TSTP Solution File: SWV419-1.030 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV419-1.030 : TPTP v8.1.0. Released v3.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 15:11:48 EDT 2022
% Result : Timeout 288.76s 181.27s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SWV419-1.030 : TPTP v8.1.0. Released v3.5.0.
% 0.08/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n017.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Sep 4 02:25:39 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 288.76/181.27 % SZS status Unsatisfiable
% 288.76/181.27 % SZS output start Proof
% 288.76/181.27 tff(node21_type, type, (
% 288.76/181.27 node21: ( $i * $i * $i * $i ) > $o)).
% 288.76/181.27 tff(s17_type, type, (
% 288.76/181.27 s17: $i)).
% 288.76/181.27 tff(s16_type, type, (
% 288.76/181.27 s16: $i)).
% 288.76/181.27 tff(c_r_type, type, (
% 288.76/181.27 c_r: $i)).
% 288.76/181.27 tff(c_e_h_3_type, type, (
% 288.76/181.27 c_e_h_3: $i)).
% 288.76/181.27 tff(m_and_h_gate_v_in2_type, type, (
% 288.76/181.27 m_and_h_gate_v_in2: ( $i * $i * $i ) > $o)).
% 288.76/181.27 tff(m_and_h_gate_h_init_v_out_type, type, (
% 288.76/181.27 m_and_h_gate_h_init_v_out: ( $i * $i * $i ) > $o)).
% 288.76/181.27 tff(c_m_type, type, (
% 288.76/181.27 c_m: $i)).
% 288.76/181.27 tff(m_c_h_element_v_out_type, type, (
% 288.76/181.27 m_c_h_element_v_out: ( $i * $i * $i ) > $o)).
% 288.76/181.27 tff(s14_type, type, (
% 288.76/181.27 s14: $i)).
% 288.76/181.27 tff(c_f_type, type, (
% 288.76/181.27 c_f: $i)).
% 288.76/181.27 tff(s13_type, type, (
% 288.76/181.27 s13: $i)).
% 288.76/181.27 tff(s12_type, type, (
% 288.76/181.27 s12: $i)).
% 288.76/181.27 tff(m_and_h_gate_v_out_type, type, (
% 288.76/181.27 m_and_h_gate_v_out: ( $i * $i * $i ) > $o)).
% 288.76/181.27 tff(s9_type, type, (
% 288.76/181.27 s9: $i)).
% 288.76/181.27 tff(c_d_type, type, (
% 288.76/181.27 c_d: $i)).
% 288.76/181.27 tff(m_mutex_h_half_v_out_type, type, (
% 288.76/181.27 m_mutex_h_half_v_out: ( $i * $i * $i ) > $o)).
% 288.76/181.27 tff(c_b_type, type, (
% 288.76/181.27 c_b: $i)).
% 288.76/181.27 tff(m_mutex_h_half_v_other_h_out_type, type, (
% 288.76/181.27 m_mutex_h_half_v_other_h_out: ( $i * $i * $i ) > $o)).
% 288.76/181.27 tff(c_a_type, type, (
% 288.76/181.27 c_a: $i)).
% 288.76/181.27 tff(m_or_h_gate_v_in1_type, type, (
% 288.76/181.27 m_or_h_gate_v_in1: ( $i * $i * $i ) > $o)).
% 288.76/181.27 tff(s8_type, type, (
% 288.76/181.27 s8: $i)).
% 288.76/181.27 tff(c_j_type, type, (
% 288.76/181.27 c_j: $i)).
% 288.76/181.27 tff(m_or_h_gate_v_out_type, type, (
% 288.76/181.27 m_or_h_gate_v_out: ( $i * $i * $i ) > $o)).
% 288.76/181.27 tff(m_and_h_gate_v_in1_type, type, (
% 288.76/181.27 m_and_h_gate_v_in1: ( $i * $i * $i ) > $o)).
% 288.76/181.27 tff(s3_type, type, (
% 288.76/181.27 s3: $i)).
% 288.76/181.27 tff(c_c_type, type, (
% 288.76/181.27 c_c: $i)).
% 288.76/181.27 tff(s4_type, type, (
% 288.76/181.27 s4: $i)).
% 288.76/181.27 tff(m_user_v_req_type, type, (
% 288.76/181.27 m_user_v_req: ( $i * $i * $i ) > $o)).
% 288.76/181.27 tff(c_u_type, type, (
% 288.76/181.27 c_u: $i)).
% 288.76/181.27 tff(m_mutex_h_half_v_inp_type, type, (
% 288.76/181.27 m_mutex_h_half_v_inp: ( $i * $i * $i ) > $o)).
% 288.76/181.27 tff(s6_type, type, (
% 288.76/181.27 s6: $i)).
% 288.76/181.27 tff(s5_type, type, (
% 288.76/181.27 s5: $i)).
% 288.76/181.27 tff(s2_type, type, (
% 288.76/181.27 s2: $i)).
% 288.76/181.27 tff(m_user_v_ack_type, type, (
% 288.76/181.27 m_user_v_ack: ( $i * $i * $i ) > $o)).
% 288.76/181.27 tff(node22_type, type, (
% 288.76/181.27 node22: ( $i * $i * $i * $i ) > $o)).
% 288.76/181.27 tff(s1_type, type, (
% 288.76/181.27 s1: $i)).
% 288.76/181.27 tff(s0_type, type, (
% 288.76/181.27 s0: $i)).
% 288.76/181.27 tff(node20_type, type, (
% 288.76/181.27 node20: ( $i * $i * $i ) > $o)).
% 288.76/181.27 tff(c_e_type, type, (
% 288.76/181.27 c_e: $i)).
% 288.76/181.27 tff(trans_type, type, (
% 288.76/181.27 trans: ( $i * $i ) > $o)).
% 288.76/181.27 tff(succ_type, type, (
% 288.76/181.27 succ: ( $i * $i ) > $o)).
% 288.76/181.27 tff(m_c_h_element_v_in1_type, type, (
% 288.76/181.27 m_c_h_element_v_in1: ( $i * $i * $i ) > $o)).
% 288.76/181.27 tff(node14_type, type, (
% 288.76/181.27 node14: ( $i * $i * $i * $i ) > $o)).
% 288.76/181.27 tff(node15_type, type, (
% 288.76/181.27 node15: ( $i * $i * $i * $i ) > $o)).
% 288.76/181.27 tff(node16_type, type, (
% 288.76/181.27 node16: ( $i * $i * $i ) > $o)).
% 288.76/181.27 tff(m_c_h_element_v_in2_type, type, (
% 288.76/181.27 m_c_h_element_v_in2: ( $i * $i * $i ) > $o)).
% 288.76/181.27 tff(c_i_type, type, (
% 288.76/181.27 c_i: $i)).
% 288.76/181.27 tff(node19_type, type, (
% 288.76/181.27 node19: ( $i * $i * $i * $i ) > $o)).
% 288.76/181.27 tff(node7_type, type, (
% 288.76/181.27 node7: ( $i * $i * $i * $i ) > $o)).
% 288.76/181.27 tff(node8_type, type, (
% 288.76/181.27 node8: ( $i * $i * $i * $i ) > $o)).
% 288.76/181.27 tff(node12_type, type, (
% 288.76/181.27 node12: ( $i * $i * $i * $i ) > $o)).
% 288.76/181.27 tff(node13_type, type, (
% 288.76/181.27 node13: ( $i * $i * $i * $i ) > $o)).
% 288.76/181.27 tff(c_h_type, type, (
% 288.76/181.27 c_h: $i)).
% 288.76/181.27 tff(node17_type, type, (
% 288.76/181.27 node17: ( $i * $i * $i ) > $o)).
% 288.76/181.27 tff(node18_type, type, (
% 288.76/181.27 node18: ( $i * $i * $i * $i ) > $o)).
% 288.76/181.27 tff(c_g_type, type, (
% 288.76/181.27 c_g: $i)).
% 288.76/181.27 tff(m_or_h_gate_v_in2_type, type, (
% 288.76/181.27 m_or_h_gate_v_in2: ( $i * $i * $i ) > $o)).
% 288.76/181.27 tff(m_cell_v_ack_type, type, (
% 288.76/181.27 m_cell_v_ack: ( $i * $i ) > $o)).
% 288.76/181.27 tff(c_q_type, type, (
% 288.76/181.27 c_q: $i)).
% 288.76/181.27 tff(c_e_h_2_type, type, (
% 288.76/181.27 c_e_h_2: $i)).
% 288.76/181.27 tff(node3_type, type, (
% 288.76/181.27 node3: ( $i * $i * $i ) > $o)).
% 288.76/181.27 tff(m_cell_v_left_type, type, (
% 288.76/181.27 m_cell_v_left: ( $i * $i ) > $o)).
% 288.76/181.27 tff(c_l_type, type, (
% 288.76/181.27 c_l: $i)).
% 288.76/181.27 tff(node5_type, type, (
% 288.76/181.27 node5: ( $i * $i * $i * $i ) > $o)).
% 288.76/181.27 tff(node6_type, type, (
% 288.76/181.27 node6: ( $i * $i * $i * $i ) > $o)).
% 288.76/181.27 tff(s7_type, type, (
% 288.76/181.27 s7: $i)).
% 288.76/181.27 tff(c_k_type, type, (
% 288.76/181.27 c_k: $i)).
% 288.76/181.27 tff(m_cell_v_req_type, type, (
% 288.76/181.27 m_cell_v_req: ( $i * $i ) > $o)).
% 288.76/181.27 tff(c_e_h_1_type, type, (
% 288.76/181.27 c_e_h_1: $i)).
% 288.76/181.27 tff(c_p_type, type, (
% 288.76/181.27 c_p: $i)).
% 288.76/181.27 tff(node1_type, type, (
% 288.76/181.27 node1: ( $i * $i * $i ) > $o)).
% 288.76/181.27 tff(m_and_h_gate_h_init_v_init_h_out_type, type, (
% 288.76/181.27 m_and_h_gate_h_init_v_init_h_out: ( $i * $i * $i ) > $o)).
% 288.76/181.27 tff(m_cell_v_token_type, type, (
% 288.76/181.27 m_cell_v_token: ( $i * $i ) > $o)).
% 288.76/181.27 tff(node11_type, type, (
% 288.76/181.27 node11: ( $i * $i * $i * $i ) > $o)).
% 288.76/181.27 tff(node10_type, type, (
% 288.76/181.27 node10: ( $i * $i * $i * $i ) > $o)).
% 288.76/181.27 tff(node9_type, type, (
% 288.76/181.27 node9: ( $i * $i * $i ) > $o)).
% 288.76/181.27 tff(m_and_h_gate_h_init_v_in2_type, type, (
% 288.76/181.27 m_and_h_gate_h_init_v_in2: ( $i * $i * $i ) > $o)).
% 288.76/181.27 tff(c_n_type, type, (
% 288.76/181.27 c_n: $i)).
% 288.76/181.27 tff(s22_type, type, (
% 288.76/181.27 s22: $i)).
% 288.76/181.27 tff(s21_type, type, (
% 288.76/181.27 s21: $i)).
% 288.76/181.27 tff(s26_type, type, (
% 288.76/181.27 s26: $i)).
% 288.76/181.27 tff(s23_type, type, (
% 288.76/181.27 s23: $i)).
% 288.76/181.27 tff(s15_type, type, (
% 288.76/181.27 s15: $i)).
% 288.76/181.27 tff(s11_type, type, (
% 288.76/181.27 s11: $i)).
% 288.76/181.27 tff(node4_type, type, (
% 288.76/181.27 node4: ( $i * $i * $i ) > $o)).
% 288.76/181.27 tff(m_and_h_gate_h_init_v_in1_type, type, (
% 288.76/181.27 m_and_h_gate_h_init_v_in1: ( $i * $i * $i ) > $o)).
% 288.76/181.27 tff(node2_type, type, (
% 288.76/181.27 node2: ( $i * $i * $i ) > $o)).
% 288.76/181.27 tff(s10_type, type, (
% 288.76/181.27 s10: $i)).
% 288.76/181.27 tff(s18_type, type, (
% 288.76/181.27 s18: $i)).
% 288.76/181.27 tff(s19_type, type, (
% 288.76/181.27 s19: $i)).
% 288.76/181.27 tff(s20_type, type, (
% 288.76/181.27 s20: $i)).
% 288.76/181.27 tff(s24_type, type, (
% 288.76/181.27 s24: $i)).
% 288.76/181.27 tff(s25_type, type, (
% 288.76/181.27 s25: $i)).
% 288.76/181.27 tff(node25_type, type, (
% 288.76/181.27 node25: $i > $o)).
% 288.76/181.27 tff(s29_type, type, (
% 288.76/181.27 s29: $i)).
% 288.76/181.27 tff(s28_type, type, (
% 288.76/181.27 s28: $i)).
% 288.76/181.27 tff(s27_type, type, (
% 288.76/181.27 s27: $i)).
% 288.76/181.27 tff(node23_type, type, (
% 288.76/181.27 node23: $i > $o)).
% 288.76/181.27 tff(node26_type, type, (
% 288.76/181.27 node26: $i > $o)).
% 288.76/181.27 tff(node24_type, type, (
% 288.76/181.27 node24: $i > $o)).
% 288.76/181.27 tff(xuntil28_type, type, (
% 288.76/181.27 xuntil28: $i > $o)).
% 288.76/181.27 tff(until27_type, type, (
% 288.76/181.27 until27: $i > $o)).
% 288.76/181.27 tff(until2p29_type, type, (
% 288.76/181.27 until2p29: $i > $o)).
% 288.76/181.27 tff(xuntil2p30_type, type, (
% 288.76/181.27 xuntil2p30: $i > $o)).
% 288.76/181.27 tff(last_type, type, (
% 288.76/181.27 last: $i > $o)).
% 288.76/181.27 tff(loop_type, type, (
% 288.76/181.27 loop: $o)).
% 288.76/181.27 tff(1,assumption,(~m_mutex_h_half_v_out(c_e_h_3, c_a, s9)), introduced(assumption)).
% 288.76/181.27 tff(2,assumption,(m_mutex_h_half_v_out(c_e_h_3, c_a, s4)), introduced(assumption)).
% 288.76/181.27 tff(3,assumption,(~m_user_v_req(c_e_h_3, c_u, s3)), introduced(assumption)).
% 288.76/181.27 tff(4,assumption,(m_and_h_gate_v_out(c_e_h_3, c_r, s2)), introduced(assumption)).
% 288.76/181.27 tff(5,assumption,(m_and_h_gate_v_out(c_e_h_3, c_r, s1)), introduced(assumption)).
% 288.76/181.27 tff(6,assumption,(node21(c_e_h_3, c_r, s0, s1)), introduced(assumption)).
% 288.76/181.27 tff(7,assumption,(m_c_h_element_v_out(c_e_h_3, c_e, s0)), introduced(assumption)).
% 288.76/181.27 tff(8,plain,
% 288.76/181.27 (^[I0: $i, I1: $i] : refl((~m_c_h_element_v_out(I0, I1, s0)) <=> (~m_c_h_element_v_out(I0, I1, s0)))),
% 288.76/181.27 inference(bind,[status(th)],[])).
% 288.76/181.27 tff(9,plain,
% 288.76/181.27 (![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0)) <=> ![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))),
% 288.76/181.27 inference(quant_intro,[status(thm)],[8])).
% 288.76/181.27 tff(10,plain,
% 288.76/181.27 (![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0)) <=> ![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))),
% 288.76/181.27 inference(rewrite,[status(thm)],[])).
% 288.76/181.27 tff(11,axiom,(![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_c_h_element_1')).
% 288.76/181.27 tff(12,plain,
% 288.76/181.27 (![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))),
% 288.76/181.27 inference(modus_ponens,[status(thm)],[11, 10])).
% 288.76/181.27 tff(13,plain,(
% 288.76/181.27 ![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))),
% 288.76/181.27 inference(skolemize,[status(sab)],[12])).
% 288.76/181.27 tff(14,plain,
% 288.76/181.27 (![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))),
% 288.76/181.27 inference(modus_ponens,[status(thm)],[13, 9])).
% 288.76/181.27 tff(15,plain,
% 288.76/181.27 ((~![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s0))),
% 288.76/181.27 inference(quant_inst,[status(thm)],[])).
% 288.76/181.27 tff(16,plain,
% 288.76/181.27 ($false),
% 288.76/181.27 inference(unit_resolution,[status(thm)],[15, 14, 7])).
% 288.76/181.27 tff(17,plain,(~m_c_h_element_v_out(c_e_h_3, c_e, s0)), inference(lemma,lemma(discharge,[]))).
% 288.76/181.27 tff(18,plain,
% 288.76/181.27 (^[I0: $i, X: $i] : refl(((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X)) <=> ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X)))),
% 288.76/181.27 inference(bind,[status(th)],[])).
% 288.76/181.27 tff(19,plain,
% 288.76/181.27 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))),
% 288.76/181.27 inference(quant_intro,[status(thm)],[18])).
% 288.76/181.27 tff(20,plain,
% 288.76/181.27 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))),
% 288.76/181.27 inference(rewrite,[status(thm)],[])).
% 288.76/181.27 tff(21,axiom,(![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_72')).
% 288.76/181.27 tff(22,plain,
% 288.76/181.27 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))),
% 288.76/181.27 inference(modus_ponens,[status(thm)],[21, 20])).
% 288.76/181.27 tff(23,plain,(
% 288.76/181.27 ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))),
% 288.76/181.27 inference(skolemize,[status(sab)],[22])).
% 288.76/181.27 tff(24,plain,
% 288.76/181.27 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))),
% 288.76/181.27 inference(modus_ponens,[status(thm)],[23, 19])).
% 288.76/181.27 tff(25,plain,
% 288.76/181.27 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s0)) | m_c_h_element_v_out(c_e_h_3, c_e, s0))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s0)) | m_c_h_element_v_out(c_e_h_3, c_e, s0))),
% 288.76/181.27 inference(rewrite,[status(thm)],[])).
% 288.76/181.27 tff(26,plain,
% 288.76/181.27 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s0)) | m_c_h_element_v_out(c_e_h_3, c_e, s0))),
% 288.76/181.27 inference(quant_inst,[status(thm)],[])).
% 288.76/181.27 tff(27,plain,
% 288.76/181.27 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s0)) | m_c_h_element_v_out(c_e_h_3, c_e, s0)),
% 288.76/181.27 inference(modus_ponens,[status(thm)],[26, 25])).
% 288.76/181.27 tff(28,plain,
% 288.76/181.27 (~m_and_h_gate_v_in1(c_e_h_3, c_r, s0)),
% 288.76/181.27 inference(unit_resolution,[status(thm)],[27, 24, 17])).
% 288.76/181.27 tff(29,plain,
% 288.76/181.27 (^[I0: $i, X: $i, I1: $i] : refl(((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X)) <=> ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X)))),
% 288.76/181.27 inference(bind,[status(th)],[])).
% 288.76/181.27 tff(30,plain,
% 288.76/181.27 (![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X)) <=> ![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))),
% 288.76/181.27 inference(quant_intro,[status(thm)],[29])).
% 288.76/181.27 tff(31,plain,
% 288.76/181.27 (![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X)) <=> ![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))),
% 288.76/181.27 inference(rewrite,[status(thm)],[])).
% 288.76/181.27 tff(32,plain,
% 288.76/181.27 (^[I0: $i, X: $i, I1: $i] : rewrite((m_and_h_gate_v_in1(I0, I1, X) | (~node20(I0, I1, X))) <=> ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X)))),
% 288.76/181.27 inference(bind,[status(th)],[])).
% 288.76/181.27 tff(33,plain,
% 288.76/181.27 (![I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_in1(I0, I1, X) | (~node20(I0, I1, X))) <=> ![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))),
% 288.76/181.27 inference(quant_intro,[status(thm)],[32])).
% 288.76/181.27 tff(34,axiom,(![I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_in1(I0, I1, X) | (~node20(I0, I1, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_and_h_gate_2')).
% 288.76/181.27 tff(35,plain,
% 288.76/181.27 (![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))),
% 288.76/181.27 inference(modus_ponens,[status(thm)],[34, 33])).
% 288.76/181.27 tff(36,plain,
% 288.76/181.27 (![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))),
% 288.76/181.27 inference(modus_ponens,[status(thm)],[35, 31])).
% 288.76/181.27 tff(37,plain,(
% 288.76/181.27 ![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))),
% 288.76/181.27 inference(skolemize,[status(sab)],[36])).
% 288.76/181.27 tff(38,plain,
% 288.76/181.27 (![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))),
% 288.76/181.27 inference(modus_ponens,[status(thm)],[37, 30])).
% 288.76/181.27 tff(39,plain,
% 288.76/181.27 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s0))),
% 288.76/181.28 inference(rewrite,[status(thm)],[])).
% 288.76/181.28 tff(40,plain,
% 288.76/181.28 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s0))),
% 288.76/181.28 inference(quant_inst,[status(thm)],[])).
% 288.76/181.28 tff(41,plain,
% 288.76/181.28 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s0)),
% 288.76/181.28 inference(modus_ponens,[status(thm)],[40, 39])).
% 288.76/181.28 tff(42,plain,
% 288.76/181.28 (~node20(c_e_h_3, c_r, s0)),
% 288.76/181.28 inference(unit_resolution,[status(thm)],[41, 38, 28])).
% 288.76/181.28 tff(43,plain,
% 288.76/181.28 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl((node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y))) <=> (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y))))),
% 288.76/181.28 inference(bind,[status(th)],[])).
% 288.76/181.28 tff(44,plain,
% 288.76/181.28 (![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))),
% 288.76/181.28 inference(quant_intro,[status(thm)],[43])).
% 288.76/181.28 tff(45,plain,
% 288.76/181.28 (![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))),
% 288.76/181.28 inference(rewrite,[status(thm)],[])).
% 288.76/181.28 tff(46,plain,
% 288.76/181.28 (^[Y: $i, I0: $i, X: $i, I1: $i] : rewrite((((~m_and_h_gate_v_out(I0, I1, Y)) | node20(I0, I1, X)) | (~node21(I0, I1, X, Y))) <=> (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y))))),
% 288.76/181.28 inference(bind,[status(th)],[])).
% 288.76/181.28 tff(47,plain,
% 288.76/181.28 (![Y: $i, I0: $i, X: $i, I1: $i] : (((~m_and_h_gate_v_out(I0, I1, Y)) | node20(I0, I1, X)) | (~node21(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))),
% 288.76/181.28 inference(quant_intro,[status(thm)],[46])).
% 288.76/181.28 tff(48,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : (((~m_and_h_gate_v_out(I0, I1, Y)) | node20(I0, I1, X)) | (~node21(I0, I1, X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_and_h_gate_5')).
% 288.76/181.28 tff(49,plain,
% 288.76/181.28 (![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))),
% 288.76/181.28 inference(modus_ponens,[status(thm)],[48, 47])).
% 288.76/181.28 tff(50,plain,
% 288.76/181.28 (![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))),
% 288.76/181.28 inference(modus_ponens,[status(thm)],[49, 45])).
% 288.76/181.28 tff(51,plain,(
% 288.76/181.28 ![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))),
% 288.76/181.28 inference(skolemize,[status(sab)],[50])).
% 288.76/181.28 tff(52,plain,
% 288.76/181.28 (![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))),
% 288.76/181.28 inference(modus_ponens,[status(thm)],[51, 44])).
% 288.76/181.28 tff(53,plain,
% 288.76/181.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s1)) | (~node21(c_e_h_3, c_r, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_r, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s1)) | (~node21(c_e_h_3, c_r, s0, s1)))),
% 288.76/181.28 inference(rewrite,[status(thm)],[])).
% 288.76/181.28 tff(54,plain,
% 288.76/181.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s1)) | (~node21(c_e_h_3, c_r, s0, s1)))),
% 288.76/181.28 inference(quant_inst,[status(thm)],[])).
% 288.76/181.28 tff(55,plain,
% 288.76/181.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_r, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s1)) | (~node21(c_e_h_3, c_r, s0, s1))),
% 288.76/181.28 inference(modus_ponens,[status(thm)],[54, 53])).
% 288.76/181.28 tff(56,plain,
% 288.76/181.28 ($false),
% 288.76/181.28 inference(unit_resolution,[status(thm)],[55, 52, 42, 6, 5])).
% 288.76/181.28 tff(57,plain,((~node21(c_e_h_3, c_r, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s1))), inference(lemma,lemma(discharge,[]))).
% 288.76/181.28 tff(58,plain,
% 288.76/181.28 (~node21(c_e_h_3, c_r, s0, s1)),
% 288.76/181.28 inference(unit_resolution,[status(thm)],[57, 5])).
% 288.76/181.28 tff(59,plain,
% 288.76/181.28 (^[Y: $i, X: $i] : refl(((~succ(X, Y)) | trans(X, Y)) <=> ((~succ(X, Y)) | trans(X, Y)))),
% 288.76/181.28 inference(bind,[status(th)],[])).
% 288.76/181.28 tff(60,plain,
% 288.76/181.28 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y)) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 288.76/181.28 inference(quant_intro,[status(thm)],[59])).
% 288.76/181.28 tff(61,plain,
% 288.76/181.28 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y)) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 288.76/181.28 inference(rewrite,[status(thm)],[])).
% 288.76/181.28 tff(62,axiom,(![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound31')).
% 288.76/181.28 tff(63,plain,
% 288.76/181.28 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 288.76/181.28 inference(modus_ponens,[status(thm)],[62, 61])).
% 288.76/181.28 tff(64,plain,(
% 288.76/181.28 ![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 288.76/181.28 inference(skolemize,[status(sab)],[63])).
% 288.76/181.28 tff(65,plain,
% 288.76/181.28 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 288.76/181.28 inference(modus_ponens,[status(thm)],[64, 60])).
% 288.76/181.28 tff(66,plain,
% 288.76/181.28 (succ(s0, s1) <=> succ(s0, s1)),
% 288.76/181.28 inference(rewrite,[status(thm)],[])).
% 288.76/181.28 tff(67,axiom,(succ(s0, s1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound1')).
% 288.76/181.28 tff(68,plain,
% 288.76/181.28 (succ(s0, s1)),
% 288.76/181.28 inference(modus_ponens,[status(thm)],[67, 66])).
% 288.76/181.28 tff(69,plain,
% 288.76/181.28 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s0, s1)) | trans(s0, s1))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s0, s1)) | trans(s0, s1))),
% 288.76/181.28 inference(rewrite,[status(thm)],[])).
% 288.76/181.28 tff(70,plain,
% 288.76/181.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s0, s1)) | trans(s0, s1))),
% 288.76/181.28 inference(quant_inst,[status(thm)],[])).
% 288.76/181.28 tff(71,plain,
% 288.76/181.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s0, s1)) | trans(s0, s1)),
% 288.76/181.28 inference(modus_ponens,[status(thm)],[70, 69])).
% 288.76/181.28 tff(72,plain,
% 288.76/181.28 (trans(s0, s1)),
% 288.76/181.28 inference(unit_resolution,[status(thm)],[71, 68, 65])).
% 288.76/181.28 tff(73,plain,
% 288.76/181.28 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl(((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y)) <=> ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y)))),
% 288.76/181.28 inference(bind,[status(th)],[])).
% 288.76/181.28 tff(74,plain,
% 288.76/181.28 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))),
% 288.76/181.28 inference(quant_intro,[status(thm)],[73])).
% 288.76/181.28 tff(75,plain,
% 288.76/181.28 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))),
% 288.76/181.28 inference(rewrite,[status(thm)],[])).
% 288.76/181.28 tff(76,plain,
% 288.76/181.28 (^[Y: $i, I0: $i, X: $i, I1: $i] : rewrite(((node21(I0, I1, X, Y) | node22(I0, I1, X, Y)) | (~trans(X, Y))) <=> ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y)))),
% 288.76/181.28 inference(bind,[status(th)],[])).
% 288.76/181.28 tff(77,plain,
% 288.76/181.28 (![Y: $i, I0: $i, X: $i, I1: $i] : ((node21(I0, I1, X, Y) | node22(I0, I1, X, Y)) | (~trans(X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))),
% 288.76/181.28 inference(quant_intro,[status(thm)],[76])).
% 288.76/181.28 tff(78,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : ((node21(I0, I1, X, Y) | node22(I0, I1, X, Y)) | (~trans(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_and_h_gate_8')).
% 288.76/181.28 tff(79,plain,
% 288.76/181.28 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))),
% 288.76/181.28 inference(modus_ponens,[status(thm)],[78, 77])).
% 288.76/181.28 tff(80,plain,
% 288.76/181.28 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))),
% 288.76/181.28 inference(modus_ponens,[status(thm)],[79, 75])).
% 288.76/181.28 tff(81,plain,(
% 288.76/181.28 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))),
% 288.76/181.28 inference(skolemize,[status(sab)],[80])).
% 288.76/181.28 tff(82,plain,
% 288.76/181.28 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))),
% 288.76/181.28 inference(modus_ponens,[status(thm)],[81, 74])).
% 288.76/181.28 tff(83,plain,
% 288.76/181.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_3, c_r, s0, s1) | node22(c_e_h_3, c_r, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_3, c_r, s0, s1) | node22(c_e_h_3, c_r, s0, s1))),
% 288.76/181.28 inference(rewrite,[status(thm)],[])).
% 288.76/181.28 tff(84,plain,
% 288.76/181.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_3, c_r, s0, s1) | node22(c_e_h_3, c_r, s0, s1))),
% 288.76/181.28 inference(quant_inst,[status(thm)],[])).
% 288.76/181.28 tff(85,plain,
% 288.76/181.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_3, c_r, s0, s1) | node22(c_e_h_3, c_r, s0, s1)),
% 288.76/181.28 inference(modus_ponens,[status(thm)],[84, 83])).
% 288.76/181.28 tff(86,plain,
% 288.76/181.28 (node21(c_e_h_3, c_r, s0, s1) | node22(c_e_h_3, c_r, s0, s1)),
% 288.76/181.28 inference(unit_resolution,[status(thm)],[85, 82, 72])).
% 288.76/181.28 tff(87,plain,
% 288.76/181.28 (node22(c_e_h_3, c_r, s0, s1)),
% 288.76/181.28 inference(unit_resolution,[status(thm)],[86, 58])).
% 288.76/181.28 tff(88,assumption,(m_and_h_gate_v_out(c_e_h_3, c_r, s0)), introduced(assumption)).
% 288.76/181.28 tff(89,plain,
% 288.76/181.28 (^[I0: $i, I1: $i] : refl((~m_and_h_gate_v_out(I0, I1, s0)) <=> (~m_and_h_gate_v_out(I0, I1, s0)))),
% 288.76/181.28 inference(bind,[status(th)],[])).
% 288.76/181.28 tff(90,plain,
% 288.76/181.28 (![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0)) <=> ![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))),
% 288.76/181.28 inference(quant_intro,[status(thm)],[89])).
% 288.76/181.28 tff(91,plain,
% 288.76/181.28 (![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0)) <=> ![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))),
% 288.76/181.28 inference(rewrite,[status(thm)],[])).
% 288.76/181.28 tff(92,axiom,(![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_and_h_gate_1')).
% 288.76/181.28 tff(93,plain,
% 288.76/181.28 (![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))),
% 288.76/181.28 inference(modus_ponens,[status(thm)],[92, 91])).
% 288.76/181.28 tff(94,plain,(
% 288.76/181.28 ![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))),
% 288.76/181.28 inference(skolemize,[status(sab)],[93])).
% 288.76/181.28 tff(95,plain,
% 288.76/181.28 (![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))),
% 288.76/181.28 inference(modus_ponens,[status(thm)],[94, 90])).
% 288.76/181.28 tff(96,plain,
% 288.76/181.28 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s0))),
% 288.76/181.28 inference(quant_inst,[status(thm)],[])).
% 288.76/181.28 tff(97,plain,
% 288.76/181.28 ($false),
% 288.76/181.28 inference(unit_resolution,[status(thm)],[96, 95, 88])).
% 288.76/181.28 tff(98,plain,(~m_and_h_gate_v_out(c_e_h_3, c_r, s0)), inference(lemma,lemma(discharge,[]))).
% 288.76/181.28 tff(99,plain,
% 288.76/181.28 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl(((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X)) <=> ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X)))),
% 288.76/181.28 inference(bind,[status(th)],[])).
% 288.76/181.28 tff(100,plain,
% 288.76/181.28 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))),
% 288.76/181.28 inference(quant_intro,[status(thm)],[99])).
% 288.76/181.28 tff(101,plain,
% 288.76/181.28 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))),
% 288.76/181.28 inference(rewrite,[status(thm)],[])).
% 288.76/181.28 tff(102,plain,
% 288.76/181.28 (^[Y: $i, I0: $i, X: $i, I1: $i] : rewrite((((~m_and_h_gate_v_out(I0, I1, Y)) | m_and_h_gate_v_out(I0, I1, X)) | (~node22(I0, I1, X, Y))) <=> ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X)))),
% 288.76/181.29 inference(bind,[status(th)],[])).
% 288.76/181.29 tff(103,plain,
% 288.76/181.29 (![Y: $i, I0: $i, X: $i, I1: $i] : (((~m_and_h_gate_v_out(I0, I1, Y)) | m_and_h_gate_v_out(I0, I1, X)) | (~node22(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))),
% 288.76/181.29 inference(quant_intro,[status(thm)],[102])).
% 288.76/181.29 tff(104,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : (((~m_and_h_gate_v_out(I0, I1, Y)) | m_and_h_gate_v_out(I0, I1, X)) | (~node22(I0, I1, X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_and_h_gate_7')).
% 288.76/181.29 tff(105,plain,
% 288.76/181.29 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))),
% 288.76/181.29 inference(modus_ponens,[status(thm)],[104, 103])).
% 288.76/181.29 tff(106,plain,
% 288.76/181.29 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))),
% 288.76/181.29 inference(modus_ponens,[status(thm)],[105, 101])).
% 288.76/181.29 tff(107,plain,(
% 288.76/181.29 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))),
% 288.76/181.29 inference(skolemize,[status(sab)],[106])).
% 288.76/181.29 tff(108,plain,
% 288.76/181.29 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))),
% 288.76/181.29 inference(modus_ponens,[status(thm)],[107, 100])).
% 288.76/181.29 tff(109,plain,
% 288.76/181.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s1)) | (~node22(c_e_h_3, c_r, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_r, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s1)) | (~node22(c_e_h_3, c_r, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_r, s0))),
% 288.76/181.29 inference(rewrite,[status(thm)],[])).
% 288.76/181.29 tff(110,plain,
% 288.76/181.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s1)) | (~node22(c_e_h_3, c_r, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_r, s0))),
% 288.76/181.29 inference(quant_inst,[status(thm)],[])).
% 288.76/181.29 tff(111,plain,
% 288.76/181.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s1)) | (~node22(c_e_h_3, c_r, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_r, s0)),
% 288.76/181.29 inference(modus_ponens,[status(thm)],[110, 109])).
% 288.76/181.29 tff(112,plain,
% 288.76/181.29 ($false),
% 288.76/181.29 inference(unit_resolution,[status(thm)],[111, 108, 98, 87, 5])).
% 288.76/181.29 tff(113,plain,(~m_and_h_gate_v_out(c_e_h_3, c_r, s1)), inference(lemma,lemma(discharge,[]))).
% 288.76/181.29 tff(114,assumption,(node22(c_e_h_3, c_r, s1, s2)), introduced(assumption)).
% 288.76/181.29 tff(115,plain,
% 288.76/181.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s2)) | (~node22(c_e_h_3, c_r, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_r, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s2)) | (~node22(c_e_h_3, c_r, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_r, s1))),
% 288.76/181.29 inference(rewrite,[status(thm)],[])).
% 288.76/181.29 tff(116,plain,
% 288.76/181.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s2)) | (~node22(c_e_h_3, c_r, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_r, s1))),
% 288.76/181.29 inference(quant_inst,[status(thm)],[])).
% 288.76/181.29 tff(117,plain,
% 288.76/181.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s2)) | (~node22(c_e_h_3, c_r, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_r, s1)),
% 288.76/181.29 inference(modus_ponens,[status(thm)],[116, 115])).
% 288.76/181.29 tff(118,plain,
% 288.76/181.29 ($false),
% 288.76/181.29 inference(unit_resolution,[status(thm)],[117, 108, 114, 113, 4])).
% 288.76/181.29 tff(119,plain,((~node22(c_e_h_3, c_r, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s2))), inference(lemma,lemma(discharge,[]))).
% 288.76/181.29 tff(120,plain,
% 288.76/181.29 (~node22(c_e_h_3, c_r, s1, s2)),
% 288.76/181.29 inference(unit_resolution,[status(thm)],[119, 4])).
% 288.76/181.29 tff(121,assumption,(m_and_h_gate_v_out(c_e_h_3, c_c, s0)), introduced(assumption)).
% 288.76/181.29 tff(122,plain,
% 288.76/181.29 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s0))),
% 288.76/181.29 inference(quant_inst,[status(thm)],[])).
% 288.76/181.29 tff(123,plain,
% 288.76/181.29 ($false),
% 288.76/181.29 inference(unit_resolution,[status(thm)],[122, 95, 121])).
% 288.76/181.29 tff(124,plain,(~m_and_h_gate_v_out(c_e_h_3, c_c, s0)), inference(lemma,lemma(discharge,[]))).
% 288.76/181.29 tff(125,plain,
% 288.76/181.29 (^[I0: $i, X: $i] : refl(((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X)) <=> ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X)))),
% 288.76/181.29 inference(bind,[status(th)],[])).
% 288.76/181.29 tff(126,plain,
% 288.76/181.29 (![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X)) <=> ![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))),
% 288.76/181.29 inference(quant_intro,[status(thm)],[125])).
% 288.76/181.29 tff(127,plain,
% 288.76/181.29 (![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X)) <=> ![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))),
% 288.76/181.29 inference(rewrite,[status(thm)],[])).
% 288.76/181.29 tff(128,axiom,(![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_20')).
% 288.76/181.29 tff(129,plain,
% 288.76/181.29 (![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))),
% 288.76/181.29 inference(modus_ponens,[status(thm)],[128, 127])).
% 288.76/181.29 tff(130,plain,(
% 288.76/181.29 ![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))),
% 288.76/181.29 inference(skolemize,[status(sab)],[129])).
% 288.76/181.29 tff(131,plain,
% 288.76/181.29 (![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))),
% 288.76/181.29 inference(modus_ponens,[status(thm)],[130, 126])).
% 288.76/181.29 tff(132,plain,
% 288.76/181.29 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s0)) | m_and_h_gate_v_out(c_e_h_3, c_c, s0))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s0)) | m_and_h_gate_v_out(c_e_h_3, c_c, s0))),
% 288.76/181.29 inference(rewrite,[status(thm)],[])).
% 288.76/181.29 tff(133,plain,
% 288.76/181.29 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s0)) | m_and_h_gate_v_out(c_e_h_3, c_c, s0))),
% 288.76/181.29 inference(quant_inst,[status(thm)],[])).
% 288.76/181.29 tff(134,plain,
% 288.76/181.29 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s0)) | m_and_h_gate_v_out(c_e_h_3, c_c, s0)),
% 288.76/181.29 inference(modus_ponens,[status(thm)],[133, 132])).
% 288.76/181.29 tff(135,plain,
% 288.76/181.29 (~m_c_h_element_v_in1(c_e_h_3, c_e, s0)),
% 288.76/181.29 inference(unit_resolution,[status(thm)],[134, 131, 124])).
% 288.76/181.29 tff(136,assumption,(m_c_h_element_v_out(c_e_h_3, c_e, s1)), introduced(assumption)).
% 288.76/181.29 tff(137,assumption,(node15(c_e_h_3, c_e, s0, s1)), introduced(assumption)).
% 288.76/181.29 tff(138,plain,
% 288.76/181.29 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl(((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X)) <=> ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X)))),
% 288.76/181.29 inference(bind,[status(th)],[])).
% 288.76/181.29 tff(139,plain,
% 288.76/181.29 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))),
% 288.76/181.29 inference(quant_intro,[status(thm)],[138])).
% 288.76/181.29 tff(140,plain,
% 288.76/181.29 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))),
% 288.76/181.29 inference(rewrite,[status(thm)],[])).
% 288.76/181.29 tff(141,plain,
% 288.76/181.29 (^[Y: $i, I0: $i, X: $i, I1: $i] : rewrite((((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X)) | (~node15(I0, I1, X, Y))) <=> ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X)))),
% 288.76/181.29 inference(bind,[status(th)],[])).
% 288.76/181.29 tff(142,plain,
% 288.76/181.29 (![Y: $i, I0: $i, X: $i, I1: $i] : (((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X)) | (~node15(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))),
% 288.76/181.29 inference(quant_intro,[status(thm)],[141])).
% 288.76/181.29 tff(143,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : (((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X)) | (~node15(I0, I1, X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_c_h_element_5')).
% 288.76/181.29 tff(144,plain,
% 288.76/181.29 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))),
% 288.76/181.29 inference(modus_ponens,[status(thm)],[143, 142])).
% 288.76/181.29 tff(145,plain,
% 288.76/181.29 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))),
% 288.76/181.29 inference(modus_ponens,[status(thm)],[144, 140])).
% 288.76/181.29 tff(146,plain,(
% 288.76/181.29 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))),
% 288.76/181.29 inference(skolemize,[status(sab)],[145])).
% 288.76/181.29 tff(147,plain,
% 288.76/181.29 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))),
% 288.76/181.29 inference(modus_ponens,[status(thm)],[146, 139])).
% 288.76/181.29 tff(148,plain,
% 288.76/181.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s1)) | (~node15(c_e_h_3, c_e, s0, s1)) | m_c_h_element_v_out(c_e_h_3, c_e, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s1)) | (~node15(c_e_h_3, c_e, s0, s1)) | m_c_h_element_v_out(c_e_h_3, c_e, s0))),
% 288.76/181.29 inference(rewrite,[status(thm)],[])).
% 288.76/181.29 tff(149,plain,
% 288.76/181.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s1)) | (~node15(c_e_h_3, c_e, s0, s1)) | m_c_h_element_v_out(c_e_h_3, c_e, s0))),
% 288.76/181.29 inference(quant_inst,[status(thm)],[])).
% 288.76/181.29 tff(150,plain,
% 288.76/181.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s1)) | (~node15(c_e_h_3, c_e, s0, s1)) | m_c_h_element_v_out(c_e_h_3, c_e, s0)),
% 288.76/181.29 inference(modus_ponens,[status(thm)],[149, 148])).
% 288.76/181.29 tff(151,plain,
% 288.76/181.29 ($false),
% 288.76/181.29 inference(unit_resolution,[status(thm)],[150, 147, 136, 17, 137])).
% 288.76/181.29 tff(152,plain,((~node15(c_e_h_3, c_e, s0, s1)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s1))), inference(lemma,lemma(discharge,[]))).
% 288.76/181.29 tff(153,plain,
% 288.76/181.29 (~node15(c_e_h_3, c_e, s0, s1)),
% 288.76/181.29 inference(unit_resolution,[status(thm)],[152, 136])).
% 288.76/181.29 tff(154,assumption,(m_and_h_gate_v_out(c_e_h_3, c_i, s0)), introduced(assumption)).
% 288.76/181.29 tff(155,plain,
% 288.76/181.29 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s0))),
% 288.76/181.29 inference(quant_inst,[status(thm)],[])).
% 288.76/181.29 tff(156,plain,
% 288.76/181.29 ($false),
% 288.76/181.29 inference(unit_resolution,[status(thm)],[155, 95, 154])).
% 288.76/181.29 tff(157,plain,(~m_and_h_gate_v_out(c_e_h_3, c_i, s0)), inference(lemma,lemma(discharge,[]))).
% 288.76/181.29 tff(158,plain,
% 288.76/181.29 (^[I0: $i, X: $i] : refl(((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X)) <=> ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X)))),
% 288.76/181.29 inference(bind,[status(th)],[])).
% 288.76/181.29 tff(159,plain,
% 288.76/181.29 (![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X)) <=> ![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))),
% 288.76/181.29 inference(quant_intro,[status(thm)],[158])).
% 288.76/181.29 tff(160,plain,
% 288.76/181.29 (![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X)) <=> ![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))),
% 288.76/181.29 inference(rewrite,[status(thm)],[])).
% 288.76/181.29 tff(161,axiom,(![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_22')).
% 288.76/181.29 tff(162,plain,
% 288.76/181.29 (![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))),
% 288.76/181.29 inference(modus_ponens,[status(thm)],[161, 160])).
% 288.76/181.29 tff(163,plain,(
% 288.76/181.29 ![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))),
% 288.76/181.29 inference(skolemize,[status(sab)],[162])).
% 288.76/181.29 tff(164,plain,
% 288.76/181.29 (![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))),
% 288.76/181.29 inference(modus_ponens,[status(thm)],[163, 159])).
% 288.76/181.29 tff(165,plain,
% 288.76/181.29 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s0)) | m_and_h_gate_v_out(c_e_h_3, c_i, s0))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s0)) | m_and_h_gate_v_out(c_e_h_3, c_i, s0))),
% 288.76/181.29 inference(rewrite,[status(thm)],[])).
% 288.76/181.29 tff(166,plain,
% 288.76/181.29 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s0)) | m_and_h_gate_v_out(c_e_h_3, c_i, s0))),
% 288.76/181.29 inference(quant_inst,[status(thm)],[])).
% 288.76/181.29 tff(167,plain,
% 288.76/181.29 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s0)) | m_and_h_gate_v_out(c_e_h_3, c_i, s0)),
% 288.76/181.29 inference(modus_ponens,[status(thm)],[166, 165])).
% 288.76/181.29 tff(168,plain,
% 288.76/181.29 (~m_c_h_element_v_in2(c_e_h_3, c_e, s0)),
% 288.76/181.29 inference(unit_resolution,[status(thm)],[167, 164, 157])).
% 288.76/181.29 tff(169,plain,
% 288.76/181.29 (^[I0: $i, X: $i, I1: $i] : refl(((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X)) <=> ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X)))),
% 288.76/181.29 inference(bind,[status(th)],[])).
% 288.76/181.29 tff(170,plain,
% 288.76/181.29 (![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X)) <=> ![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))),
% 288.76/181.29 inference(quant_intro,[status(thm)],[169])).
% 288.76/181.29 tff(171,plain,
% 288.76/181.29 (![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X)) <=> ![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))),
% 288.76/181.29 inference(rewrite,[status(thm)],[])).
% 288.76/181.29 tff(172,plain,
% 288.76/181.29 (^[I0: $i, X: $i, I1: $i] : rewrite(((m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X)) | (~node16(I0, I1, X))) <=> ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X)))),
% 288.76/181.29 inference(bind,[status(th)],[])).
% 288.76/181.29 tff(173,plain,
% 288.76/181.29 (![I0: $i, X: $i, I1: $i] : ((m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X)) | (~node16(I0, I1, X))) <=> ![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))),
% 288.76/181.29 inference(quant_intro,[status(thm)],[172])).
% 288.76/181.29 tff(174,axiom,(![I0: $i, X: $i, I1: $i] : ((m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X)) | (~node16(I0, I1, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_c_h_element_6')).
% 288.76/181.29 tff(175,plain,
% 288.76/181.29 (![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))),
% 288.85/181.30 inference(modus_ponens,[status(thm)],[174, 173])).
% 288.85/181.30 tff(176,plain,
% 288.85/181.30 (![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))),
% 288.85/181.30 inference(modus_ponens,[status(thm)],[175, 171])).
% 288.85/181.30 tff(177,plain,(
% 288.85/181.30 ![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))),
% 288.85/181.30 inference(skolemize,[status(sab)],[176])).
% 288.85/181.30 tff(178,plain,
% 288.85/181.30 (![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))),
% 288.85/181.30 inference(modus_ponens,[status(thm)],[177, 170])).
% 288.85/181.30 tff(179,plain,
% 288.85/181.30 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_e, s0)) | m_c_h_element_v_in1(c_e_h_3, c_e, s0) | m_c_h_element_v_in2(c_e_h_3, c_e, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s0)) | m_c_h_element_v_in1(c_e_h_3, c_e, s0) | m_c_h_element_v_in2(c_e_h_3, c_e, s0))),
% 288.85/181.30 inference(rewrite,[status(thm)],[])).
% 288.85/181.30 tff(180,plain,
% 288.85/181.30 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_e, s0)) | m_c_h_element_v_in1(c_e_h_3, c_e, s0) | m_c_h_element_v_in2(c_e_h_3, c_e, s0))),
% 288.85/181.30 inference(quant_inst,[status(thm)],[])).
% 288.85/181.30 tff(181,plain,
% 288.85/181.30 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s0)) | m_c_h_element_v_in1(c_e_h_3, c_e, s0) | m_c_h_element_v_in2(c_e_h_3, c_e, s0)),
% 288.85/181.30 inference(modus_ponens,[status(thm)],[180, 179])).
% 288.85/181.30 tff(182,plain,
% 288.85/181.30 ((~node16(c_e_h_3, c_e, s0)) | m_c_h_element_v_in2(c_e_h_3, c_e, s0)),
% 288.85/181.30 inference(unit_resolution,[status(thm)],[181, 178, 135])).
% 288.85/181.30 tff(183,plain,
% 288.85/181.30 (~node16(c_e_h_3, c_e, s0)),
% 288.85/181.30 inference(unit_resolution,[status(thm)],[182, 168])).
% 288.85/181.30 tff(184,plain,
% 288.85/181.30 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl(((~trans(X, Y)) | node19(I0, I1, X, Y)) <=> ((~trans(X, Y)) | node19(I0, I1, X, Y)))),
% 288.85/181.30 inference(bind,[status(th)],[])).
% 288.85/181.30 tff(185,plain,
% 288.85/181.30 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))),
% 288.85/181.30 inference(quant_intro,[status(thm)],[184])).
% 288.85/181.30 tff(186,plain,
% 288.85/181.30 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))),
% 288.85/181.30 inference(rewrite,[status(thm)],[])).
% 288.85/181.30 tff(187,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_c_h_element_14')).
% 288.85/181.30 tff(188,plain,
% 288.85/181.30 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))),
% 288.85/181.30 inference(modus_ponens,[status(thm)],[187, 186])).
% 288.85/181.30 tff(189,plain,(
% 288.85/181.30 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))),
% 288.85/181.30 inference(skolemize,[status(sab)],[188])).
% 288.85/181.30 tff(190,plain,
% 288.85/181.30 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))),
% 288.85/181.30 inference(modus_ponens,[status(thm)],[189, 185])).
% 288.85/181.30 tff(191,plain,
% 288.85/181.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s0, s1)) | node19(c_e_h_3, c_e, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s0, s1)) | node19(c_e_h_3, c_e, s0, s1))),
% 288.85/181.30 inference(rewrite,[status(thm)],[])).
% 288.85/181.30 tff(192,plain,
% 288.85/181.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s0, s1)) | node19(c_e_h_3, c_e, s0, s1))),
% 288.85/181.30 inference(quant_inst,[status(thm)],[])).
% 288.85/181.30 tff(193,plain,
% 288.85/181.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s0, s1)) | node19(c_e_h_3, c_e, s0, s1)),
% 288.85/181.30 inference(modus_ponens,[status(thm)],[192, 191])).
% 288.85/181.30 tff(194,plain,
% 288.85/181.30 (node19(c_e_h_3, c_e, s0, s1)),
% 288.85/181.30 inference(unit_resolution,[status(thm)],[193, 190, 72])).
% 288.85/181.30 tff(195,plain,
% 288.85/181.30 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl((node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y))) <=> (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y))))),
% 288.85/181.30 inference(bind,[status(th)],[])).
% 288.85/181.30 tff(196,plain,
% 288.85/181.30 (![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 288.85/181.30 inference(quant_intro,[status(thm)],[195])).
% 288.85/181.30 tff(197,plain,
% 288.85/181.30 (![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 288.85/181.30 inference(rewrite,[status(thm)],[])).
% 288.85/181.30 tff(198,plain,
% 288.85/181.30 (^[Y: $i, I0: $i, X: $i, I1: $i] : trans(monotonicity(rewrite(((node14(I0, I1, X, Y) | node15(I0, I1, X, Y)) | node16(I0, I1, X)) <=> (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y))), ((((node14(I0, I1, X, Y) | node15(I0, I1, X, Y)) | node16(I0, I1, X)) | (~node19(I0, I1, X, Y))) <=> ((node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y)) | (~node19(I0, I1, X, Y))))), rewrite(((node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y)) | (~node19(I0, I1, X, Y))) <=> (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))), ((((node14(I0, I1, X, Y) | node15(I0, I1, X, Y)) | node16(I0, I1, X)) | (~node19(I0, I1, X, Y))) <=> (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))))),
% 288.85/181.30 inference(bind,[status(th)],[])).
% 288.85/181.30 tff(199,plain,
% 288.85/181.30 (![Y: $i, I0: $i, X: $i, I1: $i] : (((node14(I0, I1, X, Y) | node15(I0, I1, X, Y)) | node16(I0, I1, X)) | (~node19(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 288.85/181.30 inference(quant_intro,[status(thm)],[198])).
% 288.85/181.30 tff(200,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : (((node14(I0, I1, X, Y) | node15(I0, I1, X, Y)) | node16(I0, I1, X)) | (~node19(I0, I1, X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_c_h_element_12')).
% 288.85/181.30 tff(201,plain,
% 288.85/181.30 (![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 288.85/181.30 inference(modus_ponens,[status(thm)],[200, 199])).
% 288.85/181.30 tff(202,plain,
% 288.85/181.30 (![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 288.85/181.30 inference(modus_ponens,[status(thm)],[201, 197])).
% 288.85/181.30 tff(203,plain,(
% 288.85/181.30 ![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 288.85/181.30 inference(skolemize,[status(sab)],[202])).
% 288.85/181.30 tff(204,plain,
% 288.85/181.30 (![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 288.85/181.30 inference(modus_ponens,[status(thm)],[203, 196])).
% 288.85/181.30 tff(205,plain,
% 288.85/181.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_3, c_e, s0, s1) | node15(c_e_h_3, c_e, s0, s1) | (~node19(c_e_h_3, c_e, s0, s1)) | node16(c_e_h_3, c_e, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_e, s0, s1) | node15(c_e_h_3, c_e, s0, s1) | (~node19(c_e_h_3, c_e, s0, s1)) | node16(c_e_h_3, c_e, s0))),
% 288.85/181.30 inference(rewrite,[status(thm)],[])).
% 288.85/181.30 tff(206,plain,
% 288.85/181.30 ((node16(c_e_h_3, c_e, s0) | node14(c_e_h_3, c_e, s0, s1) | node15(c_e_h_3, c_e, s0, s1) | (~node19(c_e_h_3, c_e, s0, s1))) <=> (node14(c_e_h_3, c_e, s0, s1) | node15(c_e_h_3, c_e, s0, s1) | (~node19(c_e_h_3, c_e, s0, s1)) | node16(c_e_h_3, c_e, s0))),
% 288.85/181.30 inference(rewrite,[status(thm)],[])).
% 288.85/181.30 tff(207,plain,
% 288.85/181.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s0) | node14(c_e_h_3, c_e, s0, s1) | node15(c_e_h_3, c_e, s0, s1) | (~node19(c_e_h_3, c_e, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_3, c_e, s0, s1) | node15(c_e_h_3, c_e, s0, s1) | (~node19(c_e_h_3, c_e, s0, s1)) | node16(c_e_h_3, c_e, s0)))),
% 288.85/181.30 inference(monotonicity,[status(thm)],[206])).
% 288.85/181.30 tff(208,plain,
% 288.85/181.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s0) | node14(c_e_h_3, c_e, s0, s1) | node15(c_e_h_3, c_e, s0, s1) | (~node19(c_e_h_3, c_e, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_e, s0, s1) | node15(c_e_h_3, c_e, s0, s1) | (~node19(c_e_h_3, c_e, s0, s1)) | node16(c_e_h_3, c_e, s0))),
% 288.85/181.30 inference(transitivity,[status(thm)],[207, 205])).
% 288.85/181.30 tff(209,plain,
% 288.85/181.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s0) | node14(c_e_h_3, c_e, s0, s1) | node15(c_e_h_3, c_e, s0, s1) | (~node19(c_e_h_3, c_e, s0, s1)))),
% 288.85/181.30 inference(quant_inst,[status(thm)],[])).
% 288.85/181.30 tff(210,plain,
% 288.85/181.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_e, s0, s1) | node15(c_e_h_3, c_e, s0, s1) | (~node19(c_e_h_3, c_e, s0, s1)) | node16(c_e_h_3, c_e, s0)),
% 288.85/181.30 inference(modus_ponens,[status(thm)],[209, 208])).
% 288.85/181.30 tff(211,plain,
% 288.85/181.30 (node14(c_e_h_3, c_e, s0, s1) | node15(c_e_h_3, c_e, s0, s1) | node16(c_e_h_3, c_e, s0)),
% 288.85/181.30 inference(unit_resolution,[status(thm)],[210, 204, 194])).
% 288.85/181.30 tff(212,plain,
% 288.85/181.30 (node14(c_e_h_3, c_e, s0, s1) | node15(c_e_h_3, c_e, s0, s1)),
% 288.85/181.30 inference(unit_resolution,[status(thm)],[211, 183])).
% 288.85/181.30 tff(213,plain,
% 288.85/181.30 (node14(c_e_h_3, c_e, s0, s1)),
% 288.85/181.30 inference(unit_resolution,[status(thm)],[212, 153])).
% 288.85/181.30 tff(214,plain,
% 288.85/181.30 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl(((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y))) <=> ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y))))),
% 288.85/181.30 inference(bind,[status(th)],[])).
% 288.85/181.30 tff(215,plain,
% 288.85/181.30 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))),
% 288.85/181.30 inference(quant_intro,[status(thm)],[214])).
% 288.85/181.30 tff(216,plain,
% 288.85/181.30 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))),
% 288.85/181.30 inference(rewrite,[status(thm)],[])).
% 288.85/181.30 tff(217,plain,
% 288.85/181.30 (^[Y: $i, I0: $i, X: $i, I1: $i] : rewrite((((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_in1(I0, I1, X)) | (~node14(I0, I1, X, Y))) <=> ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y))))),
% 288.85/181.30 inference(bind,[status(th)],[])).
% 288.85/181.30 tff(218,plain,
% 288.85/181.30 (![Y: $i, I0: $i, X: $i, I1: $i] : (((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_in1(I0, I1, X)) | (~node14(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))),
% 288.85/181.30 inference(quant_intro,[status(thm)],[217])).
% 288.85/181.30 tff(219,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : (((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_in1(I0, I1, X)) | (~node14(I0, I1, X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_c_h_element_3')).
% 288.85/181.30 tff(220,plain,
% 288.85/181.30 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))),
% 288.85/181.31 inference(modus_ponens,[status(thm)],[219, 218])).
% 288.85/181.31 tff(221,plain,
% 288.85/181.31 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))),
% 288.85/181.31 inference(modus_ponens,[status(thm)],[220, 216])).
% 288.85/181.31 tff(222,plain,(
% 288.85/181.31 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))),
% 288.85/181.31 inference(skolemize,[status(sab)],[221])).
% 288.85/181.31 tff(223,plain,
% 288.85/181.31 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))),
% 288.85/181.31 inference(modus_ponens,[status(thm)],[222, 215])).
% 288.85/181.31 tff(224,plain,
% 288.85/181.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s1)) | m_c_h_element_v_in1(c_e_h_3, c_e, s0) | (~node14(c_e_h_3, c_e, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s1)) | m_c_h_element_v_in1(c_e_h_3, c_e, s0) | (~node14(c_e_h_3, c_e, s0, s1)))),
% 288.85/181.31 inference(rewrite,[status(thm)],[])).
% 288.85/181.31 tff(225,plain,
% 288.85/181.31 (((~node14(c_e_h_3, c_e, s0, s1)) | m_c_h_element_v_in1(c_e_h_3, c_e, s0) | (~m_c_h_element_v_out(c_e_h_3, c_e, s1))) <=> ((~m_c_h_element_v_out(c_e_h_3, c_e, s1)) | m_c_h_element_v_in1(c_e_h_3, c_e, s0) | (~node14(c_e_h_3, c_e, s0, s1)))),
% 288.85/181.31 inference(rewrite,[status(thm)],[])).
% 288.85/181.31 tff(226,plain,
% 288.85/181.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s0, s1)) | m_c_h_element_v_in1(c_e_h_3, c_e, s0) | (~m_c_h_element_v_out(c_e_h_3, c_e, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s1)) | m_c_h_element_v_in1(c_e_h_3, c_e, s0) | (~node14(c_e_h_3, c_e, s0, s1))))),
% 288.85/181.31 inference(monotonicity,[status(thm)],[225])).
% 288.85/181.31 tff(227,plain,
% 288.85/181.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s0, s1)) | m_c_h_element_v_in1(c_e_h_3, c_e, s0) | (~m_c_h_element_v_out(c_e_h_3, c_e, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s1)) | m_c_h_element_v_in1(c_e_h_3, c_e, s0) | (~node14(c_e_h_3, c_e, s0, s1)))),
% 288.85/181.31 inference(transitivity,[status(thm)],[226, 224])).
% 288.85/181.31 tff(228,plain,
% 288.85/181.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s0, s1)) | m_c_h_element_v_in1(c_e_h_3, c_e, s0) | (~m_c_h_element_v_out(c_e_h_3, c_e, s1)))),
% 288.85/181.31 inference(quant_inst,[status(thm)],[])).
% 288.85/181.31 tff(229,plain,
% 288.85/181.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s1)) | m_c_h_element_v_in1(c_e_h_3, c_e, s0) | (~node14(c_e_h_3, c_e, s0, s1))),
% 288.85/181.31 inference(modus_ponens,[status(thm)],[228, 227])).
% 288.85/181.31 tff(230,plain,
% 288.85/181.31 ($false),
% 288.85/181.31 inference(unit_resolution,[status(thm)],[229, 223, 136, 213, 135])).
% 288.85/181.31 tff(231,plain,(~m_c_h_element_v_out(c_e_h_3, c_e, s1)), inference(lemma,lemma(discharge,[]))).
% 288.85/181.31 tff(232,plain,
% 288.85/181.31 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s1)) | m_c_h_element_v_out(c_e_h_3, c_e, s1))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s1)) | m_c_h_element_v_out(c_e_h_3, c_e, s1))),
% 288.85/181.31 inference(rewrite,[status(thm)],[])).
% 288.85/181.31 tff(233,plain,
% 288.85/181.31 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s1)) | m_c_h_element_v_out(c_e_h_3, c_e, s1))),
% 288.85/181.31 inference(quant_inst,[status(thm)],[])).
% 288.85/181.31 tff(234,plain,
% 288.85/181.31 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s1)) | m_c_h_element_v_out(c_e_h_3, c_e, s1)),
% 288.85/181.31 inference(modus_ponens,[status(thm)],[233, 232])).
% 288.85/181.31 tff(235,plain,
% 288.85/181.31 (~m_and_h_gate_v_in1(c_e_h_3, c_r, s1)),
% 288.85/181.31 inference(unit_resolution,[status(thm)],[234, 24, 231])).
% 288.85/181.31 tff(236,plain,
% 288.85/181.31 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s1))),
% 288.85/181.31 inference(rewrite,[status(thm)],[])).
% 288.85/181.31 tff(237,plain,
% 288.85/181.31 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s1))),
% 288.85/181.31 inference(quant_inst,[status(thm)],[])).
% 288.85/181.31 tff(238,plain,
% 288.85/181.31 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s1)),
% 288.85/181.31 inference(modus_ponens,[status(thm)],[237, 236])).
% 288.85/181.31 tff(239,plain,
% 288.85/181.31 (~node20(c_e_h_3, c_r, s1)),
% 288.85/181.31 inference(unit_resolution,[status(thm)],[238, 38, 235])).
% 288.85/181.31 tff(240,assumption,(~node20(c_e_h_3, c_r, s1)), introduced(assumption)).
% 288.85/181.31 tff(241,assumption,(node21(c_e_h_3, c_r, s1, s2)), introduced(assumption)).
% 288.85/181.31 tff(242,plain,
% 288.85/181.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s2)) | (~node21(c_e_h_3, c_r, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_r, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s2)) | (~node21(c_e_h_3, c_r, s1, s2)))),
% 288.85/181.31 inference(rewrite,[status(thm)],[])).
% 288.85/181.31 tff(243,plain,
% 288.85/181.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s2)) | (~node21(c_e_h_3, c_r, s1, s2)))),
% 288.85/181.31 inference(quant_inst,[status(thm)],[])).
% 288.85/181.31 tff(244,plain,
% 288.85/181.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_r, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s2)) | (~node21(c_e_h_3, c_r, s1, s2))),
% 288.85/181.31 inference(modus_ponens,[status(thm)],[243, 242])).
% 288.85/181.31 tff(245,plain,
% 288.85/181.31 ($false),
% 288.85/181.31 inference(unit_resolution,[status(thm)],[244, 52, 241, 4, 240])).
% 288.85/181.31 tff(246,plain,((~node21(c_e_h_3, c_r, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s2)) | node20(c_e_h_3, c_r, s1)), inference(lemma,lemma(discharge,[]))).
% 288.85/181.31 tff(247,plain,
% 288.85/181.31 ((~node21(c_e_h_3, c_r, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s2))),
% 288.85/181.31 inference(unit_resolution,[status(thm)],[246, 239])).
% 288.85/181.31 tff(248,plain,
% 288.85/181.31 (~node21(c_e_h_3, c_r, s1, s2)),
% 288.85/181.31 inference(unit_resolution,[status(thm)],[247, 4])).
% 288.85/181.31 tff(249,plain,
% 288.85/181.31 (succ(s1, s2) <=> succ(s1, s2)),
% 288.85/181.31 inference(rewrite,[status(thm)],[])).
% 288.85/181.31 tff(250,axiom,(succ(s1, s2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound2')).
% 288.85/181.31 tff(251,plain,
% 288.85/181.31 (succ(s1, s2)),
% 288.85/181.31 inference(modus_ponens,[status(thm)],[250, 249])).
% 288.85/181.31 tff(252,plain,
% 288.85/181.31 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s1, s2)) | trans(s1, s2))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s1, s2)) | trans(s1, s2))),
% 288.85/181.31 inference(rewrite,[status(thm)],[])).
% 288.85/181.31 tff(253,plain,
% 288.85/181.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s1, s2)) | trans(s1, s2))),
% 288.85/181.31 inference(quant_inst,[status(thm)],[])).
% 288.85/181.31 tff(254,plain,
% 288.85/181.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s1, s2)) | trans(s1, s2)),
% 288.85/181.31 inference(modus_ponens,[status(thm)],[253, 252])).
% 288.85/181.31 tff(255,plain,
% 288.85/181.31 (trans(s1, s2)),
% 288.85/181.31 inference(unit_resolution,[status(thm)],[254, 251, 65])).
% 288.85/181.31 tff(256,plain,
% 288.85/181.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_3, c_r, s1, s2) | node22(c_e_h_3, c_r, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_3, c_r, s1, s2) | node22(c_e_h_3, c_r, s1, s2))),
% 288.85/181.31 inference(rewrite,[status(thm)],[])).
% 288.85/181.31 tff(257,plain,
% 288.85/181.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_3, c_r, s1, s2) | node22(c_e_h_3, c_r, s1, s2))),
% 288.85/181.31 inference(quant_inst,[status(thm)],[])).
% 288.85/181.31 tff(258,plain,
% 288.85/181.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_3, c_r, s1, s2) | node22(c_e_h_3, c_r, s1, s2)),
% 288.85/181.31 inference(modus_ponens,[status(thm)],[257, 256])).
% 288.85/181.31 tff(259,plain,
% 288.85/181.31 (node21(c_e_h_3, c_r, s1, s2) | node22(c_e_h_3, c_r, s1, s2)),
% 288.85/181.31 inference(unit_resolution,[status(thm)],[258, 82, 255])).
% 288.85/181.31 tff(260,plain,
% 288.85/181.31 ($false),
% 288.85/181.31 inference(unit_resolution,[status(thm)],[259, 248, 120])).
% 288.85/181.31 tff(261,plain,(~m_and_h_gate_v_out(c_e_h_3, c_r, s2)), inference(lemma,lemma(discharge,[]))).
% 288.85/181.31 tff(262,plain,
% 288.85/181.31 (^[I0: $i, X: $i] : refl(((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X)) <=> ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X)))),
% 288.85/181.31 inference(bind,[status(th)],[])).
% 288.85/181.31 tff(263,plain,
% 288.85/181.31 (![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X)) <=> ![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))),
% 288.85/181.31 inference(quant_intro,[status(thm)],[262])).
% 288.85/181.31 tff(264,plain,
% 288.85/181.31 (![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X)) <=> ![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))),
% 288.85/181.31 inference(rewrite,[status(thm)],[])).
% 288.85/181.31 tff(265,axiom,(![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_81')).
% 288.85/181.31 tff(266,plain,
% 288.85/181.31 (![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))),
% 288.85/181.31 inference(modus_ponens,[status(thm)],[265, 264])).
% 288.85/181.31 tff(267,plain,(
% 288.85/181.31 ![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))),
% 288.85/181.31 inference(skolemize,[status(sab)],[266])).
% 288.85/181.31 tff(268,plain,
% 288.85/181.31 (![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))),
% 288.85/181.31 inference(modus_ponens,[status(thm)],[267, 263])).
% 288.85/181.31 tff(269,plain,
% 288.85/181.31 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_3, c_u, s2)) | m_and_h_gate_v_out(c_e_h_3, c_r, s2))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_3, c_u, s2)) | m_and_h_gate_v_out(c_e_h_3, c_r, s2))),
% 288.85/181.31 inference(rewrite,[status(thm)],[])).
% 288.85/181.31 tff(270,plain,
% 288.85/181.31 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_3, c_u, s2)) | m_and_h_gate_v_out(c_e_h_3, c_r, s2))),
% 288.85/181.31 inference(quant_inst,[status(thm)],[])).
% 288.85/181.31 tff(271,plain,
% 288.85/181.31 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_3, c_u, s2)) | m_and_h_gate_v_out(c_e_h_3, c_r, s2)),
% 288.85/181.31 inference(modus_ponens,[status(thm)],[270, 269])).
% 288.85/181.31 tff(272,plain,
% 288.85/181.31 (~m_user_v_ack(c_e_h_3, c_u, s2)),
% 288.85/181.31 inference(unit_resolution,[status(thm)],[271, 268, 261])).
% 288.85/181.31 tff(273,assumption,(~m_user_v_ack(c_e_h_3, c_u, s2)), introduced(assumption)).
% 288.85/181.31 tff(274,assumption,(node7(c_e_h_3, c_u, s2, s3)), introduced(assumption)).
% 288.85/181.31 tff(275,plain,
% 288.85/181.31 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl(((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y)) <=> ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y)))),
% 288.85/181.32 inference(bind,[status(th)],[])).
% 288.85/181.32 tff(276,plain,
% 288.85/181.32 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))),
% 288.85/181.32 inference(quant_intro,[status(thm)],[275])).
% 288.85/181.32 tff(277,plain,
% 288.85/181.32 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))),
% 288.85/181.32 inference(rewrite,[status(thm)],[])).
% 288.85/181.32 tff(278,plain,
% 288.85/181.32 (^[Y: $i, I0: $i, X: $i, I1: $i] : trans(monotonicity(rewrite((m_user_v_req(I0, I1, Y) | m_user_v_ack(I0, I1, X)) <=> (m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))), (((m_user_v_req(I0, I1, Y) | m_user_v_ack(I0, I1, X)) | (~node7(I0, I1, X, Y))) <=> ((m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y)) | (~node7(I0, I1, X, Y))))), rewrite(((m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y)) | (~node7(I0, I1, X, Y))) <=> ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))), (((m_user_v_req(I0, I1, Y) | m_user_v_ack(I0, I1, X)) | (~node7(I0, I1, X, Y))) <=> ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))))),
% 288.85/181.32 inference(bind,[status(th)],[])).
% 288.85/181.32 tff(279,plain,
% 288.85/181.32 (![Y: $i, I0: $i, X: $i, I1: $i] : ((m_user_v_req(I0, I1, Y) | m_user_v_ack(I0, I1, X)) | (~node7(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))),
% 288.85/181.32 inference(quant_intro,[status(thm)],[278])).
% 288.85/181.32 tff(280,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : ((m_user_v_req(I0, I1, Y) | m_user_v_ack(I0, I1, X)) | (~node7(I0, I1, X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_user_2')).
% 288.85/181.32 tff(281,plain,
% 288.85/181.32 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))),
% 288.85/181.32 inference(modus_ponens,[status(thm)],[280, 279])).
% 288.85/181.32 tff(282,plain,
% 288.85/181.32 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))),
% 288.85/181.32 inference(modus_ponens,[status(thm)],[281, 277])).
% 288.85/181.32 tff(283,plain,(
% 288.85/181.32 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))),
% 288.85/181.32 inference(skolemize,[status(sab)],[282])).
% 288.85/181.32 tff(284,plain,
% 288.85/181.32 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))),
% 288.85/181.32 inference(modus_ponens,[status(thm)],[283, 276])).
% 288.85/181.32 tff(285,plain,
% 288.85/181.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | ((~node7(c_e_h_3, c_u, s2, s3)) | m_user_v_ack(c_e_h_3, c_u, s2) | m_user_v_req(c_e_h_3, c_u, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | (~node7(c_e_h_3, c_u, s2, s3)) | m_user_v_ack(c_e_h_3, c_u, s2) | m_user_v_req(c_e_h_3, c_u, s3))),
% 288.85/181.32 inference(rewrite,[status(thm)],[])).
% 288.85/181.32 tff(286,plain,
% 288.85/181.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | ((~node7(c_e_h_3, c_u, s2, s3)) | m_user_v_ack(c_e_h_3, c_u, s2) | m_user_v_req(c_e_h_3, c_u, s3))),
% 288.85/181.32 inference(quant_inst,[status(thm)],[])).
% 288.85/181.32 tff(287,plain,
% 288.85/181.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | (~node7(c_e_h_3, c_u, s2, s3)) | m_user_v_ack(c_e_h_3, c_u, s2) | m_user_v_req(c_e_h_3, c_u, s3)),
% 288.85/181.32 inference(modus_ponens,[status(thm)],[286, 285])).
% 288.85/181.32 tff(288,plain,
% 288.85/181.32 ($false),
% 288.85/181.32 inference(unit_resolution,[status(thm)],[287, 284, 274, 3, 273])).
% 288.85/181.32 tff(289,plain,((~node7(c_e_h_3, c_u, s2, s3)) | m_user_v_req(c_e_h_3, c_u, s3) | m_user_v_ack(c_e_h_3, c_u, s2)), inference(lemma,lemma(discharge,[]))).
% 288.85/181.32 tff(290,plain,
% 288.85/181.32 (~node7(c_e_h_3, c_u, s2, s3)),
% 288.85/181.32 inference(unit_resolution,[status(thm)],[289, 3, 273])).
% 288.85/181.32 tff(291,assumption,(m_user_v_req(c_e_h_3, c_u, s2)), introduced(assumption)).
% 288.85/181.32 tff(292,assumption,(node8(c_e_h_3, c_u, s2, s3)), introduced(assumption)).
% 288.85/181.32 tff(293,plain,
% 288.85/181.32 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl((m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X))) <=> (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X))))),
% 288.85/181.32 inference(bind,[status(th)],[])).
% 288.85/181.32 tff(294,plain,
% 288.85/181.32 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))),
% 288.85/181.32 inference(quant_intro,[status(thm)],[293])).
% 288.85/181.32 tff(295,plain,
% 288.85/181.32 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))),
% 288.85/181.32 inference(rewrite,[status(thm)],[])).
% 288.85/181.32 tff(296,plain,
% 288.85/181.32 (^[Y: $i, I0: $i, X: $i, I1: $i] : trans(monotonicity(rewrite((m_user_v_req(I0, I1, Y) | (~m_user_v_req(I0, I1, X))) <=> (m_user_v_req(I0, I1, Y) | (~m_user_v_req(I0, I1, X)))), (((m_user_v_req(I0, I1, Y) | (~m_user_v_req(I0, I1, X))) | (~node8(I0, I1, X, Y))) <=> ((m_user_v_req(I0, I1, Y) | (~m_user_v_req(I0, I1, X))) | (~node8(I0, I1, X, Y))))), rewrite(((m_user_v_req(I0, I1, Y) | (~m_user_v_req(I0, I1, X))) | (~node8(I0, I1, X, Y))) <=> (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))), (((m_user_v_req(I0, I1, Y) | (~m_user_v_req(I0, I1, X))) | (~node8(I0, I1, X, Y))) <=> (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))))),
% 288.85/181.32 inference(bind,[status(th)],[])).
% 288.85/181.32 tff(297,plain,
% 288.85/181.32 (![Y: $i, I0: $i, X: $i, I1: $i] : ((m_user_v_req(I0, I1, Y) | (~m_user_v_req(I0, I1, X))) | (~node8(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))),
% 288.85/181.32 inference(quant_intro,[status(thm)],[296])).
% 288.85/181.32 tff(298,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : ((m_user_v_req(I0, I1, Y) | (~m_user_v_req(I0, I1, X))) | (~node8(I0, I1, X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_user_4')).
% 288.85/181.32 tff(299,plain,
% 288.85/181.32 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))),
% 288.85/181.32 inference(modus_ponens,[status(thm)],[298, 297])).
% 288.85/181.32 tff(300,plain,
% 288.85/181.32 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))),
% 288.85/181.32 inference(modus_ponens,[status(thm)],[299, 295])).
% 288.85/181.32 tff(301,plain,(
% 288.85/181.32 ![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))),
% 288.85/181.32 inference(skolemize,[status(sab)],[300])).
% 288.85/181.32 tff(302,plain,
% 288.85/181.32 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))),
% 288.85/181.32 inference(modus_ponens,[status(thm)],[301, 294])).
% 288.85/181.32 tff(303,plain,
% 288.85/181.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_3, c_u, s3) | (~m_user_v_req(c_e_h_3, c_u, s2)) | (~node8(c_e_h_3, c_u, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | m_user_v_req(c_e_h_3, c_u, s3) | (~m_user_v_req(c_e_h_3, c_u, s2)) | (~node8(c_e_h_3, c_u, s2, s3)))),
% 288.85/181.32 inference(rewrite,[status(thm)],[])).
% 288.85/181.32 tff(304,plain,
% 288.85/181.32 ((m_user_v_req(c_e_h_3, c_u, s3) | (~node8(c_e_h_3, c_u, s2, s3)) | (~m_user_v_req(c_e_h_3, c_u, s2))) <=> (m_user_v_req(c_e_h_3, c_u, s3) | (~m_user_v_req(c_e_h_3, c_u, s2)) | (~node8(c_e_h_3, c_u, s2, s3)))),
% 288.85/181.32 inference(rewrite,[status(thm)],[])).
% 288.85/181.32 tff(305,plain,
% 288.85/181.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_3, c_u, s3) | (~node8(c_e_h_3, c_u, s2, s3)) | (~m_user_v_req(c_e_h_3, c_u, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_3, c_u, s3) | (~m_user_v_req(c_e_h_3, c_u, s2)) | (~node8(c_e_h_3, c_u, s2, s3))))),
% 288.85/181.32 inference(monotonicity,[status(thm)],[304])).
% 288.85/181.32 tff(306,plain,
% 288.85/181.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_3, c_u, s3) | (~node8(c_e_h_3, c_u, s2, s3)) | (~m_user_v_req(c_e_h_3, c_u, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | m_user_v_req(c_e_h_3, c_u, s3) | (~m_user_v_req(c_e_h_3, c_u, s2)) | (~node8(c_e_h_3, c_u, s2, s3)))),
% 288.85/181.32 inference(transitivity,[status(thm)],[305, 303])).
% 288.85/181.32 tff(307,plain,
% 288.85/181.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_3, c_u, s3) | (~node8(c_e_h_3, c_u, s2, s3)) | (~m_user_v_req(c_e_h_3, c_u, s2)))),
% 288.85/181.32 inference(quant_inst,[status(thm)],[])).
% 288.85/181.32 tff(308,plain,
% 288.85/181.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | m_user_v_req(c_e_h_3, c_u, s3) | (~m_user_v_req(c_e_h_3, c_u, s2)) | (~node8(c_e_h_3, c_u, s2, s3))),
% 288.85/181.32 inference(modus_ponens,[status(thm)],[307, 306])).
% 288.85/181.32 tff(309,plain,
% 288.85/181.32 ($false),
% 288.85/181.32 inference(unit_resolution,[status(thm)],[308, 302, 292, 291, 3])).
% 288.85/181.32 tff(310,plain,((~node8(c_e_h_3, c_u, s2, s3)) | (~m_user_v_req(c_e_h_3, c_u, s2)) | m_user_v_req(c_e_h_3, c_u, s3)), inference(lemma,lemma(discharge,[]))).
% 288.85/181.32 tff(311,plain,
% 288.85/181.32 (~node8(c_e_h_3, c_u, s2, s3)),
% 288.85/181.32 inference(unit_resolution,[status(thm)],[310, 3, 291])).
% 288.85/181.32 tff(312,plain,
% 288.85/181.32 (succ(s2, s3) <=> succ(s2, s3)),
% 288.85/181.32 inference(rewrite,[status(thm)],[])).
% 288.85/181.32 tff(313,axiom,(succ(s2, s3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound3')).
% 288.85/181.32 tff(314,plain,
% 288.85/181.32 (succ(s2, s3)),
% 288.85/181.32 inference(modus_ponens,[status(thm)],[313, 312])).
% 288.85/181.32 tff(315,plain,
% 288.85/181.32 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s2, s3)) | trans(s2, s3))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s2, s3)) | trans(s2, s3))),
% 288.85/181.32 inference(rewrite,[status(thm)],[])).
% 288.85/181.32 tff(316,plain,
% 288.85/181.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s2, s3)) | trans(s2, s3))),
% 288.85/181.32 inference(quant_inst,[status(thm)],[])).
% 288.85/181.32 tff(317,plain,
% 288.85/181.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s2, s3)) | trans(s2, s3)),
% 288.85/181.32 inference(modus_ponens,[status(thm)],[316, 315])).
% 288.85/181.32 tff(318,plain,
% 288.85/181.32 (trans(s2, s3)),
% 288.85/181.32 inference(unit_resolution,[status(thm)],[317, 314, 65])).
% 288.85/181.32 tff(319,plain,
% 288.85/181.32 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl(((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y)) <=> ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y)))),
% 288.85/181.32 inference(bind,[status(th)],[])).
% 288.85/181.32 tff(320,plain,
% 288.85/181.32 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))),
% 288.85/181.32 inference(quant_intro,[status(thm)],[319])).
% 288.85/181.32 tff(321,plain,
% 288.85/181.32 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))),
% 288.85/181.32 inference(rewrite,[status(thm)],[])).
% 288.85/181.32 tff(322,plain,
% 288.85/181.32 (^[Y: $i, I0: $i, X: $i, I1: $i] : rewrite(((node7(I0, I1, X, Y) | node8(I0, I1, X, Y)) | (~trans(X, Y))) <=> ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y)))),
% 288.85/181.32 inference(bind,[status(th)],[])).
% 288.85/181.32 tff(323,plain,
% 288.85/181.32 (![Y: $i, I0: $i, X: $i, I1: $i] : ((node7(I0, I1, X, Y) | node8(I0, I1, X, Y)) | (~trans(X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))),
% 288.85/181.32 inference(quant_intro,[status(thm)],[322])).
% 288.85/181.32 tff(324,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : ((node7(I0, I1, X, Y) | node8(I0, I1, X, Y)) | (~trans(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_user_6')).
% 288.85/181.32 tff(325,plain,
% 288.85/181.32 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))),
% 288.85/181.33 inference(modus_ponens,[status(thm)],[324, 323])).
% 288.85/181.33 tff(326,plain,
% 288.85/181.33 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))),
% 288.85/181.33 inference(modus_ponens,[status(thm)],[325, 321])).
% 288.85/181.33 tff(327,plain,(
% 288.85/181.33 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))),
% 288.85/181.33 inference(skolemize,[status(sab)],[326])).
% 288.85/181.33 tff(328,plain,
% 288.85/181.33 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))),
% 288.85/181.33 inference(modus_ponens,[status(thm)],[327, 320])).
% 288.85/181.33 tff(329,plain,
% 288.85/181.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | ((~trans(s2, s3)) | node7(c_e_h_3, c_u, s2, s3) | node8(c_e_h_3, c_u, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | (~trans(s2, s3)) | node7(c_e_h_3, c_u, s2, s3) | node8(c_e_h_3, c_u, s2, s3))),
% 288.85/181.33 inference(rewrite,[status(thm)],[])).
% 288.85/181.33 tff(330,plain,
% 288.85/181.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | ((~trans(s2, s3)) | node7(c_e_h_3, c_u, s2, s3) | node8(c_e_h_3, c_u, s2, s3))),
% 288.85/181.33 inference(quant_inst,[status(thm)],[])).
% 288.85/181.33 tff(331,plain,
% 288.85/181.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | (~trans(s2, s3)) | node7(c_e_h_3, c_u, s2, s3) | node8(c_e_h_3, c_u, s2, s3)),
% 288.85/181.33 inference(modus_ponens,[status(thm)],[330, 329])).
% 288.85/181.33 tff(332,plain,
% 288.85/181.33 (node7(c_e_h_3, c_u, s2, s3) | node8(c_e_h_3, c_u, s2, s3)),
% 288.85/181.33 inference(unit_resolution,[status(thm)],[331, 328, 318])).
% 288.85/181.33 tff(333,plain,
% 288.85/181.33 ($false),
% 288.85/181.33 inference(unit_resolution,[status(thm)],[332, 311, 290])).
% 288.85/181.33 tff(334,plain,(m_user_v_req(c_e_h_3, c_u, s3) | (~m_user_v_req(c_e_h_3, c_u, s2)) | m_user_v_ack(c_e_h_3, c_u, s2)), inference(lemma,lemma(discharge,[]))).
% 288.85/181.33 tff(335,plain,
% 288.85/181.33 (m_user_v_req(c_e_h_3, c_u, s3) | (~m_user_v_req(c_e_h_3, c_u, s2))),
% 288.85/181.33 inference(unit_resolution,[status(thm)],[334, 272])).
% 288.85/181.33 tff(336,plain,
% 288.85/181.33 (~m_user_v_req(c_e_h_3, c_u, s2)),
% 288.85/181.33 inference(unit_resolution,[status(thm)],[335, 3])).
% 288.85/181.33 tff(337,assumption,(~m_user_v_req(c_e_h_3, c_u, s2)), introduced(assumption)).
% 288.85/181.33 tff(338,assumption,(node7(c_e_h_3, c_u, s1, s2)), introduced(assumption)).
% 288.85/181.33 tff(339,plain,
% 288.85/181.33 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_3, c_u, s1)) | m_and_h_gate_v_out(c_e_h_3, c_r, s1))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_3, c_u, s1)) | m_and_h_gate_v_out(c_e_h_3, c_r, s1))),
% 288.85/181.33 inference(rewrite,[status(thm)],[])).
% 288.85/181.33 tff(340,plain,
% 288.85/181.33 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_3, c_u, s1)) | m_and_h_gate_v_out(c_e_h_3, c_r, s1))),
% 288.85/181.33 inference(quant_inst,[status(thm)],[])).
% 288.85/181.33 tff(341,plain,
% 288.85/181.33 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_3, c_u, s1)) | m_and_h_gate_v_out(c_e_h_3, c_r, s1)),
% 288.85/181.33 inference(modus_ponens,[status(thm)],[340, 339])).
% 288.85/181.33 tff(342,plain,
% 288.85/181.33 (~m_user_v_ack(c_e_h_3, c_u, s1)),
% 288.85/181.33 inference(unit_resolution,[status(thm)],[341, 268, 113])).
% 288.85/181.33 tff(343,plain,
% 288.85/181.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | ((~node7(c_e_h_3, c_u, s1, s2)) | m_user_v_ack(c_e_h_3, c_u, s1) | m_user_v_req(c_e_h_3, c_u, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | (~node7(c_e_h_3, c_u, s1, s2)) | m_user_v_ack(c_e_h_3, c_u, s1) | m_user_v_req(c_e_h_3, c_u, s2))),
% 288.85/181.33 inference(rewrite,[status(thm)],[])).
% 288.85/181.33 tff(344,plain,
% 288.85/181.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | ((~node7(c_e_h_3, c_u, s1, s2)) | m_user_v_ack(c_e_h_3, c_u, s1) | m_user_v_req(c_e_h_3, c_u, s2))),
% 288.85/181.33 inference(quant_inst,[status(thm)],[])).
% 288.85/181.33 tff(345,plain,
% 288.85/181.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | (~node7(c_e_h_3, c_u, s1, s2)) | m_user_v_ack(c_e_h_3, c_u, s1) | m_user_v_req(c_e_h_3, c_u, s2)),
% 288.85/181.33 inference(modus_ponens,[status(thm)],[344, 343])).
% 288.85/181.33 tff(346,plain,
% 288.85/181.33 ($false),
% 288.85/181.33 inference(unit_resolution,[status(thm)],[345, 284, 342, 338, 337])).
% 288.85/181.33 tff(347,plain,((~node7(c_e_h_3, c_u, s1, s2)) | m_user_v_req(c_e_h_3, c_u, s2)), inference(lemma,lemma(discharge,[]))).
% 288.85/181.33 tff(348,plain,
% 288.85/181.33 (~node7(c_e_h_3, c_u, s1, s2)),
% 288.85/181.33 inference(unit_resolution,[status(thm)],[347, 337])).
% 288.85/181.33 tff(349,plain,
% 288.85/181.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | ((~trans(s1, s2)) | node7(c_e_h_3, c_u, s1, s2) | node8(c_e_h_3, c_u, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | (~trans(s1, s2)) | node7(c_e_h_3, c_u, s1, s2) | node8(c_e_h_3, c_u, s1, s2))),
% 288.85/181.33 inference(rewrite,[status(thm)],[])).
% 288.85/181.33 tff(350,plain,
% 288.85/181.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | ((~trans(s1, s2)) | node7(c_e_h_3, c_u, s1, s2) | node8(c_e_h_3, c_u, s1, s2))),
% 288.85/181.33 inference(quant_inst,[status(thm)],[])).
% 288.85/181.33 tff(351,plain,
% 288.85/181.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | (~trans(s1, s2)) | node7(c_e_h_3, c_u, s1, s2) | node8(c_e_h_3, c_u, s1, s2)),
% 288.85/181.33 inference(modus_ponens,[status(thm)],[350, 349])).
% 288.85/181.33 tff(352,plain,
% 288.85/181.33 (node7(c_e_h_3, c_u, s1, s2) | node8(c_e_h_3, c_u, s1, s2)),
% 288.85/181.33 inference(unit_resolution,[status(thm)],[351, 328, 255])).
% 288.85/181.33 tff(353,plain,
% 288.85/181.33 (node8(c_e_h_3, c_u, s1, s2)),
% 288.85/181.33 inference(unit_resolution,[status(thm)],[352, 348])).
% 288.85/181.33 tff(354,assumption,(m_user_v_req(c_e_h_3, c_u, s1)), introduced(assumption)).
% 288.85/181.33 tff(355,assumption,(node8(c_e_h_3, c_u, s1, s2)), introduced(assumption)).
% 288.85/181.33 tff(356,plain,
% 288.85/181.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | ((~node8(c_e_h_3, c_u, s1, s2)) | (~m_user_v_req(c_e_h_3, c_u, s1)) | m_user_v_req(c_e_h_3, c_u, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (~node8(c_e_h_3, c_u, s1, s2)) | (~m_user_v_req(c_e_h_3, c_u, s1)) | m_user_v_req(c_e_h_3, c_u, s2))),
% 288.85/181.33 inference(rewrite,[status(thm)],[])).
% 288.85/181.33 tff(357,plain,
% 288.85/181.33 ((m_user_v_req(c_e_h_3, c_u, s2) | (~node8(c_e_h_3, c_u, s1, s2)) | (~m_user_v_req(c_e_h_3, c_u, s1))) <=> ((~node8(c_e_h_3, c_u, s1, s2)) | (~m_user_v_req(c_e_h_3, c_u, s1)) | m_user_v_req(c_e_h_3, c_u, s2))),
% 288.85/181.33 inference(rewrite,[status(thm)],[])).
% 288.85/181.33 tff(358,plain,
% 288.85/181.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_3, c_u, s2) | (~node8(c_e_h_3, c_u, s1, s2)) | (~m_user_v_req(c_e_h_3, c_u, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | ((~node8(c_e_h_3, c_u, s1, s2)) | (~m_user_v_req(c_e_h_3, c_u, s1)) | m_user_v_req(c_e_h_3, c_u, s2)))),
% 288.85/181.33 inference(monotonicity,[status(thm)],[357])).
% 288.85/181.33 tff(359,plain,
% 288.85/181.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_3, c_u, s2) | (~node8(c_e_h_3, c_u, s1, s2)) | (~m_user_v_req(c_e_h_3, c_u, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (~node8(c_e_h_3, c_u, s1, s2)) | (~m_user_v_req(c_e_h_3, c_u, s1)) | m_user_v_req(c_e_h_3, c_u, s2))),
% 288.85/181.33 inference(transitivity,[status(thm)],[358, 356])).
% 288.85/181.33 tff(360,plain,
% 288.85/181.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_3, c_u, s2) | (~node8(c_e_h_3, c_u, s1, s2)) | (~m_user_v_req(c_e_h_3, c_u, s1)))),
% 288.85/181.33 inference(quant_inst,[status(thm)],[])).
% 288.85/181.33 tff(361,plain,
% 288.85/181.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (~node8(c_e_h_3, c_u, s1, s2)) | (~m_user_v_req(c_e_h_3, c_u, s1)) | m_user_v_req(c_e_h_3, c_u, s2)),
% 288.85/181.33 inference(modus_ponens,[status(thm)],[360, 359])).
% 288.85/181.33 tff(362,plain,
% 288.85/181.33 ($false),
% 288.85/181.33 inference(unit_resolution,[status(thm)],[361, 302, 355, 337, 354])).
% 288.85/181.33 tff(363,plain,((~node8(c_e_h_3, c_u, s1, s2)) | m_user_v_req(c_e_h_3, c_u, s2) | (~m_user_v_req(c_e_h_3, c_u, s1))), inference(lemma,lemma(discharge,[]))).
% 288.85/181.33 tff(364,plain,
% 288.85/181.33 (~m_user_v_req(c_e_h_3, c_u, s1)),
% 288.85/181.33 inference(unit_resolution,[status(thm)],[363, 353, 337])).
% 288.85/181.33 tff(365,assumption,(~m_user_v_req(c_e_h_3, c_u, s1)), introduced(assumption)).
% 288.85/181.33 tff(366,plain,
% 288.85/181.33 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_3, c_u, s0)) | m_and_h_gate_v_out(c_e_h_3, c_r, s0))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_3, c_u, s0)) | m_and_h_gate_v_out(c_e_h_3, c_r, s0))),
% 288.85/181.33 inference(rewrite,[status(thm)],[])).
% 288.85/181.33 tff(367,plain,
% 288.85/181.33 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_3, c_u, s0)) | m_and_h_gate_v_out(c_e_h_3, c_r, s0))),
% 288.85/181.33 inference(quant_inst,[status(thm)],[])).
% 288.85/181.33 tff(368,plain,
% 288.85/181.33 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_3, c_u, s0)) | m_and_h_gate_v_out(c_e_h_3, c_r, s0)),
% 288.85/181.33 inference(modus_ponens,[status(thm)],[367, 366])).
% 288.85/181.33 tff(369,plain,
% 288.85/181.33 (~m_user_v_ack(c_e_h_3, c_u, s0)),
% 288.85/181.33 inference(unit_resolution,[status(thm)],[368, 268, 98])).
% 288.85/181.33 tff(370,assumption,(node7(c_e_h_3, c_u, s0, s1)), introduced(assumption)).
% 288.85/181.33 tff(371,plain,
% 288.85/181.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | ((~node7(c_e_h_3, c_u, s0, s1)) | m_user_v_ack(c_e_h_3, c_u, s0) | m_user_v_req(c_e_h_3, c_u, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | (~node7(c_e_h_3, c_u, s0, s1)) | m_user_v_ack(c_e_h_3, c_u, s0) | m_user_v_req(c_e_h_3, c_u, s1))),
% 288.85/181.33 inference(rewrite,[status(thm)],[])).
% 288.85/181.33 tff(372,plain,
% 288.85/181.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | ((~node7(c_e_h_3, c_u, s0, s1)) | m_user_v_ack(c_e_h_3, c_u, s0) | m_user_v_req(c_e_h_3, c_u, s1))),
% 288.85/181.33 inference(quant_inst,[status(thm)],[])).
% 288.85/181.33 tff(373,plain,
% 288.85/181.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | (~node7(c_e_h_3, c_u, s0, s1)) | m_user_v_ack(c_e_h_3, c_u, s0) | m_user_v_req(c_e_h_3, c_u, s1)),
% 288.85/181.33 inference(modus_ponens,[status(thm)],[372, 371])).
% 288.85/181.33 tff(374,plain,
% 288.85/181.33 ($false),
% 288.85/181.33 inference(unit_resolution,[status(thm)],[373, 284, 370, 369, 365])).
% 288.85/181.33 tff(375,plain,((~node7(c_e_h_3, c_u, s0, s1)) | m_user_v_req(c_e_h_3, c_u, s1)), inference(lemma,lemma(discharge,[]))).
% 288.85/181.33 tff(376,plain,
% 288.85/181.33 (~node7(c_e_h_3, c_u, s0, s1)),
% 288.85/181.33 inference(unit_resolution,[status(thm)],[375, 364])).
% 288.85/181.33 tff(377,plain,
% 288.85/181.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | ((~trans(s0, s1)) | node7(c_e_h_3, c_u, s0, s1) | node8(c_e_h_3, c_u, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | (~trans(s0, s1)) | node7(c_e_h_3, c_u, s0, s1) | node8(c_e_h_3, c_u, s0, s1))),
% 288.85/181.33 inference(rewrite,[status(thm)],[])).
% 288.85/181.33 tff(378,plain,
% 288.85/181.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | ((~trans(s0, s1)) | node7(c_e_h_3, c_u, s0, s1) | node8(c_e_h_3, c_u, s0, s1))),
% 288.85/181.33 inference(quant_inst,[status(thm)],[])).
% 288.85/181.33 tff(379,plain,
% 288.85/181.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | (~trans(s0, s1)) | node7(c_e_h_3, c_u, s0, s1) | node8(c_e_h_3, c_u, s0, s1)),
% 288.85/181.34 inference(modus_ponens,[status(thm)],[378, 377])).
% 288.85/181.34 tff(380,plain,
% 288.85/181.34 (node7(c_e_h_3, c_u, s0, s1) | node8(c_e_h_3, c_u, s0, s1)),
% 288.85/181.34 inference(unit_resolution,[status(thm)],[379, 328, 72])).
% 288.85/181.34 tff(381,plain,
% 288.85/181.34 (node8(c_e_h_3, c_u, s0, s1)),
% 288.85/181.34 inference(unit_resolution,[status(thm)],[380, 376])).
% 288.85/181.34 tff(382,plain,
% 288.85/181.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | ((~m_user_v_req(c_e_h_3, c_u, s0)) | m_user_v_req(c_e_h_3, c_u, s1) | (~node8(c_e_h_3, c_u, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (~m_user_v_req(c_e_h_3, c_u, s0)) | m_user_v_req(c_e_h_3, c_u, s1) | (~node8(c_e_h_3, c_u, s0, s1)))),
% 288.85/181.34 inference(rewrite,[status(thm)],[])).
% 288.85/181.34 tff(383,plain,
% 288.85/181.34 ((m_user_v_req(c_e_h_3, c_u, s1) | (~node8(c_e_h_3, c_u, s0, s1)) | (~m_user_v_req(c_e_h_3, c_u, s0))) <=> ((~m_user_v_req(c_e_h_3, c_u, s0)) | m_user_v_req(c_e_h_3, c_u, s1) | (~node8(c_e_h_3, c_u, s0, s1)))),
% 288.85/181.34 inference(rewrite,[status(thm)],[])).
% 288.85/181.34 tff(384,plain,
% 288.85/181.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_3, c_u, s1) | (~node8(c_e_h_3, c_u, s0, s1)) | (~m_user_v_req(c_e_h_3, c_u, s0)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | ((~m_user_v_req(c_e_h_3, c_u, s0)) | m_user_v_req(c_e_h_3, c_u, s1) | (~node8(c_e_h_3, c_u, s0, s1))))),
% 288.85/181.34 inference(monotonicity,[status(thm)],[383])).
% 288.85/181.34 tff(385,plain,
% 288.85/181.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_3, c_u, s1) | (~node8(c_e_h_3, c_u, s0, s1)) | (~m_user_v_req(c_e_h_3, c_u, s0)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (~m_user_v_req(c_e_h_3, c_u, s0)) | m_user_v_req(c_e_h_3, c_u, s1) | (~node8(c_e_h_3, c_u, s0, s1)))),
% 288.85/181.34 inference(transitivity,[status(thm)],[384, 382])).
% 288.85/181.34 tff(386,plain,
% 288.85/181.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_3, c_u, s1) | (~node8(c_e_h_3, c_u, s0, s1)) | (~m_user_v_req(c_e_h_3, c_u, s0)))),
% 288.85/181.34 inference(quant_inst,[status(thm)],[])).
% 288.85/181.34 tff(387,plain,
% 288.85/181.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (~m_user_v_req(c_e_h_3, c_u, s0)) | m_user_v_req(c_e_h_3, c_u, s1) | (~node8(c_e_h_3, c_u, s0, s1))),
% 288.85/181.34 inference(modus_ponens,[status(thm)],[386, 385])).
% 288.85/181.34 tff(388,plain,
% 288.85/181.34 (~m_user_v_req(c_e_h_3, c_u, s0)),
% 288.85/181.34 inference(unit_resolution,[status(thm)],[387, 302, 381, 364])).
% 288.85/181.34 tff(389,plain,
% 288.85/181.34 (^[I0: $i, X: $i] : refl(((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X)) <=> ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X)))),
% 288.85/181.34 inference(bind,[status(th)],[])).
% 288.85/181.34 tff(390,plain,
% 288.85/181.34 (![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X)) <=> ![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))),
% 288.85/181.34 inference(quant_intro,[status(thm)],[389])).
% 288.85/181.34 tff(391,plain,
% 288.85/181.34 (![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X)) <=> ![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))),
% 288.85/181.34 inference(rewrite,[status(thm)],[])).
% 288.85/181.34 tff(392,axiom,(![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_2')).
% 288.85/181.34 tff(393,plain,
% 288.85/181.34 (![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))),
% 288.85/181.34 inference(modus_ponens,[status(thm)],[392, 391])).
% 288.85/181.34 tff(394,plain,(
% 288.85/181.34 ![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))),
% 288.85/181.34 inference(skolemize,[status(sab)],[393])).
% 288.85/181.34 tff(395,plain,
% 288.85/181.34 (![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))),
% 288.85/181.34 inference(modus_ponens,[status(thm)],[394, 390])).
% 288.85/181.34 tff(396,plain,
% 288.85/181.34 (((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_a, s0)) | m_user_v_req(c_e_h_3, c_u, s0))) <=> ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s0)) | m_user_v_req(c_e_h_3, c_u, s0))),
% 288.85/181.34 inference(rewrite,[status(thm)],[])).
% 288.85/181.34 tff(397,plain,
% 288.85/181.34 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_a, s0)) | m_user_v_req(c_e_h_3, c_u, s0))),
% 288.85/181.34 inference(quant_inst,[status(thm)],[])).
% 288.85/181.34 tff(398,plain,
% 288.85/181.34 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s0)) | m_user_v_req(c_e_h_3, c_u, s0)),
% 288.85/181.34 inference(modus_ponens,[status(thm)],[397, 396])).
% 288.85/181.34 tff(399,plain,
% 288.85/181.34 (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s0)),
% 288.85/181.34 inference(unit_resolution,[status(thm)],[398, 395, 388])).
% 288.85/181.34 tff(400,assumption,(~m_mutex_h_half_v_inp(c_e_h_3, c_a, s0)), introduced(assumption)).
% 288.85/181.34 tff(401,assumption,(m_mutex_h_half_v_out(c_e_h_3, c_a, s1)), introduced(assumption)).
% 288.85/181.34 tff(402,assumption,(m_mutex_h_half_v_out(c_e_h_3, c_a, s0)), introduced(assumption)).
% 288.85/181.34 tff(403,plain,
% 288.85/181.34 (^[I0: $i, I1: $i] : refl((~m_mutex_h_half_v_out(I0, I1, s0)) <=> (~m_mutex_h_half_v_out(I0, I1, s0)))),
% 288.85/181.34 inference(bind,[status(th)],[])).
% 288.85/181.34 tff(404,plain,
% 288.85/181.34 (![I0: $i, I1: $i] : (~m_mutex_h_half_v_out(I0, I1, s0)) <=> ![I0: $i, I1: $i] : (~m_mutex_h_half_v_out(I0, I1, s0))),
% 288.85/181.34 inference(quant_intro,[status(thm)],[403])).
% 288.85/181.34 tff(405,plain,
% 288.85/181.34 (![I0: $i, I1: $i] : (~m_mutex_h_half_v_out(I0, I1, s0)) <=> ![I0: $i, I1: $i] : (~m_mutex_h_half_v_out(I0, I1, s0))),
% 288.85/181.34 inference(rewrite,[status(thm)],[])).
% 288.85/181.34 tff(406,axiom,(![I0: $i, I1: $i] : (~m_mutex_h_half_v_out(I0, I1, s0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_mutex_h_half_1')).
% 288.85/181.34 tff(407,plain,
% 288.85/181.34 (![I0: $i, I1: $i] : (~m_mutex_h_half_v_out(I0, I1, s0))),
% 288.85/181.34 inference(modus_ponens,[status(thm)],[406, 405])).
% 288.85/181.34 tff(408,plain,(
% 288.85/181.34 ![I0: $i, I1: $i] : (~m_mutex_h_half_v_out(I0, I1, s0))),
% 288.85/181.34 inference(skolemize,[status(sab)],[407])).
% 288.85/181.34 tff(409,plain,
% 288.85/181.34 (![I0: $i, I1: $i] : (~m_mutex_h_half_v_out(I0, I1, s0))),
% 288.85/181.34 inference(modus_ponens,[status(thm)],[408, 404])).
% 288.85/181.34 tff(410,plain,
% 288.85/181.34 ((~![I0: $i, I1: $i] : (~m_mutex_h_half_v_out(I0, I1, s0))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s0))),
% 288.85/181.34 inference(quant_inst,[status(thm)],[])).
% 288.85/181.34 tff(411,plain,
% 288.85/181.34 ($false),
% 288.85/181.34 inference(unit_resolution,[status(thm)],[410, 409, 402])).
% 288.85/181.34 tff(412,plain,(~m_mutex_h_half_v_out(c_e_h_3, c_a, s0)), inference(lemma,lemma(discharge,[]))).
% 288.85/181.34 tff(413,assumption,(node13(c_e_h_3, c_a, s0, s1)), introduced(assumption)).
% 288.85/181.34 tff(414,plain,
% 288.85/181.34 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl(((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X)) <=> ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X)))),
% 288.85/181.34 inference(bind,[status(th)],[])).
% 288.85/181.34 tff(415,plain,
% 288.85/181.34 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))),
% 288.85/181.34 inference(quant_intro,[status(thm)],[414])).
% 288.85/181.34 tff(416,plain,
% 288.85/181.34 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))),
% 288.85/181.34 inference(rewrite,[status(thm)],[])).
% 288.85/181.34 tff(417,plain,
% 288.85/181.34 (^[Y: $i, I0: $i, X: $i, I1: $i] : rewrite((((~m_mutex_h_half_v_out(I0, I1, Y)) | m_mutex_h_half_v_out(I0, I1, X)) | (~node13(I0, I1, X, Y))) <=> ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X)))),
% 288.85/181.34 inference(bind,[status(th)],[])).
% 288.85/181.34 tff(418,plain,
% 288.85/181.34 (![Y: $i, I0: $i, X: $i, I1: $i] : (((~m_mutex_h_half_v_out(I0, I1, Y)) | m_mutex_h_half_v_out(I0, I1, X)) | (~node13(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))),
% 288.85/181.34 inference(quant_intro,[status(thm)],[417])).
% 288.85/181.34 tff(419,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : (((~m_mutex_h_half_v_out(I0, I1, Y)) | m_mutex_h_half_v_out(I0, I1, X)) | (~node13(I0, I1, X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_mutex_h_half_5')).
% 288.85/181.34 tff(420,plain,
% 288.85/181.34 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))),
% 288.85/181.34 inference(modus_ponens,[status(thm)],[419, 418])).
% 288.85/181.34 tff(421,plain,
% 288.85/181.34 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))),
% 288.85/181.34 inference(modus_ponens,[status(thm)],[420, 416])).
% 288.85/181.34 tff(422,plain,(
% 288.85/181.34 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))),
% 288.85/181.34 inference(skolemize,[status(sab)],[421])).
% 288.85/181.34 tff(423,plain,
% 288.85/181.34 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))),
% 288.85/181.34 inference(modus_ponens,[status(thm)],[422, 415])).
% 288.85/181.34 tff(424,plain,
% 288.85/181.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s1)) | (~node13(c_e_h_3, c_a, s0, s1)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s1)) | (~node13(c_e_h_3, c_a, s0, s1)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s0))),
% 288.85/181.34 inference(rewrite,[status(thm)],[])).
% 288.85/181.34 tff(425,plain,
% 288.85/181.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s1)) | (~node13(c_e_h_3, c_a, s0, s1)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s0))),
% 288.85/181.34 inference(quant_inst,[status(thm)],[])).
% 288.85/181.34 tff(426,plain,
% 288.85/181.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s1)) | (~node13(c_e_h_3, c_a, s0, s1)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s0)),
% 288.85/181.34 inference(modus_ponens,[status(thm)],[425, 424])).
% 288.85/181.34 tff(427,plain,
% 288.85/181.34 ($false),
% 288.85/181.34 inference(unit_resolution,[status(thm)],[426, 423, 413, 401, 412])).
% 288.85/181.34 tff(428,plain,((~node13(c_e_h_3, c_a, s0, s1)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s1))), inference(lemma,lemma(discharge,[]))).
% 288.85/181.34 tff(429,plain,
% 288.85/181.34 (~node13(c_e_h_3, c_a, s0, s1)),
% 288.85/181.34 inference(unit_resolution,[status(thm)],[428, 401])).
% 288.85/181.34 tff(430,plain,
% 288.85/181.34 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl(((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y)) <=> ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y)))),
% 288.85/181.34 inference(bind,[status(th)],[])).
% 288.85/181.34 tff(431,plain,
% 288.85/181.34 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))),
% 288.85/181.34 inference(quant_intro,[status(thm)],[430])).
% 288.85/181.34 tff(432,plain,
% 288.85/181.34 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))),
% 288.85/181.34 inference(rewrite,[status(thm)],[])).
% 288.85/181.34 tff(433,plain,
% 288.85/181.34 (^[Y: $i, I0: $i, X: $i, I1: $i] : rewrite(((node12(I0, I1, X, Y) | node13(I0, I1, X, Y)) | (~trans(X, Y))) <=> ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y)))),
% 288.85/181.34 inference(bind,[status(th)],[])).
% 288.85/181.34 tff(434,plain,
% 288.85/181.34 (![Y: $i, I0: $i, X: $i, I1: $i] : ((node12(I0, I1, X, Y) | node13(I0, I1, X, Y)) | (~trans(X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))),
% 288.85/181.35 inference(quant_intro,[status(thm)],[433])).
% 288.85/181.35 tff(435,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : ((node12(I0, I1, X, Y) | node13(I0, I1, X, Y)) | (~trans(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_mutex_h_half_6')).
% 288.85/181.35 tff(436,plain,
% 288.85/181.35 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))),
% 288.85/181.35 inference(modus_ponens,[status(thm)],[435, 434])).
% 288.85/181.35 tff(437,plain,
% 288.85/181.35 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))),
% 288.85/181.35 inference(modus_ponens,[status(thm)],[436, 432])).
% 288.85/181.35 tff(438,plain,(
% 288.85/181.35 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))),
% 288.85/181.35 inference(skolemize,[status(sab)],[437])).
% 288.85/181.35 tff(439,plain,
% 288.85/181.35 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))),
% 288.85/181.35 inference(modus_ponens,[status(thm)],[438, 431])).
% 288.85/181.35 tff(440,plain,
% 288.85/181.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s0, s1)) | node12(c_e_h_3, c_a, s0, s1) | node13(c_e_h_3, c_a, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s0, s1)) | node12(c_e_h_3, c_a, s0, s1) | node13(c_e_h_3, c_a, s0, s1))),
% 288.85/181.35 inference(rewrite,[status(thm)],[])).
% 288.85/181.35 tff(441,plain,
% 288.85/181.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s0, s1)) | node12(c_e_h_3, c_a, s0, s1) | node13(c_e_h_3, c_a, s0, s1))),
% 288.85/181.35 inference(quant_inst,[status(thm)],[])).
% 288.85/181.35 tff(442,plain,
% 288.85/181.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s0, s1)) | node12(c_e_h_3, c_a, s0, s1) | node13(c_e_h_3, c_a, s0, s1)),
% 288.85/181.35 inference(modus_ponens,[status(thm)],[441, 440])).
% 288.85/181.35 tff(443,plain,
% 288.85/181.35 (node12(c_e_h_3, c_a, s0, s1) | node13(c_e_h_3, c_a, s0, s1)),
% 288.85/181.35 inference(unit_resolution,[status(thm)],[442, 439, 72])).
% 288.85/181.35 tff(444,plain,
% 288.85/181.35 (node12(c_e_h_3, c_a, s0, s1)),
% 288.85/181.35 inference(unit_resolution,[status(thm)],[443, 429])).
% 288.85/181.35 tff(445,plain,
% 288.85/181.35 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl(((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y))) <=> ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y))))),
% 288.85/181.35 inference(bind,[status(th)],[])).
% 288.85/181.35 tff(446,plain,
% 288.85/181.35 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))),
% 288.85/181.35 inference(quant_intro,[status(thm)],[445])).
% 288.85/181.35 tff(447,plain,
% 288.85/181.35 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))),
% 288.85/181.35 inference(rewrite,[status(thm)],[])).
% 288.85/181.35 tff(448,plain,
% 288.85/181.35 (^[Y: $i, I0: $i, X: $i, I1: $i] : rewrite((((~m_mutex_h_half_v_out(I0, I1, Y)) | m_mutex_h_half_v_inp(I0, I1, X)) | (~node12(I0, I1, X, Y))) <=> ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y))))),
% 288.85/181.35 inference(bind,[status(th)],[])).
% 288.85/181.35 tff(449,plain,
% 288.85/181.35 (![Y: $i, I0: $i, X: $i, I1: $i] : (((~m_mutex_h_half_v_out(I0, I1, Y)) | m_mutex_h_half_v_inp(I0, I1, X)) | (~node12(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))),
% 288.85/181.35 inference(quant_intro,[status(thm)],[448])).
% 288.85/181.35 tff(450,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : (((~m_mutex_h_half_v_out(I0, I1, Y)) | m_mutex_h_half_v_inp(I0, I1, X)) | (~node12(I0, I1, X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_mutex_h_half_3')).
% 288.85/181.35 tff(451,plain,
% 288.85/181.35 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))),
% 288.85/181.35 inference(modus_ponens,[status(thm)],[450, 449])).
% 288.85/181.35 tff(452,plain,
% 288.85/181.35 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))),
% 288.85/181.35 inference(modus_ponens,[status(thm)],[451, 447])).
% 288.85/181.35 tff(453,plain,(
% 288.85/181.35 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))),
% 288.85/181.35 inference(skolemize,[status(sab)],[452])).
% 288.85/181.35 tff(454,plain,
% 288.85/181.35 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))),
% 288.85/181.35 inference(modus_ponens,[status(thm)],[453, 446])).
% 288.85/181.35 tff(455,plain,
% 288.85/181.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_3, c_a, s0) | (~node12(c_e_h_3, c_a, s0, s1)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s0) | (~node12(c_e_h_3, c_a, s0, s1)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s1)))),
% 288.85/181.35 inference(rewrite,[status(thm)],[])).
% 288.85/181.35 tff(456,plain,
% 288.85/181.35 (((~node12(c_e_h_3, c_a, s0, s1)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s0) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s1))) <=> (m_mutex_h_half_v_inp(c_e_h_3, c_a, s0) | (~node12(c_e_h_3, c_a, s0, s1)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s1)))),
% 288.85/181.35 inference(rewrite,[status(thm)],[])).
% 288.85/181.35 tff(457,plain,
% 288.85/181.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_a, s0, s1)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s0) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_3, c_a, s0) | (~node12(c_e_h_3, c_a, s0, s1)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s1))))),
% 288.85/181.35 inference(monotonicity,[status(thm)],[456])).
% 288.85/181.35 tff(458,plain,
% 288.85/181.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_a, s0, s1)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s0) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s0) | (~node12(c_e_h_3, c_a, s0, s1)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s1)))),
% 288.85/181.35 inference(transitivity,[status(thm)],[457, 455])).
% 288.85/181.35 tff(459,plain,
% 288.85/181.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_a, s0, s1)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s0) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s1)))),
% 288.85/181.35 inference(quant_inst,[status(thm)],[])).
% 288.85/181.35 tff(460,plain,
% 288.85/181.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s0) | (~node12(c_e_h_3, c_a, s0, s1)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s1))),
% 288.85/181.35 inference(modus_ponens,[status(thm)],[459, 458])).
% 288.85/181.35 tff(461,plain,
% 288.85/181.35 ($false),
% 288.85/181.35 inference(unit_resolution,[status(thm)],[460, 454, 444, 401, 400])).
% 288.85/181.35 tff(462,plain,((~m_mutex_h_half_v_out(c_e_h_3, c_a, s1)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s0)), inference(lemma,lemma(discharge,[]))).
% 288.85/181.35 tff(463,plain,
% 288.85/181.35 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s1)),
% 288.85/181.35 inference(unit_resolution,[status(thm)],[462, 399])).
% 288.85/181.35 tff(464,assumption,(m_mutex_h_half_v_out(c_e_h_3, c_a, s3)), introduced(assumption)).
% 288.85/181.35 tff(465,plain,
% 288.85/181.35 (((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_a, s2)) | m_user_v_req(c_e_h_3, c_u, s2))) <=> ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s2)) | m_user_v_req(c_e_h_3, c_u, s2))),
% 288.85/181.35 inference(rewrite,[status(thm)],[])).
% 288.85/181.35 tff(466,plain,
% 288.85/181.35 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_a, s2)) | m_user_v_req(c_e_h_3, c_u, s2))),
% 288.85/181.35 inference(quant_inst,[status(thm)],[])).
% 288.85/181.35 tff(467,plain,
% 288.85/181.35 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s2)) | m_user_v_req(c_e_h_3, c_u, s2)),
% 288.85/181.35 inference(modus_ponens,[status(thm)],[466, 465])).
% 288.85/181.35 tff(468,plain,
% 288.85/181.35 (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s2)),
% 288.85/181.35 inference(unit_resolution,[status(thm)],[467, 395, 337])).
% 288.85/181.35 tff(469,assumption,(~m_mutex_h_half_v_inp(c_e_h_3, c_a, s2)), introduced(assumption)).
% 288.85/181.35 tff(470,assumption,(node12(c_e_h_3, c_a, s2, s3)), introduced(assumption)).
% 288.85/181.35 tff(471,plain,
% 288.85/181.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s3)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s2) | (~node12(c_e_h_3, c_a, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s3)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s2) | (~node12(c_e_h_3, c_a, s2, s3)))),
% 288.85/181.35 inference(rewrite,[status(thm)],[])).
% 288.85/181.35 tff(472,plain,
% 288.85/181.35 (((~node12(c_e_h_3, c_a, s2, s3)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s2) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s3))) <=> ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s3)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s2) | (~node12(c_e_h_3, c_a, s2, s3)))),
% 288.85/181.35 inference(rewrite,[status(thm)],[])).
% 288.85/181.35 tff(473,plain,
% 288.85/181.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_a, s2, s3)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s2) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s3)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s2) | (~node12(c_e_h_3, c_a, s2, s3))))),
% 288.85/181.35 inference(monotonicity,[status(thm)],[472])).
% 288.85/181.35 tff(474,plain,
% 288.85/181.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_a, s2, s3)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s2) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s3)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s2) | (~node12(c_e_h_3, c_a, s2, s3)))),
% 288.85/181.35 inference(transitivity,[status(thm)],[473, 471])).
% 288.85/181.35 tff(475,plain,
% 288.85/181.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_a, s2, s3)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s2) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s3)))),
% 288.85/181.35 inference(quant_inst,[status(thm)],[])).
% 288.85/181.35 tff(476,plain,
% 288.85/181.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s3)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s2) | (~node12(c_e_h_3, c_a, s2, s3))),
% 288.85/181.35 inference(modus_ponens,[status(thm)],[475, 474])).
% 288.85/181.35 tff(477,plain,
% 288.85/181.35 ($false),
% 288.85/181.35 inference(unit_resolution,[status(thm)],[476, 454, 470, 469, 464])).
% 288.85/181.35 tff(478,plain,((~node12(c_e_h_3, c_a, s2, s3)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s2) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s3))), inference(lemma,lemma(discharge,[]))).
% 288.85/181.35 tff(479,plain,
% 288.85/181.35 (~node12(c_e_h_3, c_a, s2, s3)),
% 288.85/181.36 inference(unit_resolution,[status(thm)],[478, 468, 464])).
% 288.85/181.36 tff(480,plain,
% 288.85/181.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s2, s3)) | node12(c_e_h_3, c_a, s2, s3) | node13(c_e_h_3, c_a, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s2, s3)) | node12(c_e_h_3, c_a, s2, s3) | node13(c_e_h_3, c_a, s2, s3))),
% 288.85/181.36 inference(rewrite,[status(thm)],[])).
% 288.85/181.36 tff(481,plain,
% 288.85/181.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s2, s3)) | node12(c_e_h_3, c_a, s2, s3) | node13(c_e_h_3, c_a, s2, s3))),
% 288.85/181.36 inference(quant_inst,[status(thm)],[])).
% 288.85/181.36 tff(482,plain,
% 288.85/181.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s2, s3)) | node12(c_e_h_3, c_a, s2, s3) | node13(c_e_h_3, c_a, s2, s3)),
% 288.85/181.36 inference(modus_ponens,[status(thm)],[481, 480])).
% 288.85/181.36 tff(483,plain,
% 288.85/181.36 (node12(c_e_h_3, c_a, s2, s3) | node13(c_e_h_3, c_a, s2, s3)),
% 288.85/181.36 inference(unit_resolution,[status(thm)],[482, 439, 318])).
% 288.85/181.36 tff(484,plain,
% 288.85/181.36 (node13(c_e_h_3, c_a, s2, s3)),
% 288.85/181.36 inference(unit_resolution,[status(thm)],[483, 479])).
% 288.85/181.36 tff(485,plain,
% 288.85/181.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s3)) | (~node13(c_e_h_3, c_a, s2, s3)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s3)) | (~node13(c_e_h_3, c_a, s2, s3)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s2))),
% 288.85/181.36 inference(rewrite,[status(thm)],[])).
% 288.85/181.36 tff(486,plain,
% 288.85/181.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s3)) | (~node13(c_e_h_3, c_a, s2, s3)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s2))),
% 288.85/181.36 inference(quant_inst,[status(thm)],[])).
% 288.85/181.36 tff(487,plain,
% 288.85/181.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s3)) | (~node13(c_e_h_3, c_a, s2, s3)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s2)),
% 288.85/181.36 inference(modus_ponens,[status(thm)],[486, 485])).
% 288.85/181.36 tff(488,plain,
% 288.85/181.36 (m_mutex_h_half_v_out(c_e_h_3, c_a, s2)),
% 288.85/181.36 inference(unit_resolution,[status(thm)],[487, 423, 484, 464])).
% 288.85/181.36 tff(489,plain,
% 288.85/181.36 (((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_a, s1)) | m_user_v_req(c_e_h_3, c_u, s1))) <=> ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s1)) | m_user_v_req(c_e_h_3, c_u, s1))),
% 288.85/181.36 inference(rewrite,[status(thm)],[])).
% 288.85/181.36 tff(490,plain,
% 288.85/181.36 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_a, s1)) | m_user_v_req(c_e_h_3, c_u, s1))),
% 288.85/181.36 inference(quant_inst,[status(thm)],[])).
% 288.85/181.36 tff(491,plain,
% 288.85/181.36 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s1)) | m_user_v_req(c_e_h_3, c_u, s1)),
% 288.85/181.36 inference(modus_ponens,[status(thm)],[490, 489])).
% 288.85/181.36 tff(492,plain,
% 288.85/181.36 (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s1)),
% 288.85/181.36 inference(unit_resolution,[status(thm)],[491, 395, 364])).
% 288.85/181.36 tff(493,assumption,(~m_mutex_h_half_v_inp(c_e_h_3, c_a, s1)), introduced(assumption)).
% 288.85/181.36 tff(494,assumption,(m_mutex_h_half_v_out(c_e_h_3, c_a, s2)), introduced(assumption)).
% 288.85/181.36 tff(495,assumption,(node12(c_e_h_3, c_a, s1, s2)), introduced(assumption)).
% 288.85/181.36 tff(496,plain,
% 288.85/181.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_3, c_a, s1) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)) | (~node12(c_e_h_3, c_a, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s1) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)) | (~node12(c_e_h_3, c_a, s1, s2)))),
% 288.85/181.36 inference(rewrite,[status(thm)],[])).
% 288.85/181.36 tff(497,plain,
% 288.85/181.36 (((~node12(c_e_h_3, c_a, s1, s2)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s1) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2))) <=> (m_mutex_h_half_v_inp(c_e_h_3, c_a, s1) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)) | (~node12(c_e_h_3, c_a, s1, s2)))),
% 288.85/181.36 inference(rewrite,[status(thm)],[])).
% 288.85/181.36 tff(498,plain,
% 288.85/181.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_a, s1, s2)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s1) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_3, c_a, s1) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)) | (~node12(c_e_h_3, c_a, s1, s2))))),
% 288.85/181.36 inference(monotonicity,[status(thm)],[497])).
% 288.85/181.36 tff(499,plain,
% 288.85/181.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_a, s1, s2)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s1) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s1) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)) | (~node12(c_e_h_3, c_a, s1, s2)))),
% 288.85/181.36 inference(transitivity,[status(thm)],[498, 496])).
% 288.85/181.36 tff(500,plain,
% 288.85/181.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_a, s1, s2)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s1) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)))),
% 288.85/181.36 inference(quant_inst,[status(thm)],[])).
% 288.85/181.36 tff(501,plain,
% 288.85/181.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s1) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)) | (~node12(c_e_h_3, c_a, s1, s2))),
% 288.85/181.36 inference(modus_ponens,[status(thm)],[500, 499])).
% 288.85/181.36 tff(502,plain,
% 288.85/181.36 ($false),
% 288.85/181.36 inference(unit_resolution,[status(thm)],[501, 454, 495, 494, 493])).
% 288.85/181.36 tff(503,plain,((~node12(c_e_h_3, c_a, s1, s2)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s1)), inference(lemma,lemma(discharge,[]))).
% 288.85/181.36 tff(504,plain,
% 288.85/181.36 (~node12(c_e_h_3, c_a, s1, s2)),
% 288.85/181.36 inference(unit_resolution,[status(thm)],[503, 488, 492])).
% 288.85/181.36 tff(505,plain,
% 288.85/181.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s1, s2)) | node12(c_e_h_3, c_a, s1, s2) | node13(c_e_h_3, c_a, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s1, s2)) | node12(c_e_h_3, c_a, s1, s2) | node13(c_e_h_3, c_a, s1, s2))),
% 288.85/181.36 inference(rewrite,[status(thm)],[])).
% 288.85/181.36 tff(506,plain,
% 288.85/181.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s1, s2)) | node12(c_e_h_3, c_a, s1, s2) | node13(c_e_h_3, c_a, s1, s2))),
% 288.85/181.36 inference(quant_inst,[status(thm)],[])).
% 288.85/181.36 tff(507,plain,
% 288.85/181.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s1, s2)) | node12(c_e_h_3, c_a, s1, s2) | node13(c_e_h_3, c_a, s1, s2)),
% 288.85/181.36 inference(modus_ponens,[status(thm)],[506, 505])).
% 288.85/181.36 tff(508,plain,
% 288.85/181.36 (node12(c_e_h_3, c_a, s1, s2) | node13(c_e_h_3, c_a, s1, s2)),
% 288.85/181.36 inference(unit_resolution,[status(thm)],[507, 439, 255])).
% 288.85/181.36 tff(509,plain,
% 288.85/181.36 (node13(c_e_h_3, c_a, s1, s2)),
% 288.85/181.36 inference(unit_resolution,[status(thm)],[508, 504])).
% 288.85/181.36 tff(510,plain,
% 288.85/181.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)) | (~node13(c_e_h_3, c_a, s1, s2)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)) | (~node13(c_e_h_3, c_a, s1, s2)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s1))),
% 288.85/181.36 inference(rewrite,[status(thm)],[])).
% 288.85/181.36 tff(511,plain,
% 288.85/181.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)) | (~node13(c_e_h_3, c_a, s1, s2)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s1))),
% 288.85/181.36 inference(quant_inst,[status(thm)],[])).
% 288.85/181.36 tff(512,plain,
% 288.85/181.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)) | (~node13(c_e_h_3, c_a, s1, s2)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s1)),
% 288.85/181.36 inference(modus_ponens,[status(thm)],[511, 510])).
% 288.85/181.36 tff(513,plain,
% 288.85/181.36 ($false),
% 288.85/181.36 inference(unit_resolution,[status(thm)],[512, 423, 509, 488, 463])).
% 288.85/181.36 tff(514,plain,(m_user_v_req(c_e_h_3, c_u, s2) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s3))), inference(lemma,lemma(discharge,[]))).
% 288.85/181.36 tff(515,plain,
% 288.85/181.36 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s3)),
% 288.85/181.36 inference(unit_resolution,[status(thm)],[514, 336])).
% 288.85/181.36 tff(516,assumption,(~m_mutex_h_half_v_inp(c_e_h_3, c_a, s3)), introduced(assumption)).
% 288.85/181.36 tff(517,assumption,(~m_mutex_h_half_v_out(c_e_h_3, c_a, s3)), introduced(assumption)).
% 288.85/181.36 tff(518,assumption,(node13(c_e_h_3, c_a, s3, s4)), introduced(assumption)).
% 288.85/181.36 tff(519,plain,
% 288.85/181.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s4)) | (~node13(c_e_h_3, c_a, s3, s4)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s4)) | (~node13(c_e_h_3, c_a, s3, s4)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s3))),
% 288.85/181.36 inference(rewrite,[status(thm)],[])).
% 288.85/181.36 tff(520,plain,
% 288.85/181.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s4)) | (~node13(c_e_h_3, c_a, s3, s4)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s3))),
% 288.85/181.36 inference(quant_inst,[status(thm)],[])).
% 288.85/181.36 tff(521,plain,
% 288.85/181.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s4)) | (~node13(c_e_h_3, c_a, s3, s4)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s3)),
% 288.85/181.36 inference(modus_ponens,[status(thm)],[520, 519])).
% 288.85/181.36 tff(522,plain,
% 288.85/181.36 ($false),
% 288.85/181.36 inference(unit_resolution,[status(thm)],[521, 423, 518, 517, 2])).
% 288.85/181.36 tff(523,plain,((~node13(c_e_h_3, c_a, s3, s4)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s3) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s4))), inference(lemma,lemma(discharge,[]))).
% 288.85/181.36 tff(524,plain,
% 288.85/181.36 (~node13(c_e_h_3, c_a, s3, s4)),
% 288.85/181.36 inference(unit_resolution,[status(thm)],[523, 2, 517])).
% 288.85/181.36 tff(525,plain,
% 288.85/181.36 (succ(s3, s4) <=> succ(s3, s4)),
% 288.85/181.36 inference(rewrite,[status(thm)],[])).
% 288.85/181.36 tff(526,axiom,(succ(s3, s4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound4')).
% 288.85/181.36 tff(527,plain,
% 288.85/181.36 (succ(s3, s4)),
% 288.85/181.36 inference(modus_ponens,[status(thm)],[526, 525])).
% 288.85/181.36 tff(528,plain,
% 288.85/181.36 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s3, s4)) | trans(s3, s4))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s3, s4)) | trans(s3, s4))),
% 288.85/181.36 inference(rewrite,[status(thm)],[])).
% 288.85/181.36 tff(529,plain,
% 288.85/181.36 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s3, s4)) | trans(s3, s4))),
% 288.85/181.36 inference(quant_inst,[status(thm)],[])).
% 288.85/181.37 tff(530,plain,
% 288.85/181.37 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s3, s4)) | trans(s3, s4)),
% 288.85/181.37 inference(modus_ponens,[status(thm)],[529, 528])).
% 288.85/181.37 tff(531,plain,
% 288.85/181.37 (trans(s3, s4)),
% 288.85/181.37 inference(unit_resolution,[status(thm)],[530, 527, 65])).
% 288.85/181.37 tff(532,plain,
% 288.85/181.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s3, s4)) | node12(c_e_h_3, c_a, s3, s4) | node13(c_e_h_3, c_a, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s3, s4)) | node12(c_e_h_3, c_a, s3, s4) | node13(c_e_h_3, c_a, s3, s4))),
% 288.85/181.37 inference(rewrite,[status(thm)],[])).
% 288.85/181.37 tff(533,plain,
% 288.85/181.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s3, s4)) | node12(c_e_h_3, c_a, s3, s4) | node13(c_e_h_3, c_a, s3, s4))),
% 288.85/181.37 inference(quant_inst,[status(thm)],[])).
% 288.85/181.37 tff(534,plain,
% 288.85/181.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s3, s4)) | node12(c_e_h_3, c_a, s3, s4) | node13(c_e_h_3, c_a, s3, s4)),
% 288.85/181.37 inference(modus_ponens,[status(thm)],[533, 532])).
% 288.85/181.37 tff(535,plain,
% 288.85/181.37 (node12(c_e_h_3, c_a, s3, s4) | node13(c_e_h_3, c_a, s3, s4)),
% 288.85/181.37 inference(unit_resolution,[status(thm)],[534, 439, 531])).
% 288.85/181.37 tff(536,plain,
% 288.85/181.37 (node12(c_e_h_3, c_a, s3, s4)),
% 288.85/181.37 inference(unit_resolution,[status(thm)],[535, 524])).
% 288.85/181.37 tff(537,plain,
% 288.85/181.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s4)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s3) | (~node12(c_e_h_3, c_a, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s4)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s3) | (~node12(c_e_h_3, c_a, s3, s4)))),
% 288.85/181.37 inference(rewrite,[status(thm)],[])).
% 288.85/181.37 tff(538,plain,
% 288.85/181.37 (((~node12(c_e_h_3, c_a, s3, s4)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s3) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s4))) <=> ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s4)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s3) | (~node12(c_e_h_3, c_a, s3, s4)))),
% 288.85/181.37 inference(rewrite,[status(thm)],[])).
% 288.85/181.37 tff(539,plain,
% 288.85/181.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_a, s3, s4)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s3) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s4)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s3) | (~node12(c_e_h_3, c_a, s3, s4))))),
% 288.85/181.37 inference(monotonicity,[status(thm)],[538])).
% 288.85/181.37 tff(540,plain,
% 288.85/181.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_a, s3, s4)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s3) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s4)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s3) | (~node12(c_e_h_3, c_a, s3, s4)))),
% 288.85/181.37 inference(transitivity,[status(thm)],[539, 537])).
% 288.85/181.37 tff(541,plain,
% 288.85/181.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_a, s3, s4)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s3) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s4)))),
% 288.85/181.37 inference(quant_inst,[status(thm)],[])).
% 288.85/181.37 tff(542,plain,
% 288.85/181.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s4)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s3) | (~node12(c_e_h_3, c_a, s3, s4))),
% 288.85/181.37 inference(modus_ponens,[status(thm)],[541, 540])).
% 288.85/181.37 tff(543,plain,
% 288.85/181.37 ($false),
% 288.85/181.37 inference(unit_resolution,[status(thm)],[542, 454, 536, 2, 516])).
% 288.85/181.37 tff(544,plain,((~m_mutex_h_half_v_out(c_e_h_3, c_a, s4)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s3) | m_mutex_h_half_v_out(c_e_h_3, c_a, s3)), inference(lemma,lemma(discharge,[]))).
% 288.85/181.37 tff(545,plain,
% 288.85/181.37 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s3)),
% 288.85/181.37 inference(unit_resolution,[status(thm)],[544, 515, 2])).
% 288.85/181.37 tff(546,plain,
% 288.85/181.37 (((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_a, s3)) | m_user_v_req(c_e_h_3, c_u, s3))) <=> ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s3)) | m_user_v_req(c_e_h_3, c_u, s3))),
% 288.85/181.37 inference(rewrite,[status(thm)],[])).
% 288.85/181.37 tff(547,plain,
% 288.85/181.37 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_a, s3)) | m_user_v_req(c_e_h_3, c_u, s3))),
% 288.85/181.37 inference(quant_inst,[status(thm)],[])).
% 288.85/181.37 tff(548,plain,
% 288.85/181.37 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s3)) | m_user_v_req(c_e_h_3, c_u, s3)),
% 288.85/181.37 inference(modus_ponens,[status(thm)],[547, 546])).
% 288.85/181.37 tff(549,plain,
% 288.85/181.37 ($false),
% 288.85/181.37 inference(unit_resolution,[status(thm)],[548, 395, 3, 545])).
% 288.85/181.37 tff(550,plain,(m_user_v_req(c_e_h_3, c_u, s3) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s4))), inference(lemma,lemma(discharge,[]))).
% 288.85/181.37 tff(551,plain,
% 288.85/181.37 (m_user_v_req(c_e_h_3, c_u, s3)),
% 288.85/181.37 inference(unit_resolution,[status(thm)],[550, 2])).
% 288.85/181.37 tff(552,assumption,(m_and_h_gate_v_out(c_e_h_3, c_r, s3)), introduced(assumption)).
% 288.85/181.37 tff(553,assumption,(node22(c_e_h_3, c_r, s2, s3)), introduced(assumption)).
% 288.85/181.37 tff(554,plain,
% 288.85/181.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s3)) | (~node22(c_e_h_3, c_r, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_r, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s3)) | (~node22(c_e_h_3, c_r, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_r, s2))),
% 288.85/181.37 inference(rewrite,[status(thm)],[])).
% 288.85/181.37 tff(555,plain,
% 288.85/181.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s3)) | (~node22(c_e_h_3, c_r, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_r, s2))),
% 288.85/181.37 inference(quant_inst,[status(thm)],[])).
% 288.85/181.37 tff(556,plain,
% 288.85/181.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s3)) | (~node22(c_e_h_3, c_r, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_r, s2)),
% 288.85/181.37 inference(modus_ponens,[status(thm)],[555, 554])).
% 288.85/181.37 tff(557,plain,
% 288.85/181.37 ($false),
% 288.85/181.37 inference(unit_resolution,[status(thm)],[556, 108, 553, 552, 261])).
% 288.85/181.37 tff(558,plain,((~node22(c_e_h_3, c_r, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s3))), inference(lemma,lemma(discharge,[]))).
% 288.85/181.37 tff(559,plain,
% 288.85/181.37 (~node22(c_e_h_3, c_r, s2, s3)),
% 288.85/181.37 inference(unit_resolution,[status(thm)],[558, 552])).
% 288.85/181.37 tff(560,assumption,(m_c_h_element_v_out(c_e_h_3, c_e, s2)), introduced(assumption)).
% 288.85/181.37 tff(561,plain,
% 288.85/181.37 (^[I0: $i, X: $i] : refl(((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X)) <=> ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X)))),
% 288.85/181.37 inference(bind,[status(th)],[])).
% 288.85/181.37 tff(562,plain,
% 288.85/181.37 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))),
% 288.85/181.37 inference(quant_intro,[status(thm)],[561])).
% 288.85/181.37 tff(563,plain,
% 288.85/181.37 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))),
% 288.85/181.37 inference(rewrite,[status(thm)],[])).
% 288.85/181.37 tff(564,axiom,(![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_11')).
% 288.85/181.37 tff(565,plain,
% 288.85/181.37 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))),
% 288.85/181.37 inference(modus_ponens,[status(thm)],[564, 563])).
% 288.85/181.37 tff(566,plain,(
% 288.85/181.37 ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))),
% 288.85/181.37 inference(skolemize,[status(sab)],[565])).
% 288.85/181.37 tff(567,plain,
% 288.85/181.37 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))),
% 288.85/181.37 inference(modus_ponens,[status(thm)],[566, 562])).
% 288.85/181.37 tff(568,plain,
% 288.85/181.37 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_c, s0)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s0))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s0)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s0))),
% 288.85/181.37 inference(rewrite,[status(thm)],[])).
% 288.85/181.37 tff(569,plain,
% 288.85/181.37 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_c, s0)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s0))),
% 288.85/181.37 inference(quant_inst,[status(thm)],[])).
% 288.85/181.37 tff(570,plain,
% 288.85/181.37 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s0)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s0)),
% 288.85/181.37 inference(modus_ponens,[status(thm)],[569, 568])).
% 288.85/181.37 tff(571,plain,
% 288.85/181.37 (~m_and_h_gate_v_in1(c_e_h_3, c_c, s0)),
% 288.85/181.37 inference(unit_resolution,[status(thm)],[570, 567, 412])).
% 288.85/181.37 tff(572,plain,
% 288.85/181.37 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_c, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_c, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s0))),
% 288.85/181.37 inference(rewrite,[status(thm)],[])).
% 288.85/181.37 tff(573,plain,
% 288.85/181.37 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_c, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s0))),
% 288.85/181.37 inference(quant_inst,[status(thm)],[])).
% 288.85/181.37 tff(574,plain,
% 288.85/181.37 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_c, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s0)),
% 288.85/181.37 inference(modus_ponens,[status(thm)],[573, 572])).
% 288.85/181.37 tff(575,plain,
% 288.85/181.37 (~node20(c_e_h_3, c_c, s0)),
% 288.85/181.37 inference(unit_resolution,[status(thm)],[574, 38, 571])).
% 288.85/181.37 tff(576,assumption,(m_and_h_gate_v_out(c_e_h_3, c_c, s1)), introduced(assumption)).
% 288.85/181.37 tff(577,assumption,(node22(c_e_h_3, c_c, s0, s1)), introduced(assumption)).
% 288.85/181.37 tff(578,plain,
% 288.85/181.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s1)) | (~node22(c_e_h_3, c_c, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_c, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s1)) | (~node22(c_e_h_3, c_c, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_c, s0))),
% 288.85/181.37 inference(rewrite,[status(thm)],[])).
% 288.85/181.37 tff(579,plain,
% 288.85/181.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s1)) | (~node22(c_e_h_3, c_c, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_c, s0))),
% 288.85/181.37 inference(quant_inst,[status(thm)],[])).
% 288.85/181.37 tff(580,plain,
% 288.85/181.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s1)) | (~node22(c_e_h_3, c_c, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_c, s0)),
% 288.85/181.38 inference(modus_ponens,[status(thm)],[579, 578])).
% 288.85/181.38 tff(581,plain,
% 288.85/181.38 ($false),
% 288.85/181.38 inference(unit_resolution,[status(thm)],[580, 108, 124, 577, 576])).
% 288.85/181.38 tff(582,plain,((~node22(c_e_h_3, c_c, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s1))), inference(lemma,lemma(discharge,[]))).
% 288.85/181.38 tff(583,plain,
% 288.85/181.38 (~node22(c_e_h_3, c_c, s0, s1)),
% 288.85/181.38 inference(unit_resolution,[status(thm)],[582, 576])).
% 288.85/181.38 tff(584,plain,
% 288.85/181.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_3, c_c, s0, s1) | node22(c_e_h_3, c_c, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_3, c_c, s0, s1) | node22(c_e_h_3, c_c, s0, s1))),
% 288.85/181.38 inference(rewrite,[status(thm)],[])).
% 288.85/181.38 tff(585,plain,
% 288.85/181.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_3, c_c, s0, s1) | node22(c_e_h_3, c_c, s0, s1))),
% 288.85/181.38 inference(quant_inst,[status(thm)],[])).
% 288.85/181.38 tff(586,plain,
% 288.85/181.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_3, c_c, s0, s1) | node22(c_e_h_3, c_c, s0, s1)),
% 288.85/181.38 inference(modus_ponens,[status(thm)],[585, 584])).
% 288.85/181.38 tff(587,plain,
% 288.85/181.38 (node21(c_e_h_3, c_c, s0, s1) | node22(c_e_h_3, c_c, s0, s1)),
% 288.85/181.38 inference(unit_resolution,[status(thm)],[586, 82, 72])).
% 288.85/181.38 tff(588,plain,
% 288.85/181.38 (node21(c_e_h_3, c_c, s0, s1)),
% 288.85/181.38 inference(unit_resolution,[status(thm)],[587, 583])).
% 288.85/181.38 tff(589,plain,
% 288.85/181.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_c, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s1)) | (~node21(c_e_h_3, c_c, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_c, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s1)) | (~node21(c_e_h_3, c_c, s0, s1)))),
% 288.85/181.38 inference(rewrite,[status(thm)],[])).
% 288.85/181.38 tff(590,plain,
% 288.85/181.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_c, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s1)) | (~node21(c_e_h_3, c_c, s0, s1)))),
% 288.85/181.38 inference(quant_inst,[status(thm)],[])).
% 288.85/181.38 tff(591,plain,
% 288.85/181.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_c, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s1)) | (~node21(c_e_h_3, c_c, s0, s1))),
% 288.85/181.38 inference(modus_ponens,[status(thm)],[590, 589])).
% 288.85/181.38 tff(592,plain,
% 288.85/181.38 ($false),
% 288.85/181.38 inference(unit_resolution,[status(thm)],[591, 52, 588, 576, 575])).
% 288.85/181.38 tff(593,plain,(~m_and_h_gate_v_out(c_e_h_3, c_c, s1)), inference(lemma,lemma(discharge,[]))).
% 288.85/181.38 tff(594,plain,
% 288.85/181.38 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s1)) | m_and_h_gate_v_out(c_e_h_3, c_c, s1))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s1)) | m_and_h_gate_v_out(c_e_h_3, c_c, s1))),
% 288.85/181.38 inference(rewrite,[status(thm)],[])).
% 288.85/181.38 tff(595,plain,
% 288.85/181.38 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s1)) | m_and_h_gate_v_out(c_e_h_3, c_c, s1))),
% 288.85/181.38 inference(quant_inst,[status(thm)],[])).
% 288.85/181.38 tff(596,plain,
% 288.85/181.38 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s1)) | m_and_h_gate_v_out(c_e_h_3, c_c, s1)),
% 288.85/181.38 inference(modus_ponens,[status(thm)],[595, 594])).
% 288.85/181.38 tff(597,plain,
% 288.85/181.38 (~m_c_h_element_v_in1(c_e_h_3, c_e, s1)),
% 288.85/181.38 inference(unit_resolution,[status(thm)],[596, 131, 593])).
% 288.85/181.38 tff(598,assumption,(node14(c_e_h_3, c_e, s1, s2)), introduced(assumption)).
% 288.85/181.38 tff(599,plain,
% 288.85/181.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s2)) | m_c_h_element_v_in1(c_e_h_3, c_e, s1) | (~node14(c_e_h_3, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2)) | m_c_h_element_v_in1(c_e_h_3, c_e, s1) | (~node14(c_e_h_3, c_e, s1, s2)))),
% 288.85/181.38 inference(rewrite,[status(thm)],[])).
% 288.85/181.38 tff(600,plain,
% 288.85/181.38 (((~node14(c_e_h_3, c_e, s1, s2)) | m_c_h_element_v_in1(c_e_h_3, c_e, s1) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2))) <=> ((~m_c_h_element_v_out(c_e_h_3, c_e, s2)) | m_c_h_element_v_in1(c_e_h_3, c_e, s1) | (~node14(c_e_h_3, c_e, s1, s2)))),
% 288.85/181.38 inference(rewrite,[status(thm)],[])).
% 288.85/181.38 tff(601,plain,
% 288.85/181.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s1, s2)) | m_c_h_element_v_in1(c_e_h_3, c_e, s1) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s2)) | m_c_h_element_v_in1(c_e_h_3, c_e, s1) | (~node14(c_e_h_3, c_e, s1, s2))))),
% 288.85/181.38 inference(monotonicity,[status(thm)],[600])).
% 288.85/181.38 tff(602,plain,
% 288.85/181.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s1, s2)) | m_c_h_element_v_in1(c_e_h_3, c_e, s1) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2)) | m_c_h_element_v_in1(c_e_h_3, c_e, s1) | (~node14(c_e_h_3, c_e, s1, s2)))),
% 288.85/181.38 inference(transitivity,[status(thm)],[601, 599])).
% 288.85/181.38 tff(603,plain,
% 288.85/181.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s1, s2)) | m_c_h_element_v_in1(c_e_h_3, c_e, s1) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2)))),
% 288.85/181.38 inference(quant_inst,[status(thm)],[])).
% 288.85/181.38 tff(604,plain,
% 288.85/181.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2)) | m_c_h_element_v_in1(c_e_h_3, c_e, s1) | (~node14(c_e_h_3, c_e, s1, s2))),
% 288.85/181.38 inference(modus_ponens,[status(thm)],[603, 602])).
% 288.85/181.38 tff(605,plain,
% 288.85/181.38 ($false),
% 288.85/181.38 inference(unit_resolution,[status(thm)],[604, 223, 560, 598, 597])).
% 288.85/181.38 tff(606,plain,((~node14(c_e_h_3, c_e, s1, s2)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2))), inference(lemma,lemma(discharge,[]))).
% 288.85/181.38 tff(607,plain,
% 288.85/181.38 (~node14(c_e_h_3, c_e, s1, s2)),
% 288.85/181.38 inference(unit_resolution,[status(thm)],[606, 560])).
% 288.85/181.38 tff(608,assumption,(m_and_h_gate_v_out(c_e_h_3, c_i, s1)), introduced(assumption)).
% 288.85/181.38 tff(609,assumption,(m_c_h_element_v_out(c_e_h_3, c_h, s0)), introduced(assumption)).
% 288.85/181.38 tff(610,plain,
% 288.85/181.38 ((~![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s0))),
% 288.85/181.38 inference(quant_inst,[status(thm)],[])).
% 288.85/181.38 tff(611,plain,
% 288.85/181.38 ($false),
% 288.85/181.38 inference(unit_resolution,[status(thm)],[610, 14, 609])).
% 288.85/181.38 tff(612,plain,(~m_c_h_element_v_out(c_e_h_3, c_h, s0)), inference(lemma,lemma(discharge,[]))).
% 288.85/181.38 tff(613,plain,
% 288.85/181.38 (^[I0: $i, X: $i] : refl(((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X)) <=> ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X)))),
% 288.85/181.38 inference(bind,[status(th)],[])).
% 288.85/181.38 tff(614,plain,
% 288.85/181.38 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))),
% 288.85/181.38 inference(quant_intro,[status(thm)],[613])).
% 288.85/181.38 tff(615,plain,
% 288.85/181.38 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))),
% 288.85/181.39 inference(rewrite,[status(thm)],[])).
% 288.85/181.39 tff(616,axiom,(![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_36')).
% 288.85/181.39 tff(617,plain,
% 288.85/181.39 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))),
% 288.85/181.39 inference(modus_ponens,[status(thm)],[616, 615])).
% 288.85/181.39 tff(618,plain,(
% 288.85/181.39 ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))),
% 288.85/181.39 inference(skolemize,[status(sab)],[617])).
% 288.85/181.39 tff(619,plain,
% 288.85/181.39 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))),
% 288.85/181.39 inference(modus_ponens,[status(thm)],[618, 614])).
% 288.85/181.39 tff(620,plain,
% 288.85/181.39 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_i, s0)) | m_c_h_element_v_out(c_e_h_3, c_h, s0))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s0)) | m_c_h_element_v_out(c_e_h_3, c_h, s0))),
% 288.85/181.39 inference(rewrite,[status(thm)],[])).
% 288.85/181.39 tff(621,plain,
% 288.85/181.39 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_i, s0)) | m_c_h_element_v_out(c_e_h_3, c_h, s0))),
% 288.85/181.39 inference(quant_inst,[status(thm)],[])).
% 288.85/181.39 tff(622,plain,
% 288.85/181.39 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s0)) | m_c_h_element_v_out(c_e_h_3, c_h, s0)),
% 288.85/181.39 inference(modus_ponens,[status(thm)],[621, 620])).
% 288.85/181.39 tff(623,plain,
% 288.85/181.39 (~m_and_h_gate_v_in1(c_e_h_3, c_i, s0)),
% 288.85/181.39 inference(unit_resolution,[status(thm)],[622, 619, 612])).
% 288.85/181.39 tff(624,plain,
% 288.85/181.39 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_i, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s0))),
% 288.85/181.39 inference(rewrite,[status(thm)],[])).
% 288.85/181.39 tff(625,plain,
% 288.85/181.39 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s0))),
% 288.85/181.39 inference(quant_inst,[status(thm)],[])).
% 288.85/181.39 tff(626,plain,
% 288.85/181.39 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_i, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s0)),
% 288.85/181.39 inference(modus_ponens,[status(thm)],[625, 624])).
% 288.85/181.39 tff(627,plain,
% 288.85/181.39 (~node20(c_e_h_3, c_i, s0)),
% 288.85/181.39 inference(unit_resolution,[status(thm)],[626, 38, 623])).
% 288.85/181.39 tff(628,assumption,(node22(c_e_h_3, c_i, s0, s1)), introduced(assumption)).
% 288.85/181.39 tff(629,plain,
% 288.85/181.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s1)) | (~node22(c_e_h_3, c_i, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_i, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s1)) | (~node22(c_e_h_3, c_i, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_i, s0))),
% 288.85/181.39 inference(rewrite,[status(thm)],[])).
% 288.85/181.39 tff(630,plain,
% 288.85/181.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s1)) | (~node22(c_e_h_3, c_i, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_i, s0))),
% 288.85/181.39 inference(quant_inst,[status(thm)],[])).
% 288.85/181.39 tff(631,plain,
% 288.85/181.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s1)) | (~node22(c_e_h_3, c_i, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_i, s0)),
% 288.85/181.39 inference(modus_ponens,[status(thm)],[630, 629])).
% 288.85/181.39 tff(632,plain,
% 288.85/181.39 ($false),
% 288.85/181.39 inference(unit_resolution,[status(thm)],[631, 108, 628, 157, 608])).
% 288.85/181.39 tff(633,plain,((~node22(c_e_h_3, c_i, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s1))), inference(lemma,lemma(discharge,[]))).
% 288.85/181.39 tff(634,plain,
% 288.85/181.39 (~node22(c_e_h_3, c_i, s0, s1)),
% 288.85/181.39 inference(unit_resolution,[status(thm)],[633, 608])).
% 288.85/181.39 tff(635,plain,
% 288.85/181.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_3, c_i, s0, s1) | node22(c_e_h_3, c_i, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_3, c_i, s0, s1) | node22(c_e_h_3, c_i, s0, s1))),
% 288.85/181.39 inference(rewrite,[status(thm)],[])).
% 288.85/181.39 tff(636,plain,
% 288.85/181.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_3, c_i, s0, s1) | node22(c_e_h_3, c_i, s0, s1))),
% 288.85/181.39 inference(quant_inst,[status(thm)],[])).
% 288.85/181.39 tff(637,plain,
% 288.85/181.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_3, c_i, s0, s1) | node22(c_e_h_3, c_i, s0, s1)),
% 288.85/181.39 inference(modus_ponens,[status(thm)],[636, 635])).
% 288.85/181.39 tff(638,plain,
% 288.85/181.39 (node21(c_e_h_3, c_i, s0, s1) | node22(c_e_h_3, c_i, s0, s1)),
% 288.85/181.39 inference(unit_resolution,[status(thm)],[637, 82, 72])).
% 288.85/181.39 tff(639,plain,
% 288.85/181.39 (node21(c_e_h_3, c_i, s0, s1)),
% 288.85/181.39 inference(unit_resolution,[status(thm)],[638, 634])).
% 288.85/181.39 tff(640,plain,
% 288.85/181.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~node21(c_e_h_3, c_i, s0, s1)) | node20(c_e_h_3, c_i, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~node21(c_e_h_3, c_i, s0, s1)) | node20(c_e_h_3, c_i, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s1)))),
% 288.85/181.39 inference(rewrite,[status(thm)],[])).
% 288.85/181.39 tff(641,plain,
% 288.85/181.39 ((node20(c_e_h_3, c_i, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s1)) | (~node21(c_e_h_3, c_i, s0, s1))) <=> ((~node21(c_e_h_3, c_i, s0, s1)) | node20(c_e_h_3, c_i, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s1)))),
% 288.85/181.39 inference(rewrite,[status(thm)],[])).
% 288.85/181.39 tff(642,plain,
% 288.85/181.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s1)) | (~node21(c_e_h_3, c_i, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~node21(c_e_h_3, c_i, s0, s1)) | node20(c_e_h_3, c_i, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s1))))),
% 288.85/181.39 inference(monotonicity,[status(thm)],[641])).
% 288.85/181.39 tff(643,plain,
% 288.85/181.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s1)) | (~node21(c_e_h_3, c_i, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~node21(c_e_h_3, c_i, s0, s1)) | node20(c_e_h_3, c_i, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s1)))),
% 288.85/181.39 inference(transitivity,[status(thm)],[642, 640])).
% 288.85/181.39 tff(644,plain,
% 288.85/181.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s1)) | (~node21(c_e_h_3, c_i, s0, s1)))),
% 288.85/181.39 inference(quant_inst,[status(thm)],[])).
% 288.85/181.39 tff(645,plain,
% 288.85/181.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~node21(c_e_h_3, c_i, s0, s1)) | node20(c_e_h_3, c_i, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s1))),
% 288.85/181.39 inference(modus_ponens,[status(thm)],[644, 643])).
% 288.85/181.39 tff(646,plain,
% 288.85/181.39 ($false),
% 288.85/181.39 inference(unit_resolution,[status(thm)],[645, 52, 639, 627, 608])).
% 288.85/181.39 tff(647,plain,(~m_and_h_gate_v_out(c_e_h_3, c_i, s1)), inference(lemma,lemma(discharge,[]))).
% 288.85/181.39 tff(648,plain,
% 288.85/181.39 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s1)) | m_and_h_gate_v_out(c_e_h_3, c_i, s1))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s1)) | m_and_h_gate_v_out(c_e_h_3, c_i, s1))),
% 288.85/181.39 inference(rewrite,[status(thm)],[])).
% 288.85/181.39 tff(649,plain,
% 288.85/181.39 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s1)) | m_and_h_gate_v_out(c_e_h_3, c_i, s1))),
% 288.85/181.39 inference(quant_inst,[status(thm)],[])).
% 288.85/181.39 tff(650,plain,
% 288.85/181.39 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s1)) | m_and_h_gate_v_out(c_e_h_3, c_i, s1)),
% 288.85/181.39 inference(modus_ponens,[status(thm)],[649, 648])).
% 288.85/181.39 tff(651,plain,
% 288.85/181.39 (~m_c_h_element_v_in2(c_e_h_3, c_e, s1)),
% 288.85/181.39 inference(unit_resolution,[status(thm)],[650, 164, 647])).
% 288.85/181.39 tff(652,plain,
% 288.85/181.39 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_e, s1)) | m_c_h_element_v_in1(c_e_h_3, c_e, s1) | m_c_h_element_v_in2(c_e_h_3, c_e, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s1)) | m_c_h_element_v_in1(c_e_h_3, c_e, s1) | m_c_h_element_v_in2(c_e_h_3, c_e, s1))),
% 288.85/181.39 inference(rewrite,[status(thm)],[])).
% 288.85/181.39 tff(653,plain,
% 288.85/181.39 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_e, s1)) | m_c_h_element_v_in1(c_e_h_3, c_e, s1) | m_c_h_element_v_in2(c_e_h_3, c_e, s1))),
% 288.85/181.39 inference(quant_inst,[status(thm)],[])).
% 288.85/181.39 tff(654,plain,
% 288.85/181.39 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s1)) | m_c_h_element_v_in1(c_e_h_3, c_e, s1) | m_c_h_element_v_in2(c_e_h_3, c_e, s1)),
% 288.85/181.39 inference(modus_ponens,[status(thm)],[653, 652])).
% 288.85/181.39 tff(655,plain,
% 288.85/181.39 ((~node16(c_e_h_3, c_e, s1)) | m_c_h_element_v_in1(c_e_h_3, c_e, s1)),
% 288.85/181.39 inference(unit_resolution,[status(thm)],[654, 178, 651])).
% 288.85/181.39 tff(656,plain,
% 288.85/181.39 (~node16(c_e_h_3, c_e, s1)),
% 288.85/181.39 inference(unit_resolution,[status(thm)],[655, 597])).
% 288.85/181.39 tff(657,plain,
% 288.85/181.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s1, s2)) | node19(c_e_h_3, c_e, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s1, s2)) | node19(c_e_h_3, c_e, s1, s2))),
% 288.85/181.39 inference(rewrite,[status(thm)],[])).
% 288.85/181.39 tff(658,plain,
% 288.85/181.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s1, s2)) | node19(c_e_h_3, c_e, s1, s2))),
% 288.85/181.39 inference(quant_inst,[status(thm)],[])).
% 288.85/181.39 tff(659,plain,
% 288.85/181.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s1, s2)) | node19(c_e_h_3, c_e, s1, s2)),
% 288.85/181.39 inference(modus_ponens,[status(thm)],[658, 657])).
% 288.85/181.39 tff(660,plain,
% 288.85/181.39 (node19(c_e_h_3, c_e, s1, s2)),
% 288.85/181.39 inference(unit_resolution,[status(thm)],[659, 190, 255])).
% 288.85/181.39 tff(661,plain,
% 288.85/181.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_3, c_e, s1, s2) | (~node19(c_e_h_3, c_e, s1, s2)) | node14(c_e_h_3, c_e, s1, s2) | node16(c_e_h_3, c_e, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_3, c_e, s1, s2) | (~node19(c_e_h_3, c_e, s1, s2)) | node14(c_e_h_3, c_e, s1, s2) | node16(c_e_h_3, c_e, s1))),
% 288.85/181.39 inference(rewrite,[status(thm)],[])).
% 288.85/181.39 tff(662,plain,
% 288.85/181.39 ((node16(c_e_h_3, c_e, s1) | node14(c_e_h_3, c_e, s1, s2) | node15(c_e_h_3, c_e, s1, s2) | (~node19(c_e_h_3, c_e, s1, s2))) <=> (node15(c_e_h_3, c_e, s1, s2) | (~node19(c_e_h_3, c_e, s1, s2)) | node14(c_e_h_3, c_e, s1, s2) | node16(c_e_h_3, c_e, s1))),
% 288.85/181.40 inference(rewrite,[status(thm)],[])).
% 288.85/181.40 tff(663,plain,
% 288.85/181.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s1) | node14(c_e_h_3, c_e, s1, s2) | node15(c_e_h_3, c_e, s1, s2) | (~node19(c_e_h_3, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_3, c_e, s1, s2) | (~node19(c_e_h_3, c_e, s1, s2)) | node14(c_e_h_3, c_e, s1, s2) | node16(c_e_h_3, c_e, s1)))),
% 288.85/181.40 inference(monotonicity,[status(thm)],[662])).
% 288.85/181.40 tff(664,plain,
% 288.85/181.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s1) | node14(c_e_h_3, c_e, s1, s2) | node15(c_e_h_3, c_e, s1, s2) | (~node19(c_e_h_3, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_3, c_e, s1, s2) | (~node19(c_e_h_3, c_e, s1, s2)) | node14(c_e_h_3, c_e, s1, s2) | node16(c_e_h_3, c_e, s1))),
% 288.85/181.40 inference(transitivity,[status(thm)],[663, 661])).
% 288.85/181.40 tff(665,plain,
% 288.85/181.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s1) | node14(c_e_h_3, c_e, s1, s2) | node15(c_e_h_3, c_e, s1, s2) | (~node19(c_e_h_3, c_e, s1, s2)))),
% 288.85/181.40 inference(quant_inst,[status(thm)],[])).
% 288.85/181.40 tff(666,plain,
% 288.85/181.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_3, c_e, s1, s2) | (~node19(c_e_h_3, c_e, s1, s2)) | node14(c_e_h_3, c_e, s1, s2) | node16(c_e_h_3, c_e, s1)),
% 288.85/181.40 inference(modus_ponens,[status(thm)],[665, 664])).
% 288.85/181.40 tff(667,plain,
% 288.85/181.40 (node15(c_e_h_3, c_e, s1, s2) | node14(c_e_h_3, c_e, s1, s2) | node16(c_e_h_3, c_e, s1)),
% 288.85/181.40 inference(unit_resolution,[status(thm)],[666, 204, 660])).
% 288.85/181.40 tff(668,plain,
% 288.85/181.40 (node15(c_e_h_3, c_e, s1, s2) | node14(c_e_h_3, c_e, s1, s2)),
% 288.85/181.40 inference(unit_resolution,[status(thm)],[667, 656])).
% 288.85/181.40 tff(669,plain,
% 288.85/181.40 (node15(c_e_h_3, c_e, s1, s2)),
% 288.85/181.40 inference(unit_resolution,[status(thm)],[668, 607])).
% 288.85/181.40 tff(670,plain,
% 288.85/181.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s2)) | (~node15(c_e_h_3, c_e, s1, s2)) | m_c_h_element_v_out(c_e_h_3, c_e, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2)) | (~node15(c_e_h_3, c_e, s1, s2)) | m_c_h_element_v_out(c_e_h_3, c_e, s1))),
% 288.85/181.40 inference(rewrite,[status(thm)],[])).
% 288.85/181.40 tff(671,plain,
% 288.85/181.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s2)) | (~node15(c_e_h_3, c_e, s1, s2)) | m_c_h_element_v_out(c_e_h_3, c_e, s1))),
% 288.85/181.40 inference(quant_inst,[status(thm)],[])).
% 288.85/181.40 tff(672,plain,
% 288.85/181.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s2)) | (~node15(c_e_h_3, c_e, s1, s2)) | m_c_h_element_v_out(c_e_h_3, c_e, s1)),
% 288.85/181.40 inference(modus_ponens,[status(thm)],[671, 670])).
% 288.85/181.40 tff(673,plain,
% 288.85/181.40 ($false),
% 288.85/181.40 inference(unit_resolution,[status(thm)],[672, 147, 231, 560, 669])).
% 288.85/181.40 tff(674,plain,(~m_c_h_element_v_out(c_e_h_3, c_e, s2)), inference(lemma,lemma(discharge,[]))).
% 288.85/181.40 tff(675,plain,
% 288.85/181.40 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s2)) | m_c_h_element_v_out(c_e_h_3, c_e, s2))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s2)) | m_c_h_element_v_out(c_e_h_3, c_e, s2))),
% 288.85/181.40 inference(rewrite,[status(thm)],[])).
% 288.85/181.40 tff(676,plain,
% 288.85/181.40 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s2)) | m_c_h_element_v_out(c_e_h_3, c_e, s2))),
% 288.85/181.40 inference(quant_inst,[status(thm)],[])).
% 288.85/181.40 tff(677,plain,
% 288.85/181.40 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s2)) | m_c_h_element_v_out(c_e_h_3, c_e, s2)),
% 288.85/181.40 inference(modus_ponens,[status(thm)],[676, 675])).
% 288.85/181.40 tff(678,plain,
% 288.85/181.40 (~m_and_h_gate_v_in1(c_e_h_3, c_r, s2)),
% 288.85/181.40 inference(unit_resolution,[status(thm)],[677, 24, 674])).
% 288.85/181.40 tff(679,plain,
% 288.85/181.40 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s2))),
% 288.85/181.40 inference(rewrite,[status(thm)],[])).
% 288.85/181.40 tff(680,plain,
% 288.85/181.40 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s2))),
% 288.85/181.40 inference(quant_inst,[status(thm)],[])).
% 288.85/181.40 tff(681,plain,
% 288.85/181.40 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s2)),
% 288.85/181.40 inference(modus_ponens,[status(thm)],[680, 679])).
% 288.85/181.40 tff(682,plain,
% 288.85/181.40 (~node20(c_e_h_3, c_r, s2)),
% 288.85/181.40 inference(unit_resolution,[status(thm)],[681, 38, 678])).
% 288.85/181.40 tff(683,assumption,(~node20(c_e_h_3, c_r, s2)), introduced(assumption)).
% 288.85/181.40 tff(684,assumption,(node21(c_e_h_3, c_r, s2, s3)), introduced(assumption)).
% 288.85/181.40 tff(685,plain,
% 288.85/181.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s3)) | node20(c_e_h_3, c_r, s2) | (~node21(c_e_h_3, c_r, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s3)) | node20(c_e_h_3, c_r, s2) | (~node21(c_e_h_3, c_r, s2, s3)))),
% 288.85/181.40 inference(rewrite,[status(thm)],[])).
% 288.85/181.40 tff(686,plain,
% 288.85/181.40 ((node20(c_e_h_3, c_r, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s3)) | (~node21(c_e_h_3, c_r, s2, s3))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_r, s3)) | node20(c_e_h_3, c_r, s2) | (~node21(c_e_h_3, c_r, s2, s3)))),
% 288.85/181.40 inference(rewrite,[status(thm)],[])).
% 288.85/181.40 tff(687,plain,
% 288.85/181.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s3)) | (~node21(c_e_h_3, c_r, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s3)) | node20(c_e_h_3, c_r, s2) | (~node21(c_e_h_3, c_r, s2, s3))))),
% 288.85/181.40 inference(monotonicity,[status(thm)],[686])).
% 288.85/181.40 tff(688,plain,
% 288.85/181.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s3)) | (~node21(c_e_h_3, c_r, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s3)) | node20(c_e_h_3, c_r, s2) | (~node21(c_e_h_3, c_r, s2, s3)))),
% 288.85/181.40 inference(transitivity,[status(thm)],[687, 685])).
% 288.85/181.40 tff(689,plain,
% 288.85/181.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s3)) | (~node21(c_e_h_3, c_r, s2, s3)))),
% 288.85/181.40 inference(quant_inst,[status(thm)],[])).
% 288.85/181.40 tff(690,plain,
% 288.85/181.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s3)) | node20(c_e_h_3, c_r, s2) | (~node21(c_e_h_3, c_r, s2, s3))),
% 288.96/181.41 inference(modus_ponens,[status(thm)],[689, 688])).
% 288.96/181.41 tff(691,plain,
% 288.96/181.41 ($false),
% 288.96/181.41 inference(unit_resolution,[status(thm)],[690, 52, 684, 552, 683])).
% 288.96/181.41 tff(692,plain,((~node21(c_e_h_3, c_r, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s3)) | node20(c_e_h_3, c_r, s2)), inference(lemma,lemma(discharge,[]))).
% 288.96/181.41 tff(693,plain,
% 288.96/181.41 ((~node21(c_e_h_3, c_r, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s3))),
% 288.96/181.41 inference(unit_resolution,[status(thm)],[692, 682])).
% 288.96/181.41 tff(694,plain,
% 288.96/181.41 (~node21(c_e_h_3, c_r, s2, s3)),
% 288.96/181.41 inference(unit_resolution,[status(thm)],[693, 552])).
% 288.96/181.41 tff(695,plain,
% 288.96/181.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_3, c_r, s2, s3) | node22(c_e_h_3, c_r, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_3, c_r, s2, s3) | node22(c_e_h_3, c_r, s2, s3))),
% 288.96/181.41 inference(rewrite,[status(thm)],[])).
% 288.96/181.41 tff(696,plain,
% 288.96/181.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_3, c_r, s2, s3) | node22(c_e_h_3, c_r, s2, s3))),
% 288.96/181.41 inference(quant_inst,[status(thm)],[])).
% 288.96/181.41 tff(697,plain,
% 288.96/181.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_3, c_r, s2, s3) | node22(c_e_h_3, c_r, s2, s3)),
% 288.96/181.41 inference(modus_ponens,[status(thm)],[696, 695])).
% 288.96/181.41 tff(698,plain,
% 288.96/181.41 (node21(c_e_h_3, c_r, s2, s3) | node22(c_e_h_3, c_r, s2, s3)),
% 288.96/181.41 inference(unit_resolution,[status(thm)],[697, 82, 318])).
% 288.96/181.41 tff(699,plain,
% 288.96/181.41 ($false),
% 288.96/181.41 inference(unit_resolution,[status(thm)],[698, 694, 559])).
% 288.96/181.41 tff(700,plain,(~m_and_h_gate_v_out(c_e_h_3, c_r, s3)), inference(lemma,lemma(discharge,[]))).
% 288.96/181.41 tff(701,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_r, s3)), introduced(assumption)).
% 288.96/181.41 tff(702,assumption,(m_user_v_ack(c_e_h_3, c_u, s3)), introduced(assumption)).
% 288.96/181.41 tff(703,plain,
% 288.96/181.41 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_3, c_u, s3)) | m_and_h_gate_v_out(c_e_h_3, c_r, s3))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_3, c_u, s3)) | m_and_h_gate_v_out(c_e_h_3, c_r, s3))),
% 288.96/181.41 inference(rewrite,[status(thm)],[])).
% 288.96/181.41 tff(704,plain,
% 288.96/181.41 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_3, c_u, s3)) | m_and_h_gate_v_out(c_e_h_3, c_r, s3))),
% 288.96/181.41 inference(quant_inst,[status(thm)],[])).
% 288.96/181.41 tff(705,plain,
% 288.96/181.41 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_3, c_u, s3)) | m_and_h_gate_v_out(c_e_h_3, c_r, s3)),
% 288.96/181.41 inference(modus_ponens,[status(thm)],[704, 703])).
% 288.96/181.41 tff(706,plain,
% 288.96/181.41 ($false),
% 288.96/181.41 inference(unit_resolution,[status(thm)],[705, 268, 702, 701])).
% 288.96/181.41 tff(707,plain,((~m_user_v_ack(c_e_h_3, c_u, s3)) | m_and_h_gate_v_out(c_e_h_3, c_r, s3)), inference(lemma,lemma(discharge,[]))).
% 288.96/181.41 tff(708,plain,
% 288.96/181.41 (~m_user_v_ack(c_e_h_3, c_u, s3)),
% 288.96/181.41 inference(unit_resolution,[status(thm)],[707, 700])).
% 288.96/181.41 tff(709,assumption,(~m_user_v_ack(c_e_h_3, c_u, s3)), introduced(assumption)).
% 288.96/181.41 tff(710,assumption,(~m_user_v_req(c_e_h_3, c_u, s4)), introduced(assumption)).
% 288.96/181.41 tff(711,assumption,(node7(c_e_h_3, c_u, s3, s4)), introduced(assumption)).
% 288.96/181.41 tff(712,plain,
% 288.96/181.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | ((~node7(c_e_h_3, c_u, s3, s4)) | m_user_v_ack(c_e_h_3, c_u, s3) | m_user_v_req(c_e_h_3, c_u, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | (~node7(c_e_h_3, c_u, s3, s4)) | m_user_v_ack(c_e_h_3, c_u, s3) | m_user_v_req(c_e_h_3, c_u, s4))),
% 288.96/181.41 inference(rewrite,[status(thm)],[])).
% 288.96/181.41 tff(713,plain,
% 288.96/181.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | ((~node7(c_e_h_3, c_u, s3, s4)) | m_user_v_ack(c_e_h_3, c_u, s3) | m_user_v_req(c_e_h_3, c_u, s4))),
% 288.96/181.41 inference(quant_inst,[status(thm)],[])).
% 288.96/181.41 tff(714,plain,
% 288.96/181.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | (~node7(c_e_h_3, c_u, s3, s4)) | m_user_v_ack(c_e_h_3, c_u, s3) | m_user_v_req(c_e_h_3, c_u, s4)),
% 288.96/181.41 inference(modus_ponens,[status(thm)],[713, 712])).
% 288.96/181.41 tff(715,plain,
% 288.96/181.41 ($false),
% 288.96/181.41 inference(unit_resolution,[status(thm)],[714, 284, 711, 709, 710])).
% 288.96/181.41 tff(716,plain,((~node7(c_e_h_3, c_u, s3, s4)) | m_user_v_ack(c_e_h_3, c_u, s3) | m_user_v_req(c_e_h_3, c_u, s4)), inference(lemma,lemma(discharge,[]))).
% 288.96/181.41 tff(717,plain,
% 288.96/181.41 (~node7(c_e_h_3, c_u, s3, s4)),
% 288.96/181.41 inference(unit_resolution,[status(thm)],[716, 710, 709])).
% 288.96/181.41 tff(718,assumption,(m_user_v_req(c_e_h_3, c_u, s3)), introduced(assumption)).
% 288.96/181.41 tff(719,assumption,(node8(c_e_h_3, c_u, s3, s4)), introduced(assumption)).
% 288.96/181.41 tff(720,plain,
% 288.96/181.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_3, c_u, s4) | (~node8(c_e_h_3, c_u, s3, s4)) | (~m_user_v_req(c_e_h_3, c_u, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | m_user_v_req(c_e_h_3, c_u, s4) | (~node8(c_e_h_3, c_u, s3, s4)) | (~m_user_v_req(c_e_h_3, c_u, s3)))),
% 288.96/181.41 inference(rewrite,[status(thm)],[])).
% 288.96/181.41 tff(721,plain,
% 288.96/181.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_3, c_u, s4) | (~node8(c_e_h_3, c_u, s3, s4)) | (~m_user_v_req(c_e_h_3, c_u, s3)))),
% 288.96/181.41 inference(quant_inst,[status(thm)],[])).
% 288.96/181.41 tff(722,plain,
% 288.96/181.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | m_user_v_req(c_e_h_3, c_u, s4) | (~node8(c_e_h_3, c_u, s3, s4)) | (~m_user_v_req(c_e_h_3, c_u, s3))),
% 288.96/181.41 inference(modus_ponens,[status(thm)],[721, 720])).
% 288.96/181.41 tff(723,plain,
% 288.96/181.41 ($false),
% 288.96/181.41 inference(unit_resolution,[status(thm)],[722, 302, 719, 710, 718])).
% 288.96/181.41 tff(724,plain,((~node8(c_e_h_3, c_u, s3, s4)) | m_user_v_req(c_e_h_3, c_u, s4) | (~m_user_v_req(c_e_h_3, c_u, s3))), inference(lemma,lemma(discharge,[]))).
% 288.96/181.41 tff(725,plain,
% 288.96/181.41 (~node8(c_e_h_3, c_u, s3, s4)),
% 288.96/181.41 inference(unit_resolution,[status(thm)],[724, 710, 718])).
% 288.96/181.41 tff(726,plain,
% 288.96/181.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | ((~trans(s3, s4)) | node7(c_e_h_3, c_u, s3, s4) | node8(c_e_h_3, c_u, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | (~trans(s3, s4)) | node7(c_e_h_3, c_u, s3, s4) | node8(c_e_h_3, c_u, s3, s4))),
% 288.96/181.41 inference(rewrite,[status(thm)],[])).
% 288.96/181.41 tff(727,plain,
% 288.96/181.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | ((~trans(s3, s4)) | node7(c_e_h_3, c_u, s3, s4) | node8(c_e_h_3, c_u, s3, s4))),
% 288.96/181.41 inference(quant_inst,[status(thm)],[])).
% 288.96/181.41 tff(728,plain,
% 288.96/181.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | (~trans(s3, s4)) | node7(c_e_h_3, c_u, s3, s4) | node8(c_e_h_3, c_u, s3, s4)),
% 288.96/181.41 inference(modus_ponens,[status(thm)],[727, 726])).
% 288.96/181.41 tff(729,plain,
% 288.96/181.41 (node7(c_e_h_3, c_u, s3, s4) | node8(c_e_h_3, c_u, s3, s4)),
% 288.96/181.41 inference(unit_resolution,[status(thm)],[728, 328, 531])).
% 288.96/181.41 tff(730,plain,
% 288.96/181.41 ($false),
% 288.96/181.41 inference(unit_resolution,[status(thm)],[729, 725, 717])).
% 288.96/181.41 tff(731,plain,(m_user_v_req(c_e_h_3, c_u, s4) | (~m_user_v_req(c_e_h_3, c_u, s3)) | m_user_v_ack(c_e_h_3, c_u, s3)), inference(lemma,lemma(discharge,[]))).
% 288.96/181.41 tff(732,plain,
% 288.96/181.41 (m_user_v_req(c_e_h_3, c_u, s4) | (~m_user_v_req(c_e_h_3, c_u, s3))),
% 288.96/181.41 inference(unit_resolution,[status(thm)],[731, 708])).
% 288.96/181.41 tff(733,plain,
% 288.96/181.41 (m_user_v_req(c_e_h_3, c_u, s4)),
% 288.96/181.41 inference(unit_resolution,[status(thm)],[732, 551])).
% 288.96/181.41 tff(734,assumption,(m_c_h_element_v_out(c_e_h_3, c_e, s3)), introduced(assumption)).
% 288.96/181.41 tff(735,assumption,(~m_c_h_element_v_out(c_e_h_3, c_e, s2)), introduced(assumption)).
% 288.96/181.41 tff(736,assumption,(node15(c_e_h_3, c_e, s2, s3)), introduced(assumption)).
% 288.96/181.41 tff(737,plain,
% 288.96/181.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | (~node15(c_e_h_3, c_e, s2, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | (~node15(c_e_h_3, c_e, s2, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s2))),
% 288.96/181.41 inference(rewrite,[status(thm)],[])).
% 288.96/181.41 tff(738,plain,
% 288.96/181.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | (~node15(c_e_h_3, c_e, s2, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s2))),
% 288.96/181.41 inference(quant_inst,[status(thm)],[])).
% 288.96/181.41 tff(739,plain,
% 288.96/181.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | (~node15(c_e_h_3, c_e, s2, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s2)),
% 288.96/181.41 inference(modus_ponens,[status(thm)],[738, 737])).
% 288.96/181.41 tff(740,plain,
% 288.96/181.41 ($false),
% 288.96/181.41 inference(unit_resolution,[status(thm)],[739, 147, 735, 734, 736])).
% 288.96/181.41 tff(741,plain,((~node15(c_e_h_3, c_e, s2, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s2) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3))), inference(lemma,lemma(discharge,[]))).
% 288.96/181.41 tff(742,plain,
% 288.96/181.41 (~node15(c_e_h_3, c_e, s2, s3)),
% 288.96/181.41 inference(unit_resolution,[status(thm)],[741, 734, 735])).
% 288.96/181.41 tff(743,assumption,(node18(c_e_h_3, c_e, s2, s3)), introduced(assumption)).
% 288.96/181.41 tff(744,plain,
% 288.96/181.41 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl(((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y))) <=> ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y))))),
% 288.96/181.41 inference(bind,[status(th)],[])).
% 288.96/181.41 tff(745,plain,
% 288.96/181.41 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))),
% 288.96/181.41 inference(quant_intro,[status(thm)],[744])).
% 288.96/181.41 tff(746,plain,
% 288.96/181.41 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))),
% 288.96/181.41 inference(rewrite,[status(thm)],[])).
% 288.96/181.41 tff(747,plain,
% 288.96/181.41 (^[Y: $i, I0: $i, X: $i, I1: $i] : rewrite((((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X)) | (~node18(I0, I1, X, Y))) <=> ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y))))),
% 288.96/181.41 inference(bind,[status(th)],[])).
% 288.96/181.41 tff(748,plain,
% 288.96/181.41 (![Y: $i, I0: $i, X: $i, I1: $i] : (((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X)) | (~node18(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))),
% 288.96/181.41 inference(quant_intro,[status(thm)],[747])).
% 288.96/181.41 tff(749,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : (((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X)) | (~node18(I0, I1, X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_c_h_element_11')).
% 288.96/181.41 tff(750,plain,
% 288.96/181.41 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))),
% 288.96/181.41 inference(modus_ponens,[status(thm)],[749, 748])).
% 288.96/181.41 tff(751,plain,
% 288.96/181.41 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))),
% 288.96/181.41 inference(modus_ponens,[status(thm)],[750, 746])).
% 288.96/181.42 tff(752,plain,(
% 288.96/181.42 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))),
% 288.96/181.42 inference(skolemize,[status(sab)],[751])).
% 288.96/181.42 tff(753,plain,
% 288.96/181.42 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))),
% 288.96/181.42 inference(modus_ponens,[status(thm)],[752, 745])).
% 288.96/181.42 tff(754,plain,
% 288.96/181.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~node18(c_e_h_3, c_e, s2, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s2) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_3, c_e, s2, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s2) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3)))),
% 288.96/181.42 inference(rewrite,[status(thm)],[])).
% 288.96/181.42 tff(755,plain,
% 288.96/181.42 (((~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s2) | (~node18(c_e_h_3, c_e, s2, s3))) <=> ((~node18(c_e_h_3, c_e, s2, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s2) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3)))),
% 288.96/181.42 inference(rewrite,[status(thm)],[])).
% 288.96/181.42 tff(756,plain,
% 288.96/181.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s2) | (~node18(c_e_h_3, c_e, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~node18(c_e_h_3, c_e, s2, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s2) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3))))),
% 288.96/181.42 inference(monotonicity,[status(thm)],[755])).
% 288.96/181.42 tff(757,plain,
% 288.96/181.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s2) | (~node18(c_e_h_3, c_e, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_3, c_e, s2, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s2) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3)))),
% 288.96/181.42 inference(transitivity,[status(thm)],[756, 754])).
% 288.96/181.42 tff(758,plain,
% 288.96/181.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s2) | (~node18(c_e_h_3, c_e, s2, s3)))),
% 288.96/181.42 inference(quant_inst,[status(thm)],[])).
% 288.96/181.42 tff(759,plain,
% 288.96/181.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_3, c_e, s2, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s2) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3))),
% 288.96/181.42 inference(modus_ponens,[status(thm)],[758, 757])).
% 288.96/181.42 tff(760,plain,
% 288.96/181.42 ($false),
% 288.96/181.42 inference(unit_resolution,[status(thm)],[759, 753, 735, 734, 743])).
% 288.96/181.42 tff(761,plain,((~node18(c_e_h_3, c_e, s2, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s2) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3))), inference(lemma,lemma(discharge,[]))).
% 288.96/181.42 tff(762,plain,
% 288.96/181.42 (~node18(c_e_h_3, c_e, s2, s3)),
% 288.96/181.42 inference(unit_resolution,[status(thm)],[761, 734, 735])).
% 288.96/181.42 tff(763,plain,
% 288.96/181.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s2, s3)) | node19(c_e_h_3, c_e, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s2, s3)) | node19(c_e_h_3, c_e, s2, s3))),
% 288.96/181.42 inference(rewrite,[status(thm)],[])).
% 288.96/181.42 tff(764,plain,
% 288.96/181.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s2, s3)) | node19(c_e_h_3, c_e, s2, s3))),
% 288.96/181.42 inference(quant_inst,[status(thm)],[])).
% 288.96/181.42 tff(765,plain,
% 288.96/181.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s2, s3)) | node19(c_e_h_3, c_e, s2, s3)),
% 288.96/181.42 inference(modus_ponens,[status(thm)],[764, 763])).
% 288.96/181.42 tff(766,plain,
% 288.96/181.42 (node19(c_e_h_3, c_e, s2, s3)),
% 288.96/181.42 inference(unit_resolution,[status(thm)],[765, 190, 318])).
% 288.96/181.42 tff(767,plain,
% 288.96/181.42 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl((node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y))) <=> (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y))))),
% 288.96/181.42 inference(bind,[status(th)],[])).
% 288.96/181.42 tff(768,plain,
% 288.96/181.42 (![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 288.96/181.42 inference(quant_intro,[status(thm)],[767])).
% 288.96/181.42 tff(769,plain,
% 288.96/181.42 (![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 288.96/181.42 inference(rewrite,[status(thm)],[])).
% 288.96/181.42 tff(770,plain,
% 288.96/181.42 (^[Y: $i, I0: $i, X: $i, I1: $i] : rewrite(((node17(I0, I1, X) | node18(I0, I1, X, Y)) | (~node19(I0, I1, X, Y))) <=> (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y))))),
% 288.96/181.42 inference(bind,[status(th)],[])).
% 288.96/181.42 tff(771,plain,
% 288.96/181.42 (![Y: $i, I0: $i, X: $i, I1: $i] : ((node17(I0, I1, X) | node18(I0, I1, X, Y)) | (~node19(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 288.96/181.42 inference(quant_intro,[status(thm)],[770])).
% 288.96/181.42 tff(772,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : ((node17(I0, I1, X) | node18(I0, I1, X, Y)) | (~node19(I0, I1, X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_c_h_element_13')).
% 288.96/181.42 tff(773,plain,
% 288.96/181.42 (![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 288.96/181.42 inference(modus_ponens,[status(thm)],[772, 771])).
% 288.96/181.42 tff(774,plain,
% 288.96/181.42 (![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 288.96/181.42 inference(modus_ponens,[status(thm)],[773, 769])).
% 288.96/181.42 tff(775,plain,(
% 288.96/181.42 ![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 288.96/181.42 inference(skolemize,[status(sab)],[774])).
% 288.96/181.42 tff(776,plain,
% 288.96/181.42 (![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))),
% 288.96/181.42 inference(modus_ponens,[status(thm)],[775, 768])).
% 288.96/181.42 tff(777,plain,
% 288.96/181.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s2) | (~node19(c_e_h_3, c_e, s2, s3)) | node18(c_e_h_3, c_e, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_e, s2) | (~node19(c_e_h_3, c_e, s2, s3)) | node18(c_e_h_3, c_e, s2, s3))),
% 288.96/181.42 inference(rewrite,[status(thm)],[])).
% 288.96/181.42 tff(778,plain,
% 288.96/181.42 ((node17(c_e_h_3, c_e, s2) | node18(c_e_h_3, c_e, s2, s3) | (~node19(c_e_h_3, c_e, s2, s3))) <=> (node17(c_e_h_3, c_e, s2) | (~node19(c_e_h_3, c_e, s2, s3)) | node18(c_e_h_3, c_e, s2, s3))),
% 288.96/181.42 inference(rewrite,[status(thm)],[])).
% 288.96/181.42 tff(779,plain,
% 288.96/181.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s2) | node18(c_e_h_3, c_e, s2, s3) | (~node19(c_e_h_3, c_e, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s2) | (~node19(c_e_h_3, c_e, s2, s3)) | node18(c_e_h_3, c_e, s2, s3)))),
% 288.96/181.42 inference(monotonicity,[status(thm)],[778])).
% 288.96/181.42 tff(780,plain,
% 288.96/181.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s2) | node18(c_e_h_3, c_e, s2, s3) | (~node19(c_e_h_3, c_e, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_e, s2) | (~node19(c_e_h_3, c_e, s2, s3)) | node18(c_e_h_3, c_e, s2, s3))),
% 288.96/181.42 inference(transitivity,[status(thm)],[779, 777])).
% 288.96/181.42 tff(781,plain,
% 288.96/181.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s2) | node18(c_e_h_3, c_e, s2, s3) | (~node19(c_e_h_3, c_e, s2, s3)))),
% 288.96/181.42 inference(quant_inst,[status(thm)],[])).
% 288.96/181.42 tff(782,plain,
% 288.96/181.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_e, s2) | (~node19(c_e_h_3, c_e, s2, s3)) | node18(c_e_h_3, c_e, s2, s3)),
% 288.96/181.42 inference(modus_ponens,[status(thm)],[781, 780])).
% 288.96/181.42 tff(783,plain,
% 288.96/181.42 (node17(c_e_h_3, c_e, s2) | node18(c_e_h_3, c_e, s2, s3)),
% 288.96/181.42 inference(unit_resolution,[status(thm)],[782, 776, 766])).
% 288.96/181.42 tff(784,plain,
% 288.96/181.42 (node17(c_e_h_3, c_e, s2)),
% 288.96/181.42 inference(unit_resolution,[status(thm)],[783, 762])).
% 288.96/181.42 tff(785,assumption,(m_and_h_gate_v_out(c_e_h_3, c_i, s2)), introduced(assumption)).
% 288.96/181.42 tff(786,assumption,(node22(c_e_h_3, c_i, s1, s2)), introduced(assumption)).
% 288.96/181.42 tff(787,plain,
% 288.96/181.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s2)) | (~node22(c_e_h_3, c_i, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_i, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s2)) | (~node22(c_e_h_3, c_i, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_i, s1))),
% 288.96/181.42 inference(rewrite,[status(thm)],[])).
% 288.96/181.42 tff(788,plain,
% 288.96/181.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s2)) | (~node22(c_e_h_3, c_i, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_i, s1))),
% 288.96/181.42 inference(quant_inst,[status(thm)],[])).
% 288.96/181.42 tff(789,plain,
% 288.96/181.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s2)) | (~node22(c_e_h_3, c_i, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_i, s1)),
% 288.96/181.42 inference(modus_ponens,[status(thm)],[788, 787])).
% 288.96/181.42 tff(790,plain,
% 288.96/181.42 ($false),
% 288.96/181.42 inference(unit_resolution,[status(thm)],[789, 108, 786, 785, 647])).
% 288.96/181.42 tff(791,plain,((~node22(c_e_h_3, c_i, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s2))), inference(lemma,lemma(discharge,[]))).
% 288.96/181.42 tff(792,plain,
% 288.96/181.42 (~node22(c_e_h_3, c_i, s1, s2)),
% 288.96/181.42 inference(unit_resolution,[status(thm)],[791, 785])).
% 288.96/181.42 tff(793,assumption,(m_c_h_element_v_out(c_e_h_3, c_h, s1)), introduced(assumption)).
% 288.96/181.42 tff(794,assumption,(m_or_h_gate_v_out(c_e_h_3, c_g, s0)), introduced(assumption)).
% 288.96/181.42 tff(795,plain,
% 288.96/181.42 (^[I0: $i, I1: $i] : refl((~m_or_h_gate_v_out(I0, I1, s0)) <=> (~m_or_h_gate_v_out(I0, I1, s0)))),
% 288.96/181.42 inference(bind,[status(th)],[])).
% 288.96/181.42 tff(796,plain,
% 288.96/181.42 (![I0: $i, I1: $i] : (~m_or_h_gate_v_out(I0, I1, s0)) <=> ![I0: $i, I1: $i] : (~m_or_h_gate_v_out(I0, I1, s0))),
% 288.96/181.42 inference(quant_intro,[status(thm)],[795])).
% 288.96/181.42 tff(797,plain,
% 288.96/181.42 (![I0: $i, I1: $i] : (~m_or_h_gate_v_out(I0, I1, s0)) <=> ![I0: $i, I1: $i] : (~m_or_h_gate_v_out(I0, I1, s0))),
% 288.96/181.42 inference(rewrite,[status(thm)],[])).
% 288.96/181.42 tff(798,axiom,(![I0: $i, I1: $i] : (~m_or_h_gate_v_out(I0, I1, s0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_or_h_gate_1')).
% 288.96/181.42 tff(799,plain,
% 288.96/181.42 (![I0: $i, I1: $i] : (~m_or_h_gate_v_out(I0, I1, s0))),
% 288.96/181.42 inference(modus_ponens,[status(thm)],[798, 797])).
% 288.96/181.42 tff(800,plain,(
% 288.96/181.42 ![I0: $i, I1: $i] : (~m_or_h_gate_v_out(I0, I1, s0))),
% 288.96/181.42 inference(skolemize,[status(sab)],[799])).
% 288.96/181.42 tff(801,plain,
% 288.96/181.42 (![I0: $i, I1: $i] : (~m_or_h_gate_v_out(I0, I1, s0))),
% 288.96/181.42 inference(modus_ponens,[status(thm)],[800, 796])).
% 288.96/181.42 tff(802,plain,
% 288.96/181.42 ((~![I0: $i, I1: $i] : (~m_or_h_gate_v_out(I0, I1, s0))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s0))),
% 288.96/181.42 inference(quant_inst,[status(thm)],[])).
% 288.96/181.42 tff(803,plain,
% 288.96/181.42 ($false),
% 288.96/181.42 inference(unit_resolution,[status(thm)],[802, 801, 794])).
% 288.96/181.42 tff(804,plain,(~m_or_h_gate_v_out(c_e_h_3, c_g, s0)), inference(lemma,lemma(discharge,[]))).
% 288.96/181.43 tff(805,plain,
% 288.96/181.43 (^[I0: $i, X: $i] : refl(((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X)) <=> ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X)))),
% 288.96/181.43 inference(bind,[status(th)],[])).
% 288.96/181.43 tff(806,plain,
% 288.96/181.43 (![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X)) <=> ![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))),
% 288.96/181.43 inference(quant_intro,[status(thm)],[805])).
% 288.96/181.43 tff(807,plain,
% 288.96/181.43 (![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X)) <=> ![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))),
% 288.96/181.43 inference(rewrite,[status(thm)],[])).
% 288.96/181.43 tff(808,axiom,(![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_32')).
% 288.96/181.43 tff(809,plain,
% 288.96/181.43 (![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))),
% 288.96/181.43 inference(modus_ponens,[status(thm)],[808, 807])).
% 288.96/181.43 tff(810,plain,(
% 288.96/181.43 ![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))),
% 288.96/181.43 inference(skolemize,[status(sab)],[809])).
% 288.96/181.43 tff(811,plain,
% 288.96/181.43 (![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))),
% 288.96/181.43 inference(modus_ponens,[status(thm)],[810, 806])).
% 288.96/181.43 tff(812,plain,
% 288.96/181.43 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s0)) | m_or_h_gate_v_out(c_e_h_3, c_g, s0))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s0)) | m_or_h_gate_v_out(c_e_h_3, c_g, s0))),
% 288.96/181.43 inference(rewrite,[status(thm)],[])).
% 288.96/181.43 tff(813,plain,
% 288.96/181.43 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s0)) | m_or_h_gate_v_out(c_e_h_3, c_g, s0))),
% 288.96/181.43 inference(quant_inst,[status(thm)],[])).
% 288.96/181.43 tff(814,plain,
% 288.96/181.43 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s0)) | m_or_h_gate_v_out(c_e_h_3, c_g, s0)),
% 288.96/181.43 inference(modus_ponens,[status(thm)],[813, 812])).
% 288.96/181.43 tff(815,plain,
% 288.96/181.43 (~m_c_h_element_v_in1(c_e_h_3, c_h, s0)),
% 288.96/181.43 inference(unit_resolution,[status(thm)],[814, 811, 804])).
% 288.96/181.43 tff(816,assumption,(node14(c_e_h_3, c_h, s0, s1)), introduced(assumption)).
% 288.96/181.43 tff(817,plain,
% 288.96/181.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s1)) | m_c_h_element_v_in1(c_e_h_3, c_h, s0) | (~node14(c_e_h_3, c_h, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s1)) | m_c_h_element_v_in1(c_e_h_3, c_h, s0) | (~node14(c_e_h_3, c_h, s0, s1)))),
% 288.96/181.43 inference(rewrite,[status(thm)],[])).
% 288.96/181.43 tff(818,plain,
% 288.96/181.43 (((~node14(c_e_h_3, c_h, s0, s1)) | m_c_h_element_v_in1(c_e_h_3, c_h, s0) | (~m_c_h_element_v_out(c_e_h_3, c_h, s1))) <=> ((~m_c_h_element_v_out(c_e_h_3, c_h, s1)) | m_c_h_element_v_in1(c_e_h_3, c_h, s0) | (~node14(c_e_h_3, c_h, s0, s1)))),
% 288.96/181.43 inference(rewrite,[status(thm)],[])).
% 288.96/181.43 tff(819,plain,
% 288.96/181.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s0, s1)) | m_c_h_element_v_in1(c_e_h_3, c_h, s0) | (~m_c_h_element_v_out(c_e_h_3, c_h, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s1)) | m_c_h_element_v_in1(c_e_h_3, c_h, s0) | (~node14(c_e_h_3, c_h, s0, s1))))),
% 288.96/181.43 inference(monotonicity,[status(thm)],[818])).
% 288.96/181.43 tff(820,plain,
% 288.96/181.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s0, s1)) | m_c_h_element_v_in1(c_e_h_3, c_h, s0) | (~m_c_h_element_v_out(c_e_h_3, c_h, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s1)) | m_c_h_element_v_in1(c_e_h_3, c_h, s0) | (~node14(c_e_h_3, c_h, s0, s1)))),
% 288.96/181.43 inference(transitivity,[status(thm)],[819, 817])).
% 288.96/181.43 tff(821,plain,
% 288.96/181.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s0, s1)) | m_c_h_element_v_in1(c_e_h_3, c_h, s0) | (~m_c_h_element_v_out(c_e_h_3, c_h, s1)))),
% 288.96/181.43 inference(quant_inst,[status(thm)],[])).
% 288.96/181.43 tff(822,plain,
% 288.96/181.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s1)) | m_c_h_element_v_in1(c_e_h_3, c_h, s0) | (~node14(c_e_h_3, c_h, s0, s1))),
% 288.96/181.43 inference(modus_ponens,[status(thm)],[821, 820])).
% 288.96/181.43 tff(823,plain,
% 288.96/181.43 ($false),
% 288.96/181.43 inference(unit_resolution,[status(thm)],[822, 223, 793, 816, 815])).
% 288.96/181.43 tff(824,plain,((~node14(c_e_h_3, c_h, s0, s1)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s1))), inference(lemma,lemma(discharge,[]))).
% 288.96/181.43 tff(825,plain,
% 288.96/181.43 (~node14(c_e_h_3, c_h, s0, s1)),
% 288.96/181.43 inference(unit_resolution,[status(thm)],[824, 793])).
% 288.96/181.43 tff(826,assumption,(node15(c_e_h_3, c_h, s0, s1)), introduced(assumption)).
% 288.96/181.43 tff(827,plain,
% 288.96/181.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s1)) | (~node15(c_e_h_3, c_h, s0, s1)) | m_c_h_element_v_out(c_e_h_3, c_h, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s1)) | (~node15(c_e_h_3, c_h, s0, s1)) | m_c_h_element_v_out(c_e_h_3, c_h, s0))),
% 288.96/181.43 inference(rewrite,[status(thm)],[])).
% 288.96/181.43 tff(828,plain,
% 288.96/181.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s1)) | (~node15(c_e_h_3, c_h, s0, s1)) | m_c_h_element_v_out(c_e_h_3, c_h, s0))),
% 288.96/181.43 inference(quant_inst,[status(thm)],[])).
% 288.96/181.43 tff(829,plain,
% 288.96/181.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s1)) | (~node15(c_e_h_3, c_h, s0, s1)) | m_c_h_element_v_out(c_e_h_3, c_h, s0)),
% 288.96/181.43 inference(modus_ponens,[status(thm)],[828, 827])).
% 288.96/181.43 tff(830,plain,
% 288.96/181.43 ($false),
% 288.96/181.43 inference(unit_resolution,[status(thm)],[829, 147, 793, 612, 826])).
% 288.96/181.43 tff(831,plain,((~node15(c_e_h_3, c_h, s0, s1)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s1))), inference(lemma,lemma(discharge,[]))).
% 288.96/181.43 tff(832,plain,
% 288.96/181.43 (~node15(c_e_h_3, c_h, s0, s1)),
% 288.96/181.43 inference(unit_resolution,[status(thm)],[831, 793])).
% 288.96/181.43 tff(833,plain,
% 288.96/181.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s0, s1)) | node19(c_e_h_3, c_h, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s0, s1)) | node19(c_e_h_3, c_h, s0, s1))),
% 288.96/181.43 inference(rewrite,[status(thm)],[])).
% 288.96/181.43 tff(834,plain,
% 288.96/181.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s0, s1)) | node19(c_e_h_3, c_h, s0, s1))),
% 288.96/181.43 inference(quant_inst,[status(thm)],[])).
% 288.96/181.43 tff(835,plain,
% 288.96/181.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s0, s1)) | node19(c_e_h_3, c_h, s0, s1)),
% 288.96/181.43 inference(modus_ponens,[status(thm)],[834, 833])).
% 288.96/181.43 tff(836,plain,
% 288.96/181.43 (node19(c_e_h_3, c_h, s0, s1)),
% 288.96/181.43 inference(unit_resolution,[status(thm)],[835, 190, 72])).
% 288.96/181.43 tff(837,plain,
% 288.96/181.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s0) | node15(c_e_h_3, c_h, s0, s1) | (~node19(c_e_h_3, c_h, s0, s1)) | node14(c_e_h_3, c_h, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_h, s0) | node15(c_e_h_3, c_h, s0, s1) | (~node19(c_e_h_3, c_h, s0, s1)) | node14(c_e_h_3, c_h, s0, s1))),
% 288.96/181.44 inference(rewrite,[status(thm)],[])).
% 288.96/181.44 tff(838,plain,
% 288.96/181.44 ((node16(c_e_h_3, c_h, s0) | node14(c_e_h_3, c_h, s0, s1) | node15(c_e_h_3, c_h, s0, s1) | (~node19(c_e_h_3, c_h, s0, s1))) <=> (node16(c_e_h_3, c_h, s0) | node15(c_e_h_3, c_h, s0, s1) | (~node19(c_e_h_3, c_h, s0, s1)) | node14(c_e_h_3, c_h, s0, s1))),
% 288.96/181.44 inference(rewrite,[status(thm)],[])).
% 288.96/181.44 tff(839,plain,
% 288.96/181.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s0) | node14(c_e_h_3, c_h, s0, s1) | node15(c_e_h_3, c_h, s0, s1) | (~node19(c_e_h_3, c_h, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s0) | node15(c_e_h_3, c_h, s0, s1) | (~node19(c_e_h_3, c_h, s0, s1)) | node14(c_e_h_3, c_h, s0, s1)))),
% 288.96/181.44 inference(monotonicity,[status(thm)],[838])).
% 288.96/181.44 tff(840,plain,
% 288.96/181.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s0) | node14(c_e_h_3, c_h, s0, s1) | node15(c_e_h_3, c_h, s0, s1) | (~node19(c_e_h_3, c_h, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_h, s0) | node15(c_e_h_3, c_h, s0, s1) | (~node19(c_e_h_3, c_h, s0, s1)) | node14(c_e_h_3, c_h, s0, s1))),
% 288.96/181.44 inference(transitivity,[status(thm)],[839, 837])).
% 288.96/181.44 tff(841,plain,
% 288.96/181.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s0) | node14(c_e_h_3, c_h, s0, s1) | node15(c_e_h_3, c_h, s0, s1) | (~node19(c_e_h_3, c_h, s0, s1)))),
% 288.96/181.44 inference(quant_inst,[status(thm)],[])).
% 288.96/181.44 tff(842,plain,
% 288.96/181.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_h, s0) | node15(c_e_h_3, c_h, s0, s1) | (~node19(c_e_h_3, c_h, s0, s1)) | node14(c_e_h_3, c_h, s0, s1)),
% 288.96/181.44 inference(modus_ponens,[status(thm)],[841, 840])).
% 288.96/181.44 tff(843,plain,
% 288.96/181.44 (node16(c_e_h_3, c_h, s0) | node15(c_e_h_3, c_h, s0, s1) | node14(c_e_h_3, c_h, s0, s1)),
% 288.96/181.44 inference(unit_resolution,[status(thm)],[842, 204, 836])).
% 288.96/181.44 tff(844,plain,
% 288.96/181.44 (node16(c_e_h_3, c_h, s0)),
% 288.96/181.44 inference(unit_resolution,[status(thm)],[843, 832, 825])).
% 288.96/181.44 tff(845,plain,
% 288.96/181.44 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_h, s0)) | m_c_h_element_v_in1(c_e_h_3, c_h, s0) | m_c_h_element_v_in2(c_e_h_3, c_h, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_h, s0)) | m_c_h_element_v_in1(c_e_h_3, c_h, s0) | m_c_h_element_v_in2(c_e_h_3, c_h, s0))),
% 288.96/181.44 inference(rewrite,[status(thm)],[])).
% 288.96/181.44 tff(846,plain,
% 288.96/181.44 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_h, s0)) | m_c_h_element_v_in1(c_e_h_3, c_h, s0) | m_c_h_element_v_in2(c_e_h_3, c_h, s0))),
% 288.96/181.44 inference(quant_inst,[status(thm)],[])).
% 288.96/181.44 tff(847,plain,
% 288.96/181.44 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_h, s0)) | m_c_h_element_v_in1(c_e_h_3, c_h, s0) | m_c_h_element_v_in2(c_e_h_3, c_h, s0)),
% 288.96/181.44 inference(modus_ponens,[status(thm)],[846, 845])).
% 288.96/181.44 tff(848,plain,
% 288.96/181.44 ((~node16(c_e_h_3, c_h, s0)) | m_c_h_element_v_in2(c_e_h_3, c_h, s0)),
% 288.96/181.44 inference(unit_resolution,[status(thm)],[847, 178, 815])).
% 288.96/181.44 tff(849,plain,
% 288.96/181.44 (m_c_h_element_v_in2(c_e_h_3, c_h, s0)),
% 288.96/181.44 inference(unit_resolution,[status(thm)],[848, 844])).
% 288.96/181.44 tff(850,plain,
% 288.96/181.44 (^[I0: $i, X: $i, I1: $i] : refl((m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X))) <=> (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X))))),
% 288.96/181.44 inference(bind,[status(th)],[])).
% 288.96/181.44 tff(851,plain,
% 288.96/181.44 (![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X))) <=> ![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))),
% 288.96/181.44 inference(quant_intro,[status(thm)],[850])).
% 288.96/181.44 tff(852,plain,
% 288.96/181.44 (![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X))) <=> ![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))),
% 288.96/181.44 inference(rewrite,[status(thm)],[])).
% 288.96/181.44 tff(853,plain,
% 288.96/181.44 (^[I0: $i, X: $i, I1: $i] : trans(monotonicity(rewrite((m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X))) <=> (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)))), (((m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X))) | (~node17(I0, I1, X))) <=> ((m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X))) | (~node17(I0, I1, X))))), rewrite(((m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X))) | (~node17(I0, I1, X))) <=> (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))), (((m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X))) | (~node17(I0, I1, X))) <=> (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))))),
% 288.96/181.44 inference(bind,[status(th)],[])).
% 288.96/181.44 tff(854,plain,
% 288.96/181.44 (![I0: $i, X: $i, I1: $i] : ((m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X))) | (~node17(I0, I1, X))) <=> ![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))),
% 288.96/181.44 inference(quant_intro,[status(thm)],[853])).
% 288.96/181.44 tff(855,axiom,(![I0: $i, X: $i, I1: $i] : ((m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X))) | (~node17(I0, I1, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_c_h_element_8')).
% 288.96/181.44 tff(856,plain,
% 288.96/181.44 (![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))),
% 288.96/181.44 inference(modus_ponens,[status(thm)],[855, 854])).
% 288.96/181.44 tff(857,plain,
% 288.96/181.44 (![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))),
% 288.96/181.44 inference(modus_ponens,[status(thm)],[856, 852])).
% 288.96/181.44 tff(858,plain,(
% 288.96/181.44 ![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))),
% 288.96/181.44 inference(skolemize,[status(sab)],[857])).
% 288.96/181.44 tff(859,plain,
% 288.96/181.44 (![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))),
% 288.96/181.44 inference(modus_ponens,[status(thm)],[858, 851])).
% 288.96/181.44 tff(860,plain,
% 288.96/181.44 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s0)) | m_c_h_element_v_in1(c_e_h_3, c_h, s0) | (~node17(c_e_h_3, c_h, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s0)) | m_c_h_element_v_in1(c_e_h_3, c_h, s0) | (~node17(c_e_h_3, c_h, s0)))),
% 288.96/181.44 inference(rewrite,[status(thm)],[])).
% 288.96/181.44 tff(861,plain,
% 288.96/181.44 ((m_c_h_element_v_in1(c_e_h_3, c_h, s0) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s0)) | (~node17(c_e_h_3, c_h, s0))) <=> ((~m_c_h_element_v_in2(c_e_h_3, c_h, s0)) | m_c_h_element_v_in1(c_e_h_3, c_h, s0) | (~node17(c_e_h_3, c_h, s0)))),
% 288.96/181.44 inference(rewrite,[status(thm)],[])).
% 288.96/181.44 tff(862,plain,
% 288.96/181.44 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s0) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s0)) | (~node17(c_e_h_3, c_h, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s0)) | m_c_h_element_v_in1(c_e_h_3, c_h, s0) | (~node17(c_e_h_3, c_h, s0))))),
% 288.96/181.44 inference(monotonicity,[status(thm)],[861])).
% 288.96/181.44 tff(863,plain,
% 288.96/181.44 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s0) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s0)) | (~node17(c_e_h_3, c_h, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s0)) | m_c_h_element_v_in1(c_e_h_3, c_h, s0) | (~node17(c_e_h_3, c_h, s0)))),
% 288.96/181.44 inference(transitivity,[status(thm)],[862, 860])).
% 288.96/181.44 tff(864,plain,
% 288.96/181.44 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s0) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s0)) | (~node17(c_e_h_3, c_h, s0)))),
% 288.96/181.44 inference(quant_inst,[status(thm)],[])).
% 288.96/181.44 tff(865,plain,
% 288.96/181.44 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s0)) | m_c_h_element_v_in1(c_e_h_3, c_h, s0) | (~node17(c_e_h_3, c_h, s0))),
% 288.96/181.44 inference(modus_ponens,[status(thm)],[864, 863])).
% 288.96/181.44 tff(866,plain,
% 288.96/181.44 ((~m_c_h_element_v_in2(c_e_h_3, c_h, s0)) | (~node17(c_e_h_3, c_h, s0))),
% 288.96/181.44 inference(unit_resolution,[status(thm)],[865, 859, 815])).
% 288.96/181.44 tff(867,plain,
% 288.96/181.44 (~node17(c_e_h_3, c_h, s0)),
% 288.96/181.44 inference(unit_resolution,[status(thm)],[866, 849])).
% 288.96/181.44 tff(868,plain,
% 288.96/181.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_h, s0, s1)) | node18(c_e_h_3, c_h, s0, s1) | node17(c_e_h_3, c_h, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_h, s0, s1)) | node18(c_e_h_3, c_h, s0, s1) | node17(c_e_h_3, c_h, s0))),
% 288.96/181.44 inference(rewrite,[status(thm)],[])).
% 288.96/181.44 tff(869,plain,
% 288.96/181.44 ((node17(c_e_h_3, c_h, s0) | node18(c_e_h_3, c_h, s0, s1) | (~node19(c_e_h_3, c_h, s0, s1))) <=> ((~node19(c_e_h_3, c_h, s0, s1)) | node18(c_e_h_3, c_h, s0, s1) | node17(c_e_h_3, c_h, s0))),
% 288.96/181.44 inference(rewrite,[status(thm)],[])).
% 288.96/181.44 tff(870,plain,
% 288.96/181.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s0) | node18(c_e_h_3, c_h, s0, s1) | (~node19(c_e_h_3, c_h, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_h, s0, s1)) | node18(c_e_h_3, c_h, s0, s1) | node17(c_e_h_3, c_h, s0)))),
% 288.96/181.44 inference(monotonicity,[status(thm)],[869])).
% 288.96/181.44 tff(871,plain,
% 288.96/181.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s0) | node18(c_e_h_3, c_h, s0, s1) | (~node19(c_e_h_3, c_h, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_h, s0, s1)) | node18(c_e_h_3, c_h, s0, s1) | node17(c_e_h_3, c_h, s0))),
% 288.96/181.44 inference(transitivity,[status(thm)],[870, 868])).
% 288.96/181.44 tff(872,plain,
% 288.96/181.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s0) | node18(c_e_h_3, c_h, s0, s1) | (~node19(c_e_h_3, c_h, s0, s1)))),
% 288.96/181.44 inference(quant_inst,[status(thm)],[])).
% 288.96/181.44 tff(873,plain,
% 288.96/181.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_h, s0, s1)) | node18(c_e_h_3, c_h, s0, s1) | node17(c_e_h_3, c_h, s0)),
% 288.96/181.45 inference(modus_ponens,[status(thm)],[872, 871])).
% 288.96/181.45 tff(874,plain,
% 288.96/181.45 (node18(c_e_h_3, c_h, s0, s1) | node17(c_e_h_3, c_h, s0)),
% 288.96/181.45 inference(unit_resolution,[status(thm)],[873, 776, 836])).
% 288.96/181.45 tff(875,plain,
% 288.96/181.45 (node18(c_e_h_3, c_h, s0, s1)),
% 288.96/181.45 inference(unit_resolution,[status(thm)],[874, 867])).
% 288.96/181.45 tff(876,plain,
% 288.96/181.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s1)) | m_c_h_element_v_out(c_e_h_3, c_h, s0) | (~node18(c_e_h_3, c_h, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s1)) | m_c_h_element_v_out(c_e_h_3, c_h, s0) | (~node18(c_e_h_3, c_h, s0, s1)))),
% 288.96/181.45 inference(rewrite,[status(thm)],[])).
% 288.96/181.45 tff(877,plain,
% 288.96/181.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s1)) | m_c_h_element_v_out(c_e_h_3, c_h, s0) | (~node18(c_e_h_3, c_h, s0, s1)))),
% 288.96/181.45 inference(quant_inst,[status(thm)],[])).
% 288.96/181.45 tff(878,plain,
% 288.96/181.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s1)) | m_c_h_element_v_out(c_e_h_3, c_h, s0) | (~node18(c_e_h_3, c_h, s0, s1))),
% 288.96/181.45 inference(modus_ponens,[status(thm)],[877, 876])).
% 288.96/181.45 tff(879,plain,
% 288.96/181.45 ($false),
% 288.96/181.45 inference(unit_resolution,[status(thm)],[878, 753, 793, 612, 875])).
% 288.96/181.45 tff(880,plain,(~m_c_h_element_v_out(c_e_h_3, c_h, s1)), inference(lemma,lemma(discharge,[]))).
% 288.96/181.45 tff(881,plain,
% 288.96/181.45 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_i, s1)) | m_c_h_element_v_out(c_e_h_3, c_h, s1))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s1)) | m_c_h_element_v_out(c_e_h_3, c_h, s1))),
% 288.96/181.45 inference(rewrite,[status(thm)],[])).
% 288.96/181.45 tff(882,plain,
% 288.96/181.45 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_i, s1)) | m_c_h_element_v_out(c_e_h_3, c_h, s1))),
% 288.96/181.45 inference(quant_inst,[status(thm)],[])).
% 288.96/181.45 tff(883,plain,
% 288.96/181.45 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s1)) | m_c_h_element_v_out(c_e_h_3, c_h, s1)),
% 288.96/181.45 inference(modus_ponens,[status(thm)],[882, 881])).
% 288.96/181.45 tff(884,plain,
% 288.96/181.45 (~m_and_h_gate_v_in1(c_e_h_3, c_i, s1)),
% 288.96/181.45 inference(unit_resolution,[status(thm)],[883, 619, 880])).
% 288.96/181.45 tff(885,plain,
% 288.96/181.45 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_i, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s1))),
% 288.96/181.45 inference(rewrite,[status(thm)],[])).
% 288.96/181.45 tff(886,plain,
% 288.96/181.45 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s1))),
% 288.96/181.45 inference(quant_inst,[status(thm)],[])).
% 288.96/181.45 tff(887,plain,
% 288.96/181.45 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_i, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s1)),
% 288.96/181.45 inference(modus_ponens,[status(thm)],[886, 885])).
% 288.96/181.45 tff(888,plain,
% 288.96/181.45 (~node20(c_e_h_3, c_i, s1)),
% 288.96/181.45 inference(unit_resolution,[status(thm)],[887, 38, 884])).
% 288.96/181.45 tff(889,assumption,(~node20(c_e_h_3, c_i, s1)), introduced(assumption)).
% 288.96/181.45 tff(890,assumption,(node21(c_e_h_3, c_i, s1, s2)), introduced(assumption)).
% 288.96/181.45 tff(891,plain,
% 288.96/181.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s2)) | (~node21(c_e_h_3, c_i, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_i, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s2)) | (~node21(c_e_h_3, c_i, s1, s2)))),
% 288.96/181.45 inference(rewrite,[status(thm)],[])).
% 288.96/181.45 tff(892,plain,
% 288.96/181.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s2)) | (~node21(c_e_h_3, c_i, s1, s2)))),
% 288.96/181.45 inference(quant_inst,[status(thm)],[])).
% 288.96/181.45 tff(893,plain,
% 288.96/181.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_i, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s2)) | (~node21(c_e_h_3, c_i, s1, s2))),
% 288.96/181.45 inference(modus_ponens,[status(thm)],[892, 891])).
% 288.96/181.45 tff(894,plain,
% 288.96/181.45 ($false),
% 288.96/181.45 inference(unit_resolution,[status(thm)],[893, 52, 890, 785, 889])).
% 288.96/181.45 tff(895,plain,((~node21(c_e_h_3, c_i, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s2)) | node20(c_e_h_3, c_i, s1)), inference(lemma,lemma(discharge,[]))).
% 288.96/181.45 tff(896,plain,
% 288.96/181.45 ((~node21(c_e_h_3, c_i, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s2))),
% 288.96/181.45 inference(unit_resolution,[status(thm)],[895, 888])).
% 288.96/181.45 tff(897,plain,
% 288.96/181.45 (~node21(c_e_h_3, c_i, s1, s2)),
% 288.96/181.45 inference(unit_resolution,[status(thm)],[896, 785])).
% 288.96/181.45 tff(898,plain,
% 288.96/181.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_3, c_i, s1, s2) | node22(c_e_h_3, c_i, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_3, c_i, s1, s2) | node22(c_e_h_3, c_i, s1, s2))),
% 288.96/181.45 inference(rewrite,[status(thm)],[])).
% 288.96/181.45 tff(899,plain,
% 288.96/181.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_3, c_i, s1, s2) | node22(c_e_h_3, c_i, s1, s2))),
% 288.96/181.45 inference(quant_inst,[status(thm)],[])).
% 288.96/181.45 tff(900,plain,
% 288.96/181.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_3, c_i, s1, s2) | node22(c_e_h_3, c_i, s1, s2)),
% 288.96/181.45 inference(modus_ponens,[status(thm)],[899, 898])).
% 288.96/181.45 tff(901,plain,
% 288.96/181.45 (node21(c_e_h_3, c_i, s1, s2) | node22(c_e_h_3, c_i, s1, s2)),
% 288.96/181.45 inference(unit_resolution,[status(thm)],[900, 82, 255])).
% 288.96/181.45 tff(902,plain,
% 288.96/181.45 ($false),
% 288.96/181.45 inference(unit_resolution,[status(thm)],[901, 897, 792])).
% 288.96/181.45 tff(903,plain,(~m_and_h_gate_v_out(c_e_h_3, c_i, s2)), inference(lemma,lemma(discharge,[]))).
% 288.96/181.45 tff(904,plain,
% 288.96/181.45 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s2)) | m_and_h_gate_v_out(c_e_h_3, c_i, s2))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s2)) | m_and_h_gate_v_out(c_e_h_3, c_i, s2))),
% 288.96/181.45 inference(rewrite,[status(thm)],[])).
% 288.96/181.45 tff(905,plain,
% 288.96/181.45 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s2)) | m_and_h_gate_v_out(c_e_h_3, c_i, s2))),
% 288.96/181.45 inference(quant_inst,[status(thm)],[])).
% 288.96/181.45 tff(906,plain,
% 288.96/181.45 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s2)) | m_and_h_gate_v_out(c_e_h_3, c_i, s2)),
% 288.96/181.45 inference(modus_ponens,[status(thm)],[905, 904])).
% 288.96/181.45 tff(907,plain,
% 288.96/181.45 (~m_c_h_element_v_in2(c_e_h_3, c_e, s2)),
% 288.96/181.45 inference(unit_resolution,[status(thm)],[906, 164, 903])).
% 288.96/181.45 tff(908,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_e, s2)), introduced(assumption)).
% 288.96/181.45 tff(909,assumption,(node17(c_e_h_3, c_e, s2)), introduced(assumption)).
% 288.96/181.45 tff(910,plain,
% 288.96/181.45 (^[I0: $i, X: $i, I1: $i] : refl(((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X))) <=> ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X))))),
% 288.96/181.45 inference(bind,[status(th)],[])).
% 288.96/181.45 tff(911,plain,
% 288.96/181.45 (![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X))) <=> ![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))),
% 288.96/181.45 inference(quant_intro,[status(thm)],[910])).
% 288.96/181.45 tff(912,plain,
% 288.96/181.45 (![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X))) <=> ![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))),
% 288.96/181.45 inference(rewrite,[status(thm)],[])).
% 288.96/181.45 tff(913,plain,
% 288.96/181.45 (^[I0: $i, X: $i, I1: $i] : rewrite((((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X))) <=> ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X))))),
% 288.96/181.45 inference(bind,[status(th)],[])).
% 288.96/181.45 tff(914,plain,
% 288.96/181.45 (![I0: $i, X: $i, I1: $i] : (((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X))) <=> ![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))),
% 288.96/181.45 inference(quant_intro,[status(thm)],[913])).
% 288.96/181.45 tff(915,axiom,(![I0: $i, X: $i, I1: $i] : (((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_c_h_element_9')).
% 288.96/181.45 tff(916,plain,
% 288.96/181.45 (![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))),
% 288.96/181.45 inference(modus_ponens,[status(thm)],[915, 914])).
% 288.96/181.45 tff(917,plain,
% 288.96/181.45 (![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))),
% 288.96/181.45 inference(modus_ponens,[status(thm)],[916, 912])).
% 288.96/181.45 tff(918,plain,(
% 288.96/181.45 ![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))),
% 288.96/181.45 inference(skolemize,[status(sab)],[917])).
% 288.96/181.45 tff(919,plain,
% 288.96/181.45 (![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))),
% 288.96/181.45 inference(modus_ponens,[status(thm)],[918, 911])).
% 288.96/181.45 tff(920,plain,
% 288.96/181.45 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s2)) | m_c_h_element_v_in2(c_e_h_3, c_e, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s2)) | m_c_h_element_v_in2(c_e_h_3, c_e, s2))),
% 288.96/181.45 inference(rewrite,[status(thm)],[])).
% 288.96/181.45 tff(921,plain,
% 288.96/181.45 (((~m_c_h_element_v_in1(c_e_h_3, c_e, s2)) | m_c_h_element_v_in2(c_e_h_3, c_e, s2) | (~node17(c_e_h_3, c_e, s2))) <=> ((~node17(c_e_h_3, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s2)) | m_c_h_element_v_in2(c_e_h_3, c_e, s2))),
% 288.96/181.45 inference(rewrite,[status(thm)],[])).
% 288.96/181.45 tff(922,plain,
% 288.96/181.45 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s2)) | m_c_h_element_v_in2(c_e_h_3, c_e, s2) | (~node17(c_e_h_3, c_e, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s2)) | m_c_h_element_v_in2(c_e_h_3, c_e, s2)))),
% 288.96/181.45 inference(monotonicity,[status(thm)],[921])).
% 288.96/181.45 tff(923,plain,
% 288.96/181.45 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s2)) | m_c_h_element_v_in2(c_e_h_3, c_e, s2) | (~node17(c_e_h_3, c_e, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s2)) | m_c_h_element_v_in2(c_e_h_3, c_e, s2))),
% 288.96/181.46 inference(transitivity,[status(thm)],[922, 920])).
% 288.96/181.46 tff(924,plain,
% 288.96/181.46 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s2)) | m_c_h_element_v_in2(c_e_h_3, c_e, s2) | (~node17(c_e_h_3, c_e, s2)))),
% 288.96/181.46 inference(quant_inst,[status(thm)],[])).
% 288.96/181.46 tff(925,plain,
% 288.96/181.46 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s2)) | m_c_h_element_v_in2(c_e_h_3, c_e, s2)),
% 288.96/181.46 inference(modus_ponens,[status(thm)],[924, 923])).
% 288.96/181.46 tff(926,plain,
% 288.96/181.46 ((~m_c_h_element_v_in1(c_e_h_3, c_e, s2)) | m_c_h_element_v_in2(c_e_h_3, c_e, s2)),
% 288.96/181.46 inference(unit_resolution,[status(thm)],[925, 919, 909])).
% 288.96/181.46 tff(927,plain,
% 288.96/181.46 (~m_c_h_element_v_in1(c_e_h_3, c_e, s2)),
% 288.96/181.46 inference(unit_resolution,[status(thm)],[926, 908])).
% 288.96/181.46 tff(928,assumption,(~node15(c_e_h_3, c_e, s2, s3)), introduced(assumption)).
% 288.96/181.46 tff(929,plain,
% 288.96/181.46 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_e, s2)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2) | m_c_h_element_v_in2(c_e_h_3, c_e, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s2)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2) | m_c_h_element_v_in2(c_e_h_3, c_e, s2))),
% 288.96/181.46 inference(rewrite,[status(thm)],[])).
% 288.96/181.46 tff(930,plain,
% 288.96/181.46 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_e, s2)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2) | m_c_h_element_v_in2(c_e_h_3, c_e, s2))),
% 288.96/181.46 inference(quant_inst,[status(thm)],[])).
% 288.96/181.46 tff(931,plain,
% 288.96/181.46 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s2)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2) | m_c_h_element_v_in2(c_e_h_3, c_e, s2)),
% 288.96/181.46 inference(modus_ponens,[status(thm)],[930, 929])).
% 288.96/181.46 tff(932,plain,
% 288.96/181.46 (~node16(c_e_h_3, c_e, s2)),
% 288.96/181.46 inference(unit_resolution,[status(thm)],[931, 178, 927, 908])).
% 288.96/181.46 tff(933,plain,
% 288.96/181.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_3, c_e, s2, s3) | node16(c_e_h_3, c_e, s2) | (~node19(c_e_h_3, c_e, s2, s3)) | node15(c_e_h_3, c_e, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_e, s2, s3) | node16(c_e_h_3, c_e, s2) | (~node19(c_e_h_3, c_e, s2, s3)) | node15(c_e_h_3, c_e, s2, s3))),
% 288.96/181.46 inference(rewrite,[status(thm)],[])).
% 288.96/181.46 tff(934,plain,
% 288.96/181.46 ((node16(c_e_h_3, c_e, s2) | node14(c_e_h_3, c_e, s2, s3) | node15(c_e_h_3, c_e, s2, s3) | (~node19(c_e_h_3, c_e, s2, s3))) <=> (node14(c_e_h_3, c_e, s2, s3) | node16(c_e_h_3, c_e, s2) | (~node19(c_e_h_3, c_e, s2, s3)) | node15(c_e_h_3, c_e, s2, s3))),
% 288.96/181.46 inference(rewrite,[status(thm)],[])).
% 288.96/181.46 tff(935,plain,
% 288.96/181.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s2) | node14(c_e_h_3, c_e, s2, s3) | node15(c_e_h_3, c_e, s2, s3) | (~node19(c_e_h_3, c_e, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_3, c_e, s2, s3) | node16(c_e_h_3, c_e, s2) | (~node19(c_e_h_3, c_e, s2, s3)) | node15(c_e_h_3, c_e, s2, s3)))),
% 288.96/181.46 inference(monotonicity,[status(thm)],[934])).
% 288.96/181.46 tff(936,plain,
% 288.96/181.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s2) | node14(c_e_h_3, c_e, s2, s3) | node15(c_e_h_3, c_e, s2, s3) | (~node19(c_e_h_3, c_e, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_e, s2, s3) | node16(c_e_h_3, c_e, s2) | (~node19(c_e_h_3, c_e, s2, s3)) | node15(c_e_h_3, c_e, s2, s3))),
% 288.96/181.46 inference(transitivity,[status(thm)],[935, 933])).
% 288.96/181.46 tff(937,plain,
% 288.96/181.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s2) | node14(c_e_h_3, c_e, s2, s3) | node15(c_e_h_3, c_e, s2, s3) | (~node19(c_e_h_3, c_e, s2, s3)))),
% 288.96/181.46 inference(quant_inst,[status(thm)],[])).
% 288.96/181.46 tff(938,plain,
% 288.96/181.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_e, s2, s3) | node16(c_e_h_3, c_e, s2) | (~node19(c_e_h_3, c_e, s2, s3)) | node15(c_e_h_3, c_e, s2, s3)),
% 288.96/181.46 inference(modus_ponens,[status(thm)],[937, 936])).
% 288.96/181.46 tff(939,plain,
% 288.96/181.46 (node14(c_e_h_3, c_e, s2, s3) | node16(c_e_h_3, c_e, s2) | node15(c_e_h_3, c_e, s2, s3)),
% 288.96/181.46 inference(unit_resolution,[status(thm)],[938, 204, 766])).
% 288.96/181.46 tff(940,plain,
% 288.96/181.46 (node14(c_e_h_3, c_e, s2, s3)),
% 288.96/181.46 inference(unit_resolution,[status(thm)],[939, 932, 928])).
% 288.96/181.46 tff(941,plain,
% 288.96/181.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2) | (~node14(c_e_h_3, c_e, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2) | (~node14(c_e_h_3, c_e, s2, s3)))),
% 288.96/181.46 inference(rewrite,[status(thm)],[])).
% 288.96/181.46 tff(942,plain,
% 288.96/181.46 (((~node14(c_e_h_3, c_e, s2, s3)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3))) <=> ((~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2) | (~node14(c_e_h_3, c_e, s2, s3)))),
% 288.96/181.46 inference(rewrite,[status(thm)],[])).
% 288.96/181.46 tff(943,plain,
% 288.96/181.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s2, s3)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2) | (~node14(c_e_h_3, c_e, s2, s3))))),
% 288.96/181.46 inference(monotonicity,[status(thm)],[942])).
% 288.96/181.46 tff(944,plain,
% 288.96/181.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s2, s3)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2) | (~node14(c_e_h_3, c_e, s2, s3)))),
% 288.96/181.46 inference(transitivity,[status(thm)],[943, 941])).
% 288.96/181.46 tff(945,plain,
% 288.96/181.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s2, s3)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3)))),
% 288.96/181.46 inference(quant_inst,[status(thm)],[])).
% 288.96/181.46 tff(946,plain,
% 288.96/181.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | m_c_h_element_v_in1(c_e_h_3, c_e, s2) | (~node14(c_e_h_3, c_e, s2, s3))),
% 288.96/181.46 inference(modus_ponens,[status(thm)],[945, 944])).
% 288.96/181.46 tff(947,plain,
% 288.96/181.46 ($false),
% 288.96/181.46 inference(unit_resolution,[status(thm)],[946, 223, 734, 940, 927])).
% 288.96/181.46 tff(948,plain,(m_c_h_element_v_in2(c_e_h_3, c_e, s2) | (~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | node15(c_e_h_3, c_e, s2, s3) | (~node17(c_e_h_3, c_e, s2))), inference(lemma,lemma(discharge,[]))).
% 288.96/181.46 tff(949,plain,
% 288.96/181.46 ((~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | node15(c_e_h_3, c_e, s2, s3) | (~node17(c_e_h_3, c_e, s2))),
% 288.96/181.46 inference(unit_resolution,[status(thm)],[948, 907])).
% 288.96/181.46 tff(950,plain,
% 288.96/181.46 ($false),
% 288.96/181.46 inference(unit_resolution,[status(thm)],[949, 784, 742, 734])).
% 288.96/181.46 tff(951,plain,((~m_c_h_element_v_out(c_e_h_3, c_e, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s2)), inference(lemma,lemma(discharge,[]))).
% 288.96/181.46 tff(952,plain,
% 288.96/181.46 (~m_c_h_element_v_out(c_e_h_3, c_e, s3)),
% 288.96/181.46 inference(unit_resolution,[status(thm)],[951, 674])).
% 288.96/181.46 tff(953,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_r, s3)), introduced(assumption)).
% 288.96/181.46 tff(954,assumption,(~m_c_h_element_v_out(c_e_h_3, c_e, s3)), introduced(assumption)).
% 288.96/181.46 tff(955,plain,
% 288.96/181.46 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s3))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s3))),
% 288.96/181.46 inference(rewrite,[status(thm)],[])).
% 288.96/181.46 tff(956,plain,
% 288.96/181.46 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s3))),
% 288.96/181.46 inference(quant_inst,[status(thm)],[])).
% 288.96/181.46 tff(957,plain,
% 288.96/181.46 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s3)),
% 288.96/181.46 inference(modus_ponens,[status(thm)],[956, 955])).
% 288.96/181.46 tff(958,plain,
% 288.96/181.46 ($false),
% 288.96/181.46 inference(unit_resolution,[status(thm)],[957, 24, 954, 953])).
% 288.96/181.46 tff(959,plain,((~m_and_h_gate_v_in1(c_e_h_3, c_r, s3)) | m_c_h_element_v_out(c_e_h_3, c_e, s3)), inference(lemma,lemma(discharge,[]))).
% 288.96/181.46 tff(960,plain,
% 288.96/181.46 (~m_and_h_gate_v_in1(c_e_h_3, c_r, s3)),
% 288.96/181.46 inference(unit_resolution,[status(thm)],[959, 952])).
% 288.96/181.46 tff(961,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_r, s3)), introduced(assumption)).
% 288.96/181.46 tff(962,assumption,(node20(c_e_h_3, c_r, s3)), introduced(assumption)).
% 288.96/181.46 tff(963,plain,
% 288.96/181.46 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s3))),
% 288.96/181.46 inference(rewrite,[status(thm)],[])).
% 288.96/181.46 tff(964,plain,
% 288.96/181.46 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s3))),
% 288.96/181.46 inference(quant_inst,[status(thm)],[])).
% 288.96/181.46 tff(965,plain,
% 288.96/181.46 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s3)),
% 288.96/181.46 inference(modus_ponens,[status(thm)],[964, 963])).
% 288.96/181.46 tff(966,plain,
% 288.96/181.46 ($false),
% 288.96/181.46 inference(unit_resolution,[status(thm)],[965, 38, 962, 961])).
% 288.96/181.46 tff(967,plain,((~node20(c_e_h_3, c_r, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s3)), inference(lemma,lemma(discharge,[]))).
% 288.96/181.46 tff(968,plain,
% 288.96/181.46 (~node20(c_e_h_3, c_r, s3)),
% 288.96/181.46 inference(unit_resolution,[status(thm)],[967, 960])).
% 288.96/181.46 tff(969,assumption,(m_and_h_gate_v_out(c_e_h_3, c_r, s4)), introduced(assumption)).
% 288.96/181.46 tff(970,assumption,(node22(c_e_h_3, c_r, s3, s4)), introduced(assumption)).
% 288.96/181.46 tff(971,plain,
% 288.96/181.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | (~node22(c_e_h_3, c_r, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_r, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | (~node22(c_e_h_3, c_r, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_r, s3))),
% 288.96/181.47 inference(rewrite,[status(thm)],[])).
% 288.96/181.47 tff(972,plain,
% 288.96/181.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | (~node22(c_e_h_3, c_r, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_r, s3))),
% 288.96/181.47 inference(quant_inst,[status(thm)],[])).
% 288.96/181.47 tff(973,plain,
% 288.96/181.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | (~node22(c_e_h_3, c_r, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_r, s3)),
% 288.96/181.47 inference(modus_ponens,[status(thm)],[972, 971])).
% 288.96/181.47 tff(974,plain,
% 288.96/181.47 ($false),
% 288.96/181.47 inference(unit_resolution,[status(thm)],[973, 108, 970, 969, 701])).
% 288.96/181.47 tff(975,plain,((~node22(c_e_h_3, c_r, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | m_and_h_gate_v_out(c_e_h_3, c_r, s3)), inference(lemma,lemma(discharge,[]))).
% 288.96/181.47 tff(976,plain,
% 288.96/181.47 (~node22(c_e_h_3, c_r, s3, s4)),
% 288.96/181.47 inference(unit_resolution,[status(thm)],[975, 969, 701])).
% 288.96/181.47 tff(977,assumption,(~node20(c_e_h_3, c_r, s3)), introduced(assumption)).
% 288.96/181.47 tff(978,assumption,(node21(c_e_h_3, c_r, s3, s4)), introduced(assumption)).
% 288.96/181.47 tff(979,plain,
% 288.96/181.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | node20(c_e_h_3, c_r, s3) | (~node21(c_e_h_3, c_r, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | node20(c_e_h_3, c_r, s3) | (~node21(c_e_h_3, c_r, s3, s4)))),
% 288.96/181.47 inference(rewrite,[status(thm)],[])).
% 288.96/181.47 tff(980,plain,
% 288.96/181.47 ((node20(c_e_h_3, c_r, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | (~node21(c_e_h_3, c_r, s3, s4))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | node20(c_e_h_3, c_r, s3) | (~node21(c_e_h_3, c_r, s3, s4)))),
% 288.96/181.47 inference(rewrite,[status(thm)],[])).
% 288.96/181.47 tff(981,plain,
% 288.96/181.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | (~node21(c_e_h_3, c_r, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | node20(c_e_h_3, c_r, s3) | (~node21(c_e_h_3, c_r, s3, s4))))),
% 288.96/181.47 inference(monotonicity,[status(thm)],[980])).
% 288.96/181.47 tff(982,plain,
% 288.96/181.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | (~node21(c_e_h_3, c_r, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | node20(c_e_h_3, c_r, s3) | (~node21(c_e_h_3, c_r, s3, s4)))),
% 288.96/181.47 inference(transitivity,[status(thm)],[981, 979])).
% 288.96/181.47 tff(983,plain,
% 288.96/181.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | (~node21(c_e_h_3, c_r, s3, s4)))),
% 288.96/181.47 inference(quant_inst,[status(thm)],[])).
% 288.96/181.47 tff(984,plain,
% 288.96/181.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | node20(c_e_h_3, c_r, s3) | (~node21(c_e_h_3, c_r, s3, s4))),
% 288.96/181.47 inference(modus_ponens,[status(thm)],[983, 982])).
% 288.96/181.47 tff(985,plain,
% 288.96/181.47 ($false),
% 288.96/181.47 inference(unit_resolution,[status(thm)],[984, 52, 978, 969, 977])).
% 288.96/181.47 tff(986,plain,((~node21(c_e_h_3, c_r, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | node20(c_e_h_3, c_r, s3)), inference(lemma,lemma(discharge,[]))).
% 288.96/181.47 tff(987,plain,
% 288.96/181.47 (~node21(c_e_h_3, c_r, s3, s4)),
% 288.96/181.47 inference(unit_resolution,[status(thm)],[986, 969, 977])).
% 288.96/181.47 tff(988,plain,
% 288.96/181.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_3, c_r, s3, s4) | node22(c_e_h_3, c_r, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_3, c_r, s3, s4) | node22(c_e_h_3, c_r, s3, s4))),
% 288.96/181.47 inference(rewrite,[status(thm)],[])).
% 288.96/181.47 tff(989,plain,
% 288.96/181.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_3, c_r, s3, s4) | node22(c_e_h_3, c_r, s3, s4))),
% 288.96/181.47 inference(quant_inst,[status(thm)],[])).
% 288.96/181.47 tff(990,plain,
% 288.96/181.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_3, c_r, s3, s4) | node22(c_e_h_3, c_r, s3, s4)),
% 288.96/181.47 inference(modus_ponens,[status(thm)],[989, 988])).
% 288.96/181.47 tff(991,plain,
% 288.96/181.47 (node21(c_e_h_3, c_r, s3, s4) | node22(c_e_h_3, c_r, s3, s4)),
% 288.96/181.47 inference(unit_resolution,[status(thm)],[990, 82, 531])).
% 288.96/181.47 tff(992,plain,
% 288.96/181.47 ($false),
% 288.96/181.47 inference(unit_resolution,[status(thm)],[991, 987, 976])).
% 288.96/181.47 tff(993,plain,((~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | node20(c_e_h_3, c_r, s3) | m_and_h_gate_v_out(c_e_h_3, c_r, s3)), inference(lemma,lemma(discharge,[]))).
% 288.96/181.47 tff(994,plain,
% 288.96/181.47 ((~m_and_h_gate_v_out(c_e_h_3, c_r, s4)) | m_and_h_gate_v_out(c_e_h_3, c_r, s3)),
% 288.96/181.47 inference(unit_resolution,[status(thm)],[993, 968])).
% 288.96/181.47 tff(995,plain,
% 288.96/181.47 (~m_and_h_gate_v_out(c_e_h_3, c_r, s4)),
% 288.96/181.47 inference(unit_resolution,[status(thm)],[994, 700])).
% 288.96/181.47 tff(996,assumption,(m_user_v_ack(c_e_h_3, c_u, s4)), introduced(assumption)).
% 288.96/181.47 tff(997,plain,
% 288.96/181.47 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_3, c_u, s4)) | m_and_h_gate_v_out(c_e_h_3, c_r, s4))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_3, c_u, s4)) | m_and_h_gate_v_out(c_e_h_3, c_r, s4))),
% 288.96/181.47 inference(rewrite,[status(thm)],[])).
% 288.96/181.47 tff(998,plain,
% 288.96/181.47 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_3, c_u, s4)) | m_and_h_gate_v_out(c_e_h_3, c_r, s4))),
% 288.96/181.47 inference(quant_inst,[status(thm)],[])).
% 288.96/181.47 tff(999,plain,
% 288.96/181.47 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_3, c_u, s4)) | m_and_h_gate_v_out(c_e_h_3, c_r, s4)),
% 288.96/181.47 inference(modus_ponens,[status(thm)],[998, 997])).
% 288.96/181.47 tff(1000,plain,
% 288.96/181.47 ($false),
% 288.96/181.47 inference(unit_resolution,[status(thm)],[999, 268, 996, 995])).
% 288.96/181.47 tff(1001,plain,(~m_user_v_ack(c_e_h_3, c_u, s4)), inference(lemma,lemma(discharge,[]))).
% 288.96/181.47 tff(1002,assumption,(~m_user_v_ack(c_e_h_3, c_u, s4)), introduced(assumption)).
% 288.96/181.47 tff(1003,assumption,(~m_user_v_req(c_e_h_3, c_u, s5)), introduced(assumption)).
% 288.96/181.47 tff(1004,assumption,(node7(c_e_h_3, c_u, s4, s5)), introduced(assumption)).
% 288.96/181.47 tff(1005,plain,
% 288.96/181.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | ((~node7(c_e_h_3, c_u, s4, s5)) | m_user_v_ack(c_e_h_3, c_u, s4) | m_user_v_req(c_e_h_3, c_u, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | (~node7(c_e_h_3, c_u, s4, s5)) | m_user_v_ack(c_e_h_3, c_u, s4) | m_user_v_req(c_e_h_3, c_u, s5))),
% 288.96/181.47 inference(rewrite,[status(thm)],[])).
% 288.96/181.47 tff(1006,plain,
% 288.96/181.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | ((~node7(c_e_h_3, c_u, s4, s5)) | m_user_v_ack(c_e_h_3, c_u, s4) | m_user_v_req(c_e_h_3, c_u, s5))),
% 288.96/181.47 inference(quant_inst,[status(thm)],[])).
% 288.96/181.47 tff(1007,plain,
% 288.96/181.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | (~node7(c_e_h_3, c_u, s4, s5)) | m_user_v_ack(c_e_h_3, c_u, s4) | m_user_v_req(c_e_h_3, c_u, s5)),
% 288.96/181.47 inference(modus_ponens,[status(thm)],[1006, 1005])).
% 288.96/181.47 tff(1008,plain,
% 288.96/181.47 ($false),
% 288.96/181.47 inference(unit_resolution,[status(thm)],[1007, 284, 1002, 1004, 1003])).
% 288.96/181.48 tff(1009,plain,((~node7(c_e_h_3, c_u, s4, s5)) | m_user_v_ack(c_e_h_3, c_u, s4) | m_user_v_req(c_e_h_3, c_u, s5)), inference(lemma,lemma(discharge,[]))).
% 288.96/181.48 tff(1010,plain,
% 288.96/181.48 (~node7(c_e_h_3, c_u, s4, s5)),
% 288.96/181.48 inference(unit_resolution,[status(thm)],[1009, 1003, 1002])).
% 288.96/181.48 tff(1011,assumption,(m_user_v_req(c_e_h_3, c_u, s4)), introduced(assumption)).
% 288.96/181.48 tff(1012,assumption,(node8(c_e_h_3, c_u, s4, s5)), introduced(assumption)).
% 288.96/181.48 tff(1013,plain,
% 288.96/181.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | ((~m_user_v_req(c_e_h_3, c_u, s4)) | m_user_v_req(c_e_h_3, c_u, s5) | (~node8(c_e_h_3, c_u, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (~m_user_v_req(c_e_h_3, c_u, s4)) | m_user_v_req(c_e_h_3, c_u, s5) | (~node8(c_e_h_3, c_u, s4, s5)))),
% 288.96/181.48 inference(rewrite,[status(thm)],[])).
% 288.96/181.48 tff(1014,plain,
% 288.96/181.48 ((m_user_v_req(c_e_h_3, c_u, s5) | (~node8(c_e_h_3, c_u, s4, s5)) | (~m_user_v_req(c_e_h_3, c_u, s4))) <=> ((~m_user_v_req(c_e_h_3, c_u, s4)) | m_user_v_req(c_e_h_3, c_u, s5) | (~node8(c_e_h_3, c_u, s4, s5)))),
% 288.96/181.48 inference(rewrite,[status(thm)],[])).
% 288.96/181.48 tff(1015,plain,
% 288.96/181.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_3, c_u, s5) | (~node8(c_e_h_3, c_u, s4, s5)) | (~m_user_v_req(c_e_h_3, c_u, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | ((~m_user_v_req(c_e_h_3, c_u, s4)) | m_user_v_req(c_e_h_3, c_u, s5) | (~node8(c_e_h_3, c_u, s4, s5))))),
% 288.96/181.48 inference(monotonicity,[status(thm)],[1014])).
% 288.96/181.48 tff(1016,plain,
% 288.96/181.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_3, c_u, s5) | (~node8(c_e_h_3, c_u, s4, s5)) | (~m_user_v_req(c_e_h_3, c_u, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (~m_user_v_req(c_e_h_3, c_u, s4)) | m_user_v_req(c_e_h_3, c_u, s5) | (~node8(c_e_h_3, c_u, s4, s5)))),
% 288.96/181.48 inference(transitivity,[status(thm)],[1015, 1013])).
% 288.96/181.48 tff(1017,plain,
% 288.96/181.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_3, c_u, s5) | (~node8(c_e_h_3, c_u, s4, s5)) | (~m_user_v_req(c_e_h_3, c_u, s4)))),
% 288.96/181.48 inference(quant_inst,[status(thm)],[])).
% 288.96/181.48 tff(1018,plain,
% 288.96/181.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (~m_user_v_req(c_e_h_3, c_u, s4)) | m_user_v_req(c_e_h_3, c_u, s5) | (~node8(c_e_h_3, c_u, s4, s5))),
% 288.96/181.48 inference(modus_ponens,[status(thm)],[1017, 1016])).
% 288.96/181.48 tff(1019,plain,
% 288.96/181.48 ($false),
% 288.96/181.48 inference(unit_resolution,[status(thm)],[1018, 302, 1012, 1011, 1003])).
% 288.96/181.48 tff(1020,plain,((~node8(c_e_h_3, c_u, s4, s5)) | (~m_user_v_req(c_e_h_3, c_u, s4)) | m_user_v_req(c_e_h_3, c_u, s5)), inference(lemma,lemma(discharge,[]))).
% 288.96/181.48 tff(1021,plain,
% 288.96/181.48 (~node8(c_e_h_3, c_u, s4, s5)),
% 288.96/181.48 inference(unit_resolution,[status(thm)],[1020, 1003, 1011])).
% 288.96/181.48 tff(1022,plain,
% 288.96/181.48 (succ(s4, s5) <=> succ(s4, s5)),
% 288.96/181.48 inference(rewrite,[status(thm)],[])).
% 288.96/181.48 tff(1023,axiom,(succ(s4, s5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound5')).
% 288.96/181.48 tff(1024,plain,
% 288.96/181.48 (succ(s4, s5)),
% 288.96/181.48 inference(modus_ponens,[status(thm)],[1023, 1022])).
% 288.96/181.48 tff(1025,plain,
% 288.96/181.48 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s4, s5)) | trans(s4, s5))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s4, s5)) | trans(s4, s5))),
% 288.96/181.48 inference(rewrite,[status(thm)],[])).
% 288.96/181.48 tff(1026,plain,
% 288.96/181.48 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s4, s5)) | trans(s4, s5))),
% 288.96/181.48 inference(quant_inst,[status(thm)],[])).
% 288.96/181.48 tff(1027,plain,
% 288.96/181.48 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s4, s5)) | trans(s4, s5)),
% 288.96/181.48 inference(modus_ponens,[status(thm)],[1026, 1025])).
% 288.96/181.48 tff(1028,plain,
% 288.96/181.48 (trans(s4, s5)),
% 288.96/181.48 inference(unit_resolution,[status(thm)],[1027, 1024, 65])).
% 288.96/181.48 tff(1029,plain,
% 288.96/181.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | ((~trans(s4, s5)) | node7(c_e_h_3, c_u, s4, s5) | node8(c_e_h_3, c_u, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | (~trans(s4, s5)) | node7(c_e_h_3, c_u, s4, s5) | node8(c_e_h_3, c_u, s4, s5))),
% 288.96/181.48 inference(rewrite,[status(thm)],[])).
% 288.96/181.48 tff(1030,plain,
% 288.96/181.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | ((~trans(s4, s5)) | node7(c_e_h_3, c_u, s4, s5) | node8(c_e_h_3, c_u, s4, s5))),
% 288.96/181.48 inference(quant_inst,[status(thm)],[])).
% 288.96/181.48 tff(1031,plain,
% 288.96/181.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | (~trans(s4, s5)) | node7(c_e_h_3, c_u, s4, s5) | node8(c_e_h_3, c_u, s4, s5)),
% 288.96/181.48 inference(modus_ponens,[status(thm)],[1030, 1029])).
% 288.96/181.48 tff(1032,plain,
% 288.96/181.48 (node7(c_e_h_3, c_u, s4, s5) | node8(c_e_h_3, c_u, s4, s5)),
% 288.96/181.48 inference(unit_resolution,[status(thm)],[1031, 328, 1028])).
% 288.96/181.48 tff(1033,plain,
% 288.96/181.48 ($false),
% 288.96/181.48 inference(unit_resolution,[status(thm)],[1032, 1021, 1010])).
% 288.96/181.48 tff(1034,plain,(m_user_v_req(c_e_h_3, c_u, s5) | (~m_user_v_req(c_e_h_3, c_u, s4)) | m_user_v_ack(c_e_h_3, c_u, s4)), inference(lemma,lemma(discharge,[]))).
% 288.96/181.48 tff(1035,plain,
% 288.96/181.48 (m_user_v_req(c_e_h_3, c_u, s5) | (~m_user_v_req(c_e_h_3, c_u, s4))),
% 288.96/181.48 inference(unit_resolution,[status(thm)],[1034, 1001])).
% 288.96/181.48 tff(1036,plain,
% 288.96/181.48 (m_user_v_req(c_e_h_3, c_u, s5)),
% 288.96/181.48 inference(unit_resolution,[status(thm)],[1035, 733])).
% 288.96/181.48 tff(1037,assumption,(m_c_h_element_v_out(c_e_h_3, c_e, s4)), introduced(assumption)).
% 288.96/181.48 tff(1038,assumption,(m_and_h_gate_v_out(c_e_h_3, c_i, s3)), introduced(assumption)).
% 288.96/181.48 tff(1039,assumption,(node22(c_e_h_3, c_i, s2, s3)), introduced(assumption)).
% 288.96/181.48 tff(1040,plain,
% 288.96/181.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s3)) | (~node22(c_e_h_3, c_i, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_i, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s3)) | (~node22(c_e_h_3, c_i, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_i, s2))),
% 288.96/181.48 inference(rewrite,[status(thm)],[])).
% 288.96/181.48 tff(1041,plain,
% 288.96/181.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s3)) | (~node22(c_e_h_3, c_i, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_i, s2))),
% 288.96/181.48 inference(quant_inst,[status(thm)],[])).
% 288.96/181.48 tff(1042,plain,
% 288.96/181.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s3)) | (~node22(c_e_h_3, c_i, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_i, s2)),
% 288.96/181.48 inference(modus_ponens,[status(thm)],[1041, 1040])).
% 288.96/181.48 tff(1043,plain,
% 288.96/181.48 ($false),
% 288.96/181.48 inference(unit_resolution,[status(thm)],[1042, 108, 1038, 1039, 903])).
% 288.96/181.48 tff(1044,plain,((~node22(c_e_h_3, c_i, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s3))), inference(lemma,lemma(discharge,[]))).
% 288.96/181.48 tff(1045,plain,
% 288.96/181.48 (~node22(c_e_h_3, c_i, s2, s3)),
% 288.96/181.48 inference(unit_resolution,[status(thm)],[1044, 1038])).
% 288.96/181.48 tff(1046,assumption,(m_and_h_gate_v_out(c_e_h_2, c_q, s0)), introduced(assumption)).
% 288.96/181.48 tff(1047,plain,
% 288.96/181.48 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s0))),
% 288.96/181.48 inference(quant_inst,[status(thm)],[])).
% 288.96/181.48 tff(1048,plain,
% 288.96/181.48 ($false),
% 288.96/181.48 inference(unit_resolution,[status(thm)],[1047, 95, 1046])).
% 288.96/181.48 tff(1049,plain,(~m_and_h_gate_v_out(c_e_h_2, c_q, s0)), inference(lemma,lemma(discharge,[]))).
% 288.96/181.48 tff(1050,plain,
% 288.96/181.48 (^[I0: $i, X: $i, J0: $i] : refl(((~m_cell_v_left(I0, J0)) | node3(I0, J0, X)) <=> ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X)))),
% 288.96/181.48 inference(bind,[status(th)],[])).
% 288.96/181.48 tff(1051,plain,
% 288.96/181.48 (![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X)) <=> ![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))),
% 288.96/181.48 inference(quant_intro,[status(thm)],[1050])).
% 288.96/181.48 tff(1052,plain,
% 288.96/181.48 (![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X)) <=> ![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))),
% 288.96/181.48 inference(rewrite,[status(thm)],[])).
% 288.96/181.48 tff(1053,axiom,(![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_79')).
% 288.96/181.48 tff(1054,plain,
% 288.96/181.48 (![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))),
% 288.96/181.48 inference(modus_ponens,[status(thm)],[1053, 1052])).
% 288.96/181.48 tff(1055,plain,(
% 288.96/181.48 ![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))),
% 288.96/181.48 inference(skolemize,[status(sab)],[1054])).
% 288.96/181.48 tff(1056,plain,
% 288.96/181.48 (![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))),
% 288.96/181.48 inference(modus_ponens,[status(thm)],[1055, 1051])).
% 288.96/181.48 tff(1057,plain,
% 288.96/181.48 (m_cell_v_left(c_e_h_2, c_e_h_3) <=> m_cell_v_left(c_e_h_2, c_e_h_3)),
% 288.96/181.48 inference(rewrite,[status(thm)],[])).
% 288.96/181.48 tff(1058,axiom,(m_cell_v_left(c_e_h_2, c_e_h_3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_4')).
% 288.96/181.48 tff(1059,plain,
% 288.96/181.48 (m_cell_v_left(c_e_h_2, c_e_h_3)),
% 288.96/181.48 inference(modus_ponens,[status(thm)],[1058, 1057])).
% 288.96/181.48 tff(1060,plain,
% 288.96/181.48 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s0))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s0))),
% 288.96/181.48 inference(rewrite,[status(thm)],[])).
% 288.96/181.48 tff(1061,plain,
% 288.96/181.48 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s0))),
% 288.96/181.48 inference(quant_inst,[status(thm)],[])).
% 288.96/181.48 tff(1062,plain,
% 288.96/181.48 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s0)),
% 288.96/181.48 inference(modus_ponens,[status(thm)],[1061, 1060])).
% 288.96/181.48 tff(1063,plain,
% 288.96/181.48 (node3(c_e_h_2, c_e_h_3, s0)),
% 288.96/181.48 inference(unit_resolution,[status(thm)],[1062, 1059, 1056])).
% 288.96/181.48 tff(1064,plain,
% 288.96/181.48 (^[I0: $i, X: $i, J0: $i] : refl(((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X)) <=> ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X)))),
% 288.96/181.48 inference(bind,[status(th)],[])).
% 288.96/181.48 tff(1065,plain,
% 288.96/181.48 (![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X)) <=> ![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))),
% 288.96/181.48 inference(quant_intro,[status(thm)],[1064])).
% 288.96/181.48 tff(1066,plain,
% 288.96/181.48 (![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X)) <=> ![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))),
% 288.96/181.48 inference(rewrite,[status(thm)],[])).
% 288.96/181.48 tff(1067,plain,
% 288.96/181.48 (^[I0: $i, X: $i, J0: $i] : rewrite((((~m_cell_v_ack(J0, X)) | m_and_h_gate_v_out(I0, c_q, X)) | (~node3(I0, J0, X))) <=> ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X)))),
% 288.96/181.48 inference(bind,[status(th)],[])).
% 288.96/181.48 tff(1068,plain,
% 288.96/181.48 (![I0: $i, X: $i, J0: $i] : (((~m_cell_v_ack(J0, X)) | m_and_h_gate_v_out(I0, c_q, X)) | (~node3(I0, J0, X))) <=> ![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))),
% 288.96/181.48 inference(quant_intro,[status(thm)],[1067])).
% 288.96/181.48 tff(1069,axiom,(![I0: $i, X: $i, J0: $i] : (((~m_cell_v_ack(J0, X)) | m_and_h_gate_v_out(I0, c_q, X)) | (~node3(I0, J0, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_78')).
% 288.96/181.48 tff(1070,plain,
% 288.96/181.48 (![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))),
% 288.96/181.48 inference(modus_ponens,[status(thm)],[1069, 1068])).
% 288.96/181.48 tff(1071,plain,
% 288.96/181.48 (![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))),
% 288.96/181.48 inference(modus_ponens,[status(thm)],[1070, 1066])).
% 288.96/181.48 tff(1072,plain,(
% 288.96/181.48 ![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))),
% 288.96/181.48 inference(skolemize,[status(sab)],[1071])).
% 288.96/181.48 tff(1073,plain,
% 288.96/181.48 (![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))),
% 288.96/181.48 inference(modus_ponens,[status(thm)],[1072, 1065])).
% 288.96/181.48 tff(1074,plain,
% 288.96/181.48 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_3, s0)) | (~node3(c_e_h_2, c_e_h_3, s0)) | m_and_h_gate_v_out(c_e_h_2, c_q, s0))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_3, s0)) | (~node3(c_e_h_2, c_e_h_3, s0)) | m_and_h_gate_v_out(c_e_h_2, c_q, s0))),
% 288.96/181.48 inference(rewrite,[status(thm)],[])).
% 288.96/181.48 tff(1075,plain,
% 288.96/181.48 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_3, s0)) | (~node3(c_e_h_2, c_e_h_3, s0)) | m_and_h_gate_v_out(c_e_h_2, c_q, s0))),
% 288.96/181.48 inference(quant_inst,[status(thm)],[])).
% 288.96/181.48 tff(1076,plain,
% 288.96/181.48 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_3, s0)) | (~node3(c_e_h_2, c_e_h_3, s0)) | m_and_h_gate_v_out(c_e_h_2, c_q, s0)),
% 288.96/181.48 inference(modus_ponens,[status(thm)],[1075, 1074])).
% 288.96/181.48 tff(1077,plain,
% 288.96/181.48 ((~m_cell_v_ack(c_e_h_3, s0)) | m_and_h_gate_v_out(c_e_h_2, c_q, s0)),
% 288.96/181.48 inference(unit_resolution,[status(thm)],[1076, 1073, 1063])).
% 288.96/181.48 tff(1078,plain,
% 288.96/181.48 (~m_cell_v_ack(c_e_h_3, s0)),
% 288.96/181.48 inference(unit_resolution,[status(thm)],[1077, 1049])).
% 288.96/181.48 tff(1079,plain,
% 288.96/181.48 (^[I0: $i, X: $i] : refl(((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X)) <=> ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X)))),
% 288.96/181.48 inference(bind,[status(th)],[])).
% 288.96/181.48 tff(1080,plain,
% 288.96/181.48 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X)) <=> ![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))),
% 288.96/181.48 inference(quant_intro,[status(thm)],[1079])).
% 288.96/181.48 tff(1081,plain,
% 288.96/181.48 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X)) <=> ![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))),
% 288.96/181.48 inference(rewrite,[status(thm)],[])).
% 288.96/181.48 tff(1082,axiom,(![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_42')).
% 288.96/181.48 tff(1083,plain,
% 288.96/181.48 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))),
% 288.96/181.48 inference(modus_ponens,[status(thm)],[1082, 1081])).
% 288.96/181.48 tff(1084,plain,(
% 288.96/181.48 ![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))),
% 288.96/181.48 inference(skolemize,[status(sab)],[1083])).
% 288.96/181.48 tff(1085,plain,
% 288.96/181.48 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))),
% 288.96/181.48 inference(modus_ponens,[status(thm)],[1084, 1080])).
% 288.96/181.48 tff(1086,plain,
% 288.96/181.48 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_j, s0)) | m_cell_v_ack(c_e_h_3, s0))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_j, s0)) | m_cell_v_ack(c_e_h_3, s0))),
% 288.96/181.48 inference(rewrite,[status(thm)],[])).
% 288.96/181.48 tff(1087,plain,
% 288.96/181.48 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_j, s0)) | m_cell_v_ack(c_e_h_3, s0))),
% 288.96/181.48 inference(quant_inst,[status(thm)],[])).
% 288.96/181.48 tff(1088,plain,
% 288.96/181.48 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_j, s0)) | m_cell_v_ack(c_e_h_3, s0)),
% 288.96/181.48 inference(modus_ponens,[status(thm)],[1087, 1086])).
% 288.96/181.48 tff(1089,plain,
% 288.96/181.48 (~m_or_h_gate_v_in2(c_e_h_3, c_j, s0)),
% 288.96/181.49 inference(unit_resolution,[status(thm)],[1088, 1085, 1078])).
% 288.96/181.49 tff(1090,assumption,(m_and_h_gate_v_out(c_e_h_3, c_l, s0)), introduced(assumption)).
% 288.96/181.49 tff(1091,plain,
% 288.96/181.49 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s0))),
% 288.96/181.49 inference(quant_inst,[status(thm)],[])).
% 288.96/181.49 tff(1092,plain,
% 288.96/181.49 ($false),
% 288.96/181.49 inference(unit_resolution,[status(thm)],[1091, 95, 1090])).
% 288.96/181.49 tff(1093,plain,(~m_and_h_gate_v_out(c_e_h_3, c_l, s0)), inference(lemma,lemma(discharge,[]))).
% 288.96/181.49 tff(1094,plain,
% 288.96/181.49 (^[I0: $i, X: $i] : refl(((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X)) <=> ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X)))),
% 288.96/181.49 inference(bind,[status(th)],[])).
% 288.96/181.49 tff(1095,plain,
% 288.96/181.49 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X)) <=> ![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))),
% 288.96/181.49 inference(quant_intro,[status(thm)],[1094])).
% 288.96/181.49 tff(1096,plain,
% 288.96/181.49 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X)) <=> ![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))),
% 288.96/181.49 inference(rewrite,[status(thm)],[])).
% 288.96/181.49 tff(1097,axiom,(![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_40')).
% 288.96/181.49 tff(1098,plain,
% 288.96/181.49 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))),
% 288.96/181.49 inference(modus_ponens,[status(thm)],[1097, 1096])).
% 288.96/181.49 tff(1099,plain,(
% 288.96/181.49 ![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))),
% 288.96/181.49 inference(skolemize,[status(sab)],[1098])).
% 288.96/181.49 tff(1100,plain,
% 288.96/181.49 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))),
% 288.96/181.49 inference(modus_ponens,[status(thm)],[1099, 1095])).
% 288.96/181.49 tff(1101,plain,
% 288.96/181.49 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_j, s0)) | m_and_h_gate_v_out(c_e_h_3, c_l, s0))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s0)) | m_and_h_gate_v_out(c_e_h_3, c_l, s0))),
% 288.96/181.49 inference(rewrite,[status(thm)],[])).
% 288.96/181.49 tff(1102,plain,
% 288.96/181.49 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_j, s0)) | m_and_h_gate_v_out(c_e_h_3, c_l, s0))),
% 288.96/181.49 inference(quant_inst,[status(thm)],[])).
% 288.96/181.49 tff(1103,plain,
% 288.96/181.49 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s0)) | m_and_h_gate_v_out(c_e_h_3, c_l, s0)),
% 288.96/181.49 inference(modus_ponens,[status(thm)],[1102, 1101])).
% 288.96/181.49 tff(1104,plain,
% 288.96/181.49 (~m_or_h_gate_v_in1(c_e_h_3, c_j, s0)),
% 288.96/181.49 inference(unit_resolution,[status(thm)],[1103, 1100, 1093])).
% 288.96/181.49 tff(1105,assumption,(m_or_h_gate_v_out(c_e_h_3, c_j, s1)), introduced(assumption)).
% 288.96/181.49 tff(1106,assumption,(m_or_h_gate_v_out(c_e_h_3, c_j, s0)), introduced(assumption)).
% 288.96/181.49 tff(1107,plain,
% 288.96/181.49 ((~![I0: $i, I1: $i] : (~m_or_h_gate_v_out(I0, I1, s0))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s0))),
% 288.96/181.49 inference(quant_inst,[status(thm)],[])).
% 288.96/181.49 tff(1108,plain,
% 288.96/181.49 ($false),
% 288.96/181.49 inference(unit_resolution,[status(thm)],[1107, 801, 1106])).
% 288.96/181.49 tff(1109,plain,(~m_or_h_gate_v_out(c_e_h_3, c_j, s0)), inference(lemma,lemma(discharge,[]))).
% 288.96/181.49 tff(1110,assumption,(node6(c_e_h_3, c_j, s0, s1)), introduced(assumption)).
% 288.96/181.49 tff(1111,assumption,(~m_or_h_gate_v_out(c_e_h_3, c_j, s0)), introduced(assumption)).
% 288.96/181.49 tff(1112,plain,
% 288.96/181.49 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl(((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X)) <=> ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X)))),
% 288.96/181.49 inference(bind,[status(th)],[])).
% 288.96/181.49 tff(1113,plain,
% 288.96/181.49 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))),
% 288.96/181.49 inference(quant_intro,[status(thm)],[1112])).
% 288.96/181.49 tff(1114,plain,
% 288.96/181.49 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))),
% 288.96/181.49 inference(rewrite,[status(thm)],[])).
% 288.96/181.49 tff(1115,plain,
% 288.96/181.49 (^[Y: $i, I0: $i, X: $i, I1: $i] : rewrite((((~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X)) | (~node6(I0, I1, X, Y))) <=> ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X)))),
% 288.96/181.49 inference(bind,[status(th)],[])).
% 288.96/181.49 tff(1116,plain,
% 288.96/181.49 (![Y: $i, I0: $i, X: $i, I1: $i] : (((~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X)) | (~node6(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))),
% 288.96/181.49 inference(quant_intro,[status(thm)],[1115])).
% 288.96/181.49 tff(1117,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : (((~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X)) | (~node6(I0, I1, X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_or_h_gate_7')).
% 288.96/181.49 tff(1118,plain,
% 288.96/181.49 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))),
% 288.96/181.49 inference(modus_ponens,[status(thm)],[1117, 1116])).
% 288.96/181.49 tff(1119,plain,
% 288.96/181.49 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))),
% 288.96/181.49 inference(modus_ponens,[status(thm)],[1118, 1114])).
% 288.96/181.49 tff(1120,plain,(
% 288.96/181.49 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))),
% 288.96/181.49 inference(skolemize,[status(sab)],[1119])).
% 288.96/181.49 tff(1121,plain,
% 288.96/181.49 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))),
% 288.96/181.49 inference(modus_ponens,[status(thm)],[1120, 1113])).
% 288.96/181.49 tff(1122,plain,
% 288.96/181.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_3, c_j, s0) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s1)) | (~node6(c_e_h_3, c_j, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_j, s0) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s1)) | (~node6(c_e_h_3, c_j, s0, s1)))),
% 288.96/181.49 inference(rewrite,[status(thm)],[])).
% 288.96/181.49 tff(1123,plain,
% 288.96/181.49 (((~node6(c_e_h_3, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s1)) | m_or_h_gate_v_out(c_e_h_3, c_j, s0)) <=> (m_or_h_gate_v_out(c_e_h_3, c_j, s0) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s1)) | (~node6(c_e_h_3, c_j, s0, s1)))),
% 288.96/181.49 inference(rewrite,[status(thm)],[])).
% 288.96/181.49 tff(1124,plain,
% 288.96/181.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s1)) | m_or_h_gate_v_out(c_e_h_3, c_j, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_3, c_j, s0) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s1)) | (~node6(c_e_h_3, c_j, s0, s1))))),
% 288.96/181.49 inference(monotonicity,[status(thm)],[1123])).
% 288.96/181.49 tff(1125,plain,
% 288.96/181.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s1)) | m_or_h_gate_v_out(c_e_h_3, c_j, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_j, s0) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s1)) | (~node6(c_e_h_3, c_j, s0, s1)))),
% 288.96/181.49 inference(transitivity,[status(thm)],[1124, 1122])).
% 288.96/181.49 tff(1126,plain,
% 288.96/181.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s1)) | m_or_h_gate_v_out(c_e_h_3, c_j, s0))),
% 288.96/181.49 inference(quant_inst,[status(thm)],[])).
% 288.96/181.49 tff(1127,plain,
% 288.96/181.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_j, s0) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s1)) | (~node6(c_e_h_3, c_j, s0, s1))),
% 288.96/181.49 inference(modus_ponens,[status(thm)],[1126, 1125])).
% 288.96/181.49 tff(1128,plain,
% 288.96/181.49 ($false),
% 288.96/181.49 inference(unit_resolution,[status(thm)],[1127, 1121, 1105, 1111, 1110])).
% 288.96/181.49 tff(1129,plain,((~node6(c_e_h_3, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s1)) | m_or_h_gate_v_out(c_e_h_3, c_j, s0)), inference(lemma,lemma(discharge,[]))).
% 288.96/181.49 tff(1130,plain,
% 288.96/181.49 ((~node6(c_e_h_3, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s1))),
% 288.96/181.49 inference(unit_resolution,[status(thm)],[1129, 1109])).
% 288.96/181.49 tff(1131,plain,
% 288.96/181.49 (~node6(c_e_h_3, c_j, s0, s1)),
% 288.96/181.49 inference(unit_resolution,[status(thm)],[1130, 1105])).
% 288.96/181.49 tff(1132,plain,
% 288.96/181.49 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl((node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y))) <=> (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y))))),
% 288.96/181.49 inference(bind,[status(th)],[])).
% 288.96/181.49 tff(1133,plain,
% 288.96/181.49 (![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))),
% 288.96/181.49 inference(quant_intro,[status(thm)],[1132])).
% 288.96/181.49 tff(1134,plain,
% 288.96/181.49 (![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))),
% 288.96/181.49 inference(rewrite,[status(thm)],[])).
% 288.96/181.49 tff(1135,plain,
% 288.96/181.49 (^[Y: $i, I0: $i, X: $i, I1: $i] : rewrite(((node5(I0, I1, X, Y) | node6(I0, I1, X, Y)) | (~trans(X, Y))) <=> (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y))))),
% 288.96/181.49 inference(bind,[status(th)],[])).
% 288.96/181.49 tff(1136,plain,
% 288.96/181.49 (![Y: $i, I0: $i, X: $i, I1: $i] : ((node5(I0, I1, X, Y) | node6(I0, I1, X, Y)) | (~trans(X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))),
% 288.96/181.49 inference(quant_intro,[status(thm)],[1135])).
% 288.96/181.49 tff(1137,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : ((node5(I0, I1, X, Y) | node6(I0, I1, X, Y)) | (~trans(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_or_h_gate_8')).
% 288.96/181.49 tff(1138,plain,
% 288.96/181.49 (![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))),
% 288.96/181.49 inference(modus_ponens,[status(thm)],[1137, 1136])).
% 288.96/181.49 tff(1139,plain,
% 288.96/181.49 (![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))),
% 288.96/181.49 inference(modus_ponens,[status(thm)],[1138, 1134])).
% 288.96/181.49 tff(1140,plain,(
% 288.96/181.49 ![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))),
% 288.96/181.49 inference(skolemize,[status(sab)],[1139])).
% 288.96/181.49 tff(1141,plain,
% 288.96/181.49 (![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))),
% 288.96/181.49 inference(modus_ponens,[status(thm)],[1140, 1133])).
% 288.96/181.49 tff(1142,plain,
% 288.96/181.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s0, s1)) | node6(c_e_h_3, c_j, s0, s1) | node5(c_e_h_3, c_j, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s0, s1)) | node6(c_e_h_3, c_j, s0, s1) | node5(c_e_h_3, c_j, s0, s1))),
% 288.96/181.49 inference(rewrite,[status(thm)],[])).
% 288.96/181.49 tff(1143,plain,
% 288.96/181.49 ((node6(c_e_h_3, c_j, s0, s1) | node5(c_e_h_3, c_j, s0, s1) | (~trans(s0, s1))) <=> ((~trans(s0, s1)) | node6(c_e_h_3, c_j, s0, s1) | node5(c_e_h_3, c_j, s0, s1))),
% 288.96/181.49 inference(rewrite,[status(thm)],[])).
% 288.96/181.49 tff(1144,plain,
% 288.96/181.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s0, s1) | node5(c_e_h_3, c_j, s0, s1) | (~trans(s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s0, s1)) | node6(c_e_h_3, c_j, s0, s1) | node5(c_e_h_3, c_j, s0, s1)))),
% 288.96/181.50 inference(monotonicity,[status(thm)],[1143])).
% 288.96/181.50 tff(1145,plain,
% 288.96/181.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s0, s1) | node5(c_e_h_3, c_j, s0, s1) | (~trans(s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s0, s1)) | node6(c_e_h_3, c_j, s0, s1) | node5(c_e_h_3, c_j, s0, s1))),
% 288.96/181.50 inference(transitivity,[status(thm)],[1144, 1142])).
% 288.96/181.50 tff(1146,plain,
% 288.96/181.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s0, s1) | node5(c_e_h_3, c_j, s0, s1) | (~trans(s0, s1)))),
% 288.96/181.50 inference(quant_inst,[status(thm)],[])).
% 288.96/181.50 tff(1147,plain,
% 288.96/181.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s0, s1)) | node6(c_e_h_3, c_j, s0, s1) | node5(c_e_h_3, c_j, s0, s1)),
% 288.96/181.50 inference(modus_ponens,[status(thm)],[1146, 1145])).
% 288.96/181.50 tff(1148,plain,
% 288.96/181.50 (node6(c_e_h_3, c_j, s0, s1) | node5(c_e_h_3, c_j, s0, s1)),
% 288.96/181.50 inference(unit_resolution,[status(thm)],[1147, 1141, 72])).
% 288.96/181.50 tff(1149,plain,
% 288.96/181.50 (node5(c_e_h_3, c_j, s0, s1)),
% 288.96/181.50 inference(unit_resolution,[status(thm)],[1148, 1131])).
% 288.96/181.50 tff(1150,plain,
% 288.96/181.50 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl((m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y))) <=> (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y))))),
% 288.96/181.50 inference(bind,[status(th)],[])).
% 288.96/181.50 tff(1151,plain,
% 288.96/181.50 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))),
% 288.96/181.50 inference(quant_intro,[status(thm)],[1150])).
% 288.96/181.50 tff(1152,plain,
% 288.96/181.50 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))),
% 288.96/181.50 inference(rewrite,[status(thm)],[])).
% 288.96/181.50 tff(1153,plain,
% 288.96/181.50 (^[Y: $i, I0: $i, X: $i, I1: $i] : trans(monotonicity(rewrite((((~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_in1(I0, I1, X)) | m_or_h_gate_v_in2(I0, I1, X)) <=> (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~m_or_h_gate_v_out(I0, I1, Y)))), (((((~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_in1(I0, I1, X)) | m_or_h_gate_v_in2(I0, I1, X)) | (~node5(I0, I1, X, Y))) <=> ((m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~m_or_h_gate_v_out(I0, I1, Y))) | (~node5(I0, I1, X, Y))))), rewrite(((m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~m_or_h_gate_v_out(I0, I1, Y))) | (~node5(I0, I1, X, Y))) <=> (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))), (((((~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_in1(I0, I1, X)) | m_or_h_gate_v_in2(I0, I1, X)) | (~node5(I0, I1, X, Y))) <=> (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))))),
% 288.96/181.50 inference(bind,[status(th)],[])).
% 288.96/181.50 tff(1154,plain,
% 288.96/181.50 (![Y: $i, I0: $i, X: $i, I1: $i] : ((((~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_in1(I0, I1, X)) | m_or_h_gate_v_in2(I0, I1, X)) | (~node5(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))),
% 288.96/181.50 inference(quant_intro,[status(thm)],[1153])).
% 288.96/181.50 tff(1155,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : ((((~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_in1(I0, I1, X)) | m_or_h_gate_v_in2(I0, I1, X)) | (~node5(I0, I1, X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_or_h_gate_5')).
% 288.96/181.50 tff(1156,plain,
% 288.96/181.50 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))),
% 288.96/181.50 inference(modus_ponens,[status(thm)],[1155, 1154])).
% 288.96/181.50 tff(1157,plain,
% 288.96/181.50 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))),
% 288.96/181.50 inference(modus_ponens,[status(thm)],[1156, 1152])).
% 288.96/181.50 tff(1158,plain,(
% 288.96/181.50 ![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))),
% 288.96/181.50 inference(skolemize,[status(sab)],[1157])).
% 288.96/181.50 tff(1159,plain,
% 288.96/181.50 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))),
% 288.96/181.50 inference(modus_ponens,[status(thm)],[1158, 1151])).
% 288.96/181.50 tff(1160,plain,
% 288.96/181.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_3, c_j, s0) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s1)) | (~node5(c_e_h_3, c_j, s0, s1)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_3, c_j, s0) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s1)) | (~node5(c_e_h_3, c_j, s0, s1)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s0))),
% 288.96/181.50 inference(rewrite,[status(thm)],[])).
% 288.96/181.50 tff(1161,plain,
% 288.96/181.50 ((m_or_h_gate_v_in1(c_e_h_3, c_j, s0) | m_or_h_gate_v_in2(c_e_h_3, c_j, s0) | (~node5(c_e_h_3, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s1))) <=> (m_or_h_gate_v_in2(c_e_h_3, c_j, s0) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s1)) | (~node5(c_e_h_3, c_j, s0, s1)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s0))),
% 288.96/181.50 inference(rewrite,[status(thm)],[])).
% 288.96/181.50 tff(1162,plain,
% 288.96/181.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s0) | m_or_h_gate_v_in2(c_e_h_3, c_j, s0) | (~node5(c_e_h_3, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_3, c_j, s0) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s1)) | (~node5(c_e_h_3, c_j, s0, s1)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s0)))),
% 288.96/181.50 inference(monotonicity,[status(thm)],[1161])).
% 288.96/181.50 tff(1163,plain,
% 288.96/181.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s0) | m_or_h_gate_v_in2(c_e_h_3, c_j, s0) | (~node5(c_e_h_3, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_3, c_j, s0) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s1)) | (~node5(c_e_h_3, c_j, s0, s1)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s0))),
% 288.96/181.50 inference(transitivity,[status(thm)],[1162, 1160])).
% 288.96/181.50 tff(1164,plain,
% 288.96/181.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s0) | m_or_h_gate_v_in2(c_e_h_3, c_j, s0) | (~node5(c_e_h_3, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s1)))),
% 288.96/181.50 inference(quant_inst,[status(thm)],[])).
% 288.96/181.50 tff(1165,plain,
% 288.96/181.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_3, c_j, s0) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s1)) | (~node5(c_e_h_3, c_j, s0, s1)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s0)),
% 288.96/181.50 inference(modus_ponens,[status(thm)],[1164, 1163])).
% 288.96/181.50 tff(1166,plain,
% 288.96/181.50 ($false),
% 288.96/181.50 inference(unit_resolution,[status(thm)],[1165, 1159, 1105, 1149, 1104, 1089])).
% 288.96/181.50 tff(1167,plain,(~m_or_h_gate_v_out(c_e_h_3, c_j, s1)), inference(lemma,lemma(discharge,[]))).
% 288.96/181.50 tff(1168,plain,
% 288.96/181.50 (^[I0: $i, X: $i] : refl(((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X)) <=> ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X)))),
% 288.96/181.50 inference(bind,[status(th)],[])).
% 288.96/181.50 tff(1169,plain,
% 288.96/181.50 (![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X)) <=> ![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))),
% 288.96/181.50 inference(quant_intro,[status(thm)],[1168])).
% 288.96/181.50 tff(1170,plain,
% 288.96/181.50 (![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X)) <=> ![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))),
% 288.96/181.50 inference(rewrite,[status(thm)],[])).
% 288.96/181.50 tff(1171,axiom,(![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_34')).
% 288.96/181.50 tff(1172,plain,
% 288.96/181.50 (![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))),
% 288.96/181.50 inference(modus_ponens,[status(thm)],[1171, 1170])).
% 288.96/181.50 tff(1173,plain,(
% 288.96/181.50 ![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))),
% 288.96/181.50 inference(skolemize,[status(sab)],[1172])).
% 288.96/181.50 tff(1174,plain,
% 288.96/181.50 (![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))),
% 288.96/181.50 inference(modus_ponens,[status(thm)],[1173, 1169])).
% 288.96/181.50 tff(1175,plain,
% 288.96/181.50 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s1)) | m_or_h_gate_v_out(c_e_h_3, c_j, s1))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s1)) | m_or_h_gate_v_out(c_e_h_3, c_j, s1))),
% 288.96/181.50 inference(rewrite,[status(thm)],[])).
% 288.96/181.50 tff(1176,plain,
% 288.96/181.50 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s1)) | m_or_h_gate_v_out(c_e_h_3, c_j, s1))),
% 288.96/181.50 inference(quant_inst,[status(thm)],[])).
% 288.96/181.50 tff(1177,plain,
% 288.96/181.50 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s1)) | m_or_h_gate_v_out(c_e_h_3, c_j, s1)),
% 288.96/181.50 inference(modus_ponens,[status(thm)],[1176, 1175])).
% 288.96/181.50 tff(1178,plain,
% 288.96/181.50 (~m_c_h_element_v_in2(c_e_h_3, c_h, s1)),
% 288.96/181.50 inference(unit_resolution,[status(thm)],[1177, 1174, 1167])).
% 288.96/181.50 tff(1179,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_h, s1)), introduced(assumption)).
% 288.96/181.50 tff(1180,assumption,(m_c_h_element_v_out(c_e_h_3, c_h, s2)), introduced(assumption)).
% 288.96/181.50 tff(1181,assumption,(node15(c_e_h_3, c_h, s1, s2)), introduced(assumption)).
% 288.96/181.50 tff(1182,plain,
% 288.96/181.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s2)) | (~node15(c_e_h_3, c_h, s1, s2)) | m_c_h_element_v_out(c_e_h_3, c_h, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s2)) | (~node15(c_e_h_3, c_h, s1, s2)) | m_c_h_element_v_out(c_e_h_3, c_h, s1))),
% 288.96/181.50 inference(rewrite,[status(thm)],[])).
% 288.96/181.50 tff(1183,plain,
% 288.96/181.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s2)) | (~node15(c_e_h_3, c_h, s1, s2)) | m_c_h_element_v_out(c_e_h_3, c_h, s1))),
% 288.96/181.50 inference(quant_inst,[status(thm)],[])).
% 289.06/181.51 tff(1184,plain,
% 289.06/181.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s2)) | (~node15(c_e_h_3, c_h, s1, s2)) | m_c_h_element_v_out(c_e_h_3, c_h, s1)),
% 289.06/181.51 inference(modus_ponens,[status(thm)],[1183, 1182])).
% 289.06/181.51 tff(1185,plain,
% 289.06/181.51 ($false),
% 289.06/181.51 inference(unit_resolution,[status(thm)],[1184, 147, 880, 1180, 1181])).
% 289.06/181.51 tff(1186,plain,((~node15(c_e_h_3, c_h, s1, s2)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s2))), inference(lemma,lemma(discharge,[]))).
% 289.06/181.51 tff(1187,plain,
% 289.06/181.51 (~node15(c_e_h_3, c_h, s1, s2)),
% 289.06/181.51 inference(unit_resolution,[status(thm)],[1186, 1180])).
% 289.06/181.51 tff(1188,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_h, s1)), introduced(assumption)).
% 289.06/181.51 tff(1189,assumption,(~node15(c_e_h_3, c_h, s1, s2)), introduced(assumption)).
% 289.06/181.51 tff(1190,plain,
% 289.06/181.51 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_h, s1)) | m_c_h_element_v_in1(c_e_h_3, c_h, s1) | m_c_h_element_v_in2(c_e_h_3, c_h, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_h, s1)) | m_c_h_element_v_in1(c_e_h_3, c_h, s1) | m_c_h_element_v_in2(c_e_h_3, c_h, s1))),
% 289.06/181.51 inference(rewrite,[status(thm)],[])).
% 289.06/181.51 tff(1191,plain,
% 289.06/181.51 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_h, s1)) | m_c_h_element_v_in1(c_e_h_3, c_h, s1) | m_c_h_element_v_in2(c_e_h_3, c_h, s1))),
% 289.06/181.51 inference(quant_inst,[status(thm)],[])).
% 289.06/181.51 tff(1192,plain,
% 289.06/181.51 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_h, s1)) | m_c_h_element_v_in1(c_e_h_3, c_h, s1) | m_c_h_element_v_in2(c_e_h_3, c_h, s1)),
% 289.06/181.51 inference(modus_ponens,[status(thm)],[1191, 1190])).
% 289.06/181.51 tff(1193,plain,
% 289.06/181.51 ((~node16(c_e_h_3, c_h, s1)) | m_c_h_element_v_in1(c_e_h_3, c_h, s1)),
% 289.06/181.51 inference(unit_resolution,[status(thm)],[1192, 178, 1179])).
% 289.06/181.51 tff(1194,plain,
% 289.06/181.51 (~node16(c_e_h_3, c_h, s1)),
% 289.06/181.51 inference(unit_resolution,[status(thm)],[1193, 1188])).
% 289.06/181.51 tff(1195,plain,
% 289.06/181.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s1, s2)) | node19(c_e_h_3, c_h, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s1, s2)) | node19(c_e_h_3, c_h, s1, s2))),
% 289.06/181.51 inference(rewrite,[status(thm)],[])).
% 289.06/181.51 tff(1196,plain,
% 289.06/181.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s1, s2)) | node19(c_e_h_3, c_h, s1, s2))),
% 289.06/181.51 inference(quant_inst,[status(thm)],[])).
% 289.06/181.51 tff(1197,plain,
% 289.06/181.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s1, s2)) | node19(c_e_h_3, c_h, s1, s2)),
% 289.06/181.51 inference(modus_ponens,[status(thm)],[1196, 1195])).
% 289.06/181.51 tff(1198,plain,
% 289.06/181.51 (node19(c_e_h_3, c_h, s1, s2)),
% 289.06/181.51 inference(unit_resolution,[status(thm)],[1197, 190, 255])).
% 289.06/181.51 tff(1199,plain,
% 289.06/181.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s1) | (~node19(c_e_h_3, c_h, s1, s2)) | node14(c_e_h_3, c_h, s1, s2) | node15(c_e_h_3, c_h, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_h, s1) | (~node19(c_e_h_3, c_h, s1, s2)) | node14(c_e_h_3, c_h, s1, s2) | node15(c_e_h_3, c_h, s1, s2))),
% 289.06/181.51 inference(rewrite,[status(thm)],[])).
% 289.06/181.51 tff(1200,plain,
% 289.06/181.51 ((node16(c_e_h_3, c_h, s1) | node14(c_e_h_3, c_h, s1, s2) | node15(c_e_h_3, c_h, s1, s2) | (~node19(c_e_h_3, c_h, s1, s2))) <=> (node16(c_e_h_3, c_h, s1) | (~node19(c_e_h_3, c_h, s1, s2)) | node14(c_e_h_3, c_h, s1, s2) | node15(c_e_h_3, c_h, s1, s2))),
% 289.06/181.51 inference(rewrite,[status(thm)],[])).
% 289.06/181.51 tff(1201,plain,
% 289.06/181.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s1) | node14(c_e_h_3, c_h, s1, s2) | node15(c_e_h_3, c_h, s1, s2) | (~node19(c_e_h_3, c_h, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s1) | (~node19(c_e_h_3, c_h, s1, s2)) | node14(c_e_h_3, c_h, s1, s2) | node15(c_e_h_3, c_h, s1, s2)))),
% 289.06/181.51 inference(monotonicity,[status(thm)],[1200])).
% 289.06/181.51 tff(1202,plain,
% 289.06/181.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s1) | node14(c_e_h_3, c_h, s1, s2) | node15(c_e_h_3, c_h, s1, s2) | (~node19(c_e_h_3, c_h, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_h, s1) | (~node19(c_e_h_3, c_h, s1, s2)) | node14(c_e_h_3, c_h, s1, s2) | node15(c_e_h_3, c_h, s1, s2))),
% 289.06/181.51 inference(transitivity,[status(thm)],[1201, 1199])).
% 289.06/181.51 tff(1203,plain,
% 289.06/181.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s1) | node14(c_e_h_3, c_h, s1, s2) | node15(c_e_h_3, c_h, s1, s2) | (~node19(c_e_h_3, c_h, s1, s2)))),
% 289.06/181.51 inference(quant_inst,[status(thm)],[])).
% 289.06/181.51 tff(1204,plain,
% 289.06/181.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_h, s1) | (~node19(c_e_h_3, c_h, s1, s2)) | node14(c_e_h_3, c_h, s1, s2) | node15(c_e_h_3, c_h, s1, s2)),
% 289.06/181.51 inference(modus_ponens,[status(thm)],[1203, 1202])).
% 289.06/181.51 tff(1205,plain,
% 289.06/181.51 (node16(c_e_h_3, c_h, s1) | node14(c_e_h_3, c_h, s1, s2) | node15(c_e_h_3, c_h, s1, s2)),
% 289.06/181.51 inference(unit_resolution,[status(thm)],[1204, 204, 1198])).
% 289.06/181.51 tff(1206,plain,
% 289.06/181.51 (node14(c_e_h_3, c_h, s1, s2)),
% 289.06/181.51 inference(unit_resolution,[status(thm)],[1205, 1194, 1189])).
% 289.06/181.51 tff(1207,plain,
% 289.06/181.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s2)) | m_c_h_element_v_in1(c_e_h_3, c_h, s1) | (~node14(c_e_h_3, c_h, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s2)) | m_c_h_element_v_in1(c_e_h_3, c_h, s1) | (~node14(c_e_h_3, c_h, s1, s2)))),
% 289.06/181.51 inference(rewrite,[status(thm)],[])).
% 289.06/181.51 tff(1208,plain,
% 289.06/181.51 (((~node14(c_e_h_3, c_h, s1, s2)) | m_c_h_element_v_in1(c_e_h_3, c_h, s1) | (~m_c_h_element_v_out(c_e_h_3, c_h, s2))) <=> ((~m_c_h_element_v_out(c_e_h_3, c_h, s2)) | m_c_h_element_v_in1(c_e_h_3, c_h, s1) | (~node14(c_e_h_3, c_h, s1, s2)))),
% 289.06/181.51 inference(rewrite,[status(thm)],[])).
% 289.06/181.51 tff(1209,plain,
% 289.06/181.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s1, s2)) | m_c_h_element_v_in1(c_e_h_3, c_h, s1) | (~m_c_h_element_v_out(c_e_h_3, c_h, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s2)) | m_c_h_element_v_in1(c_e_h_3, c_h, s1) | (~node14(c_e_h_3, c_h, s1, s2))))),
% 289.06/181.51 inference(monotonicity,[status(thm)],[1208])).
% 289.06/181.51 tff(1210,plain,
% 289.06/181.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s1, s2)) | m_c_h_element_v_in1(c_e_h_3, c_h, s1) | (~m_c_h_element_v_out(c_e_h_3, c_h, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s2)) | m_c_h_element_v_in1(c_e_h_3, c_h, s1) | (~node14(c_e_h_3, c_h, s1, s2)))),
% 289.06/181.51 inference(transitivity,[status(thm)],[1209, 1207])).
% 289.06/181.51 tff(1211,plain,
% 289.07/181.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s1, s2)) | m_c_h_element_v_in1(c_e_h_3, c_h, s1) | (~m_c_h_element_v_out(c_e_h_3, c_h, s2)))),
% 289.07/181.52 inference(quant_inst,[status(thm)],[])).
% 289.07/181.52 tff(1212,plain,
% 289.07/181.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s2)) | m_c_h_element_v_in1(c_e_h_3, c_h, s1) | (~node14(c_e_h_3, c_h, s1, s2))),
% 289.07/181.52 inference(modus_ponens,[status(thm)],[1211, 1210])).
% 289.07/181.52 tff(1213,plain,
% 289.07/181.52 ($false),
% 289.07/181.52 inference(unit_resolution,[status(thm)],[1212, 223, 1180, 1206, 1188])).
% 289.07/181.52 tff(1214,plain,(m_c_h_element_v_in1(c_e_h_3, c_h, s1) | (~m_c_h_element_v_out(c_e_h_3, c_h, s2)) | node15(c_e_h_3, c_h, s1, s2) | m_c_h_element_v_in2(c_e_h_3, c_h, s1)), inference(lemma,lemma(discharge,[]))).
% 289.07/181.52 tff(1215,plain,
% 289.07/181.52 (m_c_h_element_v_in1(c_e_h_3, c_h, s1)),
% 289.07/181.52 inference(unit_resolution,[status(thm)],[1214, 1179, 1187, 1180])).
% 289.07/181.52 tff(1216,assumption,(node18(c_e_h_3, c_h, s1, s2)), introduced(assumption)).
% 289.07/181.52 tff(1217,plain,
% 289.07/181.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_h, s1) | (~m_c_h_element_v_out(c_e_h_3, c_h, s2)) | (~node18(c_e_h_3, c_h, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s1) | (~m_c_h_element_v_out(c_e_h_3, c_h, s2)) | (~node18(c_e_h_3, c_h, s1, s2)))),
% 289.07/181.52 inference(rewrite,[status(thm)],[])).
% 289.07/181.52 tff(1218,plain,
% 289.07/181.52 (((~m_c_h_element_v_out(c_e_h_3, c_h, s2)) | m_c_h_element_v_out(c_e_h_3, c_h, s1) | (~node18(c_e_h_3, c_h, s1, s2))) <=> (m_c_h_element_v_out(c_e_h_3, c_h, s1) | (~m_c_h_element_v_out(c_e_h_3, c_h, s2)) | (~node18(c_e_h_3, c_h, s1, s2)))),
% 289.07/181.52 inference(rewrite,[status(thm)],[])).
% 289.07/181.52 tff(1219,plain,
% 289.07/181.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s2)) | m_c_h_element_v_out(c_e_h_3, c_h, s1) | (~node18(c_e_h_3, c_h, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_h, s1) | (~m_c_h_element_v_out(c_e_h_3, c_h, s2)) | (~node18(c_e_h_3, c_h, s1, s2))))),
% 289.07/181.52 inference(monotonicity,[status(thm)],[1218])).
% 289.07/181.52 tff(1220,plain,
% 289.07/181.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s2)) | m_c_h_element_v_out(c_e_h_3, c_h, s1) | (~node18(c_e_h_3, c_h, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s1) | (~m_c_h_element_v_out(c_e_h_3, c_h, s2)) | (~node18(c_e_h_3, c_h, s1, s2)))),
% 289.07/181.52 inference(transitivity,[status(thm)],[1219, 1217])).
% 289.07/181.52 tff(1221,plain,
% 289.07/181.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s2)) | m_c_h_element_v_out(c_e_h_3, c_h, s1) | (~node18(c_e_h_3, c_h, s1, s2)))),
% 289.07/181.52 inference(quant_inst,[status(thm)],[])).
% 289.07/181.52 tff(1222,plain,
% 289.07/181.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s1) | (~m_c_h_element_v_out(c_e_h_3, c_h, s2)) | (~node18(c_e_h_3, c_h, s1, s2))),
% 289.07/181.52 inference(modus_ponens,[status(thm)],[1221, 1220])).
% 289.07/181.52 tff(1223,plain,
% 289.07/181.52 ($false),
% 289.07/181.52 inference(unit_resolution,[status(thm)],[1222, 753, 880, 1180, 1216])).
% 289.07/181.52 tff(1224,plain,((~node18(c_e_h_3, c_h, s1, s2)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s2))), inference(lemma,lemma(discharge,[]))).
% 289.07/181.52 tff(1225,plain,
% 289.07/181.52 (~node18(c_e_h_3, c_h, s1, s2)),
% 289.07/181.52 inference(unit_resolution,[status(thm)],[1224, 1180])).
% 289.07/181.52 tff(1226,plain,
% 289.07/181.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_3, c_h, s1, s2) | (~node19(c_e_h_3, c_h, s1, s2)) | node17(c_e_h_3, c_h, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_3, c_h, s1, s2) | (~node19(c_e_h_3, c_h, s1, s2)) | node17(c_e_h_3, c_h, s1))),
% 289.07/181.52 inference(rewrite,[status(thm)],[])).
% 289.07/181.52 tff(1227,plain,
% 289.07/181.52 ((node17(c_e_h_3, c_h, s1) | node18(c_e_h_3, c_h, s1, s2) | (~node19(c_e_h_3, c_h, s1, s2))) <=> (node18(c_e_h_3, c_h, s1, s2) | (~node19(c_e_h_3, c_h, s1, s2)) | node17(c_e_h_3, c_h, s1))),
% 289.07/181.52 inference(rewrite,[status(thm)],[])).
% 289.07/181.52 tff(1228,plain,
% 289.07/181.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s1) | node18(c_e_h_3, c_h, s1, s2) | (~node19(c_e_h_3, c_h, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_3, c_h, s1, s2) | (~node19(c_e_h_3, c_h, s1, s2)) | node17(c_e_h_3, c_h, s1)))),
% 289.07/181.52 inference(monotonicity,[status(thm)],[1227])).
% 289.07/181.52 tff(1229,plain,
% 289.07/181.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s1) | node18(c_e_h_3, c_h, s1, s2) | (~node19(c_e_h_3, c_h, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_3, c_h, s1, s2) | (~node19(c_e_h_3, c_h, s1, s2)) | node17(c_e_h_3, c_h, s1))),
% 289.07/181.52 inference(transitivity,[status(thm)],[1228, 1226])).
% 289.07/181.52 tff(1230,plain,
% 289.07/181.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s1) | node18(c_e_h_3, c_h, s1, s2) | (~node19(c_e_h_3, c_h, s1, s2)))),
% 289.07/181.52 inference(quant_inst,[status(thm)],[])).
% 289.07/181.52 tff(1231,plain,
% 289.07/181.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_3, c_h, s1, s2) | (~node19(c_e_h_3, c_h, s1, s2)) | node17(c_e_h_3, c_h, s1)),
% 289.07/181.52 inference(modus_ponens,[status(thm)],[1230, 1229])).
% 289.07/181.52 tff(1232,plain,
% 289.07/181.52 (node18(c_e_h_3, c_h, s1, s2) | node17(c_e_h_3, c_h, s1)),
% 289.07/181.52 inference(unit_resolution,[status(thm)],[1231, 776, 1198])).
% 289.07/181.52 tff(1233,plain,
% 289.07/181.52 (node17(c_e_h_3, c_h, s1)),
% 289.07/181.52 inference(unit_resolution,[status(thm)],[1232, 1225])).
% 289.07/181.52 tff(1234,plain,
% 289.07/181.52 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_h, s1)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s1)) | m_c_h_element_v_in2(c_e_h_3, c_h, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_h, s1)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s1)) | m_c_h_element_v_in2(c_e_h_3, c_h, s1))),
% 289.07/181.52 inference(rewrite,[status(thm)],[])).
% 289.07/181.52 tff(1235,plain,
% 289.07/181.52 (((~m_c_h_element_v_in1(c_e_h_3, c_h, s1)) | m_c_h_element_v_in2(c_e_h_3, c_h, s1) | (~node17(c_e_h_3, c_h, s1))) <=> ((~node17(c_e_h_3, c_h, s1)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s1)) | m_c_h_element_v_in2(c_e_h_3, c_h, s1))),
% 289.07/181.52 inference(rewrite,[status(thm)],[])).
% 289.07/181.52 tff(1236,plain,
% 289.07/181.52 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s1)) | m_c_h_element_v_in2(c_e_h_3, c_h, s1) | (~node17(c_e_h_3, c_h, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_h, s1)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s1)) | m_c_h_element_v_in2(c_e_h_3, c_h, s1)))),
% 289.07/181.52 inference(monotonicity,[status(thm)],[1235])).
% 289.07/181.52 tff(1237,plain,
% 289.07/181.52 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s1)) | m_c_h_element_v_in2(c_e_h_3, c_h, s1) | (~node17(c_e_h_3, c_h, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_h, s1)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s1)) | m_c_h_element_v_in2(c_e_h_3, c_h, s1))),
% 289.07/181.52 inference(transitivity,[status(thm)],[1236, 1234])).
% 289.07/181.52 tff(1238,plain,
% 289.07/181.52 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s1)) | m_c_h_element_v_in2(c_e_h_3, c_h, s1) | (~node17(c_e_h_3, c_h, s1)))),
% 289.07/181.52 inference(quant_inst,[status(thm)],[])).
% 289.07/181.52 tff(1239,plain,
% 289.07/181.52 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_h, s1)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s1)) | m_c_h_element_v_in2(c_e_h_3, c_h, s1)),
% 289.07/181.52 inference(modus_ponens,[status(thm)],[1238, 1237])).
% 289.07/181.52 tff(1240,plain,
% 289.07/181.52 ((~m_c_h_element_v_in1(c_e_h_3, c_h, s1)) | m_c_h_element_v_in2(c_e_h_3, c_h, s1)),
% 289.07/181.52 inference(unit_resolution,[status(thm)],[1239, 919, 1233])).
% 289.07/181.52 tff(1241,plain,
% 289.07/181.52 ($false),
% 289.07/181.52 inference(unit_resolution,[status(thm)],[1240, 1215, 1179])).
% 289.07/181.52 tff(1242,plain,(m_c_h_element_v_in2(c_e_h_3, c_h, s1) | (~m_c_h_element_v_out(c_e_h_3, c_h, s2))), inference(lemma,lemma(discharge,[]))).
% 289.07/181.52 tff(1243,plain,
% 289.07/181.52 (~m_c_h_element_v_out(c_e_h_3, c_h, s2)),
% 289.07/181.52 inference(unit_resolution,[status(thm)],[1242, 1178])).
% 289.07/181.52 tff(1244,plain,
% 289.07/181.52 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_i, s2)) | m_c_h_element_v_out(c_e_h_3, c_h, s2))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s2)) | m_c_h_element_v_out(c_e_h_3, c_h, s2))),
% 289.07/181.52 inference(rewrite,[status(thm)],[])).
% 289.07/181.52 tff(1245,plain,
% 289.07/181.52 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_i, s2)) | m_c_h_element_v_out(c_e_h_3, c_h, s2))),
% 289.07/181.52 inference(quant_inst,[status(thm)],[])).
% 289.07/181.52 tff(1246,plain,
% 289.07/181.52 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s2)) | m_c_h_element_v_out(c_e_h_3, c_h, s2)),
% 289.07/181.52 inference(modus_ponens,[status(thm)],[1245, 1244])).
% 289.07/181.52 tff(1247,plain,
% 289.07/181.52 (~m_and_h_gate_v_in1(c_e_h_3, c_i, s2)),
% 289.07/181.52 inference(unit_resolution,[status(thm)],[1246, 619, 1243])).
% 289.07/181.52 tff(1248,plain,
% 289.07/181.52 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_i, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s2))),
% 289.07/181.52 inference(rewrite,[status(thm)],[])).
% 289.07/181.52 tff(1249,plain,
% 289.07/181.52 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s2))),
% 289.07/181.52 inference(quant_inst,[status(thm)],[])).
% 289.07/181.52 tff(1250,plain,
% 289.07/181.52 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_i, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s2)),
% 289.07/181.52 inference(modus_ponens,[status(thm)],[1249, 1248])).
% 289.07/181.52 tff(1251,plain,
% 289.07/181.52 (~node20(c_e_h_3, c_i, s2)),
% 289.07/181.52 inference(unit_resolution,[status(thm)],[1250, 38, 1247])).
% 289.07/181.52 tff(1252,assumption,(~node20(c_e_h_3, c_i, s2)), introduced(assumption)).
% 289.07/181.52 tff(1253,assumption,(node21(c_e_h_3, c_i, s2, s3)), introduced(assumption)).
% 289.07/181.52 tff(1254,plain,
% 289.07/181.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s3)) | node20(c_e_h_3, c_i, s2) | (~node21(c_e_h_3, c_i, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s3)) | node20(c_e_h_3, c_i, s2) | (~node21(c_e_h_3, c_i, s2, s3)))),
% 289.07/181.53 inference(rewrite,[status(thm)],[])).
% 289.07/181.53 tff(1255,plain,
% 289.07/181.53 ((node20(c_e_h_3, c_i, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s3)) | (~node21(c_e_h_3, c_i, s2, s3))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_i, s3)) | node20(c_e_h_3, c_i, s2) | (~node21(c_e_h_3, c_i, s2, s3)))),
% 289.07/181.53 inference(rewrite,[status(thm)],[])).
% 289.07/181.53 tff(1256,plain,
% 289.07/181.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s3)) | (~node21(c_e_h_3, c_i, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s3)) | node20(c_e_h_3, c_i, s2) | (~node21(c_e_h_3, c_i, s2, s3))))),
% 289.07/181.53 inference(monotonicity,[status(thm)],[1255])).
% 289.07/181.53 tff(1257,plain,
% 289.07/181.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s3)) | (~node21(c_e_h_3, c_i, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s3)) | node20(c_e_h_3, c_i, s2) | (~node21(c_e_h_3, c_i, s2, s3)))),
% 289.07/181.53 inference(transitivity,[status(thm)],[1256, 1254])).
% 289.07/181.53 tff(1258,plain,
% 289.07/181.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s3)) | (~node21(c_e_h_3, c_i, s2, s3)))),
% 289.07/181.53 inference(quant_inst,[status(thm)],[])).
% 289.07/181.53 tff(1259,plain,
% 289.07/181.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s3)) | node20(c_e_h_3, c_i, s2) | (~node21(c_e_h_3, c_i, s2, s3))),
% 289.07/181.53 inference(modus_ponens,[status(thm)],[1258, 1257])).
% 289.07/181.53 tff(1260,plain,
% 289.07/181.53 ($false),
% 289.07/181.53 inference(unit_resolution,[status(thm)],[1259, 52, 1038, 1253, 1252])).
% 289.07/181.53 tff(1261,plain,((~node21(c_e_h_3, c_i, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s3)) | node20(c_e_h_3, c_i, s2)), inference(lemma,lemma(discharge,[]))).
% 289.07/181.53 tff(1262,plain,
% 289.07/181.53 ((~node21(c_e_h_3, c_i, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s3))),
% 289.07/181.53 inference(unit_resolution,[status(thm)],[1261, 1251])).
% 289.07/181.53 tff(1263,plain,
% 289.07/181.53 (~node21(c_e_h_3, c_i, s2, s3)),
% 289.07/181.53 inference(unit_resolution,[status(thm)],[1262, 1038])).
% 289.07/181.53 tff(1264,plain,
% 289.07/181.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_3, c_i, s2, s3) | node22(c_e_h_3, c_i, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_3, c_i, s2, s3) | node22(c_e_h_3, c_i, s2, s3))),
% 289.07/181.53 inference(rewrite,[status(thm)],[])).
% 289.07/181.53 tff(1265,plain,
% 289.07/181.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_3, c_i, s2, s3) | node22(c_e_h_3, c_i, s2, s3))),
% 289.07/181.53 inference(quant_inst,[status(thm)],[])).
% 289.07/181.53 tff(1266,plain,
% 289.07/181.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_3, c_i, s2, s3) | node22(c_e_h_3, c_i, s2, s3)),
% 289.07/181.53 inference(modus_ponens,[status(thm)],[1265, 1264])).
% 289.07/181.53 tff(1267,plain,
% 289.07/181.53 (node21(c_e_h_3, c_i, s2, s3) | node22(c_e_h_3, c_i, s2, s3)),
% 289.07/181.53 inference(unit_resolution,[status(thm)],[1266, 82, 318])).
% 289.07/181.53 tff(1268,plain,
% 289.07/181.53 ($false),
% 289.07/181.53 inference(unit_resolution,[status(thm)],[1267, 1263, 1045])).
% 289.07/181.53 tff(1269,plain,(~m_and_h_gate_v_out(c_e_h_3, c_i, s3)), inference(lemma,lemma(discharge,[]))).
% 289.07/181.53 tff(1270,assumption,(m_c_h_element_v_in2(c_e_h_3, c_e, s3)), introduced(assumption)).
% 289.07/181.53 tff(1271,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_i, s3)), introduced(assumption)).
% 289.07/181.53 tff(1272,plain,
% 289.07/181.53 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s3)) | m_and_h_gate_v_out(c_e_h_3, c_i, s3))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s3)) | m_and_h_gate_v_out(c_e_h_3, c_i, s3))),
% 289.07/181.53 inference(rewrite,[status(thm)],[])).
% 289.07/181.53 tff(1273,plain,
% 289.07/181.53 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s3)) | m_and_h_gate_v_out(c_e_h_3, c_i, s3))),
% 289.07/181.53 inference(quant_inst,[status(thm)],[])).
% 289.07/181.53 tff(1274,plain,
% 289.07/181.53 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s3)) | m_and_h_gate_v_out(c_e_h_3, c_i, s3)),
% 289.07/181.53 inference(modus_ponens,[status(thm)],[1273, 1272])).
% 289.07/181.53 tff(1275,plain,
% 289.07/181.53 ($false),
% 289.07/181.53 inference(unit_resolution,[status(thm)],[1274, 164, 1271, 1270])).
% 289.07/181.53 tff(1276,plain,((~m_c_h_element_v_in2(c_e_h_3, c_e, s3)) | m_and_h_gate_v_out(c_e_h_3, c_i, s3)), inference(lemma,lemma(discharge,[]))).
% 289.07/181.53 tff(1277,plain,
% 289.07/181.53 (~m_c_h_element_v_in2(c_e_h_3, c_e, s3)),
% 289.07/181.53 inference(unit_resolution,[status(thm)],[1276, 1269])).
% 289.07/181.53 tff(1278,assumption,(node15(c_e_h_3, c_e, s3, s4)), introduced(assumption)).
% 289.07/181.53 tff(1279,plain,
% 289.07/181.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s4)) | (~node15(c_e_h_3, c_e, s3, s4)) | m_c_h_element_v_out(c_e_h_3, c_e, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s4)) | (~node15(c_e_h_3, c_e, s3, s4)) | m_c_h_element_v_out(c_e_h_3, c_e, s3))),
% 289.07/181.53 inference(rewrite,[status(thm)],[])).
% 289.07/181.53 tff(1280,plain,
% 289.07/181.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s4)) | (~node15(c_e_h_3, c_e, s3, s4)) | m_c_h_element_v_out(c_e_h_3, c_e, s3))),
% 289.07/181.53 inference(quant_inst,[status(thm)],[])).
% 289.07/181.53 tff(1281,plain,
% 289.07/181.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s4)) | (~node15(c_e_h_3, c_e, s3, s4)) | m_c_h_element_v_out(c_e_h_3, c_e, s3)),
% 289.07/181.53 inference(modus_ponens,[status(thm)],[1280, 1279])).
% 289.07/181.53 tff(1282,plain,
% 289.07/181.53 ($false),
% 289.07/181.53 inference(unit_resolution,[status(thm)],[1281, 147, 1278, 1037, 954])).
% 289.07/181.53 tff(1283,plain,((~node15(c_e_h_3, c_e, s3, s4)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s4)) | m_c_h_element_v_out(c_e_h_3, c_e, s3)), inference(lemma,lemma(discharge,[]))).
% 289.07/181.53 tff(1284,plain,
% 289.07/181.53 (~node15(c_e_h_3, c_e, s3, s4)),
% 289.07/181.53 inference(unit_resolution,[status(thm)],[1283, 1037, 954])).
% 289.07/181.53 tff(1285,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_e, s3)), introduced(assumption)).
% 289.07/181.53 tff(1286,assumption,(~node15(c_e_h_3, c_e, s3, s4)), introduced(assumption)).
% 289.07/181.53 tff(1287,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_e, s3)), introduced(assumption)).
% 289.07/181.53 tff(1288,plain,
% 289.07/181.53 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_e, s3)) | m_c_h_element_v_in1(c_e_h_3, c_e, s3) | m_c_h_element_v_in2(c_e_h_3, c_e, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s3)) | m_c_h_element_v_in1(c_e_h_3, c_e, s3) | m_c_h_element_v_in2(c_e_h_3, c_e, s3))),
% 289.07/181.53 inference(rewrite,[status(thm)],[])).
% 289.07/181.53 tff(1289,plain,
% 289.07/181.53 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_e, s3)) | m_c_h_element_v_in1(c_e_h_3, c_e, s3) | m_c_h_element_v_in2(c_e_h_3, c_e, s3))),
% 289.07/181.53 inference(quant_inst,[status(thm)],[])).
% 289.07/181.53 tff(1290,plain,
% 289.07/181.53 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s3)) | m_c_h_element_v_in1(c_e_h_3, c_e, s3) | m_c_h_element_v_in2(c_e_h_3, c_e, s3)),
% 289.07/181.54 inference(modus_ponens,[status(thm)],[1289, 1288])).
% 289.07/181.54 tff(1291,plain,
% 289.07/181.54 ((~node16(c_e_h_3, c_e, s3)) | m_c_h_element_v_in1(c_e_h_3, c_e, s3)),
% 289.07/181.54 inference(unit_resolution,[status(thm)],[1290, 178, 1287])).
% 289.07/181.54 tff(1292,plain,
% 289.07/181.54 (~node16(c_e_h_3, c_e, s3)),
% 289.07/181.54 inference(unit_resolution,[status(thm)],[1291, 1285])).
% 289.07/181.54 tff(1293,plain,
% 289.07/181.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s3, s4)) | node19(c_e_h_3, c_e, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s3, s4)) | node19(c_e_h_3, c_e, s3, s4))),
% 289.07/181.54 inference(rewrite,[status(thm)],[])).
% 289.07/181.54 tff(1294,plain,
% 289.07/181.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s3, s4)) | node19(c_e_h_3, c_e, s3, s4))),
% 289.07/181.54 inference(quant_inst,[status(thm)],[])).
% 289.07/181.54 tff(1295,plain,
% 289.07/181.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s3, s4)) | node19(c_e_h_3, c_e, s3, s4)),
% 289.07/181.54 inference(modus_ponens,[status(thm)],[1294, 1293])).
% 289.07/181.54 tff(1296,plain,
% 289.07/181.54 (node19(c_e_h_3, c_e, s3, s4)),
% 289.07/181.54 inference(unit_resolution,[status(thm)],[1295, 190, 531])).
% 289.07/181.54 tff(1297,plain,
% 289.07/181.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s3) | node14(c_e_h_3, c_e, s3, s4) | node15(c_e_h_3, c_e, s3, s4) | (~node19(c_e_h_3, c_e, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_e, s3) | node14(c_e_h_3, c_e, s3, s4) | node15(c_e_h_3, c_e, s3, s4) | (~node19(c_e_h_3, c_e, s3, s4)))),
% 289.07/181.54 inference(rewrite,[status(thm)],[])).
% 289.07/181.54 tff(1298,plain,
% 289.07/181.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s3) | node14(c_e_h_3, c_e, s3, s4) | node15(c_e_h_3, c_e, s3, s4) | (~node19(c_e_h_3, c_e, s3, s4)))),
% 289.07/181.54 inference(quant_inst,[status(thm)],[])).
% 289.07/181.54 tff(1299,plain,
% 289.07/181.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_e, s3) | node14(c_e_h_3, c_e, s3, s4) | node15(c_e_h_3, c_e, s3, s4) | (~node19(c_e_h_3, c_e, s3, s4))),
% 289.07/181.54 inference(modus_ponens,[status(thm)],[1298, 1297])).
% 289.07/181.54 tff(1300,plain,
% 289.07/181.54 (node16(c_e_h_3, c_e, s3) | node14(c_e_h_3, c_e, s3, s4) | node15(c_e_h_3, c_e, s3, s4)),
% 289.07/181.54 inference(unit_resolution,[status(thm)],[1299, 204, 1296])).
% 289.07/181.54 tff(1301,plain,
% 289.07/181.54 (node14(c_e_h_3, c_e, s3, s4)),
% 289.07/181.54 inference(unit_resolution,[status(thm)],[1300, 1292, 1286])).
% 289.07/181.54 tff(1302,plain,
% 289.07/181.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s3) | (~m_c_h_element_v_out(c_e_h_3, c_e, s4)) | (~node14(c_e_h_3, c_e, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_e, s3) | (~m_c_h_element_v_out(c_e_h_3, c_e, s4)) | (~node14(c_e_h_3, c_e, s3, s4)))),
% 289.07/181.54 inference(rewrite,[status(thm)],[])).
% 289.07/181.54 tff(1303,plain,
% 289.07/181.54 (((~node14(c_e_h_3, c_e, s3, s4)) | m_c_h_element_v_in1(c_e_h_3, c_e, s3) | (~m_c_h_element_v_out(c_e_h_3, c_e, s4))) <=> (m_c_h_element_v_in1(c_e_h_3, c_e, s3) | (~m_c_h_element_v_out(c_e_h_3, c_e, s4)) | (~node14(c_e_h_3, c_e, s3, s4)))),
% 289.07/181.54 inference(rewrite,[status(thm)],[])).
% 289.07/181.54 tff(1304,plain,
% 289.07/181.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s3, s4)) | m_c_h_element_v_in1(c_e_h_3, c_e, s3) | (~m_c_h_element_v_out(c_e_h_3, c_e, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s3) | (~m_c_h_element_v_out(c_e_h_3, c_e, s4)) | (~node14(c_e_h_3, c_e, s3, s4))))),
% 289.07/181.54 inference(monotonicity,[status(thm)],[1303])).
% 289.07/181.54 tff(1305,plain,
% 289.07/181.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s3, s4)) | m_c_h_element_v_in1(c_e_h_3, c_e, s3) | (~m_c_h_element_v_out(c_e_h_3, c_e, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_e, s3) | (~m_c_h_element_v_out(c_e_h_3, c_e, s4)) | (~node14(c_e_h_3, c_e, s3, s4)))),
% 289.07/181.54 inference(transitivity,[status(thm)],[1304, 1302])).
% 289.07/181.54 tff(1306,plain,
% 289.07/181.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s3, s4)) | m_c_h_element_v_in1(c_e_h_3, c_e, s3) | (~m_c_h_element_v_out(c_e_h_3, c_e, s4)))),
% 289.07/181.54 inference(quant_inst,[status(thm)],[])).
% 289.07/181.54 tff(1307,plain,
% 289.07/181.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_e, s3) | (~m_c_h_element_v_out(c_e_h_3, c_e, s4)) | (~node14(c_e_h_3, c_e, s3, s4))),
% 289.07/181.54 inference(modus_ponens,[status(thm)],[1306, 1305])).
% 289.07/181.54 tff(1308,plain,
% 289.07/181.54 ($false),
% 289.07/181.54 inference(unit_resolution,[status(thm)],[1307, 223, 1301, 1285, 1037])).
% 289.07/181.54 tff(1309,plain,(m_c_h_element_v_in1(c_e_h_3, c_e, s3) | (~m_c_h_element_v_out(c_e_h_3, c_e, s4)) | node15(c_e_h_3, c_e, s3, s4) | m_c_h_element_v_in2(c_e_h_3, c_e, s3)), inference(lemma,lemma(discharge,[]))).
% 289.07/181.54 tff(1310,plain,
% 289.07/181.54 (m_c_h_element_v_in1(c_e_h_3, c_e, s3)),
% 289.07/181.54 inference(unit_resolution,[status(thm)],[1309, 1284, 1037, 1277])).
% 289.07/181.54 tff(1311,plain,
% 289.07/181.54 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_3, c_e, s3) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s3)) | (~node17(c_e_h_3, c_e, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_e, s3) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s3)) | (~node17(c_e_h_3, c_e, s3)))),
% 289.07/181.54 inference(rewrite,[status(thm)],[])).
% 289.07/181.54 tff(1312,plain,
% 289.07/181.54 (((~m_c_h_element_v_in1(c_e_h_3, c_e, s3)) | m_c_h_element_v_in2(c_e_h_3, c_e, s3) | (~node17(c_e_h_3, c_e, s3))) <=> (m_c_h_element_v_in2(c_e_h_3, c_e, s3) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s3)) | (~node17(c_e_h_3, c_e, s3)))),
% 289.07/181.54 inference(rewrite,[status(thm)],[])).
% 289.07/181.54 tff(1313,plain,
% 289.07/181.54 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s3)) | m_c_h_element_v_in2(c_e_h_3, c_e, s3) | (~node17(c_e_h_3, c_e, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_3, c_e, s3) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s3)) | (~node17(c_e_h_3, c_e, s3))))),
% 289.07/181.54 inference(monotonicity,[status(thm)],[1312])).
% 289.07/181.54 tff(1314,plain,
% 289.07/181.54 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s3)) | m_c_h_element_v_in2(c_e_h_3, c_e, s3) | (~node17(c_e_h_3, c_e, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_e, s3) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s3)) | (~node17(c_e_h_3, c_e, s3)))),
% 289.07/181.54 inference(transitivity,[status(thm)],[1313, 1311])).
% 289.07/181.54 tff(1315,plain,
% 289.07/181.54 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s3)) | m_c_h_element_v_in2(c_e_h_3, c_e, s3) | (~node17(c_e_h_3, c_e, s3)))),
% 289.07/181.54 inference(quant_inst,[status(thm)],[])).
% 289.07/181.54 tff(1316,plain,
% 289.07/181.54 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_e, s3) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s3)) | (~node17(c_e_h_3, c_e, s3))),
% 289.07/181.54 inference(modus_ponens,[status(thm)],[1315, 1314])).
% 289.07/181.54 tff(1317,plain,
% 289.07/181.54 ((~m_c_h_element_v_in1(c_e_h_3, c_e, s3)) | (~node17(c_e_h_3, c_e, s3))),
% 289.07/181.54 inference(unit_resolution,[status(thm)],[1316, 919, 1277])).
% 289.07/181.54 tff(1318,plain,
% 289.07/181.54 (~node17(c_e_h_3, c_e, s3)),
% 289.07/181.54 inference(unit_resolution,[status(thm)],[1317, 1310])).
% 289.07/181.54 tff(1319,plain,
% 289.07/181.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s3) | node18(c_e_h_3, c_e, s3, s4) | (~node19(c_e_h_3, c_e, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_e, s3) | node18(c_e_h_3, c_e, s3, s4) | (~node19(c_e_h_3, c_e, s3, s4)))),
% 289.07/181.54 inference(rewrite,[status(thm)],[])).
% 289.07/181.54 tff(1320,plain,
% 289.07/181.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s3) | node18(c_e_h_3, c_e, s3, s4) | (~node19(c_e_h_3, c_e, s3, s4)))),
% 289.07/181.54 inference(quant_inst,[status(thm)],[])).
% 289.07/181.54 tff(1321,plain,
% 289.07/181.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_e, s3) | node18(c_e_h_3, c_e, s3, s4) | (~node19(c_e_h_3, c_e, s3, s4))),
% 289.07/181.54 inference(modus_ponens,[status(thm)],[1320, 1319])).
% 289.07/181.54 tff(1322,plain,
% 289.07/181.54 (node17(c_e_h_3, c_e, s3) | node18(c_e_h_3, c_e, s3, s4)),
% 289.07/181.54 inference(unit_resolution,[status(thm)],[1321, 776, 1296])).
% 289.07/181.54 tff(1323,plain,
% 289.07/181.54 (node18(c_e_h_3, c_e, s3, s4)),
% 289.07/181.54 inference(unit_resolution,[status(thm)],[1322, 1318])).
% 289.07/181.54 tff(1324,plain,
% 289.07/181.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~node18(c_e_h_3, c_e, s3, s4)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s4)) | m_c_h_element_v_out(c_e_h_3, c_e, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_3, c_e, s3, s4)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s4)) | m_c_h_element_v_out(c_e_h_3, c_e, s3))),
% 289.07/181.54 inference(rewrite,[status(thm)],[])).
% 289.07/181.54 tff(1325,plain,
% 289.07/181.54 (((~m_c_h_element_v_out(c_e_h_3, c_e, s4)) | m_c_h_element_v_out(c_e_h_3, c_e, s3) | (~node18(c_e_h_3, c_e, s3, s4))) <=> ((~node18(c_e_h_3, c_e, s3, s4)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s4)) | m_c_h_element_v_out(c_e_h_3, c_e, s3))),
% 289.07/181.54 inference(rewrite,[status(thm)],[])).
% 289.07/181.54 tff(1326,plain,
% 289.07/181.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s4)) | m_c_h_element_v_out(c_e_h_3, c_e, s3) | (~node18(c_e_h_3, c_e, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~node18(c_e_h_3, c_e, s3, s4)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s4)) | m_c_h_element_v_out(c_e_h_3, c_e, s3)))),
% 289.07/181.54 inference(monotonicity,[status(thm)],[1325])).
% 289.07/181.54 tff(1327,plain,
% 289.07/181.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s4)) | m_c_h_element_v_out(c_e_h_3, c_e, s3) | (~node18(c_e_h_3, c_e, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_3, c_e, s3, s4)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s4)) | m_c_h_element_v_out(c_e_h_3, c_e, s3))),
% 289.07/181.54 inference(transitivity,[status(thm)],[1326, 1324])).
% 289.07/181.54 tff(1328,plain,
% 289.07/181.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s4)) | m_c_h_element_v_out(c_e_h_3, c_e, s3) | (~node18(c_e_h_3, c_e, s3, s4)))),
% 289.07/181.55 inference(quant_inst,[status(thm)],[])).
% 289.07/181.55 tff(1329,plain,
% 289.07/181.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_3, c_e, s3, s4)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s4)) | m_c_h_element_v_out(c_e_h_3, c_e, s3)),
% 289.07/181.55 inference(modus_ponens,[status(thm)],[1328, 1327])).
% 289.07/181.55 tff(1330,plain,
% 289.07/181.55 ($false),
% 289.07/181.55 inference(unit_resolution,[status(thm)],[1329, 753, 1323, 1037, 954])).
% 289.07/181.55 tff(1331,plain,((~m_c_h_element_v_out(c_e_h_3, c_e, s4)) | m_c_h_element_v_out(c_e_h_3, c_e, s3)), inference(lemma,lemma(discharge,[]))).
% 289.07/181.55 tff(1332,plain,
% 289.07/181.55 (~m_c_h_element_v_out(c_e_h_3, c_e, s4)),
% 289.07/181.55 inference(unit_resolution,[status(thm)],[1331, 952])).
% 289.07/181.55 tff(1333,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_r, s4)), introduced(assumption)).
% 289.07/181.55 tff(1334,assumption,(~m_c_h_element_v_out(c_e_h_3, c_e, s4)), introduced(assumption)).
% 289.07/181.55 tff(1335,plain,
% 289.07/181.55 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s4)) | m_c_h_element_v_out(c_e_h_3, c_e, s4))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s4)) | m_c_h_element_v_out(c_e_h_3, c_e, s4))),
% 289.07/181.55 inference(rewrite,[status(thm)],[])).
% 289.07/181.55 tff(1336,plain,
% 289.07/181.55 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s4)) | m_c_h_element_v_out(c_e_h_3, c_e, s4))),
% 289.07/181.55 inference(quant_inst,[status(thm)],[])).
% 289.07/181.55 tff(1337,plain,
% 289.07/181.55 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s4)) | m_c_h_element_v_out(c_e_h_3, c_e, s4)),
% 289.07/181.55 inference(modus_ponens,[status(thm)],[1336, 1335])).
% 289.07/181.55 tff(1338,plain,
% 289.07/181.55 ($false),
% 289.07/181.55 inference(unit_resolution,[status(thm)],[1337, 24, 1334, 1333])).
% 289.07/181.55 tff(1339,plain,((~m_and_h_gate_v_in1(c_e_h_3, c_r, s4)) | m_c_h_element_v_out(c_e_h_3, c_e, s4)), inference(lemma,lemma(discharge,[]))).
% 289.07/181.55 tff(1340,plain,
% 289.07/181.55 (~m_and_h_gate_v_in1(c_e_h_3, c_r, s4)),
% 289.07/181.55 inference(unit_resolution,[status(thm)],[1339, 1332])).
% 289.07/181.55 tff(1341,assumption,(node20(c_e_h_3, c_r, s4)), introduced(assumption)).
% 289.07/181.55 tff(1342,plain,
% 289.07/181.55 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s4))),
% 289.07/181.55 inference(rewrite,[status(thm)],[])).
% 289.07/181.55 tff(1343,plain,
% 289.07/181.55 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s4))),
% 289.07/181.55 inference(quant_inst,[status(thm)],[])).
% 289.07/181.55 tff(1344,plain,
% 289.07/181.55 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s4)),
% 289.07/181.55 inference(modus_ponens,[status(thm)],[1343, 1342])).
% 289.07/181.55 tff(1345,plain,
% 289.07/181.55 ($false),
% 289.07/181.55 inference(unit_resolution,[status(thm)],[1344, 38, 1341, 1340])).
% 289.07/181.55 tff(1346,plain,(~node20(c_e_h_3, c_r, s4)), inference(lemma,lemma(discharge,[]))).
% 289.07/181.55 tff(1347,assumption,(m_and_h_gate_v_out(c_e_h_3, c_r, s5)), introduced(assumption)).
% 289.07/181.55 tff(1348,assumption,(~node20(c_e_h_3, c_r, s4)), introduced(assumption)).
% 289.07/181.55 tff(1349,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_r, s4)), introduced(assumption)).
% 289.07/181.55 tff(1350,assumption,(node22(c_e_h_3, c_r, s4, s5)), introduced(assumption)).
% 289.07/181.55 tff(1351,plain,
% 289.07/181.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s5)) | (~node22(c_e_h_3, c_r, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_r, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s5)) | (~node22(c_e_h_3, c_r, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_r, s4))),
% 289.07/181.55 inference(rewrite,[status(thm)],[])).
% 289.07/181.55 tff(1352,plain,
% 289.07/181.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s5)) | (~node22(c_e_h_3, c_r, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_r, s4))),
% 289.07/181.55 inference(quant_inst,[status(thm)],[])).
% 289.07/181.55 tff(1353,plain,
% 289.07/181.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s5)) | (~node22(c_e_h_3, c_r, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_r, s4)),
% 289.07/181.55 inference(modus_ponens,[status(thm)],[1352, 1351])).
% 289.07/181.55 tff(1354,plain,
% 289.07/181.55 ($false),
% 289.07/181.55 inference(unit_resolution,[status(thm)],[1353, 108, 1350, 1349, 1347])).
% 289.07/181.55 tff(1355,plain,((~node22(c_e_h_3, c_r, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_r, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s5))), inference(lemma,lemma(discharge,[]))).
% 289.07/181.55 tff(1356,plain,
% 289.07/181.55 (~node22(c_e_h_3, c_r, s4, s5)),
% 289.07/181.55 inference(unit_resolution,[status(thm)],[1355, 1347, 1349])).
% 289.07/181.55 tff(1357,plain,
% 289.07/181.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_3, c_r, s4, s5) | node22(c_e_h_3, c_r, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_3, c_r, s4, s5) | node22(c_e_h_3, c_r, s4, s5))),
% 289.07/181.55 inference(rewrite,[status(thm)],[])).
% 289.07/181.55 tff(1358,plain,
% 289.07/181.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_3, c_r, s4, s5) | node22(c_e_h_3, c_r, s4, s5))),
% 289.07/181.55 inference(quant_inst,[status(thm)],[])).
% 289.07/181.55 tff(1359,plain,
% 289.07/181.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_3, c_r, s4, s5) | node22(c_e_h_3, c_r, s4, s5)),
% 289.07/181.55 inference(modus_ponens,[status(thm)],[1358, 1357])).
% 289.07/181.55 tff(1360,plain,
% 289.07/181.55 (node21(c_e_h_3, c_r, s4, s5) | node22(c_e_h_3, c_r, s4, s5)),
% 289.07/181.55 inference(unit_resolution,[status(thm)],[1359, 82, 1028])).
% 289.07/181.55 tff(1361,plain,
% 289.07/181.55 (node21(c_e_h_3, c_r, s4, s5)),
% 289.07/181.55 inference(unit_resolution,[status(thm)],[1360, 1356])).
% 289.07/181.55 tff(1362,plain,
% 289.07/181.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s5)) | node20(c_e_h_3, c_r, s4) | (~node21(c_e_h_3, c_r, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s5)) | node20(c_e_h_3, c_r, s4) | (~node21(c_e_h_3, c_r, s4, s5)))),
% 289.07/181.55 inference(rewrite,[status(thm)],[])).
% 289.07/181.55 tff(1363,plain,
% 289.07/181.55 ((node20(c_e_h_3, c_r, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s5)) | (~node21(c_e_h_3, c_r, s4, s5))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_r, s5)) | node20(c_e_h_3, c_r, s4) | (~node21(c_e_h_3, c_r, s4, s5)))),
% 289.07/181.55 inference(rewrite,[status(thm)],[])).
% 289.07/181.55 tff(1364,plain,
% 289.07/181.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s5)) | (~node21(c_e_h_3, c_r, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s5)) | node20(c_e_h_3, c_r, s4) | (~node21(c_e_h_3, c_r, s4, s5))))),
% 289.07/181.55 inference(monotonicity,[status(thm)],[1363])).
% 289.07/181.55 tff(1365,plain,
% 289.07/181.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s5)) | (~node21(c_e_h_3, c_r, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s5)) | node20(c_e_h_3, c_r, s4) | (~node21(c_e_h_3, c_r, s4, s5)))),
% 289.07/181.55 inference(transitivity,[status(thm)],[1364, 1362])).
% 289.07/181.55 tff(1366,plain,
% 289.07/181.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s5)) | (~node21(c_e_h_3, c_r, s4, s5)))),
% 289.07/181.55 inference(quant_inst,[status(thm)],[])).
% 289.07/181.55 tff(1367,plain,
% 289.07/181.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s5)) | node20(c_e_h_3, c_r, s4) | (~node21(c_e_h_3, c_r, s4, s5))),
% 289.07/181.55 inference(modus_ponens,[status(thm)],[1366, 1365])).
% 289.07/181.55 tff(1368,plain,
% 289.07/181.55 ($false),
% 289.07/181.55 inference(unit_resolution,[status(thm)],[1367, 52, 1361, 1348, 1347])).
% 289.07/181.55 tff(1369,plain,((~m_and_h_gate_v_out(c_e_h_3, c_r, s5)) | node20(c_e_h_3, c_r, s4) | m_and_h_gate_v_out(c_e_h_3, c_r, s4)), inference(lemma,lemma(discharge,[]))).
% 289.07/181.55 tff(1370,plain,
% 289.07/181.55 ((~m_and_h_gate_v_out(c_e_h_3, c_r, s5)) | node20(c_e_h_3, c_r, s4)),
% 289.07/181.55 inference(unit_resolution,[status(thm)],[1369, 995])).
% 289.07/181.55 tff(1371,plain,
% 289.07/181.55 (~m_and_h_gate_v_out(c_e_h_3, c_r, s5)),
% 289.07/181.55 inference(unit_resolution,[status(thm)],[1370, 1346])).
% 289.07/181.55 tff(1372,assumption,(m_user_v_ack(c_e_h_3, c_u, s5)), introduced(assumption)).
% 289.07/181.55 tff(1373,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_r, s5)), introduced(assumption)).
% 289.07/181.55 tff(1374,plain,
% 289.07/181.55 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_3, c_u, s5)) | m_and_h_gate_v_out(c_e_h_3, c_r, s5))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_3, c_u, s5)) | m_and_h_gate_v_out(c_e_h_3, c_r, s5))),
% 289.07/181.55 inference(rewrite,[status(thm)],[])).
% 289.07/181.55 tff(1375,plain,
% 289.07/181.55 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_3, c_u, s5)) | m_and_h_gate_v_out(c_e_h_3, c_r, s5))),
% 289.07/181.55 inference(quant_inst,[status(thm)],[])).
% 289.07/181.55 tff(1376,plain,
% 289.07/181.55 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_3, c_u, s5)) | m_and_h_gate_v_out(c_e_h_3, c_r, s5)),
% 289.07/181.55 inference(modus_ponens,[status(thm)],[1375, 1374])).
% 289.07/181.55 tff(1377,plain,
% 289.07/181.55 ($false),
% 289.07/181.55 inference(unit_resolution,[status(thm)],[1376, 268, 1373, 1372])).
% 289.07/181.55 tff(1378,plain,((~m_user_v_ack(c_e_h_3, c_u, s5)) | m_and_h_gate_v_out(c_e_h_3, c_r, s5)), inference(lemma,lemma(discharge,[]))).
% 289.07/181.55 tff(1379,plain,
% 289.07/181.55 (~m_user_v_ack(c_e_h_3, c_u, s5)),
% 289.07/181.55 inference(unit_resolution,[status(thm)],[1378, 1371])).
% 289.07/181.55 tff(1380,assumption,(~m_user_v_ack(c_e_h_3, c_u, s5)), introduced(assumption)).
% 289.07/181.55 tff(1381,assumption,(~m_user_v_req(c_e_h_3, c_u, s6)), introduced(assumption)).
% 289.07/181.55 tff(1382,assumption,(node7(c_e_h_3, c_u, s5, s6)), introduced(assumption)).
% 289.07/181.55 tff(1383,plain,
% 289.07/181.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | ((~node7(c_e_h_3, c_u, s5, s6)) | m_user_v_ack(c_e_h_3, c_u, s5) | m_user_v_req(c_e_h_3, c_u, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | (~node7(c_e_h_3, c_u, s5, s6)) | m_user_v_ack(c_e_h_3, c_u, s5) | m_user_v_req(c_e_h_3, c_u, s6))),
% 289.07/181.55 inference(rewrite,[status(thm)],[])).
% 289.07/181.55 tff(1384,plain,
% 289.07/181.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | ((~node7(c_e_h_3, c_u, s5, s6)) | m_user_v_ack(c_e_h_3, c_u, s5) | m_user_v_req(c_e_h_3, c_u, s6))),
% 289.07/181.55 inference(quant_inst,[status(thm)],[])).
% 289.07/181.55 tff(1385,plain,
% 289.07/181.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | (~node7(c_e_h_3, c_u, s5, s6)) | m_user_v_ack(c_e_h_3, c_u, s5) | m_user_v_req(c_e_h_3, c_u, s6)),
% 289.07/181.55 inference(modus_ponens,[status(thm)],[1384, 1383])).
% 289.07/181.56 tff(1386,plain,
% 289.07/181.56 ($false),
% 289.07/181.56 inference(unit_resolution,[status(thm)],[1385, 284, 1382, 1381, 1380])).
% 289.07/181.56 tff(1387,plain,((~node7(c_e_h_3, c_u, s5, s6)) | m_user_v_req(c_e_h_3, c_u, s6) | m_user_v_ack(c_e_h_3, c_u, s5)), inference(lemma,lemma(discharge,[]))).
% 289.07/181.56 tff(1388,plain,
% 289.07/181.56 (~node7(c_e_h_3, c_u, s5, s6)),
% 289.07/181.56 inference(unit_resolution,[status(thm)],[1387, 1381, 1380])).
% 289.07/181.56 tff(1389,assumption,(m_user_v_req(c_e_h_3, c_u, s5)), introduced(assumption)).
% 289.07/181.56 tff(1390,assumption,(node8(c_e_h_3, c_u, s5, s6)), introduced(assumption)).
% 289.07/181.56 tff(1391,plain,
% 289.07/181.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | ((~m_user_v_req(c_e_h_3, c_u, s5)) | m_user_v_req(c_e_h_3, c_u, s6) | (~node8(c_e_h_3, c_u, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (~m_user_v_req(c_e_h_3, c_u, s5)) | m_user_v_req(c_e_h_3, c_u, s6) | (~node8(c_e_h_3, c_u, s5, s6)))),
% 289.07/181.56 inference(rewrite,[status(thm)],[])).
% 289.07/181.56 tff(1392,plain,
% 289.07/181.56 ((m_user_v_req(c_e_h_3, c_u, s6) | (~node8(c_e_h_3, c_u, s5, s6)) | (~m_user_v_req(c_e_h_3, c_u, s5))) <=> ((~m_user_v_req(c_e_h_3, c_u, s5)) | m_user_v_req(c_e_h_3, c_u, s6) | (~node8(c_e_h_3, c_u, s5, s6)))),
% 289.07/181.56 inference(rewrite,[status(thm)],[])).
% 289.07/181.56 tff(1393,plain,
% 289.07/181.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_3, c_u, s6) | (~node8(c_e_h_3, c_u, s5, s6)) | (~m_user_v_req(c_e_h_3, c_u, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | ((~m_user_v_req(c_e_h_3, c_u, s5)) | m_user_v_req(c_e_h_3, c_u, s6) | (~node8(c_e_h_3, c_u, s5, s6))))),
% 289.07/181.56 inference(monotonicity,[status(thm)],[1392])).
% 289.07/181.56 tff(1394,plain,
% 289.07/181.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_3, c_u, s6) | (~node8(c_e_h_3, c_u, s5, s6)) | (~m_user_v_req(c_e_h_3, c_u, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (~m_user_v_req(c_e_h_3, c_u, s5)) | m_user_v_req(c_e_h_3, c_u, s6) | (~node8(c_e_h_3, c_u, s5, s6)))),
% 289.07/181.56 inference(transitivity,[status(thm)],[1393, 1391])).
% 289.07/181.56 tff(1395,plain,
% 289.07/181.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_3, c_u, s6) | (~node8(c_e_h_3, c_u, s5, s6)) | (~m_user_v_req(c_e_h_3, c_u, s5)))),
% 289.07/181.56 inference(quant_inst,[status(thm)],[])).
% 289.07/181.56 tff(1396,plain,
% 289.07/181.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (~m_user_v_req(c_e_h_3, c_u, s5)) | m_user_v_req(c_e_h_3, c_u, s6) | (~node8(c_e_h_3, c_u, s5, s6))),
% 289.07/181.56 inference(modus_ponens,[status(thm)],[1395, 1394])).
% 289.07/181.56 tff(1397,plain,
% 289.07/181.56 ($false),
% 289.07/181.56 inference(unit_resolution,[status(thm)],[1396, 302, 1390, 1381, 1389])).
% 289.07/181.56 tff(1398,plain,((~node8(c_e_h_3, c_u, s5, s6)) | m_user_v_req(c_e_h_3, c_u, s6) | (~m_user_v_req(c_e_h_3, c_u, s5))), inference(lemma,lemma(discharge,[]))).
% 289.07/181.56 tff(1399,plain,
% 289.07/181.56 (~node8(c_e_h_3, c_u, s5, s6)),
% 289.07/181.56 inference(unit_resolution,[status(thm)],[1398, 1381, 1389])).
% 289.07/181.56 tff(1400,plain,
% 289.07/181.56 (succ(s5, s6) <=> succ(s5, s6)),
% 289.07/181.56 inference(rewrite,[status(thm)],[])).
% 289.07/181.56 tff(1401,axiom,(succ(s5, s6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound6')).
% 289.07/181.56 tff(1402,plain,
% 289.07/181.56 (succ(s5, s6)),
% 289.07/181.56 inference(modus_ponens,[status(thm)],[1401, 1400])).
% 289.07/181.56 tff(1403,plain,
% 289.07/181.56 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s5, s6)) | trans(s5, s6))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s5, s6)) | trans(s5, s6))),
% 289.07/181.56 inference(rewrite,[status(thm)],[])).
% 289.07/181.56 tff(1404,plain,
% 289.07/181.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s5, s6)) | trans(s5, s6))),
% 289.07/181.56 inference(quant_inst,[status(thm)],[])).
% 289.07/181.56 tff(1405,plain,
% 289.07/181.56 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s5, s6)) | trans(s5, s6)),
% 289.07/181.56 inference(modus_ponens,[status(thm)],[1404, 1403])).
% 289.07/181.56 tff(1406,plain,
% 289.07/181.56 (trans(s5, s6)),
% 289.07/181.56 inference(unit_resolution,[status(thm)],[1405, 1402, 65])).
% 289.07/181.56 tff(1407,plain,
% 289.07/181.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | ((~trans(s5, s6)) | node7(c_e_h_3, c_u, s5, s6) | node8(c_e_h_3, c_u, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | (~trans(s5, s6)) | node7(c_e_h_3, c_u, s5, s6) | node8(c_e_h_3, c_u, s5, s6))),
% 289.07/181.56 inference(rewrite,[status(thm)],[])).
% 289.07/181.56 tff(1408,plain,
% 289.07/181.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | ((~trans(s5, s6)) | node7(c_e_h_3, c_u, s5, s6) | node8(c_e_h_3, c_u, s5, s6))),
% 289.07/181.56 inference(quant_inst,[status(thm)],[])).
% 289.07/181.56 tff(1409,plain,
% 289.07/181.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | (~trans(s5, s6)) | node7(c_e_h_3, c_u, s5, s6) | node8(c_e_h_3, c_u, s5, s6)),
% 289.07/181.56 inference(modus_ponens,[status(thm)],[1408, 1407])).
% 289.07/181.56 tff(1410,plain,
% 289.07/181.56 (node7(c_e_h_3, c_u, s5, s6) | node8(c_e_h_3, c_u, s5, s6)),
% 289.07/181.56 inference(unit_resolution,[status(thm)],[1409, 328, 1406])).
% 289.07/181.56 tff(1411,plain,
% 289.07/181.56 ($false),
% 289.07/181.56 inference(unit_resolution,[status(thm)],[1410, 1399, 1388])).
% 289.07/181.56 tff(1412,plain,(m_user_v_req(c_e_h_3, c_u, s6) | (~m_user_v_req(c_e_h_3, c_u, s5)) | m_user_v_ack(c_e_h_3, c_u, s5)), inference(lemma,lemma(discharge,[]))).
% 289.07/181.56 tff(1413,plain,
% 289.07/181.56 (m_user_v_req(c_e_h_3, c_u, s6) | (~m_user_v_req(c_e_h_3, c_u, s5))),
% 289.07/181.56 inference(unit_resolution,[status(thm)],[1412, 1379])).
% 289.07/181.56 tff(1414,plain,
% 289.07/181.56 (m_user_v_req(c_e_h_3, c_u, s6)),
% 289.07/181.56 inference(unit_resolution,[status(thm)],[1413, 1036])).
% 289.07/181.56 tff(1415,assumption,(~m_mutex_h_half_v_inp(c_e_h_3, c_a, s6)), introduced(assumption)).
% 289.07/181.56 tff(1416,assumption,(m_user_v_req(c_e_h_3, c_u, s6)), introduced(assumption)).
% 289.07/181.56 tff(1417,plain,
% 289.07/181.56 (^[I0: $i, X: $i] : refl(((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X)) <=> ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X)))),
% 289.07/181.56 inference(bind,[status(th)],[])).
% 289.07/181.56 tff(1418,plain,
% 289.07/181.56 (![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X)) <=> ![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))),
% 289.07/181.56 inference(quant_intro,[status(thm)],[1417])).
% 289.07/181.56 tff(1419,plain,
% 289.07/181.56 (![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X)) <=> ![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))),
% 289.07/181.56 inference(rewrite,[status(thm)],[])).
% 289.07/181.56 tff(1420,plain,
% 289.07/181.56 (^[I0: $i, X: $i] : rewrite((m_mutex_h_half_v_inp(I0, c_a, X) | (~m_user_v_req(I0, c_u, X))) <=> ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X)))),
% 289.07/181.56 inference(bind,[status(th)],[])).
% 289.07/181.56 tff(1421,plain,
% 289.07/181.56 (![I0: $i, X: $i] : (m_mutex_h_half_v_inp(I0, c_a, X) | (~m_user_v_req(I0, c_u, X))) <=> ![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))),
% 289.07/181.56 inference(quant_intro,[status(thm)],[1420])).
% 289.07/181.56 tff(1422,axiom,(![I0: $i, X: $i] : (m_mutex_h_half_v_inp(I0, c_a, X) | (~m_user_v_req(I0, c_u, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_1')).
% 289.07/181.56 tff(1423,plain,
% 289.07/181.56 (![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))),
% 289.07/181.56 inference(modus_ponens,[status(thm)],[1422, 1421])).
% 289.07/181.56 tff(1424,plain,
% 289.07/181.56 (![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))),
% 289.07/181.56 inference(modus_ponens,[status(thm)],[1423, 1419])).
% 289.07/181.56 tff(1425,plain,(
% 289.07/181.56 ![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))),
% 289.07/181.56 inference(skolemize,[status(sab)],[1424])).
% 289.07/181.56 tff(1426,plain,
% 289.07/181.56 (![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))),
% 289.07/181.56 inference(modus_ponens,[status(thm)],[1425, 1418])).
% 289.07/181.56 tff(1427,plain,
% 289.07/181.56 (((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | ((~m_user_v_req(c_e_h_3, c_u, s6)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s6))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | (~m_user_v_req(c_e_h_3, c_u, s6)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s6))),
% 289.07/181.57 inference(rewrite,[status(thm)],[])).
% 289.07/181.57 tff(1428,plain,
% 289.07/181.57 ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | ((~m_user_v_req(c_e_h_3, c_u, s6)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s6))),
% 289.07/181.57 inference(quant_inst,[status(thm)],[])).
% 289.07/181.57 tff(1429,plain,
% 289.07/181.57 ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | (~m_user_v_req(c_e_h_3, c_u, s6)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s6)),
% 289.07/181.57 inference(modus_ponens,[status(thm)],[1428, 1427])).
% 289.07/181.57 tff(1430,plain,
% 289.07/181.57 ($false),
% 289.07/181.57 inference(unit_resolution,[status(thm)],[1429, 1426, 1416, 1415])).
% 289.07/181.57 tff(1431,plain,(m_mutex_h_half_v_inp(c_e_h_3, c_a, s6) | (~m_user_v_req(c_e_h_3, c_u, s6))), inference(lemma,lemma(discharge,[]))).
% 289.07/181.57 tff(1432,plain,
% 289.07/181.57 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s6)),
% 289.07/181.57 inference(unit_resolution,[status(thm)],[1431, 1414])).
% 289.07/181.57 tff(1433,assumption,(~m_mutex_h_half_v_inp(c_e_h_3, c_a, s5)), introduced(assumption)).
% 289.07/181.57 tff(1434,plain,
% 289.07/181.57 (((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | ((~m_user_v_req(c_e_h_3, c_u, s5)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s5))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | (~m_user_v_req(c_e_h_3, c_u, s5)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s5))),
% 289.07/181.57 inference(rewrite,[status(thm)],[])).
% 289.07/181.57 tff(1435,plain,
% 289.07/181.57 ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | ((~m_user_v_req(c_e_h_3, c_u, s5)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s5))),
% 289.07/181.57 inference(quant_inst,[status(thm)],[])).
% 289.07/181.57 tff(1436,plain,
% 289.07/181.57 ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | (~m_user_v_req(c_e_h_3, c_u, s5)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s5)),
% 289.07/181.57 inference(modus_ponens,[status(thm)],[1435, 1434])).
% 289.07/181.57 tff(1437,plain,
% 289.07/181.57 ($false),
% 289.07/181.57 inference(unit_resolution,[status(thm)],[1436, 1426, 1389, 1433])).
% 289.07/181.57 tff(1438,plain,(m_mutex_h_half_v_inp(c_e_h_3, c_a, s5) | (~m_user_v_req(c_e_h_3, c_u, s5))), inference(lemma,lemma(discharge,[]))).
% 289.07/181.57 tff(1439,plain,
% 289.07/181.57 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s5)),
% 289.07/181.57 inference(unit_resolution,[status(thm)],[1438, 1036])).
% 289.07/181.57 tff(1440,assumption,(~m_mutex_h_half_v_inp(c_e_h_3, c_a, s4)), introduced(assumption)).
% 289.07/181.57 tff(1441,plain,
% 289.07/181.57 (((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | ((~m_user_v_req(c_e_h_3, c_u, s4)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s4))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | (~m_user_v_req(c_e_h_3, c_u, s4)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s4))),
% 289.07/181.57 inference(rewrite,[status(thm)],[])).
% 289.07/181.57 tff(1442,plain,
% 289.07/181.57 ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | ((~m_user_v_req(c_e_h_3, c_u, s4)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s4))),
% 289.07/181.57 inference(quant_inst,[status(thm)],[])).
% 289.07/181.57 tff(1443,plain,
% 289.07/181.57 ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | (~m_user_v_req(c_e_h_3, c_u, s4)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s4)),
% 289.07/181.57 inference(modus_ponens,[status(thm)],[1442, 1441])).
% 289.07/181.57 tff(1444,plain,
% 289.07/181.57 ($false),
% 289.07/181.57 inference(unit_resolution,[status(thm)],[1443, 1426, 1011, 1440])).
% 289.07/181.57 tff(1445,plain,(m_mutex_h_half_v_inp(c_e_h_3, c_a, s4) | (~m_user_v_req(c_e_h_3, c_u, s4))), inference(lemma,lemma(discharge,[]))).
% 289.07/181.57 tff(1446,plain,
% 289.07/181.57 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s4)),
% 289.07/181.57 inference(unit_resolution,[status(thm)],[1445, 733])).
% 289.07/181.57 tff(1447,assumption,(m_mutex_h_half_v_inp(c_e_h_3, c_a, s4)), introduced(assumption)).
% 289.07/181.57 tff(1448,assumption,(~m_mutex_h_half_v_out(c_e_h_3, c_a, s5)), introduced(assumption)).
% 289.07/181.57 tff(1449,assumption,(node13(c_e_h_3, c_a, s4, s5)), introduced(assumption)).
% 289.07/181.57 tff(1450,plain,
% 289.07/181.57 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl((m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X))) <=> (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X))))),
% 289.07/181.57 inference(bind,[status(th)],[])).
% 289.07/181.57 tff(1451,plain,
% 289.07/181.57 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))),
% 289.07/181.57 inference(quant_intro,[status(thm)],[1450])).
% 289.07/181.57 tff(1452,plain,
% 289.07/181.57 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))),
% 289.07/181.57 inference(rewrite,[status(thm)],[])).
% 289.07/181.57 tff(1453,plain,
% 289.07/181.57 (^[Y: $i, I0: $i, X: $i, I1: $i] : trans(monotonicity(rewrite((m_mutex_h_half_v_out(I0, I1, Y) | (~m_mutex_h_half_v_out(I0, I1, X))) <=> (m_mutex_h_half_v_out(I0, I1, Y) | (~m_mutex_h_half_v_out(I0, I1, X)))), (((m_mutex_h_half_v_out(I0, I1, Y) | (~m_mutex_h_half_v_out(I0, I1, X))) | (~node13(I0, I1, X, Y))) <=> ((m_mutex_h_half_v_out(I0, I1, Y) | (~m_mutex_h_half_v_out(I0, I1, X))) | (~node13(I0, I1, X, Y))))), rewrite(((m_mutex_h_half_v_out(I0, I1, Y) | (~m_mutex_h_half_v_out(I0, I1, X))) | (~node13(I0, I1, X, Y))) <=> (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))), (((m_mutex_h_half_v_out(I0, I1, Y) | (~m_mutex_h_half_v_out(I0, I1, X))) | (~node13(I0, I1, X, Y))) <=> (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))))),
% 289.07/181.57 inference(bind,[status(th)],[])).
% 289.07/181.57 tff(1454,plain,
% 289.07/181.57 (![Y: $i, I0: $i, X: $i, I1: $i] : ((m_mutex_h_half_v_out(I0, I1, Y) | (~m_mutex_h_half_v_out(I0, I1, X))) | (~node13(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))),
% 289.07/181.57 inference(quant_intro,[status(thm)],[1453])).
% 289.07/181.57 tff(1455,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : ((m_mutex_h_half_v_out(I0, I1, Y) | (~m_mutex_h_half_v_out(I0, I1, X))) | (~node13(I0, I1, X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_mutex_h_half_4')).
% 289.07/181.57 tff(1456,plain,
% 289.07/181.57 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))),
% 289.07/181.57 inference(modus_ponens,[status(thm)],[1455, 1454])).
% 289.07/181.57 tff(1457,plain,
% 289.07/181.57 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))),
% 289.07/181.57 inference(modus_ponens,[status(thm)],[1456, 1452])).
% 289.07/181.57 tff(1458,plain,(
% 289.07/181.57 ![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))),
% 289.07/181.57 inference(skolemize,[status(sab)],[1457])).
% 289.07/181.57 tff(1459,plain,
% 289.07/181.57 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))),
% 289.07/181.57 inference(modus_ponens,[status(thm)],[1458, 1451])).
% 289.07/181.57 tff(1460,plain,
% 289.07/181.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s4)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s5) | (~node13(c_e_h_3, c_a, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s4)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s5) | (~node13(c_e_h_3, c_a, s4, s5)))),
% 289.07/181.57 inference(rewrite,[status(thm)],[])).
% 289.07/181.57 tff(1461,plain,
% 289.07/181.57 ((m_mutex_h_half_v_out(c_e_h_3, c_a, s5) | (~node13(c_e_h_3, c_a, s4, s5)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s4))) <=> ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s4)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s5) | (~node13(c_e_h_3, c_a, s4, s5)))),
% 289.07/181.57 inference(rewrite,[status(thm)],[])).
% 289.07/181.57 tff(1462,plain,
% 289.07/181.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s5) | (~node13(c_e_h_3, c_a, s4, s5)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s4)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s5) | (~node13(c_e_h_3, c_a, s4, s5))))),
% 289.07/181.57 inference(monotonicity,[status(thm)],[1461])).
% 289.07/181.57 tff(1463,plain,
% 289.07/181.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s5) | (~node13(c_e_h_3, c_a, s4, s5)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s4)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s5) | (~node13(c_e_h_3, c_a, s4, s5)))),
% 289.07/181.57 inference(transitivity,[status(thm)],[1462, 1460])).
% 289.07/181.57 tff(1464,plain,
% 289.07/181.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s5) | (~node13(c_e_h_3, c_a, s4, s5)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s4)))),
% 289.07/181.57 inference(quant_inst,[status(thm)],[])).
% 289.07/181.57 tff(1465,plain,
% 289.07/181.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s4)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s5) | (~node13(c_e_h_3, c_a, s4, s5))),
% 289.07/181.57 inference(modus_ponens,[status(thm)],[1464, 1463])).
% 289.07/181.57 tff(1466,plain,
% 289.07/181.57 ($false),
% 289.07/181.57 inference(unit_resolution,[status(thm)],[1465, 1459, 1449, 2, 1448])).
% 289.07/181.57 tff(1467,plain,((~node13(c_e_h_3, c_a, s4, s5)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s4)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s5)), inference(lemma,lemma(discharge,[]))).
% 289.07/181.57 tff(1468,plain,
% 289.07/181.57 (~node13(c_e_h_3, c_a, s4, s5)),
% 289.07/181.57 inference(unit_resolution,[status(thm)],[1467, 1448, 2])).
% 289.07/181.57 tff(1469,plain,
% 289.07/181.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s4, s5)) | node12(c_e_h_3, c_a, s4, s5) | node13(c_e_h_3, c_a, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s4, s5)) | node12(c_e_h_3, c_a, s4, s5) | node13(c_e_h_3, c_a, s4, s5))),
% 289.07/181.57 inference(rewrite,[status(thm)],[])).
% 289.07/181.57 tff(1470,plain,
% 289.07/181.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s4, s5)) | node12(c_e_h_3, c_a, s4, s5) | node13(c_e_h_3, c_a, s4, s5))),
% 289.07/181.57 inference(quant_inst,[status(thm)],[])).
% 289.07/181.57 tff(1471,plain,
% 289.07/181.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s4, s5)) | node12(c_e_h_3, c_a, s4, s5) | node13(c_e_h_3, c_a, s4, s5)),
% 289.07/181.57 inference(modus_ponens,[status(thm)],[1470, 1469])).
% 289.07/181.57 tff(1472,plain,
% 289.07/181.57 (node12(c_e_h_3, c_a, s4, s5) | node13(c_e_h_3, c_a, s4, s5)),
% 289.07/181.57 inference(unit_resolution,[status(thm)],[1471, 439, 1028])).
% 289.07/181.57 tff(1473,plain,
% 289.07/181.57 (node12(c_e_h_3, c_a, s4, s5)),
% 289.07/181.57 inference(unit_resolution,[status(thm)],[1472, 1468])).
% 289.07/181.57 tff(1474,plain,
% 289.07/181.57 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl(((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y)) <=> ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y)))),
% 289.07/181.57 inference(bind,[status(th)],[])).
% 289.07/181.57 tff(1475,plain,
% 289.07/181.57 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))),
% 289.07/181.57 inference(quant_intro,[status(thm)],[1474])).
% 289.07/181.57 tff(1476,plain,
% 289.07/181.57 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))),
% 289.07/181.57 inference(rewrite,[status(thm)],[])).
% 289.07/181.57 tff(1477,plain,
% 289.07/181.57 (^[Y: $i, I0: $i, X: $i, I1: $i] : trans(monotonicity(rewrite((m_mutex_h_half_v_out(I0, I1, Y) | (~m_mutex_h_half_v_inp(I0, I1, X))) <=> ((~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))), (((m_mutex_h_half_v_out(I0, I1, Y) | (~m_mutex_h_half_v_inp(I0, I1, X))) | (~node12(I0, I1, X, Y))) <=> (((~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y)) | (~node12(I0, I1, X, Y))))), rewrite((((~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y)) | (~node12(I0, I1, X, Y))) <=> ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))), (((m_mutex_h_half_v_out(I0, I1, Y) | (~m_mutex_h_half_v_inp(I0, I1, X))) | (~node12(I0, I1, X, Y))) <=> ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))))),
% 289.07/181.57 inference(bind,[status(th)],[])).
% 289.07/181.57 tff(1478,plain,
% 289.07/181.57 (![Y: $i, I0: $i, X: $i, I1: $i] : ((m_mutex_h_half_v_out(I0, I1, Y) | (~m_mutex_h_half_v_inp(I0, I1, X))) | (~node12(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))),
% 289.07/181.57 inference(quant_intro,[status(thm)],[1477])).
% 289.07/181.57 tff(1479,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : ((m_mutex_h_half_v_out(I0, I1, Y) | (~m_mutex_h_half_v_inp(I0, I1, X))) | (~node12(I0, I1, X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_mutex_h_half_2')).
% 289.07/181.57 tff(1480,plain,
% 289.07/181.57 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))),
% 289.07/181.57 inference(modus_ponens,[status(thm)],[1479, 1478])).
% 289.07/181.57 tff(1481,plain,
% 289.07/181.57 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))),
% 289.07/181.57 inference(modus_ponens,[status(thm)],[1480, 1476])).
% 289.07/181.57 tff(1482,plain,(
% 289.07/181.57 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))),
% 289.07/181.57 inference(skolemize,[status(sab)],[1481])).
% 289.07/181.57 tff(1483,plain,
% 289.07/181.57 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))),
% 289.07/181.57 inference(modus_ponens,[status(thm)],[1482, 1475])).
% 289.07/181.57 tff(1484,plain,
% 289.07/181.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_3, c_a, s4, s5)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s4)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (~node12(c_e_h_3, c_a, s4, s5)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s4)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s5))),
% 289.07/181.57 inference(rewrite,[status(thm)],[])).
% 289.07/181.57 tff(1485,plain,
% 289.07/181.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_3, c_a, s4, s5)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s4)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s5))),
% 289.07/181.57 inference(quant_inst,[status(thm)],[])).
% 289.07/181.57 tff(1486,plain,
% 289.07/181.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (~node12(c_e_h_3, c_a, s4, s5)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s4)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s5)),
% 289.07/181.57 inference(modus_ponens,[status(thm)],[1485, 1484])).
% 289.07/181.57 tff(1487,plain,
% 289.07/181.57 ($false),
% 289.07/181.57 inference(unit_resolution,[status(thm)],[1486, 1483, 1473, 1448, 1447])).
% 289.07/181.57 tff(1488,plain,(m_mutex_h_half_v_out(c_e_h_3, c_a, s5) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s4)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s4))), inference(lemma,lemma(discharge,[]))).
% 289.07/181.58 tff(1489,plain,
% 289.07/181.58 (m_mutex_h_half_v_out(c_e_h_3, c_a, s5)),
% 289.07/181.58 inference(unit_resolution,[status(thm)],[1488, 1446, 2])).
% 289.07/181.58 tff(1490,assumption,(m_mutex_h_half_v_inp(c_e_h_3, c_a, s5)), introduced(assumption)).
% 289.07/181.58 tff(1491,assumption,(~m_mutex_h_half_v_out(c_e_h_3, c_a, s6)), introduced(assumption)).
% 289.07/181.58 tff(1492,assumption,(m_mutex_h_half_v_out(c_e_h_3, c_a, s5)), introduced(assumption)).
% 289.07/181.58 tff(1493,assumption,(node13(c_e_h_3, c_a, s5, s6)), introduced(assumption)).
% 289.07/181.58 tff(1494,plain,
% 289.07/181.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s5)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s6) | (~node13(c_e_h_3, c_a, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s5)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s6) | (~node13(c_e_h_3, c_a, s5, s6)))),
% 289.07/181.58 inference(rewrite,[status(thm)],[])).
% 289.07/181.58 tff(1495,plain,
% 289.07/181.58 ((m_mutex_h_half_v_out(c_e_h_3, c_a, s6) | (~node13(c_e_h_3, c_a, s5, s6)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s5))) <=> ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s5)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s6) | (~node13(c_e_h_3, c_a, s5, s6)))),
% 289.07/181.58 inference(rewrite,[status(thm)],[])).
% 289.07/181.58 tff(1496,plain,
% 289.07/181.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s6) | (~node13(c_e_h_3, c_a, s5, s6)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s5)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s6) | (~node13(c_e_h_3, c_a, s5, s6))))),
% 289.07/181.58 inference(monotonicity,[status(thm)],[1495])).
% 289.07/181.58 tff(1497,plain,
% 289.07/181.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s6) | (~node13(c_e_h_3, c_a, s5, s6)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s5)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s6) | (~node13(c_e_h_3, c_a, s5, s6)))),
% 289.07/181.58 inference(transitivity,[status(thm)],[1496, 1494])).
% 289.07/181.58 tff(1498,plain,
% 289.07/181.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s6) | (~node13(c_e_h_3, c_a, s5, s6)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s5)))),
% 289.07/181.58 inference(quant_inst,[status(thm)],[])).
% 289.07/181.58 tff(1499,plain,
% 289.07/181.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s5)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s6) | (~node13(c_e_h_3, c_a, s5, s6))),
% 289.07/181.58 inference(modus_ponens,[status(thm)],[1498, 1497])).
% 289.07/181.58 tff(1500,plain,
% 289.07/181.58 ($false),
% 289.07/181.58 inference(unit_resolution,[status(thm)],[1499, 1459, 1493, 1492, 1491])).
% 289.07/181.58 tff(1501,plain,((~node13(c_e_h_3, c_a, s5, s6)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s5)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s6)), inference(lemma,lemma(discharge,[]))).
% 289.07/181.58 tff(1502,plain,
% 289.07/181.58 (~node13(c_e_h_3, c_a, s5, s6)),
% 289.07/181.58 inference(unit_resolution,[status(thm)],[1501, 1491, 1492])).
% 289.07/181.58 tff(1503,plain,
% 289.07/181.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s5, s6)) | node12(c_e_h_3, c_a, s5, s6) | node13(c_e_h_3, c_a, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s5, s6)) | node12(c_e_h_3, c_a, s5, s6) | node13(c_e_h_3, c_a, s5, s6))),
% 289.07/181.58 inference(rewrite,[status(thm)],[])).
% 289.07/181.58 tff(1504,plain,
% 289.07/181.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s5, s6)) | node12(c_e_h_3, c_a, s5, s6) | node13(c_e_h_3, c_a, s5, s6))),
% 289.07/181.58 inference(quant_inst,[status(thm)],[])).
% 289.07/181.58 tff(1505,plain,
% 289.07/181.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s5, s6)) | node12(c_e_h_3, c_a, s5, s6) | node13(c_e_h_3, c_a, s5, s6)),
% 289.07/181.58 inference(modus_ponens,[status(thm)],[1504, 1503])).
% 289.07/181.58 tff(1506,plain,
% 289.07/181.58 (node12(c_e_h_3, c_a, s5, s6) | node13(c_e_h_3, c_a, s5, s6)),
% 289.07/181.58 inference(unit_resolution,[status(thm)],[1505, 439, 1406])).
% 289.07/181.58 tff(1507,plain,
% 289.07/181.58 (node12(c_e_h_3, c_a, s5, s6)),
% 289.07/181.58 inference(unit_resolution,[status(thm)],[1506, 1502])).
% 289.07/181.58 tff(1508,plain,
% 289.07/181.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_a, s5)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s6) | (~node12(c_e_h_3, c_a, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s5)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s6) | (~node12(c_e_h_3, c_a, s5, s6)))),
% 289.07/181.58 inference(rewrite,[status(thm)],[])).
% 289.07/181.58 tff(1509,plain,
% 289.07/181.58 (((~node12(c_e_h_3, c_a, s5, s6)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s5)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s6)) <=> ((~m_mutex_h_half_v_inp(c_e_h_3, c_a, s5)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s6) | (~node12(c_e_h_3, c_a, s5, s6)))),
% 289.07/181.58 inference(rewrite,[status(thm)],[])).
% 289.07/181.58 tff(1510,plain,
% 289.07/181.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_3, c_a, s5, s6)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s5)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_a, s5)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s6) | (~node12(c_e_h_3, c_a, s5, s6))))),
% 289.07/181.58 inference(monotonicity,[status(thm)],[1509])).
% 289.07/181.58 tff(1511,plain,
% 289.07/181.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_3, c_a, s5, s6)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s5)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s5)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s6) | (~node12(c_e_h_3, c_a, s5, s6)))),
% 289.07/181.58 inference(transitivity,[status(thm)],[1510, 1508])).
% 289.07/181.58 tff(1512,plain,
% 289.07/181.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_3, c_a, s5, s6)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s5)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s6))),
% 289.07/181.58 inference(quant_inst,[status(thm)],[])).
% 289.07/181.58 tff(1513,plain,
% 289.07/181.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s5)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s6) | (~node12(c_e_h_3, c_a, s5, s6))),
% 289.07/181.58 inference(modus_ponens,[status(thm)],[1512, 1511])).
% 289.07/181.58 tff(1514,plain,
% 289.07/181.58 ($false),
% 289.07/181.58 inference(unit_resolution,[status(thm)],[1513, 1483, 1507, 1491, 1490])).
% 289.07/181.58 tff(1515,plain,(m_mutex_h_half_v_out(c_e_h_3, c_a, s6) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s5)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s5))), inference(lemma,lemma(discharge,[]))).
% 289.07/181.58 tff(1516,plain,
% 289.07/181.58 (m_mutex_h_half_v_out(c_e_h_3, c_a, s6)),
% 289.07/181.58 inference(unit_resolution,[status(thm)],[1515, 1489, 1439])).
% 289.07/181.58 tff(1517,assumption,(~m_mutex_h_half_v_out(c_e_h_3, c_a, s8)), introduced(assumption)).
% 289.07/181.58 tff(1518,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_r, s5)), introduced(assumption)).
% 289.07/181.58 tff(1519,assumption,(m_and_h_gate_v_out(c_e_h_3, c_k, s0)), introduced(assumption)).
% 289.07/181.58 tff(1520,plain,
% 289.07/181.58 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s0))),
% 289.07/181.58 inference(quant_inst,[status(thm)],[])).
% 289.07/181.58 tff(1521,plain,
% 289.07/181.58 ($false),
% 289.07/181.58 inference(unit_resolution,[status(thm)],[1520, 95, 1519])).
% 289.07/181.58 tff(1522,plain,(~m_and_h_gate_v_out(c_e_h_3, c_k, s0)), inference(lemma,lemma(discharge,[]))).
% 289.07/181.58 tff(1523,plain,
% 289.07/181.58 (^[I0: $i, X: $i] : refl(((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X)) <=> ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X)))),
% 289.07/181.58 inference(bind,[status(th)],[])).
% 289.07/181.58 tff(1524,plain,
% 289.07/181.58 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))),
% 289.07/181.58 inference(quant_intro,[status(thm)],[1523])).
% 289.07/181.58 tff(1525,plain,
% 289.07/181.58 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))),
% 289.07/181.58 inference(rewrite,[status(thm)],[])).
% 289.07/181.58 tff(1526,axiom,(![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_48')).
% 289.07/181.58 tff(1527,plain,
% 289.07/181.58 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))),
% 289.07/181.58 inference(modus_ponens,[status(thm)],[1526, 1525])).
% 289.07/181.58 tff(1528,plain,(
% 289.07/181.58 ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))),
% 289.07/181.58 inference(skolemize,[status(sab)],[1527])).
% 289.07/181.58 tff(1529,plain,
% 289.07/181.58 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))),
% 289.07/181.58 inference(modus_ponens,[status(thm)],[1528, 1524])).
% 289.07/181.58 tff(1530,plain,
% 289.07/181.58 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_l, s0)) | m_and_h_gate_v_out(c_e_h_3, c_k, s0))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s0)) | m_and_h_gate_v_out(c_e_h_3, c_k, s0))),
% 289.07/181.59 inference(rewrite,[status(thm)],[])).
% 289.07/181.59 tff(1531,plain,
% 289.07/181.59 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_l, s0)) | m_and_h_gate_v_out(c_e_h_3, c_k, s0))),
% 289.07/181.59 inference(quant_inst,[status(thm)],[])).
% 289.07/181.59 tff(1532,plain,
% 289.07/181.59 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s0)) | m_and_h_gate_v_out(c_e_h_3, c_k, s0)),
% 289.07/181.59 inference(modus_ponens,[status(thm)],[1531, 1530])).
% 289.07/181.59 tff(1533,plain,
% 289.07/181.59 (~m_and_h_gate_v_in1(c_e_h_3, c_l, s0)),
% 289.07/181.59 inference(unit_resolution,[status(thm)],[1532, 1529, 1522])).
% 289.07/181.59 tff(1534,plain,
% 289.07/181.59 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_l, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_l, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s0))),
% 289.07/181.59 inference(rewrite,[status(thm)],[])).
% 289.07/181.59 tff(1535,plain,
% 289.07/181.59 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_l, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s0))),
% 289.07/181.59 inference(quant_inst,[status(thm)],[])).
% 289.07/181.59 tff(1536,plain,
% 289.07/181.59 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_l, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s0)),
% 289.07/181.59 inference(modus_ponens,[status(thm)],[1535, 1534])).
% 289.07/181.59 tff(1537,plain,
% 289.07/181.59 (~node20(c_e_h_3, c_l, s0)),
% 289.07/181.59 inference(unit_resolution,[status(thm)],[1536, 38, 1533])).
% 289.07/181.59 tff(1538,assumption,(m_and_h_gate_v_out(c_e_h_3, c_l, s1)), introduced(assumption)).
% 289.07/181.59 tff(1539,assumption,(node22(c_e_h_3, c_l, s0, s1)), introduced(assumption)).
% 289.07/181.59 tff(1540,plain,
% 289.07/181.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s1)) | (~node22(c_e_h_3, c_l, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_l, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s1)) | (~node22(c_e_h_3, c_l, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_l, s0))),
% 289.07/181.59 inference(rewrite,[status(thm)],[])).
% 289.07/181.59 tff(1541,plain,
% 289.07/181.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s1)) | (~node22(c_e_h_3, c_l, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_l, s0))),
% 289.07/181.59 inference(quant_inst,[status(thm)],[])).
% 289.07/181.59 tff(1542,plain,
% 289.07/181.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s1)) | (~node22(c_e_h_3, c_l, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_l, s0)),
% 289.07/181.59 inference(modus_ponens,[status(thm)],[1541, 1540])).
% 289.07/181.59 tff(1543,plain,
% 289.07/181.59 ($false),
% 289.07/181.59 inference(unit_resolution,[status(thm)],[1542, 108, 1538, 1539, 1093])).
% 289.07/181.59 tff(1544,plain,((~node22(c_e_h_3, c_l, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s1))), inference(lemma,lemma(discharge,[]))).
% 289.07/181.59 tff(1545,plain,
% 289.07/181.59 (~node22(c_e_h_3, c_l, s0, s1)),
% 289.07/181.59 inference(unit_resolution,[status(thm)],[1544, 1538])).
% 289.07/181.59 tff(1546,plain,
% 289.07/181.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_3, c_l, s0, s1) | node22(c_e_h_3, c_l, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_3, c_l, s0, s1) | node22(c_e_h_3, c_l, s0, s1))),
% 289.07/181.59 inference(rewrite,[status(thm)],[])).
% 289.07/181.59 tff(1547,plain,
% 289.07/181.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_3, c_l, s0, s1) | node22(c_e_h_3, c_l, s0, s1))),
% 289.07/181.59 inference(quant_inst,[status(thm)],[])).
% 289.07/181.59 tff(1548,plain,
% 289.07/181.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_3, c_l, s0, s1) | node22(c_e_h_3, c_l, s0, s1)),
% 289.07/181.59 inference(modus_ponens,[status(thm)],[1547, 1546])).
% 289.07/181.59 tff(1549,plain,
% 289.07/181.59 (node21(c_e_h_3, c_l, s0, s1) | node22(c_e_h_3, c_l, s0, s1)),
% 289.07/181.59 inference(unit_resolution,[status(thm)],[1548, 82, 72])).
% 289.07/181.59 tff(1550,plain,
% 289.07/181.59 (node21(c_e_h_3, c_l, s0, s1)),
% 289.07/181.59 inference(unit_resolution,[status(thm)],[1549, 1545])).
% 289.07/181.59 tff(1551,plain,
% 289.07/181.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s1)) | node20(c_e_h_3, c_l, s0) | (~node21(c_e_h_3, c_l, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s1)) | node20(c_e_h_3, c_l, s0) | (~node21(c_e_h_3, c_l, s0, s1)))),
% 289.07/181.59 inference(rewrite,[status(thm)],[])).
% 289.07/181.59 tff(1552,plain,
% 289.07/181.59 ((node20(c_e_h_3, c_l, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s1)) | (~node21(c_e_h_3, c_l, s0, s1))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_l, s1)) | node20(c_e_h_3, c_l, s0) | (~node21(c_e_h_3, c_l, s0, s1)))),
% 289.07/181.59 inference(rewrite,[status(thm)],[])).
% 289.07/181.59 tff(1553,plain,
% 289.07/181.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s1)) | (~node21(c_e_h_3, c_l, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s1)) | node20(c_e_h_3, c_l, s0) | (~node21(c_e_h_3, c_l, s0, s1))))),
% 289.07/181.59 inference(monotonicity,[status(thm)],[1552])).
% 289.07/181.59 tff(1554,plain,
% 289.07/181.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s1)) | (~node21(c_e_h_3, c_l, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s1)) | node20(c_e_h_3, c_l, s0) | (~node21(c_e_h_3, c_l, s0, s1)))),
% 289.07/181.59 inference(transitivity,[status(thm)],[1553, 1551])).
% 289.07/181.59 tff(1555,plain,
% 289.07/181.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s1)) | (~node21(c_e_h_3, c_l, s0, s1)))),
% 289.07/181.59 inference(quant_inst,[status(thm)],[])).
% 289.07/181.59 tff(1556,plain,
% 289.07/181.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s1)) | node20(c_e_h_3, c_l, s0) | (~node21(c_e_h_3, c_l, s0, s1))),
% 289.07/181.59 inference(modus_ponens,[status(thm)],[1555, 1554])).
% 289.07/181.59 tff(1557,plain,
% 289.07/181.59 ($false),
% 289.07/181.59 inference(unit_resolution,[status(thm)],[1556, 52, 1538, 1550, 1537])).
% 289.07/181.59 tff(1558,plain,(~m_and_h_gate_v_out(c_e_h_3, c_l, s1)), inference(lemma,lemma(discharge,[]))).
% 289.07/181.59 tff(1559,plain,
% 289.07/181.59 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_j, s1)) | m_and_h_gate_v_out(c_e_h_3, c_l, s1))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s1)) | m_and_h_gate_v_out(c_e_h_3, c_l, s1))),
% 289.07/181.59 inference(rewrite,[status(thm)],[])).
% 289.07/181.59 tff(1560,plain,
% 289.07/181.59 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_j, s1)) | m_and_h_gate_v_out(c_e_h_3, c_l, s1))),
% 289.07/181.59 inference(quant_inst,[status(thm)],[])).
% 289.07/181.59 tff(1561,plain,
% 289.07/181.59 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s1)) | m_and_h_gate_v_out(c_e_h_3, c_l, s1)),
% 289.07/181.59 inference(modus_ponens,[status(thm)],[1560, 1559])).
% 289.07/181.59 tff(1562,plain,
% 289.07/181.59 (~m_or_h_gate_v_in1(c_e_h_3, c_j, s1)),
% 289.07/181.59 inference(unit_resolution,[status(thm)],[1561, 1100, 1558])).
% 289.07/181.59 tff(1563,assumption,(m_and_h_gate_v_out(c_e_h_2, c_q, s1)), introduced(assumption)).
% 289.07/181.59 tff(1564,assumption,(node22(c_e_h_2, c_q, s0, s1)), introduced(assumption)).
% 289.07/181.59 tff(1565,plain,
% 289.07/181.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s1)) | (~node22(c_e_h_2, c_q, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_q, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s1)) | (~node22(c_e_h_2, c_q, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_q, s0))),
% 289.07/181.59 inference(rewrite,[status(thm)],[])).
% 289.07/181.59 tff(1566,plain,
% 289.07/181.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s1)) | (~node22(c_e_h_2, c_q, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_q, s0))),
% 289.07/181.59 inference(quant_inst,[status(thm)],[])).
% 289.07/181.59 tff(1567,plain,
% 289.07/181.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s1)) | (~node22(c_e_h_2, c_q, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_q, s0)),
% 289.07/181.59 inference(modus_ponens,[status(thm)],[1566, 1565])).
% 289.07/181.59 tff(1568,plain,
% 289.07/181.59 ($false),
% 289.07/181.59 inference(unit_resolution,[status(thm)],[1567, 108, 1049, 1563, 1564])).
% 289.07/181.59 tff(1569,plain,((~node22(c_e_h_2, c_q, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s1))), inference(lemma,lemma(discharge,[]))).
% 289.07/181.59 tff(1570,plain,
% 289.07/181.59 (~node22(c_e_h_2, c_q, s0, s1)),
% 289.07/181.59 inference(unit_resolution,[status(thm)],[1569, 1563])).
% 289.07/181.59 tff(1571,plain,
% 289.07/181.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_2, c_q, s0, s1) | node22(c_e_h_2, c_q, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_2, c_q, s0, s1) | node22(c_e_h_2, c_q, s0, s1))),
% 289.07/181.60 inference(rewrite,[status(thm)],[])).
% 289.07/181.60 tff(1572,plain,
% 289.07/181.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_2, c_q, s0, s1) | node22(c_e_h_2, c_q, s0, s1))),
% 289.07/181.60 inference(quant_inst,[status(thm)],[])).
% 289.07/181.60 tff(1573,plain,
% 289.07/181.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_2, c_q, s0, s1) | node22(c_e_h_2, c_q, s0, s1)),
% 289.07/181.60 inference(modus_ponens,[status(thm)],[1572, 1571])).
% 289.07/181.60 tff(1574,plain,
% 289.07/181.60 (node21(c_e_h_2, c_q, s0, s1) | node22(c_e_h_2, c_q, s0, s1)),
% 289.07/181.60 inference(unit_resolution,[status(thm)],[1573, 82, 72])).
% 289.07/181.60 tff(1575,plain,
% 289.07/181.60 (node21(c_e_h_2, c_q, s0, s1)),
% 289.07/181.60 inference(unit_resolution,[status(thm)],[1574, 1570])).
% 289.07/181.60 tff(1576,assumption,(m_c_h_element_v_out(c_e_h_2, c_f, s0)), introduced(assumption)).
% 289.07/181.60 tff(1577,plain,
% 289.07/181.60 ((~![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s0))),
% 289.07/181.60 inference(quant_inst,[status(thm)],[])).
% 289.07/181.60 tff(1578,plain,
% 289.07/181.60 ($false),
% 289.07/181.60 inference(unit_resolution,[status(thm)],[1577, 14, 1576])).
% 289.07/181.60 tff(1579,plain,(~m_c_h_element_v_out(c_e_h_2, c_f, s0)), inference(lemma,lemma(discharge,[]))).
% 289.07/181.60 tff(1580,plain,
% 289.07/181.60 (^[I0: $i, X: $i] : refl(((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X)) <=> ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X)))),
% 289.07/181.60 inference(bind,[status(th)],[])).
% 289.07/181.60 tff(1581,plain,
% 289.07/181.60 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))),
% 289.07/181.60 inference(quant_intro,[status(thm)],[1580])).
% 289.07/181.60 tff(1582,plain,
% 289.07/181.60 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))),
% 289.07/181.60 inference(rewrite,[status(thm)],[])).
% 289.07/181.60 tff(1583,axiom,(![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_68')).
% 289.07/181.60 tff(1584,plain,
% 289.07/181.60 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))),
% 289.07/181.60 inference(modus_ponens,[status(thm)],[1583, 1582])).
% 289.07/181.60 tff(1585,plain,(
% 289.07/181.60 ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))),
% 289.07/181.60 inference(skolemize,[status(sab)],[1584])).
% 289.07/181.60 tff(1586,plain,
% 289.07/181.60 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))),
% 289.07/181.60 inference(modus_ponens,[status(thm)],[1585, 1581])).
% 289.07/181.60 tff(1587,plain,
% 289.07/181.60 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_q, s0)) | m_c_h_element_v_out(c_e_h_2, c_f, s0))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_q, s0)) | m_c_h_element_v_out(c_e_h_2, c_f, s0))),
% 289.07/181.60 inference(rewrite,[status(thm)],[])).
% 289.07/181.60 tff(1588,plain,
% 289.07/181.60 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_q, s0)) | m_c_h_element_v_out(c_e_h_2, c_f, s0))),
% 289.07/181.60 inference(quant_inst,[status(thm)],[])).
% 289.07/181.60 tff(1589,plain,
% 289.07/181.60 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_q, s0)) | m_c_h_element_v_out(c_e_h_2, c_f, s0)),
% 289.07/181.60 inference(modus_ponens,[status(thm)],[1588, 1587])).
% 289.07/181.60 tff(1590,plain,
% 289.07/181.60 (~m_and_h_gate_v_in1(c_e_h_2, c_q, s0)),
% 289.07/181.60 inference(unit_resolution,[status(thm)],[1589, 1586, 1579])).
% 289.07/181.60 tff(1591,plain,
% 289.07/181.60 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_q, s0)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_q, s0)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s0))),
% 289.07/181.60 inference(rewrite,[status(thm)],[])).
% 289.07/181.60 tff(1592,plain,
% 289.07/181.60 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_q, s0)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s0))),
% 289.07/181.60 inference(quant_inst,[status(thm)],[])).
% 289.07/181.60 tff(1593,plain,
% 289.07/181.60 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_q, s0)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s0)),
% 289.07/181.60 inference(modus_ponens,[status(thm)],[1592, 1591])).
% 289.07/181.60 tff(1594,plain,
% 289.07/181.60 (~node20(c_e_h_2, c_q, s0)),
% 289.07/181.60 inference(unit_resolution,[status(thm)],[1593, 38, 1590])).
% 289.07/181.60 tff(1595,plain,
% 289.07/181.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s1)) | node20(c_e_h_2, c_q, s0) | (~node21(c_e_h_2, c_q, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s1)) | node20(c_e_h_2, c_q, s0) | (~node21(c_e_h_2, c_q, s0, s1)))),
% 289.07/181.60 inference(rewrite,[status(thm)],[])).
% 289.07/181.60 tff(1596,plain,
% 289.07/181.60 ((node20(c_e_h_2, c_q, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s1)) | (~node21(c_e_h_2, c_q, s0, s1))) <=> ((~m_and_h_gate_v_out(c_e_h_2, c_q, s1)) | node20(c_e_h_2, c_q, s0) | (~node21(c_e_h_2, c_q, s0, s1)))),
% 289.07/181.60 inference(rewrite,[status(thm)],[])).
% 289.07/181.60 tff(1597,plain,
% 289.07/181.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_q, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s1)) | (~node21(c_e_h_2, c_q, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s1)) | node20(c_e_h_2, c_q, s0) | (~node21(c_e_h_2, c_q, s0, s1))))),
% 289.07/181.60 inference(monotonicity,[status(thm)],[1596])).
% 289.07/181.60 tff(1598,plain,
% 289.07/181.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_q, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s1)) | (~node21(c_e_h_2, c_q, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s1)) | node20(c_e_h_2, c_q, s0) | (~node21(c_e_h_2, c_q, s0, s1)))),
% 289.07/181.60 inference(transitivity,[status(thm)],[1597, 1595])).
% 289.07/181.60 tff(1599,plain,
% 289.07/181.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_q, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s1)) | (~node21(c_e_h_2, c_q, s0, s1)))),
% 289.07/181.60 inference(quant_inst,[status(thm)],[])).
% 289.07/181.60 tff(1600,plain,
% 289.07/181.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s1)) | node20(c_e_h_2, c_q, s0) | (~node21(c_e_h_2, c_q, s0, s1))),
% 289.07/181.60 inference(modus_ponens,[status(thm)],[1599, 1598])).
% 289.07/181.60 tff(1601,plain,
% 289.07/181.60 ($false),
% 289.07/181.60 inference(unit_resolution,[status(thm)],[1600, 52, 1563, 1594, 1575])).
% 289.07/181.60 tff(1602,plain,(~m_and_h_gate_v_out(c_e_h_2, c_q, s1)), inference(lemma,lemma(discharge,[]))).
% 289.07/181.60 tff(1603,plain,
% 289.07/181.60 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s1))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s1))),
% 289.07/181.60 inference(rewrite,[status(thm)],[])).
% 289.07/181.60 tff(1604,plain,
% 289.07/181.60 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s1))),
% 289.07/181.60 inference(quant_inst,[status(thm)],[])).
% 289.07/181.60 tff(1605,plain,
% 289.07/181.60 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s1)),
% 289.15/181.60 inference(modus_ponens,[status(thm)],[1604, 1603])).
% 289.15/181.60 tff(1606,plain,
% 289.15/181.60 (node3(c_e_h_2, c_e_h_3, s1)),
% 289.15/181.60 inference(unit_resolution,[status(thm)],[1605, 1059, 1056])).
% 289.15/181.60 tff(1607,plain,
% 289.15/181.60 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_3, s1)) | (~node3(c_e_h_2, c_e_h_3, s1)) | m_and_h_gate_v_out(c_e_h_2, c_q, s1))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_3, s1)) | (~node3(c_e_h_2, c_e_h_3, s1)) | m_and_h_gate_v_out(c_e_h_2, c_q, s1))),
% 289.15/181.60 inference(rewrite,[status(thm)],[])).
% 289.15/181.60 tff(1608,plain,
% 289.15/181.60 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_3, s1)) | (~node3(c_e_h_2, c_e_h_3, s1)) | m_and_h_gate_v_out(c_e_h_2, c_q, s1))),
% 289.15/181.60 inference(quant_inst,[status(thm)],[])).
% 289.15/181.60 tff(1609,plain,
% 289.15/181.60 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_3, s1)) | (~node3(c_e_h_2, c_e_h_3, s1)) | m_and_h_gate_v_out(c_e_h_2, c_q, s1)),
% 289.15/181.60 inference(modus_ponens,[status(thm)],[1608, 1607])).
% 289.15/181.60 tff(1610,plain,
% 289.15/181.60 ((~m_cell_v_ack(c_e_h_3, s1)) | m_and_h_gate_v_out(c_e_h_2, c_q, s1)),
% 289.15/181.60 inference(unit_resolution,[status(thm)],[1609, 1073, 1606])).
% 289.15/181.60 tff(1611,plain,
% 289.15/181.60 (~m_cell_v_ack(c_e_h_3, s1)),
% 289.15/181.60 inference(unit_resolution,[status(thm)],[1610, 1602])).
% 289.15/181.60 tff(1612,plain,
% 289.15/181.60 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_j, s1)) | m_cell_v_ack(c_e_h_3, s1))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_j, s1)) | m_cell_v_ack(c_e_h_3, s1))),
% 289.15/181.60 inference(rewrite,[status(thm)],[])).
% 289.15/181.60 tff(1613,plain,
% 289.15/181.60 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_j, s1)) | m_cell_v_ack(c_e_h_3, s1))),
% 289.15/181.60 inference(quant_inst,[status(thm)],[])).
% 289.15/181.60 tff(1614,plain,
% 289.15/181.60 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_j, s1)) | m_cell_v_ack(c_e_h_3, s1)),
% 289.15/181.60 inference(modus_ponens,[status(thm)],[1613, 1612])).
% 289.15/181.60 tff(1615,plain,
% 289.15/181.60 (~m_or_h_gate_v_in2(c_e_h_3, c_j, s1)),
% 289.15/181.60 inference(unit_resolution,[status(thm)],[1614, 1085, 1611])).
% 289.15/181.60 tff(1616,assumption,(m_or_h_gate_v_out(c_e_h_3, c_j, s2)), introduced(assumption)).
% 289.15/181.60 tff(1617,assumption,(node6(c_e_h_3, c_j, s1, s2)), introduced(assumption)).
% 289.15/181.60 tff(1618,plain,
% 289.15/181.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_3, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s2)) | (~node6(c_e_h_3, c_j, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s2)) | (~node6(c_e_h_3, c_j, s1, s2)))),
% 289.15/181.60 inference(rewrite,[status(thm)],[])).
% 289.15/181.60 tff(1619,plain,
% 289.15/181.60 (((~node6(c_e_h_3, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s2)) | m_or_h_gate_v_out(c_e_h_3, c_j, s1)) <=> (m_or_h_gate_v_out(c_e_h_3, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s2)) | (~node6(c_e_h_3, c_j, s1, s2)))),
% 289.15/181.60 inference(rewrite,[status(thm)],[])).
% 289.15/181.60 tff(1620,plain,
% 289.15/181.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s2)) | m_or_h_gate_v_out(c_e_h_3, c_j, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_3, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s2)) | (~node6(c_e_h_3, c_j, s1, s2))))),
% 289.15/181.60 inference(monotonicity,[status(thm)],[1619])).
% 289.15/181.61 tff(1621,plain,
% 289.15/181.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s2)) | m_or_h_gate_v_out(c_e_h_3, c_j, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s2)) | (~node6(c_e_h_3, c_j, s1, s2)))),
% 289.15/181.61 inference(transitivity,[status(thm)],[1620, 1618])).
% 289.15/181.61 tff(1622,plain,
% 289.15/181.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s2)) | m_or_h_gate_v_out(c_e_h_3, c_j, s1))),
% 289.15/181.61 inference(quant_inst,[status(thm)],[])).
% 289.15/181.61 tff(1623,plain,
% 289.15/181.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s2)) | (~node6(c_e_h_3, c_j, s1, s2))),
% 289.15/181.61 inference(modus_ponens,[status(thm)],[1622, 1621])).
% 289.15/181.61 tff(1624,plain,
% 289.15/181.61 ($false),
% 289.15/181.61 inference(unit_resolution,[status(thm)],[1623, 1121, 1616, 1167, 1617])).
% 289.15/181.61 tff(1625,plain,((~node6(c_e_h_3, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s2))), inference(lemma,lemma(discharge,[]))).
% 289.15/181.61 tff(1626,plain,
% 289.15/181.61 (~node6(c_e_h_3, c_j, s1, s2)),
% 289.15/181.61 inference(unit_resolution,[status(thm)],[1625, 1616])).
% 289.15/181.61 tff(1627,plain,
% 289.15/181.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s1, s2)) | node5(c_e_h_3, c_j, s1, s2) | node6(c_e_h_3, c_j, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s1, s2)) | node5(c_e_h_3, c_j, s1, s2) | node6(c_e_h_3, c_j, s1, s2))),
% 289.15/181.61 inference(rewrite,[status(thm)],[])).
% 289.15/181.61 tff(1628,plain,
% 289.15/181.61 ((node6(c_e_h_3, c_j, s1, s2) | node5(c_e_h_3, c_j, s1, s2) | (~trans(s1, s2))) <=> ((~trans(s1, s2)) | node5(c_e_h_3, c_j, s1, s2) | node6(c_e_h_3, c_j, s1, s2))),
% 289.15/181.61 inference(rewrite,[status(thm)],[])).
% 289.15/181.61 tff(1629,plain,
% 289.15/181.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s1, s2) | node5(c_e_h_3, c_j, s1, s2) | (~trans(s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s1, s2)) | node5(c_e_h_3, c_j, s1, s2) | node6(c_e_h_3, c_j, s1, s2)))),
% 289.15/181.61 inference(monotonicity,[status(thm)],[1628])).
% 289.15/181.61 tff(1630,plain,
% 289.15/181.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s1, s2) | node5(c_e_h_3, c_j, s1, s2) | (~trans(s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s1, s2)) | node5(c_e_h_3, c_j, s1, s2) | node6(c_e_h_3, c_j, s1, s2))),
% 289.15/181.61 inference(transitivity,[status(thm)],[1629, 1627])).
% 289.15/181.61 tff(1631,plain,
% 289.15/181.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s1, s2) | node5(c_e_h_3, c_j, s1, s2) | (~trans(s1, s2)))),
% 289.15/181.61 inference(quant_inst,[status(thm)],[])).
% 289.15/181.61 tff(1632,plain,
% 289.15/181.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s1, s2)) | node5(c_e_h_3, c_j, s1, s2) | node6(c_e_h_3, c_j, s1, s2)),
% 289.15/181.61 inference(modus_ponens,[status(thm)],[1631, 1630])).
% 289.15/181.61 tff(1633,plain,
% 289.15/181.61 (node5(c_e_h_3, c_j, s1, s2) | node6(c_e_h_3, c_j, s1, s2)),
% 289.15/181.61 inference(unit_resolution,[status(thm)],[1632, 1141, 255])).
% 289.15/181.61 tff(1634,plain,
% 289.15/181.61 (node5(c_e_h_3, c_j, s1, s2)),
% 289.15/181.61 inference(unit_resolution,[status(thm)],[1633, 1626])).
% 289.15/181.61 tff(1635,plain,
% 289.15/181.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_3, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s2)) | (~node5(c_e_h_3, c_j, s1, s2)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_3, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s2)) | (~node5(c_e_h_3, c_j, s1, s2)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s1))),
% 289.15/181.61 inference(rewrite,[status(thm)],[])).
% 289.15/181.61 tff(1636,plain,
% 289.15/181.61 ((m_or_h_gate_v_in1(c_e_h_3, c_j, s1) | m_or_h_gate_v_in2(c_e_h_3, c_j, s1) | (~node5(c_e_h_3, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s2))) <=> (m_or_h_gate_v_in2(c_e_h_3, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s2)) | (~node5(c_e_h_3, c_j, s1, s2)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s1))),
% 289.15/181.61 inference(rewrite,[status(thm)],[])).
% 289.15/181.61 tff(1637,plain,
% 289.15/181.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s1) | m_or_h_gate_v_in2(c_e_h_3, c_j, s1) | (~node5(c_e_h_3, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_3, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s2)) | (~node5(c_e_h_3, c_j, s1, s2)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s1)))),
% 289.15/181.61 inference(monotonicity,[status(thm)],[1636])).
% 289.15/181.61 tff(1638,plain,
% 289.15/181.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s1) | m_or_h_gate_v_in2(c_e_h_3, c_j, s1) | (~node5(c_e_h_3, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_3, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s2)) | (~node5(c_e_h_3, c_j, s1, s2)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s1))),
% 289.15/181.61 inference(transitivity,[status(thm)],[1637, 1635])).
% 289.15/181.61 tff(1639,plain,
% 289.15/181.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s1) | m_or_h_gate_v_in2(c_e_h_3, c_j, s1) | (~node5(c_e_h_3, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s2)))),
% 289.15/181.61 inference(quant_inst,[status(thm)],[])).
% 289.15/181.61 tff(1640,plain,
% 289.15/181.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_3, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s2)) | (~node5(c_e_h_3, c_j, s1, s2)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s1)),
% 289.15/181.61 inference(modus_ponens,[status(thm)],[1639, 1638])).
% 289.15/181.61 tff(1641,plain,
% 289.15/181.61 ($false),
% 289.15/181.61 inference(unit_resolution,[status(thm)],[1640, 1159, 1616, 1634, 1615, 1562])).
% 289.15/181.61 tff(1642,plain,(~m_or_h_gate_v_out(c_e_h_3, c_j, s2)), inference(lemma,lemma(discharge,[]))).
% 289.15/181.61 tff(1643,plain,
% 289.15/181.61 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s2)) | m_or_h_gate_v_out(c_e_h_3, c_j, s2))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s2)) | m_or_h_gate_v_out(c_e_h_3, c_j, s2))),
% 289.15/181.61 inference(rewrite,[status(thm)],[])).
% 289.15/181.61 tff(1644,plain,
% 289.15/181.61 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s2)) | m_or_h_gate_v_out(c_e_h_3, c_j, s2))),
% 289.15/181.61 inference(quant_inst,[status(thm)],[])).
% 289.15/181.61 tff(1645,plain,
% 289.15/181.61 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s2)) | m_or_h_gate_v_out(c_e_h_3, c_j, s2)),
% 289.15/181.61 inference(modus_ponens,[status(thm)],[1644, 1643])).
% 289.15/181.62 tff(1646,plain,
% 289.15/181.62 (~m_c_h_element_v_in2(c_e_h_3, c_h, s2)),
% 289.15/181.62 inference(unit_resolution,[status(thm)],[1645, 1174, 1642])).
% 289.15/181.62 tff(1647,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_h, s2)), introduced(assumption)).
% 289.15/181.62 tff(1648,assumption,(m_c_h_element_v_out(c_e_h_3, c_h, s3)), introduced(assumption)).
% 289.15/181.62 tff(1649,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_h, s2)), introduced(assumption)).
% 289.15/181.62 tff(1650,assumption,(node15(c_e_h_3, c_h, s2, s3)), introduced(assumption)).
% 289.15/181.62 tff(1651,plain,
% 289.15/181.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s3)) | (~node15(c_e_h_3, c_h, s2, s3)) | m_c_h_element_v_out(c_e_h_3, c_h, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s3)) | (~node15(c_e_h_3, c_h, s2, s3)) | m_c_h_element_v_out(c_e_h_3, c_h, s2))),
% 289.15/181.62 inference(rewrite,[status(thm)],[])).
% 289.15/181.62 tff(1652,plain,
% 289.15/181.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s3)) | (~node15(c_e_h_3, c_h, s2, s3)) | m_c_h_element_v_out(c_e_h_3, c_h, s2))),
% 289.15/181.62 inference(quant_inst,[status(thm)],[])).
% 289.15/181.62 tff(1653,plain,
% 289.15/181.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s3)) | (~node15(c_e_h_3, c_h, s2, s3)) | m_c_h_element_v_out(c_e_h_3, c_h, s2)),
% 289.15/181.62 inference(modus_ponens,[status(thm)],[1652, 1651])).
% 289.15/181.62 tff(1654,plain,
% 289.15/181.62 ($false),
% 289.15/181.62 inference(unit_resolution,[status(thm)],[1653, 147, 1648, 1243, 1650])).
% 289.15/181.62 tff(1655,plain,((~node15(c_e_h_3, c_h, s2, s3)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s3))), inference(lemma,lemma(discharge,[]))).
% 289.15/181.62 tff(1656,plain,
% 289.15/181.62 (~node15(c_e_h_3, c_h, s2, s3)),
% 289.15/181.62 inference(unit_resolution,[status(thm)],[1655, 1648])).
% 289.15/181.62 tff(1657,plain,
% 289.15/181.62 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_h, s2)) | m_c_h_element_v_in1(c_e_h_3, c_h, s2) | m_c_h_element_v_in2(c_e_h_3, c_h, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_h, s2)) | m_c_h_element_v_in1(c_e_h_3, c_h, s2) | m_c_h_element_v_in2(c_e_h_3, c_h, s2))),
% 289.15/181.62 inference(rewrite,[status(thm)],[])).
% 289.15/181.62 tff(1658,plain,
% 289.15/181.62 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_h, s2)) | m_c_h_element_v_in1(c_e_h_3, c_h, s2) | m_c_h_element_v_in2(c_e_h_3, c_h, s2))),
% 289.15/181.62 inference(quant_inst,[status(thm)],[])).
% 289.15/181.62 tff(1659,plain,
% 289.15/181.62 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_h, s2)) | m_c_h_element_v_in1(c_e_h_3, c_h, s2) | m_c_h_element_v_in2(c_e_h_3, c_h, s2)),
% 289.15/181.62 inference(modus_ponens,[status(thm)],[1658, 1657])).
% 289.15/181.62 tff(1660,plain,
% 289.15/181.62 ((~node16(c_e_h_3, c_h, s2)) | m_c_h_element_v_in1(c_e_h_3, c_h, s2)),
% 289.15/181.62 inference(unit_resolution,[status(thm)],[1659, 178, 1647])).
% 289.15/181.62 tff(1661,plain,
% 289.15/181.62 (~node16(c_e_h_3, c_h, s2)),
% 289.15/181.62 inference(unit_resolution,[status(thm)],[1660, 1649])).
% 289.15/181.62 tff(1662,plain,
% 289.15/181.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s2, s3)) | node19(c_e_h_3, c_h, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s2, s3)) | node19(c_e_h_3, c_h, s2, s3))),
% 289.15/181.62 inference(rewrite,[status(thm)],[])).
% 289.15/181.62 tff(1663,plain,
% 289.15/181.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s2, s3)) | node19(c_e_h_3, c_h, s2, s3))),
% 289.15/181.62 inference(quant_inst,[status(thm)],[])).
% 289.15/181.62 tff(1664,plain,
% 289.15/181.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s2, s3)) | node19(c_e_h_3, c_h, s2, s3)),
% 289.15/181.62 inference(modus_ponens,[status(thm)],[1663, 1662])).
% 289.15/181.62 tff(1665,plain,
% 289.15/181.62 (node19(c_e_h_3, c_h, s2, s3)),
% 289.15/181.62 inference(unit_resolution,[status(thm)],[1664, 190, 318])).
% 289.15/181.62 tff(1666,plain,
% 289.15/181.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s2) | node15(c_e_h_3, c_h, s2, s3) | node14(c_e_h_3, c_h, s2, s3) | (~node19(c_e_h_3, c_h, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_h, s2) | node15(c_e_h_3, c_h, s2, s3) | node14(c_e_h_3, c_h, s2, s3) | (~node19(c_e_h_3, c_h, s2, s3)))),
% 289.15/181.62 inference(rewrite,[status(thm)],[])).
% 289.15/181.62 tff(1667,plain,
% 289.15/181.62 ((node16(c_e_h_3, c_h, s2) | node14(c_e_h_3, c_h, s2, s3) | node15(c_e_h_3, c_h, s2, s3) | (~node19(c_e_h_3, c_h, s2, s3))) <=> (node16(c_e_h_3, c_h, s2) | node15(c_e_h_3, c_h, s2, s3) | node14(c_e_h_3, c_h, s2, s3) | (~node19(c_e_h_3, c_h, s2, s3)))),
% 289.15/181.62 inference(rewrite,[status(thm)],[])).
% 289.15/181.62 tff(1668,plain,
% 289.15/181.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s2) | node14(c_e_h_3, c_h, s2, s3) | node15(c_e_h_3, c_h, s2, s3) | (~node19(c_e_h_3, c_h, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s2) | node15(c_e_h_3, c_h, s2, s3) | node14(c_e_h_3, c_h, s2, s3) | (~node19(c_e_h_3, c_h, s2, s3))))),
% 289.15/181.62 inference(monotonicity,[status(thm)],[1667])).
% 289.15/181.62 tff(1669,plain,
% 289.15/181.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s2) | node14(c_e_h_3, c_h, s2, s3) | node15(c_e_h_3, c_h, s2, s3) | (~node19(c_e_h_3, c_h, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_h, s2) | node15(c_e_h_3, c_h, s2, s3) | node14(c_e_h_3, c_h, s2, s3) | (~node19(c_e_h_3, c_h, s2, s3)))),
% 289.15/181.62 inference(transitivity,[status(thm)],[1668, 1666])).
% 289.15/181.62 tff(1670,plain,
% 289.15/181.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s2) | node14(c_e_h_3, c_h, s2, s3) | node15(c_e_h_3, c_h, s2, s3) | (~node19(c_e_h_3, c_h, s2, s3)))),
% 289.15/181.62 inference(quant_inst,[status(thm)],[])).
% 289.15/181.62 tff(1671,plain,
% 289.15/181.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_h, s2) | node15(c_e_h_3, c_h, s2, s3) | node14(c_e_h_3, c_h, s2, s3) | (~node19(c_e_h_3, c_h, s2, s3))),
% 289.15/181.62 inference(modus_ponens,[status(thm)],[1670, 1669])).
% 289.15/181.62 tff(1672,plain,
% 289.15/181.62 (node16(c_e_h_3, c_h, s2) | node15(c_e_h_3, c_h, s2, s3) | node14(c_e_h_3, c_h, s2, s3)),
% 289.15/181.62 inference(unit_resolution,[status(thm)],[1671, 204, 1665])).
% 289.15/181.62 tff(1673,plain,
% 289.15/181.62 (node14(c_e_h_3, c_h, s2, s3)),
% 289.15/181.62 inference(unit_resolution,[status(thm)],[1672, 1661, 1656])).
% 289.15/181.62 tff(1674,plain,
% 289.15/181.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s2) | (~m_c_h_element_v_out(c_e_h_3, c_h, s3)) | (~node14(c_e_h_3, c_h, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_h, s2) | (~m_c_h_element_v_out(c_e_h_3, c_h, s3)) | (~node14(c_e_h_3, c_h, s2, s3)))),
% 289.15/181.62 inference(rewrite,[status(thm)],[])).
% 289.15/181.62 tff(1675,plain,
% 289.15/181.62 (((~node14(c_e_h_3, c_h, s2, s3)) | m_c_h_element_v_in1(c_e_h_3, c_h, s2) | (~m_c_h_element_v_out(c_e_h_3, c_h, s3))) <=> (m_c_h_element_v_in1(c_e_h_3, c_h, s2) | (~m_c_h_element_v_out(c_e_h_3, c_h, s3)) | (~node14(c_e_h_3, c_h, s2, s3)))),
% 289.15/181.62 inference(rewrite,[status(thm)],[])).
% 289.15/181.63 tff(1676,plain,
% 289.15/181.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s2, s3)) | m_c_h_element_v_in1(c_e_h_3, c_h, s2) | (~m_c_h_element_v_out(c_e_h_3, c_h, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s2) | (~m_c_h_element_v_out(c_e_h_3, c_h, s3)) | (~node14(c_e_h_3, c_h, s2, s3))))),
% 289.15/181.63 inference(monotonicity,[status(thm)],[1675])).
% 289.15/181.63 tff(1677,plain,
% 289.15/181.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s2, s3)) | m_c_h_element_v_in1(c_e_h_3, c_h, s2) | (~m_c_h_element_v_out(c_e_h_3, c_h, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_h, s2) | (~m_c_h_element_v_out(c_e_h_3, c_h, s3)) | (~node14(c_e_h_3, c_h, s2, s3)))),
% 289.15/181.63 inference(transitivity,[status(thm)],[1676, 1674])).
% 289.15/181.63 tff(1678,plain,
% 289.15/181.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s2, s3)) | m_c_h_element_v_in1(c_e_h_3, c_h, s2) | (~m_c_h_element_v_out(c_e_h_3, c_h, s3)))),
% 289.15/181.63 inference(quant_inst,[status(thm)],[])).
% 289.15/181.63 tff(1679,plain,
% 289.15/181.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_h, s2) | (~m_c_h_element_v_out(c_e_h_3, c_h, s3)) | (~node14(c_e_h_3, c_h, s2, s3))),
% 289.15/181.63 inference(modus_ponens,[status(thm)],[1678, 1677])).
% 289.15/181.63 tff(1680,plain,
% 289.15/181.63 ($false),
% 289.15/181.63 inference(unit_resolution,[status(thm)],[1679, 223, 1648, 1673, 1649])).
% 289.15/181.63 tff(1681,plain,(m_c_h_element_v_in1(c_e_h_3, c_h, s2) | (~m_c_h_element_v_out(c_e_h_3, c_h, s3)) | m_c_h_element_v_in2(c_e_h_3, c_h, s2)), inference(lemma,lemma(discharge,[]))).
% 289.15/181.63 tff(1682,plain,
% 289.15/181.63 (m_c_h_element_v_in1(c_e_h_3, c_h, s2)),
% 289.15/181.63 inference(unit_resolution,[status(thm)],[1681, 1647, 1648])).
% 289.15/181.63 tff(1683,assumption,(node18(c_e_h_3, c_h, s2, s3)), introduced(assumption)).
% 289.15/181.63 tff(1684,plain,
% 289.15/181.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_h, s2) | (~m_c_h_element_v_out(c_e_h_3, c_h, s3)) | (~node18(c_e_h_3, c_h, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s2) | (~m_c_h_element_v_out(c_e_h_3, c_h, s3)) | (~node18(c_e_h_3, c_h, s2, s3)))),
% 289.15/181.63 inference(rewrite,[status(thm)],[])).
% 289.15/181.63 tff(1685,plain,
% 289.15/181.63 (((~m_c_h_element_v_out(c_e_h_3, c_h, s3)) | m_c_h_element_v_out(c_e_h_3, c_h, s2) | (~node18(c_e_h_3, c_h, s2, s3))) <=> (m_c_h_element_v_out(c_e_h_3, c_h, s2) | (~m_c_h_element_v_out(c_e_h_3, c_h, s3)) | (~node18(c_e_h_3, c_h, s2, s3)))),
% 289.15/181.63 inference(rewrite,[status(thm)],[])).
% 289.15/181.63 tff(1686,plain,
% 289.15/181.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s3)) | m_c_h_element_v_out(c_e_h_3, c_h, s2) | (~node18(c_e_h_3, c_h, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_h, s2) | (~m_c_h_element_v_out(c_e_h_3, c_h, s3)) | (~node18(c_e_h_3, c_h, s2, s3))))),
% 289.15/181.63 inference(monotonicity,[status(thm)],[1685])).
% 289.15/181.63 tff(1687,plain,
% 289.15/181.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s3)) | m_c_h_element_v_out(c_e_h_3, c_h, s2) | (~node18(c_e_h_3, c_h, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s2) | (~m_c_h_element_v_out(c_e_h_3, c_h, s3)) | (~node18(c_e_h_3, c_h, s2, s3)))),
% 289.15/181.63 inference(transitivity,[status(thm)],[1686, 1684])).
% 289.15/181.63 tff(1688,plain,
% 289.15/181.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s3)) | m_c_h_element_v_out(c_e_h_3, c_h, s2) | (~node18(c_e_h_3, c_h, s2, s3)))),
% 289.15/181.63 inference(quant_inst,[status(thm)],[])).
% 289.15/181.63 tff(1689,plain,
% 289.15/181.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s2) | (~m_c_h_element_v_out(c_e_h_3, c_h, s3)) | (~node18(c_e_h_3, c_h, s2, s3))),
% 289.15/181.63 inference(modus_ponens,[status(thm)],[1688, 1687])).
% 289.15/181.63 tff(1690,plain,
% 289.15/181.63 ($false),
% 289.15/181.63 inference(unit_resolution,[status(thm)],[1689, 753, 1648, 1243, 1683])).
% 289.15/181.63 tff(1691,plain,((~node18(c_e_h_3, c_h, s2, s3)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s3))), inference(lemma,lemma(discharge,[]))).
% 289.15/181.63 tff(1692,plain,
% 289.15/181.63 (~node18(c_e_h_3, c_h, s2, s3)),
% 289.15/181.63 inference(unit_resolution,[status(thm)],[1691, 1648])).
% 289.15/181.63 tff(1693,plain,
% 289.15/181.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s2) | (~node19(c_e_h_3, c_h, s2, s3)) | node18(c_e_h_3, c_h, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_h, s2) | (~node19(c_e_h_3, c_h, s2, s3)) | node18(c_e_h_3, c_h, s2, s3))),
% 289.15/181.63 inference(rewrite,[status(thm)],[])).
% 289.15/181.63 tff(1694,plain,
% 289.15/181.63 ((node17(c_e_h_3, c_h, s2) | node18(c_e_h_3, c_h, s2, s3) | (~node19(c_e_h_3, c_h, s2, s3))) <=> (node17(c_e_h_3, c_h, s2) | (~node19(c_e_h_3, c_h, s2, s3)) | node18(c_e_h_3, c_h, s2, s3))),
% 289.15/181.63 inference(rewrite,[status(thm)],[])).
% 289.15/181.63 tff(1695,plain,
% 289.15/181.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s2) | node18(c_e_h_3, c_h, s2, s3) | (~node19(c_e_h_3, c_h, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s2) | (~node19(c_e_h_3, c_h, s2, s3)) | node18(c_e_h_3, c_h, s2, s3)))),
% 289.15/181.63 inference(monotonicity,[status(thm)],[1694])).
% 289.15/181.63 tff(1696,plain,
% 289.15/181.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s2) | node18(c_e_h_3, c_h, s2, s3) | (~node19(c_e_h_3, c_h, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_h, s2) | (~node19(c_e_h_3, c_h, s2, s3)) | node18(c_e_h_3, c_h, s2, s3))),
% 289.15/181.63 inference(transitivity,[status(thm)],[1695, 1693])).
% 289.15/181.63 tff(1697,plain,
% 289.15/181.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s2) | node18(c_e_h_3, c_h, s2, s3) | (~node19(c_e_h_3, c_h, s2, s3)))),
% 289.15/181.63 inference(quant_inst,[status(thm)],[])).
% 289.15/181.63 tff(1698,plain,
% 289.15/181.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_h, s2) | (~node19(c_e_h_3, c_h, s2, s3)) | node18(c_e_h_3, c_h, s2, s3)),
% 289.15/181.63 inference(modus_ponens,[status(thm)],[1697, 1696])).
% 289.15/181.63 tff(1699,plain,
% 289.15/181.63 (node17(c_e_h_3, c_h, s2) | node18(c_e_h_3, c_h, s2, s3)),
% 289.15/181.63 inference(unit_resolution,[status(thm)],[1698, 776, 1665])).
% 289.15/181.63 tff(1700,plain,
% 289.15/181.63 (node17(c_e_h_3, c_h, s2)),
% 289.15/181.63 inference(unit_resolution,[status(thm)],[1699, 1692])).
% 289.15/181.63 tff(1701,plain,
% 289.15/181.63 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_h, s2)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s2)) | m_c_h_element_v_in2(c_e_h_3, c_h, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_h, s2)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s2)) | m_c_h_element_v_in2(c_e_h_3, c_h, s2))),
% 289.15/181.63 inference(rewrite,[status(thm)],[])).
% 289.15/181.63 tff(1702,plain,
% 289.15/181.63 (((~m_c_h_element_v_in1(c_e_h_3, c_h, s2)) | m_c_h_element_v_in2(c_e_h_3, c_h, s2) | (~node17(c_e_h_3, c_h, s2))) <=> ((~node17(c_e_h_3, c_h, s2)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s2)) | m_c_h_element_v_in2(c_e_h_3, c_h, s2))),
% 289.15/181.63 inference(rewrite,[status(thm)],[])).
% 289.15/181.63 tff(1703,plain,
% 289.15/181.63 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s2)) | m_c_h_element_v_in2(c_e_h_3, c_h, s2) | (~node17(c_e_h_3, c_h, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_h, s2)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s2)) | m_c_h_element_v_in2(c_e_h_3, c_h, s2)))),
% 289.15/181.63 inference(monotonicity,[status(thm)],[1702])).
% 289.15/181.63 tff(1704,plain,
% 289.15/181.63 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s2)) | m_c_h_element_v_in2(c_e_h_3, c_h, s2) | (~node17(c_e_h_3, c_h, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_h, s2)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s2)) | m_c_h_element_v_in2(c_e_h_3, c_h, s2))),
% 289.15/181.63 inference(transitivity,[status(thm)],[1703, 1701])).
% 289.15/181.63 tff(1705,plain,
% 289.15/181.63 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s2)) | m_c_h_element_v_in2(c_e_h_3, c_h, s2) | (~node17(c_e_h_3, c_h, s2)))),
% 289.15/181.63 inference(quant_inst,[status(thm)],[])).
% 289.15/181.63 tff(1706,plain,
% 289.15/181.63 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_h, s2)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s2)) | m_c_h_element_v_in2(c_e_h_3, c_h, s2)),
% 289.15/181.63 inference(modus_ponens,[status(thm)],[1705, 1704])).
% 289.15/181.63 tff(1707,plain,
% 289.15/181.63 ((~m_c_h_element_v_in1(c_e_h_3, c_h, s2)) | m_c_h_element_v_in2(c_e_h_3, c_h, s2)),
% 289.15/181.63 inference(unit_resolution,[status(thm)],[1706, 919, 1700])).
% 289.15/181.63 tff(1708,plain,
% 289.15/181.63 ($false),
% 289.15/181.63 inference(unit_resolution,[status(thm)],[1707, 1682, 1647])).
% 289.15/181.63 tff(1709,plain,(m_c_h_element_v_in2(c_e_h_3, c_h, s2) | (~m_c_h_element_v_out(c_e_h_3, c_h, s3))), inference(lemma,lemma(discharge,[]))).
% 289.15/181.63 tff(1710,plain,
% 289.15/181.63 (~m_c_h_element_v_out(c_e_h_3, c_h, s3)),
% 289.15/181.63 inference(unit_resolution,[status(thm)],[1709, 1646])).
% 289.15/181.63 tff(1711,plain,
% 289.15/181.63 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_i, s3)) | m_c_h_element_v_out(c_e_h_3, c_h, s3))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s3)) | m_c_h_element_v_out(c_e_h_3, c_h, s3))),
% 289.15/181.63 inference(rewrite,[status(thm)],[])).
% 289.15/181.63 tff(1712,plain,
% 289.15/181.63 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_i, s3)) | m_c_h_element_v_out(c_e_h_3, c_h, s3))),
% 289.15/181.63 inference(quant_inst,[status(thm)],[])).
% 289.15/181.63 tff(1713,plain,
% 289.15/181.63 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s3)) | m_c_h_element_v_out(c_e_h_3, c_h, s3)),
% 289.15/181.63 inference(modus_ponens,[status(thm)],[1712, 1711])).
% 289.15/181.63 tff(1714,plain,
% 289.15/181.63 (~m_and_h_gate_v_in1(c_e_h_3, c_i, s3)),
% 289.15/181.63 inference(unit_resolution,[status(thm)],[1713, 619, 1710])).
% 289.15/181.63 tff(1715,plain,
% 289.15/181.63 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_i, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s3))),
% 289.15/181.64 inference(rewrite,[status(thm)],[])).
% 289.15/181.64 tff(1716,plain,
% 289.15/181.64 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s3))),
% 289.15/181.64 inference(quant_inst,[status(thm)],[])).
% 289.15/181.64 tff(1717,plain,
% 289.15/181.64 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_i, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s3)),
% 289.15/181.64 inference(modus_ponens,[status(thm)],[1716, 1715])).
% 289.15/181.64 tff(1718,plain,
% 289.15/181.64 (~node20(c_e_h_3, c_i, s3)),
% 289.15/181.64 inference(unit_resolution,[status(thm)],[1717, 38, 1714])).
% 289.15/181.64 tff(1719,assumption,(m_and_h_gate_v_out(c_e_h_3, c_i, s4)), introduced(assumption)).
% 289.15/181.64 tff(1720,assumption,(node22(c_e_h_3, c_i, s3, s4)), introduced(assumption)).
% 289.15/181.64 tff(1721,plain,
% 289.15/181.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s4)) | (~node22(c_e_h_3, c_i, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_i, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s4)) | (~node22(c_e_h_3, c_i, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_i, s3))),
% 289.15/181.64 inference(rewrite,[status(thm)],[])).
% 289.15/181.64 tff(1722,plain,
% 289.15/181.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s4)) | (~node22(c_e_h_3, c_i, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_i, s3))),
% 289.15/181.64 inference(quant_inst,[status(thm)],[])).
% 289.15/181.64 tff(1723,plain,
% 289.15/181.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s4)) | (~node22(c_e_h_3, c_i, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_i, s3)),
% 289.15/181.64 inference(modus_ponens,[status(thm)],[1722, 1721])).
% 289.15/181.64 tff(1724,plain,
% 289.15/181.64 ($false),
% 289.15/181.64 inference(unit_resolution,[status(thm)],[1723, 108, 1269, 1720, 1719])).
% 289.15/181.64 tff(1725,plain,((~node22(c_e_h_3, c_i, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s4))), inference(lemma,lemma(discharge,[]))).
% 289.15/181.64 tff(1726,plain,
% 289.15/181.64 (~node22(c_e_h_3, c_i, s3, s4)),
% 289.15/181.64 inference(unit_resolution,[status(thm)],[1725, 1719])).
% 289.15/181.64 tff(1727,assumption,(~node20(c_e_h_3, c_i, s3)), introduced(assumption)).
% 289.15/181.64 tff(1728,assumption,(node21(c_e_h_3, c_i, s3, s4)), introduced(assumption)).
% 289.15/181.64 tff(1729,plain,
% 289.15/181.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s4)) | node20(c_e_h_3, c_i, s3) | (~node21(c_e_h_3, c_i, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s4)) | node20(c_e_h_3, c_i, s3) | (~node21(c_e_h_3, c_i, s3, s4)))),
% 289.15/181.64 inference(rewrite,[status(thm)],[])).
% 289.15/181.64 tff(1730,plain,
% 289.15/181.64 ((node20(c_e_h_3, c_i, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s4)) | (~node21(c_e_h_3, c_i, s3, s4))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_i, s4)) | node20(c_e_h_3, c_i, s3) | (~node21(c_e_h_3, c_i, s3, s4)))),
% 289.15/181.64 inference(rewrite,[status(thm)],[])).
% 289.15/181.64 tff(1731,plain,
% 289.15/181.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s4)) | (~node21(c_e_h_3, c_i, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s4)) | node20(c_e_h_3, c_i, s3) | (~node21(c_e_h_3, c_i, s3, s4))))),
% 289.15/181.64 inference(monotonicity,[status(thm)],[1730])).
% 289.15/181.64 tff(1732,plain,
% 289.15/181.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s4)) | (~node21(c_e_h_3, c_i, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s4)) | node20(c_e_h_3, c_i, s3) | (~node21(c_e_h_3, c_i, s3, s4)))),
% 289.15/181.64 inference(transitivity,[status(thm)],[1731, 1729])).
% 289.15/181.64 tff(1733,plain,
% 289.15/181.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s4)) | (~node21(c_e_h_3, c_i, s3, s4)))),
% 289.15/181.64 inference(quant_inst,[status(thm)],[])).
% 289.15/181.64 tff(1734,plain,
% 289.15/181.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s4)) | node20(c_e_h_3, c_i, s3) | (~node21(c_e_h_3, c_i, s3, s4))),
% 289.15/181.64 inference(modus_ponens,[status(thm)],[1733, 1732])).
% 289.15/181.64 tff(1735,plain,
% 289.15/181.64 ($false),
% 289.15/181.64 inference(unit_resolution,[status(thm)],[1734, 52, 1728, 1719, 1727])).
% 289.15/181.64 tff(1736,plain,((~node21(c_e_h_3, c_i, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s4)) | node20(c_e_h_3, c_i, s3)), inference(lemma,lemma(discharge,[]))).
% 289.15/181.64 tff(1737,plain,
% 289.15/181.64 (~node21(c_e_h_3, c_i, s3, s4)),
% 289.15/181.64 inference(unit_resolution,[status(thm)],[1736, 1719, 1727])).
% 289.15/181.64 tff(1738,plain,
% 289.15/181.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_3, c_i, s3, s4) | node22(c_e_h_3, c_i, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_3, c_i, s3, s4) | node22(c_e_h_3, c_i, s3, s4))),
% 289.15/181.64 inference(rewrite,[status(thm)],[])).
% 289.15/181.64 tff(1739,plain,
% 289.15/181.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_3, c_i, s3, s4) | node22(c_e_h_3, c_i, s3, s4))),
% 289.15/181.64 inference(quant_inst,[status(thm)],[])).
% 289.15/181.64 tff(1740,plain,
% 289.15/181.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_3, c_i, s3, s4) | node22(c_e_h_3, c_i, s3, s4)),
% 289.15/181.64 inference(modus_ponens,[status(thm)],[1739, 1738])).
% 289.15/181.64 tff(1741,plain,
% 289.15/181.64 (node21(c_e_h_3, c_i, s3, s4) | node22(c_e_h_3, c_i, s3, s4)),
% 289.15/181.64 inference(unit_resolution,[status(thm)],[1740, 82, 531])).
% 289.15/181.64 tff(1742,plain,
% 289.15/181.64 ($false),
% 289.15/181.64 inference(unit_resolution,[status(thm)],[1741, 1737, 1726])).
% 289.15/181.64 tff(1743,plain,((~m_and_h_gate_v_out(c_e_h_3, c_i, s4)) | node20(c_e_h_3, c_i, s3)), inference(lemma,lemma(discharge,[]))).
% 289.15/181.64 tff(1744,plain,
% 289.15/181.64 (~m_and_h_gate_v_out(c_e_h_3, c_i, s4)),
% 289.15/181.64 inference(unit_resolution,[status(thm)],[1743, 1718])).
% 289.15/181.64 tff(1745,assumption,(m_c_h_element_v_in2(c_e_h_3, c_e, s4)), introduced(assumption)).
% 289.15/181.64 tff(1746,plain,
% 289.15/181.64 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s4)) | m_and_h_gate_v_out(c_e_h_3, c_i, s4))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s4)) | m_and_h_gate_v_out(c_e_h_3, c_i, s4))),
% 289.15/181.64 inference(rewrite,[status(thm)],[])).
% 289.15/181.64 tff(1747,plain,
% 289.15/181.64 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s4)) | m_and_h_gate_v_out(c_e_h_3, c_i, s4))),
% 289.15/181.64 inference(quant_inst,[status(thm)],[])).
% 289.15/181.64 tff(1748,plain,
% 289.15/181.64 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s4)) | m_and_h_gate_v_out(c_e_h_3, c_i, s4)),
% 289.15/181.64 inference(modus_ponens,[status(thm)],[1747, 1746])).
% 289.15/181.64 tff(1749,plain,
% 289.15/181.64 ($false),
% 289.15/181.64 inference(unit_resolution,[status(thm)],[1748, 164, 1745, 1744])).
% 289.15/181.64 tff(1750,plain,(~m_c_h_element_v_in2(c_e_h_3, c_e, s4)), inference(lemma,lemma(discharge,[]))).
% 289.15/181.64 tff(1751,assumption,(m_c_h_element_v_out(c_e_h_3, c_e, s5)), introduced(assumption)).
% 289.15/181.64 tff(1752,assumption,(node15(c_e_h_3, c_e, s4, s5)), introduced(assumption)).
% 289.15/181.64 tff(1753,plain,
% 289.15/181.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s5)) | (~node15(c_e_h_3, c_e, s4, s5)) | m_c_h_element_v_out(c_e_h_3, c_e, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s5)) | (~node15(c_e_h_3, c_e, s4, s5)) | m_c_h_element_v_out(c_e_h_3, c_e, s4))),
% 289.15/181.64 inference(rewrite,[status(thm)],[])).
% 289.15/181.64 tff(1754,plain,
% 289.15/181.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s5)) | (~node15(c_e_h_3, c_e, s4, s5)) | m_c_h_element_v_out(c_e_h_3, c_e, s4))),
% 289.15/181.64 inference(quant_inst,[status(thm)],[])).
% 289.15/181.64 tff(1755,plain,
% 289.15/181.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s5)) | (~node15(c_e_h_3, c_e, s4, s5)) | m_c_h_element_v_out(c_e_h_3, c_e, s4)),
% 289.15/181.64 inference(modus_ponens,[status(thm)],[1754, 1753])).
% 289.15/181.64 tff(1756,plain,
% 289.15/181.64 ($false),
% 289.15/181.64 inference(unit_resolution,[status(thm)],[1755, 147, 1752, 1334, 1751])).
% 289.15/181.64 tff(1757,plain,((~node15(c_e_h_3, c_e, s4, s5)) | m_c_h_element_v_out(c_e_h_3, c_e, s4) | (~m_c_h_element_v_out(c_e_h_3, c_e, s5))), inference(lemma,lemma(discharge,[]))).
% 289.15/181.64 tff(1758,plain,
% 289.15/181.64 (~node15(c_e_h_3, c_e, s4, s5)),
% 289.15/181.64 inference(unit_resolution,[status(thm)],[1757, 1751, 1334])).
% 289.15/181.64 tff(1759,assumption,(node18(c_e_h_3, c_e, s4, s5)), introduced(assumption)).
% 289.15/181.64 tff(1760,plain,
% 289.15/181.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_e, s4) | (~node18(c_e_h_3, c_e, s4, s5)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s4) | (~node18(c_e_h_3, c_e, s4, s5)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s5)))),
% 289.15/181.64 inference(rewrite,[status(thm)],[])).
% 289.15/181.64 tff(1761,plain,
% 289.15/181.64 (((~m_c_h_element_v_out(c_e_h_3, c_e, s5)) | m_c_h_element_v_out(c_e_h_3, c_e, s4) | (~node18(c_e_h_3, c_e, s4, s5))) <=> (m_c_h_element_v_out(c_e_h_3, c_e, s4) | (~node18(c_e_h_3, c_e, s4, s5)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s5)))),
% 289.15/181.64 inference(rewrite,[status(thm)],[])).
% 289.15/181.64 tff(1762,plain,
% 289.15/181.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s5)) | m_c_h_element_v_out(c_e_h_3, c_e, s4) | (~node18(c_e_h_3, c_e, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_e, s4) | (~node18(c_e_h_3, c_e, s4, s5)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s5))))),
% 289.15/181.64 inference(monotonicity,[status(thm)],[1761])).
% 289.15/181.64 tff(1763,plain,
% 289.15/181.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s5)) | m_c_h_element_v_out(c_e_h_3, c_e, s4) | (~node18(c_e_h_3, c_e, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s4) | (~node18(c_e_h_3, c_e, s4, s5)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s5)))),
% 289.15/181.64 inference(transitivity,[status(thm)],[1762, 1760])).
% 289.15/181.64 tff(1764,plain,
% 289.15/181.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s5)) | m_c_h_element_v_out(c_e_h_3, c_e, s4) | (~node18(c_e_h_3, c_e, s4, s5)))),
% 289.15/181.64 inference(quant_inst,[status(thm)],[])).
% 289.15/181.64 tff(1765,plain,
% 289.15/181.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s4) | (~node18(c_e_h_3, c_e, s4, s5)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s5))),
% 289.15/181.65 inference(modus_ponens,[status(thm)],[1764, 1763])).
% 289.15/181.65 tff(1766,plain,
% 289.15/181.65 ($false),
% 289.15/181.65 inference(unit_resolution,[status(thm)],[1765, 753, 1759, 1334, 1751])).
% 289.15/181.65 tff(1767,plain,((~node18(c_e_h_3, c_e, s4, s5)) | m_c_h_element_v_out(c_e_h_3, c_e, s4) | (~m_c_h_element_v_out(c_e_h_3, c_e, s5))), inference(lemma,lemma(discharge,[]))).
% 289.15/181.65 tff(1768,plain,
% 289.15/181.65 (~node18(c_e_h_3, c_e, s4, s5)),
% 289.15/181.65 inference(unit_resolution,[status(thm)],[1767, 1751, 1334])).
% 289.15/181.65 tff(1769,plain,
% 289.15/181.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s4, s5)) | node19(c_e_h_3, c_e, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s4, s5)) | node19(c_e_h_3, c_e, s4, s5))),
% 289.15/181.65 inference(rewrite,[status(thm)],[])).
% 289.15/181.65 tff(1770,plain,
% 289.15/181.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s4, s5)) | node19(c_e_h_3, c_e, s4, s5))),
% 289.15/181.65 inference(quant_inst,[status(thm)],[])).
% 289.15/181.65 tff(1771,plain,
% 289.15/181.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s4, s5)) | node19(c_e_h_3, c_e, s4, s5)),
% 289.15/181.65 inference(modus_ponens,[status(thm)],[1770, 1769])).
% 289.15/181.65 tff(1772,plain,
% 289.15/181.65 (node19(c_e_h_3, c_e, s4, s5)),
% 289.15/181.65 inference(unit_resolution,[status(thm)],[1771, 190, 1028])).
% 289.15/181.65 tff(1773,plain,
% 289.15/181.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s4) | node18(c_e_h_3, c_e, s4, s5) | (~node19(c_e_h_3, c_e, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_e, s4) | node18(c_e_h_3, c_e, s4, s5) | (~node19(c_e_h_3, c_e, s4, s5)))),
% 289.15/181.65 inference(rewrite,[status(thm)],[])).
% 289.15/181.65 tff(1774,plain,
% 289.15/181.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s4) | node18(c_e_h_3, c_e, s4, s5) | (~node19(c_e_h_3, c_e, s4, s5)))),
% 289.15/181.65 inference(quant_inst,[status(thm)],[])).
% 289.15/181.65 tff(1775,plain,
% 289.15/181.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_e, s4) | node18(c_e_h_3, c_e, s4, s5) | (~node19(c_e_h_3, c_e, s4, s5))),
% 289.15/181.65 inference(modus_ponens,[status(thm)],[1774, 1773])).
% 289.15/181.65 tff(1776,plain,
% 289.15/181.65 (node17(c_e_h_3, c_e, s4) | node18(c_e_h_3, c_e, s4, s5)),
% 289.15/181.65 inference(unit_resolution,[status(thm)],[1775, 776, 1772])).
% 289.15/181.65 tff(1777,plain,
% 289.15/181.65 (node17(c_e_h_3, c_e, s4)),
% 289.15/181.65 inference(unit_resolution,[status(thm)],[1776, 1768])).
% 289.15/181.65 tff(1778,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_e, s4)), introduced(assumption)).
% 289.15/181.65 tff(1779,plain,
% 289.15/181.65 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s4)) | m_c_h_element_v_in2(c_e_h_3, c_e, s4) | (~node17(c_e_h_3, c_e, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s4)) | m_c_h_element_v_in2(c_e_h_3, c_e, s4) | (~node17(c_e_h_3, c_e, s4)))),
% 289.15/181.65 inference(rewrite,[status(thm)],[])).
% 289.15/181.65 tff(1780,plain,
% 289.15/181.65 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s4)) | m_c_h_element_v_in2(c_e_h_3, c_e, s4) | (~node17(c_e_h_3, c_e, s4)))),
% 289.15/181.65 inference(quant_inst,[status(thm)],[])).
% 289.15/181.65 tff(1781,plain,
% 289.15/181.65 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s4)) | m_c_h_element_v_in2(c_e_h_3, c_e, s4) | (~node17(c_e_h_3, c_e, s4))),
% 289.15/181.65 inference(modus_ponens,[status(thm)],[1780, 1779])).
% 289.15/181.65 tff(1782,plain,
% 289.15/181.65 ((~m_c_h_element_v_in1(c_e_h_3, c_e, s4)) | (~node17(c_e_h_3, c_e, s4))),
% 289.15/181.65 inference(unit_resolution,[status(thm)],[1781, 919, 1778])).
% 289.15/181.65 tff(1783,plain,
% 289.15/181.65 (~m_c_h_element_v_in1(c_e_h_3, c_e, s4)),
% 289.15/181.65 inference(unit_resolution,[status(thm)],[1782, 1777])).
% 289.15/181.65 tff(1784,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_e, s4)), introduced(assumption)).
% 289.15/181.65 tff(1785,assumption,(~node15(c_e_h_3, c_e, s4, s5)), introduced(assumption)).
% 289.15/181.65 tff(1786,assumption,(node17(c_e_h_3, c_e, s4)), introduced(assumption)).
% 289.15/181.65 tff(1787,plain,
% 289.15/181.65 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s4) | (~node17(c_e_h_3, c_e, s4)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_3, c_e, s4) | (~node17(c_e_h_3, c_e, s4)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s4)))),
% 289.15/181.65 inference(rewrite,[status(thm)],[])).
% 289.15/181.65 tff(1788,plain,
% 289.15/181.65 ((m_c_h_element_v_in1(c_e_h_3, c_e, s4) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s4)) | (~node17(c_e_h_3, c_e, s4))) <=> (m_c_h_element_v_in1(c_e_h_3, c_e, s4) | (~node17(c_e_h_3, c_e, s4)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s4)))),
% 289.15/181.65 inference(rewrite,[status(thm)],[])).
% 289.15/181.65 tff(1789,plain,
% 289.15/181.65 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s4) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s4)) | (~node17(c_e_h_3, c_e, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s4) | (~node17(c_e_h_3, c_e, s4)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s4))))),
% 289.15/181.65 inference(monotonicity,[status(thm)],[1788])).
% 289.15/181.65 tff(1790,plain,
% 289.15/181.65 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s4) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s4)) | (~node17(c_e_h_3, c_e, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_3, c_e, s4) | (~node17(c_e_h_3, c_e, s4)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s4)))),
% 289.15/181.65 inference(transitivity,[status(thm)],[1789, 1787])).
% 289.15/181.65 tff(1791,plain,
% 289.15/181.65 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s4) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s4)) | (~node17(c_e_h_3, c_e, s4)))),
% 289.15/181.65 inference(quant_inst,[status(thm)],[])).
% 289.15/181.65 tff(1792,plain,
% 289.15/181.65 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_3, c_e, s4) | (~node17(c_e_h_3, c_e, s4)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s4))),
% 289.15/181.65 inference(modus_ponens,[status(thm)],[1791, 1790])).
% 289.15/181.65 tff(1793,plain,
% 289.15/181.65 (m_c_h_element_v_in1(c_e_h_3, c_e, s4) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s4))),
% 289.15/181.65 inference(unit_resolution,[status(thm)],[1792, 859, 1786])).
% 289.15/181.65 tff(1794,plain,
% 289.15/181.65 (~m_c_h_element_v_in2(c_e_h_3, c_e, s4)),
% 289.15/181.65 inference(unit_resolution,[status(thm)],[1793, 1784])).
% 289.15/181.65 tff(1795,plain,
% 289.15/181.65 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_e, s4)) | m_c_h_element_v_in1(c_e_h_3, c_e, s4) | m_c_h_element_v_in2(c_e_h_3, c_e, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s4)) | m_c_h_element_v_in1(c_e_h_3, c_e, s4) | m_c_h_element_v_in2(c_e_h_3, c_e, s4))),
% 289.15/181.65 inference(rewrite,[status(thm)],[])).
% 289.15/181.65 tff(1796,plain,
% 289.15/181.65 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_e, s4)) | m_c_h_element_v_in1(c_e_h_3, c_e, s4) | m_c_h_element_v_in2(c_e_h_3, c_e, s4))),
% 289.15/181.66 inference(quant_inst,[status(thm)],[])).
% 289.15/181.66 tff(1797,plain,
% 289.15/181.66 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s4)) | m_c_h_element_v_in1(c_e_h_3, c_e, s4) | m_c_h_element_v_in2(c_e_h_3, c_e, s4)),
% 289.15/181.66 inference(modus_ponens,[status(thm)],[1796, 1795])).
% 289.15/181.66 tff(1798,plain,
% 289.15/181.66 (~node16(c_e_h_3, c_e, s4)),
% 289.15/181.66 inference(unit_resolution,[status(thm)],[1797, 178, 1794, 1784])).
% 289.15/181.66 tff(1799,plain,
% 289.15/181.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s4) | node14(c_e_h_3, c_e, s4, s5) | node15(c_e_h_3, c_e, s4, s5) | (~node19(c_e_h_3, c_e, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_e, s4) | node14(c_e_h_3, c_e, s4, s5) | node15(c_e_h_3, c_e, s4, s5) | (~node19(c_e_h_3, c_e, s4, s5)))),
% 289.15/181.66 inference(rewrite,[status(thm)],[])).
% 289.15/181.66 tff(1800,plain,
% 289.15/181.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s4) | node14(c_e_h_3, c_e, s4, s5) | node15(c_e_h_3, c_e, s4, s5) | (~node19(c_e_h_3, c_e, s4, s5)))),
% 289.15/181.66 inference(quant_inst,[status(thm)],[])).
% 289.15/181.66 tff(1801,plain,
% 289.15/181.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_e, s4) | node14(c_e_h_3, c_e, s4, s5) | node15(c_e_h_3, c_e, s4, s5) | (~node19(c_e_h_3, c_e, s4, s5))),
% 289.15/181.66 inference(modus_ponens,[status(thm)],[1800, 1799])).
% 289.15/181.66 tff(1802,plain,
% 289.15/181.66 (node16(c_e_h_3, c_e, s4) | node14(c_e_h_3, c_e, s4, s5) | node15(c_e_h_3, c_e, s4, s5)),
% 289.15/181.66 inference(unit_resolution,[status(thm)],[1801, 204, 1772])).
% 289.15/181.66 tff(1803,plain,
% 289.15/181.66 (node14(c_e_h_3, c_e, s4, s5)),
% 289.15/181.66 inference(unit_resolution,[status(thm)],[1802, 1798, 1785])).
% 289.15/181.66 tff(1804,plain,
% 289.15/181.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s4) | (~m_c_h_element_v_out(c_e_h_3, c_e, s5)) | (~node14(c_e_h_3, c_e, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_e, s4) | (~m_c_h_element_v_out(c_e_h_3, c_e, s5)) | (~node14(c_e_h_3, c_e, s4, s5)))),
% 289.15/181.66 inference(rewrite,[status(thm)],[])).
% 289.15/181.66 tff(1805,plain,
% 289.15/181.66 (((~node14(c_e_h_3, c_e, s4, s5)) | m_c_h_element_v_in1(c_e_h_3, c_e, s4) | (~m_c_h_element_v_out(c_e_h_3, c_e, s5))) <=> (m_c_h_element_v_in1(c_e_h_3, c_e, s4) | (~m_c_h_element_v_out(c_e_h_3, c_e, s5)) | (~node14(c_e_h_3, c_e, s4, s5)))),
% 289.15/181.66 inference(rewrite,[status(thm)],[])).
% 289.15/181.66 tff(1806,plain,
% 289.15/181.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s4, s5)) | m_c_h_element_v_in1(c_e_h_3, c_e, s4) | (~m_c_h_element_v_out(c_e_h_3, c_e, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s4) | (~m_c_h_element_v_out(c_e_h_3, c_e, s5)) | (~node14(c_e_h_3, c_e, s4, s5))))),
% 289.15/181.66 inference(monotonicity,[status(thm)],[1805])).
% 289.15/181.66 tff(1807,plain,
% 289.15/181.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s4, s5)) | m_c_h_element_v_in1(c_e_h_3, c_e, s4) | (~m_c_h_element_v_out(c_e_h_3, c_e, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_e, s4) | (~m_c_h_element_v_out(c_e_h_3, c_e, s5)) | (~node14(c_e_h_3, c_e, s4, s5)))),
% 289.15/181.66 inference(transitivity,[status(thm)],[1806, 1804])).
% 289.15/181.66 tff(1808,plain,
% 289.15/181.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s4, s5)) | m_c_h_element_v_in1(c_e_h_3, c_e, s4) | (~m_c_h_element_v_out(c_e_h_3, c_e, s5)))),
% 289.15/181.66 inference(quant_inst,[status(thm)],[])).
% 289.15/181.66 tff(1809,plain,
% 289.15/181.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_e, s4) | (~m_c_h_element_v_out(c_e_h_3, c_e, s5)) | (~node14(c_e_h_3, c_e, s4, s5))),
% 289.15/181.66 inference(modus_ponens,[status(thm)],[1808, 1807])).
% 289.15/181.66 tff(1810,plain,
% 289.15/181.66 ($false),
% 289.15/181.66 inference(unit_resolution,[status(thm)],[1809, 223, 1803, 1784, 1751])).
% 289.15/181.66 tff(1811,plain,(m_c_h_element_v_in1(c_e_h_3, c_e, s4) | (~m_c_h_element_v_out(c_e_h_3, c_e, s5)) | node15(c_e_h_3, c_e, s4, s5) | (~node17(c_e_h_3, c_e, s4))), inference(lemma,lemma(discharge,[]))).
% 289.15/181.66 tff(1812,plain,
% 289.15/181.66 ($false),
% 289.15/181.66 inference(unit_resolution,[status(thm)],[1811, 1783, 1777, 1751, 1758])).
% 289.15/181.66 tff(1813,plain,((~m_c_h_element_v_out(c_e_h_3, c_e, s5)) | m_c_h_element_v_in2(c_e_h_3, c_e, s4) | m_c_h_element_v_out(c_e_h_3, c_e, s4)), inference(lemma,lemma(discharge,[]))).
% 289.15/181.66 tff(1814,plain,
% 289.15/181.66 ((~m_c_h_element_v_out(c_e_h_3, c_e, s5)) | m_c_h_element_v_in2(c_e_h_3, c_e, s4)),
% 289.15/181.66 inference(unit_resolution,[status(thm)],[1813, 1332])).
% 289.15/181.66 tff(1815,plain,
% 289.15/181.66 (~m_c_h_element_v_out(c_e_h_3, c_e, s5)),
% 289.15/181.66 inference(unit_resolution,[status(thm)],[1814, 1750])).
% 289.15/181.66 tff(1816,plain,
% 289.15/181.66 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s5)) | m_c_h_element_v_out(c_e_h_3, c_e, s5))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s5)) | m_c_h_element_v_out(c_e_h_3, c_e, s5))),
% 289.15/181.66 inference(rewrite,[status(thm)],[])).
% 289.15/181.66 tff(1817,plain,
% 289.15/181.66 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s5)) | m_c_h_element_v_out(c_e_h_3, c_e, s5))),
% 289.15/181.66 inference(quant_inst,[status(thm)],[])).
% 289.15/181.66 tff(1818,plain,
% 289.15/181.66 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s5)) | m_c_h_element_v_out(c_e_h_3, c_e, s5)),
% 289.15/181.66 inference(modus_ponens,[status(thm)],[1817, 1816])).
% 289.15/181.66 tff(1819,plain,
% 289.15/181.66 ($false),
% 289.15/181.66 inference(unit_resolution,[status(thm)],[1818, 24, 1815, 1518])).
% 289.15/181.66 tff(1820,plain,(~m_and_h_gate_v_in1(c_e_h_3, c_r, s5)), inference(lemma,lemma(discharge,[]))).
% 289.15/181.66 tff(1821,plain,
% 289.15/181.66 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s5))),
% 289.15/181.66 inference(rewrite,[status(thm)],[])).
% 289.15/181.66 tff(1822,plain,
% 289.15/181.66 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s5))),
% 289.15/181.66 inference(quant_inst,[status(thm)],[])).
% 289.15/181.66 tff(1823,plain,
% 289.15/181.66 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s5)),
% 289.15/181.66 inference(modus_ponens,[status(thm)],[1822, 1821])).
% 289.15/181.66 tff(1824,plain,
% 289.15/181.66 (~node20(c_e_h_3, c_r, s5)),
% 289.15/181.66 inference(unit_resolution,[status(thm)],[1823, 38, 1820])).
% 289.15/181.66 tff(1825,assumption,(~node20(c_e_h_3, c_r, s5)), introduced(assumption)).
% 289.15/181.66 tff(1826,assumption,(~m_user_v_req(c_e_h_3, c_u, s7)), introduced(assumption)).
% 289.15/181.66 tff(1827,plain,
% 289.15/181.66 (m_user_v_req(c_e_h_3, c_u, s6)),
% 289.15/181.66 inference(unit_resolution,[status(thm)],[1412, 1380, 1389])).
% 289.15/181.66 tff(1828,assumption,(node8(c_e_h_3, c_u, s6, s7)), introduced(assumption)).
% 289.15/181.66 tff(1829,plain,
% 289.15/181.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | ((~m_user_v_req(c_e_h_3, c_u, s6)) | m_user_v_req(c_e_h_3, c_u, s7) | (~node8(c_e_h_3, c_u, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (~m_user_v_req(c_e_h_3, c_u, s6)) | m_user_v_req(c_e_h_3, c_u, s7) | (~node8(c_e_h_3, c_u, s6, s7)))),
% 289.15/181.66 inference(rewrite,[status(thm)],[])).
% 289.15/181.66 tff(1830,plain,
% 289.15/181.66 ((m_user_v_req(c_e_h_3, c_u, s7) | (~node8(c_e_h_3, c_u, s6, s7)) | (~m_user_v_req(c_e_h_3, c_u, s6))) <=> ((~m_user_v_req(c_e_h_3, c_u, s6)) | m_user_v_req(c_e_h_3, c_u, s7) | (~node8(c_e_h_3, c_u, s6, s7)))),
% 289.15/181.66 inference(rewrite,[status(thm)],[])).
% 289.15/181.66 tff(1831,plain,
% 289.15/181.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_3, c_u, s7) | (~node8(c_e_h_3, c_u, s6, s7)) | (~m_user_v_req(c_e_h_3, c_u, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | ((~m_user_v_req(c_e_h_3, c_u, s6)) | m_user_v_req(c_e_h_3, c_u, s7) | (~node8(c_e_h_3, c_u, s6, s7))))),
% 289.15/181.66 inference(monotonicity,[status(thm)],[1830])).
% 289.15/181.66 tff(1832,plain,
% 289.15/181.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_3, c_u, s7) | (~node8(c_e_h_3, c_u, s6, s7)) | (~m_user_v_req(c_e_h_3, c_u, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (~m_user_v_req(c_e_h_3, c_u, s6)) | m_user_v_req(c_e_h_3, c_u, s7) | (~node8(c_e_h_3, c_u, s6, s7)))),
% 289.15/181.66 inference(transitivity,[status(thm)],[1831, 1829])).
% 289.15/181.66 tff(1833,plain,
% 289.15/181.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_3, c_u, s7) | (~node8(c_e_h_3, c_u, s6, s7)) | (~m_user_v_req(c_e_h_3, c_u, s6)))),
% 289.15/181.66 inference(quant_inst,[status(thm)],[])).
% 289.15/181.66 tff(1834,plain,
% 289.15/181.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (~m_user_v_req(c_e_h_3, c_u, s6)) | m_user_v_req(c_e_h_3, c_u, s7) | (~node8(c_e_h_3, c_u, s6, s7))),
% 289.15/181.66 inference(modus_ponens,[status(thm)],[1833, 1832])).
% 289.15/181.66 tff(1835,plain,
% 289.15/181.66 ($false),
% 289.15/181.66 inference(unit_resolution,[status(thm)],[1834, 302, 1828, 1826, 1416])).
% 289.15/181.66 tff(1836,plain,((~node8(c_e_h_3, c_u, s6, s7)) | m_user_v_req(c_e_h_3, c_u, s7) | (~m_user_v_req(c_e_h_3, c_u, s6))), inference(lemma,lemma(discharge,[]))).
% 289.15/181.66 tff(1837,plain,
% 289.15/181.66 (~node8(c_e_h_3, c_u, s6, s7)),
% 289.15/181.66 inference(unit_resolution,[status(thm)],[1836, 1827, 1826])).
% 289.15/181.66 tff(1838,plain,
% 289.15/181.66 (succ(s6, s7) <=> succ(s6, s7)),
% 289.15/181.66 inference(rewrite,[status(thm)],[])).
% 289.15/181.66 tff(1839,axiom,(succ(s6, s7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound7')).
% 289.15/181.66 tff(1840,plain,
% 289.15/181.66 (succ(s6, s7)),
% 289.15/181.66 inference(modus_ponens,[status(thm)],[1839, 1838])).
% 289.15/181.66 tff(1841,plain,
% 289.15/181.66 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s6, s7)) | trans(s6, s7))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s6, s7)) | trans(s6, s7))),
% 289.15/181.66 inference(rewrite,[status(thm)],[])).
% 289.15/181.66 tff(1842,plain,
% 289.15/181.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s6, s7)) | trans(s6, s7))),
% 289.15/181.66 inference(quant_inst,[status(thm)],[])).
% 289.15/181.66 tff(1843,plain,
% 289.15/181.66 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s6, s7)) | trans(s6, s7)),
% 289.15/181.66 inference(modus_ponens,[status(thm)],[1842, 1841])).
% 289.15/181.66 tff(1844,plain,
% 289.15/181.66 (trans(s6, s7)),
% 289.15/181.66 inference(unit_resolution,[status(thm)],[1843, 1840, 65])).
% 289.15/181.66 tff(1845,plain,
% 289.15/181.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | ((~trans(s6, s7)) | node7(c_e_h_3, c_u, s6, s7) | node8(c_e_h_3, c_u, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | (~trans(s6, s7)) | node7(c_e_h_3, c_u, s6, s7) | node8(c_e_h_3, c_u, s6, s7))),
% 289.15/181.66 inference(rewrite,[status(thm)],[])).
% 289.15/181.66 tff(1846,plain,
% 289.15/181.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | ((~trans(s6, s7)) | node7(c_e_h_3, c_u, s6, s7) | node8(c_e_h_3, c_u, s6, s7))),
% 289.15/181.67 inference(quant_inst,[status(thm)],[])).
% 289.15/181.67 tff(1847,plain,
% 289.15/181.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | (~trans(s6, s7)) | node7(c_e_h_3, c_u, s6, s7) | node8(c_e_h_3, c_u, s6, s7)),
% 289.15/181.67 inference(modus_ponens,[status(thm)],[1846, 1845])).
% 289.15/181.67 tff(1848,plain,
% 289.15/181.67 (node7(c_e_h_3, c_u, s6, s7) | node8(c_e_h_3, c_u, s6, s7)),
% 289.15/181.67 inference(unit_resolution,[status(thm)],[1847, 328, 1844])).
% 289.15/181.67 tff(1849,plain,
% 289.15/181.67 (node7(c_e_h_3, c_u, s6, s7)),
% 289.15/181.67 inference(unit_resolution,[status(thm)],[1848, 1837])).
% 289.15/181.67 tff(1850,assumption,(node7(c_e_h_3, c_u, s6, s7)), introduced(assumption)).
% 289.15/181.67 tff(1851,assumption,(~m_user_v_ack(c_e_h_3, c_u, s6)), introduced(assumption)).
% 289.15/181.67 tff(1852,plain,
% 289.15/181.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | ((~node7(c_e_h_3, c_u, s6, s7)) | m_user_v_ack(c_e_h_3, c_u, s6) | m_user_v_req(c_e_h_3, c_u, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | (~node7(c_e_h_3, c_u, s6, s7)) | m_user_v_ack(c_e_h_3, c_u, s6) | m_user_v_req(c_e_h_3, c_u, s7))),
% 289.15/181.67 inference(rewrite,[status(thm)],[])).
% 289.15/181.67 tff(1853,plain,
% 289.15/181.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | ((~node7(c_e_h_3, c_u, s6, s7)) | m_user_v_ack(c_e_h_3, c_u, s6) | m_user_v_req(c_e_h_3, c_u, s7))),
% 289.15/181.67 inference(quant_inst,[status(thm)],[])).
% 289.15/181.67 tff(1854,plain,
% 289.15/181.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | (~node7(c_e_h_3, c_u, s6, s7)) | m_user_v_ack(c_e_h_3, c_u, s6) | m_user_v_req(c_e_h_3, c_u, s7)),
% 289.15/181.67 inference(modus_ponens,[status(thm)],[1853, 1852])).
% 289.15/181.67 tff(1855,plain,
% 289.15/181.67 ($false),
% 289.15/181.67 inference(unit_resolution,[status(thm)],[1854, 284, 1851, 1850, 1826])).
% 289.15/181.67 tff(1856,plain,((~node7(c_e_h_3, c_u, s6, s7)) | m_user_v_ack(c_e_h_3, c_u, s6) | m_user_v_req(c_e_h_3, c_u, s7)), inference(lemma,lemma(discharge,[]))).
% 289.15/181.67 tff(1857,plain,
% 289.15/181.67 (m_user_v_ack(c_e_h_3, c_u, s6)),
% 289.15/181.67 inference(unit_resolution,[status(thm)],[1856, 1849, 1826])).
% 289.15/181.67 tff(1858,plain,
% 289.15/181.67 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_3, c_u, s6)) | m_and_h_gate_v_out(c_e_h_3, c_r, s6))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_3, c_u, s6)) | m_and_h_gate_v_out(c_e_h_3, c_r, s6))),
% 289.15/181.67 inference(rewrite,[status(thm)],[])).
% 289.15/181.67 tff(1859,plain,
% 289.15/181.67 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_3, c_u, s6)) | m_and_h_gate_v_out(c_e_h_3, c_r, s6))),
% 289.15/181.67 inference(quant_inst,[status(thm)],[])).
% 289.15/181.67 tff(1860,plain,
% 289.15/181.67 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_3, c_u, s6)) | m_and_h_gate_v_out(c_e_h_3, c_r, s6)),
% 289.15/181.67 inference(modus_ponens,[status(thm)],[1859, 1858])).
% 289.15/181.67 tff(1861,plain,
% 289.15/181.67 (m_and_h_gate_v_out(c_e_h_3, c_r, s6)),
% 289.15/181.67 inference(unit_resolution,[status(thm)],[1860, 268, 1857])).
% 289.15/181.67 tff(1862,assumption,(m_and_h_gate_v_out(c_e_h_3, c_r, s6)), introduced(assumption)).
% 289.15/181.67 tff(1863,assumption,(node22(c_e_h_3, c_r, s5, s6)), introduced(assumption)).
% 289.15/181.67 tff(1864,plain,
% 289.15/181.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s6)) | (~node22(c_e_h_3, c_r, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_r, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s6)) | (~node22(c_e_h_3, c_r, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_r, s5))),
% 289.15/181.67 inference(rewrite,[status(thm)],[])).
% 289.15/181.67 tff(1865,plain,
% 289.15/181.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s6)) | (~node22(c_e_h_3, c_r, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_r, s5))),
% 289.15/181.67 inference(quant_inst,[status(thm)],[])).
% 289.15/181.67 tff(1866,plain,
% 289.15/181.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s6)) | (~node22(c_e_h_3, c_r, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_r, s5)),
% 289.15/181.67 inference(modus_ponens,[status(thm)],[1865, 1864])).
% 289.15/181.67 tff(1867,plain,
% 289.15/181.67 ($false),
% 289.15/181.67 inference(unit_resolution,[status(thm)],[1866, 108, 1373, 1863, 1862])).
% 289.15/181.67 tff(1868,plain,((~node22(c_e_h_3, c_r, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_r, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s6))), inference(lemma,lemma(discharge,[]))).
% 289.15/181.67 tff(1869,plain,
% 289.15/181.67 (~node22(c_e_h_3, c_r, s5, s6)),
% 289.15/181.67 inference(unit_resolution,[status(thm)],[1868, 1862, 1373])).
% 289.15/181.67 tff(1870,plain,
% 289.15/181.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_3, c_r, s5, s6) | node22(c_e_h_3, c_r, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_3, c_r, s5, s6) | node22(c_e_h_3, c_r, s5, s6))),
% 289.15/181.67 inference(rewrite,[status(thm)],[])).
% 289.15/181.67 tff(1871,plain,
% 289.15/181.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_3, c_r, s5, s6) | node22(c_e_h_3, c_r, s5, s6))),
% 289.15/181.67 inference(quant_inst,[status(thm)],[])).
% 289.15/181.67 tff(1872,plain,
% 289.15/181.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_3, c_r, s5, s6) | node22(c_e_h_3, c_r, s5, s6)),
% 289.15/181.67 inference(modus_ponens,[status(thm)],[1871, 1870])).
% 289.15/181.67 tff(1873,plain,
% 289.15/181.67 (node21(c_e_h_3, c_r, s5, s6) | node22(c_e_h_3, c_r, s5, s6)),
% 289.15/181.67 inference(unit_resolution,[status(thm)],[1872, 82, 1406])).
% 289.15/181.67 tff(1874,plain,
% 289.15/181.67 (node21(c_e_h_3, c_r, s5, s6)),
% 289.15/181.67 inference(unit_resolution,[status(thm)],[1873, 1869])).
% 289.15/181.67 tff(1875,plain,
% 289.15/181.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s6)) | node20(c_e_h_3, c_r, s5) | (~node21(c_e_h_3, c_r, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s6)) | node20(c_e_h_3, c_r, s5) | (~node21(c_e_h_3, c_r, s5, s6)))),
% 289.15/181.67 inference(rewrite,[status(thm)],[])).
% 289.15/181.67 tff(1876,plain,
% 289.15/181.67 ((node20(c_e_h_3, c_r, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s6)) | (~node21(c_e_h_3, c_r, s5, s6))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_r, s6)) | node20(c_e_h_3, c_r, s5) | (~node21(c_e_h_3, c_r, s5, s6)))),
% 289.15/181.67 inference(rewrite,[status(thm)],[])).
% 289.15/181.67 tff(1877,plain,
% 289.15/181.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s6)) | (~node21(c_e_h_3, c_r, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s6)) | node20(c_e_h_3, c_r, s5) | (~node21(c_e_h_3, c_r, s5, s6))))),
% 289.15/181.67 inference(monotonicity,[status(thm)],[1876])).
% 289.15/181.67 tff(1878,plain,
% 289.15/181.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s6)) | (~node21(c_e_h_3, c_r, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s6)) | node20(c_e_h_3, c_r, s5) | (~node21(c_e_h_3, c_r, s5, s6)))),
% 289.15/181.67 inference(transitivity,[status(thm)],[1877, 1875])).
% 289.15/181.67 tff(1879,plain,
% 289.15/181.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s6)) | (~node21(c_e_h_3, c_r, s5, s6)))),
% 289.15/181.68 inference(quant_inst,[status(thm)],[])).
% 289.15/181.68 tff(1880,plain,
% 289.15/181.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s6)) | node20(c_e_h_3, c_r, s5) | (~node21(c_e_h_3, c_r, s5, s6))),
% 289.15/181.68 inference(modus_ponens,[status(thm)],[1879, 1878])).
% 289.15/181.68 tff(1881,plain,
% 289.15/181.68 ($false),
% 289.15/181.68 inference(unit_resolution,[status(thm)],[1880, 52, 1874, 1825, 1862])).
% 289.15/181.68 tff(1882,plain,((~m_and_h_gate_v_out(c_e_h_3, c_r, s6)) | node20(c_e_h_3, c_r, s5) | m_and_h_gate_v_out(c_e_h_3, c_r, s5)), inference(lemma,lemma(discharge,[]))).
% 289.15/181.68 tff(1883,plain,
% 289.15/181.68 (m_and_h_gate_v_out(c_e_h_3, c_r, s5)),
% 289.15/181.68 inference(unit_resolution,[status(thm)],[1882, 1861, 1825])).
% 289.15/181.68 tff(1884,plain,
% 289.15/181.68 (^[I0: $i, X: $i] : refl((m_user_v_ack(I0, c_u, X) | (~m_and_h_gate_v_out(I0, c_r, X))) <=> (m_user_v_ack(I0, c_u, X) | (~m_and_h_gate_v_out(I0, c_r, X))))),
% 289.15/181.68 inference(bind,[status(th)],[])).
% 289.15/181.68 tff(1885,plain,
% 289.15/181.68 (![I0: $i, X: $i] : (m_user_v_ack(I0, c_u, X) | (~m_and_h_gate_v_out(I0, c_r, X))) <=> ![I0: $i, X: $i] : (m_user_v_ack(I0, c_u, X) | (~m_and_h_gate_v_out(I0, c_r, X)))),
% 289.15/181.68 inference(quant_intro,[status(thm)],[1884])).
% 289.15/181.68 tff(1886,plain,
% 289.15/181.68 (![I0: $i, X: $i] : (m_user_v_ack(I0, c_u, X) | (~m_and_h_gate_v_out(I0, c_r, X))) <=> ![I0: $i, X: $i] : (m_user_v_ack(I0, c_u, X) | (~m_and_h_gate_v_out(I0, c_r, X)))),
% 289.15/181.68 inference(rewrite,[status(thm)],[])).
% 289.15/181.68 tff(1887,axiom,(![I0: $i, X: $i] : (m_user_v_ack(I0, c_u, X) | (~m_and_h_gate_v_out(I0, c_r, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_80')).
% 289.15/181.68 tff(1888,plain,
% 289.15/181.68 (![I0: $i, X: $i] : (m_user_v_ack(I0, c_u, X) | (~m_and_h_gate_v_out(I0, c_r, X)))),
% 289.15/181.68 inference(modus_ponens,[status(thm)],[1887, 1886])).
% 289.15/181.68 tff(1889,plain,(
% 289.15/181.68 ![I0: $i, X: $i] : (m_user_v_ack(I0, c_u, X) | (~m_and_h_gate_v_out(I0, c_r, X)))),
% 289.15/181.68 inference(skolemize,[status(sab)],[1888])).
% 289.15/181.68 tff(1890,plain,
% 289.15/181.68 (![I0: $i, X: $i] : (m_user_v_ack(I0, c_u, X) | (~m_and_h_gate_v_out(I0, c_r, X)))),
% 289.15/181.68 inference(modus_ponens,[status(thm)],[1889, 1885])).
% 289.15/181.68 tff(1891,plain,
% 289.15/181.68 (((~![I0: $i, X: $i] : (m_user_v_ack(I0, c_u, X) | (~m_and_h_gate_v_out(I0, c_r, X)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s5)) | m_user_v_ack(c_e_h_3, c_u, s5))) <=> ((~![I0: $i, X: $i] : (m_user_v_ack(I0, c_u, X) | (~m_and_h_gate_v_out(I0, c_r, X)))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s5)) | m_user_v_ack(c_e_h_3, c_u, s5))),
% 289.15/181.68 inference(rewrite,[status(thm)],[])).
% 289.15/181.68 tff(1892,plain,
% 289.15/181.68 ((m_user_v_ack(c_e_h_3, c_u, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s5))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_r, s5)) | m_user_v_ack(c_e_h_3, c_u, s5))),
% 289.15/181.68 inference(rewrite,[status(thm)],[])).
% 289.15/181.68 tff(1893,plain,
% 289.15/181.68 (((~![I0: $i, X: $i] : (m_user_v_ack(I0, c_u, X) | (~m_and_h_gate_v_out(I0, c_r, X)))) | (m_user_v_ack(c_e_h_3, c_u, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s5)))) <=> ((~![I0: $i, X: $i] : (m_user_v_ack(I0, c_u, X) | (~m_and_h_gate_v_out(I0, c_r, X)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s5)) | m_user_v_ack(c_e_h_3, c_u, s5)))),
% 289.15/181.68 inference(monotonicity,[status(thm)],[1892])).
% 289.15/181.68 tff(1894,plain,
% 289.15/181.68 (((~![I0: $i, X: $i] : (m_user_v_ack(I0, c_u, X) | (~m_and_h_gate_v_out(I0, c_r, X)))) | (m_user_v_ack(c_e_h_3, c_u, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s5)))) <=> ((~![I0: $i, X: $i] : (m_user_v_ack(I0, c_u, X) | (~m_and_h_gate_v_out(I0, c_r, X)))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s5)) | m_user_v_ack(c_e_h_3, c_u, s5))),
% 289.15/181.68 inference(transitivity,[status(thm)],[1893, 1891])).
% 289.15/181.68 tff(1895,plain,
% 289.15/181.68 ((~![I0: $i, X: $i] : (m_user_v_ack(I0, c_u, X) | (~m_and_h_gate_v_out(I0, c_r, X)))) | (m_user_v_ack(c_e_h_3, c_u, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s5)))),
% 289.15/181.68 inference(quant_inst,[status(thm)],[])).
% 289.15/181.68 tff(1896,plain,
% 289.15/181.68 ((~![I0: $i, X: $i] : (m_user_v_ack(I0, c_u, X) | (~m_and_h_gate_v_out(I0, c_r, X)))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s5)) | m_user_v_ack(c_e_h_3, c_u, s5)),
% 289.15/181.68 inference(modus_ponens,[status(thm)],[1895, 1894])).
% 289.15/181.68 tff(1897,plain,
% 289.15/181.68 ($false),
% 289.15/181.68 inference(unit_resolution,[status(thm)],[1896, 1890, 1883, 1380])).
% 289.15/181.68 tff(1898,plain,(m_user_v_ack(c_e_h_3, c_u, s5) | node20(c_e_h_3, c_r, s5) | m_user_v_req(c_e_h_3, c_u, s7) | (~m_user_v_req(c_e_h_3, c_u, s5))), inference(lemma,lemma(discharge,[]))).
% 289.15/181.68 tff(1899,plain,
% 289.15/181.68 (node20(c_e_h_3, c_r, s5) | m_user_v_req(c_e_h_3, c_u, s7) | (~m_user_v_req(c_e_h_3, c_u, s5))),
% 289.15/181.68 inference(unit_resolution,[status(thm)],[1898, 1379])).
% 289.15/181.68 tff(1900,plain,
% 289.15/181.68 (m_user_v_req(c_e_h_3, c_u, s7) | (~m_user_v_req(c_e_h_3, c_u, s5))),
% 289.15/181.68 inference(unit_resolution,[status(thm)],[1899, 1824])).
% 289.15/181.68 tff(1901,plain,
% 289.15/181.68 (m_user_v_req(c_e_h_3, c_u, s7)),
% 289.15/181.68 inference(unit_resolution,[status(thm)],[1900, 1036])).
% 289.15/181.68 tff(1902,assumption,(~m_mutex_h_half_v_inp(c_e_h_3, c_a, s7)), introduced(assumption)).
% 289.15/181.68 tff(1903,assumption,(m_user_v_req(c_e_h_3, c_u, s7)), introduced(assumption)).
% 289.15/181.68 tff(1904,plain,
% 289.15/181.68 (((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | ((~m_user_v_req(c_e_h_3, c_u, s7)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s7))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | (~m_user_v_req(c_e_h_3, c_u, s7)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s7))),
% 289.15/181.68 inference(rewrite,[status(thm)],[])).
% 289.15/181.68 tff(1905,plain,
% 289.15/181.68 ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | ((~m_user_v_req(c_e_h_3, c_u, s7)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s7))),
% 289.15/181.68 inference(quant_inst,[status(thm)],[])).
% 289.15/181.68 tff(1906,plain,
% 289.15/181.68 ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | (~m_user_v_req(c_e_h_3, c_u, s7)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s7)),
% 289.15/181.68 inference(modus_ponens,[status(thm)],[1905, 1904])).
% 289.15/181.68 tff(1907,plain,
% 289.15/181.68 ($false),
% 289.15/181.68 inference(unit_resolution,[status(thm)],[1906, 1426, 1903, 1902])).
% 289.15/181.68 tff(1908,plain,(m_mutex_h_half_v_inp(c_e_h_3, c_a, s7) | (~m_user_v_req(c_e_h_3, c_u, s7))), inference(lemma,lemma(discharge,[]))).
% 289.15/181.68 tff(1909,plain,
% 289.15/181.68 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s7)),
% 289.15/181.68 inference(unit_resolution,[status(thm)],[1908, 1901])).
% 289.15/181.68 tff(1910,assumption,(m_mutex_h_half_v_out(c_e_h_3, c_a, s7)), introduced(assumption)).
% 289.15/181.68 tff(1911,assumption,(node13(c_e_h_3, c_a, s7, s8)), introduced(assumption)).
% 289.15/181.68 tff(1912,plain,
% 289.15/181.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s7)) | (~node13(c_e_h_3, c_a, s7, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s7)) | (~node13(c_e_h_3, c_a, s7, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s8))),
% 289.15/181.68 inference(rewrite,[status(thm)],[])).
% 289.15/181.68 tff(1913,plain,
% 289.15/181.68 ((m_mutex_h_half_v_out(c_e_h_3, c_a, s8) | (~node13(c_e_h_3, c_a, s7, s8)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s7))) <=> ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s7)) | (~node13(c_e_h_3, c_a, s7, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s8))),
% 289.15/181.68 inference(rewrite,[status(thm)],[])).
% 289.15/181.68 tff(1914,plain,
% 289.15/181.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s8) | (~node13(c_e_h_3, c_a, s7, s8)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s7)) | (~node13(c_e_h_3, c_a, s7, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s8)))),
% 289.15/181.68 inference(monotonicity,[status(thm)],[1913])).
% 289.15/181.68 tff(1915,plain,
% 289.15/181.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s8) | (~node13(c_e_h_3, c_a, s7, s8)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s7)) | (~node13(c_e_h_3, c_a, s7, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s8))),
% 289.15/181.68 inference(transitivity,[status(thm)],[1914, 1912])).
% 289.15/181.68 tff(1916,plain,
% 289.15/181.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s8) | (~node13(c_e_h_3, c_a, s7, s8)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s7)))),
% 289.15/181.68 inference(quant_inst,[status(thm)],[])).
% 289.15/181.68 tff(1917,plain,
% 289.15/181.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s7)) | (~node13(c_e_h_3, c_a, s7, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s8)),
% 289.15/181.68 inference(modus_ponens,[status(thm)],[1916, 1915])).
% 289.15/181.68 tff(1918,plain,
% 289.15/181.68 ($false),
% 289.15/181.68 inference(unit_resolution,[status(thm)],[1917, 1459, 1911, 1517, 1910])).
% 289.15/181.68 tff(1919,plain,((~node13(c_e_h_3, c_a, s7, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s8) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s7))), inference(lemma,lemma(discharge,[]))).
% 289.15/181.68 tff(1920,plain,
% 289.15/181.68 (~node13(c_e_h_3, c_a, s7, s8)),
% 289.15/181.68 inference(unit_resolution,[status(thm)],[1919, 1517, 1910])).
% 289.15/181.68 tff(1921,assumption,(m_mutex_h_half_v_inp(c_e_h_3, c_a, s7)), introduced(assumption)).
% 289.15/181.68 tff(1922,assumption,(node12(c_e_h_3, c_a, s7, s8)), introduced(assumption)).
% 289.15/181.68 tff(1923,plain,
% 289.15/181.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_a, s7)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s8) | (~node12(c_e_h_3, c_a, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s7)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s8) | (~node12(c_e_h_3, c_a, s7, s8)))),
% 289.15/181.68 inference(rewrite,[status(thm)],[])).
% 289.15/181.68 tff(1924,plain,
% 289.15/181.68 (((~node12(c_e_h_3, c_a, s7, s8)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s7)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s8)) <=> ((~m_mutex_h_half_v_inp(c_e_h_3, c_a, s7)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s8) | (~node12(c_e_h_3, c_a, s7, s8)))),
% 289.15/181.68 inference(rewrite,[status(thm)],[])).
% 289.15/181.68 tff(1925,plain,
% 289.15/181.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_3, c_a, s7, s8)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s7)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_a, s7)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s8) | (~node12(c_e_h_3, c_a, s7, s8))))),
% 289.15/181.68 inference(monotonicity,[status(thm)],[1924])).
% 289.15/181.68 tff(1926,plain,
% 289.15/181.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_3, c_a, s7, s8)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s7)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s7)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s8) | (~node12(c_e_h_3, c_a, s7, s8)))),
% 289.15/181.68 inference(transitivity,[status(thm)],[1925, 1923])).
% 289.15/181.68 tff(1927,plain,
% 289.15/181.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_3, c_a, s7, s8)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s7)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s8))),
% 289.15/181.68 inference(quant_inst,[status(thm)],[])).
% 289.15/181.68 tff(1928,plain,
% 289.15/181.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s7)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s8) | (~node12(c_e_h_3, c_a, s7, s8))),
% 289.23/181.69 inference(modus_ponens,[status(thm)],[1927, 1926])).
% 289.23/181.69 tff(1929,plain,
% 289.23/181.69 ($false),
% 289.23/181.69 inference(unit_resolution,[status(thm)],[1928, 1483, 1922, 1517, 1921])).
% 289.23/181.69 tff(1930,plain,((~node12(c_e_h_3, c_a, s7, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s8) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s7))), inference(lemma,lemma(discharge,[]))).
% 289.23/181.69 tff(1931,plain,
% 289.23/181.69 (~node12(c_e_h_3, c_a, s7, s8)),
% 289.23/181.69 inference(unit_resolution,[status(thm)],[1930, 1517, 1921])).
% 289.23/181.69 tff(1932,plain,
% 289.23/181.69 (succ(s7, s8) <=> succ(s7, s8)),
% 289.23/181.69 inference(rewrite,[status(thm)],[])).
% 289.23/181.69 tff(1933,axiom,(succ(s7, s8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound8')).
% 289.23/181.69 tff(1934,plain,
% 289.23/181.69 (succ(s7, s8)),
% 289.23/181.69 inference(modus_ponens,[status(thm)],[1933, 1932])).
% 289.23/181.69 tff(1935,plain,
% 289.23/181.69 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s7, s8)) | trans(s7, s8))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s7, s8)) | trans(s7, s8))),
% 289.23/181.69 inference(rewrite,[status(thm)],[])).
% 289.23/181.69 tff(1936,plain,
% 289.23/181.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s7, s8)) | trans(s7, s8))),
% 289.23/181.69 inference(quant_inst,[status(thm)],[])).
% 289.23/181.69 tff(1937,plain,
% 289.23/181.69 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s7, s8)) | trans(s7, s8)),
% 289.23/181.69 inference(modus_ponens,[status(thm)],[1936, 1935])).
% 289.23/181.69 tff(1938,plain,
% 289.23/181.69 (trans(s7, s8)),
% 289.23/181.69 inference(unit_resolution,[status(thm)],[1937, 1934, 65])).
% 289.23/181.69 tff(1939,plain,
% 289.23/181.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s7, s8)) | node12(c_e_h_3, c_a, s7, s8) | node13(c_e_h_3, c_a, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s7, s8)) | node12(c_e_h_3, c_a, s7, s8) | node13(c_e_h_3, c_a, s7, s8))),
% 289.23/181.69 inference(rewrite,[status(thm)],[])).
% 289.23/181.69 tff(1940,plain,
% 289.23/181.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s7, s8)) | node12(c_e_h_3, c_a, s7, s8) | node13(c_e_h_3, c_a, s7, s8))),
% 289.23/181.69 inference(quant_inst,[status(thm)],[])).
% 289.23/181.69 tff(1941,plain,
% 289.23/181.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s7, s8)) | node12(c_e_h_3, c_a, s7, s8) | node13(c_e_h_3, c_a, s7, s8)),
% 289.23/181.69 inference(modus_ponens,[status(thm)],[1940, 1939])).
% 289.23/181.69 tff(1942,plain,
% 289.23/181.69 (node12(c_e_h_3, c_a, s7, s8) | node13(c_e_h_3, c_a, s7, s8)),
% 289.23/181.69 inference(unit_resolution,[status(thm)],[1941, 439, 1938])).
% 289.23/181.69 tff(1943,plain,
% 289.23/181.69 ($false),
% 289.23/181.69 inference(unit_resolution,[status(thm)],[1942, 1931, 1920])).
% 289.23/181.69 tff(1944,plain,(m_mutex_h_half_v_out(c_e_h_3, c_a, s8) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s7)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s7))), inference(lemma,lemma(discharge,[]))).
% 289.23/181.69 tff(1945,plain,
% 289.23/181.69 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s7)),
% 289.23/181.69 inference(unit_resolution,[status(thm)],[1944, 1909, 1517])).
% 289.23/181.69 tff(1946,assumption,(m_mutex_h_half_v_out(c_e_h_3, c_a, s6)), introduced(assumption)).
% 289.23/181.69 tff(1947,assumption,(~m_mutex_h_half_v_out(c_e_h_3, c_a, s7)), introduced(assumption)).
% 289.23/181.69 tff(1948,assumption,(m_mutex_h_half_v_inp(c_e_h_3, c_a, s6)), introduced(assumption)).
% 289.23/181.69 tff(1949,assumption,(node12(c_e_h_3, c_a, s6, s7)), introduced(assumption)).
% 289.23/181.69 tff(1950,plain,
% 289.23/181.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_a, s6)) | (~node12(c_e_h_3, c_a, s6, s7)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s6)) | (~node12(c_e_h_3, c_a, s6, s7)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s7))),
% 289.23/181.69 inference(rewrite,[status(thm)],[])).
% 289.23/181.69 tff(1951,plain,
% 289.23/181.69 (((~node12(c_e_h_3, c_a, s6, s7)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s6)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s7)) <=> ((~m_mutex_h_half_v_inp(c_e_h_3, c_a, s6)) | (~node12(c_e_h_3, c_a, s6, s7)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s7))),
% 289.23/181.69 inference(rewrite,[status(thm)],[])).
% 289.23/181.69 tff(1952,plain,
% 289.23/181.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_3, c_a, s6, s7)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s6)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_a, s6)) | (~node12(c_e_h_3, c_a, s6, s7)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s7)))),
% 289.23/181.69 inference(monotonicity,[status(thm)],[1951])).
% 289.23/181.69 tff(1953,plain,
% 289.23/181.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_3, c_a, s6, s7)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s6)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s6)) | (~node12(c_e_h_3, c_a, s6, s7)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s7))),
% 289.23/181.69 inference(transitivity,[status(thm)],[1952, 1950])).
% 289.23/181.69 tff(1954,plain,
% 289.23/181.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_3, c_a, s6, s7)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s6)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s7))),
% 289.23/181.69 inference(quant_inst,[status(thm)],[])).
% 289.23/181.69 tff(1955,plain,
% 289.23/181.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s6)) | (~node12(c_e_h_3, c_a, s6, s7)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s7)),
% 289.23/181.69 inference(modus_ponens,[status(thm)],[1954, 1953])).
% 289.23/181.69 tff(1956,plain,
% 289.23/181.69 ($false),
% 289.23/181.69 inference(unit_resolution,[status(thm)],[1955, 1483, 1949, 1948, 1947])).
% 289.23/181.69 tff(1957,plain,((~node12(c_e_h_3, c_a, s6, s7)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s6)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s7)), inference(lemma,lemma(discharge,[]))).
% 289.23/181.69 tff(1958,plain,
% 289.23/181.69 (~node12(c_e_h_3, c_a, s6, s7)),
% 289.23/181.69 inference(unit_resolution,[status(thm)],[1957, 1947, 1948])).
% 289.23/181.69 tff(1959,plain,
% 289.23/181.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s6, s7)) | node12(c_e_h_3, c_a, s6, s7) | node13(c_e_h_3, c_a, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s6, s7)) | node12(c_e_h_3, c_a, s6, s7) | node13(c_e_h_3, c_a, s6, s7))),
% 289.23/181.69 inference(rewrite,[status(thm)],[])).
% 289.23/181.69 tff(1960,plain,
% 289.23/181.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s6, s7)) | node12(c_e_h_3, c_a, s6, s7) | node13(c_e_h_3, c_a, s6, s7))),
% 289.23/181.69 inference(quant_inst,[status(thm)],[])).
% 289.23/181.69 tff(1961,plain,
% 289.23/181.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s6, s7)) | node12(c_e_h_3, c_a, s6, s7) | node13(c_e_h_3, c_a, s6, s7)),
% 289.23/181.69 inference(modus_ponens,[status(thm)],[1960, 1959])).
% 289.23/181.69 tff(1962,plain,
% 289.23/181.69 (node12(c_e_h_3, c_a, s6, s7) | node13(c_e_h_3, c_a, s6, s7)),
% 289.23/181.69 inference(unit_resolution,[status(thm)],[1961, 439, 1844])).
% 289.23/181.69 tff(1963,plain,
% 289.23/181.69 (node13(c_e_h_3, c_a, s6, s7)),
% 289.23/181.69 inference(unit_resolution,[status(thm)],[1962, 1958])).
% 289.23/181.69 tff(1964,plain,
% 289.23/181.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s6)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s7) | (~node13(c_e_h_3, c_a, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s6)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s7) | (~node13(c_e_h_3, c_a, s6, s7)))),
% 289.23/181.70 inference(rewrite,[status(thm)],[])).
% 289.23/181.70 tff(1965,plain,
% 289.23/181.70 ((m_mutex_h_half_v_out(c_e_h_3, c_a, s7) | (~node13(c_e_h_3, c_a, s6, s7)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s6))) <=> ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s6)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s7) | (~node13(c_e_h_3, c_a, s6, s7)))),
% 289.23/181.70 inference(rewrite,[status(thm)],[])).
% 289.23/181.70 tff(1966,plain,
% 289.23/181.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s7) | (~node13(c_e_h_3, c_a, s6, s7)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s6)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s7) | (~node13(c_e_h_3, c_a, s6, s7))))),
% 289.23/181.70 inference(monotonicity,[status(thm)],[1965])).
% 289.23/181.70 tff(1967,plain,
% 289.23/181.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s7) | (~node13(c_e_h_3, c_a, s6, s7)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s6)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s7) | (~node13(c_e_h_3, c_a, s6, s7)))),
% 289.23/181.70 inference(transitivity,[status(thm)],[1966, 1964])).
% 289.23/181.70 tff(1968,plain,
% 289.23/181.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s7) | (~node13(c_e_h_3, c_a, s6, s7)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s6)))),
% 289.23/181.70 inference(quant_inst,[status(thm)],[])).
% 289.23/181.70 tff(1969,plain,
% 289.23/181.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s6)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s7) | (~node13(c_e_h_3, c_a, s6, s7))),
% 289.23/181.70 inference(modus_ponens,[status(thm)],[1968, 1967])).
% 289.23/181.70 tff(1970,plain,
% 289.23/181.70 ($false),
% 289.23/181.70 inference(unit_resolution,[status(thm)],[1969, 1459, 1963, 1947, 1946])).
% 289.23/181.70 tff(1971,plain,(m_mutex_h_half_v_out(c_e_h_3, c_a, s7) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s6)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s6))), inference(lemma,lemma(discharge,[]))).
% 289.23/181.70 tff(1972,plain,
% 289.23/181.70 ($false),
% 289.23/181.70 inference(unit_resolution,[status(thm)],[1971, 1945, 1516, 1432])).
% 289.23/181.70 tff(1973,plain,((~m_mutex_h_half_v_out(c_e_h_3, c_a, s4)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s8)), inference(lemma,lemma(discharge,[]))).
% 289.23/181.70 tff(1974,plain,
% 289.23/181.70 (m_mutex_h_half_v_out(c_e_h_3, c_a, s8)),
% 289.23/181.70 inference(unit_resolution,[status(thm)],[1973, 2])).
% 289.23/181.70 tff(1975,assumption,(m_mutex_h_half_v_inp(c_e_h_3, c_a, s8)), introduced(assumption)).
% 289.23/181.70 tff(1976,assumption,(m_mutex_h_half_v_out(c_e_h_3, c_a, s8)), introduced(assumption)).
% 289.23/181.70 tff(1977,assumption,(node13(c_e_h_3, c_a, s8, s9)), introduced(assumption)).
% 289.23/181.70 tff(1978,plain,
% 289.23/181.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s9) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s8)) | (~node13(c_e_h_3, c_a, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | m_mutex_h_half_v_out(c_e_h_3, c_a, s9) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s8)) | (~node13(c_e_h_3, c_a, s8, s9)))),
% 289.23/181.70 inference(rewrite,[status(thm)],[])).
% 289.23/181.70 tff(1979,plain,
% 289.23/181.70 ((m_mutex_h_half_v_out(c_e_h_3, c_a, s9) | (~node13(c_e_h_3, c_a, s8, s9)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s8))) <=> (m_mutex_h_half_v_out(c_e_h_3, c_a, s9) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s8)) | (~node13(c_e_h_3, c_a, s8, s9)))),
% 289.23/181.70 inference(rewrite,[status(thm)],[])).
% 289.23/181.70 tff(1980,plain,
% 289.23/181.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s9) | (~node13(c_e_h_3, c_a, s8, s9)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s9) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s8)) | (~node13(c_e_h_3, c_a, s8, s9))))),
% 289.23/181.70 inference(monotonicity,[status(thm)],[1979])).
% 289.23/181.70 tff(1981,plain,
% 289.23/181.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s9) | (~node13(c_e_h_3, c_a, s8, s9)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | m_mutex_h_half_v_out(c_e_h_3, c_a, s9) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s8)) | (~node13(c_e_h_3, c_a, s8, s9)))),
% 289.23/181.70 inference(transitivity,[status(thm)],[1980, 1978])).
% 289.23/181.70 tff(1982,plain,
% 289.23/181.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s9) | (~node13(c_e_h_3, c_a, s8, s9)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s8)))),
% 289.23/181.70 inference(quant_inst,[status(thm)],[])).
% 289.23/181.70 tff(1983,plain,
% 289.23/181.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | m_mutex_h_half_v_out(c_e_h_3, c_a, s9) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s8)) | (~node13(c_e_h_3, c_a, s8, s9))),
% 289.23/181.70 inference(modus_ponens,[status(thm)],[1982, 1981])).
% 289.23/181.70 tff(1984,plain,
% 289.23/181.70 ($false),
% 289.23/181.70 inference(unit_resolution,[status(thm)],[1983, 1459, 1977, 1976, 1])).
% 289.23/181.70 tff(1985,plain,((~node13(c_e_h_3, c_a, s8, s9)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s9)), inference(lemma,lemma(discharge,[]))).
% 289.23/181.70 tff(1986,plain,
% 289.23/181.70 (~node13(c_e_h_3, c_a, s8, s9)),
% 289.23/181.70 inference(unit_resolution,[status(thm)],[1985, 1, 1976])).
% 289.23/181.70 tff(1987,plain,
% 289.23/181.70 (succ(s8, s9) <=> succ(s8, s9)),
% 289.23/181.70 inference(rewrite,[status(thm)],[])).
% 289.23/181.70 tff(1988,axiom,(succ(s8, s9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound9')).
% 289.23/181.70 tff(1989,plain,
% 289.23/181.70 (succ(s8, s9)),
% 289.23/181.70 inference(modus_ponens,[status(thm)],[1988, 1987])).
% 289.23/181.70 tff(1990,plain,
% 289.23/181.70 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s8, s9)) | trans(s8, s9))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s8, s9)) | trans(s8, s9))),
% 289.23/181.70 inference(rewrite,[status(thm)],[])).
% 289.23/181.70 tff(1991,plain,
% 289.23/181.70 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s8, s9)) | trans(s8, s9))),
% 289.23/181.70 inference(quant_inst,[status(thm)],[])).
% 289.23/181.70 tff(1992,plain,
% 289.23/181.70 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s8, s9)) | trans(s8, s9)),
% 289.23/181.70 inference(modus_ponens,[status(thm)],[1991, 1990])).
% 289.23/181.70 tff(1993,plain,
% 289.23/181.70 (trans(s8, s9)),
% 289.23/181.70 inference(unit_resolution,[status(thm)],[1992, 1989, 65])).
% 289.23/181.70 tff(1994,plain,
% 289.23/181.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s8, s9)) | node12(c_e_h_3, c_a, s8, s9) | node13(c_e_h_3, c_a, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s8, s9)) | node12(c_e_h_3, c_a, s8, s9) | node13(c_e_h_3, c_a, s8, s9))),
% 289.23/181.70 inference(rewrite,[status(thm)],[])).
% 289.23/181.70 tff(1995,plain,
% 289.23/181.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s8, s9)) | node12(c_e_h_3, c_a, s8, s9) | node13(c_e_h_3, c_a, s8, s9))),
% 289.23/181.70 inference(quant_inst,[status(thm)],[])).
% 289.23/181.70 tff(1996,plain,
% 289.23/181.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s8, s9)) | node12(c_e_h_3, c_a, s8, s9) | node13(c_e_h_3, c_a, s8, s9)),
% 289.23/181.70 inference(modus_ponens,[status(thm)],[1995, 1994])).
% 289.23/181.70 tff(1997,plain,
% 289.23/181.70 (node12(c_e_h_3, c_a, s8, s9) | node13(c_e_h_3, c_a, s8, s9)),
% 289.23/181.70 inference(unit_resolution,[status(thm)],[1996, 439, 1993])).
% 289.23/181.70 tff(1998,plain,
% 289.23/181.70 (node12(c_e_h_3, c_a, s8, s9)),
% 289.23/181.70 inference(unit_resolution,[status(thm)],[1997, 1986])).
% 289.23/181.70 tff(1999,plain,
% 289.23/181.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_a, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s9) | (~node12(c_e_h_3, c_a, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s9) | (~node12(c_e_h_3, c_a, s8, s9)))),
% 289.23/181.70 inference(rewrite,[status(thm)],[])).
% 289.23/181.70 tff(2000,plain,
% 289.23/181.70 (((~node12(c_e_h_3, c_a, s8, s9)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s9)) <=> ((~m_mutex_h_half_v_inp(c_e_h_3, c_a, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s9) | (~node12(c_e_h_3, c_a, s8, s9)))),
% 289.23/181.70 inference(rewrite,[status(thm)],[])).
% 289.23/181.70 tff(2001,plain,
% 289.23/181.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_3, c_a, s8, s9)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_a, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s9) | (~node12(c_e_h_3, c_a, s8, s9))))),
% 289.23/181.70 inference(monotonicity,[status(thm)],[2000])).
% 289.23/181.70 tff(2002,plain,
% 289.23/181.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_3, c_a, s8, s9)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s9) | (~node12(c_e_h_3, c_a, s8, s9)))),
% 289.23/181.70 inference(transitivity,[status(thm)],[2001, 1999])).
% 289.23/181.70 tff(2003,plain,
% 289.23/181.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_3, c_a, s8, s9)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s9))),
% 289.23/181.70 inference(quant_inst,[status(thm)],[])).
% 289.23/181.70 tff(2004,plain,
% 289.23/181.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s9) | (~node12(c_e_h_3, c_a, s8, s9))),
% 289.23/181.70 inference(modus_ponens,[status(thm)],[2003, 2002])).
% 289.23/181.70 tff(2005,plain,
% 289.23/181.70 ($false),
% 289.23/181.70 inference(unit_resolution,[status(thm)],[2004, 1483, 1998, 1, 1975])).
% 289.23/181.70 tff(2006,plain,(m_mutex_h_half_v_out(c_e_h_3, c_a, s9) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s8)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s8))), inference(lemma,lemma(discharge,[]))).
% 289.23/181.70 tff(2007,plain,
% 289.23/181.70 (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s8)),
% 289.23/181.70 inference(unit_resolution,[status(thm)],[2006, 1974, 1])).
% 289.23/181.70 tff(2008,assumption,(~m_mutex_h_half_v_inp(c_e_h_3, c_a, s8)), introduced(assumption)).
% 289.23/181.70 tff(2009,assumption,(m_user_v_req(c_e_h_3, c_u, s8)), introduced(assumption)).
% 289.23/181.70 tff(2010,plain,
% 289.23/181.70 (((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | ((~m_user_v_req(c_e_h_3, c_u, s8)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s8))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | (~m_user_v_req(c_e_h_3, c_u, s8)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s8))),
% 289.23/181.70 inference(rewrite,[status(thm)],[])).
% 289.23/181.70 tff(2011,plain,
% 289.23/181.70 ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | ((~m_user_v_req(c_e_h_3, c_u, s8)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s8))),
% 289.23/181.71 inference(quant_inst,[status(thm)],[])).
% 289.23/181.71 tff(2012,plain,
% 289.23/181.71 ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | (~m_user_v_req(c_e_h_3, c_u, s8)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s8)),
% 289.23/181.71 inference(modus_ponens,[status(thm)],[2011, 2010])).
% 289.23/181.71 tff(2013,plain,
% 289.23/181.71 ($false),
% 289.23/181.71 inference(unit_resolution,[status(thm)],[2012, 1426, 2009, 2008])).
% 289.23/181.71 tff(2014,plain,(m_mutex_h_half_v_inp(c_e_h_3, c_a, s8) | (~m_user_v_req(c_e_h_3, c_u, s8))), inference(lemma,lemma(discharge,[]))).
% 289.23/181.71 tff(2015,plain,
% 289.23/181.71 (~m_user_v_req(c_e_h_3, c_u, s8)),
% 289.23/181.71 inference(unit_resolution,[status(thm)],[2014, 2007])).
% 289.23/181.71 tff(2016,assumption,(m_c_h_element_v_out(c_e_h_3, c_e, s6)), introduced(assumption)).
% 289.23/181.71 tff(2017,assumption,(~m_c_h_element_v_out(c_e_h_3, c_e, s5)), introduced(assumption)).
% 289.23/181.71 tff(2018,assumption,(node18(c_e_h_3, c_e, s5, s6)), introduced(assumption)).
% 289.23/181.71 tff(2019,plain,
% 289.23/181.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_e, s5) | (~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | (~node18(c_e_h_3, c_e, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s5) | (~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | (~node18(c_e_h_3, c_e, s5, s6)))),
% 289.23/181.71 inference(rewrite,[status(thm)],[])).
% 289.23/181.71 tff(2020,plain,
% 289.23/181.71 (((~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | m_c_h_element_v_out(c_e_h_3, c_e, s5) | (~node18(c_e_h_3, c_e, s5, s6))) <=> (m_c_h_element_v_out(c_e_h_3, c_e, s5) | (~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | (~node18(c_e_h_3, c_e, s5, s6)))),
% 289.23/181.71 inference(rewrite,[status(thm)],[])).
% 289.23/181.71 tff(2021,plain,
% 289.23/181.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | m_c_h_element_v_out(c_e_h_3, c_e, s5) | (~node18(c_e_h_3, c_e, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_e, s5) | (~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | (~node18(c_e_h_3, c_e, s5, s6))))),
% 289.23/181.71 inference(monotonicity,[status(thm)],[2020])).
% 289.23/181.71 tff(2022,plain,
% 289.23/181.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | m_c_h_element_v_out(c_e_h_3, c_e, s5) | (~node18(c_e_h_3, c_e, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s5) | (~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | (~node18(c_e_h_3, c_e, s5, s6)))),
% 289.23/181.71 inference(transitivity,[status(thm)],[2021, 2019])).
% 289.23/181.71 tff(2023,plain,
% 289.23/181.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | m_c_h_element_v_out(c_e_h_3, c_e, s5) | (~node18(c_e_h_3, c_e, s5, s6)))),
% 289.23/181.71 inference(quant_inst,[status(thm)],[])).
% 289.23/181.71 tff(2024,plain,
% 289.23/181.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s5) | (~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | (~node18(c_e_h_3, c_e, s5, s6))),
% 289.23/181.71 inference(modus_ponens,[status(thm)],[2023, 2022])).
% 289.23/181.71 tff(2025,plain,
% 289.23/181.71 ($false),
% 289.23/181.71 inference(unit_resolution,[status(thm)],[2024, 753, 2016, 2018, 2017])).
% 289.23/181.71 tff(2026,plain,((~node18(c_e_h_3, c_e, s5, s6)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | m_c_h_element_v_out(c_e_h_3, c_e, s5)), inference(lemma,lemma(discharge,[]))).
% 289.23/181.71 tff(2027,plain,
% 289.23/181.71 ((~node18(c_e_h_3, c_e, s5, s6)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s6))),
% 289.23/181.71 inference(unit_resolution,[status(thm)],[2026, 1815])).
% 289.23/181.71 tff(2028,plain,
% 289.23/181.71 (~node18(c_e_h_3, c_e, s5, s6)),
% 289.23/181.71 inference(unit_resolution,[status(thm)],[2027, 2016])).
% 289.23/181.71 tff(2029,assumption,(m_or_h_gate_v_out(c_e_h_3, c_j, s3)), introduced(assumption)).
% 289.23/181.71 tff(2030,assumption,(m_and_h_gate_v_out(c_e_h_3, c_l, s2)), introduced(assumption)).
% 289.23/181.71 tff(2031,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_l, s1)), introduced(assumption)).
% 289.23/181.71 tff(2032,assumption,(node22(c_e_h_3, c_l, s1, s2)), introduced(assumption)).
% 289.23/181.71 tff(2033,plain,
% 289.23/181.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s2)) | (~node22(c_e_h_3, c_l, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_l, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s2)) | (~node22(c_e_h_3, c_l, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_l, s1))),
% 289.23/181.71 inference(rewrite,[status(thm)],[])).
% 289.23/181.71 tff(2034,plain,
% 289.23/181.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s2)) | (~node22(c_e_h_3, c_l, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_l, s1))),
% 289.23/181.71 inference(quant_inst,[status(thm)],[])).
% 289.23/181.71 tff(2035,plain,
% 289.23/181.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s2)) | (~node22(c_e_h_3, c_l, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_l, s1)),
% 289.23/181.71 inference(modus_ponens,[status(thm)],[2034, 2033])).
% 289.23/181.71 tff(2036,plain,
% 289.23/181.71 ($false),
% 289.23/181.71 inference(unit_resolution,[status(thm)],[2035, 108, 2032, 2030, 2031])).
% 289.23/181.71 tff(2037,plain,((~node22(c_e_h_3, c_l, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s2)) | m_and_h_gate_v_out(c_e_h_3, c_l, s1)), inference(lemma,lemma(discharge,[]))).
% 289.23/181.71 tff(2038,plain,
% 289.23/181.71 ((~node22(c_e_h_3, c_l, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s2))),
% 289.23/181.71 inference(unit_resolution,[status(thm)],[2037, 1558])).
% 289.23/181.71 tff(2039,plain,
% 289.23/181.71 (~node22(c_e_h_3, c_l, s1, s2)),
% 289.23/181.71 inference(unit_resolution,[status(thm)],[2038, 2030])).
% 289.23/181.71 tff(2040,assumption,(m_and_h_gate_v_out(c_e_h_3, c_k, s1)), introduced(assumption)).
% 289.23/181.71 tff(2041,assumption,(node21(c_e_h_3, c_k, s0, s1)), introduced(assumption)).
% 289.23/181.71 tff(2042,plain,
% 289.23/181.71 (^[I0: $i, X: $i] : refl(((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X)) <=> ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X)))),
% 289.23/181.71 inference(bind,[status(th)],[])).
% 289.23/181.71 tff(2043,plain,
% 289.23/181.71 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))),
% 289.23/181.71 inference(quant_intro,[status(thm)],[2042])).
% 289.23/181.71 tff(2044,plain,
% 289.23/181.71 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))),
% 289.23/181.71 inference(rewrite,[status(thm)],[])).
% 289.23/181.71 tff(2045,axiom,(![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_44')).
% 289.23/181.71 tff(2046,plain,
% 289.23/181.71 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))),
% 289.23/181.71 inference(modus_ponens,[status(thm)],[2045, 2044])).
% 289.23/181.71 tff(2047,plain,(
% 289.23/181.71 ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))),
% 289.23/181.71 inference(skolemize,[status(sab)],[2046])).
% 289.23/181.71 tff(2048,plain,
% 289.23/181.71 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))),
% 289.23/181.71 inference(modus_ponens,[status(thm)],[2047, 2043])).
% 289.23/181.71 tff(2049,plain,
% 289.23/181.71 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_k, s0)) | m_or_h_gate_v_out(c_e_h_3, c_g, s0))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s0)) | m_or_h_gate_v_out(c_e_h_3, c_g, s0))),
% 289.23/181.71 inference(rewrite,[status(thm)],[])).
% 289.23/181.71 tff(2050,plain,
% 289.23/181.71 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_k, s0)) | m_or_h_gate_v_out(c_e_h_3, c_g, s0))),
% 289.23/181.71 inference(quant_inst,[status(thm)],[])).
% 289.23/181.71 tff(2051,plain,
% 289.23/181.71 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s0)) | m_or_h_gate_v_out(c_e_h_3, c_g, s0)),
% 289.23/181.71 inference(modus_ponens,[status(thm)],[2050, 2049])).
% 289.23/181.71 tff(2052,plain,
% 289.23/181.71 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s0)),
% 289.23/181.71 inference(unit_resolution,[status(thm)],[2051, 2048, 804])).
% 289.23/181.71 tff(2053,plain,
% 289.23/181.71 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_k, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_k, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s0))),
% 289.23/181.71 inference(rewrite,[status(thm)],[])).
% 289.23/181.71 tff(2054,plain,
% 289.23/181.71 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_k, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s0))),
% 289.23/181.71 inference(quant_inst,[status(thm)],[])).
% 289.23/181.71 tff(2055,plain,
% 289.23/181.71 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_k, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s0)),
% 289.23/181.71 inference(modus_ponens,[status(thm)],[2054, 2053])).
% 289.23/181.71 tff(2056,plain,
% 289.23/181.71 (~node20(c_e_h_3, c_k, s0)),
% 289.23/181.71 inference(unit_resolution,[status(thm)],[2055, 38, 2052])).
% 289.23/181.71 tff(2057,plain,
% 289.23/181.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_k, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s1)) | (~node21(c_e_h_3, c_k, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_k, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s1)) | (~node21(c_e_h_3, c_k, s0, s1)))),
% 289.23/181.71 inference(rewrite,[status(thm)],[])).
% 289.23/181.71 tff(2058,plain,
% 289.23/181.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_k, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s1)) | (~node21(c_e_h_3, c_k, s0, s1)))),
% 289.23/181.71 inference(quant_inst,[status(thm)],[])).
% 289.23/181.71 tff(2059,plain,
% 289.23/181.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_k, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s1)) | (~node21(c_e_h_3, c_k, s0, s1))),
% 289.23/181.71 inference(modus_ponens,[status(thm)],[2058, 2057])).
% 289.23/181.71 tff(2060,plain,
% 289.23/181.71 ($false),
% 289.23/181.71 inference(unit_resolution,[status(thm)],[2059, 52, 2056, 2041, 2040])).
% 289.23/181.71 tff(2061,plain,((~node21(c_e_h_3, c_k, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s1))), inference(lemma,lemma(discharge,[]))).
% 289.23/181.71 tff(2062,plain,
% 289.23/181.71 (~node21(c_e_h_3, c_k, s0, s1)),
% 289.23/181.71 inference(unit_resolution,[status(thm)],[2061, 2040])).
% 289.23/181.71 tff(2063,plain,
% 289.23/181.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_3, c_k, s0, s1) | node22(c_e_h_3, c_k, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_3, c_k, s0, s1) | node22(c_e_h_3, c_k, s0, s1))),
% 289.23/181.71 inference(rewrite,[status(thm)],[])).
% 289.23/181.71 tff(2064,plain,
% 289.23/181.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_3, c_k, s0, s1) | node22(c_e_h_3, c_k, s0, s1))),
% 289.23/181.71 inference(quant_inst,[status(thm)],[])).
% 289.23/181.71 tff(2065,plain,
% 289.23/181.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_3, c_k, s0, s1) | node22(c_e_h_3, c_k, s0, s1)),
% 289.23/181.71 inference(modus_ponens,[status(thm)],[2064, 2063])).
% 289.23/181.71 tff(2066,plain,
% 289.23/181.71 (node21(c_e_h_3, c_k, s0, s1) | node22(c_e_h_3, c_k, s0, s1)),
% 289.23/181.72 inference(unit_resolution,[status(thm)],[2065, 82, 72])).
% 289.23/181.72 tff(2067,plain,
% 289.23/181.72 (node22(c_e_h_3, c_k, s0, s1)),
% 289.23/181.72 inference(unit_resolution,[status(thm)],[2066, 2062])).
% 289.23/181.72 tff(2068,plain,
% 289.23/181.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s1)) | (~node22(c_e_h_3, c_k, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_k, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s1)) | (~node22(c_e_h_3, c_k, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_k, s0))),
% 289.23/181.72 inference(rewrite,[status(thm)],[])).
% 289.23/181.72 tff(2069,plain,
% 289.23/181.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s1)) | (~node22(c_e_h_3, c_k, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_k, s0))),
% 289.23/181.72 inference(quant_inst,[status(thm)],[])).
% 289.23/181.72 tff(2070,plain,
% 289.23/181.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s1)) | (~node22(c_e_h_3, c_k, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_k, s0)),
% 289.23/181.72 inference(modus_ponens,[status(thm)],[2069, 2068])).
% 289.23/181.72 tff(2071,plain,
% 289.23/181.72 ($false),
% 289.23/181.72 inference(unit_resolution,[status(thm)],[2070, 108, 2067, 1522, 2040])).
% 289.23/181.72 tff(2072,plain,(~m_and_h_gate_v_out(c_e_h_3, c_k, s1)), inference(lemma,lemma(discharge,[]))).
% 289.23/181.72 tff(2073,plain,
% 289.23/181.72 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_l, s1)) | m_and_h_gate_v_out(c_e_h_3, c_k, s1))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s1)) | m_and_h_gate_v_out(c_e_h_3, c_k, s1))),
% 289.23/181.72 inference(rewrite,[status(thm)],[])).
% 289.23/181.72 tff(2074,plain,
% 289.23/181.72 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_l, s1)) | m_and_h_gate_v_out(c_e_h_3, c_k, s1))),
% 289.23/181.72 inference(quant_inst,[status(thm)],[])).
% 289.23/181.72 tff(2075,plain,
% 289.23/181.72 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s1)) | m_and_h_gate_v_out(c_e_h_3, c_k, s1)),
% 289.23/181.72 inference(modus_ponens,[status(thm)],[2074, 2073])).
% 289.23/181.72 tff(2076,plain,
% 289.23/181.72 (~m_and_h_gate_v_in1(c_e_h_3, c_l, s1)),
% 289.23/181.72 inference(unit_resolution,[status(thm)],[2075, 1529, 2072])).
% 289.23/181.72 tff(2077,plain,
% 289.23/181.72 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_l, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_l, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s1))),
% 289.23/181.72 inference(rewrite,[status(thm)],[])).
% 289.23/181.72 tff(2078,plain,
% 289.23/181.72 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_l, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s1))),
% 289.23/181.72 inference(quant_inst,[status(thm)],[])).
% 289.23/181.72 tff(2079,plain,
% 289.23/181.72 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_l, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s1)),
% 289.23/181.72 inference(modus_ponens,[status(thm)],[2078, 2077])).
% 289.23/181.72 tff(2080,plain,
% 289.23/181.72 (~node20(c_e_h_3, c_l, s1)),
% 289.23/181.72 inference(unit_resolution,[status(thm)],[2079, 38, 2076])).
% 289.23/181.72 tff(2081,assumption,(~node20(c_e_h_3, c_l, s1)), introduced(assumption)).
% 289.23/181.72 tff(2082,assumption,(node21(c_e_h_3, c_l, s1, s2)), introduced(assumption)).
% 289.23/181.72 tff(2083,plain,
% 289.23/181.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s2)) | node20(c_e_h_3, c_l, s1) | (~node21(c_e_h_3, c_l, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s2)) | node20(c_e_h_3, c_l, s1) | (~node21(c_e_h_3, c_l, s1, s2)))),
% 289.23/181.72 inference(rewrite,[status(thm)],[])).
% 289.23/181.72 tff(2084,plain,
% 289.23/181.72 ((node20(c_e_h_3, c_l, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s2)) | (~node21(c_e_h_3, c_l, s1, s2))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_l, s2)) | node20(c_e_h_3, c_l, s1) | (~node21(c_e_h_3, c_l, s1, s2)))),
% 289.23/181.72 inference(rewrite,[status(thm)],[])).
% 289.23/181.72 tff(2085,plain,
% 289.23/181.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s2)) | (~node21(c_e_h_3, c_l, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s2)) | node20(c_e_h_3, c_l, s1) | (~node21(c_e_h_3, c_l, s1, s2))))),
% 289.23/181.72 inference(monotonicity,[status(thm)],[2084])).
% 289.23/181.72 tff(2086,plain,
% 289.23/181.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s2)) | (~node21(c_e_h_3, c_l, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s2)) | node20(c_e_h_3, c_l, s1) | (~node21(c_e_h_3, c_l, s1, s2)))),
% 289.23/181.72 inference(transitivity,[status(thm)],[2085, 2083])).
% 289.23/181.72 tff(2087,plain,
% 289.23/181.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s2)) | (~node21(c_e_h_3, c_l, s1, s2)))),
% 289.23/181.72 inference(quant_inst,[status(thm)],[])).
% 289.23/181.72 tff(2088,plain,
% 289.23/181.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s2)) | node20(c_e_h_3, c_l, s1) | (~node21(c_e_h_3, c_l, s1, s2))),
% 289.23/181.72 inference(modus_ponens,[status(thm)],[2087, 2086])).
% 289.23/181.72 tff(2089,plain,
% 289.23/181.72 ($false),
% 289.23/181.72 inference(unit_resolution,[status(thm)],[2088, 52, 2082, 2081, 2030])).
% 289.23/181.72 tff(2090,plain,((~node21(c_e_h_3, c_l, s1, s2)) | node20(c_e_h_3, c_l, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s2))), inference(lemma,lemma(discharge,[]))).
% 289.23/181.72 tff(2091,plain,
% 289.23/181.72 ((~node21(c_e_h_3, c_l, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s2))),
% 289.23/181.72 inference(unit_resolution,[status(thm)],[2090, 2080])).
% 289.23/181.72 tff(2092,plain,
% 289.23/181.72 (~node21(c_e_h_3, c_l, s1, s2)),
% 289.23/181.72 inference(unit_resolution,[status(thm)],[2091, 2030])).
% 289.23/181.72 tff(2093,plain,
% 289.23/181.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_3, c_l, s1, s2) | node22(c_e_h_3, c_l, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_3, c_l, s1, s2) | node22(c_e_h_3, c_l, s1, s2))),
% 289.23/181.72 inference(rewrite,[status(thm)],[])).
% 289.23/181.72 tff(2094,plain,
% 289.23/181.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_3, c_l, s1, s2) | node22(c_e_h_3, c_l, s1, s2))),
% 289.23/181.72 inference(quant_inst,[status(thm)],[])).
% 289.23/181.72 tff(2095,plain,
% 289.23/181.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_3, c_l, s1, s2) | node22(c_e_h_3, c_l, s1, s2)),
% 289.23/181.72 inference(modus_ponens,[status(thm)],[2094, 2093])).
% 289.23/181.72 tff(2096,plain,
% 289.23/181.72 (node21(c_e_h_3, c_l, s1, s2) | node22(c_e_h_3, c_l, s1, s2)),
% 289.23/181.72 inference(unit_resolution,[status(thm)],[2095, 82, 255])).
% 289.23/181.72 tff(2097,plain,
% 289.23/181.72 ($false),
% 289.23/181.72 inference(unit_resolution,[status(thm)],[2096, 2092, 2039])).
% 289.23/181.72 tff(2098,plain,(~m_and_h_gate_v_out(c_e_h_3, c_l, s2)), inference(lemma,lemma(discharge,[]))).
% 289.23/181.72 tff(2099,plain,
% 289.23/181.72 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_j, s2)) | m_and_h_gate_v_out(c_e_h_3, c_l, s2))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s2)) | m_and_h_gate_v_out(c_e_h_3, c_l, s2))),
% 289.23/181.72 inference(rewrite,[status(thm)],[])).
% 289.23/181.72 tff(2100,plain,
% 289.23/181.72 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_j, s2)) | m_and_h_gate_v_out(c_e_h_3, c_l, s2))),
% 289.23/181.72 inference(quant_inst,[status(thm)],[])).
% 289.23/181.72 tff(2101,plain,
% 289.23/181.72 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s2)) | m_and_h_gate_v_out(c_e_h_3, c_l, s2)),
% 289.23/181.72 inference(modus_ponens,[status(thm)],[2100, 2099])).
% 289.23/181.72 tff(2102,plain,
% 289.23/181.72 (~m_or_h_gate_v_in1(c_e_h_3, c_j, s2)),
% 289.23/181.72 inference(unit_resolution,[status(thm)],[2101, 1100, 2098])).
% 289.23/181.72 tff(2103,assumption,(m_and_h_gate_v_out(c_e_h_2, c_q, s2)), introduced(assumption)).
% 289.23/181.72 tff(2104,assumption,(node21(c_e_h_2, c_q, s1, s2)), introduced(assumption)).
% 289.23/181.72 tff(2105,assumption,(m_c_h_element_v_out(c_e_h_2, c_f, s1)), introduced(assumption)).
% 289.23/181.72 tff(2106,assumption,(m_and_h_gate_v_out(c_e_h_2, c_d, s0)), introduced(assumption)).
% 289.23/181.72 tff(2107,plain,
% 289.23/181.72 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_2, c_d, s0))),
% 289.23/181.72 inference(quant_inst,[status(thm)],[])).
% 289.23/181.72 tff(2108,plain,
% 289.23/181.72 ($false),
% 289.23/181.72 inference(unit_resolution,[status(thm)],[2107, 95, 2106])).
% 289.23/181.72 tff(2109,plain,(~m_and_h_gate_v_out(c_e_h_2, c_d, s0)), inference(lemma,lemma(discharge,[]))).
% 289.23/181.72 tff(2110,plain,
% 289.23/181.72 (^[I0: $i, X: $i] : refl(((~m_c_h_element_v_in1(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_d, X)) <=> ((~m_c_h_element_v_in1(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_d, X)))),
% 289.23/181.72 inference(bind,[status(th)],[])).
% 289.23/181.72 tff(2111,plain,
% 289.23/181.72 (![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_d, X)) <=> ![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_d, X))),
% 289.23/181.72 inference(quant_intro,[status(thm)],[2110])).
% 289.23/181.72 tff(2112,plain,
% 289.23/181.72 (![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_d, X)) <=> ![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_d, X))),
% 289.23/181.72 inference(rewrite,[status(thm)],[])).
% 289.23/181.72 tff(2113,axiom,(![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_d, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_24')).
% 289.23/181.72 tff(2114,plain,
% 289.23/181.72 (![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_d, X))),
% 289.23/181.72 inference(modus_ponens,[status(thm)],[2113, 2112])).
% 289.23/181.72 tff(2115,plain,(
% 289.23/181.72 ![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_d, X))),
% 289.23/181.72 inference(skolemize,[status(sab)],[2114])).
% 289.23/181.72 tff(2116,plain,
% 289.23/181.72 (![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_d, X))),
% 289.23/181.72 inference(modus_ponens,[status(thm)],[2115, 2111])).
% 289.23/181.72 tff(2117,plain,
% 289.23/181.72 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s0)) | m_and_h_gate_v_out(c_e_h_2, c_d, s0))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s0)) | m_and_h_gate_v_out(c_e_h_2, c_d, s0))),
% 289.23/181.72 inference(rewrite,[status(thm)],[])).
% 289.23/181.72 tff(2118,plain,
% 289.23/181.72 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s0)) | m_and_h_gate_v_out(c_e_h_2, c_d, s0))),
% 289.23/181.72 inference(quant_inst,[status(thm)],[])).
% 289.23/181.72 tff(2119,plain,
% 289.23/181.72 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s0)) | m_and_h_gate_v_out(c_e_h_2, c_d, s0)),
% 289.23/181.72 inference(modus_ponens,[status(thm)],[2118, 2117])).
% 289.23/181.72 tff(2120,plain,
% 289.23/181.72 (~m_c_h_element_v_in1(c_e_h_2, c_f, s0)),
% 289.23/181.72 inference(unit_resolution,[status(thm)],[2119, 2116, 2109])).
% 289.23/181.72 tff(2121,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_f, s0)), introduced(assumption)).
% 289.23/181.73 tff(2122,assumption,(node14(c_e_h_2, c_f, s0, s1)), introduced(assumption)).
% 289.23/181.73 tff(2123,plain,
% 289.23/181.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s1)) | m_c_h_element_v_in1(c_e_h_2, c_f, s0) | (~node14(c_e_h_2, c_f, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s1)) | m_c_h_element_v_in1(c_e_h_2, c_f, s0) | (~node14(c_e_h_2, c_f, s0, s1)))),
% 289.23/181.73 inference(rewrite,[status(thm)],[])).
% 289.23/181.73 tff(2124,plain,
% 289.23/181.73 (((~node14(c_e_h_2, c_f, s0, s1)) | m_c_h_element_v_in1(c_e_h_2, c_f, s0) | (~m_c_h_element_v_out(c_e_h_2, c_f, s1))) <=> ((~m_c_h_element_v_out(c_e_h_2, c_f, s1)) | m_c_h_element_v_in1(c_e_h_2, c_f, s0) | (~node14(c_e_h_2, c_f, s0, s1)))),
% 289.23/181.73 inference(rewrite,[status(thm)],[])).
% 289.23/181.73 tff(2125,plain,
% 289.23/181.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_f, s0, s1)) | m_c_h_element_v_in1(c_e_h_2, c_f, s0) | (~m_c_h_element_v_out(c_e_h_2, c_f, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s1)) | m_c_h_element_v_in1(c_e_h_2, c_f, s0) | (~node14(c_e_h_2, c_f, s0, s1))))),
% 289.23/181.73 inference(monotonicity,[status(thm)],[2124])).
% 289.23/181.73 tff(2126,plain,
% 289.23/181.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_f, s0, s1)) | m_c_h_element_v_in1(c_e_h_2, c_f, s0) | (~m_c_h_element_v_out(c_e_h_2, c_f, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s1)) | m_c_h_element_v_in1(c_e_h_2, c_f, s0) | (~node14(c_e_h_2, c_f, s0, s1)))),
% 289.23/181.73 inference(transitivity,[status(thm)],[2125, 2123])).
% 289.23/181.73 tff(2127,plain,
% 289.23/181.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_f, s0, s1)) | m_c_h_element_v_in1(c_e_h_2, c_f, s0) | (~m_c_h_element_v_out(c_e_h_2, c_f, s1)))),
% 289.23/181.73 inference(quant_inst,[status(thm)],[])).
% 289.23/181.73 tff(2128,plain,
% 289.23/181.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s1)) | m_c_h_element_v_in1(c_e_h_2, c_f, s0) | (~node14(c_e_h_2, c_f, s0, s1))),
% 289.23/181.73 inference(modus_ponens,[status(thm)],[2127, 2126])).
% 289.23/181.73 tff(2129,plain,
% 289.23/181.73 ($false),
% 289.23/181.73 inference(unit_resolution,[status(thm)],[2128, 223, 2105, 2122, 2121])).
% 289.23/181.73 tff(2130,plain,((~node14(c_e_h_2, c_f, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s1)) | m_c_h_element_v_in1(c_e_h_2, c_f, s0)), inference(lemma,lemma(discharge,[]))).
% 289.23/181.73 tff(2131,plain,
% 289.23/181.73 ((~node14(c_e_h_2, c_f, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s1))),
% 289.23/181.73 inference(unit_resolution,[status(thm)],[2130, 2120])).
% 289.23/181.73 tff(2132,plain,
% 289.23/181.73 (~node14(c_e_h_2, c_f, s0, s1)),
% 289.23/181.73 inference(unit_resolution,[status(thm)],[2131, 2105])).
% 289.23/181.73 tff(2133,assumption,(m_and_h_gate_v_out(c_e_h_2, c_i, s0)), introduced(assumption)).
% 289.23/181.73 tff(2134,plain,
% 289.23/181.73 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s0))),
% 289.23/181.73 inference(quant_inst,[status(thm)],[])).
% 289.23/181.73 tff(2135,plain,
% 289.23/181.73 ($false),
% 289.23/181.73 inference(unit_resolution,[status(thm)],[2134, 95, 2133])).
% 289.23/181.73 tff(2136,plain,(~m_and_h_gate_v_out(c_e_h_2, c_i, s0)), inference(lemma,lemma(discharge,[]))).
% 289.23/181.73 tff(2137,plain,
% 289.23/181.73 (^[I0: $i, X: $i] : refl(((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X)) <=> ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X)))),
% 289.23/181.73 inference(bind,[status(th)],[])).
% 289.23/181.73 tff(2138,plain,
% 289.23/181.73 (![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X)) <=> ![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))),
% 289.23/181.73 inference(quant_intro,[status(thm)],[2137])).
% 289.23/181.73 tff(2139,plain,
% 289.23/181.73 (![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X)) <=> ![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))),
% 289.23/181.73 inference(rewrite,[status(thm)],[])).
% 289.23/181.73 tff(2140,axiom,(![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_26')).
% 289.23/181.73 tff(2141,plain,
% 289.23/181.73 (![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))),
% 289.23/181.73 inference(modus_ponens,[status(thm)],[2140, 2139])).
% 289.23/181.73 tff(2142,plain,(
% 289.23/181.73 ![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))),
% 289.23/181.73 inference(skolemize,[status(sab)],[2141])).
% 289.23/181.73 tff(2143,plain,
% 289.23/181.73 (![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))),
% 289.23/181.73 inference(modus_ponens,[status(thm)],[2142, 2138])).
% 289.23/181.73 tff(2144,plain,
% 289.23/181.73 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_f, s0)) | m_and_h_gate_v_out(c_e_h_2, c_i, s0))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s0)) | m_and_h_gate_v_out(c_e_h_2, c_i, s0))),
% 289.23/181.73 inference(rewrite,[status(thm)],[])).
% 289.23/181.73 tff(2145,plain,
% 289.23/181.73 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_f, s0)) | m_and_h_gate_v_out(c_e_h_2, c_i, s0))),
% 289.23/181.73 inference(quant_inst,[status(thm)],[])).
% 289.23/181.73 tff(2146,plain,
% 289.23/181.73 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s0)) | m_and_h_gate_v_out(c_e_h_2, c_i, s0)),
% 289.23/181.73 inference(modus_ponens,[status(thm)],[2145, 2144])).
% 289.23/181.73 tff(2147,plain,
% 289.23/181.73 (~m_c_h_element_v_in2(c_e_h_2, c_f, s0)),
% 289.23/181.73 inference(unit_resolution,[status(thm)],[2146, 2143, 2136])).
% 289.23/181.73 tff(2148,plain,
% 289.23/181.73 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_f, s0)) | m_c_h_element_v_in1(c_e_h_2, c_f, s0) | m_c_h_element_v_in2(c_e_h_2, c_f, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_f, s0)) | m_c_h_element_v_in1(c_e_h_2, c_f, s0) | m_c_h_element_v_in2(c_e_h_2, c_f, s0))),
% 289.23/181.73 inference(rewrite,[status(thm)],[])).
% 289.23/181.73 tff(2149,plain,
% 289.23/181.73 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_f, s0)) | m_c_h_element_v_in1(c_e_h_2, c_f, s0) | m_c_h_element_v_in2(c_e_h_2, c_f, s0))),
% 289.23/181.73 inference(quant_inst,[status(thm)],[])).
% 289.23/181.73 tff(2150,plain,
% 289.23/181.73 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_f, s0)) | m_c_h_element_v_in1(c_e_h_2, c_f, s0) | m_c_h_element_v_in2(c_e_h_2, c_f, s0)),
% 289.23/181.73 inference(modus_ponens,[status(thm)],[2149, 2148])).
% 289.23/181.73 tff(2151,plain,
% 289.23/181.73 ((~node16(c_e_h_2, c_f, s0)) | m_c_h_element_v_in2(c_e_h_2, c_f, s0)),
% 289.23/181.73 inference(unit_resolution,[status(thm)],[2150, 178, 2120])).
% 289.23/181.73 tff(2152,plain,
% 289.23/181.73 (~node16(c_e_h_2, c_f, s0)),
% 289.23/181.73 inference(unit_resolution,[status(thm)],[2151, 2147])).
% 289.23/181.73 tff(2153,plain,
% 289.23/181.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s0, s1)) | node19(c_e_h_2, c_f, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s0, s1)) | node19(c_e_h_2, c_f, s0, s1))),
% 289.23/181.73 inference(rewrite,[status(thm)],[])).
% 289.23/181.73 tff(2154,plain,
% 289.23/181.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s0, s1)) | node19(c_e_h_2, c_f, s0, s1))),
% 289.23/181.73 inference(quant_inst,[status(thm)],[])).
% 289.23/181.73 tff(2155,plain,
% 289.23/181.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s0, s1)) | node19(c_e_h_2, c_f, s0, s1)),
% 289.23/181.74 inference(modus_ponens,[status(thm)],[2154, 2153])).
% 289.23/181.74 tff(2156,plain,
% 289.23/181.74 (node19(c_e_h_2, c_f, s0, s1)),
% 289.23/181.74 inference(unit_resolution,[status(thm)],[2155, 190, 72])).
% 289.23/181.74 tff(2157,plain,
% 289.23/181.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s0) | node14(c_e_h_2, c_f, s0, s1) | node15(c_e_h_2, c_f, s0, s1) | (~node19(c_e_h_2, c_f, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_f, s0) | node14(c_e_h_2, c_f, s0, s1) | node15(c_e_h_2, c_f, s0, s1) | (~node19(c_e_h_2, c_f, s0, s1)))),
% 289.23/181.74 inference(rewrite,[status(thm)],[])).
% 289.23/181.74 tff(2158,plain,
% 289.23/181.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s0) | node14(c_e_h_2, c_f, s0, s1) | node15(c_e_h_2, c_f, s0, s1) | (~node19(c_e_h_2, c_f, s0, s1)))),
% 289.23/181.74 inference(quant_inst,[status(thm)],[])).
% 289.23/181.74 tff(2159,plain,
% 289.23/181.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_f, s0) | node14(c_e_h_2, c_f, s0, s1) | node15(c_e_h_2, c_f, s0, s1) | (~node19(c_e_h_2, c_f, s0, s1))),
% 289.23/181.74 inference(modus_ponens,[status(thm)],[2158, 2157])).
% 289.23/181.74 tff(2160,plain,
% 289.23/181.74 (node16(c_e_h_2, c_f, s0) | node14(c_e_h_2, c_f, s0, s1) | node15(c_e_h_2, c_f, s0, s1)),
% 289.23/181.74 inference(unit_resolution,[status(thm)],[2159, 204, 2156])).
% 289.23/181.74 tff(2161,plain,
% 289.23/181.74 (node14(c_e_h_2, c_f, s0, s1) | node15(c_e_h_2, c_f, s0, s1)),
% 289.23/181.74 inference(unit_resolution,[status(thm)],[2160, 2152])).
% 289.23/181.74 tff(2162,plain,
% 289.23/181.74 (node15(c_e_h_2, c_f, s0, s1)),
% 289.23/181.74 inference(unit_resolution,[status(thm)],[2161, 2132])).
% 289.23/181.74 tff(2163,plain,
% 289.23/181.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s1)) | (~node15(c_e_h_2, c_f, s0, s1)) | m_c_h_element_v_out(c_e_h_2, c_f, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s1)) | (~node15(c_e_h_2, c_f, s0, s1)) | m_c_h_element_v_out(c_e_h_2, c_f, s0))),
% 289.23/181.74 inference(rewrite,[status(thm)],[])).
% 289.23/181.74 tff(2164,plain,
% 289.23/181.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s1)) | (~node15(c_e_h_2, c_f, s0, s1)) | m_c_h_element_v_out(c_e_h_2, c_f, s0))),
% 289.23/181.74 inference(quant_inst,[status(thm)],[])).
% 289.23/181.74 tff(2165,plain,
% 289.23/181.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s1)) | (~node15(c_e_h_2, c_f, s0, s1)) | m_c_h_element_v_out(c_e_h_2, c_f, s0)),
% 289.23/181.74 inference(modus_ponens,[status(thm)],[2164, 2163])).
% 289.23/181.74 tff(2166,plain,
% 289.23/181.74 ($false),
% 289.23/181.74 inference(unit_resolution,[status(thm)],[2165, 147, 1579, 2105, 2162])).
% 289.23/181.74 tff(2167,plain,(~m_c_h_element_v_out(c_e_h_2, c_f, s1)), inference(lemma,lemma(discharge,[]))).
% 289.23/181.74 tff(2168,plain,
% 289.23/181.74 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_q, s1)) | m_c_h_element_v_out(c_e_h_2, c_f, s1))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_q, s1)) | m_c_h_element_v_out(c_e_h_2, c_f, s1))),
% 289.23/181.74 inference(rewrite,[status(thm)],[])).
% 289.23/181.74 tff(2169,plain,
% 289.23/181.74 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_q, s1)) | m_c_h_element_v_out(c_e_h_2, c_f, s1))),
% 289.23/181.74 inference(quant_inst,[status(thm)],[])).
% 289.23/181.74 tff(2170,plain,
% 289.23/181.74 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_q, s1)) | m_c_h_element_v_out(c_e_h_2, c_f, s1)),
% 289.23/181.74 inference(modus_ponens,[status(thm)],[2169, 2168])).
% 289.23/181.74 tff(2171,plain,
% 289.23/181.74 (~m_and_h_gate_v_in1(c_e_h_2, c_q, s1)),
% 289.23/181.74 inference(unit_resolution,[status(thm)],[2170, 1586, 2167])).
% 289.23/181.74 tff(2172,plain,
% 289.23/181.74 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_q, s1)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_q, s1)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s1))),
% 289.23/181.74 inference(rewrite,[status(thm)],[])).
% 289.23/181.74 tff(2173,plain,
% 289.23/181.74 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_q, s1)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s1))),
% 289.23/181.74 inference(quant_inst,[status(thm)],[])).
% 289.23/181.74 tff(2174,plain,
% 289.23/181.74 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_q, s1)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s1)),
% 289.23/181.74 inference(modus_ponens,[status(thm)],[2173, 2172])).
% 289.23/181.74 tff(2175,plain,
% 289.23/181.74 (~node20(c_e_h_2, c_q, s1)),
% 289.23/181.74 inference(unit_resolution,[status(thm)],[2174, 38, 2171])).
% 289.23/181.74 tff(2176,plain,
% 289.23/181.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s2)) | node20(c_e_h_2, c_q, s1) | (~node21(c_e_h_2, c_q, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s2)) | node20(c_e_h_2, c_q, s1) | (~node21(c_e_h_2, c_q, s1, s2)))),
% 289.23/181.74 inference(rewrite,[status(thm)],[])).
% 289.23/181.74 tff(2177,plain,
% 289.23/181.74 ((node20(c_e_h_2, c_q, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s2)) | (~node21(c_e_h_2, c_q, s1, s2))) <=> ((~m_and_h_gate_v_out(c_e_h_2, c_q, s2)) | node20(c_e_h_2, c_q, s1) | (~node21(c_e_h_2, c_q, s1, s2)))),
% 289.23/181.74 inference(rewrite,[status(thm)],[])).
% 289.23/181.74 tff(2178,plain,
% 289.23/181.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_q, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s2)) | (~node21(c_e_h_2, c_q, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s2)) | node20(c_e_h_2, c_q, s1) | (~node21(c_e_h_2, c_q, s1, s2))))),
% 289.23/181.74 inference(monotonicity,[status(thm)],[2177])).
% 289.23/181.74 tff(2179,plain,
% 289.23/181.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_q, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s2)) | (~node21(c_e_h_2, c_q, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s2)) | node20(c_e_h_2, c_q, s1) | (~node21(c_e_h_2, c_q, s1, s2)))),
% 289.23/181.74 inference(transitivity,[status(thm)],[2178, 2176])).
% 289.23/181.74 tff(2180,plain,
% 289.23/181.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_q, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s2)) | (~node21(c_e_h_2, c_q, s1, s2)))),
% 289.23/181.74 inference(quant_inst,[status(thm)],[])).
% 289.23/181.74 tff(2181,plain,
% 289.23/181.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s2)) | node20(c_e_h_2, c_q, s1) | (~node21(c_e_h_2, c_q, s1, s2))),
% 289.23/181.74 inference(modus_ponens,[status(thm)],[2180, 2179])).
% 289.23/181.74 tff(2182,plain,
% 289.23/181.74 ($false),
% 289.23/181.74 inference(unit_resolution,[status(thm)],[2181, 52, 2103, 2175, 2104])).
% 289.23/181.74 tff(2183,plain,((~node21(c_e_h_2, c_q, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s2))), inference(lemma,lemma(discharge,[]))).
% 289.23/181.74 tff(2184,plain,
% 289.23/181.74 (~node21(c_e_h_2, c_q, s1, s2)),
% 289.23/181.74 inference(unit_resolution,[status(thm)],[2183, 2103])).
% 289.23/181.74 tff(2185,plain,
% 289.23/181.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_2, c_q, s1, s2) | node22(c_e_h_2, c_q, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_2, c_q, s1, s2) | node22(c_e_h_2, c_q, s1, s2))),
% 289.23/181.74 inference(rewrite,[status(thm)],[])).
% 289.23/181.74 tff(2186,plain,
% 289.23/181.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_2, c_q, s1, s2) | node22(c_e_h_2, c_q, s1, s2))),
% 289.23/181.74 inference(quant_inst,[status(thm)],[])).
% 289.23/181.74 tff(2187,plain,
% 289.23/181.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_2, c_q, s1, s2) | node22(c_e_h_2, c_q, s1, s2)),
% 289.23/181.74 inference(modus_ponens,[status(thm)],[2186, 2185])).
% 289.23/181.74 tff(2188,plain,
% 289.23/181.74 (node21(c_e_h_2, c_q, s1, s2) | node22(c_e_h_2, c_q, s1, s2)),
% 289.23/181.74 inference(unit_resolution,[status(thm)],[2187, 82, 255])).
% 289.23/181.74 tff(2189,plain,
% 289.23/181.74 (node22(c_e_h_2, c_q, s1, s2)),
% 289.23/181.74 inference(unit_resolution,[status(thm)],[2188, 2184])).
% 289.23/181.74 tff(2190,plain,
% 289.23/181.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s2)) | (~node22(c_e_h_2, c_q, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_q, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s2)) | (~node22(c_e_h_2, c_q, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_q, s1))),
% 289.23/181.74 inference(rewrite,[status(thm)],[])).
% 289.23/181.74 tff(2191,plain,
% 289.23/181.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s2)) | (~node22(c_e_h_2, c_q, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_q, s1))),
% 289.23/181.74 inference(quant_inst,[status(thm)],[])).
% 289.23/181.74 tff(2192,plain,
% 289.23/181.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s2)) | (~node22(c_e_h_2, c_q, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_q, s1)),
% 289.23/181.74 inference(modus_ponens,[status(thm)],[2191, 2190])).
% 289.23/181.74 tff(2193,plain,
% 289.23/181.74 ($false),
% 289.23/181.74 inference(unit_resolution,[status(thm)],[2192, 108, 1602, 2103, 2189])).
% 289.23/181.74 tff(2194,plain,(~m_and_h_gate_v_out(c_e_h_2, c_q, s2)), inference(lemma,lemma(discharge,[]))).
% 289.23/181.74 tff(2195,plain,
% 289.23/181.74 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s2))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s2))),
% 289.23/181.74 inference(rewrite,[status(thm)],[])).
% 289.23/181.74 tff(2196,plain,
% 289.23/181.74 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s2))),
% 289.23/181.74 inference(quant_inst,[status(thm)],[])).
% 289.23/181.74 tff(2197,plain,
% 289.23/181.74 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s2)),
% 289.23/181.74 inference(modus_ponens,[status(thm)],[2196, 2195])).
% 289.23/181.74 tff(2198,plain,
% 289.23/181.74 (node3(c_e_h_2, c_e_h_3, s2)),
% 289.23/181.74 inference(unit_resolution,[status(thm)],[2197, 1059, 1056])).
% 289.23/181.74 tff(2199,plain,
% 289.23/181.74 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_3, s2)) | (~node3(c_e_h_2, c_e_h_3, s2)) | m_and_h_gate_v_out(c_e_h_2, c_q, s2))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_3, s2)) | (~node3(c_e_h_2, c_e_h_3, s2)) | m_and_h_gate_v_out(c_e_h_2, c_q, s2))),
% 289.23/181.74 inference(rewrite,[status(thm)],[])).
% 289.23/181.74 tff(2200,plain,
% 289.23/181.74 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_3, s2)) | (~node3(c_e_h_2, c_e_h_3, s2)) | m_and_h_gate_v_out(c_e_h_2, c_q, s2))),
% 289.23/181.75 inference(quant_inst,[status(thm)],[])).
% 289.23/181.75 tff(2201,plain,
% 289.23/181.75 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_3, s2)) | (~node3(c_e_h_2, c_e_h_3, s2)) | m_and_h_gate_v_out(c_e_h_2, c_q, s2)),
% 289.23/181.75 inference(modus_ponens,[status(thm)],[2200, 2199])).
% 289.23/181.75 tff(2202,plain,
% 289.23/181.75 ((~m_cell_v_ack(c_e_h_3, s2)) | m_and_h_gate_v_out(c_e_h_2, c_q, s2)),
% 289.23/181.75 inference(unit_resolution,[status(thm)],[2201, 1073, 2198])).
% 289.23/181.75 tff(2203,plain,
% 289.23/181.75 (~m_cell_v_ack(c_e_h_3, s2)),
% 289.23/181.75 inference(unit_resolution,[status(thm)],[2202, 2194])).
% 289.23/181.75 tff(2204,plain,
% 289.23/181.75 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_j, s2)) | m_cell_v_ack(c_e_h_3, s2))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_j, s2)) | m_cell_v_ack(c_e_h_3, s2))),
% 289.23/181.75 inference(rewrite,[status(thm)],[])).
% 289.23/181.75 tff(2205,plain,
% 289.23/181.75 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_j, s2)) | m_cell_v_ack(c_e_h_3, s2))),
% 289.23/181.75 inference(quant_inst,[status(thm)],[])).
% 289.23/181.75 tff(2206,plain,
% 289.23/181.75 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_j, s2)) | m_cell_v_ack(c_e_h_3, s2)),
% 289.23/181.75 inference(modus_ponens,[status(thm)],[2205, 2204])).
% 289.23/181.75 tff(2207,plain,
% 289.23/181.75 (~m_or_h_gate_v_in2(c_e_h_3, c_j, s2)),
% 289.23/181.75 inference(unit_resolution,[status(thm)],[2206, 1085, 2203])).
% 289.23/181.75 tff(2208,assumption,(node5(c_e_h_3, c_j, s2, s3)), introduced(assumption)).
% 289.23/181.75 tff(2209,plain,
% 289.23/181.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_3, c_j, s3)) | (~node5(c_e_h_3, c_j, s2, s3)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s2) | m_or_h_gate_v_in1(c_e_h_3, c_j, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s3)) | (~node5(c_e_h_3, c_j, s2, s3)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s2) | m_or_h_gate_v_in1(c_e_h_3, c_j, s2))),
% 289.23/181.75 inference(rewrite,[status(thm)],[])).
% 289.23/181.75 tff(2210,plain,
% 289.23/181.75 ((m_or_h_gate_v_in1(c_e_h_3, c_j, s2) | m_or_h_gate_v_in2(c_e_h_3, c_j, s2) | (~node5(c_e_h_3, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s3))) <=> ((~m_or_h_gate_v_out(c_e_h_3, c_j, s3)) | (~node5(c_e_h_3, c_j, s2, s3)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s2) | m_or_h_gate_v_in1(c_e_h_3, c_j, s2))),
% 289.23/181.75 inference(rewrite,[status(thm)],[])).
% 289.23/181.75 tff(2211,plain,
% 289.23/181.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s2) | m_or_h_gate_v_in2(c_e_h_3, c_j, s2) | (~node5(c_e_h_3, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_3, c_j, s3)) | (~node5(c_e_h_3, c_j, s2, s3)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s2) | m_or_h_gate_v_in1(c_e_h_3, c_j, s2)))),
% 289.23/181.75 inference(monotonicity,[status(thm)],[2210])).
% 289.23/181.75 tff(2212,plain,
% 289.23/181.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s2) | m_or_h_gate_v_in2(c_e_h_3, c_j, s2) | (~node5(c_e_h_3, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s3)) | (~node5(c_e_h_3, c_j, s2, s3)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s2) | m_or_h_gate_v_in1(c_e_h_3, c_j, s2))),
% 289.23/181.75 inference(transitivity,[status(thm)],[2211, 2209])).
% 289.23/181.75 tff(2213,plain,
% 289.23/181.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s2) | m_or_h_gate_v_in2(c_e_h_3, c_j, s2) | (~node5(c_e_h_3, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s3)))),
% 289.23/181.75 inference(quant_inst,[status(thm)],[])).
% 289.23/181.75 tff(2214,plain,
% 289.23/181.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s3)) | (~node5(c_e_h_3, c_j, s2, s3)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s2) | m_or_h_gate_v_in1(c_e_h_3, c_j, s2)),
% 289.23/181.75 inference(modus_ponens,[status(thm)],[2213, 2212])).
% 289.23/181.75 tff(2215,plain,
% 289.23/181.75 ($false),
% 289.23/181.75 inference(unit_resolution,[status(thm)],[2214, 1159, 2208, 2029, 2207, 2102])).
% 289.23/181.75 tff(2216,plain,((~node5(c_e_h_3, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s3))), inference(lemma,lemma(discharge,[]))).
% 289.23/181.75 tff(2217,plain,
% 289.23/181.75 (~node5(c_e_h_3, c_j, s2, s3)),
% 289.23/181.75 inference(unit_resolution,[status(thm)],[2216, 2029])).
% 289.23/181.75 tff(2218,plain,
% 289.23/181.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s2, s3)) | node5(c_e_h_3, c_j, s2, s3) | node6(c_e_h_3, c_j, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s2, s3)) | node5(c_e_h_3, c_j, s2, s3) | node6(c_e_h_3, c_j, s2, s3))),
% 289.23/181.75 inference(rewrite,[status(thm)],[])).
% 289.23/181.75 tff(2219,plain,
% 289.23/181.75 ((node6(c_e_h_3, c_j, s2, s3) | node5(c_e_h_3, c_j, s2, s3) | (~trans(s2, s3))) <=> ((~trans(s2, s3)) | node5(c_e_h_3, c_j, s2, s3) | node6(c_e_h_3, c_j, s2, s3))),
% 289.23/181.75 inference(rewrite,[status(thm)],[])).
% 289.23/181.75 tff(2220,plain,
% 289.23/181.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s2, s3) | node5(c_e_h_3, c_j, s2, s3) | (~trans(s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s2, s3)) | node5(c_e_h_3, c_j, s2, s3) | node6(c_e_h_3, c_j, s2, s3)))),
% 289.23/181.75 inference(monotonicity,[status(thm)],[2219])).
% 289.23/181.75 tff(2221,plain,
% 289.23/181.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s2, s3) | node5(c_e_h_3, c_j, s2, s3) | (~trans(s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s2, s3)) | node5(c_e_h_3, c_j, s2, s3) | node6(c_e_h_3, c_j, s2, s3))),
% 289.23/181.75 inference(transitivity,[status(thm)],[2220, 2218])).
% 289.23/181.75 tff(2222,plain,
% 289.23/181.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s2, s3) | node5(c_e_h_3, c_j, s2, s3) | (~trans(s2, s3)))),
% 289.23/181.75 inference(quant_inst,[status(thm)],[])).
% 289.23/181.75 tff(2223,plain,
% 289.23/181.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s2, s3)) | node5(c_e_h_3, c_j, s2, s3) | node6(c_e_h_3, c_j, s2, s3)),
% 289.23/181.75 inference(modus_ponens,[status(thm)],[2222, 2221])).
% 289.23/181.75 tff(2224,plain,
% 289.23/181.75 (node5(c_e_h_3, c_j, s2, s3) | node6(c_e_h_3, c_j, s2, s3)),
% 289.23/181.75 inference(unit_resolution,[status(thm)],[2223, 1141, 318])).
% 289.23/181.75 tff(2225,plain,
% 289.23/181.75 (node6(c_e_h_3, c_j, s2, s3)),
% 289.23/181.75 inference(unit_resolution,[status(thm)],[2224, 2217])).
% 289.23/181.75 tff(2226,plain,
% 289.23/181.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_3, c_j, s3)) | m_or_h_gate_v_out(c_e_h_3, c_j, s2) | (~node6(c_e_h_3, c_j, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s3)) | m_or_h_gate_v_out(c_e_h_3, c_j, s2) | (~node6(c_e_h_3, c_j, s2, s3)))),
% 289.23/181.75 inference(rewrite,[status(thm)],[])).
% 289.23/181.75 tff(2227,plain,
% 289.23/181.75 (((~node6(c_e_h_3, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s3)) | m_or_h_gate_v_out(c_e_h_3, c_j, s2)) <=> ((~m_or_h_gate_v_out(c_e_h_3, c_j, s3)) | m_or_h_gate_v_out(c_e_h_3, c_j, s2) | (~node6(c_e_h_3, c_j, s2, s3)))),
% 289.23/181.75 inference(rewrite,[status(thm)],[])).
% 289.23/181.75 tff(2228,plain,
% 289.23/181.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s3)) | m_or_h_gate_v_out(c_e_h_3, c_j, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_3, c_j, s3)) | m_or_h_gate_v_out(c_e_h_3, c_j, s2) | (~node6(c_e_h_3, c_j, s2, s3))))),
% 289.23/181.75 inference(monotonicity,[status(thm)],[2227])).
% 289.23/181.75 tff(2229,plain,
% 289.23/181.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s3)) | m_or_h_gate_v_out(c_e_h_3, c_j, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s3)) | m_or_h_gate_v_out(c_e_h_3, c_j, s2) | (~node6(c_e_h_3, c_j, s2, s3)))),
% 289.23/181.75 inference(transitivity,[status(thm)],[2228, 2226])).
% 289.23/181.75 tff(2230,plain,
% 289.23/181.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s3)) | m_or_h_gate_v_out(c_e_h_3, c_j, s2))),
% 289.23/181.75 inference(quant_inst,[status(thm)],[])).
% 289.23/181.75 tff(2231,plain,
% 289.23/181.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s3)) | m_or_h_gate_v_out(c_e_h_3, c_j, s2) | (~node6(c_e_h_3, c_j, s2, s3))),
% 289.23/181.75 inference(modus_ponens,[status(thm)],[2230, 2229])).
% 289.23/181.75 tff(2232,plain,
% 289.23/181.75 ($false),
% 289.23/181.75 inference(unit_resolution,[status(thm)],[2231, 1121, 2225, 1642, 2029])).
% 289.23/181.75 tff(2233,plain,(~m_or_h_gate_v_out(c_e_h_3, c_j, s3)), inference(lemma,lemma(discharge,[]))).
% 289.23/181.75 tff(2234,assumption,(m_c_h_element_v_in2(c_e_h_3, c_h, s3)), introduced(assumption)).
% 289.23/181.75 tff(2235,assumption,(~m_or_h_gate_v_out(c_e_h_3, c_j, s3)), introduced(assumption)).
% 289.23/181.75 tff(2236,plain,
% 289.23/181.75 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s3)) | m_or_h_gate_v_out(c_e_h_3, c_j, s3))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s3)) | m_or_h_gate_v_out(c_e_h_3, c_j, s3))),
% 289.23/181.75 inference(rewrite,[status(thm)],[])).
% 289.23/181.75 tff(2237,plain,
% 289.23/181.75 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s3)) | m_or_h_gate_v_out(c_e_h_3, c_j, s3))),
% 289.23/181.75 inference(quant_inst,[status(thm)],[])).
% 289.23/181.75 tff(2238,plain,
% 289.23/181.75 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s3)) | m_or_h_gate_v_out(c_e_h_3, c_j, s3)),
% 289.23/181.75 inference(modus_ponens,[status(thm)],[2237, 2236])).
% 289.23/181.75 tff(2239,plain,
% 289.23/181.75 ($false),
% 289.23/181.75 inference(unit_resolution,[status(thm)],[2238, 1174, 2235, 2234])).
% 289.23/181.75 tff(2240,plain,((~m_c_h_element_v_in2(c_e_h_3, c_h, s3)) | m_or_h_gate_v_out(c_e_h_3, c_j, s3)), inference(lemma,lemma(discharge,[]))).
% 289.23/181.75 tff(2241,plain,
% 289.23/181.75 (~m_c_h_element_v_in2(c_e_h_3, c_h, s3)),
% 289.23/181.75 inference(unit_resolution,[status(thm)],[2240, 2233])).
% 289.23/181.75 tff(2242,assumption,(m_c_h_element_v_out(c_e_h_3, c_h, s4)), introduced(assumption)).
% 289.23/181.75 tff(2243,assumption,(~m_c_h_element_v_out(c_e_h_3, c_h, s3)), introduced(assumption)).
% 289.23/181.75 tff(2244,assumption,(node18(c_e_h_3, c_h, s3, s4)), introduced(assumption)).
% 289.23/181.75 tff(2245,plain,
% 289.23/181.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_h, s3) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4)) | (~node18(c_e_h_3, c_h, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s3) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4)) | (~node18(c_e_h_3, c_h, s3, s4)))),
% 289.23/181.76 inference(rewrite,[status(thm)],[])).
% 289.23/181.76 tff(2246,plain,
% 289.23/181.76 (((~m_c_h_element_v_out(c_e_h_3, c_h, s4)) | m_c_h_element_v_out(c_e_h_3, c_h, s3) | (~node18(c_e_h_3, c_h, s3, s4))) <=> (m_c_h_element_v_out(c_e_h_3, c_h, s3) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4)) | (~node18(c_e_h_3, c_h, s3, s4)))),
% 289.23/181.76 inference(rewrite,[status(thm)],[])).
% 289.23/181.76 tff(2247,plain,
% 289.23/181.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s4)) | m_c_h_element_v_out(c_e_h_3, c_h, s3) | (~node18(c_e_h_3, c_h, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_h, s3) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4)) | (~node18(c_e_h_3, c_h, s3, s4))))),
% 289.23/181.76 inference(monotonicity,[status(thm)],[2246])).
% 289.23/181.76 tff(2248,plain,
% 289.23/181.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s4)) | m_c_h_element_v_out(c_e_h_3, c_h, s3) | (~node18(c_e_h_3, c_h, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s3) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4)) | (~node18(c_e_h_3, c_h, s3, s4)))),
% 289.23/181.76 inference(transitivity,[status(thm)],[2247, 2245])).
% 289.23/181.76 tff(2249,plain,
% 289.23/181.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s4)) | m_c_h_element_v_out(c_e_h_3, c_h, s3) | (~node18(c_e_h_3, c_h, s3, s4)))),
% 289.23/181.76 inference(quant_inst,[status(thm)],[])).
% 289.23/181.76 tff(2250,plain,
% 289.23/181.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s3) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4)) | (~node18(c_e_h_3, c_h, s3, s4))),
% 289.23/181.76 inference(modus_ponens,[status(thm)],[2249, 2248])).
% 289.23/181.76 tff(2251,plain,
% 289.23/181.76 ($false),
% 289.23/181.76 inference(unit_resolution,[status(thm)],[2250, 753, 2244, 2243, 2242])).
% 289.23/181.76 tff(2252,plain,((~node18(c_e_h_3, c_h, s3, s4)) | m_c_h_element_v_out(c_e_h_3, c_h, s3) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4))), inference(lemma,lemma(discharge,[]))).
% 289.23/181.76 tff(2253,plain,
% 289.23/181.76 (~node18(c_e_h_3, c_h, s3, s4)),
% 289.23/181.76 inference(unit_resolution,[status(thm)],[2252, 2243, 2242])).
% 289.23/181.76 tff(2254,plain,
% 289.23/181.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s3, s4)) | node19(c_e_h_3, c_h, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s3, s4)) | node19(c_e_h_3, c_h, s3, s4))),
% 289.23/181.76 inference(rewrite,[status(thm)],[])).
% 289.23/181.76 tff(2255,plain,
% 289.23/181.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s3, s4)) | node19(c_e_h_3, c_h, s3, s4))),
% 289.23/181.76 inference(quant_inst,[status(thm)],[])).
% 289.23/181.76 tff(2256,plain,
% 289.23/181.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s3, s4)) | node19(c_e_h_3, c_h, s3, s4)),
% 289.23/181.76 inference(modus_ponens,[status(thm)],[2255, 2254])).
% 289.23/181.76 tff(2257,plain,
% 289.23/181.76 (node19(c_e_h_3, c_h, s3, s4)),
% 289.23/181.76 inference(unit_resolution,[status(thm)],[2256, 190, 531])).
% 289.23/181.76 tff(2258,plain,
% 289.23/181.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_3, c_h, s3, s4) | (~node19(c_e_h_3, c_h, s3, s4)) | node17(c_e_h_3, c_h, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_3, c_h, s3, s4) | (~node19(c_e_h_3, c_h, s3, s4)) | node17(c_e_h_3, c_h, s3))),
% 289.23/181.76 inference(rewrite,[status(thm)],[])).
% 289.23/181.76 tff(2259,plain,
% 289.23/181.76 ((node17(c_e_h_3, c_h, s3) | node18(c_e_h_3, c_h, s3, s4) | (~node19(c_e_h_3, c_h, s3, s4))) <=> (node18(c_e_h_3, c_h, s3, s4) | (~node19(c_e_h_3, c_h, s3, s4)) | node17(c_e_h_3, c_h, s3))),
% 289.23/181.76 inference(rewrite,[status(thm)],[])).
% 289.23/181.76 tff(2260,plain,
% 289.23/181.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s3) | node18(c_e_h_3, c_h, s3, s4) | (~node19(c_e_h_3, c_h, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_3, c_h, s3, s4) | (~node19(c_e_h_3, c_h, s3, s4)) | node17(c_e_h_3, c_h, s3)))),
% 289.23/181.76 inference(monotonicity,[status(thm)],[2259])).
% 289.23/181.76 tff(2261,plain,
% 289.23/181.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s3) | node18(c_e_h_3, c_h, s3, s4) | (~node19(c_e_h_3, c_h, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_3, c_h, s3, s4) | (~node19(c_e_h_3, c_h, s3, s4)) | node17(c_e_h_3, c_h, s3))),
% 289.23/181.76 inference(transitivity,[status(thm)],[2260, 2258])).
% 289.23/181.76 tff(2262,plain,
% 289.23/181.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s3) | node18(c_e_h_3, c_h, s3, s4) | (~node19(c_e_h_3, c_h, s3, s4)))),
% 289.23/181.76 inference(quant_inst,[status(thm)],[])).
% 289.23/181.76 tff(2263,plain,
% 289.23/181.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_3, c_h, s3, s4) | (~node19(c_e_h_3, c_h, s3, s4)) | node17(c_e_h_3, c_h, s3)),
% 289.23/181.76 inference(modus_ponens,[status(thm)],[2262, 2261])).
% 289.23/181.76 tff(2264,plain,
% 289.23/181.76 (node18(c_e_h_3, c_h, s3, s4) | node17(c_e_h_3, c_h, s3)),
% 289.23/181.76 inference(unit_resolution,[status(thm)],[2263, 776, 2257])).
% 289.23/181.76 tff(2265,plain,
% 289.23/181.76 (node17(c_e_h_3, c_h, s3)),
% 289.23/181.76 inference(unit_resolution,[status(thm)],[2264, 2253])).
% 289.23/181.76 tff(2266,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_h, s3)), introduced(assumption)).
% 289.23/181.76 tff(2267,plain,
% 289.23/181.76 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_3, c_h, s3) | (~node17(c_e_h_3, c_h, s3)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_h, s3) | (~node17(c_e_h_3, c_h, s3)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s3)))),
% 289.23/181.76 inference(rewrite,[status(thm)],[])).
% 289.23/181.76 tff(2268,plain,
% 289.23/181.76 (((~m_c_h_element_v_in1(c_e_h_3, c_h, s3)) | m_c_h_element_v_in2(c_e_h_3, c_h, s3) | (~node17(c_e_h_3, c_h, s3))) <=> (m_c_h_element_v_in2(c_e_h_3, c_h, s3) | (~node17(c_e_h_3, c_h, s3)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s3)))),
% 289.23/181.76 inference(rewrite,[status(thm)],[])).
% 289.23/181.76 tff(2269,plain,
% 289.23/181.76 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s3)) | m_c_h_element_v_in2(c_e_h_3, c_h, s3) | (~node17(c_e_h_3, c_h, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_3, c_h, s3) | (~node17(c_e_h_3, c_h, s3)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s3))))),
% 289.23/181.76 inference(monotonicity,[status(thm)],[2268])).
% 289.23/181.76 tff(2270,plain,
% 289.23/181.76 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s3)) | m_c_h_element_v_in2(c_e_h_3, c_h, s3) | (~node17(c_e_h_3, c_h, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_h, s3) | (~node17(c_e_h_3, c_h, s3)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s3)))),
% 289.23/181.77 inference(transitivity,[status(thm)],[2269, 2267])).
% 289.23/181.77 tff(2271,plain,
% 289.23/181.77 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s3)) | m_c_h_element_v_in2(c_e_h_3, c_h, s3) | (~node17(c_e_h_3, c_h, s3)))),
% 289.23/181.77 inference(quant_inst,[status(thm)],[])).
% 289.23/181.77 tff(2272,plain,
% 289.23/181.77 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_h, s3) | (~node17(c_e_h_3, c_h, s3)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s3))),
% 289.23/181.77 inference(modus_ponens,[status(thm)],[2271, 2270])).
% 289.23/181.77 tff(2273,plain,
% 289.23/181.77 ((~node17(c_e_h_3, c_h, s3)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s3))),
% 289.23/181.77 inference(unit_resolution,[status(thm)],[2272, 919, 2266])).
% 289.23/181.77 tff(2274,plain,
% 289.23/181.77 (~m_c_h_element_v_in1(c_e_h_3, c_h, s3)),
% 289.23/181.77 inference(unit_resolution,[status(thm)],[2273, 2265])).
% 289.23/181.77 tff(2275,assumption,(node15(c_e_h_3, c_h, s3, s4)), introduced(assumption)).
% 289.23/181.77 tff(2276,plain,
% 289.23/181.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s4)) | (~node15(c_e_h_3, c_h, s3, s4)) | m_c_h_element_v_out(c_e_h_3, c_h, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4)) | (~node15(c_e_h_3, c_h, s3, s4)) | m_c_h_element_v_out(c_e_h_3, c_h, s3))),
% 289.23/181.77 inference(rewrite,[status(thm)],[])).
% 289.23/181.77 tff(2277,plain,
% 289.23/181.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s4)) | (~node15(c_e_h_3, c_h, s3, s4)) | m_c_h_element_v_out(c_e_h_3, c_h, s3))),
% 289.23/181.77 inference(quant_inst,[status(thm)],[])).
% 289.23/181.77 tff(2278,plain,
% 289.23/181.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4)) | (~node15(c_e_h_3, c_h, s3, s4)) | m_c_h_element_v_out(c_e_h_3, c_h, s3)),
% 289.23/181.77 inference(modus_ponens,[status(thm)],[2277, 2276])).
% 289.23/181.77 tff(2279,plain,
% 289.23/181.77 ($false),
% 289.23/181.77 inference(unit_resolution,[status(thm)],[2278, 147, 2275, 2243, 2242])).
% 289.23/181.77 tff(2280,plain,((~node15(c_e_h_3, c_h, s3, s4)) | m_c_h_element_v_out(c_e_h_3, c_h, s3) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4))), inference(lemma,lemma(discharge,[]))).
% 289.23/181.77 tff(2281,plain,
% 289.23/181.77 (~node15(c_e_h_3, c_h, s3, s4)),
% 289.23/181.77 inference(unit_resolution,[status(thm)],[2280, 2243, 2242])).
% 289.23/181.77 tff(2282,assumption,(node17(c_e_h_3, c_h, s3)), introduced(assumption)).
% 289.23/181.77 tff(2283,assumption,(node16(c_e_h_3, c_h, s3)), introduced(assumption)).
% 289.23/181.77 tff(2284,plain,
% 289.23/181.77 (m_c_h_element_v_in2(c_e_h_3, c_h, s3) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s3))),
% 289.23/181.77 inference(unit_resolution,[status(thm)],[2272, 919, 2282])).
% 289.23/181.77 tff(2285,plain,
% 289.23/181.77 (~m_c_h_element_v_in1(c_e_h_3, c_h, s3)),
% 289.23/181.77 inference(unit_resolution,[status(thm)],[2284, 2266])).
% 289.23/181.77 tff(2286,plain,
% 289.23/181.77 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_h, s3)) | m_c_h_element_v_in1(c_e_h_3, c_h, s3) | m_c_h_element_v_in2(c_e_h_3, c_h, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_h, s3)) | m_c_h_element_v_in1(c_e_h_3, c_h, s3) | m_c_h_element_v_in2(c_e_h_3, c_h, s3))),
% 289.23/181.77 inference(rewrite,[status(thm)],[])).
% 289.23/181.77 tff(2287,plain,
% 289.23/181.77 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_h, s3)) | m_c_h_element_v_in1(c_e_h_3, c_h, s3) | m_c_h_element_v_in2(c_e_h_3, c_h, s3))),
% 289.23/181.77 inference(quant_inst,[status(thm)],[])).
% 289.23/181.77 tff(2288,plain,
% 289.23/181.77 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_h, s3)) | m_c_h_element_v_in1(c_e_h_3, c_h, s3) | m_c_h_element_v_in2(c_e_h_3, c_h, s3)),
% 289.23/181.77 inference(modus_ponens,[status(thm)],[2287, 2286])).
% 289.23/181.77 tff(2289,plain,
% 289.23/181.77 (m_c_h_element_v_in1(c_e_h_3, c_h, s3) | m_c_h_element_v_in2(c_e_h_3, c_h, s3)),
% 289.23/181.77 inference(unit_resolution,[status(thm)],[2288, 178, 2283])).
% 289.23/181.77 tff(2290,plain,
% 289.23/181.77 ($false),
% 289.23/181.77 inference(unit_resolution,[status(thm)],[2289, 2285, 2266])).
% 289.23/181.77 tff(2291,plain,(m_c_h_element_v_in2(c_e_h_3, c_h, s3) | (~node16(c_e_h_3, c_h, s3)) | (~node17(c_e_h_3, c_h, s3))), inference(lemma,lemma(discharge,[]))).
% 289.23/181.77 tff(2292,plain,
% 289.23/181.77 (m_c_h_element_v_in2(c_e_h_3, c_h, s3)),
% 289.23/181.77 inference(unit_resolution,[status(thm)],[2291, 2283, 2282])).
% 289.23/181.77 tff(2293,plain,
% 289.23/181.77 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s3) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s3)) | (~node17(c_e_h_3, c_h, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_3, c_h, s3) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s3)) | (~node17(c_e_h_3, c_h, s3)))),
% 289.23/181.77 inference(rewrite,[status(thm)],[])).
% 289.23/181.77 tff(2294,plain,
% 289.23/181.77 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s3) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s3)) | (~node17(c_e_h_3, c_h, s3)))),
% 289.23/181.77 inference(quant_inst,[status(thm)],[])).
% 289.23/181.77 tff(2295,plain,
% 289.23/181.77 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_3, c_h, s3) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s3)) | (~node17(c_e_h_3, c_h, s3))),
% 289.23/181.77 inference(modus_ponens,[status(thm)],[2294, 2293])).
% 289.23/181.77 tff(2296,plain,
% 289.23/181.77 (m_c_h_element_v_in1(c_e_h_3, c_h, s3) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s3))),
% 289.23/181.77 inference(unit_resolution,[status(thm)],[2295, 859, 2282])).
% 289.23/181.77 tff(2297,plain,
% 289.23/181.77 (m_c_h_element_v_in1(c_e_h_3, c_h, s3)),
% 289.23/181.77 inference(unit_resolution,[status(thm)],[2296, 2292])).
% 289.23/181.77 tff(2298,plain,
% 289.23/181.77 (^[I0: $i, X: $i, I1: $i] : refl(((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X))) <=> ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X))))),
% 289.23/181.77 inference(bind,[status(th)],[])).
% 289.23/181.77 tff(2299,plain,
% 289.23/181.77 (![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X))) <=> ![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))),
% 289.23/181.77 inference(quant_intro,[status(thm)],[2298])).
% 289.23/181.77 tff(2300,plain,
% 289.23/181.77 (![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X))) <=> ![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))),
% 289.23/181.77 inference(rewrite,[status(thm)],[])).
% 289.23/181.77 tff(2301,plain,
% 289.23/181.77 (^[I0: $i, X: $i, I1: $i] : rewrite((((~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X))) | (~node16(I0, I1, X))) <=> ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X))))),
% 289.23/181.77 inference(bind,[status(th)],[])).
% 289.23/181.77 tff(2302,plain,
% 289.23/181.77 (![I0: $i, X: $i, I1: $i] : (((~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X))) | (~node16(I0, I1, X))) <=> ![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))),
% 289.23/181.77 inference(quant_intro,[status(thm)],[2301])).
% 289.23/181.77 tff(2303,axiom,(![I0: $i, X: $i, I1: $i] : (((~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X))) | (~node16(I0, I1, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_c_h_element_7')).
% 289.23/181.77 tff(2304,plain,
% 289.23/181.77 (![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))),
% 289.23/181.77 inference(modus_ponens,[status(thm)],[2303, 2302])).
% 289.23/181.77 tff(2305,plain,
% 289.23/181.77 (![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))),
% 289.23/181.77 inference(modus_ponens,[status(thm)],[2304, 2300])).
% 289.23/181.77 tff(2306,plain,(
% 289.23/181.77 ![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))),
% 289.23/181.77 inference(skolemize,[status(sab)],[2305])).
% 289.23/181.77 tff(2307,plain,
% 289.23/181.77 (![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))),
% 289.23/181.77 inference(modus_ponens,[status(thm)],[2306, 2299])).
% 289.23/181.77 tff(2308,plain,
% 289.23/181.77 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s3)) | (~node16(c_e_h_3, c_h, s3)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s3)) | (~node16(c_e_h_3, c_h, s3)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s3)))),
% 289.23/181.77 inference(rewrite,[status(thm)],[])).
% 289.23/181.77 tff(2309,plain,
% 289.23/181.77 (((~node16(c_e_h_3, c_h, s3)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s3)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s3))) <=> ((~m_c_h_element_v_in2(c_e_h_3, c_h, s3)) | (~node16(c_e_h_3, c_h, s3)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s3)))),
% 289.23/181.77 inference(rewrite,[status(thm)],[])).
% 289.23/181.77 tff(2310,plain,
% 289.23/181.77 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_h, s3)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s3)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s3)) | (~node16(c_e_h_3, c_h, s3)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s3))))),
% 289.23/181.77 inference(monotonicity,[status(thm)],[2309])).
% 289.23/181.77 tff(2311,plain,
% 289.23/181.77 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_h, s3)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s3)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s3)) | (~node16(c_e_h_3, c_h, s3)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s3)))),
% 289.23/181.77 inference(transitivity,[status(thm)],[2310, 2308])).
% 289.23/181.77 tff(2312,plain,
% 289.23/181.77 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_h, s3)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s3)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s3)))),
% 289.23/181.77 inference(quant_inst,[status(thm)],[])).
% 289.23/181.77 tff(2313,plain,
% 289.23/181.77 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s3)) | (~node16(c_e_h_3, c_h, s3)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s3))),
% 289.23/181.77 inference(modus_ponens,[status(thm)],[2312, 2311])).
% 289.23/181.77 tff(2314,plain,
% 289.23/181.77 ((~m_c_h_element_v_in2(c_e_h_3, c_h, s3)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s3))),
% 289.23/181.77 inference(unit_resolution,[status(thm)],[2313, 2307, 2283])).
% 289.23/181.77 tff(2315,plain,
% 289.23/181.77 ($false),
% 289.23/181.77 inference(unit_resolution,[status(thm)],[2314, 2297, 2292])).
% 289.23/181.77 tff(2316,plain,((~node16(c_e_h_3, c_h, s3)) | (~node17(c_e_h_3, c_h, s3))), inference(lemma,lemma(discharge,[]))).
% 289.23/181.77 tff(2317,plain,
% 289.23/181.77 (~node16(c_e_h_3, c_h, s3)),
% 289.23/181.77 inference(unit_resolution,[status(thm)],[2316, 2265])).
% 289.23/181.77 tff(2318,plain,
% 289.23/181.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_3, c_h, s3, s4) | node15(c_e_h_3, c_h, s3, s4) | (~node19(c_e_h_3, c_h, s3, s4)) | node16(c_e_h_3, c_h, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_h, s3, s4) | node15(c_e_h_3, c_h, s3, s4) | (~node19(c_e_h_3, c_h, s3, s4)) | node16(c_e_h_3, c_h, s3))),
% 289.23/181.78 inference(rewrite,[status(thm)],[])).
% 289.23/181.78 tff(2319,plain,
% 289.23/181.78 ((node16(c_e_h_3, c_h, s3) | node14(c_e_h_3, c_h, s3, s4) | node15(c_e_h_3, c_h, s3, s4) | (~node19(c_e_h_3, c_h, s3, s4))) <=> (node14(c_e_h_3, c_h, s3, s4) | node15(c_e_h_3, c_h, s3, s4) | (~node19(c_e_h_3, c_h, s3, s4)) | node16(c_e_h_3, c_h, s3))),
% 289.23/181.78 inference(rewrite,[status(thm)],[])).
% 289.23/181.78 tff(2320,plain,
% 289.23/181.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s3) | node14(c_e_h_3, c_h, s3, s4) | node15(c_e_h_3, c_h, s3, s4) | (~node19(c_e_h_3, c_h, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_3, c_h, s3, s4) | node15(c_e_h_3, c_h, s3, s4) | (~node19(c_e_h_3, c_h, s3, s4)) | node16(c_e_h_3, c_h, s3)))),
% 289.23/181.78 inference(monotonicity,[status(thm)],[2319])).
% 289.23/181.78 tff(2321,plain,
% 289.23/181.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s3) | node14(c_e_h_3, c_h, s3, s4) | node15(c_e_h_3, c_h, s3, s4) | (~node19(c_e_h_3, c_h, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_h, s3, s4) | node15(c_e_h_3, c_h, s3, s4) | (~node19(c_e_h_3, c_h, s3, s4)) | node16(c_e_h_3, c_h, s3))),
% 289.23/181.78 inference(transitivity,[status(thm)],[2320, 2318])).
% 289.23/181.78 tff(2322,plain,
% 289.23/181.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s3) | node14(c_e_h_3, c_h, s3, s4) | node15(c_e_h_3, c_h, s3, s4) | (~node19(c_e_h_3, c_h, s3, s4)))),
% 289.23/181.78 inference(quant_inst,[status(thm)],[])).
% 289.23/181.78 tff(2323,plain,
% 289.23/181.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_h, s3, s4) | node15(c_e_h_3, c_h, s3, s4) | (~node19(c_e_h_3, c_h, s3, s4)) | node16(c_e_h_3, c_h, s3)),
% 289.23/181.78 inference(modus_ponens,[status(thm)],[2322, 2321])).
% 289.23/181.78 tff(2324,plain,
% 289.23/181.78 (node14(c_e_h_3, c_h, s3, s4) | node15(c_e_h_3, c_h, s3, s4) | node16(c_e_h_3, c_h, s3)),
% 289.23/181.78 inference(unit_resolution,[status(thm)],[2323, 204, 2257])).
% 289.23/181.78 tff(2325,plain,
% 289.23/181.78 (node14(c_e_h_3, c_h, s3, s4)),
% 289.23/181.78 inference(unit_resolution,[status(thm)],[2324, 2317, 2281])).
% 289.23/181.78 tff(2326,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_h, s3)), introduced(assumption)).
% 289.23/181.78 tff(2327,assumption,(node14(c_e_h_3, c_h, s3, s4)), introduced(assumption)).
% 289.23/181.78 tff(2328,plain,
% 289.23/181.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s3) | (~node14(c_e_h_3, c_h, s3, s4)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_h, s3) | (~node14(c_e_h_3, c_h, s3, s4)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4)))),
% 289.23/181.78 inference(rewrite,[status(thm)],[])).
% 289.23/181.78 tff(2329,plain,
% 289.23/181.78 (((~node14(c_e_h_3, c_h, s3, s4)) | m_c_h_element_v_in1(c_e_h_3, c_h, s3) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4))) <=> (m_c_h_element_v_in1(c_e_h_3, c_h, s3) | (~node14(c_e_h_3, c_h, s3, s4)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4)))),
% 289.23/181.78 inference(rewrite,[status(thm)],[])).
% 289.23/181.78 tff(2330,plain,
% 289.23/181.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s3, s4)) | m_c_h_element_v_in1(c_e_h_3, c_h, s3) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s3) | (~node14(c_e_h_3, c_h, s3, s4)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4))))),
% 289.32/181.78 inference(monotonicity,[status(thm)],[2329])).
% 289.32/181.78 tff(2331,plain,
% 289.32/181.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s3, s4)) | m_c_h_element_v_in1(c_e_h_3, c_h, s3) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_h, s3) | (~node14(c_e_h_3, c_h, s3, s4)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4)))),
% 289.32/181.78 inference(transitivity,[status(thm)],[2330, 2328])).
% 289.32/181.78 tff(2332,plain,
% 289.32/181.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s3, s4)) | m_c_h_element_v_in1(c_e_h_3, c_h, s3) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4)))),
% 289.32/181.78 inference(quant_inst,[status(thm)],[])).
% 289.32/181.78 tff(2333,plain,
% 289.32/181.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_h, s3) | (~node14(c_e_h_3, c_h, s3, s4)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4))),
% 289.32/181.78 inference(modus_ponens,[status(thm)],[2332, 2331])).
% 289.32/181.78 tff(2334,plain,
% 289.32/181.78 ($false),
% 289.32/181.78 inference(unit_resolution,[status(thm)],[2333, 223, 2327, 2242, 2326])).
% 289.32/181.78 tff(2335,plain,((~node14(c_e_h_3, c_h, s3, s4)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4)) | m_c_h_element_v_in1(c_e_h_3, c_h, s3)), inference(lemma,lemma(discharge,[]))).
% 289.32/181.78 tff(2336,plain,
% 289.32/181.78 ($false),
% 289.32/181.78 inference(unit_resolution,[status(thm)],[2335, 2325, 2274, 2242])).
% 289.32/181.78 tff(2337,plain,(m_c_h_element_v_out(c_e_h_3, c_h, s3) | (~m_c_h_element_v_out(c_e_h_3, c_h, s4)) | m_c_h_element_v_in2(c_e_h_3, c_h, s3)), inference(lemma,lemma(discharge,[]))).
% 289.32/181.78 tff(2338,plain,
% 289.32/181.78 ((~m_c_h_element_v_out(c_e_h_3, c_h, s4)) | m_c_h_element_v_in2(c_e_h_3, c_h, s3)),
% 289.32/181.78 inference(unit_resolution,[status(thm)],[2337, 1710])).
% 289.32/181.78 tff(2339,plain,
% 289.32/181.78 (~m_c_h_element_v_out(c_e_h_3, c_h, s4)),
% 289.32/181.78 inference(unit_resolution,[status(thm)],[2338, 2241])).
% 289.32/181.78 tff(2340,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_i, s4)), introduced(assumption)).
% 289.32/181.78 tff(2341,assumption,(~m_c_h_element_v_out(c_e_h_3, c_h, s4)), introduced(assumption)).
% 289.32/181.78 tff(2342,plain,
% 289.32/181.78 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_i, s4)) | m_c_h_element_v_out(c_e_h_3, c_h, s4))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s4)) | m_c_h_element_v_out(c_e_h_3, c_h, s4))),
% 289.32/181.78 inference(rewrite,[status(thm)],[])).
% 289.32/181.78 tff(2343,plain,
% 289.32/181.78 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_i, s4)) | m_c_h_element_v_out(c_e_h_3, c_h, s4))),
% 289.32/181.78 inference(quant_inst,[status(thm)],[])).
% 289.32/181.78 tff(2344,plain,
% 289.32/181.78 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s4)) | m_c_h_element_v_out(c_e_h_3, c_h, s4)),
% 289.32/181.78 inference(modus_ponens,[status(thm)],[2343, 2342])).
% 289.32/181.78 tff(2345,plain,
% 289.32/181.78 ($false),
% 289.32/181.78 inference(unit_resolution,[status(thm)],[2344, 619, 2341, 2340])).
% 289.32/181.78 tff(2346,plain,((~m_and_h_gate_v_in1(c_e_h_3, c_i, s4)) | m_c_h_element_v_out(c_e_h_3, c_h, s4)), inference(lemma,lemma(discharge,[]))).
% 289.32/181.78 tff(2347,plain,
% 289.32/181.78 (~m_and_h_gate_v_in1(c_e_h_3, c_i, s4)),
% 289.32/181.78 inference(unit_resolution,[status(thm)],[2346, 2339])).
% 289.32/181.78 tff(2348,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_i, s4)), introduced(assumption)).
% 289.32/181.78 tff(2349,assumption,(node20(c_e_h_3, c_i, s4)), introduced(assumption)).
% 289.32/181.78 tff(2350,plain,
% 289.32/181.78 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_i, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s4))),
% 289.32/181.78 inference(rewrite,[status(thm)],[])).
% 289.32/181.78 tff(2351,plain,
% 289.32/181.78 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s4))),
% 289.32/181.78 inference(quant_inst,[status(thm)],[])).
% 289.32/181.78 tff(2352,plain,
% 289.32/181.78 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_i, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s4)),
% 289.32/181.78 inference(modus_ponens,[status(thm)],[2351, 2350])).
% 289.32/181.78 tff(2353,plain,
% 289.32/181.78 ($false),
% 289.32/181.78 inference(unit_resolution,[status(thm)],[2352, 38, 2349, 2348])).
% 289.32/181.78 tff(2354,plain,((~node20(c_e_h_3, c_i, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s4)), inference(lemma,lemma(discharge,[]))).
% 289.32/181.78 tff(2355,plain,
% 289.32/181.78 (~node20(c_e_h_3, c_i, s4)),
% 289.32/181.78 inference(unit_resolution,[status(thm)],[2354, 2347])).
% 289.32/181.78 tff(2356,assumption,(~node20(c_e_h_3, c_i, s4)), introduced(assumption)).
% 289.32/181.78 tff(2357,assumption,(m_and_h_gate_v_out(c_e_h_3, c_i, s5)), introduced(assumption)).
% 289.32/181.78 tff(2358,assumption,(node21(c_e_h_3, c_i, s4, s5)), introduced(assumption)).
% 289.32/181.78 tff(2359,plain,
% 289.32/181.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s4) | (~node21(c_e_h_3, c_i, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_i, s4) | (~node21(c_e_h_3, c_i, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s5)))),
% 289.32/181.78 inference(rewrite,[status(thm)],[])).
% 289.32/181.78 tff(2360,plain,
% 289.32/181.78 ((node20(c_e_h_3, c_i, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s5)) | (~node21(c_e_h_3, c_i, s4, s5))) <=> (node20(c_e_h_3, c_i, s4) | (~node21(c_e_h_3, c_i, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s5)))),
% 289.32/181.78 inference(rewrite,[status(thm)],[])).
% 289.32/181.78 tff(2361,plain,
% 289.32/181.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s5)) | (~node21(c_e_h_3, c_i, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s4) | (~node21(c_e_h_3, c_i, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s5))))),
% 289.32/181.78 inference(monotonicity,[status(thm)],[2360])).
% 289.32/181.78 tff(2362,plain,
% 289.32/181.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s5)) | (~node21(c_e_h_3, c_i, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_i, s4) | (~node21(c_e_h_3, c_i, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s5)))),
% 289.32/181.78 inference(transitivity,[status(thm)],[2361, 2359])).
% 289.32/181.78 tff(2363,plain,
% 289.32/181.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s5)) | (~node21(c_e_h_3, c_i, s4, s5)))),
% 289.32/181.78 inference(quant_inst,[status(thm)],[])).
% 289.32/181.78 tff(2364,plain,
% 289.32/181.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_i, s4) | (~node21(c_e_h_3, c_i, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s5))),
% 289.32/181.78 inference(modus_ponens,[status(thm)],[2363, 2362])).
% 289.32/181.78 tff(2365,plain,
% 289.32/181.78 ($false),
% 289.32/181.78 inference(unit_resolution,[status(thm)],[2364, 52, 2358, 2357, 2356])).
% 289.32/181.78 tff(2366,plain,((~node21(c_e_h_3, c_i, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s5)) | node20(c_e_h_3, c_i, s4)), inference(lemma,lemma(discharge,[]))).
% 289.32/181.78 tff(2367,plain,
% 289.32/181.78 (~node21(c_e_h_3, c_i, s4, s5)),
% 289.32/181.78 inference(unit_resolution,[status(thm)],[2366, 2357, 2356])).
% 289.32/181.79 tff(2368,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_i, s4)), introduced(assumption)).
% 289.32/181.79 tff(2369,assumption,(node22(c_e_h_3, c_i, s4, s5)), introduced(assumption)).
% 289.32/181.79 tff(2370,plain,
% 289.32/181.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s5)) | (~node22(c_e_h_3, c_i, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_i, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s5)) | (~node22(c_e_h_3, c_i, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_i, s4))),
% 289.32/181.79 inference(rewrite,[status(thm)],[])).
% 289.32/181.79 tff(2371,plain,
% 289.32/181.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s5)) | (~node22(c_e_h_3, c_i, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_i, s4))),
% 289.32/181.79 inference(quant_inst,[status(thm)],[])).
% 289.32/181.79 tff(2372,plain,
% 289.32/181.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s5)) | (~node22(c_e_h_3, c_i, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_i, s4)),
% 289.32/181.79 inference(modus_ponens,[status(thm)],[2371, 2370])).
% 289.32/181.79 tff(2373,plain,
% 289.32/181.79 ($false),
% 289.32/181.79 inference(unit_resolution,[status(thm)],[2372, 108, 2369, 2357, 2368])).
% 289.32/181.79 tff(2374,plain,((~node22(c_e_h_3, c_i, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s5)) | m_and_h_gate_v_out(c_e_h_3, c_i, s4)), inference(lemma,lemma(discharge,[]))).
% 289.32/181.79 tff(2375,plain,
% 289.32/181.79 (~node22(c_e_h_3, c_i, s4, s5)),
% 289.32/181.79 inference(unit_resolution,[status(thm)],[2374, 2357, 2368])).
% 289.32/181.79 tff(2376,plain,
% 289.32/181.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_3, c_i, s4, s5) | node22(c_e_h_3, c_i, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_3, c_i, s4, s5) | node22(c_e_h_3, c_i, s4, s5))),
% 289.32/181.79 inference(rewrite,[status(thm)],[])).
% 289.32/181.79 tff(2377,plain,
% 289.32/181.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_3, c_i, s4, s5) | node22(c_e_h_3, c_i, s4, s5))),
% 289.32/181.79 inference(quant_inst,[status(thm)],[])).
% 289.32/181.79 tff(2378,plain,
% 289.32/181.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_3, c_i, s4, s5) | node22(c_e_h_3, c_i, s4, s5)),
% 289.32/181.79 inference(modus_ponens,[status(thm)],[2377, 2376])).
% 289.32/181.79 tff(2379,plain,
% 289.32/181.79 (node21(c_e_h_3, c_i, s4, s5) | node22(c_e_h_3, c_i, s4, s5)),
% 289.32/181.79 inference(unit_resolution,[status(thm)],[2378, 82, 1028])).
% 289.32/181.79 tff(2380,plain,
% 289.32/181.79 ($false),
% 289.32/181.79 inference(unit_resolution,[status(thm)],[2379, 2375, 2367])).
% 289.32/181.79 tff(2381,plain,((~m_and_h_gate_v_out(c_e_h_3, c_i, s5)) | m_and_h_gate_v_out(c_e_h_3, c_i, s4) | node20(c_e_h_3, c_i, s4)), inference(lemma,lemma(discharge,[]))).
% 289.32/181.79 tff(2382,plain,
% 289.32/181.79 ((~m_and_h_gate_v_out(c_e_h_3, c_i, s5)) | node20(c_e_h_3, c_i, s4)),
% 289.32/181.79 inference(unit_resolution,[status(thm)],[2381, 1744])).
% 289.32/181.79 tff(2383,plain,
% 289.32/181.79 (~m_and_h_gate_v_out(c_e_h_3, c_i, s5)),
% 289.32/181.79 inference(unit_resolution,[status(thm)],[2382, 2355])).
% 289.32/181.79 tff(2384,plain,
% 289.32/181.79 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s5)) | m_and_h_gate_v_out(c_e_h_3, c_i, s5))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s5)) | m_and_h_gate_v_out(c_e_h_3, c_i, s5))),
% 289.32/181.79 inference(rewrite,[status(thm)],[])).
% 289.32/181.79 tff(2385,plain,
% 289.32/181.79 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s5)) | m_and_h_gate_v_out(c_e_h_3, c_i, s5))),
% 289.32/181.79 inference(quant_inst,[status(thm)],[])).
% 289.33/181.79 tff(2386,plain,
% 289.33/181.79 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s5)) | m_and_h_gate_v_out(c_e_h_3, c_i, s5)),
% 289.33/181.79 inference(modus_ponens,[status(thm)],[2385, 2384])).
% 289.33/181.79 tff(2387,plain,
% 289.33/181.79 (~m_c_h_element_v_in2(c_e_h_3, c_e, s5)),
% 289.33/181.79 inference(unit_resolution,[status(thm)],[2386, 164, 2383])).
% 289.33/181.79 tff(2388,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_e, s5)), introduced(assumption)).
% 289.33/181.79 tff(2389,plain,
% 289.33/181.79 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_e, s5)) | m_c_h_element_v_in1(c_e_h_3, c_e, s5) | m_c_h_element_v_in2(c_e_h_3, c_e, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s5)) | m_c_h_element_v_in1(c_e_h_3, c_e, s5) | m_c_h_element_v_in2(c_e_h_3, c_e, s5))),
% 289.33/181.79 inference(rewrite,[status(thm)],[])).
% 289.33/181.79 tff(2390,plain,
% 289.33/181.79 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_e, s5)) | m_c_h_element_v_in1(c_e_h_3, c_e, s5) | m_c_h_element_v_in2(c_e_h_3, c_e, s5))),
% 289.33/181.79 inference(quant_inst,[status(thm)],[])).
% 289.33/181.79 tff(2391,plain,
% 289.33/181.79 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s5)) | m_c_h_element_v_in1(c_e_h_3, c_e, s5) | m_c_h_element_v_in2(c_e_h_3, c_e, s5)),
% 289.33/181.79 inference(modus_ponens,[status(thm)],[2390, 2389])).
% 289.33/181.79 tff(2392,plain,
% 289.33/181.79 ((~node16(c_e_h_3, c_e, s5)) | m_c_h_element_v_in2(c_e_h_3, c_e, s5)),
% 289.33/181.79 inference(unit_resolution,[status(thm)],[2391, 178, 2388])).
% 289.33/181.79 tff(2393,plain,
% 289.33/181.79 (~node16(c_e_h_3, c_e, s5)),
% 289.33/181.79 inference(unit_resolution,[status(thm)],[2392, 2387])).
% 289.33/181.79 tff(2394,plain,
% 289.33/181.79 (~m_c_h_element_v_in2(c_e_h_3, c_e, s4)),
% 289.33/181.79 inference(unit_resolution,[status(thm)],[1748, 164, 1744])).
% 289.33/181.79 tff(2395,plain,
% 289.33/181.79 (~m_c_h_element_v_out(c_e_h_3, c_e, s5)),
% 289.33/181.79 inference(unit_resolution,[status(thm)],[1814, 2394])).
% 289.33/181.79 tff(2396,assumption,(node15(c_e_h_3, c_e, s5, s6)), introduced(assumption)).
% 289.33/181.79 tff(2397,plain,
% 289.33/181.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | (~node15(c_e_h_3, c_e, s5, s6)) | m_c_h_element_v_out(c_e_h_3, c_e, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | (~node15(c_e_h_3, c_e, s5, s6)) | m_c_h_element_v_out(c_e_h_3, c_e, s5))),
% 289.33/181.79 inference(rewrite,[status(thm)],[])).
% 289.33/181.79 tff(2398,plain,
% 289.33/181.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | (~node15(c_e_h_3, c_e, s5, s6)) | m_c_h_element_v_out(c_e_h_3, c_e, s5))),
% 289.33/181.79 inference(quant_inst,[status(thm)],[])).
% 289.33/181.79 tff(2399,plain,
% 289.33/181.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | (~node15(c_e_h_3, c_e, s5, s6)) | m_c_h_element_v_out(c_e_h_3, c_e, s5)),
% 289.33/181.79 inference(modus_ponens,[status(thm)],[2398, 2397])).
% 289.33/181.79 tff(2400,plain,
% 289.33/181.79 ($false),
% 289.33/181.79 inference(unit_resolution,[status(thm)],[2399, 147, 2016, 2396, 2017])).
% 289.33/181.79 tff(2401,plain,((~node15(c_e_h_3, c_e, s5, s6)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | m_c_h_element_v_out(c_e_h_3, c_e, s5)), inference(lemma,lemma(discharge,[]))).
% 289.33/181.79 tff(2402,plain,
% 289.33/181.79 (~node15(c_e_h_3, c_e, s5, s6)),
% 289.33/181.79 inference(unit_resolution,[status(thm)],[2401, 2016, 2395])).
% 289.33/181.79 tff(2403,assumption,(node14(c_e_h_3, c_e, s5, s6)), introduced(assumption)).
% 289.33/181.79 tff(2404,plain,
% 289.33/181.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s5) | (~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | (~node14(c_e_h_3, c_e, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_e, s5) | (~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | (~node14(c_e_h_3, c_e, s5, s6)))),
% 289.33/181.80 inference(rewrite,[status(thm)],[])).
% 289.33/181.80 tff(2405,plain,
% 289.33/181.80 (((~node14(c_e_h_3, c_e, s5, s6)) | m_c_h_element_v_in1(c_e_h_3, c_e, s5) | (~m_c_h_element_v_out(c_e_h_3, c_e, s6))) <=> (m_c_h_element_v_in1(c_e_h_3, c_e, s5) | (~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | (~node14(c_e_h_3, c_e, s5, s6)))),
% 289.33/181.80 inference(rewrite,[status(thm)],[])).
% 289.33/181.80 tff(2406,plain,
% 289.33/181.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s5, s6)) | m_c_h_element_v_in1(c_e_h_3, c_e, s5) | (~m_c_h_element_v_out(c_e_h_3, c_e, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s5) | (~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | (~node14(c_e_h_3, c_e, s5, s6))))),
% 289.33/181.80 inference(monotonicity,[status(thm)],[2405])).
% 289.33/181.80 tff(2407,plain,
% 289.33/181.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s5, s6)) | m_c_h_element_v_in1(c_e_h_3, c_e, s5) | (~m_c_h_element_v_out(c_e_h_3, c_e, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_e, s5) | (~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | (~node14(c_e_h_3, c_e, s5, s6)))),
% 289.33/181.80 inference(transitivity,[status(thm)],[2406, 2404])).
% 289.33/181.80 tff(2408,plain,
% 289.33/181.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s5, s6)) | m_c_h_element_v_in1(c_e_h_3, c_e, s5) | (~m_c_h_element_v_out(c_e_h_3, c_e, s6)))),
% 289.33/181.80 inference(quant_inst,[status(thm)],[])).
% 289.33/181.80 tff(2409,plain,
% 289.33/181.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_e, s5) | (~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | (~node14(c_e_h_3, c_e, s5, s6))),
% 289.33/181.80 inference(modus_ponens,[status(thm)],[2408, 2407])).
% 289.33/181.80 tff(2410,plain,
% 289.33/181.80 ($false),
% 289.33/181.80 inference(unit_resolution,[status(thm)],[2409, 223, 2016, 2403, 2388])).
% 289.33/181.80 tff(2411,plain,((~node14(c_e_h_3, c_e, s5, s6)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | m_c_h_element_v_in1(c_e_h_3, c_e, s5)), inference(lemma,lemma(discharge,[]))).
% 289.33/181.80 tff(2412,plain,
% 289.33/181.80 (~node14(c_e_h_3, c_e, s5, s6)),
% 289.33/181.80 inference(unit_resolution,[status(thm)],[2411, 2016, 2388])).
% 289.33/181.80 tff(2413,plain,
% 289.33/181.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s5, s6)) | node19(c_e_h_3, c_e, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s5, s6)) | node19(c_e_h_3, c_e, s5, s6))),
% 289.33/181.80 inference(rewrite,[status(thm)],[])).
% 289.33/181.80 tff(2414,plain,
% 289.33/181.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s5, s6)) | node19(c_e_h_3, c_e, s5, s6))),
% 289.33/181.80 inference(quant_inst,[status(thm)],[])).
% 289.33/181.80 tff(2415,plain,
% 289.33/181.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s5, s6)) | node19(c_e_h_3, c_e, s5, s6)),
% 289.33/181.80 inference(modus_ponens,[status(thm)],[2414, 2413])).
% 289.33/181.80 tff(2416,plain,
% 289.33/181.80 (node19(c_e_h_3, c_e, s5, s6)),
% 289.33/181.80 inference(unit_resolution,[status(thm)],[2415, 190, 1406])).
% 289.33/181.80 tff(2417,plain,
% 289.33/181.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_e, s5, s6)) | node14(c_e_h_3, c_e, s5, s6) | node15(c_e_h_3, c_e, s5, s6) | node16(c_e_h_3, c_e, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_e, s5, s6)) | node14(c_e_h_3, c_e, s5, s6) | node15(c_e_h_3, c_e, s5, s6) | node16(c_e_h_3, c_e, s5))),
% 289.33/181.80 inference(rewrite,[status(thm)],[])).
% 289.33/181.80 tff(2418,plain,
% 289.33/181.80 ((node16(c_e_h_3, c_e, s5) | node14(c_e_h_3, c_e, s5, s6) | node15(c_e_h_3, c_e, s5, s6) | (~node19(c_e_h_3, c_e, s5, s6))) <=> ((~node19(c_e_h_3, c_e, s5, s6)) | node14(c_e_h_3, c_e, s5, s6) | node15(c_e_h_3, c_e, s5, s6) | node16(c_e_h_3, c_e, s5))),
% 289.33/181.80 inference(rewrite,[status(thm)],[])).
% 289.33/181.80 tff(2419,plain,
% 289.33/181.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s5) | node14(c_e_h_3, c_e, s5, s6) | node15(c_e_h_3, c_e, s5, s6) | (~node19(c_e_h_3, c_e, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_e, s5, s6)) | node14(c_e_h_3, c_e, s5, s6) | node15(c_e_h_3, c_e, s5, s6) | node16(c_e_h_3, c_e, s5)))),
% 289.33/181.80 inference(monotonicity,[status(thm)],[2418])).
% 289.33/181.80 tff(2420,plain,
% 289.33/181.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s5) | node14(c_e_h_3, c_e, s5, s6) | node15(c_e_h_3, c_e, s5, s6) | (~node19(c_e_h_3, c_e, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_e, s5, s6)) | node14(c_e_h_3, c_e, s5, s6) | node15(c_e_h_3, c_e, s5, s6) | node16(c_e_h_3, c_e, s5))),
% 289.33/181.80 inference(transitivity,[status(thm)],[2419, 2417])).
% 289.33/181.80 tff(2421,plain,
% 289.33/181.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s5) | node14(c_e_h_3, c_e, s5, s6) | node15(c_e_h_3, c_e, s5, s6) | (~node19(c_e_h_3, c_e, s5, s6)))),
% 289.33/181.80 inference(quant_inst,[status(thm)],[])).
% 289.33/181.80 tff(2422,plain,
% 289.33/181.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_e, s5, s6)) | node14(c_e_h_3, c_e, s5, s6) | node15(c_e_h_3, c_e, s5, s6) | node16(c_e_h_3, c_e, s5)),
% 289.33/181.80 inference(modus_ponens,[status(thm)],[2421, 2420])).
% 289.33/181.80 tff(2423,plain,
% 289.33/181.80 (node14(c_e_h_3, c_e, s5, s6) | node15(c_e_h_3, c_e, s5, s6) | node16(c_e_h_3, c_e, s5)),
% 289.33/181.80 inference(unit_resolution,[status(thm)],[2422, 204, 2416])).
% 289.33/181.80 tff(2424,plain,
% 289.33/181.80 ($false),
% 289.33/181.80 inference(unit_resolution,[status(thm)],[2423, 2412, 2402, 2393])).
% 289.33/181.80 tff(2425,plain,((~m_c_h_element_v_out(c_e_h_3, c_e, s6)) | m_c_h_element_v_in1(c_e_h_3, c_e, s5)), inference(lemma,lemma(discharge,[]))).
% 289.33/181.80 tff(2426,plain,
% 289.33/181.80 (m_c_h_element_v_in1(c_e_h_3, c_e, s5)),
% 289.33/181.80 inference(unit_resolution,[status(thm)],[2425, 2016])).
% 289.33/181.80 tff(2427,assumption,(m_c_h_element_v_in2(c_e_h_3, c_e, s5)), introduced(assumption)).
% 289.33/181.80 tff(2428,plain,
% 289.33/181.80 ($false),
% 289.33/181.80 inference(unit_resolution,[status(thm)],[2386, 164, 2383, 2427])).
% 289.33/181.80 tff(2429,plain,(~m_c_h_element_v_in2(c_e_h_3, c_e, s5)), inference(lemma,lemma(discharge,[]))).
% 289.33/181.80 tff(2430,plain,
% 289.33/181.80 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_3, c_e, s5) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s5)) | (~node17(c_e_h_3, c_e, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_e, s5) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s5)) | (~node17(c_e_h_3, c_e, s5)))),
% 289.33/181.80 inference(rewrite,[status(thm)],[])).
% 289.33/181.80 tff(2431,plain,
% 289.33/181.80 (((~m_c_h_element_v_in1(c_e_h_3, c_e, s5)) | m_c_h_element_v_in2(c_e_h_3, c_e, s5) | (~node17(c_e_h_3, c_e, s5))) <=> (m_c_h_element_v_in2(c_e_h_3, c_e, s5) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s5)) | (~node17(c_e_h_3, c_e, s5)))),
% 289.33/181.80 inference(rewrite,[status(thm)],[])).
% 289.33/181.80 tff(2432,plain,
% 289.33/181.80 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s5)) | m_c_h_element_v_in2(c_e_h_3, c_e, s5) | (~node17(c_e_h_3, c_e, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_3, c_e, s5) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s5)) | (~node17(c_e_h_3, c_e, s5))))),
% 289.33/181.80 inference(monotonicity,[status(thm)],[2431])).
% 289.33/181.80 tff(2433,plain,
% 289.33/181.80 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s5)) | m_c_h_element_v_in2(c_e_h_3, c_e, s5) | (~node17(c_e_h_3, c_e, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_e, s5) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s5)) | (~node17(c_e_h_3, c_e, s5)))),
% 289.33/181.80 inference(transitivity,[status(thm)],[2432, 2430])).
% 289.33/181.80 tff(2434,plain,
% 289.33/181.80 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s5)) | m_c_h_element_v_in2(c_e_h_3, c_e, s5) | (~node17(c_e_h_3, c_e, s5)))),
% 289.33/181.80 inference(quant_inst,[status(thm)],[])).
% 289.33/181.80 tff(2435,plain,
% 289.33/181.80 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_e, s5) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s5)) | (~node17(c_e_h_3, c_e, s5))),
% 289.33/181.80 inference(modus_ponens,[status(thm)],[2434, 2433])).
% 289.33/181.80 tff(2436,plain,
% 289.33/181.80 ((~m_c_h_element_v_in1(c_e_h_3, c_e, s5)) | (~node17(c_e_h_3, c_e, s5))),
% 289.33/181.80 inference(unit_resolution,[status(thm)],[2435, 919, 2429])).
% 289.33/181.80 tff(2437,plain,
% 289.33/181.80 (~node17(c_e_h_3, c_e, s5)),
% 289.33/181.80 inference(unit_resolution,[status(thm)],[2436, 2426])).
% 289.33/181.80 tff(2438,plain,
% 289.33/181.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s5) | (~node19(c_e_h_3, c_e, s5, s6)) | node18(c_e_h_3, c_e, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_e, s5) | (~node19(c_e_h_3, c_e, s5, s6)) | node18(c_e_h_3, c_e, s5, s6))),
% 289.33/181.80 inference(rewrite,[status(thm)],[])).
% 289.33/181.80 tff(2439,plain,
% 289.33/181.80 ((node17(c_e_h_3, c_e, s5) | node18(c_e_h_3, c_e, s5, s6) | (~node19(c_e_h_3, c_e, s5, s6))) <=> (node17(c_e_h_3, c_e, s5) | (~node19(c_e_h_3, c_e, s5, s6)) | node18(c_e_h_3, c_e, s5, s6))),
% 289.33/181.80 inference(rewrite,[status(thm)],[])).
% 289.33/181.80 tff(2440,plain,
% 289.33/181.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s5) | node18(c_e_h_3, c_e, s5, s6) | (~node19(c_e_h_3, c_e, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s5) | (~node19(c_e_h_3, c_e, s5, s6)) | node18(c_e_h_3, c_e, s5, s6)))),
% 289.33/181.80 inference(monotonicity,[status(thm)],[2439])).
% 289.33/181.80 tff(2441,plain,
% 289.33/181.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s5) | node18(c_e_h_3, c_e, s5, s6) | (~node19(c_e_h_3, c_e, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_e, s5) | (~node19(c_e_h_3, c_e, s5, s6)) | node18(c_e_h_3, c_e, s5, s6))),
% 289.33/181.80 inference(transitivity,[status(thm)],[2440, 2438])).
% 289.33/181.80 tff(2442,plain,
% 289.33/181.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s5) | node18(c_e_h_3, c_e, s5, s6) | (~node19(c_e_h_3, c_e, s5, s6)))),
% 289.33/181.80 inference(quant_inst,[status(thm)],[])).
% 289.33/181.80 tff(2443,plain,
% 289.33/181.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_e, s5) | (~node19(c_e_h_3, c_e, s5, s6)) | node18(c_e_h_3, c_e, s5, s6)),
% 289.35/181.81 inference(modus_ponens,[status(thm)],[2442, 2441])).
% 289.35/181.81 tff(2444,plain,
% 289.35/181.81 (node17(c_e_h_3, c_e, s5) | node18(c_e_h_3, c_e, s5, s6)),
% 289.35/181.81 inference(unit_resolution,[status(thm)],[2443, 776, 2416])).
% 289.35/181.81 tff(2445,plain,
% 289.35/181.81 ($false),
% 289.35/181.81 inference(unit_resolution,[status(thm)],[2444, 2437, 2028])).
% 289.35/181.81 tff(2446,plain,(~m_c_h_element_v_out(c_e_h_3, c_e, s6)), inference(lemma,lemma(discharge,[]))).
% 289.35/181.81 tff(2447,plain,
% 289.35/181.81 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s6)) | m_c_h_element_v_out(c_e_h_3, c_e, s6))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s6)) | m_c_h_element_v_out(c_e_h_3, c_e, s6))),
% 289.35/181.81 inference(rewrite,[status(thm)],[])).
% 289.35/181.81 tff(2448,plain,
% 289.35/181.81 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s6)) | m_c_h_element_v_out(c_e_h_3, c_e, s6))),
% 289.35/181.81 inference(quant_inst,[status(thm)],[])).
% 289.35/181.81 tff(2449,plain,
% 289.35/181.81 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s6)) | m_c_h_element_v_out(c_e_h_3, c_e, s6)),
% 289.35/181.81 inference(modus_ponens,[status(thm)],[2448, 2447])).
% 289.35/181.81 tff(2450,plain,
% 289.35/181.81 (~m_and_h_gate_v_in1(c_e_h_3, c_r, s6)),
% 289.35/181.81 inference(unit_resolution,[status(thm)],[2449, 24, 2446])).
% 289.35/181.81 tff(2451,plain,
% 289.35/181.81 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s6))),
% 289.35/181.81 inference(rewrite,[status(thm)],[])).
% 289.35/181.81 tff(2452,plain,
% 289.35/181.81 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s6))),
% 289.35/181.81 inference(quant_inst,[status(thm)],[])).
% 289.35/181.81 tff(2453,plain,
% 289.35/181.81 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s6)),
% 289.35/181.81 inference(modus_ponens,[status(thm)],[2452, 2451])).
% 289.35/181.81 tff(2454,plain,
% 289.35/181.81 (~node20(c_e_h_3, c_r, s6)),
% 289.35/181.81 inference(unit_resolution,[status(thm)],[2453, 38, 2450])).
% 289.35/181.81 tff(2455,plain,
% 289.35/181.81 ((~m_and_h_gate_v_out(c_e_h_3, c_r, s6)) | node20(c_e_h_3, c_r, s5)),
% 289.35/181.81 inference(unit_resolution,[status(thm)],[1882, 1371])).
% 289.35/181.81 tff(2456,plain,
% 289.35/181.81 (~m_and_h_gate_v_out(c_e_h_3, c_r, s6)),
% 289.35/181.81 inference(unit_resolution,[status(thm)],[2455, 1824])).
% 289.35/181.81 tff(2457,assumption,(~node20(c_e_h_3, c_r, s6)), introduced(assumption)).
% 289.35/181.81 tff(2458,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_r, s6)), introduced(assumption)).
% 289.35/181.81 tff(2459,assumption,(m_and_h_gate_v_out(c_e_h_3, c_r, s7)), introduced(assumption)).
% 289.35/181.81 tff(2460,assumption,(node22(c_e_h_3, c_r, s6, s7)), introduced(assumption)).
% 289.35/181.81 tff(2461,plain,
% 289.35/181.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s7)) | (~node22(c_e_h_3, c_r, s6, s7)) | m_and_h_gate_v_out(c_e_h_3, c_r, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s7)) | (~node22(c_e_h_3, c_r, s6, s7)) | m_and_h_gate_v_out(c_e_h_3, c_r, s6))),
% 289.35/181.81 inference(rewrite,[status(thm)],[])).
% 289.35/181.81 tff(2462,plain,
% 289.35/181.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s7)) | (~node22(c_e_h_3, c_r, s6, s7)) | m_and_h_gate_v_out(c_e_h_3, c_r, s6))),
% 289.35/181.81 inference(quant_inst,[status(thm)],[])).
% 289.35/181.81 tff(2463,plain,
% 289.35/181.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s7)) | (~node22(c_e_h_3, c_r, s6, s7)) | m_and_h_gate_v_out(c_e_h_3, c_r, s6)),
% 289.35/181.81 inference(modus_ponens,[status(thm)],[2462, 2461])).
% 289.35/181.81 tff(2464,plain,
% 289.35/181.81 ($false),
% 289.35/181.81 inference(unit_resolution,[status(thm)],[2463, 108, 2458, 2459, 2460])).
% 289.35/181.81 tff(2465,plain,((~node22(c_e_h_3, c_r, s6, s7)) | m_and_h_gate_v_out(c_e_h_3, c_r, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s7))), inference(lemma,lemma(discharge,[]))).
% 289.35/181.81 tff(2466,plain,
% 289.35/181.81 (~node22(c_e_h_3, c_r, s6, s7)),
% 289.35/181.81 inference(unit_resolution,[status(thm)],[2465, 2459, 2458])).
% 289.35/181.81 tff(2467,plain,
% 289.35/181.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_3, c_r, s6, s7) | node22(c_e_h_3, c_r, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_3, c_r, s6, s7) | node22(c_e_h_3, c_r, s6, s7))),
% 289.35/181.81 inference(rewrite,[status(thm)],[])).
% 289.35/181.81 tff(2468,plain,
% 289.35/181.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_3, c_r, s6, s7) | node22(c_e_h_3, c_r, s6, s7))),
% 289.35/181.81 inference(quant_inst,[status(thm)],[])).
% 289.35/181.81 tff(2469,plain,
% 289.35/181.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_3, c_r, s6, s7) | node22(c_e_h_3, c_r, s6, s7)),
% 289.35/181.81 inference(modus_ponens,[status(thm)],[2468, 2467])).
% 289.35/181.81 tff(2470,plain,
% 289.35/181.81 (node21(c_e_h_3, c_r, s6, s7) | node22(c_e_h_3, c_r, s6, s7)),
% 289.35/181.81 inference(unit_resolution,[status(thm)],[2469, 82, 1844])).
% 289.35/181.81 tff(2471,plain,
% 289.35/181.81 (node21(c_e_h_3, c_r, s6, s7)),
% 289.35/181.81 inference(unit_resolution,[status(thm)],[2470, 2466])).
% 289.35/181.81 tff(2472,plain,
% 289.35/181.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s7)) | node20(c_e_h_3, c_r, s6) | (~node21(c_e_h_3, c_r, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s7)) | node20(c_e_h_3, c_r, s6) | (~node21(c_e_h_3, c_r, s6, s7)))),
% 289.35/181.81 inference(rewrite,[status(thm)],[])).
% 289.35/181.81 tff(2473,plain,
% 289.35/181.81 ((node20(c_e_h_3, c_r, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s7)) | (~node21(c_e_h_3, c_r, s6, s7))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_r, s7)) | node20(c_e_h_3, c_r, s6) | (~node21(c_e_h_3, c_r, s6, s7)))),
% 289.35/181.81 inference(rewrite,[status(thm)],[])).
% 289.35/181.81 tff(2474,plain,
% 289.35/181.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s7)) | (~node21(c_e_h_3, c_r, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s7)) | node20(c_e_h_3, c_r, s6) | (~node21(c_e_h_3, c_r, s6, s7))))),
% 289.35/181.81 inference(monotonicity,[status(thm)],[2473])).
% 289.35/181.81 tff(2475,plain,
% 289.35/181.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s7)) | (~node21(c_e_h_3, c_r, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s7)) | node20(c_e_h_3, c_r, s6) | (~node21(c_e_h_3, c_r, s6, s7)))),
% 289.35/181.81 inference(transitivity,[status(thm)],[2474, 2472])).
% 289.35/181.81 tff(2476,plain,
% 289.35/181.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s7)) | (~node21(c_e_h_3, c_r, s6, s7)))),
% 289.35/181.81 inference(quant_inst,[status(thm)],[])).
% 289.35/181.81 tff(2477,plain,
% 289.35/181.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s7)) | node20(c_e_h_3, c_r, s6) | (~node21(c_e_h_3, c_r, s6, s7))),
% 289.36/181.82 inference(modus_ponens,[status(thm)],[2476, 2475])).
% 289.36/181.82 tff(2478,plain,
% 289.36/181.82 ($false),
% 289.36/181.82 inference(unit_resolution,[status(thm)],[2477, 52, 2459, 2471, 2457])).
% 289.36/181.82 tff(2479,plain,((~m_and_h_gate_v_out(c_e_h_3, c_r, s7)) | node20(c_e_h_3, c_r, s6) | m_and_h_gate_v_out(c_e_h_3, c_r, s6)), inference(lemma,lemma(discharge,[]))).
% 289.36/181.82 tff(2480,plain,
% 289.36/181.82 ((~m_and_h_gate_v_out(c_e_h_3, c_r, s7)) | node20(c_e_h_3, c_r, s6)),
% 289.36/181.82 inference(unit_resolution,[status(thm)],[2479, 2456])).
% 289.36/181.82 tff(2481,plain,
% 289.36/181.82 (~m_and_h_gate_v_out(c_e_h_3, c_r, s7)),
% 289.36/181.82 inference(unit_resolution,[status(thm)],[2480, 2454])).
% 289.36/181.82 tff(2482,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_r, s7)), introduced(assumption)).
% 289.36/181.82 tff(2483,assumption,(m_user_v_ack(c_e_h_3, c_u, s7)), introduced(assumption)).
% 289.36/181.82 tff(2484,plain,
% 289.36/181.82 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_3, c_u, s7)) | m_and_h_gate_v_out(c_e_h_3, c_r, s7))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_3, c_u, s7)) | m_and_h_gate_v_out(c_e_h_3, c_r, s7))),
% 289.36/181.82 inference(rewrite,[status(thm)],[])).
% 289.36/181.82 tff(2485,plain,
% 289.36/181.82 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_3, c_u, s7)) | m_and_h_gate_v_out(c_e_h_3, c_r, s7))),
% 289.36/181.82 inference(quant_inst,[status(thm)],[])).
% 289.36/181.82 tff(2486,plain,
% 289.36/181.82 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_3, c_u, s7)) | m_and_h_gate_v_out(c_e_h_3, c_r, s7)),
% 289.36/181.82 inference(modus_ponens,[status(thm)],[2485, 2484])).
% 289.36/181.82 tff(2487,plain,
% 289.36/181.82 ($false),
% 289.36/181.82 inference(unit_resolution,[status(thm)],[2486, 268, 2483, 2482])).
% 289.36/181.82 tff(2488,plain,((~m_user_v_ack(c_e_h_3, c_u, s7)) | m_and_h_gate_v_out(c_e_h_3, c_r, s7)), inference(lemma,lemma(discharge,[]))).
% 289.36/181.82 tff(2489,plain,
% 289.36/181.82 (~m_user_v_ack(c_e_h_3, c_u, s7)),
% 289.36/181.82 inference(unit_resolution,[status(thm)],[2488, 2481])).
% 289.36/181.82 tff(2490,assumption,(~m_user_v_req(c_e_h_3, c_u, s8)), introduced(assumption)).
% 289.36/181.82 tff(2491,assumption,(node8(c_e_h_3, c_u, s7, s8)), introduced(assumption)).
% 289.36/181.82 tff(2492,plain,
% 289.36/181.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_3, c_u, s8) | (~node8(c_e_h_3, c_u, s7, s8)) | (~m_user_v_req(c_e_h_3, c_u, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | m_user_v_req(c_e_h_3, c_u, s8) | (~node8(c_e_h_3, c_u, s7, s8)) | (~m_user_v_req(c_e_h_3, c_u, s7)))),
% 289.36/181.82 inference(rewrite,[status(thm)],[])).
% 289.36/181.82 tff(2493,plain,
% 289.36/181.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_3, c_u, s8) | (~node8(c_e_h_3, c_u, s7, s8)) | (~m_user_v_req(c_e_h_3, c_u, s7)))),
% 289.36/181.82 inference(quant_inst,[status(thm)],[])).
% 289.36/181.82 tff(2494,plain,
% 289.36/181.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | m_user_v_req(c_e_h_3, c_u, s8) | (~node8(c_e_h_3, c_u, s7, s8)) | (~m_user_v_req(c_e_h_3, c_u, s7))),
% 289.36/181.82 inference(modus_ponens,[status(thm)],[2493, 2492])).
% 289.36/181.82 tff(2495,plain,
% 289.36/181.82 ($false),
% 289.36/181.82 inference(unit_resolution,[status(thm)],[2494, 302, 2491, 2490, 1903])).
% 289.36/181.82 tff(2496,plain,((~node8(c_e_h_3, c_u, s7, s8)) | m_user_v_req(c_e_h_3, c_u, s8) | (~m_user_v_req(c_e_h_3, c_u, s7))), inference(lemma,lemma(discharge,[]))).
% 289.36/181.82 tff(2497,plain,
% 289.36/181.82 (~node8(c_e_h_3, c_u, s7, s8)),
% 289.36/181.82 inference(unit_resolution,[status(thm)],[2496, 2490, 1903])).
% 289.36/181.82 tff(2498,plain,
% 289.36/181.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | ((~trans(s7, s8)) | node7(c_e_h_3, c_u, s7, s8) | node8(c_e_h_3, c_u, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | (~trans(s7, s8)) | node7(c_e_h_3, c_u, s7, s8) | node8(c_e_h_3, c_u, s7, s8))),
% 289.36/181.82 inference(rewrite,[status(thm)],[])).
% 289.36/181.82 tff(2499,plain,
% 289.36/181.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | ((~trans(s7, s8)) | node7(c_e_h_3, c_u, s7, s8) | node8(c_e_h_3, c_u, s7, s8))),
% 289.36/181.82 inference(quant_inst,[status(thm)],[])).
% 289.36/181.82 tff(2500,plain,
% 289.36/181.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | (~trans(s7, s8)) | node7(c_e_h_3, c_u, s7, s8) | node8(c_e_h_3, c_u, s7, s8)),
% 289.36/181.82 inference(modus_ponens,[status(thm)],[2499, 2498])).
% 289.36/181.82 tff(2501,plain,
% 289.36/181.82 (node7(c_e_h_3, c_u, s7, s8) | node8(c_e_h_3, c_u, s7, s8)),
% 289.36/181.82 inference(unit_resolution,[status(thm)],[2500, 328, 1938])).
% 289.36/181.82 tff(2502,plain,
% 289.36/181.82 (node7(c_e_h_3, c_u, s7, s8)),
% 289.36/181.82 inference(unit_resolution,[status(thm)],[2501, 2497])).
% 289.36/181.82 tff(2503,assumption,(~m_user_v_ack(c_e_h_3, c_u, s7)), introduced(assumption)).
% 289.36/181.82 tff(2504,plain,
% 289.36/181.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | ((~node7(c_e_h_3, c_u, s7, s8)) | m_user_v_ack(c_e_h_3, c_u, s7) | m_user_v_req(c_e_h_3, c_u, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | (~node7(c_e_h_3, c_u, s7, s8)) | m_user_v_ack(c_e_h_3, c_u, s7) | m_user_v_req(c_e_h_3, c_u, s8))),
% 289.36/181.82 inference(rewrite,[status(thm)],[])).
% 289.36/181.82 tff(2505,plain,
% 289.36/181.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | ((~node7(c_e_h_3, c_u, s7, s8)) | m_user_v_ack(c_e_h_3, c_u, s7) | m_user_v_req(c_e_h_3, c_u, s8))),
% 289.36/181.82 inference(quant_inst,[status(thm)],[])).
% 289.36/181.82 tff(2506,plain,
% 289.36/181.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | (~node7(c_e_h_3, c_u, s7, s8)) | m_user_v_ack(c_e_h_3, c_u, s7) | m_user_v_req(c_e_h_3, c_u, s8)),
% 289.36/181.82 inference(modus_ponens,[status(thm)],[2505, 2504])).
% 289.36/181.82 tff(2507,plain,
% 289.36/181.82 ($false),
% 289.36/181.82 inference(unit_resolution,[status(thm)],[2506, 284, 2503, 2502, 2490])).
% 289.36/181.82 tff(2508,plain,(m_user_v_req(c_e_h_3, c_u, s8) | m_user_v_ack(c_e_h_3, c_u, s7) | (~m_user_v_req(c_e_h_3, c_u, s7))), inference(lemma,lemma(discharge,[]))).
% 289.36/181.82 tff(2509,plain,
% 289.36/181.82 (m_user_v_req(c_e_h_3, c_u, s8) | (~m_user_v_req(c_e_h_3, c_u, s7))),
% 289.36/181.82 inference(unit_resolution,[status(thm)],[2508, 2489])).
% 289.36/181.82 tff(2510,plain,
% 289.36/181.82 ($false),
% 289.36/181.82 inference(unit_resolution,[status(thm)],[2509, 1901, 2015])).
% 289.36/181.82 tff(2511,plain,((~m_mutex_h_half_v_out(c_e_h_3, c_a, s4)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s9)), inference(lemma,lemma(discharge,[]))).
% 289.36/181.82 tff(2512,plain,
% 289.36/181.82 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s4)),
% 289.36/181.82 inference(unit_resolution,[status(thm)],[2511, 1])).
% 289.36/181.82 tff(2513,assumption,(~m_mutex_h_half_v_out(c_e_h_3, c_a, s4)), introduced(assumption)).
% 289.36/181.82 tff(2514,plain,
% 289.36/181.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s3)) | (~node13(c_e_h_3, c_a, s3, s4)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s3)) | (~node13(c_e_h_3, c_a, s3, s4)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s4))),
% 289.36/181.82 inference(rewrite,[status(thm)],[])).
% 289.36/181.82 tff(2515,plain,
% 289.36/181.82 ((m_mutex_h_half_v_out(c_e_h_3, c_a, s4) | (~node13(c_e_h_3, c_a, s3, s4)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s3))) <=> ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s3)) | (~node13(c_e_h_3, c_a, s3, s4)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s4))),
% 289.36/181.82 inference(rewrite,[status(thm)],[])).
% 289.36/181.82 tff(2516,plain,
% 289.36/181.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s4) | (~node13(c_e_h_3, c_a, s3, s4)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s3)) | (~node13(c_e_h_3, c_a, s3, s4)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s4)))),
% 289.36/181.82 inference(monotonicity,[status(thm)],[2515])).
% 289.36/181.82 tff(2517,plain,
% 289.36/181.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s4) | (~node13(c_e_h_3, c_a, s3, s4)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s3)) | (~node13(c_e_h_3, c_a, s3, s4)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s4))),
% 289.36/181.82 inference(transitivity,[status(thm)],[2516, 2514])).
% 289.36/181.82 tff(2518,plain,
% 289.36/181.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s4) | (~node13(c_e_h_3, c_a, s3, s4)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s3)))),
% 289.36/181.82 inference(quant_inst,[status(thm)],[])).
% 289.36/181.82 tff(2519,plain,
% 289.36/181.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s3)) | (~node13(c_e_h_3, c_a, s3, s4)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s4)),
% 289.36/181.82 inference(modus_ponens,[status(thm)],[2518, 2517])).
% 289.36/181.82 tff(2520,plain,
% 289.36/181.82 ($false),
% 289.36/181.82 inference(unit_resolution,[status(thm)],[2519, 1459, 518, 464, 2513])).
% 289.36/181.82 tff(2521,plain,((~node13(c_e_h_3, c_a, s3, s4)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s3)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s4)), inference(lemma,lemma(discharge,[]))).
% 289.36/181.82 tff(2522,plain,
% 289.36/181.82 (~node13(c_e_h_3, c_a, s3, s4)),
% 289.36/181.82 inference(unit_resolution,[status(thm)],[2521, 464, 2513])).
% 289.36/181.82 tff(2523,plain,
% 289.36/181.82 (node12(c_e_h_3, c_a, s3, s4)),
% 289.36/181.82 inference(unit_resolution,[status(thm)],[535, 2522])).
% 289.36/181.82 tff(2524,plain,
% 289.36/181.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s4) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s3)) | (~node12(c_e_h_3, c_a, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | m_mutex_h_half_v_out(c_e_h_3, c_a, s4) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s3)) | (~node12(c_e_h_3, c_a, s3, s4)))),
% 289.36/181.82 inference(rewrite,[status(thm)],[])).
% 289.36/181.82 tff(2525,plain,
% 289.36/181.82 (((~node12(c_e_h_3, c_a, s3, s4)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s3)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s4)) <=> (m_mutex_h_half_v_out(c_e_h_3, c_a, s4) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s3)) | (~node12(c_e_h_3, c_a, s3, s4)))),
% 289.36/181.82 inference(rewrite,[status(thm)],[])).
% 289.36/181.82 tff(2526,plain,
% 289.36/181.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_3, c_a, s3, s4)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s3)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s4) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s3)) | (~node12(c_e_h_3, c_a, s3, s4))))),
% 289.36/181.82 inference(monotonicity,[status(thm)],[2525])).
% 289.36/181.82 tff(2527,plain,
% 289.36/181.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_3, c_a, s3, s4)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s3)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | m_mutex_h_half_v_out(c_e_h_3, c_a, s4) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s3)) | (~node12(c_e_h_3, c_a, s3, s4)))),
% 289.36/181.82 inference(transitivity,[status(thm)],[2526, 2524])).
% 289.36/181.82 tff(2528,plain,
% 289.36/181.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_3, c_a, s3, s4)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s3)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s4))),
% 289.36/181.83 inference(quant_inst,[status(thm)],[])).
% 289.36/181.83 tff(2529,plain,
% 289.36/181.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | m_mutex_h_half_v_out(c_e_h_3, c_a, s4) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s3)) | (~node12(c_e_h_3, c_a, s3, s4))),
% 289.36/181.83 inference(modus_ponens,[status(thm)],[2528, 2527])).
% 289.36/181.83 tff(2530,plain,
% 289.36/181.83 (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s3)),
% 289.36/181.83 inference(unit_resolution,[status(thm)],[2529, 1483, 2523, 2513])).
% 289.36/181.83 tff(2531,plain,
% 289.36/181.83 (m_user_v_req(c_e_h_3, c_u, s2)),
% 289.36/181.83 inference(unit_resolution,[status(thm)],[514, 464])).
% 289.36/181.83 tff(2532,plain,
% 289.36/181.83 (m_user_v_req(c_e_h_3, c_u, s3)),
% 289.36/181.83 inference(unit_resolution,[status(thm)],[335, 2531])).
% 289.36/181.83 tff(2533,plain,
% 289.36/181.83 (((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | ((~m_user_v_req(c_e_h_3, c_u, s3)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s3))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | (~m_user_v_req(c_e_h_3, c_u, s3)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s3))),
% 289.36/181.83 inference(rewrite,[status(thm)],[])).
% 289.36/181.83 tff(2534,plain,
% 289.36/181.83 ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | ((~m_user_v_req(c_e_h_3, c_u, s3)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s3))),
% 289.36/181.83 inference(quant_inst,[status(thm)],[])).
% 289.36/181.83 tff(2535,plain,
% 289.36/181.83 ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | (~m_user_v_req(c_e_h_3, c_u, s3)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s3)),
% 289.36/181.83 inference(modus_ponens,[status(thm)],[2534, 2533])).
% 289.36/181.83 tff(2536,plain,
% 289.36/181.83 ($false),
% 289.36/181.83 inference(unit_resolution,[status(thm)],[2535, 1426, 2532, 2530])).
% 289.36/181.83 tff(2537,plain,((~m_mutex_h_half_v_out(c_e_h_3, c_a, s3)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s4)), inference(lemma,lemma(discharge,[]))).
% 289.36/181.83 tff(2538,plain,
% 289.36/181.83 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s3)),
% 289.36/181.83 inference(unit_resolution,[status(thm)],[2537, 2512])).
% 289.36/181.83 tff(2539,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_c, s3)), introduced(assumption)).
% 289.36/181.83 tff(2540,plain,
% 289.36/181.83 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_c, s3)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s3))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s3)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s3))),
% 289.36/181.83 inference(rewrite,[status(thm)],[])).
% 289.36/181.83 tff(2541,plain,
% 289.36/181.83 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_c, s3)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s3))),
% 289.36/181.83 inference(quant_inst,[status(thm)],[])).
% 289.36/181.83 tff(2542,plain,
% 289.36/181.83 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s3)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s3)),
% 289.36/181.83 inference(modus_ponens,[status(thm)],[2541, 2540])).
% 289.36/181.83 tff(2543,plain,
% 289.36/181.83 ($false),
% 289.36/181.83 inference(unit_resolution,[status(thm)],[2542, 567, 517, 2539])).
% 289.36/181.83 tff(2544,plain,((~m_and_h_gate_v_in1(c_e_h_3, c_c, s3)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s3)), inference(lemma,lemma(discharge,[]))).
% 289.36/181.83 tff(2545,plain,
% 289.36/181.83 (~m_and_h_gate_v_in1(c_e_h_3, c_c, s3)),
% 289.36/181.83 inference(unit_resolution,[status(thm)],[2544, 2538])).
% 289.36/181.83 tff(2546,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_c, s3)), introduced(assumption)).
% 289.36/181.83 tff(2547,plain,
% 289.36/181.83 (^[I0: $i, X: $i] : refl(((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X)) <=> ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X)))),
% 289.36/181.83 inference(bind,[status(th)],[])).
% 289.36/181.83 tff(2548,plain,
% 289.36/181.83 (![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X)) <=> ![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))),
% 289.36/181.83 inference(quant_intro,[status(thm)],[2547])).
% 289.36/181.83 tff(2549,plain,
% 289.36/181.83 (![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X)) <=> ![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))),
% 289.36/181.83 inference(rewrite,[status(thm)],[])).
% 289.36/181.83 tff(2550,plain,
% 289.36/181.83 (^[I0: $i, X: $i] : rewrite((m_and_h_gate_v_in1(I0, c_c, X) | (~m_mutex_h_half_v_out(I0, c_a, X))) <=> ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X)))),
% 289.36/181.83 inference(bind,[status(th)],[])).
% 289.36/181.83 tff(2551,plain,
% 289.36/181.83 (![I0: $i, X: $i] : (m_and_h_gate_v_in1(I0, c_c, X) | (~m_mutex_h_half_v_out(I0, c_a, X))) <=> ![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))),
% 289.36/181.83 inference(quant_intro,[status(thm)],[2550])).
% 289.36/181.83 tff(2552,axiom,(![I0: $i, X: $i] : (m_and_h_gate_v_in1(I0, c_c, X) | (~m_mutex_h_half_v_out(I0, c_a, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_10')).
% 289.36/181.83 tff(2553,plain,
% 289.36/181.83 (![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))),
% 289.36/181.83 inference(modus_ponens,[status(thm)],[2552, 2551])).
% 289.36/181.83 tff(2554,plain,
% 289.36/181.83 (![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))),
% 289.36/181.83 inference(modus_ponens,[status(thm)],[2553, 2549])).
% 289.36/181.83 tff(2555,plain,(
% 289.36/181.83 ![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))),
% 289.36/181.83 inference(skolemize,[status(sab)],[2554])).
% 289.36/181.83 tff(2556,plain,
% 289.36/181.83 (![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))),
% 289.36/181.83 inference(modus_ponens,[status(thm)],[2555, 2548])).
% 289.36/181.83 tff(2557,plain,
% 289.36/181.83 (((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s3))) <=> ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s3))),
% 289.36/181.83 inference(rewrite,[status(thm)],[])).
% 289.36/181.83 tff(2558,plain,
% 289.36/181.83 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s3))),
% 289.36/181.83 inference(quant_inst,[status(thm)],[])).
% 289.36/181.83 tff(2559,plain,
% 289.36/181.83 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s3)),
% 289.36/181.83 inference(modus_ponens,[status(thm)],[2558, 2557])).
% 289.36/181.83 tff(2560,plain,
% 289.36/181.83 ($false),
% 289.36/181.83 inference(unit_resolution,[status(thm)],[2559, 2556, 464, 2546])).
% 289.36/181.83 tff(2561,plain,(m_and_h_gate_v_in1(c_e_h_3, c_c, s3) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s3))), inference(lemma,lemma(discharge,[]))).
% 289.36/181.83 tff(2562,plain,
% 289.36/181.83 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s3)),
% 289.36/181.83 inference(unit_resolution,[status(thm)],[2561, 2546])).
% 289.36/181.83 tff(2563,assumption,(node13(c_e_h_3, c_a, s2, s3)), introduced(assumption)).
% 289.36/181.83 tff(2564,plain,
% 289.36/181.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s3) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)) | (~node13(c_e_h_3, c_a, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | m_mutex_h_half_v_out(c_e_h_3, c_a, s3) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)) | (~node13(c_e_h_3, c_a, s2, s3)))),
% 289.36/181.83 inference(rewrite,[status(thm)],[])).
% 289.36/181.83 tff(2565,plain,
% 289.36/181.83 ((m_mutex_h_half_v_out(c_e_h_3, c_a, s3) | (~node13(c_e_h_3, c_a, s2, s3)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2))) <=> (m_mutex_h_half_v_out(c_e_h_3, c_a, s3) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)) | (~node13(c_e_h_3, c_a, s2, s3)))),
% 289.36/181.83 inference(rewrite,[status(thm)],[])).
% 289.36/181.83 tff(2566,plain,
% 289.36/181.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s3) | (~node13(c_e_h_3, c_a, s2, s3)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s3) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)) | (~node13(c_e_h_3, c_a, s2, s3))))),
% 289.36/181.83 inference(monotonicity,[status(thm)],[2565])).
% 289.36/181.83 tff(2567,plain,
% 289.36/181.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s3) | (~node13(c_e_h_3, c_a, s2, s3)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | m_mutex_h_half_v_out(c_e_h_3, c_a, s3) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)) | (~node13(c_e_h_3, c_a, s2, s3)))),
% 289.36/181.83 inference(transitivity,[status(thm)],[2566, 2564])).
% 289.36/181.83 tff(2568,plain,
% 289.36/181.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s3) | (~node13(c_e_h_3, c_a, s2, s3)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)))),
% 289.36/181.83 inference(quant_inst,[status(thm)],[])).
% 289.36/181.83 tff(2569,plain,
% 289.36/181.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | m_mutex_h_half_v_out(c_e_h_3, c_a, s3) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)) | (~node13(c_e_h_3, c_a, s2, s3))),
% 289.36/181.83 inference(modus_ponens,[status(thm)],[2568, 2567])).
% 289.36/181.83 tff(2570,plain,
% 289.36/181.83 ($false),
% 289.36/181.83 inference(unit_resolution,[status(thm)],[2569, 1459, 2563, 517, 494])).
% 289.36/181.83 tff(2571,plain,((~node13(c_e_h_3, c_a, s2, s3)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s3) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2))), inference(lemma,lemma(discharge,[]))).
% 289.36/181.83 tff(2572,plain,
% 289.36/181.83 (~node13(c_e_h_3, c_a, s2, s3)),
% 289.36/181.83 inference(unit_resolution,[status(thm)],[2571, 494, 517])).
% 289.36/181.83 tff(2573,plain,
% 289.36/181.83 (node12(c_e_h_3, c_a, s2, s3)),
% 289.36/181.83 inference(unit_resolution,[status(thm)],[483, 2572])).
% 289.36/181.83 tff(2574,assumption,(m_mutex_h_half_v_inp(c_e_h_3, c_a, s2)), introduced(assumption)).
% 289.36/181.83 tff(2575,plain,
% 289.36/181.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s3) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s2)) | (~node12(c_e_h_3, c_a, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | m_mutex_h_half_v_out(c_e_h_3, c_a, s3) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s2)) | (~node12(c_e_h_3, c_a, s2, s3)))),
% 289.36/181.83 inference(rewrite,[status(thm)],[])).
% 289.36/181.83 tff(2576,plain,
% 289.36/181.83 (((~node12(c_e_h_3, c_a, s2, s3)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s2)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s3)) <=> (m_mutex_h_half_v_out(c_e_h_3, c_a, s3) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s2)) | (~node12(c_e_h_3, c_a, s2, s3)))),
% 289.36/181.83 inference(rewrite,[status(thm)],[])).
% 289.36/181.83 tff(2577,plain,
% 289.36/181.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_3, c_a, s2, s3)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s2)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s3) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s2)) | (~node12(c_e_h_3, c_a, s2, s3))))),
% 289.36/181.83 inference(monotonicity,[status(thm)],[2576])).
% 289.36/181.83 tff(2578,plain,
% 289.36/181.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_3, c_a, s2, s3)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s2)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | m_mutex_h_half_v_out(c_e_h_3, c_a, s3) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s2)) | (~node12(c_e_h_3, c_a, s2, s3)))),
% 289.36/181.84 inference(transitivity,[status(thm)],[2577, 2575])).
% 289.36/181.84 tff(2579,plain,
% 289.36/181.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_3, c_a, s2, s3)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s2)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s3))),
% 289.36/181.84 inference(quant_inst,[status(thm)],[])).
% 289.36/181.84 tff(2580,plain,
% 289.36/181.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | m_mutex_h_half_v_out(c_e_h_3, c_a, s3) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s2)) | (~node12(c_e_h_3, c_a, s2, s3))),
% 289.36/181.84 inference(modus_ponens,[status(thm)],[2579, 2578])).
% 289.36/181.84 tff(2581,plain,
% 289.36/181.84 ($false),
% 289.36/181.84 inference(unit_resolution,[status(thm)],[2580, 1483, 470, 2574, 517])).
% 289.36/181.84 tff(2582,plain,((~node12(c_e_h_3, c_a, s2, s3)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s2)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s3)), inference(lemma,lemma(discharge,[]))).
% 289.36/181.84 tff(2583,plain,
% 289.36/181.84 (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s2)),
% 289.36/181.84 inference(unit_resolution,[status(thm)],[2582, 2573, 517])).
% 289.36/181.84 tff(2584,plain,
% 289.36/181.84 (~node7(c_e_h_3, c_u, s0, s1)),
% 289.36/181.84 inference(unit_resolution,[status(thm)],[375, 365])).
% 289.36/181.84 tff(2585,plain,
% 289.36/181.84 (node8(c_e_h_3, c_u, s0, s1)),
% 289.36/181.84 inference(unit_resolution,[status(thm)],[380, 2584])).
% 289.36/181.84 tff(2586,plain,
% 289.36/181.84 (~m_user_v_req(c_e_h_3, c_u, s0)),
% 289.36/181.84 inference(unit_resolution,[status(thm)],[387, 302, 2585, 365])).
% 289.36/181.84 tff(2587,plain,
% 289.36/181.84 (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s0)),
% 289.36/181.84 inference(unit_resolution,[status(thm)],[398, 395, 2586])).
% 289.36/181.84 tff(2588,plain,
% 289.36/181.84 (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s1)),
% 289.36/181.84 inference(unit_resolution,[status(thm)],[491, 395, 365])).
% 289.36/181.84 tff(2589,assumption,(~m_mutex_h_half_v_out(c_e_h_3, c_a, s1)), introduced(assumption)).
% 289.36/181.84 tff(2590,plain,
% 289.36/181.84 (~node12(c_e_h_3, c_a, s1, s2)),
% 289.36/181.84 inference(unit_resolution,[status(thm)],[503, 494, 493])).
% 289.36/181.84 tff(2591,plain,
% 289.36/181.84 (node13(c_e_h_3, c_a, s1, s2)),
% 289.36/181.84 inference(unit_resolution,[status(thm)],[508, 2590])).
% 289.36/181.84 tff(2592,plain,
% 289.36/181.84 ($false),
% 289.36/181.84 inference(unit_resolution,[status(thm)],[512, 423, 2591, 494, 2589])).
% 289.36/181.84 tff(2593,plain,((~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s1) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s1)), inference(lemma,lemma(discharge,[]))).
% 289.36/181.84 tff(2594,plain,
% 289.36/181.84 (m_mutex_h_half_v_out(c_e_h_3, c_a, s1)),
% 289.36/181.84 inference(unit_resolution,[status(thm)],[2593, 2588, 494])).
% 289.36/181.84 tff(2595,plain,
% 289.36/181.84 ($false),
% 289.36/181.84 inference(unit_resolution,[status(thm)],[462, 2594, 2587])).
% 289.36/181.84 tff(2596,plain,(m_user_v_req(c_e_h_3, c_u, s1) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2))), inference(lemma,lemma(discharge,[]))).
% 289.36/181.84 tff(2597,plain,
% 289.36/181.84 (m_user_v_req(c_e_h_3, c_u, s1)),
% 289.36/181.84 inference(unit_resolution,[status(thm)],[2596, 494])).
% 289.36/181.84 tff(2598,plain,
% 289.36/181.84 (~node8(c_e_h_3, c_u, s1, s2)),
% 289.36/181.84 inference(unit_resolution,[status(thm)],[363, 337, 354])).
% 289.36/181.84 tff(2599,plain,
% 289.36/181.84 ($false),
% 289.36/181.84 inference(unit_resolution,[status(thm)],[352, 2598, 348])).
% 289.36/181.84 tff(2600,plain,(m_user_v_req(c_e_h_3, c_u, s2) | (~m_user_v_req(c_e_h_3, c_u, s1))), inference(lemma,lemma(discharge,[]))).
% 289.36/181.84 tff(2601,plain,
% 289.36/181.84 (m_user_v_req(c_e_h_3, c_u, s2)),
% 289.36/181.84 inference(unit_resolution,[status(thm)],[2600, 2597])).
% 289.36/181.84 tff(2602,plain,
% 289.36/181.84 (((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | ((~m_user_v_req(c_e_h_3, c_u, s2)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s2))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | (~m_user_v_req(c_e_h_3, c_u, s2)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s2))),
% 289.36/181.84 inference(rewrite,[status(thm)],[])).
% 289.36/181.84 tff(2603,plain,
% 289.36/181.84 ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | ((~m_user_v_req(c_e_h_3, c_u, s2)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s2))),
% 289.36/181.84 inference(quant_inst,[status(thm)],[])).
% 289.36/181.84 tff(2604,plain,
% 289.36/181.84 ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | (~m_user_v_req(c_e_h_3, c_u, s2)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s2)),
% 289.36/181.84 inference(modus_ponens,[status(thm)],[2603, 2602])).
% 289.36/181.84 tff(2605,plain,
% 289.36/181.84 ($false),
% 289.36/181.84 inference(unit_resolution,[status(thm)],[2604, 1426, 2601, 2583])).
% 289.36/181.84 tff(2606,plain,((~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s3)), inference(lemma,lemma(discharge,[]))).
% 289.36/181.84 tff(2607,plain,
% 289.36/181.84 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)),
% 289.36/181.84 inference(unit_resolution,[status(thm)],[2606, 2562])).
% 289.36/181.84 tff(2608,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_c, s2)), introduced(assumption)).
% 289.36/181.84 tff(2609,assumption,(~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)), introduced(assumption)).
% 289.36/181.84 tff(2610,plain,
% 289.36/181.84 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_c, s2)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s2))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s2)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s2))),
% 289.36/181.84 inference(rewrite,[status(thm)],[])).
% 289.36/181.84 tff(2611,plain,
% 289.36/181.84 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_c, s2)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s2))),
% 289.36/181.84 inference(quant_inst,[status(thm)],[])).
% 289.36/181.84 tff(2612,plain,
% 289.36/181.84 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s2)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s2)),
% 289.36/181.84 inference(modus_ponens,[status(thm)],[2611, 2610])).
% 289.36/181.84 tff(2613,plain,
% 289.36/181.84 ($false),
% 289.36/181.84 inference(unit_resolution,[status(thm)],[2612, 567, 2609, 2608])).
% 289.36/181.84 tff(2614,plain,((~m_and_h_gate_v_in1(c_e_h_3, c_c, s2)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s2)), inference(lemma,lemma(discharge,[]))).
% 289.36/181.84 tff(2615,plain,
% 289.36/181.84 (~m_and_h_gate_v_in1(c_e_h_3, c_c, s2)),
% 289.36/181.84 inference(unit_resolution,[status(thm)],[2614, 2607])).
% 289.36/181.84 tff(2616,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_c, s2)), introduced(assumption)).
% 289.36/181.84 tff(2617,assumption,(node20(c_e_h_3, c_c, s2)), introduced(assumption)).
% 289.36/181.84 tff(2618,plain,
% 289.36/181.84 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_c, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_c, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s2))),
% 289.36/181.84 inference(rewrite,[status(thm)],[])).
% 289.36/181.84 tff(2619,plain,
% 289.36/181.84 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_c, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s2))),
% 289.36/181.84 inference(quant_inst,[status(thm)],[])).
% 289.36/181.84 tff(2620,plain,
% 289.36/181.84 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_c, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s2)),
% 289.36/181.84 inference(modus_ponens,[status(thm)],[2619, 2618])).
% 289.36/181.84 tff(2621,plain,
% 289.36/181.84 ($false),
% 289.36/181.84 inference(unit_resolution,[status(thm)],[2620, 38, 2617, 2616])).
% 289.36/181.84 tff(2622,plain,((~node20(c_e_h_3, c_c, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s2)), inference(lemma,lemma(discharge,[]))).
% 289.36/181.84 tff(2623,plain,
% 289.36/181.84 (~node20(c_e_h_3, c_c, s2)),
% 289.36/181.84 inference(unit_resolution,[status(thm)],[2622, 2615])).
% 289.36/181.84 tff(2624,assumption,(m_and_h_gate_v_out(c_e_h_3, c_c, s2)), introduced(assumption)).
% 289.36/181.84 tff(2625,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_c, s1)), introduced(assumption)).
% 289.36/181.84 tff(2626,assumption,(node22(c_e_h_3, c_c, s1, s2)), introduced(assumption)).
% 289.36/181.84 tff(2627,plain,
% 289.36/181.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s2)) | (~node22(c_e_h_3, c_c, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_c, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s2)) | (~node22(c_e_h_3, c_c, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_c, s1))),
% 289.36/181.84 inference(rewrite,[status(thm)],[])).
% 289.36/181.84 tff(2628,plain,
% 289.36/181.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s2)) | (~node22(c_e_h_3, c_c, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_c, s1))),
% 289.36/181.84 inference(quant_inst,[status(thm)],[])).
% 289.36/181.84 tff(2629,plain,
% 289.36/181.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s2)) | (~node22(c_e_h_3, c_c, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_c, s1)),
% 289.36/181.84 inference(modus_ponens,[status(thm)],[2628, 2627])).
% 289.36/181.84 tff(2630,plain,
% 289.36/181.84 ($false),
% 289.36/181.84 inference(unit_resolution,[status(thm)],[2629, 108, 2626, 2624, 2625])).
% 289.36/181.84 tff(2631,plain,((~node22(c_e_h_3, c_c, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s2)) | m_and_h_gate_v_out(c_e_h_3, c_c, s1)), inference(lemma,lemma(discharge,[]))).
% 289.36/181.84 tff(2632,plain,
% 289.36/181.84 ((~node22(c_e_h_3, c_c, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s2))),
% 289.36/181.84 inference(unit_resolution,[status(thm)],[2631, 593])).
% 289.36/181.84 tff(2633,plain,
% 289.36/181.84 (~node22(c_e_h_3, c_c, s1, s2)),
% 289.36/181.84 inference(unit_resolution,[status(thm)],[2632, 2624])).
% 289.36/181.84 tff(2634,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_c, s1)), introduced(assumption)).
% 289.36/181.84 tff(2635,assumption,(m_user_v_req(c_e_h_3, c_u, s0)), introduced(assumption)).
% 289.36/181.84 tff(2636,plain,
% 289.36/181.84 (^[I0: $i, I1: $i] : refl((~m_user_v_req(I0, I1, s0)) <=> (~m_user_v_req(I0, I1, s0)))),
% 289.36/181.84 inference(bind,[status(th)],[])).
% 289.36/181.84 tff(2637,plain,
% 289.36/181.84 (![I0: $i, I1: $i] : (~m_user_v_req(I0, I1, s0)) <=> ![I0: $i, I1: $i] : (~m_user_v_req(I0, I1, s0))),
% 289.36/181.84 inference(quant_intro,[status(thm)],[2636])).
% 289.36/181.84 tff(2638,plain,
% 289.36/181.84 (![I0: $i, I1: $i] : (~m_user_v_req(I0, I1, s0)) <=> ![I0: $i, I1: $i] : (~m_user_v_req(I0, I1, s0))),
% 289.36/181.84 inference(rewrite,[status(thm)],[])).
% 289.36/181.84 tff(2639,axiom,(![I0: $i, I1: $i] : (~m_user_v_req(I0, I1, s0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_user_1')).
% 289.36/181.84 tff(2640,plain,
% 289.36/181.84 (![I0: $i, I1: $i] : (~m_user_v_req(I0, I1, s0))),
% 289.36/181.84 inference(modus_ponens,[status(thm)],[2639, 2638])).
% 289.36/181.84 tff(2641,plain,(
% 289.36/181.84 ![I0: $i, I1: $i] : (~m_user_v_req(I0, I1, s0))),
% 289.36/181.84 inference(skolemize,[status(sab)],[2640])).
% 289.36/181.84 tff(2642,plain,
% 289.36/181.84 (![I0: $i, I1: $i] : (~m_user_v_req(I0, I1, s0))),
% 289.36/181.84 inference(modus_ponens,[status(thm)],[2641, 2637])).
% 289.36/181.84 tff(2643,plain,
% 289.36/181.84 ((~![I0: $i, I1: $i] : (~m_user_v_req(I0, I1, s0))) | (~m_user_v_req(c_e_h_3, c_u, s0))),
% 289.36/181.84 inference(quant_inst,[status(thm)],[])).
% 289.36/181.84 tff(2644,plain,
% 289.36/181.84 ($false),
% 289.36/181.84 inference(unit_resolution,[status(thm)],[2643, 2642, 2635])).
% 289.36/181.84 tff(2645,plain,(~m_user_v_req(c_e_h_3, c_u, s0)), inference(lemma,lemma(discharge,[]))).
% 289.36/181.84 tff(2646,plain,
% 289.36/181.84 (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s0)),
% 289.36/181.84 inference(unit_resolution,[status(thm)],[398, 395, 2645])).
% 289.36/181.84 tff(2647,plain,
% 289.36/181.84 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s1)),
% 289.36/181.84 inference(unit_resolution,[status(thm)],[462, 2646])).
% 289.36/181.84 tff(2648,plain,
% 289.36/181.84 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_c, s1)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s1))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s1)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s1))),
% 289.36/181.84 inference(rewrite,[status(thm)],[])).
% 289.36/181.84 tff(2649,plain,
% 289.36/181.84 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_c, s1)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s1))),
% 289.36/181.84 inference(quant_inst,[status(thm)],[])).
% 289.36/181.84 tff(2650,plain,
% 289.36/181.84 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s1)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s1)),
% 289.36/181.84 inference(modus_ponens,[status(thm)],[2649, 2648])).
% 289.36/181.84 tff(2651,plain,
% 289.36/181.84 ($false),
% 289.36/181.84 inference(unit_resolution,[status(thm)],[2650, 567, 2647, 2634])).
% 289.36/181.84 tff(2652,plain,(~m_and_h_gate_v_in1(c_e_h_3, c_c, s1)), inference(lemma,lemma(discharge,[]))).
% 289.36/181.84 tff(2653,plain,
% 289.36/181.84 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_c, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_c, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s1))),
% 289.36/181.85 inference(rewrite,[status(thm)],[])).
% 289.36/181.85 tff(2654,plain,
% 289.36/181.85 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_c, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s1))),
% 289.36/181.85 inference(quant_inst,[status(thm)],[])).
% 289.36/181.85 tff(2655,plain,
% 289.36/181.85 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_c, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s1)),
% 289.36/181.85 inference(modus_ponens,[status(thm)],[2654, 2653])).
% 289.36/181.85 tff(2656,plain,
% 289.36/181.85 (~node20(c_e_h_3, c_c, s1)),
% 289.36/181.85 inference(unit_resolution,[status(thm)],[2655, 38, 2652])).
% 289.36/181.85 tff(2657,assumption,(~node20(c_e_h_3, c_c, s1)), introduced(assumption)).
% 289.36/181.85 tff(2658,assumption,(node21(c_e_h_3, c_c, s1, s2)), introduced(assumption)).
% 289.36/181.85 tff(2659,plain,
% 289.36/181.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_c, s1) | (~node21(c_e_h_3, c_c, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_c, s1) | (~node21(c_e_h_3, c_c, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s2)))),
% 289.36/181.85 inference(rewrite,[status(thm)],[])).
% 289.36/181.85 tff(2660,plain,
% 289.36/181.85 ((node20(c_e_h_3, c_c, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s2)) | (~node21(c_e_h_3, c_c, s1, s2))) <=> (node20(c_e_h_3, c_c, s1) | (~node21(c_e_h_3, c_c, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s2)))),
% 289.36/181.85 inference(rewrite,[status(thm)],[])).
% 289.36/181.85 tff(2661,plain,
% 289.36/181.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_c, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s2)) | (~node21(c_e_h_3, c_c, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_c, s1) | (~node21(c_e_h_3, c_c, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s2))))),
% 289.36/181.85 inference(monotonicity,[status(thm)],[2660])).
% 289.36/181.85 tff(2662,plain,
% 289.36/181.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_c, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s2)) | (~node21(c_e_h_3, c_c, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_c, s1) | (~node21(c_e_h_3, c_c, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s2)))),
% 289.36/181.85 inference(transitivity,[status(thm)],[2661, 2659])).
% 289.36/181.85 tff(2663,plain,
% 289.36/181.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_c, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s2)) | (~node21(c_e_h_3, c_c, s1, s2)))),
% 289.36/181.85 inference(quant_inst,[status(thm)],[])).
% 289.36/181.85 tff(2664,plain,
% 289.36/181.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_c, s1) | (~node21(c_e_h_3, c_c, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s2))),
% 289.36/181.85 inference(modus_ponens,[status(thm)],[2663, 2662])).
% 289.36/181.85 tff(2665,plain,
% 289.36/181.85 ($false),
% 289.36/181.85 inference(unit_resolution,[status(thm)],[2664, 52, 2658, 2624, 2657])).
% 289.36/181.85 tff(2666,plain,((~node21(c_e_h_3, c_c, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s2)) | node20(c_e_h_3, c_c, s1)), inference(lemma,lemma(discharge,[]))).
% 289.36/181.85 tff(2667,plain,
% 289.36/181.85 ((~node21(c_e_h_3, c_c, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s2))),
% 289.36/181.85 inference(unit_resolution,[status(thm)],[2666, 2656])).
% 289.36/181.85 tff(2668,plain,
% 289.36/181.85 (~node21(c_e_h_3, c_c, s1, s2)),
% 289.36/181.85 inference(unit_resolution,[status(thm)],[2667, 2624])).
% 289.36/181.85 tff(2669,plain,
% 289.36/181.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_3, c_c, s1, s2) | node22(c_e_h_3, c_c, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_3, c_c, s1, s2) | node22(c_e_h_3, c_c, s1, s2))),
% 289.36/181.85 inference(rewrite,[status(thm)],[])).
% 289.36/181.85 tff(2670,plain,
% 289.36/181.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_3, c_c, s1, s2) | node22(c_e_h_3, c_c, s1, s2))),
% 289.36/181.85 inference(quant_inst,[status(thm)],[])).
% 289.36/181.85 tff(2671,plain,
% 289.36/181.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_3, c_c, s1, s2) | node22(c_e_h_3, c_c, s1, s2)),
% 289.36/181.85 inference(modus_ponens,[status(thm)],[2670, 2669])).
% 289.36/181.85 tff(2672,plain,
% 289.36/181.85 (node21(c_e_h_3, c_c, s1, s2) | node22(c_e_h_3, c_c, s1, s2)),
% 289.36/181.85 inference(unit_resolution,[status(thm)],[2671, 82, 255])).
% 289.36/181.85 tff(2673,plain,
% 289.36/181.85 ($false),
% 289.36/181.85 inference(unit_resolution,[status(thm)],[2672, 2668, 2633])).
% 289.36/181.85 tff(2674,plain,(~m_and_h_gate_v_out(c_e_h_3, c_c, s2)), inference(lemma,lemma(discharge,[]))).
% 289.36/181.85 tff(2675,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_c, s2)), introduced(assumption)).
% 289.36/181.85 tff(2676,assumption,(m_and_h_gate_v_out(c_e_h_3, c_c, s3)), introduced(assumption)).
% 289.36/181.85 tff(2677,assumption,(~node20(c_e_h_3, c_c, s2)), introduced(assumption)).
% 289.36/181.85 tff(2678,assumption,(node21(c_e_h_3, c_c, s2, s3)), introduced(assumption)).
% 289.36/181.85 tff(2679,plain,
% 289.36/181.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s3)) | node20(c_e_h_3, c_c, s2) | (~node21(c_e_h_3, c_c, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s3)) | node20(c_e_h_3, c_c, s2) | (~node21(c_e_h_3, c_c, s2, s3)))),
% 289.36/181.85 inference(rewrite,[status(thm)],[])).
% 289.36/181.85 tff(2680,plain,
% 289.36/181.85 ((node20(c_e_h_3, c_c, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s3)) | (~node21(c_e_h_3, c_c, s2, s3))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_c, s3)) | node20(c_e_h_3, c_c, s2) | (~node21(c_e_h_3, c_c, s2, s3)))),
% 289.36/181.85 inference(rewrite,[status(thm)],[])).
% 289.36/181.85 tff(2681,plain,
% 289.36/181.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_c, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s3)) | (~node21(c_e_h_3, c_c, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s3)) | node20(c_e_h_3, c_c, s2) | (~node21(c_e_h_3, c_c, s2, s3))))),
% 289.36/181.85 inference(monotonicity,[status(thm)],[2680])).
% 289.36/181.85 tff(2682,plain,
% 289.36/181.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_c, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s3)) | (~node21(c_e_h_3, c_c, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s3)) | node20(c_e_h_3, c_c, s2) | (~node21(c_e_h_3, c_c, s2, s3)))),
% 289.36/181.85 inference(transitivity,[status(thm)],[2681, 2679])).
% 289.36/181.85 tff(2683,plain,
% 289.36/181.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_c, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s3)) | (~node21(c_e_h_3, c_c, s2, s3)))),
% 289.36/181.85 inference(quant_inst,[status(thm)],[])).
% 289.36/181.85 tff(2684,plain,
% 289.36/181.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s3)) | node20(c_e_h_3, c_c, s2) | (~node21(c_e_h_3, c_c, s2, s3))),
% 289.36/181.85 inference(modus_ponens,[status(thm)],[2683, 2682])).
% 289.36/181.85 tff(2685,plain,
% 289.36/181.85 ($false),
% 289.36/181.85 inference(unit_resolution,[status(thm)],[2684, 52, 2678, 2676, 2677])).
% 289.36/181.85 tff(2686,plain,((~node21(c_e_h_3, c_c, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s3)) | node20(c_e_h_3, c_c, s2)), inference(lemma,lemma(discharge,[]))).
% 289.36/181.85 tff(2687,plain,
% 289.36/181.85 (~node21(c_e_h_3, c_c, s2, s3)),
% 289.36/181.85 inference(unit_resolution,[status(thm)],[2686, 2676, 2677])).
% 289.36/181.85 tff(2688,plain,
% 289.36/181.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_3, c_c, s2, s3) | node22(c_e_h_3, c_c, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_3, c_c, s2, s3) | node22(c_e_h_3, c_c, s2, s3))),
% 289.36/181.85 inference(rewrite,[status(thm)],[])).
% 289.36/181.85 tff(2689,plain,
% 289.36/181.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_3, c_c, s2, s3) | node22(c_e_h_3, c_c, s2, s3))),
% 289.36/181.85 inference(quant_inst,[status(thm)],[])).
% 289.36/181.85 tff(2690,plain,
% 289.36/181.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_3, c_c, s2, s3) | node22(c_e_h_3, c_c, s2, s3)),
% 289.36/181.85 inference(modus_ponens,[status(thm)],[2689, 2688])).
% 289.36/181.85 tff(2691,plain,
% 289.36/181.85 (node21(c_e_h_3, c_c, s2, s3) | node22(c_e_h_3, c_c, s2, s3)),
% 289.36/181.85 inference(unit_resolution,[status(thm)],[2690, 82, 318])).
% 289.36/181.85 tff(2692,plain,
% 289.36/181.85 (node22(c_e_h_3, c_c, s2, s3)),
% 289.36/181.85 inference(unit_resolution,[status(thm)],[2691, 2687])).
% 289.36/181.85 tff(2693,plain,
% 289.36/181.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s3)) | (~node22(c_e_h_3, c_c, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_c, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s3)) | (~node22(c_e_h_3, c_c, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_c, s2))),
% 289.36/181.85 inference(rewrite,[status(thm)],[])).
% 289.36/181.85 tff(2694,plain,
% 289.36/181.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s3)) | (~node22(c_e_h_3, c_c, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_c, s2))),
% 289.36/181.85 inference(quant_inst,[status(thm)],[])).
% 289.36/181.85 tff(2695,plain,
% 289.36/181.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s3)) | (~node22(c_e_h_3, c_c, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_c, s2)),
% 289.36/181.85 inference(modus_ponens,[status(thm)],[2694, 2693])).
% 289.36/181.85 tff(2696,plain,
% 289.36/181.85 ($false),
% 289.36/181.85 inference(unit_resolution,[status(thm)],[2695, 108, 2692, 2676, 2675])).
% 289.36/181.85 tff(2697,plain,((~m_and_h_gate_v_out(c_e_h_3, c_c, s3)) | m_and_h_gate_v_out(c_e_h_3, c_c, s2) | node20(c_e_h_3, c_c, s2)), inference(lemma,lemma(discharge,[]))).
% 289.36/181.85 tff(2698,plain,
% 289.36/181.85 ((~m_and_h_gate_v_out(c_e_h_3, c_c, s3)) | node20(c_e_h_3, c_c, s2)),
% 289.36/181.85 inference(unit_resolution,[status(thm)],[2697, 2674])).
% 289.36/181.85 tff(2699,plain,
% 289.36/181.85 (~m_and_h_gate_v_out(c_e_h_3, c_c, s3)),
% 289.36/181.85 inference(unit_resolution,[status(thm)],[2698, 2623])).
% 289.36/181.85 tff(2700,assumption,(m_or_h_gate_v_in1(c_e_h_3, c_g, s3)), introduced(assumption)).
% 289.36/181.85 tff(2701,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_c, s3)), introduced(assumption)).
% 289.36/181.85 tff(2702,plain,
% 289.36/181.85 (^[I0: $i, X: $i] : refl(((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X)) <=> ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X)))),
% 289.36/181.85 inference(bind,[status(th)],[])).
% 289.36/181.85 tff(2703,plain,
% 289.36/181.85 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X)) <=> ![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))),
% 289.36/181.85 inference(quant_intro,[status(thm)],[2702])).
% 289.36/181.85 tff(2704,plain,
% 289.36/181.85 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X)) <=> ![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))),
% 289.36/181.85 inference(rewrite,[status(thm)],[])).
% 289.36/181.86 tff(2705,axiom,(![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_28')).
% 289.36/181.86 tff(2706,plain,
% 289.36/181.86 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))),
% 289.36/181.86 inference(modus_ponens,[status(thm)],[2705, 2704])).
% 289.36/181.86 tff(2707,plain,(
% 289.36/181.86 ![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))),
% 289.36/181.86 inference(skolemize,[status(sab)],[2706])).
% 289.36/181.86 tff(2708,plain,
% 289.36/181.86 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))),
% 289.36/181.86 inference(modus_ponens,[status(thm)],[2707, 2703])).
% 289.36/181.86 tff(2709,plain,
% 289.36/181.86 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_g, s3)) | m_and_h_gate_v_out(c_e_h_3, c_c, s3))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s3)) | m_and_h_gate_v_out(c_e_h_3, c_c, s3))),
% 289.36/181.86 inference(rewrite,[status(thm)],[])).
% 289.36/181.86 tff(2710,plain,
% 289.36/181.86 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_g, s3)) | m_and_h_gate_v_out(c_e_h_3, c_c, s3))),
% 289.36/181.86 inference(quant_inst,[status(thm)],[])).
% 289.36/181.86 tff(2711,plain,
% 289.36/181.86 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s3)) | m_and_h_gate_v_out(c_e_h_3, c_c, s3)),
% 289.36/181.86 inference(modus_ponens,[status(thm)],[2710, 2709])).
% 289.36/181.86 tff(2712,plain,
% 289.36/181.86 ($false),
% 289.36/181.86 inference(unit_resolution,[status(thm)],[2711, 2708, 2701, 2700])).
% 289.36/181.86 tff(2713,plain,((~m_or_h_gate_v_in1(c_e_h_3, c_g, s3)) | m_and_h_gate_v_out(c_e_h_3, c_c, s3)), inference(lemma,lemma(discharge,[]))).
% 289.36/181.86 tff(2714,plain,
% 289.36/181.86 (~m_or_h_gate_v_in1(c_e_h_3, c_g, s3)),
% 289.36/181.86 inference(unit_resolution,[status(thm)],[2713, 2699])).
% 289.36/181.86 tff(2715,assumption,(node20(c_e_h_3, c_c, s3)), introduced(assumption)).
% 289.36/181.86 tff(2716,plain,
% 289.36/181.86 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_c, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_c, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s3))),
% 289.36/181.86 inference(rewrite,[status(thm)],[])).
% 289.36/181.86 tff(2717,plain,
% 289.36/181.86 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_c, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s3))),
% 289.36/181.86 inference(quant_inst,[status(thm)],[])).
% 289.36/181.86 tff(2718,plain,
% 289.36/181.86 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_c, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s3)),
% 289.36/181.86 inference(modus_ponens,[status(thm)],[2717, 2716])).
% 289.36/181.86 tff(2719,plain,
% 289.36/181.86 ($false),
% 289.36/181.86 inference(unit_resolution,[status(thm)],[2718, 38, 2715, 2546])).
% 289.36/181.86 tff(2720,plain,((~node20(c_e_h_3, c_c, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s3)), inference(lemma,lemma(discharge,[]))).
% 289.36/181.86 tff(2721,plain,
% 289.36/181.86 (~node20(c_e_h_3, c_c, s3)),
% 289.36/181.86 inference(unit_resolution,[status(thm)],[2720, 2546])).
% 289.36/181.86 tff(2722,assumption,(~node20(c_e_h_3, c_c, s3)), introduced(assumption)).
% 289.36/181.86 tff(2723,assumption,(m_and_h_gate_v_out(c_e_h_3, c_c, s4)), introduced(assumption)).
% 289.36/181.86 tff(2724,assumption,(node22(c_e_h_3, c_c, s3, s4)), introduced(assumption)).
% 289.36/181.86 tff(2725,plain,
% 289.36/181.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s4)) | (~node22(c_e_h_3, c_c, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_c, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s4)) | (~node22(c_e_h_3, c_c, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_c, s3))),
% 289.36/181.86 inference(rewrite,[status(thm)],[])).
% 289.36/181.86 tff(2726,plain,
% 289.36/181.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s4)) | (~node22(c_e_h_3, c_c, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_c, s3))),
% 289.36/181.86 inference(quant_inst,[status(thm)],[])).
% 289.36/181.86 tff(2727,plain,
% 289.36/181.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s4)) | (~node22(c_e_h_3, c_c, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_c, s3)),
% 289.36/181.86 inference(modus_ponens,[status(thm)],[2726, 2725])).
% 289.36/181.86 tff(2728,plain,
% 289.36/181.86 ($false),
% 289.36/181.86 inference(unit_resolution,[status(thm)],[2727, 108, 2724, 2723, 2701])).
% 289.36/181.86 tff(2729,plain,((~node22(c_e_h_3, c_c, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s4)) | m_and_h_gate_v_out(c_e_h_3, c_c, s3)), inference(lemma,lemma(discharge,[]))).
% 289.36/181.86 tff(2730,plain,
% 289.36/181.86 (~node22(c_e_h_3, c_c, s3, s4)),
% 289.36/181.86 inference(unit_resolution,[status(thm)],[2729, 2723, 2701])).
% 289.36/181.86 tff(2731,plain,
% 289.36/181.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_3, c_c, s3, s4) | node22(c_e_h_3, c_c, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_3, c_c, s3, s4) | node22(c_e_h_3, c_c, s3, s4))),
% 289.36/181.86 inference(rewrite,[status(thm)],[])).
% 289.36/181.86 tff(2732,plain,
% 289.36/181.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_3, c_c, s3, s4) | node22(c_e_h_3, c_c, s3, s4))),
% 289.36/181.86 inference(quant_inst,[status(thm)],[])).
% 289.36/181.86 tff(2733,plain,
% 289.36/181.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_3, c_c, s3, s4) | node22(c_e_h_3, c_c, s3, s4)),
% 289.36/181.86 inference(modus_ponens,[status(thm)],[2732, 2731])).
% 289.36/181.86 tff(2734,plain,
% 289.36/181.86 (node21(c_e_h_3, c_c, s3, s4) | node22(c_e_h_3, c_c, s3, s4)),
% 289.36/181.86 inference(unit_resolution,[status(thm)],[2733, 82, 531])).
% 289.36/181.86 tff(2735,plain,
% 289.36/181.86 (node21(c_e_h_3, c_c, s3, s4)),
% 289.36/181.86 inference(unit_resolution,[status(thm)],[2734, 2730])).
% 289.36/181.86 tff(2736,plain,
% 289.36/181.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_c, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s4)) | (~node21(c_e_h_3, c_c, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_c, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s4)) | (~node21(c_e_h_3, c_c, s3, s4)))),
% 289.36/181.86 inference(rewrite,[status(thm)],[])).
% 289.36/181.86 tff(2737,plain,
% 289.36/181.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_c, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s4)) | (~node21(c_e_h_3, c_c, s3, s4)))),
% 289.36/181.86 inference(quant_inst,[status(thm)],[])).
% 289.36/181.86 tff(2738,plain,
% 289.36/181.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_c, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s4)) | (~node21(c_e_h_3, c_c, s3, s4))),
% 289.36/181.86 inference(modus_ponens,[status(thm)],[2737, 2736])).
% 289.36/181.86 tff(2739,plain,
% 289.36/181.86 ($false),
% 289.36/181.86 inference(unit_resolution,[status(thm)],[2738, 52, 2735, 2723, 2722])).
% 289.36/181.86 tff(2740,plain,((~m_and_h_gate_v_out(c_e_h_3, c_c, s4)) | node20(c_e_h_3, c_c, s3) | m_and_h_gate_v_out(c_e_h_3, c_c, s3)), inference(lemma,lemma(discharge,[]))).
% 289.36/181.86 tff(2741,plain,
% 289.36/181.86 (~m_and_h_gate_v_out(c_e_h_3, c_c, s4)),
% 289.36/181.86 inference(unit_resolution,[status(thm)],[2740, 2699, 2721])).
% 289.36/181.86 tff(2742,assumption,(m_or_h_gate_v_in1(c_e_h_3, c_g, s4)), introduced(assumption)).
% 289.36/181.86 tff(2743,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_c, s4)), introduced(assumption)).
% 289.36/181.86 tff(2744,plain,
% 289.36/181.86 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_g, s4)) | m_and_h_gate_v_out(c_e_h_3, c_c, s4))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s4)) | m_and_h_gate_v_out(c_e_h_3, c_c, s4))),
% 289.36/181.86 inference(rewrite,[status(thm)],[])).
% 289.36/181.86 tff(2745,plain,
% 289.36/181.86 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_g, s4)) | m_and_h_gate_v_out(c_e_h_3, c_c, s4))),
% 289.36/181.86 inference(quant_inst,[status(thm)],[])).
% 289.36/181.86 tff(2746,plain,
% 289.36/181.86 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s4)) | m_and_h_gate_v_out(c_e_h_3, c_c, s4)),
% 289.36/181.86 inference(modus_ponens,[status(thm)],[2745, 2744])).
% 289.36/181.86 tff(2747,plain,
% 289.36/181.86 ($false),
% 289.36/181.86 inference(unit_resolution,[status(thm)],[2746, 2708, 2743, 2742])).
% 289.36/181.86 tff(2748,plain,((~m_or_h_gate_v_in1(c_e_h_3, c_g, s4)) | m_and_h_gate_v_out(c_e_h_3, c_c, s4)), inference(lemma,lemma(discharge,[]))).
% 289.36/181.86 tff(2749,plain,
% 289.36/181.86 (~m_or_h_gate_v_in1(c_e_h_3, c_g, s4)),
% 289.36/181.86 inference(unit_resolution,[status(thm)],[2748, 2741])).
% 289.36/181.86 tff(2750,assumption,(m_or_h_gate_v_out(c_e_h_3, c_g, s3)), introduced(assumption)).
% 289.36/181.86 tff(2751,assumption,(m_or_h_gate_v_out(c_e_h_3, c_g, s2)), introduced(assumption)).
% 289.36/181.86 tff(2752,assumption,(m_and_h_gate_v_out(c_e_h_3, c_d, s0)), introduced(assumption)).
% 289.36/181.86 tff(2753,plain,
% 289.36/181.86 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s0))),
% 289.36/181.86 inference(quant_inst,[status(thm)],[])).
% 289.36/181.86 tff(2754,plain,
% 289.36/181.86 ($false),
% 289.36/181.86 inference(unit_resolution,[status(thm)],[2753, 95, 2752])).
% 289.36/181.86 tff(2755,plain,(~m_and_h_gate_v_out(c_e_h_3, c_d, s0)), inference(lemma,lemma(discharge,[]))).
% 289.36/181.86 tff(2756,plain,
% 289.36/181.86 (^[I0: $i, X: $i] : refl(((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X)) <=> ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X)))),
% 289.36/181.86 inference(bind,[status(th)],[])).
% 289.36/181.86 tff(2757,plain,
% 289.36/181.86 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X)) <=> ![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))),
% 289.36/181.86 inference(quant_intro,[status(thm)],[2756])).
% 289.36/181.86 tff(2758,plain,
% 289.36/181.86 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X)) <=> ![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))),
% 289.36/181.86 inference(rewrite,[status(thm)],[])).
% 289.36/181.86 tff(2759,axiom,(![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_30')).
% 289.36/181.86 tff(2760,plain,
% 289.36/181.86 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))),
% 289.36/181.86 inference(modus_ponens,[status(thm)],[2759, 2758])).
% 289.36/181.86 tff(2761,plain,(
% 289.36/181.86 ![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))),
% 289.36/181.86 inference(skolemize,[status(sab)],[2760])).
% 289.36/181.86 tff(2762,plain,
% 289.36/181.86 (![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))),
% 289.36/181.86 inference(modus_ponens,[status(thm)],[2761, 2757])).
% 289.36/181.86 tff(2763,plain,
% 289.36/181.86 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_g, s0)) | m_and_h_gate_v_out(c_e_h_3, c_d, s0))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_g, s0)) | m_and_h_gate_v_out(c_e_h_3, c_d, s0))),
% 289.36/181.86 inference(rewrite,[status(thm)],[])).
% 289.36/181.86 tff(2764,plain,
% 289.36/181.86 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_g, s0)) | m_and_h_gate_v_out(c_e_h_3, c_d, s0))),
% 289.36/181.86 inference(quant_inst,[status(thm)],[])).
% 289.36/181.86 tff(2765,plain,
% 289.36/181.86 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_g, s0)) | m_and_h_gate_v_out(c_e_h_3, c_d, s0)),
% 289.36/181.86 inference(modus_ponens,[status(thm)],[2764, 2763])).
% 289.36/181.86 tff(2766,plain,
% 289.36/181.86 (~m_or_h_gate_v_in2(c_e_h_3, c_g, s0)),
% 289.36/181.86 inference(unit_resolution,[status(thm)],[2765, 2762, 2755])).
% 289.36/181.86 tff(2767,assumption,(m_or_h_gate_v_out(c_e_h_3, c_g, s1)), introduced(assumption)).
% 289.36/181.87 tff(2768,plain,
% 289.36/181.87 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_g, s0)) | m_and_h_gate_v_out(c_e_h_3, c_c, s0))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s0)) | m_and_h_gate_v_out(c_e_h_3, c_c, s0))),
% 289.36/181.87 inference(rewrite,[status(thm)],[])).
% 289.36/181.87 tff(2769,plain,
% 289.36/181.87 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_g, s0)) | m_and_h_gate_v_out(c_e_h_3, c_c, s0))),
% 289.36/181.87 inference(quant_inst,[status(thm)],[])).
% 289.36/181.87 tff(2770,plain,
% 289.36/181.87 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s0)) | m_and_h_gate_v_out(c_e_h_3, c_c, s0)),
% 289.36/181.87 inference(modus_ponens,[status(thm)],[2769, 2768])).
% 289.36/181.87 tff(2771,plain,
% 289.36/181.87 (~m_or_h_gate_v_in1(c_e_h_3, c_g, s0)),
% 289.36/181.87 inference(unit_resolution,[status(thm)],[2770, 2708, 124])).
% 289.36/181.87 tff(2772,assumption,(node6(c_e_h_3, c_g, s0, s1)), introduced(assumption)).
% 289.36/181.87 tff(2773,plain,
% 289.36/181.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s0) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s1)) | (~node6(c_e_h_3, c_g, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_g, s0) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s1)) | (~node6(c_e_h_3, c_g, s0, s1)))),
% 289.36/181.87 inference(rewrite,[status(thm)],[])).
% 289.36/181.87 tff(2774,plain,
% 289.36/181.87 (((~node6(c_e_h_3, c_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s1)) | m_or_h_gate_v_out(c_e_h_3, c_g, s0)) <=> (m_or_h_gate_v_out(c_e_h_3, c_g, s0) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s1)) | (~node6(c_e_h_3, c_g, s0, s1)))),
% 289.36/181.87 inference(rewrite,[status(thm)],[])).
% 289.36/181.87 tff(2775,plain,
% 289.36/181.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s1)) | m_or_h_gate_v_out(c_e_h_3, c_g, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s0) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s1)) | (~node6(c_e_h_3, c_g, s0, s1))))),
% 289.36/181.87 inference(monotonicity,[status(thm)],[2774])).
% 289.36/181.87 tff(2776,plain,
% 289.36/181.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s1)) | m_or_h_gate_v_out(c_e_h_3, c_g, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_g, s0) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s1)) | (~node6(c_e_h_3, c_g, s0, s1)))),
% 289.36/181.87 inference(transitivity,[status(thm)],[2775, 2773])).
% 289.36/181.87 tff(2777,plain,
% 289.36/181.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s1)) | m_or_h_gate_v_out(c_e_h_3, c_g, s0))),
% 289.36/181.87 inference(quant_inst,[status(thm)],[])).
% 289.36/181.87 tff(2778,plain,
% 289.36/181.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_g, s0) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s1)) | (~node6(c_e_h_3, c_g, s0, s1))),
% 289.36/181.87 inference(modus_ponens,[status(thm)],[2777, 2776])).
% 289.36/181.87 tff(2779,plain,
% 289.36/181.87 ($false),
% 289.36/181.87 inference(unit_resolution,[status(thm)],[2778, 1121, 804, 2772, 2767])).
% 289.36/181.87 tff(2780,plain,((~node6(c_e_h_3, c_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s1))), inference(lemma,lemma(discharge,[]))).
% 289.36/181.87 tff(2781,plain,
% 289.36/181.87 (~node6(c_e_h_3, c_g, s0, s1)),
% 289.36/181.87 inference(unit_resolution,[status(thm)],[2780, 2767])).
% 289.36/181.87 tff(2782,plain,
% 289.36/181.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s0, s1)) | node5(c_e_h_3, c_g, s0, s1) | node6(c_e_h_3, c_g, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s0, s1)) | node5(c_e_h_3, c_g, s0, s1) | node6(c_e_h_3, c_g, s0, s1))),
% 289.36/181.87 inference(rewrite,[status(thm)],[])).
% 289.36/181.87 tff(2783,plain,
% 289.36/181.87 ((node6(c_e_h_3, c_g, s0, s1) | node5(c_e_h_3, c_g, s0, s1) | (~trans(s0, s1))) <=> ((~trans(s0, s1)) | node5(c_e_h_3, c_g, s0, s1) | node6(c_e_h_3, c_g, s0, s1))),
% 289.36/181.87 inference(rewrite,[status(thm)],[])).
% 289.36/181.87 tff(2784,plain,
% 289.36/181.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s0, s1) | node5(c_e_h_3, c_g, s0, s1) | (~trans(s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s0, s1)) | node5(c_e_h_3, c_g, s0, s1) | node6(c_e_h_3, c_g, s0, s1)))),
% 289.36/181.87 inference(monotonicity,[status(thm)],[2783])).
% 289.36/181.87 tff(2785,plain,
% 289.36/181.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s0, s1) | node5(c_e_h_3, c_g, s0, s1) | (~trans(s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s0, s1)) | node5(c_e_h_3, c_g, s0, s1) | node6(c_e_h_3, c_g, s0, s1))),
% 289.36/181.87 inference(transitivity,[status(thm)],[2784, 2782])).
% 289.36/181.87 tff(2786,plain,
% 289.36/181.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s0, s1) | node5(c_e_h_3, c_g, s0, s1) | (~trans(s0, s1)))),
% 289.36/181.87 inference(quant_inst,[status(thm)],[])).
% 289.36/181.87 tff(2787,plain,
% 289.36/181.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s0, s1)) | node5(c_e_h_3, c_g, s0, s1) | node6(c_e_h_3, c_g, s0, s1)),
% 289.36/181.87 inference(modus_ponens,[status(thm)],[2786, 2785])).
% 289.36/181.87 tff(2788,plain,
% 289.36/181.87 (node5(c_e_h_3, c_g, s0, s1) | node6(c_e_h_3, c_g, s0, s1)),
% 289.36/181.87 inference(unit_resolution,[status(thm)],[2787, 1141, 72])).
% 289.36/181.87 tff(2789,plain,
% 289.36/181.87 (node5(c_e_h_3, c_g, s0, s1)),
% 289.36/181.87 inference(unit_resolution,[status(thm)],[2788, 2781])).
% 289.36/181.87 tff(2790,plain,
% 289.36/181.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~node5(c_e_h_3, c_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s1)) | m_or_h_gate_v_in2(c_e_h_3, c_g, s0) | m_or_h_gate_v_in1(c_e_h_3, c_g, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~node5(c_e_h_3, c_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s1)) | m_or_h_gate_v_in2(c_e_h_3, c_g, s0) | m_or_h_gate_v_in1(c_e_h_3, c_g, s0))),
% 289.36/181.87 inference(rewrite,[status(thm)],[])).
% 289.36/181.87 tff(2791,plain,
% 289.36/181.87 ((m_or_h_gate_v_in1(c_e_h_3, c_g, s0) | m_or_h_gate_v_in2(c_e_h_3, c_g, s0) | (~node5(c_e_h_3, c_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s1))) <=> ((~node5(c_e_h_3, c_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s1)) | m_or_h_gate_v_in2(c_e_h_3, c_g, s0) | m_or_h_gate_v_in1(c_e_h_3, c_g, s0))),
% 289.36/181.87 inference(rewrite,[status(thm)],[])).
% 289.36/181.87 tff(2792,plain,
% 289.36/181.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_g, s0) | m_or_h_gate_v_in2(c_e_h_3, c_g, s0) | (~node5(c_e_h_3, c_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~node5(c_e_h_3, c_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s1)) | m_or_h_gate_v_in2(c_e_h_3, c_g, s0) | m_or_h_gate_v_in1(c_e_h_3, c_g, s0)))),
% 289.36/181.87 inference(monotonicity,[status(thm)],[2791])).
% 289.36/181.87 tff(2793,plain,
% 289.36/181.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_g, s0) | m_or_h_gate_v_in2(c_e_h_3, c_g, s0) | (~node5(c_e_h_3, c_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~node5(c_e_h_3, c_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s1)) | m_or_h_gate_v_in2(c_e_h_3, c_g, s0) | m_or_h_gate_v_in1(c_e_h_3, c_g, s0))),
% 289.36/181.88 inference(transitivity,[status(thm)],[2792, 2790])).
% 289.36/181.88 tff(2794,plain,
% 289.36/181.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_g, s0) | m_or_h_gate_v_in2(c_e_h_3, c_g, s0) | (~node5(c_e_h_3, c_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s1)))),
% 289.36/181.88 inference(quant_inst,[status(thm)],[])).
% 289.36/181.88 tff(2795,plain,
% 289.36/181.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~node5(c_e_h_3, c_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s1)) | m_or_h_gate_v_in2(c_e_h_3, c_g, s0) | m_or_h_gate_v_in1(c_e_h_3, c_g, s0)),
% 289.36/181.88 inference(modus_ponens,[status(thm)],[2794, 2793])).
% 289.36/181.88 tff(2796,plain,
% 289.36/181.88 ($false),
% 289.36/181.88 inference(unit_resolution,[status(thm)],[2795, 1159, 2789, 2771, 2767, 2766])).
% 289.36/181.88 tff(2797,plain,(~m_or_h_gate_v_out(c_e_h_3, c_g, s1)), inference(lemma,lemma(discharge,[]))).
% 289.36/181.88 tff(2798,assumption,(m_mutex_h_half_v_out(c_e_h_3, c_b, s0)), introduced(assumption)).
% 289.36/181.88 tff(2799,plain,
% 289.36/181.88 ((~![I0: $i, I1: $i] : (~m_mutex_h_half_v_out(I0, I1, s0))) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s0))),
% 289.36/181.88 inference(quant_inst,[status(thm)],[])).
% 289.36/181.88 tff(2800,plain,
% 289.36/181.88 ($false),
% 289.36/181.88 inference(unit_resolution,[status(thm)],[2799, 409, 2798])).
% 289.36/181.88 tff(2801,plain,(~m_mutex_h_half_v_out(c_e_h_3, c_b, s0)), inference(lemma,lemma(discharge,[]))).
% 289.36/181.88 tff(2802,plain,
% 289.36/181.88 (^[I0: $i, X: $i] : refl(((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X)) <=> ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X)))),
% 289.36/181.88 inference(bind,[status(th)],[])).
% 289.36/181.88 tff(2803,plain,
% 289.36/181.88 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))),
% 289.36/181.88 inference(quant_intro,[status(thm)],[2802])).
% 289.36/181.88 tff(2804,plain,
% 289.36/181.88 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))),
% 289.36/181.88 inference(rewrite,[status(thm)],[])).
% 289.36/181.88 tff(2805,axiom,(![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_16')).
% 289.36/181.88 tff(2806,plain,
% 289.36/181.88 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))),
% 289.36/181.88 inference(modus_ponens,[status(thm)],[2805, 2804])).
% 289.36/181.88 tff(2807,plain,(
% 289.36/181.88 ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))),
% 289.36/181.88 inference(skolemize,[status(sab)],[2806])).
% 289.36/181.88 tff(2808,plain,
% 289.36/181.88 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))),
% 289.36/181.88 inference(modus_ponens,[status(thm)],[2807, 2803])).
% 289.36/181.88 tff(2809,plain,
% 289.36/181.88 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_d, s0)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s0))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_d, s0)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s0))),
% 289.36/181.88 inference(rewrite,[status(thm)],[])).
% 289.36/181.88 tff(2810,plain,
% 289.36/181.88 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_d, s0)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s0))),
% 289.36/181.88 inference(quant_inst,[status(thm)],[])).
% 289.36/181.88 tff(2811,plain,
% 289.36/181.88 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_d, s0)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s0)),
% 289.36/181.88 inference(modus_ponens,[status(thm)],[2810, 2809])).
% 289.36/181.88 tff(2812,plain,
% 289.36/181.88 (~m_and_h_gate_v_in1(c_e_h_3, c_d, s0)),
% 289.36/181.88 inference(unit_resolution,[status(thm)],[2811, 2808, 2801])).
% 289.36/181.88 tff(2813,plain,
% 289.36/181.88 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_d, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_d, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s0))),
% 289.36/181.88 inference(rewrite,[status(thm)],[])).
% 289.36/181.88 tff(2814,plain,
% 289.36/181.88 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_d, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s0))),
% 289.36/181.88 inference(quant_inst,[status(thm)],[])).
% 289.36/181.88 tff(2815,plain,
% 289.36/181.88 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_d, s0)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s0)),
% 289.36/181.88 inference(modus_ponens,[status(thm)],[2814, 2813])).
% 289.36/181.88 tff(2816,plain,
% 289.36/181.88 (~node20(c_e_h_3, c_d, s0)),
% 289.36/181.88 inference(unit_resolution,[status(thm)],[2815, 38, 2812])).
% 289.36/181.88 tff(2817,assumption,(m_and_h_gate_v_out(c_e_h_3, c_d, s1)), introduced(assumption)).
% 289.36/181.88 tff(2818,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_d, s0)), introduced(assumption)).
% 289.36/181.88 tff(2819,assumption,(node22(c_e_h_3, c_d, s0, s1)), introduced(assumption)).
% 289.36/181.88 tff(2820,plain,
% 289.36/181.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_d, s1)) | (~node22(c_e_h_3, c_d, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_d, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s1)) | (~node22(c_e_h_3, c_d, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_d, s0))),
% 289.36/181.88 inference(rewrite,[status(thm)],[])).
% 289.36/181.88 tff(2821,plain,
% 289.36/181.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_d, s1)) | (~node22(c_e_h_3, c_d, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_d, s0))),
% 289.36/181.88 inference(quant_inst,[status(thm)],[])).
% 289.36/181.88 tff(2822,plain,
% 289.36/181.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s1)) | (~node22(c_e_h_3, c_d, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_d, s0)),
% 289.36/181.88 inference(modus_ponens,[status(thm)],[2821, 2820])).
% 289.36/181.88 tff(2823,plain,
% 289.36/181.88 ($false),
% 289.36/181.88 inference(unit_resolution,[status(thm)],[2822, 108, 2819, 2818, 2817])).
% 289.36/181.88 tff(2824,plain,((~node22(c_e_h_3, c_d, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_d, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s1))), inference(lemma,lemma(discharge,[]))).
% 289.36/181.88 tff(2825,plain,
% 289.36/181.88 ((~node22(c_e_h_3, c_d, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s1))),
% 289.36/181.88 inference(unit_resolution,[status(thm)],[2824, 2755])).
% 289.36/181.88 tff(2826,plain,
% 289.36/181.88 (~node22(c_e_h_3, c_d, s0, s1)),
% 289.36/181.88 inference(unit_resolution,[status(thm)],[2825, 2817])).
% 289.36/181.88 tff(2827,plain,
% 289.36/181.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_3, c_d, s0, s1) | node22(c_e_h_3, c_d, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_3, c_d, s0, s1) | node22(c_e_h_3, c_d, s0, s1))),
% 289.36/181.88 inference(rewrite,[status(thm)],[])).
% 289.36/181.88 tff(2828,plain,
% 289.36/181.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_3, c_d, s0, s1) | node22(c_e_h_3, c_d, s0, s1))),
% 289.36/181.88 inference(quant_inst,[status(thm)],[])).
% 289.36/181.88 tff(2829,plain,
% 289.36/181.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_3, c_d, s0, s1) | node22(c_e_h_3, c_d, s0, s1)),
% 289.36/181.88 inference(modus_ponens,[status(thm)],[2828, 2827])).
% 289.36/181.88 tff(2830,plain,
% 289.36/181.88 (node21(c_e_h_3, c_d, s0, s1) | node22(c_e_h_3, c_d, s0, s1)),
% 289.36/181.88 inference(unit_resolution,[status(thm)],[2829, 82, 72])).
% 289.36/181.88 tff(2831,plain,
% 289.36/181.88 (node21(c_e_h_3, c_d, s0, s1)),
% 289.36/181.88 inference(unit_resolution,[status(thm)],[2830, 2826])).
% 289.36/181.88 tff(2832,plain,
% 289.36/181.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_d, s0) | (~node21(c_e_h_3, c_d, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_d, s0) | (~node21(c_e_h_3, c_d, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s1)))),
% 289.36/181.88 inference(rewrite,[status(thm)],[])).
% 289.36/181.88 tff(2833,plain,
% 289.36/181.88 ((node20(c_e_h_3, c_d, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s1)) | (~node21(c_e_h_3, c_d, s0, s1))) <=> (node20(c_e_h_3, c_d, s0) | (~node21(c_e_h_3, c_d, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s1)))),
% 289.36/181.88 inference(rewrite,[status(thm)],[])).
% 289.36/181.88 tff(2834,plain,
% 289.36/181.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_d, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s1)) | (~node21(c_e_h_3, c_d, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_d, s0) | (~node21(c_e_h_3, c_d, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s1))))),
% 289.36/181.88 inference(monotonicity,[status(thm)],[2833])).
% 289.36/181.88 tff(2835,plain,
% 289.36/181.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_d, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s1)) | (~node21(c_e_h_3, c_d, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_d, s0) | (~node21(c_e_h_3, c_d, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s1)))),
% 289.36/181.88 inference(transitivity,[status(thm)],[2834, 2832])).
% 289.36/181.88 tff(2836,plain,
% 289.36/181.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_d, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s1)) | (~node21(c_e_h_3, c_d, s0, s1)))),
% 289.36/181.88 inference(quant_inst,[status(thm)],[])).
% 289.36/181.88 tff(2837,plain,
% 289.36/181.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_d, s0) | (~node21(c_e_h_3, c_d, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s1))),
% 289.36/181.88 inference(modus_ponens,[status(thm)],[2836, 2835])).
% 289.36/181.88 tff(2838,plain,
% 289.36/181.88 ($false),
% 289.36/181.88 inference(unit_resolution,[status(thm)],[2837, 52, 2831, 2817, 2816])).
% 289.36/181.88 tff(2839,plain,(~m_and_h_gate_v_out(c_e_h_3, c_d, s1)), inference(lemma,lemma(discharge,[]))).
% 289.36/181.88 tff(2840,plain,
% 289.36/181.88 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_g, s1)) | m_and_h_gate_v_out(c_e_h_3, c_d, s1))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_g, s1)) | m_and_h_gate_v_out(c_e_h_3, c_d, s1))),
% 289.36/181.88 inference(rewrite,[status(thm)],[])).
% 289.36/181.88 tff(2841,plain,
% 289.36/181.88 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_g, s1)) | m_and_h_gate_v_out(c_e_h_3, c_d, s1))),
% 289.36/181.88 inference(quant_inst,[status(thm)],[])).
% 289.36/181.88 tff(2842,plain,
% 289.36/181.88 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_g, s1)) | m_and_h_gate_v_out(c_e_h_3, c_d, s1)),
% 289.36/181.88 inference(modus_ponens,[status(thm)],[2841, 2840])).
% 289.36/181.88 tff(2843,plain,
% 289.36/181.88 (~m_or_h_gate_v_in2(c_e_h_3, c_g, s1)),
% 289.36/181.89 inference(unit_resolution,[status(thm)],[2842, 2762, 2839])).
% 289.36/181.89 tff(2844,plain,
% 289.36/181.89 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_g, s1)) | m_and_h_gate_v_out(c_e_h_3, c_c, s1))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s1)) | m_and_h_gate_v_out(c_e_h_3, c_c, s1))),
% 289.36/181.89 inference(rewrite,[status(thm)],[])).
% 289.36/181.89 tff(2845,plain,
% 289.36/181.89 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_g, s1)) | m_and_h_gate_v_out(c_e_h_3, c_c, s1))),
% 289.36/181.89 inference(quant_inst,[status(thm)],[])).
% 289.36/181.89 tff(2846,plain,
% 289.36/181.89 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s1)) | m_and_h_gate_v_out(c_e_h_3, c_c, s1)),
% 289.36/181.89 inference(modus_ponens,[status(thm)],[2845, 2844])).
% 289.36/181.89 tff(2847,plain,
% 289.36/181.89 (~m_or_h_gate_v_in1(c_e_h_3, c_g, s1)),
% 289.36/181.89 inference(unit_resolution,[status(thm)],[2846, 2708, 593])).
% 289.36/181.89 tff(2848,assumption,(node5(c_e_h_3, c_g, s1, s2)), introduced(assumption)).
% 289.36/181.89 tff(2849,plain,
% 289.36/181.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_3, c_g, s2)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s1) | (~node5(c_e_h_3, c_g, s1, s2)) | m_or_h_gate_v_in2(c_e_h_3, c_g, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s2)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s1) | (~node5(c_e_h_3, c_g, s1, s2)) | m_or_h_gate_v_in2(c_e_h_3, c_g, s1))),
% 289.36/181.89 inference(rewrite,[status(thm)],[])).
% 289.36/181.89 tff(2850,plain,
% 289.36/181.89 ((m_or_h_gate_v_in1(c_e_h_3, c_g, s1) | m_or_h_gate_v_in2(c_e_h_3, c_g, s1) | (~node5(c_e_h_3, c_g, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s2))) <=> ((~m_or_h_gate_v_out(c_e_h_3, c_g, s2)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s1) | (~node5(c_e_h_3, c_g, s1, s2)) | m_or_h_gate_v_in2(c_e_h_3, c_g, s1))),
% 289.36/181.89 inference(rewrite,[status(thm)],[])).
% 289.36/181.89 tff(2851,plain,
% 289.36/181.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_g, s1) | m_or_h_gate_v_in2(c_e_h_3, c_g, s1) | (~node5(c_e_h_3, c_g, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_3, c_g, s2)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s1) | (~node5(c_e_h_3, c_g, s1, s2)) | m_or_h_gate_v_in2(c_e_h_3, c_g, s1)))),
% 289.36/181.89 inference(monotonicity,[status(thm)],[2850])).
% 289.36/181.89 tff(2852,plain,
% 289.36/181.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_g, s1) | m_or_h_gate_v_in2(c_e_h_3, c_g, s1) | (~node5(c_e_h_3, c_g, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s2)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s1) | (~node5(c_e_h_3, c_g, s1, s2)) | m_or_h_gate_v_in2(c_e_h_3, c_g, s1))),
% 289.36/181.89 inference(transitivity,[status(thm)],[2851, 2849])).
% 289.36/181.89 tff(2853,plain,
% 289.36/181.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_g, s1) | m_or_h_gate_v_in2(c_e_h_3, c_g, s1) | (~node5(c_e_h_3, c_g, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s2)))),
% 289.36/181.89 inference(quant_inst,[status(thm)],[])).
% 289.36/181.89 tff(2854,plain,
% 289.36/181.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s2)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s1) | (~node5(c_e_h_3, c_g, s1, s2)) | m_or_h_gate_v_in2(c_e_h_3, c_g, s1)),
% 289.36/181.89 inference(modus_ponens,[status(thm)],[2853, 2852])).
% 289.36/181.89 tff(2855,plain,
% 289.36/181.89 ($false),
% 289.36/181.89 inference(unit_resolution,[status(thm)],[2854, 1159, 2848, 2847, 2843, 2751])).
% 289.36/181.89 tff(2856,plain,((~node5(c_e_h_3, c_g, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s2))), inference(lemma,lemma(discharge,[]))).
% 289.36/181.89 tff(2857,plain,
% 289.36/181.89 (~node5(c_e_h_3, c_g, s1, s2)),
% 289.36/181.89 inference(unit_resolution,[status(thm)],[2856, 2751])).
% 289.36/181.89 tff(2858,plain,
% 289.36/181.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s1, s2)) | node5(c_e_h_3, c_g, s1, s2) | node6(c_e_h_3, c_g, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s1, s2)) | node5(c_e_h_3, c_g, s1, s2) | node6(c_e_h_3, c_g, s1, s2))),
% 289.36/181.89 inference(rewrite,[status(thm)],[])).
% 289.36/181.89 tff(2859,plain,
% 289.36/181.89 ((node6(c_e_h_3, c_g, s1, s2) | node5(c_e_h_3, c_g, s1, s2) | (~trans(s1, s2))) <=> ((~trans(s1, s2)) | node5(c_e_h_3, c_g, s1, s2) | node6(c_e_h_3, c_g, s1, s2))),
% 289.36/181.89 inference(rewrite,[status(thm)],[])).
% 289.36/181.89 tff(2860,plain,
% 289.36/181.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s1, s2) | node5(c_e_h_3, c_g, s1, s2) | (~trans(s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s1, s2)) | node5(c_e_h_3, c_g, s1, s2) | node6(c_e_h_3, c_g, s1, s2)))),
% 289.36/181.89 inference(monotonicity,[status(thm)],[2859])).
% 289.36/181.89 tff(2861,plain,
% 289.36/181.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s1, s2) | node5(c_e_h_3, c_g, s1, s2) | (~trans(s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s1, s2)) | node5(c_e_h_3, c_g, s1, s2) | node6(c_e_h_3, c_g, s1, s2))),
% 289.36/181.89 inference(transitivity,[status(thm)],[2860, 2858])).
% 289.36/181.89 tff(2862,plain,
% 289.36/181.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s1, s2) | node5(c_e_h_3, c_g, s1, s2) | (~trans(s1, s2)))),
% 289.36/181.89 inference(quant_inst,[status(thm)],[])).
% 289.36/181.89 tff(2863,plain,
% 289.36/181.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s1, s2)) | node5(c_e_h_3, c_g, s1, s2) | node6(c_e_h_3, c_g, s1, s2)),
% 289.36/181.89 inference(modus_ponens,[status(thm)],[2862, 2861])).
% 289.36/181.89 tff(2864,plain,
% 289.36/181.89 (node5(c_e_h_3, c_g, s1, s2) | node6(c_e_h_3, c_g, s1, s2)),
% 289.36/181.89 inference(unit_resolution,[status(thm)],[2863, 1141, 255])).
% 289.36/181.89 tff(2865,plain,
% 289.36/181.89 (node6(c_e_h_3, c_g, s1, s2)),
% 289.36/181.89 inference(unit_resolution,[status(thm)],[2864, 2857])).
% 289.36/181.89 tff(2866,plain,
% 289.36/181.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_3, c_g, s2)) | m_or_h_gate_v_out(c_e_h_3, c_g, s1) | (~node6(c_e_h_3, c_g, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s2)) | m_or_h_gate_v_out(c_e_h_3, c_g, s1) | (~node6(c_e_h_3, c_g, s1, s2)))),
% 289.36/181.89 inference(rewrite,[status(thm)],[])).
% 289.36/181.89 tff(2867,plain,
% 289.36/181.89 (((~node6(c_e_h_3, c_g, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s2)) | m_or_h_gate_v_out(c_e_h_3, c_g, s1)) <=> ((~m_or_h_gate_v_out(c_e_h_3, c_g, s2)) | m_or_h_gate_v_out(c_e_h_3, c_g, s1) | (~node6(c_e_h_3, c_g, s1, s2)))),
% 289.36/181.89 inference(rewrite,[status(thm)],[])).
% 289.36/181.89 tff(2868,plain,
% 289.36/181.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_g, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s2)) | m_or_h_gate_v_out(c_e_h_3, c_g, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_3, c_g, s2)) | m_or_h_gate_v_out(c_e_h_3, c_g, s1) | (~node6(c_e_h_3, c_g, s1, s2))))),
% 289.36/181.90 inference(monotonicity,[status(thm)],[2867])).
% 289.36/181.90 tff(2869,plain,
% 289.36/181.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_g, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s2)) | m_or_h_gate_v_out(c_e_h_3, c_g, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s2)) | m_or_h_gate_v_out(c_e_h_3, c_g, s1) | (~node6(c_e_h_3, c_g, s1, s2)))),
% 289.36/181.90 inference(transitivity,[status(thm)],[2868, 2866])).
% 289.36/181.90 tff(2870,plain,
% 289.36/181.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_g, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s2)) | m_or_h_gate_v_out(c_e_h_3, c_g, s1))),
% 289.36/181.90 inference(quant_inst,[status(thm)],[])).
% 289.36/181.90 tff(2871,plain,
% 289.36/181.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s2)) | m_or_h_gate_v_out(c_e_h_3, c_g, s1) | (~node6(c_e_h_3, c_g, s1, s2))),
% 289.36/181.90 inference(modus_ponens,[status(thm)],[2870, 2869])).
% 289.36/181.90 tff(2872,plain,
% 289.36/181.90 ($false),
% 289.36/181.90 inference(unit_resolution,[status(thm)],[2871, 1121, 2865, 2797, 2751])).
% 289.36/181.90 tff(2873,plain,(~m_or_h_gate_v_out(c_e_h_3, c_g, s2)), inference(lemma,lemma(discharge,[]))).
% 289.36/181.90 tff(2874,assumption,(node6(c_e_h_3, c_g, s2, s3)), introduced(assumption)).
% 289.36/181.90 tff(2875,plain,
% 289.36/181.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_3, c_g, s3)) | m_or_h_gate_v_out(c_e_h_3, c_g, s2) | (~node6(c_e_h_3, c_g, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s3)) | m_or_h_gate_v_out(c_e_h_3, c_g, s2) | (~node6(c_e_h_3, c_g, s2, s3)))),
% 289.36/181.90 inference(rewrite,[status(thm)],[])).
% 289.36/181.90 tff(2876,plain,
% 289.36/181.90 (((~node6(c_e_h_3, c_g, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s3)) | m_or_h_gate_v_out(c_e_h_3, c_g, s2)) <=> ((~m_or_h_gate_v_out(c_e_h_3, c_g, s3)) | m_or_h_gate_v_out(c_e_h_3, c_g, s2) | (~node6(c_e_h_3, c_g, s2, s3)))),
% 289.36/181.90 inference(rewrite,[status(thm)],[])).
% 289.36/181.90 tff(2877,plain,
% 289.36/181.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_g, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s3)) | m_or_h_gate_v_out(c_e_h_3, c_g, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_3, c_g, s3)) | m_or_h_gate_v_out(c_e_h_3, c_g, s2) | (~node6(c_e_h_3, c_g, s2, s3))))),
% 289.36/181.90 inference(monotonicity,[status(thm)],[2876])).
% 289.36/181.90 tff(2878,plain,
% 289.36/181.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_g, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s3)) | m_or_h_gate_v_out(c_e_h_3, c_g, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s3)) | m_or_h_gate_v_out(c_e_h_3, c_g, s2) | (~node6(c_e_h_3, c_g, s2, s3)))),
% 289.36/181.90 inference(transitivity,[status(thm)],[2877, 2875])).
% 289.36/181.90 tff(2879,plain,
% 289.36/181.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_g, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s3)) | m_or_h_gate_v_out(c_e_h_3, c_g, s2))),
% 289.36/181.90 inference(quant_inst,[status(thm)],[])).
% 289.36/181.90 tff(2880,plain,
% 289.36/181.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s3)) | m_or_h_gate_v_out(c_e_h_3, c_g, s2) | (~node6(c_e_h_3, c_g, s2, s3))),
% 289.36/181.90 inference(modus_ponens,[status(thm)],[2879, 2878])).
% 289.36/181.90 tff(2881,plain,
% 289.36/181.90 ($false),
% 289.36/181.90 inference(unit_resolution,[status(thm)],[2880, 1121, 2874, 2750, 2873])).
% 289.36/181.90 tff(2882,plain,((~node6(c_e_h_3, c_g, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s3))), inference(lemma,lemma(discharge,[]))).
% 289.36/181.90 tff(2883,plain,
% 289.36/181.90 (~node6(c_e_h_3, c_g, s2, s3)),
% 289.36/181.90 inference(unit_resolution,[status(thm)],[2882, 2750])).
% 289.36/181.90 tff(2884,assumption,(m_and_h_gate_v_out(c_e_h_3, c_d, s2)), introduced(assumption)).
% 289.36/181.90 tff(2885,assumption,(m_mutex_h_half_v_out(c_e_h_3, c_b, s1)), introduced(assumption)).
% 289.36/181.90 tff(2886,assumption,(node13(c_e_h_3, c_b, s0, s1)), introduced(assumption)).
% 289.36/181.90 tff(2887,plain,
% 289.36/181.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_b, s1)) | (~node13(c_e_h_3, c_b, s0, s1)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s1)) | (~node13(c_e_h_3, c_b, s0, s1)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s0))),
% 289.36/181.90 inference(rewrite,[status(thm)],[])).
% 289.36/181.90 tff(2888,plain,
% 289.36/181.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_b, s1)) | (~node13(c_e_h_3, c_b, s0, s1)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s0))),
% 289.36/181.90 inference(quant_inst,[status(thm)],[])).
% 289.36/181.90 tff(2889,plain,
% 289.36/181.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s1)) | (~node13(c_e_h_3, c_b, s0, s1)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s0)),
% 289.36/181.90 inference(modus_ponens,[status(thm)],[2888, 2887])).
% 289.36/181.90 tff(2890,plain,
% 289.36/181.90 ($false),
% 289.36/181.90 inference(unit_resolution,[status(thm)],[2889, 423, 2886, 2801, 2885])).
% 289.36/181.90 tff(2891,plain,((~node13(c_e_h_3, c_b, s0, s1)) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s1))), inference(lemma,lemma(discharge,[]))).
% 289.36/181.90 tff(2892,plain,
% 289.36/181.90 (~node13(c_e_h_3, c_b, s0, s1)),
% 289.36/181.90 inference(unit_resolution,[status(thm)],[2891, 2885])).
% 289.36/181.90 tff(2893,plain,
% 289.36/181.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s0, s1)) | node12(c_e_h_3, c_b, s0, s1) | node13(c_e_h_3, c_b, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s0, s1)) | node12(c_e_h_3, c_b, s0, s1) | node13(c_e_h_3, c_b, s0, s1))),
% 289.36/181.90 inference(rewrite,[status(thm)],[])).
% 289.36/181.90 tff(2894,plain,
% 289.36/181.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s0, s1)) | node12(c_e_h_3, c_b, s0, s1) | node13(c_e_h_3, c_b, s0, s1))),
% 289.36/181.90 inference(quant_inst,[status(thm)],[])).
% 289.36/181.90 tff(2895,plain,
% 289.36/181.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s0, s1)) | node12(c_e_h_3, c_b, s0, s1) | node13(c_e_h_3, c_b, s0, s1)),
% 289.36/181.90 inference(modus_ponens,[status(thm)],[2894, 2893])).
% 289.36/181.90 tff(2896,plain,
% 289.36/181.90 (node12(c_e_h_3, c_b, s0, s1) | node13(c_e_h_3, c_b, s0, s1)),
% 289.36/181.90 inference(unit_resolution,[status(thm)],[2895, 439, 72])).
% 289.36/181.90 tff(2897,plain,
% 289.36/181.90 (node12(c_e_h_3, c_b, s0, s1)),
% 289.36/181.90 inference(unit_resolution,[status(thm)],[2896, 2892])).
% 289.36/181.90 tff(2898,assumption,(m_and_h_gate_v_out(c_e_h_1, c_p, s0)), introduced(assumption)).
% 289.36/181.90 tff(2899,plain,
% 289.36/181.90 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s0))),
% 289.36/181.90 inference(quant_inst,[status(thm)],[])).
% 289.36/181.90 tff(2900,plain,
% 289.36/181.90 ($false),
% 289.36/181.90 inference(unit_resolution,[status(thm)],[2899, 95, 2898])).
% 289.36/181.90 tff(2901,plain,(~m_and_h_gate_v_out(c_e_h_1, c_p, s0)), inference(lemma,lemma(discharge,[]))).
% 289.36/181.90 tff(2902,plain,
% 289.36/181.90 (^[I0: $i, X: $i] : refl(((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X)) <=> ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X)))),
% 289.36/181.90 inference(bind,[status(th)],[])).
% 289.36/181.90 tff(2903,plain,
% 289.36/181.90 (![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X)) <=> ![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))),
% 289.36/181.90 inference(quant_intro,[status(thm)],[2902])).
% 289.36/181.90 tff(2904,plain,
% 289.36/181.90 (![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X)) <=> ![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))),
% 289.36/181.90 inference(rewrite,[status(thm)],[])).
% 289.36/181.90 tff(2905,axiom,(![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_76')).
% 289.36/181.90 tff(2906,plain,
% 289.36/181.90 (![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))),
% 289.36/181.90 inference(modus_ponens,[status(thm)],[2905, 2904])).
% 289.36/181.90 tff(2907,plain,(
% 289.36/181.90 ![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))),
% 289.36/181.90 inference(skolemize,[status(sab)],[2906])).
% 289.36/181.90 tff(2908,plain,
% 289.36/181.90 (![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))),
% 289.36/181.90 inference(modus_ponens,[status(thm)],[2907, 2903])).
% 289.36/181.90 tff(2909,plain,
% 289.36/181.90 (((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | ((~m_cell_v_req(c_e_h_1, s0)) | m_and_h_gate_v_out(c_e_h_1, c_p, s0))) <=> ((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | (~m_cell_v_req(c_e_h_1, s0)) | m_and_h_gate_v_out(c_e_h_1, c_p, s0))),
% 289.36/181.90 inference(rewrite,[status(thm)],[])).
% 289.36/181.90 tff(2910,plain,
% 289.36/181.90 ((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | ((~m_cell_v_req(c_e_h_1, s0)) | m_and_h_gate_v_out(c_e_h_1, c_p, s0))),
% 289.36/181.90 inference(quant_inst,[status(thm)],[])).
% 289.36/181.90 tff(2911,plain,
% 289.36/181.90 ((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | (~m_cell_v_req(c_e_h_1, s0)) | m_and_h_gate_v_out(c_e_h_1, c_p, s0)),
% 289.36/181.90 inference(modus_ponens,[status(thm)],[2910, 2909])).
% 289.36/181.90 tff(2912,plain,
% 289.36/181.90 (~m_cell_v_req(c_e_h_1, s0)),
% 289.36/181.90 inference(unit_resolution,[status(thm)],[2911, 2908, 2901])).
% 289.36/181.90 tff(2913,plain,
% 289.36/181.90 (^[I0: $i, X: $i, J0: $i] : refl(((~m_cell_v_left(I0, J0)) | node1(I0, J0, X)) <=> ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X)))),
% 289.36/181.90 inference(bind,[status(th)],[])).
% 289.36/181.90 tff(2914,plain,
% 289.36/181.90 (![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X)) <=> ![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))),
% 289.36/181.90 inference(quant_intro,[status(thm)],[2913])).
% 289.36/181.90 tff(2915,plain,
% 289.36/181.90 (![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X)) <=> ![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))),
% 289.36/181.90 inference(rewrite,[status(thm)],[])).
% 289.36/181.90 tff(2916,axiom,(![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_7')).
% 289.36/181.90 tff(2917,plain,
% 289.36/181.90 (![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))),
% 289.36/181.90 inference(modus_ponens,[status(thm)],[2916, 2915])).
% 289.36/181.90 tff(2918,plain,(
% 289.36/181.90 ![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))),
% 289.36/181.90 inference(skolemize,[status(sab)],[2917])).
% 289.36/181.90 tff(2919,plain,
% 289.36/181.90 (![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))),
% 289.36/181.90 inference(modus_ponens,[status(thm)],[2918, 2914])).
% 289.36/181.90 tff(2920,plain,
% 289.36/181.90 (m_cell_v_left(c_e_h_3, c_e_h_1) <=> m_cell_v_left(c_e_h_3, c_e_h_1)),
% 289.36/181.90 inference(rewrite,[status(thm)],[])).
% 289.36/181.90 tff(2921,axiom,(m_cell_v_left(c_e_h_3, c_e_h_1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_7')).
% 289.36/181.90 tff(2922,plain,
% 289.36/181.90 (m_cell_v_left(c_e_h_3, c_e_h_1)),
% 289.36/181.90 inference(modus_ponens,[status(thm)],[2921, 2920])).
% 289.36/181.90 tff(2923,plain,
% 289.36/181.90 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node1(c_e_h_3, c_e_h_1, s0))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node1(c_e_h_3, c_e_h_1, s0))),
% 289.45/181.91 inference(rewrite,[status(thm)],[])).
% 289.45/181.91 tff(2924,plain,
% 289.45/181.91 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node1(c_e_h_3, c_e_h_1, s0))),
% 289.45/181.91 inference(quant_inst,[status(thm)],[])).
% 289.45/181.91 tff(2925,plain,
% 289.45/181.91 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node1(c_e_h_3, c_e_h_1, s0)),
% 289.45/181.91 inference(modus_ponens,[status(thm)],[2924, 2923])).
% 289.45/181.91 tff(2926,plain,
% 289.45/181.91 (node1(c_e_h_3, c_e_h_1, s0)),
% 289.45/181.91 inference(unit_resolution,[status(thm)],[2925, 2922, 2919])).
% 289.45/181.91 tff(2927,plain,
% 289.45/181.91 (^[I0: $i, X: $i, J0: $i] : refl(((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X))) <=> ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X))))),
% 289.45/181.91 inference(bind,[status(th)],[])).
% 289.45/181.91 tff(2928,plain,
% 289.45/181.91 (![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X))) <=> ![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))),
% 289.45/181.91 inference(quant_intro,[status(thm)],[2927])).
% 289.45/181.91 tff(2929,plain,
% 289.45/181.91 (![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X))) <=> ![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))),
% 289.45/181.91 inference(rewrite,[status(thm)],[])).
% 289.45/181.91 tff(2930,plain,
% 289.45/181.91 (^[I0: $i, X: $i, J0: $i] : rewrite((((~m_mutex_h_half_v_inp(I0, c_b, X)) | m_cell_v_req(J0, X)) | (~node1(I0, J0, X))) <=> ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X))))),
% 289.45/181.91 inference(bind,[status(th)],[])).
% 289.45/181.91 tff(2931,plain,
% 289.45/181.91 (![I0: $i, X: $i, J0: $i] : (((~m_mutex_h_half_v_inp(I0, c_b, X)) | m_cell_v_req(J0, X)) | (~node1(I0, J0, X))) <=> ![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))),
% 289.45/181.91 inference(quant_intro,[status(thm)],[2930])).
% 289.45/181.91 tff(2932,axiom,(![I0: $i, X: $i, J0: $i] : (((~m_mutex_h_half_v_inp(I0, c_b, X)) | m_cell_v_req(J0, X)) | (~node1(I0, J0, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_6')).
% 289.45/181.91 tff(2933,plain,
% 289.45/181.91 (![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))),
% 289.45/181.91 inference(modus_ponens,[status(thm)],[2932, 2931])).
% 289.45/181.91 tff(2934,plain,
% 289.45/181.91 (![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))),
% 289.45/181.91 inference(modus_ponens,[status(thm)],[2933, 2929])).
% 289.45/181.91 tff(2935,plain,(
% 289.45/181.91 ![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))),
% 289.45/181.91 inference(skolemize,[status(sab)],[2934])).
% 289.45/181.91 tff(2936,plain,
% 289.45/181.91 (![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))),
% 289.45/181.91 inference(modus_ponens,[status(thm)],[2935, 2928])).
% 289.45/181.91 tff(2937,plain,
% 289.45/181.91 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_b, s0)) | (~node1(c_e_h_3, c_e_h_1, s0)) | m_cell_v_req(c_e_h_1, s0))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s0)) | (~node1(c_e_h_3, c_e_h_1, s0)) | m_cell_v_req(c_e_h_1, s0))),
% 289.45/181.91 inference(rewrite,[status(thm)],[])).
% 289.45/181.91 tff(2938,plain,
% 289.45/181.91 (((~node1(c_e_h_3, c_e_h_1, s0)) | m_cell_v_req(c_e_h_1, s0) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s0))) <=> ((~m_mutex_h_half_v_inp(c_e_h_3, c_b, s0)) | (~node1(c_e_h_3, c_e_h_1, s0)) | m_cell_v_req(c_e_h_1, s0))),
% 289.45/181.91 inference(rewrite,[status(thm)],[])).
% 289.45/181.91 tff(2939,plain,
% 289.45/181.91 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_3, c_e_h_1, s0)) | m_cell_v_req(c_e_h_1, s0) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s0)))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_b, s0)) | (~node1(c_e_h_3, c_e_h_1, s0)) | m_cell_v_req(c_e_h_1, s0)))),
% 289.45/181.91 inference(monotonicity,[status(thm)],[2938])).
% 289.45/181.91 tff(2940,plain,
% 289.45/181.91 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_3, c_e_h_1, s0)) | m_cell_v_req(c_e_h_1, s0) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s0)))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s0)) | (~node1(c_e_h_3, c_e_h_1, s0)) | m_cell_v_req(c_e_h_1, s0))),
% 289.45/181.91 inference(transitivity,[status(thm)],[2939, 2937])).
% 289.45/181.91 tff(2941,plain,
% 289.45/181.91 ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_3, c_e_h_1, s0)) | m_cell_v_req(c_e_h_1, s0) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s0)))),
% 289.45/181.91 inference(quant_inst,[status(thm)],[])).
% 289.45/181.91 tff(2942,plain,
% 289.45/181.91 ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s0)) | (~node1(c_e_h_3, c_e_h_1, s0)) | m_cell_v_req(c_e_h_1, s0)),
% 289.45/181.91 inference(modus_ponens,[status(thm)],[2941, 2940])).
% 289.45/181.91 tff(2943,plain,
% 289.45/181.91 ((~m_mutex_h_half_v_inp(c_e_h_3, c_b, s0)) | m_cell_v_req(c_e_h_1, s0)),
% 289.45/181.91 inference(unit_resolution,[status(thm)],[2942, 2936, 2926])).
% 289.45/181.91 tff(2944,plain,
% 289.45/181.91 (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s0)),
% 289.45/181.91 inference(unit_resolution,[status(thm)],[2943, 2912])).
% 289.45/181.91 tff(2945,plain,
% 289.45/181.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_3, c_b, s0) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s1)) | (~node12(c_e_h_3, c_b, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s0) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s1)) | (~node12(c_e_h_3, c_b, s0, s1)))),
% 289.45/181.91 inference(rewrite,[status(thm)],[])).
% 289.45/181.91 tff(2946,plain,
% 289.45/181.91 (((~node12(c_e_h_3, c_b, s0, s1)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s0) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s1))) <=> (m_mutex_h_half_v_inp(c_e_h_3, c_b, s0) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s1)) | (~node12(c_e_h_3, c_b, s0, s1)))),
% 289.45/181.91 inference(rewrite,[status(thm)],[])).
% 289.45/181.91 tff(2947,plain,
% 289.45/181.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_b, s0, s1)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s0) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_3, c_b, s0) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s1)) | (~node12(c_e_h_3, c_b, s0, s1))))),
% 289.45/181.91 inference(monotonicity,[status(thm)],[2946])).
% 289.45/181.91 tff(2948,plain,
% 289.45/181.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_b, s0, s1)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s0) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s0) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s1)) | (~node12(c_e_h_3, c_b, s0, s1)))),
% 289.45/181.91 inference(transitivity,[status(thm)],[2947, 2945])).
% 289.45/181.91 tff(2949,plain,
% 289.45/181.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_b, s0, s1)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s0) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s1)))),
% 289.45/181.91 inference(quant_inst,[status(thm)],[])).
% 289.45/181.91 tff(2950,plain,
% 289.45/181.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s0) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s1)) | (~node12(c_e_h_3, c_b, s0, s1))),
% 289.45/181.91 inference(modus_ponens,[status(thm)],[2949, 2948])).
% 289.45/181.91 tff(2951,plain,
% 289.45/181.91 ($false),
% 289.45/181.91 inference(unit_resolution,[status(thm)],[2950, 454, 2944, 2897, 2885])).
% 289.45/181.91 tff(2952,plain,(~m_mutex_h_half_v_out(c_e_h_3, c_b, s1)), inference(lemma,lemma(discharge,[]))).
% 289.45/181.91 tff(2953,plain,
% 289.45/181.91 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_d, s1)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s1))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_d, s1)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s1))),
% 289.45/181.91 inference(rewrite,[status(thm)],[])).
% 289.45/181.91 tff(2954,plain,
% 289.45/181.91 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_d, s1)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s1))),
% 289.45/181.91 inference(quant_inst,[status(thm)],[])).
% 289.45/181.91 tff(2955,plain,
% 289.45/181.91 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_d, s1)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s1)),
% 289.45/181.91 inference(modus_ponens,[status(thm)],[2954, 2953])).
% 289.45/181.91 tff(2956,plain,
% 289.45/181.91 (~m_and_h_gate_v_in1(c_e_h_3, c_d, s1)),
% 289.45/181.91 inference(unit_resolution,[status(thm)],[2955, 2808, 2952])).
% 289.45/181.91 tff(2957,plain,
% 289.45/181.91 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_d, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_d, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s1))),
% 289.45/181.91 inference(rewrite,[status(thm)],[])).
% 289.45/181.91 tff(2958,plain,
% 289.45/181.91 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_d, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s1))),
% 289.45/181.91 inference(quant_inst,[status(thm)],[])).
% 289.45/181.91 tff(2959,plain,
% 289.45/181.91 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_d, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s1)),
% 289.45/181.91 inference(modus_ponens,[status(thm)],[2958, 2957])).
% 289.45/181.91 tff(2960,plain,
% 289.45/181.91 (~node20(c_e_h_3, c_d, s1)),
% 289.45/181.91 inference(unit_resolution,[status(thm)],[2959, 38, 2956])).
% 289.45/181.91 tff(2961,assumption,(node21(c_e_h_3, c_d, s1, s2)), introduced(assumption)).
% 289.45/181.91 tff(2962,plain,
% 289.45/181.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_d, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s2)) | (~node21(c_e_h_3, c_d, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_d, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s2)) | (~node21(c_e_h_3, c_d, s1, s2)))),
% 289.45/181.91 inference(rewrite,[status(thm)],[])).
% 289.45/181.91 tff(2963,plain,
% 289.45/181.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_d, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s2)) | (~node21(c_e_h_3, c_d, s1, s2)))),
% 289.45/181.91 inference(quant_inst,[status(thm)],[])).
% 289.45/181.91 tff(2964,plain,
% 289.45/181.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_d, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s2)) | (~node21(c_e_h_3, c_d, s1, s2))),
% 289.45/181.91 inference(modus_ponens,[status(thm)],[2963, 2962])).
% 289.45/181.91 tff(2965,plain,
% 289.45/181.91 ($false),
% 289.45/181.91 inference(unit_resolution,[status(thm)],[2964, 52, 2961, 2960, 2884])).
% 289.45/181.91 tff(2966,plain,((~node21(c_e_h_3, c_d, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s2))), inference(lemma,lemma(discharge,[]))).
% 289.45/181.91 tff(2967,plain,
% 289.45/181.91 (~node21(c_e_h_3, c_d, s1, s2)),
% 289.45/181.91 inference(unit_resolution,[status(thm)],[2966, 2884])).
% 289.45/181.91 tff(2968,plain,
% 289.45/181.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_3, c_d, s1, s2) | node22(c_e_h_3, c_d, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_3, c_d, s1, s2) | node22(c_e_h_3, c_d, s1, s2))),
% 289.45/181.92 inference(rewrite,[status(thm)],[])).
% 289.45/181.92 tff(2969,plain,
% 289.45/181.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_3, c_d, s1, s2) | node22(c_e_h_3, c_d, s1, s2))),
% 289.45/181.92 inference(quant_inst,[status(thm)],[])).
% 289.45/181.92 tff(2970,plain,
% 289.45/181.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_3, c_d, s1, s2) | node22(c_e_h_3, c_d, s1, s2)),
% 289.45/181.92 inference(modus_ponens,[status(thm)],[2969, 2968])).
% 289.45/181.92 tff(2971,plain,
% 289.45/181.92 (node21(c_e_h_3, c_d, s1, s2) | node22(c_e_h_3, c_d, s1, s2)),
% 289.45/181.92 inference(unit_resolution,[status(thm)],[2970, 82, 255])).
% 289.45/181.92 tff(2972,plain,
% 289.45/181.92 (node22(c_e_h_3, c_d, s1, s2)),
% 289.45/181.92 inference(unit_resolution,[status(thm)],[2971, 2967])).
% 289.45/181.92 tff(2973,plain,
% 289.45/181.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_d, s2)) | (~node22(c_e_h_3, c_d, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_d, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s2)) | (~node22(c_e_h_3, c_d, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_d, s1))),
% 289.45/181.92 inference(rewrite,[status(thm)],[])).
% 289.45/181.92 tff(2974,plain,
% 289.45/181.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_d, s2)) | (~node22(c_e_h_3, c_d, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_d, s1))),
% 289.45/181.92 inference(quant_inst,[status(thm)],[])).
% 289.45/181.92 tff(2975,plain,
% 289.45/181.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s2)) | (~node22(c_e_h_3, c_d, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_d, s1)),
% 289.45/181.92 inference(modus_ponens,[status(thm)],[2974, 2973])).
% 289.45/181.92 tff(2976,plain,
% 289.45/181.92 ($false),
% 289.45/181.92 inference(unit_resolution,[status(thm)],[2975, 108, 2972, 2839, 2884])).
% 289.45/181.92 tff(2977,plain,(~m_and_h_gate_v_out(c_e_h_3, c_d, s2)), inference(lemma,lemma(discharge,[]))).
% 289.45/181.92 tff(2978,plain,
% 289.45/181.92 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_g, s2)) | m_and_h_gate_v_out(c_e_h_3, c_d, s2))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_g, s2)) | m_and_h_gate_v_out(c_e_h_3, c_d, s2))),
% 289.45/181.92 inference(rewrite,[status(thm)],[])).
% 289.45/181.92 tff(2979,plain,
% 289.45/181.92 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_g, s2)) | m_and_h_gate_v_out(c_e_h_3, c_d, s2))),
% 289.45/181.92 inference(quant_inst,[status(thm)],[])).
% 289.45/181.92 tff(2980,plain,
% 289.45/181.92 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_g, s2)) | m_and_h_gate_v_out(c_e_h_3, c_d, s2)),
% 289.45/181.92 inference(modus_ponens,[status(thm)],[2979, 2978])).
% 289.45/181.92 tff(2981,plain,
% 289.45/181.92 (~m_or_h_gate_v_in2(c_e_h_3, c_g, s2)),
% 289.45/181.92 inference(unit_resolution,[status(thm)],[2980, 2762, 2977])).
% 289.45/181.92 tff(2982,assumption,(~m_or_h_gate_v_in2(c_e_h_3, c_g, s2)), introduced(assumption)).
% 289.45/181.92 tff(2983,plain,
% 289.45/181.92 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_g, s2)) | m_and_h_gate_v_out(c_e_h_3, c_c, s2))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s2)) | m_and_h_gate_v_out(c_e_h_3, c_c, s2))),
% 289.45/181.92 inference(rewrite,[status(thm)],[])).
% 289.45/181.92 tff(2984,plain,
% 289.45/181.92 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_g, s2)) | m_and_h_gate_v_out(c_e_h_3, c_c, s2))),
% 289.45/181.92 inference(quant_inst,[status(thm)],[])).
% 289.45/181.92 tff(2985,plain,
% 289.45/181.92 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s2)) | m_and_h_gate_v_out(c_e_h_3, c_c, s2)),
% 289.45/181.92 inference(modus_ponens,[status(thm)],[2984, 2983])).
% 289.45/181.92 tff(2986,plain,
% 289.45/181.92 (~m_or_h_gate_v_in1(c_e_h_3, c_g, s2)),
% 289.45/181.92 inference(unit_resolution,[status(thm)],[2985, 2708, 2674])).
% 289.45/181.92 tff(2987,assumption,(node5(c_e_h_3, c_g, s2, s3)), introduced(assumption)).
% 289.45/181.92 tff(2988,plain,
% 289.45/181.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_3, c_g, s3)) | (~node5(c_e_h_3, c_g, s2, s3)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s2) | m_or_h_gate_v_in2(c_e_h_3, c_g, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s3)) | (~node5(c_e_h_3, c_g, s2, s3)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s2) | m_or_h_gate_v_in2(c_e_h_3, c_g, s2))),
% 289.45/181.92 inference(rewrite,[status(thm)],[])).
% 289.45/181.92 tff(2989,plain,
% 289.45/181.92 ((m_or_h_gate_v_in1(c_e_h_3, c_g, s2) | m_or_h_gate_v_in2(c_e_h_3, c_g, s2) | (~node5(c_e_h_3, c_g, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s3))) <=> ((~m_or_h_gate_v_out(c_e_h_3, c_g, s3)) | (~node5(c_e_h_3, c_g, s2, s3)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s2) | m_or_h_gate_v_in2(c_e_h_3, c_g, s2))),
% 289.45/181.92 inference(rewrite,[status(thm)],[])).
% 289.45/181.92 tff(2990,plain,
% 289.45/181.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_g, s2) | m_or_h_gate_v_in2(c_e_h_3, c_g, s2) | (~node5(c_e_h_3, c_g, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_3, c_g, s3)) | (~node5(c_e_h_3, c_g, s2, s3)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s2) | m_or_h_gate_v_in2(c_e_h_3, c_g, s2)))),
% 289.45/181.92 inference(monotonicity,[status(thm)],[2989])).
% 289.45/181.92 tff(2991,plain,
% 289.45/181.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_g, s2) | m_or_h_gate_v_in2(c_e_h_3, c_g, s2) | (~node5(c_e_h_3, c_g, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s3)) | (~node5(c_e_h_3, c_g, s2, s3)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s2) | m_or_h_gate_v_in2(c_e_h_3, c_g, s2))),
% 289.45/181.92 inference(transitivity,[status(thm)],[2990, 2988])).
% 289.45/181.92 tff(2992,plain,
% 289.45/181.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_g, s2) | m_or_h_gate_v_in2(c_e_h_3, c_g, s2) | (~node5(c_e_h_3, c_g, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s3)))),
% 289.45/181.92 inference(quant_inst,[status(thm)],[])).
% 289.45/181.92 tff(2993,plain,
% 289.45/181.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s3)) | (~node5(c_e_h_3, c_g, s2, s3)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s2) | m_or_h_gate_v_in2(c_e_h_3, c_g, s2)),
% 289.45/181.92 inference(modus_ponens,[status(thm)],[2992, 2991])).
% 289.45/181.92 tff(2994,plain,
% 289.45/181.92 ($false),
% 289.45/181.92 inference(unit_resolution,[status(thm)],[2993, 1159, 2987, 2750, 2986, 2982])).
% 289.45/181.92 tff(2995,plain,((~node5(c_e_h_3, c_g, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s3)) | m_or_h_gate_v_in2(c_e_h_3, c_g, s2)), inference(lemma,lemma(discharge,[]))).
% 289.45/181.92 tff(2996,plain,
% 289.45/181.92 ((~node5(c_e_h_3, c_g, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s3))),
% 289.45/181.92 inference(unit_resolution,[status(thm)],[2995, 2981])).
% 289.45/181.92 tff(2997,plain,
% 289.45/181.92 (~node5(c_e_h_3, c_g, s2, s3)),
% 289.45/181.92 inference(unit_resolution,[status(thm)],[2996, 2750])).
% 289.45/181.92 tff(2998,plain,
% 289.45/181.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s2, s3)) | node5(c_e_h_3, c_g, s2, s3) | node6(c_e_h_3, c_g, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s2, s3)) | node5(c_e_h_3, c_g, s2, s3) | node6(c_e_h_3, c_g, s2, s3))),
% 289.45/181.92 inference(rewrite,[status(thm)],[])).
% 289.45/181.92 tff(2999,plain,
% 289.45/181.92 ((node6(c_e_h_3, c_g, s2, s3) | node5(c_e_h_3, c_g, s2, s3) | (~trans(s2, s3))) <=> ((~trans(s2, s3)) | node5(c_e_h_3, c_g, s2, s3) | node6(c_e_h_3, c_g, s2, s3))),
% 289.45/181.92 inference(rewrite,[status(thm)],[])).
% 289.45/181.92 tff(3000,plain,
% 289.45/181.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s2, s3) | node5(c_e_h_3, c_g, s2, s3) | (~trans(s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s2, s3)) | node5(c_e_h_3, c_g, s2, s3) | node6(c_e_h_3, c_g, s2, s3)))),
% 289.45/181.92 inference(monotonicity,[status(thm)],[2999])).
% 289.45/181.92 tff(3001,plain,
% 289.45/181.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s2, s3) | node5(c_e_h_3, c_g, s2, s3) | (~trans(s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s2, s3)) | node5(c_e_h_3, c_g, s2, s3) | node6(c_e_h_3, c_g, s2, s3))),
% 289.45/181.92 inference(transitivity,[status(thm)],[3000, 2998])).
% 289.45/181.92 tff(3002,plain,
% 289.45/181.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s2, s3) | node5(c_e_h_3, c_g, s2, s3) | (~trans(s2, s3)))),
% 289.45/181.92 inference(quant_inst,[status(thm)],[])).
% 289.45/181.92 tff(3003,plain,
% 289.45/181.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s2, s3)) | node5(c_e_h_3, c_g, s2, s3) | node6(c_e_h_3, c_g, s2, s3)),
% 289.45/181.92 inference(modus_ponens,[status(thm)],[3002, 3001])).
% 289.45/181.92 tff(3004,plain,
% 289.45/181.92 (node5(c_e_h_3, c_g, s2, s3) | node6(c_e_h_3, c_g, s2, s3)),
% 289.45/181.92 inference(unit_resolution,[status(thm)],[3003, 1141, 318])).
% 289.45/181.92 tff(3005,plain,
% 289.45/181.92 ($false),
% 289.45/181.92 inference(unit_resolution,[status(thm)],[3004, 2997, 2883])).
% 289.45/181.92 tff(3006,plain,(~m_or_h_gate_v_out(c_e_h_3, c_g, s3)), inference(lemma,lemma(discharge,[]))).
% 289.45/181.92 tff(3007,assumption,(m_and_h_gate_v_out(c_e_h_3, c_d, s3)), introduced(assumption)).
% 289.45/181.92 tff(3008,assumption,(m_mutex_h_half_v_out(c_e_h_3, c_b, s2)), introduced(assumption)).
% 289.45/181.92 tff(3009,assumption,(~m_mutex_h_half_v_out(c_e_h_3, c_b, s1)), introduced(assumption)).
% 289.45/181.92 tff(3010,assumption,(node13(c_e_h_3, c_b, s1, s2)), introduced(assumption)).
% 289.45/181.92 tff(3011,plain,
% 289.45/181.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_b, s2)) | (~node13(c_e_h_3, c_b, s1, s2)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s2)) | (~node13(c_e_h_3, c_b, s1, s2)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s1))),
% 289.45/181.92 inference(rewrite,[status(thm)],[])).
% 289.45/181.92 tff(3012,plain,
% 289.45/181.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_b, s2)) | (~node13(c_e_h_3, c_b, s1, s2)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s1))),
% 289.45/181.92 inference(quant_inst,[status(thm)],[])).
% 289.45/181.92 tff(3013,plain,
% 289.45/181.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s2)) | (~node13(c_e_h_3, c_b, s1, s2)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s1)),
% 289.45/181.93 inference(modus_ponens,[status(thm)],[3012, 3011])).
% 289.45/181.93 tff(3014,plain,
% 289.45/181.93 ($false),
% 289.45/181.93 inference(unit_resolution,[status(thm)],[3013, 423, 3010, 3009, 3008])).
% 289.45/181.93 tff(3015,plain,((~node13(c_e_h_3, c_b, s1, s2)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s1) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s2))), inference(lemma,lemma(discharge,[]))).
% 289.45/181.93 tff(3016,plain,
% 289.45/181.93 ((~node13(c_e_h_3, c_b, s1, s2)) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s2))),
% 289.45/181.93 inference(unit_resolution,[status(thm)],[3015, 2952])).
% 289.45/181.93 tff(3017,plain,
% 289.45/181.93 (~node13(c_e_h_3, c_b, s1, s2)),
% 289.45/181.93 inference(unit_resolution,[status(thm)],[3016, 3008])).
% 289.45/181.93 tff(3018,plain,
% 289.45/181.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s1, s2)) | node12(c_e_h_3, c_b, s1, s2) | node13(c_e_h_3, c_b, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s1, s2)) | node12(c_e_h_3, c_b, s1, s2) | node13(c_e_h_3, c_b, s1, s2))),
% 289.45/181.93 inference(rewrite,[status(thm)],[])).
% 289.45/181.93 tff(3019,plain,
% 289.45/181.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s1, s2)) | node12(c_e_h_3, c_b, s1, s2) | node13(c_e_h_3, c_b, s1, s2))),
% 289.45/181.93 inference(quant_inst,[status(thm)],[])).
% 289.45/181.93 tff(3020,plain,
% 289.45/181.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s1, s2)) | node12(c_e_h_3, c_b, s1, s2) | node13(c_e_h_3, c_b, s1, s2)),
% 289.45/181.93 inference(modus_ponens,[status(thm)],[3019, 3018])).
% 289.45/181.93 tff(3021,plain,
% 289.45/181.93 (node12(c_e_h_3, c_b, s1, s2) | node13(c_e_h_3, c_b, s1, s2)),
% 289.45/181.93 inference(unit_resolution,[status(thm)],[3020, 439, 255])).
% 289.45/181.93 tff(3022,plain,
% 289.45/181.93 (node12(c_e_h_3, c_b, s1, s2)),
% 289.45/181.93 inference(unit_resolution,[status(thm)],[3021, 3017])).
% 289.45/181.93 tff(3023,assumption,(m_and_h_gate_v_out(c_e_h_1, c_k, s0)), introduced(assumption)).
% 289.45/181.93 tff(3024,plain,
% 289.45/181.93 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s0))),
% 289.45/181.93 inference(quant_inst,[status(thm)],[])).
% 289.45/181.93 tff(3025,plain,
% 289.45/181.93 ($false),
% 289.45/181.93 inference(unit_resolution,[status(thm)],[3024, 95, 3023])).
% 289.45/181.93 tff(3026,plain,(~m_and_h_gate_v_out(c_e_h_1, c_k, s0)), inference(lemma,lemma(discharge,[]))).
% 289.45/181.93 tff(3027,plain,
% 289.45/181.93 (^[I0: $i, X: $i] : refl(((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X)) <=> ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X)))),
% 289.45/181.93 inference(bind,[status(th)],[])).
% 289.45/181.93 tff(3028,plain,
% 289.45/181.93 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))),
% 289.45/181.93 inference(quant_intro,[status(thm)],[3027])).
% 289.45/181.93 tff(3029,plain,
% 289.45/181.93 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))),
% 289.45/181.93 inference(rewrite,[status(thm)],[])).
% 289.45/181.93 tff(3030,axiom,(![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_64')).
% 289.45/181.93 tff(3031,plain,
% 289.45/181.93 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))),
% 289.45/181.93 inference(modus_ponens,[status(thm)],[3030, 3029])).
% 289.45/181.93 tff(3032,plain,(
% 289.45/181.93 ![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))),
% 289.45/181.93 inference(skolemize,[status(sab)],[3031])).
% 289.45/181.93 tff(3033,plain,
% 289.45/181.93 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))),
% 289.45/181.93 inference(modus_ponens,[status(thm)],[3032, 3028])).
% 289.45/181.93 tff(3034,plain,
% 289.45/181.93 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_p, s0)) | m_and_h_gate_v_out(c_e_h_1, c_k, s0))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s0)) | m_and_h_gate_v_out(c_e_h_1, c_k, s0))),
% 289.45/181.93 inference(rewrite,[status(thm)],[])).
% 289.45/181.93 tff(3035,plain,
% 289.45/181.93 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_p, s0)) | m_and_h_gate_v_out(c_e_h_1, c_k, s0))),
% 289.45/181.93 inference(quant_inst,[status(thm)],[])).
% 289.45/181.93 tff(3036,plain,
% 289.45/181.93 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s0)) | m_and_h_gate_v_out(c_e_h_1, c_k, s0)),
% 289.45/181.93 inference(modus_ponens,[status(thm)],[3035, 3034])).
% 289.45/181.93 tff(3037,plain,
% 289.45/181.93 (~m_and_h_gate_v_in1(c_e_h_1, c_p, s0)),
% 289.45/181.93 inference(unit_resolution,[status(thm)],[3036, 3033, 3026])).
% 289.45/181.93 tff(3038,plain,
% 289.45/181.93 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_p, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_p, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s0))),
% 289.45/181.93 inference(rewrite,[status(thm)],[])).
% 289.45/181.93 tff(3039,plain,
% 289.45/181.93 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_p, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s0))),
% 289.45/181.93 inference(quant_inst,[status(thm)],[])).
% 289.45/181.93 tff(3040,plain,
% 289.45/181.93 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_p, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s0)),
% 289.45/181.93 inference(modus_ponens,[status(thm)],[3039, 3038])).
% 289.45/181.93 tff(3041,plain,
% 289.45/181.93 (~node20(c_e_h_1, c_p, s0)),
% 289.45/181.93 inference(unit_resolution,[status(thm)],[3040, 38, 3037])).
% 289.45/181.93 tff(3042,assumption,(m_and_h_gate_v_out(c_e_h_1, c_p, s1)), introduced(assumption)).
% 289.45/181.93 tff(3043,assumption,(node22(c_e_h_1, c_p, s0, s1)), introduced(assumption)).
% 289.45/181.93 tff(3044,plain,
% 289.45/181.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_p, s1)) | (~node22(c_e_h_1, c_p, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_p, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s1)) | (~node22(c_e_h_1, c_p, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_p, s0))),
% 289.45/181.93 inference(rewrite,[status(thm)],[])).
% 289.45/181.93 tff(3045,plain,
% 289.45/181.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_p, s1)) | (~node22(c_e_h_1, c_p, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_p, s0))),
% 289.45/181.93 inference(quant_inst,[status(thm)],[])).
% 289.45/181.93 tff(3046,plain,
% 289.45/181.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s1)) | (~node22(c_e_h_1, c_p, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_p, s0)),
% 289.45/181.93 inference(modus_ponens,[status(thm)],[3045, 3044])).
% 289.45/181.93 tff(3047,plain,
% 289.45/181.93 ($false),
% 289.45/181.93 inference(unit_resolution,[status(thm)],[3046, 108, 3043, 2901, 3042])).
% 289.45/181.93 tff(3048,plain,((~node22(c_e_h_1, c_p, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s1))), inference(lemma,lemma(discharge,[]))).
% 289.45/181.93 tff(3049,plain,
% 289.45/181.93 (~node22(c_e_h_1, c_p, s0, s1)),
% 289.45/181.93 inference(unit_resolution,[status(thm)],[3048, 3042])).
% 289.45/181.93 tff(3050,plain,
% 289.45/181.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_1, c_p, s0, s1) | node22(c_e_h_1, c_p, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_1, c_p, s0, s1) | node22(c_e_h_1, c_p, s0, s1))),
% 289.45/181.93 inference(rewrite,[status(thm)],[])).
% 289.45/181.93 tff(3051,plain,
% 289.45/181.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_1, c_p, s0, s1) | node22(c_e_h_1, c_p, s0, s1))),
% 289.45/181.93 inference(quant_inst,[status(thm)],[])).
% 289.45/181.94 tff(3052,plain,
% 289.45/181.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_1, c_p, s0, s1) | node22(c_e_h_1, c_p, s0, s1)),
% 289.45/181.94 inference(modus_ponens,[status(thm)],[3051, 3050])).
% 289.45/181.94 tff(3053,plain,
% 289.45/181.94 (node21(c_e_h_1, c_p, s0, s1) | node22(c_e_h_1, c_p, s0, s1)),
% 289.45/181.94 inference(unit_resolution,[status(thm)],[3052, 82, 72])).
% 289.45/181.94 tff(3054,plain,
% 289.45/181.94 (node21(c_e_h_1, c_p, s0, s1)),
% 289.45/181.94 inference(unit_resolution,[status(thm)],[3053, 3049])).
% 289.45/181.94 tff(3055,plain,
% 289.45/181.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_p, s1)) | node20(c_e_h_1, c_p, s0) | (~node21(c_e_h_1, c_p, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s1)) | node20(c_e_h_1, c_p, s0) | (~node21(c_e_h_1, c_p, s0, s1)))),
% 289.45/181.94 inference(rewrite,[status(thm)],[])).
% 289.45/181.94 tff(3056,plain,
% 289.45/181.94 ((node20(c_e_h_1, c_p, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s1)) | (~node21(c_e_h_1, c_p, s0, s1))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_p, s1)) | node20(c_e_h_1, c_p, s0) | (~node21(c_e_h_1, c_p, s0, s1)))),
% 289.45/181.94 inference(rewrite,[status(thm)],[])).
% 289.45/181.94 tff(3057,plain,
% 289.45/181.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_p, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s1)) | (~node21(c_e_h_1, c_p, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_p, s1)) | node20(c_e_h_1, c_p, s0) | (~node21(c_e_h_1, c_p, s0, s1))))),
% 289.45/181.94 inference(monotonicity,[status(thm)],[3056])).
% 289.45/181.94 tff(3058,plain,
% 289.45/181.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_p, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s1)) | (~node21(c_e_h_1, c_p, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s1)) | node20(c_e_h_1, c_p, s0) | (~node21(c_e_h_1, c_p, s0, s1)))),
% 289.45/181.94 inference(transitivity,[status(thm)],[3057, 3055])).
% 289.45/181.94 tff(3059,plain,
% 289.45/181.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_p, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s1)) | (~node21(c_e_h_1, c_p, s0, s1)))),
% 289.45/181.94 inference(quant_inst,[status(thm)],[])).
% 289.45/181.94 tff(3060,plain,
% 289.45/181.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s1)) | node20(c_e_h_1, c_p, s0) | (~node21(c_e_h_1, c_p, s0, s1))),
% 289.45/181.94 inference(modus_ponens,[status(thm)],[3059, 3058])).
% 289.45/181.94 tff(3061,plain,
% 289.45/181.94 ($false),
% 289.45/181.94 inference(unit_resolution,[status(thm)],[3060, 52, 3054, 3042, 3041])).
% 289.45/181.94 tff(3062,plain,(~m_and_h_gate_v_out(c_e_h_1, c_p, s1)), inference(lemma,lemma(discharge,[]))).
% 289.45/181.94 tff(3063,plain,
% 289.45/181.94 (((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | ((~m_cell_v_req(c_e_h_1, s1)) | m_and_h_gate_v_out(c_e_h_1, c_p, s1))) <=> ((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | (~m_cell_v_req(c_e_h_1, s1)) | m_and_h_gate_v_out(c_e_h_1, c_p, s1))),
% 289.45/181.94 inference(rewrite,[status(thm)],[])).
% 289.45/181.94 tff(3064,plain,
% 289.45/181.94 ((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | ((~m_cell_v_req(c_e_h_1, s1)) | m_and_h_gate_v_out(c_e_h_1, c_p, s1))),
% 289.45/181.94 inference(quant_inst,[status(thm)],[])).
% 289.45/181.94 tff(3065,plain,
% 289.45/181.94 ((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | (~m_cell_v_req(c_e_h_1, s1)) | m_and_h_gate_v_out(c_e_h_1, c_p, s1)),
% 289.45/181.94 inference(modus_ponens,[status(thm)],[3064, 3063])).
% 289.45/181.94 tff(3066,plain,
% 289.45/181.94 (~m_cell_v_req(c_e_h_1, s1)),
% 289.45/181.94 inference(unit_resolution,[status(thm)],[3065, 2908, 3062])).
% 289.45/181.94 tff(3067,plain,
% 289.45/181.94 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node1(c_e_h_3, c_e_h_1, s1))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node1(c_e_h_3, c_e_h_1, s1))),
% 289.45/181.94 inference(rewrite,[status(thm)],[])).
% 289.45/181.94 tff(3068,plain,
% 289.45/181.94 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node1(c_e_h_3, c_e_h_1, s1))),
% 289.45/181.94 inference(quant_inst,[status(thm)],[])).
% 289.45/181.94 tff(3069,plain,
% 289.45/181.94 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node1(c_e_h_3, c_e_h_1, s1)),
% 289.45/181.94 inference(modus_ponens,[status(thm)],[3068, 3067])).
% 289.45/181.94 tff(3070,plain,
% 289.45/181.94 (node1(c_e_h_3, c_e_h_1, s1)),
% 289.45/181.94 inference(unit_resolution,[status(thm)],[3069, 2922, 2919])).
% 289.45/181.94 tff(3071,plain,
% 289.45/181.94 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | (m_cell_v_req(c_e_h_1, s1) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s1)) | (~node1(c_e_h_3, c_e_h_1, s1)))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | m_cell_v_req(c_e_h_1, s1) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s1)) | (~node1(c_e_h_3, c_e_h_1, s1)))),
% 289.45/181.94 inference(rewrite,[status(thm)],[])).
% 289.45/181.94 tff(3072,plain,
% 289.45/181.94 (((~node1(c_e_h_3, c_e_h_1, s1)) | m_cell_v_req(c_e_h_1, s1) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s1))) <=> (m_cell_v_req(c_e_h_1, s1) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s1)) | (~node1(c_e_h_3, c_e_h_1, s1)))),
% 289.45/181.94 inference(rewrite,[status(thm)],[])).
% 289.45/181.94 tff(3073,plain,
% 289.45/181.94 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_3, c_e_h_1, s1)) | m_cell_v_req(c_e_h_1, s1) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s1)))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | (m_cell_v_req(c_e_h_1, s1) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s1)) | (~node1(c_e_h_3, c_e_h_1, s1))))),
% 289.45/181.94 inference(monotonicity,[status(thm)],[3072])).
% 289.45/181.94 tff(3074,plain,
% 289.45/181.94 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_3, c_e_h_1, s1)) | m_cell_v_req(c_e_h_1, s1) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s1)))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | m_cell_v_req(c_e_h_1, s1) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s1)) | (~node1(c_e_h_3, c_e_h_1, s1)))),
% 289.45/181.94 inference(transitivity,[status(thm)],[3073, 3071])).
% 289.45/181.94 tff(3075,plain,
% 289.45/181.94 ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_3, c_e_h_1, s1)) | m_cell_v_req(c_e_h_1, s1) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s1)))),
% 289.45/181.94 inference(quant_inst,[status(thm)],[])).
% 289.45/181.94 tff(3076,plain,
% 289.45/181.94 ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | m_cell_v_req(c_e_h_1, s1) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s1)) | (~node1(c_e_h_3, c_e_h_1, s1))),
% 289.45/181.94 inference(modus_ponens,[status(thm)],[3075, 3074])).
% 289.45/181.94 tff(3077,plain,
% 289.45/181.94 (m_cell_v_req(c_e_h_1, s1) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s1))),
% 289.45/181.94 inference(unit_resolution,[status(thm)],[3076, 2936, 3070])).
% 289.45/181.94 tff(3078,plain,
% 289.45/181.94 (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s1)),
% 289.45/181.94 inference(unit_resolution,[status(thm)],[3077, 3066])).
% 289.45/181.94 tff(3079,plain,
% 289.45/181.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_3, c_b, s1) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s2)) | (~node12(c_e_h_3, c_b, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s1) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s2)) | (~node12(c_e_h_3, c_b, s1, s2)))),
% 289.45/181.94 inference(rewrite,[status(thm)],[])).
% 289.45/181.94 tff(3080,plain,
% 289.45/181.94 (((~node12(c_e_h_3, c_b, s1, s2)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s1) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s2))) <=> (m_mutex_h_half_v_inp(c_e_h_3, c_b, s1) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s2)) | (~node12(c_e_h_3, c_b, s1, s2)))),
% 289.45/181.94 inference(rewrite,[status(thm)],[])).
% 289.45/181.94 tff(3081,plain,
% 289.45/181.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_b, s1, s2)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s1) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_3, c_b, s1) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s2)) | (~node12(c_e_h_3, c_b, s1, s2))))),
% 289.45/181.94 inference(monotonicity,[status(thm)],[3080])).
% 289.45/181.94 tff(3082,plain,
% 289.45/181.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_b, s1, s2)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s1) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s1) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s2)) | (~node12(c_e_h_3, c_b, s1, s2)))),
% 289.45/181.94 inference(transitivity,[status(thm)],[3081, 3079])).
% 289.45/181.94 tff(3083,plain,
% 289.45/181.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_b, s1, s2)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s1) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s2)))),
% 289.45/181.94 inference(quant_inst,[status(thm)],[])).
% 289.45/181.94 tff(3084,plain,
% 289.45/181.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s1) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s2)) | (~node12(c_e_h_3, c_b, s1, s2))),
% 289.45/181.94 inference(modus_ponens,[status(thm)],[3083, 3082])).
% 289.45/181.94 tff(3085,plain,
% 289.45/181.94 ($false),
% 289.45/181.94 inference(unit_resolution,[status(thm)],[3084, 454, 3078, 3022, 3008])).
% 289.45/181.94 tff(3086,plain,(~m_mutex_h_half_v_out(c_e_h_3, c_b, s2)), inference(lemma,lemma(discharge,[]))).
% 289.45/181.94 tff(3087,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_d, s2)), introduced(assumption)).
% 289.45/181.94 tff(3088,assumption,(~m_mutex_h_half_v_out(c_e_h_3, c_b, s2)), introduced(assumption)).
% 289.45/181.94 tff(3089,plain,
% 289.45/181.94 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_d, s2)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s2))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_d, s2)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s2))),
% 289.45/181.94 inference(rewrite,[status(thm)],[])).
% 289.45/181.94 tff(3090,plain,
% 289.45/181.94 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_d, s2)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s2))),
% 289.45/181.94 inference(quant_inst,[status(thm)],[])).
% 289.45/181.94 tff(3091,plain,
% 289.45/181.94 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_d, s2)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s2)),
% 289.45/181.94 inference(modus_ponens,[status(thm)],[3090, 3089])).
% 289.45/181.94 tff(3092,plain,
% 289.45/181.94 ($false),
% 289.45/181.94 inference(unit_resolution,[status(thm)],[3091, 2808, 3088, 3087])).
% 289.45/181.94 tff(3093,plain,((~m_and_h_gate_v_in1(c_e_h_3, c_d, s2)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s2)), inference(lemma,lemma(discharge,[]))).
% 289.45/181.94 tff(3094,plain,
% 289.45/181.94 (~m_and_h_gate_v_in1(c_e_h_3, c_d, s2)),
% 289.45/181.94 inference(unit_resolution,[status(thm)],[3093, 3086])).
% 289.45/181.94 tff(3095,plain,
% 289.45/181.94 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_d, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_d, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s2))),
% 289.45/181.95 inference(rewrite,[status(thm)],[])).
% 289.45/181.95 tff(3096,plain,
% 289.45/181.95 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_d, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s2))),
% 289.45/181.95 inference(quant_inst,[status(thm)],[])).
% 289.45/181.95 tff(3097,plain,
% 289.45/181.95 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_d, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s2)),
% 289.45/181.95 inference(modus_ponens,[status(thm)],[3096, 3095])).
% 289.45/181.95 tff(3098,plain,
% 289.45/181.95 (~node20(c_e_h_3, c_d, s2)),
% 289.45/181.95 inference(unit_resolution,[status(thm)],[3097, 38, 3094])).
% 289.45/181.95 tff(3099,assumption,(~node20(c_e_h_3, c_d, s2)), introduced(assumption)).
% 289.45/181.95 tff(3100,assumption,(node21(c_e_h_3, c_d, s2, s3)), introduced(assumption)).
% 289.45/181.95 tff(3101,plain,
% 289.45/181.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_d, s3)) | node20(c_e_h_3, c_d, s2) | (~node21(c_e_h_3, c_d, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s3)) | node20(c_e_h_3, c_d, s2) | (~node21(c_e_h_3, c_d, s2, s3)))),
% 289.45/181.95 inference(rewrite,[status(thm)],[])).
% 289.45/181.95 tff(3102,plain,
% 289.45/181.95 ((node20(c_e_h_3, c_d, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s3)) | (~node21(c_e_h_3, c_d, s2, s3))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_d, s3)) | node20(c_e_h_3, c_d, s2) | (~node21(c_e_h_3, c_d, s2, s3)))),
% 289.45/181.95 inference(rewrite,[status(thm)],[])).
% 289.45/181.95 tff(3103,plain,
% 289.45/181.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_d, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s3)) | (~node21(c_e_h_3, c_d, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_d, s3)) | node20(c_e_h_3, c_d, s2) | (~node21(c_e_h_3, c_d, s2, s3))))),
% 289.45/181.95 inference(monotonicity,[status(thm)],[3102])).
% 289.45/181.95 tff(3104,plain,
% 289.45/181.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_d, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s3)) | (~node21(c_e_h_3, c_d, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s3)) | node20(c_e_h_3, c_d, s2) | (~node21(c_e_h_3, c_d, s2, s3)))),
% 289.45/181.95 inference(transitivity,[status(thm)],[3103, 3101])).
% 289.45/181.95 tff(3105,plain,
% 289.45/181.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_d, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s3)) | (~node21(c_e_h_3, c_d, s2, s3)))),
% 289.45/181.95 inference(quant_inst,[status(thm)],[])).
% 289.45/181.95 tff(3106,plain,
% 289.45/181.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s3)) | node20(c_e_h_3, c_d, s2) | (~node21(c_e_h_3, c_d, s2, s3))),
% 289.45/181.95 inference(modus_ponens,[status(thm)],[3105, 3104])).
% 289.45/181.95 tff(3107,plain,
% 289.45/181.95 ($false),
% 289.45/181.95 inference(unit_resolution,[status(thm)],[3106, 52, 3007, 3100, 3099])).
% 289.45/181.95 tff(3108,plain,((~node21(c_e_h_3, c_d, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s3)) | node20(c_e_h_3, c_d, s2)), inference(lemma,lemma(discharge,[]))).
% 289.45/181.95 tff(3109,plain,
% 289.45/181.95 ((~node21(c_e_h_3, c_d, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s3))),
% 289.45/181.95 inference(unit_resolution,[status(thm)],[3108, 3098])).
% 289.45/181.95 tff(3110,plain,
% 289.45/181.95 (~node21(c_e_h_3, c_d, s2, s3)),
% 289.45/181.95 inference(unit_resolution,[status(thm)],[3109, 3007])).
% 289.45/181.95 tff(3111,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_d, s2)), introduced(assumption)).
% 289.45/181.95 tff(3112,assumption,(node22(c_e_h_3, c_d, s2, s3)), introduced(assumption)).
% 289.45/181.95 tff(3113,plain,
% 289.45/181.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_d, s3)) | (~node22(c_e_h_3, c_d, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_d, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s3)) | (~node22(c_e_h_3, c_d, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_d, s2))),
% 289.45/181.95 inference(rewrite,[status(thm)],[])).
% 289.45/181.95 tff(3114,plain,
% 289.45/181.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_d, s3)) | (~node22(c_e_h_3, c_d, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_d, s2))),
% 289.45/181.95 inference(quant_inst,[status(thm)],[])).
% 289.45/181.95 tff(3115,plain,
% 289.45/181.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s3)) | (~node22(c_e_h_3, c_d, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_d, s2)),
% 289.45/181.95 inference(modus_ponens,[status(thm)],[3114, 3113])).
% 289.45/181.95 tff(3116,plain,
% 289.45/181.95 ($false),
% 289.45/181.95 inference(unit_resolution,[status(thm)],[3115, 108, 3007, 3112, 3111])).
% 289.45/181.95 tff(3117,plain,((~node22(c_e_h_3, c_d, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s3)) | m_and_h_gate_v_out(c_e_h_3, c_d, s2)), inference(lemma,lemma(discharge,[]))).
% 289.45/181.95 tff(3118,plain,
% 289.45/181.95 ((~node22(c_e_h_3, c_d, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s3))),
% 289.45/181.95 inference(unit_resolution,[status(thm)],[3117, 2977])).
% 289.45/181.95 tff(3119,plain,
% 289.45/181.95 (~node22(c_e_h_3, c_d, s2, s3)),
% 289.45/181.95 inference(unit_resolution,[status(thm)],[3118, 3007])).
% 289.45/181.95 tff(3120,plain,
% 289.45/181.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_3, c_d, s2, s3) | node22(c_e_h_3, c_d, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_3, c_d, s2, s3) | node22(c_e_h_3, c_d, s2, s3))),
% 289.45/181.95 inference(rewrite,[status(thm)],[])).
% 289.45/181.95 tff(3121,plain,
% 289.45/181.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_3, c_d, s2, s3) | node22(c_e_h_3, c_d, s2, s3))),
% 289.45/181.95 inference(quant_inst,[status(thm)],[])).
% 289.45/181.95 tff(3122,plain,
% 289.45/181.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_3, c_d, s2, s3) | node22(c_e_h_3, c_d, s2, s3)),
% 289.45/181.95 inference(modus_ponens,[status(thm)],[3121, 3120])).
% 289.45/181.95 tff(3123,plain,
% 289.45/181.95 (node21(c_e_h_3, c_d, s2, s3) | node22(c_e_h_3, c_d, s2, s3)),
% 289.45/181.95 inference(unit_resolution,[status(thm)],[3122, 82, 318])).
% 289.45/181.95 tff(3124,plain,
% 289.45/181.95 ($false),
% 289.45/181.95 inference(unit_resolution,[status(thm)],[3123, 3119, 3110])).
% 289.45/181.95 tff(3125,plain,(~m_and_h_gate_v_out(c_e_h_3, c_d, s3)), inference(lemma,lemma(discharge,[]))).
% 289.45/181.95 tff(3126,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_p, s1)), introduced(assumption)).
% 289.45/181.95 tff(3127,assumption,(m_and_h_gate_v_out(c_e_h_1, c_p, s2)), introduced(assumption)).
% 289.45/181.95 tff(3128,assumption,(m_and_h_gate_v_out(c_e_h_1, c_k, s1)), introduced(assumption)).
% 289.45/181.95 tff(3129,assumption,(node21(c_e_h_1, c_k, s0, s1)), introduced(assumption)).
% 289.45/181.95 tff(3130,assumption,(m_or_h_gate_v_out(c_e_h_1, c_g, s0)), introduced(assumption)).
% 289.45/181.95 tff(3131,plain,
% 289.45/181.95 ((~![I0: $i, I1: $i] : (~m_or_h_gate_v_out(I0, I1, s0))) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s0))),
% 289.45/181.95 inference(quant_inst,[status(thm)],[])).
% 289.45/181.95 tff(3132,plain,
% 289.45/181.95 ($false),
% 289.45/181.95 inference(unit_resolution,[status(thm)],[3131, 801, 3130])).
% 289.45/181.95 tff(3133,plain,(~m_or_h_gate_v_out(c_e_h_1, c_g, s0)), inference(lemma,lemma(discharge,[]))).
% 289.45/181.95 tff(3134,plain,
% 289.45/181.95 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_k, s0)) | m_or_h_gate_v_out(c_e_h_1, c_g, s0))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_k, s0)) | m_or_h_gate_v_out(c_e_h_1, c_g, s0))),
% 289.45/181.95 inference(rewrite,[status(thm)],[])).
% 289.45/181.95 tff(3135,plain,
% 289.45/181.95 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_k, s0)) | m_or_h_gate_v_out(c_e_h_1, c_g, s0))),
% 289.45/181.95 inference(quant_inst,[status(thm)],[])).
% 289.45/181.95 tff(3136,plain,
% 289.45/181.95 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_k, s0)) | m_or_h_gate_v_out(c_e_h_1, c_g, s0)),
% 289.45/181.95 inference(modus_ponens,[status(thm)],[3135, 3134])).
% 289.45/181.95 tff(3137,plain,
% 289.45/181.95 (~m_and_h_gate_v_in1(c_e_h_1, c_k, s0)),
% 289.45/181.95 inference(unit_resolution,[status(thm)],[3136, 2048, 3133])).
% 289.45/181.95 tff(3138,plain,
% 289.45/181.95 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_k, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_k, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_k, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_k, s0))),
% 289.45/181.95 inference(rewrite,[status(thm)],[])).
% 289.45/181.95 tff(3139,plain,
% 289.45/181.95 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_k, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_k, s0))),
% 289.45/181.95 inference(quant_inst,[status(thm)],[])).
% 289.45/181.95 tff(3140,plain,
% 289.45/181.95 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_k, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_k, s0)),
% 289.45/181.95 inference(modus_ponens,[status(thm)],[3139, 3138])).
% 289.45/181.95 tff(3141,plain,
% 289.45/181.95 (~node20(c_e_h_1, c_k, s0)),
% 289.45/181.95 inference(unit_resolution,[status(thm)],[3140, 38, 3137])).
% 289.45/181.95 tff(3142,plain,
% 289.45/181.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~node21(c_e_h_1, c_k, s0, s1)) | node20(c_e_h_1, c_k, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~node21(c_e_h_1, c_k, s0, s1)) | node20(c_e_h_1, c_k, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s1)))),
% 289.45/181.95 inference(rewrite,[status(thm)],[])).
% 289.45/181.95 tff(3143,plain,
% 289.45/181.95 ((node20(c_e_h_1, c_k, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s1)) | (~node21(c_e_h_1, c_k, s0, s1))) <=> ((~node21(c_e_h_1, c_k, s0, s1)) | node20(c_e_h_1, c_k, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s1)))),
% 289.45/181.95 inference(rewrite,[status(thm)],[])).
% 289.45/181.95 tff(3144,plain,
% 289.45/181.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_k, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s1)) | (~node21(c_e_h_1, c_k, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~node21(c_e_h_1, c_k, s0, s1)) | node20(c_e_h_1, c_k, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s1))))),
% 289.45/181.95 inference(monotonicity,[status(thm)],[3143])).
% 289.45/181.95 tff(3145,plain,
% 289.45/181.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_k, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s1)) | (~node21(c_e_h_1, c_k, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~node21(c_e_h_1, c_k, s0, s1)) | node20(c_e_h_1, c_k, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s1)))),
% 289.45/181.95 inference(transitivity,[status(thm)],[3144, 3142])).
% 289.45/181.95 tff(3146,plain,
% 289.45/181.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_k, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s1)) | (~node21(c_e_h_1, c_k, s0, s1)))),
% 289.45/181.95 inference(quant_inst,[status(thm)],[])).
% 289.45/181.95 tff(3147,plain,
% 289.45/181.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~node21(c_e_h_1, c_k, s0, s1)) | node20(c_e_h_1, c_k, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s1))),
% 289.45/181.96 inference(modus_ponens,[status(thm)],[3146, 3145])).
% 289.45/181.96 tff(3148,plain,
% 289.45/181.96 ($false),
% 289.45/181.96 inference(unit_resolution,[status(thm)],[3147, 52, 3141, 3129, 3128])).
% 289.45/181.96 tff(3149,plain,((~node21(c_e_h_1, c_k, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s1))), inference(lemma,lemma(discharge,[]))).
% 289.45/181.96 tff(3150,plain,
% 289.45/181.96 (~node21(c_e_h_1, c_k, s0, s1)),
% 289.45/181.96 inference(unit_resolution,[status(thm)],[3149, 3128])).
% 289.45/181.96 tff(3151,plain,
% 289.45/181.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_1, c_k, s0, s1) | node22(c_e_h_1, c_k, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_1, c_k, s0, s1) | node22(c_e_h_1, c_k, s0, s1))),
% 289.45/181.96 inference(rewrite,[status(thm)],[])).
% 289.45/181.96 tff(3152,plain,
% 289.45/181.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_1, c_k, s0, s1) | node22(c_e_h_1, c_k, s0, s1))),
% 289.45/181.96 inference(quant_inst,[status(thm)],[])).
% 289.45/181.96 tff(3153,plain,
% 289.45/181.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_1, c_k, s0, s1) | node22(c_e_h_1, c_k, s0, s1)),
% 289.45/181.96 inference(modus_ponens,[status(thm)],[3152, 3151])).
% 289.45/181.96 tff(3154,plain,
% 289.45/181.96 (node21(c_e_h_1, c_k, s0, s1) | node22(c_e_h_1, c_k, s0, s1)),
% 289.45/181.96 inference(unit_resolution,[status(thm)],[3153, 82, 72])).
% 289.45/181.96 tff(3155,plain,
% 289.45/181.96 (node22(c_e_h_1, c_k, s0, s1)),
% 289.45/181.96 inference(unit_resolution,[status(thm)],[3154, 3150])).
% 289.45/181.96 tff(3156,plain,
% 289.45/181.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_k, s1)) | (~node22(c_e_h_1, c_k, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_k, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s1)) | (~node22(c_e_h_1, c_k, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_k, s0))),
% 289.45/181.96 inference(rewrite,[status(thm)],[])).
% 289.45/181.96 tff(3157,plain,
% 289.45/181.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_k, s1)) | (~node22(c_e_h_1, c_k, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_k, s0))),
% 289.45/181.96 inference(quant_inst,[status(thm)],[])).
% 289.45/181.96 tff(3158,plain,
% 289.45/181.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s1)) | (~node22(c_e_h_1, c_k, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_k, s0)),
% 289.45/181.96 inference(modus_ponens,[status(thm)],[3157, 3156])).
% 289.45/181.96 tff(3159,plain,
% 289.45/181.96 ($false),
% 289.45/181.96 inference(unit_resolution,[status(thm)],[3158, 108, 3155, 3128, 3026])).
% 289.45/181.96 tff(3160,plain,(~m_and_h_gate_v_out(c_e_h_1, c_k, s1)), inference(lemma,lemma(discharge,[]))).
% 289.45/181.96 tff(3161,plain,
% 289.45/181.96 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_p, s1)) | m_and_h_gate_v_out(c_e_h_1, c_k, s1))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s1)) | m_and_h_gate_v_out(c_e_h_1, c_k, s1))),
% 289.45/181.96 inference(rewrite,[status(thm)],[])).
% 289.45/181.96 tff(3162,plain,
% 289.45/181.96 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_p, s1)) | m_and_h_gate_v_out(c_e_h_1, c_k, s1))),
% 289.45/181.96 inference(quant_inst,[status(thm)],[])).
% 289.45/181.96 tff(3163,plain,
% 289.45/181.96 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s1)) | m_and_h_gate_v_out(c_e_h_1, c_k, s1)),
% 289.45/181.96 inference(modus_ponens,[status(thm)],[3162, 3161])).
% 289.45/181.96 tff(3164,plain,
% 289.45/181.96 (~m_and_h_gate_v_in1(c_e_h_1, c_p, s1)),
% 289.45/181.96 inference(unit_resolution,[status(thm)],[3163, 3033, 3160])).
% 289.45/181.96 tff(3165,plain,
% 289.45/181.96 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_p, s1)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_p, s1)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s1))),
% 289.45/181.96 inference(rewrite,[status(thm)],[])).
% 289.45/181.96 tff(3166,plain,
% 289.45/181.96 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_p, s1)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s1))),
% 289.45/181.96 inference(quant_inst,[status(thm)],[])).
% 289.45/181.96 tff(3167,plain,
% 289.45/181.96 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_p, s1)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s1)),
% 289.45/181.96 inference(modus_ponens,[status(thm)],[3166, 3165])).
% 289.45/181.96 tff(3168,plain,
% 289.45/181.96 (~node20(c_e_h_1, c_p, s1)),
% 289.45/181.96 inference(unit_resolution,[status(thm)],[3167, 38, 3164])).
% 289.45/181.96 tff(3169,assumption,(~node20(c_e_h_1, c_p, s1)), introduced(assumption)).
% 289.45/181.96 tff(3170,assumption,(node21(c_e_h_1, c_p, s1, s2)), introduced(assumption)).
% 289.45/181.96 tff(3171,plain,
% 289.45/181.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_p, s2)) | node20(c_e_h_1, c_p, s1) | (~node21(c_e_h_1, c_p, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s2)) | node20(c_e_h_1, c_p, s1) | (~node21(c_e_h_1, c_p, s1, s2)))),
% 289.45/181.96 inference(rewrite,[status(thm)],[])).
% 289.45/181.96 tff(3172,plain,
% 289.45/181.96 ((node20(c_e_h_1, c_p, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s2)) | (~node21(c_e_h_1, c_p, s1, s2))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_p, s2)) | node20(c_e_h_1, c_p, s1) | (~node21(c_e_h_1, c_p, s1, s2)))),
% 289.45/181.96 inference(rewrite,[status(thm)],[])).
% 289.45/181.96 tff(3173,plain,
% 289.45/181.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_p, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s2)) | (~node21(c_e_h_1, c_p, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_p, s2)) | node20(c_e_h_1, c_p, s1) | (~node21(c_e_h_1, c_p, s1, s2))))),
% 289.45/181.96 inference(monotonicity,[status(thm)],[3172])).
% 289.45/181.96 tff(3174,plain,
% 289.45/181.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_p, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s2)) | (~node21(c_e_h_1, c_p, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s2)) | node20(c_e_h_1, c_p, s1) | (~node21(c_e_h_1, c_p, s1, s2)))),
% 289.45/181.96 inference(transitivity,[status(thm)],[3173, 3171])).
% 289.45/181.96 tff(3175,plain,
% 289.45/181.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_p, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s2)) | (~node21(c_e_h_1, c_p, s1, s2)))),
% 289.45/181.96 inference(quant_inst,[status(thm)],[])).
% 289.45/181.96 tff(3176,plain,
% 289.45/181.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s2)) | node20(c_e_h_1, c_p, s1) | (~node21(c_e_h_1, c_p, s1, s2))),
% 289.45/181.96 inference(modus_ponens,[status(thm)],[3175, 3174])).
% 289.45/181.96 tff(3177,plain,
% 289.45/181.96 ($false),
% 289.45/181.96 inference(unit_resolution,[status(thm)],[3176, 52, 3170, 3127, 3169])).
% 289.45/181.96 tff(3178,plain,((~node21(c_e_h_1, c_p, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s2)) | node20(c_e_h_1, c_p, s1)), inference(lemma,lemma(discharge,[]))).
% 289.45/181.96 tff(3179,plain,
% 289.45/181.96 ((~node21(c_e_h_1, c_p, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s2))),
% 289.45/181.96 inference(unit_resolution,[status(thm)],[3178, 3168])).
% 289.45/181.96 tff(3180,plain,
% 289.45/181.96 (~node21(c_e_h_1, c_p, s1, s2)),
% 289.45/181.96 inference(unit_resolution,[status(thm)],[3179, 3127])).
% 289.45/181.96 tff(3181,plain,
% 289.45/181.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_1, c_p, s1, s2) | node22(c_e_h_1, c_p, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_1, c_p, s1, s2) | node22(c_e_h_1, c_p, s1, s2))),
% 289.45/181.96 inference(rewrite,[status(thm)],[])).
% 289.45/181.96 tff(3182,plain,
% 289.45/181.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_1, c_p, s1, s2) | node22(c_e_h_1, c_p, s1, s2))),
% 289.45/181.96 inference(quant_inst,[status(thm)],[])).
% 289.45/181.96 tff(3183,plain,
% 289.45/181.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_1, c_p, s1, s2) | node22(c_e_h_1, c_p, s1, s2)),
% 289.45/181.96 inference(modus_ponens,[status(thm)],[3182, 3181])).
% 289.45/181.96 tff(3184,plain,
% 289.45/181.96 (node21(c_e_h_1, c_p, s1, s2) | node22(c_e_h_1, c_p, s1, s2)),
% 289.45/181.96 inference(unit_resolution,[status(thm)],[3183, 82, 255])).
% 289.45/181.96 tff(3185,plain,
% 289.45/181.96 (node22(c_e_h_1, c_p, s1, s2)),
% 289.45/181.96 inference(unit_resolution,[status(thm)],[3184, 3180])).
% 289.45/181.96 tff(3186,plain,
% 289.45/181.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_p, s2)) | (~node22(c_e_h_1, c_p, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_p, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s2)) | (~node22(c_e_h_1, c_p, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_p, s1))),
% 289.45/181.96 inference(rewrite,[status(thm)],[])).
% 289.45/181.96 tff(3187,plain,
% 289.45/181.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_p, s2)) | (~node22(c_e_h_1, c_p, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_p, s1))),
% 289.45/181.96 inference(quant_inst,[status(thm)],[])).
% 289.45/181.96 tff(3188,plain,
% 289.45/181.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s2)) | (~node22(c_e_h_1, c_p, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_p, s1)),
% 289.45/181.96 inference(modus_ponens,[status(thm)],[3187, 3186])).
% 289.45/181.96 tff(3189,plain,
% 289.45/181.96 ($false),
% 289.45/181.96 inference(unit_resolution,[status(thm)],[3188, 108, 3185, 3127, 3126])).
% 289.45/181.96 tff(3190,plain,((~m_and_h_gate_v_out(c_e_h_1, c_p, s2)) | m_and_h_gate_v_out(c_e_h_1, c_p, s1)), inference(lemma,lemma(discharge,[]))).
% 289.45/181.96 tff(3191,plain,
% 289.45/181.96 (~m_and_h_gate_v_out(c_e_h_1, c_p, s2)),
% 289.45/181.96 inference(unit_resolution,[status(thm)],[3190, 3062])).
% 289.45/181.96 tff(3192,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_p, s2)), introduced(assumption)).
% 289.45/181.96 tff(3193,assumption,(m_cell_v_req(c_e_h_1, s2)), introduced(assumption)).
% 289.45/181.96 tff(3194,plain,
% 289.45/181.96 (((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | ((~m_cell_v_req(c_e_h_1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_p, s2))) <=> ((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | (~m_cell_v_req(c_e_h_1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_p, s2))),
% 289.45/181.96 inference(rewrite,[status(thm)],[])).
% 289.45/181.96 tff(3195,plain,
% 289.45/181.96 ((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | ((~m_cell_v_req(c_e_h_1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_p, s2))),
% 289.45/181.96 inference(quant_inst,[status(thm)],[])).
% 289.45/181.96 tff(3196,plain,
% 289.45/181.96 ((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | (~m_cell_v_req(c_e_h_1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_p, s2)),
% 289.45/181.96 inference(modus_ponens,[status(thm)],[3195, 3194])).
% 289.45/181.96 tff(3197,plain,
% 289.45/181.96 ($false),
% 289.45/181.96 inference(unit_resolution,[status(thm)],[3196, 2908, 3193, 3192])).
% 289.45/181.96 tff(3198,plain,((~m_cell_v_req(c_e_h_1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_p, s2)), inference(lemma,lemma(discharge,[]))).
% 289.45/181.96 tff(3199,plain,
% 289.45/181.96 (~m_cell_v_req(c_e_h_1, s2)),
% 289.45/181.96 inference(unit_resolution,[status(thm)],[3198, 3191])).
% 289.45/181.96 tff(3200,plain,
% 289.45/181.96 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node1(c_e_h_3, c_e_h_1, s2))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node1(c_e_h_3, c_e_h_1, s2))),
% 289.45/181.97 inference(rewrite,[status(thm)],[])).
% 289.45/181.97 tff(3201,plain,
% 289.45/181.97 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node1(c_e_h_3, c_e_h_1, s2))),
% 289.45/181.97 inference(quant_inst,[status(thm)],[])).
% 289.45/181.97 tff(3202,plain,
% 289.45/181.97 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node1(c_e_h_3, c_e_h_1, s2)),
% 289.45/181.97 inference(modus_ponens,[status(thm)],[3201, 3200])).
% 289.45/181.97 tff(3203,plain,
% 289.45/181.97 (node1(c_e_h_3, c_e_h_1, s2)),
% 289.45/181.97 inference(unit_resolution,[status(thm)],[3202, 2922, 2919])).
% 289.45/181.97 tff(3204,plain,
% 289.45/181.97 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_3, c_e_h_1, s2)) | m_cell_v_req(c_e_h_1, s2) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s2)))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | (~node1(c_e_h_3, c_e_h_1, s2)) | m_cell_v_req(c_e_h_1, s2) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s2)))),
% 289.45/181.97 inference(rewrite,[status(thm)],[])).
% 289.45/181.97 tff(3205,plain,
% 289.45/181.97 ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_3, c_e_h_1, s2)) | m_cell_v_req(c_e_h_1, s2) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s2)))),
% 289.45/181.97 inference(quant_inst,[status(thm)],[])).
% 289.45/181.97 tff(3206,plain,
% 289.45/181.97 ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | (~node1(c_e_h_3, c_e_h_1, s2)) | m_cell_v_req(c_e_h_1, s2) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s2))),
% 289.45/181.97 inference(modus_ponens,[status(thm)],[3205, 3204])).
% 289.45/181.97 tff(3207,plain,
% 289.45/181.97 (m_cell_v_req(c_e_h_1, s2) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s2))),
% 289.45/181.97 inference(unit_resolution,[status(thm)],[3206, 2936, 3203])).
% 289.45/181.97 tff(3208,plain,
% 289.45/181.97 (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s2)),
% 289.45/181.97 inference(unit_resolution,[status(thm)],[3207, 3199])).
% 289.45/181.97 tff(3209,assumption,(m_mutex_h_half_v_out(c_e_h_3, c_b, s3)), introduced(assumption)).
% 289.45/181.97 tff(3210,assumption,(node13(c_e_h_3, c_b, s2, s3)), introduced(assumption)).
% 289.45/181.97 tff(3211,plain,
% 289.45/181.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_b, s3)) | (~node13(c_e_h_3, c_b, s2, s3)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s3)) | (~node13(c_e_h_3, c_b, s2, s3)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s2))),
% 289.45/181.97 inference(rewrite,[status(thm)],[])).
% 289.45/181.97 tff(3212,plain,
% 289.45/181.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_b, s3)) | (~node13(c_e_h_3, c_b, s2, s3)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s2))),
% 289.45/181.97 inference(quant_inst,[status(thm)],[])).
% 289.45/181.97 tff(3213,plain,
% 289.45/181.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s3)) | (~node13(c_e_h_3, c_b, s2, s3)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s2)),
% 289.45/181.97 inference(modus_ponens,[status(thm)],[3212, 3211])).
% 289.45/181.97 tff(3214,plain,
% 289.45/181.97 ($false),
% 289.45/181.97 inference(unit_resolution,[status(thm)],[3213, 423, 3210, 3209, 3088])).
% 289.45/181.97 tff(3215,plain,((~node13(c_e_h_3, c_b, s2, s3)) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s3)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s2)), inference(lemma,lemma(discharge,[]))).
% 289.45/181.97 tff(3216,plain,
% 289.45/181.97 (~node13(c_e_h_3, c_b, s2, s3)),
% 289.45/181.97 inference(unit_resolution,[status(thm)],[3215, 3209, 3088])).
% 289.45/181.97 tff(3217,assumption,(~m_mutex_h_half_v_inp(c_e_h_3, c_b, s2)), introduced(assumption)).
% 289.45/181.97 tff(3218,assumption,(node12(c_e_h_3, c_b, s2, s3)), introduced(assumption)).
% 289.45/181.97 tff(3219,plain,
% 289.45/181.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_3, c_b, s2) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s3)) | (~node12(c_e_h_3, c_b, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s2) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s3)) | (~node12(c_e_h_3, c_b, s2, s3)))),
% 289.45/181.97 inference(rewrite,[status(thm)],[])).
% 289.45/181.97 tff(3220,plain,
% 289.45/181.97 (((~node12(c_e_h_3, c_b, s2, s3)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s2) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s3))) <=> (m_mutex_h_half_v_inp(c_e_h_3, c_b, s2) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s3)) | (~node12(c_e_h_3, c_b, s2, s3)))),
% 289.45/181.97 inference(rewrite,[status(thm)],[])).
% 289.45/181.97 tff(3221,plain,
% 289.45/181.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_b, s2, s3)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s2) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_3, c_b, s2) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s3)) | (~node12(c_e_h_3, c_b, s2, s3))))),
% 289.45/181.97 inference(monotonicity,[status(thm)],[3220])).
% 289.45/181.97 tff(3222,plain,
% 289.45/181.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_b, s2, s3)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s2) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s2) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s3)) | (~node12(c_e_h_3, c_b, s2, s3)))),
% 289.45/181.97 inference(transitivity,[status(thm)],[3221, 3219])).
% 289.45/181.97 tff(3223,plain,
% 289.45/181.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_b, s2, s3)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s2) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s3)))),
% 289.45/181.97 inference(quant_inst,[status(thm)],[])).
% 289.45/181.97 tff(3224,plain,
% 289.45/181.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s2) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s3)) | (~node12(c_e_h_3, c_b, s2, s3))),
% 289.45/181.97 inference(modus_ponens,[status(thm)],[3223, 3222])).
% 289.45/181.97 tff(3225,plain,
% 289.45/181.97 ($false),
% 289.45/181.97 inference(unit_resolution,[status(thm)],[3224, 454, 3217, 3218, 3209])).
% 289.45/181.97 tff(3226,plain,((~node12(c_e_h_3, c_b, s2, s3)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s2) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s3))), inference(lemma,lemma(discharge,[]))).
% 289.45/181.97 tff(3227,plain,
% 289.45/181.97 (~node12(c_e_h_3, c_b, s2, s3)),
% 289.45/181.97 inference(unit_resolution,[status(thm)],[3226, 3209, 3217])).
% 289.45/181.97 tff(3228,plain,
% 289.45/181.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s2, s3)) | node12(c_e_h_3, c_b, s2, s3) | node13(c_e_h_3, c_b, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s2, s3)) | node12(c_e_h_3, c_b, s2, s3) | node13(c_e_h_3, c_b, s2, s3))),
% 289.45/181.97 inference(rewrite,[status(thm)],[])).
% 289.45/181.97 tff(3229,plain,
% 289.45/181.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s2, s3)) | node12(c_e_h_3, c_b, s2, s3) | node13(c_e_h_3, c_b, s2, s3))),
% 289.45/181.97 inference(quant_inst,[status(thm)],[])).
% 289.45/181.97 tff(3230,plain,
% 289.45/181.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s2, s3)) | node12(c_e_h_3, c_b, s2, s3) | node13(c_e_h_3, c_b, s2, s3)),
% 289.45/181.98 inference(modus_ponens,[status(thm)],[3229, 3228])).
% 289.45/181.98 tff(3231,plain,
% 289.45/181.98 (node12(c_e_h_3, c_b, s2, s3) | node13(c_e_h_3, c_b, s2, s3)),
% 289.45/181.98 inference(unit_resolution,[status(thm)],[3230, 439, 318])).
% 289.45/181.98 tff(3232,plain,
% 289.45/181.98 ($false),
% 289.45/181.98 inference(unit_resolution,[status(thm)],[3231, 3227, 3216])).
% 289.45/181.98 tff(3233,plain,((~m_mutex_h_half_v_out(c_e_h_3, c_b, s3)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s2) | m_mutex_h_half_v_out(c_e_h_3, c_b, s2)), inference(lemma,lemma(discharge,[]))).
% 289.45/181.98 tff(3234,plain,
% 289.45/181.98 ((~m_mutex_h_half_v_out(c_e_h_3, c_b, s3)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s2)),
% 289.45/181.98 inference(unit_resolution,[status(thm)],[3233, 3208])).
% 289.45/181.98 tff(3235,plain,
% 289.45/181.98 (~m_mutex_h_half_v_out(c_e_h_3, c_b, s3)),
% 289.45/181.98 inference(unit_resolution,[status(thm)],[3234, 3086])).
% 289.45/181.98 tff(3236,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_d, s3)), introduced(assumption)).
% 289.45/181.98 tff(3237,assumption,(~m_mutex_h_half_v_out(c_e_h_3, c_b, s3)), introduced(assumption)).
% 289.45/181.98 tff(3238,plain,
% 289.45/181.98 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_d, s3)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s3))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_d, s3)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s3))),
% 289.45/181.98 inference(rewrite,[status(thm)],[])).
% 289.45/181.98 tff(3239,plain,
% 289.45/181.98 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_d, s3)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s3))),
% 289.45/181.98 inference(quant_inst,[status(thm)],[])).
% 289.45/181.98 tff(3240,plain,
% 289.45/181.98 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_d, s3)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s3)),
% 289.45/181.98 inference(modus_ponens,[status(thm)],[3239, 3238])).
% 289.45/181.98 tff(3241,plain,
% 289.45/181.98 ($false),
% 289.45/181.98 inference(unit_resolution,[status(thm)],[3240, 2808, 3237, 3236])).
% 289.45/181.98 tff(3242,plain,((~m_and_h_gate_v_in1(c_e_h_3, c_d, s3)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s3)), inference(lemma,lemma(discharge,[]))).
% 289.45/181.98 tff(3243,plain,
% 289.45/181.98 (~m_and_h_gate_v_in1(c_e_h_3, c_d, s3)),
% 289.45/181.98 inference(unit_resolution,[status(thm)],[3242, 3235])).
% 289.45/181.98 tff(3244,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_d, s3)), introduced(assumption)).
% 289.45/181.98 tff(3245,assumption,(node20(c_e_h_3, c_d, s3)), introduced(assumption)).
% 289.45/181.98 tff(3246,plain,
% 289.45/181.98 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_d, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_d, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s3))),
% 289.45/181.98 inference(rewrite,[status(thm)],[])).
% 289.45/181.98 tff(3247,plain,
% 289.45/181.98 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_d, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s3))),
% 289.45/181.98 inference(quant_inst,[status(thm)],[])).
% 289.45/181.98 tff(3248,plain,
% 289.45/181.98 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_d, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s3)),
% 289.45/181.98 inference(modus_ponens,[status(thm)],[3247, 3246])).
% 289.45/181.98 tff(3249,plain,
% 289.45/181.98 ($false),
% 289.45/181.98 inference(unit_resolution,[status(thm)],[3248, 38, 3245, 3244])).
% 289.45/181.98 tff(3250,plain,((~node20(c_e_h_3, c_d, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s3)), inference(lemma,lemma(discharge,[]))).
% 289.45/181.98 tff(3251,plain,
% 289.45/181.98 (~node20(c_e_h_3, c_d, s3)),
% 289.45/181.98 inference(unit_resolution,[status(thm)],[3250, 3243])).
% 289.45/181.98 tff(3252,assumption,(m_or_h_gate_v_out(c_e_h_3, c_g, s5)), introduced(assumption)).
% 289.45/181.98 tff(3253,assumption,(~m_or_h_gate_v_in1(c_e_h_3, c_g, s4)), introduced(assumption)).
% 289.45/181.98 tff(3254,assumption,(~node20(c_e_h_3, c_d, s3)), introduced(assumption)).
% 289.45/181.98 tff(3255,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_d, s3)), introduced(assumption)).
% 289.45/181.98 tff(3256,assumption,(m_and_h_gate_v_out(c_e_h_3, c_d, s4)), introduced(assumption)).
% 289.45/181.98 tff(3257,assumption,(node21(c_e_h_3, c_d, s3, s4)), introduced(assumption)).
% 289.45/181.98 tff(3258,plain,
% 289.45/181.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_d, s4)) | node20(c_e_h_3, c_d, s3) | (~node21(c_e_h_3, c_d, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s4)) | node20(c_e_h_3, c_d, s3) | (~node21(c_e_h_3, c_d, s3, s4)))),
% 289.45/181.98 inference(rewrite,[status(thm)],[])).
% 289.45/181.98 tff(3259,plain,
% 289.45/181.98 ((node20(c_e_h_3, c_d, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s4)) | (~node21(c_e_h_3, c_d, s3, s4))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_d, s4)) | node20(c_e_h_3, c_d, s3) | (~node21(c_e_h_3, c_d, s3, s4)))),
% 289.45/181.98 inference(rewrite,[status(thm)],[])).
% 289.45/181.98 tff(3260,plain,
% 289.45/181.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_d, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s4)) | (~node21(c_e_h_3, c_d, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_d, s4)) | node20(c_e_h_3, c_d, s3) | (~node21(c_e_h_3, c_d, s3, s4))))),
% 289.45/181.98 inference(monotonicity,[status(thm)],[3259])).
% 289.45/181.98 tff(3261,plain,
% 289.45/181.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_d, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s4)) | (~node21(c_e_h_3, c_d, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s4)) | node20(c_e_h_3, c_d, s3) | (~node21(c_e_h_3, c_d, s3, s4)))),
% 289.45/181.98 inference(transitivity,[status(thm)],[3260, 3258])).
% 289.45/181.98 tff(3262,plain,
% 289.45/181.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_d, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s4)) | (~node21(c_e_h_3, c_d, s3, s4)))),
% 289.45/181.98 inference(quant_inst,[status(thm)],[])).
% 289.45/181.98 tff(3263,plain,
% 289.45/181.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s4)) | node20(c_e_h_3, c_d, s3) | (~node21(c_e_h_3, c_d, s3, s4))),
% 289.45/181.98 inference(modus_ponens,[status(thm)],[3262, 3261])).
% 289.45/181.98 tff(3264,plain,
% 289.45/181.98 ($false),
% 289.45/181.98 inference(unit_resolution,[status(thm)],[3263, 52, 3257, 3256, 3254])).
% 289.45/181.98 tff(3265,plain,((~node21(c_e_h_3, c_d, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s4)) | node20(c_e_h_3, c_d, s3)), inference(lemma,lemma(discharge,[]))).
% 289.45/181.98 tff(3266,plain,
% 289.45/181.98 (~node21(c_e_h_3, c_d, s3, s4)),
% 289.45/181.98 inference(unit_resolution,[status(thm)],[3265, 3256, 3254])).
% 289.45/181.98 tff(3267,assumption,(node22(c_e_h_3, c_d, s3, s4)), introduced(assumption)).
% 289.45/181.98 tff(3268,plain,
% 289.45/181.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_d, s4)) | (~node22(c_e_h_3, c_d, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_d, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s4)) | (~node22(c_e_h_3, c_d, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_d, s3))),
% 289.45/181.98 inference(rewrite,[status(thm)],[])).
% 289.45/181.98 tff(3269,plain,
% 289.45/181.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_d, s4)) | (~node22(c_e_h_3, c_d, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_d, s3))),
% 289.45/181.98 inference(quant_inst,[status(thm)],[])).
% 289.45/181.98 tff(3270,plain,
% 289.45/181.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s4)) | (~node22(c_e_h_3, c_d, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_d, s3)),
% 289.45/181.98 inference(modus_ponens,[status(thm)],[3269, 3268])).
% 289.45/181.98 tff(3271,plain,
% 289.45/181.98 ($false),
% 289.45/181.98 inference(unit_resolution,[status(thm)],[3270, 108, 3267, 3255, 3256])).
% 289.45/181.98 tff(3272,plain,((~node22(c_e_h_3, c_d, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_d, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s4))), inference(lemma,lemma(discharge,[]))).
% 289.45/181.98 tff(3273,plain,
% 289.45/181.98 (~node22(c_e_h_3, c_d, s3, s4)),
% 289.45/181.98 inference(unit_resolution,[status(thm)],[3272, 3256, 3255])).
% 289.45/181.98 tff(3274,plain,
% 289.45/181.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_3, c_d, s3, s4) | node22(c_e_h_3, c_d, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_3, c_d, s3, s4) | node22(c_e_h_3, c_d, s3, s4))),
% 289.45/181.98 inference(rewrite,[status(thm)],[])).
% 289.45/181.98 tff(3275,plain,
% 289.45/181.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_3, c_d, s3, s4) | node22(c_e_h_3, c_d, s3, s4))),
% 289.45/181.98 inference(quant_inst,[status(thm)],[])).
% 289.45/181.98 tff(3276,plain,
% 289.45/181.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_3, c_d, s3, s4) | node22(c_e_h_3, c_d, s3, s4)),
% 289.45/181.98 inference(modus_ponens,[status(thm)],[3275, 3274])).
% 289.45/181.98 tff(3277,plain,
% 289.45/181.98 (node21(c_e_h_3, c_d, s3, s4) | node22(c_e_h_3, c_d, s3, s4)),
% 289.45/181.98 inference(unit_resolution,[status(thm)],[3276, 82, 531])).
% 289.45/181.98 tff(3278,plain,
% 289.45/181.98 ($false),
% 289.45/181.98 inference(unit_resolution,[status(thm)],[3277, 3273, 3266])).
% 289.45/181.98 tff(3279,plain,((~m_and_h_gate_v_out(c_e_h_3, c_d, s4)) | m_and_h_gate_v_out(c_e_h_3, c_d, s3) | node20(c_e_h_3, c_d, s3)), inference(lemma,lemma(discharge,[]))).
% 289.45/181.98 tff(3280,plain,
% 289.45/181.98 (~m_and_h_gate_v_out(c_e_h_3, c_d, s4)),
% 289.45/181.98 inference(unit_resolution,[status(thm)],[3279, 3255, 3254])).
% 289.45/181.98 tff(3281,assumption,(m_or_h_gate_v_in2(c_e_h_3, c_g, s4)), introduced(assumption)).
% 289.45/181.98 tff(3282,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_d, s4)), introduced(assumption)).
% 289.45/181.98 tff(3283,plain,
% 289.45/181.98 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_g, s4)) | m_and_h_gate_v_out(c_e_h_3, c_d, s4))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_g, s4)) | m_and_h_gate_v_out(c_e_h_3, c_d, s4))),
% 289.45/181.98 inference(rewrite,[status(thm)],[])).
% 289.45/181.98 tff(3284,plain,
% 289.45/181.98 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_g, s4)) | m_and_h_gate_v_out(c_e_h_3, c_d, s4))),
% 289.45/181.98 inference(quant_inst,[status(thm)],[])).
% 289.45/181.98 tff(3285,plain,
% 289.45/181.98 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_g, s4)) | m_and_h_gate_v_out(c_e_h_3, c_d, s4)),
% 289.45/181.98 inference(modus_ponens,[status(thm)],[3284, 3283])).
% 289.45/181.98 tff(3286,plain,
% 289.45/181.98 ($false),
% 289.45/181.98 inference(unit_resolution,[status(thm)],[3285, 2762, 3282, 3281])).
% 289.45/181.98 tff(3287,plain,((~m_or_h_gate_v_in2(c_e_h_3, c_g, s4)) | m_and_h_gate_v_out(c_e_h_3, c_d, s4)), inference(lemma,lemma(discharge,[]))).
% 289.45/181.98 tff(3288,plain,
% 289.45/181.98 (~m_or_h_gate_v_in2(c_e_h_3, c_g, s4)),
% 289.45/181.98 inference(unit_resolution,[status(thm)],[3287, 3280])).
% 289.45/181.98 tff(3289,assumption,(~m_or_h_gate_v_in2(c_e_h_3, c_g, s4)), introduced(assumption)).
% 289.45/181.98 tff(3290,assumption,(node5(c_e_h_3, c_g, s4, s5)), introduced(assumption)).
% 289.45/181.98 tff(3291,plain,
% 289.45/181.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_g, s4) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s5)) | m_or_h_gate_v_in2(c_e_h_3, c_g, s4) | (~node5(c_e_h_3, c_g, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in1(c_e_h_3, c_g, s4) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s5)) | m_or_h_gate_v_in2(c_e_h_3, c_g, s4) | (~node5(c_e_h_3, c_g, s4, s5)))),
% 289.53/181.99 inference(rewrite,[status(thm)],[])).
% 289.53/181.99 tff(3292,plain,
% 289.53/181.99 ((m_or_h_gate_v_in1(c_e_h_3, c_g, s4) | m_or_h_gate_v_in2(c_e_h_3, c_g, s4) | (~node5(c_e_h_3, c_g, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s5))) <=> (m_or_h_gate_v_in1(c_e_h_3, c_g, s4) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s5)) | m_or_h_gate_v_in2(c_e_h_3, c_g, s4) | (~node5(c_e_h_3, c_g, s4, s5)))),
% 289.53/181.99 inference(rewrite,[status(thm)],[])).
% 289.53/181.99 tff(3293,plain,
% 289.53/181.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_g, s4) | m_or_h_gate_v_in2(c_e_h_3, c_g, s4) | (~node5(c_e_h_3, c_g, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_g, s4) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s5)) | m_or_h_gate_v_in2(c_e_h_3, c_g, s4) | (~node5(c_e_h_3, c_g, s4, s5))))),
% 289.53/181.99 inference(monotonicity,[status(thm)],[3292])).
% 289.53/181.99 tff(3294,plain,
% 289.53/181.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_g, s4) | m_or_h_gate_v_in2(c_e_h_3, c_g, s4) | (~node5(c_e_h_3, c_g, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in1(c_e_h_3, c_g, s4) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s5)) | m_or_h_gate_v_in2(c_e_h_3, c_g, s4) | (~node5(c_e_h_3, c_g, s4, s5)))),
% 289.53/181.99 inference(transitivity,[status(thm)],[3293, 3291])).
% 289.53/181.99 tff(3295,plain,
% 289.53/181.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_g, s4) | m_or_h_gate_v_in2(c_e_h_3, c_g, s4) | (~node5(c_e_h_3, c_g, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s5)))),
% 289.53/181.99 inference(quant_inst,[status(thm)],[])).
% 289.53/181.99 tff(3296,plain,
% 289.53/181.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in1(c_e_h_3, c_g, s4) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s5)) | m_or_h_gate_v_in2(c_e_h_3, c_g, s4) | (~node5(c_e_h_3, c_g, s4, s5))),
% 289.53/181.99 inference(modus_ponens,[status(thm)],[3295, 3294])).
% 289.53/181.99 tff(3297,plain,
% 289.53/181.99 ($false),
% 289.53/181.99 inference(unit_resolution,[status(thm)],[3296, 1159, 3290, 3252, 3289, 3253])).
% 289.53/181.99 tff(3298,plain,((~node5(c_e_h_3, c_g, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s5)) | m_or_h_gate_v_in2(c_e_h_3, c_g, s4) | m_or_h_gate_v_in1(c_e_h_3, c_g, s4)), inference(lemma,lemma(discharge,[]))).
% 289.53/181.99 tff(3299,plain,
% 289.53/181.99 (~node5(c_e_h_3, c_g, s4, s5)),
% 289.53/181.99 inference(unit_resolution,[status(thm)],[3298, 3288, 3252, 3253])).
% 289.53/181.99 tff(3300,plain,
% 289.53/181.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s4, s5)) | node5(c_e_h_3, c_g, s4, s5) | node6(c_e_h_3, c_g, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s4, s5)) | node5(c_e_h_3, c_g, s4, s5) | node6(c_e_h_3, c_g, s4, s5))),
% 289.53/181.99 inference(rewrite,[status(thm)],[])).
% 289.53/181.99 tff(3301,plain,
% 289.53/181.99 ((node6(c_e_h_3, c_g, s4, s5) | node5(c_e_h_3, c_g, s4, s5) | (~trans(s4, s5))) <=> ((~trans(s4, s5)) | node5(c_e_h_3, c_g, s4, s5) | node6(c_e_h_3, c_g, s4, s5))),
% 289.53/181.99 inference(rewrite,[status(thm)],[])).
% 289.53/181.99 tff(3302,plain,
% 289.53/181.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s4, s5) | node5(c_e_h_3, c_g, s4, s5) | (~trans(s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s4, s5)) | node5(c_e_h_3, c_g, s4, s5) | node6(c_e_h_3, c_g, s4, s5)))),
% 289.53/181.99 inference(monotonicity,[status(thm)],[3301])).
% 289.53/181.99 tff(3303,plain,
% 289.53/181.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s4, s5) | node5(c_e_h_3, c_g, s4, s5) | (~trans(s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s4, s5)) | node5(c_e_h_3, c_g, s4, s5) | node6(c_e_h_3, c_g, s4, s5))),
% 289.53/181.99 inference(transitivity,[status(thm)],[3302, 3300])).
% 289.53/181.99 tff(3304,plain,
% 289.53/181.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s4, s5) | node5(c_e_h_3, c_g, s4, s5) | (~trans(s4, s5)))),
% 289.53/181.99 inference(quant_inst,[status(thm)],[])).
% 289.53/181.99 tff(3305,plain,
% 289.53/181.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s4, s5)) | node5(c_e_h_3, c_g, s4, s5) | node6(c_e_h_3, c_g, s4, s5)),
% 289.53/181.99 inference(modus_ponens,[status(thm)],[3304, 3303])).
% 289.53/181.99 tff(3306,plain,
% 289.53/181.99 (node5(c_e_h_3, c_g, s4, s5) | node6(c_e_h_3, c_g, s4, s5)),
% 289.53/181.99 inference(unit_resolution,[status(thm)],[3305, 1141, 1028])).
% 289.53/181.99 tff(3307,plain,
% 289.53/181.99 (node6(c_e_h_3, c_g, s4, s5)),
% 289.53/181.99 inference(unit_resolution,[status(thm)],[3306, 3299])).
% 289.53/181.99 tff(3308,assumption,(~m_or_h_gate_v_out(c_e_h_3, c_g, s4)), introduced(assumption)).
% 289.53/181.99 tff(3309,assumption,(node6(c_e_h_3, c_g, s4, s5)), introduced(assumption)).
% 289.53/181.99 tff(3310,plain,
% 289.53/181.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_3, c_g, s5)) | m_or_h_gate_v_out(c_e_h_3, c_g, s4) | (~node6(c_e_h_3, c_g, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s5)) | m_or_h_gate_v_out(c_e_h_3, c_g, s4) | (~node6(c_e_h_3, c_g, s4, s5)))),
% 289.53/181.99 inference(rewrite,[status(thm)],[])).
% 289.53/181.99 tff(3311,plain,
% 289.53/181.99 (((~node6(c_e_h_3, c_g, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s5)) | m_or_h_gate_v_out(c_e_h_3, c_g, s4)) <=> ((~m_or_h_gate_v_out(c_e_h_3, c_g, s5)) | m_or_h_gate_v_out(c_e_h_3, c_g, s4) | (~node6(c_e_h_3, c_g, s4, s5)))),
% 289.53/181.99 inference(rewrite,[status(thm)],[])).
% 289.53/181.99 tff(3312,plain,
% 289.53/181.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_g, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s5)) | m_or_h_gate_v_out(c_e_h_3, c_g, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_3, c_g, s5)) | m_or_h_gate_v_out(c_e_h_3, c_g, s4) | (~node6(c_e_h_3, c_g, s4, s5))))),
% 289.53/181.99 inference(monotonicity,[status(thm)],[3311])).
% 289.53/181.99 tff(3313,plain,
% 289.53/181.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_g, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s5)) | m_or_h_gate_v_out(c_e_h_3, c_g, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s5)) | m_or_h_gate_v_out(c_e_h_3, c_g, s4) | (~node6(c_e_h_3, c_g, s4, s5)))),
% 289.53/181.99 inference(transitivity,[status(thm)],[3312, 3310])).
% 289.53/181.99 tff(3314,plain,
% 289.53/181.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_g, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s5)) | m_or_h_gate_v_out(c_e_h_3, c_g, s4))),
% 289.53/181.99 inference(quant_inst,[status(thm)],[])).
% 289.53/181.99 tff(3315,plain,
% 289.53/181.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s5)) | m_or_h_gate_v_out(c_e_h_3, c_g, s4) | (~node6(c_e_h_3, c_g, s4, s5))),
% 289.53/181.99 inference(modus_ponens,[status(thm)],[3314, 3313])).
% 289.53/181.99 tff(3316,plain,
% 289.53/181.99 ($false),
% 289.53/181.99 inference(unit_resolution,[status(thm)],[3315, 1121, 3309, 3308, 3252])).
% 289.53/182.00 tff(3317,plain,((~node6(c_e_h_3, c_g, s4, s5)) | m_or_h_gate_v_out(c_e_h_3, c_g, s4) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s5))), inference(lemma,lemma(discharge,[]))).
% 289.53/182.00 tff(3318,plain,
% 289.53/182.00 (m_or_h_gate_v_out(c_e_h_3, c_g, s4)),
% 289.53/182.00 inference(unit_resolution,[status(thm)],[3317, 3307, 3252])).
% 289.53/182.00 tff(3319,assumption,(~m_or_h_gate_v_in1(c_e_h_3, c_g, s3)), introduced(assumption)).
% 289.53/182.00 tff(3320,assumption,(~m_or_h_gate_v_out(c_e_h_3, c_g, s3)), introduced(assumption)).
% 289.53/182.00 tff(3321,assumption,(m_or_h_gate_v_out(c_e_h_3, c_g, s4)), introduced(assumption)).
% 289.53/182.00 tff(3322,assumption,(node6(c_e_h_3, c_g, s3, s4)), introduced(assumption)).
% 289.53/182.00 tff(3323,plain,
% 289.53/182.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | m_or_h_gate_v_out(c_e_h_3, c_g, s3) | (~node6(c_e_h_3, c_g, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | m_or_h_gate_v_out(c_e_h_3, c_g, s3) | (~node6(c_e_h_3, c_g, s3, s4)))),
% 289.53/182.00 inference(rewrite,[status(thm)],[])).
% 289.53/182.00 tff(3324,plain,
% 289.53/182.00 (((~node6(c_e_h_3, c_g, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | m_or_h_gate_v_out(c_e_h_3, c_g, s3)) <=> ((~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | m_or_h_gate_v_out(c_e_h_3, c_g, s3) | (~node6(c_e_h_3, c_g, s3, s4)))),
% 289.53/182.00 inference(rewrite,[status(thm)],[])).
% 289.53/182.00 tff(3325,plain,
% 289.53/182.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_g, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | m_or_h_gate_v_out(c_e_h_3, c_g, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | m_or_h_gate_v_out(c_e_h_3, c_g, s3) | (~node6(c_e_h_3, c_g, s3, s4))))),
% 289.53/182.00 inference(monotonicity,[status(thm)],[3324])).
% 289.53/182.00 tff(3326,plain,
% 289.53/182.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_g, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | m_or_h_gate_v_out(c_e_h_3, c_g, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | m_or_h_gate_v_out(c_e_h_3, c_g, s3) | (~node6(c_e_h_3, c_g, s3, s4)))),
% 289.53/182.00 inference(transitivity,[status(thm)],[3325, 3323])).
% 289.53/182.00 tff(3327,plain,
% 289.53/182.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_g, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | m_or_h_gate_v_out(c_e_h_3, c_g, s3))),
% 289.53/182.00 inference(quant_inst,[status(thm)],[])).
% 289.53/182.00 tff(3328,plain,
% 289.53/182.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | m_or_h_gate_v_out(c_e_h_3, c_g, s3) | (~node6(c_e_h_3, c_g, s3, s4))),
% 289.53/182.00 inference(modus_ponens,[status(thm)],[3327, 3326])).
% 289.53/182.00 tff(3329,plain,
% 289.53/182.00 ($false),
% 289.53/182.00 inference(unit_resolution,[status(thm)],[3328, 1121, 3322, 3321, 3320])).
% 289.53/182.00 tff(3330,plain,((~node6(c_e_h_3, c_g, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | m_or_h_gate_v_out(c_e_h_3, c_g, s3)), inference(lemma,lemma(discharge,[]))).
% 289.53/182.00 tff(3331,plain,
% 289.53/182.00 (~node6(c_e_h_3, c_g, s3, s4)),
% 289.53/182.00 inference(unit_resolution,[status(thm)],[3330, 3318, 3320])).
% 289.53/182.00 tff(3332,plain,
% 289.53/182.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s3, s4)) | node6(c_e_h_3, c_g, s3, s4) | node5(c_e_h_3, c_g, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s3, s4)) | node6(c_e_h_3, c_g, s3, s4) | node5(c_e_h_3, c_g, s3, s4))),
% 289.53/182.00 inference(rewrite,[status(thm)],[])).
% 289.53/182.00 tff(3333,plain,
% 289.53/182.00 ((node6(c_e_h_3, c_g, s3, s4) | node5(c_e_h_3, c_g, s3, s4) | (~trans(s3, s4))) <=> ((~trans(s3, s4)) | node6(c_e_h_3, c_g, s3, s4) | node5(c_e_h_3, c_g, s3, s4))),
% 289.53/182.00 inference(rewrite,[status(thm)],[])).
% 289.53/182.00 tff(3334,plain,
% 289.53/182.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s3, s4) | node5(c_e_h_3, c_g, s3, s4) | (~trans(s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s3, s4)) | node6(c_e_h_3, c_g, s3, s4) | node5(c_e_h_3, c_g, s3, s4)))),
% 289.53/182.00 inference(monotonicity,[status(thm)],[3333])).
% 289.53/182.00 tff(3335,plain,
% 289.53/182.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s3, s4) | node5(c_e_h_3, c_g, s3, s4) | (~trans(s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s3, s4)) | node6(c_e_h_3, c_g, s3, s4) | node5(c_e_h_3, c_g, s3, s4))),
% 289.53/182.00 inference(transitivity,[status(thm)],[3334, 3332])).
% 289.53/182.00 tff(3336,plain,
% 289.53/182.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s3, s4) | node5(c_e_h_3, c_g, s3, s4) | (~trans(s3, s4)))),
% 289.53/182.00 inference(quant_inst,[status(thm)],[])).
% 289.53/182.00 tff(3337,plain,
% 289.53/182.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s3, s4)) | node6(c_e_h_3, c_g, s3, s4) | node5(c_e_h_3, c_g, s3, s4)),
% 289.53/182.00 inference(modus_ponens,[status(thm)],[3336, 3335])).
% 289.53/182.00 tff(3338,plain,
% 289.53/182.00 (node6(c_e_h_3, c_g, s3, s4) | node5(c_e_h_3, c_g, s3, s4)),
% 289.53/182.00 inference(unit_resolution,[status(thm)],[3337, 1141, 531])).
% 289.53/182.00 tff(3339,plain,
% 289.53/182.00 (node5(c_e_h_3, c_g, s3, s4)),
% 289.53/182.00 inference(unit_resolution,[status(thm)],[3338, 3331])).
% 289.53/182.00 tff(3340,assumption,(~m_or_h_gate_v_in2(c_e_h_3, c_g, s3)), introduced(assumption)).
% 289.53/182.00 tff(3341,assumption,(node5(c_e_h_3, c_g, s3, s4)), introduced(assumption)).
% 289.53/182.00 tff(3342,plain,
% 289.53/182.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_3, c_g, s3) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s3) | (~node5(c_e_h_3, c_g, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_3, c_g, s3) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s3) | (~node5(c_e_h_3, c_g, s3, s4)))),
% 289.53/182.00 inference(rewrite,[status(thm)],[])).
% 289.53/182.00 tff(3343,plain,
% 289.53/182.00 ((m_or_h_gate_v_in1(c_e_h_3, c_g, s3) | m_or_h_gate_v_in2(c_e_h_3, c_g, s3) | (~node5(c_e_h_3, c_g, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4))) <=> (m_or_h_gate_v_in2(c_e_h_3, c_g, s3) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s3) | (~node5(c_e_h_3, c_g, s3, s4)))),
% 289.53/182.00 inference(rewrite,[status(thm)],[])).
% 289.53/182.00 tff(3344,plain,
% 289.53/182.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_g, s3) | m_or_h_gate_v_in2(c_e_h_3, c_g, s3) | (~node5(c_e_h_3, c_g, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_3, c_g, s3) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s3) | (~node5(c_e_h_3, c_g, s3, s4))))),
% 289.53/182.00 inference(monotonicity,[status(thm)],[3343])).
% 289.53/182.00 tff(3345,plain,
% 289.53/182.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_g, s3) | m_or_h_gate_v_in2(c_e_h_3, c_g, s3) | (~node5(c_e_h_3, c_g, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_3, c_g, s3) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s3) | (~node5(c_e_h_3, c_g, s3, s4)))),
% 289.53/182.00 inference(transitivity,[status(thm)],[3344, 3342])).
% 289.53/182.00 tff(3346,plain,
% 289.53/182.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_g, s3) | m_or_h_gate_v_in2(c_e_h_3, c_g, s3) | (~node5(c_e_h_3, c_g, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)))),
% 289.53/182.00 inference(quant_inst,[status(thm)],[])).
% 289.53/182.00 tff(3347,plain,
% 289.53/182.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_3, c_g, s3) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s3) | (~node5(c_e_h_3, c_g, s3, s4))),
% 289.53/182.00 inference(modus_ponens,[status(thm)],[3346, 3345])).
% 289.53/182.00 tff(3348,plain,
% 289.53/182.00 ($false),
% 289.53/182.00 inference(unit_resolution,[status(thm)],[3347, 1159, 3341, 3321, 3319, 3340])).
% 289.53/182.00 tff(3349,plain,((~node5(c_e_h_3, c_g, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s3) | m_or_h_gate_v_in2(c_e_h_3, c_g, s3)), inference(lemma,lemma(discharge,[]))).
% 289.53/182.00 tff(3350,plain,
% 289.53/182.00 (m_or_h_gate_v_in2(c_e_h_3, c_g, s3)),
% 289.53/182.00 inference(unit_resolution,[status(thm)],[3349, 3339, 3319, 3318])).
% 289.53/182.00 tff(3351,plain,
% 289.53/182.00 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_g, s3)) | m_and_h_gate_v_out(c_e_h_3, c_d, s3))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_g, s3)) | m_and_h_gate_v_out(c_e_h_3, c_d, s3))),
% 289.53/182.00 inference(rewrite,[status(thm)],[])).
% 289.53/182.00 tff(3352,plain,
% 289.53/182.00 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_g, s3)) | m_and_h_gate_v_out(c_e_h_3, c_d, s3))),
% 289.53/182.00 inference(quant_inst,[status(thm)],[])).
% 289.53/182.00 tff(3353,plain,
% 289.53/182.00 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_g, s3)) | m_and_h_gate_v_out(c_e_h_3, c_d, s3)),
% 289.53/182.00 inference(modus_ponens,[status(thm)],[3352, 3351])).
% 289.53/182.00 tff(3354,plain,
% 289.53/182.00 ($false),
% 289.53/182.00 inference(unit_resolution,[status(thm)],[3353, 2762, 3255, 3350])).
% 289.53/182.00 tff(3355,plain,(m_and_h_gate_v_out(c_e_h_3, c_d, s3) | m_or_h_gate_v_in1(c_e_h_3, c_g, s3) | m_or_h_gate_v_out(c_e_h_3, c_g, s3) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s5)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s4) | node20(c_e_h_3, c_d, s3)), inference(lemma,lemma(discharge,[]))).
% 289.53/182.00 tff(3356,plain,
% 289.53/182.00 (m_and_h_gate_v_out(c_e_h_3, c_d, s3) | m_or_h_gate_v_in1(c_e_h_3, c_g, s3) | m_or_h_gate_v_out(c_e_h_3, c_g, s3) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s5)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s4)),
% 289.53/182.00 inference(unit_resolution,[status(thm)],[3355, 3251])).
% 289.53/182.00 tff(3357,plain,
% 289.53/182.00 (m_or_h_gate_v_in1(c_e_h_3, c_g, s3) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s5)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s4)),
% 289.53/182.00 inference(unit_resolution,[status(thm)],[3356, 3125, 3006])).
% 289.53/182.00 tff(3358,plain,
% 289.53/182.00 (~m_or_h_gate_v_out(c_e_h_3, c_g, s5)),
% 289.53/182.00 inference(unit_resolution,[status(thm)],[3357, 2749, 2714])).
% 289.53/182.00 tff(3359,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_k, s5)), introduced(assumption)).
% 289.53/182.00 tff(3360,assumption,(~m_or_h_gate_v_out(c_e_h_3, c_g, s5)), introduced(assumption)).
% 289.53/182.00 tff(3361,plain,
% 289.53/182.00 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_k, s5)) | m_or_h_gate_v_out(c_e_h_3, c_g, s5))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s5)) | m_or_h_gate_v_out(c_e_h_3, c_g, s5))),
% 289.53/182.00 inference(rewrite,[status(thm)],[])).
% 289.53/182.01 tff(3362,plain,
% 289.53/182.01 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_k, s5)) | m_or_h_gate_v_out(c_e_h_3, c_g, s5))),
% 289.53/182.01 inference(quant_inst,[status(thm)],[])).
% 289.53/182.01 tff(3363,plain,
% 289.53/182.01 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s5)) | m_or_h_gate_v_out(c_e_h_3, c_g, s5)),
% 289.53/182.01 inference(modus_ponens,[status(thm)],[3362, 3361])).
% 289.53/182.01 tff(3364,plain,
% 289.53/182.01 ($false),
% 289.53/182.01 inference(unit_resolution,[status(thm)],[3363, 2048, 3360, 3359])).
% 289.53/182.01 tff(3365,plain,((~m_and_h_gate_v_in1(c_e_h_3, c_k, s5)) | m_or_h_gate_v_out(c_e_h_3, c_g, s5)), inference(lemma,lemma(discharge,[]))).
% 289.53/182.01 tff(3366,plain,
% 289.53/182.01 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s5)),
% 289.53/182.01 inference(unit_resolution,[status(thm)],[3365, 3358])).
% 289.53/182.01 tff(3367,assumption,(m_or_h_gate_v_out(c_e_h_3, c_j, s8)), introduced(assumption)).
% 289.53/182.01 tff(3368,plain,
% 289.53/182.01 (~m_or_h_gate_v_in2(c_e_h_3, c_g, s3)),
% 289.53/182.01 inference(unit_resolution,[status(thm)],[3353, 2762, 3255])).
% 289.53/182.01 tff(3369,plain,
% 289.53/182.01 (~node5(c_e_h_3, c_g, s3, s4)),
% 289.53/182.01 inference(unit_resolution,[status(thm)],[3349, 3368, 3319, 3321])).
% 289.53/182.01 tff(3370,plain,
% 289.53/182.01 (node6(c_e_h_3, c_g, s3, s4)),
% 289.53/182.01 inference(unit_resolution,[status(thm)],[3338, 3369])).
% 289.53/182.01 tff(3371,plain,
% 289.53/182.01 (m_or_h_gate_v_out(c_e_h_3, c_g, s3)),
% 289.53/182.01 inference(unit_resolution,[status(thm)],[3330, 3370, 3321])).
% 289.53/182.01 tff(3372,plain,
% 289.53/182.01 (~node5(c_e_h_3, c_g, s2, s3)),
% 289.53/182.01 inference(unit_resolution,[status(thm)],[2995, 3371, 2982])).
% 289.53/182.01 tff(3373,plain,
% 289.53/182.01 (node6(c_e_h_3, c_g, s2, s3)),
% 289.53/182.01 inference(unit_resolution,[status(thm)],[3004, 3372])).
% 289.53/182.01 tff(3374,plain,
% 289.53/182.01 ($false),
% 289.53/182.01 inference(unit_resolution,[status(thm)],[2880, 1121, 3373, 3371, 2873])).
% 289.53/182.01 tff(3375,plain,(m_or_h_gate_v_in2(c_e_h_3, c_g, s2) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s3) | m_and_h_gate_v_out(c_e_h_3, c_d, s3)), inference(lemma,lemma(discharge,[]))).
% 289.53/182.01 tff(3376,plain,
% 289.53/182.01 ((~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s3) | m_and_h_gate_v_out(c_e_h_3, c_d, s3)),
% 289.53/182.01 inference(unit_resolution,[status(thm)],[3375, 2981])).
% 289.53/182.01 tff(3377,plain,
% 289.53/182.01 ((~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s3)),
% 289.53/182.01 inference(unit_resolution,[status(thm)],[3376, 3125])).
% 289.53/182.01 tff(3378,plain,
% 289.53/182.01 (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)),
% 289.53/182.01 inference(unit_resolution,[status(thm)],[3377, 2714])).
% 289.53/182.01 tff(3379,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_k, s4)), introduced(assumption)).
% 289.53/182.01 tff(3380,plain,
% 289.53/182.01 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_k, s4)) | m_or_h_gate_v_out(c_e_h_3, c_g, s4))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s4)) | m_or_h_gate_v_out(c_e_h_3, c_g, s4))),
% 289.53/182.01 inference(rewrite,[status(thm)],[])).
% 289.53/182.01 tff(3381,plain,
% 289.53/182.01 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_k, s4)) | m_or_h_gate_v_out(c_e_h_3, c_g, s4))),
% 289.53/182.01 inference(quant_inst,[status(thm)],[])).
% 289.53/182.01 tff(3382,plain,
% 289.53/182.01 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s4)) | m_or_h_gate_v_out(c_e_h_3, c_g, s4)),
% 289.53/182.01 inference(modus_ponens,[status(thm)],[3381, 3380])).
% 289.53/182.01 tff(3383,plain,
% 289.53/182.01 ($false),
% 289.53/182.01 inference(unit_resolution,[status(thm)],[3382, 2048, 3308, 3379])).
% 289.53/182.01 tff(3384,plain,((~m_and_h_gate_v_in1(c_e_h_3, c_k, s4)) | m_or_h_gate_v_out(c_e_h_3, c_g, s4)), inference(lemma,lemma(discharge,[]))).
% 289.53/182.01 tff(3385,plain,
% 289.53/182.01 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s4)),
% 289.53/182.01 inference(unit_resolution,[status(thm)],[3384, 3378])).
% 289.53/182.01 tff(3386,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_k, s4)), introduced(assumption)).
% 289.53/182.01 tff(3387,assumption,(node20(c_e_h_3, c_k, s4)), introduced(assumption)).
% 289.53/182.01 tff(3388,plain,
% 289.53/182.01 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_k, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_k, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s4))),
% 289.53/182.01 inference(rewrite,[status(thm)],[])).
% 289.53/182.01 tff(3389,plain,
% 289.53/182.01 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_k, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s4))),
% 289.53/182.01 inference(quant_inst,[status(thm)],[])).
% 289.53/182.01 tff(3390,plain,
% 289.53/182.01 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_k, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s4)),
% 289.53/182.01 inference(modus_ponens,[status(thm)],[3389, 3388])).
% 289.53/182.01 tff(3391,plain,
% 289.53/182.01 ($false),
% 289.53/182.01 inference(unit_resolution,[status(thm)],[3390, 38, 3387, 3386])).
% 289.53/182.01 tff(3392,plain,((~node20(c_e_h_3, c_k, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s4)), inference(lemma,lemma(discharge,[]))).
% 289.53/182.01 tff(3393,plain,
% 289.53/182.01 (~node20(c_e_h_3, c_k, s4)),
% 289.53/182.01 inference(unit_resolution,[status(thm)],[3392, 3385])).
% 289.53/182.01 tff(3394,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_k, s3)), introduced(assumption)).
% 289.53/182.01 tff(3395,plain,
% 289.53/182.01 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_k, s3)) | m_or_h_gate_v_out(c_e_h_3, c_g, s3))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s3)) | m_or_h_gate_v_out(c_e_h_3, c_g, s3))),
% 289.53/182.01 inference(rewrite,[status(thm)],[])).
% 289.53/182.01 tff(3396,plain,
% 289.53/182.01 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_k, s3)) | m_or_h_gate_v_out(c_e_h_3, c_g, s3))),
% 289.53/182.01 inference(quant_inst,[status(thm)],[])).
% 289.53/182.01 tff(3397,plain,
% 289.53/182.01 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s3)) | m_or_h_gate_v_out(c_e_h_3, c_g, s3)),
% 289.53/182.01 inference(modus_ponens,[status(thm)],[3396, 3395])).
% 289.53/182.01 tff(3398,plain,
% 289.53/182.01 ($false),
% 289.53/182.01 inference(unit_resolution,[status(thm)],[3397, 2048, 3320, 3394])).
% 289.53/182.01 tff(3399,plain,((~m_and_h_gate_v_in1(c_e_h_3, c_k, s3)) | m_or_h_gate_v_out(c_e_h_3, c_g, s3)), inference(lemma,lemma(discharge,[]))).
% 289.53/182.01 tff(3400,plain,
% 289.53/182.01 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s3)),
% 289.53/182.01 inference(unit_resolution,[status(thm)],[3399, 3006])).
% 289.53/182.01 tff(3401,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_k, s3)), introduced(assumption)).
% 289.53/182.01 tff(3402,assumption,(node20(c_e_h_3, c_k, s3)), introduced(assumption)).
% 289.53/182.01 tff(3403,plain,
% 289.53/182.01 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_k, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_k, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s3))),
% 289.53/182.01 inference(rewrite,[status(thm)],[])).
% 289.53/182.01 tff(3404,plain,
% 289.53/182.01 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_k, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s3))),
% 289.53/182.01 inference(quant_inst,[status(thm)],[])).
% 289.53/182.01 tff(3405,plain,
% 289.53/182.01 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_k, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s3)),
% 289.53/182.01 inference(modus_ponens,[status(thm)],[3404, 3403])).
% 289.53/182.01 tff(3406,plain,
% 289.53/182.01 ($false),
% 289.53/182.01 inference(unit_resolution,[status(thm)],[3405, 38, 3402, 3401])).
% 289.53/182.01 tff(3407,plain,(m_and_h_gate_v_in1(c_e_h_3, c_k, s3) | (~node20(c_e_h_3, c_k, s3))), inference(lemma,lemma(discharge,[]))).
% 289.53/182.01 tff(3408,plain,
% 289.53/182.01 (~node20(c_e_h_3, c_k, s3)),
% 289.53/182.01 inference(unit_resolution,[status(thm)],[3407, 3400])).
% 289.53/182.01 tff(3409,assumption,(m_and_h_gate_v_out(c_e_h_3, c_k, s2)), introduced(assumption)).
% 289.53/182.01 tff(3410,plain,
% 289.53/182.01 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_k, s1)) | m_or_h_gate_v_out(c_e_h_3, c_g, s1))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s1)) | m_or_h_gate_v_out(c_e_h_3, c_g, s1))),
% 289.53/182.01 inference(rewrite,[status(thm)],[])).
% 289.53/182.01 tff(3411,plain,
% 289.53/182.01 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_k, s1)) | m_or_h_gate_v_out(c_e_h_3, c_g, s1))),
% 289.53/182.01 inference(quant_inst,[status(thm)],[])).
% 289.53/182.01 tff(3412,plain,
% 289.53/182.01 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s1)) | m_or_h_gate_v_out(c_e_h_3, c_g, s1)),
% 289.53/182.01 inference(modus_ponens,[status(thm)],[3411, 3410])).
% 289.53/182.01 tff(3413,plain,
% 289.53/182.01 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s1)),
% 289.53/182.01 inference(unit_resolution,[status(thm)],[3412, 2048, 2797])).
% 289.53/182.01 tff(3414,plain,
% 289.53/182.01 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_k, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_k, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s1))),
% 289.53/182.01 inference(rewrite,[status(thm)],[])).
% 289.53/182.01 tff(3415,plain,
% 289.53/182.01 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_k, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s1))),
% 289.53/182.01 inference(quant_inst,[status(thm)],[])).
% 289.53/182.01 tff(3416,plain,
% 289.53/182.01 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_k, s1)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s1)),
% 289.53/182.01 inference(modus_ponens,[status(thm)],[3415, 3414])).
% 289.53/182.01 tff(3417,plain,
% 289.53/182.01 (~node20(c_e_h_3, c_k, s1)),
% 289.53/182.01 inference(unit_resolution,[status(thm)],[3416, 38, 3413])).
% 289.53/182.01 tff(3418,assumption,(node22(c_e_h_3, c_k, s1, s2)), introduced(assumption)).
% 289.53/182.01 tff(3419,plain,
% 289.53/182.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s2)) | (~node22(c_e_h_3, c_k, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_k, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s2)) | (~node22(c_e_h_3, c_k, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_k, s1))),
% 289.53/182.01 inference(rewrite,[status(thm)],[])).
% 289.53/182.01 tff(3420,plain,
% 289.53/182.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s2)) | (~node22(c_e_h_3, c_k, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_k, s1))),
% 289.53/182.01 inference(quant_inst,[status(thm)],[])).
% 289.53/182.01 tff(3421,plain,
% 289.53/182.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s2)) | (~node22(c_e_h_3, c_k, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_k, s1)),
% 289.53/182.01 inference(modus_ponens,[status(thm)],[3420, 3419])).
% 289.53/182.01 tff(3422,plain,
% 289.53/182.01 ($false),
% 289.53/182.01 inference(unit_resolution,[status(thm)],[3421, 108, 3418, 2072, 3409])).
% 289.53/182.01 tff(3423,plain,((~node22(c_e_h_3, c_k, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s2))), inference(lemma,lemma(discharge,[]))).
% 289.53/182.01 tff(3424,plain,
% 289.53/182.01 (~node22(c_e_h_3, c_k, s1, s2)),
% 289.53/182.01 inference(unit_resolution,[status(thm)],[3423, 3409])).
% 289.53/182.01 tff(3425,plain,
% 289.53/182.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_3, c_k, s1, s2) | node22(c_e_h_3, c_k, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_3, c_k, s1, s2) | node22(c_e_h_3, c_k, s1, s2))),
% 289.53/182.01 inference(rewrite,[status(thm)],[])).
% 289.53/182.01 tff(3426,plain,
% 289.53/182.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_3, c_k, s1, s2) | node22(c_e_h_3, c_k, s1, s2))),
% 289.53/182.01 inference(quant_inst,[status(thm)],[])).
% 289.53/182.01 tff(3427,plain,
% 289.53/182.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_3, c_k, s1, s2) | node22(c_e_h_3, c_k, s1, s2)),
% 289.53/182.02 inference(modus_ponens,[status(thm)],[3426, 3425])).
% 289.53/182.02 tff(3428,plain,
% 289.53/182.02 (node21(c_e_h_3, c_k, s1, s2) | node22(c_e_h_3, c_k, s1, s2)),
% 289.53/182.02 inference(unit_resolution,[status(thm)],[3427, 82, 255])).
% 289.53/182.02 tff(3429,plain,
% 289.53/182.02 (node21(c_e_h_3, c_k, s1, s2)),
% 289.53/182.02 inference(unit_resolution,[status(thm)],[3428, 3424])).
% 289.53/182.02 tff(3430,plain,
% 289.53/182.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_k, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s2)) | (~node21(c_e_h_3, c_k, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_k, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s2)) | (~node21(c_e_h_3, c_k, s1, s2)))),
% 289.53/182.02 inference(rewrite,[status(thm)],[])).
% 289.53/182.02 tff(3431,plain,
% 289.53/182.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_k, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s2)) | (~node21(c_e_h_3, c_k, s1, s2)))),
% 289.53/182.02 inference(quant_inst,[status(thm)],[])).
% 289.53/182.02 tff(3432,plain,
% 289.53/182.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_k, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s2)) | (~node21(c_e_h_3, c_k, s1, s2))),
% 289.53/182.02 inference(modus_ponens,[status(thm)],[3431, 3430])).
% 289.53/182.02 tff(3433,plain,
% 289.53/182.02 ($false),
% 289.53/182.02 inference(unit_resolution,[status(thm)],[3432, 52, 3429, 3417, 3409])).
% 289.53/182.02 tff(3434,plain,(~m_and_h_gate_v_out(c_e_h_3, c_k, s2)), inference(lemma,lemma(discharge,[]))).
% 289.53/182.02 tff(3435,assumption,(m_and_h_gate_v_out(c_e_h_3, c_k, s3)), introduced(assumption)).
% 289.53/182.02 tff(3436,plain,
% 289.53/182.02 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_k, s2)) | m_or_h_gate_v_out(c_e_h_3, c_g, s2))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s2)) | m_or_h_gate_v_out(c_e_h_3, c_g, s2))),
% 289.53/182.02 inference(rewrite,[status(thm)],[])).
% 289.53/182.02 tff(3437,plain,
% 289.53/182.02 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_k, s2)) | m_or_h_gate_v_out(c_e_h_3, c_g, s2))),
% 289.53/182.02 inference(quant_inst,[status(thm)],[])).
% 289.53/182.02 tff(3438,plain,
% 289.53/182.02 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s2)) | m_or_h_gate_v_out(c_e_h_3, c_g, s2)),
% 289.53/182.02 inference(modus_ponens,[status(thm)],[3437, 3436])).
% 289.53/182.02 tff(3439,plain,
% 289.53/182.02 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s2)),
% 289.53/182.02 inference(unit_resolution,[status(thm)],[3438, 2048, 2873])).
% 289.53/182.02 tff(3440,plain,
% 289.53/182.02 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_k, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_k, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s2))),
% 289.53/182.02 inference(rewrite,[status(thm)],[])).
% 289.53/182.02 tff(3441,plain,
% 289.53/182.02 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_k, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s2))),
% 289.53/182.02 inference(quant_inst,[status(thm)],[])).
% 289.53/182.02 tff(3442,plain,
% 289.53/182.02 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_k, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s2)),
% 289.53/182.02 inference(modus_ponens,[status(thm)],[3441, 3440])).
% 289.53/182.02 tff(3443,plain,
% 289.53/182.02 (~node20(c_e_h_3, c_k, s2)),
% 289.53/182.02 inference(unit_resolution,[status(thm)],[3442, 38, 3439])).
% 289.53/182.02 tff(3444,assumption,(node21(c_e_h_3, c_k, s2, s3)), introduced(assumption)).
% 289.53/182.02 tff(3445,plain,
% 289.53/182.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_k, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s3)) | (~node21(c_e_h_3, c_k, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_k, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s3)) | (~node21(c_e_h_3, c_k, s2, s3)))),
% 289.53/182.02 inference(rewrite,[status(thm)],[])).
% 289.53/182.02 tff(3446,plain,
% 289.53/182.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_k, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s3)) | (~node21(c_e_h_3, c_k, s2, s3)))),
% 289.53/182.02 inference(quant_inst,[status(thm)],[])).
% 289.53/182.02 tff(3447,plain,
% 289.53/182.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_k, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s3)) | (~node21(c_e_h_3, c_k, s2, s3))),
% 289.53/182.02 inference(modus_ponens,[status(thm)],[3446, 3445])).
% 289.53/182.02 tff(3448,plain,
% 289.53/182.02 ($false),
% 289.53/182.02 inference(unit_resolution,[status(thm)],[3447, 52, 3444, 3435, 3443])).
% 289.53/182.02 tff(3449,plain,((~node21(c_e_h_3, c_k, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s3))), inference(lemma,lemma(discharge,[]))).
% 289.53/182.02 tff(3450,plain,
% 289.53/182.02 (~node21(c_e_h_3, c_k, s2, s3)),
% 289.53/182.02 inference(unit_resolution,[status(thm)],[3449, 3435])).
% 289.53/182.02 tff(3451,plain,
% 289.53/182.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_3, c_k, s2, s3) | node22(c_e_h_3, c_k, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_3, c_k, s2, s3) | node22(c_e_h_3, c_k, s2, s3))),
% 289.53/182.02 inference(rewrite,[status(thm)],[])).
% 289.53/182.02 tff(3452,plain,
% 289.53/182.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_3, c_k, s2, s3) | node22(c_e_h_3, c_k, s2, s3))),
% 289.53/182.02 inference(quant_inst,[status(thm)],[])).
% 289.53/182.02 tff(3453,plain,
% 289.53/182.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_3, c_k, s2, s3) | node22(c_e_h_3, c_k, s2, s3)),
% 289.53/182.02 inference(modus_ponens,[status(thm)],[3452, 3451])).
% 289.53/182.02 tff(3454,plain,
% 289.53/182.02 (node21(c_e_h_3, c_k, s2, s3) | node22(c_e_h_3, c_k, s2, s3)),
% 289.53/182.02 inference(unit_resolution,[status(thm)],[3453, 82, 318])).
% 289.53/182.02 tff(3455,plain,
% 289.53/182.02 (node22(c_e_h_3, c_k, s2, s3)),
% 289.53/182.02 inference(unit_resolution,[status(thm)],[3454, 3450])).
% 289.53/182.02 tff(3456,plain,
% 289.53/182.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s3)) | (~node22(c_e_h_3, c_k, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_k, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s3)) | (~node22(c_e_h_3, c_k, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_k, s2))),
% 289.53/182.02 inference(rewrite,[status(thm)],[])).
% 289.53/182.02 tff(3457,plain,
% 289.53/182.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s3)) | (~node22(c_e_h_3, c_k, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_k, s2))),
% 289.53/182.02 inference(quant_inst,[status(thm)],[])).
% 289.53/182.02 tff(3458,plain,
% 289.53/182.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s3)) | (~node22(c_e_h_3, c_k, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_k, s2)),
% 289.53/182.02 inference(modus_ponens,[status(thm)],[3457, 3456])).
% 289.53/182.02 tff(3459,plain,
% 289.53/182.02 ($false),
% 289.53/182.02 inference(unit_resolution,[status(thm)],[3458, 108, 3455, 3435, 3434])).
% 289.53/182.02 tff(3460,plain,(~m_and_h_gate_v_out(c_e_h_3, c_k, s3)), inference(lemma,lemma(discharge,[]))).
% 289.53/182.02 tff(3461,assumption,(m_and_h_gate_v_out(c_e_h_3, c_k, s4)), introduced(assumption)).
% 289.53/182.02 tff(3462,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_k, s3)), introduced(assumption)).
% 289.53/182.02 tff(3463,assumption,(~node20(c_e_h_3, c_k, s3)), introduced(assumption)).
% 289.53/182.03 tff(3464,assumption,(node21(c_e_h_3, c_k, s3, s4)), introduced(assumption)).
% 289.53/182.03 tff(3465,plain,
% 289.53/182.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s4)) | node20(c_e_h_3, c_k, s3) | (~node21(c_e_h_3, c_k, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s4)) | node20(c_e_h_3, c_k, s3) | (~node21(c_e_h_3, c_k, s3, s4)))),
% 289.53/182.03 inference(rewrite,[status(thm)],[])).
% 289.53/182.03 tff(3466,plain,
% 289.53/182.03 ((node20(c_e_h_3, c_k, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s4)) | (~node21(c_e_h_3, c_k, s3, s4))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_k, s4)) | node20(c_e_h_3, c_k, s3) | (~node21(c_e_h_3, c_k, s3, s4)))),
% 289.53/182.03 inference(rewrite,[status(thm)],[])).
% 289.53/182.03 tff(3467,plain,
% 289.53/182.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_k, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s4)) | (~node21(c_e_h_3, c_k, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s4)) | node20(c_e_h_3, c_k, s3) | (~node21(c_e_h_3, c_k, s3, s4))))),
% 289.53/182.03 inference(monotonicity,[status(thm)],[3466])).
% 289.53/182.03 tff(3468,plain,
% 289.53/182.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_k, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s4)) | (~node21(c_e_h_3, c_k, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s4)) | node20(c_e_h_3, c_k, s3) | (~node21(c_e_h_3, c_k, s3, s4)))),
% 289.53/182.03 inference(transitivity,[status(thm)],[3467, 3465])).
% 289.53/182.03 tff(3469,plain,
% 289.53/182.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_k, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s4)) | (~node21(c_e_h_3, c_k, s3, s4)))),
% 289.53/182.03 inference(quant_inst,[status(thm)],[])).
% 289.53/182.03 tff(3470,plain,
% 289.53/182.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s4)) | node20(c_e_h_3, c_k, s3) | (~node21(c_e_h_3, c_k, s3, s4))),
% 289.53/182.03 inference(modus_ponens,[status(thm)],[3469, 3468])).
% 289.53/182.03 tff(3471,plain,
% 289.53/182.03 ($false),
% 289.53/182.03 inference(unit_resolution,[status(thm)],[3470, 52, 3464, 3463, 3461])).
% 289.53/182.03 tff(3472,plain,((~node21(c_e_h_3, c_k, s3, s4)) | node20(c_e_h_3, c_k, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s4))), inference(lemma,lemma(discharge,[]))).
% 289.53/182.03 tff(3473,plain,
% 289.53/182.03 (~node21(c_e_h_3, c_k, s3, s4)),
% 289.53/182.03 inference(unit_resolution,[status(thm)],[3472, 3461, 3463])).
% 289.53/182.03 tff(3474,plain,
% 289.53/182.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_3, c_k, s3, s4) | node22(c_e_h_3, c_k, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_3, c_k, s3, s4) | node22(c_e_h_3, c_k, s3, s4))),
% 289.53/182.03 inference(rewrite,[status(thm)],[])).
% 289.53/182.03 tff(3475,plain,
% 289.53/182.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_3, c_k, s3, s4) | node22(c_e_h_3, c_k, s3, s4))),
% 289.53/182.03 inference(quant_inst,[status(thm)],[])).
% 289.53/182.03 tff(3476,plain,
% 289.53/182.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_3, c_k, s3, s4) | node22(c_e_h_3, c_k, s3, s4)),
% 289.53/182.03 inference(modus_ponens,[status(thm)],[3475, 3474])).
% 289.53/182.03 tff(3477,plain,
% 289.53/182.03 (node21(c_e_h_3, c_k, s3, s4) | node22(c_e_h_3, c_k, s3, s4)),
% 289.53/182.03 inference(unit_resolution,[status(thm)],[3476, 82, 531])).
% 289.53/182.03 tff(3478,plain,
% 289.53/182.03 (node22(c_e_h_3, c_k, s3, s4)),
% 289.53/182.03 inference(unit_resolution,[status(thm)],[3477, 3473])).
% 289.53/182.03 tff(3479,plain,
% 289.53/182.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s4)) | (~node22(c_e_h_3, c_k, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_k, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s4)) | (~node22(c_e_h_3, c_k, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_k, s3))),
% 289.53/182.03 inference(rewrite,[status(thm)],[])).
% 289.53/182.03 tff(3480,plain,
% 289.53/182.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s4)) | (~node22(c_e_h_3, c_k, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_k, s3))),
% 289.53/182.03 inference(quant_inst,[status(thm)],[])).
% 289.53/182.03 tff(3481,plain,
% 289.53/182.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s4)) | (~node22(c_e_h_3, c_k, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_k, s3)),
% 289.53/182.03 inference(modus_ponens,[status(thm)],[3480, 3479])).
% 289.53/182.03 tff(3482,plain,
% 289.53/182.03 ($false),
% 289.53/182.03 inference(unit_resolution,[status(thm)],[3481, 108, 3478, 3462, 3461])).
% 289.53/182.03 tff(3483,plain,((~m_and_h_gate_v_out(c_e_h_3, c_k, s4)) | m_and_h_gate_v_out(c_e_h_3, c_k, s3) | node20(c_e_h_3, c_k, s3)), inference(lemma,lemma(discharge,[]))).
% 289.53/182.03 tff(3484,plain,
% 289.53/182.03 ((~m_and_h_gate_v_out(c_e_h_3, c_k, s4)) | node20(c_e_h_3, c_k, s3)),
% 289.53/182.03 inference(unit_resolution,[status(thm)],[3483, 3460])).
% 289.53/182.03 tff(3485,plain,
% 289.53/182.03 (~m_and_h_gate_v_out(c_e_h_3, c_k, s4)),
% 289.53/182.03 inference(unit_resolution,[status(thm)],[3484, 3408])).
% 289.53/182.03 tff(3486,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_k, s4)), introduced(assumption)).
% 289.53/182.03 tff(3487,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_l, s4)), introduced(assumption)).
% 289.53/182.03 tff(3488,plain,
% 289.53/182.03 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_l, s4)) | m_and_h_gate_v_out(c_e_h_3, c_k, s4))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s4)) | m_and_h_gate_v_out(c_e_h_3, c_k, s4))),
% 289.53/182.03 inference(rewrite,[status(thm)],[])).
% 289.53/182.03 tff(3489,plain,
% 289.53/182.03 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_l, s4)) | m_and_h_gate_v_out(c_e_h_3, c_k, s4))),
% 289.53/182.03 inference(quant_inst,[status(thm)],[])).
% 289.53/182.03 tff(3490,plain,
% 289.53/182.03 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s4)) | m_and_h_gate_v_out(c_e_h_3, c_k, s4)),
% 289.53/182.03 inference(modus_ponens,[status(thm)],[3489, 3488])).
% 289.53/182.03 tff(3491,plain,
% 289.53/182.03 ($false),
% 289.53/182.03 inference(unit_resolution,[status(thm)],[3490, 1529, 3486, 3487])).
% 289.53/182.03 tff(3492,plain,((~m_and_h_gate_v_in1(c_e_h_3, c_l, s4)) | m_and_h_gate_v_out(c_e_h_3, c_k, s4)), inference(lemma,lemma(discharge,[]))).
% 289.53/182.03 tff(3493,plain,
% 289.53/182.03 (~m_and_h_gate_v_in1(c_e_h_3, c_l, s4)),
% 289.53/182.03 inference(unit_resolution,[status(thm)],[3492, 3486])).
% 289.53/182.03 tff(3494,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_l, s4)), introduced(assumption)).
% 289.53/182.03 tff(3495,assumption,(node20(c_e_h_3, c_l, s4)), introduced(assumption)).
% 289.53/182.03 tff(3496,plain,
% 289.53/182.03 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_l, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_l, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s4))),
% 289.53/182.03 inference(rewrite,[status(thm)],[])).
% 289.53/182.03 tff(3497,plain,
% 289.53/182.03 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_l, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s4))),
% 289.53/182.03 inference(quant_inst,[status(thm)],[])).
% 289.53/182.03 tff(3498,plain,
% 289.53/182.03 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_l, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s4)),
% 289.53/182.03 inference(modus_ponens,[status(thm)],[3497, 3496])).
% 289.53/182.03 tff(3499,plain,
% 289.53/182.03 ($false),
% 289.53/182.03 inference(unit_resolution,[status(thm)],[3498, 38, 3495, 3494])).
% 289.53/182.03 tff(3500,plain,((~node20(c_e_h_3, c_l, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s4)), inference(lemma,lemma(discharge,[]))).
% 289.53/182.03 tff(3501,plain,
% 289.53/182.03 (~node20(c_e_h_3, c_l, s4)),
% 289.53/182.03 inference(unit_resolution,[status(thm)],[3500, 3493])).
% 289.53/182.03 tff(3502,assumption,(m_and_h_gate_v_out(c_e_h_3, c_l, s5)), introduced(assumption)).
% 289.53/182.03 tff(3503,assumption,(m_and_h_gate_v_out(c_e_h_3, c_l, s3)), introduced(assumption)).
% 289.53/182.03 tff(3504,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_l, s2)), introduced(assumption)).
% 289.53/182.03 tff(3505,assumption,(node22(c_e_h_3, c_l, s2, s3)), introduced(assumption)).
% 289.53/182.03 tff(3506,plain,
% 289.53/182.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s3)) | (~node22(c_e_h_3, c_l, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_l, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s3)) | (~node22(c_e_h_3, c_l, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_l, s2))),
% 289.53/182.03 inference(rewrite,[status(thm)],[])).
% 289.53/182.03 tff(3507,plain,
% 289.53/182.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s3)) | (~node22(c_e_h_3, c_l, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_l, s2))),
% 289.53/182.03 inference(quant_inst,[status(thm)],[])).
% 289.53/182.03 tff(3508,plain,
% 289.53/182.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s3)) | (~node22(c_e_h_3, c_l, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_l, s2)),
% 289.53/182.03 inference(modus_ponens,[status(thm)],[3507, 3506])).
% 289.53/182.03 tff(3509,plain,
% 289.53/182.03 ($false),
% 289.53/182.03 inference(unit_resolution,[status(thm)],[3508, 108, 3505, 3503, 3504])).
% 289.53/182.03 tff(3510,plain,((~node22(c_e_h_3, c_l, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s3)) | m_and_h_gate_v_out(c_e_h_3, c_l, s2)), inference(lemma,lemma(discharge,[]))).
% 289.53/182.03 tff(3511,plain,
% 289.53/182.03 ((~node22(c_e_h_3, c_l, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s3))),
% 289.53/182.03 inference(unit_resolution,[status(thm)],[3510, 2098])).
% 289.53/182.03 tff(3512,plain,
% 289.53/182.03 (~node22(c_e_h_3, c_l, s2, s3)),
% 289.53/182.03 inference(unit_resolution,[status(thm)],[3511, 3503])).
% 289.53/182.03 tff(3513,plain,
% 289.53/182.03 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_l, s2)) | m_and_h_gate_v_out(c_e_h_3, c_k, s2))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s2)) | m_and_h_gate_v_out(c_e_h_3, c_k, s2))),
% 289.53/182.03 inference(rewrite,[status(thm)],[])).
% 289.53/182.03 tff(3514,plain,
% 289.53/182.03 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_l, s2)) | m_and_h_gate_v_out(c_e_h_3, c_k, s2))),
% 289.53/182.03 inference(quant_inst,[status(thm)],[])).
% 289.53/182.03 tff(3515,plain,
% 289.53/182.03 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s2)) | m_and_h_gate_v_out(c_e_h_3, c_k, s2)),
% 289.53/182.03 inference(modus_ponens,[status(thm)],[3514, 3513])).
% 289.53/182.03 tff(3516,plain,
% 289.53/182.03 (~m_and_h_gate_v_in1(c_e_h_3, c_l, s2)),
% 289.53/182.03 inference(unit_resolution,[status(thm)],[3515, 1529, 3434])).
% 289.53/182.03 tff(3517,plain,
% 289.53/182.03 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_l, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_l, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s2))),
% 289.53/182.03 inference(rewrite,[status(thm)],[])).
% 289.53/182.03 tff(3518,plain,
% 289.53/182.03 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_l, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s2))),
% 289.53/182.04 inference(quant_inst,[status(thm)],[])).
% 289.53/182.04 tff(3519,plain,
% 289.53/182.04 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_l, s2)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s2)),
% 289.53/182.04 inference(modus_ponens,[status(thm)],[3518, 3517])).
% 289.53/182.04 tff(3520,plain,
% 289.53/182.04 (~node20(c_e_h_3, c_l, s2)),
% 289.53/182.04 inference(unit_resolution,[status(thm)],[3519, 38, 3516])).
% 289.53/182.04 tff(3521,assumption,(~node20(c_e_h_3, c_l, s2)), introduced(assumption)).
% 289.53/182.04 tff(3522,assumption,(node21(c_e_h_3, c_l, s2, s3)), introduced(assumption)).
% 289.53/182.04 tff(3523,plain,
% 289.53/182.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s3)) | node20(c_e_h_3, c_l, s2) | (~node21(c_e_h_3, c_l, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s3)) | node20(c_e_h_3, c_l, s2) | (~node21(c_e_h_3, c_l, s2, s3)))),
% 289.53/182.04 inference(rewrite,[status(thm)],[])).
% 289.53/182.04 tff(3524,plain,
% 289.53/182.04 ((node20(c_e_h_3, c_l, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s3)) | (~node21(c_e_h_3, c_l, s2, s3))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_l, s3)) | node20(c_e_h_3, c_l, s2) | (~node21(c_e_h_3, c_l, s2, s3)))),
% 289.53/182.04 inference(rewrite,[status(thm)],[])).
% 289.53/182.04 tff(3525,plain,
% 289.53/182.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s3)) | (~node21(c_e_h_3, c_l, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s3)) | node20(c_e_h_3, c_l, s2) | (~node21(c_e_h_3, c_l, s2, s3))))),
% 289.53/182.04 inference(monotonicity,[status(thm)],[3524])).
% 289.53/182.04 tff(3526,plain,
% 289.53/182.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s3)) | (~node21(c_e_h_3, c_l, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s3)) | node20(c_e_h_3, c_l, s2) | (~node21(c_e_h_3, c_l, s2, s3)))),
% 289.53/182.04 inference(transitivity,[status(thm)],[3525, 3523])).
% 289.53/182.04 tff(3527,plain,
% 289.53/182.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s3)) | (~node21(c_e_h_3, c_l, s2, s3)))),
% 289.53/182.04 inference(quant_inst,[status(thm)],[])).
% 289.53/182.04 tff(3528,plain,
% 289.53/182.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s3)) | node20(c_e_h_3, c_l, s2) | (~node21(c_e_h_3, c_l, s2, s3))),
% 289.53/182.04 inference(modus_ponens,[status(thm)],[3527, 3526])).
% 289.53/182.04 tff(3529,plain,
% 289.53/182.04 ($false),
% 289.53/182.04 inference(unit_resolution,[status(thm)],[3528, 52, 3522, 3503, 3521])).
% 289.53/182.04 tff(3530,plain,((~node21(c_e_h_3, c_l, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s3)) | node20(c_e_h_3, c_l, s2)), inference(lemma,lemma(discharge,[]))).
% 289.53/182.04 tff(3531,plain,
% 289.53/182.04 (~node21(c_e_h_3, c_l, s2, s3)),
% 289.53/182.04 inference(unit_resolution,[status(thm)],[3530, 3503, 3520])).
% 289.53/182.04 tff(3532,plain,
% 289.53/182.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_3, c_l, s2, s3) | node22(c_e_h_3, c_l, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_3, c_l, s2, s3) | node22(c_e_h_3, c_l, s2, s3))),
% 289.53/182.04 inference(rewrite,[status(thm)],[])).
% 289.53/182.04 tff(3533,plain,
% 289.53/182.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_3, c_l, s2, s3) | node22(c_e_h_3, c_l, s2, s3))),
% 289.53/182.04 inference(quant_inst,[status(thm)],[])).
% 289.53/182.04 tff(3534,plain,
% 289.53/182.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_3, c_l, s2, s3) | node22(c_e_h_3, c_l, s2, s3)),
% 289.53/182.04 inference(modus_ponens,[status(thm)],[3533, 3532])).
% 289.53/182.04 tff(3535,plain,
% 289.53/182.04 (node21(c_e_h_3, c_l, s2, s3) | node22(c_e_h_3, c_l, s2, s3)),
% 289.53/182.04 inference(unit_resolution,[status(thm)],[3534, 82, 318])).
% 289.53/182.04 tff(3536,plain,
% 289.53/182.04 ($false),
% 289.53/182.04 inference(unit_resolution,[status(thm)],[3535, 3531, 3512])).
% 289.53/182.04 tff(3537,plain,(~m_and_h_gate_v_out(c_e_h_3, c_l, s3)), inference(lemma,lemma(discharge,[]))).
% 289.53/182.04 tff(3538,plain,
% 289.53/182.04 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_l, s3)) | m_and_h_gate_v_out(c_e_h_3, c_k, s3))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s3)) | m_and_h_gate_v_out(c_e_h_3, c_k, s3))),
% 289.53/182.04 inference(rewrite,[status(thm)],[])).
% 289.53/182.04 tff(3539,plain,
% 289.53/182.04 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_l, s3)) | m_and_h_gate_v_out(c_e_h_3, c_k, s3))),
% 289.53/182.04 inference(quant_inst,[status(thm)],[])).
% 289.53/182.04 tff(3540,plain,
% 289.53/182.04 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s3)) | m_and_h_gate_v_out(c_e_h_3, c_k, s3)),
% 289.53/182.04 inference(modus_ponens,[status(thm)],[3539, 3538])).
% 289.53/182.04 tff(3541,plain,
% 289.53/182.04 (~m_and_h_gate_v_in1(c_e_h_3, c_l, s3)),
% 289.53/182.04 inference(unit_resolution,[status(thm)],[3540, 1529, 3460])).
% 289.53/182.04 tff(3542,plain,
% 289.53/182.04 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_l, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_l, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s3))),
% 289.53/182.04 inference(rewrite,[status(thm)],[])).
% 289.53/182.04 tff(3543,plain,
% 289.53/182.04 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_l, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s3))),
% 289.53/182.04 inference(quant_inst,[status(thm)],[])).
% 289.53/182.04 tff(3544,plain,
% 289.53/182.04 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_l, s3)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s3)),
% 289.53/182.04 inference(modus_ponens,[status(thm)],[3543, 3542])).
% 289.53/182.04 tff(3545,plain,
% 289.53/182.04 (~node20(c_e_h_3, c_l, s3)),
% 289.53/182.04 inference(unit_resolution,[status(thm)],[3544, 38, 3541])).
% 289.53/182.04 tff(3546,assumption,(~node20(c_e_h_3, c_l, s3)), introduced(assumption)).
% 289.53/182.04 tff(3547,assumption,(m_and_h_gate_v_out(c_e_h_3, c_l, s4)), introduced(assumption)).
% 289.53/182.04 tff(3548,assumption,(node21(c_e_h_3, c_l, s3, s4)), introduced(assumption)).
% 289.53/182.04 tff(3549,plain,
% 289.53/182.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s3) | (~node21(c_e_h_3, c_l, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_l, s3) | (~node21(c_e_h_3, c_l, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s4)))),
% 289.53/182.04 inference(rewrite,[status(thm)],[])).
% 289.53/182.04 tff(3550,plain,
% 289.53/182.04 ((node20(c_e_h_3, c_l, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s4)) | (~node21(c_e_h_3, c_l, s3, s4))) <=> (node20(c_e_h_3, c_l, s3) | (~node21(c_e_h_3, c_l, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s4)))),
% 289.53/182.04 inference(rewrite,[status(thm)],[])).
% 289.53/182.04 tff(3551,plain,
% 289.53/182.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s4)) | (~node21(c_e_h_3, c_l, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s3) | (~node21(c_e_h_3, c_l, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s4))))),
% 289.53/182.04 inference(monotonicity,[status(thm)],[3550])).
% 289.53/182.04 tff(3552,plain,
% 289.53/182.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s4)) | (~node21(c_e_h_3, c_l, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_l, s3) | (~node21(c_e_h_3, c_l, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s4)))),
% 289.53/182.04 inference(transitivity,[status(thm)],[3551, 3549])).
% 289.53/182.04 tff(3553,plain,
% 289.53/182.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s4)) | (~node21(c_e_h_3, c_l, s3, s4)))),
% 289.53/182.04 inference(quant_inst,[status(thm)],[])).
% 289.53/182.04 tff(3554,plain,
% 289.53/182.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_l, s3) | (~node21(c_e_h_3, c_l, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s4))),
% 289.53/182.04 inference(modus_ponens,[status(thm)],[3553, 3552])).
% 289.53/182.04 tff(3555,plain,
% 289.53/182.04 ($false),
% 289.53/182.04 inference(unit_resolution,[status(thm)],[3554, 52, 3548, 3546, 3547])).
% 289.53/182.04 tff(3556,plain,((~node21(c_e_h_3, c_l, s3, s4)) | node20(c_e_h_3, c_l, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s4))), inference(lemma,lemma(discharge,[]))).
% 289.53/182.04 tff(3557,plain,
% 289.53/182.04 (~node21(c_e_h_3, c_l, s3, s4)),
% 289.53/182.04 inference(unit_resolution,[status(thm)],[3556, 3547, 3546])).
% 289.53/182.04 tff(3558,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_l, s3)), introduced(assumption)).
% 289.53/182.04 tff(3559,assumption,(node22(c_e_h_3, c_l, s3, s4)), introduced(assumption)).
% 289.53/182.04 tff(3560,plain,
% 289.53/182.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s4)) | (~node22(c_e_h_3, c_l, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_l, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s4)) | (~node22(c_e_h_3, c_l, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_l, s3))),
% 289.53/182.04 inference(rewrite,[status(thm)],[])).
% 289.53/182.04 tff(3561,plain,
% 289.53/182.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s4)) | (~node22(c_e_h_3, c_l, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_l, s3))),
% 289.53/182.04 inference(quant_inst,[status(thm)],[])).
% 289.53/182.04 tff(3562,plain,
% 289.53/182.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s4)) | (~node22(c_e_h_3, c_l, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_l, s3)),
% 289.53/182.04 inference(modus_ponens,[status(thm)],[3561, 3560])).
% 289.53/182.04 tff(3563,plain,
% 289.53/182.04 ($false),
% 289.53/182.04 inference(unit_resolution,[status(thm)],[3562, 108, 3559, 3558, 3547])).
% 289.53/182.04 tff(3564,plain,((~node22(c_e_h_3, c_l, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_l, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s4))), inference(lemma,lemma(discharge,[]))).
% 289.53/182.04 tff(3565,plain,
% 289.53/182.04 (~node22(c_e_h_3, c_l, s3, s4)),
% 289.53/182.04 inference(unit_resolution,[status(thm)],[3564, 3547, 3558])).
% 289.53/182.04 tff(3566,plain,
% 289.53/182.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_3, c_l, s3, s4) | node22(c_e_h_3, c_l, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_3, c_l, s3, s4) | node22(c_e_h_3, c_l, s3, s4))),
% 289.53/182.04 inference(rewrite,[status(thm)],[])).
% 289.53/182.04 tff(3567,plain,
% 289.53/182.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_3, c_l, s3, s4) | node22(c_e_h_3, c_l, s3, s4))),
% 289.53/182.04 inference(quant_inst,[status(thm)],[])).
% 289.53/182.04 tff(3568,plain,
% 289.53/182.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_3, c_l, s3, s4) | node22(c_e_h_3, c_l, s3, s4)),
% 289.53/182.05 inference(modus_ponens,[status(thm)],[3567, 3566])).
% 289.53/182.05 tff(3569,plain,
% 289.53/182.05 (node21(c_e_h_3, c_l, s3, s4) | node22(c_e_h_3, c_l, s3, s4)),
% 289.53/182.05 inference(unit_resolution,[status(thm)],[3568, 82, 531])).
% 289.53/182.05 tff(3570,plain,
% 289.53/182.05 ($false),
% 289.53/182.05 inference(unit_resolution,[status(thm)],[3569, 3565, 3557])).
% 289.53/182.05 tff(3571,plain,((~m_and_h_gate_v_out(c_e_h_3, c_l, s4)) | m_and_h_gate_v_out(c_e_h_3, c_l, s3) | node20(c_e_h_3, c_l, s3)), inference(lemma,lemma(discharge,[]))).
% 289.53/182.05 tff(3572,plain,
% 289.53/182.05 (~m_and_h_gate_v_out(c_e_h_3, c_l, s4)),
% 289.53/182.05 inference(unit_resolution,[status(thm)],[3571, 3545, 3537])).
% 289.53/182.05 tff(3573,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_l, s4)), introduced(assumption)).
% 289.53/182.05 tff(3574,assumption,(node22(c_e_h_3, c_l, s4, s5)), introduced(assumption)).
% 289.53/182.05 tff(3575,plain,
% 289.53/182.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s5)) | (~node22(c_e_h_3, c_l, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_l, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s5)) | (~node22(c_e_h_3, c_l, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_l, s4))),
% 289.53/182.05 inference(rewrite,[status(thm)],[])).
% 289.53/182.05 tff(3576,plain,
% 289.53/182.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s5)) | (~node22(c_e_h_3, c_l, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_l, s4))),
% 289.53/182.05 inference(quant_inst,[status(thm)],[])).
% 289.53/182.05 tff(3577,plain,
% 289.53/182.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s5)) | (~node22(c_e_h_3, c_l, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_l, s4)),
% 289.53/182.05 inference(modus_ponens,[status(thm)],[3576, 3575])).
% 289.53/182.05 tff(3578,plain,
% 289.53/182.05 ($false),
% 289.53/182.05 inference(unit_resolution,[status(thm)],[3577, 108, 3574, 3573, 3502])).
% 289.53/182.05 tff(3579,plain,((~node22(c_e_h_3, c_l, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_l, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s5))), inference(lemma,lemma(discharge,[]))).
% 289.53/182.05 tff(3580,plain,
% 289.53/182.05 ((~node22(c_e_h_3, c_l, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s5))),
% 289.53/182.05 inference(unit_resolution,[status(thm)],[3579, 3572])).
% 289.53/182.05 tff(3581,plain,
% 289.53/182.05 (~node22(c_e_h_3, c_l, s4, s5)),
% 289.53/182.05 inference(unit_resolution,[status(thm)],[3580, 3502])).
% 289.53/182.05 tff(3582,assumption,(~node20(c_e_h_3, c_l, s4)), introduced(assumption)).
% 289.53/182.05 tff(3583,assumption,(node21(c_e_h_3, c_l, s4, s5)), introduced(assumption)).
% 289.53/182.05 tff(3584,plain,
% 289.53/182.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s4) | (~node21(c_e_h_3, c_l, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_l, s4) | (~node21(c_e_h_3, c_l, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s5)))),
% 289.53/182.05 inference(rewrite,[status(thm)],[])).
% 289.53/182.05 tff(3585,plain,
% 289.53/182.05 ((node20(c_e_h_3, c_l, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s5)) | (~node21(c_e_h_3, c_l, s4, s5))) <=> (node20(c_e_h_3, c_l, s4) | (~node21(c_e_h_3, c_l, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s5)))),
% 289.53/182.05 inference(rewrite,[status(thm)],[])).
% 289.53/182.05 tff(3586,plain,
% 289.53/182.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s5)) | (~node21(c_e_h_3, c_l, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s4) | (~node21(c_e_h_3, c_l, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s5))))),
% 289.53/182.05 inference(monotonicity,[status(thm)],[3585])).
% 289.53/182.05 tff(3587,plain,
% 289.53/182.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s5)) | (~node21(c_e_h_3, c_l, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_l, s4) | (~node21(c_e_h_3, c_l, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s5)))),
% 289.53/182.05 inference(transitivity,[status(thm)],[3586, 3584])).
% 289.53/182.05 tff(3588,plain,
% 289.53/182.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s5)) | (~node21(c_e_h_3, c_l, s4, s5)))),
% 289.53/182.05 inference(quant_inst,[status(thm)],[])).
% 289.53/182.05 tff(3589,plain,
% 289.53/182.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_l, s4) | (~node21(c_e_h_3, c_l, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s5))),
% 289.53/182.05 inference(modus_ponens,[status(thm)],[3588, 3587])).
% 289.53/182.05 tff(3590,plain,
% 289.53/182.05 ($false),
% 289.53/182.05 inference(unit_resolution,[status(thm)],[3589, 52, 3583, 3502, 3582])).
% 289.53/182.05 tff(3591,plain,((~node21(c_e_h_3, c_l, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s5)) | node20(c_e_h_3, c_l, s4)), inference(lemma,lemma(discharge,[]))).
% 289.53/182.05 tff(3592,plain,
% 289.53/182.05 (~node21(c_e_h_3, c_l, s4, s5)),
% 289.53/182.05 inference(unit_resolution,[status(thm)],[3591, 3502, 3582])).
% 289.53/182.05 tff(3593,plain,
% 289.53/182.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_3, c_l, s4, s5) | node22(c_e_h_3, c_l, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_3, c_l, s4, s5) | node22(c_e_h_3, c_l, s4, s5))),
% 289.53/182.05 inference(rewrite,[status(thm)],[])).
% 289.53/182.05 tff(3594,plain,
% 289.53/182.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_3, c_l, s4, s5) | node22(c_e_h_3, c_l, s4, s5))),
% 289.53/182.05 inference(quant_inst,[status(thm)],[])).
% 289.53/182.05 tff(3595,plain,
% 289.53/182.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_3, c_l, s4, s5) | node22(c_e_h_3, c_l, s4, s5)),
% 289.53/182.05 inference(modus_ponens,[status(thm)],[3594, 3593])).
% 289.53/182.05 tff(3596,plain,
% 289.53/182.05 (node21(c_e_h_3, c_l, s4, s5) | node22(c_e_h_3, c_l, s4, s5)),
% 289.53/182.05 inference(unit_resolution,[status(thm)],[3595, 82, 1028])).
% 289.53/182.05 tff(3597,plain,
% 289.53/182.05 ($false),
% 289.53/182.05 inference(unit_resolution,[status(thm)],[3596, 3592, 3581])).
% 289.53/182.05 tff(3598,plain,((~m_and_h_gate_v_out(c_e_h_3, c_l, s5)) | node20(c_e_h_3, c_l, s4)), inference(lemma,lemma(discharge,[]))).
% 289.53/182.05 tff(3599,plain,
% 289.53/182.05 (~m_and_h_gate_v_out(c_e_h_3, c_l, s5)),
% 289.53/182.05 inference(unit_resolution,[status(thm)],[3598, 3501])).
% 289.53/182.05 tff(3600,assumption,(m_or_h_gate_v_in1(c_e_h_3, c_j, s5)), introduced(assumption)).
% 289.53/182.05 tff(3601,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_l, s5)), introduced(assumption)).
% 289.53/182.05 tff(3602,plain,
% 289.53/182.05 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_j, s5)) | m_and_h_gate_v_out(c_e_h_3, c_l, s5))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s5)) | m_and_h_gate_v_out(c_e_h_3, c_l, s5))),
% 289.53/182.05 inference(rewrite,[status(thm)],[])).
% 289.53/182.05 tff(3603,plain,
% 289.53/182.05 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_j, s5)) | m_and_h_gate_v_out(c_e_h_3, c_l, s5))),
% 289.53/182.05 inference(quant_inst,[status(thm)],[])).
% 289.53/182.05 tff(3604,plain,
% 289.53/182.05 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s5)) | m_and_h_gate_v_out(c_e_h_3, c_l, s5)),
% 289.53/182.05 inference(modus_ponens,[status(thm)],[3603, 3602])).
% 289.53/182.05 tff(3605,plain,
% 289.53/182.05 ($false),
% 289.53/182.05 inference(unit_resolution,[status(thm)],[3604, 1100, 3601, 3600])).
% 289.53/182.05 tff(3606,plain,((~m_or_h_gate_v_in1(c_e_h_3, c_j, s5)) | m_and_h_gate_v_out(c_e_h_3, c_l, s5)), inference(lemma,lemma(discharge,[]))).
% 289.53/182.05 tff(3607,plain,
% 289.53/182.05 (~m_or_h_gate_v_in1(c_e_h_3, c_j, s5)),
% 289.53/182.05 inference(unit_resolution,[status(thm)],[3606, 3599])).
% 289.53/182.05 tff(3608,assumption,(m_or_h_gate_v_out(c_e_h_3, c_j, s6)), introduced(assumption)).
% 289.53/182.05 tff(3609,assumption,(m_or_h_gate_v_in1(c_e_h_3, c_j, s3)), introduced(assumption)).
% 289.53/182.05 tff(3610,plain,
% 289.53/182.05 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_j, s3)) | m_and_h_gate_v_out(c_e_h_3, c_l, s3))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s3)) | m_and_h_gate_v_out(c_e_h_3, c_l, s3))),
% 289.53/182.05 inference(rewrite,[status(thm)],[])).
% 289.53/182.05 tff(3611,plain,
% 289.53/182.05 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_j, s3)) | m_and_h_gate_v_out(c_e_h_3, c_l, s3))),
% 289.53/182.05 inference(quant_inst,[status(thm)],[])).
% 289.53/182.05 tff(3612,plain,
% 289.53/182.05 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s3)) | m_and_h_gate_v_out(c_e_h_3, c_l, s3)),
% 289.53/182.05 inference(modus_ponens,[status(thm)],[3611, 3610])).
% 289.53/182.05 tff(3613,plain,
% 289.53/182.05 ($false),
% 289.53/182.05 inference(unit_resolution,[status(thm)],[3612, 1100, 3558, 3609])).
% 289.53/182.05 tff(3614,plain,((~m_or_h_gate_v_in1(c_e_h_3, c_j, s3)) | m_and_h_gate_v_out(c_e_h_3, c_l, s3)), inference(lemma,lemma(discharge,[]))).
% 289.53/182.05 tff(3615,plain,
% 289.53/182.05 (~m_or_h_gate_v_in1(c_e_h_3, c_j, s3)),
% 289.53/182.05 inference(unit_resolution,[status(thm)],[3614, 3537])).
% 289.53/182.05 tff(3616,assumption,(m_or_h_gate_v_out(c_e_h_3, c_j, s5)), introduced(assumption)).
% 289.53/182.05 tff(3617,assumption,(~m_or_h_gate_v_in1(c_e_h_3, c_j, s3)), introduced(assumption)).
% 289.53/182.05 tff(3618,plain,
% 289.53/182.05 (^[I0: $i, X: $i] : refl(((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X)) <=> ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X)))),
% 289.53/182.05 inference(bind,[status(th)],[])).
% 289.53/182.05 tff(3619,plain,
% 289.53/182.05 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X))),
% 289.53/182.05 inference(quant_intro,[status(thm)],[3618])).
% 289.53/182.05 tff(3620,plain,
% 289.53/182.05 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X))),
% 289.53/182.05 inference(rewrite,[status(thm)],[])).
% 289.53/182.05 tff(3621,plain,
% 289.53/182.05 (^[I0: $i, X: $i] : rewrite((m_or_h_gate_v_in1(I0, c_j, X) | (~m_and_h_gate_v_out(I0, c_l, X))) <=> ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X)))),
% 289.53/182.05 inference(bind,[status(th)],[])).
% 289.53/182.05 tff(3622,plain,
% 289.53/182.05 (![I0: $i, X: $i] : (m_or_h_gate_v_in1(I0, c_j, X) | (~m_and_h_gate_v_out(I0, c_l, X))) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X))),
% 289.53/182.05 inference(quant_intro,[status(thm)],[3621])).
% 289.53/182.05 tff(3623,axiom,(![I0: $i, X: $i] : (m_or_h_gate_v_in1(I0, c_j, X) | (~m_and_h_gate_v_out(I0, c_l, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_39')).
% 289.53/182.05 tff(3624,plain,
% 289.53/182.05 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X))),
% 289.53/182.05 inference(modus_ponens,[status(thm)],[3623, 3622])).
% 289.53/182.05 tff(3625,plain,
% 289.53/182.05 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X))),
% 289.53/182.05 inference(modus_ponens,[status(thm)],[3624, 3620])).
% 289.53/182.05 tff(3626,plain,(
% 289.53/182.05 ![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X))),
% 289.53/182.05 inference(skolemize,[status(sab)],[3625])).
% 289.53/182.05 tff(3627,plain,
% 289.53/182.05 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X))),
% 289.53/182.05 inference(modus_ponens,[status(thm)],[3626, 3619])).
% 289.53/182.05 tff(3628,plain,
% 289.53/182.05 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s3)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s3))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s3)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s3))),
% 289.53/182.06 inference(rewrite,[status(thm)],[])).
% 289.53/182.06 tff(3629,plain,
% 289.53/182.06 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s3)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s3))),
% 289.53/182.06 inference(quant_inst,[status(thm)],[])).
% 289.53/182.06 tff(3630,plain,
% 289.53/182.06 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s3)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s3)),
% 289.53/182.06 inference(modus_ponens,[status(thm)],[3629, 3628])).
% 289.53/182.06 tff(3631,plain,
% 289.53/182.06 ($false),
% 289.53/182.06 inference(unit_resolution,[status(thm)],[3630, 3627, 3503, 3617])).
% 289.53/182.06 tff(3632,plain,((~m_and_h_gate_v_out(c_e_h_3, c_l, s3)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s3)), inference(lemma,lemma(discharge,[]))).
% 289.53/182.06 tff(3633,plain,
% 289.53/182.06 (~m_and_h_gate_v_out(c_e_h_3, c_l, s3)),
% 289.53/182.06 inference(unit_resolution,[status(thm)],[3632, 3617])).
% 289.53/182.06 tff(3634,plain,
% 289.53/182.06 (~m_and_h_gate_v_out(c_e_h_3, c_l, s4)),
% 289.53/182.06 inference(unit_resolution,[status(thm)],[3571, 3633, 3546])).
% 289.53/182.06 tff(3635,assumption,(m_or_h_gate_v_in1(c_e_h_3, c_j, s4)), introduced(assumption)).
% 289.53/182.06 tff(3636,plain,
% 289.53/182.06 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_j, s4)) | m_and_h_gate_v_out(c_e_h_3, c_l, s4))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s4)) | m_and_h_gate_v_out(c_e_h_3, c_l, s4))),
% 289.53/182.06 inference(rewrite,[status(thm)],[])).
% 289.53/182.06 tff(3637,plain,
% 289.53/182.06 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_j, s4)) | m_and_h_gate_v_out(c_e_h_3, c_l, s4))),
% 289.53/182.06 inference(quant_inst,[status(thm)],[])).
% 289.53/182.06 tff(3638,plain,
% 289.53/182.06 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s4)) | m_and_h_gate_v_out(c_e_h_3, c_l, s4)),
% 289.53/182.06 inference(modus_ponens,[status(thm)],[3637, 3636])).
% 289.53/182.06 tff(3639,plain,
% 289.53/182.06 ($false),
% 289.53/182.06 inference(unit_resolution,[status(thm)],[3638, 1100, 3635, 3573])).
% 289.53/182.06 tff(3640,plain,((~m_or_h_gate_v_in1(c_e_h_3, c_j, s4)) | m_and_h_gate_v_out(c_e_h_3, c_l, s4)), inference(lemma,lemma(discharge,[]))).
% 289.53/182.06 tff(3641,plain,
% 289.53/182.06 (~m_or_h_gate_v_in1(c_e_h_3, c_j, s4)),
% 289.53/182.06 inference(unit_resolution,[status(thm)],[3640, 3634])).
% 289.53/182.06 tff(3642,assumption,(m_and_h_gate_v_out(c_e_h_2, c_q, s3)), introduced(assumption)).
% 289.53/182.06 tff(3643,assumption,(m_c_h_element_v_out(c_e_h_2, c_f, s2)), introduced(assumption)).
% 289.53/182.06 tff(3644,assumption,(node18(c_e_h_2, c_f, s1, s2)), introduced(assumption)).
% 289.53/182.06 tff(3645,plain,
% 289.53/182.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s2)) | m_c_h_element_v_out(c_e_h_2, c_f, s1) | (~node18(c_e_h_2, c_f, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s2)) | m_c_h_element_v_out(c_e_h_2, c_f, s1) | (~node18(c_e_h_2, c_f, s1, s2)))),
% 289.53/182.06 inference(rewrite,[status(thm)],[])).
% 289.53/182.06 tff(3646,plain,
% 289.53/182.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s2)) | m_c_h_element_v_out(c_e_h_2, c_f, s1) | (~node18(c_e_h_2, c_f, s1, s2)))),
% 289.53/182.06 inference(quant_inst,[status(thm)],[])).
% 289.53/182.06 tff(3647,plain,
% 289.53/182.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s2)) | m_c_h_element_v_out(c_e_h_2, c_f, s1) | (~node18(c_e_h_2, c_f, s1, s2))),
% 289.53/182.06 inference(modus_ponens,[status(thm)],[3646, 3645])).
% 289.53/182.06 tff(3648,plain,
% 289.53/182.06 ($false),
% 289.53/182.06 inference(unit_resolution,[status(thm)],[3647, 753, 3643, 2167, 3644])).
% 289.53/182.06 tff(3649,plain,((~node18(c_e_h_2, c_f, s1, s2)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s2))), inference(lemma,lemma(discharge,[]))).
% 289.53/182.06 tff(3650,plain,
% 289.53/182.06 (~node18(c_e_h_2, c_f, s1, s2)),
% 289.53/182.06 inference(unit_resolution,[status(thm)],[3649, 3643])).
% 289.53/182.06 tff(3651,plain,
% 289.53/182.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s1, s2)) | node19(c_e_h_2, c_f, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s1, s2)) | node19(c_e_h_2, c_f, s1, s2))),
% 289.53/182.06 inference(rewrite,[status(thm)],[])).
% 289.53/182.06 tff(3652,plain,
% 289.53/182.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s1, s2)) | node19(c_e_h_2, c_f, s1, s2))),
% 289.53/182.06 inference(quant_inst,[status(thm)],[])).
% 289.53/182.06 tff(3653,plain,
% 289.53/182.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s1, s2)) | node19(c_e_h_2, c_f, s1, s2)),
% 289.53/182.06 inference(modus_ponens,[status(thm)],[3652, 3651])).
% 289.53/182.06 tff(3654,plain,
% 289.53/182.06 (node19(c_e_h_2, c_f, s1, s2)),
% 289.53/182.06 inference(unit_resolution,[status(thm)],[3653, 190, 255])).
% 289.53/182.06 tff(3655,plain,
% 289.53/182.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_f, s1, s2)) | node18(c_e_h_2, c_f, s1, s2) | node17(c_e_h_2, c_f, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_f, s1, s2)) | node18(c_e_h_2, c_f, s1, s2) | node17(c_e_h_2, c_f, s1))),
% 289.53/182.06 inference(rewrite,[status(thm)],[])).
% 289.53/182.06 tff(3656,plain,
% 289.53/182.06 ((node17(c_e_h_2, c_f, s1) | node18(c_e_h_2, c_f, s1, s2) | (~node19(c_e_h_2, c_f, s1, s2))) <=> ((~node19(c_e_h_2, c_f, s1, s2)) | node18(c_e_h_2, c_f, s1, s2) | node17(c_e_h_2, c_f, s1))),
% 289.53/182.06 inference(rewrite,[status(thm)],[])).
% 289.53/182.06 tff(3657,plain,
% 289.53/182.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s1) | node18(c_e_h_2, c_f, s1, s2) | (~node19(c_e_h_2, c_f, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_f, s1, s2)) | node18(c_e_h_2, c_f, s1, s2) | node17(c_e_h_2, c_f, s1)))),
% 289.53/182.06 inference(monotonicity,[status(thm)],[3656])).
% 289.53/182.06 tff(3658,plain,
% 289.53/182.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s1) | node18(c_e_h_2, c_f, s1, s2) | (~node19(c_e_h_2, c_f, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_f, s1, s2)) | node18(c_e_h_2, c_f, s1, s2) | node17(c_e_h_2, c_f, s1))),
% 289.53/182.06 inference(transitivity,[status(thm)],[3657, 3655])).
% 289.53/182.06 tff(3659,plain,
% 289.53/182.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s1) | node18(c_e_h_2, c_f, s1, s2) | (~node19(c_e_h_2, c_f, s1, s2)))),
% 289.53/182.06 inference(quant_inst,[status(thm)],[])).
% 289.53/182.06 tff(3660,plain,
% 289.53/182.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_f, s1, s2)) | node18(c_e_h_2, c_f, s1, s2) | node17(c_e_h_2, c_f, s1)),
% 289.53/182.06 inference(modus_ponens,[status(thm)],[3659, 3658])).
% 289.53/182.06 tff(3661,plain,
% 289.53/182.06 (node18(c_e_h_2, c_f, s1, s2) | node17(c_e_h_2, c_f, s1)),
% 289.53/182.06 inference(unit_resolution,[status(thm)],[3660, 776, 3654])).
% 289.53/182.06 tff(3662,plain,
% 289.53/182.06 (node17(c_e_h_2, c_f, s1)),
% 289.53/182.06 inference(unit_resolution,[status(thm)],[3661, 3650])).
% 289.53/182.06 tff(3663,assumption,(node17(c_e_h_2, c_f, s1)), introduced(assumption)).
% 289.53/182.06 tff(3664,assumption,(node16(c_e_h_2, c_f, s1)), introduced(assumption)).
% 289.53/182.06 tff(3665,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_f, s1)), introduced(assumption)).
% 289.53/182.06 tff(3666,plain,
% 289.53/182.06 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_2, c_f, s1) | (~node17(c_e_h_2, c_f, s1)) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_f, s1) | (~node17(c_e_h_2, c_f, s1)) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s1)))),
% 289.53/182.07 inference(rewrite,[status(thm)],[])).
% 289.53/182.07 tff(3667,plain,
% 289.53/182.07 (((~m_c_h_element_v_in1(c_e_h_2, c_f, s1)) | m_c_h_element_v_in2(c_e_h_2, c_f, s1) | (~node17(c_e_h_2, c_f, s1))) <=> (m_c_h_element_v_in2(c_e_h_2, c_f, s1) | (~node17(c_e_h_2, c_f, s1)) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s1)))),
% 289.53/182.07 inference(rewrite,[status(thm)],[])).
% 289.53/182.07 tff(3668,plain,
% 289.53/182.07 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s1)) | m_c_h_element_v_in2(c_e_h_2, c_f, s1) | (~node17(c_e_h_2, c_f, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_2, c_f, s1) | (~node17(c_e_h_2, c_f, s1)) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s1))))),
% 289.53/182.07 inference(monotonicity,[status(thm)],[3667])).
% 289.53/182.07 tff(3669,plain,
% 289.53/182.07 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s1)) | m_c_h_element_v_in2(c_e_h_2, c_f, s1) | (~node17(c_e_h_2, c_f, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_f, s1) | (~node17(c_e_h_2, c_f, s1)) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s1)))),
% 289.53/182.07 inference(transitivity,[status(thm)],[3668, 3666])).
% 289.53/182.07 tff(3670,plain,
% 289.53/182.07 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s1)) | m_c_h_element_v_in2(c_e_h_2, c_f, s1) | (~node17(c_e_h_2, c_f, s1)))),
% 289.53/182.07 inference(quant_inst,[status(thm)],[])).
% 289.53/182.07 tff(3671,plain,
% 289.53/182.07 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_f, s1) | (~node17(c_e_h_2, c_f, s1)) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s1))),
% 289.53/182.07 inference(modus_ponens,[status(thm)],[3670, 3669])).
% 289.53/182.07 tff(3672,plain,
% 289.53/182.07 (m_c_h_element_v_in2(c_e_h_2, c_f, s1) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s1))),
% 289.53/182.07 inference(unit_resolution,[status(thm)],[3671, 919, 3663])).
% 289.53/182.07 tff(3673,plain,
% 289.53/182.07 (~m_c_h_element_v_in1(c_e_h_2, c_f, s1)),
% 289.53/182.07 inference(unit_resolution,[status(thm)],[3672, 3665])).
% 289.53/182.07 tff(3674,plain,
% 289.53/182.07 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_f, s1)) | m_c_h_element_v_in1(c_e_h_2, c_f, s1) | m_c_h_element_v_in2(c_e_h_2, c_f, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_f, s1)) | m_c_h_element_v_in1(c_e_h_2, c_f, s1) | m_c_h_element_v_in2(c_e_h_2, c_f, s1))),
% 289.53/182.07 inference(rewrite,[status(thm)],[])).
% 289.53/182.07 tff(3675,plain,
% 289.53/182.07 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_f, s1)) | m_c_h_element_v_in1(c_e_h_2, c_f, s1) | m_c_h_element_v_in2(c_e_h_2, c_f, s1))),
% 289.53/182.07 inference(quant_inst,[status(thm)],[])).
% 289.53/182.07 tff(3676,plain,
% 289.53/182.07 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_f, s1)) | m_c_h_element_v_in1(c_e_h_2, c_f, s1) | m_c_h_element_v_in2(c_e_h_2, c_f, s1)),
% 289.53/182.07 inference(modus_ponens,[status(thm)],[3675, 3674])).
% 289.53/182.07 tff(3677,plain,
% 289.53/182.07 (m_c_h_element_v_in1(c_e_h_2, c_f, s1) | m_c_h_element_v_in2(c_e_h_2, c_f, s1)),
% 289.53/182.07 inference(unit_resolution,[status(thm)],[3676, 178, 3664])).
% 289.53/182.07 tff(3678,plain,
% 289.53/182.07 ($false),
% 289.53/182.07 inference(unit_resolution,[status(thm)],[3677, 3673, 3665])).
% 289.53/182.07 tff(3679,plain,(m_c_h_element_v_in2(c_e_h_2, c_f, s1) | (~node16(c_e_h_2, c_f, s1)) | (~node17(c_e_h_2, c_f, s1))), inference(lemma,lemma(discharge,[]))).
% 289.53/182.07 tff(3680,plain,
% 289.53/182.07 (m_c_h_element_v_in2(c_e_h_2, c_f, s1)),
% 289.53/182.07 inference(unit_resolution,[status(thm)],[3679, 3664, 3663])).
% 289.53/182.07 tff(3681,plain,
% 289.53/182.07 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_f, s1) | (~node17(c_e_h_2, c_f, s1)) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_f, s1) | (~node17(c_e_h_2, c_f, s1)) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s1)))),
% 289.53/182.07 inference(rewrite,[status(thm)],[])).
% 289.53/182.07 tff(3682,plain,
% 289.53/182.07 ((m_c_h_element_v_in1(c_e_h_2, c_f, s1) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s1)) | (~node17(c_e_h_2, c_f, s1))) <=> (m_c_h_element_v_in1(c_e_h_2, c_f, s1) | (~node17(c_e_h_2, c_f, s1)) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s1)))),
% 289.53/182.07 inference(rewrite,[status(thm)],[])).
% 289.53/182.07 tff(3683,plain,
% 289.53/182.07 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_f, s1) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s1)) | (~node17(c_e_h_2, c_f, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_f, s1) | (~node17(c_e_h_2, c_f, s1)) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s1))))),
% 289.53/182.07 inference(monotonicity,[status(thm)],[3682])).
% 289.53/182.07 tff(3684,plain,
% 289.53/182.07 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_f, s1) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s1)) | (~node17(c_e_h_2, c_f, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_f, s1) | (~node17(c_e_h_2, c_f, s1)) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s1)))),
% 289.53/182.07 inference(transitivity,[status(thm)],[3683, 3681])).
% 289.53/182.07 tff(3685,plain,
% 289.53/182.07 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_f, s1) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s1)) | (~node17(c_e_h_2, c_f, s1)))),
% 289.53/182.07 inference(quant_inst,[status(thm)],[])).
% 289.53/182.07 tff(3686,plain,
% 289.53/182.07 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_f, s1) | (~node17(c_e_h_2, c_f, s1)) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s1))),
% 289.53/182.07 inference(modus_ponens,[status(thm)],[3685, 3684])).
% 289.53/182.07 tff(3687,plain,
% 289.53/182.07 (m_c_h_element_v_in1(c_e_h_2, c_f, s1) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s1))),
% 289.53/182.07 inference(unit_resolution,[status(thm)],[3686, 859, 3663])).
% 289.53/182.07 tff(3688,plain,
% 289.53/182.07 (m_c_h_element_v_in1(c_e_h_2, c_f, s1)),
% 289.53/182.07 inference(unit_resolution,[status(thm)],[3687, 3680])).
% 289.53/182.07 tff(3689,plain,
% 289.53/182.07 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_2, c_f, s1)) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s1)) | (~node16(c_e_h_2, c_f, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s1)) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s1)) | (~node16(c_e_h_2, c_f, s1)))),
% 289.53/182.07 inference(rewrite,[status(thm)],[])).
% 289.53/182.07 tff(3690,plain,
% 289.53/182.07 (((~node16(c_e_h_2, c_f, s1)) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s1)) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s1))) <=> ((~m_c_h_element_v_in2(c_e_h_2, c_f, s1)) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s1)) | (~node16(c_e_h_2, c_f, s1)))),
% 289.53/182.07 inference(rewrite,[status(thm)],[])).
% 289.53/182.07 tff(3691,plain,
% 289.53/182.07 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_2, c_f, s1)) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s1)) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_2, c_f, s1)) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s1)) | (~node16(c_e_h_2, c_f, s1))))),
% 289.53/182.07 inference(monotonicity,[status(thm)],[3690])).
% 289.53/182.07 tff(3692,plain,
% 289.53/182.07 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_2, c_f, s1)) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s1)) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s1)) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s1)) | (~node16(c_e_h_2, c_f, s1)))),
% 289.53/182.07 inference(transitivity,[status(thm)],[3691, 3689])).
% 289.53/182.07 tff(3693,plain,
% 289.53/182.07 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_2, c_f, s1)) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s1)) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s1)))),
% 289.53/182.07 inference(quant_inst,[status(thm)],[])).
% 289.53/182.07 tff(3694,plain,
% 289.53/182.07 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s1)) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s1)) | (~node16(c_e_h_2, c_f, s1))),
% 289.53/182.07 inference(modus_ponens,[status(thm)],[3693, 3692])).
% 289.53/182.07 tff(3695,plain,
% 289.53/182.07 ((~m_c_h_element_v_in2(c_e_h_2, c_f, s1)) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s1))),
% 289.53/182.07 inference(unit_resolution,[status(thm)],[3694, 2307, 3664])).
% 289.53/182.07 tff(3696,plain,
% 289.53/182.07 ($false),
% 289.53/182.07 inference(unit_resolution,[status(thm)],[3695, 3688, 3680])).
% 289.53/182.07 tff(3697,plain,((~node16(c_e_h_2, c_f, s1)) | (~node17(c_e_h_2, c_f, s1))), inference(lemma,lemma(discharge,[]))).
% 289.53/182.07 tff(3698,plain,
% 289.53/182.07 (~node16(c_e_h_2, c_f, s1)),
% 289.53/182.07 inference(unit_resolution,[status(thm)],[3697, 3662])).
% 289.53/182.07 tff(3699,assumption,(m_and_h_gate_v_out(c_e_h_2, c_i, s1)), introduced(assumption)).
% 289.53/182.07 tff(3700,assumption,(m_c_h_element_v_out(c_e_h_2, c_h, s0)), introduced(assumption)).
% 289.53/182.07 tff(3701,plain,
% 289.53/182.07 ((~![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s0))),
% 289.53/182.07 inference(quant_inst,[status(thm)],[])).
% 289.53/182.07 tff(3702,plain,
% 289.53/182.07 ($false),
% 289.53/182.07 inference(unit_resolution,[status(thm)],[3701, 14, 3700])).
% 289.53/182.07 tff(3703,plain,(~m_c_h_element_v_out(c_e_h_2, c_h, s0)), inference(lemma,lemma(discharge,[]))).
% 289.53/182.07 tff(3704,plain,
% 289.53/182.07 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s0)) | m_c_h_element_v_out(c_e_h_2, c_h, s0))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s0)) | m_c_h_element_v_out(c_e_h_2, c_h, s0))),
% 289.53/182.07 inference(rewrite,[status(thm)],[])).
% 289.53/182.07 tff(3705,plain,
% 289.53/182.07 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s0)) | m_c_h_element_v_out(c_e_h_2, c_h, s0))),
% 289.53/182.07 inference(quant_inst,[status(thm)],[])).
% 289.53/182.07 tff(3706,plain,
% 289.53/182.07 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s0)) | m_c_h_element_v_out(c_e_h_2, c_h, s0)),
% 289.53/182.07 inference(modus_ponens,[status(thm)],[3705, 3704])).
% 289.53/182.07 tff(3707,plain,
% 289.53/182.07 (~m_and_h_gate_v_in1(c_e_h_2, c_i, s0)),
% 289.53/182.07 inference(unit_resolution,[status(thm)],[3706, 619, 3703])).
% 289.53/182.07 tff(3708,plain,
% 289.53/182.07 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s0)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s0)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s0))),
% 289.53/182.07 inference(rewrite,[status(thm)],[])).
% 289.53/182.07 tff(3709,plain,
% 289.53/182.08 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s0)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s0))),
% 289.53/182.08 inference(quant_inst,[status(thm)],[])).
% 289.53/182.08 tff(3710,plain,
% 289.53/182.08 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s0)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s0)),
% 289.53/182.08 inference(modus_ponens,[status(thm)],[3709, 3708])).
% 289.53/182.08 tff(3711,plain,
% 289.53/182.08 (~node20(c_e_h_2, c_i, s0)),
% 289.53/182.08 inference(unit_resolution,[status(thm)],[3710, 38, 3707])).
% 289.53/182.08 tff(3712,assumption,(node21(c_e_h_2, c_i, s0, s1)), introduced(assumption)).
% 289.53/182.08 tff(3713,plain,
% 289.53/182.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s1)) | node20(c_e_h_2, c_i, s0) | (~node21(c_e_h_2, c_i, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s1)) | node20(c_e_h_2, c_i, s0) | (~node21(c_e_h_2, c_i, s0, s1)))),
% 289.53/182.08 inference(rewrite,[status(thm)],[])).
% 289.53/182.08 tff(3714,plain,
% 289.53/182.08 ((node20(c_e_h_2, c_i, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s1)) | (~node21(c_e_h_2, c_i, s0, s1))) <=> ((~m_and_h_gate_v_out(c_e_h_2, c_i, s1)) | node20(c_e_h_2, c_i, s0) | (~node21(c_e_h_2, c_i, s0, s1)))),
% 289.53/182.08 inference(rewrite,[status(thm)],[])).
% 289.53/182.08 tff(3715,plain,
% 289.53/182.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s1)) | (~node21(c_e_h_2, c_i, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s1)) | node20(c_e_h_2, c_i, s0) | (~node21(c_e_h_2, c_i, s0, s1))))),
% 289.53/182.08 inference(monotonicity,[status(thm)],[3714])).
% 289.53/182.08 tff(3716,plain,
% 289.53/182.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s1)) | (~node21(c_e_h_2, c_i, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s1)) | node20(c_e_h_2, c_i, s0) | (~node21(c_e_h_2, c_i, s0, s1)))),
% 289.53/182.08 inference(transitivity,[status(thm)],[3715, 3713])).
% 289.53/182.08 tff(3717,plain,
% 289.53/182.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s1)) | (~node21(c_e_h_2, c_i, s0, s1)))),
% 289.53/182.08 inference(quant_inst,[status(thm)],[])).
% 289.53/182.08 tff(3718,plain,
% 289.53/182.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s1)) | node20(c_e_h_2, c_i, s0) | (~node21(c_e_h_2, c_i, s0, s1))),
% 289.53/182.08 inference(modus_ponens,[status(thm)],[3717, 3716])).
% 289.53/182.08 tff(3719,plain,
% 289.53/182.08 ($false),
% 289.53/182.08 inference(unit_resolution,[status(thm)],[3718, 52, 3712, 3699, 3711])).
% 289.53/182.08 tff(3720,plain,((~node21(c_e_h_2, c_i, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s1))), inference(lemma,lemma(discharge,[]))).
% 289.53/182.08 tff(3721,plain,
% 289.53/182.08 (~node21(c_e_h_2, c_i, s0, s1)),
% 289.53/182.08 inference(unit_resolution,[status(thm)],[3720, 3699])).
% 289.53/182.08 tff(3722,plain,
% 289.53/182.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_2, c_i, s0, s1) | node22(c_e_h_2, c_i, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_2, c_i, s0, s1) | node22(c_e_h_2, c_i, s0, s1))),
% 289.53/182.08 inference(rewrite,[status(thm)],[])).
% 289.53/182.08 tff(3723,plain,
% 289.53/182.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_2, c_i, s0, s1) | node22(c_e_h_2, c_i, s0, s1))),
% 289.53/182.08 inference(quant_inst,[status(thm)],[])).
% 289.53/182.09 tff(3724,plain,
% 289.53/182.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_2, c_i, s0, s1) | node22(c_e_h_2, c_i, s0, s1)),
% 289.53/182.09 inference(modus_ponens,[status(thm)],[3723, 3722])).
% 289.53/182.09 tff(3725,plain,
% 289.53/182.09 (node21(c_e_h_2, c_i, s0, s1) | node22(c_e_h_2, c_i, s0, s1)),
% 289.53/182.09 inference(unit_resolution,[status(thm)],[3724, 82, 72])).
% 289.53/182.09 tff(3726,plain,
% 289.53/182.09 (node22(c_e_h_2, c_i, s0, s1)),
% 289.53/182.09 inference(unit_resolution,[status(thm)],[3725, 3721])).
% 289.53/182.09 tff(3727,plain,
% 289.53/182.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s1)) | (~node22(c_e_h_2, c_i, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_i, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s1)) | (~node22(c_e_h_2, c_i, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_i, s0))),
% 289.53/182.09 inference(rewrite,[status(thm)],[])).
% 289.53/182.09 tff(3728,plain,
% 289.53/182.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s1)) | (~node22(c_e_h_2, c_i, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_i, s0))),
% 289.53/182.09 inference(quant_inst,[status(thm)],[])).
% 289.53/182.09 tff(3729,plain,
% 289.53/182.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s1)) | (~node22(c_e_h_2, c_i, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_i, s0)),
% 289.53/182.09 inference(modus_ponens,[status(thm)],[3728, 3727])).
% 289.53/182.09 tff(3730,plain,
% 289.53/182.09 ($false),
% 289.53/182.09 inference(unit_resolution,[status(thm)],[3729, 108, 3726, 3699, 2136])).
% 289.53/182.09 tff(3731,plain,(~m_and_h_gate_v_out(c_e_h_2, c_i, s1)), inference(lemma,lemma(discharge,[]))).
% 289.53/182.09 tff(3732,plain,
% 289.53/182.09 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_f, s1)) | m_and_h_gate_v_out(c_e_h_2, c_i, s1))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s1)) | m_and_h_gate_v_out(c_e_h_2, c_i, s1))),
% 289.53/182.09 inference(rewrite,[status(thm)],[])).
% 289.53/182.09 tff(3733,plain,
% 289.53/182.09 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_f, s1)) | m_and_h_gate_v_out(c_e_h_2, c_i, s1))),
% 289.53/182.09 inference(quant_inst,[status(thm)],[])).
% 289.53/182.09 tff(3734,plain,
% 289.53/182.09 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s1)) | m_and_h_gate_v_out(c_e_h_2, c_i, s1)),
% 289.53/182.09 inference(modus_ponens,[status(thm)],[3733, 3732])).
% 289.53/182.09 tff(3735,plain,
% 289.53/182.09 (~m_c_h_element_v_in2(c_e_h_2, c_f, s1)),
% 289.53/182.09 inference(unit_resolution,[status(thm)],[3734, 2143, 3731])).
% 289.53/182.09 tff(3736,plain,
% 289.53/182.09 ((~node17(c_e_h_2, c_f, s1)) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s1))),
% 289.53/182.09 inference(unit_resolution,[status(thm)],[3671, 919, 3735])).
% 289.53/182.09 tff(3737,plain,
% 289.53/182.09 (~m_c_h_element_v_in1(c_e_h_2, c_f, s1)),
% 289.53/182.09 inference(unit_resolution,[status(thm)],[3736, 3662])).
% 289.53/182.09 tff(3738,assumption,(node14(c_e_h_2, c_f, s1, s2)), introduced(assumption)).
% 289.53/182.09 tff(3739,plain,
% 289.53/182.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s2)) | m_c_h_element_v_in1(c_e_h_2, c_f, s1) | (~node14(c_e_h_2, c_f, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s2)) | m_c_h_element_v_in1(c_e_h_2, c_f, s1) | (~node14(c_e_h_2, c_f, s1, s2)))),
% 289.53/182.09 inference(rewrite,[status(thm)],[])).
% 289.53/182.09 tff(3740,plain,
% 289.53/182.09 (((~node14(c_e_h_2, c_f, s1, s2)) | m_c_h_element_v_in1(c_e_h_2, c_f, s1) | (~m_c_h_element_v_out(c_e_h_2, c_f, s2))) <=> ((~m_c_h_element_v_out(c_e_h_2, c_f, s2)) | m_c_h_element_v_in1(c_e_h_2, c_f, s1) | (~node14(c_e_h_2, c_f, s1, s2)))),
% 289.62/182.10 inference(rewrite,[status(thm)],[])).
% 289.62/182.10 tff(3741,plain,
% 289.62/182.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_f, s1, s2)) | m_c_h_element_v_in1(c_e_h_2, c_f, s1) | (~m_c_h_element_v_out(c_e_h_2, c_f, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s2)) | m_c_h_element_v_in1(c_e_h_2, c_f, s1) | (~node14(c_e_h_2, c_f, s1, s2))))),
% 289.62/182.10 inference(monotonicity,[status(thm)],[3740])).
% 289.62/182.10 tff(3742,plain,
% 289.62/182.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_f, s1, s2)) | m_c_h_element_v_in1(c_e_h_2, c_f, s1) | (~m_c_h_element_v_out(c_e_h_2, c_f, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s2)) | m_c_h_element_v_in1(c_e_h_2, c_f, s1) | (~node14(c_e_h_2, c_f, s1, s2)))),
% 289.62/182.10 inference(transitivity,[status(thm)],[3741, 3739])).
% 289.62/182.10 tff(3743,plain,
% 289.62/182.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_f, s1, s2)) | m_c_h_element_v_in1(c_e_h_2, c_f, s1) | (~m_c_h_element_v_out(c_e_h_2, c_f, s2)))),
% 289.62/182.10 inference(quant_inst,[status(thm)],[])).
% 289.62/182.10 tff(3744,plain,
% 289.62/182.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s2)) | m_c_h_element_v_in1(c_e_h_2, c_f, s1) | (~node14(c_e_h_2, c_f, s1, s2))),
% 289.62/182.10 inference(modus_ponens,[status(thm)],[3743, 3742])).
% 289.62/182.10 tff(3745,plain,
% 289.62/182.10 ($false),
% 289.62/182.10 inference(unit_resolution,[status(thm)],[3744, 223, 3643, 3738, 3737])).
% 289.62/182.10 tff(3746,plain,((~node14(c_e_h_2, c_f, s1, s2)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s2))), inference(lemma,lemma(discharge,[]))).
% 289.62/182.10 tff(3747,plain,
% 289.62/182.10 (~node14(c_e_h_2, c_f, s1, s2)),
% 289.62/182.10 inference(unit_resolution,[status(thm)],[3746, 3643])).
% 289.62/182.10 tff(3748,plain,
% 289.62/182.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_f, s1, s2)) | node15(c_e_h_2, c_f, s1, s2) | node16(c_e_h_2, c_f, s1) | node14(c_e_h_2, c_f, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_f, s1, s2)) | node15(c_e_h_2, c_f, s1, s2) | node16(c_e_h_2, c_f, s1) | node14(c_e_h_2, c_f, s1, s2))),
% 289.62/182.10 inference(rewrite,[status(thm)],[])).
% 289.62/182.10 tff(3749,plain,
% 289.62/182.10 ((node16(c_e_h_2, c_f, s1) | node14(c_e_h_2, c_f, s1, s2) | node15(c_e_h_2, c_f, s1, s2) | (~node19(c_e_h_2, c_f, s1, s2))) <=> ((~node19(c_e_h_2, c_f, s1, s2)) | node15(c_e_h_2, c_f, s1, s2) | node16(c_e_h_2, c_f, s1) | node14(c_e_h_2, c_f, s1, s2))),
% 289.62/182.10 inference(rewrite,[status(thm)],[])).
% 289.62/182.10 tff(3750,plain,
% 289.62/182.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s1) | node14(c_e_h_2, c_f, s1, s2) | node15(c_e_h_2, c_f, s1, s2) | (~node19(c_e_h_2, c_f, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_f, s1, s2)) | node15(c_e_h_2, c_f, s1, s2) | node16(c_e_h_2, c_f, s1) | node14(c_e_h_2, c_f, s1, s2)))),
% 289.62/182.10 inference(monotonicity,[status(thm)],[3749])).
% 289.62/182.10 tff(3751,plain,
% 289.62/182.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s1) | node14(c_e_h_2, c_f, s1, s2) | node15(c_e_h_2, c_f, s1, s2) | (~node19(c_e_h_2, c_f, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_f, s1, s2)) | node15(c_e_h_2, c_f, s1, s2) | node16(c_e_h_2, c_f, s1) | node14(c_e_h_2, c_f, s1, s2))),
% 289.62/182.10 inference(transitivity,[status(thm)],[3750, 3748])).
% 289.62/182.10 tff(3752,plain,
% 289.62/182.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s1) | node14(c_e_h_2, c_f, s1, s2) | node15(c_e_h_2, c_f, s1, s2) | (~node19(c_e_h_2, c_f, s1, s2)))),
% 289.62/182.10 inference(quant_inst,[status(thm)],[])).
% 289.62/182.10 tff(3753,plain,
% 289.62/182.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_f, s1, s2)) | node15(c_e_h_2, c_f, s1, s2) | node16(c_e_h_2, c_f, s1) | node14(c_e_h_2, c_f, s1, s2)),
% 289.62/182.10 inference(modus_ponens,[status(thm)],[3752, 3751])).
% 289.62/182.10 tff(3754,plain,
% 289.62/182.10 (node15(c_e_h_2, c_f, s1, s2) | node16(c_e_h_2, c_f, s1) | node14(c_e_h_2, c_f, s1, s2)),
% 289.62/182.10 inference(unit_resolution,[status(thm)],[3753, 204, 3654])).
% 289.62/182.10 tff(3755,plain,
% 289.62/182.10 (node15(c_e_h_2, c_f, s1, s2)),
% 289.62/182.10 inference(unit_resolution,[status(thm)],[3754, 3747, 3698])).
% 289.62/182.10 tff(3756,plain,
% 289.62/182.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s2)) | (~node15(c_e_h_2, c_f, s1, s2)) | m_c_h_element_v_out(c_e_h_2, c_f, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s2)) | (~node15(c_e_h_2, c_f, s1, s2)) | m_c_h_element_v_out(c_e_h_2, c_f, s1))),
% 289.62/182.10 inference(rewrite,[status(thm)],[])).
% 289.62/182.10 tff(3757,plain,
% 289.62/182.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s2)) | (~node15(c_e_h_2, c_f, s1, s2)) | m_c_h_element_v_out(c_e_h_2, c_f, s1))),
% 289.62/182.10 inference(quant_inst,[status(thm)],[])).
% 289.62/182.10 tff(3758,plain,
% 289.62/182.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s2)) | (~node15(c_e_h_2, c_f, s1, s2)) | m_c_h_element_v_out(c_e_h_2, c_f, s1)),
% 289.62/182.10 inference(modus_ponens,[status(thm)],[3757, 3756])).
% 289.62/182.10 tff(3759,plain,
% 289.62/182.10 ($false),
% 289.62/182.10 inference(unit_resolution,[status(thm)],[3758, 147, 3643, 2167, 3755])).
% 289.62/182.10 tff(3760,plain,(~m_c_h_element_v_out(c_e_h_2, c_f, s2)), inference(lemma,lemma(discharge,[]))).
% 289.62/182.10 tff(3761,plain,
% 289.62/182.10 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_q, s2)) | m_c_h_element_v_out(c_e_h_2, c_f, s2))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_q, s2)) | m_c_h_element_v_out(c_e_h_2, c_f, s2))),
% 289.62/182.10 inference(rewrite,[status(thm)],[])).
% 289.62/182.10 tff(3762,plain,
% 289.62/182.10 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_q, s2)) | m_c_h_element_v_out(c_e_h_2, c_f, s2))),
% 289.62/182.10 inference(quant_inst,[status(thm)],[])).
% 289.62/182.10 tff(3763,plain,
% 289.62/182.10 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_q, s2)) | m_c_h_element_v_out(c_e_h_2, c_f, s2)),
% 289.62/182.10 inference(modus_ponens,[status(thm)],[3762, 3761])).
% 289.62/182.10 tff(3764,plain,
% 289.62/182.10 (~m_and_h_gate_v_in1(c_e_h_2, c_q, s2)),
% 289.62/182.10 inference(unit_resolution,[status(thm)],[3763, 1586, 3760])).
% 289.62/182.10 tff(3765,plain,
% 289.62/182.10 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_q, s2)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_q, s2)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s2))),
% 289.62/182.10 inference(rewrite,[status(thm)],[])).
% 289.62/182.10 tff(3766,plain,
% 289.64/182.11 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_q, s2)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s2))),
% 289.64/182.11 inference(quant_inst,[status(thm)],[])).
% 289.64/182.11 tff(3767,plain,
% 289.64/182.11 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_q, s2)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s2)),
% 289.64/182.11 inference(modus_ponens,[status(thm)],[3766, 3765])).
% 289.64/182.11 tff(3768,plain,
% 289.64/182.11 (~node20(c_e_h_2, c_q, s2)),
% 289.64/182.11 inference(unit_resolution,[status(thm)],[3767, 38, 3764])).
% 289.64/182.11 tff(3769,assumption,(~node20(c_e_h_2, c_q, s2)), introduced(assumption)).
% 289.64/182.11 tff(3770,assumption,(node21(c_e_h_2, c_q, s2, s3)), introduced(assumption)).
% 289.64/182.11 tff(3771,plain,
% 289.64/182.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_q, s2) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s3)) | (~node21(c_e_h_2, c_q, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_q, s2) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s3)) | (~node21(c_e_h_2, c_q, s2, s3)))),
% 289.64/182.11 inference(rewrite,[status(thm)],[])).
% 289.64/182.11 tff(3772,plain,
% 289.64/182.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_q, s2) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s3)) | (~node21(c_e_h_2, c_q, s2, s3)))),
% 289.64/182.11 inference(quant_inst,[status(thm)],[])).
% 289.64/182.11 tff(3773,plain,
% 289.64/182.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_q, s2) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s3)) | (~node21(c_e_h_2, c_q, s2, s3))),
% 289.64/182.11 inference(modus_ponens,[status(thm)],[3772, 3771])).
% 289.64/182.11 tff(3774,plain,
% 289.64/182.11 ($false),
% 289.64/182.11 inference(unit_resolution,[status(thm)],[3773, 52, 3642, 3770, 3769])).
% 289.64/182.11 tff(3775,plain,((~node21(c_e_h_2, c_q, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s3)) | node20(c_e_h_2, c_q, s2)), inference(lemma,lemma(discharge,[]))).
% 289.64/182.11 tff(3776,plain,
% 289.64/182.11 ((~node21(c_e_h_2, c_q, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s3))),
% 289.64/182.11 inference(unit_resolution,[status(thm)],[3775, 3768])).
% 289.64/182.11 tff(3777,plain,
% 289.64/182.11 (~node21(c_e_h_2, c_q, s2, s3)),
% 289.64/182.11 inference(unit_resolution,[status(thm)],[3776, 3642])).
% 289.64/182.11 tff(3778,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_q, s2)), introduced(assumption)).
% 289.64/182.11 tff(3779,assumption,(node22(c_e_h_2, c_q, s2, s3)), introduced(assumption)).
% 289.64/182.11 tff(3780,plain,
% 289.64/182.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s3)) | (~node22(c_e_h_2, c_q, s2, s3)) | m_and_h_gate_v_out(c_e_h_2, c_q, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s3)) | (~node22(c_e_h_2, c_q, s2, s3)) | m_and_h_gate_v_out(c_e_h_2, c_q, s2))),
% 289.64/182.11 inference(rewrite,[status(thm)],[])).
% 289.64/182.11 tff(3781,plain,
% 289.64/182.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s3)) | (~node22(c_e_h_2, c_q, s2, s3)) | m_and_h_gate_v_out(c_e_h_2, c_q, s2))),
% 289.64/182.11 inference(quant_inst,[status(thm)],[])).
% 289.64/182.11 tff(3782,plain,
% 289.64/182.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s3)) | (~node22(c_e_h_2, c_q, s2, s3)) | m_and_h_gate_v_out(c_e_h_2, c_q, s2)),
% 289.64/182.11 inference(modus_ponens,[status(thm)],[3781, 3780])).
% 289.64/182.11 tff(3783,plain,
% 289.64/182.11 ($false),
% 289.64/182.11 inference(unit_resolution,[status(thm)],[3782, 108, 3778, 3642, 3779])).
% 289.64/182.11 tff(3784,plain,((~node22(c_e_h_2, c_q, s2, s3)) | m_and_h_gate_v_out(c_e_h_2, c_q, s2) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s3))), inference(lemma,lemma(discharge,[]))).
% 289.64/182.11 tff(3785,plain,
% 289.64/182.11 (~node22(c_e_h_2, c_q, s2, s3)),
% 289.64/182.11 inference(unit_resolution,[status(thm)],[3784, 3642, 3778])).
% 289.64/182.11 tff(3786,plain,
% 289.64/182.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_2, c_q, s2, s3) | node22(c_e_h_2, c_q, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_2, c_q, s2, s3) | node22(c_e_h_2, c_q, s2, s3))),
% 289.64/182.11 inference(rewrite,[status(thm)],[])).
% 289.64/182.11 tff(3787,plain,
% 289.64/182.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_2, c_q, s2, s3) | node22(c_e_h_2, c_q, s2, s3))),
% 289.64/182.11 inference(quant_inst,[status(thm)],[])).
% 289.64/182.11 tff(3788,plain,
% 289.64/182.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_2, c_q, s2, s3) | node22(c_e_h_2, c_q, s2, s3)),
% 289.64/182.11 inference(modus_ponens,[status(thm)],[3787, 3786])).
% 289.64/182.11 tff(3789,plain,
% 289.64/182.11 (node21(c_e_h_2, c_q, s2, s3) | node22(c_e_h_2, c_q, s2, s3)),
% 289.64/182.11 inference(unit_resolution,[status(thm)],[3788, 82, 318])).
% 289.64/182.11 tff(3790,plain,
% 289.64/182.11 ($false),
% 289.64/182.11 inference(unit_resolution,[status(thm)],[3789, 3785, 3777])).
% 289.64/182.11 tff(3791,plain,((~m_and_h_gate_v_out(c_e_h_2, c_q, s3)) | m_and_h_gate_v_out(c_e_h_2, c_q, s2)), inference(lemma,lemma(discharge,[]))).
% 289.64/182.11 tff(3792,plain,
% 289.64/182.11 (~m_and_h_gate_v_out(c_e_h_2, c_q, s3)),
% 289.64/182.11 inference(unit_resolution,[status(thm)],[3791, 2194])).
% 289.64/182.11 tff(3793,assumption,(m_c_h_element_v_out(c_e_h_2, c_f, s3)), introduced(assumption)).
% 289.64/182.11 tff(3794,assumption,(~m_c_h_element_v_out(c_e_h_2, c_f, s2)), introduced(assumption)).
% 289.64/182.11 tff(3795,assumption,(node18(c_e_h_2, c_f, s2, s3)), introduced(assumption)).
% 289.64/182.11 tff(3796,plain,
% 289.64/182.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_f, s2) | (~m_c_h_element_v_out(c_e_h_2, c_f, s3)) | (~node18(c_e_h_2, c_f, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_f, s2) | (~m_c_h_element_v_out(c_e_h_2, c_f, s3)) | (~node18(c_e_h_2, c_f, s2, s3)))),
% 289.64/182.11 inference(rewrite,[status(thm)],[])).
% 289.64/182.11 tff(3797,plain,
% 289.64/182.11 (((~m_c_h_element_v_out(c_e_h_2, c_f, s3)) | m_c_h_element_v_out(c_e_h_2, c_f, s2) | (~node18(c_e_h_2, c_f, s2, s3))) <=> (m_c_h_element_v_out(c_e_h_2, c_f, s2) | (~m_c_h_element_v_out(c_e_h_2, c_f, s3)) | (~node18(c_e_h_2, c_f, s2, s3)))),
% 289.64/182.11 inference(rewrite,[status(thm)],[])).
% 289.64/182.11 tff(3798,plain,
% 289.64/182.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s3)) | m_c_h_element_v_out(c_e_h_2, c_f, s2) | (~node18(c_e_h_2, c_f, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_f, s2) | (~m_c_h_element_v_out(c_e_h_2, c_f, s3)) | (~node18(c_e_h_2, c_f, s2, s3))))),
% 289.64/182.11 inference(monotonicity,[status(thm)],[3797])).
% 289.64/182.11 tff(3799,plain,
% 289.64/182.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s3)) | m_c_h_element_v_out(c_e_h_2, c_f, s2) | (~node18(c_e_h_2, c_f, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_f, s2) | (~m_c_h_element_v_out(c_e_h_2, c_f, s3)) | (~node18(c_e_h_2, c_f, s2, s3)))),
% 289.64/182.11 inference(transitivity,[status(thm)],[3798, 3796])).
% 289.64/182.11 tff(3800,plain,
% 289.64/182.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s3)) | m_c_h_element_v_out(c_e_h_2, c_f, s2) | (~node18(c_e_h_2, c_f, s2, s3)))),
% 289.64/182.11 inference(quant_inst,[status(thm)],[])).
% 289.64/182.11 tff(3801,plain,
% 289.64/182.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_f, s2) | (~m_c_h_element_v_out(c_e_h_2, c_f, s3)) | (~node18(c_e_h_2, c_f, s2, s3))),
% 289.64/182.11 inference(modus_ponens,[status(thm)],[3800, 3799])).
% 289.64/182.11 tff(3802,plain,
% 289.64/182.11 ($false),
% 289.64/182.11 inference(unit_resolution,[status(thm)],[3801, 753, 3793, 3794, 3795])).
% 289.64/182.11 tff(3803,plain,((~node18(c_e_h_2, c_f, s2, s3)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s3)) | m_c_h_element_v_out(c_e_h_2, c_f, s2)), inference(lemma,lemma(discharge,[]))).
% 289.64/182.11 tff(3804,plain,
% 289.64/182.11 (~node18(c_e_h_2, c_f, s2, s3)),
% 289.64/182.11 inference(unit_resolution,[status(thm)],[3803, 3794, 3793])).
% 289.64/182.11 tff(3805,plain,
% 289.64/182.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s2, s3)) | node19(c_e_h_2, c_f, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s2, s3)) | node19(c_e_h_2, c_f, s2, s3))),
% 289.64/182.11 inference(rewrite,[status(thm)],[])).
% 289.64/182.11 tff(3806,plain,
% 289.64/182.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s2, s3)) | node19(c_e_h_2, c_f, s2, s3))),
% 289.64/182.11 inference(quant_inst,[status(thm)],[])).
% 289.64/182.11 tff(3807,plain,
% 289.64/182.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s2, s3)) | node19(c_e_h_2, c_f, s2, s3)),
% 289.64/182.11 inference(modus_ponens,[status(thm)],[3806, 3805])).
% 289.64/182.11 tff(3808,plain,
% 289.64/182.11 (node19(c_e_h_2, c_f, s2, s3)),
% 289.64/182.11 inference(unit_resolution,[status(thm)],[3807, 190, 318])).
% 289.64/182.11 tff(3809,plain,
% 289.64/182.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s2) | (~node19(c_e_h_2, c_f, s2, s3)) | node18(c_e_h_2, c_f, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_f, s2) | (~node19(c_e_h_2, c_f, s2, s3)) | node18(c_e_h_2, c_f, s2, s3))),
% 289.64/182.11 inference(rewrite,[status(thm)],[])).
% 289.64/182.11 tff(3810,plain,
% 289.64/182.11 ((node17(c_e_h_2, c_f, s2) | node18(c_e_h_2, c_f, s2, s3) | (~node19(c_e_h_2, c_f, s2, s3))) <=> (node17(c_e_h_2, c_f, s2) | (~node19(c_e_h_2, c_f, s2, s3)) | node18(c_e_h_2, c_f, s2, s3))),
% 289.64/182.11 inference(rewrite,[status(thm)],[])).
% 289.64/182.11 tff(3811,plain,
% 289.64/182.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s2) | node18(c_e_h_2, c_f, s2, s3) | (~node19(c_e_h_2, c_f, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s2) | (~node19(c_e_h_2, c_f, s2, s3)) | node18(c_e_h_2, c_f, s2, s3)))),
% 289.64/182.11 inference(monotonicity,[status(thm)],[3810])).
% 289.64/182.11 tff(3812,plain,
% 289.64/182.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s2) | node18(c_e_h_2, c_f, s2, s3) | (~node19(c_e_h_2, c_f, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_f, s2) | (~node19(c_e_h_2, c_f, s2, s3)) | node18(c_e_h_2, c_f, s2, s3))),
% 289.64/182.11 inference(transitivity,[status(thm)],[3811, 3809])).
% 289.64/182.11 tff(3813,plain,
% 289.64/182.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s2) | node18(c_e_h_2, c_f, s2, s3) | (~node19(c_e_h_2, c_f, s2, s3)))),
% 289.64/182.11 inference(quant_inst,[status(thm)],[])).
% 289.64/182.11 tff(3814,plain,
% 289.64/182.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_f, s2) | (~node19(c_e_h_2, c_f, s2, s3)) | node18(c_e_h_2, c_f, s2, s3)),
% 289.64/182.11 inference(modus_ponens,[status(thm)],[3813, 3812])).
% 289.64/182.11 tff(3815,plain,
% 289.64/182.11 (node17(c_e_h_2, c_f, s2) | node18(c_e_h_2, c_f, s2, s3)),
% 289.64/182.11 inference(unit_resolution,[status(thm)],[3814, 776, 3808])).
% 289.64/182.11 tff(3816,plain,
% 289.64/182.11 (node17(c_e_h_2, c_f, s2)),
% 289.64/182.11 inference(unit_resolution,[status(thm)],[3815, 3804])).
% 289.64/182.11 tff(3817,assumption,(node15(c_e_h_2, c_f, s2, s3)), introduced(assumption)).
% 289.64/182.12 tff(3818,plain,
% 289.64/182.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s3)) | (~node15(c_e_h_2, c_f, s2, s3)) | m_c_h_element_v_out(c_e_h_2, c_f, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s3)) | (~node15(c_e_h_2, c_f, s2, s3)) | m_c_h_element_v_out(c_e_h_2, c_f, s2))),
% 289.64/182.12 inference(rewrite,[status(thm)],[])).
% 289.64/182.12 tff(3819,plain,
% 289.64/182.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s3)) | (~node15(c_e_h_2, c_f, s2, s3)) | m_c_h_element_v_out(c_e_h_2, c_f, s2))),
% 289.64/182.12 inference(quant_inst,[status(thm)],[])).
% 289.64/182.12 tff(3820,plain,
% 289.64/182.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s3)) | (~node15(c_e_h_2, c_f, s2, s3)) | m_c_h_element_v_out(c_e_h_2, c_f, s2)),
% 289.64/182.12 inference(modus_ponens,[status(thm)],[3819, 3818])).
% 289.64/182.12 tff(3821,plain,
% 289.64/182.12 ($false),
% 289.64/182.12 inference(unit_resolution,[status(thm)],[3820, 147, 3793, 3794, 3817])).
% 289.64/182.12 tff(3822,plain,((~node15(c_e_h_2, c_f, s2, s3)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s3)) | m_c_h_element_v_out(c_e_h_2, c_f, s2)), inference(lemma,lemma(discharge,[]))).
% 289.64/182.12 tff(3823,plain,
% 289.64/182.12 (~node15(c_e_h_2, c_f, s2, s3)),
% 289.64/182.12 inference(unit_resolution,[status(thm)],[3822, 3794, 3793])).
% 289.64/182.12 tff(3824,assumption,(m_and_h_gate_v_out(c_e_h_2, c_i, s2)), introduced(assumption)).
% 289.64/182.12 tff(3825,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_i, s1)), introduced(assumption)).
% 289.64/182.12 tff(3826,assumption,(node22(c_e_h_2, c_i, s1, s2)), introduced(assumption)).
% 289.64/182.12 tff(3827,plain,
% 289.64/182.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s2)) | (~node22(c_e_h_2, c_i, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_i, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s2)) | (~node22(c_e_h_2, c_i, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_i, s1))),
% 289.64/182.12 inference(rewrite,[status(thm)],[])).
% 289.64/182.12 tff(3828,plain,
% 289.64/182.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s2)) | (~node22(c_e_h_2, c_i, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_i, s1))),
% 289.64/182.12 inference(quant_inst,[status(thm)],[])).
% 289.64/182.12 tff(3829,plain,
% 289.64/182.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s2)) | (~node22(c_e_h_2, c_i, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_i, s1)),
% 289.64/182.12 inference(modus_ponens,[status(thm)],[3828, 3827])).
% 289.64/182.12 tff(3830,plain,
% 289.64/182.12 ($false),
% 289.64/182.12 inference(unit_resolution,[status(thm)],[3829, 108, 3826, 3824, 3825])).
% 289.64/182.12 tff(3831,plain,((~node22(c_e_h_2, c_i, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s2)) | m_and_h_gate_v_out(c_e_h_2, c_i, s1)), inference(lemma,lemma(discharge,[]))).
% 289.64/182.12 tff(3832,plain,
% 289.64/182.12 ((~node22(c_e_h_2, c_i, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s2))),
% 289.64/182.12 inference(unit_resolution,[status(thm)],[3831, 3731])).
% 289.64/182.12 tff(3833,plain,
% 289.64/182.12 (~node22(c_e_h_2, c_i, s1, s2)),
% 289.64/182.12 inference(unit_resolution,[status(thm)],[3832, 3824])).
% 289.64/182.12 tff(3834,assumption,(m_c_h_element_v_out(c_e_h_2, c_h, s1)), introduced(assumption)).
% 289.64/182.12 tff(3835,assumption,(node14(c_e_h_2, c_h, s0, s1)), introduced(assumption)).
% 289.64/182.12 tff(3836,assumption,(m_or_h_gate_v_out(c_e_h_2, c_g, s0)), introduced(assumption)).
% 289.64/182.12 tff(3837,plain,
% 289.64/182.12 ((~![I0: $i, I1: $i] : (~m_or_h_gate_v_out(I0, I1, s0))) | (~m_or_h_gate_v_out(c_e_h_2, c_g, s0))),
% 289.64/182.12 inference(quant_inst,[status(thm)],[])).
% 289.64/182.12 tff(3838,plain,
% 289.64/182.12 ($false),
% 289.64/182.12 inference(unit_resolution,[status(thm)],[3837, 801, 3836])).
% 289.64/182.12 tff(3839,plain,(~m_or_h_gate_v_out(c_e_h_2, c_g, s0)), inference(lemma,lemma(discharge,[]))).
% 289.64/182.12 tff(3840,plain,
% 289.64/182.12 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s0)) | m_or_h_gate_v_out(c_e_h_2, c_g, s0))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s0)) | m_or_h_gate_v_out(c_e_h_2, c_g, s0))),
% 289.64/182.12 inference(rewrite,[status(thm)],[])).
% 289.64/182.12 tff(3841,plain,
% 289.64/182.12 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s0)) | m_or_h_gate_v_out(c_e_h_2, c_g, s0))),
% 289.64/182.12 inference(quant_inst,[status(thm)],[])).
% 289.64/182.12 tff(3842,plain,
% 289.64/182.12 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s0)) | m_or_h_gate_v_out(c_e_h_2, c_g, s0)),
% 289.64/182.12 inference(modus_ponens,[status(thm)],[3841, 3840])).
% 289.64/182.12 tff(3843,plain,
% 289.64/182.12 (~m_c_h_element_v_in1(c_e_h_2, c_h, s0)),
% 289.64/182.12 inference(unit_resolution,[status(thm)],[3842, 811, 3839])).
% 289.64/182.12 tff(3844,plain,
% 289.64/182.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s0) | (~node14(c_e_h_2, c_h, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s0) | (~node14(c_e_h_2, c_h, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s1)))),
% 289.64/182.12 inference(rewrite,[status(thm)],[])).
% 289.64/182.12 tff(3845,plain,
% 289.64/182.12 (((~node14(c_e_h_2, c_h, s0, s1)) | m_c_h_element_v_in1(c_e_h_2, c_h, s0) | (~m_c_h_element_v_out(c_e_h_2, c_h, s1))) <=> (m_c_h_element_v_in1(c_e_h_2, c_h, s0) | (~node14(c_e_h_2, c_h, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s1)))),
% 289.64/182.12 inference(rewrite,[status(thm)],[])).
% 289.64/182.12 tff(3846,plain,
% 289.64/182.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s0, s1)) | m_c_h_element_v_in1(c_e_h_2, c_h, s0) | (~m_c_h_element_v_out(c_e_h_2, c_h, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s0) | (~node14(c_e_h_2, c_h, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s1))))),
% 289.64/182.12 inference(monotonicity,[status(thm)],[3845])).
% 289.64/182.12 tff(3847,plain,
% 289.64/182.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s0, s1)) | m_c_h_element_v_in1(c_e_h_2, c_h, s0) | (~m_c_h_element_v_out(c_e_h_2, c_h, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s0) | (~node14(c_e_h_2, c_h, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s1)))),
% 289.64/182.12 inference(transitivity,[status(thm)],[3846, 3844])).
% 289.64/182.12 tff(3848,plain,
% 289.64/182.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s0, s1)) | m_c_h_element_v_in1(c_e_h_2, c_h, s0) | (~m_c_h_element_v_out(c_e_h_2, c_h, s1)))),
% 289.64/182.12 inference(quant_inst,[status(thm)],[])).
% 289.64/182.12 tff(3849,plain,
% 289.64/182.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s0) | (~node14(c_e_h_2, c_h, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s1))),
% 289.64/182.12 inference(modus_ponens,[status(thm)],[3848, 3847])).
% 289.64/182.12 tff(3850,plain,
% 289.64/182.12 ($false),
% 289.64/182.12 inference(unit_resolution,[status(thm)],[3849, 223, 3834, 3843, 3835])).
% 289.64/182.12 tff(3851,plain,((~node14(c_e_h_2, c_h, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s1))), inference(lemma,lemma(discharge,[]))).
% 289.65/182.12 tff(3852,plain,
% 289.65/182.12 (~node14(c_e_h_2, c_h, s0, s1)),
% 289.65/182.12 inference(unit_resolution,[status(thm)],[3851, 3834])).
% 289.65/182.12 tff(3853,assumption,(m_or_h_gate_v_out(c_e_h_2, c_j, s0)), introduced(assumption)).
% 289.65/182.12 tff(3854,plain,
% 289.65/182.12 ((~![I0: $i, I1: $i] : (~m_or_h_gate_v_out(I0, I1, s0))) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s0))),
% 289.65/182.12 inference(quant_inst,[status(thm)],[])).
% 289.65/182.12 tff(3855,plain,
% 289.65/182.12 ($false),
% 289.65/182.12 inference(unit_resolution,[status(thm)],[3854, 801, 3853])).
% 289.65/182.12 tff(3856,plain,(~m_or_h_gate_v_out(c_e_h_2, c_j, s0)), inference(lemma,lemma(discharge,[]))).
% 289.65/182.12 tff(3857,plain,
% 289.65/182.12 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s0)) | m_or_h_gate_v_out(c_e_h_2, c_j, s0))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s0)) | m_or_h_gate_v_out(c_e_h_2, c_j, s0))),
% 289.65/182.12 inference(rewrite,[status(thm)],[])).
% 289.65/182.12 tff(3858,plain,
% 289.65/182.12 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s0)) | m_or_h_gate_v_out(c_e_h_2, c_j, s0))),
% 289.65/182.12 inference(quant_inst,[status(thm)],[])).
% 289.65/182.12 tff(3859,plain,
% 289.65/182.12 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s0)) | m_or_h_gate_v_out(c_e_h_2, c_j, s0)),
% 289.65/182.12 inference(modus_ponens,[status(thm)],[3858, 3857])).
% 289.65/182.12 tff(3860,plain,
% 289.65/182.12 (~m_c_h_element_v_in2(c_e_h_2, c_h, s0)),
% 289.65/182.12 inference(unit_resolution,[status(thm)],[3859, 1174, 3856])).
% 289.65/182.12 tff(3861,plain,
% 289.65/182.12 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_h, s0)) | m_c_h_element_v_in1(c_e_h_2, c_h, s0) | m_c_h_element_v_in2(c_e_h_2, c_h, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_h, s0)) | m_c_h_element_v_in1(c_e_h_2, c_h, s0) | m_c_h_element_v_in2(c_e_h_2, c_h, s0))),
% 289.65/182.12 inference(rewrite,[status(thm)],[])).
% 289.65/182.12 tff(3862,plain,
% 289.65/182.12 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_h, s0)) | m_c_h_element_v_in1(c_e_h_2, c_h, s0) | m_c_h_element_v_in2(c_e_h_2, c_h, s0))),
% 289.65/182.12 inference(quant_inst,[status(thm)],[])).
% 289.65/182.12 tff(3863,plain,
% 289.65/182.12 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_h, s0)) | m_c_h_element_v_in1(c_e_h_2, c_h, s0) | m_c_h_element_v_in2(c_e_h_2, c_h, s0)),
% 289.65/182.12 inference(modus_ponens,[status(thm)],[3862, 3861])).
% 289.65/182.12 tff(3864,plain,
% 289.65/182.12 ((~node16(c_e_h_2, c_h, s0)) | m_c_h_element_v_in1(c_e_h_2, c_h, s0)),
% 289.65/182.12 inference(unit_resolution,[status(thm)],[3863, 178, 3860])).
% 289.65/182.12 tff(3865,plain,
% 289.65/182.12 (~node16(c_e_h_2, c_h, s0)),
% 289.65/182.12 inference(unit_resolution,[status(thm)],[3864, 3843])).
% 289.65/182.12 tff(3866,plain,
% 289.65/182.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s0, s1)) | node19(c_e_h_2, c_h, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s0, s1)) | node19(c_e_h_2, c_h, s0, s1))),
% 289.65/182.12 inference(rewrite,[status(thm)],[])).
% 289.65/182.12 tff(3867,plain,
% 289.65/182.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s0, s1)) | node19(c_e_h_2, c_h, s0, s1))),
% 289.65/182.12 inference(quant_inst,[status(thm)],[])).
% 289.65/182.12 tff(3868,plain,
% 289.65/182.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s0, s1)) | node19(c_e_h_2, c_h, s0, s1)),
% 289.65/182.12 inference(modus_ponens,[status(thm)],[3867, 3866])).
% 289.65/182.12 tff(3869,plain,
% 289.65/182.12 (node19(c_e_h_2, c_h, s0, s1)),
% 289.65/182.12 inference(unit_resolution,[status(thm)],[3868, 190, 72])).
% 289.65/182.12 tff(3870,plain,
% 289.65/182.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s0) | node14(c_e_h_2, c_h, s0, s1) | node15(c_e_h_2, c_h, s0, s1) | (~node19(c_e_h_2, c_h, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s0) | node14(c_e_h_2, c_h, s0, s1) | node15(c_e_h_2, c_h, s0, s1) | (~node19(c_e_h_2, c_h, s0, s1)))),
% 289.65/182.13 inference(rewrite,[status(thm)],[])).
% 289.65/182.13 tff(3871,plain,
% 289.65/182.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s0) | node14(c_e_h_2, c_h, s0, s1) | node15(c_e_h_2, c_h, s0, s1) | (~node19(c_e_h_2, c_h, s0, s1)))),
% 289.65/182.13 inference(quant_inst,[status(thm)],[])).
% 289.65/182.13 tff(3872,plain,
% 289.65/182.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s0) | node14(c_e_h_2, c_h, s0, s1) | node15(c_e_h_2, c_h, s0, s1) | (~node19(c_e_h_2, c_h, s0, s1))),
% 289.65/182.13 inference(modus_ponens,[status(thm)],[3871, 3870])).
% 289.65/182.13 tff(3873,plain,
% 289.65/182.13 (node16(c_e_h_2, c_h, s0) | node14(c_e_h_2, c_h, s0, s1) | node15(c_e_h_2, c_h, s0, s1)),
% 289.65/182.13 inference(unit_resolution,[status(thm)],[3872, 204, 3869])).
% 289.65/182.13 tff(3874,plain,
% 289.65/182.13 (node14(c_e_h_2, c_h, s0, s1) | node15(c_e_h_2, c_h, s0, s1)),
% 289.65/182.13 inference(unit_resolution,[status(thm)],[3873, 3865])).
% 289.65/182.13 tff(3875,plain,
% 289.65/182.13 (node15(c_e_h_2, c_h, s0, s1)),
% 289.65/182.13 inference(unit_resolution,[status(thm)],[3874, 3852])).
% 289.65/182.13 tff(3876,plain,
% 289.65/182.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s1)) | (~node15(c_e_h_2, c_h, s0, s1)) | m_c_h_element_v_out(c_e_h_2, c_h, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s1)) | (~node15(c_e_h_2, c_h, s0, s1)) | m_c_h_element_v_out(c_e_h_2, c_h, s0))),
% 289.65/182.13 inference(rewrite,[status(thm)],[])).
% 289.65/182.13 tff(3877,plain,
% 289.65/182.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s1)) | (~node15(c_e_h_2, c_h, s0, s1)) | m_c_h_element_v_out(c_e_h_2, c_h, s0))),
% 289.65/182.13 inference(quant_inst,[status(thm)],[])).
% 289.65/182.13 tff(3878,plain,
% 289.65/182.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s1)) | (~node15(c_e_h_2, c_h, s0, s1)) | m_c_h_element_v_out(c_e_h_2, c_h, s0)),
% 289.65/182.13 inference(modus_ponens,[status(thm)],[3877, 3876])).
% 289.65/182.13 tff(3879,plain,
% 289.65/182.13 ($false),
% 289.65/182.13 inference(unit_resolution,[status(thm)],[3878, 147, 3834, 3703, 3875])).
% 289.65/182.13 tff(3880,plain,(~m_c_h_element_v_out(c_e_h_2, c_h, s1)), inference(lemma,lemma(discharge,[]))).
% 289.65/182.13 tff(3881,plain,
% 289.65/182.13 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s1)) | m_c_h_element_v_out(c_e_h_2, c_h, s1))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s1)) | m_c_h_element_v_out(c_e_h_2, c_h, s1))),
% 289.65/182.13 inference(rewrite,[status(thm)],[])).
% 289.65/182.13 tff(3882,plain,
% 289.65/182.13 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s1)) | m_c_h_element_v_out(c_e_h_2, c_h, s1))),
% 289.65/182.13 inference(quant_inst,[status(thm)],[])).
% 289.65/182.13 tff(3883,plain,
% 289.65/182.13 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s1)) | m_c_h_element_v_out(c_e_h_2, c_h, s1)),
% 289.65/182.13 inference(modus_ponens,[status(thm)],[3882, 3881])).
% 289.65/182.13 tff(3884,plain,
% 289.65/182.13 (~m_and_h_gate_v_in1(c_e_h_2, c_i, s1)),
% 289.65/182.13 inference(unit_resolution,[status(thm)],[3883, 619, 3880])).
% 289.65/182.13 tff(3885,plain,
% 289.65/182.13 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s1)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s1)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s1))),
% 289.65/182.13 inference(rewrite,[status(thm)],[])).
% 289.65/182.13 tff(3886,plain,
% 289.65/182.13 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s1)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s1))),
% 289.65/182.13 inference(quant_inst,[status(thm)],[])).
% 289.65/182.13 tff(3887,plain,
% 289.65/182.13 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s1)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s1)),
% 289.65/182.13 inference(modus_ponens,[status(thm)],[3886, 3885])).
% 289.65/182.13 tff(3888,plain,
% 289.65/182.13 (~node20(c_e_h_2, c_i, s1)),
% 289.65/182.13 inference(unit_resolution,[status(thm)],[3887, 38, 3884])).
% 289.65/182.13 tff(3889,assumption,(~node20(c_e_h_2, c_i, s1)), introduced(assumption)).
% 289.65/182.13 tff(3890,assumption,(node21(c_e_h_2, c_i, s1, s2)), introduced(assumption)).
% 289.65/182.13 tff(3891,plain,
% 289.65/182.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s2)) | (~node21(c_e_h_2, c_i, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s2)) | (~node21(c_e_h_2, c_i, s1, s2)))),
% 289.65/182.13 inference(rewrite,[status(thm)],[])).
% 289.65/182.13 tff(3892,plain,
% 289.65/182.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s2)) | (~node21(c_e_h_2, c_i, s1, s2)))),
% 289.65/182.13 inference(quant_inst,[status(thm)],[])).
% 289.65/182.13 tff(3893,plain,
% 289.65/182.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s2)) | (~node21(c_e_h_2, c_i, s1, s2))),
% 289.65/182.13 inference(modus_ponens,[status(thm)],[3892, 3891])).
% 289.65/182.13 tff(3894,plain,
% 289.65/182.13 ($false),
% 289.65/182.13 inference(unit_resolution,[status(thm)],[3893, 52, 3890, 3824, 3889])).
% 289.65/182.13 tff(3895,plain,((~node21(c_e_h_2, c_i, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s2)) | node20(c_e_h_2, c_i, s1)), inference(lemma,lemma(discharge,[]))).
% 289.65/182.13 tff(3896,plain,
% 289.65/182.13 (~node21(c_e_h_2, c_i, s1, s2)),
% 289.65/182.13 inference(unit_resolution,[status(thm)],[3895, 3824, 3888])).
% 289.65/182.13 tff(3897,plain,
% 289.65/182.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_2, c_i, s1, s2) | node22(c_e_h_2, c_i, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_2, c_i, s1, s2) | node22(c_e_h_2, c_i, s1, s2))),
% 289.65/182.13 inference(rewrite,[status(thm)],[])).
% 289.65/182.13 tff(3898,plain,
% 289.65/182.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_2, c_i, s1, s2) | node22(c_e_h_2, c_i, s1, s2))),
% 289.65/182.13 inference(quant_inst,[status(thm)],[])).
% 289.65/182.13 tff(3899,plain,
% 289.65/182.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_2, c_i, s1, s2) | node22(c_e_h_2, c_i, s1, s2)),
% 289.65/182.13 inference(modus_ponens,[status(thm)],[3898, 3897])).
% 289.65/182.13 tff(3900,plain,
% 289.65/182.13 (node21(c_e_h_2, c_i, s1, s2) | node22(c_e_h_2, c_i, s1, s2)),
% 289.65/182.13 inference(unit_resolution,[status(thm)],[3899, 82, 255])).
% 289.65/182.13 tff(3901,plain,
% 289.65/182.13 ($false),
% 289.65/182.13 inference(unit_resolution,[status(thm)],[3900, 3896, 3833])).
% 289.65/182.13 tff(3902,plain,(~m_and_h_gate_v_out(c_e_h_2, c_i, s2)), inference(lemma,lemma(discharge,[]))).
% 289.65/182.13 tff(3903,plain,
% 289.65/182.13 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_f, s2)) | m_and_h_gate_v_out(c_e_h_2, c_i, s2))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s2)) | m_and_h_gate_v_out(c_e_h_2, c_i, s2))),
% 289.65/182.14 inference(rewrite,[status(thm)],[])).
% 289.65/182.14 tff(3904,plain,
% 289.65/182.14 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_f, s2)) | m_and_h_gate_v_out(c_e_h_2, c_i, s2))),
% 289.65/182.14 inference(quant_inst,[status(thm)],[])).
% 289.65/182.14 tff(3905,plain,
% 289.65/182.14 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s2)) | m_and_h_gate_v_out(c_e_h_2, c_i, s2)),
% 289.65/182.14 inference(modus_ponens,[status(thm)],[3904, 3903])).
% 289.65/182.14 tff(3906,plain,
% 289.65/182.14 (~m_c_h_element_v_in2(c_e_h_2, c_f, s2)),
% 289.65/182.14 inference(unit_resolution,[status(thm)],[3905, 2143, 3902])).
% 289.65/182.14 tff(3907,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_f, s2)), introduced(assumption)).
% 289.65/182.14 tff(3908,assumption,(~node15(c_e_h_2, c_f, s2, s3)), introduced(assumption)).
% 289.65/182.14 tff(3909,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_f, s2)), introduced(assumption)).
% 289.65/182.14 tff(3910,plain,
% 289.65/182.14 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_f, s2)) | m_c_h_element_v_in1(c_e_h_2, c_f, s2) | m_c_h_element_v_in2(c_e_h_2, c_f, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_f, s2)) | m_c_h_element_v_in1(c_e_h_2, c_f, s2) | m_c_h_element_v_in2(c_e_h_2, c_f, s2))),
% 289.65/182.14 inference(rewrite,[status(thm)],[])).
% 289.65/182.14 tff(3911,plain,
% 289.65/182.14 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_f, s2)) | m_c_h_element_v_in1(c_e_h_2, c_f, s2) | m_c_h_element_v_in2(c_e_h_2, c_f, s2))),
% 289.65/182.14 inference(quant_inst,[status(thm)],[])).
% 289.65/182.14 tff(3912,plain,
% 289.65/182.14 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_f, s2)) | m_c_h_element_v_in1(c_e_h_2, c_f, s2) | m_c_h_element_v_in2(c_e_h_2, c_f, s2)),
% 289.65/182.14 inference(modus_ponens,[status(thm)],[3911, 3910])).
% 289.65/182.14 tff(3913,plain,
% 289.65/182.14 ((~node16(c_e_h_2, c_f, s2)) | m_c_h_element_v_in1(c_e_h_2, c_f, s2)),
% 289.65/182.14 inference(unit_resolution,[status(thm)],[3912, 178, 3909])).
% 289.65/182.14 tff(3914,plain,
% 289.65/182.14 (~node16(c_e_h_2, c_f, s2)),
% 289.65/182.14 inference(unit_resolution,[status(thm)],[3913, 3907])).
% 289.65/182.14 tff(3915,plain,
% 289.65/182.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s2) | node15(c_e_h_2, c_f, s2, s3) | (~node19(c_e_h_2, c_f, s2, s3)) | node14(c_e_h_2, c_f, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_f, s2) | node15(c_e_h_2, c_f, s2, s3) | (~node19(c_e_h_2, c_f, s2, s3)) | node14(c_e_h_2, c_f, s2, s3))),
% 289.65/182.14 inference(rewrite,[status(thm)],[])).
% 289.65/182.14 tff(3916,plain,
% 289.65/182.14 ((node16(c_e_h_2, c_f, s2) | node14(c_e_h_2, c_f, s2, s3) | node15(c_e_h_2, c_f, s2, s3) | (~node19(c_e_h_2, c_f, s2, s3))) <=> (node16(c_e_h_2, c_f, s2) | node15(c_e_h_2, c_f, s2, s3) | (~node19(c_e_h_2, c_f, s2, s3)) | node14(c_e_h_2, c_f, s2, s3))),
% 289.65/182.14 inference(rewrite,[status(thm)],[])).
% 289.65/182.14 tff(3917,plain,
% 289.65/182.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s2) | node14(c_e_h_2, c_f, s2, s3) | node15(c_e_h_2, c_f, s2, s3) | (~node19(c_e_h_2, c_f, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s2) | node15(c_e_h_2, c_f, s2, s3) | (~node19(c_e_h_2, c_f, s2, s3)) | node14(c_e_h_2, c_f, s2, s3)))),
% 289.65/182.14 inference(monotonicity,[status(thm)],[3916])).
% 289.65/182.14 tff(3918,plain,
% 289.65/182.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s2) | node14(c_e_h_2, c_f, s2, s3) | node15(c_e_h_2, c_f, s2, s3) | (~node19(c_e_h_2, c_f, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_f, s2) | node15(c_e_h_2, c_f, s2, s3) | (~node19(c_e_h_2, c_f, s2, s3)) | node14(c_e_h_2, c_f, s2, s3))),
% 289.65/182.14 inference(transitivity,[status(thm)],[3917, 3915])).
% 289.65/182.14 tff(3919,plain,
% 289.65/182.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s2) | node14(c_e_h_2, c_f, s2, s3) | node15(c_e_h_2, c_f, s2, s3) | (~node19(c_e_h_2, c_f, s2, s3)))),
% 289.65/182.14 inference(quant_inst,[status(thm)],[])).
% 289.65/182.14 tff(3920,plain,
% 289.65/182.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_f, s2) | node15(c_e_h_2, c_f, s2, s3) | (~node19(c_e_h_2, c_f, s2, s3)) | node14(c_e_h_2, c_f, s2, s3)),
% 289.65/182.14 inference(modus_ponens,[status(thm)],[3919, 3918])).
% 289.65/182.14 tff(3921,plain,
% 289.65/182.14 (node16(c_e_h_2, c_f, s2) | node15(c_e_h_2, c_f, s2, s3) | node14(c_e_h_2, c_f, s2, s3)),
% 289.65/182.14 inference(unit_resolution,[status(thm)],[3920, 204, 3808])).
% 289.65/182.14 tff(3922,plain,
% 289.65/182.14 (node14(c_e_h_2, c_f, s2, s3)),
% 289.65/182.14 inference(unit_resolution,[status(thm)],[3921, 3914, 3908])).
% 289.65/182.14 tff(3923,plain,
% 289.65/182.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s3)) | m_c_h_element_v_in1(c_e_h_2, c_f, s2) | (~node14(c_e_h_2, c_f, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s3)) | m_c_h_element_v_in1(c_e_h_2, c_f, s2) | (~node14(c_e_h_2, c_f, s2, s3)))),
% 289.65/182.14 inference(rewrite,[status(thm)],[])).
% 289.65/182.14 tff(3924,plain,
% 289.65/182.14 (((~node14(c_e_h_2, c_f, s2, s3)) | m_c_h_element_v_in1(c_e_h_2, c_f, s2) | (~m_c_h_element_v_out(c_e_h_2, c_f, s3))) <=> ((~m_c_h_element_v_out(c_e_h_2, c_f, s3)) | m_c_h_element_v_in1(c_e_h_2, c_f, s2) | (~node14(c_e_h_2, c_f, s2, s3)))),
% 289.65/182.14 inference(rewrite,[status(thm)],[])).
% 289.65/182.14 tff(3925,plain,
% 289.65/182.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_f, s2, s3)) | m_c_h_element_v_in1(c_e_h_2, c_f, s2) | (~m_c_h_element_v_out(c_e_h_2, c_f, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s3)) | m_c_h_element_v_in1(c_e_h_2, c_f, s2) | (~node14(c_e_h_2, c_f, s2, s3))))),
% 289.65/182.14 inference(monotonicity,[status(thm)],[3924])).
% 289.65/182.14 tff(3926,plain,
% 289.65/182.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_f, s2, s3)) | m_c_h_element_v_in1(c_e_h_2, c_f, s2) | (~m_c_h_element_v_out(c_e_h_2, c_f, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s3)) | m_c_h_element_v_in1(c_e_h_2, c_f, s2) | (~node14(c_e_h_2, c_f, s2, s3)))),
% 289.65/182.14 inference(transitivity,[status(thm)],[3925, 3923])).
% 289.65/182.14 tff(3927,plain,
% 289.65/182.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_f, s2, s3)) | m_c_h_element_v_in1(c_e_h_2, c_f, s2) | (~m_c_h_element_v_out(c_e_h_2, c_f, s3)))),
% 289.65/182.14 inference(quant_inst,[status(thm)],[])).
% 289.65/182.14 tff(3928,plain,
% 289.65/182.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s3)) | m_c_h_element_v_in1(c_e_h_2, c_f, s2) | (~node14(c_e_h_2, c_f, s2, s3))),
% 289.65/182.14 inference(modus_ponens,[status(thm)],[3927, 3926])).
% 289.65/182.14 tff(3929,plain,
% 289.65/182.14 ($false),
% 289.65/182.14 inference(unit_resolution,[status(thm)],[3928, 223, 3793, 3922, 3907])).
% 289.65/182.14 tff(3930,plain,(m_c_h_element_v_in1(c_e_h_2, c_f, s2) | (~m_c_h_element_v_out(c_e_h_2, c_f, s3)) | node15(c_e_h_2, c_f, s2, s3) | m_c_h_element_v_in2(c_e_h_2, c_f, s2)), inference(lemma,lemma(discharge,[]))).
% 289.65/182.14 tff(3931,plain,
% 289.65/182.14 (m_c_h_element_v_in1(c_e_h_2, c_f, s2) | (~m_c_h_element_v_out(c_e_h_2, c_f, s3)) | node15(c_e_h_2, c_f, s2, s3)),
% 289.65/182.14 inference(unit_resolution,[status(thm)],[3930, 3906])).
% 289.65/182.14 tff(3932,plain,
% 289.65/182.14 (m_c_h_element_v_in1(c_e_h_2, c_f, s2)),
% 289.65/182.14 inference(unit_resolution,[status(thm)],[3931, 3823, 3793])).
% 289.65/182.14 tff(3933,plain,
% 289.65/182.14 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_2, c_f, s2) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s2)) | (~node17(c_e_h_2, c_f, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_f, s2) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s2)) | (~node17(c_e_h_2, c_f, s2)))),
% 289.65/182.14 inference(rewrite,[status(thm)],[])).
% 289.65/182.14 tff(3934,plain,
% 289.65/182.14 (((~m_c_h_element_v_in1(c_e_h_2, c_f, s2)) | m_c_h_element_v_in2(c_e_h_2, c_f, s2) | (~node17(c_e_h_2, c_f, s2))) <=> (m_c_h_element_v_in2(c_e_h_2, c_f, s2) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s2)) | (~node17(c_e_h_2, c_f, s2)))),
% 289.65/182.14 inference(rewrite,[status(thm)],[])).
% 289.65/182.14 tff(3935,plain,
% 289.65/182.14 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s2)) | m_c_h_element_v_in2(c_e_h_2, c_f, s2) | (~node17(c_e_h_2, c_f, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_2, c_f, s2) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s2)) | (~node17(c_e_h_2, c_f, s2))))),
% 289.65/182.14 inference(monotonicity,[status(thm)],[3934])).
% 289.65/182.14 tff(3936,plain,
% 289.65/182.14 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s2)) | m_c_h_element_v_in2(c_e_h_2, c_f, s2) | (~node17(c_e_h_2, c_f, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_f, s2) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s2)) | (~node17(c_e_h_2, c_f, s2)))),
% 289.65/182.14 inference(transitivity,[status(thm)],[3935, 3933])).
% 289.65/182.14 tff(3937,plain,
% 289.65/182.14 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s2)) | m_c_h_element_v_in2(c_e_h_2, c_f, s2) | (~node17(c_e_h_2, c_f, s2)))),
% 289.65/182.14 inference(quant_inst,[status(thm)],[])).
% 289.65/182.14 tff(3938,plain,
% 289.65/182.14 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_f, s2) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s2)) | (~node17(c_e_h_2, c_f, s2))),
% 289.65/182.14 inference(modus_ponens,[status(thm)],[3937, 3936])).
% 289.65/182.14 tff(3939,plain,
% 289.65/182.14 ((~m_c_h_element_v_in1(c_e_h_2, c_f, s2)) | (~node17(c_e_h_2, c_f, s2))),
% 289.65/182.14 inference(unit_resolution,[status(thm)],[3938, 919, 3906])).
% 289.65/182.14 tff(3940,plain,
% 289.65/182.14 ($false),
% 289.65/182.14 inference(unit_resolution,[status(thm)],[3939, 3932, 3816])).
% 289.65/182.14 tff(3941,plain,(m_c_h_element_v_out(c_e_h_2, c_f, s2) | (~m_c_h_element_v_out(c_e_h_2, c_f, s3))), inference(lemma,lemma(discharge,[]))).
% 289.65/182.14 tff(3942,plain,
% 289.65/182.14 (~m_c_h_element_v_out(c_e_h_2, c_f, s3)),
% 289.65/182.14 inference(unit_resolution,[status(thm)],[3941, 3760])).
% 289.65/182.14 tff(3943,plain,
% 289.65/182.14 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_q, s3)) | m_c_h_element_v_out(c_e_h_2, c_f, s3))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_q, s3)) | m_c_h_element_v_out(c_e_h_2, c_f, s3))),
% 289.65/182.14 inference(rewrite,[status(thm)],[])).
% 289.65/182.14 tff(3944,plain,
% 289.65/182.14 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_q, s3)) | m_c_h_element_v_out(c_e_h_2, c_f, s3))),
% 289.65/182.15 inference(quant_inst,[status(thm)],[])).
% 289.65/182.15 tff(3945,plain,
% 289.65/182.15 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_q, s3)) | m_c_h_element_v_out(c_e_h_2, c_f, s3)),
% 289.65/182.15 inference(modus_ponens,[status(thm)],[3944, 3943])).
% 289.65/182.15 tff(3946,plain,
% 289.65/182.15 (~m_and_h_gate_v_in1(c_e_h_2, c_q, s3)),
% 289.65/182.15 inference(unit_resolution,[status(thm)],[3945, 1586, 3942])).
% 289.65/182.15 tff(3947,plain,
% 289.65/182.15 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_q, s3)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_q, s3)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s3))),
% 289.65/182.15 inference(rewrite,[status(thm)],[])).
% 289.65/182.15 tff(3948,plain,
% 289.65/182.15 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_q, s3)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s3))),
% 289.65/182.15 inference(quant_inst,[status(thm)],[])).
% 289.65/182.15 tff(3949,plain,
% 289.65/182.15 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_q, s3)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s3)),
% 289.65/182.15 inference(modus_ponens,[status(thm)],[3948, 3947])).
% 289.65/182.15 tff(3950,plain,
% 289.65/182.15 (~node20(c_e_h_2, c_q, s3)),
% 289.65/182.15 inference(unit_resolution,[status(thm)],[3949, 38, 3946])).
% 289.65/182.15 tff(3951,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_q, s3)), introduced(assumption)).
% 289.65/182.15 tff(3952,assumption,(m_and_h_gate_v_out(c_e_h_2, c_q, s4)), introduced(assumption)).
% 289.65/182.15 tff(3953,assumption,(~node20(c_e_h_2, c_q, s3)), introduced(assumption)).
% 289.65/182.15 tff(3954,assumption,(node21(c_e_h_2, c_q, s3, s4)), introduced(assumption)).
% 289.65/182.15 tff(3955,plain,
% 289.65/182.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_q, s3) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s4)) | (~node21(c_e_h_2, c_q, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_q, s3) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s4)) | (~node21(c_e_h_2, c_q, s3, s4)))),
% 289.65/182.15 inference(rewrite,[status(thm)],[])).
% 289.65/182.15 tff(3956,plain,
% 289.65/182.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_q, s3) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s4)) | (~node21(c_e_h_2, c_q, s3, s4)))),
% 289.65/182.15 inference(quant_inst,[status(thm)],[])).
% 289.65/182.15 tff(3957,plain,
% 289.65/182.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_q, s3) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s4)) | (~node21(c_e_h_2, c_q, s3, s4))),
% 289.65/182.15 inference(modus_ponens,[status(thm)],[3956, 3955])).
% 289.65/182.15 tff(3958,plain,
% 289.65/182.15 ($false),
% 289.65/182.15 inference(unit_resolution,[status(thm)],[3957, 52, 3954, 3952, 3953])).
% 289.65/182.15 tff(3959,plain,((~node21(c_e_h_2, c_q, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s4)) | node20(c_e_h_2, c_q, s3)), inference(lemma,lemma(discharge,[]))).
% 289.65/182.15 tff(3960,plain,
% 289.65/182.15 (~node21(c_e_h_2, c_q, s3, s4)),
% 289.65/182.15 inference(unit_resolution,[status(thm)],[3959, 3952, 3953])).
% 289.65/182.15 tff(3961,plain,
% 289.65/182.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_2, c_q, s3, s4) | node22(c_e_h_2, c_q, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_2, c_q, s3, s4) | node22(c_e_h_2, c_q, s3, s4))),
% 289.65/182.15 inference(rewrite,[status(thm)],[])).
% 289.65/182.15 tff(3962,plain,
% 289.65/182.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_2, c_q, s3, s4) | node22(c_e_h_2, c_q, s3, s4))),
% 289.65/182.15 inference(quant_inst,[status(thm)],[])).
% 289.65/182.15 tff(3963,plain,
% 289.65/182.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_2, c_q, s3, s4) | node22(c_e_h_2, c_q, s3, s4)),
% 289.65/182.15 inference(modus_ponens,[status(thm)],[3962, 3961])).
% 289.65/182.15 tff(3964,plain,
% 289.65/182.15 (node21(c_e_h_2, c_q, s3, s4) | node22(c_e_h_2, c_q, s3, s4)),
% 289.65/182.15 inference(unit_resolution,[status(thm)],[3963, 82, 531])).
% 289.65/182.15 tff(3965,plain,
% 289.65/182.15 (node22(c_e_h_2, c_q, s3, s4)),
% 289.65/182.15 inference(unit_resolution,[status(thm)],[3964, 3960])).
% 289.65/182.15 tff(3966,plain,
% 289.65/182.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s4)) | (~node22(c_e_h_2, c_q, s3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_q, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s4)) | (~node22(c_e_h_2, c_q, s3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_q, s3))),
% 289.65/182.15 inference(rewrite,[status(thm)],[])).
% 289.65/182.15 tff(3967,plain,
% 289.65/182.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s4)) | (~node22(c_e_h_2, c_q, s3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_q, s3))),
% 289.65/182.15 inference(quant_inst,[status(thm)],[])).
% 289.65/182.15 tff(3968,plain,
% 289.65/182.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s4)) | (~node22(c_e_h_2, c_q, s3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_q, s3)),
% 289.65/182.15 inference(modus_ponens,[status(thm)],[3967, 3966])).
% 289.65/182.15 tff(3969,plain,
% 289.65/182.15 ($false),
% 289.65/182.15 inference(unit_resolution,[status(thm)],[3968, 108, 3965, 3952, 3951])).
% 289.65/182.15 tff(3970,plain,((~m_and_h_gate_v_out(c_e_h_2, c_q, s4)) | m_and_h_gate_v_out(c_e_h_2, c_q, s3) | node20(c_e_h_2, c_q, s3)), inference(lemma,lemma(discharge,[]))).
% 289.65/182.15 tff(3971,plain,
% 289.65/182.15 ((~m_and_h_gate_v_out(c_e_h_2, c_q, s4)) | m_and_h_gate_v_out(c_e_h_2, c_q, s3)),
% 289.65/182.15 inference(unit_resolution,[status(thm)],[3970, 3950])).
% 289.65/182.15 tff(3972,plain,
% 289.65/182.15 (~m_and_h_gate_v_out(c_e_h_2, c_q, s4)),
% 289.65/182.15 inference(unit_resolution,[status(thm)],[3971, 3792])).
% 289.65/182.15 tff(3973,plain,
% 289.65/182.15 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s4))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s4))),
% 289.65/182.15 inference(rewrite,[status(thm)],[])).
% 289.65/182.15 tff(3974,plain,
% 289.65/182.15 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s4))),
% 289.65/182.15 inference(quant_inst,[status(thm)],[])).
% 289.65/182.15 tff(3975,plain,
% 289.65/182.15 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s4)),
% 289.65/182.15 inference(modus_ponens,[status(thm)],[3974, 3973])).
% 289.65/182.15 tff(3976,plain,
% 289.65/182.15 (node3(c_e_h_2, c_e_h_3, s4)),
% 289.65/182.15 inference(unit_resolution,[status(thm)],[3975, 1059, 1056])).
% 289.65/182.15 tff(3977,plain,
% 289.65/182.15 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_3, s4)) | (~node3(c_e_h_2, c_e_h_3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_q, s4))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_3, s4)) | (~node3(c_e_h_2, c_e_h_3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_q, s4))),
% 289.65/182.15 inference(rewrite,[status(thm)],[])).
% 289.65/182.15 tff(3978,plain,
% 289.65/182.15 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_3, s4)) | (~node3(c_e_h_2, c_e_h_3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_q, s4))),
% 289.65/182.15 inference(quant_inst,[status(thm)],[])).
% 289.65/182.15 tff(3979,plain,
% 289.65/182.15 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_3, s4)) | (~node3(c_e_h_2, c_e_h_3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_q, s4)),
% 289.65/182.16 inference(modus_ponens,[status(thm)],[3978, 3977])).
% 289.65/182.16 tff(3980,plain,
% 289.65/182.16 ((~m_cell_v_ack(c_e_h_3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_q, s4)),
% 289.65/182.16 inference(unit_resolution,[status(thm)],[3979, 1073, 3976])).
% 289.65/182.16 tff(3981,plain,
% 289.65/182.16 (~m_cell_v_ack(c_e_h_3, s4)),
% 289.65/182.16 inference(unit_resolution,[status(thm)],[3980, 3972])).
% 289.65/182.16 tff(3982,plain,
% 289.65/182.16 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_j, s4)) | m_cell_v_ack(c_e_h_3, s4))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_j, s4)) | m_cell_v_ack(c_e_h_3, s4))),
% 289.65/182.16 inference(rewrite,[status(thm)],[])).
% 289.65/182.16 tff(3983,plain,
% 289.65/182.16 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_j, s4)) | m_cell_v_ack(c_e_h_3, s4))),
% 289.65/182.16 inference(quant_inst,[status(thm)],[])).
% 289.65/182.16 tff(3984,plain,
% 289.65/182.16 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_j, s4)) | m_cell_v_ack(c_e_h_3, s4)),
% 289.65/182.16 inference(modus_ponens,[status(thm)],[3983, 3982])).
% 289.65/182.16 tff(3985,plain,
% 289.65/182.16 (~m_or_h_gate_v_in2(c_e_h_3, c_j, s4)),
% 289.65/182.16 inference(unit_resolution,[status(thm)],[3984, 1085, 3981])).
% 289.65/182.16 tff(3986,assumption,(~m_or_h_gate_v_in1(c_e_h_3, c_j, s4)), introduced(assumption)).
% 289.65/182.16 tff(3987,assumption,(~m_or_h_gate_v_in2(c_e_h_3, c_j, s4)), introduced(assumption)).
% 289.65/182.16 tff(3988,assumption,(node5(c_e_h_3, c_j, s4, s5)), introduced(assumption)).
% 289.65/182.16 tff(3989,plain,
% 289.65/182.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_3, c_j, s5)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s4) | m_or_h_gate_v_in1(c_e_h_3, c_j, s4) | (~node5(c_e_h_3, c_j, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s5)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s4) | m_or_h_gate_v_in1(c_e_h_3, c_j, s4) | (~node5(c_e_h_3, c_j, s4, s5)))),
% 289.65/182.16 inference(rewrite,[status(thm)],[])).
% 289.65/182.16 tff(3990,plain,
% 289.65/182.16 ((m_or_h_gate_v_in1(c_e_h_3, c_j, s4) | m_or_h_gate_v_in2(c_e_h_3, c_j, s4) | (~node5(c_e_h_3, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s5))) <=> ((~m_or_h_gate_v_out(c_e_h_3, c_j, s5)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s4) | m_or_h_gate_v_in1(c_e_h_3, c_j, s4) | (~node5(c_e_h_3, c_j, s4, s5)))),
% 289.65/182.16 inference(rewrite,[status(thm)],[])).
% 289.65/182.16 tff(3991,plain,
% 289.65/182.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s4) | m_or_h_gate_v_in2(c_e_h_3, c_j, s4) | (~node5(c_e_h_3, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_3, c_j, s5)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s4) | m_or_h_gate_v_in1(c_e_h_3, c_j, s4) | (~node5(c_e_h_3, c_j, s4, s5))))),
% 289.65/182.16 inference(monotonicity,[status(thm)],[3990])).
% 289.65/182.16 tff(3992,plain,
% 289.65/182.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s4) | m_or_h_gate_v_in2(c_e_h_3, c_j, s4) | (~node5(c_e_h_3, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s5)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s4) | m_or_h_gate_v_in1(c_e_h_3, c_j, s4) | (~node5(c_e_h_3, c_j, s4, s5)))),
% 289.65/182.16 inference(transitivity,[status(thm)],[3991, 3989])).
% 289.65/182.16 tff(3993,plain,
% 289.65/182.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s4) | m_or_h_gate_v_in2(c_e_h_3, c_j, s4) | (~node5(c_e_h_3, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s5)))),
% 289.65/182.16 inference(quant_inst,[status(thm)],[])).
% 289.65/182.16 tff(3994,plain,
% 289.65/182.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s5)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s4) | m_or_h_gate_v_in1(c_e_h_3, c_j, s4) | (~node5(c_e_h_3, c_j, s4, s5))),
% 289.65/182.16 inference(modus_ponens,[status(thm)],[3993, 3992])).
% 289.65/182.16 tff(3995,plain,
% 289.65/182.16 ($false),
% 289.65/182.16 inference(unit_resolution,[status(thm)],[3994, 1159, 3988, 3987, 3616, 3986])).
% 289.65/182.16 tff(3996,plain,((~node5(c_e_h_3, c_j, s4, s5)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s5)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s4)), inference(lemma,lemma(discharge,[]))).
% 289.65/182.16 tff(3997,plain,
% 289.65/182.16 ((~node5(c_e_h_3, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s5)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s4)),
% 289.65/182.16 inference(unit_resolution,[status(thm)],[3996, 3985])).
% 289.65/182.16 tff(3998,plain,
% 289.65/182.16 (~node5(c_e_h_3, c_j, s4, s5)),
% 289.65/182.16 inference(unit_resolution,[status(thm)],[3997, 3641, 3616])).
% 289.65/182.16 tff(3999,plain,
% 289.65/182.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s4, s5)) | node5(c_e_h_3, c_j, s4, s5) | node6(c_e_h_3, c_j, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s4, s5)) | node5(c_e_h_3, c_j, s4, s5) | node6(c_e_h_3, c_j, s4, s5))),
% 289.65/182.16 inference(rewrite,[status(thm)],[])).
% 289.65/182.16 tff(4000,plain,
% 289.65/182.16 ((node6(c_e_h_3, c_j, s4, s5) | node5(c_e_h_3, c_j, s4, s5) | (~trans(s4, s5))) <=> ((~trans(s4, s5)) | node5(c_e_h_3, c_j, s4, s5) | node6(c_e_h_3, c_j, s4, s5))),
% 289.65/182.16 inference(rewrite,[status(thm)],[])).
% 289.65/182.16 tff(4001,plain,
% 289.65/182.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s4, s5) | node5(c_e_h_3, c_j, s4, s5) | (~trans(s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s4, s5)) | node5(c_e_h_3, c_j, s4, s5) | node6(c_e_h_3, c_j, s4, s5)))),
% 289.65/182.16 inference(monotonicity,[status(thm)],[4000])).
% 289.65/182.16 tff(4002,plain,
% 289.65/182.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s4, s5) | node5(c_e_h_3, c_j, s4, s5) | (~trans(s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s4, s5)) | node5(c_e_h_3, c_j, s4, s5) | node6(c_e_h_3, c_j, s4, s5))),
% 289.65/182.16 inference(transitivity,[status(thm)],[4001, 3999])).
% 289.65/182.16 tff(4003,plain,
% 289.65/182.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s4, s5) | node5(c_e_h_3, c_j, s4, s5) | (~trans(s4, s5)))),
% 289.65/182.16 inference(quant_inst,[status(thm)],[])).
% 289.65/182.16 tff(4004,plain,
% 289.65/182.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s4, s5)) | node5(c_e_h_3, c_j, s4, s5) | node6(c_e_h_3, c_j, s4, s5)),
% 289.65/182.16 inference(modus_ponens,[status(thm)],[4003, 4002])).
% 289.65/182.16 tff(4005,plain,
% 289.65/182.16 (node5(c_e_h_3, c_j, s4, s5) | node6(c_e_h_3, c_j, s4, s5)),
% 289.65/182.16 inference(unit_resolution,[status(thm)],[4004, 1141, 1028])).
% 289.65/182.16 tff(4006,plain,
% 289.65/182.16 (node6(c_e_h_3, c_j, s4, s5)),
% 289.65/182.16 inference(unit_resolution,[status(thm)],[4005, 3998])).
% 289.65/182.16 tff(4007,assumption,(~m_or_h_gate_v_out(c_e_h_3, c_j, s4)), introduced(assumption)).
% 289.65/182.16 tff(4008,assumption,(node6(c_e_h_3, c_j, s4, s5)), introduced(assumption)).
% 289.65/182.16 tff(4009,plain,
% 289.65/182.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_3, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s5)) | (~node6(c_e_h_3, c_j, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s5)) | (~node6(c_e_h_3, c_j, s4, s5)))),
% 289.65/182.16 inference(rewrite,[status(thm)],[])).
% 289.65/182.16 tff(4010,plain,
% 289.65/182.16 (((~node6(c_e_h_3, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s5)) | m_or_h_gate_v_out(c_e_h_3, c_j, s4)) <=> (m_or_h_gate_v_out(c_e_h_3, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s5)) | (~node6(c_e_h_3, c_j, s4, s5)))),
% 289.65/182.16 inference(rewrite,[status(thm)],[])).
% 289.65/182.16 tff(4011,plain,
% 289.65/182.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s5)) | m_or_h_gate_v_out(c_e_h_3, c_j, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_3, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s5)) | (~node6(c_e_h_3, c_j, s4, s5))))),
% 289.65/182.16 inference(monotonicity,[status(thm)],[4010])).
% 289.65/182.16 tff(4012,plain,
% 289.65/182.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s5)) | m_or_h_gate_v_out(c_e_h_3, c_j, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s5)) | (~node6(c_e_h_3, c_j, s4, s5)))),
% 289.65/182.16 inference(transitivity,[status(thm)],[4011, 4009])).
% 289.65/182.16 tff(4013,plain,
% 289.65/182.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s5)) | m_or_h_gate_v_out(c_e_h_3, c_j, s4))),
% 289.65/182.16 inference(quant_inst,[status(thm)],[])).
% 289.65/182.16 tff(4014,plain,
% 289.65/182.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s5)) | (~node6(c_e_h_3, c_j, s4, s5))),
% 289.65/182.16 inference(modus_ponens,[status(thm)],[4013, 4012])).
% 289.65/182.16 tff(4015,plain,
% 289.65/182.16 ($false),
% 289.65/182.16 inference(unit_resolution,[status(thm)],[4014, 1121, 4008, 3616, 4007])).
% 289.65/182.16 tff(4016,plain,((~node6(c_e_h_3, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s5)) | m_or_h_gate_v_out(c_e_h_3, c_j, s4)), inference(lemma,lemma(discharge,[]))).
% 289.65/182.16 tff(4017,plain,
% 289.65/182.16 (m_or_h_gate_v_out(c_e_h_3, c_j, s4)),
% 289.65/182.16 inference(unit_resolution,[status(thm)],[4016, 4006, 3616])).
% 289.65/182.16 tff(4018,assumption,(m_or_h_gate_v_out(c_e_h_3, c_j, s4)), introduced(assumption)).
% 289.65/182.16 tff(4019,assumption,(node6(c_e_h_3, c_j, s3, s4)), introduced(assumption)).
% 289.65/182.16 tff(4020,plain,
% 289.65/182.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_3, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s4)) | (~node6(c_e_h_3, c_j, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s4)) | (~node6(c_e_h_3, c_j, s3, s4)))),
% 289.65/182.16 inference(rewrite,[status(thm)],[])).
% 289.65/182.16 tff(4021,plain,
% 289.65/182.16 (((~node6(c_e_h_3, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s4)) | m_or_h_gate_v_out(c_e_h_3, c_j, s3)) <=> (m_or_h_gate_v_out(c_e_h_3, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s4)) | (~node6(c_e_h_3, c_j, s3, s4)))),
% 289.65/182.16 inference(rewrite,[status(thm)],[])).
% 289.65/182.16 tff(4022,plain,
% 289.65/182.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s4)) | m_or_h_gate_v_out(c_e_h_3, c_j, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_3, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s4)) | (~node6(c_e_h_3, c_j, s3, s4))))),
% 289.65/182.17 inference(monotonicity,[status(thm)],[4021])).
% 289.65/182.17 tff(4023,plain,
% 289.65/182.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s4)) | m_or_h_gate_v_out(c_e_h_3, c_j, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s4)) | (~node6(c_e_h_3, c_j, s3, s4)))),
% 289.65/182.17 inference(transitivity,[status(thm)],[4022, 4020])).
% 289.65/182.17 tff(4024,plain,
% 289.65/182.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s4)) | m_or_h_gate_v_out(c_e_h_3, c_j, s3))),
% 289.65/182.17 inference(quant_inst,[status(thm)],[])).
% 289.65/182.17 tff(4025,plain,
% 289.65/182.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s4)) | (~node6(c_e_h_3, c_j, s3, s4))),
% 289.65/182.17 inference(modus_ponens,[status(thm)],[4024, 4023])).
% 289.65/182.17 tff(4026,plain,
% 289.65/182.17 ($false),
% 289.65/182.17 inference(unit_resolution,[status(thm)],[4025, 1121, 4019, 4018, 2235])).
% 289.65/182.17 tff(4027,plain,((~node6(c_e_h_3, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s4)) | m_or_h_gate_v_out(c_e_h_3, c_j, s3)), inference(lemma,lemma(discharge,[]))).
% 289.65/182.17 tff(4028,plain,
% 289.65/182.17 (~node6(c_e_h_3, c_j, s3, s4)),
% 289.65/182.17 inference(unit_resolution,[status(thm)],[4027, 4017, 2235])).
% 289.65/182.17 tff(4029,plain,
% 289.65/182.17 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s3))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s3))),
% 289.65/182.17 inference(rewrite,[status(thm)],[])).
% 289.65/182.17 tff(4030,plain,
% 289.65/182.17 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s3))),
% 289.65/182.17 inference(quant_inst,[status(thm)],[])).
% 289.65/182.17 tff(4031,plain,
% 289.65/182.17 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s3)),
% 289.65/182.17 inference(modus_ponens,[status(thm)],[4030, 4029])).
% 289.65/182.17 tff(4032,plain,
% 289.65/182.17 (node3(c_e_h_2, c_e_h_3, s3)),
% 289.65/182.17 inference(unit_resolution,[status(thm)],[4031, 1059, 1056])).
% 289.65/182.17 tff(4033,plain,
% 289.65/182.17 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_3, s3)) | (~node3(c_e_h_2, c_e_h_3, s3)) | m_and_h_gate_v_out(c_e_h_2, c_q, s3))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_3, s3)) | (~node3(c_e_h_2, c_e_h_3, s3)) | m_and_h_gate_v_out(c_e_h_2, c_q, s3))),
% 289.65/182.17 inference(rewrite,[status(thm)],[])).
% 289.65/182.17 tff(4034,plain,
% 289.65/182.17 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_3, s3)) | (~node3(c_e_h_2, c_e_h_3, s3)) | m_and_h_gate_v_out(c_e_h_2, c_q, s3))),
% 289.65/182.17 inference(quant_inst,[status(thm)],[])).
% 289.65/182.17 tff(4035,plain,
% 289.65/182.17 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_3, s3)) | (~node3(c_e_h_2, c_e_h_3, s3)) | m_and_h_gate_v_out(c_e_h_2, c_q, s3)),
% 289.65/182.17 inference(modus_ponens,[status(thm)],[4034, 4033])).
% 289.65/182.17 tff(4036,plain,
% 289.65/182.17 ((~m_cell_v_ack(c_e_h_3, s3)) | m_and_h_gate_v_out(c_e_h_2, c_q, s3)),
% 289.65/182.17 inference(unit_resolution,[status(thm)],[4035, 1073, 4032])).
% 289.65/182.17 tff(4037,plain,
% 289.65/182.17 (~m_cell_v_ack(c_e_h_3, s3)),
% 289.65/182.17 inference(unit_resolution,[status(thm)],[4036, 3792])).
% 289.65/182.17 tff(4038,plain,
% 289.65/182.17 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_j, s3)) | m_cell_v_ack(c_e_h_3, s3))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_j, s3)) | m_cell_v_ack(c_e_h_3, s3))),
% 289.65/182.17 inference(rewrite,[status(thm)],[])).
% 289.65/182.17 tff(4039,plain,
% 289.65/182.17 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_j, s3)) | m_cell_v_ack(c_e_h_3, s3))),
% 289.65/182.17 inference(quant_inst,[status(thm)],[])).
% 289.65/182.17 tff(4040,plain,
% 289.65/182.17 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_j, s3)) | m_cell_v_ack(c_e_h_3, s3)),
% 289.65/182.17 inference(modus_ponens,[status(thm)],[4039, 4038])).
% 289.65/182.17 tff(4041,plain,
% 289.65/182.17 (~m_or_h_gate_v_in2(c_e_h_3, c_j, s3)),
% 289.65/182.17 inference(unit_resolution,[status(thm)],[4040, 1085, 4037])).
% 289.65/182.17 tff(4042,assumption,(~m_or_h_gate_v_in2(c_e_h_3, c_j, s3)), introduced(assumption)).
% 289.65/182.17 tff(4043,assumption,(node5(c_e_h_3, c_j, s3, s4)), introduced(assumption)).
% 289.65/182.17 tff(4044,plain,
% 289.65/182.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s3) | m_or_h_gate_v_in2(c_e_h_3, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s4)) | (~node5(c_e_h_3, c_j, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in1(c_e_h_3, c_j, s3) | m_or_h_gate_v_in2(c_e_h_3, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s4)) | (~node5(c_e_h_3, c_j, s3, s4)))),
% 289.65/182.17 inference(rewrite,[status(thm)],[])).
% 289.65/182.17 tff(4045,plain,
% 289.65/182.17 ((m_or_h_gate_v_in1(c_e_h_3, c_j, s3) | m_or_h_gate_v_in2(c_e_h_3, c_j, s3) | (~node5(c_e_h_3, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s4))) <=> (m_or_h_gate_v_in1(c_e_h_3, c_j, s3) | m_or_h_gate_v_in2(c_e_h_3, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s4)) | (~node5(c_e_h_3, c_j, s3, s4)))),
% 289.65/182.17 inference(rewrite,[status(thm)],[])).
% 289.65/182.17 tff(4046,plain,
% 289.65/182.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s3) | m_or_h_gate_v_in2(c_e_h_3, c_j, s3) | (~node5(c_e_h_3, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s3) | m_or_h_gate_v_in2(c_e_h_3, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s4)) | (~node5(c_e_h_3, c_j, s3, s4))))),
% 289.65/182.17 inference(monotonicity,[status(thm)],[4045])).
% 289.65/182.17 tff(4047,plain,
% 289.65/182.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s3) | m_or_h_gate_v_in2(c_e_h_3, c_j, s3) | (~node5(c_e_h_3, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in1(c_e_h_3, c_j, s3) | m_or_h_gate_v_in2(c_e_h_3, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s4)) | (~node5(c_e_h_3, c_j, s3, s4)))),
% 289.65/182.17 inference(transitivity,[status(thm)],[4046, 4044])).
% 289.65/182.17 tff(4048,plain,
% 289.65/182.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s3) | m_or_h_gate_v_in2(c_e_h_3, c_j, s3) | (~node5(c_e_h_3, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s4)))),
% 289.65/182.17 inference(quant_inst,[status(thm)],[])).
% 289.65/182.17 tff(4049,plain,
% 289.65/182.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in1(c_e_h_3, c_j, s3) | m_or_h_gate_v_in2(c_e_h_3, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s4)) | (~node5(c_e_h_3, c_j, s3, s4))),
% 289.65/182.18 inference(modus_ponens,[status(thm)],[4048, 4047])).
% 289.65/182.18 tff(4050,plain,
% 289.65/182.18 ($false),
% 289.65/182.18 inference(unit_resolution,[status(thm)],[4049, 1159, 4043, 4018, 4042, 3617])).
% 289.65/182.18 tff(4051,plain,((~node5(c_e_h_3, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s4)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s3) | m_or_h_gate_v_in1(c_e_h_3, c_j, s3)), inference(lemma,lemma(discharge,[]))).
% 289.65/182.18 tff(4052,plain,
% 289.65/182.18 ((~node5(c_e_h_3, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s4)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s3)),
% 289.65/182.18 inference(unit_resolution,[status(thm)],[4051, 4041])).
% 289.65/182.18 tff(4053,plain,
% 289.65/182.18 (~node5(c_e_h_3, c_j, s3, s4)),
% 289.65/182.18 inference(unit_resolution,[status(thm)],[4052, 4017, 3617])).
% 289.65/182.18 tff(4054,plain,
% 289.65/182.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s3, s4)) | node6(c_e_h_3, c_j, s3, s4) | node5(c_e_h_3, c_j, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s3, s4)) | node6(c_e_h_3, c_j, s3, s4) | node5(c_e_h_3, c_j, s3, s4))),
% 289.65/182.18 inference(rewrite,[status(thm)],[])).
% 289.65/182.18 tff(4055,plain,
% 289.65/182.18 ((node6(c_e_h_3, c_j, s3, s4) | node5(c_e_h_3, c_j, s3, s4) | (~trans(s3, s4))) <=> ((~trans(s3, s4)) | node6(c_e_h_3, c_j, s3, s4) | node5(c_e_h_3, c_j, s3, s4))),
% 289.65/182.18 inference(rewrite,[status(thm)],[])).
% 289.65/182.18 tff(4056,plain,
% 289.65/182.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s3, s4) | node5(c_e_h_3, c_j, s3, s4) | (~trans(s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s3, s4)) | node6(c_e_h_3, c_j, s3, s4) | node5(c_e_h_3, c_j, s3, s4)))),
% 289.65/182.18 inference(monotonicity,[status(thm)],[4055])).
% 289.65/182.18 tff(4057,plain,
% 289.65/182.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s3, s4) | node5(c_e_h_3, c_j, s3, s4) | (~trans(s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s3, s4)) | node6(c_e_h_3, c_j, s3, s4) | node5(c_e_h_3, c_j, s3, s4))),
% 289.65/182.18 inference(transitivity,[status(thm)],[4056, 4054])).
% 289.65/182.18 tff(4058,plain,
% 289.65/182.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s3, s4) | node5(c_e_h_3, c_j, s3, s4) | (~trans(s3, s4)))),
% 289.65/182.18 inference(quant_inst,[status(thm)],[])).
% 289.65/182.18 tff(4059,plain,
% 289.65/182.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s3, s4)) | node6(c_e_h_3, c_j, s3, s4) | node5(c_e_h_3, c_j, s3, s4)),
% 289.65/182.18 inference(modus_ponens,[status(thm)],[4058, 4057])).
% 289.65/182.18 tff(4060,plain,
% 289.65/182.18 (node6(c_e_h_3, c_j, s3, s4) | node5(c_e_h_3, c_j, s3, s4)),
% 289.65/182.18 inference(unit_resolution,[status(thm)],[4059, 1141, 531])).
% 289.65/182.18 tff(4061,plain,
% 289.65/182.18 ($false),
% 289.65/182.18 inference(unit_resolution,[status(thm)],[4060, 4053, 4028])).
% 289.65/182.18 tff(4062,plain,(m_or_h_gate_v_in1(c_e_h_3, c_j, s3) | m_or_h_gate_v_out(c_e_h_3, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s5)) | node20(c_e_h_3, c_l, s3)), inference(lemma,lemma(discharge,[]))).
% 289.65/182.18 tff(4063,plain,
% 289.65/182.18 (m_or_h_gate_v_in1(c_e_h_3, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s5)) | node20(c_e_h_3, c_l, s3)),
% 289.65/182.18 inference(unit_resolution,[status(thm)],[4062, 2233])).
% 289.65/182.18 tff(4064,plain,
% 289.65/182.18 (~m_or_h_gate_v_out(c_e_h_3, c_j, s5)),
% 289.65/182.18 inference(unit_resolution,[status(thm)],[4063, 3545, 3615])).
% 289.65/182.18 tff(4065,assumption,(~m_or_h_gate_v_out(c_e_h_3, c_j, s5)), introduced(assumption)).
% 289.65/182.18 tff(4066,assumption,(node6(c_e_h_3, c_j, s5, s6)), introduced(assumption)).
% 289.65/182.18 tff(4067,plain,
% 289.65/182.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_3, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s6)) | (~node6(c_e_h_3, c_j, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s6)) | (~node6(c_e_h_3, c_j, s5, s6)))),
% 289.65/182.18 inference(rewrite,[status(thm)],[])).
% 289.65/182.18 tff(4068,plain,
% 289.65/182.18 (((~node6(c_e_h_3, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s6)) | m_or_h_gate_v_out(c_e_h_3, c_j, s5)) <=> (m_or_h_gate_v_out(c_e_h_3, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s6)) | (~node6(c_e_h_3, c_j, s5, s6)))),
% 289.65/182.18 inference(rewrite,[status(thm)],[])).
% 289.65/182.18 tff(4069,plain,
% 289.65/182.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s6)) | m_or_h_gate_v_out(c_e_h_3, c_j, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_3, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s6)) | (~node6(c_e_h_3, c_j, s5, s6))))),
% 289.65/182.18 inference(monotonicity,[status(thm)],[4068])).
% 289.65/182.18 tff(4070,plain,
% 289.65/182.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s6)) | m_or_h_gate_v_out(c_e_h_3, c_j, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s6)) | (~node6(c_e_h_3, c_j, s5, s6)))),
% 289.65/182.18 inference(transitivity,[status(thm)],[4069, 4067])).
% 289.65/182.18 tff(4071,plain,
% 289.65/182.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s6)) | m_or_h_gate_v_out(c_e_h_3, c_j, s5))),
% 289.65/182.18 inference(quant_inst,[status(thm)],[])).
% 289.65/182.18 tff(4072,plain,
% 289.65/182.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s6)) | (~node6(c_e_h_3, c_j, s5, s6))),
% 289.65/182.18 inference(modus_ponens,[status(thm)],[4071, 4070])).
% 289.65/182.18 tff(4073,plain,
% 289.65/182.18 ($false),
% 289.65/182.18 inference(unit_resolution,[status(thm)],[4072, 1121, 3608, 4066, 4065])).
% 289.65/182.18 tff(4074,plain,((~node6(c_e_h_3, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s6)) | m_or_h_gate_v_out(c_e_h_3, c_j, s5)), inference(lemma,lemma(discharge,[]))).
% 289.65/182.18 tff(4075,plain,
% 289.65/182.18 ((~node6(c_e_h_3, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s6))),
% 289.65/182.18 inference(unit_resolution,[status(thm)],[4074, 4064])).
% 289.65/182.18 tff(4076,plain,
% 289.65/182.18 (~node6(c_e_h_3, c_j, s5, s6)),
% 289.65/182.18 inference(unit_resolution,[status(thm)],[4075, 3608])).
% 289.65/182.18 tff(4077,assumption,(~m_or_h_gate_v_in1(c_e_h_3, c_j, s5)), introduced(assumption)).
% 289.65/182.18 tff(4078,assumption,(m_c_h_element_v_out(c_e_h_2, c_f, s4)), introduced(assumption)).
% 289.65/182.18 tff(4079,assumption,(~m_c_h_element_v_out(c_e_h_2, c_f, s3)), introduced(assumption)).
% 289.65/182.18 tff(4080,assumption,(node18(c_e_h_2, c_f, s3, s4)), introduced(assumption)).
% 289.65/182.18 tff(4081,plain,
% 289.65/182.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_f, s3) | (~m_c_h_element_v_out(c_e_h_2, c_f, s4)) | (~node18(c_e_h_2, c_f, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_f, s3) | (~m_c_h_element_v_out(c_e_h_2, c_f, s4)) | (~node18(c_e_h_2, c_f, s3, s4)))),
% 289.65/182.18 inference(rewrite,[status(thm)],[])).
% 289.65/182.18 tff(4082,plain,
% 289.65/182.18 (((~m_c_h_element_v_out(c_e_h_2, c_f, s4)) | m_c_h_element_v_out(c_e_h_2, c_f, s3) | (~node18(c_e_h_2, c_f, s3, s4))) <=> (m_c_h_element_v_out(c_e_h_2, c_f, s3) | (~m_c_h_element_v_out(c_e_h_2, c_f, s4)) | (~node18(c_e_h_2, c_f, s3, s4)))),
% 289.65/182.18 inference(rewrite,[status(thm)],[])).
% 289.65/182.18 tff(4083,plain,
% 289.65/182.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s4)) | m_c_h_element_v_out(c_e_h_2, c_f, s3) | (~node18(c_e_h_2, c_f, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_f, s3) | (~m_c_h_element_v_out(c_e_h_2, c_f, s4)) | (~node18(c_e_h_2, c_f, s3, s4))))),
% 289.65/182.18 inference(monotonicity,[status(thm)],[4082])).
% 289.65/182.18 tff(4084,plain,
% 289.65/182.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s4)) | m_c_h_element_v_out(c_e_h_2, c_f, s3) | (~node18(c_e_h_2, c_f, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_f, s3) | (~m_c_h_element_v_out(c_e_h_2, c_f, s4)) | (~node18(c_e_h_2, c_f, s3, s4)))),
% 289.65/182.18 inference(transitivity,[status(thm)],[4083, 4081])).
% 289.65/182.18 tff(4085,plain,
% 289.65/182.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s4)) | m_c_h_element_v_out(c_e_h_2, c_f, s3) | (~node18(c_e_h_2, c_f, s3, s4)))),
% 289.65/182.18 inference(quant_inst,[status(thm)],[])).
% 289.65/182.18 tff(4086,plain,
% 289.65/182.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_f, s3) | (~m_c_h_element_v_out(c_e_h_2, c_f, s4)) | (~node18(c_e_h_2, c_f, s3, s4))),
% 289.65/182.18 inference(modus_ponens,[status(thm)],[4085, 4084])).
% 289.65/182.18 tff(4087,plain,
% 289.65/182.18 ($false),
% 289.65/182.18 inference(unit_resolution,[status(thm)],[4086, 753, 4080, 4079, 4078])).
% 289.65/182.18 tff(4088,plain,((~node18(c_e_h_2, c_f, s3, s4)) | m_c_h_element_v_out(c_e_h_2, c_f, s3) | (~m_c_h_element_v_out(c_e_h_2, c_f, s4))), inference(lemma,lemma(discharge,[]))).
% 289.65/182.18 tff(4089,plain,
% 289.65/182.18 ((~node18(c_e_h_2, c_f, s3, s4)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s4))),
% 289.65/182.18 inference(unit_resolution,[status(thm)],[4088, 3942])).
% 289.65/182.18 tff(4090,plain,
% 289.65/182.18 (~node18(c_e_h_2, c_f, s3, s4)),
% 289.65/182.18 inference(unit_resolution,[status(thm)],[4089, 4078])).
% 289.65/182.18 tff(4091,assumption,(m_and_h_gate_v_out(c_e_h_2, c_i, s3)), introduced(assumption)).
% 289.65/182.18 tff(4092,assumption,(node22(c_e_h_2, c_i, s2, s3)), introduced(assumption)).
% 289.65/182.18 tff(4093,plain,
% 289.65/182.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s3)) | (~node22(c_e_h_2, c_i, s2, s3)) | m_and_h_gate_v_out(c_e_h_2, c_i, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s3)) | (~node22(c_e_h_2, c_i, s2, s3)) | m_and_h_gate_v_out(c_e_h_2, c_i, s2))),
% 289.65/182.18 inference(rewrite,[status(thm)],[])).
% 289.65/182.18 tff(4094,plain,
% 289.65/182.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s3)) | (~node22(c_e_h_2, c_i, s2, s3)) | m_and_h_gate_v_out(c_e_h_2, c_i, s2))),
% 289.65/182.18 inference(quant_inst,[status(thm)],[])).
% 289.65/182.18 tff(4095,plain,
% 289.65/182.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s3)) | (~node22(c_e_h_2, c_i, s2, s3)) | m_and_h_gate_v_out(c_e_h_2, c_i, s2)),
% 289.65/182.18 inference(modus_ponens,[status(thm)],[4094, 4093])).
% 289.65/182.18 tff(4096,plain,
% 289.65/182.18 ($false),
% 289.65/182.18 inference(unit_resolution,[status(thm)],[4095, 108, 4091, 3902, 4092])).
% 289.65/182.18 tff(4097,plain,((~node22(c_e_h_2, c_i, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s3))), inference(lemma,lemma(discharge,[]))).
% 289.65/182.18 tff(4098,plain,
% 289.65/182.18 (~node22(c_e_h_2, c_i, s2, s3)),
% 289.65/182.18 inference(unit_resolution,[status(thm)],[4097, 4091])).
% 289.65/182.18 tff(4099,plain,
% 289.65/182.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_2, c_i, s2, s3) | node22(c_e_h_2, c_i, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_2, c_i, s2, s3) | node22(c_e_h_2, c_i, s2, s3))),
% 289.65/182.19 inference(rewrite,[status(thm)],[])).
% 289.65/182.19 tff(4100,plain,
% 289.65/182.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_2, c_i, s2, s3) | node22(c_e_h_2, c_i, s2, s3))),
% 289.65/182.19 inference(quant_inst,[status(thm)],[])).
% 289.65/182.19 tff(4101,plain,
% 289.65/182.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_2, c_i, s2, s3) | node22(c_e_h_2, c_i, s2, s3)),
% 289.65/182.19 inference(modus_ponens,[status(thm)],[4100, 4099])).
% 289.65/182.19 tff(4102,plain,
% 289.65/182.19 (node21(c_e_h_2, c_i, s2, s3) | node22(c_e_h_2, c_i, s2, s3)),
% 289.65/182.19 inference(unit_resolution,[status(thm)],[4101, 82, 318])).
% 289.65/182.19 tff(4103,plain,
% 289.65/182.19 (node21(c_e_h_2, c_i, s2, s3)),
% 289.65/182.19 inference(unit_resolution,[status(thm)],[4102, 4098])).
% 289.65/182.19 tff(4104,assumption,(m_c_h_element_v_out(c_e_h_2, c_h, s2)), introduced(assumption)).
% 289.65/182.19 tff(4105,plain,
% 289.65/182.19 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_g, s0)) | m_and_h_gate_v_out(c_e_h_2, c_d, s0))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_g, s0)) | m_and_h_gate_v_out(c_e_h_2, c_d, s0))),
% 289.65/182.19 inference(rewrite,[status(thm)],[])).
% 289.65/182.19 tff(4106,plain,
% 289.65/182.19 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_g, s0)) | m_and_h_gate_v_out(c_e_h_2, c_d, s0))),
% 289.65/182.19 inference(quant_inst,[status(thm)],[])).
% 289.65/182.19 tff(4107,plain,
% 289.65/182.19 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_g, s0)) | m_and_h_gate_v_out(c_e_h_2, c_d, s0)),
% 289.65/182.19 inference(modus_ponens,[status(thm)],[4106, 4105])).
% 289.65/182.19 tff(4108,plain,
% 289.65/182.19 (~m_or_h_gate_v_in2(c_e_h_2, c_g, s0)),
% 289.65/182.19 inference(unit_resolution,[status(thm)],[4107, 2762, 2109])).
% 289.65/182.19 tff(4109,assumption,(m_or_h_gate_v_out(c_e_h_2, c_g, s1)), introduced(assumption)).
% 289.65/182.19 tff(4110,assumption,(m_and_h_gate_v_out(c_e_h_2, c_c, s0)), introduced(assumption)).
% 289.65/182.19 tff(4111,plain,
% 289.65/182.19 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_2, c_c, s0))),
% 289.65/182.19 inference(quant_inst,[status(thm)],[])).
% 289.65/182.19 tff(4112,plain,
% 289.65/182.19 ($false),
% 289.65/182.19 inference(unit_resolution,[status(thm)],[4111, 95, 4110])).
% 289.65/182.19 tff(4113,plain,(~m_and_h_gate_v_out(c_e_h_2, c_c, s0)), inference(lemma,lemma(discharge,[]))).
% 289.65/182.19 tff(4114,plain,
% 289.65/182.19 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_or_h_gate_v_in1(c_e_h_2, c_g, s0)) | m_and_h_gate_v_out(c_e_h_2, c_c, s0))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_g, s0)) | m_and_h_gate_v_out(c_e_h_2, c_c, s0))),
% 289.65/182.19 inference(rewrite,[status(thm)],[])).
% 289.65/182.19 tff(4115,plain,
% 289.65/182.19 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_or_h_gate_v_in1(c_e_h_2, c_g, s0)) | m_and_h_gate_v_out(c_e_h_2, c_c, s0))),
% 289.65/182.19 inference(quant_inst,[status(thm)],[])).
% 289.65/182.19 tff(4116,plain,
% 289.65/182.19 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_g, s0)) | m_and_h_gate_v_out(c_e_h_2, c_c, s0)),
% 289.65/182.19 inference(modus_ponens,[status(thm)],[4115, 4114])).
% 289.65/182.19 tff(4117,plain,
% 289.65/182.19 (~m_or_h_gate_v_in1(c_e_h_2, c_g, s0)),
% 289.65/182.19 inference(unit_resolution,[status(thm)],[4116, 2708, 4113])).
% 289.65/182.19 tff(4118,assumption,(node6(c_e_h_2, c_g, s0, s1)), introduced(assumption)).
% 289.65/182.19 tff(4119,plain,
% 289.65/182.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_g, s0, s1)) | m_or_h_gate_v_out(c_e_h_2, c_g, s0) | (~m_or_h_gate_v_out(c_e_h_2, c_g, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~node6(c_e_h_2, c_g, s0, s1)) | m_or_h_gate_v_out(c_e_h_2, c_g, s0) | (~m_or_h_gate_v_out(c_e_h_2, c_g, s1)))),
% 289.65/182.19 inference(rewrite,[status(thm)],[])).
% 289.65/182.19 tff(4120,plain,
% 289.65/182.19 (((~node6(c_e_h_2, c_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_2, c_g, s1)) | m_or_h_gate_v_out(c_e_h_2, c_g, s0)) <=> ((~node6(c_e_h_2, c_g, s0, s1)) | m_or_h_gate_v_out(c_e_h_2, c_g, s0) | (~m_or_h_gate_v_out(c_e_h_2, c_g, s1)))),
% 289.65/182.19 inference(rewrite,[status(thm)],[])).
% 289.65/182.19 tff(4121,plain,
% 289.65/182.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_2, c_g, s1)) | m_or_h_gate_v_out(c_e_h_2, c_g, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_g, s0, s1)) | m_or_h_gate_v_out(c_e_h_2, c_g, s0) | (~m_or_h_gate_v_out(c_e_h_2, c_g, s1))))),
% 289.65/182.19 inference(monotonicity,[status(thm)],[4120])).
% 289.65/182.19 tff(4122,plain,
% 289.65/182.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_2, c_g, s1)) | m_or_h_gate_v_out(c_e_h_2, c_g, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~node6(c_e_h_2, c_g, s0, s1)) | m_or_h_gate_v_out(c_e_h_2, c_g, s0) | (~m_or_h_gate_v_out(c_e_h_2, c_g, s1)))),
% 289.65/182.19 inference(transitivity,[status(thm)],[4121, 4119])).
% 289.65/182.19 tff(4123,plain,
% 289.65/182.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_2, c_g, s1)) | m_or_h_gate_v_out(c_e_h_2, c_g, s0))),
% 289.65/182.19 inference(quant_inst,[status(thm)],[])).
% 289.65/182.19 tff(4124,plain,
% 289.65/182.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~node6(c_e_h_2, c_g, s0, s1)) | m_or_h_gate_v_out(c_e_h_2, c_g, s0) | (~m_or_h_gate_v_out(c_e_h_2, c_g, s1))),
% 289.65/182.19 inference(modus_ponens,[status(thm)],[4123, 4122])).
% 289.65/182.19 tff(4125,plain,
% 289.65/182.19 ($false),
% 289.65/182.19 inference(unit_resolution,[status(thm)],[4124, 1121, 4118, 3839, 4109])).
% 289.65/182.19 tff(4126,plain,((~node6(c_e_h_2, c_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_2, c_g, s1))), inference(lemma,lemma(discharge,[]))).
% 289.65/182.19 tff(4127,plain,
% 289.65/182.19 (~node6(c_e_h_2, c_g, s0, s1)),
% 289.65/182.19 inference(unit_resolution,[status(thm)],[4126, 4109])).
% 289.65/182.19 tff(4128,plain,
% 289.65/182.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s0, s1)) | node5(c_e_h_2, c_g, s0, s1) | node6(c_e_h_2, c_g, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s0, s1)) | node5(c_e_h_2, c_g, s0, s1) | node6(c_e_h_2, c_g, s0, s1))),
% 289.65/182.19 inference(rewrite,[status(thm)],[])).
% 289.65/182.19 tff(4129,plain,
% 289.65/182.19 ((node6(c_e_h_2, c_g, s0, s1) | node5(c_e_h_2, c_g, s0, s1) | (~trans(s0, s1))) <=> ((~trans(s0, s1)) | node5(c_e_h_2, c_g, s0, s1) | node6(c_e_h_2, c_g, s0, s1))),
% 289.65/182.19 inference(rewrite,[status(thm)],[])).
% 289.65/182.19 tff(4130,plain,
% 289.65/182.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_g, s0, s1) | node5(c_e_h_2, c_g, s0, s1) | (~trans(s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s0, s1)) | node5(c_e_h_2, c_g, s0, s1) | node6(c_e_h_2, c_g, s0, s1)))),
% 289.65/182.19 inference(monotonicity,[status(thm)],[4129])).
% 289.65/182.19 tff(4131,plain,
% 289.65/182.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_g, s0, s1) | node5(c_e_h_2, c_g, s0, s1) | (~trans(s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s0, s1)) | node5(c_e_h_2, c_g, s0, s1) | node6(c_e_h_2, c_g, s0, s1))),
% 289.65/182.19 inference(transitivity,[status(thm)],[4130, 4128])).
% 289.65/182.19 tff(4132,plain,
% 289.65/182.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_g, s0, s1) | node5(c_e_h_2, c_g, s0, s1) | (~trans(s0, s1)))),
% 289.65/182.19 inference(quant_inst,[status(thm)],[])).
% 289.65/182.19 tff(4133,plain,
% 289.65/182.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s0, s1)) | node5(c_e_h_2, c_g, s0, s1) | node6(c_e_h_2, c_g, s0, s1)),
% 289.65/182.19 inference(modus_ponens,[status(thm)],[4132, 4131])).
% 289.65/182.19 tff(4134,plain,
% 289.65/182.19 (node5(c_e_h_2, c_g, s0, s1) | node6(c_e_h_2, c_g, s0, s1)),
% 289.65/182.19 inference(unit_resolution,[status(thm)],[4133, 1141, 72])).
% 289.65/182.19 tff(4135,plain,
% 289.65/182.19 (node5(c_e_h_2, c_g, s0, s1)),
% 289.65/182.19 inference(unit_resolution,[status(thm)],[4134, 4127])).
% 289.65/182.19 tff(4136,plain,
% 289.65/182.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_2, c_g, s1)) | m_or_h_gate_v_in1(c_e_h_2, c_g, s0) | m_or_h_gate_v_in2(c_e_h_2, c_g, s0) | (~node5(c_e_h_2, c_g, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_2, c_g, s1)) | m_or_h_gate_v_in1(c_e_h_2, c_g, s0) | m_or_h_gate_v_in2(c_e_h_2, c_g, s0) | (~node5(c_e_h_2, c_g, s0, s1)))),
% 289.65/182.19 inference(rewrite,[status(thm)],[])).
% 289.65/182.19 tff(4137,plain,
% 289.65/182.19 ((m_or_h_gate_v_in1(c_e_h_2, c_g, s0) | m_or_h_gate_v_in2(c_e_h_2, c_g, s0) | (~node5(c_e_h_2, c_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_2, c_g, s1))) <=> ((~m_or_h_gate_v_out(c_e_h_2, c_g, s1)) | m_or_h_gate_v_in1(c_e_h_2, c_g, s0) | m_or_h_gate_v_in2(c_e_h_2, c_g, s0) | (~node5(c_e_h_2, c_g, s0, s1)))),
% 289.65/182.19 inference(rewrite,[status(thm)],[])).
% 289.65/182.19 tff(4138,plain,
% 289.65/182.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_g, s0) | m_or_h_gate_v_in2(c_e_h_2, c_g, s0) | (~node5(c_e_h_2, c_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_2, c_g, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_2, c_g, s1)) | m_or_h_gate_v_in1(c_e_h_2, c_g, s0) | m_or_h_gate_v_in2(c_e_h_2, c_g, s0) | (~node5(c_e_h_2, c_g, s0, s1))))),
% 289.65/182.19 inference(monotonicity,[status(thm)],[4137])).
% 289.65/182.19 tff(4139,plain,
% 289.65/182.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_g, s0) | m_or_h_gate_v_in2(c_e_h_2, c_g, s0) | (~node5(c_e_h_2, c_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_2, c_g, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_2, c_g, s1)) | m_or_h_gate_v_in1(c_e_h_2, c_g, s0) | m_or_h_gate_v_in2(c_e_h_2, c_g, s0) | (~node5(c_e_h_2, c_g, s0, s1)))),
% 289.65/182.19 inference(transitivity,[status(thm)],[4138, 4136])).
% 289.65/182.19 tff(4140,plain,
% 289.65/182.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_g, s0) | m_or_h_gate_v_in2(c_e_h_2, c_g, s0) | (~node5(c_e_h_2, c_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_2, c_g, s1)))),
% 289.65/182.19 inference(quant_inst,[status(thm)],[])).
% 289.65/182.19 tff(4141,plain,
% 289.65/182.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_2, c_g, s1)) | m_or_h_gate_v_in1(c_e_h_2, c_g, s0) | m_or_h_gate_v_in2(c_e_h_2, c_g, s0) | (~node5(c_e_h_2, c_g, s0, s1))),
% 289.65/182.19 inference(modus_ponens,[status(thm)],[4140, 4139])).
% 289.65/182.20 tff(4142,plain,
% 289.65/182.20 ($false),
% 289.65/182.20 inference(unit_resolution,[status(thm)],[4141, 1159, 4135, 4117, 4109, 4108])).
% 289.65/182.20 tff(4143,plain,(~m_or_h_gate_v_out(c_e_h_2, c_g, s1)), inference(lemma,lemma(discharge,[]))).
% 289.65/182.20 tff(4144,plain,
% 289.65/182.20 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s1)) | m_or_h_gate_v_out(c_e_h_2, c_g, s1))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s1)) | m_or_h_gate_v_out(c_e_h_2, c_g, s1))),
% 289.65/182.20 inference(rewrite,[status(thm)],[])).
% 289.65/182.20 tff(4145,plain,
% 289.65/182.20 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s1)) | m_or_h_gate_v_out(c_e_h_2, c_g, s1))),
% 289.65/182.20 inference(quant_inst,[status(thm)],[])).
% 289.65/182.20 tff(4146,plain,
% 289.65/182.20 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s1)) | m_or_h_gate_v_out(c_e_h_2, c_g, s1)),
% 289.65/182.20 inference(modus_ponens,[status(thm)],[4145, 4144])).
% 289.65/182.20 tff(4147,plain,
% 289.65/182.20 (~m_c_h_element_v_in1(c_e_h_2, c_h, s1)),
% 289.65/182.20 inference(unit_resolution,[status(thm)],[4146, 811, 4143])).
% 289.65/182.20 tff(4148,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_h, s1)), introduced(assumption)).
% 289.65/182.20 tff(4149,assumption,(node14(c_e_h_2, c_h, s1, s2)), introduced(assumption)).
% 289.65/182.20 tff(4150,plain,
% 289.65/182.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s2)) | m_c_h_element_v_in1(c_e_h_2, c_h, s1) | (~node14(c_e_h_2, c_h, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s2)) | m_c_h_element_v_in1(c_e_h_2, c_h, s1) | (~node14(c_e_h_2, c_h, s1, s2)))),
% 289.65/182.20 inference(rewrite,[status(thm)],[])).
% 289.65/182.20 tff(4151,plain,
% 289.65/182.20 (((~node14(c_e_h_2, c_h, s1, s2)) | m_c_h_element_v_in1(c_e_h_2, c_h, s1) | (~m_c_h_element_v_out(c_e_h_2, c_h, s2))) <=> ((~m_c_h_element_v_out(c_e_h_2, c_h, s2)) | m_c_h_element_v_in1(c_e_h_2, c_h, s1) | (~node14(c_e_h_2, c_h, s1, s2)))),
% 289.65/182.20 inference(rewrite,[status(thm)],[])).
% 289.65/182.20 tff(4152,plain,
% 289.65/182.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s1, s2)) | m_c_h_element_v_in1(c_e_h_2, c_h, s1) | (~m_c_h_element_v_out(c_e_h_2, c_h, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s2)) | m_c_h_element_v_in1(c_e_h_2, c_h, s1) | (~node14(c_e_h_2, c_h, s1, s2))))),
% 289.65/182.20 inference(monotonicity,[status(thm)],[4151])).
% 289.65/182.20 tff(4153,plain,
% 289.65/182.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s1, s2)) | m_c_h_element_v_in1(c_e_h_2, c_h, s1) | (~m_c_h_element_v_out(c_e_h_2, c_h, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s2)) | m_c_h_element_v_in1(c_e_h_2, c_h, s1) | (~node14(c_e_h_2, c_h, s1, s2)))),
% 289.65/182.20 inference(transitivity,[status(thm)],[4152, 4150])).
% 289.65/182.20 tff(4154,plain,
% 289.65/182.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s1, s2)) | m_c_h_element_v_in1(c_e_h_2, c_h, s1) | (~m_c_h_element_v_out(c_e_h_2, c_h, s2)))),
% 289.65/182.20 inference(quant_inst,[status(thm)],[])).
% 289.65/182.20 tff(4155,plain,
% 289.65/182.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s2)) | m_c_h_element_v_in1(c_e_h_2, c_h, s1) | (~node14(c_e_h_2, c_h, s1, s2))),
% 289.65/182.20 inference(modus_ponens,[status(thm)],[4154, 4153])).
% 289.65/182.20 tff(4156,plain,
% 289.65/182.20 ($false),
% 289.65/182.20 inference(unit_resolution,[status(thm)],[4155, 223, 4104, 4149, 4148])).
% 289.65/182.20 tff(4157,plain,((~node14(c_e_h_2, c_h, s1, s2)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s2)) | m_c_h_element_v_in1(c_e_h_2, c_h, s1)), inference(lemma,lemma(discharge,[]))).
% 289.65/182.20 tff(4158,plain,
% 289.65/182.20 ((~node14(c_e_h_2, c_h, s1, s2)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s2))),
% 289.65/182.20 inference(unit_resolution,[status(thm)],[4157, 4147])).
% 289.65/182.20 tff(4159,plain,
% 289.65/182.20 (~node14(c_e_h_2, c_h, s1, s2)),
% 289.65/182.20 inference(unit_resolution,[status(thm)],[4158, 4104])).
% 289.65/182.20 tff(4160,assumption,(m_and_h_gate_v_out(c_e_h_1, c_q, s0)), introduced(assumption)).
% 289.65/182.20 tff(4161,plain,
% 289.65/182.20 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s0))),
% 289.65/182.20 inference(quant_inst,[status(thm)],[])).
% 289.65/182.20 tff(4162,plain,
% 289.65/182.20 ($false),
% 289.65/182.20 inference(unit_resolution,[status(thm)],[4161, 95, 4160])).
% 289.65/182.20 tff(4163,plain,(~m_and_h_gate_v_out(c_e_h_1, c_q, s0)), inference(lemma,lemma(discharge,[]))).
% 289.65/182.20 tff(4164,plain,
% 289.65/182.20 (m_cell_v_left(c_e_h_1, c_e_h_2) <=> m_cell_v_left(c_e_h_1, c_e_h_2)),
% 289.65/182.20 inference(rewrite,[status(thm)],[])).
% 289.65/182.20 tff(4165,axiom,(m_cell_v_left(c_e_h_1, c_e_h_2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_1')).
% 289.65/182.20 tff(4166,plain,
% 289.65/182.20 (m_cell_v_left(c_e_h_1, c_e_h_2)),
% 289.65/182.20 inference(modus_ponens,[status(thm)],[4165, 4164])).
% 289.65/182.20 tff(4167,plain,
% 289.65/182.20 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s0))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s0))),
% 289.65/182.20 inference(rewrite,[status(thm)],[])).
% 289.65/182.20 tff(4168,plain,
% 289.65/182.20 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s0))),
% 289.65/182.20 inference(quant_inst,[status(thm)],[])).
% 289.65/182.20 tff(4169,plain,
% 289.65/182.20 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s0)),
% 289.65/182.20 inference(modus_ponens,[status(thm)],[4168, 4167])).
% 289.65/182.20 tff(4170,plain,
% 289.65/182.20 (node3(c_e_h_1, c_e_h_2, s0)),
% 289.65/182.20 inference(unit_resolution,[status(thm)],[4169, 4166, 1056])).
% 289.65/182.20 tff(4171,plain,
% 289.65/182.20 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s0)) | (~node3(c_e_h_1, c_e_h_2, s0)) | m_and_h_gate_v_out(c_e_h_1, c_q, s0))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s0)) | (~node3(c_e_h_1, c_e_h_2, s0)) | m_and_h_gate_v_out(c_e_h_1, c_q, s0))),
% 289.65/182.20 inference(rewrite,[status(thm)],[])).
% 289.65/182.20 tff(4172,plain,
% 289.65/182.20 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s0)) | (~node3(c_e_h_1, c_e_h_2, s0)) | m_and_h_gate_v_out(c_e_h_1, c_q, s0))),
% 289.65/182.20 inference(quant_inst,[status(thm)],[])).
% 289.65/182.20 tff(4173,plain,
% 289.65/182.20 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s0)) | (~node3(c_e_h_1, c_e_h_2, s0)) | m_and_h_gate_v_out(c_e_h_1, c_q, s0)),
% 289.65/182.20 inference(modus_ponens,[status(thm)],[4172, 4171])).
% 289.65/182.20 tff(4174,plain,
% 289.65/182.20 ((~m_cell_v_ack(c_e_h_2, s0)) | m_and_h_gate_v_out(c_e_h_1, c_q, s0)),
% 289.65/182.20 inference(unit_resolution,[status(thm)],[4173, 1073, 4170])).
% 289.65/182.20 tff(4175,plain,
% 289.65/182.20 (~m_cell_v_ack(c_e_h_2, s0)),
% 289.65/182.20 inference(unit_resolution,[status(thm)],[4174, 4163])).
% 289.65/182.20 tff(4176,plain,
% 289.65/182.20 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s0)) | m_cell_v_ack(c_e_h_2, s0))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s0)) | m_cell_v_ack(c_e_h_2, s0))),
% 289.65/182.20 inference(rewrite,[status(thm)],[])).
% 289.65/182.20 tff(4177,plain,
% 289.65/182.20 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s0)) | m_cell_v_ack(c_e_h_2, s0))),
% 289.65/182.21 inference(quant_inst,[status(thm)],[])).
% 289.65/182.21 tff(4178,plain,
% 289.65/182.21 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s0)) | m_cell_v_ack(c_e_h_2, s0)),
% 289.65/182.21 inference(modus_ponens,[status(thm)],[4177, 4176])).
% 289.65/182.21 tff(4179,plain,
% 289.65/182.21 (~m_or_h_gate_v_in2(c_e_h_2, c_j, s0)),
% 289.65/182.21 inference(unit_resolution,[status(thm)],[4178, 1085, 4175])).
% 289.65/182.21 tff(4180,assumption,(m_and_h_gate_v_out(c_e_h_2, c_l, s0)), introduced(assumption)).
% 289.65/182.21 tff(4181,plain,
% 289.65/182.21 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s0))),
% 289.65/182.21 inference(quant_inst,[status(thm)],[])).
% 289.65/182.21 tff(4182,plain,
% 289.65/182.21 ($false),
% 289.65/182.21 inference(unit_resolution,[status(thm)],[4181, 95, 4180])).
% 289.65/182.21 tff(4183,plain,(~m_and_h_gate_v_out(c_e_h_2, c_l, s0)), inference(lemma,lemma(discharge,[]))).
% 289.65/182.21 tff(4184,plain,
% 289.65/182.21 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_2, c_j, s0)) | m_and_h_gate_v_out(c_e_h_2, c_l, s0))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_j, s0)) | m_and_h_gate_v_out(c_e_h_2, c_l, s0))),
% 289.65/182.21 inference(rewrite,[status(thm)],[])).
% 289.65/182.21 tff(4185,plain,
% 289.65/182.21 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_2, c_j, s0)) | m_and_h_gate_v_out(c_e_h_2, c_l, s0))),
% 289.65/182.21 inference(quant_inst,[status(thm)],[])).
% 289.65/182.21 tff(4186,plain,
% 289.65/182.21 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_j, s0)) | m_and_h_gate_v_out(c_e_h_2, c_l, s0)),
% 289.65/182.21 inference(modus_ponens,[status(thm)],[4185, 4184])).
% 289.65/182.21 tff(4187,plain,
% 289.65/182.21 (~m_or_h_gate_v_in1(c_e_h_2, c_j, s0)),
% 289.65/182.21 inference(unit_resolution,[status(thm)],[4186, 1100, 4183])).
% 289.65/182.21 tff(4188,assumption,(m_or_h_gate_v_out(c_e_h_2, c_j, s1)), introduced(assumption)).
% 289.65/182.21 tff(4189,assumption,(node6(c_e_h_2, c_j, s0, s1)), introduced(assumption)).
% 289.65/182.21 tff(4190,plain,
% 289.65/182.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_2, c_j, s0) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s1)) | (~node6(c_e_h_2, c_j, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s0) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s1)) | (~node6(c_e_h_2, c_j, s0, s1)))),
% 289.65/182.21 inference(rewrite,[status(thm)],[])).
% 289.65/182.21 tff(4191,plain,
% 289.65/182.21 (((~node6(c_e_h_2, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s1)) | m_or_h_gate_v_out(c_e_h_2, c_j, s0)) <=> (m_or_h_gate_v_out(c_e_h_2, c_j, s0) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s1)) | (~node6(c_e_h_2, c_j, s0, s1)))),
% 289.65/182.21 inference(rewrite,[status(thm)],[])).
% 289.65/182.21 tff(4192,plain,
% 289.65/182.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s1)) | m_or_h_gate_v_out(c_e_h_2, c_j, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_2, c_j, s0) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s1)) | (~node6(c_e_h_2, c_j, s0, s1))))),
% 289.65/182.21 inference(monotonicity,[status(thm)],[4191])).
% 289.65/182.21 tff(4193,plain,
% 289.65/182.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s1)) | m_or_h_gate_v_out(c_e_h_2, c_j, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s0) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s1)) | (~node6(c_e_h_2, c_j, s0, s1)))),
% 289.65/182.21 inference(transitivity,[status(thm)],[4192, 4190])).
% 289.65/182.21 tff(4194,plain,
% 289.65/182.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s1)) | m_or_h_gate_v_out(c_e_h_2, c_j, s0))),
% 289.65/182.21 inference(quant_inst,[status(thm)],[])).
% 289.65/182.21 tff(4195,plain,
% 289.65/182.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s0) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s1)) | (~node6(c_e_h_2, c_j, s0, s1))),
% 289.65/182.21 inference(modus_ponens,[status(thm)],[4194, 4193])).
% 289.65/182.21 tff(4196,plain,
% 289.65/182.21 ($false),
% 289.65/182.21 inference(unit_resolution,[status(thm)],[4195, 1121, 3856, 4188, 4189])).
% 289.65/182.21 tff(4197,plain,((~node6(c_e_h_2, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s1))), inference(lemma,lemma(discharge,[]))).
% 289.65/182.21 tff(4198,plain,
% 289.65/182.21 (~node6(c_e_h_2, c_j, s0, s1)),
% 289.65/182.21 inference(unit_resolution,[status(thm)],[4197, 4188])).
% 289.65/182.21 tff(4199,plain,
% 289.65/182.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s0, s1)) | node6(c_e_h_2, c_j, s0, s1) | node5(c_e_h_2, c_j, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s0, s1)) | node6(c_e_h_2, c_j, s0, s1) | node5(c_e_h_2, c_j, s0, s1))),
% 289.65/182.21 inference(rewrite,[status(thm)],[])).
% 289.65/182.21 tff(4200,plain,
% 289.65/182.21 ((node6(c_e_h_2, c_j, s0, s1) | node5(c_e_h_2, c_j, s0, s1) | (~trans(s0, s1))) <=> ((~trans(s0, s1)) | node6(c_e_h_2, c_j, s0, s1) | node5(c_e_h_2, c_j, s0, s1))),
% 289.65/182.21 inference(rewrite,[status(thm)],[])).
% 289.65/182.21 tff(4201,plain,
% 289.65/182.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s0, s1) | node5(c_e_h_2, c_j, s0, s1) | (~trans(s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s0, s1)) | node6(c_e_h_2, c_j, s0, s1) | node5(c_e_h_2, c_j, s0, s1)))),
% 289.65/182.21 inference(monotonicity,[status(thm)],[4200])).
% 289.65/182.21 tff(4202,plain,
% 289.65/182.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s0, s1) | node5(c_e_h_2, c_j, s0, s1) | (~trans(s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s0, s1)) | node6(c_e_h_2, c_j, s0, s1) | node5(c_e_h_2, c_j, s0, s1))),
% 289.65/182.21 inference(transitivity,[status(thm)],[4201, 4199])).
% 289.65/182.21 tff(4203,plain,
% 289.65/182.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s0, s1) | node5(c_e_h_2, c_j, s0, s1) | (~trans(s0, s1)))),
% 289.65/182.21 inference(quant_inst,[status(thm)],[])).
% 289.65/182.21 tff(4204,plain,
% 289.65/182.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s0, s1)) | node6(c_e_h_2, c_j, s0, s1) | node5(c_e_h_2, c_j, s0, s1)),
% 289.65/182.21 inference(modus_ponens,[status(thm)],[4203, 4202])).
% 289.65/182.21 tff(4205,plain,
% 289.65/182.21 (node6(c_e_h_2, c_j, s0, s1) | node5(c_e_h_2, c_j, s0, s1)),
% 289.65/182.21 inference(unit_resolution,[status(thm)],[4204, 1141, 72])).
% 289.65/182.21 tff(4206,plain,
% 289.65/182.21 (node5(c_e_h_2, c_j, s0, s1)),
% 289.65/182.21 inference(unit_resolution,[status(thm)],[4205, 4198])).
% 289.65/182.21 tff(4207,plain,
% 289.65/182.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_2, c_j, s0) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s1)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s0) | (~node5(c_e_h_2, c_j, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_2, c_j, s0) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s1)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s0) | (~node5(c_e_h_2, c_j, s0, s1)))),
% 289.65/182.21 inference(rewrite,[status(thm)],[])).
% 289.65/182.21 tff(4208,plain,
% 289.65/182.21 ((m_or_h_gate_v_in1(c_e_h_2, c_j, s0) | m_or_h_gate_v_in2(c_e_h_2, c_j, s0) | (~node5(c_e_h_2, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s1))) <=> (m_or_h_gate_v_in2(c_e_h_2, c_j, s0) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s1)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s0) | (~node5(c_e_h_2, c_j, s0, s1)))),
% 289.74/182.21 inference(rewrite,[status(thm)],[])).
% 289.74/182.21 tff(4209,plain,
% 289.74/182.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s0) | m_or_h_gate_v_in2(c_e_h_2, c_j, s0) | (~node5(c_e_h_2, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_2, c_j, s0) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s1)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s0) | (~node5(c_e_h_2, c_j, s0, s1))))),
% 289.74/182.21 inference(monotonicity,[status(thm)],[4208])).
% 289.74/182.21 tff(4210,plain,
% 289.74/182.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s0) | m_or_h_gate_v_in2(c_e_h_2, c_j, s0) | (~node5(c_e_h_2, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_2, c_j, s0) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s1)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s0) | (~node5(c_e_h_2, c_j, s0, s1)))),
% 289.74/182.21 inference(transitivity,[status(thm)],[4209, 4207])).
% 289.74/182.21 tff(4211,plain,
% 289.74/182.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s0) | m_or_h_gate_v_in2(c_e_h_2, c_j, s0) | (~node5(c_e_h_2, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s1)))),
% 289.74/182.21 inference(quant_inst,[status(thm)],[])).
% 289.74/182.21 tff(4212,plain,
% 289.74/182.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_2, c_j, s0) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s1)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s0) | (~node5(c_e_h_2, c_j, s0, s1))),
% 289.74/182.21 inference(modus_ponens,[status(thm)],[4211, 4210])).
% 289.74/182.21 tff(4213,plain,
% 289.74/182.21 ($false),
% 289.74/182.21 inference(unit_resolution,[status(thm)],[4212, 1159, 4188, 4206, 4187, 4179])).
% 289.74/182.21 tff(4214,plain,(~m_or_h_gate_v_out(c_e_h_2, c_j, s1)), inference(lemma,lemma(discharge,[]))).
% 289.74/182.21 tff(4215,plain,
% 289.74/182.21 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s1)) | m_or_h_gate_v_out(c_e_h_2, c_j, s1))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s1)) | m_or_h_gate_v_out(c_e_h_2, c_j, s1))),
% 289.74/182.21 inference(rewrite,[status(thm)],[])).
% 289.74/182.21 tff(4216,plain,
% 289.74/182.21 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s1)) | m_or_h_gate_v_out(c_e_h_2, c_j, s1))),
% 289.74/182.21 inference(quant_inst,[status(thm)],[])).
% 289.74/182.21 tff(4217,plain,
% 289.74/182.21 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s1)) | m_or_h_gate_v_out(c_e_h_2, c_j, s1)),
% 289.74/182.21 inference(modus_ponens,[status(thm)],[4216, 4215])).
% 289.74/182.21 tff(4218,plain,
% 289.74/182.21 (~m_c_h_element_v_in2(c_e_h_2, c_h, s1)),
% 289.74/182.21 inference(unit_resolution,[status(thm)],[4217, 1174, 4214])).
% 289.74/182.21 tff(4219,plain,
% 289.74/182.21 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_h, s1)) | m_c_h_element_v_in1(c_e_h_2, c_h, s1) | m_c_h_element_v_in2(c_e_h_2, c_h, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_h, s1)) | m_c_h_element_v_in1(c_e_h_2, c_h, s1) | m_c_h_element_v_in2(c_e_h_2, c_h, s1))),
% 289.74/182.22 inference(rewrite,[status(thm)],[])).
% 289.74/182.22 tff(4220,plain,
% 289.74/182.22 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_h, s1)) | m_c_h_element_v_in1(c_e_h_2, c_h, s1) | m_c_h_element_v_in2(c_e_h_2, c_h, s1))),
% 289.74/182.22 inference(quant_inst,[status(thm)],[])).
% 289.74/182.22 tff(4221,plain,
% 289.74/182.22 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_h, s1)) | m_c_h_element_v_in1(c_e_h_2, c_h, s1) | m_c_h_element_v_in2(c_e_h_2, c_h, s1)),
% 289.74/182.22 inference(modus_ponens,[status(thm)],[4220, 4219])).
% 289.74/182.22 tff(4222,plain,
% 289.74/182.22 ((~node16(c_e_h_2, c_h, s1)) | m_c_h_element_v_in2(c_e_h_2, c_h, s1)),
% 289.74/182.22 inference(unit_resolution,[status(thm)],[4221, 178, 4147])).
% 289.74/182.22 tff(4223,plain,
% 289.74/182.22 (~node16(c_e_h_2, c_h, s1)),
% 289.74/182.22 inference(unit_resolution,[status(thm)],[4222, 4218])).
% 289.74/182.22 tff(4224,plain,
% 289.74/182.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s1, s2)) | node19(c_e_h_2, c_h, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s1, s2)) | node19(c_e_h_2, c_h, s1, s2))),
% 289.74/182.22 inference(rewrite,[status(thm)],[])).
% 289.74/182.22 tff(4225,plain,
% 289.74/182.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s1, s2)) | node19(c_e_h_2, c_h, s1, s2))),
% 289.74/182.22 inference(quant_inst,[status(thm)],[])).
% 289.74/182.22 tff(4226,plain,
% 289.74/182.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s1, s2)) | node19(c_e_h_2, c_h, s1, s2)),
% 289.74/182.22 inference(modus_ponens,[status(thm)],[4225, 4224])).
% 289.74/182.22 tff(4227,plain,
% 289.74/182.22 (node19(c_e_h_2, c_h, s1, s2)),
% 289.74/182.22 inference(unit_resolution,[status(thm)],[4226, 190, 255])).
% 289.74/182.22 tff(4228,plain,
% 289.74/182.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s1) | (~node19(c_e_h_2, c_h, s1, s2)) | node14(c_e_h_2, c_h, s1, s2) | node15(c_e_h_2, c_h, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s1) | (~node19(c_e_h_2, c_h, s1, s2)) | node14(c_e_h_2, c_h, s1, s2) | node15(c_e_h_2, c_h, s1, s2))),
% 289.74/182.22 inference(rewrite,[status(thm)],[])).
% 289.74/182.22 tff(4229,plain,
% 289.74/182.22 ((node16(c_e_h_2, c_h, s1) | node14(c_e_h_2, c_h, s1, s2) | node15(c_e_h_2, c_h, s1, s2) | (~node19(c_e_h_2, c_h, s1, s2))) <=> (node16(c_e_h_2, c_h, s1) | (~node19(c_e_h_2, c_h, s1, s2)) | node14(c_e_h_2, c_h, s1, s2) | node15(c_e_h_2, c_h, s1, s2))),
% 289.74/182.22 inference(rewrite,[status(thm)],[])).
% 289.74/182.22 tff(4230,plain,
% 289.74/182.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s1) | node14(c_e_h_2, c_h, s1, s2) | node15(c_e_h_2, c_h, s1, s2) | (~node19(c_e_h_2, c_h, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s1) | (~node19(c_e_h_2, c_h, s1, s2)) | node14(c_e_h_2, c_h, s1, s2) | node15(c_e_h_2, c_h, s1, s2)))),
% 289.74/182.22 inference(monotonicity,[status(thm)],[4229])).
% 289.74/182.22 tff(4231,plain,
% 289.74/182.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s1) | node14(c_e_h_2, c_h, s1, s2) | node15(c_e_h_2, c_h, s1, s2) | (~node19(c_e_h_2, c_h, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s1) | (~node19(c_e_h_2, c_h, s1, s2)) | node14(c_e_h_2, c_h, s1, s2) | node15(c_e_h_2, c_h, s1, s2))),
% 289.74/182.22 inference(transitivity,[status(thm)],[4230, 4228])).
% 289.74/182.22 tff(4232,plain,
% 289.74/182.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s1) | node14(c_e_h_2, c_h, s1, s2) | node15(c_e_h_2, c_h, s1, s2) | (~node19(c_e_h_2, c_h, s1, s2)))),
% 289.74/182.22 inference(quant_inst,[status(thm)],[])).
% 289.74/182.22 tff(4233,plain,
% 289.74/182.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s1) | (~node19(c_e_h_2, c_h, s1, s2)) | node14(c_e_h_2, c_h, s1, s2) | node15(c_e_h_2, c_h, s1, s2)),
% 289.74/182.22 inference(modus_ponens,[status(thm)],[4232, 4231])).
% 289.74/182.22 tff(4234,plain,
% 289.74/182.22 (node16(c_e_h_2, c_h, s1) | node14(c_e_h_2, c_h, s1, s2) | node15(c_e_h_2, c_h, s1, s2)),
% 289.74/182.22 inference(unit_resolution,[status(thm)],[4233, 204, 4227])).
% 289.74/182.22 tff(4235,plain,
% 289.74/182.22 (node14(c_e_h_2, c_h, s1, s2) | node15(c_e_h_2, c_h, s1, s2)),
% 289.74/182.22 inference(unit_resolution,[status(thm)],[4234, 4223])).
% 289.74/182.22 tff(4236,plain,
% 289.74/182.22 (node15(c_e_h_2, c_h, s1, s2)),
% 289.74/182.22 inference(unit_resolution,[status(thm)],[4235, 4159])).
% 289.74/182.22 tff(4237,plain,
% 289.74/182.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s2)) | (~node15(c_e_h_2, c_h, s1, s2)) | m_c_h_element_v_out(c_e_h_2, c_h, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s2)) | (~node15(c_e_h_2, c_h, s1, s2)) | m_c_h_element_v_out(c_e_h_2, c_h, s1))),
% 289.74/182.22 inference(rewrite,[status(thm)],[])).
% 289.74/182.22 tff(4238,plain,
% 289.74/182.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s2)) | (~node15(c_e_h_2, c_h, s1, s2)) | m_c_h_element_v_out(c_e_h_2, c_h, s1))),
% 289.74/182.22 inference(quant_inst,[status(thm)],[])).
% 289.74/182.22 tff(4239,plain,
% 289.74/182.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s2)) | (~node15(c_e_h_2, c_h, s1, s2)) | m_c_h_element_v_out(c_e_h_2, c_h, s1)),
% 289.74/182.22 inference(modus_ponens,[status(thm)],[4238, 4237])).
% 289.74/182.22 tff(4240,plain,
% 289.74/182.22 ($false),
% 289.74/182.22 inference(unit_resolution,[status(thm)],[4239, 147, 4104, 3880, 4236])).
% 289.74/182.22 tff(4241,plain,(~m_c_h_element_v_out(c_e_h_2, c_h, s2)), inference(lemma,lemma(discharge,[]))).
% 289.74/182.22 tff(4242,plain,
% 289.74/182.22 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s2)) | m_c_h_element_v_out(c_e_h_2, c_h, s2))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s2)) | m_c_h_element_v_out(c_e_h_2, c_h, s2))),
% 289.74/182.22 inference(rewrite,[status(thm)],[])).
% 289.74/182.22 tff(4243,plain,
% 289.74/182.22 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s2)) | m_c_h_element_v_out(c_e_h_2, c_h, s2))),
% 289.74/182.22 inference(quant_inst,[status(thm)],[])).
% 289.74/182.22 tff(4244,plain,
% 289.74/182.22 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s2)) | m_c_h_element_v_out(c_e_h_2, c_h, s2)),
% 289.74/182.22 inference(modus_ponens,[status(thm)],[4243, 4242])).
% 289.74/182.22 tff(4245,plain,
% 289.74/182.22 (~m_and_h_gate_v_in1(c_e_h_2, c_i, s2)),
% 289.74/182.22 inference(unit_resolution,[status(thm)],[4244, 619, 4241])).
% 289.74/182.22 tff(4246,plain,
% 289.74/182.22 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s2)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s2)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s2))),
% 289.74/182.22 inference(rewrite,[status(thm)],[])).
% 289.74/182.22 tff(4247,plain,
% 289.74/182.22 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s2)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s2))),
% 289.74/182.22 inference(quant_inst,[status(thm)],[])).
% 289.74/182.22 tff(4248,plain,
% 289.74/182.22 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s2)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s2)),
% 289.74/182.23 inference(modus_ponens,[status(thm)],[4247, 4246])).
% 289.74/182.23 tff(4249,plain,
% 289.74/182.23 (~node20(c_e_h_2, c_i, s2)),
% 289.74/182.23 inference(unit_resolution,[status(thm)],[4248, 38, 4245])).
% 289.74/182.23 tff(4250,plain,
% 289.74/182.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s3)) | node20(c_e_h_2, c_i, s2) | (~node21(c_e_h_2, c_i, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s3)) | node20(c_e_h_2, c_i, s2) | (~node21(c_e_h_2, c_i, s2, s3)))),
% 289.74/182.23 inference(rewrite,[status(thm)],[])).
% 289.74/182.23 tff(4251,plain,
% 289.74/182.23 ((node20(c_e_h_2, c_i, s2) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s3)) | (~node21(c_e_h_2, c_i, s2, s3))) <=> ((~m_and_h_gate_v_out(c_e_h_2, c_i, s3)) | node20(c_e_h_2, c_i, s2) | (~node21(c_e_h_2, c_i, s2, s3)))),
% 289.74/182.23 inference(rewrite,[status(thm)],[])).
% 289.74/182.23 tff(4252,plain,
% 289.74/182.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s2) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s3)) | (~node21(c_e_h_2, c_i, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s3)) | node20(c_e_h_2, c_i, s2) | (~node21(c_e_h_2, c_i, s2, s3))))),
% 289.74/182.23 inference(monotonicity,[status(thm)],[4251])).
% 289.74/182.23 tff(4253,plain,
% 289.74/182.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s2) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s3)) | (~node21(c_e_h_2, c_i, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s3)) | node20(c_e_h_2, c_i, s2) | (~node21(c_e_h_2, c_i, s2, s3)))),
% 289.74/182.23 inference(transitivity,[status(thm)],[4252, 4250])).
% 289.74/182.23 tff(4254,plain,
% 289.74/182.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s2) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s3)) | (~node21(c_e_h_2, c_i, s2, s3)))),
% 289.74/182.23 inference(quant_inst,[status(thm)],[])).
% 289.74/182.23 tff(4255,plain,
% 289.74/182.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s3)) | node20(c_e_h_2, c_i, s2) | (~node21(c_e_h_2, c_i, s2, s3))),
% 289.74/182.23 inference(modus_ponens,[status(thm)],[4254, 4253])).
% 289.74/182.23 tff(4256,plain,
% 289.74/182.23 ($false),
% 289.74/182.23 inference(unit_resolution,[status(thm)],[4255, 52, 4091, 4249, 4103])).
% 289.74/182.23 tff(4257,plain,(~m_and_h_gate_v_out(c_e_h_2, c_i, s3)), inference(lemma,lemma(discharge,[]))).
% 289.74/182.23 tff(4258,plain,
% 289.74/182.23 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_f, s3)) | m_and_h_gate_v_out(c_e_h_2, c_i, s3))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s3)) | m_and_h_gate_v_out(c_e_h_2, c_i, s3))),
% 289.74/182.23 inference(rewrite,[status(thm)],[])).
% 289.74/182.23 tff(4259,plain,
% 289.74/182.23 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_f, s3)) | m_and_h_gate_v_out(c_e_h_2, c_i, s3))),
% 289.74/182.23 inference(quant_inst,[status(thm)],[])).
% 289.74/182.23 tff(4260,plain,
% 289.74/182.23 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s3)) | m_and_h_gate_v_out(c_e_h_2, c_i, s3)),
% 289.74/182.23 inference(modus_ponens,[status(thm)],[4259, 4258])).
% 289.74/182.23 tff(4261,plain,
% 289.74/182.23 (~m_c_h_element_v_in2(c_e_h_2, c_f, s3)),
% 289.74/182.23 inference(unit_resolution,[status(thm)],[4260, 2143, 4257])).
% 289.74/182.23 tff(4262,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_f, s3)), introduced(assumption)).
% 289.74/182.23 tff(4263,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_f, s3)), introduced(assumption)).
% 289.74/182.23 tff(4264,assumption,(node15(c_e_h_2, c_f, s3, s4)), introduced(assumption)).
% 289.74/182.23 tff(4265,plain,
% 289.74/182.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s4)) | (~node15(c_e_h_2, c_f, s3, s4)) | m_c_h_element_v_out(c_e_h_2, c_f, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s4)) | (~node15(c_e_h_2, c_f, s3, s4)) | m_c_h_element_v_out(c_e_h_2, c_f, s3))),
% 289.74/182.23 inference(rewrite,[status(thm)],[])).
% 289.74/182.23 tff(4266,plain,
% 289.74/182.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s4)) | (~node15(c_e_h_2, c_f, s3, s4)) | m_c_h_element_v_out(c_e_h_2, c_f, s3))),
% 289.74/182.23 inference(quant_inst,[status(thm)],[])).
% 289.74/182.23 tff(4267,plain,
% 289.74/182.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s4)) | (~node15(c_e_h_2, c_f, s3, s4)) | m_c_h_element_v_out(c_e_h_2, c_f, s3)),
% 289.74/182.23 inference(modus_ponens,[status(thm)],[4266, 4265])).
% 289.74/182.23 tff(4268,plain,
% 289.74/182.23 ($false),
% 289.74/182.23 inference(unit_resolution,[status(thm)],[4267, 147, 4264, 4079, 4078])).
% 289.74/182.23 tff(4269,plain,((~node15(c_e_h_2, c_f, s3, s4)) | m_c_h_element_v_out(c_e_h_2, c_f, s3) | (~m_c_h_element_v_out(c_e_h_2, c_f, s4))), inference(lemma,lemma(discharge,[]))).
% 289.74/182.23 tff(4270,plain,
% 289.74/182.23 (~node15(c_e_h_2, c_f, s3, s4)),
% 289.74/182.23 inference(unit_resolution,[status(thm)],[4269, 4078, 4079])).
% 289.74/182.23 tff(4271,assumption,(~node15(c_e_h_2, c_f, s3, s4)), introduced(assumption)).
% 289.74/182.23 tff(4272,plain,
% 289.74/182.23 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_f, s3)) | m_c_h_element_v_in1(c_e_h_2, c_f, s3) | m_c_h_element_v_in2(c_e_h_2, c_f, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_f, s3)) | m_c_h_element_v_in1(c_e_h_2, c_f, s3) | m_c_h_element_v_in2(c_e_h_2, c_f, s3))),
% 289.74/182.23 inference(rewrite,[status(thm)],[])).
% 289.74/182.23 tff(4273,plain,
% 289.74/182.23 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_f, s3)) | m_c_h_element_v_in1(c_e_h_2, c_f, s3) | m_c_h_element_v_in2(c_e_h_2, c_f, s3))),
% 289.74/182.23 inference(quant_inst,[status(thm)],[])).
% 289.74/182.23 tff(4274,plain,
% 289.74/182.23 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_f, s3)) | m_c_h_element_v_in1(c_e_h_2, c_f, s3) | m_c_h_element_v_in2(c_e_h_2, c_f, s3)),
% 289.74/182.23 inference(modus_ponens,[status(thm)],[4273, 4272])).
% 289.74/182.23 tff(4275,plain,
% 289.74/182.23 ((~node16(c_e_h_2, c_f, s3)) | m_c_h_element_v_in1(c_e_h_2, c_f, s3)),
% 289.74/182.23 inference(unit_resolution,[status(thm)],[4274, 178, 4262])).
% 289.74/182.23 tff(4276,plain,
% 289.74/182.23 (~node16(c_e_h_2, c_f, s3)),
% 289.74/182.23 inference(unit_resolution,[status(thm)],[4275, 4263])).
% 289.74/182.23 tff(4277,plain,
% 289.74/182.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s3, s4)) | node19(c_e_h_2, c_f, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s3, s4)) | node19(c_e_h_2, c_f, s3, s4))),
% 289.74/182.23 inference(rewrite,[status(thm)],[])).
% 289.74/182.23 tff(4278,plain,
% 289.74/182.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s3, s4)) | node19(c_e_h_2, c_f, s3, s4))),
% 289.74/182.23 inference(quant_inst,[status(thm)],[])).
% 289.74/182.23 tff(4279,plain,
% 289.74/182.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s3, s4)) | node19(c_e_h_2, c_f, s3, s4)),
% 289.74/182.23 inference(modus_ponens,[status(thm)],[4278, 4277])).
% 289.74/182.23 tff(4280,plain,
% 289.74/182.23 (node19(c_e_h_2, c_f, s3, s4)),
% 289.74/182.23 inference(unit_resolution,[status(thm)],[4279, 190, 531])).
% 289.74/182.23 tff(4281,plain,
% 289.74/182.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_f, s3, s4)) | node15(c_e_h_2, c_f, s3, s4) | node16(c_e_h_2, c_f, s3) | node14(c_e_h_2, c_f, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_f, s3, s4)) | node15(c_e_h_2, c_f, s3, s4) | node16(c_e_h_2, c_f, s3) | node14(c_e_h_2, c_f, s3, s4))),
% 289.74/182.23 inference(rewrite,[status(thm)],[])).
% 289.74/182.23 tff(4282,plain,
% 289.74/182.23 ((node16(c_e_h_2, c_f, s3) | node14(c_e_h_2, c_f, s3, s4) | node15(c_e_h_2, c_f, s3, s4) | (~node19(c_e_h_2, c_f, s3, s4))) <=> ((~node19(c_e_h_2, c_f, s3, s4)) | node15(c_e_h_2, c_f, s3, s4) | node16(c_e_h_2, c_f, s3) | node14(c_e_h_2, c_f, s3, s4))),
% 289.74/182.23 inference(rewrite,[status(thm)],[])).
% 289.74/182.23 tff(4283,plain,
% 289.74/182.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s3) | node14(c_e_h_2, c_f, s3, s4) | node15(c_e_h_2, c_f, s3, s4) | (~node19(c_e_h_2, c_f, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_f, s3, s4)) | node15(c_e_h_2, c_f, s3, s4) | node16(c_e_h_2, c_f, s3) | node14(c_e_h_2, c_f, s3, s4)))),
% 289.74/182.23 inference(monotonicity,[status(thm)],[4282])).
% 289.74/182.23 tff(4284,plain,
% 289.74/182.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s3) | node14(c_e_h_2, c_f, s3, s4) | node15(c_e_h_2, c_f, s3, s4) | (~node19(c_e_h_2, c_f, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_f, s3, s4)) | node15(c_e_h_2, c_f, s3, s4) | node16(c_e_h_2, c_f, s3) | node14(c_e_h_2, c_f, s3, s4))),
% 289.74/182.23 inference(transitivity,[status(thm)],[4283, 4281])).
% 289.74/182.23 tff(4285,plain,
% 289.74/182.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s3) | node14(c_e_h_2, c_f, s3, s4) | node15(c_e_h_2, c_f, s3, s4) | (~node19(c_e_h_2, c_f, s3, s4)))),
% 289.74/182.23 inference(quant_inst,[status(thm)],[])).
% 289.74/182.23 tff(4286,plain,
% 289.74/182.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_f, s3, s4)) | node15(c_e_h_2, c_f, s3, s4) | node16(c_e_h_2, c_f, s3) | node14(c_e_h_2, c_f, s3, s4)),
% 289.74/182.23 inference(modus_ponens,[status(thm)],[4285, 4284])).
% 289.74/182.23 tff(4287,plain,
% 289.74/182.23 (node15(c_e_h_2, c_f, s3, s4) | node16(c_e_h_2, c_f, s3) | node14(c_e_h_2, c_f, s3, s4)),
% 289.74/182.23 inference(unit_resolution,[status(thm)],[4286, 204, 4280])).
% 289.74/182.23 tff(4288,plain,
% 289.74/182.23 (node14(c_e_h_2, c_f, s3, s4)),
% 289.74/182.23 inference(unit_resolution,[status(thm)],[4287, 4276, 4271])).
% 289.74/182.23 tff(4289,plain,
% 289.74/182.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_f, s3, s4)) | m_c_h_element_v_in1(c_e_h_2, c_f, s3) | (~m_c_h_element_v_out(c_e_h_2, c_f, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_2, c_f, s3, s4)) | m_c_h_element_v_in1(c_e_h_2, c_f, s3) | (~m_c_h_element_v_out(c_e_h_2, c_f, s4)))),
% 289.74/182.23 inference(rewrite,[status(thm)],[])).
% 289.74/182.23 tff(4290,plain,
% 289.74/182.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_f, s3, s4)) | m_c_h_element_v_in1(c_e_h_2, c_f, s3) | (~m_c_h_element_v_out(c_e_h_2, c_f, s4)))),
% 289.74/182.23 inference(quant_inst,[status(thm)],[])).
% 289.74/182.23 tff(4291,plain,
% 289.74/182.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_2, c_f, s3, s4)) | m_c_h_element_v_in1(c_e_h_2, c_f, s3) | (~m_c_h_element_v_out(c_e_h_2, c_f, s4))),
% 289.74/182.24 inference(modus_ponens,[status(thm)],[4290, 4289])).
% 289.74/182.24 tff(4292,plain,
% 289.74/182.24 ($false),
% 289.74/182.24 inference(unit_resolution,[status(thm)],[4291, 223, 4288, 4078, 4263])).
% 289.74/182.24 tff(4293,plain,(m_c_h_element_v_in1(c_e_h_2, c_f, s3) | (~m_c_h_element_v_out(c_e_h_2, c_f, s4)) | node15(c_e_h_2, c_f, s3, s4) | m_c_h_element_v_in2(c_e_h_2, c_f, s3)), inference(lemma,lemma(discharge,[]))).
% 289.74/182.24 tff(4294,plain,
% 289.74/182.24 ($false),
% 289.74/182.24 inference(unit_resolution,[status(thm)],[4293, 4270, 4078, 4263, 4262])).
% 289.74/182.24 tff(4295,plain,((~m_c_h_element_v_out(c_e_h_2, c_f, s4)) | m_c_h_element_v_in1(c_e_h_2, c_f, s3) | m_c_h_element_v_in2(c_e_h_2, c_f, s3) | m_c_h_element_v_out(c_e_h_2, c_f, s3)), inference(lemma,lemma(discharge,[]))).
% 289.74/182.24 tff(4296,plain,
% 289.74/182.24 ((~m_c_h_element_v_out(c_e_h_2, c_f, s4)) | m_c_h_element_v_in1(c_e_h_2, c_f, s3) | m_c_h_element_v_in2(c_e_h_2, c_f, s3)),
% 289.74/182.24 inference(unit_resolution,[status(thm)],[4295, 3942])).
% 289.74/182.24 tff(4297,plain,
% 289.74/182.24 ((~m_c_h_element_v_out(c_e_h_2, c_f, s4)) | m_c_h_element_v_in1(c_e_h_2, c_f, s3)),
% 289.74/182.24 inference(unit_resolution,[status(thm)],[4296, 4261])).
% 289.74/182.24 tff(4298,plain,
% 289.74/182.24 (m_c_h_element_v_in1(c_e_h_2, c_f, s3)),
% 289.74/182.24 inference(unit_resolution,[status(thm)],[4297, 4078])).
% 289.74/182.24 tff(4299,plain,
% 289.74/182.24 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s3)) | (~node17(c_e_h_2, c_f, s3)) | m_c_h_element_v_in2(c_e_h_2, c_f, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s3)) | (~node17(c_e_h_2, c_f, s3)) | m_c_h_element_v_in2(c_e_h_2, c_f, s3))),
% 289.74/182.24 inference(rewrite,[status(thm)],[])).
% 289.74/182.24 tff(4300,plain,
% 289.74/182.24 (((~m_c_h_element_v_in1(c_e_h_2, c_f, s3)) | m_c_h_element_v_in2(c_e_h_2, c_f, s3) | (~node17(c_e_h_2, c_f, s3))) <=> ((~m_c_h_element_v_in1(c_e_h_2, c_f, s3)) | (~node17(c_e_h_2, c_f, s3)) | m_c_h_element_v_in2(c_e_h_2, c_f, s3))),
% 289.74/182.24 inference(rewrite,[status(thm)],[])).
% 289.74/182.24 tff(4301,plain,
% 289.74/182.24 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s3)) | m_c_h_element_v_in2(c_e_h_2, c_f, s3) | (~node17(c_e_h_2, c_f, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s3)) | (~node17(c_e_h_2, c_f, s3)) | m_c_h_element_v_in2(c_e_h_2, c_f, s3)))),
% 289.74/182.24 inference(monotonicity,[status(thm)],[4300])).
% 289.74/182.24 tff(4302,plain,
% 289.74/182.24 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s3)) | m_c_h_element_v_in2(c_e_h_2, c_f, s3) | (~node17(c_e_h_2, c_f, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s3)) | (~node17(c_e_h_2, c_f, s3)) | m_c_h_element_v_in2(c_e_h_2, c_f, s3))),
% 289.74/182.24 inference(transitivity,[status(thm)],[4301, 4299])).
% 289.74/182.24 tff(4303,plain,
% 289.74/182.24 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s3)) | m_c_h_element_v_in2(c_e_h_2, c_f, s3) | (~node17(c_e_h_2, c_f, s3)))),
% 289.74/182.24 inference(quant_inst,[status(thm)],[])).
% 289.74/182.24 tff(4304,plain,
% 289.74/182.24 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s3)) | (~node17(c_e_h_2, c_f, s3)) | m_c_h_element_v_in2(c_e_h_2, c_f, s3)),
% 289.74/182.24 inference(modus_ponens,[status(thm)],[4303, 4302])).
% 289.74/182.24 tff(4305,plain,
% 289.74/182.24 ((~m_c_h_element_v_in1(c_e_h_2, c_f, s3)) | (~node17(c_e_h_2, c_f, s3))),
% 289.74/182.24 inference(unit_resolution,[status(thm)],[4304, 919, 4261])).
% 289.74/182.24 tff(4306,plain,
% 289.74/182.24 (~node17(c_e_h_2, c_f, s3)),
% 289.74/182.24 inference(unit_resolution,[status(thm)],[4305, 4298])).
% 289.74/182.24 tff(4307,plain,
% 289.74/182.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_f, s3, s4)) | node17(c_e_h_2, c_f, s3) | node18(c_e_h_2, c_f, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_f, s3, s4)) | node17(c_e_h_2, c_f, s3) | node18(c_e_h_2, c_f, s3, s4))),
% 289.74/182.24 inference(rewrite,[status(thm)],[])).
% 289.74/182.24 tff(4308,plain,
% 289.74/182.24 ((node17(c_e_h_2, c_f, s3) | node18(c_e_h_2, c_f, s3, s4) | (~node19(c_e_h_2, c_f, s3, s4))) <=> ((~node19(c_e_h_2, c_f, s3, s4)) | node17(c_e_h_2, c_f, s3) | node18(c_e_h_2, c_f, s3, s4))),
% 289.74/182.24 inference(rewrite,[status(thm)],[])).
% 289.74/182.24 tff(4309,plain,
% 289.74/182.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s3) | node18(c_e_h_2, c_f, s3, s4) | (~node19(c_e_h_2, c_f, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_f, s3, s4)) | node17(c_e_h_2, c_f, s3) | node18(c_e_h_2, c_f, s3, s4)))),
% 289.74/182.24 inference(monotonicity,[status(thm)],[4308])).
% 289.74/182.24 tff(4310,plain,
% 289.74/182.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s3) | node18(c_e_h_2, c_f, s3, s4) | (~node19(c_e_h_2, c_f, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_f, s3, s4)) | node17(c_e_h_2, c_f, s3) | node18(c_e_h_2, c_f, s3, s4))),
% 289.74/182.24 inference(transitivity,[status(thm)],[4309, 4307])).
% 289.74/182.24 tff(4311,plain,
% 289.74/182.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s3) | node18(c_e_h_2, c_f, s3, s4) | (~node19(c_e_h_2, c_f, s3, s4)))),
% 289.74/182.24 inference(quant_inst,[status(thm)],[])).
% 289.74/182.24 tff(4312,plain,
% 289.74/182.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_f, s3, s4)) | node17(c_e_h_2, c_f, s3) | node18(c_e_h_2, c_f, s3, s4)),
% 289.74/182.24 inference(modus_ponens,[status(thm)],[4311, 4310])).
% 289.74/182.24 tff(4313,plain,
% 289.74/182.24 (node17(c_e_h_2, c_f, s3) | node18(c_e_h_2, c_f, s3, s4)),
% 289.74/182.24 inference(unit_resolution,[status(thm)],[4312, 776, 4280])).
% 289.74/182.24 tff(4314,plain,
% 289.74/182.24 ($false),
% 289.74/182.24 inference(unit_resolution,[status(thm)],[4313, 4306, 4090])).
% 289.74/182.24 tff(4315,plain,(~m_c_h_element_v_out(c_e_h_2, c_f, s4)), inference(lemma,lemma(discharge,[]))).
% 289.74/182.24 tff(4316,assumption,(m_and_h_gate_v_in1(c_e_h_2, c_q, s4)), introduced(assumption)).
% 289.74/182.24 tff(4317,assumption,(~m_c_h_element_v_out(c_e_h_2, c_f, s4)), introduced(assumption)).
% 289.74/182.24 tff(4318,plain,
% 289.74/182.24 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_q, s4)) | m_c_h_element_v_out(c_e_h_2, c_f, s4))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_q, s4)) | m_c_h_element_v_out(c_e_h_2, c_f, s4))),
% 289.74/182.24 inference(rewrite,[status(thm)],[])).
% 289.74/182.24 tff(4319,plain,
% 289.74/182.24 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_q, s4)) | m_c_h_element_v_out(c_e_h_2, c_f, s4))),
% 289.74/182.24 inference(quant_inst,[status(thm)],[])).
% 289.74/182.24 tff(4320,plain,
% 289.74/182.24 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_q, s4)) | m_c_h_element_v_out(c_e_h_2, c_f, s4)),
% 289.74/182.24 inference(modus_ponens,[status(thm)],[4319, 4318])).
% 289.74/182.24 tff(4321,plain,
% 289.74/182.24 ($false),
% 289.74/182.24 inference(unit_resolution,[status(thm)],[4320, 1586, 4317, 4316])).
% 289.74/182.24 tff(4322,plain,((~m_and_h_gate_v_in1(c_e_h_2, c_q, s4)) | m_c_h_element_v_out(c_e_h_2, c_f, s4)), inference(lemma,lemma(discharge,[]))).
% 289.74/182.24 tff(4323,plain,
% 289.74/182.24 (~m_and_h_gate_v_in1(c_e_h_2, c_q, s4)),
% 289.74/182.24 inference(unit_resolution,[status(thm)],[4322, 4315])).
% 289.74/182.24 tff(4324,assumption,(node20(c_e_h_2, c_q, s4)), introduced(assumption)).
% 289.74/182.24 tff(4325,assumption,(~m_and_h_gate_v_in1(c_e_h_2, c_q, s4)), introduced(assumption)).
% 289.74/182.24 tff(4326,plain,
% 289.74/182.24 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_q, s4)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_q, s4)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s4))),
% 289.74/182.24 inference(rewrite,[status(thm)],[])).
% 289.74/182.24 tff(4327,plain,
% 289.74/182.24 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_q, s4)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s4))),
% 289.74/182.24 inference(quant_inst,[status(thm)],[])).
% 289.74/182.24 tff(4328,plain,
% 289.74/182.24 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_q, s4)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s4)),
% 289.74/182.24 inference(modus_ponens,[status(thm)],[4327, 4326])).
% 289.74/182.24 tff(4329,plain,
% 289.74/182.24 ($false),
% 289.74/182.24 inference(unit_resolution,[status(thm)],[4328, 38, 4325, 4324])).
% 289.74/182.24 tff(4330,plain,(m_and_h_gate_v_in1(c_e_h_2, c_q, s4) | (~node20(c_e_h_2, c_q, s4))), inference(lemma,lemma(discharge,[]))).
% 289.74/182.24 tff(4331,plain,
% 289.74/182.24 (~node20(c_e_h_2, c_q, s4)),
% 289.74/182.24 inference(unit_resolution,[status(thm)],[4330, 4323])).
% 289.74/182.24 tff(4332,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_q, s4)), introduced(assumption)).
% 289.74/182.24 tff(4333,assumption,(~node20(c_e_h_2, c_q, s4)), introduced(assumption)).
% 289.74/182.24 tff(4334,assumption,(m_and_h_gate_v_out(c_e_h_2, c_q, s5)), introduced(assumption)).
% 289.74/182.24 tff(4335,assumption,(node21(c_e_h_2, c_q, s4, s5)), introduced(assumption)).
% 289.74/182.24 tff(4336,plain,
% 289.74/182.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_q, s4) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s5)) | (~node21(c_e_h_2, c_q, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_q, s4) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s5)) | (~node21(c_e_h_2, c_q, s4, s5)))),
% 289.74/182.24 inference(rewrite,[status(thm)],[])).
% 289.74/182.24 tff(4337,plain,
% 289.74/182.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_q, s4) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s5)) | (~node21(c_e_h_2, c_q, s4, s5)))),
% 289.74/182.24 inference(quant_inst,[status(thm)],[])).
% 289.74/182.24 tff(4338,plain,
% 289.74/182.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_q, s4) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s5)) | (~node21(c_e_h_2, c_q, s4, s5))),
% 289.74/182.24 inference(modus_ponens,[status(thm)],[4337, 4336])).
% 289.74/182.24 tff(4339,plain,
% 289.74/182.24 ($false),
% 289.74/182.24 inference(unit_resolution,[status(thm)],[4338, 52, 4334, 4335, 4333])).
% 289.74/182.24 tff(4340,plain,((~node21(c_e_h_2, c_q, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s5)) | node20(c_e_h_2, c_q, s4)), inference(lemma,lemma(discharge,[]))).
% 289.74/182.24 tff(4341,plain,
% 289.74/182.24 (~node21(c_e_h_2, c_q, s4, s5)),
% 289.74/182.24 inference(unit_resolution,[status(thm)],[4340, 4334, 4333])).
% 289.74/182.24 tff(4342,plain,
% 289.74/182.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_2, c_q, s4, s5) | node22(c_e_h_2, c_q, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_2, c_q, s4, s5) | node22(c_e_h_2, c_q, s4, s5))),
% 289.74/182.24 inference(rewrite,[status(thm)],[])).
% 289.74/182.24 tff(4343,plain,
% 289.74/182.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_2, c_q, s4, s5) | node22(c_e_h_2, c_q, s4, s5))),
% 289.74/182.24 inference(quant_inst,[status(thm)],[])).
% 289.74/182.24 tff(4344,plain,
% 289.74/182.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_2, c_q, s4, s5) | node22(c_e_h_2, c_q, s4, s5)),
% 289.74/182.24 inference(modus_ponens,[status(thm)],[4343, 4342])).
% 289.74/182.24 tff(4345,plain,
% 289.74/182.24 (node21(c_e_h_2, c_q, s4, s5) | node22(c_e_h_2, c_q, s4, s5)),
% 289.74/182.24 inference(unit_resolution,[status(thm)],[4344, 82, 1028])).
% 289.74/182.25 tff(4346,plain,
% 289.74/182.25 (node22(c_e_h_2, c_q, s4, s5)),
% 289.74/182.25 inference(unit_resolution,[status(thm)],[4345, 4341])).
% 289.74/182.25 tff(4347,plain,
% 289.74/182.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s5)) | (~node22(c_e_h_2, c_q, s4, s5)) | m_and_h_gate_v_out(c_e_h_2, c_q, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s5)) | (~node22(c_e_h_2, c_q, s4, s5)) | m_and_h_gate_v_out(c_e_h_2, c_q, s4))),
% 289.74/182.25 inference(rewrite,[status(thm)],[])).
% 289.74/182.25 tff(4348,plain,
% 289.74/182.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s5)) | (~node22(c_e_h_2, c_q, s4, s5)) | m_and_h_gate_v_out(c_e_h_2, c_q, s4))),
% 289.74/182.25 inference(quant_inst,[status(thm)],[])).
% 289.74/182.25 tff(4349,plain,
% 289.74/182.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s5)) | (~node22(c_e_h_2, c_q, s4, s5)) | m_and_h_gate_v_out(c_e_h_2, c_q, s4)),
% 289.74/182.25 inference(modus_ponens,[status(thm)],[4348, 4347])).
% 289.74/182.25 tff(4350,plain,
% 289.74/182.25 ($false),
% 289.74/182.25 inference(unit_resolution,[status(thm)],[4349, 108, 4334, 4346, 4332])).
% 289.74/182.25 tff(4351,plain,((~m_and_h_gate_v_out(c_e_h_2, c_q, s5)) | m_and_h_gate_v_out(c_e_h_2, c_q, s4) | node20(c_e_h_2, c_q, s4)), inference(lemma,lemma(discharge,[]))).
% 289.74/182.25 tff(4352,plain,
% 289.74/182.25 ((~m_and_h_gate_v_out(c_e_h_2, c_q, s5)) | m_and_h_gate_v_out(c_e_h_2, c_q, s4)),
% 289.74/182.25 inference(unit_resolution,[status(thm)],[4351, 4331])).
% 289.74/182.25 tff(4353,plain,
% 289.74/182.25 (~m_and_h_gate_v_out(c_e_h_2, c_q, s5)),
% 289.74/182.25 inference(unit_resolution,[status(thm)],[4352, 3972])).
% 289.74/182.25 tff(4354,plain,
% 289.74/182.25 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s5))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s5))),
% 289.74/182.25 inference(rewrite,[status(thm)],[])).
% 289.74/182.25 tff(4355,plain,
% 289.74/182.25 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s5))),
% 289.74/182.25 inference(quant_inst,[status(thm)],[])).
% 289.74/182.25 tff(4356,plain,
% 289.74/182.25 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s5)),
% 289.74/182.25 inference(modus_ponens,[status(thm)],[4355, 4354])).
% 289.74/182.25 tff(4357,plain,
% 289.74/182.25 (node3(c_e_h_2, c_e_h_3, s5)),
% 289.74/182.25 inference(unit_resolution,[status(thm)],[4356, 1059, 1056])).
% 289.74/182.25 tff(4358,plain,
% 289.74/182.25 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_3, s5)) | (~node3(c_e_h_2, c_e_h_3, s5)) | m_and_h_gate_v_out(c_e_h_2, c_q, s5))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_3, s5)) | (~node3(c_e_h_2, c_e_h_3, s5)) | m_and_h_gate_v_out(c_e_h_2, c_q, s5))),
% 289.74/182.25 inference(rewrite,[status(thm)],[])).
% 289.74/182.25 tff(4359,plain,
% 289.74/182.25 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_3, s5)) | (~node3(c_e_h_2, c_e_h_3, s5)) | m_and_h_gate_v_out(c_e_h_2, c_q, s5))),
% 289.74/182.25 inference(quant_inst,[status(thm)],[])).
% 289.74/182.25 tff(4360,plain,
% 289.74/182.25 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_3, s5)) | (~node3(c_e_h_2, c_e_h_3, s5)) | m_and_h_gate_v_out(c_e_h_2, c_q, s5)),
% 289.74/182.25 inference(modus_ponens,[status(thm)],[4359, 4358])).
% 289.74/182.25 tff(4361,plain,
% 289.74/182.25 ((~m_cell_v_ack(c_e_h_3, s5)) | m_and_h_gate_v_out(c_e_h_2, c_q, s5)),
% 289.74/182.25 inference(unit_resolution,[status(thm)],[4360, 1073, 4357])).
% 289.74/182.25 tff(4362,plain,
% 289.74/182.25 (~m_cell_v_ack(c_e_h_3, s5)),
% 289.74/182.25 inference(unit_resolution,[status(thm)],[4361, 4353])).
% 289.74/182.25 tff(4363,plain,
% 289.74/182.25 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_j, s5)) | m_cell_v_ack(c_e_h_3, s5))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_j, s5)) | m_cell_v_ack(c_e_h_3, s5))),
% 289.74/182.25 inference(rewrite,[status(thm)],[])).
% 289.74/182.25 tff(4364,plain,
% 289.74/182.25 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_j, s5)) | m_cell_v_ack(c_e_h_3, s5))),
% 289.74/182.25 inference(quant_inst,[status(thm)],[])).
% 289.74/182.25 tff(4365,plain,
% 289.74/182.25 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_j, s5)) | m_cell_v_ack(c_e_h_3, s5)),
% 289.74/182.25 inference(modus_ponens,[status(thm)],[4364, 4363])).
% 289.74/182.25 tff(4366,plain,
% 289.74/182.25 (~m_or_h_gate_v_in2(c_e_h_3, c_j, s5)),
% 289.74/182.25 inference(unit_resolution,[status(thm)],[4365, 1085, 4362])).
% 289.74/182.25 tff(4367,assumption,(node5(c_e_h_3, c_j, s5, s6)), introduced(assumption)).
% 289.74/182.25 tff(4368,plain,
% 289.74/182.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_3, c_j, s5) | (~node5(c_e_h_3, c_j, s5, s6)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_3, c_j, s5) | (~node5(c_e_h_3, c_j, s5, s6)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s6)))),
% 289.74/182.25 inference(rewrite,[status(thm)],[])).
% 289.74/182.25 tff(4369,plain,
% 289.74/182.25 ((m_or_h_gate_v_in1(c_e_h_3, c_j, s5) | m_or_h_gate_v_in2(c_e_h_3, c_j, s5) | (~node5(c_e_h_3, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s6))) <=> (m_or_h_gate_v_in2(c_e_h_3, c_j, s5) | (~node5(c_e_h_3, c_j, s5, s6)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s6)))),
% 289.74/182.25 inference(rewrite,[status(thm)],[])).
% 289.74/182.25 tff(4370,plain,
% 289.74/182.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s5) | m_or_h_gate_v_in2(c_e_h_3, c_j, s5) | (~node5(c_e_h_3, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_3, c_j, s5) | (~node5(c_e_h_3, c_j, s5, s6)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s6))))),
% 289.74/182.25 inference(monotonicity,[status(thm)],[4369])).
% 289.74/182.25 tff(4371,plain,
% 289.74/182.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s5) | m_or_h_gate_v_in2(c_e_h_3, c_j, s5) | (~node5(c_e_h_3, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_3, c_j, s5) | (~node5(c_e_h_3, c_j, s5, s6)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s6)))),
% 289.74/182.25 inference(transitivity,[status(thm)],[4370, 4368])).
% 289.74/182.25 tff(4372,plain,
% 289.74/182.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s5) | m_or_h_gate_v_in2(c_e_h_3, c_j, s5) | (~node5(c_e_h_3, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s6)))),
% 289.74/182.25 inference(quant_inst,[status(thm)],[])).
% 289.74/182.25 tff(4373,plain,
% 289.74/182.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_3, c_j, s5) | (~node5(c_e_h_3, c_j, s5, s6)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s6))),
% 289.74/182.26 inference(modus_ponens,[status(thm)],[4372, 4371])).
% 289.74/182.26 tff(4374,plain,
% 289.74/182.26 ($false),
% 289.74/182.26 inference(unit_resolution,[status(thm)],[4373, 1159, 3608, 4367, 4366, 4077])).
% 289.74/182.26 tff(4375,plain,((~node5(c_e_h_3, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s6)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s5)), inference(lemma,lemma(discharge,[]))).
% 289.74/182.26 tff(4376,plain,
% 289.74/182.26 (~node5(c_e_h_3, c_j, s5, s6)),
% 289.74/182.26 inference(unit_resolution,[status(thm)],[4375, 3608, 4077])).
% 289.74/182.26 tff(4377,plain,
% 289.74/182.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s5, s6)) | node5(c_e_h_3, c_j, s5, s6) | node6(c_e_h_3, c_j, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s5, s6)) | node5(c_e_h_3, c_j, s5, s6) | node6(c_e_h_3, c_j, s5, s6))),
% 289.74/182.26 inference(rewrite,[status(thm)],[])).
% 289.74/182.26 tff(4378,plain,
% 289.74/182.26 ((node6(c_e_h_3, c_j, s5, s6) | node5(c_e_h_3, c_j, s5, s6) | (~trans(s5, s6))) <=> ((~trans(s5, s6)) | node5(c_e_h_3, c_j, s5, s6) | node6(c_e_h_3, c_j, s5, s6))),
% 289.74/182.26 inference(rewrite,[status(thm)],[])).
% 289.74/182.26 tff(4379,plain,
% 289.74/182.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s5, s6) | node5(c_e_h_3, c_j, s5, s6) | (~trans(s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s5, s6)) | node5(c_e_h_3, c_j, s5, s6) | node6(c_e_h_3, c_j, s5, s6)))),
% 289.74/182.26 inference(monotonicity,[status(thm)],[4378])).
% 289.74/182.26 tff(4380,plain,
% 289.74/182.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s5, s6) | node5(c_e_h_3, c_j, s5, s6) | (~trans(s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s5, s6)) | node5(c_e_h_3, c_j, s5, s6) | node6(c_e_h_3, c_j, s5, s6))),
% 289.74/182.26 inference(transitivity,[status(thm)],[4379, 4377])).
% 289.74/182.26 tff(4381,plain,
% 289.74/182.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s5, s6) | node5(c_e_h_3, c_j, s5, s6) | (~trans(s5, s6)))),
% 289.74/182.26 inference(quant_inst,[status(thm)],[])).
% 289.74/182.26 tff(4382,plain,
% 289.74/182.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s5, s6)) | node5(c_e_h_3, c_j, s5, s6) | node6(c_e_h_3, c_j, s5, s6)),
% 289.74/182.26 inference(modus_ponens,[status(thm)],[4381, 4380])).
% 289.74/182.26 tff(4383,plain,
% 289.74/182.26 (node5(c_e_h_3, c_j, s5, s6) | node6(c_e_h_3, c_j, s5, s6)),
% 289.74/182.26 inference(unit_resolution,[status(thm)],[4382, 1141, 1406])).
% 289.74/182.26 tff(4384,plain,
% 289.74/182.26 ($false),
% 289.74/182.26 inference(unit_resolution,[status(thm)],[4383, 4376, 4076])).
% 289.74/182.26 tff(4385,plain,((~m_or_h_gate_v_out(c_e_h_3, c_j, s6)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s5)), inference(lemma,lemma(discharge,[]))).
% 289.74/182.26 tff(4386,plain,
% 289.74/182.26 (~m_or_h_gate_v_out(c_e_h_3, c_j, s6)),
% 289.74/182.26 inference(unit_resolution,[status(thm)],[4385, 3607])).
% 289.74/182.26 tff(4387,assumption,(~node20(c_e_h_3, c_k, s4)), introduced(assumption)).
% 289.74/182.26 tff(4388,assumption,(m_and_h_gate_v_out(c_e_h_3, c_k, s5)), introduced(assumption)).
% 289.74/182.26 tff(4389,assumption,(node22(c_e_h_3, c_k, s4, s5)), introduced(assumption)).
% 289.74/182.26 tff(4390,plain,
% 289.74/182.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s5)) | (~node22(c_e_h_3, c_k, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_k, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s5)) | (~node22(c_e_h_3, c_k, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_k, s4))),
% 289.74/182.26 inference(rewrite,[status(thm)],[])).
% 289.74/182.26 tff(4391,plain,
% 289.74/182.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s5)) | (~node22(c_e_h_3, c_k, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_k, s4))),
% 289.74/182.26 inference(quant_inst,[status(thm)],[])).
% 289.74/182.26 tff(4392,plain,
% 289.74/182.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s5)) | (~node22(c_e_h_3, c_k, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_k, s4)),
% 289.74/182.26 inference(modus_ponens,[status(thm)],[4391, 4390])).
% 289.74/182.26 tff(4393,plain,
% 289.74/182.26 ($false),
% 289.74/182.26 inference(unit_resolution,[status(thm)],[4392, 108, 4389, 3486, 4388])).
% 289.74/182.26 tff(4394,plain,((~node22(c_e_h_3, c_k, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_k, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s5))), inference(lemma,lemma(discharge,[]))).
% 289.74/182.26 tff(4395,plain,
% 289.74/182.26 (~node22(c_e_h_3, c_k, s4, s5)),
% 289.74/182.26 inference(unit_resolution,[status(thm)],[4394, 4388, 3486])).
% 289.74/182.26 tff(4396,plain,
% 289.74/182.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_3, c_k, s4, s5) | node22(c_e_h_3, c_k, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_3, c_k, s4, s5) | node22(c_e_h_3, c_k, s4, s5))),
% 289.74/182.26 inference(rewrite,[status(thm)],[])).
% 289.74/182.26 tff(4397,plain,
% 289.74/182.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_3, c_k, s4, s5) | node22(c_e_h_3, c_k, s4, s5))),
% 289.74/182.26 inference(quant_inst,[status(thm)],[])).
% 289.74/182.26 tff(4398,plain,
% 289.74/182.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_3, c_k, s4, s5) | node22(c_e_h_3, c_k, s4, s5)),
% 289.74/182.26 inference(modus_ponens,[status(thm)],[4397, 4396])).
% 289.74/182.26 tff(4399,plain,
% 289.74/182.26 (node21(c_e_h_3, c_k, s4, s5) | node22(c_e_h_3, c_k, s4, s5)),
% 289.74/182.26 inference(unit_resolution,[status(thm)],[4398, 82, 1028])).
% 289.74/182.26 tff(4400,plain,
% 289.74/182.26 (node21(c_e_h_3, c_k, s4, s5)),
% 289.74/182.26 inference(unit_resolution,[status(thm)],[4399, 4395])).
% 289.74/182.26 tff(4401,plain,
% 289.74/182.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_k, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s5)) | (~node21(c_e_h_3, c_k, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_k, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s5)) | (~node21(c_e_h_3, c_k, s4, s5)))),
% 289.74/182.26 inference(rewrite,[status(thm)],[])).
% 289.74/182.26 tff(4402,plain,
% 289.74/182.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_k, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s5)) | (~node21(c_e_h_3, c_k, s4, s5)))),
% 289.74/182.26 inference(quant_inst,[status(thm)],[])).
% 289.74/182.26 tff(4403,plain,
% 289.74/182.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_k, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s5)) | (~node21(c_e_h_3, c_k, s4, s5))),
% 289.74/182.26 inference(modus_ponens,[status(thm)],[4402, 4401])).
% 289.74/182.26 tff(4404,plain,
% 289.74/182.26 ($false),
% 289.74/182.26 inference(unit_resolution,[status(thm)],[4403, 52, 4400, 4387, 4388])).
% 289.74/182.26 tff(4405,plain,((~m_and_h_gate_v_out(c_e_h_3, c_k, s5)) | node20(c_e_h_3, c_k, s4) | m_and_h_gate_v_out(c_e_h_3, c_k, s4)), inference(lemma,lemma(discharge,[]))).
% 289.74/182.26 tff(4406,plain,
% 289.74/182.26 (~m_and_h_gate_v_out(c_e_h_3, c_k, s5)),
% 289.74/182.26 inference(unit_resolution,[status(thm)],[4405, 3486, 4387])).
% 289.74/182.26 tff(4407,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_l, s5)), introduced(assumption)).
% 289.74/182.26 tff(4408,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_k, s5)), introduced(assumption)).
% 289.74/182.26 tff(4409,plain,
% 289.74/182.26 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_l, s5)) | m_and_h_gate_v_out(c_e_h_3, c_k, s5))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s5)) | m_and_h_gate_v_out(c_e_h_3, c_k, s5))),
% 289.74/182.26 inference(rewrite,[status(thm)],[])).
% 289.74/182.26 tff(4410,plain,
% 289.74/182.26 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_l, s5)) | m_and_h_gate_v_out(c_e_h_3, c_k, s5))),
% 289.74/182.26 inference(quant_inst,[status(thm)],[])).
% 289.74/182.26 tff(4411,plain,
% 289.74/182.26 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s5)) | m_and_h_gate_v_out(c_e_h_3, c_k, s5)),
% 289.74/182.26 inference(modus_ponens,[status(thm)],[4410, 4409])).
% 289.74/182.26 tff(4412,plain,
% 289.74/182.26 ($false),
% 289.74/182.26 inference(unit_resolution,[status(thm)],[4411, 1529, 4408, 4407])).
% 289.74/182.26 tff(4413,plain,((~m_and_h_gate_v_in1(c_e_h_3, c_l, s5)) | m_and_h_gate_v_out(c_e_h_3, c_k, s5)), inference(lemma,lemma(discharge,[]))).
% 289.74/182.26 tff(4414,plain,
% 289.74/182.26 (~m_and_h_gate_v_in1(c_e_h_3, c_l, s5)),
% 289.74/182.26 inference(unit_resolution,[status(thm)],[4413, 4406])).
% 289.74/182.26 tff(4415,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_l, s5)), introduced(assumption)).
% 289.74/182.26 tff(4416,assumption,(node20(c_e_h_3, c_l, s5)), introduced(assumption)).
% 289.74/182.26 tff(4417,plain,
% 289.74/182.26 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_l, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_l, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s5))),
% 289.74/182.26 inference(rewrite,[status(thm)],[])).
% 289.74/182.26 tff(4418,plain,
% 289.74/182.26 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_l, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s5))),
% 289.74/182.26 inference(quant_inst,[status(thm)],[])).
% 289.74/182.26 tff(4419,plain,
% 289.74/182.26 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_l, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s5)),
% 289.74/182.26 inference(modus_ponens,[status(thm)],[4418, 4417])).
% 289.74/182.26 tff(4420,plain,
% 289.74/182.26 ($false),
% 289.74/182.26 inference(unit_resolution,[status(thm)],[4419, 38, 4416, 4415])).
% 289.74/182.26 tff(4421,plain,((~node20(c_e_h_3, c_l, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s5)), inference(lemma,lemma(discharge,[]))).
% 289.74/182.26 tff(4422,plain,
% 289.74/182.26 (~node20(c_e_h_3, c_l, s5)),
% 289.74/182.26 inference(unit_resolution,[status(thm)],[4421, 4414])).
% 289.74/182.26 tff(4423,assumption,(m_and_h_gate_v_out(c_e_h_3, c_l, s6)), introduced(assumption)).
% 289.74/182.26 tff(4424,assumption,(node22(c_e_h_3, c_l, s5, s6)), introduced(assumption)).
% 289.74/182.26 tff(4425,plain,
% 289.74/182.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s6)) | (~node22(c_e_h_3, c_l, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_l, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s6)) | (~node22(c_e_h_3, c_l, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_l, s5))),
% 289.74/182.26 inference(rewrite,[status(thm)],[])).
% 289.74/182.26 tff(4426,plain,
% 289.74/182.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s6)) | (~node22(c_e_h_3, c_l, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_l, s5))),
% 289.74/182.26 inference(quant_inst,[status(thm)],[])).
% 289.74/182.26 tff(4427,plain,
% 289.74/182.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s6)) | (~node22(c_e_h_3, c_l, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_l, s5)),
% 289.74/182.26 inference(modus_ponens,[status(thm)],[4426, 4425])).
% 289.74/182.26 tff(4428,plain,
% 289.74/182.26 ($false),
% 289.74/182.26 inference(unit_resolution,[status(thm)],[4427, 108, 3601, 4424, 4423])).
% 289.74/182.26 tff(4429,plain,((~node22(c_e_h_3, c_l, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_l, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s6))), inference(lemma,lemma(discharge,[]))).
% 289.74/182.26 tff(4430,plain,
% 289.74/182.26 (~node22(c_e_h_3, c_l, s5, s6)),
% 289.74/182.26 inference(unit_resolution,[status(thm)],[4429, 4423, 3601])).
% 289.74/182.26 tff(4431,assumption,(~node20(c_e_h_3, c_l, s5)), introduced(assumption)).
% 289.74/182.27 tff(4432,assumption,(node21(c_e_h_3, c_l, s5, s6)), introduced(assumption)).
% 289.74/182.27 tff(4433,plain,
% 289.74/182.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s5) | (~node21(c_e_h_3, c_l, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_l, s5) | (~node21(c_e_h_3, c_l, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s6)))),
% 289.74/182.27 inference(rewrite,[status(thm)],[])).
% 289.74/182.27 tff(4434,plain,
% 289.74/182.27 ((node20(c_e_h_3, c_l, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s6)) | (~node21(c_e_h_3, c_l, s5, s6))) <=> (node20(c_e_h_3, c_l, s5) | (~node21(c_e_h_3, c_l, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s6)))),
% 289.74/182.27 inference(rewrite,[status(thm)],[])).
% 289.74/182.27 tff(4435,plain,
% 289.74/182.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s6)) | (~node21(c_e_h_3, c_l, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s5) | (~node21(c_e_h_3, c_l, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s6))))),
% 289.74/182.27 inference(monotonicity,[status(thm)],[4434])).
% 289.74/182.27 tff(4436,plain,
% 289.74/182.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s6)) | (~node21(c_e_h_3, c_l, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_l, s5) | (~node21(c_e_h_3, c_l, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s6)))),
% 289.74/182.27 inference(transitivity,[status(thm)],[4435, 4433])).
% 289.74/182.27 tff(4437,plain,
% 289.74/182.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s6)) | (~node21(c_e_h_3, c_l, s5, s6)))),
% 289.74/182.27 inference(quant_inst,[status(thm)],[])).
% 289.74/182.27 tff(4438,plain,
% 289.74/182.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_l, s5) | (~node21(c_e_h_3, c_l, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s6))),
% 289.74/182.27 inference(modus_ponens,[status(thm)],[4437, 4436])).
% 289.74/182.27 tff(4439,plain,
% 289.74/182.27 ($false),
% 289.74/182.27 inference(unit_resolution,[status(thm)],[4438, 52, 4432, 4423, 4431])).
% 289.74/182.27 tff(4440,plain,((~node21(c_e_h_3, c_l, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s6)) | node20(c_e_h_3, c_l, s5)), inference(lemma,lemma(discharge,[]))).
% 289.74/182.27 tff(4441,plain,
% 289.74/182.27 (~node21(c_e_h_3, c_l, s5, s6)),
% 289.74/182.27 inference(unit_resolution,[status(thm)],[4440, 4423, 4431])).
% 289.74/182.27 tff(4442,plain,
% 289.74/182.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_3, c_l, s5, s6) | node22(c_e_h_3, c_l, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_3, c_l, s5, s6) | node22(c_e_h_3, c_l, s5, s6))),
% 289.74/182.27 inference(rewrite,[status(thm)],[])).
% 289.74/182.27 tff(4443,plain,
% 289.74/182.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_3, c_l, s5, s6) | node22(c_e_h_3, c_l, s5, s6))),
% 289.74/182.27 inference(quant_inst,[status(thm)],[])).
% 289.74/182.27 tff(4444,plain,
% 289.74/182.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_3, c_l, s5, s6) | node22(c_e_h_3, c_l, s5, s6)),
% 289.74/182.27 inference(modus_ponens,[status(thm)],[4443, 4442])).
% 289.74/182.27 tff(4445,plain,
% 289.74/182.27 (node21(c_e_h_3, c_l, s5, s6) | node22(c_e_h_3, c_l, s5, s6)),
% 289.74/182.27 inference(unit_resolution,[status(thm)],[4444, 82, 1406])).
% 289.74/182.27 tff(4446,plain,
% 289.74/182.27 ($false),
% 289.74/182.27 inference(unit_resolution,[status(thm)],[4445, 4441, 4430])).
% 289.74/182.27 tff(4447,plain,((~m_and_h_gate_v_out(c_e_h_3, c_l, s6)) | node20(c_e_h_3, c_l, s5) | m_and_h_gate_v_out(c_e_h_3, c_l, s5)), inference(lemma,lemma(discharge,[]))).
% 289.74/182.27 tff(4448,plain,
% 289.74/182.27 (~m_and_h_gate_v_out(c_e_h_3, c_l, s6)),
% 289.74/182.27 inference(unit_resolution,[status(thm)],[4447, 4422, 3599])).
% 289.74/182.27 tff(4449,assumption,(~node20(c_e_h_3, c_k, s5)), introduced(assumption)).
% 289.74/182.27 tff(4450,assumption,(m_and_h_gate_v_out(c_e_h_3, c_k, s6)), introduced(assumption)).
% 289.74/182.27 tff(4451,assumption,(node21(c_e_h_3, c_k, s5, s6)), introduced(assumption)).
% 289.74/182.27 tff(4452,plain,
% 289.74/182.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_k, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s6)) | (~node21(c_e_h_3, c_k, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_k, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s6)) | (~node21(c_e_h_3, c_k, s5, s6)))),
% 289.74/182.27 inference(rewrite,[status(thm)],[])).
% 289.74/182.27 tff(4453,plain,
% 289.74/182.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_k, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s6)) | (~node21(c_e_h_3, c_k, s5, s6)))),
% 289.74/182.27 inference(quant_inst,[status(thm)],[])).
% 289.74/182.27 tff(4454,plain,
% 289.74/182.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_k, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s6)) | (~node21(c_e_h_3, c_k, s5, s6))),
% 289.74/182.27 inference(modus_ponens,[status(thm)],[4453, 4452])).
% 289.74/182.27 tff(4455,plain,
% 289.74/182.27 ($false),
% 289.74/182.27 inference(unit_resolution,[status(thm)],[4454, 52, 4451, 4449, 4450])).
% 289.74/182.27 tff(4456,plain,((~node21(c_e_h_3, c_k, s5, s6)) | node20(c_e_h_3, c_k, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s6))), inference(lemma,lemma(discharge,[]))).
% 289.74/182.27 tff(4457,plain,
% 289.74/182.27 (~node21(c_e_h_3, c_k, s5, s6)),
% 289.74/182.27 inference(unit_resolution,[status(thm)],[4456, 4450, 4449])).
% 289.74/182.27 tff(4458,plain,
% 289.74/182.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_3, c_k, s5, s6) | node22(c_e_h_3, c_k, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_3, c_k, s5, s6) | node22(c_e_h_3, c_k, s5, s6))),
% 289.74/182.27 inference(rewrite,[status(thm)],[])).
% 289.74/182.27 tff(4459,plain,
% 289.74/182.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_3, c_k, s5, s6) | node22(c_e_h_3, c_k, s5, s6))),
% 289.74/182.27 inference(quant_inst,[status(thm)],[])).
% 289.74/182.27 tff(4460,plain,
% 289.74/182.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_3, c_k, s5, s6) | node22(c_e_h_3, c_k, s5, s6)),
% 289.74/182.27 inference(modus_ponens,[status(thm)],[4459, 4458])).
% 289.74/182.27 tff(4461,plain,
% 289.74/182.27 (node21(c_e_h_3, c_k, s5, s6) | node22(c_e_h_3, c_k, s5, s6)),
% 289.74/182.27 inference(unit_resolution,[status(thm)],[4460, 82, 1406])).
% 289.74/182.27 tff(4462,plain,
% 289.74/182.27 (node22(c_e_h_3, c_k, s5, s6)),
% 289.74/182.27 inference(unit_resolution,[status(thm)],[4461, 4457])).
% 289.74/182.27 tff(4463,plain,
% 289.74/182.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s6)) | (~node22(c_e_h_3, c_k, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_k, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s6)) | (~node22(c_e_h_3, c_k, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_k, s5))),
% 289.74/182.27 inference(rewrite,[status(thm)],[])).
% 289.74/182.27 tff(4464,plain,
% 289.74/182.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s6)) | (~node22(c_e_h_3, c_k, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_k, s5))),
% 289.74/182.27 inference(quant_inst,[status(thm)],[])).
% 289.74/182.27 tff(4465,plain,
% 289.74/182.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s6)) | (~node22(c_e_h_3, c_k, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_k, s5)),
% 289.74/182.27 inference(modus_ponens,[status(thm)],[4464, 4463])).
% 289.74/182.27 tff(4466,plain,
% 289.74/182.27 ($false),
% 289.74/182.27 inference(unit_resolution,[status(thm)],[4465, 108, 4462, 4408, 4450])).
% 289.74/182.27 tff(4467,plain,((~m_and_h_gate_v_out(c_e_h_3, c_k, s6)) | m_and_h_gate_v_out(c_e_h_3, c_k, s5) | node20(c_e_h_3, c_k, s5)), inference(lemma,lemma(discharge,[]))).
% 289.74/182.27 tff(4468,plain,
% 289.74/182.27 (~m_and_h_gate_v_out(c_e_h_3, c_k, s6)),
% 289.74/182.27 inference(unit_resolution,[status(thm)],[4467, 4406, 4449])).
% 289.74/182.27 tff(4469,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_k, s6)), introduced(assumption)).
% 289.74/182.27 tff(4470,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_l, s6)), introduced(assumption)).
% 289.74/182.27 tff(4471,plain,
% 289.74/182.27 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_l, s6)) | m_and_h_gate_v_out(c_e_h_3, c_k, s6))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s6)) | m_and_h_gate_v_out(c_e_h_3, c_k, s6))),
% 289.74/182.27 inference(rewrite,[status(thm)],[])).
% 289.74/182.27 tff(4472,plain,
% 289.74/182.27 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_l, s6)) | m_and_h_gate_v_out(c_e_h_3, c_k, s6))),
% 289.74/182.27 inference(quant_inst,[status(thm)],[])).
% 289.74/182.27 tff(4473,plain,
% 289.74/182.27 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s6)) | m_and_h_gate_v_out(c_e_h_3, c_k, s6)),
% 289.74/182.27 inference(modus_ponens,[status(thm)],[4472, 4471])).
% 289.74/182.27 tff(4474,plain,
% 289.74/182.27 ($false),
% 289.74/182.27 inference(unit_resolution,[status(thm)],[4473, 1529, 4470, 4469])).
% 289.74/182.27 tff(4475,plain,((~m_and_h_gate_v_in1(c_e_h_3, c_l, s6)) | m_and_h_gate_v_out(c_e_h_3, c_k, s6)), inference(lemma,lemma(discharge,[]))).
% 289.74/182.27 tff(4476,plain,
% 289.74/182.27 (~m_and_h_gate_v_in1(c_e_h_3, c_l, s6)),
% 289.74/182.27 inference(unit_resolution,[status(thm)],[4475, 4468])).
% 289.74/182.27 tff(4477,assumption,(node20(c_e_h_3, c_l, s6)), introduced(assumption)).
% 289.74/182.27 tff(4478,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_l, s6)), introduced(assumption)).
% 289.74/182.27 tff(4479,plain,
% 289.74/182.27 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_l, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_l, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s6))),
% 289.74/182.27 inference(rewrite,[status(thm)],[])).
% 289.74/182.27 tff(4480,plain,
% 289.74/182.27 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_l, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s6))),
% 289.74/182.27 inference(quant_inst,[status(thm)],[])).
% 289.74/182.27 tff(4481,plain,
% 289.74/182.27 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_l, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s6)),
% 289.74/182.27 inference(modus_ponens,[status(thm)],[4480, 4479])).
% 289.74/182.27 tff(4482,plain,
% 289.74/182.27 ($false),
% 289.74/182.27 inference(unit_resolution,[status(thm)],[4481, 38, 4478, 4477])).
% 289.74/182.27 tff(4483,plain,((~node20(c_e_h_3, c_l, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s6)), inference(lemma,lemma(discharge,[]))).
% 289.74/182.27 tff(4484,plain,
% 289.74/182.27 (~node20(c_e_h_3, c_l, s6)),
% 289.74/182.27 inference(unit_resolution,[status(thm)],[4483, 4476])).
% 289.74/182.27 tff(4485,assumption,(~m_or_h_gate_v_out(c_e_h_3, c_j, s6)), introduced(assumption)).
% 289.74/182.27 tff(4486,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_l, s6)), introduced(assumption)).
% 289.74/182.27 tff(4487,assumption,(m_or_h_gate_v_in1(c_e_h_3, c_j, s6)), introduced(assumption)).
% 289.74/182.27 tff(4488,plain,
% 289.74/182.27 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_j, s6)) | m_and_h_gate_v_out(c_e_h_3, c_l, s6))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s6)) | m_and_h_gate_v_out(c_e_h_3, c_l, s6))),
% 289.74/182.28 inference(rewrite,[status(thm)],[])).
% 289.74/182.28 tff(4489,plain,
% 289.74/182.28 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_j, s6)) | m_and_h_gate_v_out(c_e_h_3, c_l, s6))),
% 289.74/182.28 inference(quant_inst,[status(thm)],[])).
% 289.74/182.28 tff(4490,plain,
% 289.74/182.28 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s6)) | m_and_h_gate_v_out(c_e_h_3, c_l, s6)),
% 289.74/182.28 inference(modus_ponens,[status(thm)],[4489, 4488])).
% 289.74/182.28 tff(4491,plain,
% 289.74/182.28 ($false),
% 289.74/182.28 inference(unit_resolution,[status(thm)],[4490, 1100, 4487, 4486])).
% 289.74/182.28 tff(4492,plain,((~m_or_h_gate_v_in1(c_e_h_3, c_j, s6)) | m_and_h_gate_v_out(c_e_h_3, c_l, s6)), inference(lemma,lemma(discharge,[]))).
% 289.74/182.28 tff(4493,plain,
% 289.74/182.28 (~m_or_h_gate_v_in1(c_e_h_3, c_j, s6)),
% 289.74/182.28 inference(unit_resolution,[status(thm)],[4492, 4486])).
% 289.74/182.28 tff(4494,assumption,(~m_or_h_gate_v_in1(c_e_h_3, c_j, s6)), introduced(assumption)).
% 289.74/182.28 tff(4495,assumption,(m_or_h_gate_v_out(c_e_h_3, c_j, s7)), introduced(assumption)).
% 289.74/182.28 tff(4496,assumption,(m_and_h_gate_v_out(c_e_h_2, c_q, s6)), introduced(assumption)).
% 289.74/182.28 tff(4497,assumption,(m_and_h_gate_v_out(c_e_h_2, c_l, s1)), introduced(assumption)).
% 289.74/182.28 tff(4498,assumption,(node22(c_e_h_2, c_l, s0, s1)), introduced(assumption)).
% 289.74/182.28 tff(4499,plain,
% 289.74/182.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s1)) | (~node22(c_e_h_2, c_l, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_l, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s1)) | (~node22(c_e_h_2, c_l, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_l, s0))),
% 289.74/182.28 inference(rewrite,[status(thm)],[])).
% 289.74/182.28 tff(4500,plain,
% 289.74/182.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s1)) | (~node22(c_e_h_2, c_l, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_l, s0))),
% 289.74/182.28 inference(quant_inst,[status(thm)],[])).
% 289.74/182.28 tff(4501,plain,
% 289.74/182.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s1)) | (~node22(c_e_h_2, c_l, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_l, s0)),
% 289.74/182.28 inference(modus_ponens,[status(thm)],[4500, 4499])).
% 289.74/182.28 tff(4502,plain,
% 289.74/182.28 ($false),
% 289.74/182.28 inference(unit_resolution,[status(thm)],[4501, 108, 4183, 4498, 4497])).
% 289.74/182.28 tff(4503,plain,((~node22(c_e_h_2, c_l, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s1))), inference(lemma,lemma(discharge,[]))).
% 289.74/182.28 tff(4504,plain,
% 289.74/182.28 (~node22(c_e_h_2, c_l, s0, s1)),
% 289.74/182.28 inference(unit_resolution,[status(thm)],[4503, 4497])).
% 289.74/182.28 tff(4505,plain,
% 289.74/182.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_2, c_l, s0, s1) | node22(c_e_h_2, c_l, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_2, c_l, s0, s1) | node22(c_e_h_2, c_l, s0, s1))),
% 289.74/182.28 inference(rewrite,[status(thm)],[])).
% 289.74/182.28 tff(4506,plain,
% 289.74/182.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_2, c_l, s0, s1) | node22(c_e_h_2, c_l, s0, s1))),
% 289.74/182.28 inference(quant_inst,[status(thm)],[])).
% 289.74/182.28 tff(4507,plain,
% 289.74/182.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_2, c_l, s0, s1) | node22(c_e_h_2, c_l, s0, s1)),
% 289.74/182.28 inference(modus_ponens,[status(thm)],[4506, 4505])).
% 289.74/182.28 tff(4508,plain,
% 289.74/182.28 (node21(c_e_h_2, c_l, s0, s1) | node22(c_e_h_2, c_l, s0, s1)),
% 289.74/182.28 inference(unit_resolution,[status(thm)],[4507, 82, 72])).
% 289.74/182.28 tff(4509,plain,
% 289.74/182.28 (node21(c_e_h_2, c_l, s0, s1)),
% 289.74/182.28 inference(unit_resolution,[status(thm)],[4508, 4504])).
% 289.74/182.28 tff(4510,assumption,(m_cell_v_token(c_e_h_2, s0)), introduced(assumption)).
% 289.74/182.28 tff(4511,plain,
% 289.74/182.28 (^[X: $i] : refl((~m_cell_v_token(c_e_h_2, X)) <=> (~m_cell_v_token(c_e_h_2, X)))),
% 289.74/182.28 inference(bind,[status(th)],[])).
% 289.74/182.28 tff(4512,plain,
% 289.74/182.28 (![X: $i] : (~m_cell_v_token(c_e_h_2, X)) <=> ![X: $i] : (~m_cell_v_token(c_e_h_2, X))),
% 289.74/182.28 inference(quant_intro,[status(thm)],[4511])).
% 289.74/182.28 tff(4513,plain,
% 289.74/182.28 (![X: $i] : (~m_cell_v_token(c_e_h_2, X)) <=> ![X: $i] : (~m_cell_v_token(c_e_h_2, X))),
% 289.74/182.28 inference(rewrite,[status(thm)],[])).
% 289.74/182.28 tff(4514,axiom,(![X: $i] : (~m_cell_v_token(c_e_h_2, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_6')).
% 289.74/182.28 tff(4515,plain,
% 289.74/182.28 (![X: $i] : (~m_cell_v_token(c_e_h_2, X))),
% 289.74/182.28 inference(modus_ponens,[status(thm)],[4514, 4513])).
% 289.74/182.28 tff(4516,plain,(
% 289.74/182.28 ![X: $i] : (~m_cell_v_token(c_e_h_2, X))),
% 289.74/182.28 inference(skolemize,[status(sab)],[4515])).
% 289.74/182.28 tff(4517,plain,
% 289.74/182.28 (![X: $i] : (~m_cell_v_token(c_e_h_2, X))),
% 289.74/182.28 inference(modus_ponens,[status(thm)],[4516, 4512])).
% 289.74/182.28 tff(4518,plain,
% 289.74/182.28 ((~![X: $i] : (~m_cell_v_token(c_e_h_2, X))) | (~m_cell_v_token(c_e_h_2, s0))),
% 289.74/182.28 inference(quant_inst,[status(thm)],[])).
% 289.74/182.28 tff(4519,plain,
% 289.74/182.28 ($false),
% 289.74/182.28 inference(unit_resolution,[status(thm)],[4518, 4517, 4510])).
% 289.74/182.28 tff(4520,plain,(~m_cell_v_token(c_e_h_2, s0)), inference(lemma,lemma(discharge,[]))).
% 289.74/182.28 tff(4521,plain,
% 289.74/182.28 (^[I0: $i, X: $i] : refl(((~m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) | m_cell_v_token(I0, X)) <=> ((~m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) | m_cell_v_token(I0, X)))),
% 289.74/182.28 inference(bind,[status(th)],[])).
% 289.74/182.28 tff(4522,plain,
% 289.74/182.28 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) | m_cell_v_token(I0, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) | m_cell_v_token(I0, X))),
% 289.74/182.28 inference(quant_intro,[status(thm)],[4521])).
% 289.74/182.28 tff(4523,plain,
% 289.74/182.28 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) | m_cell_v_token(I0, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) | m_cell_v_token(I0, X))),
% 289.74/182.28 inference(rewrite,[status(thm)],[])).
% 289.74/182.28 tff(4524,axiom,(![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) | m_cell_v_token(I0, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_56')).
% 289.74/182.28 tff(4525,plain,
% 289.74/182.28 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) | m_cell_v_token(I0, X))),
% 289.74/182.28 inference(modus_ponens,[status(thm)],[4524, 4523])).
% 289.74/182.28 tff(4526,plain,(
% 289.74/182.28 ![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) | m_cell_v_token(I0, X))),
% 289.74/182.28 inference(skolemize,[status(sab)],[4525])).
% 289.74/182.28 tff(4527,plain,
% 289.74/182.28 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) | m_cell_v_token(I0, X))),
% 289.74/182.28 inference(modus_ponens,[status(thm)],[4526, 4522])).
% 289.74/182.28 tff(4528,plain,
% 289.74/182.28 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) | m_cell_v_token(I0, X))) | ((~m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_m, s0)) | m_cell_v_token(c_e_h_2, s0))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) | m_cell_v_token(I0, X))) | (~m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_m, s0)) | m_cell_v_token(c_e_h_2, s0))),
% 289.74/182.28 inference(rewrite,[status(thm)],[])).
% 289.74/182.28 tff(4529,plain,
% 289.74/182.28 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) | m_cell_v_token(I0, X))) | ((~m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_m, s0)) | m_cell_v_token(c_e_h_2, s0))),
% 289.74/182.28 inference(quant_inst,[status(thm)],[])).
% 289.74/182.28 tff(4530,plain,
% 289.74/182.28 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) | m_cell_v_token(I0, X))) | (~m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_m, s0)) | m_cell_v_token(c_e_h_2, s0)),
% 289.74/182.28 inference(modus_ponens,[status(thm)],[4529, 4528])).
% 289.74/182.28 tff(4531,plain,
% 289.74/182.28 (~m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_m, s0)),
% 289.74/182.28 inference(unit_resolution,[status(thm)],[4530, 4527, 4520])).
% 289.74/182.28 tff(4532,plain,
% 289.74/182.28 (^[I0: $i, I1: $i] : refl(((~m_and_h_gate_h_init_v_out(I0, I1, s0)) | m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) <=> ((~m_and_h_gate_h_init_v_out(I0, I1, s0)) | m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)))),
% 289.74/182.28 inference(bind,[status(th)],[])).
% 289.74/182.28 tff(4533,plain,
% 289.74/182.28 (![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, s0)) | m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) <=> ![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, s0)) | m_and_h_gate_h_init_v_init_h_out(I0, I1, s0))),
% 289.74/182.28 inference(quant_intro,[status(thm)],[4532])).
% 289.74/182.28 tff(4534,plain,
% 289.74/182.28 (![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, s0)) | m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) <=> ![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, s0)) | m_and_h_gate_h_init_v_init_h_out(I0, I1, s0))),
% 289.74/182.28 inference(rewrite,[status(thm)],[])).
% 289.74/182.28 tff(4535,axiom,(![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, s0)) | m_and_h_gate_h_init_v_init_h_out(I0, I1, s0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_and_h_gate_h_init_2')).
% 289.74/182.28 tff(4536,plain,
% 289.74/182.28 (![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, s0)) | m_and_h_gate_h_init_v_init_h_out(I0, I1, s0))),
% 289.74/182.28 inference(modus_ponens,[status(thm)],[4535, 4534])).
% 289.74/182.28 tff(4537,plain,(
% 289.74/182.28 ![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, s0)) | m_and_h_gate_h_init_v_init_h_out(I0, I1, s0))),
% 289.74/182.28 inference(skolemize,[status(sab)],[4536])).
% 289.74/182.28 tff(4538,plain,
% 289.74/182.28 (![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, s0)) | m_and_h_gate_h_init_v_init_h_out(I0, I1, s0))),
% 289.74/182.28 inference(modus_ponens,[status(thm)],[4537, 4533])).
% 289.74/182.28 tff(4539,plain,
% 289.74/182.28 (((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, s0)) | m_and_h_gate_h_init_v_init_h_out(I0, I1, s0))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0)) | m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_m, s0))) <=> ((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, s0)) | m_and_h_gate_h_init_v_init_h_out(I0, I1, s0))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0)) | m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_m, s0))),
% 289.74/182.28 inference(rewrite,[status(thm)],[])).
% 289.74/182.28 tff(4540,plain,
% 289.74/182.28 ((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, s0)) | m_and_h_gate_h_init_v_init_h_out(I0, I1, s0))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0)) | m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_m, s0))),
% 289.74/182.28 inference(quant_inst,[status(thm)],[])).
% 289.74/182.28 tff(4541,plain,
% 289.74/182.28 ((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, s0)) | m_and_h_gate_h_init_v_init_h_out(I0, I1, s0))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0)) | m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_m, s0)),
% 289.74/182.28 inference(modus_ponens,[status(thm)],[4540, 4539])).
% 289.74/182.28 tff(4542,plain,
% 289.74/182.28 (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0)),
% 289.74/182.28 inference(unit_resolution,[status(thm)],[4541, 4538, 4531])).
% 289.74/182.28 tff(4543,plain,
% 289.74/182.28 (^[I0: $i, X: $i] : refl(((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X)) <=> ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X)))),
% 289.74/182.28 inference(bind,[status(th)],[])).
% 289.74/182.28 tff(4544,plain,
% 289.74/182.28 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))),
% 289.74/182.28 inference(quant_intro,[status(thm)],[4543])).
% 289.74/182.28 tff(4545,plain,
% 289.74/182.28 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))),
% 289.74/182.28 inference(rewrite,[status(thm)],[])).
% 289.74/182.28 tff(4546,axiom,(![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_50')).
% 289.74/182.28 tff(4547,plain,
% 289.74/182.28 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))),
% 289.74/182.28 inference(modus_ponens,[status(thm)],[4546, 4545])).
% 289.74/182.28 tff(4548,plain,(
% 289.74/182.28 ![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))),
% 289.74/182.28 inference(skolemize,[status(sab)],[4547])).
% 289.74/182.28 tff(4549,plain,
% 289.74/182.28 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))),
% 289.74/182.28 inference(modus_ponens,[status(thm)],[4548, 4544])).
% 289.74/182.28 tff(4550,plain,
% 289.74/182.28 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_l, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_l, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0))),
% 289.74/182.28 inference(rewrite,[status(thm)],[])).
% 289.74/182.28 tff(4551,plain,
% 289.74/182.28 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_l, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0))),
% 289.74/182.28 inference(quant_inst,[status(thm)],[])).
% 289.74/182.28 tff(4552,plain,
% 289.74/182.28 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_l, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0)),
% 289.74/182.28 inference(modus_ponens,[status(thm)],[4551, 4550])).
% 289.74/182.28 tff(4553,plain,
% 289.74/182.28 (~m_and_h_gate_v_in2(c_e_h_2, c_l, s0)),
% 289.74/182.28 inference(unit_resolution,[status(thm)],[4552, 4549, 4542])).
% 289.74/182.28 tff(4554,plain,
% 289.74/182.28 (^[I0: $i, X: $i, I1: $i] : refl(((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X)) <=> ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X)))),
% 289.74/182.28 inference(bind,[status(th)],[])).
% 289.74/182.28 tff(4555,plain,
% 289.74/182.28 (![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X)) <=> ![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))),
% 289.74/182.28 inference(quant_intro,[status(thm)],[4554])).
% 289.74/182.28 tff(4556,plain,
% 289.74/182.28 (![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X)) <=> ![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))),
% 289.74/182.28 inference(rewrite,[status(thm)],[])).
% 289.74/182.28 tff(4557,plain,
% 289.74/182.28 (^[I0: $i, X: $i, I1: $i] : rewrite((m_and_h_gate_v_in2(I0, I1, X) | (~node20(I0, I1, X))) <=> ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X)))),
% 289.74/182.28 inference(bind,[status(th)],[])).
% 289.74/182.28 tff(4558,plain,
% 289.74/182.28 (![I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_in2(I0, I1, X) | (~node20(I0, I1, X))) <=> ![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))),
% 289.74/182.28 inference(quant_intro,[status(thm)],[4557])).
% 289.74/182.28 tff(4559,axiom,(![I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_in2(I0, I1, X) | (~node20(I0, I1, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_and_h_gate_3')).
% 289.74/182.28 tff(4560,plain,
% 289.74/182.28 (![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))),
% 289.74/182.28 inference(modus_ponens,[status(thm)],[4559, 4558])).
% 289.74/182.28 tff(4561,plain,
% 289.74/182.28 (![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))),
% 289.74/182.28 inference(modus_ponens,[status(thm)],[4560, 4556])).
% 289.74/182.28 tff(4562,plain,(
% 289.74/182.28 ![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))),
% 289.74/182.28 inference(skolemize,[status(sab)],[4561])).
% 289.74/182.28 tff(4563,plain,
% 289.74/182.28 (![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))),
% 289.74/182.28 inference(modus_ponens,[status(thm)],[4562, 4555])).
% 289.74/182.28 tff(4564,plain,
% 289.74/182.28 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_l, s0)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_l, s0)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s0))),
% 289.74/182.28 inference(rewrite,[status(thm)],[])).
% 289.74/182.28 tff(4565,plain,
% 289.74/182.28 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_l, s0)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s0))),
% 289.74/182.28 inference(quant_inst,[status(thm)],[])).
% 289.74/182.28 tff(4566,plain,
% 289.74/182.28 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_l, s0)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s0)),
% 289.74/182.28 inference(modus_ponens,[status(thm)],[4565, 4564])).
% 289.74/182.28 tff(4567,plain,
% 289.74/182.28 (~node20(c_e_h_2, c_l, s0)),
% 289.74/182.28 inference(unit_resolution,[status(thm)],[4566, 4563, 4553])).
% 289.74/182.28 tff(4568,plain,
% 289.82/182.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_l, s0) | (~node21(c_e_h_2, c_l, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_l, s0) | (~node21(c_e_h_2, c_l, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s1)))),
% 289.82/182.29 inference(rewrite,[status(thm)],[])).
% 289.82/182.29 tff(4569,plain,
% 289.82/182.29 ((node20(c_e_h_2, c_l, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s1)) | (~node21(c_e_h_2, c_l, s0, s1))) <=> (node20(c_e_h_2, c_l, s0) | (~node21(c_e_h_2, c_l, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s1)))),
% 289.82/182.29 inference(rewrite,[status(thm)],[])).
% 289.82/182.29 tff(4570,plain,
% 289.82/182.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_l, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s1)) | (~node21(c_e_h_2, c_l, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_l, s0) | (~node21(c_e_h_2, c_l, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s1))))),
% 289.82/182.29 inference(monotonicity,[status(thm)],[4569])).
% 289.82/182.29 tff(4571,plain,
% 289.82/182.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_l, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s1)) | (~node21(c_e_h_2, c_l, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_l, s0) | (~node21(c_e_h_2, c_l, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s1)))),
% 289.82/182.29 inference(transitivity,[status(thm)],[4570, 4568])).
% 289.82/182.29 tff(4572,plain,
% 289.82/182.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_l, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s1)) | (~node21(c_e_h_2, c_l, s0, s1)))),
% 289.82/182.29 inference(quant_inst,[status(thm)],[])).
% 289.82/182.29 tff(4573,plain,
% 289.82/182.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_l, s0) | (~node21(c_e_h_2, c_l, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s1))),
% 289.82/182.29 inference(modus_ponens,[status(thm)],[4572, 4571])).
% 289.82/182.29 tff(4574,plain,
% 289.82/182.29 ($false),
% 289.82/182.29 inference(unit_resolution,[status(thm)],[4573, 52, 4567, 4509, 4497])).
% 289.82/182.29 tff(4575,plain,(~m_and_h_gate_v_out(c_e_h_2, c_l, s1)), inference(lemma,lemma(discharge,[]))).
% 289.82/182.29 tff(4576,plain,
% 289.82/182.29 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_2, c_j, s1)) | m_and_h_gate_v_out(c_e_h_2, c_l, s1))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_j, s1)) | m_and_h_gate_v_out(c_e_h_2, c_l, s1))),
% 289.82/182.29 inference(rewrite,[status(thm)],[])).
% 289.82/182.29 tff(4577,plain,
% 289.82/182.29 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_2, c_j, s1)) | m_and_h_gate_v_out(c_e_h_2, c_l, s1))),
% 289.82/182.29 inference(quant_inst,[status(thm)],[])).
% 289.82/182.29 tff(4578,plain,
% 289.82/182.29 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_j, s1)) | m_and_h_gate_v_out(c_e_h_2, c_l, s1)),
% 289.82/182.29 inference(modus_ponens,[status(thm)],[4577, 4576])).
% 289.82/182.29 tff(4579,plain,
% 289.82/182.29 (~m_or_h_gate_v_in1(c_e_h_2, c_j, s1)),
% 289.82/182.29 inference(unit_resolution,[status(thm)],[4578, 1100, 4575])).
% 289.82/182.29 tff(4580,assumption,(m_c_h_element_v_out(c_e_h_1, c_f, s0)), introduced(assumption)).
% 289.82/182.29 tff(4581,plain,
% 289.82/182.29 ((~![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s0))),
% 289.82/182.29 inference(quant_inst,[status(thm)],[])).
% 289.82/182.29 tff(4582,plain,
% 289.82/182.29 ($false),
% 289.82/182.29 inference(unit_resolution,[status(thm)],[4581, 14, 4580])).
% 289.82/182.29 tff(4583,plain,(~m_c_h_element_v_out(c_e_h_1, c_f, s0)), inference(lemma,lemma(discharge,[]))).
% 289.82/182.29 tff(4584,plain,
% 289.82/182.29 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s0)) | m_c_h_element_v_out(c_e_h_1, c_f, s0))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s0)) | m_c_h_element_v_out(c_e_h_1, c_f, s0))),
% 289.82/182.29 inference(rewrite,[status(thm)],[])).
% 289.82/182.29 tff(4585,plain,
% 289.82/182.29 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s0)) | m_c_h_element_v_out(c_e_h_1, c_f, s0))),
% 289.82/182.29 inference(quant_inst,[status(thm)],[])).
% 289.82/182.29 tff(4586,plain,
% 289.82/182.29 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s0)) | m_c_h_element_v_out(c_e_h_1, c_f, s0)),
% 289.82/182.29 inference(modus_ponens,[status(thm)],[4585, 4584])).
% 289.82/182.29 tff(4587,plain,
% 289.82/182.29 (~m_and_h_gate_v_in1(c_e_h_1, c_q, s0)),
% 289.82/182.29 inference(unit_resolution,[status(thm)],[4586, 1586, 4583])).
% 289.82/182.29 tff(4588,plain,
% 289.82/182.29 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s0))),
% 289.82/182.29 inference(rewrite,[status(thm)],[])).
% 289.82/182.29 tff(4589,plain,
% 289.82/182.29 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s0))),
% 289.82/182.29 inference(quant_inst,[status(thm)],[])).
% 289.82/182.29 tff(4590,plain,
% 289.82/182.29 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s0)),
% 289.82/182.29 inference(modus_ponens,[status(thm)],[4589, 4588])).
% 289.82/182.29 tff(4591,plain,
% 289.82/182.29 (~node20(c_e_h_1, c_q, s0)),
% 289.82/182.29 inference(unit_resolution,[status(thm)],[4590, 38, 4587])).
% 289.82/182.29 tff(4592,assumption,(m_and_h_gate_v_out(c_e_h_1, c_q, s1)), introduced(assumption)).
% 289.82/182.29 tff(4593,assumption,(node22(c_e_h_1, c_q, s0, s1)), introduced(assumption)).
% 289.82/182.29 tff(4594,plain,
% 289.82/182.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s1)) | (~node22(c_e_h_1, c_q, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_q, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s1)) | (~node22(c_e_h_1, c_q, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_q, s0))),
% 289.82/182.29 inference(rewrite,[status(thm)],[])).
% 289.82/182.29 tff(4595,plain,
% 289.82/182.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s1)) | (~node22(c_e_h_1, c_q, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_q, s0))),
% 289.82/182.29 inference(quant_inst,[status(thm)],[])).
% 289.82/182.29 tff(4596,plain,
% 289.82/182.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s1)) | (~node22(c_e_h_1, c_q, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_q, s0)),
% 289.82/182.29 inference(modus_ponens,[status(thm)],[4595, 4594])).
% 289.82/182.29 tff(4597,plain,
% 289.82/182.29 ($false),
% 289.82/182.29 inference(unit_resolution,[status(thm)],[4596, 108, 4592, 4163, 4593])).
% 289.82/182.29 tff(4598,plain,((~node22(c_e_h_1, c_q, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s1))), inference(lemma,lemma(discharge,[]))).
% 289.82/182.29 tff(4599,plain,
% 289.82/182.29 (~node22(c_e_h_1, c_q, s0, s1)),
% 289.82/182.29 inference(unit_resolution,[status(thm)],[4598, 4592])).
% 289.82/182.29 tff(4600,plain,
% 289.82/182.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_1, c_q, s0, s1) | node22(c_e_h_1, c_q, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_1, c_q, s0, s1) | node22(c_e_h_1, c_q, s0, s1))),
% 289.82/182.30 inference(rewrite,[status(thm)],[])).
% 289.82/182.30 tff(4601,plain,
% 289.82/182.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_1, c_q, s0, s1) | node22(c_e_h_1, c_q, s0, s1))),
% 289.82/182.30 inference(quant_inst,[status(thm)],[])).
% 289.82/182.30 tff(4602,plain,
% 289.82/182.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_1, c_q, s0, s1) | node22(c_e_h_1, c_q, s0, s1)),
% 289.82/182.30 inference(modus_ponens,[status(thm)],[4601, 4600])).
% 289.82/182.30 tff(4603,plain,
% 289.82/182.30 (node21(c_e_h_1, c_q, s0, s1) | node22(c_e_h_1, c_q, s0, s1)),
% 289.82/182.30 inference(unit_resolution,[status(thm)],[4602, 82, 72])).
% 289.82/182.30 tff(4604,plain,
% 289.82/182.30 (node21(c_e_h_1, c_q, s0, s1)),
% 289.82/182.30 inference(unit_resolution,[status(thm)],[4603, 4599])).
% 289.82/182.30 tff(4605,plain,
% 289.82/182.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s1)) | (~node21(c_e_h_1, c_q, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_q, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s1)) | (~node21(c_e_h_1, c_q, s0, s1)))),
% 289.82/182.30 inference(rewrite,[status(thm)],[])).
% 289.82/182.30 tff(4606,plain,
% 289.82/182.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s1)) | (~node21(c_e_h_1, c_q, s0, s1)))),
% 289.82/182.30 inference(quant_inst,[status(thm)],[])).
% 289.82/182.30 tff(4607,plain,
% 289.82/182.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_q, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s1)) | (~node21(c_e_h_1, c_q, s0, s1))),
% 289.82/182.30 inference(modus_ponens,[status(thm)],[4606, 4605])).
% 289.82/182.30 tff(4608,plain,
% 289.82/182.30 ($false),
% 289.82/182.30 inference(unit_resolution,[status(thm)],[4607, 52, 4592, 4604, 4591])).
% 289.82/182.30 tff(4609,plain,(~m_and_h_gate_v_out(c_e_h_1, c_q, s1)), inference(lemma,lemma(discharge,[]))).
% 289.82/182.30 tff(4610,plain,
% 289.82/182.30 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s1))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s1))),
% 289.82/182.30 inference(rewrite,[status(thm)],[])).
% 289.82/182.30 tff(4611,plain,
% 289.82/182.30 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s1))),
% 289.82/182.30 inference(quant_inst,[status(thm)],[])).
% 289.82/182.30 tff(4612,plain,
% 289.82/182.30 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s1)),
% 289.82/182.30 inference(modus_ponens,[status(thm)],[4611, 4610])).
% 289.82/182.30 tff(4613,plain,
% 289.82/182.30 (node3(c_e_h_1, c_e_h_2, s1)),
% 289.82/182.30 inference(unit_resolution,[status(thm)],[4612, 4166, 1056])).
% 289.82/182.30 tff(4614,plain,
% 289.82/182.30 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s1)) | (~node3(c_e_h_1, c_e_h_2, s1)) | m_and_h_gate_v_out(c_e_h_1, c_q, s1))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s1)) | (~node3(c_e_h_1, c_e_h_2, s1)) | m_and_h_gate_v_out(c_e_h_1, c_q, s1))),
% 289.82/182.30 inference(rewrite,[status(thm)],[])).
% 289.82/182.30 tff(4615,plain,
% 289.82/182.30 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s1)) | (~node3(c_e_h_1, c_e_h_2, s1)) | m_and_h_gate_v_out(c_e_h_1, c_q, s1))),
% 289.82/182.30 inference(quant_inst,[status(thm)],[])).
% 289.82/182.30 tff(4616,plain,
% 289.82/182.30 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s1)) | (~node3(c_e_h_1, c_e_h_2, s1)) | m_and_h_gate_v_out(c_e_h_1, c_q, s1)),
% 289.82/182.30 inference(modus_ponens,[status(thm)],[4615, 4614])).
% 289.82/182.30 tff(4617,plain,
% 289.82/182.30 ((~m_cell_v_ack(c_e_h_2, s1)) | m_and_h_gate_v_out(c_e_h_1, c_q, s1)),
% 289.82/182.30 inference(unit_resolution,[status(thm)],[4616, 1073, 4613])).
% 289.82/182.30 tff(4618,plain,
% 289.82/182.30 (~m_cell_v_ack(c_e_h_2, s1)),
% 289.82/182.30 inference(unit_resolution,[status(thm)],[4617, 4609])).
% 289.82/182.30 tff(4619,plain,
% 289.82/182.30 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s1)) | m_cell_v_ack(c_e_h_2, s1))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s1)) | m_cell_v_ack(c_e_h_2, s1))),
% 289.82/182.30 inference(rewrite,[status(thm)],[])).
% 289.82/182.30 tff(4620,plain,
% 289.82/182.30 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s1)) | m_cell_v_ack(c_e_h_2, s1))),
% 289.82/182.30 inference(quant_inst,[status(thm)],[])).
% 289.82/182.30 tff(4621,plain,
% 289.82/182.30 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s1)) | m_cell_v_ack(c_e_h_2, s1)),
% 289.82/182.30 inference(modus_ponens,[status(thm)],[4620, 4619])).
% 289.82/182.30 tff(4622,plain,
% 289.82/182.30 (~m_or_h_gate_v_in2(c_e_h_2, c_j, s1)),
% 289.82/182.30 inference(unit_resolution,[status(thm)],[4621, 1085, 4618])).
% 289.82/182.30 tff(4623,assumption,(~m_or_h_gate_v_in1(c_e_h_2, c_j, s1)), introduced(assumption)).
% 289.82/182.30 tff(4624,assumption,(~m_or_h_gate_v_in2(c_e_h_2, c_j, s1)), introduced(assumption)).
% 289.82/182.30 tff(4625,assumption,(m_or_h_gate_v_out(c_e_h_2, c_j, s2)), introduced(assumption)).
% 289.82/182.30 tff(4626,assumption,(node5(c_e_h_2, c_j, s1, s2)), introduced(assumption)).
% 289.82/182.30 tff(4627,plain,
% 289.82/182.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_2, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s2)) | (~node5(c_e_h_2, c_j, s1, s2)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_2, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s2)) | (~node5(c_e_h_2, c_j, s1, s2)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s1))),
% 289.82/182.30 inference(rewrite,[status(thm)],[])).
% 289.82/182.30 tff(4628,plain,
% 289.82/182.30 ((m_or_h_gate_v_in1(c_e_h_2, c_j, s1) | m_or_h_gate_v_in2(c_e_h_2, c_j, s1) | (~node5(c_e_h_2, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s2))) <=> (m_or_h_gate_v_in2(c_e_h_2, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s2)) | (~node5(c_e_h_2, c_j, s1, s2)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s1))),
% 289.82/182.30 inference(rewrite,[status(thm)],[])).
% 289.82/182.30 tff(4629,plain,
% 289.82/182.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s1) | m_or_h_gate_v_in2(c_e_h_2, c_j, s1) | (~node5(c_e_h_2, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_2, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s2)) | (~node5(c_e_h_2, c_j, s1, s2)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s1)))),
% 289.82/182.30 inference(monotonicity,[status(thm)],[4628])).
% 289.82/182.30 tff(4630,plain,
% 289.82/182.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s1) | m_or_h_gate_v_in2(c_e_h_2, c_j, s1) | (~node5(c_e_h_2, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_2, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s2)) | (~node5(c_e_h_2, c_j, s1, s2)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s1))),
% 289.82/182.30 inference(transitivity,[status(thm)],[4629, 4627])).
% 289.82/182.30 tff(4631,plain,
% 289.82/182.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s1) | m_or_h_gate_v_in2(c_e_h_2, c_j, s1) | (~node5(c_e_h_2, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s2)))),
% 289.82/182.30 inference(quant_inst,[status(thm)],[])).
% 289.82/182.30 tff(4632,plain,
% 289.82/182.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_2, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s2)) | (~node5(c_e_h_2, c_j, s1, s2)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s1)),
% 289.82/182.30 inference(modus_ponens,[status(thm)],[4631, 4630])).
% 289.82/182.30 tff(4633,plain,
% 289.82/182.30 ($false),
% 289.82/182.30 inference(unit_resolution,[status(thm)],[4632, 1159, 4625, 4626, 4624, 4623])).
% 289.82/182.30 tff(4634,plain,((~node5(c_e_h_2, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s2)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s1) | m_or_h_gate_v_in1(c_e_h_2, c_j, s1)), inference(lemma,lemma(discharge,[]))).
% 289.82/182.30 tff(4635,plain,
% 289.82/182.30 (~node5(c_e_h_2, c_j, s1, s2)),
% 289.82/182.30 inference(unit_resolution,[status(thm)],[4634, 4625, 4624, 4623])).
% 289.82/182.30 tff(4636,plain,
% 289.82/182.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s1, s2)) | node6(c_e_h_2, c_j, s1, s2) | node5(c_e_h_2, c_j, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s1, s2)) | node6(c_e_h_2, c_j, s1, s2) | node5(c_e_h_2, c_j, s1, s2))),
% 289.82/182.30 inference(rewrite,[status(thm)],[])).
% 289.82/182.30 tff(4637,plain,
% 289.82/182.30 ((node6(c_e_h_2, c_j, s1, s2) | node5(c_e_h_2, c_j, s1, s2) | (~trans(s1, s2))) <=> ((~trans(s1, s2)) | node6(c_e_h_2, c_j, s1, s2) | node5(c_e_h_2, c_j, s1, s2))),
% 289.82/182.30 inference(rewrite,[status(thm)],[])).
% 289.82/182.30 tff(4638,plain,
% 289.82/182.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s1, s2) | node5(c_e_h_2, c_j, s1, s2) | (~trans(s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s1, s2)) | node6(c_e_h_2, c_j, s1, s2) | node5(c_e_h_2, c_j, s1, s2)))),
% 289.82/182.30 inference(monotonicity,[status(thm)],[4637])).
% 289.82/182.30 tff(4639,plain,
% 289.82/182.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s1, s2) | node5(c_e_h_2, c_j, s1, s2) | (~trans(s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s1, s2)) | node6(c_e_h_2, c_j, s1, s2) | node5(c_e_h_2, c_j, s1, s2))),
% 289.82/182.30 inference(transitivity,[status(thm)],[4638, 4636])).
% 289.82/182.30 tff(4640,plain,
% 289.82/182.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s1, s2) | node5(c_e_h_2, c_j, s1, s2) | (~trans(s1, s2)))),
% 289.82/182.30 inference(quant_inst,[status(thm)],[])).
% 289.82/182.30 tff(4641,plain,
% 289.82/182.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s1, s2)) | node6(c_e_h_2, c_j, s1, s2) | node5(c_e_h_2, c_j, s1, s2)),
% 289.82/182.30 inference(modus_ponens,[status(thm)],[4640, 4639])).
% 289.82/182.30 tff(4642,plain,
% 289.82/182.30 (node6(c_e_h_2, c_j, s1, s2) | node5(c_e_h_2, c_j, s1, s2)),
% 289.82/182.30 inference(unit_resolution,[status(thm)],[4641, 1141, 255])).
% 289.82/182.30 tff(4643,plain,
% 289.82/182.30 (node6(c_e_h_2, c_j, s1, s2)),
% 289.82/182.30 inference(unit_resolution,[status(thm)],[4642, 4635])).
% 289.82/182.30 tff(4644,assumption,(~m_or_h_gate_v_out(c_e_h_2, c_j, s1)), introduced(assumption)).
% 289.82/182.30 tff(4645,plain,
% 289.82/182.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_2, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s2)) | (~node6(c_e_h_2, c_j, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s2)) | (~node6(c_e_h_2, c_j, s1, s2)))),
% 289.82/182.30 inference(rewrite,[status(thm)],[])).
% 289.82/182.31 tff(4646,plain,
% 289.82/182.31 (((~node6(c_e_h_2, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s2)) | m_or_h_gate_v_out(c_e_h_2, c_j, s1)) <=> (m_or_h_gate_v_out(c_e_h_2, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s2)) | (~node6(c_e_h_2, c_j, s1, s2)))),
% 289.82/182.31 inference(rewrite,[status(thm)],[])).
% 289.82/182.31 tff(4647,plain,
% 289.82/182.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s2)) | m_or_h_gate_v_out(c_e_h_2, c_j, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_2, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s2)) | (~node6(c_e_h_2, c_j, s1, s2))))),
% 289.82/182.31 inference(monotonicity,[status(thm)],[4646])).
% 289.82/182.31 tff(4648,plain,
% 289.82/182.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s2)) | m_or_h_gate_v_out(c_e_h_2, c_j, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s2)) | (~node6(c_e_h_2, c_j, s1, s2)))),
% 289.82/182.31 inference(transitivity,[status(thm)],[4647, 4645])).
% 289.82/182.31 tff(4649,plain,
% 289.82/182.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s2)) | m_or_h_gate_v_out(c_e_h_2, c_j, s1))),
% 289.82/182.31 inference(quant_inst,[status(thm)],[])).
% 289.82/182.31 tff(4650,plain,
% 289.82/182.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s2)) | (~node6(c_e_h_2, c_j, s1, s2))),
% 289.82/182.31 inference(modus_ponens,[status(thm)],[4649, 4648])).
% 289.82/182.31 tff(4651,plain,
% 289.82/182.31 ($false),
% 289.82/182.31 inference(unit_resolution,[status(thm)],[4650, 1121, 4644, 4625, 4643])).
% 289.82/182.31 tff(4652,plain,((~m_or_h_gate_v_out(c_e_h_2, c_j, s2)) | m_or_h_gate_v_out(c_e_h_2, c_j, s1) | m_or_h_gate_v_in2(c_e_h_2, c_j, s1) | m_or_h_gate_v_in1(c_e_h_2, c_j, s1)), inference(lemma,lemma(discharge,[]))).
% 289.82/182.31 tff(4653,plain,
% 289.82/182.31 ((~m_or_h_gate_v_out(c_e_h_2, c_j, s2)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s1) | m_or_h_gate_v_in1(c_e_h_2, c_j, s1)),
% 289.82/182.31 inference(unit_resolution,[status(thm)],[4652, 4214])).
% 289.82/182.31 tff(4654,plain,
% 289.82/182.31 ((~m_or_h_gate_v_out(c_e_h_2, c_j, s2)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s1)),
% 289.82/182.31 inference(unit_resolution,[status(thm)],[4653, 4622])).
% 289.82/182.31 tff(4655,plain,
% 289.82/182.31 (~m_or_h_gate_v_out(c_e_h_2, c_j, s2)),
% 289.82/182.31 inference(unit_resolution,[status(thm)],[4654, 4579])).
% 289.82/182.31 tff(4656,plain,
% 289.82/182.31 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s2)) | m_or_h_gate_v_out(c_e_h_2, c_j, s2))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s2)) | m_or_h_gate_v_out(c_e_h_2, c_j, s2))),
% 289.82/182.31 inference(rewrite,[status(thm)],[])).
% 289.82/182.31 tff(4657,plain,
% 289.82/182.31 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s2)) | m_or_h_gate_v_out(c_e_h_2, c_j, s2))),
% 289.82/182.31 inference(quant_inst,[status(thm)],[])).
% 289.82/182.31 tff(4658,plain,
% 289.82/182.31 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s2)) | m_or_h_gate_v_out(c_e_h_2, c_j, s2)),
% 289.82/182.31 inference(modus_ponens,[status(thm)],[4657, 4656])).
% 289.82/182.31 tff(4659,plain,
% 289.82/182.31 (~m_c_h_element_v_in2(c_e_h_2, c_h, s2)),
% 289.82/182.31 inference(unit_resolution,[status(thm)],[4658, 1174, 4655])).
% 289.82/182.31 tff(4660,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_h, s2)), introduced(assumption)).
% 289.82/182.31 tff(4661,assumption,(~m_c_h_element_v_out(c_e_h_2, c_h, s2)), introduced(assumption)).
% 289.82/182.31 tff(4662,assumption,(m_c_h_element_v_out(c_e_h_2, c_h, s3)), introduced(assumption)).
% 289.82/182.31 tff(4663,assumption,(node15(c_e_h_2, c_h, s2, s3)), introduced(assumption)).
% 289.82/182.31 tff(4664,plain,
% 289.82/182.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | (~node15(c_e_h_2, c_h, s2, s3)) | m_c_h_element_v_out(c_e_h_2, c_h, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | (~node15(c_e_h_2, c_h, s2, s3)) | m_c_h_element_v_out(c_e_h_2, c_h, s2))),
% 289.82/182.31 inference(rewrite,[status(thm)],[])).
% 289.82/182.31 tff(4665,plain,
% 289.82/182.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | (~node15(c_e_h_2, c_h, s2, s3)) | m_c_h_element_v_out(c_e_h_2, c_h, s2))),
% 289.82/182.31 inference(quant_inst,[status(thm)],[])).
% 289.82/182.31 tff(4666,plain,
% 289.82/182.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | (~node15(c_e_h_2, c_h, s2, s3)) | m_c_h_element_v_out(c_e_h_2, c_h, s2)),
% 289.82/182.31 inference(modus_ponens,[status(thm)],[4665, 4664])).
% 289.82/182.31 tff(4667,plain,
% 289.82/182.31 ($false),
% 289.82/182.31 inference(unit_resolution,[status(thm)],[4666, 147, 4661, 4662, 4663])).
% 289.82/182.31 tff(4668,plain,((~node15(c_e_h_2, c_h, s2, s3)) | m_c_h_element_v_out(c_e_h_2, c_h, s2) | (~m_c_h_element_v_out(c_e_h_2, c_h, s3))), inference(lemma,lemma(discharge,[]))).
% 289.82/182.31 tff(4669,plain,
% 289.82/182.31 (~node15(c_e_h_2, c_h, s2, s3)),
% 289.82/182.31 inference(unit_resolution,[status(thm)],[4668, 4662, 4661])).
% 289.82/182.31 tff(4670,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_h, s2)), introduced(assumption)).
% 289.82/182.31 tff(4671,assumption,(~node15(c_e_h_2, c_h, s2, s3)), introduced(assumption)).
% 289.82/182.31 tff(4672,plain,
% 289.82/182.31 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_h, s2)) | m_c_h_element_v_in1(c_e_h_2, c_h, s2) | m_c_h_element_v_in2(c_e_h_2, c_h, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_h, s2)) | m_c_h_element_v_in1(c_e_h_2, c_h, s2) | m_c_h_element_v_in2(c_e_h_2, c_h, s2))),
% 289.82/182.31 inference(rewrite,[status(thm)],[])).
% 289.82/182.31 tff(4673,plain,
% 289.82/182.31 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_h, s2)) | m_c_h_element_v_in1(c_e_h_2, c_h, s2) | m_c_h_element_v_in2(c_e_h_2, c_h, s2))),
% 289.82/182.31 inference(quant_inst,[status(thm)],[])).
% 289.82/182.31 tff(4674,plain,
% 289.82/182.31 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_h, s2)) | m_c_h_element_v_in1(c_e_h_2, c_h, s2) | m_c_h_element_v_in2(c_e_h_2, c_h, s2)),
% 289.82/182.31 inference(modus_ponens,[status(thm)],[4673, 4672])).
% 289.82/182.31 tff(4675,plain,
% 289.82/182.31 ((~node16(c_e_h_2, c_h, s2)) | m_c_h_element_v_in1(c_e_h_2, c_h, s2)),
% 289.82/182.31 inference(unit_resolution,[status(thm)],[4674, 178, 4660])).
% 289.82/182.31 tff(4676,plain,
% 289.82/182.31 (~node16(c_e_h_2, c_h, s2)),
% 289.82/182.31 inference(unit_resolution,[status(thm)],[4675, 4670])).
% 289.82/182.31 tff(4677,plain,
% 289.82/182.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s2, s3)) | node19(c_e_h_2, c_h, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s2, s3)) | node19(c_e_h_2, c_h, s2, s3))),
% 289.82/182.31 inference(rewrite,[status(thm)],[])).
% 289.82/182.31 tff(4678,plain,
% 289.82/182.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s2, s3)) | node19(c_e_h_2, c_h, s2, s3))),
% 289.82/182.31 inference(quant_inst,[status(thm)],[])).
% 289.82/182.31 tff(4679,plain,
% 289.82/182.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s2, s3)) | node19(c_e_h_2, c_h, s2, s3)),
% 289.82/182.31 inference(modus_ponens,[status(thm)],[4678, 4677])).
% 289.82/182.31 tff(4680,plain,
% 289.82/182.31 (node19(c_e_h_2, c_h, s2, s3)),
% 289.82/182.31 inference(unit_resolution,[status(thm)],[4679, 190, 318])).
% 289.82/182.31 tff(4681,plain,
% 289.82/182.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_h, s2, s3)) | node16(c_e_h_2, c_h, s2) | node15(c_e_h_2, c_h, s2, s3) | node14(c_e_h_2, c_h, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_h, s2, s3)) | node16(c_e_h_2, c_h, s2) | node15(c_e_h_2, c_h, s2, s3) | node14(c_e_h_2, c_h, s2, s3))),
% 289.82/182.31 inference(rewrite,[status(thm)],[])).
% 289.82/182.31 tff(4682,plain,
% 289.82/182.31 ((node16(c_e_h_2, c_h, s2) | node14(c_e_h_2, c_h, s2, s3) | node15(c_e_h_2, c_h, s2, s3) | (~node19(c_e_h_2, c_h, s2, s3))) <=> ((~node19(c_e_h_2, c_h, s2, s3)) | node16(c_e_h_2, c_h, s2) | node15(c_e_h_2, c_h, s2, s3) | node14(c_e_h_2, c_h, s2, s3))),
% 289.82/182.31 inference(rewrite,[status(thm)],[])).
% 289.82/182.31 tff(4683,plain,
% 289.82/182.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s2) | node14(c_e_h_2, c_h, s2, s3) | node15(c_e_h_2, c_h, s2, s3) | (~node19(c_e_h_2, c_h, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_h, s2, s3)) | node16(c_e_h_2, c_h, s2) | node15(c_e_h_2, c_h, s2, s3) | node14(c_e_h_2, c_h, s2, s3)))),
% 289.82/182.31 inference(monotonicity,[status(thm)],[4682])).
% 289.82/182.31 tff(4684,plain,
% 289.82/182.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s2) | node14(c_e_h_2, c_h, s2, s3) | node15(c_e_h_2, c_h, s2, s3) | (~node19(c_e_h_2, c_h, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_h, s2, s3)) | node16(c_e_h_2, c_h, s2) | node15(c_e_h_2, c_h, s2, s3) | node14(c_e_h_2, c_h, s2, s3))),
% 289.82/182.31 inference(transitivity,[status(thm)],[4683, 4681])).
% 289.82/182.31 tff(4685,plain,
% 289.82/182.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s2) | node14(c_e_h_2, c_h, s2, s3) | node15(c_e_h_2, c_h, s2, s3) | (~node19(c_e_h_2, c_h, s2, s3)))),
% 289.82/182.31 inference(quant_inst,[status(thm)],[])).
% 289.82/182.31 tff(4686,plain,
% 289.82/182.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_h, s2, s3)) | node16(c_e_h_2, c_h, s2) | node15(c_e_h_2, c_h, s2, s3) | node14(c_e_h_2, c_h, s2, s3)),
% 289.82/182.31 inference(modus_ponens,[status(thm)],[4685, 4684])).
% 289.82/182.31 tff(4687,plain,
% 289.82/182.31 (node16(c_e_h_2, c_h, s2) | node15(c_e_h_2, c_h, s2, s3) | node14(c_e_h_2, c_h, s2, s3)),
% 289.82/182.31 inference(unit_resolution,[status(thm)],[4686, 204, 4680])).
% 289.82/182.31 tff(4688,plain,
% 289.82/182.31 (node14(c_e_h_2, c_h, s2, s3)),
% 289.82/182.31 inference(unit_resolution,[status(thm)],[4687, 4676, 4671])).
% 289.82/182.31 tff(4689,plain,
% 289.82/182.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | m_c_h_element_v_in1(c_e_h_2, c_h, s2) | (~node14(c_e_h_2, c_h, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | m_c_h_element_v_in1(c_e_h_2, c_h, s2) | (~node14(c_e_h_2, c_h, s2, s3)))),
% 289.82/182.31 inference(rewrite,[status(thm)],[])).
% 289.82/182.31 tff(4690,plain,
% 289.82/182.31 (((~node14(c_e_h_2, c_h, s2, s3)) | m_c_h_element_v_in1(c_e_h_2, c_h, s2) | (~m_c_h_element_v_out(c_e_h_2, c_h, s3))) <=> ((~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | m_c_h_element_v_in1(c_e_h_2, c_h, s2) | (~node14(c_e_h_2, c_h, s2, s3)))),
% 289.82/182.31 inference(rewrite,[status(thm)],[])).
% 289.82/182.31 tff(4691,plain,
% 289.82/182.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s2, s3)) | m_c_h_element_v_in1(c_e_h_2, c_h, s2) | (~m_c_h_element_v_out(c_e_h_2, c_h, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | m_c_h_element_v_in1(c_e_h_2, c_h, s2) | (~node14(c_e_h_2, c_h, s2, s3))))),
% 289.82/182.32 inference(monotonicity,[status(thm)],[4690])).
% 289.82/182.32 tff(4692,plain,
% 289.82/182.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s2, s3)) | m_c_h_element_v_in1(c_e_h_2, c_h, s2) | (~m_c_h_element_v_out(c_e_h_2, c_h, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | m_c_h_element_v_in1(c_e_h_2, c_h, s2) | (~node14(c_e_h_2, c_h, s2, s3)))),
% 289.82/182.32 inference(transitivity,[status(thm)],[4691, 4689])).
% 289.82/182.32 tff(4693,plain,
% 289.82/182.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s2, s3)) | m_c_h_element_v_in1(c_e_h_2, c_h, s2) | (~m_c_h_element_v_out(c_e_h_2, c_h, s3)))),
% 289.82/182.32 inference(quant_inst,[status(thm)],[])).
% 289.82/182.32 tff(4694,plain,
% 289.82/182.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | m_c_h_element_v_in1(c_e_h_2, c_h, s2) | (~node14(c_e_h_2, c_h, s2, s3))),
% 289.82/182.32 inference(modus_ponens,[status(thm)],[4693, 4692])).
% 289.82/182.32 tff(4695,plain,
% 289.82/182.32 ($false),
% 289.82/182.32 inference(unit_resolution,[status(thm)],[4694, 223, 4662, 4688, 4670])).
% 289.82/182.32 tff(4696,plain,(m_c_h_element_v_in1(c_e_h_2, c_h, s2) | (~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | node15(c_e_h_2, c_h, s2, s3) | m_c_h_element_v_in2(c_e_h_2, c_h, s2)), inference(lemma,lemma(discharge,[]))).
% 289.82/182.32 tff(4697,plain,
% 289.82/182.32 (m_c_h_element_v_in1(c_e_h_2, c_h, s2)),
% 289.82/182.32 inference(unit_resolution,[status(thm)],[4696, 4662, 4669, 4660])).
% 289.82/182.32 tff(4698,plain,
% 289.82/182.32 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_2, c_h, s2) | (~node17(c_e_h_2, c_h, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_h, s2) | (~node17(c_e_h_2, c_h, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s2)))),
% 289.82/182.32 inference(rewrite,[status(thm)],[])).
% 289.82/182.32 tff(4699,plain,
% 289.82/182.32 (((~m_c_h_element_v_in1(c_e_h_2, c_h, s2)) | m_c_h_element_v_in2(c_e_h_2, c_h, s2) | (~node17(c_e_h_2, c_h, s2))) <=> (m_c_h_element_v_in2(c_e_h_2, c_h, s2) | (~node17(c_e_h_2, c_h, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s2)))),
% 289.82/182.32 inference(rewrite,[status(thm)],[])).
% 289.82/182.32 tff(4700,plain,
% 289.82/182.32 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s2)) | m_c_h_element_v_in2(c_e_h_2, c_h, s2) | (~node17(c_e_h_2, c_h, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_2, c_h, s2) | (~node17(c_e_h_2, c_h, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s2))))),
% 289.82/182.32 inference(monotonicity,[status(thm)],[4699])).
% 289.82/182.32 tff(4701,plain,
% 289.82/182.32 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s2)) | m_c_h_element_v_in2(c_e_h_2, c_h, s2) | (~node17(c_e_h_2, c_h, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_h, s2) | (~node17(c_e_h_2, c_h, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s2)))),
% 289.82/182.32 inference(transitivity,[status(thm)],[4700, 4698])).
% 289.82/182.32 tff(4702,plain,
% 289.82/182.32 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s2)) | m_c_h_element_v_in2(c_e_h_2, c_h, s2) | (~node17(c_e_h_2, c_h, s2)))),
% 289.82/182.32 inference(quant_inst,[status(thm)],[])).
% 289.82/182.32 tff(4703,plain,
% 289.82/182.32 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_h, s2) | (~node17(c_e_h_2, c_h, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s2))),
% 289.82/182.32 inference(modus_ponens,[status(thm)],[4702, 4701])).
% 289.82/182.32 tff(4704,plain,
% 289.82/182.32 ((~node17(c_e_h_2, c_h, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s2))),
% 289.82/182.32 inference(unit_resolution,[status(thm)],[4703, 919, 4660])).
% 289.82/182.32 tff(4705,plain,
% 289.82/182.32 (~node17(c_e_h_2, c_h, s2)),
% 289.82/182.32 inference(unit_resolution,[status(thm)],[4704, 4697])).
% 289.82/182.32 tff(4706,plain,
% 289.82/182.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_h, s2, s3)) | node18(c_e_h_2, c_h, s2, s3) | node17(c_e_h_2, c_h, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_h, s2, s3)) | node18(c_e_h_2, c_h, s2, s3) | node17(c_e_h_2, c_h, s2))),
% 289.82/182.32 inference(rewrite,[status(thm)],[])).
% 289.82/182.32 tff(4707,plain,
% 289.82/182.32 ((node17(c_e_h_2, c_h, s2) | node18(c_e_h_2, c_h, s2, s3) | (~node19(c_e_h_2, c_h, s2, s3))) <=> ((~node19(c_e_h_2, c_h, s2, s3)) | node18(c_e_h_2, c_h, s2, s3) | node17(c_e_h_2, c_h, s2))),
% 289.82/182.32 inference(rewrite,[status(thm)],[])).
% 289.82/182.32 tff(4708,plain,
% 289.82/182.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s2) | node18(c_e_h_2, c_h, s2, s3) | (~node19(c_e_h_2, c_h, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_h, s2, s3)) | node18(c_e_h_2, c_h, s2, s3) | node17(c_e_h_2, c_h, s2)))),
% 289.82/182.32 inference(monotonicity,[status(thm)],[4707])).
% 289.82/182.32 tff(4709,plain,
% 289.82/182.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s2) | node18(c_e_h_2, c_h, s2, s3) | (~node19(c_e_h_2, c_h, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_h, s2, s3)) | node18(c_e_h_2, c_h, s2, s3) | node17(c_e_h_2, c_h, s2))),
% 289.82/182.32 inference(transitivity,[status(thm)],[4708, 4706])).
% 289.82/182.32 tff(4710,plain,
% 289.82/182.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s2) | node18(c_e_h_2, c_h, s2, s3) | (~node19(c_e_h_2, c_h, s2, s3)))),
% 289.82/182.32 inference(quant_inst,[status(thm)],[])).
% 289.82/182.32 tff(4711,plain,
% 289.82/182.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_h, s2, s3)) | node18(c_e_h_2, c_h, s2, s3) | node17(c_e_h_2, c_h, s2)),
% 289.82/182.32 inference(modus_ponens,[status(thm)],[4710, 4709])).
% 289.82/182.32 tff(4712,plain,
% 289.82/182.32 (node18(c_e_h_2, c_h, s2, s3) | node17(c_e_h_2, c_h, s2)),
% 289.82/182.32 inference(unit_resolution,[status(thm)],[4711, 776, 4680])).
% 289.82/182.32 tff(4713,plain,
% 289.82/182.32 (node18(c_e_h_2, c_h, s2, s3)),
% 289.82/182.32 inference(unit_resolution,[status(thm)],[4712, 4705])).
% 289.82/182.32 tff(4714,plain,
% 289.82/182.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_h, s2) | (~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | (~node18(c_e_h_2, c_h, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s2) | (~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | (~node18(c_e_h_2, c_h, s2, s3)))),
% 289.82/182.32 inference(rewrite,[status(thm)],[])).
% 289.82/182.32 tff(4715,plain,
% 289.82/182.32 (((~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | m_c_h_element_v_out(c_e_h_2, c_h, s2) | (~node18(c_e_h_2, c_h, s2, s3))) <=> (m_c_h_element_v_out(c_e_h_2, c_h, s2) | (~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | (~node18(c_e_h_2, c_h, s2, s3)))),
% 289.82/182.32 inference(rewrite,[status(thm)],[])).
% 289.82/182.32 tff(4716,plain,
% 289.82/182.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | m_c_h_element_v_out(c_e_h_2, c_h, s2) | (~node18(c_e_h_2, c_h, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_h, s2) | (~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | (~node18(c_e_h_2, c_h, s2, s3))))),
% 289.82/182.32 inference(monotonicity,[status(thm)],[4715])).
% 289.82/182.32 tff(4717,plain,
% 289.82/182.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | m_c_h_element_v_out(c_e_h_2, c_h, s2) | (~node18(c_e_h_2, c_h, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s2) | (~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | (~node18(c_e_h_2, c_h, s2, s3)))),
% 289.82/182.32 inference(transitivity,[status(thm)],[4716, 4714])).
% 289.82/182.32 tff(4718,plain,
% 289.82/182.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | m_c_h_element_v_out(c_e_h_2, c_h, s2) | (~node18(c_e_h_2, c_h, s2, s3)))),
% 289.82/182.32 inference(quant_inst,[status(thm)],[])).
% 289.82/182.32 tff(4719,plain,
% 289.82/182.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s2) | (~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | (~node18(c_e_h_2, c_h, s2, s3))),
% 289.82/182.32 inference(modus_ponens,[status(thm)],[4718, 4717])).
% 289.82/182.32 tff(4720,plain,
% 289.82/182.32 ($false),
% 289.82/182.32 inference(unit_resolution,[status(thm)],[4719, 753, 4661, 4662, 4713])).
% 289.82/182.32 tff(4721,plain,((~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | m_c_h_element_v_out(c_e_h_2, c_h, s2) | m_c_h_element_v_in2(c_e_h_2, c_h, s2)), inference(lemma,lemma(discharge,[]))).
% 289.82/182.32 tff(4722,plain,
% 289.82/182.32 ((~m_c_h_element_v_out(c_e_h_2, c_h, s3)) | m_c_h_element_v_in2(c_e_h_2, c_h, s2)),
% 289.82/182.32 inference(unit_resolution,[status(thm)],[4721, 4241])).
% 289.82/182.32 tff(4723,plain,
% 289.82/182.32 (~m_c_h_element_v_out(c_e_h_2, c_h, s3)),
% 289.82/182.32 inference(unit_resolution,[status(thm)],[4722, 4659])).
% 289.82/182.32 tff(4724,assumption,(m_and_h_gate_v_in1(c_e_h_2, c_i, s3)), introduced(assumption)).
% 289.82/182.32 tff(4725,assumption,(~m_c_h_element_v_out(c_e_h_2, c_h, s3)), introduced(assumption)).
% 289.82/182.32 tff(4726,plain,
% 289.82/182.32 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s3)) | m_c_h_element_v_out(c_e_h_2, c_h, s3))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s3)) | m_c_h_element_v_out(c_e_h_2, c_h, s3))),
% 289.82/182.32 inference(rewrite,[status(thm)],[])).
% 289.82/182.32 tff(4727,plain,
% 289.82/182.32 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s3)) | m_c_h_element_v_out(c_e_h_2, c_h, s3))),
% 289.82/182.32 inference(quant_inst,[status(thm)],[])).
% 289.82/182.32 tff(4728,plain,
% 289.82/182.32 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s3)) | m_c_h_element_v_out(c_e_h_2, c_h, s3)),
% 289.82/182.32 inference(modus_ponens,[status(thm)],[4727, 4726])).
% 289.82/182.32 tff(4729,plain,
% 289.82/182.32 ($false),
% 289.82/182.32 inference(unit_resolution,[status(thm)],[4728, 619, 4725, 4724])).
% 289.82/182.32 tff(4730,plain,((~m_and_h_gate_v_in1(c_e_h_2, c_i, s3)) | m_c_h_element_v_out(c_e_h_2, c_h, s3)), inference(lemma,lemma(discharge,[]))).
% 289.82/182.32 tff(4731,plain,
% 289.82/182.32 (~m_and_h_gate_v_in1(c_e_h_2, c_i, s3)),
% 289.82/182.32 inference(unit_resolution,[status(thm)],[4730, 4723])).
% 289.82/182.32 tff(4732,assumption,(node20(c_e_h_2, c_i, s3)), introduced(assumption)).
% 289.82/182.33 tff(4733,assumption,(~m_and_h_gate_v_in1(c_e_h_2, c_i, s3)), introduced(assumption)).
% 289.82/182.33 tff(4734,plain,
% 289.82/182.33 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s3)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s3)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s3))),
% 289.82/182.33 inference(rewrite,[status(thm)],[])).
% 289.82/182.33 tff(4735,plain,
% 289.82/182.33 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s3)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s3))),
% 289.82/182.33 inference(quant_inst,[status(thm)],[])).
% 289.82/182.33 tff(4736,plain,
% 289.82/182.33 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s3)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s3)),
% 289.82/182.33 inference(modus_ponens,[status(thm)],[4735, 4734])).
% 289.82/182.33 tff(4737,plain,
% 289.82/182.33 ($false),
% 289.82/182.33 inference(unit_resolution,[status(thm)],[4736, 38, 4733, 4732])).
% 289.82/182.33 tff(4738,plain,((~node20(c_e_h_2, c_i, s3)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s3)), inference(lemma,lemma(discharge,[]))).
% 289.82/182.33 tff(4739,plain,
% 289.82/182.33 (~node20(c_e_h_2, c_i, s3)),
% 289.82/182.33 inference(unit_resolution,[status(thm)],[4738, 4731])).
% 289.82/182.33 tff(4740,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_i, s3)), introduced(assumption)).
% 289.82/182.33 tff(4741,assumption,(m_and_h_gate_v_out(c_e_h_2, c_i, s4)), introduced(assumption)).
% 289.82/182.33 tff(4742,assumption,(~node20(c_e_h_2, c_i, s3)), introduced(assumption)).
% 289.82/182.33 tff(4743,assumption,(node21(c_e_h_2, c_i, s3, s4)), introduced(assumption)).
% 289.82/182.33 tff(4744,plain,
% 289.82/182.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s4)) | (~node21(c_e_h_2, c_i, s3, s4)) | node20(c_e_h_2, c_i, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s4)) | (~node21(c_e_h_2, c_i, s3, s4)) | node20(c_e_h_2, c_i, s3))),
% 289.82/182.33 inference(rewrite,[status(thm)],[])).
% 289.82/182.33 tff(4745,plain,
% 289.82/182.33 ((node20(c_e_h_2, c_i, s3) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s4)) | (~node21(c_e_h_2, c_i, s3, s4))) <=> ((~m_and_h_gate_v_out(c_e_h_2, c_i, s4)) | (~node21(c_e_h_2, c_i, s3, s4)) | node20(c_e_h_2, c_i, s3))),
% 289.82/182.33 inference(rewrite,[status(thm)],[])).
% 289.82/182.33 tff(4746,plain,
% 289.82/182.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s3) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s4)) | (~node21(c_e_h_2, c_i, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s4)) | (~node21(c_e_h_2, c_i, s3, s4)) | node20(c_e_h_2, c_i, s3)))),
% 289.82/182.33 inference(monotonicity,[status(thm)],[4745])).
% 289.82/182.33 tff(4747,plain,
% 289.82/182.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s3) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s4)) | (~node21(c_e_h_2, c_i, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s4)) | (~node21(c_e_h_2, c_i, s3, s4)) | node20(c_e_h_2, c_i, s3))),
% 289.82/182.33 inference(transitivity,[status(thm)],[4746, 4744])).
% 289.82/182.33 tff(4748,plain,
% 289.82/182.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s3) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s4)) | (~node21(c_e_h_2, c_i, s3, s4)))),
% 289.82/182.33 inference(quant_inst,[status(thm)],[])).
% 289.82/182.33 tff(4749,plain,
% 289.82/182.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s4)) | (~node21(c_e_h_2, c_i, s3, s4)) | node20(c_e_h_2, c_i, s3)),
% 289.82/182.33 inference(modus_ponens,[status(thm)],[4748, 4747])).
% 289.82/182.33 tff(4750,plain,
% 289.82/182.33 ($false),
% 289.82/182.33 inference(unit_resolution,[status(thm)],[4749, 52, 4743, 4742, 4741])).
% 289.82/182.33 tff(4751,plain,((~node21(c_e_h_2, c_i, s3, s4)) | node20(c_e_h_2, c_i, s3) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s4))), inference(lemma,lemma(discharge,[]))).
% 289.82/182.33 tff(4752,plain,
% 289.82/182.33 (~node21(c_e_h_2, c_i, s3, s4)),
% 289.82/182.33 inference(unit_resolution,[status(thm)],[4751, 4741, 4742])).
% 289.82/182.33 tff(4753,plain,
% 289.82/182.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_2, c_i, s3, s4) | node22(c_e_h_2, c_i, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_2, c_i, s3, s4) | node22(c_e_h_2, c_i, s3, s4))),
% 289.82/182.33 inference(rewrite,[status(thm)],[])).
% 289.82/182.33 tff(4754,plain,
% 289.82/182.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_2, c_i, s3, s4) | node22(c_e_h_2, c_i, s3, s4))),
% 289.82/182.33 inference(quant_inst,[status(thm)],[])).
% 289.82/182.33 tff(4755,plain,
% 289.82/182.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_2, c_i, s3, s4) | node22(c_e_h_2, c_i, s3, s4)),
% 289.82/182.33 inference(modus_ponens,[status(thm)],[4754, 4753])).
% 289.82/182.33 tff(4756,plain,
% 289.82/182.33 (node21(c_e_h_2, c_i, s3, s4) | node22(c_e_h_2, c_i, s3, s4)),
% 289.82/182.33 inference(unit_resolution,[status(thm)],[4755, 82, 531])).
% 289.82/182.33 tff(4757,plain,
% 289.82/182.33 (node22(c_e_h_2, c_i, s3, s4)),
% 289.82/182.33 inference(unit_resolution,[status(thm)],[4756, 4752])).
% 289.82/182.33 tff(4758,plain,
% 289.82/182.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s4)) | (~node22(c_e_h_2, c_i, s3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_i, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s4)) | (~node22(c_e_h_2, c_i, s3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_i, s3))),
% 289.82/182.33 inference(rewrite,[status(thm)],[])).
% 289.82/182.33 tff(4759,plain,
% 289.82/182.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s4)) | (~node22(c_e_h_2, c_i, s3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_i, s3))),
% 289.82/182.33 inference(quant_inst,[status(thm)],[])).
% 289.82/182.33 tff(4760,plain,
% 289.82/182.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s4)) | (~node22(c_e_h_2, c_i, s3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_i, s3)),
% 289.82/182.33 inference(modus_ponens,[status(thm)],[4759, 4758])).
% 289.82/182.33 tff(4761,plain,
% 289.82/182.33 ($false),
% 289.82/182.33 inference(unit_resolution,[status(thm)],[4760, 108, 4757, 4741, 4740])).
% 289.82/182.33 tff(4762,plain,((~m_and_h_gate_v_out(c_e_h_2, c_i, s4)) | m_and_h_gate_v_out(c_e_h_2, c_i, s3) | node20(c_e_h_2, c_i, s3)), inference(lemma,lemma(discharge,[]))).
% 289.82/182.33 tff(4763,plain,
% 289.82/182.33 ((~m_and_h_gate_v_out(c_e_h_2, c_i, s4)) | node20(c_e_h_2, c_i, s3)),
% 289.82/182.33 inference(unit_resolution,[status(thm)],[4762, 4257])).
% 289.82/182.33 tff(4764,plain,
% 289.82/182.33 (~m_and_h_gate_v_out(c_e_h_2, c_i, s4)),
% 289.82/182.33 inference(unit_resolution,[status(thm)],[4763, 4739])).
% 289.82/182.33 tff(4765,assumption,(m_c_h_element_v_in2(c_e_h_2, c_f, s4)), introduced(assumption)).
% 289.82/182.33 tff(4766,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_i, s4)), introduced(assumption)).
% 289.82/182.33 tff(4767,plain,
% 289.82/182.33 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_f, s4)) | m_and_h_gate_v_out(c_e_h_2, c_i, s4))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s4)) | m_and_h_gate_v_out(c_e_h_2, c_i, s4))),
% 289.82/182.33 inference(rewrite,[status(thm)],[])).
% 289.82/182.33 tff(4768,plain,
% 289.82/182.33 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_f, s4)) | m_and_h_gate_v_out(c_e_h_2, c_i, s4))),
% 289.82/182.33 inference(quant_inst,[status(thm)],[])).
% 289.82/182.34 tff(4769,plain,
% 289.82/182.34 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s4)) | m_and_h_gate_v_out(c_e_h_2, c_i, s4)),
% 289.82/182.34 inference(modus_ponens,[status(thm)],[4768, 4767])).
% 289.82/182.34 tff(4770,plain,
% 289.82/182.34 ($false),
% 289.82/182.34 inference(unit_resolution,[status(thm)],[4769, 2143, 4766, 4765])).
% 289.82/182.34 tff(4771,plain,((~m_c_h_element_v_in2(c_e_h_2, c_f, s4)) | m_and_h_gate_v_out(c_e_h_2, c_i, s4)), inference(lemma,lemma(discharge,[]))).
% 289.82/182.34 tff(4772,plain,
% 289.82/182.34 (~m_c_h_element_v_in2(c_e_h_2, c_f, s4)),
% 289.82/182.34 inference(unit_resolution,[status(thm)],[4771, 4764])).
% 289.82/182.34 tff(4773,assumption,(m_c_h_element_v_out(c_e_h_2, c_f, s5)), introduced(assumption)).
% 289.82/182.34 tff(4774,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_f, s4)), introduced(assumption)).
% 289.82/182.34 tff(4775,assumption,(node15(c_e_h_2, c_f, s4, s5)), introduced(assumption)).
% 289.82/182.34 tff(4776,plain,
% 289.82/182.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s5)) | (~node15(c_e_h_2, c_f, s4, s5)) | m_c_h_element_v_out(c_e_h_2, c_f, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s5)) | (~node15(c_e_h_2, c_f, s4, s5)) | m_c_h_element_v_out(c_e_h_2, c_f, s4))),
% 289.82/182.34 inference(rewrite,[status(thm)],[])).
% 289.82/182.34 tff(4777,plain,
% 289.82/182.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s5)) | (~node15(c_e_h_2, c_f, s4, s5)) | m_c_h_element_v_out(c_e_h_2, c_f, s4))),
% 289.82/182.34 inference(quant_inst,[status(thm)],[])).
% 289.82/182.34 tff(4778,plain,
% 289.82/182.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s5)) | (~node15(c_e_h_2, c_f, s4, s5)) | m_c_h_element_v_out(c_e_h_2, c_f, s4)),
% 289.82/182.34 inference(modus_ponens,[status(thm)],[4777, 4776])).
% 289.82/182.34 tff(4779,plain,
% 289.82/182.34 ($false),
% 289.82/182.34 inference(unit_resolution,[status(thm)],[4778, 147, 4773, 4775, 4317])).
% 289.82/182.34 tff(4780,plain,((~node15(c_e_h_2, c_f, s4, s5)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s5)) | m_c_h_element_v_out(c_e_h_2, c_f, s4)), inference(lemma,lemma(discharge,[]))).
% 289.82/182.34 tff(4781,plain,
% 289.82/182.34 (~node15(c_e_h_2, c_f, s4, s5)),
% 289.82/182.34 inference(unit_resolution,[status(thm)],[4780, 4317, 4773])).
% 289.82/182.34 tff(4782,assumption,(~node15(c_e_h_2, c_f, s4, s5)), introduced(assumption)).
% 289.82/182.34 tff(4783,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_f, s4)), introduced(assumption)).
% 289.82/182.34 tff(4784,assumption,(node14(c_e_h_2, c_f, s4, s5)), introduced(assumption)).
% 289.82/182.34 tff(4785,plain,
% 289.82/182.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_f, s4) | (~node14(c_e_h_2, c_f, s4, s5)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_f, s4) | (~node14(c_e_h_2, c_f, s4, s5)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s5)))),
% 289.82/182.34 inference(rewrite,[status(thm)],[])).
% 289.82/182.34 tff(4786,plain,
% 289.82/182.34 (((~node14(c_e_h_2, c_f, s4, s5)) | m_c_h_element_v_in1(c_e_h_2, c_f, s4) | (~m_c_h_element_v_out(c_e_h_2, c_f, s5))) <=> (m_c_h_element_v_in1(c_e_h_2, c_f, s4) | (~node14(c_e_h_2, c_f, s4, s5)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s5)))),
% 289.82/182.34 inference(rewrite,[status(thm)],[])).
% 289.82/182.34 tff(4787,plain,
% 289.82/182.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_f, s4, s5)) | m_c_h_element_v_in1(c_e_h_2, c_f, s4) | (~m_c_h_element_v_out(c_e_h_2, c_f, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_f, s4) | (~node14(c_e_h_2, c_f, s4, s5)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s5))))),
% 289.82/182.34 inference(monotonicity,[status(thm)],[4786])).
% 289.82/182.34 tff(4788,plain,
% 289.82/182.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_f, s4, s5)) | m_c_h_element_v_in1(c_e_h_2, c_f, s4) | (~m_c_h_element_v_out(c_e_h_2, c_f, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_f, s4) | (~node14(c_e_h_2, c_f, s4, s5)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s5)))),
% 289.82/182.34 inference(transitivity,[status(thm)],[4787, 4785])).
% 289.82/182.34 tff(4789,plain,
% 289.82/182.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_f, s4, s5)) | m_c_h_element_v_in1(c_e_h_2, c_f, s4) | (~m_c_h_element_v_out(c_e_h_2, c_f, s5)))),
% 289.82/182.34 inference(quant_inst,[status(thm)],[])).
% 289.82/182.34 tff(4790,plain,
% 289.82/182.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_f, s4) | (~node14(c_e_h_2, c_f, s4, s5)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s5))),
% 289.82/182.34 inference(modus_ponens,[status(thm)],[4789, 4788])).
% 289.82/182.34 tff(4791,plain,
% 289.82/182.34 ($false),
% 289.82/182.34 inference(unit_resolution,[status(thm)],[4790, 223, 4773, 4784, 4783])).
% 289.82/182.34 tff(4792,plain,((~node14(c_e_h_2, c_f, s4, s5)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s5)) | m_c_h_element_v_in1(c_e_h_2, c_f, s4)), inference(lemma,lemma(discharge,[]))).
% 289.82/182.34 tff(4793,plain,
% 289.82/182.34 (~node14(c_e_h_2, c_f, s4, s5)),
% 289.82/182.34 inference(unit_resolution,[status(thm)],[4792, 4783, 4773])).
% 289.82/182.34 tff(4794,plain,
% 289.82/182.34 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_f, s4)) | m_c_h_element_v_in1(c_e_h_2, c_f, s4) | m_c_h_element_v_in2(c_e_h_2, c_f, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_f, s4)) | m_c_h_element_v_in1(c_e_h_2, c_f, s4) | m_c_h_element_v_in2(c_e_h_2, c_f, s4))),
% 289.82/182.34 inference(rewrite,[status(thm)],[])).
% 289.82/182.34 tff(4795,plain,
% 289.82/182.34 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_f, s4)) | m_c_h_element_v_in1(c_e_h_2, c_f, s4) | m_c_h_element_v_in2(c_e_h_2, c_f, s4))),
% 289.82/182.34 inference(quant_inst,[status(thm)],[])).
% 289.82/182.34 tff(4796,plain,
% 289.82/182.34 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_f, s4)) | m_c_h_element_v_in1(c_e_h_2, c_f, s4) | m_c_h_element_v_in2(c_e_h_2, c_f, s4)),
% 289.82/182.34 inference(modus_ponens,[status(thm)],[4795, 4794])).
% 289.82/182.34 tff(4797,plain,
% 289.82/182.34 ((~node16(c_e_h_2, c_f, s4)) | m_c_h_element_v_in1(c_e_h_2, c_f, s4)),
% 289.82/182.34 inference(unit_resolution,[status(thm)],[4796, 178, 4774])).
% 289.82/182.34 tff(4798,plain,
% 289.82/182.34 (~node16(c_e_h_2, c_f, s4)),
% 289.82/182.34 inference(unit_resolution,[status(thm)],[4797, 4783])).
% 289.82/182.34 tff(4799,plain,
% 289.82/182.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s4, s5)) | node19(c_e_h_2, c_f, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s4, s5)) | node19(c_e_h_2, c_f, s4, s5))),
% 289.82/182.34 inference(rewrite,[status(thm)],[])).
% 289.82/182.34 tff(4800,plain,
% 289.82/182.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s4, s5)) | node19(c_e_h_2, c_f, s4, s5))),
% 289.82/182.34 inference(quant_inst,[status(thm)],[])).
% 289.82/182.34 tff(4801,plain,
% 289.82/182.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s4, s5)) | node19(c_e_h_2, c_f, s4, s5)),
% 289.82/182.34 inference(modus_ponens,[status(thm)],[4800, 4799])).
% 289.82/182.34 tff(4802,plain,
% 289.82/182.34 (node19(c_e_h_2, c_f, s4, s5)),
% 289.82/182.34 inference(unit_resolution,[status(thm)],[4801, 190, 1028])).
% 289.82/182.34 tff(4803,plain,
% 289.82/182.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s4) | node15(c_e_h_2, c_f, s4, s5) | (~node19(c_e_h_2, c_f, s4, s5)) | node14(c_e_h_2, c_f, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_f, s4) | node15(c_e_h_2, c_f, s4, s5) | (~node19(c_e_h_2, c_f, s4, s5)) | node14(c_e_h_2, c_f, s4, s5))),
% 289.82/182.34 inference(rewrite,[status(thm)],[])).
% 289.82/182.34 tff(4804,plain,
% 289.82/182.34 ((node16(c_e_h_2, c_f, s4) | node14(c_e_h_2, c_f, s4, s5) | node15(c_e_h_2, c_f, s4, s5) | (~node19(c_e_h_2, c_f, s4, s5))) <=> (node16(c_e_h_2, c_f, s4) | node15(c_e_h_2, c_f, s4, s5) | (~node19(c_e_h_2, c_f, s4, s5)) | node14(c_e_h_2, c_f, s4, s5))),
% 289.82/182.34 inference(rewrite,[status(thm)],[])).
% 289.82/182.34 tff(4805,plain,
% 289.82/182.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s4) | node14(c_e_h_2, c_f, s4, s5) | node15(c_e_h_2, c_f, s4, s5) | (~node19(c_e_h_2, c_f, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s4) | node15(c_e_h_2, c_f, s4, s5) | (~node19(c_e_h_2, c_f, s4, s5)) | node14(c_e_h_2, c_f, s4, s5)))),
% 289.82/182.34 inference(monotonicity,[status(thm)],[4804])).
% 289.82/182.34 tff(4806,plain,
% 289.82/182.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s4) | node14(c_e_h_2, c_f, s4, s5) | node15(c_e_h_2, c_f, s4, s5) | (~node19(c_e_h_2, c_f, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_f, s4) | node15(c_e_h_2, c_f, s4, s5) | (~node19(c_e_h_2, c_f, s4, s5)) | node14(c_e_h_2, c_f, s4, s5))),
% 289.82/182.34 inference(transitivity,[status(thm)],[4805, 4803])).
% 289.82/182.34 tff(4807,plain,
% 289.82/182.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s4) | node14(c_e_h_2, c_f, s4, s5) | node15(c_e_h_2, c_f, s4, s5) | (~node19(c_e_h_2, c_f, s4, s5)))),
% 289.82/182.34 inference(quant_inst,[status(thm)],[])).
% 289.82/182.34 tff(4808,plain,
% 289.82/182.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_f, s4) | node15(c_e_h_2, c_f, s4, s5) | (~node19(c_e_h_2, c_f, s4, s5)) | node14(c_e_h_2, c_f, s4, s5)),
% 289.82/182.34 inference(modus_ponens,[status(thm)],[4807, 4806])).
% 289.82/182.34 tff(4809,plain,
% 289.82/182.34 (node16(c_e_h_2, c_f, s4) | node15(c_e_h_2, c_f, s4, s5) | node14(c_e_h_2, c_f, s4, s5)),
% 289.82/182.34 inference(unit_resolution,[status(thm)],[4808, 204, 4802])).
% 289.82/182.34 tff(4810,plain,
% 289.82/182.34 ($false),
% 289.82/182.34 inference(unit_resolution,[status(thm)],[4809, 4798, 4793, 4782])).
% 289.82/182.34 tff(4811,plain,(m_c_h_element_v_in1(c_e_h_2, c_f, s4) | node15(c_e_h_2, c_f, s4, s5) | m_c_h_element_v_in2(c_e_h_2, c_f, s4) | (~m_c_h_element_v_out(c_e_h_2, c_f, s5))), inference(lemma,lemma(discharge,[]))).
% 289.82/182.34 tff(4812,plain,
% 289.82/182.34 (m_c_h_element_v_in1(c_e_h_2, c_f, s4)),
% 289.82/182.34 inference(unit_resolution,[status(thm)],[4811, 4781, 4774, 4773])).
% 289.82/182.34 tff(4813,plain,
% 289.82/182.34 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s4)) | m_c_h_element_v_in2(c_e_h_2, c_f, s4) | (~node17(c_e_h_2, c_f, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s4)) | m_c_h_element_v_in2(c_e_h_2, c_f, s4) | (~node17(c_e_h_2, c_f, s4)))),
% 289.82/182.34 inference(rewrite,[status(thm)],[])).
% 289.82/182.34 tff(4814,plain,
% 289.82/182.34 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s4)) | m_c_h_element_v_in2(c_e_h_2, c_f, s4) | (~node17(c_e_h_2, c_f, s4)))),
% 289.82/182.34 inference(quant_inst,[status(thm)],[])).
% 289.82/182.35 tff(4815,plain,
% 289.82/182.35 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s4)) | m_c_h_element_v_in2(c_e_h_2, c_f, s4) | (~node17(c_e_h_2, c_f, s4))),
% 289.82/182.35 inference(modus_ponens,[status(thm)],[4814, 4813])).
% 289.82/182.35 tff(4816,plain,
% 289.82/182.35 ((~m_c_h_element_v_in1(c_e_h_2, c_f, s4)) | (~node17(c_e_h_2, c_f, s4))),
% 289.82/182.35 inference(unit_resolution,[status(thm)],[4815, 919, 4774])).
% 289.82/182.35 tff(4817,plain,
% 289.82/182.35 (~node17(c_e_h_2, c_f, s4)),
% 289.82/182.35 inference(unit_resolution,[status(thm)],[4816, 4812])).
% 289.82/182.35 tff(4818,plain,
% 289.82/182.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_f, s4, s5)) | node18(c_e_h_2, c_f, s4, s5) | node17(c_e_h_2, c_f, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_f, s4, s5)) | node18(c_e_h_2, c_f, s4, s5) | node17(c_e_h_2, c_f, s4))),
% 289.82/182.35 inference(rewrite,[status(thm)],[])).
% 289.82/182.35 tff(4819,plain,
% 289.82/182.35 ((node17(c_e_h_2, c_f, s4) | node18(c_e_h_2, c_f, s4, s5) | (~node19(c_e_h_2, c_f, s4, s5))) <=> ((~node19(c_e_h_2, c_f, s4, s5)) | node18(c_e_h_2, c_f, s4, s5) | node17(c_e_h_2, c_f, s4))),
% 289.82/182.35 inference(rewrite,[status(thm)],[])).
% 289.82/182.35 tff(4820,plain,
% 289.82/182.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s4) | node18(c_e_h_2, c_f, s4, s5) | (~node19(c_e_h_2, c_f, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_f, s4, s5)) | node18(c_e_h_2, c_f, s4, s5) | node17(c_e_h_2, c_f, s4)))),
% 289.82/182.35 inference(monotonicity,[status(thm)],[4819])).
% 289.82/182.35 tff(4821,plain,
% 289.82/182.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s4) | node18(c_e_h_2, c_f, s4, s5) | (~node19(c_e_h_2, c_f, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_f, s4, s5)) | node18(c_e_h_2, c_f, s4, s5) | node17(c_e_h_2, c_f, s4))),
% 289.82/182.35 inference(transitivity,[status(thm)],[4820, 4818])).
% 289.82/182.35 tff(4822,plain,
% 289.82/182.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s4) | node18(c_e_h_2, c_f, s4, s5) | (~node19(c_e_h_2, c_f, s4, s5)))),
% 289.82/182.35 inference(quant_inst,[status(thm)],[])).
% 289.82/182.35 tff(4823,plain,
% 289.82/182.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_f, s4, s5)) | node18(c_e_h_2, c_f, s4, s5) | node17(c_e_h_2, c_f, s4)),
% 289.82/182.35 inference(modus_ponens,[status(thm)],[4822, 4821])).
% 289.82/182.35 tff(4824,plain,
% 289.82/182.35 (node18(c_e_h_2, c_f, s4, s5) | node17(c_e_h_2, c_f, s4)),
% 289.82/182.35 inference(unit_resolution,[status(thm)],[4823, 776, 4802])).
% 289.82/182.35 tff(4825,plain,
% 289.82/182.35 (node18(c_e_h_2, c_f, s4, s5)),
% 289.82/182.35 inference(unit_resolution,[status(thm)],[4824, 4817])).
% 289.82/182.35 tff(4826,plain,
% 289.82/182.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_f, s4) | (~node18(c_e_h_2, c_f, s4, s5)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_f, s4) | (~node18(c_e_h_2, c_f, s4, s5)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s5)))),
% 289.82/182.35 inference(rewrite,[status(thm)],[])).
% 289.82/182.35 tff(4827,plain,
% 289.82/182.35 (((~m_c_h_element_v_out(c_e_h_2, c_f, s5)) | m_c_h_element_v_out(c_e_h_2, c_f, s4) | (~node18(c_e_h_2, c_f, s4, s5))) <=> (m_c_h_element_v_out(c_e_h_2, c_f, s4) | (~node18(c_e_h_2, c_f, s4, s5)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s5)))),
% 289.82/182.35 inference(rewrite,[status(thm)],[])).
% 289.82/182.35 tff(4828,plain,
% 289.82/182.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s5)) | m_c_h_element_v_out(c_e_h_2, c_f, s4) | (~node18(c_e_h_2, c_f, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_f, s4) | (~node18(c_e_h_2, c_f, s4, s5)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s5))))),
% 289.82/182.35 inference(monotonicity,[status(thm)],[4827])).
% 289.82/182.35 tff(4829,plain,
% 289.82/182.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s5)) | m_c_h_element_v_out(c_e_h_2, c_f, s4) | (~node18(c_e_h_2, c_f, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_f, s4) | (~node18(c_e_h_2, c_f, s4, s5)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s5)))),
% 289.82/182.35 inference(transitivity,[status(thm)],[4828, 4826])).
% 289.82/182.35 tff(4830,plain,
% 289.82/182.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s5)) | m_c_h_element_v_out(c_e_h_2, c_f, s4) | (~node18(c_e_h_2, c_f, s4, s5)))),
% 289.82/182.35 inference(quant_inst,[status(thm)],[])).
% 289.82/182.35 tff(4831,plain,
% 289.82/182.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_f, s4) | (~node18(c_e_h_2, c_f, s4, s5)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s5))),
% 289.82/182.35 inference(modus_ponens,[status(thm)],[4830, 4829])).
% 289.82/182.35 tff(4832,plain,
% 289.82/182.35 ($false),
% 289.82/182.35 inference(unit_resolution,[status(thm)],[4831, 753, 4773, 4825, 4317])).
% 289.82/182.35 tff(4833,plain,(m_c_h_element_v_out(c_e_h_2, c_f, s4) | (~m_c_h_element_v_out(c_e_h_2, c_f, s5)) | m_c_h_element_v_in2(c_e_h_2, c_f, s4)), inference(lemma,lemma(discharge,[]))).
% 289.82/182.35 tff(4834,plain,
% 289.82/182.35 (m_c_h_element_v_out(c_e_h_2, c_f, s4) | (~m_c_h_element_v_out(c_e_h_2, c_f, s5))),
% 289.82/182.35 inference(unit_resolution,[status(thm)],[4833, 4772])).
% 289.82/182.35 tff(4835,plain,
% 289.82/182.35 (~m_c_h_element_v_out(c_e_h_2, c_f, s5)),
% 289.82/182.35 inference(unit_resolution,[status(thm)],[4834, 4315])).
% 289.82/182.35 tff(4836,plain,
% 289.82/182.35 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_q, s5)) | m_c_h_element_v_out(c_e_h_2, c_f, s5))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_q, s5)) | m_c_h_element_v_out(c_e_h_2, c_f, s5))),
% 289.82/182.35 inference(rewrite,[status(thm)],[])).
% 289.82/182.35 tff(4837,plain,
% 289.82/182.35 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_q, s5)) | m_c_h_element_v_out(c_e_h_2, c_f, s5))),
% 289.82/182.35 inference(quant_inst,[status(thm)],[])).
% 289.82/182.35 tff(4838,plain,
% 289.82/182.35 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_q, s5)) | m_c_h_element_v_out(c_e_h_2, c_f, s5)),
% 289.82/182.35 inference(modus_ponens,[status(thm)],[4837, 4836])).
% 289.82/182.35 tff(4839,plain,
% 289.82/182.35 (~m_and_h_gate_v_in1(c_e_h_2, c_q, s5)),
% 289.82/182.35 inference(unit_resolution,[status(thm)],[4838, 1586, 4835])).
% 289.82/182.35 tff(4840,plain,
% 289.82/182.35 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_q, s5)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_q, s5)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s5))),
% 289.82/182.35 inference(rewrite,[status(thm)],[])).
% 289.82/182.35 tff(4841,plain,
% 289.82/182.35 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_q, s5)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s5))),
% 289.82/182.35 inference(quant_inst,[status(thm)],[])).
% 289.82/182.35 tff(4842,plain,
% 289.82/182.35 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_q, s5)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s5)),
% 289.82/182.35 inference(modus_ponens,[status(thm)],[4841, 4840])).
% 289.82/182.35 tff(4843,plain,
% 289.82/182.35 (~node20(c_e_h_2, c_q, s5)),
% 289.82/182.35 inference(unit_resolution,[status(thm)],[4842, 38, 4839])).
% 289.82/182.35 tff(4844,assumption,(node21(c_e_h_2, c_q, s5, s6)), introduced(assumption)).
% 289.82/182.35 tff(4845,plain,
% 289.82/182.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_q, s5) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s6)) | (~node21(c_e_h_2, c_q, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_q, s5) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s6)) | (~node21(c_e_h_2, c_q, s5, s6)))),
% 289.82/182.35 inference(rewrite,[status(thm)],[])).
% 289.82/182.35 tff(4846,plain,
% 289.82/182.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_q, s5) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s6)) | (~node21(c_e_h_2, c_q, s5, s6)))),
% 289.82/182.35 inference(quant_inst,[status(thm)],[])).
% 289.82/182.35 tff(4847,plain,
% 289.82/182.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_q, s5) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s6)) | (~node21(c_e_h_2, c_q, s5, s6))),
% 289.82/182.35 inference(modus_ponens,[status(thm)],[4846, 4845])).
% 289.82/182.35 tff(4848,plain,
% 289.82/182.35 ($false),
% 289.82/182.35 inference(unit_resolution,[status(thm)],[4847, 52, 4496, 4844, 4843])).
% 289.82/182.35 tff(4849,plain,((~node21(c_e_h_2, c_q, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s6))), inference(lemma,lemma(discharge,[]))).
% 289.82/182.35 tff(4850,plain,
% 289.82/182.35 (~node21(c_e_h_2, c_q, s5, s6)),
% 289.82/182.35 inference(unit_resolution,[status(thm)],[4849, 4496])).
% 289.82/182.35 tff(4851,plain,
% 289.82/182.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_2, c_q, s5, s6) | node22(c_e_h_2, c_q, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_2, c_q, s5, s6) | node22(c_e_h_2, c_q, s5, s6))),
% 289.82/182.35 inference(rewrite,[status(thm)],[])).
% 289.82/182.35 tff(4852,plain,
% 289.82/182.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_2, c_q, s5, s6) | node22(c_e_h_2, c_q, s5, s6))),
% 289.82/182.35 inference(quant_inst,[status(thm)],[])).
% 289.82/182.35 tff(4853,plain,
% 289.82/182.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_2, c_q, s5, s6) | node22(c_e_h_2, c_q, s5, s6)),
% 289.82/182.35 inference(modus_ponens,[status(thm)],[4852, 4851])).
% 289.82/182.35 tff(4854,plain,
% 289.82/182.35 (node21(c_e_h_2, c_q, s5, s6) | node22(c_e_h_2, c_q, s5, s6)),
% 289.82/182.35 inference(unit_resolution,[status(thm)],[4853, 82, 1406])).
% 289.82/182.35 tff(4855,plain,
% 289.82/182.35 (node22(c_e_h_2, c_q, s5, s6)),
% 289.82/182.35 inference(unit_resolution,[status(thm)],[4854, 4850])).
% 289.82/182.35 tff(4856,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_q, s5)), introduced(assumption)).
% 289.82/182.35 tff(4857,plain,
% 289.82/182.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s6)) | (~node22(c_e_h_2, c_q, s5, s6)) | m_and_h_gate_v_out(c_e_h_2, c_q, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s6)) | (~node22(c_e_h_2, c_q, s5, s6)) | m_and_h_gate_v_out(c_e_h_2, c_q, s5))),
% 289.82/182.35 inference(rewrite,[status(thm)],[])).
% 289.82/182.35 tff(4858,plain,
% 289.82/182.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s6)) | (~node22(c_e_h_2, c_q, s5, s6)) | m_and_h_gate_v_out(c_e_h_2, c_q, s5))),
% 289.82/182.35 inference(quant_inst,[status(thm)],[])).
% 289.82/182.35 tff(4859,plain,
% 289.82/182.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s6)) | (~node22(c_e_h_2, c_q, s5, s6)) | m_and_h_gate_v_out(c_e_h_2, c_q, s5)),
% 289.82/182.36 inference(modus_ponens,[status(thm)],[4858, 4857])).
% 289.82/182.36 tff(4860,plain,
% 289.82/182.36 ($false),
% 289.82/182.36 inference(unit_resolution,[status(thm)],[4859, 108, 4856, 4496, 4855])).
% 289.82/182.36 tff(4861,plain,((~m_and_h_gate_v_out(c_e_h_2, c_q, s6)) | m_and_h_gate_v_out(c_e_h_2, c_q, s5)), inference(lemma,lemma(discharge,[]))).
% 289.82/182.36 tff(4862,plain,
% 289.82/182.36 (~m_and_h_gate_v_out(c_e_h_2, c_q, s6)),
% 289.82/182.36 inference(unit_resolution,[status(thm)],[4861, 4353])).
% 289.82/182.36 tff(4863,plain,
% 289.82/182.36 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s6))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s6))),
% 289.82/182.36 inference(rewrite,[status(thm)],[])).
% 289.82/182.36 tff(4864,plain,
% 289.82/182.36 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s6))),
% 289.82/182.36 inference(quant_inst,[status(thm)],[])).
% 289.82/182.36 tff(4865,plain,
% 289.82/182.36 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s6)),
% 289.82/182.36 inference(modus_ponens,[status(thm)],[4864, 4863])).
% 289.82/182.36 tff(4866,plain,
% 289.82/182.36 (node3(c_e_h_2, c_e_h_3, s6)),
% 289.82/182.36 inference(unit_resolution,[status(thm)],[4865, 1059, 1056])).
% 289.82/182.36 tff(4867,plain,
% 289.82/182.36 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_3, s6)) | (~node3(c_e_h_2, c_e_h_3, s6)) | m_and_h_gate_v_out(c_e_h_2, c_q, s6))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_3, s6)) | (~node3(c_e_h_2, c_e_h_3, s6)) | m_and_h_gate_v_out(c_e_h_2, c_q, s6))),
% 289.82/182.36 inference(rewrite,[status(thm)],[])).
% 289.82/182.36 tff(4868,plain,
% 289.82/182.36 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_3, s6)) | (~node3(c_e_h_2, c_e_h_3, s6)) | m_and_h_gate_v_out(c_e_h_2, c_q, s6))),
% 289.82/182.36 inference(quant_inst,[status(thm)],[])).
% 289.82/182.36 tff(4869,plain,
% 289.82/182.36 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_3, s6)) | (~node3(c_e_h_2, c_e_h_3, s6)) | m_and_h_gate_v_out(c_e_h_2, c_q, s6)),
% 289.82/182.36 inference(modus_ponens,[status(thm)],[4868, 4867])).
% 289.82/182.36 tff(4870,plain,
% 289.82/182.36 ((~m_cell_v_ack(c_e_h_3, s6)) | m_and_h_gate_v_out(c_e_h_2, c_q, s6)),
% 289.82/182.36 inference(unit_resolution,[status(thm)],[4869, 1073, 4866])).
% 289.82/182.36 tff(4871,plain,
% 289.82/182.36 (~m_cell_v_ack(c_e_h_3, s6)),
% 289.82/182.36 inference(unit_resolution,[status(thm)],[4870, 4862])).
% 289.82/182.36 tff(4872,plain,
% 289.82/182.36 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_j, s6)) | m_cell_v_ack(c_e_h_3, s6))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_j, s6)) | m_cell_v_ack(c_e_h_3, s6))),
% 289.82/182.36 inference(rewrite,[status(thm)],[])).
% 289.82/182.36 tff(4873,plain,
% 289.82/182.36 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_j, s6)) | m_cell_v_ack(c_e_h_3, s6))),
% 289.82/182.36 inference(quant_inst,[status(thm)],[])).
% 289.82/182.36 tff(4874,plain,
% 289.82/182.36 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_j, s6)) | m_cell_v_ack(c_e_h_3, s6)),
% 289.82/182.36 inference(modus_ponens,[status(thm)],[4873, 4872])).
% 289.82/182.36 tff(4875,plain,
% 289.82/182.36 (~m_or_h_gate_v_in2(c_e_h_3, c_j, s6)),
% 289.82/182.36 inference(unit_resolution,[status(thm)],[4874, 1085, 4871])).
% 289.82/182.36 tff(4876,assumption,(node5(c_e_h_3, c_j, s6, s7)), introduced(assumption)).
% 289.82/182.36 tff(4877,plain,
% 289.82/182.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s6) | m_or_h_gate_v_in1(c_e_h_3, c_j, s6) | (~node5(c_e_h_3, c_j, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s6) | m_or_h_gate_v_in1(c_e_h_3, c_j, s6) | (~node5(c_e_h_3, c_j, s6, s7)))),
% 289.82/182.36 inference(rewrite,[status(thm)],[])).
% 289.82/182.36 tff(4878,plain,
% 289.82/182.36 ((m_or_h_gate_v_in1(c_e_h_3, c_j, s6) | m_or_h_gate_v_in2(c_e_h_3, c_j, s6) | (~node5(c_e_h_3, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7))) <=> ((~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s6) | m_or_h_gate_v_in1(c_e_h_3, c_j, s6) | (~node5(c_e_h_3, c_j, s6, s7)))),
% 289.82/182.36 inference(rewrite,[status(thm)],[])).
% 289.82/182.36 tff(4879,plain,
% 289.82/182.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s6) | m_or_h_gate_v_in2(c_e_h_3, c_j, s6) | (~node5(c_e_h_3, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s6) | m_or_h_gate_v_in1(c_e_h_3, c_j, s6) | (~node5(c_e_h_3, c_j, s6, s7))))),
% 289.82/182.36 inference(monotonicity,[status(thm)],[4878])).
% 289.82/182.36 tff(4880,plain,
% 289.82/182.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s6) | m_or_h_gate_v_in2(c_e_h_3, c_j, s6) | (~node5(c_e_h_3, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s6) | m_or_h_gate_v_in1(c_e_h_3, c_j, s6) | (~node5(c_e_h_3, c_j, s6, s7)))),
% 289.82/182.36 inference(transitivity,[status(thm)],[4879, 4877])).
% 289.82/182.36 tff(4881,plain,
% 289.82/182.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s6) | m_or_h_gate_v_in2(c_e_h_3, c_j, s6) | (~node5(c_e_h_3, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)))),
% 289.82/182.36 inference(quant_inst,[status(thm)],[])).
% 289.82/182.36 tff(4882,plain,
% 289.82/182.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s6) | m_or_h_gate_v_in1(c_e_h_3, c_j, s6) | (~node5(c_e_h_3, c_j, s6, s7))),
% 289.82/182.36 inference(modus_ponens,[status(thm)],[4881, 4880])).
% 289.82/182.36 tff(4883,plain,
% 289.82/182.36 ($false),
% 289.82/182.36 inference(unit_resolution,[status(thm)],[4882, 1159, 4495, 4876, 4875, 4494])).
% 289.82/182.36 tff(4884,plain,((~node5(c_e_h_3, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s6)), inference(lemma,lemma(discharge,[]))).
% 289.82/182.36 tff(4885,plain,
% 289.82/182.36 (~node5(c_e_h_3, c_j, s6, s7)),
% 289.82/182.36 inference(unit_resolution,[status(thm)],[4884, 4495, 4494])).
% 289.82/182.36 tff(4886,assumption,(node6(c_e_h_3, c_j, s6, s7)), introduced(assumption)).
% 289.82/182.36 tff(4887,plain,
% 289.82/182.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | m_or_h_gate_v_out(c_e_h_3, c_j, s6) | (~node6(c_e_h_3, c_j, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | m_or_h_gate_v_out(c_e_h_3, c_j, s6) | (~node6(c_e_h_3, c_j, s6, s7)))),
% 289.82/182.36 inference(rewrite,[status(thm)],[])).
% 289.82/182.36 tff(4888,plain,
% 289.82/182.36 (((~node6(c_e_h_3, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | m_or_h_gate_v_out(c_e_h_3, c_j, s6)) <=> ((~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | m_or_h_gate_v_out(c_e_h_3, c_j, s6) | (~node6(c_e_h_3, c_j, s6, s7)))),
% 289.82/182.37 inference(rewrite,[status(thm)],[])).
% 289.82/182.37 tff(4889,plain,
% 289.82/182.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | m_or_h_gate_v_out(c_e_h_3, c_j, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | m_or_h_gate_v_out(c_e_h_3, c_j, s6) | (~node6(c_e_h_3, c_j, s6, s7))))),
% 289.82/182.37 inference(monotonicity,[status(thm)],[4888])).
% 289.82/182.37 tff(4890,plain,
% 289.82/182.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | m_or_h_gate_v_out(c_e_h_3, c_j, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | m_or_h_gate_v_out(c_e_h_3, c_j, s6) | (~node6(c_e_h_3, c_j, s6, s7)))),
% 289.82/182.37 inference(transitivity,[status(thm)],[4889, 4887])).
% 289.82/182.37 tff(4891,plain,
% 289.82/182.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | m_or_h_gate_v_out(c_e_h_3, c_j, s6))),
% 289.82/182.37 inference(quant_inst,[status(thm)],[])).
% 289.82/182.37 tff(4892,plain,
% 289.82/182.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | m_or_h_gate_v_out(c_e_h_3, c_j, s6) | (~node6(c_e_h_3, c_j, s6, s7))),
% 289.82/182.37 inference(modus_ponens,[status(thm)],[4891, 4890])).
% 289.82/182.37 tff(4893,plain,
% 289.82/182.37 ($false),
% 289.82/182.37 inference(unit_resolution,[status(thm)],[4892, 1121, 4495, 4485, 4886])).
% 289.82/182.37 tff(4894,plain,((~node6(c_e_h_3, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | m_or_h_gate_v_out(c_e_h_3, c_j, s6)), inference(lemma,lemma(discharge,[]))).
% 289.82/182.37 tff(4895,plain,
% 289.82/182.37 (~node6(c_e_h_3, c_j, s6, s7)),
% 289.82/182.37 inference(unit_resolution,[status(thm)],[4894, 4495, 4485])).
% 289.82/182.37 tff(4896,plain,
% 289.82/182.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s6, s7)) | node6(c_e_h_3, c_j, s6, s7) | node5(c_e_h_3, c_j, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s6, s7)) | node6(c_e_h_3, c_j, s6, s7) | node5(c_e_h_3, c_j, s6, s7))),
% 289.82/182.37 inference(rewrite,[status(thm)],[])).
% 289.82/182.37 tff(4897,plain,
% 289.82/182.37 ((node6(c_e_h_3, c_j, s6, s7) | node5(c_e_h_3, c_j, s6, s7) | (~trans(s6, s7))) <=> ((~trans(s6, s7)) | node6(c_e_h_3, c_j, s6, s7) | node5(c_e_h_3, c_j, s6, s7))),
% 289.82/182.37 inference(rewrite,[status(thm)],[])).
% 289.82/182.37 tff(4898,plain,
% 289.82/182.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s6, s7) | node5(c_e_h_3, c_j, s6, s7) | (~trans(s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s6, s7)) | node6(c_e_h_3, c_j, s6, s7) | node5(c_e_h_3, c_j, s6, s7)))),
% 289.82/182.37 inference(monotonicity,[status(thm)],[4897])).
% 289.82/182.37 tff(4899,plain,
% 289.82/182.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s6, s7) | node5(c_e_h_3, c_j, s6, s7) | (~trans(s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s6, s7)) | node6(c_e_h_3, c_j, s6, s7) | node5(c_e_h_3, c_j, s6, s7))),
% 289.82/182.37 inference(transitivity,[status(thm)],[4898, 4896])).
% 289.82/182.37 tff(4900,plain,
% 289.82/182.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s6, s7) | node5(c_e_h_3, c_j, s6, s7) | (~trans(s6, s7)))),
% 289.82/182.37 inference(quant_inst,[status(thm)],[])).
% 289.82/182.37 tff(4901,plain,
% 289.82/182.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s6, s7)) | node6(c_e_h_3, c_j, s6, s7) | node5(c_e_h_3, c_j, s6, s7)),
% 289.82/182.37 inference(modus_ponens,[status(thm)],[4900, 4899])).
% 289.82/182.37 tff(4902,plain,
% 289.82/182.37 (node6(c_e_h_3, c_j, s6, s7) | node5(c_e_h_3, c_j, s6, s7)),
% 289.82/182.37 inference(unit_resolution,[status(thm)],[4901, 1141, 1844])).
% 289.82/182.37 tff(4903,plain,
% 289.82/182.37 ($false),
% 289.82/182.37 inference(unit_resolution,[status(thm)],[4902, 4895, 4885])).
% 289.82/182.37 tff(4904,plain,((~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | m_or_h_gate_v_out(c_e_h_3, c_j, s6) | m_or_h_gate_v_in1(c_e_h_3, c_j, s6)), inference(lemma,lemma(discharge,[]))).
% 289.82/182.37 tff(4905,plain,
% 289.82/182.37 (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)),
% 289.82/182.37 inference(unit_resolution,[status(thm)],[4904, 4493, 4485])).
% 289.82/182.37 tff(4906,assumption,(~m_or_h_gate_v_in1(c_e_h_3, c_j, s7)), introduced(assumption)).
% 289.82/182.37 tff(4907,assumption,(m_and_h_gate_v_out(c_e_h_2, c_q, s7)), introduced(assumption)).
% 289.82/182.37 tff(4908,assumption,(m_and_h_gate_v_out(c_e_h_2, c_l, s2)), introduced(assumption)).
% 289.82/182.37 tff(4909,assumption,(node22(c_e_h_2, c_l, s1, s2)), introduced(assumption)).
% 289.82/182.37 tff(4910,plain,
% 289.82/182.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s2)) | (~node22(c_e_h_2, c_l, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_l, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s2)) | (~node22(c_e_h_2, c_l, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_l, s1))),
% 289.82/182.37 inference(rewrite,[status(thm)],[])).
% 289.82/182.37 tff(4911,plain,
% 289.82/182.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s2)) | (~node22(c_e_h_2, c_l, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_l, s1))),
% 289.82/182.37 inference(quant_inst,[status(thm)],[])).
% 289.82/182.37 tff(4912,plain,
% 289.82/182.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s2)) | (~node22(c_e_h_2, c_l, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_l, s1)),
% 289.82/182.37 inference(modus_ponens,[status(thm)],[4911, 4910])).
% 289.82/182.37 tff(4913,plain,
% 289.82/182.37 ($false),
% 289.82/182.37 inference(unit_resolution,[status(thm)],[4912, 108, 4909, 4575, 4908])).
% 289.82/182.37 tff(4914,plain,((~node22(c_e_h_2, c_l, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s2))), inference(lemma,lemma(discharge,[]))).
% 289.82/182.37 tff(4915,plain,
% 289.82/182.37 (~node22(c_e_h_2, c_l, s1, s2)),
% 289.82/182.37 inference(unit_resolution,[status(thm)],[4914, 4908])).
% 289.82/182.37 tff(4916,plain,
% 289.82/182.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_2, c_l, s1, s2) | node22(c_e_h_2, c_l, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_2, c_l, s1, s2) | node22(c_e_h_2, c_l, s1, s2))),
% 289.82/182.37 inference(rewrite,[status(thm)],[])).
% 289.82/182.37 tff(4917,plain,
% 289.82/182.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_2, c_l, s1, s2) | node22(c_e_h_2, c_l, s1, s2))),
% 289.82/182.37 inference(quant_inst,[status(thm)],[])).
% 289.82/182.37 tff(4918,plain,
% 289.82/182.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_2, c_l, s1, s2) | node22(c_e_h_2, c_l, s1, s2)),
% 289.82/182.37 inference(modus_ponens,[status(thm)],[4917, 4916])).
% 289.82/182.37 tff(4919,plain,
% 289.82/182.37 (node21(c_e_h_2, c_l, s1, s2) | node22(c_e_h_2, c_l, s1, s2)),
% 289.82/182.37 inference(unit_resolution,[status(thm)],[4918, 82, 255])).
% 289.82/182.37 tff(4920,plain,
% 289.82/182.37 (node21(c_e_h_2, c_l, s1, s2)),
% 289.82/182.37 inference(unit_resolution,[status(thm)],[4919, 4915])).
% 289.82/182.37 tff(4921,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)), introduced(assumption)).
% 289.82/182.37 tff(4922,assumption,(node10(c_e_h_2, c_m, s0, s1)), introduced(assumption)).
% 289.82/182.37 tff(4923,plain,
% 289.82/182.37 (^[I0: $i, X: $i] : refl((m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X)) <=> (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X)))),
% 289.90/182.37 inference(bind,[status(th)],[])).
% 289.90/182.37 tff(4924,plain,
% 289.90/182.37 (![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X)) <=> ![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))),
% 289.90/182.37 inference(quant_intro,[status(thm)],[4923])).
% 289.90/182.37 tff(4925,plain,
% 289.90/182.37 (![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X)) <=> ![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))),
% 289.90/182.37 inference(rewrite,[status(thm)],[])).
% 289.90/182.37 tff(4926,plain,
% 289.90/182.37 (^[I0: $i, X: $i] : rewrite((m_and_h_gate_h_init_v_init_h_out(I0, c_n, X) | m_cell_v_token(I0, X)) <=> (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X)))),
% 289.90/182.37 inference(bind,[status(th)],[])).
% 289.90/182.37 tff(4927,plain,
% 289.90/182.37 (![I0: $i, X: $i] : (m_and_h_gate_h_init_v_init_h_out(I0, c_n, X) | m_cell_v_token(I0, X)) <=> ![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))),
% 289.90/182.37 inference(quant_intro,[status(thm)],[4926])).
% 289.90/182.37 tff(4928,axiom,(![I0: $i, X: $i] : (m_and_h_gate_h_init_v_init_h_out(I0, c_n, X) | m_cell_v_token(I0, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_61')).
% 289.90/182.37 tff(4929,plain,
% 289.90/182.37 (![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))),
% 289.90/182.37 inference(modus_ponens,[status(thm)],[4928, 4927])).
% 289.90/182.37 tff(4930,plain,
% 289.90/182.37 (![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))),
% 289.90/182.37 inference(modus_ponens,[status(thm)],[4929, 4925])).
% 289.90/182.37 tff(4931,plain,(
% 289.90/182.37 ![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))),
% 289.90/182.37 inference(skolemize,[status(sab)],[4930])).
% 289.90/182.37 tff(4932,plain,
% 289.90/182.37 (![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))),
% 289.90/182.37 inference(modus_ponens,[status(thm)],[4931, 4924])).
% 289.90/182.37 tff(4933,plain,
% 289.90/182.37 (((~![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))) | (m_cell_v_token(c_e_h_2, s0) | m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_n, s0))) <=> ((~![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))) | m_cell_v_token(c_e_h_2, s0) | m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_n, s0))),
% 289.90/182.37 inference(rewrite,[status(thm)],[])).
% 289.90/182.37 tff(4934,plain,
% 289.90/182.37 ((~![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))) | (m_cell_v_token(c_e_h_2, s0) | m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_n, s0))),
% 289.90/182.37 inference(quant_inst,[status(thm)],[])).
% 289.90/182.37 tff(4935,plain,
% 289.90/182.37 ((~![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))) | m_cell_v_token(c_e_h_2, s0) | m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_n, s0)),
% 289.90/182.37 inference(modus_ponens,[status(thm)],[4934, 4933])).
% 289.90/182.37 tff(4936,plain,
% 289.90/182.37 (m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_n, s0)),
% 289.90/182.37 inference(unit_resolution,[status(thm)],[4935, 4932, 4520])).
% 289.90/182.37 tff(4937,plain,
% 289.90/182.37 (^[I0: $i, I1: $i] : refl(((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0)) <=> ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0)))),
% 289.90/182.37 inference(bind,[status(th)],[])).
% 289.90/182.37 tff(4938,plain,
% 289.90/182.37 (![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0)) <=> ![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0))),
% 289.90/182.37 inference(quant_intro,[status(thm)],[4937])).
% 289.90/182.37 tff(4939,plain,
% 289.90/182.37 (![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0)) <=> ![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0))),
% 289.90/182.37 inference(rewrite,[status(thm)],[])).
% 289.90/182.37 tff(4940,plain,
% 289.90/182.37 (^[I0: $i, I1: $i] : rewrite((m_and_h_gate_h_init_v_out(I0, I1, s0) | (~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0))) <=> ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0)))),
% 289.90/182.37 inference(bind,[status(th)],[])).
% 289.90/182.37 tff(4941,plain,
% 289.90/182.37 (![I0: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, s0) | (~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0))) <=> ![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0))),
% 289.90/182.37 inference(quant_intro,[status(thm)],[4940])).
% 289.90/182.37 tff(4942,axiom,(![I0: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, s0) | (~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_and_h_gate_h_init_1')).
% 289.90/182.37 tff(4943,plain,
% 289.90/182.37 (![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0))),
% 289.90/182.37 inference(modus_ponens,[status(thm)],[4942, 4941])).
% 289.90/182.37 tff(4944,plain,
% 289.90/182.37 (![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0))),
% 289.90/182.37 inference(modus_ponens,[status(thm)],[4943, 4939])).
% 289.90/182.37 tff(4945,plain,(
% 289.90/182.37 ![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0))),
% 289.90/182.37 inference(skolemize,[status(sab)],[4944])).
% 289.90/182.37 tff(4946,plain,
% 289.90/182.37 (![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0))),
% 289.90/182.37 inference(modus_ponens,[status(thm)],[4945, 4938])).
% 289.90/182.37 tff(4947,plain,
% 289.90/182.37 (((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0))) | ((~m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0))) <=> ((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0))) | (~m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0))),
% 289.90/182.37 inference(rewrite,[status(thm)],[])).
% 289.90/182.37 tff(4948,plain,
% 289.90/182.37 ((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0))) | ((~m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0))),
% 289.90/182.37 inference(quant_inst,[status(thm)],[])).
% 289.90/182.37 tff(4949,plain,
% 289.90/182.37 ((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0))) | (~m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0)),
% 289.90/182.37 inference(modus_ponens,[status(thm)],[4948, 4947])).
% 289.90/182.37 tff(4950,plain,
% 289.90/182.37 ((~m_and_h_gate_h_init_v_init_h_out(c_e_h_2, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0)),
% 289.90/182.37 inference(unit_resolution,[status(thm)],[4949, 4946])).
% 289.90/182.37 tff(4951,plain,
% 289.90/182.37 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0)),
% 289.90/182.37 inference(unit_resolution,[status(thm)],[4950, 4936])).
% 289.90/182.37 tff(4952,plain,
% 289.90/182.37 (^[I0: $i, X: $i] : refl(((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X))) <=> ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X))))),
% 289.90/182.37 inference(bind,[status(th)],[])).
% 289.90/182.37 tff(4953,plain,
% 289.90/182.37 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X))) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))),
% 289.90/182.37 inference(quant_intro,[status(thm)],[4952])).
% 289.90/182.37 tff(4954,plain,
% 289.90/182.37 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X))) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))),
% 289.90/182.37 inference(rewrite,[status(thm)],[])).
% 289.90/182.37 tff(4955,axiom,(![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_54')).
% 289.90/182.37 tff(4956,plain,
% 289.90/182.37 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))),
% 289.90/182.37 inference(modus_ponens,[status(thm)],[4955, 4954])).
% 289.90/182.37 tff(4957,plain,(
% 289.90/182.37 ![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))),
% 289.90/182.37 inference(skolemize,[status(sab)],[4956])).
% 289.90/182.38 tff(4958,plain,
% 289.90/182.38 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))),
% 289.90/182.38 inference(modus_ponens,[status(thm)],[4957, 4953])).
% 289.90/182.38 tff(4959,plain,
% 289.90/182.38 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s0)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s0)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0)))),
% 289.90/182.38 inference(rewrite,[status(thm)],[])).
% 289.90/182.38 tff(4960,plain,
% 289.90/182.38 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s0)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0)))),
% 289.90/182.38 inference(quant_inst,[status(thm)],[])).
% 289.90/182.38 tff(4961,plain,
% 289.90/182.38 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s0)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0))),
% 289.90/182.38 inference(modus_ponens,[status(thm)],[4960, 4959])).
% 289.90/182.38 tff(4962,plain,
% 289.90/182.38 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s0)),
% 289.90/182.38 inference(unit_resolution,[status(thm)],[4961, 4958, 4951])).
% 289.90/182.38 tff(4963,plain,
% 289.90/182.38 (^[I0: $i, X: $i, I1: $i] : refl(((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X)) <=> ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X)))),
% 289.90/182.38 inference(bind,[status(th)],[])).
% 289.90/182.38 tff(4964,plain,
% 289.90/182.38 (![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X)) <=> ![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))),
% 289.90/182.38 inference(quant_intro,[status(thm)],[4963])).
% 289.90/182.38 tff(4965,plain,
% 289.90/182.38 (![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X)) <=> ![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))),
% 289.90/182.38 inference(rewrite,[status(thm)],[])).
% 289.90/182.38 tff(4966,plain,
% 289.90/182.38 (^[I0: $i, X: $i, I1: $i] : rewrite((m_and_h_gate_h_init_v_in2(I0, I1, X) | (~node9(I0, I1, X))) <=> ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X)))),
% 289.90/182.38 inference(bind,[status(th)],[])).
% 289.90/182.38 tff(4967,plain,
% 289.90/182.38 (![I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_in2(I0, I1, X) | (~node9(I0, I1, X))) <=> ![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))),
% 289.90/182.38 inference(quant_intro,[status(thm)],[4966])).
% 289.90/182.38 tff(4968,axiom,(![I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_in2(I0, I1, X) | (~node9(I0, I1, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_and_h_gate_h_init_4')).
% 289.90/182.38 tff(4969,plain,
% 289.90/182.38 (![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))),
% 289.90/182.38 inference(modus_ponens,[status(thm)],[4968, 4967])).
% 289.90/182.38 tff(4970,plain,
% 289.90/182.38 (![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))),
% 289.90/182.38 inference(modus_ponens,[status(thm)],[4969, 4965])).
% 289.90/182.38 tff(4971,plain,(
% 289.90/182.38 ![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))),
% 289.90/182.38 inference(skolemize,[status(sab)],[4970])).
% 289.90/182.38 tff(4972,plain,
% 289.90/182.38 (![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))),
% 289.90/182.38 inference(modus_ponens,[status(thm)],[4971, 4964])).
% 289.90/182.38 tff(4973,plain,
% 289.90/182.38 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s0)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s0)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s0))),
% 289.90/182.38 inference(rewrite,[status(thm)],[])).
% 289.90/182.38 tff(4974,plain,
% 289.90/182.38 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s0)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s0))),
% 289.90/182.38 inference(quant_inst,[status(thm)],[])).
% 289.91/182.38 tff(4975,plain,
% 289.91/182.38 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s0)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s0)),
% 289.91/182.38 inference(modus_ponens,[status(thm)],[4974, 4973])).
% 289.91/182.38 tff(4976,plain,
% 289.91/182.38 (~node9(c_e_h_2, c_m, s0)),
% 289.91/182.38 inference(unit_resolution,[status(thm)],[4975, 4972, 4962])).
% 289.91/182.38 tff(4977,plain,
% 289.91/182.38 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl((node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y))) <=> (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y))))),
% 289.91/182.38 inference(bind,[status(th)],[])).
% 289.91/182.38 tff(4978,plain,
% 289.91/182.38 (![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))),
% 289.91/182.38 inference(quant_intro,[status(thm)],[4977])).
% 289.91/182.38 tff(4979,plain,
% 289.91/182.38 (![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))),
% 289.91/182.38 inference(rewrite,[status(thm)],[])).
% 289.91/182.38 tff(4980,plain,
% 289.91/182.38 (^[Y: $i, I0: $i, X: $i, I1: $i] : rewrite((((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | node9(I0, I1, X)) | (~node10(I0, I1, X, Y))) <=> (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y))))),
% 289.91/182.38 inference(bind,[status(th)],[])).
% 289.91/182.38 tff(4981,plain,
% 289.91/182.38 (![Y: $i, I0: $i, X: $i, I1: $i] : (((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | node9(I0, I1, X)) | (~node10(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))),
% 289.91/182.38 inference(quant_intro,[status(thm)],[4980])).
% 289.91/182.38 tff(4982,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : (((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | node9(I0, I1, X)) | (~node10(I0, I1, X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_and_h_gate_h_init_6')).
% 289.91/182.38 tff(4983,plain,
% 289.91/182.38 (![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))),
% 289.91/182.38 inference(modus_ponens,[status(thm)],[4982, 4981])).
% 289.91/182.38 tff(4984,plain,
% 289.91/182.38 (![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))),
% 289.91/182.38 inference(modus_ponens,[status(thm)],[4983, 4979])).
% 289.91/182.38 tff(4985,plain,(
% 289.91/182.38 ![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))),
% 289.91/182.38 inference(skolemize,[status(sab)],[4984])).
% 289.91/182.38 tff(4986,plain,
% 289.91/182.38 (![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))),
% 289.91/182.38 inference(modus_ponens,[status(thm)],[4985, 4978])).
% 289.91/182.38 tff(4987,plain,
% 289.91/182.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s0) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)) | (~node10(c_e_h_2, c_m, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_2, c_m, s0) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)) | (~node10(c_e_h_2, c_m, s0, s1)))),
% 289.91/182.38 inference(rewrite,[status(thm)],[])).
% 289.91/182.38 tff(4988,plain,
% 289.91/182.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s0) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)) | (~node10(c_e_h_2, c_m, s0, s1)))),
% 289.91/182.38 inference(quant_inst,[status(thm)],[])).
% 289.91/182.38 tff(4989,plain,
% 289.91/182.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_2, c_m, s0) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)) | (~node10(c_e_h_2, c_m, s0, s1))),
% 289.91/182.38 inference(modus_ponens,[status(thm)],[4988, 4987])).
% 289.91/182.38 tff(4990,plain,
% 289.91/182.38 ($false),
% 289.91/182.38 inference(unit_resolution,[status(thm)],[4989, 4986, 4976, 4921, 4922])).
% 289.91/182.38 tff(4991,plain,((~node10(c_e_h_2, c_m, s0, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1))), inference(lemma,lemma(discharge,[]))).
% 289.91/182.38 tff(4992,plain,
% 289.91/182.38 (~node10(c_e_h_2, c_m, s0, s1)),
% 289.91/182.38 inference(unit_resolution,[status(thm)],[4991, 4921])).
% 289.91/182.38 tff(4993,plain,
% 289.91/182.38 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl(((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y)) <=> ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y)))),
% 289.91/182.38 inference(bind,[status(th)],[])).
% 289.91/182.38 tff(4994,plain,
% 289.91/182.38 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))),
% 289.91/182.38 inference(quant_intro,[status(thm)],[4993])).
% 289.91/182.38 tff(4995,plain,
% 289.91/182.38 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))),
% 289.91/182.38 inference(rewrite,[status(thm)],[])).
% 289.91/182.38 tff(4996,plain,
% 289.91/182.38 (^[Y: $i, I0: $i, X: $i, I1: $i] : rewrite(((node10(I0, I1, X, Y) | node11(I0, I1, X, Y)) | (~trans(X, Y))) <=> ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y)))),
% 289.91/182.38 inference(bind,[status(th)],[])).
% 289.91/182.38 tff(4997,plain,
% 289.91/182.38 (![Y: $i, I0: $i, X: $i, I1: $i] : ((node10(I0, I1, X, Y) | node11(I0, I1, X, Y)) | (~trans(X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))),
% 289.91/182.38 inference(quant_intro,[status(thm)],[4996])).
% 289.91/182.38 tff(4998,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : ((node10(I0, I1, X, Y) | node11(I0, I1, X, Y)) | (~trans(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_and_h_gate_h_init_9')).
% 289.91/182.38 tff(4999,plain,
% 289.91/182.38 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))),
% 289.91/182.38 inference(modus_ponens,[status(thm)],[4998, 4997])).
% 289.91/182.38 tff(5000,plain,
% 289.91/182.38 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))),
% 289.91/182.38 inference(modus_ponens,[status(thm)],[4999, 4995])).
% 289.91/182.38 tff(5001,plain,(
% 289.91/182.38 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))),
% 289.91/182.38 inference(skolemize,[status(sab)],[5000])).
% 289.91/182.38 tff(5002,plain,
% 289.91/182.38 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))),
% 289.91/182.38 inference(modus_ponens,[status(thm)],[5001, 4994])).
% 289.91/182.38 tff(5003,plain,
% 289.91/182.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s0, s1)) | node10(c_e_h_2, c_m, s0, s1) | node11(c_e_h_2, c_m, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s0, s1)) | node10(c_e_h_2, c_m, s0, s1) | node11(c_e_h_2, c_m, s0, s1))),
% 289.91/182.38 inference(rewrite,[status(thm)],[])).
% 289.91/182.38 tff(5004,plain,
% 289.91/182.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s0, s1)) | node10(c_e_h_2, c_m, s0, s1) | node11(c_e_h_2, c_m, s0, s1))),
% 289.91/182.38 inference(quant_inst,[status(thm)],[])).
% 289.91/182.38 tff(5005,plain,
% 289.91/182.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s0, s1)) | node10(c_e_h_2, c_m, s0, s1) | node11(c_e_h_2, c_m, s0, s1)),
% 289.91/182.38 inference(modus_ponens,[status(thm)],[5004, 5003])).
% 289.91/182.38 tff(5006,plain,
% 289.91/182.38 (node10(c_e_h_2, c_m, s0, s1) | node11(c_e_h_2, c_m, s0, s1)),
% 289.91/182.38 inference(unit_resolution,[status(thm)],[5005, 5002, 72])).
% 289.91/182.38 tff(5007,plain,
% 289.91/182.38 (node11(c_e_h_2, c_m, s0, s1)),
% 289.91/182.38 inference(unit_resolution,[status(thm)],[5006, 4992])).
% 289.91/182.38 tff(5008,plain,
% 289.91/182.38 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl(((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X)) <=> ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X)))),
% 289.91/182.38 inference(bind,[status(th)],[])).
% 289.91/182.38 tff(5009,plain,
% 289.91/182.38 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))),
% 289.91/182.38 inference(quant_intro,[status(thm)],[5008])).
% 289.91/182.38 tff(5010,plain,
% 289.91/182.38 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))),
% 289.91/182.38 inference(rewrite,[status(thm)],[])).
% 289.91/182.38 tff(5011,plain,
% 289.91/182.38 (^[Y: $i, I0: $i, X: $i, I1: $i] : rewrite((((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X)) | (~node11(I0, I1, X, Y))) <=> ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X)))),
% 289.91/182.38 inference(bind,[status(th)],[])).
% 289.91/182.38 tff(5012,plain,
% 289.91/182.38 (![Y: $i, I0: $i, X: $i, I1: $i] : (((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X)) | (~node11(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))),
% 289.91/182.38 inference(quant_intro,[status(thm)],[5011])).
% 289.91/182.38 tff(5013,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : (((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X)) | (~node11(I0, I1, X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_and_h_gate_h_init_8')).
% 289.91/182.38 tff(5014,plain,
% 289.91/182.38 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))),
% 289.91/182.38 inference(modus_ponens,[status(thm)],[5013, 5012])).
% 289.91/182.38 tff(5015,plain,
% 289.91/182.38 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))),
% 289.91/182.38 inference(modus_ponens,[status(thm)],[5014, 5010])).
% 289.91/182.38 tff(5016,plain,(
% 289.91/182.38 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))),
% 289.91/182.38 inference(skolemize,[status(sab)],[5015])).
% 289.91/182.38 tff(5017,plain,
% 289.91/182.38 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))),
% 289.91/182.38 inference(modus_ponens,[status(thm)],[5016, 5009])).
% 289.91/182.38 tff(5018,plain,
% 289.91/182.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)) | (~node11(c_e_h_2, c_m, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)) | (~node11(c_e_h_2, c_m, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0))),
% 289.91/182.38 inference(rewrite,[status(thm)],[])).
% 289.91/182.38 tff(5019,plain,
% 289.91/182.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)) | (~node11(c_e_h_2, c_m, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0))),
% 289.91/182.38 inference(quant_inst,[status(thm)],[])).
% 289.91/182.38 tff(5020,plain,
% 289.91/182.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)) | (~node11(c_e_h_2, c_m, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0)),
% 289.91/182.38 inference(modus_ponens,[status(thm)],[5019, 5018])).
% 289.91/182.38 tff(5021,plain,
% 289.91/182.38 ($false),
% 289.91/182.38 inference(unit_resolution,[status(thm)],[5020, 5017, 4542, 4921, 5007])).
% 289.91/182.38 tff(5022,plain,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)), inference(lemma,lemma(discharge,[]))).
% 289.91/182.38 tff(5023,plain,
% 289.91/182.38 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_l, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_l, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1))),
% 289.91/182.39 inference(rewrite,[status(thm)],[])).
% 289.91/182.39 tff(5024,plain,
% 289.91/182.39 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_l, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1))),
% 289.91/182.39 inference(quant_inst,[status(thm)],[])).
% 289.91/182.39 tff(5025,plain,
% 289.91/182.39 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_l, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)),
% 289.91/182.39 inference(modus_ponens,[status(thm)],[5024, 5023])).
% 289.91/182.39 tff(5026,plain,
% 289.91/182.39 (~m_and_h_gate_v_in2(c_e_h_2, c_l, s1)),
% 289.91/182.39 inference(unit_resolution,[status(thm)],[5025, 4549, 5022])).
% 289.91/182.39 tff(5027,plain,
% 289.91/182.39 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_l, s1)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_l, s1)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s1))),
% 289.91/182.39 inference(rewrite,[status(thm)],[])).
% 289.91/182.39 tff(5028,plain,
% 289.91/182.39 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_l, s1)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s1))),
% 289.91/182.39 inference(quant_inst,[status(thm)],[])).
% 289.91/182.39 tff(5029,plain,
% 289.91/182.39 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_l, s1)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s1)),
% 289.91/182.39 inference(modus_ponens,[status(thm)],[5028, 5027])).
% 289.91/182.39 tff(5030,plain,
% 289.91/182.39 (~node20(c_e_h_2, c_l, s1)),
% 289.91/182.39 inference(unit_resolution,[status(thm)],[5029, 4563, 5026])).
% 289.91/182.39 tff(5031,plain,
% 289.91/182.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_l, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s2)) | (~node21(c_e_h_2, c_l, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_l, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s2)) | (~node21(c_e_h_2, c_l, s1, s2)))),
% 289.91/182.39 inference(rewrite,[status(thm)],[])).
% 289.91/182.39 tff(5032,plain,
% 289.91/182.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_l, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s2)) | (~node21(c_e_h_2, c_l, s1, s2)))),
% 289.91/182.39 inference(quant_inst,[status(thm)],[])).
% 289.91/182.39 tff(5033,plain,
% 289.91/182.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_l, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s2)) | (~node21(c_e_h_2, c_l, s1, s2))),
% 289.91/182.39 inference(modus_ponens,[status(thm)],[5032, 5031])).
% 289.91/182.39 tff(5034,plain,
% 289.91/182.39 ($false),
% 289.91/182.39 inference(unit_resolution,[status(thm)],[5033, 52, 5030, 4920, 4908])).
% 289.91/182.39 tff(5035,plain,(~m_and_h_gate_v_out(c_e_h_2, c_l, s2)), inference(lemma,lemma(discharge,[]))).
% 289.91/182.39 tff(5036,plain,
% 289.91/182.39 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_2, c_j, s2)) | m_and_h_gate_v_out(c_e_h_2, c_l, s2))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_j, s2)) | m_and_h_gate_v_out(c_e_h_2, c_l, s2))),
% 289.91/182.39 inference(rewrite,[status(thm)],[])).
% 289.91/182.39 tff(5037,plain,
% 289.91/182.39 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_2, c_j, s2)) | m_and_h_gate_v_out(c_e_h_2, c_l, s2))),
% 289.91/182.39 inference(quant_inst,[status(thm)],[])).
% 289.91/182.39 tff(5038,plain,
% 289.91/182.39 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_j, s2)) | m_and_h_gate_v_out(c_e_h_2, c_l, s2)),
% 289.91/182.39 inference(modus_ponens,[status(thm)],[5037, 5036])).
% 289.91/182.39 tff(5039,plain,
% 289.91/182.39 (~m_or_h_gate_v_in1(c_e_h_2, c_j, s2)),
% 289.91/182.39 inference(unit_resolution,[status(thm)],[5038, 1100, 5035])).
% 289.91/182.39 tff(5040,assumption,(m_c_h_element_v_out(c_e_h_1, c_f, s1)), introduced(assumption)).
% 289.91/182.39 tff(5041,assumption,(m_and_h_gate_v_out(c_e_h_1, c_d, s0)), introduced(assumption)).
% 289.91/182.39 tff(5042,plain,
% 289.91/182.39 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s0))),
% 289.91/182.39 inference(quant_inst,[status(thm)],[])).
% 289.91/182.39 tff(5043,plain,
% 289.91/182.39 ($false),
% 289.91/182.39 inference(unit_resolution,[status(thm)],[5042, 95, 5041])).
% 289.91/182.39 tff(5044,plain,(~m_and_h_gate_v_out(c_e_h_1, c_d, s0)), inference(lemma,lemma(discharge,[]))).
% 289.91/182.39 tff(5045,plain,
% 289.91/182.39 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s0)) | m_and_h_gate_v_out(c_e_h_1, c_d, s0))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s0)) | m_and_h_gate_v_out(c_e_h_1, c_d, s0))),
% 289.91/182.39 inference(rewrite,[status(thm)],[])).
% 289.91/182.39 tff(5046,plain,
% 289.91/182.39 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s0)) | m_and_h_gate_v_out(c_e_h_1, c_d, s0))),
% 289.91/182.39 inference(quant_inst,[status(thm)],[])).
% 289.91/182.39 tff(5047,plain,
% 289.91/182.39 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s0)) | m_and_h_gate_v_out(c_e_h_1, c_d, s0)),
% 289.91/182.39 inference(modus_ponens,[status(thm)],[5046, 5045])).
% 289.91/182.39 tff(5048,plain,
% 289.91/182.39 (~m_c_h_element_v_in1(c_e_h_1, c_f, s0)),
% 289.91/182.39 inference(unit_resolution,[status(thm)],[5047, 2116, 5044])).
% 289.91/182.39 tff(5049,assumption,(node14(c_e_h_1, c_f, s0, s1)), introduced(assumption)).
% 289.91/182.39 tff(5050,plain,
% 289.91/182.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s1)) | (~node14(c_e_h_1, c_f, s0, s1)) | m_c_h_element_v_in1(c_e_h_1, c_f, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s1)) | (~node14(c_e_h_1, c_f, s0, s1)) | m_c_h_element_v_in1(c_e_h_1, c_f, s0))),
% 289.91/182.39 inference(rewrite,[status(thm)],[])).
% 289.91/182.39 tff(5051,plain,
% 289.91/182.39 (((~node14(c_e_h_1, c_f, s0, s1)) | m_c_h_element_v_in1(c_e_h_1, c_f, s0) | (~m_c_h_element_v_out(c_e_h_1, c_f, s1))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_f, s1)) | (~node14(c_e_h_1, c_f, s0, s1)) | m_c_h_element_v_in1(c_e_h_1, c_f, s0))),
% 289.91/182.39 inference(rewrite,[status(thm)],[])).
% 289.91/182.39 tff(5052,plain,
% 289.91/182.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s0, s1)) | m_c_h_element_v_in1(c_e_h_1, c_f, s0) | (~m_c_h_element_v_out(c_e_h_1, c_f, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s1)) | (~node14(c_e_h_1, c_f, s0, s1)) | m_c_h_element_v_in1(c_e_h_1, c_f, s0)))),
% 289.91/182.39 inference(monotonicity,[status(thm)],[5051])).
% 289.91/182.39 tff(5053,plain,
% 289.91/182.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s0, s1)) | m_c_h_element_v_in1(c_e_h_1, c_f, s0) | (~m_c_h_element_v_out(c_e_h_1, c_f, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s1)) | (~node14(c_e_h_1, c_f, s0, s1)) | m_c_h_element_v_in1(c_e_h_1, c_f, s0))),
% 289.91/182.39 inference(transitivity,[status(thm)],[5052, 5050])).
% 289.91/182.39 tff(5054,plain,
% 289.91/182.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s0, s1)) | m_c_h_element_v_in1(c_e_h_1, c_f, s0) | (~m_c_h_element_v_out(c_e_h_1, c_f, s1)))),
% 289.91/182.39 inference(quant_inst,[status(thm)],[])).
% 289.91/182.39 tff(5055,plain,
% 289.91/182.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s1)) | (~node14(c_e_h_1, c_f, s0, s1)) | m_c_h_element_v_in1(c_e_h_1, c_f, s0)),
% 289.91/182.39 inference(modus_ponens,[status(thm)],[5054, 5053])).
% 289.91/182.39 tff(5056,plain,
% 289.91/182.39 ($false),
% 289.91/182.39 inference(unit_resolution,[status(thm)],[5055, 223, 5040, 5049, 5048])).
% 289.91/182.39 tff(5057,plain,((~node14(c_e_h_1, c_f, s0, s1)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s1))), inference(lemma,lemma(discharge,[]))).
% 289.91/182.39 tff(5058,plain,
% 289.91/182.39 (~node14(c_e_h_1, c_f, s0, s1)),
% 289.91/182.39 inference(unit_resolution,[status(thm)],[5057, 5040])).
% 289.91/182.39 tff(5059,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s0)), introduced(assumption)).
% 289.91/182.39 tff(5060,plain,
% 289.91/182.39 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s0))),
% 289.91/182.39 inference(quant_inst,[status(thm)],[])).
% 289.91/182.39 tff(5061,plain,
% 289.91/182.39 ($false),
% 289.91/182.39 inference(unit_resolution,[status(thm)],[5060, 95, 5059])).
% 289.91/182.39 tff(5062,plain,(~m_and_h_gate_v_out(c_e_h_1, c_i, s0)), inference(lemma,lemma(discharge,[]))).
% 289.91/182.39 tff(5063,plain,
% 289.91/182.39 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s0)) | m_and_h_gate_v_out(c_e_h_1, c_i, s0))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s0)) | m_and_h_gate_v_out(c_e_h_1, c_i, s0))),
% 289.91/182.39 inference(rewrite,[status(thm)],[])).
% 289.91/182.39 tff(5064,plain,
% 289.91/182.39 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s0)) | m_and_h_gate_v_out(c_e_h_1, c_i, s0))),
% 289.91/182.39 inference(quant_inst,[status(thm)],[])).
% 289.91/182.39 tff(5065,plain,
% 289.91/182.39 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s0)) | m_and_h_gate_v_out(c_e_h_1, c_i, s0)),
% 289.91/182.39 inference(modus_ponens,[status(thm)],[5064, 5063])).
% 289.91/182.39 tff(5066,plain,
% 289.91/182.39 (~m_c_h_element_v_in2(c_e_h_1, c_f, s0)),
% 289.91/182.39 inference(unit_resolution,[status(thm)],[5065, 2143, 5062])).
% 289.91/182.39 tff(5067,plain,
% 289.91/182.39 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s0)) | m_c_h_element_v_in1(c_e_h_1, c_f, s0) | m_c_h_element_v_in2(c_e_h_1, c_f, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s0)) | m_c_h_element_v_in1(c_e_h_1, c_f, s0) | m_c_h_element_v_in2(c_e_h_1, c_f, s0))),
% 289.91/182.39 inference(rewrite,[status(thm)],[])).
% 289.91/182.39 tff(5068,plain,
% 289.91/182.39 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s0)) | m_c_h_element_v_in1(c_e_h_1, c_f, s0) | m_c_h_element_v_in2(c_e_h_1, c_f, s0))),
% 289.91/182.39 inference(quant_inst,[status(thm)],[])).
% 289.91/182.39 tff(5069,plain,
% 289.91/182.39 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s0)) | m_c_h_element_v_in1(c_e_h_1, c_f, s0) | m_c_h_element_v_in2(c_e_h_1, c_f, s0)),
% 289.91/182.39 inference(modus_ponens,[status(thm)],[5068, 5067])).
% 289.91/182.39 tff(5070,plain,
% 289.91/182.39 ((~node16(c_e_h_1, c_f, s0)) | m_c_h_element_v_in1(c_e_h_1, c_f, s0)),
% 289.91/182.39 inference(unit_resolution,[status(thm)],[5069, 178, 5066])).
% 289.91/182.39 tff(5071,plain,
% 289.91/182.39 (~node16(c_e_h_1, c_f, s0)),
% 289.91/182.39 inference(unit_resolution,[status(thm)],[5070, 5048])).
% 289.91/182.39 tff(5072,plain,
% 289.91/182.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s0, s1)) | node19(c_e_h_1, c_f, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s0, s1)) | node19(c_e_h_1, c_f, s0, s1))),
% 289.91/182.39 inference(rewrite,[status(thm)],[])).
% 289.91/182.39 tff(5073,plain,
% 289.91/182.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s0, s1)) | node19(c_e_h_1, c_f, s0, s1))),
% 289.91/182.40 inference(quant_inst,[status(thm)],[])).
% 289.91/182.40 tff(5074,plain,
% 289.91/182.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s0, s1)) | node19(c_e_h_1, c_f, s0, s1)),
% 289.91/182.40 inference(modus_ponens,[status(thm)],[5073, 5072])).
% 289.91/182.40 tff(5075,plain,
% 289.91/182.40 (node19(c_e_h_1, c_f, s0, s1)),
% 289.91/182.40 inference(unit_resolution,[status(thm)],[5074, 190, 72])).
% 289.91/182.40 tff(5076,plain,
% 289.91/182.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_1, c_f, s0, s1) | (~node19(c_e_h_1, c_f, s0, s1)) | node14(c_e_h_1, c_f, s0, s1) | node16(c_e_h_1, c_f, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_f, s0, s1) | (~node19(c_e_h_1, c_f, s0, s1)) | node14(c_e_h_1, c_f, s0, s1) | node16(c_e_h_1, c_f, s0))),
% 289.91/182.40 inference(rewrite,[status(thm)],[])).
% 289.91/182.40 tff(5077,plain,
% 289.91/182.40 ((node16(c_e_h_1, c_f, s0) | node14(c_e_h_1, c_f, s0, s1) | node15(c_e_h_1, c_f, s0, s1) | (~node19(c_e_h_1, c_f, s0, s1))) <=> (node15(c_e_h_1, c_f, s0, s1) | (~node19(c_e_h_1, c_f, s0, s1)) | node14(c_e_h_1, c_f, s0, s1) | node16(c_e_h_1, c_f, s0))),
% 289.91/182.40 inference(rewrite,[status(thm)],[])).
% 289.91/182.40 tff(5078,plain,
% 289.91/182.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s0) | node14(c_e_h_1, c_f, s0, s1) | node15(c_e_h_1, c_f, s0, s1) | (~node19(c_e_h_1, c_f, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_1, c_f, s0, s1) | (~node19(c_e_h_1, c_f, s0, s1)) | node14(c_e_h_1, c_f, s0, s1) | node16(c_e_h_1, c_f, s0)))),
% 289.91/182.40 inference(monotonicity,[status(thm)],[5077])).
% 289.91/182.40 tff(5079,plain,
% 289.91/182.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s0) | node14(c_e_h_1, c_f, s0, s1) | node15(c_e_h_1, c_f, s0, s1) | (~node19(c_e_h_1, c_f, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_f, s0, s1) | (~node19(c_e_h_1, c_f, s0, s1)) | node14(c_e_h_1, c_f, s0, s1) | node16(c_e_h_1, c_f, s0))),
% 289.91/182.40 inference(transitivity,[status(thm)],[5078, 5076])).
% 289.91/182.40 tff(5080,plain,
% 289.91/182.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s0) | node14(c_e_h_1, c_f, s0, s1) | node15(c_e_h_1, c_f, s0, s1) | (~node19(c_e_h_1, c_f, s0, s1)))),
% 289.91/182.40 inference(quant_inst,[status(thm)],[])).
% 289.91/182.40 tff(5081,plain,
% 289.91/182.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_f, s0, s1) | (~node19(c_e_h_1, c_f, s0, s1)) | node14(c_e_h_1, c_f, s0, s1) | node16(c_e_h_1, c_f, s0)),
% 289.91/182.40 inference(modus_ponens,[status(thm)],[5080, 5079])).
% 289.91/182.40 tff(5082,plain,
% 289.91/182.40 (node15(c_e_h_1, c_f, s0, s1) | node14(c_e_h_1, c_f, s0, s1) | node16(c_e_h_1, c_f, s0)),
% 289.91/182.40 inference(unit_resolution,[status(thm)],[5081, 204, 5075])).
% 289.91/182.40 tff(5083,plain,
% 289.91/182.40 (node15(c_e_h_1, c_f, s0, s1) | node14(c_e_h_1, c_f, s0, s1)),
% 289.91/182.40 inference(unit_resolution,[status(thm)],[5082, 5071])).
% 289.91/182.40 tff(5084,plain,
% 289.91/182.40 (node15(c_e_h_1, c_f, s0, s1)),
% 289.91/182.40 inference(unit_resolution,[status(thm)],[5083, 5058])).
% 289.91/182.40 tff(5085,plain,
% 289.91/182.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s1)) | (~node15(c_e_h_1, c_f, s0, s1)) | m_c_h_element_v_out(c_e_h_1, c_f, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s1)) | (~node15(c_e_h_1, c_f, s0, s1)) | m_c_h_element_v_out(c_e_h_1, c_f, s0))),
% 289.91/182.40 inference(rewrite,[status(thm)],[])).
% 289.91/182.40 tff(5086,plain,
% 289.91/182.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s1)) | (~node15(c_e_h_1, c_f, s0, s1)) | m_c_h_element_v_out(c_e_h_1, c_f, s0))),
% 289.91/182.40 inference(quant_inst,[status(thm)],[])).
% 289.91/182.40 tff(5087,plain,
% 289.91/182.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s1)) | (~node15(c_e_h_1, c_f, s0, s1)) | m_c_h_element_v_out(c_e_h_1, c_f, s0)),
% 289.91/182.40 inference(modus_ponens,[status(thm)],[5086, 5085])).
% 289.91/182.40 tff(5088,plain,
% 289.91/182.40 ($false),
% 289.91/182.40 inference(unit_resolution,[status(thm)],[5087, 147, 5040, 4583, 5084])).
% 289.91/182.40 tff(5089,plain,(~m_c_h_element_v_out(c_e_h_1, c_f, s1)), inference(lemma,lemma(discharge,[]))).
% 289.91/182.40 tff(5090,plain,
% 289.91/182.40 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s1)) | m_c_h_element_v_out(c_e_h_1, c_f, s1))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s1)) | m_c_h_element_v_out(c_e_h_1, c_f, s1))),
% 289.91/182.40 inference(rewrite,[status(thm)],[])).
% 289.91/182.40 tff(5091,plain,
% 289.91/182.40 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s1)) | m_c_h_element_v_out(c_e_h_1, c_f, s1))),
% 289.91/182.40 inference(quant_inst,[status(thm)],[])).
% 289.91/182.40 tff(5092,plain,
% 289.91/182.40 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s1)) | m_c_h_element_v_out(c_e_h_1, c_f, s1)),
% 289.91/182.40 inference(modus_ponens,[status(thm)],[5091, 5090])).
% 289.91/182.40 tff(5093,plain,
% 289.91/182.40 (~m_and_h_gate_v_in1(c_e_h_1, c_q, s1)),
% 289.91/182.40 inference(unit_resolution,[status(thm)],[5092, 1586, 5089])).
% 289.91/182.40 tff(5094,plain,
% 289.91/182.40 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s1)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s1)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s1))),
% 289.91/182.40 inference(rewrite,[status(thm)],[])).
% 289.91/182.40 tff(5095,plain,
% 289.91/182.40 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s1)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s1))),
% 289.91/182.40 inference(quant_inst,[status(thm)],[])).
% 289.91/182.40 tff(5096,plain,
% 289.91/182.40 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s1)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s1)),
% 289.91/182.40 inference(modus_ponens,[status(thm)],[5095, 5094])).
% 289.91/182.40 tff(5097,plain,
% 289.91/182.40 (~node20(c_e_h_1, c_q, s1)),
% 289.91/182.40 inference(unit_resolution,[status(thm)],[5096, 38, 5093])).
% 289.91/182.40 tff(5098,assumption,(~node20(c_e_h_1, c_q, s1)), introduced(assumption)).
% 289.91/182.40 tff(5099,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_q, s1)), introduced(assumption)).
% 289.91/182.40 tff(5100,assumption,(m_and_h_gate_v_out(c_e_h_1, c_q, s2)), introduced(assumption)).
% 289.91/182.40 tff(5101,assumption,(node22(c_e_h_1, c_q, s1, s2)), introduced(assumption)).
% 289.91/182.40 tff(5102,plain,
% 289.91/182.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s2)) | (~node22(c_e_h_1, c_q, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_q, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s2)) | (~node22(c_e_h_1, c_q, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_q, s1))),
% 289.91/182.40 inference(rewrite,[status(thm)],[])).
% 289.91/182.40 tff(5103,plain,
% 289.91/182.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s2)) | (~node22(c_e_h_1, c_q, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_q, s1))),
% 289.91/182.40 inference(quant_inst,[status(thm)],[])).
% 289.94/182.40 tff(5104,plain,
% 289.94/182.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s2)) | (~node22(c_e_h_1, c_q, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_q, s1)),
% 289.94/182.40 inference(modus_ponens,[status(thm)],[5103, 5102])).
% 289.94/182.40 tff(5105,plain,
% 289.94/182.40 ($false),
% 289.94/182.40 inference(unit_resolution,[status(thm)],[5104, 108, 5099, 5100, 5101])).
% 289.94/182.40 tff(5106,plain,((~node22(c_e_h_1, c_q, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_q, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s2))), inference(lemma,lemma(discharge,[]))).
% 289.94/182.40 tff(5107,plain,
% 289.94/182.40 (~node22(c_e_h_1, c_q, s1, s2)),
% 289.94/182.40 inference(unit_resolution,[status(thm)],[5106, 5100, 5099])).
% 289.94/182.40 tff(5108,plain,
% 289.94/182.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_1, c_q, s1, s2) | node22(c_e_h_1, c_q, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_1, c_q, s1, s2) | node22(c_e_h_1, c_q, s1, s2))),
% 289.94/182.40 inference(rewrite,[status(thm)],[])).
% 289.94/182.40 tff(5109,plain,
% 289.94/182.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_1, c_q, s1, s2) | node22(c_e_h_1, c_q, s1, s2))),
% 289.94/182.40 inference(quant_inst,[status(thm)],[])).
% 289.94/182.40 tff(5110,plain,
% 289.94/182.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_1, c_q, s1, s2) | node22(c_e_h_1, c_q, s1, s2)),
% 289.94/182.40 inference(modus_ponens,[status(thm)],[5109, 5108])).
% 289.94/182.40 tff(5111,plain,
% 289.94/182.40 (node21(c_e_h_1, c_q, s1, s2) | node22(c_e_h_1, c_q, s1, s2)),
% 289.94/182.40 inference(unit_resolution,[status(thm)],[5110, 82, 255])).
% 289.94/182.40 tff(5112,plain,
% 289.94/182.40 (node21(c_e_h_1, c_q, s1, s2)),
% 289.94/182.40 inference(unit_resolution,[status(thm)],[5111, 5107])).
% 289.94/182.40 tff(5113,plain,
% 289.94/182.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s2)) | node20(c_e_h_1, c_q, s1) | (~node21(c_e_h_1, c_q, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s2)) | node20(c_e_h_1, c_q, s1) | (~node21(c_e_h_1, c_q, s1, s2)))),
% 289.94/182.40 inference(rewrite,[status(thm)],[])).
% 289.94/182.40 tff(5114,plain,
% 289.94/182.40 ((node20(c_e_h_1, c_q, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s2)) | (~node21(c_e_h_1, c_q, s1, s2))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_q, s2)) | node20(c_e_h_1, c_q, s1) | (~node21(c_e_h_1, c_q, s1, s2)))),
% 289.94/182.40 inference(rewrite,[status(thm)],[])).
% 289.94/182.40 tff(5115,plain,
% 289.94/182.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s2)) | (~node21(c_e_h_1, c_q, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s2)) | node20(c_e_h_1, c_q, s1) | (~node21(c_e_h_1, c_q, s1, s2))))),
% 289.94/182.40 inference(monotonicity,[status(thm)],[5114])).
% 289.94/182.40 tff(5116,plain,
% 289.94/182.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s2)) | (~node21(c_e_h_1, c_q, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s2)) | node20(c_e_h_1, c_q, s1) | (~node21(c_e_h_1, c_q, s1, s2)))),
% 289.94/182.40 inference(transitivity,[status(thm)],[5115, 5113])).
% 289.94/182.40 tff(5117,plain,
% 289.94/182.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s2)) | (~node21(c_e_h_1, c_q, s1, s2)))),
% 289.94/182.40 inference(quant_inst,[status(thm)],[])).
% 289.94/182.40 tff(5118,plain,
% 289.94/182.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s2)) | node20(c_e_h_1, c_q, s1) | (~node21(c_e_h_1, c_q, s1, s2))),
% 289.94/182.41 inference(modus_ponens,[status(thm)],[5117, 5116])).
% 289.94/182.41 tff(5119,plain,
% 289.94/182.41 ($false),
% 289.94/182.41 inference(unit_resolution,[status(thm)],[5118, 52, 5100, 5112, 5098])).
% 289.94/182.41 tff(5120,plain,((~m_and_h_gate_v_out(c_e_h_1, c_q, s2)) | node20(c_e_h_1, c_q, s1) | m_and_h_gate_v_out(c_e_h_1, c_q, s1)), inference(lemma,lemma(discharge,[]))).
% 289.94/182.41 tff(5121,plain,
% 289.94/182.41 ((~m_and_h_gate_v_out(c_e_h_1, c_q, s2)) | node20(c_e_h_1, c_q, s1)),
% 289.94/182.41 inference(unit_resolution,[status(thm)],[5120, 4609])).
% 289.94/182.41 tff(5122,plain,
% 289.94/182.41 (~m_and_h_gate_v_out(c_e_h_1, c_q, s2)),
% 289.94/182.41 inference(unit_resolution,[status(thm)],[5121, 5097])).
% 289.94/182.41 tff(5123,plain,
% 289.94/182.41 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s2))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s2))),
% 289.94/182.41 inference(rewrite,[status(thm)],[])).
% 289.94/182.41 tff(5124,plain,
% 289.94/182.41 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s2))),
% 289.94/182.41 inference(quant_inst,[status(thm)],[])).
% 289.94/182.41 tff(5125,plain,
% 289.94/182.41 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s2)),
% 289.94/182.41 inference(modus_ponens,[status(thm)],[5124, 5123])).
% 289.94/182.41 tff(5126,plain,
% 289.94/182.41 (node3(c_e_h_1, c_e_h_2, s2)),
% 289.94/182.41 inference(unit_resolution,[status(thm)],[5125, 4166, 1056])).
% 289.94/182.41 tff(5127,plain,
% 289.94/182.41 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s2)) | (~node3(c_e_h_1, c_e_h_2, s2)) | m_and_h_gate_v_out(c_e_h_1, c_q, s2))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s2)) | (~node3(c_e_h_1, c_e_h_2, s2)) | m_and_h_gate_v_out(c_e_h_1, c_q, s2))),
% 289.94/182.41 inference(rewrite,[status(thm)],[])).
% 289.94/182.41 tff(5128,plain,
% 289.94/182.41 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s2)) | (~node3(c_e_h_1, c_e_h_2, s2)) | m_and_h_gate_v_out(c_e_h_1, c_q, s2))),
% 289.94/182.41 inference(quant_inst,[status(thm)],[])).
% 289.94/182.41 tff(5129,plain,
% 289.94/182.41 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s2)) | (~node3(c_e_h_1, c_e_h_2, s2)) | m_and_h_gate_v_out(c_e_h_1, c_q, s2)),
% 289.94/182.41 inference(modus_ponens,[status(thm)],[5128, 5127])).
% 289.94/182.41 tff(5130,plain,
% 289.94/182.41 ((~m_cell_v_ack(c_e_h_2, s2)) | m_and_h_gate_v_out(c_e_h_1, c_q, s2)),
% 289.94/182.41 inference(unit_resolution,[status(thm)],[5129, 1073, 5126])).
% 289.94/182.41 tff(5131,plain,
% 289.94/182.41 (~m_cell_v_ack(c_e_h_2, s2)),
% 289.94/182.41 inference(unit_resolution,[status(thm)],[5130, 5122])).
% 289.94/182.41 tff(5132,plain,
% 289.94/182.41 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s2)) | m_cell_v_ack(c_e_h_2, s2))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s2)) | m_cell_v_ack(c_e_h_2, s2))),
% 289.94/182.41 inference(rewrite,[status(thm)],[])).
% 289.94/182.41 tff(5133,plain,
% 289.94/182.41 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s2)) | m_cell_v_ack(c_e_h_2, s2))),
% 289.94/182.41 inference(quant_inst,[status(thm)],[])).
% 289.94/182.41 tff(5134,plain,
% 289.94/182.41 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s2)) | m_cell_v_ack(c_e_h_2, s2)),
% 289.94/182.41 inference(modus_ponens,[status(thm)],[5133, 5132])).
% 289.94/182.41 tff(5135,plain,
% 289.94/182.41 (~m_or_h_gate_v_in2(c_e_h_2, c_j, s2)),
% 289.94/182.41 inference(unit_resolution,[status(thm)],[5134, 1085, 5131])).
% 289.94/182.41 tff(5136,assumption,(m_or_h_gate_v_out(c_e_h_2, c_j, s3)), introduced(assumption)).
% 289.94/182.41 tff(5137,assumption,(node6(c_e_h_2, c_j, s2, s3)), introduced(assumption)).
% 289.94/182.41 tff(5138,assumption,(~m_or_h_gate_v_out(c_e_h_2, c_j, s2)), introduced(assumption)).
% 289.94/182.41 tff(5139,plain,
% 289.94/182.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_2, c_j, s3)) | m_or_h_gate_v_out(c_e_h_2, c_j, s2) | (~node6(c_e_h_2, c_j, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s3)) | m_or_h_gate_v_out(c_e_h_2, c_j, s2) | (~node6(c_e_h_2, c_j, s2, s3)))),
% 289.94/182.41 inference(rewrite,[status(thm)],[])).
% 289.94/182.41 tff(5140,plain,
% 289.94/182.41 (((~node6(c_e_h_2, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s3)) | m_or_h_gate_v_out(c_e_h_2, c_j, s2)) <=> ((~m_or_h_gate_v_out(c_e_h_2, c_j, s3)) | m_or_h_gate_v_out(c_e_h_2, c_j, s2) | (~node6(c_e_h_2, c_j, s2, s3)))),
% 289.94/182.41 inference(rewrite,[status(thm)],[])).
% 289.94/182.41 tff(5141,plain,
% 289.94/182.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s3)) | m_or_h_gate_v_out(c_e_h_2, c_j, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_2, c_j, s3)) | m_or_h_gate_v_out(c_e_h_2, c_j, s2) | (~node6(c_e_h_2, c_j, s2, s3))))),
% 289.94/182.41 inference(monotonicity,[status(thm)],[5140])).
% 289.94/182.41 tff(5142,plain,
% 289.94/182.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s3)) | m_or_h_gate_v_out(c_e_h_2, c_j, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s3)) | m_or_h_gate_v_out(c_e_h_2, c_j, s2) | (~node6(c_e_h_2, c_j, s2, s3)))),
% 289.94/182.41 inference(transitivity,[status(thm)],[5141, 5139])).
% 289.94/182.41 tff(5143,plain,
% 289.94/182.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s3)) | m_or_h_gate_v_out(c_e_h_2, c_j, s2))),
% 289.94/182.41 inference(quant_inst,[status(thm)],[])).
% 289.94/182.41 tff(5144,plain,
% 289.94/182.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s3)) | m_or_h_gate_v_out(c_e_h_2, c_j, s2) | (~node6(c_e_h_2, c_j, s2, s3))),
% 289.94/182.41 inference(modus_ponens,[status(thm)],[5143, 5142])).
% 289.94/182.41 tff(5145,plain,
% 289.94/182.41 ($false),
% 289.94/182.41 inference(unit_resolution,[status(thm)],[5144, 1121, 5136, 5138, 5137])).
% 289.94/182.41 tff(5146,plain,((~node6(c_e_h_2, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s3)) | m_or_h_gate_v_out(c_e_h_2, c_j, s2)), inference(lemma,lemma(discharge,[]))).
% 289.94/182.41 tff(5147,plain,
% 289.94/182.41 ((~node6(c_e_h_2, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s3))),
% 289.94/182.41 inference(unit_resolution,[status(thm)],[5146, 4655])).
% 289.94/182.41 tff(5148,plain,
% 289.94/182.41 (~node6(c_e_h_2, c_j, s2, s3)),
% 289.94/182.41 inference(unit_resolution,[status(thm)],[5147, 5136])).
% 289.94/182.41 tff(5149,plain,
% 289.94/182.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s2, s3)) | node6(c_e_h_2, c_j, s2, s3) | node5(c_e_h_2, c_j, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s2, s3)) | node6(c_e_h_2, c_j, s2, s3) | node5(c_e_h_2, c_j, s2, s3))),
% 289.94/182.41 inference(rewrite,[status(thm)],[])).
% 289.94/182.41 tff(5150,plain,
% 289.94/182.41 ((node6(c_e_h_2, c_j, s2, s3) | node5(c_e_h_2, c_j, s2, s3) | (~trans(s2, s3))) <=> ((~trans(s2, s3)) | node6(c_e_h_2, c_j, s2, s3) | node5(c_e_h_2, c_j, s2, s3))),
% 289.94/182.41 inference(rewrite,[status(thm)],[])).
% 289.94/182.41 tff(5151,plain,
% 289.94/182.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s2, s3) | node5(c_e_h_2, c_j, s2, s3) | (~trans(s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s2, s3)) | node6(c_e_h_2, c_j, s2, s3) | node5(c_e_h_2, c_j, s2, s3)))),
% 289.94/182.42 inference(monotonicity,[status(thm)],[5150])).
% 289.94/182.42 tff(5152,plain,
% 289.94/182.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s2, s3) | node5(c_e_h_2, c_j, s2, s3) | (~trans(s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s2, s3)) | node6(c_e_h_2, c_j, s2, s3) | node5(c_e_h_2, c_j, s2, s3))),
% 289.94/182.42 inference(transitivity,[status(thm)],[5151, 5149])).
% 289.94/182.42 tff(5153,plain,
% 289.94/182.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s2, s3) | node5(c_e_h_2, c_j, s2, s3) | (~trans(s2, s3)))),
% 289.94/182.42 inference(quant_inst,[status(thm)],[])).
% 289.94/182.42 tff(5154,plain,
% 289.94/182.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s2, s3)) | node6(c_e_h_2, c_j, s2, s3) | node5(c_e_h_2, c_j, s2, s3)),
% 289.94/182.42 inference(modus_ponens,[status(thm)],[5153, 5152])).
% 289.94/182.42 tff(5155,plain,
% 289.94/182.42 (node6(c_e_h_2, c_j, s2, s3) | node5(c_e_h_2, c_j, s2, s3)),
% 289.94/182.42 inference(unit_resolution,[status(thm)],[5154, 1141, 318])).
% 289.94/182.42 tff(5156,plain,
% 289.94/182.42 (node5(c_e_h_2, c_j, s2, s3)),
% 289.94/182.42 inference(unit_resolution,[status(thm)],[5155, 5148])).
% 289.94/182.42 tff(5157,plain,
% 289.94/182.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_2, c_j, s3)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s2) | (~node5(c_e_h_2, c_j, s2, s3)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s3)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s2) | (~node5(c_e_h_2, c_j, s2, s3)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s2))),
% 289.94/182.42 inference(rewrite,[status(thm)],[])).
% 289.94/182.42 tff(5158,plain,
% 289.94/182.42 ((m_or_h_gate_v_in1(c_e_h_2, c_j, s2) | m_or_h_gate_v_in2(c_e_h_2, c_j, s2) | (~node5(c_e_h_2, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s3))) <=> ((~m_or_h_gate_v_out(c_e_h_2, c_j, s3)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s2) | (~node5(c_e_h_2, c_j, s2, s3)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s2))),
% 289.94/182.42 inference(rewrite,[status(thm)],[])).
% 289.94/182.42 tff(5159,plain,
% 289.94/182.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s2) | m_or_h_gate_v_in2(c_e_h_2, c_j, s2) | (~node5(c_e_h_2, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_2, c_j, s3)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s2) | (~node5(c_e_h_2, c_j, s2, s3)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s2)))),
% 289.94/182.42 inference(monotonicity,[status(thm)],[5158])).
% 289.94/182.42 tff(5160,plain,
% 289.94/182.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s2) | m_or_h_gate_v_in2(c_e_h_2, c_j, s2) | (~node5(c_e_h_2, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s3)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s2) | (~node5(c_e_h_2, c_j, s2, s3)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s2))),
% 289.94/182.42 inference(transitivity,[status(thm)],[5159, 5157])).
% 289.94/182.42 tff(5161,plain,
% 289.94/182.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s2) | m_or_h_gate_v_in2(c_e_h_2, c_j, s2) | (~node5(c_e_h_2, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s3)))),
% 289.94/182.42 inference(quant_inst,[status(thm)],[])).
% 289.94/182.42 tff(5162,plain,
% 289.94/182.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s3)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s2) | (~node5(c_e_h_2, c_j, s2, s3)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s2)),
% 289.94/182.42 inference(modus_ponens,[status(thm)],[5161, 5160])).
% 289.94/182.42 tff(5163,plain,
% 289.94/182.42 ($false),
% 289.94/182.42 inference(unit_resolution,[status(thm)],[5162, 1159, 5136, 5156, 5135, 5039])).
% 289.94/182.42 tff(5164,plain,(~m_or_h_gate_v_out(c_e_h_2, c_j, s3)), inference(lemma,lemma(discharge,[]))).
% 289.94/182.42 tff(5165,plain,
% 289.94/182.42 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s3)) | m_or_h_gate_v_out(c_e_h_2, c_j, s3))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s3)) | m_or_h_gate_v_out(c_e_h_2, c_j, s3))),
% 289.94/182.42 inference(rewrite,[status(thm)],[])).
% 289.94/182.42 tff(5166,plain,
% 289.94/182.42 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s3)) | m_or_h_gate_v_out(c_e_h_2, c_j, s3))),
% 289.94/182.42 inference(quant_inst,[status(thm)],[])).
% 289.94/182.42 tff(5167,plain,
% 289.94/182.42 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s3)) | m_or_h_gate_v_out(c_e_h_2, c_j, s3)),
% 289.94/182.42 inference(modus_ponens,[status(thm)],[5166, 5165])).
% 289.94/182.42 tff(5168,plain,
% 289.94/182.42 (~m_c_h_element_v_in2(c_e_h_2, c_h, s3)),
% 289.94/182.42 inference(unit_resolution,[status(thm)],[5167, 1174, 5164])).
% 289.94/182.42 tff(5169,assumption,(m_and_h_gate_v_out(c_e_h_2, c_i, s5)), introduced(assumption)).
% 289.94/182.42 tff(5170,plain,
% 289.94/182.42 (~m_and_h_gate_v_in1(c_e_h_2, c_i, s3)),
% 289.94/182.42 inference(unit_resolution,[status(thm)],[4730, 4725])).
% 289.94/182.42 tff(5171,plain,
% 289.94/182.42 (~node20(c_e_h_2, c_i, s3)),
% 289.94/182.42 inference(unit_resolution,[status(thm)],[4738, 5170])).
% 289.94/182.42 tff(5172,plain,
% 289.94/182.42 (~m_and_h_gate_v_out(c_e_h_2, c_i, s4)),
% 289.94/182.42 inference(unit_resolution,[status(thm)],[4762, 5171, 4740])).
% 289.94/182.42 tff(5173,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_h, s3)), introduced(assumption)).
% 289.94/182.42 tff(5174,assumption,(m_c_h_element_v_out(c_e_h_2, c_h, s4)), introduced(assumption)).
% 289.94/182.42 tff(5175,assumption,(node18(c_e_h_2, c_h, s3, s4)), introduced(assumption)).
% 289.94/182.42 tff(5176,plain,
% 289.94/182.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_h, s3) | (~m_c_h_element_v_out(c_e_h_2, c_h, s4)) | (~node18(c_e_h_2, c_h, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s3) | (~m_c_h_element_v_out(c_e_h_2, c_h, s4)) | (~node18(c_e_h_2, c_h, s3, s4)))),
% 289.94/182.42 inference(rewrite,[status(thm)],[])).
% 289.94/182.42 tff(5177,plain,
% 289.94/182.42 (((~m_c_h_element_v_out(c_e_h_2, c_h, s4)) | m_c_h_element_v_out(c_e_h_2, c_h, s3) | (~node18(c_e_h_2, c_h, s3, s4))) <=> (m_c_h_element_v_out(c_e_h_2, c_h, s3) | (~m_c_h_element_v_out(c_e_h_2, c_h, s4)) | (~node18(c_e_h_2, c_h, s3, s4)))),
% 289.94/182.42 inference(rewrite,[status(thm)],[])).
% 289.94/182.42 tff(5178,plain,
% 289.94/182.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s4)) | m_c_h_element_v_out(c_e_h_2, c_h, s3) | (~node18(c_e_h_2, c_h, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_h, s3) | (~m_c_h_element_v_out(c_e_h_2, c_h, s4)) | (~node18(c_e_h_2, c_h, s3, s4))))),
% 289.94/182.42 inference(monotonicity,[status(thm)],[5177])).
% 289.94/182.42 tff(5179,plain,
% 289.94/182.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s4)) | m_c_h_element_v_out(c_e_h_2, c_h, s3) | (~node18(c_e_h_2, c_h, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s3) | (~m_c_h_element_v_out(c_e_h_2, c_h, s4)) | (~node18(c_e_h_2, c_h, s3, s4)))),
% 289.95/182.42 inference(transitivity,[status(thm)],[5178, 5176])).
% 289.95/182.42 tff(5180,plain,
% 289.95/182.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s4)) | m_c_h_element_v_out(c_e_h_2, c_h, s3) | (~node18(c_e_h_2, c_h, s3, s4)))),
% 289.95/182.42 inference(quant_inst,[status(thm)],[])).
% 289.95/182.42 tff(5181,plain,
% 289.95/182.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s3) | (~m_c_h_element_v_out(c_e_h_2, c_h, s4)) | (~node18(c_e_h_2, c_h, s3, s4))),
% 289.95/182.42 inference(modus_ponens,[status(thm)],[5180, 5179])).
% 289.95/182.42 tff(5182,plain,
% 289.95/182.42 ($false),
% 289.95/182.42 inference(unit_resolution,[status(thm)],[5181, 753, 5175, 4725, 5174])).
% 289.95/182.42 tff(5183,plain,((~node18(c_e_h_2, c_h, s3, s4)) | m_c_h_element_v_out(c_e_h_2, c_h, s3) | (~m_c_h_element_v_out(c_e_h_2, c_h, s4))), inference(lemma,lemma(discharge,[]))).
% 289.95/182.42 tff(5184,plain,
% 289.95/182.42 (~node18(c_e_h_2, c_h, s3, s4)),
% 289.95/182.42 inference(unit_resolution,[status(thm)],[5183, 4725, 5174])).
% 289.95/182.42 tff(5185,plain,
% 289.95/182.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s3, s4)) | node19(c_e_h_2, c_h, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s3, s4)) | node19(c_e_h_2, c_h, s3, s4))),
% 289.95/182.42 inference(rewrite,[status(thm)],[])).
% 289.95/182.42 tff(5186,plain,
% 289.95/182.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s3, s4)) | node19(c_e_h_2, c_h, s3, s4))),
% 289.95/182.42 inference(quant_inst,[status(thm)],[])).
% 289.95/182.42 tff(5187,plain,
% 289.95/182.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s3, s4)) | node19(c_e_h_2, c_h, s3, s4)),
% 289.95/182.42 inference(modus_ponens,[status(thm)],[5186, 5185])).
% 289.95/182.42 tff(5188,plain,
% 289.95/182.42 (node19(c_e_h_2, c_h, s3, s4)),
% 289.95/182.42 inference(unit_resolution,[status(thm)],[5187, 190, 531])).
% 289.95/182.42 tff(5189,plain,
% 289.95/182.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_h, s3, s4)) | node17(c_e_h_2, c_h, s3) | node18(c_e_h_2, c_h, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_h, s3, s4)) | node17(c_e_h_2, c_h, s3) | node18(c_e_h_2, c_h, s3, s4))),
% 289.95/182.42 inference(rewrite,[status(thm)],[])).
% 289.95/182.42 tff(5190,plain,
% 289.95/182.42 ((node17(c_e_h_2, c_h, s3) | node18(c_e_h_2, c_h, s3, s4) | (~node19(c_e_h_2, c_h, s3, s4))) <=> ((~node19(c_e_h_2, c_h, s3, s4)) | node17(c_e_h_2, c_h, s3) | node18(c_e_h_2, c_h, s3, s4))),
% 289.95/182.42 inference(rewrite,[status(thm)],[])).
% 289.95/182.42 tff(5191,plain,
% 289.95/182.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s3) | node18(c_e_h_2, c_h, s3, s4) | (~node19(c_e_h_2, c_h, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_h, s3, s4)) | node17(c_e_h_2, c_h, s3) | node18(c_e_h_2, c_h, s3, s4)))),
% 289.95/182.42 inference(monotonicity,[status(thm)],[5190])).
% 289.95/182.42 tff(5192,plain,
% 289.95/182.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s3) | node18(c_e_h_2, c_h, s3, s4) | (~node19(c_e_h_2, c_h, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_h, s3, s4)) | node17(c_e_h_2, c_h, s3) | node18(c_e_h_2, c_h, s3, s4))),
% 289.95/182.43 inference(transitivity,[status(thm)],[5191, 5189])).
% 289.95/182.43 tff(5193,plain,
% 289.95/182.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s3) | node18(c_e_h_2, c_h, s3, s4) | (~node19(c_e_h_2, c_h, s3, s4)))),
% 289.95/182.43 inference(quant_inst,[status(thm)],[])).
% 289.95/182.43 tff(5194,plain,
% 289.95/182.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_h, s3, s4)) | node17(c_e_h_2, c_h, s3) | node18(c_e_h_2, c_h, s3, s4)),
% 289.95/182.43 inference(modus_ponens,[status(thm)],[5193, 5192])).
% 289.95/182.43 tff(5195,plain,
% 289.95/182.43 (node17(c_e_h_2, c_h, s3) | node18(c_e_h_2, c_h, s3, s4)),
% 289.95/182.43 inference(unit_resolution,[status(thm)],[5194, 776, 5188])).
% 289.95/182.43 tff(5196,plain,
% 289.95/182.43 (node17(c_e_h_2, c_h, s3)),
% 289.95/182.43 inference(unit_resolution,[status(thm)],[5195, 5184])).
% 289.95/182.43 tff(5197,plain,
% 289.95/182.43 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s3)) | m_c_h_element_v_in2(c_e_h_2, c_h, s3) | (~node17(c_e_h_2, c_h, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s3)) | m_c_h_element_v_in2(c_e_h_2, c_h, s3) | (~node17(c_e_h_2, c_h, s3)))),
% 289.95/182.43 inference(rewrite,[status(thm)],[])).
% 289.95/182.43 tff(5198,plain,
% 289.95/182.43 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s3)) | m_c_h_element_v_in2(c_e_h_2, c_h, s3) | (~node17(c_e_h_2, c_h, s3)))),
% 289.95/182.43 inference(quant_inst,[status(thm)],[])).
% 289.95/182.43 tff(5199,plain,
% 289.95/182.43 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s3)) | m_c_h_element_v_in2(c_e_h_2, c_h, s3) | (~node17(c_e_h_2, c_h, s3))),
% 289.95/182.43 inference(modus_ponens,[status(thm)],[5198, 5197])).
% 289.95/182.43 tff(5200,plain,
% 289.95/182.43 ((~m_c_h_element_v_in1(c_e_h_2, c_h, s3)) | m_c_h_element_v_in2(c_e_h_2, c_h, s3)),
% 289.95/182.43 inference(unit_resolution,[status(thm)],[5199, 919, 5196])).
% 289.95/182.43 tff(5201,plain,
% 289.95/182.43 (~m_c_h_element_v_in1(c_e_h_2, c_h, s3)),
% 289.95/182.43 inference(unit_resolution,[status(thm)],[5200, 5173])).
% 289.95/182.43 tff(5202,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_h, s3)), introduced(assumption)).
% 289.95/182.43 tff(5203,assumption,(~node16(c_e_h_2, c_h, s3)), introduced(assumption)).
% 289.95/182.43 tff(5204,assumption,(node15(c_e_h_2, c_h, s3, s4)), introduced(assumption)).
% 289.95/182.43 tff(5205,plain,
% 289.95/182.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s4)) | (~node15(c_e_h_2, c_h, s3, s4)) | m_c_h_element_v_out(c_e_h_2, c_h, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s4)) | (~node15(c_e_h_2, c_h, s3, s4)) | m_c_h_element_v_out(c_e_h_2, c_h, s3))),
% 289.95/182.43 inference(rewrite,[status(thm)],[])).
% 289.95/182.43 tff(5206,plain,
% 289.95/182.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s4)) | (~node15(c_e_h_2, c_h, s3, s4)) | m_c_h_element_v_out(c_e_h_2, c_h, s3))),
% 289.95/182.43 inference(quant_inst,[status(thm)],[])).
% 289.95/182.43 tff(5207,plain,
% 289.95/182.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s4)) | (~node15(c_e_h_2, c_h, s3, s4)) | m_c_h_element_v_out(c_e_h_2, c_h, s3)),
% 289.95/182.43 inference(modus_ponens,[status(thm)],[5206, 5205])).
% 289.95/182.43 tff(5208,plain,
% 289.95/182.43 ($false),
% 289.95/182.43 inference(unit_resolution,[status(thm)],[5207, 147, 5204, 4725, 5174])).
% 289.95/182.43 tff(5209,plain,((~node15(c_e_h_2, c_h, s3, s4)) | m_c_h_element_v_out(c_e_h_2, c_h, s3) | (~m_c_h_element_v_out(c_e_h_2, c_h, s4))), inference(lemma,lemma(discharge,[]))).
% 289.95/182.43 tff(5210,plain,
% 289.95/182.43 (~node15(c_e_h_2, c_h, s3, s4)),
% 289.95/182.43 inference(unit_resolution,[status(thm)],[5209, 5174, 4725])).
% 289.95/182.43 tff(5211,plain,
% 289.95/182.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_2, c_h, s3, s4) | (~node19(c_e_h_2, c_h, s3, s4)) | node16(c_e_h_2, c_h, s3) | node15(c_e_h_2, c_h, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_2, c_h, s3, s4) | (~node19(c_e_h_2, c_h, s3, s4)) | node16(c_e_h_2, c_h, s3) | node15(c_e_h_2, c_h, s3, s4))),
% 289.95/182.43 inference(rewrite,[status(thm)],[])).
% 289.95/182.43 tff(5212,plain,
% 289.95/182.43 ((node16(c_e_h_2, c_h, s3) | node14(c_e_h_2, c_h, s3, s4) | node15(c_e_h_2, c_h, s3, s4) | (~node19(c_e_h_2, c_h, s3, s4))) <=> (node14(c_e_h_2, c_h, s3, s4) | (~node19(c_e_h_2, c_h, s3, s4)) | node16(c_e_h_2, c_h, s3) | node15(c_e_h_2, c_h, s3, s4))),
% 289.95/182.43 inference(rewrite,[status(thm)],[])).
% 289.95/182.43 tff(5213,plain,
% 289.95/182.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s3) | node14(c_e_h_2, c_h, s3, s4) | node15(c_e_h_2, c_h, s3, s4) | (~node19(c_e_h_2, c_h, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_2, c_h, s3, s4) | (~node19(c_e_h_2, c_h, s3, s4)) | node16(c_e_h_2, c_h, s3) | node15(c_e_h_2, c_h, s3, s4)))),
% 289.95/182.43 inference(monotonicity,[status(thm)],[5212])).
% 289.95/182.43 tff(5214,plain,
% 289.95/182.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s3) | node14(c_e_h_2, c_h, s3, s4) | node15(c_e_h_2, c_h, s3, s4) | (~node19(c_e_h_2, c_h, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_2, c_h, s3, s4) | (~node19(c_e_h_2, c_h, s3, s4)) | node16(c_e_h_2, c_h, s3) | node15(c_e_h_2, c_h, s3, s4))),
% 289.95/182.43 inference(transitivity,[status(thm)],[5213, 5211])).
% 289.95/182.43 tff(5215,plain,
% 289.95/182.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s3) | node14(c_e_h_2, c_h, s3, s4) | node15(c_e_h_2, c_h, s3, s4) | (~node19(c_e_h_2, c_h, s3, s4)))),
% 289.95/182.43 inference(quant_inst,[status(thm)],[])).
% 289.95/182.43 tff(5216,plain,
% 289.95/182.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_2, c_h, s3, s4) | (~node19(c_e_h_2, c_h, s3, s4)) | node16(c_e_h_2, c_h, s3) | node15(c_e_h_2, c_h, s3, s4)),
% 289.95/182.43 inference(modus_ponens,[status(thm)],[5215, 5214])).
% 289.95/182.43 tff(5217,plain,
% 289.95/182.43 (node14(c_e_h_2, c_h, s3, s4) | node16(c_e_h_2, c_h, s3) | node15(c_e_h_2, c_h, s3, s4)),
% 289.95/182.43 inference(unit_resolution,[status(thm)],[5216, 204, 5188])).
% 289.95/182.43 tff(5218,plain,
% 289.95/182.43 (node14(c_e_h_2, c_h, s3, s4)),
% 289.95/182.43 inference(unit_resolution,[status(thm)],[5217, 5210, 5203])).
% 289.95/182.43 tff(5219,plain,
% 289.95/182.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s3, s4)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s4)) | m_c_h_element_v_in1(c_e_h_2, c_h, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_2, c_h, s3, s4)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s4)) | m_c_h_element_v_in1(c_e_h_2, c_h, s3))),
% 289.95/182.43 inference(rewrite,[status(thm)],[])).
% 289.95/182.43 tff(5220,plain,
% 289.95/182.43 (((~node14(c_e_h_2, c_h, s3, s4)) | m_c_h_element_v_in1(c_e_h_2, c_h, s3) | (~m_c_h_element_v_out(c_e_h_2, c_h, s4))) <=> ((~node14(c_e_h_2, c_h, s3, s4)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s4)) | m_c_h_element_v_in1(c_e_h_2, c_h, s3))),
% 289.95/182.43 inference(rewrite,[status(thm)],[])).
% 289.95/182.43 tff(5221,plain,
% 289.95/182.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s3, s4)) | m_c_h_element_v_in1(c_e_h_2, c_h, s3) | (~m_c_h_element_v_out(c_e_h_2, c_h, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s3, s4)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s4)) | m_c_h_element_v_in1(c_e_h_2, c_h, s3)))),
% 289.95/182.43 inference(monotonicity,[status(thm)],[5220])).
% 289.95/182.43 tff(5222,plain,
% 289.95/182.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s3, s4)) | m_c_h_element_v_in1(c_e_h_2, c_h, s3) | (~m_c_h_element_v_out(c_e_h_2, c_h, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_2, c_h, s3, s4)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s4)) | m_c_h_element_v_in1(c_e_h_2, c_h, s3))),
% 289.95/182.43 inference(transitivity,[status(thm)],[5221, 5219])).
% 289.95/182.43 tff(5223,plain,
% 289.95/182.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s3, s4)) | m_c_h_element_v_in1(c_e_h_2, c_h, s3) | (~m_c_h_element_v_out(c_e_h_2, c_h, s4)))),
% 289.95/182.43 inference(quant_inst,[status(thm)],[])).
% 289.95/182.43 tff(5224,plain,
% 289.95/182.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_2, c_h, s3, s4)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s4)) | m_c_h_element_v_in1(c_e_h_2, c_h, s3)),
% 289.95/182.43 inference(modus_ponens,[status(thm)],[5223, 5222])).
% 289.95/182.43 tff(5225,plain,
% 289.95/182.43 ($false),
% 289.95/182.43 inference(unit_resolution,[status(thm)],[5224, 223, 5218, 5202, 5174])).
% 289.95/182.43 tff(5226,plain,((~m_c_h_element_v_out(c_e_h_2, c_h, s4)) | m_c_h_element_v_in1(c_e_h_2, c_h, s3) | node16(c_e_h_2, c_h, s3) | m_c_h_element_v_out(c_e_h_2, c_h, s3)), inference(lemma,lemma(discharge,[]))).
% 289.95/182.43 tff(5227,plain,
% 289.95/182.43 (node16(c_e_h_2, c_h, s3)),
% 289.95/182.43 inference(unit_resolution,[status(thm)],[5226, 5201, 5174, 4725])).
% 289.95/182.43 tff(5228,plain,
% 289.95/182.43 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_h, s3)) | m_c_h_element_v_in1(c_e_h_2, c_h, s3) | m_c_h_element_v_in2(c_e_h_2, c_h, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_h, s3)) | m_c_h_element_v_in1(c_e_h_2, c_h, s3) | m_c_h_element_v_in2(c_e_h_2, c_h, s3))),
% 289.95/182.43 inference(rewrite,[status(thm)],[])).
% 289.95/182.43 tff(5229,plain,
% 289.95/182.43 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_h, s3)) | m_c_h_element_v_in1(c_e_h_2, c_h, s3) | m_c_h_element_v_in2(c_e_h_2, c_h, s3))),
% 289.95/182.43 inference(quant_inst,[status(thm)],[])).
% 289.95/182.43 tff(5230,plain,
% 289.95/182.43 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_h, s3)) | m_c_h_element_v_in1(c_e_h_2, c_h, s3) | m_c_h_element_v_in2(c_e_h_2, c_h, s3)),
% 289.95/182.43 inference(modus_ponens,[status(thm)],[5229, 5228])).
% 289.95/182.43 tff(5231,plain,
% 289.95/182.43 ($false),
% 289.95/182.43 inference(unit_resolution,[status(thm)],[5230, 178, 5227, 5201, 5173])).
% 289.95/182.43 tff(5232,plain,(m_c_h_element_v_in2(c_e_h_2, c_h, s3) | (~m_c_h_element_v_out(c_e_h_2, c_h, s4)) | m_c_h_element_v_out(c_e_h_2, c_h, s3)), inference(lemma,lemma(discharge,[]))).
% 289.95/182.43 tff(5233,plain,
% 289.95/182.43 (~m_c_h_element_v_out(c_e_h_2, c_h, s4)),
% 289.95/182.43 inference(unit_resolution,[status(thm)],[5232, 4725, 5173])).
% 289.95/182.43 tff(5234,assumption,(m_and_h_gate_v_in1(c_e_h_2, c_i, s4)), introduced(assumption)).
% 289.95/182.43 tff(5235,assumption,(~m_c_h_element_v_out(c_e_h_2, c_h, s4)), introduced(assumption)).
% 289.95/182.43 tff(5236,plain,
% 289.95/182.43 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s4)) | m_c_h_element_v_out(c_e_h_2, c_h, s4))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s4)) | m_c_h_element_v_out(c_e_h_2, c_h, s4))),
% 289.95/182.44 inference(rewrite,[status(thm)],[])).
% 289.95/182.44 tff(5237,plain,
% 289.95/182.44 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s4)) | m_c_h_element_v_out(c_e_h_2, c_h, s4))),
% 289.95/182.44 inference(quant_inst,[status(thm)],[])).
% 289.95/182.44 tff(5238,plain,
% 289.95/182.44 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s4)) | m_c_h_element_v_out(c_e_h_2, c_h, s4)),
% 289.95/182.44 inference(modus_ponens,[status(thm)],[5237, 5236])).
% 289.95/182.44 tff(5239,plain,
% 289.95/182.44 ($false),
% 289.95/182.44 inference(unit_resolution,[status(thm)],[5238, 619, 5235, 5234])).
% 289.95/182.44 tff(5240,plain,((~m_and_h_gate_v_in1(c_e_h_2, c_i, s4)) | m_c_h_element_v_out(c_e_h_2, c_h, s4)), inference(lemma,lemma(discharge,[]))).
% 289.95/182.44 tff(5241,plain,
% 289.95/182.44 (~m_and_h_gate_v_in1(c_e_h_2, c_i, s4)),
% 289.95/182.44 inference(unit_resolution,[status(thm)],[5240, 5233])).
% 289.95/182.44 tff(5242,assumption,(~m_and_h_gate_v_in1(c_e_h_2, c_i, s4)), introduced(assumption)).
% 289.95/182.44 tff(5243,assumption,(node20(c_e_h_2, c_i, s4)), introduced(assumption)).
% 289.95/182.44 tff(5244,plain,
% 289.95/182.44 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s4)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s4)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s4))),
% 289.95/182.44 inference(rewrite,[status(thm)],[])).
% 289.95/182.44 tff(5245,plain,
% 289.95/182.44 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s4)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s4))),
% 289.95/182.44 inference(quant_inst,[status(thm)],[])).
% 289.95/182.44 tff(5246,plain,
% 289.95/182.44 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s4)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s4)),
% 289.95/182.44 inference(modus_ponens,[status(thm)],[5245, 5244])).
% 289.95/182.44 tff(5247,plain,
% 289.95/182.44 ($false),
% 289.95/182.44 inference(unit_resolution,[status(thm)],[5246, 38, 5243, 5242])).
% 289.95/182.44 tff(5248,plain,((~node20(c_e_h_2, c_i, s4)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s4)), inference(lemma,lemma(discharge,[]))).
% 289.95/182.44 tff(5249,plain,
% 289.95/182.44 (~node20(c_e_h_2, c_i, s4)),
% 289.95/182.44 inference(unit_resolution,[status(thm)],[5248, 5241])).
% 289.95/182.44 tff(5250,assumption,(~node20(c_e_h_2, c_i, s4)), introduced(assumption)).
% 289.95/182.44 tff(5251,assumption,(node21(c_e_h_2, c_i, s4, s5)), introduced(assumption)).
% 289.95/182.44 tff(5252,plain,
% 289.95/182.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s4) | (~node21(c_e_h_2, c_i, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s4) | (~node21(c_e_h_2, c_i, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s5)))),
% 289.95/182.44 inference(rewrite,[status(thm)],[])).
% 289.95/182.44 tff(5253,plain,
% 289.95/182.44 ((node20(c_e_h_2, c_i, s4) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s5)) | (~node21(c_e_h_2, c_i, s4, s5))) <=> (node20(c_e_h_2, c_i, s4) | (~node21(c_e_h_2, c_i, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s5)))),
% 289.95/182.44 inference(rewrite,[status(thm)],[])).
% 289.95/182.44 tff(5254,plain,
% 289.95/182.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s4) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s5)) | (~node21(c_e_h_2, c_i, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s4) | (~node21(c_e_h_2, c_i, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s5))))),
% 289.95/182.44 inference(monotonicity,[status(thm)],[5253])).
% 289.95/182.44 tff(5255,plain,
% 289.95/182.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s4) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s5)) | (~node21(c_e_h_2, c_i, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s4) | (~node21(c_e_h_2, c_i, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s5)))),
% 289.95/182.44 inference(transitivity,[status(thm)],[5254, 5252])).
% 289.95/182.44 tff(5256,plain,
% 289.95/182.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s4) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s5)) | (~node21(c_e_h_2, c_i, s4, s5)))),
% 289.95/182.44 inference(quant_inst,[status(thm)],[])).
% 289.95/182.44 tff(5257,plain,
% 289.95/182.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s4) | (~node21(c_e_h_2, c_i, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s5))),
% 289.95/182.44 inference(modus_ponens,[status(thm)],[5256, 5255])).
% 289.95/182.44 tff(5258,plain,
% 289.95/182.44 ($false),
% 289.95/182.44 inference(unit_resolution,[status(thm)],[5257, 52, 5251, 5169, 5250])).
% 289.95/182.44 tff(5259,plain,((~node21(c_e_h_2, c_i, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s5)) | node20(c_e_h_2, c_i, s4)), inference(lemma,lemma(discharge,[]))).
% 289.95/182.44 tff(5260,plain,
% 289.95/182.44 (~node21(c_e_h_2, c_i, s4, s5)),
% 289.95/182.44 inference(unit_resolution,[status(thm)],[5259, 5169, 5250])).
% 289.95/182.44 tff(5261,assumption,(node22(c_e_h_2, c_i, s4, s5)), introduced(assumption)).
% 289.95/182.44 tff(5262,plain,
% 289.95/182.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s5)) | (~node22(c_e_h_2, c_i, s4, s5)) | m_and_h_gate_v_out(c_e_h_2, c_i, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s5)) | (~node22(c_e_h_2, c_i, s4, s5)) | m_and_h_gate_v_out(c_e_h_2, c_i, s4))),
% 289.95/182.44 inference(rewrite,[status(thm)],[])).
% 289.95/182.44 tff(5263,plain,
% 289.95/182.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s5)) | (~node22(c_e_h_2, c_i, s4, s5)) | m_and_h_gate_v_out(c_e_h_2, c_i, s4))),
% 289.95/182.44 inference(quant_inst,[status(thm)],[])).
% 289.95/182.44 tff(5264,plain,
% 289.95/182.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s5)) | (~node22(c_e_h_2, c_i, s4, s5)) | m_and_h_gate_v_out(c_e_h_2, c_i, s4)),
% 289.95/182.44 inference(modus_ponens,[status(thm)],[5263, 5262])).
% 289.95/182.44 tff(5265,plain,
% 289.95/182.44 ($false),
% 289.95/182.44 inference(unit_resolution,[status(thm)],[5264, 108, 5261, 4766, 5169])).
% 289.95/182.44 tff(5266,plain,((~node22(c_e_h_2, c_i, s4, s5)) | m_and_h_gate_v_out(c_e_h_2, c_i, s4) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s5))), inference(lemma,lemma(discharge,[]))).
% 289.95/182.44 tff(5267,plain,
% 289.95/182.44 (~node22(c_e_h_2, c_i, s4, s5)),
% 289.95/182.44 inference(unit_resolution,[status(thm)],[5266, 5169, 4766])).
% 289.95/182.44 tff(5268,plain,
% 289.95/182.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_2, c_i, s4, s5) | node22(c_e_h_2, c_i, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_2, c_i, s4, s5) | node22(c_e_h_2, c_i, s4, s5))),
% 289.95/182.44 inference(rewrite,[status(thm)],[])).
% 289.95/182.44 tff(5269,plain,
% 289.95/182.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_2, c_i, s4, s5) | node22(c_e_h_2, c_i, s4, s5))),
% 289.95/182.44 inference(quant_inst,[status(thm)],[])).
% 289.95/182.44 tff(5270,plain,
% 289.95/182.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_2, c_i, s4, s5) | node22(c_e_h_2, c_i, s4, s5)),
% 289.95/182.44 inference(modus_ponens,[status(thm)],[5269, 5268])).
% 289.95/182.44 tff(5271,plain,
% 289.95/182.44 (node21(c_e_h_2, c_i, s4, s5) | node22(c_e_h_2, c_i, s4, s5)),
% 289.95/182.44 inference(unit_resolution,[status(thm)],[5270, 82, 1028])).
% 289.95/182.44 tff(5272,plain,
% 289.95/182.44 ($false),
% 289.95/182.44 inference(unit_resolution,[status(thm)],[5271, 5267, 5260])).
% 289.95/182.44 tff(5273,plain,((~m_and_h_gate_v_out(c_e_h_2, c_i, s5)) | m_and_h_gate_v_out(c_e_h_2, c_i, s4) | node20(c_e_h_2, c_i, s4)), inference(lemma,lemma(discharge,[]))).
% 289.95/182.44 tff(5274,plain,
% 289.95/182.44 ($false),
% 289.95/182.44 inference(unit_resolution,[status(thm)],[5273, 5249, 5172, 5169])).
% 289.95/182.44 tff(5275,plain,(m_c_h_element_v_out(c_e_h_2, c_h, s3) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s5)) | m_and_h_gate_v_out(c_e_h_2, c_i, s3) | m_c_h_element_v_in2(c_e_h_2, c_h, s3)), inference(lemma,lemma(discharge,[]))).
% 289.95/182.44 tff(5276,plain,
% 289.95/182.44 (m_c_h_element_v_out(c_e_h_2, c_h, s3) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s5)) | m_c_h_element_v_in2(c_e_h_2, c_h, s3)),
% 289.95/182.44 inference(unit_resolution,[status(thm)],[5275, 4257])).
% 289.95/182.44 tff(5277,plain,
% 289.95/182.44 ((~m_and_h_gate_v_out(c_e_h_2, c_i, s5)) | m_c_h_element_v_in2(c_e_h_2, c_h, s3)),
% 289.95/182.44 inference(unit_resolution,[status(thm)],[5276, 4723])).
% 289.95/182.44 tff(5278,plain,
% 289.95/182.44 (~m_and_h_gate_v_out(c_e_h_2, c_i, s5)),
% 289.95/182.44 inference(unit_resolution,[status(thm)],[5277, 5168])).
% 289.95/182.44 tff(5279,assumption,(m_c_h_element_v_in2(c_e_h_2, c_f, s5)), introduced(assumption)).
% 289.95/182.44 tff(5280,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_i, s5)), introduced(assumption)).
% 289.95/182.44 tff(5281,plain,
% 289.95/182.44 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_f, s5)) | m_and_h_gate_v_out(c_e_h_2, c_i, s5))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s5)) | m_and_h_gate_v_out(c_e_h_2, c_i, s5))),
% 289.95/182.44 inference(rewrite,[status(thm)],[])).
% 289.95/182.44 tff(5282,plain,
% 289.95/182.44 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_f, s5)) | m_and_h_gate_v_out(c_e_h_2, c_i, s5))),
% 289.95/182.44 inference(quant_inst,[status(thm)],[])).
% 289.95/182.44 tff(5283,plain,
% 289.95/182.44 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s5)) | m_and_h_gate_v_out(c_e_h_2, c_i, s5)),
% 289.95/182.44 inference(modus_ponens,[status(thm)],[5282, 5281])).
% 289.95/182.44 tff(5284,plain,
% 289.95/182.44 ($false),
% 289.95/182.44 inference(unit_resolution,[status(thm)],[5283, 2143, 5280, 5279])).
% 289.95/182.44 tff(5285,plain,((~m_c_h_element_v_in2(c_e_h_2, c_f, s5)) | m_and_h_gate_v_out(c_e_h_2, c_i, s5)), inference(lemma,lemma(discharge,[]))).
% 289.95/182.44 tff(5286,plain,
% 289.95/182.44 (~m_c_h_element_v_in2(c_e_h_2, c_f, s5)),
% 289.95/182.44 inference(unit_resolution,[status(thm)],[5285, 5278])).
% 289.95/182.44 tff(5287,assumption,(m_c_h_element_v_out(c_e_h_2, c_f, s6)), introduced(assumption)).
% 289.95/182.44 tff(5288,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_f, s5)), introduced(assumption)).
% 289.95/182.44 tff(5289,assumption,(~m_c_h_element_v_out(c_e_h_2, c_f, s5)), introduced(assumption)).
% 289.95/182.44 tff(5290,assumption,(node15(c_e_h_2, c_f, s5, s6)), introduced(assumption)).
% 289.95/182.44 tff(5291,plain,
% 289.95/182.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s6)) | (~node15(c_e_h_2, c_f, s5, s6)) | m_c_h_element_v_out(c_e_h_2, c_f, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s6)) | (~node15(c_e_h_2, c_f, s5, s6)) | m_c_h_element_v_out(c_e_h_2, c_f, s5))),
% 289.95/182.44 inference(rewrite,[status(thm)],[])).
% 289.95/182.44 tff(5292,plain,
% 289.95/182.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s6)) | (~node15(c_e_h_2, c_f, s5, s6)) | m_c_h_element_v_out(c_e_h_2, c_f, s5))),
% 289.95/182.44 inference(quant_inst,[status(thm)],[])).
% 289.95/182.44 tff(5293,plain,
% 289.95/182.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s6)) | (~node15(c_e_h_2, c_f, s5, s6)) | m_c_h_element_v_out(c_e_h_2, c_f, s5)),
% 289.95/182.44 inference(modus_ponens,[status(thm)],[5292, 5291])).
% 289.95/182.44 tff(5294,plain,
% 289.95/182.44 ($false),
% 289.95/182.44 inference(unit_resolution,[status(thm)],[5293, 147, 5289, 5287, 5290])).
% 289.95/182.45 tff(5295,plain,((~node15(c_e_h_2, c_f, s5, s6)) | m_c_h_element_v_out(c_e_h_2, c_f, s5) | (~m_c_h_element_v_out(c_e_h_2, c_f, s6))), inference(lemma,lemma(discharge,[]))).
% 289.95/182.45 tff(5296,plain,
% 289.95/182.45 (~node15(c_e_h_2, c_f, s5, s6)),
% 289.95/182.45 inference(unit_resolution,[status(thm)],[5295, 5287, 5289])).
% 289.95/182.45 tff(5297,assumption,(~node15(c_e_h_2, c_f, s5, s6)), introduced(assumption)).
% 289.95/182.45 tff(5298,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_f, s5)), introduced(assumption)).
% 289.95/182.45 tff(5299,assumption,(node14(c_e_h_2, c_f, s5, s6)), introduced(assumption)).
% 289.95/182.45 tff(5300,plain,
% 289.95/182.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s6)) | m_c_h_element_v_in1(c_e_h_2, c_f, s5) | (~node14(c_e_h_2, c_f, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s6)) | m_c_h_element_v_in1(c_e_h_2, c_f, s5) | (~node14(c_e_h_2, c_f, s5, s6)))),
% 289.95/182.45 inference(rewrite,[status(thm)],[])).
% 289.95/182.45 tff(5301,plain,
% 289.95/182.45 (((~node14(c_e_h_2, c_f, s5, s6)) | m_c_h_element_v_in1(c_e_h_2, c_f, s5) | (~m_c_h_element_v_out(c_e_h_2, c_f, s6))) <=> ((~m_c_h_element_v_out(c_e_h_2, c_f, s6)) | m_c_h_element_v_in1(c_e_h_2, c_f, s5) | (~node14(c_e_h_2, c_f, s5, s6)))),
% 289.95/182.45 inference(rewrite,[status(thm)],[])).
% 289.95/182.45 tff(5302,plain,
% 289.95/182.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_f, s5, s6)) | m_c_h_element_v_in1(c_e_h_2, c_f, s5) | (~m_c_h_element_v_out(c_e_h_2, c_f, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s6)) | m_c_h_element_v_in1(c_e_h_2, c_f, s5) | (~node14(c_e_h_2, c_f, s5, s6))))),
% 289.95/182.45 inference(monotonicity,[status(thm)],[5301])).
% 289.95/182.45 tff(5303,plain,
% 289.95/182.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_f, s5, s6)) | m_c_h_element_v_in1(c_e_h_2, c_f, s5) | (~m_c_h_element_v_out(c_e_h_2, c_f, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s6)) | m_c_h_element_v_in1(c_e_h_2, c_f, s5) | (~node14(c_e_h_2, c_f, s5, s6)))),
% 289.95/182.45 inference(transitivity,[status(thm)],[5302, 5300])).
% 289.95/182.45 tff(5304,plain,
% 289.95/182.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_f, s5, s6)) | m_c_h_element_v_in1(c_e_h_2, c_f, s5) | (~m_c_h_element_v_out(c_e_h_2, c_f, s6)))),
% 289.95/182.45 inference(quant_inst,[status(thm)],[])).
% 289.95/182.45 tff(5305,plain,
% 289.95/182.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s6)) | m_c_h_element_v_in1(c_e_h_2, c_f, s5) | (~node14(c_e_h_2, c_f, s5, s6))),
% 289.95/182.45 inference(modus_ponens,[status(thm)],[5304, 5303])).
% 289.95/182.45 tff(5306,plain,
% 289.95/182.45 ($false),
% 289.95/182.45 inference(unit_resolution,[status(thm)],[5305, 223, 5287, 5299, 5298])).
% 289.95/182.45 tff(5307,plain,((~node14(c_e_h_2, c_f, s5, s6)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s6)) | m_c_h_element_v_in1(c_e_h_2, c_f, s5)), inference(lemma,lemma(discharge,[]))).
% 289.95/182.45 tff(5308,plain,
% 289.95/182.45 (~node14(c_e_h_2, c_f, s5, s6)),
% 289.95/182.45 inference(unit_resolution,[status(thm)],[5307, 5298, 5287])).
% 289.95/182.45 tff(5309,plain,
% 289.95/182.45 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_f, s5)) | m_c_h_element_v_in1(c_e_h_2, c_f, s5) | m_c_h_element_v_in2(c_e_h_2, c_f, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_f, s5)) | m_c_h_element_v_in1(c_e_h_2, c_f, s5) | m_c_h_element_v_in2(c_e_h_2, c_f, s5))),
% 289.95/182.45 inference(rewrite,[status(thm)],[])).
% 289.95/182.45 tff(5310,plain,
% 289.95/182.45 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_f, s5)) | m_c_h_element_v_in1(c_e_h_2, c_f, s5) | m_c_h_element_v_in2(c_e_h_2, c_f, s5))),
% 289.95/182.45 inference(quant_inst,[status(thm)],[])).
% 289.95/182.45 tff(5311,plain,
% 289.95/182.45 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_f, s5)) | m_c_h_element_v_in1(c_e_h_2, c_f, s5) | m_c_h_element_v_in2(c_e_h_2, c_f, s5)),
% 289.95/182.45 inference(modus_ponens,[status(thm)],[5310, 5309])).
% 289.95/182.45 tff(5312,plain,
% 289.95/182.45 ((~node16(c_e_h_2, c_f, s5)) | m_c_h_element_v_in1(c_e_h_2, c_f, s5)),
% 289.95/182.45 inference(unit_resolution,[status(thm)],[5311, 178, 5288])).
% 289.95/182.45 tff(5313,plain,
% 289.95/182.45 (~node16(c_e_h_2, c_f, s5)),
% 289.95/182.45 inference(unit_resolution,[status(thm)],[5312, 5298])).
% 289.95/182.45 tff(5314,plain,
% 289.95/182.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s5, s6)) | node19(c_e_h_2, c_f, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s5, s6)) | node19(c_e_h_2, c_f, s5, s6))),
% 289.95/182.45 inference(rewrite,[status(thm)],[])).
% 289.95/182.45 tff(5315,plain,
% 289.95/182.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s5, s6)) | node19(c_e_h_2, c_f, s5, s6))),
% 289.95/182.45 inference(quant_inst,[status(thm)],[])).
% 289.95/182.45 tff(5316,plain,
% 289.95/182.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s5, s6)) | node19(c_e_h_2, c_f, s5, s6)),
% 289.95/182.45 inference(modus_ponens,[status(thm)],[5315, 5314])).
% 289.95/182.45 tff(5317,plain,
% 289.95/182.45 (node19(c_e_h_2, c_f, s5, s6)),
% 289.95/182.45 inference(unit_resolution,[status(thm)],[5316, 190, 1406])).
% 289.95/182.45 tff(5318,plain,
% 289.95/182.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_f, s5, s6)) | node16(c_e_h_2, c_f, s5) | node14(c_e_h_2, c_f, s5, s6) | node15(c_e_h_2, c_f, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_f, s5, s6)) | node16(c_e_h_2, c_f, s5) | node14(c_e_h_2, c_f, s5, s6) | node15(c_e_h_2, c_f, s5, s6))),
% 289.95/182.45 inference(rewrite,[status(thm)],[])).
% 289.95/182.45 tff(5319,plain,
% 289.95/182.45 ((node16(c_e_h_2, c_f, s5) | node14(c_e_h_2, c_f, s5, s6) | node15(c_e_h_2, c_f, s5, s6) | (~node19(c_e_h_2, c_f, s5, s6))) <=> ((~node19(c_e_h_2, c_f, s5, s6)) | node16(c_e_h_2, c_f, s5) | node14(c_e_h_2, c_f, s5, s6) | node15(c_e_h_2, c_f, s5, s6))),
% 289.95/182.45 inference(rewrite,[status(thm)],[])).
% 289.95/182.45 tff(5320,plain,
% 289.95/182.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s5) | node14(c_e_h_2, c_f, s5, s6) | node15(c_e_h_2, c_f, s5, s6) | (~node19(c_e_h_2, c_f, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_f, s5, s6)) | node16(c_e_h_2, c_f, s5) | node14(c_e_h_2, c_f, s5, s6) | node15(c_e_h_2, c_f, s5, s6)))),
% 289.95/182.45 inference(monotonicity,[status(thm)],[5319])).
% 289.95/182.45 tff(5321,plain,
% 289.95/182.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s5) | node14(c_e_h_2, c_f, s5, s6) | node15(c_e_h_2, c_f, s5, s6) | (~node19(c_e_h_2, c_f, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_f, s5, s6)) | node16(c_e_h_2, c_f, s5) | node14(c_e_h_2, c_f, s5, s6) | node15(c_e_h_2, c_f, s5, s6))),
% 289.95/182.45 inference(transitivity,[status(thm)],[5320, 5318])).
% 289.95/182.45 tff(5322,plain,
% 289.95/182.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s5) | node14(c_e_h_2, c_f, s5, s6) | node15(c_e_h_2, c_f, s5, s6) | (~node19(c_e_h_2, c_f, s5, s6)))),
% 289.95/182.46 inference(quant_inst,[status(thm)],[])).
% 289.95/182.46 tff(5323,plain,
% 289.95/182.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_f, s5, s6)) | node16(c_e_h_2, c_f, s5) | node14(c_e_h_2, c_f, s5, s6) | node15(c_e_h_2, c_f, s5, s6)),
% 289.95/182.46 inference(modus_ponens,[status(thm)],[5322, 5321])).
% 289.95/182.46 tff(5324,plain,
% 289.95/182.46 (node16(c_e_h_2, c_f, s5) | node14(c_e_h_2, c_f, s5, s6) | node15(c_e_h_2, c_f, s5, s6)),
% 289.95/182.46 inference(unit_resolution,[status(thm)],[5323, 204, 5317])).
% 289.95/182.46 tff(5325,plain,
% 289.95/182.46 ($false),
% 289.95/182.46 inference(unit_resolution,[status(thm)],[5324, 5313, 5308, 5297])).
% 289.95/182.46 tff(5326,plain,(m_c_h_element_v_in1(c_e_h_2, c_f, s5) | node15(c_e_h_2, c_f, s5, s6) | m_c_h_element_v_in2(c_e_h_2, c_f, s5) | (~m_c_h_element_v_out(c_e_h_2, c_f, s6))), inference(lemma,lemma(discharge,[]))).
% 289.95/182.46 tff(5327,plain,
% 289.95/182.46 (m_c_h_element_v_in1(c_e_h_2, c_f, s5)),
% 289.95/182.46 inference(unit_resolution,[status(thm)],[5326, 5296, 5288, 5287])).
% 289.95/182.46 tff(5328,plain,
% 289.95/182.46 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_f, s5)) | m_c_h_element_v_in2(c_e_h_2, c_f, s5) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_f, s5)) | m_c_h_element_v_in2(c_e_h_2, c_f, s5) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s5)))),
% 289.95/182.46 inference(rewrite,[status(thm)],[])).
% 289.95/182.46 tff(5329,plain,
% 289.95/182.46 (((~m_c_h_element_v_in1(c_e_h_2, c_f, s5)) | m_c_h_element_v_in2(c_e_h_2, c_f, s5) | (~node17(c_e_h_2, c_f, s5))) <=> ((~node17(c_e_h_2, c_f, s5)) | m_c_h_element_v_in2(c_e_h_2, c_f, s5) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s5)))),
% 289.95/182.46 inference(rewrite,[status(thm)],[])).
% 289.95/182.46 tff(5330,plain,
% 289.95/182.46 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s5)) | m_c_h_element_v_in2(c_e_h_2, c_f, s5) | (~node17(c_e_h_2, c_f, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_f, s5)) | m_c_h_element_v_in2(c_e_h_2, c_f, s5) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s5))))),
% 289.95/182.46 inference(monotonicity,[status(thm)],[5329])).
% 289.95/182.46 tff(5331,plain,
% 289.95/182.46 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s5)) | m_c_h_element_v_in2(c_e_h_2, c_f, s5) | (~node17(c_e_h_2, c_f, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_f, s5)) | m_c_h_element_v_in2(c_e_h_2, c_f, s5) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s5)))),
% 289.95/182.46 inference(transitivity,[status(thm)],[5330, 5328])).
% 289.95/182.46 tff(5332,plain,
% 289.95/182.46 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s5)) | m_c_h_element_v_in2(c_e_h_2, c_f, s5) | (~node17(c_e_h_2, c_f, s5)))),
% 289.95/182.46 inference(quant_inst,[status(thm)],[])).
% 289.95/182.46 tff(5333,plain,
% 289.95/182.46 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_f, s5)) | m_c_h_element_v_in2(c_e_h_2, c_f, s5) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s5))),
% 289.95/182.46 inference(modus_ponens,[status(thm)],[5332, 5331])).
% 289.95/182.46 tff(5334,plain,
% 289.95/182.46 ((~node17(c_e_h_2, c_f, s5)) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s5))),
% 289.95/182.46 inference(unit_resolution,[status(thm)],[5333, 919, 5288])).
% 289.95/182.46 tff(5335,plain,
% 289.95/182.46 (~node17(c_e_h_2, c_f, s5)),
% 289.95/182.46 inference(unit_resolution,[status(thm)],[5334, 5327])).
% 289.95/182.46 tff(5336,plain,
% 289.95/182.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_f, s5, s6)) | node18(c_e_h_2, c_f, s5, s6) | node17(c_e_h_2, c_f, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_f, s5, s6)) | node18(c_e_h_2, c_f, s5, s6) | node17(c_e_h_2, c_f, s5))),
% 289.95/182.46 inference(rewrite,[status(thm)],[])).
% 289.95/182.46 tff(5337,plain,
% 289.95/182.46 ((node17(c_e_h_2, c_f, s5) | node18(c_e_h_2, c_f, s5, s6) | (~node19(c_e_h_2, c_f, s5, s6))) <=> ((~node19(c_e_h_2, c_f, s5, s6)) | node18(c_e_h_2, c_f, s5, s6) | node17(c_e_h_2, c_f, s5))),
% 289.95/182.46 inference(rewrite,[status(thm)],[])).
% 289.95/182.46 tff(5338,plain,
% 289.95/182.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s5) | node18(c_e_h_2, c_f, s5, s6) | (~node19(c_e_h_2, c_f, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_f, s5, s6)) | node18(c_e_h_2, c_f, s5, s6) | node17(c_e_h_2, c_f, s5)))),
% 289.95/182.46 inference(monotonicity,[status(thm)],[5337])).
% 289.95/182.46 tff(5339,plain,
% 289.95/182.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s5) | node18(c_e_h_2, c_f, s5, s6) | (~node19(c_e_h_2, c_f, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_f, s5, s6)) | node18(c_e_h_2, c_f, s5, s6) | node17(c_e_h_2, c_f, s5))),
% 289.95/182.46 inference(transitivity,[status(thm)],[5338, 5336])).
% 289.95/182.46 tff(5340,plain,
% 289.95/182.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s5) | node18(c_e_h_2, c_f, s5, s6) | (~node19(c_e_h_2, c_f, s5, s6)))),
% 289.95/182.46 inference(quant_inst,[status(thm)],[])).
% 289.95/182.46 tff(5341,plain,
% 289.95/182.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_f, s5, s6)) | node18(c_e_h_2, c_f, s5, s6) | node17(c_e_h_2, c_f, s5)),
% 289.95/182.46 inference(modus_ponens,[status(thm)],[5340, 5339])).
% 289.95/182.46 tff(5342,plain,
% 289.95/182.46 (node18(c_e_h_2, c_f, s5, s6) | node17(c_e_h_2, c_f, s5)),
% 289.95/182.46 inference(unit_resolution,[status(thm)],[5341, 776, 5317])).
% 289.95/182.46 tff(5343,plain,
% 289.95/182.46 (node18(c_e_h_2, c_f, s5, s6)),
% 289.95/182.46 inference(unit_resolution,[status(thm)],[5342, 5335])).
% 289.95/182.46 tff(5344,plain,
% 289.95/182.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_f, s5) | (~m_c_h_element_v_out(c_e_h_2, c_f, s6)) | (~node18(c_e_h_2, c_f, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_f, s5) | (~m_c_h_element_v_out(c_e_h_2, c_f, s6)) | (~node18(c_e_h_2, c_f, s5, s6)))),
% 289.95/182.46 inference(rewrite,[status(thm)],[])).
% 289.95/182.46 tff(5345,plain,
% 289.95/182.46 (((~m_c_h_element_v_out(c_e_h_2, c_f, s6)) | m_c_h_element_v_out(c_e_h_2, c_f, s5) | (~node18(c_e_h_2, c_f, s5, s6))) <=> (m_c_h_element_v_out(c_e_h_2, c_f, s5) | (~m_c_h_element_v_out(c_e_h_2, c_f, s6)) | (~node18(c_e_h_2, c_f, s5, s6)))),
% 289.95/182.46 inference(rewrite,[status(thm)],[])).
% 289.95/182.46 tff(5346,plain,
% 289.95/182.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s6)) | m_c_h_element_v_out(c_e_h_2, c_f, s5) | (~node18(c_e_h_2, c_f, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_f, s5) | (~m_c_h_element_v_out(c_e_h_2, c_f, s6)) | (~node18(c_e_h_2, c_f, s5, s6))))),
% 289.95/182.46 inference(monotonicity,[status(thm)],[5345])).
% 289.95/182.46 tff(5347,plain,
% 289.95/182.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s6)) | m_c_h_element_v_out(c_e_h_2, c_f, s5) | (~node18(c_e_h_2, c_f, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_f, s5) | (~m_c_h_element_v_out(c_e_h_2, c_f, s6)) | (~node18(c_e_h_2, c_f, s5, s6)))),
% 289.95/182.46 inference(transitivity,[status(thm)],[5346, 5344])).
% 289.95/182.46 tff(5348,plain,
% 289.95/182.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s6)) | m_c_h_element_v_out(c_e_h_2, c_f, s5) | (~node18(c_e_h_2, c_f, s5, s6)))),
% 289.95/182.46 inference(quant_inst,[status(thm)],[])).
% 289.95/182.46 tff(5349,plain,
% 289.95/182.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_f, s5) | (~m_c_h_element_v_out(c_e_h_2, c_f, s6)) | (~node18(c_e_h_2, c_f, s5, s6))),
% 289.95/182.46 inference(modus_ponens,[status(thm)],[5348, 5347])).
% 289.95/182.46 tff(5350,plain,
% 289.95/182.46 ($false),
% 289.95/182.46 inference(unit_resolution,[status(thm)],[5349, 753, 5289, 5287, 5343])).
% 289.95/182.46 tff(5351,plain,((~m_c_h_element_v_out(c_e_h_2, c_f, s6)) | m_c_h_element_v_out(c_e_h_2, c_f, s5) | m_c_h_element_v_in2(c_e_h_2, c_f, s5)), inference(lemma,lemma(discharge,[]))).
% 289.95/182.46 tff(5352,plain,
% 289.95/182.46 ((~m_c_h_element_v_out(c_e_h_2, c_f, s6)) | m_c_h_element_v_in2(c_e_h_2, c_f, s5)),
% 289.95/182.46 inference(unit_resolution,[status(thm)],[5351, 4835])).
% 289.95/182.46 tff(5353,plain,
% 289.95/182.46 (~m_c_h_element_v_out(c_e_h_2, c_f, s6)),
% 289.95/182.46 inference(unit_resolution,[status(thm)],[5352, 5286])).
% 289.95/182.46 tff(5354,plain,
% 289.95/182.46 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_q, s6)) | m_c_h_element_v_out(c_e_h_2, c_f, s6))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_q, s6)) | m_c_h_element_v_out(c_e_h_2, c_f, s6))),
% 289.95/182.46 inference(rewrite,[status(thm)],[])).
% 289.95/182.46 tff(5355,plain,
% 289.95/182.46 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_q, s6)) | m_c_h_element_v_out(c_e_h_2, c_f, s6))),
% 289.95/182.46 inference(quant_inst,[status(thm)],[])).
% 289.95/182.46 tff(5356,plain,
% 289.95/182.46 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_q, s6)) | m_c_h_element_v_out(c_e_h_2, c_f, s6)),
% 289.95/182.46 inference(modus_ponens,[status(thm)],[5355, 5354])).
% 289.95/182.46 tff(5357,plain,
% 289.95/182.46 (~m_and_h_gate_v_in1(c_e_h_2, c_q, s6)),
% 289.95/182.46 inference(unit_resolution,[status(thm)],[5356, 1586, 5353])).
% 289.95/182.46 tff(5358,plain,
% 289.95/182.46 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_q, s6)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_q, s6)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s6))),
% 289.95/182.46 inference(rewrite,[status(thm)],[])).
% 289.95/182.46 tff(5359,plain,
% 289.95/182.46 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_q, s6)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s6))),
% 289.95/182.46 inference(quant_inst,[status(thm)],[])).
% 289.95/182.46 tff(5360,plain,
% 289.95/182.46 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_q, s6)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s6)),
% 289.95/182.46 inference(modus_ponens,[status(thm)],[5359, 5358])).
% 289.95/182.46 tff(5361,plain,
% 289.95/182.46 (~node20(c_e_h_2, c_q, s6)),
% 289.95/182.46 inference(unit_resolution,[status(thm)],[5360, 38, 5357])).
% 289.95/182.46 tff(5362,assumption,(node21(c_e_h_2, c_q, s6, s7)), introduced(assumption)).
% 289.95/182.46 tff(5363,plain,
% 289.95/182.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s7)) | node20(c_e_h_2, c_q, s6) | (~node21(c_e_h_2, c_q, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s7)) | node20(c_e_h_2, c_q, s6) | (~node21(c_e_h_2, c_q, s6, s7)))),
% 289.95/182.46 inference(rewrite,[status(thm)],[])).
% 289.95/182.46 tff(5364,plain,
% 289.95/182.46 ((node20(c_e_h_2, c_q, s6) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s7)) | (~node21(c_e_h_2, c_q, s6, s7))) <=> ((~m_and_h_gate_v_out(c_e_h_2, c_q, s7)) | node20(c_e_h_2, c_q, s6) | (~node21(c_e_h_2, c_q, s6, s7)))),
% 289.95/182.47 inference(rewrite,[status(thm)],[])).
% 289.95/182.47 tff(5365,plain,
% 289.95/182.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_q, s6) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s7)) | (~node21(c_e_h_2, c_q, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s7)) | node20(c_e_h_2, c_q, s6) | (~node21(c_e_h_2, c_q, s6, s7))))),
% 289.95/182.47 inference(monotonicity,[status(thm)],[5364])).
% 289.95/182.47 tff(5366,plain,
% 289.95/182.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_q, s6) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s7)) | (~node21(c_e_h_2, c_q, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s7)) | node20(c_e_h_2, c_q, s6) | (~node21(c_e_h_2, c_q, s6, s7)))),
% 289.95/182.47 inference(transitivity,[status(thm)],[5365, 5363])).
% 289.95/182.47 tff(5367,plain,
% 289.95/182.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_q, s6) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s7)) | (~node21(c_e_h_2, c_q, s6, s7)))),
% 289.95/182.47 inference(quant_inst,[status(thm)],[])).
% 289.95/182.47 tff(5368,plain,
% 289.95/182.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s7)) | node20(c_e_h_2, c_q, s6) | (~node21(c_e_h_2, c_q, s6, s7))),
% 289.95/182.47 inference(modus_ponens,[status(thm)],[5367, 5366])).
% 289.95/182.47 tff(5369,plain,
% 289.95/182.47 ($false),
% 289.95/182.47 inference(unit_resolution,[status(thm)],[5368, 52, 4907, 5362, 5361])).
% 289.95/182.47 tff(5370,plain,((~node21(c_e_h_2, c_q, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s7))), inference(lemma,lemma(discharge,[]))).
% 289.95/182.47 tff(5371,plain,
% 289.95/182.47 (~node21(c_e_h_2, c_q, s6, s7)),
% 289.95/182.47 inference(unit_resolution,[status(thm)],[5370, 4907])).
% 289.95/182.47 tff(5372,plain,
% 289.95/182.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_2, c_q, s6, s7) | node22(c_e_h_2, c_q, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_2, c_q, s6, s7) | node22(c_e_h_2, c_q, s6, s7))),
% 289.95/182.47 inference(rewrite,[status(thm)],[])).
% 289.95/182.47 tff(5373,plain,
% 289.95/182.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_2, c_q, s6, s7) | node22(c_e_h_2, c_q, s6, s7))),
% 289.95/182.47 inference(quant_inst,[status(thm)],[])).
% 289.95/182.47 tff(5374,plain,
% 289.95/182.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_2, c_q, s6, s7) | node22(c_e_h_2, c_q, s6, s7)),
% 289.95/182.47 inference(modus_ponens,[status(thm)],[5373, 5372])).
% 289.95/182.47 tff(5375,plain,
% 289.95/182.47 (node21(c_e_h_2, c_q, s6, s7) | node22(c_e_h_2, c_q, s6, s7)),
% 289.95/182.47 inference(unit_resolution,[status(thm)],[5374, 82, 1844])).
% 289.95/182.47 tff(5376,plain,
% 289.95/182.47 (node22(c_e_h_2, c_q, s6, s7)),
% 289.95/182.47 inference(unit_resolution,[status(thm)],[5375, 5371])).
% 289.95/182.47 tff(5377,plain,
% 289.95/182.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s7)) | (~node22(c_e_h_2, c_q, s6, s7)) | m_and_h_gate_v_out(c_e_h_2, c_q, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s7)) | (~node22(c_e_h_2, c_q, s6, s7)) | m_and_h_gate_v_out(c_e_h_2, c_q, s6))),
% 289.95/182.47 inference(rewrite,[status(thm)],[])).
% 289.95/182.47 tff(5378,plain,
% 289.95/182.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s7)) | (~node22(c_e_h_2, c_q, s6, s7)) | m_and_h_gate_v_out(c_e_h_2, c_q, s6))),
% 289.95/182.47 inference(quant_inst,[status(thm)],[])).
% 289.95/182.47 tff(5379,plain,
% 289.95/182.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s7)) | (~node22(c_e_h_2, c_q, s6, s7)) | m_and_h_gate_v_out(c_e_h_2, c_q, s6)),
% 289.95/182.47 inference(modus_ponens,[status(thm)],[5378, 5377])).
% 289.95/182.47 tff(5380,plain,
% 289.95/182.47 ($false),
% 289.95/182.47 inference(unit_resolution,[status(thm)],[5379, 108, 4907, 4862, 5376])).
% 289.95/182.47 tff(5381,plain,(~m_and_h_gate_v_out(c_e_h_2, c_q, s7)), inference(lemma,lemma(discharge,[]))).
% 289.95/182.47 tff(5382,plain,
% 289.95/182.47 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s7))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s7))),
% 289.95/182.47 inference(rewrite,[status(thm)],[])).
% 289.95/182.47 tff(5383,plain,
% 289.95/182.47 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s7))),
% 289.95/182.47 inference(quant_inst,[status(thm)],[])).
% 289.95/182.47 tff(5384,plain,
% 289.95/182.47 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s7)),
% 289.95/182.47 inference(modus_ponens,[status(thm)],[5383, 5382])).
% 289.95/182.47 tff(5385,plain,
% 289.95/182.47 (node3(c_e_h_2, c_e_h_3, s7)),
% 289.95/182.47 inference(unit_resolution,[status(thm)],[5384, 1059, 1056])).
% 289.95/182.47 tff(5386,plain,
% 289.95/182.47 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_3, s7)) | (~node3(c_e_h_2, c_e_h_3, s7)) | m_and_h_gate_v_out(c_e_h_2, c_q, s7))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_3, s7)) | (~node3(c_e_h_2, c_e_h_3, s7)) | m_and_h_gate_v_out(c_e_h_2, c_q, s7))),
% 289.95/182.47 inference(rewrite,[status(thm)],[])).
% 289.95/182.47 tff(5387,plain,
% 289.95/182.47 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_3, s7)) | (~node3(c_e_h_2, c_e_h_3, s7)) | m_and_h_gate_v_out(c_e_h_2, c_q, s7))),
% 289.95/182.47 inference(quant_inst,[status(thm)],[])).
% 289.95/182.47 tff(5388,plain,
% 289.95/182.47 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_3, s7)) | (~node3(c_e_h_2, c_e_h_3, s7)) | m_and_h_gate_v_out(c_e_h_2, c_q, s7)),
% 289.95/182.47 inference(modus_ponens,[status(thm)],[5387, 5386])).
% 289.95/182.47 tff(5389,plain,
% 289.95/182.47 ((~m_cell_v_ack(c_e_h_3, s7)) | m_and_h_gate_v_out(c_e_h_2, c_q, s7)),
% 289.95/182.47 inference(unit_resolution,[status(thm)],[5388, 1073, 5385])).
% 289.95/182.47 tff(5390,plain,
% 289.95/182.47 (~m_cell_v_ack(c_e_h_3, s7)),
% 289.95/182.47 inference(unit_resolution,[status(thm)],[5389, 5381])).
% 289.95/182.47 tff(5391,plain,
% 289.95/182.47 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_j, s7)) | m_cell_v_ack(c_e_h_3, s7))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_j, s7)) | m_cell_v_ack(c_e_h_3, s7))),
% 289.95/182.47 inference(rewrite,[status(thm)],[])).
% 289.95/182.47 tff(5392,plain,
% 289.95/182.47 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_j, s7)) | m_cell_v_ack(c_e_h_3, s7))),
% 289.95/182.47 inference(quant_inst,[status(thm)],[])).
% 289.95/182.47 tff(5393,plain,
% 289.95/182.47 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_j, s7)) | m_cell_v_ack(c_e_h_3, s7)),
% 289.95/182.47 inference(modus_ponens,[status(thm)],[5392, 5391])).
% 289.95/182.47 tff(5394,plain,
% 289.95/182.47 (~m_or_h_gate_v_in2(c_e_h_3, c_j, s7)),
% 289.95/182.47 inference(unit_resolution,[status(thm)],[5393, 1085, 5390])).
% 289.95/182.47 tff(5395,assumption,(~m_or_h_gate_v_out(c_e_h_3, c_j, s7)), introduced(assumption)).
% 289.95/182.47 tff(5396,assumption,(node6(c_e_h_3, c_j, s7, s8)), introduced(assumption)).
% 289.95/182.47 tff(5397,plain,
% 289.95/182.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_3, c_j, s7) | (~node6(c_e_h_3, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_j, s7) | (~node6(c_e_h_3, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s8)))),
% 289.95/182.47 inference(rewrite,[status(thm)],[])).
% 289.95/182.47 tff(5398,plain,
% 289.95/182.47 (((~node6(c_e_h_3, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s8)) | m_or_h_gate_v_out(c_e_h_3, c_j, s7)) <=> (m_or_h_gate_v_out(c_e_h_3, c_j, s7) | (~node6(c_e_h_3, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s8)))),
% 289.95/182.47 inference(rewrite,[status(thm)],[])).
% 289.95/182.47 tff(5399,plain,
% 289.95/182.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s8)) | m_or_h_gate_v_out(c_e_h_3, c_j, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_3, c_j, s7) | (~node6(c_e_h_3, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s8))))),
% 289.95/182.47 inference(monotonicity,[status(thm)],[5398])).
% 289.95/182.47 tff(5400,plain,
% 289.95/182.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s8)) | m_or_h_gate_v_out(c_e_h_3, c_j, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_j, s7) | (~node6(c_e_h_3, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s8)))),
% 289.95/182.47 inference(transitivity,[status(thm)],[5399, 5397])).
% 289.95/182.47 tff(5401,plain,
% 289.95/182.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s8)) | m_or_h_gate_v_out(c_e_h_3, c_j, s7))),
% 289.95/182.47 inference(quant_inst,[status(thm)],[])).
% 289.95/182.47 tff(5402,plain,
% 289.95/182.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_j, s7) | (~node6(c_e_h_3, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s8))),
% 289.95/182.47 inference(modus_ponens,[status(thm)],[5401, 5400])).
% 289.95/182.47 tff(5403,plain,
% 289.95/182.47 ($false),
% 289.95/182.47 inference(unit_resolution,[status(thm)],[5402, 1121, 5395, 3367, 5396])).
% 289.95/182.47 tff(5404,plain,((~node6(c_e_h_3, c_j, s7, s8)) | m_or_h_gate_v_out(c_e_h_3, c_j, s7) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s8))), inference(lemma,lemma(discharge,[]))).
% 289.95/182.47 tff(5405,plain,
% 289.95/182.47 (~node6(c_e_h_3, c_j, s7, s8)),
% 289.95/182.47 inference(unit_resolution,[status(thm)],[5404, 3367, 5395])).
% 289.95/182.47 tff(5406,plain,
% 289.95/182.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s7, s8)) | node5(c_e_h_3, c_j, s7, s8) | node6(c_e_h_3, c_j, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s7, s8)) | node5(c_e_h_3, c_j, s7, s8) | node6(c_e_h_3, c_j, s7, s8))),
% 289.95/182.47 inference(rewrite,[status(thm)],[])).
% 289.95/182.47 tff(5407,plain,
% 289.95/182.47 ((node6(c_e_h_3, c_j, s7, s8) | node5(c_e_h_3, c_j, s7, s8) | (~trans(s7, s8))) <=> ((~trans(s7, s8)) | node5(c_e_h_3, c_j, s7, s8) | node6(c_e_h_3, c_j, s7, s8))),
% 289.95/182.47 inference(rewrite,[status(thm)],[])).
% 289.95/182.47 tff(5408,plain,
% 289.95/182.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s7, s8) | node5(c_e_h_3, c_j, s7, s8) | (~trans(s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s7, s8)) | node5(c_e_h_3, c_j, s7, s8) | node6(c_e_h_3, c_j, s7, s8)))),
% 289.95/182.47 inference(monotonicity,[status(thm)],[5407])).
% 289.95/182.48 tff(5409,plain,
% 289.95/182.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s7, s8) | node5(c_e_h_3, c_j, s7, s8) | (~trans(s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s7, s8)) | node5(c_e_h_3, c_j, s7, s8) | node6(c_e_h_3, c_j, s7, s8))),
% 289.95/182.48 inference(transitivity,[status(thm)],[5408, 5406])).
% 289.95/182.48 tff(5410,plain,
% 289.95/182.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s7, s8) | node5(c_e_h_3, c_j, s7, s8) | (~trans(s7, s8)))),
% 289.95/182.48 inference(quant_inst,[status(thm)],[])).
% 289.95/182.48 tff(5411,plain,
% 289.95/182.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s7, s8)) | node5(c_e_h_3, c_j, s7, s8) | node6(c_e_h_3, c_j, s7, s8)),
% 289.95/182.48 inference(modus_ponens,[status(thm)],[5410, 5409])).
% 289.95/182.48 tff(5412,plain,
% 289.95/182.48 (node5(c_e_h_3, c_j, s7, s8) | node6(c_e_h_3, c_j, s7, s8)),
% 289.95/182.48 inference(unit_resolution,[status(thm)],[5411, 1141, 1938])).
% 289.95/182.48 tff(5413,plain,
% 289.95/182.48 (node5(c_e_h_3, c_j, s7, s8)),
% 289.95/182.48 inference(unit_resolution,[status(thm)],[5412, 5405])).
% 289.95/182.48 tff(5414,plain,
% 289.95/182.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_3, c_j, s7) | m_or_h_gate_v_in1(c_e_h_3, c_j, s7) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s8)) | (~node5(c_e_h_3, c_j, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_3, c_j, s7) | m_or_h_gate_v_in1(c_e_h_3, c_j, s7) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s8)) | (~node5(c_e_h_3, c_j, s7, s8)))),
% 289.95/182.48 inference(rewrite,[status(thm)],[])).
% 289.95/182.48 tff(5415,plain,
% 289.95/182.48 ((m_or_h_gate_v_in1(c_e_h_3, c_j, s7) | m_or_h_gate_v_in2(c_e_h_3, c_j, s7) | (~node5(c_e_h_3, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s8))) <=> (m_or_h_gate_v_in2(c_e_h_3, c_j, s7) | m_or_h_gate_v_in1(c_e_h_3, c_j, s7) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s8)) | (~node5(c_e_h_3, c_j, s7, s8)))),
% 289.95/182.48 inference(rewrite,[status(thm)],[])).
% 289.95/182.48 tff(5416,plain,
% 289.95/182.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s7) | m_or_h_gate_v_in2(c_e_h_3, c_j, s7) | (~node5(c_e_h_3, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_3, c_j, s7) | m_or_h_gate_v_in1(c_e_h_3, c_j, s7) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s8)) | (~node5(c_e_h_3, c_j, s7, s8))))),
% 289.95/182.48 inference(monotonicity,[status(thm)],[5415])).
% 289.95/182.48 tff(5417,plain,
% 289.95/182.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s7) | m_or_h_gate_v_in2(c_e_h_3, c_j, s7) | (~node5(c_e_h_3, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_3, c_j, s7) | m_or_h_gate_v_in1(c_e_h_3, c_j, s7) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s8)) | (~node5(c_e_h_3, c_j, s7, s8)))),
% 289.95/182.48 inference(transitivity,[status(thm)],[5416, 5414])).
% 289.95/182.48 tff(5418,plain,
% 289.95/182.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s7) | m_or_h_gate_v_in2(c_e_h_3, c_j, s7) | (~node5(c_e_h_3, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s8)))),
% 289.95/182.48 inference(quant_inst,[status(thm)],[])).
% 289.95/182.48 tff(5419,plain,
% 289.95/182.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_3, c_j, s7) | m_or_h_gate_v_in1(c_e_h_3, c_j, s7) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s8)) | (~node5(c_e_h_3, c_j, s7, s8))),
% 289.95/182.48 inference(modus_ponens,[status(thm)],[5418, 5417])).
% 289.95/182.48 tff(5420,plain,
% 289.95/182.48 ($false),
% 289.95/182.48 inference(unit_resolution,[status(thm)],[5419, 1159, 3367, 5413, 5394, 4906])).
% 289.95/182.48 tff(5421,plain,((~m_or_h_gate_v_out(c_e_h_3, c_j, s8)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s7) | m_or_h_gate_v_out(c_e_h_3, c_j, s7)), inference(lemma,lemma(discharge,[]))).
% 289.95/182.48 tff(5422,plain,
% 289.95/182.48 (m_or_h_gate_v_in1(c_e_h_3, c_j, s7)),
% 289.95/182.48 inference(unit_resolution,[status(thm)],[5421, 4905, 3367])).
% 289.95/182.48 tff(5423,assumption,(~node20(c_e_h_3, c_l, s6)), introduced(assumption)).
% 289.95/182.48 tff(5424,assumption,(m_and_h_gate_v_out(c_e_h_3, c_l, s7)), introduced(assumption)).
% 289.95/182.48 tff(5425,assumption,(node22(c_e_h_3, c_l, s6, s7)), introduced(assumption)).
% 289.95/182.48 tff(5426,plain,
% 289.95/182.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s7)) | (~node22(c_e_h_3, c_l, s6, s7)) | m_and_h_gate_v_out(c_e_h_3, c_l, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s7)) | (~node22(c_e_h_3, c_l, s6, s7)) | m_and_h_gate_v_out(c_e_h_3, c_l, s6))),
% 289.95/182.48 inference(rewrite,[status(thm)],[])).
% 289.95/182.48 tff(5427,plain,
% 289.95/182.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s7)) | (~node22(c_e_h_3, c_l, s6, s7)) | m_and_h_gate_v_out(c_e_h_3, c_l, s6))),
% 289.95/182.48 inference(quant_inst,[status(thm)],[])).
% 289.95/182.48 tff(5428,plain,
% 289.95/182.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s7)) | (~node22(c_e_h_3, c_l, s6, s7)) | m_and_h_gate_v_out(c_e_h_3, c_l, s6)),
% 289.95/182.48 inference(modus_ponens,[status(thm)],[5427, 5426])).
% 289.95/182.48 tff(5429,plain,
% 289.95/182.48 ($false),
% 289.95/182.48 inference(unit_resolution,[status(thm)],[5428, 108, 5425, 4486, 5424])).
% 289.95/182.48 tff(5430,plain,((~node22(c_e_h_3, c_l, s6, s7)) | m_and_h_gate_v_out(c_e_h_3, c_l, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s7))), inference(lemma,lemma(discharge,[]))).
% 289.95/182.48 tff(5431,plain,
% 289.95/182.48 (~node22(c_e_h_3, c_l, s6, s7)),
% 289.95/182.48 inference(unit_resolution,[status(thm)],[5430, 5424, 4486])).
% 289.95/182.48 tff(5432,plain,
% 289.95/182.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_3, c_l, s6, s7) | node22(c_e_h_3, c_l, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_3, c_l, s6, s7) | node22(c_e_h_3, c_l, s6, s7))),
% 289.95/182.48 inference(rewrite,[status(thm)],[])).
% 289.95/182.48 tff(5433,plain,
% 289.95/182.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_3, c_l, s6, s7) | node22(c_e_h_3, c_l, s6, s7))),
% 289.95/182.48 inference(quant_inst,[status(thm)],[])).
% 289.95/182.48 tff(5434,plain,
% 289.95/182.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_3, c_l, s6, s7) | node22(c_e_h_3, c_l, s6, s7)),
% 289.95/182.48 inference(modus_ponens,[status(thm)],[5433, 5432])).
% 289.95/182.48 tff(5435,plain,
% 289.95/182.48 (node21(c_e_h_3, c_l, s6, s7) | node22(c_e_h_3, c_l, s6, s7)),
% 289.95/182.48 inference(unit_resolution,[status(thm)],[5434, 82, 1844])).
% 289.95/182.48 tff(5436,plain,
% 289.95/182.48 (node21(c_e_h_3, c_l, s6, s7)),
% 289.95/182.48 inference(unit_resolution,[status(thm)],[5435, 5431])).
% 289.95/182.48 tff(5437,plain,
% 289.95/182.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s7)) | (~node21(c_e_h_3, c_l, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_l, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s7)) | (~node21(c_e_h_3, c_l, s6, s7)))),
% 289.95/182.48 inference(rewrite,[status(thm)],[])).
% 289.95/182.48 tff(5438,plain,
% 289.95/182.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s7)) | (~node21(c_e_h_3, c_l, s6, s7)))),
% 289.95/182.48 inference(quant_inst,[status(thm)],[])).
% 289.95/182.48 tff(5439,plain,
% 289.95/182.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_l, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s7)) | (~node21(c_e_h_3, c_l, s6, s7))),
% 289.95/182.48 inference(modus_ponens,[status(thm)],[5438, 5437])).
% 289.95/182.48 tff(5440,plain,
% 289.95/182.48 ($false),
% 289.95/182.48 inference(unit_resolution,[status(thm)],[5439, 52, 5436, 5424, 5423])).
% 289.95/182.48 tff(5441,plain,((~m_and_h_gate_v_out(c_e_h_3, c_l, s7)) | node20(c_e_h_3, c_l, s6) | m_and_h_gate_v_out(c_e_h_3, c_l, s6)), inference(lemma,lemma(discharge,[]))).
% 289.95/182.48 tff(5442,plain,
% 289.95/182.48 (~m_and_h_gate_v_out(c_e_h_3, c_l, s7)),
% 289.95/182.48 inference(unit_resolution,[status(thm)],[5441, 4486, 5423])).
% 289.95/182.48 tff(5443,plain,
% 289.95/182.48 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_j, s7)) | m_and_h_gate_v_out(c_e_h_3, c_l, s7))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s7)) | m_and_h_gate_v_out(c_e_h_3, c_l, s7))),
% 289.95/182.48 inference(rewrite,[status(thm)],[])).
% 289.95/182.48 tff(5444,plain,
% 289.95/182.48 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_j, s7)) | m_and_h_gate_v_out(c_e_h_3, c_l, s7))),
% 289.95/182.48 inference(quant_inst,[status(thm)],[])).
% 289.95/182.48 tff(5445,plain,
% 289.95/182.48 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s7)) | m_and_h_gate_v_out(c_e_h_3, c_l, s7)),
% 289.95/182.48 inference(modus_ponens,[status(thm)],[5444, 5443])).
% 289.95/182.48 tff(5446,plain,
% 289.95/182.48 ($false),
% 289.95/182.48 inference(unit_resolution,[status(thm)],[5445, 1100, 5442, 5422])).
% 289.95/182.48 tff(5447,plain,(m_and_h_gate_v_out(c_e_h_3, c_l, s6) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s8)) | m_or_h_gate_v_out(c_e_h_3, c_j, s6) | node20(c_e_h_3, c_l, s6)), inference(lemma,lemma(discharge,[]))).
% 289.95/182.48 tff(5448,plain,
% 289.95/182.48 ($false),
% 289.95/182.48 inference(unit_resolution,[status(thm)],[5447, 4484, 4448, 3367, 4386])).
% 289.95/182.48 tff(5449,plain,(m_and_h_gate_v_out(c_e_h_3, c_k, s4) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s8)) | node20(c_e_h_3, c_k, s5) | node20(c_e_h_3, c_k, s4)), inference(lemma,lemma(discharge,[]))).
% 289.95/182.48 tff(5450,plain,
% 289.95/182.48 ((~m_or_h_gate_v_out(c_e_h_3, c_j, s8)) | node20(c_e_h_3, c_k, s5) | node20(c_e_h_3, c_k, s4)),
% 289.95/182.48 inference(unit_resolution,[status(thm)],[5449, 3485])).
% 289.95/182.48 tff(5451,plain,
% 289.95/182.48 (node20(c_e_h_3, c_k, s5)),
% 289.95/182.48 inference(unit_resolution,[status(thm)],[5450, 3393, 3367])).
% 289.95/182.48 tff(5452,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_k, s5)), introduced(assumption)).
% 289.95/182.48 tff(5453,assumption,(node20(c_e_h_3, c_k, s5)), introduced(assumption)).
% 289.95/182.48 tff(5454,plain,
% 289.95/182.48 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_k, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_k, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s5))),
% 289.95/182.48 inference(rewrite,[status(thm)],[])).
% 289.95/182.48 tff(5455,plain,
% 289.95/182.48 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_k, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s5))),
% 289.95/182.48 inference(quant_inst,[status(thm)],[])).
% 289.95/182.48 tff(5456,plain,
% 289.95/182.48 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_k, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s5)),
% 289.95/182.48 inference(modus_ponens,[status(thm)],[5455, 5454])).
% 289.95/182.48 tff(5457,plain,
% 289.95/182.48 ($false),
% 289.95/182.48 inference(unit_resolution,[status(thm)],[5456, 38, 5453, 5452])).
% 289.95/182.49 tff(5458,plain,((~node20(c_e_h_3, c_k, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s5)), inference(lemma,lemma(discharge,[]))).
% 289.95/182.49 tff(5459,plain,
% 289.95/182.49 ($false),
% 289.95/182.49 inference(unit_resolution,[status(thm)],[5458, 5451, 3366])).
% 289.95/182.49 tff(5460,plain,(m_and_h_gate_v_in1(c_e_h_3, c_c, s3) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s8))), inference(lemma,lemma(discharge,[]))).
% 289.95/182.49 tff(5461,plain,
% 289.95/182.49 (~m_or_h_gate_v_out(c_e_h_3, c_j, s8)),
% 289.95/182.49 inference(unit_resolution,[status(thm)],[5460, 2545])).
% 289.95/182.49 tff(5462,assumption,(~m_or_h_gate_v_out(c_e_h_3, c_j, s9)), introduced(assumption)).
% 289.95/182.49 tff(5463,assumption,(~node4(c_e_h_3, c_j, s8)), introduced(assumption)).
% 289.95/182.49 tff(5464,assumption,(node6(c_e_h_3, c_j, s8, s9)), introduced(assumption)).
% 289.95/182.49 tff(5465,plain,
% 289.95/182.49 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl((m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X))) <=> (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X))))),
% 289.95/182.49 inference(bind,[status(th)],[])).
% 289.95/182.49 tff(5466,plain,
% 289.95/182.49 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))),
% 289.95/182.49 inference(quant_intro,[status(thm)],[5465])).
% 289.95/182.49 tff(5467,plain,
% 289.95/182.49 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))),
% 289.95/182.49 inference(rewrite,[status(thm)],[])).
% 289.95/182.49 tff(5468,plain,
% 289.95/182.49 (^[Y: $i, I0: $i, X: $i, I1: $i] : trans(monotonicity(rewrite((m_or_h_gate_v_out(I0, I1, Y) | (~m_or_h_gate_v_out(I0, I1, X))) <=> (m_or_h_gate_v_out(I0, I1, Y) | (~m_or_h_gate_v_out(I0, I1, X)))), (((m_or_h_gate_v_out(I0, I1, Y) | (~m_or_h_gate_v_out(I0, I1, X))) | (~node6(I0, I1, X, Y))) <=> ((m_or_h_gate_v_out(I0, I1, Y) | (~m_or_h_gate_v_out(I0, I1, X))) | (~node6(I0, I1, X, Y))))), rewrite(((m_or_h_gate_v_out(I0, I1, Y) | (~m_or_h_gate_v_out(I0, I1, X))) | (~node6(I0, I1, X, Y))) <=> (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))), (((m_or_h_gate_v_out(I0, I1, Y) | (~m_or_h_gate_v_out(I0, I1, X))) | (~node6(I0, I1, X, Y))) <=> (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))))),
% 289.95/182.49 inference(bind,[status(th)],[])).
% 289.95/182.49 tff(5469,plain,
% 289.95/182.49 (![Y: $i, I0: $i, X: $i, I1: $i] : ((m_or_h_gate_v_out(I0, I1, Y) | (~m_or_h_gate_v_out(I0, I1, X))) | (~node6(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))),
% 289.95/182.49 inference(quant_intro,[status(thm)],[5468])).
% 289.95/182.49 tff(5470,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : ((m_or_h_gate_v_out(I0, I1, Y) | (~m_or_h_gate_v_out(I0, I1, X))) | (~node6(I0, I1, X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_or_h_gate_6')).
% 289.95/182.49 tff(5471,plain,
% 289.95/182.49 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))),
% 289.95/182.49 inference(modus_ponens,[status(thm)],[5470, 5469])).
% 289.95/182.49 tff(5472,plain,
% 289.95/182.49 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))),
% 289.95/182.49 inference(modus_ponens,[status(thm)],[5471, 5467])).
% 289.95/182.49 tff(5473,plain,(
% 289.95/182.49 ![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))),
% 289.95/182.49 inference(skolemize,[status(sab)],[5472])).
% 289.95/182.49 tff(5474,plain,
% 289.95/182.49 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))),
% 289.95/182.49 inference(modus_ponens,[status(thm)],[5473, 5466])).
% 289.95/182.49 tff(5475,plain,
% 289.95/182.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_3, c_j, s9) | (~node6(c_e_h_3, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | m_or_h_gate_v_out(c_e_h_3, c_j, s9) | (~node6(c_e_h_3, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s8)))),
% 289.95/182.49 inference(rewrite,[status(thm)],[])).
% 289.95/182.49 tff(5476,plain,
% 289.95/182.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_3, c_j, s9) | (~node6(c_e_h_3, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s8)))),
% 289.95/182.49 inference(quant_inst,[status(thm)],[])).
% 289.95/182.49 tff(5477,plain,
% 289.95/182.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | m_or_h_gate_v_out(c_e_h_3, c_j, s9) | (~node6(c_e_h_3, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s8))),
% 289.95/182.49 inference(modus_ponens,[status(thm)],[5476, 5475])).
% 289.95/182.49 tff(5478,plain,
% 289.95/182.49 ($false),
% 289.95/182.49 inference(unit_resolution,[status(thm)],[5477, 5474, 5462, 3367, 5464])).
% 289.95/182.49 tff(5479,plain,((~node6(c_e_h_3, c_j, s8, s9)) | m_or_h_gate_v_out(c_e_h_3, c_j, s9) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s8))), inference(lemma,lemma(discharge,[]))).
% 289.95/182.49 tff(5480,plain,
% 289.95/182.49 (~node6(c_e_h_3, c_j, s8, s9)),
% 289.95/182.49 inference(unit_resolution,[status(thm)],[5479, 5462, 3367])).
% 289.95/182.49 tff(5481,plain,
% 289.95/182.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s8, s9)) | node5(c_e_h_3, c_j, s8, s9) | node6(c_e_h_3, c_j, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s8, s9)) | node5(c_e_h_3, c_j, s8, s9) | node6(c_e_h_3, c_j, s8, s9))),
% 289.95/182.49 inference(rewrite,[status(thm)],[])).
% 289.95/182.49 tff(5482,plain,
% 289.95/182.49 ((node6(c_e_h_3, c_j, s8, s9) | node5(c_e_h_3, c_j, s8, s9) | (~trans(s8, s9))) <=> ((~trans(s8, s9)) | node5(c_e_h_3, c_j, s8, s9) | node6(c_e_h_3, c_j, s8, s9))),
% 289.95/182.49 inference(rewrite,[status(thm)],[])).
% 289.95/182.49 tff(5483,plain,
% 289.95/182.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s8, s9) | node5(c_e_h_3, c_j, s8, s9) | (~trans(s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s8, s9)) | node5(c_e_h_3, c_j, s8, s9) | node6(c_e_h_3, c_j, s8, s9)))),
% 289.95/182.49 inference(monotonicity,[status(thm)],[5482])).
% 289.95/182.49 tff(5484,plain,
% 289.95/182.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s8, s9) | node5(c_e_h_3, c_j, s8, s9) | (~trans(s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s8, s9)) | node5(c_e_h_3, c_j, s8, s9) | node6(c_e_h_3, c_j, s8, s9))),
% 289.95/182.49 inference(transitivity,[status(thm)],[5483, 5481])).
% 289.95/182.49 tff(5485,plain,
% 289.95/182.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s8, s9) | node5(c_e_h_3, c_j, s8, s9) | (~trans(s8, s9)))),
% 289.95/182.49 inference(quant_inst,[status(thm)],[])).
% 289.95/182.49 tff(5486,plain,
% 289.95/182.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s8, s9)) | node5(c_e_h_3, c_j, s8, s9) | node6(c_e_h_3, c_j, s8, s9)),
% 289.95/182.49 inference(modus_ponens,[status(thm)],[5485, 5484])).
% 289.95/182.49 tff(5487,plain,
% 289.95/182.49 (node5(c_e_h_3, c_j, s8, s9) | node6(c_e_h_3, c_j, s8, s9)),
% 289.95/182.49 inference(unit_resolution,[status(thm)],[5486, 1141, 1993])).
% 289.95/182.49 tff(5488,plain,
% 289.95/182.49 (node5(c_e_h_3, c_j, s8, s9)),
% 289.95/182.49 inference(unit_resolution,[status(thm)],[5487, 5480])).
% 289.95/182.49 tff(5489,plain,
% 289.95/182.49 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl((node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y)) <=> (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y)))),
% 289.95/182.49 inference(bind,[status(th)],[])).
% 289.95/182.49 tff(5490,plain,
% 289.95/182.49 (![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))),
% 289.95/182.49 inference(quant_intro,[status(thm)],[5489])).
% 289.95/182.49 tff(5491,plain,
% 289.95/182.49 (![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))),
% 289.95/182.49 inference(rewrite,[status(thm)],[])).
% 289.95/182.49 tff(5492,plain,
% 289.95/182.49 (^[Y: $i, I0: $i, X: $i, I1: $i] : rewrite(((m_or_h_gate_v_out(I0, I1, Y) | node4(I0, I1, X)) | (~node5(I0, I1, X, Y))) <=> (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y)))),
% 289.95/182.49 inference(bind,[status(th)],[])).
% 289.95/182.49 tff(5493,plain,
% 289.95/182.49 (![Y: $i, I0: $i, X: $i, I1: $i] : ((m_or_h_gate_v_out(I0, I1, Y) | node4(I0, I1, X)) | (~node5(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))),
% 289.95/182.49 inference(quant_intro,[status(thm)],[5492])).
% 289.95/182.49 tff(5494,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : ((m_or_h_gate_v_out(I0, I1, Y) | node4(I0, I1, X)) | (~node5(I0, I1, X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_or_h_gate_4')).
% 289.95/182.49 tff(5495,plain,
% 289.95/182.49 (![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))),
% 289.95/182.49 inference(modus_ponens,[status(thm)],[5494, 5493])).
% 289.95/182.49 tff(5496,plain,
% 289.95/182.49 (![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))),
% 289.95/182.49 inference(modus_ponens,[status(thm)],[5495, 5491])).
% 289.95/182.49 tff(5497,plain,(
% 289.95/182.49 ![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))),
% 289.95/182.49 inference(skolemize,[status(sab)],[5496])).
% 289.95/182.49 tff(5498,plain,
% 289.95/182.49 (![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))),
% 289.95/182.49 inference(modus_ponens,[status(thm)],[5497, 5490])).
% 289.95/182.49 tff(5499,plain,
% 289.95/182.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (m_or_h_gate_v_out(c_e_h_3, c_j, s9) | node4(c_e_h_3, c_j, s8) | (~node5(c_e_h_3, c_j, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | m_or_h_gate_v_out(c_e_h_3, c_j, s9) | node4(c_e_h_3, c_j, s8) | (~node5(c_e_h_3, c_j, s8, s9)))),
% 289.95/182.49 inference(rewrite,[status(thm)],[])).
% 289.95/182.49 tff(5500,plain,
% 289.95/182.49 ((node4(c_e_h_3, c_j, s8) | (~node5(c_e_h_3, c_j, s8, s9)) | m_or_h_gate_v_out(c_e_h_3, c_j, s9)) <=> (m_or_h_gate_v_out(c_e_h_3, c_j, s9) | node4(c_e_h_3, c_j, s8) | (~node5(c_e_h_3, c_j, s8, s9)))),
% 289.95/182.49 inference(rewrite,[status(thm)],[])).
% 289.95/182.49 tff(5501,plain,
% 289.95/182.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_3, c_j, s8) | (~node5(c_e_h_3, c_j, s8, s9)) | m_or_h_gate_v_out(c_e_h_3, c_j, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (m_or_h_gate_v_out(c_e_h_3, c_j, s9) | node4(c_e_h_3, c_j, s8) | (~node5(c_e_h_3, c_j, s8, s9))))),
% 289.95/182.49 inference(monotonicity,[status(thm)],[5500])).
% 289.95/182.49 tff(5502,plain,
% 289.95/182.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_3, c_j, s8) | (~node5(c_e_h_3, c_j, s8, s9)) | m_or_h_gate_v_out(c_e_h_3, c_j, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | m_or_h_gate_v_out(c_e_h_3, c_j, s9) | node4(c_e_h_3, c_j, s8) | (~node5(c_e_h_3, c_j, s8, s9)))),
% 289.95/182.49 inference(transitivity,[status(thm)],[5501, 5499])).
% 289.95/182.49 tff(5503,plain,
% 289.95/182.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_3, c_j, s8) | (~node5(c_e_h_3, c_j, s8, s9)) | m_or_h_gate_v_out(c_e_h_3, c_j, s9))),
% 289.95/182.49 inference(quant_inst,[status(thm)],[])).
% 289.95/182.49 tff(5504,plain,
% 289.95/182.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | m_or_h_gate_v_out(c_e_h_3, c_j, s9) | node4(c_e_h_3, c_j, s8) | (~node5(c_e_h_3, c_j, s8, s9))),
% 289.95/182.50 inference(modus_ponens,[status(thm)],[5503, 5502])).
% 289.95/182.50 tff(5505,plain,
% 289.95/182.50 ($false),
% 289.95/182.50 inference(unit_resolution,[status(thm)],[5504, 5498, 5462, 5488, 5463])).
% 289.95/182.50 tff(5506,plain,(m_or_h_gate_v_out(c_e_h_3, c_j, s9) | node4(c_e_h_3, c_j, s8) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s8))), inference(lemma,lemma(discharge,[]))).
% 289.95/182.50 tff(5507,plain,
% 289.95/182.50 (node4(c_e_h_3, c_j, s8)),
% 289.95/182.50 inference(unit_resolution,[status(thm)],[5506, 3367, 5462])).
% 289.95/182.50 tff(5508,assumption,(node4(c_e_h_3, c_j, s8)), introduced(assumption)).
% 289.95/182.50 tff(5509,assumption,(m_or_h_gate_v_in1(c_e_h_3, c_j, s8)), introduced(assumption)).
% 289.95/182.50 tff(5510,plain,
% 289.95/182.50 (^[I0: $i, X: $i, I1: $i] : refl(((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X))) <=> ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X))))),
% 289.95/182.50 inference(bind,[status(th)],[])).
% 289.95/182.50 tff(5511,plain,
% 289.95/182.50 (![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X))) <=> ![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))),
% 289.95/182.50 inference(quant_intro,[status(thm)],[5510])).
% 289.95/182.50 tff(5512,plain,
% 289.95/182.50 (![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X))) <=> ![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))),
% 289.95/182.50 inference(rewrite,[status(thm)],[])).
% 289.95/182.50 tff(5513,axiom,(![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_or_h_gate_2')).
% 289.95/182.50 tff(5514,plain,
% 289.95/182.50 (![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))),
% 289.95/182.50 inference(modus_ponens,[status(thm)],[5513, 5512])).
% 289.95/182.50 tff(5515,plain,(
% 289.95/182.50 ![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))),
% 289.95/182.50 inference(skolemize,[status(sab)],[5514])).
% 289.95/182.50 tff(5516,plain,
% 289.95/182.50 (![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))),
% 289.95/182.50 inference(modus_ponens,[status(thm)],[5515, 5511])).
% 289.95/182.50 tff(5517,plain,
% 289.95/182.50 (((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_j, s8)) | (~node4(c_e_h_3, c_j, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s8)) | (~node4(c_e_h_3, c_j, s8)))),
% 289.95/182.50 inference(rewrite,[status(thm)],[])).
% 289.95/182.50 tff(5518,plain,
% 289.95/182.50 ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_j, s8)) | (~node4(c_e_h_3, c_j, s8)))),
% 289.95/182.50 inference(quant_inst,[status(thm)],[])).
% 289.95/182.50 tff(5519,plain,
% 289.95/182.50 ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s8)) | (~node4(c_e_h_3, c_j, s8))),
% 289.95/182.50 inference(modus_ponens,[status(thm)],[5518, 5517])).
% 289.95/182.50 tff(5520,plain,
% 289.95/182.50 ($false),
% 289.95/182.50 inference(unit_resolution,[status(thm)],[5519, 5516, 5509, 5508])).
% 289.95/182.50 tff(5521,plain,((~node4(c_e_h_3, c_j, s8)) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s8))), inference(lemma,lemma(discharge,[]))).
% 289.95/182.50 tff(5522,plain,
% 289.95/182.50 (~m_or_h_gate_v_in1(c_e_h_3, c_j, s8)),
% 289.95/182.50 inference(unit_resolution,[status(thm)],[5521, 5507])).
% 289.95/182.50 tff(5523,assumption,(~m_or_h_gate_v_in1(c_e_h_3, c_j, s8)), introduced(assumption)).
% 289.95/182.50 tff(5524,assumption,(m_and_h_gate_v_out(c_e_h_3, c_l, s8)), introduced(assumption)).
% 289.95/182.50 tff(5525,plain,
% 289.95/182.50 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s8)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s8))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s8)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s8))),
% 289.95/182.50 inference(rewrite,[status(thm)],[])).
% 289.95/182.50 tff(5526,plain,
% 289.95/182.50 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s8)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s8))),
% 289.95/182.50 inference(quant_inst,[status(thm)],[])).
% 289.95/182.50 tff(5527,plain,
% 289.95/182.50 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s8)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s8)),
% 289.95/182.50 inference(modus_ponens,[status(thm)],[5526, 5525])).
% 289.95/182.50 tff(5528,plain,
% 289.95/182.50 ($false),
% 289.95/182.50 inference(unit_resolution,[status(thm)],[5527, 3627, 5524, 5523])).
% 289.95/182.50 tff(5529,plain,((~m_and_h_gate_v_out(c_e_h_3, c_l, s8)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s8)), inference(lemma,lemma(discharge,[]))).
% 289.95/182.50 tff(5530,plain,
% 289.95/182.50 (~m_and_h_gate_v_out(c_e_h_3, c_l, s8)),
% 289.95/182.50 inference(unit_resolution,[status(thm)],[5529, 5522])).
% 289.95/182.50 tff(5531,plain,
% 289.95/182.50 (m_and_h_gate_v_in1(c_e_h_3, c_c, s3)),
% 289.95/182.50 inference(unit_resolution,[status(thm)],[5460, 3367])).
% 289.95/182.50 tff(5532,assumption,(m_and_h_gate_v_out(c_e_h_3, c_q, s2)), introduced(assumption)).
% 289.95/182.50 tff(5533,assumption,(node21(c_e_h_3, c_q, s1, s2)), introduced(assumption)).
% 289.95/182.50 tff(5534,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1)), introduced(assumption)).
% 289.95/182.50 tff(5535,assumption,(node11(c_e_h_3, c_n, s0, s1)), introduced(assumption)).
% 289.95/182.50 tff(5536,assumption,(~m_cell_v_token(c_e_h_3, s0)), introduced(assumption)).
% 289.95/182.50 tff(5537,plain,
% 289.95/182.50 (^[X: $i] : refl(m_cell_v_token(c_e_h_3, X) <=> m_cell_v_token(c_e_h_3, X))),
% 289.95/182.50 inference(bind,[status(th)],[])).
% 289.95/182.50 tff(5538,plain,
% 289.95/182.50 (![X: $i] : m_cell_v_token(c_e_h_3, X) <=> ![X: $i] : m_cell_v_token(c_e_h_3, X)),
% 289.95/182.50 inference(quant_intro,[status(thm)],[5537])).
% 289.95/182.50 tff(5539,plain,
% 289.95/182.50 (![X: $i] : m_cell_v_token(c_e_h_3, X) <=> ![X: $i] : m_cell_v_token(c_e_h_3, X)),
% 289.95/182.50 inference(rewrite,[status(thm)],[])).
% 289.95/182.50 tff(5540,axiom,(![X: $i] : m_cell_v_token(c_e_h_3, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_9')).
% 289.95/182.50 tff(5541,plain,
% 289.95/182.50 (![X: $i] : m_cell_v_token(c_e_h_3, X)),
% 289.95/182.50 inference(modus_ponens,[status(thm)],[5540, 5539])).
% 289.95/182.50 tff(5542,plain,(
% 289.95/182.50 ![X: $i] : m_cell_v_token(c_e_h_3, X)),
% 289.95/182.50 inference(skolemize,[status(sab)],[5541])).
% 289.95/182.50 tff(5543,plain,
% 289.95/182.50 (![X: $i] : m_cell_v_token(c_e_h_3, X)),
% 289.95/182.50 inference(modus_ponens,[status(thm)],[5542, 5538])).
% 289.95/182.50 tff(5544,plain,
% 289.95/182.50 ((~![X: $i] : m_cell_v_token(c_e_h_3, X)) | m_cell_v_token(c_e_h_3, s0)),
% 289.95/182.50 inference(quant_inst,[status(thm)],[])).
% 289.95/182.50 tff(5545,plain,
% 289.95/182.50 ($false),
% 289.95/182.50 inference(unit_resolution,[status(thm)],[5544, 5543, 5536])).
% 289.95/182.50 tff(5546,plain,(m_cell_v_token(c_e_h_3, s0)), inference(lemma,lemma(discharge,[]))).
% 289.95/182.50 tff(5547,plain,
% 289.95/182.50 (^[I0: $i, X: $i] : refl(((~m_cell_v_token(I0, X)) | (~m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))) <=> ((~m_cell_v_token(I0, X)) | (~m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))))),
% 289.95/182.50 inference(bind,[status(th)],[])).
% 289.95/182.50 tff(5548,plain,
% 289.95/182.50 (![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | (~m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))) <=> ![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | (~m_and_h_gate_h_init_v_init_h_out(I0, c_n, X)))),
% 289.95/182.50 inference(quant_intro,[status(thm)],[5547])).
% 289.95/182.50 tff(5549,plain,
% 289.95/182.50 (![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | (~m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))) <=> ![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | (~m_and_h_gate_h_init_v_init_h_out(I0, c_n, X)))),
% 289.95/182.50 inference(rewrite,[status(thm)],[])).
% 289.95/182.50 tff(5550,plain,
% 289.95/182.50 (^[I0: $i, X: $i] : rewrite(((~m_and_h_gate_h_init_v_init_h_out(I0, c_n, X)) | (~m_cell_v_token(I0, X))) <=> ((~m_cell_v_token(I0, X)) | (~m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))))),
% 289.95/182.50 inference(bind,[status(th)],[])).
% 289.95/182.50 tff(5551,plain,
% 289.95/182.50 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, c_n, X)) | (~m_cell_v_token(I0, X))) <=> ![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | (~m_and_h_gate_h_init_v_init_h_out(I0, c_n, X)))),
% 289.95/182.50 inference(quant_intro,[status(thm)],[5550])).
% 289.95/182.50 tff(5552,axiom,(![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, c_n, X)) | (~m_cell_v_token(I0, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_62')).
% 289.95/182.50 tff(5553,plain,
% 289.95/182.50 (![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | (~m_and_h_gate_h_init_v_init_h_out(I0, c_n, X)))),
% 289.95/182.50 inference(modus_ponens,[status(thm)],[5552, 5551])).
% 289.95/182.50 tff(5554,plain,
% 289.95/182.50 (![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | (~m_and_h_gate_h_init_v_init_h_out(I0, c_n, X)))),
% 289.95/182.50 inference(modus_ponens,[status(thm)],[5553, 5549])).
% 289.95/182.50 tff(5555,plain,(
% 289.95/182.50 ![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | (~m_and_h_gate_h_init_v_init_h_out(I0, c_n, X)))),
% 289.95/182.50 inference(skolemize,[status(sab)],[5554])).
% 289.95/182.50 tff(5556,plain,
% 289.95/182.50 (![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | (~m_and_h_gate_h_init_v_init_h_out(I0, c_n, X)))),
% 289.95/182.50 inference(modus_ponens,[status(thm)],[5555, 5548])).
% 289.95/182.50 tff(5557,plain,
% 289.95/182.50 (((~![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | (~m_and_h_gate_h_init_v_init_h_out(I0, c_n, X)))) | ((~m_cell_v_token(c_e_h_3, s0)) | (~m_and_h_gate_h_init_v_init_h_out(c_e_h_3, c_n, s0)))) <=> ((~![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | (~m_and_h_gate_h_init_v_init_h_out(I0, c_n, X)))) | (~m_cell_v_token(c_e_h_3, s0)) | (~m_and_h_gate_h_init_v_init_h_out(c_e_h_3, c_n, s0)))),
% 289.95/182.50 inference(rewrite,[status(thm)],[])).
% 289.95/182.50 tff(5558,plain,
% 289.95/182.50 ((~![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | (~m_and_h_gate_h_init_v_init_h_out(I0, c_n, X)))) | ((~m_cell_v_token(c_e_h_3, s0)) | (~m_and_h_gate_h_init_v_init_h_out(c_e_h_3, c_n, s0)))),
% 289.95/182.50 inference(quant_inst,[status(thm)],[])).
% 289.95/182.50 tff(5559,plain,
% 289.95/182.50 ((~![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | (~m_and_h_gate_h_init_v_init_h_out(I0, c_n, X)))) | (~m_cell_v_token(c_e_h_3, s0)) | (~m_and_h_gate_h_init_v_init_h_out(c_e_h_3, c_n, s0))),
% 289.95/182.50 inference(modus_ponens,[status(thm)],[5558, 5557])).
% 289.95/182.50 tff(5560,plain,
% 289.95/182.50 (~m_and_h_gate_h_init_v_init_h_out(c_e_h_3, c_n, s0)),
% 289.95/182.50 inference(unit_resolution,[status(thm)],[5559, 5556, 5546])).
% 289.95/182.50 tff(5561,plain,
% 289.95/182.50 (((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, s0)) | m_and_h_gate_h_init_v_init_h_out(I0, I1, s0))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s0)) | m_and_h_gate_h_init_v_init_h_out(c_e_h_3, c_n, s0))) <=> ((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, s0)) | m_and_h_gate_h_init_v_init_h_out(I0, I1, s0))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s0)) | m_and_h_gate_h_init_v_init_h_out(c_e_h_3, c_n, s0))),
% 289.95/182.50 inference(rewrite,[status(thm)],[])).
% 289.95/182.50 tff(5562,plain,
% 289.95/182.50 ((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, s0)) | m_and_h_gate_h_init_v_init_h_out(I0, I1, s0))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s0)) | m_and_h_gate_h_init_v_init_h_out(c_e_h_3, c_n, s0))),
% 289.95/182.50 inference(quant_inst,[status(thm)],[])).
% 289.95/182.50 tff(5563,plain,
% 289.95/182.50 ((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, s0)) | m_and_h_gate_h_init_v_init_h_out(I0, I1, s0))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s0)) | m_and_h_gate_h_init_v_init_h_out(c_e_h_3, c_n, s0)),
% 289.95/182.50 inference(modus_ponens,[status(thm)],[5562, 5561])).
% 289.95/182.50 tff(5564,plain,
% 289.95/182.50 (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s0)),
% 289.95/182.50 inference(unit_resolution,[status(thm)],[5563, 4538, 5560])).
% 289.95/182.50 tff(5565,plain,
% 289.95/182.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1)) | (~node11(c_e_h_3, c_n, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1)) | (~node11(c_e_h_3, c_n, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s0))),
% 289.95/182.50 inference(rewrite,[status(thm)],[])).
% 289.95/182.50 tff(5566,plain,
% 289.95/182.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1)) | (~node11(c_e_h_3, c_n, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s0))),
% 289.95/182.50 inference(quant_inst,[status(thm)],[])).
% 289.95/182.50 tff(5567,plain,
% 289.95/182.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1)) | (~node11(c_e_h_3, c_n, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s0)),
% 289.95/182.50 inference(modus_ponens,[status(thm)],[5566, 5565])).
% 289.95/182.50 tff(5568,plain,
% 289.95/182.50 ($false),
% 289.95/182.50 inference(unit_resolution,[status(thm)],[5567, 5017, 5564, 5534, 5535])).
% 289.95/182.50 tff(5569,plain,((~node11(c_e_h_3, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1))), inference(lemma,lemma(discharge,[]))).
% 289.95/182.50 tff(5570,plain,
% 289.95/182.50 (~node11(c_e_h_3, c_n, s0, s1)),
% 289.95/182.50 inference(unit_resolution,[status(thm)],[5569, 5534])).
% 289.95/182.50 tff(5571,plain,
% 289.95/182.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s0, s1)) | node10(c_e_h_3, c_n, s0, s1) | node11(c_e_h_3, c_n, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s0, s1)) | node10(c_e_h_3, c_n, s0, s1) | node11(c_e_h_3, c_n, s0, s1))),
% 289.95/182.50 inference(rewrite,[status(thm)],[])).
% 289.95/182.50 tff(5572,plain,
% 289.95/182.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s0, s1)) | node10(c_e_h_3, c_n, s0, s1) | node11(c_e_h_3, c_n, s0, s1))),
% 289.95/182.50 inference(quant_inst,[status(thm)],[])).
% 289.95/182.50 tff(5573,plain,
% 289.95/182.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s0, s1)) | node10(c_e_h_3, c_n, s0, s1) | node11(c_e_h_3, c_n, s0, s1)),
% 289.95/182.50 inference(modus_ponens,[status(thm)],[5572, 5571])).
% 289.95/182.50 tff(5574,plain,
% 289.95/182.50 (node10(c_e_h_3, c_n, s0, s1) | node11(c_e_h_3, c_n, s0, s1)),
% 289.95/182.50 inference(unit_resolution,[status(thm)],[5573, 5002, 72])).
% 289.95/182.50 tff(5575,plain,
% 289.95/182.50 (node10(c_e_h_3, c_n, s0, s1)),
% 289.95/182.50 inference(unit_resolution,[status(thm)],[5574, 5570])).
% 289.95/182.50 tff(5576,plain,
% 289.95/182.50 (^[I0: $i, X: $i] : refl(((~m_cell_v_token(I0, X)) | m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) <=> ((~m_cell_v_token(I0, X)) | m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)))),
% 289.95/182.50 inference(bind,[status(th)],[])).
% 289.95/182.50 tff(5577,plain,
% 289.95/182.50 (![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) <=> ![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | m_and_h_gate_h_init_v_init_h_out(I0, c_m, X))),
% 289.95/182.50 inference(quant_intro,[status(thm)],[5576])).
% 289.95/182.50 tff(5578,plain,
% 289.95/182.50 (![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) <=> ![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | m_and_h_gate_h_init_v_init_h_out(I0, c_m, X))),
% 289.95/182.50 inference(rewrite,[status(thm)],[])).
% 289.95/182.50 tff(5579,plain,
% 289.95/182.50 (^[I0: $i, X: $i] : rewrite((m_and_h_gate_h_init_v_init_h_out(I0, c_m, X) | (~m_cell_v_token(I0, X))) <=> ((~m_cell_v_token(I0, X)) | m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)))),
% 289.95/182.50 inference(bind,[status(th)],[])).
% 289.95/182.50 tff(5580,plain,
% 289.95/182.50 (![I0: $i, X: $i] : (m_and_h_gate_h_init_v_init_h_out(I0, c_m, X) | (~m_cell_v_token(I0, X))) <=> ![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | m_and_h_gate_h_init_v_init_h_out(I0, c_m, X))),
% 289.95/182.50 inference(quant_intro,[status(thm)],[5579])).
% 289.95/182.50 tff(5581,axiom,(![I0: $i, X: $i] : (m_and_h_gate_h_init_v_init_h_out(I0, c_m, X) | (~m_cell_v_token(I0, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_55')).
% 289.95/182.50 tff(5582,plain,
% 289.95/182.50 (![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | m_and_h_gate_h_init_v_init_h_out(I0, c_m, X))),
% 289.95/182.50 inference(modus_ponens,[status(thm)],[5581, 5580])).
% 289.95/182.50 tff(5583,plain,
% 289.95/182.50 (![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | m_and_h_gate_h_init_v_init_h_out(I0, c_m, X))),
% 289.95/182.50 inference(modus_ponens,[status(thm)],[5582, 5578])).
% 289.95/182.50 tff(5584,plain,(
% 289.95/182.50 ![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | m_and_h_gate_h_init_v_init_h_out(I0, c_m, X))),
% 289.95/182.50 inference(skolemize,[status(sab)],[5583])).
% 289.95/182.50 tff(5585,plain,
% 289.95/182.50 (![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | m_and_h_gate_h_init_v_init_h_out(I0, c_m, X))),
% 289.95/182.50 inference(modus_ponens,[status(thm)],[5584, 5577])).
% 289.95/182.50 tff(5586,plain,
% 289.95/182.50 (((~![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | m_and_h_gate_h_init_v_init_h_out(I0, c_m, X))) | ((~m_cell_v_token(c_e_h_3, s0)) | m_and_h_gate_h_init_v_init_h_out(c_e_h_3, c_m, s0))) <=> ((~![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | m_and_h_gate_h_init_v_init_h_out(I0, c_m, X))) | (~m_cell_v_token(c_e_h_3, s0)) | m_and_h_gate_h_init_v_init_h_out(c_e_h_3, c_m, s0))),
% 289.95/182.50 inference(rewrite,[status(thm)],[])).
% 289.95/182.50 tff(5587,plain,
% 289.95/182.51 ((~![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | m_and_h_gate_h_init_v_init_h_out(I0, c_m, X))) | ((~m_cell_v_token(c_e_h_3, s0)) | m_and_h_gate_h_init_v_init_h_out(c_e_h_3, c_m, s0))),
% 289.95/182.51 inference(quant_inst,[status(thm)],[])).
% 289.95/182.51 tff(5588,plain,
% 289.95/182.51 ((~![I0: $i, X: $i] : ((~m_cell_v_token(I0, X)) | m_and_h_gate_h_init_v_init_h_out(I0, c_m, X))) | (~m_cell_v_token(c_e_h_3, s0)) | m_and_h_gate_h_init_v_init_h_out(c_e_h_3, c_m, s0)),
% 289.95/182.51 inference(modus_ponens,[status(thm)],[5587, 5586])).
% 289.95/182.51 tff(5589,plain,
% 289.95/182.51 (m_and_h_gate_h_init_v_init_h_out(c_e_h_3, c_m, s0)),
% 289.95/182.51 inference(unit_resolution,[status(thm)],[5588, 5585, 5546])).
% 289.95/182.51 tff(5590,plain,
% 289.95/182.51 (((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0))) | ((~m_and_h_gate_h_init_v_init_h_out(c_e_h_3, c_m, s0)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s0))) <=> ((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0))) | (~m_and_h_gate_h_init_v_init_h_out(c_e_h_3, c_m, s0)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s0))),
% 289.95/182.51 inference(rewrite,[status(thm)],[])).
% 289.95/182.51 tff(5591,plain,
% 289.95/182.51 ((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0))) | ((~m_and_h_gate_h_init_v_init_h_out(c_e_h_3, c_m, s0)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s0))),
% 289.95/182.51 inference(quant_inst,[status(thm)],[])).
% 289.95/182.51 tff(5592,plain,
% 289.95/182.51 ((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0))) | (~m_and_h_gate_h_init_v_init_h_out(c_e_h_3, c_m, s0)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s0)),
% 289.95/182.51 inference(modus_ponens,[status(thm)],[5591, 5590])).
% 289.95/182.51 tff(5593,plain,
% 289.95/182.51 ((~m_and_h_gate_h_init_v_init_h_out(c_e_h_3, c_m, s0)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s0)),
% 289.95/182.51 inference(unit_resolution,[status(thm)],[5592, 4946])).
% 289.95/182.51 tff(5594,plain,
% 289.95/182.51 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s0)),
% 289.95/182.51 inference(unit_resolution,[status(thm)],[5593, 5589])).
% 289.95/182.51 tff(5595,plain,
% 289.95/182.51 (^[I0: $i, X: $i] : refl(((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X))) <=> ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X))))),
% 289.95/182.51 inference(bind,[status(th)],[])).
% 289.95/182.51 tff(5596,plain,
% 289.95/182.51 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X))) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))),
% 289.95/182.51 inference(quant_intro,[status(thm)],[5595])).
% 289.95/182.51 tff(5597,plain,
% 289.95/182.51 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X))) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))),
% 289.95/182.51 inference(rewrite,[status(thm)],[])).
% 289.95/182.51 tff(5598,axiom,(![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_60')).
% 289.95/182.51 tff(5599,plain,
% 289.95/182.51 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))),
% 289.95/182.51 inference(modus_ponens,[status(thm)],[5598, 5597])).
% 289.95/182.51 tff(5600,plain,(
% 289.95/182.51 ![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))),
% 289.95/182.51 inference(skolemize,[status(sab)],[5599])).
% 289.95/182.51 tff(5601,plain,
% 289.95/182.51 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))),
% 289.95/182.51 inference(modus_ponens,[status(thm)],[5600, 5596])).
% 289.95/182.51 tff(5602,plain,
% 289.95/182.51 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s0)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s0)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s0)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s0)))),
% 289.95/182.51 inference(rewrite,[status(thm)],[])).
% 289.95/182.51 tff(5603,plain,
% 289.95/182.51 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s0)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s0)))),
% 289.95/182.51 inference(quant_inst,[status(thm)],[])).
% 289.95/182.51 tff(5604,plain,
% 289.95/182.51 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s0)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s0))),
% 289.95/182.51 inference(modus_ponens,[status(thm)],[5603, 5602])).
% 289.95/182.51 tff(5605,plain,
% 289.95/182.51 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s0)),
% 289.95/182.51 inference(unit_resolution,[status(thm)],[5604, 5601, 5594])).
% 289.95/182.51 tff(5606,plain,
% 289.95/182.51 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s0)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s0)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s0))),
% 289.95/182.51 inference(rewrite,[status(thm)],[])).
% 289.95/182.51 tff(5607,plain,
% 289.95/182.51 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s0)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s0))),
% 289.95/182.51 inference(quant_inst,[status(thm)],[])).
% 289.95/182.51 tff(5608,plain,
% 289.95/182.51 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s0)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s0)),
% 289.95/182.51 inference(modus_ponens,[status(thm)],[5607, 5606])).
% 289.95/182.51 tff(5609,plain,
% 289.95/182.51 (~node9(c_e_h_3, c_n, s0)),
% 289.95/182.51 inference(unit_resolution,[status(thm)],[5608, 4972, 5605])).
% 289.95/182.51 tff(5610,plain,
% 289.95/182.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s0) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1)) | (~node10(c_e_h_3, c_n, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_3, c_n, s0) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1)) | (~node10(c_e_h_3, c_n, s0, s1)))),
% 289.95/182.51 inference(rewrite,[status(thm)],[])).
% 289.95/182.51 tff(5611,plain,
% 289.95/182.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s0) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1)) | (~node10(c_e_h_3, c_n, s0, s1)))),
% 289.95/182.51 inference(quant_inst,[status(thm)],[])).
% 289.95/182.51 tff(5612,plain,
% 289.95/182.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_3, c_n, s0) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1)) | (~node10(c_e_h_3, c_n, s0, s1))),
% 289.95/182.51 inference(modus_ponens,[status(thm)],[5611, 5610])).
% 289.95/182.51 tff(5613,plain,
% 289.95/182.51 ($false),
% 289.95/182.51 inference(unit_resolution,[status(thm)],[5612, 4986, 5609, 5534, 5575])).
% 289.95/182.51 tff(5614,plain,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1)), inference(lemma,lemma(discharge,[]))).
% 289.95/182.51 tff(5615,plain,
% 289.95/182.51 (^[I0: $i, X: $i] : refl(((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X)) <=> ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X)))),
% 289.95/182.51 inference(bind,[status(th)],[])).
% 289.95/182.51 tff(5616,plain,
% 289.95/182.51 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))),
% 289.95/182.51 inference(quant_intro,[status(thm)],[5615])).
% 289.95/182.51 tff(5617,plain,
% 289.95/182.51 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))),
% 289.95/182.51 inference(rewrite,[status(thm)],[])).
% 289.95/182.51 tff(5618,axiom,(![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_70')).
% 289.95/182.51 tff(5619,plain,
% 289.95/182.51 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))),
% 289.95/182.51 inference(modus_ponens,[status(thm)],[5618, 5617])).
% 289.95/182.51 tff(5620,plain,(
% 289.95/182.51 ![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))),
% 289.95/182.51 inference(skolemize,[status(sab)],[5619])).
% 289.95/182.51 tff(5621,plain,
% 289.95/182.51 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))),
% 289.95/182.51 inference(modus_ponens,[status(thm)],[5620, 5616])).
% 289.95/182.51 tff(5622,plain,
% 289.95/182.51 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s1)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s1)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1))),
% 289.95/182.51 inference(rewrite,[status(thm)],[])).
% 289.95/182.51 tff(5623,plain,
% 289.95/182.51 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s1)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1))),
% 289.95/182.51 inference(quant_inst,[status(thm)],[])).
% 289.95/182.51 tff(5624,plain,
% 289.95/182.51 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s1)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1)),
% 289.95/182.51 inference(modus_ponens,[status(thm)],[5623, 5622])).
% 289.95/182.51 tff(5625,plain,
% 289.95/182.51 (~m_and_h_gate_v_in2(c_e_h_3, c_q, s1)),
% 289.95/182.51 inference(unit_resolution,[status(thm)],[5624, 5621, 5614])).
% 289.95/182.51 tff(5626,plain,
% 289.95/182.51 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s1)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s1)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s1))),
% 289.95/182.51 inference(rewrite,[status(thm)],[])).
% 289.95/182.51 tff(5627,plain,
% 289.95/182.51 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s1)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s1))),
% 289.95/182.51 inference(quant_inst,[status(thm)],[])).
% 289.95/182.51 tff(5628,plain,
% 289.95/182.51 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s1)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s1)),
% 289.95/182.51 inference(modus_ponens,[status(thm)],[5627, 5626])).
% 289.95/182.51 tff(5629,plain,
% 289.95/182.51 (~node20(c_e_h_3, c_q, s1)),
% 289.95/182.51 inference(unit_resolution,[status(thm)],[5628, 4563, 5625])).
% 289.95/182.51 tff(5630,plain,
% 289.95/182.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s2)) | (~node21(c_e_h_3, c_q, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_q, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s2)) | (~node21(c_e_h_3, c_q, s1, s2)))),
% 289.95/182.51 inference(rewrite,[status(thm)],[])).
% 289.95/182.51 tff(5631,plain,
% 289.95/182.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s2)) | (~node21(c_e_h_3, c_q, s1, s2)))),
% 289.95/182.51 inference(quant_inst,[status(thm)],[])).
% 289.95/182.51 tff(5632,plain,
% 289.95/182.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_q, s1) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s2)) | (~node21(c_e_h_3, c_q, s1, s2))),
% 289.95/182.51 inference(modus_ponens,[status(thm)],[5631, 5630])).
% 289.95/182.51 tff(5633,plain,
% 289.95/182.51 ($false),
% 289.95/182.51 inference(unit_resolution,[status(thm)],[5632, 52, 5532, 5629, 5533])).
% 289.95/182.51 tff(5634,plain,((~node21(c_e_h_3, c_q, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s2))), inference(lemma,lemma(discharge,[]))).
% 289.95/182.51 tff(5635,plain,
% 289.95/182.51 (~node21(c_e_h_3, c_q, s1, s2)),
% 289.95/182.51 inference(unit_resolution,[status(thm)],[5634, 5532])).
% 289.95/182.51 tff(5636,plain,
% 289.95/182.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_3, c_q, s1, s2) | node22(c_e_h_3, c_q, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_3, c_q, s1, s2) | node22(c_e_h_3, c_q, s1, s2))),
% 290.04/182.52 inference(rewrite,[status(thm)],[])).
% 290.04/182.52 tff(5637,plain,
% 290.04/182.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_3, c_q, s1, s2) | node22(c_e_h_3, c_q, s1, s2))),
% 290.04/182.52 inference(quant_inst,[status(thm)],[])).
% 290.04/182.52 tff(5638,plain,
% 290.04/182.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_3, c_q, s1, s2) | node22(c_e_h_3, c_q, s1, s2)),
% 290.04/182.52 inference(modus_ponens,[status(thm)],[5637, 5636])).
% 290.04/182.52 tff(5639,plain,
% 290.04/182.52 (node21(c_e_h_3, c_q, s1, s2) | node22(c_e_h_3, c_q, s1, s2)),
% 290.04/182.52 inference(unit_resolution,[status(thm)],[5638, 82, 255])).
% 290.04/182.52 tff(5640,plain,
% 290.04/182.52 (node22(c_e_h_3, c_q, s1, s2)),
% 290.04/182.52 inference(unit_resolution,[status(thm)],[5639, 5635])).
% 290.04/182.52 tff(5641,assumption,(m_and_h_gate_v_out(c_e_h_3, c_q, s1)), introduced(assumption)).
% 290.04/182.52 tff(5642,assumption,(node22(c_e_h_3, c_q, s0, s1)), introduced(assumption)).
% 290.04/182.52 tff(5643,assumption,(m_and_h_gate_v_out(c_e_h_3, c_q, s0)), introduced(assumption)).
% 290.04/182.52 tff(5644,plain,
% 290.04/182.52 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s0))),
% 290.04/182.52 inference(quant_inst,[status(thm)],[])).
% 290.04/182.52 tff(5645,plain,
% 290.04/182.52 ($false),
% 290.04/182.52 inference(unit_resolution,[status(thm)],[5644, 95, 5643])).
% 290.04/182.52 tff(5646,plain,(~m_and_h_gate_v_out(c_e_h_3, c_q, s0)), inference(lemma,lemma(discharge,[]))).
% 290.04/182.52 tff(5647,plain,
% 290.04/182.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s1)) | (~node22(c_e_h_3, c_q, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_q, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s1)) | (~node22(c_e_h_3, c_q, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_q, s0))),
% 290.04/182.52 inference(rewrite,[status(thm)],[])).
% 290.04/182.52 tff(5648,plain,
% 290.04/182.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s1)) | (~node22(c_e_h_3, c_q, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_q, s0))),
% 290.04/182.52 inference(quant_inst,[status(thm)],[])).
% 290.04/182.52 tff(5649,plain,
% 290.04/182.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s1)) | (~node22(c_e_h_3, c_q, s0, s1)) | m_and_h_gate_v_out(c_e_h_3, c_q, s0)),
% 290.04/182.52 inference(modus_ponens,[status(thm)],[5648, 5647])).
% 290.04/182.52 tff(5650,plain,
% 290.04/182.52 ($false),
% 290.04/182.52 inference(unit_resolution,[status(thm)],[5649, 108, 5646, 5641, 5642])).
% 290.04/182.52 tff(5651,plain,((~node22(c_e_h_3, c_q, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s1))), inference(lemma,lemma(discharge,[]))).
% 290.04/182.52 tff(5652,plain,
% 290.04/182.52 (~node22(c_e_h_3, c_q, s0, s1)),
% 290.04/182.52 inference(unit_resolution,[status(thm)],[5651, 5641])).
% 290.04/182.52 tff(5653,plain,
% 290.04/182.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_3, c_q, s0, s1) | node22(c_e_h_3, c_q, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_3, c_q, s0, s1) | node22(c_e_h_3, c_q, s0, s1))),
% 290.04/182.52 inference(rewrite,[status(thm)],[])).
% 290.04/182.52 tff(5654,plain,
% 290.04/182.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_3, c_q, s0, s1) | node22(c_e_h_3, c_q, s0, s1))),
% 290.04/182.52 inference(quant_inst,[status(thm)],[])).
% 290.04/182.52 tff(5655,plain,
% 290.04/182.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_3, c_q, s0, s1) | node22(c_e_h_3, c_q, s0, s1)),
% 290.04/182.52 inference(modus_ponens,[status(thm)],[5654, 5653])).
% 290.04/182.52 tff(5656,plain,
% 290.04/182.52 (node21(c_e_h_3, c_q, s0, s1) | node22(c_e_h_3, c_q, s0, s1)),
% 290.04/182.52 inference(unit_resolution,[status(thm)],[5655, 82, 72])).
% 290.04/182.52 tff(5657,plain,
% 290.04/182.52 (node21(c_e_h_3, c_q, s0, s1)),
% 290.04/182.52 inference(unit_resolution,[status(thm)],[5656, 5652])).
% 290.04/182.52 tff(5658,plain,
% 290.04/182.52 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s0)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s0))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s0)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s0))),
% 290.04/182.52 inference(rewrite,[status(thm)],[])).
% 290.04/182.52 tff(5659,plain,
% 290.04/182.52 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s0)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s0))),
% 290.04/182.52 inference(quant_inst,[status(thm)],[])).
% 290.04/182.52 tff(5660,plain,
% 290.04/182.52 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s0)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s0)),
% 290.04/182.52 inference(modus_ponens,[status(thm)],[5659, 5658])).
% 290.04/182.52 tff(5661,plain,
% 290.04/182.52 (~m_and_h_gate_v_in2(c_e_h_3, c_q, s0)),
% 290.04/182.52 inference(unit_resolution,[status(thm)],[5660, 5621, 5564])).
% 290.04/182.52 tff(5662,plain,
% 290.04/182.52 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s0)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s0)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s0))),
% 290.04/182.52 inference(rewrite,[status(thm)],[])).
% 290.04/182.52 tff(5663,plain,
% 290.04/182.52 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s0)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s0))),
% 290.04/182.52 inference(quant_inst,[status(thm)],[])).
% 290.04/182.52 tff(5664,plain,
% 290.04/182.52 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s0)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s0)),
% 290.04/182.52 inference(modus_ponens,[status(thm)],[5663, 5662])).
% 290.04/182.52 tff(5665,plain,
% 290.04/182.52 (~node20(c_e_h_3, c_q, s0)),
% 290.04/182.52 inference(unit_resolution,[status(thm)],[5664, 4563, 5661])).
% 290.04/182.52 tff(5666,plain,
% 290.04/182.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s1)) | (~node21(c_e_h_3, c_q, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_q, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s1)) | (~node21(c_e_h_3, c_q, s0, s1)))),
% 290.04/182.52 inference(rewrite,[status(thm)],[])).
% 290.04/182.52 tff(5667,plain,
% 290.04/182.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s1)) | (~node21(c_e_h_3, c_q, s0, s1)))),
% 290.04/182.52 inference(quant_inst,[status(thm)],[])).
% 290.04/182.52 tff(5668,plain,
% 290.04/182.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_q, s0) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s1)) | (~node21(c_e_h_3, c_q, s0, s1))),
% 290.04/182.52 inference(modus_ponens,[status(thm)],[5667, 5666])).
% 290.04/182.52 tff(5669,plain,
% 290.04/182.52 ($false),
% 290.04/182.52 inference(unit_resolution,[status(thm)],[5668, 52, 5665, 5641, 5657])).
% 290.04/182.52 tff(5670,plain,(~m_and_h_gate_v_out(c_e_h_3, c_q, s1)), inference(lemma,lemma(discharge,[]))).
% 290.04/182.52 tff(5671,plain,
% 290.04/182.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s2)) | (~node22(c_e_h_3, c_q, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_q, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s2)) | (~node22(c_e_h_3, c_q, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_q, s1))),
% 290.04/182.52 inference(rewrite,[status(thm)],[])).
% 290.04/182.52 tff(5672,plain,
% 290.04/182.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s2)) | (~node22(c_e_h_3, c_q, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_q, s1))),
% 290.04/182.52 inference(quant_inst,[status(thm)],[])).
% 290.04/182.52 tff(5673,plain,
% 290.04/182.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s2)) | (~node22(c_e_h_3, c_q, s1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_q, s1)),
% 290.04/182.52 inference(modus_ponens,[status(thm)],[5672, 5671])).
% 290.04/182.52 tff(5674,plain,
% 290.04/182.52 ($false),
% 290.04/182.52 inference(unit_resolution,[status(thm)],[5673, 108, 5670, 5532, 5640])).
% 290.04/182.52 tff(5675,plain,(~m_and_h_gate_v_out(c_e_h_3, c_q, s2)), inference(lemma,lemma(discharge,[]))).
% 290.04/182.52 tff(5676,assumption,(m_and_h_gate_v_out(c_e_h_3, c_q, s3)), introduced(assumption)).
% 290.04/182.52 tff(5677,assumption,(node21(c_e_h_3, c_q, s2, s3)), introduced(assumption)).
% 290.04/182.52 tff(5678,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s2)), introduced(assumption)).
% 290.04/182.52 tff(5679,assumption,(m_c_h_element_v_out(c_e_h_3, c_f, s0)), introduced(assumption)).
% 290.04/182.52 tff(5680,plain,
% 290.04/182.52 ((~![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s0))),
% 290.04/182.52 inference(quant_inst,[status(thm)],[])).
% 290.04/182.52 tff(5681,plain,
% 290.04/182.52 ($false),
% 290.04/182.52 inference(unit_resolution,[status(thm)],[5680, 14, 5679])).
% 290.04/182.52 tff(5682,plain,(~m_c_h_element_v_out(c_e_h_3, c_f, s0)), inference(lemma,lemma(discharge,[]))).
% 290.04/182.52 tff(5683,plain,
% 290.04/182.52 (^[I0: $i, X: $i] : refl((m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X)) <=> (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X)))),
% 290.04/182.52 inference(bind,[status(th)],[])).
% 290.04/182.52 tff(5684,plain,
% 290.04/182.52 (![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X)) <=> ![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))),
% 290.04/182.52 inference(quant_intro,[status(thm)],[5683])).
% 290.04/182.52 tff(5685,plain,
% 290.04/182.52 (![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X)) <=> ![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))),
% 290.04/182.52 inference(rewrite,[status(thm)],[])).
% 290.04/182.52 tff(5686,axiom,(![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_51')).
% 290.04/182.52 tff(5687,plain,
% 290.04/182.52 (![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))),
% 290.04/182.52 inference(modus_ponens,[status(thm)],[5686, 5685])).
% 290.04/182.52 tff(5688,plain,(
% 290.04/182.52 ![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))),
% 290.04/182.52 inference(skolemize,[status(sab)],[5687])).
% 290.04/182.52 tff(5689,plain,
% 290.04/182.52 (![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))),
% 290.04/182.52 inference(modus_ponens,[status(thm)],[5688, 5684])).
% 290.04/182.52 tff(5690,plain,
% 290.04/182.52 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s0) | m_c_h_element_v_out(c_e_h_3, c_f, s0))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s0) | m_c_h_element_v_out(c_e_h_3, c_f, s0))),
% 290.04/182.52 inference(rewrite,[status(thm)],[])).
% 290.04/182.52 tff(5691,plain,
% 290.04/182.52 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s0) | m_c_h_element_v_out(c_e_h_3, c_f, s0))),
% 290.04/182.52 inference(quant_inst,[status(thm)],[])).
% 290.04/182.52 tff(5692,plain,
% 290.04/182.52 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s0) | m_c_h_element_v_out(c_e_h_3, c_f, s0)),
% 290.04/182.52 inference(modus_ponens,[status(thm)],[5691, 5690])).
% 290.04/182.52 tff(5693,plain,
% 290.04/182.52 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s0) | m_c_h_element_v_out(c_e_h_3, c_f, s0)),
% 290.04/182.52 inference(unit_resolution,[status(thm)],[5692, 5689])).
% 290.04/182.52 tff(5694,plain,
% 290.04/182.52 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s0)),
% 290.04/182.52 inference(unit_resolution,[status(thm)],[5693, 5682])).
% 290.04/182.52 tff(5695,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s0)), introduced(assumption)).
% 290.04/182.52 tff(5696,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1)), introduced(assumption)).
% 290.04/182.52 tff(5697,assumption,(node10(c_e_h_3, c_m, s0, s1)), introduced(assumption)).
% 290.04/182.52 tff(5698,plain,
% 290.04/182.52 (^[I0: $i, X: $i] : refl((m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X)) <=> (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X)))),
% 290.04/182.52 inference(bind,[status(th)],[])).
% 290.04/182.52 tff(5699,plain,
% 290.04/182.52 (![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X)) <=> ![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))),
% 290.04/182.52 inference(quant_intro,[status(thm)],[5698])).
% 290.04/182.52 tff(5700,plain,
% 290.04/182.52 (![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X)) <=> ![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))),
% 290.04/182.52 inference(rewrite,[status(thm)],[])).
% 290.04/182.52 tff(5701,axiom,(![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_53')).
% 290.04/182.52 tff(5702,plain,
% 290.04/182.52 (![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))),
% 290.04/182.52 inference(modus_ponens,[status(thm)],[5701, 5700])).
% 290.04/182.52 tff(5703,plain,(
% 290.04/182.52 ![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))),
% 290.04/182.52 inference(skolemize,[status(sab)],[5702])).
% 290.04/182.52 tff(5704,plain,
% 290.04/182.52 (![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))),
% 290.04/182.52 inference(modus_ponens,[status(thm)],[5703, 5699])).
% 290.04/182.52 tff(5705,plain,
% 290.04/182.52 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s0) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s0))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s0) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s0))),
% 290.04/182.52 inference(rewrite,[status(thm)],[])).
% 290.04/182.52 tff(5706,plain,
% 290.04/182.52 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s0) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s0))),
% 290.04/182.52 inference(quant_inst,[status(thm)],[])).
% 290.04/182.52 tff(5707,plain,
% 290.04/182.52 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s0) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s0)),
% 290.04/182.52 inference(modus_ponens,[status(thm)],[5706, 5705])).
% 290.04/182.52 tff(5708,plain,
% 290.04/182.52 (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s0)),
% 290.04/182.52 inference(unit_resolution,[status(thm)],[5707, 5704, 5564])).
% 290.04/182.52 tff(5709,plain,
% 290.04/182.52 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl(((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y)) <=> ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y)))),
% 290.04/182.52 inference(bind,[status(th)],[])).
% 290.04/182.52 tff(5710,plain,
% 290.04/182.52 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))),
% 290.04/182.52 inference(quant_intro,[status(thm)],[5709])).
% 290.04/182.52 tff(5711,plain,
% 290.04/182.52 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))),
% 290.04/182.53 inference(rewrite,[status(thm)],[])).
% 290.04/182.53 tff(5712,plain,
% 290.04/182.53 (^[Y: $i, I0: $i, X: $i, I1: $i] : trans(monotonicity(trans(monotonicity(rewrite((m_and_h_gate_h_init_v_out(I0, I1, Y) | (~m_and_h_gate_h_init_v_in1(I0, I1, X))) <=> ((~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))), (((m_and_h_gate_h_init_v_out(I0, I1, Y) | (~m_and_h_gate_h_init_v_in1(I0, I1, X))) | (~m_and_h_gate_h_init_v_in2(I0, I1, X))) <=> (((~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X))))), rewrite((((~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X))) <=> ((~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))), (((m_and_h_gate_h_init_v_out(I0, I1, Y) | (~m_and_h_gate_h_init_v_in1(I0, I1, X))) | (~m_and_h_gate_h_init_v_in2(I0, I1, X))) <=> ((~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y)))), ((((m_and_h_gate_h_init_v_out(I0, I1, Y) | (~m_and_h_gate_h_init_v_in1(I0, I1, X))) | (~m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node10(I0, I1, X, Y))) <=> (((~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y))))), rewrite((((~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y))) <=> ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))), ((((m_and_h_gate_h_init_v_out(I0, I1, Y) | (~m_and_h_gate_h_init_v_in1(I0, I1, X))) | (~m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node10(I0, I1, X, Y))) <=> ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))))),
% 290.04/182.53 inference(bind,[status(th)],[])).
% 290.04/182.53 tff(5713,plain,
% 290.04/182.53 (![Y: $i, I0: $i, X: $i, I1: $i] : (((m_and_h_gate_h_init_v_out(I0, I1, Y) | (~m_and_h_gate_h_init_v_in1(I0, I1, X))) | (~m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node10(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))),
% 290.04/182.53 inference(quant_intro,[status(thm)],[5712])).
% 290.04/182.53 tff(5714,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : (((m_and_h_gate_h_init_v_out(I0, I1, Y) | (~m_and_h_gate_h_init_v_in1(I0, I1, X))) | (~m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node10(I0, I1, X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_and_h_gate_h_init_5')).
% 290.04/182.53 tff(5715,plain,
% 290.04/182.53 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))),
% 290.04/182.53 inference(modus_ponens,[status(thm)],[5714, 5713])).
% 290.04/182.53 tff(5716,plain,
% 290.04/182.53 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))),
% 290.04/182.53 inference(modus_ponens,[status(thm)],[5715, 5711])).
% 290.04/182.53 tff(5717,plain,(
% 290.04/182.53 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))),
% 290.04/182.53 inference(skolemize,[status(sab)],[5716])).
% 290.04/182.53 tff(5718,plain,
% 290.04/182.53 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))),
% 290.04/182.53 inference(modus_ponens,[status(thm)],[5717, 5710])).
% 290.04/182.53 tff(5719,plain,
% 290.04/182.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s0)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s0)) | (~node10(c_e_h_3, c_m, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s0)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s0)) | (~node10(c_e_h_3, c_m, s0, s1)))),
% 290.04/182.53 inference(rewrite,[status(thm)],[])).
% 290.04/182.53 tff(5720,plain,
% 290.04/182.53 (((~node10(c_e_h_3, c_m, s0, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s0)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s0)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1)) <=> (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s0)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s0)) | (~node10(c_e_h_3, c_m, s0, s1)))),
% 290.04/182.53 inference(rewrite,[status(thm)],[])).
% 290.04/182.53 tff(5721,plain,
% 290.04/182.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s0, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s0)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s0)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s0)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s0)) | (~node10(c_e_h_3, c_m, s0, s1))))),
% 290.04/182.53 inference(monotonicity,[status(thm)],[5720])).
% 290.04/182.53 tff(5722,plain,
% 290.04/182.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s0, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s0)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s0)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s0)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s0)) | (~node10(c_e_h_3, c_m, s0, s1)))),
% 290.04/182.53 inference(transitivity,[status(thm)],[5721, 5719])).
% 290.04/182.53 tff(5723,plain,
% 290.04/182.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s0, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s0)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s0)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1))),
% 290.04/182.53 inference(quant_inst,[status(thm)],[])).
% 290.04/182.53 tff(5724,plain,
% 290.04/182.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s0)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s0)) | (~node10(c_e_h_3, c_m, s0, s1))),
% 290.04/182.53 inference(modus_ponens,[status(thm)],[5723, 5722])).
% 290.04/182.53 tff(5725,plain,
% 290.04/182.53 ($false),
% 290.04/182.53 inference(unit_resolution,[status(thm)],[5724, 5718, 5708, 5695, 5696, 5697])).
% 290.04/182.53 tff(5726,plain,((~node10(c_e_h_3, c_m, s0, s1)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s0)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1)), inference(lemma,lemma(discharge,[]))).
% 290.04/182.53 tff(5727,plain,
% 290.04/182.53 (~node10(c_e_h_3, c_m, s0, s1)),
% 290.04/182.53 inference(unit_resolution,[status(thm)],[5726, 5696, 5695])).
% 290.04/182.53 tff(5728,plain,
% 290.04/182.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s0, s1)) | node10(c_e_h_3, c_m, s0, s1) | node11(c_e_h_3, c_m, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s0, s1)) | node10(c_e_h_3, c_m, s0, s1) | node11(c_e_h_3, c_m, s0, s1))),
% 290.04/182.53 inference(rewrite,[status(thm)],[])).
% 290.04/182.53 tff(5729,plain,
% 290.04/182.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s0, s1)) | node10(c_e_h_3, c_m, s0, s1) | node11(c_e_h_3, c_m, s0, s1))),
% 290.04/182.53 inference(quant_inst,[status(thm)],[])).
% 290.04/182.53 tff(5730,plain,
% 290.04/182.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s0, s1)) | node10(c_e_h_3, c_m, s0, s1) | node11(c_e_h_3, c_m, s0, s1)),
% 290.04/182.53 inference(modus_ponens,[status(thm)],[5729, 5728])).
% 290.04/182.53 tff(5731,plain,
% 290.04/182.53 (node10(c_e_h_3, c_m, s0, s1) | node11(c_e_h_3, c_m, s0, s1)),
% 290.04/182.53 inference(unit_resolution,[status(thm)],[5730, 5002, 72])).
% 290.04/182.53 tff(5732,plain,
% 290.04/182.53 (node11(c_e_h_3, c_m, s0, s1)),
% 290.04/182.53 inference(unit_resolution,[status(thm)],[5731, 5727])).
% 290.04/182.53 tff(5733,plain,
% 290.04/182.53 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl((m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X))) <=> (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X))))),
% 290.04/182.53 inference(bind,[status(th)],[])).
% 290.04/182.53 tff(5734,plain,
% 290.04/182.53 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))),
% 290.04/182.53 inference(quant_intro,[status(thm)],[5733])).
% 290.04/182.53 tff(5735,plain,
% 290.04/182.53 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))),
% 290.04/182.53 inference(rewrite,[status(thm)],[])).
% 290.04/182.53 tff(5736,plain,
% 290.04/182.53 (^[Y: $i, I0: $i, X: $i, I1: $i] : trans(monotonicity(rewrite((m_and_h_gate_h_init_v_out(I0, I1, Y) | (~m_and_h_gate_h_init_v_out(I0, I1, X))) <=> (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))), (((m_and_h_gate_h_init_v_out(I0, I1, Y) | (~m_and_h_gate_h_init_v_out(I0, I1, X))) | (~node11(I0, I1, X, Y))) <=> ((m_and_h_gate_h_init_v_out(I0, I1, Y) | (~m_and_h_gate_h_init_v_out(I0, I1, X))) | (~node11(I0, I1, X, Y))))), rewrite(((m_and_h_gate_h_init_v_out(I0, I1, Y) | (~m_and_h_gate_h_init_v_out(I0, I1, X))) | (~node11(I0, I1, X, Y))) <=> (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))), (((m_and_h_gate_h_init_v_out(I0, I1, Y) | (~m_and_h_gate_h_init_v_out(I0, I1, X))) | (~node11(I0, I1, X, Y))) <=> (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))))),
% 290.04/182.53 inference(bind,[status(th)],[])).
% 290.04/182.53 tff(5737,plain,
% 290.04/182.53 (![Y: $i, I0: $i, X: $i, I1: $i] : ((m_and_h_gate_h_init_v_out(I0, I1, Y) | (~m_and_h_gate_h_init_v_out(I0, I1, X))) | (~node11(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))),
% 290.04/182.53 inference(quant_intro,[status(thm)],[5736])).
% 290.04/182.53 tff(5738,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : ((m_and_h_gate_h_init_v_out(I0, I1, Y) | (~m_and_h_gate_h_init_v_out(I0, I1, X))) | (~node11(I0, I1, X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_and_h_gate_h_init_7')).
% 290.04/182.53 tff(5739,plain,
% 290.04/182.53 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))),
% 290.04/182.53 inference(modus_ponens,[status(thm)],[5738, 5737])).
% 290.04/182.53 tff(5740,plain,
% 290.04/182.53 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))),
% 290.04/182.53 inference(modus_ponens,[status(thm)],[5739, 5735])).
% 290.04/182.53 tff(5741,plain,(
% 290.04/182.53 ![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))),
% 290.04/182.53 inference(skolemize,[status(sab)],[5740])).
% 290.04/182.53 tff(5742,plain,
% 290.04/182.53 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))),
% 290.04/182.53 inference(modus_ponens,[status(thm)],[5741, 5734])).
% 290.04/182.53 tff(5743,plain,
% 290.04/182.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s0)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1) | (~node11(c_e_h_3, c_m, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s0)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1) | (~node11(c_e_h_3, c_m, s0, s1)))),
% 290.04/182.53 inference(rewrite,[status(thm)],[])).
% 290.04/182.53 tff(5744,plain,
% 290.04/182.53 ((m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1) | (~node11(c_e_h_3, c_m, s0, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s0))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s0)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1) | (~node11(c_e_h_3, c_m, s0, s1)))),
% 290.04/182.53 inference(rewrite,[status(thm)],[])).
% 290.04/182.53 tff(5745,plain,
% 290.04/182.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1) | (~node11(c_e_h_3, c_m, s0, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s0)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s0)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1) | (~node11(c_e_h_3, c_m, s0, s1))))),
% 290.04/182.53 inference(monotonicity,[status(thm)],[5744])).
% 290.04/182.53 tff(5746,plain,
% 290.04/182.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1) | (~node11(c_e_h_3, c_m, s0, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s0)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s0)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1) | (~node11(c_e_h_3, c_m, s0, s1)))),
% 290.04/182.53 inference(transitivity,[status(thm)],[5745, 5743])).
% 290.04/182.53 tff(5747,plain,
% 290.04/182.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1) | (~node11(c_e_h_3, c_m, s0, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s0)))),
% 290.04/182.54 inference(quant_inst,[status(thm)],[])).
% 290.04/182.54 tff(5748,plain,
% 290.04/182.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s0)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1) | (~node11(c_e_h_3, c_m, s0, s1))),
% 290.04/182.54 inference(modus_ponens,[status(thm)],[5747, 5746])).
% 290.04/182.54 tff(5749,plain,
% 290.04/182.54 ($false),
% 290.04/182.54 inference(unit_resolution,[status(thm)],[5748, 5742, 5594, 5696, 5732])).
% 290.04/182.54 tff(5750,plain,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s0))), inference(lemma,lemma(discharge,[]))).
% 290.04/182.54 tff(5751,plain,
% 290.04/182.54 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1)),
% 290.04/182.54 inference(unit_resolution,[status(thm)],[5750, 5694])).
% 290.04/182.54 tff(5752,plain,
% 290.04/182.54 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1)))),
% 290.04/182.54 inference(rewrite,[status(thm)],[])).
% 290.04/182.54 tff(5753,plain,
% 290.04/182.54 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1)))),
% 290.04/182.54 inference(quant_inst,[status(thm)],[])).
% 290.04/182.54 tff(5754,plain,
% 290.04/182.54 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1))),
% 290.04/182.54 inference(modus_ponens,[status(thm)],[5753, 5752])).
% 290.04/182.54 tff(5755,plain,
% 290.04/182.54 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s1)),
% 290.04/182.54 inference(unit_resolution,[status(thm)],[5754, 5601, 5751])).
% 290.04/182.54 tff(5756,plain,
% 290.04/182.54 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s1)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s1)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s1))),
% 290.04/182.54 inference(rewrite,[status(thm)],[])).
% 290.04/182.54 tff(5757,plain,
% 290.04/182.54 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s1)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s1))),
% 290.04/182.54 inference(quant_inst,[status(thm)],[])).
% 290.04/182.54 tff(5758,plain,
% 290.04/182.54 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s1)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s1)),
% 290.04/182.54 inference(modus_ponens,[status(thm)],[5757, 5756])).
% 290.04/182.54 tff(5759,plain,
% 290.04/182.54 (~node9(c_e_h_3, c_n, s1)),
% 290.04/182.54 inference(unit_resolution,[status(thm)],[5758, 4972, 5755])).
% 290.04/182.54 tff(5760,assumption,(node10(c_e_h_3, c_n, s1, s2)), introduced(assumption)).
% 290.04/182.54 tff(5761,plain,
% 290.04/182.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s1) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s2)) | (~node10(c_e_h_3, c_n, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_3, c_n, s1) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s2)) | (~node10(c_e_h_3, c_n, s1, s2)))),
% 290.04/182.54 inference(rewrite,[status(thm)],[])).
% 290.04/182.54 tff(5762,plain,
% 290.04/182.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s1) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s2)) | (~node10(c_e_h_3, c_n, s1, s2)))),
% 290.04/182.54 inference(quant_inst,[status(thm)],[])).
% 290.04/182.54 tff(5763,plain,
% 290.04/182.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_3, c_n, s1) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s2)) | (~node10(c_e_h_3, c_n, s1, s2))),
% 290.04/182.54 inference(modus_ponens,[status(thm)],[5762, 5761])).
% 290.04/182.54 tff(5764,plain,
% 290.04/182.54 ($false),
% 290.04/182.54 inference(unit_resolution,[status(thm)],[5763, 4986, 5678, 5760, 5759])).
% 290.04/182.54 tff(5765,plain,((~node10(c_e_h_3, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s2))), inference(lemma,lemma(discharge,[]))).
% 290.04/182.54 tff(5766,plain,
% 290.04/182.54 (~node10(c_e_h_3, c_n, s1, s2)),
% 290.04/182.54 inference(unit_resolution,[status(thm)],[5765, 5678])).
% 290.04/182.54 tff(5767,plain,
% 290.04/182.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s1, s2)) | node10(c_e_h_3, c_n, s1, s2) | node11(c_e_h_3, c_n, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s1, s2)) | node10(c_e_h_3, c_n, s1, s2) | node11(c_e_h_3, c_n, s1, s2))),
% 290.04/182.54 inference(rewrite,[status(thm)],[])).
% 290.04/182.54 tff(5768,plain,
% 290.04/182.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s1, s2)) | node10(c_e_h_3, c_n, s1, s2) | node11(c_e_h_3, c_n, s1, s2))),
% 290.04/182.54 inference(quant_inst,[status(thm)],[])).
% 290.04/182.54 tff(5769,plain,
% 290.04/182.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s1, s2)) | node10(c_e_h_3, c_n, s1, s2) | node11(c_e_h_3, c_n, s1, s2)),
% 290.04/182.54 inference(modus_ponens,[status(thm)],[5768, 5767])).
% 290.04/182.54 tff(5770,plain,
% 290.04/182.54 (node10(c_e_h_3, c_n, s1, s2) | node11(c_e_h_3, c_n, s1, s2)),
% 290.04/182.54 inference(unit_resolution,[status(thm)],[5769, 5002, 255])).
% 290.04/182.54 tff(5771,plain,
% 290.04/182.54 (node11(c_e_h_3, c_n, s1, s2)),
% 290.04/182.54 inference(unit_resolution,[status(thm)],[5770, 5766])).
% 290.04/182.54 tff(5772,plain,
% 290.04/182.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s2)) | (~node11(c_e_h_3, c_n, s1, s2)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s2)) | (~node11(c_e_h_3, c_n, s1, s2)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1))),
% 290.04/182.54 inference(rewrite,[status(thm)],[])).
% 290.04/182.54 tff(5773,plain,
% 290.04/182.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s2)) | (~node11(c_e_h_3, c_n, s1, s2)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1))),
% 290.04/182.54 inference(quant_inst,[status(thm)],[])).
% 290.04/182.54 tff(5774,plain,
% 290.04/182.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s2)) | (~node11(c_e_h_3, c_n, s1, s2)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1)),
% 290.04/182.54 inference(modus_ponens,[status(thm)],[5773, 5772])).
% 290.04/182.54 tff(5775,plain,
% 290.04/182.54 ($false),
% 290.04/182.54 inference(unit_resolution,[status(thm)],[5774, 5017, 5614, 5678, 5771])).
% 290.04/182.54 tff(5776,plain,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s2)), inference(lemma,lemma(discharge,[]))).
% 290.04/182.54 tff(5777,plain,
% 290.04/182.54 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s2)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s2))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s2)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s2))),
% 290.04/182.54 inference(rewrite,[status(thm)],[])).
% 290.04/182.54 tff(5778,plain,
% 290.04/182.54 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s2)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s2))),
% 290.04/182.54 inference(quant_inst,[status(thm)],[])).
% 290.04/182.54 tff(5779,plain,
% 290.04/182.54 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s2)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s2)),
% 290.04/182.54 inference(modus_ponens,[status(thm)],[5778, 5777])).
% 290.04/182.54 tff(5780,plain,
% 290.04/182.54 (~m_and_h_gate_v_in2(c_e_h_3, c_q, s2)),
% 290.04/182.54 inference(unit_resolution,[status(thm)],[5779, 5621, 5776])).
% 290.04/182.54 tff(5781,plain,
% 290.04/182.54 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s2)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s2)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s2))),
% 290.04/182.54 inference(rewrite,[status(thm)],[])).
% 290.04/182.54 tff(5782,plain,
% 290.04/182.54 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s2)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s2))),
% 290.04/182.54 inference(quant_inst,[status(thm)],[])).
% 290.04/182.54 tff(5783,plain,
% 290.04/182.54 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s2)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s2)),
% 290.04/182.55 inference(modus_ponens,[status(thm)],[5782, 5781])).
% 290.04/182.55 tff(5784,plain,
% 290.04/182.55 (~node20(c_e_h_3, c_q, s2)),
% 290.04/182.55 inference(unit_resolution,[status(thm)],[5783, 4563, 5780])).
% 290.04/182.55 tff(5785,plain,
% 290.04/182.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s3)) | node20(c_e_h_3, c_q, s2) | (~node21(c_e_h_3, c_q, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s3)) | node20(c_e_h_3, c_q, s2) | (~node21(c_e_h_3, c_q, s2, s3)))),
% 290.04/182.55 inference(rewrite,[status(thm)],[])).
% 290.04/182.55 tff(5786,plain,
% 290.04/182.55 ((node20(c_e_h_3, c_q, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s3)) | (~node21(c_e_h_3, c_q, s2, s3))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_q, s3)) | node20(c_e_h_3, c_q, s2) | (~node21(c_e_h_3, c_q, s2, s3)))),
% 290.04/182.55 inference(rewrite,[status(thm)],[])).
% 290.04/182.55 tff(5787,plain,
% 290.04/182.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s3)) | (~node21(c_e_h_3, c_q, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s3)) | node20(c_e_h_3, c_q, s2) | (~node21(c_e_h_3, c_q, s2, s3))))),
% 290.04/182.55 inference(monotonicity,[status(thm)],[5786])).
% 290.04/182.55 tff(5788,plain,
% 290.04/182.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s3)) | (~node21(c_e_h_3, c_q, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s3)) | node20(c_e_h_3, c_q, s2) | (~node21(c_e_h_3, c_q, s2, s3)))),
% 290.04/182.55 inference(transitivity,[status(thm)],[5787, 5785])).
% 290.04/182.55 tff(5789,plain,
% 290.04/182.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s2) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s3)) | (~node21(c_e_h_3, c_q, s2, s3)))),
% 290.04/182.55 inference(quant_inst,[status(thm)],[])).
% 290.04/182.55 tff(5790,plain,
% 290.04/182.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s3)) | node20(c_e_h_3, c_q, s2) | (~node21(c_e_h_3, c_q, s2, s3))),
% 290.04/182.55 inference(modus_ponens,[status(thm)],[5789, 5788])).
% 290.04/182.55 tff(5791,plain,
% 290.04/182.55 ($false),
% 290.04/182.55 inference(unit_resolution,[status(thm)],[5790, 52, 5676, 5784, 5677])).
% 290.04/182.55 tff(5792,plain,((~node21(c_e_h_3, c_q, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s3))), inference(lemma,lemma(discharge,[]))).
% 290.04/182.55 tff(5793,plain,
% 290.04/182.55 (~node21(c_e_h_3, c_q, s2, s3)),
% 290.04/182.55 inference(unit_resolution,[status(thm)],[5792, 5676])).
% 290.04/182.55 tff(5794,plain,
% 290.04/182.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_3, c_q, s2, s3) | node22(c_e_h_3, c_q, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_3, c_q, s2, s3) | node22(c_e_h_3, c_q, s2, s3))),
% 290.04/182.55 inference(rewrite,[status(thm)],[])).
% 290.04/182.55 tff(5795,plain,
% 290.04/182.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_3, c_q, s2, s3) | node22(c_e_h_3, c_q, s2, s3))),
% 290.04/182.55 inference(quant_inst,[status(thm)],[])).
% 290.04/182.55 tff(5796,plain,
% 290.04/182.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_3, c_q, s2, s3) | node22(c_e_h_3, c_q, s2, s3)),
% 290.04/182.55 inference(modus_ponens,[status(thm)],[5795, 5794])).
% 290.04/182.55 tff(5797,plain,
% 290.04/182.55 (node21(c_e_h_3, c_q, s2, s3) | node22(c_e_h_3, c_q, s2, s3)),
% 290.04/182.55 inference(unit_resolution,[status(thm)],[5796, 82, 318])).
% 290.04/182.55 tff(5798,plain,
% 290.04/182.55 (node22(c_e_h_3, c_q, s2, s3)),
% 290.04/182.55 inference(unit_resolution,[status(thm)],[5797, 5793])).
% 290.04/182.55 tff(5799,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_q, s2)), introduced(assumption)).
% 290.04/182.55 tff(5800,plain,
% 290.04/182.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s3)) | (~node22(c_e_h_3, c_q, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_q, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s3)) | (~node22(c_e_h_3, c_q, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_q, s2))),
% 290.04/182.55 inference(rewrite,[status(thm)],[])).
% 290.04/182.55 tff(5801,plain,
% 290.04/182.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s3)) | (~node22(c_e_h_3, c_q, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_q, s2))),
% 290.04/182.55 inference(quant_inst,[status(thm)],[])).
% 290.04/182.55 tff(5802,plain,
% 290.04/182.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s3)) | (~node22(c_e_h_3, c_q, s2, s3)) | m_and_h_gate_v_out(c_e_h_3, c_q, s2)),
% 290.04/182.55 inference(modus_ponens,[status(thm)],[5801, 5800])).
% 290.04/182.55 tff(5803,plain,
% 290.04/182.55 ($false),
% 290.04/182.55 inference(unit_resolution,[status(thm)],[5802, 108, 5676, 5799, 5798])).
% 290.04/182.55 tff(5804,plain,((~m_and_h_gate_v_out(c_e_h_3, c_q, s3)) | m_and_h_gate_v_out(c_e_h_3, c_q, s2)), inference(lemma,lemma(discharge,[]))).
% 290.04/182.55 tff(5805,plain,
% 290.04/182.55 (~m_and_h_gate_v_out(c_e_h_3, c_q, s3)),
% 290.04/182.55 inference(unit_resolution,[status(thm)],[5804, 5675])).
% 290.04/182.55 tff(5806,plain,
% 290.04/182.55 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s3))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s3))),
% 290.04/182.55 inference(rewrite,[status(thm)],[])).
% 290.04/182.55 tff(5807,plain,
% 290.04/182.55 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s3))),
% 290.04/182.55 inference(quant_inst,[status(thm)],[])).
% 290.04/182.55 tff(5808,plain,
% 290.04/182.55 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s3)),
% 290.04/182.55 inference(modus_ponens,[status(thm)],[5807, 5806])).
% 290.04/182.55 tff(5809,plain,
% 290.04/182.55 (node3(c_e_h_3, c_e_h_1, s3)),
% 290.04/182.55 inference(unit_resolution,[status(thm)],[5808, 2922, 1056])).
% 290.04/182.55 tff(5810,plain,
% 290.04/182.55 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s3)) | (~node3(c_e_h_3, c_e_h_1, s3)) | m_and_h_gate_v_out(c_e_h_3, c_q, s3))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s3)) | (~node3(c_e_h_3, c_e_h_1, s3)) | m_and_h_gate_v_out(c_e_h_3, c_q, s3))),
% 290.04/182.55 inference(rewrite,[status(thm)],[])).
% 290.04/182.55 tff(5811,plain,
% 290.04/182.55 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s3)) | (~node3(c_e_h_3, c_e_h_1, s3)) | m_and_h_gate_v_out(c_e_h_3, c_q, s3))),
% 290.04/182.55 inference(quant_inst,[status(thm)],[])).
% 290.04/182.55 tff(5812,plain,
% 290.04/182.55 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s3)) | (~node3(c_e_h_3, c_e_h_1, s3)) | m_and_h_gate_v_out(c_e_h_3, c_q, s3)),
% 290.04/182.55 inference(modus_ponens,[status(thm)],[5811, 5810])).
% 290.04/182.55 tff(5813,plain,
% 290.04/182.55 ((~m_cell_v_ack(c_e_h_1, s3)) | m_and_h_gate_v_out(c_e_h_3, c_q, s3)),
% 290.04/182.55 inference(unit_resolution,[status(thm)],[5812, 1073, 5809])).
% 290.04/182.55 tff(5814,plain,
% 290.04/182.55 (~m_cell_v_ack(c_e_h_1, s3)),
% 290.04/182.55 inference(unit_resolution,[status(thm)],[5813, 5805])).
% 290.04/182.55 tff(5815,plain,
% 290.04/182.55 (^[I0: $i, X: $i, J0: $i] : refl(((~m_cell_v_left(I0, J0)) | node2(I0, J0, X)) <=> ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X)))),
% 290.04/182.55 inference(bind,[status(th)],[])).
% 290.04/182.55 tff(5816,plain,
% 290.04/182.55 (![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X)) <=> ![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))),
% 290.04/182.55 inference(quant_intro,[status(thm)],[5815])).
% 290.04/182.55 tff(5817,plain,
% 290.04/182.55 (![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X)) <=> ![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))),
% 290.04/182.55 inference(rewrite,[status(thm)],[])).
% 290.04/182.55 tff(5818,axiom,(![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_14')).
% 290.04/182.55 tff(5819,plain,
% 290.04/182.55 (![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))),
% 290.04/182.55 inference(modus_ponens,[status(thm)],[5818, 5817])).
% 290.04/182.55 tff(5820,plain,(
% 290.04/182.55 ![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))),
% 290.04/182.55 inference(skolemize,[status(sab)],[5819])).
% 290.04/182.55 tff(5821,plain,
% 290.04/182.55 (![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))),
% 290.04/182.55 inference(modus_ponens,[status(thm)],[5820, 5816])).
% 290.04/182.55 tff(5822,plain,
% 290.04/182.55 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node2(c_e_h_3, c_e_h_1, s3))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node2(c_e_h_3, c_e_h_1, s3))),
% 290.04/182.55 inference(rewrite,[status(thm)],[])).
% 290.04/182.55 tff(5823,plain,
% 290.04/182.55 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node2(c_e_h_3, c_e_h_1, s3))),
% 290.04/182.55 inference(quant_inst,[status(thm)],[])).
% 290.04/182.55 tff(5824,plain,
% 290.04/182.55 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node2(c_e_h_3, c_e_h_1, s3)),
% 290.04/182.55 inference(modus_ponens,[status(thm)],[5823, 5822])).
% 290.04/182.55 tff(5825,plain,
% 290.04/182.55 (node2(c_e_h_3, c_e_h_1, s3)),
% 290.04/182.55 inference(unit_resolution,[status(thm)],[5824, 2922, 5821])).
% 290.04/182.55 tff(5826,plain,
% 290.04/182.55 (^[I0: $i, X: $i, J0: $i] : refl(((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X)) <=> ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X)))),
% 290.04/182.55 inference(bind,[status(th)],[])).
% 290.04/182.55 tff(5827,plain,
% 290.04/182.55 (![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X)) <=> ![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))),
% 290.04/182.55 inference(quant_intro,[status(thm)],[5826])).
% 290.04/182.55 tff(5828,plain,
% 290.04/182.55 (![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X)) <=> ![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))),
% 290.04/182.55 inference(rewrite,[status(thm)],[])).
% 290.04/182.55 tff(5829,plain,
% 290.04/182.55 (^[I0: $i, X: $i, J0: $i] : trans(monotonicity(rewrite((m_and_h_gate_v_in2(I0, c_c, X) | m_cell_v_ack(J0, X)) <=> (m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))), (((m_and_h_gate_v_in2(I0, c_c, X) | m_cell_v_ack(J0, X)) | (~node2(I0, J0, X))) <=> ((m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X)) | (~node2(I0, J0, X))))), rewrite(((m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X)) | (~node2(I0, J0, X))) <=> ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))), (((m_and_h_gate_v_in2(I0, c_c, X) | m_cell_v_ack(J0, X)) | (~node2(I0, J0, X))) <=> ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))))),
% 290.04/182.55 inference(bind,[status(th)],[])).
% 290.04/182.55 tff(5830,plain,
% 290.04/182.55 (![I0: $i, X: $i, J0: $i] : ((m_and_h_gate_v_in2(I0, c_c, X) | m_cell_v_ack(J0, X)) | (~node2(I0, J0, X))) <=> ![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))),
% 290.04/182.55 inference(quant_intro,[status(thm)],[5829])).
% 290.04/182.55 tff(5831,axiom,(![I0: $i, X: $i, J0: $i] : ((m_and_h_gate_v_in2(I0, c_c, X) | m_cell_v_ack(J0, X)) | (~node2(I0, J0, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_12')).
% 290.04/182.55 tff(5832,plain,
% 290.04/182.55 (![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))),
% 290.04/182.55 inference(modus_ponens,[status(thm)],[5831, 5830])).
% 290.04/182.55 tff(5833,plain,
% 290.04/182.55 (![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))),
% 290.04/182.55 inference(modus_ponens,[status(thm)],[5832, 5828])).
% 290.04/182.55 tff(5834,plain,(
% 290.04/182.55 ![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))),
% 290.04/182.55 inference(skolemize,[status(sab)],[5833])).
% 290.04/182.55 tff(5835,plain,
% 290.04/182.55 (![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))),
% 290.04/182.55 inference(modus_ponens,[status(thm)],[5834, 5827])).
% 290.04/182.55 tff(5836,plain,
% 290.04/182.55 (((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | ((~node2(c_e_h_3, c_e_h_1, s3)) | m_cell_v_ack(c_e_h_1, s3) | m_and_h_gate_v_in2(c_e_h_3, c_c, s3))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | (~node2(c_e_h_3, c_e_h_1, s3)) | m_cell_v_ack(c_e_h_1, s3) | m_and_h_gate_v_in2(c_e_h_3, c_c, s3))),
% 290.04/182.55 inference(rewrite,[status(thm)],[])).
% 290.04/182.55 tff(5837,plain,
% 290.04/182.55 ((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | ((~node2(c_e_h_3, c_e_h_1, s3)) | m_cell_v_ack(c_e_h_1, s3) | m_and_h_gate_v_in2(c_e_h_3, c_c, s3))),
% 290.04/182.55 inference(quant_inst,[status(thm)],[])).
% 290.04/182.55 tff(5838,plain,
% 290.04/182.55 ((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | (~node2(c_e_h_3, c_e_h_1, s3)) | m_cell_v_ack(c_e_h_1, s3) | m_and_h_gate_v_in2(c_e_h_3, c_c, s3)),
% 290.04/182.55 inference(modus_ponens,[status(thm)],[5837, 5836])).
% 290.04/182.55 tff(5839,plain,
% 290.04/182.55 (m_cell_v_ack(c_e_h_1, s3) | m_and_h_gate_v_in2(c_e_h_3, c_c, s3)),
% 290.04/182.55 inference(unit_resolution,[status(thm)],[5838, 5835, 5825])).
% 290.04/182.55 tff(5840,plain,
% 290.04/182.55 (m_and_h_gate_v_in2(c_e_h_3, c_c, s3)),
% 290.04/182.55 inference(unit_resolution,[status(thm)],[5839, 5814])).
% 290.04/182.55 tff(5841,assumption,(node21(c_e_h_3, c_c, s3, s4)), introduced(assumption)).
% 290.04/182.55 tff(5842,plain,
% 290.04/182.55 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl(((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y)) <=> ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y)))),
% 290.04/182.55 inference(bind,[status(th)],[])).
% 290.04/182.55 tff(5843,plain,
% 290.04/182.55 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))),
% 290.04/182.55 inference(quant_intro,[status(thm)],[5842])).
% 290.04/182.55 tff(5844,plain,
% 290.04/182.55 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))),
% 290.04/182.55 inference(rewrite,[status(thm)],[])).
% 290.04/182.55 tff(5845,plain,
% 290.04/182.55 (^[Y: $i, I0: $i, X: $i, I1: $i] : trans(monotonicity(trans(monotonicity(rewrite((m_and_h_gate_v_out(I0, I1, Y) | (~m_and_h_gate_v_in1(I0, I1, X))) <=> ((~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))), (((m_and_h_gate_v_out(I0, I1, Y) | (~m_and_h_gate_v_in1(I0, I1, X))) | (~m_and_h_gate_v_in2(I0, I1, X))) <=> (((~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y)) | (~m_and_h_gate_v_in2(I0, I1, X))))), rewrite((((~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y)) | (~m_and_h_gate_v_in2(I0, I1, X))) <=> ((~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))), (((m_and_h_gate_v_out(I0, I1, Y) | (~m_and_h_gate_v_in1(I0, I1, X))) | (~m_and_h_gate_v_in2(I0, I1, X))) <=> ((~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y)))), ((((m_and_h_gate_v_out(I0, I1, Y) | (~m_and_h_gate_v_in1(I0, I1, X))) | (~m_and_h_gate_v_in2(I0, I1, X))) | (~node21(I0, I1, X, Y))) <=> (((~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y))))), rewrite((((~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y))) <=> ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))), ((((m_and_h_gate_v_out(I0, I1, Y) | (~m_and_h_gate_v_in1(I0, I1, X))) | (~m_and_h_gate_v_in2(I0, I1, X))) | (~node21(I0, I1, X, Y))) <=> ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))))),
% 290.04/182.56 inference(bind,[status(th)],[])).
% 290.04/182.56 tff(5846,plain,
% 290.04/182.56 (![Y: $i, I0: $i, X: $i, I1: $i] : (((m_and_h_gate_v_out(I0, I1, Y) | (~m_and_h_gate_v_in1(I0, I1, X))) | (~m_and_h_gate_v_in2(I0, I1, X))) | (~node21(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))),
% 290.04/182.56 inference(quant_intro,[status(thm)],[5845])).
% 290.04/182.56 tff(5847,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : (((m_and_h_gate_v_out(I0, I1, Y) | (~m_and_h_gate_v_in1(I0, I1, X))) | (~m_and_h_gate_v_in2(I0, I1, X))) | (~node21(I0, I1, X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_and_h_gate_4')).
% 290.04/182.56 tff(5848,plain,
% 290.04/182.56 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))),
% 290.04/182.56 inference(modus_ponens,[status(thm)],[5847, 5846])).
% 290.04/182.56 tff(5849,plain,
% 290.04/182.56 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))),
% 290.04/182.56 inference(modus_ponens,[status(thm)],[5848, 5844])).
% 290.04/182.56 tff(5850,plain,(
% 290.04/182.56 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))),
% 290.04/182.56 inference(skolemize,[status(sab)],[5849])).
% 290.04/182.56 tff(5851,plain,
% 290.04/182.56 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))),
% 290.04/182.56 inference(modus_ponens,[status(thm)],[5850, 5843])).
% 290.04/182.56 tff(5852,plain,
% 290.04/182.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_c, s3)) | m_and_h_gate_v_out(c_e_h_3, c_c, s4) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s3)) | (~node21(c_e_h_3, c_c, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s3)) | m_and_h_gate_v_out(c_e_h_3, c_c, s4) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s3)) | (~node21(c_e_h_3, c_c, s3, s4)))),
% 290.04/182.56 inference(rewrite,[status(thm)],[])).
% 290.04/182.56 tff(5853,plain,
% 290.04/182.56 (((~node21(c_e_h_3, c_c, s3, s4)) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s3)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s3)) | m_and_h_gate_v_out(c_e_h_3, c_c, s4)) <=> ((~m_and_h_gate_v_in1(c_e_h_3, c_c, s3)) | m_and_h_gate_v_out(c_e_h_3, c_c, s4) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s3)) | (~node21(c_e_h_3, c_c, s3, s4)))),
% 290.04/182.56 inference(rewrite,[status(thm)],[])).
% 290.04/182.56 tff(5854,plain,
% 290.04/182.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_c, s3, s4)) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s3)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s3)) | m_and_h_gate_v_out(c_e_h_3, c_c, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_c, s3)) | m_and_h_gate_v_out(c_e_h_3, c_c, s4) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s3)) | (~node21(c_e_h_3, c_c, s3, s4))))),
% 290.04/182.56 inference(monotonicity,[status(thm)],[5853])).
% 290.04/182.56 tff(5855,plain,
% 290.04/182.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_c, s3, s4)) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s3)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s3)) | m_and_h_gate_v_out(c_e_h_3, c_c, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s3)) | m_and_h_gate_v_out(c_e_h_3, c_c, s4) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s3)) | (~node21(c_e_h_3, c_c, s3, s4)))),
% 290.04/182.56 inference(transitivity,[status(thm)],[5854, 5852])).
% 290.04/182.56 tff(5856,plain,
% 290.04/182.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_c, s3, s4)) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s3)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s3)) | m_and_h_gate_v_out(c_e_h_3, c_c, s4))),
% 290.04/182.56 inference(quant_inst,[status(thm)],[])).
% 290.04/182.56 tff(5857,plain,
% 290.04/182.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s3)) | m_and_h_gate_v_out(c_e_h_3, c_c, s4) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s3)) | (~node21(c_e_h_3, c_c, s3, s4))),
% 290.04/182.56 inference(modus_ponens,[status(thm)],[5856, 5855])).
% 290.04/182.56 tff(5858,plain,
% 290.04/182.56 ($false),
% 290.04/182.56 inference(unit_resolution,[status(thm)],[5857, 5851, 5841, 5840, 2743, 2539])).
% 290.04/182.56 tff(5859,plain,((~node21(c_e_h_3, c_c, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_c, s4) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s3))), inference(lemma,lemma(discharge,[]))).
% 290.04/182.56 tff(5860,plain,
% 290.04/182.56 (~node21(c_e_h_3, c_c, s3, s4)),
% 290.04/182.56 inference(unit_resolution,[status(thm)],[5859, 2743, 5531])).
% 290.04/182.56 tff(5861,plain,
% 290.04/182.56 (node22(c_e_h_3, c_c, s3, s4)),
% 290.04/182.56 inference(unit_resolution,[status(thm)],[2734, 5860])).
% 290.04/182.56 tff(5862,plain,
% 290.04/182.56 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl((m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X))) <=> (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X))))),
% 290.04/182.56 inference(bind,[status(th)],[])).
% 290.04/182.56 tff(5863,plain,
% 290.04/182.56 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))),
% 290.04/182.56 inference(quant_intro,[status(thm)],[5862])).
% 290.04/182.56 tff(5864,plain,
% 290.04/182.56 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))),
% 290.04/182.56 inference(rewrite,[status(thm)],[])).
% 290.04/182.56 tff(5865,plain,
% 290.04/182.56 (^[Y: $i, I0: $i, X: $i, I1: $i] : trans(monotonicity(rewrite((m_and_h_gate_v_out(I0, I1, Y) | (~m_and_h_gate_v_out(I0, I1, X))) <=> (m_and_h_gate_v_out(I0, I1, Y) | (~m_and_h_gate_v_out(I0, I1, X)))), (((m_and_h_gate_v_out(I0, I1, Y) | (~m_and_h_gate_v_out(I0, I1, X))) | (~node22(I0, I1, X, Y))) <=> ((m_and_h_gate_v_out(I0, I1, Y) | (~m_and_h_gate_v_out(I0, I1, X))) | (~node22(I0, I1, X, Y))))), rewrite(((m_and_h_gate_v_out(I0, I1, Y) | (~m_and_h_gate_v_out(I0, I1, X))) | (~node22(I0, I1, X, Y))) <=> (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))), (((m_and_h_gate_v_out(I0, I1, Y) | (~m_and_h_gate_v_out(I0, I1, X))) | (~node22(I0, I1, X, Y))) <=> (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))))),
% 290.04/182.56 inference(bind,[status(th)],[])).
% 290.04/182.56 tff(5866,plain,
% 290.04/182.56 (![Y: $i, I0: $i, X: $i, I1: $i] : ((m_and_h_gate_v_out(I0, I1, Y) | (~m_and_h_gate_v_out(I0, I1, X))) | (~node22(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))),
% 290.04/182.56 inference(quant_intro,[status(thm)],[5865])).
% 290.04/182.56 tff(5867,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : ((m_and_h_gate_v_out(I0, I1, Y) | (~m_and_h_gate_v_out(I0, I1, X))) | (~node22(I0, I1, X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_and_h_gate_6')).
% 290.04/182.56 tff(5868,plain,
% 290.04/182.56 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))),
% 290.04/182.56 inference(modus_ponens,[status(thm)],[5867, 5866])).
% 290.04/182.56 tff(5869,plain,
% 290.04/182.56 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))),
% 290.04/182.56 inference(modus_ponens,[status(thm)],[5868, 5864])).
% 290.04/182.56 tff(5870,plain,(
% 290.04/182.56 ![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))),
% 290.04/182.56 inference(skolemize,[status(sab)],[5869])).
% 290.04/182.56 tff(5871,plain,
% 290.04/182.56 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))),
% 290.04/182.56 inference(modus_ponens,[status(thm)],[5870, 5863])).
% 290.04/182.56 tff(5872,plain,
% 290.04/182.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_c, s4) | (~node22(c_e_h_3, c_c, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | m_and_h_gate_v_out(c_e_h_3, c_c, s4) | (~node22(c_e_h_3, c_c, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s3)))),
% 290.04/182.56 inference(rewrite,[status(thm)],[])).
% 290.04/182.56 tff(5873,plain,
% 290.04/182.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_c, s4) | (~node22(c_e_h_3, c_c, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s3)))),
% 290.04/182.56 inference(quant_inst,[status(thm)],[])).
% 290.04/182.56 tff(5874,plain,
% 290.04/182.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | m_and_h_gate_v_out(c_e_h_3, c_c, s4) | (~node22(c_e_h_3, c_c, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s3))),
% 290.04/182.56 inference(modus_ponens,[status(thm)],[5873, 5872])).
% 290.04/182.56 tff(5875,plain,
% 290.04/182.56 (~m_and_h_gate_v_out(c_e_h_3, c_c, s3)),
% 290.04/182.56 inference(unit_resolution,[status(thm)],[5874, 5871, 5861, 2743])).
% 290.04/182.56 tff(5876,plain,
% 290.04/182.56 (~m_or_h_gate_v_in1(c_e_h_3, c_g, s3)),
% 290.04/182.56 inference(unit_resolution,[status(thm)],[2713, 5875])).
% 290.04/182.56 tff(5877,plain,
% 290.04/182.56 (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)),
% 290.04/182.56 inference(unit_resolution,[status(thm)],[3377, 5876])).
% 290.04/182.56 tff(5878,plain,
% 290.04/182.56 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s4)),
% 290.04/182.56 inference(unit_resolution,[status(thm)],[3384, 5877])).
% 290.04/182.56 tff(5879,plain,
% 290.04/182.56 (~node20(c_e_h_3, c_k, s4)),
% 290.04/182.56 inference(unit_resolution,[status(thm)],[3392, 5878])).
% 290.04/182.56 tff(5880,plain,
% 290.04/182.56 (~m_or_h_gate_v_in1(c_e_h_3, c_g, s4)),
% 290.04/182.56 inference(unit_resolution,[status(thm)],[2748, 2743])).
% 290.04/182.56 tff(5881,plain,
% 290.04/182.56 (~m_or_h_gate_v_out(c_e_h_3, c_g, s5)),
% 290.04/182.56 inference(unit_resolution,[status(thm)],[3357, 5876, 5880])).
% 290.04/182.56 tff(5882,plain,
% 290.04/182.56 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s5)),
% 290.04/182.56 inference(unit_resolution,[status(thm)],[3365, 5881])).
% 290.04/182.56 tff(5883,plain,
% 290.04/182.56 (~node20(c_e_h_3, c_k, s5)),
% 290.04/182.56 inference(unit_resolution,[status(thm)],[5458, 5882])).
% 290.04/182.56 tff(5884,plain,
% 290.04/182.56 ($false),
% 290.04/182.56 inference(unit_resolution,[status(thm)],[5450, 5883, 5879, 3367])).
% 290.04/182.56 tff(5885,plain,(m_and_h_gate_v_out(c_e_h_3, c_c, s4) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s8))), inference(lemma,lemma(discharge,[]))).
% 290.04/182.56 tff(5886,plain,
% 290.04/182.56 (m_and_h_gate_v_out(c_e_h_3, c_c, s4)),
% 290.04/182.57 inference(unit_resolution,[status(thm)],[5885, 3367])).
% 290.04/182.57 tff(5887,plain,
% 290.04/182.57 (^[I0: $i, X: $i] : refl(((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X)) <=> ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X)))),
% 290.04/182.57 inference(bind,[status(th)],[])).
% 290.04/182.57 tff(5888,plain,
% 290.04/182.57 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))),
% 290.04/182.57 inference(quant_intro,[status(thm)],[5887])).
% 290.04/182.57 tff(5889,plain,
% 290.04/182.57 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))),
% 290.04/182.57 inference(rewrite,[status(thm)],[])).
% 290.04/182.57 tff(5890,plain,
% 290.04/182.57 (^[I0: $i, X: $i] : rewrite((m_or_h_gate_v_in1(I0, c_g, X) | (~m_and_h_gate_v_out(I0, c_c, X))) <=> ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X)))),
% 290.04/182.57 inference(bind,[status(th)],[])).
% 290.04/182.57 tff(5891,plain,
% 290.04/182.57 (![I0: $i, X: $i] : (m_or_h_gate_v_in1(I0, c_g, X) | (~m_and_h_gate_v_out(I0, c_c, X))) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))),
% 290.04/182.57 inference(quant_intro,[status(thm)],[5890])).
% 290.04/182.57 tff(5892,axiom,(![I0: $i, X: $i] : (m_or_h_gate_v_in1(I0, c_g, X) | (~m_and_h_gate_v_out(I0, c_c, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_27')).
% 290.04/182.57 tff(5893,plain,
% 290.04/182.57 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))),
% 290.04/182.57 inference(modus_ponens,[status(thm)],[5892, 5891])).
% 290.04/182.57 tff(5894,plain,
% 290.04/182.57 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))),
% 290.04/182.57 inference(modus_ponens,[status(thm)],[5893, 5889])).
% 290.04/182.57 tff(5895,plain,(
% 290.04/182.57 ![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))),
% 290.04/182.57 inference(skolemize,[status(sab)],[5894])).
% 290.04/182.57 tff(5896,plain,
% 290.04/182.57 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))),
% 290.04/182.57 inference(modus_ponens,[status(thm)],[5895, 5888])).
% 290.04/182.57 tff(5897,plain,
% 290.04/182.57 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s4)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s4))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s4)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s4))),
% 290.04/182.57 inference(rewrite,[status(thm)],[])).
% 290.04/182.57 tff(5898,plain,
% 290.04/182.57 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s4)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s4))),
% 290.04/182.57 inference(quant_inst,[status(thm)],[])).
% 290.04/182.57 tff(5899,plain,
% 290.04/182.57 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s4)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s4)),
% 290.04/182.57 inference(modus_ponens,[status(thm)],[5898, 5897])).
% 290.04/182.57 tff(5900,plain,
% 290.04/182.57 (m_or_h_gate_v_in1(c_e_h_3, c_g, s4)),
% 290.04/182.57 inference(unit_resolution,[status(thm)],[5899, 5896, 5886])).
% 290.04/182.57 tff(5901,plain,
% 290.04/182.57 (((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_g, s4)) | (~node4(c_e_h_3, c_g, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s4)) | (~node4(c_e_h_3, c_g, s4)))),
% 290.04/182.57 inference(rewrite,[status(thm)],[])).
% 290.04/182.57 tff(5902,plain,
% 290.04/182.57 ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_g, s4)) | (~node4(c_e_h_3, c_g, s4)))),
% 290.04/182.57 inference(quant_inst,[status(thm)],[])).
% 290.04/182.57 tff(5903,plain,
% 290.04/182.57 ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s4)) | (~node4(c_e_h_3, c_g, s4))),
% 290.04/182.57 inference(modus_ponens,[status(thm)],[5902, 5901])).
% 290.04/182.57 tff(5904,plain,
% 290.04/182.57 (~node4(c_e_h_3, c_g, s4)),
% 290.04/182.57 inference(unit_resolution,[status(thm)],[5903, 5516, 5900])).
% 290.04/182.57 tff(5905,assumption,(~node4(c_e_h_3, c_g, s4)), introduced(assumption)).
% 290.04/182.57 tff(5906,plain,
% 290.04/182.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_3, c_g, s4) | (~node5(c_e_h_3, c_g, s4, s5)) | m_or_h_gate_v_out(c_e_h_3, c_g, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | node4(c_e_h_3, c_g, s4) | (~node5(c_e_h_3, c_g, s4, s5)) | m_or_h_gate_v_out(c_e_h_3, c_g, s5))),
% 290.04/182.57 inference(rewrite,[status(thm)],[])).
% 290.04/182.57 tff(5907,plain,
% 290.04/182.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_3, c_g, s4) | (~node5(c_e_h_3, c_g, s4, s5)) | m_or_h_gate_v_out(c_e_h_3, c_g, s5))),
% 290.04/182.57 inference(quant_inst,[status(thm)],[])).
% 290.04/182.57 tff(5908,plain,
% 290.04/182.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | node4(c_e_h_3, c_g, s4) | (~node5(c_e_h_3, c_g, s4, s5)) | m_or_h_gate_v_out(c_e_h_3, c_g, s5)),
% 290.04/182.57 inference(modus_ponens,[status(thm)],[5907, 5906])).
% 290.04/182.57 tff(5909,plain,
% 290.04/182.57 ($false),
% 290.04/182.57 inference(unit_resolution,[status(thm)],[5908, 5498, 3290, 5905, 3360])).
% 290.04/182.57 tff(5910,plain,((~node5(c_e_h_3, c_g, s4, s5)) | node4(c_e_h_3, c_g, s4) | m_or_h_gate_v_out(c_e_h_3, c_g, s5)), inference(lemma,lemma(discharge,[]))).
% 290.04/182.57 tff(5911,plain,
% 290.04/182.57 (~node5(c_e_h_3, c_g, s4, s5)),
% 290.04/182.57 inference(unit_resolution,[status(thm)],[5910, 3360, 5905])).
% 290.04/182.57 tff(5912,plain,
% 290.04/182.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s5) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | (~node6(c_e_h_3, c_g, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | m_or_h_gate_v_out(c_e_h_3, c_g, s5) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | (~node6(c_e_h_3, c_g, s4, s5)))),
% 290.04/182.57 inference(rewrite,[status(thm)],[])).
% 290.04/182.57 tff(5913,plain,
% 290.04/182.57 ((m_or_h_gate_v_out(c_e_h_3, c_g, s5) | (~node6(c_e_h_3, c_g, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4))) <=> (m_or_h_gate_v_out(c_e_h_3, c_g, s5) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | (~node6(c_e_h_3, c_g, s4, s5)))),
% 290.04/182.57 inference(rewrite,[status(thm)],[])).
% 290.04/182.57 tff(5914,plain,
% 290.04/182.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s5) | (~node6(c_e_h_3, c_g, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s5) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | (~node6(c_e_h_3, c_g, s4, s5))))),
% 290.04/182.57 inference(monotonicity,[status(thm)],[5913])).
% 290.04/182.57 tff(5915,plain,
% 290.04/182.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s5) | (~node6(c_e_h_3, c_g, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | m_or_h_gate_v_out(c_e_h_3, c_g, s5) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | (~node6(c_e_h_3, c_g, s4, s5)))),
% 290.04/182.57 inference(transitivity,[status(thm)],[5914, 5912])).
% 290.04/182.57 tff(5916,plain,
% 290.04/182.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s5) | (~node6(c_e_h_3, c_g, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)))),
% 290.04/182.57 inference(quant_inst,[status(thm)],[])).
% 290.04/182.57 tff(5917,plain,
% 290.04/182.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | m_or_h_gate_v_out(c_e_h_3, c_g, s5) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | (~node6(c_e_h_3, c_g, s4, s5))),
% 290.04/182.57 inference(modus_ponens,[status(thm)],[5916, 5915])).
% 290.04/182.57 tff(5918,plain,
% 290.04/182.57 ($false),
% 290.04/182.57 inference(unit_resolution,[status(thm)],[5917, 5474, 3309, 3321, 3360])).
% 290.04/182.57 tff(5919,plain,((~node6(c_e_h_3, c_g, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | m_or_h_gate_v_out(c_e_h_3, c_g, s5)), inference(lemma,lemma(discharge,[]))).
% 290.04/182.57 tff(5920,plain,
% 290.04/182.57 (~node6(c_e_h_3, c_g, s4, s5)),
% 290.04/182.57 inference(unit_resolution,[status(thm)],[5919, 3360, 3321])).
% 290.04/182.57 tff(5921,plain,
% 290.04/182.57 ($false),
% 290.04/182.57 inference(unit_resolution,[status(thm)],[3306, 5920, 5911])).
% 290.04/182.57 tff(5922,plain,(m_or_h_gate_v_out(c_e_h_3, c_g, s5) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | node4(c_e_h_3, c_g, s4)), inference(lemma,lemma(discharge,[]))).
% 290.04/182.57 tff(5923,plain,
% 290.04/182.57 (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)),
% 290.04/182.57 inference(unit_resolution,[status(thm)],[5922, 3360, 5904])).
% 290.04/182.57 tff(5924,plain,
% 290.04/182.57 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s4)),
% 290.04/182.57 inference(unit_resolution,[status(thm)],[3384, 5923])).
% 290.04/182.57 tff(5925,plain,
% 290.04/182.57 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s5)),
% 290.04/182.57 inference(unit_resolution,[status(thm)],[3365, 3360])).
% 290.04/182.57 tff(5926,plain,
% 290.04/182.57 (~node20(c_e_h_3, c_k, s5)),
% 290.04/182.57 inference(unit_resolution,[status(thm)],[5458, 5925])).
% 290.04/182.57 tff(5927,plain,
% 290.04/182.57 (node20(c_e_h_3, c_k, s4)),
% 290.04/182.57 inference(unit_resolution,[status(thm)],[5450, 5926, 3367])).
% 290.04/182.57 tff(5928,plain,
% 290.04/182.57 ($false),
% 290.04/182.57 inference(unit_resolution,[status(thm)],[3392, 5927, 5924])).
% 290.04/182.57 tff(5929,plain,(m_or_h_gate_v_out(c_e_h_3, c_g, s5) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s8))), inference(lemma,lemma(discharge,[]))).
% 290.04/182.57 tff(5930,plain,
% 290.04/182.57 (m_or_h_gate_v_out(c_e_h_3, c_g, s5)),
% 290.04/182.57 inference(unit_resolution,[status(thm)],[5929, 3367])).
% 290.04/182.57 tff(5931,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_c, s5)), introduced(assumption)).
% 290.04/182.57 tff(5932,assumption,(m_and_h_gate_v_out(c_e_h_3, c_q, s4)), introduced(assumption)).
% 290.04/182.57 tff(5933,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3)), introduced(assumption)).
% 290.04/182.57 tff(5934,assumption,(node11(c_e_h_3, c_n, s2, s3)), introduced(assumption)).
% 290.04/182.57 tff(5935,plain,
% 290.04/182.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3)) | (~node11(c_e_h_3, c_n, s2, s3)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3)) | (~node11(c_e_h_3, c_n, s2, s3)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s2))),
% 290.04/182.57 inference(rewrite,[status(thm)],[])).
% 290.04/182.57 tff(5936,plain,
% 290.04/182.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3)) | (~node11(c_e_h_3, c_n, s2, s3)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s2))),
% 290.04/182.57 inference(quant_inst,[status(thm)],[])).
% 290.04/182.57 tff(5937,plain,
% 290.04/182.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3)) | (~node11(c_e_h_3, c_n, s2, s3)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s2)),
% 290.04/182.57 inference(modus_ponens,[status(thm)],[5936, 5935])).
% 290.04/182.57 tff(5938,plain,
% 290.04/182.57 ($false),
% 290.04/182.57 inference(unit_resolution,[status(thm)],[5937, 5017, 5933, 5776, 5934])).
% 290.04/182.57 tff(5939,plain,((~node11(c_e_h_3, c_n, s2, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3))), inference(lemma,lemma(discharge,[]))).
% 290.04/182.57 tff(5940,plain,
% 290.04/182.57 (~node11(c_e_h_3, c_n, s2, s3)),
% 290.04/182.57 inference(unit_resolution,[status(thm)],[5939, 5933])).
% 290.04/182.57 tff(5941,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2)), introduced(assumption)).
% 290.04/182.57 tff(5942,plain,
% 290.04/182.57 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s1) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s1) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1))),
% 290.04/182.58 inference(rewrite,[status(thm)],[])).
% 290.04/182.58 tff(5943,plain,
% 290.04/182.58 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s1) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1))),
% 290.04/182.58 inference(quant_inst,[status(thm)],[])).
% 290.04/182.58 tff(5944,plain,
% 290.04/182.58 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s1) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1)),
% 290.04/182.58 inference(modus_ponens,[status(thm)],[5943, 5942])).
% 290.04/182.58 tff(5945,plain,
% 290.04/182.58 (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s1) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s1)),
% 290.04/182.58 inference(unit_resolution,[status(thm)],[5944, 5704])).
% 290.04/182.58 tff(5946,plain,
% 290.04/182.58 (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s1)),
% 290.04/182.58 inference(unit_resolution,[status(thm)],[5945, 5614])).
% 290.04/182.58 tff(5947,assumption,(~m_c_h_element_v_out(c_e_h_3, c_f, s0)), introduced(assumption)).
% 290.04/182.58 tff(5948,plain,
% 290.04/182.58 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s0)),
% 290.04/182.58 inference(unit_resolution,[status(thm)],[5693, 5947])).
% 290.04/182.58 tff(5949,plain,
% 290.04/182.58 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1)),
% 290.04/182.58 inference(unit_resolution,[status(thm)],[5750, 5948])).
% 290.04/182.58 tff(5950,assumption,(node11(c_e_h_3, c_m, s1, s2)), introduced(assumption)).
% 290.04/182.58 tff(5951,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1)), introduced(assumption)).
% 290.04/182.58 tff(5952,plain,
% 290.04/182.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2) | (~node11(c_e_h_3, c_m, s1, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2) | (~node11(c_e_h_3, c_m, s1, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1)))),
% 290.04/182.58 inference(rewrite,[status(thm)],[])).
% 290.04/182.58 tff(5953,plain,
% 290.04/182.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2) | (~node11(c_e_h_3, c_m, s1, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1)))),
% 290.04/182.58 inference(quant_inst,[status(thm)],[])).
% 290.04/182.58 tff(5954,plain,
% 290.04/182.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2) | (~node11(c_e_h_3, c_m, s1, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1))),
% 290.04/182.58 inference(modus_ponens,[status(thm)],[5953, 5952])).
% 290.04/182.58 tff(5955,plain,
% 290.04/182.58 ($false),
% 290.04/182.58 inference(unit_resolution,[status(thm)],[5954, 5742, 5951, 5950, 5941])).
% 290.04/182.58 tff(5956,plain,((~node11(c_e_h_3, c_m, s1, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s1)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2)), inference(lemma,lemma(discharge,[]))).
% 290.04/182.58 tff(5957,plain,
% 290.04/182.58 (~node11(c_e_h_3, c_m, s1, s2)),
% 290.04/182.58 inference(unit_resolution,[status(thm)],[5956, 5949, 5941])).
% 290.04/182.58 tff(5958,plain,
% 290.04/182.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s1, s2)) | node10(c_e_h_3, c_m, s1, s2) | node11(c_e_h_3, c_m, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s1, s2)) | node10(c_e_h_3, c_m, s1, s2) | node11(c_e_h_3, c_m, s1, s2))),
% 290.04/182.58 inference(rewrite,[status(thm)],[])).
% 290.04/182.58 tff(5959,plain,
% 290.04/182.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s1, s2)) | node10(c_e_h_3, c_m, s1, s2) | node11(c_e_h_3, c_m, s1, s2))),
% 290.04/182.58 inference(quant_inst,[status(thm)],[])).
% 290.04/182.58 tff(5960,plain,
% 290.04/182.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s1, s2)) | node10(c_e_h_3, c_m, s1, s2) | node11(c_e_h_3, c_m, s1, s2)),
% 290.04/182.58 inference(modus_ponens,[status(thm)],[5959, 5958])).
% 290.04/182.58 tff(5961,plain,
% 290.04/182.58 (node10(c_e_h_3, c_m, s1, s2) | node11(c_e_h_3, c_m, s1, s2)),
% 290.04/182.58 inference(unit_resolution,[status(thm)],[5960, 5002, 255])).
% 290.04/182.58 tff(5962,plain,
% 290.04/182.58 (node10(c_e_h_3, c_m, s1, s2)),
% 290.04/182.58 inference(unit_resolution,[status(thm)],[5961, 5957])).
% 290.04/182.58 tff(5963,assumption,(node18(c_e_h_3, c_f, s0, s1)), introduced(assumption)).
% 290.04/182.58 tff(5964,plain,
% 290.04/182.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_f, s0) | (~m_c_h_element_v_out(c_e_h_3, c_f, s1)) | (~node18(c_e_h_3, c_f, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s0) | (~m_c_h_element_v_out(c_e_h_3, c_f, s1)) | (~node18(c_e_h_3, c_f, s0, s1)))),
% 290.04/182.58 inference(rewrite,[status(thm)],[])).
% 290.04/182.58 tff(5965,plain,
% 290.04/182.58 (((~m_c_h_element_v_out(c_e_h_3, c_f, s1)) | m_c_h_element_v_out(c_e_h_3, c_f, s0) | (~node18(c_e_h_3, c_f, s0, s1))) <=> (m_c_h_element_v_out(c_e_h_3, c_f, s0) | (~m_c_h_element_v_out(c_e_h_3, c_f, s1)) | (~node18(c_e_h_3, c_f, s0, s1)))),
% 290.04/182.58 inference(rewrite,[status(thm)],[])).
% 290.04/182.58 tff(5966,plain,
% 290.04/182.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s1)) | m_c_h_element_v_out(c_e_h_3, c_f, s0) | (~node18(c_e_h_3, c_f, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_f, s0) | (~m_c_h_element_v_out(c_e_h_3, c_f, s1)) | (~node18(c_e_h_3, c_f, s0, s1))))),
% 290.04/182.58 inference(monotonicity,[status(thm)],[5965])).
% 290.04/182.58 tff(5967,plain,
% 290.04/182.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s1)) | m_c_h_element_v_out(c_e_h_3, c_f, s0) | (~node18(c_e_h_3, c_f, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s0) | (~m_c_h_element_v_out(c_e_h_3, c_f, s1)) | (~node18(c_e_h_3, c_f, s0, s1)))),
% 290.04/182.58 inference(transitivity,[status(thm)],[5966, 5964])).
% 290.04/182.58 tff(5968,plain,
% 290.04/182.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s1)) | m_c_h_element_v_out(c_e_h_3, c_f, s0) | (~node18(c_e_h_3, c_f, s0, s1)))),
% 290.04/182.58 inference(quant_inst,[status(thm)],[])).
% 290.04/182.58 tff(5969,plain,
% 290.04/182.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s0) | (~m_c_h_element_v_out(c_e_h_3, c_f, s1)) | (~node18(c_e_h_3, c_f, s0, s1))),
% 290.04/182.58 inference(modus_ponens,[status(thm)],[5968, 5967])).
% 290.04/182.58 tff(5970,plain,
% 290.04/182.58 (m_c_h_element_v_out(c_e_h_3, c_f, s0) | (~m_c_h_element_v_out(c_e_h_3, c_f, s1))),
% 290.04/182.58 inference(unit_resolution,[status(thm)],[5969, 753, 5963])).
% 290.04/182.58 tff(5971,plain,
% 290.04/182.58 (~m_c_h_element_v_out(c_e_h_3, c_f, s1)),
% 290.04/182.58 inference(unit_resolution,[status(thm)],[5970, 5947])).
% 290.04/182.58 tff(5972,plain,
% 290.04/182.58 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s1) | m_c_h_element_v_out(c_e_h_3, c_f, s1))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s1) | m_c_h_element_v_out(c_e_h_3, c_f, s1))),
% 290.04/182.58 inference(rewrite,[status(thm)],[])).
% 290.04/182.58 tff(5973,plain,
% 290.04/182.58 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s1) | m_c_h_element_v_out(c_e_h_3, c_f, s1))),
% 290.04/182.58 inference(quant_inst,[status(thm)],[])).
% 290.04/182.58 tff(5974,plain,
% 290.04/182.58 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s1) | m_c_h_element_v_out(c_e_h_3, c_f, s1)),
% 290.04/182.58 inference(modus_ponens,[status(thm)],[5973, 5972])).
% 290.04/182.58 tff(5975,plain,
% 290.04/182.58 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s1) | m_c_h_element_v_out(c_e_h_3, c_f, s1)),
% 290.04/182.58 inference(unit_resolution,[status(thm)],[5974, 5689])).
% 290.04/182.58 tff(5976,plain,
% 290.04/182.58 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s1)),
% 290.04/182.58 inference(unit_resolution,[status(thm)],[5975, 5971])).
% 290.04/182.58 tff(5977,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s1)), introduced(assumption)).
% 290.04/182.58 tff(5978,plain,
% 290.04/182.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s1)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s1)) | (~node10(c_e_h_3, c_m, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s1)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s1)) | (~node10(c_e_h_3, c_m, s1, s2)))),
% 290.04/182.58 inference(rewrite,[status(thm)],[])).
% 290.04/182.58 tff(5979,plain,
% 290.04/182.58 (((~node10(c_e_h_3, c_m, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s1)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s1)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2)) <=> ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s1)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s1)) | (~node10(c_e_h_3, c_m, s1, s2)))),
% 290.04/182.58 inference(rewrite,[status(thm)],[])).
% 290.04/182.58 tff(5980,plain,
% 290.04/182.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s1)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s1)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s1)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s1)) | (~node10(c_e_h_3, c_m, s1, s2))))),
% 290.04/182.58 inference(monotonicity,[status(thm)],[5979])).
% 290.04/182.58 tff(5981,plain,
% 290.04/182.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s1)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s1)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s1)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s1)) | (~node10(c_e_h_3, c_m, s1, s2)))),
% 290.04/182.58 inference(transitivity,[status(thm)],[5980, 5978])).
% 290.04/182.58 tff(5982,plain,
% 290.04/182.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s1)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s1)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2))),
% 290.04/182.58 inference(quant_inst,[status(thm)],[])).
% 290.04/182.58 tff(5983,plain,
% 290.04/182.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s1)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s1)) | (~node10(c_e_h_3, c_m, s1, s2))),
% 290.12/182.59 inference(modus_ponens,[status(thm)],[5982, 5981])).
% 290.12/182.59 tff(5984,plain,
% 290.12/182.59 ($false),
% 290.12/182.59 inference(unit_resolution,[status(thm)],[5983, 5718, 5977, 5976, 5962, 5941])).
% 290.12/182.59 tff(5985,plain,(m_c_h_element_v_out(c_e_h_3, c_f, s0) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s1)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2) | (~node18(c_e_h_3, c_f, s0, s1))), inference(lemma,lemma(discharge,[]))).
% 290.12/182.59 tff(5986,plain,
% 290.12/182.59 ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s1)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2) | (~node18(c_e_h_3, c_f, s0, s1))),
% 290.12/182.59 inference(unit_resolution,[status(thm)],[5985, 5682])).
% 290.12/182.59 tff(5987,plain,
% 290.12/182.59 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2) | (~node18(c_e_h_3, c_f, s0, s1))),
% 290.12/182.59 inference(unit_resolution,[status(thm)],[5986, 5946])).
% 290.12/182.59 tff(5988,plain,
% 290.12/182.59 (~node18(c_e_h_3, c_f, s0, s1)),
% 290.12/182.59 inference(unit_resolution,[status(thm)],[5987, 5941])).
% 290.12/182.59 tff(5989,plain,
% 290.12/182.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s0, s1)) | node19(c_e_h_3, c_f, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s0, s1)) | node19(c_e_h_3, c_f, s0, s1))),
% 290.12/182.59 inference(rewrite,[status(thm)],[])).
% 290.12/182.59 tff(5990,plain,
% 290.12/182.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s0, s1)) | node19(c_e_h_3, c_f, s0, s1))),
% 290.12/182.59 inference(quant_inst,[status(thm)],[])).
% 290.12/182.59 tff(5991,plain,
% 290.12/182.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s0, s1)) | node19(c_e_h_3, c_f, s0, s1)),
% 290.12/182.59 inference(modus_ponens,[status(thm)],[5990, 5989])).
% 290.12/182.59 tff(5992,plain,
% 290.12/182.59 (node19(c_e_h_3, c_f, s0, s1)),
% 290.12/182.59 inference(unit_resolution,[status(thm)],[5991, 190, 72])).
% 290.12/182.59 tff(5993,plain,
% 290.12/182.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_f, s0, s1)) | node18(c_e_h_3, c_f, s0, s1) | node17(c_e_h_3, c_f, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s0, s1)) | node18(c_e_h_3, c_f, s0, s1) | node17(c_e_h_3, c_f, s0))),
% 290.12/182.59 inference(rewrite,[status(thm)],[])).
% 290.12/182.59 tff(5994,plain,
% 290.12/182.59 ((node17(c_e_h_3, c_f, s0) | node18(c_e_h_3, c_f, s0, s1) | (~node19(c_e_h_3, c_f, s0, s1))) <=> ((~node19(c_e_h_3, c_f, s0, s1)) | node18(c_e_h_3, c_f, s0, s1) | node17(c_e_h_3, c_f, s0))),
% 290.12/182.59 inference(rewrite,[status(thm)],[])).
% 290.12/182.59 tff(5995,plain,
% 290.12/182.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s0) | node18(c_e_h_3, c_f, s0, s1) | (~node19(c_e_h_3, c_f, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_f, s0, s1)) | node18(c_e_h_3, c_f, s0, s1) | node17(c_e_h_3, c_f, s0)))),
% 290.12/182.59 inference(monotonicity,[status(thm)],[5994])).
% 290.12/182.59 tff(5996,plain,
% 290.12/182.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s0) | node18(c_e_h_3, c_f, s0, s1) | (~node19(c_e_h_3, c_f, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s0, s1)) | node18(c_e_h_3, c_f, s0, s1) | node17(c_e_h_3, c_f, s0))),
% 290.12/182.59 inference(transitivity,[status(thm)],[5995, 5993])).
% 290.12/182.59 tff(5997,plain,
% 290.12/182.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s0) | node18(c_e_h_3, c_f, s0, s1) | (~node19(c_e_h_3, c_f, s0, s1)))),
% 290.12/182.59 inference(quant_inst,[status(thm)],[])).
% 290.12/182.59 tff(5998,plain,
% 290.12/182.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s0, s1)) | node18(c_e_h_3, c_f, s0, s1) | node17(c_e_h_3, c_f, s0)),
% 290.12/182.59 inference(modus_ponens,[status(thm)],[5997, 5996])).
% 290.12/182.59 tff(5999,plain,
% 290.12/182.59 (node18(c_e_h_3, c_f, s0, s1) | node17(c_e_h_3, c_f, s0)),
% 290.12/182.59 inference(unit_resolution,[status(thm)],[5998, 776, 5992])).
% 290.12/182.59 tff(6000,plain,
% 290.12/182.59 (node17(c_e_h_3, c_f, s0)),
% 290.12/182.59 inference(unit_resolution,[status(thm)],[5999, 5988])).
% 290.12/182.59 tff(6001,plain,
% 290.12/182.59 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s0)) | m_and_h_gate_v_out(c_e_h_3, c_i, s0))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s0)) | m_and_h_gate_v_out(c_e_h_3, c_i, s0))),
% 290.12/182.59 inference(rewrite,[status(thm)],[])).
% 290.12/182.59 tff(6002,plain,
% 290.12/182.59 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s0)) | m_and_h_gate_v_out(c_e_h_3, c_i, s0))),
% 290.12/182.59 inference(quant_inst,[status(thm)],[])).
% 290.12/182.59 tff(6003,plain,
% 290.12/182.59 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s0)) | m_and_h_gate_v_out(c_e_h_3, c_i, s0)),
% 290.12/182.59 inference(modus_ponens,[status(thm)],[6002, 6001])).
% 290.12/182.59 tff(6004,plain,
% 290.12/182.59 (~m_c_h_element_v_in2(c_e_h_3, c_f, s0)),
% 290.12/182.59 inference(unit_resolution,[status(thm)],[6003, 2143, 157])).
% 290.12/182.59 tff(6005,plain,
% 290.12/182.59 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s0)) | (~node17(c_e_h_3, c_f, s0)) | m_c_h_element_v_in2(c_e_h_3, c_f, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s0)) | (~node17(c_e_h_3, c_f, s0)) | m_c_h_element_v_in2(c_e_h_3, c_f, s0))),
% 290.12/182.59 inference(rewrite,[status(thm)],[])).
% 290.12/182.59 tff(6006,plain,
% 290.12/182.59 (((~m_c_h_element_v_in1(c_e_h_3, c_f, s0)) | m_c_h_element_v_in2(c_e_h_3, c_f, s0) | (~node17(c_e_h_3, c_f, s0))) <=> ((~m_c_h_element_v_in1(c_e_h_3, c_f, s0)) | (~node17(c_e_h_3, c_f, s0)) | m_c_h_element_v_in2(c_e_h_3, c_f, s0))),
% 290.12/182.59 inference(rewrite,[status(thm)],[])).
% 290.12/182.59 tff(6007,plain,
% 290.12/182.59 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s0)) | m_c_h_element_v_in2(c_e_h_3, c_f, s0) | (~node17(c_e_h_3, c_f, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s0)) | (~node17(c_e_h_3, c_f, s0)) | m_c_h_element_v_in2(c_e_h_3, c_f, s0)))),
% 290.12/182.59 inference(monotonicity,[status(thm)],[6006])).
% 290.12/182.59 tff(6008,plain,
% 290.12/182.59 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s0)) | m_c_h_element_v_in2(c_e_h_3, c_f, s0) | (~node17(c_e_h_3, c_f, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s0)) | (~node17(c_e_h_3, c_f, s0)) | m_c_h_element_v_in2(c_e_h_3, c_f, s0))),
% 290.12/182.59 inference(transitivity,[status(thm)],[6007, 6005])).
% 290.12/182.59 tff(6009,plain,
% 290.12/182.59 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s0)) | m_c_h_element_v_in2(c_e_h_3, c_f, s0) | (~node17(c_e_h_3, c_f, s0)))),
% 290.12/182.59 inference(quant_inst,[status(thm)],[])).
% 290.12/182.59 tff(6010,plain,
% 290.12/182.59 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s0)) | (~node17(c_e_h_3, c_f, s0)) | m_c_h_element_v_in2(c_e_h_3, c_f, s0)),
% 290.12/182.59 inference(modus_ponens,[status(thm)],[6009, 6008])).
% 290.12/182.59 tff(6011,plain,
% 290.12/182.59 ((~m_c_h_element_v_in1(c_e_h_3, c_f, s0)) | (~node17(c_e_h_3, c_f, s0))),
% 290.12/182.59 inference(unit_resolution,[status(thm)],[6010, 919, 6004])).
% 290.12/182.59 tff(6012,plain,
% 290.12/182.59 (~m_c_h_element_v_in1(c_e_h_3, c_f, s0)),
% 290.12/182.59 inference(unit_resolution,[status(thm)],[6011, 6000])).
% 290.12/182.59 tff(6013,plain,
% 290.12/182.59 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s0)) | m_c_h_element_v_in1(c_e_h_3, c_f, s0) | m_c_h_element_v_in2(c_e_h_3, c_f, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s0)) | m_c_h_element_v_in1(c_e_h_3, c_f, s0) | m_c_h_element_v_in2(c_e_h_3, c_f, s0))),
% 290.12/182.59 inference(rewrite,[status(thm)],[])).
% 290.12/182.59 tff(6014,plain,
% 290.12/182.59 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s0)) | m_c_h_element_v_in1(c_e_h_3, c_f, s0) | m_c_h_element_v_in2(c_e_h_3, c_f, s0))),
% 290.12/182.59 inference(quant_inst,[status(thm)],[])).
% 290.12/182.59 tff(6015,plain,
% 290.12/182.59 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s0)) | m_c_h_element_v_in1(c_e_h_3, c_f, s0) | m_c_h_element_v_in2(c_e_h_3, c_f, s0)),
% 290.12/182.59 inference(modus_ponens,[status(thm)],[6014, 6013])).
% 290.12/182.59 tff(6016,plain,
% 290.12/182.59 ((~node16(c_e_h_3, c_f, s0)) | m_c_h_element_v_in1(c_e_h_3, c_f, s0)),
% 290.12/182.59 inference(unit_resolution,[status(thm)],[6015, 178, 6004])).
% 290.12/182.59 tff(6017,plain,
% 290.12/182.59 (~node16(c_e_h_3, c_f, s0)),
% 290.12/182.59 inference(unit_resolution,[status(thm)],[6016, 6012])).
% 290.12/182.59 tff(6018,plain,
% 290.12/182.59 ((~node11(c_e_h_3, c_m, s1, s2)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2)),
% 290.12/182.59 inference(unit_resolution,[status(thm)],[5956, 5751])).
% 290.12/182.59 tff(6019,plain,
% 290.12/182.59 (~node11(c_e_h_3, c_m, s1, s2)),
% 290.12/182.59 inference(unit_resolution,[status(thm)],[6018, 5941])).
% 290.12/182.59 tff(6020,plain,
% 290.12/182.59 (node10(c_e_h_3, c_m, s1, s2)),
% 290.12/182.59 inference(unit_resolution,[status(thm)],[5961, 6019])).
% 290.12/182.59 tff(6021,plain,
% 290.12/182.59 (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s1)),
% 290.12/182.59 inference(unit_resolution,[status(thm)],[5983, 5718, 5946, 6020, 5941])).
% 290.12/182.59 tff(6022,plain,
% 290.12/182.59 (m_c_h_element_v_out(c_e_h_3, c_f, s1)),
% 290.12/182.59 inference(unit_resolution,[status(thm)],[5975, 6021])).
% 290.12/182.59 tff(6023,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_f, s0)), introduced(assumption)).
% 290.12/182.59 tff(6024,assumption,(node14(c_e_h_3, c_f, s0, s1)), introduced(assumption)).
% 290.12/182.59 tff(6025,assumption,(m_c_h_element_v_out(c_e_h_3, c_f, s1)), introduced(assumption)).
% 290.12/182.59 tff(6026,plain,
% 290.12/182.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s1)) | (~node14(c_e_h_3, c_f, s0, s1)) | m_c_h_element_v_in1(c_e_h_3, c_f, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s1)) | (~node14(c_e_h_3, c_f, s0, s1)) | m_c_h_element_v_in1(c_e_h_3, c_f, s0))),
% 290.12/182.59 inference(rewrite,[status(thm)],[])).
% 290.12/182.59 tff(6027,plain,
% 290.12/182.59 (((~node14(c_e_h_3, c_f, s0, s1)) | m_c_h_element_v_in1(c_e_h_3, c_f, s0) | (~m_c_h_element_v_out(c_e_h_3, c_f, s1))) <=> ((~m_c_h_element_v_out(c_e_h_3, c_f, s1)) | (~node14(c_e_h_3, c_f, s0, s1)) | m_c_h_element_v_in1(c_e_h_3, c_f, s0))),
% 290.12/182.59 inference(rewrite,[status(thm)],[])).
% 290.12/182.59 tff(6028,plain,
% 290.12/182.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s0, s1)) | m_c_h_element_v_in1(c_e_h_3, c_f, s0) | (~m_c_h_element_v_out(c_e_h_3, c_f, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s1)) | (~node14(c_e_h_3, c_f, s0, s1)) | m_c_h_element_v_in1(c_e_h_3, c_f, s0)))),
% 290.12/182.59 inference(monotonicity,[status(thm)],[6027])).
% 290.12/182.59 tff(6029,plain,
% 290.12/182.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s0, s1)) | m_c_h_element_v_in1(c_e_h_3, c_f, s0) | (~m_c_h_element_v_out(c_e_h_3, c_f, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s1)) | (~node14(c_e_h_3, c_f, s0, s1)) | m_c_h_element_v_in1(c_e_h_3, c_f, s0))),
% 290.12/182.60 inference(transitivity,[status(thm)],[6028, 6026])).
% 290.12/182.60 tff(6030,plain,
% 290.12/182.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s0, s1)) | m_c_h_element_v_in1(c_e_h_3, c_f, s0) | (~m_c_h_element_v_out(c_e_h_3, c_f, s1)))),
% 290.12/182.60 inference(quant_inst,[status(thm)],[])).
% 290.12/182.60 tff(6031,plain,
% 290.12/182.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s1)) | (~node14(c_e_h_3, c_f, s0, s1)) | m_c_h_element_v_in1(c_e_h_3, c_f, s0)),
% 290.12/182.60 inference(modus_ponens,[status(thm)],[6030, 6029])).
% 290.12/182.60 tff(6032,plain,
% 290.12/182.60 ($false),
% 290.12/182.60 inference(unit_resolution,[status(thm)],[6031, 223, 6025, 6024, 6023])).
% 290.12/182.60 tff(6033,plain,((~node14(c_e_h_3, c_f, s0, s1)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s1)) | m_c_h_element_v_in1(c_e_h_3, c_f, s0)), inference(lemma,lemma(discharge,[]))).
% 290.12/182.60 tff(6034,plain,
% 290.12/182.60 (~node14(c_e_h_3, c_f, s0, s1)),
% 290.12/182.60 inference(unit_resolution,[status(thm)],[6033, 6022, 6012])).
% 290.12/182.60 tff(6035,plain,
% 290.12/182.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s0) | (~node19(c_e_h_3, c_f, s0, s1)) | node14(c_e_h_3, c_f, s0, s1) | node15(c_e_h_3, c_f, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_f, s0) | (~node19(c_e_h_3, c_f, s0, s1)) | node14(c_e_h_3, c_f, s0, s1) | node15(c_e_h_3, c_f, s0, s1))),
% 290.12/182.60 inference(rewrite,[status(thm)],[])).
% 290.12/182.60 tff(6036,plain,
% 290.12/182.60 ((node16(c_e_h_3, c_f, s0) | node14(c_e_h_3, c_f, s0, s1) | node15(c_e_h_3, c_f, s0, s1) | (~node19(c_e_h_3, c_f, s0, s1))) <=> (node16(c_e_h_3, c_f, s0) | (~node19(c_e_h_3, c_f, s0, s1)) | node14(c_e_h_3, c_f, s0, s1) | node15(c_e_h_3, c_f, s0, s1))),
% 290.12/182.60 inference(rewrite,[status(thm)],[])).
% 290.12/182.60 tff(6037,plain,
% 290.12/182.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s0) | node14(c_e_h_3, c_f, s0, s1) | node15(c_e_h_3, c_f, s0, s1) | (~node19(c_e_h_3, c_f, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s0) | (~node19(c_e_h_3, c_f, s0, s1)) | node14(c_e_h_3, c_f, s0, s1) | node15(c_e_h_3, c_f, s0, s1)))),
% 290.12/182.60 inference(monotonicity,[status(thm)],[6036])).
% 290.12/182.60 tff(6038,plain,
% 290.12/182.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s0) | node14(c_e_h_3, c_f, s0, s1) | node15(c_e_h_3, c_f, s0, s1) | (~node19(c_e_h_3, c_f, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_f, s0) | (~node19(c_e_h_3, c_f, s0, s1)) | node14(c_e_h_3, c_f, s0, s1) | node15(c_e_h_3, c_f, s0, s1))),
% 290.12/182.60 inference(transitivity,[status(thm)],[6037, 6035])).
% 290.12/182.60 tff(6039,plain,
% 290.12/182.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s0) | node14(c_e_h_3, c_f, s0, s1) | node15(c_e_h_3, c_f, s0, s1) | (~node19(c_e_h_3, c_f, s0, s1)))),
% 290.12/182.60 inference(quant_inst,[status(thm)],[])).
% 290.12/182.60 tff(6040,plain,
% 290.12/182.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_f, s0) | (~node19(c_e_h_3, c_f, s0, s1)) | node14(c_e_h_3, c_f, s0, s1) | node15(c_e_h_3, c_f, s0, s1)),
% 290.12/182.60 inference(modus_ponens,[status(thm)],[6039, 6038])).
% 290.12/182.60 tff(6041,plain,
% 290.12/182.60 (node16(c_e_h_3, c_f, s0) | node14(c_e_h_3, c_f, s0, s1) | node15(c_e_h_3, c_f, s0, s1)),
% 290.12/182.60 inference(unit_resolution,[status(thm)],[6040, 204, 5992])).
% 290.12/182.60 tff(6042,plain,
% 290.12/182.60 (node15(c_e_h_3, c_f, s0, s1)),
% 290.12/182.60 inference(unit_resolution,[status(thm)],[6041, 6034, 6017])).
% 290.12/182.60 tff(6043,plain,
% 290.12/182.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s1)) | (~node15(c_e_h_3, c_f, s0, s1)) | m_c_h_element_v_out(c_e_h_3, c_f, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s1)) | (~node15(c_e_h_3, c_f, s0, s1)) | m_c_h_element_v_out(c_e_h_3, c_f, s0))),
% 290.12/182.60 inference(rewrite,[status(thm)],[])).
% 290.12/182.60 tff(6044,plain,
% 290.12/182.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s1)) | (~node15(c_e_h_3, c_f, s0, s1)) | m_c_h_element_v_out(c_e_h_3, c_f, s0))),
% 290.12/182.60 inference(quant_inst,[status(thm)],[])).
% 290.12/182.60 tff(6045,plain,
% 290.12/182.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s1)) | (~node15(c_e_h_3, c_f, s0, s1)) | m_c_h_element_v_out(c_e_h_3, c_f, s0)),
% 290.12/182.60 inference(modus_ponens,[status(thm)],[6044, 6043])).
% 290.12/182.60 tff(6046,plain,
% 290.12/182.60 ($false),
% 290.12/182.60 inference(unit_resolution,[status(thm)],[6045, 147, 5682, 6022, 6042])).
% 290.12/182.60 tff(6047,plain,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2)), inference(lemma,lemma(discharge,[]))).
% 290.12/182.60 tff(6048,plain,
% 290.12/182.60 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2)))),
% 290.12/182.60 inference(rewrite,[status(thm)],[])).
% 290.12/182.60 tff(6049,plain,
% 290.12/182.60 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2)))),
% 290.12/182.60 inference(quant_inst,[status(thm)],[])).
% 290.12/182.60 tff(6050,plain,
% 290.12/182.60 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2))),
% 290.12/182.60 inference(modus_ponens,[status(thm)],[6049, 6048])).
% 290.12/182.60 tff(6051,plain,
% 290.12/182.60 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s2)),
% 290.12/182.60 inference(unit_resolution,[status(thm)],[6050, 5601, 6047])).
% 290.12/182.60 tff(6052,plain,
% 290.12/182.60 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s2)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s2)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s2))),
% 290.12/182.60 inference(rewrite,[status(thm)],[])).
% 290.12/182.60 tff(6053,plain,
% 290.12/182.60 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s2)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s2))),
% 290.12/182.60 inference(quant_inst,[status(thm)],[])).
% 290.12/182.60 tff(6054,plain,
% 290.12/182.60 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s2)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s2)),
% 290.12/182.60 inference(modus_ponens,[status(thm)],[6053, 6052])).
% 290.12/182.60 tff(6055,plain,
% 290.12/182.60 (~node9(c_e_h_3, c_n, s2)),
% 290.12/182.60 inference(unit_resolution,[status(thm)],[6054, 4972, 6051])).
% 290.12/182.60 tff(6056,assumption,(~node9(c_e_h_3, c_n, s2)), introduced(assumption)).
% 290.12/182.60 tff(6057,assumption,(node10(c_e_h_3, c_n, s2, s3)), introduced(assumption)).
% 290.12/182.61 tff(6058,plain,
% 290.12/182.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3)) | node9(c_e_h_3, c_n, s2) | (~node10(c_e_h_3, c_n, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3)) | node9(c_e_h_3, c_n, s2) | (~node10(c_e_h_3, c_n, s2, s3)))),
% 290.12/182.61 inference(rewrite,[status(thm)],[])).
% 290.12/182.61 tff(6059,plain,
% 290.12/182.61 ((node9(c_e_h_3, c_n, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3)) | (~node10(c_e_h_3, c_n, s2, s3))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3)) | node9(c_e_h_3, c_n, s2) | (~node10(c_e_h_3, c_n, s2, s3)))),
% 290.12/182.61 inference(rewrite,[status(thm)],[])).
% 290.12/182.61 tff(6060,plain,
% 290.12/182.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3)) | (~node10(c_e_h_3, c_n, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3)) | node9(c_e_h_3, c_n, s2) | (~node10(c_e_h_3, c_n, s2, s3))))),
% 290.12/182.61 inference(monotonicity,[status(thm)],[6059])).
% 290.12/182.61 tff(6061,plain,
% 290.12/182.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3)) | (~node10(c_e_h_3, c_n, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3)) | node9(c_e_h_3, c_n, s2) | (~node10(c_e_h_3, c_n, s2, s3)))),
% 290.12/182.61 inference(transitivity,[status(thm)],[6060, 6058])).
% 290.12/182.61 tff(6062,plain,
% 290.12/182.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3)) | (~node10(c_e_h_3, c_n, s2, s3)))),
% 290.12/182.61 inference(quant_inst,[status(thm)],[])).
% 290.12/182.61 tff(6063,plain,
% 290.12/182.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3)) | node9(c_e_h_3, c_n, s2) | (~node10(c_e_h_3, c_n, s2, s3))),
% 290.12/182.61 inference(modus_ponens,[status(thm)],[6062, 6061])).
% 290.12/182.61 tff(6064,plain,
% 290.12/182.61 ($false),
% 290.12/182.61 inference(unit_resolution,[status(thm)],[6063, 4986, 5933, 6057, 6056])).
% 290.12/182.61 tff(6065,plain,((~node10(c_e_h_3, c_n, s2, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3)) | node9(c_e_h_3, c_n, s2)), inference(lemma,lemma(discharge,[]))).
% 290.12/182.61 tff(6066,plain,
% 290.12/182.61 ((~node10(c_e_h_3, c_n, s2, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3))),
% 290.12/182.61 inference(unit_resolution,[status(thm)],[6065, 6055])).
% 290.12/182.61 tff(6067,plain,
% 290.12/182.61 (~node10(c_e_h_3, c_n, s2, s3)),
% 290.12/182.61 inference(unit_resolution,[status(thm)],[6066, 5933])).
% 290.12/182.61 tff(6068,plain,
% 290.12/182.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s2, s3)) | node10(c_e_h_3, c_n, s2, s3) | node11(c_e_h_3, c_n, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s2, s3)) | node10(c_e_h_3, c_n, s2, s3) | node11(c_e_h_3, c_n, s2, s3))),
% 290.12/182.61 inference(rewrite,[status(thm)],[])).
% 290.12/182.61 tff(6069,plain,
% 290.12/182.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s2, s3)) | node10(c_e_h_3, c_n, s2, s3) | node11(c_e_h_3, c_n, s2, s3))),
% 290.12/182.61 inference(quant_inst,[status(thm)],[])).
% 290.12/182.61 tff(6070,plain,
% 290.12/182.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s2, s3)) | node10(c_e_h_3, c_n, s2, s3) | node11(c_e_h_3, c_n, s2, s3)),
% 290.12/182.61 inference(modus_ponens,[status(thm)],[6069, 6068])).
% 290.12/182.61 tff(6071,plain,
% 290.12/182.61 (node10(c_e_h_3, c_n, s2, s3) | node11(c_e_h_3, c_n, s2, s3)),
% 290.12/182.61 inference(unit_resolution,[status(thm)],[6070, 5002, 318])).
% 290.12/182.61 tff(6072,plain,
% 290.12/182.61 ($false),
% 290.12/182.61 inference(unit_resolution,[status(thm)],[6071, 6067, 5940])).
% 290.12/182.61 tff(6073,plain,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3)), inference(lemma,lemma(discharge,[]))).
% 290.12/182.61 tff(6074,plain,
% 290.12/182.61 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s3)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s3)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3))),
% 290.12/182.61 inference(rewrite,[status(thm)],[])).
% 290.12/182.61 tff(6075,plain,
% 290.12/182.61 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s3)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3))),
% 290.12/182.61 inference(quant_inst,[status(thm)],[])).
% 290.12/182.61 tff(6076,plain,
% 290.12/182.61 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s3)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3)),
% 290.12/182.61 inference(modus_ponens,[status(thm)],[6075, 6074])).
% 290.12/182.61 tff(6077,plain,
% 290.12/182.61 (~m_and_h_gate_v_in2(c_e_h_3, c_q, s3)),
% 290.12/182.61 inference(unit_resolution,[status(thm)],[6076, 5621, 6073])).
% 290.12/182.61 tff(6078,plain,
% 290.12/182.61 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s3)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s3)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s3))),
% 290.12/182.61 inference(rewrite,[status(thm)],[])).
% 290.12/182.61 tff(6079,plain,
% 290.12/182.61 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s3)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s3))),
% 290.12/182.61 inference(quant_inst,[status(thm)],[])).
% 290.12/182.61 tff(6080,plain,
% 290.12/182.61 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s3)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s3)),
% 290.12/182.61 inference(modus_ponens,[status(thm)],[6079, 6078])).
% 290.12/182.61 tff(6081,plain,
% 290.12/182.61 (~node20(c_e_h_3, c_q, s3)),
% 290.12/182.61 inference(unit_resolution,[status(thm)],[6080, 4563, 6077])).
% 290.12/182.61 tff(6082,assumption,(node21(c_e_h_3, c_q, s3, s4)), introduced(assumption)).
% 290.12/182.61 tff(6083,plain,
% 290.12/182.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s4)) | (~node21(c_e_h_3, c_q, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_q, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s4)) | (~node21(c_e_h_3, c_q, s3, s4)))),
% 290.12/182.61 inference(rewrite,[status(thm)],[])).
% 290.12/182.61 tff(6084,plain,
% 290.12/182.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s4)) | (~node21(c_e_h_3, c_q, s3, s4)))),
% 290.12/182.61 inference(quant_inst,[status(thm)],[])).
% 290.12/182.61 tff(6085,plain,
% 290.12/182.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_q, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s4)) | (~node21(c_e_h_3, c_q, s3, s4))),
% 290.12/182.61 inference(modus_ponens,[status(thm)],[6084, 6083])).
% 290.12/182.61 tff(6086,plain,
% 290.12/182.61 ($false),
% 290.12/182.61 inference(unit_resolution,[status(thm)],[6085, 52, 5932, 6082, 6081])).
% 290.12/182.61 tff(6087,plain,((~node21(c_e_h_3, c_q, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s4))), inference(lemma,lemma(discharge,[]))).
% 290.12/182.61 tff(6088,plain,
% 290.12/182.61 (~node21(c_e_h_3, c_q, s3, s4)),
% 290.12/182.61 inference(unit_resolution,[status(thm)],[6087, 5932])).
% 290.12/182.61 tff(6089,assumption,(node22(c_e_h_3, c_q, s3, s4)), introduced(assumption)).
% 290.12/182.61 tff(6090,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_q, s3)), introduced(assumption)).
% 290.12/182.61 tff(6091,plain,
% 290.12/182.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s4)) | (~node22(c_e_h_3, c_q, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_q, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s4)) | (~node22(c_e_h_3, c_q, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_q, s3))),
% 290.12/182.61 inference(rewrite,[status(thm)],[])).
% 290.12/182.61 tff(6092,plain,
% 290.12/182.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s4)) | (~node22(c_e_h_3, c_q, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_q, s3))),
% 290.12/182.61 inference(quant_inst,[status(thm)],[])).
% 290.12/182.61 tff(6093,plain,
% 290.12/182.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s4)) | (~node22(c_e_h_3, c_q, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_q, s3)),
% 290.12/182.61 inference(modus_ponens,[status(thm)],[6092, 6091])).
% 290.12/182.61 tff(6094,plain,
% 290.12/182.61 ($false),
% 290.12/182.61 inference(unit_resolution,[status(thm)],[6093, 108, 6090, 5932, 6089])).
% 290.12/182.61 tff(6095,plain,((~node22(c_e_h_3, c_q, s3, s4)) | m_and_h_gate_v_out(c_e_h_3, c_q, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s4))), inference(lemma,lemma(discharge,[]))).
% 290.12/182.61 tff(6096,plain,
% 290.12/182.61 ((~node22(c_e_h_3, c_q, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s4))),
% 290.12/182.61 inference(unit_resolution,[status(thm)],[6095, 5805])).
% 290.12/182.61 tff(6097,plain,
% 290.12/182.61 (~node22(c_e_h_3, c_q, s3, s4)),
% 290.12/182.61 inference(unit_resolution,[status(thm)],[6096, 5932])).
% 290.12/182.61 tff(6098,plain,
% 290.12/182.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_3, c_q, s3, s4) | node22(c_e_h_3, c_q, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_3, c_q, s3, s4) | node22(c_e_h_3, c_q, s3, s4))),
% 290.12/182.61 inference(rewrite,[status(thm)],[])).
% 290.12/182.61 tff(6099,plain,
% 290.12/182.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_3, c_q, s3, s4) | node22(c_e_h_3, c_q, s3, s4))),
% 290.12/182.61 inference(quant_inst,[status(thm)],[])).
% 290.12/182.61 tff(6100,plain,
% 290.12/182.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_3, c_q, s3, s4) | node22(c_e_h_3, c_q, s3, s4)),
% 290.12/182.61 inference(modus_ponens,[status(thm)],[6099, 6098])).
% 290.12/182.61 tff(6101,plain,
% 290.12/182.61 (node21(c_e_h_3, c_q, s3, s4) | node22(c_e_h_3, c_q, s3, s4)),
% 290.12/182.61 inference(unit_resolution,[status(thm)],[6100, 82, 531])).
% 290.12/182.61 tff(6102,plain,
% 290.12/182.61 ($false),
% 290.12/182.61 inference(unit_resolution,[status(thm)],[6101, 6097, 6088])).
% 290.12/182.61 tff(6103,plain,(~m_and_h_gate_v_out(c_e_h_3, c_q, s4)), inference(lemma,lemma(discharge,[]))).
% 290.12/182.61 tff(6104,plain,
% 290.12/182.61 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s4))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s4))),
% 290.12/182.61 inference(rewrite,[status(thm)],[])).
% 290.12/182.61 tff(6105,plain,
% 290.12/182.61 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s4))),
% 290.12/182.61 inference(quant_inst,[status(thm)],[])).
% 290.12/182.61 tff(6106,plain,
% 290.12/182.61 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s4)),
% 290.12/182.61 inference(modus_ponens,[status(thm)],[6105, 6104])).
% 290.12/182.61 tff(6107,plain,
% 290.12/182.61 (node3(c_e_h_3, c_e_h_1, s4)),
% 290.12/182.61 inference(unit_resolution,[status(thm)],[6106, 2922, 1056])).
% 290.12/182.61 tff(6108,plain,
% 290.12/182.61 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s4)) | (~node3(c_e_h_3, c_e_h_1, s4)) | m_and_h_gate_v_out(c_e_h_3, c_q, s4))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s4)) | (~node3(c_e_h_3, c_e_h_1, s4)) | m_and_h_gate_v_out(c_e_h_3, c_q, s4))),
% 290.12/182.62 inference(rewrite,[status(thm)],[])).
% 290.12/182.62 tff(6109,plain,
% 290.12/182.62 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s4)) | (~node3(c_e_h_3, c_e_h_1, s4)) | m_and_h_gate_v_out(c_e_h_3, c_q, s4))),
% 290.12/182.62 inference(quant_inst,[status(thm)],[])).
% 290.12/182.62 tff(6110,plain,
% 290.12/182.62 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s4)) | (~node3(c_e_h_3, c_e_h_1, s4)) | m_and_h_gate_v_out(c_e_h_3, c_q, s4)),
% 290.12/182.62 inference(modus_ponens,[status(thm)],[6109, 6108])).
% 290.12/182.62 tff(6111,plain,
% 290.12/182.62 ((~m_cell_v_ack(c_e_h_1, s4)) | m_and_h_gate_v_out(c_e_h_3, c_q, s4)),
% 290.12/182.62 inference(unit_resolution,[status(thm)],[6110, 1073, 6107])).
% 290.12/182.62 tff(6112,plain,
% 290.12/182.62 (~m_cell_v_ack(c_e_h_1, s4)),
% 290.12/182.62 inference(unit_resolution,[status(thm)],[6111, 6103])).
% 290.12/182.62 tff(6113,plain,
% 290.12/182.62 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node2(c_e_h_3, c_e_h_1, s4))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node2(c_e_h_3, c_e_h_1, s4))),
% 290.12/182.62 inference(rewrite,[status(thm)],[])).
% 290.12/182.62 tff(6114,plain,
% 290.12/182.62 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node2(c_e_h_3, c_e_h_1, s4))),
% 290.12/182.62 inference(quant_inst,[status(thm)],[])).
% 290.12/182.62 tff(6115,plain,
% 290.12/182.62 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node2(c_e_h_3, c_e_h_1, s4)),
% 290.12/182.62 inference(modus_ponens,[status(thm)],[6114, 6113])).
% 290.12/182.62 tff(6116,plain,
% 290.12/182.62 (node2(c_e_h_3, c_e_h_1, s4)),
% 290.12/182.62 inference(unit_resolution,[status(thm)],[6115, 2922, 5821])).
% 290.12/182.62 tff(6117,plain,
% 290.12/182.62 (((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | ((~node2(c_e_h_3, c_e_h_1, s4)) | m_cell_v_ack(c_e_h_1, s4) | m_and_h_gate_v_in2(c_e_h_3, c_c, s4))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | (~node2(c_e_h_3, c_e_h_1, s4)) | m_cell_v_ack(c_e_h_1, s4) | m_and_h_gate_v_in2(c_e_h_3, c_c, s4))),
% 290.12/182.62 inference(rewrite,[status(thm)],[])).
% 290.12/182.62 tff(6118,plain,
% 290.12/182.62 ((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | ((~node2(c_e_h_3, c_e_h_1, s4)) | m_cell_v_ack(c_e_h_1, s4) | m_and_h_gate_v_in2(c_e_h_3, c_c, s4))),
% 290.12/182.62 inference(quant_inst,[status(thm)],[])).
% 290.12/182.62 tff(6119,plain,
% 290.12/182.62 ((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | (~node2(c_e_h_3, c_e_h_1, s4)) | m_cell_v_ack(c_e_h_1, s4) | m_and_h_gate_v_in2(c_e_h_3, c_c, s4)),
% 290.12/182.62 inference(modus_ponens,[status(thm)],[6118, 6117])).
% 290.12/182.62 tff(6120,plain,
% 290.12/182.62 (m_cell_v_ack(c_e_h_1, s4) | m_and_h_gate_v_in2(c_e_h_3, c_c, s4)),
% 290.12/182.62 inference(unit_resolution,[status(thm)],[6119, 5835, 6116])).
% 290.12/182.62 tff(6121,plain,
% 290.12/182.62 (m_and_h_gate_v_in2(c_e_h_3, c_c, s4)),
% 290.12/182.62 inference(unit_resolution,[status(thm)],[6120, 6112])).
% 290.12/182.62 tff(6122,assumption,(node22(c_e_h_3, c_c, s4, s5)), introduced(assumption)).
% 290.12/182.62 tff(6123,plain,
% 290.12/182.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s4)) | m_and_h_gate_v_out(c_e_h_3, c_c, s5) | (~node22(c_e_h_3, c_c, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s4)) | m_and_h_gate_v_out(c_e_h_3, c_c, s5) | (~node22(c_e_h_3, c_c, s4, s5)))),
% 290.12/182.62 inference(rewrite,[status(thm)],[])).
% 290.12/182.62 tff(6124,plain,
% 290.12/182.62 ((m_and_h_gate_v_out(c_e_h_3, c_c, s5) | (~node22(c_e_h_3, c_c, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s4))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_c, s4)) | m_and_h_gate_v_out(c_e_h_3, c_c, s5) | (~node22(c_e_h_3, c_c, s4, s5)))),
% 290.12/182.62 inference(rewrite,[status(thm)],[])).
% 290.12/182.62 tff(6125,plain,
% 290.12/182.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_c, s5) | (~node22(c_e_h_3, c_c, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s4)) | m_and_h_gate_v_out(c_e_h_3, c_c, s5) | (~node22(c_e_h_3, c_c, s4, s5))))),
% 290.12/182.62 inference(monotonicity,[status(thm)],[6124])).
% 290.12/182.62 tff(6126,plain,
% 290.12/182.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_c, s5) | (~node22(c_e_h_3, c_c, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s4)) | m_and_h_gate_v_out(c_e_h_3, c_c, s5) | (~node22(c_e_h_3, c_c, s4, s5)))),
% 290.12/182.62 inference(transitivity,[status(thm)],[6125, 6123])).
% 290.12/182.62 tff(6127,plain,
% 290.12/182.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_c, s5) | (~node22(c_e_h_3, c_c, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s4)))),
% 290.12/182.62 inference(quant_inst,[status(thm)],[])).
% 290.12/182.62 tff(6128,plain,
% 290.12/182.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s4)) | m_and_h_gate_v_out(c_e_h_3, c_c, s5) | (~node22(c_e_h_3, c_c, s4, s5))),
% 290.12/182.62 inference(modus_ponens,[status(thm)],[6127, 6126])).
% 290.12/182.62 tff(6129,plain,
% 290.12/182.62 ($false),
% 290.12/182.62 inference(unit_resolution,[status(thm)],[6128, 5871, 6122, 2723, 5931])).
% 290.12/182.62 tff(6130,plain,((~node22(c_e_h_3, c_c, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s4)) | m_and_h_gate_v_out(c_e_h_3, c_c, s5)), inference(lemma,lemma(discharge,[]))).
% 290.12/182.62 tff(6131,plain,
% 290.12/182.62 (~node22(c_e_h_3, c_c, s4, s5)),
% 290.12/182.62 inference(unit_resolution,[status(thm)],[6130, 2723, 5931])).
% 290.12/182.62 tff(6132,plain,
% 290.12/182.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_3, c_c, s4, s5) | node22(c_e_h_3, c_c, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_3, c_c, s4, s5) | node22(c_e_h_3, c_c, s4, s5))),
% 290.12/182.62 inference(rewrite,[status(thm)],[])).
% 290.12/182.62 tff(6133,plain,
% 290.12/182.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_3, c_c, s4, s5) | node22(c_e_h_3, c_c, s4, s5))),
% 290.12/182.62 inference(quant_inst,[status(thm)],[])).
% 290.12/182.62 tff(6134,plain,
% 290.12/182.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_3, c_c, s4, s5) | node22(c_e_h_3, c_c, s4, s5)),
% 290.12/182.62 inference(modus_ponens,[status(thm)],[6133, 6132])).
% 290.12/182.62 tff(6135,plain,
% 290.12/182.62 (node21(c_e_h_3, c_c, s4, s5) | node22(c_e_h_3, c_c, s4, s5)),
% 290.12/182.62 inference(unit_resolution,[status(thm)],[6134, 82, 1028])).
% 290.12/182.62 tff(6136,plain,
% 290.12/182.62 (node21(c_e_h_3, c_c, s4, s5)),
% 290.12/182.62 inference(unit_resolution,[status(thm)],[6135, 6131])).
% 290.12/182.62 tff(6137,plain,
% 290.12/182.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_c, s4, s5)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s4)) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s4)) | m_and_h_gate_v_out(c_e_h_3, c_c, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~node21(c_e_h_3, c_c, s4, s5)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s4)) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s4)) | m_and_h_gate_v_out(c_e_h_3, c_c, s5))),
% 290.12/182.62 inference(rewrite,[status(thm)],[])).
% 290.12/182.62 tff(6138,plain,
% 290.12/182.62 (((~node21(c_e_h_3, c_c, s4, s5)) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s4)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s4)) | m_and_h_gate_v_out(c_e_h_3, c_c, s5)) <=> ((~node21(c_e_h_3, c_c, s4, s5)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s4)) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s4)) | m_and_h_gate_v_out(c_e_h_3, c_c, s5))),
% 290.12/182.62 inference(rewrite,[status(thm)],[])).
% 290.12/182.62 tff(6139,plain,
% 290.12/182.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_c, s4, s5)) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s4)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s4)) | m_and_h_gate_v_out(c_e_h_3, c_c, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_c, s4, s5)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s4)) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s4)) | m_and_h_gate_v_out(c_e_h_3, c_c, s5)))),
% 290.12/182.62 inference(monotonicity,[status(thm)],[6138])).
% 290.12/182.62 tff(6140,plain,
% 290.12/182.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_c, s4, s5)) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s4)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s4)) | m_and_h_gate_v_out(c_e_h_3, c_c, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~node21(c_e_h_3, c_c, s4, s5)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s4)) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s4)) | m_and_h_gate_v_out(c_e_h_3, c_c, s5))),
% 290.12/182.62 inference(transitivity,[status(thm)],[6139, 6137])).
% 290.12/182.62 tff(6141,plain,
% 290.12/182.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_c, s4, s5)) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s4)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s4)) | m_and_h_gate_v_out(c_e_h_3, c_c, s5))),
% 290.12/182.62 inference(quant_inst,[status(thm)],[])).
% 290.12/182.62 tff(6142,plain,
% 290.12/182.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~node21(c_e_h_3, c_c, s4, s5)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s4)) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s4)) | m_and_h_gate_v_out(c_e_h_3, c_c, s5)),
% 290.12/182.62 inference(modus_ponens,[status(thm)],[6141, 6140])).
% 290.12/182.62 tff(6143,plain,
% 290.12/182.62 (~m_and_h_gate_v_in1(c_e_h_3, c_c, s4)),
% 290.12/182.62 inference(unit_resolution,[status(thm)],[6142, 5851, 6136, 6121, 5931])).
% 290.12/182.62 tff(6144,plain,
% 290.12/182.62 (((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s4))) <=> ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s4))),
% 290.12/182.62 inference(rewrite,[status(thm)],[])).
% 290.12/182.62 tff(6145,plain,
% 290.12/182.62 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s4))),
% 290.12/182.62 inference(quant_inst,[status(thm)],[])).
% 290.12/182.62 tff(6146,plain,
% 290.12/182.62 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s4)),
% 290.12/182.62 inference(modus_ponens,[status(thm)],[6145, 6144])).
% 290.12/182.62 tff(6147,plain,
% 290.12/182.62 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s4)),
% 290.12/182.62 inference(unit_resolution,[status(thm)],[6146, 2556, 6143])).
% 290.12/182.63 tff(6148,plain,
% 290.12/182.63 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s3)),
% 290.12/182.63 inference(unit_resolution,[status(thm)],[2537, 6147])).
% 290.12/182.63 tff(6149,plain,
% 290.12/182.63 (~m_and_h_gate_v_in1(c_e_h_3, c_c, s3)),
% 290.12/182.63 inference(unit_resolution,[status(thm)],[2544, 6148])).
% 290.12/182.63 tff(6150,plain,
% 290.12/182.63 (~node20(c_e_h_3, c_c, s3)),
% 290.12/182.63 inference(unit_resolution,[status(thm)],[2718, 38, 6149])).
% 290.12/182.63 tff(6151,plain,
% 290.12/182.63 (m_and_h_gate_v_out(c_e_h_3, c_c, s3)),
% 290.12/182.63 inference(unit_resolution,[status(thm)],[2740, 6150, 2723])).
% 290.12/182.63 tff(6152,plain,
% 290.12/182.63 (node20(c_e_h_3, c_c, s2)),
% 290.12/182.63 inference(unit_resolution,[status(thm)],[2697, 6151, 2675])).
% 290.12/182.63 tff(6153,plain,
% 290.12/182.63 (m_and_h_gate_v_in1(c_e_h_3, c_c, s2)),
% 290.12/182.63 inference(unit_resolution,[status(thm)],[2620, 38, 6152])).
% 290.12/182.63 tff(6154,plain,
% 290.12/182.63 (m_mutex_h_half_v_out(c_e_h_3, c_a, s2)),
% 290.12/182.63 inference(unit_resolution,[status(thm)],[2612, 567, 6153])).
% 290.12/182.63 tff(6155,plain,
% 290.12/182.63 (~node13(c_e_h_3, c_a, s2, s3)),
% 290.12/182.63 inference(unit_resolution,[status(thm)],[2571, 6154, 6148])).
% 290.12/182.63 tff(6156,plain,
% 290.12/182.63 (node12(c_e_h_3, c_a, s2, s3)),
% 290.12/182.63 inference(unit_resolution,[status(thm)],[483, 6155])).
% 290.12/182.63 tff(6157,plain,
% 290.12/182.63 (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s2)),
% 290.12/182.63 inference(unit_resolution,[status(thm)],[2582, 6156, 6148])).
% 290.12/182.63 tff(6158,plain,
% 290.12/182.63 (~m_user_v_req(c_e_h_3, c_u, s2)),
% 290.12/182.63 inference(unit_resolution,[status(thm)],[2604, 1426, 6157])).
% 290.12/182.63 tff(6159,plain,
% 290.12/182.63 (~node7(c_e_h_3, c_u, s1, s2)),
% 290.12/182.63 inference(unit_resolution,[status(thm)],[347, 6158])).
% 290.12/182.63 tff(6160,plain,
% 290.12/182.63 (node8(c_e_h_3, c_u, s1, s2)),
% 290.12/182.63 inference(unit_resolution,[status(thm)],[352, 6159])).
% 290.12/182.63 tff(6161,plain,
% 290.12/182.63 (~m_user_v_req(c_e_h_3, c_u, s1)),
% 290.12/182.63 inference(unit_resolution,[status(thm)],[363, 6160, 6158])).
% 290.12/182.63 tff(6162,plain,
% 290.12/182.63 (~node7(c_e_h_3, c_u, s0, s1)),
% 290.12/182.63 inference(unit_resolution,[status(thm)],[375, 6161])).
% 290.12/182.63 tff(6163,plain,
% 290.12/182.63 (node8(c_e_h_3, c_u, s0, s1)),
% 290.12/182.63 inference(unit_resolution,[status(thm)],[380, 6162])).
% 290.12/182.63 tff(6164,plain,
% 290.12/182.63 (~m_user_v_req(c_e_h_3, c_u, s0)),
% 290.12/182.63 inference(unit_resolution,[status(thm)],[387, 302, 6163, 6161])).
% 290.12/182.63 tff(6165,plain,
% 290.12/182.63 (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s0)),
% 290.12/182.63 inference(unit_resolution,[status(thm)],[398, 395, 6164])).
% 290.12/182.63 tff(6166,plain,
% 290.12/182.63 (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s1)),
% 290.12/182.63 inference(unit_resolution,[status(thm)],[491, 395, 6161])).
% 290.12/182.63 tff(6167,plain,
% 290.12/182.63 (m_mutex_h_half_v_out(c_e_h_3, c_a, s1)),
% 290.12/182.63 inference(unit_resolution,[status(thm)],[2593, 6166, 6154])).
% 290.12/182.63 tff(6168,plain,
% 290.12/182.63 ($false),
% 290.12/182.63 inference(unit_resolution,[status(thm)],[462, 6167, 6165])).
% 290.12/182.63 tff(6169,plain,((~m_and_h_gate_v_out(c_e_h_3, c_c, s4)) | m_and_h_gate_v_out(c_e_h_3, c_c, s2) | m_and_h_gate_v_out(c_e_h_3, c_c, s5)), inference(lemma,lemma(discharge,[]))).
% 290.12/182.63 tff(6170,plain,
% 290.12/182.63 ((~m_and_h_gate_v_out(c_e_h_3, c_c, s4)) | m_and_h_gate_v_out(c_e_h_3, c_c, s5)),
% 290.12/182.63 inference(unit_resolution,[status(thm)],[6169, 2674])).
% 290.12/182.63 tff(6171,plain,
% 290.12/182.63 (m_and_h_gate_v_out(c_e_h_3, c_c, s5)),
% 290.12/182.63 inference(unit_resolution,[status(thm)],[6170, 5886])).
% 290.12/182.63 tff(6172,assumption,(~m_or_h_gate_v_in1(c_e_h_3, c_g, s5)), introduced(assumption)).
% 290.12/182.63 tff(6173,assumption,(m_and_h_gate_v_out(c_e_h_3, c_c, s5)), introduced(assumption)).
% 290.12/182.63 tff(6174,plain,
% 290.12/182.63 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s5)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s5))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s5)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s5))),
% 290.12/182.63 inference(rewrite,[status(thm)],[])).
% 290.12/182.63 tff(6175,plain,
% 290.12/182.63 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s5)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s5))),
% 290.12/182.63 inference(quant_inst,[status(thm)],[])).
% 290.12/182.63 tff(6176,plain,
% 290.12/182.63 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s5)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s5)),
% 290.12/182.63 inference(modus_ponens,[status(thm)],[6175, 6174])).
% 290.12/182.63 tff(6177,plain,
% 290.12/182.63 ($false),
% 290.12/182.63 inference(unit_resolution,[status(thm)],[6176, 5896, 6173, 6172])).
% 290.12/182.63 tff(6178,plain,(m_or_h_gate_v_in1(c_e_h_3, c_g, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s5))), inference(lemma,lemma(discharge,[]))).
% 290.12/182.63 tff(6179,plain,
% 290.12/182.63 (m_or_h_gate_v_in1(c_e_h_3, c_g, s5)),
% 290.12/182.63 inference(unit_resolution,[status(thm)],[6178, 6171])).
% 290.12/182.63 tff(6180,assumption,(m_or_h_gate_v_in1(c_e_h_3, c_g, s5)), introduced(assumption)).
% 290.12/182.63 tff(6181,assumption,(node4(c_e_h_3, c_g, s5)), introduced(assumption)).
% 290.12/182.63 tff(6182,plain,
% 290.12/182.63 (((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_g, s5)) | (~node4(c_e_h_3, c_g, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s5)) | (~node4(c_e_h_3, c_g, s5)))),
% 290.12/182.63 inference(rewrite,[status(thm)],[])).
% 290.12/182.63 tff(6183,plain,
% 290.12/182.63 ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_g, s5)) | (~node4(c_e_h_3, c_g, s5)))),
% 290.12/182.63 inference(quant_inst,[status(thm)],[])).
% 290.12/182.63 tff(6184,plain,
% 290.12/182.63 ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s5)) | (~node4(c_e_h_3, c_g, s5))),
% 290.12/182.63 inference(modus_ponens,[status(thm)],[6183, 6182])).
% 290.12/182.63 tff(6185,plain,
% 290.12/182.63 ($false),
% 290.12/182.63 inference(unit_resolution,[status(thm)],[6184, 5516, 6181, 6180])).
% 290.12/182.63 tff(6186,plain,((~node4(c_e_h_3, c_g, s5)) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s5))), inference(lemma,lemma(discharge,[]))).
% 290.12/182.63 tff(6187,plain,
% 290.12/182.63 (~node4(c_e_h_3, c_g, s5)),
% 290.12/182.63 inference(unit_resolution,[status(thm)],[6186, 6179])).
% 290.12/182.63 tff(6188,assumption,(~node4(c_e_h_3, c_g, s5)), introduced(assumption)).
% 290.12/182.63 tff(6189,assumption,(~m_or_h_gate_v_out(c_e_h_3, c_g, s6)), introduced(assumption)).
% 290.12/182.63 tff(6190,assumption,(node5(c_e_h_3, c_g, s5, s6)), introduced(assumption)).
% 290.12/182.63 tff(6191,plain,
% 290.12/182.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s6) | node4(c_e_h_3, c_g, s5) | (~node5(c_e_h_3, c_g, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | m_or_h_gate_v_out(c_e_h_3, c_g, s6) | node4(c_e_h_3, c_g, s5) | (~node5(c_e_h_3, c_g, s5, s6)))),
% 290.12/182.63 inference(rewrite,[status(thm)],[])).
% 290.12/182.63 tff(6192,plain,
% 290.12/182.63 ((node4(c_e_h_3, c_g, s5) | (~node5(c_e_h_3, c_g, s5, s6)) | m_or_h_gate_v_out(c_e_h_3, c_g, s6)) <=> (m_or_h_gate_v_out(c_e_h_3, c_g, s6) | node4(c_e_h_3, c_g, s5) | (~node5(c_e_h_3, c_g, s5, s6)))),
% 290.12/182.63 inference(rewrite,[status(thm)],[])).
% 290.12/182.63 tff(6193,plain,
% 290.12/182.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_3, c_g, s5) | (~node5(c_e_h_3, c_g, s5, s6)) | m_or_h_gate_v_out(c_e_h_3, c_g, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s6) | node4(c_e_h_3, c_g, s5) | (~node5(c_e_h_3, c_g, s5, s6))))),
% 290.12/182.63 inference(monotonicity,[status(thm)],[6192])).
% 290.12/182.63 tff(6194,plain,
% 290.12/182.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_3, c_g, s5) | (~node5(c_e_h_3, c_g, s5, s6)) | m_or_h_gate_v_out(c_e_h_3, c_g, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | m_or_h_gate_v_out(c_e_h_3, c_g, s6) | node4(c_e_h_3, c_g, s5) | (~node5(c_e_h_3, c_g, s5, s6)))),
% 290.12/182.63 inference(transitivity,[status(thm)],[6193, 6191])).
% 290.12/182.63 tff(6195,plain,
% 290.12/182.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_3, c_g, s5) | (~node5(c_e_h_3, c_g, s5, s6)) | m_or_h_gate_v_out(c_e_h_3, c_g, s6))),
% 290.12/182.63 inference(quant_inst,[status(thm)],[])).
% 290.12/182.63 tff(6196,plain,
% 290.12/182.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | m_or_h_gate_v_out(c_e_h_3, c_g, s6) | node4(c_e_h_3, c_g, s5) | (~node5(c_e_h_3, c_g, s5, s6))),
% 290.12/182.63 inference(modus_ponens,[status(thm)],[6195, 6194])).
% 290.12/182.63 tff(6197,plain,
% 290.12/182.63 ($false),
% 290.12/182.63 inference(unit_resolution,[status(thm)],[6196, 5498, 6190, 6189, 6188])).
% 290.12/182.63 tff(6198,plain,((~node5(c_e_h_3, c_g, s5, s6)) | m_or_h_gate_v_out(c_e_h_3, c_g, s6) | node4(c_e_h_3, c_g, s5)), inference(lemma,lemma(discharge,[]))).
% 290.12/182.63 tff(6199,plain,
% 290.12/182.63 (~node5(c_e_h_3, c_g, s5, s6)),
% 290.12/182.63 inference(unit_resolution,[status(thm)],[6198, 6189, 6188])).
% 290.12/182.63 tff(6200,assumption,(node6(c_e_h_3, c_g, s5, s6)), introduced(assumption)).
% 290.12/182.63 tff(6201,plain,
% 290.12/182.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | ((~m_or_h_gate_v_out(c_e_h_3, c_g, s5)) | m_or_h_gate_v_out(c_e_h_3, c_g, s6) | (~node6(c_e_h_3, c_g, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s5)) | m_or_h_gate_v_out(c_e_h_3, c_g, s6) | (~node6(c_e_h_3, c_g, s5, s6)))),
% 290.12/182.63 inference(rewrite,[status(thm)],[])).
% 290.12/182.63 tff(6202,plain,
% 290.12/182.63 ((m_or_h_gate_v_out(c_e_h_3, c_g, s6) | (~node6(c_e_h_3, c_g, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s5))) <=> ((~m_or_h_gate_v_out(c_e_h_3, c_g, s5)) | m_or_h_gate_v_out(c_e_h_3, c_g, s6) | (~node6(c_e_h_3, c_g, s5, s6)))),
% 290.12/182.63 inference(rewrite,[status(thm)],[])).
% 290.12/182.63 tff(6203,plain,
% 290.12/182.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s6) | (~node6(c_e_h_3, c_g, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | ((~m_or_h_gate_v_out(c_e_h_3, c_g, s5)) | m_or_h_gate_v_out(c_e_h_3, c_g, s6) | (~node6(c_e_h_3, c_g, s5, s6))))),
% 290.12/182.63 inference(monotonicity,[status(thm)],[6202])).
% 290.12/182.63 tff(6204,plain,
% 290.12/182.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s6) | (~node6(c_e_h_3, c_g, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s5)) | m_or_h_gate_v_out(c_e_h_3, c_g, s6) | (~node6(c_e_h_3, c_g, s5, s6)))),
% 290.12/182.63 inference(transitivity,[status(thm)],[6203, 6201])).
% 290.12/182.63 tff(6205,plain,
% 290.12/182.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s6) | (~node6(c_e_h_3, c_g, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s5)))),
% 290.12/182.63 inference(quant_inst,[status(thm)],[])).
% 290.12/182.63 tff(6206,plain,
% 290.12/182.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s5)) | m_or_h_gate_v_out(c_e_h_3, c_g, s6) | (~node6(c_e_h_3, c_g, s5, s6))),
% 290.12/182.63 inference(modus_ponens,[status(thm)],[6205, 6204])).
% 290.12/182.63 tff(6207,plain,
% 290.12/182.63 ($false),
% 290.12/182.63 inference(unit_resolution,[status(thm)],[6206, 5474, 6200, 3252, 6189])).
% 290.12/182.63 tff(6208,plain,((~node6(c_e_h_3, c_g, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s5)) | m_or_h_gate_v_out(c_e_h_3, c_g, s6)), inference(lemma,lemma(discharge,[]))).
% 290.12/182.63 tff(6209,plain,
% 290.12/182.63 (~node6(c_e_h_3, c_g, s5, s6)),
% 290.12/182.63 inference(unit_resolution,[status(thm)],[6208, 6189, 3252])).
% 290.12/182.63 tff(6210,plain,
% 290.12/182.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s5, s6)) | node5(c_e_h_3, c_g, s5, s6) | node6(c_e_h_3, c_g, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s5, s6)) | node5(c_e_h_3, c_g, s5, s6) | node6(c_e_h_3, c_g, s5, s6))),
% 290.12/182.63 inference(rewrite,[status(thm)],[])).
% 290.12/182.63 tff(6211,plain,
% 290.12/182.63 ((node6(c_e_h_3, c_g, s5, s6) | node5(c_e_h_3, c_g, s5, s6) | (~trans(s5, s6))) <=> ((~trans(s5, s6)) | node5(c_e_h_3, c_g, s5, s6) | node6(c_e_h_3, c_g, s5, s6))),
% 290.12/182.64 inference(rewrite,[status(thm)],[])).
% 290.12/182.64 tff(6212,plain,
% 290.12/182.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s5, s6) | node5(c_e_h_3, c_g, s5, s6) | (~trans(s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s5, s6)) | node5(c_e_h_3, c_g, s5, s6) | node6(c_e_h_3, c_g, s5, s6)))),
% 290.12/182.64 inference(monotonicity,[status(thm)],[6211])).
% 290.12/182.64 tff(6213,plain,
% 290.12/182.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s5, s6) | node5(c_e_h_3, c_g, s5, s6) | (~trans(s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s5, s6)) | node5(c_e_h_3, c_g, s5, s6) | node6(c_e_h_3, c_g, s5, s6))),
% 290.12/182.64 inference(transitivity,[status(thm)],[6212, 6210])).
% 290.12/182.64 tff(6214,plain,
% 290.12/182.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s5, s6) | node5(c_e_h_3, c_g, s5, s6) | (~trans(s5, s6)))),
% 290.12/182.64 inference(quant_inst,[status(thm)],[])).
% 290.12/182.64 tff(6215,plain,
% 290.12/182.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s5, s6)) | node5(c_e_h_3, c_g, s5, s6) | node6(c_e_h_3, c_g, s5, s6)),
% 290.12/182.64 inference(modus_ponens,[status(thm)],[6214, 6213])).
% 290.12/182.64 tff(6216,plain,
% 290.12/182.64 (node5(c_e_h_3, c_g, s5, s6) | node6(c_e_h_3, c_g, s5, s6)),
% 290.12/182.64 inference(unit_resolution,[status(thm)],[6215, 1141, 1406])).
% 290.12/182.64 tff(6217,plain,
% 290.12/182.64 ($false),
% 290.12/182.64 inference(unit_resolution,[status(thm)],[6216, 6209, 6199])).
% 290.12/182.64 tff(6218,plain,(m_or_h_gate_v_out(c_e_h_3, c_g, s6) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s5)) | node4(c_e_h_3, c_g, s5)), inference(lemma,lemma(discharge,[]))).
% 290.12/182.64 tff(6219,plain,
% 290.12/182.64 (m_or_h_gate_v_out(c_e_h_3, c_g, s6)),
% 290.12/182.64 inference(unit_resolution,[status(thm)],[6218, 6187, 5930])).
% 290.12/182.64 tff(6220,plain,
% 290.12/182.64 (^[I0: $i, X: $i] : refl(((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X)) <=> ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X)))),
% 290.12/182.64 inference(bind,[status(th)],[])).
% 290.12/182.64 tff(6221,plain,
% 290.12/182.64 (![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X)) <=> ![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X))),
% 290.12/182.64 inference(quant_intro,[status(thm)],[6220])).
% 290.12/182.64 tff(6222,plain,
% 290.12/182.64 (![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X)) <=> ![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X))),
% 290.12/182.64 inference(rewrite,[status(thm)],[])).
% 290.12/182.64 tff(6223,plain,
% 290.12/182.64 (^[I0: $i, X: $i] : rewrite((m_and_h_gate_v_in1(I0, c_k, X) | (~m_or_h_gate_v_out(I0, c_g, X))) <=> ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X)))),
% 290.12/182.64 inference(bind,[status(th)],[])).
% 290.12/182.64 tff(6224,plain,
% 290.12/182.64 (![I0: $i, X: $i] : (m_and_h_gate_v_in1(I0, c_k, X) | (~m_or_h_gate_v_out(I0, c_g, X))) <=> ![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X))),
% 290.12/182.64 inference(quant_intro,[status(thm)],[6223])).
% 290.12/182.64 tff(6225,axiom,(![I0: $i, X: $i] : (m_and_h_gate_v_in1(I0, c_k, X) | (~m_or_h_gate_v_out(I0, c_g, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_43')).
% 290.12/182.64 tff(6226,plain,
% 290.12/182.64 (![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X))),
% 290.12/182.64 inference(modus_ponens,[status(thm)],[6225, 6224])).
% 290.12/182.64 tff(6227,plain,
% 290.12/182.64 (![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X))),
% 290.12/182.64 inference(modus_ponens,[status(thm)],[6226, 6222])).
% 290.12/182.64 tff(6228,plain,(
% 290.12/182.64 ![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X))),
% 290.12/182.64 inference(skolemize,[status(sab)],[6227])).
% 290.12/182.64 tff(6229,plain,
% 290.12/182.64 (![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X))),
% 290.12/182.64 inference(modus_ponens,[status(thm)],[6228, 6221])).
% 290.12/182.64 tff(6230,plain,
% 290.12/182.64 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X))) | ((~m_or_h_gate_v_out(c_e_h_3, c_g, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s6))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s6))),
% 290.12/182.64 inference(rewrite,[status(thm)],[])).
% 290.12/182.64 tff(6231,plain,
% 290.12/182.64 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X))) | ((~m_or_h_gate_v_out(c_e_h_3, c_g, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s6))),
% 290.12/182.64 inference(quant_inst,[status(thm)],[])).
% 290.12/182.64 tff(6232,plain,
% 290.12/182.64 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s6)),
% 290.12/182.64 inference(modus_ponens,[status(thm)],[6231, 6230])).
% 290.12/182.64 tff(6233,plain,
% 290.12/182.64 (m_and_h_gate_v_in1(c_e_h_3, c_k, s6)),
% 290.12/182.64 inference(unit_resolution,[status(thm)],[6232, 6229, 6219])).
% 290.12/182.64 tff(6234,plain,
% 290.12/182.64 (~m_and_h_gate_v_in1(c_e_h_3, c_l, s4)),
% 290.12/182.64 inference(unit_resolution,[status(thm)],[3492, 3485])).
% 290.12/182.64 tff(6235,plain,
% 290.12/182.64 (~node20(c_e_h_3, c_l, s4)),
% 290.12/182.64 inference(unit_resolution,[status(thm)],[3500, 6234])).
% 290.12/182.64 tff(6236,plain,
% 290.12/182.64 (~m_and_h_gate_v_out(c_e_h_3, c_l, s5)),
% 290.12/182.64 inference(unit_resolution,[status(thm)],[3598, 6235])).
% 290.12/182.64 tff(6237,plain,
% 290.12/182.64 (~m_or_h_gate_v_in1(c_e_h_3, c_j, s5)),
% 290.12/182.64 inference(unit_resolution,[status(thm)],[3606, 6236])).
% 290.12/182.64 tff(6238,plain,
% 290.12/182.64 (~m_or_h_gate_v_out(c_e_h_3, c_j, s6)),
% 290.12/182.64 inference(unit_resolution,[status(thm)],[4385, 6237])).
% 290.12/182.64 tff(6239,plain,
% 290.12/182.64 (m_and_h_gate_v_out(c_e_h_3, c_l, s6) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s8)) | node20(c_e_h_3, c_l, s6)),
% 290.12/182.64 inference(unit_resolution,[status(thm)],[5447, 6238])).
% 290.12/182.64 tff(6240,plain,
% 290.12/182.64 (node20(c_e_h_3, c_l, s6)),
% 290.12/182.64 inference(unit_resolution,[status(thm)],[6239, 4486, 3367])).
% 290.12/182.64 tff(6241,plain,
% 290.12/182.64 (m_and_h_gate_v_in1(c_e_h_3, c_l, s6)),
% 290.12/182.64 inference(unit_resolution,[status(thm)],[4483, 6240])).
% 290.12/182.64 tff(6242,plain,
% 290.12/182.64 (m_and_h_gate_v_out(c_e_h_3, c_k, s6)),
% 290.12/182.64 inference(unit_resolution,[status(thm)],[4475, 6241])).
% 290.12/182.64 tff(6243,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_k, s7)), introduced(assumption)).
% 290.12/182.64 tff(6244,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_k, s6)), introduced(assumption)).
% 290.12/182.64 tff(6245,assumption,(~m_and_h_gate_v_in2(c_e_h_3, c_k, s6)), introduced(assumption)).
% 290.12/182.64 tff(6246,plain,
% 290.12/182.64 ((~node6(c_e_h_3, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s4))),
% 290.12/182.64 inference(unit_resolution,[status(thm)],[4027, 2233])).
% 290.12/182.64 tff(6247,plain,
% 290.12/182.64 (~node6(c_e_h_3, c_j, s3, s4)),
% 290.12/182.64 inference(unit_resolution,[status(thm)],[6246, 4018])).
% 290.12/182.64 tff(6248,plain,
% 290.12/182.64 ((~node5(c_e_h_3, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s4))),
% 290.12/182.64 inference(unit_resolution,[status(thm)],[4052, 3615])).
% 290.12/182.64 tff(6249,plain,
% 290.12/182.64 (~node5(c_e_h_3, c_j, s3, s4)),
% 290.12/182.64 inference(unit_resolution,[status(thm)],[6248, 4018])).
% 290.12/182.64 tff(6250,plain,
% 290.12/182.64 ($false),
% 290.12/182.64 inference(unit_resolution,[status(thm)],[4060, 6249, 6247])).
% 290.12/182.64 tff(6251,plain,(~m_or_h_gate_v_out(c_e_h_3, c_j, s4)), inference(lemma,lemma(discharge,[]))).
% 290.12/182.64 tff(6252,assumption,(m_c_h_element_v_in2(c_e_h_3, c_h, s4)), introduced(assumption)).
% 290.12/182.64 tff(6253,plain,
% 290.12/182.64 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s4)) | m_or_h_gate_v_out(c_e_h_3, c_j, s4))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s4)) | m_or_h_gate_v_out(c_e_h_3, c_j, s4))),
% 290.12/182.64 inference(rewrite,[status(thm)],[])).
% 290.12/182.64 tff(6254,plain,
% 290.12/182.64 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s4)) | m_or_h_gate_v_out(c_e_h_3, c_j, s4))),
% 290.12/182.64 inference(quant_inst,[status(thm)],[])).
% 290.12/182.64 tff(6255,plain,
% 290.12/182.64 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s4)) | m_or_h_gate_v_out(c_e_h_3, c_j, s4)),
% 290.12/182.64 inference(modus_ponens,[status(thm)],[6254, 6253])).
% 290.12/182.64 tff(6256,plain,
% 290.12/182.64 ($false),
% 290.12/182.64 inference(unit_resolution,[status(thm)],[6255, 1174, 6252, 4007])).
% 290.12/182.64 tff(6257,plain,((~m_c_h_element_v_in2(c_e_h_3, c_h, s4)) | m_or_h_gate_v_out(c_e_h_3, c_j, s4)), inference(lemma,lemma(discharge,[]))).
% 290.12/182.64 tff(6258,plain,
% 290.12/182.64 (~m_c_h_element_v_in2(c_e_h_3, c_h, s4)),
% 290.12/182.64 inference(unit_resolution,[status(thm)],[6257, 6251])).
% 290.12/182.64 tff(6259,assumption,(m_c_h_element_v_out(c_e_h_3, c_h, s5)), introduced(assumption)).
% 290.12/182.64 tff(6260,assumption,(node18(c_e_h_3, c_h, s4, s5)), introduced(assumption)).
% 290.12/182.64 tff(6261,plain,
% 290.12/182.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s5)) | m_c_h_element_v_out(c_e_h_3, c_h, s4) | (~node18(c_e_h_3, c_h, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s5)) | m_c_h_element_v_out(c_e_h_3, c_h, s4) | (~node18(c_e_h_3, c_h, s4, s5)))),
% 290.12/182.64 inference(rewrite,[status(thm)],[])).
% 290.12/182.64 tff(6262,plain,
% 290.12/182.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s5)) | m_c_h_element_v_out(c_e_h_3, c_h, s4) | (~node18(c_e_h_3, c_h, s4, s5)))),
% 290.12/182.64 inference(quant_inst,[status(thm)],[])).
% 290.12/182.64 tff(6263,plain,
% 290.12/182.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s5)) | m_c_h_element_v_out(c_e_h_3, c_h, s4) | (~node18(c_e_h_3, c_h, s4, s5))),
% 290.12/182.64 inference(modus_ponens,[status(thm)],[6262, 6261])).
% 290.12/182.64 tff(6264,plain,
% 290.12/182.64 ($false),
% 290.12/182.64 inference(unit_resolution,[status(thm)],[6263, 753, 6259, 6260, 2341])).
% 290.12/182.64 tff(6265,plain,((~node18(c_e_h_3, c_h, s4, s5)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s5)) | m_c_h_element_v_out(c_e_h_3, c_h, s4)), inference(lemma,lemma(discharge,[]))).
% 290.12/182.64 tff(6266,plain,
% 290.12/182.64 (~node18(c_e_h_3, c_h, s4, s5)),
% 290.12/182.64 inference(unit_resolution,[status(thm)],[6265, 6259, 2341])).
% 290.12/182.64 tff(6267,plain,
% 290.12/182.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s4, s5)) | node19(c_e_h_3, c_h, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s4, s5)) | node19(c_e_h_3, c_h, s4, s5))),
% 290.12/182.64 inference(rewrite,[status(thm)],[])).
% 290.12/182.64 tff(6268,plain,
% 290.12/182.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s4, s5)) | node19(c_e_h_3, c_h, s4, s5))),
% 290.12/182.64 inference(quant_inst,[status(thm)],[])).
% 290.12/182.64 tff(6269,plain,
% 290.12/182.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s4, s5)) | node19(c_e_h_3, c_h, s4, s5)),
% 290.12/182.64 inference(modus_ponens,[status(thm)],[6268, 6267])).
% 290.12/182.64 tff(6270,plain,
% 290.12/182.64 (node19(c_e_h_3, c_h, s4, s5)),
% 290.12/182.64 inference(unit_resolution,[status(thm)],[6269, 190, 1028])).
% 290.12/182.64 tff(6271,plain,
% 290.12/182.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s4) | node18(c_e_h_3, c_h, s4, s5) | (~node19(c_e_h_3, c_h, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_h, s4) | node18(c_e_h_3, c_h, s4, s5) | (~node19(c_e_h_3, c_h, s4, s5)))),
% 290.12/182.64 inference(rewrite,[status(thm)],[])).
% 290.12/182.64 tff(6272,plain,
% 290.12/182.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s4) | node18(c_e_h_3, c_h, s4, s5) | (~node19(c_e_h_3, c_h, s4, s5)))),
% 290.12/182.64 inference(quant_inst,[status(thm)],[])).
% 290.12/182.64 tff(6273,plain,
% 290.12/182.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_h, s4) | node18(c_e_h_3, c_h, s4, s5) | (~node19(c_e_h_3, c_h, s4, s5))),
% 290.12/182.64 inference(modus_ponens,[status(thm)],[6272, 6271])).
% 290.12/182.64 tff(6274,plain,
% 290.12/182.64 (node17(c_e_h_3, c_h, s4) | node18(c_e_h_3, c_h, s4, s5)),
% 290.12/182.65 inference(unit_resolution,[status(thm)],[6273, 776, 6270])).
% 290.12/182.65 tff(6275,plain,
% 290.12/182.65 (node17(c_e_h_3, c_h, s4)),
% 290.12/182.65 inference(unit_resolution,[status(thm)],[6274, 6266])).
% 290.12/182.65 tff(6276,assumption,(~node14(c_e_h_3, c_h, s4, s5)), introduced(assumption)).
% 290.12/182.65 tff(6277,assumption,(node15(c_e_h_3, c_h, s4, s5)), introduced(assumption)).
% 290.12/182.65 tff(6278,plain,
% 290.12/182.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s5)) | (~node15(c_e_h_3, c_h, s4, s5)) | m_c_h_element_v_out(c_e_h_3, c_h, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s5)) | (~node15(c_e_h_3, c_h, s4, s5)) | m_c_h_element_v_out(c_e_h_3, c_h, s4))),
% 290.12/182.65 inference(rewrite,[status(thm)],[])).
% 290.12/182.65 tff(6279,plain,
% 290.12/182.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s5)) | (~node15(c_e_h_3, c_h, s4, s5)) | m_c_h_element_v_out(c_e_h_3, c_h, s4))),
% 290.12/182.65 inference(quant_inst,[status(thm)],[])).
% 290.12/182.65 tff(6280,plain,
% 290.12/182.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s5)) | (~node15(c_e_h_3, c_h, s4, s5)) | m_c_h_element_v_out(c_e_h_3, c_h, s4)),
% 290.12/182.65 inference(modus_ponens,[status(thm)],[6279, 6278])).
% 290.12/182.65 tff(6281,plain,
% 290.12/182.65 ($false),
% 290.12/182.65 inference(unit_resolution,[status(thm)],[6280, 147, 6259, 6277, 2341])).
% 290.12/182.65 tff(6282,plain,((~node15(c_e_h_3, c_h, s4, s5)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s5)) | m_c_h_element_v_out(c_e_h_3, c_h, s4)), inference(lemma,lemma(discharge,[]))).
% 290.12/182.65 tff(6283,plain,
% 290.12/182.65 (~node15(c_e_h_3, c_h, s4, s5)),
% 290.12/182.65 inference(unit_resolution,[status(thm)],[6282, 2341, 6259])).
% 290.12/182.65 tff(6284,plain,
% 290.12/182.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_3, c_h, s4, s5) | node16(c_e_h_3, c_h, s4) | node15(c_e_h_3, c_h, s4, s5) | (~node19(c_e_h_3, c_h, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_h, s4, s5) | node16(c_e_h_3, c_h, s4) | node15(c_e_h_3, c_h, s4, s5) | (~node19(c_e_h_3, c_h, s4, s5)))),
% 290.12/182.65 inference(rewrite,[status(thm)],[])).
% 290.12/182.65 tff(6285,plain,
% 290.12/182.65 ((node16(c_e_h_3, c_h, s4) | node14(c_e_h_3, c_h, s4, s5) | node15(c_e_h_3, c_h, s4, s5) | (~node19(c_e_h_3, c_h, s4, s5))) <=> (node14(c_e_h_3, c_h, s4, s5) | node16(c_e_h_3, c_h, s4) | node15(c_e_h_3, c_h, s4, s5) | (~node19(c_e_h_3, c_h, s4, s5)))),
% 290.12/182.65 inference(rewrite,[status(thm)],[])).
% 290.12/182.65 tff(6286,plain,
% 290.12/182.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s4) | node14(c_e_h_3, c_h, s4, s5) | node15(c_e_h_3, c_h, s4, s5) | (~node19(c_e_h_3, c_h, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_3, c_h, s4, s5) | node16(c_e_h_3, c_h, s4) | node15(c_e_h_3, c_h, s4, s5) | (~node19(c_e_h_3, c_h, s4, s5))))),
% 290.12/182.65 inference(monotonicity,[status(thm)],[6285])).
% 290.12/182.65 tff(6287,plain,
% 290.12/182.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s4) | node14(c_e_h_3, c_h, s4, s5) | node15(c_e_h_3, c_h, s4, s5) | (~node19(c_e_h_3, c_h, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_h, s4, s5) | node16(c_e_h_3, c_h, s4) | node15(c_e_h_3, c_h, s4, s5) | (~node19(c_e_h_3, c_h, s4, s5)))),
% 290.12/182.65 inference(transitivity,[status(thm)],[6286, 6284])).
% 290.12/182.65 tff(6288,plain,
% 290.12/182.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s4) | node14(c_e_h_3, c_h, s4, s5) | node15(c_e_h_3, c_h, s4, s5) | (~node19(c_e_h_3, c_h, s4, s5)))),
% 290.12/182.65 inference(quant_inst,[status(thm)],[])).
% 290.12/182.65 tff(6289,plain,
% 290.12/182.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_h, s4, s5) | node16(c_e_h_3, c_h, s4) | node15(c_e_h_3, c_h, s4, s5) | (~node19(c_e_h_3, c_h, s4, s5))),
% 290.12/182.65 inference(modus_ponens,[status(thm)],[6288, 6287])).
% 290.12/182.65 tff(6290,plain,
% 290.12/182.65 (node14(c_e_h_3, c_h, s4, s5) | node16(c_e_h_3, c_h, s4) | node15(c_e_h_3, c_h, s4, s5)),
% 290.12/182.65 inference(unit_resolution,[status(thm)],[6289, 204, 6270])).
% 290.12/182.65 tff(6291,plain,
% 290.12/182.65 (node16(c_e_h_3, c_h, s4)),
% 290.12/182.65 inference(unit_resolution,[status(thm)],[6290, 6283, 6276])).
% 290.12/182.65 tff(6292,plain,
% 290.12/182.65 (~node18(c_e_h_3, c_h, s4, s5)),
% 290.12/182.65 inference(unit_resolution,[status(thm)],[6265, 2341, 6259])).
% 290.12/182.65 tff(6293,plain,
% 290.12/182.65 (node17(c_e_h_3, c_h, s4)),
% 290.12/182.65 inference(unit_resolution,[status(thm)],[6274, 6292])).
% 290.12/182.65 tff(6294,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_h, s4)), introduced(assumption)).
% 290.12/182.65 tff(6295,assumption,(node16(c_e_h_3, c_h, s4)), introduced(assumption)).
% 290.12/182.65 tff(6296,plain,
% 290.12/182.65 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_h, s4)) | m_c_h_element_v_in1(c_e_h_3, c_h, s4) | m_c_h_element_v_in2(c_e_h_3, c_h, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_h, s4)) | m_c_h_element_v_in1(c_e_h_3, c_h, s4) | m_c_h_element_v_in2(c_e_h_3, c_h, s4))),
% 290.12/182.65 inference(rewrite,[status(thm)],[])).
% 290.12/182.65 tff(6297,plain,
% 290.12/182.65 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_h, s4)) | m_c_h_element_v_in1(c_e_h_3, c_h, s4) | m_c_h_element_v_in2(c_e_h_3, c_h, s4))),
% 290.12/182.65 inference(quant_inst,[status(thm)],[])).
% 290.12/182.65 tff(6298,plain,
% 290.12/182.65 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_h, s4)) | m_c_h_element_v_in1(c_e_h_3, c_h, s4) | m_c_h_element_v_in2(c_e_h_3, c_h, s4)),
% 290.12/182.65 inference(modus_ponens,[status(thm)],[6297, 6296])).
% 290.12/182.65 tff(6299,plain,
% 290.12/182.65 (m_c_h_element_v_in1(c_e_h_3, c_h, s4) | m_c_h_element_v_in2(c_e_h_3, c_h, s4)),
% 290.12/182.65 inference(unit_resolution,[status(thm)],[6298, 178, 6295])).
% 290.12/182.65 tff(6300,plain,
% 290.12/182.65 (m_c_h_element_v_in1(c_e_h_3, c_h, s4)),
% 290.12/182.65 inference(unit_resolution,[status(thm)],[6299, 6294])).
% 290.12/182.65 tff(6301,assumption,(node17(c_e_h_3, c_h, s4)), introduced(assumption)).
% 290.12/182.65 tff(6302,plain,
% 290.12/182.65 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_3, c_h, s4) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s4)) | (~node17(c_e_h_3, c_h, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_h, s4) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s4)) | (~node17(c_e_h_3, c_h, s4)))),
% 290.12/182.65 inference(rewrite,[status(thm)],[])).
% 290.12/182.65 tff(6303,plain,
% 290.12/182.65 (((~m_c_h_element_v_in1(c_e_h_3, c_h, s4)) | m_c_h_element_v_in2(c_e_h_3, c_h, s4) | (~node17(c_e_h_3, c_h, s4))) <=> (m_c_h_element_v_in2(c_e_h_3, c_h, s4) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s4)) | (~node17(c_e_h_3, c_h, s4)))),
% 290.12/182.65 inference(rewrite,[status(thm)],[])).
% 290.12/182.65 tff(6304,plain,
% 290.12/182.65 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s4)) | m_c_h_element_v_in2(c_e_h_3, c_h, s4) | (~node17(c_e_h_3, c_h, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_3, c_h, s4) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s4)) | (~node17(c_e_h_3, c_h, s4))))),
% 290.12/182.66 inference(monotonicity,[status(thm)],[6303])).
% 290.12/182.66 tff(6305,plain,
% 290.12/182.66 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s4)) | m_c_h_element_v_in2(c_e_h_3, c_h, s4) | (~node17(c_e_h_3, c_h, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_h, s4) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s4)) | (~node17(c_e_h_3, c_h, s4)))),
% 290.12/182.66 inference(transitivity,[status(thm)],[6304, 6302])).
% 290.12/182.66 tff(6306,plain,
% 290.12/182.66 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s4)) | m_c_h_element_v_in2(c_e_h_3, c_h, s4) | (~node17(c_e_h_3, c_h, s4)))),
% 290.12/182.66 inference(quant_inst,[status(thm)],[])).
% 290.12/182.66 tff(6307,plain,
% 290.12/182.66 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_h, s4) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s4)) | (~node17(c_e_h_3, c_h, s4))),
% 290.12/182.66 inference(modus_ponens,[status(thm)],[6306, 6305])).
% 290.12/182.66 tff(6308,plain,
% 290.12/182.66 (m_c_h_element_v_in2(c_e_h_3, c_h, s4) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s4))),
% 290.12/182.66 inference(unit_resolution,[status(thm)],[6307, 919, 6301])).
% 290.12/182.66 tff(6309,plain,
% 290.12/182.66 ($false),
% 290.12/182.66 inference(unit_resolution,[status(thm)],[6308, 6300, 6294])).
% 290.12/182.66 tff(6310,plain,(m_c_h_element_v_in2(c_e_h_3, c_h, s4) | (~node17(c_e_h_3, c_h, s4)) | (~node16(c_e_h_3, c_h, s4))), inference(lemma,lemma(discharge,[]))).
% 290.12/182.66 tff(6311,plain,
% 290.12/182.66 (m_c_h_element_v_in2(c_e_h_3, c_h, s4)),
% 290.12/182.66 inference(unit_resolution,[status(thm)],[6310, 6293, 6291])).
% 290.12/182.66 tff(6312,plain,
% 290.12/182.66 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s4)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s4)) | (~node16(c_e_h_3, c_h, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s4)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s4)) | (~node16(c_e_h_3, c_h, s4)))),
% 290.12/182.66 inference(rewrite,[status(thm)],[])).
% 290.12/182.66 tff(6313,plain,
% 290.12/182.66 (((~node16(c_e_h_3, c_h, s4)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s4)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s4))) <=> ((~m_c_h_element_v_in2(c_e_h_3, c_h, s4)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s4)) | (~node16(c_e_h_3, c_h, s4)))),
% 290.12/182.66 inference(rewrite,[status(thm)],[])).
% 290.12/182.66 tff(6314,plain,
% 290.12/182.66 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_h, s4)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s4)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s4)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s4)) | (~node16(c_e_h_3, c_h, s4))))),
% 290.12/182.66 inference(monotonicity,[status(thm)],[6313])).
% 290.12/182.66 tff(6315,plain,
% 290.12/182.66 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_h, s4)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s4)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s4)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s4)) | (~node16(c_e_h_3, c_h, s4)))),
% 290.12/182.66 inference(transitivity,[status(thm)],[6314, 6312])).
% 290.12/182.66 tff(6316,plain,
% 290.12/182.66 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_h, s4)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s4)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s4)))),
% 290.12/182.66 inference(quant_inst,[status(thm)],[])).
% 290.12/182.66 tff(6317,plain,
% 290.12/182.66 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s4)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s4)) | (~node16(c_e_h_3, c_h, s4))),
% 290.12/182.66 inference(modus_ponens,[status(thm)],[6316, 6315])).
% 290.12/182.66 tff(6318,plain,
% 290.12/182.66 ((~m_c_h_element_v_in2(c_e_h_3, c_h, s4)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s4))),
% 290.12/182.66 inference(unit_resolution,[status(thm)],[6317, 2307, 6291])).
% 290.12/182.66 tff(6319,plain,
% 290.12/182.66 (~m_c_h_element_v_in1(c_e_h_3, c_h, s4)),
% 290.12/182.66 inference(unit_resolution,[status(thm)],[6318, 6311])).
% 290.12/182.66 tff(6320,plain,
% 290.12/182.66 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s4)) | m_c_h_element_v_in1(c_e_h_3, c_h, s4) | (~node17(c_e_h_3, c_h, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s4)) | m_c_h_element_v_in1(c_e_h_3, c_h, s4) | (~node17(c_e_h_3, c_h, s4)))),
% 290.12/182.66 inference(rewrite,[status(thm)],[])).
% 290.12/182.66 tff(6321,plain,
% 290.12/182.66 ((m_c_h_element_v_in1(c_e_h_3, c_h, s4) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s4)) | (~node17(c_e_h_3, c_h, s4))) <=> ((~m_c_h_element_v_in2(c_e_h_3, c_h, s4)) | m_c_h_element_v_in1(c_e_h_3, c_h, s4) | (~node17(c_e_h_3, c_h, s4)))),
% 290.12/182.66 inference(rewrite,[status(thm)],[])).
% 290.12/182.66 tff(6322,plain,
% 290.12/182.66 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s4) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s4)) | (~node17(c_e_h_3, c_h, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s4)) | m_c_h_element_v_in1(c_e_h_3, c_h, s4) | (~node17(c_e_h_3, c_h, s4))))),
% 290.12/182.66 inference(monotonicity,[status(thm)],[6321])).
% 290.12/182.66 tff(6323,plain,
% 290.12/182.66 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s4) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s4)) | (~node17(c_e_h_3, c_h, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s4)) | m_c_h_element_v_in1(c_e_h_3, c_h, s4) | (~node17(c_e_h_3, c_h, s4)))),
% 290.12/182.66 inference(transitivity,[status(thm)],[6322, 6320])).
% 290.12/182.66 tff(6324,plain,
% 290.12/182.66 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s4) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s4)) | (~node17(c_e_h_3, c_h, s4)))),
% 290.12/182.66 inference(quant_inst,[status(thm)],[])).
% 290.12/182.66 tff(6325,plain,
% 290.12/182.66 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s4)) | m_c_h_element_v_in1(c_e_h_3, c_h, s4) | (~node17(c_e_h_3, c_h, s4))),
% 290.12/182.66 inference(modus_ponens,[status(thm)],[6324, 6323])).
% 290.12/182.66 tff(6326,plain,
% 290.12/182.66 ((~m_c_h_element_v_in2(c_e_h_3, c_h, s4)) | m_c_h_element_v_in1(c_e_h_3, c_h, s4)),
% 290.12/182.66 inference(unit_resolution,[status(thm)],[6325, 859, 6293])).
% 290.12/182.66 tff(6327,plain,
% 290.12/182.66 ($false),
% 290.12/182.66 inference(unit_resolution,[status(thm)],[6326, 6319, 6311])).
% 290.12/182.66 tff(6328,plain,(m_c_h_element_v_out(c_e_h_3, c_h, s4) | (~m_c_h_element_v_out(c_e_h_3, c_h, s5)) | node14(c_e_h_3, c_h, s4, s5)), inference(lemma,lemma(discharge,[]))).
% 290.12/182.66 tff(6329,plain,
% 290.12/182.66 (node14(c_e_h_3, c_h, s4, s5)),
% 290.12/182.66 inference(unit_resolution,[status(thm)],[6328, 6259, 2341])).
% 290.12/182.66 tff(6330,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_h, s4)), introduced(assumption)).
% 290.12/182.66 tff(6331,assumption,(node14(c_e_h_3, c_h, s4, s5)), introduced(assumption)).
% 290.12/182.66 tff(6332,plain,
% 290.12/182.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s4) | (~m_c_h_element_v_out(c_e_h_3, c_h, s5)) | (~node14(c_e_h_3, c_h, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_h, s4) | (~m_c_h_element_v_out(c_e_h_3, c_h, s5)) | (~node14(c_e_h_3, c_h, s4, s5)))),
% 290.12/182.66 inference(rewrite,[status(thm)],[])).
% 290.12/182.66 tff(6333,plain,
% 290.12/182.66 (((~node14(c_e_h_3, c_h, s4, s5)) | m_c_h_element_v_in1(c_e_h_3, c_h, s4) | (~m_c_h_element_v_out(c_e_h_3, c_h, s5))) <=> (m_c_h_element_v_in1(c_e_h_3, c_h, s4) | (~m_c_h_element_v_out(c_e_h_3, c_h, s5)) | (~node14(c_e_h_3, c_h, s4, s5)))),
% 290.12/182.66 inference(rewrite,[status(thm)],[])).
% 290.12/182.66 tff(6334,plain,
% 290.12/182.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s4, s5)) | m_c_h_element_v_in1(c_e_h_3, c_h, s4) | (~m_c_h_element_v_out(c_e_h_3, c_h, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s4) | (~m_c_h_element_v_out(c_e_h_3, c_h, s5)) | (~node14(c_e_h_3, c_h, s4, s5))))),
% 290.12/182.66 inference(monotonicity,[status(thm)],[6333])).
% 290.12/182.66 tff(6335,plain,
% 290.12/182.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s4, s5)) | m_c_h_element_v_in1(c_e_h_3, c_h, s4) | (~m_c_h_element_v_out(c_e_h_3, c_h, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_h, s4) | (~m_c_h_element_v_out(c_e_h_3, c_h, s5)) | (~node14(c_e_h_3, c_h, s4, s5)))),
% 290.12/182.66 inference(transitivity,[status(thm)],[6334, 6332])).
% 290.12/182.66 tff(6336,plain,
% 290.12/182.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s4, s5)) | m_c_h_element_v_in1(c_e_h_3, c_h, s4) | (~m_c_h_element_v_out(c_e_h_3, c_h, s5)))),
% 290.12/182.66 inference(quant_inst,[status(thm)],[])).
% 290.12/182.66 tff(6337,plain,
% 290.12/182.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_h, s4) | (~m_c_h_element_v_out(c_e_h_3, c_h, s5)) | (~node14(c_e_h_3, c_h, s4, s5))),
% 290.12/182.66 inference(modus_ponens,[status(thm)],[6336, 6335])).
% 290.12/182.66 tff(6338,plain,
% 290.12/182.66 ($false),
% 290.12/182.66 inference(unit_resolution,[status(thm)],[6337, 223, 6259, 6331, 6330])).
% 290.12/182.66 tff(6339,plain,((~node14(c_e_h_3, c_h, s4, s5)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s5)) | m_c_h_element_v_in1(c_e_h_3, c_h, s4)), inference(lemma,lemma(discharge,[]))).
% 290.12/182.66 tff(6340,plain,
% 290.12/182.66 (m_c_h_element_v_in1(c_e_h_3, c_h, s4)),
% 290.12/182.66 inference(unit_resolution,[status(thm)],[6339, 6329, 6259])).
% 290.12/182.66 tff(6341,plain,
% 290.12/182.66 ((~m_c_h_element_v_in1(c_e_h_3, c_h, s4)) | (~node17(c_e_h_3, c_h, s4))),
% 290.12/182.66 inference(unit_resolution,[status(thm)],[6307, 919, 6294])).
% 290.12/182.66 tff(6342,plain,
% 290.12/182.66 ($false),
% 290.12/182.66 inference(unit_resolution,[status(thm)],[6341, 6340, 6275])).
% 290.12/182.66 tff(6343,plain,((~m_c_h_element_v_out(c_e_h_3, c_h, s5)) | m_c_h_element_v_in2(c_e_h_3, c_h, s4) | m_c_h_element_v_out(c_e_h_3, c_h, s4)), inference(lemma,lemma(discharge,[]))).
% 290.12/182.66 tff(6344,plain,
% 290.12/182.66 ((~m_c_h_element_v_out(c_e_h_3, c_h, s5)) | m_c_h_element_v_in2(c_e_h_3, c_h, s4)),
% 290.12/182.66 inference(unit_resolution,[status(thm)],[6343, 2339])).
% 290.12/182.66 tff(6345,plain,
% 290.12/182.66 (~m_c_h_element_v_out(c_e_h_3, c_h, s5)),
% 290.12/182.66 inference(unit_resolution,[status(thm)],[6344, 6258])).
% 290.12/182.66 tff(6346,assumption,(m_c_h_element_v_in2(c_e_h_3, c_h, s5)), introduced(assumption)).
% 290.12/182.66 tff(6347,plain,
% 290.12/182.66 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s5)) | m_or_h_gate_v_out(c_e_h_3, c_j, s5))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s5)) | m_or_h_gate_v_out(c_e_h_3, c_j, s5))),
% 290.12/182.67 inference(rewrite,[status(thm)],[])).
% 290.12/182.67 tff(6348,plain,
% 290.12/182.67 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s5)) | m_or_h_gate_v_out(c_e_h_3, c_j, s5))),
% 290.12/182.67 inference(quant_inst,[status(thm)],[])).
% 290.12/182.67 tff(6349,plain,
% 290.12/182.67 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s5)) | m_or_h_gate_v_out(c_e_h_3, c_j, s5)),
% 290.12/182.67 inference(modus_ponens,[status(thm)],[6348, 6347])).
% 290.12/182.67 tff(6350,plain,
% 290.12/182.67 ($false),
% 290.12/182.67 inference(unit_resolution,[status(thm)],[6349, 1174, 4065, 6346])).
% 290.12/182.67 tff(6351,plain,(m_or_h_gate_v_out(c_e_h_3, c_j, s5) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s5))), inference(lemma,lemma(discharge,[]))).
% 290.12/182.67 tff(6352,plain,
% 290.12/182.67 (~m_c_h_element_v_in2(c_e_h_3, c_h, s5)),
% 290.12/182.67 inference(unit_resolution,[status(thm)],[6351, 4064])).
% 290.12/182.67 tff(6353,assumption,(m_c_h_element_v_out(c_e_h_3, c_h, s6)), introduced(assumption)).
% 290.12/182.67 tff(6354,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_h, s5)), introduced(assumption)).
% 290.12/182.67 tff(6355,assumption,(~m_c_h_element_v_out(c_e_h_3, c_h, s5)), introduced(assumption)).
% 290.12/182.67 tff(6356,assumption,(node15(c_e_h_3, c_h, s5, s6)), introduced(assumption)).
% 290.12/182.67 tff(6357,plain,
% 290.12/182.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s6)) | (~node15(c_e_h_3, c_h, s5, s6)) | m_c_h_element_v_out(c_e_h_3, c_h, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s6)) | (~node15(c_e_h_3, c_h, s5, s6)) | m_c_h_element_v_out(c_e_h_3, c_h, s5))),
% 290.12/182.67 inference(rewrite,[status(thm)],[])).
% 290.12/182.67 tff(6358,plain,
% 290.12/182.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s6)) | (~node15(c_e_h_3, c_h, s5, s6)) | m_c_h_element_v_out(c_e_h_3, c_h, s5))),
% 290.12/182.67 inference(quant_inst,[status(thm)],[])).
% 290.12/182.67 tff(6359,plain,
% 290.12/182.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s6)) | (~node15(c_e_h_3, c_h, s5, s6)) | m_c_h_element_v_out(c_e_h_3, c_h, s5)),
% 290.12/182.67 inference(modus_ponens,[status(thm)],[6358, 6357])).
% 290.12/182.67 tff(6360,plain,
% 290.12/182.67 ($false),
% 290.12/182.67 inference(unit_resolution,[status(thm)],[6359, 147, 6355, 6356, 6353])).
% 290.12/182.67 tff(6361,plain,((~node15(c_e_h_3, c_h, s5, s6)) | m_c_h_element_v_out(c_e_h_3, c_h, s5) | (~m_c_h_element_v_out(c_e_h_3, c_h, s6))), inference(lemma,lemma(discharge,[]))).
% 290.12/182.67 tff(6362,plain,
% 290.12/182.67 (~node15(c_e_h_3, c_h, s5, s6)),
% 290.12/182.67 inference(unit_resolution,[status(thm)],[6361, 6353, 6355])).
% 290.12/182.67 tff(6363,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_h, s5)), introduced(assumption)).
% 290.12/182.67 tff(6364,assumption,(~node15(c_e_h_3, c_h, s5, s6)), introduced(assumption)).
% 290.12/182.67 tff(6365,plain,
% 290.12/182.67 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_h, s5)) | m_c_h_element_v_in1(c_e_h_3, c_h, s5) | m_c_h_element_v_in2(c_e_h_3, c_h, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_h, s5)) | m_c_h_element_v_in1(c_e_h_3, c_h, s5) | m_c_h_element_v_in2(c_e_h_3, c_h, s5))),
% 290.12/182.67 inference(rewrite,[status(thm)],[])).
% 290.12/182.67 tff(6366,plain,
% 290.12/182.67 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_h, s5)) | m_c_h_element_v_in1(c_e_h_3, c_h, s5) | m_c_h_element_v_in2(c_e_h_3, c_h, s5))),
% 290.12/182.67 inference(quant_inst,[status(thm)],[])).
% 290.12/182.67 tff(6367,plain,
% 290.12/182.67 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_h, s5)) | m_c_h_element_v_in1(c_e_h_3, c_h, s5) | m_c_h_element_v_in2(c_e_h_3, c_h, s5)),
% 290.12/182.67 inference(modus_ponens,[status(thm)],[6366, 6365])).
% 290.12/182.67 tff(6368,plain,
% 290.12/182.67 ((~node16(c_e_h_3, c_h, s5)) | m_c_h_element_v_in1(c_e_h_3, c_h, s5)),
% 290.12/182.67 inference(unit_resolution,[status(thm)],[6367, 178, 6354])).
% 290.12/182.67 tff(6369,plain,
% 290.12/182.67 (~node16(c_e_h_3, c_h, s5)),
% 290.12/182.67 inference(unit_resolution,[status(thm)],[6368, 6363])).
% 290.12/182.67 tff(6370,plain,
% 290.12/182.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s5, s6)) | node19(c_e_h_3, c_h, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s5, s6)) | node19(c_e_h_3, c_h, s5, s6))),
% 290.12/182.67 inference(rewrite,[status(thm)],[])).
% 290.12/182.67 tff(6371,plain,
% 290.12/182.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s5, s6)) | node19(c_e_h_3, c_h, s5, s6))),
% 290.12/182.67 inference(quant_inst,[status(thm)],[])).
% 290.12/182.67 tff(6372,plain,
% 290.12/182.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s5, s6)) | node19(c_e_h_3, c_h, s5, s6)),
% 290.12/182.67 inference(modus_ponens,[status(thm)],[6371, 6370])).
% 290.12/182.67 tff(6373,plain,
% 290.12/182.67 (node19(c_e_h_3, c_h, s5, s6)),
% 290.12/182.67 inference(unit_resolution,[status(thm)],[6372, 190, 1406])).
% 290.12/182.67 tff(6374,plain,
% 290.12/182.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s5) | (~node19(c_e_h_3, c_h, s5, s6)) | node14(c_e_h_3, c_h, s5, s6) | node15(c_e_h_3, c_h, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_h, s5) | (~node19(c_e_h_3, c_h, s5, s6)) | node14(c_e_h_3, c_h, s5, s6) | node15(c_e_h_3, c_h, s5, s6))),
% 290.12/182.67 inference(rewrite,[status(thm)],[])).
% 290.12/182.67 tff(6375,plain,
% 290.12/182.67 ((node16(c_e_h_3, c_h, s5) | node14(c_e_h_3, c_h, s5, s6) | node15(c_e_h_3, c_h, s5, s6) | (~node19(c_e_h_3, c_h, s5, s6))) <=> (node16(c_e_h_3, c_h, s5) | (~node19(c_e_h_3, c_h, s5, s6)) | node14(c_e_h_3, c_h, s5, s6) | node15(c_e_h_3, c_h, s5, s6))),
% 290.12/182.67 inference(rewrite,[status(thm)],[])).
% 290.12/182.67 tff(6376,plain,
% 290.12/182.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s5) | node14(c_e_h_3, c_h, s5, s6) | node15(c_e_h_3, c_h, s5, s6) | (~node19(c_e_h_3, c_h, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s5) | (~node19(c_e_h_3, c_h, s5, s6)) | node14(c_e_h_3, c_h, s5, s6) | node15(c_e_h_3, c_h, s5, s6)))),
% 290.12/182.67 inference(monotonicity,[status(thm)],[6375])).
% 290.12/182.67 tff(6377,plain,
% 290.12/182.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s5) | node14(c_e_h_3, c_h, s5, s6) | node15(c_e_h_3, c_h, s5, s6) | (~node19(c_e_h_3, c_h, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_h, s5) | (~node19(c_e_h_3, c_h, s5, s6)) | node14(c_e_h_3, c_h, s5, s6) | node15(c_e_h_3, c_h, s5, s6))),
% 290.12/182.67 inference(transitivity,[status(thm)],[6376, 6374])).
% 290.12/182.67 tff(6378,plain,
% 290.12/182.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s5) | node14(c_e_h_3, c_h, s5, s6) | node15(c_e_h_3, c_h, s5, s6) | (~node19(c_e_h_3, c_h, s5, s6)))),
% 290.12/182.67 inference(quant_inst,[status(thm)],[])).
% 290.12/182.67 tff(6379,plain,
% 290.12/182.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_h, s5) | (~node19(c_e_h_3, c_h, s5, s6)) | node14(c_e_h_3, c_h, s5, s6) | node15(c_e_h_3, c_h, s5, s6)),
% 290.12/182.67 inference(modus_ponens,[status(thm)],[6378, 6377])).
% 290.12/182.67 tff(6380,plain,
% 290.12/182.67 (node16(c_e_h_3, c_h, s5) | node14(c_e_h_3, c_h, s5, s6) | node15(c_e_h_3, c_h, s5, s6)),
% 290.12/182.67 inference(unit_resolution,[status(thm)],[6379, 204, 6373])).
% 290.12/182.67 tff(6381,plain,
% 290.12/182.67 (node14(c_e_h_3, c_h, s5, s6)),
% 290.12/182.67 inference(unit_resolution,[status(thm)],[6380, 6369, 6364])).
% 290.12/182.67 tff(6382,plain,
% 290.12/182.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s5) | (~m_c_h_element_v_out(c_e_h_3, c_h, s6)) | (~node14(c_e_h_3, c_h, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_h, s5) | (~m_c_h_element_v_out(c_e_h_3, c_h, s6)) | (~node14(c_e_h_3, c_h, s5, s6)))),
% 290.12/182.67 inference(rewrite,[status(thm)],[])).
% 290.12/182.67 tff(6383,plain,
% 290.12/182.67 (((~node14(c_e_h_3, c_h, s5, s6)) | m_c_h_element_v_in1(c_e_h_3, c_h, s5) | (~m_c_h_element_v_out(c_e_h_3, c_h, s6))) <=> (m_c_h_element_v_in1(c_e_h_3, c_h, s5) | (~m_c_h_element_v_out(c_e_h_3, c_h, s6)) | (~node14(c_e_h_3, c_h, s5, s6)))),
% 290.12/182.67 inference(rewrite,[status(thm)],[])).
% 290.12/182.67 tff(6384,plain,
% 290.12/182.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s5, s6)) | m_c_h_element_v_in1(c_e_h_3, c_h, s5) | (~m_c_h_element_v_out(c_e_h_3, c_h, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s5) | (~m_c_h_element_v_out(c_e_h_3, c_h, s6)) | (~node14(c_e_h_3, c_h, s5, s6))))),
% 290.12/182.67 inference(monotonicity,[status(thm)],[6383])).
% 290.12/182.67 tff(6385,plain,
% 290.12/182.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s5, s6)) | m_c_h_element_v_in1(c_e_h_3, c_h, s5) | (~m_c_h_element_v_out(c_e_h_3, c_h, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_h, s5) | (~m_c_h_element_v_out(c_e_h_3, c_h, s6)) | (~node14(c_e_h_3, c_h, s5, s6)))),
% 290.12/182.67 inference(transitivity,[status(thm)],[6384, 6382])).
% 290.12/182.67 tff(6386,plain,
% 290.12/182.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s5, s6)) | m_c_h_element_v_in1(c_e_h_3, c_h, s5) | (~m_c_h_element_v_out(c_e_h_3, c_h, s6)))),
% 290.12/182.67 inference(quant_inst,[status(thm)],[])).
% 290.12/182.67 tff(6387,plain,
% 290.12/182.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_h, s5) | (~m_c_h_element_v_out(c_e_h_3, c_h, s6)) | (~node14(c_e_h_3, c_h, s5, s6))),
% 290.12/182.67 inference(modus_ponens,[status(thm)],[6386, 6385])).
% 290.12/182.67 tff(6388,plain,
% 290.12/182.67 ($false),
% 290.12/182.67 inference(unit_resolution,[status(thm)],[6387, 223, 6381, 6363, 6353])).
% 290.12/182.67 tff(6389,plain,(m_c_h_element_v_in1(c_e_h_3, c_h, s5) | (~m_c_h_element_v_out(c_e_h_3, c_h, s6)) | node15(c_e_h_3, c_h, s5, s6) | m_c_h_element_v_in2(c_e_h_3, c_h, s5)), inference(lemma,lemma(discharge,[]))).
% 290.12/182.67 tff(6390,plain,
% 290.12/182.67 (m_c_h_element_v_in1(c_e_h_3, c_h, s5)),
% 290.12/182.67 inference(unit_resolution,[status(thm)],[6389, 6353, 6362, 6354])).
% 290.12/182.67 tff(6391,plain,
% 290.12/182.67 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s5)) | m_c_h_element_v_in2(c_e_h_3, c_h, s5) | (~node17(c_e_h_3, c_h, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s5)) | m_c_h_element_v_in2(c_e_h_3, c_h, s5) | (~node17(c_e_h_3, c_h, s5)))),
% 290.12/182.67 inference(rewrite,[status(thm)],[])).
% 290.12/182.67 tff(6392,plain,
% 290.12/182.67 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s5)) | m_c_h_element_v_in2(c_e_h_3, c_h, s5) | (~node17(c_e_h_3, c_h, s5)))),
% 290.12/182.68 inference(quant_inst,[status(thm)],[])).
% 290.12/182.68 tff(6393,plain,
% 290.12/182.68 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s5)) | m_c_h_element_v_in2(c_e_h_3, c_h, s5) | (~node17(c_e_h_3, c_h, s5))),
% 290.12/182.68 inference(modus_ponens,[status(thm)],[6392, 6391])).
% 290.12/182.68 tff(6394,plain,
% 290.12/182.68 ((~m_c_h_element_v_in1(c_e_h_3, c_h, s5)) | (~node17(c_e_h_3, c_h, s5))),
% 290.12/182.68 inference(unit_resolution,[status(thm)],[6393, 919, 6354])).
% 290.12/182.68 tff(6395,plain,
% 290.12/182.68 (~node17(c_e_h_3, c_h, s5)),
% 290.12/182.68 inference(unit_resolution,[status(thm)],[6394, 6390])).
% 290.12/182.68 tff(6396,plain,
% 290.12/182.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s5) | (~node19(c_e_h_3, c_h, s5, s6)) | node18(c_e_h_3, c_h, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_h, s5) | (~node19(c_e_h_3, c_h, s5, s6)) | node18(c_e_h_3, c_h, s5, s6))),
% 290.12/182.68 inference(rewrite,[status(thm)],[])).
% 290.12/182.68 tff(6397,plain,
% 290.12/182.68 ((node17(c_e_h_3, c_h, s5) | node18(c_e_h_3, c_h, s5, s6) | (~node19(c_e_h_3, c_h, s5, s6))) <=> (node17(c_e_h_3, c_h, s5) | (~node19(c_e_h_3, c_h, s5, s6)) | node18(c_e_h_3, c_h, s5, s6))),
% 290.12/182.68 inference(rewrite,[status(thm)],[])).
% 290.12/182.68 tff(6398,plain,
% 290.12/182.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s5) | node18(c_e_h_3, c_h, s5, s6) | (~node19(c_e_h_3, c_h, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s5) | (~node19(c_e_h_3, c_h, s5, s6)) | node18(c_e_h_3, c_h, s5, s6)))),
% 290.12/182.68 inference(monotonicity,[status(thm)],[6397])).
% 290.12/182.68 tff(6399,plain,
% 290.12/182.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s5) | node18(c_e_h_3, c_h, s5, s6) | (~node19(c_e_h_3, c_h, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_h, s5) | (~node19(c_e_h_3, c_h, s5, s6)) | node18(c_e_h_3, c_h, s5, s6))),
% 290.12/182.68 inference(transitivity,[status(thm)],[6398, 6396])).
% 290.12/182.68 tff(6400,plain,
% 290.12/182.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s5) | node18(c_e_h_3, c_h, s5, s6) | (~node19(c_e_h_3, c_h, s5, s6)))),
% 290.12/182.68 inference(quant_inst,[status(thm)],[])).
% 290.12/182.68 tff(6401,plain,
% 290.12/182.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_h, s5) | (~node19(c_e_h_3, c_h, s5, s6)) | node18(c_e_h_3, c_h, s5, s6)),
% 290.12/182.68 inference(modus_ponens,[status(thm)],[6400, 6399])).
% 290.12/182.68 tff(6402,plain,
% 290.12/182.68 (node17(c_e_h_3, c_h, s5) | node18(c_e_h_3, c_h, s5, s6)),
% 290.12/182.68 inference(unit_resolution,[status(thm)],[6401, 776, 6373])).
% 290.12/182.68 tff(6403,plain,
% 290.12/182.68 (node18(c_e_h_3, c_h, s5, s6)),
% 290.12/182.68 inference(unit_resolution,[status(thm)],[6402, 6395])).
% 290.12/182.68 tff(6404,plain,
% 290.12/182.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_h, s5) | (~m_c_h_element_v_out(c_e_h_3, c_h, s6)) | (~node18(c_e_h_3, c_h, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s5) | (~m_c_h_element_v_out(c_e_h_3, c_h, s6)) | (~node18(c_e_h_3, c_h, s5, s6)))),
% 290.12/182.68 inference(rewrite,[status(thm)],[])).
% 290.12/182.68 tff(6405,plain,
% 290.12/182.68 (((~m_c_h_element_v_out(c_e_h_3, c_h, s6)) | m_c_h_element_v_out(c_e_h_3, c_h, s5) | (~node18(c_e_h_3, c_h, s5, s6))) <=> (m_c_h_element_v_out(c_e_h_3, c_h, s5) | (~m_c_h_element_v_out(c_e_h_3, c_h, s6)) | (~node18(c_e_h_3, c_h, s5, s6)))),
% 290.12/182.68 inference(rewrite,[status(thm)],[])).
% 290.12/182.68 tff(6406,plain,
% 290.12/182.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s6)) | m_c_h_element_v_out(c_e_h_3, c_h, s5) | (~node18(c_e_h_3, c_h, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_h, s5) | (~m_c_h_element_v_out(c_e_h_3, c_h, s6)) | (~node18(c_e_h_3, c_h, s5, s6))))),
% 290.12/182.68 inference(monotonicity,[status(thm)],[6405])).
% 290.12/182.68 tff(6407,plain,
% 290.12/182.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s6)) | m_c_h_element_v_out(c_e_h_3, c_h, s5) | (~node18(c_e_h_3, c_h, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s5) | (~m_c_h_element_v_out(c_e_h_3, c_h, s6)) | (~node18(c_e_h_3, c_h, s5, s6)))),
% 290.12/182.68 inference(transitivity,[status(thm)],[6406, 6404])).
% 290.12/182.68 tff(6408,plain,
% 290.12/182.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s6)) | m_c_h_element_v_out(c_e_h_3, c_h, s5) | (~node18(c_e_h_3, c_h, s5, s6)))),
% 290.12/182.68 inference(quant_inst,[status(thm)],[])).
% 290.12/182.68 tff(6409,plain,
% 290.12/182.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s5) | (~m_c_h_element_v_out(c_e_h_3, c_h, s6)) | (~node18(c_e_h_3, c_h, s5, s6))),
% 290.12/182.68 inference(modus_ponens,[status(thm)],[6408, 6407])).
% 290.12/182.68 tff(6410,plain,
% 290.12/182.68 ($false),
% 290.12/182.68 inference(unit_resolution,[status(thm)],[6409, 753, 6355, 6403, 6353])).
% 290.12/182.68 tff(6411,plain,((~m_c_h_element_v_out(c_e_h_3, c_h, s6)) | m_c_h_element_v_out(c_e_h_3, c_h, s5) | m_c_h_element_v_in2(c_e_h_3, c_h, s5)), inference(lemma,lemma(discharge,[]))).
% 290.12/182.68 tff(6412,plain,
% 290.12/182.68 ((~m_c_h_element_v_out(c_e_h_3, c_h, s6)) | m_c_h_element_v_out(c_e_h_3, c_h, s5)),
% 290.12/182.68 inference(unit_resolution,[status(thm)],[6411, 6352])).
% 290.12/182.68 tff(6413,plain,
% 290.12/182.68 (~m_c_h_element_v_out(c_e_h_3, c_h, s6)),
% 290.12/182.68 inference(unit_resolution,[status(thm)],[6412, 6345])).
% 290.12/182.68 tff(6414,plain,
% 290.12/182.68 (^[I0: $i, X: $i] : refl((m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X)) <=> (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X)))),
% 290.12/182.68 inference(bind,[status(th)],[])).
% 290.12/182.68 tff(6415,plain,
% 290.12/182.68 (![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X)) <=> ![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))),
% 290.12/182.68 inference(quant_intro,[status(thm)],[6414])).
% 290.12/182.68 tff(6416,plain,
% 290.12/182.68 (![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X)) <=> ![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))),
% 290.12/182.68 inference(rewrite,[status(thm)],[])).
% 290.12/182.68 tff(6417,axiom,(![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_45')).
% 290.12/182.68 tff(6418,plain,
% 290.12/182.68 (![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))),
% 290.12/182.68 inference(modus_ponens,[status(thm)],[6417, 6416])).
% 290.12/182.68 tff(6419,plain,(
% 290.12/182.68 ![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))),
% 290.12/182.68 inference(skolemize,[status(sab)],[6418])).
% 290.12/182.68 tff(6420,plain,
% 290.12/182.68 (![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))),
% 290.12/182.68 inference(modus_ponens,[status(thm)],[6419, 6415])).
% 290.12/182.68 tff(6421,plain,
% 290.12/182.68 (((~![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))) | (m_and_h_gate_v_in2(c_e_h_3, c_k, s6) | m_c_h_element_v_out(c_e_h_3, c_h, s6))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))) | m_and_h_gate_v_in2(c_e_h_3, c_k, s6) | m_c_h_element_v_out(c_e_h_3, c_h, s6))),
% 290.12/182.68 inference(rewrite,[status(thm)],[])).
% 290.12/182.68 tff(6422,plain,
% 290.21/182.69 ((~![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))) | (m_and_h_gate_v_in2(c_e_h_3, c_k, s6) | m_c_h_element_v_out(c_e_h_3, c_h, s6))),
% 290.21/182.69 inference(quant_inst,[status(thm)],[])).
% 290.21/182.69 tff(6423,plain,
% 290.21/182.69 ((~![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))) | m_and_h_gate_v_in2(c_e_h_3, c_k, s6) | m_c_h_element_v_out(c_e_h_3, c_h, s6)),
% 290.21/182.69 inference(modus_ponens,[status(thm)],[6422, 6421])).
% 290.21/182.69 tff(6424,plain,
% 290.21/182.69 ($false),
% 290.21/182.69 inference(unit_resolution,[status(thm)],[6423, 6420, 6413, 6245])).
% 290.21/182.69 tff(6425,plain,(m_and_h_gate_v_in2(c_e_h_3, c_k, s6)), inference(lemma,lemma(discharge,[]))).
% 290.21/182.69 tff(6426,assumption,(node21(c_e_h_3, c_k, s6, s7)), introduced(assumption)).
% 290.21/182.69 tff(6427,plain,
% 290.21/182.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_k, s6)) | m_and_h_gate_v_out(c_e_h_3, c_k, s7) | (~node21(c_e_h_3, c_k, s6, s7)) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s6)) | m_and_h_gate_v_out(c_e_h_3, c_k, s7) | (~node21(c_e_h_3, c_k, s6, s7)) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s6)))),
% 290.21/182.69 inference(rewrite,[status(thm)],[])).
% 290.21/182.69 tff(6428,plain,
% 290.21/182.69 (((~node21(c_e_h_3, c_k, s6, s7)) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s6)) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s6)) | m_and_h_gate_v_out(c_e_h_3, c_k, s7)) <=> ((~m_and_h_gate_v_in1(c_e_h_3, c_k, s6)) | m_and_h_gate_v_out(c_e_h_3, c_k, s7) | (~node21(c_e_h_3, c_k, s6, s7)) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s6)))),
% 290.21/182.69 inference(rewrite,[status(thm)],[])).
% 290.21/182.69 tff(6429,plain,
% 290.21/182.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_k, s6, s7)) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s6)) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s6)) | m_and_h_gate_v_out(c_e_h_3, c_k, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_k, s6)) | m_and_h_gate_v_out(c_e_h_3, c_k, s7) | (~node21(c_e_h_3, c_k, s6, s7)) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s6))))),
% 290.21/182.69 inference(monotonicity,[status(thm)],[6428])).
% 290.21/182.69 tff(6430,plain,
% 290.21/182.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_k, s6, s7)) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s6)) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s6)) | m_and_h_gate_v_out(c_e_h_3, c_k, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s6)) | m_and_h_gate_v_out(c_e_h_3, c_k, s7) | (~node21(c_e_h_3, c_k, s6, s7)) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s6)))),
% 290.21/182.69 inference(transitivity,[status(thm)],[6429, 6427])).
% 290.21/182.69 tff(6431,plain,
% 290.21/182.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_k, s6, s7)) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s6)) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s6)) | m_and_h_gate_v_out(c_e_h_3, c_k, s7))),
% 290.21/182.69 inference(quant_inst,[status(thm)],[])).
% 290.21/182.69 tff(6432,plain,
% 290.21/182.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s6)) | m_and_h_gate_v_out(c_e_h_3, c_k, s7) | (~node21(c_e_h_3, c_k, s6, s7)) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s6))),
% 290.21/182.69 inference(modus_ponens,[status(thm)],[6431, 6430])).
% 290.21/182.69 tff(6433,plain,
% 290.21/182.69 ($false),
% 290.21/182.69 inference(unit_resolution,[status(thm)],[6432, 5851, 6426, 6243, 6425, 6244])).
% 290.21/182.69 tff(6434,plain,((~node21(c_e_h_3, c_k, s6, s7)) | m_and_h_gate_v_out(c_e_h_3, c_k, s7) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s6))), inference(lemma,lemma(discharge,[]))).
% 290.21/182.69 tff(6435,plain,
% 290.21/182.69 (~node21(c_e_h_3, c_k, s6, s7)),
% 290.21/182.69 inference(unit_resolution,[status(thm)],[6434, 6243, 6244])).
% 290.21/182.69 tff(6436,plain,
% 290.21/182.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_3, c_k, s6, s7) | node22(c_e_h_3, c_k, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_3, c_k, s6, s7) | node22(c_e_h_3, c_k, s6, s7))),
% 290.21/182.69 inference(rewrite,[status(thm)],[])).
% 290.21/182.69 tff(6437,plain,
% 290.21/182.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_3, c_k, s6, s7) | node22(c_e_h_3, c_k, s6, s7))),
% 290.21/182.69 inference(quant_inst,[status(thm)],[])).
% 290.21/182.69 tff(6438,plain,
% 290.21/182.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_3, c_k, s6, s7) | node22(c_e_h_3, c_k, s6, s7)),
% 290.21/182.69 inference(modus_ponens,[status(thm)],[6437, 6436])).
% 290.21/182.69 tff(6439,plain,
% 290.21/182.69 (node21(c_e_h_3, c_k, s6, s7) | node22(c_e_h_3, c_k, s6, s7)),
% 290.21/182.69 inference(unit_resolution,[status(thm)],[6438, 82, 1844])).
% 290.21/182.69 tff(6440,plain,
% 290.21/182.69 (node22(c_e_h_3, c_k, s6, s7)),
% 290.21/182.69 inference(unit_resolution,[status(thm)],[6439, 6435])).
% 290.21/182.69 tff(6441,plain,
% 290.21/182.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s6)) | m_and_h_gate_v_out(c_e_h_3, c_k, s7) | (~node22(c_e_h_3, c_k, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s6)) | m_and_h_gate_v_out(c_e_h_3, c_k, s7) | (~node22(c_e_h_3, c_k, s6, s7)))),
% 290.21/182.69 inference(rewrite,[status(thm)],[])).
% 290.21/182.69 tff(6442,plain,
% 290.21/182.69 ((m_and_h_gate_v_out(c_e_h_3, c_k, s7) | (~node22(c_e_h_3, c_k, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s6))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_k, s6)) | m_and_h_gate_v_out(c_e_h_3, c_k, s7) | (~node22(c_e_h_3, c_k, s6, s7)))),
% 290.21/182.69 inference(rewrite,[status(thm)],[])).
% 290.21/182.69 tff(6443,plain,
% 290.21/182.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_k, s7) | (~node22(c_e_h_3, c_k, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s6)) | m_and_h_gate_v_out(c_e_h_3, c_k, s7) | (~node22(c_e_h_3, c_k, s6, s7))))),
% 290.21/182.69 inference(monotonicity,[status(thm)],[6442])).
% 290.21/182.69 tff(6444,plain,
% 290.21/182.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_k, s7) | (~node22(c_e_h_3, c_k, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s6)) | m_and_h_gate_v_out(c_e_h_3, c_k, s7) | (~node22(c_e_h_3, c_k, s6, s7)))),
% 290.21/182.69 inference(transitivity,[status(thm)],[6443, 6441])).
% 290.21/182.69 tff(6445,plain,
% 290.21/182.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_k, s7) | (~node22(c_e_h_3, c_k, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s6)))),
% 290.21/182.69 inference(quant_inst,[status(thm)],[])).
% 290.21/182.69 tff(6446,plain,
% 290.21/182.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s6)) | m_and_h_gate_v_out(c_e_h_3, c_k, s7) | (~node22(c_e_h_3, c_k, s6, s7))),
% 290.21/182.69 inference(modus_ponens,[status(thm)],[6445, 6444])).
% 290.21/182.69 tff(6447,plain,
% 290.21/182.69 ($false),
% 290.21/182.69 inference(unit_resolution,[status(thm)],[6446, 5871, 6440, 6243, 4450])).
% 290.21/182.69 tff(6448,plain,(m_and_h_gate_v_out(c_e_h_3, c_k, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s6)) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s6))), inference(lemma,lemma(discharge,[]))).
% 290.21/182.69 tff(6449,plain,
% 290.21/182.69 (m_and_h_gate_v_out(c_e_h_3, c_k, s7)),
% 290.21/182.69 inference(unit_resolution,[status(thm)],[6448, 6242, 6233])).
% 290.21/182.69 tff(6450,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_l, s8)), introduced(assumption)).
% 290.21/182.69 tff(6451,plain,
% 290.21/182.69 ((~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s6)),
% 290.21/182.69 inference(unit_resolution,[status(thm)],[4904, 6238])).
% 290.21/182.69 tff(6452,plain,
% 290.21/182.69 (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)),
% 290.21/182.69 inference(unit_resolution,[status(thm)],[6451, 4493])).
% 290.21/182.69 tff(6453,plain,
% 290.21/182.69 (m_or_h_gate_v_in1(c_e_h_3, c_j, s7)),
% 290.21/182.69 inference(unit_resolution,[status(thm)],[5421, 6452, 3367])).
% 290.21/182.69 tff(6454,assumption,(m_or_h_gate_v_in1(c_e_h_3, c_j, s7)), introduced(assumption)).
% 290.21/182.69 tff(6455,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_l, s7)), introduced(assumption)).
% 290.21/182.69 tff(6456,plain,
% 290.21/182.69 ($false),
% 290.21/182.69 inference(unit_resolution,[status(thm)],[5445, 1100, 6455, 6454])).
% 290.21/182.69 tff(6457,plain,((~m_or_h_gate_v_in1(c_e_h_3, c_j, s7)) | m_and_h_gate_v_out(c_e_h_3, c_l, s7)), inference(lemma,lemma(discharge,[]))).
% 290.21/182.69 tff(6458,plain,
% 290.21/182.69 (m_and_h_gate_v_out(c_e_h_3, c_l, s7)),
% 290.21/182.69 inference(unit_resolution,[status(thm)],[6457, 6453])).
% 290.21/182.69 tff(6459,assumption,(node22(c_e_h_3, c_l, s7, s8)), introduced(assumption)).
% 290.21/182.69 tff(6460,plain,
% 290.21/182.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s7)) | m_and_h_gate_v_out(c_e_h_3, c_l, s8) | (~node22(c_e_h_3, c_l, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s7)) | m_and_h_gate_v_out(c_e_h_3, c_l, s8) | (~node22(c_e_h_3, c_l, s7, s8)))),
% 290.21/182.69 inference(rewrite,[status(thm)],[])).
% 290.21/182.69 tff(6461,plain,
% 290.21/182.69 ((m_and_h_gate_v_out(c_e_h_3, c_l, s8) | (~node22(c_e_h_3, c_l, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s7))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_l, s7)) | m_and_h_gate_v_out(c_e_h_3, c_l, s8) | (~node22(c_e_h_3, c_l, s7, s8)))),
% 290.21/182.69 inference(rewrite,[status(thm)],[])).
% 290.21/182.69 tff(6462,plain,
% 290.21/182.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_l, s8) | (~node22(c_e_h_3, c_l, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s7)) | m_and_h_gate_v_out(c_e_h_3, c_l, s8) | (~node22(c_e_h_3, c_l, s7, s8))))),
% 290.21/182.69 inference(monotonicity,[status(thm)],[6461])).
% 290.21/182.69 tff(6463,plain,
% 290.21/182.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_l, s8) | (~node22(c_e_h_3, c_l, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s7)) | m_and_h_gate_v_out(c_e_h_3, c_l, s8) | (~node22(c_e_h_3, c_l, s7, s8)))),
% 290.21/182.69 inference(transitivity,[status(thm)],[6462, 6460])).
% 290.21/182.69 tff(6464,plain,
% 290.21/182.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_l, s8) | (~node22(c_e_h_3, c_l, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s7)))),
% 290.21/182.69 inference(quant_inst,[status(thm)],[])).
% 290.21/182.69 tff(6465,plain,
% 290.21/182.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s7)) | m_and_h_gate_v_out(c_e_h_3, c_l, s8) | (~node22(c_e_h_3, c_l, s7, s8))),
% 290.22/182.70 inference(modus_ponens,[status(thm)],[6464, 6463])).
% 290.22/182.70 tff(6466,plain,
% 290.22/182.70 ($false),
% 290.22/182.70 inference(unit_resolution,[status(thm)],[6465, 5871, 6459, 6450, 5424])).
% 290.22/182.70 tff(6467,plain,((~node22(c_e_h_3, c_l, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_l, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s7))), inference(lemma,lemma(discharge,[]))).
% 290.22/182.70 tff(6468,plain,
% 290.22/182.70 (~node22(c_e_h_3, c_l, s7, s8)),
% 290.22/182.70 inference(unit_resolution,[status(thm)],[6467, 6450, 5424])).
% 290.22/182.70 tff(6469,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_l, s7)), introduced(assumption)).
% 290.22/182.70 tff(6470,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_i, s5)), introduced(assumption)).
% 290.22/182.70 tff(6471,assumption,(m_c_h_element_v_in2(c_e_h_3, c_f, s5)), introduced(assumption)).
% 290.22/182.70 tff(6472,plain,
% 290.22/182.70 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s5)) | m_and_h_gate_v_out(c_e_h_3, c_i, s5))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s5)) | m_and_h_gate_v_out(c_e_h_3, c_i, s5))),
% 290.22/182.70 inference(rewrite,[status(thm)],[])).
% 290.22/182.70 tff(6473,plain,
% 290.22/182.70 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s5)) | m_and_h_gate_v_out(c_e_h_3, c_i, s5))),
% 290.22/182.70 inference(quant_inst,[status(thm)],[])).
% 290.22/182.70 tff(6474,plain,
% 290.22/182.70 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s5)) | m_and_h_gate_v_out(c_e_h_3, c_i, s5)),
% 290.22/182.70 inference(modus_ponens,[status(thm)],[6473, 6472])).
% 290.22/182.70 tff(6475,plain,
% 290.22/182.70 ($false),
% 290.22/182.70 inference(unit_resolution,[status(thm)],[6474, 2143, 6471, 6470])).
% 290.22/182.70 tff(6476,plain,((~m_c_h_element_v_in2(c_e_h_3, c_f, s5)) | m_and_h_gate_v_out(c_e_h_3, c_i, s5)), inference(lemma,lemma(discharge,[]))).
% 290.22/182.70 tff(6477,plain,
% 290.22/182.70 (~m_c_h_element_v_in2(c_e_h_3, c_f, s5)),
% 290.22/182.70 inference(unit_resolution,[status(thm)],[6476, 2383])).
% 290.22/182.70 tff(6478,assumption,(m_c_h_element_v_in2(c_e_h_3, c_f, s4)), introduced(assumption)).
% 290.22/182.70 tff(6479,plain,
% 290.22/182.70 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s4)) | m_and_h_gate_v_out(c_e_h_3, c_i, s4))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s4)) | m_and_h_gate_v_out(c_e_h_3, c_i, s4))),
% 290.22/182.70 inference(rewrite,[status(thm)],[])).
% 290.22/182.70 tff(6480,plain,
% 290.22/182.70 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s4)) | m_and_h_gate_v_out(c_e_h_3, c_i, s4))),
% 290.22/182.70 inference(quant_inst,[status(thm)],[])).
% 290.22/182.70 tff(6481,plain,
% 290.22/182.70 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s4)) | m_and_h_gate_v_out(c_e_h_3, c_i, s4)),
% 290.22/182.70 inference(modus_ponens,[status(thm)],[6480, 6479])).
% 290.22/182.70 tff(6482,plain,
% 290.22/182.70 ($false),
% 290.22/182.70 inference(unit_resolution,[status(thm)],[6481, 2143, 2368, 6478])).
% 290.22/182.70 tff(6483,plain,((~m_c_h_element_v_in2(c_e_h_3, c_f, s4)) | m_and_h_gate_v_out(c_e_h_3, c_i, s4)), inference(lemma,lemma(discharge,[]))).
% 290.22/182.70 tff(6484,plain,
% 290.22/182.70 (~m_c_h_element_v_in2(c_e_h_3, c_f, s4)),
% 290.22/182.70 inference(unit_resolution,[status(thm)],[6483, 1744])).
% 290.22/182.70 tff(6485,assumption,(m_c_h_element_v_out(c_e_h_3, c_f, s5)), introduced(assumption)).
% 290.22/182.70 tff(6486,plain,
% 290.22/182.70 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s3)) | m_and_h_gate_v_out(c_e_h_3, c_i, s3))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s3)) | m_and_h_gate_v_out(c_e_h_3, c_i, s3))),
% 290.22/182.70 inference(rewrite,[status(thm)],[])).
% 290.22/182.70 tff(6487,plain,
% 290.22/182.70 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s3)) | m_and_h_gate_v_out(c_e_h_3, c_i, s3))),
% 290.22/182.70 inference(quant_inst,[status(thm)],[])).
% 290.22/182.70 tff(6488,plain,
% 290.22/182.70 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s3)) | m_and_h_gate_v_out(c_e_h_3, c_i, s3)),
% 290.22/182.70 inference(modus_ponens,[status(thm)],[6487, 6486])).
% 290.22/182.70 tff(6489,plain,
% 290.22/182.70 (~m_c_h_element_v_in2(c_e_h_3, c_f, s3)),
% 290.22/182.70 inference(unit_resolution,[status(thm)],[6488, 2143, 1269])).
% 290.22/182.70 tff(6490,assumption,(m_c_h_element_v_out(c_e_h_3, c_f, s4)), introduced(assumption)).
% 290.22/182.70 tff(6491,plain,
% 290.22/182.70 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s2)) | m_and_h_gate_v_out(c_e_h_3, c_i, s2))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s2)) | m_and_h_gate_v_out(c_e_h_3, c_i, s2))),
% 290.22/182.70 inference(rewrite,[status(thm)],[])).
% 290.22/182.70 tff(6492,plain,
% 290.22/182.70 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s2)) | m_and_h_gate_v_out(c_e_h_3, c_i, s2))),
% 290.22/182.70 inference(quant_inst,[status(thm)],[])).
% 290.22/182.70 tff(6493,plain,
% 290.22/182.70 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s2)) | m_and_h_gate_v_out(c_e_h_3, c_i, s2)),
% 290.22/182.70 inference(modus_ponens,[status(thm)],[6492, 6491])).
% 290.22/182.70 tff(6494,plain,
% 290.22/182.70 (~m_c_h_element_v_in2(c_e_h_3, c_f, s2)),
% 290.22/182.70 inference(unit_resolution,[status(thm)],[6493, 2143, 903])).
% 290.22/182.70 tff(6495,assumption,(node15(c_e_h_3, c_f, s0, s1)), introduced(assumption)).
% 290.22/182.70 tff(6496,plain,
% 290.22/182.70 ($false),
% 290.22/182.70 inference(unit_resolution,[status(thm)],[6045, 147, 5682, 6025, 6495])).
% 290.22/182.70 tff(6497,plain,((~node15(c_e_h_3, c_f, s0, s1)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s1))), inference(lemma,lemma(discharge,[]))).
% 290.22/182.70 tff(6498,plain,
% 290.22/182.70 (~node15(c_e_h_3, c_f, s0, s1)),
% 290.22/182.70 inference(unit_resolution,[status(thm)],[6497, 6025])).
% 290.22/182.70 tff(6499,plain,
% 290.22/182.70 (~node16(c_e_h_3, c_f, s0)),
% 290.22/182.70 inference(unit_resolution,[status(thm)],[6016, 6023])).
% 290.22/182.70 tff(6500,plain,
% 290.22/182.70 (~node14(c_e_h_3, c_f, s0, s1)),
% 290.22/182.70 inference(unit_resolution,[status(thm)],[6033, 6023, 6025])).
% 290.22/182.70 tff(6501,plain,
% 290.22/182.70 ($false),
% 290.22/182.70 inference(unit_resolution,[status(thm)],[6041, 6500, 6499, 6498])).
% 290.22/182.70 tff(6502,plain,(m_c_h_element_v_in1(c_e_h_3, c_f, s0) | (~m_c_h_element_v_out(c_e_h_3, c_f, s1))), inference(lemma,lemma(discharge,[]))).
% 290.22/182.70 tff(6503,plain,
% 290.22/182.70 (m_c_h_element_v_in1(c_e_h_3, c_f, s0)),
% 290.22/182.70 inference(unit_resolution,[status(thm)],[6502, 6025])).
% 290.22/182.70 tff(6504,plain,
% 290.22/182.70 (~node17(c_e_h_3, c_f, s0)),
% 290.22/182.70 inference(unit_resolution,[status(thm)],[6011, 6503])).
% 290.22/182.70 tff(6505,plain,
% 290.22/182.70 (node18(c_e_h_3, c_f, s0, s1)),
% 290.22/182.70 inference(unit_resolution,[status(thm)],[5999, 6504])).
% 290.22/182.70 tff(6506,plain,
% 290.22/182.70 ($false),
% 290.22/182.70 inference(unit_resolution,[status(thm)],[5969, 753, 5682, 6025, 6505])).
% 290.22/182.70 tff(6507,plain,(~m_c_h_element_v_out(c_e_h_3, c_f, s1)), inference(lemma,lemma(discharge,[]))).
% 290.22/182.70 tff(6508,assumption,(m_c_h_element_v_out(c_e_h_3, c_f, s2)), introduced(assumption)).
% 290.22/182.70 tff(6509,assumption,(~m_c_h_element_v_out(c_e_h_3, c_f, s1)), introduced(assumption)).
% 290.22/182.70 tff(6510,assumption,(node18(c_e_h_3, c_f, s1, s2)), introduced(assumption)).
% 290.22/182.70 tff(6511,plain,
% 290.22/182.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_f, s1) | (~m_c_h_element_v_out(c_e_h_3, c_f, s2)) | (~node18(c_e_h_3, c_f, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s1) | (~m_c_h_element_v_out(c_e_h_3, c_f, s2)) | (~node18(c_e_h_3, c_f, s1, s2)))),
% 290.22/182.70 inference(rewrite,[status(thm)],[])).
% 290.22/182.70 tff(6512,plain,
% 290.22/182.70 (((~m_c_h_element_v_out(c_e_h_3, c_f, s2)) | m_c_h_element_v_out(c_e_h_3, c_f, s1) | (~node18(c_e_h_3, c_f, s1, s2))) <=> (m_c_h_element_v_out(c_e_h_3, c_f, s1) | (~m_c_h_element_v_out(c_e_h_3, c_f, s2)) | (~node18(c_e_h_3, c_f, s1, s2)))),
% 290.22/182.70 inference(rewrite,[status(thm)],[])).
% 290.22/182.70 tff(6513,plain,
% 290.22/182.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s2)) | m_c_h_element_v_out(c_e_h_3, c_f, s1) | (~node18(c_e_h_3, c_f, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_f, s1) | (~m_c_h_element_v_out(c_e_h_3, c_f, s2)) | (~node18(c_e_h_3, c_f, s1, s2))))),
% 290.22/182.70 inference(monotonicity,[status(thm)],[6512])).
% 290.22/182.70 tff(6514,plain,
% 290.22/182.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s2)) | m_c_h_element_v_out(c_e_h_3, c_f, s1) | (~node18(c_e_h_3, c_f, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s1) | (~m_c_h_element_v_out(c_e_h_3, c_f, s2)) | (~node18(c_e_h_3, c_f, s1, s2)))),
% 290.22/182.70 inference(transitivity,[status(thm)],[6513, 6511])).
% 290.22/182.70 tff(6515,plain,
% 290.22/182.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s2)) | m_c_h_element_v_out(c_e_h_3, c_f, s1) | (~node18(c_e_h_3, c_f, s1, s2)))),
% 290.22/182.70 inference(quant_inst,[status(thm)],[])).
% 290.22/182.70 tff(6516,plain,
% 290.22/182.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s1) | (~m_c_h_element_v_out(c_e_h_3, c_f, s2)) | (~node18(c_e_h_3, c_f, s1, s2))),
% 290.22/182.70 inference(modus_ponens,[status(thm)],[6515, 6514])).
% 290.22/182.70 tff(6517,plain,
% 290.22/182.70 ($false),
% 290.22/182.70 inference(unit_resolution,[status(thm)],[6516, 753, 6509, 6508, 6510])).
% 290.22/182.70 tff(6518,plain,((~node18(c_e_h_3, c_f, s1, s2)) | m_c_h_element_v_out(c_e_h_3, c_f, s1) | (~m_c_h_element_v_out(c_e_h_3, c_f, s2))), inference(lemma,lemma(discharge,[]))).
% 290.22/182.70 tff(6519,plain,
% 290.22/182.70 (~node18(c_e_h_3, c_f, s1, s2)),
% 290.22/182.70 inference(unit_resolution,[status(thm)],[6518, 6509, 6508])).
% 290.22/182.70 tff(6520,plain,
% 290.22/182.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s1, s2)) | node19(c_e_h_3, c_f, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s1, s2)) | node19(c_e_h_3, c_f, s1, s2))),
% 290.22/182.70 inference(rewrite,[status(thm)],[])).
% 290.22/182.70 tff(6521,plain,
% 290.22/182.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s1, s2)) | node19(c_e_h_3, c_f, s1, s2))),
% 290.22/182.70 inference(quant_inst,[status(thm)],[])).
% 290.22/182.70 tff(6522,plain,
% 290.22/182.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s1, s2)) | node19(c_e_h_3, c_f, s1, s2)),
% 290.22/182.70 inference(modus_ponens,[status(thm)],[6521, 6520])).
% 290.22/182.70 tff(6523,plain,
% 290.22/182.70 (node19(c_e_h_3, c_f, s1, s2)),
% 290.22/182.70 inference(unit_resolution,[status(thm)],[6522, 190, 255])).
% 290.22/182.70 tff(6524,plain,
% 290.22/182.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_3, c_f, s1, s2) | (~node19(c_e_h_3, c_f, s1, s2)) | node17(c_e_h_3, c_f, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_3, c_f, s1, s2) | (~node19(c_e_h_3, c_f, s1, s2)) | node17(c_e_h_3, c_f, s1))),
% 290.22/182.70 inference(rewrite,[status(thm)],[])).
% 290.22/182.70 tff(6525,plain,
% 290.22/182.70 ((node17(c_e_h_3, c_f, s1) | node18(c_e_h_3, c_f, s1, s2) | (~node19(c_e_h_3, c_f, s1, s2))) <=> (node18(c_e_h_3, c_f, s1, s2) | (~node19(c_e_h_3, c_f, s1, s2)) | node17(c_e_h_3, c_f, s1))),
% 290.22/182.70 inference(rewrite,[status(thm)],[])).
% 290.22/182.70 tff(6526,plain,
% 290.22/182.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s1) | node18(c_e_h_3, c_f, s1, s2) | (~node19(c_e_h_3, c_f, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_3, c_f, s1, s2) | (~node19(c_e_h_3, c_f, s1, s2)) | node17(c_e_h_3, c_f, s1)))),
% 290.22/182.71 inference(monotonicity,[status(thm)],[6525])).
% 290.22/182.71 tff(6527,plain,
% 290.22/182.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s1) | node18(c_e_h_3, c_f, s1, s2) | (~node19(c_e_h_3, c_f, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_3, c_f, s1, s2) | (~node19(c_e_h_3, c_f, s1, s2)) | node17(c_e_h_3, c_f, s1))),
% 290.22/182.71 inference(transitivity,[status(thm)],[6526, 6524])).
% 290.22/182.71 tff(6528,plain,
% 290.22/182.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s1) | node18(c_e_h_3, c_f, s1, s2) | (~node19(c_e_h_3, c_f, s1, s2)))),
% 290.22/182.71 inference(quant_inst,[status(thm)],[])).
% 290.22/182.71 tff(6529,plain,
% 290.22/182.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_3, c_f, s1, s2) | (~node19(c_e_h_3, c_f, s1, s2)) | node17(c_e_h_3, c_f, s1)),
% 290.22/182.71 inference(modus_ponens,[status(thm)],[6528, 6527])).
% 290.22/182.71 tff(6530,plain,
% 290.22/182.71 (node18(c_e_h_3, c_f, s1, s2) | node17(c_e_h_3, c_f, s1)),
% 290.22/182.71 inference(unit_resolution,[status(thm)],[6529, 776, 6523])).
% 290.22/182.71 tff(6531,plain,
% 290.22/182.71 (node17(c_e_h_3, c_f, s1)),
% 290.22/182.71 inference(unit_resolution,[status(thm)],[6530, 6519])).
% 290.22/182.71 tff(6532,plain,
% 290.22/182.71 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s1)) | m_and_h_gate_v_out(c_e_h_3, c_i, s1))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s1)) | m_and_h_gate_v_out(c_e_h_3, c_i, s1))),
% 290.22/182.71 inference(rewrite,[status(thm)],[])).
% 290.22/182.71 tff(6533,plain,
% 290.22/182.71 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s1)) | m_and_h_gate_v_out(c_e_h_3, c_i, s1))),
% 290.22/182.71 inference(quant_inst,[status(thm)],[])).
% 290.22/182.71 tff(6534,plain,
% 290.22/182.71 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s1)) | m_and_h_gate_v_out(c_e_h_3, c_i, s1)),
% 290.22/182.71 inference(modus_ponens,[status(thm)],[6533, 6532])).
% 290.22/182.71 tff(6535,plain,
% 290.22/182.71 (~m_c_h_element_v_in2(c_e_h_3, c_f, s1)),
% 290.22/182.71 inference(unit_resolution,[status(thm)],[6534, 2143, 647])).
% 290.22/182.71 tff(6536,plain,
% 290.22/182.71 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_f, s1)) | m_c_h_element_v_in2(c_e_h_3, c_f, s1) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_f, s1)) | m_c_h_element_v_in2(c_e_h_3, c_f, s1) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s1)))),
% 290.22/182.71 inference(rewrite,[status(thm)],[])).
% 290.22/182.71 tff(6537,plain,
% 290.22/182.71 (((~m_c_h_element_v_in1(c_e_h_3, c_f, s1)) | m_c_h_element_v_in2(c_e_h_3, c_f, s1) | (~node17(c_e_h_3, c_f, s1))) <=> ((~node17(c_e_h_3, c_f, s1)) | m_c_h_element_v_in2(c_e_h_3, c_f, s1) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s1)))),
% 290.22/182.71 inference(rewrite,[status(thm)],[])).
% 290.22/182.71 tff(6538,plain,
% 290.22/182.71 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s1)) | m_c_h_element_v_in2(c_e_h_3, c_f, s1) | (~node17(c_e_h_3, c_f, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_f, s1)) | m_c_h_element_v_in2(c_e_h_3, c_f, s1) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s1))))),
% 290.22/182.71 inference(monotonicity,[status(thm)],[6537])).
% 290.22/182.71 tff(6539,plain,
% 290.22/182.71 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s1)) | m_c_h_element_v_in2(c_e_h_3, c_f, s1) | (~node17(c_e_h_3, c_f, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_f, s1)) | m_c_h_element_v_in2(c_e_h_3, c_f, s1) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s1)))),
% 290.22/182.71 inference(transitivity,[status(thm)],[6538, 6536])).
% 290.22/182.71 tff(6540,plain,
% 290.22/182.71 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s1)) | m_c_h_element_v_in2(c_e_h_3, c_f, s1) | (~node17(c_e_h_3, c_f, s1)))),
% 290.22/182.71 inference(quant_inst,[status(thm)],[])).
% 290.22/182.71 tff(6541,plain,
% 290.22/182.71 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_f, s1)) | m_c_h_element_v_in2(c_e_h_3, c_f, s1) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s1))),
% 290.22/182.71 inference(modus_ponens,[status(thm)],[6540, 6539])).
% 290.22/182.71 tff(6542,plain,
% 290.22/182.71 ((~node17(c_e_h_3, c_f, s1)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s1))),
% 290.22/182.71 inference(unit_resolution,[status(thm)],[6541, 919, 6535])).
% 290.22/182.71 tff(6543,plain,
% 290.22/182.71 (~m_c_h_element_v_in1(c_e_h_3, c_f, s1)),
% 290.22/182.71 inference(unit_resolution,[status(thm)],[6542, 6531])).
% 290.22/182.71 tff(6544,plain,
% 290.22/182.71 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s1)) | m_c_h_element_v_in1(c_e_h_3, c_f, s1) | m_c_h_element_v_in2(c_e_h_3, c_f, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s1)) | m_c_h_element_v_in1(c_e_h_3, c_f, s1) | m_c_h_element_v_in2(c_e_h_3, c_f, s1))),
% 290.22/182.71 inference(rewrite,[status(thm)],[])).
% 290.22/182.71 tff(6545,plain,
% 290.22/182.71 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s1)) | m_c_h_element_v_in1(c_e_h_3, c_f, s1) | m_c_h_element_v_in2(c_e_h_3, c_f, s1))),
% 290.22/182.71 inference(quant_inst,[status(thm)],[])).
% 290.22/182.71 tff(6546,plain,
% 290.22/182.71 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s1)) | m_c_h_element_v_in1(c_e_h_3, c_f, s1) | m_c_h_element_v_in2(c_e_h_3, c_f, s1)),
% 290.22/182.71 inference(modus_ponens,[status(thm)],[6545, 6544])).
% 290.22/182.71 tff(6547,plain,
% 290.22/182.71 ((~node16(c_e_h_3, c_f, s1)) | m_c_h_element_v_in1(c_e_h_3, c_f, s1)),
% 290.22/182.71 inference(unit_resolution,[status(thm)],[6546, 178, 6535])).
% 290.22/182.71 tff(6548,plain,
% 290.22/182.71 (~node16(c_e_h_3, c_f, s1)),
% 290.22/182.71 inference(unit_resolution,[status(thm)],[6547, 6543])).
% 290.22/182.71 tff(6549,assumption,(node15(c_e_h_3, c_f, s1, s2)), introduced(assumption)).
% 290.22/182.71 tff(6550,plain,
% 290.22/182.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s2)) | (~node15(c_e_h_3, c_f, s1, s2)) | m_c_h_element_v_out(c_e_h_3, c_f, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s2)) | (~node15(c_e_h_3, c_f, s1, s2)) | m_c_h_element_v_out(c_e_h_3, c_f, s1))),
% 290.22/182.71 inference(rewrite,[status(thm)],[])).
% 290.22/182.71 tff(6551,plain,
% 290.22/182.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s2)) | (~node15(c_e_h_3, c_f, s1, s2)) | m_c_h_element_v_out(c_e_h_3, c_f, s1))),
% 290.22/182.71 inference(quant_inst,[status(thm)],[])).
% 290.22/182.71 tff(6552,plain,
% 290.22/182.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s2)) | (~node15(c_e_h_3, c_f, s1, s2)) | m_c_h_element_v_out(c_e_h_3, c_f, s1)),
% 290.22/182.71 inference(modus_ponens,[status(thm)],[6551, 6550])).
% 290.22/182.71 tff(6553,plain,
% 290.22/182.71 ($false),
% 290.22/182.71 inference(unit_resolution,[status(thm)],[6552, 147, 6509, 6508, 6549])).
% 290.22/182.71 tff(6554,plain,((~node15(c_e_h_3, c_f, s1, s2)) | m_c_h_element_v_out(c_e_h_3, c_f, s1) | (~m_c_h_element_v_out(c_e_h_3, c_f, s2))), inference(lemma,lemma(discharge,[]))).
% 290.22/182.71 tff(6555,plain,
% 290.22/182.71 (~node15(c_e_h_3, c_f, s1, s2)),
% 290.22/182.71 inference(unit_resolution,[status(thm)],[6554, 6509, 6508])).
% 290.22/182.71 tff(6556,plain,
% 290.22/182.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_f, s1, s2)) | node15(c_e_h_3, c_f, s1, s2) | node14(c_e_h_3, c_f, s1, s2) | node16(c_e_h_3, c_f, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s1, s2)) | node15(c_e_h_3, c_f, s1, s2) | node14(c_e_h_3, c_f, s1, s2) | node16(c_e_h_3, c_f, s1))),
% 290.22/182.71 inference(rewrite,[status(thm)],[])).
% 290.22/182.71 tff(6557,plain,
% 290.22/182.71 ((node16(c_e_h_3, c_f, s1) | node14(c_e_h_3, c_f, s1, s2) | node15(c_e_h_3, c_f, s1, s2) | (~node19(c_e_h_3, c_f, s1, s2))) <=> ((~node19(c_e_h_3, c_f, s1, s2)) | node15(c_e_h_3, c_f, s1, s2) | node14(c_e_h_3, c_f, s1, s2) | node16(c_e_h_3, c_f, s1))),
% 290.22/182.71 inference(rewrite,[status(thm)],[])).
% 290.22/182.71 tff(6558,plain,
% 290.22/182.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s1) | node14(c_e_h_3, c_f, s1, s2) | node15(c_e_h_3, c_f, s1, s2) | (~node19(c_e_h_3, c_f, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_f, s1, s2)) | node15(c_e_h_3, c_f, s1, s2) | node14(c_e_h_3, c_f, s1, s2) | node16(c_e_h_3, c_f, s1)))),
% 290.22/182.71 inference(monotonicity,[status(thm)],[6557])).
% 290.22/182.71 tff(6559,plain,
% 290.22/182.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s1) | node14(c_e_h_3, c_f, s1, s2) | node15(c_e_h_3, c_f, s1, s2) | (~node19(c_e_h_3, c_f, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s1, s2)) | node15(c_e_h_3, c_f, s1, s2) | node14(c_e_h_3, c_f, s1, s2) | node16(c_e_h_3, c_f, s1))),
% 290.22/182.72 inference(transitivity,[status(thm)],[6558, 6556])).
% 290.22/182.72 tff(6560,plain,
% 290.22/182.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s1) | node14(c_e_h_3, c_f, s1, s2) | node15(c_e_h_3, c_f, s1, s2) | (~node19(c_e_h_3, c_f, s1, s2)))),
% 290.22/182.72 inference(quant_inst,[status(thm)],[])).
% 290.22/182.72 tff(6561,plain,
% 290.22/182.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s1, s2)) | node15(c_e_h_3, c_f, s1, s2) | node14(c_e_h_3, c_f, s1, s2) | node16(c_e_h_3, c_f, s1)),
% 290.22/182.72 inference(modus_ponens,[status(thm)],[6560, 6559])).
% 290.22/182.72 tff(6562,plain,
% 290.22/182.72 (node15(c_e_h_3, c_f, s1, s2) | node14(c_e_h_3, c_f, s1, s2) | node16(c_e_h_3, c_f, s1)),
% 290.22/182.72 inference(unit_resolution,[status(thm)],[6561, 204, 6523])).
% 290.22/182.72 tff(6563,plain,
% 290.22/182.72 (node14(c_e_h_3, c_f, s1, s2)),
% 290.22/182.72 inference(unit_resolution,[status(thm)],[6562, 6555, 6548])).
% 290.22/182.72 tff(6564,plain,
% 290.22/182.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s2)) | m_c_h_element_v_in1(c_e_h_3, c_f, s1) | (~node14(c_e_h_3, c_f, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s2)) | m_c_h_element_v_in1(c_e_h_3, c_f, s1) | (~node14(c_e_h_3, c_f, s1, s2)))),
% 290.22/182.72 inference(rewrite,[status(thm)],[])).
% 290.22/182.72 tff(6565,plain,
% 290.22/182.72 (((~node14(c_e_h_3, c_f, s1, s2)) | m_c_h_element_v_in1(c_e_h_3, c_f, s1) | (~m_c_h_element_v_out(c_e_h_3, c_f, s2))) <=> ((~m_c_h_element_v_out(c_e_h_3, c_f, s2)) | m_c_h_element_v_in1(c_e_h_3, c_f, s1) | (~node14(c_e_h_3, c_f, s1, s2)))),
% 290.22/182.72 inference(rewrite,[status(thm)],[])).
% 290.22/182.72 tff(6566,plain,
% 290.22/182.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s1, s2)) | m_c_h_element_v_in1(c_e_h_3, c_f, s1) | (~m_c_h_element_v_out(c_e_h_3, c_f, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s2)) | m_c_h_element_v_in1(c_e_h_3, c_f, s1) | (~node14(c_e_h_3, c_f, s1, s2))))),
% 290.22/182.72 inference(monotonicity,[status(thm)],[6565])).
% 290.22/182.72 tff(6567,plain,
% 290.22/182.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s1, s2)) | m_c_h_element_v_in1(c_e_h_3, c_f, s1) | (~m_c_h_element_v_out(c_e_h_3, c_f, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s2)) | m_c_h_element_v_in1(c_e_h_3, c_f, s1) | (~node14(c_e_h_3, c_f, s1, s2)))),
% 290.22/182.72 inference(transitivity,[status(thm)],[6566, 6564])).
% 290.22/182.72 tff(6568,plain,
% 290.22/182.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s1, s2)) | m_c_h_element_v_in1(c_e_h_3, c_f, s1) | (~m_c_h_element_v_out(c_e_h_3, c_f, s2)))),
% 290.22/182.72 inference(quant_inst,[status(thm)],[])).
% 290.22/182.72 tff(6569,plain,
% 290.22/182.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s2)) | m_c_h_element_v_in1(c_e_h_3, c_f, s1) | (~node14(c_e_h_3, c_f, s1, s2))),
% 290.22/182.72 inference(modus_ponens,[status(thm)],[6568, 6567])).
% 290.22/182.72 tff(6570,plain,
% 290.22/182.72 ($false),
% 290.22/182.72 inference(unit_resolution,[status(thm)],[6569, 223, 6508, 6563, 6543])).
% 290.22/182.72 tff(6571,plain,(m_c_h_element_v_out(c_e_h_3, c_f, s1) | (~m_c_h_element_v_out(c_e_h_3, c_f, s2))), inference(lemma,lemma(discharge,[]))).
% 290.22/182.72 tff(6572,plain,
% 290.22/182.72 (~m_c_h_element_v_out(c_e_h_3, c_f, s2)),
% 290.22/182.72 inference(unit_resolution,[status(thm)],[6571, 6507])).
% 290.22/182.72 tff(6573,assumption,(m_c_h_element_v_out(c_e_h_3, c_f, s3)), introduced(assumption)).
% 290.22/182.72 tff(6574,assumption,(~m_c_h_element_v_out(c_e_h_3, c_f, s2)), introduced(assumption)).
% 290.22/182.72 tff(6575,assumption,(node18(c_e_h_3, c_f, s2, s3)), introduced(assumption)).
% 290.22/182.72 tff(6576,plain,
% 290.22/182.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s3)) | m_c_h_element_v_out(c_e_h_3, c_f, s2) | (~node18(c_e_h_3, c_f, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s3)) | m_c_h_element_v_out(c_e_h_3, c_f, s2) | (~node18(c_e_h_3, c_f, s2, s3)))),
% 290.22/182.72 inference(rewrite,[status(thm)],[])).
% 290.22/182.72 tff(6577,plain,
% 290.22/182.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s3)) | m_c_h_element_v_out(c_e_h_3, c_f, s2) | (~node18(c_e_h_3, c_f, s2, s3)))),
% 290.22/182.72 inference(quant_inst,[status(thm)],[])).
% 290.22/182.72 tff(6578,plain,
% 290.22/182.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s3)) | m_c_h_element_v_out(c_e_h_3, c_f, s2) | (~node18(c_e_h_3, c_f, s2, s3))),
% 290.22/182.72 inference(modus_ponens,[status(thm)],[6577, 6576])).
% 290.22/182.72 tff(6579,plain,
% 290.22/182.72 ($false),
% 290.22/182.72 inference(unit_resolution,[status(thm)],[6578, 753, 6574, 6575, 6573])).
% 290.22/182.72 tff(6580,plain,((~node18(c_e_h_3, c_f, s2, s3)) | m_c_h_element_v_out(c_e_h_3, c_f, s2) | (~m_c_h_element_v_out(c_e_h_3, c_f, s3))), inference(lemma,lemma(discharge,[]))).
% 290.25/182.72 tff(6581,plain,
% 290.25/182.72 (~node18(c_e_h_3, c_f, s2, s3)),
% 290.25/182.72 inference(unit_resolution,[status(thm)],[6580, 6574, 6573])).
% 290.25/182.72 tff(6582,plain,
% 290.25/182.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s2, s3)) | node19(c_e_h_3, c_f, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s2, s3)) | node19(c_e_h_3, c_f, s2, s3))),
% 290.25/182.72 inference(rewrite,[status(thm)],[])).
% 290.25/182.72 tff(6583,plain,
% 290.25/182.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s2, s3)) | node19(c_e_h_3, c_f, s2, s3))),
% 290.25/182.72 inference(quant_inst,[status(thm)],[])).
% 290.25/182.72 tff(6584,plain,
% 290.25/182.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s2, s3)) | node19(c_e_h_3, c_f, s2, s3)),
% 290.25/182.72 inference(modus_ponens,[status(thm)],[6583, 6582])).
% 290.25/182.72 tff(6585,plain,
% 290.25/182.72 (node19(c_e_h_3, c_f, s2, s3)),
% 290.25/182.72 inference(unit_resolution,[status(thm)],[6584, 190, 318])).
% 290.25/182.72 tff(6586,plain,
% 290.25/182.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_f, s2, s3)) | node18(c_e_h_3, c_f, s2, s3) | node17(c_e_h_3, c_f, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s2, s3)) | node18(c_e_h_3, c_f, s2, s3) | node17(c_e_h_3, c_f, s2))),
% 290.25/182.72 inference(rewrite,[status(thm)],[])).
% 290.25/182.72 tff(6587,plain,
% 290.25/182.72 ((node17(c_e_h_3, c_f, s2) | node18(c_e_h_3, c_f, s2, s3) | (~node19(c_e_h_3, c_f, s2, s3))) <=> ((~node19(c_e_h_3, c_f, s2, s3)) | node18(c_e_h_3, c_f, s2, s3) | node17(c_e_h_3, c_f, s2))),
% 290.25/182.72 inference(rewrite,[status(thm)],[])).
% 290.25/182.72 tff(6588,plain,
% 290.25/182.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s2) | node18(c_e_h_3, c_f, s2, s3) | (~node19(c_e_h_3, c_f, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_f, s2, s3)) | node18(c_e_h_3, c_f, s2, s3) | node17(c_e_h_3, c_f, s2)))),
% 290.25/182.72 inference(monotonicity,[status(thm)],[6587])).
% 290.25/182.72 tff(6589,plain,
% 290.25/182.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s2) | node18(c_e_h_3, c_f, s2, s3) | (~node19(c_e_h_3, c_f, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s2, s3)) | node18(c_e_h_3, c_f, s2, s3) | node17(c_e_h_3, c_f, s2))),
% 290.25/182.72 inference(transitivity,[status(thm)],[6588, 6586])).
% 290.25/182.72 tff(6590,plain,
% 290.25/182.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s2) | node18(c_e_h_3, c_f, s2, s3) | (~node19(c_e_h_3, c_f, s2, s3)))),
% 290.25/182.72 inference(quant_inst,[status(thm)],[])).
% 290.25/182.72 tff(6591,plain,
% 290.25/182.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s2, s3)) | node18(c_e_h_3, c_f, s2, s3) | node17(c_e_h_3, c_f, s2)),
% 290.25/182.72 inference(modus_ponens,[status(thm)],[6590, 6589])).
% 290.25/182.72 tff(6592,plain,
% 290.25/182.72 (node18(c_e_h_3, c_f, s2, s3) | node17(c_e_h_3, c_f, s2)),
% 290.25/182.72 inference(unit_resolution,[status(thm)],[6591, 776, 6585])).
% 290.25/182.72 tff(6593,plain,
% 290.25/182.72 (node17(c_e_h_3, c_f, s2)),
% 290.25/182.72 inference(unit_resolution,[status(thm)],[6592, 6581])).
% 290.25/182.72 tff(6594,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_f, s2)), introduced(assumption)).
% 290.25/182.72 tff(6595,plain,
% 290.25/182.72 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_3, c_f, s2) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s2)) | (~node17(c_e_h_3, c_f, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_f, s2) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s2)) | (~node17(c_e_h_3, c_f, s2)))),
% 290.25/182.73 inference(rewrite,[status(thm)],[])).
% 290.25/182.73 tff(6596,plain,
% 290.25/182.73 (((~m_c_h_element_v_in1(c_e_h_3, c_f, s2)) | m_c_h_element_v_in2(c_e_h_3, c_f, s2) | (~node17(c_e_h_3, c_f, s2))) <=> (m_c_h_element_v_in2(c_e_h_3, c_f, s2) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s2)) | (~node17(c_e_h_3, c_f, s2)))),
% 290.25/182.73 inference(rewrite,[status(thm)],[])).
% 290.25/182.73 tff(6597,plain,
% 290.25/182.73 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s2)) | m_c_h_element_v_in2(c_e_h_3, c_f, s2) | (~node17(c_e_h_3, c_f, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_3, c_f, s2) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s2)) | (~node17(c_e_h_3, c_f, s2))))),
% 290.25/182.73 inference(monotonicity,[status(thm)],[6596])).
% 290.25/182.73 tff(6598,plain,
% 290.25/182.73 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s2)) | m_c_h_element_v_in2(c_e_h_3, c_f, s2) | (~node17(c_e_h_3, c_f, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_f, s2) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s2)) | (~node17(c_e_h_3, c_f, s2)))),
% 290.25/182.73 inference(transitivity,[status(thm)],[6597, 6595])).
% 290.25/182.73 tff(6599,plain,
% 290.25/182.73 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s2)) | m_c_h_element_v_in2(c_e_h_3, c_f, s2) | (~node17(c_e_h_3, c_f, s2)))),
% 290.25/182.73 inference(quant_inst,[status(thm)],[])).
% 290.25/182.73 tff(6600,plain,
% 290.25/182.73 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_f, s2) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s2)) | (~node17(c_e_h_3, c_f, s2))),
% 290.25/182.73 inference(modus_ponens,[status(thm)],[6599, 6598])).
% 290.25/182.73 tff(6601,plain,
% 290.25/182.73 ((~m_c_h_element_v_in1(c_e_h_3, c_f, s2)) | (~node17(c_e_h_3, c_f, s2))),
% 290.25/182.73 inference(unit_resolution,[status(thm)],[6600, 919, 6594])).
% 290.25/182.73 tff(6602,plain,
% 290.25/182.73 (~m_c_h_element_v_in1(c_e_h_3, c_f, s2)),
% 290.25/182.73 inference(unit_resolution,[status(thm)],[6601, 6593])).
% 290.25/182.73 tff(6603,assumption,(node15(c_e_h_3, c_f, s2, s3)), introduced(assumption)).
% 290.25/182.73 tff(6604,plain,
% 290.25/182.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s3)) | (~node15(c_e_h_3, c_f, s2, s3)) | m_c_h_element_v_out(c_e_h_3, c_f, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s3)) | (~node15(c_e_h_3, c_f, s2, s3)) | m_c_h_element_v_out(c_e_h_3, c_f, s2))),
% 290.25/182.73 inference(rewrite,[status(thm)],[])).
% 290.25/182.73 tff(6605,plain,
% 290.25/182.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s3)) | (~node15(c_e_h_3, c_f, s2, s3)) | m_c_h_element_v_out(c_e_h_3, c_f, s2))),
% 290.25/182.73 inference(quant_inst,[status(thm)],[])).
% 290.25/182.73 tff(6606,plain,
% 290.25/182.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s3)) | (~node15(c_e_h_3, c_f, s2, s3)) | m_c_h_element_v_out(c_e_h_3, c_f, s2)),
% 290.25/182.73 inference(modus_ponens,[status(thm)],[6605, 6604])).
% 290.25/182.73 tff(6607,plain,
% 290.25/182.73 ($false),
% 290.25/182.73 inference(unit_resolution,[status(thm)],[6606, 147, 6574, 6603, 6573])).
% 290.25/182.73 tff(6608,plain,((~node15(c_e_h_3, c_f, s2, s3)) | m_c_h_element_v_out(c_e_h_3, c_f, s2) | (~m_c_h_element_v_out(c_e_h_3, c_f, s3))), inference(lemma,lemma(discharge,[]))).
% 290.25/182.73 tff(6609,plain,
% 290.25/182.73 (~node15(c_e_h_3, c_f, s2, s3)),
% 290.25/182.73 inference(unit_resolution,[status(thm)],[6608, 6574, 6573])).
% 290.25/182.73 tff(6610,plain,
% 290.25/182.73 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s2)) | m_c_h_element_v_in1(c_e_h_3, c_f, s2) | m_c_h_element_v_in2(c_e_h_3, c_f, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s2)) | m_c_h_element_v_in1(c_e_h_3, c_f, s2) | m_c_h_element_v_in2(c_e_h_3, c_f, s2))),
% 290.25/182.73 inference(rewrite,[status(thm)],[])).
% 290.25/182.73 tff(6611,plain,
% 290.25/182.73 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s2)) | m_c_h_element_v_in1(c_e_h_3, c_f, s2) | m_c_h_element_v_in2(c_e_h_3, c_f, s2))),
% 290.25/182.73 inference(quant_inst,[status(thm)],[])).
% 290.25/182.73 tff(6612,plain,
% 290.25/182.73 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s2)) | m_c_h_element_v_in1(c_e_h_3, c_f, s2) | m_c_h_element_v_in2(c_e_h_3, c_f, s2)),
% 290.25/182.73 inference(modus_ponens,[status(thm)],[6611, 6610])).
% 290.25/182.73 tff(6613,plain,
% 290.25/182.73 ((~node16(c_e_h_3, c_f, s2)) | m_c_h_element_v_in1(c_e_h_3, c_f, s2)),
% 290.25/182.73 inference(unit_resolution,[status(thm)],[6612, 178, 6594])).
% 290.25/182.73 tff(6614,plain,
% 290.25/182.73 (~node16(c_e_h_3, c_f, s2)),
% 290.25/182.73 inference(unit_resolution,[status(thm)],[6613, 6602])).
% 290.25/182.73 tff(6615,plain,
% 290.25/182.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_f, s2, s3)) | node14(c_e_h_3, c_f, s2, s3) | node15(c_e_h_3, c_f, s2, s3) | node16(c_e_h_3, c_f, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s2, s3)) | node14(c_e_h_3, c_f, s2, s3) | node15(c_e_h_3, c_f, s2, s3) | node16(c_e_h_3, c_f, s2))),
% 290.25/182.73 inference(rewrite,[status(thm)],[])).
% 290.25/182.73 tff(6616,plain,
% 290.25/182.73 ((node16(c_e_h_3, c_f, s2) | node14(c_e_h_3, c_f, s2, s3) | node15(c_e_h_3, c_f, s2, s3) | (~node19(c_e_h_3, c_f, s2, s3))) <=> ((~node19(c_e_h_3, c_f, s2, s3)) | node14(c_e_h_3, c_f, s2, s3) | node15(c_e_h_3, c_f, s2, s3) | node16(c_e_h_3, c_f, s2))),
% 290.25/182.73 inference(rewrite,[status(thm)],[])).
% 290.25/182.73 tff(6617,plain,
% 290.25/182.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s2) | node14(c_e_h_3, c_f, s2, s3) | node15(c_e_h_3, c_f, s2, s3) | (~node19(c_e_h_3, c_f, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_f, s2, s3)) | node14(c_e_h_3, c_f, s2, s3) | node15(c_e_h_3, c_f, s2, s3) | node16(c_e_h_3, c_f, s2)))),
% 290.25/182.73 inference(monotonicity,[status(thm)],[6616])).
% 290.25/182.73 tff(6618,plain,
% 290.25/182.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s2) | node14(c_e_h_3, c_f, s2, s3) | node15(c_e_h_3, c_f, s2, s3) | (~node19(c_e_h_3, c_f, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s2, s3)) | node14(c_e_h_3, c_f, s2, s3) | node15(c_e_h_3, c_f, s2, s3) | node16(c_e_h_3, c_f, s2))),
% 290.25/182.73 inference(transitivity,[status(thm)],[6617, 6615])).
% 290.25/182.73 tff(6619,plain,
% 290.25/182.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s2) | node14(c_e_h_3, c_f, s2, s3) | node15(c_e_h_3, c_f, s2, s3) | (~node19(c_e_h_3, c_f, s2, s3)))),
% 290.25/182.73 inference(quant_inst,[status(thm)],[])).
% 290.25/182.73 tff(6620,plain,
% 290.25/182.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s2, s3)) | node14(c_e_h_3, c_f, s2, s3) | node15(c_e_h_3, c_f, s2, s3) | node16(c_e_h_3, c_f, s2)),
% 290.25/182.73 inference(modus_ponens,[status(thm)],[6619, 6618])).
% 290.25/182.73 tff(6621,plain,
% 290.25/182.73 (node14(c_e_h_3, c_f, s2, s3) | node15(c_e_h_3, c_f, s2, s3) | node16(c_e_h_3, c_f, s2)),
% 290.25/182.73 inference(unit_resolution,[status(thm)],[6620, 204, 6585])).
% 290.25/182.73 tff(6622,plain,
% 290.25/182.73 (node14(c_e_h_3, c_f, s2, s3)),
% 290.25/182.73 inference(unit_resolution,[status(thm)],[6621, 6614, 6609])).
% 290.25/182.73 tff(6623,plain,
% 290.25/182.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s3)) | m_c_h_element_v_in1(c_e_h_3, c_f, s2) | (~node14(c_e_h_3, c_f, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s3)) | m_c_h_element_v_in1(c_e_h_3, c_f, s2) | (~node14(c_e_h_3, c_f, s2, s3)))),
% 290.25/182.73 inference(rewrite,[status(thm)],[])).
% 290.25/182.73 tff(6624,plain,
% 290.25/182.73 (((~node14(c_e_h_3, c_f, s2, s3)) | m_c_h_element_v_in1(c_e_h_3, c_f, s2) | (~m_c_h_element_v_out(c_e_h_3, c_f, s3))) <=> ((~m_c_h_element_v_out(c_e_h_3, c_f, s3)) | m_c_h_element_v_in1(c_e_h_3, c_f, s2) | (~node14(c_e_h_3, c_f, s2, s3)))),
% 290.25/182.73 inference(rewrite,[status(thm)],[])).
% 290.25/182.73 tff(6625,plain,
% 290.25/182.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s2, s3)) | m_c_h_element_v_in1(c_e_h_3, c_f, s2) | (~m_c_h_element_v_out(c_e_h_3, c_f, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s3)) | m_c_h_element_v_in1(c_e_h_3, c_f, s2) | (~node14(c_e_h_3, c_f, s2, s3))))),
% 290.25/182.73 inference(monotonicity,[status(thm)],[6624])).
% 290.25/182.73 tff(6626,plain,
% 290.25/182.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s2, s3)) | m_c_h_element_v_in1(c_e_h_3, c_f, s2) | (~m_c_h_element_v_out(c_e_h_3, c_f, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s3)) | m_c_h_element_v_in1(c_e_h_3, c_f, s2) | (~node14(c_e_h_3, c_f, s2, s3)))),
% 290.25/182.73 inference(transitivity,[status(thm)],[6625, 6623])).
% 290.25/182.73 tff(6627,plain,
% 290.25/182.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s2, s3)) | m_c_h_element_v_in1(c_e_h_3, c_f, s2) | (~m_c_h_element_v_out(c_e_h_3, c_f, s3)))),
% 290.25/182.73 inference(quant_inst,[status(thm)],[])).
% 290.25/182.73 tff(6628,plain,
% 290.25/182.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s3)) | m_c_h_element_v_in1(c_e_h_3, c_f, s2) | (~node14(c_e_h_3, c_f, s2, s3))),
% 290.25/182.73 inference(modus_ponens,[status(thm)],[6627, 6626])).
% 290.25/182.73 tff(6629,plain,
% 290.25/182.73 ($false),
% 290.25/182.73 inference(unit_resolution,[status(thm)],[6628, 223, 6622, 6573, 6602])).
% 290.25/182.73 tff(6630,plain,(m_c_h_element_v_out(c_e_h_3, c_f, s2) | (~m_c_h_element_v_out(c_e_h_3, c_f, s3)) | m_c_h_element_v_in2(c_e_h_3, c_f, s2)), inference(lemma,lemma(discharge,[]))).
% 290.25/182.73 tff(6631,plain,
% 290.25/182.73 ((~m_c_h_element_v_out(c_e_h_3, c_f, s3)) | m_c_h_element_v_in2(c_e_h_3, c_f, s2)),
% 290.25/182.73 inference(unit_resolution,[status(thm)],[6630, 6572])).
% 290.25/182.73 tff(6632,plain,
% 290.25/182.73 (~m_c_h_element_v_out(c_e_h_3, c_f, s3)),
% 290.25/182.73 inference(unit_resolution,[status(thm)],[6631, 6494])).
% 290.25/182.73 tff(6633,assumption,(node15(c_e_h_3, c_f, s3, s4)), introduced(assumption)).
% 290.25/182.73 tff(6634,plain,
% 290.25/182.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s4)) | (~node15(c_e_h_3, c_f, s3, s4)) | m_c_h_element_v_out(c_e_h_3, c_f, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s4)) | (~node15(c_e_h_3, c_f, s3, s4)) | m_c_h_element_v_out(c_e_h_3, c_f, s3))),
% 290.25/182.74 inference(rewrite,[status(thm)],[])).
% 290.25/182.74 tff(6635,plain,
% 290.25/182.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s4)) | (~node15(c_e_h_3, c_f, s3, s4)) | m_c_h_element_v_out(c_e_h_3, c_f, s3))),
% 290.25/182.74 inference(quant_inst,[status(thm)],[])).
% 290.25/182.74 tff(6636,plain,
% 290.25/182.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s4)) | (~node15(c_e_h_3, c_f, s3, s4)) | m_c_h_element_v_out(c_e_h_3, c_f, s3)),
% 290.25/182.74 inference(modus_ponens,[status(thm)],[6635, 6634])).
% 290.25/182.74 tff(6637,plain,
% 290.25/182.74 ($false),
% 290.25/182.74 inference(unit_resolution,[status(thm)],[6636, 147, 6633, 6632, 6490])).
% 290.25/182.74 tff(6638,plain,((~node15(c_e_h_3, c_f, s3, s4)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s4))), inference(lemma,lemma(discharge,[]))).
% 290.25/182.74 tff(6639,plain,
% 290.25/182.74 (~node15(c_e_h_3, c_f, s3, s4)),
% 290.25/182.74 inference(unit_resolution,[status(thm)],[6638, 6490])).
% 290.25/182.74 tff(6640,assumption,(node18(c_e_h_3, c_f, s3, s4)), introduced(assumption)).
% 290.25/182.74 tff(6641,plain,
% 290.25/182.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~node18(c_e_h_3, c_f, s3, s4)) | m_c_h_element_v_out(c_e_h_3, c_f, s3) | (~m_c_h_element_v_out(c_e_h_3, c_f, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_3, c_f, s3, s4)) | m_c_h_element_v_out(c_e_h_3, c_f, s3) | (~m_c_h_element_v_out(c_e_h_3, c_f, s4)))),
% 290.25/182.74 inference(rewrite,[status(thm)],[])).
% 290.25/182.74 tff(6642,plain,
% 290.25/182.74 (((~m_c_h_element_v_out(c_e_h_3, c_f, s4)) | m_c_h_element_v_out(c_e_h_3, c_f, s3) | (~node18(c_e_h_3, c_f, s3, s4))) <=> ((~node18(c_e_h_3, c_f, s3, s4)) | m_c_h_element_v_out(c_e_h_3, c_f, s3) | (~m_c_h_element_v_out(c_e_h_3, c_f, s4)))),
% 290.25/182.74 inference(rewrite,[status(thm)],[])).
% 290.25/182.74 tff(6643,plain,
% 290.25/182.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s4)) | m_c_h_element_v_out(c_e_h_3, c_f, s3) | (~node18(c_e_h_3, c_f, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~node18(c_e_h_3, c_f, s3, s4)) | m_c_h_element_v_out(c_e_h_3, c_f, s3) | (~m_c_h_element_v_out(c_e_h_3, c_f, s4))))),
% 290.25/182.74 inference(monotonicity,[status(thm)],[6642])).
% 290.25/182.74 tff(6644,plain,
% 290.25/182.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s4)) | m_c_h_element_v_out(c_e_h_3, c_f, s3) | (~node18(c_e_h_3, c_f, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_3, c_f, s3, s4)) | m_c_h_element_v_out(c_e_h_3, c_f, s3) | (~m_c_h_element_v_out(c_e_h_3, c_f, s4)))),
% 290.25/182.74 inference(transitivity,[status(thm)],[6643, 6641])).
% 290.25/182.74 tff(6645,plain,
% 290.25/182.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s4)) | m_c_h_element_v_out(c_e_h_3, c_f, s3) | (~node18(c_e_h_3, c_f, s3, s4)))),
% 290.25/182.74 inference(quant_inst,[status(thm)],[])).
% 290.25/182.74 tff(6646,plain,
% 290.25/182.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_3, c_f, s3, s4)) | m_c_h_element_v_out(c_e_h_3, c_f, s3) | (~m_c_h_element_v_out(c_e_h_3, c_f, s4))),
% 290.25/182.74 inference(modus_ponens,[status(thm)],[6645, 6644])).
% 290.25/182.74 tff(6647,plain,
% 290.25/182.74 ($false),
% 290.25/182.74 inference(unit_resolution,[status(thm)],[6646, 753, 6640, 6632, 6490])).
% 290.25/182.74 tff(6648,plain,((~node18(c_e_h_3, c_f, s3, s4)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s4))), inference(lemma,lemma(discharge,[]))).
% 290.25/182.74 tff(6649,plain,
% 290.25/182.74 (~node18(c_e_h_3, c_f, s3, s4)),
% 290.25/182.74 inference(unit_resolution,[status(thm)],[6648, 6490])).
% 290.25/182.74 tff(6650,plain,
% 290.25/182.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s3, s4)) | node19(c_e_h_3, c_f, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s3, s4)) | node19(c_e_h_3, c_f, s3, s4))),
% 290.25/182.74 inference(rewrite,[status(thm)],[])).
% 290.25/182.74 tff(6651,plain,
% 290.25/182.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s3, s4)) | node19(c_e_h_3, c_f, s3, s4))),
% 290.25/182.74 inference(quant_inst,[status(thm)],[])).
% 290.25/182.74 tff(6652,plain,
% 290.25/182.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s3, s4)) | node19(c_e_h_3, c_f, s3, s4)),
% 290.25/182.74 inference(modus_ponens,[status(thm)],[6651, 6650])).
% 290.25/182.74 tff(6653,plain,
% 290.25/182.74 (node19(c_e_h_3, c_f, s3, s4)),
% 290.25/182.74 inference(unit_resolution,[status(thm)],[6652, 190, 531])).
% 290.25/182.74 tff(6654,plain,
% 290.25/182.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s3) | node18(c_e_h_3, c_f, s3, s4) | (~node19(c_e_h_3, c_f, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_f, s3) | node18(c_e_h_3, c_f, s3, s4) | (~node19(c_e_h_3, c_f, s3, s4)))),
% 290.25/182.74 inference(rewrite,[status(thm)],[])).
% 290.25/182.74 tff(6655,plain,
% 290.25/182.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s3) | node18(c_e_h_3, c_f, s3, s4) | (~node19(c_e_h_3, c_f, s3, s4)))),
% 290.25/182.74 inference(quant_inst,[status(thm)],[])).
% 290.25/182.74 tff(6656,plain,
% 290.25/182.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_f, s3) | node18(c_e_h_3, c_f, s3, s4) | (~node19(c_e_h_3, c_f, s3, s4))),
% 290.25/182.74 inference(modus_ponens,[status(thm)],[6655, 6654])).
% 290.25/182.74 tff(6657,plain,
% 290.25/182.74 (node17(c_e_h_3, c_f, s3) | node18(c_e_h_3, c_f, s3, s4)),
% 290.25/182.74 inference(unit_resolution,[status(thm)],[6656, 776, 6653])).
% 290.25/182.74 tff(6658,plain,
% 290.25/182.74 (node17(c_e_h_3, c_f, s3)),
% 290.25/182.74 inference(unit_resolution,[status(thm)],[6657, 6649])).
% 290.25/182.74 tff(6659,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_f, s3)), introduced(assumption)).
% 290.25/182.74 tff(6660,plain,
% 290.25/182.74 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s3)) | (~node17(c_e_h_3, c_f, s3)) | m_c_h_element_v_in2(c_e_h_3, c_f, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s3)) | (~node17(c_e_h_3, c_f, s3)) | m_c_h_element_v_in2(c_e_h_3, c_f, s3))),
% 290.25/182.74 inference(rewrite,[status(thm)],[])).
% 290.25/182.74 tff(6661,plain,
% 290.25/182.74 (((~m_c_h_element_v_in1(c_e_h_3, c_f, s3)) | m_c_h_element_v_in2(c_e_h_3, c_f, s3) | (~node17(c_e_h_3, c_f, s3))) <=> ((~m_c_h_element_v_in1(c_e_h_3, c_f, s3)) | (~node17(c_e_h_3, c_f, s3)) | m_c_h_element_v_in2(c_e_h_3, c_f, s3))),
% 290.25/182.74 inference(rewrite,[status(thm)],[])).
% 290.25/182.74 tff(6662,plain,
% 290.25/182.74 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s3)) | m_c_h_element_v_in2(c_e_h_3, c_f, s3) | (~node17(c_e_h_3, c_f, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s3)) | (~node17(c_e_h_3, c_f, s3)) | m_c_h_element_v_in2(c_e_h_3, c_f, s3)))),
% 290.25/182.74 inference(monotonicity,[status(thm)],[6661])).
% 290.25/182.74 tff(6663,plain,
% 290.25/182.74 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s3)) | m_c_h_element_v_in2(c_e_h_3, c_f, s3) | (~node17(c_e_h_3, c_f, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s3)) | (~node17(c_e_h_3, c_f, s3)) | m_c_h_element_v_in2(c_e_h_3, c_f, s3))),
% 290.25/182.75 inference(transitivity,[status(thm)],[6662, 6660])).
% 290.25/182.75 tff(6664,plain,
% 290.25/182.75 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s3)) | m_c_h_element_v_in2(c_e_h_3, c_f, s3) | (~node17(c_e_h_3, c_f, s3)))),
% 290.25/182.75 inference(quant_inst,[status(thm)],[])).
% 290.25/182.75 tff(6665,plain,
% 290.25/182.75 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s3)) | (~node17(c_e_h_3, c_f, s3)) | m_c_h_element_v_in2(c_e_h_3, c_f, s3)),
% 290.25/182.75 inference(modus_ponens,[status(thm)],[6664, 6663])).
% 290.25/182.75 tff(6666,plain,
% 290.25/182.75 ((~m_c_h_element_v_in1(c_e_h_3, c_f, s3)) | (~node17(c_e_h_3, c_f, s3))),
% 290.25/182.75 inference(unit_resolution,[status(thm)],[6665, 919, 6659])).
% 290.25/182.75 tff(6667,plain,
% 290.25/182.75 (~m_c_h_element_v_in1(c_e_h_3, c_f, s3)),
% 290.25/182.75 inference(unit_resolution,[status(thm)],[6666, 6658])).
% 290.25/182.75 tff(6668,assumption,(~node15(c_e_h_3, c_f, s3, s4)), introduced(assumption)).
% 290.25/182.75 tff(6669,assumption,(node17(c_e_h_3, c_f, s3)), introduced(assumption)).
% 290.25/182.75 tff(6670,assumption,(node16(c_e_h_3, c_f, s3)), introduced(assumption)).
% 290.25/182.75 tff(6671,plain,
% 290.25/182.75 ((~m_c_h_element_v_in1(c_e_h_3, c_f, s3)) | m_c_h_element_v_in2(c_e_h_3, c_f, s3)),
% 290.25/182.75 inference(unit_resolution,[status(thm)],[6665, 919, 6669])).
% 290.25/182.75 tff(6672,plain,
% 290.25/182.75 (~m_c_h_element_v_in1(c_e_h_3, c_f, s3)),
% 290.25/182.75 inference(unit_resolution,[status(thm)],[6671, 6659])).
% 290.25/182.75 tff(6673,plain,
% 290.25/182.75 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s3)) | m_c_h_element_v_in1(c_e_h_3, c_f, s3) | m_c_h_element_v_in2(c_e_h_3, c_f, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s3)) | m_c_h_element_v_in1(c_e_h_3, c_f, s3) | m_c_h_element_v_in2(c_e_h_3, c_f, s3))),
% 290.25/182.75 inference(rewrite,[status(thm)],[])).
% 290.25/182.75 tff(6674,plain,
% 290.25/182.75 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s3)) | m_c_h_element_v_in1(c_e_h_3, c_f, s3) | m_c_h_element_v_in2(c_e_h_3, c_f, s3))),
% 290.25/182.75 inference(quant_inst,[status(thm)],[])).
% 290.25/182.75 tff(6675,plain,
% 290.25/182.75 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s3)) | m_c_h_element_v_in1(c_e_h_3, c_f, s3) | m_c_h_element_v_in2(c_e_h_3, c_f, s3)),
% 290.25/182.75 inference(modus_ponens,[status(thm)],[6674, 6673])).
% 290.25/182.75 tff(6676,plain,
% 290.25/182.75 (m_c_h_element_v_in1(c_e_h_3, c_f, s3) | m_c_h_element_v_in2(c_e_h_3, c_f, s3)),
% 290.25/182.75 inference(unit_resolution,[status(thm)],[6675, 178, 6670])).
% 290.25/182.75 tff(6677,plain,
% 290.25/182.75 ($false),
% 290.25/182.75 inference(unit_resolution,[status(thm)],[6676, 6672, 6659])).
% 290.25/182.75 tff(6678,plain,(m_c_h_element_v_in2(c_e_h_3, c_f, s3) | (~node16(c_e_h_3, c_f, s3)) | (~node17(c_e_h_3, c_f, s3))), inference(lemma,lemma(discharge,[]))).
% 290.25/182.75 tff(6679,plain,
% 290.25/182.75 (m_c_h_element_v_in2(c_e_h_3, c_f, s3)),
% 290.25/182.75 inference(unit_resolution,[status(thm)],[6678, 6670, 6669])).
% 290.25/182.75 tff(6680,plain,
% 290.25/182.75 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_f, s3)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s3)) | m_c_h_element_v_in1(c_e_h_3, c_f, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_f, s3)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s3)) | m_c_h_element_v_in1(c_e_h_3, c_f, s3))),
% 290.25/182.75 inference(rewrite,[status(thm)],[])).
% 290.25/182.75 tff(6681,plain,
% 290.25/182.75 ((m_c_h_element_v_in1(c_e_h_3, c_f, s3) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s3)) | (~node17(c_e_h_3, c_f, s3))) <=> ((~node17(c_e_h_3, c_f, s3)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s3)) | m_c_h_element_v_in1(c_e_h_3, c_f, s3))),
% 290.25/182.75 inference(rewrite,[status(thm)],[])).
% 290.25/182.75 tff(6682,plain,
% 290.25/182.75 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s3) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s3)) | (~node17(c_e_h_3, c_f, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_f, s3)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s3)) | m_c_h_element_v_in1(c_e_h_3, c_f, s3)))),
% 290.25/182.75 inference(monotonicity,[status(thm)],[6681])).
% 290.25/182.75 tff(6683,plain,
% 290.25/182.75 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s3) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s3)) | (~node17(c_e_h_3, c_f, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_f, s3)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s3)) | m_c_h_element_v_in1(c_e_h_3, c_f, s3))),
% 290.25/182.75 inference(transitivity,[status(thm)],[6682, 6680])).
% 290.25/182.75 tff(6684,plain,
% 290.25/182.75 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s3) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s3)) | (~node17(c_e_h_3, c_f, s3)))),
% 290.25/182.75 inference(quant_inst,[status(thm)],[])).
% 290.25/182.75 tff(6685,plain,
% 290.25/182.75 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_f, s3)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s3)) | m_c_h_element_v_in1(c_e_h_3, c_f, s3)),
% 290.25/182.75 inference(modus_ponens,[status(thm)],[6684, 6683])).
% 290.25/182.75 tff(6686,plain,
% 290.25/182.75 ((~m_c_h_element_v_in2(c_e_h_3, c_f, s3)) | m_c_h_element_v_in1(c_e_h_3, c_f, s3)),
% 290.25/182.75 inference(unit_resolution,[status(thm)],[6685, 859, 6669])).
% 290.25/182.75 tff(6687,plain,
% 290.25/182.75 (m_c_h_element_v_in1(c_e_h_3, c_f, s3)),
% 290.25/182.75 inference(unit_resolution,[status(thm)],[6686, 6679])).
% 290.25/182.75 tff(6688,plain,
% 290.25/182.75 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s3)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s3)) | (~node16(c_e_h_3, c_f, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s3)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s3)) | (~node16(c_e_h_3, c_f, s3)))),
% 290.25/182.75 inference(rewrite,[status(thm)],[])).
% 290.25/182.75 tff(6689,plain,
% 290.25/182.75 (((~node16(c_e_h_3, c_f, s3)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s3)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s3))) <=> ((~m_c_h_element_v_in1(c_e_h_3, c_f, s3)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s3)) | (~node16(c_e_h_3, c_f, s3)))),
% 290.25/182.75 inference(rewrite,[status(thm)],[])).
% 290.25/182.75 tff(6690,plain,
% 290.25/182.75 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_f, s3)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s3)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s3)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s3)) | (~node16(c_e_h_3, c_f, s3))))),
% 290.25/182.75 inference(monotonicity,[status(thm)],[6689])).
% 290.25/182.75 tff(6691,plain,
% 290.25/182.75 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_f, s3)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s3)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s3)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s3)) | (~node16(c_e_h_3, c_f, s3)))),
% 290.25/182.75 inference(transitivity,[status(thm)],[6690, 6688])).
% 290.25/182.75 tff(6692,plain,
% 290.25/182.75 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_f, s3)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s3)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s3)))),
% 290.25/182.75 inference(quant_inst,[status(thm)],[])).
% 290.25/182.75 tff(6693,plain,
% 290.25/182.75 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s3)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s3)) | (~node16(c_e_h_3, c_f, s3))),
% 290.25/182.75 inference(modus_ponens,[status(thm)],[6692, 6691])).
% 290.25/182.75 tff(6694,plain,
% 290.25/182.75 ((~m_c_h_element_v_in1(c_e_h_3, c_f, s3)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s3))),
% 290.25/182.75 inference(unit_resolution,[status(thm)],[6693, 2307, 6670])).
% 290.25/182.75 tff(6695,plain,
% 290.25/182.75 ($false),
% 290.25/182.75 inference(unit_resolution,[status(thm)],[6694, 6687, 6679])).
% 290.25/182.75 tff(6696,plain,((~node16(c_e_h_3, c_f, s3)) | (~node17(c_e_h_3, c_f, s3))), inference(lemma,lemma(discharge,[]))).
% 290.25/182.75 tff(6697,plain,
% 290.25/182.75 (~node16(c_e_h_3, c_f, s3)),
% 290.25/182.75 inference(unit_resolution,[status(thm)],[6696, 6658])).
% 290.25/182.75 tff(6698,plain,
% 290.25/182.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_3, c_f, s3, s4) | node15(c_e_h_3, c_f, s3, s4) | node16(c_e_h_3, c_f, s3) | (~node19(c_e_h_3, c_f, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_f, s3, s4) | node15(c_e_h_3, c_f, s3, s4) | node16(c_e_h_3, c_f, s3) | (~node19(c_e_h_3, c_f, s3, s4)))),
% 290.25/182.75 inference(rewrite,[status(thm)],[])).
% 290.25/182.75 tff(6699,plain,
% 290.25/182.75 ((node16(c_e_h_3, c_f, s3) | node14(c_e_h_3, c_f, s3, s4) | node15(c_e_h_3, c_f, s3, s4) | (~node19(c_e_h_3, c_f, s3, s4))) <=> (node14(c_e_h_3, c_f, s3, s4) | node15(c_e_h_3, c_f, s3, s4) | node16(c_e_h_3, c_f, s3) | (~node19(c_e_h_3, c_f, s3, s4)))),
% 290.25/182.75 inference(rewrite,[status(thm)],[])).
% 290.25/182.75 tff(6700,plain,
% 290.25/182.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s3) | node14(c_e_h_3, c_f, s3, s4) | node15(c_e_h_3, c_f, s3, s4) | (~node19(c_e_h_3, c_f, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_3, c_f, s3, s4) | node15(c_e_h_3, c_f, s3, s4) | node16(c_e_h_3, c_f, s3) | (~node19(c_e_h_3, c_f, s3, s4))))),
% 290.25/182.75 inference(monotonicity,[status(thm)],[6699])).
% 290.25/182.75 tff(6701,plain,
% 290.25/182.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s3) | node14(c_e_h_3, c_f, s3, s4) | node15(c_e_h_3, c_f, s3, s4) | (~node19(c_e_h_3, c_f, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_f, s3, s4) | node15(c_e_h_3, c_f, s3, s4) | node16(c_e_h_3, c_f, s3) | (~node19(c_e_h_3, c_f, s3, s4)))),
% 290.25/182.75 inference(transitivity,[status(thm)],[6700, 6698])).
% 290.25/182.75 tff(6702,plain,
% 290.25/182.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s3) | node14(c_e_h_3, c_f, s3, s4) | node15(c_e_h_3, c_f, s3, s4) | (~node19(c_e_h_3, c_f, s3, s4)))),
% 290.25/182.75 inference(quant_inst,[status(thm)],[])).
% 290.25/182.75 tff(6703,plain,
% 290.25/182.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_f, s3, s4) | node15(c_e_h_3, c_f, s3, s4) | node16(c_e_h_3, c_f, s3) | (~node19(c_e_h_3, c_f, s3, s4))),
% 290.25/182.75 inference(modus_ponens,[status(thm)],[6702, 6701])).
% 290.25/182.75 tff(6704,plain,
% 290.25/182.75 (node14(c_e_h_3, c_f, s3, s4) | node15(c_e_h_3, c_f, s3, s4) | node16(c_e_h_3, c_f, s3)),
% 290.25/182.75 inference(unit_resolution,[status(thm)],[6703, 204, 6653])).
% 290.25/182.75 tff(6705,plain,
% 290.25/182.76 (node14(c_e_h_3, c_f, s3, s4)),
% 290.25/182.76 inference(unit_resolution,[status(thm)],[6704, 6697, 6668])).
% 290.25/182.76 tff(6706,plain,
% 290.25/182.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s3) | (~m_c_h_element_v_out(c_e_h_3, c_f, s4)) | (~node14(c_e_h_3, c_f, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_f, s3) | (~m_c_h_element_v_out(c_e_h_3, c_f, s4)) | (~node14(c_e_h_3, c_f, s3, s4)))),
% 290.25/182.76 inference(rewrite,[status(thm)],[])).
% 290.25/182.76 tff(6707,plain,
% 290.25/182.76 (((~node14(c_e_h_3, c_f, s3, s4)) | m_c_h_element_v_in1(c_e_h_3, c_f, s3) | (~m_c_h_element_v_out(c_e_h_3, c_f, s4))) <=> (m_c_h_element_v_in1(c_e_h_3, c_f, s3) | (~m_c_h_element_v_out(c_e_h_3, c_f, s4)) | (~node14(c_e_h_3, c_f, s3, s4)))),
% 290.25/182.76 inference(rewrite,[status(thm)],[])).
% 290.25/182.76 tff(6708,plain,
% 290.25/182.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s3, s4)) | m_c_h_element_v_in1(c_e_h_3, c_f, s3) | (~m_c_h_element_v_out(c_e_h_3, c_f, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s3) | (~m_c_h_element_v_out(c_e_h_3, c_f, s4)) | (~node14(c_e_h_3, c_f, s3, s4))))),
% 290.25/182.76 inference(monotonicity,[status(thm)],[6707])).
% 290.25/182.76 tff(6709,plain,
% 290.25/182.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s3, s4)) | m_c_h_element_v_in1(c_e_h_3, c_f, s3) | (~m_c_h_element_v_out(c_e_h_3, c_f, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_f, s3) | (~m_c_h_element_v_out(c_e_h_3, c_f, s4)) | (~node14(c_e_h_3, c_f, s3, s4)))),
% 290.25/182.76 inference(transitivity,[status(thm)],[6708, 6706])).
% 290.25/182.76 tff(6710,plain,
% 290.25/182.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s3, s4)) | m_c_h_element_v_in1(c_e_h_3, c_f, s3) | (~m_c_h_element_v_out(c_e_h_3, c_f, s4)))),
% 290.25/182.76 inference(quant_inst,[status(thm)],[])).
% 290.25/182.76 tff(6711,plain,
% 290.25/182.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_f, s3) | (~m_c_h_element_v_out(c_e_h_3, c_f, s4)) | (~node14(c_e_h_3, c_f, s3, s4))),
% 290.25/182.76 inference(modus_ponens,[status(thm)],[6710, 6709])).
% 290.25/182.76 tff(6712,plain,
% 290.25/182.76 ($false),
% 290.25/182.76 inference(unit_resolution,[status(thm)],[6711, 223, 6705, 6667, 6490])).
% 290.25/182.76 tff(6713,plain,((~m_c_h_element_v_out(c_e_h_3, c_f, s4)) | node15(c_e_h_3, c_f, s3, s4) | m_c_h_element_v_in2(c_e_h_3, c_f, s3)), inference(lemma,lemma(discharge,[]))).
% 290.25/182.76 tff(6714,plain,
% 290.25/182.76 ($false),
% 290.25/182.76 inference(unit_resolution,[status(thm)],[6713, 6639, 6490, 6489])).
% 290.25/182.76 tff(6715,plain,(~m_c_h_element_v_out(c_e_h_3, c_f, s4)), inference(lemma,lemma(discharge,[]))).
% 290.25/182.76 tff(6716,assumption,(~m_c_h_element_v_out(c_e_h_3, c_f, s4)), introduced(assumption)).
% 290.25/182.76 tff(6717,assumption,(node18(c_e_h_3, c_f, s4, s5)), introduced(assumption)).
% 290.25/182.76 tff(6718,plain,
% 290.25/182.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_f, s4) | (~m_c_h_element_v_out(c_e_h_3, c_f, s5)) | (~node18(c_e_h_3, c_f, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s4) | (~m_c_h_element_v_out(c_e_h_3, c_f, s5)) | (~node18(c_e_h_3, c_f, s4, s5)))),
% 290.25/182.76 inference(rewrite,[status(thm)],[])).
% 290.25/182.76 tff(6719,plain,
% 290.25/182.76 (((~m_c_h_element_v_out(c_e_h_3, c_f, s5)) | m_c_h_element_v_out(c_e_h_3, c_f, s4) | (~node18(c_e_h_3, c_f, s4, s5))) <=> (m_c_h_element_v_out(c_e_h_3, c_f, s4) | (~m_c_h_element_v_out(c_e_h_3, c_f, s5)) | (~node18(c_e_h_3, c_f, s4, s5)))),
% 290.25/182.76 inference(rewrite,[status(thm)],[])).
% 290.25/182.76 tff(6720,plain,
% 290.25/182.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s5)) | m_c_h_element_v_out(c_e_h_3, c_f, s4) | (~node18(c_e_h_3, c_f, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_f, s4) | (~m_c_h_element_v_out(c_e_h_3, c_f, s5)) | (~node18(c_e_h_3, c_f, s4, s5))))),
% 290.25/182.76 inference(monotonicity,[status(thm)],[6719])).
% 290.25/182.76 tff(6721,plain,
% 290.25/182.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s5)) | m_c_h_element_v_out(c_e_h_3, c_f, s4) | (~node18(c_e_h_3, c_f, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s4) | (~m_c_h_element_v_out(c_e_h_3, c_f, s5)) | (~node18(c_e_h_3, c_f, s4, s5)))),
% 290.25/182.76 inference(transitivity,[status(thm)],[6720, 6718])).
% 290.25/182.76 tff(6722,plain,
% 290.25/182.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s5)) | m_c_h_element_v_out(c_e_h_3, c_f, s4) | (~node18(c_e_h_3, c_f, s4, s5)))),
% 290.25/182.76 inference(quant_inst,[status(thm)],[])).
% 290.25/182.76 tff(6723,plain,
% 290.25/182.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s4) | (~m_c_h_element_v_out(c_e_h_3, c_f, s5)) | (~node18(c_e_h_3, c_f, s4, s5))),
% 290.25/182.76 inference(modus_ponens,[status(thm)],[6722, 6721])).
% 290.25/182.76 tff(6724,plain,
% 290.25/182.76 ($false),
% 290.25/182.76 inference(unit_resolution,[status(thm)],[6723, 753, 6717, 6716, 6485])).
% 290.25/182.76 tff(6725,plain,((~node18(c_e_h_3, c_f, s4, s5)) | m_c_h_element_v_out(c_e_h_3, c_f, s4) | (~m_c_h_element_v_out(c_e_h_3, c_f, s5))), inference(lemma,lemma(discharge,[]))).
% 290.25/182.76 tff(6726,plain,
% 290.25/182.76 ((~node18(c_e_h_3, c_f, s4, s5)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s5))),
% 290.25/182.76 inference(unit_resolution,[status(thm)],[6725, 6715])).
% 290.25/182.76 tff(6727,plain,
% 290.25/182.76 (~node18(c_e_h_3, c_f, s4, s5)),
% 290.25/182.76 inference(unit_resolution,[status(thm)],[6726, 6485])).
% 290.25/182.76 tff(6728,plain,
% 290.25/182.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s4, s5)) | node19(c_e_h_3, c_f, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s4, s5)) | node19(c_e_h_3, c_f, s4, s5))),
% 290.25/182.76 inference(rewrite,[status(thm)],[])).
% 290.25/182.76 tff(6729,plain,
% 290.25/182.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s4, s5)) | node19(c_e_h_3, c_f, s4, s5))),
% 290.25/182.76 inference(quant_inst,[status(thm)],[])).
% 290.25/182.76 tff(6730,plain,
% 290.25/182.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s4, s5)) | node19(c_e_h_3, c_f, s4, s5)),
% 290.25/182.76 inference(modus_ponens,[status(thm)],[6729, 6728])).
% 290.25/182.76 tff(6731,plain,
% 290.25/182.76 (node19(c_e_h_3, c_f, s4, s5)),
% 290.25/182.76 inference(unit_resolution,[status(thm)],[6730, 190, 1028])).
% 290.25/182.76 tff(6732,plain,
% 290.25/182.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_f, s4, s5)) | node18(c_e_h_3, c_f, s4, s5) | node17(c_e_h_3, c_f, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s4, s5)) | node18(c_e_h_3, c_f, s4, s5) | node17(c_e_h_3, c_f, s4))),
% 290.25/182.76 inference(rewrite,[status(thm)],[])).
% 290.25/182.76 tff(6733,plain,
% 290.25/182.76 ((node17(c_e_h_3, c_f, s4) | node18(c_e_h_3, c_f, s4, s5) | (~node19(c_e_h_3, c_f, s4, s5))) <=> ((~node19(c_e_h_3, c_f, s4, s5)) | node18(c_e_h_3, c_f, s4, s5) | node17(c_e_h_3, c_f, s4))),
% 290.25/182.76 inference(rewrite,[status(thm)],[])).
% 290.25/182.76 tff(6734,plain,
% 290.25/182.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s4) | node18(c_e_h_3, c_f, s4, s5) | (~node19(c_e_h_3, c_f, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_f, s4, s5)) | node18(c_e_h_3, c_f, s4, s5) | node17(c_e_h_3, c_f, s4)))),
% 290.25/182.76 inference(monotonicity,[status(thm)],[6733])).
% 290.25/182.76 tff(6735,plain,
% 290.25/182.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s4) | node18(c_e_h_3, c_f, s4, s5) | (~node19(c_e_h_3, c_f, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s4, s5)) | node18(c_e_h_3, c_f, s4, s5) | node17(c_e_h_3, c_f, s4))),
% 290.25/182.76 inference(transitivity,[status(thm)],[6734, 6732])).
% 290.25/182.76 tff(6736,plain,
% 290.25/182.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s4) | node18(c_e_h_3, c_f, s4, s5) | (~node19(c_e_h_3, c_f, s4, s5)))),
% 290.25/182.76 inference(quant_inst,[status(thm)],[])).
% 290.25/182.76 tff(6737,plain,
% 290.25/182.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s4, s5)) | node18(c_e_h_3, c_f, s4, s5) | node17(c_e_h_3, c_f, s4)),
% 290.25/182.76 inference(modus_ponens,[status(thm)],[6736, 6735])).
% 290.25/182.76 tff(6738,plain,
% 290.25/182.76 (node18(c_e_h_3, c_f, s4, s5) | node17(c_e_h_3, c_f, s4)),
% 290.25/182.76 inference(unit_resolution,[status(thm)],[6737, 776, 6731])).
% 290.25/182.76 tff(6739,plain,
% 290.25/182.76 (node17(c_e_h_3, c_f, s4)),
% 290.25/182.76 inference(unit_resolution,[status(thm)],[6738, 6727])).
% 290.25/182.76 tff(6740,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_f, s4)), introduced(assumption)).
% 290.25/182.76 tff(6741,plain,
% 290.25/182.76 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s4)) | (~node17(c_e_h_3, c_f, s4)) | m_c_h_element_v_in2(c_e_h_3, c_f, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s4)) | (~node17(c_e_h_3, c_f, s4)) | m_c_h_element_v_in2(c_e_h_3, c_f, s4))),
% 290.25/182.76 inference(rewrite,[status(thm)],[])).
% 290.25/182.76 tff(6742,plain,
% 290.25/182.76 (((~m_c_h_element_v_in1(c_e_h_3, c_f, s4)) | m_c_h_element_v_in2(c_e_h_3, c_f, s4) | (~node17(c_e_h_3, c_f, s4))) <=> ((~m_c_h_element_v_in1(c_e_h_3, c_f, s4)) | (~node17(c_e_h_3, c_f, s4)) | m_c_h_element_v_in2(c_e_h_3, c_f, s4))),
% 290.25/182.76 inference(rewrite,[status(thm)],[])).
% 290.25/182.76 tff(6743,plain,
% 290.25/182.76 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s4)) | m_c_h_element_v_in2(c_e_h_3, c_f, s4) | (~node17(c_e_h_3, c_f, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s4)) | (~node17(c_e_h_3, c_f, s4)) | m_c_h_element_v_in2(c_e_h_3, c_f, s4)))),
% 290.25/182.76 inference(monotonicity,[status(thm)],[6742])).
% 290.25/182.76 tff(6744,plain,
% 290.25/182.76 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s4)) | m_c_h_element_v_in2(c_e_h_3, c_f, s4) | (~node17(c_e_h_3, c_f, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s4)) | (~node17(c_e_h_3, c_f, s4)) | m_c_h_element_v_in2(c_e_h_3, c_f, s4))),
% 290.25/182.76 inference(transitivity,[status(thm)],[6743, 6741])).
% 290.25/182.76 tff(6745,plain,
% 290.25/182.76 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s4)) | m_c_h_element_v_in2(c_e_h_3, c_f, s4) | (~node17(c_e_h_3, c_f, s4)))),
% 290.25/182.77 inference(quant_inst,[status(thm)],[])).
% 290.25/182.77 tff(6746,plain,
% 290.25/182.77 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s4)) | (~node17(c_e_h_3, c_f, s4)) | m_c_h_element_v_in2(c_e_h_3, c_f, s4)),
% 290.25/182.77 inference(modus_ponens,[status(thm)],[6745, 6744])).
% 290.25/182.77 tff(6747,plain,
% 290.25/182.77 ((~m_c_h_element_v_in1(c_e_h_3, c_f, s4)) | (~node17(c_e_h_3, c_f, s4))),
% 290.25/182.77 inference(unit_resolution,[status(thm)],[6746, 919, 6740])).
% 290.25/182.77 tff(6748,plain,
% 290.25/182.77 (~m_c_h_element_v_in1(c_e_h_3, c_f, s4)),
% 290.25/182.77 inference(unit_resolution,[status(thm)],[6747, 6739])).
% 290.25/182.77 tff(6749,assumption,(node15(c_e_h_3, c_f, s4, s5)), introduced(assumption)).
% 290.25/182.77 tff(6750,plain,
% 290.25/182.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s5)) | (~node15(c_e_h_3, c_f, s4, s5)) | m_c_h_element_v_out(c_e_h_3, c_f, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s5)) | (~node15(c_e_h_3, c_f, s4, s5)) | m_c_h_element_v_out(c_e_h_3, c_f, s4))),
% 290.25/182.77 inference(rewrite,[status(thm)],[])).
% 290.25/182.77 tff(6751,plain,
% 290.25/182.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s5)) | (~node15(c_e_h_3, c_f, s4, s5)) | m_c_h_element_v_out(c_e_h_3, c_f, s4))),
% 290.25/182.77 inference(quant_inst,[status(thm)],[])).
% 290.25/182.77 tff(6752,plain,
% 290.25/182.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s5)) | (~node15(c_e_h_3, c_f, s4, s5)) | m_c_h_element_v_out(c_e_h_3, c_f, s4)),
% 290.25/182.77 inference(modus_ponens,[status(thm)],[6751, 6750])).
% 290.25/182.77 tff(6753,plain,
% 290.25/182.77 ($false),
% 290.25/182.77 inference(unit_resolution,[status(thm)],[6752, 147, 6749, 6715, 6485])).
% 290.25/182.77 tff(6754,plain,((~node15(c_e_h_3, c_f, s4, s5)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s5))), inference(lemma,lemma(discharge,[]))).
% 290.25/182.77 tff(6755,plain,
% 290.25/182.77 (~node15(c_e_h_3, c_f, s4, s5)),
% 290.25/182.77 inference(unit_resolution,[status(thm)],[6754, 6485])).
% 290.25/182.77 tff(6756,assumption,(node17(c_e_h_3, c_f, s4)), introduced(assumption)).
% 290.25/182.77 tff(6757,assumption,(node16(c_e_h_3, c_f, s4)), introduced(assumption)).
% 290.25/182.77 tff(6758,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_f, s4)), introduced(assumption)).
% 290.25/182.77 tff(6759,plain,
% 290.25/182.77 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s4) | (~node17(c_e_h_3, c_f, s4)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_3, c_f, s4) | (~node17(c_e_h_3, c_f, s4)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s4)))),
% 290.25/182.77 inference(rewrite,[status(thm)],[])).
% 290.25/182.77 tff(6760,plain,
% 290.25/182.77 ((m_c_h_element_v_in1(c_e_h_3, c_f, s4) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s4)) | (~node17(c_e_h_3, c_f, s4))) <=> (m_c_h_element_v_in1(c_e_h_3, c_f, s4) | (~node17(c_e_h_3, c_f, s4)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s4)))),
% 290.25/182.77 inference(rewrite,[status(thm)],[])).
% 290.25/182.77 tff(6761,plain,
% 290.25/182.77 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s4) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s4)) | (~node17(c_e_h_3, c_f, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s4) | (~node17(c_e_h_3, c_f, s4)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s4))))),
% 290.25/182.77 inference(monotonicity,[status(thm)],[6760])).
% 290.25/182.77 tff(6762,plain,
% 290.25/182.77 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s4) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s4)) | (~node17(c_e_h_3, c_f, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_3, c_f, s4) | (~node17(c_e_h_3, c_f, s4)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s4)))),
% 290.25/182.77 inference(transitivity,[status(thm)],[6761, 6759])).
% 290.25/182.77 tff(6763,plain,
% 290.25/182.77 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s4) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s4)) | (~node17(c_e_h_3, c_f, s4)))),
% 290.25/182.77 inference(quant_inst,[status(thm)],[])).
% 290.25/182.77 tff(6764,plain,
% 290.25/182.77 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_3, c_f, s4) | (~node17(c_e_h_3, c_f, s4)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s4))),
% 290.25/182.77 inference(modus_ponens,[status(thm)],[6763, 6762])).
% 290.25/182.77 tff(6765,plain,
% 290.25/182.77 (m_c_h_element_v_in1(c_e_h_3, c_f, s4) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s4))),
% 290.25/182.77 inference(unit_resolution,[status(thm)],[6764, 859, 6756])).
% 290.25/182.77 tff(6766,plain,
% 290.25/182.77 (~m_c_h_element_v_in2(c_e_h_3, c_f, s4)),
% 290.25/182.77 inference(unit_resolution,[status(thm)],[6765, 6758])).
% 290.25/182.77 tff(6767,plain,
% 290.25/182.77 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s4)) | m_c_h_element_v_in1(c_e_h_3, c_f, s4) | m_c_h_element_v_in2(c_e_h_3, c_f, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s4)) | m_c_h_element_v_in1(c_e_h_3, c_f, s4) | m_c_h_element_v_in2(c_e_h_3, c_f, s4))),
% 290.25/182.77 inference(rewrite,[status(thm)],[])).
% 290.25/182.77 tff(6768,plain,
% 290.25/182.77 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s4)) | m_c_h_element_v_in1(c_e_h_3, c_f, s4) | m_c_h_element_v_in2(c_e_h_3, c_f, s4))),
% 290.25/182.77 inference(quant_inst,[status(thm)],[])).
% 290.25/182.77 tff(6769,plain,
% 290.25/182.77 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s4)) | m_c_h_element_v_in1(c_e_h_3, c_f, s4) | m_c_h_element_v_in2(c_e_h_3, c_f, s4)),
% 290.25/182.77 inference(modus_ponens,[status(thm)],[6768, 6767])).
% 290.25/182.77 tff(6770,plain,
% 290.25/182.77 (m_c_h_element_v_in1(c_e_h_3, c_f, s4) | m_c_h_element_v_in2(c_e_h_3, c_f, s4)),
% 290.25/182.77 inference(unit_resolution,[status(thm)],[6769, 178, 6757])).
% 290.25/182.77 tff(6771,plain,
% 290.25/182.77 ($false),
% 290.25/182.77 inference(unit_resolution,[status(thm)],[6770, 6766, 6758])).
% 290.25/182.77 tff(6772,plain,(m_c_h_element_v_in1(c_e_h_3, c_f, s4) | (~node16(c_e_h_3, c_f, s4)) | (~node17(c_e_h_3, c_f, s4))), inference(lemma,lemma(discharge,[]))).
% 290.25/182.77 tff(6773,plain,
% 290.25/182.77 (m_c_h_element_v_in1(c_e_h_3, c_f, s4)),
% 290.25/182.77 inference(unit_resolution,[status(thm)],[6772, 6757, 6756])).
% 290.25/182.77 tff(6774,plain,
% 290.25/182.77 ((~m_c_h_element_v_in1(c_e_h_3, c_f, s4)) | m_c_h_element_v_in2(c_e_h_3, c_f, s4)),
% 290.25/182.77 inference(unit_resolution,[status(thm)],[6746, 919, 6756])).
% 290.25/182.77 tff(6775,plain,
% 290.25/182.77 (m_c_h_element_v_in2(c_e_h_3, c_f, s4)),
% 290.25/182.77 inference(unit_resolution,[status(thm)],[6774, 6773])).
% 290.25/182.77 tff(6776,plain,
% 290.25/182.77 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s4)) | (~node16(c_e_h_3, c_f, s4)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s4)) | (~node16(c_e_h_3, c_f, s4)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s4)))),
% 290.25/182.77 inference(rewrite,[status(thm)],[])).
% 290.25/182.77 tff(6777,plain,
% 290.25/182.77 (((~node16(c_e_h_3, c_f, s4)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s4)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s4))) <=> ((~m_c_h_element_v_in1(c_e_h_3, c_f, s4)) | (~node16(c_e_h_3, c_f, s4)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s4)))),
% 290.25/182.78 inference(rewrite,[status(thm)],[])).
% 290.25/182.78 tff(6778,plain,
% 290.25/182.78 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_f, s4)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s4)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s4)) | (~node16(c_e_h_3, c_f, s4)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s4))))),
% 290.25/182.78 inference(monotonicity,[status(thm)],[6777])).
% 290.25/182.78 tff(6779,plain,
% 290.25/182.78 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_f, s4)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s4)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s4)) | (~node16(c_e_h_3, c_f, s4)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s4)))),
% 290.25/182.78 inference(transitivity,[status(thm)],[6778, 6776])).
% 290.25/182.78 tff(6780,plain,
% 290.25/182.78 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_f, s4)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s4)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s4)))),
% 290.25/182.78 inference(quant_inst,[status(thm)],[])).
% 290.25/182.78 tff(6781,plain,
% 290.25/182.78 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s4)) | (~node16(c_e_h_3, c_f, s4)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s4))),
% 290.25/182.78 inference(modus_ponens,[status(thm)],[6780, 6779])).
% 290.25/182.78 tff(6782,plain,
% 290.25/182.78 ((~m_c_h_element_v_in1(c_e_h_3, c_f, s4)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s4))),
% 290.25/182.78 inference(unit_resolution,[status(thm)],[6781, 2307, 6757])).
% 290.25/182.78 tff(6783,plain,
% 290.25/182.78 ($false),
% 290.25/182.78 inference(unit_resolution,[status(thm)],[6782, 6775, 6773])).
% 290.25/182.78 tff(6784,plain,((~node16(c_e_h_3, c_f, s4)) | (~node17(c_e_h_3, c_f, s4))), inference(lemma,lemma(discharge,[]))).
% 290.25/182.78 tff(6785,plain,
% 290.25/182.78 (~node16(c_e_h_3, c_f, s4)),
% 290.25/182.78 inference(unit_resolution,[status(thm)],[6784, 6739])).
% 290.25/182.78 tff(6786,plain,
% 290.25/182.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_3, c_f, s4, s5) | node15(c_e_h_3, c_f, s4, s5) | (~node19(c_e_h_3, c_f, s4, s5)) | node16(c_e_h_3, c_f, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_f, s4, s5) | node15(c_e_h_3, c_f, s4, s5) | (~node19(c_e_h_3, c_f, s4, s5)) | node16(c_e_h_3, c_f, s4))),
% 290.25/182.78 inference(rewrite,[status(thm)],[])).
% 290.25/182.78 tff(6787,plain,
% 290.25/182.78 ((node16(c_e_h_3, c_f, s4) | node14(c_e_h_3, c_f, s4, s5) | node15(c_e_h_3, c_f, s4, s5) | (~node19(c_e_h_3, c_f, s4, s5))) <=> (node14(c_e_h_3, c_f, s4, s5) | node15(c_e_h_3, c_f, s4, s5) | (~node19(c_e_h_3, c_f, s4, s5)) | node16(c_e_h_3, c_f, s4))),
% 290.25/182.78 inference(rewrite,[status(thm)],[])).
% 290.25/182.78 tff(6788,plain,
% 290.25/182.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s4) | node14(c_e_h_3, c_f, s4, s5) | node15(c_e_h_3, c_f, s4, s5) | (~node19(c_e_h_3, c_f, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_3, c_f, s4, s5) | node15(c_e_h_3, c_f, s4, s5) | (~node19(c_e_h_3, c_f, s4, s5)) | node16(c_e_h_3, c_f, s4)))),
% 290.25/182.78 inference(monotonicity,[status(thm)],[6787])).
% 290.25/182.78 tff(6789,plain,
% 290.25/182.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s4) | node14(c_e_h_3, c_f, s4, s5) | node15(c_e_h_3, c_f, s4, s5) | (~node19(c_e_h_3, c_f, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_f, s4, s5) | node15(c_e_h_3, c_f, s4, s5) | (~node19(c_e_h_3, c_f, s4, s5)) | node16(c_e_h_3, c_f, s4))),
% 290.25/182.78 inference(transitivity,[status(thm)],[6788, 6786])).
% 290.25/182.78 tff(6790,plain,
% 290.25/182.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s4) | node14(c_e_h_3, c_f, s4, s5) | node15(c_e_h_3, c_f, s4, s5) | (~node19(c_e_h_3, c_f, s4, s5)))),
% 290.25/182.78 inference(quant_inst,[status(thm)],[])).
% 290.25/182.78 tff(6791,plain,
% 290.25/182.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_f, s4, s5) | node15(c_e_h_3, c_f, s4, s5) | (~node19(c_e_h_3, c_f, s4, s5)) | node16(c_e_h_3, c_f, s4)),
% 290.25/182.78 inference(modus_ponens,[status(thm)],[6790, 6789])).
% 290.25/182.78 tff(6792,plain,
% 290.25/182.78 (node14(c_e_h_3, c_f, s4, s5) | node15(c_e_h_3, c_f, s4, s5) | node16(c_e_h_3, c_f, s4)),
% 290.25/182.78 inference(unit_resolution,[status(thm)],[6791, 204, 6731])).
% 290.25/182.78 tff(6793,plain,
% 290.25/182.78 (node14(c_e_h_3, c_f, s4, s5)),
% 290.25/182.78 inference(unit_resolution,[status(thm)],[6792, 6785, 6755])).
% 290.25/182.78 tff(6794,assumption,(node14(c_e_h_3, c_f, s4, s5)), introduced(assumption)).
% 290.25/182.78 tff(6795,plain,
% 290.25/182.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s4) | (~node14(c_e_h_3, c_f, s4, s5)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_f, s4) | (~node14(c_e_h_3, c_f, s4, s5)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s5)))),
% 290.25/182.78 inference(rewrite,[status(thm)],[])).
% 290.25/182.78 tff(6796,plain,
% 290.25/182.78 (((~node14(c_e_h_3, c_f, s4, s5)) | m_c_h_element_v_in1(c_e_h_3, c_f, s4) | (~m_c_h_element_v_out(c_e_h_3, c_f, s5))) <=> (m_c_h_element_v_in1(c_e_h_3, c_f, s4) | (~node14(c_e_h_3, c_f, s4, s5)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s5)))),
% 290.25/182.78 inference(rewrite,[status(thm)],[])).
% 290.25/182.78 tff(6797,plain,
% 290.25/182.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s4, s5)) | m_c_h_element_v_in1(c_e_h_3, c_f, s4) | (~m_c_h_element_v_out(c_e_h_3, c_f, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s4) | (~node14(c_e_h_3, c_f, s4, s5)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s5))))),
% 290.25/182.78 inference(monotonicity,[status(thm)],[6796])).
% 290.25/182.78 tff(6798,plain,
% 290.25/182.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s4, s5)) | m_c_h_element_v_in1(c_e_h_3, c_f, s4) | (~m_c_h_element_v_out(c_e_h_3, c_f, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_f, s4) | (~node14(c_e_h_3, c_f, s4, s5)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s5)))),
% 290.25/182.78 inference(transitivity,[status(thm)],[6797, 6795])).
% 290.25/182.78 tff(6799,plain,
% 290.25/182.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s4, s5)) | m_c_h_element_v_in1(c_e_h_3, c_f, s4) | (~m_c_h_element_v_out(c_e_h_3, c_f, s5)))),
% 290.25/182.78 inference(quant_inst,[status(thm)],[])).
% 290.25/182.78 tff(6800,plain,
% 290.25/182.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_f, s4) | (~node14(c_e_h_3, c_f, s4, s5)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s5))),
% 290.25/182.78 inference(modus_ponens,[status(thm)],[6799, 6798])).
% 290.25/182.78 tff(6801,plain,
% 290.25/182.78 ($false),
% 290.25/182.78 inference(unit_resolution,[status(thm)],[6800, 223, 6794, 6485, 6758])).
% 290.25/182.78 tff(6802,plain,((~node14(c_e_h_3, c_f, s4, s5)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s5)) | m_c_h_element_v_in1(c_e_h_3, c_f, s4)), inference(lemma,lemma(discharge,[]))).
% 290.25/182.78 tff(6803,plain,
% 290.25/182.78 ($false),
% 290.25/182.78 inference(unit_resolution,[status(thm)],[6802, 6793, 6748, 6485])).
% 290.25/182.78 tff(6804,plain,((~m_c_h_element_v_out(c_e_h_3, c_f, s5)) | m_c_h_element_v_in2(c_e_h_3, c_f, s4)), inference(lemma,lemma(discharge,[]))).
% 290.25/182.78 tff(6805,plain,
% 290.25/182.78 (~m_c_h_element_v_out(c_e_h_3, c_f, s5)),
% 290.25/182.78 inference(unit_resolution,[status(thm)],[6804, 6484])).
% 290.25/182.78 tff(6806,assumption,(~m_c_h_element_v_out(c_e_h_3, c_f, s5)), introduced(assumption)).
% 290.25/182.78 tff(6807,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_f, s5)), introduced(assumption)).
% 290.25/182.78 tff(6808,assumption,(m_c_h_element_v_out(c_e_h_3, c_f, s6)), introduced(assumption)).
% 290.25/182.78 tff(6809,assumption,(node18(c_e_h_3, c_f, s5, s6)), introduced(assumption)).
% 290.25/182.78 tff(6810,plain,
% 290.25/182.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_f, s5) | (~node18(c_e_h_3, c_f, s5, s6)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s5) | (~node18(c_e_h_3, c_f, s5, s6)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s6)))),
% 290.25/182.78 inference(rewrite,[status(thm)],[])).
% 290.25/182.78 tff(6811,plain,
% 290.25/182.78 (((~m_c_h_element_v_out(c_e_h_3, c_f, s6)) | m_c_h_element_v_out(c_e_h_3, c_f, s5) | (~node18(c_e_h_3, c_f, s5, s6))) <=> (m_c_h_element_v_out(c_e_h_3, c_f, s5) | (~node18(c_e_h_3, c_f, s5, s6)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s6)))),
% 290.25/182.78 inference(rewrite,[status(thm)],[])).
% 290.25/182.78 tff(6812,plain,
% 290.25/182.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s6)) | m_c_h_element_v_out(c_e_h_3, c_f, s5) | (~node18(c_e_h_3, c_f, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_f, s5) | (~node18(c_e_h_3, c_f, s5, s6)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s6))))),
% 290.25/182.78 inference(monotonicity,[status(thm)],[6811])).
% 290.25/182.78 tff(6813,plain,
% 290.25/182.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s6)) | m_c_h_element_v_out(c_e_h_3, c_f, s5) | (~node18(c_e_h_3, c_f, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s5) | (~node18(c_e_h_3, c_f, s5, s6)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s6)))),
% 290.25/182.78 inference(transitivity,[status(thm)],[6812, 6810])).
% 290.25/182.78 tff(6814,plain,
% 290.25/182.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s6)) | m_c_h_element_v_out(c_e_h_3, c_f, s5) | (~node18(c_e_h_3, c_f, s5, s6)))),
% 290.25/182.78 inference(quant_inst,[status(thm)],[])).
% 290.25/182.78 tff(6815,plain,
% 290.25/182.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s5) | (~node18(c_e_h_3, c_f, s5, s6)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s6))),
% 290.25/182.78 inference(modus_ponens,[status(thm)],[6814, 6813])).
% 290.25/182.78 tff(6816,plain,
% 290.25/182.78 ($false),
% 290.25/182.78 inference(unit_resolution,[status(thm)],[6815, 753, 6808, 6809, 6806])).
% 290.25/182.78 tff(6817,plain,((~node18(c_e_h_3, c_f, s5, s6)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s6)) | m_c_h_element_v_out(c_e_h_3, c_f, s5)), inference(lemma,lemma(discharge,[]))).
% 290.25/182.78 tff(6818,plain,
% 290.25/182.78 (~node18(c_e_h_3, c_f, s5, s6)),
% 290.25/182.78 inference(unit_resolution,[status(thm)],[6817, 6806, 6808])).
% 290.25/182.78 tff(6819,plain,
% 290.25/182.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s5, s6)) | node19(c_e_h_3, c_f, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s5, s6)) | node19(c_e_h_3, c_f, s5, s6))),
% 290.25/182.79 inference(rewrite,[status(thm)],[])).
% 290.25/182.79 tff(6820,plain,
% 290.25/182.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s5, s6)) | node19(c_e_h_3, c_f, s5, s6))),
% 290.25/182.79 inference(quant_inst,[status(thm)],[])).
% 290.25/182.79 tff(6821,plain,
% 290.25/182.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s5, s6)) | node19(c_e_h_3, c_f, s5, s6)),
% 290.25/182.79 inference(modus_ponens,[status(thm)],[6820, 6819])).
% 290.25/182.79 tff(6822,plain,
% 290.25/182.79 (node19(c_e_h_3, c_f, s5, s6)),
% 290.25/182.79 inference(unit_resolution,[status(thm)],[6821, 190, 1406])).
% 290.25/182.79 tff(6823,plain,
% 290.25/182.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s5) | (~node19(c_e_h_3, c_f, s5, s6)) | node18(c_e_h_3, c_f, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_f, s5) | (~node19(c_e_h_3, c_f, s5, s6)) | node18(c_e_h_3, c_f, s5, s6))),
% 290.25/182.79 inference(rewrite,[status(thm)],[])).
% 290.25/182.79 tff(6824,plain,
% 290.25/182.79 ((node17(c_e_h_3, c_f, s5) | node18(c_e_h_3, c_f, s5, s6) | (~node19(c_e_h_3, c_f, s5, s6))) <=> (node17(c_e_h_3, c_f, s5) | (~node19(c_e_h_3, c_f, s5, s6)) | node18(c_e_h_3, c_f, s5, s6))),
% 290.25/182.79 inference(rewrite,[status(thm)],[])).
% 290.25/182.79 tff(6825,plain,
% 290.25/182.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s5) | node18(c_e_h_3, c_f, s5, s6) | (~node19(c_e_h_3, c_f, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s5) | (~node19(c_e_h_3, c_f, s5, s6)) | node18(c_e_h_3, c_f, s5, s6)))),
% 290.25/182.79 inference(monotonicity,[status(thm)],[6824])).
% 290.25/182.79 tff(6826,plain,
% 290.25/182.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s5) | node18(c_e_h_3, c_f, s5, s6) | (~node19(c_e_h_3, c_f, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_f, s5) | (~node19(c_e_h_3, c_f, s5, s6)) | node18(c_e_h_3, c_f, s5, s6))),
% 290.25/182.79 inference(transitivity,[status(thm)],[6825, 6823])).
% 290.25/182.79 tff(6827,plain,
% 290.25/182.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s5) | node18(c_e_h_3, c_f, s5, s6) | (~node19(c_e_h_3, c_f, s5, s6)))),
% 290.25/182.79 inference(quant_inst,[status(thm)],[])).
% 290.25/182.79 tff(6828,plain,
% 290.25/182.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_f, s5) | (~node19(c_e_h_3, c_f, s5, s6)) | node18(c_e_h_3, c_f, s5, s6)),
% 290.25/182.79 inference(modus_ponens,[status(thm)],[6827, 6826])).
% 290.25/182.79 tff(6829,plain,
% 290.25/182.79 (node17(c_e_h_3, c_f, s5) | node18(c_e_h_3, c_f, s5, s6)),
% 290.25/182.79 inference(unit_resolution,[status(thm)],[6828, 776, 6822])).
% 290.25/182.79 tff(6830,plain,
% 290.25/182.79 (node17(c_e_h_3, c_f, s5)),
% 290.25/182.79 inference(unit_resolution,[status(thm)],[6829, 6818])).
% 290.25/182.79 tff(6831,plain,
% 290.25/182.79 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_f, s5)) | m_c_h_element_v_in2(c_e_h_3, c_f, s5) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_f, s5)) | m_c_h_element_v_in2(c_e_h_3, c_f, s5) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s5)))),
% 290.25/182.79 inference(rewrite,[status(thm)],[])).
% 290.25/182.79 tff(6832,plain,
% 290.25/182.79 (((~m_c_h_element_v_in1(c_e_h_3, c_f, s5)) | m_c_h_element_v_in2(c_e_h_3, c_f, s5) | (~node17(c_e_h_3, c_f, s5))) <=> ((~node17(c_e_h_3, c_f, s5)) | m_c_h_element_v_in2(c_e_h_3, c_f, s5) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s5)))),
% 290.25/182.79 inference(rewrite,[status(thm)],[])).
% 290.25/182.79 tff(6833,plain,
% 290.25/182.79 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s5)) | m_c_h_element_v_in2(c_e_h_3, c_f, s5) | (~node17(c_e_h_3, c_f, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_f, s5)) | m_c_h_element_v_in2(c_e_h_3, c_f, s5) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s5))))),
% 290.25/182.79 inference(monotonicity,[status(thm)],[6832])).
% 290.25/182.79 tff(6834,plain,
% 290.25/182.79 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s5)) | m_c_h_element_v_in2(c_e_h_3, c_f, s5) | (~node17(c_e_h_3, c_f, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_f, s5)) | m_c_h_element_v_in2(c_e_h_3, c_f, s5) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s5)))),
% 290.25/182.79 inference(transitivity,[status(thm)],[6833, 6831])).
% 290.25/182.79 tff(6835,plain,
% 290.25/182.79 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s5)) | m_c_h_element_v_in2(c_e_h_3, c_f, s5) | (~node17(c_e_h_3, c_f, s5)))),
% 290.25/182.79 inference(quant_inst,[status(thm)],[])).
% 290.25/182.79 tff(6836,plain,
% 290.25/182.79 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_f, s5)) | m_c_h_element_v_in2(c_e_h_3, c_f, s5) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s5))),
% 290.25/182.79 inference(modus_ponens,[status(thm)],[6835, 6834])).
% 290.25/182.79 tff(6837,plain,
% 290.25/182.79 ((~node17(c_e_h_3, c_f, s5)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s5))),
% 290.25/182.79 inference(unit_resolution,[status(thm)],[6836, 919, 6807])).
% 290.25/182.79 tff(6838,plain,
% 290.25/182.79 (~m_c_h_element_v_in1(c_e_h_3, c_f, s5)),
% 290.25/182.79 inference(unit_resolution,[status(thm)],[6837, 6830])).
% 290.25/182.79 tff(6839,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_f, s5)), introduced(assumption)).
% 290.25/182.79 tff(6840,assumption,(~node15(c_e_h_3, c_f, s5, s6)), introduced(assumption)).
% 290.25/182.79 tff(6841,plain,
% 290.25/182.79 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s5)) | m_c_h_element_v_in1(c_e_h_3, c_f, s5) | m_c_h_element_v_in2(c_e_h_3, c_f, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s5)) | m_c_h_element_v_in1(c_e_h_3, c_f, s5) | m_c_h_element_v_in2(c_e_h_3, c_f, s5))),
% 290.25/182.79 inference(rewrite,[status(thm)],[])).
% 290.25/182.79 tff(6842,plain,
% 290.25/182.79 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s5)) | m_c_h_element_v_in1(c_e_h_3, c_f, s5) | m_c_h_element_v_in2(c_e_h_3, c_f, s5))),
% 290.25/182.79 inference(quant_inst,[status(thm)],[])).
% 290.25/182.79 tff(6843,plain,
% 290.25/182.79 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s5)) | m_c_h_element_v_in1(c_e_h_3, c_f, s5) | m_c_h_element_v_in2(c_e_h_3, c_f, s5)),
% 290.25/182.79 inference(modus_ponens,[status(thm)],[6842, 6841])).
% 290.25/182.79 tff(6844,plain,
% 290.25/182.79 ((~node16(c_e_h_3, c_f, s5)) | m_c_h_element_v_in1(c_e_h_3, c_f, s5)),
% 290.25/182.79 inference(unit_resolution,[status(thm)],[6843, 178, 6807])).
% 290.25/182.79 tff(6845,plain,
% 290.25/182.79 (~node16(c_e_h_3, c_f, s5)),
% 290.25/182.79 inference(unit_resolution,[status(thm)],[6844, 6839])).
% 290.25/182.79 tff(6846,plain,
% 290.25/182.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_3, c_f, s5, s6) | (~node19(c_e_h_3, c_f, s5, s6)) | node16(c_e_h_3, c_f, s5) | node15(c_e_h_3, c_f, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_f, s5, s6) | (~node19(c_e_h_3, c_f, s5, s6)) | node16(c_e_h_3, c_f, s5) | node15(c_e_h_3, c_f, s5, s6))),
% 290.25/182.80 inference(rewrite,[status(thm)],[])).
% 290.25/182.80 tff(6847,plain,
% 290.25/182.80 ((node16(c_e_h_3, c_f, s5) | node14(c_e_h_3, c_f, s5, s6) | node15(c_e_h_3, c_f, s5, s6) | (~node19(c_e_h_3, c_f, s5, s6))) <=> (node14(c_e_h_3, c_f, s5, s6) | (~node19(c_e_h_3, c_f, s5, s6)) | node16(c_e_h_3, c_f, s5) | node15(c_e_h_3, c_f, s5, s6))),
% 290.25/182.80 inference(rewrite,[status(thm)],[])).
% 290.25/182.80 tff(6848,plain,
% 290.25/182.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s5) | node14(c_e_h_3, c_f, s5, s6) | node15(c_e_h_3, c_f, s5, s6) | (~node19(c_e_h_3, c_f, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_3, c_f, s5, s6) | (~node19(c_e_h_3, c_f, s5, s6)) | node16(c_e_h_3, c_f, s5) | node15(c_e_h_3, c_f, s5, s6)))),
% 290.25/182.80 inference(monotonicity,[status(thm)],[6847])).
% 290.25/182.80 tff(6849,plain,
% 290.25/182.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s5) | node14(c_e_h_3, c_f, s5, s6) | node15(c_e_h_3, c_f, s5, s6) | (~node19(c_e_h_3, c_f, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_f, s5, s6) | (~node19(c_e_h_3, c_f, s5, s6)) | node16(c_e_h_3, c_f, s5) | node15(c_e_h_3, c_f, s5, s6))),
% 290.25/182.80 inference(transitivity,[status(thm)],[6848, 6846])).
% 290.25/182.80 tff(6850,plain,
% 290.25/182.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s5) | node14(c_e_h_3, c_f, s5, s6) | node15(c_e_h_3, c_f, s5, s6) | (~node19(c_e_h_3, c_f, s5, s6)))),
% 290.25/182.80 inference(quant_inst,[status(thm)],[])).
% 290.25/182.80 tff(6851,plain,
% 290.25/182.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_f, s5, s6) | (~node19(c_e_h_3, c_f, s5, s6)) | node16(c_e_h_3, c_f, s5) | node15(c_e_h_3, c_f, s5, s6)),
% 290.25/182.80 inference(modus_ponens,[status(thm)],[6850, 6849])).
% 290.25/182.80 tff(6852,plain,
% 290.25/182.80 (node14(c_e_h_3, c_f, s5, s6) | node16(c_e_h_3, c_f, s5) | node15(c_e_h_3, c_f, s5, s6)),
% 290.25/182.80 inference(unit_resolution,[status(thm)],[6851, 204, 6822])).
% 290.25/182.80 tff(6853,plain,
% 290.25/182.80 (node14(c_e_h_3, c_f, s5, s6)),
% 290.25/182.80 inference(unit_resolution,[status(thm)],[6852, 6845, 6840])).
% 290.25/182.80 tff(6854,plain,
% 290.25/182.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s5) | (~node14(c_e_h_3, c_f, s5, s6)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_f, s5) | (~node14(c_e_h_3, c_f, s5, s6)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s6)))),
% 290.25/182.80 inference(rewrite,[status(thm)],[])).
% 290.25/182.80 tff(6855,plain,
% 290.25/182.80 (((~node14(c_e_h_3, c_f, s5, s6)) | m_c_h_element_v_in1(c_e_h_3, c_f, s5) | (~m_c_h_element_v_out(c_e_h_3, c_f, s6))) <=> (m_c_h_element_v_in1(c_e_h_3, c_f, s5) | (~node14(c_e_h_3, c_f, s5, s6)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s6)))),
% 290.25/182.80 inference(rewrite,[status(thm)],[])).
% 290.25/182.80 tff(6856,plain,
% 290.25/182.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s5, s6)) | m_c_h_element_v_in1(c_e_h_3, c_f, s5) | (~m_c_h_element_v_out(c_e_h_3, c_f, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s5) | (~node14(c_e_h_3, c_f, s5, s6)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s6))))),
% 290.25/182.80 inference(monotonicity,[status(thm)],[6855])).
% 290.25/182.80 tff(6857,plain,
% 290.25/182.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s5, s6)) | m_c_h_element_v_in1(c_e_h_3, c_f, s5) | (~m_c_h_element_v_out(c_e_h_3, c_f, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_f, s5) | (~node14(c_e_h_3, c_f, s5, s6)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s6)))),
% 290.33/182.80 inference(transitivity,[status(thm)],[6856, 6854])).
% 290.33/182.80 tff(6858,plain,
% 290.33/182.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s5, s6)) | m_c_h_element_v_in1(c_e_h_3, c_f, s5) | (~m_c_h_element_v_out(c_e_h_3, c_f, s6)))),
% 290.33/182.80 inference(quant_inst,[status(thm)],[])).
% 290.33/182.80 tff(6859,plain,
% 290.33/182.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_f, s5) | (~node14(c_e_h_3, c_f, s5, s6)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s6))),
% 290.33/182.80 inference(modus_ponens,[status(thm)],[6858, 6857])).
% 290.33/182.80 tff(6860,plain,
% 290.33/182.80 ($false),
% 290.33/182.80 inference(unit_resolution,[status(thm)],[6859, 223, 6808, 6853, 6839])).
% 290.33/182.80 tff(6861,plain,(m_c_h_element_v_in1(c_e_h_3, c_f, s5) | (~m_c_h_element_v_out(c_e_h_3, c_f, s6)) | node15(c_e_h_3, c_f, s5, s6) | m_c_h_element_v_in2(c_e_h_3, c_f, s5)), inference(lemma,lemma(discharge,[]))).
% 290.33/182.80 tff(6862,plain,
% 290.33/182.80 (node15(c_e_h_3, c_f, s5, s6)),
% 290.33/182.80 inference(unit_resolution,[status(thm)],[6861, 6838, 6808, 6807])).
% 290.33/182.80 tff(6863,plain,
% 290.33/182.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s6)) | (~node15(c_e_h_3, c_f, s5, s6)) | m_c_h_element_v_out(c_e_h_3, c_f, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s6)) | (~node15(c_e_h_3, c_f, s5, s6)) | m_c_h_element_v_out(c_e_h_3, c_f, s5))),
% 290.33/182.80 inference(rewrite,[status(thm)],[])).
% 290.33/182.80 tff(6864,plain,
% 290.33/182.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s6)) | (~node15(c_e_h_3, c_f, s5, s6)) | m_c_h_element_v_out(c_e_h_3, c_f, s5))),
% 290.33/182.80 inference(quant_inst,[status(thm)],[])).
% 290.33/182.80 tff(6865,plain,
% 290.33/182.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s6)) | (~node15(c_e_h_3, c_f, s5, s6)) | m_c_h_element_v_out(c_e_h_3, c_f, s5)),
% 290.33/182.80 inference(modus_ponens,[status(thm)],[6864, 6863])).
% 290.33/182.80 tff(6866,plain,
% 290.33/182.80 ($false),
% 290.33/182.80 inference(unit_resolution,[status(thm)],[6865, 147, 6808, 6862, 6806])).
% 290.33/182.80 tff(6867,plain,(m_c_h_element_v_out(c_e_h_3, c_f, s5) | (~m_c_h_element_v_out(c_e_h_3, c_f, s6)) | m_c_h_element_v_in2(c_e_h_3, c_f, s5)), inference(lemma,lemma(discharge,[]))).
% 290.33/182.80 tff(6868,plain,
% 290.33/182.80 ((~m_c_h_element_v_out(c_e_h_3, c_f, s6)) | m_c_h_element_v_in2(c_e_h_3, c_f, s5)),
% 290.33/182.80 inference(unit_resolution,[status(thm)],[6867, 6805])).
% 290.33/182.80 tff(6869,plain,
% 290.33/182.80 (~m_c_h_element_v_out(c_e_h_3, c_f, s6)),
% 290.33/182.80 inference(unit_resolution,[status(thm)],[6868, 6477])).
% 290.33/182.80 tff(6870,plain,
% 290.33/182.80 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6) | m_c_h_element_v_out(c_e_h_3, c_f, s6))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6) | m_c_h_element_v_out(c_e_h_3, c_f, s6))),
% 290.33/182.80 inference(rewrite,[status(thm)],[])).
% 290.33/182.80 tff(6871,plain,
% 290.33/182.80 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6) | m_c_h_element_v_out(c_e_h_3, c_f, s6))),
% 290.33/182.80 inference(quant_inst,[status(thm)],[])).
% 290.33/182.80 tff(6872,plain,
% 290.33/182.80 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6) | m_c_h_element_v_out(c_e_h_3, c_f, s6)),
% 290.33/182.80 inference(modus_ponens,[status(thm)],[6871, 6870])).
% 290.33/182.80 tff(6873,plain,
% 290.33/182.80 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6) | m_c_h_element_v_out(c_e_h_3, c_f, s6)),
% 290.33/182.80 inference(unit_resolution,[status(thm)],[6872, 5689])).
% 290.33/182.80 tff(6874,plain,
% 290.33/182.80 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6)),
% 290.33/182.80 inference(unit_resolution,[status(thm)],[6873, 6869])).
% 290.33/182.80 tff(6875,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s5)), introduced(assumption)).
% 290.33/182.80 tff(6876,plain,
% 290.33/182.80 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s5) | m_c_h_element_v_out(c_e_h_3, c_f, s5))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s5) | m_c_h_element_v_out(c_e_h_3, c_f, s5))),
% 290.33/182.80 inference(rewrite,[status(thm)],[])).
% 290.33/182.80 tff(6877,plain,
% 290.33/182.80 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s5) | m_c_h_element_v_out(c_e_h_3, c_f, s5))),
% 290.33/182.80 inference(quant_inst,[status(thm)],[])).
% 290.33/182.80 tff(6878,plain,
% 290.33/182.80 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s5) | m_c_h_element_v_out(c_e_h_3, c_f, s5)),
% 290.33/182.80 inference(modus_ponens,[status(thm)],[6877, 6876])).
% 290.33/182.80 tff(6879,plain,
% 290.33/182.80 ($false),
% 290.33/182.80 inference(unit_resolution,[status(thm)],[6878, 5689, 6806, 6875])).
% 290.33/182.80 tff(6880,plain,(m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s5) | m_c_h_element_v_out(c_e_h_3, c_f, s5)), inference(lemma,lemma(discharge,[]))).
% 290.33/182.80 tff(6881,plain,
% 290.33/182.80 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s5)),
% 290.33/182.80 inference(unit_resolution,[status(thm)],[6880, 6805])).
% 290.33/182.80 tff(6882,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s5)), introduced(assumption)).
% 290.33/182.80 tff(6883,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s3)), introduced(assumption)).
% 290.33/182.80 tff(6884,assumption,(~m_c_h_element_v_out(c_e_h_3, c_f, s3)), introduced(assumption)).
% 290.33/182.80 tff(6885,plain,
% 290.33/182.80 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s3) | m_c_h_element_v_out(c_e_h_3, c_f, s3))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s3) | m_c_h_element_v_out(c_e_h_3, c_f, s3))),
% 290.33/182.80 inference(rewrite,[status(thm)],[])).
% 290.33/182.80 tff(6886,plain,
% 290.33/182.80 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s3) | m_c_h_element_v_out(c_e_h_3, c_f, s3))),
% 290.33/182.80 inference(quant_inst,[status(thm)],[])).
% 290.33/182.80 tff(6887,plain,
% 290.33/182.80 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s3) | m_c_h_element_v_out(c_e_h_3, c_f, s3)),
% 290.33/182.80 inference(modus_ponens,[status(thm)],[6886, 6885])).
% 290.33/182.80 tff(6888,plain,
% 290.33/182.80 ($false),
% 290.33/182.80 inference(unit_resolution,[status(thm)],[6887, 5689, 6884, 6883])).
% 290.33/182.80 tff(6889,plain,(m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s3) | m_c_h_element_v_out(c_e_h_3, c_f, s3)), inference(lemma,lemma(discharge,[]))).
% 290.33/182.80 tff(6890,plain,
% 290.33/182.80 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s3)),
% 290.33/182.80 inference(unit_resolution,[status(thm)],[6889, 6632])).
% 290.33/182.80 tff(6891,plain,
% 290.33/182.80 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s2) | m_c_h_element_v_out(c_e_h_3, c_f, s2))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s2) | m_c_h_element_v_out(c_e_h_3, c_f, s2))),
% 290.33/182.80 inference(rewrite,[status(thm)],[])).
% 290.33/182.80 tff(6892,plain,
% 290.33/182.80 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s2) | m_c_h_element_v_out(c_e_h_3, c_f, s2))),
% 290.33/182.81 inference(quant_inst,[status(thm)],[])).
% 290.33/182.81 tff(6893,plain,
% 290.33/182.81 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s2) | m_c_h_element_v_out(c_e_h_3, c_f, s2)),
% 290.33/182.81 inference(modus_ponens,[status(thm)],[6892, 6891])).
% 290.33/182.81 tff(6894,plain,
% 290.33/182.81 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s2) | m_c_h_element_v_out(c_e_h_3, c_f, s2)),
% 290.33/182.81 inference(unit_resolution,[status(thm)],[6893, 5689])).
% 290.33/182.81 tff(6895,plain,
% 290.33/182.81 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s2)),
% 290.33/182.81 inference(unit_resolution,[status(thm)],[6894, 6572])).
% 290.33/182.81 tff(6896,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3)), introduced(assumption)).
% 290.33/182.81 tff(6897,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s2)), introduced(assumption)).
% 290.33/182.81 tff(6898,assumption,(node10(c_e_h_3, c_m, s2, s3)), introduced(assumption)).
% 290.33/182.81 tff(6899,plain,
% 290.33/182.81 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s2) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s2))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s2) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s2))),
% 290.33/182.81 inference(rewrite,[status(thm)],[])).
% 290.33/182.81 tff(6900,plain,
% 290.33/182.81 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s2) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s2))),
% 290.33/182.81 inference(quant_inst,[status(thm)],[])).
% 290.33/182.81 tff(6901,plain,
% 290.33/182.81 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s2) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s2)),
% 290.33/182.81 inference(modus_ponens,[status(thm)],[6900, 6899])).
% 290.33/182.81 tff(6902,plain,
% 290.33/182.81 (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s2) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s2)),
% 290.33/182.81 inference(unit_resolution,[status(thm)],[6901, 5704])).
% 290.33/182.81 tff(6903,plain,
% 290.33/182.81 (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s2)),
% 290.33/182.81 inference(unit_resolution,[status(thm)],[6902, 5776])).
% 290.33/182.81 tff(6904,plain,
% 290.33/182.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s2)) | (~node10(c_e_h_3, c_m, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s2)) | (~node10(c_e_h_3, c_m, s2, s3)))),
% 290.33/182.81 inference(rewrite,[status(thm)],[])).
% 290.33/182.81 tff(6905,plain,
% 290.33/182.81 (((~node10(c_e_h_3, c_m, s2, s3)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s2)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s2)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3)) <=> (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s2)) | (~node10(c_e_h_3, c_m, s2, s3)))),
% 290.33/182.81 inference(rewrite,[status(thm)],[])).
% 290.33/182.81 tff(6906,plain,
% 290.33/182.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s2, s3)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s2)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s2)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s2)) | (~node10(c_e_h_3, c_m, s2, s3))))),
% 290.33/182.81 inference(monotonicity,[status(thm)],[6905])).
% 290.33/182.81 tff(6907,plain,
% 290.33/182.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s2, s3)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s2)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s2)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s2)) | (~node10(c_e_h_3, c_m, s2, s3)))),
% 290.33/182.81 inference(transitivity,[status(thm)],[6906, 6904])).
% 290.33/182.81 tff(6908,plain,
% 290.33/182.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s2, s3)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s2)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s2)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3))),
% 290.33/182.81 inference(quant_inst,[status(thm)],[])).
% 290.33/182.81 tff(6909,plain,
% 290.33/182.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s2)) | (~node10(c_e_h_3, c_m, s2, s3))),
% 290.33/182.81 inference(modus_ponens,[status(thm)],[6908, 6907])).
% 290.33/182.81 tff(6910,plain,
% 290.33/182.81 ($false),
% 290.33/182.81 inference(unit_resolution,[status(thm)],[6909, 5718, 6897, 6903, 6898, 6896])).
% 290.33/182.81 tff(6911,plain,((~node10(c_e_h_3, c_m, s2, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s2)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3)), inference(lemma,lemma(discharge,[]))).
% 290.33/182.81 tff(6912,plain,
% 290.33/182.81 (~node10(c_e_h_3, c_m, s2, s3)),
% 290.33/182.81 inference(unit_resolution,[status(thm)],[6911, 6896, 6897])).
% 290.33/182.81 tff(6913,plain,
% 290.33/182.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s2, s3)) | node10(c_e_h_3, c_m, s2, s3) | node11(c_e_h_3, c_m, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s2, s3)) | node10(c_e_h_3, c_m, s2, s3) | node11(c_e_h_3, c_m, s2, s3))),
% 290.33/182.81 inference(rewrite,[status(thm)],[])).
% 290.33/182.81 tff(6914,plain,
% 290.33/182.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s2, s3)) | node10(c_e_h_3, c_m, s2, s3) | node11(c_e_h_3, c_m, s2, s3))),
% 290.33/182.81 inference(quant_inst,[status(thm)],[])).
% 290.33/182.81 tff(6915,plain,
% 290.33/182.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s2, s3)) | node10(c_e_h_3, c_m, s2, s3) | node11(c_e_h_3, c_m, s2, s3)),
% 290.33/182.81 inference(modus_ponens,[status(thm)],[6914, 6913])).
% 290.33/182.81 tff(6916,plain,
% 290.33/182.81 (node10(c_e_h_3, c_m, s2, s3) | node11(c_e_h_3, c_m, s2, s3)),
% 290.33/182.81 inference(unit_resolution,[status(thm)],[6915, 5002, 318])).
% 290.33/182.81 tff(6917,plain,
% 290.33/182.81 (node11(c_e_h_3, c_m, s2, s3)),
% 290.33/182.81 inference(unit_resolution,[status(thm)],[6916, 6912])).
% 290.33/182.81 tff(6918,plain,
% 290.33/182.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2)) | (~node11(c_e_h_3, c_m, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2)) | (~node11(c_e_h_3, c_m, s2, s3)))),
% 290.33/182.81 inference(rewrite,[status(thm)],[])).
% 290.33/182.81 tff(6919,plain,
% 290.33/182.81 ((m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3) | (~node11(c_e_h_3, c_m, s2, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2))) <=> (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2)) | (~node11(c_e_h_3, c_m, s2, s3)))),
% 290.33/182.81 inference(rewrite,[status(thm)],[])).
% 290.33/182.81 tff(6920,plain,
% 290.33/182.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3) | (~node11(c_e_h_3, c_m, s2, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2)) | (~node11(c_e_h_3, c_m, s2, s3))))),
% 290.33/182.81 inference(monotonicity,[status(thm)],[6919])).
% 290.33/182.81 tff(6921,plain,
% 290.33/182.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3) | (~node11(c_e_h_3, c_m, s2, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2)) | (~node11(c_e_h_3, c_m, s2, s3)))),
% 290.33/182.81 inference(transitivity,[status(thm)],[6920, 6918])).
% 290.33/182.81 tff(6922,plain,
% 290.33/182.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3) | (~node11(c_e_h_3, c_m, s2, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2)))),
% 290.33/182.81 inference(quant_inst,[status(thm)],[])).
% 290.33/182.81 tff(6923,plain,
% 290.33/182.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s2)) | (~node11(c_e_h_3, c_m, s2, s3))),
% 290.33/182.81 inference(modus_ponens,[status(thm)],[6922, 6921])).
% 290.33/182.81 tff(6924,plain,
% 290.33/182.81 ($false),
% 290.33/182.81 inference(unit_resolution,[status(thm)],[6923, 5742, 6917, 6047, 6896])).
% 290.33/182.81 tff(6925,plain,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s2))), inference(lemma,lemma(discharge,[]))).
% 290.33/182.81 tff(6926,plain,
% 290.33/182.81 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3)),
% 290.33/182.81 inference(unit_resolution,[status(thm)],[6925, 6895])).
% 290.33/182.81 tff(6927,plain,
% 290.33/182.81 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s3) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s3) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3))),
% 290.33/182.81 inference(rewrite,[status(thm)],[])).
% 290.33/182.81 tff(6928,plain,
% 290.33/182.81 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s3) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3))),
% 290.33/182.81 inference(quant_inst,[status(thm)],[])).
% 290.33/182.81 tff(6929,plain,
% 290.33/182.81 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s3) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3)),
% 290.33/182.81 inference(modus_ponens,[status(thm)],[6928, 6927])).
% 290.33/182.81 tff(6930,plain,
% 290.33/182.81 (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s3) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3)),
% 290.33/182.81 inference(unit_resolution,[status(thm)],[6929, 5704])).
% 290.33/182.81 tff(6931,plain,
% 290.33/182.81 (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s3)),
% 290.33/182.81 inference(unit_resolution,[status(thm)],[6930, 6073])).
% 290.33/182.81 tff(6932,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3)), introduced(assumption)).
% 290.33/182.82 tff(6933,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4)), introduced(assumption)).
% 290.33/182.82 tff(6934,assumption,(node11(c_e_h_3, c_m, s3, s4)), introduced(assumption)).
% 290.33/182.82 tff(6935,plain,
% 290.33/182.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4) | (~node11(c_e_h_3, c_m, s3, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4) | (~node11(c_e_h_3, c_m, s3, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3)))),
% 290.33/182.82 inference(rewrite,[status(thm)],[])).
% 290.33/182.82 tff(6936,plain,
% 290.33/182.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4) | (~node11(c_e_h_3, c_m, s3, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3)))),
% 290.33/182.82 inference(quant_inst,[status(thm)],[])).
% 290.33/182.82 tff(6937,plain,
% 290.33/182.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4) | (~node11(c_e_h_3, c_m, s3, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3))),
% 290.33/182.82 inference(modus_ponens,[status(thm)],[6936, 6935])).
% 290.33/182.82 tff(6938,plain,
% 290.33/182.82 ($false),
% 290.33/182.82 inference(unit_resolution,[status(thm)],[6937, 5742, 6933, 6934, 6932])).
% 290.33/182.82 tff(6939,plain,((~node11(c_e_h_3, c_m, s3, s4)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3))), inference(lemma,lemma(discharge,[]))).
% 290.33/182.82 tff(6940,plain,
% 290.33/182.82 (~node11(c_e_h_3, c_m, s3, s4)),
% 290.33/182.82 inference(unit_resolution,[status(thm)],[6939, 6933, 6932])).
% 290.33/182.82 tff(6941,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s3)), introduced(assumption)).
% 290.33/182.82 tff(6942,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s3)), introduced(assumption)).
% 290.33/182.82 tff(6943,assumption,(node10(c_e_h_3, c_m, s3, s4)), introduced(assumption)).
% 290.33/182.82 tff(6944,plain,
% 290.33/182.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s3)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4) | (~node10(c_e_h_3, c_m, s3, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s3)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4) | (~node10(c_e_h_3, c_m, s3, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s3)))),
% 290.33/182.82 inference(rewrite,[status(thm)],[])).
% 290.33/182.82 tff(6945,plain,
% 290.33/182.82 (((~node10(c_e_h_3, c_m, s3, s4)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s3)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4)) <=> ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s3)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4) | (~node10(c_e_h_3, c_m, s3, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s3)))),
% 290.33/182.82 inference(rewrite,[status(thm)],[])).
% 290.33/182.82 tff(6946,plain,
% 290.33/182.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s3, s4)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s3)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s3)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4) | (~node10(c_e_h_3, c_m, s3, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s3))))),
% 290.33/182.82 inference(monotonicity,[status(thm)],[6945])).
% 290.33/182.82 tff(6947,plain,
% 290.33/182.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s3, s4)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s3)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s3)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4) | (~node10(c_e_h_3, c_m, s3, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s3)))),
% 290.33/182.82 inference(transitivity,[status(thm)],[6946, 6944])).
% 290.33/182.82 tff(6948,plain,
% 290.33/182.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s3, s4)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s3)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4))),
% 290.33/182.82 inference(quant_inst,[status(thm)],[])).
% 290.33/182.82 tff(6949,plain,
% 290.33/182.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s3)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4) | (~node10(c_e_h_3, c_m, s3, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s3))),
% 290.33/182.82 inference(modus_ponens,[status(thm)],[6948, 6947])).
% 290.33/182.82 tff(6950,plain,
% 290.33/182.82 ($false),
% 290.33/182.82 inference(unit_resolution,[status(thm)],[6949, 5718, 6941, 6933, 6943, 6942])).
% 290.33/182.82 tff(6951,plain,((~node10(c_e_h_3, c_m, s3, s4)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s3)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s3))), inference(lemma,lemma(discharge,[]))).
% 290.33/182.82 tff(6952,plain,
% 290.33/182.82 (~node10(c_e_h_3, c_m, s3, s4)),
% 290.33/182.82 inference(unit_resolution,[status(thm)],[6951, 6933, 6942, 6941])).
% 290.33/182.82 tff(6953,plain,
% 290.33/182.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s3, s4)) | node10(c_e_h_3, c_m, s3, s4) | node11(c_e_h_3, c_m, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s3, s4)) | node10(c_e_h_3, c_m, s3, s4) | node11(c_e_h_3, c_m, s3, s4))),
% 290.33/182.82 inference(rewrite,[status(thm)],[])).
% 290.33/182.82 tff(6954,plain,
% 290.33/182.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s3, s4)) | node10(c_e_h_3, c_m, s3, s4) | node11(c_e_h_3, c_m, s3, s4))),
% 290.33/182.82 inference(quant_inst,[status(thm)],[])).
% 290.33/182.82 tff(6955,plain,
% 290.33/182.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s3, s4)) | node10(c_e_h_3, c_m, s3, s4) | node11(c_e_h_3, c_m, s3, s4)),
% 290.33/182.82 inference(modus_ponens,[status(thm)],[6954, 6953])).
% 290.33/182.82 tff(6956,plain,
% 290.33/182.82 (node10(c_e_h_3, c_m, s3, s4) | node11(c_e_h_3, c_m, s3, s4)),
% 290.33/182.82 inference(unit_resolution,[status(thm)],[6955, 5002, 531])).
% 290.33/182.82 tff(6957,plain,
% 290.33/182.82 ($false),
% 290.33/182.82 inference(unit_resolution,[status(thm)],[6956, 6952, 6940])).
% 290.33/182.82 tff(6958,plain,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s3)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3))), inference(lemma,lemma(discharge,[]))).
% 290.33/182.82 tff(6959,plain,
% 290.33/182.82 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3))),
% 290.33/182.82 inference(unit_resolution,[status(thm)],[6958, 6931])).
% 290.33/182.82 tff(6960,plain,
% 290.33/182.82 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s3))),
% 290.33/182.82 inference(unit_resolution,[status(thm)],[6959, 6926])).
% 290.33/182.82 tff(6961,plain,
% 290.33/182.82 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4)),
% 290.33/182.82 inference(unit_resolution,[status(thm)],[6960, 6890])).
% 290.33/182.82 tff(6962,plain,
% 290.33/182.82 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4)))),
% 290.33/182.82 inference(rewrite,[status(thm)],[])).
% 290.33/182.82 tff(6963,plain,
% 290.33/182.82 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4)))),
% 290.33/182.82 inference(quant_inst,[status(thm)],[])).
% 290.33/182.82 tff(6964,plain,
% 290.33/182.82 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4))),
% 290.33/182.82 inference(modus_ponens,[status(thm)],[6963, 6962])).
% 290.33/182.82 tff(6965,plain,
% 290.33/182.82 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s4)),
% 290.33/182.82 inference(unit_resolution,[status(thm)],[6964, 5601, 6961])).
% 290.33/182.82 tff(6966,plain,
% 290.33/182.82 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s4)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s4)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s4))),
% 290.33/182.82 inference(rewrite,[status(thm)],[])).
% 290.33/182.82 tff(6967,plain,
% 290.33/182.82 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s4)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s4))),
% 290.33/182.82 inference(quant_inst,[status(thm)],[])).
% 290.33/182.82 tff(6968,plain,
% 290.33/182.82 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s4)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s4)),
% 290.33/182.82 inference(modus_ponens,[status(thm)],[6967, 6966])).
% 290.33/182.82 tff(6969,plain,
% 290.33/182.82 (~node9(c_e_h_3, c_n, s4)),
% 290.33/182.82 inference(unit_resolution,[status(thm)],[6968, 4972, 6965])).
% 290.33/182.82 tff(6970,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5)), introduced(assumption)).
% 290.33/182.82 tff(6971,assumption,(node11(c_e_h_3, c_n, s4, s5)), introduced(assumption)).
% 290.33/182.82 tff(6972,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4)), introduced(assumption)).
% 290.33/182.82 tff(6973,plain,
% 290.33/182.82 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3)))),
% 290.33/182.82 inference(rewrite,[status(thm)],[])).
% 290.33/182.82 tff(6974,plain,
% 290.33/182.82 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3)))),
% 290.33/182.82 inference(quant_inst,[status(thm)],[])).
% 290.33/182.82 tff(6975,plain,
% 290.33/182.82 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s3))),
% 290.33/182.82 inference(modus_ponens,[status(thm)],[6974, 6973])).
% 290.33/182.82 tff(6976,plain,
% 290.33/182.82 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s3)),
% 290.33/182.82 inference(unit_resolution,[status(thm)],[6975, 5601, 6926])).
% 290.33/182.82 tff(6977,plain,
% 290.33/182.82 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s3)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s3)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s3))),
% 290.33/182.83 inference(rewrite,[status(thm)],[])).
% 290.33/182.83 tff(6978,plain,
% 290.33/182.83 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s3)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s3))),
% 290.33/182.83 inference(quant_inst,[status(thm)],[])).
% 290.33/182.83 tff(6979,plain,
% 290.33/182.83 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s3)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s3)),
% 290.33/182.83 inference(modus_ponens,[status(thm)],[6978, 6977])).
% 290.33/182.83 tff(6980,plain,
% 290.33/182.83 (~node9(c_e_h_3, c_n, s3)),
% 290.33/182.83 inference(unit_resolution,[status(thm)],[6979, 4972, 6976])).
% 290.33/182.83 tff(6981,assumption,(node10(c_e_h_3, c_n, s3, s4)), introduced(assumption)).
% 290.33/182.83 tff(6982,plain,
% 290.33/182.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4)) | node9(c_e_h_3, c_n, s3) | (~node10(c_e_h_3, c_n, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4)) | node9(c_e_h_3, c_n, s3) | (~node10(c_e_h_3, c_n, s3, s4)))),
% 290.33/182.83 inference(rewrite,[status(thm)],[])).
% 290.33/182.83 tff(6983,plain,
% 290.33/182.83 ((node9(c_e_h_3, c_n, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4)) | (~node10(c_e_h_3, c_n, s3, s4))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4)) | node9(c_e_h_3, c_n, s3) | (~node10(c_e_h_3, c_n, s3, s4)))),
% 290.33/182.83 inference(rewrite,[status(thm)],[])).
% 290.33/182.83 tff(6984,plain,
% 290.33/182.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4)) | (~node10(c_e_h_3, c_n, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4)) | node9(c_e_h_3, c_n, s3) | (~node10(c_e_h_3, c_n, s3, s4))))),
% 290.33/182.83 inference(monotonicity,[status(thm)],[6983])).
% 290.33/182.83 tff(6985,plain,
% 290.33/182.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4)) | (~node10(c_e_h_3, c_n, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4)) | node9(c_e_h_3, c_n, s3) | (~node10(c_e_h_3, c_n, s3, s4)))),
% 290.33/182.83 inference(transitivity,[status(thm)],[6984, 6982])).
% 290.33/182.83 tff(6986,plain,
% 290.33/182.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4)) | (~node10(c_e_h_3, c_n, s3, s4)))),
% 290.33/182.83 inference(quant_inst,[status(thm)],[])).
% 290.33/182.83 tff(6987,plain,
% 290.33/182.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4)) | node9(c_e_h_3, c_n, s3) | (~node10(c_e_h_3, c_n, s3, s4))),
% 290.33/182.83 inference(modus_ponens,[status(thm)],[6986, 6985])).
% 290.33/182.83 tff(6988,plain,
% 290.33/182.83 ($false),
% 290.33/182.83 inference(unit_resolution,[status(thm)],[6987, 4986, 6972, 6981, 6980])).
% 290.33/182.83 tff(6989,plain,((~node10(c_e_h_3, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4))), inference(lemma,lemma(discharge,[]))).
% 290.33/182.83 tff(6990,plain,
% 290.33/182.83 (~node10(c_e_h_3, c_n, s3, s4)),
% 290.33/182.83 inference(unit_resolution,[status(thm)],[6989, 6972])).
% 290.33/182.83 tff(6991,plain,
% 290.33/182.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s3, s4)) | node10(c_e_h_3, c_n, s3, s4) | node11(c_e_h_3, c_n, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s3, s4)) | node10(c_e_h_3, c_n, s3, s4) | node11(c_e_h_3, c_n, s3, s4))),
% 290.33/182.83 inference(rewrite,[status(thm)],[])).
% 290.33/182.83 tff(6992,plain,
% 290.33/182.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s3, s4)) | node10(c_e_h_3, c_n, s3, s4) | node11(c_e_h_3, c_n, s3, s4))),
% 290.33/182.83 inference(quant_inst,[status(thm)],[])).
% 290.33/182.83 tff(6993,plain,
% 290.33/182.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s3, s4)) | node10(c_e_h_3, c_n, s3, s4) | node11(c_e_h_3, c_n, s3, s4)),
% 290.33/182.83 inference(modus_ponens,[status(thm)],[6992, 6991])).
% 290.33/182.83 tff(6994,plain,
% 290.33/182.83 (node10(c_e_h_3, c_n, s3, s4) | node11(c_e_h_3, c_n, s3, s4)),
% 290.33/182.83 inference(unit_resolution,[status(thm)],[6993, 5002, 531])).
% 290.33/182.83 tff(6995,plain,
% 290.33/182.83 (node11(c_e_h_3, c_n, s3, s4)),
% 290.33/182.83 inference(unit_resolution,[status(thm)],[6994, 6990])).
% 290.33/182.83 tff(6996,plain,
% 290.33/182.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4)) | (~node11(c_e_h_3, c_n, s3, s4)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4)) | (~node11(c_e_h_3, c_n, s3, s4)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3))),
% 290.33/182.83 inference(rewrite,[status(thm)],[])).
% 290.33/182.83 tff(6997,plain,
% 290.33/182.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4)) | (~node11(c_e_h_3, c_n, s3, s4)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3))),
% 290.33/182.83 inference(quant_inst,[status(thm)],[])).
% 290.33/182.83 tff(6998,plain,
% 290.33/182.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4)) | (~node11(c_e_h_3, c_n, s3, s4)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s3)),
% 290.33/182.83 inference(modus_ponens,[status(thm)],[6997, 6996])).
% 290.33/182.83 tff(6999,plain,
% 290.33/182.83 ($false),
% 290.33/182.83 inference(unit_resolution,[status(thm)],[6998, 5017, 6073, 6972, 6995])).
% 290.33/182.83 tff(7000,plain,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4)), inference(lemma,lemma(discharge,[]))).
% 290.33/182.83 tff(7001,plain,
% 290.33/182.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5)) | (~node11(c_e_h_3, c_n, s4, s5)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5)) | (~node11(c_e_h_3, c_n, s4, s5)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4))),
% 290.33/182.83 inference(rewrite,[status(thm)],[])).
% 290.33/182.83 tff(7002,plain,
% 290.33/182.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5)) | (~node11(c_e_h_3, c_n, s4, s5)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4))),
% 290.33/182.83 inference(quant_inst,[status(thm)],[])).
% 290.33/182.83 tff(7003,plain,
% 290.33/182.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5)) | (~node11(c_e_h_3, c_n, s4, s5)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4)),
% 290.33/182.83 inference(modus_ponens,[status(thm)],[7002, 7001])).
% 290.33/182.83 tff(7004,plain,
% 290.33/182.83 ($false),
% 290.33/182.83 inference(unit_resolution,[status(thm)],[7003, 5017, 7000, 6971, 6970])).
% 290.33/182.83 tff(7005,plain,((~node11(c_e_h_3, c_n, s4, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5))), inference(lemma,lemma(discharge,[]))).
% 290.33/182.83 tff(7006,plain,
% 290.33/182.83 (~node11(c_e_h_3, c_n, s4, s5)),
% 290.33/182.83 inference(unit_resolution,[status(thm)],[7005, 6970])).
% 290.33/182.83 tff(7007,plain,
% 290.33/182.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s4, s5)) | node10(c_e_h_3, c_n, s4, s5) | node11(c_e_h_3, c_n, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s4, s5)) | node10(c_e_h_3, c_n, s4, s5) | node11(c_e_h_3, c_n, s4, s5))),
% 290.33/182.83 inference(rewrite,[status(thm)],[])).
% 290.33/182.83 tff(7008,plain,
% 290.33/182.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s4, s5)) | node10(c_e_h_3, c_n, s4, s5) | node11(c_e_h_3, c_n, s4, s5))),
% 290.33/182.83 inference(quant_inst,[status(thm)],[])).
% 290.33/182.83 tff(7009,plain,
% 290.33/182.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s4, s5)) | node10(c_e_h_3, c_n, s4, s5) | node11(c_e_h_3, c_n, s4, s5)),
% 290.33/182.83 inference(modus_ponens,[status(thm)],[7008, 7007])).
% 290.33/182.83 tff(7010,plain,
% 290.33/182.83 (node10(c_e_h_3, c_n, s4, s5) | node11(c_e_h_3, c_n, s4, s5)),
% 290.33/182.83 inference(unit_resolution,[status(thm)],[7009, 5002, 1028])).
% 290.33/182.83 tff(7011,plain,
% 290.33/182.83 (node10(c_e_h_3, c_n, s4, s5)),
% 290.33/182.83 inference(unit_resolution,[status(thm)],[7010, 7006])).
% 290.33/182.83 tff(7012,plain,
% 290.33/182.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5)) | (~node10(c_e_h_3, c_n, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_3, c_n, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5)) | (~node10(c_e_h_3, c_n, s4, s5)))),
% 290.33/182.83 inference(rewrite,[status(thm)],[])).
% 290.33/182.83 tff(7013,plain,
% 290.33/182.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5)) | (~node10(c_e_h_3, c_n, s4, s5)))),
% 290.33/182.83 inference(quant_inst,[status(thm)],[])).
% 290.33/182.83 tff(7014,plain,
% 290.33/182.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_3, c_n, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5)) | (~node10(c_e_h_3, c_n, s4, s5))),
% 290.33/182.83 inference(modus_ponens,[status(thm)],[7013, 7012])).
% 290.33/182.83 tff(7015,plain,
% 290.33/182.83 ($false),
% 290.33/182.83 inference(unit_resolution,[status(thm)],[7014, 4986, 7011, 6970, 6969])).
% 290.33/182.83 tff(7016,plain,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5)), inference(lemma,lemma(discharge,[]))).
% 290.33/182.83 tff(7017,plain,
% 290.33/182.83 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s5) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s5) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5))),
% 290.33/182.83 inference(rewrite,[status(thm)],[])).
% 290.33/182.83 tff(7018,plain,
% 290.33/182.83 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s5) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5))),
% 290.33/182.83 inference(quant_inst,[status(thm)],[])).
% 290.33/182.83 tff(7019,plain,
% 290.33/182.83 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s5) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5)),
% 290.33/182.83 inference(modus_ponens,[status(thm)],[7018, 7017])).
% 290.33/182.83 tff(7020,plain,
% 290.33/182.83 (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s5)),
% 290.33/182.83 inference(unit_resolution,[status(thm)],[7019, 5704, 7016])).
% 290.33/182.83 tff(7021,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)), introduced(assumption)).
% 290.33/182.83 tff(7022,plain,
% 290.33/182.83 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s4) | m_c_h_element_v_out(c_e_h_3, c_f, s4))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s4) | m_c_h_element_v_out(c_e_h_3, c_f, s4))),
% 290.33/182.84 inference(rewrite,[status(thm)],[])).
% 290.33/182.84 tff(7023,plain,
% 290.33/182.84 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s4) | m_c_h_element_v_out(c_e_h_3, c_f, s4))),
% 290.33/182.84 inference(quant_inst,[status(thm)],[])).
% 290.33/182.84 tff(7024,plain,
% 290.33/182.84 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s4) | m_c_h_element_v_out(c_e_h_3, c_f, s4)),
% 290.33/182.84 inference(modus_ponens,[status(thm)],[7023, 7022])).
% 290.33/182.84 tff(7025,plain,
% 290.33/182.84 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s4)),
% 290.33/182.84 inference(unit_resolution,[status(thm)],[7024, 5689, 6715])).
% 290.33/182.84 tff(7026,plain,
% 290.33/182.84 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s4) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s4) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4))),
% 290.33/182.84 inference(rewrite,[status(thm)],[])).
% 290.33/182.84 tff(7027,plain,
% 290.33/182.84 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s4) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4))),
% 290.33/182.84 inference(quant_inst,[status(thm)],[])).
% 290.33/182.84 tff(7028,plain,
% 290.33/182.84 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s4) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4)),
% 290.33/182.84 inference(modus_ponens,[status(thm)],[7027, 7026])).
% 290.33/182.84 tff(7029,plain,
% 290.33/182.84 (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s4) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4)),
% 290.33/182.84 inference(unit_resolution,[status(thm)],[7028, 5704])).
% 290.33/182.84 tff(7030,plain,
% 290.33/182.84 (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s4)),
% 290.33/182.84 inference(unit_resolution,[status(thm)],[7029, 7000])).
% 290.33/182.84 tff(7031,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s4)), introduced(assumption)).
% 290.33/182.84 tff(7032,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4)), introduced(assumption)).
% 290.33/182.84 tff(7033,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5)), introduced(assumption)).
% 290.33/182.84 tff(7034,assumption,(node11(c_e_h_3, c_m, s4, s5)), introduced(assumption)).
% 290.33/182.84 tff(7035,plain,
% 290.33/182.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5) | (~node11(c_e_h_3, c_m, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5) | (~node11(c_e_h_3, c_m, s4, s5)))),
% 290.33/182.84 inference(rewrite,[status(thm)],[])).
% 290.33/182.84 tff(7036,plain,
% 290.33/182.84 ((m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5) | (~node11(c_e_h_3, c_m, s4, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5) | (~node11(c_e_h_3, c_m, s4, s5)))),
% 290.33/182.84 inference(rewrite,[status(thm)],[])).
% 290.33/182.84 tff(7037,plain,
% 290.33/182.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5) | (~node11(c_e_h_3, c_m, s4, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5) | (~node11(c_e_h_3, c_m, s4, s5))))),
% 290.33/182.84 inference(monotonicity,[status(thm)],[7036])).
% 290.33/182.84 tff(7038,plain,
% 290.33/182.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5) | (~node11(c_e_h_3, c_m, s4, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5) | (~node11(c_e_h_3, c_m, s4, s5)))),
% 290.33/182.84 inference(transitivity,[status(thm)],[7037, 7035])).
% 290.33/182.84 tff(7039,plain,
% 290.33/182.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5) | (~node11(c_e_h_3, c_m, s4, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4)))),
% 290.33/182.84 inference(quant_inst,[status(thm)],[])).
% 290.33/182.84 tff(7040,plain,
% 290.33/182.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5) | (~node11(c_e_h_3, c_m, s4, s5))),
% 290.33/182.84 inference(modus_ponens,[status(thm)],[7039, 7038])).
% 290.33/182.84 tff(7041,plain,
% 290.33/182.84 ($false),
% 290.33/182.84 inference(unit_resolution,[status(thm)],[7040, 5742, 7032, 7033, 7034])).
% 290.33/182.84 tff(7042,plain,((~node11(c_e_h_3, c_m, s4, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5)), inference(lemma,lemma(discharge,[]))).
% 290.33/182.84 tff(7043,plain,
% 290.33/182.84 (~node11(c_e_h_3, c_m, s4, s5)),
% 290.33/182.84 inference(unit_resolution,[status(thm)],[7042, 7033, 7032])).
% 290.33/182.84 tff(7044,plain,
% 290.33/182.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s4, s5)) | node10(c_e_h_3, c_m, s4, s5) | node11(c_e_h_3, c_m, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s4, s5)) | node10(c_e_h_3, c_m, s4, s5) | node11(c_e_h_3, c_m, s4, s5))),
% 290.33/182.84 inference(rewrite,[status(thm)],[])).
% 290.33/182.84 tff(7045,plain,
% 290.33/182.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s4, s5)) | node10(c_e_h_3, c_m, s4, s5) | node11(c_e_h_3, c_m, s4, s5))),
% 290.33/182.84 inference(quant_inst,[status(thm)],[])).
% 290.33/182.84 tff(7046,plain,
% 290.33/182.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s4, s5)) | node10(c_e_h_3, c_m, s4, s5) | node11(c_e_h_3, c_m, s4, s5)),
% 290.33/182.84 inference(modus_ponens,[status(thm)],[7045, 7044])).
% 290.33/182.84 tff(7047,plain,
% 290.33/182.84 (node10(c_e_h_3, c_m, s4, s5) | node11(c_e_h_3, c_m, s4, s5)),
% 290.33/182.84 inference(unit_resolution,[status(thm)],[7046, 5002, 1028])).
% 290.33/182.84 tff(7048,plain,
% 290.33/182.84 (node10(c_e_h_3, c_m, s4, s5)),
% 290.33/182.84 inference(unit_resolution,[status(thm)],[7047, 7043])).
% 290.33/182.84 tff(7049,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s4)), introduced(assumption)).
% 290.33/182.84 tff(7050,plain,
% 290.33/182.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s4)) | (~node10(c_e_h_3, c_m, s4, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s4)) | (~node10(c_e_h_3, c_m, s4, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s4)))),
% 290.33/182.84 inference(rewrite,[status(thm)],[])).
% 290.33/182.84 tff(7051,plain,
% 290.33/182.84 (((~node10(c_e_h_3, c_m, s4, s5)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s4)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5)) <=> (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s4)) | (~node10(c_e_h_3, c_m, s4, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s4)))),
% 290.33/182.84 inference(rewrite,[status(thm)],[])).
% 290.33/182.84 tff(7052,plain,
% 290.33/182.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s4, s5)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s4)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s4)) | (~node10(c_e_h_3, c_m, s4, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s4))))),
% 290.33/182.84 inference(monotonicity,[status(thm)],[7051])).
% 290.33/182.84 tff(7053,plain,
% 290.33/182.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s4, s5)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s4)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s4)) | (~node10(c_e_h_3, c_m, s4, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s4)))),
% 290.33/182.84 inference(transitivity,[status(thm)],[7052, 7050])).
% 290.33/182.84 tff(7054,plain,
% 290.33/182.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s4, s5)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s4)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5))),
% 290.33/182.84 inference(quant_inst,[status(thm)],[])).
% 290.33/182.84 tff(7055,plain,
% 290.33/182.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s4)) | (~node10(c_e_h_3, c_m, s4, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s4))),
% 290.33/182.84 inference(modus_ponens,[status(thm)],[7054, 7053])).
% 290.33/182.84 tff(7056,plain,
% 290.33/182.84 ($false),
% 290.33/182.84 inference(unit_resolution,[status(thm)],[7055, 5718, 7049, 7033, 7048, 7031])).
% 290.33/182.84 tff(7057,plain,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4))), inference(lemma,lemma(discharge,[]))).
% 290.33/182.84 tff(7058,plain,
% 290.33/182.84 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s4))),
% 290.33/182.84 inference(unit_resolution,[status(thm)],[7057, 7030])).
% 290.33/182.84 tff(7059,plain,
% 290.33/182.84 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s4))),
% 290.33/182.84 inference(unit_resolution,[status(thm)],[7058, 6961])).
% 290.33/182.84 tff(7060,plain,
% 290.33/182.84 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5)),
% 290.33/182.84 inference(unit_resolution,[status(thm)],[7059, 7025])).
% 290.33/182.84 tff(7061,assumption,(node11(c_e_h_3, c_m, s5, s6)), introduced(assumption)).
% 290.33/182.84 tff(7062,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5)), introduced(assumption)).
% 290.33/182.84 tff(7063,plain,
% 290.33/182.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5)) | (~node11(c_e_h_3, c_m, s5, s6)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5)) | (~node11(c_e_h_3, c_m, s5, s6)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6))),
% 290.33/182.85 inference(rewrite,[status(thm)],[])).
% 290.33/182.85 tff(7064,plain,
% 290.33/182.85 ((m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6) | (~node11(c_e_h_3, c_m, s5, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5)) | (~node11(c_e_h_3, c_m, s5, s6)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6))),
% 290.33/182.85 inference(rewrite,[status(thm)],[])).
% 290.33/182.85 tff(7065,plain,
% 290.33/182.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6) | (~node11(c_e_h_3, c_m, s5, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5)) | (~node11(c_e_h_3, c_m, s5, s6)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)))),
% 290.33/182.85 inference(monotonicity,[status(thm)],[7064])).
% 290.33/182.85 tff(7066,plain,
% 290.33/182.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6) | (~node11(c_e_h_3, c_m, s5, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5)) | (~node11(c_e_h_3, c_m, s5, s6)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6))),
% 290.33/182.85 inference(transitivity,[status(thm)],[7065, 7063])).
% 290.33/182.85 tff(7067,plain,
% 290.33/182.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6) | (~node11(c_e_h_3, c_m, s5, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5)))),
% 290.33/182.85 inference(quant_inst,[status(thm)],[])).
% 290.33/182.85 tff(7068,plain,
% 290.33/182.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5)) | (~node11(c_e_h_3, c_m, s5, s6)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)),
% 290.33/182.85 inference(modus_ponens,[status(thm)],[7067, 7066])).
% 290.33/182.85 tff(7069,plain,
% 290.33/182.85 ($false),
% 290.33/182.85 inference(unit_resolution,[status(thm)],[7068, 5742, 7062, 7061, 7021])).
% 290.33/182.85 tff(7070,plain,((~node11(c_e_h_3, c_m, s5, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)), inference(lemma,lemma(discharge,[]))).
% 290.33/182.85 tff(7071,plain,
% 290.33/182.85 ((~node11(c_e_h_3, c_m, s5, s6)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)),
% 290.33/182.85 inference(unit_resolution,[status(thm)],[7070, 7060])).
% 290.33/182.85 tff(7072,plain,
% 290.33/182.85 (~node11(c_e_h_3, c_m, s5, s6)),
% 290.33/182.85 inference(unit_resolution,[status(thm)],[7071, 7021])).
% 290.33/182.85 tff(7073,plain,
% 290.33/182.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s5, s6)) | node10(c_e_h_3, c_m, s5, s6) | node11(c_e_h_3, c_m, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s5, s6)) | node10(c_e_h_3, c_m, s5, s6) | node11(c_e_h_3, c_m, s5, s6))),
% 290.33/182.85 inference(rewrite,[status(thm)],[])).
% 290.33/182.85 tff(7074,plain,
% 290.33/182.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s5, s6)) | node10(c_e_h_3, c_m, s5, s6) | node11(c_e_h_3, c_m, s5, s6))),
% 290.33/182.85 inference(quant_inst,[status(thm)],[])).
% 290.33/182.85 tff(7075,plain,
% 290.33/182.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s5, s6)) | node10(c_e_h_3, c_m, s5, s6) | node11(c_e_h_3, c_m, s5, s6)),
% 290.33/182.85 inference(modus_ponens,[status(thm)],[7074, 7073])).
% 290.33/182.85 tff(7076,plain,
% 290.33/182.85 (node10(c_e_h_3, c_m, s5, s6) | node11(c_e_h_3, c_m, s5, s6)),
% 290.33/182.85 inference(unit_resolution,[status(thm)],[7075, 5002, 1406])).
% 290.33/182.85 tff(7077,plain,
% 290.33/182.85 (node10(c_e_h_3, c_m, s5, s6)),
% 290.33/182.85 inference(unit_resolution,[status(thm)],[7076, 7072])).
% 290.33/182.85 tff(7078,plain,
% 290.33/182.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s5, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s5)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~node10(c_e_h_3, c_m, s5, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s5)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s5)))),
% 290.33/182.85 inference(rewrite,[status(thm)],[])).
% 290.33/182.85 tff(7079,plain,
% 290.33/182.85 (((~node10(c_e_h_3, c_m, s5, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s5)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)) <=> ((~node10(c_e_h_3, c_m, s5, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s5)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s5)))),
% 290.33/182.85 inference(rewrite,[status(thm)],[])).
% 290.33/182.85 tff(7080,plain,
% 290.33/182.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s5, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s5)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s5, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s5)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s5))))),
% 290.33/182.85 inference(monotonicity,[status(thm)],[7079])).
% 290.33/182.85 tff(7081,plain,
% 290.33/182.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s5, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s5)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~node10(c_e_h_3, c_m, s5, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s5)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s5)))),
% 290.33/182.85 inference(transitivity,[status(thm)],[7080, 7078])).
% 290.33/182.85 tff(7082,plain,
% 290.33/182.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s5, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s5)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6))),
% 290.33/182.85 inference(quant_inst,[status(thm)],[])).
% 290.33/182.85 tff(7083,plain,
% 290.33/182.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~node10(c_e_h_3, c_m, s5, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s5)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s5))),
% 290.33/182.85 inference(modus_ponens,[status(thm)],[7082, 7081])).
% 290.33/182.85 tff(7084,plain,
% 290.33/182.85 ($false),
% 290.33/182.85 inference(unit_resolution,[status(thm)],[7083, 5718, 7077, 7021, 7020, 6882])).
% 290.33/182.85 tff(7085,plain,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s5))), inference(lemma,lemma(discharge,[]))).
% 290.33/182.85 tff(7086,plain,
% 290.33/182.85 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)),
% 290.33/182.85 inference(unit_resolution,[status(thm)],[7085, 6881])).
% 290.33/182.85 tff(7087,plain,
% 290.33/182.85 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5)))),
% 290.33/182.85 inference(rewrite,[status(thm)],[])).
% 290.33/182.85 tff(7088,plain,
% 290.33/182.85 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5)))),
% 290.33/182.85 inference(quant_inst,[status(thm)],[])).
% 290.33/182.85 tff(7089,plain,
% 290.33/182.85 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s5))),
% 290.33/182.85 inference(modus_ponens,[status(thm)],[7088, 7087])).
% 290.33/182.85 tff(7090,plain,
% 290.33/182.85 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s5)),
% 290.33/182.85 inference(unit_resolution,[status(thm)],[7089, 5601, 7060])).
% 290.33/182.85 tff(7091,plain,
% 290.33/182.85 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s5)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s5)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s5))),
% 290.33/182.85 inference(rewrite,[status(thm)],[])).
% 290.33/182.85 tff(7092,plain,
% 290.33/182.85 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s5)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s5))),
% 290.33/182.85 inference(quant_inst,[status(thm)],[])).
% 290.33/182.85 tff(7093,plain,
% 290.33/182.85 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s5)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s5)),
% 290.33/182.85 inference(modus_ponens,[status(thm)],[7092, 7091])).
% 290.33/182.85 tff(7094,plain,
% 290.33/182.85 (~node9(c_e_h_3, c_n, s5)),
% 290.33/182.85 inference(unit_resolution,[status(thm)],[7093, 4972, 7090])).
% 290.33/182.85 tff(7095,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6)), introduced(assumption)).
% 290.33/182.85 tff(7096,assumption,(node11(c_e_h_3, c_n, s5, s6)), introduced(assumption)).
% 290.33/182.85 tff(7097,plain,
% 290.33/182.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6)) | (~node11(c_e_h_3, c_n, s5, s6)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6)) | (~node11(c_e_h_3, c_n, s5, s6)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5))),
% 290.33/182.85 inference(rewrite,[status(thm)],[])).
% 290.33/182.85 tff(7098,plain,
% 290.33/182.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6)) | (~node11(c_e_h_3, c_n, s5, s6)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5))),
% 290.33/182.85 inference(quant_inst,[status(thm)],[])).
% 290.33/182.85 tff(7099,plain,
% 290.33/182.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6)) | (~node11(c_e_h_3, c_n, s5, s6)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5)),
% 290.33/182.85 inference(modus_ponens,[status(thm)],[7098, 7097])).
% 290.33/182.85 tff(7100,plain,
% 290.33/182.85 ($false),
% 290.33/182.85 inference(unit_resolution,[status(thm)],[7099, 5017, 7096, 7016, 7095])).
% 290.33/182.85 tff(7101,plain,((~node11(c_e_h_3, c_n, s5, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6))), inference(lemma,lemma(discharge,[]))).
% 290.33/182.85 tff(7102,plain,
% 290.33/182.85 (~node11(c_e_h_3, c_n, s5, s6)),
% 290.33/182.85 inference(unit_resolution,[status(thm)],[7101, 7095])).
% 290.33/182.86 tff(7103,plain,
% 290.33/182.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s5, s6)) | node10(c_e_h_3, c_n, s5, s6) | node11(c_e_h_3, c_n, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s5, s6)) | node10(c_e_h_3, c_n, s5, s6) | node11(c_e_h_3, c_n, s5, s6))),
% 290.33/182.86 inference(rewrite,[status(thm)],[])).
% 290.33/182.86 tff(7104,plain,
% 290.33/182.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s5, s6)) | node10(c_e_h_3, c_n, s5, s6) | node11(c_e_h_3, c_n, s5, s6))),
% 290.33/182.86 inference(quant_inst,[status(thm)],[])).
% 290.33/182.86 tff(7105,plain,
% 290.33/182.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s5, s6)) | node10(c_e_h_3, c_n, s5, s6) | node11(c_e_h_3, c_n, s5, s6)),
% 290.33/182.86 inference(modus_ponens,[status(thm)],[7104, 7103])).
% 290.33/182.86 tff(7106,plain,
% 290.33/182.86 (node10(c_e_h_3, c_n, s5, s6) | node11(c_e_h_3, c_n, s5, s6)),
% 290.33/182.86 inference(unit_resolution,[status(thm)],[7105, 5002, 1406])).
% 290.33/182.86 tff(7107,plain,
% 290.33/182.86 (node10(c_e_h_3, c_n, s5, s6)),
% 290.33/182.86 inference(unit_resolution,[status(thm)],[7106, 7102])).
% 290.33/182.86 tff(7108,plain,
% 290.33/182.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6)) | (~node10(c_e_h_3, c_n, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_3, c_n, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6)) | (~node10(c_e_h_3, c_n, s5, s6)))),
% 290.33/182.86 inference(rewrite,[status(thm)],[])).
% 290.33/182.86 tff(7109,plain,
% 290.33/182.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6)) | (~node10(c_e_h_3, c_n, s5, s6)))),
% 290.33/182.86 inference(quant_inst,[status(thm)],[])).
% 290.33/182.86 tff(7110,plain,
% 290.33/182.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_3, c_n, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6)) | (~node10(c_e_h_3, c_n, s5, s6))),
% 290.33/182.86 inference(modus_ponens,[status(thm)],[7109, 7108])).
% 290.33/182.86 tff(7111,plain,
% 290.33/182.86 ($false),
% 290.33/182.86 inference(unit_resolution,[status(thm)],[7110, 4986, 7107, 7095, 7094])).
% 290.33/182.86 tff(7112,plain,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6)), inference(lemma,lemma(discharge,[]))).
% 290.33/182.86 tff(7113,plain,
% 290.33/182.86 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s6) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s6) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6))),
% 290.33/182.86 inference(rewrite,[status(thm)],[])).
% 290.33/182.86 tff(7114,plain,
% 290.33/182.86 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s6) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6))),
% 290.33/182.86 inference(quant_inst,[status(thm)],[])).
% 290.33/182.86 tff(7115,plain,
% 290.33/182.86 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s6) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6)),
% 290.33/182.86 inference(modus_ponens,[status(thm)],[7114, 7113])).
% 290.33/182.86 tff(7116,plain,
% 290.33/182.86 (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s6)),
% 290.33/182.86 inference(unit_resolution,[status(thm)],[7115, 5704, 7112])).
% 290.33/182.86 tff(7117,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6)), introduced(assumption)).
% 290.33/182.86 tff(7118,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s6)), introduced(assumption)).
% 290.33/182.86 tff(7119,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7)), introduced(assumption)).
% 290.33/182.86 tff(7120,assumption,(node10(c_e_h_3, c_m, s6, s7)), introduced(assumption)).
% 290.33/182.86 tff(7121,plain,
% 290.33/182.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6)) | (~node10(c_e_h_3, c_m, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6)) | (~node10(c_e_h_3, c_m, s6, s7)))),
% 290.33/182.86 inference(rewrite,[status(thm)],[])).
% 290.33/182.86 tff(7122,plain,
% 290.33/182.86 (((~node10(c_e_h_3, c_m, s6, s7)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7)) <=> (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6)) | (~node10(c_e_h_3, c_m, s6, s7)))),
% 290.33/182.86 inference(rewrite,[status(thm)],[])).
% 290.33/182.86 tff(7123,plain,
% 290.33/182.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s6, s7)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6)) | (~node10(c_e_h_3, c_m, s6, s7))))),
% 290.33/182.86 inference(monotonicity,[status(thm)],[7122])).
% 290.33/182.86 tff(7124,plain,
% 290.33/182.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s6, s7)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6)) | (~node10(c_e_h_3, c_m, s6, s7)))),
% 290.33/182.86 inference(transitivity,[status(thm)],[7123, 7121])).
% 290.33/182.86 tff(7125,plain,
% 290.33/182.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s6, s7)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7))),
% 290.33/182.86 inference(quant_inst,[status(thm)],[])).
% 290.33/182.86 tff(7126,plain,
% 290.33/182.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6)) | (~node10(c_e_h_3, c_m, s6, s7))),
% 290.33/182.86 inference(modus_ponens,[status(thm)],[7125, 7124])).
% 290.33/182.86 tff(7127,plain,
% 290.33/182.86 ($false),
% 290.33/182.86 inference(unit_resolution,[status(thm)],[7126, 5718, 7119, 7117, 7120, 7118])).
% 290.33/182.86 tff(7128,plain,((~node10(c_e_h_3, c_m, s6, s7)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s6))), inference(lemma,lemma(discharge,[]))).
% 290.33/182.86 tff(7129,plain,
% 290.33/182.86 (~node10(c_e_h_3, c_m, s6, s7)),
% 290.33/182.86 inference(unit_resolution,[status(thm)],[7128, 7119, 7118, 7117])).
% 290.33/182.86 tff(7130,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)), introduced(assumption)).
% 290.33/182.86 tff(7131,assumption,(node11(c_e_h_3, c_m, s6, s7)), introduced(assumption)).
% 290.33/182.86 tff(7132,plain,
% 290.33/182.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)) | (~node11(c_e_h_3, c_m, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)) | (~node11(c_e_h_3, c_m, s6, s7)))),
% 290.33/182.86 inference(rewrite,[status(thm)],[])).
% 290.33/182.86 tff(7133,plain,
% 290.33/182.86 ((m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7) | (~node11(c_e_h_3, c_m, s6, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6))) <=> (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)) | (~node11(c_e_h_3, c_m, s6, s7)))),
% 290.33/182.86 inference(rewrite,[status(thm)],[])).
% 290.33/182.86 tff(7134,plain,
% 290.33/182.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7) | (~node11(c_e_h_3, c_m, s6, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)) | (~node11(c_e_h_3, c_m, s6, s7))))),
% 290.33/182.86 inference(monotonicity,[status(thm)],[7133])).
% 290.33/182.86 tff(7135,plain,
% 290.33/182.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7) | (~node11(c_e_h_3, c_m, s6, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)) | (~node11(c_e_h_3, c_m, s6, s7)))),
% 290.33/182.86 inference(transitivity,[status(thm)],[7134, 7132])).
% 290.33/182.86 tff(7136,plain,
% 290.33/182.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7) | (~node11(c_e_h_3, c_m, s6, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)))),
% 290.33/182.86 inference(quant_inst,[status(thm)],[])).
% 290.33/182.86 tff(7137,plain,
% 290.33/182.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)) | (~node11(c_e_h_3, c_m, s6, s7))),
% 290.33/182.86 inference(modus_ponens,[status(thm)],[7136, 7135])).
% 290.33/182.86 tff(7138,plain,
% 290.33/182.86 ($false),
% 290.33/182.86 inference(unit_resolution,[status(thm)],[7137, 5742, 7119, 7131, 7130])).
% 290.33/182.86 tff(7139,plain,((~node11(c_e_h_3, c_m, s6, s7)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6))), inference(lemma,lemma(discharge,[]))).
% 290.33/182.86 tff(7140,plain,
% 290.33/182.86 (~node11(c_e_h_3, c_m, s6, s7)),
% 290.33/182.86 inference(unit_resolution,[status(thm)],[7139, 7119, 7130])).
% 290.33/182.86 tff(7141,plain,
% 290.33/182.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s6, s7)) | node10(c_e_h_3, c_m, s6, s7) | node11(c_e_h_3, c_m, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s6, s7)) | node10(c_e_h_3, c_m, s6, s7) | node11(c_e_h_3, c_m, s6, s7))),
% 290.33/182.86 inference(rewrite,[status(thm)],[])).
% 290.33/182.86 tff(7142,plain,
% 290.33/182.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s6, s7)) | node10(c_e_h_3, c_m, s6, s7) | node11(c_e_h_3, c_m, s6, s7))),
% 290.33/182.87 inference(quant_inst,[status(thm)],[])).
% 290.33/182.87 tff(7143,plain,
% 290.33/182.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s6, s7)) | node10(c_e_h_3, c_m, s6, s7) | node11(c_e_h_3, c_m, s6, s7)),
% 290.33/182.87 inference(modus_ponens,[status(thm)],[7142, 7141])).
% 290.33/182.87 tff(7144,plain,
% 290.33/182.87 (node10(c_e_h_3, c_m, s6, s7) | node11(c_e_h_3, c_m, s6, s7)),
% 290.33/182.87 inference(unit_resolution,[status(thm)],[7143, 5002, 1844])).
% 290.33/182.87 tff(7145,plain,
% 290.33/182.87 ($false),
% 290.33/182.87 inference(unit_resolution,[status(thm)],[7144, 7140, 7129])).
% 290.33/182.87 tff(7146,plain,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6))), inference(lemma,lemma(discharge,[]))).
% 290.33/182.87 tff(7147,plain,
% 290.33/182.87 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6))),
% 290.33/182.87 inference(unit_resolution,[status(thm)],[7146, 7116])).
% 290.33/182.87 tff(7148,plain,
% 290.33/182.87 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6))),
% 290.33/182.87 inference(unit_resolution,[status(thm)],[7147, 7086])).
% 290.33/182.87 tff(7149,plain,
% 290.33/182.87 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7)),
% 290.33/182.87 inference(unit_resolution,[status(thm)],[7148, 6874])).
% 290.33/182.87 tff(7150,plain,
% 290.33/182.87 (^[I0: $i, X: $i] : refl(((~m_and_h_gate_h_init_v_out(I0, c_m, X)) | m_and_h_gate_v_in2(I0, c_l, X)) <=> ((~m_and_h_gate_h_init_v_out(I0, c_m, X)) | m_and_h_gate_v_in2(I0, c_l, X)))),
% 290.33/182.87 inference(bind,[status(th)],[])).
% 290.33/182.87 tff(7151,plain,
% 290.33/182.87 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_m, X)) | m_and_h_gate_v_in2(I0, c_l, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_m, X)) | m_and_h_gate_v_in2(I0, c_l, X))),
% 290.33/182.87 inference(quant_intro,[status(thm)],[7150])).
% 290.33/182.87 tff(7152,plain,
% 290.33/182.87 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_m, X)) | m_and_h_gate_v_in2(I0, c_l, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_m, X)) | m_and_h_gate_v_in2(I0, c_l, X))),
% 290.33/182.87 inference(rewrite,[status(thm)],[])).
% 290.33/182.87 tff(7153,plain,
% 290.33/182.87 (^[I0: $i, X: $i] : rewrite((m_and_h_gate_v_in2(I0, c_l, X) | (~m_and_h_gate_h_init_v_out(I0, c_m, X))) <=> ((~m_and_h_gate_h_init_v_out(I0, c_m, X)) | m_and_h_gate_v_in2(I0, c_l, X)))),
% 290.33/182.87 inference(bind,[status(th)],[])).
% 290.33/182.87 tff(7154,plain,
% 290.33/182.87 (![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_l, X) | (~m_and_h_gate_h_init_v_out(I0, c_m, X))) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_m, X)) | m_and_h_gate_v_in2(I0, c_l, X))),
% 290.33/182.87 inference(quant_intro,[status(thm)],[7153])).
% 290.33/182.87 tff(7155,axiom,(![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_l, X) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_49')).
% 290.33/182.87 tff(7156,plain,
% 290.33/182.87 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_m, X)) | m_and_h_gate_v_in2(I0, c_l, X))),
% 290.33/182.87 inference(modus_ponens,[status(thm)],[7155, 7154])).
% 290.33/182.87 tff(7157,plain,
% 290.33/182.87 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_m, X)) | m_and_h_gate_v_in2(I0, c_l, X))),
% 290.33/182.87 inference(modus_ponens,[status(thm)],[7156, 7152])).
% 290.33/182.87 tff(7158,plain,(
% 290.33/182.87 ![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_m, X)) | m_and_h_gate_v_in2(I0, c_l, X))),
% 290.33/182.87 inference(skolemize,[status(sab)],[7157])).
% 290.33/182.87 tff(7159,plain,
% 290.33/182.87 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_m, X)) | m_and_h_gate_v_in2(I0, c_l, X))),
% 290.33/182.87 inference(modus_ponens,[status(thm)],[7158, 7151])).
% 290.33/182.87 tff(7160,plain,
% 290.33/182.87 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_m, X)) | m_and_h_gate_v_in2(I0, c_l, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7)) | m_and_h_gate_v_in2(c_e_h_3, c_l, s7))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_m, X)) | m_and_h_gate_v_in2(I0, c_l, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7)) | m_and_h_gate_v_in2(c_e_h_3, c_l, s7))),
% 290.33/182.87 inference(rewrite,[status(thm)],[])).
% 290.33/182.87 tff(7161,plain,
% 290.33/182.87 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_m, X)) | m_and_h_gate_v_in2(I0, c_l, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7)) | m_and_h_gate_v_in2(c_e_h_3, c_l, s7))),
% 290.33/182.87 inference(quant_inst,[status(thm)],[])).
% 290.33/182.87 tff(7162,plain,
% 290.33/182.87 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_m, X)) | m_and_h_gate_v_in2(I0, c_l, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7)) | m_and_h_gate_v_in2(c_e_h_3, c_l, s7)),
% 290.33/182.87 inference(modus_ponens,[status(thm)],[7161, 7160])).
% 290.33/182.87 tff(7163,plain,
% 290.33/182.87 (m_and_h_gate_v_in2(c_e_h_3, c_l, s7)),
% 290.33/182.87 inference(unit_resolution,[status(thm)],[7162, 7159, 7149])).
% 290.33/182.87 tff(7164,assumption,(node21(c_e_h_3, c_l, s7, s8)), introduced(assumption)).
% 290.33/182.87 tff(7165,plain,
% 290.33/182.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_l, s7)) | (~m_and_h_gate_v_in2(c_e_h_3, c_l, s7)) | (~node21(c_e_h_3, c_l, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_l, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s7)) | (~m_and_h_gate_v_in2(c_e_h_3, c_l, s7)) | (~node21(c_e_h_3, c_l, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_l, s8))),
% 290.33/182.87 inference(rewrite,[status(thm)],[])).
% 290.33/182.87 tff(7166,plain,
% 290.33/182.87 (((~node21(c_e_h_3, c_l, s7, s8)) | (~m_and_h_gate_v_in2(c_e_h_3, c_l, s7)) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s7)) | m_and_h_gate_v_out(c_e_h_3, c_l, s8)) <=> ((~m_and_h_gate_v_in1(c_e_h_3, c_l, s7)) | (~m_and_h_gate_v_in2(c_e_h_3, c_l, s7)) | (~node21(c_e_h_3, c_l, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_l, s8))),
% 290.33/182.87 inference(rewrite,[status(thm)],[])).
% 290.33/182.87 tff(7167,plain,
% 290.33/182.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_l, s7, s8)) | (~m_and_h_gate_v_in2(c_e_h_3, c_l, s7)) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s7)) | m_and_h_gate_v_out(c_e_h_3, c_l, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_l, s7)) | (~m_and_h_gate_v_in2(c_e_h_3, c_l, s7)) | (~node21(c_e_h_3, c_l, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_l, s8)))),
% 290.33/182.87 inference(monotonicity,[status(thm)],[7166])).
% 290.33/182.87 tff(7168,plain,
% 290.33/182.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_l, s7, s8)) | (~m_and_h_gate_v_in2(c_e_h_3, c_l, s7)) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s7)) | m_and_h_gate_v_out(c_e_h_3, c_l, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s7)) | (~m_and_h_gate_v_in2(c_e_h_3, c_l, s7)) | (~node21(c_e_h_3, c_l, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_l, s8))),
% 290.33/182.87 inference(transitivity,[status(thm)],[7167, 7165])).
% 290.33/182.87 tff(7169,plain,
% 290.33/182.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_l, s7, s8)) | (~m_and_h_gate_v_in2(c_e_h_3, c_l, s7)) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s7)) | m_and_h_gate_v_out(c_e_h_3, c_l, s8))),
% 290.33/182.87 inference(quant_inst,[status(thm)],[])).
% 290.33/182.87 tff(7170,plain,
% 290.33/182.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s7)) | (~m_and_h_gate_v_in2(c_e_h_3, c_l, s7)) | (~node21(c_e_h_3, c_l, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_l, s8)),
% 290.33/182.87 inference(modus_ponens,[status(thm)],[7169, 7168])).
% 290.33/182.87 tff(7171,plain,
% 290.40/182.87 ($false),
% 290.40/182.87 inference(unit_resolution,[status(thm)],[7170, 5851, 7164, 7163, 6450, 6469])).
% 290.40/182.87 tff(7172,plain,((~node21(c_e_h_3, c_l, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_l, s8) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s7))), inference(lemma,lemma(discharge,[]))).
% 290.40/182.87 tff(7173,plain,
% 290.40/182.87 (~node21(c_e_h_3, c_l, s7, s8)),
% 290.40/182.87 inference(unit_resolution,[status(thm)],[7172, 6450, 6469])).
% 290.40/182.87 tff(7174,plain,
% 290.40/182.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_3, c_l, s7, s8) | node22(c_e_h_3, c_l, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_3, c_l, s7, s8) | node22(c_e_h_3, c_l, s7, s8))),
% 290.40/182.87 inference(rewrite,[status(thm)],[])).
% 290.40/182.87 tff(7175,plain,
% 290.40/182.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_3, c_l, s7, s8) | node22(c_e_h_3, c_l, s7, s8))),
% 290.40/182.87 inference(quant_inst,[status(thm)],[])).
% 290.40/182.87 tff(7176,plain,
% 290.40/182.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_3, c_l, s7, s8) | node22(c_e_h_3, c_l, s7, s8)),
% 290.40/182.87 inference(modus_ponens,[status(thm)],[7175, 7174])).
% 290.40/182.87 tff(7177,plain,
% 290.40/182.87 (node21(c_e_h_3, c_l, s7, s8) | node22(c_e_h_3, c_l, s7, s8)),
% 290.40/182.87 inference(unit_resolution,[status(thm)],[7176, 82, 1938])).
% 290.40/182.87 tff(7178,plain,
% 290.40/182.87 ($false),
% 290.40/182.87 inference(unit_resolution,[status(thm)],[7177, 7173, 6468])).
% 290.40/182.87 tff(7179,plain,(m_and_h_gate_v_out(c_e_h_3, c_l, s8) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s7)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s7))), inference(lemma,lemma(discharge,[]))).
% 290.40/182.87 tff(7180,plain,
% 290.40/182.87 (~m_and_h_gate_v_in1(c_e_h_3, c_l, s7)),
% 290.40/182.87 inference(unit_resolution,[status(thm)],[7179, 6458, 6450])).
% 290.40/182.87 tff(7181,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_l, s7)), introduced(assumption)).
% 290.40/182.87 tff(7182,assumption,(m_and_h_gate_v_out(c_e_h_3, c_k, s7)), introduced(assumption)).
% 290.40/182.87 tff(7183,plain,
% 290.40/182.87 (^[I0: $i, X: $i] : refl(((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_l, X)) <=> ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_l, X)))),
% 290.40/182.87 inference(bind,[status(th)],[])).
% 290.40/182.87 tff(7184,plain,
% 290.40/182.87 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_l, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_l, X))),
% 290.40/182.87 inference(quant_intro,[status(thm)],[7183])).
% 290.40/182.87 tff(7185,plain,
% 290.40/182.87 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_l, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_l, X))),
% 290.40/182.87 inference(rewrite,[status(thm)],[])).
% 290.40/182.87 tff(7186,plain,
% 290.40/182.87 (^[I0: $i, X: $i] : rewrite((m_and_h_gate_v_in1(I0, c_l, X) | (~m_and_h_gate_v_out(I0, c_k, X))) <=> ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_l, X)))),
% 290.40/182.87 inference(bind,[status(th)],[])).
% 290.40/182.87 tff(7187,plain,
% 290.40/182.87 (![I0: $i, X: $i] : (m_and_h_gate_v_in1(I0, c_l, X) | (~m_and_h_gate_v_out(I0, c_k, X))) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_l, X))),
% 290.40/182.87 inference(quant_intro,[status(thm)],[7186])).
% 290.40/182.87 tff(7188,axiom,(![I0: $i, X: $i] : (m_and_h_gate_v_in1(I0, c_l, X) | (~m_and_h_gate_v_out(I0, c_k, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_47')).
% 290.40/182.87 tff(7189,plain,
% 290.40/182.87 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_l, X))),
% 290.40/182.87 inference(modus_ponens,[status(thm)],[7188, 7187])).
% 290.40/182.87 tff(7190,plain,
% 290.40/182.87 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_l, X))),
% 290.40/182.87 inference(modus_ponens,[status(thm)],[7189, 7185])).
% 290.40/182.87 tff(7191,plain,(
% 290.40/182.87 ![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_l, X))),
% 290.40/182.87 inference(skolemize,[status(sab)],[7190])).
% 290.40/182.87 tff(7192,plain,
% 290.40/182.87 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_l, X))),
% 290.40/182.87 inference(modus_ponens,[status(thm)],[7191, 7184])).
% 290.40/182.88 tff(7193,plain,
% 290.40/182.88 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_l, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s7))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_l, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s7))),
% 290.40/182.88 inference(rewrite,[status(thm)],[])).
% 290.40/182.88 tff(7194,plain,
% 290.40/182.88 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_l, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s7))),
% 290.40/182.88 inference(quant_inst,[status(thm)],[])).
% 290.40/182.88 tff(7195,plain,
% 290.40/182.88 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_l, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s7)),
% 290.40/182.88 inference(modus_ponens,[status(thm)],[7194, 7193])).
% 290.40/182.88 tff(7196,plain,
% 290.40/182.88 ($false),
% 290.40/182.88 inference(unit_resolution,[status(thm)],[7195, 7192, 7182, 7181])).
% 290.40/182.88 tff(7197,plain,((~m_and_h_gate_v_out(c_e_h_3, c_k, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s7)), inference(lemma,lemma(discharge,[]))).
% 290.40/182.88 tff(7198,plain,
% 290.40/182.88 ($false),
% 290.40/182.88 inference(unit_resolution,[status(thm)],[7197, 7180, 6449])).
% 290.40/182.88 tff(7199,plain,(m_and_h_gate_v_out(c_e_h_3, c_l, s6) | m_and_h_gate_v_out(c_e_h_3, c_l, s8) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s8))), inference(lemma,lemma(discharge,[]))).
% 290.40/182.88 tff(7200,plain,
% 290.40/182.88 (m_and_h_gate_v_out(c_e_h_3, c_l, s6)),
% 290.40/182.88 inference(unit_resolution,[status(thm)],[7199, 5530, 3367])).
% 290.40/182.88 tff(7201,plain,
% 290.40/182.88 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X))) | ((~m_or_h_gate_v_out(c_e_h_3, c_g, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s5))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s5))),
% 290.40/182.88 inference(rewrite,[status(thm)],[])).
% 290.40/182.88 tff(7202,plain,
% 290.40/182.88 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X))) | ((~m_or_h_gate_v_out(c_e_h_3, c_g, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s5))),
% 290.40/182.88 inference(quant_inst,[status(thm)],[])).
% 290.40/182.88 tff(7203,plain,
% 290.40/182.88 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s5)),
% 290.40/182.88 inference(modus_ponens,[status(thm)],[7202, 7201])).
% 290.40/182.88 tff(7204,plain,
% 290.40/182.88 ($false),
% 290.40/182.88 inference(unit_resolution,[status(thm)],[7203, 6229, 3252, 5452])).
% 290.40/182.88 tff(7205,plain,(m_and_h_gate_v_in1(c_e_h_3, c_k, s5) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s5))), inference(lemma,lemma(discharge,[]))).
% 290.40/182.88 tff(7206,plain,
% 290.40/182.88 (m_and_h_gate_v_in1(c_e_h_3, c_k, s5)),
% 290.40/182.88 inference(unit_resolution,[status(thm)],[7205, 5930])).
% 290.40/182.88 tff(7207,plain,
% 290.40/182.88 ((~m_and_h_gate_v_out(c_e_h_3, c_l, s6)) | node20(c_e_h_3, c_l, s5)),
% 290.40/182.88 inference(unit_resolution,[status(thm)],[4447, 6236])).
% 290.40/182.88 tff(7208,plain,
% 290.40/182.88 (node20(c_e_h_3, c_l, s5)),
% 290.40/182.88 inference(unit_resolution,[status(thm)],[7207, 7200])).
% 290.40/182.88 tff(7209,plain,
% 290.40/182.88 (m_and_h_gate_v_in1(c_e_h_3, c_l, s5)),
% 290.40/182.88 inference(unit_resolution,[status(thm)],[4421, 7208])).
% 290.40/182.88 tff(7210,plain,
% 290.40/182.88 (m_and_h_gate_v_out(c_e_h_3, c_k, s5)),
% 290.40/182.88 inference(unit_resolution,[status(thm)],[4413, 7209])).
% 290.40/182.88 tff(7211,plain,
% 290.40/182.88 (((~![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))) | (m_and_h_gate_v_in2(c_e_h_3, c_k, s5) | m_c_h_element_v_out(c_e_h_3, c_h, s5))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))) | m_and_h_gate_v_in2(c_e_h_3, c_k, s5) | m_c_h_element_v_out(c_e_h_3, c_h, s5))),
% 290.40/182.88 inference(rewrite,[status(thm)],[])).
% 290.40/182.88 tff(7212,plain,
% 290.40/182.88 ((~![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))) | (m_and_h_gate_v_in2(c_e_h_3, c_k, s5) | m_c_h_element_v_out(c_e_h_3, c_h, s5))),
% 290.40/182.88 inference(quant_inst,[status(thm)],[])).
% 290.40/182.88 tff(7213,plain,
% 290.40/182.88 ((~![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))) | m_and_h_gate_v_in2(c_e_h_3, c_k, s5) | m_c_h_element_v_out(c_e_h_3, c_h, s5)),
% 290.40/182.88 inference(modus_ponens,[status(thm)],[7212, 7211])).
% 290.40/182.88 tff(7214,plain,
% 290.40/182.88 (m_and_h_gate_v_in2(c_e_h_3, c_k, s5) | m_c_h_element_v_out(c_e_h_3, c_h, s5)),
% 290.40/182.88 inference(unit_resolution,[status(thm)],[7213, 6420])).
% 290.40/182.88 tff(7215,plain,
% 290.40/182.88 (m_and_h_gate_v_in2(c_e_h_3, c_k, s5)),
% 290.40/182.88 inference(unit_resolution,[status(thm)],[7214, 6345])).
% 290.40/182.88 tff(7216,plain,
% 290.40/182.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_k, s5)) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s5)) | m_and_h_gate_v_out(c_e_h_3, c_k, s6) | (~node21(c_e_h_3, c_k, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s5)) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s5)) | m_and_h_gate_v_out(c_e_h_3, c_k, s6) | (~node21(c_e_h_3, c_k, s5, s6)))),
% 290.40/182.88 inference(rewrite,[status(thm)],[])).
% 290.40/182.88 tff(7217,plain,
% 290.40/182.88 (((~node21(c_e_h_3, c_k, s5, s6)) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s5)) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s5)) | m_and_h_gate_v_out(c_e_h_3, c_k, s6)) <=> ((~m_and_h_gate_v_in1(c_e_h_3, c_k, s5)) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s5)) | m_and_h_gate_v_out(c_e_h_3, c_k, s6) | (~node21(c_e_h_3, c_k, s5, s6)))),
% 290.40/182.88 inference(rewrite,[status(thm)],[])).
% 290.40/182.88 tff(7218,plain,
% 290.40/182.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_k, s5, s6)) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s5)) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s5)) | m_and_h_gate_v_out(c_e_h_3, c_k, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_k, s5)) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s5)) | m_and_h_gate_v_out(c_e_h_3, c_k, s6) | (~node21(c_e_h_3, c_k, s5, s6))))),
% 290.40/182.88 inference(monotonicity,[status(thm)],[7217])).
% 290.40/182.88 tff(7219,plain,
% 290.40/182.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_k, s5, s6)) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s5)) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s5)) | m_and_h_gate_v_out(c_e_h_3, c_k, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s5)) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s5)) | m_and_h_gate_v_out(c_e_h_3, c_k, s6) | (~node21(c_e_h_3, c_k, s5, s6)))),
% 290.40/182.88 inference(transitivity,[status(thm)],[7218, 7216])).
% 290.40/182.88 tff(7220,plain,
% 290.40/182.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_k, s5, s6)) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s5)) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s5)) | m_and_h_gate_v_out(c_e_h_3, c_k, s6))),
% 290.40/182.88 inference(quant_inst,[status(thm)],[])).
% 290.40/182.88 tff(7221,plain,
% 290.40/182.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s5)) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s5)) | m_and_h_gate_v_out(c_e_h_3, c_k, s6) | (~node21(c_e_h_3, c_k, s5, s6))),
% 290.40/182.88 inference(modus_ponens,[status(thm)],[7220, 7219])).
% 290.40/182.88 tff(7222,plain,
% 290.40/182.88 ($false),
% 290.40/182.88 inference(unit_resolution,[status(thm)],[7221, 5851, 7215, 4451, 4469, 3359])).
% 290.40/182.88 tff(7223,plain,((~node21(c_e_h_3, c_k, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_k, s6) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s5))), inference(lemma,lemma(discharge,[]))).
% 290.40/182.88 tff(7224,plain,
% 290.40/182.88 (~node21(c_e_h_3, c_k, s5, s6)),
% 290.40/182.88 inference(unit_resolution,[status(thm)],[7223, 4469, 3359])).
% 290.40/182.88 tff(7225,assumption,(node22(c_e_h_3, c_k, s5, s6)), introduced(assumption)).
% 290.40/182.88 tff(7226,plain,
% 290.40/182.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s5)) | m_and_h_gate_v_out(c_e_h_3, c_k, s6) | (~node22(c_e_h_3, c_k, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s5)) | m_and_h_gate_v_out(c_e_h_3, c_k, s6) | (~node22(c_e_h_3, c_k, s5, s6)))),
% 290.40/182.88 inference(rewrite,[status(thm)],[])).
% 290.40/182.88 tff(7227,plain,
% 290.40/182.88 ((m_and_h_gate_v_out(c_e_h_3, c_k, s6) | (~node22(c_e_h_3, c_k, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s5))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_k, s5)) | m_and_h_gate_v_out(c_e_h_3, c_k, s6) | (~node22(c_e_h_3, c_k, s5, s6)))),
% 290.40/182.88 inference(rewrite,[status(thm)],[])).
% 290.40/182.88 tff(7228,plain,
% 290.40/182.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_k, s6) | (~node22(c_e_h_3, c_k, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s5)) | m_and_h_gate_v_out(c_e_h_3, c_k, s6) | (~node22(c_e_h_3, c_k, s5, s6))))),
% 290.40/182.88 inference(monotonicity,[status(thm)],[7227])).
% 290.40/182.88 tff(7229,plain,
% 290.40/182.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_k, s6) | (~node22(c_e_h_3, c_k, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s5)) | m_and_h_gate_v_out(c_e_h_3, c_k, s6) | (~node22(c_e_h_3, c_k, s5, s6)))),
% 290.40/182.88 inference(transitivity,[status(thm)],[7228, 7226])).
% 290.40/182.88 tff(7230,plain,
% 290.40/182.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_k, s6) | (~node22(c_e_h_3, c_k, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s5)))),
% 290.40/182.88 inference(quant_inst,[status(thm)],[])).
% 290.40/182.88 tff(7231,plain,
% 290.40/182.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s5)) | m_and_h_gate_v_out(c_e_h_3, c_k, s6) | (~node22(c_e_h_3, c_k, s5, s6))),
% 290.40/182.88 inference(modus_ponens,[status(thm)],[7230, 7229])).
% 290.40/182.88 tff(7232,plain,
% 290.40/182.88 ($false),
% 290.40/182.88 inference(unit_resolution,[status(thm)],[7231, 5871, 7225, 4388, 4469])).
% 290.40/182.88 tff(7233,plain,((~node22(c_e_h_3, c_k, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s5)) | m_and_h_gate_v_out(c_e_h_3, c_k, s6)), inference(lemma,lemma(discharge,[]))).
% 290.40/182.88 tff(7234,plain,
% 290.40/182.88 (~node22(c_e_h_3, c_k, s5, s6)),
% 290.40/182.88 inference(unit_resolution,[status(thm)],[7233, 4469, 4388])).
% 290.40/182.88 tff(7235,plain,
% 290.40/182.88 ($false),
% 290.40/182.88 inference(unit_resolution,[status(thm)],[4461, 7234, 7224])).
% 290.40/182.88 tff(7236,plain,(m_and_h_gate_v_out(c_e_h_3, c_k, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s5)) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s5))), inference(lemma,lemma(discharge,[]))).
% 290.40/182.88 tff(7237,plain,
% 290.40/182.88 (m_and_h_gate_v_out(c_e_h_3, c_k, s6)),
% 290.40/182.88 inference(unit_resolution,[status(thm)],[7236, 7210, 7206])).
% 290.40/182.88 tff(7238,plain,
% 290.40/182.88 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_l, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s6))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_l, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s6))),
% 290.40/182.88 inference(rewrite,[status(thm)],[])).
% 290.40/182.88 tff(7239,plain,
% 290.40/182.88 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_l, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s6))),
% 290.40/182.89 inference(quant_inst,[status(thm)],[])).
% 290.40/182.89 tff(7240,plain,
% 290.40/182.89 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_l, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s6)),
% 290.40/182.89 inference(modus_ponens,[status(thm)],[7239, 7238])).
% 290.40/182.89 tff(7241,plain,
% 290.40/182.89 ($false),
% 290.40/182.89 inference(unit_resolution,[status(thm)],[7240, 7192, 4478, 4450])).
% 290.40/182.89 tff(7242,plain,(m_and_h_gate_v_in1(c_e_h_3, c_l, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s6))), inference(lemma,lemma(discharge,[]))).
% 290.40/182.89 tff(7243,plain,
% 290.40/182.89 (m_and_h_gate_v_in1(c_e_h_3, c_l, s6)),
% 290.40/182.89 inference(unit_resolution,[status(thm)],[7242, 7237])).
% 290.40/182.89 tff(7244,plain,
% 290.40/182.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s6)) | m_and_h_gate_v_out(c_e_h_3, c_l, s7) | (~node22(c_e_h_3, c_l, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s6)) | m_and_h_gate_v_out(c_e_h_3, c_l, s7) | (~node22(c_e_h_3, c_l, s6, s7)))),
% 290.40/182.89 inference(rewrite,[status(thm)],[])).
% 290.40/182.89 tff(7245,plain,
% 290.40/182.89 ((m_and_h_gate_v_out(c_e_h_3, c_l, s7) | (~node22(c_e_h_3, c_l, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s6))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_l, s6)) | m_and_h_gate_v_out(c_e_h_3, c_l, s7) | (~node22(c_e_h_3, c_l, s6, s7)))),
% 290.40/182.89 inference(rewrite,[status(thm)],[])).
% 290.40/182.89 tff(7246,plain,
% 290.40/182.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_l, s7) | (~node22(c_e_h_3, c_l, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s6)) | m_and_h_gate_v_out(c_e_h_3, c_l, s7) | (~node22(c_e_h_3, c_l, s6, s7))))),
% 290.40/182.89 inference(monotonicity,[status(thm)],[7245])).
% 290.40/182.89 tff(7247,plain,
% 290.40/182.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_l, s7) | (~node22(c_e_h_3, c_l, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s6)) | m_and_h_gate_v_out(c_e_h_3, c_l, s7) | (~node22(c_e_h_3, c_l, s6, s7)))),
% 290.40/182.89 inference(transitivity,[status(thm)],[7246, 7244])).
% 290.40/182.89 tff(7248,plain,
% 290.40/182.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_l, s7) | (~node22(c_e_h_3, c_l, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s6)))),
% 290.40/182.89 inference(quant_inst,[status(thm)],[])).
% 290.40/182.89 tff(7249,plain,
% 290.40/182.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s6)) | m_and_h_gate_v_out(c_e_h_3, c_l, s7) | (~node22(c_e_h_3, c_l, s6, s7))),
% 290.40/182.89 inference(modus_ponens,[status(thm)],[7248, 7247])).
% 290.40/182.89 tff(7250,plain,
% 290.40/182.89 ($false),
% 290.40/182.89 inference(unit_resolution,[status(thm)],[7249, 5871, 5425, 4423, 6455])).
% 290.40/182.89 tff(7251,plain,((~node22(c_e_h_3, c_l, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s6)) | m_and_h_gate_v_out(c_e_h_3, c_l, s7)), inference(lemma,lemma(discharge,[]))).
% 290.40/182.89 tff(7252,plain,
% 290.40/182.89 (~node22(c_e_h_3, c_l, s6, s7)),
% 290.40/182.89 inference(unit_resolution,[status(thm)],[7251, 6455, 4423])).
% 290.40/182.89 tff(7253,plain,
% 290.40/182.89 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_m, X)) | m_and_h_gate_v_in2(I0, c_l, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)) | m_and_h_gate_v_in2(c_e_h_3, c_l, s6))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_m, X)) | m_and_h_gate_v_in2(I0, c_l, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)) | m_and_h_gate_v_in2(c_e_h_3, c_l, s6))),
% 290.40/182.89 inference(rewrite,[status(thm)],[])).
% 290.40/182.89 tff(7254,plain,
% 290.40/182.89 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_m, X)) | m_and_h_gate_v_in2(I0, c_l, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)) | m_and_h_gate_v_in2(c_e_h_3, c_l, s6))),
% 290.40/182.89 inference(quant_inst,[status(thm)],[])).
% 290.40/182.89 tff(7255,plain,
% 290.40/182.89 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_m, X)) | m_and_h_gate_v_in2(I0, c_l, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)) | m_and_h_gate_v_in2(c_e_h_3, c_l, s6)),
% 290.40/182.89 inference(modus_ponens,[status(thm)],[7254, 7253])).
% 290.40/182.89 tff(7256,plain,
% 290.40/182.89 (m_and_h_gate_v_in2(c_e_h_3, c_l, s6)),
% 290.40/182.89 inference(unit_resolution,[status(thm)],[7255, 7159, 7086])).
% 290.40/182.89 tff(7257,assumption,(node21(c_e_h_3, c_l, s6, s7)), introduced(assumption)).
% 290.40/182.89 tff(7258,plain,
% 290.40/182.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_l, s6)) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s6)) | m_and_h_gate_v_out(c_e_h_3, c_l, s7) | (~node21(c_e_h_3, c_l, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in2(c_e_h_3, c_l, s6)) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s6)) | m_and_h_gate_v_out(c_e_h_3, c_l, s7) | (~node21(c_e_h_3, c_l, s6, s7)))),
% 290.40/182.89 inference(rewrite,[status(thm)],[])).
% 290.40/182.89 tff(7259,plain,
% 290.40/182.89 (((~node21(c_e_h_3, c_l, s6, s7)) | (~m_and_h_gate_v_in2(c_e_h_3, c_l, s6)) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s6)) | m_and_h_gate_v_out(c_e_h_3, c_l, s7)) <=> ((~m_and_h_gate_v_in2(c_e_h_3, c_l, s6)) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s6)) | m_and_h_gate_v_out(c_e_h_3, c_l, s7) | (~node21(c_e_h_3, c_l, s6, s7)))),
% 290.40/182.89 inference(rewrite,[status(thm)],[])).
% 290.40/182.89 tff(7260,plain,
% 290.40/182.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_l, s6, s7)) | (~m_and_h_gate_v_in2(c_e_h_3, c_l, s6)) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s6)) | m_and_h_gate_v_out(c_e_h_3, c_l, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_l, s6)) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s6)) | m_and_h_gate_v_out(c_e_h_3, c_l, s7) | (~node21(c_e_h_3, c_l, s6, s7))))),
% 290.40/182.89 inference(monotonicity,[status(thm)],[7259])).
% 290.40/182.89 tff(7261,plain,
% 290.40/182.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_l, s6, s7)) | (~m_and_h_gate_v_in2(c_e_h_3, c_l, s6)) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s6)) | m_and_h_gate_v_out(c_e_h_3, c_l, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in2(c_e_h_3, c_l, s6)) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s6)) | m_and_h_gate_v_out(c_e_h_3, c_l, s7) | (~node21(c_e_h_3, c_l, s6, s7)))),
% 290.40/182.89 inference(transitivity,[status(thm)],[7260, 7258])).
% 290.40/182.89 tff(7262,plain,
% 290.40/182.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_l, s6, s7)) | (~m_and_h_gate_v_in2(c_e_h_3, c_l, s6)) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s6)) | m_and_h_gate_v_out(c_e_h_3, c_l, s7))),
% 290.40/182.89 inference(quant_inst,[status(thm)],[])).
% 290.40/182.89 tff(7263,plain,
% 290.40/182.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in2(c_e_h_3, c_l, s6)) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s6)) | m_and_h_gate_v_out(c_e_h_3, c_l, s7) | (~node21(c_e_h_3, c_l, s6, s7))),
% 290.40/182.89 inference(modus_ponens,[status(thm)],[7262, 7261])).
% 290.40/182.89 tff(7264,plain,
% 290.40/182.89 ($false),
% 290.40/182.89 inference(unit_resolution,[status(thm)],[7263, 5851, 7257, 6455, 7256, 4470])).
% 290.40/182.89 tff(7265,plain,((~node21(c_e_h_3, c_l, s6, s7)) | m_and_h_gate_v_out(c_e_h_3, c_l, s7) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s6))), inference(lemma,lemma(discharge,[]))).
% 290.40/182.89 tff(7266,plain,
% 290.40/182.89 (~node21(c_e_h_3, c_l, s6, s7)),
% 290.40/182.89 inference(unit_resolution,[status(thm)],[7265, 6455, 4470])).
% 290.40/182.89 tff(7267,plain,
% 290.40/182.89 ($false),
% 290.40/182.89 inference(unit_resolution,[status(thm)],[5435, 7266, 7252])).
% 290.40/182.89 tff(7268,plain,(m_and_h_gate_v_out(c_e_h_3, c_l, s7) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s6)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s6))), inference(lemma,lemma(discharge,[]))).
% 290.40/182.89 tff(7269,plain,
% 290.40/182.89 (m_and_h_gate_v_out(c_e_h_3, c_l, s7)),
% 290.40/182.89 inference(unit_resolution,[status(thm)],[7268, 7243, 7200])).
% 290.40/182.89 tff(7270,plain,
% 290.40/182.89 (m_and_h_gate_v_out(c_e_h_3, c_k, s7)),
% 290.40/182.89 inference(unit_resolution,[status(thm)],[6448, 7237, 6233])).
% 290.40/182.89 tff(7271,plain,
% 290.40/182.89 (m_and_h_gate_v_in1(c_e_h_3, c_l, s7)),
% 290.40/182.89 inference(unit_resolution,[status(thm)],[7197, 7270])).
% 290.40/182.89 tff(7272,plain,
% 290.40/182.89 ($false),
% 290.40/182.89 inference(unit_resolution,[status(thm)],[7179, 7271, 7269, 5530])).
% 290.40/182.89 tff(7273,plain,((~m_or_h_gate_v_out(c_e_h_3, c_j, s8)) | m_or_h_gate_v_out(c_e_h_3, c_j, s9)), inference(lemma,lemma(discharge,[]))).
% 290.40/182.89 tff(7274,plain,
% 290.40/182.89 (~m_or_h_gate_v_out(c_e_h_3, c_j, s8)),
% 290.40/182.89 inference(unit_resolution,[status(thm)],[7273, 5462])).
% 290.40/182.89 tff(7275,assumption,(~m_or_h_gate_v_out(c_e_h_3, c_j, s8)), introduced(assumption)).
% 290.40/182.89 tff(7276,assumption,(node20(c_e_h_3, c_i, s11)), introduced(assumption)).
% 290.40/182.89 tff(7277,plain,
% 290.40/182.89 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s11)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s11))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_i, s11)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s11))),
% 290.40/182.89 inference(rewrite,[status(thm)],[])).
% 290.40/182.89 tff(7278,plain,
% 290.40/182.89 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s11)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s11))),
% 290.40/182.89 inference(quant_inst,[status(thm)],[])).
% 290.40/182.89 tff(7279,plain,
% 290.40/182.89 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_i, s11)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s11)),
% 290.40/182.89 inference(modus_ponens,[status(thm)],[7278, 7277])).
% 290.40/182.89 tff(7280,plain,
% 290.40/182.89 (m_and_h_gate_v_in1(c_e_h_3, c_i, s11)),
% 290.40/182.89 inference(unit_resolution,[status(thm)],[7279, 38, 7276])).
% 290.40/182.89 tff(7281,plain,
% 290.40/182.89 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_i, s11)) | m_c_h_element_v_out(c_e_h_3, c_h, s11))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s11)) | m_c_h_element_v_out(c_e_h_3, c_h, s11))),
% 290.40/182.89 inference(rewrite,[status(thm)],[])).
% 290.40/182.89 tff(7282,plain,
% 290.40/182.89 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_i, s11)) | m_c_h_element_v_out(c_e_h_3, c_h, s11))),
% 290.40/182.89 inference(quant_inst,[status(thm)],[])).
% 290.40/182.89 tff(7283,plain,
% 290.40/182.89 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s11)) | m_c_h_element_v_out(c_e_h_3, c_h, s11)),
% 290.40/182.89 inference(modus_ponens,[status(thm)],[7282, 7281])).
% 290.40/182.89 tff(7284,plain,
% 290.40/182.89 (m_c_h_element_v_out(c_e_h_3, c_h, s11)),
% 290.40/182.89 inference(unit_resolution,[status(thm)],[7283, 619, 7280])).
% 290.40/182.89 tff(7285,plain,
% 290.40/182.89 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s11)) | m_and_h_gate_v_in2(c_e_h_3, c_i, s11))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_i, s11)) | m_and_h_gate_v_in2(c_e_h_3, c_i, s11))),
% 290.40/182.90 inference(rewrite,[status(thm)],[])).
% 290.40/182.90 tff(7286,plain,
% 290.40/182.90 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s11)) | m_and_h_gate_v_in2(c_e_h_3, c_i, s11))),
% 290.40/182.90 inference(quant_inst,[status(thm)],[])).
% 290.40/182.90 tff(7287,plain,
% 290.40/182.90 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_i, s11)) | m_and_h_gate_v_in2(c_e_h_3, c_i, s11)),
% 290.40/182.90 inference(modus_ponens,[status(thm)],[7286, 7285])).
% 290.40/182.90 tff(7288,plain,
% 290.40/182.90 (m_and_h_gate_v_in2(c_e_h_3, c_i, s11)),
% 290.40/182.90 inference(unit_resolution,[status(thm)],[7287, 4563, 7276])).
% 290.40/182.90 tff(7289,plain,
% 290.40/182.90 (^[I0: $i, X: $i] : refl(((~m_and_h_gate_v_in2(I0, c_i, X)) | (~m_or_h_gate_v_out(I0, c_j, X))) <=> ((~m_and_h_gate_v_in2(I0, c_i, X)) | (~m_or_h_gate_v_out(I0, c_j, X))))),
% 290.40/182.90 inference(bind,[status(th)],[])).
% 290.40/182.90 tff(7290,plain,
% 290.40/182.90 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_i, X)) | (~m_or_h_gate_v_out(I0, c_j, X))) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_i, X)) | (~m_or_h_gate_v_out(I0, c_j, X)))),
% 290.40/182.90 inference(quant_intro,[status(thm)],[7289])).
% 290.40/182.90 tff(7291,plain,
% 290.40/182.90 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_i, X)) | (~m_or_h_gate_v_out(I0, c_j, X))) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_i, X)) | (~m_or_h_gate_v_out(I0, c_j, X)))),
% 290.40/182.90 inference(rewrite,[status(thm)],[])).
% 290.40/182.90 tff(7292,axiom,(![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_i, X)) | (~m_or_h_gate_v_out(I0, c_j, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_38')).
% 290.40/182.90 tff(7293,plain,
% 290.40/182.90 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_i, X)) | (~m_or_h_gate_v_out(I0, c_j, X)))),
% 290.40/182.90 inference(modus_ponens,[status(thm)],[7292, 7291])).
% 290.40/182.90 tff(7294,plain,(
% 290.40/182.90 ![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_i, X)) | (~m_or_h_gate_v_out(I0, c_j, X)))),
% 290.40/182.90 inference(skolemize,[status(sab)],[7293])).
% 290.40/182.90 tff(7295,plain,
% 290.40/182.90 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_i, X)) | (~m_or_h_gate_v_out(I0, c_j, X)))),
% 290.40/182.90 inference(modus_ponens,[status(thm)],[7294, 7290])).
% 290.40/182.90 tff(7296,plain,
% 290.40/182.90 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_i, X)) | (~m_or_h_gate_v_out(I0, c_j, X)))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_i, s11)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s11)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_i, X)) | (~m_or_h_gate_v_out(I0, c_j, X)))) | (~m_and_h_gate_v_in2(c_e_h_3, c_i, s11)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s11)))),
% 290.40/182.90 inference(rewrite,[status(thm)],[])).
% 290.40/182.90 tff(7297,plain,
% 290.40/182.90 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_i, X)) | (~m_or_h_gate_v_out(I0, c_j, X)))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_i, s11)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s11)))),
% 290.40/182.90 inference(quant_inst,[status(thm)],[])).
% 290.40/182.90 tff(7298,plain,
% 290.40/182.90 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_i, X)) | (~m_or_h_gate_v_out(I0, c_j, X)))) | (~m_and_h_gate_v_in2(c_e_h_3, c_i, s11)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s11))),
% 290.40/182.90 inference(modus_ponens,[status(thm)],[7297, 7296])).
% 290.40/182.90 tff(7299,plain,
% 290.40/182.90 (~m_or_h_gate_v_out(c_e_h_3, c_j, s11)),
% 290.40/182.90 inference(unit_resolution,[status(thm)],[7298, 7295, 7288])).
% 290.40/182.90 tff(7300,assumption,(m_c_h_element_v_out(c_e_h_3, c_h, s9)), introduced(assumption)).
% 290.40/182.90 tff(7301,plain,
% 290.40/182.90 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s8)) | m_or_h_gate_v_out(c_e_h_3, c_j, s8))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s8)) | m_or_h_gate_v_out(c_e_h_3, c_j, s8))),
% 290.40/182.90 inference(rewrite,[status(thm)],[])).
% 290.40/182.90 tff(7302,plain,
% 290.40/182.90 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s8)) | m_or_h_gate_v_out(c_e_h_3, c_j, s8))),
% 290.40/182.90 inference(quant_inst,[status(thm)],[])).
% 290.40/182.90 tff(7303,plain,
% 290.40/182.90 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s8)) | m_or_h_gate_v_out(c_e_h_3, c_j, s8)),
% 290.40/182.90 inference(modus_ponens,[status(thm)],[7302, 7301])).
% 290.40/182.90 tff(7304,plain,
% 290.40/182.90 (~m_c_h_element_v_in2(c_e_h_3, c_h, s8)),
% 290.40/182.90 inference(unit_resolution,[status(thm)],[7303, 1174, 7275])).
% 290.40/182.90 tff(7305,assumption,(~m_c_h_element_v_out(c_e_h_3, c_h, s8)), introduced(assumption)).
% 290.40/182.90 tff(7306,assumption,(node15(c_e_h_3, c_h, s8, s9)), introduced(assumption)).
% 290.40/182.90 tff(7307,plain,
% 290.40/182.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s9)) | (~node15(c_e_h_3, c_h, s8, s9)) | m_c_h_element_v_out(c_e_h_3, c_h, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s9)) | (~node15(c_e_h_3, c_h, s8, s9)) | m_c_h_element_v_out(c_e_h_3, c_h, s8))),
% 290.40/182.90 inference(rewrite,[status(thm)],[])).
% 290.40/182.90 tff(7308,plain,
% 290.40/182.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s9)) | (~node15(c_e_h_3, c_h, s8, s9)) | m_c_h_element_v_out(c_e_h_3, c_h, s8))),
% 290.40/182.90 inference(quant_inst,[status(thm)],[])).
% 290.40/182.90 tff(7309,plain,
% 290.40/182.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s9)) | (~node15(c_e_h_3, c_h, s8, s9)) | m_c_h_element_v_out(c_e_h_3, c_h, s8)),
% 290.40/182.90 inference(modus_ponens,[status(thm)],[7308, 7307])).
% 290.40/182.90 tff(7310,plain,
% 290.40/182.90 ($false),
% 290.40/182.90 inference(unit_resolution,[status(thm)],[7309, 147, 7305, 7300, 7306])).
% 290.40/182.90 tff(7311,plain,((~node15(c_e_h_3, c_h, s8, s9)) | m_c_h_element_v_out(c_e_h_3, c_h, s8) | (~m_c_h_element_v_out(c_e_h_3, c_h, s9))), inference(lemma,lemma(discharge,[]))).
% 290.40/182.90 tff(7312,plain,
% 290.40/182.90 (~node15(c_e_h_3, c_h, s8, s9)),
% 290.40/182.90 inference(unit_resolution,[status(thm)],[7311, 7300, 7305])).
% 290.40/182.90 tff(7313,assumption,(node18(c_e_h_3, c_h, s8, s9)), introduced(assumption)).
% 290.40/182.90 tff(7314,plain,
% 290.40/182.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s9)) | m_c_h_element_v_out(c_e_h_3, c_h, s8) | (~node18(c_e_h_3, c_h, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s9)) | m_c_h_element_v_out(c_e_h_3, c_h, s8) | (~node18(c_e_h_3, c_h, s8, s9)))),
% 290.40/182.90 inference(rewrite,[status(thm)],[])).
% 290.40/182.90 tff(7315,plain,
% 290.40/182.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s9)) | m_c_h_element_v_out(c_e_h_3, c_h, s8) | (~node18(c_e_h_3, c_h, s8, s9)))),
% 290.40/182.90 inference(quant_inst,[status(thm)],[])).
% 290.40/182.90 tff(7316,plain,
% 290.40/182.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s9)) | m_c_h_element_v_out(c_e_h_3, c_h, s8) | (~node18(c_e_h_3, c_h, s8, s9))),
% 290.40/182.90 inference(modus_ponens,[status(thm)],[7315, 7314])).
% 290.40/182.90 tff(7317,plain,
% 290.40/182.90 ($false),
% 290.40/182.90 inference(unit_resolution,[status(thm)],[7316, 753, 7305, 7300, 7313])).
% 290.40/182.90 tff(7318,plain,((~node18(c_e_h_3, c_h, s8, s9)) | m_c_h_element_v_out(c_e_h_3, c_h, s8) | (~m_c_h_element_v_out(c_e_h_3, c_h, s9))), inference(lemma,lemma(discharge,[]))).
% 290.40/182.90 tff(7319,plain,
% 290.40/182.90 (~node18(c_e_h_3, c_h, s8, s9)),
% 290.40/182.90 inference(unit_resolution,[status(thm)],[7318, 7300, 7305])).
% 290.40/182.90 tff(7320,plain,
% 290.40/182.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s8, s9)) | node19(c_e_h_3, c_h, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s8, s9)) | node19(c_e_h_3, c_h, s8, s9))),
% 290.40/182.90 inference(rewrite,[status(thm)],[])).
% 290.40/182.90 tff(7321,plain,
% 290.40/182.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s8, s9)) | node19(c_e_h_3, c_h, s8, s9))),
% 290.40/182.90 inference(quant_inst,[status(thm)],[])).
% 290.40/182.90 tff(7322,plain,
% 290.40/182.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s8, s9)) | node19(c_e_h_3, c_h, s8, s9)),
% 290.40/182.90 inference(modus_ponens,[status(thm)],[7321, 7320])).
% 290.40/182.90 tff(7323,plain,
% 290.40/182.90 (node19(c_e_h_3, c_h, s8, s9)),
% 290.40/182.90 inference(unit_resolution,[status(thm)],[7322, 190, 1993])).
% 290.40/182.90 tff(7324,plain,
% 290.40/182.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s8) | (~node19(c_e_h_3, c_h, s8, s9)) | node18(c_e_h_3, c_h, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_h, s8) | (~node19(c_e_h_3, c_h, s8, s9)) | node18(c_e_h_3, c_h, s8, s9))),
% 290.40/182.90 inference(rewrite,[status(thm)],[])).
% 290.40/182.90 tff(7325,plain,
% 290.40/182.90 ((node17(c_e_h_3, c_h, s8) | node18(c_e_h_3, c_h, s8, s9) | (~node19(c_e_h_3, c_h, s8, s9))) <=> (node17(c_e_h_3, c_h, s8) | (~node19(c_e_h_3, c_h, s8, s9)) | node18(c_e_h_3, c_h, s8, s9))),
% 290.40/182.90 inference(rewrite,[status(thm)],[])).
% 290.40/182.90 tff(7326,plain,
% 290.40/182.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s8) | node18(c_e_h_3, c_h, s8, s9) | (~node19(c_e_h_3, c_h, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s8) | (~node19(c_e_h_3, c_h, s8, s9)) | node18(c_e_h_3, c_h, s8, s9)))),
% 290.40/182.90 inference(monotonicity,[status(thm)],[7325])).
% 290.40/182.90 tff(7327,plain,
% 290.40/182.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s8) | node18(c_e_h_3, c_h, s8, s9) | (~node19(c_e_h_3, c_h, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_h, s8) | (~node19(c_e_h_3, c_h, s8, s9)) | node18(c_e_h_3, c_h, s8, s9))),
% 290.40/182.90 inference(transitivity,[status(thm)],[7326, 7324])).
% 290.40/182.90 tff(7328,plain,
% 290.40/182.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s8) | node18(c_e_h_3, c_h, s8, s9) | (~node19(c_e_h_3, c_h, s8, s9)))),
% 290.40/182.90 inference(quant_inst,[status(thm)],[])).
% 290.40/182.90 tff(7329,plain,
% 290.40/182.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_h, s8) | (~node19(c_e_h_3, c_h, s8, s9)) | node18(c_e_h_3, c_h, s8, s9)),
% 290.40/182.90 inference(modus_ponens,[status(thm)],[7328, 7327])).
% 290.40/182.90 tff(7330,plain,
% 290.40/182.90 (node17(c_e_h_3, c_h, s8) | node18(c_e_h_3, c_h, s8, s9)),
% 290.40/182.90 inference(unit_resolution,[status(thm)],[7329, 776, 7323])).
% 290.40/182.90 tff(7331,plain,
% 290.40/182.90 (node17(c_e_h_3, c_h, s8)),
% 290.40/182.90 inference(unit_resolution,[status(thm)],[7330, 7319])).
% 290.40/182.90 tff(7332,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_h, s8)), introduced(assumption)).
% 290.40/182.90 tff(7333,plain,
% 290.40/182.90 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s8)) | m_c_h_element_v_in2(c_e_h_3, c_h, s8) | (~node17(c_e_h_3, c_h, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s8)) | m_c_h_element_v_in2(c_e_h_3, c_h, s8) | (~node17(c_e_h_3, c_h, s8)))),
% 290.40/182.90 inference(rewrite,[status(thm)],[])).
% 290.40/182.90 tff(7334,plain,
% 290.40/182.90 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s8)) | m_c_h_element_v_in2(c_e_h_3, c_h, s8) | (~node17(c_e_h_3, c_h, s8)))),
% 290.40/182.90 inference(quant_inst,[status(thm)],[])).
% 290.40/182.90 tff(7335,plain,
% 290.40/182.90 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s8)) | m_c_h_element_v_in2(c_e_h_3, c_h, s8) | (~node17(c_e_h_3, c_h, s8))),
% 290.40/182.90 inference(modus_ponens,[status(thm)],[7334, 7333])).
% 290.40/182.91 tff(7336,plain,
% 290.40/182.91 ((~m_c_h_element_v_in1(c_e_h_3, c_h, s8)) | (~node17(c_e_h_3, c_h, s8))),
% 290.40/182.91 inference(unit_resolution,[status(thm)],[7335, 919, 7332])).
% 290.40/182.91 tff(7337,plain,
% 290.40/182.91 (~m_c_h_element_v_in1(c_e_h_3, c_h, s8)),
% 290.40/182.91 inference(unit_resolution,[status(thm)],[7336, 7331])).
% 290.40/182.91 tff(7338,plain,
% 290.40/182.91 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_h, s8)) | m_c_h_element_v_in1(c_e_h_3, c_h, s8) | m_c_h_element_v_in2(c_e_h_3, c_h, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_h, s8)) | m_c_h_element_v_in1(c_e_h_3, c_h, s8) | m_c_h_element_v_in2(c_e_h_3, c_h, s8))),
% 290.40/182.91 inference(rewrite,[status(thm)],[])).
% 290.40/182.91 tff(7339,plain,
% 290.40/182.91 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_h, s8)) | m_c_h_element_v_in1(c_e_h_3, c_h, s8) | m_c_h_element_v_in2(c_e_h_3, c_h, s8))),
% 290.40/182.91 inference(quant_inst,[status(thm)],[])).
% 290.40/182.91 tff(7340,plain,
% 290.40/182.91 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_h, s8)) | m_c_h_element_v_in1(c_e_h_3, c_h, s8) | m_c_h_element_v_in2(c_e_h_3, c_h, s8)),
% 290.40/182.91 inference(modus_ponens,[status(thm)],[7339, 7338])).
% 290.40/182.91 tff(7341,plain,
% 290.40/182.91 ((~node16(c_e_h_3, c_h, s8)) | m_c_h_element_v_in1(c_e_h_3, c_h, s8)),
% 290.40/182.91 inference(unit_resolution,[status(thm)],[7340, 178, 7332])).
% 290.40/182.91 tff(7342,plain,
% 290.40/182.91 (~node16(c_e_h_3, c_h, s8)),
% 290.40/182.91 inference(unit_resolution,[status(thm)],[7341, 7337])).
% 290.40/182.91 tff(7343,plain,
% 290.40/182.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s8) | node15(c_e_h_3, c_h, s8, s9) | (~node19(c_e_h_3, c_h, s8, s9)) | node14(c_e_h_3, c_h, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_h, s8) | node15(c_e_h_3, c_h, s8, s9) | (~node19(c_e_h_3, c_h, s8, s9)) | node14(c_e_h_3, c_h, s8, s9))),
% 290.40/182.91 inference(rewrite,[status(thm)],[])).
% 290.40/182.91 tff(7344,plain,
% 290.40/182.91 ((node16(c_e_h_3, c_h, s8) | node14(c_e_h_3, c_h, s8, s9) | node15(c_e_h_3, c_h, s8, s9) | (~node19(c_e_h_3, c_h, s8, s9))) <=> (node16(c_e_h_3, c_h, s8) | node15(c_e_h_3, c_h, s8, s9) | (~node19(c_e_h_3, c_h, s8, s9)) | node14(c_e_h_3, c_h, s8, s9))),
% 290.40/182.91 inference(rewrite,[status(thm)],[])).
% 290.40/182.91 tff(7345,plain,
% 290.40/182.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s8) | node14(c_e_h_3, c_h, s8, s9) | node15(c_e_h_3, c_h, s8, s9) | (~node19(c_e_h_3, c_h, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s8) | node15(c_e_h_3, c_h, s8, s9) | (~node19(c_e_h_3, c_h, s8, s9)) | node14(c_e_h_3, c_h, s8, s9)))),
% 290.40/182.91 inference(monotonicity,[status(thm)],[7344])).
% 290.40/182.91 tff(7346,plain,
% 290.40/182.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s8) | node14(c_e_h_3, c_h, s8, s9) | node15(c_e_h_3, c_h, s8, s9) | (~node19(c_e_h_3, c_h, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_h, s8) | node15(c_e_h_3, c_h, s8, s9) | (~node19(c_e_h_3, c_h, s8, s9)) | node14(c_e_h_3, c_h, s8, s9))),
% 290.40/182.91 inference(transitivity,[status(thm)],[7345, 7343])).
% 290.40/182.91 tff(7347,plain,
% 290.40/182.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s8) | node14(c_e_h_3, c_h, s8, s9) | node15(c_e_h_3, c_h, s8, s9) | (~node19(c_e_h_3, c_h, s8, s9)))),
% 290.40/182.91 inference(quant_inst,[status(thm)],[])).
% 290.40/182.91 tff(7348,plain,
% 290.40/182.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_h, s8) | node15(c_e_h_3, c_h, s8, s9) | (~node19(c_e_h_3, c_h, s8, s9)) | node14(c_e_h_3, c_h, s8, s9)),
% 290.40/182.91 inference(modus_ponens,[status(thm)],[7347, 7346])).
% 290.40/182.91 tff(7349,plain,
% 290.40/182.91 (node16(c_e_h_3, c_h, s8) | node15(c_e_h_3, c_h, s8, s9) | node14(c_e_h_3, c_h, s8, s9)),
% 290.40/182.91 inference(unit_resolution,[status(thm)],[7348, 204, 7323])).
% 290.40/182.91 tff(7350,plain,
% 290.40/182.91 (node14(c_e_h_3, c_h, s8, s9)),
% 290.40/182.91 inference(unit_resolution,[status(thm)],[7349, 7342, 7312])).
% 290.40/182.91 tff(7351,plain,
% 290.40/182.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s9)) | m_c_h_element_v_in1(c_e_h_3, c_h, s8) | (~node14(c_e_h_3, c_h, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s9)) | m_c_h_element_v_in1(c_e_h_3, c_h, s8) | (~node14(c_e_h_3, c_h, s8, s9)))),
% 290.40/182.91 inference(rewrite,[status(thm)],[])).
% 290.40/182.91 tff(7352,plain,
% 290.40/182.91 (((~node14(c_e_h_3, c_h, s8, s9)) | m_c_h_element_v_in1(c_e_h_3, c_h, s8) | (~m_c_h_element_v_out(c_e_h_3, c_h, s9))) <=> ((~m_c_h_element_v_out(c_e_h_3, c_h, s9)) | m_c_h_element_v_in1(c_e_h_3, c_h, s8) | (~node14(c_e_h_3, c_h, s8, s9)))),
% 290.40/182.91 inference(rewrite,[status(thm)],[])).
% 290.40/182.91 tff(7353,plain,
% 290.40/182.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s8, s9)) | m_c_h_element_v_in1(c_e_h_3, c_h, s8) | (~m_c_h_element_v_out(c_e_h_3, c_h, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s9)) | m_c_h_element_v_in1(c_e_h_3, c_h, s8) | (~node14(c_e_h_3, c_h, s8, s9))))),
% 290.40/182.91 inference(monotonicity,[status(thm)],[7352])).
% 290.40/182.91 tff(7354,plain,
% 290.40/182.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s8, s9)) | m_c_h_element_v_in1(c_e_h_3, c_h, s8) | (~m_c_h_element_v_out(c_e_h_3, c_h, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s9)) | m_c_h_element_v_in1(c_e_h_3, c_h, s8) | (~node14(c_e_h_3, c_h, s8, s9)))),
% 290.40/182.91 inference(transitivity,[status(thm)],[7353, 7351])).
% 290.40/182.91 tff(7355,plain,
% 290.40/182.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s8, s9)) | m_c_h_element_v_in1(c_e_h_3, c_h, s8) | (~m_c_h_element_v_out(c_e_h_3, c_h, s9)))),
% 290.40/182.91 inference(quant_inst,[status(thm)],[])).
% 290.40/182.91 tff(7356,plain,
% 290.40/182.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s9)) | m_c_h_element_v_in1(c_e_h_3, c_h, s8) | (~node14(c_e_h_3, c_h, s8, s9))),
% 290.40/182.91 inference(modus_ponens,[status(thm)],[7355, 7354])).
% 290.40/182.91 tff(7357,plain,
% 290.40/182.91 ($false),
% 290.40/182.91 inference(unit_resolution,[status(thm)],[7356, 223, 7300, 7337, 7350])).
% 290.40/182.91 tff(7358,plain,((~m_c_h_element_v_out(c_e_h_3, c_h, s9)) | m_c_h_element_v_in2(c_e_h_3, c_h, s8) | m_c_h_element_v_out(c_e_h_3, c_h, s8)), inference(lemma,lemma(discharge,[]))).
% 290.40/182.91 tff(7359,plain,
% 290.40/182.91 (m_c_h_element_v_out(c_e_h_3, c_h, s8)),
% 290.40/182.91 inference(unit_resolution,[status(thm)],[7358, 7304, 7300])).
% 290.40/182.91 tff(7360,assumption,(m_or_h_gate_v_in2(c_e_h_3, c_g, s3)), introduced(assumption)).
% 290.40/182.91 tff(7361,plain,
% 290.40/182.91 ($false),
% 290.40/182.91 inference(unit_resolution,[status(thm)],[3353, 2762, 3255, 7360])).
% 290.40/182.91 tff(7362,plain,((~m_or_h_gate_v_in2(c_e_h_3, c_g, s3)) | m_and_h_gate_v_out(c_e_h_3, c_d, s3)), inference(lemma,lemma(discharge,[]))).
% 290.40/182.91 tff(7363,plain,
% 290.40/182.92 (~m_or_h_gate_v_in2(c_e_h_3, c_g, s3)),
% 290.40/182.92 inference(unit_resolution,[status(thm)],[7362, 3125])).
% 290.40/182.92 tff(7364,plain,
% 290.40/182.92 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s3)),
% 290.40/182.92 inference(unit_resolution,[status(thm)],[3399, 3320])).
% 290.40/182.92 tff(7365,plain,
% 290.40/182.92 (~node20(c_e_h_3, c_k, s3)),
% 290.40/182.92 inference(unit_resolution,[status(thm)],[3407, 7364])).
% 290.40/182.92 tff(7366,plain,
% 290.40/182.92 (~m_and_h_gate_v_out(c_e_h_3, c_k, s4)),
% 290.40/182.92 inference(unit_resolution,[status(thm)],[3484, 7365])).
% 290.40/182.92 tff(7367,assumption,(m_c_h_element_v_out(c_e_h_3, c_h, s8)), introduced(assumption)).
% 290.40/182.92 tff(7368,plain,
% 290.40/182.92 (~m_and_h_gate_v_in1(c_e_h_3, c_l, s4)),
% 290.40/182.92 inference(unit_resolution,[status(thm)],[3492, 7366])).
% 290.40/182.92 tff(7369,plain,
% 290.40/182.92 (~node20(c_e_h_3, c_l, s4)),
% 290.40/182.92 inference(unit_resolution,[status(thm)],[3500, 7368])).
% 290.40/182.92 tff(7370,plain,
% 290.40/182.92 (~m_and_h_gate_v_out(c_e_h_3, c_l, s5)),
% 290.40/182.92 inference(unit_resolution,[status(thm)],[3598, 3582])).
% 290.40/182.92 tff(7371,plain,
% 290.40/182.92 (~m_and_h_gate_v_in1(c_e_h_3, c_l, s5)),
% 290.40/182.92 inference(unit_resolution,[status(thm)],[4411, 1529, 4408])).
% 290.40/182.92 tff(7372,plain,
% 290.40/182.92 (~node20(c_e_h_3, c_l, s5)),
% 290.40/182.92 inference(unit_resolution,[status(thm)],[4419, 38, 7371])).
% 290.40/182.92 tff(7373,plain,
% 290.40/182.92 (~m_and_h_gate_v_out(c_e_h_3, c_l, s6)),
% 290.40/182.92 inference(unit_resolution,[status(thm)],[4447, 7372, 7370])).
% 290.40/182.92 tff(7374,plain,
% 290.40/182.92 (~m_or_h_gate_v_in1(c_e_h_3, c_j, s6)),
% 290.40/182.92 inference(unit_resolution,[status(thm)],[4492, 7373])).
% 290.40/182.92 tff(7375,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_h, s6)), introduced(assumption)).
% 290.40/182.92 tff(7376,plain,
% 290.40/182.92 (^[I0: $i, X: $i] : refl(((~m_or_h_gate_v_out(I0, c_j, X)) | m_c_h_element_v_in2(I0, c_h, X)) <=> ((~m_or_h_gate_v_out(I0, c_j, X)) | m_c_h_element_v_in2(I0, c_h, X)))),
% 290.40/182.92 inference(bind,[status(th)],[])).
% 290.40/182.92 tff(7377,plain,
% 290.40/182.92 (![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_j, X)) | m_c_h_element_v_in2(I0, c_h, X)) <=> ![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_j, X)) | m_c_h_element_v_in2(I0, c_h, X))),
% 290.40/182.92 inference(quant_intro,[status(thm)],[7376])).
% 290.40/182.92 tff(7378,plain,
% 290.40/182.92 (![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_j, X)) | m_c_h_element_v_in2(I0, c_h, X)) <=> ![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_j, X)) | m_c_h_element_v_in2(I0, c_h, X))),
% 290.40/182.92 inference(rewrite,[status(thm)],[])).
% 290.40/182.92 tff(7379,plain,
% 290.40/182.92 (^[I0: $i, X: $i] : rewrite((m_c_h_element_v_in2(I0, c_h, X) | (~m_or_h_gate_v_out(I0, c_j, X))) <=> ((~m_or_h_gate_v_out(I0, c_j, X)) | m_c_h_element_v_in2(I0, c_h, X)))),
% 290.40/182.92 inference(bind,[status(th)],[])).
% 290.40/182.92 tff(7380,plain,
% 290.40/182.92 (![I0: $i, X: $i] : (m_c_h_element_v_in2(I0, c_h, X) | (~m_or_h_gate_v_out(I0, c_j, X))) <=> ![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_j, X)) | m_c_h_element_v_in2(I0, c_h, X))),
% 290.40/182.92 inference(quant_intro,[status(thm)],[7379])).
% 290.40/182.92 tff(7381,axiom,(![I0: $i, X: $i] : (m_c_h_element_v_in2(I0, c_h, X) | (~m_or_h_gate_v_out(I0, c_j, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_33')).
% 290.40/182.92 tff(7382,plain,
% 290.40/182.92 (![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_j, X)) | m_c_h_element_v_in2(I0, c_h, X))),
% 290.40/182.92 inference(modus_ponens,[status(thm)],[7381, 7380])).
% 290.40/182.92 tff(7383,plain,
% 290.40/182.92 (![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_j, X)) | m_c_h_element_v_in2(I0, c_h, X))),
% 290.40/182.92 inference(modus_ponens,[status(thm)],[7382, 7378])).
% 290.40/182.92 tff(7384,plain,(
% 290.40/182.92 ![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_j, X)) | m_c_h_element_v_in2(I0, c_h, X))),
% 290.40/182.92 inference(skolemize,[status(sab)],[7383])).
% 290.40/182.92 tff(7385,plain,
% 290.40/182.92 (![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_j, X)) | m_c_h_element_v_in2(I0, c_h, X))),
% 290.40/182.92 inference(modus_ponens,[status(thm)],[7384, 7377])).
% 290.40/182.92 tff(7386,plain,
% 290.40/182.92 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_j, X)) | m_c_h_element_v_in2(I0, c_h, X))) | ((~m_or_h_gate_v_out(c_e_h_3, c_j, s6)) | m_c_h_element_v_in2(c_e_h_3, c_h, s6))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_j, X)) | m_c_h_element_v_in2(I0, c_h, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s6)) | m_c_h_element_v_in2(c_e_h_3, c_h, s6))),
% 290.40/182.92 inference(rewrite,[status(thm)],[])).
% 290.40/182.92 tff(7387,plain,
% 290.40/182.92 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_j, X)) | m_c_h_element_v_in2(I0, c_h, X))) | ((~m_or_h_gate_v_out(c_e_h_3, c_j, s6)) | m_c_h_element_v_in2(c_e_h_3, c_h, s6))),
% 290.40/182.92 inference(quant_inst,[status(thm)],[])).
% 290.40/182.92 tff(7388,plain,
% 290.40/182.92 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_j, X)) | m_c_h_element_v_in2(I0, c_h, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s6)) | m_c_h_element_v_in2(c_e_h_3, c_h, s6)),
% 290.40/182.92 inference(modus_ponens,[status(thm)],[7387, 7386])).
% 290.40/182.92 tff(7389,plain,
% 290.40/182.92 ($false),
% 290.40/182.92 inference(unit_resolution,[status(thm)],[7388, 7385, 3608, 7375])).
% 290.40/182.92 tff(7390,plain,((~m_or_h_gate_v_out(c_e_h_3, c_j, s6)) | m_c_h_element_v_in2(c_e_h_3, c_h, s6)), inference(lemma,lemma(discharge,[]))).
% 290.40/182.92 tff(7391,plain,
% 290.40/182.92 (~m_or_h_gate_v_out(c_e_h_3, c_j, s6)),
% 290.40/182.92 inference(unit_resolution,[status(thm)],[7390, 7375])).
% 290.40/182.92 tff(7392,assumption,(m_c_h_element_v_out(c_e_h_3, c_h, s7)), introduced(assumption)).
% 290.40/182.92 tff(7393,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_h, s6)), introduced(assumption)).
% 290.40/182.92 tff(7394,assumption,(~m_c_h_element_v_out(c_e_h_3, c_h, s6)), introduced(assumption)).
% 290.40/182.92 tff(7395,assumption,(~node16(c_e_h_3, c_h, s6)), introduced(assumption)).
% 290.40/182.92 tff(7396,assumption,(node14(c_e_h_3, c_h, s6, s7)), introduced(assumption)).
% 290.40/182.92 tff(7397,plain,
% 290.40/182.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s7)) | m_c_h_element_v_in1(c_e_h_3, c_h, s6) | (~node14(c_e_h_3, c_h, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s7)) | m_c_h_element_v_in1(c_e_h_3, c_h, s6) | (~node14(c_e_h_3, c_h, s6, s7)))),
% 290.40/182.92 inference(rewrite,[status(thm)],[])).
% 290.40/182.92 tff(7398,plain,
% 290.40/182.92 (((~node14(c_e_h_3, c_h, s6, s7)) | m_c_h_element_v_in1(c_e_h_3, c_h, s6) | (~m_c_h_element_v_out(c_e_h_3, c_h, s7))) <=> ((~m_c_h_element_v_out(c_e_h_3, c_h, s7)) | m_c_h_element_v_in1(c_e_h_3, c_h, s6) | (~node14(c_e_h_3, c_h, s6, s7)))),
% 290.40/182.92 inference(rewrite,[status(thm)],[])).
% 290.40/182.92 tff(7399,plain,
% 290.40/182.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s6, s7)) | m_c_h_element_v_in1(c_e_h_3, c_h, s6) | (~m_c_h_element_v_out(c_e_h_3, c_h, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s7)) | m_c_h_element_v_in1(c_e_h_3, c_h, s6) | (~node14(c_e_h_3, c_h, s6, s7))))),
% 290.40/182.92 inference(monotonicity,[status(thm)],[7398])).
% 290.40/182.92 tff(7400,plain,
% 290.40/182.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s6, s7)) | m_c_h_element_v_in1(c_e_h_3, c_h, s6) | (~m_c_h_element_v_out(c_e_h_3, c_h, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s7)) | m_c_h_element_v_in1(c_e_h_3, c_h, s6) | (~node14(c_e_h_3, c_h, s6, s7)))),
% 290.40/182.92 inference(transitivity,[status(thm)],[7399, 7397])).
% 290.40/182.92 tff(7401,plain,
% 290.40/182.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s6, s7)) | m_c_h_element_v_in1(c_e_h_3, c_h, s6) | (~m_c_h_element_v_out(c_e_h_3, c_h, s7)))),
% 290.40/182.92 inference(quant_inst,[status(thm)],[])).
% 290.40/182.92 tff(7402,plain,
% 290.40/182.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s7)) | m_c_h_element_v_in1(c_e_h_3, c_h, s6) | (~node14(c_e_h_3, c_h, s6, s7))),
% 290.40/182.92 inference(modus_ponens,[status(thm)],[7401, 7400])).
% 290.40/182.92 tff(7403,plain,
% 290.40/182.92 ($false),
% 290.40/182.92 inference(unit_resolution,[status(thm)],[7402, 223, 7392, 7396, 7393])).
% 290.40/182.92 tff(7404,plain,((~node14(c_e_h_3, c_h, s6, s7)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s7)) | m_c_h_element_v_in1(c_e_h_3, c_h, s6)), inference(lemma,lemma(discharge,[]))).
% 290.40/182.92 tff(7405,plain,
% 290.40/182.92 (~node14(c_e_h_3, c_h, s6, s7)),
% 290.40/182.92 inference(unit_resolution,[status(thm)],[7404, 7392, 7393])).
% 290.40/182.92 tff(7406,plain,
% 290.40/182.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s6, s7)) | node19(c_e_h_3, c_h, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s6, s7)) | node19(c_e_h_3, c_h, s6, s7))),
% 290.40/182.92 inference(rewrite,[status(thm)],[])).
% 290.40/182.92 tff(7407,plain,
% 290.40/182.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s6, s7)) | node19(c_e_h_3, c_h, s6, s7))),
% 290.40/182.92 inference(quant_inst,[status(thm)],[])).
% 290.40/182.92 tff(7408,plain,
% 290.40/182.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s6, s7)) | node19(c_e_h_3, c_h, s6, s7)),
% 290.40/182.92 inference(modus_ponens,[status(thm)],[7407, 7406])).
% 290.40/182.92 tff(7409,plain,
% 290.40/182.92 (node19(c_e_h_3, c_h, s6, s7)),
% 290.40/182.92 inference(unit_resolution,[status(thm)],[7408, 190, 1844])).
% 290.40/182.92 tff(7410,plain,
% 290.40/182.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s6) | node15(c_e_h_3, c_h, s6, s7) | node14(c_e_h_3, c_h, s6, s7) | (~node19(c_e_h_3, c_h, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_h, s6) | node15(c_e_h_3, c_h, s6, s7) | node14(c_e_h_3, c_h, s6, s7) | (~node19(c_e_h_3, c_h, s6, s7)))),
% 290.40/182.92 inference(rewrite,[status(thm)],[])).
% 290.40/182.92 tff(7411,plain,
% 290.40/182.92 ((node16(c_e_h_3, c_h, s6) | node14(c_e_h_3, c_h, s6, s7) | node15(c_e_h_3, c_h, s6, s7) | (~node19(c_e_h_3, c_h, s6, s7))) <=> (node16(c_e_h_3, c_h, s6) | node15(c_e_h_3, c_h, s6, s7) | node14(c_e_h_3, c_h, s6, s7) | (~node19(c_e_h_3, c_h, s6, s7)))),
% 290.40/182.92 inference(rewrite,[status(thm)],[])).
% 290.40/182.92 tff(7412,plain,
% 290.40/182.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s6) | node14(c_e_h_3, c_h, s6, s7) | node15(c_e_h_3, c_h, s6, s7) | (~node19(c_e_h_3, c_h, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s6) | node15(c_e_h_3, c_h, s6, s7) | node14(c_e_h_3, c_h, s6, s7) | (~node19(c_e_h_3, c_h, s6, s7))))),
% 290.40/182.92 inference(monotonicity,[status(thm)],[7411])).
% 290.40/182.92 tff(7413,plain,
% 290.40/182.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s6) | node14(c_e_h_3, c_h, s6, s7) | node15(c_e_h_3, c_h, s6, s7) | (~node19(c_e_h_3, c_h, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_h, s6) | node15(c_e_h_3, c_h, s6, s7) | node14(c_e_h_3, c_h, s6, s7) | (~node19(c_e_h_3, c_h, s6, s7)))),
% 290.40/182.92 inference(transitivity,[status(thm)],[7412, 7410])).
% 290.40/182.92 tff(7414,plain,
% 290.40/182.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s6) | node14(c_e_h_3, c_h, s6, s7) | node15(c_e_h_3, c_h, s6, s7) | (~node19(c_e_h_3, c_h, s6, s7)))),
% 290.40/182.92 inference(quant_inst,[status(thm)],[])).
% 290.40/182.92 tff(7415,plain,
% 290.40/182.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_h, s6) | node15(c_e_h_3, c_h, s6, s7) | node14(c_e_h_3, c_h, s6, s7) | (~node19(c_e_h_3, c_h, s6, s7))),
% 290.40/182.92 inference(modus_ponens,[status(thm)],[7414, 7413])).
% 290.40/182.92 tff(7416,plain,
% 290.40/182.92 (node16(c_e_h_3, c_h, s6) | node15(c_e_h_3, c_h, s6, s7) | node14(c_e_h_3, c_h, s6, s7)),
% 290.40/182.92 inference(unit_resolution,[status(thm)],[7415, 204, 7409])).
% 290.40/182.92 tff(7417,plain,
% 290.40/182.92 (node15(c_e_h_3, c_h, s6, s7)),
% 290.40/182.92 inference(unit_resolution,[status(thm)],[7416, 7405, 7395])).
% 290.40/182.92 tff(7418,plain,
% 290.40/182.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s7)) | (~node15(c_e_h_3, c_h, s6, s7)) | m_c_h_element_v_out(c_e_h_3, c_h, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s7)) | (~node15(c_e_h_3, c_h, s6, s7)) | m_c_h_element_v_out(c_e_h_3, c_h, s6))),
% 290.40/182.93 inference(rewrite,[status(thm)],[])).
% 290.40/182.93 tff(7419,plain,
% 290.40/182.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s7)) | (~node15(c_e_h_3, c_h, s6, s7)) | m_c_h_element_v_out(c_e_h_3, c_h, s6))),
% 290.40/182.93 inference(quant_inst,[status(thm)],[])).
% 290.40/182.93 tff(7420,plain,
% 290.40/182.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s7)) | (~node15(c_e_h_3, c_h, s6, s7)) | m_c_h_element_v_out(c_e_h_3, c_h, s6)),
% 290.40/182.93 inference(modus_ponens,[status(thm)],[7419, 7418])).
% 290.40/182.93 tff(7421,plain,
% 290.40/182.93 ($false),
% 290.40/182.93 inference(unit_resolution,[status(thm)],[7420, 147, 7392, 7394, 7417])).
% 290.40/182.93 tff(7422,plain,((~m_c_h_element_v_out(c_e_h_3, c_h, s7)) | m_c_h_element_v_out(c_e_h_3, c_h, s6) | node16(c_e_h_3, c_h, s6) | m_c_h_element_v_in1(c_e_h_3, c_h, s6)), inference(lemma,lemma(discharge,[]))).
% 290.40/182.93 tff(7423,plain,
% 290.40/182.93 (node16(c_e_h_3, c_h, s6)),
% 290.40/182.93 inference(unit_resolution,[status(thm)],[7422, 7393, 7394, 7392])).
% 290.40/182.93 tff(7424,plain,
% 290.40/182.93 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_h, s6)) | m_c_h_element_v_in1(c_e_h_3, c_h, s6) | m_c_h_element_v_in2(c_e_h_3, c_h, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_h, s6)) | m_c_h_element_v_in1(c_e_h_3, c_h, s6) | m_c_h_element_v_in2(c_e_h_3, c_h, s6))),
% 290.40/182.93 inference(rewrite,[status(thm)],[])).
% 290.40/182.93 tff(7425,plain,
% 290.40/182.93 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_h, s6)) | m_c_h_element_v_in1(c_e_h_3, c_h, s6) | m_c_h_element_v_in2(c_e_h_3, c_h, s6))),
% 290.40/182.93 inference(quant_inst,[status(thm)],[])).
% 290.40/182.93 tff(7426,plain,
% 290.40/182.93 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_h, s6)) | m_c_h_element_v_in1(c_e_h_3, c_h, s6) | m_c_h_element_v_in2(c_e_h_3, c_h, s6)),
% 290.40/182.93 inference(modus_ponens,[status(thm)],[7425, 7424])).
% 290.40/182.93 tff(7427,plain,
% 290.40/182.93 ((~node16(c_e_h_3, c_h, s6)) | m_c_h_element_v_in1(c_e_h_3, c_h, s6)),
% 290.40/182.93 inference(unit_resolution,[status(thm)],[7426, 178, 7375])).
% 290.40/182.93 tff(7428,plain,
% 290.40/182.93 ($false),
% 290.40/182.93 inference(unit_resolution,[status(thm)],[7427, 7423, 7393])).
% 290.40/182.93 tff(7429,plain,(m_c_h_element_v_in1(c_e_h_3, c_h, s6) | m_c_h_element_v_in2(c_e_h_3, c_h, s6) | m_c_h_element_v_out(c_e_h_3, c_h, s6) | (~m_c_h_element_v_out(c_e_h_3, c_h, s7))), inference(lemma,lemma(discharge,[]))).
% 290.40/182.93 tff(7430,plain,
% 290.40/182.93 (m_c_h_element_v_in1(c_e_h_3, c_h, s6) | m_c_h_element_v_in2(c_e_h_3, c_h, s6) | (~m_c_h_element_v_out(c_e_h_3, c_h, s7))),
% 290.40/182.93 inference(unit_resolution,[status(thm)],[7429, 6413])).
% 290.40/182.93 tff(7431,plain,
% 290.40/182.93 (m_c_h_element_v_in1(c_e_h_3, c_h, s6)),
% 290.40/182.93 inference(unit_resolution,[status(thm)],[7430, 7392, 7375])).
% 290.40/182.93 tff(7432,plain,
% 290.40/182.93 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_h, s6)) | m_c_h_element_v_in2(c_e_h_3, c_h, s6) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_h, s6)) | m_c_h_element_v_in2(c_e_h_3, c_h, s6) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s6)))),
% 290.40/182.93 inference(rewrite,[status(thm)],[])).
% 290.40/182.93 tff(7433,plain,
% 290.40/182.93 (((~m_c_h_element_v_in1(c_e_h_3, c_h, s6)) | m_c_h_element_v_in2(c_e_h_3, c_h, s6) | (~node17(c_e_h_3, c_h, s6))) <=> ((~node17(c_e_h_3, c_h, s6)) | m_c_h_element_v_in2(c_e_h_3, c_h, s6) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s6)))),
% 290.40/182.93 inference(rewrite,[status(thm)],[])).
% 290.40/182.93 tff(7434,plain,
% 290.40/182.93 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s6)) | m_c_h_element_v_in2(c_e_h_3, c_h, s6) | (~node17(c_e_h_3, c_h, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_h, s6)) | m_c_h_element_v_in2(c_e_h_3, c_h, s6) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s6))))),
% 290.40/182.93 inference(monotonicity,[status(thm)],[7433])).
% 290.40/182.93 tff(7435,plain,
% 290.40/182.93 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s6)) | m_c_h_element_v_in2(c_e_h_3, c_h, s6) | (~node17(c_e_h_3, c_h, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_h, s6)) | m_c_h_element_v_in2(c_e_h_3, c_h, s6) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s6)))),
% 290.40/182.93 inference(transitivity,[status(thm)],[7434, 7432])).
% 290.40/182.93 tff(7436,plain,
% 290.40/182.93 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s6)) | m_c_h_element_v_in2(c_e_h_3, c_h, s6) | (~node17(c_e_h_3, c_h, s6)))),
% 290.40/182.93 inference(quant_inst,[status(thm)],[])).
% 290.40/182.93 tff(7437,plain,
% 290.40/182.93 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_h, s6)) | m_c_h_element_v_in2(c_e_h_3, c_h, s6) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s6))),
% 290.40/182.93 inference(modus_ponens,[status(thm)],[7436, 7435])).
% 290.40/182.93 tff(7438,plain,
% 290.40/182.93 ((~node17(c_e_h_3, c_h, s6)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s6))),
% 290.40/182.93 inference(unit_resolution,[status(thm)],[7437, 919, 7375])).
% 290.40/182.93 tff(7439,plain,
% 290.40/182.93 (~node17(c_e_h_3, c_h, s6)),
% 290.40/182.93 inference(unit_resolution,[status(thm)],[7438, 7431])).
% 290.40/182.93 tff(7440,plain,
% 290.40/182.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s6) | node18(c_e_h_3, c_h, s6, s7) | (~node19(c_e_h_3, c_h, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_h, s6) | node18(c_e_h_3, c_h, s6, s7) | (~node19(c_e_h_3, c_h, s6, s7)))),
% 290.40/182.93 inference(rewrite,[status(thm)],[])).
% 290.40/182.93 tff(7441,plain,
% 290.40/182.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s6) | node18(c_e_h_3, c_h, s6, s7) | (~node19(c_e_h_3, c_h, s6, s7)))),
% 290.40/182.93 inference(quant_inst,[status(thm)],[])).
% 290.40/182.93 tff(7442,plain,
% 290.40/182.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_h, s6) | node18(c_e_h_3, c_h, s6, s7) | (~node19(c_e_h_3, c_h, s6, s7))),
% 290.40/182.93 inference(modus_ponens,[status(thm)],[7441, 7440])).
% 290.40/182.93 tff(7443,plain,
% 290.40/182.93 (node17(c_e_h_3, c_h, s6) | node18(c_e_h_3, c_h, s6, s7)),
% 290.40/182.93 inference(unit_resolution,[status(thm)],[7442, 776, 7409])).
% 290.40/182.93 tff(7444,plain,
% 290.40/182.93 (node18(c_e_h_3, c_h, s6, s7)),
% 290.40/182.93 inference(unit_resolution,[status(thm)],[7443, 7439])).
% 290.40/182.93 tff(7445,plain,
% 290.40/182.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s7)) | m_c_h_element_v_out(c_e_h_3, c_h, s6) | (~node18(c_e_h_3, c_h, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s7)) | m_c_h_element_v_out(c_e_h_3, c_h, s6) | (~node18(c_e_h_3, c_h, s6, s7)))),
% 290.40/182.93 inference(rewrite,[status(thm)],[])).
% 290.40/182.93 tff(7446,plain,
% 290.40/182.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s7)) | m_c_h_element_v_out(c_e_h_3, c_h, s6) | (~node18(c_e_h_3, c_h, s6, s7)))),
% 290.40/182.93 inference(quant_inst,[status(thm)],[])).
% 290.40/182.93 tff(7447,plain,
% 290.40/182.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s7)) | m_c_h_element_v_out(c_e_h_3, c_h, s6) | (~node18(c_e_h_3, c_h, s6, s7))),
% 290.40/182.93 inference(modus_ponens,[status(thm)],[7446, 7445])).
% 290.40/182.93 tff(7448,plain,
% 290.40/182.93 ($false),
% 290.40/182.93 inference(unit_resolution,[status(thm)],[7447, 753, 7392, 6413, 7444])).
% 290.40/182.93 tff(7449,plain,((~m_c_h_element_v_out(c_e_h_3, c_h, s7)) | m_c_h_element_v_in2(c_e_h_3, c_h, s6)), inference(lemma,lemma(discharge,[]))).
% 290.40/182.93 tff(7450,plain,
% 290.40/182.93 (~m_c_h_element_v_out(c_e_h_3, c_h, s7)),
% 290.40/182.93 inference(unit_resolution,[status(thm)],[7449, 7375])).
% 290.40/182.93 tff(7451,assumption,(node15(c_e_h_3, c_h, s7, s8)), introduced(assumption)).
% 290.40/182.93 tff(7452,assumption,(~m_c_h_element_v_out(c_e_h_3, c_h, s7)), introduced(assumption)).
% 290.40/182.93 tff(7453,plain,
% 290.40/182.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | (~node15(c_e_h_3, c_h, s7, s8)) | m_c_h_element_v_out(c_e_h_3, c_h, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | (~node15(c_e_h_3, c_h, s7, s8)) | m_c_h_element_v_out(c_e_h_3, c_h, s7))),
% 290.40/182.93 inference(rewrite,[status(thm)],[])).
% 290.40/182.93 tff(7454,plain,
% 290.40/182.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | (~node15(c_e_h_3, c_h, s7, s8)) | m_c_h_element_v_out(c_e_h_3, c_h, s7))),
% 290.40/182.93 inference(quant_inst,[status(thm)],[])).
% 290.40/182.93 tff(7455,plain,
% 290.40/182.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | (~node15(c_e_h_3, c_h, s7, s8)) | m_c_h_element_v_out(c_e_h_3, c_h, s7)),
% 290.40/182.93 inference(modus_ponens,[status(thm)],[7454, 7453])).
% 290.40/182.93 tff(7456,plain,
% 290.40/182.93 ($false),
% 290.40/182.93 inference(unit_resolution,[status(thm)],[7455, 147, 7452, 7367, 7451])).
% 290.40/182.93 tff(7457,plain,((~node15(c_e_h_3, c_h, s7, s8)) | m_c_h_element_v_out(c_e_h_3, c_h, s7) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8))), inference(lemma,lemma(discharge,[]))).
% 290.40/182.93 tff(7458,plain,
% 290.40/182.93 (~node15(c_e_h_3, c_h, s7, s8)),
% 290.40/182.93 inference(unit_resolution,[status(thm)],[7457, 7450, 7367])).
% 290.40/182.93 tff(7459,assumption,(node18(c_e_h_3, c_h, s7, s8)), introduced(assumption)).
% 290.40/182.93 tff(7460,plain,
% 290.40/182.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_h, s7) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | (~node18(c_e_h_3, c_h, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s7) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | (~node18(c_e_h_3, c_h, s7, s8)))),
% 290.40/182.93 inference(rewrite,[status(thm)],[])).
% 290.40/182.93 tff(7461,plain,
% 290.40/182.93 (((~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | m_c_h_element_v_out(c_e_h_3, c_h, s7) | (~node18(c_e_h_3, c_h, s7, s8))) <=> (m_c_h_element_v_out(c_e_h_3, c_h, s7) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | (~node18(c_e_h_3, c_h, s7, s8)))),
% 290.40/182.93 inference(rewrite,[status(thm)],[])).
% 290.40/182.93 tff(7462,plain,
% 290.40/182.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | m_c_h_element_v_out(c_e_h_3, c_h, s7) | (~node18(c_e_h_3, c_h, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_h, s7) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | (~node18(c_e_h_3, c_h, s7, s8))))),
% 290.40/182.94 inference(monotonicity,[status(thm)],[7461])).
% 290.40/182.94 tff(7463,plain,
% 290.40/182.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | m_c_h_element_v_out(c_e_h_3, c_h, s7) | (~node18(c_e_h_3, c_h, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s7) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | (~node18(c_e_h_3, c_h, s7, s8)))),
% 290.40/182.94 inference(transitivity,[status(thm)],[7462, 7460])).
% 290.40/182.94 tff(7464,plain,
% 290.40/182.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | m_c_h_element_v_out(c_e_h_3, c_h, s7) | (~node18(c_e_h_3, c_h, s7, s8)))),
% 290.40/182.94 inference(quant_inst,[status(thm)],[])).
% 290.40/182.94 tff(7465,plain,
% 290.40/182.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s7) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | (~node18(c_e_h_3, c_h, s7, s8))),
% 290.40/182.94 inference(modus_ponens,[status(thm)],[7464, 7463])).
% 290.40/182.94 tff(7466,plain,
% 290.40/182.94 ($false),
% 290.40/182.94 inference(unit_resolution,[status(thm)],[7465, 753, 7452, 7367, 7459])).
% 290.40/182.94 tff(7467,plain,((~node18(c_e_h_3, c_h, s7, s8)) | m_c_h_element_v_out(c_e_h_3, c_h, s7) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8))), inference(lemma,lemma(discharge,[]))).
% 290.40/182.94 tff(7468,plain,
% 290.40/182.94 (~node18(c_e_h_3, c_h, s7, s8)),
% 290.40/182.94 inference(unit_resolution,[status(thm)],[7467, 7450, 7367])).
% 290.40/182.94 tff(7469,plain,
% 290.40/182.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s7, s8)) | node19(c_e_h_3, c_h, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s7, s8)) | node19(c_e_h_3, c_h, s7, s8))),
% 290.40/182.94 inference(rewrite,[status(thm)],[])).
% 290.40/182.94 tff(7470,plain,
% 290.40/182.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s7, s8)) | node19(c_e_h_3, c_h, s7, s8))),
% 290.40/182.94 inference(quant_inst,[status(thm)],[])).
% 290.40/182.94 tff(7471,plain,
% 290.40/182.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s7, s8)) | node19(c_e_h_3, c_h, s7, s8)),
% 290.40/182.94 inference(modus_ponens,[status(thm)],[7470, 7469])).
% 290.40/182.94 tff(7472,plain,
% 290.40/182.94 (node19(c_e_h_3, c_h, s7, s8)),
% 290.40/182.94 inference(unit_resolution,[status(thm)],[7471, 190, 1938])).
% 290.40/182.94 tff(7473,plain,
% 290.40/182.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s7) | (~node19(c_e_h_3, c_h, s7, s8)) | node18(c_e_h_3, c_h, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_h, s7) | (~node19(c_e_h_3, c_h, s7, s8)) | node18(c_e_h_3, c_h, s7, s8))),
% 290.40/182.94 inference(rewrite,[status(thm)],[])).
% 290.40/182.94 tff(7474,plain,
% 290.40/182.94 ((node17(c_e_h_3, c_h, s7) | node18(c_e_h_3, c_h, s7, s8) | (~node19(c_e_h_3, c_h, s7, s8))) <=> (node17(c_e_h_3, c_h, s7) | (~node19(c_e_h_3, c_h, s7, s8)) | node18(c_e_h_3, c_h, s7, s8))),
% 290.40/182.94 inference(rewrite,[status(thm)],[])).
% 290.40/182.94 tff(7475,plain,
% 290.40/182.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s7) | node18(c_e_h_3, c_h, s7, s8) | (~node19(c_e_h_3, c_h, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s7) | (~node19(c_e_h_3, c_h, s7, s8)) | node18(c_e_h_3, c_h, s7, s8)))),
% 290.40/182.94 inference(monotonicity,[status(thm)],[7474])).
% 290.40/182.94 tff(7476,plain,
% 290.40/182.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s7) | node18(c_e_h_3, c_h, s7, s8) | (~node19(c_e_h_3, c_h, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_h, s7) | (~node19(c_e_h_3, c_h, s7, s8)) | node18(c_e_h_3, c_h, s7, s8))),
% 290.40/182.94 inference(transitivity,[status(thm)],[7475, 7473])).
% 290.40/182.94 tff(7477,plain,
% 290.40/182.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s7) | node18(c_e_h_3, c_h, s7, s8) | (~node19(c_e_h_3, c_h, s7, s8)))),
% 290.40/182.94 inference(quant_inst,[status(thm)],[])).
% 290.40/182.94 tff(7478,plain,
% 290.40/182.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_h, s7) | (~node19(c_e_h_3, c_h, s7, s8)) | node18(c_e_h_3, c_h, s7, s8)),
% 290.40/182.94 inference(modus_ponens,[status(thm)],[7477, 7476])).
% 290.40/182.94 tff(7479,plain,
% 290.40/182.94 (node17(c_e_h_3, c_h, s7) | node18(c_e_h_3, c_h, s7, s8)),
% 290.40/182.94 inference(unit_resolution,[status(thm)],[7478, 776, 7472])).
% 290.40/182.94 tff(7480,plain,
% 290.40/182.94 (node17(c_e_h_3, c_h, s7)),
% 290.40/182.94 inference(unit_resolution,[status(thm)],[7479, 7468])).
% 290.40/182.94 tff(7481,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_h, s7)), introduced(assumption)).
% 290.40/182.94 tff(7482,assumption,(node17(c_e_h_3, c_h, s7)), introduced(assumption)).
% 290.40/182.94 tff(7483,plain,
% 290.40/182.94 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_h, s7)) | m_c_h_element_v_in1(c_e_h_3, c_h, s7) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_h, s7)) | m_c_h_element_v_in1(c_e_h_3, c_h, s7) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s7)))),
% 290.40/182.94 inference(rewrite,[status(thm)],[])).
% 290.40/182.94 tff(7484,plain,
% 290.40/182.94 ((m_c_h_element_v_in1(c_e_h_3, c_h, s7) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s7)) | (~node17(c_e_h_3, c_h, s7))) <=> ((~node17(c_e_h_3, c_h, s7)) | m_c_h_element_v_in1(c_e_h_3, c_h, s7) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s7)))),
% 290.40/182.94 inference(rewrite,[status(thm)],[])).
% 290.40/182.94 tff(7485,plain,
% 290.40/182.94 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s7) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s7)) | (~node17(c_e_h_3, c_h, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_h, s7)) | m_c_h_element_v_in1(c_e_h_3, c_h, s7) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s7))))),
% 290.40/182.94 inference(monotonicity,[status(thm)],[7484])).
% 290.40/182.94 tff(7486,plain,
% 290.40/182.94 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s7) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s7)) | (~node17(c_e_h_3, c_h, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_h, s7)) | m_c_h_element_v_in1(c_e_h_3, c_h, s7) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s7)))),
% 290.40/182.94 inference(transitivity,[status(thm)],[7485, 7483])).
% 290.40/182.94 tff(7487,plain,
% 290.40/182.94 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s7) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s7)) | (~node17(c_e_h_3, c_h, s7)))),
% 290.40/182.94 inference(quant_inst,[status(thm)],[])).
% 290.40/182.94 tff(7488,plain,
% 290.40/182.94 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_h, s7)) | m_c_h_element_v_in1(c_e_h_3, c_h, s7) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s7))),
% 290.40/182.94 inference(modus_ponens,[status(thm)],[7487, 7486])).
% 290.40/182.94 tff(7489,plain,
% 290.40/182.94 (m_c_h_element_v_in1(c_e_h_3, c_h, s7) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s7))),
% 290.40/182.94 inference(unit_resolution,[status(thm)],[7488, 859, 7482])).
% 290.40/182.94 tff(7490,plain,
% 290.40/182.94 (~m_c_h_element_v_in2(c_e_h_3, c_h, s7)),
% 290.40/182.94 inference(unit_resolution,[status(thm)],[7489, 7481])).
% 290.40/182.95 tff(7491,assumption,(~node15(c_e_h_3, c_h, s7, s8)), introduced(assumption)).
% 290.40/182.95 tff(7492,assumption,(node14(c_e_h_3, c_h, s7, s8)), introduced(assumption)).
% 290.40/182.95 tff(7493,plain,
% 290.40/182.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s7) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | (~node14(c_e_h_3, c_h, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_h, s7) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | (~node14(c_e_h_3, c_h, s7, s8)))),
% 290.40/182.95 inference(rewrite,[status(thm)],[])).
% 290.40/182.95 tff(7494,plain,
% 290.40/182.95 (((~node14(c_e_h_3, c_h, s7, s8)) | m_c_h_element_v_in1(c_e_h_3, c_h, s7) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8))) <=> (m_c_h_element_v_in1(c_e_h_3, c_h, s7) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | (~node14(c_e_h_3, c_h, s7, s8)))),
% 290.40/182.95 inference(rewrite,[status(thm)],[])).
% 290.40/182.95 tff(7495,plain,
% 290.40/182.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s7, s8)) | m_c_h_element_v_in1(c_e_h_3, c_h, s7) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s7) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | (~node14(c_e_h_3, c_h, s7, s8))))),
% 290.40/182.95 inference(monotonicity,[status(thm)],[7494])).
% 290.40/182.95 tff(7496,plain,
% 290.40/182.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s7, s8)) | m_c_h_element_v_in1(c_e_h_3, c_h, s7) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_h, s7) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | (~node14(c_e_h_3, c_h, s7, s8)))),
% 290.40/182.95 inference(transitivity,[status(thm)],[7495, 7493])).
% 290.40/182.95 tff(7497,plain,
% 290.40/182.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s7, s8)) | m_c_h_element_v_in1(c_e_h_3, c_h, s7) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8)))),
% 290.40/182.95 inference(quant_inst,[status(thm)],[])).
% 290.40/182.95 tff(7498,plain,
% 290.40/182.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_h, s7) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | (~node14(c_e_h_3, c_h, s7, s8))),
% 290.40/182.95 inference(modus_ponens,[status(thm)],[7497, 7496])).
% 290.40/182.95 tff(7499,plain,
% 290.40/182.95 ($false),
% 290.40/182.95 inference(unit_resolution,[status(thm)],[7498, 223, 7367, 7492, 7481])).
% 290.40/182.95 tff(7500,plain,((~node14(c_e_h_3, c_h, s7, s8)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | m_c_h_element_v_in1(c_e_h_3, c_h, s7)), inference(lemma,lemma(discharge,[]))).
% 290.40/182.95 tff(7501,plain,
% 290.40/182.95 (~node14(c_e_h_3, c_h, s7, s8)),
% 290.40/182.95 inference(unit_resolution,[status(thm)],[7500, 7481, 7367])).
% 290.40/182.95 tff(7502,plain,
% 290.40/182.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s7) | node14(c_e_h_3, c_h, s7, s8) | node15(c_e_h_3, c_h, s7, s8) | (~node19(c_e_h_3, c_h, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_h, s7) | node14(c_e_h_3, c_h, s7, s8) | node15(c_e_h_3, c_h, s7, s8) | (~node19(c_e_h_3, c_h, s7, s8)))),
% 290.40/182.95 inference(rewrite,[status(thm)],[])).
% 290.40/182.95 tff(7503,plain,
% 290.40/182.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s7) | node14(c_e_h_3, c_h, s7, s8) | node15(c_e_h_3, c_h, s7, s8) | (~node19(c_e_h_3, c_h, s7, s8)))),
% 290.40/182.95 inference(quant_inst,[status(thm)],[])).
% 290.40/182.95 tff(7504,plain,
% 290.40/182.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_h, s7) | node14(c_e_h_3, c_h, s7, s8) | node15(c_e_h_3, c_h, s7, s8) | (~node19(c_e_h_3, c_h, s7, s8))),
% 290.40/182.95 inference(modus_ponens,[status(thm)],[7503, 7502])).
% 290.40/182.95 tff(7505,plain,
% 290.40/182.95 (node16(c_e_h_3, c_h, s7) | node14(c_e_h_3, c_h, s7, s8) | node15(c_e_h_3, c_h, s7, s8)),
% 290.40/182.95 inference(unit_resolution,[status(thm)],[7504, 204, 7472])).
% 290.40/182.95 tff(7506,plain,
% 290.40/182.95 (node16(c_e_h_3, c_h, s7)),
% 290.40/182.95 inference(unit_resolution,[status(thm)],[7505, 7501, 7491])).
% 290.40/182.95 tff(7507,plain,
% 290.40/182.95 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_h, s7)) | m_c_h_element_v_in1(c_e_h_3, c_h, s7) | m_c_h_element_v_in2(c_e_h_3, c_h, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_h, s7)) | m_c_h_element_v_in1(c_e_h_3, c_h, s7) | m_c_h_element_v_in2(c_e_h_3, c_h, s7))),
% 290.40/182.95 inference(rewrite,[status(thm)],[])).
% 290.40/182.95 tff(7508,plain,
% 290.40/182.95 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_h, s7)) | m_c_h_element_v_in1(c_e_h_3, c_h, s7) | m_c_h_element_v_in2(c_e_h_3, c_h, s7))),
% 290.40/182.95 inference(quant_inst,[status(thm)],[])).
% 290.40/182.95 tff(7509,plain,
% 290.40/182.95 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_h, s7)) | m_c_h_element_v_in1(c_e_h_3, c_h, s7) | m_c_h_element_v_in2(c_e_h_3, c_h, s7)),
% 290.40/182.95 inference(modus_ponens,[status(thm)],[7508, 7507])).
% 290.40/182.95 tff(7510,plain,
% 290.40/182.95 ($false),
% 290.40/182.95 inference(unit_resolution,[status(thm)],[7509, 178, 7506, 7481, 7490])).
% 290.40/182.95 tff(7511,plain,(m_c_h_element_v_in1(c_e_h_3, c_h, s7) | node15(c_e_h_3, c_h, s7, s8) | (~node17(c_e_h_3, c_h, s7)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8))), inference(lemma,lemma(discharge,[]))).
% 290.40/182.95 tff(7512,plain,
% 290.40/182.95 (m_c_h_element_v_in1(c_e_h_3, c_h, s7)),
% 290.40/182.95 inference(unit_resolution,[status(thm)],[7511, 7480, 7367, 7458])).
% 290.40/182.95 tff(7513,plain,
% 290.40/182.95 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_h, s7)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s7)) | m_c_h_element_v_in2(c_e_h_3, c_h, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_h, s7)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s7)) | m_c_h_element_v_in2(c_e_h_3, c_h, s7))),
% 290.40/182.95 inference(rewrite,[status(thm)],[])).
% 290.40/182.95 tff(7514,plain,
% 290.40/182.95 (((~m_c_h_element_v_in1(c_e_h_3, c_h, s7)) | m_c_h_element_v_in2(c_e_h_3, c_h, s7) | (~node17(c_e_h_3, c_h, s7))) <=> ((~node17(c_e_h_3, c_h, s7)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s7)) | m_c_h_element_v_in2(c_e_h_3, c_h, s7))),
% 290.40/182.95 inference(rewrite,[status(thm)],[])).
% 290.40/182.95 tff(7515,plain,
% 290.40/182.95 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s7)) | m_c_h_element_v_in2(c_e_h_3, c_h, s7) | (~node17(c_e_h_3, c_h, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_h, s7)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s7)) | m_c_h_element_v_in2(c_e_h_3, c_h, s7)))),
% 290.40/182.95 inference(monotonicity,[status(thm)],[7514])).
% 290.40/182.95 tff(7516,plain,
% 290.40/182.95 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s7)) | m_c_h_element_v_in2(c_e_h_3, c_h, s7) | (~node17(c_e_h_3, c_h, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_h, s7)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s7)) | m_c_h_element_v_in2(c_e_h_3, c_h, s7))),
% 290.40/182.95 inference(transitivity,[status(thm)],[7515, 7513])).
% 290.40/182.95 tff(7517,plain,
% 290.40/182.95 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s7)) | m_c_h_element_v_in2(c_e_h_3, c_h, s7) | (~node17(c_e_h_3, c_h, s7)))),
% 290.40/182.95 inference(quant_inst,[status(thm)],[])).
% 290.40/182.95 tff(7518,plain,
% 290.40/182.95 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_h, s7)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s7)) | m_c_h_element_v_in2(c_e_h_3, c_h, s7)),
% 290.40/182.95 inference(modus_ponens,[status(thm)],[7517, 7516])).
% 290.40/182.95 tff(7519,plain,
% 290.40/182.95 (m_c_h_element_v_in2(c_e_h_3, c_h, s7)),
% 290.40/182.95 inference(unit_resolution,[status(thm)],[7518, 919, 7480, 7512])).
% 290.40/182.95 tff(7520,plain,
% 290.40/182.95 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s7)) | m_or_h_gate_v_out(c_e_h_3, c_j, s7))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s7)) | m_or_h_gate_v_out(c_e_h_3, c_j, s7))),
% 290.40/182.95 inference(rewrite,[status(thm)],[])).
% 290.40/182.95 tff(7521,plain,
% 290.40/182.95 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s7)) | m_or_h_gate_v_out(c_e_h_3, c_j, s7))),
% 290.40/182.95 inference(quant_inst,[status(thm)],[])).
% 290.40/182.95 tff(7522,plain,
% 290.40/182.95 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s7)) | m_or_h_gate_v_out(c_e_h_3, c_j, s7)),
% 290.40/182.95 inference(modus_ponens,[status(thm)],[7521, 7520])).
% 290.40/182.95 tff(7523,plain,
% 290.40/182.95 (m_or_h_gate_v_out(c_e_h_3, c_j, s7)),
% 290.40/182.95 inference(unit_resolution,[status(thm)],[7522, 1174, 7519])).
% 290.40/182.95 tff(7524,plain,
% 290.40/182.95 (~node6(c_e_h_3, c_j, s6, s7)),
% 290.40/182.95 inference(unit_resolution,[status(thm)],[4894, 7523, 7391])).
% 290.40/182.95 tff(7525,plain,
% 290.40/182.95 (~node5(c_e_h_3, c_j, s6, s7)),
% 290.40/182.95 inference(unit_resolution,[status(thm)],[4884, 7523, 4494])).
% 290.40/182.95 tff(7526,plain,
% 290.40/182.95 ($false),
% 290.40/182.95 inference(unit_resolution,[status(thm)],[4902, 7525, 7524])).
% 290.40/182.95 tff(7527,plain,(m_c_h_element_v_in2(c_e_h_3, c_h, s6) | m_or_h_gate_v_in1(c_e_h_3, c_j, s6) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8))), inference(lemma,lemma(discharge,[]))).
% 290.40/182.95 tff(7528,plain,
% 290.40/182.95 (m_c_h_element_v_in2(c_e_h_3, c_h, s6)),
% 290.40/182.95 inference(unit_resolution,[status(thm)],[7527, 7374, 7367])).
% 290.40/182.95 tff(7529,assumption,(m_c_h_element_v_in2(c_e_h_3, c_h, s6)), introduced(assumption)).
% 290.40/182.95 tff(7530,plain,
% 290.40/182.95 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s6)) | m_or_h_gate_v_out(c_e_h_3, c_j, s6))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s6)) | m_or_h_gate_v_out(c_e_h_3, c_j, s6))),
% 290.40/182.95 inference(rewrite,[status(thm)],[])).
% 290.40/182.95 tff(7531,plain,
% 290.40/182.95 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s6)) | m_or_h_gate_v_out(c_e_h_3, c_j, s6))),
% 290.40/182.95 inference(quant_inst,[status(thm)],[])).
% 290.40/182.95 tff(7532,plain,
% 290.40/182.95 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s6)) | m_or_h_gate_v_out(c_e_h_3, c_j, s6)),
% 290.40/182.95 inference(modus_ponens,[status(thm)],[7531, 7530])).
% 290.40/182.95 tff(7533,plain,
% 290.40/182.95 ($false),
% 290.40/182.95 inference(unit_resolution,[status(thm)],[7532, 1174, 4485, 7529])).
% 290.40/182.95 tff(7534,plain,(m_or_h_gate_v_out(c_e_h_3, c_j, s6) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s6))), inference(lemma,lemma(discharge,[]))).
% 290.40/182.95 tff(7535,plain,
% 290.40/182.95 (m_or_h_gate_v_out(c_e_h_3, c_j, s6)),
% 290.40/182.95 inference(unit_resolution,[status(thm)],[7534, 7528])).
% 290.40/182.95 tff(7536,plain,
% 290.40/182.95 (~node6(c_e_h_3, c_j, s5, s6)),
% 290.40/182.95 inference(unit_resolution,[status(thm)],[4075, 7535])).
% 290.40/182.95 tff(7537,plain,
% 290.40/182.95 (~m_or_h_gate_v_in1(c_e_h_3, c_j, s5)),
% 290.40/182.96 inference(unit_resolution,[status(thm)],[3604, 1100, 7370])).
% 290.40/182.96 tff(7538,plain,
% 290.40/182.96 (~node5(c_e_h_3, c_j, s5, s6)),
% 290.40/182.96 inference(unit_resolution,[status(thm)],[4375, 7535, 7537])).
% 290.40/182.96 tff(7539,plain,
% 290.40/182.96 ($false),
% 290.40/182.96 inference(unit_resolution,[status(thm)],[4383, 7538, 7536])).
% 290.40/182.96 tff(7540,plain,(node20(c_e_h_3, c_l, s4) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | m_and_h_gate_v_out(c_e_h_3, c_k, s5)), inference(lemma,lemma(discharge,[]))).
% 290.40/182.96 tff(7541,plain,
% 290.40/182.96 (m_and_h_gate_v_out(c_e_h_3, c_k, s5)),
% 290.40/182.96 inference(unit_resolution,[status(thm)],[7540, 7369, 7367])).
% 290.40/182.96 tff(7542,plain,
% 290.40/182.96 (node20(c_e_h_3, c_k, s4)),
% 290.40/182.96 inference(unit_resolution,[status(thm)],[4405, 7541, 7366])).
% 290.40/182.96 tff(7543,plain,
% 290.40/182.96 (m_and_h_gate_v_in1(c_e_h_3, c_k, s4)),
% 290.40/182.96 inference(unit_resolution,[status(thm)],[3390, 38, 7542])).
% 290.40/182.96 tff(7544,plain,
% 290.40/182.96 (~node6(c_e_h_3, c_g, s3, s4)),
% 290.40/182.96 inference(unit_resolution,[status(thm)],[3330, 3321, 3320])).
% 290.40/182.96 tff(7545,plain,
% 290.40/182.96 (~node5(c_e_h_3, c_g, s3, s4)),
% 290.40/182.96 inference(unit_resolution,[status(thm)],[3349, 3321, 3319, 3340])).
% 290.40/182.96 tff(7546,plain,
% 290.40/182.96 ($false),
% 290.40/182.96 inference(unit_resolution,[status(thm)],[3338, 7545, 7544])).
% 290.40/182.96 tff(7547,plain,((~m_or_h_gate_v_out(c_e_h_3, c_g, s4)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s3) | m_or_h_gate_v_in2(c_e_h_3, c_g, s3) | m_or_h_gate_v_out(c_e_h_3, c_g, s3)), inference(lemma,lemma(discharge,[]))).
% 290.40/182.96 tff(7548,plain,
% 290.40/182.96 (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)),
% 290.40/182.96 inference(unit_resolution,[status(thm)],[7547, 3320, 3340, 3319])).
% 290.40/182.96 tff(7549,plain,
% 290.40/182.96 ($false),
% 290.40/182.96 inference(unit_resolution,[status(thm)],[3382, 2048, 7548, 7543])).
% 290.40/182.96 tff(7550,plain,(m_or_h_gate_v_out(c_e_h_3, c_g, s3) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | m_or_h_gate_v_in2(c_e_h_3, c_g, s3) | m_or_h_gate_v_in1(c_e_h_3, c_g, s3)), inference(lemma,lemma(discharge,[]))).
% 290.40/182.96 tff(7551,plain,
% 290.40/182.96 ((~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s3)),
% 290.40/182.96 inference(unit_resolution,[status(thm)],[7550, 7363, 3006])).
% 290.40/182.96 tff(7552,plain,
% 290.40/182.96 (m_or_h_gate_v_in1(c_e_h_3, c_g, s3)),
% 290.40/182.96 inference(unit_resolution,[status(thm)],[7551, 7359])).
% 290.40/182.96 tff(7553,plain,
% 290.40/182.96 (m_and_h_gate_v_out(c_e_h_3, c_c, s3)),
% 290.40/182.96 inference(unit_resolution,[status(thm)],[2713, 7552])).
% 290.40/182.96 tff(7554,plain,
% 290.40/182.96 ($false),
% 290.40/182.96 inference(unit_resolution,[status(thm)],[7540, 3501, 4406, 7367])).
% 290.40/182.96 tff(7555,plain,(m_and_h_gate_v_out(c_e_h_3, c_k, s4) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | node20(c_e_h_3, c_k, s4)), inference(lemma,lemma(discharge,[]))).
% 290.40/182.96 tff(7556,plain,
% 290.40/182.96 ((~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | node20(c_e_h_3, c_k, s4)),
% 290.40/182.96 inference(unit_resolution,[status(thm)],[7555, 3485])).
% 290.40/182.96 tff(7557,plain,
% 290.40/182.96 (node20(c_e_h_3, c_k, s4)),
% 290.40/182.96 inference(unit_resolution,[status(thm)],[7556, 7359])).
% 290.40/182.96 tff(7558,plain,
% 290.40/182.96 (m_and_h_gate_v_in1(c_e_h_3, c_k, s4)),
% 290.40/182.96 inference(unit_resolution,[status(thm)],[3392, 7557])).
% 290.40/182.96 tff(7559,plain,
% 290.40/182.96 (m_or_h_gate_v_out(c_e_h_3, c_g, s4)),
% 290.40/182.96 inference(unit_resolution,[status(thm)],[3384, 7558])).
% 290.40/182.96 tff(7560,plain,
% 290.40/182.96 ((~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | m_and_h_gate_v_out(c_e_h_3, c_k, s5)),
% 290.40/182.96 inference(unit_resolution,[status(thm)],[7540, 6235])).
% 290.40/182.96 tff(7561,plain,
% 290.40/182.96 (m_and_h_gate_v_out(c_e_h_3, c_k, s5)),
% 290.40/182.96 inference(unit_resolution,[status(thm)],[7560, 7359])).
% 290.40/182.96 tff(7562,plain,
% 290.40/182.96 (~m_c_h_element_v_in2(c_e_h_3, c_h, s6)),
% 290.40/182.96 inference(unit_resolution,[status(thm)],[7534, 6238])).
% 290.40/182.96 tff(7563,plain,
% 290.40/182.96 (m_or_h_gate_v_in1(c_e_h_3, c_j, s6) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8))),
% 290.40/182.96 inference(unit_resolution,[status(thm)],[7527, 7562])).
% 290.40/182.96 tff(7564,plain,
% 290.40/182.96 (m_or_h_gate_v_in1(c_e_h_3, c_j, s6)),
% 290.40/182.96 inference(unit_resolution,[status(thm)],[7563, 7359])).
% 290.40/182.96 tff(7565,plain,
% 290.40/182.96 (m_and_h_gate_v_out(c_e_h_3, c_l, s6)),
% 290.40/182.96 inference(unit_resolution,[status(thm)],[4492, 7564])).
% 290.40/182.96 tff(7566,plain,
% 290.40/182.96 (~m_c_h_element_v_out(c_e_h_3, c_h, s7)),
% 290.40/182.96 inference(unit_resolution,[status(thm)],[7449, 7562])).
% 290.40/182.96 tff(7567,plain,
% 290.40/182.96 (~node18(c_e_h_3, c_h, s7, s8)),
% 290.40/182.96 inference(unit_resolution,[status(thm)],[7467, 7452, 7367])).
% 290.40/182.96 tff(7568,plain,
% 290.40/182.96 (node17(c_e_h_3, c_h, s7)),
% 290.40/182.96 inference(unit_resolution,[status(thm)],[7479, 7567])).
% 290.40/182.96 tff(7569,plain,
% 290.40/182.96 (~node15(c_e_h_3, c_h, s7, s8)),
% 290.40/182.96 inference(unit_resolution,[status(thm)],[7457, 7452, 7367])).
% 290.40/182.96 tff(7570,plain,
% 290.40/182.96 (m_c_h_element_v_in1(c_e_h_3, c_h, s7)),
% 290.40/182.96 inference(unit_resolution,[status(thm)],[7511, 7568, 7367, 7569])).
% 290.40/182.96 tff(7571,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_h, s7)), introduced(assumption)).
% 290.40/182.96 tff(7572,plain,
% 290.40/182.96 ((~node17(c_e_h_3, c_h, s7)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s7))),
% 290.40/182.96 inference(unit_resolution,[status(thm)],[7518, 919, 7571])).
% 290.40/182.96 tff(7573,plain,
% 290.40/182.96 ($false),
% 290.40/182.96 inference(unit_resolution,[status(thm)],[7572, 7570, 7568])).
% 290.40/182.96 tff(7574,plain,(m_c_h_element_v_out(c_e_h_3, c_h, s7) | m_c_h_element_v_in2(c_e_h_3, c_h, s7) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8))), inference(lemma,lemma(discharge,[]))).
% 290.40/182.96 tff(7575,plain,
% 290.40/182.96 (m_c_h_element_v_in2(c_e_h_3, c_h, s7) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8))),
% 290.40/182.96 inference(unit_resolution,[status(thm)],[7574, 7566])).
% 290.40/182.96 tff(7576,plain,
% 290.40/182.96 (m_c_h_element_v_in2(c_e_h_3, c_h, s7)),
% 290.40/182.96 inference(unit_resolution,[status(thm)],[7575, 7359])).
% 290.40/182.96 tff(7577,plain,
% 290.40/182.96 (m_or_h_gate_v_out(c_e_h_3, c_j, s7)),
% 290.40/182.96 inference(unit_resolution,[status(thm)],[7522, 1174, 7576])).
% 290.40/182.96 tff(7578,plain,
% 290.40/182.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | ((~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | m_or_h_gate_v_out(c_e_h_3, c_j, s8) | (~node6(c_e_h_3, c_j, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | m_or_h_gate_v_out(c_e_h_3, c_j, s8) | (~node6(c_e_h_3, c_j, s7, s8)))),
% 290.40/182.96 inference(rewrite,[status(thm)],[])).
% 290.40/182.96 tff(7579,plain,
% 290.40/182.96 ((m_or_h_gate_v_out(c_e_h_3, c_j, s8) | (~node6(c_e_h_3, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7))) <=> ((~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | m_or_h_gate_v_out(c_e_h_3, c_j, s8) | (~node6(c_e_h_3, c_j, s7, s8)))),
% 290.40/182.96 inference(rewrite,[status(thm)],[])).
% 290.40/182.96 tff(7580,plain,
% 290.40/182.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_3, c_j, s8) | (~node6(c_e_h_3, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | ((~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | m_or_h_gate_v_out(c_e_h_3, c_j, s8) | (~node6(c_e_h_3, c_j, s7, s8))))),
% 290.40/182.96 inference(monotonicity,[status(thm)],[7579])).
% 290.40/182.96 tff(7581,plain,
% 290.40/182.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_3, c_j, s8) | (~node6(c_e_h_3, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | m_or_h_gate_v_out(c_e_h_3, c_j, s8) | (~node6(c_e_h_3, c_j, s7, s8)))),
% 290.40/182.96 inference(transitivity,[status(thm)],[7580, 7578])).
% 290.40/182.96 tff(7582,plain,
% 290.40/182.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_3, c_j, s8) | (~node6(c_e_h_3, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)))),
% 290.40/182.96 inference(quant_inst,[status(thm)],[])).
% 290.40/182.96 tff(7583,plain,
% 290.40/182.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | m_or_h_gate_v_out(c_e_h_3, c_j, s8) | (~node6(c_e_h_3, c_j, s7, s8))),
% 290.40/182.96 inference(modus_ponens,[status(thm)],[7582, 7581])).
% 290.40/182.96 tff(7584,plain,
% 290.40/182.96 ($false),
% 290.40/182.96 inference(unit_resolution,[status(thm)],[7583, 5474, 4495, 7275, 5396])).
% 290.40/182.96 tff(7585,plain,((~node6(c_e_h_3, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s7)) | m_or_h_gate_v_out(c_e_h_3, c_j, s8)), inference(lemma,lemma(discharge,[]))).
% 290.40/182.96 tff(7586,plain,
% 290.40/182.96 (~node6(c_e_h_3, c_j, s7, s8)),
% 290.40/182.96 inference(unit_resolution,[status(thm)],[7585, 7577, 7275])).
% 290.40/182.96 tff(7587,plain,
% 290.40/182.96 (node5(c_e_h_3, c_j, s7, s8)),
% 290.40/182.96 inference(unit_resolution,[status(thm)],[5412, 7586])).
% 290.40/182.96 tff(7588,assumption,(~node4(c_e_h_3, c_j, s7)), introduced(assumption)).
% 290.40/182.96 tff(7589,assumption,(node5(c_e_h_3, c_j, s7, s8)), introduced(assumption)).
% 290.40/182.96 tff(7590,plain,
% 290.40/182.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (m_or_h_gate_v_out(c_e_h_3, c_j, s8) | (~node5(c_e_h_3, c_j, s7, s8)) | node4(c_e_h_3, c_j, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | m_or_h_gate_v_out(c_e_h_3, c_j, s8) | (~node5(c_e_h_3, c_j, s7, s8)) | node4(c_e_h_3, c_j, s7))),
% 290.40/182.96 inference(rewrite,[status(thm)],[])).
% 290.40/182.96 tff(7591,plain,
% 290.40/182.96 ((node4(c_e_h_3, c_j, s7) | (~node5(c_e_h_3, c_j, s7, s8)) | m_or_h_gate_v_out(c_e_h_3, c_j, s8)) <=> (m_or_h_gate_v_out(c_e_h_3, c_j, s8) | (~node5(c_e_h_3, c_j, s7, s8)) | node4(c_e_h_3, c_j, s7))),
% 290.40/182.96 inference(rewrite,[status(thm)],[])).
% 290.40/182.96 tff(7592,plain,
% 290.40/182.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_3, c_j, s7) | (~node5(c_e_h_3, c_j, s7, s8)) | m_or_h_gate_v_out(c_e_h_3, c_j, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (m_or_h_gate_v_out(c_e_h_3, c_j, s8) | (~node5(c_e_h_3, c_j, s7, s8)) | node4(c_e_h_3, c_j, s7)))),
% 290.40/182.96 inference(monotonicity,[status(thm)],[7591])).
% 290.40/182.96 tff(7593,plain,
% 290.40/182.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_3, c_j, s7) | (~node5(c_e_h_3, c_j, s7, s8)) | m_or_h_gate_v_out(c_e_h_3, c_j, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | m_or_h_gate_v_out(c_e_h_3, c_j, s8) | (~node5(c_e_h_3, c_j, s7, s8)) | node4(c_e_h_3, c_j, s7))),
% 290.40/182.96 inference(transitivity,[status(thm)],[7592, 7590])).
% 290.40/182.96 tff(7594,plain,
% 290.40/182.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_3, c_j, s7) | (~node5(c_e_h_3, c_j, s7, s8)) | m_or_h_gate_v_out(c_e_h_3, c_j, s8))),
% 290.40/182.96 inference(quant_inst,[status(thm)],[])).
% 290.40/182.96 tff(7595,plain,
% 290.40/182.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | m_or_h_gate_v_out(c_e_h_3, c_j, s8) | (~node5(c_e_h_3, c_j, s7, s8)) | node4(c_e_h_3, c_j, s7)),
% 290.40/182.96 inference(modus_ponens,[status(thm)],[7594, 7593])).
% 290.40/182.96 tff(7596,plain,
% 290.40/182.96 ($false),
% 290.40/182.96 inference(unit_resolution,[status(thm)],[7595, 5498, 7275, 7589, 7588])).
% 290.40/182.96 tff(7597,plain,((~node5(c_e_h_3, c_j, s7, s8)) | m_or_h_gate_v_out(c_e_h_3, c_j, s8) | node4(c_e_h_3, c_j, s7)), inference(lemma,lemma(discharge,[]))).
% 290.40/182.96 tff(7598,plain,
% 290.40/182.96 (node4(c_e_h_3, c_j, s7)),
% 290.40/182.96 inference(unit_resolution,[status(thm)],[7597, 7587, 7275])).
% 290.40/182.96 tff(7599,plain,
% 290.40/182.96 (((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_j, s7)) | (~node4(c_e_h_3, c_j, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s7)) | (~node4(c_e_h_3, c_j, s7)))),
% 290.40/182.96 inference(rewrite,[status(thm)],[])).
% 290.40/182.96 tff(7600,plain,
% 290.40/182.96 ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_j, s7)) | (~node4(c_e_h_3, c_j, s7)))),
% 290.40/182.96 inference(quant_inst,[status(thm)],[])).
% 290.40/182.96 tff(7601,plain,
% 290.40/182.96 ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s7)) | (~node4(c_e_h_3, c_j, s7))),
% 290.40/182.96 inference(modus_ponens,[status(thm)],[7600, 7599])).
% 290.40/182.96 tff(7602,plain,
% 290.40/182.96 (~m_or_h_gate_v_in1(c_e_h_3, c_j, s7)),
% 290.40/182.96 inference(unit_resolution,[status(thm)],[7601, 5516, 7598])).
% 290.40/182.96 tff(7603,plain,
% 290.40/182.96 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s7)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s7))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s7)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s7))),
% 290.40/182.97 inference(rewrite,[status(thm)],[])).
% 290.40/182.97 tff(7604,plain,
% 290.40/182.97 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s7)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s7))),
% 290.40/182.97 inference(quant_inst,[status(thm)],[])).
% 290.40/182.97 tff(7605,plain,
% 290.40/182.97 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s7)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s7)),
% 290.40/182.97 inference(modus_ponens,[status(thm)],[7604, 7603])).
% 290.40/182.97 tff(7606,plain,
% 290.40/182.97 ($false),
% 290.40/182.97 inference(unit_resolution,[status(thm)],[7605, 3627, 5424, 4906])).
% 290.40/182.97 tff(7607,plain,(m_or_h_gate_v_in1(c_e_h_3, c_j, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s7))), inference(lemma,lemma(discharge,[]))).
% 290.40/182.97 tff(7608,plain,
% 290.40/182.97 (~m_and_h_gate_v_out(c_e_h_3, c_l, s7)),
% 290.40/182.97 inference(unit_resolution,[status(thm)],[7607, 7602])).
% 290.40/182.97 tff(7609,plain,
% 290.40/182.97 (~m_and_h_gate_v_in1(c_e_h_3, c_l, s6)),
% 290.40/182.97 inference(unit_resolution,[status(thm)],[7268, 7608, 7565])).
% 290.40/182.97 tff(7610,plain,
% 290.40/182.97 (~m_and_h_gate_v_out(c_e_h_3, c_k, s6)),
% 290.40/182.97 inference(unit_resolution,[status(thm)],[7242, 7609])).
% 290.40/182.97 tff(7611,plain,
% 290.40/182.97 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s5)),
% 290.40/182.97 inference(unit_resolution,[status(thm)],[7236, 7610, 7561])).
% 290.40/182.97 tff(7612,plain,
% 290.40/182.97 (~m_or_h_gate_v_out(c_e_h_3, c_g, s5)),
% 290.40/182.97 inference(unit_resolution,[status(thm)],[7205, 7611])).
% 290.40/182.97 tff(7613,plain,
% 290.40/182.97 (node4(c_e_h_3, c_g, s4)),
% 290.40/182.97 inference(unit_resolution,[status(thm)],[5922, 7612, 7559])).
% 290.40/182.97 tff(7614,plain,
% 290.40/182.97 (~m_or_h_gate_v_in1(c_e_h_3, c_g, s4)),
% 290.40/182.97 inference(unit_resolution,[status(thm)],[5903, 5516, 7613])).
% 290.40/182.97 tff(7615,plain,
% 290.40/182.97 (~m_and_h_gate_v_out(c_e_h_3, c_c, s4)),
% 290.40/182.97 inference(unit_resolution,[status(thm)],[5899, 5896, 7614])).
% 290.40/182.97 tff(7616,plain,
% 290.40/182.97 (node20(c_e_h_3, c_c, s2)),
% 290.40/182.97 inference(unit_resolution,[status(thm)],[2698, 7553])).
% 290.40/182.97 tff(7617,plain,
% 290.40/182.97 (m_and_h_gate_v_in1(c_e_h_3, c_c, s2)),
% 290.40/182.97 inference(unit_resolution,[status(thm)],[2622, 7616])).
% 290.40/182.97 tff(7618,plain,
% 290.40/182.97 (m_mutex_h_half_v_out(c_e_h_3, c_a, s2)),
% 290.40/182.97 inference(unit_resolution,[status(thm)],[2614, 7617])).
% 290.40/182.97 tff(7619,plain,
% 290.40/182.97 (m_mutex_h_half_v_out(c_e_h_3, c_a, s3)),
% 290.40/182.97 inference(unit_resolution,[status(thm)],[2606, 7618])).
% 290.40/182.97 tff(7620,plain,
% 290.40/182.97 (m_and_h_gate_v_in1(c_e_h_3, c_c, s3)),
% 290.40/182.97 inference(unit_resolution,[status(thm)],[2561, 7619])).
% 290.40/182.97 tff(7621,plain,
% 290.40/182.97 (~node21(c_e_h_3, c_c, s3, s4)),
% 290.40/182.97 inference(unit_resolution,[status(thm)],[5859, 7615, 7620])).
% 290.40/182.97 tff(7622,plain,
% 290.40/182.97 (node22(c_e_h_3, c_c, s3, s4)),
% 290.40/182.97 inference(unit_resolution,[status(thm)],[2734, 7621])).
% 290.40/182.97 tff(7623,plain,
% 290.40/182.97 ($false),
% 290.40/182.97 inference(unit_resolution,[status(thm)],[5874, 5871, 7622, 7615, 7553])).
% 290.40/182.97 tff(7624,plain,(m_or_h_gate_v_out(c_e_h_3, c_j, s8) | (~m_c_h_element_v_out(c_e_h_3, c_h, s9))), inference(lemma,lemma(discharge,[]))).
% 290.40/182.97 tff(7625,plain,
% 290.40/182.97 (~m_c_h_element_v_out(c_e_h_3, c_h, s9)),
% 290.40/182.97 inference(unit_resolution,[status(thm)],[7624, 7275])).
% 290.40/182.97 tff(7626,assumption,(m_c_h_element_v_out(c_e_h_3, c_h, s11)), introduced(assumption)).
% 290.40/182.97 tff(7627,assumption,(~m_or_h_gate_v_out(c_e_h_3, c_j, s11)), introduced(assumption)).
% 290.40/182.97 tff(7628,plain,
% 290.40/182.97 (~node20(c_e_h_3, c_k, s5)),
% 290.40/182.97 inference(unit_resolution,[status(thm)],[5458, 5452])).
% 290.40/182.97 tff(7629,plain,
% 290.40/182.97 (~m_or_h_gate_v_out(c_e_h_3, c_g, s5)),
% 290.40/182.97 inference(unit_resolution,[status(thm)],[7205, 5452])).
% 290.40/182.97 tff(7630,plain,
% 290.40/182.97 (~m_c_h_element_v_out(c_e_h_3, c_h, s8)),
% 290.40/182.97 inference(unit_resolution,[status(thm)],[7556, 4387])).
% 290.40/182.97 tff(7631,plain,
% 290.40/182.97 ($false),
% 290.40/182.97 inference(unit_resolution,[status(thm)],[4447, 4422, 3599, 4423])).
% 290.40/182.97 tff(7632,plain,(m_and_h_gate_v_out(c_e_h_3, c_k, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s6)) | node20(c_e_h_3, c_k, s4)), inference(lemma,lemma(discharge,[]))).
% 290.40/182.97 tff(7633,plain,
% 290.40/182.97 ((~m_and_h_gate_v_out(c_e_h_3, c_l, s6)) | node20(c_e_h_3, c_k, s4)),
% 290.40/182.97 inference(unit_resolution,[status(thm)],[7632, 3485])).
% 290.40/182.97 tff(7634,plain,
% 290.40/182.97 (~m_and_h_gate_v_out(c_e_h_3, c_l, s6)),
% 290.40/182.97 inference(unit_resolution,[status(thm)],[7633, 4387])).
% 290.40/182.97 tff(7635,plain,
% 290.40/182.97 ((~m_and_h_gate_v_out(c_e_h_3, c_k, s5)) | node20(c_e_h_3, c_k, s4)),
% 290.40/182.97 inference(unit_resolution,[status(thm)],[4405, 3485])).
% 290.40/182.97 tff(7636,plain,
% 290.40/182.97 (~m_and_h_gate_v_out(c_e_h_3, c_k, s5)),
% 290.40/182.97 inference(unit_resolution,[status(thm)],[7635, 4387])).
% 290.40/182.97 tff(7637,plain,
% 290.40/182.97 (~m_and_h_gate_v_out(c_e_h_3, c_k, s6)),
% 290.40/182.97 inference(unit_resolution,[status(thm)],[4467, 7636, 4449])).
% 290.40/182.97 tff(7638,plain,
% 290.40/182.97 (~m_and_h_gate_v_in1(c_e_h_3, c_l, s6)),
% 290.40/182.97 inference(unit_resolution,[status(thm)],[4475, 7637])).
% 290.40/182.97 tff(7639,plain,
% 290.40/182.97 (~node20(c_e_h_3, c_l, s6)),
% 290.40/182.97 inference(unit_resolution,[status(thm)],[4483, 7638])).
% 290.40/182.97 tff(7640,plain,
% 290.40/182.97 (~m_and_h_gate_v_out(c_e_h_3, c_l, s7)),
% 290.40/182.97 inference(unit_resolution,[status(thm)],[5441, 7639, 7634])).
% 290.40/182.97 tff(7641,plain,
% 290.40/182.97 (((~![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))) | (m_and_h_gate_v_in2(c_e_h_3, c_k, s8) | m_c_h_element_v_out(c_e_h_3, c_h, s8))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))) | m_and_h_gate_v_in2(c_e_h_3, c_k, s8) | m_c_h_element_v_out(c_e_h_3, c_h, s8))),
% 290.40/182.97 inference(rewrite,[status(thm)],[])).
% 290.40/182.97 tff(7642,plain,
% 290.40/182.97 ((~![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))) | (m_and_h_gate_v_in2(c_e_h_3, c_k, s8) | m_c_h_element_v_out(c_e_h_3, c_h, s8))),
% 290.40/182.97 inference(quant_inst,[status(thm)],[])).
% 290.40/182.97 tff(7643,plain,
% 290.40/182.97 ((~![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))) | m_and_h_gate_v_in2(c_e_h_3, c_k, s8) | m_c_h_element_v_out(c_e_h_3, c_h, s8)),
% 290.40/182.97 inference(modus_ponens,[status(thm)],[7642, 7641])).
% 290.40/182.97 tff(7644,plain,
% 290.40/182.97 (m_and_h_gate_v_in2(c_e_h_3, c_k, s8) | m_c_h_element_v_out(c_e_h_3, c_h, s8)),
% 290.40/182.97 inference(unit_resolution,[status(thm)],[7643, 6420])).
% 290.40/182.97 tff(7645,plain,
% 290.40/182.97 (m_and_h_gate_v_in2(c_e_h_3, c_k, s8)),
% 290.40/182.97 inference(unit_resolution,[status(thm)],[7644, 7630])).
% 290.40/182.97 tff(7646,plain,
% 290.40/182.97 (~m_and_h_gate_v_in1(c_e_h_3, c_l, s6)),
% 290.40/182.97 inference(unit_resolution,[status(thm)],[4475, 4469])).
% 290.40/182.97 tff(7647,plain,
% 290.40/182.97 (~node20(c_e_h_3, c_l, s6)),
% 290.40/182.97 inference(unit_resolution,[status(thm)],[4483, 7646])).
% 290.40/182.97 tff(7648,plain,
% 290.40/182.97 (~m_and_h_gate_v_out(c_e_h_3, c_l, s7)),
% 290.40/182.97 inference(unit_resolution,[status(thm)],[5441, 7647, 7634])).
% 290.40/182.97 tff(7649,assumption,(~m_c_h_element_v_out(c_e_h_3, c_h, s9)), introduced(assumption)).
% 290.40/182.97 tff(7650,plain,
% 290.40/182.97 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s9)) | m_or_h_gate_v_out(c_e_h_3, c_j, s9))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s9)) | m_or_h_gate_v_out(c_e_h_3, c_j, s9))),
% 290.40/182.97 inference(rewrite,[status(thm)],[])).
% 290.40/182.97 tff(7651,plain,
% 290.40/182.97 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s9)) | m_or_h_gate_v_out(c_e_h_3, c_j, s9))),
% 290.40/182.97 inference(quant_inst,[status(thm)],[])).
% 290.40/182.97 tff(7652,plain,
% 290.40/182.97 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s9)) | m_or_h_gate_v_out(c_e_h_3, c_j, s9)),
% 290.40/182.97 inference(modus_ponens,[status(thm)],[7651, 7650])).
% 290.40/182.97 tff(7653,plain,
% 290.40/182.97 (~m_c_h_element_v_in2(c_e_h_3, c_h, s9)),
% 290.40/182.97 inference(unit_resolution,[status(thm)],[7652, 1174, 5462])).
% 290.40/182.97 tff(7654,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_h, s9)), introduced(assumption)).
% 290.40/182.97 tff(7655,assumption,(m_c_h_element_v_out(c_e_h_3, c_h, s10)), introduced(assumption)).
% 290.40/182.97 tff(7656,assumption,(node15(c_e_h_3, c_h, s9, s10)), introduced(assumption)).
% 290.40/182.97 tff(7657,plain,
% 290.40/182.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s10)) | (~node15(c_e_h_3, c_h, s9, s10)) | m_c_h_element_v_out(c_e_h_3, c_h, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s10)) | (~node15(c_e_h_3, c_h, s9, s10)) | m_c_h_element_v_out(c_e_h_3, c_h, s9))),
% 290.50/182.97 inference(rewrite,[status(thm)],[])).
% 290.50/182.97 tff(7658,plain,
% 290.50/182.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s10)) | (~node15(c_e_h_3, c_h, s9, s10)) | m_c_h_element_v_out(c_e_h_3, c_h, s9))),
% 290.50/182.97 inference(quant_inst,[status(thm)],[])).
% 290.50/182.97 tff(7659,plain,
% 290.50/182.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s10)) | (~node15(c_e_h_3, c_h, s9, s10)) | m_c_h_element_v_out(c_e_h_3, c_h, s9)),
% 290.50/182.97 inference(modus_ponens,[status(thm)],[7658, 7657])).
% 290.50/182.97 tff(7660,plain,
% 290.50/182.97 ($false),
% 290.50/182.97 inference(unit_resolution,[status(thm)],[7659, 147, 7655, 7649, 7656])).
% 290.50/182.97 tff(7661,plain,((~node15(c_e_h_3, c_h, s9, s10)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s10)) | m_c_h_element_v_out(c_e_h_3, c_h, s9)), inference(lemma,lemma(discharge,[]))).
% 290.50/182.97 tff(7662,plain,
% 290.50/182.97 (~node15(c_e_h_3, c_h, s9, s10)),
% 290.50/182.97 inference(unit_resolution,[status(thm)],[7661, 7649, 7655])).
% 290.50/182.97 tff(7663,assumption,(~node15(c_e_h_3, c_h, s9, s10)), introduced(assumption)).
% 290.50/182.97 tff(7664,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_h, s9)), introduced(assumption)).
% 290.50/182.97 tff(7665,plain,
% 290.50/182.97 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_h, s9)) | m_c_h_element_v_in1(c_e_h_3, c_h, s9) | m_c_h_element_v_in2(c_e_h_3, c_h, s9))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_h, s9)) | m_c_h_element_v_in1(c_e_h_3, c_h, s9) | m_c_h_element_v_in2(c_e_h_3, c_h, s9))),
% 290.50/182.97 inference(rewrite,[status(thm)],[])).
% 290.50/182.97 tff(7666,plain,
% 290.50/182.97 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_h, s9)) | m_c_h_element_v_in1(c_e_h_3, c_h, s9) | m_c_h_element_v_in2(c_e_h_3, c_h, s9))),
% 290.50/182.97 inference(quant_inst,[status(thm)],[])).
% 290.50/182.97 tff(7667,plain,
% 290.50/182.97 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_h, s9)) | m_c_h_element_v_in1(c_e_h_3, c_h, s9) | m_c_h_element_v_in2(c_e_h_3, c_h, s9)),
% 290.50/182.97 inference(modus_ponens,[status(thm)],[7666, 7665])).
% 290.50/182.97 tff(7668,plain,
% 290.50/182.97 ((~node16(c_e_h_3, c_h, s9)) | m_c_h_element_v_in1(c_e_h_3, c_h, s9)),
% 290.50/182.97 inference(unit_resolution,[status(thm)],[7667, 178, 7654])).
% 290.50/182.97 tff(7669,plain,
% 290.50/182.97 (~node16(c_e_h_3, c_h, s9)),
% 290.50/182.97 inference(unit_resolution,[status(thm)],[7668, 7664])).
% 290.50/182.97 tff(7670,plain,
% 290.50/182.97 (succ(s9, s10) <=> succ(s9, s10)),
% 290.50/182.97 inference(rewrite,[status(thm)],[])).
% 290.50/182.97 tff(7671,axiom,(succ(s9, s10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound10')).
% 290.50/182.97 tff(7672,plain,
% 290.50/182.97 (succ(s9, s10)),
% 290.50/182.97 inference(modus_ponens,[status(thm)],[7671, 7670])).
% 290.50/182.97 tff(7673,plain,
% 290.50/182.97 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s9, s10)) | trans(s9, s10))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s9, s10)) | trans(s9, s10))),
% 290.50/182.97 inference(rewrite,[status(thm)],[])).
% 290.50/182.97 tff(7674,plain,
% 290.50/182.97 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s9, s10)) | trans(s9, s10))),
% 290.50/182.97 inference(quant_inst,[status(thm)],[])).
% 290.50/182.97 tff(7675,plain,
% 290.50/182.97 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s9, s10)) | trans(s9, s10)),
% 290.50/182.97 inference(modus_ponens,[status(thm)],[7674, 7673])).
% 290.50/182.97 tff(7676,plain,
% 290.50/182.97 (trans(s9, s10)),
% 290.50/182.97 inference(unit_resolution,[status(thm)],[7675, 7672, 65])).
% 290.50/182.97 tff(7677,plain,
% 290.50/182.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s9, s10)) | node19(c_e_h_3, c_h, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s9, s10)) | node19(c_e_h_3, c_h, s9, s10))),
% 290.50/182.98 inference(rewrite,[status(thm)],[])).
% 290.50/182.98 tff(7678,plain,
% 290.50/182.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s9, s10)) | node19(c_e_h_3, c_h, s9, s10))),
% 290.50/182.98 inference(quant_inst,[status(thm)],[])).
% 290.50/182.98 tff(7679,plain,
% 290.50/182.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s9, s10)) | node19(c_e_h_3, c_h, s9, s10)),
% 290.50/182.98 inference(modus_ponens,[status(thm)],[7678, 7677])).
% 290.50/182.98 tff(7680,plain,
% 290.50/182.98 (node19(c_e_h_3, c_h, s9, s10)),
% 290.50/182.98 inference(unit_resolution,[status(thm)],[7679, 190, 7676])).
% 290.50/182.98 tff(7681,plain,
% 290.50/182.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s9) | node15(c_e_h_3, c_h, s9, s10) | node14(c_e_h_3, c_h, s9, s10) | (~node19(c_e_h_3, c_h, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_h, s9) | node15(c_e_h_3, c_h, s9, s10) | node14(c_e_h_3, c_h, s9, s10) | (~node19(c_e_h_3, c_h, s9, s10)))),
% 290.50/182.98 inference(rewrite,[status(thm)],[])).
% 290.50/182.98 tff(7682,plain,
% 290.50/182.98 ((node16(c_e_h_3, c_h, s9) | node14(c_e_h_3, c_h, s9, s10) | node15(c_e_h_3, c_h, s9, s10) | (~node19(c_e_h_3, c_h, s9, s10))) <=> (node16(c_e_h_3, c_h, s9) | node15(c_e_h_3, c_h, s9, s10) | node14(c_e_h_3, c_h, s9, s10) | (~node19(c_e_h_3, c_h, s9, s10)))),
% 290.50/182.98 inference(rewrite,[status(thm)],[])).
% 290.50/182.98 tff(7683,plain,
% 290.50/182.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s9) | node14(c_e_h_3, c_h, s9, s10) | node15(c_e_h_3, c_h, s9, s10) | (~node19(c_e_h_3, c_h, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s9) | node15(c_e_h_3, c_h, s9, s10) | node14(c_e_h_3, c_h, s9, s10) | (~node19(c_e_h_3, c_h, s9, s10))))),
% 290.50/182.98 inference(monotonicity,[status(thm)],[7682])).
% 290.50/182.98 tff(7684,plain,
% 290.50/182.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s9) | node14(c_e_h_3, c_h, s9, s10) | node15(c_e_h_3, c_h, s9, s10) | (~node19(c_e_h_3, c_h, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_h, s9) | node15(c_e_h_3, c_h, s9, s10) | node14(c_e_h_3, c_h, s9, s10) | (~node19(c_e_h_3, c_h, s9, s10)))),
% 290.50/182.98 inference(transitivity,[status(thm)],[7683, 7681])).
% 290.50/182.98 tff(7685,plain,
% 290.50/182.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s9) | node14(c_e_h_3, c_h, s9, s10) | node15(c_e_h_3, c_h, s9, s10) | (~node19(c_e_h_3, c_h, s9, s10)))),
% 290.50/182.98 inference(quant_inst,[status(thm)],[])).
% 290.50/182.98 tff(7686,plain,
% 290.50/182.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_h, s9) | node15(c_e_h_3, c_h, s9, s10) | node14(c_e_h_3, c_h, s9, s10) | (~node19(c_e_h_3, c_h, s9, s10))),
% 290.50/182.98 inference(modus_ponens,[status(thm)],[7685, 7684])).
% 290.50/182.98 tff(7687,plain,
% 290.50/182.98 (node16(c_e_h_3, c_h, s9) | node15(c_e_h_3, c_h, s9, s10) | node14(c_e_h_3, c_h, s9, s10)),
% 290.50/182.98 inference(unit_resolution,[status(thm)],[7686, 204, 7680])).
% 290.50/182.98 tff(7688,plain,
% 290.50/182.98 (node14(c_e_h_3, c_h, s9, s10)),
% 290.50/182.98 inference(unit_resolution,[status(thm)],[7687, 7669, 7663])).
% 290.50/182.98 tff(7689,plain,
% 290.50/182.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s9) | (~m_c_h_element_v_out(c_e_h_3, c_h, s10)) | (~node14(c_e_h_3, c_h, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_h, s9) | (~m_c_h_element_v_out(c_e_h_3, c_h, s10)) | (~node14(c_e_h_3, c_h, s9, s10)))),
% 290.50/182.98 inference(rewrite,[status(thm)],[])).
% 290.50/182.98 tff(7690,plain,
% 290.50/182.98 (((~node14(c_e_h_3, c_h, s9, s10)) | m_c_h_element_v_in1(c_e_h_3, c_h, s9) | (~m_c_h_element_v_out(c_e_h_3, c_h, s10))) <=> (m_c_h_element_v_in1(c_e_h_3, c_h, s9) | (~m_c_h_element_v_out(c_e_h_3, c_h, s10)) | (~node14(c_e_h_3, c_h, s9, s10)))),
% 290.50/182.98 inference(rewrite,[status(thm)],[])).
% 290.50/182.98 tff(7691,plain,
% 290.50/182.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s9, s10)) | m_c_h_element_v_in1(c_e_h_3, c_h, s9) | (~m_c_h_element_v_out(c_e_h_3, c_h, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s9) | (~m_c_h_element_v_out(c_e_h_3, c_h, s10)) | (~node14(c_e_h_3, c_h, s9, s10))))),
% 290.50/182.98 inference(monotonicity,[status(thm)],[7690])).
% 290.50/182.98 tff(7692,plain,
% 290.50/182.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s9, s10)) | m_c_h_element_v_in1(c_e_h_3, c_h, s9) | (~m_c_h_element_v_out(c_e_h_3, c_h, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_h, s9) | (~m_c_h_element_v_out(c_e_h_3, c_h, s10)) | (~node14(c_e_h_3, c_h, s9, s10)))),
% 290.50/182.98 inference(transitivity,[status(thm)],[7691, 7689])).
% 290.50/182.98 tff(7693,plain,
% 290.50/182.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s9, s10)) | m_c_h_element_v_in1(c_e_h_3, c_h, s9) | (~m_c_h_element_v_out(c_e_h_3, c_h, s10)))),
% 290.50/182.98 inference(quant_inst,[status(thm)],[])).
% 290.50/182.98 tff(7694,plain,
% 290.50/182.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_h, s9) | (~m_c_h_element_v_out(c_e_h_3, c_h, s10)) | (~node14(c_e_h_3, c_h, s9, s10))),
% 290.50/182.98 inference(modus_ponens,[status(thm)],[7693, 7692])).
% 290.50/182.98 tff(7695,plain,
% 290.50/182.98 ($false),
% 290.50/182.98 inference(unit_resolution,[status(thm)],[7694, 223, 7655, 7664, 7688])).
% 290.50/182.98 tff(7696,plain,(m_c_h_element_v_in1(c_e_h_3, c_h, s9) | (~m_c_h_element_v_out(c_e_h_3, c_h, s10)) | node15(c_e_h_3, c_h, s9, s10) | m_c_h_element_v_in2(c_e_h_3, c_h, s9)), inference(lemma,lemma(discharge,[]))).
% 290.50/182.98 tff(7697,plain,
% 290.50/182.98 (m_c_h_element_v_in1(c_e_h_3, c_h, s9)),
% 290.50/182.98 inference(unit_resolution,[status(thm)],[7696, 7662, 7655, 7654])).
% 290.50/182.98 tff(7698,plain,
% 290.50/182.98 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_h, s9)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s9)) | m_c_h_element_v_in2(c_e_h_3, c_h, s9))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_h, s9)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s9)) | m_c_h_element_v_in2(c_e_h_3, c_h, s9))),
% 290.50/182.98 inference(rewrite,[status(thm)],[])).
% 290.50/182.98 tff(7699,plain,
% 290.50/182.98 (((~m_c_h_element_v_in1(c_e_h_3, c_h, s9)) | m_c_h_element_v_in2(c_e_h_3, c_h, s9) | (~node17(c_e_h_3, c_h, s9))) <=> ((~node17(c_e_h_3, c_h, s9)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s9)) | m_c_h_element_v_in2(c_e_h_3, c_h, s9))),
% 290.50/182.98 inference(rewrite,[status(thm)],[])).
% 290.50/182.98 tff(7700,plain,
% 290.50/182.98 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s9)) | m_c_h_element_v_in2(c_e_h_3, c_h, s9) | (~node17(c_e_h_3, c_h, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_h, s9)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s9)) | m_c_h_element_v_in2(c_e_h_3, c_h, s9)))),
% 290.50/182.98 inference(monotonicity,[status(thm)],[7699])).
% 290.50/182.98 tff(7701,plain,
% 290.50/182.98 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s9)) | m_c_h_element_v_in2(c_e_h_3, c_h, s9) | (~node17(c_e_h_3, c_h, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_h, s9)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s9)) | m_c_h_element_v_in2(c_e_h_3, c_h, s9))),
% 290.50/182.98 inference(transitivity,[status(thm)],[7700, 7698])).
% 290.50/182.98 tff(7702,plain,
% 290.50/182.98 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s9)) | m_c_h_element_v_in2(c_e_h_3, c_h, s9) | (~node17(c_e_h_3, c_h, s9)))),
% 290.50/182.98 inference(quant_inst,[status(thm)],[])).
% 290.50/182.98 tff(7703,plain,
% 290.50/182.98 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_h, s9)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s9)) | m_c_h_element_v_in2(c_e_h_3, c_h, s9)),
% 290.50/182.98 inference(modus_ponens,[status(thm)],[7702, 7701])).
% 290.50/182.98 tff(7704,plain,
% 290.50/182.98 ((~node17(c_e_h_3, c_h, s9)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s9))),
% 290.50/182.98 inference(unit_resolution,[status(thm)],[7703, 919, 7654])).
% 290.50/182.98 tff(7705,plain,
% 290.50/182.98 (~node17(c_e_h_3, c_h, s9)),
% 290.50/182.98 inference(unit_resolution,[status(thm)],[7704, 7697])).
% 290.50/182.98 tff(7706,plain,
% 290.50/182.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s9) | (~node19(c_e_h_3, c_h, s9, s10)) | node18(c_e_h_3, c_h, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_h, s9) | (~node19(c_e_h_3, c_h, s9, s10)) | node18(c_e_h_3, c_h, s9, s10))),
% 290.50/182.98 inference(rewrite,[status(thm)],[])).
% 290.50/182.98 tff(7707,plain,
% 290.50/182.98 ((node17(c_e_h_3, c_h, s9) | node18(c_e_h_3, c_h, s9, s10) | (~node19(c_e_h_3, c_h, s9, s10))) <=> (node17(c_e_h_3, c_h, s9) | (~node19(c_e_h_3, c_h, s9, s10)) | node18(c_e_h_3, c_h, s9, s10))),
% 290.50/182.98 inference(rewrite,[status(thm)],[])).
% 290.50/182.98 tff(7708,plain,
% 290.50/182.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s9) | node18(c_e_h_3, c_h, s9, s10) | (~node19(c_e_h_3, c_h, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s9) | (~node19(c_e_h_3, c_h, s9, s10)) | node18(c_e_h_3, c_h, s9, s10)))),
% 290.50/182.98 inference(monotonicity,[status(thm)],[7707])).
% 290.50/182.98 tff(7709,plain,
% 290.50/182.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s9) | node18(c_e_h_3, c_h, s9, s10) | (~node19(c_e_h_3, c_h, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_h, s9) | (~node19(c_e_h_3, c_h, s9, s10)) | node18(c_e_h_3, c_h, s9, s10))),
% 290.50/182.98 inference(transitivity,[status(thm)],[7708, 7706])).
% 290.50/182.98 tff(7710,plain,
% 290.50/182.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s9) | node18(c_e_h_3, c_h, s9, s10) | (~node19(c_e_h_3, c_h, s9, s10)))),
% 290.50/182.98 inference(quant_inst,[status(thm)],[])).
% 290.50/182.98 tff(7711,plain,
% 290.50/182.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_h, s9) | (~node19(c_e_h_3, c_h, s9, s10)) | node18(c_e_h_3, c_h, s9, s10)),
% 290.50/182.98 inference(modus_ponens,[status(thm)],[7710, 7709])).
% 290.50/182.98 tff(7712,plain,
% 290.50/182.98 (node17(c_e_h_3, c_h, s9) | node18(c_e_h_3, c_h, s9, s10)),
% 290.50/182.98 inference(unit_resolution,[status(thm)],[7711, 776, 7680])).
% 290.50/182.98 tff(7713,plain,
% 290.50/182.98 (node18(c_e_h_3, c_h, s9, s10)),
% 290.50/182.98 inference(unit_resolution,[status(thm)],[7712, 7705])).
% 290.50/182.99 tff(7714,plain,
% 290.50/182.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_h, s9) | (~m_c_h_element_v_out(c_e_h_3, c_h, s10)) | (~node18(c_e_h_3, c_h, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s9) | (~m_c_h_element_v_out(c_e_h_3, c_h, s10)) | (~node18(c_e_h_3, c_h, s9, s10)))),
% 290.50/182.99 inference(rewrite,[status(thm)],[])).
% 290.50/182.99 tff(7715,plain,
% 290.50/182.99 (((~m_c_h_element_v_out(c_e_h_3, c_h, s10)) | m_c_h_element_v_out(c_e_h_3, c_h, s9) | (~node18(c_e_h_3, c_h, s9, s10))) <=> (m_c_h_element_v_out(c_e_h_3, c_h, s9) | (~m_c_h_element_v_out(c_e_h_3, c_h, s10)) | (~node18(c_e_h_3, c_h, s9, s10)))),
% 290.50/182.99 inference(rewrite,[status(thm)],[])).
% 290.50/182.99 tff(7716,plain,
% 290.50/182.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s10)) | m_c_h_element_v_out(c_e_h_3, c_h, s9) | (~node18(c_e_h_3, c_h, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_h, s9) | (~m_c_h_element_v_out(c_e_h_3, c_h, s10)) | (~node18(c_e_h_3, c_h, s9, s10))))),
% 290.50/182.99 inference(monotonicity,[status(thm)],[7715])).
% 290.50/182.99 tff(7717,plain,
% 290.50/182.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s10)) | m_c_h_element_v_out(c_e_h_3, c_h, s9) | (~node18(c_e_h_3, c_h, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s9) | (~m_c_h_element_v_out(c_e_h_3, c_h, s10)) | (~node18(c_e_h_3, c_h, s9, s10)))),
% 290.50/182.99 inference(transitivity,[status(thm)],[7716, 7714])).
% 290.50/182.99 tff(7718,plain,
% 290.50/182.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s10)) | m_c_h_element_v_out(c_e_h_3, c_h, s9) | (~node18(c_e_h_3, c_h, s9, s10)))),
% 290.50/182.99 inference(quant_inst,[status(thm)],[])).
% 290.50/182.99 tff(7719,plain,
% 290.50/182.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s9) | (~m_c_h_element_v_out(c_e_h_3, c_h, s10)) | (~node18(c_e_h_3, c_h, s9, s10))),
% 290.50/182.99 inference(modus_ponens,[status(thm)],[7718, 7717])).
% 290.50/182.99 tff(7720,plain,
% 290.50/182.99 ($false),
% 290.50/182.99 inference(unit_resolution,[status(thm)],[7719, 753, 7655, 7649, 7713])).
% 290.50/182.99 tff(7721,plain,(m_c_h_element_v_out(c_e_h_3, c_h, s9) | (~m_c_h_element_v_out(c_e_h_3, c_h, s10)) | m_c_h_element_v_in2(c_e_h_3, c_h, s9)), inference(lemma,lemma(discharge,[]))).
% 290.50/182.99 tff(7722,plain,
% 290.50/182.99 (~m_c_h_element_v_out(c_e_h_3, c_h, s10)),
% 290.50/182.99 inference(unit_resolution,[status(thm)],[7721, 7653, 7649])).
% 290.50/182.99 tff(7723,assumption,(~m_c_h_element_v_out(c_e_h_3, c_h, s10)), introduced(assumption)).
% 290.50/182.99 tff(7724,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_h, s10)), introduced(assumption)).
% 290.50/182.99 tff(7725,assumption,(node15(c_e_h_3, c_h, s10, s11)), introduced(assumption)).
% 290.50/182.99 tff(7726,plain,
% 290.50/182.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s11)) | (~node15(c_e_h_3, c_h, s10, s11)) | m_c_h_element_v_out(c_e_h_3, c_h, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s11)) | (~node15(c_e_h_3, c_h, s10, s11)) | m_c_h_element_v_out(c_e_h_3, c_h, s10))),
% 290.50/182.99 inference(rewrite,[status(thm)],[])).
% 290.50/182.99 tff(7727,plain,
% 290.50/182.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s11)) | (~node15(c_e_h_3, c_h, s10, s11)) | m_c_h_element_v_out(c_e_h_3, c_h, s10))),
% 290.50/182.99 inference(quant_inst,[status(thm)],[])).
% 290.50/182.99 tff(7728,plain,
% 290.50/182.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s11)) | (~node15(c_e_h_3, c_h, s10, s11)) | m_c_h_element_v_out(c_e_h_3, c_h, s10)),
% 290.50/182.99 inference(modus_ponens,[status(thm)],[7727, 7726])).
% 290.50/182.99 tff(7729,plain,
% 290.50/182.99 ($false),
% 290.50/182.99 inference(unit_resolution,[status(thm)],[7728, 147, 7626, 7723, 7725])).
% 290.50/182.99 tff(7730,plain,((~node15(c_e_h_3, c_h, s10, s11)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s11)) | m_c_h_element_v_out(c_e_h_3, c_h, s10)), inference(lemma,lemma(discharge,[]))).
% 290.50/182.99 tff(7731,plain,
% 290.50/182.99 (~node15(c_e_h_3, c_h, s10, s11)),
% 290.50/182.99 inference(unit_resolution,[status(thm)],[7730, 7723, 7626])).
% 290.50/182.99 tff(7732,assumption,(node18(c_e_h_3, c_h, s10, s11)), introduced(assumption)).
% 290.50/182.99 tff(7733,plain,
% 290.50/182.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_h, s10) | (~m_c_h_element_v_out(c_e_h_3, c_h, s11)) | (~node18(c_e_h_3, c_h, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s10) | (~m_c_h_element_v_out(c_e_h_3, c_h, s11)) | (~node18(c_e_h_3, c_h, s10, s11)))),
% 290.50/182.99 inference(rewrite,[status(thm)],[])).
% 290.50/182.99 tff(7734,plain,
% 290.50/182.99 (((~m_c_h_element_v_out(c_e_h_3, c_h, s11)) | m_c_h_element_v_out(c_e_h_3, c_h, s10) | (~node18(c_e_h_3, c_h, s10, s11))) <=> (m_c_h_element_v_out(c_e_h_3, c_h, s10) | (~m_c_h_element_v_out(c_e_h_3, c_h, s11)) | (~node18(c_e_h_3, c_h, s10, s11)))),
% 290.50/182.99 inference(rewrite,[status(thm)],[])).
% 290.50/182.99 tff(7735,plain,
% 290.50/182.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s11)) | m_c_h_element_v_out(c_e_h_3, c_h, s10) | (~node18(c_e_h_3, c_h, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_h, s10) | (~m_c_h_element_v_out(c_e_h_3, c_h, s11)) | (~node18(c_e_h_3, c_h, s10, s11))))),
% 290.50/182.99 inference(monotonicity,[status(thm)],[7734])).
% 290.50/182.99 tff(7736,plain,
% 290.50/182.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s11)) | m_c_h_element_v_out(c_e_h_3, c_h, s10) | (~node18(c_e_h_3, c_h, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s10) | (~m_c_h_element_v_out(c_e_h_3, c_h, s11)) | (~node18(c_e_h_3, c_h, s10, s11)))),
% 290.50/182.99 inference(transitivity,[status(thm)],[7735, 7733])).
% 290.50/182.99 tff(7737,plain,
% 290.50/182.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s11)) | m_c_h_element_v_out(c_e_h_3, c_h, s10) | (~node18(c_e_h_3, c_h, s10, s11)))),
% 290.50/182.99 inference(quant_inst,[status(thm)],[])).
% 290.50/182.99 tff(7738,plain,
% 290.50/182.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s10) | (~m_c_h_element_v_out(c_e_h_3, c_h, s11)) | (~node18(c_e_h_3, c_h, s10, s11))),
% 290.50/182.99 inference(modus_ponens,[status(thm)],[7737, 7736])).
% 290.50/182.99 tff(7739,plain,
% 290.50/182.99 ($false),
% 290.50/182.99 inference(unit_resolution,[status(thm)],[7738, 753, 7626, 7723, 7732])).
% 290.50/182.99 tff(7740,plain,((~node18(c_e_h_3, c_h, s10, s11)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s11)) | m_c_h_element_v_out(c_e_h_3, c_h, s10)), inference(lemma,lemma(discharge,[]))).
% 290.50/182.99 tff(7741,plain,
% 290.50/182.99 (~node18(c_e_h_3, c_h, s10, s11)),
% 290.52/183.00 inference(unit_resolution,[status(thm)],[7740, 7723, 7626])).
% 290.52/183.00 tff(7742,plain,
% 290.52/183.00 (succ(s10, s11) <=> succ(s10, s11)),
% 290.52/183.00 inference(rewrite,[status(thm)],[])).
% 290.52/183.00 tff(7743,axiom,(succ(s10, s11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound11')).
% 290.52/183.00 tff(7744,plain,
% 290.52/183.00 (succ(s10, s11)),
% 290.52/183.00 inference(modus_ponens,[status(thm)],[7743, 7742])).
% 290.52/183.00 tff(7745,plain,
% 290.52/183.00 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s10, s11)) | trans(s10, s11))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s10, s11)) | trans(s10, s11))),
% 290.52/183.00 inference(rewrite,[status(thm)],[])).
% 290.52/183.00 tff(7746,plain,
% 290.52/183.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s10, s11)) | trans(s10, s11))),
% 290.52/183.00 inference(quant_inst,[status(thm)],[])).
% 290.52/183.00 tff(7747,plain,
% 290.52/183.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s10, s11)) | trans(s10, s11)),
% 290.52/183.00 inference(modus_ponens,[status(thm)],[7746, 7745])).
% 290.52/183.00 tff(7748,plain,
% 290.52/183.00 (trans(s10, s11)),
% 290.52/183.00 inference(unit_resolution,[status(thm)],[7747, 7744, 65])).
% 290.52/183.00 tff(7749,plain,
% 290.52/183.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s10, s11)) | node19(c_e_h_3, c_h, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s10, s11)) | node19(c_e_h_3, c_h, s10, s11))),
% 290.52/183.00 inference(rewrite,[status(thm)],[])).
% 290.52/183.00 tff(7750,plain,
% 290.52/183.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s10, s11)) | node19(c_e_h_3, c_h, s10, s11))),
% 290.52/183.00 inference(quant_inst,[status(thm)],[])).
% 290.52/183.00 tff(7751,plain,
% 290.52/183.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s10, s11)) | node19(c_e_h_3, c_h, s10, s11)),
% 290.52/183.00 inference(modus_ponens,[status(thm)],[7750, 7749])).
% 290.52/183.00 tff(7752,plain,
% 290.52/183.00 (node19(c_e_h_3, c_h, s10, s11)),
% 290.52/183.00 inference(unit_resolution,[status(thm)],[7751, 190, 7748])).
% 290.52/183.00 tff(7753,plain,
% 290.52/183.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s10) | (~node19(c_e_h_3, c_h, s10, s11)) | node18(c_e_h_3, c_h, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_h, s10) | (~node19(c_e_h_3, c_h, s10, s11)) | node18(c_e_h_3, c_h, s10, s11))),
% 290.52/183.00 inference(rewrite,[status(thm)],[])).
% 290.52/183.00 tff(7754,plain,
% 290.52/183.00 ((node17(c_e_h_3, c_h, s10) | node18(c_e_h_3, c_h, s10, s11) | (~node19(c_e_h_3, c_h, s10, s11))) <=> (node17(c_e_h_3, c_h, s10) | (~node19(c_e_h_3, c_h, s10, s11)) | node18(c_e_h_3, c_h, s10, s11))),
% 290.52/183.00 inference(rewrite,[status(thm)],[])).
% 290.52/183.00 tff(7755,plain,
% 290.52/183.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s10) | node18(c_e_h_3, c_h, s10, s11) | (~node19(c_e_h_3, c_h, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s10) | (~node19(c_e_h_3, c_h, s10, s11)) | node18(c_e_h_3, c_h, s10, s11)))),
% 290.52/183.00 inference(monotonicity,[status(thm)],[7754])).
% 290.52/183.00 tff(7756,plain,
% 290.52/183.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s10) | node18(c_e_h_3, c_h, s10, s11) | (~node19(c_e_h_3, c_h, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_h, s10) | (~node19(c_e_h_3, c_h, s10, s11)) | node18(c_e_h_3, c_h, s10, s11))),
% 290.52/183.00 inference(transitivity,[status(thm)],[7755, 7753])).
% 290.52/183.00 tff(7757,plain,
% 290.52/183.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s10) | node18(c_e_h_3, c_h, s10, s11) | (~node19(c_e_h_3, c_h, s10, s11)))),
% 290.52/183.00 inference(quant_inst,[status(thm)],[])).
% 290.52/183.00 tff(7758,plain,
% 290.52/183.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_h, s10) | (~node19(c_e_h_3, c_h, s10, s11)) | node18(c_e_h_3, c_h, s10, s11)),
% 290.52/183.00 inference(modus_ponens,[status(thm)],[7757, 7756])).
% 290.52/183.00 tff(7759,plain,
% 290.52/183.00 (node17(c_e_h_3, c_h, s10) | node18(c_e_h_3, c_h, s10, s11)),
% 290.52/183.00 inference(unit_resolution,[status(thm)],[7758, 776, 7752])).
% 290.52/183.00 tff(7760,plain,
% 290.52/183.00 (node17(c_e_h_3, c_h, s10)),
% 290.52/183.00 inference(unit_resolution,[status(thm)],[7759, 7741])).
% 290.52/183.00 tff(7761,assumption,(node17(c_e_h_3, c_h, s10)), introduced(assumption)).
% 290.52/183.00 tff(7762,plain,
% 290.52/183.00 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s10)) | m_c_h_element_v_in1(c_e_h_3, c_h, s10) | (~node17(c_e_h_3, c_h, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s10)) | m_c_h_element_v_in1(c_e_h_3, c_h, s10) | (~node17(c_e_h_3, c_h, s10)))),
% 290.52/183.00 inference(rewrite,[status(thm)],[])).
% 290.52/183.00 tff(7763,plain,
% 290.52/183.00 ((m_c_h_element_v_in1(c_e_h_3, c_h, s10) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s10)) | (~node17(c_e_h_3, c_h, s10))) <=> ((~m_c_h_element_v_in2(c_e_h_3, c_h, s10)) | m_c_h_element_v_in1(c_e_h_3, c_h, s10) | (~node17(c_e_h_3, c_h, s10)))),
% 290.52/183.00 inference(rewrite,[status(thm)],[])).
% 290.52/183.00 tff(7764,plain,
% 290.52/183.00 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s10) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s10)) | (~node17(c_e_h_3, c_h, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s10)) | m_c_h_element_v_in1(c_e_h_3, c_h, s10) | (~node17(c_e_h_3, c_h, s10))))),
% 290.52/183.00 inference(monotonicity,[status(thm)],[7763])).
% 290.52/183.00 tff(7765,plain,
% 290.52/183.00 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s10) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s10)) | (~node17(c_e_h_3, c_h, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s10)) | m_c_h_element_v_in1(c_e_h_3, c_h, s10) | (~node17(c_e_h_3, c_h, s10)))),
% 290.52/183.00 inference(transitivity,[status(thm)],[7764, 7762])).
% 290.52/183.00 tff(7766,plain,
% 290.52/183.00 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s10) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s10)) | (~node17(c_e_h_3, c_h, s10)))),
% 290.52/183.00 inference(quant_inst,[status(thm)],[])).
% 290.52/183.00 tff(7767,plain,
% 290.52/183.00 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s10)) | m_c_h_element_v_in1(c_e_h_3, c_h, s10) | (~node17(c_e_h_3, c_h, s10))),
% 290.52/183.00 inference(modus_ponens,[status(thm)],[7766, 7765])).
% 290.52/183.00 tff(7768,plain,
% 290.52/183.00 ((~m_c_h_element_v_in2(c_e_h_3, c_h, s10)) | m_c_h_element_v_in1(c_e_h_3, c_h, s10)),
% 290.52/183.00 inference(unit_resolution,[status(thm)],[7767, 859, 7761])).
% 290.52/183.00 tff(7769,plain,
% 290.52/183.00 (~m_c_h_element_v_in2(c_e_h_3, c_h, s10)),
% 290.52/183.00 inference(unit_resolution,[status(thm)],[7768, 7724])).
% 290.52/183.00 tff(7770,assumption,(~node15(c_e_h_3, c_h, s10, s11)), introduced(assumption)).
% 290.52/183.00 tff(7771,assumption,(node14(c_e_h_3, c_h, s10, s11)), introduced(assumption)).
% 290.52/183.00 tff(7772,plain,
% 290.52/183.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s10) | (~m_c_h_element_v_out(c_e_h_3, c_h, s11)) | (~node14(c_e_h_3, c_h, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_h, s10) | (~m_c_h_element_v_out(c_e_h_3, c_h, s11)) | (~node14(c_e_h_3, c_h, s10, s11)))),
% 290.52/183.00 inference(rewrite,[status(thm)],[])).
% 290.52/183.00 tff(7773,plain,
% 290.52/183.00 (((~node14(c_e_h_3, c_h, s10, s11)) | m_c_h_element_v_in1(c_e_h_3, c_h, s10) | (~m_c_h_element_v_out(c_e_h_3, c_h, s11))) <=> (m_c_h_element_v_in1(c_e_h_3, c_h, s10) | (~m_c_h_element_v_out(c_e_h_3, c_h, s11)) | (~node14(c_e_h_3, c_h, s10, s11)))),
% 290.52/183.00 inference(rewrite,[status(thm)],[])).
% 290.52/183.00 tff(7774,plain,
% 290.52/183.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s10, s11)) | m_c_h_element_v_in1(c_e_h_3, c_h, s10) | (~m_c_h_element_v_out(c_e_h_3, c_h, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s10) | (~m_c_h_element_v_out(c_e_h_3, c_h, s11)) | (~node14(c_e_h_3, c_h, s10, s11))))),
% 290.52/183.00 inference(monotonicity,[status(thm)],[7773])).
% 290.52/183.00 tff(7775,plain,
% 290.52/183.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s10, s11)) | m_c_h_element_v_in1(c_e_h_3, c_h, s10) | (~m_c_h_element_v_out(c_e_h_3, c_h, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_h, s10) | (~m_c_h_element_v_out(c_e_h_3, c_h, s11)) | (~node14(c_e_h_3, c_h, s10, s11)))),
% 290.52/183.00 inference(transitivity,[status(thm)],[7774, 7772])).
% 290.52/183.00 tff(7776,plain,
% 290.52/183.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s10, s11)) | m_c_h_element_v_in1(c_e_h_3, c_h, s10) | (~m_c_h_element_v_out(c_e_h_3, c_h, s11)))),
% 290.52/183.00 inference(quant_inst,[status(thm)],[])).
% 290.52/183.00 tff(7777,plain,
% 290.52/183.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_h, s10) | (~m_c_h_element_v_out(c_e_h_3, c_h, s11)) | (~node14(c_e_h_3, c_h, s10, s11))),
% 290.52/183.00 inference(modus_ponens,[status(thm)],[7776, 7775])).
% 290.52/183.00 tff(7778,plain,
% 290.52/183.00 ($false),
% 290.52/183.00 inference(unit_resolution,[status(thm)],[7777, 223, 7626, 7724, 7771])).
% 290.52/183.00 tff(7779,plain,((~node14(c_e_h_3, c_h, s10, s11)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s11)) | m_c_h_element_v_in1(c_e_h_3, c_h, s10)), inference(lemma,lemma(discharge,[]))).
% 290.52/183.00 tff(7780,plain,
% 290.52/183.00 (~node14(c_e_h_3, c_h, s10, s11)),
% 290.52/183.00 inference(unit_resolution,[status(thm)],[7779, 7724, 7626])).
% 290.52/183.00 tff(7781,plain,
% 290.52/183.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s10) | (~node19(c_e_h_3, c_h, s10, s11)) | node14(c_e_h_3, c_h, s10, s11) | node15(c_e_h_3, c_h, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_h, s10) | (~node19(c_e_h_3, c_h, s10, s11)) | node14(c_e_h_3, c_h, s10, s11) | node15(c_e_h_3, c_h, s10, s11))),
% 290.52/183.00 inference(rewrite,[status(thm)],[])).
% 290.52/183.00 tff(7782,plain,
% 290.52/183.00 ((node16(c_e_h_3, c_h, s10) | node14(c_e_h_3, c_h, s10, s11) | node15(c_e_h_3, c_h, s10, s11) | (~node19(c_e_h_3, c_h, s10, s11))) <=> (node16(c_e_h_3, c_h, s10) | (~node19(c_e_h_3, c_h, s10, s11)) | node14(c_e_h_3, c_h, s10, s11) | node15(c_e_h_3, c_h, s10, s11))),
% 290.52/183.00 inference(rewrite,[status(thm)],[])).
% 290.52/183.00 tff(7783,plain,
% 290.52/183.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s10) | node14(c_e_h_3, c_h, s10, s11) | node15(c_e_h_3, c_h, s10, s11) | (~node19(c_e_h_3, c_h, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s10) | (~node19(c_e_h_3, c_h, s10, s11)) | node14(c_e_h_3, c_h, s10, s11) | node15(c_e_h_3, c_h, s10, s11)))),
% 290.52/183.00 inference(monotonicity,[status(thm)],[7782])).
% 290.52/183.01 tff(7784,plain,
% 290.52/183.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s10) | node14(c_e_h_3, c_h, s10, s11) | node15(c_e_h_3, c_h, s10, s11) | (~node19(c_e_h_3, c_h, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_h, s10) | (~node19(c_e_h_3, c_h, s10, s11)) | node14(c_e_h_3, c_h, s10, s11) | node15(c_e_h_3, c_h, s10, s11))),
% 290.52/183.01 inference(transitivity,[status(thm)],[7783, 7781])).
% 290.52/183.01 tff(7785,plain,
% 290.52/183.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s10) | node14(c_e_h_3, c_h, s10, s11) | node15(c_e_h_3, c_h, s10, s11) | (~node19(c_e_h_3, c_h, s10, s11)))),
% 290.52/183.01 inference(quant_inst,[status(thm)],[])).
% 290.52/183.01 tff(7786,plain,
% 290.52/183.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_h, s10) | (~node19(c_e_h_3, c_h, s10, s11)) | node14(c_e_h_3, c_h, s10, s11) | node15(c_e_h_3, c_h, s10, s11)),
% 290.52/183.01 inference(modus_ponens,[status(thm)],[7785, 7784])).
% 290.52/183.01 tff(7787,plain,
% 290.52/183.01 (node16(c_e_h_3, c_h, s10) | node14(c_e_h_3, c_h, s10, s11) | node15(c_e_h_3, c_h, s10, s11)),
% 290.52/183.01 inference(unit_resolution,[status(thm)],[7786, 204, 7752])).
% 290.52/183.01 tff(7788,plain,
% 290.52/183.01 (node16(c_e_h_3, c_h, s10)),
% 290.52/183.01 inference(unit_resolution,[status(thm)],[7787, 7780, 7770])).
% 290.52/183.01 tff(7789,plain,
% 290.52/183.01 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_h, s10)) | m_c_h_element_v_in1(c_e_h_3, c_h, s10) | m_c_h_element_v_in2(c_e_h_3, c_h, s10))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_h, s10)) | m_c_h_element_v_in1(c_e_h_3, c_h, s10) | m_c_h_element_v_in2(c_e_h_3, c_h, s10))),
% 290.52/183.01 inference(rewrite,[status(thm)],[])).
% 290.52/183.01 tff(7790,plain,
% 290.52/183.01 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_h, s10)) | m_c_h_element_v_in1(c_e_h_3, c_h, s10) | m_c_h_element_v_in2(c_e_h_3, c_h, s10))),
% 290.52/183.01 inference(quant_inst,[status(thm)],[])).
% 290.52/183.01 tff(7791,plain,
% 290.52/183.01 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_h, s10)) | m_c_h_element_v_in1(c_e_h_3, c_h, s10) | m_c_h_element_v_in2(c_e_h_3, c_h, s10)),
% 290.52/183.01 inference(modus_ponens,[status(thm)],[7790, 7789])).
% 290.52/183.01 tff(7792,plain,
% 290.52/183.01 ($false),
% 290.52/183.01 inference(unit_resolution,[status(thm)],[7791, 178, 7724, 7788, 7769])).
% 290.52/183.01 tff(7793,plain,(m_c_h_element_v_in1(c_e_h_3, c_h, s10) | node15(c_e_h_3, c_h, s10, s11) | (~node17(c_e_h_3, c_h, s10)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s11))), inference(lemma,lemma(discharge,[]))).
% 290.52/183.01 tff(7794,plain,
% 290.52/183.01 ($false),
% 290.52/183.01 inference(unit_resolution,[status(thm)],[7793, 7760, 7731, 7626, 7724])).
% 290.52/183.01 tff(7795,plain,(m_c_h_element_v_out(c_e_h_3, c_h, s10) | (~m_c_h_element_v_out(c_e_h_3, c_h, s11)) | m_c_h_element_v_in1(c_e_h_3, c_h, s10)), inference(lemma,lemma(discharge,[]))).
% 290.52/183.01 tff(7796,plain,
% 290.52/183.01 (m_c_h_element_v_in1(c_e_h_3, c_h, s10)),
% 290.52/183.01 inference(unit_resolution,[status(thm)],[7795, 7723, 7626])).
% 290.52/183.01 tff(7797,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_h, s10)), introduced(assumption)).
% 290.52/183.01 tff(7798,plain,
% 290.52/183.01 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_3, c_h, s10) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s10)) | (~node17(c_e_h_3, c_h, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_h, s10) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s10)) | (~node17(c_e_h_3, c_h, s10)))),
% 290.52/183.01 inference(rewrite,[status(thm)],[])).
% 290.52/183.01 tff(7799,plain,
% 290.52/183.01 (((~m_c_h_element_v_in1(c_e_h_3, c_h, s10)) | m_c_h_element_v_in2(c_e_h_3, c_h, s10) | (~node17(c_e_h_3, c_h, s10))) <=> (m_c_h_element_v_in2(c_e_h_3, c_h, s10) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s10)) | (~node17(c_e_h_3, c_h, s10)))),
% 290.52/183.01 inference(rewrite,[status(thm)],[])).
% 290.52/183.01 tff(7800,plain,
% 290.52/183.01 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s10)) | m_c_h_element_v_in2(c_e_h_3, c_h, s10) | (~node17(c_e_h_3, c_h, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_3, c_h, s10) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s10)) | (~node17(c_e_h_3, c_h, s10))))),
% 290.52/183.01 inference(monotonicity,[status(thm)],[7799])).
% 290.52/183.01 tff(7801,plain,
% 290.52/183.01 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s10)) | m_c_h_element_v_in2(c_e_h_3, c_h, s10) | (~node17(c_e_h_3, c_h, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_h, s10) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s10)) | (~node17(c_e_h_3, c_h, s10)))),
% 290.52/183.01 inference(transitivity,[status(thm)],[7800, 7798])).
% 290.52/183.01 tff(7802,plain,
% 290.52/183.01 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s10)) | m_c_h_element_v_in2(c_e_h_3, c_h, s10) | (~node17(c_e_h_3, c_h, s10)))),
% 290.52/183.01 inference(quant_inst,[status(thm)],[])).
% 290.52/183.01 tff(7803,plain,
% 290.52/183.01 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_h, s10) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s10)) | (~node17(c_e_h_3, c_h, s10))),
% 290.52/183.01 inference(modus_ponens,[status(thm)],[7802, 7801])).
% 290.52/183.01 tff(7804,plain,
% 290.52/183.01 ((~m_c_h_element_v_in1(c_e_h_3, c_h, s10)) | (~node17(c_e_h_3, c_h, s10))),
% 290.52/183.01 inference(unit_resolution,[status(thm)],[7803, 919, 7797])).
% 290.52/183.01 tff(7805,plain,
% 290.52/183.01 ($false),
% 290.52/183.01 inference(unit_resolution,[status(thm)],[7804, 7760, 7796])).
% 290.52/183.01 tff(7806,plain,(m_c_h_element_v_out(c_e_h_3, c_h, s10) | m_c_h_element_v_in2(c_e_h_3, c_h, s10) | (~m_c_h_element_v_out(c_e_h_3, c_h, s11))), inference(lemma,lemma(discharge,[]))).
% 290.52/183.01 tff(7807,plain,
% 290.52/183.01 (m_c_h_element_v_in2(c_e_h_3, c_h, s10)),
% 290.52/183.01 inference(unit_resolution,[status(thm)],[7806, 7722, 7626])).
% 290.52/183.01 tff(7808,plain,
% 290.52/183.01 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s10)) | m_or_h_gate_v_out(c_e_h_3, c_j, s10))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s10)) | m_or_h_gate_v_out(c_e_h_3, c_j, s10))),
% 290.52/183.01 inference(rewrite,[status(thm)],[])).
% 290.52/183.01 tff(7809,plain,
% 290.52/183.01 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s10)) | m_or_h_gate_v_out(c_e_h_3, c_j, s10))),
% 290.52/183.01 inference(quant_inst,[status(thm)],[])).
% 290.52/183.01 tff(7810,plain,
% 290.52/183.01 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s10)) | m_or_h_gate_v_out(c_e_h_3, c_j, s10)),
% 290.52/183.01 inference(modus_ponens,[status(thm)],[7809, 7808])).
% 290.52/183.01 tff(7811,plain,
% 290.52/183.01 (m_or_h_gate_v_out(c_e_h_3, c_j, s10)),
% 290.52/183.01 inference(unit_resolution,[status(thm)],[7810, 1174, 7807])).
% 290.52/183.01 tff(7812,assumption,(m_and_h_gate_v_out(c_e_h_2, c_q, s9)), introduced(assumption)).
% 290.52/183.01 tff(7813,assumption,(node21(c_e_h_2, c_q, s8, s9)), introduced(assumption)).
% 290.52/183.01 tff(7814,assumption,(m_and_h_gate_v_out(c_e_h_2, c_i, s7)), introduced(assumption)).
% 290.52/183.01 tff(7815,assumption,(node22(c_e_h_2, c_i, s6, s7)), introduced(assumption)).
% 290.52/183.01 tff(7816,assumption,(m_or_h_gate_v_out(c_e_h_2, c_j, s4)), introduced(assumption)).
% 290.52/183.01 tff(7817,assumption,(node6(c_e_h_2, c_j, s3, s4)), introduced(assumption)).
% 290.52/183.01 tff(7818,assumption,(~m_or_h_gate_v_out(c_e_h_2, c_j, s3)), introduced(assumption)).
% 290.52/183.01 tff(7819,plain,
% 290.52/183.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_2, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s4)) | (~node6(c_e_h_2, c_j, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s4)) | (~node6(c_e_h_2, c_j, s3, s4)))),
% 290.52/183.01 inference(rewrite,[status(thm)],[])).
% 290.52/183.01 tff(7820,plain,
% 290.52/183.01 (((~node6(c_e_h_2, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s4)) | m_or_h_gate_v_out(c_e_h_2, c_j, s3)) <=> (m_or_h_gate_v_out(c_e_h_2, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s4)) | (~node6(c_e_h_2, c_j, s3, s4)))),
% 290.52/183.01 inference(rewrite,[status(thm)],[])).
% 290.52/183.01 tff(7821,plain,
% 290.52/183.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s4)) | m_or_h_gate_v_out(c_e_h_2, c_j, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_2, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s4)) | (~node6(c_e_h_2, c_j, s3, s4))))),
% 290.52/183.01 inference(monotonicity,[status(thm)],[7820])).
% 290.52/183.01 tff(7822,plain,
% 290.52/183.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s4)) | m_or_h_gate_v_out(c_e_h_2, c_j, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s4)) | (~node6(c_e_h_2, c_j, s3, s4)))),
% 290.52/183.01 inference(transitivity,[status(thm)],[7821, 7819])).
% 290.52/183.01 tff(7823,plain,
% 290.52/183.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s4)) | m_or_h_gate_v_out(c_e_h_2, c_j, s3))),
% 290.52/183.01 inference(quant_inst,[status(thm)],[])).
% 290.52/183.01 tff(7824,plain,
% 290.52/183.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s4)) | (~node6(c_e_h_2, c_j, s3, s4))),
% 290.52/183.01 inference(modus_ponens,[status(thm)],[7823, 7822])).
% 290.52/183.01 tff(7825,plain,
% 290.52/183.01 ($false),
% 290.52/183.01 inference(unit_resolution,[status(thm)],[7824, 1121, 7816, 7818, 7817])).
% 290.52/183.01 tff(7826,plain,((~node6(c_e_h_2, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s4)) | m_or_h_gate_v_out(c_e_h_2, c_j, s3)), inference(lemma,lemma(discharge,[]))).
% 290.52/183.01 tff(7827,plain,
% 290.52/183.01 ((~node6(c_e_h_2, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s4))),
% 290.52/183.01 inference(unit_resolution,[status(thm)],[7826, 5164])).
% 290.52/183.01 tff(7828,plain,
% 290.52/183.01 (~node6(c_e_h_2, c_j, s3, s4)),
% 290.52/183.01 inference(unit_resolution,[status(thm)],[7827, 7816])).
% 290.52/183.01 tff(7829,assumption,(m_and_h_gate_v_out(c_e_h_2, c_l, s3)), introduced(assumption)).
% 290.52/183.01 tff(7830,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1)), introduced(assumption)).
% 290.52/183.01 tff(7831,assumption,(node11(c_e_h_2, c_n, s0, s1)), introduced(assumption)).
% 290.52/183.01 tff(7832,plain,
% 290.52/183.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1) | (~node11(c_e_h_2, c_n, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1) | (~node11(c_e_h_2, c_n, s0, s1)))),
% 290.52/183.02 inference(rewrite,[status(thm)],[])).
% 290.52/183.02 tff(7833,plain,
% 290.52/183.02 ((m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1) | (~node11(c_e_h_2, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1) | (~node11(c_e_h_2, c_n, s0, s1)))),
% 290.52/183.02 inference(rewrite,[status(thm)],[])).
% 290.52/183.02 tff(7834,plain,
% 290.52/183.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1) | (~node11(c_e_h_2, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1) | (~node11(c_e_h_2, c_n, s0, s1))))),
% 290.52/183.02 inference(monotonicity,[status(thm)],[7833])).
% 290.52/183.02 tff(7835,plain,
% 290.52/183.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1) | (~node11(c_e_h_2, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1) | (~node11(c_e_h_2, c_n, s0, s1)))),
% 290.52/183.02 inference(transitivity,[status(thm)],[7834, 7832])).
% 290.52/183.02 tff(7836,plain,
% 290.52/183.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1) | (~node11(c_e_h_2, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0)))),
% 290.52/183.02 inference(quant_inst,[status(thm)],[])).
% 290.52/183.02 tff(7837,plain,
% 290.52/183.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1) | (~node11(c_e_h_2, c_n, s0, s1))),
% 290.52/183.02 inference(modus_ponens,[status(thm)],[7836, 7835])).
% 290.52/183.02 tff(7838,plain,
% 290.52/183.02 ($false),
% 290.52/183.02 inference(unit_resolution,[status(thm)],[7837, 5742, 4951, 7830, 7831])).
% 290.52/183.02 tff(7839,plain,((~node11(c_e_h_2, c_n, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1)), inference(lemma,lemma(discharge,[]))).
% 290.52/183.02 tff(7840,plain,
% 290.52/183.02 (~node11(c_e_h_2, c_n, s0, s1)),
% 290.52/183.02 inference(unit_resolution,[status(thm)],[7839, 7830])).
% 290.52/183.02 tff(7841,plain,
% 290.52/183.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s0, s1)) | node10(c_e_h_2, c_n, s0, s1) | node11(c_e_h_2, c_n, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s0, s1)) | node10(c_e_h_2, c_n, s0, s1) | node11(c_e_h_2, c_n, s0, s1))),
% 290.52/183.02 inference(rewrite,[status(thm)],[])).
% 290.52/183.02 tff(7842,plain,
% 290.52/183.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s0, s1)) | node10(c_e_h_2, c_n, s0, s1) | node11(c_e_h_2, c_n, s0, s1))),
% 290.52/183.02 inference(quant_inst,[status(thm)],[])).
% 290.52/183.02 tff(7843,plain,
% 290.52/183.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s0, s1)) | node10(c_e_h_2, c_n, s0, s1) | node11(c_e_h_2, c_n, s0, s1)),
% 290.52/183.02 inference(modus_ponens,[status(thm)],[7842, 7841])).
% 290.52/183.02 tff(7844,plain,
% 290.52/183.02 (node10(c_e_h_2, c_n, s0, s1) | node11(c_e_h_2, c_n, s0, s1)),
% 290.52/183.02 inference(unit_resolution,[status(thm)],[7843, 5002, 72])).
% 290.52/183.02 tff(7845,plain,
% 290.52/183.02 (node10(c_e_h_2, c_n, s0, s1)),
% 290.52/183.02 inference(unit_resolution,[status(thm)],[7844, 7840])).
% 290.52/183.02 tff(7846,assumption,(m_c_h_element_v_out(c_e_h_2, c_e, s0)), introduced(assumption)).
% 290.52/183.02 tff(7847,plain,
% 290.52/183.02 ((~![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s0))),
% 290.55/183.02 inference(quant_inst,[status(thm)],[])).
% 290.55/183.02 tff(7848,plain,
% 290.55/183.02 ($false),
% 290.55/183.02 inference(unit_resolution,[status(thm)],[7847, 14, 7846])).
% 290.55/183.02 tff(7849,plain,(~m_c_h_element_v_out(c_e_h_2, c_e, s0)), inference(lemma,lemma(discharge,[]))).
% 290.55/183.02 tff(7850,plain,
% 290.55/183.02 (^[I0: $i, X: $i] : refl((m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X)) <=> (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X)))),
% 290.55/183.02 inference(bind,[status(th)],[])).
% 290.55/183.02 tff(7851,plain,
% 290.55/183.02 (![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X)) <=> ![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))),
% 290.55/183.02 inference(quant_intro,[status(thm)],[7850])).
% 290.55/183.02 tff(7852,plain,
% 290.55/183.02 (![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X)) <=> ![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))),
% 290.55/183.02 inference(rewrite,[status(thm)],[])).
% 290.55/183.02 tff(7853,axiom,(![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_57')).
% 290.55/183.02 tff(7854,plain,
% 290.55/183.02 (![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))),
% 290.55/183.02 inference(modus_ponens,[status(thm)],[7853, 7852])).
% 290.55/183.02 tff(7855,plain,(
% 290.55/183.02 ![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))),
% 290.55/183.02 inference(skolemize,[status(sab)],[7854])).
% 290.55/183.02 tff(7856,plain,
% 290.55/183.02 (![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))),
% 290.55/183.02 inference(modus_ponens,[status(thm)],[7855, 7851])).
% 290.55/183.02 tff(7857,plain,
% 290.55/183.02 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s0) | m_c_h_element_v_out(c_e_h_2, c_e, s0))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s0) | m_c_h_element_v_out(c_e_h_2, c_e, s0))),
% 290.55/183.02 inference(rewrite,[status(thm)],[])).
% 290.55/183.02 tff(7858,plain,
% 290.55/183.02 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s0) | m_c_h_element_v_out(c_e_h_2, c_e, s0))),
% 290.55/183.02 inference(quant_inst,[status(thm)],[])).
% 290.55/183.02 tff(7859,plain,
% 290.55/183.02 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s0) | m_c_h_element_v_out(c_e_h_2, c_e, s0)),
% 290.55/183.02 inference(modus_ponens,[status(thm)],[7858, 7857])).
% 290.55/183.02 tff(7860,plain,
% 290.55/183.02 (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s0) | m_c_h_element_v_out(c_e_h_2, c_e, s0)),
% 290.55/183.02 inference(unit_resolution,[status(thm)],[7859, 7856])).
% 290.55/183.02 tff(7861,plain,
% 290.55/183.02 (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s0)),
% 290.55/183.02 inference(unit_resolution,[status(thm)],[7860, 7849])).
% 290.55/183.02 tff(7862,plain,
% 290.55/183.02 (^[I0: $i, X: $i] : refl((m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X)) <=> (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X)))),
% 290.55/183.02 inference(bind,[status(th)],[])).
% 290.55/183.02 tff(7863,plain,
% 290.55/183.02 (![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X)) <=> ![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))),
% 290.55/183.02 inference(quant_intro,[status(thm)],[7862])).
% 290.55/183.02 tff(7864,plain,
% 290.55/183.02 (![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X)) <=> ![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))),
% 290.55/183.02 inference(rewrite,[status(thm)],[])).
% 290.55/183.02 tff(7865,axiom,(![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_59')).
% 290.55/183.02 tff(7866,plain,
% 290.55/183.02 (![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))),
% 290.55/183.02 inference(modus_ponens,[status(thm)],[7865, 7864])).
% 290.55/183.02 tff(7867,plain,(
% 290.55/183.02 ![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))),
% 290.55/183.02 inference(skolemize,[status(sab)],[7866])).
% 290.55/183.02 tff(7868,plain,
% 290.55/183.02 (![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))),
% 290.55/183.02 inference(modus_ponens,[status(thm)],[7867, 7863])).
% 290.55/183.02 tff(7869,plain,
% 290.55/183.02 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s0) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s0) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0))),
% 290.55/183.02 inference(rewrite,[status(thm)],[])).
% 290.55/183.02 tff(7870,plain,
% 290.55/183.02 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s0) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0))),
% 290.55/183.02 inference(quant_inst,[status(thm)],[])).
% 290.55/183.02 tff(7871,plain,
% 290.55/183.02 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s0) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s0)),
% 290.55/183.02 inference(modus_ponens,[status(thm)],[7870, 7869])).
% 290.55/183.02 tff(7872,plain,
% 290.55/183.02 (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s0)),
% 290.55/183.02 inference(unit_resolution,[status(thm)],[7871, 7868, 4542])).
% 290.55/183.02 tff(7873,plain,
% 290.55/183.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s0)) | (~node10(c_e_h_2, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s0)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s0)) | (~node10(c_e_h_2, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s0)))),
% 290.55/183.02 inference(rewrite,[status(thm)],[])).
% 290.55/183.02 tff(7874,plain,
% 290.55/183.02 (((~node10(c_e_h_2, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s0)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1)) <=> (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s0)) | (~node10(c_e_h_2, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s0)))),
% 290.55/183.02 inference(rewrite,[status(thm)],[])).
% 290.55/183.02 tff(7875,plain,
% 290.55/183.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s0)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s0)) | (~node10(c_e_h_2, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s0))))),
% 290.55/183.02 inference(monotonicity,[status(thm)],[7874])).
% 290.55/183.02 tff(7876,plain,
% 290.55/183.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s0)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s0)) | (~node10(c_e_h_2, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s0)))),
% 290.55/183.03 inference(transitivity,[status(thm)],[7875, 7873])).
% 290.55/183.03 tff(7877,plain,
% 290.55/183.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s0)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1))),
% 290.55/183.03 inference(quant_inst,[status(thm)],[])).
% 290.55/183.03 tff(7878,plain,
% 290.55/183.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s0)) | (~node10(c_e_h_2, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s0))),
% 290.55/183.03 inference(modus_ponens,[status(thm)],[7877, 7876])).
% 290.55/183.03 tff(7879,plain,
% 290.55/183.03 ($false),
% 290.55/183.03 inference(unit_resolution,[status(thm)],[7878, 5718, 7872, 7830, 7861, 7845])).
% 290.55/183.03 tff(7880,plain,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1)), inference(lemma,lemma(discharge,[]))).
% 290.55/183.03 tff(7881,plain,
% 290.55/183.03 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1)))),
% 290.55/183.03 inference(rewrite,[status(thm)],[])).
% 290.55/183.03 tff(7882,plain,
% 290.55/183.03 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1)))),
% 290.55/183.03 inference(quant_inst,[status(thm)],[])).
% 290.55/183.03 tff(7883,plain,
% 290.55/183.03 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1))),
% 290.55/183.03 inference(modus_ponens,[status(thm)],[7882, 7881])).
% 290.55/183.03 tff(7884,plain,
% 290.55/183.03 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s1)),
% 290.55/183.03 inference(unit_resolution,[status(thm)],[7883, 4958, 7880])).
% 290.55/183.03 tff(7885,plain,
% 290.55/183.03 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s1)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s1)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s1))),
% 290.55/183.03 inference(rewrite,[status(thm)],[])).
% 290.55/183.03 tff(7886,plain,
% 290.55/183.03 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s1)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s1))),
% 290.55/183.03 inference(quant_inst,[status(thm)],[])).
% 290.55/183.03 tff(7887,plain,
% 290.55/183.03 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s1)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s1)),
% 290.55/183.03 inference(modus_ponens,[status(thm)],[7886, 7885])).
% 290.55/183.03 tff(7888,plain,
% 290.55/183.03 (~node9(c_e_h_2, c_m, s1)),
% 290.55/183.03 inference(unit_resolution,[status(thm)],[7887, 4972, 7884])).
% 290.55/183.03 tff(7889,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)), introduced(assumption)).
% 290.55/183.03 tff(7890,assumption,(~node9(c_e_h_2, c_m, s1)), introduced(assumption)).
% 290.55/183.03 tff(7891,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)), introduced(assumption)).
% 290.55/183.03 tff(7892,assumption,(node11(c_e_h_2, c_m, s1, s2)), introduced(assumption)).
% 290.55/183.03 tff(7893,plain,
% 290.55/183.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)) | (~node11(c_e_h_2, c_m, s1, s2)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)) | (~node11(c_e_h_2, c_m, s1, s2)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1))),
% 290.55/183.03 inference(rewrite,[status(thm)],[])).
% 290.55/183.03 tff(7894,plain,
% 290.55/183.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)) | (~node11(c_e_h_2, c_m, s1, s2)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1))),
% 290.55/183.03 inference(quant_inst,[status(thm)],[])).
% 290.55/183.03 tff(7895,plain,
% 290.55/183.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)) | (~node11(c_e_h_2, c_m, s1, s2)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)),
% 290.55/183.03 inference(modus_ponens,[status(thm)],[7894, 7893])).
% 290.55/183.03 tff(7896,plain,
% 290.55/183.03 ($false),
% 290.55/183.03 inference(unit_resolution,[status(thm)],[7895, 5017, 7891, 7892, 7889])).
% 290.55/183.03 tff(7897,plain,((~node11(c_e_h_2, c_m, s1, s2)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2))), inference(lemma,lemma(discharge,[]))).
% 290.55/183.03 tff(7898,plain,
% 290.55/183.03 (~node11(c_e_h_2, c_m, s1, s2)),
% 290.55/183.03 inference(unit_resolution,[status(thm)],[7897, 7889, 7891])).
% 290.55/183.03 tff(7899,plain,
% 290.55/183.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s1, s2)) | node10(c_e_h_2, c_m, s1, s2) | node11(c_e_h_2, c_m, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s1, s2)) | node10(c_e_h_2, c_m, s1, s2) | node11(c_e_h_2, c_m, s1, s2))),
% 290.55/183.03 inference(rewrite,[status(thm)],[])).
% 290.55/183.03 tff(7900,plain,
% 290.55/183.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s1, s2)) | node10(c_e_h_2, c_m, s1, s2) | node11(c_e_h_2, c_m, s1, s2))),
% 290.55/183.03 inference(quant_inst,[status(thm)],[])).
% 290.55/183.03 tff(7901,plain,
% 290.55/183.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s1, s2)) | node10(c_e_h_2, c_m, s1, s2) | node11(c_e_h_2, c_m, s1, s2)),
% 290.55/183.03 inference(modus_ponens,[status(thm)],[7900, 7899])).
% 290.55/183.03 tff(7902,plain,
% 290.55/183.03 (node10(c_e_h_2, c_m, s1, s2) | node11(c_e_h_2, c_m, s1, s2)),
% 290.55/183.03 inference(unit_resolution,[status(thm)],[7901, 5002, 255])).
% 290.55/183.03 tff(7903,plain,
% 290.55/183.03 (node10(c_e_h_2, c_m, s1, s2)),
% 290.55/183.03 inference(unit_resolution,[status(thm)],[7902, 7898])).
% 290.55/183.03 tff(7904,plain,
% 290.55/183.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s1) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)) | (~node10(c_e_h_2, c_m, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_2, c_m, s1) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)) | (~node10(c_e_h_2, c_m, s1, s2)))),
% 290.55/183.03 inference(rewrite,[status(thm)],[])).
% 290.55/183.03 tff(7905,plain,
% 290.55/183.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s1) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)) | (~node10(c_e_h_2, c_m, s1, s2)))),
% 290.55/183.03 inference(quant_inst,[status(thm)],[])).
% 290.55/183.03 tff(7906,plain,
% 290.55/183.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_2, c_m, s1) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)) | (~node10(c_e_h_2, c_m, s1, s2))),
% 290.55/183.03 inference(modus_ponens,[status(thm)],[7905, 7904])).
% 290.55/183.03 tff(7907,plain,
% 290.55/183.03 ($false),
% 290.55/183.03 inference(unit_resolution,[status(thm)],[7906, 4986, 7903, 7890, 7889])).
% 290.55/183.03 tff(7908,plain,((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)) | node9(c_e_h_2, c_m, s1) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)), inference(lemma,lemma(discharge,[]))).
% 290.55/183.03 tff(7909,plain,
% 290.55/183.03 (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)),
% 290.55/183.03 inference(unit_resolution,[status(thm)],[7908, 5022, 7888])).
% 290.55/183.03 tff(7910,plain,
% 290.55/183.03 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_l, s2)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_l, s2)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2))),
% 290.55/183.03 inference(rewrite,[status(thm)],[])).
% 290.55/183.03 tff(7911,plain,
% 290.55/183.03 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_l, s2)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2))),
% 290.55/183.03 inference(quant_inst,[status(thm)],[])).
% 290.55/183.03 tff(7912,plain,
% 290.55/183.03 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_l, s2)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)),
% 290.55/183.03 inference(modus_ponens,[status(thm)],[7911, 7910])).
% 290.55/183.03 tff(7913,plain,
% 290.55/183.03 (~m_and_h_gate_v_in2(c_e_h_2, c_l, s2)),
% 290.55/183.03 inference(unit_resolution,[status(thm)],[7912, 4549, 7909])).
% 290.55/183.03 tff(7914,plain,
% 290.55/183.03 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_l, s2)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_l, s2)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s2))),
% 290.55/183.03 inference(rewrite,[status(thm)],[])).
% 290.55/183.03 tff(7915,plain,
% 290.55/183.03 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_l, s2)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s2))),
% 290.55/183.03 inference(quant_inst,[status(thm)],[])).
% 290.55/183.03 tff(7916,plain,
% 290.55/183.03 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_l, s2)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s2)),
% 290.55/183.03 inference(modus_ponens,[status(thm)],[7915, 7914])).
% 290.55/183.03 tff(7917,plain,
% 290.55/183.03 (~node20(c_e_h_2, c_l, s2)),
% 290.55/183.03 inference(unit_resolution,[status(thm)],[7916, 4563, 7913])).
% 290.55/183.03 tff(7918,assumption,(node21(c_e_h_2, c_l, s2, s3)), introduced(assumption)).
% 290.55/183.03 tff(7919,plain,
% 290.55/183.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s3)) | node20(c_e_h_2, c_l, s2) | (~node21(c_e_h_2, c_l, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s3)) | node20(c_e_h_2, c_l, s2) | (~node21(c_e_h_2, c_l, s2, s3)))),
% 290.55/183.03 inference(rewrite,[status(thm)],[])).
% 290.55/183.03 tff(7920,plain,
% 290.55/183.03 ((node20(c_e_h_2, c_l, s2) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s3)) | (~node21(c_e_h_2, c_l, s2, s3))) <=> ((~m_and_h_gate_v_out(c_e_h_2, c_l, s3)) | node20(c_e_h_2, c_l, s2) | (~node21(c_e_h_2, c_l, s2, s3)))),
% 290.55/183.03 inference(rewrite,[status(thm)],[])).
% 290.55/183.03 tff(7921,plain,
% 290.55/183.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_l, s2) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s3)) | (~node21(c_e_h_2, c_l, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s3)) | node20(c_e_h_2, c_l, s2) | (~node21(c_e_h_2, c_l, s2, s3))))),
% 290.55/183.03 inference(monotonicity,[status(thm)],[7920])).
% 290.55/183.03 tff(7922,plain,
% 290.55/183.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_l, s2) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s3)) | (~node21(c_e_h_2, c_l, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s3)) | node20(c_e_h_2, c_l, s2) | (~node21(c_e_h_2, c_l, s2, s3)))),
% 290.55/183.04 inference(transitivity,[status(thm)],[7921, 7919])).
% 290.55/183.04 tff(7923,plain,
% 290.55/183.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_l, s2) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s3)) | (~node21(c_e_h_2, c_l, s2, s3)))),
% 290.55/183.04 inference(quant_inst,[status(thm)],[])).
% 290.55/183.04 tff(7924,plain,
% 290.55/183.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s3)) | node20(c_e_h_2, c_l, s2) | (~node21(c_e_h_2, c_l, s2, s3))),
% 290.55/183.04 inference(modus_ponens,[status(thm)],[7923, 7922])).
% 290.55/183.04 tff(7925,plain,
% 290.55/183.04 ($false),
% 290.55/183.04 inference(unit_resolution,[status(thm)],[7924, 52, 7829, 7918, 7917])).
% 290.55/183.04 tff(7926,plain,((~node21(c_e_h_2, c_l, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s3))), inference(lemma,lemma(discharge,[]))).
% 290.55/183.04 tff(7927,plain,
% 290.55/183.04 (~node21(c_e_h_2, c_l, s2, s3)),
% 290.55/183.04 inference(unit_resolution,[status(thm)],[7926, 7829])).
% 290.55/183.04 tff(7928,plain,
% 290.55/183.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_2, c_l, s2, s3) | node22(c_e_h_2, c_l, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_2, c_l, s2, s3) | node22(c_e_h_2, c_l, s2, s3))),
% 290.55/183.04 inference(rewrite,[status(thm)],[])).
% 290.55/183.04 tff(7929,plain,
% 290.55/183.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_2, c_l, s2, s3) | node22(c_e_h_2, c_l, s2, s3))),
% 290.55/183.04 inference(quant_inst,[status(thm)],[])).
% 290.55/183.04 tff(7930,plain,
% 290.55/183.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_2, c_l, s2, s3) | node22(c_e_h_2, c_l, s2, s3)),
% 290.55/183.04 inference(modus_ponens,[status(thm)],[7929, 7928])).
% 290.55/183.04 tff(7931,plain,
% 290.55/183.04 (node21(c_e_h_2, c_l, s2, s3) | node22(c_e_h_2, c_l, s2, s3)),
% 290.55/183.04 inference(unit_resolution,[status(thm)],[7930, 82, 318])).
% 290.55/183.04 tff(7932,plain,
% 290.55/183.04 (node22(c_e_h_2, c_l, s2, s3)),
% 290.55/183.04 inference(unit_resolution,[status(thm)],[7931, 7927])).
% 290.55/183.04 tff(7933,plain,
% 290.55/183.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s3)) | (~node22(c_e_h_2, c_l, s2, s3)) | m_and_h_gate_v_out(c_e_h_2, c_l, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s3)) | (~node22(c_e_h_2, c_l, s2, s3)) | m_and_h_gate_v_out(c_e_h_2, c_l, s2))),
% 290.55/183.04 inference(rewrite,[status(thm)],[])).
% 290.55/183.04 tff(7934,plain,
% 290.55/183.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s3)) | (~node22(c_e_h_2, c_l, s2, s3)) | m_and_h_gate_v_out(c_e_h_2, c_l, s2))),
% 290.55/183.04 inference(quant_inst,[status(thm)],[])).
% 290.55/183.04 tff(7935,plain,
% 290.55/183.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s3)) | (~node22(c_e_h_2, c_l, s2, s3)) | m_and_h_gate_v_out(c_e_h_2, c_l, s2)),
% 290.55/183.04 inference(modus_ponens,[status(thm)],[7934, 7933])).
% 290.55/183.04 tff(7936,plain,
% 290.55/183.04 ($false),
% 290.55/183.04 inference(unit_resolution,[status(thm)],[7935, 108, 7829, 7932, 5035])).
% 290.55/183.04 tff(7937,plain,(~m_and_h_gate_v_out(c_e_h_2, c_l, s3)), inference(lemma,lemma(discharge,[]))).
% 290.55/183.04 tff(7938,assumption,(m_or_h_gate_v_in1(c_e_h_2, c_j, s3)), introduced(assumption)).
% 290.55/183.04 tff(7939,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_l, s3)), introduced(assumption)).
% 290.55/183.04 tff(7940,plain,
% 290.55/183.04 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_2, c_j, s3)) | m_and_h_gate_v_out(c_e_h_2, c_l, s3))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_j, s3)) | m_and_h_gate_v_out(c_e_h_2, c_l, s3))),
% 290.55/183.04 inference(rewrite,[status(thm)],[])).
% 290.55/183.04 tff(7941,plain,
% 290.55/183.04 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_2, c_j, s3)) | m_and_h_gate_v_out(c_e_h_2, c_l, s3))),
% 290.55/183.04 inference(quant_inst,[status(thm)],[])).
% 290.55/183.04 tff(7942,plain,
% 290.55/183.04 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_j, s3)) | m_and_h_gate_v_out(c_e_h_2, c_l, s3)),
% 290.55/183.04 inference(modus_ponens,[status(thm)],[7941, 7940])).
% 290.55/183.04 tff(7943,plain,
% 290.55/183.04 ($false),
% 290.55/183.04 inference(unit_resolution,[status(thm)],[7942, 1100, 7939, 7938])).
% 290.55/183.04 tff(7944,plain,((~m_or_h_gate_v_in1(c_e_h_2, c_j, s3)) | m_and_h_gate_v_out(c_e_h_2, c_l, s3)), inference(lemma,lemma(discharge,[]))).
% 290.55/183.04 tff(7945,plain,
% 290.55/183.04 (~m_or_h_gate_v_in1(c_e_h_2, c_j, s3)),
% 290.55/183.04 inference(unit_resolution,[status(thm)],[7944, 7937])).
% 290.55/183.04 tff(7946,assumption,(m_c_h_element_v_out(c_e_h_1, c_f, s2)), introduced(assumption)).
% 290.55/183.04 tff(7947,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_f, s1)), introduced(assumption)).
% 290.55/183.04 tff(7948,assumption,(node15(c_e_h_1, c_f, s1, s2)), introduced(assumption)).
% 290.55/183.04 tff(7949,plain,
% 290.55/183.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s2)) | (~node15(c_e_h_1, c_f, s1, s2)) | m_c_h_element_v_out(c_e_h_1, c_f, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s2)) | (~node15(c_e_h_1, c_f, s1, s2)) | m_c_h_element_v_out(c_e_h_1, c_f, s1))),
% 290.55/183.04 inference(rewrite,[status(thm)],[])).
% 290.55/183.04 tff(7950,plain,
% 290.55/183.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s2)) | (~node15(c_e_h_1, c_f, s1, s2)) | m_c_h_element_v_out(c_e_h_1, c_f, s1))),
% 290.55/183.04 inference(quant_inst,[status(thm)],[])).
% 290.55/183.04 tff(7951,plain,
% 290.55/183.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s2)) | (~node15(c_e_h_1, c_f, s1, s2)) | m_c_h_element_v_out(c_e_h_1, c_f, s1)),
% 290.55/183.04 inference(modus_ponens,[status(thm)],[7950, 7949])).
% 290.55/183.04 tff(7952,plain,
% 290.55/183.04 ($false),
% 290.55/183.04 inference(unit_resolution,[status(thm)],[7951, 147, 5089, 7946, 7948])).
% 290.55/183.04 tff(7953,plain,((~node15(c_e_h_1, c_f, s1, s2)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s2))), inference(lemma,lemma(discharge,[]))).
% 290.55/183.04 tff(7954,plain,
% 290.55/183.04 (~node15(c_e_h_1, c_f, s1, s2)),
% 290.55/183.04 inference(unit_resolution,[status(thm)],[7953, 7946])).
% 290.55/183.04 tff(7955,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s1)), introduced(assumption)).
% 290.55/183.04 tff(7956,assumption,(node21(c_e_h_1, c_i, s0, s1)), introduced(assumption)).
% 290.55/183.04 tff(7957,assumption,(m_c_h_element_v_out(c_e_h_1, c_h, s0)), introduced(assumption)).
% 290.55/183.04 tff(7958,plain,
% 290.55/183.04 ((~![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s0))),
% 290.55/183.04 inference(quant_inst,[status(thm)],[])).
% 290.55/183.04 tff(7959,plain,
% 290.55/183.04 ($false),
% 290.55/183.04 inference(unit_resolution,[status(thm)],[7958, 14, 7957])).
% 290.55/183.04 tff(7960,plain,(~m_c_h_element_v_out(c_e_h_1, c_h, s0)), inference(lemma,lemma(discharge,[]))).
% 290.55/183.04 tff(7961,plain,
% 290.55/183.04 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s0)) | m_c_h_element_v_out(c_e_h_1, c_h, s0))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s0)) | m_c_h_element_v_out(c_e_h_1, c_h, s0))),
% 290.55/183.04 inference(rewrite,[status(thm)],[])).
% 290.55/183.04 tff(7962,plain,
% 290.55/183.04 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s0)) | m_c_h_element_v_out(c_e_h_1, c_h, s0))),
% 290.55/183.04 inference(quant_inst,[status(thm)],[])).
% 290.55/183.04 tff(7963,plain,
% 290.55/183.04 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s0)) | m_c_h_element_v_out(c_e_h_1, c_h, s0)),
% 290.55/183.04 inference(modus_ponens,[status(thm)],[7962, 7961])).
% 290.55/183.04 tff(7964,plain,
% 290.55/183.04 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s0)),
% 290.55/183.04 inference(unit_resolution,[status(thm)],[7963, 619, 7960])).
% 290.55/183.04 tff(7965,plain,
% 290.55/183.04 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s0))),
% 290.55/183.04 inference(rewrite,[status(thm)],[])).
% 290.55/183.04 tff(7966,plain,
% 290.55/183.04 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s0))),
% 290.55/183.04 inference(quant_inst,[status(thm)],[])).
% 290.55/183.04 tff(7967,plain,
% 290.55/183.04 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s0)),
% 290.55/183.04 inference(modus_ponens,[status(thm)],[7966, 7965])).
% 290.55/183.04 tff(7968,plain,
% 290.55/183.04 (~node20(c_e_h_1, c_i, s0)),
% 290.55/183.04 inference(unit_resolution,[status(thm)],[7967, 38, 7964])).
% 290.55/183.04 tff(7969,plain,
% 290.55/183.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s1)) | (~node21(c_e_h_1, c_i, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s1)) | (~node21(c_e_h_1, c_i, s0, s1)))),
% 290.55/183.04 inference(rewrite,[status(thm)],[])).
% 290.55/183.04 tff(7970,plain,
% 290.55/183.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s1)) | (~node21(c_e_h_1, c_i, s0, s1)))),
% 290.55/183.04 inference(quant_inst,[status(thm)],[])).
% 290.55/183.04 tff(7971,plain,
% 290.55/183.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s1)) | (~node21(c_e_h_1, c_i, s0, s1))),
% 290.55/183.04 inference(modus_ponens,[status(thm)],[7970, 7969])).
% 290.55/183.04 tff(7972,plain,
% 290.55/183.04 ($false),
% 290.55/183.04 inference(unit_resolution,[status(thm)],[7971, 52, 7968, 7956, 7955])).
% 290.55/183.04 tff(7973,plain,((~node21(c_e_h_1, c_i, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s1))), inference(lemma,lemma(discharge,[]))).
% 290.55/183.04 tff(7974,plain,
% 290.55/183.04 (~node21(c_e_h_1, c_i, s0, s1)),
% 290.55/183.04 inference(unit_resolution,[status(thm)],[7973, 7955])).
% 290.55/183.04 tff(7975,plain,
% 290.55/183.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_1, c_i, s0, s1) | node22(c_e_h_1, c_i, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_1, c_i, s0, s1) | node22(c_e_h_1, c_i, s0, s1))),
% 290.55/183.04 inference(rewrite,[status(thm)],[])).
% 290.55/183.04 tff(7976,plain,
% 290.55/183.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_1, c_i, s0, s1) | node22(c_e_h_1, c_i, s0, s1))),
% 290.55/183.04 inference(quant_inst,[status(thm)],[])).
% 290.55/183.04 tff(7977,plain,
% 290.55/183.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_1, c_i, s0, s1) | node22(c_e_h_1, c_i, s0, s1)),
% 290.55/183.04 inference(modus_ponens,[status(thm)],[7976, 7975])).
% 290.55/183.04 tff(7978,plain,
% 290.55/183.04 (node21(c_e_h_1, c_i, s0, s1) | node22(c_e_h_1, c_i, s0, s1)),
% 290.55/183.04 inference(unit_resolution,[status(thm)],[7977, 82, 72])).
% 290.55/183.04 tff(7979,plain,
% 290.55/183.04 (node22(c_e_h_1, c_i, s0, s1)),
% 290.55/183.04 inference(unit_resolution,[status(thm)],[7978, 7974])).
% 290.55/183.04 tff(7980,plain,
% 290.55/183.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s1)) | (~node22(c_e_h_1, c_i, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_i, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s1)) | (~node22(c_e_h_1, c_i, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_i, s0))),
% 290.55/183.05 inference(rewrite,[status(thm)],[])).
% 290.55/183.05 tff(7981,plain,
% 290.55/183.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s1)) | (~node22(c_e_h_1, c_i, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_i, s0))),
% 290.55/183.05 inference(quant_inst,[status(thm)],[])).
% 290.55/183.05 tff(7982,plain,
% 290.55/183.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s1)) | (~node22(c_e_h_1, c_i, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_i, s0)),
% 290.55/183.05 inference(modus_ponens,[status(thm)],[7981, 7980])).
% 290.55/183.05 tff(7983,plain,
% 290.55/183.05 ($false),
% 290.55/183.05 inference(unit_resolution,[status(thm)],[7982, 108, 5062, 7979, 7955])).
% 290.55/183.05 tff(7984,plain,(~m_and_h_gate_v_out(c_e_h_1, c_i, s1)), inference(lemma,lemma(discharge,[]))).
% 290.55/183.05 tff(7985,plain,
% 290.55/183.05 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s1)) | m_and_h_gate_v_out(c_e_h_1, c_i, s1))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s1)) | m_and_h_gate_v_out(c_e_h_1, c_i, s1))),
% 290.55/183.05 inference(rewrite,[status(thm)],[])).
% 290.55/183.05 tff(7986,plain,
% 290.55/183.05 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s1)) | m_and_h_gate_v_out(c_e_h_1, c_i, s1))),
% 290.55/183.05 inference(quant_inst,[status(thm)],[])).
% 290.55/183.05 tff(7987,plain,
% 290.55/183.05 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s1)) | m_and_h_gate_v_out(c_e_h_1, c_i, s1)),
% 290.55/183.05 inference(modus_ponens,[status(thm)],[7986, 7985])).
% 290.55/183.05 tff(7988,plain,
% 290.55/183.05 (~m_c_h_element_v_in2(c_e_h_1, c_f, s1)),
% 290.55/183.05 inference(unit_resolution,[status(thm)],[7987, 2143, 7984])).
% 290.55/183.05 tff(7989,plain,
% 290.55/183.05 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s1)) | m_c_h_element_v_in1(c_e_h_1, c_f, s1) | m_c_h_element_v_in2(c_e_h_1, c_f, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s1)) | m_c_h_element_v_in1(c_e_h_1, c_f, s1) | m_c_h_element_v_in2(c_e_h_1, c_f, s1))),
% 290.55/183.05 inference(rewrite,[status(thm)],[])).
% 290.55/183.05 tff(7990,plain,
% 290.55/183.05 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s1)) | m_c_h_element_v_in1(c_e_h_1, c_f, s1) | m_c_h_element_v_in2(c_e_h_1, c_f, s1))),
% 290.55/183.05 inference(quant_inst,[status(thm)],[])).
% 290.55/183.05 tff(7991,plain,
% 290.55/183.05 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s1)) | m_c_h_element_v_in1(c_e_h_1, c_f, s1) | m_c_h_element_v_in2(c_e_h_1, c_f, s1)),
% 290.55/183.05 inference(modus_ponens,[status(thm)],[7990, 7989])).
% 290.55/183.05 tff(7992,plain,
% 290.55/183.05 ((~node16(c_e_h_1, c_f, s1)) | m_c_h_element_v_in1(c_e_h_1, c_f, s1)),
% 290.55/183.05 inference(unit_resolution,[status(thm)],[7991, 178, 7988])).
% 290.55/183.05 tff(7993,plain,
% 290.55/183.05 (~node16(c_e_h_1, c_f, s1)),
% 290.55/183.05 inference(unit_resolution,[status(thm)],[7992, 7947])).
% 290.55/183.05 tff(7994,plain,
% 290.55/183.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s1, s2)) | node19(c_e_h_1, c_f, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s1, s2)) | node19(c_e_h_1, c_f, s1, s2))),
% 290.55/183.05 inference(rewrite,[status(thm)],[])).
% 290.55/183.05 tff(7995,plain,
% 290.55/183.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s1, s2)) | node19(c_e_h_1, c_f, s1, s2))),
% 290.55/183.05 inference(quant_inst,[status(thm)],[])).
% 290.55/183.05 tff(7996,plain,
% 290.55/183.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s1, s2)) | node19(c_e_h_1, c_f, s1, s2)),
% 290.55/183.05 inference(modus_ponens,[status(thm)],[7995, 7994])).
% 290.55/183.05 tff(7997,plain,
% 290.55/183.05 (node19(c_e_h_1, c_f, s1, s2)),
% 290.55/183.05 inference(unit_resolution,[status(thm)],[7996, 190, 255])).
% 290.55/183.05 tff(7998,plain,
% 290.55/183.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_f, s1, s2)) | node15(c_e_h_1, c_f, s1, s2) | node16(c_e_h_1, c_f, s1) | node14(c_e_h_1, c_f, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s1, s2)) | node15(c_e_h_1, c_f, s1, s2) | node16(c_e_h_1, c_f, s1) | node14(c_e_h_1, c_f, s1, s2))),
% 290.55/183.05 inference(rewrite,[status(thm)],[])).
% 290.55/183.05 tff(7999,plain,
% 290.55/183.05 ((node16(c_e_h_1, c_f, s1) | node14(c_e_h_1, c_f, s1, s2) | node15(c_e_h_1, c_f, s1, s2) | (~node19(c_e_h_1, c_f, s1, s2))) <=> ((~node19(c_e_h_1, c_f, s1, s2)) | node15(c_e_h_1, c_f, s1, s2) | node16(c_e_h_1, c_f, s1) | node14(c_e_h_1, c_f, s1, s2))),
% 290.55/183.05 inference(rewrite,[status(thm)],[])).
% 290.55/183.05 tff(8000,plain,
% 290.55/183.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s1) | node14(c_e_h_1, c_f, s1, s2) | node15(c_e_h_1, c_f, s1, s2) | (~node19(c_e_h_1, c_f, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_f, s1, s2)) | node15(c_e_h_1, c_f, s1, s2) | node16(c_e_h_1, c_f, s1) | node14(c_e_h_1, c_f, s1, s2)))),
% 290.55/183.05 inference(monotonicity,[status(thm)],[7999])).
% 290.55/183.05 tff(8001,plain,
% 290.55/183.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s1) | node14(c_e_h_1, c_f, s1, s2) | node15(c_e_h_1, c_f, s1, s2) | (~node19(c_e_h_1, c_f, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s1, s2)) | node15(c_e_h_1, c_f, s1, s2) | node16(c_e_h_1, c_f, s1) | node14(c_e_h_1, c_f, s1, s2))),
% 290.55/183.05 inference(transitivity,[status(thm)],[8000, 7998])).
% 290.55/183.05 tff(8002,plain,
% 290.55/183.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s1) | node14(c_e_h_1, c_f, s1, s2) | node15(c_e_h_1, c_f, s1, s2) | (~node19(c_e_h_1, c_f, s1, s2)))),
% 290.55/183.05 inference(quant_inst,[status(thm)],[])).
% 290.55/183.05 tff(8003,plain,
% 290.55/183.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s1, s2)) | node15(c_e_h_1, c_f, s1, s2) | node16(c_e_h_1, c_f, s1) | node14(c_e_h_1, c_f, s1, s2)),
% 290.55/183.05 inference(modus_ponens,[status(thm)],[8002, 8001])).
% 290.55/183.05 tff(8004,plain,
% 290.55/183.05 (node15(c_e_h_1, c_f, s1, s2) | node16(c_e_h_1, c_f, s1) | node14(c_e_h_1, c_f, s1, s2)),
% 290.55/183.05 inference(unit_resolution,[status(thm)],[8003, 204, 7997])).
% 290.55/183.05 tff(8005,plain,
% 290.55/183.05 (node14(c_e_h_1, c_f, s1, s2)),
% 290.55/183.05 inference(unit_resolution,[status(thm)],[8004, 7993, 7954])).
% 290.55/183.05 tff(8006,plain,
% 290.55/183.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s2)) | m_c_h_element_v_in1(c_e_h_1, c_f, s1) | (~node14(c_e_h_1, c_f, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s2)) | m_c_h_element_v_in1(c_e_h_1, c_f, s1) | (~node14(c_e_h_1, c_f, s1, s2)))),
% 290.55/183.05 inference(rewrite,[status(thm)],[])).
% 290.55/183.06 tff(8007,plain,
% 290.55/183.06 (((~node14(c_e_h_1, c_f, s1, s2)) | m_c_h_element_v_in1(c_e_h_1, c_f, s1) | (~m_c_h_element_v_out(c_e_h_1, c_f, s2))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_f, s2)) | m_c_h_element_v_in1(c_e_h_1, c_f, s1) | (~node14(c_e_h_1, c_f, s1, s2)))),
% 290.55/183.06 inference(rewrite,[status(thm)],[])).
% 290.55/183.06 tff(8008,plain,
% 290.55/183.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s1, s2)) | m_c_h_element_v_in1(c_e_h_1, c_f, s1) | (~m_c_h_element_v_out(c_e_h_1, c_f, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s2)) | m_c_h_element_v_in1(c_e_h_1, c_f, s1) | (~node14(c_e_h_1, c_f, s1, s2))))),
% 290.55/183.06 inference(monotonicity,[status(thm)],[8007])).
% 290.55/183.06 tff(8009,plain,
% 290.55/183.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s1, s2)) | m_c_h_element_v_in1(c_e_h_1, c_f, s1) | (~m_c_h_element_v_out(c_e_h_1, c_f, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s2)) | m_c_h_element_v_in1(c_e_h_1, c_f, s1) | (~node14(c_e_h_1, c_f, s1, s2)))),
% 290.55/183.06 inference(transitivity,[status(thm)],[8008, 8006])).
% 290.55/183.06 tff(8010,plain,
% 290.55/183.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s1, s2)) | m_c_h_element_v_in1(c_e_h_1, c_f, s1) | (~m_c_h_element_v_out(c_e_h_1, c_f, s2)))),
% 290.55/183.06 inference(quant_inst,[status(thm)],[])).
% 290.55/183.06 tff(8011,plain,
% 290.55/183.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s2)) | m_c_h_element_v_in1(c_e_h_1, c_f, s1) | (~node14(c_e_h_1, c_f, s1, s2))),
% 290.55/183.06 inference(modus_ponens,[status(thm)],[8010, 8009])).
% 290.55/183.06 tff(8012,plain,
% 290.55/183.06 ($false),
% 290.55/183.06 inference(unit_resolution,[status(thm)],[8011, 223, 7946, 8005, 7947])).
% 290.55/183.06 tff(8013,plain,(m_c_h_element_v_in1(c_e_h_1, c_f, s1) | (~m_c_h_element_v_out(c_e_h_1, c_f, s2))), inference(lemma,lemma(discharge,[]))).
% 290.55/183.06 tff(8014,plain,
% 290.55/183.06 (m_c_h_element_v_in1(c_e_h_1, c_f, s1)),
% 290.55/183.06 inference(unit_resolution,[status(thm)],[8013, 7946])).
% 290.55/183.06 tff(8015,plain,
% 290.55/183.06 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_f, s1) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s1)) | (~node17(c_e_h_1, c_f, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_f, s1) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s1)) | (~node17(c_e_h_1, c_f, s1)))),
% 290.55/183.06 inference(rewrite,[status(thm)],[])).
% 290.55/183.06 tff(8016,plain,
% 290.55/183.06 (((~m_c_h_element_v_in1(c_e_h_1, c_f, s1)) | m_c_h_element_v_in2(c_e_h_1, c_f, s1) | (~node17(c_e_h_1, c_f, s1))) <=> (m_c_h_element_v_in2(c_e_h_1, c_f, s1) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s1)) | (~node17(c_e_h_1, c_f, s1)))),
% 290.55/183.06 inference(rewrite,[status(thm)],[])).
% 290.55/183.06 tff(8017,plain,
% 290.55/183.06 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s1)) | m_c_h_element_v_in2(c_e_h_1, c_f, s1) | (~node17(c_e_h_1, c_f, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_f, s1) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s1)) | (~node17(c_e_h_1, c_f, s1))))),
% 290.55/183.06 inference(monotonicity,[status(thm)],[8016])).
% 290.55/183.06 tff(8018,plain,
% 290.55/183.06 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s1)) | m_c_h_element_v_in2(c_e_h_1, c_f, s1) | (~node17(c_e_h_1, c_f, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_f, s1) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s1)) | (~node17(c_e_h_1, c_f, s1)))),
% 290.55/183.06 inference(transitivity,[status(thm)],[8017, 8015])).
% 290.55/183.06 tff(8019,plain,
% 290.55/183.06 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s1)) | m_c_h_element_v_in2(c_e_h_1, c_f, s1) | (~node17(c_e_h_1, c_f, s1)))),
% 290.55/183.06 inference(quant_inst,[status(thm)],[])).
% 290.55/183.06 tff(8020,plain,
% 290.55/183.06 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_f, s1) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s1)) | (~node17(c_e_h_1, c_f, s1))),
% 290.55/183.06 inference(modus_ponens,[status(thm)],[8019, 8018])).
% 290.55/183.06 tff(8021,plain,
% 290.55/183.06 ((~m_c_h_element_v_in1(c_e_h_1, c_f, s1)) | (~node17(c_e_h_1, c_f, s1))),
% 290.55/183.06 inference(unit_resolution,[status(thm)],[8020, 919, 7988])).
% 290.55/183.06 tff(8022,plain,
% 290.55/183.06 (~node17(c_e_h_1, c_f, s1)),
% 290.55/183.06 inference(unit_resolution,[status(thm)],[8021, 8014])).
% 290.55/183.06 tff(8023,plain,
% 290.55/183.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_f, s1, s2)) | node18(c_e_h_1, c_f, s1, s2) | node17(c_e_h_1, c_f, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s1, s2)) | node18(c_e_h_1, c_f, s1, s2) | node17(c_e_h_1, c_f, s1))),
% 290.55/183.06 inference(rewrite,[status(thm)],[])).
% 290.55/183.06 tff(8024,plain,
% 290.55/183.06 ((node17(c_e_h_1, c_f, s1) | node18(c_e_h_1, c_f, s1, s2) | (~node19(c_e_h_1, c_f, s1, s2))) <=> ((~node19(c_e_h_1, c_f, s1, s2)) | node18(c_e_h_1, c_f, s1, s2) | node17(c_e_h_1, c_f, s1))),
% 290.55/183.06 inference(rewrite,[status(thm)],[])).
% 290.55/183.06 tff(8025,plain,
% 290.55/183.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s1) | node18(c_e_h_1, c_f, s1, s2) | (~node19(c_e_h_1, c_f, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_f, s1, s2)) | node18(c_e_h_1, c_f, s1, s2) | node17(c_e_h_1, c_f, s1)))),
% 290.55/183.06 inference(monotonicity,[status(thm)],[8024])).
% 290.55/183.06 tff(8026,plain,
% 290.55/183.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s1) | node18(c_e_h_1, c_f, s1, s2) | (~node19(c_e_h_1, c_f, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s1, s2)) | node18(c_e_h_1, c_f, s1, s2) | node17(c_e_h_1, c_f, s1))),
% 290.55/183.06 inference(transitivity,[status(thm)],[8025, 8023])).
% 290.55/183.06 tff(8027,plain,
% 290.55/183.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s1) | node18(c_e_h_1, c_f, s1, s2) | (~node19(c_e_h_1, c_f, s1, s2)))),
% 290.55/183.06 inference(quant_inst,[status(thm)],[])).
% 290.55/183.06 tff(8028,plain,
% 290.55/183.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s1, s2)) | node18(c_e_h_1, c_f, s1, s2) | node17(c_e_h_1, c_f, s1)),
% 290.55/183.06 inference(modus_ponens,[status(thm)],[8027, 8026])).
% 290.55/183.06 tff(8029,plain,
% 290.55/183.06 (node18(c_e_h_1, c_f, s1, s2) | node17(c_e_h_1, c_f, s1)),
% 290.55/183.06 inference(unit_resolution,[status(thm)],[8028, 776, 7997])).
% 290.55/183.06 tff(8030,plain,
% 290.55/183.06 (node18(c_e_h_1, c_f, s1, s2)),
% 290.55/183.06 inference(unit_resolution,[status(thm)],[8029, 8022])).
% 290.55/183.06 tff(8031,plain,
% 290.55/183.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_f, s1) | (~m_c_h_element_v_out(c_e_h_1, c_f, s2)) | (~node18(c_e_h_1, c_f, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s1) | (~m_c_h_element_v_out(c_e_h_1, c_f, s2)) | (~node18(c_e_h_1, c_f, s1, s2)))),
% 290.55/183.06 inference(rewrite,[status(thm)],[])).
% 290.55/183.06 tff(8032,plain,
% 290.55/183.06 (((~m_c_h_element_v_out(c_e_h_1, c_f, s2)) | m_c_h_element_v_out(c_e_h_1, c_f, s1) | (~node18(c_e_h_1, c_f, s1, s2))) <=> (m_c_h_element_v_out(c_e_h_1, c_f, s1) | (~m_c_h_element_v_out(c_e_h_1, c_f, s2)) | (~node18(c_e_h_1, c_f, s1, s2)))),
% 290.55/183.06 inference(rewrite,[status(thm)],[])).
% 290.55/183.06 tff(8033,plain,
% 290.55/183.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s2)) | m_c_h_element_v_out(c_e_h_1, c_f, s1) | (~node18(c_e_h_1, c_f, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_f, s1) | (~m_c_h_element_v_out(c_e_h_1, c_f, s2)) | (~node18(c_e_h_1, c_f, s1, s2))))),
% 290.55/183.06 inference(monotonicity,[status(thm)],[8032])).
% 290.55/183.06 tff(8034,plain,
% 290.55/183.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s2)) | m_c_h_element_v_out(c_e_h_1, c_f, s1) | (~node18(c_e_h_1, c_f, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s1) | (~m_c_h_element_v_out(c_e_h_1, c_f, s2)) | (~node18(c_e_h_1, c_f, s1, s2)))),
% 290.55/183.06 inference(transitivity,[status(thm)],[8033, 8031])).
% 290.55/183.06 tff(8035,plain,
% 290.55/183.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s2)) | m_c_h_element_v_out(c_e_h_1, c_f, s1) | (~node18(c_e_h_1, c_f, s1, s2)))),
% 290.55/183.06 inference(quant_inst,[status(thm)],[])).
% 290.55/183.06 tff(8036,plain,
% 290.55/183.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s1) | (~m_c_h_element_v_out(c_e_h_1, c_f, s2)) | (~node18(c_e_h_1, c_f, s1, s2))),
% 290.55/183.06 inference(modus_ponens,[status(thm)],[8035, 8034])).
% 290.55/183.06 tff(8037,plain,
% 290.55/183.06 ($false),
% 290.55/183.06 inference(unit_resolution,[status(thm)],[8036, 753, 5089, 7946, 8030])).
% 290.55/183.06 tff(8038,plain,(~m_c_h_element_v_out(c_e_h_1, c_f, s2)), inference(lemma,lemma(discharge,[]))).
% 290.55/183.06 tff(8039,assumption,(m_and_h_gate_v_in1(c_e_h_1, c_q, s2)), introduced(assumption)).
% 290.55/183.06 tff(8040,assumption,(~m_c_h_element_v_out(c_e_h_1, c_f, s2)), introduced(assumption)).
% 290.55/183.06 tff(8041,plain,
% 290.55/183.06 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s2)) | m_c_h_element_v_out(c_e_h_1, c_f, s2))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s2)) | m_c_h_element_v_out(c_e_h_1, c_f, s2))),
% 290.55/183.06 inference(rewrite,[status(thm)],[])).
% 290.55/183.06 tff(8042,plain,
% 290.55/183.06 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s2)) | m_c_h_element_v_out(c_e_h_1, c_f, s2))),
% 290.55/183.06 inference(quant_inst,[status(thm)],[])).
% 290.55/183.06 tff(8043,plain,
% 290.55/183.06 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s2)) | m_c_h_element_v_out(c_e_h_1, c_f, s2)),
% 290.55/183.06 inference(modus_ponens,[status(thm)],[8042, 8041])).
% 290.55/183.06 tff(8044,plain,
% 290.55/183.06 ($false),
% 290.55/183.06 inference(unit_resolution,[status(thm)],[8043, 1586, 8040, 8039])).
% 290.55/183.06 tff(8045,plain,(m_c_h_element_v_out(c_e_h_1, c_f, s2) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s2))), inference(lemma,lemma(discharge,[]))).
% 290.55/183.06 tff(8046,plain,
% 290.55/183.06 (~m_and_h_gate_v_in1(c_e_h_1, c_q, s2)),
% 290.55/183.06 inference(unit_resolution,[status(thm)],[8045, 8038])).
% 290.55/183.06 tff(8047,assumption,(~m_and_h_gate_v_in1(c_e_h_1, c_q, s2)), introduced(assumption)).
% 290.55/183.06 tff(8048,assumption,(node20(c_e_h_1, c_q, s2)), introduced(assumption)).
% 290.55/183.07 tff(8049,plain,
% 290.55/183.07 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s2)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s2)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s2))),
% 290.55/183.07 inference(rewrite,[status(thm)],[])).
% 290.55/183.07 tff(8050,plain,
% 290.55/183.07 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s2)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s2))),
% 290.55/183.07 inference(quant_inst,[status(thm)],[])).
% 290.55/183.07 tff(8051,plain,
% 290.55/183.07 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s2)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s2)),
% 290.55/183.07 inference(modus_ponens,[status(thm)],[8050, 8049])).
% 290.55/183.07 tff(8052,plain,
% 290.55/183.07 ($false),
% 290.55/183.07 inference(unit_resolution,[status(thm)],[8051, 38, 8048, 8047])).
% 290.55/183.07 tff(8053,plain,(m_and_h_gate_v_in1(c_e_h_1, c_q, s2) | (~node20(c_e_h_1, c_q, s2))), inference(lemma,lemma(discharge,[]))).
% 290.55/183.07 tff(8054,plain,
% 290.55/183.07 (~node20(c_e_h_1, c_q, s2)),
% 290.55/183.07 inference(unit_resolution,[status(thm)],[8053, 8046])).
% 290.55/183.07 tff(8055,assumption,(~node20(c_e_h_1, c_q, s2)), introduced(assumption)).
% 290.55/183.07 tff(8056,assumption,(m_and_h_gate_v_out(c_e_h_1, c_q, s3)), introduced(assumption)).
% 290.55/183.07 tff(8057,assumption,(node21(c_e_h_1, c_q, s2, s3)), introduced(assumption)).
% 290.55/183.07 tff(8058,plain,
% 290.55/183.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s3)) | node20(c_e_h_1, c_q, s2) | (~node21(c_e_h_1, c_q, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s3)) | node20(c_e_h_1, c_q, s2) | (~node21(c_e_h_1, c_q, s2, s3)))),
% 290.55/183.07 inference(rewrite,[status(thm)],[])).
% 290.55/183.07 tff(8059,plain,
% 290.55/183.07 ((node20(c_e_h_1, c_q, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s3)) | (~node21(c_e_h_1, c_q, s2, s3))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_q, s3)) | node20(c_e_h_1, c_q, s2) | (~node21(c_e_h_1, c_q, s2, s3)))),
% 290.55/183.07 inference(rewrite,[status(thm)],[])).
% 290.55/183.07 tff(8060,plain,
% 290.55/183.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s3)) | (~node21(c_e_h_1, c_q, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s3)) | node20(c_e_h_1, c_q, s2) | (~node21(c_e_h_1, c_q, s2, s3))))),
% 290.55/183.07 inference(monotonicity,[status(thm)],[8059])).
% 290.55/183.07 tff(8061,plain,
% 290.55/183.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s3)) | (~node21(c_e_h_1, c_q, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s3)) | node20(c_e_h_1, c_q, s2) | (~node21(c_e_h_1, c_q, s2, s3)))),
% 290.55/183.07 inference(transitivity,[status(thm)],[8060, 8058])).
% 290.55/183.07 tff(8062,plain,
% 290.55/183.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s3)) | (~node21(c_e_h_1, c_q, s2, s3)))),
% 290.55/183.07 inference(quant_inst,[status(thm)],[])).
% 290.55/183.07 tff(8063,plain,
% 290.55/183.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s3)) | node20(c_e_h_1, c_q, s2) | (~node21(c_e_h_1, c_q, s2, s3))),
% 290.55/183.07 inference(modus_ponens,[status(thm)],[8062, 8061])).
% 290.55/183.07 tff(8064,plain,
% 290.55/183.07 ($false),
% 290.55/183.07 inference(unit_resolution,[status(thm)],[8063, 52, 8056, 8057, 8055])).
% 290.55/183.07 tff(8065,plain,((~node21(c_e_h_1, c_q, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s3)) | node20(c_e_h_1, c_q, s2)), inference(lemma,lemma(discharge,[]))).
% 290.55/183.07 tff(8066,plain,
% 290.55/183.07 (~node21(c_e_h_1, c_q, s2, s3)),
% 290.55/183.07 inference(unit_resolution,[status(thm)],[8065, 8056, 8055])).
% 290.55/183.07 tff(8067,plain,
% 290.55/183.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_1, c_q, s2, s3) | node22(c_e_h_1, c_q, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_1, c_q, s2, s3) | node22(c_e_h_1, c_q, s2, s3))),
% 290.55/183.07 inference(rewrite,[status(thm)],[])).
% 290.55/183.07 tff(8068,plain,
% 290.55/183.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_1, c_q, s2, s3) | node22(c_e_h_1, c_q, s2, s3))),
% 290.55/183.07 inference(quant_inst,[status(thm)],[])).
% 290.55/183.07 tff(8069,plain,
% 290.55/183.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_1, c_q, s2, s3) | node22(c_e_h_1, c_q, s2, s3)),
% 290.55/183.07 inference(modus_ponens,[status(thm)],[8068, 8067])).
% 290.55/183.07 tff(8070,plain,
% 290.55/183.07 (node21(c_e_h_1, c_q, s2, s3) | node22(c_e_h_1, c_q, s2, s3)),
% 290.55/183.07 inference(unit_resolution,[status(thm)],[8069, 82, 318])).
% 290.55/183.07 tff(8071,plain,
% 290.55/183.07 (node22(c_e_h_1, c_q, s2, s3)),
% 290.55/183.07 inference(unit_resolution,[status(thm)],[8070, 8066])).
% 290.55/183.07 tff(8072,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_q, s2)), introduced(assumption)).
% 290.55/183.07 tff(8073,plain,
% 290.55/183.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s3)) | (~node22(c_e_h_1, c_q, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_q, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s3)) | (~node22(c_e_h_1, c_q, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_q, s2))),
% 290.55/183.07 inference(rewrite,[status(thm)],[])).
% 290.55/183.07 tff(8074,plain,
% 290.55/183.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s3)) | (~node22(c_e_h_1, c_q, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_q, s2))),
% 290.55/183.07 inference(quant_inst,[status(thm)],[])).
% 290.55/183.07 tff(8075,plain,
% 290.55/183.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s3)) | (~node22(c_e_h_1, c_q, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_q, s2)),
% 290.55/183.07 inference(modus_ponens,[status(thm)],[8074, 8073])).
% 290.55/183.07 tff(8076,plain,
% 290.55/183.07 ($false),
% 290.55/183.07 inference(unit_resolution,[status(thm)],[8075, 108, 8056, 8072, 8071])).
% 290.55/183.07 tff(8077,plain,((~m_and_h_gate_v_out(c_e_h_1, c_q, s3)) | m_and_h_gate_v_out(c_e_h_1, c_q, s2) | node20(c_e_h_1, c_q, s2)), inference(lemma,lemma(discharge,[]))).
% 290.55/183.07 tff(8078,plain,
% 290.55/183.07 ((~m_and_h_gate_v_out(c_e_h_1, c_q, s3)) | node20(c_e_h_1, c_q, s2)),
% 290.55/183.07 inference(unit_resolution,[status(thm)],[8077, 5122])).
% 290.55/183.07 tff(8079,plain,
% 290.55/183.07 (~m_and_h_gate_v_out(c_e_h_1, c_q, s3)),
% 290.55/183.07 inference(unit_resolution,[status(thm)],[8078, 8054])).
% 290.55/183.07 tff(8080,plain,
% 290.55/183.07 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s3))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s3))),
% 290.55/183.07 inference(rewrite,[status(thm)],[])).
% 290.55/183.07 tff(8081,plain,
% 290.55/183.07 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s3))),
% 290.55/183.07 inference(quant_inst,[status(thm)],[])).
% 290.55/183.07 tff(8082,plain,
% 290.55/183.07 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s3)),
% 290.55/183.07 inference(modus_ponens,[status(thm)],[8081, 8080])).
% 290.55/183.07 tff(8083,plain,
% 290.55/183.07 (node3(c_e_h_1, c_e_h_2, s3)),
% 290.55/183.07 inference(unit_resolution,[status(thm)],[8082, 4166, 1056])).
% 290.55/183.07 tff(8084,plain,
% 290.55/183.07 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s3)) | (~node3(c_e_h_1, c_e_h_2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_q, s3))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s3)) | (~node3(c_e_h_1, c_e_h_2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_q, s3))),
% 290.55/183.07 inference(rewrite,[status(thm)],[])).
% 290.55/183.07 tff(8085,plain,
% 290.55/183.07 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s3)) | (~node3(c_e_h_1, c_e_h_2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_q, s3))),
% 290.55/183.07 inference(quant_inst,[status(thm)],[])).
% 290.55/183.07 tff(8086,plain,
% 290.55/183.07 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s3)) | (~node3(c_e_h_1, c_e_h_2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_q, s3)),
% 290.55/183.07 inference(modus_ponens,[status(thm)],[8085, 8084])).
% 290.55/183.07 tff(8087,plain,
% 290.55/183.07 ((~m_cell_v_ack(c_e_h_2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_q, s3)),
% 290.55/183.07 inference(unit_resolution,[status(thm)],[8086, 1073, 8083])).
% 290.55/183.07 tff(8088,plain,
% 290.55/183.07 (~m_cell_v_ack(c_e_h_2, s3)),
% 290.55/183.07 inference(unit_resolution,[status(thm)],[8087, 8079])).
% 290.55/183.07 tff(8089,plain,
% 290.55/183.07 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s3)) | m_cell_v_ack(c_e_h_2, s3))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s3)) | m_cell_v_ack(c_e_h_2, s3))),
% 290.55/183.07 inference(rewrite,[status(thm)],[])).
% 290.55/183.07 tff(8090,plain,
% 290.55/183.07 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s3)) | m_cell_v_ack(c_e_h_2, s3))),
% 290.55/183.07 inference(quant_inst,[status(thm)],[])).
% 290.55/183.07 tff(8091,plain,
% 290.55/183.07 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s3)) | m_cell_v_ack(c_e_h_2, s3)),
% 290.55/183.07 inference(modus_ponens,[status(thm)],[8090, 8089])).
% 290.55/183.07 tff(8092,plain,
% 290.55/183.07 (~m_or_h_gate_v_in2(c_e_h_2, c_j, s3)),
% 290.55/183.07 inference(unit_resolution,[status(thm)],[8091, 1085, 8088])).
% 290.55/183.07 tff(8093,assumption,(~m_or_h_gate_v_in2(c_e_h_2, c_j, s3)), introduced(assumption)).
% 290.55/183.07 tff(8094,assumption,(~m_or_h_gate_v_in1(c_e_h_2, c_j, s3)), introduced(assumption)).
% 290.55/183.07 tff(8095,assumption,(node5(c_e_h_2, c_j, s3, s4)), introduced(assumption)).
% 290.55/183.07 tff(8096,plain,
% 290.55/183.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~node5(c_e_h_2, c_j, s3, s4)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s4)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~node5(c_e_h_2, c_j, s3, s4)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s4)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s3))),
% 290.55/183.07 inference(rewrite,[status(thm)],[])).
% 290.55/183.07 tff(8097,plain,
% 290.55/183.07 ((m_or_h_gate_v_in1(c_e_h_2, c_j, s3) | m_or_h_gate_v_in2(c_e_h_2, c_j, s3) | (~node5(c_e_h_2, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s4))) <=> ((~node5(c_e_h_2, c_j, s3, s4)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s4)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s3))),
% 290.55/183.07 inference(rewrite,[status(thm)],[])).
% 290.55/183.07 tff(8098,plain,
% 290.55/183.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s3) | m_or_h_gate_v_in2(c_e_h_2, c_j, s3) | (~node5(c_e_h_2, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~node5(c_e_h_2, c_j, s3, s4)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s4)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s3)))),
% 290.55/183.08 inference(monotonicity,[status(thm)],[8097])).
% 290.55/183.08 tff(8099,plain,
% 290.55/183.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s3) | m_or_h_gate_v_in2(c_e_h_2, c_j, s3) | (~node5(c_e_h_2, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~node5(c_e_h_2, c_j, s3, s4)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s4)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s3))),
% 290.55/183.08 inference(transitivity,[status(thm)],[8098, 8096])).
% 290.55/183.08 tff(8100,plain,
% 290.55/183.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s3) | m_or_h_gate_v_in2(c_e_h_2, c_j, s3) | (~node5(c_e_h_2, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s4)))),
% 290.55/183.08 inference(quant_inst,[status(thm)],[])).
% 290.55/183.08 tff(8101,plain,
% 290.55/183.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~node5(c_e_h_2, c_j, s3, s4)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s4)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s3)),
% 290.55/183.08 inference(modus_ponens,[status(thm)],[8100, 8099])).
% 290.55/183.08 tff(8102,plain,
% 290.55/183.08 ($false),
% 290.55/183.08 inference(unit_resolution,[status(thm)],[8101, 1159, 7816, 8095, 8094, 8093])).
% 290.55/183.08 tff(8103,plain,((~node5(c_e_h_2, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s4)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s3) | m_or_h_gate_v_in2(c_e_h_2, c_j, s3)), inference(lemma,lemma(discharge,[]))).
% 290.55/183.08 tff(8104,plain,
% 290.55/183.08 ((~node5(c_e_h_2, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s4)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s3)),
% 290.55/183.08 inference(unit_resolution,[status(thm)],[8103, 8092])).
% 290.55/183.08 tff(8105,plain,
% 290.55/183.08 ((~node5(c_e_h_2, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s4))),
% 290.55/183.08 inference(unit_resolution,[status(thm)],[8104, 7945])).
% 290.55/183.08 tff(8106,plain,
% 290.55/183.08 (~node5(c_e_h_2, c_j, s3, s4)),
% 290.55/183.08 inference(unit_resolution,[status(thm)],[8105, 7816])).
% 290.55/183.08 tff(8107,plain,
% 290.55/183.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s3, s4)) | node5(c_e_h_2, c_j, s3, s4) | node6(c_e_h_2, c_j, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s3, s4)) | node5(c_e_h_2, c_j, s3, s4) | node6(c_e_h_2, c_j, s3, s4))),
% 290.55/183.08 inference(rewrite,[status(thm)],[])).
% 290.55/183.08 tff(8108,plain,
% 290.55/183.08 ((node6(c_e_h_2, c_j, s3, s4) | node5(c_e_h_2, c_j, s3, s4) | (~trans(s3, s4))) <=> ((~trans(s3, s4)) | node5(c_e_h_2, c_j, s3, s4) | node6(c_e_h_2, c_j, s3, s4))),
% 290.55/183.08 inference(rewrite,[status(thm)],[])).
% 290.55/183.08 tff(8109,plain,
% 290.55/183.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s3, s4) | node5(c_e_h_2, c_j, s3, s4) | (~trans(s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s3, s4)) | node5(c_e_h_2, c_j, s3, s4) | node6(c_e_h_2, c_j, s3, s4)))),
% 290.55/183.08 inference(monotonicity,[status(thm)],[8108])).
% 290.55/183.08 tff(8110,plain,
% 290.55/183.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s3, s4) | node5(c_e_h_2, c_j, s3, s4) | (~trans(s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s3, s4)) | node5(c_e_h_2, c_j, s3, s4) | node6(c_e_h_2, c_j, s3, s4))),
% 290.55/183.08 inference(transitivity,[status(thm)],[8109, 8107])).
% 290.55/183.08 tff(8111,plain,
% 290.55/183.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s3, s4) | node5(c_e_h_2, c_j, s3, s4) | (~trans(s3, s4)))),
% 290.55/183.08 inference(quant_inst,[status(thm)],[])).
% 290.55/183.08 tff(8112,plain,
% 290.55/183.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s3, s4)) | node5(c_e_h_2, c_j, s3, s4) | node6(c_e_h_2, c_j, s3, s4)),
% 290.55/183.08 inference(modus_ponens,[status(thm)],[8111, 8110])).
% 290.55/183.08 tff(8113,plain,
% 290.55/183.08 (node5(c_e_h_2, c_j, s3, s4) | node6(c_e_h_2, c_j, s3, s4)),
% 290.55/183.08 inference(unit_resolution,[status(thm)],[8112, 1141, 531])).
% 290.55/183.08 tff(8114,plain,
% 290.55/183.08 ($false),
% 290.55/183.08 inference(unit_resolution,[status(thm)],[8113, 8106, 7828])).
% 290.55/183.08 tff(8115,plain,(~m_or_h_gate_v_out(c_e_h_2, c_j, s4)), inference(lemma,lemma(discharge,[]))).
% 290.55/183.08 tff(8116,plain,
% 290.55/183.08 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s4)) | m_or_h_gate_v_out(c_e_h_2, c_j, s4))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s4)) | m_or_h_gate_v_out(c_e_h_2, c_j, s4))),
% 290.55/183.08 inference(rewrite,[status(thm)],[])).
% 290.55/183.08 tff(8117,plain,
% 290.55/183.08 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s4)) | m_or_h_gate_v_out(c_e_h_2, c_j, s4))),
% 290.55/183.08 inference(quant_inst,[status(thm)],[])).
% 290.55/183.08 tff(8118,plain,
% 290.55/183.08 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s4)) | m_or_h_gate_v_out(c_e_h_2, c_j, s4)),
% 290.55/183.08 inference(modus_ponens,[status(thm)],[8117, 8116])).
% 290.55/183.08 tff(8119,plain,
% 290.55/183.08 (~m_c_h_element_v_in2(c_e_h_2, c_h, s4)),
% 290.55/183.08 inference(unit_resolution,[status(thm)],[8118, 1174, 8115])).
% 290.55/183.08 tff(8120,plain,
% 290.55/183.08 (m_c_h_element_v_in2(c_e_h_2, c_h, s3) | (~m_c_h_element_v_out(c_e_h_2, c_h, s4))),
% 290.55/183.08 inference(unit_resolution,[status(thm)],[5232, 4723])).
% 290.55/183.08 tff(8121,plain,
% 290.55/183.08 (~m_c_h_element_v_out(c_e_h_2, c_h, s4)),
% 290.55/183.08 inference(unit_resolution,[status(thm)],[8120, 5168])).
% 290.55/183.08 tff(8122,assumption,(m_c_h_element_v_out(c_e_h_2, c_h, s5)), introduced(assumption)).
% 290.55/183.08 tff(8123,assumption,(node18(c_e_h_2, c_h, s4, s5)), introduced(assumption)).
% 290.55/183.08 tff(8124,plain,
% 290.55/183.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~node18(c_e_h_2, c_h, s4, s5)) | m_c_h_element_v_out(c_e_h_2, c_h, s4) | (~m_c_h_element_v_out(c_e_h_2, c_h, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_2, c_h, s4, s5)) | m_c_h_element_v_out(c_e_h_2, c_h, s4) | (~m_c_h_element_v_out(c_e_h_2, c_h, s5)))),
% 290.55/183.08 inference(rewrite,[status(thm)],[])).
% 290.55/183.08 tff(8125,plain,
% 290.55/183.08 (((~m_c_h_element_v_out(c_e_h_2, c_h, s5)) | m_c_h_element_v_out(c_e_h_2, c_h, s4) | (~node18(c_e_h_2, c_h, s4, s5))) <=> ((~node18(c_e_h_2, c_h, s4, s5)) | m_c_h_element_v_out(c_e_h_2, c_h, s4) | (~m_c_h_element_v_out(c_e_h_2, c_h, s5)))),
% 290.55/183.08 inference(rewrite,[status(thm)],[])).
% 290.55/183.08 tff(8126,plain,
% 290.55/183.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s5)) | m_c_h_element_v_out(c_e_h_2, c_h, s4) | (~node18(c_e_h_2, c_h, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~node18(c_e_h_2, c_h, s4, s5)) | m_c_h_element_v_out(c_e_h_2, c_h, s4) | (~m_c_h_element_v_out(c_e_h_2, c_h, s5))))),
% 290.55/183.08 inference(monotonicity,[status(thm)],[8125])).
% 290.55/183.08 tff(8127,plain,
% 290.55/183.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s5)) | m_c_h_element_v_out(c_e_h_2, c_h, s4) | (~node18(c_e_h_2, c_h, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_2, c_h, s4, s5)) | m_c_h_element_v_out(c_e_h_2, c_h, s4) | (~m_c_h_element_v_out(c_e_h_2, c_h, s5)))),
% 290.55/183.09 inference(transitivity,[status(thm)],[8126, 8124])).
% 290.55/183.09 tff(8128,plain,
% 290.55/183.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s5)) | m_c_h_element_v_out(c_e_h_2, c_h, s4) | (~node18(c_e_h_2, c_h, s4, s5)))),
% 290.55/183.09 inference(quant_inst,[status(thm)],[])).
% 290.55/183.09 tff(8129,plain,
% 290.55/183.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_2, c_h, s4, s5)) | m_c_h_element_v_out(c_e_h_2, c_h, s4) | (~m_c_h_element_v_out(c_e_h_2, c_h, s5))),
% 290.55/183.09 inference(modus_ponens,[status(thm)],[8128, 8127])).
% 290.55/183.09 tff(8130,plain,
% 290.55/183.09 ($false),
% 290.55/183.09 inference(unit_resolution,[status(thm)],[8129, 753, 8123, 5235, 8122])).
% 290.55/183.09 tff(8131,plain,((~node18(c_e_h_2, c_h, s4, s5)) | m_c_h_element_v_out(c_e_h_2, c_h, s4) | (~m_c_h_element_v_out(c_e_h_2, c_h, s5))), inference(lemma,lemma(discharge,[]))).
% 290.55/183.09 tff(8132,plain,
% 290.55/183.09 (~node18(c_e_h_2, c_h, s4, s5)),
% 290.55/183.09 inference(unit_resolution,[status(thm)],[8131, 8122, 5235])).
% 290.55/183.09 tff(8133,plain,
% 290.55/183.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s4, s5)) | node19(c_e_h_2, c_h, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s4, s5)) | node19(c_e_h_2, c_h, s4, s5))),
% 290.55/183.09 inference(rewrite,[status(thm)],[])).
% 290.55/183.09 tff(8134,plain,
% 290.55/183.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s4, s5)) | node19(c_e_h_2, c_h, s4, s5))),
% 290.55/183.09 inference(quant_inst,[status(thm)],[])).
% 290.55/183.09 tff(8135,plain,
% 290.55/183.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s4, s5)) | node19(c_e_h_2, c_h, s4, s5)),
% 290.55/183.09 inference(modus_ponens,[status(thm)],[8134, 8133])).
% 290.55/183.09 tff(8136,plain,
% 290.55/183.09 (node19(c_e_h_2, c_h, s4, s5)),
% 290.55/183.09 inference(unit_resolution,[status(thm)],[8135, 190, 1028])).
% 290.55/183.09 tff(8137,plain,
% 290.55/183.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_2, c_h, s4, s5) | (~node19(c_e_h_2, c_h, s4, s5)) | node17(c_e_h_2, c_h, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_2, c_h, s4, s5) | (~node19(c_e_h_2, c_h, s4, s5)) | node17(c_e_h_2, c_h, s4))),
% 290.55/183.09 inference(rewrite,[status(thm)],[])).
% 290.55/183.09 tff(8138,plain,
% 290.55/183.09 ((node17(c_e_h_2, c_h, s4) | node18(c_e_h_2, c_h, s4, s5) | (~node19(c_e_h_2, c_h, s4, s5))) <=> (node18(c_e_h_2, c_h, s4, s5) | (~node19(c_e_h_2, c_h, s4, s5)) | node17(c_e_h_2, c_h, s4))),
% 290.55/183.09 inference(rewrite,[status(thm)],[])).
% 290.55/183.09 tff(8139,plain,
% 290.55/183.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s4) | node18(c_e_h_2, c_h, s4, s5) | (~node19(c_e_h_2, c_h, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_2, c_h, s4, s5) | (~node19(c_e_h_2, c_h, s4, s5)) | node17(c_e_h_2, c_h, s4)))),
% 290.55/183.09 inference(monotonicity,[status(thm)],[8138])).
% 290.55/183.09 tff(8140,plain,
% 290.55/183.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s4) | node18(c_e_h_2, c_h, s4, s5) | (~node19(c_e_h_2, c_h, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_2, c_h, s4, s5) | (~node19(c_e_h_2, c_h, s4, s5)) | node17(c_e_h_2, c_h, s4))),
% 290.55/183.09 inference(transitivity,[status(thm)],[8139, 8137])).
% 290.55/183.09 tff(8141,plain,
% 290.55/183.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s4) | node18(c_e_h_2, c_h, s4, s5) | (~node19(c_e_h_2, c_h, s4, s5)))),
% 290.55/183.09 inference(quant_inst,[status(thm)],[])).
% 290.55/183.09 tff(8142,plain,
% 290.55/183.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_2, c_h, s4, s5) | (~node19(c_e_h_2, c_h, s4, s5)) | node17(c_e_h_2, c_h, s4)),
% 290.55/183.09 inference(modus_ponens,[status(thm)],[8141, 8140])).
% 290.55/183.09 tff(8143,plain,
% 290.55/183.09 (node18(c_e_h_2, c_h, s4, s5) | node17(c_e_h_2, c_h, s4)),
% 290.55/183.09 inference(unit_resolution,[status(thm)],[8142, 776, 8136])).
% 290.55/183.09 tff(8144,plain,
% 290.55/183.09 (node17(c_e_h_2, c_h, s4)),
% 290.55/183.09 inference(unit_resolution,[status(thm)],[8143, 8132])).
% 290.55/183.09 tff(8145,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_h, s4)), introduced(assumption)).
% 290.55/183.09 tff(8146,plain,
% 290.55/183.09 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s4)) | m_c_h_element_v_in2(c_e_h_2, c_h, s4) | (~node17(c_e_h_2, c_h, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s4)) | m_c_h_element_v_in2(c_e_h_2, c_h, s4) | (~node17(c_e_h_2, c_h, s4)))),
% 290.55/183.09 inference(rewrite,[status(thm)],[])).
% 290.55/183.09 tff(8147,plain,
% 290.55/183.09 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s4)) | m_c_h_element_v_in2(c_e_h_2, c_h, s4) | (~node17(c_e_h_2, c_h, s4)))),
% 290.55/183.09 inference(quant_inst,[status(thm)],[])).
% 290.55/183.09 tff(8148,plain,
% 290.55/183.09 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s4)) | m_c_h_element_v_in2(c_e_h_2, c_h, s4) | (~node17(c_e_h_2, c_h, s4))),
% 290.55/183.09 inference(modus_ponens,[status(thm)],[8147, 8146])).
% 290.55/183.09 tff(8149,plain,
% 290.55/183.09 ((~m_c_h_element_v_in1(c_e_h_2, c_h, s4)) | (~node17(c_e_h_2, c_h, s4))),
% 290.55/183.09 inference(unit_resolution,[status(thm)],[8148, 919, 8145])).
% 290.55/183.09 tff(8150,plain,
% 290.55/183.09 (~m_c_h_element_v_in1(c_e_h_2, c_h, s4)),
% 290.55/183.09 inference(unit_resolution,[status(thm)],[8149, 8144])).
% 290.55/183.09 tff(8151,plain,
% 290.55/183.09 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_h, s4)) | m_c_h_element_v_in1(c_e_h_2, c_h, s4) | m_c_h_element_v_in2(c_e_h_2, c_h, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_h, s4)) | m_c_h_element_v_in1(c_e_h_2, c_h, s4) | m_c_h_element_v_in2(c_e_h_2, c_h, s4))),
% 290.55/183.09 inference(rewrite,[status(thm)],[])).
% 290.55/183.09 tff(8152,plain,
% 290.55/183.09 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_h, s4)) | m_c_h_element_v_in1(c_e_h_2, c_h, s4) | m_c_h_element_v_in2(c_e_h_2, c_h, s4))),
% 290.55/183.09 inference(quant_inst,[status(thm)],[])).
% 290.55/183.09 tff(8153,plain,
% 290.55/183.09 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_h, s4)) | m_c_h_element_v_in1(c_e_h_2, c_h, s4) | m_c_h_element_v_in2(c_e_h_2, c_h, s4)),
% 290.55/183.09 inference(modus_ponens,[status(thm)],[8152, 8151])).
% 290.55/183.09 tff(8154,plain,
% 290.55/183.09 ((~node16(c_e_h_2, c_h, s4)) | m_c_h_element_v_in1(c_e_h_2, c_h, s4)),
% 290.55/183.09 inference(unit_resolution,[status(thm)],[8153, 178, 8145])).
% 290.55/183.09 tff(8155,plain,
% 290.55/183.09 (~node16(c_e_h_2, c_h, s4)),
% 290.55/183.09 inference(unit_resolution,[status(thm)],[8154, 8150])).
% 290.55/183.09 tff(8156,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_h, s4)), introduced(assumption)).
% 290.55/183.09 tff(8157,assumption,(~node16(c_e_h_2, c_h, s4)), introduced(assumption)).
% 290.55/183.09 tff(8158,assumption,(node15(c_e_h_2, c_h, s4, s5)), introduced(assumption)).
% 290.55/183.09 tff(8159,plain,
% 290.55/183.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s5)) | (~node15(c_e_h_2, c_h, s4, s5)) | m_c_h_element_v_out(c_e_h_2, c_h, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s5)) | (~node15(c_e_h_2, c_h, s4, s5)) | m_c_h_element_v_out(c_e_h_2, c_h, s4))),
% 290.55/183.09 inference(rewrite,[status(thm)],[])).
% 290.55/183.09 tff(8160,plain,
% 290.55/183.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s5)) | (~node15(c_e_h_2, c_h, s4, s5)) | m_c_h_element_v_out(c_e_h_2, c_h, s4))),
% 290.55/183.09 inference(quant_inst,[status(thm)],[])).
% 290.55/183.09 tff(8161,plain,
% 290.55/183.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s5)) | (~node15(c_e_h_2, c_h, s4, s5)) | m_c_h_element_v_out(c_e_h_2, c_h, s4)),
% 290.55/183.09 inference(modus_ponens,[status(thm)],[8160, 8159])).
% 290.55/183.09 tff(8162,plain,
% 290.55/183.09 ($false),
% 290.55/183.09 inference(unit_resolution,[status(thm)],[8161, 147, 8158, 5235, 8122])).
% 290.55/183.09 tff(8163,plain,((~node15(c_e_h_2, c_h, s4, s5)) | m_c_h_element_v_out(c_e_h_2, c_h, s4) | (~m_c_h_element_v_out(c_e_h_2, c_h, s5))), inference(lemma,lemma(discharge,[]))).
% 290.55/183.09 tff(8164,plain,
% 290.55/183.09 (~node15(c_e_h_2, c_h, s4, s5)),
% 290.55/183.09 inference(unit_resolution,[status(thm)],[8163, 8122, 5235])).
% 290.55/183.09 tff(8165,plain,
% 290.55/183.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_2, c_h, s4, s5) | node14(c_e_h_2, c_h, s4, s5) | (~node19(c_e_h_2, c_h, s4, s5)) | node16(c_e_h_2, c_h, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_2, c_h, s4, s5) | node14(c_e_h_2, c_h, s4, s5) | (~node19(c_e_h_2, c_h, s4, s5)) | node16(c_e_h_2, c_h, s4))),
% 290.55/183.09 inference(rewrite,[status(thm)],[])).
% 290.55/183.09 tff(8166,plain,
% 290.55/183.09 ((node16(c_e_h_2, c_h, s4) | node14(c_e_h_2, c_h, s4, s5) | node15(c_e_h_2, c_h, s4, s5) | (~node19(c_e_h_2, c_h, s4, s5))) <=> (node15(c_e_h_2, c_h, s4, s5) | node14(c_e_h_2, c_h, s4, s5) | (~node19(c_e_h_2, c_h, s4, s5)) | node16(c_e_h_2, c_h, s4))),
% 290.55/183.09 inference(rewrite,[status(thm)],[])).
% 290.55/183.09 tff(8167,plain,
% 290.55/183.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s4) | node14(c_e_h_2, c_h, s4, s5) | node15(c_e_h_2, c_h, s4, s5) | (~node19(c_e_h_2, c_h, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_2, c_h, s4, s5) | node14(c_e_h_2, c_h, s4, s5) | (~node19(c_e_h_2, c_h, s4, s5)) | node16(c_e_h_2, c_h, s4)))),
% 290.55/183.09 inference(monotonicity,[status(thm)],[8166])).
% 290.55/183.09 tff(8168,plain,
% 290.55/183.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s4) | node14(c_e_h_2, c_h, s4, s5) | node15(c_e_h_2, c_h, s4, s5) | (~node19(c_e_h_2, c_h, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_2, c_h, s4, s5) | node14(c_e_h_2, c_h, s4, s5) | (~node19(c_e_h_2, c_h, s4, s5)) | node16(c_e_h_2, c_h, s4))),
% 290.55/183.09 inference(transitivity,[status(thm)],[8167, 8165])).
% 290.55/183.09 tff(8169,plain,
% 290.55/183.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s4) | node14(c_e_h_2, c_h, s4, s5) | node15(c_e_h_2, c_h, s4, s5) | (~node19(c_e_h_2, c_h, s4, s5)))),
% 290.55/183.09 inference(quant_inst,[status(thm)],[])).
% 290.55/183.09 tff(8170,plain,
% 290.55/183.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_2, c_h, s4, s5) | node14(c_e_h_2, c_h, s4, s5) | (~node19(c_e_h_2, c_h, s4, s5)) | node16(c_e_h_2, c_h, s4)),
% 290.55/183.09 inference(modus_ponens,[status(thm)],[8169, 8168])).
% 290.55/183.09 tff(8171,plain,
% 290.55/183.09 (node15(c_e_h_2, c_h, s4, s5) | node14(c_e_h_2, c_h, s4, s5) | node16(c_e_h_2, c_h, s4)),
% 290.55/183.09 inference(unit_resolution,[status(thm)],[8170, 204, 8136])).
% 290.63/183.10 tff(8172,plain,
% 290.63/183.10 (node14(c_e_h_2, c_h, s4, s5)),
% 290.63/183.10 inference(unit_resolution,[status(thm)],[8171, 8164, 8157])).
% 290.63/183.10 tff(8173,plain,
% 290.63/183.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s4) | (~m_c_h_element_v_out(c_e_h_2, c_h, s5)) | (~node14(c_e_h_2, c_h, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s4) | (~m_c_h_element_v_out(c_e_h_2, c_h, s5)) | (~node14(c_e_h_2, c_h, s4, s5)))),
% 290.63/183.10 inference(rewrite,[status(thm)],[])).
% 290.63/183.10 tff(8174,plain,
% 290.63/183.10 (((~node14(c_e_h_2, c_h, s4, s5)) | m_c_h_element_v_in1(c_e_h_2, c_h, s4) | (~m_c_h_element_v_out(c_e_h_2, c_h, s5))) <=> (m_c_h_element_v_in1(c_e_h_2, c_h, s4) | (~m_c_h_element_v_out(c_e_h_2, c_h, s5)) | (~node14(c_e_h_2, c_h, s4, s5)))),
% 290.63/183.10 inference(rewrite,[status(thm)],[])).
% 290.63/183.10 tff(8175,plain,
% 290.63/183.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s4, s5)) | m_c_h_element_v_in1(c_e_h_2, c_h, s4) | (~m_c_h_element_v_out(c_e_h_2, c_h, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s4) | (~m_c_h_element_v_out(c_e_h_2, c_h, s5)) | (~node14(c_e_h_2, c_h, s4, s5))))),
% 290.63/183.10 inference(monotonicity,[status(thm)],[8174])).
% 290.63/183.10 tff(8176,plain,
% 290.63/183.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s4, s5)) | m_c_h_element_v_in1(c_e_h_2, c_h, s4) | (~m_c_h_element_v_out(c_e_h_2, c_h, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s4) | (~m_c_h_element_v_out(c_e_h_2, c_h, s5)) | (~node14(c_e_h_2, c_h, s4, s5)))),
% 290.63/183.10 inference(transitivity,[status(thm)],[8175, 8173])).
% 290.63/183.10 tff(8177,plain,
% 290.63/183.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s4, s5)) | m_c_h_element_v_in1(c_e_h_2, c_h, s4) | (~m_c_h_element_v_out(c_e_h_2, c_h, s5)))),
% 290.63/183.10 inference(quant_inst,[status(thm)],[])).
% 290.63/183.10 tff(8178,plain,
% 290.63/183.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s4) | (~m_c_h_element_v_out(c_e_h_2, c_h, s5)) | (~node14(c_e_h_2, c_h, s4, s5))),
% 290.63/183.10 inference(modus_ponens,[status(thm)],[8177, 8176])).
% 290.63/183.10 tff(8179,plain,
% 290.63/183.10 ($false),
% 290.63/183.10 inference(unit_resolution,[status(thm)],[8178, 223, 8172, 8156, 8122])).
% 290.63/183.10 tff(8180,plain,((~m_c_h_element_v_out(c_e_h_2, c_h, s5)) | m_c_h_element_v_in1(c_e_h_2, c_h, s4) | node16(c_e_h_2, c_h, s4) | m_c_h_element_v_out(c_e_h_2, c_h, s4)), inference(lemma,lemma(discharge,[]))).
% 290.63/183.10 tff(8181,plain,
% 290.63/183.10 ($false),
% 290.63/183.10 inference(unit_resolution,[status(thm)],[8180, 8155, 8150, 5235, 8122])).
% 290.63/183.10 tff(8182,plain,((~m_c_h_element_v_out(c_e_h_2, c_h, s5)) | m_c_h_element_v_out(c_e_h_2, c_h, s4) | m_c_h_element_v_in2(c_e_h_2, c_h, s4)), inference(lemma,lemma(discharge,[]))).
% 290.63/183.10 tff(8183,plain,
% 290.63/183.10 ((~m_c_h_element_v_out(c_e_h_2, c_h, s5)) | m_c_h_element_v_in2(c_e_h_2, c_h, s4)),
% 290.63/183.10 inference(unit_resolution,[status(thm)],[8182, 8121])).
% 290.63/183.10 tff(8184,plain,
% 290.63/183.10 (~m_c_h_element_v_out(c_e_h_2, c_h, s5)),
% 290.63/183.10 inference(unit_resolution,[status(thm)],[8183, 8119])).
% 290.63/183.10 tff(8185,assumption,(m_and_h_gate_v_in1(c_e_h_2, c_i, s5)), introduced(assumption)).
% 290.63/183.10 tff(8186,assumption,(~m_c_h_element_v_out(c_e_h_2, c_h, s5)), introduced(assumption)).
% 290.63/183.10 tff(8187,plain,
% 290.63/183.10 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s5)) | m_c_h_element_v_out(c_e_h_2, c_h, s5))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s5)) | m_c_h_element_v_out(c_e_h_2, c_h, s5))),
% 290.63/183.10 inference(rewrite,[status(thm)],[])).
% 290.63/183.10 tff(8188,plain,
% 290.63/183.10 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s5)) | m_c_h_element_v_out(c_e_h_2, c_h, s5))),
% 290.63/183.10 inference(quant_inst,[status(thm)],[])).
% 290.63/183.10 tff(8189,plain,
% 290.63/183.10 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s5)) | m_c_h_element_v_out(c_e_h_2, c_h, s5)),
% 290.63/183.10 inference(modus_ponens,[status(thm)],[8188, 8187])).
% 290.63/183.10 tff(8190,plain,
% 290.63/183.10 ($false),
% 290.63/183.10 inference(unit_resolution,[status(thm)],[8189, 619, 8186, 8185])).
% 290.63/183.10 tff(8191,plain,((~m_and_h_gate_v_in1(c_e_h_2, c_i, s5)) | m_c_h_element_v_out(c_e_h_2, c_h, s5)), inference(lemma,lemma(discharge,[]))).
% 290.63/183.10 tff(8192,plain,
% 290.63/183.10 (~m_and_h_gate_v_in1(c_e_h_2, c_i, s5)),
% 290.63/183.10 inference(unit_resolution,[status(thm)],[8191, 8184])).
% 290.63/183.10 tff(8193,assumption,(~m_and_h_gate_v_in1(c_e_h_2, c_i, s5)), introduced(assumption)).
% 290.63/183.10 tff(8194,assumption,(node20(c_e_h_2, c_i, s5)), introduced(assumption)).
% 290.63/183.10 tff(8195,plain,
% 290.63/183.10 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s5)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s5)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s5))),
% 290.63/183.10 inference(rewrite,[status(thm)],[])).
% 290.63/183.10 tff(8196,plain,
% 290.63/183.10 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s5)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s5))),
% 290.63/183.10 inference(quant_inst,[status(thm)],[])).
% 290.63/183.10 tff(8197,plain,
% 290.63/183.10 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s5)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s5)),
% 290.63/183.10 inference(modus_ponens,[status(thm)],[8196, 8195])).
% 290.63/183.10 tff(8198,plain,
% 290.63/183.10 ($false),
% 290.63/183.10 inference(unit_resolution,[status(thm)],[8197, 38, 8194, 8193])).
% 290.63/183.10 tff(8199,plain,((~node20(c_e_h_2, c_i, s5)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s5)), inference(lemma,lemma(discharge,[]))).
% 290.63/183.10 tff(8200,plain,
% 290.63/183.10 (~node20(c_e_h_2, c_i, s5)),
% 290.63/183.10 inference(unit_resolution,[status(thm)],[8199, 8192])).
% 290.63/183.10 tff(8201,assumption,(m_and_h_gate_v_out(c_e_h_2, c_i, s6)), introduced(assumption)).
% 290.63/183.10 tff(8202,assumption,(node22(c_e_h_2, c_i, s5, s6)), introduced(assumption)).
% 290.63/183.10 tff(8203,plain,
% 290.63/183.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s6)) | (~node22(c_e_h_2, c_i, s5, s6)) | m_and_h_gate_v_out(c_e_h_2, c_i, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s6)) | (~node22(c_e_h_2, c_i, s5, s6)) | m_and_h_gate_v_out(c_e_h_2, c_i, s5))),
% 290.63/183.10 inference(rewrite,[status(thm)],[])).
% 290.63/183.10 tff(8204,plain,
% 290.63/183.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s6)) | (~node22(c_e_h_2, c_i, s5, s6)) | m_and_h_gate_v_out(c_e_h_2, c_i, s5))),
% 290.63/183.10 inference(quant_inst,[status(thm)],[])).
% 290.63/183.10 tff(8205,plain,
% 290.63/183.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s6)) | (~node22(c_e_h_2, c_i, s5, s6)) | m_and_h_gate_v_out(c_e_h_2, c_i, s5)),
% 290.63/183.10 inference(modus_ponens,[status(thm)],[8204, 8203])).
% 290.63/183.10 tff(8206,plain,
% 290.63/183.10 ($false),
% 290.63/183.10 inference(unit_resolution,[status(thm)],[8205, 108, 8202, 5280, 8201])).
% 290.63/183.10 tff(8207,plain,((~node22(c_e_h_2, c_i, s5, s6)) | m_and_h_gate_v_out(c_e_h_2, c_i, s5) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s6))), inference(lemma,lemma(discharge,[]))).
% 290.63/183.10 tff(8208,plain,
% 290.63/183.10 (~node22(c_e_h_2, c_i, s5, s6)),
% 290.63/183.11 inference(unit_resolution,[status(thm)],[8207, 8201, 5280])).
% 290.63/183.11 tff(8209,assumption,(~node20(c_e_h_2, c_i, s5)), introduced(assumption)).
% 290.63/183.11 tff(8210,assumption,(node21(c_e_h_2, c_i, s5, s6)), introduced(assumption)).
% 290.63/183.11 tff(8211,plain,
% 290.63/183.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s5) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s6)) | (~node21(c_e_h_2, c_i, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s5) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s6)) | (~node21(c_e_h_2, c_i, s5, s6)))),
% 290.63/183.11 inference(rewrite,[status(thm)],[])).
% 290.63/183.11 tff(8212,plain,
% 290.63/183.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s5) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s6)) | (~node21(c_e_h_2, c_i, s5, s6)))),
% 290.63/183.11 inference(quant_inst,[status(thm)],[])).
% 290.63/183.11 tff(8213,plain,
% 290.63/183.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s5) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s6)) | (~node21(c_e_h_2, c_i, s5, s6))),
% 290.63/183.11 inference(modus_ponens,[status(thm)],[8212, 8211])).
% 290.63/183.11 tff(8214,plain,
% 290.63/183.11 ($false),
% 290.63/183.11 inference(unit_resolution,[status(thm)],[8213, 52, 8210, 8201, 8209])).
% 290.63/183.11 tff(8215,plain,((~node21(c_e_h_2, c_i, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s6)) | node20(c_e_h_2, c_i, s5)), inference(lemma,lemma(discharge,[]))).
% 290.63/183.11 tff(8216,plain,
% 290.63/183.11 (~node21(c_e_h_2, c_i, s5, s6)),
% 290.63/183.11 inference(unit_resolution,[status(thm)],[8215, 8201, 8209])).
% 290.63/183.11 tff(8217,plain,
% 290.63/183.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_2, c_i, s5, s6) | node22(c_e_h_2, c_i, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_2, c_i, s5, s6) | node22(c_e_h_2, c_i, s5, s6))),
% 290.63/183.11 inference(rewrite,[status(thm)],[])).
% 290.63/183.11 tff(8218,plain,
% 290.63/183.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_2, c_i, s5, s6) | node22(c_e_h_2, c_i, s5, s6))),
% 290.63/183.11 inference(quant_inst,[status(thm)],[])).
% 290.63/183.11 tff(8219,plain,
% 290.63/183.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_2, c_i, s5, s6) | node22(c_e_h_2, c_i, s5, s6)),
% 290.63/183.11 inference(modus_ponens,[status(thm)],[8218, 8217])).
% 290.63/183.11 tff(8220,plain,
% 290.63/183.11 (node21(c_e_h_2, c_i, s5, s6) | node22(c_e_h_2, c_i, s5, s6)),
% 290.63/183.11 inference(unit_resolution,[status(thm)],[8219, 82, 1406])).
% 290.63/183.11 tff(8221,plain,
% 290.63/183.11 ($false),
% 290.63/183.11 inference(unit_resolution,[status(thm)],[8220, 8216, 8208])).
% 290.63/183.11 tff(8222,plain,((~m_and_h_gate_v_out(c_e_h_2, c_i, s6)) | node20(c_e_h_2, c_i, s5) | m_and_h_gate_v_out(c_e_h_2, c_i, s5)), inference(lemma,lemma(discharge,[]))).
% 290.63/183.11 tff(8223,plain,
% 290.63/183.11 ((~m_and_h_gate_v_out(c_e_h_2, c_i, s6)) | node20(c_e_h_2, c_i, s5)),
% 290.63/183.11 inference(unit_resolution,[status(thm)],[8222, 5278])).
% 290.63/183.11 tff(8224,plain,
% 290.63/183.11 (~m_and_h_gate_v_out(c_e_h_2, c_i, s6)),
% 290.63/183.11 inference(unit_resolution,[status(thm)],[8223, 8200])).
% 290.63/183.11 tff(8225,plain,
% 290.63/183.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s7)) | (~node22(c_e_h_2, c_i, s6, s7)) | m_and_h_gate_v_out(c_e_h_2, c_i, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s7)) | (~node22(c_e_h_2, c_i, s6, s7)) | m_and_h_gate_v_out(c_e_h_2, c_i, s6))),
% 290.63/183.11 inference(rewrite,[status(thm)],[])).
% 290.63/183.11 tff(8226,plain,
% 290.63/183.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s7)) | (~node22(c_e_h_2, c_i, s6, s7)) | m_and_h_gate_v_out(c_e_h_2, c_i, s6))),
% 290.63/183.11 inference(quant_inst,[status(thm)],[])).
% 290.63/183.11 tff(8227,plain,
% 290.63/183.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s7)) | (~node22(c_e_h_2, c_i, s6, s7)) | m_and_h_gate_v_out(c_e_h_2, c_i, s6)),
% 290.63/183.11 inference(modus_ponens,[status(thm)],[8226, 8225])).
% 290.63/183.11 tff(8228,plain,
% 290.63/183.11 ($false),
% 290.63/183.11 inference(unit_resolution,[status(thm)],[8227, 108, 8224, 7814, 7815])).
% 290.63/183.11 tff(8229,plain,((~node22(c_e_h_2, c_i, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s7))), inference(lemma,lemma(discharge,[]))).
% 290.63/183.11 tff(8230,plain,
% 290.63/183.11 (~node22(c_e_h_2, c_i, s6, s7)),
% 290.63/183.11 inference(unit_resolution,[status(thm)],[8229, 7814])).
% 290.63/183.11 tff(8231,assumption,(m_and_h_gate_v_out(c_e_h_2, c_l, s4)), introduced(assumption)).
% 290.63/183.11 tff(8232,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)), introduced(assumption)).
% 290.63/183.11 tff(8233,assumption,(node11(c_e_h_2, c_m, s2, s3)), introduced(assumption)).
% 290.63/183.11 tff(8234,plain,
% 290.63/183.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)) | (~node11(c_e_h_2, c_m, s2, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)) | (~node11(c_e_h_2, c_m, s2, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2))),
% 290.63/183.11 inference(rewrite,[status(thm)],[])).
% 290.63/183.11 tff(8235,plain,
% 290.63/183.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)) | (~node11(c_e_h_2, c_m, s2, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2))),
% 290.63/183.11 inference(quant_inst,[status(thm)],[])).
% 290.63/183.11 tff(8236,plain,
% 290.63/183.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)) | (~node11(c_e_h_2, c_m, s2, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)),
% 290.63/183.11 inference(modus_ponens,[status(thm)],[8235, 8234])).
% 290.63/183.11 tff(8237,plain,
% 290.63/183.11 ($false),
% 290.63/183.11 inference(unit_resolution,[status(thm)],[8236, 5017, 7909, 8233, 8232])).
% 290.63/183.11 tff(8238,plain,((~node11(c_e_h_2, c_m, s2, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3))), inference(lemma,lemma(discharge,[]))).
% 290.63/183.11 tff(8239,plain,
% 290.63/183.11 (~node11(c_e_h_2, c_m, s2, s3)),
% 290.63/183.11 inference(unit_resolution,[status(thm)],[8238, 8232])).
% 290.63/183.11 tff(8240,plain,
% 290.63/183.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s2, s3)) | node10(c_e_h_2, c_m, s2, s3) | node11(c_e_h_2, c_m, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s2, s3)) | node10(c_e_h_2, c_m, s2, s3) | node11(c_e_h_2, c_m, s2, s3))),
% 290.63/183.11 inference(rewrite,[status(thm)],[])).
% 290.63/183.11 tff(8241,plain,
% 290.63/183.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s2, s3)) | node10(c_e_h_2, c_m, s2, s3) | node11(c_e_h_2, c_m, s2, s3))),
% 290.63/183.11 inference(quant_inst,[status(thm)],[])).
% 290.63/183.11 tff(8242,plain,
% 290.63/183.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s2, s3)) | node10(c_e_h_2, c_m, s2, s3) | node11(c_e_h_2, c_m, s2, s3)),
% 290.63/183.11 inference(modus_ponens,[status(thm)],[8241, 8240])).
% 290.63/183.11 tff(8243,plain,
% 290.63/183.11 (node10(c_e_h_2, c_m, s2, s3) | node11(c_e_h_2, c_m, s2, s3)),
% 290.63/183.11 inference(unit_resolution,[status(thm)],[8242, 5002, 318])).
% 290.63/183.11 tff(8244,plain,
% 290.63/183.11 (node10(c_e_h_2, c_m, s2, s3)),
% 290.63/183.11 inference(unit_resolution,[status(thm)],[8243, 8239])).
% 290.63/183.11 tff(8245,assumption,(m_c_h_element_v_out(c_e_h_2, c_e, s1)), introduced(assumption)).
% 290.63/183.11 tff(8246,assumption,(node18(c_e_h_2, c_e, s0, s1)), introduced(assumption)).
% 290.63/183.11 tff(8247,plain,
% 290.63/183.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_e, s0) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1)) | (~node18(c_e_h_2, c_e, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_e, s0) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1)) | (~node18(c_e_h_2, c_e, s0, s1)))),
% 290.63/183.11 inference(rewrite,[status(thm)],[])).
% 290.63/183.11 tff(8248,plain,
% 290.63/183.11 (((~m_c_h_element_v_out(c_e_h_2, c_e, s1)) | m_c_h_element_v_out(c_e_h_2, c_e, s0) | (~node18(c_e_h_2, c_e, s0, s1))) <=> (m_c_h_element_v_out(c_e_h_2, c_e, s0) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1)) | (~node18(c_e_h_2, c_e, s0, s1)))),
% 290.63/183.11 inference(rewrite,[status(thm)],[])).
% 290.63/183.11 tff(8249,plain,
% 290.63/183.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s1)) | m_c_h_element_v_out(c_e_h_2, c_e, s0) | (~node18(c_e_h_2, c_e, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_e, s0) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1)) | (~node18(c_e_h_2, c_e, s0, s1))))),
% 290.63/183.11 inference(monotonicity,[status(thm)],[8248])).
% 290.63/183.11 tff(8250,plain,
% 290.63/183.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s1)) | m_c_h_element_v_out(c_e_h_2, c_e, s0) | (~node18(c_e_h_2, c_e, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_e, s0) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1)) | (~node18(c_e_h_2, c_e, s0, s1)))),
% 290.63/183.11 inference(transitivity,[status(thm)],[8249, 8247])).
% 290.63/183.11 tff(8251,plain,
% 290.63/183.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s1)) | m_c_h_element_v_out(c_e_h_2, c_e, s0) | (~node18(c_e_h_2, c_e, s0, s1)))),
% 290.63/183.11 inference(quant_inst,[status(thm)],[])).
% 290.63/183.11 tff(8252,plain,
% 290.63/183.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_e, s0) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1)) | (~node18(c_e_h_2, c_e, s0, s1))),
% 290.63/183.11 inference(modus_ponens,[status(thm)],[8251, 8250])).
% 290.63/183.11 tff(8253,plain,
% 290.63/183.11 ($false),
% 290.63/183.11 inference(unit_resolution,[status(thm)],[8252, 753, 8245, 7849, 8246])).
% 290.63/183.11 tff(8254,plain,((~node18(c_e_h_2, c_e, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1))), inference(lemma,lemma(discharge,[]))).
% 290.63/183.11 tff(8255,plain,
% 290.63/183.11 (~node18(c_e_h_2, c_e, s0, s1)),
% 290.63/183.11 inference(unit_resolution,[status(thm)],[8254, 8245])).
% 290.63/183.11 tff(8256,plain,
% 290.63/183.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s0, s1)) | node19(c_e_h_2, c_e, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s0, s1)) | node19(c_e_h_2, c_e, s0, s1))),
% 290.63/183.11 inference(rewrite,[status(thm)],[])).
% 290.63/183.11 tff(8257,plain,
% 290.63/183.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s0, s1)) | node19(c_e_h_2, c_e, s0, s1))),
% 290.63/183.11 inference(quant_inst,[status(thm)],[])).
% 290.63/183.11 tff(8258,plain,
% 290.63/183.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s0, s1)) | node19(c_e_h_2, c_e, s0, s1)),
% 290.63/183.11 inference(modus_ponens,[status(thm)],[8257, 8256])).
% 290.63/183.11 tff(8259,plain,
% 290.63/183.11 (node19(c_e_h_2, c_e, s0, s1)),
% 290.63/183.11 inference(unit_resolution,[status(thm)],[8258, 190, 72])).
% 290.63/183.11 tff(8260,plain,
% 290.63/183.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_2, c_e, s0, s1) | (~node19(c_e_h_2, c_e, s0, s1)) | node17(c_e_h_2, c_e, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_2, c_e, s0, s1) | (~node19(c_e_h_2, c_e, s0, s1)) | node17(c_e_h_2, c_e, s0))),
% 290.63/183.12 inference(rewrite,[status(thm)],[])).
% 290.63/183.12 tff(8261,plain,
% 290.63/183.12 ((node17(c_e_h_2, c_e, s0) | node18(c_e_h_2, c_e, s0, s1) | (~node19(c_e_h_2, c_e, s0, s1))) <=> (node18(c_e_h_2, c_e, s0, s1) | (~node19(c_e_h_2, c_e, s0, s1)) | node17(c_e_h_2, c_e, s0))),
% 290.63/183.12 inference(rewrite,[status(thm)],[])).
% 290.63/183.12 tff(8262,plain,
% 290.63/183.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s0) | node18(c_e_h_2, c_e, s0, s1) | (~node19(c_e_h_2, c_e, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_2, c_e, s0, s1) | (~node19(c_e_h_2, c_e, s0, s1)) | node17(c_e_h_2, c_e, s0)))),
% 290.63/183.12 inference(monotonicity,[status(thm)],[8261])).
% 290.63/183.12 tff(8263,plain,
% 290.63/183.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s0) | node18(c_e_h_2, c_e, s0, s1) | (~node19(c_e_h_2, c_e, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_2, c_e, s0, s1) | (~node19(c_e_h_2, c_e, s0, s1)) | node17(c_e_h_2, c_e, s0))),
% 290.63/183.12 inference(transitivity,[status(thm)],[8262, 8260])).
% 290.63/183.12 tff(8264,plain,
% 290.63/183.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s0) | node18(c_e_h_2, c_e, s0, s1) | (~node19(c_e_h_2, c_e, s0, s1)))),
% 290.63/183.12 inference(quant_inst,[status(thm)],[])).
% 290.63/183.12 tff(8265,plain,
% 290.63/183.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_2, c_e, s0, s1) | (~node19(c_e_h_2, c_e, s0, s1)) | node17(c_e_h_2, c_e, s0)),
% 290.63/183.12 inference(modus_ponens,[status(thm)],[8264, 8263])).
% 290.63/183.12 tff(8266,plain,
% 290.63/183.12 (node18(c_e_h_2, c_e, s0, s1) | node17(c_e_h_2, c_e, s0)),
% 290.63/183.12 inference(unit_resolution,[status(thm)],[8265, 776, 8259])).
% 290.63/183.12 tff(8267,plain,
% 290.63/183.12 (node17(c_e_h_2, c_e, s0)),
% 290.63/183.12 inference(unit_resolution,[status(thm)],[8266, 8255])).
% 290.63/183.12 tff(8268,plain,
% 290.63/183.12 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s0)) | m_and_h_gate_v_out(c_e_h_2, c_c, s0))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s0)) | m_and_h_gate_v_out(c_e_h_2, c_c, s0))),
% 290.63/183.12 inference(rewrite,[status(thm)],[])).
% 290.63/183.12 tff(8269,plain,
% 290.63/183.12 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s0)) | m_and_h_gate_v_out(c_e_h_2, c_c, s0))),
% 290.63/183.12 inference(quant_inst,[status(thm)],[])).
% 290.63/183.12 tff(8270,plain,
% 290.63/183.12 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s0)) | m_and_h_gate_v_out(c_e_h_2, c_c, s0)),
% 290.63/183.12 inference(modus_ponens,[status(thm)],[8269, 8268])).
% 290.63/183.12 tff(8271,plain,
% 290.63/183.12 (~m_c_h_element_v_in1(c_e_h_2, c_e, s0)),
% 290.63/183.12 inference(unit_resolution,[status(thm)],[8270, 131, 4113])).
% 290.63/183.12 tff(8272,plain,
% 290.63/183.12 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_e, s0)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s0)) | m_c_h_element_v_in1(c_e_h_2, c_e, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_e, s0)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s0)) | m_c_h_element_v_in1(c_e_h_2, c_e, s0))),
% 290.63/183.12 inference(rewrite,[status(thm)],[])).
% 290.63/183.12 tff(8273,plain,
% 290.63/183.12 ((m_c_h_element_v_in1(c_e_h_2, c_e, s0) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s0)) | (~node17(c_e_h_2, c_e, s0))) <=> ((~node17(c_e_h_2, c_e, s0)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s0)) | m_c_h_element_v_in1(c_e_h_2, c_e, s0))),
% 290.63/183.12 inference(rewrite,[status(thm)],[])).
% 290.63/183.12 tff(8274,plain,
% 290.63/183.12 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s0) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s0)) | (~node17(c_e_h_2, c_e, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_e, s0)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s0)) | m_c_h_element_v_in1(c_e_h_2, c_e, s0)))),
% 290.63/183.12 inference(monotonicity,[status(thm)],[8273])).
% 290.63/183.12 tff(8275,plain,
% 290.63/183.12 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s0) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s0)) | (~node17(c_e_h_2, c_e, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_e, s0)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s0)) | m_c_h_element_v_in1(c_e_h_2, c_e, s0))),
% 290.63/183.12 inference(transitivity,[status(thm)],[8274, 8272])).
% 290.63/183.12 tff(8276,plain,
% 290.63/183.12 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s0) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s0)) | (~node17(c_e_h_2, c_e, s0)))),
% 290.63/183.12 inference(quant_inst,[status(thm)],[])).
% 290.63/183.12 tff(8277,plain,
% 290.63/183.12 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_e, s0)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s0)) | m_c_h_element_v_in1(c_e_h_2, c_e, s0)),
% 290.63/183.12 inference(modus_ponens,[status(thm)],[8276, 8275])).
% 290.63/183.12 tff(8278,plain,
% 290.63/183.12 ((~node17(c_e_h_2, c_e, s0)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s0))),
% 290.63/183.12 inference(unit_resolution,[status(thm)],[8277, 859, 8271])).
% 290.63/183.12 tff(8279,plain,
% 290.63/183.12 (~m_c_h_element_v_in2(c_e_h_2, c_e, s0)),
% 290.63/183.12 inference(unit_resolution,[status(thm)],[8278, 8267])).
% 290.63/183.12 tff(8280,plain,
% 290.63/183.12 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_e, s0)) | m_c_h_element_v_in1(c_e_h_2, c_e, s0) | m_c_h_element_v_in2(c_e_h_2, c_e, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s0)) | m_c_h_element_v_in1(c_e_h_2, c_e, s0) | m_c_h_element_v_in2(c_e_h_2, c_e, s0))),
% 290.63/183.12 inference(rewrite,[status(thm)],[])).
% 290.63/183.12 tff(8281,plain,
% 290.63/183.12 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_e, s0)) | m_c_h_element_v_in1(c_e_h_2, c_e, s0) | m_c_h_element_v_in2(c_e_h_2, c_e, s0))),
% 290.63/183.12 inference(quant_inst,[status(thm)],[])).
% 290.63/183.12 tff(8282,plain,
% 290.63/183.12 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s0)) | m_c_h_element_v_in1(c_e_h_2, c_e, s0) | m_c_h_element_v_in2(c_e_h_2, c_e, s0)),
% 290.63/183.12 inference(modus_ponens,[status(thm)],[8281, 8280])).
% 290.63/183.12 tff(8283,plain,
% 290.63/183.12 ((~node16(c_e_h_2, c_e, s0)) | m_c_h_element_v_in2(c_e_h_2, c_e, s0)),
% 290.63/183.12 inference(unit_resolution,[status(thm)],[8282, 178, 8271])).
% 290.63/183.12 tff(8284,plain,
% 290.63/183.12 (~node16(c_e_h_2, c_e, s0)),
% 290.63/183.12 inference(unit_resolution,[status(thm)],[8283, 8279])).
% 290.63/183.12 tff(8285,assumption,(node14(c_e_h_2, c_e, s0, s1)), introduced(assumption)).
% 290.63/183.12 tff(8286,plain,
% 290.63/183.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s1)) | m_c_h_element_v_in1(c_e_h_2, c_e, s0) | (~node14(c_e_h_2, c_e, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1)) | m_c_h_element_v_in1(c_e_h_2, c_e, s0) | (~node14(c_e_h_2, c_e, s0, s1)))),
% 290.63/183.12 inference(rewrite,[status(thm)],[])).
% 290.63/183.12 tff(8287,plain,
% 290.63/183.12 (((~node14(c_e_h_2, c_e, s0, s1)) | m_c_h_element_v_in1(c_e_h_2, c_e, s0) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1))) <=> ((~m_c_h_element_v_out(c_e_h_2, c_e, s1)) | m_c_h_element_v_in1(c_e_h_2, c_e, s0) | (~node14(c_e_h_2, c_e, s0, s1)))),
% 290.63/183.12 inference(rewrite,[status(thm)],[])).
% 290.63/183.12 tff(8288,plain,
% 290.63/183.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s0, s1)) | m_c_h_element_v_in1(c_e_h_2, c_e, s0) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s1)) | m_c_h_element_v_in1(c_e_h_2, c_e, s0) | (~node14(c_e_h_2, c_e, s0, s1))))),
% 290.63/183.12 inference(monotonicity,[status(thm)],[8287])).
% 290.63/183.12 tff(8289,plain,
% 290.63/183.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s0, s1)) | m_c_h_element_v_in1(c_e_h_2, c_e, s0) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1)) | m_c_h_element_v_in1(c_e_h_2, c_e, s0) | (~node14(c_e_h_2, c_e, s0, s1)))),
% 290.63/183.12 inference(transitivity,[status(thm)],[8288, 8286])).
% 290.63/183.12 tff(8290,plain,
% 290.63/183.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s0, s1)) | m_c_h_element_v_in1(c_e_h_2, c_e, s0) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1)))),
% 290.63/183.12 inference(quant_inst,[status(thm)],[])).
% 290.63/183.12 tff(8291,plain,
% 290.63/183.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1)) | m_c_h_element_v_in1(c_e_h_2, c_e, s0) | (~node14(c_e_h_2, c_e, s0, s1))),
% 290.63/183.12 inference(modus_ponens,[status(thm)],[8290, 8289])).
% 290.63/183.12 tff(8292,plain,
% 290.63/183.12 ($false),
% 290.63/183.12 inference(unit_resolution,[status(thm)],[8291, 223, 8245, 8285, 8271])).
% 290.63/183.12 tff(8293,plain,((~node14(c_e_h_2, c_e, s0, s1)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1))), inference(lemma,lemma(discharge,[]))).
% 290.63/183.12 tff(8294,plain,
% 290.63/183.12 (~node14(c_e_h_2, c_e, s0, s1)),
% 290.63/183.12 inference(unit_resolution,[status(thm)],[8293, 8245])).
% 290.63/183.12 tff(8295,plain,
% 290.63/183.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s0) | node14(c_e_h_2, c_e, s0, s1) | node15(c_e_h_2, c_e, s0, s1) | (~node19(c_e_h_2, c_e, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_e, s0) | node14(c_e_h_2, c_e, s0, s1) | node15(c_e_h_2, c_e, s0, s1) | (~node19(c_e_h_2, c_e, s0, s1)))),
% 290.63/183.12 inference(rewrite,[status(thm)],[])).
% 290.63/183.12 tff(8296,plain,
% 290.63/183.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s0) | node14(c_e_h_2, c_e, s0, s1) | node15(c_e_h_2, c_e, s0, s1) | (~node19(c_e_h_2, c_e, s0, s1)))),
% 290.63/183.12 inference(quant_inst,[status(thm)],[])).
% 290.63/183.12 tff(8297,plain,
% 290.63/183.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_e, s0) | node14(c_e_h_2, c_e, s0, s1) | node15(c_e_h_2, c_e, s0, s1) | (~node19(c_e_h_2, c_e, s0, s1))),
% 290.63/183.12 inference(modus_ponens,[status(thm)],[8296, 8295])).
% 290.63/183.12 tff(8298,plain,
% 290.63/183.12 (node16(c_e_h_2, c_e, s0) | node14(c_e_h_2, c_e, s0, s1) | node15(c_e_h_2, c_e, s0, s1)),
% 290.63/183.12 inference(unit_resolution,[status(thm)],[8297, 204, 8259])).
% 290.63/183.12 tff(8299,plain,
% 290.63/183.12 (node15(c_e_h_2, c_e, s0, s1)),
% 290.63/183.12 inference(unit_resolution,[status(thm)],[8298, 8294, 8284])).
% 290.63/183.12 tff(8300,plain,
% 290.63/183.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s1)) | (~node15(c_e_h_2, c_e, s0, s1)) | m_c_h_element_v_out(c_e_h_2, c_e, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1)) | (~node15(c_e_h_2, c_e, s0, s1)) | m_c_h_element_v_out(c_e_h_2, c_e, s0))),
% 290.63/183.13 inference(rewrite,[status(thm)],[])).
% 290.63/183.13 tff(8301,plain,
% 290.63/183.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s1)) | (~node15(c_e_h_2, c_e, s0, s1)) | m_c_h_element_v_out(c_e_h_2, c_e, s0))),
% 290.63/183.13 inference(quant_inst,[status(thm)],[])).
% 290.63/183.13 tff(8302,plain,
% 290.63/183.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s1)) | (~node15(c_e_h_2, c_e, s0, s1)) | m_c_h_element_v_out(c_e_h_2, c_e, s0)),
% 290.63/183.13 inference(modus_ponens,[status(thm)],[8301, 8300])).
% 290.63/183.13 tff(8303,plain,
% 290.63/183.13 ($false),
% 290.63/183.13 inference(unit_resolution,[status(thm)],[8302, 147, 8245, 7849, 8299])).
% 290.63/183.13 tff(8304,plain,(~m_c_h_element_v_out(c_e_h_2, c_e, s1)), inference(lemma,lemma(discharge,[]))).
% 290.63/183.13 tff(8305,plain,
% 290.63/183.13 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1) | m_c_h_element_v_out(c_e_h_2, c_e, s1))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1) | m_c_h_element_v_out(c_e_h_2, c_e, s1))),
% 290.63/183.13 inference(rewrite,[status(thm)],[])).
% 290.63/183.13 tff(8306,plain,
% 290.63/183.13 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1) | m_c_h_element_v_out(c_e_h_2, c_e, s1))),
% 290.63/183.13 inference(quant_inst,[status(thm)],[])).
% 290.63/183.13 tff(8307,plain,
% 290.63/183.13 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1) | m_c_h_element_v_out(c_e_h_2, c_e, s1)),
% 290.63/183.13 inference(modus_ponens,[status(thm)],[8306, 8305])).
% 290.63/183.13 tff(8308,plain,
% 290.63/183.13 (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1) | m_c_h_element_v_out(c_e_h_2, c_e, s1)),
% 290.63/183.13 inference(unit_resolution,[status(thm)],[8307, 7856])).
% 290.63/183.13 tff(8309,plain,
% 290.63/183.13 (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1)),
% 290.63/183.13 inference(unit_resolution,[status(thm)],[8308, 8304])).
% 290.63/183.13 tff(8310,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2)), introduced(assumption)).
% 290.63/183.13 tff(8311,assumption,(node11(c_e_h_2, c_n, s1, s2)), introduced(assumption)).
% 290.63/183.13 tff(8312,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1)), introduced(assumption)).
% 290.63/183.13 tff(8313,plain,
% 290.63/183.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2) | (~node11(c_e_h_2, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2) | (~node11(c_e_h_2, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1)))),
% 290.63/183.13 inference(rewrite,[status(thm)],[])).
% 290.63/183.13 tff(8314,plain,
% 290.63/183.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2) | (~node11(c_e_h_2, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1)))),
% 290.63/183.13 inference(quant_inst,[status(thm)],[])).
% 290.63/183.13 tff(8315,plain,
% 290.63/183.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2) | (~node11(c_e_h_2, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1))),
% 290.63/183.13 inference(modus_ponens,[status(thm)],[8314, 8313])).
% 290.63/183.13 tff(8316,plain,
% 290.63/183.13 ($false),
% 290.63/183.13 inference(unit_resolution,[status(thm)],[8315, 5742, 8310, 8312, 8311])).
% 290.63/183.13 tff(8317,plain,((~node11(c_e_h_2, c_n, s1, s2)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s1))), inference(lemma,lemma(discharge,[]))).
% 290.63/183.13 tff(8318,plain,
% 290.63/183.13 ((~node11(c_e_h_2, c_n, s1, s2)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2)),
% 290.63/183.13 inference(unit_resolution,[status(thm)],[8317, 7880])).
% 290.63/183.13 tff(8319,plain,
% 290.63/183.13 (~node11(c_e_h_2, c_n, s1, s2)),
% 290.63/183.13 inference(unit_resolution,[status(thm)],[8318, 8310])).
% 290.63/183.13 tff(8320,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1)), introduced(assumption)).
% 290.63/183.13 tff(8321,plain,
% 290.63/183.13 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1))),
% 290.63/183.13 inference(rewrite,[status(thm)],[])).
% 290.63/183.13 tff(8322,plain,
% 290.63/183.13 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1))),
% 290.63/183.13 inference(quant_inst,[status(thm)],[])).
% 290.63/183.13 tff(8323,plain,
% 290.63/183.13 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)),
% 290.63/183.13 inference(modus_ponens,[status(thm)],[8322, 8321])).
% 290.63/183.13 tff(8324,plain,
% 290.63/183.13 (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s1)),
% 290.63/183.13 inference(unit_resolution,[status(thm)],[8323, 7868])).
% 290.63/183.13 tff(8325,plain,
% 290.63/183.13 (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1)),
% 290.63/183.13 inference(unit_resolution,[status(thm)],[8324, 5022])).
% 290.63/183.13 tff(8326,assumption,(node10(c_e_h_2, c_n, s1, s2)), introduced(assumption)).
% 290.63/183.13 tff(8327,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1)), introduced(assumption)).
% 290.63/183.13 tff(8328,plain,
% 290.63/183.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1)) | (~node10(c_e_h_2, c_n, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1)) | (~node10(c_e_h_2, c_n, s1, s2)))),
% 290.63/183.13 inference(rewrite,[status(thm)],[])).
% 290.63/183.13 tff(8329,plain,
% 290.63/183.13 (((~node10(c_e_h_2, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2)) <=> (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1)) | (~node10(c_e_h_2, c_n, s1, s2)))),
% 290.63/183.13 inference(rewrite,[status(thm)],[])).
% 290.63/183.13 tff(8330,plain,
% 290.63/183.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1)) | (~node10(c_e_h_2, c_n, s1, s2))))),
% 290.63/183.13 inference(monotonicity,[status(thm)],[8329])).
% 290.63/183.13 tff(8331,plain,
% 290.63/183.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1)) | (~node10(c_e_h_2, c_n, s1, s2)))),
% 290.63/183.13 inference(transitivity,[status(thm)],[8330, 8328])).
% 290.63/183.13 tff(8332,plain,
% 290.63/183.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2))),
% 290.63/183.13 inference(quant_inst,[status(thm)],[])).
% 290.63/183.13 tff(8333,plain,
% 290.63/183.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1)) | (~node10(c_e_h_2, c_n, s1, s2))),
% 290.63/183.13 inference(modus_ponens,[status(thm)],[8332, 8331])).
% 290.63/183.13 tff(8334,plain,
% 290.63/183.13 ($false),
% 290.63/183.13 inference(unit_resolution,[status(thm)],[8333, 5718, 8320, 8310, 8327, 8326])).
% 290.63/183.13 tff(8335,plain,((~node10(c_e_h_2, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s1))), inference(lemma,lemma(discharge,[]))).
% 290.63/183.13 tff(8336,plain,
% 290.63/183.13 ((~node10(c_e_h_2, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2)),
% 290.63/183.13 inference(unit_resolution,[status(thm)],[8335, 8325])).
% 290.63/183.13 tff(8337,plain,
% 290.63/183.13 (~node10(c_e_h_2, c_n, s1, s2)),
% 290.63/183.13 inference(unit_resolution,[status(thm)],[8336, 8310, 8320])).
% 290.63/183.13 tff(8338,plain,
% 290.63/183.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s1, s2)) | node10(c_e_h_2, c_n, s1, s2) | node11(c_e_h_2, c_n, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s1, s2)) | node10(c_e_h_2, c_n, s1, s2) | node11(c_e_h_2, c_n, s1, s2))),
% 290.63/183.13 inference(rewrite,[status(thm)],[])).
% 290.63/183.13 tff(8339,plain,
% 290.63/183.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s1, s2)) | node10(c_e_h_2, c_n, s1, s2) | node11(c_e_h_2, c_n, s1, s2))),
% 290.63/183.13 inference(quant_inst,[status(thm)],[])).
% 290.63/183.13 tff(8340,plain,
% 290.63/183.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s1, s2)) | node10(c_e_h_2, c_n, s1, s2) | node11(c_e_h_2, c_n, s1, s2)),
% 290.63/183.13 inference(modus_ponens,[status(thm)],[8339, 8338])).
% 290.63/183.13 tff(8341,plain,
% 290.63/183.13 (node10(c_e_h_2, c_n, s1, s2) | node11(c_e_h_2, c_n, s1, s2)),
% 290.63/183.13 inference(unit_resolution,[status(thm)],[8340, 5002, 255])).
% 290.63/183.13 tff(8342,plain,
% 290.63/183.13 ($false),
% 290.63/183.13 inference(unit_resolution,[status(thm)],[8341, 8337, 8319])).
% 290.63/183.13 tff(8343,plain,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s1))), inference(lemma,lemma(discharge,[]))).
% 290.63/183.13 tff(8344,plain,
% 290.63/183.13 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2)),
% 290.63/183.13 inference(unit_resolution,[status(thm)],[8343, 8309])).
% 290.63/183.13 tff(8345,plain,
% 290.63/183.13 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2)))),
% 290.63/183.14 inference(rewrite,[status(thm)],[])).
% 290.63/183.14 tff(8346,plain,
% 290.63/183.14 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2)))),
% 290.63/183.14 inference(quant_inst,[status(thm)],[])).
% 290.63/183.14 tff(8347,plain,
% 290.63/183.14 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2))),
% 290.63/183.14 inference(modus_ponens,[status(thm)],[8346, 8345])).
% 290.63/183.14 tff(8348,plain,
% 290.63/183.14 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s2)),
% 290.63/183.14 inference(unit_resolution,[status(thm)],[8347, 4958, 8344])).
% 290.63/183.14 tff(8349,plain,
% 290.63/183.14 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s2)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s2)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s2))),
% 290.63/183.14 inference(rewrite,[status(thm)],[])).
% 290.63/183.14 tff(8350,plain,
% 290.63/183.14 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s2)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s2))),
% 290.63/183.14 inference(quant_inst,[status(thm)],[])).
% 290.63/183.14 tff(8351,plain,
% 290.63/183.14 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s2)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s2)),
% 290.63/183.14 inference(modus_ponens,[status(thm)],[8350, 8349])).
% 290.63/183.14 tff(8352,plain,
% 290.63/183.14 (~node9(c_e_h_2, c_m, s2)),
% 290.63/183.14 inference(unit_resolution,[status(thm)],[8351, 4972, 8348])).
% 290.63/183.14 tff(8353,plain,
% 290.63/183.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)) | node9(c_e_h_2, c_m, s2) | (~node10(c_e_h_2, c_m, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)) | node9(c_e_h_2, c_m, s2) | (~node10(c_e_h_2, c_m, s2, s3)))),
% 290.63/183.14 inference(rewrite,[status(thm)],[])).
% 290.63/183.14 tff(8354,plain,
% 290.63/183.14 ((node9(c_e_h_2, c_m, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)) | (~node10(c_e_h_2, c_m, s2, s3))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)) | node9(c_e_h_2, c_m, s2) | (~node10(c_e_h_2, c_m, s2, s3)))),
% 290.63/183.14 inference(rewrite,[status(thm)],[])).
% 290.63/183.14 tff(8355,plain,
% 290.63/183.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)) | (~node10(c_e_h_2, c_m, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)) | node9(c_e_h_2, c_m, s2) | (~node10(c_e_h_2, c_m, s2, s3))))),
% 290.63/183.14 inference(monotonicity,[status(thm)],[8354])).
% 290.63/183.14 tff(8356,plain,
% 290.63/183.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)) | (~node10(c_e_h_2, c_m, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)) | node9(c_e_h_2, c_m, s2) | (~node10(c_e_h_2, c_m, s2, s3)))),
% 290.63/183.14 inference(transitivity,[status(thm)],[8355, 8353])).
% 290.63/183.14 tff(8357,plain,
% 290.63/183.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)) | (~node10(c_e_h_2, c_m, s2, s3)))),
% 290.63/183.14 inference(quant_inst,[status(thm)],[])).
% 290.63/183.14 tff(8358,plain,
% 290.63/183.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)) | node9(c_e_h_2, c_m, s2) | (~node10(c_e_h_2, c_m, s2, s3))),
% 290.63/183.14 inference(modus_ponens,[status(thm)],[8357, 8356])).
% 290.63/183.14 tff(8359,plain,
% 290.63/183.14 ($false),
% 290.63/183.14 inference(unit_resolution,[status(thm)],[8358, 4986, 8352, 8244, 8232])).
% 290.63/183.14 tff(8360,plain,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)), inference(lemma,lemma(discharge,[]))).
% 290.63/183.14 tff(8361,plain,
% 290.63/183.14 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_l, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_l, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3))),
% 290.63/183.14 inference(rewrite,[status(thm)],[])).
% 290.63/183.14 tff(8362,plain,
% 290.63/183.14 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_l, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3))),
% 290.63/183.14 inference(quant_inst,[status(thm)],[])).
% 290.63/183.14 tff(8363,plain,
% 290.63/183.14 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_l, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)),
% 290.63/183.14 inference(modus_ponens,[status(thm)],[8362, 8361])).
% 290.63/183.14 tff(8364,plain,
% 290.63/183.14 (~m_and_h_gate_v_in2(c_e_h_2, c_l, s3)),
% 290.63/183.14 inference(unit_resolution,[status(thm)],[8363, 4549, 8360])).
% 290.63/183.14 tff(8365,plain,
% 290.63/183.14 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_l, s3)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_l, s3)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s3))),
% 290.63/183.14 inference(rewrite,[status(thm)],[])).
% 290.63/183.14 tff(8366,plain,
% 290.63/183.14 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_l, s3)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s3))),
% 290.63/183.14 inference(quant_inst,[status(thm)],[])).
% 290.63/183.14 tff(8367,plain,
% 290.63/183.14 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_l, s3)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s3)),
% 290.63/183.14 inference(modus_ponens,[status(thm)],[8366, 8365])).
% 290.63/183.14 tff(8368,plain,
% 290.63/183.14 (~node20(c_e_h_2, c_l, s3)),
% 290.63/183.14 inference(unit_resolution,[status(thm)],[8367, 4563, 8364])).
% 290.63/183.14 tff(8369,assumption,(~node20(c_e_h_2, c_l, s3)), introduced(assumption)).
% 290.63/183.14 tff(8370,assumption,(node21(c_e_h_2, c_l, s3, s4)), introduced(assumption)).
% 290.63/183.14 tff(8371,plain,
% 290.63/183.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_l, s3) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s4)) | (~node21(c_e_h_2, c_l, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_l, s3) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s4)) | (~node21(c_e_h_2, c_l, s3, s4)))),
% 290.63/183.14 inference(rewrite,[status(thm)],[])).
% 290.63/183.14 tff(8372,plain,
% 290.63/183.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_l, s3) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s4)) | (~node21(c_e_h_2, c_l, s3, s4)))),
% 290.63/183.14 inference(quant_inst,[status(thm)],[])).
% 290.63/183.14 tff(8373,plain,
% 290.63/183.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_l, s3) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s4)) | (~node21(c_e_h_2, c_l, s3, s4))),
% 290.63/183.14 inference(modus_ponens,[status(thm)],[8372, 8371])).
% 290.63/183.14 tff(8374,plain,
% 290.63/183.14 ($false),
% 290.63/183.14 inference(unit_resolution,[status(thm)],[8373, 52, 8370, 8369, 8231])).
% 290.63/183.14 tff(8375,plain,((~node21(c_e_h_2, c_l, s3, s4)) | node20(c_e_h_2, c_l, s3) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s4))), inference(lemma,lemma(discharge,[]))).
% 290.63/183.14 tff(8376,plain,
% 290.63/183.14 ((~node21(c_e_h_2, c_l, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s4))),
% 290.63/183.14 inference(unit_resolution,[status(thm)],[8375, 8368])).
% 290.63/183.14 tff(8377,plain,
% 290.63/183.14 (~node21(c_e_h_2, c_l, s3, s4)),
% 290.63/183.14 inference(unit_resolution,[status(thm)],[8376, 8231])).
% 290.63/183.14 tff(8378,plain,
% 290.63/183.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_2, c_l, s3, s4) | node22(c_e_h_2, c_l, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_2, c_l, s3, s4) | node22(c_e_h_2, c_l, s3, s4))),
% 290.63/183.14 inference(rewrite,[status(thm)],[])).
% 290.63/183.14 tff(8379,plain,
% 290.63/183.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_2, c_l, s3, s4) | node22(c_e_h_2, c_l, s3, s4))),
% 290.63/183.14 inference(quant_inst,[status(thm)],[])).
% 290.63/183.14 tff(8380,plain,
% 290.63/183.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_2, c_l, s3, s4) | node22(c_e_h_2, c_l, s3, s4)),
% 290.63/183.14 inference(modus_ponens,[status(thm)],[8379, 8378])).
% 290.63/183.14 tff(8381,plain,
% 290.63/183.14 (node21(c_e_h_2, c_l, s3, s4) | node22(c_e_h_2, c_l, s3, s4)),
% 290.63/183.14 inference(unit_resolution,[status(thm)],[8380, 82, 531])).
% 290.63/183.14 tff(8382,plain,
% 290.63/183.14 (node22(c_e_h_2, c_l, s3, s4)),
% 290.63/183.14 inference(unit_resolution,[status(thm)],[8381, 8377])).
% 290.63/183.14 tff(8383,plain,
% 290.63/183.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s4)) | (~node22(c_e_h_2, c_l, s3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_l, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s4)) | (~node22(c_e_h_2, c_l, s3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_l, s3))),
% 290.63/183.14 inference(rewrite,[status(thm)],[])).
% 290.63/183.14 tff(8384,plain,
% 290.63/183.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s4)) | (~node22(c_e_h_2, c_l, s3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_l, s3))),
% 290.63/183.14 inference(quant_inst,[status(thm)],[])).
% 290.63/183.14 tff(8385,plain,
% 290.63/183.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s4)) | (~node22(c_e_h_2, c_l, s3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_l, s3)),
% 290.63/183.14 inference(modus_ponens,[status(thm)],[8384, 8383])).
% 290.63/183.14 tff(8386,plain,
% 290.63/183.14 ($false),
% 290.63/183.14 inference(unit_resolution,[status(thm)],[8385, 108, 8382, 8231, 7939])).
% 290.63/183.14 tff(8387,plain,((~m_and_h_gate_v_out(c_e_h_2, c_l, s4)) | m_and_h_gate_v_out(c_e_h_2, c_l, s3)), inference(lemma,lemma(discharge,[]))).
% 290.63/183.14 tff(8388,plain,
% 290.63/183.14 (~m_and_h_gate_v_out(c_e_h_2, c_l, s4)),
% 290.63/183.14 inference(unit_resolution,[status(thm)],[8387, 7937])).
% 290.63/183.14 tff(8389,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_l, s4)), introduced(assumption)).
% 290.63/183.14 tff(8390,assumption,(m_or_h_gate_v_in1(c_e_h_2, c_j, s4)), introduced(assumption)).
% 290.63/183.14 tff(8391,plain,
% 290.63/183.14 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_2, c_j, s4)) | m_and_h_gate_v_out(c_e_h_2, c_l, s4))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_j, s4)) | m_and_h_gate_v_out(c_e_h_2, c_l, s4))),
% 290.63/183.14 inference(rewrite,[status(thm)],[])).
% 290.63/183.14 tff(8392,plain,
% 290.63/183.14 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_2, c_j, s4)) | m_and_h_gate_v_out(c_e_h_2, c_l, s4))),
% 290.63/183.15 inference(quant_inst,[status(thm)],[])).
% 290.63/183.15 tff(8393,plain,
% 290.63/183.15 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_j, s4)) | m_and_h_gate_v_out(c_e_h_2, c_l, s4)),
% 290.63/183.15 inference(modus_ponens,[status(thm)],[8392, 8391])).
% 290.63/183.15 tff(8394,plain,
% 290.63/183.15 ($false),
% 290.63/183.15 inference(unit_resolution,[status(thm)],[8393, 1100, 8390, 8389])).
% 290.63/183.15 tff(8395,plain,((~m_or_h_gate_v_in1(c_e_h_2, c_j, s4)) | m_and_h_gate_v_out(c_e_h_2, c_l, s4)), inference(lemma,lemma(discharge,[]))).
% 290.63/183.15 tff(8396,plain,
% 290.63/183.15 (~m_or_h_gate_v_in1(c_e_h_2, c_j, s4)),
% 290.63/183.15 inference(unit_resolution,[status(thm)],[8395, 8388])).
% 290.63/183.15 tff(8397,assumption,(m_c_h_element_v_out(c_e_h_1, c_f, s3)), introduced(assumption)).
% 290.63/183.15 tff(8398,assumption,(node18(c_e_h_1, c_f, s2, s3)), introduced(assumption)).
% 290.63/183.15 tff(8399,plain,
% 290.63/183.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s3)) | m_c_h_element_v_out(c_e_h_1, c_f, s2) | (~node18(c_e_h_1, c_f, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s3)) | m_c_h_element_v_out(c_e_h_1, c_f, s2) | (~node18(c_e_h_1, c_f, s2, s3)))),
% 290.63/183.15 inference(rewrite,[status(thm)],[])).
% 290.63/183.15 tff(8400,plain,
% 290.63/183.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s3)) | m_c_h_element_v_out(c_e_h_1, c_f, s2) | (~node18(c_e_h_1, c_f, s2, s3)))),
% 290.63/183.15 inference(quant_inst,[status(thm)],[])).
% 290.63/183.15 tff(8401,plain,
% 290.63/183.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s3)) | m_c_h_element_v_out(c_e_h_1, c_f, s2) | (~node18(c_e_h_1, c_f, s2, s3))),
% 290.63/183.15 inference(modus_ponens,[status(thm)],[8400, 8399])).
% 290.63/183.15 tff(8402,plain,
% 290.63/183.15 ($false),
% 290.63/183.15 inference(unit_resolution,[status(thm)],[8401, 753, 8040, 8397, 8398])).
% 290.63/183.15 tff(8403,plain,((~node18(c_e_h_1, c_f, s2, s3)) | m_c_h_element_v_out(c_e_h_1, c_f, s2) | (~m_c_h_element_v_out(c_e_h_1, c_f, s3))), inference(lemma,lemma(discharge,[]))).
% 290.63/183.15 tff(8404,plain,
% 290.63/183.15 (~node18(c_e_h_1, c_f, s2, s3)),
% 290.63/183.15 inference(unit_resolution,[status(thm)],[8403, 8397, 8040])).
% 290.63/183.15 tff(8405,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_f, s2)), introduced(assumption)).
% 290.63/183.15 tff(8406,assumption,(m_c_h_element_v_out(c_e_h_1, c_h, s1)), introduced(assumption)).
% 290.63/183.15 tff(8407,assumption,(node15(c_e_h_1, c_h, s0, s1)), introduced(assumption)).
% 290.63/183.15 tff(8408,plain,
% 290.63/183.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s1)) | (~node15(c_e_h_1, c_h, s0, s1)) | m_c_h_element_v_out(c_e_h_1, c_h, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s1)) | (~node15(c_e_h_1, c_h, s0, s1)) | m_c_h_element_v_out(c_e_h_1, c_h, s0))),
% 290.63/183.15 inference(rewrite,[status(thm)],[])).
% 290.63/183.15 tff(8409,plain,
% 290.63/183.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s1)) | (~node15(c_e_h_1, c_h, s0, s1)) | m_c_h_element_v_out(c_e_h_1, c_h, s0))),
% 290.63/183.15 inference(quant_inst,[status(thm)],[])).
% 290.63/183.15 tff(8410,plain,
% 290.63/183.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s1)) | (~node15(c_e_h_1, c_h, s0, s1)) | m_c_h_element_v_out(c_e_h_1, c_h, s0)),
% 290.63/183.15 inference(modus_ponens,[status(thm)],[8409, 8408])).
% 290.63/183.15 tff(8411,plain,
% 290.63/183.15 ($false),
% 290.63/183.15 inference(unit_resolution,[status(thm)],[8410, 147, 8406, 7960, 8407])).
% 290.63/183.15 tff(8412,plain,((~node15(c_e_h_1, c_h, s0, s1)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s1))), inference(lemma,lemma(discharge,[]))).
% 290.63/183.15 tff(8413,plain,
% 290.63/183.15 (~node15(c_e_h_1, c_h, s0, s1)),
% 290.63/183.15 inference(unit_resolution,[status(thm)],[8412, 8406])).
% 290.63/183.15 tff(8414,plain,
% 290.63/183.15 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s0)) | m_or_h_gate_v_out(c_e_h_1, c_g, s0))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s0)) | m_or_h_gate_v_out(c_e_h_1, c_g, s0))),
% 290.63/183.15 inference(rewrite,[status(thm)],[])).
% 290.63/183.15 tff(8415,plain,
% 290.63/183.15 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s0)) | m_or_h_gate_v_out(c_e_h_1, c_g, s0))),
% 290.63/183.15 inference(quant_inst,[status(thm)],[])).
% 290.63/183.15 tff(8416,plain,
% 290.63/183.15 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s0)) | m_or_h_gate_v_out(c_e_h_1, c_g, s0)),
% 290.63/183.15 inference(modus_ponens,[status(thm)],[8415, 8414])).
% 290.63/183.15 tff(8417,plain,
% 290.63/183.15 (~m_c_h_element_v_in1(c_e_h_1, c_h, s0)),
% 290.63/183.15 inference(unit_resolution,[status(thm)],[8416, 811, 3133])).
% 290.63/183.15 tff(8418,assumption,(m_or_h_gate_v_out(c_e_h_1, c_j, s0)), introduced(assumption)).
% 290.63/183.15 tff(8419,plain,
% 290.63/183.15 ((~![I0: $i, I1: $i] : (~m_or_h_gate_v_out(I0, I1, s0))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s0))),
% 290.63/183.15 inference(quant_inst,[status(thm)],[])).
% 290.63/183.15 tff(8420,plain,
% 290.63/183.15 ($false),
% 290.63/183.15 inference(unit_resolution,[status(thm)],[8419, 801, 8418])).
% 290.63/183.15 tff(8421,plain,(~m_or_h_gate_v_out(c_e_h_1, c_j, s0)), inference(lemma,lemma(discharge,[]))).
% 290.63/183.15 tff(8422,plain,
% 290.63/183.15 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s0)) | m_or_h_gate_v_out(c_e_h_1, c_j, s0))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s0)) | m_or_h_gate_v_out(c_e_h_1, c_j, s0))),
% 290.63/183.15 inference(rewrite,[status(thm)],[])).
% 290.63/183.15 tff(8423,plain,
% 290.63/183.15 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s0)) | m_or_h_gate_v_out(c_e_h_1, c_j, s0))),
% 290.63/183.15 inference(quant_inst,[status(thm)],[])).
% 290.63/183.15 tff(8424,plain,
% 290.63/183.15 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s0)) | m_or_h_gate_v_out(c_e_h_1, c_j, s0)),
% 290.63/183.15 inference(modus_ponens,[status(thm)],[8423, 8422])).
% 290.63/183.15 tff(8425,plain,
% 290.63/183.15 (~m_c_h_element_v_in2(c_e_h_1, c_h, s0)),
% 290.63/183.15 inference(unit_resolution,[status(thm)],[8424, 1174, 8421])).
% 290.63/183.15 tff(8426,plain,
% 290.63/183.15 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s0)) | m_c_h_element_v_in1(c_e_h_1, c_h, s0) | m_c_h_element_v_in2(c_e_h_1, c_h, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s0)) | m_c_h_element_v_in1(c_e_h_1, c_h, s0) | m_c_h_element_v_in2(c_e_h_1, c_h, s0))),
% 290.63/183.15 inference(rewrite,[status(thm)],[])).
% 290.63/183.15 tff(8427,plain,
% 290.63/183.15 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s0)) | m_c_h_element_v_in1(c_e_h_1, c_h, s0) | m_c_h_element_v_in2(c_e_h_1, c_h, s0))),
% 290.63/183.15 inference(quant_inst,[status(thm)],[])).
% 290.63/183.15 tff(8428,plain,
% 290.63/183.15 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s0)) | m_c_h_element_v_in1(c_e_h_1, c_h, s0) | m_c_h_element_v_in2(c_e_h_1, c_h, s0)),
% 290.63/183.15 inference(modus_ponens,[status(thm)],[8427, 8426])).
% 290.63/183.15 tff(8429,plain,
% 290.63/183.15 ((~node16(c_e_h_1, c_h, s0)) | m_c_h_element_v_in1(c_e_h_1, c_h, s0)),
% 290.63/183.15 inference(unit_resolution,[status(thm)],[8428, 178, 8425])).
% 290.63/183.15 tff(8430,plain,
% 290.63/183.15 (~node16(c_e_h_1, c_h, s0)),
% 290.63/183.15 inference(unit_resolution,[status(thm)],[8429, 8417])).
% 290.63/183.16 tff(8431,plain,
% 290.63/183.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s0, s1)) | node19(c_e_h_1, c_h, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s0, s1)) | node19(c_e_h_1, c_h, s0, s1))),
% 290.63/183.16 inference(rewrite,[status(thm)],[])).
% 290.63/183.16 tff(8432,plain,
% 290.63/183.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s0, s1)) | node19(c_e_h_1, c_h, s0, s1))),
% 290.63/183.16 inference(quant_inst,[status(thm)],[])).
% 290.63/183.16 tff(8433,plain,
% 290.63/183.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s0, s1)) | node19(c_e_h_1, c_h, s0, s1)),
% 290.63/183.16 inference(modus_ponens,[status(thm)],[8432, 8431])).
% 290.63/183.16 tff(8434,plain,
% 290.63/183.16 (node19(c_e_h_1, c_h, s0, s1)),
% 290.63/183.16 inference(unit_resolution,[status(thm)],[8433, 190, 72])).
% 290.63/183.16 tff(8435,plain,
% 290.63/183.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_1, c_h, s0, s1) | node16(c_e_h_1, c_h, s0) | (~node19(c_e_h_1, c_h, s0, s1)) | node15(c_e_h_1, c_h, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_h, s0, s1) | node16(c_e_h_1, c_h, s0) | (~node19(c_e_h_1, c_h, s0, s1)) | node15(c_e_h_1, c_h, s0, s1))),
% 290.63/183.16 inference(rewrite,[status(thm)],[])).
% 290.63/183.16 tff(8436,plain,
% 290.63/183.16 ((node16(c_e_h_1, c_h, s0) | node14(c_e_h_1, c_h, s0, s1) | node15(c_e_h_1, c_h, s0, s1) | (~node19(c_e_h_1, c_h, s0, s1))) <=> (node14(c_e_h_1, c_h, s0, s1) | node16(c_e_h_1, c_h, s0) | (~node19(c_e_h_1, c_h, s0, s1)) | node15(c_e_h_1, c_h, s0, s1))),
% 290.63/183.16 inference(rewrite,[status(thm)],[])).
% 290.63/183.16 tff(8437,plain,
% 290.63/183.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s0) | node14(c_e_h_1, c_h, s0, s1) | node15(c_e_h_1, c_h, s0, s1) | (~node19(c_e_h_1, c_h, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_1, c_h, s0, s1) | node16(c_e_h_1, c_h, s0) | (~node19(c_e_h_1, c_h, s0, s1)) | node15(c_e_h_1, c_h, s0, s1)))),
% 290.63/183.16 inference(monotonicity,[status(thm)],[8436])).
% 290.63/183.16 tff(8438,plain,
% 290.63/183.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s0) | node14(c_e_h_1, c_h, s0, s1) | node15(c_e_h_1, c_h, s0, s1) | (~node19(c_e_h_1, c_h, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_h, s0, s1) | node16(c_e_h_1, c_h, s0) | (~node19(c_e_h_1, c_h, s0, s1)) | node15(c_e_h_1, c_h, s0, s1))),
% 290.63/183.16 inference(transitivity,[status(thm)],[8437, 8435])).
% 290.63/183.16 tff(8439,plain,
% 290.63/183.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s0) | node14(c_e_h_1, c_h, s0, s1) | node15(c_e_h_1, c_h, s0, s1) | (~node19(c_e_h_1, c_h, s0, s1)))),
% 290.63/183.16 inference(quant_inst,[status(thm)],[])).
% 290.63/183.16 tff(8440,plain,
% 290.63/183.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_h, s0, s1) | node16(c_e_h_1, c_h, s0) | (~node19(c_e_h_1, c_h, s0, s1)) | node15(c_e_h_1, c_h, s0, s1)),
% 290.63/183.16 inference(modus_ponens,[status(thm)],[8439, 8438])).
% 290.63/183.16 tff(8441,plain,
% 290.63/183.16 (node14(c_e_h_1, c_h, s0, s1) | node16(c_e_h_1, c_h, s0) | node15(c_e_h_1, c_h, s0, s1)),
% 290.63/183.16 inference(unit_resolution,[status(thm)],[8440, 204, 8434])).
% 290.63/183.16 tff(8442,plain,
% 290.63/183.16 (node14(c_e_h_1, c_h, s0, s1) | node15(c_e_h_1, c_h, s0, s1)),
% 290.63/183.16 inference(unit_resolution,[status(thm)],[8441, 8430])).
% 290.63/183.16 tff(8443,plain,
% 290.63/183.16 (node14(c_e_h_1, c_h, s0, s1)),
% 290.63/183.16 inference(unit_resolution,[status(thm)],[8442, 8413])).
% 290.63/183.16 tff(8444,plain,
% 290.63/183.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s1)) | m_c_h_element_v_in1(c_e_h_1, c_h, s0) | (~node14(c_e_h_1, c_h, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s1)) | m_c_h_element_v_in1(c_e_h_1, c_h, s0) | (~node14(c_e_h_1, c_h, s0, s1)))),
% 290.63/183.16 inference(rewrite,[status(thm)],[])).
% 290.63/183.16 tff(8445,plain,
% 290.63/183.16 (((~node14(c_e_h_1, c_h, s0, s1)) | m_c_h_element_v_in1(c_e_h_1, c_h, s0) | (~m_c_h_element_v_out(c_e_h_1, c_h, s1))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_h, s1)) | m_c_h_element_v_in1(c_e_h_1, c_h, s0) | (~node14(c_e_h_1, c_h, s0, s1)))),
% 290.63/183.16 inference(rewrite,[status(thm)],[])).
% 290.63/183.16 tff(8446,plain,
% 290.63/183.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s0, s1)) | m_c_h_element_v_in1(c_e_h_1, c_h, s0) | (~m_c_h_element_v_out(c_e_h_1, c_h, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s1)) | m_c_h_element_v_in1(c_e_h_1, c_h, s0) | (~node14(c_e_h_1, c_h, s0, s1))))),
% 290.63/183.16 inference(monotonicity,[status(thm)],[8445])).
% 290.63/183.16 tff(8447,plain,
% 290.63/183.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s0, s1)) | m_c_h_element_v_in1(c_e_h_1, c_h, s0) | (~m_c_h_element_v_out(c_e_h_1, c_h, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s1)) | m_c_h_element_v_in1(c_e_h_1, c_h, s0) | (~node14(c_e_h_1, c_h, s0, s1)))),
% 290.63/183.16 inference(transitivity,[status(thm)],[8446, 8444])).
% 290.63/183.16 tff(8448,plain,
% 290.63/183.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s0, s1)) | m_c_h_element_v_in1(c_e_h_1, c_h, s0) | (~m_c_h_element_v_out(c_e_h_1, c_h, s1)))),
% 290.63/183.16 inference(quant_inst,[status(thm)],[])).
% 290.63/183.16 tff(8449,plain,
% 290.63/183.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s1)) | m_c_h_element_v_in1(c_e_h_1, c_h, s0) | (~node14(c_e_h_1, c_h, s0, s1))),
% 290.63/183.16 inference(modus_ponens,[status(thm)],[8448, 8447])).
% 290.63/183.16 tff(8450,plain,
% 290.63/183.16 ($false),
% 290.63/183.16 inference(unit_resolution,[status(thm)],[8449, 223, 8406, 8417, 8443])).
% 290.63/183.16 tff(8451,plain,(~m_c_h_element_v_out(c_e_h_1, c_h, s1)), inference(lemma,lemma(discharge,[]))).
% 290.63/183.16 tff(8452,plain,
% 290.63/183.16 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s1)) | m_c_h_element_v_out(c_e_h_1, c_h, s1))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s1)) | m_c_h_element_v_out(c_e_h_1, c_h, s1))),
% 290.63/183.16 inference(rewrite,[status(thm)],[])).
% 290.63/183.16 tff(8453,plain,
% 290.63/183.16 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s1)) | m_c_h_element_v_out(c_e_h_1, c_h, s1))),
% 290.63/183.16 inference(quant_inst,[status(thm)],[])).
% 290.63/183.16 tff(8454,plain,
% 290.63/183.16 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s1)) | m_c_h_element_v_out(c_e_h_1, c_h, s1)),
% 290.63/183.16 inference(modus_ponens,[status(thm)],[8453, 8452])).
% 290.63/183.16 tff(8455,plain,
% 290.63/183.16 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s1)),
% 290.63/183.16 inference(unit_resolution,[status(thm)],[8454, 619, 8451])).
% 290.63/183.16 tff(8456,plain,
% 290.63/183.16 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s1)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s1)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s1))),
% 290.63/183.16 inference(rewrite,[status(thm)],[])).
% 290.63/183.16 tff(8457,plain,
% 290.63/183.16 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s1)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s1))),
% 290.63/183.16 inference(quant_inst,[status(thm)],[])).
% 290.63/183.16 tff(8458,plain,
% 290.63/183.16 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s1)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s1)),
% 290.63/183.16 inference(modus_ponens,[status(thm)],[8457, 8456])).
% 290.63/183.16 tff(8459,plain,
% 290.63/183.16 (~node20(c_e_h_1, c_i, s1)),
% 290.63/183.16 inference(unit_resolution,[status(thm)],[8458, 38, 8455])).
% 290.63/183.16 tff(8460,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s2)), introduced(assumption)).
% 290.63/183.16 tff(8461,assumption,(node22(c_e_h_1, c_i, s1, s2)), introduced(assumption)).
% 290.63/183.16 tff(8462,plain,
% 290.63/183.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s2)) | (~node22(c_e_h_1, c_i, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_i, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s2)) | (~node22(c_e_h_1, c_i, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_i, s1))),
% 290.63/183.16 inference(rewrite,[status(thm)],[])).
% 290.63/183.16 tff(8463,plain,
% 290.63/183.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s2)) | (~node22(c_e_h_1, c_i, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_i, s1))),
% 290.63/183.16 inference(quant_inst,[status(thm)],[])).
% 290.63/183.16 tff(8464,plain,
% 290.63/183.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s2)) | (~node22(c_e_h_1, c_i, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_i, s1)),
% 290.63/183.16 inference(modus_ponens,[status(thm)],[8463, 8462])).
% 290.63/183.16 tff(8465,plain,
% 290.63/183.16 ($false),
% 290.63/183.16 inference(unit_resolution,[status(thm)],[8464, 108, 7984, 8460, 8461])).
% 290.63/183.16 tff(8466,plain,((~node22(c_e_h_1, c_i, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s2))), inference(lemma,lemma(discharge,[]))).
% 290.63/183.16 tff(8467,plain,
% 290.63/183.16 (~node22(c_e_h_1, c_i, s1, s2)),
% 290.63/183.16 inference(unit_resolution,[status(thm)],[8466, 8460])).
% 290.63/183.16 tff(8468,plain,
% 290.63/183.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_1, c_i, s1, s2) | node22(c_e_h_1, c_i, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_1, c_i, s1, s2) | node22(c_e_h_1, c_i, s1, s2))),
% 290.63/183.16 inference(rewrite,[status(thm)],[])).
% 290.63/183.16 tff(8469,plain,
% 290.63/183.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_1, c_i, s1, s2) | node22(c_e_h_1, c_i, s1, s2))),
% 290.63/183.16 inference(quant_inst,[status(thm)],[])).
% 290.63/183.16 tff(8470,plain,
% 290.63/183.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_1, c_i, s1, s2) | node22(c_e_h_1, c_i, s1, s2)),
% 290.63/183.16 inference(modus_ponens,[status(thm)],[8469, 8468])).
% 290.63/183.16 tff(8471,plain,
% 290.63/183.16 (node21(c_e_h_1, c_i, s1, s2) | node22(c_e_h_1, c_i, s1, s2)),
% 290.63/183.16 inference(unit_resolution,[status(thm)],[8470, 82, 255])).
% 290.63/183.16 tff(8472,plain,
% 290.63/183.16 (node21(c_e_h_1, c_i, s1, s2)),
% 290.63/183.16 inference(unit_resolution,[status(thm)],[8471, 8467])).
% 290.63/183.16 tff(8473,plain,
% 290.63/183.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s2)) | (~node21(c_e_h_1, c_i, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s2)) | (~node21(c_e_h_1, c_i, s1, s2)))),
% 290.63/183.17 inference(rewrite,[status(thm)],[])).
% 290.63/183.17 tff(8474,plain,
% 290.63/183.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s2)) | (~node21(c_e_h_1, c_i, s1, s2)))),
% 290.63/183.17 inference(quant_inst,[status(thm)],[])).
% 290.63/183.17 tff(8475,plain,
% 290.63/183.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s2)) | (~node21(c_e_h_1, c_i, s1, s2))),
% 290.63/183.17 inference(modus_ponens,[status(thm)],[8474, 8473])).
% 290.63/183.17 tff(8476,plain,
% 290.63/183.17 ($false),
% 290.63/183.17 inference(unit_resolution,[status(thm)],[8475, 52, 8460, 8472, 8459])).
% 290.63/183.17 tff(8477,plain,(~m_and_h_gate_v_out(c_e_h_1, c_i, s2)), inference(lemma,lemma(discharge,[]))).
% 290.63/183.17 tff(8478,plain,
% 290.63/183.17 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s2)) | m_and_h_gate_v_out(c_e_h_1, c_i, s2))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s2)) | m_and_h_gate_v_out(c_e_h_1, c_i, s2))),
% 290.63/183.17 inference(rewrite,[status(thm)],[])).
% 290.63/183.17 tff(8479,plain,
% 290.63/183.17 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s2)) | m_and_h_gate_v_out(c_e_h_1, c_i, s2))),
% 290.63/183.17 inference(quant_inst,[status(thm)],[])).
% 290.63/183.17 tff(8480,plain,
% 290.63/183.17 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s2)) | m_and_h_gate_v_out(c_e_h_1, c_i, s2)),
% 290.63/183.17 inference(modus_ponens,[status(thm)],[8479, 8478])).
% 290.63/183.17 tff(8481,plain,
% 290.63/183.17 (~m_c_h_element_v_in2(c_e_h_1, c_f, s2)),
% 290.63/183.17 inference(unit_resolution,[status(thm)],[8480, 2143, 8477])).
% 290.63/183.17 tff(8482,plain,
% 290.63/183.17 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s2)) | m_c_h_element_v_in1(c_e_h_1, c_f, s2) | m_c_h_element_v_in2(c_e_h_1, c_f, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s2)) | m_c_h_element_v_in1(c_e_h_1, c_f, s2) | m_c_h_element_v_in2(c_e_h_1, c_f, s2))),
% 290.63/183.17 inference(rewrite,[status(thm)],[])).
% 290.63/183.17 tff(8483,plain,
% 290.63/183.17 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s2)) | m_c_h_element_v_in1(c_e_h_1, c_f, s2) | m_c_h_element_v_in2(c_e_h_1, c_f, s2))),
% 290.63/183.17 inference(quant_inst,[status(thm)],[])).
% 290.63/183.17 tff(8484,plain,
% 290.63/183.17 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s2)) | m_c_h_element_v_in1(c_e_h_1, c_f, s2) | m_c_h_element_v_in2(c_e_h_1, c_f, s2)),
% 290.63/183.17 inference(modus_ponens,[status(thm)],[8483, 8482])).
% 290.63/183.17 tff(8485,plain,
% 290.63/183.17 ((~node16(c_e_h_1, c_f, s2)) | m_c_h_element_v_in1(c_e_h_1, c_f, s2)),
% 290.63/183.17 inference(unit_resolution,[status(thm)],[8484, 178, 8481])).
% 290.63/183.17 tff(8486,plain,
% 290.63/183.17 (~node16(c_e_h_1, c_f, s2)),
% 290.63/183.17 inference(unit_resolution,[status(thm)],[8485, 8405])).
% 290.63/183.17 tff(8487,assumption,(node15(c_e_h_1, c_f, s2, s3)), introduced(assumption)).
% 290.63/183.17 tff(8488,plain,
% 290.63/183.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s3)) | (~node15(c_e_h_1, c_f, s2, s3)) | m_c_h_element_v_out(c_e_h_1, c_f, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s3)) | (~node15(c_e_h_1, c_f, s2, s3)) | m_c_h_element_v_out(c_e_h_1, c_f, s2))),
% 290.63/183.17 inference(rewrite,[status(thm)],[])).
% 290.63/183.17 tff(8489,plain,
% 290.63/183.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s3)) | (~node15(c_e_h_1, c_f, s2, s3)) | m_c_h_element_v_out(c_e_h_1, c_f, s2))),
% 290.63/183.17 inference(quant_inst,[status(thm)],[])).
% 290.63/183.17 tff(8490,plain,
% 290.63/183.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s3)) | (~node15(c_e_h_1, c_f, s2, s3)) | m_c_h_element_v_out(c_e_h_1, c_f, s2)),
% 290.63/183.17 inference(modus_ponens,[status(thm)],[8489, 8488])).
% 290.63/183.17 tff(8491,plain,
% 290.63/183.17 ($false),
% 290.63/183.17 inference(unit_resolution,[status(thm)],[8490, 147, 8040, 8397, 8487])).
% 290.63/183.17 tff(8492,plain,((~node15(c_e_h_1, c_f, s2, s3)) | m_c_h_element_v_out(c_e_h_1, c_f, s2) | (~m_c_h_element_v_out(c_e_h_1, c_f, s3))), inference(lemma,lemma(discharge,[]))).
% 290.63/183.17 tff(8493,plain,
% 290.63/183.17 (~node15(c_e_h_1, c_f, s2, s3)),
% 290.63/183.17 inference(unit_resolution,[status(thm)],[8492, 8397, 8040])).
% 290.63/183.17 tff(8494,plain,
% 290.63/183.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s2, s3)) | node19(c_e_h_1, c_f, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s2, s3)) | node19(c_e_h_1, c_f, s2, s3))),
% 290.63/183.17 inference(rewrite,[status(thm)],[])).
% 290.63/183.17 tff(8495,plain,
% 290.63/183.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s2, s3)) | node19(c_e_h_1, c_f, s2, s3))),
% 290.63/183.17 inference(quant_inst,[status(thm)],[])).
% 290.63/183.17 tff(8496,plain,
% 290.63/183.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s2, s3)) | node19(c_e_h_1, c_f, s2, s3)),
% 290.63/183.17 inference(modus_ponens,[status(thm)],[8495, 8494])).
% 290.63/183.17 tff(8497,plain,
% 290.63/183.17 (node19(c_e_h_1, c_f, s2, s3)),
% 290.63/183.17 inference(unit_resolution,[status(thm)],[8496, 190, 318])).
% 290.63/183.17 tff(8498,plain,
% 290.63/183.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_f, s2, s3)) | node16(c_e_h_1, c_f, s2) | node14(c_e_h_1, c_f, s2, s3) | node15(c_e_h_1, c_f, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s2, s3)) | node16(c_e_h_1, c_f, s2) | node14(c_e_h_1, c_f, s2, s3) | node15(c_e_h_1, c_f, s2, s3))),
% 290.63/183.17 inference(rewrite,[status(thm)],[])).
% 290.63/183.17 tff(8499,plain,
% 290.63/183.17 ((node16(c_e_h_1, c_f, s2) | node14(c_e_h_1, c_f, s2, s3) | node15(c_e_h_1, c_f, s2, s3) | (~node19(c_e_h_1, c_f, s2, s3))) <=> ((~node19(c_e_h_1, c_f, s2, s3)) | node16(c_e_h_1, c_f, s2) | node14(c_e_h_1, c_f, s2, s3) | node15(c_e_h_1, c_f, s2, s3))),
% 290.63/183.17 inference(rewrite,[status(thm)],[])).
% 290.63/183.17 tff(8500,plain,
% 290.63/183.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s2) | node14(c_e_h_1, c_f, s2, s3) | node15(c_e_h_1, c_f, s2, s3) | (~node19(c_e_h_1, c_f, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_f, s2, s3)) | node16(c_e_h_1, c_f, s2) | node14(c_e_h_1, c_f, s2, s3) | node15(c_e_h_1, c_f, s2, s3)))),
% 290.63/183.17 inference(monotonicity,[status(thm)],[8499])).
% 290.63/183.17 tff(8501,plain,
% 290.63/183.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s2) | node14(c_e_h_1, c_f, s2, s3) | node15(c_e_h_1, c_f, s2, s3) | (~node19(c_e_h_1, c_f, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s2, s3)) | node16(c_e_h_1, c_f, s2) | node14(c_e_h_1, c_f, s2, s3) | node15(c_e_h_1, c_f, s2, s3))),
% 290.63/183.17 inference(transitivity,[status(thm)],[8500, 8498])).
% 290.63/183.17 tff(8502,plain,
% 290.63/183.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s2) | node14(c_e_h_1, c_f, s2, s3) | node15(c_e_h_1, c_f, s2, s3) | (~node19(c_e_h_1, c_f, s2, s3)))),
% 290.63/183.18 inference(quant_inst,[status(thm)],[])).
% 290.63/183.18 tff(8503,plain,
% 290.63/183.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s2, s3)) | node16(c_e_h_1, c_f, s2) | node14(c_e_h_1, c_f, s2, s3) | node15(c_e_h_1, c_f, s2, s3)),
% 290.63/183.18 inference(modus_ponens,[status(thm)],[8502, 8501])).
% 290.63/183.18 tff(8504,plain,
% 290.63/183.18 (node16(c_e_h_1, c_f, s2) | node14(c_e_h_1, c_f, s2, s3) | node15(c_e_h_1, c_f, s2, s3)),
% 290.63/183.18 inference(unit_resolution,[status(thm)],[8503, 204, 8497])).
% 290.63/183.18 tff(8505,plain,
% 290.63/183.18 (node14(c_e_h_1, c_f, s2, s3)),
% 290.63/183.18 inference(unit_resolution,[status(thm)],[8504, 8493, 8486])).
% 290.63/183.18 tff(8506,plain,
% 290.63/183.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s3)) | m_c_h_element_v_in1(c_e_h_1, c_f, s2) | (~node14(c_e_h_1, c_f, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s3)) | m_c_h_element_v_in1(c_e_h_1, c_f, s2) | (~node14(c_e_h_1, c_f, s2, s3)))),
% 290.63/183.18 inference(rewrite,[status(thm)],[])).
% 290.63/183.18 tff(8507,plain,
% 290.63/183.18 (((~node14(c_e_h_1, c_f, s2, s3)) | m_c_h_element_v_in1(c_e_h_1, c_f, s2) | (~m_c_h_element_v_out(c_e_h_1, c_f, s3))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_f, s3)) | m_c_h_element_v_in1(c_e_h_1, c_f, s2) | (~node14(c_e_h_1, c_f, s2, s3)))),
% 290.63/183.18 inference(rewrite,[status(thm)],[])).
% 290.63/183.18 tff(8508,plain,
% 290.63/183.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s2, s3)) | m_c_h_element_v_in1(c_e_h_1, c_f, s2) | (~m_c_h_element_v_out(c_e_h_1, c_f, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s3)) | m_c_h_element_v_in1(c_e_h_1, c_f, s2) | (~node14(c_e_h_1, c_f, s2, s3))))),
% 290.63/183.18 inference(monotonicity,[status(thm)],[8507])).
% 290.63/183.18 tff(8509,plain,
% 290.63/183.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s2, s3)) | m_c_h_element_v_in1(c_e_h_1, c_f, s2) | (~m_c_h_element_v_out(c_e_h_1, c_f, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s3)) | m_c_h_element_v_in1(c_e_h_1, c_f, s2) | (~node14(c_e_h_1, c_f, s2, s3)))),
% 290.63/183.18 inference(transitivity,[status(thm)],[8508, 8506])).
% 290.63/183.18 tff(8510,plain,
% 290.63/183.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s2, s3)) | m_c_h_element_v_in1(c_e_h_1, c_f, s2) | (~m_c_h_element_v_out(c_e_h_1, c_f, s3)))),
% 290.63/183.18 inference(quant_inst,[status(thm)],[])).
% 290.63/183.18 tff(8511,plain,
% 290.63/183.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s3)) | m_c_h_element_v_in1(c_e_h_1, c_f, s2) | (~node14(c_e_h_1, c_f, s2, s3))),
% 290.63/183.18 inference(modus_ponens,[status(thm)],[8510, 8509])).
% 290.63/183.18 tff(8512,plain,
% 290.63/183.18 ($false),
% 290.63/183.18 inference(unit_resolution,[status(thm)],[8511, 223, 8397, 8505, 8405])).
% 290.63/183.18 tff(8513,plain,((~m_c_h_element_v_out(c_e_h_1, c_f, s3)) | m_c_h_element_v_in1(c_e_h_1, c_f, s2) | m_c_h_element_v_out(c_e_h_1, c_f, s2)), inference(lemma,lemma(discharge,[]))).
% 290.63/183.18 tff(8514,plain,
% 290.63/183.18 (m_c_h_element_v_in1(c_e_h_1, c_f, s2)),
% 290.63/183.18 inference(unit_resolution,[status(thm)],[8513, 8397, 8040])).
% 290.63/183.18 tff(8515,plain,
% 290.63/183.18 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_f, s2)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s2)) | m_c_h_element_v_in2(c_e_h_1, c_f, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_f, s2)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s2)) | m_c_h_element_v_in2(c_e_h_1, c_f, s2))),
% 290.63/183.18 inference(rewrite,[status(thm)],[])).
% 290.63/183.18 tff(8516,plain,
% 290.63/183.18 (((~m_c_h_element_v_in1(c_e_h_1, c_f, s2)) | m_c_h_element_v_in2(c_e_h_1, c_f, s2) | (~node17(c_e_h_1, c_f, s2))) <=> ((~node17(c_e_h_1, c_f, s2)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s2)) | m_c_h_element_v_in2(c_e_h_1, c_f, s2))),
% 290.63/183.18 inference(rewrite,[status(thm)],[])).
% 290.63/183.18 tff(8517,plain,
% 290.63/183.18 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s2)) | m_c_h_element_v_in2(c_e_h_1, c_f, s2) | (~node17(c_e_h_1, c_f, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_f, s2)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s2)) | m_c_h_element_v_in2(c_e_h_1, c_f, s2)))),
% 290.63/183.18 inference(monotonicity,[status(thm)],[8516])).
% 290.63/183.18 tff(8518,plain,
% 290.63/183.18 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s2)) | m_c_h_element_v_in2(c_e_h_1, c_f, s2) | (~node17(c_e_h_1, c_f, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_f, s2)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s2)) | m_c_h_element_v_in2(c_e_h_1, c_f, s2))),
% 290.63/183.18 inference(transitivity,[status(thm)],[8517, 8515])).
% 290.63/183.18 tff(8519,plain,
% 290.63/183.18 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s2)) | m_c_h_element_v_in2(c_e_h_1, c_f, s2) | (~node17(c_e_h_1, c_f, s2)))),
% 290.63/183.18 inference(quant_inst,[status(thm)],[])).
% 290.63/183.18 tff(8520,plain,
% 290.63/183.18 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_f, s2)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s2)) | m_c_h_element_v_in2(c_e_h_1, c_f, s2)),
% 290.63/183.18 inference(modus_ponens,[status(thm)],[8519, 8518])).
% 290.63/183.18 tff(8521,plain,
% 290.63/183.18 ((~node17(c_e_h_1, c_f, s2)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s2))),
% 290.63/183.18 inference(unit_resolution,[status(thm)],[8520, 919, 8481])).
% 290.63/183.18 tff(8522,plain,
% 290.63/183.18 (~node17(c_e_h_1, c_f, s2)),
% 290.63/183.18 inference(unit_resolution,[status(thm)],[8521, 8514])).
% 290.63/183.18 tff(8523,plain,
% 290.63/183.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s2) | (~node19(c_e_h_1, c_f, s2, s3)) | node18(c_e_h_1, c_f, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_f, s2) | (~node19(c_e_h_1, c_f, s2, s3)) | node18(c_e_h_1, c_f, s2, s3))),
% 290.63/183.18 inference(rewrite,[status(thm)],[])).
% 290.63/183.18 tff(8524,plain,
% 290.63/183.18 ((node17(c_e_h_1, c_f, s2) | node18(c_e_h_1, c_f, s2, s3) | (~node19(c_e_h_1, c_f, s2, s3))) <=> (node17(c_e_h_1, c_f, s2) | (~node19(c_e_h_1, c_f, s2, s3)) | node18(c_e_h_1, c_f, s2, s3))),
% 290.63/183.18 inference(rewrite,[status(thm)],[])).
% 290.63/183.18 tff(8525,plain,
% 290.63/183.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s2) | node18(c_e_h_1, c_f, s2, s3) | (~node19(c_e_h_1, c_f, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s2) | (~node19(c_e_h_1, c_f, s2, s3)) | node18(c_e_h_1, c_f, s2, s3)))),
% 290.63/183.18 inference(monotonicity,[status(thm)],[8524])).
% 290.63/183.18 tff(8526,plain,
% 290.63/183.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s2) | node18(c_e_h_1, c_f, s2, s3) | (~node19(c_e_h_1, c_f, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_f, s2) | (~node19(c_e_h_1, c_f, s2, s3)) | node18(c_e_h_1, c_f, s2, s3))),
% 290.63/183.18 inference(transitivity,[status(thm)],[8525, 8523])).
% 290.63/183.18 tff(8527,plain,
% 290.63/183.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s2) | node18(c_e_h_1, c_f, s2, s3) | (~node19(c_e_h_1, c_f, s2, s3)))),
% 290.63/183.18 inference(quant_inst,[status(thm)],[])).
% 290.63/183.18 tff(8528,plain,
% 290.63/183.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_f, s2) | (~node19(c_e_h_1, c_f, s2, s3)) | node18(c_e_h_1, c_f, s2, s3)),
% 290.63/183.18 inference(modus_ponens,[status(thm)],[8527, 8526])).
% 290.63/183.18 tff(8529,plain,
% 290.63/183.18 (node17(c_e_h_1, c_f, s2) | node18(c_e_h_1, c_f, s2, s3)),
% 290.63/183.18 inference(unit_resolution,[status(thm)],[8528, 776, 8497])).
% 290.63/183.18 tff(8530,plain,
% 290.63/183.18 ($false),
% 290.63/183.18 inference(unit_resolution,[status(thm)],[8529, 8522, 8404])).
% 290.63/183.18 tff(8531,plain,((~m_c_h_element_v_out(c_e_h_1, c_f, s3)) | m_c_h_element_v_out(c_e_h_1, c_f, s2)), inference(lemma,lemma(discharge,[]))).
% 290.63/183.18 tff(8532,plain,
% 290.63/183.18 (~m_c_h_element_v_out(c_e_h_1, c_f, s3)),
% 290.63/183.18 inference(unit_resolution,[status(thm)],[8531, 8038])).
% 290.63/183.18 tff(8533,plain,
% 290.63/183.18 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s3)) | m_c_h_element_v_out(c_e_h_1, c_f, s3))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s3)) | m_c_h_element_v_out(c_e_h_1, c_f, s3))),
% 290.63/183.18 inference(rewrite,[status(thm)],[])).
% 290.63/183.18 tff(8534,plain,
% 290.63/183.18 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s3)) | m_c_h_element_v_out(c_e_h_1, c_f, s3))),
% 290.63/183.18 inference(quant_inst,[status(thm)],[])).
% 290.63/183.18 tff(8535,plain,
% 290.63/183.18 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s3)) | m_c_h_element_v_out(c_e_h_1, c_f, s3)),
% 290.63/183.18 inference(modus_ponens,[status(thm)],[8534, 8533])).
% 290.63/183.18 tff(8536,plain,
% 290.63/183.18 (~m_and_h_gate_v_in1(c_e_h_1, c_q, s3)),
% 290.63/183.18 inference(unit_resolution,[status(thm)],[8535, 1586, 8532])).
% 290.63/183.18 tff(8537,plain,
% 290.63/183.18 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s3)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s3)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s3))),
% 290.63/183.18 inference(rewrite,[status(thm)],[])).
% 290.63/183.18 tff(8538,plain,
% 290.63/183.18 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s3)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s3))),
% 290.63/183.18 inference(quant_inst,[status(thm)],[])).
% 290.63/183.18 tff(8539,plain,
% 290.63/183.18 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s3)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s3)),
% 290.63/183.18 inference(modus_ponens,[status(thm)],[8538, 8537])).
% 290.63/183.18 tff(8540,plain,
% 290.63/183.18 (~node20(c_e_h_1, c_q, s3)),
% 290.63/183.18 inference(unit_resolution,[status(thm)],[8539, 38, 8536])).
% 290.63/183.18 tff(8541,assumption,(m_and_h_gate_v_out(c_e_h_1, c_q, s4)), introduced(assumption)).
% 290.63/183.18 tff(8542,assumption,(~node20(c_e_h_1, c_q, s3)), introduced(assumption)).
% 290.63/183.18 tff(8543,assumption,(node21(c_e_h_1, c_q, s3, s4)), introduced(assumption)).
% 290.63/183.18 tff(8544,plain,
% 290.63/183.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s4)) | node20(c_e_h_1, c_q, s3) | (~node21(c_e_h_1, c_q, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s4)) | node20(c_e_h_1, c_q, s3) | (~node21(c_e_h_1, c_q, s3, s4)))),
% 290.63/183.18 inference(rewrite,[status(thm)],[])).
% 290.63/183.18 tff(8545,plain,
% 290.63/183.18 ((node20(c_e_h_1, c_q, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s4)) | (~node21(c_e_h_1, c_q, s3, s4))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_q, s4)) | node20(c_e_h_1, c_q, s3) | (~node21(c_e_h_1, c_q, s3, s4)))),
% 290.63/183.19 inference(rewrite,[status(thm)],[])).
% 290.63/183.19 tff(8546,plain,
% 290.63/183.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s4)) | (~node21(c_e_h_1, c_q, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s4)) | node20(c_e_h_1, c_q, s3) | (~node21(c_e_h_1, c_q, s3, s4))))),
% 290.63/183.19 inference(monotonicity,[status(thm)],[8545])).
% 290.63/183.19 tff(8547,plain,
% 290.63/183.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s4)) | (~node21(c_e_h_1, c_q, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s4)) | node20(c_e_h_1, c_q, s3) | (~node21(c_e_h_1, c_q, s3, s4)))),
% 290.63/183.19 inference(transitivity,[status(thm)],[8546, 8544])).
% 290.63/183.19 tff(8548,plain,
% 290.63/183.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s4)) | (~node21(c_e_h_1, c_q, s3, s4)))),
% 290.63/183.19 inference(quant_inst,[status(thm)],[])).
% 290.63/183.19 tff(8549,plain,
% 290.63/183.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s4)) | node20(c_e_h_1, c_q, s3) | (~node21(c_e_h_1, c_q, s3, s4))),
% 290.63/183.19 inference(modus_ponens,[status(thm)],[8548, 8547])).
% 290.63/183.19 tff(8550,plain,
% 290.63/183.19 ($false),
% 290.63/183.19 inference(unit_resolution,[status(thm)],[8549, 52, 8543, 8541, 8542])).
% 290.63/183.19 tff(8551,plain,((~node21(c_e_h_1, c_q, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s4)) | node20(c_e_h_1, c_q, s3)), inference(lemma,lemma(discharge,[]))).
% 290.63/183.19 tff(8552,plain,
% 290.63/183.19 (~node21(c_e_h_1, c_q, s3, s4)),
% 290.63/183.19 inference(unit_resolution,[status(thm)],[8551, 8541, 8542])).
% 290.63/183.19 tff(8553,plain,
% 290.63/183.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_1, c_q, s3, s4) | node22(c_e_h_1, c_q, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_1, c_q, s3, s4) | node22(c_e_h_1, c_q, s3, s4))),
% 290.63/183.19 inference(rewrite,[status(thm)],[])).
% 290.63/183.19 tff(8554,plain,
% 290.63/183.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_1, c_q, s3, s4) | node22(c_e_h_1, c_q, s3, s4))),
% 290.63/183.19 inference(quant_inst,[status(thm)],[])).
% 290.63/183.19 tff(8555,plain,
% 290.63/183.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_1, c_q, s3, s4) | node22(c_e_h_1, c_q, s3, s4)),
% 290.63/183.19 inference(modus_ponens,[status(thm)],[8554, 8553])).
% 290.63/183.19 tff(8556,plain,
% 290.63/183.19 (node21(c_e_h_1, c_q, s3, s4) | node22(c_e_h_1, c_q, s3, s4)),
% 290.63/183.19 inference(unit_resolution,[status(thm)],[8555, 82, 531])).
% 290.63/183.19 tff(8557,plain,
% 290.63/183.19 (node22(c_e_h_1, c_q, s3, s4)),
% 290.63/183.19 inference(unit_resolution,[status(thm)],[8556, 8552])).
% 290.63/183.19 tff(8558,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_q, s3)), introduced(assumption)).
% 290.63/183.19 tff(8559,plain,
% 290.63/183.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s4)) | (~node22(c_e_h_1, c_q, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_q, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s4)) | (~node22(c_e_h_1, c_q, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_q, s3))),
% 290.63/183.19 inference(rewrite,[status(thm)],[])).
% 290.63/183.19 tff(8560,plain,
% 290.63/183.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s4)) | (~node22(c_e_h_1, c_q, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_q, s3))),
% 290.72/183.19 inference(quant_inst,[status(thm)],[])).
% 290.72/183.19 tff(8561,plain,
% 290.72/183.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s4)) | (~node22(c_e_h_1, c_q, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_q, s3)),
% 290.72/183.19 inference(modus_ponens,[status(thm)],[8560, 8559])).
% 290.72/183.19 tff(8562,plain,
% 290.72/183.19 ($false),
% 290.72/183.19 inference(unit_resolution,[status(thm)],[8561, 108, 8558, 8557, 8541])).
% 290.72/183.19 tff(8563,plain,((~m_and_h_gate_v_out(c_e_h_1, c_q, s4)) | m_and_h_gate_v_out(c_e_h_1, c_q, s3) | node20(c_e_h_1, c_q, s3)), inference(lemma,lemma(discharge,[]))).
% 290.72/183.19 tff(8564,plain,
% 290.72/183.19 (~m_and_h_gate_v_out(c_e_h_1, c_q, s4)),
% 290.72/183.19 inference(unit_resolution,[status(thm)],[8563, 8540, 8079])).
% 290.72/183.19 tff(8565,plain,
% 290.72/183.19 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s4))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s4))),
% 290.72/183.19 inference(rewrite,[status(thm)],[])).
% 290.72/183.19 tff(8566,plain,
% 290.72/183.19 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s4))),
% 290.72/183.19 inference(quant_inst,[status(thm)],[])).
% 290.72/183.19 tff(8567,plain,
% 290.72/183.19 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s4)),
% 290.72/183.19 inference(modus_ponens,[status(thm)],[8566, 8565])).
% 290.72/183.19 tff(8568,plain,
% 290.72/183.19 (node3(c_e_h_1, c_e_h_2, s4)),
% 290.72/183.19 inference(unit_resolution,[status(thm)],[8567, 4166, 1056])).
% 290.72/183.19 tff(8569,plain,
% 290.72/183.19 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s4)) | (~node3(c_e_h_1, c_e_h_2, s4)) | m_and_h_gate_v_out(c_e_h_1, c_q, s4))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s4)) | (~node3(c_e_h_1, c_e_h_2, s4)) | m_and_h_gate_v_out(c_e_h_1, c_q, s4))),
% 290.72/183.19 inference(rewrite,[status(thm)],[])).
% 290.72/183.19 tff(8570,plain,
% 290.72/183.19 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s4)) | (~node3(c_e_h_1, c_e_h_2, s4)) | m_and_h_gate_v_out(c_e_h_1, c_q, s4))),
% 290.72/183.19 inference(quant_inst,[status(thm)],[])).
% 290.72/183.19 tff(8571,plain,
% 290.72/183.19 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s4)) | (~node3(c_e_h_1, c_e_h_2, s4)) | m_and_h_gate_v_out(c_e_h_1, c_q, s4)),
% 290.72/183.19 inference(modus_ponens,[status(thm)],[8570, 8569])).
% 290.72/183.19 tff(8572,plain,
% 290.72/183.19 ((~m_cell_v_ack(c_e_h_2, s4)) | m_and_h_gate_v_out(c_e_h_1, c_q, s4)),
% 290.72/183.19 inference(unit_resolution,[status(thm)],[8571, 1073, 8568])).
% 290.72/183.19 tff(8573,plain,
% 290.72/183.19 (~m_cell_v_ack(c_e_h_2, s4)),
% 290.72/183.19 inference(unit_resolution,[status(thm)],[8572, 8564])).
% 290.72/183.19 tff(8574,plain,
% 290.72/183.19 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s4)) | m_cell_v_ack(c_e_h_2, s4))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s4)) | m_cell_v_ack(c_e_h_2, s4))),
% 290.72/183.19 inference(rewrite,[status(thm)],[])).
% 290.72/183.19 tff(8575,plain,
% 290.72/183.19 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s4)) | m_cell_v_ack(c_e_h_2, s4))),
% 290.72/183.19 inference(quant_inst,[status(thm)],[])).
% 290.72/183.19 tff(8576,plain,
% 290.72/183.19 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s4)) | m_cell_v_ack(c_e_h_2, s4)),
% 290.72/183.19 inference(modus_ponens,[status(thm)],[8575, 8574])).
% 290.72/183.19 tff(8577,plain,
% 290.72/183.19 (~m_or_h_gate_v_in2(c_e_h_2, c_j, s4)),
% 290.72/183.19 inference(unit_resolution,[status(thm)],[8576, 1085, 8573])).
% 290.72/183.19 tff(8578,assumption,(~m_or_h_gate_v_out(c_e_h_2, c_j, s4)), introduced(assumption)).
% 290.72/183.19 tff(8579,assumption,(m_or_h_gate_v_out(c_e_h_2, c_j, s5)), introduced(assumption)).
% 290.72/183.19 tff(8580,assumption,(node6(c_e_h_2, c_j, s4, s5)), introduced(assumption)).
% 290.72/183.19 tff(8581,plain,
% 290.72/183.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_2, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s5)) | (~node6(c_e_h_2, c_j, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s5)) | (~node6(c_e_h_2, c_j, s4, s5)))),
% 290.72/183.19 inference(rewrite,[status(thm)],[])).
% 290.72/183.19 tff(8582,plain,
% 290.72/183.19 (((~node6(c_e_h_2, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s5)) | m_or_h_gate_v_out(c_e_h_2, c_j, s4)) <=> (m_or_h_gate_v_out(c_e_h_2, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s5)) | (~node6(c_e_h_2, c_j, s4, s5)))),
% 290.72/183.19 inference(rewrite,[status(thm)],[])).
% 290.72/183.19 tff(8583,plain,
% 290.72/183.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s5)) | m_or_h_gate_v_out(c_e_h_2, c_j, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_2, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s5)) | (~node6(c_e_h_2, c_j, s4, s5))))),
% 290.72/183.19 inference(monotonicity,[status(thm)],[8582])).
% 290.72/183.19 tff(8584,plain,
% 290.72/183.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s5)) | m_or_h_gate_v_out(c_e_h_2, c_j, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s5)) | (~node6(c_e_h_2, c_j, s4, s5)))),
% 290.72/183.19 inference(transitivity,[status(thm)],[8583, 8581])).
% 290.72/183.19 tff(8585,plain,
% 290.72/183.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s5)) | m_or_h_gate_v_out(c_e_h_2, c_j, s4))),
% 290.72/183.19 inference(quant_inst,[status(thm)],[])).
% 290.72/183.19 tff(8586,plain,
% 290.72/183.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s5)) | (~node6(c_e_h_2, c_j, s4, s5))),
% 290.72/183.19 inference(modus_ponens,[status(thm)],[8585, 8584])).
% 290.72/183.19 tff(8587,plain,
% 290.72/183.19 ($false),
% 290.72/183.19 inference(unit_resolution,[status(thm)],[8586, 1121, 8578, 8580, 8579])).
% 290.72/183.19 tff(8588,plain,((~node6(c_e_h_2, c_j, s4, s5)) | m_or_h_gate_v_out(c_e_h_2, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s5))), inference(lemma,lemma(discharge,[]))).
% 290.72/183.19 tff(8589,plain,
% 290.72/183.19 (~node6(c_e_h_2, c_j, s4, s5)),
% 290.72/183.19 inference(unit_resolution,[status(thm)],[8588, 8579, 8578])).
% 290.72/183.19 tff(8590,assumption,(~m_or_h_gate_v_in2(c_e_h_2, c_j, s4)), introduced(assumption)).
% 290.72/183.19 tff(8591,assumption,(~m_or_h_gate_v_in1(c_e_h_2, c_j, s4)), introduced(assumption)).
% 290.72/183.19 tff(8592,assumption,(node5(c_e_h_2, c_j, s4, s5)), introduced(assumption)).
% 290.72/183.19 tff(8593,plain,
% 290.72/183.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~node5(c_e_h_2, c_j, s4, s5)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s4) | m_or_h_gate_v_in1(c_e_h_2, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~node5(c_e_h_2, c_j, s4, s5)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s4) | m_or_h_gate_v_in1(c_e_h_2, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s5)))),
% 290.72/183.20 inference(rewrite,[status(thm)],[])).
% 290.72/183.20 tff(8594,plain,
% 290.72/183.20 ((m_or_h_gate_v_in1(c_e_h_2, c_j, s4) | m_or_h_gate_v_in2(c_e_h_2, c_j, s4) | (~node5(c_e_h_2, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s5))) <=> ((~node5(c_e_h_2, c_j, s4, s5)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s4) | m_or_h_gate_v_in1(c_e_h_2, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s5)))),
% 290.72/183.20 inference(rewrite,[status(thm)],[])).
% 290.72/183.20 tff(8595,plain,
% 290.72/183.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s4) | m_or_h_gate_v_in2(c_e_h_2, c_j, s4) | (~node5(c_e_h_2, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~node5(c_e_h_2, c_j, s4, s5)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s4) | m_or_h_gate_v_in1(c_e_h_2, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s5))))),
% 290.72/183.20 inference(monotonicity,[status(thm)],[8594])).
% 290.72/183.20 tff(8596,plain,
% 290.72/183.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s4) | m_or_h_gate_v_in2(c_e_h_2, c_j, s4) | (~node5(c_e_h_2, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~node5(c_e_h_2, c_j, s4, s5)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s4) | m_or_h_gate_v_in1(c_e_h_2, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s5)))),
% 290.72/183.20 inference(transitivity,[status(thm)],[8595, 8593])).
% 290.72/183.20 tff(8597,plain,
% 290.72/183.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s4) | m_or_h_gate_v_in2(c_e_h_2, c_j, s4) | (~node5(c_e_h_2, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s5)))),
% 290.72/183.20 inference(quant_inst,[status(thm)],[])).
% 290.72/183.20 tff(8598,plain,
% 290.72/183.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~node5(c_e_h_2, c_j, s4, s5)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s4) | m_or_h_gate_v_in1(c_e_h_2, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s5))),
% 290.72/183.20 inference(modus_ponens,[status(thm)],[8597, 8596])).
% 290.72/183.20 tff(8599,plain,
% 290.72/183.20 ($false),
% 290.72/183.20 inference(unit_resolution,[status(thm)],[8598, 1159, 8592, 8590, 8579, 8591])).
% 290.72/183.20 tff(8600,plain,((~node5(c_e_h_2, c_j, s4, s5)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s5)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s4)), inference(lemma,lemma(discharge,[]))).
% 290.72/183.20 tff(8601,plain,
% 290.72/183.20 (~node5(c_e_h_2, c_j, s4, s5)),
% 290.72/183.20 inference(unit_resolution,[status(thm)],[8600, 8579, 8591, 8590])).
% 290.72/183.20 tff(8602,plain,
% 290.72/183.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s4, s5)) | node5(c_e_h_2, c_j, s4, s5) | node6(c_e_h_2, c_j, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s4, s5)) | node5(c_e_h_2, c_j, s4, s5) | node6(c_e_h_2, c_j, s4, s5))),
% 290.72/183.20 inference(rewrite,[status(thm)],[])).
% 290.72/183.20 tff(8603,plain,
% 290.72/183.20 ((node6(c_e_h_2, c_j, s4, s5) | node5(c_e_h_2, c_j, s4, s5) | (~trans(s4, s5))) <=> ((~trans(s4, s5)) | node5(c_e_h_2, c_j, s4, s5) | node6(c_e_h_2, c_j, s4, s5))),
% 290.72/183.20 inference(rewrite,[status(thm)],[])).
% 290.72/183.20 tff(8604,plain,
% 290.72/183.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s4, s5) | node5(c_e_h_2, c_j, s4, s5) | (~trans(s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s4, s5)) | node5(c_e_h_2, c_j, s4, s5) | node6(c_e_h_2, c_j, s4, s5)))),
% 290.72/183.20 inference(monotonicity,[status(thm)],[8603])).
% 290.72/183.20 tff(8605,plain,
% 290.72/183.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s4, s5) | node5(c_e_h_2, c_j, s4, s5) | (~trans(s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s4, s5)) | node5(c_e_h_2, c_j, s4, s5) | node6(c_e_h_2, c_j, s4, s5))),
% 290.72/183.20 inference(transitivity,[status(thm)],[8604, 8602])).
% 290.72/183.20 tff(8606,plain,
% 290.72/183.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s4, s5) | node5(c_e_h_2, c_j, s4, s5) | (~trans(s4, s5)))),
% 290.72/183.20 inference(quant_inst,[status(thm)],[])).
% 290.72/183.20 tff(8607,plain,
% 290.72/183.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s4, s5)) | node5(c_e_h_2, c_j, s4, s5) | node6(c_e_h_2, c_j, s4, s5)),
% 290.72/183.20 inference(modus_ponens,[status(thm)],[8606, 8605])).
% 290.72/183.20 tff(8608,plain,
% 290.72/183.20 (node5(c_e_h_2, c_j, s4, s5) | node6(c_e_h_2, c_j, s4, s5)),
% 290.72/183.20 inference(unit_resolution,[status(thm)],[8607, 1141, 1028])).
% 290.72/183.20 tff(8609,plain,
% 290.72/183.20 ($false),
% 290.72/183.20 inference(unit_resolution,[status(thm)],[8608, 8601, 8589])).
% 290.72/183.20 tff(8610,plain,((~m_or_h_gate_v_out(c_e_h_2, c_j, s5)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s4) | m_or_h_gate_v_in2(c_e_h_2, c_j, s4) | m_or_h_gate_v_out(c_e_h_2, c_j, s4)), inference(lemma,lemma(discharge,[]))).
% 290.72/183.20 tff(8611,plain,
% 290.72/183.20 ((~m_or_h_gate_v_out(c_e_h_2, c_j, s5)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s4) | m_or_h_gate_v_out(c_e_h_2, c_j, s4)),
% 290.72/183.20 inference(unit_resolution,[status(thm)],[8610, 8577])).
% 290.72/183.20 tff(8612,plain,
% 290.72/183.20 ((~m_or_h_gate_v_out(c_e_h_2, c_j, s5)) | m_or_h_gate_v_out(c_e_h_2, c_j, s4)),
% 290.72/183.20 inference(unit_resolution,[status(thm)],[8611, 8396])).
% 290.72/183.20 tff(8613,plain,
% 290.72/183.20 (~m_or_h_gate_v_out(c_e_h_2, c_j, s5)),
% 290.72/183.20 inference(unit_resolution,[status(thm)],[8612, 8115])).
% 290.72/183.20 tff(8614,assumption,(m_c_h_element_v_in2(c_e_h_2, c_h, s5)), introduced(assumption)).
% 290.72/183.20 tff(8615,assumption,(~m_or_h_gate_v_out(c_e_h_2, c_j, s5)), introduced(assumption)).
% 290.72/183.20 tff(8616,plain,
% 290.72/183.20 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s5)) | m_or_h_gate_v_out(c_e_h_2, c_j, s5))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s5)) | m_or_h_gate_v_out(c_e_h_2, c_j, s5))),
% 290.72/183.20 inference(rewrite,[status(thm)],[])).
% 290.72/183.20 tff(8617,plain,
% 290.72/183.20 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s5)) | m_or_h_gate_v_out(c_e_h_2, c_j, s5))),
% 290.72/183.20 inference(quant_inst,[status(thm)],[])).
% 290.72/183.20 tff(8618,plain,
% 290.72/183.20 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s5)) | m_or_h_gate_v_out(c_e_h_2, c_j, s5)),
% 290.72/183.20 inference(modus_ponens,[status(thm)],[8617, 8616])).
% 290.72/183.20 tff(8619,plain,
% 290.72/183.20 ($false),
% 290.72/183.20 inference(unit_resolution,[status(thm)],[8618, 1174, 8615, 8614])).
% 290.72/183.20 tff(8620,plain,((~m_c_h_element_v_in2(c_e_h_2, c_h, s5)) | m_or_h_gate_v_out(c_e_h_2, c_j, s5)), inference(lemma,lemma(discharge,[]))).
% 290.72/183.20 tff(8621,plain,
% 290.72/183.20 (~m_c_h_element_v_in2(c_e_h_2, c_h, s5)),
% 290.72/183.20 inference(unit_resolution,[status(thm)],[8620, 8613])).
% 290.72/183.20 tff(8622,assumption,(m_c_h_element_v_out(c_e_h_2, c_h, s6)), introduced(assumption)).
% 290.72/183.20 tff(8623,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_h, s5)), introduced(assumption)).
% 290.72/183.20 tff(8624,assumption,(~node16(c_e_h_2, c_h, s5)), introduced(assumption)).
% 290.72/183.20 tff(8625,assumption,(node15(c_e_h_2, c_h, s5, s6)), introduced(assumption)).
% 290.72/183.20 tff(8626,plain,
% 290.72/183.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | (~node15(c_e_h_2, c_h, s5, s6)) | m_c_h_element_v_out(c_e_h_2, c_h, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | (~node15(c_e_h_2, c_h, s5, s6)) | m_c_h_element_v_out(c_e_h_2, c_h, s5))),
% 290.72/183.21 inference(rewrite,[status(thm)],[])).
% 290.72/183.21 tff(8627,plain,
% 290.72/183.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | (~node15(c_e_h_2, c_h, s5, s6)) | m_c_h_element_v_out(c_e_h_2, c_h, s5))),
% 290.72/183.21 inference(quant_inst,[status(thm)],[])).
% 290.72/183.21 tff(8628,plain,
% 290.72/183.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | (~node15(c_e_h_2, c_h, s5, s6)) | m_c_h_element_v_out(c_e_h_2, c_h, s5)),
% 290.72/183.21 inference(modus_ponens,[status(thm)],[8627, 8626])).
% 290.72/183.21 tff(8629,plain,
% 290.72/183.21 ($false),
% 290.72/183.21 inference(unit_resolution,[status(thm)],[8628, 147, 8622, 8625, 8186])).
% 290.72/183.21 tff(8630,plain,((~node15(c_e_h_2, c_h, s5, s6)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | m_c_h_element_v_out(c_e_h_2, c_h, s5)), inference(lemma,lemma(discharge,[]))).
% 290.72/183.21 tff(8631,plain,
% 290.72/183.21 (~node15(c_e_h_2, c_h, s5, s6)),
% 290.72/183.21 inference(unit_resolution,[status(thm)],[8630, 8622, 8186])).
% 290.72/183.21 tff(8632,plain,
% 290.72/183.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s5, s6)) | node19(c_e_h_2, c_h, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s5, s6)) | node19(c_e_h_2, c_h, s5, s6))),
% 290.72/183.21 inference(rewrite,[status(thm)],[])).
% 290.72/183.21 tff(8633,plain,
% 290.72/183.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s5, s6)) | node19(c_e_h_2, c_h, s5, s6))),
% 290.72/183.21 inference(quant_inst,[status(thm)],[])).
% 290.72/183.21 tff(8634,plain,
% 290.72/183.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s5, s6)) | node19(c_e_h_2, c_h, s5, s6)),
% 290.72/183.21 inference(modus_ponens,[status(thm)],[8633, 8632])).
% 290.72/183.21 tff(8635,plain,
% 290.72/183.21 (node19(c_e_h_2, c_h, s5, s6)),
% 290.72/183.21 inference(unit_resolution,[status(thm)],[8634, 190, 1406])).
% 290.72/183.21 tff(8636,plain,
% 290.72/183.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_h, s5, s6)) | node16(c_e_h_2, c_h, s5) | node15(c_e_h_2, c_h, s5, s6) | node14(c_e_h_2, c_h, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_h, s5, s6)) | node16(c_e_h_2, c_h, s5) | node15(c_e_h_2, c_h, s5, s6) | node14(c_e_h_2, c_h, s5, s6))),
% 290.72/183.21 inference(rewrite,[status(thm)],[])).
% 290.72/183.21 tff(8637,plain,
% 290.72/183.21 ((node16(c_e_h_2, c_h, s5) | node14(c_e_h_2, c_h, s5, s6) | node15(c_e_h_2, c_h, s5, s6) | (~node19(c_e_h_2, c_h, s5, s6))) <=> ((~node19(c_e_h_2, c_h, s5, s6)) | node16(c_e_h_2, c_h, s5) | node15(c_e_h_2, c_h, s5, s6) | node14(c_e_h_2, c_h, s5, s6))),
% 290.72/183.21 inference(rewrite,[status(thm)],[])).
% 290.72/183.21 tff(8638,plain,
% 290.72/183.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s5) | node14(c_e_h_2, c_h, s5, s6) | node15(c_e_h_2, c_h, s5, s6) | (~node19(c_e_h_2, c_h, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_h, s5, s6)) | node16(c_e_h_2, c_h, s5) | node15(c_e_h_2, c_h, s5, s6) | node14(c_e_h_2, c_h, s5, s6)))),
% 290.72/183.21 inference(monotonicity,[status(thm)],[8637])).
% 290.72/183.21 tff(8639,plain,
% 290.72/183.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s5) | node14(c_e_h_2, c_h, s5, s6) | node15(c_e_h_2, c_h, s5, s6) | (~node19(c_e_h_2, c_h, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_h, s5, s6)) | node16(c_e_h_2, c_h, s5) | node15(c_e_h_2, c_h, s5, s6) | node14(c_e_h_2, c_h, s5, s6))),
% 290.72/183.21 inference(transitivity,[status(thm)],[8638, 8636])).
% 290.72/183.21 tff(8640,plain,
% 290.72/183.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s5) | node14(c_e_h_2, c_h, s5, s6) | node15(c_e_h_2, c_h, s5, s6) | (~node19(c_e_h_2, c_h, s5, s6)))),
% 290.72/183.21 inference(quant_inst,[status(thm)],[])).
% 290.72/183.21 tff(8641,plain,
% 290.72/183.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_h, s5, s6)) | node16(c_e_h_2, c_h, s5) | node15(c_e_h_2, c_h, s5, s6) | node14(c_e_h_2, c_h, s5, s6)),
% 290.72/183.21 inference(modus_ponens,[status(thm)],[8640, 8639])).
% 290.72/183.21 tff(8642,plain,
% 290.72/183.21 (node16(c_e_h_2, c_h, s5) | node15(c_e_h_2, c_h, s5, s6) | node14(c_e_h_2, c_h, s5, s6)),
% 290.72/183.21 inference(unit_resolution,[status(thm)],[8641, 204, 8635])).
% 290.72/183.21 tff(8643,plain,
% 290.72/183.21 (node14(c_e_h_2, c_h, s5, s6)),
% 290.72/183.21 inference(unit_resolution,[status(thm)],[8642, 8631, 8624])).
% 290.72/183.21 tff(8644,plain,
% 290.72/183.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s5) | (~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | (~node14(c_e_h_2, c_h, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s5) | (~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | (~node14(c_e_h_2, c_h, s5, s6)))),
% 290.72/183.21 inference(rewrite,[status(thm)],[])).
% 290.72/183.21 tff(8645,plain,
% 290.72/183.21 (((~node14(c_e_h_2, c_h, s5, s6)) | m_c_h_element_v_in1(c_e_h_2, c_h, s5) | (~m_c_h_element_v_out(c_e_h_2, c_h, s6))) <=> (m_c_h_element_v_in1(c_e_h_2, c_h, s5) | (~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | (~node14(c_e_h_2, c_h, s5, s6)))),
% 290.72/183.21 inference(rewrite,[status(thm)],[])).
% 290.72/183.21 tff(8646,plain,
% 290.72/183.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s5, s6)) | m_c_h_element_v_in1(c_e_h_2, c_h, s5) | (~m_c_h_element_v_out(c_e_h_2, c_h, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s5) | (~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | (~node14(c_e_h_2, c_h, s5, s6))))),
% 290.72/183.21 inference(monotonicity,[status(thm)],[8645])).
% 290.72/183.21 tff(8647,plain,
% 290.72/183.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s5, s6)) | m_c_h_element_v_in1(c_e_h_2, c_h, s5) | (~m_c_h_element_v_out(c_e_h_2, c_h, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s5) | (~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | (~node14(c_e_h_2, c_h, s5, s6)))),
% 290.72/183.21 inference(transitivity,[status(thm)],[8646, 8644])).
% 290.72/183.21 tff(8648,plain,
% 290.72/183.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s5, s6)) | m_c_h_element_v_in1(c_e_h_2, c_h, s5) | (~m_c_h_element_v_out(c_e_h_2, c_h, s6)))),
% 290.72/183.21 inference(quant_inst,[status(thm)],[])).
% 290.72/183.21 tff(8649,plain,
% 290.72/183.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s5) | (~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | (~node14(c_e_h_2, c_h, s5, s6))),
% 290.72/183.21 inference(modus_ponens,[status(thm)],[8648, 8647])).
% 290.72/183.21 tff(8650,plain,
% 290.72/183.21 ($false),
% 290.72/183.21 inference(unit_resolution,[status(thm)],[8649, 223, 8622, 8643, 8623])).
% 290.72/183.21 tff(8651,plain,((~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | m_c_h_element_v_in1(c_e_h_2, c_h, s5) | node16(c_e_h_2, c_h, s5) | m_c_h_element_v_out(c_e_h_2, c_h, s5)), inference(lemma,lemma(discharge,[]))).
% 290.72/183.21 tff(8652,plain,
% 290.72/183.21 (node16(c_e_h_2, c_h, s5)),
% 290.72/183.21 inference(unit_resolution,[status(thm)],[8651, 8186, 8622, 8623])).
% 290.72/183.21 tff(8653,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_h, s5)), introduced(assumption)).
% 290.72/183.21 tff(8654,assumption,(node16(c_e_h_2, c_h, s5)), introduced(assumption)).
% 290.72/183.21 tff(8655,plain,
% 290.72/183.21 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_h, s5)) | m_c_h_element_v_in1(c_e_h_2, c_h, s5) | m_c_h_element_v_in2(c_e_h_2, c_h, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_h, s5)) | m_c_h_element_v_in1(c_e_h_2, c_h, s5) | m_c_h_element_v_in2(c_e_h_2, c_h, s5))),
% 290.72/183.21 inference(rewrite,[status(thm)],[])).
% 290.72/183.21 tff(8656,plain,
% 290.72/183.21 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_h, s5)) | m_c_h_element_v_in1(c_e_h_2, c_h, s5) | m_c_h_element_v_in2(c_e_h_2, c_h, s5))),
% 290.72/183.21 inference(quant_inst,[status(thm)],[])).
% 290.72/183.21 tff(8657,plain,
% 290.72/183.21 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_h, s5)) | m_c_h_element_v_in1(c_e_h_2, c_h, s5) | m_c_h_element_v_in2(c_e_h_2, c_h, s5)),
% 290.72/183.21 inference(modus_ponens,[status(thm)],[8656, 8655])).
% 290.72/183.21 tff(8658,plain,
% 290.72/183.21 ($false),
% 290.72/183.21 inference(unit_resolution,[status(thm)],[8657, 178, 8654, 8623, 8653])).
% 290.72/183.21 tff(8659,plain,((~node16(c_e_h_2, c_h, s5)) | m_c_h_element_v_in1(c_e_h_2, c_h, s5) | m_c_h_element_v_in2(c_e_h_2, c_h, s5)), inference(lemma,lemma(discharge,[]))).
% 290.72/183.21 tff(8660,plain,
% 290.72/183.21 (m_c_h_element_v_in2(c_e_h_2, c_h, s5)),
% 290.72/183.21 inference(unit_resolution,[status(thm)],[8659, 8652, 8623])).
% 290.72/183.21 tff(8661,plain,
% 290.72/183.21 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s5) | (~node17(c_e_h_2, c_h, s5)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s5) | (~node17(c_e_h_2, c_h, s5)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s5)))),
% 290.72/183.21 inference(rewrite,[status(thm)],[])).
% 290.72/183.21 tff(8662,plain,
% 290.72/183.21 ((m_c_h_element_v_in1(c_e_h_2, c_h, s5) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s5)) | (~node17(c_e_h_2, c_h, s5))) <=> (m_c_h_element_v_in1(c_e_h_2, c_h, s5) | (~node17(c_e_h_2, c_h, s5)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s5)))),
% 290.72/183.21 inference(rewrite,[status(thm)],[])).
% 290.72/183.21 tff(8663,plain,
% 290.72/183.21 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s5) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s5)) | (~node17(c_e_h_2, c_h, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s5) | (~node17(c_e_h_2, c_h, s5)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s5))))),
% 290.72/183.21 inference(monotonicity,[status(thm)],[8662])).
% 290.72/183.21 tff(8664,plain,
% 290.72/183.21 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s5) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s5)) | (~node17(c_e_h_2, c_h, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s5) | (~node17(c_e_h_2, c_h, s5)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s5)))),
% 290.72/183.21 inference(transitivity,[status(thm)],[8663, 8661])).
% 290.72/183.21 tff(8665,plain,
% 290.72/183.21 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s5) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s5)) | (~node17(c_e_h_2, c_h, s5)))),
% 290.72/183.21 inference(quant_inst,[status(thm)],[])).
% 290.72/183.21 tff(8666,plain,
% 290.72/183.22 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s5) | (~node17(c_e_h_2, c_h, s5)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s5))),
% 290.72/183.22 inference(modus_ponens,[status(thm)],[8665, 8664])).
% 290.72/183.22 tff(8667,plain,
% 290.72/183.22 ((~node17(c_e_h_2, c_h, s5)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s5))),
% 290.72/183.22 inference(unit_resolution,[status(thm)],[8666, 859, 8623])).
% 290.72/183.22 tff(8668,plain,
% 290.72/183.22 (~node17(c_e_h_2, c_h, s5)),
% 290.72/183.22 inference(unit_resolution,[status(thm)],[8667, 8660])).
% 290.72/183.22 tff(8669,plain,
% 290.72/183.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_h, s5, s6)) | node18(c_e_h_2, c_h, s5, s6) | node17(c_e_h_2, c_h, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_h, s5, s6)) | node18(c_e_h_2, c_h, s5, s6) | node17(c_e_h_2, c_h, s5))),
% 290.72/183.22 inference(rewrite,[status(thm)],[])).
% 290.72/183.22 tff(8670,plain,
% 290.72/183.22 ((node17(c_e_h_2, c_h, s5) | node18(c_e_h_2, c_h, s5, s6) | (~node19(c_e_h_2, c_h, s5, s6))) <=> ((~node19(c_e_h_2, c_h, s5, s6)) | node18(c_e_h_2, c_h, s5, s6) | node17(c_e_h_2, c_h, s5))),
% 290.72/183.22 inference(rewrite,[status(thm)],[])).
% 290.72/183.22 tff(8671,plain,
% 290.72/183.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s5) | node18(c_e_h_2, c_h, s5, s6) | (~node19(c_e_h_2, c_h, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_h, s5, s6)) | node18(c_e_h_2, c_h, s5, s6) | node17(c_e_h_2, c_h, s5)))),
% 290.72/183.22 inference(monotonicity,[status(thm)],[8670])).
% 290.72/183.22 tff(8672,plain,
% 290.72/183.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s5) | node18(c_e_h_2, c_h, s5, s6) | (~node19(c_e_h_2, c_h, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_h, s5, s6)) | node18(c_e_h_2, c_h, s5, s6) | node17(c_e_h_2, c_h, s5))),
% 290.72/183.22 inference(transitivity,[status(thm)],[8671, 8669])).
% 290.72/183.22 tff(8673,plain,
% 290.72/183.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s5) | node18(c_e_h_2, c_h, s5, s6) | (~node19(c_e_h_2, c_h, s5, s6)))),
% 290.72/183.22 inference(quant_inst,[status(thm)],[])).
% 290.72/183.22 tff(8674,plain,
% 290.72/183.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_h, s5, s6)) | node18(c_e_h_2, c_h, s5, s6) | node17(c_e_h_2, c_h, s5)),
% 290.72/183.22 inference(modus_ponens,[status(thm)],[8673, 8672])).
% 290.72/183.22 tff(8675,plain,
% 290.72/183.22 (node18(c_e_h_2, c_h, s5, s6) | node17(c_e_h_2, c_h, s5)),
% 290.72/183.22 inference(unit_resolution,[status(thm)],[8674, 776, 8635])).
% 290.72/183.22 tff(8676,plain,
% 290.72/183.22 (node18(c_e_h_2, c_h, s5, s6)),
% 290.72/183.22 inference(unit_resolution,[status(thm)],[8675, 8668])).
% 290.72/183.22 tff(8677,plain,
% 290.72/183.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_h, s5) | (~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | (~node18(c_e_h_2, c_h, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s5) | (~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | (~node18(c_e_h_2, c_h, s5, s6)))),
% 290.72/183.22 inference(rewrite,[status(thm)],[])).
% 290.72/183.22 tff(8678,plain,
% 290.72/183.22 (((~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | m_c_h_element_v_out(c_e_h_2, c_h, s5) | (~node18(c_e_h_2, c_h, s5, s6))) <=> (m_c_h_element_v_out(c_e_h_2, c_h, s5) | (~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | (~node18(c_e_h_2, c_h, s5, s6)))),
% 290.72/183.22 inference(rewrite,[status(thm)],[])).
% 290.72/183.22 tff(8679,plain,
% 290.72/183.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | m_c_h_element_v_out(c_e_h_2, c_h, s5) | (~node18(c_e_h_2, c_h, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_h, s5) | (~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | (~node18(c_e_h_2, c_h, s5, s6))))),
% 290.72/183.22 inference(monotonicity,[status(thm)],[8678])).
% 290.72/183.22 tff(8680,plain,
% 290.72/183.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | m_c_h_element_v_out(c_e_h_2, c_h, s5) | (~node18(c_e_h_2, c_h, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s5) | (~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | (~node18(c_e_h_2, c_h, s5, s6)))),
% 290.72/183.22 inference(transitivity,[status(thm)],[8679, 8677])).
% 290.72/183.22 tff(8681,plain,
% 290.72/183.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | m_c_h_element_v_out(c_e_h_2, c_h, s5) | (~node18(c_e_h_2, c_h, s5, s6)))),
% 290.72/183.22 inference(quant_inst,[status(thm)],[])).
% 290.72/183.22 tff(8682,plain,
% 290.72/183.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s5) | (~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | (~node18(c_e_h_2, c_h, s5, s6))),
% 290.72/183.22 inference(modus_ponens,[status(thm)],[8681, 8680])).
% 290.72/183.22 tff(8683,plain,
% 290.72/183.22 ($false),
% 290.72/183.22 inference(unit_resolution,[status(thm)],[8682, 753, 8622, 8676, 8186])).
% 290.72/183.22 tff(8684,plain,(m_c_h_element_v_out(c_e_h_2, c_h, s5) | (~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | m_c_h_element_v_in1(c_e_h_2, c_h, s5)), inference(lemma,lemma(discharge,[]))).
% 290.72/183.22 tff(8685,plain,
% 290.72/183.22 ((~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | m_c_h_element_v_in1(c_e_h_2, c_h, s5)),
% 290.72/183.22 inference(unit_resolution,[status(thm)],[8684, 8184])).
% 290.72/183.22 tff(8686,plain,
% 290.72/183.22 (m_c_h_element_v_in1(c_e_h_2, c_h, s5)),
% 290.72/183.22 inference(unit_resolution,[status(thm)],[8685, 8622])).
% 290.72/183.22 tff(8687,assumption,(node18(c_e_h_2, c_h, s5, s6)), introduced(assumption)).
% 290.72/183.22 tff(8688,plain,
% 290.72/183.22 ($false),
% 290.72/183.22 inference(unit_resolution,[status(thm)],[8682, 753, 8622, 8687, 8186])).
% 290.72/183.22 tff(8689,plain,((~node18(c_e_h_2, c_h, s5, s6)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s6)) | m_c_h_element_v_out(c_e_h_2, c_h, s5)), inference(lemma,lemma(discharge,[]))).
% 290.72/183.22 tff(8690,plain,
% 290.72/183.22 ((~node18(c_e_h_2, c_h, s5, s6)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s6))),
% 290.72/183.22 inference(unit_resolution,[status(thm)],[8689, 8184])).
% 290.72/183.22 tff(8691,plain,
% 290.72/183.22 (~node18(c_e_h_2, c_h, s5, s6)),
% 290.72/183.22 inference(unit_resolution,[status(thm)],[8690, 8622])).
% 290.72/183.22 tff(8692,plain,
% 290.72/183.22 (node17(c_e_h_2, c_h, s5)),
% 290.72/183.22 inference(unit_resolution,[status(thm)],[8675, 8691])).
% 290.72/183.22 tff(8693,plain,
% 290.72/183.22 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_h, s5)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s5)) | m_c_h_element_v_in2(c_e_h_2, c_h, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_h, s5)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s5)) | m_c_h_element_v_in2(c_e_h_2, c_h, s5))),
% 290.72/183.22 inference(rewrite,[status(thm)],[])).
% 290.72/183.22 tff(8694,plain,
% 290.72/183.22 (((~m_c_h_element_v_in1(c_e_h_2, c_h, s5)) | m_c_h_element_v_in2(c_e_h_2, c_h, s5) | (~node17(c_e_h_2, c_h, s5))) <=> ((~node17(c_e_h_2, c_h, s5)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s5)) | m_c_h_element_v_in2(c_e_h_2, c_h, s5))),
% 290.72/183.22 inference(rewrite,[status(thm)],[])).
% 290.72/183.22 tff(8695,plain,
% 290.72/183.22 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s5)) | m_c_h_element_v_in2(c_e_h_2, c_h, s5) | (~node17(c_e_h_2, c_h, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_h, s5)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s5)) | m_c_h_element_v_in2(c_e_h_2, c_h, s5)))),
% 290.72/183.22 inference(monotonicity,[status(thm)],[8694])).
% 290.72/183.22 tff(8696,plain,
% 290.72/183.22 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s5)) | m_c_h_element_v_in2(c_e_h_2, c_h, s5) | (~node17(c_e_h_2, c_h, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_h, s5)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s5)) | m_c_h_element_v_in2(c_e_h_2, c_h, s5))),
% 290.72/183.22 inference(transitivity,[status(thm)],[8695, 8693])).
% 290.72/183.22 tff(8697,plain,
% 290.72/183.22 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s5)) | m_c_h_element_v_in2(c_e_h_2, c_h, s5) | (~node17(c_e_h_2, c_h, s5)))),
% 290.72/183.22 inference(quant_inst,[status(thm)],[])).
% 290.72/183.22 tff(8698,plain,
% 290.72/183.22 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_h, s5)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s5)) | m_c_h_element_v_in2(c_e_h_2, c_h, s5)),
% 290.72/183.22 inference(modus_ponens,[status(thm)],[8697, 8696])).
% 290.72/183.22 tff(8699,plain,
% 290.72/183.22 ($false),
% 290.72/183.22 inference(unit_resolution,[status(thm)],[8698, 919, 8692, 8686, 8621])).
% 290.72/183.22 tff(8700,plain,(~m_c_h_element_v_out(c_e_h_2, c_h, s6)), inference(lemma,lemma(discharge,[]))).
% 290.72/183.22 tff(8701,plain,
% 290.72/183.22 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s6)) | m_c_h_element_v_out(c_e_h_2, c_h, s6))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s6)) | m_c_h_element_v_out(c_e_h_2, c_h, s6))),
% 290.72/183.22 inference(rewrite,[status(thm)],[])).
% 290.72/183.22 tff(8702,plain,
% 290.72/183.22 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s6)) | m_c_h_element_v_out(c_e_h_2, c_h, s6))),
% 290.72/183.22 inference(quant_inst,[status(thm)],[])).
% 290.72/183.22 tff(8703,plain,
% 290.72/183.22 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s6)) | m_c_h_element_v_out(c_e_h_2, c_h, s6)),
% 290.72/183.22 inference(modus_ponens,[status(thm)],[8702, 8701])).
% 290.72/183.22 tff(8704,plain,
% 290.72/183.22 (~m_and_h_gate_v_in1(c_e_h_2, c_i, s6)),
% 290.72/183.22 inference(unit_resolution,[status(thm)],[8703, 619, 8700])).
% 290.72/183.22 tff(8705,plain,
% 290.72/183.22 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s6)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s6)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s6))),
% 290.72/183.22 inference(rewrite,[status(thm)],[])).
% 290.72/183.22 tff(8706,plain,
% 290.72/183.22 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s6)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s6))),
% 290.72/183.22 inference(quant_inst,[status(thm)],[])).
% 290.72/183.22 tff(8707,plain,
% 290.72/183.22 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s6)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s6)),
% 290.72/183.22 inference(modus_ponens,[status(thm)],[8706, 8705])).
% 290.72/183.22 tff(8708,plain,
% 290.72/183.22 (~node20(c_e_h_2, c_i, s6)),
% 290.72/183.22 inference(unit_resolution,[status(thm)],[8707, 38, 8704])).
% 290.72/183.22 tff(8709,assumption,(~node20(c_e_h_2, c_i, s6)), introduced(assumption)).
% 290.72/183.22 tff(8710,assumption,(node21(c_e_h_2, c_i, s6, s7)), introduced(assumption)).
% 290.72/183.22 tff(8711,plain,
% 290.72/183.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s7)) | node20(c_e_h_2, c_i, s6) | (~node21(c_e_h_2, c_i, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s7)) | node20(c_e_h_2, c_i, s6) | (~node21(c_e_h_2, c_i, s6, s7)))),
% 290.72/183.23 inference(rewrite,[status(thm)],[])).
% 290.72/183.23 tff(8712,plain,
% 290.72/183.23 ((node20(c_e_h_2, c_i, s6) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s7)) | (~node21(c_e_h_2, c_i, s6, s7))) <=> ((~m_and_h_gate_v_out(c_e_h_2, c_i, s7)) | node20(c_e_h_2, c_i, s6) | (~node21(c_e_h_2, c_i, s6, s7)))),
% 290.72/183.23 inference(rewrite,[status(thm)],[])).
% 290.72/183.23 tff(8713,plain,
% 290.72/183.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s6) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s7)) | (~node21(c_e_h_2, c_i, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s7)) | node20(c_e_h_2, c_i, s6) | (~node21(c_e_h_2, c_i, s6, s7))))),
% 290.72/183.23 inference(monotonicity,[status(thm)],[8712])).
% 290.72/183.23 tff(8714,plain,
% 290.72/183.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s6) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s7)) | (~node21(c_e_h_2, c_i, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s7)) | node20(c_e_h_2, c_i, s6) | (~node21(c_e_h_2, c_i, s6, s7)))),
% 290.72/183.23 inference(transitivity,[status(thm)],[8713, 8711])).
% 290.72/183.23 tff(8715,plain,
% 290.72/183.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s6) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s7)) | (~node21(c_e_h_2, c_i, s6, s7)))),
% 290.72/183.23 inference(quant_inst,[status(thm)],[])).
% 290.72/183.23 tff(8716,plain,
% 290.72/183.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s7)) | node20(c_e_h_2, c_i, s6) | (~node21(c_e_h_2, c_i, s6, s7))),
% 290.72/183.23 inference(modus_ponens,[status(thm)],[8715, 8714])).
% 290.72/183.23 tff(8717,plain,
% 290.72/183.23 ($false),
% 290.72/183.23 inference(unit_resolution,[status(thm)],[8716, 52, 7814, 8710, 8709])).
% 290.72/183.23 tff(8718,plain,((~node21(c_e_h_2, c_i, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s7)) | node20(c_e_h_2, c_i, s6)), inference(lemma,lemma(discharge,[]))).
% 290.72/183.23 tff(8719,plain,
% 290.72/183.23 (~node21(c_e_h_2, c_i, s6, s7)),
% 290.72/183.23 inference(unit_resolution,[status(thm)],[8718, 7814, 8708])).
% 290.72/183.23 tff(8720,plain,
% 290.72/183.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_2, c_i, s6, s7) | node22(c_e_h_2, c_i, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_2, c_i, s6, s7) | node22(c_e_h_2, c_i, s6, s7))),
% 290.72/183.23 inference(rewrite,[status(thm)],[])).
% 290.72/183.23 tff(8721,plain,
% 290.72/183.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_2, c_i, s6, s7) | node22(c_e_h_2, c_i, s6, s7))),
% 290.72/183.23 inference(quant_inst,[status(thm)],[])).
% 290.72/183.23 tff(8722,plain,
% 290.72/183.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_2, c_i, s6, s7) | node22(c_e_h_2, c_i, s6, s7)),
% 290.72/183.23 inference(modus_ponens,[status(thm)],[8721, 8720])).
% 290.72/183.23 tff(8723,plain,
% 290.72/183.23 (node21(c_e_h_2, c_i, s6, s7) | node22(c_e_h_2, c_i, s6, s7)),
% 290.72/183.23 inference(unit_resolution,[status(thm)],[8722, 82, 1844])).
% 290.72/183.23 tff(8724,plain,
% 290.72/183.23 ($false),
% 290.72/183.23 inference(unit_resolution,[status(thm)],[8723, 8719, 8230])).
% 290.72/183.23 tff(8725,plain,(~m_and_h_gate_v_out(c_e_h_2, c_i, s7)), inference(lemma,lemma(discharge,[]))).
% 290.72/183.23 tff(8726,assumption,(m_c_h_element_v_in2(c_e_h_2, c_f, s7)), introduced(assumption)).
% 290.72/183.23 tff(8727,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_i, s7)), introduced(assumption)).
% 290.72/183.23 tff(8728,plain,
% 290.72/183.23 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_f, s7)) | m_and_h_gate_v_out(c_e_h_2, c_i, s7))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s7)) | m_and_h_gate_v_out(c_e_h_2, c_i, s7))),
% 290.72/183.23 inference(rewrite,[status(thm)],[])).
% 290.72/183.23 tff(8729,plain,
% 290.72/183.23 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_f, s7)) | m_and_h_gate_v_out(c_e_h_2, c_i, s7))),
% 290.72/183.23 inference(quant_inst,[status(thm)],[])).
% 290.72/183.23 tff(8730,plain,
% 290.72/183.23 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s7)) | m_and_h_gate_v_out(c_e_h_2, c_i, s7)),
% 290.72/183.23 inference(modus_ponens,[status(thm)],[8729, 8728])).
% 290.72/183.23 tff(8731,plain,
% 290.72/183.23 ($false),
% 290.72/183.23 inference(unit_resolution,[status(thm)],[8730, 2143, 8727, 8726])).
% 290.72/183.23 tff(8732,plain,((~m_c_h_element_v_in2(c_e_h_2, c_f, s7)) | m_and_h_gate_v_out(c_e_h_2, c_i, s7)), inference(lemma,lemma(discharge,[]))).
% 290.72/183.23 tff(8733,plain,
% 290.72/183.23 (~m_c_h_element_v_in2(c_e_h_2, c_f, s7)),
% 290.72/183.23 inference(unit_resolution,[status(thm)],[8732, 8725])).
% 290.72/183.23 tff(8734,assumption,(m_c_h_element_v_in2(c_e_h_2, c_f, s6)), introduced(assumption)).
% 290.72/183.23 tff(8735,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_i, s6)), introduced(assumption)).
% 290.72/183.23 tff(8736,plain,
% 290.72/183.23 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_f, s6)) | m_and_h_gate_v_out(c_e_h_2, c_i, s6))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s6)) | m_and_h_gate_v_out(c_e_h_2, c_i, s6))),
% 290.72/183.23 inference(rewrite,[status(thm)],[])).
% 290.72/183.23 tff(8737,plain,
% 290.72/183.23 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_f, s6)) | m_and_h_gate_v_out(c_e_h_2, c_i, s6))),
% 290.72/183.23 inference(quant_inst,[status(thm)],[])).
% 290.72/183.23 tff(8738,plain,
% 290.72/183.23 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s6)) | m_and_h_gate_v_out(c_e_h_2, c_i, s6)),
% 290.72/183.23 inference(modus_ponens,[status(thm)],[8737, 8736])).
% 290.72/183.23 tff(8739,plain,
% 290.72/183.23 ($false),
% 290.72/183.23 inference(unit_resolution,[status(thm)],[8738, 2143, 8735, 8734])).
% 290.72/183.23 tff(8740,plain,((~m_c_h_element_v_in2(c_e_h_2, c_f, s6)) | m_and_h_gate_v_out(c_e_h_2, c_i, s6)), inference(lemma,lemma(discharge,[]))).
% 290.72/183.23 tff(8741,plain,
% 290.72/183.23 (~m_c_h_element_v_in2(c_e_h_2, c_f, s6)),
% 290.72/183.23 inference(unit_resolution,[status(thm)],[8740, 8224])).
% 290.72/183.23 tff(8742,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_f, s6)), introduced(assumption)).
% 290.72/183.23 tff(8743,assumption,(m_c_h_element_v_out(c_e_h_2, c_f, s7)), introduced(assumption)).
% 290.72/183.23 tff(8744,assumption,(~m_c_h_element_v_out(c_e_h_2, c_f, s6)), introduced(assumption)).
% 290.72/183.23 tff(8745,assumption,(node15(c_e_h_2, c_f, s6, s7)), introduced(assumption)).
% 290.72/183.23 tff(8746,plain,
% 290.72/183.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s7)) | (~node15(c_e_h_2, c_f, s6, s7)) | m_c_h_element_v_out(c_e_h_2, c_f, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s7)) | (~node15(c_e_h_2, c_f, s6, s7)) | m_c_h_element_v_out(c_e_h_2, c_f, s6))),
% 290.72/183.23 inference(rewrite,[status(thm)],[])).
% 290.72/183.23 tff(8747,plain,
% 290.72/183.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s7)) | (~node15(c_e_h_2, c_f, s6, s7)) | m_c_h_element_v_out(c_e_h_2, c_f, s6))),
% 290.72/183.23 inference(quant_inst,[status(thm)],[])).
% 290.72/183.23 tff(8748,plain,
% 290.72/183.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s7)) | (~node15(c_e_h_2, c_f, s6, s7)) | m_c_h_element_v_out(c_e_h_2, c_f, s6)),
% 290.72/183.23 inference(modus_ponens,[status(thm)],[8747, 8746])).
% 290.72/183.23 tff(8749,plain,
% 290.72/183.23 ($false),
% 290.72/183.23 inference(unit_resolution,[status(thm)],[8748, 147, 8743, 8744, 8745])).
% 290.72/183.23 tff(8750,plain,((~node15(c_e_h_2, c_f, s6, s7)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s7)) | m_c_h_element_v_out(c_e_h_2, c_f, s6)), inference(lemma,lemma(discharge,[]))).
% 290.72/183.23 tff(8751,plain,
% 290.72/183.23 (~node15(c_e_h_2, c_f, s6, s7)),
% 290.72/183.23 inference(unit_resolution,[status(thm)],[8750, 8744, 8743])).
% 290.72/183.23 tff(8752,assumption,(~node15(c_e_h_2, c_f, s6, s7)), introduced(assumption)).
% 290.72/183.23 tff(8753,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_f, s6)), introduced(assumption)).
% 290.72/183.23 tff(8754,plain,
% 290.72/183.23 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_f, s6)) | m_c_h_element_v_in1(c_e_h_2, c_f, s6) | m_c_h_element_v_in2(c_e_h_2, c_f, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_f, s6)) | m_c_h_element_v_in1(c_e_h_2, c_f, s6) | m_c_h_element_v_in2(c_e_h_2, c_f, s6))),
% 290.72/183.23 inference(rewrite,[status(thm)],[])).
% 290.72/183.23 tff(8755,plain,
% 290.72/183.23 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_f, s6)) | m_c_h_element_v_in1(c_e_h_2, c_f, s6) | m_c_h_element_v_in2(c_e_h_2, c_f, s6))),
% 290.72/183.23 inference(quant_inst,[status(thm)],[])).
% 290.72/183.23 tff(8756,plain,
% 290.72/183.23 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_f, s6)) | m_c_h_element_v_in1(c_e_h_2, c_f, s6) | m_c_h_element_v_in2(c_e_h_2, c_f, s6)),
% 290.72/183.23 inference(modus_ponens,[status(thm)],[8755, 8754])).
% 290.72/183.23 tff(8757,plain,
% 290.72/183.23 ((~node16(c_e_h_2, c_f, s6)) | m_c_h_element_v_in1(c_e_h_2, c_f, s6)),
% 290.72/183.23 inference(unit_resolution,[status(thm)],[8756, 178, 8742])).
% 290.72/183.23 tff(8758,plain,
% 290.72/183.23 (~node16(c_e_h_2, c_f, s6)),
% 290.72/183.23 inference(unit_resolution,[status(thm)],[8757, 8753])).
% 290.72/183.23 tff(8759,assumption,(node14(c_e_h_2, c_f, s6, s7)), introduced(assumption)).
% 290.72/183.23 tff(8760,plain,
% 290.72/183.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s7)) | m_c_h_element_v_in1(c_e_h_2, c_f, s6) | (~node14(c_e_h_2, c_f, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s7)) | m_c_h_element_v_in1(c_e_h_2, c_f, s6) | (~node14(c_e_h_2, c_f, s6, s7)))),
% 290.72/183.23 inference(rewrite,[status(thm)],[])).
% 290.72/183.23 tff(8761,plain,
% 290.72/183.23 (((~node14(c_e_h_2, c_f, s6, s7)) | m_c_h_element_v_in1(c_e_h_2, c_f, s6) | (~m_c_h_element_v_out(c_e_h_2, c_f, s7))) <=> ((~m_c_h_element_v_out(c_e_h_2, c_f, s7)) | m_c_h_element_v_in1(c_e_h_2, c_f, s6) | (~node14(c_e_h_2, c_f, s6, s7)))),
% 290.72/183.23 inference(rewrite,[status(thm)],[])).
% 290.72/183.23 tff(8762,plain,
% 290.72/183.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_f, s6, s7)) | m_c_h_element_v_in1(c_e_h_2, c_f, s6) | (~m_c_h_element_v_out(c_e_h_2, c_f, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s7)) | m_c_h_element_v_in1(c_e_h_2, c_f, s6) | (~node14(c_e_h_2, c_f, s6, s7))))),
% 290.72/183.23 inference(monotonicity,[status(thm)],[8761])).
% 290.72/183.23 tff(8763,plain,
% 290.72/183.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_f, s6, s7)) | m_c_h_element_v_in1(c_e_h_2, c_f, s6) | (~m_c_h_element_v_out(c_e_h_2, c_f, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s7)) | m_c_h_element_v_in1(c_e_h_2, c_f, s6) | (~node14(c_e_h_2, c_f, s6, s7)))),
% 290.72/183.24 inference(transitivity,[status(thm)],[8762, 8760])).
% 290.72/183.24 tff(8764,plain,
% 290.72/183.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_f, s6, s7)) | m_c_h_element_v_in1(c_e_h_2, c_f, s6) | (~m_c_h_element_v_out(c_e_h_2, c_f, s7)))),
% 290.72/183.24 inference(quant_inst,[status(thm)],[])).
% 290.72/183.24 tff(8765,plain,
% 290.72/183.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s7)) | m_c_h_element_v_in1(c_e_h_2, c_f, s6) | (~node14(c_e_h_2, c_f, s6, s7))),
% 290.72/183.24 inference(modus_ponens,[status(thm)],[8764, 8763])).
% 290.72/183.24 tff(8766,plain,
% 290.72/183.24 ($false),
% 290.72/183.24 inference(unit_resolution,[status(thm)],[8765, 223, 8743, 8759, 8753])).
% 290.72/183.24 tff(8767,plain,((~node14(c_e_h_2, c_f, s6, s7)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s7)) | m_c_h_element_v_in1(c_e_h_2, c_f, s6)), inference(lemma,lemma(discharge,[]))).
% 290.72/183.24 tff(8768,plain,
% 290.72/183.24 (~node14(c_e_h_2, c_f, s6, s7)),
% 290.72/183.24 inference(unit_resolution,[status(thm)],[8767, 8753, 8743])).
% 290.72/183.24 tff(8769,plain,
% 290.72/183.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s6, s7)) | node19(c_e_h_2, c_f, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s6, s7)) | node19(c_e_h_2, c_f, s6, s7))),
% 290.72/183.24 inference(rewrite,[status(thm)],[])).
% 290.72/183.24 tff(8770,plain,
% 290.72/183.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s6, s7)) | node19(c_e_h_2, c_f, s6, s7))),
% 290.72/183.24 inference(quant_inst,[status(thm)],[])).
% 290.72/183.24 tff(8771,plain,
% 290.72/183.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s6, s7)) | node19(c_e_h_2, c_f, s6, s7)),
% 290.72/183.24 inference(modus_ponens,[status(thm)],[8770, 8769])).
% 290.72/183.24 tff(8772,plain,
% 290.72/183.24 (node19(c_e_h_2, c_f, s6, s7)),
% 290.72/183.24 inference(unit_resolution,[status(thm)],[8771, 190, 1844])).
% 290.72/183.24 tff(8773,plain,
% 290.72/183.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s6) | node15(c_e_h_2, c_f, s6, s7) | node14(c_e_h_2, c_f, s6, s7) | (~node19(c_e_h_2, c_f, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_f, s6) | node15(c_e_h_2, c_f, s6, s7) | node14(c_e_h_2, c_f, s6, s7) | (~node19(c_e_h_2, c_f, s6, s7)))),
% 290.72/183.24 inference(rewrite,[status(thm)],[])).
% 290.72/183.24 tff(8774,plain,
% 290.72/183.24 ((node16(c_e_h_2, c_f, s6) | node14(c_e_h_2, c_f, s6, s7) | node15(c_e_h_2, c_f, s6, s7) | (~node19(c_e_h_2, c_f, s6, s7))) <=> (node16(c_e_h_2, c_f, s6) | node15(c_e_h_2, c_f, s6, s7) | node14(c_e_h_2, c_f, s6, s7) | (~node19(c_e_h_2, c_f, s6, s7)))),
% 290.72/183.24 inference(rewrite,[status(thm)],[])).
% 290.72/183.24 tff(8775,plain,
% 290.72/183.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s6) | node14(c_e_h_2, c_f, s6, s7) | node15(c_e_h_2, c_f, s6, s7) | (~node19(c_e_h_2, c_f, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s6) | node15(c_e_h_2, c_f, s6, s7) | node14(c_e_h_2, c_f, s6, s7) | (~node19(c_e_h_2, c_f, s6, s7))))),
% 290.72/183.24 inference(monotonicity,[status(thm)],[8774])).
% 290.72/183.24 tff(8776,plain,
% 290.72/183.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s6) | node14(c_e_h_2, c_f, s6, s7) | node15(c_e_h_2, c_f, s6, s7) | (~node19(c_e_h_2, c_f, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_f, s6) | node15(c_e_h_2, c_f, s6, s7) | node14(c_e_h_2, c_f, s6, s7) | (~node19(c_e_h_2, c_f, s6, s7)))),
% 290.72/183.24 inference(transitivity,[status(thm)],[8775, 8773])).
% 290.72/183.24 tff(8777,plain,
% 290.72/183.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s6) | node14(c_e_h_2, c_f, s6, s7) | node15(c_e_h_2, c_f, s6, s7) | (~node19(c_e_h_2, c_f, s6, s7)))),
% 290.72/183.24 inference(quant_inst,[status(thm)],[])).
% 290.72/183.24 tff(8778,plain,
% 290.72/183.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_f, s6) | node15(c_e_h_2, c_f, s6, s7) | node14(c_e_h_2, c_f, s6, s7) | (~node19(c_e_h_2, c_f, s6, s7))),
% 290.72/183.24 inference(modus_ponens,[status(thm)],[8777, 8776])).
% 290.72/183.24 tff(8779,plain,
% 290.72/183.24 (node16(c_e_h_2, c_f, s6) | node15(c_e_h_2, c_f, s6, s7) | node14(c_e_h_2, c_f, s6, s7)),
% 290.72/183.24 inference(unit_resolution,[status(thm)],[8778, 204, 8772])).
% 290.72/183.24 tff(8780,plain,
% 290.72/183.24 ($false),
% 290.72/183.24 inference(unit_resolution,[status(thm)],[8779, 8768, 8758, 8752])).
% 290.72/183.24 tff(8781,plain,(m_c_h_element_v_in1(c_e_h_2, c_f, s6) | node15(c_e_h_2, c_f, s6, s7) | (~m_c_h_element_v_out(c_e_h_2, c_f, s7)) | m_c_h_element_v_in2(c_e_h_2, c_f, s6)), inference(lemma,lemma(discharge,[]))).
% 290.72/183.24 tff(8782,plain,
% 290.72/183.24 (m_c_h_element_v_in1(c_e_h_2, c_f, s6)),
% 290.72/183.24 inference(unit_resolution,[status(thm)],[8781, 8751, 8743, 8742])).
% 290.72/183.24 tff(8783,plain,
% 290.72/183.24 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s6)) | (~node17(c_e_h_2, c_f, s6)) | m_c_h_element_v_in2(c_e_h_2, c_f, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s6)) | (~node17(c_e_h_2, c_f, s6)) | m_c_h_element_v_in2(c_e_h_2, c_f, s6))),
% 290.72/183.24 inference(rewrite,[status(thm)],[])).
% 290.72/183.24 tff(8784,plain,
% 290.72/183.24 (((~m_c_h_element_v_in1(c_e_h_2, c_f, s6)) | m_c_h_element_v_in2(c_e_h_2, c_f, s6) | (~node17(c_e_h_2, c_f, s6))) <=> ((~m_c_h_element_v_in1(c_e_h_2, c_f, s6)) | (~node17(c_e_h_2, c_f, s6)) | m_c_h_element_v_in2(c_e_h_2, c_f, s6))),
% 290.72/183.24 inference(rewrite,[status(thm)],[])).
% 290.72/183.24 tff(8785,plain,
% 290.72/183.24 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s6)) | m_c_h_element_v_in2(c_e_h_2, c_f, s6) | (~node17(c_e_h_2, c_f, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s6)) | (~node17(c_e_h_2, c_f, s6)) | m_c_h_element_v_in2(c_e_h_2, c_f, s6)))),
% 290.72/183.24 inference(monotonicity,[status(thm)],[8784])).
% 290.72/183.24 tff(8786,plain,
% 290.72/183.24 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s6)) | m_c_h_element_v_in2(c_e_h_2, c_f, s6) | (~node17(c_e_h_2, c_f, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s6)) | (~node17(c_e_h_2, c_f, s6)) | m_c_h_element_v_in2(c_e_h_2, c_f, s6))),
% 290.72/183.24 inference(transitivity,[status(thm)],[8785, 8783])).
% 290.72/183.24 tff(8787,plain,
% 290.72/183.24 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s6)) | m_c_h_element_v_in2(c_e_h_2, c_f, s6) | (~node17(c_e_h_2, c_f, s6)))),
% 290.72/183.24 inference(quant_inst,[status(thm)],[])).
% 290.72/183.24 tff(8788,plain,
% 290.72/183.24 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s6)) | (~node17(c_e_h_2, c_f, s6)) | m_c_h_element_v_in2(c_e_h_2, c_f, s6)),
% 290.72/183.24 inference(modus_ponens,[status(thm)],[8787, 8786])).
% 290.72/183.24 tff(8789,plain,
% 290.72/183.24 ((~m_c_h_element_v_in1(c_e_h_2, c_f, s6)) | (~node17(c_e_h_2, c_f, s6))),
% 290.72/183.24 inference(unit_resolution,[status(thm)],[8788, 919, 8742])).
% 290.72/183.24 tff(8790,plain,
% 290.72/183.24 (~node17(c_e_h_2, c_f, s6)),
% 290.72/183.24 inference(unit_resolution,[status(thm)],[8789, 8782])).
% 290.72/183.25 tff(8791,plain,
% 290.72/183.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s6) | node18(c_e_h_2, c_f, s6, s7) | (~node19(c_e_h_2, c_f, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_f, s6) | node18(c_e_h_2, c_f, s6, s7) | (~node19(c_e_h_2, c_f, s6, s7)))),
% 290.72/183.25 inference(rewrite,[status(thm)],[])).
% 290.72/183.25 tff(8792,plain,
% 290.72/183.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s6) | node18(c_e_h_2, c_f, s6, s7) | (~node19(c_e_h_2, c_f, s6, s7)))),
% 290.72/183.25 inference(quant_inst,[status(thm)],[])).
% 290.72/183.25 tff(8793,plain,
% 290.72/183.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_f, s6) | node18(c_e_h_2, c_f, s6, s7) | (~node19(c_e_h_2, c_f, s6, s7))),
% 290.72/183.25 inference(modus_ponens,[status(thm)],[8792, 8791])).
% 290.72/183.25 tff(8794,plain,
% 290.72/183.25 (node17(c_e_h_2, c_f, s6) | node18(c_e_h_2, c_f, s6, s7)),
% 290.72/183.25 inference(unit_resolution,[status(thm)],[8793, 776, 8772])).
% 290.72/183.25 tff(8795,plain,
% 290.72/183.25 (node18(c_e_h_2, c_f, s6, s7)),
% 290.72/183.25 inference(unit_resolution,[status(thm)],[8794, 8790])).
% 290.72/183.25 tff(8796,plain,
% 290.72/183.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s7)) | m_c_h_element_v_out(c_e_h_2, c_f, s6) | (~node18(c_e_h_2, c_f, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s7)) | m_c_h_element_v_out(c_e_h_2, c_f, s6) | (~node18(c_e_h_2, c_f, s6, s7)))),
% 290.72/183.25 inference(rewrite,[status(thm)],[])).
% 290.72/183.25 tff(8797,plain,
% 290.72/183.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s7)) | m_c_h_element_v_out(c_e_h_2, c_f, s6) | (~node18(c_e_h_2, c_f, s6, s7)))),
% 290.72/183.25 inference(quant_inst,[status(thm)],[])).
% 290.72/183.25 tff(8798,plain,
% 290.72/183.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s7)) | m_c_h_element_v_out(c_e_h_2, c_f, s6) | (~node18(c_e_h_2, c_f, s6, s7))),
% 290.72/183.25 inference(modus_ponens,[status(thm)],[8797, 8796])).
% 290.72/183.25 tff(8799,plain,
% 290.72/183.25 ($false),
% 290.72/183.25 inference(unit_resolution,[status(thm)],[8798, 753, 8743, 8744, 8795])).
% 290.72/183.25 tff(8800,plain,(m_c_h_element_v_out(c_e_h_2, c_f, s6) | (~m_c_h_element_v_out(c_e_h_2, c_f, s7)) | m_c_h_element_v_in2(c_e_h_2, c_f, s6)), inference(lemma,lemma(discharge,[]))).
% 290.72/183.25 tff(8801,plain,
% 290.72/183.25 ((~m_c_h_element_v_out(c_e_h_2, c_f, s7)) | m_c_h_element_v_in2(c_e_h_2, c_f, s6)),
% 290.72/183.25 inference(unit_resolution,[status(thm)],[8800, 5353])).
% 290.72/183.25 tff(8802,plain,
% 290.72/183.25 (~m_c_h_element_v_out(c_e_h_2, c_f, s7)),
% 290.72/183.25 inference(unit_resolution,[status(thm)],[8801, 8741])).
% 290.72/183.25 tff(8803,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_f, s7)), introduced(assumption)).
% 290.72/183.25 tff(8804,assumption,(m_c_h_element_v_out(c_e_h_2, c_f, s8)), introduced(assumption)).
% 290.72/183.25 tff(8805,assumption,(~m_c_h_element_v_out(c_e_h_2, c_f, s7)), introduced(assumption)).
% 290.72/183.25 tff(8806,assumption,(node15(c_e_h_2, c_f, s7, s8)), introduced(assumption)).
% 290.72/183.25 tff(8807,plain,
% 290.72/183.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s8)) | (~node15(c_e_h_2, c_f, s7, s8)) | m_c_h_element_v_out(c_e_h_2, c_f, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s8)) | (~node15(c_e_h_2, c_f, s7, s8)) | m_c_h_element_v_out(c_e_h_2, c_f, s7))),
% 290.72/183.25 inference(rewrite,[status(thm)],[])).
% 290.72/183.25 tff(8808,plain,
% 290.72/183.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s8)) | (~node15(c_e_h_2, c_f, s7, s8)) | m_c_h_element_v_out(c_e_h_2, c_f, s7))),
% 290.72/183.25 inference(quant_inst,[status(thm)],[])).
% 290.72/183.25 tff(8809,plain,
% 290.72/183.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s8)) | (~node15(c_e_h_2, c_f, s7, s8)) | m_c_h_element_v_out(c_e_h_2, c_f, s7)),
% 290.72/183.25 inference(modus_ponens,[status(thm)],[8808, 8807])).
% 290.72/183.25 tff(8810,plain,
% 290.72/183.25 ($false),
% 290.72/183.25 inference(unit_resolution,[status(thm)],[8809, 147, 8805, 8804, 8806])).
% 290.72/183.25 tff(8811,plain,((~node15(c_e_h_2, c_f, s7, s8)) | m_c_h_element_v_out(c_e_h_2, c_f, s7) | (~m_c_h_element_v_out(c_e_h_2, c_f, s8))), inference(lemma,lemma(discharge,[]))).
% 290.72/183.25 tff(8812,plain,
% 290.72/183.25 (~node15(c_e_h_2, c_f, s7, s8)),
% 290.72/183.25 inference(unit_resolution,[status(thm)],[8811, 8805, 8804])).
% 290.72/183.25 tff(8813,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_f, s7)), introduced(assumption)).
% 290.72/183.25 tff(8814,assumption,(~node15(c_e_h_2, c_f, s7, s8)), introduced(assumption)).
% 290.72/183.25 tff(8815,plain,
% 290.72/183.25 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_f, s7)) | m_c_h_element_v_in1(c_e_h_2, c_f, s7) | m_c_h_element_v_in2(c_e_h_2, c_f, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_f, s7)) | m_c_h_element_v_in1(c_e_h_2, c_f, s7) | m_c_h_element_v_in2(c_e_h_2, c_f, s7))),
% 290.72/183.25 inference(rewrite,[status(thm)],[])).
% 290.72/183.25 tff(8816,plain,
% 290.72/183.25 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_f, s7)) | m_c_h_element_v_in1(c_e_h_2, c_f, s7) | m_c_h_element_v_in2(c_e_h_2, c_f, s7))),
% 290.72/183.25 inference(quant_inst,[status(thm)],[])).
% 290.72/183.25 tff(8817,plain,
% 290.72/183.25 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_f, s7)) | m_c_h_element_v_in1(c_e_h_2, c_f, s7) | m_c_h_element_v_in2(c_e_h_2, c_f, s7)),
% 290.72/183.25 inference(modus_ponens,[status(thm)],[8816, 8815])).
% 290.72/183.25 tff(8818,plain,
% 290.72/183.25 ((~node16(c_e_h_2, c_f, s7)) | m_c_h_element_v_in1(c_e_h_2, c_f, s7)),
% 290.72/183.25 inference(unit_resolution,[status(thm)],[8817, 178, 8803])).
% 290.72/183.25 tff(8819,plain,
% 290.72/183.25 (~node16(c_e_h_2, c_f, s7)),
% 290.72/183.25 inference(unit_resolution,[status(thm)],[8818, 8813])).
% 290.72/183.25 tff(8820,plain,
% 290.72/183.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s7, s8)) | node19(c_e_h_2, c_f, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s7, s8)) | node19(c_e_h_2, c_f, s7, s8))),
% 290.72/183.25 inference(rewrite,[status(thm)],[])).
% 290.72/183.25 tff(8821,plain,
% 290.72/183.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s7, s8)) | node19(c_e_h_2, c_f, s7, s8))),
% 290.72/183.25 inference(quant_inst,[status(thm)],[])).
% 290.72/183.25 tff(8822,plain,
% 290.72/183.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s7, s8)) | node19(c_e_h_2, c_f, s7, s8)),
% 290.72/183.25 inference(modus_ponens,[status(thm)],[8821, 8820])).
% 290.72/183.25 tff(8823,plain,
% 290.72/183.25 (node19(c_e_h_2, c_f, s7, s8)),
% 290.72/183.25 inference(unit_resolution,[status(thm)],[8822, 190, 1938])).
% 290.72/183.25 tff(8824,plain,
% 290.72/183.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s7) | node15(c_e_h_2, c_f, s7, s8) | (~node19(c_e_h_2, c_f, s7, s8)) | node14(c_e_h_2, c_f, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_f, s7) | node15(c_e_h_2, c_f, s7, s8) | (~node19(c_e_h_2, c_f, s7, s8)) | node14(c_e_h_2, c_f, s7, s8))),
% 290.72/183.25 inference(rewrite,[status(thm)],[])).
% 290.72/183.25 tff(8825,plain,
% 290.72/183.25 ((node16(c_e_h_2, c_f, s7) | node14(c_e_h_2, c_f, s7, s8) | node15(c_e_h_2, c_f, s7, s8) | (~node19(c_e_h_2, c_f, s7, s8))) <=> (node16(c_e_h_2, c_f, s7) | node15(c_e_h_2, c_f, s7, s8) | (~node19(c_e_h_2, c_f, s7, s8)) | node14(c_e_h_2, c_f, s7, s8))),
% 290.72/183.25 inference(rewrite,[status(thm)],[])).
% 290.72/183.25 tff(8826,plain,
% 290.72/183.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s7) | node14(c_e_h_2, c_f, s7, s8) | node15(c_e_h_2, c_f, s7, s8) | (~node19(c_e_h_2, c_f, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s7) | node15(c_e_h_2, c_f, s7, s8) | (~node19(c_e_h_2, c_f, s7, s8)) | node14(c_e_h_2, c_f, s7, s8)))),
% 290.72/183.25 inference(monotonicity,[status(thm)],[8825])).
% 290.72/183.25 tff(8827,plain,
% 290.72/183.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s7) | node14(c_e_h_2, c_f, s7, s8) | node15(c_e_h_2, c_f, s7, s8) | (~node19(c_e_h_2, c_f, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_f, s7) | node15(c_e_h_2, c_f, s7, s8) | (~node19(c_e_h_2, c_f, s7, s8)) | node14(c_e_h_2, c_f, s7, s8))),
% 290.72/183.25 inference(transitivity,[status(thm)],[8826, 8824])).
% 290.72/183.25 tff(8828,plain,
% 290.72/183.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s7) | node14(c_e_h_2, c_f, s7, s8) | node15(c_e_h_2, c_f, s7, s8) | (~node19(c_e_h_2, c_f, s7, s8)))),
% 290.72/183.25 inference(quant_inst,[status(thm)],[])).
% 290.72/183.25 tff(8829,plain,
% 290.72/183.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_f, s7) | node15(c_e_h_2, c_f, s7, s8) | (~node19(c_e_h_2, c_f, s7, s8)) | node14(c_e_h_2, c_f, s7, s8)),
% 290.72/183.25 inference(modus_ponens,[status(thm)],[8828, 8827])).
% 290.72/183.25 tff(8830,plain,
% 290.72/183.25 (node16(c_e_h_2, c_f, s7) | node15(c_e_h_2, c_f, s7, s8) | node14(c_e_h_2, c_f, s7, s8)),
% 290.72/183.25 inference(unit_resolution,[status(thm)],[8829, 204, 8823])).
% 290.72/183.25 tff(8831,plain,
% 290.72/183.25 (node14(c_e_h_2, c_f, s7, s8)),
% 290.72/183.25 inference(unit_resolution,[status(thm)],[8830, 8819, 8814])).
% 290.72/183.25 tff(8832,plain,
% 290.72/183.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s8)) | m_c_h_element_v_in1(c_e_h_2, c_f, s7) | (~node14(c_e_h_2, c_f, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s8)) | m_c_h_element_v_in1(c_e_h_2, c_f, s7) | (~node14(c_e_h_2, c_f, s7, s8)))),
% 290.72/183.25 inference(rewrite,[status(thm)],[])).
% 290.72/183.25 tff(8833,plain,
% 290.72/183.25 (((~node14(c_e_h_2, c_f, s7, s8)) | m_c_h_element_v_in1(c_e_h_2, c_f, s7) | (~m_c_h_element_v_out(c_e_h_2, c_f, s8))) <=> ((~m_c_h_element_v_out(c_e_h_2, c_f, s8)) | m_c_h_element_v_in1(c_e_h_2, c_f, s7) | (~node14(c_e_h_2, c_f, s7, s8)))),
% 290.72/183.25 inference(rewrite,[status(thm)],[])).
% 290.72/183.25 tff(8834,plain,
% 290.72/183.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_f, s7, s8)) | m_c_h_element_v_in1(c_e_h_2, c_f, s7) | (~m_c_h_element_v_out(c_e_h_2, c_f, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s8)) | m_c_h_element_v_in1(c_e_h_2, c_f, s7) | (~node14(c_e_h_2, c_f, s7, s8))))),
% 290.72/183.25 inference(monotonicity,[status(thm)],[8833])).
% 290.72/183.25 tff(8835,plain,
% 290.72/183.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_f, s7, s8)) | m_c_h_element_v_in1(c_e_h_2, c_f, s7) | (~m_c_h_element_v_out(c_e_h_2, c_f, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s8)) | m_c_h_element_v_in1(c_e_h_2, c_f, s7) | (~node14(c_e_h_2, c_f, s7, s8)))),
% 290.72/183.26 inference(transitivity,[status(thm)],[8834, 8832])).
% 290.72/183.26 tff(8836,plain,
% 290.72/183.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_f, s7, s8)) | m_c_h_element_v_in1(c_e_h_2, c_f, s7) | (~m_c_h_element_v_out(c_e_h_2, c_f, s8)))),
% 290.72/183.26 inference(quant_inst,[status(thm)],[])).
% 290.72/183.26 tff(8837,plain,
% 290.72/183.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s8)) | m_c_h_element_v_in1(c_e_h_2, c_f, s7) | (~node14(c_e_h_2, c_f, s7, s8))),
% 290.72/183.26 inference(modus_ponens,[status(thm)],[8836, 8835])).
% 290.72/183.26 tff(8838,plain,
% 290.72/183.26 ($false),
% 290.72/183.26 inference(unit_resolution,[status(thm)],[8837, 223, 8804, 8831, 8813])).
% 290.72/183.26 tff(8839,plain,(m_c_h_element_v_in1(c_e_h_2, c_f, s7) | (~m_c_h_element_v_out(c_e_h_2, c_f, s8)) | node15(c_e_h_2, c_f, s7, s8) | m_c_h_element_v_in2(c_e_h_2, c_f, s7)), inference(lemma,lemma(discharge,[]))).
% 290.72/183.26 tff(8840,plain,
% 290.72/183.26 (m_c_h_element_v_in1(c_e_h_2, c_f, s7)),
% 290.72/183.26 inference(unit_resolution,[status(thm)],[8839, 8812, 8804, 8803])).
% 290.72/183.26 tff(8841,plain,
% 290.72/183.26 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s7)) | m_c_h_element_v_in2(c_e_h_2, c_f, s7) | (~node17(c_e_h_2, c_f, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s7)) | m_c_h_element_v_in2(c_e_h_2, c_f, s7) | (~node17(c_e_h_2, c_f, s7)))),
% 290.72/183.26 inference(rewrite,[status(thm)],[])).
% 290.72/183.26 tff(8842,plain,
% 290.72/183.26 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s7)) | m_c_h_element_v_in2(c_e_h_2, c_f, s7) | (~node17(c_e_h_2, c_f, s7)))),
% 290.72/183.26 inference(quant_inst,[status(thm)],[])).
% 290.72/183.26 tff(8843,plain,
% 290.72/183.26 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s7)) | m_c_h_element_v_in2(c_e_h_2, c_f, s7) | (~node17(c_e_h_2, c_f, s7))),
% 290.72/183.26 inference(modus_ponens,[status(thm)],[8842, 8841])).
% 290.72/183.26 tff(8844,plain,
% 290.72/183.26 ((~m_c_h_element_v_in1(c_e_h_2, c_f, s7)) | (~node17(c_e_h_2, c_f, s7))),
% 290.72/183.26 inference(unit_resolution,[status(thm)],[8843, 919, 8803])).
% 290.72/183.26 tff(8845,plain,
% 290.72/183.26 (~node17(c_e_h_2, c_f, s7)),
% 290.72/183.26 inference(unit_resolution,[status(thm)],[8844, 8840])).
% 290.72/183.26 tff(8846,plain,
% 290.72/183.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s7) | (~node19(c_e_h_2, c_f, s7, s8)) | node18(c_e_h_2, c_f, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_f, s7) | (~node19(c_e_h_2, c_f, s7, s8)) | node18(c_e_h_2, c_f, s7, s8))),
% 290.72/183.26 inference(rewrite,[status(thm)],[])).
% 290.72/183.26 tff(8847,plain,
% 290.72/183.26 ((node17(c_e_h_2, c_f, s7) | node18(c_e_h_2, c_f, s7, s8) | (~node19(c_e_h_2, c_f, s7, s8))) <=> (node17(c_e_h_2, c_f, s7) | (~node19(c_e_h_2, c_f, s7, s8)) | node18(c_e_h_2, c_f, s7, s8))),
% 290.72/183.26 inference(rewrite,[status(thm)],[])).
% 290.72/183.26 tff(8848,plain,
% 290.72/183.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s7) | node18(c_e_h_2, c_f, s7, s8) | (~node19(c_e_h_2, c_f, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s7) | (~node19(c_e_h_2, c_f, s7, s8)) | node18(c_e_h_2, c_f, s7, s8)))),
% 290.72/183.26 inference(monotonicity,[status(thm)],[8847])).
% 290.72/183.26 tff(8849,plain,
% 290.72/183.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s7) | node18(c_e_h_2, c_f, s7, s8) | (~node19(c_e_h_2, c_f, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_f, s7) | (~node19(c_e_h_2, c_f, s7, s8)) | node18(c_e_h_2, c_f, s7, s8))),
% 290.72/183.26 inference(transitivity,[status(thm)],[8848, 8846])).
% 290.72/183.26 tff(8850,plain,
% 290.72/183.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s7) | node18(c_e_h_2, c_f, s7, s8) | (~node19(c_e_h_2, c_f, s7, s8)))),
% 290.72/183.26 inference(quant_inst,[status(thm)],[])).
% 290.72/183.26 tff(8851,plain,
% 290.72/183.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_f, s7) | (~node19(c_e_h_2, c_f, s7, s8)) | node18(c_e_h_2, c_f, s7, s8)),
% 290.72/183.26 inference(modus_ponens,[status(thm)],[8850, 8849])).
% 290.72/183.26 tff(8852,plain,
% 290.72/183.26 (node17(c_e_h_2, c_f, s7) | node18(c_e_h_2, c_f, s7, s8)),
% 290.72/183.26 inference(unit_resolution,[status(thm)],[8851, 776, 8823])).
% 290.72/183.26 tff(8853,plain,
% 290.72/183.26 (node18(c_e_h_2, c_f, s7, s8)),
% 290.72/183.26 inference(unit_resolution,[status(thm)],[8852, 8845])).
% 290.72/183.26 tff(8854,plain,
% 290.72/183.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_f, s7) | (~m_c_h_element_v_out(c_e_h_2, c_f, s8)) | (~node18(c_e_h_2, c_f, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_f, s7) | (~m_c_h_element_v_out(c_e_h_2, c_f, s8)) | (~node18(c_e_h_2, c_f, s7, s8)))),
% 290.72/183.26 inference(rewrite,[status(thm)],[])).
% 290.72/183.26 tff(8855,plain,
% 290.72/183.26 (((~m_c_h_element_v_out(c_e_h_2, c_f, s8)) | m_c_h_element_v_out(c_e_h_2, c_f, s7) | (~node18(c_e_h_2, c_f, s7, s8))) <=> (m_c_h_element_v_out(c_e_h_2, c_f, s7) | (~m_c_h_element_v_out(c_e_h_2, c_f, s8)) | (~node18(c_e_h_2, c_f, s7, s8)))),
% 290.72/183.26 inference(rewrite,[status(thm)],[])).
% 290.72/183.26 tff(8856,plain,
% 290.72/183.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s8)) | m_c_h_element_v_out(c_e_h_2, c_f, s7) | (~node18(c_e_h_2, c_f, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_f, s7) | (~m_c_h_element_v_out(c_e_h_2, c_f, s8)) | (~node18(c_e_h_2, c_f, s7, s8))))),
% 290.72/183.26 inference(monotonicity,[status(thm)],[8855])).
% 290.72/183.26 tff(8857,plain,
% 290.72/183.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s8)) | m_c_h_element_v_out(c_e_h_2, c_f, s7) | (~node18(c_e_h_2, c_f, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_f, s7) | (~m_c_h_element_v_out(c_e_h_2, c_f, s8)) | (~node18(c_e_h_2, c_f, s7, s8)))),
% 290.72/183.26 inference(transitivity,[status(thm)],[8856, 8854])).
% 290.72/183.26 tff(8858,plain,
% 290.72/183.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s8)) | m_c_h_element_v_out(c_e_h_2, c_f, s7) | (~node18(c_e_h_2, c_f, s7, s8)))),
% 290.72/183.26 inference(quant_inst,[status(thm)],[])).
% 290.72/183.26 tff(8859,plain,
% 290.72/183.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_f, s7) | (~m_c_h_element_v_out(c_e_h_2, c_f, s8)) | (~node18(c_e_h_2, c_f, s7, s8))),
% 290.72/183.26 inference(modus_ponens,[status(thm)],[8858, 8857])).
% 290.72/183.26 tff(8860,plain,
% 290.72/183.26 ($false),
% 290.72/183.26 inference(unit_resolution,[status(thm)],[8859, 753, 8805, 8804, 8853])).
% 290.72/183.26 tff(8861,plain,(m_c_h_element_v_out(c_e_h_2, c_f, s7) | (~m_c_h_element_v_out(c_e_h_2, c_f, s8)) | m_c_h_element_v_in2(c_e_h_2, c_f, s7)), inference(lemma,lemma(discharge,[]))).
% 290.72/183.27 tff(8862,plain,
% 290.72/183.27 ((~m_c_h_element_v_out(c_e_h_2, c_f, s8)) | m_c_h_element_v_in2(c_e_h_2, c_f, s7)),
% 290.72/183.27 inference(unit_resolution,[status(thm)],[8861, 8802])).
% 290.72/183.27 tff(8863,plain,
% 290.72/183.27 (~m_c_h_element_v_out(c_e_h_2, c_f, s8)),
% 290.72/183.27 inference(unit_resolution,[status(thm)],[8862, 8733])).
% 290.72/183.27 tff(8864,plain,
% 290.72/183.27 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_q, s8)) | m_c_h_element_v_out(c_e_h_2, c_f, s8))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_q, s8)) | m_c_h_element_v_out(c_e_h_2, c_f, s8))),
% 290.72/183.27 inference(rewrite,[status(thm)],[])).
% 290.72/183.27 tff(8865,plain,
% 290.72/183.27 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_q, s8)) | m_c_h_element_v_out(c_e_h_2, c_f, s8))),
% 290.72/183.27 inference(quant_inst,[status(thm)],[])).
% 290.72/183.27 tff(8866,plain,
% 290.72/183.27 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_q, s8)) | m_c_h_element_v_out(c_e_h_2, c_f, s8)),
% 290.72/183.27 inference(modus_ponens,[status(thm)],[8865, 8864])).
% 290.72/183.27 tff(8867,plain,
% 290.72/183.27 (~m_and_h_gate_v_in1(c_e_h_2, c_q, s8)),
% 290.72/183.27 inference(unit_resolution,[status(thm)],[8866, 1586, 8863])).
% 290.72/183.27 tff(8868,plain,
% 290.72/183.27 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_q, s8)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_q, s8)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s8))),
% 290.72/183.27 inference(rewrite,[status(thm)],[])).
% 290.72/183.27 tff(8869,plain,
% 290.72/183.27 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_q, s8)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s8))),
% 290.72/183.27 inference(quant_inst,[status(thm)],[])).
% 290.72/183.27 tff(8870,plain,
% 290.72/183.27 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_q, s8)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s8)),
% 290.72/183.27 inference(modus_ponens,[status(thm)],[8869, 8868])).
% 290.72/183.27 tff(8871,plain,
% 290.72/183.27 (~node20(c_e_h_2, c_q, s8)),
% 290.72/183.27 inference(unit_resolution,[status(thm)],[8870, 38, 8867])).
% 290.72/183.27 tff(8872,plain,
% 290.72/183.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s9)) | node20(c_e_h_2, c_q, s8) | (~node21(c_e_h_2, c_q, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s9)) | node20(c_e_h_2, c_q, s8) | (~node21(c_e_h_2, c_q, s8, s9)))),
% 290.72/183.27 inference(rewrite,[status(thm)],[])).
% 290.72/183.27 tff(8873,plain,
% 290.72/183.27 ((node20(c_e_h_2, c_q, s8) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s9)) | (~node21(c_e_h_2, c_q, s8, s9))) <=> ((~m_and_h_gate_v_out(c_e_h_2, c_q, s9)) | node20(c_e_h_2, c_q, s8) | (~node21(c_e_h_2, c_q, s8, s9)))),
% 290.72/183.27 inference(rewrite,[status(thm)],[])).
% 290.72/183.27 tff(8874,plain,
% 290.72/183.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_q, s8) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s9)) | (~node21(c_e_h_2, c_q, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s9)) | node20(c_e_h_2, c_q, s8) | (~node21(c_e_h_2, c_q, s8, s9))))),
% 290.72/183.27 inference(monotonicity,[status(thm)],[8873])).
% 290.72/183.27 tff(8875,plain,
% 290.72/183.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_q, s8) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s9)) | (~node21(c_e_h_2, c_q, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s9)) | node20(c_e_h_2, c_q, s8) | (~node21(c_e_h_2, c_q, s8, s9)))),
% 290.72/183.27 inference(transitivity,[status(thm)],[8874, 8872])).
% 290.72/183.27 tff(8876,plain,
% 290.72/183.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_q, s8) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s9)) | (~node21(c_e_h_2, c_q, s8, s9)))),
% 290.72/183.27 inference(quant_inst,[status(thm)],[])).
% 290.72/183.27 tff(8877,plain,
% 290.72/183.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s9)) | node20(c_e_h_2, c_q, s8) | (~node21(c_e_h_2, c_q, s8, s9))),
% 290.72/183.27 inference(modus_ponens,[status(thm)],[8876, 8875])).
% 290.72/183.27 tff(8878,plain,
% 290.72/183.27 ($false),
% 290.72/183.27 inference(unit_resolution,[status(thm)],[8877, 52, 7812, 8871, 7813])).
% 290.72/183.27 tff(8879,plain,((~node21(c_e_h_2, c_q, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s9))), inference(lemma,lemma(discharge,[]))).
% 290.72/183.27 tff(8880,plain,
% 290.72/183.27 (~node21(c_e_h_2, c_q, s8, s9)),
% 290.72/183.27 inference(unit_resolution,[status(thm)],[8879, 7812])).
% 290.72/183.27 tff(8881,assumption,(m_and_h_gate_v_out(c_e_h_2, c_q, s8)), introduced(assumption)).
% 290.72/183.27 tff(8882,plain,
% 290.72/183.27 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_q, s7)) | m_c_h_element_v_out(c_e_h_2, c_f, s7))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_q, s7)) | m_c_h_element_v_out(c_e_h_2, c_f, s7))),
% 290.72/183.27 inference(rewrite,[status(thm)],[])).
% 290.72/183.27 tff(8883,plain,
% 290.72/183.27 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_q, s7)) | m_c_h_element_v_out(c_e_h_2, c_f, s7))),
% 290.72/183.27 inference(quant_inst,[status(thm)],[])).
% 290.72/183.27 tff(8884,plain,
% 290.72/183.27 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_q, s7)) | m_c_h_element_v_out(c_e_h_2, c_f, s7)),
% 290.72/183.27 inference(modus_ponens,[status(thm)],[8883, 8882])).
% 290.72/183.27 tff(8885,plain,
% 290.72/183.27 (~m_and_h_gate_v_in1(c_e_h_2, c_q, s7)),
% 290.72/183.27 inference(unit_resolution,[status(thm)],[8884, 1586, 8802])).
% 290.72/183.27 tff(8886,plain,
% 290.72/183.27 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_q, s7)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_q, s7)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s7))),
% 290.72/183.27 inference(rewrite,[status(thm)],[])).
% 290.72/183.27 tff(8887,plain,
% 290.72/183.27 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_q, s7)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s7))),
% 290.72/183.27 inference(quant_inst,[status(thm)],[])).
% 290.72/183.27 tff(8888,plain,
% 290.72/183.27 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_q, s7)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s7)),
% 290.72/183.27 inference(modus_ponens,[status(thm)],[8887, 8886])).
% 290.72/183.27 tff(8889,plain,
% 290.72/183.27 (~node20(c_e_h_2, c_q, s7)),
% 290.72/183.27 inference(unit_resolution,[status(thm)],[8888, 38, 8885])).
% 290.72/183.27 tff(8890,assumption,(node21(c_e_h_2, c_q, s7, s8)), introduced(assumption)).
% 290.72/183.27 tff(8891,plain,
% 290.72/183.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_q, s7) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s8)) | (~node21(c_e_h_2, c_q, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_q, s7) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s8)) | (~node21(c_e_h_2, c_q, s7, s8)))),
% 290.72/183.27 inference(rewrite,[status(thm)],[])).
% 290.72/183.27 tff(8892,plain,
% 290.72/183.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_q, s7) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s8)) | (~node21(c_e_h_2, c_q, s7, s8)))),
% 290.72/183.27 inference(quant_inst,[status(thm)],[])).
% 290.72/183.27 tff(8893,plain,
% 290.72/183.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_q, s7) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s8)) | (~node21(c_e_h_2, c_q, s7, s8))),
% 290.72/183.27 inference(modus_ponens,[status(thm)],[8892, 8891])).
% 290.72/183.27 tff(8894,plain,
% 290.72/183.27 ($false),
% 290.72/183.27 inference(unit_resolution,[status(thm)],[8893, 52, 8881, 8890, 8889])).
% 290.72/183.27 tff(8895,plain,((~node21(c_e_h_2, c_q, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s8))), inference(lemma,lemma(discharge,[]))).
% 290.72/183.27 tff(8896,plain,
% 290.72/183.27 (~node21(c_e_h_2, c_q, s7, s8)),
% 290.72/183.27 inference(unit_resolution,[status(thm)],[8895, 8881])).
% 290.72/183.27 tff(8897,assumption,(node22(c_e_h_2, c_q, s7, s8)), introduced(assumption)).
% 290.72/183.27 tff(8898,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_q, s7)), introduced(assumption)).
% 290.72/183.27 tff(8899,plain,
% 290.72/183.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s8)) | (~node22(c_e_h_2, c_q, s7, s8)) | m_and_h_gate_v_out(c_e_h_2, c_q, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s8)) | (~node22(c_e_h_2, c_q, s7, s8)) | m_and_h_gate_v_out(c_e_h_2, c_q, s7))),
% 290.72/183.27 inference(rewrite,[status(thm)],[])).
% 290.72/183.27 tff(8900,plain,
% 290.72/183.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s8)) | (~node22(c_e_h_2, c_q, s7, s8)) | m_and_h_gate_v_out(c_e_h_2, c_q, s7))),
% 290.72/183.27 inference(quant_inst,[status(thm)],[])).
% 290.72/183.27 tff(8901,plain,
% 290.72/183.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s8)) | (~node22(c_e_h_2, c_q, s7, s8)) | m_and_h_gate_v_out(c_e_h_2, c_q, s7)),
% 290.72/183.27 inference(modus_ponens,[status(thm)],[8900, 8899])).
% 290.72/183.27 tff(8902,plain,
% 290.72/183.27 ($false),
% 290.72/183.27 inference(unit_resolution,[status(thm)],[8901, 108, 8898, 8881, 8897])).
% 290.72/183.27 tff(8903,plain,((~node22(c_e_h_2, c_q, s7, s8)) | m_and_h_gate_v_out(c_e_h_2, c_q, s7) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s8))), inference(lemma,lemma(discharge,[]))).
% 290.72/183.27 tff(8904,plain,
% 290.72/183.27 ((~node22(c_e_h_2, c_q, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s8))),
% 290.72/183.27 inference(unit_resolution,[status(thm)],[8903, 5381])).
% 290.72/183.27 tff(8905,plain,
% 290.72/183.27 (~node22(c_e_h_2, c_q, s7, s8)),
% 290.72/183.27 inference(unit_resolution,[status(thm)],[8904, 8881])).
% 290.72/183.27 tff(8906,plain,
% 290.72/183.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_2, c_q, s7, s8) | node22(c_e_h_2, c_q, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_2, c_q, s7, s8) | node22(c_e_h_2, c_q, s7, s8))),
% 290.72/183.27 inference(rewrite,[status(thm)],[])).
% 290.72/183.27 tff(8907,plain,
% 290.72/183.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_2, c_q, s7, s8) | node22(c_e_h_2, c_q, s7, s8))),
% 290.72/183.27 inference(quant_inst,[status(thm)],[])).
% 290.72/183.27 tff(8908,plain,
% 290.72/183.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_2, c_q, s7, s8) | node22(c_e_h_2, c_q, s7, s8)),
% 290.72/183.27 inference(modus_ponens,[status(thm)],[8907, 8906])).
% 290.72/183.27 tff(8909,plain,
% 290.72/183.27 (node21(c_e_h_2, c_q, s7, s8) | node22(c_e_h_2, c_q, s7, s8)),
% 290.72/183.27 inference(unit_resolution,[status(thm)],[8908, 82, 1938])).
% 290.72/183.27 tff(8910,plain,
% 290.72/183.27 ($false),
% 290.72/183.27 inference(unit_resolution,[status(thm)],[8909, 8905, 8896])).
% 290.72/183.27 tff(8911,plain,(~m_and_h_gate_v_out(c_e_h_2, c_q, s8)), inference(lemma,lemma(discharge,[]))).
% 290.72/183.27 tff(8912,assumption,(node22(c_e_h_2, c_q, s8, s9)), introduced(assumption)).
% 290.72/183.27 tff(8913,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_q, s8)), introduced(assumption)).
% 290.72/183.27 tff(8914,plain,
% 290.72/183.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s9)) | (~node22(c_e_h_2, c_q, s8, s9)) | m_and_h_gate_v_out(c_e_h_2, c_q, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s9)) | (~node22(c_e_h_2, c_q, s8, s9)) | m_and_h_gate_v_out(c_e_h_2, c_q, s8))),
% 290.72/183.28 inference(rewrite,[status(thm)],[])).
% 290.72/183.28 tff(8915,plain,
% 290.72/183.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s9)) | (~node22(c_e_h_2, c_q, s8, s9)) | m_and_h_gate_v_out(c_e_h_2, c_q, s8))),
% 290.72/183.28 inference(quant_inst,[status(thm)],[])).
% 290.72/183.28 tff(8916,plain,
% 290.72/183.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s9)) | (~node22(c_e_h_2, c_q, s8, s9)) | m_and_h_gate_v_out(c_e_h_2, c_q, s8)),
% 290.72/183.28 inference(modus_ponens,[status(thm)],[8915, 8914])).
% 290.72/183.28 tff(8917,plain,
% 290.72/183.28 ($false),
% 290.72/183.28 inference(unit_resolution,[status(thm)],[8916, 108, 7812, 8913, 8912])).
% 290.72/183.28 tff(8918,plain,((~node22(c_e_h_2, c_q, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s9)) | m_and_h_gate_v_out(c_e_h_2, c_q, s8)), inference(lemma,lemma(discharge,[]))).
% 290.72/183.28 tff(8919,plain,
% 290.72/183.28 (~node22(c_e_h_2, c_q, s8, s9)),
% 290.72/183.28 inference(unit_resolution,[status(thm)],[8918, 7812, 8911])).
% 290.72/183.28 tff(8920,plain,
% 290.72/183.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s8, s9)) | node21(c_e_h_2, c_q, s8, s9) | node22(c_e_h_2, c_q, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_2, c_q, s8, s9) | node22(c_e_h_2, c_q, s8, s9))),
% 290.72/183.28 inference(rewrite,[status(thm)],[])).
% 290.72/183.28 tff(8921,plain,
% 290.72/183.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s8, s9)) | node21(c_e_h_2, c_q, s8, s9) | node22(c_e_h_2, c_q, s8, s9))),
% 290.72/183.28 inference(quant_inst,[status(thm)],[])).
% 290.72/183.28 tff(8922,plain,
% 290.72/183.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_2, c_q, s8, s9) | node22(c_e_h_2, c_q, s8, s9)),
% 290.72/183.28 inference(modus_ponens,[status(thm)],[8921, 8920])).
% 290.72/183.28 tff(8923,plain,
% 290.72/183.28 (node21(c_e_h_2, c_q, s8, s9) | node22(c_e_h_2, c_q, s8, s9)),
% 290.72/183.28 inference(unit_resolution,[status(thm)],[8922, 82, 1993])).
% 290.72/183.28 tff(8924,plain,
% 290.72/183.28 ($false),
% 290.72/183.28 inference(unit_resolution,[status(thm)],[8923, 8919, 8880])).
% 290.72/183.28 tff(8925,plain,(~m_and_h_gate_v_out(c_e_h_2, c_q, s9)), inference(lemma,lemma(discharge,[]))).
% 290.72/183.28 tff(8926,plain,
% 290.72/183.28 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s9))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s9))),
% 290.72/183.28 inference(rewrite,[status(thm)],[])).
% 290.72/183.28 tff(8927,plain,
% 290.72/183.28 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s9))),
% 290.72/183.28 inference(quant_inst,[status(thm)],[])).
% 290.72/183.28 tff(8928,plain,
% 290.72/183.28 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s9)),
% 290.72/183.28 inference(modus_ponens,[status(thm)],[8927, 8926])).
% 290.72/183.28 tff(8929,plain,
% 290.72/183.28 (node3(c_e_h_2, c_e_h_3, s9)),
% 290.72/183.28 inference(unit_resolution,[status(thm)],[8928, 1059, 1056])).
% 290.72/183.28 tff(8930,plain,
% 290.72/183.28 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_3, s9)) | (~node3(c_e_h_2, c_e_h_3, s9)) | m_and_h_gate_v_out(c_e_h_2, c_q, s9))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_3, s9)) | (~node3(c_e_h_2, c_e_h_3, s9)) | m_and_h_gate_v_out(c_e_h_2, c_q, s9))),
% 290.72/183.28 inference(rewrite,[status(thm)],[])).
% 290.72/183.28 tff(8931,plain,
% 290.72/183.28 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_3, s9)) | (~node3(c_e_h_2, c_e_h_3, s9)) | m_and_h_gate_v_out(c_e_h_2, c_q, s9))),
% 290.72/183.28 inference(quant_inst,[status(thm)],[])).
% 290.72/183.28 tff(8932,plain,
% 290.72/183.28 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_3, s9)) | (~node3(c_e_h_2, c_e_h_3, s9)) | m_and_h_gate_v_out(c_e_h_2, c_q, s9)),
% 290.72/183.28 inference(modus_ponens,[status(thm)],[8931, 8930])).
% 290.72/183.28 tff(8933,plain,
% 290.72/183.28 ((~m_cell_v_ack(c_e_h_3, s9)) | m_and_h_gate_v_out(c_e_h_2, c_q, s9)),
% 290.72/183.28 inference(unit_resolution,[status(thm)],[8932, 1073, 8929])).
% 290.72/183.28 tff(8934,plain,
% 290.72/183.28 (~m_cell_v_ack(c_e_h_3, s9)),
% 290.72/183.28 inference(unit_resolution,[status(thm)],[8933, 8925])).
% 290.72/183.28 tff(8935,plain,
% 290.72/183.28 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_j, s9)) | m_cell_v_ack(c_e_h_3, s9))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_j, s9)) | m_cell_v_ack(c_e_h_3, s9))),
% 290.72/183.28 inference(rewrite,[status(thm)],[])).
% 290.72/183.28 tff(8936,plain,
% 290.72/183.28 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_j, s9)) | m_cell_v_ack(c_e_h_3, s9))),
% 290.72/183.28 inference(quant_inst,[status(thm)],[])).
% 290.72/183.28 tff(8937,plain,
% 290.72/183.28 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_j, s9)) | m_cell_v_ack(c_e_h_3, s9)),
% 290.72/183.28 inference(modus_ponens,[status(thm)],[8936, 8935])).
% 290.72/183.28 tff(8938,plain,
% 290.72/183.28 (~m_or_h_gate_v_in2(c_e_h_3, c_j, s9)),
% 290.72/183.28 inference(unit_resolution,[status(thm)],[8937, 1085, 8934])).
% 290.72/183.28 tff(8939,assumption,(m_or_h_gate_v_out(c_e_h_3, c_j, s10)), introduced(assumption)).
% 290.72/183.28 tff(8940,assumption,(node6(c_e_h_3, c_j, s9, s10)), introduced(assumption)).
% 290.72/183.28 tff(8941,plain,
% 290.72/183.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_3, c_j, s9) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s10)) | (~node6(c_e_h_3, c_j, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_j, s9) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s10)) | (~node6(c_e_h_3, c_j, s9, s10)))),
% 290.72/183.28 inference(rewrite,[status(thm)],[])).
% 290.72/183.28 tff(8942,plain,
% 290.72/183.28 (((~node6(c_e_h_3, c_j, s9, s10)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s10)) | m_or_h_gate_v_out(c_e_h_3, c_j, s9)) <=> (m_or_h_gate_v_out(c_e_h_3, c_j, s9) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s10)) | (~node6(c_e_h_3, c_j, s9, s10)))),
% 290.72/183.28 inference(rewrite,[status(thm)],[])).
% 290.72/183.28 tff(8943,plain,
% 290.72/183.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s9, s10)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s10)) | m_or_h_gate_v_out(c_e_h_3, c_j, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_3, c_j, s9) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s10)) | (~node6(c_e_h_3, c_j, s9, s10))))),
% 290.72/183.28 inference(monotonicity,[status(thm)],[8942])).
% 290.72/183.28 tff(8944,plain,
% 290.72/183.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s9, s10)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s10)) | m_or_h_gate_v_out(c_e_h_3, c_j, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_j, s9) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s10)) | (~node6(c_e_h_3, c_j, s9, s10)))),
% 290.72/183.28 inference(transitivity,[status(thm)],[8943, 8941])).
% 290.72/183.28 tff(8945,plain,
% 290.72/183.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s9, s10)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s10)) | m_or_h_gate_v_out(c_e_h_3, c_j, s9))),
% 290.72/183.28 inference(quant_inst,[status(thm)],[])).
% 290.72/183.28 tff(8946,plain,
% 290.72/183.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_j, s9) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s10)) | (~node6(c_e_h_3, c_j, s9, s10))),
% 290.72/183.28 inference(modus_ponens,[status(thm)],[8945, 8944])).
% 290.72/183.28 tff(8947,plain,
% 290.72/183.28 ($false),
% 290.72/183.28 inference(unit_resolution,[status(thm)],[8946, 1121, 5462, 8939, 8940])).
% 290.72/183.28 tff(8948,plain,((~node6(c_e_h_3, c_j, s9, s10)) | m_or_h_gate_v_out(c_e_h_3, c_j, s9) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s10))), inference(lemma,lemma(discharge,[]))).
% 290.72/183.28 tff(8949,plain,
% 290.72/183.28 (~node6(c_e_h_3, c_j, s9, s10)),
% 290.72/183.28 inference(unit_resolution,[status(thm)],[8948, 8939, 5462])).
% 290.72/183.28 tff(8950,assumption,(~m_or_h_gate_v_in1(c_e_h_3, c_j, s9)), introduced(assumption)).
% 290.72/183.28 tff(8951,assumption,(~m_or_h_gate_v_in2(c_e_h_3, c_j, s9)), introduced(assumption)).
% 290.72/183.28 tff(8952,assumption,(node5(c_e_h_3, c_j, s9, s10)), introduced(assumption)).
% 290.72/183.28 tff(8953,plain,
% 290.72/183.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_3, c_j, s9) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s10)) | (~node5(c_e_h_3, c_j, s9, s10)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_3, c_j, s9) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s10)) | (~node5(c_e_h_3, c_j, s9, s10)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s9))),
% 290.72/183.28 inference(rewrite,[status(thm)],[])).
% 290.72/183.28 tff(8954,plain,
% 290.72/183.28 ((m_or_h_gate_v_in1(c_e_h_3, c_j, s9) | m_or_h_gate_v_in2(c_e_h_3, c_j, s9) | (~node5(c_e_h_3, c_j, s9, s10)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s10))) <=> (m_or_h_gate_v_in2(c_e_h_3, c_j, s9) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s10)) | (~node5(c_e_h_3, c_j, s9, s10)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s9))),
% 290.72/183.28 inference(rewrite,[status(thm)],[])).
% 290.72/183.28 tff(8955,plain,
% 290.72/183.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s9) | m_or_h_gate_v_in2(c_e_h_3, c_j, s9) | (~node5(c_e_h_3, c_j, s9, s10)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_3, c_j, s9) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s10)) | (~node5(c_e_h_3, c_j, s9, s10)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s9)))),
% 290.72/183.28 inference(monotonicity,[status(thm)],[8954])).
% 290.72/183.28 tff(8956,plain,
% 290.72/183.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s9) | m_or_h_gate_v_in2(c_e_h_3, c_j, s9) | (~node5(c_e_h_3, c_j, s9, s10)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_3, c_j, s9) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s10)) | (~node5(c_e_h_3, c_j, s9, s10)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s9))),
% 290.72/183.28 inference(transitivity,[status(thm)],[8955, 8953])).
% 290.72/183.28 tff(8957,plain,
% 290.72/183.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s9) | m_or_h_gate_v_in2(c_e_h_3, c_j, s9) | (~node5(c_e_h_3, c_j, s9, s10)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s10)))),
% 290.72/183.28 inference(quant_inst,[status(thm)],[])).
% 290.72/183.28 tff(8958,plain,
% 290.72/183.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_3, c_j, s9) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s10)) | (~node5(c_e_h_3, c_j, s9, s10)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s9)),
% 290.82/183.29 inference(modus_ponens,[status(thm)],[8957, 8956])).
% 290.82/183.29 tff(8959,plain,
% 290.82/183.29 ($false),
% 290.82/183.29 inference(unit_resolution,[status(thm)],[8958, 1159, 8939, 8952, 8950, 8951])).
% 290.82/183.29 tff(8960,plain,((~node5(c_e_h_3, c_j, s9, s10)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s10)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s9) | m_or_h_gate_v_in2(c_e_h_3, c_j, s9)), inference(lemma,lemma(discharge,[]))).
% 290.82/183.29 tff(8961,plain,
% 290.82/183.29 (~node5(c_e_h_3, c_j, s9, s10)),
% 290.82/183.29 inference(unit_resolution,[status(thm)],[8960, 8939, 8951, 8950])).
% 290.82/183.29 tff(8962,plain,
% 290.82/183.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s9, s10)) | node5(c_e_h_3, c_j, s9, s10) | node6(c_e_h_3, c_j, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s9, s10)) | node5(c_e_h_3, c_j, s9, s10) | node6(c_e_h_3, c_j, s9, s10))),
% 290.82/183.29 inference(rewrite,[status(thm)],[])).
% 290.82/183.29 tff(8963,plain,
% 290.82/183.29 ((node6(c_e_h_3, c_j, s9, s10) | node5(c_e_h_3, c_j, s9, s10) | (~trans(s9, s10))) <=> ((~trans(s9, s10)) | node5(c_e_h_3, c_j, s9, s10) | node6(c_e_h_3, c_j, s9, s10))),
% 290.82/183.29 inference(rewrite,[status(thm)],[])).
% 290.82/183.29 tff(8964,plain,
% 290.82/183.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s9, s10) | node5(c_e_h_3, c_j, s9, s10) | (~trans(s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s9, s10)) | node5(c_e_h_3, c_j, s9, s10) | node6(c_e_h_3, c_j, s9, s10)))),
% 290.82/183.29 inference(monotonicity,[status(thm)],[8963])).
% 290.82/183.29 tff(8965,plain,
% 290.82/183.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s9, s10) | node5(c_e_h_3, c_j, s9, s10) | (~trans(s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s9, s10)) | node5(c_e_h_3, c_j, s9, s10) | node6(c_e_h_3, c_j, s9, s10))),
% 290.82/183.29 inference(transitivity,[status(thm)],[8964, 8962])).
% 290.82/183.29 tff(8966,plain,
% 290.82/183.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s9, s10) | node5(c_e_h_3, c_j, s9, s10) | (~trans(s9, s10)))),
% 290.82/183.29 inference(quant_inst,[status(thm)],[])).
% 290.82/183.29 tff(8967,plain,
% 290.82/183.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s9, s10)) | node5(c_e_h_3, c_j, s9, s10) | node6(c_e_h_3, c_j, s9, s10)),
% 290.82/183.29 inference(modus_ponens,[status(thm)],[8966, 8965])).
% 290.82/183.29 tff(8968,plain,
% 290.82/183.29 (node5(c_e_h_3, c_j, s9, s10) | node6(c_e_h_3, c_j, s9, s10)),
% 290.82/183.29 inference(unit_resolution,[status(thm)],[8967, 1141, 7676])).
% 290.82/183.29 tff(8969,plain,
% 290.82/183.29 ($false),
% 290.82/183.29 inference(unit_resolution,[status(thm)],[8968, 8961, 8949])).
% 290.82/183.29 tff(8970,plain,((~m_or_h_gate_v_out(c_e_h_3, c_j, s10)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s9) | m_or_h_gate_v_in1(c_e_h_3, c_j, s9) | m_or_h_gate_v_out(c_e_h_3, c_j, s9)), inference(lemma,lemma(discharge,[]))).
% 290.82/183.29 tff(8971,plain,
% 290.82/183.29 ((~m_or_h_gate_v_out(c_e_h_3, c_j, s10)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s9) | m_or_h_gate_v_out(c_e_h_3, c_j, s9)),
% 290.82/183.29 inference(unit_resolution,[status(thm)],[8970, 8938])).
% 290.82/183.29 tff(8972,plain,
% 290.82/183.29 (m_or_h_gate_v_in1(c_e_h_3, c_j, s9)),
% 290.82/183.29 inference(unit_resolution,[status(thm)],[8971, 7811, 5462])).
% 290.82/183.29 tff(8973,assumption,(m_or_h_gate_v_in1(c_e_h_3, c_j, s9)), introduced(assumption)).
% 290.82/183.29 tff(8974,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_l, s9)), introduced(assumption)).
% 290.82/183.29 tff(8975,plain,
% 290.82/183.29 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_j, s9)) | m_and_h_gate_v_out(c_e_h_3, c_l, s9))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s9)) | m_and_h_gate_v_out(c_e_h_3, c_l, s9))),
% 290.82/183.29 inference(rewrite,[status(thm)],[])).
% 290.82/183.29 tff(8976,plain,
% 290.82/183.29 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_j, s9)) | m_and_h_gate_v_out(c_e_h_3, c_l, s9))),
% 290.82/183.29 inference(quant_inst,[status(thm)],[])).
% 290.82/183.29 tff(8977,plain,
% 290.82/183.29 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s9)) | m_and_h_gate_v_out(c_e_h_3, c_l, s9)),
% 290.82/183.29 inference(modus_ponens,[status(thm)],[8976, 8975])).
% 290.82/183.29 tff(8978,plain,
% 290.82/183.29 ($false),
% 290.82/183.29 inference(unit_resolution,[status(thm)],[8977, 1100, 8974, 8973])).
% 290.82/183.29 tff(8979,plain,((~m_or_h_gate_v_in1(c_e_h_3, c_j, s9)) | m_and_h_gate_v_out(c_e_h_3, c_l, s9)), inference(lemma,lemma(discharge,[]))).
% 290.82/183.29 tff(8980,plain,
% 290.82/183.29 (m_and_h_gate_v_out(c_e_h_3, c_l, s9)),
% 290.82/183.29 inference(unit_resolution,[status(thm)],[8979, 8972])).
% 290.82/183.29 tff(8981,assumption,(m_and_h_gate_v_in2(c_e_h_3, c_k, s8)), introduced(assumption)).
% 290.82/183.29 tff(8982,assumption,(node6(c_e_h_3, c_j, s10, s11)), introduced(assumption)).
% 290.82/183.29 tff(8983,plain,
% 290.82/183.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | ((~m_or_h_gate_v_out(c_e_h_3, c_j, s10)) | m_or_h_gate_v_out(c_e_h_3, c_j, s11) | (~node6(c_e_h_3, c_j, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s10)) | m_or_h_gate_v_out(c_e_h_3, c_j, s11) | (~node6(c_e_h_3, c_j, s10, s11)))),
% 290.82/183.29 inference(rewrite,[status(thm)],[])).
% 290.82/183.29 tff(8984,plain,
% 290.82/183.29 ((m_or_h_gate_v_out(c_e_h_3, c_j, s11) | (~node6(c_e_h_3, c_j, s10, s11)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s10))) <=> ((~m_or_h_gate_v_out(c_e_h_3, c_j, s10)) | m_or_h_gate_v_out(c_e_h_3, c_j, s11) | (~node6(c_e_h_3, c_j, s10, s11)))),
% 290.82/183.29 inference(rewrite,[status(thm)],[])).
% 290.82/183.29 tff(8985,plain,
% 290.82/183.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_3, c_j, s11) | (~node6(c_e_h_3, c_j, s10, s11)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | ((~m_or_h_gate_v_out(c_e_h_3, c_j, s10)) | m_or_h_gate_v_out(c_e_h_3, c_j, s11) | (~node6(c_e_h_3, c_j, s10, s11))))),
% 290.82/183.29 inference(monotonicity,[status(thm)],[8984])).
% 290.82/183.29 tff(8986,plain,
% 290.82/183.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_3, c_j, s11) | (~node6(c_e_h_3, c_j, s10, s11)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s10)) | m_or_h_gate_v_out(c_e_h_3, c_j, s11) | (~node6(c_e_h_3, c_j, s10, s11)))),
% 290.82/183.29 inference(transitivity,[status(thm)],[8985, 8983])).
% 290.82/183.29 tff(8987,plain,
% 290.82/183.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_3, c_j, s11) | (~node6(c_e_h_3, c_j, s10, s11)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s10)))),
% 290.82/183.29 inference(quant_inst,[status(thm)],[])).
% 290.82/183.29 tff(8988,plain,
% 290.82/183.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s10)) | m_or_h_gate_v_out(c_e_h_3, c_j, s11) | (~node6(c_e_h_3, c_j, s10, s11))),
% 290.82/183.29 inference(modus_ponens,[status(thm)],[8987, 8986])).
% 290.82/183.29 tff(8989,plain,
% 290.82/183.29 ($false),
% 290.82/183.29 inference(unit_resolution,[status(thm)],[8988, 5474, 8939, 7627, 8982])).
% 290.82/183.29 tff(8990,plain,((~node6(c_e_h_3, c_j, s10, s11)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s10)) | m_or_h_gate_v_out(c_e_h_3, c_j, s11)), inference(lemma,lemma(discharge,[]))).
% 290.82/183.29 tff(8991,plain,
% 290.82/183.29 (~node6(c_e_h_3, c_j, s10, s11)),
% 290.82/183.29 inference(unit_resolution,[status(thm)],[8990, 7811, 7627])).
% 290.82/183.30 tff(8992,plain,
% 290.82/183.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s10, s11)) | node5(c_e_h_3, c_j, s10, s11) | node6(c_e_h_3, c_j, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s10, s11)) | node5(c_e_h_3, c_j, s10, s11) | node6(c_e_h_3, c_j, s10, s11))),
% 290.82/183.30 inference(rewrite,[status(thm)],[])).
% 290.82/183.30 tff(8993,plain,
% 290.82/183.30 ((node6(c_e_h_3, c_j, s10, s11) | node5(c_e_h_3, c_j, s10, s11) | (~trans(s10, s11))) <=> ((~trans(s10, s11)) | node5(c_e_h_3, c_j, s10, s11) | node6(c_e_h_3, c_j, s10, s11))),
% 290.82/183.30 inference(rewrite,[status(thm)],[])).
% 290.82/183.30 tff(8994,plain,
% 290.82/183.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s10, s11) | node5(c_e_h_3, c_j, s10, s11) | (~trans(s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s10, s11)) | node5(c_e_h_3, c_j, s10, s11) | node6(c_e_h_3, c_j, s10, s11)))),
% 290.82/183.30 inference(monotonicity,[status(thm)],[8993])).
% 290.82/183.30 tff(8995,plain,
% 290.82/183.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s10, s11) | node5(c_e_h_3, c_j, s10, s11) | (~trans(s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s10, s11)) | node5(c_e_h_3, c_j, s10, s11) | node6(c_e_h_3, c_j, s10, s11))),
% 290.82/183.30 inference(transitivity,[status(thm)],[8994, 8992])).
% 290.82/183.30 tff(8996,plain,
% 290.82/183.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s10, s11) | node5(c_e_h_3, c_j, s10, s11) | (~trans(s10, s11)))),
% 290.82/183.30 inference(quant_inst,[status(thm)],[])).
% 290.82/183.30 tff(8997,plain,
% 290.82/183.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s10, s11)) | node5(c_e_h_3, c_j, s10, s11) | node6(c_e_h_3, c_j, s10, s11)),
% 290.82/183.30 inference(modus_ponens,[status(thm)],[8996, 8995])).
% 290.82/183.30 tff(8998,plain,
% 290.82/183.30 (node5(c_e_h_3, c_j, s10, s11) | node6(c_e_h_3, c_j, s10, s11)),
% 290.82/183.30 inference(unit_resolution,[status(thm)],[8997, 1141, 7748])).
% 290.82/183.30 tff(8999,plain,
% 290.82/183.30 (node5(c_e_h_3, c_j, s10, s11)),
% 290.82/183.30 inference(unit_resolution,[status(thm)],[8998, 8991])).
% 290.82/183.30 tff(9000,assumption,(~node4(c_e_h_3, c_j, s10)), introduced(assumption)).
% 290.82/183.30 tff(9001,assumption,(node5(c_e_h_3, c_j, s10, s11)), introduced(assumption)).
% 290.82/183.30 tff(9002,plain,
% 290.82/183.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_3, c_j, s10) | m_or_h_gate_v_out(c_e_h_3, c_j, s11) | (~node5(c_e_h_3, c_j, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | node4(c_e_h_3, c_j, s10) | m_or_h_gate_v_out(c_e_h_3, c_j, s11) | (~node5(c_e_h_3, c_j, s10, s11)))),
% 290.82/183.30 inference(rewrite,[status(thm)],[])).
% 290.82/183.30 tff(9003,plain,
% 290.82/183.30 ((node4(c_e_h_3, c_j, s10) | (~node5(c_e_h_3, c_j, s10, s11)) | m_or_h_gate_v_out(c_e_h_3, c_j, s11)) <=> (node4(c_e_h_3, c_j, s10) | m_or_h_gate_v_out(c_e_h_3, c_j, s11) | (~node5(c_e_h_3, c_j, s10, s11)))),
% 290.82/183.30 inference(rewrite,[status(thm)],[])).
% 290.82/183.30 tff(9004,plain,
% 290.82/183.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_3, c_j, s10) | (~node5(c_e_h_3, c_j, s10, s11)) | m_or_h_gate_v_out(c_e_h_3, c_j, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_3, c_j, s10) | m_or_h_gate_v_out(c_e_h_3, c_j, s11) | (~node5(c_e_h_3, c_j, s10, s11))))),
% 290.82/183.30 inference(monotonicity,[status(thm)],[9003])).
% 290.82/183.30 tff(9005,plain,
% 290.82/183.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_3, c_j, s10) | (~node5(c_e_h_3, c_j, s10, s11)) | m_or_h_gate_v_out(c_e_h_3, c_j, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | node4(c_e_h_3, c_j, s10) | m_or_h_gate_v_out(c_e_h_3, c_j, s11) | (~node5(c_e_h_3, c_j, s10, s11)))),
% 290.82/183.30 inference(transitivity,[status(thm)],[9004, 9002])).
% 290.82/183.30 tff(9006,plain,
% 290.82/183.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_3, c_j, s10) | (~node5(c_e_h_3, c_j, s10, s11)) | m_or_h_gate_v_out(c_e_h_3, c_j, s11))),
% 290.82/183.30 inference(quant_inst,[status(thm)],[])).
% 290.82/183.30 tff(9007,plain,
% 290.82/183.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | node4(c_e_h_3, c_j, s10) | m_or_h_gate_v_out(c_e_h_3, c_j, s11) | (~node5(c_e_h_3, c_j, s10, s11))),
% 290.82/183.30 inference(modus_ponens,[status(thm)],[9006, 9005])).
% 290.82/183.30 tff(9008,plain,
% 290.82/183.30 ($false),
% 290.82/183.30 inference(unit_resolution,[status(thm)],[9007, 5498, 7627, 9001, 9000])).
% 290.82/183.30 tff(9009,plain,((~node5(c_e_h_3, c_j, s10, s11)) | m_or_h_gate_v_out(c_e_h_3, c_j, s11) | node4(c_e_h_3, c_j, s10)), inference(lemma,lemma(discharge,[]))).
% 290.82/183.30 tff(9010,plain,
% 290.82/183.30 (node4(c_e_h_3, c_j, s10)),
% 290.82/183.30 inference(unit_resolution,[status(thm)],[9009, 8999, 7627])).
% 290.82/183.30 tff(9011,plain,
% 290.82/183.30 (((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_j, s10)) | (~node4(c_e_h_3, c_j, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s10)) | (~node4(c_e_h_3, c_j, s10)))),
% 290.82/183.30 inference(rewrite,[status(thm)],[])).
% 290.82/183.30 tff(9012,plain,
% 290.82/183.30 ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_j, s10)) | (~node4(c_e_h_3, c_j, s10)))),
% 290.82/183.30 inference(quant_inst,[status(thm)],[])).
% 290.82/183.30 tff(9013,plain,
% 290.82/183.30 ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s10)) | (~node4(c_e_h_3, c_j, s10))),
% 290.82/183.30 inference(modus_ponens,[status(thm)],[9012, 9011])).
% 290.82/183.30 tff(9014,plain,
% 290.82/183.30 (~m_or_h_gate_v_in1(c_e_h_3, c_j, s10)),
% 290.82/183.30 inference(unit_resolution,[status(thm)],[9013, 5516, 9010])).
% 290.82/183.30 tff(9015,plain,
% 290.82/183.30 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s10)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s10))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s10)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s10))),
% 290.82/183.30 inference(rewrite,[status(thm)],[])).
% 290.82/183.30 tff(9016,plain,
% 290.82/183.30 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s10)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s10))),
% 290.82/183.30 inference(quant_inst,[status(thm)],[])).
% 290.82/183.30 tff(9017,plain,
% 290.82/183.30 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s10)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s10)),
% 290.82/183.30 inference(modus_ponens,[status(thm)],[9016, 9015])).
% 290.82/183.30 tff(9018,plain,
% 290.82/183.30 (~m_and_h_gate_v_out(c_e_h_3, c_l, s10)),
% 290.82/183.30 inference(unit_resolution,[status(thm)],[9017, 3627, 9014])).
% 290.82/183.30 tff(9019,assumption,(m_and_h_gate_v_out(c_e_h_3, c_l, s9)), introduced(assumption)).
% 290.82/183.30 tff(9020,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_l, s10)), introduced(assumption)).
% 290.82/183.30 tff(9021,assumption,(node22(c_e_h_3, c_l, s9, s10)), introduced(assumption)).
% 290.82/183.30 tff(9022,plain,
% 290.82/183.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_l, s10) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s9)) | (~node22(c_e_h_3, c_l, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | m_and_h_gate_v_out(c_e_h_3, c_l, s10) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s9)) | (~node22(c_e_h_3, c_l, s9, s10)))),
% 290.82/183.30 inference(rewrite,[status(thm)],[])).
% 290.82/183.30 tff(9023,plain,
% 290.82/183.30 ((m_and_h_gate_v_out(c_e_h_3, c_l, s10) | (~node22(c_e_h_3, c_l, s9, s10)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s9))) <=> (m_and_h_gate_v_out(c_e_h_3, c_l, s10) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s9)) | (~node22(c_e_h_3, c_l, s9, s10)))),
% 290.82/183.30 inference(rewrite,[status(thm)],[])).
% 290.82/183.30 tff(9024,plain,
% 290.82/183.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_l, s10) | (~node22(c_e_h_3, c_l, s9, s10)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_l, s10) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s9)) | (~node22(c_e_h_3, c_l, s9, s10))))),
% 290.82/183.30 inference(monotonicity,[status(thm)],[9023])).
% 290.82/183.30 tff(9025,plain,
% 290.82/183.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_l, s10) | (~node22(c_e_h_3, c_l, s9, s10)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | m_and_h_gate_v_out(c_e_h_3, c_l, s10) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s9)) | (~node22(c_e_h_3, c_l, s9, s10)))),
% 290.82/183.30 inference(transitivity,[status(thm)],[9024, 9022])).
% 290.82/183.30 tff(9026,plain,
% 290.82/183.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_l, s10) | (~node22(c_e_h_3, c_l, s9, s10)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s9)))),
% 290.82/183.30 inference(quant_inst,[status(thm)],[])).
% 290.82/183.30 tff(9027,plain,
% 290.82/183.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | m_and_h_gate_v_out(c_e_h_3, c_l, s10) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s9)) | (~node22(c_e_h_3, c_l, s9, s10))),
% 290.82/183.30 inference(modus_ponens,[status(thm)],[9026, 9025])).
% 290.82/183.30 tff(9028,plain,
% 290.82/183.30 ($false),
% 290.82/183.30 inference(unit_resolution,[status(thm)],[9027, 5871, 9021, 9020, 9019])).
% 290.82/183.30 tff(9029,plain,((~node22(c_e_h_3, c_l, s9, s10)) | m_and_h_gate_v_out(c_e_h_3, c_l, s10) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s9))), inference(lemma,lemma(discharge,[]))).
% 290.82/183.30 tff(9030,plain,
% 290.82/183.30 (~node22(c_e_h_3, c_l, s9, s10)),
% 290.82/183.30 inference(unit_resolution,[status(thm)],[9029, 9018, 8980])).
% 290.82/183.30 tff(9031,plain,
% 290.82/183.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s9, s10)) | node21(c_e_h_3, c_l, s9, s10) | node22(c_e_h_3, c_l, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s9, s10)) | node21(c_e_h_3, c_l, s9, s10) | node22(c_e_h_3, c_l, s9, s10))),
% 290.82/183.30 inference(rewrite,[status(thm)],[])).
% 290.82/183.30 tff(9032,plain,
% 290.82/183.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s9, s10)) | node21(c_e_h_3, c_l, s9, s10) | node22(c_e_h_3, c_l, s9, s10))),
% 290.82/183.30 inference(quant_inst,[status(thm)],[])).
% 290.82/183.30 tff(9033,plain,
% 290.82/183.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s9, s10)) | node21(c_e_h_3, c_l, s9, s10) | node22(c_e_h_3, c_l, s9, s10)),
% 290.82/183.30 inference(modus_ponens,[status(thm)],[9032, 9031])).
% 290.82/183.30 tff(9034,plain,
% 290.82/183.30 (node21(c_e_h_3, c_l, s9, s10) | node22(c_e_h_3, c_l, s9, s10)),
% 290.82/183.30 inference(unit_resolution,[status(thm)],[9033, 82, 7676])).
% 290.82/183.30 tff(9035,plain,
% 290.82/183.30 (node21(c_e_h_3, c_l, s9, s10)),
% 290.82/183.30 inference(unit_resolution,[status(thm)],[9034, 9030])).
% 290.82/183.30 tff(9036,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_l, s9)), introduced(assumption)).
% 290.82/183.30 tff(9037,plain,
% 290.82/183.30 (~m_c_h_element_v_in2(c_e_h_3, c_h, s3)),
% 290.82/183.30 inference(unit_resolution,[status(thm)],[2240, 2235])).
% 290.82/183.30 tff(9038,plain,
% 290.82/183.30 (~m_c_h_element_v_out(c_e_h_3, c_h, s4)),
% 290.82/183.30 inference(unit_resolution,[status(thm)],[2338, 9037])).
% 290.82/183.30 tff(9039,plain,
% 290.82/183.30 (~m_c_h_element_v_out(c_e_h_3, c_h, s4)),
% 290.82/183.31 inference(unit_resolution,[status(thm)],[2337, 2266, 1710])).
% 290.82/183.31 tff(9040,assumption,(m_and_h_gate_v_out(c_e_h_3, c_i, s6)), introduced(assumption)).
% 290.82/183.31 tff(9041,plain,
% 290.82/183.31 (~m_and_h_gate_v_in1(c_e_h_3, c_i, s4)),
% 290.82/183.31 inference(unit_resolution,[status(thm)],[2346, 9039])).
% 290.82/183.31 tff(9042,plain,
% 290.82/183.31 (~node20(c_e_h_3, c_i, s4)),
% 290.82/183.31 inference(unit_resolution,[status(thm)],[2354, 9041])).
% 290.82/183.31 tff(9043,plain,
% 290.82/183.31 (~m_and_h_gate_v_out(c_e_h_3, c_i, s5)),
% 290.82/183.31 inference(unit_resolution,[status(thm)],[2381, 9042, 1744])).
% 290.82/183.31 tff(9044,assumption,(node22(c_e_h_3, c_i, s5, s6)), introduced(assumption)).
% 290.82/183.31 tff(9045,plain,
% 290.82/183.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s6)) | (~node22(c_e_h_3, c_i, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_i, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s6)) | (~node22(c_e_h_3, c_i, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_i, s5))),
% 290.82/183.31 inference(rewrite,[status(thm)],[])).
% 290.82/183.31 tff(9046,plain,
% 290.82/183.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s6)) | (~node22(c_e_h_3, c_i, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_i, s5))),
% 290.82/183.31 inference(quant_inst,[status(thm)],[])).
% 290.82/183.31 tff(9047,plain,
% 290.82/183.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s6)) | (~node22(c_e_h_3, c_i, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_i, s5)),
% 290.82/183.31 inference(modus_ponens,[status(thm)],[9046, 9045])).
% 290.82/183.31 tff(9048,plain,
% 290.82/183.31 ($false),
% 290.82/183.31 inference(unit_resolution,[status(thm)],[9047, 108, 9044, 6470, 9040])).
% 290.82/183.31 tff(9049,plain,((~node22(c_e_h_3, c_i, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_i, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s6))), inference(lemma,lemma(discharge,[]))).
% 290.82/183.31 tff(9050,plain,
% 290.82/183.31 (~node22(c_e_h_3, c_i, s5, s6)),
% 290.82/183.31 inference(unit_resolution,[status(thm)],[9049, 9040, 6470])).
% 290.82/183.31 tff(9051,assumption,(~node20(c_e_h_3, c_i, s5)), introduced(assumption)).
% 290.82/183.31 tff(9052,assumption,(node21(c_e_h_3, c_i, s5, s6)), introduced(assumption)).
% 290.82/183.31 tff(9053,plain,
% 290.82/183.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s6)) | (~node21(c_e_h_3, c_i, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_i, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s6)) | (~node21(c_e_h_3, c_i, s5, s6)))),
% 290.82/183.31 inference(rewrite,[status(thm)],[])).
% 290.82/183.31 tff(9054,plain,
% 290.82/183.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s6)) | (~node21(c_e_h_3, c_i, s5, s6)))),
% 290.82/183.31 inference(quant_inst,[status(thm)],[])).
% 290.82/183.31 tff(9055,plain,
% 290.82/183.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_i, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s6)) | (~node21(c_e_h_3, c_i, s5, s6))),
% 290.82/183.31 inference(modus_ponens,[status(thm)],[9054, 9053])).
% 290.82/183.31 tff(9056,plain,
% 290.82/183.31 ($false),
% 290.82/183.31 inference(unit_resolution,[status(thm)],[9055, 52, 9052, 9040, 9051])).
% 290.82/183.31 tff(9057,plain,((~node21(c_e_h_3, c_i, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s6)) | node20(c_e_h_3, c_i, s5)), inference(lemma,lemma(discharge,[]))).
% 290.82/183.31 tff(9058,plain,
% 290.82/183.31 (~node21(c_e_h_3, c_i, s5, s6)),
% 290.82/183.31 inference(unit_resolution,[status(thm)],[9057, 9040, 9051])).
% 290.82/183.31 tff(9059,plain,
% 290.82/183.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_3, c_i, s5, s6) | node22(c_e_h_3, c_i, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_3, c_i, s5, s6) | node22(c_e_h_3, c_i, s5, s6))),
% 290.84/183.31 inference(rewrite,[status(thm)],[])).
% 290.84/183.31 tff(9060,plain,
% 290.84/183.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_3, c_i, s5, s6) | node22(c_e_h_3, c_i, s5, s6))),
% 290.84/183.31 inference(quant_inst,[status(thm)],[])).
% 290.84/183.31 tff(9061,plain,
% 290.84/183.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_3, c_i, s5, s6) | node22(c_e_h_3, c_i, s5, s6)),
% 290.84/183.31 inference(modus_ponens,[status(thm)],[9060, 9059])).
% 290.84/183.31 tff(9062,plain,
% 290.84/183.31 (node21(c_e_h_3, c_i, s5, s6) | node22(c_e_h_3, c_i, s5, s6)),
% 290.84/183.31 inference(unit_resolution,[status(thm)],[9061, 82, 1406])).
% 290.84/183.31 tff(9063,plain,
% 290.84/183.31 ($false),
% 290.84/183.31 inference(unit_resolution,[status(thm)],[9062, 9058, 9050])).
% 290.84/183.31 tff(9064,plain,((~m_and_h_gate_v_out(c_e_h_3, c_i, s6)) | node20(c_e_h_3, c_i, s5) | m_and_h_gate_v_out(c_e_h_3, c_i, s5)), inference(lemma,lemma(discharge,[]))).
% 290.84/183.31 tff(9065,plain,
% 290.84/183.31 (node20(c_e_h_3, c_i, s5)),
% 290.84/183.31 inference(unit_resolution,[status(thm)],[9064, 9043, 9040])).
% 290.84/183.31 tff(9066,plain,
% 290.84/183.31 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_i, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s5))),
% 290.84/183.31 inference(rewrite,[status(thm)],[])).
% 290.84/183.31 tff(9067,plain,
% 290.84/183.31 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s5))),
% 290.84/183.31 inference(quant_inst,[status(thm)],[])).
% 290.84/183.31 tff(9068,plain,
% 290.84/183.31 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_i, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s5)),
% 290.84/183.31 inference(modus_ponens,[status(thm)],[9067, 9066])).
% 290.84/183.31 tff(9069,plain,
% 290.84/183.31 (m_and_h_gate_v_in1(c_e_h_3, c_i, s5)),
% 290.84/183.31 inference(unit_resolution,[status(thm)],[9068, 38, 9065])).
% 290.84/183.31 tff(9070,plain,
% 290.84/183.31 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_i, s5)) | m_c_h_element_v_out(c_e_h_3, c_h, s5))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s5)) | m_c_h_element_v_out(c_e_h_3, c_h, s5))),
% 290.84/183.31 inference(rewrite,[status(thm)],[])).
% 290.84/183.31 tff(9071,plain,
% 290.84/183.31 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_i, s5)) | m_c_h_element_v_out(c_e_h_3, c_h, s5))),
% 290.84/183.31 inference(quant_inst,[status(thm)],[])).
% 290.84/183.31 tff(9072,plain,
% 290.84/183.31 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s5)) | m_c_h_element_v_out(c_e_h_3, c_h, s5)),
% 290.84/183.31 inference(modus_ponens,[status(thm)],[9071, 9070])).
% 290.84/183.31 tff(9073,plain,
% 290.84/183.31 (m_c_h_element_v_out(c_e_h_3, c_h, s5)),
% 290.84/183.31 inference(unit_resolution,[status(thm)],[9072, 619, 9069])).
% 290.84/183.31 tff(9074,plain,
% 290.84/183.31 (m_c_h_element_v_in2(c_e_h_3, c_h, s4)),
% 290.84/183.31 inference(unit_resolution,[status(thm)],[6343, 9073, 9039])).
% 290.84/183.31 tff(9075,plain,
% 290.84/183.31 (m_or_h_gate_v_out(c_e_h_3, c_j, s4)),
% 290.84/183.31 inference(unit_resolution,[status(thm)],[6257, 9074])).
% 290.84/183.31 tff(9076,plain,
% 290.84/183.31 (~node5(c_e_h_3, c_j, s3, s4)),
% 290.84/183.31 inference(unit_resolution,[status(thm)],[4052, 9075, 3617])).
% 290.84/183.31 tff(9077,plain,
% 290.84/183.31 (node6(c_e_h_3, c_j, s3, s4)),
% 290.84/183.31 inference(unit_resolution,[status(thm)],[4060, 9076])).
% 290.84/183.31 tff(9078,plain,
% 290.84/183.31 (m_or_h_gate_v_out(c_e_h_3, c_j, s3)),
% 290.84/183.31 inference(unit_resolution,[status(thm)],[4027, 9077, 9075])).
% 290.84/183.31 tff(9079,plain,
% 290.84/183.31 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_j, X)) | m_c_h_element_v_in2(I0, c_h, X))) | ((~m_or_h_gate_v_out(c_e_h_3, c_j, s3)) | m_c_h_element_v_in2(c_e_h_3, c_h, s3))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_j, X)) | m_c_h_element_v_in2(I0, c_h, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s3)) | m_c_h_element_v_in2(c_e_h_3, c_h, s3))),
% 290.84/183.31 inference(rewrite,[status(thm)],[])).
% 290.84/183.31 tff(9080,plain,
% 290.84/183.31 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_j, X)) | m_c_h_element_v_in2(I0, c_h, X))) | ((~m_or_h_gate_v_out(c_e_h_3, c_j, s3)) | m_c_h_element_v_in2(c_e_h_3, c_h, s3))),
% 290.84/183.31 inference(quant_inst,[status(thm)],[])).
% 290.84/183.31 tff(9081,plain,
% 290.84/183.31 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_j, X)) | m_c_h_element_v_in2(I0, c_h, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s3)) | m_c_h_element_v_in2(c_e_h_3, c_h, s3)),
% 290.84/183.31 inference(modus_ponens,[status(thm)],[9080, 9079])).
% 290.84/183.31 tff(9082,plain,
% 290.84/183.31 ($false),
% 290.84/183.31 inference(unit_resolution,[status(thm)],[9081, 7385, 9078, 2266])).
% 290.84/183.31 tff(9083,plain,(m_c_h_element_v_in2(c_e_h_3, c_h, s3) | m_or_h_gate_v_in1(c_e_h_3, c_j, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s6))), inference(lemma,lemma(discharge,[]))).
% 290.84/183.31 tff(9084,plain,
% 290.84/183.31 (~m_and_h_gate_v_out(c_e_h_3, c_i, s6)),
% 290.84/183.31 inference(unit_resolution,[status(thm)],[9083, 9037, 3617])).
% 290.84/183.31 tff(9085,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_i, s6)), introduced(assumption)).
% 290.84/183.31 tff(9086,assumption,(m_c_h_element_v_in2(c_e_h_3, c_f, s6)), introduced(assumption)).
% 290.84/183.31 tff(9087,plain,
% 290.84/183.31 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s6)) | m_and_h_gate_v_out(c_e_h_3, c_i, s6))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s6)) | m_and_h_gate_v_out(c_e_h_3, c_i, s6))),
% 290.84/183.31 inference(rewrite,[status(thm)],[])).
% 290.84/183.31 tff(9088,plain,
% 290.84/183.31 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s6)) | m_and_h_gate_v_out(c_e_h_3, c_i, s6))),
% 290.84/183.31 inference(quant_inst,[status(thm)],[])).
% 290.84/183.31 tff(9089,plain,
% 290.84/183.31 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s6)) | m_and_h_gate_v_out(c_e_h_3, c_i, s6)),
% 290.84/183.31 inference(modus_ponens,[status(thm)],[9088, 9087])).
% 290.84/183.31 tff(9090,plain,
% 290.84/183.31 ($false),
% 290.84/183.31 inference(unit_resolution,[status(thm)],[9089, 2143, 9086, 9085])).
% 290.84/183.31 tff(9091,plain,((~m_c_h_element_v_in2(c_e_h_3, c_f, s6)) | m_and_h_gate_v_out(c_e_h_3, c_i, s6)), inference(lemma,lemma(discharge,[]))).
% 290.84/183.31 tff(9092,plain,
% 290.84/183.31 (~m_c_h_element_v_in2(c_e_h_3, c_f, s6)),
% 290.84/183.31 inference(unit_resolution,[status(thm)],[9091, 9084])).
% 290.84/183.31 tff(9093,plain,
% 290.84/183.31 (~m_and_h_gate_v_in1(c_e_h_3, c_i, s4)),
% 290.84/183.31 inference(unit_resolution,[status(thm)],[2346, 9038])).
% 290.84/183.31 tff(9094,plain,
% 290.84/183.31 (~node20(c_e_h_3, c_i, s4)),
% 290.84/183.31 inference(unit_resolution,[status(thm)],[2354, 9093])).
% 290.84/183.31 tff(9095,plain,
% 290.84/183.31 (~m_and_h_gate_v_out(c_e_h_3, c_i, s5)),
% 290.84/183.31 inference(unit_resolution,[status(thm)],[2382, 9094])).
% 290.84/183.31 tff(9096,plain,
% 290.84/183.31 (~m_c_h_element_v_in2(c_e_h_3, c_f, s5)),
% 290.84/183.31 inference(unit_resolution,[status(thm)],[6476, 9095])).
% 290.84/183.31 tff(9097,plain,
% 290.84/183.31 (~m_c_h_element_v_out(c_e_h_3, c_f, s6)),
% 290.84/183.31 inference(unit_resolution,[status(thm)],[6868, 9096])).
% 290.84/183.31 tff(9098,assumption,(~m_c_h_element_v_out(c_e_h_3, c_f, s6)), introduced(assumption)).
% 290.84/183.31 tff(9099,assumption,(m_c_h_element_v_out(c_e_h_3, c_f, s7)), introduced(assumption)).
% 290.84/183.31 tff(9100,assumption,(node18(c_e_h_3, c_f, s6, s7)), introduced(assumption)).
% 290.84/183.31 tff(9101,plain,
% 290.84/183.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s7)) | m_c_h_element_v_out(c_e_h_3, c_f, s6) | (~node18(c_e_h_3, c_f, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s7)) | m_c_h_element_v_out(c_e_h_3, c_f, s6) | (~node18(c_e_h_3, c_f, s6, s7)))),
% 290.84/183.31 inference(rewrite,[status(thm)],[])).
% 290.84/183.31 tff(9102,plain,
% 290.84/183.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s7)) | m_c_h_element_v_out(c_e_h_3, c_f, s6) | (~node18(c_e_h_3, c_f, s6, s7)))),
% 290.84/183.32 inference(quant_inst,[status(thm)],[])).
% 290.84/183.32 tff(9103,plain,
% 290.84/183.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s7)) | m_c_h_element_v_out(c_e_h_3, c_f, s6) | (~node18(c_e_h_3, c_f, s6, s7))),
% 290.84/183.32 inference(modus_ponens,[status(thm)],[9102, 9101])).
% 290.84/183.32 tff(9104,plain,
% 290.84/183.32 ($false),
% 290.84/183.32 inference(unit_resolution,[status(thm)],[9103, 753, 9099, 9098, 9100])).
% 290.84/183.32 tff(9105,plain,((~node18(c_e_h_3, c_f, s6, s7)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s7)) | m_c_h_element_v_out(c_e_h_3, c_f, s6)), inference(lemma,lemma(discharge,[]))).
% 290.84/183.32 tff(9106,plain,
% 290.84/183.32 (~node18(c_e_h_3, c_f, s6, s7)),
% 290.84/183.32 inference(unit_resolution,[status(thm)],[9105, 9099, 9098])).
% 290.84/183.32 tff(9107,assumption,(node15(c_e_h_3, c_f, s6, s7)), introduced(assumption)).
% 290.84/183.32 tff(9108,plain,
% 290.84/183.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s7)) | (~node15(c_e_h_3, c_f, s6, s7)) | m_c_h_element_v_out(c_e_h_3, c_f, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s7)) | (~node15(c_e_h_3, c_f, s6, s7)) | m_c_h_element_v_out(c_e_h_3, c_f, s6))),
% 290.84/183.32 inference(rewrite,[status(thm)],[])).
% 290.84/183.32 tff(9109,plain,
% 290.84/183.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s7)) | (~node15(c_e_h_3, c_f, s6, s7)) | m_c_h_element_v_out(c_e_h_3, c_f, s6))),
% 290.84/183.32 inference(quant_inst,[status(thm)],[])).
% 290.84/183.32 tff(9110,plain,
% 290.84/183.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s7)) | (~node15(c_e_h_3, c_f, s6, s7)) | m_c_h_element_v_out(c_e_h_3, c_f, s6)),
% 290.84/183.32 inference(modus_ponens,[status(thm)],[9109, 9108])).
% 290.84/183.32 tff(9111,plain,
% 290.84/183.32 ($false),
% 290.84/183.32 inference(unit_resolution,[status(thm)],[9110, 147, 9099, 9098, 9107])).
% 290.84/183.32 tff(9112,plain,((~node15(c_e_h_3, c_f, s6, s7)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s7)) | m_c_h_element_v_out(c_e_h_3, c_f, s6)), inference(lemma,lemma(discharge,[]))).
% 290.84/183.32 tff(9113,plain,
% 290.84/183.32 (~node15(c_e_h_3, c_f, s6, s7)),
% 290.84/183.32 inference(unit_resolution,[status(thm)],[9112, 9099, 9098])).
% 290.84/183.32 tff(9114,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_f, s6)), introduced(assumption)).
% 290.84/183.32 tff(9115,assumption,(node17(c_e_h_3, c_f, s6)), introduced(assumption)).
% 290.84/183.32 tff(9116,plain,
% 290.84/183.32 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_f, s6)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s6)) | m_c_h_element_v_in2(c_e_h_3, c_f, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_f, s6)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s6)) | m_c_h_element_v_in2(c_e_h_3, c_f, s6))),
% 290.84/183.32 inference(rewrite,[status(thm)],[])).
% 290.84/183.32 tff(9117,plain,
% 290.84/183.32 (((~m_c_h_element_v_in1(c_e_h_3, c_f, s6)) | m_c_h_element_v_in2(c_e_h_3, c_f, s6) | (~node17(c_e_h_3, c_f, s6))) <=> ((~node17(c_e_h_3, c_f, s6)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s6)) | m_c_h_element_v_in2(c_e_h_3, c_f, s6))),
% 290.84/183.32 inference(rewrite,[status(thm)],[])).
% 290.84/183.32 tff(9118,plain,
% 290.84/183.32 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s6)) | m_c_h_element_v_in2(c_e_h_3, c_f, s6) | (~node17(c_e_h_3, c_f, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_f, s6)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s6)) | m_c_h_element_v_in2(c_e_h_3, c_f, s6)))),
% 290.84/183.32 inference(monotonicity,[status(thm)],[9117])).
% 290.85/183.32 tff(9119,plain,
% 290.85/183.32 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s6)) | m_c_h_element_v_in2(c_e_h_3, c_f, s6) | (~node17(c_e_h_3, c_f, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_f, s6)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s6)) | m_c_h_element_v_in2(c_e_h_3, c_f, s6))),
% 290.85/183.32 inference(transitivity,[status(thm)],[9118, 9116])).
% 290.85/183.32 tff(9120,plain,
% 290.85/183.32 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s6)) | m_c_h_element_v_in2(c_e_h_3, c_f, s6) | (~node17(c_e_h_3, c_f, s6)))),
% 290.85/183.32 inference(quant_inst,[status(thm)],[])).
% 290.85/183.32 tff(9121,plain,
% 290.85/183.32 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_f, s6)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s6)) | m_c_h_element_v_in2(c_e_h_3, c_f, s6)),
% 290.85/183.32 inference(modus_ponens,[status(thm)],[9120, 9119])).
% 290.85/183.32 tff(9122,plain,
% 290.85/183.32 ((~m_c_h_element_v_in1(c_e_h_3, c_f, s6)) | m_c_h_element_v_in2(c_e_h_3, c_f, s6)),
% 290.85/183.32 inference(unit_resolution,[status(thm)],[9121, 919, 9115])).
% 290.85/183.32 tff(9123,plain,
% 290.85/183.32 (~m_c_h_element_v_in1(c_e_h_3, c_f, s6)),
% 290.85/183.32 inference(unit_resolution,[status(thm)],[9122, 9114])).
% 290.85/183.32 tff(9124,assumption,(~node15(c_e_h_3, c_f, s6, s7)), introduced(assumption)).
% 290.85/183.32 tff(9125,plain,
% 290.85/183.32 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s6)) | m_c_h_element_v_in1(c_e_h_3, c_f, s6) | m_c_h_element_v_in2(c_e_h_3, c_f, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s6)) | m_c_h_element_v_in1(c_e_h_3, c_f, s6) | m_c_h_element_v_in2(c_e_h_3, c_f, s6))),
% 290.85/183.32 inference(rewrite,[status(thm)],[])).
% 290.85/183.32 tff(9126,plain,
% 290.85/183.32 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s6)) | m_c_h_element_v_in1(c_e_h_3, c_f, s6) | m_c_h_element_v_in2(c_e_h_3, c_f, s6))),
% 290.85/183.32 inference(quant_inst,[status(thm)],[])).
% 290.85/183.32 tff(9127,plain,
% 290.85/183.32 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s6)) | m_c_h_element_v_in1(c_e_h_3, c_f, s6) | m_c_h_element_v_in2(c_e_h_3, c_f, s6)),
% 290.85/183.32 inference(modus_ponens,[status(thm)],[9126, 9125])).
% 290.85/183.32 tff(9128,plain,
% 290.85/183.32 (~node16(c_e_h_3, c_f, s6)),
% 290.85/183.32 inference(unit_resolution,[status(thm)],[9127, 178, 9114, 9123])).
% 290.85/183.32 tff(9129,plain,
% 290.85/183.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s6, s7)) | node19(c_e_h_3, c_f, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s6, s7)) | node19(c_e_h_3, c_f, s6, s7))),
% 290.85/183.32 inference(rewrite,[status(thm)],[])).
% 290.85/183.32 tff(9130,plain,
% 290.85/183.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s6, s7)) | node19(c_e_h_3, c_f, s6, s7))),
% 290.85/183.32 inference(quant_inst,[status(thm)],[])).
% 290.85/183.32 tff(9131,plain,
% 290.85/183.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s6, s7)) | node19(c_e_h_3, c_f, s6, s7)),
% 290.85/183.32 inference(modus_ponens,[status(thm)],[9130, 9129])).
% 290.85/183.32 tff(9132,plain,
% 290.85/183.32 (node19(c_e_h_3, c_f, s6, s7)),
% 290.85/183.32 inference(unit_resolution,[status(thm)],[9131, 190, 1844])).
% 290.85/183.32 tff(9133,plain,
% 290.85/183.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s6) | node15(c_e_h_3, c_f, s6, s7) | (~node19(c_e_h_3, c_f, s6, s7)) | node14(c_e_h_3, c_f, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_f, s6) | node15(c_e_h_3, c_f, s6, s7) | (~node19(c_e_h_3, c_f, s6, s7)) | node14(c_e_h_3, c_f, s6, s7))),
% 290.85/183.33 inference(rewrite,[status(thm)],[])).
% 290.85/183.33 tff(9134,plain,
% 290.85/183.33 ((node16(c_e_h_3, c_f, s6) | node14(c_e_h_3, c_f, s6, s7) | node15(c_e_h_3, c_f, s6, s7) | (~node19(c_e_h_3, c_f, s6, s7))) <=> (node16(c_e_h_3, c_f, s6) | node15(c_e_h_3, c_f, s6, s7) | (~node19(c_e_h_3, c_f, s6, s7)) | node14(c_e_h_3, c_f, s6, s7))),
% 290.85/183.33 inference(rewrite,[status(thm)],[])).
% 290.85/183.33 tff(9135,plain,
% 290.85/183.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s6) | node14(c_e_h_3, c_f, s6, s7) | node15(c_e_h_3, c_f, s6, s7) | (~node19(c_e_h_3, c_f, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s6) | node15(c_e_h_3, c_f, s6, s7) | (~node19(c_e_h_3, c_f, s6, s7)) | node14(c_e_h_3, c_f, s6, s7)))),
% 290.85/183.33 inference(monotonicity,[status(thm)],[9134])).
% 290.85/183.33 tff(9136,plain,
% 290.85/183.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s6) | node14(c_e_h_3, c_f, s6, s7) | node15(c_e_h_3, c_f, s6, s7) | (~node19(c_e_h_3, c_f, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_f, s6) | node15(c_e_h_3, c_f, s6, s7) | (~node19(c_e_h_3, c_f, s6, s7)) | node14(c_e_h_3, c_f, s6, s7))),
% 290.85/183.33 inference(transitivity,[status(thm)],[9135, 9133])).
% 290.85/183.33 tff(9137,plain,
% 290.85/183.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s6) | node14(c_e_h_3, c_f, s6, s7) | node15(c_e_h_3, c_f, s6, s7) | (~node19(c_e_h_3, c_f, s6, s7)))),
% 290.85/183.33 inference(quant_inst,[status(thm)],[])).
% 290.85/183.33 tff(9138,plain,
% 290.85/183.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_f, s6) | node15(c_e_h_3, c_f, s6, s7) | (~node19(c_e_h_3, c_f, s6, s7)) | node14(c_e_h_3, c_f, s6, s7)),
% 290.85/183.33 inference(modus_ponens,[status(thm)],[9137, 9136])).
% 290.85/183.33 tff(9139,plain,
% 290.85/183.33 (node16(c_e_h_3, c_f, s6) | node15(c_e_h_3, c_f, s6, s7) | node14(c_e_h_3, c_f, s6, s7)),
% 290.85/183.33 inference(unit_resolution,[status(thm)],[9138, 204, 9132])).
% 290.85/183.33 tff(9140,plain,
% 290.85/183.33 (node14(c_e_h_3, c_f, s6, s7)),
% 290.85/183.33 inference(unit_resolution,[status(thm)],[9139, 9128, 9124])).
% 290.85/183.33 tff(9141,plain,
% 290.85/183.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s7)) | m_c_h_element_v_in1(c_e_h_3, c_f, s6) | (~node14(c_e_h_3, c_f, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s7)) | m_c_h_element_v_in1(c_e_h_3, c_f, s6) | (~node14(c_e_h_3, c_f, s6, s7)))),
% 290.85/183.33 inference(rewrite,[status(thm)],[])).
% 290.85/183.33 tff(9142,plain,
% 290.85/183.33 (((~node14(c_e_h_3, c_f, s6, s7)) | m_c_h_element_v_in1(c_e_h_3, c_f, s6) | (~m_c_h_element_v_out(c_e_h_3, c_f, s7))) <=> ((~m_c_h_element_v_out(c_e_h_3, c_f, s7)) | m_c_h_element_v_in1(c_e_h_3, c_f, s6) | (~node14(c_e_h_3, c_f, s6, s7)))),
% 290.85/183.33 inference(rewrite,[status(thm)],[])).
% 290.85/183.33 tff(9143,plain,
% 290.85/183.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s6, s7)) | m_c_h_element_v_in1(c_e_h_3, c_f, s6) | (~m_c_h_element_v_out(c_e_h_3, c_f, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s7)) | m_c_h_element_v_in1(c_e_h_3, c_f, s6) | (~node14(c_e_h_3, c_f, s6, s7))))),
% 290.85/183.33 inference(monotonicity,[status(thm)],[9142])).
% 290.85/183.33 tff(9144,plain,
% 290.85/183.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s6, s7)) | m_c_h_element_v_in1(c_e_h_3, c_f, s6) | (~m_c_h_element_v_out(c_e_h_3, c_f, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s7)) | m_c_h_element_v_in1(c_e_h_3, c_f, s6) | (~node14(c_e_h_3, c_f, s6, s7)))),
% 290.85/183.33 inference(transitivity,[status(thm)],[9143, 9141])).
% 290.85/183.33 tff(9145,plain,
% 290.85/183.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s6, s7)) | m_c_h_element_v_in1(c_e_h_3, c_f, s6) | (~m_c_h_element_v_out(c_e_h_3, c_f, s7)))),
% 290.85/183.33 inference(quant_inst,[status(thm)],[])).
% 290.85/183.33 tff(9146,plain,
% 290.85/183.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s7)) | m_c_h_element_v_in1(c_e_h_3, c_f, s6) | (~node14(c_e_h_3, c_f, s6, s7))),
% 290.85/183.33 inference(modus_ponens,[status(thm)],[9145, 9144])).
% 290.85/183.33 tff(9147,plain,
% 290.85/183.33 ($false),
% 290.85/183.33 inference(unit_resolution,[status(thm)],[9146, 223, 9099, 9140, 9123])).
% 290.85/183.33 tff(9148,plain,(m_c_h_element_v_in2(c_e_h_3, c_f, s6) | (~m_c_h_element_v_out(c_e_h_3, c_f, s7)) | node15(c_e_h_3, c_f, s6, s7) | (~node17(c_e_h_3, c_f, s6))), inference(lemma,lemma(discharge,[]))).
% 290.85/183.33 tff(9149,plain,
% 290.85/183.33 (~node17(c_e_h_3, c_f, s6)),
% 290.85/183.33 inference(unit_resolution,[status(thm)],[9148, 9099, 9114, 9113])).
% 290.85/183.33 tff(9150,plain,
% 290.85/183.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s6) | (~node19(c_e_h_3, c_f, s6, s7)) | node18(c_e_h_3, c_f, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_f, s6) | (~node19(c_e_h_3, c_f, s6, s7)) | node18(c_e_h_3, c_f, s6, s7))),
% 290.85/183.33 inference(rewrite,[status(thm)],[])).
% 290.85/183.33 tff(9151,plain,
% 290.85/183.33 ((node17(c_e_h_3, c_f, s6) | node18(c_e_h_3, c_f, s6, s7) | (~node19(c_e_h_3, c_f, s6, s7))) <=> (node17(c_e_h_3, c_f, s6) | (~node19(c_e_h_3, c_f, s6, s7)) | node18(c_e_h_3, c_f, s6, s7))),
% 290.85/183.33 inference(rewrite,[status(thm)],[])).
% 290.85/183.33 tff(9152,plain,
% 290.85/183.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s6) | node18(c_e_h_3, c_f, s6, s7) | (~node19(c_e_h_3, c_f, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s6) | (~node19(c_e_h_3, c_f, s6, s7)) | node18(c_e_h_3, c_f, s6, s7)))),
% 290.85/183.33 inference(monotonicity,[status(thm)],[9151])).
% 290.85/183.33 tff(9153,plain,
% 290.85/183.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s6) | node18(c_e_h_3, c_f, s6, s7) | (~node19(c_e_h_3, c_f, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_f, s6) | (~node19(c_e_h_3, c_f, s6, s7)) | node18(c_e_h_3, c_f, s6, s7))),
% 290.85/183.33 inference(transitivity,[status(thm)],[9152, 9150])).
% 290.85/183.33 tff(9154,plain,
% 290.85/183.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s6) | node18(c_e_h_3, c_f, s6, s7) | (~node19(c_e_h_3, c_f, s6, s7)))),
% 290.85/183.33 inference(quant_inst,[status(thm)],[])).
% 290.85/183.33 tff(9155,plain,
% 290.85/183.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_f, s6) | (~node19(c_e_h_3, c_f, s6, s7)) | node18(c_e_h_3, c_f, s6, s7)),
% 290.85/183.33 inference(modus_ponens,[status(thm)],[9154, 9153])).
% 290.85/183.33 tff(9156,plain,
% 290.85/183.33 (node17(c_e_h_3, c_f, s6) | node18(c_e_h_3, c_f, s6, s7)),
% 290.85/183.33 inference(unit_resolution,[status(thm)],[9155, 776, 9132])).
% 290.85/183.33 tff(9157,plain,
% 290.85/183.33 ($false),
% 290.85/183.33 inference(unit_resolution,[status(thm)],[9156, 9149, 9106])).
% 290.85/183.33 tff(9158,plain,((~m_c_h_element_v_out(c_e_h_3, c_f, s7)) | m_c_h_element_v_in2(c_e_h_3, c_f, s6) | m_c_h_element_v_out(c_e_h_3, c_f, s6)), inference(lemma,lemma(discharge,[]))).
% 290.85/183.33 tff(9159,plain,
% 290.85/183.33 (~m_c_h_element_v_out(c_e_h_3, c_f, s7)),
% 290.85/183.33 inference(unit_resolution,[status(thm)],[9158, 9097, 9092])).
% 290.85/183.33 tff(9160,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9)), introduced(assumption)).
% 290.85/183.33 tff(9161,plain,
% 290.85/183.33 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6)),
% 290.85/183.33 inference(unit_resolution,[status(thm)],[6873, 9097])).
% 290.85/183.33 tff(9162,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_f, s7)), introduced(assumption)).
% 290.85/183.33 tff(9163,assumption,(~m_c_h_element_v_out(c_e_h_3, c_f, s7)), introduced(assumption)).
% 290.85/183.33 tff(9164,assumption,(m_c_h_element_v_out(c_e_h_3, c_f, s8)), introduced(assumption)).
% 290.85/183.33 tff(9165,assumption,(node18(c_e_h_3, c_f, s7, s8)), introduced(assumption)).
% 290.85/183.33 tff(9166,plain,
% 290.85/183.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_f, s7) | (~m_c_h_element_v_out(c_e_h_3, c_f, s8)) | (~node18(c_e_h_3, c_f, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s7) | (~m_c_h_element_v_out(c_e_h_3, c_f, s8)) | (~node18(c_e_h_3, c_f, s7, s8)))),
% 290.85/183.33 inference(rewrite,[status(thm)],[])).
% 290.85/183.33 tff(9167,plain,
% 290.85/183.33 (((~m_c_h_element_v_out(c_e_h_3, c_f, s8)) | m_c_h_element_v_out(c_e_h_3, c_f, s7) | (~node18(c_e_h_3, c_f, s7, s8))) <=> (m_c_h_element_v_out(c_e_h_3, c_f, s7) | (~m_c_h_element_v_out(c_e_h_3, c_f, s8)) | (~node18(c_e_h_3, c_f, s7, s8)))),
% 290.85/183.33 inference(rewrite,[status(thm)],[])).
% 290.85/183.33 tff(9168,plain,
% 290.85/183.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s8)) | m_c_h_element_v_out(c_e_h_3, c_f, s7) | (~node18(c_e_h_3, c_f, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_f, s7) | (~m_c_h_element_v_out(c_e_h_3, c_f, s8)) | (~node18(c_e_h_3, c_f, s7, s8))))),
% 290.85/183.33 inference(monotonicity,[status(thm)],[9167])).
% 290.85/183.33 tff(9169,plain,
% 290.85/183.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s8)) | m_c_h_element_v_out(c_e_h_3, c_f, s7) | (~node18(c_e_h_3, c_f, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s7) | (~m_c_h_element_v_out(c_e_h_3, c_f, s8)) | (~node18(c_e_h_3, c_f, s7, s8)))),
% 290.85/183.33 inference(transitivity,[status(thm)],[9168, 9166])).
% 290.85/183.33 tff(9170,plain,
% 290.85/183.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s8)) | m_c_h_element_v_out(c_e_h_3, c_f, s7) | (~node18(c_e_h_3, c_f, s7, s8)))),
% 290.85/183.33 inference(quant_inst,[status(thm)],[])).
% 290.85/183.33 tff(9171,plain,
% 290.85/183.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s7) | (~m_c_h_element_v_out(c_e_h_3, c_f, s8)) | (~node18(c_e_h_3, c_f, s7, s8))),
% 290.85/183.33 inference(modus_ponens,[status(thm)],[9170, 9169])).
% 290.85/183.33 tff(9172,plain,
% 290.85/183.33 ($false),
% 290.85/183.33 inference(unit_resolution,[status(thm)],[9171, 753, 9163, 9164, 9165])).
% 290.85/183.33 tff(9173,plain,((~node18(c_e_h_3, c_f, s7, s8)) | m_c_h_element_v_out(c_e_h_3, c_f, s7) | (~m_c_h_element_v_out(c_e_h_3, c_f, s8))), inference(lemma,lemma(discharge,[]))).
% 290.85/183.33 tff(9174,plain,
% 290.85/183.33 (~node18(c_e_h_3, c_f, s7, s8)),
% 290.85/183.33 inference(unit_resolution,[status(thm)],[9173, 9164, 9163])).
% 290.85/183.33 tff(9175,plain,
% 290.85/183.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s7, s8)) | node19(c_e_h_3, c_f, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s7, s8)) | node19(c_e_h_3, c_f, s7, s8))),
% 290.85/183.34 inference(rewrite,[status(thm)],[])).
% 290.85/183.34 tff(9176,plain,
% 290.85/183.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s7, s8)) | node19(c_e_h_3, c_f, s7, s8))),
% 290.85/183.34 inference(quant_inst,[status(thm)],[])).
% 290.85/183.34 tff(9177,plain,
% 290.85/183.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s7, s8)) | node19(c_e_h_3, c_f, s7, s8)),
% 290.85/183.34 inference(modus_ponens,[status(thm)],[9176, 9175])).
% 290.85/183.34 tff(9178,plain,
% 290.85/183.34 (node19(c_e_h_3, c_f, s7, s8)),
% 290.85/183.34 inference(unit_resolution,[status(thm)],[9177, 190, 1938])).
% 290.85/183.34 tff(9179,plain,
% 290.85/183.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_3, c_f, s7, s8) | (~node19(c_e_h_3, c_f, s7, s8)) | node17(c_e_h_3, c_f, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_3, c_f, s7, s8) | (~node19(c_e_h_3, c_f, s7, s8)) | node17(c_e_h_3, c_f, s7))),
% 290.85/183.34 inference(rewrite,[status(thm)],[])).
% 290.85/183.34 tff(9180,plain,
% 290.85/183.34 ((node17(c_e_h_3, c_f, s7) | node18(c_e_h_3, c_f, s7, s8) | (~node19(c_e_h_3, c_f, s7, s8))) <=> (node18(c_e_h_3, c_f, s7, s8) | (~node19(c_e_h_3, c_f, s7, s8)) | node17(c_e_h_3, c_f, s7))),
% 290.85/183.34 inference(rewrite,[status(thm)],[])).
% 290.85/183.34 tff(9181,plain,
% 290.85/183.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s7) | node18(c_e_h_3, c_f, s7, s8) | (~node19(c_e_h_3, c_f, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_3, c_f, s7, s8) | (~node19(c_e_h_3, c_f, s7, s8)) | node17(c_e_h_3, c_f, s7)))),
% 290.85/183.34 inference(monotonicity,[status(thm)],[9180])).
% 290.85/183.34 tff(9182,plain,
% 290.85/183.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s7) | node18(c_e_h_3, c_f, s7, s8) | (~node19(c_e_h_3, c_f, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_3, c_f, s7, s8) | (~node19(c_e_h_3, c_f, s7, s8)) | node17(c_e_h_3, c_f, s7))),
% 290.85/183.34 inference(transitivity,[status(thm)],[9181, 9179])).
% 290.85/183.34 tff(9183,plain,
% 290.85/183.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s7) | node18(c_e_h_3, c_f, s7, s8) | (~node19(c_e_h_3, c_f, s7, s8)))),
% 290.85/183.34 inference(quant_inst,[status(thm)],[])).
% 290.85/183.34 tff(9184,plain,
% 290.85/183.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_3, c_f, s7, s8) | (~node19(c_e_h_3, c_f, s7, s8)) | node17(c_e_h_3, c_f, s7)),
% 290.85/183.34 inference(modus_ponens,[status(thm)],[9183, 9182])).
% 290.85/183.34 tff(9185,plain,
% 290.85/183.34 (node18(c_e_h_3, c_f, s7, s8) | node17(c_e_h_3, c_f, s7)),
% 290.85/183.34 inference(unit_resolution,[status(thm)],[9184, 776, 9178])).
% 290.85/183.34 tff(9186,plain,
% 290.85/183.34 (node17(c_e_h_3, c_f, s7)),
% 290.85/183.34 inference(unit_resolution,[status(thm)],[9185, 9174])).
% 290.85/183.34 tff(9187,plain,
% 290.85/183.34 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_3, c_f, s7) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s7)) | (~node17(c_e_h_3, c_f, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_f, s7) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s7)) | (~node17(c_e_h_3, c_f, s7)))),
% 290.85/183.34 inference(rewrite,[status(thm)],[])).
% 290.85/183.34 tff(9188,plain,
% 290.85/183.34 (((~m_c_h_element_v_in1(c_e_h_3, c_f, s7)) | m_c_h_element_v_in2(c_e_h_3, c_f, s7) | (~node17(c_e_h_3, c_f, s7))) <=> (m_c_h_element_v_in2(c_e_h_3, c_f, s7) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s7)) | (~node17(c_e_h_3, c_f, s7)))),
% 290.85/183.34 inference(rewrite,[status(thm)],[])).
% 290.85/183.34 tff(9189,plain,
% 290.85/183.34 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s7)) | m_c_h_element_v_in2(c_e_h_3, c_f, s7) | (~node17(c_e_h_3, c_f, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_3, c_f, s7) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s7)) | (~node17(c_e_h_3, c_f, s7))))),
% 290.85/183.34 inference(monotonicity,[status(thm)],[9188])).
% 290.85/183.34 tff(9190,plain,
% 290.85/183.34 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s7)) | m_c_h_element_v_in2(c_e_h_3, c_f, s7) | (~node17(c_e_h_3, c_f, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_f, s7) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s7)) | (~node17(c_e_h_3, c_f, s7)))),
% 290.85/183.34 inference(transitivity,[status(thm)],[9189, 9187])).
% 290.85/183.34 tff(9191,plain,
% 290.85/183.34 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s7)) | m_c_h_element_v_in2(c_e_h_3, c_f, s7) | (~node17(c_e_h_3, c_f, s7)))),
% 290.85/183.34 inference(quant_inst,[status(thm)],[])).
% 290.85/183.34 tff(9192,plain,
% 290.85/183.34 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_f, s7) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s7)) | (~node17(c_e_h_3, c_f, s7))),
% 290.85/183.34 inference(modus_ponens,[status(thm)],[9191, 9190])).
% 290.85/183.34 tff(9193,plain,
% 290.85/183.34 ((~m_c_h_element_v_in1(c_e_h_3, c_f, s7)) | (~node17(c_e_h_3, c_f, s7))),
% 290.85/183.34 inference(unit_resolution,[status(thm)],[9192, 919, 9162])).
% 290.85/183.34 tff(9194,plain,
% 290.85/183.34 (~m_c_h_element_v_in1(c_e_h_3, c_f, s7)),
% 290.85/183.34 inference(unit_resolution,[status(thm)],[9193, 9186])).
% 290.85/183.34 tff(9195,assumption,(node15(c_e_h_3, c_f, s7, s8)), introduced(assumption)).
% 290.85/183.34 tff(9196,plain,
% 290.85/183.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s8)) | (~node15(c_e_h_3, c_f, s7, s8)) | m_c_h_element_v_out(c_e_h_3, c_f, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s8)) | (~node15(c_e_h_3, c_f, s7, s8)) | m_c_h_element_v_out(c_e_h_3, c_f, s7))),
% 290.85/183.34 inference(rewrite,[status(thm)],[])).
% 290.85/183.34 tff(9197,plain,
% 290.85/183.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s8)) | (~node15(c_e_h_3, c_f, s7, s8)) | m_c_h_element_v_out(c_e_h_3, c_f, s7))),
% 290.85/183.34 inference(quant_inst,[status(thm)],[])).
% 290.85/183.34 tff(9198,plain,
% 290.85/183.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s8)) | (~node15(c_e_h_3, c_f, s7, s8)) | m_c_h_element_v_out(c_e_h_3, c_f, s7)),
% 290.85/183.34 inference(modus_ponens,[status(thm)],[9197, 9196])).
% 290.85/183.34 tff(9199,plain,
% 290.85/183.34 ($false),
% 290.85/183.34 inference(unit_resolution,[status(thm)],[9198, 147, 9163, 9164, 9195])).
% 290.85/183.34 tff(9200,plain,((~node15(c_e_h_3, c_f, s7, s8)) | m_c_h_element_v_out(c_e_h_3, c_f, s7) | (~m_c_h_element_v_out(c_e_h_3, c_f, s8))), inference(lemma,lemma(discharge,[]))).
% 290.85/183.34 tff(9201,plain,
% 290.85/183.34 (~node15(c_e_h_3, c_f, s7, s8)),
% 290.85/183.34 inference(unit_resolution,[status(thm)],[9200, 9164, 9163])).
% 290.85/183.34 tff(9202,assumption,(node17(c_e_h_3, c_f, s7)), introduced(assumption)).
% 290.85/183.34 tff(9203,assumption,(node16(c_e_h_3, c_f, s7)), introduced(assumption)).
% 290.85/183.34 tff(9204,plain,
% 290.85/183.34 (m_c_h_element_v_in2(c_e_h_3, c_f, s7) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s7))),
% 290.85/183.34 inference(unit_resolution,[status(thm)],[9192, 919, 9202])).
% 290.85/183.34 tff(9205,plain,
% 290.85/183.34 (~m_c_h_element_v_in1(c_e_h_3, c_f, s7)),
% 290.85/183.34 inference(unit_resolution,[status(thm)],[9204, 9162])).
% 290.85/183.34 tff(9206,plain,
% 290.85/183.34 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s7)) | m_c_h_element_v_in1(c_e_h_3, c_f, s7) | m_c_h_element_v_in2(c_e_h_3, c_f, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s7)) | m_c_h_element_v_in1(c_e_h_3, c_f, s7) | m_c_h_element_v_in2(c_e_h_3, c_f, s7))),
% 290.85/183.34 inference(rewrite,[status(thm)],[])).
% 290.85/183.34 tff(9207,plain,
% 290.85/183.34 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s7)) | m_c_h_element_v_in1(c_e_h_3, c_f, s7) | m_c_h_element_v_in2(c_e_h_3, c_f, s7))),
% 290.85/183.34 inference(quant_inst,[status(thm)],[])).
% 290.85/183.34 tff(9208,plain,
% 290.85/183.34 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s7)) | m_c_h_element_v_in1(c_e_h_3, c_f, s7) | m_c_h_element_v_in2(c_e_h_3, c_f, s7)),
% 290.85/183.34 inference(modus_ponens,[status(thm)],[9207, 9206])).
% 290.85/183.34 tff(9209,plain,
% 290.85/183.34 (m_c_h_element_v_in1(c_e_h_3, c_f, s7) | m_c_h_element_v_in2(c_e_h_3, c_f, s7)),
% 290.85/183.34 inference(unit_resolution,[status(thm)],[9208, 178, 9203])).
% 290.85/183.34 tff(9210,plain,
% 290.85/183.34 ($false),
% 290.85/183.34 inference(unit_resolution,[status(thm)],[9209, 9205, 9162])).
% 290.85/183.34 tff(9211,plain,(m_c_h_element_v_in2(c_e_h_3, c_f, s7) | (~node16(c_e_h_3, c_f, s7)) | (~node17(c_e_h_3, c_f, s7))), inference(lemma,lemma(discharge,[]))).
% 290.85/183.34 tff(9212,plain,
% 290.85/183.34 (m_c_h_element_v_in2(c_e_h_3, c_f, s7)),
% 290.85/183.34 inference(unit_resolution,[status(thm)],[9211, 9203, 9202])).
% 290.85/183.34 tff(9213,plain,
% 290.85/183.34 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s7) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s7)) | (~node17(c_e_h_3, c_f, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_3, c_f, s7) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s7)) | (~node17(c_e_h_3, c_f, s7)))),
% 290.85/183.34 inference(rewrite,[status(thm)],[])).
% 290.85/183.34 tff(9214,plain,
% 290.85/183.34 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s7) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s7)) | (~node17(c_e_h_3, c_f, s7)))),
% 290.85/183.34 inference(quant_inst,[status(thm)],[])).
% 290.85/183.34 tff(9215,plain,
% 290.85/183.34 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_3, c_f, s7) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s7)) | (~node17(c_e_h_3, c_f, s7))),
% 290.85/183.34 inference(modus_ponens,[status(thm)],[9214, 9213])).
% 290.85/183.34 tff(9216,plain,
% 290.85/183.34 (m_c_h_element_v_in1(c_e_h_3, c_f, s7) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s7))),
% 290.85/183.34 inference(unit_resolution,[status(thm)],[9215, 859, 9202])).
% 290.85/183.34 tff(9217,plain,
% 290.85/183.34 (m_c_h_element_v_in1(c_e_h_3, c_f, s7)),
% 290.85/183.34 inference(unit_resolution,[status(thm)],[9216, 9212])).
% 290.85/183.34 tff(9218,plain,
% 290.85/183.34 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_f, s7)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s7)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~node16(c_e_h_3, c_f, s7)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s7)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s7)))),
% 290.85/183.34 inference(rewrite,[status(thm)],[])).
% 290.85/183.34 tff(9219,plain,
% 290.85/183.34 (((~node16(c_e_h_3, c_f, s7)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s7)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s7))) <=> ((~node16(c_e_h_3, c_f, s7)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s7)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s7)))),
% 290.85/183.34 inference(rewrite,[status(thm)],[])).
% 290.85/183.34 tff(9220,plain,
% 290.85/183.34 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_f, s7)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s7)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_f, s7)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s7)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s7))))),
% 290.85/183.35 inference(monotonicity,[status(thm)],[9219])).
% 290.85/183.35 tff(9221,plain,
% 290.85/183.35 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_f, s7)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s7)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~node16(c_e_h_3, c_f, s7)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s7)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s7)))),
% 290.85/183.35 inference(transitivity,[status(thm)],[9220, 9218])).
% 290.85/183.35 tff(9222,plain,
% 290.85/183.35 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_f, s7)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s7)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s7)))),
% 290.85/183.35 inference(quant_inst,[status(thm)],[])).
% 290.85/183.35 tff(9223,plain,
% 290.85/183.35 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~node16(c_e_h_3, c_f, s7)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s7)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s7))),
% 290.85/183.35 inference(modus_ponens,[status(thm)],[9222, 9221])).
% 290.85/183.35 tff(9224,plain,
% 290.85/183.35 ((~m_c_h_element_v_in2(c_e_h_3, c_f, s7)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s7))),
% 290.85/183.35 inference(unit_resolution,[status(thm)],[9223, 2307, 9203])).
% 290.85/183.35 tff(9225,plain,
% 290.85/183.35 ($false),
% 290.85/183.35 inference(unit_resolution,[status(thm)],[9224, 9217, 9212])).
% 290.85/183.35 tff(9226,plain,((~node16(c_e_h_3, c_f, s7)) | (~node17(c_e_h_3, c_f, s7))), inference(lemma,lemma(discharge,[]))).
% 290.85/183.35 tff(9227,plain,
% 290.85/183.35 (~node16(c_e_h_3, c_f, s7)),
% 290.85/183.35 inference(unit_resolution,[status(thm)],[9226, 9186])).
% 290.85/183.35 tff(9228,plain,
% 290.85/183.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_3, c_f, s7, s8) | (~node19(c_e_h_3, c_f, s7, s8)) | node15(c_e_h_3, c_f, s7, s8) | node16(c_e_h_3, c_f, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_f, s7, s8) | (~node19(c_e_h_3, c_f, s7, s8)) | node15(c_e_h_3, c_f, s7, s8) | node16(c_e_h_3, c_f, s7))),
% 290.85/183.35 inference(rewrite,[status(thm)],[])).
% 290.85/183.35 tff(9229,plain,
% 290.85/183.35 ((node16(c_e_h_3, c_f, s7) | node14(c_e_h_3, c_f, s7, s8) | node15(c_e_h_3, c_f, s7, s8) | (~node19(c_e_h_3, c_f, s7, s8))) <=> (node14(c_e_h_3, c_f, s7, s8) | (~node19(c_e_h_3, c_f, s7, s8)) | node15(c_e_h_3, c_f, s7, s8) | node16(c_e_h_3, c_f, s7))),
% 290.85/183.35 inference(rewrite,[status(thm)],[])).
% 290.85/183.35 tff(9230,plain,
% 290.85/183.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s7) | node14(c_e_h_3, c_f, s7, s8) | node15(c_e_h_3, c_f, s7, s8) | (~node19(c_e_h_3, c_f, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_3, c_f, s7, s8) | (~node19(c_e_h_3, c_f, s7, s8)) | node15(c_e_h_3, c_f, s7, s8) | node16(c_e_h_3, c_f, s7)))),
% 290.85/183.35 inference(monotonicity,[status(thm)],[9229])).
% 290.85/183.35 tff(9231,plain,
% 290.85/183.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s7) | node14(c_e_h_3, c_f, s7, s8) | node15(c_e_h_3, c_f, s7, s8) | (~node19(c_e_h_3, c_f, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_f, s7, s8) | (~node19(c_e_h_3, c_f, s7, s8)) | node15(c_e_h_3, c_f, s7, s8) | node16(c_e_h_3, c_f, s7))),
% 290.85/183.35 inference(transitivity,[status(thm)],[9230, 9228])).
% 290.85/183.35 tff(9232,plain,
% 290.85/183.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s7) | node14(c_e_h_3, c_f, s7, s8) | node15(c_e_h_3, c_f, s7, s8) | (~node19(c_e_h_3, c_f, s7, s8)))),
% 290.85/183.35 inference(quant_inst,[status(thm)],[])).
% 290.85/183.35 tff(9233,plain,
% 290.85/183.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_f, s7, s8) | (~node19(c_e_h_3, c_f, s7, s8)) | node15(c_e_h_3, c_f, s7, s8) | node16(c_e_h_3, c_f, s7)),
% 290.85/183.35 inference(modus_ponens,[status(thm)],[9232, 9231])).
% 290.85/183.35 tff(9234,plain,
% 290.85/183.35 (node14(c_e_h_3, c_f, s7, s8) | node15(c_e_h_3, c_f, s7, s8) | node16(c_e_h_3, c_f, s7)),
% 290.85/183.35 inference(unit_resolution,[status(thm)],[9233, 204, 9178])).
% 290.85/183.35 tff(9235,plain,
% 290.85/183.35 (node14(c_e_h_3, c_f, s7, s8)),
% 290.85/183.35 inference(unit_resolution,[status(thm)],[9234, 9227, 9201])).
% 290.85/183.35 tff(9236,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_f, s7)), introduced(assumption)).
% 290.85/183.35 tff(9237,assumption,(node14(c_e_h_3, c_f, s7, s8)), introduced(assumption)).
% 290.85/183.35 tff(9238,plain,
% 290.85/183.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s8)) | m_c_h_element_v_in1(c_e_h_3, c_f, s7) | (~node14(c_e_h_3, c_f, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s8)) | m_c_h_element_v_in1(c_e_h_3, c_f, s7) | (~node14(c_e_h_3, c_f, s7, s8)))),
% 290.85/183.35 inference(rewrite,[status(thm)],[])).
% 290.85/183.35 tff(9239,plain,
% 290.85/183.35 (((~node14(c_e_h_3, c_f, s7, s8)) | m_c_h_element_v_in1(c_e_h_3, c_f, s7) | (~m_c_h_element_v_out(c_e_h_3, c_f, s8))) <=> ((~m_c_h_element_v_out(c_e_h_3, c_f, s8)) | m_c_h_element_v_in1(c_e_h_3, c_f, s7) | (~node14(c_e_h_3, c_f, s7, s8)))),
% 290.85/183.35 inference(rewrite,[status(thm)],[])).
% 290.85/183.35 tff(9240,plain,
% 290.85/183.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s7, s8)) | m_c_h_element_v_in1(c_e_h_3, c_f, s7) | (~m_c_h_element_v_out(c_e_h_3, c_f, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s8)) | m_c_h_element_v_in1(c_e_h_3, c_f, s7) | (~node14(c_e_h_3, c_f, s7, s8))))),
% 290.85/183.35 inference(monotonicity,[status(thm)],[9239])).
% 290.85/183.35 tff(9241,plain,
% 290.85/183.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s7, s8)) | m_c_h_element_v_in1(c_e_h_3, c_f, s7) | (~m_c_h_element_v_out(c_e_h_3, c_f, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s8)) | m_c_h_element_v_in1(c_e_h_3, c_f, s7) | (~node14(c_e_h_3, c_f, s7, s8)))),
% 290.85/183.35 inference(transitivity,[status(thm)],[9240, 9238])).
% 290.85/183.35 tff(9242,plain,
% 290.85/183.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s7, s8)) | m_c_h_element_v_in1(c_e_h_3, c_f, s7) | (~m_c_h_element_v_out(c_e_h_3, c_f, s8)))),
% 290.85/183.35 inference(quant_inst,[status(thm)],[])).
% 290.85/183.35 tff(9243,plain,
% 290.85/183.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s8)) | m_c_h_element_v_in1(c_e_h_3, c_f, s7) | (~node14(c_e_h_3, c_f, s7, s8))),
% 290.85/183.35 inference(modus_ponens,[status(thm)],[9242, 9241])).
% 290.85/183.35 tff(9244,plain,
% 290.85/183.35 ($false),
% 290.85/183.35 inference(unit_resolution,[status(thm)],[9243, 223, 9164, 9237, 9236])).
% 290.85/183.35 tff(9245,plain,((~node14(c_e_h_3, c_f, s7, s8)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s8)) | m_c_h_element_v_in1(c_e_h_3, c_f, s7)), inference(lemma,lemma(discharge,[]))).
% 290.85/183.36 tff(9246,plain,
% 290.85/183.36 ($false),
% 290.85/183.36 inference(unit_resolution,[status(thm)],[9245, 9235, 9194, 9164])).
% 290.85/183.36 tff(9247,plain,((~m_c_h_element_v_out(c_e_h_3, c_f, s8)) | m_c_h_element_v_in2(c_e_h_3, c_f, s7) | m_c_h_element_v_out(c_e_h_3, c_f, s7)), inference(lemma,lemma(discharge,[]))).
% 290.85/183.36 tff(9248,plain,
% 290.85/183.36 (~m_c_h_element_v_out(c_e_h_3, c_f, s8)),
% 290.85/183.36 inference(unit_resolution,[status(thm)],[9247, 9163, 9162])).
% 290.85/183.36 tff(9249,plain,
% 290.85/183.36 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7) | m_c_h_element_v_out(c_e_h_3, c_f, s7))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7) | m_c_h_element_v_out(c_e_h_3, c_f, s7))),
% 290.85/183.36 inference(rewrite,[status(thm)],[])).
% 290.85/183.36 tff(9250,plain,
% 290.85/183.36 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7) | m_c_h_element_v_out(c_e_h_3, c_f, s7))),
% 290.85/183.36 inference(quant_inst,[status(thm)],[])).
% 290.85/183.36 tff(9251,plain,
% 290.85/183.36 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7) | m_c_h_element_v_out(c_e_h_3, c_f, s7)),
% 290.85/183.36 inference(modus_ponens,[status(thm)],[9250, 9249])).
% 290.85/183.36 tff(9252,plain,
% 290.85/183.36 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7) | m_c_h_element_v_out(c_e_h_3, c_f, s7)),
% 290.85/183.36 inference(unit_resolution,[status(thm)],[9251, 5689])).
% 290.85/183.36 tff(9253,plain,
% 290.85/183.36 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7)),
% 290.85/183.36 inference(unit_resolution,[status(thm)],[9252, 9163])).
% 290.85/183.36 tff(9254,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s8)), introduced(assumption)).
% 290.85/183.36 tff(9255,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7)), introduced(assumption)).
% 290.85/183.36 tff(9256,plain,
% 290.85/183.36 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7)),
% 290.85/183.36 inference(unit_resolution,[status(thm)],[7147, 7130, 7117])).
% 290.85/183.36 tff(9257,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7)), introduced(assumption)).
% 290.85/183.36 tff(9258,plain,
% 290.85/183.36 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7)))),
% 290.85/183.36 inference(rewrite,[status(thm)],[])).
% 290.85/183.36 tff(9259,plain,
% 290.85/183.36 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7)))),
% 290.85/183.36 inference(quant_inst,[status(thm)],[])).
% 290.85/183.36 tff(9260,plain,
% 290.85/183.36 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7))),
% 290.85/183.36 inference(modus_ponens,[status(thm)],[9259, 9258])).
% 290.85/183.36 tff(9261,plain,
% 290.85/183.36 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s7)),
% 290.85/183.36 inference(unit_resolution,[status(thm)],[9260, 5601, 9257])).
% 290.85/183.36 tff(9262,plain,
% 290.85/183.36 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s7)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s7)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s7))),
% 290.85/183.36 inference(rewrite,[status(thm)],[])).
% 290.85/183.36 tff(9263,plain,
% 290.85/183.36 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s7)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s7))),
% 290.85/183.36 inference(quant_inst,[status(thm)],[])).
% 290.85/183.36 tff(9264,plain,
% 290.85/183.36 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s7)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s7)),
% 290.85/183.36 inference(modus_ponens,[status(thm)],[9263, 9262])).
% 290.85/183.36 tff(9265,plain,
% 290.85/183.36 (~node9(c_e_h_3, c_n, s7)),
% 290.85/183.36 inference(unit_resolution,[status(thm)],[9264, 4972, 9261])).
% 290.85/183.36 tff(9266,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)), introduced(assumption)).
% 290.85/183.36 tff(9267,plain,
% 290.85/183.36 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s7) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s7) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7))),
% 290.85/183.36 inference(rewrite,[status(thm)],[])).
% 290.85/183.36 tff(9268,plain,
% 290.85/183.36 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s7) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7))),
% 290.85/183.36 inference(quant_inst,[status(thm)],[])).
% 290.85/183.36 tff(9269,plain,
% 290.85/183.36 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s7) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)),
% 290.85/183.36 inference(modus_ponens,[status(thm)],[9268, 9267])).
% 290.85/183.36 tff(9270,plain,
% 290.85/183.36 (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s7) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)),
% 290.85/183.36 inference(unit_resolution,[status(thm)],[9269, 5704])).
% 290.85/183.36 tff(9271,plain,
% 290.85/183.36 (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s7)),
% 290.85/183.36 inference(unit_resolution,[status(thm)],[9270, 9266])).
% 290.85/183.36 tff(9272,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8)), introduced(assumption)).
% 290.85/183.36 tff(9273,assumption,(node11(c_e_h_3, c_m, s7, s8)), introduced(assumption)).
% 290.85/183.36 tff(9274,plain,
% 290.85/183.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8) | (~node11(c_e_h_3, c_m, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8) | (~node11(c_e_h_3, c_m, s7, s8)))),
% 290.85/183.36 inference(rewrite,[status(thm)],[])).
% 290.85/183.36 tff(9275,plain,
% 290.85/183.36 ((m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8) | (~node11(c_e_h_3, c_m, s7, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8) | (~node11(c_e_h_3, c_m, s7, s8)))),
% 290.85/183.36 inference(rewrite,[status(thm)],[])).
% 290.85/183.36 tff(9276,plain,
% 290.85/183.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8) | (~node11(c_e_h_3, c_m, s7, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8) | (~node11(c_e_h_3, c_m, s7, s8))))),
% 290.85/183.36 inference(monotonicity,[status(thm)],[9275])).
% 290.85/183.36 tff(9277,plain,
% 290.85/183.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8) | (~node11(c_e_h_3, c_m, s7, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8) | (~node11(c_e_h_3, c_m, s7, s8)))),
% 290.85/183.36 inference(transitivity,[status(thm)],[9276, 9274])).
% 290.85/183.36 tff(9278,plain,
% 290.85/183.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8) | (~node11(c_e_h_3, c_m, s7, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7)))),
% 290.85/183.36 inference(quant_inst,[status(thm)],[])).
% 290.85/183.36 tff(9279,plain,
% 290.85/183.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8) | (~node11(c_e_h_3, c_m, s7, s8))),
% 290.85/183.36 inference(modus_ponens,[status(thm)],[9278, 9277])).
% 290.85/183.36 tff(9280,plain,
% 290.85/183.36 ($false),
% 290.85/183.36 inference(unit_resolution,[status(thm)],[9279, 5742, 9257, 9272, 9273])).
% 290.85/183.36 tff(9281,plain,((~node11(c_e_h_3, c_m, s7, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8)), inference(lemma,lemma(discharge,[]))).
% 290.85/183.36 tff(9282,plain,
% 290.85/183.36 (~node11(c_e_h_3, c_m, s7, s8)),
% 290.85/183.36 inference(unit_resolution,[status(thm)],[9281, 9272, 9257])).
% 290.85/183.36 tff(9283,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s7)), introduced(assumption)).
% 290.85/183.36 tff(9284,assumption,(node10(c_e_h_3, c_m, s7, s8)), introduced(assumption)).
% 290.85/183.36 tff(9285,plain,
% 290.85/183.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s7)) | (~node10(c_e_h_3, c_m, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s7)) | (~node10(c_e_h_3, c_m, s7, s8)))),
% 290.85/183.36 inference(rewrite,[status(thm)],[])).
% 290.85/183.36 tff(9286,plain,
% 290.85/183.36 (((~node10(c_e_h_3, c_m, s7, s8)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8)) <=> ((~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s7)) | (~node10(c_e_h_3, c_m, s7, s8)))),
% 290.85/183.36 inference(rewrite,[status(thm)],[])).
% 290.85/183.36 tff(9287,plain,
% 290.85/183.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s7, s8)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s7)) | (~node10(c_e_h_3, c_m, s7, s8))))),
% 290.85/183.36 inference(monotonicity,[status(thm)],[9286])).
% 290.85/183.36 tff(9288,plain,
% 290.85/183.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s7, s8)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s7)) | (~node10(c_e_h_3, c_m, s7, s8)))),
% 290.85/183.36 inference(transitivity,[status(thm)],[9287, 9285])).
% 290.85/183.37 tff(9289,plain,
% 290.85/183.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s7, s8)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8))),
% 290.85/183.37 inference(quant_inst,[status(thm)],[])).
% 290.85/183.37 tff(9290,plain,
% 290.85/183.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s7)) | (~node10(c_e_h_3, c_m, s7, s8))),
% 290.85/183.37 inference(modus_ponens,[status(thm)],[9289, 9288])).
% 290.85/183.37 tff(9291,plain,
% 290.85/183.37 ($false),
% 290.85/183.37 inference(unit_resolution,[status(thm)],[9290, 5718, 9255, 9283, 9272, 9284])).
% 290.85/183.37 tff(9292,plain,((~node10(c_e_h_3, c_m, s7, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s7)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8)), inference(lemma,lemma(discharge,[]))).
% 290.85/183.37 tff(9293,plain,
% 290.85/183.37 (~node10(c_e_h_3, c_m, s7, s8)),
% 290.85/183.37 inference(unit_resolution,[status(thm)],[9292, 9272, 9255, 9283])).
% 290.85/183.37 tff(9294,plain,
% 290.85/183.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s7, s8)) | node10(c_e_h_3, c_m, s7, s8) | node11(c_e_h_3, c_m, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s7, s8)) | node10(c_e_h_3, c_m, s7, s8) | node11(c_e_h_3, c_m, s7, s8))),
% 290.85/183.37 inference(rewrite,[status(thm)],[])).
% 290.85/183.37 tff(9295,plain,
% 290.85/183.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s7, s8)) | node10(c_e_h_3, c_m, s7, s8) | node11(c_e_h_3, c_m, s7, s8))),
% 290.85/183.37 inference(quant_inst,[status(thm)],[])).
% 290.85/183.37 tff(9296,plain,
% 290.85/183.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s7, s8)) | node10(c_e_h_3, c_m, s7, s8) | node11(c_e_h_3, c_m, s7, s8)),
% 290.85/183.37 inference(modus_ponens,[status(thm)],[9295, 9294])).
% 290.85/183.37 tff(9297,plain,
% 290.85/183.37 (node10(c_e_h_3, c_m, s7, s8) | node11(c_e_h_3, c_m, s7, s8)),
% 290.85/183.37 inference(unit_resolution,[status(thm)],[9296, 5002, 1938])).
% 290.85/183.37 tff(9298,plain,
% 290.85/183.37 ($false),
% 290.85/183.37 inference(unit_resolution,[status(thm)],[9297, 9293, 9282])).
% 290.85/183.37 tff(9299,plain,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7))), inference(lemma,lemma(discharge,[]))).
% 290.85/183.37 tff(9300,plain,
% 290.85/183.37 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8)),
% 290.85/183.37 inference(unit_resolution,[status(thm)],[9299, 9271, 9255, 9257])).
% 290.85/183.37 tff(9301,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8)), introduced(assumption)).
% 290.85/183.37 tff(9302,assumption,(node11(c_e_h_3, c_m, s8, s9)), introduced(assumption)).
% 290.85/183.37 tff(9303,plain,
% 290.85/183.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8)) | (~node11(c_e_h_3, c_m, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8)) | (~node11(c_e_h_3, c_m, s8, s9)))),
% 290.85/183.37 inference(rewrite,[status(thm)],[])).
% 290.85/183.37 tff(9304,plain,
% 290.85/183.37 ((m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9) | (~node11(c_e_h_3, c_m, s8, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8))) <=> (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8)) | (~node11(c_e_h_3, c_m, s8, s9)))),
% 290.85/183.37 inference(rewrite,[status(thm)],[])).
% 290.85/183.37 tff(9305,plain,
% 290.85/183.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9) | (~node11(c_e_h_3, c_m, s8, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8)) | (~node11(c_e_h_3, c_m, s8, s9))))),
% 290.85/183.37 inference(monotonicity,[status(thm)],[9304])).
% 290.85/183.37 tff(9306,plain,
% 290.85/183.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9) | (~node11(c_e_h_3, c_m, s8, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8)) | (~node11(c_e_h_3, c_m, s8, s9)))),
% 290.85/183.37 inference(transitivity,[status(thm)],[9305, 9303])).
% 290.85/183.37 tff(9307,plain,
% 290.85/183.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9) | (~node11(c_e_h_3, c_m, s8, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8)))),
% 290.85/183.37 inference(quant_inst,[status(thm)],[])).
% 290.85/183.37 tff(9308,plain,
% 290.85/183.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8)) | (~node11(c_e_h_3, c_m, s8, s9))),
% 290.85/183.37 inference(modus_ponens,[status(thm)],[9307, 9306])).
% 290.85/183.37 tff(9309,plain,
% 290.85/183.37 ($false),
% 290.85/183.37 inference(unit_resolution,[status(thm)],[9308, 5742, 9160, 9301, 9302])).
% 290.85/183.37 tff(9310,plain,((~node11(c_e_h_3, c_m, s8, s9)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8))), inference(lemma,lemma(discharge,[]))).
% 290.85/183.37 tff(9311,plain,
% 290.85/183.37 (~node11(c_e_h_3, c_m, s8, s9)),
% 290.85/183.37 inference(unit_resolution,[status(thm)],[9310, 9160, 9301])).
% 290.85/183.37 tff(9312,plain,
% 290.85/183.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s8, s9)) | node10(c_e_h_3, c_m, s8, s9) | node11(c_e_h_3, c_m, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s8, s9)) | node10(c_e_h_3, c_m, s8, s9) | node11(c_e_h_3, c_m, s8, s9))),
% 290.85/183.37 inference(rewrite,[status(thm)],[])).
% 290.85/183.37 tff(9313,plain,
% 290.85/183.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s8, s9)) | node10(c_e_h_3, c_m, s8, s9) | node11(c_e_h_3, c_m, s8, s9))),
% 290.85/183.37 inference(quant_inst,[status(thm)],[])).
% 290.85/183.37 tff(9314,plain,
% 290.85/183.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s8, s9)) | node10(c_e_h_3, c_m, s8, s9) | node11(c_e_h_3, c_m, s8, s9)),
% 290.85/183.37 inference(modus_ponens,[status(thm)],[9313, 9312])).
% 290.85/183.37 tff(9315,plain,
% 290.85/183.37 (node10(c_e_h_3, c_m, s8, s9) | node11(c_e_h_3, c_m, s8, s9)),
% 290.85/183.37 inference(unit_resolution,[status(thm)],[9314, 5002, 1993])).
% 290.85/183.37 tff(9316,plain,
% 290.85/183.37 (node10(c_e_h_3, c_m, s8, s9)),
% 290.85/183.37 inference(unit_resolution,[status(thm)],[9315, 9311])).
% 290.85/183.37 tff(9317,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s8)), introduced(assumption)).
% 290.85/183.37 tff(9318,plain,
% 290.85/183.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s8)) | (~node10(c_e_h_3, c_m, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s8)) | (~node10(c_e_h_3, c_m, s8, s9)))),
% 290.85/183.37 inference(rewrite,[status(thm)],[])).
% 290.85/183.37 tff(9319,plain,
% 290.85/183.37 (((~node10(c_e_h_3, c_m, s8, s9)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s8)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9)) <=> (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s8)) | (~node10(c_e_h_3, c_m, s8, s9)))),
% 290.85/183.37 inference(rewrite,[status(thm)],[])).
% 290.85/183.37 tff(9320,plain,
% 290.85/183.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s8, s9)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s8)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s8)) | (~node10(c_e_h_3, c_m, s8, s9))))),
% 290.85/183.37 inference(monotonicity,[status(thm)],[9319])).
% 290.85/183.37 tff(9321,plain,
% 290.85/183.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s8, s9)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s8)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s8)) | (~node10(c_e_h_3, c_m, s8, s9)))),
% 290.85/183.37 inference(transitivity,[status(thm)],[9320, 9318])).
% 290.85/183.37 tff(9322,plain,
% 290.85/183.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s8, s9)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s8)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9))),
% 290.85/183.37 inference(quant_inst,[status(thm)],[])).
% 290.85/183.37 tff(9323,plain,
% 290.85/183.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s8)) | (~node10(c_e_h_3, c_m, s8, s9))),
% 290.85/183.37 inference(modus_ponens,[status(thm)],[9322, 9321])).
% 290.85/183.37 tff(9324,plain,
% 290.85/183.37 ($false),
% 290.85/183.37 inference(unit_resolution,[status(thm)],[9323, 5718, 9160, 9317, 9254, 9316])).
% 290.85/183.37 tff(9325,plain,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8))), inference(lemma,lemma(discharge,[]))).
% 290.85/183.37 tff(9326,plain,
% 290.85/183.37 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s8)),
% 290.85/183.37 inference(unit_resolution,[status(thm)],[9325, 9300, 9254, 9160])).
% 290.85/183.37 tff(9327,plain,
% 290.85/183.37 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s8) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s8) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8))),
% 290.85/183.38 inference(rewrite,[status(thm)],[])).
% 290.85/183.38 tff(9328,plain,
% 290.85/183.38 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s8) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8))),
% 290.85/183.38 inference(quant_inst,[status(thm)],[])).
% 290.85/183.38 tff(9329,plain,
% 290.85/183.38 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s8) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8)),
% 290.85/183.38 inference(modus_ponens,[status(thm)],[9328, 9327])).
% 290.85/183.38 tff(9330,plain,
% 290.85/183.38 (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s8) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8)),
% 290.85/183.38 inference(unit_resolution,[status(thm)],[9329, 5704])).
% 290.85/183.38 tff(9331,plain,
% 290.85/183.38 (m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8)),
% 290.85/183.38 inference(unit_resolution,[status(thm)],[9330, 9326])).
% 290.85/183.38 tff(9332,assumption,(node11(c_e_h_3, c_n, s7, s8)), introduced(assumption)).
% 290.85/183.38 tff(9333,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8)), introduced(assumption)).
% 290.85/183.38 tff(9334,plain,
% 290.85/183.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8)) | (~node11(c_e_h_3, c_n, s7, s8)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8)) | (~node11(c_e_h_3, c_n, s7, s8)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7))),
% 290.85/183.38 inference(rewrite,[status(thm)],[])).
% 290.85/183.38 tff(9335,plain,
% 290.85/183.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8)) | (~node11(c_e_h_3, c_n, s7, s8)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7))),
% 290.85/183.38 inference(quant_inst,[status(thm)],[])).
% 290.85/183.38 tff(9336,plain,
% 290.85/183.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8)) | (~node11(c_e_h_3, c_n, s7, s8)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)),
% 290.85/183.38 inference(modus_ponens,[status(thm)],[9335, 9334])).
% 290.85/183.38 tff(9337,plain,
% 290.85/183.38 ($false),
% 290.85/183.38 inference(unit_resolution,[status(thm)],[9336, 5017, 9266, 9333, 9332])).
% 290.85/183.38 tff(9338,plain,((~node11(c_e_h_3, c_n, s7, s8)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8))), inference(lemma,lemma(discharge,[]))).
% 290.85/183.38 tff(9339,plain,
% 290.85/183.38 (~node11(c_e_h_3, c_n, s7, s8)),
% 290.85/183.38 inference(unit_resolution,[status(thm)],[9338, 9331, 9266])).
% 290.85/183.38 tff(9340,plain,
% 290.85/183.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s7, s8)) | node10(c_e_h_3, c_n, s7, s8) | node11(c_e_h_3, c_n, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s7, s8)) | node10(c_e_h_3, c_n, s7, s8) | node11(c_e_h_3, c_n, s7, s8))),
% 290.85/183.38 inference(rewrite,[status(thm)],[])).
% 290.85/183.38 tff(9341,plain,
% 290.85/183.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s7, s8)) | node10(c_e_h_3, c_n, s7, s8) | node11(c_e_h_3, c_n, s7, s8))),
% 290.85/183.38 inference(quant_inst,[status(thm)],[])).
% 290.85/183.38 tff(9342,plain,
% 290.85/183.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s7, s8)) | node10(c_e_h_3, c_n, s7, s8) | node11(c_e_h_3, c_n, s7, s8)),
% 290.85/183.38 inference(modus_ponens,[status(thm)],[9341, 9340])).
% 290.85/183.38 tff(9343,plain,
% 290.85/183.38 (node10(c_e_h_3, c_n, s7, s8) | node11(c_e_h_3, c_n, s7, s8)),
% 290.85/183.38 inference(unit_resolution,[status(thm)],[9342, 5002, 1938])).
% 290.85/183.38 tff(9344,plain,
% 290.85/183.38 (node10(c_e_h_3, c_n, s7, s8)),
% 290.85/183.38 inference(unit_resolution,[status(thm)],[9343, 9339])).
% 290.85/183.38 tff(9345,plain,
% 290.85/183.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8)) | (~node10(c_e_h_3, c_n, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_3, c_n, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8)) | (~node10(c_e_h_3, c_n, s7, s8)))),
% 290.85/183.38 inference(rewrite,[status(thm)],[])).
% 290.85/183.38 tff(9346,plain,
% 290.85/183.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8)) | (~node10(c_e_h_3, c_n, s7, s8)))),
% 290.85/183.38 inference(quant_inst,[status(thm)],[])).
% 290.85/183.38 tff(9347,plain,
% 290.85/183.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_3, c_n, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8)) | (~node10(c_e_h_3, c_n, s7, s8))),
% 290.85/183.38 inference(modus_ponens,[status(thm)],[9346, 9345])).
% 290.85/183.38 tff(9348,plain,
% 290.85/183.38 ($false),
% 290.85/183.38 inference(unit_resolution,[status(thm)],[9347, 4986, 9331, 9344, 9265])).
% 290.85/183.38 tff(9349,plain,(m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s8)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7))), inference(lemma,lemma(discharge,[]))).
% 290.85/183.38 tff(9350,plain,
% 290.85/183.38 (m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)),
% 290.85/183.38 inference(unit_resolution,[status(thm)],[9349, 9256, 9160, 9255, 9254])).
% 290.85/183.38 tff(9351,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6)), introduced(assumption)).
% 290.85/183.38 tff(9352,assumption,(node11(c_e_h_3, c_n, s6, s7)), introduced(assumption)).
% 290.85/183.38 tff(9353,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)), introduced(assumption)).
% 290.85/183.38 tff(9354,plain,
% 290.85/183.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)) | (~node11(c_e_h_3, c_n, s6, s7)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)) | (~node11(c_e_h_3, c_n, s6, s7)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6))),
% 290.85/183.38 inference(rewrite,[status(thm)],[])).
% 290.85/183.38 tff(9355,plain,
% 290.85/183.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)) | (~node11(c_e_h_3, c_n, s6, s7)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6))),
% 290.85/183.38 inference(quant_inst,[status(thm)],[])).
% 290.85/183.38 tff(9356,plain,
% 290.85/183.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)) | (~node11(c_e_h_3, c_n, s6, s7)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6)),
% 290.85/183.38 inference(modus_ponens,[status(thm)],[9355, 9354])).
% 290.85/183.38 tff(9357,plain,
% 290.85/183.38 ($false),
% 290.85/183.38 inference(unit_resolution,[status(thm)],[9356, 5017, 9353, 9352, 9351])).
% 290.85/183.38 tff(9358,plain,((~node11(c_e_h_3, c_n, s6, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6)), inference(lemma,lemma(discharge,[]))).
% 290.85/183.38 tff(9359,plain,
% 290.85/183.38 ((~node11(c_e_h_3, c_n, s6, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7))),
% 290.85/183.38 inference(unit_resolution,[status(thm)],[9358, 7112])).
% 290.85/183.38 tff(9360,plain,
% 290.85/183.38 (~node11(c_e_h_3, c_n, s6, s7)),
% 290.85/183.38 inference(unit_resolution,[status(thm)],[9359, 9350])).
% 290.85/183.38 tff(9361,plain,
% 290.85/183.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s6, s7)) | node10(c_e_h_3, c_n, s6, s7) | node11(c_e_h_3, c_n, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s6, s7)) | node10(c_e_h_3, c_n, s6, s7) | node11(c_e_h_3, c_n, s6, s7))),
% 290.85/183.38 inference(rewrite,[status(thm)],[])).
% 290.85/183.38 tff(9362,plain,
% 290.85/183.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s6, s7)) | node10(c_e_h_3, c_n, s6, s7) | node11(c_e_h_3, c_n, s6, s7))),
% 290.85/183.38 inference(quant_inst,[status(thm)],[])).
% 290.85/183.38 tff(9363,plain,
% 290.85/183.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s6, s7)) | node10(c_e_h_3, c_n, s6, s7) | node11(c_e_h_3, c_n, s6, s7)),
% 290.85/183.38 inference(modus_ponens,[status(thm)],[9362, 9361])).
% 290.85/183.38 tff(9364,plain,
% 290.85/183.38 (node10(c_e_h_3, c_n, s6, s7) | node11(c_e_h_3, c_n, s6, s7)),
% 290.85/183.38 inference(unit_resolution,[status(thm)],[9363, 5002, 1844])).
% 290.85/183.38 tff(9365,plain,
% 290.85/183.38 (node10(c_e_h_3, c_n, s6, s7)),
% 290.85/183.38 inference(unit_resolution,[status(thm)],[9364, 9360])).
% 290.85/183.38 tff(9366,plain,
% 290.85/183.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)) | node9(c_e_h_3, c_n, s6) | (~node10(c_e_h_3, c_n, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)) | node9(c_e_h_3, c_n, s6) | (~node10(c_e_h_3, c_n, s6, s7)))),
% 290.85/183.38 inference(rewrite,[status(thm)],[])).
% 290.85/183.38 tff(9367,plain,
% 290.85/183.38 ((node9(c_e_h_3, c_n, s6) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)) | (~node10(c_e_h_3, c_n, s6, s7))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)) | node9(c_e_h_3, c_n, s6) | (~node10(c_e_h_3, c_n, s6, s7)))),
% 290.85/183.38 inference(rewrite,[status(thm)],[])).
% 290.85/183.38 tff(9368,plain,
% 290.85/183.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s6) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)) | (~node10(c_e_h_3, c_n, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)) | node9(c_e_h_3, c_n, s6) | (~node10(c_e_h_3, c_n, s6, s7))))),
% 290.85/183.38 inference(monotonicity,[status(thm)],[9367])).
% 290.85/183.38 tff(9369,plain,
% 290.85/183.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s6) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)) | (~node10(c_e_h_3, c_n, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)) | node9(c_e_h_3, c_n, s6) | (~node10(c_e_h_3, c_n, s6, s7)))),
% 290.85/183.38 inference(transitivity,[status(thm)],[9368, 9366])).
% 290.85/183.38 tff(9370,plain,
% 290.85/183.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s6) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)) | (~node10(c_e_h_3, c_n, s6, s7)))),
% 290.85/183.38 inference(quant_inst,[status(thm)],[])).
% 290.85/183.38 tff(9371,plain,
% 290.85/183.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)) | node9(c_e_h_3, c_n, s6) | (~node10(c_e_h_3, c_n, s6, s7))),
% 290.85/183.38 inference(modus_ponens,[status(thm)],[9370, 9369])).
% 290.85/183.38 tff(9372,plain,
% 290.85/183.38 (node9(c_e_h_3, c_n, s6)),
% 290.85/183.38 inference(unit_resolution,[status(thm)],[9371, 4986, 9350, 9365])).
% 290.85/183.38 tff(9373,plain,
% 290.85/183.38 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s6)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s6)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s6))),
% 290.85/183.38 inference(rewrite,[status(thm)],[])).
% 290.85/183.38 tff(9374,plain,
% 290.85/183.38 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s6)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s6))),
% 290.85/183.39 inference(quant_inst,[status(thm)],[])).
% 290.85/183.39 tff(9375,plain,
% 290.85/183.39 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s6)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s6)),
% 290.85/183.39 inference(modus_ponens,[status(thm)],[9374, 9373])).
% 290.85/183.39 tff(9376,plain,
% 290.85/183.39 (m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s6)),
% 290.85/183.39 inference(unit_resolution,[status(thm)],[9375, 4972, 9372])).
% 290.85/183.39 tff(9377,plain,
% 290.85/183.39 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)))),
% 290.85/183.39 inference(rewrite,[status(thm)],[])).
% 290.85/183.39 tff(9378,plain,
% 290.85/183.39 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)))),
% 290.85/183.39 inference(quant_inst,[status(thm)],[])).
% 290.85/183.39 tff(9379,plain,
% 290.85/183.39 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6))),
% 290.85/183.39 inference(modus_ponens,[status(thm)],[9378, 9377])).
% 290.85/183.39 tff(9380,plain,
% 290.85/183.39 ($false),
% 290.85/183.39 inference(unit_resolution,[status(thm)],[9379, 5601, 7130, 9376])).
% 290.85/183.39 tff(9381,plain,((~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6))), inference(lemma,lemma(discharge,[]))).
% 290.85/183.39 tff(9382,plain,
% 290.85/183.39 (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s8)),
% 290.85/183.39 inference(unit_resolution,[status(thm)],[9381, 9253, 9160, 7130, 7117])).
% 290.85/183.39 tff(9383,plain,
% 290.85/183.39 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s8) | m_c_h_element_v_out(c_e_h_3, c_f, s8))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s8) | m_c_h_element_v_out(c_e_h_3, c_f, s8))),
% 290.85/183.39 inference(rewrite,[status(thm)],[])).
% 290.85/183.39 tff(9384,plain,
% 290.85/183.39 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s8) | m_c_h_element_v_out(c_e_h_3, c_f, s8))),
% 290.85/183.39 inference(quant_inst,[status(thm)],[])).
% 290.85/183.39 tff(9385,plain,
% 290.85/183.39 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s8) | m_c_h_element_v_out(c_e_h_3, c_f, s8)),
% 290.85/183.39 inference(modus_ponens,[status(thm)],[9384, 9383])).
% 290.85/183.39 tff(9386,plain,
% 290.85/183.39 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s8) | m_c_h_element_v_out(c_e_h_3, c_f, s8)),
% 290.85/183.39 inference(unit_resolution,[status(thm)],[9385, 5689])).
% 290.85/183.39 tff(9387,plain,
% 290.85/183.39 ($false),
% 290.85/183.39 inference(unit_resolution,[status(thm)],[9386, 9382, 9248])).
% 290.85/183.39 tff(9388,plain,(m_c_h_element_v_out(c_e_h_3, c_f, s7) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6)) | m_c_h_element_v_in2(c_e_h_3, c_f, s7)), inference(lemma,lemma(discharge,[]))).
% 290.85/183.39 tff(9389,plain,
% 290.85/183.39 (m_c_h_element_v_out(c_e_h_3, c_f, s7) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s6)) | m_c_h_element_v_in2(c_e_h_3, c_f, s7)),
% 290.85/183.39 inference(unit_resolution,[status(thm)],[9388, 7086])).
% 290.85/183.39 tff(9390,plain,
% 290.85/183.39 (m_c_h_element_v_in2(c_e_h_3, c_f, s7)),
% 290.85/183.39 inference(unit_resolution,[status(thm)],[9389, 9161, 9160, 9159])).
% 290.85/183.39 tff(9391,assumption,(m_c_h_element_v_in2(c_e_h_3, c_f, s7)), introduced(assumption)).
% 290.85/183.39 tff(9392,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_i, s7)), introduced(assumption)).
% 290.85/183.39 tff(9393,plain,
% 290.85/183.39 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s7)) | m_and_h_gate_v_out(c_e_h_3, c_i, s7))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s7)) | m_and_h_gate_v_out(c_e_h_3, c_i, s7))),
% 290.85/183.39 inference(rewrite,[status(thm)],[])).
% 290.85/183.39 tff(9394,plain,
% 290.85/183.39 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s7)) | m_and_h_gate_v_out(c_e_h_3, c_i, s7))),
% 290.85/183.39 inference(quant_inst,[status(thm)],[])).
% 290.85/183.39 tff(9395,plain,
% 290.85/183.39 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s7)) | m_and_h_gate_v_out(c_e_h_3, c_i, s7)),
% 290.85/183.39 inference(modus_ponens,[status(thm)],[9394, 9393])).
% 290.85/183.39 tff(9396,plain,
% 290.85/183.39 ($false),
% 290.85/183.39 inference(unit_resolution,[status(thm)],[9395, 2143, 9392, 9391])).
% 290.85/183.39 tff(9397,plain,((~m_c_h_element_v_in2(c_e_h_3, c_f, s7)) | m_and_h_gate_v_out(c_e_h_3, c_i, s7)), inference(lemma,lemma(discharge,[]))).
% 290.85/183.39 tff(9398,plain,
% 290.85/183.39 (m_and_h_gate_v_out(c_e_h_3, c_i, s7)),
% 290.85/183.39 inference(unit_resolution,[status(thm)],[9397, 9390])).
% 290.85/183.39 tff(9399,assumption,(m_and_h_gate_v_out(c_e_h_3, c_i, s7)), introduced(assumption)).
% 290.85/183.39 tff(9400,assumption,(node22(c_e_h_3, c_i, s6, s7)), introduced(assumption)).
% 290.85/183.39 tff(9401,plain,
% 290.85/183.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s7)) | (~node22(c_e_h_3, c_i, s6, s7)) | m_and_h_gate_v_out(c_e_h_3, c_i, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s7)) | (~node22(c_e_h_3, c_i, s6, s7)) | m_and_h_gate_v_out(c_e_h_3, c_i, s6))),
% 290.85/183.39 inference(rewrite,[status(thm)],[])).
% 290.85/183.39 tff(9402,plain,
% 290.85/183.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s7)) | (~node22(c_e_h_3, c_i, s6, s7)) | m_and_h_gate_v_out(c_e_h_3, c_i, s6))),
% 290.85/183.39 inference(quant_inst,[status(thm)],[])).
% 290.85/183.39 tff(9403,plain,
% 290.85/183.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s7)) | (~node22(c_e_h_3, c_i, s6, s7)) | m_and_h_gate_v_out(c_e_h_3, c_i, s6)),
% 290.85/183.39 inference(modus_ponens,[status(thm)],[9402, 9401])).
% 290.85/183.39 tff(9404,plain,
% 290.85/183.39 ($false),
% 290.85/183.39 inference(unit_resolution,[status(thm)],[9403, 108, 9399, 9085, 9400])).
% 290.85/183.39 tff(9405,plain,((~node22(c_e_h_3, c_i, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s7)) | m_and_h_gate_v_out(c_e_h_3, c_i, s6)), inference(lemma,lemma(discharge,[]))).
% 290.85/183.39 tff(9406,plain,
% 290.85/183.39 (~node22(c_e_h_3, c_i, s6, s7)),
% 290.85/183.39 inference(unit_resolution,[status(thm)],[9405, 9399, 9085])).
% 290.85/183.39 tff(9407,assumption,(~node20(c_e_h_3, c_i, s6)), introduced(assumption)).
% 290.85/183.39 tff(9408,assumption,(node21(c_e_h_3, c_i, s6, s7)), introduced(assumption)).
% 290.85/183.39 tff(9409,plain,
% 290.85/183.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s7)) | (~node21(c_e_h_3, c_i, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_i, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s7)) | (~node21(c_e_h_3, c_i, s6, s7)))),
% 290.85/183.39 inference(rewrite,[status(thm)],[])).
% 290.85/183.39 tff(9410,plain,
% 290.85/183.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s7)) | (~node21(c_e_h_3, c_i, s6, s7)))),
% 290.85/183.39 inference(quant_inst,[status(thm)],[])).
% 290.85/183.39 tff(9411,plain,
% 290.85/183.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_i, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s7)) | (~node21(c_e_h_3, c_i, s6, s7))),
% 290.85/183.39 inference(modus_ponens,[status(thm)],[9410, 9409])).
% 290.85/183.39 tff(9412,plain,
% 290.85/183.39 ($false),
% 290.85/183.39 inference(unit_resolution,[status(thm)],[9411, 52, 9399, 9408, 9407])).
% 290.85/183.39 tff(9413,plain,((~node21(c_e_h_3, c_i, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s7)) | node20(c_e_h_3, c_i, s6)), inference(lemma,lemma(discharge,[]))).
% 290.85/183.39 tff(9414,plain,
% 290.85/183.39 (~node21(c_e_h_3, c_i, s6, s7)),
% 290.85/183.39 inference(unit_resolution,[status(thm)],[9413, 9399, 9407])).
% 290.85/183.39 tff(9415,plain,
% 290.85/183.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_3, c_i, s6, s7) | node22(c_e_h_3, c_i, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_3, c_i, s6, s7) | node22(c_e_h_3, c_i, s6, s7))),
% 290.85/183.39 inference(rewrite,[status(thm)],[])).
% 290.85/183.39 tff(9416,plain,
% 290.85/183.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_3, c_i, s6, s7) | node22(c_e_h_3, c_i, s6, s7))),
% 290.85/183.39 inference(quant_inst,[status(thm)],[])).
% 290.85/183.39 tff(9417,plain,
% 290.85/183.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_3, c_i, s6, s7) | node22(c_e_h_3, c_i, s6, s7)),
% 290.85/183.39 inference(modus_ponens,[status(thm)],[9416, 9415])).
% 290.85/183.39 tff(9418,plain,
% 290.85/183.39 (node21(c_e_h_3, c_i, s6, s7) | node22(c_e_h_3, c_i, s6, s7)),
% 290.85/183.39 inference(unit_resolution,[status(thm)],[9417, 82, 1844])).
% 290.85/183.39 tff(9419,plain,
% 290.85/183.39 ($false),
% 290.85/183.39 inference(unit_resolution,[status(thm)],[9418, 9414, 9406])).
% 290.85/183.39 tff(9420,plain,((~m_and_h_gate_v_out(c_e_h_3, c_i, s7)) | node20(c_e_h_3, c_i, s6) | m_and_h_gate_v_out(c_e_h_3, c_i, s6)), inference(lemma,lemma(discharge,[]))).
% 290.85/183.39 tff(9421,plain,
% 290.85/183.39 (node20(c_e_h_3, c_i, s6)),
% 290.85/183.39 inference(unit_resolution,[status(thm)],[9420, 9398, 9084])).
% 290.85/183.39 tff(9422,assumption,(node20(c_e_h_3, c_i, s6)), introduced(assumption)).
% 290.85/183.39 tff(9423,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_i, s6)), introduced(assumption)).
% 290.85/183.39 tff(9424,plain,
% 290.85/183.39 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_i, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s6))),
% 290.85/183.39 inference(rewrite,[status(thm)],[])).
% 290.85/183.39 tff(9425,plain,
% 290.85/183.39 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s6))),
% 290.85/183.39 inference(quant_inst,[status(thm)],[])).
% 290.85/183.39 tff(9426,plain,
% 290.85/183.39 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_i, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s6)),
% 290.85/183.39 inference(modus_ponens,[status(thm)],[9425, 9424])).
% 290.85/183.39 tff(9427,plain,
% 290.85/183.39 ($false),
% 290.85/183.39 inference(unit_resolution,[status(thm)],[9426, 38, 9423, 9422])).
% 290.85/183.39 tff(9428,plain,((~node20(c_e_h_3, c_i, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s6)), inference(lemma,lemma(discharge,[]))).
% 290.85/183.39 tff(9429,plain,
% 290.85/183.39 (m_and_h_gate_v_in1(c_e_h_3, c_i, s6)),
% 290.85/183.39 inference(unit_resolution,[status(thm)],[9428, 9421])).
% 290.85/183.39 tff(9430,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_i, s6)), introduced(assumption)).
% 290.85/183.39 tff(9431,plain,
% 290.85/183.39 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_i, s6)) | m_c_h_element_v_out(c_e_h_3, c_h, s6))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s6)) | m_c_h_element_v_out(c_e_h_3, c_h, s6))),
% 290.85/183.39 inference(rewrite,[status(thm)],[])).
% 290.85/183.39 tff(9432,plain,
% 290.85/183.39 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_i, s6)) | m_c_h_element_v_out(c_e_h_3, c_h, s6))),
% 290.85/183.40 inference(quant_inst,[status(thm)],[])).
% 290.85/183.40 tff(9433,plain,
% 290.85/183.40 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s6)) | m_c_h_element_v_out(c_e_h_3, c_h, s6)),
% 290.85/183.40 inference(modus_ponens,[status(thm)],[9432, 9431])).
% 290.85/183.40 tff(9434,plain,
% 290.85/183.40 ($false),
% 290.85/183.40 inference(unit_resolution,[status(thm)],[9433, 619, 7394, 9430])).
% 290.85/183.40 tff(9435,plain,((~m_and_h_gate_v_in1(c_e_h_3, c_i, s6)) | m_c_h_element_v_out(c_e_h_3, c_h, s6)), inference(lemma,lemma(discharge,[]))).
% 290.85/183.40 tff(9436,plain,
% 290.85/183.40 (m_c_h_element_v_out(c_e_h_3, c_h, s6)),
% 290.85/183.40 inference(unit_resolution,[status(thm)],[9435, 9429])).
% 290.85/183.40 tff(9437,plain,
% 290.85/183.40 (m_c_h_element_v_out(c_e_h_3, c_h, s5)),
% 290.85/183.40 inference(unit_resolution,[status(thm)],[6411, 9436, 6354])).
% 290.85/183.40 tff(9438,plain,
% 290.85/183.40 (m_c_h_element_v_in2(c_e_h_3, c_h, s4)),
% 290.85/183.40 inference(unit_resolution,[status(thm)],[6343, 9437, 9038])).
% 290.85/183.40 tff(9439,plain,
% 290.85/183.40 (m_or_h_gate_v_out(c_e_h_3, c_j, s4)),
% 290.85/183.40 inference(unit_resolution,[status(thm)],[6257, 9438])).
% 290.85/183.40 tff(9440,plain,
% 290.85/183.40 (~node6(c_e_h_3, c_j, s3, s4)),
% 290.85/183.40 inference(unit_resolution,[status(thm)],[4027, 9439, 2235])).
% 290.85/183.40 tff(9441,plain,
% 290.85/183.40 (~node5(c_e_h_3, c_j, s3, s4)),
% 290.85/183.40 inference(unit_resolution,[status(thm)],[4052, 9439, 3617])).
% 290.85/183.40 tff(9442,plain,
% 290.85/183.40 ($false),
% 290.85/183.40 inference(unit_resolution,[status(thm)],[4060, 9441, 9440])).
% 290.85/183.40 tff(9443,plain,(m_or_h_gate_v_out(c_e_h_3, c_j, s3) | m_or_h_gate_v_in1(c_e_h_3, c_j, s3) | m_c_h_element_v_in2(c_e_h_3, c_h, s5) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9)), inference(lemma,lemma(discharge,[]))).
% 290.85/183.40 tff(9444,plain,
% 290.85/183.40 (m_or_h_gate_v_in1(c_e_h_3, c_j, s3) | m_c_h_element_v_in2(c_e_h_3, c_h, s5) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9)),
% 290.85/183.40 inference(unit_resolution,[status(thm)],[9443, 2233])).
% 290.85/183.40 tff(9445,plain,
% 290.85/183.40 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9)),
% 290.85/183.40 inference(unit_resolution,[status(thm)],[9444, 6352, 3615])).
% 290.85/183.40 tff(9446,plain,
% 290.85/183.40 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_m, X)) | m_and_h_gate_v_in2(I0, c_l, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9)) | m_and_h_gate_v_in2(c_e_h_3, c_l, s9))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_m, X)) | m_and_h_gate_v_in2(I0, c_l, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9)) | m_and_h_gate_v_in2(c_e_h_3, c_l, s9))),
% 290.85/183.40 inference(rewrite,[status(thm)],[])).
% 290.85/183.40 tff(9447,plain,
% 290.85/183.40 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_m, X)) | m_and_h_gate_v_in2(I0, c_l, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9)) | m_and_h_gate_v_in2(c_e_h_3, c_l, s9))),
% 290.85/183.40 inference(quant_inst,[status(thm)],[])).
% 290.85/183.40 tff(9448,plain,
% 290.85/183.40 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_m, X)) | m_and_h_gate_v_in2(I0, c_l, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9)) | m_and_h_gate_v_in2(c_e_h_3, c_l, s9)),
% 290.85/183.40 inference(modus_ponens,[status(thm)],[9447, 9446])).
% 290.85/183.40 tff(9449,plain,
% 290.85/183.40 (m_and_h_gate_v_in2(c_e_h_3, c_l, s9)),
% 290.85/183.40 inference(unit_resolution,[status(thm)],[9448, 7159, 9445])).
% 290.85/183.40 tff(9450,assumption,(node21(c_e_h_3, c_l, s9, s10)), introduced(assumption)).
% 290.85/183.40 tff(9451,plain,
% 290.85/183.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (m_and_h_gate_v_out(c_e_h_3, c_l, s10) | (~m_and_h_gate_v_in2(c_e_h_3, c_l, s9)) | (~node21(c_e_h_3, c_l, s9, s10)) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | m_and_h_gate_v_out(c_e_h_3, c_l, s10) | (~m_and_h_gate_v_in2(c_e_h_3, c_l, s9)) | (~node21(c_e_h_3, c_l, s9, s10)) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s9)))),
% 290.85/183.40 inference(rewrite,[status(thm)],[])).
% 290.85/183.40 tff(9452,plain,
% 290.85/183.40 (((~node21(c_e_h_3, c_l, s9, s10)) | (~m_and_h_gate_v_in2(c_e_h_3, c_l, s9)) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s9)) | m_and_h_gate_v_out(c_e_h_3, c_l, s10)) <=> (m_and_h_gate_v_out(c_e_h_3, c_l, s10) | (~m_and_h_gate_v_in2(c_e_h_3, c_l, s9)) | (~node21(c_e_h_3, c_l, s9, s10)) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s9)))),
% 290.85/183.40 inference(rewrite,[status(thm)],[])).
% 290.85/183.40 tff(9453,plain,
% 290.85/183.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_l, s9, s10)) | (~m_and_h_gate_v_in2(c_e_h_3, c_l, s9)) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s9)) | m_and_h_gate_v_out(c_e_h_3, c_l, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (m_and_h_gate_v_out(c_e_h_3, c_l, s10) | (~m_and_h_gate_v_in2(c_e_h_3, c_l, s9)) | (~node21(c_e_h_3, c_l, s9, s10)) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s9))))),
% 290.85/183.40 inference(monotonicity,[status(thm)],[9452])).
% 290.85/183.40 tff(9454,plain,
% 290.85/183.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_l, s9, s10)) | (~m_and_h_gate_v_in2(c_e_h_3, c_l, s9)) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s9)) | m_and_h_gate_v_out(c_e_h_3, c_l, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | m_and_h_gate_v_out(c_e_h_3, c_l, s10) | (~m_and_h_gate_v_in2(c_e_h_3, c_l, s9)) | (~node21(c_e_h_3, c_l, s9, s10)) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s9)))),
% 290.85/183.40 inference(transitivity,[status(thm)],[9453, 9451])).
% 290.85/183.40 tff(9455,plain,
% 290.85/183.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_l, s9, s10)) | (~m_and_h_gate_v_in2(c_e_h_3, c_l, s9)) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s9)) | m_and_h_gate_v_out(c_e_h_3, c_l, s10))),
% 290.85/183.40 inference(quant_inst,[status(thm)],[])).
% 290.85/183.40 tff(9456,plain,
% 290.85/183.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | m_and_h_gate_v_out(c_e_h_3, c_l, s10) | (~m_and_h_gate_v_in2(c_e_h_3, c_l, s9)) | (~node21(c_e_h_3, c_l, s9, s10)) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s9))),
% 290.85/183.40 inference(modus_ponens,[status(thm)],[9455, 9454])).
% 290.85/183.40 tff(9457,plain,
% 290.85/183.40 ($false),
% 290.85/183.40 inference(unit_resolution,[status(thm)],[9456, 5851, 9450, 9449, 9020, 9036])).
% 290.85/183.40 tff(9458,plain,((~node21(c_e_h_3, c_l, s9, s10)) | m_and_h_gate_v_out(c_e_h_3, c_l, s10) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s9))), inference(lemma,lemma(discharge,[]))).
% 290.85/183.40 tff(9459,plain,
% 290.85/183.40 (~m_and_h_gate_v_in1(c_e_h_3, c_l, s9)),
% 290.85/183.40 inference(unit_resolution,[status(thm)],[9458, 9035, 9018])).
% 290.85/183.40 tff(9460,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_l, s9)), introduced(assumption)).
% 290.85/183.40 tff(9461,assumption,(m_and_h_gate_v_out(c_e_h_3, c_k, s9)), introduced(assumption)).
% 290.85/183.40 tff(9462,plain,
% 290.85/183.40 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_l, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s9)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s9))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_l, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s9)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s9))),
% 290.85/183.40 inference(rewrite,[status(thm)],[])).
% 290.85/183.40 tff(9463,plain,
% 290.85/183.40 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_l, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s9)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s9))),
% 290.85/183.40 inference(quant_inst,[status(thm)],[])).
% 290.85/183.40 tff(9464,plain,
% 290.85/183.40 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_l, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s9)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s9)),
% 290.85/183.40 inference(modus_ponens,[status(thm)],[9463, 9462])).
% 290.85/183.40 tff(9465,plain,
% 290.85/183.40 ($false),
% 290.85/183.40 inference(unit_resolution,[status(thm)],[9464, 7192, 9461, 9460])).
% 290.85/183.40 tff(9466,plain,((~m_and_h_gate_v_out(c_e_h_3, c_k, s9)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s9)), inference(lemma,lemma(discharge,[]))).
% 290.85/183.40 tff(9467,plain,
% 290.85/183.40 (~m_and_h_gate_v_out(c_e_h_3, c_k, s9)),
% 290.85/183.40 inference(unit_resolution,[status(thm)],[9466, 9459])).
% 290.85/183.40 tff(9468,assumption,(m_and_h_gate_v_out(c_e_h_3, c_k, s8)), introduced(assumption)).
% 290.85/183.40 tff(9469,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_k, s9)), introduced(assumption)).
% 290.85/183.40 tff(9470,assumption,(node22(c_e_h_3, c_k, s8, s9)), introduced(assumption)).
% 290.85/183.40 tff(9471,plain,
% 290.85/183.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s8)) | m_and_h_gate_v_out(c_e_h_3, c_k, s9) | (~node22(c_e_h_3, c_k, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s8)) | m_and_h_gate_v_out(c_e_h_3, c_k, s9) | (~node22(c_e_h_3, c_k, s8, s9)))),
% 290.85/183.40 inference(rewrite,[status(thm)],[])).
% 290.85/183.40 tff(9472,plain,
% 290.85/183.40 ((m_and_h_gate_v_out(c_e_h_3, c_k, s9) | (~node22(c_e_h_3, c_k, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s8))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_k, s8)) | m_and_h_gate_v_out(c_e_h_3, c_k, s9) | (~node22(c_e_h_3, c_k, s8, s9)))),
% 290.85/183.40 inference(rewrite,[status(thm)],[])).
% 290.85/183.40 tff(9473,plain,
% 290.85/183.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_k, s9) | (~node22(c_e_h_3, c_k, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s8)) | m_and_h_gate_v_out(c_e_h_3, c_k, s9) | (~node22(c_e_h_3, c_k, s8, s9))))),
% 290.85/183.40 inference(monotonicity,[status(thm)],[9472])).
% 290.85/183.40 tff(9474,plain,
% 290.85/183.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_k, s9) | (~node22(c_e_h_3, c_k, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s8)) | m_and_h_gate_v_out(c_e_h_3, c_k, s9) | (~node22(c_e_h_3, c_k, s8, s9)))),
% 290.85/183.40 inference(transitivity,[status(thm)],[9473, 9471])).
% 290.85/183.40 tff(9475,plain,
% 290.85/183.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_k, s9) | (~node22(c_e_h_3, c_k, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s8)))),
% 290.85/183.40 inference(quant_inst,[status(thm)],[])).
% 290.85/183.40 tff(9476,plain,
% 290.85/183.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s8)) | m_and_h_gate_v_out(c_e_h_3, c_k, s9) | (~node22(c_e_h_3, c_k, s8, s9))),
% 290.85/183.40 inference(modus_ponens,[status(thm)],[9475, 9474])).
% 290.85/183.40 tff(9477,plain,
% 290.85/183.40 ($false),
% 290.85/183.40 inference(unit_resolution,[status(thm)],[9476, 5871, 9470, 9468, 9469])).
% 290.85/183.40 tff(9478,plain,((~node22(c_e_h_3, c_k, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s8)) | m_and_h_gate_v_out(c_e_h_3, c_k, s9)), inference(lemma,lemma(discharge,[]))).
% 290.85/183.40 tff(9479,plain,
% 290.85/183.40 (~node22(c_e_h_3, c_k, s8, s9)),
% 290.85/183.40 inference(unit_resolution,[status(thm)],[9478, 9468, 9469])).
% 290.85/183.40 tff(9480,plain,
% 290.85/183.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s8, s9)) | node21(c_e_h_3, c_k, s8, s9) | node22(c_e_h_3, c_k, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_3, c_k, s8, s9) | node22(c_e_h_3, c_k, s8, s9))),
% 290.85/183.40 inference(rewrite,[status(thm)],[])).
% 290.85/183.40 tff(9481,plain,
% 290.85/183.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s8, s9)) | node21(c_e_h_3, c_k, s8, s9) | node22(c_e_h_3, c_k, s8, s9))),
% 290.94/183.41 inference(quant_inst,[status(thm)],[])).
% 290.94/183.41 tff(9482,plain,
% 290.94/183.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_3, c_k, s8, s9) | node22(c_e_h_3, c_k, s8, s9)),
% 290.94/183.41 inference(modus_ponens,[status(thm)],[9481, 9480])).
% 290.94/183.41 tff(9483,plain,
% 290.94/183.41 (node21(c_e_h_3, c_k, s8, s9) | node22(c_e_h_3, c_k, s8, s9)),
% 290.94/183.41 inference(unit_resolution,[status(thm)],[9482, 82, 1993])).
% 290.94/183.41 tff(9484,plain,
% 290.94/183.41 (node21(c_e_h_3, c_k, s8, s9)),
% 290.94/183.41 inference(unit_resolution,[status(thm)],[9483, 9479])).
% 290.94/183.41 tff(9485,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_k, s8)), introduced(assumption)).
% 290.94/183.41 tff(9486,assumption,(node21(c_e_h_3, c_k, s8, s9)), introduced(assumption)).
% 290.94/183.41 tff(9487,plain,
% 290.94/183.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_k, s8)) | m_and_h_gate_v_out(c_e_h_3, c_k, s9) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s8)) | (~node21(c_e_h_3, c_k, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s8)) | m_and_h_gate_v_out(c_e_h_3, c_k, s9) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s8)) | (~node21(c_e_h_3, c_k, s8, s9)))),
% 290.94/183.41 inference(rewrite,[status(thm)],[])).
% 290.94/183.41 tff(9488,plain,
% 290.94/183.41 (((~node21(c_e_h_3, c_k, s8, s9)) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s8)) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s8)) | m_and_h_gate_v_out(c_e_h_3, c_k, s9)) <=> ((~m_and_h_gate_v_in2(c_e_h_3, c_k, s8)) | m_and_h_gate_v_out(c_e_h_3, c_k, s9) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s8)) | (~node21(c_e_h_3, c_k, s8, s9)))),
% 290.94/183.41 inference(rewrite,[status(thm)],[])).
% 290.94/183.41 tff(9489,plain,
% 290.94/183.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_k, s8, s9)) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s8)) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s8)) | m_and_h_gate_v_out(c_e_h_3, c_k, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_k, s8)) | m_and_h_gate_v_out(c_e_h_3, c_k, s9) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s8)) | (~node21(c_e_h_3, c_k, s8, s9))))),
% 290.94/183.41 inference(monotonicity,[status(thm)],[9488])).
% 290.94/183.41 tff(9490,plain,
% 290.94/183.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_k, s8, s9)) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s8)) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s8)) | m_and_h_gate_v_out(c_e_h_3, c_k, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s8)) | m_and_h_gate_v_out(c_e_h_3, c_k, s9) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s8)) | (~node21(c_e_h_3, c_k, s8, s9)))),
% 290.94/183.41 inference(transitivity,[status(thm)],[9489, 9487])).
% 290.94/183.41 tff(9491,plain,
% 290.94/183.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_k, s8, s9)) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s8)) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s8)) | m_and_h_gate_v_out(c_e_h_3, c_k, s9))),
% 290.94/183.41 inference(quant_inst,[status(thm)],[])).
% 290.94/183.41 tff(9492,plain,
% 290.94/183.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s8)) | m_and_h_gate_v_out(c_e_h_3, c_k, s9) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s8)) | (~node21(c_e_h_3, c_k, s8, s9))),
% 290.94/183.41 inference(modus_ponens,[status(thm)],[9491, 9490])).
% 290.94/183.41 tff(9493,plain,
% 290.94/183.41 ($false),
% 290.94/183.41 inference(unit_resolution,[status(thm)],[9492, 5851, 8981, 9486, 9469, 9485])).
% 290.94/183.41 tff(9494,plain,((~node21(c_e_h_3, c_k, s8, s9)) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s8)) | m_and_h_gate_v_out(c_e_h_3, c_k, s9) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s8))), inference(lemma,lemma(discharge,[]))).
% 290.94/183.41 tff(9495,plain,
% 290.94/183.41 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s8)),
% 290.94/183.41 inference(unit_resolution,[status(thm)],[9494, 9484, 8981, 9469])).
% 290.94/183.41 tff(9496,plain,
% 290.94/183.41 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X))) | ((~m_or_h_gate_v_out(c_e_h_3, c_g, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s8))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s8))),
% 290.94/183.41 inference(rewrite,[status(thm)],[])).
% 290.94/183.41 tff(9497,plain,
% 290.94/183.41 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X))) | ((~m_or_h_gate_v_out(c_e_h_3, c_g, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s8))),
% 290.94/183.41 inference(quant_inst,[status(thm)],[])).
% 290.94/183.41 tff(9498,plain,
% 290.94/183.41 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s8)),
% 290.94/183.41 inference(modus_ponens,[status(thm)],[9497, 9496])).
% 290.94/183.41 tff(9499,plain,
% 290.94/183.41 (~m_or_h_gate_v_out(c_e_h_3, c_g, s8)),
% 290.94/183.41 inference(unit_resolution,[status(thm)],[9498, 6229, 9495])).
% 290.94/183.41 tff(9500,assumption,(~m_or_h_gate_v_out(c_e_h_3, c_g, s8)), introduced(assumption)).
% 290.94/183.41 tff(9501,assumption,(m_or_h_gate_v_out(c_e_h_3, c_g, s7)), introduced(assumption)).
% 290.94/183.41 tff(9502,assumption,(~node4(c_e_h_3, c_g, s7)), introduced(assumption)).
% 290.94/183.41 tff(9503,assumption,(node5(c_e_h_3, c_g, s7, s8)), introduced(assumption)).
% 290.94/183.41 tff(9504,plain,
% 290.94/183.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | ((~node5(c_e_h_3, c_g, s7, s8)) | m_or_h_gate_v_out(c_e_h_3, c_g, s8) | node4(c_e_h_3, c_g, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (~node5(c_e_h_3, c_g, s7, s8)) | m_or_h_gate_v_out(c_e_h_3, c_g, s8) | node4(c_e_h_3, c_g, s7))),
% 290.94/183.41 inference(rewrite,[status(thm)],[])).
% 290.94/183.41 tff(9505,plain,
% 290.94/183.41 ((node4(c_e_h_3, c_g, s7) | (~node5(c_e_h_3, c_g, s7, s8)) | m_or_h_gate_v_out(c_e_h_3, c_g, s8)) <=> ((~node5(c_e_h_3, c_g, s7, s8)) | m_or_h_gate_v_out(c_e_h_3, c_g, s8) | node4(c_e_h_3, c_g, s7))),
% 290.94/183.41 inference(rewrite,[status(thm)],[])).
% 290.94/183.41 tff(9506,plain,
% 290.94/183.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_3, c_g, s7) | (~node5(c_e_h_3, c_g, s7, s8)) | m_or_h_gate_v_out(c_e_h_3, c_g, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | ((~node5(c_e_h_3, c_g, s7, s8)) | m_or_h_gate_v_out(c_e_h_3, c_g, s8) | node4(c_e_h_3, c_g, s7)))),
% 290.94/183.41 inference(monotonicity,[status(thm)],[9505])).
% 290.94/183.41 tff(9507,plain,
% 290.94/183.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_3, c_g, s7) | (~node5(c_e_h_3, c_g, s7, s8)) | m_or_h_gate_v_out(c_e_h_3, c_g, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (~node5(c_e_h_3, c_g, s7, s8)) | m_or_h_gate_v_out(c_e_h_3, c_g, s8) | node4(c_e_h_3, c_g, s7))),
% 290.94/183.41 inference(transitivity,[status(thm)],[9506, 9504])).
% 290.94/183.41 tff(9508,plain,
% 290.94/183.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_3, c_g, s7) | (~node5(c_e_h_3, c_g, s7, s8)) | m_or_h_gate_v_out(c_e_h_3, c_g, s8))),
% 290.94/183.41 inference(quant_inst,[status(thm)],[])).
% 290.94/183.41 tff(9509,plain,
% 290.94/183.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (~node5(c_e_h_3, c_g, s7, s8)) | m_or_h_gate_v_out(c_e_h_3, c_g, s8) | node4(c_e_h_3, c_g, s7)),
% 290.94/183.42 inference(modus_ponens,[status(thm)],[9508, 9507])).
% 290.94/183.42 tff(9510,plain,
% 290.94/183.42 ($false),
% 290.94/183.42 inference(unit_resolution,[status(thm)],[9509, 5498, 9503, 9502, 9500])).
% 290.94/183.42 tff(9511,plain,((~node5(c_e_h_3, c_g, s7, s8)) | node4(c_e_h_3, c_g, s7) | m_or_h_gate_v_out(c_e_h_3, c_g, s8)), inference(lemma,lemma(discharge,[]))).
% 290.94/183.42 tff(9512,plain,
% 290.94/183.42 (~node5(c_e_h_3, c_g, s7, s8)),
% 290.94/183.42 inference(unit_resolution,[status(thm)],[9511, 9500, 9502])).
% 290.94/183.42 tff(9513,plain,
% 290.94/183.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s7, s8)) | node6(c_e_h_3, c_g, s7, s8) | node5(c_e_h_3, c_g, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s7, s8)) | node6(c_e_h_3, c_g, s7, s8) | node5(c_e_h_3, c_g, s7, s8))),
% 290.94/183.42 inference(rewrite,[status(thm)],[])).
% 290.94/183.42 tff(9514,plain,
% 290.94/183.42 ((node6(c_e_h_3, c_g, s7, s8) | node5(c_e_h_3, c_g, s7, s8) | (~trans(s7, s8))) <=> ((~trans(s7, s8)) | node6(c_e_h_3, c_g, s7, s8) | node5(c_e_h_3, c_g, s7, s8))),
% 290.94/183.42 inference(rewrite,[status(thm)],[])).
% 290.94/183.42 tff(9515,plain,
% 290.94/183.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s7, s8) | node5(c_e_h_3, c_g, s7, s8) | (~trans(s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s7, s8)) | node6(c_e_h_3, c_g, s7, s8) | node5(c_e_h_3, c_g, s7, s8)))),
% 290.94/183.42 inference(monotonicity,[status(thm)],[9514])).
% 290.94/183.42 tff(9516,plain,
% 290.94/183.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s7, s8) | node5(c_e_h_3, c_g, s7, s8) | (~trans(s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s7, s8)) | node6(c_e_h_3, c_g, s7, s8) | node5(c_e_h_3, c_g, s7, s8))),
% 290.94/183.42 inference(transitivity,[status(thm)],[9515, 9513])).
% 290.94/183.42 tff(9517,plain,
% 290.94/183.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s7, s8) | node5(c_e_h_3, c_g, s7, s8) | (~trans(s7, s8)))),
% 290.94/183.42 inference(quant_inst,[status(thm)],[])).
% 290.94/183.42 tff(9518,plain,
% 290.94/183.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s7, s8)) | node6(c_e_h_3, c_g, s7, s8) | node5(c_e_h_3, c_g, s7, s8)),
% 290.94/183.42 inference(modus_ponens,[status(thm)],[9517, 9516])).
% 290.94/183.42 tff(9519,plain,
% 290.94/183.42 (node6(c_e_h_3, c_g, s7, s8) | node5(c_e_h_3, c_g, s7, s8)),
% 290.94/183.42 inference(unit_resolution,[status(thm)],[9518, 1141, 1938])).
% 290.94/183.42 tff(9520,plain,
% 290.94/183.42 (node6(c_e_h_3, c_g, s7, s8)),
% 290.94/183.42 inference(unit_resolution,[status(thm)],[9519, 9512])).
% 290.94/183.42 tff(9521,plain,
% 290.94/183.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | ((~m_or_h_gate_v_out(c_e_h_3, c_g, s7)) | (~node6(c_e_h_3, c_g, s7, s8)) | m_or_h_gate_v_out(c_e_h_3, c_g, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s7)) | (~node6(c_e_h_3, c_g, s7, s8)) | m_or_h_gate_v_out(c_e_h_3, c_g, s8))),
% 290.94/183.42 inference(rewrite,[status(thm)],[])).
% 290.94/183.42 tff(9522,plain,
% 290.94/183.42 ((m_or_h_gate_v_out(c_e_h_3, c_g, s8) | (~node6(c_e_h_3, c_g, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s7))) <=> ((~m_or_h_gate_v_out(c_e_h_3, c_g, s7)) | (~node6(c_e_h_3, c_g, s7, s8)) | m_or_h_gate_v_out(c_e_h_3, c_g, s8))),
% 290.94/183.42 inference(rewrite,[status(thm)],[])).
% 290.94/183.42 tff(9523,plain,
% 290.94/183.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s8) | (~node6(c_e_h_3, c_g, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | ((~m_or_h_gate_v_out(c_e_h_3, c_g, s7)) | (~node6(c_e_h_3, c_g, s7, s8)) | m_or_h_gate_v_out(c_e_h_3, c_g, s8)))),
% 290.94/183.42 inference(monotonicity,[status(thm)],[9522])).
% 290.94/183.42 tff(9524,plain,
% 290.94/183.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s8) | (~node6(c_e_h_3, c_g, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s7)) | (~node6(c_e_h_3, c_g, s7, s8)) | m_or_h_gate_v_out(c_e_h_3, c_g, s8))),
% 290.94/183.42 inference(transitivity,[status(thm)],[9523, 9521])).
% 290.94/183.42 tff(9525,plain,
% 290.94/183.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s8) | (~node6(c_e_h_3, c_g, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s7)))),
% 290.94/183.42 inference(quant_inst,[status(thm)],[])).
% 290.94/183.42 tff(9526,plain,
% 290.94/183.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s7)) | (~node6(c_e_h_3, c_g, s7, s8)) | m_or_h_gate_v_out(c_e_h_3, c_g, s8)),
% 290.94/183.42 inference(modus_ponens,[status(thm)],[9525, 9524])).
% 290.94/183.42 tff(9527,plain,
% 290.94/183.42 ($false),
% 290.94/183.42 inference(unit_resolution,[status(thm)],[9526, 5474, 9520, 9501, 9500])).
% 290.94/183.42 tff(9528,plain,(m_or_h_gate_v_out(c_e_h_3, c_g, s8) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s7)) | node4(c_e_h_3, c_g, s7)), inference(lemma,lemma(discharge,[]))).
% 290.94/183.42 tff(9529,plain,
% 290.94/183.42 (node4(c_e_h_3, c_g, s7)),
% 290.94/183.42 inference(unit_resolution,[status(thm)],[9528, 9501, 9500])).
% 290.94/183.42 tff(9530,plain,
% 290.94/183.42 (((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_g, s7)) | (~node4(c_e_h_3, c_g, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s7)) | (~node4(c_e_h_3, c_g, s7)))),
% 290.94/183.42 inference(rewrite,[status(thm)],[])).
% 290.94/183.42 tff(9531,plain,
% 290.94/183.42 ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_g, s7)) | (~node4(c_e_h_3, c_g, s7)))),
% 290.94/183.42 inference(quant_inst,[status(thm)],[])).
% 290.94/183.42 tff(9532,plain,
% 290.94/183.42 ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s7)) | (~node4(c_e_h_3, c_g, s7))),
% 290.94/183.42 inference(modus_ponens,[status(thm)],[9531, 9530])).
% 290.94/183.42 tff(9533,plain,
% 290.94/183.42 (~m_or_h_gate_v_in1(c_e_h_3, c_g, s7)),
% 290.94/183.42 inference(unit_resolution,[status(thm)],[9532, 5516, 9529])).
% 290.94/183.42 tff(9534,plain,
% 290.94/183.42 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s7)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s7))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s7)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s7))),
% 290.94/183.42 inference(rewrite,[status(thm)],[])).
% 290.94/183.42 tff(9535,plain,
% 290.94/183.42 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s7)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s7))),
% 290.94/183.42 inference(quant_inst,[status(thm)],[])).
% 290.94/183.42 tff(9536,plain,
% 290.94/183.42 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s7)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s7)),
% 290.94/183.42 inference(modus_ponens,[status(thm)],[9535, 9534])).
% 290.94/183.42 tff(9537,plain,
% 290.94/183.42 (~m_and_h_gate_v_out(c_e_h_3, c_c, s7)),
% 290.94/183.42 inference(unit_resolution,[status(thm)],[9536, 5896, 9533])).
% 290.94/183.42 tff(9538,assumption,(m_and_h_gate_v_out(c_e_h_1, c_p, s3)), introduced(assumption)).
% 290.94/183.42 tff(9539,assumption,(m_and_h_gate_v_in1(c_e_h_1, c_p, s2)), introduced(assumption)).
% 290.94/183.42 tff(9540,plain,
% 290.94/183.42 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_g, s0)) | m_and_h_gate_v_out(c_e_h_1, c_d, s0))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_g, s0)) | m_and_h_gate_v_out(c_e_h_1, c_d, s0))),
% 290.94/183.42 inference(rewrite,[status(thm)],[])).
% 290.94/183.42 tff(9541,plain,
% 290.94/183.42 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_g, s0)) | m_and_h_gate_v_out(c_e_h_1, c_d, s0))),
% 290.94/183.42 inference(quant_inst,[status(thm)],[])).
% 290.94/183.42 tff(9542,plain,
% 290.94/183.42 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_g, s0)) | m_and_h_gate_v_out(c_e_h_1, c_d, s0)),
% 290.94/183.42 inference(modus_ponens,[status(thm)],[9541, 9540])).
% 290.94/183.42 tff(9543,plain,
% 290.94/183.42 (~m_or_h_gate_v_in2(c_e_h_1, c_g, s0)),
% 290.94/183.42 inference(unit_resolution,[status(thm)],[9542, 2762, 5044])).
% 290.94/183.42 tff(9544,assumption,(m_or_h_gate_v_out(c_e_h_1, c_g, s1)), introduced(assumption)).
% 290.94/183.42 tff(9545,assumption,(m_and_h_gate_v_out(c_e_h_1, c_c, s0)), introduced(assumption)).
% 290.94/183.42 tff(9546,plain,
% 290.94/183.42 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s0))),
% 290.94/183.42 inference(quant_inst,[status(thm)],[])).
% 290.94/183.42 tff(9547,plain,
% 290.94/183.42 ($false),
% 290.94/183.42 inference(unit_resolution,[status(thm)],[9546, 95, 9545])).
% 290.94/183.42 tff(9548,plain,(~m_and_h_gate_v_out(c_e_h_1, c_c, s0)), inference(lemma,lemma(discharge,[]))).
% 290.94/183.42 tff(9549,plain,
% 290.94/183.42 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_g, s0)) | m_and_h_gate_v_out(c_e_h_1, c_c, s0))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_g, s0)) | m_and_h_gate_v_out(c_e_h_1, c_c, s0))),
% 290.94/183.42 inference(rewrite,[status(thm)],[])).
% 290.94/183.42 tff(9550,plain,
% 290.94/183.42 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_g, s0)) | m_and_h_gate_v_out(c_e_h_1, c_c, s0))),
% 290.94/183.42 inference(quant_inst,[status(thm)],[])).
% 290.94/183.42 tff(9551,plain,
% 290.94/183.42 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_g, s0)) | m_and_h_gate_v_out(c_e_h_1, c_c, s0)),
% 290.94/183.42 inference(modus_ponens,[status(thm)],[9550, 9549])).
% 290.94/183.42 tff(9552,plain,
% 290.94/183.42 (~m_or_h_gate_v_in1(c_e_h_1, c_g, s0)),
% 290.94/183.42 inference(unit_resolution,[status(thm)],[9551, 2708, 9548])).
% 290.94/183.42 tff(9553,assumption,(node6(c_e_h_1, c_g, s0, s1)), introduced(assumption)).
% 290.94/183.42 tff(9554,plain,
% 290.94/183.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_g, s0) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s1)) | (~node6(c_e_h_1, c_g, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_g, s0) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s1)) | (~node6(c_e_h_1, c_g, s0, s1)))),
% 290.94/183.42 inference(rewrite,[status(thm)],[])).
% 290.94/183.42 tff(9555,plain,
% 290.94/183.42 (((~node6(c_e_h_1, c_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s1)) | m_or_h_gate_v_out(c_e_h_1, c_g, s0)) <=> (m_or_h_gate_v_out(c_e_h_1, c_g, s0) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s1)) | (~node6(c_e_h_1, c_g, s0, s1)))),
% 290.94/183.42 inference(rewrite,[status(thm)],[])).
% 290.94/183.42 tff(9556,plain,
% 290.94/183.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s1)) | m_or_h_gate_v_out(c_e_h_1, c_g, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_g, s0) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s1)) | (~node6(c_e_h_1, c_g, s0, s1))))),
% 290.94/183.42 inference(monotonicity,[status(thm)],[9555])).
% 290.94/183.42 tff(9557,plain,
% 290.94/183.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s1)) | m_or_h_gate_v_out(c_e_h_1, c_g, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_g, s0) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s1)) | (~node6(c_e_h_1, c_g, s0, s1)))),
% 290.94/183.43 inference(transitivity,[status(thm)],[9556, 9554])).
% 290.94/183.43 tff(9558,plain,
% 290.94/183.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s1)) | m_or_h_gate_v_out(c_e_h_1, c_g, s0))),
% 290.94/183.43 inference(quant_inst,[status(thm)],[])).
% 290.94/183.43 tff(9559,plain,
% 290.94/183.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_g, s0) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s1)) | (~node6(c_e_h_1, c_g, s0, s1))),
% 290.94/183.43 inference(modus_ponens,[status(thm)],[9558, 9557])).
% 290.94/183.43 tff(9560,plain,
% 290.94/183.43 ($false),
% 290.94/183.43 inference(unit_resolution,[status(thm)],[9559, 1121, 9553, 3133, 9544])).
% 290.94/183.43 tff(9561,plain,((~node6(c_e_h_1, c_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s1))), inference(lemma,lemma(discharge,[]))).
% 290.94/183.43 tff(9562,plain,
% 290.94/183.43 (~node6(c_e_h_1, c_g, s0, s1)),
% 290.94/183.43 inference(unit_resolution,[status(thm)],[9561, 9544])).
% 290.94/183.43 tff(9563,plain,
% 290.94/183.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s0, s1)) | node5(c_e_h_1, c_g, s0, s1) | node6(c_e_h_1, c_g, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s0, s1)) | node5(c_e_h_1, c_g, s0, s1) | node6(c_e_h_1, c_g, s0, s1))),
% 290.94/183.43 inference(rewrite,[status(thm)],[])).
% 290.94/183.43 tff(9564,plain,
% 290.94/183.43 ((node6(c_e_h_1, c_g, s0, s1) | node5(c_e_h_1, c_g, s0, s1) | (~trans(s0, s1))) <=> ((~trans(s0, s1)) | node5(c_e_h_1, c_g, s0, s1) | node6(c_e_h_1, c_g, s0, s1))),
% 290.94/183.43 inference(rewrite,[status(thm)],[])).
% 290.94/183.43 tff(9565,plain,
% 290.94/183.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_g, s0, s1) | node5(c_e_h_1, c_g, s0, s1) | (~trans(s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s0, s1)) | node5(c_e_h_1, c_g, s0, s1) | node6(c_e_h_1, c_g, s0, s1)))),
% 290.94/183.43 inference(monotonicity,[status(thm)],[9564])).
% 290.94/183.43 tff(9566,plain,
% 290.94/183.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_g, s0, s1) | node5(c_e_h_1, c_g, s0, s1) | (~trans(s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s0, s1)) | node5(c_e_h_1, c_g, s0, s1) | node6(c_e_h_1, c_g, s0, s1))),
% 290.94/183.43 inference(transitivity,[status(thm)],[9565, 9563])).
% 290.94/183.43 tff(9567,plain,
% 290.94/183.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_g, s0, s1) | node5(c_e_h_1, c_g, s0, s1) | (~trans(s0, s1)))),
% 290.94/183.43 inference(quant_inst,[status(thm)],[])).
% 290.94/183.43 tff(9568,plain,
% 290.94/183.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s0, s1)) | node5(c_e_h_1, c_g, s0, s1) | node6(c_e_h_1, c_g, s0, s1)),
% 290.94/183.43 inference(modus_ponens,[status(thm)],[9567, 9566])).
% 290.94/183.43 tff(9569,plain,
% 290.94/183.43 (node5(c_e_h_1, c_g, s0, s1) | node6(c_e_h_1, c_g, s0, s1)),
% 290.94/183.43 inference(unit_resolution,[status(thm)],[9568, 1141, 72])).
% 290.94/183.43 tff(9570,plain,
% 290.94/183.43 (node5(c_e_h_1, c_g, s0, s1)),
% 290.94/183.43 inference(unit_resolution,[status(thm)],[9569, 9562])).
% 290.94/183.43 tff(9571,plain,
% 290.94/183.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_1, c_g, s0) | m_or_h_gate_v_in1(c_e_h_1, c_g, s0) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s1)) | (~node5(c_e_h_1, c_g, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_1, c_g, s0) | m_or_h_gate_v_in1(c_e_h_1, c_g, s0) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s1)) | (~node5(c_e_h_1, c_g, s0, s1)))),
% 290.94/183.43 inference(rewrite,[status(thm)],[])).
% 290.94/183.43 tff(9572,plain,
% 290.94/183.43 ((m_or_h_gate_v_in1(c_e_h_1, c_g, s0) | m_or_h_gate_v_in2(c_e_h_1, c_g, s0) | (~node5(c_e_h_1, c_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s1))) <=> (m_or_h_gate_v_in2(c_e_h_1, c_g, s0) | m_or_h_gate_v_in1(c_e_h_1, c_g, s0) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s1)) | (~node5(c_e_h_1, c_g, s0, s1)))),
% 290.94/183.43 inference(rewrite,[status(thm)],[])).
% 290.94/183.43 tff(9573,plain,
% 290.94/183.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_g, s0) | m_or_h_gate_v_in2(c_e_h_1, c_g, s0) | (~node5(c_e_h_1, c_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_1, c_g, s0) | m_or_h_gate_v_in1(c_e_h_1, c_g, s0) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s1)) | (~node5(c_e_h_1, c_g, s0, s1))))),
% 290.94/183.43 inference(monotonicity,[status(thm)],[9572])).
% 290.94/183.43 tff(9574,plain,
% 290.94/183.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_g, s0) | m_or_h_gate_v_in2(c_e_h_1, c_g, s0) | (~node5(c_e_h_1, c_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_1, c_g, s0) | m_or_h_gate_v_in1(c_e_h_1, c_g, s0) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s1)) | (~node5(c_e_h_1, c_g, s0, s1)))),
% 290.94/183.43 inference(transitivity,[status(thm)],[9573, 9571])).
% 290.94/183.43 tff(9575,plain,
% 290.94/183.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_g, s0) | m_or_h_gate_v_in2(c_e_h_1, c_g, s0) | (~node5(c_e_h_1, c_g, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s1)))),
% 290.94/183.43 inference(quant_inst,[status(thm)],[])).
% 290.94/183.43 tff(9576,plain,
% 290.94/183.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_1, c_g, s0) | m_or_h_gate_v_in1(c_e_h_1, c_g, s0) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s1)) | (~node5(c_e_h_1, c_g, s0, s1))),
% 290.94/183.43 inference(modus_ponens,[status(thm)],[9575, 9574])).
% 290.94/183.43 tff(9577,plain,
% 290.94/183.43 ($false),
% 290.94/183.43 inference(unit_resolution,[status(thm)],[9576, 1159, 9570, 9552, 9544, 9543])).
% 290.94/183.43 tff(9578,plain,(~m_or_h_gate_v_out(c_e_h_1, c_g, s1)), inference(lemma,lemma(discharge,[]))).
% 290.94/183.43 tff(9579,plain,
% 290.94/183.43 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_k, s1)) | m_or_h_gate_v_out(c_e_h_1, c_g, s1))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_k, s1)) | m_or_h_gate_v_out(c_e_h_1, c_g, s1))),
% 290.94/183.43 inference(rewrite,[status(thm)],[])).
% 290.94/183.43 tff(9580,plain,
% 290.94/183.43 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_k, s1)) | m_or_h_gate_v_out(c_e_h_1, c_g, s1))),
% 290.94/183.43 inference(quant_inst,[status(thm)],[])).
% 290.94/183.43 tff(9581,plain,
% 290.94/183.43 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_k, s1)) | m_or_h_gate_v_out(c_e_h_1, c_g, s1)),
% 290.94/183.43 inference(modus_ponens,[status(thm)],[9580, 9579])).
% 290.94/183.43 tff(9582,plain,
% 290.94/183.43 (~m_and_h_gate_v_in1(c_e_h_1, c_k, s1)),
% 290.94/183.43 inference(unit_resolution,[status(thm)],[9581, 2048, 9578])).
% 290.94/183.43 tff(9583,plain,
% 290.94/183.43 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_k, s1)) | m_and_h_gate_v_in1(c_e_h_1, c_k, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_k, s1)) | m_and_h_gate_v_in1(c_e_h_1, c_k, s1))),
% 290.94/183.43 inference(rewrite,[status(thm)],[])).
% 290.94/183.43 tff(9584,plain,
% 290.94/183.43 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_k, s1)) | m_and_h_gate_v_in1(c_e_h_1, c_k, s1))),
% 290.94/183.43 inference(quant_inst,[status(thm)],[])).
% 290.94/183.43 tff(9585,plain,
% 290.94/183.43 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_k, s1)) | m_and_h_gate_v_in1(c_e_h_1, c_k, s1)),
% 290.94/183.43 inference(modus_ponens,[status(thm)],[9584, 9583])).
% 290.94/183.43 tff(9586,plain,
% 290.94/183.43 (~node20(c_e_h_1, c_k, s1)),
% 290.94/183.43 inference(unit_resolution,[status(thm)],[9585, 38, 9582])).
% 290.94/183.43 tff(9587,assumption,(m_and_h_gate_v_out(c_e_h_1, c_k, s2)), introduced(assumption)).
% 290.94/183.43 tff(9588,assumption,(~node20(c_e_h_1, c_k, s1)), introduced(assumption)).
% 290.94/183.43 tff(9589,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_k, s1)), introduced(assumption)).
% 290.94/183.43 tff(9590,assumption,(node22(c_e_h_1, c_k, s1, s2)), introduced(assumption)).
% 290.94/183.43 tff(9591,plain,
% 290.94/183.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_k, s2)) | (~node22(c_e_h_1, c_k, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_k, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s2)) | (~node22(c_e_h_1, c_k, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_k, s1))),
% 290.94/183.43 inference(rewrite,[status(thm)],[])).
% 290.94/183.43 tff(9592,plain,
% 290.94/183.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_k, s2)) | (~node22(c_e_h_1, c_k, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_k, s1))),
% 290.94/183.43 inference(quant_inst,[status(thm)],[])).
% 290.94/183.43 tff(9593,plain,
% 290.94/183.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s2)) | (~node22(c_e_h_1, c_k, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_k, s1)),
% 290.94/183.43 inference(modus_ponens,[status(thm)],[9592, 9591])).
% 290.94/183.43 tff(9594,plain,
% 290.94/183.43 ($false),
% 290.94/183.43 inference(unit_resolution,[status(thm)],[9593, 108, 9590, 9589, 9587])).
% 290.94/183.43 tff(9595,plain,((~node22(c_e_h_1, c_k, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_k, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s2))), inference(lemma,lemma(discharge,[]))).
% 290.94/183.43 tff(9596,plain,
% 290.94/183.43 (~node22(c_e_h_1, c_k, s1, s2)),
% 290.94/183.43 inference(unit_resolution,[status(thm)],[9595, 9587, 9589])).
% 290.94/183.43 tff(9597,plain,
% 290.94/183.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_1, c_k, s1, s2) | node22(c_e_h_1, c_k, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_1, c_k, s1, s2) | node22(c_e_h_1, c_k, s1, s2))),
% 290.94/183.44 inference(rewrite,[status(thm)],[])).
% 290.94/183.44 tff(9598,plain,
% 290.94/183.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_1, c_k, s1, s2) | node22(c_e_h_1, c_k, s1, s2))),
% 290.94/183.44 inference(quant_inst,[status(thm)],[])).
% 290.94/183.44 tff(9599,plain,
% 290.94/183.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_1, c_k, s1, s2) | node22(c_e_h_1, c_k, s1, s2)),
% 290.94/183.44 inference(modus_ponens,[status(thm)],[9598, 9597])).
% 290.94/183.44 tff(9600,plain,
% 290.94/183.44 (node21(c_e_h_1, c_k, s1, s2) | node22(c_e_h_1, c_k, s1, s2)),
% 290.94/183.44 inference(unit_resolution,[status(thm)],[9599, 82, 255])).
% 290.94/183.44 tff(9601,plain,
% 290.94/183.44 (node21(c_e_h_1, c_k, s1, s2)),
% 290.94/183.44 inference(unit_resolution,[status(thm)],[9600, 9596])).
% 290.94/183.44 tff(9602,plain,
% 290.94/183.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_k, s2)) | node20(c_e_h_1, c_k, s1) | (~node21(c_e_h_1, c_k, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s2)) | node20(c_e_h_1, c_k, s1) | (~node21(c_e_h_1, c_k, s1, s2)))),
% 290.94/183.44 inference(rewrite,[status(thm)],[])).
% 290.94/183.44 tff(9603,plain,
% 290.94/183.44 ((node20(c_e_h_1, c_k, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s2)) | (~node21(c_e_h_1, c_k, s1, s2))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_k, s2)) | node20(c_e_h_1, c_k, s1) | (~node21(c_e_h_1, c_k, s1, s2)))),
% 290.94/183.44 inference(rewrite,[status(thm)],[])).
% 290.94/183.44 tff(9604,plain,
% 290.94/183.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_k, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s2)) | (~node21(c_e_h_1, c_k, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_k, s2)) | node20(c_e_h_1, c_k, s1) | (~node21(c_e_h_1, c_k, s1, s2))))),
% 290.94/183.44 inference(monotonicity,[status(thm)],[9603])).
% 290.94/183.44 tff(9605,plain,
% 290.94/183.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_k, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s2)) | (~node21(c_e_h_1, c_k, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s2)) | node20(c_e_h_1, c_k, s1) | (~node21(c_e_h_1, c_k, s1, s2)))),
% 290.94/183.44 inference(transitivity,[status(thm)],[9604, 9602])).
% 290.94/183.44 tff(9606,plain,
% 290.94/183.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_k, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s2)) | (~node21(c_e_h_1, c_k, s1, s2)))),
% 290.94/183.44 inference(quant_inst,[status(thm)],[])).
% 290.94/183.44 tff(9607,plain,
% 290.94/183.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s2)) | node20(c_e_h_1, c_k, s1) | (~node21(c_e_h_1, c_k, s1, s2))),
% 290.94/183.44 inference(modus_ponens,[status(thm)],[9606, 9605])).
% 290.94/183.44 tff(9608,plain,
% 290.94/183.44 ($false),
% 290.94/183.44 inference(unit_resolution,[status(thm)],[9607, 52, 9601, 9588, 9587])).
% 290.94/183.44 tff(9609,plain,((~m_and_h_gate_v_out(c_e_h_1, c_k, s2)) | node20(c_e_h_1, c_k, s1) | m_and_h_gate_v_out(c_e_h_1, c_k, s1)), inference(lemma,lemma(discharge,[]))).
% 290.94/183.44 tff(9610,plain,
% 290.94/183.44 ((~m_and_h_gate_v_out(c_e_h_1, c_k, s2)) | m_and_h_gate_v_out(c_e_h_1, c_k, s1)),
% 290.94/183.44 inference(unit_resolution,[status(thm)],[9609, 9586])).
% 290.94/183.44 tff(9611,plain,
% 290.94/183.44 (~m_and_h_gate_v_out(c_e_h_1, c_k, s2)),
% 290.94/183.44 inference(unit_resolution,[status(thm)],[9610, 3160])).
% 290.94/183.44 tff(9612,plain,
% 290.94/183.44 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_p, s2)) | m_and_h_gate_v_out(c_e_h_1, c_k, s2))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s2)) | m_and_h_gate_v_out(c_e_h_1, c_k, s2))),
% 290.94/183.44 inference(rewrite,[status(thm)],[])).
% 290.94/183.44 tff(9613,plain,
% 290.94/183.44 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_p, s2)) | m_and_h_gate_v_out(c_e_h_1, c_k, s2))),
% 290.94/183.44 inference(quant_inst,[status(thm)],[])).
% 290.94/183.44 tff(9614,plain,
% 290.94/183.44 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s2)) | m_and_h_gate_v_out(c_e_h_1, c_k, s2)),
% 290.94/183.44 inference(modus_ponens,[status(thm)],[9613, 9612])).
% 290.94/183.44 tff(9615,plain,
% 290.94/183.44 ($false),
% 290.94/183.44 inference(unit_resolution,[status(thm)],[9614, 3033, 9611, 9539])).
% 290.94/183.44 tff(9616,plain,(~m_and_h_gate_v_in1(c_e_h_1, c_p, s2)), inference(lemma,lemma(discharge,[]))).
% 290.94/183.44 tff(9617,plain,
% 290.94/183.44 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_p, s2)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_p, s2)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s2))),
% 290.94/183.44 inference(rewrite,[status(thm)],[])).
% 290.94/183.44 tff(9618,plain,
% 290.94/183.44 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_p, s2)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s2))),
% 290.94/183.44 inference(quant_inst,[status(thm)],[])).
% 290.94/183.44 tff(9619,plain,
% 290.94/183.44 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_p, s2)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s2)),
% 290.94/183.44 inference(modus_ponens,[status(thm)],[9618, 9617])).
% 290.94/183.44 tff(9620,plain,
% 290.94/183.44 (~node20(c_e_h_1, c_p, s2)),
% 290.94/183.44 inference(unit_resolution,[status(thm)],[9619, 38, 9616])).
% 290.94/183.44 tff(9621,assumption,(~node20(c_e_h_1, c_p, s2)), introduced(assumption)).
% 290.94/183.44 tff(9622,assumption,(node21(c_e_h_1, c_p, s2, s3)), introduced(assumption)).
% 290.94/183.44 tff(9623,plain,
% 290.94/183.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_p, s3)) | (~node21(c_e_h_1, c_p, s2, s3)) | node20(c_e_h_1, c_p, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s3)) | (~node21(c_e_h_1, c_p, s2, s3)) | node20(c_e_h_1, c_p, s2))),
% 290.94/183.44 inference(rewrite,[status(thm)],[])).
% 290.94/183.44 tff(9624,plain,
% 290.94/183.44 ((node20(c_e_h_1, c_p, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s3)) | (~node21(c_e_h_1, c_p, s2, s3))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_p, s3)) | (~node21(c_e_h_1, c_p, s2, s3)) | node20(c_e_h_1, c_p, s2))),
% 290.94/183.44 inference(rewrite,[status(thm)],[])).
% 290.94/183.44 tff(9625,plain,
% 290.94/183.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_p, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s3)) | (~node21(c_e_h_1, c_p, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_p, s3)) | (~node21(c_e_h_1, c_p, s2, s3)) | node20(c_e_h_1, c_p, s2)))),
% 290.94/183.44 inference(monotonicity,[status(thm)],[9624])).
% 290.94/183.44 tff(9626,plain,
% 290.94/183.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_p, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s3)) | (~node21(c_e_h_1, c_p, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s3)) | (~node21(c_e_h_1, c_p, s2, s3)) | node20(c_e_h_1, c_p, s2))),
% 290.94/183.44 inference(transitivity,[status(thm)],[9625, 9623])).
% 290.94/183.44 tff(9627,plain,
% 290.94/183.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_p, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s3)) | (~node21(c_e_h_1, c_p, s2, s3)))),
% 290.94/183.44 inference(quant_inst,[status(thm)],[])).
% 290.94/183.44 tff(9628,plain,
% 290.94/183.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s3)) | (~node21(c_e_h_1, c_p, s2, s3)) | node20(c_e_h_1, c_p, s2)),
% 290.94/183.44 inference(modus_ponens,[status(thm)],[9627, 9626])).
% 290.94/183.44 tff(9629,plain,
% 290.94/183.44 ($false),
% 290.94/183.44 inference(unit_resolution,[status(thm)],[9628, 52, 9622, 9538, 9621])).
% 290.94/183.44 tff(9630,plain,((~node21(c_e_h_1, c_p, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s3)) | node20(c_e_h_1, c_p, s2)), inference(lemma,lemma(discharge,[]))).
% 290.94/183.44 tff(9631,plain,
% 290.94/183.44 ((~node21(c_e_h_1, c_p, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s3))),
% 290.94/183.44 inference(unit_resolution,[status(thm)],[9630, 9620])).
% 290.94/183.44 tff(9632,plain,
% 290.94/183.44 (~node21(c_e_h_1, c_p, s2, s3)),
% 290.94/183.44 inference(unit_resolution,[status(thm)],[9631, 9538])).
% 290.94/183.44 tff(9633,assumption,(node22(c_e_h_1, c_p, s2, s3)), introduced(assumption)).
% 290.94/183.45 tff(9634,plain,
% 290.94/183.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_p, s3)) | (~node22(c_e_h_1, c_p, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_p, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s3)) | (~node22(c_e_h_1, c_p, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_p, s2))),
% 290.94/183.45 inference(rewrite,[status(thm)],[])).
% 290.94/183.45 tff(9635,plain,
% 290.94/183.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_p, s3)) | (~node22(c_e_h_1, c_p, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_p, s2))),
% 290.94/183.45 inference(quant_inst,[status(thm)],[])).
% 290.94/183.45 tff(9636,plain,
% 290.94/183.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s3)) | (~node22(c_e_h_1, c_p, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_p, s2)),
% 290.94/183.45 inference(modus_ponens,[status(thm)],[9635, 9634])).
% 290.94/183.45 tff(9637,plain,
% 290.94/183.45 ($false),
% 290.94/183.45 inference(unit_resolution,[status(thm)],[9636, 108, 9633, 9538, 3192])).
% 290.94/183.45 tff(9638,plain,((~node22(c_e_h_1, c_p, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s3)) | m_and_h_gate_v_out(c_e_h_1, c_p, s2)), inference(lemma,lemma(discharge,[]))).
% 290.94/183.45 tff(9639,plain,
% 290.94/183.45 (~node22(c_e_h_1, c_p, s2, s3)),
% 290.94/183.45 inference(unit_resolution,[status(thm)],[9638, 9538, 3192])).
% 290.94/183.45 tff(9640,plain,
% 290.94/183.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_1, c_p, s2, s3) | node22(c_e_h_1, c_p, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_1, c_p, s2, s3) | node22(c_e_h_1, c_p, s2, s3))),
% 290.94/183.45 inference(rewrite,[status(thm)],[])).
% 290.94/183.45 tff(9641,plain,
% 290.94/183.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_1, c_p, s2, s3) | node22(c_e_h_1, c_p, s2, s3))),
% 290.94/183.45 inference(quant_inst,[status(thm)],[])).
% 290.94/183.45 tff(9642,plain,
% 290.94/183.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_1, c_p, s2, s3) | node22(c_e_h_1, c_p, s2, s3)),
% 290.94/183.45 inference(modus_ponens,[status(thm)],[9641, 9640])).
% 290.94/183.45 tff(9643,plain,
% 290.94/183.45 (node21(c_e_h_1, c_p, s2, s3) | node22(c_e_h_1, c_p, s2, s3)),
% 290.94/183.45 inference(unit_resolution,[status(thm)],[9642, 82, 318])).
% 290.94/183.45 tff(9644,plain,
% 290.94/183.45 ($false),
% 290.94/183.45 inference(unit_resolution,[status(thm)],[9643, 9639, 9632])).
% 290.94/183.45 tff(9645,plain,((~m_and_h_gate_v_out(c_e_h_1, c_p, s3)) | m_and_h_gate_v_out(c_e_h_1, c_p, s2)), inference(lemma,lemma(discharge,[]))).
% 290.94/183.45 tff(9646,plain,
% 290.94/183.45 (~m_and_h_gate_v_out(c_e_h_1, c_p, s3)),
% 290.94/183.45 inference(unit_resolution,[status(thm)],[9645, 3191])).
% 290.94/183.45 tff(9647,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_p, s3)), introduced(assumption)).
% 290.94/183.45 tff(9648,assumption,(m_cell_v_req(c_e_h_1, s3)), introduced(assumption)).
% 290.94/183.45 tff(9649,plain,
% 290.94/183.45 (((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | ((~m_cell_v_req(c_e_h_1, s3)) | m_and_h_gate_v_out(c_e_h_1, c_p, s3))) <=> ((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | (~m_cell_v_req(c_e_h_1, s3)) | m_and_h_gate_v_out(c_e_h_1, c_p, s3))),
% 290.94/183.45 inference(rewrite,[status(thm)],[])).
% 290.94/183.45 tff(9650,plain,
% 290.94/183.45 ((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | ((~m_cell_v_req(c_e_h_1, s3)) | m_and_h_gate_v_out(c_e_h_1, c_p, s3))),
% 290.94/183.45 inference(quant_inst,[status(thm)],[])).
% 290.94/183.45 tff(9651,plain,
% 290.94/183.45 ((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | (~m_cell_v_req(c_e_h_1, s3)) | m_and_h_gate_v_out(c_e_h_1, c_p, s3)),
% 290.94/183.45 inference(modus_ponens,[status(thm)],[9650, 9649])).
% 290.94/183.45 tff(9652,plain,
% 290.94/183.45 ($false),
% 290.94/183.45 inference(unit_resolution,[status(thm)],[9651, 2908, 9648, 9647])).
% 290.94/183.45 tff(9653,plain,((~m_cell_v_req(c_e_h_1, s3)) | m_and_h_gate_v_out(c_e_h_1, c_p, s3)), inference(lemma,lemma(discharge,[]))).
% 290.94/183.45 tff(9654,plain,
% 290.94/183.45 (~m_cell_v_req(c_e_h_1, s3)),
% 290.94/183.45 inference(unit_resolution,[status(thm)],[9653, 9646])).
% 290.94/183.45 tff(9655,plain,
% 290.94/183.45 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node1(c_e_h_3, c_e_h_1, s3))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node1(c_e_h_3, c_e_h_1, s3))),
% 290.94/183.45 inference(rewrite,[status(thm)],[])).
% 290.94/183.45 tff(9656,plain,
% 290.94/183.45 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node1(c_e_h_3, c_e_h_1, s3))),
% 290.94/183.45 inference(quant_inst,[status(thm)],[])).
% 290.94/183.45 tff(9657,plain,
% 290.94/183.45 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node1(c_e_h_3, c_e_h_1, s3)),
% 290.94/183.45 inference(modus_ponens,[status(thm)],[9656, 9655])).
% 290.94/183.45 tff(9658,plain,
% 290.94/183.45 (node1(c_e_h_3, c_e_h_1, s3)),
% 290.94/183.45 inference(unit_resolution,[status(thm)],[9657, 2922, 2919])).
% 290.94/183.45 tff(9659,plain,
% 290.94/183.45 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_3, c_e_h_1, s3)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s3)) | m_cell_v_req(c_e_h_1, s3))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | (~node1(c_e_h_3, c_e_h_1, s3)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s3)) | m_cell_v_req(c_e_h_1, s3))),
% 290.94/183.45 inference(rewrite,[status(thm)],[])).
% 290.94/183.45 tff(9660,plain,
% 290.94/183.45 (((~node1(c_e_h_3, c_e_h_1, s3)) | m_cell_v_req(c_e_h_1, s3) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s3))) <=> ((~node1(c_e_h_3, c_e_h_1, s3)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s3)) | m_cell_v_req(c_e_h_1, s3))),
% 290.94/183.45 inference(rewrite,[status(thm)],[])).
% 290.94/183.45 tff(9661,plain,
% 290.94/183.45 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_3, c_e_h_1, s3)) | m_cell_v_req(c_e_h_1, s3) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s3)))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_3, c_e_h_1, s3)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s3)) | m_cell_v_req(c_e_h_1, s3)))),
% 290.94/183.45 inference(monotonicity,[status(thm)],[9660])).
% 290.94/183.45 tff(9662,plain,
% 290.94/183.45 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_3, c_e_h_1, s3)) | m_cell_v_req(c_e_h_1, s3) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s3)))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | (~node1(c_e_h_3, c_e_h_1, s3)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s3)) | m_cell_v_req(c_e_h_1, s3))),
% 290.94/183.45 inference(transitivity,[status(thm)],[9661, 9659])).
% 290.94/183.45 tff(9663,plain,
% 290.94/183.45 ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_3, c_e_h_1, s3)) | m_cell_v_req(c_e_h_1, s3) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s3)))),
% 290.94/183.45 inference(quant_inst,[status(thm)],[])).
% 290.94/183.45 tff(9664,plain,
% 290.94/183.45 ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | (~node1(c_e_h_3, c_e_h_1, s3)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s3)) | m_cell_v_req(c_e_h_1, s3)),
% 290.94/183.45 inference(modus_ponens,[status(thm)],[9663, 9662])).
% 290.94/183.45 tff(9665,plain,
% 290.94/183.45 ((~m_mutex_h_half_v_inp(c_e_h_3, c_b, s3)) | m_cell_v_req(c_e_h_1, s3)),
% 290.94/183.45 inference(unit_resolution,[status(thm)],[9664, 2936, 9658])).
% 290.94/183.45 tff(9666,plain,
% 290.94/183.45 (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s3)),
% 290.94/183.45 inference(unit_resolution,[status(thm)],[9665, 9654])).
% 290.94/183.45 tff(9667,assumption,(m_and_h_gate_v_out(c_e_h_3, c_d, s5)), introduced(assumption)).
% 290.94/183.45 tff(9668,plain,
% 290.94/183.45 (~m_and_h_gate_v_in1(c_e_h_3, c_d, s3)),
% 290.94/183.45 inference(unit_resolution,[status(thm)],[3242, 3237])).
% 290.94/183.46 tff(9669,plain,
% 290.94/183.46 (~node20(c_e_h_3, c_d, s3)),
% 290.94/183.46 inference(unit_resolution,[status(thm)],[3250, 9668])).
% 290.94/183.46 tff(9670,plain,
% 290.94/183.46 (~m_and_h_gate_v_out(c_e_h_3, c_d, s4)),
% 290.94/183.46 inference(unit_resolution,[status(thm)],[3279, 9669, 3255])).
% 290.94/183.46 tff(9671,assumption,(~m_mutex_h_half_v_inp(c_e_h_3, c_b, s3)), introduced(assumption)).
% 290.94/183.46 tff(9672,assumption,(m_mutex_h_half_v_out(c_e_h_3, c_b, s4)), introduced(assumption)).
% 290.94/183.46 tff(9673,assumption,(node13(c_e_h_3, c_b, s3, s4)), introduced(assumption)).
% 290.94/183.46 tff(9674,plain,
% 290.94/183.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_b, s4)) | (~node13(c_e_h_3, c_b, s3, s4)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s4)) | (~node13(c_e_h_3, c_b, s3, s4)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s3))),
% 290.94/183.46 inference(rewrite,[status(thm)],[])).
% 290.94/183.46 tff(9675,plain,
% 290.94/183.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_b, s4)) | (~node13(c_e_h_3, c_b, s3, s4)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s3))),
% 290.94/183.46 inference(quant_inst,[status(thm)],[])).
% 290.94/183.46 tff(9676,plain,
% 290.94/183.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s4)) | (~node13(c_e_h_3, c_b, s3, s4)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s3)),
% 290.94/183.46 inference(modus_ponens,[status(thm)],[9675, 9674])).
% 290.94/183.46 tff(9677,plain,
% 290.94/183.46 ($false),
% 290.94/183.46 inference(unit_resolution,[status(thm)],[9676, 423, 9673, 3237, 9672])).
% 290.94/183.46 tff(9678,plain,((~node13(c_e_h_3, c_b, s3, s4)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s3) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s4))), inference(lemma,lemma(discharge,[]))).
% 290.94/183.46 tff(9679,plain,
% 290.94/183.46 (~node13(c_e_h_3, c_b, s3, s4)),
% 290.94/183.46 inference(unit_resolution,[status(thm)],[9678, 9672, 3237])).
% 290.94/183.46 tff(9680,plain,
% 290.94/183.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s3, s4)) | node12(c_e_h_3, c_b, s3, s4) | node13(c_e_h_3, c_b, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s3, s4)) | node12(c_e_h_3, c_b, s3, s4) | node13(c_e_h_3, c_b, s3, s4))),
% 290.94/183.46 inference(rewrite,[status(thm)],[])).
% 290.94/183.46 tff(9681,plain,
% 290.94/183.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s3, s4)) | node12(c_e_h_3, c_b, s3, s4) | node13(c_e_h_3, c_b, s3, s4))),
% 290.94/183.46 inference(quant_inst,[status(thm)],[])).
% 290.94/183.46 tff(9682,plain,
% 290.94/183.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s3, s4)) | node12(c_e_h_3, c_b, s3, s4) | node13(c_e_h_3, c_b, s3, s4)),
% 290.94/183.46 inference(modus_ponens,[status(thm)],[9681, 9680])).
% 290.94/183.46 tff(9683,plain,
% 290.94/183.46 (node12(c_e_h_3, c_b, s3, s4) | node13(c_e_h_3, c_b, s3, s4)),
% 290.94/183.46 inference(unit_resolution,[status(thm)],[9682, 439, 531])).
% 290.94/183.46 tff(9684,plain,
% 290.94/183.46 (node12(c_e_h_3, c_b, s3, s4)),
% 290.94/183.46 inference(unit_resolution,[status(thm)],[9683, 9679])).
% 290.94/183.46 tff(9685,plain,
% 290.94/183.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_3, c_b, s3) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s4)) | (~node12(c_e_h_3, c_b, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s3) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s4)) | (~node12(c_e_h_3, c_b, s3, s4)))),
% 290.94/183.46 inference(rewrite,[status(thm)],[])).
% 290.94/183.46 tff(9686,plain,
% 290.94/183.46 (((~node12(c_e_h_3, c_b, s3, s4)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s3) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s4))) <=> (m_mutex_h_half_v_inp(c_e_h_3, c_b, s3) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s4)) | (~node12(c_e_h_3, c_b, s3, s4)))),
% 290.94/183.46 inference(rewrite,[status(thm)],[])).
% 290.94/183.46 tff(9687,plain,
% 290.94/183.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_b, s3, s4)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s3) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_3, c_b, s3) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s4)) | (~node12(c_e_h_3, c_b, s3, s4))))),
% 290.94/183.46 inference(monotonicity,[status(thm)],[9686])).
% 290.94/183.46 tff(9688,plain,
% 290.94/183.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_b, s3, s4)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s3) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s3) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s4)) | (~node12(c_e_h_3, c_b, s3, s4)))),
% 290.94/183.46 inference(transitivity,[status(thm)],[9687, 9685])).
% 290.94/183.46 tff(9689,plain,
% 290.94/183.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_b, s3, s4)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s3) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s4)))),
% 290.94/183.46 inference(quant_inst,[status(thm)],[])).
% 290.94/183.46 tff(9690,plain,
% 290.94/183.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s3) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s4)) | (~node12(c_e_h_3, c_b, s3, s4))),
% 290.94/183.46 inference(modus_ponens,[status(thm)],[9689, 9688])).
% 290.94/183.46 tff(9691,plain,
% 290.94/183.46 ($false),
% 290.94/183.46 inference(unit_resolution,[status(thm)],[9690, 454, 9671, 9684, 9672])).
% 290.94/183.46 tff(9692,plain,((~m_mutex_h_half_v_out(c_e_h_3, c_b, s4)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s3) | m_mutex_h_half_v_out(c_e_h_3, c_b, s3)), inference(lemma,lemma(discharge,[]))).
% 290.94/183.46 tff(9693,plain,
% 290.94/183.46 (~m_mutex_h_half_v_out(c_e_h_3, c_b, s4)),
% 290.94/183.46 inference(unit_resolution,[status(thm)],[9692, 3237, 9671])).
% 290.94/183.46 tff(9694,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_d, s4)), introduced(assumption)).
% 290.94/183.46 tff(9695,assumption,(~m_mutex_h_half_v_out(c_e_h_3, c_b, s4)), introduced(assumption)).
% 290.94/183.46 tff(9696,plain,
% 290.94/183.46 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_d, s4)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s4))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_d, s4)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s4))),
% 290.94/183.46 inference(rewrite,[status(thm)],[])).
% 290.94/183.46 tff(9697,plain,
% 290.94/183.46 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_d, s4)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s4))),
% 290.94/183.46 inference(quant_inst,[status(thm)],[])).
% 290.94/183.46 tff(9698,plain,
% 290.94/183.46 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_d, s4)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s4)),
% 290.94/183.46 inference(modus_ponens,[status(thm)],[9697, 9696])).
% 290.94/183.46 tff(9699,plain,
% 290.94/183.46 ($false),
% 290.94/183.46 inference(unit_resolution,[status(thm)],[9698, 2808, 9695, 9694])).
% 290.94/183.46 tff(9700,plain,((~m_and_h_gate_v_in1(c_e_h_3, c_d, s4)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s4)), inference(lemma,lemma(discharge,[]))).
% 290.94/183.46 tff(9701,plain,
% 290.94/183.46 (~m_and_h_gate_v_in1(c_e_h_3, c_d, s4)),
% 290.94/183.46 inference(unit_resolution,[status(thm)],[9700, 9693])).
% 290.94/183.46 tff(9702,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_d, s4)), introduced(assumption)).
% 290.94/183.46 tff(9703,assumption,(node20(c_e_h_3, c_d, s4)), introduced(assumption)).
% 290.94/183.46 tff(9704,plain,
% 290.94/183.46 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_d, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_d, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s4))),
% 290.94/183.46 inference(rewrite,[status(thm)],[])).
% 290.94/183.46 tff(9705,plain,
% 290.94/183.46 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_d, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s4))),
% 290.94/183.46 inference(quant_inst,[status(thm)],[])).
% 290.94/183.46 tff(9706,plain,
% 290.94/183.46 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_d, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s4)),
% 290.94/183.46 inference(modus_ponens,[status(thm)],[9705, 9704])).
% 290.94/183.46 tff(9707,plain,
% 290.94/183.46 ($false),
% 290.94/183.46 inference(unit_resolution,[status(thm)],[9706, 38, 9703, 9702])).
% 290.94/183.46 tff(9708,plain,((~node20(c_e_h_3, c_d, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s4)), inference(lemma,lemma(discharge,[]))).
% 290.94/183.46 tff(9709,plain,
% 290.94/183.46 (~node20(c_e_h_3, c_d, s4)),
% 290.94/183.46 inference(unit_resolution,[status(thm)],[9708, 9701])).
% 290.94/183.46 tff(9710,assumption,(~node20(c_e_h_3, c_d, s4)), introduced(assumption)).
% 290.94/183.46 tff(9711,assumption,(node21(c_e_h_3, c_d, s4, s5)), introduced(assumption)).
% 290.94/183.46 tff(9712,plain,
% 290.94/183.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_d, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s5)) | (~node21(c_e_h_3, c_d, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_d, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s5)) | (~node21(c_e_h_3, c_d, s4, s5)))),
% 290.94/183.46 inference(rewrite,[status(thm)],[])).
% 290.94/183.46 tff(9713,plain,
% 290.94/183.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_d, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s5)) | (~node21(c_e_h_3, c_d, s4, s5)))),
% 290.94/183.46 inference(quant_inst,[status(thm)],[])).
% 290.94/183.46 tff(9714,plain,
% 290.94/183.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_d, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s5)) | (~node21(c_e_h_3, c_d, s4, s5))),
% 290.94/183.46 inference(modus_ponens,[status(thm)],[9713, 9712])).
% 290.94/183.46 tff(9715,plain,
% 290.94/183.46 ($false),
% 290.94/183.46 inference(unit_resolution,[status(thm)],[9714, 52, 9711, 9667, 9710])).
% 290.94/183.46 tff(9716,plain,((~node21(c_e_h_3, c_d, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s5)) | node20(c_e_h_3, c_d, s4)), inference(lemma,lemma(discharge,[]))).
% 290.94/183.46 tff(9717,plain,
% 290.94/183.46 (~node21(c_e_h_3, c_d, s4, s5)),
% 290.94/183.46 inference(unit_resolution,[status(thm)],[9716, 9667, 9710])).
% 290.94/183.46 tff(9718,plain,
% 290.94/183.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_3, c_d, s4, s5) | node22(c_e_h_3, c_d, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_3, c_d, s4, s5) | node22(c_e_h_3, c_d, s4, s5))),
% 290.94/183.46 inference(rewrite,[status(thm)],[])).
% 290.94/183.46 tff(9719,plain,
% 290.94/183.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_3, c_d, s4, s5) | node22(c_e_h_3, c_d, s4, s5))),
% 290.94/183.46 inference(quant_inst,[status(thm)],[])).
% 290.94/183.46 tff(9720,plain,
% 290.94/183.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_3, c_d, s4, s5) | node22(c_e_h_3, c_d, s4, s5)),
% 290.94/183.46 inference(modus_ponens,[status(thm)],[9719, 9718])).
% 290.94/183.46 tff(9721,plain,
% 290.94/183.46 (node21(c_e_h_3, c_d, s4, s5) | node22(c_e_h_3, c_d, s4, s5)),
% 290.94/183.46 inference(unit_resolution,[status(thm)],[9720, 82, 1028])).
% 290.94/183.46 tff(9722,plain,
% 290.94/183.46 (node22(c_e_h_3, c_d, s4, s5)),
% 290.94/183.46 inference(unit_resolution,[status(thm)],[9721, 9717])).
% 290.94/183.46 tff(9723,plain,
% 290.94/183.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_d, s5)) | (~node22(c_e_h_3, c_d, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_d, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s5)) | (~node22(c_e_h_3, c_d, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_d, s4))),
% 290.94/183.46 inference(rewrite,[status(thm)],[])).
% 290.94/183.46 tff(9724,plain,
% 290.94/183.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_d, s5)) | (~node22(c_e_h_3, c_d, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_d, s4))),
% 290.94/183.46 inference(quant_inst,[status(thm)],[])).
% 290.94/183.46 tff(9725,plain,
% 290.94/183.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s5)) | (~node22(c_e_h_3, c_d, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_d, s4)),
% 290.94/183.46 inference(modus_ponens,[status(thm)],[9724, 9723])).
% 290.94/183.46 tff(9726,plain,
% 290.94/183.46 ($false),
% 290.94/183.46 inference(unit_resolution,[status(thm)],[9725, 108, 9722, 3282, 9667])).
% 290.94/183.46 tff(9727,plain,((~m_and_h_gate_v_out(c_e_h_3, c_d, s5)) | m_and_h_gate_v_out(c_e_h_3, c_d, s4) | node20(c_e_h_3, c_d, s4)), inference(lemma,lemma(discharge,[]))).
% 290.94/183.46 tff(9728,plain,
% 290.94/183.46 ($false),
% 290.94/183.46 inference(unit_resolution,[status(thm)],[9727, 9709, 9670, 9667])).
% 290.94/183.46 tff(9729,plain,(m_mutex_h_half_v_out(c_e_h_3, c_b, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s5)) | m_and_h_gate_v_out(c_e_h_3, c_d, s3) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s3)), inference(lemma,lemma(discharge,[]))).
% 290.94/183.46 tff(9730,plain,
% 290.94/183.46 (m_mutex_h_half_v_out(c_e_h_3, c_b, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s5)) | m_and_h_gate_v_out(c_e_h_3, c_d, s3)),
% 290.94/183.46 inference(unit_resolution,[status(thm)],[9729, 9666])).
% 290.94/183.46 tff(9731,plain,
% 290.94/183.46 ((~m_and_h_gate_v_out(c_e_h_3, c_d, s5)) | m_and_h_gate_v_out(c_e_h_3, c_d, s3)),
% 290.94/183.46 inference(unit_resolution,[status(thm)],[9730, 3235])).
% 290.94/183.46 tff(9732,plain,
% 290.94/183.46 (~m_and_h_gate_v_out(c_e_h_3, c_d, s5)),
% 290.94/183.46 inference(unit_resolution,[status(thm)],[9731, 3125])).
% 290.94/183.46 tff(9733,assumption,(m_or_h_gate_v_in2(c_e_h_3, c_g, s5)), introduced(assumption)).
% 290.94/183.46 tff(9734,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_d, s5)), introduced(assumption)).
% 290.94/183.46 tff(9735,plain,
% 290.94/183.46 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_g, s5)) | m_and_h_gate_v_out(c_e_h_3, c_d, s5))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_g, s5)) | m_and_h_gate_v_out(c_e_h_3, c_d, s5))),
% 290.94/183.46 inference(rewrite,[status(thm)],[])).
% 290.94/183.46 tff(9736,plain,
% 290.94/183.46 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_g, s5)) | m_and_h_gate_v_out(c_e_h_3, c_d, s5))),
% 290.94/183.46 inference(quant_inst,[status(thm)],[])).
% 290.94/183.46 tff(9737,plain,
% 290.94/183.46 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_g, s5)) | m_and_h_gate_v_out(c_e_h_3, c_d, s5)),
% 290.94/183.46 inference(modus_ponens,[status(thm)],[9736, 9735])).
% 290.94/183.46 tff(9738,plain,
% 290.94/183.46 ($false),
% 290.94/183.46 inference(unit_resolution,[status(thm)],[9737, 2762, 9734, 9733])).
% 290.94/183.46 tff(9739,plain,((~m_or_h_gate_v_in2(c_e_h_3, c_g, s5)) | m_and_h_gate_v_out(c_e_h_3, c_d, s5)), inference(lemma,lemma(discharge,[]))).
% 290.94/183.46 tff(9740,plain,
% 290.94/183.46 (~m_or_h_gate_v_in2(c_e_h_3, c_g, s5)),
% 290.94/183.46 inference(unit_resolution,[status(thm)],[9739, 9732])).
% 290.94/183.46 tff(9741,assumption,(m_mutex_h_half_v_out(c_e_h_3, c_b, s5)), introduced(assumption)).
% 290.94/183.46 tff(9742,assumption,(m_and_h_gate_v_out(c_e_h_1, c_k, s3)), introduced(assumption)).
% 290.94/183.46 tff(9743,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_k, s2)), introduced(assumption)).
% 290.94/183.46 tff(9744,assumption,(m_mutex_h_half_v_out(c_e_h_1, c_b, s0)), introduced(assumption)).
% 290.94/183.46 tff(9745,plain,
% 290.94/183.46 ((~![I0: $i, I1: $i] : (~m_mutex_h_half_v_out(I0, I1, s0))) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s0))),
% 290.94/183.46 inference(quant_inst,[status(thm)],[])).
% 290.94/183.46 tff(9746,plain,
% 290.94/183.46 ($false),
% 290.94/183.47 inference(unit_resolution,[status(thm)],[9745, 409, 9744])).
% 290.94/183.47 tff(9747,plain,(~m_mutex_h_half_v_out(c_e_h_1, c_b, s0)), inference(lemma,lemma(discharge,[]))).
% 290.94/183.47 tff(9748,plain,
% 290.94/183.47 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_d, s0)) | m_mutex_h_half_v_out(c_e_h_1, c_b, s0))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_d, s0)) | m_mutex_h_half_v_out(c_e_h_1, c_b, s0))),
% 290.94/183.47 inference(rewrite,[status(thm)],[])).
% 290.94/183.47 tff(9749,plain,
% 290.94/183.47 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_d, s0)) | m_mutex_h_half_v_out(c_e_h_1, c_b, s0))),
% 290.94/183.47 inference(quant_inst,[status(thm)],[])).
% 290.94/183.47 tff(9750,plain,
% 290.94/183.47 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_d, s0)) | m_mutex_h_half_v_out(c_e_h_1, c_b, s0)),
% 290.94/183.47 inference(modus_ponens,[status(thm)],[9749, 9748])).
% 290.94/183.47 tff(9751,plain,
% 290.94/183.47 (~m_and_h_gate_v_in1(c_e_h_1, c_d, s0)),
% 290.94/183.47 inference(unit_resolution,[status(thm)],[9750, 2808, 9747])).
% 290.94/183.47 tff(9752,plain,
% 290.94/183.47 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_d, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_d, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_d, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_d, s0))),
% 290.94/183.47 inference(rewrite,[status(thm)],[])).
% 290.94/183.47 tff(9753,plain,
% 290.94/183.47 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_d, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_d, s0))),
% 290.94/183.47 inference(quant_inst,[status(thm)],[])).
% 290.94/183.47 tff(9754,plain,
% 290.94/183.47 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_d, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_d, s0)),
% 290.94/183.47 inference(modus_ponens,[status(thm)],[9753, 9752])).
% 290.94/183.47 tff(9755,plain,
% 290.94/183.47 (~node20(c_e_h_1, c_d, s0)),
% 290.94/183.47 inference(unit_resolution,[status(thm)],[9754, 38, 9751])).
% 290.94/183.47 tff(9756,assumption,(m_and_h_gate_v_out(c_e_h_1, c_d, s1)), introduced(assumption)).
% 290.94/183.47 tff(9757,assumption,(node22(c_e_h_1, c_d, s0, s1)), introduced(assumption)).
% 290.94/183.47 tff(9758,plain,
% 290.94/183.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_d, s1)) | (~node22(c_e_h_1, c_d, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_d, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s1)) | (~node22(c_e_h_1, c_d, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_d, s0))),
% 290.94/183.47 inference(rewrite,[status(thm)],[])).
% 290.94/183.47 tff(9759,plain,
% 290.94/183.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_d, s1)) | (~node22(c_e_h_1, c_d, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_d, s0))),
% 290.94/183.47 inference(quant_inst,[status(thm)],[])).
% 290.94/183.47 tff(9760,plain,
% 290.94/183.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s1)) | (~node22(c_e_h_1, c_d, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_d, s0)),
% 290.94/183.47 inference(modus_ponens,[status(thm)],[9759, 9758])).
% 290.94/183.47 tff(9761,plain,
% 290.94/183.47 ($false),
% 290.94/183.47 inference(unit_resolution,[status(thm)],[9760, 108, 5044, 9757, 9756])).
% 290.94/183.47 tff(9762,plain,((~node22(c_e_h_1, c_d, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s1))), inference(lemma,lemma(discharge,[]))).
% 290.94/183.47 tff(9763,plain,
% 290.94/183.47 (~node22(c_e_h_1, c_d, s0, s1)),
% 290.94/183.47 inference(unit_resolution,[status(thm)],[9762, 9756])).
% 290.94/183.47 tff(9764,plain,
% 290.94/183.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_1, c_d, s0, s1) | node22(c_e_h_1, c_d, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_1, c_d, s0, s1) | node22(c_e_h_1, c_d, s0, s1))),
% 290.94/183.47 inference(rewrite,[status(thm)],[])).
% 290.94/183.47 tff(9765,plain,
% 290.94/183.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_1, c_d, s0, s1) | node22(c_e_h_1, c_d, s0, s1))),
% 290.94/183.47 inference(quant_inst,[status(thm)],[])).
% 290.94/183.47 tff(9766,plain,
% 290.94/183.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_1, c_d, s0, s1) | node22(c_e_h_1, c_d, s0, s1)),
% 290.94/183.47 inference(modus_ponens,[status(thm)],[9765, 9764])).
% 290.94/183.47 tff(9767,plain,
% 290.94/183.47 (node21(c_e_h_1, c_d, s0, s1) | node22(c_e_h_1, c_d, s0, s1)),
% 290.94/183.47 inference(unit_resolution,[status(thm)],[9766, 82, 72])).
% 290.94/183.47 tff(9768,plain,
% 290.94/183.47 (node21(c_e_h_1, c_d, s0, s1)),
% 290.94/183.47 inference(unit_resolution,[status(thm)],[9767, 9763])).
% 290.94/183.47 tff(9769,plain,
% 290.94/183.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_d, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s1)) | (~node21(c_e_h_1, c_d, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_d, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s1)) | (~node21(c_e_h_1, c_d, s0, s1)))),
% 290.94/183.47 inference(rewrite,[status(thm)],[])).
% 290.94/183.47 tff(9770,plain,
% 290.94/183.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_d, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s1)) | (~node21(c_e_h_1, c_d, s0, s1)))),
% 290.94/183.47 inference(quant_inst,[status(thm)],[])).
% 290.94/183.47 tff(9771,plain,
% 290.94/183.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_d, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s1)) | (~node21(c_e_h_1, c_d, s0, s1))),
% 290.94/183.47 inference(modus_ponens,[status(thm)],[9770, 9769])).
% 290.94/183.47 tff(9772,plain,
% 290.94/183.47 ($false),
% 290.94/183.47 inference(unit_resolution,[status(thm)],[9771, 52, 9768, 9756, 9755])).
% 290.94/183.47 tff(9773,plain,(~m_and_h_gate_v_out(c_e_h_1, c_d, s1)), inference(lemma,lemma(discharge,[]))).
% 290.94/183.47 tff(9774,plain,
% 290.94/183.47 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_g, s1)) | m_and_h_gate_v_out(c_e_h_1, c_d, s1))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_g, s1)) | m_and_h_gate_v_out(c_e_h_1, c_d, s1))),
% 290.94/183.47 inference(rewrite,[status(thm)],[])).
% 290.94/183.47 tff(9775,plain,
% 290.94/183.47 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_g, s1)) | m_and_h_gate_v_out(c_e_h_1, c_d, s1))),
% 290.94/183.47 inference(quant_inst,[status(thm)],[])).
% 290.94/183.47 tff(9776,plain,
% 290.94/183.47 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_g, s1)) | m_and_h_gate_v_out(c_e_h_1, c_d, s1)),
% 290.94/183.47 inference(modus_ponens,[status(thm)],[9775, 9774])).
% 290.94/183.47 tff(9777,plain,
% 290.94/183.47 (~m_or_h_gate_v_in2(c_e_h_1, c_g, s1)),
% 290.94/183.47 inference(unit_resolution,[status(thm)],[9776, 2762, 9773])).
% 290.94/183.47 tff(9778,assumption,(m_and_h_gate_v_out(c_e_h_1, c_c, s1)), introduced(assumption)).
% 290.94/183.47 tff(9779,assumption,(m_mutex_h_half_v_out(c_e_h_1, c_a, s0)), introduced(assumption)).
% 290.94/183.47 tff(9780,plain,
% 290.94/183.47 ((~![I0: $i, I1: $i] : (~m_mutex_h_half_v_out(I0, I1, s0))) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s0))),
% 290.94/183.47 inference(quant_inst,[status(thm)],[])).
% 290.94/183.47 tff(9781,plain,
% 290.94/183.47 ($false),
% 290.94/183.47 inference(unit_resolution,[status(thm)],[9780, 409, 9779])).
% 290.94/183.47 tff(9782,plain,(~m_mutex_h_half_v_out(c_e_h_1, c_a, s0)), inference(lemma,lemma(discharge,[]))).
% 290.94/183.47 tff(9783,plain,
% 290.94/183.47 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_c, s0)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s0))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s0)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s0))),
% 290.94/183.48 inference(rewrite,[status(thm)],[])).
% 290.94/183.48 tff(9784,plain,
% 290.94/183.48 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_c, s0)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s0))),
% 290.94/183.48 inference(quant_inst,[status(thm)],[])).
% 290.94/183.48 tff(9785,plain,
% 290.94/183.48 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s0)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s0)),
% 290.94/183.48 inference(modus_ponens,[status(thm)],[9784, 9783])).
% 290.94/183.48 tff(9786,plain,
% 290.94/183.48 (~m_and_h_gate_v_in1(c_e_h_1, c_c, s0)),
% 290.94/183.48 inference(unit_resolution,[status(thm)],[9785, 567, 9782])).
% 290.94/183.48 tff(9787,plain,
% 290.94/183.48 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_c, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_c, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s0))),
% 290.94/183.48 inference(rewrite,[status(thm)],[])).
% 290.94/183.48 tff(9788,plain,
% 290.94/183.48 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_c, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s0))),
% 290.94/183.48 inference(quant_inst,[status(thm)],[])).
% 290.94/183.48 tff(9789,plain,
% 290.94/183.48 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_c, s0)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s0)),
% 290.94/183.48 inference(modus_ponens,[status(thm)],[9788, 9787])).
% 290.94/183.48 tff(9790,plain,
% 290.94/183.48 (~node20(c_e_h_1, c_c, s0)),
% 290.94/183.48 inference(unit_resolution,[status(thm)],[9789, 38, 9786])).
% 290.94/183.48 tff(9791,assumption,(node21(c_e_h_1, c_c, s0, s1)), introduced(assumption)).
% 290.94/183.48 tff(9792,plain,
% 290.94/183.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_c, s1)) | node20(c_e_h_1, c_c, s0) | (~node21(c_e_h_1, c_c, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s1)) | node20(c_e_h_1, c_c, s0) | (~node21(c_e_h_1, c_c, s0, s1)))),
% 290.94/183.48 inference(rewrite,[status(thm)],[])).
% 290.94/183.48 tff(9793,plain,
% 290.94/183.48 ((node20(c_e_h_1, c_c, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s1)) | (~node21(c_e_h_1, c_c, s0, s1))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_c, s1)) | node20(c_e_h_1, c_c, s0) | (~node21(c_e_h_1, c_c, s0, s1)))),
% 290.94/183.48 inference(rewrite,[status(thm)],[])).
% 290.94/183.48 tff(9794,plain,
% 290.94/183.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_c, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s1)) | (~node21(c_e_h_1, c_c, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_c, s1)) | node20(c_e_h_1, c_c, s0) | (~node21(c_e_h_1, c_c, s0, s1))))),
% 290.94/183.48 inference(monotonicity,[status(thm)],[9793])).
% 290.94/183.48 tff(9795,plain,
% 290.94/183.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_c, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s1)) | (~node21(c_e_h_1, c_c, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s1)) | node20(c_e_h_1, c_c, s0) | (~node21(c_e_h_1, c_c, s0, s1)))),
% 290.94/183.48 inference(transitivity,[status(thm)],[9794, 9792])).
% 290.94/183.48 tff(9796,plain,
% 290.94/183.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_c, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s1)) | (~node21(c_e_h_1, c_c, s0, s1)))),
% 290.94/183.48 inference(quant_inst,[status(thm)],[])).
% 290.94/183.48 tff(9797,plain,
% 290.94/183.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s1)) | node20(c_e_h_1, c_c, s0) | (~node21(c_e_h_1, c_c, s0, s1))),
% 290.94/183.48 inference(modus_ponens,[status(thm)],[9796, 9795])).
% 290.94/183.48 tff(9798,plain,
% 290.94/183.48 ($false),
% 290.94/183.48 inference(unit_resolution,[status(thm)],[9797, 52, 9791, 9790, 9778])).
% 290.94/183.48 tff(9799,plain,((~node21(c_e_h_1, c_c, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s1))), inference(lemma,lemma(discharge,[]))).
% 290.94/183.48 tff(9800,plain,
% 290.94/183.48 (~node21(c_e_h_1, c_c, s0, s1)),
% 290.94/183.48 inference(unit_resolution,[status(thm)],[9799, 9778])).
% 290.94/183.48 tff(9801,plain,
% 290.94/183.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_1, c_c, s0, s1) | node22(c_e_h_1, c_c, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_1, c_c, s0, s1) | node22(c_e_h_1, c_c, s0, s1))),
% 290.94/183.48 inference(rewrite,[status(thm)],[])).
% 290.94/183.48 tff(9802,plain,
% 290.94/183.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_1, c_c, s0, s1) | node22(c_e_h_1, c_c, s0, s1))),
% 290.94/183.48 inference(quant_inst,[status(thm)],[])).
% 290.94/183.48 tff(9803,plain,
% 290.94/183.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_1, c_c, s0, s1) | node22(c_e_h_1, c_c, s0, s1)),
% 290.94/183.48 inference(modus_ponens,[status(thm)],[9802, 9801])).
% 290.94/183.48 tff(9804,plain,
% 290.94/183.48 (node21(c_e_h_1, c_c, s0, s1) | node22(c_e_h_1, c_c, s0, s1)),
% 290.94/183.48 inference(unit_resolution,[status(thm)],[9803, 82, 72])).
% 290.94/183.48 tff(9805,plain,
% 290.94/183.48 (node22(c_e_h_1, c_c, s0, s1)),
% 290.94/183.48 inference(unit_resolution,[status(thm)],[9804, 9800])).
% 290.94/183.48 tff(9806,plain,
% 290.94/183.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_c, s1)) | (~node22(c_e_h_1, c_c, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_c, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s1)) | (~node22(c_e_h_1, c_c, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_c, s0))),
% 290.94/183.48 inference(rewrite,[status(thm)],[])).
% 290.94/183.48 tff(9807,plain,
% 290.94/183.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_c, s1)) | (~node22(c_e_h_1, c_c, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_c, s0))),
% 290.94/183.48 inference(quant_inst,[status(thm)],[])).
% 290.94/183.48 tff(9808,plain,
% 290.94/183.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s1)) | (~node22(c_e_h_1, c_c, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_c, s0)),
% 290.94/183.48 inference(modus_ponens,[status(thm)],[9807, 9806])).
% 290.94/183.48 tff(9809,plain,
% 290.94/183.48 ($false),
% 290.94/183.48 inference(unit_resolution,[status(thm)],[9808, 108, 9548, 9805, 9778])).
% 290.94/183.48 tff(9810,plain,(~m_and_h_gate_v_out(c_e_h_1, c_c, s1)), inference(lemma,lemma(discharge,[]))).
% 290.94/183.48 tff(9811,plain,
% 290.94/183.48 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_g, s1)) | m_and_h_gate_v_out(c_e_h_1, c_c, s1))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_g, s1)) | m_and_h_gate_v_out(c_e_h_1, c_c, s1))),
% 290.94/183.48 inference(rewrite,[status(thm)],[])).
% 290.94/183.48 tff(9812,plain,
% 290.94/183.48 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_g, s1)) | m_and_h_gate_v_out(c_e_h_1, c_c, s1))),
% 290.94/183.48 inference(quant_inst,[status(thm)],[])).
% 290.94/183.48 tff(9813,plain,
% 290.94/183.48 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_g, s1)) | m_and_h_gate_v_out(c_e_h_1, c_c, s1)),
% 290.94/183.48 inference(modus_ponens,[status(thm)],[9812, 9811])).
% 290.94/183.48 tff(9814,plain,
% 291.01/183.48 (~m_or_h_gate_v_in1(c_e_h_1, c_g, s1)),
% 291.01/183.48 inference(unit_resolution,[status(thm)],[9813, 2708, 9810])).
% 291.01/183.48 tff(9815,assumption,(m_or_h_gate_v_out(c_e_h_1, c_g, s2)), introduced(assumption)).
% 291.01/183.48 tff(9816,assumption,(~m_or_h_gate_v_out(c_e_h_1, c_g, s1)), introduced(assumption)).
% 291.01/183.48 tff(9817,assumption,(node6(c_e_h_1, c_g, s1, s2)), introduced(assumption)).
% 291.01/183.48 tff(9818,plain,
% 291.01/183.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_1, c_g, s2)) | m_or_h_gate_v_out(c_e_h_1, c_g, s1) | (~node6(c_e_h_1, c_g, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s2)) | m_or_h_gate_v_out(c_e_h_1, c_g, s1) | (~node6(c_e_h_1, c_g, s1, s2)))),
% 291.01/183.48 inference(rewrite,[status(thm)],[])).
% 291.01/183.48 tff(9819,plain,
% 291.01/183.48 (((~node6(c_e_h_1, c_g, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s2)) | m_or_h_gate_v_out(c_e_h_1, c_g, s1)) <=> ((~m_or_h_gate_v_out(c_e_h_1, c_g, s2)) | m_or_h_gate_v_out(c_e_h_1, c_g, s1) | (~node6(c_e_h_1, c_g, s1, s2)))),
% 291.01/183.48 inference(rewrite,[status(thm)],[])).
% 291.01/183.48 tff(9820,plain,
% 291.01/183.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_g, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s2)) | m_or_h_gate_v_out(c_e_h_1, c_g, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_1, c_g, s2)) | m_or_h_gate_v_out(c_e_h_1, c_g, s1) | (~node6(c_e_h_1, c_g, s1, s2))))),
% 291.01/183.48 inference(monotonicity,[status(thm)],[9819])).
% 291.01/183.48 tff(9821,plain,
% 291.01/183.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_g, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s2)) | m_or_h_gate_v_out(c_e_h_1, c_g, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s2)) | m_or_h_gate_v_out(c_e_h_1, c_g, s1) | (~node6(c_e_h_1, c_g, s1, s2)))),
% 291.01/183.48 inference(transitivity,[status(thm)],[9820, 9818])).
% 291.01/183.48 tff(9822,plain,
% 291.01/183.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_g, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s2)) | m_or_h_gate_v_out(c_e_h_1, c_g, s1))),
% 291.01/183.48 inference(quant_inst,[status(thm)],[])).
% 291.01/183.48 tff(9823,plain,
% 291.01/183.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s2)) | m_or_h_gate_v_out(c_e_h_1, c_g, s1) | (~node6(c_e_h_1, c_g, s1, s2))),
% 291.01/183.48 inference(modus_ponens,[status(thm)],[9822, 9821])).
% 291.01/183.48 tff(9824,plain,
% 291.01/183.48 ($false),
% 291.01/183.48 inference(unit_resolution,[status(thm)],[9823, 1121, 9817, 9816, 9815])).
% 291.01/183.48 tff(9825,plain,((~node6(c_e_h_1, c_g, s1, s2)) | m_or_h_gate_v_out(c_e_h_1, c_g, s1) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s2))), inference(lemma,lemma(discharge,[]))).
% 291.01/183.48 tff(9826,plain,
% 291.01/183.48 ((~node6(c_e_h_1, c_g, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s2))),
% 291.01/183.48 inference(unit_resolution,[status(thm)],[9825, 9578])).
% 291.01/183.48 tff(9827,plain,
% 291.01/183.48 (~node6(c_e_h_1, c_g, s1, s2)),
% 291.01/183.48 inference(unit_resolution,[status(thm)],[9826, 9815])).
% 291.01/183.48 tff(9828,plain,
% 291.01/183.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s1, s2)) | node5(c_e_h_1, c_g, s1, s2) | node6(c_e_h_1, c_g, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s1, s2)) | node5(c_e_h_1, c_g, s1, s2) | node6(c_e_h_1, c_g, s1, s2))),
% 291.01/183.48 inference(rewrite,[status(thm)],[])).
% 291.01/183.48 tff(9829,plain,
% 291.01/183.48 ((node6(c_e_h_1, c_g, s1, s2) | node5(c_e_h_1, c_g, s1, s2) | (~trans(s1, s2))) <=> ((~trans(s1, s2)) | node5(c_e_h_1, c_g, s1, s2) | node6(c_e_h_1, c_g, s1, s2))),
% 291.01/183.49 inference(rewrite,[status(thm)],[])).
% 291.01/183.49 tff(9830,plain,
% 291.01/183.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_g, s1, s2) | node5(c_e_h_1, c_g, s1, s2) | (~trans(s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s1, s2)) | node5(c_e_h_1, c_g, s1, s2) | node6(c_e_h_1, c_g, s1, s2)))),
% 291.01/183.49 inference(monotonicity,[status(thm)],[9829])).
% 291.01/183.49 tff(9831,plain,
% 291.01/183.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_g, s1, s2) | node5(c_e_h_1, c_g, s1, s2) | (~trans(s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s1, s2)) | node5(c_e_h_1, c_g, s1, s2) | node6(c_e_h_1, c_g, s1, s2))),
% 291.01/183.49 inference(transitivity,[status(thm)],[9830, 9828])).
% 291.01/183.49 tff(9832,plain,
% 291.01/183.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_g, s1, s2) | node5(c_e_h_1, c_g, s1, s2) | (~trans(s1, s2)))),
% 291.01/183.49 inference(quant_inst,[status(thm)],[])).
% 291.01/183.49 tff(9833,plain,
% 291.01/183.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s1, s2)) | node5(c_e_h_1, c_g, s1, s2) | node6(c_e_h_1, c_g, s1, s2)),
% 291.01/183.49 inference(modus_ponens,[status(thm)],[9832, 9831])).
% 291.01/183.49 tff(9834,plain,
% 291.01/183.49 (node5(c_e_h_1, c_g, s1, s2) | node6(c_e_h_1, c_g, s1, s2)),
% 291.01/183.49 inference(unit_resolution,[status(thm)],[9833, 1141, 255])).
% 291.01/183.49 tff(9835,plain,
% 291.01/183.49 (node5(c_e_h_1, c_g, s1, s2)),
% 291.01/183.49 inference(unit_resolution,[status(thm)],[9834, 9827])).
% 291.01/183.49 tff(9836,plain,
% 291.01/183.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_1, c_g, s2)) | m_or_h_gate_v_in2(c_e_h_1, c_g, s1) | (~node5(c_e_h_1, c_g, s1, s2)) | m_or_h_gate_v_in1(c_e_h_1, c_g, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s2)) | m_or_h_gate_v_in2(c_e_h_1, c_g, s1) | (~node5(c_e_h_1, c_g, s1, s2)) | m_or_h_gate_v_in1(c_e_h_1, c_g, s1))),
% 291.01/183.49 inference(rewrite,[status(thm)],[])).
% 291.01/183.49 tff(9837,plain,
% 291.01/183.49 ((m_or_h_gate_v_in1(c_e_h_1, c_g, s1) | m_or_h_gate_v_in2(c_e_h_1, c_g, s1) | (~node5(c_e_h_1, c_g, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s2))) <=> ((~m_or_h_gate_v_out(c_e_h_1, c_g, s2)) | m_or_h_gate_v_in2(c_e_h_1, c_g, s1) | (~node5(c_e_h_1, c_g, s1, s2)) | m_or_h_gate_v_in1(c_e_h_1, c_g, s1))),
% 291.01/183.49 inference(rewrite,[status(thm)],[])).
% 291.01/183.49 tff(9838,plain,
% 291.01/183.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_g, s1) | m_or_h_gate_v_in2(c_e_h_1, c_g, s1) | (~node5(c_e_h_1, c_g, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_1, c_g, s2)) | m_or_h_gate_v_in2(c_e_h_1, c_g, s1) | (~node5(c_e_h_1, c_g, s1, s2)) | m_or_h_gate_v_in1(c_e_h_1, c_g, s1)))),
% 291.01/183.49 inference(monotonicity,[status(thm)],[9837])).
% 291.01/183.49 tff(9839,plain,
% 291.01/183.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_g, s1) | m_or_h_gate_v_in2(c_e_h_1, c_g, s1) | (~node5(c_e_h_1, c_g, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s2)) | m_or_h_gate_v_in2(c_e_h_1, c_g, s1) | (~node5(c_e_h_1, c_g, s1, s2)) | m_or_h_gate_v_in1(c_e_h_1, c_g, s1))),
% 291.01/183.49 inference(transitivity,[status(thm)],[9838, 9836])).
% 291.01/183.49 tff(9840,plain,
% 291.01/183.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_g, s1) | m_or_h_gate_v_in2(c_e_h_1, c_g, s1) | (~node5(c_e_h_1, c_g, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s2)))),
% 291.01/183.49 inference(quant_inst,[status(thm)],[])).
% 291.01/183.49 tff(9841,plain,
% 291.01/183.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s2)) | m_or_h_gate_v_in2(c_e_h_1, c_g, s1) | (~node5(c_e_h_1, c_g, s1, s2)) | m_or_h_gate_v_in1(c_e_h_1, c_g, s1)),
% 291.01/183.49 inference(modus_ponens,[status(thm)],[9840, 9839])).
% 291.01/183.49 tff(9842,plain,
% 291.01/183.49 ($false),
% 291.01/183.49 inference(unit_resolution,[status(thm)],[9841, 1159, 9835, 9815, 9814, 9777])).
% 291.01/183.49 tff(9843,plain,(~m_or_h_gate_v_out(c_e_h_1, c_g, s2)), inference(lemma,lemma(discharge,[]))).
% 291.01/183.49 tff(9844,assumption,(m_and_h_gate_v_in1(c_e_h_1, c_k, s2)), introduced(assumption)).
% 291.01/183.49 tff(9845,assumption,(~m_or_h_gate_v_out(c_e_h_1, c_g, s2)), introduced(assumption)).
% 291.01/183.49 tff(9846,plain,
% 291.01/183.49 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_k, s2)) | m_or_h_gate_v_out(c_e_h_1, c_g, s2))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_k, s2)) | m_or_h_gate_v_out(c_e_h_1, c_g, s2))),
% 291.01/183.49 inference(rewrite,[status(thm)],[])).
% 291.01/183.49 tff(9847,plain,
% 291.01/183.49 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_k, s2)) | m_or_h_gate_v_out(c_e_h_1, c_g, s2))),
% 291.01/183.49 inference(quant_inst,[status(thm)],[])).
% 291.01/183.49 tff(9848,plain,
% 291.01/183.49 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_k, s2)) | m_or_h_gate_v_out(c_e_h_1, c_g, s2)),
% 291.01/183.49 inference(modus_ponens,[status(thm)],[9847, 9846])).
% 291.01/183.49 tff(9849,plain,
% 291.01/183.49 ($false),
% 291.01/183.49 inference(unit_resolution,[status(thm)],[9848, 2048, 9845, 9844])).
% 291.01/183.49 tff(9850,plain,((~m_and_h_gate_v_in1(c_e_h_1, c_k, s2)) | m_or_h_gate_v_out(c_e_h_1, c_g, s2)), inference(lemma,lemma(discharge,[]))).
% 291.01/183.49 tff(9851,plain,
% 291.01/183.49 (~m_and_h_gate_v_in1(c_e_h_1, c_k, s2)),
% 291.01/183.49 inference(unit_resolution,[status(thm)],[9850, 9843])).
% 291.01/183.49 tff(9852,assumption,(node20(c_e_h_1, c_k, s2)), introduced(assumption)).
% 291.01/183.49 tff(9853,assumption,(~m_and_h_gate_v_in1(c_e_h_1, c_k, s2)), introduced(assumption)).
% 291.01/183.49 tff(9854,plain,
% 291.01/183.49 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_k, s2)) | m_and_h_gate_v_in1(c_e_h_1, c_k, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_k, s2)) | m_and_h_gate_v_in1(c_e_h_1, c_k, s2))),
% 291.01/183.49 inference(rewrite,[status(thm)],[])).
% 291.01/183.49 tff(9855,plain,
% 291.01/183.49 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_k, s2)) | m_and_h_gate_v_in1(c_e_h_1, c_k, s2))),
% 291.01/183.49 inference(quant_inst,[status(thm)],[])).
% 291.01/183.49 tff(9856,plain,
% 291.01/183.49 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_k, s2)) | m_and_h_gate_v_in1(c_e_h_1, c_k, s2)),
% 291.01/183.49 inference(modus_ponens,[status(thm)],[9855, 9854])).
% 291.01/183.49 tff(9857,plain,
% 291.01/183.49 ($false),
% 291.01/183.49 inference(unit_resolution,[status(thm)],[9856, 38, 9853, 9852])).
% 291.01/183.49 tff(9858,plain,((~node20(c_e_h_1, c_k, s2)) | m_and_h_gate_v_in1(c_e_h_1, c_k, s2)), inference(lemma,lemma(discharge,[]))).
% 291.01/183.49 tff(9859,plain,
% 291.01/183.49 (~node20(c_e_h_1, c_k, s2)),
% 291.01/183.49 inference(unit_resolution,[status(thm)],[9858, 9851])).
% 291.01/183.49 tff(9860,assumption,(~node20(c_e_h_1, c_k, s2)), introduced(assumption)).
% 291.01/183.49 tff(9861,assumption,(node21(c_e_h_1, c_k, s2, s3)), introduced(assumption)).
% 291.01/183.49 tff(9862,plain,
% 291.01/183.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_k, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s3)) | (~node21(c_e_h_1, c_k, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_k, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s3)) | (~node21(c_e_h_1, c_k, s2, s3)))),
% 291.01/183.50 inference(rewrite,[status(thm)],[])).
% 291.01/183.50 tff(9863,plain,
% 291.01/183.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_k, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s3)) | (~node21(c_e_h_1, c_k, s2, s3)))),
% 291.01/183.50 inference(quant_inst,[status(thm)],[])).
% 291.01/183.50 tff(9864,plain,
% 291.01/183.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_k, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s3)) | (~node21(c_e_h_1, c_k, s2, s3))),
% 291.01/183.50 inference(modus_ponens,[status(thm)],[9863, 9862])).
% 291.01/183.50 tff(9865,plain,
% 291.01/183.50 ($false),
% 291.01/183.50 inference(unit_resolution,[status(thm)],[9864, 52, 9861, 9742, 9860])).
% 291.01/183.50 tff(9866,plain,((~node21(c_e_h_1, c_k, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s3)) | node20(c_e_h_1, c_k, s2)), inference(lemma,lemma(discharge,[]))).
% 291.01/183.50 tff(9867,plain,
% 291.01/183.50 ((~node21(c_e_h_1, c_k, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s3))),
% 291.01/183.50 inference(unit_resolution,[status(thm)],[9866, 9859])).
% 291.01/183.50 tff(9868,plain,
% 291.01/183.50 (~node21(c_e_h_1, c_k, s2, s3)),
% 291.01/183.50 inference(unit_resolution,[status(thm)],[9867, 9742])).
% 291.01/183.50 tff(9869,plain,
% 291.01/183.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_1, c_k, s2, s3) | node22(c_e_h_1, c_k, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_1, c_k, s2, s3) | node22(c_e_h_1, c_k, s2, s3))),
% 291.01/183.50 inference(rewrite,[status(thm)],[])).
% 291.01/183.50 tff(9870,plain,
% 291.01/183.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_1, c_k, s2, s3) | node22(c_e_h_1, c_k, s2, s3))),
% 291.01/183.50 inference(quant_inst,[status(thm)],[])).
% 291.01/183.50 tff(9871,plain,
% 291.01/183.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_1, c_k, s2, s3) | node22(c_e_h_1, c_k, s2, s3)),
% 291.01/183.50 inference(modus_ponens,[status(thm)],[9870, 9869])).
% 291.01/183.50 tff(9872,plain,
% 291.01/183.50 (node21(c_e_h_1, c_k, s2, s3) | node22(c_e_h_1, c_k, s2, s3)),
% 291.01/183.50 inference(unit_resolution,[status(thm)],[9871, 82, 318])).
% 291.01/183.50 tff(9873,plain,
% 291.01/183.50 (node22(c_e_h_1, c_k, s2, s3)),
% 291.01/183.50 inference(unit_resolution,[status(thm)],[9872, 9868])).
% 291.01/183.50 tff(9874,plain,
% 291.01/183.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_k, s3)) | (~node22(c_e_h_1, c_k, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_k, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s3)) | (~node22(c_e_h_1, c_k, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_k, s2))),
% 291.01/183.50 inference(rewrite,[status(thm)],[])).
% 291.01/183.50 tff(9875,plain,
% 291.01/183.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_k, s3)) | (~node22(c_e_h_1, c_k, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_k, s2))),
% 291.01/183.50 inference(quant_inst,[status(thm)],[])).
% 291.01/183.50 tff(9876,plain,
% 291.01/183.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s3)) | (~node22(c_e_h_1, c_k, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_k, s2)),
% 291.01/183.50 inference(modus_ponens,[status(thm)],[9875, 9874])).
% 291.01/183.50 tff(9877,plain,
% 291.01/183.50 ($false),
% 291.01/183.50 inference(unit_resolution,[status(thm)],[9876, 108, 9873, 9743, 9742])).
% 291.01/183.50 tff(9878,plain,((~m_and_h_gate_v_out(c_e_h_1, c_k, s3)) | m_and_h_gate_v_out(c_e_h_1, c_k, s2)), inference(lemma,lemma(discharge,[]))).
% 291.01/183.50 tff(9879,plain,
% 291.01/183.50 (~m_and_h_gate_v_out(c_e_h_1, c_k, s3)),
% 291.01/183.50 inference(unit_resolution,[status(thm)],[9878, 9611])).
% 291.01/183.50 tff(9880,assumption,(~m_and_h_gate_v_in1(c_e_h_1, c_p, s2)), introduced(assumption)).
% 291.01/183.50 tff(9881,plain,
% 291.01/183.50 (~node20(c_e_h_1, c_p, s2)),
% 291.01/183.50 inference(unit_resolution,[status(thm)],[9619, 38, 9880])).
% 291.01/183.50 tff(9882,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_k, s3)), introduced(assumption)).
% 291.01/183.50 tff(9883,plain,
% 291.01/183.50 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_p, s3)) | m_and_h_gate_v_out(c_e_h_1, c_k, s3))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s3)) | m_and_h_gate_v_out(c_e_h_1, c_k, s3))),
% 291.01/183.50 inference(rewrite,[status(thm)],[])).
% 291.01/183.50 tff(9884,plain,
% 291.01/183.50 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_p, s3)) | m_and_h_gate_v_out(c_e_h_1, c_k, s3))),
% 291.01/183.50 inference(quant_inst,[status(thm)],[])).
% 291.01/183.50 tff(9885,plain,
% 291.01/183.50 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s3)) | m_and_h_gate_v_out(c_e_h_1, c_k, s3)),
% 291.01/183.50 inference(modus_ponens,[status(thm)],[9884, 9883])).
% 291.01/183.50 tff(9886,plain,
% 291.01/183.50 (~m_and_h_gate_v_in1(c_e_h_1, c_p, s3)),
% 291.01/183.50 inference(unit_resolution,[status(thm)],[9885, 3033, 9882])).
% 291.01/183.50 tff(9887,plain,
% 291.01/183.50 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_p, s3)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_p, s3)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s3))),
% 291.01/183.50 inference(rewrite,[status(thm)],[])).
% 291.01/183.50 tff(9888,plain,
% 291.01/183.50 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_p, s3)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s3))),
% 291.01/183.50 inference(quant_inst,[status(thm)],[])).
% 291.01/183.50 tff(9889,plain,
% 291.01/183.50 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_p, s3)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s3)),
% 291.01/183.50 inference(modus_ponens,[status(thm)],[9888, 9887])).
% 291.01/183.50 tff(9890,plain,
% 291.01/183.50 (~node20(c_e_h_1, c_p, s3)),
% 291.01/183.50 inference(unit_resolution,[status(thm)],[9889, 38, 9886])).
% 291.01/183.50 tff(9891,plain,
% 291.01/183.50 (~m_cell_v_req(c_e_h_1, s3)),
% 291.01/183.50 inference(unit_resolution,[status(thm)],[9651, 2908, 9647])).
% 291.01/183.50 tff(9892,plain,
% 291.01/183.50 (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s3)),
% 291.01/183.50 inference(unit_resolution,[status(thm)],[9665, 9891])).
% 291.01/183.50 tff(9893,plain,
% 291.01/183.50 (~m_mutex_h_half_v_out(c_e_h_3, c_b, s4)),
% 291.01/183.50 inference(unit_resolution,[status(thm)],[9692, 9892, 3237])).
% 291.01/183.50 tff(9894,assumption,(node13(c_e_h_3, c_b, s4, s5)), introduced(assumption)).
% 291.01/183.50 tff(9895,plain,
% 291.01/183.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_b, s5)) | (~node13(c_e_h_3, c_b, s4, s5)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s5)) | (~node13(c_e_h_3, c_b, s4, s5)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s4))),
% 291.01/183.50 inference(rewrite,[status(thm)],[])).
% 291.01/183.50 tff(9896,plain,
% 291.01/183.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_b, s5)) | (~node13(c_e_h_3, c_b, s4, s5)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s4))),
% 291.01/183.50 inference(quant_inst,[status(thm)],[])).
% 291.01/183.50 tff(9897,plain,
% 291.01/183.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s5)) | (~node13(c_e_h_3, c_b, s4, s5)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s4)),
% 291.01/183.50 inference(modus_ponens,[status(thm)],[9896, 9895])).
% 291.01/183.50 tff(9898,plain,
% 291.01/183.50 ($false),
% 291.01/183.50 inference(unit_resolution,[status(thm)],[9897, 423, 9894, 9741, 9695])).
% 291.01/183.50 tff(9899,plain,((~node13(c_e_h_3, c_b, s4, s5)) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s5)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s4)), inference(lemma,lemma(discharge,[]))).
% 291.01/183.50 tff(9900,plain,
% 291.01/183.50 (~node13(c_e_h_3, c_b, s4, s5)),
% 291.01/183.50 inference(unit_resolution,[status(thm)],[9899, 9893, 9741])).
% 291.01/183.50 tff(9901,plain,
% 291.01/183.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s4, s5)) | node12(c_e_h_3, c_b, s4, s5) | node13(c_e_h_3, c_b, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s4, s5)) | node12(c_e_h_3, c_b, s4, s5) | node13(c_e_h_3, c_b, s4, s5))),
% 291.01/183.50 inference(rewrite,[status(thm)],[])).
% 291.01/183.50 tff(9902,plain,
% 291.01/183.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s4, s5)) | node12(c_e_h_3, c_b, s4, s5) | node13(c_e_h_3, c_b, s4, s5))),
% 291.01/183.50 inference(quant_inst,[status(thm)],[])).
% 291.01/183.50 tff(9903,plain,
% 291.01/183.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s4, s5)) | node12(c_e_h_3, c_b, s4, s5) | node13(c_e_h_3, c_b, s4, s5)),
% 291.01/183.50 inference(modus_ponens,[status(thm)],[9902, 9901])).
% 291.01/183.50 tff(9904,plain,
% 291.01/183.50 (node12(c_e_h_3, c_b, s4, s5) | node13(c_e_h_3, c_b, s4, s5)),
% 291.01/183.50 inference(unit_resolution,[status(thm)],[9903, 439, 1028])).
% 291.01/183.50 tff(9905,plain,
% 291.01/183.50 (node12(c_e_h_3, c_b, s4, s5)),
% 291.01/183.50 inference(unit_resolution,[status(thm)],[9904, 9900])).
% 291.01/183.50 tff(9906,plain,
% 291.01/183.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_b, s5)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s4) | (~node12(c_e_h_3, c_b, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s5)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s4) | (~node12(c_e_h_3, c_b, s4, s5)))),
% 291.01/183.50 inference(rewrite,[status(thm)],[])).
% 291.01/183.50 tff(9907,plain,
% 291.01/183.50 (((~node12(c_e_h_3, c_b, s4, s5)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s4) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s5))) <=> ((~m_mutex_h_half_v_out(c_e_h_3, c_b, s5)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s4) | (~node12(c_e_h_3, c_b, s4, s5)))),
% 291.01/183.50 inference(rewrite,[status(thm)],[])).
% 291.01/183.50 tff(9908,plain,
% 291.01/183.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_b, s4, s5)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s4) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_b, s5)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s4) | (~node12(c_e_h_3, c_b, s4, s5))))),
% 291.01/183.50 inference(monotonicity,[status(thm)],[9907])).
% 291.01/183.50 tff(9909,plain,
% 291.01/183.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_b, s4, s5)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s4) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s5)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s4) | (~node12(c_e_h_3, c_b, s4, s5)))),
% 291.01/183.50 inference(transitivity,[status(thm)],[9908, 9906])).
% 291.01/183.50 tff(9910,plain,
% 291.01/183.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_b, s4, s5)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s4) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s5)))),
% 291.01/183.50 inference(quant_inst,[status(thm)],[])).
% 291.01/183.50 tff(9911,plain,
% 291.01/183.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s5)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s4) | (~node12(c_e_h_3, c_b, s4, s5))),
% 291.01/183.51 inference(modus_ponens,[status(thm)],[9910, 9909])).
% 291.01/183.51 tff(9912,plain,
% 291.01/183.51 (m_mutex_h_half_v_inp(c_e_h_3, c_b, s4)),
% 291.01/183.51 inference(unit_resolution,[status(thm)],[9911, 454, 9905, 9741])).
% 291.01/183.51 tff(9913,plain,
% 291.01/183.51 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node1(c_e_h_3, c_e_h_1, s4))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node1(c_e_h_3, c_e_h_1, s4))),
% 291.01/183.51 inference(rewrite,[status(thm)],[])).
% 291.01/183.51 tff(9914,plain,
% 291.01/183.51 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node1(c_e_h_3, c_e_h_1, s4))),
% 291.01/183.51 inference(quant_inst,[status(thm)],[])).
% 291.01/183.51 tff(9915,plain,
% 291.01/183.51 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node1(c_e_h_3, c_e_h_1, s4)),
% 291.01/183.51 inference(modus_ponens,[status(thm)],[9914, 9913])).
% 291.01/183.51 tff(9916,plain,
% 291.01/183.51 (node1(c_e_h_3, c_e_h_1, s4)),
% 291.01/183.51 inference(unit_resolution,[status(thm)],[9915, 2922, 2919])).
% 291.01/183.51 tff(9917,plain,
% 291.01/183.51 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | (m_cell_v_req(c_e_h_1, s4) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s4)) | (~node1(c_e_h_3, c_e_h_1, s4)))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | m_cell_v_req(c_e_h_1, s4) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s4)) | (~node1(c_e_h_3, c_e_h_1, s4)))),
% 291.01/183.51 inference(rewrite,[status(thm)],[])).
% 291.01/183.51 tff(9918,plain,
% 291.01/183.51 (((~node1(c_e_h_3, c_e_h_1, s4)) | m_cell_v_req(c_e_h_1, s4) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s4))) <=> (m_cell_v_req(c_e_h_1, s4) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s4)) | (~node1(c_e_h_3, c_e_h_1, s4)))),
% 291.01/183.51 inference(rewrite,[status(thm)],[])).
% 291.01/183.51 tff(9919,plain,
% 291.01/183.51 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_3, c_e_h_1, s4)) | m_cell_v_req(c_e_h_1, s4) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s4)))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | (m_cell_v_req(c_e_h_1, s4) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s4)) | (~node1(c_e_h_3, c_e_h_1, s4))))),
% 291.01/183.51 inference(monotonicity,[status(thm)],[9918])).
% 291.01/183.51 tff(9920,plain,
% 291.01/183.51 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_3, c_e_h_1, s4)) | m_cell_v_req(c_e_h_1, s4) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s4)))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | m_cell_v_req(c_e_h_1, s4) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s4)) | (~node1(c_e_h_3, c_e_h_1, s4)))),
% 291.01/183.51 inference(transitivity,[status(thm)],[9919, 9917])).
% 291.01/183.51 tff(9921,plain,
% 291.01/183.51 ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_3, c_e_h_1, s4)) | m_cell_v_req(c_e_h_1, s4) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s4)))),
% 291.01/183.51 inference(quant_inst,[status(thm)],[])).
% 291.01/183.51 tff(9922,plain,
% 291.01/183.51 ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | m_cell_v_req(c_e_h_1, s4) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s4)) | (~node1(c_e_h_3, c_e_h_1, s4))),
% 291.01/183.51 inference(modus_ponens,[status(thm)],[9921, 9920])).
% 291.01/183.51 tff(9923,plain,
% 291.01/183.51 (m_cell_v_req(c_e_h_1, s4) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s4))),
% 291.01/183.51 inference(unit_resolution,[status(thm)],[9922, 2936, 9916])).
% 291.01/183.51 tff(9924,plain,
% 291.01/183.51 (m_cell_v_req(c_e_h_1, s4)),
% 291.01/183.51 inference(unit_resolution,[status(thm)],[9923, 9912])).
% 291.01/183.51 tff(9925,plain,
% 291.01/183.51 (((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | ((~m_cell_v_req(c_e_h_1, s4)) | m_and_h_gate_v_out(c_e_h_1, c_p, s4))) <=> ((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | (~m_cell_v_req(c_e_h_1, s4)) | m_and_h_gate_v_out(c_e_h_1, c_p, s4))),
% 291.01/183.51 inference(rewrite,[status(thm)],[])).
% 291.01/183.51 tff(9926,plain,
% 291.01/183.51 ((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | ((~m_cell_v_req(c_e_h_1, s4)) | m_and_h_gate_v_out(c_e_h_1, c_p, s4))),
% 291.01/183.51 inference(quant_inst,[status(thm)],[])).
% 291.01/183.51 tff(9927,plain,
% 291.01/183.51 ((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | (~m_cell_v_req(c_e_h_1, s4)) | m_and_h_gate_v_out(c_e_h_1, c_p, s4)),
% 291.01/183.51 inference(modus_ponens,[status(thm)],[9926, 9925])).
% 291.01/183.51 tff(9928,plain,
% 291.01/183.51 (m_and_h_gate_v_out(c_e_h_1, c_p, s4)),
% 291.01/183.51 inference(unit_resolution,[status(thm)],[9927, 2908, 9924])).
% 291.01/183.51 tff(9929,assumption,(~node20(c_e_h_1, c_p, s3)), introduced(assumption)).
% 291.01/183.51 tff(9930,assumption,(m_and_h_gate_v_out(c_e_h_1, c_p, s4)), introduced(assumption)).
% 291.01/183.51 tff(9931,assumption,(node22(c_e_h_1, c_p, s3, s4)), introduced(assumption)).
% 291.01/183.51 tff(9932,plain,
% 291.01/183.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_p, s4)) | (~node22(c_e_h_1, c_p, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_p, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s4)) | (~node22(c_e_h_1, c_p, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_p, s3))),
% 291.01/183.51 inference(rewrite,[status(thm)],[])).
% 291.01/183.51 tff(9933,plain,
% 291.01/183.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_p, s4)) | (~node22(c_e_h_1, c_p, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_p, s3))),
% 291.01/183.51 inference(quant_inst,[status(thm)],[])).
% 291.01/183.51 tff(9934,plain,
% 291.01/183.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s4)) | (~node22(c_e_h_1, c_p, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_p, s3)),
% 291.01/183.51 inference(modus_ponens,[status(thm)],[9933, 9932])).
% 291.01/183.51 tff(9935,plain,
% 291.01/183.51 ($false),
% 291.01/183.51 inference(unit_resolution,[status(thm)],[9934, 108, 9931, 9647, 9930])).
% 291.01/183.51 tff(9936,plain,((~node22(c_e_h_1, c_p, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_p, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s4))), inference(lemma,lemma(discharge,[]))).
% 291.01/183.51 tff(9937,plain,
% 291.01/183.51 (~node22(c_e_h_1, c_p, s3, s4)),
% 291.01/183.51 inference(unit_resolution,[status(thm)],[9936, 9647, 9928])).
% 291.01/183.51 tff(9938,plain,
% 291.01/183.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_1, c_p, s3, s4) | node22(c_e_h_1, c_p, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_1, c_p, s3, s4) | node22(c_e_h_1, c_p, s3, s4))),
% 291.01/183.51 inference(rewrite,[status(thm)],[])).
% 291.01/183.51 tff(9939,plain,
% 291.01/183.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_1, c_p, s3, s4) | node22(c_e_h_1, c_p, s3, s4))),
% 291.01/183.51 inference(quant_inst,[status(thm)],[])).
% 291.01/183.51 tff(9940,plain,
% 291.01/183.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_1, c_p, s3, s4) | node22(c_e_h_1, c_p, s3, s4)),
% 291.01/183.51 inference(modus_ponens,[status(thm)],[9939, 9938])).
% 291.01/183.51 tff(9941,plain,
% 291.01/183.51 (node21(c_e_h_1, c_p, s3, s4) | node22(c_e_h_1, c_p, s3, s4)),
% 291.01/183.51 inference(unit_resolution,[status(thm)],[9940, 82, 531])).
% 291.01/183.51 tff(9942,plain,
% 291.01/183.51 (node21(c_e_h_1, c_p, s3, s4)),
% 291.01/183.51 inference(unit_resolution,[status(thm)],[9941, 9937])).
% 291.01/183.51 tff(9943,plain,
% 291.01/183.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_p, s4)) | node20(c_e_h_1, c_p, s3) | (~node21(c_e_h_1, c_p, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s4)) | node20(c_e_h_1, c_p, s3) | (~node21(c_e_h_1, c_p, s3, s4)))),
% 291.01/183.51 inference(rewrite,[status(thm)],[])).
% 291.01/183.51 tff(9944,plain,
% 291.01/183.51 ((node20(c_e_h_1, c_p, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s4)) | (~node21(c_e_h_1, c_p, s3, s4))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_p, s4)) | node20(c_e_h_1, c_p, s3) | (~node21(c_e_h_1, c_p, s3, s4)))),
% 291.01/183.51 inference(rewrite,[status(thm)],[])).
% 291.01/183.51 tff(9945,plain,
% 291.01/183.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_p, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s4)) | (~node21(c_e_h_1, c_p, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_p, s4)) | node20(c_e_h_1, c_p, s3) | (~node21(c_e_h_1, c_p, s3, s4))))),
% 291.01/183.51 inference(monotonicity,[status(thm)],[9944])).
% 291.01/183.51 tff(9946,plain,
% 291.01/183.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_p, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s4)) | (~node21(c_e_h_1, c_p, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s4)) | node20(c_e_h_1, c_p, s3) | (~node21(c_e_h_1, c_p, s3, s4)))),
% 291.01/183.51 inference(transitivity,[status(thm)],[9945, 9943])).
% 291.01/183.51 tff(9947,plain,
% 291.01/183.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_p, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s4)) | (~node21(c_e_h_1, c_p, s3, s4)))),
% 291.01/183.51 inference(quant_inst,[status(thm)],[])).
% 291.01/183.51 tff(9948,plain,
% 291.01/183.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s4)) | node20(c_e_h_1, c_p, s3) | (~node21(c_e_h_1, c_p, s3, s4))),
% 291.01/183.51 inference(modus_ponens,[status(thm)],[9947, 9946])).
% 291.01/183.51 tff(9949,plain,
% 291.01/183.51 ($false),
% 291.01/183.51 inference(unit_resolution,[status(thm)],[9948, 52, 9942, 9929, 9928])).
% 291.01/183.51 tff(9950,plain,(m_and_h_gate_v_out(c_e_h_1, c_p, s3) | node20(c_e_h_1, c_p, s3) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s5)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s3)), inference(lemma,lemma(discharge,[]))).
% 291.01/183.51 tff(9951,plain,
% 291.01/183.51 (m_and_h_gate_v_out(c_e_h_1, c_p, s3)),
% 291.01/183.51 inference(unit_resolution,[status(thm)],[9950, 9890, 9741, 3237])).
% 291.01/183.51 tff(9952,plain,
% 291.01/183.51 (~node22(c_e_h_1, c_p, s2, s3)),
% 291.01/183.51 inference(unit_resolution,[status(thm)],[9638, 9951, 3192])).
% 291.01/183.51 tff(9953,plain,
% 291.01/183.51 (node21(c_e_h_1, c_p, s2, s3)),
% 291.01/183.51 inference(unit_resolution,[status(thm)],[9643, 9952])).
% 291.01/183.51 tff(9954,plain,
% 291.01/183.51 ($false),
% 291.01/183.51 inference(unit_resolution,[status(thm)],[9628, 52, 9953, 9951, 9881])).
% 291.01/183.51 tff(9955,plain,(m_and_h_gate_v_in1(c_e_h_1, c_p, s2) | m_and_h_gate_v_out(c_e_h_1, c_p, s2) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s5)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s3) | m_and_h_gate_v_out(c_e_h_1, c_k, s3)), inference(lemma,lemma(discharge,[]))).
% 291.01/183.51 tff(9956,plain,
% 291.01/183.51 (m_and_h_gate_v_in1(c_e_h_1, c_p, s2) | m_and_h_gate_v_out(c_e_h_1, c_p, s2) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s5)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s3)),
% 291.01/183.51 inference(unit_resolution,[status(thm)],[9955, 9879])).
% 291.01/183.51 tff(9957,plain,
% 291.01/183.51 (m_and_h_gate_v_out(c_e_h_1, c_p, s2) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s5)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s3)),
% 291.01/183.51 inference(unit_resolution,[status(thm)],[9956, 9616])).
% 291.01/183.51 tff(9958,plain,
% 291.01/183.51 (m_mutex_h_half_v_out(c_e_h_3, c_b, s3)),
% 291.01/183.51 inference(unit_resolution,[status(thm)],[9957, 3192, 9741])).
% 291.01/183.51 tff(9959,plain,
% 291.01/183.51 (~m_cell_v_req(c_e_h_1, s2)),
% 291.01/183.51 inference(unit_resolution,[status(thm)],[3198, 3192])).
% 291.01/183.51 tff(9960,plain,
% 291.01/183.51 (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s2)),
% 291.01/183.51 inference(unit_resolution,[status(thm)],[3207, 9959])).
% 291.01/183.52 tff(9961,plain,
% 291.01/183.52 ($false),
% 291.01/183.52 inference(unit_resolution,[status(thm)],[3233, 9960, 9958, 3088])).
% 291.01/183.52 tff(9962,plain,(m_and_h_gate_v_out(c_e_h_1, c_p, s2) | m_mutex_h_half_v_out(c_e_h_3, c_b, s2) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s5))), inference(lemma,lemma(discharge,[]))).
% 291.01/183.52 tff(9963,plain,
% 291.01/183.52 (m_mutex_h_half_v_out(c_e_h_3, c_b, s2) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s5))),
% 291.01/183.52 inference(unit_resolution,[status(thm)],[9962, 3191])).
% 291.01/183.52 tff(9964,plain,
% 291.01/183.52 (~m_mutex_h_half_v_out(c_e_h_3, c_b, s5)),
% 291.01/183.52 inference(unit_resolution,[status(thm)],[9963, 3086])).
% 291.01/183.52 tff(9965,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_d, s5)), introduced(assumption)).
% 291.01/183.52 tff(9966,assumption,(~m_mutex_h_half_v_out(c_e_h_3, c_b, s5)), introduced(assumption)).
% 291.01/183.52 tff(9967,plain,
% 291.01/183.52 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_d, s5)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s5))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_d, s5)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s5))),
% 291.01/183.52 inference(rewrite,[status(thm)],[])).
% 291.01/183.52 tff(9968,plain,
% 291.01/183.52 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_d, s5)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s5))),
% 291.01/183.52 inference(quant_inst,[status(thm)],[])).
% 291.01/183.52 tff(9969,plain,
% 291.01/183.52 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_d, s5)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s5)),
% 291.01/183.52 inference(modus_ponens,[status(thm)],[9968, 9967])).
% 291.01/183.52 tff(9970,plain,
% 291.01/183.52 ($false),
% 291.01/183.52 inference(unit_resolution,[status(thm)],[9969, 2808, 9966, 9965])).
% 291.01/183.52 tff(9971,plain,((~m_and_h_gate_v_in1(c_e_h_3, c_d, s5)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s5)), inference(lemma,lemma(discharge,[]))).
% 291.01/183.52 tff(9972,plain,
% 291.01/183.52 (~m_and_h_gate_v_in1(c_e_h_3, c_d, s5)),
% 291.01/183.52 inference(unit_resolution,[status(thm)],[9971, 9964])).
% 291.01/183.52 tff(9973,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_d, s5)), introduced(assumption)).
% 291.01/183.52 tff(9974,assumption,(node20(c_e_h_3, c_d, s5)), introduced(assumption)).
% 291.01/183.52 tff(9975,plain,
% 291.01/183.52 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_d, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_d, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s5))),
% 291.01/183.52 inference(rewrite,[status(thm)],[])).
% 291.01/183.52 tff(9976,plain,
% 291.01/183.52 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_d, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s5))),
% 291.01/183.52 inference(quant_inst,[status(thm)],[])).
% 291.01/183.52 tff(9977,plain,
% 291.01/183.52 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_d, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s5)),
% 291.01/183.52 inference(modus_ponens,[status(thm)],[9976, 9975])).
% 291.01/183.52 tff(9978,plain,
% 291.01/183.52 ($false),
% 291.01/183.52 inference(unit_resolution,[status(thm)],[9977, 38, 9974, 9973])).
% 291.01/183.52 tff(9979,plain,((~node20(c_e_h_3, c_d, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s5)), inference(lemma,lemma(discharge,[]))).
% 291.01/183.52 tff(9980,plain,
% 291.01/183.52 (~node20(c_e_h_3, c_d, s5)),
% 291.01/183.52 inference(unit_resolution,[status(thm)],[9979, 9972])).
% 291.01/183.52 tff(9981,assumption,(m_and_h_gate_v_out(c_e_h_3, c_d, s6)), introduced(assumption)).
% 291.01/183.52 tff(9982,assumption,(node22(c_e_h_3, c_d, s5, s6)), introduced(assumption)).
% 291.01/183.52 tff(9983,plain,
% 291.01/183.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_d, s6)) | (~node22(c_e_h_3, c_d, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_d, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s6)) | (~node22(c_e_h_3, c_d, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_d, s5))),
% 291.01/183.52 inference(rewrite,[status(thm)],[])).
% 291.01/183.52 tff(9984,plain,
% 291.01/183.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_d, s6)) | (~node22(c_e_h_3, c_d, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_d, s5))),
% 291.01/183.52 inference(quant_inst,[status(thm)],[])).
% 291.01/183.52 tff(9985,plain,
% 291.01/183.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s6)) | (~node22(c_e_h_3, c_d, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_d, s5)),
% 291.01/183.52 inference(modus_ponens,[status(thm)],[9984, 9983])).
% 291.01/183.52 tff(9986,plain,
% 291.01/183.52 ($false),
% 291.01/183.52 inference(unit_resolution,[status(thm)],[9985, 108, 9982, 9734, 9981])).
% 291.01/183.52 tff(9987,plain,((~node22(c_e_h_3, c_d, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_d, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s6))), inference(lemma,lemma(discharge,[]))).
% 291.01/183.52 tff(9988,plain,
% 291.01/183.52 (~node22(c_e_h_3, c_d, s5, s6)),
% 291.01/183.52 inference(unit_resolution,[status(thm)],[9987, 9981, 9734])).
% 291.01/183.52 tff(9989,assumption,(~node20(c_e_h_3, c_d, s5)), introduced(assumption)).
% 291.01/183.52 tff(9990,assumption,(node21(c_e_h_3, c_d, s5, s6)), introduced(assumption)).
% 291.01/183.52 tff(9991,plain,
% 291.01/183.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_d, s5) | (~node21(c_e_h_3, c_d, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_d, s5) | (~node21(c_e_h_3, c_d, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s6)))),
% 291.01/183.52 inference(rewrite,[status(thm)],[])).
% 291.01/183.52 tff(9992,plain,
% 291.01/183.52 ((node20(c_e_h_3, c_d, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s6)) | (~node21(c_e_h_3, c_d, s5, s6))) <=> (node20(c_e_h_3, c_d, s5) | (~node21(c_e_h_3, c_d, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s6)))),
% 291.01/183.52 inference(rewrite,[status(thm)],[])).
% 291.01/183.52 tff(9993,plain,
% 291.01/183.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_d, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s6)) | (~node21(c_e_h_3, c_d, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_d, s5) | (~node21(c_e_h_3, c_d, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s6))))),
% 291.01/183.52 inference(monotonicity,[status(thm)],[9992])).
% 291.01/183.52 tff(9994,plain,
% 291.01/183.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_d, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s6)) | (~node21(c_e_h_3, c_d, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_d, s5) | (~node21(c_e_h_3, c_d, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s6)))),
% 291.01/183.52 inference(transitivity,[status(thm)],[9993, 9991])).
% 291.01/183.52 tff(9995,plain,
% 291.01/183.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_d, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s6)) | (~node21(c_e_h_3, c_d, s5, s6)))),
% 291.01/183.52 inference(quant_inst,[status(thm)],[])).
% 291.01/183.52 tff(9996,plain,
% 291.01/183.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_d, s5) | (~node21(c_e_h_3, c_d, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s6))),
% 291.01/183.52 inference(modus_ponens,[status(thm)],[9995, 9994])).
% 291.01/183.52 tff(9997,plain,
% 291.01/183.52 ($false),
% 291.01/183.52 inference(unit_resolution,[status(thm)],[9996, 52, 9990, 9981, 9989])).
% 291.01/183.52 tff(9998,plain,((~node21(c_e_h_3, c_d, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s6)) | node20(c_e_h_3, c_d, s5)), inference(lemma,lemma(discharge,[]))).
% 291.01/183.52 tff(9999,plain,
% 291.01/183.52 (~node21(c_e_h_3, c_d, s5, s6)),
% 291.01/183.52 inference(unit_resolution,[status(thm)],[9998, 9981, 9989])).
% 291.01/183.52 tff(10000,plain,
% 291.01/183.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_3, c_d, s5, s6) | node22(c_e_h_3, c_d, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_3, c_d, s5, s6) | node22(c_e_h_3, c_d, s5, s6))),
% 291.01/183.52 inference(rewrite,[status(thm)],[])).
% 291.01/183.52 tff(10001,plain,
% 291.01/183.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_3, c_d, s5, s6) | node22(c_e_h_3, c_d, s5, s6))),
% 291.01/183.52 inference(quant_inst,[status(thm)],[])).
% 291.01/183.52 tff(10002,plain,
% 291.01/183.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_3, c_d, s5, s6) | node22(c_e_h_3, c_d, s5, s6)),
% 291.01/183.52 inference(modus_ponens,[status(thm)],[10001, 10000])).
% 291.01/183.52 tff(10003,plain,
% 291.01/183.52 (node21(c_e_h_3, c_d, s5, s6) | node22(c_e_h_3, c_d, s5, s6)),
% 291.01/183.52 inference(unit_resolution,[status(thm)],[10002, 82, 1406])).
% 291.01/183.52 tff(10004,plain,
% 291.01/183.52 ($false),
% 291.01/183.52 inference(unit_resolution,[status(thm)],[10003, 9999, 9988])).
% 291.01/183.52 tff(10005,plain,((~m_and_h_gate_v_out(c_e_h_3, c_d, s6)) | node20(c_e_h_3, c_d, s5) | m_and_h_gate_v_out(c_e_h_3, c_d, s5)), inference(lemma,lemma(discharge,[]))).
% 291.01/183.52 tff(10006,plain,
% 291.01/183.52 ((~m_and_h_gate_v_out(c_e_h_3, c_d, s6)) | m_and_h_gate_v_out(c_e_h_3, c_d, s5)),
% 291.01/183.52 inference(unit_resolution,[status(thm)],[10005, 9980])).
% 291.01/183.52 tff(10007,plain,
% 291.01/183.52 (~m_and_h_gate_v_out(c_e_h_3, c_d, s6)),
% 291.01/183.52 inference(unit_resolution,[status(thm)],[10006, 9732])).
% 291.01/183.52 tff(10008,assumption,(m_or_h_gate_v_in2(c_e_h_3, c_g, s6)), introduced(assumption)).
% 291.01/183.52 tff(10009,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_d, s6)), introduced(assumption)).
% 291.01/183.52 tff(10010,plain,
% 291.01/183.52 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_g, s6)) | m_and_h_gate_v_out(c_e_h_3, c_d, s6))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_g, s6)) | m_and_h_gate_v_out(c_e_h_3, c_d, s6))),
% 291.01/183.52 inference(rewrite,[status(thm)],[])).
% 291.01/183.52 tff(10011,plain,
% 291.01/183.52 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_g, s6)) | m_and_h_gate_v_out(c_e_h_3, c_d, s6))),
% 291.01/183.52 inference(quant_inst,[status(thm)],[])).
% 291.01/183.52 tff(10012,plain,
% 291.01/183.52 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_g, s6)) | m_and_h_gate_v_out(c_e_h_3, c_d, s6)),
% 291.01/183.52 inference(modus_ponens,[status(thm)],[10011, 10010])).
% 291.01/183.52 tff(10013,plain,
% 291.01/183.52 ($false),
% 291.01/183.52 inference(unit_resolution,[status(thm)],[10012, 2762, 10009, 10008])).
% 291.01/183.52 tff(10014,plain,((~m_or_h_gate_v_in2(c_e_h_3, c_g, s6)) | m_and_h_gate_v_out(c_e_h_3, c_d, s6)), inference(lemma,lemma(discharge,[]))).
% 291.01/183.52 tff(10015,plain,
% 291.01/183.52 (~m_or_h_gate_v_in2(c_e_h_3, c_g, s6)),
% 291.01/183.52 inference(unit_resolution,[status(thm)],[10014, 10007])).
% 291.01/183.52 tff(10016,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_c, s7)), introduced(assumption)).
% 291.01/183.52 tff(10017,assumption,(~m_or_h_gate_v_in2(c_e_h_3, c_g, s5)), introduced(assumption)).
% 291.01/183.52 tff(10018,assumption,(~m_or_h_gate_v_in2(c_e_h_3, c_g, s6)), introduced(assumption)).
% 291.01/183.52 tff(10019,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_c, s4)), introduced(assumption)).
% 291.01/183.52 tff(10020,plain,
% 291.01/183.52 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_c, s4)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s4))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s4)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s4))),
% 291.01/183.52 inference(rewrite,[status(thm)],[])).
% 291.01/183.52 tff(10021,plain,
% 291.01/183.52 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_c, s4)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s4))),
% 291.01/183.52 inference(quant_inst,[status(thm)],[])).
% 291.01/183.52 tff(10022,plain,
% 291.01/183.53 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s4)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s4)),
% 291.01/183.53 inference(modus_ponens,[status(thm)],[10021, 10020])).
% 291.01/183.53 tff(10023,plain,
% 291.01/183.53 ($false),
% 291.01/183.53 inference(unit_resolution,[status(thm)],[10022, 567, 2513, 10019])).
% 291.01/183.53 tff(10024,plain,((~m_and_h_gate_v_in1(c_e_h_3, c_c, s4)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s4)), inference(lemma,lemma(discharge,[]))).
% 291.01/183.53 tff(10025,plain,
% 291.01/183.53 (~m_and_h_gate_v_in1(c_e_h_3, c_c, s4)),
% 291.01/183.53 inference(unit_resolution,[status(thm)],[10024, 2513])).
% 291.01/183.53 tff(10026,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_c, s4)), introduced(assumption)).
% 291.01/183.53 tff(10027,assumption,(node20(c_e_h_3, c_c, s4)), introduced(assumption)).
% 291.01/183.53 tff(10028,plain,
% 291.01/183.53 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_c, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_c, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s4))),
% 291.01/183.53 inference(rewrite,[status(thm)],[])).
% 291.01/183.53 tff(10029,plain,
% 291.01/183.53 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_c, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s4))),
% 291.01/183.53 inference(quant_inst,[status(thm)],[])).
% 291.01/183.53 tff(10030,plain,
% 291.01/183.53 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_c, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s4)),
% 291.01/183.53 inference(modus_ponens,[status(thm)],[10029, 10028])).
% 291.01/183.53 tff(10031,plain,
% 291.01/183.53 ($false),
% 291.01/183.53 inference(unit_resolution,[status(thm)],[10030, 38, 10027, 10026])).
% 291.01/183.53 tff(10032,plain,((~node20(c_e_h_3, c_c, s4)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s4)), inference(lemma,lemma(discharge,[]))).
% 291.01/183.53 tff(10033,plain,
% 291.01/183.53 (~node20(c_e_h_3, c_c, s4)),
% 291.01/183.53 inference(unit_resolution,[status(thm)],[10032, 10025])).
% 291.01/183.53 tff(10034,plain,
% 291.01/183.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s5)) | (~node22(c_e_h_3, c_c, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_c, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s5)) | (~node22(c_e_h_3, c_c, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_c, s4))),
% 291.01/183.53 inference(rewrite,[status(thm)],[])).
% 291.01/183.53 tff(10035,plain,
% 291.01/183.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s5)) | (~node22(c_e_h_3, c_c, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_c, s4))),
% 291.01/183.53 inference(quant_inst,[status(thm)],[])).
% 291.01/183.53 tff(10036,plain,
% 291.01/183.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s5)) | (~node22(c_e_h_3, c_c, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_c, s4)),
% 291.01/183.53 inference(modus_ponens,[status(thm)],[10035, 10034])).
% 291.01/183.53 tff(10037,plain,
% 291.01/183.53 ($false),
% 291.01/183.53 inference(unit_resolution,[status(thm)],[10036, 108, 6122, 2743, 6173])).
% 291.01/183.53 tff(10038,plain,((~node22(c_e_h_3, c_c, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_c, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s5))), inference(lemma,lemma(discharge,[]))).
% 291.01/183.53 tff(10039,plain,
% 291.01/183.53 (~node22(c_e_h_3, c_c, s4, s5)),
% 291.01/183.53 inference(unit_resolution,[status(thm)],[10038, 6173, 2743])).
% 291.01/183.53 tff(10040,assumption,(~node20(c_e_h_3, c_c, s4)), introduced(assumption)).
% 291.01/183.53 tff(10041,assumption,(node21(c_e_h_3, c_c, s4, s5)), introduced(assumption)).
% 291.01/183.53 tff(10042,plain,
% 291.01/183.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~node21(c_e_h_3, c_c, s4, s5)) | node20(c_e_h_3, c_c, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~node21(c_e_h_3, c_c, s4, s5)) | node20(c_e_h_3, c_c, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s5)))),
% 291.01/183.53 inference(rewrite,[status(thm)],[])).
% 291.01/183.53 tff(10043,plain,
% 291.01/183.53 ((node20(c_e_h_3, c_c, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s5)) | (~node21(c_e_h_3, c_c, s4, s5))) <=> ((~node21(c_e_h_3, c_c, s4, s5)) | node20(c_e_h_3, c_c, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s5)))),
% 291.01/183.53 inference(rewrite,[status(thm)],[])).
% 291.01/183.53 tff(10044,plain,
% 291.01/183.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_c, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s5)) | (~node21(c_e_h_3, c_c, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~node21(c_e_h_3, c_c, s4, s5)) | node20(c_e_h_3, c_c, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s5))))),
% 291.01/183.53 inference(monotonicity,[status(thm)],[10043])).
% 291.01/183.53 tff(10045,plain,
% 291.01/183.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_c, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s5)) | (~node21(c_e_h_3, c_c, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~node21(c_e_h_3, c_c, s4, s5)) | node20(c_e_h_3, c_c, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s5)))),
% 291.01/183.53 inference(transitivity,[status(thm)],[10044, 10042])).
% 291.01/183.53 tff(10046,plain,
% 291.01/183.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_c, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s5)) | (~node21(c_e_h_3, c_c, s4, s5)))),
% 291.01/183.53 inference(quant_inst,[status(thm)],[])).
% 291.01/183.53 tff(10047,plain,
% 291.01/183.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~node21(c_e_h_3, c_c, s4, s5)) | node20(c_e_h_3, c_c, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s5))),
% 291.01/183.53 inference(modus_ponens,[status(thm)],[10046, 10045])).
% 291.01/183.53 tff(10048,plain,
% 291.01/183.53 ($false),
% 291.01/183.53 inference(unit_resolution,[status(thm)],[10047, 52, 10041, 6173, 10040])).
% 291.01/183.53 tff(10049,plain,((~node21(c_e_h_3, c_c, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s5)) | node20(c_e_h_3, c_c, s4)), inference(lemma,lemma(discharge,[]))).
% 291.01/183.53 tff(10050,plain,
% 291.01/183.53 (~node21(c_e_h_3, c_c, s4, s5)),
% 291.01/183.53 inference(unit_resolution,[status(thm)],[10049, 6173, 10040])).
% 291.01/183.53 tff(10051,plain,
% 291.01/183.53 ($false),
% 291.01/183.53 inference(unit_resolution,[status(thm)],[6135, 10050, 10039])).
% 291.01/183.53 tff(10052,plain,((~m_and_h_gate_v_out(c_e_h_3, c_c, s5)) | node20(c_e_h_3, c_c, s4) | m_and_h_gate_v_out(c_e_h_3, c_c, s4)), inference(lemma,lemma(discharge,[]))).
% 291.01/183.53 tff(10053,plain,
% 291.01/183.53 (~m_and_h_gate_v_out(c_e_h_3, c_c, s5)),
% 291.01/183.53 inference(unit_resolution,[status(thm)],[10052, 10033, 2743])).
% 291.01/183.53 tff(10054,plain,
% 291.01/183.53 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_g, s5)) | m_and_h_gate_v_out(c_e_h_3, c_c, s5))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s5)) | m_and_h_gate_v_out(c_e_h_3, c_c, s5))),
% 291.01/183.53 inference(rewrite,[status(thm)],[])).
% 291.01/183.53 tff(10055,plain,
% 291.01/183.53 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_g, s5)) | m_and_h_gate_v_out(c_e_h_3, c_c, s5))),
% 291.01/183.53 inference(quant_inst,[status(thm)],[])).
% 291.01/183.53 tff(10056,plain,
% 291.01/183.53 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s5)) | m_and_h_gate_v_out(c_e_h_3, c_c, s5)),
% 291.01/183.53 inference(modus_ponens,[status(thm)],[10055, 10054])).
% 291.01/183.53 tff(10057,plain,
% 291.01/183.53 ($false),
% 291.01/183.53 inference(unit_resolution,[status(thm)],[10056, 2708, 5931, 6180])).
% 291.01/183.53 tff(10058,plain,((~m_or_h_gate_v_in1(c_e_h_3, c_g, s5)) | m_and_h_gate_v_out(c_e_h_3, c_c, s5)), inference(lemma,lemma(discharge,[]))).
% 291.01/183.53 tff(10059,plain,
% 291.01/183.53 (~m_or_h_gate_v_in1(c_e_h_3, c_g, s5)),
% 291.01/183.53 inference(unit_resolution,[status(thm)],[10058, 10053])).
% 291.01/183.54 tff(10060,assumption,(m_and_h_gate_v_out(c_e_h_3, c_c, s6)), introduced(assumption)).
% 291.01/183.54 tff(10061,assumption,(node22(c_e_h_3, c_c, s6, s7)), introduced(assumption)).
% 291.01/183.54 tff(10062,plain,
% 291.01/183.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s6)) | m_and_h_gate_v_out(c_e_h_3, c_c, s7) | (~node22(c_e_h_3, c_c, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s6)) | m_and_h_gate_v_out(c_e_h_3, c_c, s7) | (~node22(c_e_h_3, c_c, s6, s7)))),
% 291.01/183.54 inference(rewrite,[status(thm)],[])).
% 291.01/183.54 tff(10063,plain,
% 291.01/183.54 ((m_and_h_gate_v_out(c_e_h_3, c_c, s7) | (~node22(c_e_h_3, c_c, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s6))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_c, s6)) | m_and_h_gate_v_out(c_e_h_3, c_c, s7) | (~node22(c_e_h_3, c_c, s6, s7)))),
% 291.01/183.54 inference(rewrite,[status(thm)],[])).
% 291.01/183.54 tff(10064,plain,
% 291.01/183.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_c, s7) | (~node22(c_e_h_3, c_c, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s6)) | m_and_h_gate_v_out(c_e_h_3, c_c, s7) | (~node22(c_e_h_3, c_c, s6, s7))))),
% 291.01/183.54 inference(monotonicity,[status(thm)],[10063])).
% 291.01/183.54 tff(10065,plain,
% 291.01/183.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_c, s7) | (~node22(c_e_h_3, c_c, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s6)) | m_and_h_gate_v_out(c_e_h_3, c_c, s7) | (~node22(c_e_h_3, c_c, s6, s7)))),
% 291.01/183.54 inference(transitivity,[status(thm)],[10064, 10062])).
% 291.01/183.54 tff(10066,plain,
% 291.01/183.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_c, s7) | (~node22(c_e_h_3, c_c, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s6)))),
% 291.01/183.54 inference(quant_inst,[status(thm)],[])).
% 291.01/183.54 tff(10067,plain,
% 291.01/183.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s6)) | m_and_h_gate_v_out(c_e_h_3, c_c, s7) | (~node22(c_e_h_3, c_c, s6, s7))),
% 291.01/183.54 inference(modus_ponens,[status(thm)],[10066, 10065])).
% 291.01/183.54 tff(10068,plain,
% 291.01/183.54 ($false),
% 291.01/183.54 inference(unit_resolution,[status(thm)],[10067, 5871, 10060, 10016, 10061])).
% 291.01/183.54 tff(10069,plain,((~node22(c_e_h_3, c_c, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s6)) | m_and_h_gate_v_out(c_e_h_3, c_c, s7)), inference(lemma,lemma(discharge,[]))).
% 291.01/183.54 tff(10070,plain,
% 291.01/183.54 (~node22(c_e_h_3, c_c, s6, s7)),
% 291.01/183.54 inference(unit_resolution,[status(thm)],[10069, 10060, 10016])).
% 291.01/183.54 tff(10071,plain,
% 291.01/183.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_3, c_c, s6, s7) | node22(c_e_h_3, c_c, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_3, c_c, s6, s7) | node22(c_e_h_3, c_c, s6, s7))),
% 291.01/183.54 inference(rewrite,[status(thm)],[])).
% 291.01/183.54 tff(10072,plain,
% 291.01/183.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_3, c_c, s6, s7) | node22(c_e_h_3, c_c, s6, s7))),
% 291.01/183.54 inference(quant_inst,[status(thm)],[])).
% 291.01/183.54 tff(10073,plain,
% 291.01/183.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_3, c_c, s6, s7) | node22(c_e_h_3, c_c, s6, s7)),
% 291.01/183.54 inference(modus_ponens,[status(thm)],[10072, 10071])).
% 291.01/183.54 tff(10074,plain,
% 291.01/183.54 (node21(c_e_h_3, c_c, s6, s7) | node22(c_e_h_3, c_c, s6, s7)),
% 291.01/183.54 inference(unit_resolution,[status(thm)],[10073, 82, 1844])).
% 291.01/183.54 tff(10075,plain,
% 291.01/183.54 (node21(c_e_h_3, c_c, s6, s7)),
% 291.01/183.54 inference(unit_resolution,[status(thm)],[10074, 10070])).
% 291.01/183.54 tff(10076,assumption,(m_and_h_gate_v_out(c_e_h_3, c_q, s6)), introduced(assumption)).
% 291.01/183.54 tff(10077,plain,
% 291.01/183.54 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s5)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s5)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5))),
% 291.01/183.54 inference(rewrite,[status(thm)],[])).
% 291.01/183.54 tff(10078,plain,
% 291.01/183.54 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s5)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5))),
% 291.01/183.54 inference(quant_inst,[status(thm)],[])).
% 291.01/183.54 tff(10079,plain,
% 291.01/183.54 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s5)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s5)),
% 291.01/183.54 inference(modus_ponens,[status(thm)],[10078, 10077])).
% 291.01/183.54 tff(10080,plain,
% 291.01/183.54 (~m_and_h_gate_v_in2(c_e_h_3, c_q, s5)),
% 291.01/183.54 inference(unit_resolution,[status(thm)],[10079, 5621, 7016])).
% 291.01/183.54 tff(10081,plain,
% 291.01/183.54 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s5)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s5)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s5))),
% 291.01/183.54 inference(rewrite,[status(thm)],[])).
% 291.01/183.54 tff(10082,plain,
% 291.01/183.54 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s5)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s5))),
% 291.01/183.54 inference(quant_inst,[status(thm)],[])).
% 291.01/183.54 tff(10083,plain,
% 291.01/183.54 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s5)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s5)),
% 291.01/183.54 inference(modus_ponens,[status(thm)],[10082, 10081])).
% 291.01/183.54 tff(10084,plain,
% 291.01/183.54 (~node20(c_e_h_3, c_q, s5)),
% 291.01/183.54 inference(unit_resolution,[status(thm)],[10083, 4563, 10080])).
% 291.01/183.54 tff(10085,assumption,(node21(c_e_h_3, c_q, s5, s6)), introduced(assumption)).
% 291.01/183.54 tff(10086,plain,
% 291.01/183.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s6)) | (~node21(c_e_h_3, c_q, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_q, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s6)) | (~node21(c_e_h_3, c_q, s5, s6)))),
% 291.01/183.54 inference(rewrite,[status(thm)],[])).
% 291.01/183.54 tff(10087,plain,
% 291.01/183.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s6)) | (~node21(c_e_h_3, c_q, s5, s6)))),
% 291.01/183.54 inference(quant_inst,[status(thm)],[])).
% 291.01/183.54 tff(10088,plain,
% 291.01/183.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_q, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s6)) | (~node21(c_e_h_3, c_q, s5, s6))),
% 291.01/183.54 inference(modus_ponens,[status(thm)],[10087, 10086])).
% 291.01/183.54 tff(10089,plain,
% 291.01/183.54 ($false),
% 291.01/183.54 inference(unit_resolution,[status(thm)],[10088, 52, 10076, 10085, 10084])).
% 291.01/183.54 tff(10090,plain,((~node21(c_e_h_3, c_q, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s6))), inference(lemma,lemma(discharge,[]))).
% 291.01/183.54 tff(10091,plain,
% 291.01/183.54 (~node21(c_e_h_3, c_q, s5, s6)),
% 291.01/183.54 inference(unit_resolution,[status(thm)],[10090, 10076])).
% 291.01/183.54 tff(10092,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_q, s4)), introduced(assumption)).
% 291.01/183.54 tff(10093,assumption,(m_and_h_gate_v_out(c_e_h_3, c_q, s5)), introduced(assumption)).
% 291.01/183.54 tff(10094,plain,
% 291.01/183.54 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s4)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s4)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4))),
% 291.01/183.54 inference(rewrite,[status(thm)],[])).
% 291.01/183.54 tff(10095,plain,
% 291.01/183.54 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s4)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4))),
% 291.01/183.54 inference(quant_inst,[status(thm)],[])).
% 291.01/183.54 tff(10096,plain,
% 291.01/183.54 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s4)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s4)),
% 291.01/183.54 inference(modus_ponens,[status(thm)],[10095, 10094])).
% 291.01/183.54 tff(10097,plain,
% 291.01/183.54 (~m_and_h_gate_v_in2(c_e_h_3, c_q, s4)),
% 291.01/183.54 inference(unit_resolution,[status(thm)],[10096, 5621, 7000])).
% 291.01/183.54 tff(10098,plain,
% 291.01/183.54 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s4)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s4)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s4))),
% 291.01/183.54 inference(rewrite,[status(thm)],[])).
% 291.01/183.54 tff(10099,plain,
% 291.01/183.54 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s4)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s4))),
% 291.01/183.54 inference(quant_inst,[status(thm)],[])).
% 291.01/183.54 tff(10100,plain,
% 291.01/183.54 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s4)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s4)),
% 291.01/183.54 inference(modus_ponens,[status(thm)],[10099, 10098])).
% 291.01/183.54 tff(10101,plain,
% 291.01/183.54 (~node20(c_e_h_3, c_q, s4)),
% 291.01/183.54 inference(unit_resolution,[status(thm)],[10100, 4563, 10097])).
% 291.01/183.54 tff(10102,assumption,(node21(c_e_h_3, c_q, s4, s5)), introduced(assumption)).
% 291.01/183.54 tff(10103,plain,
% 291.01/183.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s5)) | node20(c_e_h_3, c_q, s4) | (~node21(c_e_h_3, c_q, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s5)) | node20(c_e_h_3, c_q, s4) | (~node21(c_e_h_3, c_q, s4, s5)))),
% 291.01/183.54 inference(rewrite,[status(thm)],[])).
% 291.01/183.54 tff(10104,plain,
% 291.01/183.54 ((node20(c_e_h_3, c_q, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s5)) | (~node21(c_e_h_3, c_q, s4, s5))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_q, s5)) | node20(c_e_h_3, c_q, s4) | (~node21(c_e_h_3, c_q, s4, s5)))),
% 291.01/183.54 inference(rewrite,[status(thm)],[])).
% 291.01/183.54 tff(10105,plain,
% 291.01/183.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s5)) | (~node21(c_e_h_3, c_q, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s5)) | node20(c_e_h_3, c_q, s4) | (~node21(c_e_h_3, c_q, s4, s5))))),
% 291.01/183.54 inference(monotonicity,[status(thm)],[10104])).
% 291.01/183.54 tff(10106,plain,
% 291.01/183.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s5)) | (~node21(c_e_h_3, c_q, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s5)) | node20(c_e_h_3, c_q, s4) | (~node21(c_e_h_3, c_q, s4, s5)))),
% 291.01/183.55 inference(transitivity,[status(thm)],[10105, 10103])).
% 291.01/183.55 tff(10107,plain,
% 291.01/183.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s5)) | (~node21(c_e_h_3, c_q, s4, s5)))),
% 291.01/183.55 inference(quant_inst,[status(thm)],[])).
% 291.01/183.55 tff(10108,plain,
% 291.01/183.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s5)) | node20(c_e_h_3, c_q, s4) | (~node21(c_e_h_3, c_q, s4, s5))),
% 291.01/183.55 inference(modus_ponens,[status(thm)],[10107, 10106])).
% 291.01/183.55 tff(10109,plain,
% 291.01/183.55 ($false),
% 291.01/183.55 inference(unit_resolution,[status(thm)],[10108, 52, 10093, 10102, 10101])).
% 291.01/183.55 tff(10110,plain,((~node21(c_e_h_3, c_q, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s5))), inference(lemma,lemma(discharge,[]))).
% 291.01/183.55 tff(10111,plain,
% 291.01/183.55 (~node21(c_e_h_3, c_q, s4, s5)),
% 291.01/183.55 inference(unit_resolution,[status(thm)],[10110, 10093])).
% 291.01/183.55 tff(10112,plain,
% 291.01/183.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_3, c_q, s4, s5) | node22(c_e_h_3, c_q, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_3, c_q, s4, s5) | node22(c_e_h_3, c_q, s4, s5))),
% 291.01/183.55 inference(rewrite,[status(thm)],[])).
% 291.01/183.55 tff(10113,plain,
% 291.01/183.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_3, c_q, s4, s5) | node22(c_e_h_3, c_q, s4, s5))),
% 291.01/183.55 inference(quant_inst,[status(thm)],[])).
% 291.01/183.55 tff(10114,plain,
% 291.01/183.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_3, c_q, s4, s5) | node22(c_e_h_3, c_q, s4, s5)),
% 291.01/183.55 inference(modus_ponens,[status(thm)],[10113, 10112])).
% 291.01/183.55 tff(10115,plain,
% 291.01/183.55 (node21(c_e_h_3, c_q, s4, s5) | node22(c_e_h_3, c_q, s4, s5)),
% 291.01/183.55 inference(unit_resolution,[status(thm)],[10114, 82, 1028])).
% 291.01/183.55 tff(10116,plain,
% 291.01/183.55 (node22(c_e_h_3, c_q, s4, s5)),
% 291.01/183.55 inference(unit_resolution,[status(thm)],[10115, 10111])).
% 291.01/183.55 tff(10117,plain,
% 291.01/183.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s5)) | (~node22(c_e_h_3, c_q, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_q, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s5)) | (~node22(c_e_h_3, c_q, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_q, s4))),
% 291.01/183.55 inference(rewrite,[status(thm)],[])).
% 291.01/183.55 tff(10118,plain,
% 291.01/183.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s5)) | (~node22(c_e_h_3, c_q, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_q, s4))),
% 291.01/183.55 inference(quant_inst,[status(thm)],[])).
% 291.01/183.55 tff(10119,plain,
% 291.01/183.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s5)) | (~node22(c_e_h_3, c_q, s4, s5)) | m_and_h_gate_v_out(c_e_h_3, c_q, s4)),
% 291.01/183.55 inference(modus_ponens,[status(thm)],[10118, 10117])).
% 291.01/183.55 tff(10120,plain,
% 291.01/183.55 ($false),
% 291.01/183.55 inference(unit_resolution,[status(thm)],[10119, 108, 10093, 10116, 10092])).
% 291.01/183.55 tff(10121,plain,((~m_and_h_gate_v_out(c_e_h_3, c_q, s5)) | m_and_h_gate_v_out(c_e_h_3, c_q, s4)), inference(lemma,lemma(discharge,[]))).
% 291.01/183.55 tff(10122,plain,
% 291.01/183.55 (~m_and_h_gate_v_out(c_e_h_3, c_q, s5)),
% 291.01/183.55 inference(unit_resolution,[status(thm)],[10121, 6103])).
% 291.01/183.55 tff(10123,assumption,(node22(c_e_h_3, c_q, s5, s6)), introduced(assumption)).
% 291.01/183.55 tff(10124,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_q, s5)), introduced(assumption)).
% 291.01/183.55 tff(10125,plain,
% 291.01/183.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s6)) | (~node22(c_e_h_3, c_q, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_q, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s6)) | (~node22(c_e_h_3, c_q, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_q, s5))),
% 291.01/183.55 inference(rewrite,[status(thm)],[])).
% 291.01/183.55 tff(10126,plain,
% 291.01/183.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s6)) | (~node22(c_e_h_3, c_q, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_q, s5))),
% 291.01/183.55 inference(quant_inst,[status(thm)],[])).
% 291.01/183.55 tff(10127,plain,
% 291.01/183.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s6)) | (~node22(c_e_h_3, c_q, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_q, s5)),
% 291.01/183.55 inference(modus_ponens,[status(thm)],[10126, 10125])).
% 291.01/183.55 tff(10128,plain,
% 291.01/183.55 ($false),
% 291.01/183.55 inference(unit_resolution,[status(thm)],[10127, 108, 10124, 10076, 10123])).
% 291.01/183.55 tff(10129,plain,((~node22(c_e_h_3, c_q, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_q, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s6))), inference(lemma,lemma(discharge,[]))).
% 291.01/183.55 tff(10130,plain,
% 291.01/183.55 ((~node22(c_e_h_3, c_q, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s6))),
% 291.01/183.55 inference(unit_resolution,[status(thm)],[10129, 10122])).
% 291.01/183.55 tff(10131,plain,
% 291.01/183.55 (~node22(c_e_h_3, c_q, s5, s6)),
% 291.01/183.55 inference(unit_resolution,[status(thm)],[10130, 10076])).
% 291.01/183.55 tff(10132,plain,
% 291.01/183.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_3, c_q, s5, s6) | node22(c_e_h_3, c_q, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_3, c_q, s5, s6) | node22(c_e_h_3, c_q, s5, s6))),
% 291.01/183.55 inference(rewrite,[status(thm)],[])).
% 291.01/183.55 tff(10133,plain,
% 291.01/183.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_3, c_q, s5, s6) | node22(c_e_h_3, c_q, s5, s6))),
% 291.01/183.55 inference(quant_inst,[status(thm)],[])).
% 291.01/183.55 tff(10134,plain,
% 291.01/183.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_3, c_q, s5, s6) | node22(c_e_h_3, c_q, s5, s6)),
% 291.01/183.55 inference(modus_ponens,[status(thm)],[10133, 10132])).
% 291.01/183.55 tff(10135,plain,
% 291.01/183.55 (node21(c_e_h_3, c_q, s5, s6) | node22(c_e_h_3, c_q, s5, s6)),
% 291.01/183.55 inference(unit_resolution,[status(thm)],[10134, 82, 1406])).
% 291.01/183.55 tff(10136,plain,
% 291.01/183.55 ($false),
% 291.01/183.55 inference(unit_resolution,[status(thm)],[10135, 10131, 10091])).
% 291.01/183.55 tff(10137,plain,(~m_and_h_gate_v_out(c_e_h_3, c_q, s6)), inference(lemma,lemma(discharge,[]))).
% 291.01/183.55 tff(10138,plain,
% 291.01/183.55 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s6))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s6))),
% 291.01/183.55 inference(rewrite,[status(thm)],[])).
% 291.01/183.55 tff(10139,plain,
% 291.01/183.55 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s6))),
% 291.01/183.55 inference(quant_inst,[status(thm)],[])).
% 291.01/183.55 tff(10140,plain,
% 291.01/183.55 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s6)),
% 291.01/183.55 inference(modus_ponens,[status(thm)],[10139, 10138])).
% 291.01/183.55 tff(10141,plain,
% 291.01/183.55 (node3(c_e_h_3, c_e_h_1, s6)),
% 291.01/183.55 inference(unit_resolution,[status(thm)],[10140, 2922, 1056])).
% 291.01/183.55 tff(10142,plain,
% 291.01/183.55 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s6)) | (~node3(c_e_h_3, c_e_h_1, s6)) | m_and_h_gate_v_out(c_e_h_3, c_q, s6))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s6)) | (~node3(c_e_h_3, c_e_h_1, s6)) | m_and_h_gate_v_out(c_e_h_3, c_q, s6))),
% 291.01/183.55 inference(rewrite,[status(thm)],[])).
% 291.01/183.55 tff(10143,plain,
% 291.01/183.55 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s6)) | (~node3(c_e_h_3, c_e_h_1, s6)) | m_and_h_gate_v_out(c_e_h_3, c_q, s6))),
% 291.01/183.55 inference(quant_inst,[status(thm)],[])).
% 291.01/183.55 tff(10144,plain,
% 291.01/183.55 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s6)) | (~node3(c_e_h_3, c_e_h_1, s6)) | m_and_h_gate_v_out(c_e_h_3, c_q, s6)),
% 291.01/183.55 inference(modus_ponens,[status(thm)],[10143, 10142])).
% 291.01/183.55 tff(10145,plain,
% 291.01/183.55 ((~m_cell_v_ack(c_e_h_1, s6)) | m_and_h_gate_v_out(c_e_h_3, c_q, s6)),
% 291.01/183.55 inference(unit_resolution,[status(thm)],[10144, 1073, 10141])).
% 291.01/183.55 tff(10146,plain,
% 291.01/183.55 (~m_cell_v_ack(c_e_h_1, s6)),
% 291.01/183.55 inference(unit_resolution,[status(thm)],[10145, 10137])).
% 291.01/183.55 tff(10147,plain,
% 291.01/183.55 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node2(c_e_h_3, c_e_h_1, s6))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node2(c_e_h_3, c_e_h_1, s6))),
% 291.01/183.55 inference(rewrite,[status(thm)],[])).
% 291.01/183.55 tff(10148,plain,
% 291.01/183.55 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node2(c_e_h_3, c_e_h_1, s6))),
% 291.01/183.55 inference(quant_inst,[status(thm)],[])).
% 291.01/183.55 tff(10149,plain,
% 291.01/183.55 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node2(c_e_h_3, c_e_h_1, s6)),
% 291.01/183.55 inference(modus_ponens,[status(thm)],[10148, 10147])).
% 291.01/183.55 tff(10150,plain,
% 291.01/183.55 (node2(c_e_h_3, c_e_h_1, s6)),
% 291.01/183.55 inference(unit_resolution,[status(thm)],[10149, 2922, 5821])).
% 291.01/183.55 tff(10151,plain,
% 291.01/183.55 (((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | ((~node2(c_e_h_3, c_e_h_1, s6)) | m_cell_v_ack(c_e_h_1, s6) | m_and_h_gate_v_in2(c_e_h_3, c_c, s6))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | (~node2(c_e_h_3, c_e_h_1, s6)) | m_cell_v_ack(c_e_h_1, s6) | m_and_h_gate_v_in2(c_e_h_3, c_c, s6))),
% 291.01/183.55 inference(rewrite,[status(thm)],[])).
% 291.01/183.55 tff(10152,plain,
% 291.01/183.55 ((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | ((~node2(c_e_h_3, c_e_h_1, s6)) | m_cell_v_ack(c_e_h_1, s6) | m_and_h_gate_v_in2(c_e_h_3, c_c, s6))),
% 291.01/183.55 inference(quant_inst,[status(thm)],[])).
% 291.01/183.55 tff(10153,plain,
% 291.01/183.55 ((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | (~node2(c_e_h_3, c_e_h_1, s6)) | m_cell_v_ack(c_e_h_1, s6) | m_and_h_gate_v_in2(c_e_h_3, c_c, s6)),
% 291.01/183.55 inference(modus_ponens,[status(thm)],[10152, 10151])).
% 291.01/183.55 tff(10154,plain,
% 291.01/183.55 (m_cell_v_ack(c_e_h_1, s6) | m_and_h_gate_v_in2(c_e_h_3, c_c, s6)),
% 291.01/183.55 inference(unit_resolution,[status(thm)],[10153, 5835, 10150])).
% 291.01/183.55 tff(10155,plain,
% 291.01/183.55 (m_and_h_gate_v_in2(c_e_h_3, c_c, s6)),
% 291.01/183.55 inference(unit_resolution,[status(thm)],[10154, 10146])).
% 291.01/183.55 tff(10156,plain,
% 291.01/183.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_c, s6)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s6)) | m_and_h_gate_v_out(c_e_h_3, c_c, s7) | (~node21(c_e_h_3, c_c, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s6)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s6)) | m_and_h_gate_v_out(c_e_h_3, c_c, s7) | (~node21(c_e_h_3, c_c, s6, s7)))),
% 291.01/183.56 inference(rewrite,[status(thm)],[])).
% 291.01/183.56 tff(10157,plain,
% 291.01/183.56 (((~node21(c_e_h_3, c_c, s6, s7)) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s6)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s6)) | m_and_h_gate_v_out(c_e_h_3, c_c, s7)) <=> ((~m_and_h_gate_v_in2(c_e_h_3, c_c, s6)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s6)) | m_and_h_gate_v_out(c_e_h_3, c_c, s7) | (~node21(c_e_h_3, c_c, s6, s7)))),
% 291.01/183.56 inference(rewrite,[status(thm)],[])).
% 291.01/183.56 tff(10158,plain,
% 291.01/183.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_c, s6, s7)) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s6)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s6)) | m_and_h_gate_v_out(c_e_h_3, c_c, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_c, s6)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s6)) | m_and_h_gate_v_out(c_e_h_3, c_c, s7) | (~node21(c_e_h_3, c_c, s6, s7))))),
% 291.01/183.56 inference(monotonicity,[status(thm)],[10157])).
% 291.01/183.56 tff(10159,plain,
% 291.01/183.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_c, s6, s7)) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s6)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s6)) | m_and_h_gate_v_out(c_e_h_3, c_c, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s6)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s6)) | m_and_h_gate_v_out(c_e_h_3, c_c, s7) | (~node21(c_e_h_3, c_c, s6, s7)))),
% 291.01/183.56 inference(transitivity,[status(thm)],[10158, 10156])).
% 291.01/183.56 tff(10160,plain,
% 291.01/183.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_c, s6, s7)) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s6)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s6)) | m_and_h_gate_v_out(c_e_h_3, c_c, s7))),
% 291.01/183.56 inference(quant_inst,[status(thm)],[])).
% 291.01/183.56 tff(10161,plain,
% 291.01/183.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s6)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s6)) | m_and_h_gate_v_out(c_e_h_3, c_c, s7) | (~node21(c_e_h_3, c_c, s6, s7))),
% 291.01/183.56 inference(modus_ponens,[status(thm)],[10160, 10159])).
% 291.01/183.56 tff(10162,plain,
% 291.01/183.56 (~m_and_h_gate_v_in1(c_e_h_3, c_c, s6)),
% 291.01/183.56 inference(unit_resolution,[status(thm)],[10161, 5851, 10155, 10016, 10075])).
% 291.01/183.56 tff(10163,assumption,(~node20(c_e_h_3, c_c, s5)), introduced(assumption)).
% 291.01/183.56 tff(10164,assumption,(node21(c_e_h_3, c_c, s5, s6)), introduced(assumption)).
% 291.01/183.56 tff(10165,plain,
% 291.01/183.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_c, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s6)) | (~node21(c_e_h_3, c_c, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_c, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s6)) | (~node21(c_e_h_3, c_c, s5, s6)))),
% 291.01/183.56 inference(rewrite,[status(thm)],[])).
% 291.01/183.56 tff(10166,plain,
% 291.01/183.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_c, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s6)) | (~node21(c_e_h_3, c_c, s5, s6)))),
% 291.01/183.56 inference(quant_inst,[status(thm)],[])).
% 291.01/183.56 tff(10167,plain,
% 291.01/183.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_c, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s6)) | (~node21(c_e_h_3, c_c, s5, s6))),
% 291.01/183.56 inference(modus_ponens,[status(thm)],[10166, 10165])).
% 291.01/183.56 tff(10168,plain,
% 291.01/183.56 ($false),
% 291.01/183.56 inference(unit_resolution,[status(thm)],[10167, 52, 10164, 10163, 10060])).
% 291.01/183.56 tff(10169,plain,((~node21(c_e_h_3, c_c, s5, s6)) | node20(c_e_h_3, c_c, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s6))), inference(lemma,lemma(discharge,[]))).
% 291.01/183.56 tff(10170,plain,
% 291.01/183.56 (~node21(c_e_h_3, c_c, s5, s6)),
% 291.01/183.56 inference(unit_resolution,[status(thm)],[10169, 10060, 10163])).
% 291.01/183.56 tff(10171,plain,
% 291.01/183.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_3, c_c, s5, s6) | node22(c_e_h_3, c_c, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_3, c_c, s5, s6) | node22(c_e_h_3, c_c, s5, s6))),
% 291.01/183.56 inference(rewrite,[status(thm)],[])).
% 291.01/183.56 tff(10172,plain,
% 291.01/183.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_3, c_c, s5, s6) | node22(c_e_h_3, c_c, s5, s6))),
% 291.01/183.56 inference(quant_inst,[status(thm)],[])).
% 291.01/183.56 tff(10173,plain,
% 291.01/183.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_3, c_c, s5, s6) | node22(c_e_h_3, c_c, s5, s6)),
% 291.01/183.56 inference(modus_ponens,[status(thm)],[10172, 10171])).
% 291.01/183.56 tff(10174,plain,
% 291.01/183.56 (node21(c_e_h_3, c_c, s5, s6) | node22(c_e_h_3, c_c, s5, s6)),
% 291.01/183.56 inference(unit_resolution,[status(thm)],[10173, 82, 1406])).
% 291.01/183.56 tff(10175,plain,
% 291.01/183.56 (node22(c_e_h_3, c_c, s5, s6)),
% 291.01/183.56 inference(unit_resolution,[status(thm)],[10174, 10170])).
% 291.01/183.56 tff(10176,plain,
% 291.01/183.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s6)) | (~node22(c_e_h_3, c_c, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_c, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s6)) | (~node22(c_e_h_3, c_c, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_c, s5))),
% 291.01/183.56 inference(rewrite,[status(thm)],[])).
% 291.01/183.56 tff(10177,plain,
% 291.01/183.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s6)) | (~node22(c_e_h_3, c_c, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_c, s5))),
% 291.01/183.56 inference(quant_inst,[status(thm)],[])).
% 291.01/183.56 tff(10178,plain,
% 291.01/183.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s6)) | (~node22(c_e_h_3, c_c, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_c, s5)),
% 291.01/183.56 inference(modus_ponens,[status(thm)],[10177, 10176])).
% 291.01/183.56 tff(10179,plain,
% 291.01/183.56 ($false),
% 291.01/183.56 inference(unit_resolution,[status(thm)],[10178, 108, 5931, 10175, 10060])).
% 291.01/183.56 tff(10180,plain,((~m_and_h_gate_v_out(c_e_h_3, c_c, s6)) | m_and_h_gate_v_out(c_e_h_3, c_c, s5) | node20(c_e_h_3, c_c, s5)), inference(lemma,lemma(discharge,[]))).
% 291.01/183.56 tff(10181,plain,
% 291.01/183.56 (node20(c_e_h_3, c_c, s5)),
% 291.01/183.56 inference(unit_resolution,[status(thm)],[10180, 10060, 5931])).
% 291.01/183.56 tff(10182,plain,
% 291.01/183.56 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_c, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_c, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s5))),
% 291.01/183.56 inference(rewrite,[status(thm)],[])).
% 291.01/183.56 tff(10183,plain,
% 291.01/183.56 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_c, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s5))),
% 291.01/183.56 inference(quant_inst,[status(thm)],[])).
% 291.01/183.56 tff(10184,plain,
% 291.01/183.56 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_c, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s5)),
% 291.01/183.56 inference(modus_ponens,[status(thm)],[10183, 10182])).
% 291.01/183.56 tff(10185,plain,
% 291.01/183.56 (m_and_h_gate_v_in1(c_e_h_3, c_c, s5)),
% 291.01/183.57 inference(unit_resolution,[status(thm)],[10184, 38, 10181])).
% 291.01/183.57 tff(10186,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_c, s5)), introduced(assumption)).
% 291.01/183.57 tff(10187,plain,
% 291.01/183.57 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_c, s5)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s5))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s5)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s5))),
% 291.01/183.57 inference(rewrite,[status(thm)],[])).
% 291.01/183.57 tff(10188,plain,
% 291.01/183.57 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_c, s5)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s5))),
% 291.01/183.57 inference(quant_inst,[status(thm)],[])).
% 291.01/183.57 tff(10189,plain,
% 291.01/183.57 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s5)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s5)),
% 291.01/183.57 inference(modus_ponens,[status(thm)],[10188, 10187])).
% 291.01/183.57 tff(10190,plain,
% 291.01/183.57 ($false),
% 291.01/183.57 inference(unit_resolution,[status(thm)],[10189, 567, 1448, 10186])).
% 291.01/183.57 tff(10191,plain,((~m_and_h_gate_v_in1(c_e_h_3, c_c, s5)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s5)), inference(lemma,lemma(discharge,[]))).
% 291.01/183.57 tff(10192,plain,
% 291.01/183.57 (m_mutex_h_half_v_out(c_e_h_3, c_a, s5)),
% 291.01/183.57 inference(unit_resolution,[status(thm)],[10191, 10185])).
% 291.01/183.57 tff(10193,plain,
% 291.01/183.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s5)) | (~node13(c_e_h_3, c_a, s4, s5)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s5)) | (~node13(c_e_h_3, c_a, s4, s5)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s4))),
% 291.01/183.57 inference(rewrite,[status(thm)],[])).
% 291.01/183.57 tff(10194,plain,
% 291.01/183.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s5)) | (~node13(c_e_h_3, c_a, s4, s5)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s4))),
% 291.01/183.57 inference(quant_inst,[status(thm)],[])).
% 291.01/183.57 tff(10195,plain,
% 291.01/183.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s5)) | (~node13(c_e_h_3, c_a, s4, s5)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s4)),
% 291.01/183.57 inference(modus_ponens,[status(thm)],[10194, 10193])).
% 291.01/183.57 tff(10196,plain,
% 291.01/183.57 ($false),
% 291.01/183.57 inference(unit_resolution,[status(thm)],[10195, 423, 1449, 2513, 1492])).
% 291.01/183.57 tff(10197,plain,((~node13(c_e_h_3, c_a, s4, s5)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s4) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s5))), inference(lemma,lemma(discharge,[]))).
% 291.01/183.57 tff(10198,plain,
% 291.01/183.57 (~node13(c_e_h_3, c_a, s4, s5)),
% 291.01/183.57 inference(unit_resolution,[status(thm)],[10197, 1492, 2513])).
% 291.01/183.57 tff(10199,assumption,(node12(c_e_h_3, c_a, s4, s5)), introduced(assumption)).
% 291.01/183.57 tff(10200,plain,
% 291.01/183.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_3, c_a, s4) | (~node12(c_e_h_3, c_a, s4, s5)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s4) | (~node12(c_e_h_3, c_a, s4, s5)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s5)))),
% 291.01/183.57 inference(rewrite,[status(thm)],[])).
% 291.01/183.57 tff(10201,plain,
% 291.01/183.57 (((~node12(c_e_h_3, c_a, s4, s5)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s4) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s5))) <=> (m_mutex_h_half_v_inp(c_e_h_3, c_a, s4) | (~node12(c_e_h_3, c_a, s4, s5)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s5)))),
% 291.01/183.57 inference(rewrite,[status(thm)],[])).
% 291.01/183.57 tff(10202,plain,
% 291.01/183.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_a, s4, s5)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s4) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_3, c_a, s4) | (~node12(c_e_h_3, c_a, s4, s5)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s5))))),
% 291.01/183.57 inference(monotonicity,[status(thm)],[10201])).
% 291.01/183.57 tff(10203,plain,
% 291.01/183.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_a, s4, s5)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s4) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s4) | (~node12(c_e_h_3, c_a, s4, s5)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s5)))),
% 291.01/183.57 inference(transitivity,[status(thm)],[10202, 10200])).
% 291.01/183.57 tff(10204,plain,
% 291.01/183.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_a, s4, s5)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s4) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s5)))),
% 291.01/183.57 inference(quant_inst,[status(thm)],[])).
% 291.01/183.57 tff(10205,plain,
% 291.01/183.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s4) | (~node12(c_e_h_3, c_a, s4, s5)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s5))),
% 291.01/183.57 inference(modus_ponens,[status(thm)],[10204, 10203])).
% 291.01/183.57 tff(10206,plain,
% 291.01/183.57 ($false),
% 291.01/183.57 inference(unit_resolution,[status(thm)],[10205, 454, 10199, 1492, 1440])).
% 291.01/183.57 tff(10207,plain,((~node12(c_e_h_3, c_a, s4, s5)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s5)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s4)), inference(lemma,lemma(discharge,[]))).
% 291.01/183.57 tff(10208,plain,
% 291.01/183.57 (~node12(c_e_h_3, c_a, s4, s5)),
% 291.01/183.57 inference(unit_resolution,[status(thm)],[10207, 1492, 1440])).
% 291.01/183.57 tff(10209,plain,
% 291.01/183.57 ($false),
% 291.01/183.57 inference(unit_resolution,[status(thm)],[1472, 10208, 10198])).
% 291.01/183.57 tff(10210,plain,((~m_mutex_h_half_v_out(c_e_h_3, c_a, s5)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s4) | m_mutex_h_half_v_out(c_e_h_3, c_a, s4)), inference(lemma,lemma(discharge,[]))).
% 291.01/183.57 tff(10211,plain,
% 291.01/183.57 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s4)),
% 291.01/183.57 inference(unit_resolution,[status(thm)],[10210, 10192, 2513])).
% 291.01/183.57 tff(10212,plain,
% 291.01/183.57 (((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_a, s4)) | m_user_v_req(c_e_h_3, c_u, s4))) <=> ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s4)) | m_user_v_req(c_e_h_3, c_u, s4))),
% 291.01/183.57 inference(rewrite,[status(thm)],[])).
% 291.01/183.57 tff(10213,plain,
% 291.01/183.57 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_a, s4)) | m_user_v_req(c_e_h_3, c_u, s4))),
% 291.01/183.57 inference(quant_inst,[status(thm)],[])).
% 291.01/183.57 tff(10214,plain,
% 291.01/183.57 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s4)) | m_user_v_req(c_e_h_3, c_u, s4)),
% 291.01/183.57 inference(modus_ponens,[status(thm)],[10213, 10212])).
% 291.01/183.57 tff(10215,plain,
% 291.01/183.57 (m_user_v_req(c_e_h_3, c_u, s4)),
% 291.01/183.57 inference(unit_resolution,[status(thm)],[10214, 395, 10211])).
% 291.01/183.57 tff(10216,plain,
% 291.01/183.57 (m_user_v_req(c_e_h_3, c_u, s5)),
% 291.01/183.57 inference(unit_resolution,[status(thm)],[1035, 10215])).
% 291.01/183.57 tff(10217,plain,
% 291.01/183.57 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s5)),
% 291.01/183.57 inference(unit_resolution,[status(thm)],[1438, 10216])).
% 291.01/183.57 tff(10218,plain,
% 291.01/183.57 (m_mutex_h_half_v_out(c_e_h_3, c_a, s6)),
% 291.01/183.57 inference(unit_resolution,[status(thm)],[1515, 10217, 10192])).
% 291.01/183.57 tff(10219,plain,
% 291.01/183.57 (((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s6))) <=> ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s6))),
% 291.10/183.57 inference(rewrite,[status(thm)],[])).
% 291.10/183.57 tff(10220,plain,
% 291.10/183.57 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s6))),
% 291.10/183.57 inference(quant_inst,[status(thm)],[])).
% 291.10/183.57 tff(10221,plain,
% 291.10/183.57 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s6)),
% 291.10/183.57 inference(modus_ponens,[status(thm)],[10220, 10219])).
% 291.10/183.57 tff(10222,plain,
% 291.10/183.57 ($false),
% 291.10/183.57 inference(unit_resolution,[status(thm)],[10221, 2556, 10218, 10162])).
% 291.10/183.57 tff(10223,plain,((~m_and_h_gate_v_out(c_e_h_3, c_c, s6)) | m_and_h_gate_v_out(c_e_h_3, c_c, s7) | m_mutex_h_half_v_out(c_e_h_3, c_a, s4) | m_and_h_gate_v_out(c_e_h_3, c_c, s5)), inference(lemma,lemma(discharge,[]))).
% 291.10/183.57 tff(10224,plain,
% 291.10/183.57 (~m_and_h_gate_v_out(c_e_h_3, c_c, s6)),
% 291.10/183.57 inference(unit_resolution,[status(thm)],[10223, 2513, 10016, 10053])).
% 291.10/183.57 tff(10225,assumption,(m_or_h_gate_v_in1(c_e_h_3, c_g, s6)), introduced(assumption)).
% 291.10/183.57 tff(10226,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_c, s6)), introduced(assumption)).
% 291.10/183.57 tff(10227,plain,
% 291.10/183.57 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_g, s6)) | m_and_h_gate_v_out(c_e_h_3, c_c, s6))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s6)) | m_and_h_gate_v_out(c_e_h_3, c_c, s6))),
% 291.10/183.57 inference(rewrite,[status(thm)],[])).
% 291.10/183.57 tff(10228,plain,
% 291.10/183.57 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_g, s6)) | m_and_h_gate_v_out(c_e_h_3, c_c, s6))),
% 291.10/183.57 inference(quant_inst,[status(thm)],[])).
% 291.10/183.57 tff(10229,plain,
% 291.10/183.57 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s6)) | m_and_h_gate_v_out(c_e_h_3, c_c, s6)),
% 291.10/183.57 inference(modus_ponens,[status(thm)],[10228, 10227])).
% 291.10/183.57 tff(10230,plain,
% 291.10/183.57 ($false),
% 291.10/183.57 inference(unit_resolution,[status(thm)],[10229, 2708, 10226, 10225])).
% 291.10/183.57 tff(10231,plain,((~m_or_h_gate_v_in1(c_e_h_3, c_g, s6)) | m_and_h_gate_v_out(c_e_h_3, c_c, s6)), inference(lemma,lemma(discharge,[]))).
% 291.10/183.57 tff(10232,plain,
% 291.10/183.57 (~m_or_h_gate_v_in1(c_e_h_3, c_g, s6)),
% 291.10/183.57 inference(unit_resolution,[status(thm)],[10231, 10224])).
% 291.10/183.57 tff(10233,assumption,(~m_or_h_gate_v_in1(c_e_h_3, c_g, s6)), introduced(assumption)).
% 291.10/183.57 tff(10234,assumption,(node6(c_e_h_3, c_g, s6, s7)), introduced(assumption)).
% 291.10/183.57 tff(10235,plain,
% 291.10/183.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_3, c_g, s7)) | m_or_h_gate_v_out(c_e_h_3, c_g, s6) | (~node6(c_e_h_3, c_g, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s7)) | m_or_h_gate_v_out(c_e_h_3, c_g, s6) | (~node6(c_e_h_3, c_g, s6, s7)))),
% 291.10/183.57 inference(rewrite,[status(thm)],[])).
% 291.10/183.57 tff(10236,plain,
% 291.10/183.57 (((~node6(c_e_h_3, c_g, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s7)) | m_or_h_gate_v_out(c_e_h_3, c_g, s6)) <=> ((~m_or_h_gate_v_out(c_e_h_3, c_g, s7)) | m_or_h_gate_v_out(c_e_h_3, c_g, s6) | (~node6(c_e_h_3, c_g, s6, s7)))),
% 291.10/183.57 inference(rewrite,[status(thm)],[])).
% 291.10/183.57 tff(10237,plain,
% 291.10/183.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_g, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s7)) | m_or_h_gate_v_out(c_e_h_3, c_g, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_3, c_g, s7)) | m_or_h_gate_v_out(c_e_h_3, c_g, s6) | (~node6(c_e_h_3, c_g, s6, s7))))),
% 291.10/183.58 inference(monotonicity,[status(thm)],[10236])).
% 291.10/183.58 tff(10238,plain,
% 291.10/183.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_g, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s7)) | m_or_h_gate_v_out(c_e_h_3, c_g, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s7)) | m_or_h_gate_v_out(c_e_h_3, c_g, s6) | (~node6(c_e_h_3, c_g, s6, s7)))),
% 291.10/183.58 inference(transitivity,[status(thm)],[10237, 10235])).
% 291.10/183.58 tff(10239,plain,
% 291.10/183.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_g, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s7)) | m_or_h_gate_v_out(c_e_h_3, c_g, s6))),
% 291.10/183.58 inference(quant_inst,[status(thm)],[])).
% 291.10/183.58 tff(10240,plain,
% 291.10/183.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s7)) | m_or_h_gate_v_out(c_e_h_3, c_g, s6) | (~node6(c_e_h_3, c_g, s6, s7))),
% 291.10/183.58 inference(modus_ponens,[status(thm)],[10239, 10238])).
% 291.10/183.58 tff(10241,plain,
% 291.10/183.58 ($false),
% 291.10/183.58 inference(unit_resolution,[status(thm)],[10240, 1121, 10234, 9501, 6189])).
% 291.10/183.58 tff(10242,plain,((~node6(c_e_h_3, c_g, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s7)) | m_or_h_gate_v_out(c_e_h_3, c_g, s6)), inference(lemma,lemma(discharge,[]))).
% 291.10/183.58 tff(10243,plain,
% 291.10/183.58 (~node6(c_e_h_3, c_g, s6, s7)),
% 291.10/183.58 inference(unit_resolution,[status(thm)],[10242, 9501, 6189])).
% 291.10/183.58 tff(10244,plain,
% 291.10/183.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s6, s7)) | node5(c_e_h_3, c_g, s6, s7) | node6(c_e_h_3, c_g, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s6, s7)) | node5(c_e_h_3, c_g, s6, s7) | node6(c_e_h_3, c_g, s6, s7))),
% 291.10/183.58 inference(rewrite,[status(thm)],[])).
% 291.10/183.58 tff(10245,plain,
% 291.10/183.58 ((node6(c_e_h_3, c_g, s6, s7) | node5(c_e_h_3, c_g, s6, s7) | (~trans(s6, s7))) <=> ((~trans(s6, s7)) | node5(c_e_h_3, c_g, s6, s7) | node6(c_e_h_3, c_g, s6, s7))),
% 291.10/183.58 inference(rewrite,[status(thm)],[])).
% 291.10/183.58 tff(10246,plain,
% 291.10/183.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s6, s7) | node5(c_e_h_3, c_g, s6, s7) | (~trans(s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s6, s7)) | node5(c_e_h_3, c_g, s6, s7) | node6(c_e_h_3, c_g, s6, s7)))),
% 291.10/183.58 inference(monotonicity,[status(thm)],[10245])).
% 291.10/183.58 tff(10247,plain,
% 291.10/183.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s6, s7) | node5(c_e_h_3, c_g, s6, s7) | (~trans(s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s6, s7)) | node5(c_e_h_3, c_g, s6, s7) | node6(c_e_h_3, c_g, s6, s7))),
% 291.10/183.58 inference(transitivity,[status(thm)],[10246, 10244])).
% 291.10/183.58 tff(10248,plain,
% 291.10/183.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s6, s7) | node5(c_e_h_3, c_g, s6, s7) | (~trans(s6, s7)))),
% 291.10/183.58 inference(quant_inst,[status(thm)],[])).
% 291.10/183.58 tff(10249,plain,
% 291.10/183.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s6, s7)) | node5(c_e_h_3, c_g, s6, s7) | node6(c_e_h_3, c_g, s6, s7)),
% 291.10/183.58 inference(modus_ponens,[status(thm)],[10248, 10247])).
% 291.10/183.58 tff(10250,plain,
% 291.10/183.58 (node5(c_e_h_3, c_g, s6, s7) | node6(c_e_h_3, c_g, s6, s7)),
% 291.10/183.58 inference(unit_resolution,[status(thm)],[10249, 1141, 1844])).
% 291.10/183.58 tff(10251,plain,
% 291.10/183.58 (node5(c_e_h_3, c_g, s6, s7)),
% 291.10/183.58 inference(unit_resolution,[status(thm)],[10250, 10243])).
% 291.10/183.58 tff(10252,plain,
% 291.10/183.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_3, c_g, s7)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s6) | m_or_h_gate_v_in2(c_e_h_3, c_g, s6) | (~node5(c_e_h_3, c_g, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s7)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s6) | m_or_h_gate_v_in2(c_e_h_3, c_g, s6) | (~node5(c_e_h_3, c_g, s6, s7)))),
% 291.10/183.58 inference(rewrite,[status(thm)],[])).
% 291.10/183.58 tff(10253,plain,
% 291.10/183.58 ((m_or_h_gate_v_in1(c_e_h_3, c_g, s6) | m_or_h_gate_v_in2(c_e_h_3, c_g, s6) | (~node5(c_e_h_3, c_g, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s7))) <=> ((~m_or_h_gate_v_out(c_e_h_3, c_g, s7)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s6) | m_or_h_gate_v_in2(c_e_h_3, c_g, s6) | (~node5(c_e_h_3, c_g, s6, s7)))),
% 291.10/183.58 inference(rewrite,[status(thm)],[])).
% 291.10/183.58 tff(10254,plain,
% 291.10/183.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_g, s6) | m_or_h_gate_v_in2(c_e_h_3, c_g, s6) | (~node5(c_e_h_3, c_g, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_3, c_g, s7)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s6) | m_or_h_gate_v_in2(c_e_h_3, c_g, s6) | (~node5(c_e_h_3, c_g, s6, s7))))),
% 291.10/183.58 inference(monotonicity,[status(thm)],[10253])).
% 291.10/183.58 tff(10255,plain,
% 291.10/183.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_g, s6) | m_or_h_gate_v_in2(c_e_h_3, c_g, s6) | (~node5(c_e_h_3, c_g, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s7)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s6) | m_or_h_gate_v_in2(c_e_h_3, c_g, s6) | (~node5(c_e_h_3, c_g, s6, s7)))),
% 291.10/183.58 inference(transitivity,[status(thm)],[10254, 10252])).
% 291.10/183.58 tff(10256,plain,
% 291.10/183.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_g, s6) | m_or_h_gate_v_in2(c_e_h_3, c_g, s6) | (~node5(c_e_h_3, c_g, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s7)))),
% 291.10/183.58 inference(quant_inst,[status(thm)],[])).
% 291.10/183.58 tff(10257,plain,
% 291.10/183.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s7)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s6) | m_or_h_gate_v_in2(c_e_h_3, c_g, s6) | (~node5(c_e_h_3, c_g, s6, s7))),
% 291.10/183.58 inference(modus_ponens,[status(thm)],[10256, 10255])).
% 291.10/183.58 tff(10258,plain,
% 291.10/183.58 ($false),
% 291.10/183.58 inference(unit_resolution,[status(thm)],[10257, 1159, 10251, 9501, 10018, 10233])).
% 291.10/183.58 tff(10259,plain,((~m_or_h_gate_v_out(c_e_h_3, c_g, s7)) | m_or_h_gate_v_in2(c_e_h_3, c_g, s6) | m_or_h_gate_v_in1(c_e_h_3, c_g, s6) | m_or_h_gate_v_out(c_e_h_3, c_g, s6)), inference(lemma,lemma(discharge,[]))).
% 291.10/183.58 tff(10260,plain,
% 291.10/183.58 (m_or_h_gate_v_out(c_e_h_3, c_g, s6)),
% 291.10/183.58 inference(unit_resolution,[status(thm)],[10259, 10232, 10018, 9501])).
% 291.10/183.58 tff(10261,assumption,(m_or_h_gate_v_out(c_e_h_3, c_g, s6)), introduced(assumption)).
% 291.10/183.58 tff(10262,plain,
% 291.10/183.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s5) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s6)) | (~node6(c_e_h_3, c_g, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_g, s5) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s6)) | (~node6(c_e_h_3, c_g, s5, s6)))),
% 291.10/183.59 inference(rewrite,[status(thm)],[])).
% 291.10/183.59 tff(10263,plain,
% 291.10/183.59 (((~node6(c_e_h_3, c_g, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s6)) | m_or_h_gate_v_out(c_e_h_3, c_g, s5)) <=> (m_or_h_gate_v_out(c_e_h_3, c_g, s5) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s6)) | (~node6(c_e_h_3, c_g, s5, s6)))),
% 291.10/183.59 inference(rewrite,[status(thm)],[])).
% 291.10/183.59 tff(10264,plain,
% 291.10/183.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_g, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s6)) | m_or_h_gate_v_out(c_e_h_3, c_g, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s5) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s6)) | (~node6(c_e_h_3, c_g, s5, s6))))),
% 291.10/183.59 inference(monotonicity,[status(thm)],[10263])).
% 291.10/183.59 tff(10265,plain,
% 291.10/183.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_g, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s6)) | m_or_h_gate_v_out(c_e_h_3, c_g, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_g, s5) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s6)) | (~node6(c_e_h_3, c_g, s5, s6)))),
% 291.10/183.59 inference(transitivity,[status(thm)],[10264, 10262])).
% 291.10/183.59 tff(10266,plain,
% 291.10/183.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_g, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s6)) | m_or_h_gate_v_out(c_e_h_3, c_g, s5))),
% 291.10/183.59 inference(quant_inst,[status(thm)],[])).
% 291.10/183.59 tff(10267,plain,
% 291.10/183.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_g, s5) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s6)) | (~node6(c_e_h_3, c_g, s5, s6))),
% 291.10/183.59 inference(modus_ponens,[status(thm)],[10266, 10265])).
% 291.10/183.59 tff(10268,plain,
% 291.10/183.59 ($false),
% 291.10/183.59 inference(unit_resolution,[status(thm)],[10267, 1121, 6200, 3360, 10261])).
% 291.10/183.59 tff(10269,plain,((~node6(c_e_h_3, c_g, s5, s6)) | m_or_h_gate_v_out(c_e_h_3, c_g, s5) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s6))), inference(lemma,lemma(discharge,[]))).
% 291.10/183.59 tff(10270,plain,
% 291.10/183.59 (~node6(c_e_h_3, c_g, s5, s6)),
% 291.10/183.59 inference(unit_resolution,[status(thm)],[10269, 10260, 3360])).
% 291.10/183.59 tff(10271,plain,
% 291.10/183.59 (node5(c_e_h_3, c_g, s5, s6)),
% 291.10/183.59 inference(unit_resolution,[status(thm)],[6216, 10270])).
% 291.10/183.59 tff(10272,plain,
% 291.10/183.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_3, c_g, s5) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s6)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s5) | (~node5(c_e_h_3, c_g, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_3, c_g, s5) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s6)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s5) | (~node5(c_e_h_3, c_g, s5, s6)))),
% 291.11/183.59 inference(rewrite,[status(thm)],[])).
% 291.11/183.59 tff(10273,plain,
% 291.11/183.59 ((m_or_h_gate_v_in1(c_e_h_3, c_g, s5) | m_or_h_gate_v_in2(c_e_h_3, c_g, s5) | (~node5(c_e_h_3, c_g, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s6))) <=> (m_or_h_gate_v_in2(c_e_h_3, c_g, s5) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s6)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s5) | (~node5(c_e_h_3, c_g, s5, s6)))),
% 291.11/183.59 inference(rewrite,[status(thm)],[])).
% 291.11/183.59 tff(10274,plain,
% 291.11/183.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_g, s5) | m_or_h_gate_v_in2(c_e_h_3, c_g, s5) | (~node5(c_e_h_3, c_g, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_3, c_g, s5) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s6)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s5) | (~node5(c_e_h_3, c_g, s5, s6))))),
% 291.11/183.59 inference(monotonicity,[status(thm)],[10273])).
% 291.11/183.59 tff(10275,plain,
% 291.11/183.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_g, s5) | m_or_h_gate_v_in2(c_e_h_3, c_g, s5) | (~node5(c_e_h_3, c_g, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_3, c_g, s5) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s6)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s5) | (~node5(c_e_h_3, c_g, s5, s6)))),
% 291.11/183.59 inference(transitivity,[status(thm)],[10274, 10272])).
% 291.11/183.59 tff(10276,plain,
% 291.11/183.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_g, s5) | m_or_h_gate_v_in2(c_e_h_3, c_g, s5) | (~node5(c_e_h_3, c_g, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s6)))),
% 291.11/183.59 inference(quant_inst,[status(thm)],[])).
% 291.11/183.59 tff(10277,plain,
% 291.11/183.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_3, c_g, s5) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s6)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s5) | (~node5(c_e_h_3, c_g, s5, s6))),
% 291.11/183.59 inference(modus_ponens,[status(thm)],[10276, 10275])).
% 291.11/183.59 tff(10278,plain,
% 291.11/183.59 ($false),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[10277, 1159, 10271, 10260, 10017, 10059])).
% 291.11/183.59 tff(10279,plain,(m_mutex_h_half_v_out(c_e_h_3, c_a, s4) | m_or_h_gate_v_in2(c_e_h_3, c_g, s5) | m_or_h_gate_v_out(c_e_h_3, c_g, s5) | m_or_h_gate_v_in2(c_e_h_3, c_g, s6) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s7)) | m_and_h_gate_v_out(c_e_h_3, c_c, s7) | m_and_h_gate_v_out(c_e_h_3, c_c, s4)), inference(lemma,lemma(discharge,[]))).
% 291.11/183.59 tff(10280,plain,
% 291.11/183.59 (m_mutex_h_half_v_out(c_e_h_3, c_a, s4)),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[10279, 10018, 9501, 3360, 10017, 10016, 2743])).
% 291.11/183.59 tff(10281,plain,
% 291.11/183.59 (m_user_v_req(c_e_h_3, c_u, s3)),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[550, 10280])).
% 291.11/183.59 tff(10282,plain,
% 291.11/183.59 (m_user_v_req(c_e_h_3, c_u, s4)),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[732, 10281])).
% 291.11/183.59 tff(10283,plain,
% 291.11/183.59 (m_user_v_req(c_e_h_3, c_u, s5)),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[1035, 10282])).
% 291.11/183.59 tff(10284,plain,
% 291.11/183.59 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s5)),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[1438, 10283])).
% 291.11/183.59 tff(10285,plain,
% 291.11/183.59 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s4)),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[1445, 10282])).
% 291.11/183.59 tff(10286,plain,
% 291.11/183.59 (m_mutex_h_half_v_out(c_e_h_3, c_a, s5)),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[1488, 10285, 10280])).
% 291.11/183.59 tff(10287,plain,
% 291.11/183.59 (m_or_h_gate_v_in1(c_e_h_3, c_g, s6)),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[10259, 10018, 6189, 9501])).
% 291.11/183.59 tff(10288,plain,
% 291.11/183.59 (m_and_h_gate_v_out(c_e_h_3, c_c, s6)),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[10231, 10287])).
% 291.11/183.59 tff(10289,plain,
% 291.11/183.59 (~node22(c_e_h_3, c_c, s6, s7)),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[10069, 10288, 10016])).
% 291.11/183.59 tff(10290,plain,
% 291.11/183.59 (node21(c_e_h_3, c_c, s6, s7)),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[10074, 10289])).
% 291.11/183.59 tff(10291,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_c, s6)), introduced(assumption)).
% 291.11/183.59 tff(10292,assumption,(node21(c_e_h_3, c_c, s6, s7)), introduced(assumption)).
% 291.11/183.59 tff(10293,plain,
% 291.11/183.59 ($false),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[10161, 5851, 10155, 10016, 10292, 10291])).
% 291.11/183.59 tff(10294,plain,((~node21(c_e_h_3, c_c, s6, s7)) | m_and_h_gate_v_out(c_e_h_3, c_c, s7) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s6))), inference(lemma,lemma(discharge,[]))).
% 291.11/183.59 tff(10295,plain,
% 291.11/183.59 (~m_and_h_gate_v_in1(c_e_h_3, c_c, s6)),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[10294, 10290, 10016])).
% 291.11/183.59 tff(10296,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_c, s6)), introduced(assumption)).
% 291.11/183.59 tff(10297,plain,
% 291.11/183.59 ($false),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[10221, 2556, 1946, 10296])).
% 291.11/183.59 tff(10298,plain,(m_and_h_gate_v_in1(c_e_h_3, c_c, s6) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s6))), inference(lemma,lemma(discharge,[]))).
% 291.11/183.59 tff(10299,plain,
% 291.11/183.59 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s6)),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[10298, 10295])).
% 291.11/183.59 tff(10300,plain,
% 291.11/183.59 ($false),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[1515, 10299, 10286, 10284])).
% 291.11/183.59 tff(10301,plain,(m_or_h_gate_v_in2(c_e_h_3, c_g, s6) | m_and_h_gate_v_out(c_e_h_3, c_c, s7) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s7)) | m_or_h_gate_v_out(c_e_h_3, c_g, s5) | m_or_h_gate_v_in2(c_e_h_3, c_g, s5) | m_and_h_gate_v_out(c_e_h_3, c_c, s4) | m_or_h_gate_v_out(c_e_h_3, c_g, s6)), inference(lemma,lemma(discharge,[]))).
% 291.11/183.59 tff(10302,plain,
% 291.11/183.59 (m_and_h_gate_v_out(c_e_h_3, c_c, s7) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s7)) | m_or_h_gate_v_out(c_e_h_3, c_g, s5) | m_and_h_gate_v_out(c_e_h_3, c_c, s4) | m_or_h_gate_v_out(c_e_h_3, c_g, s6)),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[10301, 10015, 9740])).
% 291.11/183.59 tff(10303,plain,
% 291.11/183.59 (m_or_h_gate_v_out(c_e_h_3, c_g, s6)),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[10302, 9537, 9501, 3360, 2743])).
% 291.11/183.59 tff(10304,plain,
% 291.11/183.59 ((~m_and_h_gate_v_out(c_e_h_3, c_d, s4)) | m_and_h_gate_v_out(c_e_h_3, c_d, s3)),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[3279, 3251])).
% 291.11/183.59 tff(10305,plain,
% 291.11/183.59 (~m_and_h_gate_v_out(c_e_h_3, c_d, s4)),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[10304, 3125])).
% 291.11/183.59 tff(10306,plain,
% 291.11/183.59 (~m_or_h_gate_v_in2(c_e_h_3, c_g, s4)),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[3287, 10305])).
% 291.11/183.59 tff(10307,plain,
% 291.11/183.59 (~m_or_h_gate_v_in1(c_e_h_3, c_g, s5)),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[10058, 5931])).
% 291.11/183.59 tff(10308,plain,
% 291.11/183.59 ($false),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[10277, 1159, 6190, 10261, 10017, 6172])).
% 291.11/183.59 tff(10309,plain,((~node5(c_e_h_3, c_g, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s6)) | m_or_h_gate_v_in2(c_e_h_3, c_g, s5) | m_or_h_gate_v_in1(c_e_h_3, c_g, s5)), inference(lemma,lemma(discharge,[]))).
% 291.11/183.59 tff(10310,plain,
% 291.11/183.59 (~node5(c_e_h_3, c_g, s5, s6)),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[10309, 10307, 10017, 10261])).
% 291.11/183.59 tff(10311,plain,
% 291.11/183.59 (node6(c_e_h_3, c_g, s5, s6)),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[6216, 10310])).
% 291.11/183.59 tff(10312,plain,
% 291.11/183.59 (m_or_h_gate_v_out(c_e_h_3, c_g, s5)),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[10269, 10311, 10261])).
% 291.11/183.59 tff(10313,plain,
% 291.11/183.59 (~node6(c_e_h_3, c_g, s4, s5)),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[3317, 10312, 3308])).
% 291.11/183.59 tff(10314,plain,
% 291.11/183.59 (~m_and_h_gate_v_out(c_e_h_3, c_c, s4)),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[6170, 5931])).
% 291.11/183.59 tff(10315,plain,
% 291.11/183.59 (~m_or_h_gate_v_in1(c_e_h_3, c_g, s4)),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[2748, 10314])).
% 291.11/183.59 tff(10316,plain,
% 291.11/183.59 (~node5(c_e_h_3, c_g, s4, s5)),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[3298, 10312, 10315, 3289])).
% 291.11/183.59 tff(10317,plain,
% 291.11/183.59 ($false),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[3306, 10316, 10313])).
% 291.11/183.59 tff(10318,plain,(m_and_h_gate_v_out(c_e_h_3, c_c, s5) | m_or_h_gate_v_in2(c_e_h_3, c_g, s4) | m_or_h_gate_v_out(c_e_h_3, c_g, s4) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s6)) | m_or_h_gate_v_in2(c_e_h_3, c_g, s5)), inference(lemma,lemma(discharge,[]))).
% 291.11/183.59 tff(10319,plain,
% 291.11/183.59 (m_and_h_gate_v_out(c_e_h_3, c_c, s5) | m_or_h_gate_v_out(c_e_h_3, c_g, s4) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s6))),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[10318, 10306, 9740])).
% 291.11/183.59 tff(10320,plain,
% 291.11/183.59 (m_and_h_gate_v_out(c_e_h_3, c_c, s5)),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[10319, 10303, 3308])).
% 291.11/183.59 tff(10321,plain,
% 291.11/183.59 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s3)),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[2537, 2513])).
% 291.11/183.59 tff(10322,plain,
% 291.11/183.59 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[2606, 10321])).
% 291.11/183.59 tff(10323,plain,
% 291.11/183.59 (~m_and_h_gate_v_in1(c_e_h_3, c_c, s2)),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[2614, 10322])).
% 291.11/183.59 tff(10324,plain,
% 291.11/183.59 (~node20(c_e_h_3, c_c, s2)),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[2622, 10323])).
% 291.11/183.59 tff(10325,plain,
% 291.11/183.59 (~m_and_h_gate_v_in1(c_e_h_3, c_c, s3)),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[2544, 10321])).
% 291.11/183.59 tff(10326,plain,
% 291.11/183.59 (~node20(c_e_h_3, c_c, s3)),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[2720, 10325])).
% 291.11/183.59 tff(10327,plain,
% 291.11/183.59 (m_and_h_gate_v_out(c_e_h_3, c_c, s4)),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[10052, 10033, 6173])).
% 291.11/183.59 tff(10328,plain,
% 291.11/183.59 (m_and_h_gate_v_out(c_e_h_3, c_c, s3)),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[2740, 10327, 10326])).
% 291.11/183.59 tff(10329,plain,
% 291.11/183.59 ($false),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[2698, 10328, 10324])).
% 291.11/183.59 tff(10330,plain,(m_mutex_h_half_v_out(c_e_h_3, c_a, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s5))), inference(lemma,lemma(discharge,[]))).
% 291.11/183.59 tff(10331,plain,
% 291.11/183.59 (m_mutex_h_half_v_out(c_e_h_3, c_a, s4)),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[10330, 10320])).
% 291.11/183.59 tff(10332,plain,
% 291.11/183.59 (m_user_v_req(c_e_h_3, c_u, s3)),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[550, 10331])).
% 291.11/183.59 tff(10333,plain,
% 291.11/183.59 (m_user_v_req(c_e_h_3, c_u, s4)),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[732, 10332])).
% 291.11/183.59 tff(10334,plain,
% 291.11/183.59 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s4)),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[1445, 10333])).
% 291.11/183.59 tff(10335,plain,
% 291.11/183.59 (m_mutex_h_half_v_out(c_e_h_3, c_a, s5)),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[1488, 10334, 10331])).
% 291.11/183.59 tff(10336,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_c, s5)), introduced(assumption)).
% 291.11/183.59 tff(10337,plain,
% 291.11/183.59 (((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s5))) <=> ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s5))),
% 291.11/183.59 inference(rewrite,[status(thm)],[])).
% 291.11/183.59 tff(10338,plain,
% 291.11/183.59 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s5))),
% 291.11/183.59 inference(quant_inst,[status(thm)],[])).
% 291.11/183.59 tff(10339,plain,
% 291.11/183.59 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s5)),
% 291.11/183.59 inference(modus_ponens,[status(thm)],[10338, 10337])).
% 291.11/183.59 tff(10340,plain,
% 291.11/183.59 ($false),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[10339, 2556, 1492, 10336])).
% 291.11/183.59 tff(10341,plain,(m_and_h_gate_v_in1(c_e_h_3, c_c, s5) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s5))), inference(lemma,lemma(discharge,[]))).
% 291.11/183.59 tff(10342,plain,
% 291.11/183.59 (m_and_h_gate_v_in1(c_e_h_3, c_c, s5)),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[10341, 10335])).
% 291.11/183.59 tff(10343,plain,
% 291.11/183.59 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s5))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s5))),
% 291.11/183.59 inference(rewrite,[status(thm)],[])).
% 291.11/183.59 tff(10344,plain,
% 291.11/183.59 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s5))),
% 291.11/183.59 inference(quant_inst,[status(thm)],[])).
% 291.11/183.59 tff(10345,plain,
% 291.11/183.59 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s5)),
% 291.11/183.59 inference(modus_ponens,[status(thm)],[10344, 10343])).
% 291.11/183.59 tff(10346,plain,
% 291.11/183.59 (node3(c_e_h_3, c_e_h_1, s5)),
% 291.11/183.59 inference(unit_resolution,[status(thm)],[10345, 2922, 1056])).
% 291.11/183.60 tff(10347,plain,
% 291.11/183.60 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s5)) | (~node3(c_e_h_3, c_e_h_1, s5)) | m_and_h_gate_v_out(c_e_h_3, c_q, s5))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s5)) | (~node3(c_e_h_3, c_e_h_1, s5)) | m_and_h_gate_v_out(c_e_h_3, c_q, s5))),
% 291.11/183.60 inference(rewrite,[status(thm)],[])).
% 291.11/183.60 tff(10348,plain,
% 291.11/183.60 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s5)) | (~node3(c_e_h_3, c_e_h_1, s5)) | m_and_h_gate_v_out(c_e_h_3, c_q, s5))),
% 291.11/183.60 inference(quant_inst,[status(thm)],[])).
% 291.11/183.60 tff(10349,plain,
% 291.11/183.60 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s5)) | (~node3(c_e_h_3, c_e_h_1, s5)) | m_and_h_gate_v_out(c_e_h_3, c_q, s5)),
% 291.11/183.60 inference(modus_ponens,[status(thm)],[10348, 10347])).
% 291.11/183.60 tff(10350,plain,
% 291.11/183.60 ((~m_cell_v_ack(c_e_h_1, s5)) | m_and_h_gate_v_out(c_e_h_3, c_q, s5)),
% 291.11/183.60 inference(unit_resolution,[status(thm)],[10349, 1073, 10346])).
% 291.11/183.60 tff(10351,plain,
% 291.11/183.60 (~m_cell_v_ack(c_e_h_1, s5)),
% 291.11/183.60 inference(unit_resolution,[status(thm)],[10350, 10122])).
% 291.11/183.60 tff(10352,plain,
% 291.11/183.60 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node2(c_e_h_3, c_e_h_1, s5))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node2(c_e_h_3, c_e_h_1, s5))),
% 291.11/183.60 inference(rewrite,[status(thm)],[])).
% 291.11/183.60 tff(10353,plain,
% 291.11/183.60 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node2(c_e_h_3, c_e_h_1, s5))),
% 291.11/183.60 inference(quant_inst,[status(thm)],[])).
% 291.11/183.60 tff(10354,plain,
% 291.11/183.60 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node2(c_e_h_3, c_e_h_1, s5)),
% 291.11/183.60 inference(modus_ponens,[status(thm)],[10353, 10352])).
% 291.11/183.60 tff(10355,plain,
% 291.11/183.60 (node2(c_e_h_3, c_e_h_1, s5)),
% 291.11/183.60 inference(unit_resolution,[status(thm)],[10354, 2922, 5821])).
% 291.11/183.60 tff(10356,plain,
% 291.11/183.60 (((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | ((~node2(c_e_h_3, c_e_h_1, s5)) | m_cell_v_ack(c_e_h_1, s5) | m_and_h_gate_v_in2(c_e_h_3, c_c, s5))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | (~node2(c_e_h_3, c_e_h_1, s5)) | m_cell_v_ack(c_e_h_1, s5) | m_and_h_gate_v_in2(c_e_h_3, c_c, s5))),
% 291.11/183.60 inference(rewrite,[status(thm)],[])).
% 291.11/183.60 tff(10357,plain,
% 291.11/183.60 ((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | ((~node2(c_e_h_3, c_e_h_1, s5)) | m_cell_v_ack(c_e_h_1, s5) | m_and_h_gate_v_in2(c_e_h_3, c_c, s5))),
% 291.11/183.60 inference(quant_inst,[status(thm)],[])).
% 291.11/183.60 tff(10358,plain,
% 291.11/183.60 ((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | (~node2(c_e_h_3, c_e_h_1, s5)) | m_cell_v_ack(c_e_h_1, s5) | m_and_h_gate_v_in2(c_e_h_3, c_c, s5)),
% 291.11/183.60 inference(modus_ponens,[status(thm)],[10357, 10356])).
% 291.11/183.60 tff(10359,plain,
% 291.11/183.60 (m_cell_v_ack(c_e_h_1, s5) | m_and_h_gate_v_in2(c_e_h_3, c_c, s5)),
% 291.11/183.60 inference(unit_resolution,[status(thm)],[10358, 5835, 10355])).
% 291.11/183.60 tff(10360,plain,
% 291.11/183.60 (m_and_h_gate_v_in2(c_e_h_3, c_c, s5)),
% 291.11/183.60 inference(unit_resolution,[status(thm)],[10359, 10351])).
% 291.11/183.60 tff(10361,plain,
% 291.11/183.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_c, s5)) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s5)) | (~node21(c_e_h_3, c_c, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_c, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s5)) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s5)) | (~node21(c_e_h_3, c_c, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_c, s6))),
% 291.11/183.60 inference(rewrite,[status(thm)],[])).
% 291.11/183.60 tff(10362,plain,
% 291.11/183.60 (((~node21(c_e_h_3, c_c, s5, s6)) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s5)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s5)) | m_and_h_gate_v_out(c_e_h_3, c_c, s6)) <=> ((~m_and_h_gate_v_in1(c_e_h_3, c_c, s5)) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s5)) | (~node21(c_e_h_3, c_c, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_c, s6))),
% 291.11/183.60 inference(rewrite,[status(thm)],[])).
% 291.11/183.60 tff(10363,plain,
% 291.11/183.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_c, s5, s6)) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s5)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s5)) | m_and_h_gate_v_out(c_e_h_3, c_c, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_c, s5)) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s5)) | (~node21(c_e_h_3, c_c, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_c, s6)))),
% 291.11/183.60 inference(monotonicity,[status(thm)],[10362])).
% 291.11/183.60 tff(10364,plain,
% 291.11/183.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_c, s5, s6)) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s5)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s5)) | m_and_h_gate_v_out(c_e_h_3, c_c, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s5)) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s5)) | (~node21(c_e_h_3, c_c, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_c, s6))),
% 291.11/183.60 inference(transitivity,[status(thm)],[10363, 10361])).
% 291.11/183.60 tff(10365,plain,
% 291.11/183.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_c, s5, s6)) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s5)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s5)) | m_and_h_gate_v_out(c_e_h_3, c_c, s6))),
% 291.11/183.60 inference(quant_inst,[status(thm)],[])).
% 291.11/183.60 tff(10366,plain,
% 291.11/183.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s5)) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s5)) | (~node21(c_e_h_3, c_c, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_c, s6)),
% 291.11/183.60 inference(modus_ponens,[status(thm)],[10365, 10364])).
% 291.11/183.60 tff(10367,plain,
% 291.11/183.60 ($false),
% 291.11/183.60 inference(unit_resolution,[status(thm)],[10366, 5851, 10360, 10164, 10226, 10186])).
% 291.11/183.60 tff(10368,plain,((~node21(c_e_h_3, c_c, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_c, s6) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s5))), inference(lemma,lemma(discharge,[]))).
% 291.11/183.60 tff(10369,plain,
% 291.11/183.60 (~node21(c_e_h_3, c_c, s5, s6)),
% 291.11/183.60 inference(unit_resolution,[status(thm)],[10368, 10226, 10186])).
% 291.11/183.60 tff(10370,plain,
% 291.11/183.60 (node22(c_e_h_3, c_c, s5, s6)),
% 291.11/183.60 inference(unit_resolution,[status(thm)],[10174, 10369])).
% 291.11/183.60 tff(10371,plain,
% 291.11/183.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s5)) | (~node22(c_e_h_3, c_c, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_c, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s5)) | (~node22(c_e_h_3, c_c, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_c, s6))),
% 291.11/183.60 inference(rewrite,[status(thm)],[])).
% 291.11/183.60 tff(10372,plain,
% 291.11/183.60 ((m_and_h_gate_v_out(c_e_h_3, c_c, s6) | (~node22(c_e_h_3, c_c, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s5))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_c, s5)) | (~node22(c_e_h_3, c_c, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_c, s6))),
% 291.11/183.60 inference(rewrite,[status(thm)],[])).
% 291.11/183.60 tff(10373,plain,
% 291.11/183.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_c, s6) | (~node22(c_e_h_3, c_c, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s5)) | (~node22(c_e_h_3, c_c, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_c, s6)))),
% 291.11/183.60 inference(monotonicity,[status(thm)],[10372])).
% 291.11/183.60 tff(10374,plain,
% 291.11/183.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_c, s6) | (~node22(c_e_h_3, c_c, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s5)) | (~node22(c_e_h_3, c_c, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_c, s6))),
% 291.11/183.60 inference(transitivity,[status(thm)],[10373, 10371])).
% 291.11/183.60 tff(10375,plain,
% 291.11/183.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_c, s6) | (~node22(c_e_h_3, c_c, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s5)))),
% 291.11/183.60 inference(quant_inst,[status(thm)],[])).
% 291.11/183.60 tff(10376,plain,
% 291.11/183.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s5)) | (~node22(c_e_h_3, c_c, s5, s6)) | m_and_h_gate_v_out(c_e_h_3, c_c, s6)),
% 291.11/183.60 inference(modus_ponens,[status(thm)],[10375, 10374])).
% 291.11/183.60 tff(10377,plain,
% 291.11/183.60 ($false),
% 291.11/183.60 inference(unit_resolution,[status(thm)],[10376, 5871, 6173, 10370, 10226])).
% 291.11/183.60 tff(10378,plain,(m_and_h_gate_v_out(c_e_h_3, c_c, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s5)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s5))), inference(lemma,lemma(discharge,[]))).
% 291.11/183.60 tff(10379,plain,
% 291.11/183.60 (m_and_h_gate_v_out(c_e_h_3, c_c, s6)),
% 291.11/183.60 inference(unit_resolution,[status(thm)],[10378, 10342, 10320])).
% 291.11/183.60 tff(10380,plain,
% 291.11/183.60 (~node22(c_e_h_3, c_c, s6, s7)),
% 291.11/183.60 inference(unit_resolution,[status(thm)],[10069, 10379, 9537])).
% 291.11/183.60 tff(10381,plain,
% 291.11/183.60 (m_user_v_req(c_e_h_3, c_u, s5)),
% 291.11/183.60 inference(unit_resolution,[status(thm)],[1035, 10333])).
% 291.11/183.60 tff(10382,plain,
% 291.11/183.60 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s5)),
% 291.11/183.60 inference(unit_resolution,[status(thm)],[1438, 10381])).
% 291.11/183.60 tff(10383,plain,
% 291.11/183.60 (m_mutex_h_half_v_out(c_e_h_3, c_a, s6)),
% 291.11/183.60 inference(unit_resolution,[status(thm)],[1515, 10335, 10382])).
% 291.11/183.60 tff(10384,plain,
% 291.11/183.60 (m_and_h_gate_v_in1(c_e_h_3, c_c, s6)),
% 291.11/183.60 inference(unit_resolution,[status(thm)],[10298, 10383])).
% 291.11/183.60 tff(10385,plain,
% 291.11/183.60 (~node21(c_e_h_3, c_c, s6, s7)),
% 291.11/183.60 inference(unit_resolution,[status(thm)],[10294, 10384, 9537])).
% 291.11/183.60 tff(10386,plain,
% 291.11/183.60 ($false),
% 291.11/183.60 inference(unit_resolution,[status(thm)],[10074, 10385, 10380])).
% 291.11/183.60 tff(10387,plain,((~m_or_h_gate_v_out(c_e_h_3, c_g, s7)) | m_or_h_gate_v_out(c_e_h_3, c_g, s4) | m_or_h_gate_v_out(c_e_h_3, c_g, s5) | m_and_h_gate_v_out(c_e_h_3, c_c, s4) | m_or_h_gate_v_out(c_e_h_3, c_g, s8)), inference(lemma,lemma(discharge,[]))).
% 291.11/183.60 tff(10388,plain,
% 291.11/183.60 (~m_or_h_gate_v_out(c_e_h_3, c_g, s7)),
% 291.11/183.60 inference(unit_resolution,[status(thm)],[10387, 9499, 3360, 2743, 3308])).
% 291.11/183.60 tff(10389,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_k, s7)), introduced(assumption)).
% 291.11/183.60 tff(10390,assumption,(~m_or_h_gate_v_out(c_e_h_3, c_g, s7)), introduced(assumption)).
% 291.11/183.60 tff(10391,plain,
% 291.11/183.60 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_k, s7)) | m_or_h_gate_v_out(c_e_h_3, c_g, s7))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s7)) | m_or_h_gate_v_out(c_e_h_3, c_g, s7))),
% 291.11/183.61 inference(rewrite,[status(thm)],[])).
% 291.11/183.61 tff(10392,plain,
% 291.11/183.61 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_k, s7)) | m_or_h_gate_v_out(c_e_h_3, c_g, s7))),
% 291.11/183.61 inference(quant_inst,[status(thm)],[])).
% 291.11/183.61 tff(10393,plain,
% 291.11/183.61 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s7)) | m_or_h_gate_v_out(c_e_h_3, c_g, s7)),
% 291.11/183.61 inference(modus_ponens,[status(thm)],[10392, 10391])).
% 291.11/183.61 tff(10394,plain,
% 291.11/183.61 ($false),
% 291.11/183.61 inference(unit_resolution,[status(thm)],[10393, 2048, 10390, 10389])).
% 291.11/183.61 tff(10395,plain,((~m_and_h_gate_v_in1(c_e_h_3, c_k, s7)) | m_or_h_gate_v_out(c_e_h_3, c_g, s7)), inference(lemma,lemma(discharge,[]))).
% 291.11/183.61 tff(10396,plain,
% 291.11/183.61 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s7)),
% 291.11/183.61 inference(unit_resolution,[status(thm)],[10395, 10388])).
% 291.11/183.61 tff(10397,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_k, s7)), introduced(assumption)).
% 291.11/183.61 tff(10398,assumption,(node20(c_e_h_3, c_k, s7)), introduced(assumption)).
% 291.11/183.61 tff(10399,plain,
% 291.11/183.61 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_k, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_k, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s7))),
% 291.11/183.61 inference(rewrite,[status(thm)],[])).
% 291.11/183.61 tff(10400,plain,
% 291.11/183.61 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_k, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s7))),
% 291.11/183.61 inference(quant_inst,[status(thm)],[])).
% 291.11/183.61 tff(10401,plain,
% 291.11/183.61 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_k, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s7)),
% 291.11/183.61 inference(modus_ponens,[status(thm)],[10400, 10399])).
% 291.11/183.61 tff(10402,plain,
% 291.11/183.61 ($false),
% 291.11/183.61 inference(unit_resolution,[status(thm)],[10401, 38, 10398, 10397])).
% 291.11/183.61 tff(10403,plain,((~node20(c_e_h_3, c_k, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s7)), inference(lemma,lemma(discharge,[]))).
% 291.11/183.61 tff(10404,plain,
% 291.11/183.61 (~node20(c_e_h_3, c_k, s7)),
% 291.11/183.61 inference(unit_resolution,[status(thm)],[10403, 10396])).
% 291.11/183.61 tff(10405,assumption,(node22(c_e_h_3, c_k, s7, s8)), introduced(assumption)).
% 291.11/183.61 tff(10406,plain,
% 291.11/183.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s8)) | (~node22(c_e_h_3, c_k, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_k, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s8)) | (~node22(c_e_h_3, c_k, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_k, s7))),
% 291.11/183.61 inference(rewrite,[status(thm)],[])).
% 291.11/183.61 tff(10407,plain,
% 291.11/183.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s8)) | (~node22(c_e_h_3, c_k, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_k, s7))),
% 291.11/183.61 inference(quant_inst,[status(thm)],[])).
% 291.11/183.61 tff(10408,plain,
% 291.11/183.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s8)) | (~node22(c_e_h_3, c_k, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_k, s7)),
% 291.11/183.61 inference(modus_ponens,[status(thm)],[10407, 10406])).
% 291.11/183.61 tff(10409,plain,
% 291.11/183.61 ($false),
% 291.11/183.61 inference(unit_resolution,[status(thm)],[10408, 108, 10405, 6243, 9468])).
% 291.11/183.61 tff(10410,plain,((~node22(c_e_h_3, c_k, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_k, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s8))), inference(lemma,lemma(discharge,[]))).
% 291.11/183.61 tff(10411,plain,
% 291.11/183.61 (~node22(c_e_h_3, c_k, s7, s8)),
% 291.11/183.61 inference(unit_resolution,[status(thm)],[10410, 9468, 6243])).
% 291.11/183.61 tff(10412,assumption,(~node20(c_e_h_3, c_k, s7)), introduced(assumption)).
% 291.14/183.61 tff(10413,assumption,(node21(c_e_h_3, c_k, s7, s8)), introduced(assumption)).
% 291.14/183.61 tff(10414,plain,
% 291.14/183.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_k, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s8)) | (~node21(c_e_h_3, c_k, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_k, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s8)) | (~node21(c_e_h_3, c_k, s7, s8)))),
% 291.14/183.61 inference(rewrite,[status(thm)],[])).
% 291.14/183.61 tff(10415,plain,
% 291.14/183.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_k, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s8)) | (~node21(c_e_h_3, c_k, s7, s8)))),
% 291.14/183.61 inference(quant_inst,[status(thm)],[])).
% 291.14/183.61 tff(10416,plain,
% 291.14/183.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_k, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s8)) | (~node21(c_e_h_3, c_k, s7, s8))),
% 291.14/183.61 inference(modus_ponens,[status(thm)],[10415, 10414])).
% 291.14/183.61 tff(10417,plain,
% 291.14/183.61 ($false),
% 291.14/183.61 inference(unit_resolution,[status(thm)],[10416, 52, 10413, 9468, 10412])).
% 291.14/183.61 tff(10418,plain,((~node21(c_e_h_3, c_k, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s8)) | node20(c_e_h_3, c_k, s7)), inference(lemma,lemma(discharge,[]))).
% 291.14/183.61 tff(10419,plain,
% 291.14/183.61 (~node21(c_e_h_3, c_k, s7, s8)),
% 291.14/183.61 inference(unit_resolution,[status(thm)],[10418, 9468, 10412])).
% 291.14/183.61 tff(10420,plain,
% 291.14/183.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_3, c_k, s7, s8) | node22(c_e_h_3, c_k, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_3, c_k, s7, s8) | node22(c_e_h_3, c_k, s7, s8))),
% 291.14/183.61 inference(rewrite,[status(thm)],[])).
% 291.14/183.61 tff(10421,plain,
% 291.14/183.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_3, c_k, s7, s8) | node22(c_e_h_3, c_k, s7, s8))),
% 291.14/183.61 inference(quant_inst,[status(thm)],[])).
% 291.14/183.61 tff(10422,plain,
% 291.14/183.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_3, c_k, s7, s8) | node22(c_e_h_3, c_k, s7, s8)),
% 291.14/183.61 inference(modus_ponens,[status(thm)],[10421, 10420])).
% 291.14/183.61 tff(10423,plain,
% 291.14/183.61 (node21(c_e_h_3, c_k, s7, s8) | node22(c_e_h_3, c_k, s7, s8)),
% 291.14/183.61 inference(unit_resolution,[status(thm)],[10422, 82, 1938])).
% 291.14/183.61 tff(10424,plain,
% 291.14/183.61 ($false),
% 291.14/183.61 inference(unit_resolution,[status(thm)],[10423, 10419, 10411])).
% 291.14/183.61 tff(10425,plain,((~m_and_h_gate_v_out(c_e_h_3, c_k, s8)) | node20(c_e_h_3, c_k, s7) | m_and_h_gate_v_out(c_e_h_3, c_k, s7)), inference(lemma,lemma(discharge,[]))).
% 291.14/183.61 tff(10426,plain,
% 291.14/183.61 (m_and_h_gate_v_out(c_e_h_3, c_k, s7)),
% 291.14/183.61 inference(unit_resolution,[status(thm)],[10425, 10404, 9468])).
% 291.14/183.61 tff(10427,assumption,(~node20(c_e_h_3, c_k, s6)), introduced(assumption)).
% 291.14/183.61 tff(10428,assumption,(node22(c_e_h_3, c_k, s6, s7)), introduced(assumption)).
% 291.14/183.61 tff(10429,plain,
% 291.14/183.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s7)) | (~node22(c_e_h_3, c_k, s6, s7)) | m_and_h_gate_v_out(c_e_h_3, c_k, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s7)) | (~node22(c_e_h_3, c_k, s6, s7)) | m_and_h_gate_v_out(c_e_h_3, c_k, s6))),
% 291.14/183.61 inference(rewrite,[status(thm)],[])).
% 291.14/183.61 tff(10430,plain,
% 291.14/183.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s7)) | (~node22(c_e_h_3, c_k, s6, s7)) | m_and_h_gate_v_out(c_e_h_3, c_k, s6))),
% 291.14/183.62 inference(quant_inst,[status(thm)],[])).
% 291.14/183.62 tff(10431,plain,
% 291.14/183.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s7)) | (~node22(c_e_h_3, c_k, s6, s7)) | m_and_h_gate_v_out(c_e_h_3, c_k, s6)),
% 291.14/183.62 inference(modus_ponens,[status(thm)],[10430, 10429])).
% 291.14/183.62 tff(10432,plain,
% 291.14/183.62 ($false),
% 291.14/183.62 inference(unit_resolution,[status(thm)],[10431, 108, 10428, 7182, 4469])).
% 291.14/183.62 tff(10433,plain,((~node22(c_e_h_3, c_k, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s7)) | m_and_h_gate_v_out(c_e_h_3, c_k, s6)), inference(lemma,lemma(discharge,[]))).
% 291.14/183.62 tff(10434,plain,
% 291.14/183.62 (~node22(c_e_h_3, c_k, s6, s7)),
% 291.14/183.62 inference(unit_resolution,[status(thm)],[10433, 7182, 4469])).
% 291.14/183.62 tff(10435,plain,
% 291.14/183.62 (node21(c_e_h_3, c_k, s6, s7)),
% 291.14/183.62 inference(unit_resolution,[status(thm)],[6439, 10434])).
% 291.14/183.62 tff(10436,plain,
% 291.14/183.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_k, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s7)) | (~node21(c_e_h_3, c_k, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_k, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s7)) | (~node21(c_e_h_3, c_k, s6, s7)))),
% 291.14/183.62 inference(rewrite,[status(thm)],[])).
% 291.14/183.62 tff(10437,plain,
% 291.14/183.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_k, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s7)) | (~node21(c_e_h_3, c_k, s6, s7)))),
% 291.14/183.62 inference(quant_inst,[status(thm)],[])).
% 291.14/183.62 tff(10438,plain,
% 291.14/183.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_k, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s7)) | (~node21(c_e_h_3, c_k, s6, s7))),
% 291.14/183.62 inference(modus_ponens,[status(thm)],[10437, 10436])).
% 291.14/183.62 tff(10439,plain,
% 291.14/183.62 ($false),
% 291.14/183.62 inference(unit_resolution,[status(thm)],[10438, 52, 10435, 10427, 7182])).
% 291.14/183.62 tff(10440,plain,((~m_and_h_gate_v_out(c_e_h_3, c_k, s7)) | node20(c_e_h_3, c_k, s6) | m_and_h_gate_v_out(c_e_h_3, c_k, s6)), inference(lemma,lemma(discharge,[]))).
% 291.14/183.62 tff(10441,plain,
% 291.14/183.62 (node20(c_e_h_3, c_k, s6)),
% 291.14/183.62 inference(unit_resolution,[status(thm)],[10440, 10426, 4469])).
% 291.14/183.62 tff(10442,plain,
% 291.14/183.62 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_k, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_k, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s6))),
% 291.14/183.62 inference(rewrite,[status(thm)],[])).
% 291.14/183.62 tff(10443,plain,
% 291.14/183.62 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_k, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s6))),
% 291.14/183.62 inference(quant_inst,[status(thm)],[])).
% 291.14/183.62 tff(10444,plain,
% 291.14/183.62 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_k, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s6)),
% 291.14/183.62 inference(modus_ponens,[status(thm)],[10443, 10442])).
% 291.14/183.62 tff(10445,plain,
% 291.14/183.62 (m_and_h_gate_v_in1(c_e_h_3, c_k, s6)),
% 291.14/183.62 inference(unit_resolution,[status(thm)],[10444, 38, 10441])).
% 291.14/183.62 tff(10446,plain,
% 291.14/183.62 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_k, s6)) | m_or_h_gate_v_out(c_e_h_3, c_g, s6))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s6)) | m_or_h_gate_v_out(c_e_h_3, c_g, s6))),
% 291.14/183.62 inference(rewrite,[status(thm)],[])).
% 291.14/183.62 tff(10447,plain,
% 291.14/183.62 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_k, s6)) | m_or_h_gate_v_out(c_e_h_3, c_g, s6))),
% 291.14/183.62 inference(quant_inst,[status(thm)],[])).
% 291.14/183.62 tff(10448,plain,
% 291.14/183.62 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s6)) | m_or_h_gate_v_out(c_e_h_3, c_g, s6)),
% 291.14/183.62 inference(modus_ponens,[status(thm)],[10447, 10446])).
% 291.14/183.62 tff(10449,plain,
% 291.14/183.62 (m_or_h_gate_v_out(c_e_h_3, c_g, s6)),
% 291.14/183.62 inference(unit_resolution,[status(thm)],[10448, 2048, 10445])).
% 291.14/183.62 tff(10450,plain,
% 291.14/183.62 (m_and_h_gate_v_out(c_e_h_3, c_c, s5)),
% 291.14/183.62 inference(unit_resolution,[status(thm)],[10319, 10449, 3308])).
% 291.14/183.62 tff(10451,plain,
% 291.14/183.62 (m_mutex_h_half_v_out(c_e_h_3, c_a, s4)),
% 291.14/183.62 inference(unit_resolution,[status(thm)],[10330, 10450])).
% 291.14/183.62 tff(10452,plain,
% 291.14/183.62 (m_user_v_req(c_e_h_3, c_u, s3)),
% 291.14/183.62 inference(unit_resolution,[status(thm)],[550, 10451])).
% 291.14/183.62 tff(10453,plain,
% 291.14/183.62 (m_user_v_req(c_e_h_3, c_u, s4)),
% 291.14/183.62 inference(unit_resolution,[status(thm)],[732, 10452])).
% 291.14/183.62 tff(10454,plain,
% 291.14/183.62 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s4)),
% 291.14/183.62 inference(unit_resolution,[status(thm)],[1445, 10453])).
% 291.14/183.62 tff(10455,plain,
% 291.14/183.62 (~m_or_h_gate_v_out(c_e_h_3, c_g, s5)),
% 291.14/183.62 inference(unit_resolution,[status(thm)],[3356, 2749, 3125, 3006, 2714])).
% 291.14/183.62 tff(10456,plain,
% 291.14/183.62 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s5)),
% 291.14/183.62 inference(unit_resolution,[status(thm)],[3365, 10455])).
% 291.14/183.62 tff(10457,plain,
% 291.14/183.62 (~node20(c_e_h_3, c_k, s5)),
% 291.14/183.62 inference(unit_resolution,[status(thm)],[5458, 10456])).
% 291.14/183.62 tff(10458,plain,
% 291.14/183.62 (~m_and_h_gate_v_out(c_e_h_3, c_k, s6)),
% 291.14/183.62 inference(unit_resolution,[status(thm)],[4467, 10457, 4408])).
% 291.14/183.62 tff(10459,plain,
% 291.14/183.62 (node20(c_e_h_3, c_k, s6)),
% 291.14/183.62 inference(unit_resolution,[status(thm)],[10440, 10458, 7182])).
% 291.14/183.62 tff(10460,plain,
% 291.14/183.62 (m_and_h_gate_v_in1(c_e_h_3, c_k, s6)),
% 291.14/183.62 inference(unit_resolution,[status(thm)],[10444, 38, 10459])).
% 291.14/183.62 tff(10461,plain,
% 291.14/183.62 (m_or_h_gate_v_out(c_e_h_3, c_g, s6)),
% 291.14/183.62 inference(unit_resolution,[status(thm)],[10448, 2048, 10460])).
% 291.14/183.62 tff(10462,plain,
% 291.14/183.62 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X))) | ((~m_or_h_gate_v_out(c_e_h_3, c_g, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s7))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s7))),
% 291.14/183.62 inference(rewrite,[status(thm)],[])).
% 291.14/183.62 tff(10463,plain,
% 291.14/183.62 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X))) | ((~m_or_h_gate_v_out(c_e_h_3, c_g, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s7))),
% 291.14/183.62 inference(quant_inst,[status(thm)],[])).
% 291.14/183.62 tff(10464,plain,
% 291.14/183.62 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s7)),
% 291.14/183.62 inference(modus_ponens,[status(thm)],[10463, 10462])).
% 291.14/183.62 tff(10465,plain,
% 291.14/183.62 (~m_or_h_gate_v_out(c_e_h_3, c_g, s7)),
% 291.14/183.62 inference(unit_resolution,[status(thm)],[10464, 6229, 10397])).
% 291.14/183.62 tff(10466,assumption,(~node4(c_e_h_3, c_g, s6)), introduced(assumption)).
% 291.14/183.62 tff(10467,assumption,(node5(c_e_h_3, c_g, s6, s7)), introduced(assumption)).
% 291.14/183.62 tff(10468,plain,
% 291.14/183.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s7) | node4(c_e_h_3, c_g, s6) | (~node5(c_e_h_3, c_g, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | m_or_h_gate_v_out(c_e_h_3, c_g, s7) | node4(c_e_h_3, c_g, s6) | (~node5(c_e_h_3, c_g, s6, s7)))),
% 291.14/183.62 inference(rewrite,[status(thm)],[])).
% 291.14/183.62 tff(10469,plain,
% 291.14/183.62 ((node4(c_e_h_3, c_g, s6) | (~node5(c_e_h_3, c_g, s6, s7)) | m_or_h_gate_v_out(c_e_h_3, c_g, s7)) <=> (m_or_h_gate_v_out(c_e_h_3, c_g, s7) | node4(c_e_h_3, c_g, s6) | (~node5(c_e_h_3, c_g, s6, s7)))),
% 291.14/183.62 inference(rewrite,[status(thm)],[])).
% 291.14/183.62 tff(10470,plain,
% 291.14/183.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_3, c_g, s6) | (~node5(c_e_h_3, c_g, s6, s7)) | m_or_h_gate_v_out(c_e_h_3, c_g, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s7) | node4(c_e_h_3, c_g, s6) | (~node5(c_e_h_3, c_g, s6, s7))))),
% 291.15/183.62 inference(monotonicity,[status(thm)],[10469])).
% 291.15/183.62 tff(10471,plain,
% 291.15/183.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_3, c_g, s6) | (~node5(c_e_h_3, c_g, s6, s7)) | m_or_h_gate_v_out(c_e_h_3, c_g, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | m_or_h_gate_v_out(c_e_h_3, c_g, s7) | node4(c_e_h_3, c_g, s6) | (~node5(c_e_h_3, c_g, s6, s7)))),
% 291.15/183.62 inference(transitivity,[status(thm)],[10470, 10468])).
% 291.15/183.62 tff(10472,plain,
% 291.15/183.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_3, c_g, s6) | (~node5(c_e_h_3, c_g, s6, s7)) | m_or_h_gate_v_out(c_e_h_3, c_g, s7))),
% 291.15/183.62 inference(quant_inst,[status(thm)],[])).
% 291.15/183.62 tff(10473,plain,
% 291.15/183.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | m_or_h_gate_v_out(c_e_h_3, c_g, s7) | node4(c_e_h_3, c_g, s6) | (~node5(c_e_h_3, c_g, s6, s7))),
% 291.15/183.62 inference(modus_ponens,[status(thm)],[10472, 10471])).
% 291.15/183.62 tff(10474,plain,
% 291.15/183.62 ($false),
% 291.15/183.62 inference(unit_resolution,[status(thm)],[10473, 5498, 10467, 10390, 10466])).
% 291.15/183.62 tff(10475,plain,((~node5(c_e_h_3, c_g, s6, s7)) | m_or_h_gate_v_out(c_e_h_3, c_g, s7) | node4(c_e_h_3, c_g, s6)), inference(lemma,lemma(discharge,[]))).
% 291.15/183.62 tff(10476,plain,
% 291.15/183.62 (~node5(c_e_h_3, c_g, s6, s7)),
% 291.15/183.62 inference(unit_resolution,[status(thm)],[10475, 10390, 10466])).
% 291.15/183.62 tff(10477,plain,
% 291.15/183.62 (node6(c_e_h_3, c_g, s6, s7)),
% 291.15/183.62 inference(unit_resolution,[status(thm)],[10250, 10476])).
% 291.15/183.62 tff(10478,plain,
% 291.15/183.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s7) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s6)) | (~node6(c_e_h_3, c_g, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | m_or_h_gate_v_out(c_e_h_3, c_g, s7) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s6)) | (~node6(c_e_h_3, c_g, s6, s7)))),
% 291.15/183.62 inference(rewrite,[status(thm)],[])).
% 291.15/183.62 tff(10479,plain,
% 291.15/183.62 ((m_or_h_gate_v_out(c_e_h_3, c_g, s7) | (~node6(c_e_h_3, c_g, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s6))) <=> (m_or_h_gate_v_out(c_e_h_3, c_g, s7) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s6)) | (~node6(c_e_h_3, c_g, s6, s7)))),
% 291.15/183.62 inference(rewrite,[status(thm)],[])).
% 291.15/183.62 tff(10480,plain,
% 291.15/183.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s7) | (~node6(c_e_h_3, c_g, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s7) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s6)) | (~node6(c_e_h_3, c_g, s6, s7))))),
% 291.15/183.62 inference(monotonicity,[status(thm)],[10479])).
% 291.15/183.62 tff(10481,plain,
% 291.15/183.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s7) | (~node6(c_e_h_3, c_g, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | m_or_h_gate_v_out(c_e_h_3, c_g, s7) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s6)) | (~node6(c_e_h_3, c_g, s6, s7)))),
% 291.15/183.62 inference(transitivity,[status(thm)],[10480, 10478])).
% 291.15/183.62 tff(10482,plain,
% 291.15/183.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s7) | (~node6(c_e_h_3, c_g, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s6)))),
% 291.15/183.62 inference(quant_inst,[status(thm)],[])).
% 291.15/183.62 tff(10483,plain,
% 291.15/183.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | m_or_h_gate_v_out(c_e_h_3, c_g, s7) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s6)) | (~node6(c_e_h_3, c_g, s6, s7))),
% 291.15/183.63 inference(modus_ponens,[status(thm)],[10482, 10481])).
% 291.15/183.63 tff(10484,plain,
% 291.15/183.63 ($false),
% 291.15/183.63 inference(unit_resolution,[status(thm)],[10483, 5474, 10477, 10390, 10261])).
% 291.15/183.63 tff(10485,plain,(m_or_h_gate_v_out(c_e_h_3, c_g, s7) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s6)) | node4(c_e_h_3, c_g, s6)), inference(lemma,lemma(discharge,[]))).
% 291.15/183.63 tff(10486,plain,
% 291.15/183.63 (node4(c_e_h_3, c_g, s6)),
% 291.15/183.63 inference(unit_resolution,[status(thm)],[10485, 10465, 10461])).
% 291.15/183.63 tff(10487,plain,
% 291.15/183.63 (((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_g, s6)) | (~node4(c_e_h_3, c_g, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s6)) | (~node4(c_e_h_3, c_g, s6)))),
% 291.15/183.63 inference(rewrite,[status(thm)],[])).
% 291.15/183.63 tff(10488,plain,
% 291.15/183.63 ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_g, s6)) | (~node4(c_e_h_3, c_g, s6)))),
% 291.15/183.63 inference(quant_inst,[status(thm)],[])).
% 291.15/183.63 tff(10489,plain,
% 291.15/183.63 ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s6)) | (~node4(c_e_h_3, c_g, s6))),
% 291.15/183.63 inference(modus_ponens,[status(thm)],[10488, 10487])).
% 291.15/183.63 tff(10490,plain,
% 291.15/183.63 (~m_or_h_gate_v_in1(c_e_h_3, c_g, s6)),
% 291.15/183.63 inference(unit_resolution,[status(thm)],[10489, 5516, 10486])).
% 291.15/183.63 tff(10491,plain,
% 291.15/183.63 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s6)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s6))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s6)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s6))),
% 291.15/183.63 inference(rewrite,[status(thm)],[])).
% 291.15/183.63 tff(10492,plain,
% 291.15/183.63 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s6)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s6))),
% 291.15/183.63 inference(quant_inst,[status(thm)],[])).
% 291.15/183.63 tff(10493,plain,
% 291.15/183.63 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s6)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s6)),
% 291.15/183.63 inference(modus_ponens,[status(thm)],[10492, 10491])).
% 291.15/183.63 tff(10494,plain,
% 291.15/183.63 (~m_and_h_gate_v_out(c_e_h_3, c_c, s6)),
% 291.15/183.63 inference(unit_resolution,[status(thm)],[10493, 5896, 10490])).
% 291.15/183.63 tff(10495,plain,
% 291.15/183.63 (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)),
% 291.15/183.63 inference(unit_resolution,[status(thm)],[3376, 2714, 3125])).
% 291.15/183.63 tff(10496,plain,
% 291.15/183.63 (m_and_h_gate_v_out(c_e_h_3, c_c, s5)),
% 291.15/183.63 inference(unit_resolution,[status(thm)],[10318, 10461, 10306, 10495, 9740])).
% 291.15/183.63 tff(10497,plain,
% 291.15/183.63 (m_mutex_h_half_v_out(c_e_h_3, c_a, s4)),
% 291.15/183.63 inference(unit_resolution,[status(thm)],[10330, 10496])).
% 291.15/183.63 tff(10498,plain,
% 291.15/183.63 (m_mutex_h_half_v_out(c_e_h_3, c_a, s5)),
% 291.15/183.63 inference(unit_resolution,[status(thm)],[1488, 10497, 1447])).
% 291.15/183.63 tff(10499,plain,
% 291.15/183.63 (m_and_h_gate_v_in1(c_e_h_3, c_c, s5)),
% 291.15/183.63 inference(unit_resolution,[status(thm)],[10341, 10498])).
% 291.15/183.63 tff(10500,plain,
% 291.15/183.63 (~node21(c_e_h_3, c_c, s5, s6)),
% 291.15/183.63 inference(unit_resolution,[status(thm)],[10368, 10494, 10499])).
% 291.15/183.63 tff(10501,plain,
% 291.15/183.63 (node22(c_e_h_3, c_c, s5, s6)),
% 291.15/183.63 inference(unit_resolution,[status(thm)],[10174, 10500])).
% 291.15/183.63 tff(10502,plain,
% 291.15/183.63 ($false),
% 291.15/183.63 inference(unit_resolution,[status(thm)],[10376, 5871, 10496, 10501, 10494])).
% 291.15/183.63 tff(10503,plain,(m_and_h_gate_v_in1(c_e_h_3, c_c, s3) | m_and_h_gate_v_in1(c_e_h_3, c_k, s7) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s4)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s7)) | m_and_h_gate_v_out(c_e_h_3, c_k, s5)), inference(lemma,lemma(discharge,[]))).
% 291.15/183.63 tff(10504,plain,
% 291.15/183.63 (m_and_h_gate_v_in1(c_e_h_3, c_c, s3)),
% 291.15/183.63 inference(unit_resolution,[status(thm)],[10503, 10454, 10426, 10396, 4408])).
% 291.15/183.63 tff(10505,plain,
% 291.15/183.63 (m_mutex_h_half_v_out(c_e_h_3, c_a, s5)),
% 291.15/183.63 inference(unit_resolution,[status(thm)],[1488, 10454, 10451])).
% 291.15/183.63 tff(10506,plain,
% 291.15/183.63 (m_and_h_gate_v_in1(c_e_h_3, c_c, s5)),
% 291.15/183.63 inference(unit_resolution,[status(thm)],[10341, 10505])).
% 291.15/183.63 tff(10507,plain,
% 291.15/183.63 (~node21(c_e_h_3, c_c, s3, s4)),
% 291.15/183.63 inference(unit_resolution,[status(thm)],[5859, 2743, 2539])).
% 291.15/183.63 tff(10508,plain,
% 291.15/183.63 (node22(c_e_h_3, c_c, s3, s4)),
% 291.15/183.63 inference(unit_resolution,[status(thm)],[2734, 10507])).
% 291.15/183.63 tff(10509,plain,
% 291.15/183.63 (~m_and_h_gate_v_out(c_e_h_3, c_c, s3)),
% 291.15/183.63 inference(unit_resolution,[status(thm)],[5874, 5871, 10508, 2743])).
% 291.15/183.63 tff(10510,plain,
% 291.15/183.63 (~m_or_h_gate_v_in1(c_e_h_3, c_g, s3)),
% 291.15/183.63 inference(unit_resolution,[status(thm)],[2713, 10509])).
% 291.15/183.63 tff(10511,plain,
% 291.15/183.63 (~m_or_h_gate_v_out(c_e_h_3, c_g, s5)),
% 291.15/183.63 inference(unit_resolution,[status(thm)],[3356, 10510, 3125, 3006, 5880])).
% 291.15/183.63 tff(10512,plain,
% 291.15/183.63 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s5)),
% 291.15/183.63 inference(unit_resolution,[status(thm)],[3365, 10511])).
% 291.15/183.63 tff(10513,plain,
% 291.15/183.63 (~node20(c_e_h_3, c_k, s5)),
% 291.15/183.63 inference(unit_resolution,[status(thm)],[5458, 10512])).
% 291.15/183.63 tff(10514,plain,
% 291.15/183.63 (~m_and_h_gate_v_out(c_e_h_3, c_k, s6)),
% 291.15/183.63 inference(unit_resolution,[status(thm)],[4467, 10513, 4408])).
% 291.15/183.63 tff(10515,plain,
% 291.15/183.63 (node20(c_e_h_3, c_k, s6)),
% 291.15/183.63 inference(unit_resolution,[status(thm)],[10440, 10514, 7182])).
% 291.15/183.63 tff(10516,plain,
% 291.15/183.63 (m_and_h_gate_v_in1(c_e_h_3, c_k, s6)),
% 291.15/183.63 inference(unit_resolution,[status(thm)],[10444, 38, 10515])).
% 291.15/183.63 tff(10517,plain,
% 291.15/183.63 (m_or_h_gate_v_out(c_e_h_3, c_g, s6)),
% 291.15/183.63 inference(unit_resolution,[status(thm)],[10448, 2048, 10516])).
% 291.15/183.63 tff(10518,plain,
% 291.15/183.63 (node4(c_e_h_3, c_g, s6)),
% 291.15/183.63 inference(unit_resolution,[status(thm)],[10485, 10517, 10390])).
% 291.15/183.63 tff(10519,plain,
% 291.15/183.63 (~m_or_h_gate_v_in1(c_e_h_3, c_g, s6)),
% 291.15/183.63 inference(unit_resolution,[status(thm)],[10489, 5516, 10518])).
% 291.15/183.63 tff(10520,plain,
% 291.15/183.63 (~m_and_h_gate_v_out(c_e_h_3, c_c, s6)),
% 291.15/183.63 inference(unit_resolution,[status(thm)],[10493, 5896, 10519])).
% 291.15/183.63 tff(10521,plain,
% 291.15/183.63 (~node21(c_e_h_3, c_c, s5, s6)),
% 291.15/183.63 inference(unit_resolution,[status(thm)],[10368, 10520, 10186])).
% 291.15/183.63 tff(10522,plain,
% 291.15/183.63 (node22(c_e_h_3, c_c, s5, s6)),
% 291.15/183.63 inference(unit_resolution,[status(thm)],[10174, 10521])).
% 291.15/183.63 tff(10523,plain,
% 291.15/183.63 (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)),
% 291.15/183.63 inference(unit_resolution,[status(thm)],[3376, 10510, 3125])).
% 291.15/183.63 tff(10524,plain,
% 291.15/183.63 (m_and_h_gate_v_out(c_e_h_3, c_c, s5)),
% 291.15/183.63 inference(unit_resolution,[status(thm)],[10318, 10517, 10306, 10523, 9740])).
% 291.15/183.63 tff(10525,plain,
% 291.15/183.63 ($false),
% 291.15/183.63 inference(unit_resolution,[status(thm)],[10376, 5871, 10524, 10522, 10520])).
% 291.15/183.63 tff(10526,plain,(m_and_h_gate_v_out(c_e_h_3, c_c, s4) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s5)) | m_or_h_gate_v_out(c_e_h_3, c_g, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s7)) | m_and_h_gate_v_out(c_e_h_3, c_k, s5) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s3))), inference(lemma,lemma(discharge,[]))).
% 291.15/183.63 tff(10527,plain,
% 291.15/183.63 ($false),
% 291.15/183.63 inference(unit_resolution,[status(thm)],[10526, 10506, 10504, 2743, 10388, 4408, 10426])).
% 291.15/183.63 tff(10528,plain,((~m_and_h_gate_v_out(c_e_h_3, c_k, s8)) | m_and_h_gate_v_out(c_e_h_3, c_c, s4) | m_and_h_gate_v_out(c_e_h_3, c_k, s5) | m_or_h_gate_v_out(c_e_h_3, c_g, s4) | m_and_h_gate_v_out(c_e_h_3, c_k, s6) | m_or_h_gate_v_out(c_e_h_3, c_g, s5) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s8)) | m_and_h_gate_v_out(c_e_h_3, c_k, s9)), inference(lemma,lemma(discharge,[]))).
% 291.15/183.63 tff(10529,plain,
% 291.15/183.63 (~m_and_h_gate_v_out(c_e_h_3, c_k, s8)),
% 291.15/183.63 inference(unit_resolution,[status(thm)],[10528, 9467, 4408, 3308, 4469, 3360, 8981, 2743])).
% 291.15/183.63 tff(10530,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_l, s8)), introduced(assumption)).
% 291.15/183.63 tff(10531,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_k, s8)), introduced(assumption)).
% 291.15/183.63 tff(10532,plain,
% 291.15/183.63 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_l, s8)) | m_and_h_gate_v_out(c_e_h_3, c_k, s8))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s8)) | m_and_h_gate_v_out(c_e_h_3, c_k, s8))),
% 291.15/183.63 inference(rewrite,[status(thm)],[])).
% 291.15/183.63 tff(10533,plain,
% 291.15/183.63 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_l, s8)) | m_and_h_gate_v_out(c_e_h_3, c_k, s8))),
% 291.15/183.63 inference(quant_inst,[status(thm)],[])).
% 291.15/183.63 tff(10534,plain,
% 291.15/183.63 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s8)) | m_and_h_gate_v_out(c_e_h_3, c_k, s8)),
% 291.15/183.63 inference(modus_ponens,[status(thm)],[10533, 10532])).
% 291.15/183.63 tff(10535,plain,
% 291.15/183.63 ($false),
% 291.15/183.63 inference(unit_resolution,[status(thm)],[10534, 1529, 10531, 10530])).
% 291.15/183.63 tff(10536,plain,((~m_and_h_gate_v_in1(c_e_h_3, c_l, s8)) | m_and_h_gate_v_out(c_e_h_3, c_k, s8)), inference(lemma,lemma(discharge,[]))).
% 291.15/183.63 tff(10537,plain,
% 291.15/183.63 (~m_and_h_gate_v_in1(c_e_h_3, c_l, s8)),
% 291.15/183.63 inference(unit_resolution,[status(thm)],[10536, 10529])).
% 291.15/183.63 tff(10538,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_l, s8)), introduced(assumption)).
% 291.15/183.63 tff(10539,assumption,(node20(c_e_h_3, c_l, s8)), introduced(assumption)).
% 291.15/183.63 tff(10540,plain,
% 291.15/183.63 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_l, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_l, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s8))),
% 291.15/183.63 inference(rewrite,[status(thm)],[])).
% 291.15/183.63 tff(10541,plain,
% 291.15/183.63 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_l, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s8))),
% 291.15/183.63 inference(quant_inst,[status(thm)],[])).
% 291.15/183.63 tff(10542,plain,
% 291.15/183.63 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_l, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s8)),
% 291.15/183.63 inference(modus_ponens,[status(thm)],[10541, 10540])).
% 291.15/183.63 tff(10543,plain,
% 291.15/183.63 ($false),
% 291.15/183.63 inference(unit_resolution,[status(thm)],[10542, 38, 10539, 10538])).
% 291.15/183.63 tff(10544,plain,((~node20(c_e_h_3, c_l, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s8)), inference(lemma,lemma(discharge,[]))).
% 291.15/183.63 tff(10545,plain,
% 291.15/183.63 (~node20(c_e_h_3, c_l, s8)),
% 291.15/183.63 inference(unit_resolution,[status(thm)],[10544, 10537])).
% 291.15/183.63 tff(10546,assumption,(node22(c_e_h_3, c_l, s8, s9)), introduced(assumption)).
% 291.15/183.63 tff(10547,plain,
% 291.15/183.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s9)) | (~node22(c_e_h_3, c_l, s8, s9)) | m_and_h_gate_v_out(c_e_h_3, c_l, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s9)) | (~node22(c_e_h_3, c_l, s8, s9)) | m_and_h_gate_v_out(c_e_h_3, c_l, s8))),
% 291.15/183.63 inference(rewrite,[status(thm)],[])).
% 291.15/183.63 tff(10548,plain,
% 291.15/183.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s9)) | (~node22(c_e_h_3, c_l, s8, s9)) | m_and_h_gate_v_out(c_e_h_3, c_l, s8))),
% 291.15/183.63 inference(quant_inst,[status(thm)],[])).
% 291.15/183.63 tff(10549,plain,
% 291.15/183.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s9)) | (~node22(c_e_h_3, c_l, s8, s9)) | m_and_h_gate_v_out(c_e_h_3, c_l, s8)),
% 291.15/183.63 inference(modus_ponens,[status(thm)],[10548, 10547])).
% 291.15/183.63 tff(10550,plain,
% 291.15/183.63 ($false),
% 291.15/183.63 inference(unit_resolution,[status(thm)],[10549, 108, 9019, 10546, 6450])).
% 291.15/183.63 tff(10551,plain,((~node22(c_e_h_3, c_l, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s9)) | m_and_h_gate_v_out(c_e_h_3, c_l, s8)), inference(lemma,lemma(discharge,[]))).
% 291.15/183.63 tff(10552,plain,
% 291.15/183.63 (~node22(c_e_h_3, c_l, s8, s9)),
% 291.15/183.63 inference(unit_resolution,[status(thm)],[10551, 9019, 6450])).
% 291.15/183.63 tff(10553,assumption,(~node20(c_e_h_3, c_l, s8)), introduced(assumption)).
% 291.15/183.63 tff(10554,assumption,(node21(c_e_h_3, c_l, s8, s9)), introduced(assumption)).
% 291.15/183.64 tff(10555,plain,
% 291.15/183.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s9)) | node20(c_e_h_3, c_l, s8) | (~node21(c_e_h_3, c_l, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s9)) | node20(c_e_h_3, c_l, s8) | (~node21(c_e_h_3, c_l, s8, s9)))),
% 291.15/183.64 inference(rewrite,[status(thm)],[])).
% 291.15/183.64 tff(10556,plain,
% 291.15/183.64 ((node20(c_e_h_3, c_l, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s9)) | (~node21(c_e_h_3, c_l, s8, s9))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_l, s9)) | node20(c_e_h_3, c_l, s8) | (~node21(c_e_h_3, c_l, s8, s9)))),
% 291.15/183.64 inference(rewrite,[status(thm)],[])).
% 291.15/183.64 tff(10557,plain,
% 291.15/183.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s9)) | (~node21(c_e_h_3, c_l, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s9)) | node20(c_e_h_3, c_l, s8) | (~node21(c_e_h_3, c_l, s8, s9))))),
% 291.15/183.64 inference(monotonicity,[status(thm)],[10556])).
% 291.15/183.64 tff(10558,plain,
% 291.15/183.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s9)) | (~node21(c_e_h_3, c_l, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s9)) | node20(c_e_h_3, c_l, s8) | (~node21(c_e_h_3, c_l, s8, s9)))),
% 291.15/183.64 inference(transitivity,[status(thm)],[10557, 10555])).
% 291.15/183.64 tff(10559,plain,
% 291.15/183.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s9)) | (~node21(c_e_h_3, c_l, s8, s9)))),
% 291.15/183.64 inference(quant_inst,[status(thm)],[])).
% 291.15/183.64 tff(10560,plain,
% 291.15/183.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s9)) | node20(c_e_h_3, c_l, s8) | (~node21(c_e_h_3, c_l, s8, s9))),
% 291.15/183.64 inference(modus_ponens,[status(thm)],[10559, 10558])).
% 291.15/183.64 tff(10561,plain,
% 291.15/183.64 ($false),
% 291.15/183.64 inference(unit_resolution,[status(thm)],[10560, 52, 9019, 10554, 10553])).
% 291.15/183.64 tff(10562,plain,((~node21(c_e_h_3, c_l, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s9)) | node20(c_e_h_3, c_l, s8)), inference(lemma,lemma(discharge,[]))).
% 291.15/183.64 tff(10563,plain,
% 291.15/183.64 (~node21(c_e_h_3, c_l, s8, s9)),
% 291.15/183.64 inference(unit_resolution,[status(thm)],[10562, 9019, 10553])).
% 291.15/183.64 tff(10564,plain,
% 291.15/183.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s8, s9)) | node21(c_e_h_3, c_l, s8, s9) | node22(c_e_h_3, c_l, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_3, c_l, s8, s9) | node22(c_e_h_3, c_l, s8, s9))),
% 291.15/183.64 inference(rewrite,[status(thm)],[])).
% 291.15/183.64 tff(10565,plain,
% 291.15/183.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s8, s9)) | node21(c_e_h_3, c_l, s8, s9) | node22(c_e_h_3, c_l, s8, s9))),
% 291.15/183.64 inference(quant_inst,[status(thm)],[])).
% 291.15/183.64 tff(10566,plain,
% 291.15/183.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_3, c_l, s8, s9) | node22(c_e_h_3, c_l, s8, s9)),
% 291.15/183.64 inference(modus_ponens,[status(thm)],[10565, 10564])).
% 291.15/183.64 tff(10567,plain,
% 291.15/183.64 (node21(c_e_h_3, c_l, s8, s9) | node22(c_e_h_3, c_l, s8, s9)),
% 291.15/183.64 inference(unit_resolution,[status(thm)],[10566, 82, 1993])).
% 291.15/183.64 tff(10568,plain,
% 291.15/183.64 ($false),
% 291.15/183.64 inference(unit_resolution,[status(thm)],[10567, 10563, 10552])).
% 291.15/183.64 tff(10569,plain,((~m_and_h_gate_v_out(c_e_h_3, c_l, s9)) | node20(c_e_h_3, c_l, s8) | m_and_h_gate_v_out(c_e_h_3, c_l, s8)), inference(lemma,lemma(discharge,[]))).
% 291.15/183.64 tff(10570,plain,
% 291.15/183.64 (m_and_h_gate_v_out(c_e_h_3, c_l, s8)),
% 291.15/183.64 inference(unit_resolution,[status(thm)],[10569, 10545, 8980])).
% 291.15/183.64 tff(10571,plain,
% 291.15/183.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s8)) | (~node22(c_e_h_3, c_l, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_l, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s8)) | (~node22(c_e_h_3, c_l, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_l, s7))),
% 291.15/183.64 inference(rewrite,[status(thm)],[])).
% 291.15/183.64 tff(10572,plain,
% 291.15/183.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s8)) | (~node22(c_e_h_3, c_l, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_l, s7))),
% 291.15/183.64 inference(quant_inst,[status(thm)],[])).
% 291.15/183.64 tff(10573,plain,
% 291.15/183.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s8)) | (~node22(c_e_h_3, c_l, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_l, s7)),
% 291.15/183.64 inference(modus_ponens,[status(thm)],[10572, 10571])).
% 291.15/183.64 tff(10574,plain,
% 291.15/183.64 ($false),
% 291.15/183.64 inference(unit_resolution,[status(thm)],[10573, 108, 6459, 6455, 5524])).
% 291.15/183.64 tff(10575,plain,((~node22(c_e_h_3, c_l, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_l, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s8))), inference(lemma,lemma(discharge,[]))).
% 291.15/183.64 tff(10576,plain,
% 291.15/183.64 (~node22(c_e_h_3, c_l, s7, s8)),
% 291.15/183.64 inference(unit_resolution,[status(thm)],[10575, 5524, 6455])).
% 291.15/183.64 tff(10577,assumption,(~node20(c_e_h_3, c_l, s7)), introduced(assumption)).
% 291.15/183.64 tff(10578,plain,
% 291.15/183.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s7) | (~node21(c_e_h_3, c_l, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_l, s7) | (~node21(c_e_h_3, c_l, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s8)))),
% 291.15/183.64 inference(rewrite,[status(thm)],[])).
% 291.15/183.64 tff(10579,plain,
% 291.15/183.64 ((node20(c_e_h_3, c_l, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s8)) | (~node21(c_e_h_3, c_l, s7, s8))) <=> (node20(c_e_h_3, c_l, s7) | (~node21(c_e_h_3, c_l, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s8)))),
% 291.15/183.64 inference(rewrite,[status(thm)],[])).
% 291.15/183.64 tff(10580,plain,
% 291.15/183.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s8)) | (~node21(c_e_h_3, c_l, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s7) | (~node21(c_e_h_3, c_l, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s8))))),
% 291.15/183.64 inference(monotonicity,[status(thm)],[10579])).
% 291.15/183.64 tff(10581,plain,
% 291.15/183.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s8)) | (~node21(c_e_h_3, c_l, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_l, s7) | (~node21(c_e_h_3, c_l, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s8)))),
% 291.15/183.64 inference(transitivity,[status(thm)],[10580, 10578])).
% 291.15/183.64 tff(10582,plain,
% 291.15/183.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s8)) | (~node21(c_e_h_3, c_l, s7, s8)))),
% 291.15/183.64 inference(quant_inst,[status(thm)],[])).
% 291.15/183.64 tff(10583,plain,
% 291.15/183.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_l, s7) | (~node21(c_e_h_3, c_l, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s8))),
% 291.15/183.64 inference(modus_ponens,[status(thm)],[10582, 10581])).
% 291.15/183.64 tff(10584,plain,
% 291.15/183.64 ($false),
% 291.15/183.64 inference(unit_resolution,[status(thm)],[10583, 52, 7164, 5524, 10577])).
% 291.15/183.64 tff(10585,plain,((~node21(c_e_h_3, c_l, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s8)) | node20(c_e_h_3, c_l, s7)), inference(lemma,lemma(discharge,[]))).
% 291.15/183.64 tff(10586,plain,
% 291.15/183.64 (~node21(c_e_h_3, c_l, s7, s8)),
% 291.15/183.64 inference(unit_resolution,[status(thm)],[10585, 5524, 10577])).
% 291.15/183.64 tff(10587,plain,
% 291.15/183.64 ($false),
% 291.15/183.64 inference(unit_resolution,[status(thm)],[7177, 10586, 10576])).
% 291.15/183.64 tff(10588,plain,((~m_and_h_gate_v_out(c_e_h_3, c_l, s8)) | node20(c_e_h_3, c_l, s7) | m_and_h_gate_v_out(c_e_h_3, c_l, s7)), inference(lemma,lemma(discharge,[]))).
% 291.15/183.64 tff(10589,plain,
% 291.15/183.64 (node20(c_e_h_3, c_l, s7)),
% 291.15/183.64 inference(unit_resolution,[status(thm)],[10588, 10570, 6455])).
% 291.15/183.64 tff(10590,assumption,(node20(c_e_h_3, c_l, s7)), introduced(assumption)).
% 291.15/183.64 tff(10591,plain,
% 291.15/183.64 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_l, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_l, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s7))),
% 291.15/183.64 inference(rewrite,[status(thm)],[])).
% 291.15/183.64 tff(10592,plain,
% 291.15/183.64 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_l, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s7))),
% 291.15/183.64 inference(quant_inst,[status(thm)],[])).
% 291.15/183.64 tff(10593,plain,
% 291.15/183.64 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_l, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s7)),
% 291.15/183.64 inference(modus_ponens,[status(thm)],[10592, 10591])).
% 291.15/183.64 tff(10594,plain,
% 291.15/183.64 ($false),
% 291.15/183.64 inference(unit_resolution,[status(thm)],[10593, 38, 10590, 7181])).
% 291.15/183.64 tff(10595,plain,((~node20(c_e_h_3, c_l, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s7)), inference(lemma,lemma(discharge,[]))).
% 291.15/183.64 tff(10596,plain,
% 291.15/183.64 (m_and_h_gate_v_in1(c_e_h_3, c_l, s7)),
% 291.15/183.64 inference(unit_resolution,[status(thm)],[10595, 10589])).
% 291.15/183.64 tff(10597,plain,
% 291.15/183.64 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_l, s7)) | m_and_h_gate_v_out(c_e_h_3, c_k, s7))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s7)) | m_and_h_gate_v_out(c_e_h_3, c_k, s7))),
% 291.15/183.64 inference(rewrite,[status(thm)],[])).
% 291.15/183.64 tff(10598,plain,
% 291.15/183.64 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_l, s7)) | m_and_h_gate_v_out(c_e_h_3, c_k, s7))),
% 291.15/183.64 inference(quant_inst,[status(thm)],[])).
% 291.15/183.64 tff(10599,plain,
% 291.15/183.64 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s7)) | m_and_h_gate_v_out(c_e_h_3, c_k, s7)),
% 291.15/183.64 inference(modus_ponens,[status(thm)],[10598, 10597])).
% 291.15/183.64 tff(10600,plain,
% 291.15/183.64 ($false),
% 291.15/183.64 inference(unit_resolution,[status(thm)],[10599, 1529, 6243, 6469])).
% 291.15/183.64 tff(10601,plain,((~m_and_h_gate_v_in1(c_e_h_3, c_l, s7)) | m_and_h_gate_v_out(c_e_h_3, c_k, s7)), inference(lemma,lemma(discharge,[]))).
% 291.15/183.64 tff(10602,plain,
% 291.15/183.64 (m_and_h_gate_v_out(c_e_h_3, c_k, s7)),
% 291.15/183.64 inference(unit_resolution,[status(thm)],[10601, 10596])).
% 291.15/183.64 tff(10603,plain,
% 291.15/183.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s7)) | m_and_h_gate_v_out(c_e_h_3, c_k, s8) | (~node22(c_e_h_3, c_k, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s7)) | m_and_h_gate_v_out(c_e_h_3, c_k, s8) | (~node22(c_e_h_3, c_k, s7, s8)))),
% 291.15/183.65 inference(rewrite,[status(thm)],[])).
% 291.15/183.65 tff(10604,plain,
% 291.15/183.65 ((m_and_h_gate_v_out(c_e_h_3, c_k, s8) | (~node22(c_e_h_3, c_k, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s7))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_k, s7)) | m_and_h_gate_v_out(c_e_h_3, c_k, s8) | (~node22(c_e_h_3, c_k, s7, s8)))),
% 291.15/183.65 inference(rewrite,[status(thm)],[])).
% 291.15/183.65 tff(10605,plain,
% 291.15/183.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_k, s8) | (~node22(c_e_h_3, c_k, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s7)) | m_and_h_gate_v_out(c_e_h_3, c_k, s8) | (~node22(c_e_h_3, c_k, s7, s8))))),
% 291.15/183.65 inference(monotonicity,[status(thm)],[10604])).
% 291.15/183.65 tff(10606,plain,
% 291.15/183.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_k, s8) | (~node22(c_e_h_3, c_k, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s7)) | m_and_h_gate_v_out(c_e_h_3, c_k, s8) | (~node22(c_e_h_3, c_k, s7, s8)))),
% 291.15/183.65 inference(transitivity,[status(thm)],[10605, 10603])).
% 291.15/183.65 tff(10607,plain,
% 291.15/183.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_k, s8) | (~node22(c_e_h_3, c_k, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s7)))),
% 291.15/183.65 inference(quant_inst,[status(thm)],[])).
% 291.15/183.65 tff(10608,plain,
% 291.15/183.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s7)) | m_and_h_gate_v_out(c_e_h_3, c_k, s8) | (~node22(c_e_h_3, c_k, s7, s8))),
% 291.15/183.65 inference(modus_ponens,[status(thm)],[10607, 10606])).
% 291.15/183.65 tff(10609,plain,
% 291.15/183.65 ($false),
% 291.15/183.65 inference(unit_resolution,[status(thm)],[10608, 5871, 10405, 7182, 10531])).
% 291.15/183.65 tff(10610,plain,((~node22(c_e_h_3, c_k, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s7)) | m_and_h_gate_v_out(c_e_h_3, c_k, s8)), inference(lemma,lemma(discharge,[]))).
% 291.15/183.65 tff(10611,plain,
% 291.15/183.65 (~node22(c_e_h_3, c_k, s7, s8)),
% 291.15/183.65 inference(unit_resolution,[status(thm)],[10610, 10602, 10529])).
% 291.15/183.65 tff(10612,plain,
% 291.15/183.65 (node21(c_e_h_3, c_k, s7, s8)),
% 291.15/183.65 inference(unit_resolution,[status(thm)],[10423, 10611])).
% 291.15/183.65 tff(10613,plain,
% 291.15/183.65 (((~![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))) | (m_and_h_gate_v_in2(c_e_h_3, c_k, s7) | m_c_h_element_v_out(c_e_h_3, c_h, s7))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))) | m_and_h_gate_v_in2(c_e_h_3, c_k, s7) | m_c_h_element_v_out(c_e_h_3, c_h, s7))),
% 291.15/183.65 inference(rewrite,[status(thm)],[])).
% 291.15/183.65 tff(10614,plain,
% 291.15/183.65 ((~![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))) | (m_and_h_gate_v_in2(c_e_h_3, c_k, s7) | m_c_h_element_v_out(c_e_h_3, c_h, s7))),
% 291.15/183.65 inference(quant_inst,[status(thm)],[])).
% 291.15/183.65 tff(10615,plain,
% 291.15/183.65 ((~![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))) | m_and_h_gate_v_in2(c_e_h_3, c_k, s7) | m_c_h_element_v_out(c_e_h_3, c_h, s7)),
% 291.15/183.65 inference(modus_ponens,[status(thm)],[10614, 10613])).
% 291.15/183.65 tff(10616,plain,
% 291.15/183.65 (m_and_h_gate_v_in2(c_e_h_3, c_k, s7) | m_c_h_element_v_out(c_e_h_3, c_h, s7)),
% 291.15/183.65 inference(unit_resolution,[status(thm)],[10615, 6420])).
% 291.15/183.65 tff(10617,plain,
% 291.15/183.65 (m_and_h_gate_v_in2(c_e_h_3, c_k, s7)),
% 291.15/183.65 inference(unit_resolution,[status(thm)],[10616, 7566])).
% 291.15/183.65 tff(10618,plain,
% 291.15/183.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_k, s7)) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s7)) | m_and_h_gate_v_out(c_e_h_3, c_k, s8) | (~node21(c_e_h_3, c_k, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s7)) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s7)) | m_and_h_gate_v_out(c_e_h_3, c_k, s8) | (~node21(c_e_h_3, c_k, s7, s8)))),
% 291.15/183.65 inference(rewrite,[status(thm)],[])).
% 291.15/183.65 tff(10619,plain,
% 291.15/183.65 (((~node21(c_e_h_3, c_k, s7, s8)) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s7)) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s7)) | m_and_h_gate_v_out(c_e_h_3, c_k, s8)) <=> ((~m_and_h_gate_v_in1(c_e_h_3, c_k, s7)) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s7)) | m_and_h_gate_v_out(c_e_h_3, c_k, s8) | (~node21(c_e_h_3, c_k, s7, s8)))),
% 291.15/183.65 inference(rewrite,[status(thm)],[])).
% 291.15/183.65 tff(10620,plain,
% 291.15/183.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_k, s7, s8)) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s7)) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s7)) | m_and_h_gate_v_out(c_e_h_3, c_k, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_k, s7)) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s7)) | m_and_h_gate_v_out(c_e_h_3, c_k, s8) | (~node21(c_e_h_3, c_k, s7, s8))))),
% 291.15/183.65 inference(monotonicity,[status(thm)],[10619])).
% 291.15/183.65 tff(10621,plain,
% 291.15/183.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_k, s7, s8)) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s7)) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s7)) | m_and_h_gate_v_out(c_e_h_3, c_k, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s7)) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s7)) | m_and_h_gate_v_out(c_e_h_3, c_k, s8) | (~node21(c_e_h_3, c_k, s7, s8)))),
% 291.15/183.65 inference(transitivity,[status(thm)],[10620, 10618])).
% 291.15/183.65 tff(10622,plain,
% 291.15/183.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_k, s7, s8)) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s7)) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s7)) | m_and_h_gate_v_out(c_e_h_3, c_k, s8))),
% 291.15/183.65 inference(quant_inst,[status(thm)],[])).
% 291.15/183.65 tff(10623,plain,
% 291.15/183.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s7)) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s7)) | m_and_h_gate_v_out(c_e_h_3, c_k, s8) | (~node21(c_e_h_3, c_k, s7, s8))),
% 291.15/183.65 inference(modus_ponens,[status(thm)],[10622, 10621])).
% 291.15/183.65 tff(10624,plain,
% 291.15/183.65 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s7)),
% 291.15/183.65 inference(unit_resolution,[status(thm)],[10623, 5851, 10617, 10612, 10529])).
% 291.15/183.65 tff(10625,plain,
% 291.15/183.65 (~m_or_h_gate_v_out(c_e_h_3, c_g, s7)),
% 291.15/183.65 inference(unit_resolution,[status(thm)],[10464, 6229, 10624])).
% 291.15/183.65 tff(10626,plain,
% 291.15/183.65 (node20(c_e_h_3, c_k, s6)),
% 291.15/183.65 inference(unit_resolution,[status(thm)],[10440, 10602, 4469])).
% 291.15/183.65 tff(10627,plain,
% 291.15/183.65 (m_and_h_gate_v_in1(c_e_h_3, c_k, s6)),
% 291.15/183.65 inference(unit_resolution,[status(thm)],[10444, 38, 10626])).
% 291.15/183.65 tff(10628,plain,
% 291.15/183.65 (m_or_h_gate_v_out(c_e_h_3, c_g, s6)),
% 291.15/183.65 inference(unit_resolution,[status(thm)],[10448, 2048, 10627])).
% 291.15/183.65 tff(10629,plain,
% 291.15/183.65 (m_and_h_gate_v_out(c_e_h_3, c_c, s5)),
% 291.15/183.65 inference(unit_resolution,[status(thm)],[10319, 10628, 3308])).
% 291.15/183.65 tff(10630,plain,
% 291.15/183.65 (m_mutex_h_half_v_out(c_e_h_3, c_a, s4)),
% 291.15/183.65 inference(unit_resolution,[status(thm)],[10330, 10629])).
% 291.15/183.65 tff(10631,plain,
% 291.15/183.65 (m_user_v_req(c_e_h_3, c_u, s3)),
% 291.15/183.65 inference(unit_resolution,[status(thm)],[550, 10630])).
% 291.15/183.65 tff(10632,plain,
% 291.15/183.65 (m_user_v_req(c_e_h_3, c_u, s4)),
% 291.15/183.65 inference(unit_resolution,[status(thm)],[732, 10631])).
% 291.15/183.65 tff(10633,plain,
% 291.15/183.65 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s4)),
% 291.15/183.65 inference(unit_resolution,[status(thm)],[1445, 10632])).
% 291.15/183.65 tff(10634,plain,
% 291.15/183.65 (m_and_h_gate_v_in1(c_e_h_3, c_c, s3)),
% 291.15/183.65 inference(unit_resolution,[status(thm)],[10503, 10633, 10602, 10624, 4408])).
% 291.15/183.65 tff(10635,plain,
% 291.15/183.65 (m_mutex_h_half_v_out(c_e_h_3, c_a, s5)),
% 291.15/183.65 inference(unit_resolution,[status(thm)],[1488, 10633, 10630])).
% 291.15/183.65 tff(10636,plain,
% 291.15/183.65 (m_and_h_gate_v_in1(c_e_h_3, c_c, s5)),
% 291.15/183.65 inference(unit_resolution,[status(thm)],[10341, 10635])).
% 291.15/183.65 tff(10637,plain,
% 291.15/183.65 ($false),
% 291.15/183.65 inference(unit_resolution,[status(thm)],[10526, 10636, 10634, 2743, 10625, 4408, 10602])).
% 291.15/183.65 tff(10638,plain,(m_or_h_gate_v_out(c_e_h_3, c_j, s9) | m_and_h_gate_v_out(c_e_h_3, c_c, s4) | m_and_h_gate_v_out(c_e_h_3, c_k, s5) | m_or_h_gate_v_out(c_e_h_3, c_g, s4) | m_and_h_gate_v_out(c_e_h_3, c_k, s6) | m_and_h_gate_v_out(c_e_h_3, c_l, s7) | m_or_h_gate_v_out(c_e_h_3, c_g, s5) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s8)) | m_or_h_gate_v_out(c_e_h_3, c_j, s11) | (~m_c_h_element_v_out(c_e_h_3, c_h, s11)) | m_c_h_element_v_out(c_e_h_3, c_h, s9)), inference(lemma,lemma(discharge,[]))).
% 291.15/183.65 tff(10639,plain,
% 291.15/183.65 (m_or_h_gate_v_out(c_e_h_3, c_j, s9)),
% 291.15/183.65 inference(unit_resolution,[status(thm)],[10638, 3308, 7636, 2743, 4469, 7648, 3360, 7645, 7627, 7626, 7625])).
% 291.15/183.65 tff(10640,plain,
% 291.15/183.65 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s8))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s8))),
% 291.15/183.65 inference(rewrite,[status(thm)],[])).
% 291.15/183.65 tff(10641,plain,
% 291.15/183.65 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s8))),
% 291.15/183.65 inference(quant_inst,[status(thm)],[])).
% 291.15/183.65 tff(10642,plain,
% 291.15/183.65 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s8)),
% 291.15/183.65 inference(modus_ponens,[status(thm)],[10641, 10640])).
% 291.15/183.65 tff(10643,plain,
% 291.15/183.65 (node3(c_e_h_2, c_e_h_3, s8)),
% 291.15/183.65 inference(unit_resolution,[status(thm)],[10642, 1059, 1056])).
% 291.15/183.65 tff(10644,plain,
% 291.15/183.65 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_3, s8)) | (~node3(c_e_h_2, c_e_h_3, s8)) | m_and_h_gate_v_out(c_e_h_2, c_q, s8))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_3, s8)) | (~node3(c_e_h_2, c_e_h_3, s8)) | m_and_h_gate_v_out(c_e_h_2, c_q, s8))),
% 291.15/183.65 inference(rewrite,[status(thm)],[])).
% 291.15/183.65 tff(10645,plain,
% 291.15/183.65 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_3, s8)) | (~node3(c_e_h_2, c_e_h_3, s8)) | m_and_h_gate_v_out(c_e_h_2, c_q, s8))),
% 291.15/183.65 inference(quant_inst,[status(thm)],[])).
% 291.15/183.65 tff(10646,plain,
% 291.15/183.65 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_3, s8)) | (~node3(c_e_h_2, c_e_h_3, s8)) | m_and_h_gate_v_out(c_e_h_2, c_q, s8)),
% 291.15/183.65 inference(modus_ponens,[status(thm)],[10645, 10644])).
% 291.15/183.65 tff(10647,plain,
% 291.15/183.65 ((~m_cell_v_ack(c_e_h_3, s8)) | m_and_h_gate_v_out(c_e_h_2, c_q, s8)),
% 291.15/183.65 inference(unit_resolution,[status(thm)],[10646, 1073, 10643])).
% 291.15/183.65 tff(10648,plain,
% 291.15/183.65 (~m_cell_v_ack(c_e_h_3, s8)),
% 291.15/183.65 inference(unit_resolution,[status(thm)],[10647, 8911])).
% 291.15/183.65 tff(10649,plain,
% 291.15/183.65 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_j, s8)) | m_cell_v_ack(c_e_h_3, s8))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_j, s8)) | m_cell_v_ack(c_e_h_3, s8))),
% 291.15/183.66 inference(rewrite,[status(thm)],[])).
% 291.15/183.66 tff(10650,plain,
% 291.15/183.66 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_j, s8)) | m_cell_v_ack(c_e_h_3, s8))),
% 291.15/183.66 inference(quant_inst,[status(thm)],[])).
% 291.15/183.66 tff(10651,plain,
% 291.15/183.66 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_j, s8)) | m_cell_v_ack(c_e_h_3, s8)),
% 291.15/183.66 inference(modus_ponens,[status(thm)],[10650, 10649])).
% 291.15/183.66 tff(10652,plain,
% 291.15/183.66 (~m_or_h_gate_v_in2(c_e_h_3, c_j, s8)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[10651, 1085, 10648])).
% 291.15/183.66 tff(10653,assumption,(m_or_h_gate_v_out(c_e_h_3, c_j, s9)), introduced(assumption)).
% 291.15/183.66 tff(10654,plain,
% 291.15/183.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_3, c_j, s9)) | m_or_h_gate_v_out(c_e_h_3, c_j, s8) | (~node6(c_e_h_3, c_j, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s9)) | m_or_h_gate_v_out(c_e_h_3, c_j, s8) | (~node6(c_e_h_3, c_j, s8, s9)))),
% 291.15/183.66 inference(rewrite,[status(thm)],[])).
% 291.15/183.66 tff(10655,plain,
% 291.15/183.66 (((~node6(c_e_h_3, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s9)) | m_or_h_gate_v_out(c_e_h_3, c_j, s8)) <=> ((~m_or_h_gate_v_out(c_e_h_3, c_j, s9)) | m_or_h_gate_v_out(c_e_h_3, c_j, s8) | (~node6(c_e_h_3, c_j, s8, s9)))),
% 291.15/183.66 inference(rewrite,[status(thm)],[])).
% 291.15/183.66 tff(10656,plain,
% 291.15/183.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s9)) | m_or_h_gate_v_out(c_e_h_3, c_j, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_3, c_j, s9)) | m_or_h_gate_v_out(c_e_h_3, c_j, s8) | (~node6(c_e_h_3, c_j, s8, s9))))),
% 291.15/183.66 inference(monotonicity,[status(thm)],[10655])).
% 291.15/183.66 tff(10657,plain,
% 291.15/183.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s9)) | m_or_h_gate_v_out(c_e_h_3, c_j, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s9)) | m_or_h_gate_v_out(c_e_h_3, c_j, s8) | (~node6(c_e_h_3, c_j, s8, s9)))),
% 291.15/183.66 inference(transitivity,[status(thm)],[10656, 10654])).
% 291.15/183.66 tff(10658,plain,
% 291.15/183.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s9)) | m_or_h_gate_v_out(c_e_h_3, c_j, s8))),
% 291.15/183.66 inference(quant_inst,[status(thm)],[])).
% 291.15/183.66 tff(10659,plain,
% 291.15/183.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s9)) | m_or_h_gate_v_out(c_e_h_3, c_j, s8) | (~node6(c_e_h_3, c_j, s8, s9))),
% 291.15/183.66 inference(modus_ponens,[status(thm)],[10658, 10657])).
% 291.15/183.66 tff(10660,plain,
% 291.15/183.66 ($false),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[10659, 1121, 10653, 7275, 5464])).
% 291.15/183.66 tff(10661,plain,((~node6(c_e_h_3, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s9)) | m_or_h_gate_v_out(c_e_h_3, c_j, s8)), inference(lemma,lemma(discharge,[]))).
% 291.15/183.66 tff(10662,plain,
% 291.15/183.66 (~node6(c_e_h_3, c_j, s8, s9)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[10661, 10653, 7275])).
% 291.15/183.66 tff(10663,assumption,(~m_or_h_gate_v_in2(c_e_h_3, c_j, s8)), introduced(assumption)).
% 291.15/183.66 tff(10664,assumption,(node5(c_e_h_3, c_j, s8, s9)), introduced(assumption)).
% 291.15/183.66 tff(10665,plain,
% 291.15/183.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_3, c_j, s9)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s8) | (~node5(c_e_h_3, c_j, s8, s9)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s9)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s8) | (~node5(c_e_h_3, c_j, s8, s9)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s8))),
% 291.15/183.66 inference(rewrite,[status(thm)],[])).
% 291.15/183.66 tff(10666,plain,
% 291.15/183.66 ((m_or_h_gate_v_in1(c_e_h_3, c_j, s8) | m_or_h_gate_v_in2(c_e_h_3, c_j, s8) | (~node5(c_e_h_3, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s9))) <=> ((~m_or_h_gate_v_out(c_e_h_3, c_j, s9)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s8) | (~node5(c_e_h_3, c_j, s8, s9)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s8))),
% 291.15/183.66 inference(rewrite,[status(thm)],[])).
% 291.15/183.66 tff(10667,plain,
% 291.15/183.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s8) | m_or_h_gate_v_in2(c_e_h_3, c_j, s8) | (~node5(c_e_h_3, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_3, c_j, s9)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s8) | (~node5(c_e_h_3, c_j, s8, s9)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s8)))),
% 291.15/183.66 inference(monotonicity,[status(thm)],[10666])).
% 291.15/183.66 tff(10668,plain,
% 291.15/183.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s8) | m_or_h_gate_v_in2(c_e_h_3, c_j, s8) | (~node5(c_e_h_3, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s9)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s8) | (~node5(c_e_h_3, c_j, s8, s9)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s8))),
% 291.15/183.66 inference(transitivity,[status(thm)],[10667, 10665])).
% 291.15/183.66 tff(10669,plain,
% 291.15/183.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s8) | m_or_h_gate_v_in2(c_e_h_3, c_j, s8) | (~node5(c_e_h_3, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s9)))),
% 291.15/183.66 inference(quant_inst,[status(thm)],[])).
% 291.15/183.66 tff(10670,plain,
% 291.15/183.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s9)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s8) | (~node5(c_e_h_3, c_j, s8, s9)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s8)),
% 291.15/183.66 inference(modus_ponens,[status(thm)],[10669, 10668])).
% 291.15/183.66 tff(10671,plain,
% 291.15/183.66 ($false),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[10670, 1159, 10653, 10664, 5523, 10663])).
% 291.15/183.66 tff(10672,plain,((~node5(c_e_h_3, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s9)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s8) | m_or_h_gate_v_in2(c_e_h_3, c_j, s8)), inference(lemma,lemma(discharge,[]))).
% 291.15/183.66 tff(10673,plain,
% 291.15/183.66 (~node5(c_e_h_3, c_j, s8, s9)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[10672, 10653, 5523, 10663])).
% 291.15/183.66 tff(10674,plain,
% 291.15/183.66 ($false),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[5487, 10673, 10662])).
% 291.15/183.66 tff(10675,plain,((~m_or_h_gate_v_out(c_e_h_3, c_j, s9)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s8) | m_or_h_gate_v_in2(c_e_h_3, c_j, s8) | m_or_h_gate_v_out(c_e_h_3, c_j, s8)), inference(lemma,lemma(discharge,[]))).
% 291.15/183.66 tff(10676,plain,
% 291.15/183.66 ((~m_or_h_gate_v_out(c_e_h_3, c_j, s9)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s8) | m_or_h_gate_v_out(c_e_h_3, c_j, s8)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[10675, 10652])).
% 291.15/183.66 tff(10677,plain,
% 291.15/183.66 (m_or_h_gate_v_in1(c_e_h_3, c_j, s8)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[10676, 10639, 7275])).
% 291.15/183.66 tff(10678,plain,
% 291.15/183.66 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_j, s8)) | m_and_h_gate_v_out(c_e_h_3, c_l, s8))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s8)) | m_and_h_gate_v_out(c_e_h_3, c_l, s8))),
% 291.15/183.66 inference(rewrite,[status(thm)],[])).
% 291.15/183.66 tff(10679,plain,
% 291.15/183.66 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_j, s8)) | m_and_h_gate_v_out(c_e_h_3, c_l, s8))),
% 291.15/183.66 inference(quant_inst,[status(thm)],[])).
% 291.15/183.66 tff(10680,plain,
% 291.15/183.66 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s8)) | m_and_h_gate_v_out(c_e_h_3, c_l, s8)),
% 291.15/183.66 inference(modus_ponens,[status(thm)],[10679, 10678])).
% 291.15/183.66 tff(10681,plain,
% 291.15/183.66 ($false),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[10680, 1100, 6450, 5509])).
% 291.15/183.66 tff(10682,plain,((~m_or_h_gate_v_in1(c_e_h_3, c_j, s8)) | m_and_h_gate_v_out(c_e_h_3, c_l, s8)), inference(lemma,lemma(discharge,[]))).
% 291.15/183.66 tff(10683,plain,
% 291.15/183.66 (m_and_h_gate_v_out(c_e_h_3, c_l, s8)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[10682, 10677])).
% 291.15/183.66 tff(10684,plain,
% 291.15/183.66 (~m_and_h_gate_v_out(c_e_h_3, c_k, s5)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[4405, 4387, 3485])).
% 291.15/183.66 tff(10685,plain,
% 291.15/183.66 (~m_and_h_gate_v_out(c_e_h_3, c_l, s6)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[7632, 4387, 3485])).
% 291.15/183.66 tff(10686,plain,
% 291.15/183.66 (~m_and_h_gate_v_in1(c_e_h_3, c_l, s7)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[10601, 6243])).
% 291.15/183.66 tff(10687,plain,
% 291.15/183.66 (~node20(c_e_h_3, c_l, s7)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[10595, 10686])).
% 291.15/183.66 tff(10688,plain,
% 291.15/183.66 (node20(c_e_h_3, c_k, s5)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[5449, 3367, 4387, 3485])).
% 291.15/183.66 tff(10689,plain,
% 291.15/183.66 (m_and_h_gate_v_in1(c_e_h_3, c_k, s5)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[5458, 10688])).
% 291.15/183.66 tff(10690,plain,
% 291.15/183.66 (m_or_h_gate_v_out(c_e_h_3, c_g, s5)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[3365, 10689])).
% 291.15/183.66 tff(10691,plain,
% 291.15/183.66 (~m_and_h_gate_v_in1(c_e_h_3, c_l, s5)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[4413, 10684])).
% 291.15/183.66 tff(10692,plain,
% 291.15/183.66 (~node20(c_e_h_3, c_l, s5)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[4421, 10691])).
% 291.15/183.66 tff(10693,plain,
% 291.15/183.66 (~m_and_h_gate_v_out(c_e_h_3, c_l, s6)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[4447, 3601, 4431])).
% 291.15/183.66 tff(10694,plain,
% 291.15/183.66 (~m_or_h_gate_v_in1(c_e_h_3, c_j, s5)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[3606, 3601])).
% 291.15/183.66 tff(10695,plain,
% 291.15/183.66 (~m_or_h_gate_v_out(c_e_h_3, c_j, s6)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[4385, 10694])).
% 291.15/183.66 tff(10696,plain,
% 291.15/183.66 ($false),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[5447, 10695, 10693, 3367, 5423])).
% 291.15/183.66 tff(10697,plain,(m_and_h_gate_v_out(c_e_h_3, c_l, s5) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s8)) | node20(c_e_h_3, c_l, s6) | node20(c_e_h_3, c_l, s5)), inference(lemma,lemma(discharge,[]))).
% 291.15/183.66 tff(10698,plain,
% 291.15/183.66 (node20(c_e_h_3, c_l, s6)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[10697, 3367, 6236, 10692])).
% 291.15/183.66 tff(10699,plain,
% 291.15/183.66 (m_and_h_gate_v_in1(c_e_h_3, c_l, s6)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[4483, 10698])).
% 291.15/183.66 tff(10700,plain,
% 291.15/183.66 (m_and_h_gate_v_out(c_e_h_3, c_k, s6)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[4475, 10699])).
% 291.15/183.66 tff(10701,plain,
% 291.15/183.66 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s6)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[6448, 10700, 6243])).
% 291.15/183.66 tff(10702,plain,
% 291.15/183.66 (~m_or_h_gate_v_out(c_e_h_3, c_g, s6)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[6232, 6229, 10701])).
% 291.15/183.66 tff(10703,plain,
% 291.15/183.66 (node4(c_e_h_3, c_g, s5)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[6218, 10702, 10690])).
% 291.15/183.66 tff(10704,plain,
% 291.15/183.66 (~m_or_h_gate_v_in1(c_e_h_3, c_g, s5)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[6184, 5516, 10703])).
% 291.15/183.66 tff(10705,plain,
% 291.15/183.66 (~m_and_h_gate_v_out(c_e_h_3, c_c, s5)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[6178, 10704])).
% 291.15/183.66 tff(10706,plain,
% 291.15/183.66 (~m_and_h_gate_v_out(c_e_h_3, c_c, s4)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[6170, 10705])).
% 291.15/183.66 tff(10707,plain,
% 291.15/183.66 (~m_or_h_gate_v_in1(c_e_h_3, c_g, s4)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[2748, 10706])).
% 291.15/183.66 tff(10708,plain,
% 291.15/183.66 (m_or_h_gate_v_in1(c_e_h_3, c_g, s3)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[3356, 10707, 3125, 3006, 10690])).
% 291.15/183.66 tff(10709,plain,
% 291.15/183.66 (m_and_h_gate_v_out(c_e_h_3, c_c, s3)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[2713, 10708])).
% 291.15/183.66 tff(10710,plain,
% 291.15/183.66 (node20(c_e_h_3, c_c, s2)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[2698, 10709])).
% 291.15/183.66 tff(10711,plain,
% 291.15/183.66 (m_and_h_gate_v_in1(c_e_h_3, c_c, s2)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[2622, 10710])).
% 291.15/183.66 tff(10712,plain,
% 291.15/183.66 (m_mutex_h_half_v_out(c_e_h_3, c_a, s2)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[2614, 10711])).
% 291.15/183.66 tff(10713,plain,
% 291.15/183.66 (m_mutex_h_half_v_out(c_e_h_3, c_a, s3)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[2606, 10712])).
% 291.15/183.66 tff(10714,plain,
% 291.15/183.66 (m_and_h_gate_v_in1(c_e_h_3, c_c, s3)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[2561, 10713])).
% 291.15/183.66 tff(10715,plain,
% 291.15/183.66 (~node21(c_e_h_3, c_c, s3, s4)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[5859, 10706, 10714])).
% 291.15/183.66 tff(10716,plain,
% 291.15/183.66 (node22(c_e_h_3, c_c, s3, s4)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[2734, 10715])).
% 291.15/183.66 tff(10717,plain,
% 291.15/183.66 ($false),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[5874, 5871, 10716, 10706, 10709])).
% 291.15/183.66 tff(10718,plain,((~m_or_h_gate_v_out(c_e_h_3, c_j, s8)) | m_and_h_gate_v_out(c_e_h_3, c_k, s7) | node20(c_e_h_3, c_k, s4)), inference(lemma,lemma(discharge,[]))).
% 291.15/183.66 tff(10719,plain,
% 291.15/183.66 (~m_or_h_gate_v_out(c_e_h_3, c_j, s8)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[10718, 6243, 4387])).
% 291.15/183.66 tff(10720,plain,
% 291.15/183.66 (m_or_h_gate_v_in1(c_e_h_3, c_j, s8)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[10676, 10719, 10653])).
% 291.15/183.66 tff(10721,plain,
% 291.15/183.66 (m_and_h_gate_v_out(c_e_h_3, c_l, s8)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[10682, 10720])).
% 291.15/183.66 tff(10722,plain,
% 291.15/183.66 (m_and_h_gate_v_out(c_e_h_3, c_l, s7)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[10588, 10721, 10687])).
% 291.15/183.66 tff(10723,plain,
% 291.15/183.66 (node20(c_e_h_3, c_l, s6)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[5441, 10722, 10685])).
% 291.15/183.66 tff(10724,plain,
% 291.15/183.66 (m_and_h_gate_v_in1(c_e_h_3, c_l, s6)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[4483, 10723])).
% 291.15/183.66 tff(10725,plain,
% 291.15/183.66 (m_and_h_gate_v_out(c_e_h_3, c_k, s6)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[4475, 10724])).
% 291.15/183.66 tff(10726,plain,
% 291.15/183.66 (node20(c_e_h_3, c_k, s5)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[4467, 10725, 10684])).
% 291.15/183.66 tff(10727,plain,
% 291.15/183.66 (m_and_h_gate_v_in1(c_e_h_3, c_k, s5)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[5458, 10726])).
% 291.15/183.66 tff(10728,plain,
% 291.15/183.66 (m_or_h_gate_v_out(c_e_h_3, c_g, s5)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[3365, 10727])).
% 291.15/183.66 tff(10729,plain,
% 291.15/183.66 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s6)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[6448, 10725, 6243])).
% 291.15/183.66 tff(10730,plain,
% 291.15/183.66 (~m_or_h_gate_v_out(c_e_h_3, c_g, s6)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[6232, 6229, 10729])).
% 291.15/183.66 tff(10731,plain,
% 291.15/183.66 (node4(c_e_h_3, c_g, s5)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[6218, 10730, 10728])).
% 291.15/183.66 tff(10732,plain,
% 291.15/183.66 (~m_or_h_gate_v_in1(c_e_h_3, c_g, s5)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[6184, 5516, 10731])).
% 291.15/183.66 tff(10733,plain,
% 291.15/183.66 (~m_and_h_gate_v_out(c_e_h_3, c_c, s5)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[6178, 10732])).
% 291.15/183.66 tff(10734,plain,
% 291.15/183.66 (~m_and_h_gate_v_out(c_e_h_3, c_c, s4)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[6170, 10733])).
% 291.15/183.66 tff(10735,plain,
% 291.15/183.66 (~m_or_h_gate_v_in1(c_e_h_3, c_g, s4)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[2748, 10734])).
% 291.15/183.66 tff(10736,plain,
% 291.15/183.66 (m_or_h_gate_v_in1(c_e_h_3, c_g, s3)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[3356, 10735, 3125, 3006, 10728])).
% 291.15/183.66 tff(10737,plain,
% 291.15/183.66 (m_and_h_gate_v_out(c_e_h_3, c_c, s3)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[2713, 10736])).
% 291.15/183.66 tff(10738,plain,
% 291.15/183.66 (node20(c_e_h_3, c_c, s2)),
% 291.15/183.66 inference(unit_resolution,[status(thm)],[2698, 10737])).
% 291.15/183.67 tff(10739,plain,
% 291.15/183.67 (m_and_h_gate_v_in1(c_e_h_3, c_c, s2)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[2622, 10738])).
% 291.15/183.67 tff(10740,plain,
% 291.15/183.67 (m_mutex_h_half_v_out(c_e_h_3, c_a, s2)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[2614, 10739])).
% 291.15/183.67 tff(10741,plain,
% 291.15/183.67 (m_mutex_h_half_v_out(c_e_h_3, c_a, s3)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[2606, 10740])).
% 291.15/183.67 tff(10742,plain,
% 291.15/183.67 (m_and_h_gate_v_in1(c_e_h_3, c_c, s3)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[2561, 10741])).
% 291.15/183.67 tff(10743,plain,
% 291.15/183.67 (~node21(c_e_h_3, c_c, s3, s4)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[5859, 10742, 10734])).
% 291.15/183.67 tff(10744,plain,
% 291.15/183.67 (node22(c_e_h_3, c_c, s3, s4)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[2734, 10743])).
% 291.15/183.67 tff(10745,plain,
% 291.15/183.67 ($false),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[5874, 5871, 10744, 10734, 10737])).
% 291.15/183.67 tff(10746,plain,(m_and_h_gate_v_out(c_e_h_3, c_k, s7) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s9)) | node20(c_e_h_3, c_k, s4)), inference(lemma,lemma(discharge,[]))).
% 291.15/183.67 tff(10747,plain,
% 291.15/183.67 (m_and_h_gate_v_out(c_e_h_3, c_k, s7)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[10746, 10639, 4387])).
% 291.15/183.67 tff(10748,plain,
% 291.15/183.67 (m_and_h_gate_v_out(c_e_h_3, c_k, s7)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[10746, 10653, 4387])).
% 291.15/183.67 tff(10749,plain,
% 291.15/183.67 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s4)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[550, 3])).
% 291.15/183.67 tff(10750,plain,
% 291.15/183.67 (~m_and_h_gate_v_out(c_e_h_3, c_c, s5)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[10330, 10749])).
% 291.15/183.67 tff(10751,plain,
% 291.15/183.67 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s2)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[2606, 515])).
% 291.15/183.67 tff(10752,plain,
% 291.15/183.67 (~m_and_h_gate_v_in1(c_e_h_3, c_c, s2)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[2614, 10751])).
% 291.15/183.67 tff(10753,plain,
% 291.15/183.67 (~node20(c_e_h_3, c_c, s2)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[2622, 10752])).
% 291.15/183.67 tff(10754,plain,
% 291.15/183.67 (~m_and_h_gate_v_out(c_e_h_3, c_c, s3)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[2698, 10753])).
% 291.15/183.67 tff(10755,plain,
% 291.15/183.67 (~m_or_h_gate_v_in1(c_e_h_3, c_g, s3)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[2713, 10754])).
% 291.15/183.67 tff(10756,plain,
% 291.15/183.67 (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[3376, 10755, 3125])).
% 291.15/183.67 tff(10757,plain,
% 291.15/183.67 (~m_or_h_gate_v_out(c_e_h_3, c_g, s6)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[10318, 10756, 10306, 10750, 9740])).
% 291.15/183.67 tff(10758,plain,
% 291.15/183.67 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s6)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[10448, 2048, 10757])).
% 291.15/183.67 tff(10759,plain,
% 291.15/183.67 (~m_and_h_gate_v_out(c_e_h_3, c_c, s4)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[6170, 10750])).
% 291.15/183.67 tff(10760,plain,
% 291.15/183.67 (~m_or_h_gate_v_in1(c_e_h_3, c_g, s4)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[2748, 10759])).
% 291.15/183.67 tff(10761,plain,
% 291.15/183.67 (~m_or_h_gate_v_out(c_e_h_3, c_g, s5)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[3356, 10755, 3125, 3006, 10760])).
% 291.15/183.67 tff(10762,plain,
% 291.15/183.67 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s5)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[3365, 10761])).
% 291.15/183.67 tff(10763,plain,
% 291.15/183.67 (~node20(c_e_h_3, c_k, s5)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[5458, 10762])).
% 291.15/183.67 tff(10764,plain,
% 291.15/183.67 (~m_and_h_gate_v_out(c_e_h_3, c_k, s6)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[4467, 10763, 10684])).
% 291.15/183.67 tff(10765,plain,
% 291.15/183.67 (~m_and_h_gate_v_in1(c_e_h_3, c_l, s6)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[4475, 10764])).
% 291.15/183.67 tff(10766,plain,
% 291.15/183.67 (~node20(c_e_h_3, c_l, s6)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[4483, 10765])).
% 291.15/183.67 tff(10767,plain,
% 291.15/183.67 (~m_and_h_gate_v_out(c_e_h_3, c_l, s7)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[5441, 10766, 10685])).
% 291.15/183.67 tff(10768,plain,
% 291.15/183.67 (~m_or_h_gate_v_out(c_e_h_3, c_j, s8)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[5449, 10763, 4387, 3485])).
% 291.15/183.67 tff(10769,plain,
% 291.15/183.67 (m_or_h_gate_v_in1(c_e_h_3, c_j, s8)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[10676, 10768, 10653])).
% 291.15/183.67 tff(10770,plain,
% 291.15/183.67 (m_and_h_gate_v_out(c_e_h_3, c_l, s8)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[10682, 10769])).
% 291.15/183.67 tff(10771,plain,
% 291.15/183.67 (node20(c_e_h_3, c_l, s7)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[10588, 10770, 10767])).
% 291.15/183.67 tff(10772,plain,
% 291.15/183.67 (m_and_h_gate_v_in1(c_e_h_3, c_l, s7)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[10595, 10771])).
% 291.15/183.67 tff(10773,plain,
% 291.15/183.67 (m_and_h_gate_v_out(c_e_h_3, c_k, s7)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[10601, 10772])).
% 291.15/183.67 tff(10774,plain,
% 291.15/183.67 (node20(c_e_h_3, c_k, s6)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[10440, 10773, 10764])).
% 291.15/183.67 tff(10775,plain,
% 291.15/183.67 ($false),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[10444, 38, 10774, 10758])).
% 291.15/183.67 tff(10776,plain,(m_user_v_req(c_e_h_3, c_u, s3) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s9)) | node20(c_e_h_3, c_k, s4)), inference(lemma,lemma(discharge,[]))).
% 291.15/183.67 tff(10777,plain,
% 291.15/183.67 (m_user_v_req(c_e_h_3, c_u, s3)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[10776, 10653, 4387])).
% 291.15/183.67 tff(10778,plain,
% 291.15/183.67 (m_user_v_req(c_e_h_3, c_u, s4)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[732, 10777])).
% 291.15/183.67 tff(10779,plain,
% 291.15/183.67 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s4)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[1445, 10778])).
% 291.15/183.67 tff(10780,plain,
% 291.15/183.67 (m_and_h_gate_v_in1(c_e_h_3, c_c, s3)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[10503, 10779, 10397, 10748, 10684])).
% 291.15/183.67 tff(10781,plain,
% 291.15/183.67 (m_mutex_h_half_v_out(c_e_h_3, c_a, s3)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[2544, 10780])).
% 291.15/183.67 tff(10782,plain,
% 291.15/183.67 (m_mutex_h_half_v_out(c_e_h_3, c_a, s4)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[2537, 10781])).
% 291.15/183.67 tff(10783,plain,
% 291.15/183.67 (m_mutex_h_half_v_out(c_e_h_3, c_a, s5)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[1488, 10782, 10779])).
% 291.15/183.67 tff(10784,plain,
% 291.15/183.67 (m_and_h_gate_v_in1(c_e_h_3, c_c, s5)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[10341, 10783])).
% 291.15/183.67 tff(10785,plain,
% 291.15/183.67 (m_and_h_gate_v_out(c_e_h_3, c_c, s4)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[10526, 10784, 10465, 10748, 10684, 10780])).
% 291.15/183.67 tff(10786,plain,
% 291.15/183.67 (m_and_h_gate_v_out(c_e_h_3, c_c, s5)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[6170, 10785])).
% 291.15/183.67 tff(10787,plain,
% 291.15/183.67 (m_or_h_gate_v_in1(c_e_h_3, c_g, s5)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[6178, 10786])).
% 291.15/183.67 tff(10788,plain,
% 291.15/183.67 (m_and_h_gate_v_out(c_e_h_3, c_c, s6)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[10378, 10786, 10784])).
% 291.15/183.67 tff(10789,plain,
% 291.15/183.67 (m_or_h_gate_v_in1(c_e_h_3, c_g, s6)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[10493, 5896, 10788])).
% 291.15/183.67 tff(10790,plain,
% 291.15/183.67 (~node4(c_e_h_3, c_g, s6)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[10489, 5516, 10789])).
% 291.15/183.67 tff(10791,plain,
% 291.15/183.67 (~m_or_h_gate_v_out(c_e_h_3, c_g, s6)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[10485, 10790, 10465])).
% 291.15/183.67 tff(10792,plain,
% 291.15/183.67 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s6)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[10448, 2048, 10791])).
% 291.15/183.67 tff(10793,plain,
% 291.15/183.67 (~node20(c_e_h_3, c_k, s6)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[10444, 38, 10792])).
% 291.15/183.67 tff(10794,plain,
% 291.15/183.67 (m_and_h_gate_v_out(c_e_h_3, c_k, s6)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[10440, 10793, 10748])).
% 291.15/183.67 tff(10795,plain,
% 291.15/183.67 (node20(c_e_h_3, c_k, s5)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[4467, 10794, 10684])).
% 291.15/183.67 tff(10796,plain,
% 291.15/183.67 (m_and_h_gate_v_in1(c_e_h_3, c_k, s5)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[5458, 10795])).
% 291.15/183.67 tff(10797,plain,
% 291.15/183.67 (m_or_h_gate_v_out(c_e_h_3, c_g, s5)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[3365, 10796])).
% 291.15/183.67 tff(10798,plain,
% 291.15/183.67 (node4(c_e_h_3, c_g, s5)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[6218, 10797, 10791])).
% 291.15/183.67 tff(10799,plain,
% 291.15/183.67 ($false),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[6184, 5516, 10798, 10787])).
% 291.15/183.67 tff(10800,plain,((~m_or_h_gate_v_out(c_e_h_3, c_j, s9)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s7) | node20(c_e_h_3, c_k, s4)), inference(lemma,lemma(discharge,[]))).
% 291.15/183.67 tff(10801,plain,
% 291.15/183.67 (m_and_h_gate_v_in1(c_e_h_3, c_k, s7)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[10800, 10639, 4387])).
% 291.15/183.67 tff(10802,plain,
% 291.15/183.67 (~node22(c_e_h_3, c_k, s7, s8)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[10610, 10531, 7182])).
% 291.15/183.67 tff(10803,plain,
% 291.15/183.67 (node21(c_e_h_3, c_k, s7, s8)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[10423, 10802])).
% 291.15/183.67 tff(10804,plain,
% 291.15/183.67 ($false),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[10623, 5851, 10617, 10803, 10531, 10389])).
% 291.15/183.67 tff(10805,plain,(m_and_h_gate_v_out(c_e_h_3, c_k, s8) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s7)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s7))), inference(lemma,lemma(discharge,[]))).
% 291.15/183.67 tff(10806,plain,
% 291.15/183.67 (m_and_h_gate_v_out(c_e_h_3, c_k, s8)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[10805, 10801, 10747])).
% 291.15/183.67 tff(10807,plain,
% 291.15/183.67 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_l, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s8))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_l, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s8))),
% 291.15/183.67 inference(rewrite,[status(thm)],[])).
% 291.15/183.67 tff(10808,plain,
% 291.15/183.67 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_l, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s8))),
% 291.15/183.67 inference(quant_inst,[status(thm)],[])).
% 291.15/183.67 tff(10809,plain,
% 291.15/183.67 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_l, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s8)),
% 291.15/183.67 inference(modus_ponens,[status(thm)],[10808, 10807])).
% 291.15/183.67 tff(10810,plain,
% 291.15/183.67 (m_and_h_gate_v_in1(c_e_h_3, c_l, s8)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[10809, 7192, 10806])).
% 291.15/183.67 tff(10811,plain,
% 291.15/183.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_l, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s8)) | (~node22(c_e_h_3, c_l, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | m_and_h_gate_v_out(c_e_h_3, c_l, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s8)) | (~node22(c_e_h_3, c_l, s8, s9)))),
% 291.15/183.67 inference(rewrite,[status(thm)],[])).
% 291.15/183.67 tff(10812,plain,
% 291.15/183.67 ((m_and_h_gate_v_out(c_e_h_3, c_l, s9) | (~node22(c_e_h_3, c_l, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s8))) <=> (m_and_h_gate_v_out(c_e_h_3, c_l, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s8)) | (~node22(c_e_h_3, c_l, s8, s9)))),
% 291.15/183.67 inference(rewrite,[status(thm)],[])).
% 291.15/183.67 tff(10813,plain,
% 291.15/183.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_l, s9) | (~node22(c_e_h_3, c_l, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_l, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s8)) | (~node22(c_e_h_3, c_l, s8, s9))))),
% 291.15/183.67 inference(monotonicity,[status(thm)],[10812])).
% 291.15/183.67 tff(10814,plain,
% 291.15/183.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_l, s9) | (~node22(c_e_h_3, c_l, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | m_and_h_gate_v_out(c_e_h_3, c_l, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s8)) | (~node22(c_e_h_3, c_l, s8, s9)))),
% 291.15/183.67 inference(transitivity,[status(thm)],[10813, 10811])).
% 291.15/183.67 tff(10815,plain,
% 291.15/183.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_l, s9) | (~node22(c_e_h_3, c_l, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s8)))),
% 291.15/183.67 inference(quant_inst,[status(thm)],[])).
% 291.15/183.67 tff(10816,plain,
% 291.15/183.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | m_and_h_gate_v_out(c_e_h_3, c_l, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s8)) | (~node22(c_e_h_3, c_l, s8, s9))),
% 291.15/183.67 inference(modus_ponens,[status(thm)],[10815, 10814])).
% 291.15/183.67 tff(10817,plain,
% 291.15/183.67 ($false),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[10816, 5871, 8974, 10546, 5524])).
% 291.15/183.67 tff(10818,plain,((~node22(c_e_h_3, c_l, s8, s9)) | m_and_h_gate_v_out(c_e_h_3, c_l, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s8))), inference(lemma,lemma(discharge,[]))).
% 291.15/183.67 tff(10819,plain,
% 291.15/183.67 (~node22(c_e_h_3, c_l, s8, s9)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[10818, 8974, 5524])).
% 291.15/183.67 tff(10820,plain,
% 291.15/183.67 (m_or_h_gate_v_in1(c_e_h_3, c_j, s3) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s6))),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[9083, 2241])).
% 291.15/183.67 tff(10821,plain,
% 291.15/183.67 (~m_and_h_gate_v_out(c_e_h_3, c_i, s6)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[10820, 3615])).
% 291.15/183.67 tff(10822,plain,
% 291.15/183.67 (~m_c_h_element_v_in2(c_e_h_3, c_f, s6)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[9091, 10821])).
% 291.15/183.67 tff(10823,plain,
% 291.15/183.67 ((~m_c_h_element_v_out(c_e_h_3, c_f, s7)) | m_c_h_element_v_in2(c_e_h_3, c_f, s6)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[9158, 6869])).
% 291.15/183.67 tff(10824,plain,
% 291.15/183.67 (~m_c_h_element_v_out(c_e_h_3, c_f, s7)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[10823, 10822])).
% 291.15/183.67 tff(10825,plain,
% 291.15/183.67 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[9252, 10824])).
% 291.15/183.67 tff(10826,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s6)), introduced(assumption)).
% 291.15/183.67 tff(10827,plain,
% 291.15/183.67 ($false),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[9379, 5601, 7130, 10826])).
% 291.15/183.67 tff(10828,plain,((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s6))), inference(lemma,lemma(discharge,[]))).
% 291.15/183.67 tff(10829,plain,
% 291.15/183.67 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s6)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[10828, 7086])).
% 291.15/183.67 tff(10830,assumption,(node9(c_e_h_3, c_n, s6)), introduced(assumption)).
% 291.15/183.67 tff(10831,assumption,(~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s6)), introduced(assumption)).
% 291.15/183.67 tff(10832,plain,
% 291.15/183.67 ($false),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[9375, 4972, 10831, 10830])).
% 291.15/183.67 tff(10833,plain,((~node9(c_e_h_3, c_n, s6)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s6)), inference(lemma,lemma(discharge,[]))).
% 291.15/183.67 tff(10834,plain,
% 291.15/183.67 (~node9(c_e_h_3, c_n, s6)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[10833, 10829])).
% 291.15/183.67 tff(10835,assumption,(~node9(c_e_h_3, c_n, s6)), introduced(assumption)).
% 291.15/183.67 tff(10836,plain,
% 291.15/183.67 (~node11(c_e_h_3, c_n, s6, s7)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[9359, 9353])).
% 291.15/183.67 tff(10837,plain,
% 291.15/183.67 (node10(c_e_h_3, c_n, s6, s7)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[9364, 10836])).
% 291.15/183.67 tff(10838,plain,
% 291.15/183.67 ($false),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[9371, 4986, 9353, 10837, 10835])).
% 291.15/183.67 tff(10839,plain,((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)) | node9(c_e_h_3, c_n, s6)), inference(lemma,lemma(discharge,[]))).
% 291.15/183.67 tff(10840,plain,
% 291.15/183.67 (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[10839, 10834])).
% 291.15/183.67 tff(10841,plain,
% 291.15/183.67 (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s7)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[9270, 10840])).
% 291.15/183.67 tff(10842,plain,
% 291.15/183.67 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s7))),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[9299, 10841])).
% 291.15/183.67 tff(10843,plain,
% 291.15/183.67 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s7))),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[10842, 7149])).
% 291.15/183.67 tff(10844,plain,
% 291.15/183.67 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8)),
% 291.15/183.67 inference(unit_resolution,[status(thm)],[10843, 10825])).
% 291.15/183.67 tff(10845,plain,
% 291.15/183.67 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_m, X)) | m_and_h_gate_v_in2(I0, c_l, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8)) | m_and_h_gate_v_in2(c_e_h_3, c_l, s8))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_m, X)) | m_and_h_gate_v_in2(I0, c_l, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8)) | m_and_h_gate_v_in2(c_e_h_3, c_l, s8))),
% 291.15/183.67 inference(rewrite,[status(thm)],[])).
% 291.15/183.67 tff(10846,plain,
% 291.15/183.67 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_m, X)) | m_and_h_gate_v_in2(I0, c_l, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8)) | m_and_h_gate_v_in2(c_e_h_3, c_l, s8))),
% 291.15/183.68 inference(quant_inst,[status(thm)],[])).
% 291.15/183.68 tff(10847,plain,
% 291.15/183.68 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_m, X)) | m_and_h_gate_v_in2(I0, c_l, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8)) | m_and_h_gate_v_in2(c_e_h_3, c_l, s8)),
% 291.15/183.68 inference(modus_ponens,[status(thm)],[10846, 10845])).
% 291.15/183.68 tff(10848,plain,
% 291.15/183.68 (m_and_h_gate_v_in2(c_e_h_3, c_l, s8)),
% 291.15/183.68 inference(unit_resolution,[status(thm)],[10847, 7159, 10844])).
% 291.15/183.68 tff(10849,plain,
% 291.15/183.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_l, s8)) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s8)) | m_and_h_gate_v_out(c_e_h_3, c_l, s9) | (~node21(c_e_h_3, c_l, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in2(c_e_h_3, c_l, s8)) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s8)) | m_and_h_gate_v_out(c_e_h_3, c_l, s9) | (~node21(c_e_h_3, c_l, s8, s9)))),
% 291.15/183.68 inference(rewrite,[status(thm)],[])).
% 291.15/183.68 tff(10850,plain,
% 291.15/183.68 (((~node21(c_e_h_3, c_l, s8, s9)) | (~m_and_h_gate_v_in2(c_e_h_3, c_l, s8)) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s8)) | m_and_h_gate_v_out(c_e_h_3, c_l, s9)) <=> ((~m_and_h_gate_v_in2(c_e_h_3, c_l, s8)) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s8)) | m_and_h_gate_v_out(c_e_h_3, c_l, s9) | (~node21(c_e_h_3, c_l, s8, s9)))),
% 291.15/183.68 inference(rewrite,[status(thm)],[])).
% 291.15/183.68 tff(10851,plain,
% 291.15/183.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_l, s8, s9)) | (~m_and_h_gate_v_in2(c_e_h_3, c_l, s8)) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s8)) | m_and_h_gate_v_out(c_e_h_3, c_l, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_l, s8)) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s8)) | m_and_h_gate_v_out(c_e_h_3, c_l, s9) | (~node21(c_e_h_3, c_l, s8, s9))))),
% 291.15/183.68 inference(monotonicity,[status(thm)],[10850])).
% 291.15/183.68 tff(10852,plain,
% 291.15/183.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_l, s8, s9)) | (~m_and_h_gate_v_in2(c_e_h_3, c_l, s8)) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s8)) | m_and_h_gate_v_out(c_e_h_3, c_l, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in2(c_e_h_3, c_l, s8)) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s8)) | m_and_h_gate_v_out(c_e_h_3, c_l, s9) | (~node21(c_e_h_3, c_l, s8, s9)))),
% 291.15/183.68 inference(transitivity,[status(thm)],[10851, 10849])).
% 291.15/183.68 tff(10853,plain,
% 291.15/183.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_l, s8, s9)) | (~m_and_h_gate_v_in2(c_e_h_3, c_l, s8)) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s8)) | m_and_h_gate_v_out(c_e_h_3, c_l, s9))),
% 291.15/183.68 inference(quant_inst,[status(thm)],[])).
% 291.15/183.68 tff(10854,plain,
% 291.15/183.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in2(c_e_h_3, c_l, s8)) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s8)) | m_and_h_gate_v_out(c_e_h_3, c_l, s9) | (~node21(c_e_h_3, c_l, s8, s9))),
% 291.15/183.68 inference(modus_ponens,[status(thm)],[10853, 10852])).
% 291.15/183.68 tff(10855,plain,
% 291.15/183.68 ($false),
% 291.15/183.68 inference(unit_resolution,[status(thm)],[10854, 5851, 10848, 8974, 10554, 10530])).
% 291.15/183.68 tff(10856,plain,((~node21(c_e_h_3, c_l, s8, s9)) | m_and_h_gate_v_out(c_e_h_3, c_l, s9) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s8))), inference(lemma,lemma(discharge,[]))).
% 291.15/183.68 tff(10857,plain,
% 291.15/183.68 (~node21(c_e_h_3, c_l, s8, s9)),
% 291.15/183.68 inference(unit_resolution,[status(thm)],[10856, 8974, 10530])).
% 291.15/183.68 tff(10858,plain,
% 291.15/183.68 ($false),
% 291.15/183.68 inference(unit_resolution,[status(thm)],[10567, 10857, 10819])).
% 291.15/183.68 tff(10859,plain,(m_and_h_gate_v_out(c_e_h_3, c_l, s9) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s8)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s8))), inference(lemma,lemma(discharge,[]))).
% 291.15/183.68 tff(10860,plain,
% 291.15/183.68 (m_and_h_gate_v_out(c_e_h_3, c_l, s9)),
% 291.15/183.68 inference(unit_resolution,[status(thm)],[10859, 10810, 10683])).
% 291.15/183.68 tff(10861,plain,
% 291.15/183.68 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s9)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s9))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s9)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s9))),
% 291.15/183.68 inference(rewrite,[status(thm)],[])).
% 291.15/183.68 tff(10862,plain,
% 291.15/183.68 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s9)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s9))),
% 291.15/183.68 inference(quant_inst,[status(thm)],[])).
% 291.15/183.68 tff(10863,plain,
% 291.15/183.68 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_l, X)) | m_or_h_gate_v_in1(I0, c_j, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s9)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s9)),
% 291.15/183.68 inference(modus_ponens,[status(thm)],[10862, 10861])).
% 291.15/183.68 tff(10864,plain,
% 291.15/183.68 ($false),
% 291.15/183.68 inference(unit_resolution,[status(thm)],[10863, 3627, 9019, 8950])).
% 291.15/183.68 tff(10865,plain,((~m_and_h_gate_v_out(c_e_h_3, c_l, s9)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s9)), inference(lemma,lemma(discharge,[]))).
% 291.15/183.68 tff(10866,plain,
% 291.15/183.68 (m_or_h_gate_v_in1(c_e_h_3, c_j, s9)),
% 291.15/183.68 inference(unit_resolution,[status(thm)],[10865, 10860])).
% 291.15/183.68 tff(10867,assumption,(node4(c_e_h_3, c_j, s9)), introduced(assumption)).
% 291.15/183.68 tff(10868,plain,
% 291.15/183.68 (((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_j, s9)) | (~node4(c_e_h_3, c_j, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s9)) | (~node4(c_e_h_3, c_j, s9)))),
% 291.15/183.68 inference(rewrite,[status(thm)],[])).
% 291.15/183.68 tff(10869,plain,
% 291.15/183.68 ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_j, s9)) | (~node4(c_e_h_3, c_j, s9)))),
% 291.15/183.68 inference(quant_inst,[status(thm)],[])).
% 291.15/183.68 tff(10870,plain,
% 291.15/183.68 ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s9)) | (~node4(c_e_h_3, c_j, s9))),
% 291.15/183.68 inference(modus_ponens,[status(thm)],[10869, 10868])).
% 291.15/183.68 tff(10871,plain,
% 291.15/183.68 ($false),
% 291.15/183.68 inference(unit_resolution,[status(thm)],[10870, 5516, 10867, 8973])).
% 291.15/183.68 tff(10872,plain,((~node4(c_e_h_3, c_j, s9)) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s9))), inference(lemma,lemma(discharge,[]))).
% 291.15/183.68 tff(10873,plain,
% 291.15/183.68 (~node4(c_e_h_3, c_j, s9)),
% 291.15/183.68 inference(unit_resolution,[status(thm)],[10872, 10866])).
% 291.15/183.68 tff(10874,assumption,(~node4(c_e_h_3, c_j, s9)), introduced(assumption)).
% 291.15/183.68 tff(10875,assumption,(~m_or_h_gate_v_out(c_e_h_3, c_j, s10)), introduced(assumption)).
% 291.15/183.68 tff(10876,plain,
% 291.15/183.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (m_or_h_gate_v_out(c_e_h_3, c_j, s10) | node4(c_e_h_3, c_j, s9) | (~node5(c_e_h_3, c_j, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | m_or_h_gate_v_out(c_e_h_3, c_j, s10) | node4(c_e_h_3, c_j, s9) | (~node5(c_e_h_3, c_j, s9, s10)))),
% 291.15/183.68 inference(rewrite,[status(thm)],[])).
% 291.15/183.68 tff(10877,plain,
% 291.15/183.68 ((node4(c_e_h_3, c_j, s9) | (~node5(c_e_h_3, c_j, s9, s10)) | m_or_h_gate_v_out(c_e_h_3, c_j, s10)) <=> (m_or_h_gate_v_out(c_e_h_3, c_j, s10) | node4(c_e_h_3, c_j, s9) | (~node5(c_e_h_3, c_j, s9, s10)))),
% 291.15/183.69 inference(rewrite,[status(thm)],[])).
% 291.15/183.69 tff(10878,plain,
% 291.15/183.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_3, c_j, s9) | (~node5(c_e_h_3, c_j, s9, s10)) | m_or_h_gate_v_out(c_e_h_3, c_j, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (m_or_h_gate_v_out(c_e_h_3, c_j, s10) | node4(c_e_h_3, c_j, s9) | (~node5(c_e_h_3, c_j, s9, s10))))),
% 291.15/183.69 inference(monotonicity,[status(thm)],[10877])).
% 291.15/183.69 tff(10879,plain,
% 291.15/183.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_3, c_j, s9) | (~node5(c_e_h_3, c_j, s9, s10)) | m_or_h_gate_v_out(c_e_h_3, c_j, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | m_or_h_gate_v_out(c_e_h_3, c_j, s10) | node4(c_e_h_3, c_j, s9) | (~node5(c_e_h_3, c_j, s9, s10)))),
% 291.15/183.69 inference(transitivity,[status(thm)],[10878, 10876])).
% 291.15/183.69 tff(10880,plain,
% 291.15/183.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_3, c_j, s9) | (~node5(c_e_h_3, c_j, s9, s10)) | m_or_h_gate_v_out(c_e_h_3, c_j, s10))),
% 291.15/183.69 inference(quant_inst,[status(thm)],[])).
% 291.15/183.69 tff(10881,plain,
% 291.15/183.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | m_or_h_gate_v_out(c_e_h_3, c_j, s10) | node4(c_e_h_3, c_j, s9) | (~node5(c_e_h_3, c_j, s9, s10))),
% 291.15/183.69 inference(modus_ponens,[status(thm)],[10880, 10879])).
% 291.15/183.69 tff(10882,plain,
% 291.15/183.69 ($false),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[10881, 5498, 10875, 8952, 10874])).
% 291.15/183.69 tff(10883,plain,((~node5(c_e_h_3, c_j, s9, s10)) | m_or_h_gate_v_out(c_e_h_3, c_j, s10) | node4(c_e_h_3, c_j, s9)), inference(lemma,lemma(discharge,[]))).
% 291.15/183.69 tff(10884,plain,
% 291.15/183.69 (~node5(c_e_h_3, c_j, s9, s10)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[10883, 10875, 10874])).
% 291.15/183.69 tff(10885,plain,
% 291.15/183.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | ((~m_or_h_gate_v_out(c_e_h_3, c_j, s9)) | m_or_h_gate_v_out(c_e_h_3, c_j, s10) | (~node6(c_e_h_3, c_j, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s9)) | m_or_h_gate_v_out(c_e_h_3, c_j, s10) | (~node6(c_e_h_3, c_j, s9, s10)))),
% 291.15/183.69 inference(rewrite,[status(thm)],[])).
% 291.15/183.69 tff(10886,plain,
% 291.15/183.69 ((m_or_h_gate_v_out(c_e_h_3, c_j, s10) | (~node6(c_e_h_3, c_j, s9, s10)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s9))) <=> ((~m_or_h_gate_v_out(c_e_h_3, c_j, s9)) | m_or_h_gate_v_out(c_e_h_3, c_j, s10) | (~node6(c_e_h_3, c_j, s9, s10)))),
% 291.15/183.69 inference(rewrite,[status(thm)],[])).
% 291.15/183.69 tff(10887,plain,
% 291.15/183.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_3, c_j, s10) | (~node6(c_e_h_3, c_j, s9, s10)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | ((~m_or_h_gate_v_out(c_e_h_3, c_j, s9)) | m_or_h_gate_v_out(c_e_h_3, c_j, s10) | (~node6(c_e_h_3, c_j, s9, s10))))),
% 291.15/183.69 inference(monotonicity,[status(thm)],[10886])).
% 291.15/183.69 tff(10888,plain,
% 291.15/183.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_3, c_j, s10) | (~node6(c_e_h_3, c_j, s9, s10)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s9)) | m_or_h_gate_v_out(c_e_h_3, c_j, s10) | (~node6(c_e_h_3, c_j, s9, s10)))),
% 291.15/183.69 inference(transitivity,[status(thm)],[10887, 10885])).
% 291.15/183.69 tff(10889,plain,
% 291.15/183.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_3, c_j, s10) | (~node6(c_e_h_3, c_j, s9, s10)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s9)))),
% 291.15/183.69 inference(quant_inst,[status(thm)],[])).
% 291.15/183.69 tff(10890,plain,
% 291.15/183.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s9)) | m_or_h_gate_v_out(c_e_h_3, c_j, s10) | (~node6(c_e_h_3, c_j, s9, s10))),
% 291.15/183.69 inference(modus_ponens,[status(thm)],[10889, 10888])).
% 291.15/183.69 tff(10891,plain,
% 291.15/183.69 ($false),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[10890, 5474, 10653, 10875, 8940])).
% 291.15/183.69 tff(10892,plain,((~node6(c_e_h_3, c_j, s9, s10)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s9)) | m_or_h_gate_v_out(c_e_h_3, c_j, s10)), inference(lemma,lemma(discharge,[]))).
% 291.15/183.69 tff(10893,plain,
% 291.15/183.69 (~node6(c_e_h_3, c_j, s9, s10)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[10892, 10875, 10653])).
% 291.15/183.69 tff(10894,plain,
% 291.15/183.69 ($false),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[8968, 10893, 10884])).
% 291.15/183.69 tff(10895,plain,(m_or_h_gate_v_out(c_e_h_3, c_j, s10) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s9)) | node4(c_e_h_3, c_j, s9)), inference(lemma,lemma(discharge,[]))).
% 291.15/183.69 tff(10896,plain,
% 291.15/183.69 (m_or_h_gate_v_out(c_e_h_3, c_j, s10)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[10895, 10873, 10639])).
% 291.15/183.69 tff(10897,plain,
% 291.15/183.69 (~node6(c_e_h_3, c_j, s10, s11)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[8990, 10896, 7627])).
% 291.15/183.69 tff(10898,plain,
% 291.15/183.69 (node5(c_e_h_3, c_j, s10, s11)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[8998, 10897])).
% 291.15/183.69 tff(10899,plain,
% 291.15/183.69 (node4(c_e_h_3, c_j, s10)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[9009, 10898, 7627])).
% 291.15/183.69 tff(10900,plain,
% 291.15/183.69 (~m_or_h_gate_v_in1(c_e_h_3, c_j, s10)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[9013, 5516, 10899])).
% 291.15/183.69 tff(10901,plain,
% 291.15/183.69 (m_and_h_gate_v_out(c_e_h_3, c_k, s9)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[10528, 10806, 7636, 3308, 4469, 3360, 7645, 2743])).
% 291.15/183.69 tff(10902,plain,
% 291.15/183.69 (m_and_h_gate_v_in1(c_e_h_3, c_l, s9)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[9466, 10901])).
% 291.15/183.69 tff(10903,plain,
% 291.15/183.69 (~node22(c_e_h_3, c_l, s9, s10)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[9029, 9020, 9019])).
% 291.15/183.69 tff(10904,plain,
% 291.15/183.69 (~node21(c_e_h_3, c_l, s9, s10)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[9458, 9020, 9036])).
% 291.15/183.69 tff(10905,plain,
% 291.15/183.69 ($false),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[9034, 10904, 10903])).
% 291.15/183.69 tff(10906,plain,(m_and_h_gate_v_out(c_e_h_3, c_l, s10) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s9)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s9))), inference(lemma,lemma(discharge,[]))).
% 291.15/183.69 tff(10907,plain,
% 291.15/183.69 (m_and_h_gate_v_out(c_e_h_3, c_l, s10)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[10906, 10902, 10860])).
% 291.15/183.69 tff(10908,plain,
% 291.15/183.69 ($false),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[9017, 3627, 10907, 10900])).
% 291.15/183.69 tff(10909,plain,(m_or_h_gate_v_out(c_e_h_3, c_g, s4) | m_or_h_gate_v_out(c_e_h_3, c_j, s11) | m_and_h_gate_v_out(c_e_h_3, c_k, s6) | m_or_h_gate_v_out(c_e_h_3, c_g, s5) | m_and_h_gate_v_out(c_e_h_3, c_c, s4) | m_or_h_gate_v_out(c_e_h_3, c_j, s8) | node20(c_e_h_3, c_k, s4) | (~m_c_h_element_v_out(c_e_h_3, c_h, s11))), inference(lemma,lemma(discharge,[]))).
% 291.15/183.69 tff(10910,plain,
% 291.15/183.69 (m_or_h_gate_v_out(c_e_h_3, c_g, s4)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[10909, 2743, 4469, 3360, 7627, 7275, 4387, 7626])).
% 291.15/183.69 tff(10911,plain,
% 291.15/183.69 (m_or_h_gate_v_in1(c_e_h_3, c_g, s3)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[3377, 10910])).
% 291.15/183.69 tff(10912,plain,
% 291.15/183.69 (m_and_h_gate_v_out(c_e_h_3, c_c, s3)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[2713, 10911])).
% 291.15/183.69 tff(10913,plain,
% 291.15/183.69 (node20(c_e_h_3, c_c, s2)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[2698, 10912])).
% 291.15/183.69 tff(10914,plain,
% 291.15/183.69 (m_and_h_gate_v_in1(c_e_h_3, c_c, s2)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[2622, 10913])).
% 291.15/183.69 tff(10915,plain,
% 291.15/183.69 (m_mutex_h_half_v_out(c_e_h_3, c_a, s2)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[2614, 10914])).
% 291.15/183.69 tff(10916,plain,
% 291.15/183.69 (m_mutex_h_half_v_out(c_e_h_3, c_a, s3)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[2606, 10915])).
% 291.15/183.69 tff(10917,plain,
% 291.15/183.69 (m_and_h_gate_v_in1(c_e_h_3, c_c, s3)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[2561, 10916])).
% 291.15/183.69 tff(10918,plain,
% 291.15/183.69 (~node21(c_e_h_3, c_c, s3, s4)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[5859, 10917, 2743])).
% 291.15/183.69 tff(10919,plain,
% 291.15/183.69 (node22(c_e_h_3, c_c, s3, s4)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[2734, 10918])).
% 291.15/183.69 tff(10920,plain,
% 291.15/183.69 ($false),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[5874, 5871, 10919, 2743, 10912])).
% 291.15/183.69 tff(10921,plain,(m_and_h_gate_v_out(c_e_h_3, c_c, s4) | m_and_h_gate_v_out(c_e_h_3, c_k, s6) | m_or_h_gate_v_out(c_e_h_3, c_g, s5) | m_or_h_gate_v_out(c_e_h_3, c_j, s11) | m_or_h_gate_v_out(c_e_h_3, c_j, s8) | node20(c_e_h_3, c_k, s4) | (~m_c_h_element_v_out(c_e_h_3, c_h, s11))), inference(lemma,lemma(discharge,[]))).
% 291.15/183.69 tff(10922,plain,
% 291.15/183.69 (m_and_h_gate_v_out(c_e_h_3, c_c, s4)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[10921, 7637, 3360, 7627, 7275, 4387, 7626])).
% 291.15/183.69 tff(10923,plain,
% 291.15/183.69 (m_and_h_gate_v_out(c_e_h_3, c_c, s5)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[6170, 10922])).
% 291.15/183.69 tff(10924,plain,
% 291.15/183.69 (m_mutex_h_half_v_out(c_e_h_3, c_a, s4)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[10330, 10923])).
% 291.15/183.69 tff(10925,plain,
% 291.15/183.69 (m_user_v_req(c_e_h_3, c_u, s3)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[550, 10924])).
% 291.15/183.69 tff(10926,plain,
% 291.15/183.69 (m_user_v_req(c_e_h_3, c_u, s4)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[732, 10925])).
% 291.15/183.69 tff(10927,plain,
% 291.15/183.69 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s4)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[1445, 10926])).
% 291.15/183.69 tff(10928,plain,
% 291.15/183.69 (m_mutex_h_half_v_out(c_e_h_3, c_a, s5)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[1488, 10927, 10924])).
% 291.15/183.69 tff(10929,plain,
% 291.15/183.69 (m_and_h_gate_v_in1(c_e_h_3, c_c, s5)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[10341, 10928])).
% 291.15/183.69 tff(10930,plain,
% 291.15/183.69 (m_and_h_gate_v_out(c_e_h_3, c_c, s6)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[10378, 10929, 10923])).
% 291.15/183.69 tff(10931,plain,
% 291.15/183.69 (m_user_v_req(c_e_h_3, c_u, s5)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[1035, 10926])).
% 291.15/183.69 tff(10932,plain,
% 291.15/183.69 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s5)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[1438, 10931])).
% 291.15/183.69 tff(10933,plain,
% 291.15/183.69 (m_mutex_h_half_v_out(c_e_h_3, c_a, s6)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[1515, 10928, 10932])).
% 291.15/183.69 tff(10934,plain,
% 291.15/183.69 (m_and_h_gate_v_in1(c_e_h_3, c_c, s6)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[10298, 10933])).
% 291.15/183.69 tff(10935,plain,
% 291.15/183.69 (~node22(c_e_h_3, c_c, s6, s7)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[10069, 10016, 10060])).
% 291.15/183.69 tff(10936,plain,
% 291.15/183.69 (~node21(c_e_h_3, c_c, s6, s7)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[10294, 10016, 10291])).
% 291.15/183.69 tff(10937,plain,
% 291.15/183.69 ($false),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[10074, 10936, 10935])).
% 291.15/183.69 tff(10938,plain,(m_and_h_gate_v_out(c_e_h_3, c_c, s7) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s6)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s6))), inference(lemma,lemma(discharge,[]))).
% 291.15/183.69 tff(10939,plain,
% 291.15/183.69 (m_and_h_gate_v_out(c_e_h_3, c_c, s7)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[10938, 10934, 10930])).
% 291.15/183.69 tff(10940,plain,
% 291.15/183.69 (m_or_h_gate_v_in1(c_e_h_3, c_g, s7)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[9536, 5896, 10939])).
% 291.15/183.69 tff(10941,plain,
% 291.15/183.69 (~node4(c_e_h_3, c_g, s7)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[9532, 5516, 10940])).
% 291.15/183.69 tff(10942,plain,
% 291.15/183.69 (~m_and_h_gate_v_out(c_e_h_3, c_l, s8)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[10588, 10687, 6455])).
% 291.15/183.69 tff(10943,plain,
% 291.15/183.69 (~m_or_h_gate_v_out(c_e_h_3, c_j, s9)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[10746, 6243, 4387])).
% 291.15/183.69 tff(10944,plain,
% 291.15/183.69 (~m_or_h_gate_v_in1(c_e_h_3, c_j, s8)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[10682, 10942])).
% 291.15/183.69 tff(10945,plain,
% 291.15/183.69 (~m_c_h_element_v_out(c_e_h_3, c_h, s9)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[7358, 7304, 7305])).
% 291.15/183.69 tff(10946,plain,
% 291.15/183.69 (m_c_h_element_v_in2(c_e_h_3, c_h, s9)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[7721, 10945, 7655])).
% 291.15/183.69 tff(10947,plain,
% 291.15/183.69 (m_or_h_gate_v_out(c_e_h_3, c_j, s9)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[7652, 1174, 10946])).
% 291.15/183.69 tff(10948,plain,
% 291.15/183.69 (~node6(c_e_h_3, c_j, s8, s9)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[10661, 10947, 7275])).
% 291.15/183.69 tff(10949,plain,
% 291.15/183.69 (~node5(c_e_h_3, c_j, s8, s9)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[10672, 10947, 5523, 10663])).
% 291.15/183.69 tff(10950,plain,
% 291.15/183.69 ($false),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[5487, 10949, 10948])).
% 291.15/183.69 tff(10951,plain,(m_or_h_gate_v_out(c_e_h_3, c_j, s8) | m_or_h_gate_v_in1(c_e_h_3, c_j, s8) | m_or_h_gate_v_in2(c_e_h_3, c_j, s8) | (~m_c_h_element_v_out(c_e_h_3, c_h, s10)) | m_c_h_element_v_out(c_e_h_3, c_h, s8)), inference(lemma,lemma(discharge,[]))).
% 291.15/183.69 tff(10952,plain,
% 291.15/183.69 (m_or_h_gate_v_out(c_e_h_3, c_j, s8) | m_or_h_gate_v_in1(c_e_h_3, c_j, s8) | (~m_c_h_element_v_out(c_e_h_3, c_h, s10)) | m_c_h_element_v_out(c_e_h_3, c_h, s8)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[10951, 10652])).
% 291.15/183.69 tff(10953,plain,
% 291.15/183.69 (~m_c_h_element_v_out(c_e_h_3, c_h, s10)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[10952, 10944, 7275, 7630])).
% 291.15/183.69 tff(10954,plain,
% 291.15/183.69 (m_c_h_element_v_in2(c_e_h_3, c_h, s10)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[7806, 10953, 7626])).
% 291.15/183.69 tff(10955,plain,
% 291.15/183.69 (m_or_h_gate_v_out(c_e_h_3, c_j, s10)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[7810, 1174, 10954])).
% 291.15/183.69 tff(10956,plain,
% 291.15/183.69 (m_or_h_gate_v_in1(c_e_h_3, c_j, s9)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[8971, 10955, 10943])).
% 291.15/183.69 tff(10957,plain,
% 291.15/183.69 (m_and_h_gate_v_out(c_e_h_3, c_l, s9)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[8979, 10956])).
% 291.15/183.69 tff(10958,plain,
% 291.15/183.69 (node20(c_e_h_3, c_l, s8)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[10569, 10957, 10942])).
% 291.15/183.69 tff(10959,plain,
% 291.15/183.69 (m_and_h_gate_v_in1(c_e_h_3, c_l, s8)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[10544, 10958])).
% 291.15/183.69 tff(10960,plain,
% 291.15/183.69 (m_and_h_gate_v_out(c_e_h_3, c_k, s8)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[10536, 10959])).
% 291.15/183.69 tff(10961,plain,
% 291.15/183.69 (~node6(c_e_h_3, c_j, s10, s11)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[8990, 10955, 7627])).
% 291.15/183.69 tff(10962,plain,
% 291.15/183.69 (node5(c_e_h_3, c_j, s10, s11)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[8998, 10961])).
% 291.15/183.69 tff(10963,plain,
% 291.15/183.69 (node4(c_e_h_3, c_j, s10)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[9009, 10962, 7627])).
% 291.15/183.69 tff(10964,plain,
% 291.15/183.69 (~m_or_h_gate_v_in1(c_e_h_3, c_j, s10)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[9013, 5516, 10963])).
% 291.15/183.69 tff(10965,plain,
% 291.15/183.69 (~m_and_h_gate_v_out(c_e_h_3, c_l, s10)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[9017, 3627, 10964])).
% 291.15/183.69 tff(10966,plain,
% 291.15/183.69 (~m_and_h_gate_v_in1(c_e_h_3, c_l, s9)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[10906, 10965, 10957])).
% 291.15/183.69 tff(10967,plain,
% 291.15/183.69 (~m_and_h_gate_v_out(c_e_h_3, c_k, s9)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[9466, 10966])).
% 291.15/183.69 tff(10968,plain,
% 291.15/183.69 (~node22(c_e_h_3, c_k, s8, s9)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[9478, 10967, 10960])).
% 291.15/183.69 tff(10969,plain,
% 291.15/183.69 (~node20(c_e_h_3, c_l, s7)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[10593, 38, 10686])).
% 291.15/183.69 tff(10970,plain,
% 291.15/183.69 (~m_and_h_gate_v_out(c_e_h_3, c_l, s8)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[10588, 10969, 6455])).
% 291.15/183.69 tff(10971,plain,
% 291.15/183.69 (~m_or_h_gate_v_in1(c_e_h_3, c_j, s8)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[10682, 10970])).
% 291.15/183.69 tff(10972,plain,
% 291.15/183.69 (~m_c_h_element_v_out(c_e_h_3, c_h, s10)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[10952, 10971, 7305, 7275])).
% 291.15/183.69 tff(10973,plain,
% 291.15/183.69 (m_c_h_element_v_in2(c_e_h_3, c_h, s10)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[7806, 10972, 7626])).
% 291.15/183.69 tff(10974,plain,
% 291.15/183.69 (~m_or_h_gate_v_out(c_e_h_3, c_j, s9)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[10676, 10971, 7275])).
% 291.15/183.69 tff(10975,plain,
% 291.15/183.69 (~m_and_h_gate_v_out(c_e_h_3, c_k, s8)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[10425, 6243, 10412])).
% 291.15/183.69 tff(10976,plain,
% 291.15/183.69 (~m_and_h_gate_v_in1(c_e_h_3, c_l, s8)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[10536, 10975])).
% 291.15/183.69 tff(10977,plain,
% 291.15/183.69 (~node20(c_e_h_3, c_l, s8)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[10544, 10976])).
% 291.15/183.69 tff(10978,plain,
% 291.15/183.69 (~m_and_h_gate_v_out(c_e_h_3, c_l, s9)),
% 291.15/183.69 inference(unit_resolution,[status(thm)],[10569, 10970, 10977])).
% 291.15/183.70 tff(10979,plain,
% 291.15/183.70 (~m_or_h_gate_v_in1(c_e_h_3, c_j, s9)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[8979, 10978])).
% 291.15/183.70 tff(10980,plain,
% 291.15/183.70 (~m_or_h_gate_v_out(c_e_h_3, c_j, s10)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[8971, 10979, 10974])).
% 291.15/183.70 tff(10981,plain,
% 291.15/183.70 ($false),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[7810, 1174, 10980, 10973])).
% 291.15/183.70 tff(10982,plain,(m_and_h_gate_v_out(c_e_h_3, c_k, s7) | (~m_c_h_element_v_out(c_e_h_3, c_h, s11)) | m_c_h_element_v_out(c_e_h_3, c_h, s8) | m_or_h_gate_v_out(c_e_h_3, c_j, s8) | m_and_h_gate_v_out(c_e_h_3, c_l, s7) | node20(c_e_h_3, c_k, s7)), inference(lemma,lemma(discharge,[]))).
% 291.15/183.70 tff(10983,plain,
% 291.15/183.70 (node20(c_e_h_3, c_k, s7)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[10982, 6243, 7626, 7630, 6455, 7275])).
% 291.15/183.70 tff(10984,plain,
% 291.15/183.70 (m_and_h_gate_v_in1(c_e_h_3, c_k, s7)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[10403, 10983])).
% 291.15/183.70 tff(10985,plain,
% 291.15/183.70 (m_or_h_gate_v_out(c_e_h_3, c_g, s7)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[10395, 10984])).
% 291.15/183.70 tff(10986,plain,
% 291.15/183.70 (m_or_h_gate_v_out(c_e_h_3, c_g, s8)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[9528, 10985, 9502])).
% 291.15/183.70 tff(10987,plain,
% 291.15/183.70 (m_and_h_gate_v_in1(c_e_h_3, c_k, s8)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[9498, 6229, 10986])).
% 291.15/183.70 tff(10988,plain,
% 291.15/183.70 (~node21(c_e_h_3, c_k, s8, s9)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[9494, 10967, 7645, 10987])).
% 291.15/183.70 tff(10989,plain,
% 291.15/183.70 ($false),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[9483, 10988, 10968])).
% 291.15/183.70 tff(10990,plain,(m_and_h_gate_v_out(c_e_h_3, c_k, s7) | m_or_h_gate_v_out(c_e_h_3, c_j, s11) | (~m_c_h_element_v_out(c_e_h_3, c_h, s11)) | m_or_h_gate_v_out(c_e_h_3, c_j, s8) | node4(c_e_h_3, c_g, s7) | m_and_h_gate_v_out(c_e_h_3, c_l, s7) | node20(c_e_h_3, c_k, s4)), inference(lemma,lemma(discharge,[]))).
% 291.15/183.70 tff(10991,plain,
% 291.15/183.70 (m_and_h_gate_v_out(c_e_h_3, c_k, s7)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[10990, 10941, 7626, 7275, 7627, 7640, 4387])).
% 291.15/183.70 tff(10992,plain,
% 291.15/183.70 (node20(c_e_h_3, c_k, s6)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[10440, 10991, 7637])).
% 291.15/183.70 tff(10993,plain,
% 291.15/183.70 (m_and_h_gate_v_in1(c_e_h_3, c_k, s6)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[10444, 38, 10992])).
% 291.15/183.70 tff(10994,plain,
% 291.15/183.70 (m_or_h_gate_v_out(c_e_h_3, c_g, s6)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[10448, 2048, 10993])).
% 291.15/183.70 tff(10995,plain,
% 291.15/183.70 ($false),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[10493, 5896, 10060, 10233])).
% 291.15/183.70 tff(10996,plain,(m_or_h_gate_v_in1(c_e_h_3, c_g, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s6))), inference(lemma,lemma(discharge,[]))).
% 291.15/183.70 tff(10997,plain,
% 291.15/183.70 (m_or_h_gate_v_in1(c_e_h_3, c_g, s6)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[10996, 10930])).
% 291.15/183.70 tff(10998,plain,
% 291.15/183.70 (~node4(c_e_h_3, c_g, s6)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[10489, 5516, 10997])).
% 291.15/183.70 tff(10999,plain,
% 291.15/183.70 (m_or_h_gate_v_out(c_e_h_3, c_g, s7)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[10485, 10998, 10994])).
% 291.15/183.70 tff(11000,plain,
% 291.15/183.70 ($false),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[10464, 6229, 9501, 10397])).
% 291.15/183.70 tff(11001,plain,(m_and_h_gate_v_in1(c_e_h_3, c_k, s7) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s7))), inference(lemma,lemma(discharge,[]))).
% 291.15/183.70 tff(11002,plain,
% 291.15/183.70 (m_and_h_gate_v_in1(c_e_h_3, c_k, s7)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[11001, 10999])).
% 291.15/183.70 tff(11003,plain,
% 291.15/183.70 (m_and_h_gate_v_out(c_e_h_3, c_k, s8)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[10805, 11002, 10991])).
% 291.15/183.70 tff(11004,plain,
% 291.15/183.70 ($false),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[10809, 7192, 9468, 10538])).
% 291.15/183.70 tff(11005,plain,(m_and_h_gate_v_in1(c_e_h_3, c_l, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s8))), inference(lemma,lemma(discharge,[]))).
% 291.15/183.70 tff(11006,plain,
% 291.15/183.70 (m_and_h_gate_v_in1(c_e_h_3, c_l, s8)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[11005, 11003])).
% 291.15/183.70 tff(11007,plain,
% 291.15/183.70 (~m_c_h_element_v_out(c_e_h_3, c_h, s10)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[10952, 5523, 7275, 7305])).
% 291.15/183.70 tff(11008,plain,
% 291.15/183.70 (m_c_h_element_v_in2(c_e_h_3, c_h, s10)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[7806, 11007, 7626])).
% 291.15/183.70 tff(11009,plain,
% 291.15/183.70 (~m_or_h_gate_v_out(c_e_h_3, c_j, s9)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[10676, 5523, 7275])).
% 291.15/183.70 tff(11010,plain,
% 291.15/183.70 (~m_or_h_gate_v_out(c_e_h_3, c_j, s10)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[8971, 11009, 8950])).
% 291.15/183.70 tff(11011,plain,
% 291.15/183.70 ($false),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[7810, 1174, 11010, 11008])).
% 291.15/183.70 tff(11012,plain,(m_or_h_gate_v_in1(c_e_h_3, c_j, s8) | (~m_c_h_element_v_out(c_e_h_3, c_h, s11)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s9) | m_or_h_gate_v_out(c_e_h_3, c_j, s8) | m_c_h_element_v_out(c_e_h_3, c_h, s8)), inference(lemma,lemma(discharge,[]))).
% 291.15/183.70 tff(11013,plain,
% 291.15/183.70 (m_or_h_gate_v_in1(c_e_h_3, c_j, s8)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[11012, 8950, 7626, 7275, 7305])).
% 291.15/183.70 tff(11014,plain,
% 291.15/183.70 (~m_and_h_gate_v_out(c_e_h_3, c_l, s9)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[10865, 8950])).
% 291.15/183.70 tff(11015,plain,
% 291.15/183.70 (~m_and_h_gate_v_out(c_e_h_3, c_l, s8)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[10859, 11014, 10530])).
% 291.15/183.70 tff(11016,plain,
% 291.15/183.70 ($false),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[10682, 11015, 11013])).
% 291.15/183.70 tff(11017,plain,(m_or_h_gate_v_in1(c_e_h_3, c_j, s9) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s8)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s11)) | m_or_h_gate_v_out(c_e_h_3, c_j, s8) | m_c_h_element_v_out(c_e_h_3, c_h, s8)), inference(lemma,lemma(discharge,[]))).
% 291.15/183.70 tff(11018,plain,
% 291.15/183.70 (m_or_h_gate_v_in1(c_e_h_3, c_j, s9)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[11017, 11006, 7626, 7275, 7630])).
% 291.15/183.70 tff(11019,plain,
% 291.15/183.70 (~node4(c_e_h_3, c_j, s9)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[10872, 11018])).
% 291.15/183.70 tff(11020,plain,
% 291.15/183.70 (m_or_h_gate_v_out(c_e_h_3, c_g, s8)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[9528, 10999, 10941])).
% 291.15/183.70 tff(11021,plain,
% 291.15/183.70 (m_and_h_gate_v_in1(c_e_h_3, c_k, s8)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[9498, 6229, 11020])).
% 291.15/183.70 tff(11022,plain,
% 291.15/183.70 (~node22(c_e_h_3, c_k, s8, s9)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[9478, 9469, 9468])).
% 291.15/183.70 tff(11023,plain,
% 291.15/183.70 (~node21(c_e_h_3, c_k, s8, s9)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[9494, 9469, 8981, 9485])).
% 291.15/183.70 tff(11024,plain,
% 291.15/183.70 ($false),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[9483, 11023, 11022])).
% 291.15/183.70 tff(11025,plain,(m_and_h_gate_v_out(c_e_h_3, c_k, s9) | (~m_and_h_gate_v_in2(c_e_h_3, c_k, s8)) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s8)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s8))), inference(lemma,lemma(discharge,[]))).
% 291.15/183.70 tff(11026,plain,
% 291.15/183.70 (m_and_h_gate_v_out(c_e_h_3, c_k, s9)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[11025, 7645, 11021, 11003])).
% 291.15/183.70 tff(11027,plain,
% 291.15/183.70 (m_and_h_gate_v_in1(c_e_h_3, c_l, s9)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[9466, 11026])).
% 291.15/183.70 tff(11028,plain,
% 291.15/183.70 (m_and_h_gate_v_out(c_e_h_3, c_l, s9)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[8979, 11018])).
% 291.15/183.70 tff(11029,plain,
% 291.15/183.70 (m_and_h_gate_v_out(c_e_h_3, c_l, s10)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[10906, 11028, 11027])).
% 291.15/183.70 tff(11030,assumption,(~m_or_h_gate_v_in1(c_e_h_3, c_j, s10)), introduced(assumption)).
% 291.15/183.70 tff(11031,assumption,(m_and_h_gate_v_out(c_e_h_3, c_l, s10)), introduced(assumption)).
% 291.15/183.70 tff(11032,plain,
% 291.15/183.70 ($false),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[9017, 3627, 11031, 11030])).
% 291.15/183.70 tff(11033,plain,(m_or_h_gate_v_in1(c_e_h_3, c_j, s10) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s10))), inference(lemma,lemma(discharge,[]))).
% 291.15/183.70 tff(11034,plain,
% 291.15/183.70 (m_or_h_gate_v_in1(c_e_h_3, c_j, s10)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[11033, 11029])).
% 291.15/183.70 tff(11035,plain,
% 291.15/183.70 (~node4(c_e_h_3, c_j, s10)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[9013, 5516, 11034])).
% 291.15/183.70 tff(11036,plain,
% 291.15/183.70 (~node5(c_e_h_3, c_j, s10, s11)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[9009, 11035, 7627])).
% 291.15/183.70 tff(11037,plain,
% 291.15/183.70 (node6(c_e_h_3, c_j, s10, s11)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[8998, 11036])).
% 291.15/183.70 tff(11038,plain,
% 291.15/183.70 (~m_or_h_gate_v_out(c_e_h_3, c_j, s10)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[8990, 11037, 7627])).
% 291.15/183.70 tff(11039,plain,
% 291.15/183.70 (~m_or_h_gate_v_out(c_e_h_3, c_j, s9)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[10895, 11038, 11019])).
% 291.15/183.70 tff(11040,plain,
% 291.15/183.70 (~m_c_h_element_v_in2(c_e_h_3, c_h, s9)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[7652, 1174, 11039])).
% 291.15/183.70 tff(11041,plain,
% 291.15/183.70 (~m_c_h_element_v_in2(c_e_h_3, c_h, s10)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[7810, 1174, 11038])).
% 291.15/183.70 tff(11042,plain,
% 291.15/183.70 (m_c_h_element_v_out(c_e_h_3, c_h, s10)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[7806, 11041, 7626])).
% 291.15/183.70 tff(11043,plain,
% 291.15/183.70 ($false),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[7721, 11042, 11040, 7625])).
% 291.15/183.70 tff(11044,plain,(node20(c_e_h_3, c_k, s4) | (~m_c_h_element_v_out(c_e_h_3, c_h, s11)) | m_or_h_gate_v_out(c_e_h_3, c_j, s11) | m_or_h_gate_v_out(c_e_h_3, c_j, s8) | m_or_h_gate_v_out(c_e_h_3, c_g, s5) | node20(c_e_h_3, c_k, s5)), inference(lemma,lemma(discharge,[]))).
% 291.15/183.70 tff(11045,plain,
% 291.15/183.70 (node20(c_e_h_3, c_k, s4)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[11044, 7629, 7627, 7275, 7626, 7628])).
% 291.15/183.70 tff(11046,plain,
% 291.15/183.70 (m_and_h_gate_v_in1(c_e_h_3, c_k, s4)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[3392, 11045])).
% 291.15/183.70 tff(11047,plain,
% 291.15/183.70 (m_or_h_gate_v_out(c_e_h_3, c_g, s4)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[3384, 11046])).
% 291.15/183.70 tff(11048,plain,
% 291.15/183.70 (m_or_h_gate_v_in1(c_e_h_3, c_g, s3)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[3377, 11047])).
% 291.15/183.70 tff(11049,plain,
% 291.15/183.70 (m_and_h_gate_v_out(c_e_h_3, c_c, s3)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[2713, 11048])).
% 291.15/183.70 tff(11050,plain,
% 291.15/183.70 (node4(c_e_h_3, c_g, s4)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[5922, 11047, 7629])).
% 291.15/183.70 tff(11051,plain,
% 291.15/183.70 (~m_or_h_gate_v_in1(c_e_h_3, c_g, s4)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[5903, 5516, 11050])).
% 291.15/183.70 tff(11052,plain,
% 291.15/183.70 (~m_and_h_gate_v_out(c_e_h_3, c_c, s4)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[5899, 5896, 11051])).
% 291.15/183.70 tff(11053,plain,
% 291.15/183.70 (node20(c_e_h_3, c_c, s2)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[2698, 11049])).
% 291.15/183.70 tff(11054,plain,
% 291.15/183.70 (m_and_h_gate_v_in1(c_e_h_3, c_c, s2)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[2622, 11053])).
% 291.15/183.70 tff(11055,plain,
% 291.15/183.70 (m_mutex_h_half_v_out(c_e_h_3, c_a, s2)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[2614, 11054])).
% 291.15/183.70 tff(11056,plain,
% 291.15/183.70 (m_mutex_h_half_v_out(c_e_h_3, c_a, s3)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[2606, 11055])).
% 291.15/183.70 tff(11057,plain,
% 291.15/183.70 (m_and_h_gate_v_in1(c_e_h_3, c_c, s3)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[2561, 11056])).
% 291.15/183.70 tff(11058,plain,
% 291.15/183.70 (~node21(c_e_h_3, c_c, s3, s4)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[5859, 11052, 11057])).
% 291.15/183.70 tff(11059,plain,
% 291.15/183.70 (node22(c_e_h_3, c_c, s3, s4)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[2734, 11058])).
% 291.15/183.70 tff(11060,plain,
% 291.15/183.70 ($false),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[5874, 5871, 11059, 11052, 11049])).
% 291.15/183.70 tff(11061,plain,(m_and_h_gate_v_in1(c_e_h_3, c_k, s5) | m_or_h_gate_v_out(c_e_h_3, c_j, s11) | m_or_h_gate_v_out(c_e_h_3, c_j, s8) | (~m_c_h_element_v_out(c_e_h_3, c_h, s11))), inference(lemma,lemma(discharge,[]))).
% 291.15/183.70 tff(11062,plain,
% 291.15/183.70 (m_and_h_gate_v_in1(c_e_h_3, c_k, s5)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[11061, 7275, 7627, 7626])).
% 291.15/183.70 tff(11063,plain,
% 291.15/183.70 (~m_and_h_gate_v_in1(c_e_h_3, c_l, s8)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[10536, 10531])).
% 291.15/183.70 tff(11064,plain,
% 291.15/183.70 (~node20(c_e_h_3, c_l, s8)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[10544, 11063])).
% 291.15/183.70 tff(11065,plain,
% 291.15/183.70 (m_or_h_gate_v_out(c_e_h_3, c_g, s5)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[3365, 3359])).
% 291.15/183.70 tff(11066,plain,
% 291.15/183.70 (m_or_h_gate_v_in1(c_e_h_3, c_g, s3)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[3357, 5880, 3252])).
% 291.15/183.70 tff(11067,plain,
% 291.15/183.70 (m_and_h_gate_v_out(c_e_h_3, c_c, s3)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[2713, 11066])).
% 291.15/183.70 tff(11068,plain,
% 291.15/183.70 (node20(c_e_h_3, c_c, s2)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[2698, 11067])).
% 291.15/183.70 tff(11069,plain,
% 291.15/183.70 (m_and_h_gate_v_in1(c_e_h_3, c_c, s2)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[2622, 11068])).
% 291.15/183.70 tff(11070,plain,
% 291.15/183.70 (m_mutex_h_half_v_out(c_e_h_3, c_a, s2)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[2614, 11069])).
% 291.15/183.70 tff(11071,plain,
% 291.15/183.70 (m_mutex_h_half_v_out(c_e_h_3, c_a, s3)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[2606, 11070])).
% 291.15/183.70 tff(11072,plain,
% 291.15/183.70 (m_and_h_gate_v_in1(c_e_h_3, c_c, s3)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[2561, 11071])).
% 291.15/183.70 tff(11073,plain,
% 291.15/183.70 (~node21(c_e_h_3, c_c, s3, s4)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[5859, 11072, 2743])).
% 291.15/183.70 tff(11074,plain,
% 291.15/183.70 (node22(c_e_h_3, c_c, s3, s4)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[2734, 11073])).
% 291.15/183.70 tff(11075,plain,
% 291.15/183.70 ($false),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[5874, 5871, 11074, 2743, 11067])).
% 291.15/183.70 tff(11076,plain,(m_and_h_gate_v_out(c_e_h_3, c_c, s4) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s5))), inference(lemma,lemma(discharge,[]))).
% 291.15/183.70 tff(11077,plain,
% 291.15/183.70 (m_and_h_gate_v_out(c_e_h_3, c_c, s4)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[11076, 11065])).
% 291.15/183.70 tff(11078,plain,
% 291.15/183.70 (m_and_h_gate_v_out(c_e_h_3, c_c, s5)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[6170, 11077])).
% 291.15/183.70 tff(11079,plain,
% 291.15/183.70 (m_or_h_gate_v_in1(c_e_h_3, c_g, s5)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[6178, 11078])).
% 291.15/183.70 tff(11080,plain,
% 291.15/183.70 (~node4(c_e_h_3, c_g, s5)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[6186, 11079])).
% 291.15/183.70 tff(11081,plain,
% 291.15/183.70 (m_or_h_gate_v_out(c_e_h_3, c_g, s6)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[6218, 11080, 11065])).
% 291.15/183.70 tff(11082,plain,
% 291.15/183.70 (m_mutex_h_half_v_out(c_e_h_3, c_a, s4)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[10330, 11078])).
% 291.15/183.70 tff(11083,plain,
% 291.15/183.70 (m_user_v_req(c_e_h_3, c_u, s3)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[550, 11082])).
% 291.15/183.70 tff(11084,plain,
% 291.15/183.70 (m_user_v_req(c_e_h_3, c_u, s4)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[732, 11083])).
% 291.15/183.70 tff(11085,plain,
% 291.15/183.70 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s4)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[1445, 11084])).
% 291.15/183.70 tff(11086,plain,
% 291.15/183.70 (m_mutex_h_half_v_out(c_e_h_3, c_a, s5)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[1488, 11085, 11082])).
% 291.15/183.70 tff(11087,plain,
% 291.15/183.70 (m_and_h_gate_v_in1(c_e_h_3, c_c, s5)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[10341, 11086])).
% 291.15/183.70 tff(11088,plain,
% 291.15/183.70 (m_and_h_gate_v_out(c_e_h_3, c_c, s6)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[10378, 11087, 11078])).
% 291.15/183.70 tff(11089,plain,
% 291.15/183.70 (m_or_h_gate_v_in1(c_e_h_3, c_g, s6)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[10996, 11088])).
% 291.15/183.70 tff(11090,assumption,(node4(c_e_h_3, c_g, s6)), introduced(assumption)).
% 291.15/183.70 tff(11091,plain,
% 291.15/183.70 ($false),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[10489, 5516, 11090, 10225])).
% 291.15/183.70 tff(11092,plain,((~node4(c_e_h_3, c_g, s6)) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s6))), inference(lemma,lemma(discharge,[]))).
% 291.15/183.70 tff(11093,plain,
% 291.15/183.70 (~node4(c_e_h_3, c_g, s6)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[11092, 11089])).
% 291.15/183.70 tff(11094,plain,
% 291.15/183.70 (m_or_h_gate_v_out(c_e_h_3, c_g, s7)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[10485, 11093, 11081])).
% 291.15/183.70 tff(11095,plain,
% 291.15/183.70 (m_and_h_gate_v_in1(c_e_h_3, c_k, s7)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[11001, 11094])).
% 291.15/183.70 tff(11096,plain,
% 291.15/183.70 (~m_and_h_gate_v_out(c_e_h_3, c_k, s7)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[10805, 10531, 11095])).
% 291.15/183.70 tff(11097,plain,
% 291.15/183.70 (~m_and_h_gate_v_in1(c_e_h_3, c_l, s7)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[10601, 11096])).
% 291.15/183.70 tff(11098,plain,
% 291.15/183.70 (~node20(c_e_h_3, c_l, s7)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[10595, 11097])).
% 291.15/183.70 tff(11099,plain,
% 291.15/183.70 (m_and_h_gate_v_in1(c_e_h_3, c_k, s6)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[6232, 6229, 11081])).
% 291.15/183.70 tff(11100,plain,
% 291.15/183.70 (~m_and_h_gate_v_out(c_e_h_3, c_k, s6)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[6448, 11096, 11099])).
% 291.15/183.70 tff(11101,plain,
% 291.15/183.70 (~m_and_h_gate_v_in1(c_e_h_3, c_l, s6)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[4475, 11100])).
% 291.15/183.70 tff(11102,plain,
% 291.15/183.70 (~node20(c_e_h_3, c_l, s6)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[4483, 11101])).
% 291.15/183.70 tff(11103,plain,
% 291.15/183.70 (~m_and_h_gate_v_out(c_e_h_3, c_k, s5)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[7236, 11100, 3359])).
% 291.15/183.70 tff(11104,plain,
% 291.15/183.70 (~m_and_h_gate_v_in1(c_e_h_3, c_l, s5)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[4413, 11103])).
% 291.15/183.70 tff(11105,plain,
% 291.15/183.70 (~node20(c_e_h_3, c_l, s5)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[4421, 11104])).
% 291.15/183.70 tff(11106,plain,
% 291.15/183.70 (~m_and_h_gate_v_out(c_e_h_3, c_l, s6)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[7207, 11105])).
% 291.15/183.70 tff(11107,plain,
% 291.15/183.70 (~m_and_h_gate_v_out(c_e_h_3, c_l, s7)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[5441, 11106, 11102])).
% 291.15/183.70 tff(11108,plain,
% 291.15/183.70 (~m_and_h_gate_v_out(c_e_h_3, c_l, s8)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[10588, 11107, 11098])).
% 291.15/183.70 tff(11109,plain,
% 291.15/183.70 (~m_and_h_gate_v_out(c_e_h_3, c_l, s9)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[10569, 11108, 11064])).
% 291.15/183.70 tff(11110,plain,
% 291.15/183.70 (~m_c_h_element_v_out(c_e_h_3, c_h, s8)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[7560, 11103])).
% 291.15/183.70 tff(11111,plain,
% 291.15/183.70 (~m_or_h_gate_v_in1(c_e_h_3, c_j, s8)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[10682, 11108])).
% 291.15/183.70 tff(11112,plain,
% 291.15/183.70 (m_or_h_gate_v_in1(c_e_h_3, c_j, s9)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[11012, 11111, 7626, 7275, 11110])).
% 291.15/183.70 tff(11113,plain,
% 291.15/183.70 ($false),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[8979, 11112, 11109])).
% 291.15/183.70 tff(11114,plain,(m_and_h_gate_v_out(c_e_h_3, c_k, s8) | (~m_c_h_element_v_out(c_e_h_3, c_h, s11)) | m_or_h_gate_v_out(c_e_h_3, c_j, s8) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s5))), inference(lemma,lemma(discharge,[]))).
% 291.15/183.70 tff(11115,plain,
% 291.15/183.70 (m_and_h_gate_v_out(c_e_h_3, c_k, s8)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[11114, 7275, 7626, 3359])).
% 291.15/183.70 tff(11116,plain,
% 291.15/183.70 (m_and_h_gate_v_in1(c_e_h_3, c_l, s8)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[11005, 11115])).
% 291.15/183.70 tff(11117,plain,
% 291.15/183.70 (~m_and_h_gate_v_out(c_e_h_3, c_l, s8)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[10859, 11014, 11116])).
% 291.15/183.70 tff(11118,plain,
% 291.15/183.70 (m_c_h_element_v_out(c_e_h_3, c_h, s8)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[11017, 8950, 7626, 7275, 11116])).
% 291.15/183.70 tff(11119,plain,
% 291.15/183.70 (m_or_h_gate_v_in1(c_e_h_3, c_j, s6)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[7563, 11118])).
% 291.15/183.70 tff(11120,plain,
% 291.15/183.70 (m_and_h_gate_v_out(c_e_h_3, c_l, s6)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[4492, 11119])).
% 291.15/183.70 tff(11121,plain,
% 291.15/183.70 (m_and_h_gate_v_out(c_e_h_3, c_k, s5)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[7560, 11118])).
% 291.15/183.70 tff(11122,plain,
% 291.15/183.70 (m_and_h_gate_v_out(c_e_h_3, c_k, s6)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[7236, 11121, 3359])).
% 291.15/183.70 tff(11123,plain,
% 291.15/183.70 (m_and_h_gate_v_in1(c_e_h_3, c_l, s6)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[7242, 11122])).
% 291.15/183.70 tff(11124,plain,
% 291.15/183.70 (m_and_h_gate_v_out(c_e_h_3, c_l, s7)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[7268, 11123, 11120])).
% 291.15/183.70 tff(11125,plain,
% 291.15/183.70 (m_and_h_gate_v_out(c_e_h_3, c_k, s7)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[6448, 11122, 11099])).
% 291.15/183.70 tff(11126,plain,
% 291.15/183.70 (m_and_h_gate_v_in1(c_e_h_3, c_l, s7)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[7197, 11125])).
% 291.15/183.70 tff(11127,plain,
% 291.15/183.70 ($false),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[7179, 11126, 11124, 11117])).
% 291.15/183.70 tff(11128,plain,(m_or_h_gate_v_in1(c_e_h_3, c_j, s9) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s5)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s11)) | m_or_h_gate_v_out(c_e_h_3, c_j, s8)), inference(lemma,lemma(discharge,[]))).
% 291.15/183.70 tff(11129,plain,
% 291.15/183.70 (m_or_h_gate_v_in1(c_e_h_3, c_j, s9)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[11128, 11062, 7626, 7275])).
% 291.15/183.70 tff(11130,plain,
% 291.15/183.70 (~node4(c_e_h_3, c_j, s9)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[10872, 11129])).
% 291.15/183.70 tff(11131,plain,
% 291.15/183.70 (m_and_h_gate_v_out(c_e_h_3, c_l, s9)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[8979, 11129])).
% 291.15/183.70 tff(11132,plain,
% 291.15/183.70 (m_and_h_gate_v_out(c_e_h_3, c_k, s8)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[11114, 7275, 7626, 11062])).
% 291.15/183.70 tff(11133,plain,
% 291.15/183.70 (m_or_h_gate_v_out(c_e_h_3, c_g, s5)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[3365, 11062])).
% 291.15/183.70 tff(11134,plain,
% 291.15/183.70 (m_and_h_gate_v_out(c_e_h_3, c_c, s4)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[11076, 11133])).
% 291.15/183.70 tff(11135,plain,
% 291.15/183.70 (m_and_h_gate_v_out(c_e_h_3, c_c, s5)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[6170, 11134])).
% 291.15/183.70 tff(11136,plain,
% 291.15/183.70 (m_or_h_gate_v_in1(c_e_h_3, c_g, s5)),
% 291.15/183.70 inference(unit_resolution,[status(thm)],[6178, 11135])).
% 291.23/183.71 tff(11137,plain,
% 291.23/183.71 (~node4(c_e_h_3, c_g, s5)),
% 291.23/183.71 inference(unit_resolution,[status(thm)],[6186, 11136])).
% 291.23/183.71 tff(11138,plain,
% 291.23/183.71 (m_or_h_gate_v_out(c_e_h_3, c_g, s6)),
% 291.23/183.71 inference(unit_resolution,[status(thm)],[6218, 11137, 11133])).
% 291.23/183.71 tff(11139,plain,
% 291.23/183.71 (m_mutex_h_half_v_out(c_e_h_3, c_a, s4)),
% 291.23/183.71 inference(unit_resolution,[status(thm)],[10330, 11135])).
% 291.23/183.71 tff(11140,plain,
% 291.23/183.71 (m_user_v_req(c_e_h_3, c_u, s3)),
% 291.23/183.71 inference(unit_resolution,[status(thm)],[550, 11139])).
% 291.23/183.71 tff(11141,plain,
% 291.23/183.71 (m_user_v_req(c_e_h_3, c_u, s4)),
% 291.23/183.71 inference(unit_resolution,[status(thm)],[732, 11140])).
% 291.23/183.71 tff(11142,plain,
% 291.23/183.71 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s4)),
% 291.23/183.71 inference(unit_resolution,[status(thm)],[1445, 11141])).
% 291.23/183.71 tff(11143,plain,
% 291.23/183.71 (m_mutex_h_half_v_out(c_e_h_3, c_a, s5)),
% 291.23/183.71 inference(unit_resolution,[status(thm)],[1488, 11142, 11139])).
% 291.23/183.71 tff(11144,plain,
% 291.23/183.71 (m_and_h_gate_v_in1(c_e_h_3, c_c, s5)),
% 291.23/183.71 inference(unit_resolution,[status(thm)],[10341, 11143])).
% 291.23/183.71 tff(11145,plain,
% 291.23/183.71 (m_and_h_gate_v_out(c_e_h_3, c_c, s6)),
% 291.23/183.71 inference(unit_resolution,[status(thm)],[10378, 11144, 11135])).
% 291.23/183.71 tff(11146,plain,
% 291.23/183.71 (m_or_h_gate_v_in1(c_e_h_3, c_g, s6)),
% 291.23/183.71 inference(unit_resolution,[status(thm)],[10996, 11145])).
% 291.23/183.71 tff(11147,plain,
% 291.23/183.71 (~node4(c_e_h_3, c_g, s6)),
% 291.23/183.71 inference(unit_resolution,[status(thm)],[11092, 11146])).
% 291.23/183.71 tff(11148,plain,
% 291.23/183.71 (m_or_h_gate_v_out(c_e_h_3, c_g, s7)),
% 291.23/183.71 inference(unit_resolution,[status(thm)],[10485, 11147, 11138])).
% 291.23/183.71 tff(11149,plain,
% 291.23/183.71 (m_user_v_req(c_e_h_3, c_u, s5)),
% 291.23/183.71 inference(unit_resolution,[status(thm)],[1035, 11141])).
% 291.23/183.71 tff(11150,plain,
% 291.23/183.71 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s5)),
% 291.23/183.71 inference(unit_resolution,[status(thm)],[1438, 11149])).
% 291.23/183.71 tff(11151,plain,
% 291.23/183.71 (m_mutex_h_half_v_out(c_e_h_3, c_a, s6)),
% 291.23/183.71 inference(unit_resolution,[status(thm)],[1515, 11143, 11150])).
% 291.23/183.71 tff(11152,plain,
% 291.23/183.71 (m_and_h_gate_v_in1(c_e_h_3, c_c, s6)),
% 291.23/183.71 inference(unit_resolution,[status(thm)],[10298, 11151])).
% 291.23/183.71 tff(11153,plain,
% 291.23/183.71 (m_and_h_gate_v_out(c_e_h_3, c_c, s7)),
% 291.23/183.71 inference(unit_resolution,[status(thm)],[10938, 11145, 11152])).
% 291.23/183.71 tff(11154,assumption,(~m_or_h_gate_v_in1(c_e_h_3, c_g, s7)), introduced(assumption)).
% 291.23/183.71 tff(11155,assumption,(m_and_h_gate_v_out(c_e_h_3, c_c, s7)), introduced(assumption)).
% 291.23/183.71 tff(11156,plain,
% 291.23/183.71 ($false),
% 291.23/183.71 inference(unit_resolution,[status(thm)],[9536, 5896, 11155, 11154])).
% 291.23/183.71 tff(11157,plain,(m_or_h_gate_v_in1(c_e_h_3, c_g, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s7))), inference(lemma,lemma(discharge,[]))).
% 291.23/183.71 tff(11158,plain,
% 291.23/183.71 (m_or_h_gate_v_in1(c_e_h_3, c_g, s7)),
% 291.23/183.71 inference(unit_resolution,[status(thm)],[11157, 11153])).
% 291.23/183.71 tff(11159,plain,
% 291.23/183.71 (~node4(c_e_h_3, c_g, s7)),
% 291.23/183.71 inference(unit_resolution,[status(thm)],[9532, 5516, 11158])).
% 291.23/183.71 tff(11160,plain,
% 291.23/183.71 (m_or_h_gate_v_out(c_e_h_3, c_g, s8)),
% 291.23/183.71 inference(unit_resolution,[status(thm)],[9528, 11159, 11148])).
% 291.23/183.71 tff(11161,assumption,(m_or_h_gate_v_out(c_e_h_3, c_g, s8)), introduced(assumption)).
% 291.23/183.71 tff(11162,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_h, s8)), introduced(assumption)).
% 291.23/183.71 tff(11163,plain,
% 291.23/183.71 (^[I0: $i, X: $i] : refl(((~m_or_h_gate_v_out(I0, c_g, X)) | m_c_h_element_v_in1(I0, c_h, X)) <=> ((~m_or_h_gate_v_out(I0, c_g, X)) | m_c_h_element_v_in1(I0, c_h, X)))),
% 291.23/183.71 inference(bind,[status(th)],[])).
% 291.23/183.71 tff(11164,plain,
% 291.23/183.71 (![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_c_h_element_v_in1(I0, c_h, X)) <=> ![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_c_h_element_v_in1(I0, c_h, X))),
% 291.23/183.71 inference(quant_intro,[status(thm)],[11163])).
% 291.23/183.71 tff(11165,plain,
% 291.23/183.71 (![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_c_h_element_v_in1(I0, c_h, X)) <=> ![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_c_h_element_v_in1(I0, c_h, X))),
% 291.23/183.71 inference(rewrite,[status(thm)],[])).
% 291.23/183.71 tff(11166,plain,
% 291.23/183.71 (^[I0: $i, X: $i] : rewrite((m_c_h_element_v_in1(I0, c_h, X) | (~m_or_h_gate_v_out(I0, c_g, X))) <=> ((~m_or_h_gate_v_out(I0, c_g, X)) | m_c_h_element_v_in1(I0, c_h, X)))),
% 291.23/183.71 inference(bind,[status(th)],[])).
% 291.23/183.71 tff(11167,plain,
% 291.23/183.71 (![I0: $i, X: $i] : (m_c_h_element_v_in1(I0, c_h, X) | (~m_or_h_gate_v_out(I0, c_g, X))) <=> ![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_c_h_element_v_in1(I0, c_h, X))),
% 291.23/183.71 inference(quant_intro,[status(thm)],[11166])).
% 291.23/183.71 tff(11168,axiom,(![I0: $i, X: $i] : (m_c_h_element_v_in1(I0, c_h, X) | (~m_or_h_gate_v_out(I0, c_g, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_31')).
% 291.23/183.71 tff(11169,plain,
% 291.23/183.71 (![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_c_h_element_v_in1(I0, c_h, X))),
% 291.23/183.71 inference(modus_ponens,[status(thm)],[11168, 11167])).
% 291.23/183.71 tff(11170,plain,
% 291.23/183.71 (![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_c_h_element_v_in1(I0, c_h, X))),
% 291.23/183.71 inference(modus_ponens,[status(thm)],[11169, 11165])).
% 291.23/183.71 tff(11171,plain,(
% 291.23/183.71 ![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_c_h_element_v_in1(I0, c_h, X))),
% 291.23/183.71 inference(skolemize,[status(sab)],[11170])).
% 291.23/183.71 tff(11172,plain,
% 291.23/183.71 (![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_c_h_element_v_in1(I0, c_h, X))),
% 291.23/183.71 inference(modus_ponens,[status(thm)],[11171, 11164])).
% 291.23/183.71 tff(11173,plain,
% 291.23/183.71 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_c_h_element_v_in1(I0, c_h, X))) | ((~m_or_h_gate_v_out(c_e_h_3, c_g, s8)) | m_c_h_element_v_in1(c_e_h_3, c_h, s8))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_c_h_element_v_in1(I0, c_h, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s8)) | m_c_h_element_v_in1(c_e_h_3, c_h, s8))),
% 291.23/183.71 inference(rewrite,[status(thm)],[])).
% 291.23/183.71 tff(11174,plain,
% 291.23/183.71 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_c_h_element_v_in1(I0, c_h, X))) | ((~m_or_h_gate_v_out(c_e_h_3, c_g, s8)) | m_c_h_element_v_in1(c_e_h_3, c_h, s8))),
% 291.23/183.71 inference(quant_inst,[status(thm)],[])).
% 291.23/183.71 tff(11175,plain,
% 291.23/183.71 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_c_h_element_v_in1(I0, c_h, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s8)) | m_c_h_element_v_in1(c_e_h_3, c_h, s8)),
% 291.23/183.71 inference(modus_ponens,[status(thm)],[11174, 11173])).
% 291.23/183.71 tff(11176,plain,
% 291.23/183.71 ($false),
% 291.23/183.71 inference(unit_resolution,[status(thm)],[11175, 11172, 11162, 11161])).
% 291.23/183.71 tff(11177,plain,((~m_or_h_gate_v_out(c_e_h_3, c_g, s8)) | m_c_h_element_v_in1(c_e_h_3, c_h, s8)), inference(lemma,lemma(discharge,[]))).
% 291.23/183.71 tff(11178,plain,
% 291.23/183.71 (m_c_h_element_v_in1(c_e_h_3, c_h, s8)),
% 291.23/183.71 inference(unit_resolution,[status(thm)],[11177, 11160])).
% 291.23/183.71 tff(11179,plain,
% 291.23/183.71 ((~m_c_h_element_v_in1(c_e_h_3, c_h, s8)) | (~node17(c_e_h_3, c_h, s8))),
% 291.23/183.71 inference(unit_resolution,[status(thm)],[7335, 919, 7304])).
% 291.23/183.71 tff(11180,plain,
% 291.23/183.71 (~node17(c_e_h_3, c_h, s8)),
% 291.23/183.71 inference(unit_resolution,[status(thm)],[11179, 11178])).
% 291.23/183.71 tff(11181,plain,
% 291.23/183.71 (node18(c_e_h_3, c_h, s8, s9)),
% 291.23/183.71 inference(unit_resolution,[status(thm)],[7330, 11180])).
% 291.23/183.71 tff(11182,plain,
% 291.23/183.71 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl((m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_out(I0, I1, X)) | (~node18(I0, I1, X, Y))) <=> (m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_out(I0, I1, X)) | (~node18(I0, I1, X, Y))))),
% 291.23/183.71 inference(bind,[status(th)],[])).
% 291.23/183.71 tff(11183,plain,
% 291.23/183.71 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_out(I0, I1, X)) | (~node18(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_out(I0, I1, X)) | (~node18(I0, I1, X, Y)))),
% 291.23/183.71 inference(quant_intro,[status(thm)],[11182])).
% 291.23/183.71 tff(11184,plain,
% 291.23/183.71 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_out(I0, I1, X)) | (~node18(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_out(I0, I1, X)) | (~node18(I0, I1, X, Y)))),
% 291.23/183.71 inference(rewrite,[status(thm)],[])).
% 291.23/183.71 tff(11185,plain,
% 291.23/183.71 (^[Y: $i, I0: $i, X: $i, I1: $i] : trans(monotonicity(rewrite((m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_out(I0, I1, X))) <=> (m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_out(I0, I1, X)))), (((m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_out(I0, I1, X))) | (~node18(I0, I1, X, Y))) <=> ((m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_out(I0, I1, X))) | (~node18(I0, I1, X, Y))))), rewrite(((m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_out(I0, I1, X))) | (~node18(I0, I1, X, Y))) <=> (m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_out(I0, I1, X)) | (~node18(I0, I1, X, Y)))), (((m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_out(I0, I1, X))) | (~node18(I0, I1, X, Y))) <=> (m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_out(I0, I1, X)) | (~node18(I0, I1, X, Y)))))),
% 291.23/183.71 inference(bind,[status(th)],[])).
% 291.23/183.71 tff(11186,plain,
% 291.23/183.71 (![Y: $i, I0: $i, X: $i, I1: $i] : ((m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_out(I0, I1, X))) | (~node18(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_out(I0, I1, X)) | (~node18(I0, I1, X, Y)))),
% 291.23/183.71 inference(quant_intro,[status(thm)],[11185])).
% 291.23/183.71 tff(11187,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : ((m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_out(I0, I1, X))) | (~node18(I0, I1, X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_c_h_element_10')).
% 291.23/183.71 tff(11188,plain,
% 291.23/183.71 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_out(I0, I1, X)) | (~node18(I0, I1, X, Y)))),
% 291.23/183.71 inference(modus_ponens,[status(thm)],[11187, 11186])).
% 291.23/183.71 tff(11189,plain,
% 291.23/183.71 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_out(I0, I1, X)) | (~node18(I0, I1, X, Y)))),
% 291.23/183.71 inference(modus_ponens,[status(thm)],[11188, 11184])).
% 291.23/183.71 tff(11190,plain,(
% 291.23/183.71 ![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_out(I0, I1, X)) | (~node18(I0, I1, X, Y)))),
% 291.23/183.71 inference(skolemize,[status(sab)],[11189])).
% 291.23/183.71 tff(11191,plain,
% 291.23/183.71 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_out(I0, I1, X)) | (~node18(I0, I1, X, Y)))),
% 291.23/183.71 inference(modus_ponens,[status(thm)],[11190, 11183])).
% 291.23/183.71 tff(11192,plain,
% 291.23/183.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_out(I0, I1, X)) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_h, s9) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | (~node18(c_e_h_3, c_h, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_out(I0, I1, X)) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s9) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | (~node18(c_e_h_3, c_h, s8, s9)))),
% 291.23/183.71 inference(rewrite,[status(thm)],[])).
% 291.23/183.71 tff(11193,plain,
% 291.23/183.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_out(I0, I1, X)) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_h, s9) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | (~node18(c_e_h_3, c_h, s8, s9)))),
% 291.23/183.71 inference(quant_inst,[status(thm)],[])).
% 291.23/183.71 tff(11194,plain,
% 291.23/183.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_out(I0, I1, X)) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s9) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | (~node18(c_e_h_3, c_h, s8, s9))),
% 291.23/183.71 inference(modus_ponens,[status(thm)],[11193, 11192])).
% 291.23/183.71 tff(11195,plain,
% 291.23/183.71 (~m_c_h_element_v_out(c_e_h_3, c_h, s8)),
% 291.23/183.71 inference(unit_resolution,[status(thm)],[11194, 11191, 7625, 11181])).
% 291.23/183.71 tff(11196,plain,
% 291.23/183.71 (m_and_h_gate_v_in2(c_e_h_3, c_k, s8)),
% 291.23/183.71 inference(unit_resolution,[status(thm)],[7644, 11195])).
% 291.23/183.71 tff(11197,plain,
% 291.23/183.71 (m_and_h_gate_v_in1(c_e_h_3, c_k, s8)),
% 291.23/183.71 inference(unit_resolution,[status(thm)],[9498, 6229, 11160])).
% 291.23/183.71 tff(11198,plain,
% 291.23/183.71 (m_and_h_gate_v_out(c_e_h_3, c_k, s9)),
% 291.23/183.71 inference(unit_resolution,[status(thm)],[11025, 11197, 11196, 11132])).
% 291.23/183.71 tff(11199,plain,
% 291.23/183.71 (m_and_h_gate_v_in1(c_e_h_3, c_l, s9)),
% 291.23/183.71 inference(unit_resolution,[status(thm)],[9466, 11198])).
% 291.23/183.71 tff(11200,plain,
% 291.23/183.71 (m_and_h_gate_v_out(c_e_h_3, c_l, s10)),
% 291.23/183.71 inference(unit_resolution,[status(thm)],[10906, 11199, 11131])).
% 291.23/183.71 tff(11201,plain,
% 291.23/183.71 (m_or_h_gate_v_in1(c_e_h_3, c_j, s10)),
% 291.23/183.71 inference(unit_resolution,[status(thm)],[11033, 11200])).
% 291.23/183.71 tff(11202,assumption,(m_or_h_gate_v_in1(c_e_h_3, c_j, s10)), introduced(assumption)).
% 291.23/183.71 tff(11203,assumption,(node4(c_e_h_3, c_j, s10)), introduced(assumption)).
% 291.23/183.71 tff(11204,plain,
% 291.23/183.71 ($false),
% 291.23/183.71 inference(unit_resolution,[status(thm)],[9013, 5516, 11203, 11202])).
% 291.23/183.71 tff(11205,plain,((~node4(c_e_h_3, c_j, s10)) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s10))), inference(lemma,lemma(discharge,[]))).
% 291.23/183.71 tff(11206,plain,
% 291.23/183.71 (~node4(c_e_h_3, c_j, s10)),
% 291.23/183.71 inference(unit_resolution,[status(thm)],[11205, 11201])).
% 291.23/183.71 tff(11207,plain,
% 291.23/183.71 (~node5(c_e_h_3, c_j, s10, s11)),
% 291.23/183.71 inference(unit_resolution,[status(thm)],[9009, 11206, 7627])).
% 291.23/183.71 tff(11208,plain,
% 291.23/183.71 (node6(c_e_h_3, c_j, s10, s11)),
% 291.23/183.71 inference(unit_resolution,[status(thm)],[8998, 11207])).
% 291.23/183.71 tff(11209,plain,
% 291.23/183.71 (~m_or_h_gate_v_out(c_e_h_3, c_j, s10)),
% 291.23/183.71 inference(unit_resolution,[status(thm)],[8990, 11208, 7627])).
% 291.23/183.71 tff(11210,plain,
% 291.23/183.71 (~m_or_h_gate_v_out(c_e_h_3, c_j, s9)),
% 291.23/183.71 inference(unit_resolution,[status(thm)],[10895, 11209, 11130])).
% 291.23/183.71 tff(11211,plain,
% 291.23/183.71 (~m_c_h_element_v_in2(c_e_h_3, c_h, s9)),
% 291.23/183.71 inference(unit_resolution,[status(thm)],[7652, 1174, 11210])).
% 291.23/183.71 tff(11212,plain,
% 291.23/183.71 (~m_c_h_element_v_in2(c_e_h_3, c_h, s10)),
% 291.23/183.71 inference(unit_resolution,[status(thm)],[7810, 1174, 11209])).
% 291.23/183.71 tff(11213,plain,
% 291.23/183.71 (m_c_h_element_v_out(c_e_h_3, c_h, s10)),
% 291.23/183.71 inference(unit_resolution,[status(thm)],[7806, 11212, 7626])).
% 291.23/183.71 tff(11214,plain,
% 291.23/183.71 ($false),
% 291.23/183.71 inference(unit_resolution,[status(thm)],[7721, 11213, 11211, 7625])).
% 291.23/183.71 tff(11215,plain,(m_or_h_gate_v_out(c_e_h_3, c_j, s8) | (~m_c_h_element_v_out(c_e_h_3, c_h, s11)) | m_or_h_gate_v_out(c_e_h_3, c_j, s11)), inference(lemma,lemma(discharge,[]))).
% 291.23/183.71 tff(11216,plain,
% 291.23/183.71 ($false),
% 291.23/183.71 inference(unit_resolution,[status(thm)],[11215, 7299, 7284, 7275])).
% 291.23/183.71 tff(11217,plain,((~node20(c_e_h_3, c_i, s11)) | m_or_h_gate_v_out(c_e_h_3, c_j, s8)), inference(lemma,lemma(discharge,[]))).
% 291.23/183.71 tff(11218,plain,
% 291.23/183.71 (~node20(c_e_h_3, c_i, s11)),
% 291.23/183.71 inference(unit_resolution,[status(thm)],[11217, 7274])).
% 291.23/183.71 tff(11219,plain,
% 291.23/183.71 (~m_c_h_element_v_out(c_e_h_3, c_h, s9)),
% 291.23/183.71 inference(unit_resolution,[status(thm)],[7624, 7274])).
% 291.23/183.71 tff(11220,plain,
% 291.23/183.71 (~m_c_h_element_v_out(c_e_h_3, c_h, s10)),
% 291.23/183.71 inference(unit_resolution,[status(thm)],[7721, 7653, 11219])).
% 291.23/183.71 tff(11221,plain,
% 291.23/183.71 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_i, s10)) | m_c_h_element_v_out(c_e_h_3, c_h, s10))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s10)) | m_c_h_element_v_out(c_e_h_3, c_h, s10))),
% 291.23/183.71 inference(rewrite,[status(thm)],[])).
% 291.23/183.71 tff(11222,plain,
% 291.23/183.71 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_i, s10)) | m_c_h_element_v_out(c_e_h_3, c_h, s10))),
% 291.23/183.71 inference(quant_inst,[status(thm)],[])).
% 291.23/183.71 tff(11223,plain,
% 291.23/183.71 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s10)) | m_c_h_element_v_out(c_e_h_3, c_h, s10)),
% 291.23/183.71 inference(modus_ponens,[status(thm)],[11222, 11221])).
% 291.23/183.71 tff(11224,plain,
% 291.23/183.71 (~m_and_h_gate_v_in1(c_e_h_3, c_i, s10)),
% 291.23/183.71 inference(unit_resolution,[status(thm)],[11223, 619, 11220])).
% 291.23/183.71 tff(11225,plain,
% 291.23/183.71 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s10)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s10))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_i, s10)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s10))),
% 291.23/183.71 inference(rewrite,[status(thm)],[])).
% 291.23/183.71 tff(11226,plain,
% 291.23/183.71 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s10)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s10))),
% 291.23/183.71 inference(quant_inst,[status(thm)],[])).
% 291.23/183.71 tff(11227,plain,
% 291.23/183.71 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_i, s10)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s10)),
% 291.23/183.71 inference(modus_ponens,[status(thm)],[11226, 11225])).
% 291.23/183.71 tff(11228,plain,
% 291.23/183.72 (~node20(c_e_h_3, c_i, s10)),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[11227, 38, 11224])).
% 291.23/183.72 tff(11229,assumption,(node20(c_e_h_3, c_i, s8)), introduced(assumption)).
% 291.23/183.72 tff(11230,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_i, s8)), introduced(assumption)).
% 291.23/183.72 tff(11231,plain,
% 291.23/183.72 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_i, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s8))),
% 291.23/183.72 inference(rewrite,[status(thm)],[])).
% 291.23/183.72 tff(11232,plain,
% 291.23/183.72 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s8))),
% 291.23/183.72 inference(quant_inst,[status(thm)],[])).
% 291.23/183.72 tff(11233,plain,
% 291.23/183.72 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_i, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s8)),
% 291.23/183.72 inference(modus_ponens,[status(thm)],[11232, 11231])).
% 291.23/183.72 tff(11234,plain,
% 291.23/183.72 ($false),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[11233, 38, 11229, 11230])).
% 291.23/183.72 tff(11235,plain,(m_and_h_gate_v_in1(c_e_h_3, c_i, s8) | (~node20(c_e_h_3, c_i, s8))), inference(lemma,lemma(discharge,[]))).
% 291.23/183.72 tff(11236,plain,
% 291.23/183.72 (m_and_h_gate_v_in1(c_e_h_3, c_i, s8)),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[11235, 11229])).
% 291.23/183.72 tff(11237,assumption,(~m_and_h_gate_v_in2(c_e_h_3, c_i, s8)), introduced(assumption)).
% 291.23/183.72 tff(11238,plain,
% 291.23/183.72 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s8)) | m_and_h_gate_v_in2(c_e_h_3, c_i, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_i, s8)) | m_and_h_gate_v_in2(c_e_h_3, c_i, s8))),
% 291.23/183.72 inference(rewrite,[status(thm)],[])).
% 291.23/183.72 tff(11239,plain,
% 291.23/183.72 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s8)) | m_and_h_gate_v_in2(c_e_h_3, c_i, s8))),
% 291.23/183.72 inference(quant_inst,[status(thm)],[])).
% 291.23/183.72 tff(11240,plain,
% 291.23/183.72 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_i, s8)) | m_and_h_gate_v_in2(c_e_h_3, c_i, s8)),
% 291.23/183.72 inference(modus_ponens,[status(thm)],[11239, 11238])).
% 291.23/183.72 tff(11241,plain,
% 291.23/183.72 ($false),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[11240, 4563, 11237, 11229])).
% 291.23/183.72 tff(11242,plain,(m_and_h_gate_v_in2(c_e_h_3, c_i, s8) | (~node20(c_e_h_3, c_i, s8))), inference(lemma,lemma(discharge,[]))).
% 291.23/183.72 tff(11243,plain,
% 291.23/183.72 (m_and_h_gate_v_in2(c_e_h_3, c_i, s8)),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[11242, 11229])).
% 291.23/183.72 tff(11244,plain,
% 291.23/183.72 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_i, X)) | (~m_or_h_gate_v_out(I0, c_j, X)))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_i, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s8)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_i, X)) | (~m_or_h_gate_v_out(I0, c_j, X)))) | (~m_and_h_gate_v_in2(c_e_h_3, c_i, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s8)))),
% 291.23/183.72 inference(rewrite,[status(thm)],[])).
% 291.23/183.72 tff(11245,plain,
% 291.23/183.72 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_i, X)) | (~m_or_h_gate_v_out(I0, c_j, X)))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_i, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s8)))),
% 291.23/183.72 inference(quant_inst,[status(thm)],[])).
% 291.23/183.72 tff(11246,plain,
% 291.23/183.72 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_i, X)) | (~m_or_h_gate_v_out(I0, c_j, X)))) | (~m_and_h_gate_v_in2(c_e_h_3, c_i, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s8))),
% 291.23/183.72 inference(modus_ponens,[status(thm)],[11245, 11244])).
% 291.23/183.72 tff(11247,plain,
% 291.23/183.72 (~m_or_h_gate_v_out(c_e_h_3, c_j, s8)),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[11246, 7295, 11243])).
% 291.23/183.72 tff(11248,plain,
% 291.23/183.72 (~m_c_h_element_v_in2(c_e_h_3, c_h, s8)),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[7303, 1174, 11247])).
% 291.23/183.72 tff(11249,plain,
% 291.23/183.72 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_i, s8)) | m_c_h_element_v_out(c_e_h_3, c_h, s8))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s8)) | m_c_h_element_v_out(c_e_h_3, c_h, s8))),
% 291.23/183.72 inference(rewrite,[status(thm)],[])).
% 291.23/183.72 tff(11250,plain,
% 291.23/183.72 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_i, s8)) | m_c_h_element_v_out(c_e_h_3, c_h, s8))),
% 291.23/183.72 inference(quant_inst,[status(thm)],[])).
% 291.23/183.72 tff(11251,plain,
% 291.23/183.72 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s8)) | m_c_h_element_v_out(c_e_h_3, c_h, s8)),
% 291.23/183.72 inference(modus_ponens,[status(thm)],[11250, 11249])).
% 291.23/183.72 tff(11252,plain,
% 291.23/183.72 (m_c_h_element_v_out(c_e_h_3, c_h, s8)),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[11251, 619, 11236])).
% 291.23/183.72 tff(11253,plain,
% 291.23/183.72 (~m_c_h_element_v_out(c_e_h_3, c_h, s9)),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[7624, 11247])).
% 291.23/183.72 tff(11254,plain,
% 291.23/183.72 ($false),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[11194, 11191, 7367, 7649, 7313])).
% 291.23/183.72 tff(11255,plain,((~node18(c_e_h_3, c_h, s8, s9)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | m_c_h_element_v_out(c_e_h_3, c_h, s9)), inference(lemma,lemma(discharge,[]))).
% 291.23/183.72 tff(11256,plain,
% 291.23/183.72 (~node18(c_e_h_3, c_h, s8, s9)),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[11255, 11253, 11252])).
% 291.23/183.72 tff(11257,plain,
% 291.23/183.72 (node17(c_e_h_3, c_h, s8)),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[7330, 11256])).
% 291.23/183.72 tff(11258,plain,
% 291.23/183.72 (~node18(c_e_h_3, c_h, s7, s8)),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[7467, 7367, 7452])).
% 291.23/183.72 tff(11259,plain,
% 291.23/183.72 (~node15(c_e_h_3, c_h, s7, s8)),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[7457, 7367, 7452])).
% 291.23/183.72 tff(11260,plain,
% 291.23/183.72 (~node17(c_e_h_3, c_h, s7)),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[7511, 7367, 7481, 11259])).
% 291.23/183.72 tff(11261,plain,
% 291.23/183.72 ($false),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[7479, 11260, 11258])).
% 291.23/183.72 tff(11262,plain,((~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | m_c_h_element_v_in1(c_e_h_3, c_h, s7) | m_c_h_element_v_out(c_e_h_3, c_h, s7)), inference(lemma,lemma(discharge,[]))).
% 291.23/183.72 tff(11263,plain,
% 291.23/183.72 ((~m_c_h_element_v_out(c_e_h_3, c_h, s8)) | m_c_h_element_v_in1(c_e_h_3, c_h, s7)),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[11262, 7566])).
% 291.23/183.72 tff(11264,plain,
% 291.23/183.72 (m_c_h_element_v_in1(c_e_h_3, c_h, s7)),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[11263, 11252])).
% 291.23/183.72 tff(11265,assumption,(m_c_h_element_v_in1(c_e_h_3, c_h, s7)), introduced(assumption)).
% 291.23/183.72 tff(11266,plain,
% 291.23/183.72 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s7)) | m_or_h_gate_v_out(c_e_h_3, c_g, s7))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s7)) | m_or_h_gate_v_out(c_e_h_3, c_g, s7))),
% 291.23/183.72 inference(rewrite,[status(thm)],[])).
% 291.23/183.72 tff(11267,plain,
% 291.23/183.72 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s7)) | m_or_h_gate_v_out(c_e_h_3, c_g, s7))),
% 291.23/183.72 inference(quant_inst,[status(thm)],[])).
% 291.23/183.72 tff(11268,plain,
% 291.23/183.72 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s7)) | m_or_h_gate_v_out(c_e_h_3, c_g, s7)),
% 291.23/183.72 inference(modus_ponens,[status(thm)],[11267, 11266])).
% 291.23/183.72 tff(11269,plain,
% 291.23/183.72 ($false),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[11268, 811, 10390, 11265])).
% 291.23/183.72 tff(11270,plain,((~m_c_h_element_v_in1(c_e_h_3, c_h, s7)) | m_or_h_gate_v_out(c_e_h_3, c_g, s7)), inference(lemma,lemma(discharge,[]))).
% 291.23/183.72 tff(11271,plain,
% 291.23/183.72 (m_or_h_gate_v_out(c_e_h_3, c_g, s7)),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[11270, 11264])).
% 291.23/183.72 tff(11272,plain,
% 291.23/183.72 (m_or_h_gate_v_out(c_e_h_3, c_g, s8)),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[9528, 11271, 9502])).
% 291.23/183.72 tff(11273,plain,
% 291.23/183.72 (m_c_h_element_v_in1(c_e_h_3, c_h, s8)),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[11177, 11272])).
% 291.23/183.72 tff(11274,plain,
% 291.23/183.72 ($false),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[7335, 919, 11273, 11257, 11248])).
% 291.23/183.72 tff(11275,plain,((~node20(c_e_h_3, c_i, s8)) | node4(c_e_h_3, c_g, s7)), inference(lemma,lemma(discharge,[]))).
% 291.23/183.72 tff(11276,plain,
% 291.23/183.72 (node4(c_e_h_3, c_g, s7)),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[11275, 11229])).
% 291.23/183.72 tff(11277,assumption,(m_or_h_gate_v_in1(c_e_h_3, c_g, s7)), introduced(assumption)).
% 291.23/183.72 tff(11278,assumption,(node4(c_e_h_3, c_g, s7)), introduced(assumption)).
% 291.23/183.72 tff(11279,plain,
% 291.23/183.72 ($false),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[9532, 5516, 11278, 11277])).
% 291.23/183.72 tff(11280,plain,((~node4(c_e_h_3, c_g, s7)) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s7))), inference(lemma,lemma(discharge,[]))).
% 291.23/183.72 tff(11281,plain,
% 291.23/183.72 (~m_or_h_gate_v_in1(c_e_h_3, c_g, s7)),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[11280, 11276])).
% 291.23/183.72 tff(11282,plain,
% 291.23/183.72 (~m_and_h_gate_v_out(c_e_h_3, c_c, s7)),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[11157, 11281])).
% 291.23/183.72 tff(11283,plain,
% 291.23/183.72 (m_mutex_h_half_v_out(c_e_h_3, c_a, s4)),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[10330, 6173])).
% 291.23/183.72 tff(11284,plain,
% 291.23/183.72 (m_user_v_req(c_e_h_3, c_u, s3)),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[550, 11283])).
% 291.23/183.72 tff(11285,plain,
% 291.23/183.72 (m_user_v_req(c_e_h_3, c_u, s4)),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[732, 11284])).
% 291.23/183.72 tff(11286,plain,
% 291.23/183.72 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s4)),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[1445, 11285])).
% 291.23/183.72 tff(11287,plain,
% 291.23/183.72 (m_mutex_h_half_v_out(c_e_h_3, c_a, s5)),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[1488, 11286, 11283])).
% 291.23/183.72 tff(11288,plain,
% 291.23/183.72 (m_and_h_gate_v_in1(c_e_h_3, c_c, s5)),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[10341, 11287])).
% 291.23/183.72 tff(11289,plain,
% 291.23/183.72 (m_and_h_gate_v_out(c_e_h_3, c_c, s6)),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[10378, 11288, 6173])).
% 291.23/183.72 tff(11290,plain,
% 291.23/183.72 (m_user_v_req(c_e_h_3, c_u, s5)),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[1035, 11285])).
% 291.23/183.72 tff(11291,plain,
% 291.23/183.72 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s5)),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[1438, 11290])).
% 291.23/183.72 tff(11292,plain,
% 291.23/183.72 (m_mutex_h_half_v_out(c_e_h_3, c_a, s6)),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[1515, 11287, 11291])).
% 291.23/183.72 tff(11293,plain,
% 291.23/183.72 (m_and_h_gate_v_in1(c_e_h_3, c_c, s6)),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[10298, 11292])).
% 291.23/183.72 tff(11294,plain,
% 291.23/183.72 ($false),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[10938, 11293, 11289, 10016])).
% 291.23/183.72 tff(11295,plain,((~m_and_h_gate_v_out(c_e_h_3, c_c, s5)) | m_and_h_gate_v_out(c_e_h_3, c_c, s7)), inference(lemma,lemma(discharge,[]))).
% 291.23/183.72 tff(11296,plain,
% 291.23/183.72 (~m_and_h_gate_v_out(c_e_h_3, c_c, s5)),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[11295, 11282])).
% 291.23/183.72 tff(11297,plain,
% 291.23/183.72 (~m_and_h_gate_v_out(c_e_h_3, c_c, s4)),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[6170, 11296])).
% 291.23/183.72 tff(11298,plain,
% 291.23/183.72 (node20(c_e_h_3, c_c, s2)),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[2698, 2676])).
% 291.23/183.72 tff(11299,plain,
% 291.23/183.72 (m_and_h_gate_v_in1(c_e_h_3, c_c, s2)),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[2622, 11298])).
% 291.23/183.72 tff(11300,plain,
% 291.23/183.72 (m_mutex_h_half_v_out(c_e_h_3, c_a, s2)),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[2614, 11299])).
% 291.23/183.72 tff(11301,plain,
% 291.23/183.72 (m_mutex_h_half_v_out(c_e_h_3, c_a, s3)),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[2606, 11300])).
% 291.23/183.72 tff(11302,plain,
% 291.23/183.72 (m_and_h_gate_v_in1(c_e_h_3, c_c, s3)),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[2561, 11301])).
% 291.23/183.72 tff(11303,plain,
% 291.23/183.72 (~node21(c_e_h_3, c_c, s3, s4)),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[5859, 11302, 2743])).
% 291.23/183.72 tff(11304,plain,
% 291.23/183.72 (node22(c_e_h_3, c_c, s3, s4)),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[2734, 11303])).
% 291.23/183.72 tff(11305,plain,
% 291.23/183.72 ($false),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[5874, 5871, 11304, 2743, 2676])).
% 291.23/183.72 tff(11306,plain,((~m_and_h_gate_v_out(c_e_h_3, c_c, s3)) | m_and_h_gate_v_out(c_e_h_3, c_c, s4)), inference(lemma,lemma(discharge,[]))).
% 291.23/183.72 tff(11307,plain,
% 291.23/183.72 (~m_and_h_gate_v_out(c_e_h_3, c_c, s3)),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[11306, 11297])).
% 291.23/183.72 tff(11308,plain,
% 291.23/183.72 (~m_or_h_gate_v_in1(c_e_h_3, c_g, s3)),
% 291.23/183.72 inference(unit_resolution,[status(thm)],[2713, 11307])).
% 291.23/183.73 tff(11309,plain,
% 291.23/183.73 (~m_c_h_element_v_out(c_e_h_3, c_h, s8)),
% 291.23/183.73 inference(unit_resolution,[status(thm)],[7551, 11308])).
% 291.23/183.73 tff(11310,plain,
% 291.23/183.73 ($false),
% 291.23/183.73 inference(unit_resolution,[status(thm)],[11251, 619, 11309, 11236])).
% 291.23/183.73 tff(11311,plain,(~node20(c_e_h_3, c_i, s8)), inference(lemma,lemma(discharge,[]))).
% 291.23/183.73 tff(11312,assumption,(m_and_h_gate_v_out(c_e_h_3, c_i, s8)), introduced(assumption)).
% 291.23/183.73 tff(11313,assumption,(node22(c_e_h_3, c_i, s7, s8)), introduced(assumption)).
% 291.23/183.73 tff(11314,plain,
% 291.23/183.73 (~m_and_h_gate_v_in1(c_e_h_3, c_i, s6)),
% 291.23/183.73 inference(unit_resolution,[status(thm)],[9435, 6413])).
% 291.23/183.73 tff(11315,plain,
% 291.23/183.73 (~node20(c_e_h_3, c_i, s6)),
% 291.23/183.73 inference(unit_resolution,[status(thm)],[9428, 11314])).
% 291.23/183.73 tff(11316,plain,
% 291.23/183.73 ((~m_and_h_gate_v_out(c_e_h_3, c_i, s7)) | node20(c_e_h_3, c_i, s6)),
% 291.23/183.73 inference(unit_resolution,[status(thm)],[9420, 10821])).
% 291.23/183.73 tff(11317,plain,
% 291.23/183.73 (~m_and_h_gate_v_out(c_e_h_3, c_i, s7)),
% 291.23/183.73 inference(unit_resolution,[status(thm)],[11316, 11315])).
% 291.23/183.73 tff(11318,plain,
% 291.23/183.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s8)) | (~node22(c_e_h_3, c_i, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_i, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s8)) | (~node22(c_e_h_3, c_i, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_i, s7))),
% 291.23/183.73 inference(rewrite,[status(thm)],[])).
% 291.23/183.73 tff(11319,plain,
% 291.23/183.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s8)) | (~node22(c_e_h_3, c_i, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_i, s7))),
% 291.23/183.73 inference(quant_inst,[status(thm)],[])).
% 291.23/183.73 tff(11320,plain,
% 291.23/183.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s8)) | (~node22(c_e_h_3, c_i, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_i, s7)),
% 291.23/183.73 inference(modus_ponens,[status(thm)],[11319, 11318])).
% 291.23/183.73 tff(11321,plain,
% 291.23/183.73 ($false),
% 291.23/183.73 inference(unit_resolution,[status(thm)],[11320, 108, 11317, 11313, 11312])).
% 291.23/183.73 tff(11322,plain,((~node22(c_e_h_3, c_i, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s8))), inference(lemma,lemma(discharge,[]))).
% 291.23/183.73 tff(11323,plain,
% 291.23/183.73 (~node22(c_e_h_3, c_i, s7, s8)),
% 291.23/183.73 inference(unit_resolution,[status(thm)],[11322, 11312])).
% 291.23/183.73 tff(11324,plain,
% 291.23/183.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_3, c_i, s7, s8) | node22(c_e_h_3, c_i, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_3, c_i, s7, s8) | node22(c_e_h_3, c_i, s7, s8))),
% 291.23/183.73 inference(rewrite,[status(thm)],[])).
% 291.23/183.73 tff(11325,plain,
% 291.23/183.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_3, c_i, s7, s8) | node22(c_e_h_3, c_i, s7, s8))),
% 291.23/183.73 inference(quant_inst,[status(thm)],[])).
% 291.23/183.73 tff(11326,plain,
% 291.23/183.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_3, c_i, s7, s8) | node22(c_e_h_3, c_i, s7, s8)),
% 291.23/183.73 inference(modus_ponens,[status(thm)],[11325, 11324])).
% 291.23/183.73 tff(11327,plain,
% 291.23/183.73 (node21(c_e_h_3, c_i, s7, s8) | node22(c_e_h_3, c_i, s7, s8)),
% 291.23/183.73 inference(unit_resolution,[status(thm)],[11326, 82, 1938])).
% 291.23/183.73 tff(11328,plain,
% 291.23/183.73 (node21(c_e_h_3, c_i, s7, s8)),
% 291.23/183.73 inference(unit_resolution,[status(thm)],[11327, 11323])).
% 291.23/183.73 tff(11329,plain,
% 291.23/183.73 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_i, s7)) | m_c_h_element_v_out(c_e_h_3, c_h, s7))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s7)) | m_c_h_element_v_out(c_e_h_3, c_h, s7))),
% 291.23/183.73 inference(rewrite,[status(thm)],[])).
% 291.23/183.73 tff(11330,plain,
% 291.23/183.73 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_i, s7)) | m_c_h_element_v_out(c_e_h_3, c_h, s7))),
% 291.23/183.73 inference(quant_inst,[status(thm)],[])).
% 291.23/183.73 tff(11331,plain,
% 291.23/183.73 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s7)) | m_c_h_element_v_out(c_e_h_3, c_h, s7)),
% 291.23/183.73 inference(modus_ponens,[status(thm)],[11330, 11329])).
% 291.23/183.73 tff(11332,plain,
% 291.23/183.73 (~m_and_h_gate_v_in1(c_e_h_3, c_i, s7)),
% 291.23/183.73 inference(unit_resolution,[status(thm)],[11331, 619, 7566])).
% 291.23/183.73 tff(11333,plain,
% 291.23/183.73 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_i, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s7))),
% 291.23/183.73 inference(rewrite,[status(thm)],[])).
% 291.23/183.73 tff(11334,plain,
% 291.23/183.73 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s7))),
% 291.23/183.73 inference(quant_inst,[status(thm)],[])).
% 291.23/183.73 tff(11335,plain,
% 291.23/183.73 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_i, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s7)),
% 291.23/183.73 inference(modus_ponens,[status(thm)],[11334, 11333])).
% 291.23/183.73 tff(11336,plain,
% 291.23/183.73 (~node20(c_e_h_3, c_i, s7)),
% 291.23/183.73 inference(unit_resolution,[status(thm)],[11335, 38, 11332])).
% 291.23/183.73 tff(11337,plain,
% 291.23/183.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s8)) | node20(c_e_h_3, c_i, s7) | (~node21(c_e_h_3, c_i, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s8)) | node20(c_e_h_3, c_i, s7) | (~node21(c_e_h_3, c_i, s7, s8)))),
% 291.23/183.73 inference(rewrite,[status(thm)],[])).
% 291.23/183.73 tff(11338,plain,
% 291.23/183.73 ((node20(c_e_h_3, c_i, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s8)) | (~node21(c_e_h_3, c_i, s7, s8))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_i, s8)) | node20(c_e_h_3, c_i, s7) | (~node21(c_e_h_3, c_i, s7, s8)))),
% 291.23/183.73 inference(rewrite,[status(thm)],[])).
% 291.23/183.73 tff(11339,plain,
% 291.23/183.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s8)) | (~node21(c_e_h_3, c_i, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s8)) | node20(c_e_h_3, c_i, s7) | (~node21(c_e_h_3, c_i, s7, s8))))),
% 291.23/183.73 inference(monotonicity,[status(thm)],[11338])).
% 291.23/183.73 tff(11340,plain,
% 291.23/183.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s8)) | (~node21(c_e_h_3, c_i, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s8)) | node20(c_e_h_3, c_i, s7) | (~node21(c_e_h_3, c_i, s7, s8)))),
% 291.23/183.73 inference(transitivity,[status(thm)],[11339, 11337])).
% 291.23/183.73 tff(11341,plain,
% 291.23/183.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s8)) | (~node21(c_e_h_3, c_i, s7, s8)))),
% 291.23/183.73 inference(quant_inst,[status(thm)],[])).
% 291.23/183.73 tff(11342,plain,
% 291.23/183.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s8)) | node20(c_e_h_3, c_i, s7) | (~node21(c_e_h_3, c_i, s7, s8))),
% 291.23/183.73 inference(modus_ponens,[status(thm)],[11341, 11340])).
% 291.23/183.73 tff(11343,plain,
% 291.23/183.73 ($false),
% 291.23/183.73 inference(unit_resolution,[status(thm)],[11342, 52, 11336, 11328, 11312])).
% 291.23/183.73 tff(11344,plain,(~m_and_h_gate_v_out(c_e_h_3, c_i, s8)), inference(lemma,lemma(discharge,[]))).
% 291.23/183.73 tff(11345,assumption,(~node20(c_e_h_3, c_i, s8)), introduced(assumption)).
% 291.23/183.73 tff(11346,assumption,(m_and_h_gate_v_out(c_e_h_3, c_i, s9)), introduced(assumption)).
% 291.23/183.73 tff(11347,assumption,(node21(c_e_h_3, c_i, s8, s9)), introduced(assumption)).
% 291.23/183.73 tff(11348,plain,
% 291.23/183.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s9)) | (~node21(c_e_h_3, c_i, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_i, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s9)) | (~node21(c_e_h_3, c_i, s8, s9)))),
% 291.23/183.73 inference(rewrite,[status(thm)],[])).
% 291.23/183.73 tff(11349,plain,
% 291.23/183.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s9)) | (~node21(c_e_h_3, c_i, s8, s9)))),
% 291.23/183.73 inference(quant_inst,[status(thm)],[])).
% 291.23/183.73 tff(11350,plain,
% 291.23/183.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_i, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s9)) | (~node21(c_e_h_3, c_i, s8, s9))),
% 291.23/183.73 inference(modus_ponens,[status(thm)],[11349, 11348])).
% 291.23/183.73 tff(11351,plain,
% 291.23/183.73 ($false),
% 291.23/183.73 inference(unit_resolution,[status(thm)],[11350, 52, 11346, 11347, 11345])).
% 291.23/183.73 tff(11352,plain,((~node21(c_e_h_3, c_i, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s9)) | node20(c_e_h_3, c_i, s8)), inference(lemma,lemma(discharge,[]))).
% 291.23/183.73 tff(11353,plain,
% 291.23/183.73 (~node21(c_e_h_3, c_i, s8, s9)),
% 291.23/183.73 inference(unit_resolution,[status(thm)],[11352, 11346, 11345])).
% 291.23/183.73 tff(11354,plain,
% 291.23/183.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s8, s9)) | node21(c_e_h_3, c_i, s8, s9) | node22(c_e_h_3, c_i, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_3, c_i, s8, s9) | node22(c_e_h_3, c_i, s8, s9))),
% 291.23/183.73 inference(rewrite,[status(thm)],[])).
% 291.23/183.73 tff(11355,plain,
% 291.23/183.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s8, s9)) | node21(c_e_h_3, c_i, s8, s9) | node22(c_e_h_3, c_i, s8, s9))),
% 291.23/183.73 inference(quant_inst,[status(thm)],[])).
% 291.23/183.73 tff(11356,plain,
% 291.23/183.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_3, c_i, s8, s9) | node22(c_e_h_3, c_i, s8, s9)),
% 291.23/183.73 inference(modus_ponens,[status(thm)],[11355, 11354])).
% 291.23/183.73 tff(11357,plain,
% 291.23/183.73 (node21(c_e_h_3, c_i, s8, s9) | node22(c_e_h_3, c_i, s8, s9)),
% 291.23/183.73 inference(unit_resolution,[status(thm)],[11356, 82, 1993])).
% 291.23/183.73 tff(11358,plain,
% 291.23/183.73 (node22(c_e_h_3, c_i, s8, s9)),
% 291.23/183.73 inference(unit_resolution,[status(thm)],[11357, 11353])).
% 291.23/183.73 tff(11359,plain,
% 291.23/183.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s9)) | (~node22(c_e_h_3, c_i, s8, s9)) | m_and_h_gate_v_out(c_e_h_3, c_i, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s9)) | (~node22(c_e_h_3, c_i, s8, s9)) | m_and_h_gate_v_out(c_e_h_3, c_i, s8))),
% 291.23/183.73 inference(rewrite,[status(thm)],[])).
% 291.23/183.73 tff(11360,plain,
% 291.23/183.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s9)) | (~node22(c_e_h_3, c_i, s8, s9)) | m_and_h_gate_v_out(c_e_h_3, c_i, s8))),
% 291.23/183.74 inference(quant_inst,[status(thm)],[])).
% 291.23/183.74 tff(11361,plain,
% 291.23/183.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s9)) | (~node22(c_e_h_3, c_i, s8, s9)) | m_and_h_gate_v_out(c_e_h_3, c_i, s8)),
% 291.23/183.74 inference(modus_ponens,[status(thm)],[11360, 11359])).
% 291.23/183.74 tff(11362,plain,
% 291.23/183.74 ($false),
% 291.23/183.74 inference(unit_resolution,[status(thm)],[11361, 108, 11346, 11358, 11344])).
% 291.23/183.74 tff(11363,plain,((~m_and_h_gate_v_out(c_e_h_3, c_i, s9)) | node20(c_e_h_3, c_i, s8)), inference(lemma,lemma(discharge,[]))).
% 291.23/183.74 tff(11364,plain,
% 291.23/183.74 (~m_and_h_gate_v_out(c_e_h_3, c_i, s9)),
% 291.23/183.74 inference(unit_resolution,[status(thm)],[11363, 11311])).
% 291.23/183.74 tff(11365,assumption,(node20(c_e_h_3, c_i, s9)), introduced(assumption)).
% 291.23/183.74 tff(11366,plain,
% 291.23/183.74 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s9)) | m_and_h_gate_v_in2(c_e_h_3, c_i, s9))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_i, s9)) | m_and_h_gate_v_in2(c_e_h_3, c_i, s9))),
% 291.23/183.74 inference(rewrite,[status(thm)],[])).
% 291.23/183.74 tff(11367,plain,
% 291.23/183.74 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s9)) | m_and_h_gate_v_in2(c_e_h_3, c_i, s9))),
% 291.23/183.74 inference(quant_inst,[status(thm)],[])).
% 291.23/183.74 tff(11368,plain,
% 291.23/183.74 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_i, s9)) | m_and_h_gate_v_in2(c_e_h_3, c_i, s9)),
% 291.23/183.74 inference(modus_ponens,[status(thm)],[11367, 11366])).
% 291.23/183.74 tff(11369,plain,
% 291.23/183.74 (m_and_h_gate_v_in2(c_e_h_3, c_i, s9)),
% 291.23/183.74 inference(unit_resolution,[status(thm)],[11368, 4563, 11365])).
% 291.23/183.74 tff(11370,plain,
% 291.23/183.74 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_i, X)) | (~m_or_h_gate_v_out(I0, c_j, X)))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_i, s9)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s9)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_i, X)) | (~m_or_h_gate_v_out(I0, c_j, X)))) | (~m_and_h_gate_v_in2(c_e_h_3, c_i, s9)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s9)))),
% 291.23/183.74 inference(rewrite,[status(thm)],[])).
% 291.23/183.74 tff(11371,plain,
% 291.23/183.74 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_i, X)) | (~m_or_h_gate_v_out(I0, c_j, X)))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_i, s9)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s9)))),
% 291.23/183.74 inference(quant_inst,[status(thm)],[])).
% 291.23/183.74 tff(11372,plain,
% 291.23/183.74 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_i, X)) | (~m_or_h_gate_v_out(I0, c_j, X)))) | (~m_and_h_gate_v_in2(c_e_h_3, c_i, s9)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s9))),
% 291.23/183.74 inference(modus_ponens,[status(thm)],[11371, 11370])).
% 291.23/183.74 tff(11373,plain,
% 291.23/183.74 (~m_or_h_gate_v_out(c_e_h_3, c_j, s9)),
% 291.23/183.74 inference(unit_resolution,[status(thm)],[11372, 7295, 11369])).
% 291.23/183.74 tff(11374,plain,
% 291.23/183.74 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s9)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s9))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_i, s9)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s9))),
% 291.23/183.74 inference(rewrite,[status(thm)],[])).
% 291.23/183.74 tff(11375,plain,
% 291.23/183.74 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s9)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s9))),
% 291.23/183.74 inference(quant_inst,[status(thm)],[])).
% 291.23/183.74 tff(11376,plain,
% 291.23/183.74 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_i, s9)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s9)),
% 291.23/183.74 inference(modus_ponens,[status(thm)],[11375, 11374])).
% 291.23/183.74 tff(11377,plain,
% 291.23/183.74 (m_and_h_gate_v_in1(c_e_h_3, c_i, s9)),
% 291.23/183.74 inference(unit_resolution,[status(thm)],[11376, 38, 11365])).
% 291.23/183.74 tff(11378,plain,
% 291.23/183.74 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_i, s9)) | m_c_h_element_v_out(c_e_h_3, c_h, s9))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s9)) | m_c_h_element_v_out(c_e_h_3, c_h, s9))),
% 291.23/183.74 inference(rewrite,[status(thm)],[])).
% 291.23/183.74 tff(11379,plain,
% 291.23/183.74 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_i, s9)) | m_c_h_element_v_out(c_e_h_3, c_h, s9))),
% 291.23/183.74 inference(quant_inst,[status(thm)],[])).
% 291.23/183.74 tff(11380,plain,
% 291.23/183.74 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s9)) | m_c_h_element_v_out(c_e_h_3, c_h, s9)),
% 291.23/183.74 inference(modus_ponens,[status(thm)],[11379, 11378])).
% 291.23/183.74 tff(11381,plain,
% 291.23/183.74 (m_c_h_element_v_out(c_e_h_3, c_h, s9)),
% 291.23/183.74 inference(unit_resolution,[status(thm)],[11380, 619, 11377])).
% 291.23/183.74 tff(11382,plain,
% 291.23/183.74 (m_or_h_gate_v_out(c_e_h_3, c_j, s8)),
% 291.23/183.74 inference(unit_resolution,[status(thm)],[7624, 11381])).
% 291.23/183.74 tff(11383,plain,
% 291.23/183.74 ($false),
% 291.23/183.74 inference(unit_resolution,[status(thm)],[7273, 11382, 11373])).
% 291.23/183.74 tff(11384,plain,(~node20(c_e_h_3, c_i, s9)), inference(lemma,lemma(discharge,[]))).
% 291.23/183.74 tff(11385,assumption,(~node20(c_e_h_3, c_i, s9)), introduced(assumption)).
% 291.23/183.74 tff(11386,assumption,(m_and_h_gate_v_out(c_e_h_3, c_i, s10)), introduced(assumption)).
% 291.23/183.74 tff(11387,assumption,(node21(c_e_h_3, c_i, s9, s10)), introduced(assumption)).
% 291.23/183.74 tff(11388,plain,
% 291.23/183.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s10)) | (~node21(c_e_h_3, c_i, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_i, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s10)) | (~node21(c_e_h_3, c_i, s9, s10)))),
% 291.23/183.74 inference(rewrite,[status(thm)],[])).
% 291.23/183.74 tff(11389,plain,
% 291.23/183.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s10)) | (~node21(c_e_h_3, c_i, s9, s10)))),
% 291.23/183.74 inference(quant_inst,[status(thm)],[])).
% 291.23/183.74 tff(11390,plain,
% 291.23/183.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_i, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s10)) | (~node21(c_e_h_3, c_i, s9, s10))),
% 291.23/183.74 inference(modus_ponens,[status(thm)],[11389, 11388])).
% 291.23/183.74 tff(11391,plain,
% 291.23/183.74 ($false),
% 291.23/183.74 inference(unit_resolution,[status(thm)],[11390, 52, 11386, 11387, 11385])).
% 291.23/183.74 tff(11392,plain,((~node21(c_e_h_3, c_i, s9, s10)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s10)) | node20(c_e_h_3, c_i, s9)), inference(lemma,lemma(discharge,[]))).
% 291.23/183.74 tff(11393,plain,
% 291.23/183.74 (~node21(c_e_h_3, c_i, s9, s10)),
% 291.23/183.74 inference(unit_resolution,[status(thm)],[11392, 11386, 11385])).
% 291.23/183.74 tff(11394,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_i, s9)), introduced(assumption)).
% 291.23/183.74 tff(11395,assumption,(node22(c_e_h_3, c_i, s9, s10)), introduced(assumption)).
% 291.23/183.74 tff(11396,plain,
% 291.23/183.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s10)) | (~node22(c_e_h_3, c_i, s9, s10)) | m_and_h_gate_v_out(c_e_h_3, c_i, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s10)) | (~node22(c_e_h_3, c_i, s9, s10)) | m_and_h_gate_v_out(c_e_h_3, c_i, s9))),
% 291.23/183.74 inference(rewrite,[status(thm)],[])).
% 291.23/183.74 tff(11397,plain,
% 291.23/183.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s10)) | (~node22(c_e_h_3, c_i, s9, s10)) | m_and_h_gate_v_out(c_e_h_3, c_i, s9))),
% 291.23/183.74 inference(quant_inst,[status(thm)],[])).
% 291.23/183.74 tff(11398,plain,
% 291.23/183.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s10)) | (~node22(c_e_h_3, c_i, s9, s10)) | m_and_h_gate_v_out(c_e_h_3, c_i, s9)),
% 291.23/183.74 inference(modus_ponens,[status(thm)],[11397, 11396])).
% 291.23/183.74 tff(11399,plain,
% 291.23/183.74 ($false),
% 291.23/183.74 inference(unit_resolution,[status(thm)],[11398, 108, 11386, 11394, 11395])).
% 291.23/183.74 tff(11400,plain,((~node22(c_e_h_3, c_i, s9, s10)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s10)) | m_and_h_gate_v_out(c_e_h_3, c_i, s9)), inference(lemma,lemma(discharge,[]))).
% 291.23/183.74 tff(11401,plain,
% 291.23/183.74 (~node22(c_e_h_3, c_i, s9, s10)),
% 291.23/183.74 inference(unit_resolution,[status(thm)],[11400, 11386, 11394])).
% 291.23/183.74 tff(11402,plain,
% 291.23/183.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s9, s10)) | node21(c_e_h_3, c_i, s9, s10) | node22(c_e_h_3, c_i, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s9, s10)) | node21(c_e_h_3, c_i, s9, s10) | node22(c_e_h_3, c_i, s9, s10))),
% 291.23/183.74 inference(rewrite,[status(thm)],[])).
% 291.23/183.74 tff(11403,plain,
% 291.23/183.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s9, s10)) | node21(c_e_h_3, c_i, s9, s10) | node22(c_e_h_3, c_i, s9, s10))),
% 291.23/183.74 inference(quant_inst,[status(thm)],[])).
% 291.23/183.74 tff(11404,plain,
% 291.23/183.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s9, s10)) | node21(c_e_h_3, c_i, s9, s10) | node22(c_e_h_3, c_i, s9, s10)),
% 291.23/183.74 inference(modus_ponens,[status(thm)],[11403, 11402])).
% 291.23/183.74 tff(11405,plain,
% 291.23/183.74 (node21(c_e_h_3, c_i, s9, s10) | node22(c_e_h_3, c_i, s9, s10)),
% 291.23/183.74 inference(unit_resolution,[status(thm)],[11404, 82, 7676])).
% 291.23/183.74 tff(11406,plain,
% 291.23/183.74 ($false),
% 291.23/183.74 inference(unit_resolution,[status(thm)],[11405, 11401, 11393])).
% 291.23/183.74 tff(11407,plain,((~m_and_h_gate_v_out(c_e_h_3, c_i, s10)) | m_and_h_gate_v_out(c_e_h_3, c_i, s9) | node20(c_e_h_3, c_i, s9)), inference(lemma,lemma(discharge,[]))).
% 291.23/183.74 tff(11408,plain,
% 291.23/183.74 ((~m_and_h_gate_v_out(c_e_h_3, c_i, s10)) | m_and_h_gate_v_out(c_e_h_3, c_i, s9)),
% 291.23/183.74 inference(unit_resolution,[status(thm)],[11407, 11384])).
% 291.23/183.74 tff(11409,plain,
% 291.23/183.74 (~m_and_h_gate_v_out(c_e_h_3, c_i, s10)),
% 291.23/183.74 inference(unit_resolution,[status(thm)],[11408, 11364])).
% 291.23/183.74 tff(11410,assumption,(~node20(c_e_h_3, c_i, s10)), introduced(assumption)).
% 291.23/183.74 tff(11411,assumption,(m_and_h_gate_v_out(c_e_h_3, c_i, s11)), introduced(assumption)).
% 291.23/183.74 tff(11412,assumption,(node21(c_e_h_3, c_i, s10, s11)), introduced(assumption)).
% 291.23/183.74 tff(11413,plain,
% 291.23/183.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s11)) | node20(c_e_h_3, c_i, s10) | (~node21(c_e_h_3, c_i, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s11)) | node20(c_e_h_3, c_i, s10) | (~node21(c_e_h_3, c_i, s10, s11)))),
% 291.23/183.74 inference(rewrite,[status(thm)],[])).
% 291.23/183.74 tff(11414,plain,
% 291.23/183.74 ((node20(c_e_h_3, c_i, s10) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s11)) | (~node21(c_e_h_3, c_i, s10, s11))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_i, s11)) | node20(c_e_h_3, c_i, s10) | (~node21(c_e_h_3, c_i, s10, s11)))),
% 291.23/183.74 inference(rewrite,[status(thm)],[])).
% 291.23/183.74 tff(11415,plain,
% 291.23/183.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s10) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s11)) | (~node21(c_e_h_3, c_i, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s11)) | node20(c_e_h_3, c_i, s10) | (~node21(c_e_h_3, c_i, s10, s11))))),
% 291.23/183.74 inference(monotonicity,[status(thm)],[11414])).
% 291.23/183.74 tff(11416,plain,
% 291.23/183.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s10) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s11)) | (~node21(c_e_h_3, c_i, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s11)) | node20(c_e_h_3, c_i, s10) | (~node21(c_e_h_3, c_i, s10, s11)))),
% 291.23/183.75 inference(transitivity,[status(thm)],[11415, 11413])).
% 291.23/183.75 tff(11417,plain,
% 291.23/183.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s10) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s11)) | (~node21(c_e_h_3, c_i, s10, s11)))),
% 291.23/183.75 inference(quant_inst,[status(thm)],[])).
% 291.23/183.75 tff(11418,plain,
% 291.23/183.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s11)) | node20(c_e_h_3, c_i, s10) | (~node21(c_e_h_3, c_i, s10, s11))),
% 291.23/183.75 inference(modus_ponens,[status(thm)],[11417, 11416])).
% 291.23/183.75 tff(11419,plain,
% 291.23/183.75 ($false),
% 291.23/183.75 inference(unit_resolution,[status(thm)],[11418, 52, 11411, 11412, 11410])).
% 291.23/183.75 tff(11420,plain,((~node21(c_e_h_3, c_i, s10, s11)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s11)) | node20(c_e_h_3, c_i, s10)), inference(lemma,lemma(discharge,[]))).
% 291.23/183.75 tff(11421,plain,
% 291.23/183.75 (~node21(c_e_h_3, c_i, s10, s11)),
% 291.23/183.75 inference(unit_resolution,[status(thm)],[11420, 11411, 11410])).
% 291.23/183.75 tff(11422,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_i, s10)), introduced(assumption)).
% 291.23/183.75 tff(11423,assumption,(node22(c_e_h_3, c_i, s10, s11)), introduced(assumption)).
% 291.23/183.75 tff(11424,plain,
% 291.23/183.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s11)) | (~node22(c_e_h_3, c_i, s10, s11)) | m_and_h_gate_v_out(c_e_h_3, c_i, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s11)) | (~node22(c_e_h_3, c_i, s10, s11)) | m_and_h_gate_v_out(c_e_h_3, c_i, s10))),
% 291.23/183.75 inference(rewrite,[status(thm)],[])).
% 291.23/183.75 tff(11425,plain,
% 291.23/183.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s11)) | (~node22(c_e_h_3, c_i, s10, s11)) | m_and_h_gate_v_out(c_e_h_3, c_i, s10))),
% 291.23/183.75 inference(quant_inst,[status(thm)],[])).
% 291.23/183.75 tff(11426,plain,
% 291.23/183.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s11)) | (~node22(c_e_h_3, c_i, s10, s11)) | m_and_h_gate_v_out(c_e_h_3, c_i, s10)),
% 291.23/183.75 inference(modus_ponens,[status(thm)],[11425, 11424])).
% 291.23/183.75 tff(11427,plain,
% 291.23/183.75 ($false),
% 291.23/183.75 inference(unit_resolution,[status(thm)],[11426, 108, 11411, 11423, 11422])).
% 291.23/183.75 tff(11428,plain,((~node22(c_e_h_3, c_i, s10, s11)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s11)) | m_and_h_gate_v_out(c_e_h_3, c_i, s10)), inference(lemma,lemma(discharge,[]))).
% 291.23/183.75 tff(11429,plain,
% 291.23/183.75 (~node22(c_e_h_3, c_i, s10, s11)),
% 291.23/183.75 inference(unit_resolution,[status(thm)],[11428, 11411, 11422])).
% 291.23/183.75 tff(11430,plain,
% 291.23/183.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s10, s11)) | node21(c_e_h_3, c_i, s10, s11) | node22(c_e_h_3, c_i, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s10, s11)) | node21(c_e_h_3, c_i, s10, s11) | node22(c_e_h_3, c_i, s10, s11))),
% 291.23/183.75 inference(rewrite,[status(thm)],[])).
% 291.23/183.75 tff(11431,plain,
% 291.23/183.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s10, s11)) | node21(c_e_h_3, c_i, s10, s11) | node22(c_e_h_3, c_i, s10, s11))),
% 291.23/183.75 inference(quant_inst,[status(thm)],[])).
% 291.23/183.75 tff(11432,plain,
% 291.23/183.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s10, s11)) | node21(c_e_h_3, c_i, s10, s11) | node22(c_e_h_3, c_i, s10, s11)),
% 291.23/183.75 inference(modus_ponens,[status(thm)],[11431, 11430])).
% 291.23/183.75 tff(11433,plain,
% 291.23/183.75 (node21(c_e_h_3, c_i, s10, s11) | node22(c_e_h_3, c_i, s10, s11)),
% 291.23/183.75 inference(unit_resolution,[status(thm)],[11432, 82, 7748])).
% 291.23/183.75 tff(11434,plain,
% 291.23/183.75 ($false),
% 291.23/183.75 inference(unit_resolution,[status(thm)],[11433, 11429, 11421])).
% 291.23/183.75 tff(11435,plain,((~m_and_h_gate_v_out(c_e_h_3, c_i, s11)) | m_and_h_gate_v_out(c_e_h_3, c_i, s10) | node20(c_e_h_3, c_i, s10)), inference(lemma,lemma(discharge,[]))).
% 291.23/183.75 tff(11436,plain,
% 291.23/183.75 ((~m_and_h_gate_v_out(c_e_h_3, c_i, s11)) | node20(c_e_h_3, c_i, s10)),
% 291.23/183.75 inference(unit_resolution,[status(thm)],[11435, 11409])).
% 291.23/183.75 tff(11437,plain,
% 291.23/183.75 (~m_and_h_gate_v_out(c_e_h_3, c_i, s11)),
% 291.23/183.75 inference(unit_resolution,[status(thm)],[11436, 11228])).
% 291.23/183.75 tff(11438,assumption,(~node20(c_e_h_3, c_i, s11)), introduced(assumption)).
% 291.23/183.75 tff(11439,assumption,(m_and_h_gate_v_out(c_e_h_3, c_i, s12)), introduced(assumption)).
% 291.23/183.75 tff(11440,assumption,(node21(c_e_h_3, c_i, s11, s12)), introduced(assumption)).
% 291.23/183.75 tff(11441,plain,
% 291.23/183.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s11) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s12)) | (~node21(c_e_h_3, c_i, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_i, s11) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s12)) | (~node21(c_e_h_3, c_i, s11, s12)))),
% 291.23/183.75 inference(rewrite,[status(thm)],[])).
% 291.23/183.75 tff(11442,plain,
% 291.23/183.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s11) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s12)) | (~node21(c_e_h_3, c_i, s11, s12)))),
% 291.23/183.75 inference(quant_inst,[status(thm)],[])).
% 291.23/183.75 tff(11443,plain,
% 291.23/183.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_i, s11) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s12)) | (~node21(c_e_h_3, c_i, s11, s12))),
% 291.23/183.75 inference(modus_ponens,[status(thm)],[11442, 11441])).
% 291.23/183.75 tff(11444,plain,
% 291.23/183.75 ($false),
% 291.23/183.75 inference(unit_resolution,[status(thm)],[11443, 52, 11439, 11440, 11438])).
% 291.23/183.75 tff(11445,plain,((~node21(c_e_h_3, c_i, s11, s12)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s12)) | node20(c_e_h_3, c_i, s11)), inference(lemma,lemma(discharge,[]))).
% 291.23/183.75 tff(11446,plain,
% 291.23/183.75 (~node21(c_e_h_3, c_i, s11, s12)),
% 291.23/183.75 inference(unit_resolution,[status(thm)],[11445, 11439, 11438])).
% 291.23/183.75 tff(11447,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_i, s11)), introduced(assumption)).
% 291.23/183.75 tff(11448,assumption,(node22(c_e_h_3, c_i, s11, s12)), introduced(assumption)).
% 291.23/183.75 tff(11449,plain,
% 291.23/183.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s12)) | (~node22(c_e_h_3, c_i, s11, s12)) | m_and_h_gate_v_out(c_e_h_3, c_i, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s12)) | (~node22(c_e_h_3, c_i, s11, s12)) | m_and_h_gate_v_out(c_e_h_3, c_i, s11))),
% 291.23/183.75 inference(rewrite,[status(thm)],[])).
% 291.23/183.75 tff(11450,plain,
% 291.23/183.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s12)) | (~node22(c_e_h_3, c_i, s11, s12)) | m_and_h_gate_v_out(c_e_h_3, c_i, s11))),
% 291.23/183.75 inference(quant_inst,[status(thm)],[])).
% 291.23/183.75 tff(11451,plain,
% 291.23/183.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s12)) | (~node22(c_e_h_3, c_i, s11, s12)) | m_and_h_gate_v_out(c_e_h_3, c_i, s11)),
% 291.23/183.75 inference(modus_ponens,[status(thm)],[11450, 11449])).
% 291.23/183.75 tff(11452,plain,
% 291.23/183.75 ($false),
% 291.23/183.75 inference(unit_resolution,[status(thm)],[11451, 108, 11447, 11439, 11448])).
% 291.23/183.75 tff(11453,plain,((~node22(c_e_h_3, c_i, s11, s12)) | m_and_h_gate_v_out(c_e_h_3, c_i, s11) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s12))), inference(lemma,lemma(discharge,[]))).
% 291.23/183.75 tff(11454,plain,
% 291.23/183.75 (~node22(c_e_h_3, c_i, s11, s12)),
% 291.23/183.75 inference(unit_resolution,[status(thm)],[11453, 11439, 11447])).
% 291.23/183.75 tff(11455,plain,
% 291.23/183.75 (succ(s11, s12) <=> succ(s11, s12)),
% 291.23/183.75 inference(rewrite,[status(thm)],[])).
% 291.23/183.75 tff(11456,axiom,(succ(s11, s12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound12')).
% 291.23/183.75 tff(11457,plain,
% 291.23/183.75 (succ(s11, s12)),
% 291.23/183.75 inference(modus_ponens,[status(thm)],[11456, 11455])).
% 291.23/183.75 tff(11458,plain,
% 291.23/183.75 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s11, s12)) | trans(s11, s12))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s11, s12)) | trans(s11, s12))),
% 291.23/183.75 inference(rewrite,[status(thm)],[])).
% 291.23/183.75 tff(11459,plain,
% 291.23/183.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s11, s12)) | trans(s11, s12))),
% 291.23/183.75 inference(quant_inst,[status(thm)],[])).
% 291.23/183.75 tff(11460,plain,
% 291.23/183.75 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s11, s12)) | trans(s11, s12)),
% 291.23/183.75 inference(modus_ponens,[status(thm)],[11459, 11458])).
% 291.23/183.75 tff(11461,plain,
% 291.23/183.75 (trans(s11, s12)),
% 291.23/183.75 inference(unit_resolution,[status(thm)],[11460, 11457, 65])).
% 291.23/183.75 tff(11462,plain,
% 291.23/183.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s11, s12)) | node21(c_e_h_3, c_i, s11, s12) | node22(c_e_h_3, c_i, s11, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s11, s12)) | node21(c_e_h_3, c_i, s11, s12) | node22(c_e_h_3, c_i, s11, s12))),
% 291.23/183.75 inference(rewrite,[status(thm)],[])).
% 291.23/183.75 tff(11463,plain,
% 291.23/183.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s11, s12)) | node21(c_e_h_3, c_i, s11, s12) | node22(c_e_h_3, c_i, s11, s12))),
% 291.23/183.75 inference(quant_inst,[status(thm)],[])).
% 291.23/183.75 tff(11464,plain,
% 291.23/183.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s11, s12)) | node21(c_e_h_3, c_i, s11, s12) | node22(c_e_h_3, c_i, s11, s12)),
% 291.23/183.75 inference(modus_ponens,[status(thm)],[11463, 11462])).
% 291.23/183.75 tff(11465,plain,
% 291.23/183.75 (node21(c_e_h_3, c_i, s11, s12) | node22(c_e_h_3, c_i, s11, s12)),
% 291.23/183.75 inference(unit_resolution,[status(thm)],[11464, 82, 11461])).
% 291.23/183.75 tff(11466,plain,
% 291.23/183.75 ($false),
% 291.23/183.75 inference(unit_resolution,[status(thm)],[11465, 11454, 11446])).
% 291.23/183.75 tff(11467,plain,((~m_and_h_gate_v_out(c_e_h_3, c_i, s12)) | m_and_h_gate_v_out(c_e_h_3, c_i, s11) | node20(c_e_h_3, c_i, s11)), inference(lemma,lemma(discharge,[]))).
% 291.23/183.75 tff(11468,plain,
% 291.23/183.75 (~m_and_h_gate_v_out(c_e_h_3, c_i, s12)),
% 291.23/183.75 inference(unit_resolution,[status(thm)],[11467, 11437, 11218])).
% 291.23/183.75 tff(11469,assumption,(m_c_h_element_v_in2(c_e_h_3, c_f, s11)), introduced(assumption)).
% 291.23/183.75 tff(11470,plain,
% 291.23/183.75 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s11)) | m_and_h_gate_v_out(c_e_h_3, c_i, s11))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s11)) | m_and_h_gate_v_out(c_e_h_3, c_i, s11))),
% 291.23/183.75 inference(rewrite,[status(thm)],[])).
% 291.23/183.75 tff(11471,plain,
% 291.23/183.75 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s11)) | m_and_h_gate_v_out(c_e_h_3, c_i, s11))),
% 291.23/183.75 inference(quant_inst,[status(thm)],[])).
% 291.23/183.75 tff(11472,plain,
% 291.23/183.75 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s11)) | m_and_h_gate_v_out(c_e_h_3, c_i, s11)),
% 291.23/183.75 inference(modus_ponens,[status(thm)],[11471, 11470])).
% 291.23/183.75 tff(11473,plain,
% 291.23/183.75 ($false),
% 291.23/183.75 inference(unit_resolution,[status(thm)],[11472, 2143, 11469, 11447])).
% 291.23/183.75 tff(11474,plain,((~m_c_h_element_v_in2(c_e_h_3, c_f, s11)) | m_and_h_gate_v_out(c_e_h_3, c_i, s11)), inference(lemma,lemma(discharge,[]))).
% 291.23/183.75 tff(11475,plain,
% 291.23/183.75 (~m_c_h_element_v_in2(c_e_h_3, c_f, s11)),
% 291.23/183.75 inference(unit_resolution,[status(thm)],[11474, 11437])).
% 291.23/183.75 tff(11476,assumption,(m_c_h_element_v_in2(c_e_h_3, c_f, s9)), introduced(assumption)).
% 291.23/183.76 tff(11477,plain,
% 291.23/183.76 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s9)) | m_and_h_gate_v_out(c_e_h_3, c_i, s9))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s9)) | m_and_h_gate_v_out(c_e_h_3, c_i, s9))),
% 291.23/183.76 inference(rewrite,[status(thm)],[])).
% 291.23/183.76 tff(11478,plain,
% 291.23/183.76 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s9)) | m_and_h_gate_v_out(c_e_h_3, c_i, s9))),
% 291.23/183.76 inference(quant_inst,[status(thm)],[])).
% 291.23/183.76 tff(11479,plain,
% 291.23/183.76 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s9)) | m_and_h_gate_v_out(c_e_h_3, c_i, s9)),
% 291.23/183.76 inference(modus_ponens,[status(thm)],[11478, 11477])).
% 291.23/183.76 tff(11480,plain,
% 291.23/183.76 ($false),
% 291.23/183.76 inference(unit_resolution,[status(thm)],[11479, 2143, 11476, 11394])).
% 291.23/183.76 tff(11481,plain,((~m_c_h_element_v_in2(c_e_h_3, c_f, s9)) | m_and_h_gate_v_out(c_e_h_3, c_i, s9)), inference(lemma,lemma(discharge,[]))).
% 291.23/183.76 tff(11482,plain,
% 291.23/183.76 (~m_c_h_element_v_in2(c_e_h_3, c_f, s9)),
% 291.23/183.76 inference(unit_resolution,[status(thm)],[11481, 11364])).
% 291.23/183.76 tff(11483,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_i, s8)), introduced(assumption)).
% 291.23/183.76 tff(11484,assumption,(m_c_h_element_v_in2(c_e_h_3, c_f, s8)), introduced(assumption)).
% 291.23/183.76 tff(11485,plain,
% 291.23/183.76 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s8)) | m_and_h_gate_v_out(c_e_h_3, c_i, s8))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s8)) | m_and_h_gate_v_out(c_e_h_3, c_i, s8))),
% 291.23/183.76 inference(rewrite,[status(thm)],[])).
% 291.23/183.76 tff(11486,plain,
% 291.23/183.76 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s8)) | m_and_h_gate_v_out(c_e_h_3, c_i, s8))),
% 291.23/183.76 inference(quant_inst,[status(thm)],[])).
% 291.23/183.76 tff(11487,plain,
% 291.23/183.76 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s8)) | m_and_h_gate_v_out(c_e_h_3, c_i, s8)),
% 291.23/183.76 inference(modus_ponens,[status(thm)],[11486, 11485])).
% 291.23/183.76 tff(11488,plain,
% 291.23/183.76 ($false),
% 291.23/183.76 inference(unit_resolution,[status(thm)],[11487, 2143, 11484, 11483])).
% 291.23/183.76 tff(11489,plain,((~m_c_h_element_v_in2(c_e_h_3, c_f, s8)) | m_and_h_gate_v_out(c_e_h_3, c_i, s8)), inference(lemma,lemma(discharge,[]))).
% 291.23/183.76 tff(11490,plain,
% 291.23/183.76 (~m_c_h_element_v_in2(c_e_h_3, c_f, s8)),
% 291.23/183.76 inference(unit_resolution,[status(thm)],[11489, 11344])).
% 291.23/183.76 tff(11491,assumption,(m_c_h_element_v_out(c_e_h_3, c_f, s9)), introduced(assumption)).
% 291.23/183.76 tff(11492,plain,
% 291.23/183.76 (~m_c_h_element_v_in2(c_e_h_3, c_f, s7)),
% 291.23/183.76 inference(unit_resolution,[status(thm)],[9397, 11317])).
% 291.23/183.76 tff(11493,plain,
% 291.23/183.76 ((~m_c_h_element_v_out(c_e_h_3, c_f, s8)) | m_c_h_element_v_in2(c_e_h_3, c_f, s7)),
% 291.23/183.76 inference(unit_resolution,[status(thm)],[9247, 10824])).
% 291.23/183.76 tff(11494,plain,
% 291.23/183.76 (~m_c_h_element_v_out(c_e_h_3, c_f, s8)),
% 291.23/183.76 inference(unit_resolution,[status(thm)],[11493, 11492])).
% 291.23/183.76 tff(11495,assumption,(~m_c_h_element_v_out(c_e_h_3, c_f, s8)), introduced(assumption)).
% 291.23/183.76 tff(11496,assumption,(node18(c_e_h_3, c_f, s8, s9)), introduced(assumption)).
% 291.23/183.76 tff(11497,plain,
% 291.23/183.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_f, s8) | (~m_c_h_element_v_out(c_e_h_3, c_f, s9)) | (~node18(c_e_h_3, c_f, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s8) | (~m_c_h_element_v_out(c_e_h_3, c_f, s9)) | (~node18(c_e_h_3, c_f, s8, s9)))),
% 291.23/183.76 inference(rewrite,[status(thm)],[])).
% 291.23/183.76 tff(11498,plain,
% 291.23/183.76 (((~m_c_h_element_v_out(c_e_h_3, c_f, s9)) | m_c_h_element_v_out(c_e_h_3, c_f, s8) | (~node18(c_e_h_3, c_f, s8, s9))) <=> (m_c_h_element_v_out(c_e_h_3, c_f, s8) | (~m_c_h_element_v_out(c_e_h_3, c_f, s9)) | (~node18(c_e_h_3, c_f, s8, s9)))),
% 291.23/183.76 inference(rewrite,[status(thm)],[])).
% 291.23/183.76 tff(11499,plain,
% 291.23/183.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s9)) | m_c_h_element_v_out(c_e_h_3, c_f, s8) | (~node18(c_e_h_3, c_f, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_f, s8) | (~m_c_h_element_v_out(c_e_h_3, c_f, s9)) | (~node18(c_e_h_3, c_f, s8, s9))))),
% 291.23/183.76 inference(monotonicity,[status(thm)],[11498])).
% 291.23/183.76 tff(11500,plain,
% 291.23/183.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s9)) | m_c_h_element_v_out(c_e_h_3, c_f, s8) | (~node18(c_e_h_3, c_f, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s8) | (~m_c_h_element_v_out(c_e_h_3, c_f, s9)) | (~node18(c_e_h_3, c_f, s8, s9)))),
% 291.23/183.76 inference(transitivity,[status(thm)],[11499, 11497])).
% 291.23/183.76 tff(11501,plain,
% 291.23/183.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s9)) | m_c_h_element_v_out(c_e_h_3, c_f, s8) | (~node18(c_e_h_3, c_f, s8, s9)))),
% 291.23/183.76 inference(quant_inst,[status(thm)],[])).
% 291.23/183.76 tff(11502,plain,
% 291.23/183.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s8) | (~m_c_h_element_v_out(c_e_h_3, c_f, s9)) | (~node18(c_e_h_3, c_f, s8, s9))),
% 291.23/183.76 inference(modus_ponens,[status(thm)],[11501, 11500])).
% 291.23/183.76 tff(11503,plain,
% 291.23/183.76 ($false),
% 291.23/183.76 inference(unit_resolution,[status(thm)],[11502, 753, 11495, 11491, 11496])).
% 291.23/183.76 tff(11504,plain,((~node18(c_e_h_3, c_f, s8, s9)) | m_c_h_element_v_out(c_e_h_3, c_f, s8) | (~m_c_h_element_v_out(c_e_h_3, c_f, s9))), inference(lemma,lemma(discharge,[]))).
% 291.23/183.76 tff(11505,plain,
% 291.23/183.76 (~node18(c_e_h_3, c_f, s8, s9)),
% 291.23/183.76 inference(unit_resolution,[status(thm)],[11504, 11491, 11495])).
% 291.23/183.76 tff(11506,plain,
% 291.23/183.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s8, s9)) | node19(c_e_h_3, c_f, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s8, s9)) | node19(c_e_h_3, c_f, s8, s9))),
% 291.23/183.76 inference(rewrite,[status(thm)],[])).
% 291.23/183.76 tff(11507,plain,
% 291.23/183.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s8, s9)) | node19(c_e_h_3, c_f, s8, s9))),
% 291.23/183.76 inference(quant_inst,[status(thm)],[])).
% 291.23/183.76 tff(11508,plain,
% 291.23/183.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s8, s9)) | node19(c_e_h_3, c_f, s8, s9)),
% 291.23/183.76 inference(modus_ponens,[status(thm)],[11507, 11506])).
% 291.23/183.76 tff(11509,plain,
% 291.23/183.76 (node19(c_e_h_3, c_f, s8, s9)),
% 291.23/183.76 inference(unit_resolution,[status(thm)],[11508, 190, 1993])).
% 291.23/183.76 tff(11510,plain,
% 291.23/183.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s8) | (~node19(c_e_h_3, c_f, s8, s9)) | node18(c_e_h_3, c_f, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_f, s8) | (~node19(c_e_h_3, c_f, s8, s9)) | node18(c_e_h_3, c_f, s8, s9))),
% 291.23/183.76 inference(rewrite,[status(thm)],[])).
% 291.23/183.76 tff(11511,plain,
% 291.23/183.76 ((node17(c_e_h_3, c_f, s8) | node18(c_e_h_3, c_f, s8, s9) | (~node19(c_e_h_3, c_f, s8, s9))) <=> (node17(c_e_h_3, c_f, s8) | (~node19(c_e_h_3, c_f, s8, s9)) | node18(c_e_h_3, c_f, s8, s9))),
% 291.23/183.76 inference(rewrite,[status(thm)],[])).
% 291.23/183.76 tff(11512,plain,
% 291.23/183.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s8) | node18(c_e_h_3, c_f, s8, s9) | (~node19(c_e_h_3, c_f, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s8) | (~node19(c_e_h_3, c_f, s8, s9)) | node18(c_e_h_3, c_f, s8, s9)))),
% 291.23/183.77 inference(monotonicity,[status(thm)],[11511])).
% 291.23/183.77 tff(11513,plain,
% 291.23/183.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s8) | node18(c_e_h_3, c_f, s8, s9) | (~node19(c_e_h_3, c_f, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_f, s8) | (~node19(c_e_h_3, c_f, s8, s9)) | node18(c_e_h_3, c_f, s8, s9))),
% 291.23/183.77 inference(transitivity,[status(thm)],[11512, 11510])).
% 291.23/183.77 tff(11514,plain,
% 291.23/183.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s8) | node18(c_e_h_3, c_f, s8, s9) | (~node19(c_e_h_3, c_f, s8, s9)))),
% 291.23/183.77 inference(quant_inst,[status(thm)],[])).
% 291.23/183.77 tff(11515,plain,
% 291.23/183.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_f, s8) | (~node19(c_e_h_3, c_f, s8, s9)) | node18(c_e_h_3, c_f, s8, s9)),
% 291.23/183.77 inference(modus_ponens,[status(thm)],[11514, 11513])).
% 291.23/183.77 tff(11516,plain,
% 291.23/183.77 (node17(c_e_h_3, c_f, s8) | node18(c_e_h_3, c_f, s8, s9)),
% 291.23/183.77 inference(unit_resolution,[status(thm)],[11515, 776, 11509])).
% 291.23/183.77 tff(11517,plain,
% 291.23/183.77 (node17(c_e_h_3, c_f, s8)),
% 291.23/183.77 inference(unit_resolution,[status(thm)],[11516, 11505])).
% 291.23/183.77 tff(11518,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_f, s8)), introduced(assumption)).
% 291.23/183.77 tff(11519,assumption,(node14(c_e_h_3, c_f, s8, s9)), introduced(assumption)).
% 291.23/183.77 tff(11520,plain,
% 291.23/183.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s9)) | m_c_h_element_v_in1(c_e_h_3, c_f, s8) | (~node14(c_e_h_3, c_f, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s9)) | m_c_h_element_v_in1(c_e_h_3, c_f, s8) | (~node14(c_e_h_3, c_f, s8, s9)))),
% 291.23/183.77 inference(rewrite,[status(thm)],[])).
% 291.23/183.77 tff(11521,plain,
% 291.23/183.77 (((~node14(c_e_h_3, c_f, s8, s9)) | m_c_h_element_v_in1(c_e_h_3, c_f, s8) | (~m_c_h_element_v_out(c_e_h_3, c_f, s9))) <=> ((~m_c_h_element_v_out(c_e_h_3, c_f, s9)) | m_c_h_element_v_in1(c_e_h_3, c_f, s8) | (~node14(c_e_h_3, c_f, s8, s9)))),
% 291.23/183.77 inference(rewrite,[status(thm)],[])).
% 291.23/183.77 tff(11522,plain,
% 291.23/183.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s8, s9)) | m_c_h_element_v_in1(c_e_h_3, c_f, s8) | (~m_c_h_element_v_out(c_e_h_3, c_f, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s9)) | m_c_h_element_v_in1(c_e_h_3, c_f, s8) | (~node14(c_e_h_3, c_f, s8, s9))))),
% 291.23/183.77 inference(monotonicity,[status(thm)],[11521])).
% 291.23/183.77 tff(11523,plain,
% 291.23/183.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s8, s9)) | m_c_h_element_v_in1(c_e_h_3, c_f, s8) | (~m_c_h_element_v_out(c_e_h_3, c_f, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s9)) | m_c_h_element_v_in1(c_e_h_3, c_f, s8) | (~node14(c_e_h_3, c_f, s8, s9)))),
% 291.23/183.77 inference(transitivity,[status(thm)],[11522, 11520])).
% 291.23/183.77 tff(11524,plain,
% 291.23/183.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s8, s9)) | m_c_h_element_v_in1(c_e_h_3, c_f, s8) | (~m_c_h_element_v_out(c_e_h_3, c_f, s9)))),
% 291.23/183.77 inference(quant_inst,[status(thm)],[])).
% 291.23/183.77 tff(11525,plain,
% 291.23/183.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s9)) | m_c_h_element_v_in1(c_e_h_3, c_f, s8) | (~node14(c_e_h_3, c_f, s8, s9))),
% 291.23/183.77 inference(modus_ponens,[status(thm)],[11524, 11523])).
% 291.23/183.77 tff(11526,plain,
% 291.23/183.77 ($false),
% 291.23/183.77 inference(unit_resolution,[status(thm)],[11525, 223, 11491, 11519, 11518])).
% 291.23/183.77 tff(11527,plain,((~node14(c_e_h_3, c_f, s8, s9)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s9)) | m_c_h_element_v_in1(c_e_h_3, c_f, s8)), inference(lemma,lemma(discharge,[]))).
% 291.23/183.77 tff(11528,plain,
% 291.23/183.77 (~node14(c_e_h_3, c_f, s8, s9)),
% 291.23/183.77 inference(unit_resolution,[status(thm)],[11527, 11491, 11518])).
% 291.23/183.77 tff(11529,assumption,(node15(c_e_h_3, c_f, s8, s9)), introduced(assumption)).
% 291.23/183.77 tff(11530,plain,
% 291.23/183.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s9)) | (~node15(c_e_h_3, c_f, s8, s9)) | m_c_h_element_v_out(c_e_h_3, c_f, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s9)) | (~node15(c_e_h_3, c_f, s8, s9)) | m_c_h_element_v_out(c_e_h_3, c_f, s8))),
% 291.23/183.77 inference(rewrite,[status(thm)],[])).
% 291.23/183.77 tff(11531,plain,
% 291.23/183.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s9)) | (~node15(c_e_h_3, c_f, s8, s9)) | m_c_h_element_v_out(c_e_h_3, c_f, s8))),
% 291.23/183.77 inference(quant_inst,[status(thm)],[])).
% 291.23/183.77 tff(11532,plain,
% 291.23/183.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s9)) | (~node15(c_e_h_3, c_f, s8, s9)) | m_c_h_element_v_out(c_e_h_3, c_f, s8)),
% 291.23/183.77 inference(modus_ponens,[status(thm)],[11531, 11530])).
% 291.23/183.77 tff(11533,plain,
% 291.23/183.77 ($false),
% 291.23/183.77 inference(unit_resolution,[status(thm)],[11532, 147, 11495, 11491, 11529])).
% 291.23/183.77 tff(11534,plain,((~node15(c_e_h_3, c_f, s8, s9)) | m_c_h_element_v_out(c_e_h_3, c_f, s8) | (~m_c_h_element_v_out(c_e_h_3, c_f, s9))), inference(lemma,lemma(discharge,[]))).
% 291.23/183.77 tff(11535,plain,
% 291.23/183.77 (~node15(c_e_h_3, c_f, s8, s9)),
% 291.23/183.77 inference(unit_resolution,[status(thm)],[11534, 11491, 11495])).
% 291.23/183.77 tff(11536,plain,
% 291.23/183.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s8) | (~node19(c_e_h_3, c_f, s8, s9)) | node15(c_e_h_3, c_f, s8, s9) | node14(c_e_h_3, c_f, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_f, s8) | (~node19(c_e_h_3, c_f, s8, s9)) | node15(c_e_h_3, c_f, s8, s9) | node14(c_e_h_3, c_f, s8, s9))),
% 291.23/183.77 inference(rewrite,[status(thm)],[])).
% 291.23/183.77 tff(11537,plain,
% 291.23/183.77 ((node16(c_e_h_3, c_f, s8) | node14(c_e_h_3, c_f, s8, s9) | node15(c_e_h_3, c_f, s8, s9) | (~node19(c_e_h_3, c_f, s8, s9))) <=> (node16(c_e_h_3, c_f, s8) | (~node19(c_e_h_3, c_f, s8, s9)) | node15(c_e_h_3, c_f, s8, s9) | node14(c_e_h_3, c_f, s8, s9))),
% 291.23/183.77 inference(rewrite,[status(thm)],[])).
% 291.23/183.77 tff(11538,plain,
% 291.23/183.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s8) | node14(c_e_h_3, c_f, s8, s9) | node15(c_e_h_3, c_f, s8, s9) | (~node19(c_e_h_3, c_f, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s8) | (~node19(c_e_h_3, c_f, s8, s9)) | node15(c_e_h_3, c_f, s8, s9) | node14(c_e_h_3, c_f, s8, s9)))),
% 291.23/183.77 inference(monotonicity,[status(thm)],[11537])).
% 291.23/183.77 tff(11539,plain,
% 291.23/183.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s8) | node14(c_e_h_3, c_f, s8, s9) | node15(c_e_h_3, c_f, s8, s9) | (~node19(c_e_h_3, c_f, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_f, s8) | (~node19(c_e_h_3, c_f, s8, s9)) | node15(c_e_h_3, c_f, s8, s9) | node14(c_e_h_3, c_f, s8, s9))),
% 291.23/183.77 inference(transitivity,[status(thm)],[11538, 11536])).
% 291.23/183.77 tff(11540,plain,
% 291.23/183.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s8) | node14(c_e_h_3, c_f, s8, s9) | node15(c_e_h_3, c_f, s8, s9) | (~node19(c_e_h_3, c_f, s8, s9)))),
% 291.23/183.77 inference(quant_inst,[status(thm)],[])).
% 291.23/183.77 tff(11541,plain,
% 291.23/183.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_f, s8) | (~node19(c_e_h_3, c_f, s8, s9)) | node15(c_e_h_3, c_f, s8, s9) | node14(c_e_h_3, c_f, s8, s9)),
% 291.23/183.77 inference(modus_ponens,[status(thm)],[11540, 11539])).
% 291.23/183.77 tff(11542,plain,
% 291.23/183.77 (node16(c_e_h_3, c_f, s8) | node15(c_e_h_3, c_f, s8, s9) | node14(c_e_h_3, c_f, s8, s9)),
% 291.23/183.77 inference(unit_resolution,[status(thm)],[11541, 204, 11509])).
% 291.23/183.77 tff(11543,plain,
% 291.23/183.77 (node16(c_e_h_3, c_f, s8)),
% 291.23/183.77 inference(unit_resolution,[status(thm)],[11542, 11535, 11528])).
% 291.23/183.77 tff(11544,assumption,(node17(c_e_h_3, c_f, s8)), introduced(assumption)).
% 291.23/183.77 tff(11545,assumption,(node16(c_e_h_3, c_f, s8)), introduced(assumption)).
% 291.23/183.77 tff(11546,plain,
% 291.23/183.77 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s8) | (~node17(c_e_h_3, c_f, s8)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_3, c_f, s8) | (~node17(c_e_h_3, c_f, s8)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s8)))),
% 291.23/183.77 inference(rewrite,[status(thm)],[])).
% 291.23/183.77 tff(11547,plain,
% 291.23/183.77 ((m_c_h_element_v_in1(c_e_h_3, c_f, s8) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s8)) | (~node17(c_e_h_3, c_f, s8))) <=> (m_c_h_element_v_in1(c_e_h_3, c_f, s8) | (~node17(c_e_h_3, c_f, s8)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s8)))),
% 291.23/183.77 inference(rewrite,[status(thm)],[])).
% 291.23/183.77 tff(11548,plain,
% 291.23/183.77 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s8) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s8)) | (~node17(c_e_h_3, c_f, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s8) | (~node17(c_e_h_3, c_f, s8)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s8))))),
% 291.23/183.77 inference(monotonicity,[status(thm)],[11547])).
% 291.23/183.77 tff(11549,plain,
% 291.23/183.77 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s8) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s8)) | (~node17(c_e_h_3, c_f, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_3, c_f, s8) | (~node17(c_e_h_3, c_f, s8)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s8)))),
% 291.23/183.77 inference(transitivity,[status(thm)],[11548, 11546])).
% 291.23/183.77 tff(11550,plain,
% 291.23/183.77 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s8) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s8)) | (~node17(c_e_h_3, c_f, s8)))),
% 291.23/183.77 inference(quant_inst,[status(thm)],[])).
% 291.23/183.77 tff(11551,plain,
% 291.23/183.77 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_3, c_f, s8) | (~node17(c_e_h_3, c_f, s8)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s8))),
% 291.23/183.78 inference(modus_ponens,[status(thm)],[11550, 11549])).
% 291.23/183.78 tff(11552,plain,
% 291.23/183.78 (m_c_h_element_v_in1(c_e_h_3, c_f, s8) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s8))),
% 291.23/183.78 inference(unit_resolution,[status(thm)],[11551, 859, 11544])).
% 291.23/183.78 tff(11553,plain,
% 291.23/183.78 (~m_c_h_element_v_in2(c_e_h_3, c_f, s8)),
% 291.23/183.78 inference(unit_resolution,[status(thm)],[11552, 11518])).
% 291.23/183.78 tff(11554,plain,
% 291.23/183.78 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s8)) | m_c_h_element_v_in1(c_e_h_3, c_f, s8) | m_c_h_element_v_in2(c_e_h_3, c_f, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s8)) | m_c_h_element_v_in1(c_e_h_3, c_f, s8) | m_c_h_element_v_in2(c_e_h_3, c_f, s8))),
% 291.23/183.78 inference(rewrite,[status(thm)],[])).
% 291.23/183.78 tff(11555,plain,
% 291.23/183.78 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s8)) | m_c_h_element_v_in1(c_e_h_3, c_f, s8) | m_c_h_element_v_in2(c_e_h_3, c_f, s8))),
% 291.23/183.78 inference(quant_inst,[status(thm)],[])).
% 291.23/183.78 tff(11556,plain,
% 291.23/183.78 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s8)) | m_c_h_element_v_in1(c_e_h_3, c_f, s8) | m_c_h_element_v_in2(c_e_h_3, c_f, s8)),
% 291.23/183.78 inference(modus_ponens,[status(thm)],[11555, 11554])).
% 291.23/183.78 tff(11557,plain,
% 291.23/183.78 (m_c_h_element_v_in1(c_e_h_3, c_f, s8) | m_c_h_element_v_in2(c_e_h_3, c_f, s8)),
% 291.23/183.78 inference(unit_resolution,[status(thm)],[11556, 178, 11545])).
% 291.23/183.78 tff(11558,plain,
% 291.23/183.78 ($false),
% 291.23/183.78 inference(unit_resolution,[status(thm)],[11557, 11553, 11518])).
% 291.23/183.78 tff(11559,plain,(m_c_h_element_v_in1(c_e_h_3, c_f, s8) | (~node16(c_e_h_3, c_f, s8)) | (~node17(c_e_h_3, c_f, s8))), inference(lemma,lemma(discharge,[]))).
% 291.23/183.78 tff(11560,plain,
% 291.23/183.78 (m_c_h_element_v_in1(c_e_h_3, c_f, s8)),
% 291.23/183.78 inference(unit_resolution,[status(thm)],[11559, 11545, 11544])).
% 291.23/183.78 tff(11561,plain,
% 291.23/183.78 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s8)) | m_c_h_element_v_in2(c_e_h_3, c_f, s8) | (~node17(c_e_h_3, c_f, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s8)) | m_c_h_element_v_in2(c_e_h_3, c_f, s8) | (~node17(c_e_h_3, c_f, s8)))),
% 291.23/183.78 inference(rewrite,[status(thm)],[])).
% 291.23/183.78 tff(11562,plain,
% 291.23/183.78 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s8)) | m_c_h_element_v_in2(c_e_h_3, c_f, s8) | (~node17(c_e_h_3, c_f, s8)))),
% 291.23/183.78 inference(quant_inst,[status(thm)],[])).
% 291.23/183.78 tff(11563,plain,
% 291.23/183.78 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s8)) | m_c_h_element_v_in2(c_e_h_3, c_f, s8) | (~node17(c_e_h_3, c_f, s8))),
% 291.23/183.78 inference(modus_ponens,[status(thm)],[11562, 11561])).
% 291.23/183.78 tff(11564,plain,
% 291.23/183.78 ((~m_c_h_element_v_in1(c_e_h_3, c_f, s8)) | m_c_h_element_v_in2(c_e_h_3, c_f, s8)),
% 291.23/183.78 inference(unit_resolution,[status(thm)],[11563, 919, 11544])).
% 291.23/183.78 tff(11565,plain,
% 291.23/183.78 (m_c_h_element_v_in2(c_e_h_3, c_f, s8)),
% 291.23/183.78 inference(unit_resolution,[status(thm)],[11564, 11560])).
% 291.23/183.78 tff(11566,plain,
% 291.23/183.78 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_f, s8)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s8)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~node16(c_e_h_3, c_f, s8)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s8)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s8)))),
% 291.23/183.78 inference(rewrite,[status(thm)],[])).
% 291.23/183.78 tff(11567,plain,
% 291.23/183.78 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_f, s8)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s8)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s8)))),
% 291.23/183.78 inference(quant_inst,[status(thm)],[])).
% 291.23/183.78 tff(11568,plain,
% 291.23/183.78 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~node16(c_e_h_3, c_f, s8)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s8)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s8))),
% 291.23/183.78 inference(modus_ponens,[status(thm)],[11567, 11566])).
% 291.23/183.78 tff(11569,plain,
% 291.23/183.78 ((~m_c_h_element_v_in1(c_e_h_3, c_f, s8)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s8))),
% 291.23/183.78 inference(unit_resolution,[status(thm)],[11568, 2307, 11545])).
% 291.23/183.78 tff(11570,plain,
% 291.23/183.78 ($false),
% 291.23/183.78 inference(unit_resolution,[status(thm)],[11569, 11565, 11560])).
% 291.23/183.78 tff(11571,plain,((~node16(c_e_h_3, c_f, s8)) | (~node17(c_e_h_3, c_f, s8))), inference(lemma,lemma(discharge,[]))).
% 291.23/183.78 tff(11572,plain,
% 291.23/183.78 ($false),
% 291.23/183.78 inference(unit_resolution,[status(thm)],[11571, 11543, 11517])).
% 291.23/183.78 tff(11573,plain,((~m_c_h_element_v_out(c_e_h_3, c_f, s9)) | m_c_h_element_v_out(c_e_h_3, c_f, s8) | m_c_h_element_v_in1(c_e_h_3, c_f, s8)), inference(lemma,lemma(discharge,[]))).
% 291.23/183.78 tff(11574,plain,
% 291.23/183.78 ((~m_c_h_element_v_out(c_e_h_3, c_f, s9)) | m_c_h_element_v_in1(c_e_h_3, c_f, s8)),
% 291.23/183.78 inference(unit_resolution,[status(thm)],[11573, 11494])).
% 291.23/183.78 tff(11575,plain,
% 291.23/183.78 (m_c_h_element_v_in1(c_e_h_3, c_f, s8)),
% 291.23/183.78 inference(unit_resolution,[status(thm)],[11574, 11491])).
% 291.23/183.78 tff(11576,plain,
% 291.23/183.78 ((~node18(c_e_h_3, c_f, s8, s9)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s9))),
% 291.23/183.78 inference(unit_resolution,[status(thm)],[11504, 11494])).
% 291.23/183.78 tff(11577,plain,
% 291.23/183.78 (~node18(c_e_h_3, c_f, s8, s9)),
% 291.23/183.78 inference(unit_resolution,[status(thm)],[11576, 11491])).
% 291.23/183.78 tff(11578,plain,
% 291.23/183.78 (node17(c_e_h_3, c_f, s8)),
% 291.23/183.78 inference(unit_resolution,[status(thm)],[11516, 11577])).
% 291.23/183.78 tff(11579,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_f, s8)), introduced(assumption)).
% 291.23/183.78 tff(11580,plain,
% 291.23/183.78 ((~m_c_h_element_v_in1(c_e_h_3, c_f, s8)) | (~node17(c_e_h_3, c_f, s8))),
% 291.23/183.78 inference(unit_resolution,[status(thm)],[11563, 919, 11579])).
% 291.23/183.78 tff(11581,plain,
% 291.23/183.78 ($false),
% 291.23/183.78 inference(unit_resolution,[status(thm)],[11580, 11578, 11575])).
% 291.23/183.78 tff(11582,plain,((~m_c_h_element_v_out(c_e_h_3, c_f, s9)) | m_c_h_element_v_in2(c_e_h_3, c_f, s8)), inference(lemma,lemma(discharge,[]))).
% 291.23/183.78 tff(11583,plain,
% 291.23/183.78 (~m_c_h_element_v_out(c_e_h_3, c_f, s9)),
% 291.23/183.78 inference(unit_resolution,[status(thm)],[11582, 11490])).
% 291.23/183.78 tff(11584,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_f, s9)), introduced(assumption)).
% 291.23/183.78 tff(11585,assumption,(m_c_h_element_v_out(c_e_h_3, c_f, s10)), introduced(assumption)).
% 291.23/183.78 tff(11586,assumption,(~m_c_h_element_v_out(c_e_h_3, c_f, s9)), introduced(assumption)).
% 291.23/183.78 tff(11587,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_f, s9)), introduced(assumption)).
% 291.23/183.78 tff(11588,assumption,(~node16(c_e_h_3, c_f, s9)), introduced(assumption)).
% 291.23/183.78 tff(11589,assumption,(node14(c_e_h_3, c_f, s9, s10)), introduced(assumption)).
% 291.23/183.78 tff(11590,plain,
% 291.23/183.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s10)) | (~node14(c_e_h_3, c_f, s9, s10)) | m_c_h_element_v_in1(c_e_h_3, c_f, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s10)) | (~node14(c_e_h_3, c_f, s9, s10)) | m_c_h_element_v_in1(c_e_h_3, c_f, s9))),
% 291.23/183.78 inference(rewrite,[status(thm)],[])).
% 291.23/183.78 tff(11591,plain,
% 291.23/183.78 (((~node14(c_e_h_3, c_f, s9, s10)) | m_c_h_element_v_in1(c_e_h_3, c_f, s9) | (~m_c_h_element_v_out(c_e_h_3, c_f, s10))) <=> ((~m_c_h_element_v_out(c_e_h_3, c_f, s10)) | (~node14(c_e_h_3, c_f, s9, s10)) | m_c_h_element_v_in1(c_e_h_3, c_f, s9))),
% 291.31/183.80 inference(rewrite,[status(thm)],[])).
% 291.31/183.80 tff(11592,plain,
% 291.31/183.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s9, s10)) | m_c_h_element_v_in1(c_e_h_3, c_f, s9) | (~m_c_h_element_v_out(c_e_h_3, c_f, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s10)) | (~node14(c_e_h_3, c_f, s9, s10)) | m_c_h_element_v_in1(c_e_h_3, c_f, s9)))),
% 291.31/183.80 inference(monotonicity,[status(thm)],[11591])).
% 291.31/183.80 tff(11593,plain,
% 291.31/183.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s9, s10)) | m_c_h_element_v_in1(c_e_h_3, c_f, s9) | (~m_c_h_element_v_out(c_e_h_3, c_f, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s10)) | (~node14(c_e_h_3, c_f, s9, s10)) | m_c_h_element_v_in1(c_e_h_3, c_f, s9))),
% 291.31/183.80 inference(transitivity,[status(thm)],[11592, 11590])).
% 291.31/183.80 tff(11594,plain,
% 291.31/183.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s9, s10)) | m_c_h_element_v_in1(c_e_h_3, c_f, s9) | (~m_c_h_element_v_out(c_e_h_3, c_f, s10)))),
% 291.31/183.80 inference(quant_inst,[status(thm)],[])).
% 291.31/183.80 tff(11595,plain,
% 291.31/183.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s10)) | (~node14(c_e_h_3, c_f, s9, s10)) | m_c_h_element_v_in1(c_e_h_3, c_f, s9)),
% 291.31/183.80 inference(modus_ponens,[status(thm)],[11594, 11593])).
% 291.31/183.80 tff(11596,plain,
% 291.31/183.80 ($false),
% 291.31/183.80 inference(unit_resolution,[status(thm)],[11595, 223, 11585, 11589, 11587])).
% 291.31/183.80 tff(11597,plain,((~node14(c_e_h_3, c_f, s9, s10)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s10)) | m_c_h_element_v_in1(c_e_h_3, c_f, s9)), inference(lemma,lemma(discharge,[]))).
% 291.31/183.80 tff(11598,plain,
% 291.31/183.80 (~node14(c_e_h_3, c_f, s9, s10)),
% 291.31/183.80 inference(unit_resolution,[status(thm)],[11597, 11585, 11587])).
% 291.31/183.80 tff(11599,plain,
% 291.31/183.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s9, s10)) | node19(c_e_h_3, c_f, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s9, s10)) | node19(c_e_h_3, c_f, s9, s10))),
% 291.31/183.80 inference(rewrite,[status(thm)],[])).
% 291.31/183.80 tff(11600,plain,
% 291.31/183.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s9, s10)) | node19(c_e_h_3, c_f, s9, s10))),
% 291.31/183.80 inference(quant_inst,[status(thm)],[])).
% 291.31/183.80 tff(11601,plain,
% 291.31/183.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s9, s10)) | node19(c_e_h_3, c_f, s9, s10)),
% 291.31/183.80 inference(modus_ponens,[status(thm)],[11600, 11599])).
% 291.31/183.80 tff(11602,plain,
% 291.31/183.80 (node19(c_e_h_3, c_f, s9, s10)),
% 291.31/183.80 inference(unit_resolution,[status(thm)],[11601, 190, 7676])).
% 291.31/183.80 tff(11603,plain,
% 291.31/183.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_f, s9, s10)) | node14(c_e_h_3, c_f, s9, s10) | node15(c_e_h_3, c_f, s9, s10) | node16(c_e_h_3, c_f, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s9, s10)) | node14(c_e_h_3, c_f, s9, s10) | node15(c_e_h_3, c_f, s9, s10) | node16(c_e_h_3, c_f, s9))),
% 291.31/183.80 inference(rewrite,[status(thm)],[])).
% 291.31/183.80 tff(11604,plain,
% 291.31/183.80 ((node16(c_e_h_3, c_f, s9) | node14(c_e_h_3, c_f, s9, s10) | node15(c_e_h_3, c_f, s9, s10) | (~node19(c_e_h_3, c_f, s9, s10))) <=> ((~node19(c_e_h_3, c_f, s9, s10)) | node14(c_e_h_3, c_f, s9, s10) | node15(c_e_h_3, c_f, s9, s10) | node16(c_e_h_3, c_f, s9))),
% 291.31/183.80 inference(rewrite,[status(thm)],[])).
% 291.31/183.80 tff(11605,plain,
% 291.31/183.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s9) | node14(c_e_h_3, c_f, s9, s10) | node15(c_e_h_3, c_f, s9, s10) | (~node19(c_e_h_3, c_f, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_f, s9, s10)) | node14(c_e_h_3, c_f, s9, s10) | node15(c_e_h_3, c_f, s9, s10) | node16(c_e_h_3, c_f, s9)))),
% 291.31/183.80 inference(monotonicity,[status(thm)],[11604])).
% 291.31/183.80 tff(11606,plain,
% 291.31/183.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s9) | node14(c_e_h_3, c_f, s9, s10) | node15(c_e_h_3, c_f, s9, s10) | (~node19(c_e_h_3, c_f, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s9, s10)) | node14(c_e_h_3, c_f, s9, s10) | node15(c_e_h_3, c_f, s9, s10) | node16(c_e_h_3, c_f, s9))),
% 291.31/183.80 inference(transitivity,[status(thm)],[11605, 11603])).
% 291.31/183.80 tff(11607,plain,
% 291.31/183.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s9) | node14(c_e_h_3, c_f, s9, s10) | node15(c_e_h_3, c_f, s9, s10) | (~node19(c_e_h_3, c_f, s9, s10)))),
% 291.31/183.80 inference(quant_inst,[status(thm)],[])).
% 291.31/183.80 tff(11608,plain,
% 291.31/183.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s9, s10)) | node14(c_e_h_3, c_f, s9, s10) | node15(c_e_h_3, c_f, s9, s10) | node16(c_e_h_3, c_f, s9)),
% 291.31/183.80 inference(modus_ponens,[status(thm)],[11607, 11606])).
% 291.31/183.80 tff(11609,plain,
% 291.31/183.80 (node14(c_e_h_3, c_f, s9, s10) | node15(c_e_h_3, c_f, s9, s10) | node16(c_e_h_3, c_f, s9)),
% 291.31/183.80 inference(unit_resolution,[status(thm)],[11608, 204, 11602])).
% 291.31/183.80 tff(11610,plain,
% 291.31/183.80 (node15(c_e_h_3, c_f, s9, s10)),
% 291.31/183.80 inference(unit_resolution,[status(thm)],[11609, 11598, 11588])).
% 291.31/183.80 tff(11611,plain,
% 291.31/183.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s10)) | (~node15(c_e_h_3, c_f, s9, s10)) | m_c_h_element_v_out(c_e_h_3, c_f, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s10)) | (~node15(c_e_h_3, c_f, s9, s10)) | m_c_h_element_v_out(c_e_h_3, c_f, s9))),
% 291.31/183.80 inference(rewrite,[status(thm)],[])).
% 291.31/183.80 tff(11612,plain,
% 291.31/183.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s10)) | (~node15(c_e_h_3, c_f, s9, s10)) | m_c_h_element_v_out(c_e_h_3, c_f, s9))),
% 291.31/183.80 inference(quant_inst,[status(thm)],[])).
% 291.31/183.80 tff(11613,plain,
% 291.31/183.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s10)) | (~node15(c_e_h_3, c_f, s9, s10)) | m_c_h_element_v_out(c_e_h_3, c_f, s9)),
% 291.31/183.80 inference(modus_ponens,[status(thm)],[11612, 11611])).
% 291.31/183.80 tff(11614,plain,
% 291.31/183.80 ($false),
% 291.31/183.80 inference(unit_resolution,[status(thm)],[11613, 147, 11585, 11586, 11610])).
% 291.31/183.80 tff(11615,plain,((~m_c_h_element_v_out(c_e_h_3, c_f, s10)) | m_c_h_element_v_out(c_e_h_3, c_f, s9) | node16(c_e_h_3, c_f, s9) | m_c_h_element_v_in1(c_e_h_3, c_f, s9)), inference(lemma,lemma(discharge,[]))).
% 291.31/183.80 tff(11616,plain,
% 291.31/183.80 (node16(c_e_h_3, c_f, s9)),
% 291.31/183.80 inference(unit_resolution,[status(thm)],[11615, 11585, 11587, 11586])).
% 291.31/183.80 tff(11617,assumption,(node18(c_e_h_3, c_f, s9, s10)), introduced(assumption)).
% 291.31/183.80 tff(11618,plain,
% 291.31/183.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_f, s9) | (~m_c_h_element_v_out(c_e_h_3, c_f, s10)) | (~node18(c_e_h_3, c_f, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s9) | (~m_c_h_element_v_out(c_e_h_3, c_f, s10)) | (~node18(c_e_h_3, c_f, s9, s10)))),
% 291.31/183.81 inference(rewrite,[status(thm)],[])).
% 291.31/183.81 tff(11619,plain,
% 291.31/183.81 (((~m_c_h_element_v_out(c_e_h_3, c_f, s10)) | m_c_h_element_v_out(c_e_h_3, c_f, s9) | (~node18(c_e_h_3, c_f, s9, s10))) <=> (m_c_h_element_v_out(c_e_h_3, c_f, s9) | (~m_c_h_element_v_out(c_e_h_3, c_f, s10)) | (~node18(c_e_h_3, c_f, s9, s10)))),
% 291.31/183.81 inference(rewrite,[status(thm)],[])).
% 291.31/183.81 tff(11620,plain,
% 291.31/183.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s10)) | m_c_h_element_v_out(c_e_h_3, c_f, s9) | (~node18(c_e_h_3, c_f, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_f, s9) | (~m_c_h_element_v_out(c_e_h_3, c_f, s10)) | (~node18(c_e_h_3, c_f, s9, s10))))),
% 291.31/183.81 inference(monotonicity,[status(thm)],[11619])).
% 291.31/183.81 tff(11621,plain,
% 291.31/183.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s10)) | m_c_h_element_v_out(c_e_h_3, c_f, s9) | (~node18(c_e_h_3, c_f, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s9) | (~m_c_h_element_v_out(c_e_h_3, c_f, s10)) | (~node18(c_e_h_3, c_f, s9, s10)))),
% 291.31/183.81 inference(transitivity,[status(thm)],[11620, 11618])).
% 291.31/183.81 tff(11622,plain,
% 291.31/183.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s10)) | m_c_h_element_v_out(c_e_h_3, c_f, s9) | (~node18(c_e_h_3, c_f, s9, s10)))),
% 291.31/183.81 inference(quant_inst,[status(thm)],[])).
% 291.31/183.81 tff(11623,plain,
% 291.31/183.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s9) | (~m_c_h_element_v_out(c_e_h_3, c_f, s10)) | (~node18(c_e_h_3, c_f, s9, s10))),
% 291.31/183.81 inference(modus_ponens,[status(thm)],[11622, 11621])).
% 291.31/183.81 tff(11624,plain,
% 291.31/183.81 ($false),
% 291.31/183.81 inference(unit_resolution,[status(thm)],[11623, 753, 11585, 11586, 11617])).
% 291.31/183.81 tff(11625,plain,((~node18(c_e_h_3, c_f, s9, s10)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s10)) | m_c_h_element_v_out(c_e_h_3, c_f, s9)), inference(lemma,lemma(discharge,[]))).
% 291.31/183.81 tff(11626,plain,
% 291.31/183.81 (~node18(c_e_h_3, c_f, s9, s10)),
% 291.31/183.81 inference(unit_resolution,[status(thm)],[11625, 11585, 11586])).
% 291.31/183.81 tff(11627,plain,
% 291.31/183.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_f, s9, s10)) | node18(c_e_h_3, c_f, s9, s10) | node17(c_e_h_3, c_f, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s9, s10)) | node18(c_e_h_3, c_f, s9, s10) | node17(c_e_h_3, c_f, s9))),
% 291.31/183.81 inference(rewrite,[status(thm)],[])).
% 291.31/183.81 tff(11628,plain,
% 291.31/183.81 ((node17(c_e_h_3, c_f, s9) | node18(c_e_h_3, c_f, s9, s10) | (~node19(c_e_h_3, c_f, s9, s10))) <=> ((~node19(c_e_h_3, c_f, s9, s10)) | node18(c_e_h_3, c_f, s9, s10) | node17(c_e_h_3, c_f, s9))),
% 291.31/183.81 inference(rewrite,[status(thm)],[])).
% 291.31/183.81 tff(11629,plain,
% 291.31/183.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s9) | node18(c_e_h_3, c_f, s9, s10) | (~node19(c_e_h_3, c_f, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_f, s9, s10)) | node18(c_e_h_3, c_f, s9, s10) | node17(c_e_h_3, c_f, s9)))),
% 291.31/183.81 inference(monotonicity,[status(thm)],[11628])).
% 291.31/183.81 tff(11630,plain,
% 291.31/183.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s9) | node18(c_e_h_3, c_f, s9, s10) | (~node19(c_e_h_3, c_f, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s9, s10)) | node18(c_e_h_3, c_f, s9, s10) | node17(c_e_h_3, c_f, s9))),
% 291.31/183.81 inference(transitivity,[status(thm)],[11629, 11627])).
% 291.31/183.81 tff(11631,plain,
% 291.31/183.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s9) | node18(c_e_h_3, c_f, s9, s10) | (~node19(c_e_h_3, c_f, s9, s10)))),
% 291.31/183.81 inference(quant_inst,[status(thm)],[])).
% 291.31/183.81 tff(11632,plain,
% 291.31/183.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s9, s10)) | node18(c_e_h_3, c_f, s9, s10) | node17(c_e_h_3, c_f, s9)),
% 291.31/183.81 inference(modus_ponens,[status(thm)],[11631, 11630])).
% 291.31/183.81 tff(11633,plain,
% 291.31/183.81 (node18(c_e_h_3, c_f, s9, s10) | node17(c_e_h_3, c_f, s9)),
% 291.31/183.81 inference(unit_resolution,[status(thm)],[11632, 776, 11602])).
% 291.31/183.81 tff(11634,plain,
% 291.31/183.81 (node17(c_e_h_3, c_f, s9)),
% 291.31/183.81 inference(unit_resolution,[status(thm)],[11633, 11626])).
% 291.31/183.81 tff(11635,assumption,(node17(c_e_h_3, c_f, s9)), introduced(assumption)).
% 291.31/183.81 tff(11636,assumption,(node16(c_e_h_3, c_f, s9)), introduced(assumption)).
% 291.31/183.81 tff(11637,plain,
% 291.31/183.81 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s9)) | (~node17(c_e_h_3, c_f, s9)) | m_c_h_element_v_in1(c_e_h_3, c_f, s9))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s9)) | (~node17(c_e_h_3, c_f, s9)) | m_c_h_element_v_in1(c_e_h_3, c_f, s9))),
% 291.31/183.81 inference(rewrite,[status(thm)],[])).
% 291.31/183.81 tff(11638,plain,
% 291.31/183.81 ((m_c_h_element_v_in1(c_e_h_3, c_f, s9) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s9)) | (~node17(c_e_h_3, c_f, s9))) <=> ((~m_c_h_element_v_in2(c_e_h_3, c_f, s9)) | (~node17(c_e_h_3, c_f, s9)) | m_c_h_element_v_in1(c_e_h_3, c_f, s9))),
% 291.31/183.81 inference(rewrite,[status(thm)],[])).
% 291.31/183.81 tff(11639,plain,
% 291.31/183.81 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s9) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s9)) | (~node17(c_e_h_3, c_f, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s9)) | (~node17(c_e_h_3, c_f, s9)) | m_c_h_element_v_in1(c_e_h_3, c_f, s9)))),
% 291.31/183.81 inference(monotonicity,[status(thm)],[11638])).
% 291.31/183.81 tff(11640,plain,
% 291.31/183.81 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s9) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s9)) | (~node17(c_e_h_3, c_f, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s9)) | (~node17(c_e_h_3, c_f, s9)) | m_c_h_element_v_in1(c_e_h_3, c_f, s9))),
% 291.31/183.81 inference(transitivity,[status(thm)],[11639, 11637])).
% 291.31/183.81 tff(11641,plain,
% 291.31/183.81 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s9) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s9)) | (~node17(c_e_h_3, c_f, s9)))),
% 291.31/183.81 inference(quant_inst,[status(thm)],[])).
% 291.31/183.81 tff(11642,plain,
% 291.31/183.81 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s9)) | (~node17(c_e_h_3, c_f, s9)) | m_c_h_element_v_in1(c_e_h_3, c_f, s9)),
% 291.31/183.81 inference(modus_ponens,[status(thm)],[11641, 11640])).
% 291.31/183.81 tff(11643,plain,
% 291.31/183.81 ((~m_c_h_element_v_in2(c_e_h_3, c_f, s9)) | m_c_h_element_v_in1(c_e_h_3, c_f, s9)),
% 291.31/183.81 inference(unit_resolution,[status(thm)],[11642, 859, 11635])).
% 291.31/183.81 tff(11644,plain,
% 291.31/183.81 (~m_c_h_element_v_in2(c_e_h_3, c_f, s9)),
% 291.31/183.81 inference(unit_resolution,[status(thm)],[11643, 11587])).
% 291.31/183.81 tff(11645,plain,
% 291.31/183.81 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s9)) | m_c_h_element_v_in1(c_e_h_3, c_f, s9) | m_c_h_element_v_in2(c_e_h_3, c_f, s9))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s9)) | m_c_h_element_v_in1(c_e_h_3, c_f, s9) | m_c_h_element_v_in2(c_e_h_3, c_f, s9))),
% 291.31/183.81 inference(rewrite,[status(thm)],[])).
% 291.31/183.81 tff(11646,plain,
% 291.31/183.81 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s9)) | m_c_h_element_v_in1(c_e_h_3, c_f, s9) | m_c_h_element_v_in2(c_e_h_3, c_f, s9))),
% 291.31/183.81 inference(quant_inst,[status(thm)],[])).
% 291.31/183.81 tff(11647,plain,
% 291.31/183.81 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s9)) | m_c_h_element_v_in1(c_e_h_3, c_f, s9) | m_c_h_element_v_in2(c_e_h_3, c_f, s9)),
% 291.31/183.81 inference(modus_ponens,[status(thm)],[11646, 11645])).
% 291.31/183.81 tff(11648,plain,
% 291.31/183.81 (m_c_h_element_v_in1(c_e_h_3, c_f, s9) | m_c_h_element_v_in2(c_e_h_3, c_f, s9)),
% 291.31/183.81 inference(unit_resolution,[status(thm)],[11647, 178, 11636])).
% 291.31/183.81 tff(11649,plain,
% 291.31/183.81 ($false),
% 291.31/183.81 inference(unit_resolution,[status(thm)],[11648, 11644, 11587])).
% 291.31/183.81 tff(11650,plain,(m_c_h_element_v_in1(c_e_h_3, c_f, s9) | (~node16(c_e_h_3, c_f, s9)) | (~node17(c_e_h_3, c_f, s9))), inference(lemma,lemma(discharge,[]))).
% 291.31/183.81 tff(11651,plain,
% 291.31/183.81 (m_c_h_element_v_in1(c_e_h_3, c_f, s9)),
% 291.31/183.81 inference(unit_resolution,[status(thm)],[11650, 11636, 11635])).
% 291.31/183.81 tff(11652,plain,
% 291.31/183.81 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_f, s9)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s9)) | m_c_h_element_v_in2(c_e_h_3, c_f, s9))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_f, s9)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s9)) | m_c_h_element_v_in2(c_e_h_3, c_f, s9))),
% 291.31/183.81 inference(rewrite,[status(thm)],[])).
% 291.31/183.81 tff(11653,plain,
% 291.31/183.81 (((~m_c_h_element_v_in1(c_e_h_3, c_f, s9)) | m_c_h_element_v_in2(c_e_h_3, c_f, s9) | (~node17(c_e_h_3, c_f, s9))) <=> ((~node17(c_e_h_3, c_f, s9)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s9)) | m_c_h_element_v_in2(c_e_h_3, c_f, s9))),
% 291.31/183.81 inference(rewrite,[status(thm)],[])).
% 291.31/183.81 tff(11654,plain,
% 291.31/183.81 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s9)) | m_c_h_element_v_in2(c_e_h_3, c_f, s9) | (~node17(c_e_h_3, c_f, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_f, s9)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s9)) | m_c_h_element_v_in2(c_e_h_3, c_f, s9)))),
% 291.31/183.81 inference(monotonicity,[status(thm)],[11653])).
% 291.31/183.81 tff(11655,plain,
% 291.31/183.81 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s9)) | m_c_h_element_v_in2(c_e_h_3, c_f, s9) | (~node17(c_e_h_3, c_f, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_f, s9)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s9)) | m_c_h_element_v_in2(c_e_h_3, c_f, s9))),
% 291.31/183.81 inference(transitivity,[status(thm)],[11654, 11652])).
% 291.31/183.81 tff(11656,plain,
% 291.31/183.81 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s9)) | m_c_h_element_v_in2(c_e_h_3, c_f, s9) | (~node17(c_e_h_3, c_f, s9)))),
% 291.31/183.82 inference(quant_inst,[status(thm)],[])).
% 291.31/183.82 tff(11657,plain,
% 291.31/183.82 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_f, s9)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s9)) | m_c_h_element_v_in2(c_e_h_3, c_f, s9)),
% 291.31/183.82 inference(modus_ponens,[status(thm)],[11656, 11655])).
% 291.31/183.82 tff(11658,plain,
% 291.31/183.82 ((~m_c_h_element_v_in1(c_e_h_3, c_f, s9)) | m_c_h_element_v_in2(c_e_h_3, c_f, s9)),
% 291.31/183.82 inference(unit_resolution,[status(thm)],[11657, 919, 11635])).
% 291.31/183.82 tff(11659,plain,
% 291.31/183.82 (m_c_h_element_v_in2(c_e_h_3, c_f, s9)),
% 291.31/183.82 inference(unit_resolution,[status(thm)],[11658, 11651])).
% 291.31/183.82 tff(11660,plain,
% 291.31/183.82 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s9)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s9)) | (~node16(c_e_h_3, c_f, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s9)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s9)) | (~node16(c_e_h_3, c_f, s9)))),
% 291.31/183.82 inference(rewrite,[status(thm)],[])).
% 291.31/183.82 tff(11661,plain,
% 291.31/183.82 (((~node16(c_e_h_3, c_f, s9)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s9)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s9))) <=> ((~m_c_h_element_v_in2(c_e_h_3, c_f, s9)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s9)) | (~node16(c_e_h_3, c_f, s9)))),
% 291.31/183.82 inference(rewrite,[status(thm)],[])).
% 291.31/183.82 tff(11662,plain,
% 291.31/183.82 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_f, s9)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s9)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s9)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s9)) | (~node16(c_e_h_3, c_f, s9))))),
% 291.31/183.82 inference(monotonicity,[status(thm)],[11661])).
% 291.31/183.82 tff(11663,plain,
% 291.31/183.82 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_f, s9)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s9)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s9)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s9)) | (~node16(c_e_h_3, c_f, s9)))),
% 291.31/183.82 inference(transitivity,[status(thm)],[11662, 11660])).
% 291.31/183.82 tff(11664,plain,
% 291.31/183.82 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_f, s9)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s9)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s9)))),
% 291.31/183.82 inference(quant_inst,[status(thm)],[])).
% 291.31/183.82 tff(11665,plain,
% 291.31/183.82 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s9)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s9)) | (~node16(c_e_h_3, c_f, s9))),
% 291.31/183.82 inference(modus_ponens,[status(thm)],[11664, 11663])).
% 291.31/183.82 tff(11666,plain,
% 291.31/183.82 ((~m_c_h_element_v_in2(c_e_h_3, c_f, s9)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s9))),
% 291.31/183.82 inference(unit_resolution,[status(thm)],[11665, 2307, 11636])).
% 291.31/183.82 tff(11667,plain,
% 291.31/183.82 ($false),
% 291.31/183.82 inference(unit_resolution,[status(thm)],[11666, 11659, 11651])).
% 291.31/183.82 tff(11668,plain,((~node16(c_e_h_3, c_f, s9)) | (~node17(c_e_h_3, c_f, s9))), inference(lemma,lemma(discharge,[]))).
% 291.31/183.82 tff(11669,plain,
% 291.31/183.82 ($false),
% 291.31/183.82 inference(unit_resolution,[status(thm)],[11668, 11634, 11616])).
% 291.31/183.82 tff(11670,plain,((~m_c_h_element_v_out(c_e_h_3, c_f, s10)) | m_c_h_element_v_in1(c_e_h_3, c_f, s9) | m_c_h_element_v_out(c_e_h_3, c_f, s9)), inference(lemma,lemma(discharge,[]))).
% 291.31/183.82 tff(11671,plain,
% 291.31/183.82 (m_c_h_element_v_in1(c_e_h_3, c_f, s9)),
% 291.31/183.82 inference(unit_resolution,[status(thm)],[11670, 11586, 11585])).
% 291.31/183.82 tff(11672,plain,
% 291.31/183.82 (~node18(c_e_h_3, c_f, s9, s10)),
% 291.31/183.82 inference(unit_resolution,[status(thm)],[11625, 11586, 11585])).
% 291.31/183.82 tff(11673,plain,
% 291.31/183.82 (node17(c_e_h_3, c_f, s9)),
% 291.31/183.82 inference(unit_resolution,[status(thm)],[11633, 11672])).
% 291.31/183.82 tff(11674,plain,
% 291.31/183.82 ($false),
% 291.31/183.82 inference(unit_resolution,[status(thm)],[11657, 919, 11673, 11671, 11584])).
% 291.31/183.82 tff(11675,plain,(m_c_h_element_v_out(c_e_h_3, c_f, s9) | m_c_h_element_v_in2(c_e_h_3, c_f, s9) | (~m_c_h_element_v_out(c_e_h_3, c_f, s10))), inference(lemma,lemma(discharge,[]))).
% 291.31/183.82 tff(11676,plain,
% 291.31/183.82 (m_c_h_element_v_in2(c_e_h_3, c_f, s9) | (~m_c_h_element_v_out(c_e_h_3, c_f, s10))),
% 291.31/183.82 inference(unit_resolution,[status(thm)],[11675, 11583])).
% 291.31/183.82 tff(11677,plain,
% 291.31/183.82 (~m_c_h_element_v_out(c_e_h_3, c_f, s10)),
% 291.31/183.82 inference(unit_resolution,[status(thm)],[11676, 11482])).
% 291.31/183.82 tff(11678,assumption,(m_c_h_element_v_in2(c_e_h_3, c_f, s10)), introduced(assumption)).
% 291.31/183.82 tff(11679,plain,
% 291.31/183.82 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s10)) | m_and_h_gate_v_out(c_e_h_3, c_i, s10))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s10)) | m_and_h_gate_v_out(c_e_h_3, c_i, s10))),
% 291.31/183.82 inference(rewrite,[status(thm)],[])).
% 291.31/183.82 tff(11680,plain,
% 291.31/183.82 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s10)) | m_and_h_gate_v_out(c_e_h_3, c_i, s10))),
% 291.31/183.82 inference(quant_inst,[status(thm)],[])).
% 291.31/183.82 tff(11681,plain,
% 291.31/183.82 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s10)) | m_and_h_gate_v_out(c_e_h_3, c_i, s10)),
% 291.31/183.82 inference(modus_ponens,[status(thm)],[11680, 11679])).
% 291.31/183.82 tff(11682,plain,
% 291.31/183.82 ($false),
% 291.31/183.82 inference(unit_resolution,[status(thm)],[11681, 2143, 11422, 11678])).
% 291.31/183.82 tff(11683,plain,((~m_c_h_element_v_in2(c_e_h_3, c_f, s10)) | m_and_h_gate_v_out(c_e_h_3, c_i, s10)), inference(lemma,lemma(discharge,[]))).
% 291.31/183.82 tff(11684,plain,
% 291.31/183.82 (~m_c_h_element_v_in2(c_e_h_3, c_f, s10)),
% 291.31/183.82 inference(unit_resolution,[status(thm)],[11683, 11409])).
% 291.31/183.82 tff(11685,assumption,(m_c_h_element_v_out(c_e_h_3, c_f, s11)), introduced(assumption)).
% 291.31/183.82 tff(11686,assumption,(~m_c_h_element_v_out(c_e_h_3, c_f, s10)), introduced(assumption)).
% 291.31/183.82 tff(11687,assumption,(node18(c_e_h_3, c_f, s10, s11)), introduced(assumption)).
% 291.31/183.82 tff(11688,plain,
% 291.31/183.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_f, s10) | (~m_c_h_element_v_out(c_e_h_3, c_f, s11)) | (~node18(c_e_h_3, c_f, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s10) | (~m_c_h_element_v_out(c_e_h_3, c_f, s11)) | (~node18(c_e_h_3, c_f, s10, s11)))),
% 291.31/183.82 inference(rewrite,[status(thm)],[])).
% 291.31/183.82 tff(11689,plain,
% 291.31/183.82 (((~m_c_h_element_v_out(c_e_h_3, c_f, s11)) | m_c_h_element_v_out(c_e_h_3, c_f, s10) | (~node18(c_e_h_3, c_f, s10, s11))) <=> (m_c_h_element_v_out(c_e_h_3, c_f, s10) | (~m_c_h_element_v_out(c_e_h_3, c_f, s11)) | (~node18(c_e_h_3, c_f, s10, s11)))),
% 291.31/183.82 inference(rewrite,[status(thm)],[])).
% 291.31/183.82 tff(11690,plain,
% 291.31/183.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s11)) | m_c_h_element_v_out(c_e_h_3, c_f, s10) | (~node18(c_e_h_3, c_f, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_f, s10) | (~m_c_h_element_v_out(c_e_h_3, c_f, s11)) | (~node18(c_e_h_3, c_f, s10, s11))))),
% 291.31/183.82 inference(monotonicity,[status(thm)],[11689])).
% 291.31/183.82 tff(11691,plain,
% 291.31/183.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s11)) | m_c_h_element_v_out(c_e_h_3, c_f, s10) | (~node18(c_e_h_3, c_f, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s10) | (~m_c_h_element_v_out(c_e_h_3, c_f, s11)) | (~node18(c_e_h_3, c_f, s10, s11)))),
% 291.31/183.82 inference(transitivity,[status(thm)],[11690, 11688])).
% 291.31/183.82 tff(11692,plain,
% 291.31/183.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s11)) | m_c_h_element_v_out(c_e_h_3, c_f, s10) | (~node18(c_e_h_3, c_f, s10, s11)))),
% 291.31/183.82 inference(quant_inst,[status(thm)],[])).
% 291.31/183.82 tff(11693,plain,
% 291.31/183.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s10) | (~m_c_h_element_v_out(c_e_h_3, c_f, s11)) | (~node18(c_e_h_3, c_f, s10, s11))),
% 291.31/183.82 inference(modus_ponens,[status(thm)],[11692, 11691])).
% 291.31/183.82 tff(11694,plain,
% 291.31/183.82 ($false),
% 291.31/183.82 inference(unit_resolution,[status(thm)],[11693, 753, 11686, 11685, 11687])).
% 291.31/183.82 tff(11695,plain,((~node18(c_e_h_3, c_f, s10, s11)) | m_c_h_element_v_out(c_e_h_3, c_f, s10) | (~m_c_h_element_v_out(c_e_h_3, c_f, s11))), inference(lemma,lemma(discharge,[]))).
% 291.31/183.82 tff(11696,plain,
% 291.31/183.82 (~node18(c_e_h_3, c_f, s10, s11)),
% 291.31/183.82 inference(unit_resolution,[status(thm)],[11695, 11686, 11685])).
% 291.31/183.82 tff(11697,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_f, s10)), introduced(assumption)).
% 291.31/183.82 tff(11698,assumption,(node14(c_e_h_3, c_f, s10, s11)), introduced(assumption)).
% 291.31/183.82 tff(11699,plain,
% 291.31/183.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s11)) | m_c_h_element_v_in1(c_e_h_3, c_f, s10) | (~node14(c_e_h_3, c_f, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s11)) | m_c_h_element_v_in1(c_e_h_3, c_f, s10) | (~node14(c_e_h_3, c_f, s10, s11)))),
% 291.31/183.82 inference(rewrite,[status(thm)],[])).
% 291.31/183.82 tff(11700,plain,
% 291.31/183.82 (((~node14(c_e_h_3, c_f, s10, s11)) | m_c_h_element_v_in1(c_e_h_3, c_f, s10) | (~m_c_h_element_v_out(c_e_h_3, c_f, s11))) <=> ((~m_c_h_element_v_out(c_e_h_3, c_f, s11)) | m_c_h_element_v_in1(c_e_h_3, c_f, s10) | (~node14(c_e_h_3, c_f, s10, s11)))),
% 291.31/183.82 inference(rewrite,[status(thm)],[])).
% 291.31/183.82 tff(11701,plain,
% 291.31/183.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s10, s11)) | m_c_h_element_v_in1(c_e_h_3, c_f, s10) | (~m_c_h_element_v_out(c_e_h_3, c_f, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s11)) | m_c_h_element_v_in1(c_e_h_3, c_f, s10) | (~node14(c_e_h_3, c_f, s10, s11))))),
% 291.31/183.82 inference(monotonicity,[status(thm)],[11700])).
% 291.31/183.82 tff(11702,plain,
% 291.31/183.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s10, s11)) | m_c_h_element_v_in1(c_e_h_3, c_f, s10) | (~m_c_h_element_v_out(c_e_h_3, c_f, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s11)) | m_c_h_element_v_in1(c_e_h_3, c_f, s10) | (~node14(c_e_h_3, c_f, s10, s11)))),
% 291.31/183.82 inference(transitivity,[status(thm)],[11701, 11699])).
% 291.31/183.82 tff(11703,plain,
% 291.31/183.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s10, s11)) | m_c_h_element_v_in1(c_e_h_3, c_f, s10) | (~m_c_h_element_v_out(c_e_h_3, c_f, s11)))),
% 291.31/183.83 inference(quant_inst,[status(thm)],[])).
% 291.31/183.83 tff(11704,plain,
% 291.31/183.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s11)) | m_c_h_element_v_in1(c_e_h_3, c_f, s10) | (~node14(c_e_h_3, c_f, s10, s11))),
% 291.31/183.83 inference(modus_ponens,[status(thm)],[11703, 11702])).
% 291.31/183.83 tff(11705,plain,
% 291.31/183.83 ($false),
% 291.31/183.83 inference(unit_resolution,[status(thm)],[11704, 223, 11685, 11698, 11697])).
% 291.31/183.83 tff(11706,plain,((~node14(c_e_h_3, c_f, s10, s11)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s11)) | m_c_h_element_v_in1(c_e_h_3, c_f, s10)), inference(lemma,lemma(discharge,[]))).
% 291.31/183.83 tff(11707,plain,
% 291.31/183.83 (~node14(c_e_h_3, c_f, s10, s11)),
% 291.31/183.83 inference(unit_resolution,[status(thm)],[11706, 11685, 11697])).
% 291.31/183.83 tff(11708,plain,
% 291.31/183.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s10, s11)) | node19(c_e_h_3, c_f, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s10, s11)) | node19(c_e_h_3, c_f, s10, s11))),
% 291.31/183.83 inference(rewrite,[status(thm)],[])).
% 291.31/183.83 tff(11709,plain,
% 291.31/183.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s10, s11)) | node19(c_e_h_3, c_f, s10, s11))),
% 291.31/183.83 inference(quant_inst,[status(thm)],[])).
% 291.31/183.83 tff(11710,plain,
% 291.31/183.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s10, s11)) | node19(c_e_h_3, c_f, s10, s11)),
% 291.31/183.83 inference(modus_ponens,[status(thm)],[11709, 11708])).
% 291.31/183.83 tff(11711,plain,
% 291.31/183.83 (node19(c_e_h_3, c_f, s10, s11)),
% 291.31/183.83 inference(unit_resolution,[status(thm)],[11710, 190, 7748])).
% 291.31/183.83 tff(11712,plain,
% 291.31/183.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_3, c_f, s10, s11) | (~node19(c_e_h_3, c_f, s10, s11)) | node17(c_e_h_3, c_f, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_3, c_f, s10, s11) | (~node19(c_e_h_3, c_f, s10, s11)) | node17(c_e_h_3, c_f, s10))),
% 291.31/183.83 inference(rewrite,[status(thm)],[])).
% 291.31/183.83 tff(11713,plain,
% 291.31/183.83 ((node17(c_e_h_3, c_f, s10) | node18(c_e_h_3, c_f, s10, s11) | (~node19(c_e_h_3, c_f, s10, s11))) <=> (node18(c_e_h_3, c_f, s10, s11) | (~node19(c_e_h_3, c_f, s10, s11)) | node17(c_e_h_3, c_f, s10))),
% 291.31/183.83 inference(rewrite,[status(thm)],[])).
% 291.31/183.83 tff(11714,plain,
% 291.31/183.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s10) | node18(c_e_h_3, c_f, s10, s11) | (~node19(c_e_h_3, c_f, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_3, c_f, s10, s11) | (~node19(c_e_h_3, c_f, s10, s11)) | node17(c_e_h_3, c_f, s10)))),
% 291.31/183.83 inference(monotonicity,[status(thm)],[11713])).
% 291.31/183.83 tff(11715,plain,
% 291.31/183.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s10) | node18(c_e_h_3, c_f, s10, s11) | (~node19(c_e_h_3, c_f, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_3, c_f, s10, s11) | (~node19(c_e_h_3, c_f, s10, s11)) | node17(c_e_h_3, c_f, s10))),
% 291.31/183.83 inference(transitivity,[status(thm)],[11714, 11712])).
% 291.31/183.83 tff(11716,plain,
% 291.31/183.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s10) | node18(c_e_h_3, c_f, s10, s11) | (~node19(c_e_h_3, c_f, s10, s11)))),
% 291.31/183.83 inference(quant_inst,[status(thm)],[])).
% 291.31/183.83 tff(11717,plain,
% 291.31/183.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_3, c_f, s10, s11) | (~node19(c_e_h_3, c_f, s10, s11)) | node17(c_e_h_3, c_f, s10)),
% 291.31/183.83 inference(modus_ponens,[status(thm)],[11716, 11715])).
% 291.31/183.83 tff(11718,plain,
% 291.31/183.83 (node18(c_e_h_3, c_f, s10, s11) | node17(c_e_h_3, c_f, s10)),
% 291.31/183.83 inference(unit_resolution,[status(thm)],[11717, 776, 11711])).
% 291.31/183.83 tff(11719,plain,
% 291.31/183.83 (node17(c_e_h_3, c_f, s10)),
% 291.31/183.83 inference(unit_resolution,[status(thm)],[11718, 11696])).
% 291.31/183.83 tff(11720,assumption,(node16(c_e_h_3, c_f, s10)), introduced(assumption)).
% 291.31/183.83 tff(11721,plain,
% 291.31/183.83 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s10)) | m_c_h_element_v_in1(c_e_h_3, c_f, s10) | m_c_h_element_v_in2(c_e_h_3, c_f, s10))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s10)) | m_c_h_element_v_in1(c_e_h_3, c_f, s10) | m_c_h_element_v_in2(c_e_h_3, c_f, s10))),
% 291.31/183.83 inference(rewrite,[status(thm)],[])).
% 291.31/183.83 tff(11722,plain,
% 291.31/183.83 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s10)) | m_c_h_element_v_in1(c_e_h_3, c_f, s10) | m_c_h_element_v_in2(c_e_h_3, c_f, s10))),
% 291.31/183.83 inference(quant_inst,[status(thm)],[])).
% 291.31/183.83 tff(11723,plain,
% 291.31/183.83 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s10)) | m_c_h_element_v_in1(c_e_h_3, c_f, s10) | m_c_h_element_v_in2(c_e_h_3, c_f, s10)),
% 291.31/183.83 inference(modus_ponens,[status(thm)],[11722, 11721])).
% 291.31/183.83 tff(11724,plain,
% 291.31/183.83 (m_c_h_element_v_in1(c_e_h_3, c_f, s10) | m_c_h_element_v_in2(c_e_h_3, c_f, s10)),
% 291.31/183.83 inference(unit_resolution,[status(thm)],[11723, 178, 11720])).
% 291.31/183.83 tff(11725,plain,
% 291.31/183.83 (m_c_h_element_v_in2(c_e_h_3, c_f, s10)),
% 291.31/183.83 inference(unit_resolution,[status(thm)],[11724, 11697])).
% 291.31/183.83 tff(11726,assumption,(node17(c_e_h_3, c_f, s10)), introduced(assumption)).
% 291.31/183.83 tff(11727,plain,
% 291.31/183.83 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s10)) | m_c_h_element_v_in1(c_e_h_3, c_f, s10) | (~node17(c_e_h_3, c_f, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s10)) | m_c_h_element_v_in1(c_e_h_3, c_f, s10) | (~node17(c_e_h_3, c_f, s10)))),
% 291.31/183.83 inference(rewrite,[status(thm)],[])).
% 291.31/183.83 tff(11728,plain,
% 291.31/183.83 ((m_c_h_element_v_in1(c_e_h_3, c_f, s10) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s10)) | (~node17(c_e_h_3, c_f, s10))) <=> ((~m_c_h_element_v_in2(c_e_h_3, c_f, s10)) | m_c_h_element_v_in1(c_e_h_3, c_f, s10) | (~node17(c_e_h_3, c_f, s10)))),
% 291.31/183.83 inference(rewrite,[status(thm)],[])).
% 291.31/183.83 tff(11729,plain,
% 291.31/183.83 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s10) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s10)) | (~node17(c_e_h_3, c_f, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s10)) | m_c_h_element_v_in1(c_e_h_3, c_f, s10) | (~node17(c_e_h_3, c_f, s10))))),
% 291.31/183.83 inference(monotonicity,[status(thm)],[11728])).
% 291.31/183.83 tff(11730,plain,
% 291.31/183.83 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s10) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s10)) | (~node17(c_e_h_3, c_f, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s10)) | m_c_h_element_v_in1(c_e_h_3, c_f, s10) | (~node17(c_e_h_3, c_f, s10)))),
% 291.31/183.83 inference(transitivity,[status(thm)],[11729, 11727])).
% 291.31/183.83 tff(11731,plain,
% 291.31/183.83 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s10) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s10)) | (~node17(c_e_h_3, c_f, s10)))),
% 291.31/183.83 inference(quant_inst,[status(thm)],[])).
% 291.31/183.83 tff(11732,plain,
% 291.31/183.83 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s10)) | m_c_h_element_v_in1(c_e_h_3, c_f, s10) | (~node17(c_e_h_3, c_f, s10))),
% 291.31/183.83 inference(modus_ponens,[status(thm)],[11731, 11730])).
% 291.31/183.83 tff(11733,plain,
% 291.31/183.83 ((~m_c_h_element_v_in2(c_e_h_3, c_f, s10)) | m_c_h_element_v_in1(c_e_h_3, c_f, s10)),
% 291.31/183.83 inference(unit_resolution,[status(thm)],[11732, 859, 11726])).
% 291.31/183.83 tff(11734,plain,
% 291.31/183.83 ($false),
% 291.31/183.83 inference(unit_resolution,[status(thm)],[11733, 11725, 11697])).
% 291.31/183.83 tff(11735,plain,(m_c_h_element_v_in1(c_e_h_3, c_f, s10) | (~node17(c_e_h_3, c_f, s10)) | (~node16(c_e_h_3, c_f, s10))), inference(lemma,lemma(discharge,[]))).
% 291.31/183.83 tff(11736,plain,
% 291.31/183.83 (~node16(c_e_h_3, c_f, s10)),
% 291.31/183.83 inference(unit_resolution,[status(thm)],[11735, 11719, 11697])).
% 291.31/183.83 tff(11737,plain,
% 291.31/183.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_f, s10, s11)) | node15(c_e_h_3, c_f, s10, s11) | node14(c_e_h_3, c_f, s10, s11) | node16(c_e_h_3, c_f, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s10, s11)) | node15(c_e_h_3, c_f, s10, s11) | node14(c_e_h_3, c_f, s10, s11) | node16(c_e_h_3, c_f, s10))),
% 291.31/183.83 inference(rewrite,[status(thm)],[])).
% 291.31/183.83 tff(11738,plain,
% 291.31/183.83 ((node16(c_e_h_3, c_f, s10) | node14(c_e_h_3, c_f, s10, s11) | node15(c_e_h_3, c_f, s10, s11) | (~node19(c_e_h_3, c_f, s10, s11))) <=> ((~node19(c_e_h_3, c_f, s10, s11)) | node15(c_e_h_3, c_f, s10, s11) | node14(c_e_h_3, c_f, s10, s11) | node16(c_e_h_3, c_f, s10))),
% 291.31/183.83 inference(rewrite,[status(thm)],[])).
% 291.31/183.83 tff(11739,plain,
% 291.31/183.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s10) | node14(c_e_h_3, c_f, s10, s11) | node15(c_e_h_3, c_f, s10, s11) | (~node19(c_e_h_3, c_f, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_f, s10, s11)) | node15(c_e_h_3, c_f, s10, s11) | node14(c_e_h_3, c_f, s10, s11) | node16(c_e_h_3, c_f, s10)))),
% 291.31/183.83 inference(monotonicity,[status(thm)],[11738])).
% 291.31/183.83 tff(11740,plain,
% 291.31/183.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s10) | node14(c_e_h_3, c_f, s10, s11) | node15(c_e_h_3, c_f, s10, s11) | (~node19(c_e_h_3, c_f, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s10, s11)) | node15(c_e_h_3, c_f, s10, s11) | node14(c_e_h_3, c_f, s10, s11) | node16(c_e_h_3, c_f, s10))),
% 291.31/183.83 inference(transitivity,[status(thm)],[11739, 11737])).
% 291.31/183.83 tff(11741,plain,
% 291.31/183.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s10) | node14(c_e_h_3, c_f, s10, s11) | node15(c_e_h_3, c_f, s10, s11) | (~node19(c_e_h_3, c_f, s10, s11)))),
% 291.31/183.83 inference(quant_inst,[status(thm)],[])).
% 291.31/183.83 tff(11742,plain,
% 291.31/183.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s10, s11)) | node15(c_e_h_3, c_f, s10, s11) | node14(c_e_h_3, c_f, s10, s11) | node16(c_e_h_3, c_f, s10)),
% 291.31/183.83 inference(modus_ponens,[status(thm)],[11741, 11740])).
% 291.31/183.83 tff(11743,plain,
% 291.31/183.83 (node15(c_e_h_3, c_f, s10, s11) | node14(c_e_h_3, c_f, s10, s11) | node16(c_e_h_3, c_f, s10)),
% 291.31/183.83 inference(unit_resolution,[status(thm)],[11742, 204, 11711])).
% 291.31/183.83 tff(11744,plain,
% 291.31/183.83 (node15(c_e_h_3, c_f, s10, s11)),
% 291.31/183.83 inference(unit_resolution,[status(thm)],[11743, 11736, 11707])).
% 291.31/183.83 tff(11745,plain,
% 291.31/183.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s11)) | (~node15(c_e_h_3, c_f, s10, s11)) | m_c_h_element_v_out(c_e_h_3, c_f, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s11)) | (~node15(c_e_h_3, c_f, s10, s11)) | m_c_h_element_v_out(c_e_h_3, c_f, s10))),
% 291.31/183.84 inference(rewrite,[status(thm)],[])).
% 291.31/183.84 tff(11746,plain,
% 291.31/183.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s11)) | (~node15(c_e_h_3, c_f, s10, s11)) | m_c_h_element_v_out(c_e_h_3, c_f, s10))),
% 291.31/183.84 inference(quant_inst,[status(thm)],[])).
% 291.31/183.84 tff(11747,plain,
% 291.31/183.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s11)) | (~node15(c_e_h_3, c_f, s10, s11)) | m_c_h_element_v_out(c_e_h_3, c_f, s10)),
% 291.31/183.84 inference(modus_ponens,[status(thm)],[11746, 11745])).
% 291.31/183.84 tff(11748,plain,
% 291.31/183.84 ($false),
% 291.31/183.84 inference(unit_resolution,[status(thm)],[11747, 147, 11686, 11685, 11744])).
% 291.31/183.84 tff(11749,plain,(m_c_h_element_v_out(c_e_h_3, c_f, s10) | (~m_c_h_element_v_out(c_e_h_3, c_f, s11)) | m_c_h_element_v_in1(c_e_h_3, c_f, s10)), inference(lemma,lemma(discharge,[]))).
% 291.31/183.84 tff(11750,plain,
% 291.31/183.84 (m_c_h_element_v_in1(c_e_h_3, c_f, s10)),
% 291.31/183.84 inference(unit_resolution,[status(thm)],[11749, 11686, 11685])).
% 291.31/183.84 tff(11751,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_f, s10)), introduced(assumption)).
% 291.31/183.84 tff(11752,plain,
% 291.31/183.84 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s10)) | m_c_h_element_v_in2(c_e_h_3, c_f, s10) | (~node17(c_e_h_3, c_f, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s10)) | m_c_h_element_v_in2(c_e_h_3, c_f, s10) | (~node17(c_e_h_3, c_f, s10)))),
% 291.31/183.84 inference(rewrite,[status(thm)],[])).
% 291.31/183.84 tff(11753,plain,
% 291.31/183.84 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s10)) | m_c_h_element_v_in2(c_e_h_3, c_f, s10) | (~node17(c_e_h_3, c_f, s10)))),
% 291.31/183.84 inference(quant_inst,[status(thm)],[])).
% 291.31/183.84 tff(11754,plain,
% 291.31/183.84 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s10)) | m_c_h_element_v_in2(c_e_h_3, c_f, s10) | (~node17(c_e_h_3, c_f, s10))),
% 291.31/183.84 inference(modus_ponens,[status(thm)],[11753, 11752])).
% 291.31/183.84 tff(11755,plain,
% 291.31/183.84 ((~m_c_h_element_v_in1(c_e_h_3, c_f, s10)) | (~node17(c_e_h_3, c_f, s10))),
% 291.31/183.84 inference(unit_resolution,[status(thm)],[11754, 919, 11751])).
% 291.31/183.84 tff(11756,plain,
% 291.31/183.84 (~node17(c_e_h_3, c_f, s10)),
% 291.31/183.84 inference(unit_resolution,[status(thm)],[11755, 11750])).
% 291.31/183.84 tff(11757,plain,
% 291.31/183.84 ($false),
% 291.31/183.84 inference(unit_resolution,[status(thm)],[11718, 11756, 11696])).
% 291.31/183.84 tff(11758,plain,(m_c_h_element_v_out(c_e_h_3, c_f, s10) | m_c_h_element_v_in2(c_e_h_3, c_f, s10) | (~m_c_h_element_v_out(c_e_h_3, c_f, s11))), inference(lemma,lemma(discharge,[]))).
% 291.31/183.84 tff(11759,plain,
% 291.31/183.84 (~m_c_h_element_v_out(c_e_h_3, c_f, s11)),
% 291.31/183.84 inference(unit_resolution,[status(thm)],[11758, 11684, 11677])).
% 291.31/183.84 tff(11760,assumption,(m_c_h_element_v_out(c_e_h_3, c_f, s12)), introduced(assumption)).
% 291.31/183.84 tff(11761,assumption,(~m_c_h_element_v_out(c_e_h_3, c_f, s11)), introduced(assumption)).
% 291.31/183.84 tff(11762,assumption,(node18(c_e_h_3, c_f, s11, s12)), introduced(assumption)).
% 291.31/183.84 tff(11763,plain,
% 291.31/183.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_f, s11) | (~m_c_h_element_v_out(c_e_h_3, c_f, s12)) | (~node18(c_e_h_3, c_f, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s11) | (~m_c_h_element_v_out(c_e_h_3, c_f, s12)) | (~node18(c_e_h_3, c_f, s11, s12)))),
% 291.31/183.84 inference(rewrite,[status(thm)],[])).
% 291.31/183.84 tff(11764,plain,
% 291.31/183.84 (((~m_c_h_element_v_out(c_e_h_3, c_f, s12)) | m_c_h_element_v_out(c_e_h_3, c_f, s11) | (~node18(c_e_h_3, c_f, s11, s12))) <=> (m_c_h_element_v_out(c_e_h_3, c_f, s11) | (~m_c_h_element_v_out(c_e_h_3, c_f, s12)) | (~node18(c_e_h_3, c_f, s11, s12)))),
% 291.31/183.84 inference(rewrite,[status(thm)],[])).
% 291.31/183.84 tff(11765,plain,
% 291.31/183.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s12)) | m_c_h_element_v_out(c_e_h_3, c_f, s11) | (~node18(c_e_h_3, c_f, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_f, s11) | (~m_c_h_element_v_out(c_e_h_3, c_f, s12)) | (~node18(c_e_h_3, c_f, s11, s12))))),
% 291.31/183.84 inference(monotonicity,[status(thm)],[11764])).
% 291.31/183.84 tff(11766,plain,
% 291.31/183.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s12)) | m_c_h_element_v_out(c_e_h_3, c_f, s11) | (~node18(c_e_h_3, c_f, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s11) | (~m_c_h_element_v_out(c_e_h_3, c_f, s12)) | (~node18(c_e_h_3, c_f, s11, s12)))),
% 291.31/183.84 inference(transitivity,[status(thm)],[11765, 11763])).
% 291.31/183.84 tff(11767,plain,
% 291.31/183.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s12)) | m_c_h_element_v_out(c_e_h_3, c_f, s11) | (~node18(c_e_h_3, c_f, s11, s12)))),
% 291.31/183.84 inference(quant_inst,[status(thm)],[])).
% 291.31/183.84 tff(11768,plain,
% 291.31/183.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s11) | (~m_c_h_element_v_out(c_e_h_3, c_f, s12)) | (~node18(c_e_h_3, c_f, s11, s12))),
% 291.31/183.84 inference(modus_ponens,[status(thm)],[11767, 11766])).
% 291.31/183.84 tff(11769,plain,
% 291.31/183.84 ($false),
% 291.31/183.84 inference(unit_resolution,[status(thm)],[11768, 753, 11760, 11761, 11762])).
% 291.31/183.84 tff(11770,plain,((~node18(c_e_h_3, c_f, s11, s12)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s12)) | m_c_h_element_v_out(c_e_h_3, c_f, s11)), inference(lemma,lemma(discharge,[]))).
% 291.31/183.84 tff(11771,plain,
% 291.31/183.84 (~node18(c_e_h_3, c_f, s11, s12)),
% 291.31/183.84 inference(unit_resolution,[status(thm)],[11770, 11760, 11761])).
% 291.31/183.84 tff(11772,plain,
% 291.31/183.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s11, s12)) | node19(c_e_h_3, c_f, s11, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s11, s12)) | node19(c_e_h_3, c_f, s11, s12))),
% 291.31/183.84 inference(rewrite,[status(thm)],[])).
% 291.31/183.84 tff(11773,plain,
% 291.31/183.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s11, s12)) | node19(c_e_h_3, c_f, s11, s12))),
% 291.31/183.84 inference(quant_inst,[status(thm)],[])).
% 291.31/183.84 tff(11774,plain,
% 291.31/183.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s11, s12)) | node19(c_e_h_3, c_f, s11, s12)),
% 291.31/183.84 inference(modus_ponens,[status(thm)],[11773, 11772])).
% 291.31/183.84 tff(11775,plain,
% 291.31/183.84 (node19(c_e_h_3, c_f, s11, s12)),
% 291.31/183.84 inference(unit_resolution,[status(thm)],[11774, 190, 11461])).
% 291.31/183.84 tff(11776,plain,
% 291.31/183.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_f, s11, s12)) | node18(c_e_h_3, c_f, s11, s12) | node17(c_e_h_3, c_f, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s11, s12)) | node18(c_e_h_3, c_f, s11, s12) | node17(c_e_h_3, c_f, s11))),
% 291.31/183.85 inference(rewrite,[status(thm)],[])).
% 291.31/183.85 tff(11777,plain,
% 291.31/183.85 ((node17(c_e_h_3, c_f, s11) | node18(c_e_h_3, c_f, s11, s12) | (~node19(c_e_h_3, c_f, s11, s12))) <=> ((~node19(c_e_h_3, c_f, s11, s12)) | node18(c_e_h_3, c_f, s11, s12) | node17(c_e_h_3, c_f, s11))),
% 291.31/183.85 inference(rewrite,[status(thm)],[])).
% 291.31/183.85 tff(11778,plain,
% 291.31/183.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s11) | node18(c_e_h_3, c_f, s11, s12) | (~node19(c_e_h_3, c_f, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_f, s11, s12)) | node18(c_e_h_3, c_f, s11, s12) | node17(c_e_h_3, c_f, s11)))),
% 291.31/183.85 inference(monotonicity,[status(thm)],[11777])).
% 291.31/183.85 tff(11779,plain,
% 291.31/183.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s11) | node18(c_e_h_3, c_f, s11, s12) | (~node19(c_e_h_3, c_f, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s11, s12)) | node18(c_e_h_3, c_f, s11, s12) | node17(c_e_h_3, c_f, s11))),
% 291.31/183.85 inference(transitivity,[status(thm)],[11778, 11776])).
% 291.31/183.85 tff(11780,plain,
% 291.31/183.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s11) | node18(c_e_h_3, c_f, s11, s12) | (~node19(c_e_h_3, c_f, s11, s12)))),
% 291.31/183.85 inference(quant_inst,[status(thm)],[])).
% 291.31/183.85 tff(11781,plain,
% 291.31/183.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s11, s12)) | node18(c_e_h_3, c_f, s11, s12) | node17(c_e_h_3, c_f, s11)),
% 291.31/183.85 inference(modus_ponens,[status(thm)],[11780, 11779])).
% 291.31/183.85 tff(11782,plain,
% 291.31/183.85 (node18(c_e_h_3, c_f, s11, s12) | node17(c_e_h_3, c_f, s11)),
% 291.31/183.85 inference(unit_resolution,[status(thm)],[11781, 776, 11775])).
% 291.31/183.85 tff(11783,plain,
% 291.31/183.85 (node17(c_e_h_3, c_f, s11)),
% 291.31/183.85 inference(unit_resolution,[status(thm)],[11782, 11771])).
% 291.31/183.85 tff(11784,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_f, s11)), introduced(assumption)).
% 291.31/183.85 tff(11785,assumption,(node17(c_e_h_3, c_f, s11)), introduced(assumption)).
% 291.31/183.85 tff(11786,plain,
% 291.31/183.85 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_f, s11)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s11)) | m_c_h_element_v_in2(c_e_h_3, c_f, s11))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_f, s11)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s11)) | m_c_h_element_v_in2(c_e_h_3, c_f, s11))),
% 291.31/183.85 inference(rewrite,[status(thm)],[])).
% 291.31/183.85 tff(11787,plain,
% 291.31/183.85 (((~m_c_h_element_v_in1(c_e_h_3, c_f, s11)) | m_c_h_element_v_in2(c_e_h_3, c_f, s11) | (~node17(c_e_h_3, c_f, s11))) <=> ((~node17(c_e_h_3, c_f, s11)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s11)) | m_c_h_element_v_in2(c_e_h_3, c_f, s11))),
% 291.31/183.85 inference(rewrite,[status(thm)],[])).
% 291.31/183.85 tff(11788,plain,
% 291.31/183.85 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s11)) | m_c_h_element_v_in2(c_e_h_3, c_f, s11) | (~node17(c_e_h_3, c_f, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_f, s11)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s11)) | m_c_h_element_v_in2(c_e_h_3, c_f, s11)))),
% 291.31/183.85 inference(monotonicity,[status(thm)],[11787])).
% 291.31/183.85 tff(11789,plain,
% 291.31/183.85 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s11)) | m_c_h_element_v_in2(c_e_h_3, c_f, s11) | (~node17(c_e_h_3, c_f, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_f, s11)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s11)) | m_c_h_element_v_in2(c_e_h_3, c_f, s11))),
% 291.31/183.85 inference(transitivity,[status(thm)],[11788, 11786])).
% 291.31/183.85 tff(11790,plain,
% 291.31/183.85 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s11)) | m_c_h_element_v_in2(c_e_h_3, c_f, s11) | (~node17(c_e_h_3, c_f, s11)))),
% 291.31/183.85 inference(quant_inst,[status(thm)],[])).
% 291.31/183.85 tff(11791,plain,
% 291.31/183.85 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_f, s11)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s11)) | m_c_h_element_v_in2(c_e_h_3, c_f, s11)),
% 291.31/183.85 inference(modus_ponens,[status(thm)],[11790, 11789])).
% 291.31/183.85 tff(11792,plain,
% 291.31/183.85 ((~m_c_h_element_v_in1(c_e_h_3, c_f, s11)) | m_c_h_element_v_in2(c_e_h_3, c_f, s11)),
% 291.31/183.85 inference(unit_resolution,[status(thm)],[11791, 919, 11785])).
% 291.31/183.85 tff(11793,plain,
% 291.31/183.85 (~m_c_h_element_v_in1(c_e_h_3, c_f, s11)),
% 291.31/183.85 inference(unit_resolution,[status(thm)],[11792, 11784])).
% 291.31/183.85 tff(11794,assumption,(node16(c_e_h_3, c_f, s11)), introduced(assumption)).
% 291.31/183.85 tff(11795,plain,
% 291.31/183.85 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s11)) | m_c_h_element_v_in1(c_e_h_3, c_f, s11) | m_c_h_element_v_in2(c_e_h_3, c_f, s11))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s11)) | m_c_h_element_v_in1(c_e_h_3, c_f, s11) | m_c_h_element_v_in2(c_e_h_3, c_f, s11))),
% 291.31/183.85 inference(rewrite,[status(thm)],[])).
% 291.31/183.85 tff(11796,plain,
% 291.31/183.85 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s11)) | m_c_h_element_v_in1(c_e_h_3, c_f, s11) | m_c_h_element_v_in2(c_e_h_3, c_f, s11))),
% 291.31/183.85 inference(quant_inst,[status(thm)],[])).
% 291.31/183.85 tff(11797,plain,
% 291.31/183.85 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s11)) | m_c_h_element_v_in1(c_e_h_3, c_f, s11) | m_c_h_element_v_in2(c_e_h_3, c_f, s11)),
% 291.31/183.85 inference(modus_ponens,[status(thm)],[11796, 11795])).
% 291.31/183.85 tff(11798,plain,
% 291.31/183.85 (m_c_h_element_v_in1(c_e_h_3, c_f, s11) | m_c_h_element_v_in2(c_e_h_3, c_f, s11)),
% 291.31/183.85 inference(unit_resolution,[status(thm)],[11797, 178, 11794])).
% 291.31/183.85 tff(11799,plain,
% 291.31/183.85 ($false),
% 291.31/183.85 inference(unit_resolution,[status(thm)],[11798, 11793, 11784])).
% 291.31/183.85 tff(11800,plain,(m_c_h_element_v_in2(c_e_h_3, c_f, s11) | (~node16(c_e_h_3, c_f, s11)) | (~node17(c_e_h_3, c_f, s11))), inference(lemma,lemma(discharge,[]))).
% 291.31/183.85 tff(11801,plain,
% 291.31/183.85 (~node16(c_e_h_3, c_f, s11)),
% 291.31/183.85 inference(unit_resolution,[status(thm)],[11800, 11784, 11783])).
% 291.31/183.85 tff(11802,plain,
% 291.31/183.85 ((~m_c_h_element_v_in1(c_e_h_3, c_f, s11)) | m_c_h_element_v_in2(c_e_h_3, c_f, s11)),
% 291.31/183.85 inference(unit_resolution,[status(thm)],[11791, 919, 11783])).
% 291.31/183.85 tff(11803,plain,
% 291.31/183.85 (~m_c_h_element_v_in1(c_e_h_3, c_f, s11)),
% 291.31/183.85 inference(unit_resolution,[status(thm)],[11802, 11784])).
% 291.31/183.85 tff(11804,assumption,(~node16(c_e_h_3, c_f, s11)), introduced(assumption)).
% 291.31/183.85 tff(11805,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_f, s11)), introduced(assumption)).
% 291.31/183.85 tff(11806,assumption,(node14(c_e_h_3, c_f, s11, s12)), introduced(assumption)).
% 291.31/183.85 tff(11807,plain,
% 291.31/183.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s12)) | m_c_h_element_v_in1(c_e_h_3, c_f, s11) | (~node14(c_e_h_3, c_f, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s12)) | m_c_h_element_v_in1(c_e_h_3, c_f, s11) | (~node14(c_e_h_3, c_f, s11, s12)))),
% 291.31/183.85 inference(rewrite,[status(thm)],[])).
% 291.31/183.85 tff(11808,plain,
% 291.31/183.85 (((~node14(c_e_h_3, c_f, s11, s12)) | m_c_h_element_v_in1(c_e_h_3, c_f, s11) | (~m_c_h_element_v_out(c_e_h_3, c_f, s12))) <=> ((~m_c_h_element_v_out(c_e_h_3, c_f, s12)) | m_c_h_element_v_in1(c_e_h_3, c_f, s11) | (~node14(c_e_h_3, c_f, s11, s12)))),
% 291.31/183.85 inference(rewrite,[status(thm)],[])).
% 291.31/183.85 tff(11809,plain,
% 291.31/183.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s11, s12)) | m_c_h_element_v_in1(c_e_h_3, c_f, s11) | (~m_c_h_element_v_out(c_e_h_3, c_f, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s12)) | m_c_h_element_v_in1(c_e_h_3, c_f, s11) | (~node14(c_e_h_3, c_f, s11, s12))))),
% 291.31/183.85 inference(monotonicity,[status(thm)],[11808])).
% 291.31/183.85 tff(11810,plain,
% 291.31/183.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s11, s12)) | m_c_h_element_v_in1(c_e_h_3, c_f, s11) | (~m_c_h_element_v_out(c_e_h_3, c_f, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s12)) | m_c_h_element_v_in1(c_e_h_3, c_f, s11) | (~node14(c_e_h_3, c_f, s11, s12)))),
% 291.31/183.85 inference(transitivity,[status(thm)],[11809, 11807])).
% 291.31/183.85 tff(11811,plain,
% 291.31/183.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s11, s12)) | m_c_h_element_v_in1(c_e_h_3, c_f, s11) | (~m_c_h_element_v_out(c_e_h_3, c_f, s12)))),
% 291.31/183.85 inference(quant_inst,[status(thm)],[])).
% 291.31/183.85 tff(11812,plain,
% 291.31/183.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s12)) | m_c_h_element_v_in1(c_e_h_3, c_f, s11) | (~node14(c_e_h_3, c_f, s11, s12))),
% 291.31/183.85 inference(modus_ponens,[status(thm)],[11811, 11810])).
% 291.31/183.85 tff(11813,plain,
% 291.31/183.85 ($false),
% 291.31/183.85 inference(unit_resolution,[status(thm)],[11812, 223, 11760, 11806, 11805])).
% 291.31/183.85 tff(11814,plain,((~node14(c_e_h_3, c_f, s11, s12)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s12)) | m_c_h_element_v_in1(c_e_h_3, c_f, s11)), inference(lemma,lemma(discharge,[]))).
% 291.31/183.85 tff(11815,plain,
% 291.31/183.85 (~node14(c_e_h_3, c_f, s11, s12)),
% 291.31/183.85 inference(unit_resolution,[status(thm)],[11814, 11760, 11805])).
% 291.31/183.85 tff(11816,plain,
% 291.31/183.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_f, s11, s12)) | node14(c_e_h_3, c_f, s11, s12) | node15(c_e_h_3, c_f, s11, s12) | node16(c_e_h_3, c_f, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s11, s12)) | node14(c_e_h_3, c_f, s11, s12) | node15(c_e_h_3, c_f, s11, s12) | node16(c_e_h_3, c_f, s11))),
% 291.31/183.85 inference(rewrite,[status(thm)],[])).
% 291.31/183.85 tff(11817,plain,
% 291.31/183.85 ((node16(c_e_h_3, c_f, s11) | node14(c_e_h_3, c_f, s11, s12) | node15(c_e_h_3, c_f, s11, s12) | (~node19(c_e_h_3, c_f, s11, s12))) <=> ((~node19(c_e_h_3, c_f, s11, s12)) | node14(c_e_h_3, c_f, s11, s12) | node15(c_e_h_3, c_f, s11, s12) | node16(c_e_h_3, c_f, s11))),
% 291.31/183.85 inference(rewrite,[status(thm)],[])).
% 291.31/183.85 tff(11818,plain,
% 291.31/183.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s11) | node14(c_e_h_3, c_f, s11, s12) | node15(c_e_h_3, c_f, s11, s12) | (~node19(c_e_h_3, c_f, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_f, s11, s12)) | node14(c_e_h_3, c_f, s11, s12) | node15(c_e_h_3, c_f, s11, s12) | node16(c_e_h_3, c_f, s11)))),
% 291.31/183.86 inference(monotonicity,[status(thm)],[11817])).
% 291.31/183.86 tff(11819,plain,
% 291.31/183.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s11) | node14(c_e_h_3, c_f, s11, s12) | node15(c_e_h_3, c_f, s11, s12) | (~node19(c_e_h_3, c_f, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s11, s12)) | node14(c_e_h_3, c_f, s11, s12) | node15(c_e_h_3, c_f, s11, s12) | node16(c_e_h_3, c_f, s11))),
% 291.31/183.86 inference(transitivity,[status(thm)],[11818, 11816])).
% 291.31/183.86 tff(11820,plain,
% 291.31/183.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s11) | node14(c_e_h_3, c_f, s11, s12) | node15(c_e_h_3, c_f, s11, s12) | (~node19(c_e_h_3, c_f, s11, s12)))),
% 291.31/183.86 inference(quant_inst,[status(thm)],[])).
% 291.31/183.86 tff(11821,plain,
% 291.31/183.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s11, s12)) | node14(c_e_h_3, c_f, s11, s12) | node15(c_e_h_3, c_f, s11, s12) | node16(c_e_h_3, c_f, s11)),
% 291.31/183.86 inference(modus_ponens,[status(thm)],[11820, 11819])).
% 291.31/183.86 tff(11822,plain,
% 291.31/183.86 (node14(c_e_h_3, c_f, s11, s12) | node15(c_e_h_3, c_f, s11, s12) | node16(c_e_h_3, c_f, s11)),
% 291.31/183.86 inference(unit_resolution,[status(thm)],[11821, 204, 11775])).
% 291.31/183.86 tff(11823,plain,
% 291.31/183.86 (node15(c_e_h_3, c_f, s11, s12)),
% 291.31/183.86 inference(unit_resolution,[status(thm)],[11822, 11815, 11804])).
% 291.31/183.86 tff(11824,plain,
% 291.31/183.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s12)) | (~node15(c_e_h_3, c_f, s11, s12)) | m_c_h_element_v_out(c_e_h_3, c_f, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s12)) | (~node15(c_e_h_3, c_f, s11, s12)) | m_c_h_element_v_out(c_e_h_3, c_f, s11))),
% 291.31/183.86 inference(rewrite,[status(thm)],[])).
% 291.31/183.86 tff(11825,plain,
% 291.31/183.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s12)) | (~node15(c_e_h_3, c_f, s11, s12)) | m_c_h_element_v_out(c_e_h_3, c_f, s11))),
% 291.31/183.86 inference(quant_inst,[status(thm)],[])).
% 291.31/183.86 tff(11826,plain,
% 291.31/183.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s12)) | (~node15(c_e_h_3, c_f, s11, s12)) | m_c_h_element_v_out(c_e_h_3, c_f, s11)),
% 291.31/183.86 inference(modus_ponens,[status(thm)],[11825, 11824])).
% 291.31/183.86 tff(11827,plain,
% 291.31/183.86 ($false),
% 291.31/183.86 inference(unit_resolution,[status(thm)],[11826, 147, 11760, 11761, 11823])).
% 291.31/183.86 tff(11828,plain,((~m_c_h_element_v_out(c_e_h_3, c_f, s12)) | m_c_h_element_v_out(c_e_h_3, c_f, s11) | node16(c_e_h_3, c_f, s11) | m_c_h_element_v_in1(c_e_h_3, c_f, s11)), inference(lemma,lemma(discharge,[]))).
% 291.31/183.86 tff(11829,plain,
% 291.31/183.86 ($false),
% 291.31/183.86 inference(unit_resolution,[status(thm)],[11828, 11803, 11801, 11761, 11760])).
% 291.31/183.86 tff(11830,plain,(m_c_h_element_v_in2(c_e_h_3, c_f, s11) | m_c_h_element_v_out(c_e_h_3, c_f, s11) | (~m_c_h_element_v_out(c_e_h_3, c_f, s12))), inference(lemma,lemma(discharge,[]))).
% 291.31/183.86 tff(11831,plain,
% 291.31/183.86 (m_c_h_element_v_in2(c_e_h_3, c_f, s11) | (~m_c_h_element_v_out(c_e_h_3, c_f, s12))),
% 291.31/183.86 inference(unit_resolution,[status(thm)],[11830, 11759])).
% 291.31/183.86 tff(11832,plain,
% 291.31/183.86 (~m_c_h_element_v_out(c_e_h_3, c_f, s12)),
% 291.31/183.86 inference(unit_resolution,[status(thm)],[11831, 11475])).
% 291.31/183.86 tff(11833,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_i, s12)), introduced(assumption)).
% 291.31/183.86 tff(11834,assumption,(m_c_h_element_v_in2(c_e_h_3, c_f, s12)), introduced(assumption)).
% 291.31/183.86 tff(11835,plain,
% 291.31/183.86 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s12)) | m_and_h_gate_v_out(c_e_h_3, c_i, s12))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s12)) | m_and_h_gate_v_out(c_e_h_3, c_i, s12))),
% 291.31/183.86 inference(rewrite,[status(thm)],[])).
% 291.31/183.86 tff(11836,plain,
% 291.31/183.86 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s12)) | m_and_h_gate_v_out(c_e_h_3, c_i, s12))),
% 291.31/183.86 inference(quant_inst,[status(thm)],[])).
% 291.31/183.86 tff(11837,plain,
% 291.31/183.86 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s12)) | m_and_h_gate_v_out(c_e_h_3, c_i, s12)),
% 291.31/183.86 inference(modus_ponens,[status(thm)],[11836, 11835])).
% 291.31/183.86 tff(11838,plain,
% 291.31/183.86 ($false),
% 291.31/183.86 inference(unit_resolution,[status(thm)],[11837, 2143, 11834, 11833])).
% 291.31/183.86 tff(11839,plain,((~m_c_h_element_v_in2(c_e_h_3, c_f, s12)) | m_and_h_gate_v_out(c_e_h_3, c_i, s12)), inference(lemma,lemma(discharge,[]))).
% 291.31/183.86 tff(11840,plain,
% 291.31/183.86 (~m_c_h_element_v_in2(c_e_h_3, c_f, s12)),
% 291.31/183.86 inference(unit_resolution,[status(thm)],[11839, 11468])).
% 291.31/183.86 tff(11841,assumption,(~m_c_h_element_v_out(c_e_h_3, c_f, s12)), introduced(assumption)).
% 291.31/183.86 tff(11842,assumption,(m_c_h_element_v_out(c_e_h_3, c_f, s13)), introduced(assumption)).
% 291.31/183.86 tff(11843,assumption,(node18(c_e_h_3, c_f, s12, s13)), introduced(assumption)).
% 291.31/183.86 tff(11844,plain,
% 291.31/183.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s13)) | m_c_h_element_v_out(c_e_h_3, c_f, s12) | (~node18(c_e_h_3, c_f, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s13)) | m_c_h_element_v_out(c_e_h_3, c_f, s12) | (~node18(c_e_h_3, c_f, s12, s13)))),
% 291.31/183.86 inference(rewrite,[status(thm)],[])).
% 291.31/183.86 tff(11845,plain,
% 291.31/183.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s13)) | m_c_h_element_v_out(c_e_h_3, c_f, s12) | (~node18(c_e_h_3, c_f, s12, s13)))),
% 291.31/183.86 inference(quant_inst,[status(thm)],[])).
% 291.31/183.86 tff(11846,plain,
% 291.31/183.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s13)) | m_c_h_element_v_out(c_e_h_3, c_f, s12) | (~node18(c_e_h_3, c_f, s12, s13))),
% 291.31/183.86 inference(modus_ponens,[status(thm)],[11845, 11844])).
% 291.31/183.86 tff(11847,plain,
% 291.31/183.86 ($false),
% 291.31/183.86 inference(unit_resolution,[status(thm)],[11846, 753, 11841, 11842, 11843])).
% 291.31/183.86 tff(11848,plain,((~node18(c_e_h_3, c_f, s12, s13)) | m_c_h_element_v_out(c_e_h_3, c_f, s12) | (~m_c_h_element_v_out(c_e_h_3, c_f, s13))), inference(lemma,lemma(discharge,[]))).
% 291.31/183.86 tff(11849,plain,
% 291.31/183.86 (~node18(c_e_h_3, c_f, s12, s13)),
% 291.31/183.86 inference(unit_resolution,[status(thm)],[11848, 11842, 11841])).
% 291.31/183.86 tff(11850,plain,
% 291.31/183.86 (succ(s12, s13) <=> succ(s12, s13)),
% 291.31/183.86 inference(rewrite,[status(thm)],[])).
% 291.31/183.86 tff(11851,axiom,(succ(s12, s13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound13')).
% 291.31/183.86 tff(11852,plain,
% 291.31/183.86 (succ(s12, s13)),
% 291.31/183.86 inference(modus_ponens,[status(thm)],[11851, 11850])).
% 291.31/183.86 tff(11853,plain,
% 291.31/183.86 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s12, s13)) | trans(s12, s13))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s12, s13)) | trans(s12, s13))),
% 291.31/183.86 inference(rewrite,[status(thm)],[])).
% 291.31/183.86 tff(11854,plain,
% 291.31/183.86 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s12, s13)) | trans(s12, s13))),
% 291.31/183.86 inference(quant_inst,[status(thm)],[])).
% 291.31/183.86 tff(11855,plain,
% 291.31/183.86 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s12, s13)) | trans(s12, s13)),
% 291.31/183.86 inference(modus_ponens,[status(thm)],[11854, 11853])).
% 291.31/183.86 tff(11856,plain,
% 291.31/183.86 (trans(s12, s13)),
% 291.31/183.86 inference(unit_resolution,[status(thm)],[11855, 11852, 65])).
% 291.31/183.86 tff(11857,plain,
% 291.31/183.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s12, s13)) | node19(c_e_h_3, c_f, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s12, s13)) | node19(c_e_h_3, c_f, s12, s13))),
% 291.31/183.86 inference(rewrite,[status(thm)],[])).
% 291.31/183.86 tff(11858,plain,
% 291.31/183.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s12, s13)) | node19(c_e_h_3, c_f, s12, s13))),
% 291.31/183.86 inference(quant_inst,[status(thm)],[])).
% 291.31/183.86 tff(11859,plain,
% 291.31/183.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s12, s13)) | node19(c_e_h_3, c_f, s12, s13)),
% 291.31/183.86 inference(modus_ponens,[status(thm)],[11858, 11857])).
% 291.31/183.86 tff(11860,plain,
% 291.31/183.86 (node19(c_e_h_3, c_f, s12, s13)),
% 291.31/183.86 inference(unit_resolution,[status(thm)],[11859, 190, 11856])).
% 291.31/183.86 tff(11861,plain,
% 291.31/183.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s12) | node18(c_e_h_3, c_f, s12, s13) | (~node19(c_e_h_3, c_f, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_f, s12) | node18(c_e_h_3, c_f, s12, s13) | (~node19(c_e_h_3, c_f, s12, s13)))),
% 291.31/183.86 inference(rewrite,[status(thm)],[])).
% 291.31/183.86 tff(11862,plain,
% 291.31/183.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s12) | node18(c_e_h_3, c_f, s12, s13) | (~node19(c_e_h_3, c_f, s12, s13)))),
% 291.31/183.86 inference(quant_inst,[status(thm)],[])).
% 291.31/183.86 tff(11863,plain,
% 291.31/183.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_f, s12) | node18(c_e_h_3, c_f, s12, s13) | (~node19(c_e_h_3, c_f, s12, s13))),
% 291.31/183.86 inference(modus_ponens,[status(thm)],[11862, 11861])).
% 291.31/183.86 tff(11864,plain,
% 291.31/183.86 (node17(c_e_h_3, c_f, s12) | node18(c_e_h_3, c_f, s12, s13)),
% 291.31/183.86 inference(unit_resolution,[status(thm)],[11863, 776, 11860])).
% 291.31/183.86 tff(11865,plain,
% 291.31/183.86 (node17(c_e_h_3, c_f, s12)),
% 291.31/183.86 inference(unit_resolution,[status(thm)],[11864, 11849])).
% 291.31/183.86 tff(11866,assumption,(node15(c_e_h_3, c_f, s12, s13)), introduced(assumption)).
% 291.31/183.86 tff(11867,plain,
% 291.31/183.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s13)) | (~node15(c_e_h_3, c_f, s12, s13)) | m_c_h_element_v_out(c_e_h_3, c_f, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s13)) | (~node15(c_e_h_3, c_f, s12, s13)) | m_c_h_element_v_out(c_e_h_3, c_f, s12))),
% 291.31/183.86 inference(rewrite,[status(thm)],[])).
% 291.31/183.86 tff(11868,plain,
% 291.31/183.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s13)) | (~node15(c_e_h_3, c_f, s12, s13)) | m_c_h_element_v_out(c_e_h_3, c_f, s12))),
% 291.31/183.86 inference(quant_inst,[status(thm)],[])).
% 291.31/183.86 tff(11869,plain,
% 291.31/183.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s13)) | (~node15(c_e_h_3, c_f, s12, s13)) | m_c_h_element_v_out(c_e_h_3, c_f, s12)),
% 291.31/183.86 inference(modus_ponens,[status(thm)],[11868, 11867])).
% 291.31/183.86 tff(11870,plain,
% 291.31/183.86 ($false),
% 291.31/183.86 inference(unit_resolution,[status(thm)],[11869, 147, 11841, 11842, 11866])).
% 291.31/183.86 tff(11871,plain,((~node15(c_e_h_3, c_f, s12, s13)) | m_c_h_element_v_out(c_e_h_3, c_f, s12) | (~m_c_h_element_v_out(c_e_h_3, c_f, s13))), inference(lemma,lemma(discharge,[]))).
% 291.31/183.86 tff(11872,plain,
% 291.31/183.86 (~node15(c_e_h_3, c_f, s12, s13)),
% 291.31/183.86 inference(unit_resolution,[status(thm)],[11871, 11842, 11841])).
% 291.31/183.86 tff(11873,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_f, s12)), introduced(assumption)).
% 291.31/183.86 tff(11874,assumption,(~node15(c_e_h_3, c_f, s12, s13)), introduced(assumption)).
% 291.31/183.87 tff(11875,assumption,(node17(c_e_h_3, c_f, s12)), introduced(assumption)).
% 291.31/183.87 tff(11876,plain,
% 291.31/183.87 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s12) | (~node17(c_e_h_3, c_f, s12)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_3, c_f, s12) | (~node17(c_e_h_3, c_f, s12)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s12)))),
% 291.31/183.87 inference(rewrite,[status(thm)],[])).
% 291.31/183.87 tff(11877,plain,
% 291.31/183.87 ((m_c_h_element_v_in1(c_e_h_3, c_f, s12) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s12)) | (~node17(c_e_h_3, c_f, s12))) <=> (m_c_h_element_v_in1(c_e_h_3, c_f, s12) | (~node17(c_e_h_3, c_f, s12)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s12)))),
% 291.31/183.87 inference(rewrite,[status(thm)],[])).
% 291.31/183.87 tff(11878,plain,
% 291.31/183.87 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s12) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s12)) | (~node17(c_e_h_3, c_f, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s12) | (~node17(c_e_h_3, c_f, s12)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s12))))),
% 291.31/183.87 inference(monotonicity,[status(thm)],[11877])).
% 291.31/183.87 tff(11879,plain,
% 291.31/183.87 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s12) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s12)) | (~node17(c_e_h_3, c_f, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_3, c_f, s12) | (~node17(c_e_h_3, c_f, s12)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s12)))),
% 291.31/183.87 inference(transitivity,[status(thm)],[11878, 11876])).
% 291.31/183.87 tff(11880,plain,
% 291.31/183.87 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s12) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s12)) | (~node17(c_e_h_3, c_f, s12)))),
% 291.31/183.87 inference(quant_inst,[status(thm)],[])).
% 291.31/183.87 tff(11881,plain,
% 291.31/183.87 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_3, c_f, s12) | (~node17(c_e_h_3, c_f, s12)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s12))),
% 291.31/183.87 inference(modus_ponens,[status(thm)],[11880, 11879])).
% 291.31/183.87 tff(11882,plain,
% 291.31/183.87 (m_c_h_element_v_in1(c_e_h_3, c_f, s12) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s12))),
% 291.31/183.87 inference(unit_resolution,[status(thm)],[11881, 859, 11875])).
% 291.31/183.87 tff(11883,plain,
% 291.31/183.87 (~m_c_h_element_v_in2(c_e_h_3, c_f, s12)),
% 291.31/183.87 inference(unit_resolution,[status(thm)],[11882, 11873])).
% 291.31/183.87 tff(11884,plain,
% 291.31/183.87 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s12)) | m_c_h_element_v_in1(c_e_h_3, c_f, s12) | m_c_h_element_v_in2(c_e_h_3, c_f, s12))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s12)) | m_c_h_element_v_in1(c_e_h_3, c_f, s12) | m_c_h_element_v_in2(c_e_h_3, c_f, s12))),
% 291.31/183.87 inference(rewrite,[status(thm)],[])).
% 291.31/183.87 tff(11885,plain,
% 291.31/183.87 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s12)) | m_c_h_element_v_in1(c_e_h_3, c_f, s12) | m_c_h_element_v_in2(c_e_h_3, c_f, s12))),
% 291.31/183.87 inference(quant_inst,[status(thm)],[])).
% 291.31/183.87 tff(11886,plain,
% 291.31/183.87 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s12)) | m_c_h_element_v_in1(c_e_h_3, c_f, s12) | m_c_h_element_v_in2(c_e_h_3, c_f, s12)),
% 291.31/183.87 inference(modus_ponens,[status(thm)],[11885, 11884])).
% 291.31/183.87 tff(11887,plain,
% 291.31/183.87 (~node16(c_e_h_3, c_f, s12)),
% 291.31/183.87 inference(unit_resolution,[status(thm)],[11886, 178, 11873, 11883])).
% 291.31/183.87 tff(11888,plain,
% 291.31/183.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s12) | node14(c_e_h_3, c_f, s12, s13) | (~node19(c_e_h_3, c_f, s12, s13)) | node15(c_e_h_3, c_f, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_f, s12) | node14(c_e_h_3, c_f, s12, s13) | (~node19(c_e_h_3, c_f, s12, s13)) | node15(c_e_h_3, c_f, s12, s13))),
% 291.31/183.87 inference(rewrite,[status(thm)],[])).
% 291.31/183.87 tff(11889,plain,
% 291.31/183.87 ((node16(c_e_h_3, c_f, s12) | node14(c_e_h_3, c_f, s12, s13) | node15(c_e_h_3, c_f, s12, s13) | (~node19(c_e_h_3, c_f, s12, s13))) <=> (node16(c_e_h_3, c_f, s12) | node14(c_e_h_3, c_f, s12, s13) | (~node19(c_e_h_3, c_f, s12, s13)) | node15(c_e_h_3, c_f, s12, s13))),
% 291.31/183.87 inference(rewrite,[status(thm)],[])).
% 291.31/183.87 tff(11890,plain,
% 291.31/183.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s12) | node14(c_e_h_3, c_f, s12, s13) | node15(c_e_h_3, c_f, s12, s13) | (~node19(c_e_h_3, c_f, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s12) | node14(c_e_h_3, c_f, s12, s13) | (~node19(c_e_h_3, c_f, s12, s13)) | node15(c_e_h_3, c_f, s12, s13)))),
% 291.31/183.87 inference(monotonicity,[status(thm)],[11889])).
% 291.31/183.87 tff(11891,plain,
% 291.31/183.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s12) | node14(c_e_h_3, c_f, s12, s13) | node15(c_e_h_3, c_f, s12, s13) | (~node19(c_e_h_3, c_f, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_f, s12) | node14(c_e_h_3, c_f, s12, s13) | (~node19(c_e_h_3, c_f, s12, s13)) | node15(c_e_h_3, c_f, s12, s13))),
% 291.31/183.87 inference(transitivity,[status(thm)],[11890, 11888])).
% 291.31/183.87 tff(11892,plain,
% 291.31/183.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s12) | node14(c_e_h_3, c_f, s12, s13) | node15(c_e_h_3, c_f, s12, s13) | (~node19(c_e_h_3, c_f, s12, s13)))),
% 291.31/183.87 inference(quant_inst,[status(thm)],[])).
% 291.31/183.87 tff(11893,plain,
% 291.31/183.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_f, s12) | node14(c_e_h_3, c_f, s12, s13) | (~node19(c_e_h_3, c_f, s12, s13)) | node15(c_e_h_3, c_f, s12, s13)),
% 291.31/183.87 inference(modus_ponens,[status(thm)],[11892, 11891])).
% 291.31/183.87 tff(11894,plain,
% 291.31/183.87 (node16(c_e_h_3, c_f, s12) | node14(c_e_h_3, c_f, s12, s13) | node15(c_e_h_3, c_f, s12, s13)),
% 291.31/183.87 inference(unit_resolution,[status(thm)],[11893, 204, 11860])).
% 291.31/183.87 tff(11895,plain,
% 291.31/183.87 (node14(c_e_h_3, c_f, s12, s13)),
% 291.31/183.87 inference(unit_resolution,[status(thm)],[11894, 11887, 11874])).
% 291.31/183.87 tff(11896,plain,
% 291.31/183.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s13)) | m_c_h_element_v_in1(c_e_h_3, c_f, s12) | (~node14(c_e_h_3, c_f, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s13)) | m_c_h_element_v_in1(c_e_h_3, c_f, s12) | (~node14(c_e_h_3, c_f, s12, s13)))),
% 291.31/183.87 inference(rewrite,[status(thm)],[])).
% 291.31/183.87 tff(11897,plain,
% 291.31/183.87 (((~node14(c_e_h_3, c_f, s12, s13)) | m_c_h_element_v_in1(c_e_h_3, c_f, s12) | (~m_c_h_element_v_out(c_e_h_3, c_f, s13))) <=> ((~m_c_h_element_v_out(c_e_h_3, c_f, s13)) | m_c_h_element_v_in1(c_e_h_3, c_f, s12) | (~node14(c_e_h_3, c_f, s12, s13)))),
% 291.31/183.88 inference(rewrite,[status(thm)],[])).
% 291.31/183.88 tff(11898,plain,
% 291.31/183.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s12, s13)) | m_c_h_element_v_in1(c_e_h_3, c_f, s12) | (~m_c_h_element_v_out(c_e_h_3, c_f, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s13)) | m_c_h_element_v_in1(c_e_h_3, c_f, s12) | (~node14(c_e_h_3, c_f, s12, s13))))),
% 291.31/183.88 inference(monotonicity,[status(thm)],[11897])).
% 291.31/183.88 tff(11899,plain,
% 291.31/183.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s12, s13)) | m_c_h_element_v_in1(c_e_h_3, c_f, s12) | (~m_c_h_element_v_out(c_e_h_3, c_f, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s13)) | m_c_h_element_v_in1(c_e_h_3, c_f, s12) | (~node14(c_e_h_3, c_f, s12, s13)))),
% 291.31/183.88 inference(transitivity,[status(thm)],[11898, 11896])).
% 291.31/183.88 tff(11900,plain,
% 291.31/183.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s12, s13)) | m_c_h_element_v_in1(c_e_h_3, c_f, s12) | (~m_c_h_element_v_out(c_e_h_3, c_f, s13)))),
% 291.31/183.88 inference(quant_inst,[status(thm)],[])).
% 291.31/183.88 tff(11901,plain,
% 291.31/183.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s13)) | m_c_h_element_v_in1(c_e_h_3, c_f, s12) | (~node14(c_e_h_3, c_f, s12, s13))),
% 291.31/183.88 inference(modus_ponens,[status(thm)],[11900, 11899])).
% 291.31/183.88 tff(11902,plain,
% 291.31/183.88 ($false),
% 291.31/183.88 inference(unit_resolution,[status(thm)],[11901, 223, 11842, 11895, 11873])).
% 291.31/183.88 tff(11903,plain,(m_c_h_element_v_in1(c_e_h_3, c_f, s12) | (~m_c_h_element_v_out(c_e_h_3, c_f, s13)) | node15(c_e_h_3, c_f, s12, s13) | (~node17(c_e_h_3, c_f, s12))), inference(lemma,lemma(discharge,[]))).
% 291.31/183.88 tff(11904,plain,
% 291.31/183.88 (m_c_h_element_v_in1(c_e_h_3, c_f, s12)),
% 291.31/183.88 inference(unit_resolution,[status(thm)],[11903, 11865, 11872, 11842])).
% 291.31/183.88 tff(11905,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_f, s12)), introduced(assumption)).
% 291.31/183.88 tff(11906,plain,
% 291.31/183.88 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s12)) | (~node17(c_e_h_3, c_f, s12)) | m_c_h_element_v_in2(c_e_h_3, c_f, s12))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s12)) | (~node17(c_e_h_3, c_f, s12)) | m_c_h_element_v_in2(c_e_h_3, c_f, s12))),
% 291.31/183.88 inference(rewrite,[status(thm)],[])).
% 291.31/183.88 tff(11907,plain,
% 291.31/183.88 (((~m_c_h_element_v_in1(c_e_h_3, c_f, s12)) | m_c_h_element_v_in2(c_e_h_3, c_f, s12) | (~node17(c_e_h_3, c_f, s12))) <=> ((~m_c_h_element_v_in1(c_e_h_3, c_f, s12)) | (~node17(c_e_h_3, c_f, s12)) | m_c_h_element_v_in2(c_e_h_3, c_f, s12))),
% 291.31/183.88 inference(rewrite,[status(thm)],[])).
% 291.31/183.88 tff(11908,plain,
% 291.31/183.88 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s12)) | m_c_h_element_v_in2(c_e_h_3, c_f, s12) | (~node17(c_e_h_3, c_f, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s12)) | (~node17(c_e_h_3, c_f, s12)) | m_c_h_element_v_in2(c_e_h_3, c_f, s12)))),
% 291.31/183.88 inference(monotonicity,[status(thm)],[11907])).
% 291.31/183.88 tff(11909,plain,
% 291.31/183.88 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s12)) | m_c_h_element_v_in2(c_e_h_3, c_f, s12) | (~node17(c_e_h_3, c_f, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s12)) | (~node17(c_e_h_3, c_f, s12)) | m_c_h_element_v_in2(c_e_h_3, c_f, s12))),
% 291.31/183.88 inference(transitivity,[status(thm)],[11908, 11906])).
% 291.31/183.88 tff(11910,plain,
% 291.31/183.88 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s12)) | m_c_h_element_v_in2(c_e_h_3, c_f, s12) | (~node17(c_e_h_3, c_f, s12)))),
% 291.31/183.88 inference(quant_inst,[status(thm)],[])).
% 291.31/183.88 tff(11911,plain,
% 291.31/183.88 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s12)) | (~node17(c_e_h_3, c_f, s12)) | m_c_h_element_v_in2(c_e_h_3, c_f, s12)),
% 291.31/183.88 inference(modus_ponens,[status(thm)],[11910, 11909])).
% 291.31/183.88 tff(11912,plain,
% 291.31/183.88 ((~m_c_h_element_v_in1(c_e_h_3, c_f, s12)) | (~node17(c_e_h_3, c_f, s12))),
% 291.31/183.88 inference(unit_resolution,[status(thm)],[11911, 919, 11905])).
% 291.31/183.88 tff(11913,plain,
% 291.31/183.88 ($false),
% 291.31/183.88 inference(unit_resolution,[status(thm)],[11912, 11904, 11865])).
% 291.31/183.88 tff(11914,plain,((~m_c_h_element_v_out(c_e_h_3, c_f, s13)) | m_c_h_element_v_in2(c_e_h_3, c_f, s12) | m_c_h_element_v_out(c_e_h_3, c_f, s12)), inference(lemma,lemma(discharge,[]))).
% 291.31/183.88 tff(11915,plain,
% 291.31/183.88 (~m_c_h_element_v_out(c_e_h_3, c_f, s13)),
% 291.31/183.88 inference(unit_resolution,[status(thm)],[11914, 11840, 11832])).
% 291.31/183.88 tff(11916,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_d, s16)), introduced(assumption)).
% 291.31/183.88 tff(11917,assumption,(m_c_h_element_v_in1(c_e_h_3, c_f, s16)), introduced(assumption)).
% 291.31/183.88 tff(11918,plain,
% 291.31/183.88 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s16)) | m_and_h_gate_v_out(c_e_h_3, c_d, s16))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s16)) | m_and_h_gate_v_out(c_e_h_3, c_d, s16))),
% 291.31/183.88 inference(rewrite,[status(thm)],[])).
% 291.31/183.88 tff(11919,plain,
% 291.31/183.88 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s16)) | m_and_h_gate_v_out(c_e_h_3, c_d, s16))),
% 291.31/183.88 inference(quant_inst,[status(thm)],[])).
% 291.31/183.88 tff(11920,plain,
% 291.31/183.88 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s16)) | m_and_h_gate_v_out(c_e_h_3, c_d, s16)),
% 291.31/183.88 inference(modus_ponens,[status(thm)],[11919, 11918])).
% 291.31/183.88 tff(11921,plain,
% 291.31/183.88 ($false),
% 291.31/183.88 inference(unit_resolution,[status(thm)],[11920, 2116, 11917, 11916])).
% 291.31/183.88 tff(11922,plain,((~m_c_h_element_v_in1(c_e_h_3, c_f, s16)) | m_and_h_gate_v_out(c_e_h_3, c_d, s16)), inference(lemma,lemma(discharge,[]))).
% 291.31/183.88 tff(11923,plain,
% 291.31/183.88 (~m_c_h_element_v_in1(c_e_h_3, c_f, s16)),
% 291.31/183.88 inference(unit_resolution,[status(thm)],[11922, 11916])).
% 291.31/183.88 tff(11924,assumption,(~m_c_h_element_v_out(c_e_h_3, c_f, s16)), introduced(assumption)).
% 291.31/183.88 tff(11925,assumption,(m_c_h_element_v_out(c_e_h_3, c_f, s17)), introduced(assumption)).
% 291.31/183.88 tff(11926,assumption,(node18(c_e_h_3, c_f, s16, s17)), introduced(assumption)).
% 291.31/183.88 tff(11927,plain,
% 291.31/183.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_f, s16) | (~m_c_h_element_v_out(c_e_h_3, c_f, s17)) | (~node18(c_e_h_3, c_f, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s16) | (~m_c_h_element_v_out(c_e_h_3, c_f, s17)) | (~node18(c_e_h_3, c_f, s16, s17)))),
% 291.31/183.88 inference(rewrite,[status(thm)],[])).
% 291.31/183.88 tff(11928,plain,
% 291.31/183.88 (((~m_c_h_element_v_out(c_e_h_3, c_f, s17)) | m_c_h_element_v_out(c_e_h_3, c_f, s16) | (~node18(c_e_h_3, c_f, s16, s17))) <=> (m_c_h_element_v_out(c_e_h_3, c_f, s16) | (~m_c_h_element_v_out(c_e_h_3, c_f, s17)) | (~node18(c_e_h_3, c_f, s16, s17)))),
% 291.31/183.88 inference(rewrite,[status(thm)],[])).
% 291.31/183.88 tff(11929,plain,
% 291.31/183.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s17)) | m_c_h_element_v_out(c_e_h_3, c_f, s16) | (~node18(c_e_h_3, c_f, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_f, s16) | (~m_c_h_element_v_out(c_e_h_3, c_f, s17)) | (~node18(c_e_h_3, c_f, s16, s17))))),
% 291.31/183.88 inference(monotonicity,[status(thm)],[11928])).
% 291.31/183.88 tff(11930,plain,
% 291.31/183.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s17)) | m_c_h_element_v_out(c_e_h_3, c_f, s16) | (~node18(c_e_h_3, c_f, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s16) | (~m_c_h_element_v_out(c_e_h_3, c_f, s17)) | (~node18(c_e_h_3, c_f, s16, s17)))),
% 291.31/183.88 inference(transitivity,[status(thm)],[11929, 11927])).
% 291.31/183.88 tff(11931,plain,
% 291.31/183.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s17)) | m_c_h_element_v_out(c_e_h_3, c_f, s16) | (~node18(c_e_h_3, c_f, s16, s17)))),
% 291.31/183.88 inference(quant_inst,[status(thm)],[])).
% 291.31/183.88 tff(11932,plain,
% 291.31/183.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s16) | (~m_c_h_element_v_out(c_e_h_3, c_f, s17)) | (~node18(c_e_h_3, c_f, s16, s17))),
% 291.31/183.88 inference(modus_ponens,[status(thm)],[11931, 11930])).
% 291.31/183.88 tff(11933,plain,
% 291.31/183.88 ($false),
% 291.31/183.88 inference(unit_resolution,[status(thm)],[11932, 753, 11925, 11924, 11926])).
% 291.31/183.88 tff(11934,plain,((~node18(c_e_h_3, c_f, s16, s17)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s17)) | m_c_h_element_v_out(c_e_h_3, c_f, s16)), inference(lemma,lemma(discharge,[]))).
% 291.31/183.88 tff(11935,plain,
% 291.31/183.88 (~node18(c_e_h_3, c_f, s16, s17)),
% 291.31/183.88 inference(unit_resolution,[status(thm)],[11934, 11925, 11924])).
% 291.31/183.88 tff(11936,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_f, s16)), introduced(assumption)).
% 291.31/183.88 tff(11937,assumption,(node15(c_e_h_3, c_f, s16, s17)), introduced(assumption)).
% 291.31/183.88 tff(11938,plain,
% 291.31/183.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s17)) | (~node15(c_e_h_3, c_f, s16, s17)) | m_c_h_element_v_out(c_e_h_3, c_f, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s17)) | (~node15(c_e_h_3, c_f, s16, s17)) | m_c_h_element_v_out(c_e_h_3, c_f, s16))),
% 291.31/183.88 inference(rewrite,[status(thm)],[])).
% 291.31/183.88 tff(11939,plain,
% 291.31/183.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s17)) | (~node15(c_e_h_3, c_f, s16, s17)) | m_c_h_element_v_out(c_e_h_3, c_f, s16))),
% 291.31/183.88 inference(quant_inst,[status(thm)],[])).
% 291.31/183.88 tff(11940,plain,
% 291.31/183.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s17)) | (~node15(c_e_h_3, c_f, s16, s17)) | m_c_h_element_v_out(c_e_h_3, c_f, s16)),
% 291.31/183.88 inference(modus_ponens,[status(thm)],[11939, 11938])).
% 291.31/183.88 tff(11941,plain,
% 291.31/183.88 ($false),
% 291.31/183.88 inference(unit_resolution,[status(thm)],[11940, 147, 11925, 11924, 11937])).
% 291.31/183.88 tff(11942,plain,((~node15(c_e_h_3, c_f, s16, s17)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s17)) | m_c_h_element_v_out(c_e_h_3, c_f, s16)), inference(lemma,lemma(discharge,[]))).
% 291.40/183.89 tff(11943,plain,
% 291.40/183.89 (~node15(c_e_h_3, c_f, s16, s17)),
% 291.40/183.89 inference(unit_resolution,[status(thm)],[11942, 11925, 11924])).
% 291.40/183.89 tff(11944,assumption,(~node15(c_e_h_3, c_f, s16, s17)), introduced(assumption)).
% 291.40/183.89 tff(11945,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_f, s16)), introduced(assumption)).
% 291.40/183.89 tff(11946,plain,
% 291.40/183.89 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s16)) | m_c_h_element_v_in1(c_e_h_3, c_f, s16) | m_c_h_element_v_in2(c_e_h_3, c_f, s16))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s16)) | m_c_h_element_v_in1(c_e_h_3, c_f, s16) | m_c_h_element_v_in2(c_e_h_3, c_f, s16))),
% 291.40/183.89 inference(rewrite,[status(thm)],[])).
% 291.40/183.89 tff(11947,plain,
% 291.40/183.89 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s16)) | m_c_h_element_v_in1(c_e_h_3, c_f, s16) | m_c_h_element_v_in2(c_e_h_3, c_f, s16))),
% 291.40/183.89 inference(quant_inst,[status(thm)],[])).
% 291.40/183.89 tff(11948,plain,
% 291.40/183.89 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s16)) | m_c_h_element_v_in1(c_e_h_3, c_f, s16) | m_c_h_element_v_in2(c_e_h_3, c_f, s16)),
% 291.40/183.89 inference(modus_ponens,[status(thm)],[11947, 11946])).
% 291.40/183.89 tff(11949,plain,
% 291.40/183.89 ((~node16(c_e_h_3, c_f, s16)) | m_c_h_element_v_in1(c_e_h_3, c_f, s16)),
% 291.40/183.89 inference(unit_resolution,[status(thm)],[11948, 178, 11936])).
% 291.40/183.89 tff(11950,plain,
% 291.40/183.89 (~node16(c_e_h_3, c_f, s16)),
% 291.40/183.89 inference(unit_resolution,[status(thm)],[11949, 11945])).
% 291.40/183.89 tff(11951,assumption,(node14(c_e_h_3, c_f, s16, s17)), introduced(assumption)).
% 291.40/183.89 tff(11952,plain,
% 291.40/183.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s17)) | m_c_h_element_v_in1(c_e_h_3, c_f, s16) | (~node14(c_e_h_3, c_f, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s17)) | m_c_h_element_v_in1(c_e_h_3, c_f, s16) | (~node14(c_e_h_3, c_f, s16, s17)))),
% 291.40/183.89 inference(rewrite,[status(thm)],[])).
% 291.40/183.89 tff(11953,plain,
% 291.40/183.89 (((~node14(c_e_h_3, c_f, s16, s17)) | m_c_h_element_v_in1(c_e_h_3, c_f, s16) | (~m_c_h_element_v_out(c_e_h_3, c_f, s17))) <=> ((~m_c_h_element_v_out(c_e_h_3, c_f, s17)) | m_c_h_element_v_in1(c_e_h_3, c_f, s16) | (~node14(c_e_h_3, c_f, s16, s17)))),
% 291.40/183.89 inference(rewrite,[status(thm)],[])).
% 291.40/183.89 tff(11954,plain,
% 291.40/183.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s16, s17)) | m_c_h_element_v_in1(c_e_h_3, c_f, s16) | (~m_c_h_element_v_out(c_e_h_3, c_f, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s17)) | m_c_h_element_v_in1(c_e_h_3, c_f, s16) | (~node14(c_e_h_3, c_f, s16, s17))))),
% 291.40/183.89 inference(monotonicity,[status(thm)],[11953])).
% 291.40/183.89 tff(11955,plain,
% 291.40/183.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s16, s17)) | m_c_h_element_v_in1(c_e_h_3, c_f, s16) | (~m_c_h_element_v_out(c_e_h_3, c_f, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s17)) | m_c_h_element_v_in1(c_e_h_3, c_f, s16) | (~node14(c_e_h_3, c_f, s16, s17)))),
% 291.40/183.89 inference(transitivity,[status(thm)],[11954, 11952])).
% 291.40/183.89 tff(11956,plain,
% 291.40/183.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s16, s17)) | m_c_h_element_v_in1(c_e_h_3, c_f, s16) | (~m_c_h_element_v_out(c_e_h_3, c_f, s17)))),
% 291.40/183.89 inference(quant_inst,[status(thm)],[])).
% 291.40/183.89 tff(11957,plain,
% 291.40/183.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s17)) | m_c_h_element_v_in1(c_e_h_3, c_f, s16) | (~node14(c_e_h_3, c_f, s16, s17))),
% 291.40/183.89 inference(modus_ponens,[status(thm)],[11956, 11955])).
% 291.40/183.89 tff(11958,plain,
% 291.40/183.89 ($false),
% 291.40/183.89 inference(unit_resolution,[status(thm)],[11957, 223, 11925, 11951, 11945])).
% 291.40/183.89 tff(11959,plain,((~node14(c_e_h_3, c_f, s16, s17)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s17)) | m_c_h_element_v_in1(c_e_h_3, c_f, s16)), inference(lemma,lemma(discharge,[]))).
% 291.40/183.89 tff(11960,plain,
% 291.40/183.89 (~node14(c_e_h_3, c_f, s16, s17)),
% 291.40/183.89 inference(unit_resolution,[status(thm)],[11959, 11945, 11925])).
% 291.40/183.89 tff(11961,plain,
% 291.40/183.89 (succ(s16, s17) <=> succ(s16, s17)),
% 291.40/183.89 inference(rewrite,[status(thm)],[])).
% 291.40/183.89 tff(11962,axiom,(succ(s16, s17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound17')).
% 291.40/183.89 tff(11963,plain,
% 291.40/183.89 (succ(s16, s17)),
% 291.40/183.89 inference(modus_ponens,[status(thm)],[11962, 11961])).
% 291.40/183.89 tff(11964,plain,
% 291.40/183.89 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s16, s17)) | trans(s16, s17))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s16, s17)) | trans(s16, s17))),
% 291.40/183.89 inference(rewrite,[status(thm)],[])).
% 291.40/183.89 tff(11965,plain,
% 291.40/183.89 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s16, s17)) | trans(s16, s17))),
% 291.40/183.89 inference(quant_inst,[status(thm)],[])).
% 291.40/183.89 tff(11966,plain,
% 291.40/183.89 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s16, s17)) | trans(s16, s17)),
% 291.40/183.89 inference(modus_ponens,[status(thm)],[11965, 11964])).
% 291.40/183.89 tff(11967,plain,
% 291.40/183.89 (trans(s16, s17)),
% 291.40/183.89 inference(unit_resolution,[status(thm)],[11966, 11963, 65])).
% 291.40/183.89 tff(11968,plain,
% 291.40/183.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s16, s17)) | node19(c_e_h_3, c_f, s16, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s16, s17)) | node19(c_e_h_3, c_f, s16, s17))),
% 291.40/183.89 inference(rewrite,[status(thm)],[])).
% 291.40/183.89 tff(11969,plain,
% 291.40/183.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s16, s17)) | node19(c_e_h_3, c_f, s16, s17))),
% 291.40/183.89 inference(quant_inst,[status(thm)],[])).
% 291.40/183.89 tff(11970,plain,
% 291.40/183.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s16, s17)) | node19(c_e_h_3, c_f, s16, s17)),
% 291.40/183.89 inference(modus_ponens,[status(thm)],[11969, 11968])).
% 291.40/183.89 tff(11971,plain,
% 291.40/183.89 (node19(c_e_h_3, c_f, s16, s17)),
% 291.40/183.89 inference(unit_resolution,[status(thm)],[11970, 190, 11967])).
% 291.40/183.89 tff(11972,plain,
% 291.40/183.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_3, c_f, s16, s17) | node16(c_e_h_3, c_f, s16) | node15(c_e_h_3, c_f, s16, s17) | (~node19(c_e_h_3, c_f, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_f, s16, s17) | node16(c_e_h_3, c_f, s16) | node15(c_e_h_3, c_f, s16, s17) | (~node19(c_e_h_3, c_f, s16, s17)))),
% 291.40/183.89 inference(rewrite,[status(thm)],[])).
% 291.40/183.89 tff(11973,plain,
% 291.40/183.89 ((node16(c_e_h_3, c_f, s16) | node14(c_e_h_3, c_f, s16, s17) | node15(c_e_h_3, c_f, s16, s17) | (~node19(c_e_h_3, c_f, s16, s17))) <=> (node14(c_e_h_3, c_f, s16, s17) | node16(c_e_h_3, c_f, s16) | node15(c_e_h_3, c_f, s16, s17) | (~node19(c_e_h_3, c_f, s16, s17)))),
% 291.40/183.89 inference(rewrite,[status(thm)],[])).
% 291.40/183.89 tff(11974,plain,
% 291.40/183.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s16) | node14(c_e_h_3, c_f, s16, s17) | node15(c_e_h_3, c_f, s16, s17) | (~node19(c_e_h_3, c_f, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_3, c_f, s16, s17) | node16(c_e_h_3, c_f, s16) | node15(c_e_h_3, c_f, s16, s17) | (~node19(c_e_h_3, c_f, s16, s17))))),
% 291.40/183.89 inference(monotonicity,[status(thm)],[11973])).
% 291.40/183.89 tff(11975,plain,
% 291.40/183.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s16) | node14(c_e_h_3, c_f, s16, s17) | node15(c_e_h_3, c_f, s16, s17) | (~node19(c_e_h_3, c_f, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_f, s16, s17) | node16(c_e_h_3, c_f, s16) | node15(c_e_h_3, c_f, s16, s17) | (~node19(c_e_h_3, c_f, s16, s17)))),
% 291.40/183.89 inference(transitivity,[status(thm)],[11974, 11972])).
% 291.40/183.89 tff(11976,plain,
% 291.40/183.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s16) | node14(c_e_h_3, c_f, s16, s17) | node15(c_e_h_3, c_f, s16, s17) | (~node19(c_e_h_3, c_f, s16, s17)))),
% 291.40/183.89 inference(quant_inst,[status(thm)],[])).
% 291.40/183.89 tff(11977,plain,
% 291.40/183.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_f, s16, s17) | node16(c_e_h_3, c_f, s16) | node15(c_e_h_3, c_f, s16, s17) | (~node19(c_e_h_3, c_f, s16, s17))),
% 291.40/183.89 inference(modus_ponens,[status(thm)],[11976, 11975])).
% 291.40/183.89 tff(11978,plain,
% 291.40/183.89 (node14(c_e_h_3, c_f, s16, s17) | node16(c_e_h_3, c_f, s16) | node15(c_e_h_3, c_f, s16, s17)),
% 291.40/183.89 inference(unit_resolution,[status(thm)],[11977, 204, 11971])).
% 291.40/183.89 tff(11979,plain,
% 291.40/183.89 ($false),
% 291.40/183.89 inference(unit_resolution,[status(thm)],[11978, 11960, 11950, 11944])).
% 291.40/183.89 tff(11980,plain,(m_c_h_element_v_in1(c_e_h_3, c_f, s16) | node15(c_e_h_3, c_f, s16, s17) | (~m_c_h_element_v_out(c_e_h_3, c_f, s17)) | m_c_h_element_v_in2(c_e_h_3, c_f, s16)), inference(lemma,lemma(discharge,[]))).
% 291.40/183.89 tff(11981,plain,
% 291.40/183.89 (m_c_h_element_v_in1(c_e_h_3, c_f, s16)),
% 291.40/183.89 inference(unit_resolution,[status(thm)],[11980, 11943, 11925, 11936])).
% 291.40/183.89 tff(11982,plain,
% 291.40/183.89 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s16)) | (~node17(c_e_h_3, c_f, s16)) | m_c_h_element_v_in2(c_e_h_3, c_f, s16))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s16)) | (~node17(c_e_h_3, c_f, s16)) | m_c_h_element_v_in2(c_e_h_3, c_f, s16))),
% 291.40/183.89 inference(rewrite,[status(thm)],[])).
% 291.40/183.89 tff(11983,plain,
% 291.40/183.89 (((~m_c_h_element_v_in1(c_e_h_3, c_f, s16)) | m_c_h_element_v_in2(c_e_h_3, c_f, s16) | (~node17(c_e_h_3, c_f, s16))) <=> ((~m_c_h_element_v_in1(c_e_h_3, c_f, s16)) | (~node17(c_e_h_3, c_f, s16)) | m_c_h_element_v_in2(c_e_h_3, c_f, s16))),
% 291.40/183.89 inference(rewrite,[status(thm)],[])).
% 291.40/183.89 tff(11984,plain,
% 291.40/183.89 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s16)) | m_c_h_element_v_in2(c_e_h_3, c_f, s16) | (~node17(c_e_h_3, c_f, s16)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s16)) | (~node17(c_e_h_3, c_f, s16)) | m_c_h_element_v_in2(c_e_h_3, c_f, s16)))),
% 291.40/183.89 inference(monotonicity,[status(thm)],[11983])).
% 291.40/183.89 tff(11985,plain,
% 291.40/183.89 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s16)) | m_c_h_element_v_in2(c_e_h_3, c_f, s16) | (~node17(c_e_h_3, c_f, s16)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s16)) | (~node17(c_e_h_3, c_f, s16)) | m_c_h_element_v_in2(c_e_h_3, c_f, s16))),
% 291.40/183.89 inference(transitivity,[status(thm)],[11984, 11982])).
% 291.40/183.90 tff(11986,plain,
% 291.40/183.90 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s16)) | m_c_h_element_v_in2(c_e_h_3, c_f, s16) | (~node17(c_e_h_3, c_f, s16)))),
% 291.40/183.90 inference(quant_inst,[status(thm)],[])).
% 291.40/183.90 tff(11987,plain,
% 291.40/183.90 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s16)) | (~node17(c_e_h_3, c_f, s16)) | m_c_h_element_v_in2(c_e_h_3, c_f, s16)),
% 291.40/183.90 inference(modus_ponens,[status(thm)],[11986, 11985])).
% 291.40/183.90 tff(11988,plain,
% 291.40/183.90 ((~m_c_h_element_v_in1(c_e_h_3, c_f, s16)) | (~node17(c_e_h_3, c_f, s16))),
% 291.40/183.90 inference(unit_resolution,[status(thm)],[11987, 919, 11936])).
% 291.40/183.90 tff(11989,plain,
% 291.40/183.90 (~node17(c_e_h_3, c_f, s16)),
% 291.40/183.90 inference(unit_resolution,[status(thm)],[11988, 11981])).
% 291.40/183.90 tff(11990,plain,
% 291.40/183.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s16) | (~node19(c_e_h_3, c_f, s16, s17)) | node18(c_e_h_3, c_f, s16, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_f, s16) | (~node19(c_e_h_3, c_f, s16, s17)) | node18(c_e_h_3, c_f, s16, s17))),
% 291.40/183.90 inference(rewrite,[status(thm)],[])).
% 291.40/183.90 tff(11991,plain,
% 291.40/183.90 ((node17(c_e_h_3, c_f, s16) | node18(c_e_h_3, c_f, s16, s17) | (~node19(c_e_h_3, c_f, s16, s17))) <=> (node17(c_e_h_3, c_f, s16) | (~node19(c_e_h_3, c_f, s16, s17)) | node18(c_e_h_3, c_f, s16, s17))),
% 291.40/183.90 inference(rewrite,[status(thm)],[])).
% 291.40/183.90 tff(11992,plain,
% 291.40/183.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s16) | node18(c_e_h_3, c_f, s16, s17) | (~node19(c_e_h_3, c_f, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s16) | (~node19(c_e_h_3, c_f, s16, s17)) | node18(c_e_h_3, c_f, s16, s17)))),
% 291.40/183.90 inference(monotonicity,[status(thm)],[11991])).
% 291.40/183.90 tff(11993,plain,
% 291.40/183.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s16) | node18(c_e_h_3, c_f, s16, s17) | (~node19(c_e_h_3, c_f, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_f, s16) | (~node19(c_e_h_3, c_f, s16, s17)) | node18(c_e_h_3, c_f, s16, s17))),
% 291.40/183.90 inference(transitivity,[status(thm)],[11992, 11990])).
% 291.40/183.90 tff(11994,plain,
% 291.40/183.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s16) | node18(c_e_h_3, c_f, s16, s17) | (~node19(c_e_h_3, c_f, s16, s17)))),
% 291.40/183.90 inference(quant_inst,[status(thm)],[])).
% 291.40/183.90 tff(11995,plain,
% 291.40/183.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_f, s16) | (~node19(c_e_h_3, c_f, s16, s17)) | node18(c_e_h_3, c_f, s16, s17)),
% 291.40/183.90 inference(modus_ponens,[status(thm)],[11994, 11993])).
% 291.40/183.90 tff(11996,plain,
% 291.40/183.90 (node17(c_e_h_3, c_f, s16) | node18(c_e_h_3, c_f, s16, s17)),
% 291.40/183.90 inference(unit_resolution,[status(thm)],[11995, 776, 11971])).
% 291.40/183.90 tff(11997,plain,
% 291.40/183.90 (node18(c_e_h_3, c_f, s16, s17)),
% 291.40/183.90 inference(unit_resolution,[status(thm)],[11996, 11989])).
% 291.40/183.90 tff(11998,plain,
% 291.40/183.90 ($false),
% 291.40/183.90 inference(unit_resolution,[status(thm)],[11932, 753, 11925, 11924, 11997])).
% 291.40/183.90 tff(11999,plain,((~m_c_h_element_v_out(c_e_h_3, c_f, s17)) | m_c_h_element_v_out(c_e_h_3, c_f, s16) | m_c_h_element_v_in2(c_e_h_3, c_f, s16)), inference(lemma,lemma(discharge,[]))).
% 291.40/183.90 tff(12000,plain,
% 291.40/183.90 (m_c_h_element_v_in2(c_e_h_3, c_f, s16)),
% 291.40/183.90 inference(unit_resolution,[status(thm)],[11999, 11925, 11924])).
% 291.40/183.90 tff(12001,plain,
% 291.40/183.90 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_f, s16)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s16)) | m_c_h_element_v_in1(c_e_h_3, c_f, s16))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_f, s16)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s16)) | m_c_h_element_v_in1(c_e_h_3, c_f, s16))),
% 291.41/183.90 inference(rewrite,[status(thm)],[])).
% 291.41/183.90 tff(12002,plain,
% 291.41/183.90 ((m_c_h_element_v_in1(c_e_h_3, c_f, s16) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s16)) | (~node17(c_e_h_3, c_f, s16))) <=> ((~node17(c_e_h_3, c_f, s16)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s16)) | m_c_h_element_v_in1(c_e_h_3, c_f, s16))),
% 291.41/183.90 inference(rewrite,[status(thm)],[])).
% 291.41/183.90 tff(12003,plain,
% 291.41/183.90 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s16) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s16)) | (~node17(c_e_h_3, c_f, s16)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_f, s16)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s16)) | m_c_h_element_v_in1(c_e_h_3, c_f, s16)))),
% 291.41/183.90 inference(monotonicity,[status(thm)],[12002])).
% 291.41/183.90 tff(12004,plain,
% 291.41/183.90 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s16) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s16)) | (~node17(c_e_h_3, c_f, s16)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_f, s16)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s16)) | m_c_h_element_v_in1(c_e_h_3, c_f, s16))),
% 291.41/183.90 inference(transitivity,[status(thm)],[12003, 12001])).
% 291.41/183.90 tff(12005,plain,
% 291.41/183.90 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s16) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s16)) | (~node17(c_e_h_3, c_f, s16)))),
% 291.41/183.90 inference(quant_inst,[status(thm)],[])).
% 291.41/183.90 tff(12006,plain,
% 291.41/183.90 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_f, s16)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s16)) | m_c_h_element_v_in1(c_e_h_3, c_f, s16)),
% 291.41/183.90 inference(modus_ponens,[status(thm)],[12005, 12004])).
% 291.41/183.90 tff(12007,plain,
% 291.41/183.90 ((~node17(c_e_h_3, c_f, s16)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s16))),
% 291.41/183.90 inference(unit_resolution,[status(thm)],[12006, 859, 11945])).
% 291.41/183.90 tff(12008,plain,
% 291.41/183.90 (~node17(c_e_h_3, c_f, s16)),
% 291.41/183.90 inference(unit_resolution,[status(thm)],[12007, 12000])).
% 291.41/183.90 tff(12009,plain,
% 291.41/183.90 ($false),
% 291.41/183.90 inference(unit_resolution,[status(thm)],[11996, 12008, 11935])).
% 291.41/183.90 tff(12010,plain,((~m_c_h_element_v_out(c_e_h_3, c_f, s17)) | m_c_h_element_v_in1(c_e_h_3, c_f, s16) | m_c_h_element_v_out(c_e_h_3, c_f, s16)), inference(lemma,lemma(discharge,[]))).
% 291.41/183.90 tff(12011,plain,
% 291.41/183.90 (~m_c_h_element_v_out(c_e_h_3, c_f, s17)),
% 291.41/183.90 inference(unit_resolution,[status(thm)],[12010, 11924, 11923])).
% 291.41/183.90 tff(12012,assumption,(m_c_h_element_v_in2(c_e_h_3, c_e, s9)), introduced(assumption)).
% 291.41/183.90 tff(12013,plain,
% 291.41/183.90 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s9)) | m_and_h_gate_v_out(c_e_h_3, c_i, s9))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s9)) | m_and_h_gate_v_out(c_e_h_3, c_i, s9))),
% 291.41/183.90 inference(rewrite,[status(thm)],[])).
% 291.41/183.90 tff(12014,plain,
% 291.41/183.90 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s9)) | m_and_h_gate_v_out(c_e_h_3, c_i, s9))),
% 291.41/183.90 inference(quant_inst,[status(thm)],[])).
% 291.41/183.90 tff(12015,plain,
% 291.41/183.90 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s9)) | m_and_h_gate_v_out(c_e_h_3, c_i, s9)),
% 291.41/183.90 inference(modus_ponens,[status(thm)],[12014, 12013])).
% 291.41/183.90 tff(12016,plain,
% 291.41/183.90 ($false),
% 291.41/183.90 inference(unit_resolution,[status(thm)],[12015, 164, 12012, 11394])).
% 291.41/183.90 tff(12017,plain,((~m_c_h_element_v_in2(c_e_h_3, c_e, s9)) | m_and_h_gate_v_out(c_e_h_3, c_i, s9)), inference(lemma,lemma(discharge,[]))).
% 291.41/183.90 tff(12018,plain,
% 291.41/183.90 (~m_c_h_element_v_in2(c_e_h_3, c_e, s9)),
% 291.41/183.90 inference(unit_resolution,[status(thm)],[12017, 11364])).
% 291.41/183.90 tff(12019,assumption,(m_c_h_element_v_out(c_e_h_3, c_e, s9)), introduced(assumption)).
% 291.41/183.90 tff(12020,assumption,(m_c_h_element_v_out(c_e_h_3, c_e, s8)), introduced(assumption)).
% 291.41/183.90 tff(12021,plain,
% 291.41/183.90 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s7)) | m_and_h_gate_v_out(c_e_h_3, c_i, s7))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s7)) | m_and_h_gate_v_out(c_e_h_3, c_i, s7))),
% 291.41/183.90 inference(rewrite,[status(thm)],[])).
% 291.41/183.90 tff(12022,plain,
% 291.41/183.90 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s7)) | m_and_h_gate_v_out(c_e_h_3, c_i, s7))),
% 291.41/183.90 inference(quant_inst,[status(thm)],[])).
% 291.41/183.90 tff(12023,plain,
% 291.41/183.90 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s7)) | m_and_h_gate_v_out(c_e_h_3, c_i, s7)),
% 291.41/183.90 inference(modus_ponens,[status(thm)],[12022, 12021])).
% 291.41/183.90 tff(12024,plain,
% 291.41/183.90 (~m_c_h_element_v_in2(c_e_h_3, c_e, s7)),
% 291.41/183.90 inference(unit_resolution,[status(thm)],[12023, 164, 11317])).
% 291.41/183.90 tff(12025,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_e, s7)), introduced(assumption)).
% 291.41/183.90 tff(12026,plain,
% 291.41/183.90 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_e, s7)) | m_c_h_element_v_in1(c_e_h_3, c_e, s7) | m_c_h_element_v_in2(c_e_h_3, c_e, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s7)) | m_c_h_element_v_in1(c_e_h_3, c_e, s7) | m_c_h_element_v_in2(c_e_h_3, c_e, s7))),
% 291.41/183.90 inference(rewrite,[status(thm)],[])).
% 291.41/183.90 tff(12027,plain,
% 291.41/183.90 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_e, s7)) | m_c_h_element_v_in1(c_e_h_3, c_e, s7) | m_c_h_element_v_in2(c_e_h_3, c_e, s7))),
% 291.41/183.90 inference(quant_inst,[status(thm)],[])).
% 291.41/183.90 tff(12028,plain,
% 291.41/183.90 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s7)) | m_c_h_element_v_in1(c_e_h_3, c_e, s7) | m_c_h_element_v_in2(c_e_h_3, c_e, s7)),
% 291.41/183.90 inference(modus_ponens,[status(thm)],[12027, 12026])).
% 291.41/183.90 tff(12029,plain,
% 291.41/183.90 ((~node16(c_e_h_3, c_e, s7)) | m_c_h_element_v_in2(c_e_h_3, c_e, s7)),
% 291.41/183.90 inference(unit_resolution,[status(thm)],[12028, 178, 12025])).
% 291.41/183.90 tff(12030,plain,
% 291.41/183.90 (~node16(c_e_h_3, c_e, s7)),
% 291.41/183.90 inference(unit_resolution,[status(thm)],[12029, 12024])).
% 291.41/183.90 tff(12031,assumption,(node14(c_e_h_3, c_e, s7, s8)), introduced(assumption)).
% 291.41/183.90 tff(12032,plain,
% 291.41/183.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s8)) | (~node14(c_e_h_3, c_e, s7, s8)) | m_c_h_element_v_in1(c_e_h_3, c_e, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s8)) | (~node14(c_e_h_3, c_e, s7, s8)) | m_c_h_element_v_in1(c_e_h_3, c_e, s7))),
% 291.41/183.90 inference(rewrite,[status(thm)],[])).
% 291.41/183.90 tff(12033,plain,
% 291.41/183.90 (((~node14(c_e_h_3, c_e, s7, s8)) | m_c_h_element_v_in1(c_e_h_3, c_e, s7) | (~m_c_h_element_v_out(c_e_h_3, c_e, s8))) <=> ((~m_c_h_element_v_out(c_e_h_3, c_e, s8)) | (~node14(c_e_h_3, c_e, s7, s8)) | m_c_h_element_v_in1(c_e_h_3, c_e, s7))),
% 291.41/183.90 inference(rewrite,[status(thm)],[])).
% 291.41/183.91 tff(12034,plain,
% 291.41/183.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s7, s8)) | m_c_h_element_v_in1(c_e_h_3, c_e, s7) | (~m_c_h_element_v_out(c_e_h_3, c_e, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s8)) | (~node14(c_e_h_3, c_e, s7, s8)) | m_c_h_element_v_in1(c_e_h_3, c_e, s7)))),
% 291.41/183.91 inference(monotonicity,[status(thm)],[12033])).
% 291.41/183.91 tff(12035,plain,
% 291.41/183.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s7, s8)) | m_c_h_element_v_in1(c_e_h_3, c_e, s7) | (~m_c_h_element_v_out(c_e_h_3, c_e, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s8)) | (~node14(c_e_h_3, c_e, s7, s8)) | m_c_h_element_v_in1(c_e_h_3, c_e, s7))),
% 291.41/183.91 inference(transitivity,[status(thm)],[12034, 12032])).
% 291.41/183.91 tff(12036,plain,
% 291.41/183.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s7, s8)) | m_c_h_element_v_in1(c_e_h_3, c_e, s7) | (~m_c_h_element_v_out(c_e_h_3, c_e, s8)))),
% 291.41/183.91 inference(quant_inst,[status(thm)],[])).
% 291.41/183.91 tff(12037,plain,
% 291.41/183.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s8)) | (~node14(c_e_h_3, c_e, s7, s8)) | m_c_h_element_v_in1(c_e_h_3, c_e, s7)),
% 291.41/183.91 inference(modus_ponens,[status(thm)],[12036, 12035])).
% 291.41/183.91 tff(12038,plain,
% 291.41/183.91 ($false),
% 291.41/183.91 inference(unit_resolution,[status(thm)],[12037, 223, 12020, 12031, 12025])).
% 291.41/183.91 tff(12039,plain,((~node14(c_e_h_3, c_e, s7, s8)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s8)) | m_c_h_element_v_in1(c_e_h_3, c_e, s7)), inference(lemma,lemma(discharge,[]))).
% 291.41/183.91 tff(12040,plain,
% 291.41/183.91 (~node14(c_e_h_3, c_e, s7, s8)),
% 291.41/183.91 inference(unit_resolution,[status(thm)],[12039, 12020, 12025])).
% 291.41/183.91 tff(12041,assumption,(m_c_h_element_v_in2(c_e_h_3, c_e, s6)), introduced(assumption)).
% 291.41/183.91 tff(12042,plain,
% 291.41/183.91 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s6)) | m_and_h_gate_v_out(c_e_h_3, c_i, s6))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s6)) | m_and_h_gate_v_out(c_e_h_3, c_i, s6))),
% 291.41/183.91 inference(rewrite,[status(thm)],[])).
% 291.41/183.91 tff(12043,plain,
% 291.41/183.91 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s6)) | m_and_h_gate_v_out(c_e_h_3, c_i, s6))),
% 291.41/183.91 inference(quant_inst,[status(thm)],[])).
% 291.41/183.91 tff(12044,plain,
% 291.41/183.91 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s6)) | m_and_h_gate_v_out(c_e_h_3, c_i, s6)),
% 291.41/183.91 inference(modus_ponens,[status(thm)],[12043, 12042])).
% 291.41/183.91 tff(12045,plain,
% 291.41/183.91 ($false),
% 291.41/183.91 inference(unit_resolution,[status(thm)],[12044, 164, 9085, 12041])).
% 291.41/183.91 tff(12046,plain,((~m_c_h_element_v_in2(c_e_h_3, c_e, s6)) | m_and_h_gate_v_out(c_e_h_3, c_i, s6)), inference(lemma,lemma(discharge,[]))).
% 291.41/183.91 tff(12047,plain,
% 291.41/183.91 (~m_c_h_element_v_in2(c_e_h_3, c_e, s6)),
% 291.41/183.91 inference(unit_resolution,[status(thm)],[12046, 10821])).
% 291.41/183.91 tff(12048,assumption,(m_c_h_element_v_out(c_e_h_3, c_e, s7)), introduced(assumption)).
% 291.41/183.91 tff(12049,assumption,(~m_c_h_element_v_out(c_e_h_3, c_e, s6)), introduced(assumption)).
% 291.41/183.91 tff(12050,assumption,(node18(c_e_h_3, c_e, s6, s7)), introduced(assumption)).
% 291.41/183.91 tff(12051,plain,
% 291.41/183.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | m_c_h_element_v_out(c_e_h_3, c_e, s6) | (~node18(c_e_h_3, c_e, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | m_c_h_element_v_out(c_e_h_3, c_e, s6) | (~node18(c_e_h_3, c_e, s6, s7)))),
% 291.42/183.91 inference(rewrite,[status(thm)],[])).
% 291.42/183.91 tff(12052,plain,
% 291.42/183.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | m_c_h_element_v_out(c_e_h_3, c_e, s6) | (~node18(c_e_h_3, c_e, s6, s7)))),
% 291.42/183.91 inference(quant_inst,[status(thm)],[])).
% 291.42/183.91 tff(12053,plain,
% 291.42/183.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | m_c_h_element_v_out(c_e_h_3, c_e, s6) | (~node18(c_e_h_3, c_e, s6, s7))),
% 291.42/183.91 inference(modus_ponens,[status(thm)],[12052, 12051])).
% 291.42/183.91 tff(12054,plain,
% 291.42/183.91 ($false),
% 291.42/183.91 inference(unit_resolution,[status(thm)],[12053, 753, 12048, 12049, 12050])).
% 291.42/183.91 tff(12055,plain,((~node18(c_e_h_3, c_e, s6, s7)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | m_c_h_element_v_out(c_e_h_3, c_e, s6)), inference(lemma,lemma(discharge,[]))).
% 291.42/183.91 tff(12056,plain,
% 291.42/183.91 (~node18(c_e_h_3, c_e, s6, s7)),
% 291.42/183.91 inference(unit_resolution,[status(thm)],[12055, 12049, 12048])).
% 291.42/183.91 tff(12057,plain,
% 291.42/183.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s6, s7)) | node19(c_e_h_3, c_e, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s6, s7)) | node19(c_e_h_3, c_e, s6, s7))),
% 291.42/183.91 inference(rewrite,[status(thm)],[])).
% 291.42/183.91 tff(12058,plain,
% 291.42/183.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s6, s7)) | node19(c_e_h_3, c_e, s6, s7))),
% 291.42/183.91 inference(quant_inst,[status(thm)],[])).
% 291.42/183.91 tff(12059,plain,
% 291.42/183.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s6, s7)) | node19(c_e_h_3, c_e, s6, s7)),
% 291.42/183.91 inference(modus_ponens,[status(thm)],[12058, 12057])).
% 291.42/183.91 tff(12060,plain,
% 291.42/183.91 (node19(c_e_h_3, c_e, s6, s7)),
% 291.42/183.91 inference(unit_resolution,[status(thm)],[12059, 190, 1844])).
% 291.42/183.91 tff(12061,plain,
% 291.42/183.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s6) | (~node19(c_e_h_3, c_e, s6, s7)) | node18(c_e_h_3, c_e, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_e, s6) | (~node19(c_e_h_3, c_e, s6, s7)) | node18(c_e_h_3, c_e, s6, s7))),
% 291.42/183.91 inference(rewrite,[status(thm)],[])).
% 291.42/183.91 tff(12062,plain,
% 291.42/183.91 ((node17(c_e_h_3, c_e, s6) | node18(c_e_h_3, c_e, s6, s7) | (~node19(c_e_h_3, c_e, s6, s7))) <=> (node17(c_e_h_3, c_e, s6) | (~node19(c_e_h_3, c_e, s6, s7)) | node18(c_e_h_3, c_e, s6, s7))),
% 291.42/183.91 inference(rewrite,[status(thm)],[])).
% 291.42/183.91 tff(12063,plain,
% 291.42/183.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s6) | node18(c_e_h_3, c_e, s6, s7) | (~node19(c_e_h_3, c_e, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s6) | (~node19(c_e_h_3, c_e, s6, s7)) | node18(c_e_h_3, c_e, s6, s7)))),
% 291.42/183.91 inference(monotonicity,[status(thm)],[12062])).
% 291.42/183.91 tff(12064,plain,
% 291.42/183.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s6) | node18(c_e_h_3, c_e, s6, s7) | (~node19(c_e_h_3, c_e, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_e, s6) | (~node19(c_e_h_3, c_e, s6, s7)) | node18(c_e_h_3, c_e, s6, s7))),
% 291.42/183.91 inference(transitivity,[status(thm)],[12063, 12061])).
% 291.42/183.91 tff(12065,plain,
% 291.42/183.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s6) | node18(c_e_h_3, c_e, s6, s7) | (~node19(c_e_h_3, c_e, s6, s7)))),
% 291.42/183.92 inference(quant_inst,[status(thm)],[])).
% 291.42/183.92 tff(12066,plain,
% 291.42/183.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_e, s6) | (~node19(c_e_h_3, c_e, s6, s7)) | node18(c_e_h_3, c_e, s6, s7)),
% 291.42/183.92 inference(modus_ponens,[status(thm)],[12065, 12064])).
% 291.42/183.92 tff(12067,plain,
% 291.42/183.92 (node17(c_e_h_3, c_e, s6) | node18(c_e_h_3, c_e, s6, s7)),
% 291.42/183.92 inference(unit_resolution,[status(thm)],[12066, 776, 12060])).
% 291.42/183.92 tff(12068,plain,
% 291.42/183.92 (node17(c_e_h_3, c_e, s6)),
% 291.42/183.92 inference(unit_resolution,[status(thm)],[12067, 12056])).
% 291.42/183.92 tff(12069,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_e, s6)), introduced(assumption)).
% 291.42/183.92 tff(12070,plain,
% 291.42/183.92 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_3, c_e, s6) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s6)) | (~node17(c_e_h_3, c_e, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_e, s6) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s6)) | (~node17(c_e_h_3, c_e, s6)))),
% 291.42/183.92 inference(rewrite,[status(thm)],[])).
% 291.42/183.92 tff(12071,plain,
% 291.42/183.92 (((~m_c_h_element_v_in1(c_e_h_3, c_e, s6)) | m_c_h_element_v_in2(c_e_h_3, c_e, s6) | (~node17(c_e_h_3, c_e, s6))) <=> (m_c_h_element_v_in2(c_e_h_3, c_e, s6) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s6)) | (~node17(c_e_h_3, c_e, s6)))),
% 291.42/183.92 inference(rewrite,[status(thm)],[])).
% 291.42/183.92 tff(12072,plain,
% 291.42/183.92 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s6)) | m_c_h_element_v_in2(c_e_h_3, c_e, s6) | (~node17(c_e_h_3, c_e, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_3, c_e, s6) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s6)) | (~node17(c_e_h_3, c_e, s6))))),
% 291.42/183.92 inference(monotonicity,[status(thm)],[12071])).
% 291.42/183.92 tff(12073,plain,
% 291.42/183.92 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s6)) | m_c_h_element_v_in2(c_e_h_3, c_e, s6) | (~node17(c_e_h_3, c_e, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_e, s6) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s6)) | (~node17(c_e_h_3, c_e, s6)))),
% 291.42/183.92 inference(transitivity,[status(thm)],[12072, 12070])).
% 291.42/183.92 tff(12074,plain,
% 291.42/183.92 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s6)) | m_c_h_element_v_in2(c_e_h_3, c_e, s6) | (~node17(c_e_h_3, c_e, s6)))),
% 291.42/183.92 inference(quant_inst,[status(thm)],[])).
% 291.42/183.92 tff(12075,plain,
% 291.42/183.92 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_e, s6) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s6)) | (~node17(c_e_h_3, c_e, s6))),
% 291.42/183.92 inference(modus_ponens,[status(thm)],[12074, 12073])).
% 291.42/183.92 tff(12076,plain,
% 291.42/183.92 ((~m_c_h_element_v_in1(c_e_h_3, c_e, s6)) | (~node17(c_e_h_3, c_e, s6))),
% 291.42/183.92 inference(unit_resolution,[status(thm)],[12075, 919, 12069])).
% 291.42/183.92 tff(12077,plain,
% 291.42/183.92 (~m_c_h_element_v_in1(c_e_h_3, c_e, s6)),
% 291.42/183.92 inference(unit_resolution,[status(thm)],[12076, 12068])).
% 291.42/183.92 tff(12078,assumption,(node15(c_e_h_3, c_e, s6, s7)), introduced(assumption)).
% 291.42/183.92 tff(12079,plain,
% 291.42/183.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | (~node15(c_e_h_3, c_e, s6, s7)) | m_c_h_element_v_out(c_e_h_3, c_e, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | (~node15(c_e_h_3, c_e, s6, s7)) | m_c_h_element_v_out(c_e_h_3, c_e, s6))),
% 291.42/183.92 inference(rewrite,[status(thm)],[])).
% 291.42/183.92 tff(12080,plain,
% 291.42/183.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | (~node15(c_e_h_3, c_e, s6, s7)) | m_c_h_element_v_out(c_e_h_3, c_e, s6))),
% 291.42/183.92 inference(quant_inst,[status(thm)],[])).
% 291.42/183.92 tff(12081,plain,
% 291.42/183.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | (~node15(c_e_h_3, c_e, s6, s7)) | m_c_h_element_v_out(c_e_h_3, c_e, s6)),
% 291.42/183.92 inference(modus_ponens,[status(thm)],[12080, 12079])).
% 291.42/183.92 tff(12082,plain,
% 291.42/183.92 ($false),
% 291.42/183.92 inference(unit_resolution,[status(thm)],[12081, 147, 12048, 12049, 12078])).
% 291.42/183.92 tff(12083,plain,((~node15(c_e_h_3, c_e, s6, s7)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | m_c_h_element_v_out(c_e_h_3, c_e, s6)), inference(lemma,lemma(discharge,[]))).
% 291.42/183.92 tff(12084,plain,
% 291.42/183.92 (~node15(c_e_h_3, c_e, s6, s7)),
% 291.42/183.92 inference(unit_resolution,[status(thm)],[12083, 12049, 12048])).
% 291.42/183.92 tff(12085,assumption,(node17(c_e_h_3, c_e, s6)), introduced(assumption)).
% 291.42/183.92 tff(12086,assumption,(node16(c_e_h_3, c_e, s6)), introduced(assumption)).
% 291.42/183.92 tff(12087,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_e, s6)), introduced(assumption)).
% 291.42/183.92 tff(12088,plain,
% 291.42/183.92 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s6)) | (~node17(c_e_h_3, c_e, s6)) | m_c_h_element_v_in1(c_e_h_3, c_e, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s6)) | (~node17(c_e_h_3, c_e, s6)) | m_c_h_element_v_in1(c_e_h_3, c_e, s6))),
% 291.42/183.92 inference(rewrite,[status(thm)],[])).
% 291.42/183.92 tff(12089,plain,
% 291.42/183.92 ((m_c_h_element_v_in1(c_e_h_3, c_e, s6) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s6)) | (~node17(c_e_h_3, c_e, s6))) <=> ((~m_c_h_element_v_in2(c_e_h_3, c_e, s6)) | (~node17(c_e_h_3, c_e, s6)) | m_c_h_element_v_in1(c_e_h_3, c_e, s6))),
% 291.42/183.92 inference(rewrite,[status(thm)],[])).
% 291.42/183.92 tff(12090,plain,
% 291.42/183.92 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s6) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s6)) | (~node17(c_e_h_3, c_e, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s6)) | (~node17(c_e_h_3, c_e, s6)) | m_c_h_element_v_in1(c_e_h_3, c_e, s6)))),
% 291.42/183.92 inference(monotonicity,[status(thm)],[12089])).
% 291.42/183.92 tff(12091,plain,
% 291.42/183.92 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s6) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s6)) | (~node17(c_e_h_3, c_e, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s6)) | (~node17(c_e_h_3, c_e, s6)) | m_c_h_element_v_in1(c_e_h_3, c_e, s6))),
% 291.42/183.92 inference(transitivity,[status(thm)],[12090, 12088])).
% 291.42/183.92 tff(12092,plain,
% 291.42/183.92 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s6) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s6)) | (~node17(c_e_h_3, c_e, s6)))),
% 291.42/183.92 inference(quant_inst,[status(thm)],[])).
% 291.42/183.92 tff(12093,plain,
% 291.42/183.92 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s6)) | (~node17(c_e_h_3, c_e, s6)) | m_c_h_element_v_in1(c_e_h_3, c_e, s6)),
% 291.42/183.92 inference(modus_ponens,[status(thm)],[12092, 12091])).
% 291.42/183.92 tff(12094,plain,
% 291.42/183.92 ((~m_c_h_element_v_in2(c_e_h_3, c_e, s6)) | m_c_h_element_v_in1(c_e_h_3, c_e, s6)),
% 291.42/183.92 inference(unit_resolution,[status(thm)],[12093, 859, 12085])).
% 291.42/183.92 tff(12095,plain,
% 291.42/183.92 (~m_c_h_element_v_in2(c_e_h_3, c_e, s6)),
% 291.42/183.92 inference(unit_resolution,[status(thm)],[12094, 12087])).
% 291.42/183.92 tff(12096,plain,
% 291.42/183.92 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_e, s6)) | m_c_h_element_v_in1(c_e_h_3, c_e, s6) | m_c_h_element_v_in2(c_e_h_3, c_e, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s6)) | m_c_h_element_v_in1(c_e_h_3, c_e, s6) | m_c_h_element_v_in2(c_e_h_3, c_e, s6))),
% 291.42/183.92 inference(rewrite,[status(thm)],[])).
% 291.42/183.92 tff(12097,plain,
% 291.42/183.92 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_e, s6)) | m_c_h_element_v_in1(c_e_h_3, c_e, s6) | m_c_h_element_v_in2(c_e_h_3, c_e, s6))),
% 291.42/183.92 inference(quant_inst,[status(thm)],[])).
% 291.42/183.92 tff(12098,plain,
% 291.42/183.92 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s6)) | m_c_h_element_v_in1(c_e_h_3, c_e, s6) | m_c_h_element_v_in2(c_e_h_3, c_e, s6)),
% 291.42/183.92 inference(modus_ponens,[status(thm)],[12097, 12096])).
% 291.42/183.92 tff(12099,plain,
% 291.42/183.92 (m_c_h_element_v_in1(c_e_h_3, c_e, s6) | m_c_h_element_v_in2(c_e_h_3, c_e, s6)),
% 291.42/183.92 inference(unit_resolution,[status(thm)],[12098, 178, 12086])).
% 291.42/183.92 tff(12100,plain,
% 291.42/183.92 ($false),
% 291.42/183.92 inference(unit_resolution,[status(thm)],[12099, 12095, 12087])).
% 291.42/183.92 tff(12101,plain,(m_c_h_element_v_in1(c_e_h_3, c_e, s6) | (~node16(c_e_h_3, c_e, s6)) | (~node17(c_e_h_3, c_e, s6))), inference(lemma,lemma(discharge,[]))).
% 291.42/183.92 tff(12102,plain,
% 291.42/183.92 (m_c_h_element_v_in1(c_e_h_3, c_e, s6)),
% 291.42/183.92 inference(unit_resolution,[status(thm)],[12101, 12086, 12085])).
% 291.42/183.92 tff(12103,plain,
% 291.42/183.92 (m_c_h_element_v_in2(c_e_h_3, c_e, s6) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s6))),
% 291.42/183.92 inference(unit_resolution,[status(thm)],[12075, 919, 12085])).
% 291.42/183.92 tff(12104,plain,
% 291.42/183.92 (m_c_h_element_v_in2(c_e_h_3, c_e, s6)),
% 291.42/183.92 inference(unit_resolution,[status(thm)],[12103, 12102])).
% 291.42/183.92 tff(12105,plain,
% 291.42/183.92 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s6)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s6)) | (~node16(c_e_h_3, c_e, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s6)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s6)) | (~node16(c_e_h_3, c_e, s6)))),
% 291.42/183.92 inference(rewrite,[status(thm)],[])).
% 291.42/183.92 tff(12106,plain,
% 291.42/183.92 (((~node16(c_e_h_3, c_e, s6)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s6)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s6))) <=> ((~m_c_h_element_v_in1(c_e_h_3, c_e, s6)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s6)) | (~node16(c_e_h_3, c_e, s6)))),
% 291.42/183.92 inference(rewrite,[status(thm)],[])).
% 291.42/183.92 tff(12107,plain,
% 291.42/183.92 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_e, s6)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s6)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s6)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s6)) | (~node16(c_e_h_3, c_e, s6))))),
% 291.42/183.92 inference(monotonicity,[status(thm)],[12106])).
% 291.42/183.92 tff(12108,plain,
% 291.42/183.92 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_e, s6)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s6)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s6)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s6)) | (~node16(c_e_h_3, c_e, s6)))),
% 291.42/183.93 inference(transitivity,[status(thm)],[12107, 12105])).
% 291.42/183.93 tff(12109,plain,
% 291.42/183.93 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_e, s6)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s6)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s6)))),
% 291.42/183.93 inference(quant_inst,[status(thm)],[])).
% 291.42/183.93 tff(12110,plain,
% 291.42/183.93 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s6)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s6)) | (~node16(c_e_h_3, c_e, s6))),
% 291.42/183.93 inference(modus_ponens,[status(thm)],[12109, 12108])).
% 291.42/183.93 tff(12111,plain,
% 291.42/183.93 ((~m_c_h_element_v_in1(c_e_h_3, c_e, s6)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s6))),
% 291.42/183.93 inference(unit_resolution,[status(thm)],[12110, 2307, 12086])).
% 291.42/183.93 tff(12112,plain,
% 291.42/183.93 ($false),
% 291.42/183.93 inference(unit_resolution,[status(thm)],[12111, 12104, 12102])).
% 291.42/183.93 tff(12113,plain,((~node16(c_e_h_3, c_e, s6)) | (~node17(c_e_h_3, c_e, s6))), inference(lemma,lemma(discharge,[]))).
% 291.42/183.93 tff(12114,plain,
% 291.42/183.93 (~node16(c_e_h_3, c_e, s6)),
% 291.42/183.93 inference(unit_resolution,[status(thm)],[12113, 12068])).
% 291.42/183.93 tff(12115,plain,
% 291.42/183.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s6) | (~node19(c_e_h_3, c_e, s6, s7)) | node15(c_e_h_3, c_e, s6, s7) | node14(c_e_h_3, c_e, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_e, s6) | (~node19(c_e_h_3, c_e, s6, s7)) | node15(c_e_h_3, c_e, s6, s7) | node14(c_e_h_3, c_e, s6, s7))),
% 291.42/183.93 inference(rewrite,[status(thm)],[])).
% 291.42/183.93 tff(12116,plain,
% 291.42/183.93 ((node16(c_e_h_3, c_e, s6) | node14(c_e_h_3, c_e, s6, s7) | node15(c_e_h_3, c_e, s6, s7) | (~node19(c_e_h_3, c_e, s6, s7))) <=> (node16(c_e_h_3, c_e, s6) | (~node19(c_e_h_3, c_e, s6, s7)) | node15(c_e_h_3, c_e, s6, s7) | node14(c_e_h_3, c_e, s6, s7))),
% 291.42/183.93 inference(rewrite,[status(thm)],[])).
% 291.42/183.93 tff(12117,plain,
% 291.42/183.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s6) | node14(c_e_h_3, c_e, s6, s7) | node15(c_e_h_3, c_e, s6, s7) | (~node19(c_e_h_3, c_e, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s6) | (~node19(c_e_h_3, c_e, s6, s7)) | node15(c_e_h_3, c_e, s6, s7) | node14(c_e_h_3, c_e, s6, s7)))),
% 291.42/183.93 inference(monotonicity,[status(thm)],[12116])).
% 291.42/183.93 tff(12118,plain,
% 291.42/183.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s6) | node14(c_e_h_3, c_e, s6, s7) | node15(c_e_h_3, c_e, s6, s7) | (~node19(c_e_h_3, c_e, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_e, s6) | (~node19(c_e_h_3, c_e, s6, s7)) | node15(c_e_h_3, c_e, s6, s7) | node14(c_e_h_3, c_e, s6, s7))),
% 291.42/183.93 inference(transitivity,[status(thm)],[12117, 12115])).
% 291.42/183.93 tff(12119,plain,
% 291.42/183.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s6) | node14(c_e_h_3, c_e, s6, s7) | node15(c_e_h_3, c_e, s6, s7) | (~node19(c_e_h_3, c_e, s6, s7)))),
% 291.42/183.93 inference(quant_inst,[status(thm)],[])).
% 291.42/183.93 tff(12120,plain,
% 291.42/183.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_e, s6) | (~node19(c_e_h_3, c_e, s6, s7)) | node15(c_e_h_3, c_e, s6, s7) | node14(c_e_h_3, c_e, s6, s7)),
% 291.42/183.93 inference(modus_ponens,[status(thm)],[12119, 12118])).
% 291.42/183.93 tff(12121,plain,
% 291.42/183.93 (node16(c_e_h_3, c_e, s6) | node15(c_e_h_3, c_e, s6, s7) | node14(c_e_h_3, c_e, s6, s7)),
% 291.42/183.93 inference(unit_resolution,[status(thm)],[12120, 204, 12060])).
% 291.42/183.93 tff(12122,plain,
% 291.42/183.93 (node14(c_e_h_3, c_e, s6, s7)),
% 291.42/183.93 inference(unit_resolution,[status(thm)],[12121, 12114, 12084])).
% 291.42/183.93 tff(12123,assumption,(node14(c_e_h_3, c_e, s6, s7)), introduced(assumption)).
% 291.42/183.93 tff(12124,plain,
% 291.42/183.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | m_c_h_element_v_in1(c_e_h_3, c_e, s6) | (~node14(c_e_h_3, c_e, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | m_c_h_element_v_in1(c_e_h_3, c_e, s6) | (~node14(c_e_h_3, c_e, s6, s7)))),
% 291.42/183.93 inference(rewrite,[status(thm)],[])).
% 291.42/183.93 tff(12125,plain,
% 291.42/183.93 (((~node14(c_e_h_3, c_e, s6, s7)) | m_c_h_element_v_in1(c_e_h_3, c_e, s6) | (~m_c_h_element_v_out(c_e_h_3, c_e, s7))) <=> ((~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | m_c_h_element_v_in1(c_e_h_3, c_e, s6) | (~node14(c_e_h_3, c_e, s6, s7)))),
% 291.42/183.93 inference(rewrite,[status(thm)],[])).
% 291.42/183.93 tff(12126,plain,
% 291.42/183.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s6, s7)) | m_c_h_element_v_in1(c_e_h_3, c_e, s6) | (~m_c_h_element_v_out(c_e_h_3, c_e, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | m_c_h_element_v_in1(c_e_h_3, c_e, s6) | (~node14(c_e_h_3, c_e, s6, s7))))),
% 291.42/183.93 inference(monotonicity,[status(thm)],[12125])).
% 291.42/183.93 tff(12127,plain,
% 291.42/183.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s6, s7)) | m_c_h_element_v_in1(c_e_h_3, c_e, s6) | (~m_c_h_element_v_out(c_e_h_3, c_e, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | m_c_h_element_v_in1(c_e_h_3, c_e, s6) | (~node14(c_e_h_3, c_e, s6, s7)))),
% 291.42/183.93 inference(transitivity,[status(thm)],[12126, 12124])).
% 291.42/183.93 tff(12128,plain,
% 291.42/183.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s6, s7)) | m_c_h_element_v_in1(c_e_h_3, c_e, s6) | (~m_c_h_element_v_out(c_e_h_3, c_e, s7)))),
% 291.42/183.93 inference(quant_inst,[status(thm)],[])).
% 291.42/183.93 tff(12129,plain,
% 291.42/183.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | m_c_h_element_v_in1(c_e_h_3, c_e, s6) | (~node14(c_e_h_3, c_e, s6, s7))),
% 291.42/183.93 inference(modus_ponens,[status(thm)],[12128, 12127])).
% 291.42/183.93 tff(12130,plain,
% 291.42/183.93 ($false),
% 291.42/183.93 inference(unit_resolution,[status(thm)],[12129, 223, 12048, 12123, 12087])).
% 291.42/183.93 tff(12131,plain,((~node14(c_e_h_3, c_e, s6, s7)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | m_c_h_element_v_in1(c_e_h_3, c_e, s6)), inference(lemma,lemma(discharge,[]))).
% 291.42/183.93 tff(12132,plain,
% 291.42/183.93 ($false),
% 291.42/183.93 inference(unit_resolution,[status(thm)],[12131, 12122, 12077, 12048])).
% 291.42/183.93 tff(12133,plain,(m_c_h_element_v_out(c_e_h_3, c_e, s6) | (~m_c_h_element_v_out(c_e_h_3, c_e, s7)) | m_c_h_element_v_in2(c_e_h_3, c_e, s6)), inference(lemma,lemma(discharge,[]))).
% 291.42/183.93 tff(12134,plain,
% 291.42/183.93 (m_c_h_element_v_out(c_e_h_3, c_e, s6) | (~m_c_h_element_v_out(c_e_h_3, c_e, s7))),
% 291.42/183.93 inference(unit_resolution,[status(thm)],[12133, 12047])).
% 291.42/183.93 tff(12135,plain,
% 291.42/183.93 (~m_c_h_element_v_out(c_e_h_3, c_e, s7)),
% 291.42/183.93 inference(unit_resolution,[status(thm)],[12134, 2446])).
% 291.42/183.93 tff(12136,assumption,(node15(c_e_h_3, c_e, s7, s8)), introduced(assumption)).
% 291.42/183.93 tff(12137,assumption,(~m_c_h_element_v_out(c_e_h_3, c_e, s7)), introduced(assumption)).
% 291.42/183.93 tff(12138,plain,
% 291.42/183.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s8)) | (~node15(c_e_h_3, c_e, s7, s8)) | m_c_h_element_v_out(c_e_h_3, c_e, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s8)) | (~node15(c_e_h_3, c_e, s7, s8)) | m_c_h_element_v_out(c_e_h_3, c_e, s7))),
% 291.42/183.93 inference(rewrite,[status(thm)],[])).
% 291.42/183.93 tff(12139,plain,
% 291.42/183.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s8)) | (~node15(c_e_h_3, c_e, s7, s8)) | m_c_h_element_v_out(c_e_h_3, c_e, s7))),
% 291.42/183.93 inference(quant_inst,[status(thm)],[])).
% 291.42/183.93 tff(12140,plain,
% 291.42/183.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s8)) | (~node15(c_e_h_3, c_e, s7, s8)) | m_c_h_element_v_out(c_e_h_3, c_e, s7)),
% 291.42/183.93 inference(modus_ponens,[status(thm)],[12139, 12138])).
% 291.42/183.93 tff(12141,plain,
% 291.42/183.93 ($false),
% 291.42/183.93 inference(unit_resolution,[status(thm)],[12140, 147, 12137, 12020, 12136])).
% 291.42/183.93 tff(12142,plain,((~node15(c_e_h_3, c_e, s7, s8)) | m_c_h_element_v_out(c_e_h_3, c_e, s7) | (~m_c_h_element_v_out(c_e_h_3, c_e, s8))), inference(lemma,lemma(discharge,[]))).
% 291.42/183.93 tff(12143,plain,
% 291.42/183.93 ((~node15(c_e_h_3, c_e, s7, s8)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s8))),
% 291.42/183.93 inference(unit_resolution,[status(thm)],[12142, 12135])).
% 291.42/183.93 tff(12144,plain,
% 291.42/183.93 (~node15(c_e_h_3, c_e, s7, s8)),
% 291.42/183.93 inference(unit_resolution,[status(thm)],[12143, 12020])).
% 291.42/183.93 tff(12145,plain,
% 291.42/183.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s7, s8)) | node19(c_e_h_3, c_e, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s7, s8)) | node19(c_e_h_3, c_e, s7, s8))),
% 291.42/183.93 inference(rewrite,[status(thm)],[])).
% 291.42/183.93 tff(12146,plain,
% 291.42/183.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s7, s8)) | node19(c_e_h_3, c_e, s7, s8))),
% 291.42/183.93 inference(quant_inst,[status(thm)],[])).
% 291.42/183.93 tff(12147,plain,
% 291.42/183.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s7, s8)) | node19(c_e_h_3, c_e, s7, s8)),
% 291.42/183.93 inference(modus_ponens,[status(thm)],[12146, 12145])).
% 291.42/183.93 tff(12148,plain,
% 291.42/183.93 (node19(c_e_h_3, c_e, s7, s8)),
% 291.42/183.93 inference(unit_resolution,[status(thm)],[12147, 190, 1938])).
% 291.42/183.93 tff(12149,plain,
% 291.42/183.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_3, c_e, s7, s8) | node15(c_e_h_3, c_e, s7, s8) | (~node19(c_e_h_3, c_e, s7, s8)) | node16(c_e_h_3, c_e, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_e, s7, s8) | node15(c_e_h_3, c_e, s7, s8) | (~node19(c_e_h_3, c_e, s7, s8)) | node16(c_e_h_3, c_e, s7))),
% 291.42/183.93 inference(rewrite,[status(thm)],[])).
% 291.42/183.93 tff(12150,plain,
% 291.42/183.93 ((node16(c_e_h_3, c_e, s7) | node14(c_e_h_3, c_e, s7, s8) | node15(c_e_h_3, c_e, s7, s8) | (~node19(c_e_h_3, c_e, s7, s8))) <=> (node14(c_e_h_3, c_e, s7, s8) | node15(c_e_h_3, c_e, s7, s8) | (~node19(c_e_h_3, c_e, s7, s8)) | node16(c_e_h_3, c_e, s7))),
% 291.42/183.93 inference(rewrite,[status(thm)],[])).
% 291.42/183.93 tff(12151,plain,
% 291.42/183.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s7) | node14(c_e_h_3, c_e, s7, s8) | node15(c_e_h_3, c_e, s7, s8) | (~node19(c_e_h_3, c_e, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_3, c_e, s7, s8) | node15(c_e_h_3, c_e, s7, s8) | (~node19(c_e_h_3, c_e, s7, s8)) | node16(c_e_h_3, c_e, s7)))),
% 291.42/183.93 inference(monotonicity,[status(thm)],[12150])).
% 291.42/183.94 tff(12152,plain,
% 291.42/183.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s7) | node14(c_e_h_3, c_e, s7, s8) | node15(c_e_h_3, c_e, s7, s8) | (~node19(c_e_h_3, c_e, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_e, s7, s8) | node15(c_e_h_3, c_e, s7, s8) | (~node19(c_e_h_3, c_e, s7, s8)) | node16(c_e_h_3, c_e, s7))),
% 291.42/183.94 inference(transitivity,[status(thm)],[12151, 12149])).
% 291.42/183.94 tff(12153,plain,
% 291.42/183.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s7) | node14(c_e_h_3, c_e, s7, s8) | node15(c_e_h_3, c_e, s7, s8) | (~node19(c_e_h_3, c_e, s7, s8)))),
% 291.42/183.94 inference(quant_inst,[status(thm)],[])).
% 291.42/183.94 tff(12154,plain,
% 291.42/183.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_e, s7, s8) | node15(c_e_h_3, c_e, s7, s8) | (~node19(c_e_h_3, c_e, s7, s8)) | node16(c_e_h_3, c_e, s7)),
% 291.42/183.94 inference(modus_ponens,[status(thm)],[12153, 12152])).
% 291.42/183.94 tff(12155,plain,
% 291.42/183.94 (node14(c_e_h_3, c_e, s7, s8) | node15(c_e_h_3, c_e, s7, s8) | node16(c_e_h_3, c_e, s7)),
% 291.42/183.94 inference(unit_resolution,[status(thm)],[12154, 204, 12148])).
% 291.42/183.94 tff(12156,plain,
% 291.42/183.94 ($false),
% 291.42/183.94 inference(unit_resolution,[status(thm)],[12155, 12144, 12040, 12030])).
% 291.42/183.94 tff(12157,plain,((~m_c_h_element_v_out(c_e_h_3, c_e, s8)) | m_c_h_element_v_in1(c_e_h_3, c_e, s7)), inference(lemma,lemma(discharge,[]))).
% 291.42/183.94 tff(12158,plain,
% 291.42/183.94 (m_c_h_element_v_in1(c_e_h_3, c_e, s7)),
% 291.42/183.94 inference(unit_resolution,[status(thm)],[12157, 12020])).
% 291.42/183.94 tff(12159,assumption,(node18(c_e_h_3, c_e, s7, s8)), introduced(assumption)).
% 291.42/183.94 tff(12160,plain,
% 291.42/183.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_e, s7) | (~m_c_h_element_v_out(c_e_h_3, c_e, s8)) | (~node18(c_e_h_3, c_e, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s7) | (~m_c_h_element_v_out(c_e_h_3, c_e, s8)) | (~node18(c_e_h_3, c_e, s7, s8)))),
% 291.42/183.94 inference(rewrite,[status(thm)],[])).
% 291.42/183.94 tff(12161,plain,
% 291.42/183.94 (((~m_c_h_element_v_out(c_e_h_3, c_e, s8)) | m_c_h_element_v_out(c_e_h_3, c_e, s7) | (~node18(c_e_h_3, c_e, s7, s8))) <=> (m_c_h_element_v_out(c_e_h_3, c_e, s7) | (~m_c_h_element_v_out(c_e_h_3, c_e, s8)) | (~node18(c_e_h_3, c_e, s7, s8)))),
% 291.42/183.94 inference(rewrite,[status(thm)],[])).
% 291.42/183.94 tff(12162,plain,
% 291.42/183.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s8)) | m_c_h_element_v_out(c_e_h_3, c_e, s7) | (~node18(c_e_h_3, c_e, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_e, s7) | (~m_c_h_element_v_out(c_e_h_3, c_e, s8)) | (~node18(c_e_h_3, c_e, s7, s8))))),
% 291.42/183.94 inference(monotonicity,[status(thm)],[12161])).
% 291.42/183.94 tff(12163,plain,
% 291.42/183.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s8)) | m_c_h_element_v_out(c_e_h_3, c_e, s7) | (~node18(c_e_h_3, c_e, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s7) | (~m_c_h_element_v_out(c_e_h_3, c_e, s8)) | (~node18(c_e_h_3, c_e, s7, s8)))),
% 291.42/183.94 inference(transitivity,[status(thm)],[12162, 12160])).
% 291.42/183.94 tff(12164,plain,
% 291.42/183.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s8)) | m_c_h_element_v_out(c_e_h_3, c_e, s7) | (~node18(c_e_h_3, c_e, s7, s8)))),
% 291.42/183.94 inference(quant_inst,[status(thm)],[])).
% 291.42/183.94 tff(12165,plain,
% 291.42/183.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s7) | (~m_c_h_element_v_out(c_e_h_3, c_e, s8)) | (~node18(c_e_h_3, c_e, s7, s8))),
% 291.42/183.94 inference(modus_ponens,[status(thm)],[12164, 12163])).
% 291.42/183.94 tff(12166,plain,
% 291.42/183.94 ($false),
% 291.42/183.94 inference(unit_resolution,[status(thm)],[12165, 753, 12137, 12020, 12159])).
% 291.42/183.94 tff(12167,plain,((~node18(c_e_h_3, c_e, s7, s8)) | m_c_h_element_v_out(c_e_h_3, c_e, s7) | (~m_c_h_element_v_out(c_e_h_3, c_e, s8))), inference(lemma,lemma(discharge,[]))).
% 291.42/183.94 tff(12168,plain,
% 291.42/183.94 ((~node18(c_e_h_3, c_e, s7, s8)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s8))),
% 291.42/183.94 inference(unit_resolution,[status(thm)],[12167, 12135])).
% 291.42/183.94 tff(12169,plain,
% 291.42/183.94 (~node18(c_e_h_3, c_e, s7, s8)),
% 291.42/183.94 inference(unit_resolution,[status(thm)],[12168, 12020])).
% 291.42/183.94 tff(12170,plain,
% 291.42/183.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_3, c_e, s7, s8) | (~node19(c_e_h_3, c_e, s7, s8)) | node17(c_e_h_3, c_e, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_3, c_e, s7, s8) | (~node19(c_e_h_3, c_e, s7, s8)) | node17(c_e_h_3, c_e, s7))),
% 291.42/183.94 inference(rewrite,[status(thm)],[])).
% 291.42/183.94 tff(12171,plain,
% 291.42/183.94 ((node17(c_e_h_3, c_e, s7) | node18(c_e_h_3, c_e, s7, s8) | (~node19(c_e_h_3, c_e, s7, s8))) <=> (node18(c_e_h_3, c_e, s7, s8) | (~node19(c_e_h_3, c_e, s7, s8)) | node17(c_e_h_3, c_e, s7))),
% 291.42/183.94 inference(rewrite,[status(thm)],[])).
% 291.42/183.94 tff(12172,plain,
% 291.42/183.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s7) | node18(c_e_h_3, c_e, s7, s8) | (~node19(c_e_h_3, c_e, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_3, c_e, s7, s8) | (~node19(c_e_h_3, c_e, s7, s8)) | node17(c_e_h_3, c_e, s7)))),
% 291.42/183.94 inference(monotonicity,[status(thm)],[12171])).
% 291.42/183.94 tff(12173,plain,
% 291.42/183.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s7) | node18(c_e_h_3, c_e, s7, s8) | (~node19(c_e_h_3, c_e, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_3, c_e, s7, s8) | (~node19(c_e_h_3, c_e, s7, s8)) | node17(c_e_h_3, c_e, s7))),
% 291.42/183.94 inference(transitivity,[status(thm)],[12172, 12170])).
% 291.42/183.94 tff(12174,plain,
% 291.42/183.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s7) | node18(c_e_h_3, c_e, s7, s8) | (~node19(c_e_h_3, c_e, s7, s8)))),
% 291.42/183.94 inference(quant_inst,[status(thm)],[])).
% 291.42/183.94 tff(12175,plain,
% 291.42/183.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_3, c_e, s7, s8) | (~node19(c_e_h_3, c_e, s7, s8)) | node17(c_e_h_3, c_e, s7)),
% 291.42/183.94 inference(modus_ponens,[status(thm)],[12174, 12173])).
% 291.42/183.94 tff(12176,plain,
% 291.42/183.94 (node18(c_e_h_3, c_e, s7, s8) | node17(c_e_h_3, c_e, s7)),
% 291.42/183.94 inference(unit_resolution,[status(thm)],[12175, 776, 12148])).
% 291.42/183.94 tff(12177,plain,
% 291.42/183.94 (node17(c_e_h_3, c_e, s7)),
% 291.42/183.94 inference(unit_resolution,[status(thm)],[12176, 12169])).
% 291.42/183.94 tff(12178,assumption,(m_c_h_element_v_in2(c_e_h_3, c_e, s7)), introduced(assumption)).
% 291.42/183.94 tff(12179,plain,
% 291.42/183.94 ($false),
% 291.42/183.94 inference(unit_resolution,[status(thm)],[12023, 164, 12178, 11317])).
% 291.42/183.94 tff(12180,plain,(~m_c_h_element_v_in2(c_e_h_3, c_e, s7)), inference(lemma,lemma(discharge,[]))).
% 291.42/183.94 tff(12181,plain,
% 291.42/183.94 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s7)) | m_c_h_element_v_in2(c_e_h_3, c_e, s7) | (~node17(c_e_h_3, c_e, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s7)) | m_c_h_element_v_in2(c_e_h_3, c_e, s7) | (~node17(c_e_h_3, c_e, s7)))),
% 291.42/183.95 inference(rewrite,[status(thm)],[])).
% 291.42/183.95 tff(12182,plain,
% 291.42/183.95 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s7)) | m_c_h_element_v_in2(c_e_h_3, c_e, s7) | (~node17(c_e_h_3, c_e, s7)))),
% 291.42/183.95 inference(quant_inst,[status(thm)],[])).
% 291.42/183.95 tff(12183,plain,
% 291.42/183.95 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s7)) | m_c_h_element_v_in2(c_e_h_3, c_e, s7) | (~node17(c_e_h_3, c_e, s7))),
% 291.42/183.95 inference(modus_ponens,[status(thm)],[12182, 12181])).
% 291.42/183.95 tff(12184,plain,
% 291.42/183.95 ((~m_c_h_element_v_in1(c_e_h_3, c_e, s7)) | (~node17(c_e_h_3, c_e, s7))),
% 291.42/183.95 inference(unit_resolution,[status(thm)],[12183, 919, 12180])).
% 291.42/183.95 tff(12185,plain,
% 291.42/183.95 ($false),
% 291.42/183.95 inference(unit_resolution,[status(thm)],[12184, 12177, 12158])).
% 291.42/183.95 tff(12186,plain,(~m_c_h_element_v_out(c_e_h_3, c_e, s8)), inference(lemma,lemma(discharge,[]))).
% 291.42/183.95 tff(12187,assumption,(node18(c_e_h_3, c_e, s8, s9)), introduced(assumption)).
% 291.42/183.95 tff(12188,assumption,(~m_c_h_element_v_out(c_e_h_3, c_e, s8)), introduced(assumption)).
% 291.42/183.95 tff(12189,plain,
% 291.42/183.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_e, s8) | (~m_c_h_element_v_out(c_e_h_3, c_e, s9)) | (~node18(c_e_h_3, c_e, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s8) | (~m_c_h_element_v_out(c_e_h_3, c_e, s9)) | (~node18(c_e_h_3, c_e, s8, s9)))),
% 291.42/183.95 inference(rewrite,[status(thm)],[])).
% 291.42/183.95 tff(12190,plain,
% 291.42/183.95 (((~m_c_h_element_v_out(c_e_h_3, c_e, s9)) | m_c_h_element_v_out(c_e_h_3, c_e, s8) | (~node18(c_e_h_3, c_e, s8, s9))) <=> (m_c_h_element_v_out(c_e_h_3, c_e, s8) | (~m_c_h_element_v_out(c_e_h_3, c_e, s9)) | (~node18(c_e_h_3, c_e, s8, s9)))),
% 291.42/183.95 inference(rewrite,[status(thm)],[])).
% 291.42/183.95 tff(12191,plain,
% 291.42/183.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s9)) | m_c_h_element_v_out(c_e_h_3, c_e, s8) | (~node18(c_e_h_3, c_e, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_e, s8) | (~m_c_h_element_v_out(c_e_h_3, c_e, s9)) | (~node18(c_e_h_3, c_e, s8, s9))))),
% 291.42/183.95 inference(monotonicity,[status(thm)],[12190])).
% 291.42/183.95 tff(12192,plain,
% 291.42/183.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s9)) | m_c_h_element_v_out(c_e_h_3, c_e, s8) | (~node18(c_e_h_3, c_e, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s8) | (~m_c_h_element_v_out(c_e_h_3, c_e, s9)) | (~node18(c_e_h_3, c_e, s8, s9)))),
% 291.42/183.95 inference(transitivity,[status(thm)],[12191, 12189])).
% 291.42/183.95 tff(12193,plain,
% 291.42/183.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s9)) | m_c_h_element_v_out(c_e_h_3, c_e, s8) | (~node18(c_e_h_3, c_e, s8, s9)))),
% 291.42/183.95 inference(quant_inst,[status(thm)],[])).
% 291.42/183.95 tff(12194,plain,
% 291.42/183.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s8) | (~m_c_h_element_v_out(c_e_h_3, c_e, s9)) | (~node18(c_e_h_3, c_e, s8, s9))),
% 291.42/183.95 inference(modus_ponens,[status(thm)],[12193, 12192])).
% 291.42/183.95 tff(12195,plain,
% 291.42/183.95 ($false),
% 291.42/183.95 inference(unit_resolution,[status(thm)],[12194, 753, 12188, 12019, 12187])).
% 291.42/183.95 tff(12196,plain,((~node18(c_e_h_3, c_e, s8, s9)) | m_c_h_element_v_out(c_e_h_3, c_e, s8) | (~m_c_h_element_v_out(c_e_h_3, c_e, s9))), inference(lemma,lemma(discharge,[]))).
% 291.42/183.95 tff(12197,plain,
% 291.42/183.95 ((~node18(c_e_h_3, c_e, s8, s9)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s9))),
% 291.42/183.95 inference(unit_resolution,[status(thm)],[12196, 12186])).
% 291.42/183.95 tff(12198,plain,
% 291.42/183.95 (~node18(c_e_h_3, c_e, s8, s9)),
% 291.42/183.95 inference(unit_resolution,[status(thm)],[12197, 12019])).
% 291.42/183.95 tff(12199,plain,
% 291.42/183.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s8, s9)) | node19(c_e_h_3, c_e, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s8, s9)) | node19(c_e_h_3, c_e, s8, s9))),
% 291.42/183.95 inference(rewrite,[status(thm)],[])).
% 291.42/183.95 tff(12200,plain,
% 291.42/183.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s8, s9)) | node19(c_e_h_3, c_e, s8, s9))),
% 291.42/183.95 inference(quant_inst,[status(thm)],[])).
% 291.42/183.95 tff(12201,plain,
% 291.42/183.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s8, s9)) | node19(c_e_h_3, c_e, s8, s9)),
% 291.42/183.95 inference(modus_ponens,[status(thm)],[12200, 12199])).
% 291.42/183.95 tff(12202,plain,
% 291.42/183.95 (node19(c_e_h_3, c_e, s8, s9)),
% 291.42/183.95 inference(unit_resolution,[status(thm)],[12201, 190, 1993])).
% 291.42/183.95 tff(12203,plain,
% 291.42/183.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s8) | node18(c_e_h_3, c_e, s8, s9) | (~node19(c_e_h_3, c_e, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_e, s8) | node18(c_e_h_3, c_e, s8, s9) | (~node19(c_e_h_3, c_e, s8, s9)))),
% 291.42/183.95 inference(rewrite,[status(thm)],[])).
% 291.42/183.95 tff(12204,plain,
% 291.42/183.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s8) | node18(c_e_h_3, c_e, s8, s9) | (~node19(c_e_h_3, c_e, s8, s9)))),
% 291.42/183.95 inference(quant_inst,[status(thm)],[])).
% 291.42/183.95 tff(12205,plain,
% 291.42/183.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_e, s8) | node18(c_e_h_3, c_e, s8, s9) | (~node19(c_e_h_3, c_e, s8, s9))),
% 291.42/183.95 inference(modus_ponens,[status(thm)],[12204, 12203])).
% 291.42/183.95 tff(12206,plain,
% 291.42/183.95 (node17(c_e_h_3, c_e, s8) | node18(c_e_h_3, c_e, s8, s9)),
% 291.42/183.95 inference(unit_resolution,[status(thm)],[12205, 776, 12202])).
% 291.42/183.95 tff(12207,plain,
% 291.42/183.95 (node17(c_e_h_3, c_e, s8)),
% 291.42/183.95 inference(unit_resolution,[status(thm)],[12206, 12198])).
% 291.42/183.95 tff(12208,assumption,(node15(c_e_h_3, c_e, s8, s9)), introduced(assumption)).
% 291.42/183.95 tff(12209,plain,
% 291.42/183.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s9)) | (~node15(c_e_h_3, c_e, s8, s9)) | m_c_h_element_v_out(c_e_h_3, c_e, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s9)) | (~node15(c_e_h_3, c_e, s8, s9)) | m_c_h_element_v_out(c_e_h_3, c_e, s8))),
% 291.42/183.95 inference(rewrite,[status(thm)],[])).
% 291.42/183.95 tff(12210,plain,
% 291.42/183.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s9)) | (~node15(c_e_h_3, c_e, s8, s9)) | m_c_h_element_v_out(c_e_h_3, c_e, s8))),
% 291.42/183.95 inference(quant_inst,[status(thm)],[])).
% 291.42/183.95 tff(12211,plain,
% 291.42/183.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s9)) | (~node15(c_e_h_3, c_e, s8, s9)) | m_c_h_element_v_out(c_e_h_3, c_e, s8)),
% 291.42/183.95 inference(modus_ponens,[status(thm)],[12210, 12209])).
% 291.42/183.95 tff(12212,plain,
% 291.42/183.95 ($false),
% 291.42/183.95 inference(unit_resolution,[status(thm)],[12211, 147, 12188, 12019, 12208])).
% 291.42/183.95 tff(12213,plain,((~node15(c_e_h_3, c_e, s8, s9)) | m_c_h_element_v_out(c_e_h_3, c_e, s8) | (~m_c_h_element_v_out(c_e_h_3, c_e, s9))), inference(lemma,lemma(discharge,[]))).
% 291.42/183.95 tff(12214,plain,
% 291.42/183.95 ((~node15(c_e_h_3, c_e, s8, s9)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s9))),
% 291.42/183.95 inference(unit_resolution,[status(thm)],[12213, 12186])).
% 291.42/183.95 tff(12215,plain,
% 291.42/183.95 (~node15(c_e_h_3, c_e, s8, s9)),
% 291.42/183.95 inference(unit_resolution,[status(thm)],[12214, 12019])).
% 291.42/183.95 tff(12216,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_e, s8)), introduced(assumption)).
% 291.42/183.95 tff(12217,assumption,(node14(c_e_h_3, c_e, s8, s9)), introduced(assumption)).
% 291.42/183.95 tff(12218,plain,
% 291.42/183.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s9)) | m_c_h_element_v_in1(c_e_h_3, c_e, s8) | (~node14(c_e_h_3, c_e, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s9)) | m_c_h_element_v_in1(c_e_h_3, c_e, s8) | (~node14(c_e_h_3, c_e, s8, s9)))),
% 291.42/183.95 inference(rewrite,[status(thm)],[])).
% 291.42/183.95 tff(12219,plain,
% 291.42/183.95 (((~node14(c_e_h_3, c_e, s8, s9)) | m_c_h_element_v_in1(c_e_h_3, c_e, s8) | (~m_c_h_element_v_out(c_e_h_3, c_e, s9))) <=> ((~m_c_h_element_v_out(c_e_h_3, c_e, s9)) | m_c_h_element_v_in1(c_e_h_3, c_e, s8) | (~node14(c_e_h_3, c_e, s8, s9)))),
% 291.42/183.95 inference(rewrite,[status(thm)],[])).
% 291.42/183.95 tff(12220,plain,
% 291.42/183.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s8, s9)) | m_c_h_element_v_in1(c_e_h_3, c_e, s8) | (~m_c_h_element_v_out(c_e_h_3, c_e, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s9)) | m_c_h_element_v_in1(c_e_h_3, c_e, s8) | (~node14(c_e_h_3, c_e, s8, s9))))),
% 291.42/183.95 inference(monotonicity,[status(thm)],[12219])).
% 291.42/183.95 tff(12221,plain,
% 291.42/183.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s8, s9)) | m_c_h_element_v_in1(c_e_h_3, c_e, s8) | (~m_c_h_element_v_out(c_e_h_3, c_e, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s9)) | m_c_h_element_v_in1(c_e_h_3, c_e, s8) | (~node14(c_e_h_3, c_e, s8, s9)))),
% 291.42/183.95 inference(transitivity,[status(thm)],[12220, 12218])).
% 291.42/183.95 tff(12222,plain,
% 291.42/183.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s8, s9)) | m_c_h_element_v_in1(c_e_h_3, c_e, s8) | (~m_c_h_element_v_out(c_e_h_3, c_e, s9)))),
% 291.42/183.95 inference(quant_inst,[status(thm)],[])).
% 291.42/183.95 tff(12223,plain,
% 291.42/183.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s9)) | m_c_h_element_v_in1(c_e_h_3, c_e, s8) | (~node14(c_e_h_3, c_e, s8, s9))),
% 291.42/183.95 inference(modus_ponens,[status(thm)],[12222, 12221])).
% 291.42/183.95 tff(12224,plain,
% 291.42/183.95 ($false),
% 291.42/183.95 inference(unit_resolution,[status(thm)],[12223, 223, 12019, 12217, 12216])).
% 291.42/183.95 tff(12225,plain,((~node14(c_e_h_3, c_e, s8, s9)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s9)) | m_c_h_element_v_in1(c_e_h_3, c_e, s8)), inference(lemma,lemma(discharge,[]))).
% 291.42/183.95 tff(12226,plain,
% 291.42/183.95 (~node14(c_e_h_3, c_e, s8, s9)),
% 291.42/183.95 inference(unit_resolution,[status(thm)],[12225, 12019, 12216])).
% 291.42/183.95 tff(12227,plain,
% 291.42/183.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s8) | node15(c_e_h_3, c_e, s8, s9) | (~node19(c_e_h_3, c_e, s8, s9)) | node14(c_e_h_3, c_e, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_e, s8) | node15(c_e_h_3, c_e, s8, s9) | (~node19(c_e_h_3, c_e, s8, s9)) | node14(c_e_h_3, c_e, s8, s9))),
% 291.42/183.96 inference(rewrite,[status(thm)],[])).
% 291.42/183.96 tff(12228,plain,
% 291.42/183.96 ((node16(c_e_h_3, c_e, s8) | node14(c_e_h_3, c_e, s8, s9) | node15(c_e_h_3, c_e, s8, s9) | (~node19(c_e_h_3, c_e, s8, s9))) <=> (node16(c_e_h_3, c_e, s8) | node15(c_e_h_3, c_e, s8, s9) | (~node19(c_e_h_3, c_e, s8, s9)) | node14(c_e_h_3, c_e, s8, s9))),
% 291.42/183.96 inference(rewrite,[status(thm)],[])).
% 291.42/183.96 tff(12229,plain,
% 291.42/183.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s8) | node14(c_e_h_3, c_e, s8, s9) | node15(c_e_h_3, c_e, s8, s9) | (~node19(c_e_h_3, c_e, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s8) | node15(c_e_h_3, c_e, s8, s9) | (~node19(c_e_h_3, c_e, s8, s9)) | node14(c_e_h_3, c_e, s8, s9)))),
% 291.42/183.96 inference(monotonicity,[status(thm)],[12228])).
% 291.42/183.96 tff(12230,plain,
% 291.42/183.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s8) | node14(c_e_h_3, c_e, s8, s9) | node15(c_e_h_3, c_e, s8, s9) | (~node19(c_e_h_3, c_e, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_e, s8) | node15(c_e_h_3, c_e, s8, s9) | (~node19(c_e_h_3, c_e, s8, s9)) | node14(c_e_h_3, c_e, s8, s9))),
% 291.42/183.96 inference(transitivity,[status(thm)],[12229, 12227])).
% 291.42/183.96 tff(12231,plain,
% 291.42/183.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s8) | node14(c_e_h_3, c_e, s8, s9) | node15(c_e_h_3, c_e, s8, s9) | (~node19(c_e_h_3, c_e, s8, s9)))),
% 291.42/183.96 inference(quant_inst,[status(thm)],[])).
% 291.42/183.96 tff(12232,plain,
% 291.42/183.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_e, s8) | node15(c_e_h_3, c_e, s8, s9) | (~node19(c_e_h_3, c_e, s8, s9)) | node14(c_e_h_3, c_e, s8, s9)),
% 291.42/183.96 inference(modus_ponens,[status(thm)],[12231, 12230])).
% 291.42/183.96 tff(12233,plain,
% 291.42/183.96 (node16(c_e_h_3, c_e, s8) | node15(c_e_h_3, c_e, s8, s9) | node14(c_e_h_3, c_e, s8, s9)),
% 291.42/183.96 inference(unit_resolution,[status(thm)],[12232, 204, 12202])).
% 291.42/183.96 tff(12234,plain,
% 291.42/183.96 (node16(c_e_h_3, c_e, s8)),
% 291.42/183.96 inference(unit_resolution,[status(thm)],[12233, 12226, 12215])).
% 291.42/183.96 tff(12235,assumption,(node17(c_e_h_3, c_e, s8)), introduced(assumption)).
% 291.42/183.96 tff(12236,assumption,(node16(c_e_h_3, c_e, s8)), introduced(assumption)).
% 291.42/183.96 tff(12237,assumption,(m_c_h_element_v_in1(c_e_h_3, c_e, s8)), introduced(assumption)).
% 291.42/183.96 tff(12238,plain,
% 291.42/183.96 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_e, s8)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s8)) | m_c_h_element_v_in2(c_e_h_3, c_e, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_e, s8)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s8)) | m_c_h_element_v_in2(c_e_h_3, c_e, s8))),
% 291.42/183.96 inference(rewrite,[status(thm)],[])).
% 291.42/183.96 tff(12239,plain,
% 291.42/183.96 (((~m_c_h_element_v_in1(c_e_h_3, c_e, s8)) | m_c_h_element_v_in2(c_e_h_3, c_e, s8) | (~node17(c_e_h_3, c_e, s8))) <=> ((~node17(c_e_h_3, c_e, s8)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s8)) | m_c_h_element_v_in2(c_e_h_3, c_e, s8))),
% 291.42/183.96 inference(rewrite,[status(thm)],[])).
% 291.42/183.96 tff(12240,plain,
% 291.42/183.96 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s8)) | m_c_h_element_v_in2(c_e_h_3, c_e, s8) | (~node17(c_e_h_3, c_e, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_e, s8)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s8)) | m_c_h_element_v_in2(c_e_h_3, c_e, s8)))),
% 291.42/183.96 inference(monotonicity,[status(thm)],[12239])).
% 291.42/183.96 tff(12241,plain,
% 291.42/183.96 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s8)) | m_c_h_element_v_in2(c_e_h_3, c_e, s8) | (~node17(c_e_h_3, c_e, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_e, s8)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s8)) | m_c_h_element_v_in2(c_e_h_3, c_e, s8))),
% 291.42/183.96 inference(transitivity,[status(thm)],[12240, 12238])).
% 291.42/183.96 tff(12242,plain,
% 291.42/183.96 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s8)) | m_c_h_element_v_in2(c_e_h_3, c_e, s8) | (~node17(c_e_h_3, c_e, s8)))),
% 291.42/183.96 inference(quant_inst,[status(thm)],[])).
% 291.42/183.96 tff(12243,plain,
% 291.42/183.96 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_e, s8)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s8)) | m_c_h_element_v_in2(c_e_h_3, c_e, s8)),
% 291.42/183.96 inference(modus_ponens,[status(thm)],[12242, 12241])).
% 291.42/183.96 tff(12244,plain,
% 291.42/183.96 ((~m_c_h_element_v_in1(c_e_h_3, c_e, s8)) | m_c_h_element_v_in2(c_e_h_3, c_e, s8)),
% 291.42/183.96 inference(unit_resolution,[status(thm)],[12243, 919, 12235])).
% 291.42/183.96 tff(12245,plain,
% 291.42/183.96 (m_c_h_element_v_in2(c_e_h_3, c_e, s8)),
% 291.42/183.96 inference(unit_resolution,[status(thm)],[12244, 12237])).
% 291.42/183.96 tff(12246,plain,
% 291.42/183.96 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_e, s8)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s8)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~node16(c_e_h_3, c_e, s8)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s8)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s8)))),
% 291.42/183.96 inference(rewrite,[status(thm)],[])).
% 291.42/183.96 tff(12247,plain,
% 291.42/183.96 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_e, s8)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s8)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s8)))),
% 291.42/183.96 inference(quant_inst,[status(thm)],[])).
% 291.42/183.96 tff(12248,plain,
% 291.42/183.96 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~node16(c_e_h_3, c_e, s8)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s8)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s8))),
% 291.42/183.96 inference(modus_ponens,[status(thm)],[12247, 12246])).
% 291.42/183.96 tff(12249,plain,
% 291.42/183.96 ((~m_c_h_element_v_in1(c_e_h_3, c_e, s8)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s8))),
% 291.42/183.96 inference(unit_resolution,[status(thm)],[12248, 2307, 12236])).
% 291.42/183.96 tff(12250,plain,
% 291.42/183.96 ($false),
% 291.42/183.96 inference(unit_resolution,[status(thm)],[12249, 12245, 12237])).
% 291.42/183.96 tff(12251,plain,((~m_c_h_element_v_in1(c_e_h_3, c_e, s8)) | (~node16(c_e_h_3, c_e, s8)) | (~node17(c_e_h_3, c_e, s8))), inference(lemma,lemma(discharge,[]))).
% 291.42/183.96 tff(12252,plain,
% 291.42/183.96 (~m_c_h_element_v_in1(c_e_h_3, c_e, s8)),
% 291.42/183.96 inference(unit_resolution,[status(thm)],[12251, 12236, 12235])).
% 291.42/183.96 tff(12253,plain,
% 291.42/183.96 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s8) | (~node17(c_e_h_3, c_e, s8)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_3, c_e, s8) | (~node17(c_e_h_3, c_e, s8)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s8)))),
% 291.42/183.96 inference(rewrite,[status(thm)],[])).
% 291.42/183.96 tff(12254,plain,
% 291.42/183.96 ((m_c_h_element_v_in1(c_e_h_3, c_e, s8) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s8)) | (~node17(c_e_h_3, c_e, s8))) <=> (m_c_h_element_v_in1(c_e_h_3, c_e, s8) | (~node17(c_e_h_3, c_e, s8)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s8)))),
% 291.42/183.96 inference(rewrite,[status(thm)],[])).
% 291.42/183.96 tff(12255,plain,
% 291.42/183.96 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s8) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s8)) | (~node17(c_e_h_3, c_e, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s8) | (~node17(c_e_h_3, c_e, s8)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s8))))),
% 291.42/183.96 inference(monotonicity,[status(thm)],[12254])).
% 291.42/183.96 tff(12256,plain,
% 291.42/183.96 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s8) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s8)) | (~node17(c_e_h_3, c_e, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_3, c_e, s8) | (~node17(c_e_h_3, c_e, s8)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s8)))),
% 291.42/183.96 inference(transitivity,[status(thm)],[12255, 12253])).
% 291.42/183.96 tff(12257,plain,
% 291.42/183.96 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s8) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s8)) | (~node17(c_e_h_3, c_e, s8)))),
% 291.42/183.96 inference(quant_inst,[status(thm)],[])).
% 291.42/183.96 tff(12258,plain,
% 291.42/183.96 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_3, c_e, s8) | (~node17(c_e_h_3, c_e, s8)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s8))),
% 291.42/183.96 inference(modus_ponens,[status(thm)],[12257, 12256])).
% 291.42/183.96 tff(12259,plain,
% 291.42/183.96 (m_c_h_element_v_in1(c_e_h_3, c_e, s8) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s8))),
% 291.42/183.96 inference(unit_resolution,[status(thm)],[12258, 859, 12235])).
% 291.42/183.96 tff(12260,plain,
% 291.42/183.96 (~m_c_h_element_v_in2(c_e_h_3, c_e, s8)),
% 291.42/183.96 inference(unit_resolution,[status(thm)],[12259, 12252])).
% 291.42/183.96 tff(12261,plain,
% 291.42/183.96 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_e, s8)) | m_c_h_element_v_in1(c_e_h_3, c_e, s8) | m_c_h_element_v_in2(c_e_h_3, c_e, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s8)) | m_c_h_element_v_in1(c_e_h_3, c_e, s8) | m_c_h_element_v_in2(c_e_h_3, c_e, s8))),
% 291.42/183.96 inference(rewrite,[status(thm)],[])).
% 291.42/183.96 tff(12262,plain,
% 291.42/183.96 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_e, s8)) | m_c_h_element_v_in1(c_e_h_3, c_e, s8) | m_c_h_element_v_in2(c_e_h_3, c_e, s8))),
% 291.42/183.96 inference(quant_inst,[status(thm)],[])).
% 291.42/183.96 tff(12263,plain,
% 291.42/183.96 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s8)) | m_c_h_element_v_in1(c_e_h_3, c_e, s8) | m_c_h_element_v_in2(c_e_h_3, c_e, s8)),
% 291.42/183.96 inference(modus_ponens,[status(thm)],[12262, 12261])).
% 291.42/183.96 tff(12264,plain,
% 291.42/183.96 (m_c_h_element_v_in1(c_e_h_3, c_e, s8) | m_c_h_element_v_in2(c_e_h_3, c_e, s8)),
% 291.42/183.96 inference(unit_resolution,[status(thm)],[12263, 178, 12236])).
% 291.42/183.96 tff(12265,plain,
% 291.42/183.96 ($false),
% 291.42/183.96 inference(unit_resolution,[status(thm)],[12264, 12260, 12252])).
% 291.42/183.96 tff(12266,plain,((~node16(c_e_h_3, c_e, s8)) | (~node17(c_e_h_3, c_e, s8))), inference(lemma,lemma(discharge,[]))).
% 291.42/183.96 tff(12267,plain,
% 291.42/183.96 ($false),
% 291.42/183.96 inference(unit_resolution,[status(thm)],[12266, 12234, 12207])).
% 291.42/183.96 tff(12268,plain,((~m_c_h_element_v_out(c_e_h_3, c_e, s9)) | m_c_h_element_v_in1(c_e_h_3, c_e, s8)), inference(lemma,lemma(discharge,[]))).
% 291.42/183.97 tff(12269,plain,
% 291.42/183.97 (m_c_h_element_v_in1(c_e_h_3, c_e, s8)),
% 291.42/183.97 inference(unit_resolution,[status(thm)],[12268, 12019])).
% 291.42/183.97 tff(12270,plain,
% 291.42/183.97 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s8)) | m_and_h_gate_v_out(c_e_h_3, c_i, s8))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s8)) | m_and_h_gate_v_out(c_e_h_3, c_i, s8))),
% 291.42/183.97 inference(rewrite,[status(thm)],[])).
% 291.42/183.97 tff(12271,plain,
% 291.42/183.97 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s8)) | m_and_h_gate_v_out(c_e_h_3, c_i, s8))),
% 291.42/183.97 inference(quant_inst,[status(thm)],[])).
% 291.42/183.97 tff(12272,plain,
% 291.42/183.97 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s8)) | m_and_h_gate_v_out(c_e_h_3, c_i, s8)),
% 291.42/183.97 inference(modus_ponens,[status(thm)],[12271, 12270])).
% 291.42/183.97 tff(12273,plain,
% 291.42/183.97 (~m_c_h_element_v_in2(c_e_h_3, c_e, s8)),
% 291.42/183.97 inference(unit_resolution,[status(thm)],[12272, 164, 11344])).
% 291.42/183.97 tff(12274,plain,
% 291.42/183.97 ((~node17(c_e_h_3, c_e, s8)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s8))),
% 291.42/183.97 inference(unit_resolution,[status(thm)],[12243, 919, 12273])).
% 291.42/183.97 tff(12275,plain,
% 291.42/183.97 ($false),
% 291.42/183.97 inference(unit_resolution,[status(thm)],[12274, 12207, 12269])).
% 291.42/183.97 tff(12276,plain,(~m_c_h_element_v_out(c_e_h_3, c_e, s9)), inference(lemma,lemma(discharge,[]))).
% 291.42/183.97 tff(12277,assumption,(m_c_h_element_v_out(c_e_h_3, c_e, s10)), introduced(assumption)).
% 291.42/183.97 tff(12278,assumption,(~m_c_h_element_v_out(c_e_h_3, c_e, s9)), introduced(assumption)).
% 291.42/183.97 tff(12279,assumption,(node18(c_e_h_3, c_e, s9, s10)), introduced(assumption)).
% 291.42/183.97 tff(12280,plain,
% 291.42/183.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_e, s9) | (~m_c_h_element_v_out(c_e_h_3, c_e, s10)) | (~node18(c_e_h_3, c_e, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s9) | (~m_c_h_element_v_out(c_e_h_3, c_e, s10)) | (~node18(c_e_h_3, c_e, s9, s10)))),
% 291.42/183.97 inference(rewrite,[status(thm)],[])).
% 291.42/183.97 tff(12281,plain,
% 291.42/183.97 (((~m_c_h_element_v_out(c_e_h_3, c_e, s10)) | m_c_h_element_v_out(c_e_h_3, c_e, s9) | (~node18(c_e_h_3, c_e, s9, s10))) <=> (m_c_h_element_v_out(c_e_h_3, c_e, s9) | (~m_c_h_element_v_out(c_e_h_3, c_e, s10)) | (~node18(c_e_h_3, c_e, s9, s10)))),
% 291.42/183.97 inference(rewrite,[status(thm)],[])).
% 291.42/183.97 tff(12282,plain,
% 291.42/183.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s10)) | m_c_h_element_v_out(c_e_h_3, c_e, s9) | (~node18(c_e_h_3, c_e, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_e, s9) | (~m_c_h_element_v_out(c_e_h_3, c_e, s10)) | (~node18(c_e_h_3, c_e, s9, s10))))),
% 291.42/183.97 inference(monotonicity,[status(thm)],[12281])).
% 291.42/183.97 tff(12283,plain,
% 291.42/183.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s10)) | m_c_h_element_v_out(c_e_h_3, c_e, s9) | (~node18(c_e_h_3, c_e, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s9) | (~m_c_h_element_v_out(c_e_h_3, c_e, s10)) | (~node18(c_e_h_3, c_e, s9, s10)))),
% 291.42/183.97 inference(transitivity,[status(thm)],[12282, 12280])).
% 291.42/183.97 tff(12284,plain,
% 291.42/183.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s10)) | m_c_h_element_v_out(c_e_h_3, c_e, s9) | (~node18(c_e_h_3, c_e, s9, s10)))),
% 291.42/183.97 inference(quant_inst,[status(thm)],[])).
% 291.42/183.97 tff(12285,plain,
% 291.42/183.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s9) | (~m_c_h_element_v_out(c_e_h_3, c_e, s10)) | (~node18(c_e_h_3, c_e, s9, s10))),
% 291.42/183.97 inference(modus_ponens,[status(thm)],[12284, 12283])).
% 291.42/183.97 tff(12286,plain,
% 291.42/183.97 ($false),
% 291.42/183.97 inference(unit_resolution,[status(thm)],[12285, 753, 12277, 12278, 12279])).
% 291.42/183.97 tff(12287,plain,((~node18(c_e_h_3, c_e, s9, s10)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s10)) | m_c_h_element_v_out(c_e_h_3, c_e, s9)), inference(lemma,lemma(discharge,[]))).
% 291.42/183.97 tff(12288,plain,
% 291.42/183.97 (~node18(c_e_h_3, c_e, s9, s10)),
% 291.42/183.97 inference(unit_resolution,[status(thm)],[12287, 12278, 12277])).
% 291.42/183.97 tff(12289,plain,
% 291.42/183.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s9, s10)) | node19(c_e_h_3, c_e, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s9, s10)) | node19(c_e_h_3, c_e, s9, s10))),
% 291.42/183.97 inference(rewrite,[status(thm)],[])).
% 291.42/183.97 tff(12290,plain,
% 291.42/183.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s9, s10)) | node19(c_e_h_3, c_e, s9, s10))),
% 291.42/183.97 inference(quant_inst,[status(thm)],[])).
% 291.42/183.97 tff(12291,plain,
% 291.42/183.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s9, s10)) | node19(c_e_h_3, c_e, s9, s10)),
% 291.42/183.97 inference(modus_ponens,[status(thm)],[12290, 12289])).
% 291.42/183.97 tff(12292,plain,
% 291.42/183.97 (node19(c_e_h_3, c_e, s9, s10)),
% 291.42/183.97 inference(unit_resolution,[status(thm)],[12291, 190, 7676])).
% 291.42/183.97 tff(12293,plain,
% 291.42/183.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s9) | (~node19(c_e_h_3, c_e, s9, s10)) | node18(c_e_h_3, c_e, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_e, s9) | (~node19(c_e_h_3, c_e, s9, s10)) | node18(c_e_h_3, c_e, s9, s10))),
% 291.42/183.97 inference(rewrite,[status(thm)],[])).
% 291.42/183.97 tff(12294,plain,
% 291.42/183.97 ((node17(c_e_h_3, c_e, s9) | node18(c_e_h_3, c_e, s9, s10) | (~node19(c_e_h_3, c_e, s9, s10))) <=> (node17(c_e_h_3, c_e, s9) | (~node19(c_e_h_3, c_e, s9, s10)) | node18(c_e_h_3, c_e, s9, s10))),
% 291.42/183.97 inference(rewrite,[status(thm)],[])).
% 291.42/183.97 tff(12295,plain,
% 291.42/183.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s9) | node18(c_e_h_3, c_e, s9, s10) | (~node19(c_e_h_3, c_e, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s9) | (~node19(c_e_h_3, c_e, s9, s10)) | node18(c_e_h_3, c_e, s9, s10)))),
% 291.42/183.97 inference(monotonicity,[status(thm)],[12294])).
% 291.42/183.97 tff(12296,plain,
% 291.42/183.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s9) | node18(c_e_h_3, c_e, s9, s10) | (~node19(c_e_h_3, c_e, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_e, s9) | (~node19(c_e_h_3, c_e, s9, s10)) | node18(c_e_h_3, c_e, s9, s10))),
% 291.42/183.97 inference(transitivity,[status(thm)],[12295, 12293])).
% 291.42/183.97 tff(12297,plain,
% 291.42/183.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s9) | node18(c_e_h_3, c_e, s9, s10) | (~node19(c_e_h_3, c_e, s9, s10)))),
% 291.42/183.97 inference(quant_inst,[status(thm)],[])).
% 291.42/183.97 tff(12298,plain,
% 291.42/183.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_e, s9) | (~node19(c_e_h_3, c_e, s9, s10)) | node18(c_e_h_3, c_e, s9, s10)),
% 291.42/183.97 inference(modus_ponens,[status(thm)],[12297, 12296])).
% 291.42/183.97 tff(12299,plain,
% 291.42/183.97 (node17(c_e_h_3, c_e, s9) | node18(c_e_h_3, c_e, s9, s10)),
% 291.42/183.97 inference(unit_resolution,[status(thm)],[12298, 776, 12292])).
% 291.42/183.98 tff(12300,plain,
% 291.42/183.98 (node17(c_e_h_3, c_e, s9)),
% 291.42/183.98 inference(unit_resolution,[status(thm)],[12299, 12288])).
% 291.42/183.98 tff(12301,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_e, s9)), introduced(assumption)).
% 291.42/183.98 tff(12302,plain,
% 291.42/183.98 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s9)) | m_c_h_element_v_in2(c_e_h_3, c_e, s9) | (~node17(c_e_h_3, c_e, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s9)) | m_c_h_element_v_in2(c_e_h_3, c_e, s9) | (~node17(c_e_h_3, c_e, s9)))),
% 291.42/183.98 inference(rewrite,[status(thm)],[])).
% 291.42/183.98 tff(12303,plain,
% 291.42/183.98 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s9)) | m_c_h_element_v_in2(c_e_h_3, c_e, s9) | (~node17(c_e_h_3, c_e, s9)))),
% 291.42/183.98 inference(quant_inst,[status(thm)],[])).
% 291.42/183.98 tff(12304,plain,
% 291.42/183.98 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s9)) | m_c_h_element_v_in2(c_e_h_3, c_e, s9) | (~node17(c_e_h_3, c_e, s9))),
% 291.42/183.98 inference(modus_ponens,[status(thm)],[12303, 12302])).
% 291.42/183.98 tff(12305,plain,
% 291.42/183.98 ((~m_c_h_element_v_in1(c_e_h_3, c_e, s9)) | (~node17(c_e_h_3, c_e, s9))),
% 291.42/183.98 inference(unit_resolution,[status(thm)],[12304, 919, 12301])).
% 291.42/183.98 tff(12306,plain,
% 291.42/183.98 (~m_c_h_element_v_in1(c_e_h_3, c_e, s9)),
% 291.42/183.98 inference(unit_resolution,[status(thm)],[12305, 12300])).
% 291.42/183.98 tff(12307,assumption,(node15(c_e_h_3, c_e, s9, s10)), introduced(assumption)).
% 291.42/183.98 tff(12308,plain,
% 291.42/183.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s10)) | (~node15(c_e_h_3, c_e, s9, s10)) | m_c_h_element_v_out(c_e_h_3, c_e, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s10)) | (~node15(c_e_h_3, c_e, s9, s10)) | m_c_h_element_v_out(c_e_h_3, c_e, s9))),
% 291.42/183.98 inference(rewrite,[status(thm)],[])).
% 291.42/183.98 tff(12309,plain,
% 291.42/183.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s10)) | (~node15(c_e_h_3, c_e, s9, s10)) | m_c_h_element_v_out(c_e_h_3, c_e, s9))),
% 291.42/183.98 inference(quant_inst,[status(thm)],[])).
% 291.42/183.98 tff(12310,plain,
% 291.42/183.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s10)) | (~node15(c_e_h_3, c_e, s9, s10)) | m_c_h_element_v_out(c_e_h_3, c_e, s9)),
% 291.42/183.98 inference(modus_ponens,[status(thm)],[12309, 12308])).
% 291.42/183.98 tff(12311,plain,
% 291.42/183.98 ($false),
% 291.42/183.98 inference(unit_resolution,[status(thm)],[12310, 147, 12277, 12278, 12307])).
% 291.42/183.98 tff(12312,plain,((~node15(c_e_h_3, c_e, s9, s10)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s10)) | m_c_h_element_v_out(c_e_h_3, c_e, s9)), inference(lemma,lemma(discharge,[]))).
% 291.42/183.98 tff(12313,plain,
% 291.42/183.98 (~node15(c_e_h_3, c_e, s9, s10)),
% 291.42/183.98 inference(unit_resolution,[status(thm)],[12312, 12278, 12277])).
% 291.42/183.98 tff(12314,assumption,(node17(c_e_h_3, c_e, s9)), introduced(assumption)).
% 291.42/183.98 tff(12315,assumption,(node16(c_e_h_3, c_e, s9)), introduced(assumption)).
% 291.42/183.98 tff(12316,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_e, s9)), introduced(assumption)).
% 291.42/183.98 tff(12317,plain,
% 291.42/183.98 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s9) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s9)) | (~node17(c_e_h_3, c_e, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_3, c_e, s9) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s9)) | (~node17(c_e_h_3, c_e, s9)))),
% 291.42/183.98 inference(rewrite,[status(thm)],[])).
% 291.42/183.98 tff(12318,plain,
% 291.42/183.98 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s9) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s9)) | (~node17(c_e_h_3, c_e, s9)))),
% 291.42/183.98 inference(quant_inst,[status(thm)],[])).
% 291.42/183.98 tff(12319,plain,
% 291.42/183.98 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_3, c_e, s9) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s9)) | (~node17(c_e_h_3, c_e, s9))),
% 291.42/183.98 inference(modus_ponens,[status(thm)],[12318, 12317])).
% 291.42/183.98 tff(12320,plain,
% 291.42/183.98 (m_c_h_element_v_in1(c_e_h_3, c_e, s9) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s9))),
% 291.42/183.98 inference(unit_resolution,[status(thm)],[12319, 859, 12314])).
% 291.42/183.98 tff(12321,plain,
% 291.42/183.98 (~m_c_h_element_v_in2(c_e_h_3, c_e, s9)),
% 291.42/183.98 inference(unit_resolution,[status(thm)],[12320, 12316])).
% 291.42/183.98 tff(12322,plain,
% 291.42/183.98 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_e, s9)) | m_c_h_element_v_in1(c_e_h_3, c_e, s9) | m_c_h_element_v_in2(c_e_h_3, c_e, s9))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s9)) | m_c_h_element_v_in1(c_e_h_3, c_e, s9) | m_c_h_element_v_in2(c_e_h_3, c_e, s9))),
% 291.42/183.98 inference(rewrite,[status(thm)],[])).
% 291.42/183.98 tff(12323,plain,
% 291.42/183.98 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_e, s9)) | m_c_h_element_v_in1(c_e_h_3, c_e, s9) | m_c_h_element_v_in2(c_e_h_3, c_e, s9))),
% 291.42/183.98 inference(quant_inst,[status(thm)],[])).
% 291.42/183.98 tff(12324,plain,
% 291.42/183.98 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s9)) | m_c_h_element_v_in1(c_e_h_3, c_e, s9) | m_c_h_element_v_in2(c_e_h_3, c_e, s9)),
% 291.42/183.98 inference(modus_ponens,[status(thm)],[12323, 12322])).
% 291.42/183.98 tff(12325,plain,
% 291.42/183.98 (m_c_h_element_v_in1(c_e_h_3, c_e, s9) | m_c_h_element_v_in2(c_e_h_3, c_e, s9)),
% 291.42/183.98 inference(unit_resolution,[status(thm)],[12324, 178, 12315])).
% 291.42/183.98 tff(12326,plain,
% 291.42/183.98 ($false),
% 291.42/183.98 inference(unit_resolution,[status(thm)],[12325, 12321, 12316])).
% 291.42/183.98 tff(12327,plain,(m_c_h_element_v_in1(c_e_h_3, c_e, s9) | (~node16(c_e_h_3, c_e, s9)) | (~node17(c_e_h_3, c_e, s9))), inference(lemma,lemma(discharge,[]))).
% 291.42/183.98 tff(12328,plain,
% 291.42/183.98 (m_c_h_element_v_in1(c_e_h_3, c_e, s9)),
% 291.42/183.98 inference(unit_resolution,[status(thm)],[12327, 12315, 12314])).
% 291.42/183.98 tff(12329,plain,
% 291.42/183.98 ((~m_c_h_element_v_in1(c_e_h_3, c_e, s9)) | m_c_h_element_v_in2(c_e_h_3, c_e, s9)),
% 291.42/183.98 inference(unit_resolution,[status(thm)],[12304, 919, 12314])).
% 291.42/183.98 tff(12330,plain,
% 291.42/183.98 (m_c_h_element_v_in2(c_e_h_3, c_e, s9)),
% 291.42/183.98 inference(unit_resolution,[status(thm)],[12329, 12328])).
% 291.42/183.98 tff(12331,plain,
% 291.42/183.98 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s9)) | (~node16(c_e_h_3, c_e, s9)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s9)) | (~node16(c_e_h_3, c_e, s9)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s9)))),
% 291.42/183.98 inference(rewrite,[status(thm)],[])).
% 291.42/183.98 tff(12332,plain,
% 291.42/183.98 (((~node16(c_e_h_3, c_e, s9)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s9)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s9))) <=> ((~m_c_h_element_v_in1(c_e_h_3, c_e, s9)) | (~node16(c_e_h_3, c_e, s9)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s9)))),
% 291.42/183.98 inference(rewrite,[status(thm)],[])).
% 291.42/183.98 tff(12333,plain,
% 291.42/183.98 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_e, s9)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s9)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s9)) | (~node16(c_e_h_3, c_e, s9)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s9))))),
% 291.42/183.98 inference(monotonicity,[status(thm)],[12332])).
% 291.42/183.98 tff(12334,plain,
% 291.42/183.98 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_e, s9)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s9)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s9)) | (~node16(c_e_h_3, c_e, s9)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s9)))),
% 291.42/183.98 inference(transitivity,[status(thm)],[12333, 12331])).
% 291.42/183.98 tff(12335,plain,
% 291.42/183.98 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_e, s9)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s9)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s9)))),
% 291.42/183.98 inference(quant_inst,[status(thm)],[])).
% 291.42/183.98 tff(12336,plain,
% 291.42/183.98 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s9)) | (~node16(c_e_h_3, c_e, s9)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s9))),
% 291.42/183.98 inference(modus_ponens,[status(thm)],[12335, 12334])).
% 291.42/183.98 tff(12337,plain,
% 291.42/183.98 ((~m_c_h_element_v_in1(c_e_h_3, c_e, s9)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s9))),
% 291.42/183.98 inference(unit_resolution,[status(thm)],[12336, 2307, 12315])).
% 291.42/183.98 tff(12338,plain,
% 291.42/183.98 ($false),
% 291.42/183.98 inference(unit_resolution,[status(thm)],[12337, 12330, 12328])).
% 291.42/183.98 tff(12339,plain,((~node16(c_e_h_3, c_e, s9)) | (~node17(c_e_h_3, c_e, s9))), inference(lemma,lemma(discharge,[]))).
% 291.42/183.98 tff(12340,plain,
% 291.42/183.98 (~node16(c_e_h_3, c_e, s9)),
% 291.42/183.98 inference(unit_resolution,[status(thm)],[12339, 12300])).
% 291.42/183.98 tff(12341,plain,
% 291.42/183.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_3, c_e, s9, s10) | node16(c_e_h_3, c_e, s9) | (~node19(c_e_h_3, c_e, s9, s10)) | node15(c_e_h_3, c_e, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_e, s9, s10) | node16(c_e_h_3, c_e, s9) | (~node19(c_e_h_3, c_e, s9, s10)) | node15(c_e_h_3, c_e, s9, s10))),
% 291.42/183.98 inference(rewrite,[status(thm)],[])).
% 291.42/183.98 tff(12342,plain,
% 291.42/183.98 ((node16(c_e_h_3, c_e, s9) | node14(c_e_h_3, c_e, s9, s10) | node15(c_e_h_3, c_e, s9, s10) | (~node19(c_e_h_3, c_e, s9, s10))) <=> (node14(c_e_h_3, c_e, s9, s10) | node16(c_e_h_3, c_e, s9) | (~node19(c_e_h_3, c_e, s9, s10)) | node15(c_e_h_3, c_e, s9, s10))),
% 291.42/183.98 inference(rewrite,[status(thm)],[])).
% 291.42/183.98 tff(12343,plain,
% 291.42/183.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s9) | node14(c_e_h_3, c_e, s9, s10) | node15(c_e_h_3, c_e, s9, s10) | (~node19(c_e_h_3, c_e, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_3, c_e, s9, s10) | node16(c_e_h_3, c_e, s9) | (~node19(c_e_h_3, c_e, s9, s10)) | node15(c_e_h_3, c_e, s9, s10)))),
% 291.42/183.98 inference(monotonicity,[status(thm)],[12342])).
% 291.42/183.98 tff(12344,plain,
% 291.42/183.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s9) | node14(c_e_h_3, c_e, s9, s10) | node15(c_e_h_3, c_e, s9, s10) | (~node19(c_e_h_3, c_e, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_e, s9, s10) | node16(c_e_h_3, c_e, s9) | (~node19(c_e_h_3, c_e, s9, s10)) | node15(c_e_h_3, c_e, s9, s10))),
% 291.42/183.99 inference(transitivity,[status(thm)],[12343, 12341])).
% 291.42/183.99 tff(12345,plain,
% 291.42/183.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s9) | node14(c_e_h_3, c_e, s9, s10) | node15(c_e_h_3, c_e, s9, s10) | (~node19(c_e_h_3, c_e, s9, s10)))),
% 291.42/183.99 inference(quant_inst,[status(thm)],[])).
% 291.42/183.99 tff(12346,plain,
% 291.42/183.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_e, s9, s10) | node16(c_e_h_3, c_e, s9) | (~node19(c_e_h_3, c_e, s9, s10)) | node15(c_e_h_3, c_e, s9, s10)),
% 291.42/183.99 inference(modus_ponens,[status(thm)],[12345, 12344])).
% 291.42/183.99 tff(12347,plain,
% 291.42/183.99 (node14(c_e_h_3, c_e, s9, s10) | node16(c_e_h_3, c_e, s9) | node15(c_e_h_3, c_e, s9, s10)),
% 291.42/183.99 inference(unit_resolution,[status(thm)],[12346, 204, 12292])).
% 291.42/183.99 tff(12348,plain,
% 291.42/183.99 (node14(c_e_h_3, c_e, s9, s10)),
% 291.42/183.99 inference(unit_resolution,[status(thm)],[12347, 12340, 12313])).
% 291.42/183.99 tff(12349,assumption,(node14(c_e_h_3, c_e, s9, s10)), introduced(assumption)).
% 291.42/183.99 tff(12350,plain,
% 291.42/183.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s10)) | m_c_h_element_v_in1(c_e_h_3, c_e, s9) | (~node14(c_e_h_3, c_e, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s10)) | m_c_h_element_v_in1(c_e_h_3, c_e, s9) | (~node14(c_e_h_3, c_e, s9, s10)))),
% 291.42/183.99 inference(rewrite,[status(thm)],[])).
% 291.42/183.99 tff(12351,plain,
% 291.42/183.99 (((~node14(c_e_h_3, c_e, s9, s10)) | m_c_h_element_v_in1(c_e_h_3, c_e, s9) | (~m_c_h_element_v_out(c_e_h_3, c_e, s10))) <=> ((~m_c_h_element_v_out(c_e_h_3, c_e, s10)) | m_c_h_element_v_in1(c_e_h_3, c_e, s9) | (~node14(c_e_h_3, c_e, s9, s10)))),
% 291.42/183.99 inference(rewrite,[status(thm)],[])).
% 291.42/183.99 tff(12352,plain,
% 291.42/183.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s9, s10)) | m_c_h_element_v_in1(c_e_h_3, c_e, s9) | (~m_c_h_element_v_out(c_e_h_3, c_e, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s10)) | m_c_h_element_v_in1(c_e_h_3, c_e, s9) | (~node14(c_e_h_3, c_e, s9, s10))))),
% 291.42/183.99 inference(monotonicity,[status(thm)],[12351])).
% 291.42/183.99 tff(12353,plain,
% 291.42/183.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s9, s10)) | m_c_h_element_v_in1(c_e_h_3, c_e, s9) | (~m_c_h_element_v_out(c_e_h_3, c_e, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s10)) | m_c_h_element_v_in1(c_e_h_3, c_e, s9) | (~node14(c_e_h_3, c_e, s9, s10)))),
% 291.42/183.99 inference(transitivity,[status(thm)],[12352, 12350])).
% 291.42/183.99 tff(12354,plain,
% 291.42/183.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s9, s10)) | m_c_h_element_v_in1(c_e_h_3, c_e, s9) | (~m_c_h_element_v_out(c_e_h_3, c_e, s10)))),
% 291.42/183.99 inference(quant_inst,[status(thm)],[])).
% 291.42/183.99 tff(12355,plain,
% 291.42/183.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s10)) | m_c_h_element_v_in1(c_e_h_3, c_e, s9) | (~node14(c_e_h_3, c_e, s9, s10))),
% 291.42/183.99 inference(modus_ponens,[status(thm)],[12354, 12353])).
% 291.42/183.99 tff(12356,plain,
% 291.42/183.99 ($false),
% 291.42/183.99 inference(unit_resolution,[status(thm)],[12355, 223, 12277, 12349, 12316])).
% 291.42/183.99 tff(12357,plain,((~node14(c_e_h_3, c_e, s9, s10)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s10)) | m_c_h_element_v_in1(c_e_h_3, c_e, s9)), inference(lemma,lemma(discharge,[]))).
% 291.42/183.99 tff(12358,plain,
% 291.42/183.99 ($false),
% 291.42/183.99 inference(unit_resolution,[status(thm)],[12357, 12348, 12306, 12277])).
% 291.42/183.99 tff(12359,plain,(m_c_h_element_v_out(c_e_h_3, c_e, s9) | (~m_c_h_element_v_out(c_e_h_3, c_e, s10)) | m_c_h_element_v_in2(c_e_h_3, c_e, s9)), inference(lemma,lemma(discharge,[]))).
% 291.42/183.99 tff(12360,plain,
% 291.42/183.99 ((~m_c_h_element_v_out(c_e_h_3, c_e, s10)) | m_c_h_element_v_in2(c_e_h_3, c_e, s9)),
% 291.42/183.99 inference(unit_resolution,[status(thm)],[12359, 12276])).
% 291.42/183.99 tff(12361,plain,
% 291.42/183.99 (~m_c_h_element_v_out(c_e_h_3, c_e, s10)),
% 291.42/183.99 inference(unit_resolution,[status(thm)],[12360, 12018])).
% 291.42/183.99 tff(12362,assumption,(m_c_h_element_v_out(c_e_h_3, c_e, s12)), introduced(assumption)).
% 291.42/183.99 tff(12363,assumption,(~m_c_h_element_v_out(c_e_h_3, c_e, s10)), introduced(assumption)).
% 291.42/183.99 tff(12364,assumption,(m_c_h_element_v_in2(c_e_h_3, c_e, s10)), introduced(assumption)).
% 291.42/183.99 tff(12365,plain,
% 291.42/183.99 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s10)) | m_and_h_gate_v_out(c_e_h_3, c_i, s10))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s10)) | m_and_h_gate_v_out(c_e_h_3, c_i, s10))),
% 291.42/183.99 inference(rewrite,[status(thm)],[])).
% 291.42/183.99 tff(12366,plain,
% 291.42/183.99 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s10)) | m_and_h_gate_v_out(c_e_h_3, c_i, s10))),
% 291.42/183.99 inference(quant_inst,[status(thm)],[])).
% 291.42/183.99 tff(12367,plain,
% 291.42/183.99 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s10)) | m_and_h_gate_v_out(c_e_h_3, c_i, s10)),
% 291.42/183.99 inference(modus_ponens,[status(thm)],[12366, 12365])).
% 291.42/183.99 tff(12368,plain,
% 291.42/183.99 ($false),
% 291.42/183.99 inference(unit_resolution,[status(thm)],[12367, 164, 12364, 11422])).
% 291.42/183.99 tff(12369,plain,((~m_c_h_element_v_in2(c_e_h_3, c_e, s10)) | m_and_h_gate_v_out(c_e_h_3, c_i, s10)), inference(lemma,lemma(discharge,[]))).
% 291.42/183.99 tff(12370,plain,
% 291.42/183.99 (~m_c_h_element_v_in2(c_e_h_3, c_e, s10)),
% 291.42/183.99 inference(unit_resolution,[status(thm)],[12369, 11422])).
% 291.42/183.99 tff(12371,assumption,(m_c_h_element_v_out(c_e_h_3, c_e, s11)), introduced(assumption)).
% 291.42/183.99 tff(12372,assumption,(node18(c_e_h_3, c_e, s10, s11)), introduced(assumption)).
% 291.42/183.99 tff(12373,plain,
% 291.42/183.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s11)) | m_c_h_element_v_out(c_e_h_3, c_e, s10) | (~node18(c_e_h_3, c_e, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s11)) | m_c_h_element_v_out(c_e_h_3, c_e, s10) | (~node18(c_e_h_3, c_e, s10, s11)))),
% 291.42/183.99 inference(rewrite,[status(thm)],[])).
% 291.42/183.99 tff(12374,plain,
% 291.42/183.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s11)) | m_c_h_element_v_out(c_e_h_3, c_e, s10) | (~node18(c_e_h_3, c_e, s10, s11)))),
% 291.42/183.99 inference(quant_inst,[status(thm)],[])).
% 291.42/183.99 tff(12375,plain,
% 291.42/183.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s11)) | m_c_h_element_v_out(c_e_h_3, c_e, s10) | (~node18(c_e_h_3, c_e, s10, s11))),
% 291.42/183.99 inference(modus_ponens,[status(thm)],[12374, 12373])).
% 291.42/183.99 tff(12376,plain,
% 291.42/183.99 ($false),
% 291.42/183.99 inference(unit_resolution,[status(thm)],[12375, 753, 12371, 12363, 12372])).
% 291.42/183.99 tff(12377,plain,((~node18(c_e_h_3, c_e, s10, s11)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s11)) | m_c_h_element_v_out(c_e_h_3, c_e, s10)), inference(lemma,lemma(discharge,[]))).
% 291.42/183.99 tff(12378,plain,
% 291.42/183.99 (~node18(c_e_h_3, c_e, s10, s11)),
% 291.42/183.99 inference(unit_resolution,[status(thm)],[12377, 12371, 12363])).
% 291.42/183.99 tff(12379,assumption,(node15(c_e_h_3, c_e, s10, s11)), introduced(assumption)).
% 291.42/183.99 tff(12380,plain,
% 291.42/183.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s11)) | (~node15(c_e_h_3, c_e, s10, s11)) | m_c_h_element_v_out(c_e_h_3, c_e, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s11)) | (~node15(c_e_h_3, c_e, s10, s11)) | m_c_h_element_v_out(c_e_h_3, c_e, s10))),
% 291.42/183.99 inference(rewrite,[status(thm)],[])).
% 291.42/183.99 tff(12381,plain,
% 291.42/183.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s11)) | (~node15(c_e_h_3, c_e, s10, s11)) | m_c_h_element_v_out(c_e_h_3, c_e, s10))),
% 291.42/183.99 inference(quant_inst,[status(thm)],[])).
% 291.42/183.99 tff(12382,plain,
% 291.42/183.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s11)) | (~node15(c_e_h_3, c_e, s10, s11)) | m_c_h_element_v_out(c_e_h_3, c_e, s10)),
% 291.42/183.99 inference(modus_ponens,[status(thm)],[12381, 12380])).
% 291.42/183.99 tff(12383,plain,
% 291.42/183.99 ($false),
% 291.42/183.99 inference(unit_resolution,[status(thm)],[12382, 147, 12371, 12363, 12379])).
% 291.42/183.99 tff(12384,plain,((~node15(c_e_h_3, c_e, s10, s11)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s11)) | m_c_h_element_v_out(c_e_h_3, c_e, s10)), inference(lemma,lemma(discharge,[]))).
% 291.42/183.99 tff(12385,plain,
% 291.42/183.99 (~node15(c_e_h_3, c_e, s10, s11)),
% 291.42/183.99 inference(unit_resolution,[status(thm)],[12384, 12371, 12363])).
% 291.42/183.99 tff(12386,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_e, s10)), introduced(assumption)).
% 291.42/183.99 tff(12387,assumption,(node17(c_e_h_3, c_e, s10)), introduced(assumption)).
% 291.42/183.99 tff(12388,plain,
% 291.42/183.99 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_e, s10)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s10)) | m_c_h_element_v_in2(c_e_h_3, c_e, s10))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_e, s10)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s10)) | m_c_h_element_v_in2(c_e_h_3, c_e, s10))),
% 291.42/183.99 inference(rewrite,[status(thm)],[])).
% 291.42/183.99 tff(12389,plain,
% 291.42/183.99 (((~m_c_h_element_v_in1(c_e_h_3, c_e, s10)) | m_c_h_element_v_in2(c_e_h_3, c_e, s10) | (~node17(c_e_h_3, c_e, s10))) <=> ((~node17(c_e_h_3, c_e, s10)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s10)) | m_c_h_element_v_in2(c_e_h_3, c_e, s10))),
% 291.42/183.99 inference(rewrite,[status(thm)],[])).
% 291.42/183.99 tff(12390,plain,
% 291.42/183.99 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s10)) | m_c_h_element_v_in2(c_e_h_3, c_e, s10) | (~node17(c_e_h_3, c_e, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_e, s10)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s10)) | m_c_h_element_v_in2(c_e_h_3, c_e, s10)))),
% 291.42/183.99 inference(monotonicity,[status(thm)],[12389])).
% 291.42/183.99 tff(12391,plain,
% 291.42/183.99 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s10)) | m_c_h_element_v_in2(c_e_h_3, c_e, s10) | (~node17(c_e_h_3, c_e, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_e, s10)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s10)) | m_c_h_element_v_in2(c_e_h_3, c_e, s10))),
% 291.42/183.99 inference(transitivity,[status(thm)],[12390, 12388])).
% 291.42/183.99 tff(12392,plain,
% 291.42/183.99 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s10)) | m_c_h_element_v_in2(c_e_h_3, c_e, s10) | (~node17(c_e_h_3, c_e, s10)))),
% 291.42/184.00 inference(quant_inst,[status(thm)],[])).
% 291.42/184.00 tff(12393,plain,
% 291.42/184.00 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_e, s10)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s10)) | m_c_h_element_v_in2(c_e_h_3, c_e, s10)),
% 291.42/184.00 inference(modus_ponens,[status(thm)],[12392, 12391])).
% 291.42/184.00 tff(12394,plain,
% 291.42/184.00 ((~m_c_h_element_v_in1(c_e_h_3, c_e, s10)) | m_c_h_element_v_in2(c_e_h_3, c_e, s10)),
% 291.42/184.00 inference(unit_resolution,[status(thm)],[12393, 919, 12387])).
% 291.42/184.00 tff(12395,plain,
% 291.42/184.00 (~m_c_h_element_v_in1(c_e_h_3, c_e, s10)),
% 291.42/184.00 inference(unit_resolution,[status(thm)],[12394, 12386])).
% 291.42/184.00 tff(12396,assumption,(~node15(c_e_h_3, c_e, s10, s11)), introduced(assumption)).
% 291.42/184.00 tff(12397,plain,
% 291.42/184.00 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_e, s10)) | m_c_h_element_v_in1(c_e_h_3, c_e, s10) | m_c_h_element_v_in2(c_e_h_3, c_e, s10))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s10)) | m_c_h_element_v_in1(c_e_h_3, c_e, s10) | m_c_h_element_v_in2(c_e_h_3, c_e, s10))),
% 291.42/184.00 inference(rewrite,[status(thm)],[])).
% 291.42/184.00 tff(12398,plain,
% 291.42/184.00 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_e, s10)) | m_c_h_element_v_in1(c_e_h_3, c_e, s10) | m_c_h_element_v_in2(c_e_h_3, c_e, s10))),
% 291.42/184.00 inference(quant_inst,[status(thm)],[])).
% 291.42/184.00 tff(12399,plain,
% 291.42/184.00 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s10)) | m_c_h_element_v_in1(c_e_h_3, c_e, s10) | m_c_h_element_v_in2(c_e_h_3, c_e, s10)),
% 291.42/184.00 inference(modus_ponens,[status(thm)],[12398, 12397])).
% 291.42/184.00 tff(12400,plain,
% 291.42/184.00 (~node16(c_e_h_3, c_e, s10)),
% 291.42/184.00 inference(unit_resolution,[status(thm)],[12399, 178, 12395, 12386])).
% 291.42/184.00 tff(12401,plain,
% 291.42/184.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s10, s11)) | node19(c_e_h_3, c_e, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s10, s11)) | node19(c_e_h_3, c_e, s10, s11))),
% 291.42/184.00 inference(rewrite,[status(thm)],[])).
% 291.42/184.00 tff(12402,plain,
% 291.42/184.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s10, s11)) | node19(c_e_h_3, c_e, s10, s11))),
% 291.42/184.00 inference(quant_inst,[status(thm)],[])).
% 291.42/184.00 tff(12403,plain,
% 291.42/184.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s10, s11)) | node19(c_e_h_3, c_e, s10, s11)),
% 291.42/184.00 inference(modus_ponens,[status(thm)],[12402, 12401])).
% 291.42/184.00 tff(12404,plain,
% 291.42/184.00 (node19(c_e_h_3, c_e, s10, s11)),
% 291.42/184.00 inference(unit_resolution,[status(thm)],[12403, 190, 7748])).
% 291.42/184.00 tff(12405,plain,
% 291.42/184.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_3, c_e, s10, s11) | (~node19(c_e_h_3, c_e, s10, s11)) | node14(c_e_h_3, c_e, s10, s11) | node16(c_e_h_3, c_e, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_3, c_e, s10, s11) | (~node19(c_e_h_3, c_e, s10, s11)) | node14(c_e_h_3, c_e, s10, s11) | node16(c_e_h_3, c_e, s10))),
% 291.42/184.00 inference(rewrite,[status(thm)],[])).
% 291.42/184.00 tff(12406,plain,
% 291.42/184.00 ((node16(c_e_h_3, c_e, s10) | node14(c_e_h_3, c_e, s10, s11) | node15(c_e_h_3, c_e, s10, s11) | (~node19(c_e_h_3, c_e, s10, s11))) <=> (node15(c_e_h_3, c_e, s10, s11) | (~node19(c_e_h_3, c_e, s10, s11)) | node14(c_e_h_3, c_e, s10, s11) | node16(c_e_h_3, c_e, s10))),
% 291.42/184.00 inference(rewrite,[status(thm)],[])).
% 291.42/184.00 tff(12407,plain,
% 291.42/184.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s10) | node14(c_e_h_3, c_e, s10, s11) | node15(c_e_h_3, c_e, s10, s11) | (~node19(c_e_h_3, c_e, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_3, c_e, s10, s11) | (~node19(c_e_h_3, c_e, s10, s11)) | node14(c_e_h_3, c_e, s10, s11) | node16(c_e_h_3, c_e, s10)))),
% 291.42/184.00 inference(monotonicity,[status(thm)],[12406])).
% 291.42/184.00 tff(12408,plain,
% 291.42/184.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s10) | node14(c_e_h_3, c_e, s10, s11) | node15(c_e_h_3, c_e, s10, s11) | (~node19(c_e_h_3, c_e, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_3, c_e, s10, s11) | (~node19(c_e_h_3, c_e, s10, s11)) | node14(c_e_h_3, c_e, s10, s11) | node16(c_e_h_3, c_e, s10))),
% 291.42/184.00 inference(transitivity,[status(thm)],[12407, 12405])).
% 291.42/184.00 tff(12409,plain,
% 291.42/184.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s10) | node14(c_e_h_3, c_e, s10, s11) | node15(c_e_h_3, c_e, s10, s11) | (~node19(c_e_h_3, c_e, s10, s11)))),
% 291.42/184.00 inference(quant_inst,[status(thm)],[])).
% 291.42/184.00 tff(12410,plain,
% 291.42/184.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_3, c_e, s10, s11) | (~node19(c_e_h_3, c_e, s10, s11)) | node14(c_e_h_3, c_e, s10, s11) | node16(c_e_h_3, c_e, s10)),
% 291.42/184.00 inference(modus_ponens,[status(thm)],[12409, 12408])).
% 291.42/184.00 tff(12411,plain,
% 291.42/184.00 (node15(c_e_h_3, c_e, s10, s11) | node14(c_e_h_3, c_e, s10, s11) | node16(c_e_h_3, c_e, s10)),
% 291.42/184.00 inference(unit_resolution,[status(thm)],[12410, 204, 12404])).
% 291.42/184.00 tff(12412,plain,
% 291.42/184.00 (node14(c_e_h_3, c_e, s10, s11)),
% 291.42/184.00 inference(unit_resolution,[status(thm)],[12411, 12400, 12396])).
% 291.42/184.00 tff(12413,plain,
% 291.42/184.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s11)) | m_c_h_element_v_in1(c_e_h_3, c_e, s10) | (~node14(c_e_h_3, c_e, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s11)) | m_c_h_element_v_in1(c_e_h_3, c_e, s10) | (~node14(c_e_h_3, c_e, s10, s11)))),
% 291.42/184.00 inference(rewrite,[status(thm)],[])).
% 291.42/184.00 tff(12414,plain,
% 291.42/184.00 (((~node14(c_e_h_3, c_e, s10, s11)) | m_c_h_element_v_in1(c_e_h_3, c_e, s10) | (~m_c_h_element_v_out(c_e_h_3, c_e, s11))) <=> ((~m_c_h_element_v_out(c_e_h_3, c_e, s11)) | m_c_h_element_v_in1(c_e_h_3, c_e, s10) | (~node14(c_e_h_3, c_e, s10, s11)))),
% 291.42/184.00 inference(rewrite,[status(thm)],[])).
% 291.42/184.00 tff(12415,plain,
% 291.42/184.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s10, s11)) | m_c_h_element_v_in1(c_e_h_3, c_e, s10) | (~m_c_h_element_v_out(c_e_h_3, c_e, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s11)) | m_c_h_element_v_in1(c_e_h_3, c_e, s10) | (~node14(c_e_h_3, c_e, s10, s11))))),
% 291.42/184.00 inference(monotonicity,[status(thm)],[12414])).
% 291.42/184.00 tff(12416,plain,
% 291.42/184.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s10, s11)) | m_c_h_element_v_in1(c_e_h_3, c_e, s10) | (~m_c_h_element_v_out(c_e_h_3, c_e, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s11)) | m_c_h_element_v_in1(c_e_h_3, c_e, s10) | (~node14(c_e_h_3, c_e, s10, s11)))),
% 291.42/184.00 inference(transitivity,[status(thm)],[12415, 12413])).
% 291.42/184.00 tff(12417,plain,
% 291.42/184.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s10, s11)) | m_c_h_element_v_in1(c_e_h_3, c_e, s10) | (~m_c_h_element_v_out(c_e_h_3, c_e, s11)))),
% 291.42/184.01 inference(quant_inst,[status(thm)],[])).
% 291.42/184.01 tff(12418,plain,
% 291.42/184.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s11)) | m_c_h_element_v_in1(c_e_h_3, c_e, s10) | (~node14(c_e_h_3, c_e, s10, s11))),
% 291.42/184.01 inference(modus_ponens,[status(thm)],[12417, 12416])).
% 291.42/184.01 tff(12419,plain,
% 291.42/184.01 ($false),
% 291.42/184.01 inference(unit_resolution,[status(thm)],[12418, 223, 12371, 12412, 12395])).
% 291.42/184.01 tff(12420,plain,(m_c_h_element_v_in2(c_e_h_3, c_e, s10) | (~m_c_h_element_v_out(c_e_h_3, c_e, s11)) | node15(c_e_h_3, c_e, s10, s11) | (~node17(c_e_h_3, c_e, s10))), inference(lemma,lemma(discharge,[]))).
% 291.42/184.01 tff(12421,plain,
% 291.42/184.01 (~node17(c_e_h_3, c_e, s10)),
% 291.42/184.01 inference(unit_resolution,[status(thm)],[12420, 12371, 12386, 12385])).
% 291.42/184.01 tff(12422,plain,
% 291.42/184.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_3, c_e, s10, s11) | (~node19(c_e_h_3, c_e, s10, s11)) | node17(c_e_h_3, c_e, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_3, c_e, s10, s11) | (~node19(c_e_h_3, c_e, s10, s11)) | node17(c_e_h_3, c_e, s10))),
% 291.42/184.01 inference(rewrite,[status(thm)],[])).
% 291.42/184.01 tff(12423,plain,
% 291.42/184.01 ((node17(c_e_h_3, c_e, s10) | node18(c_e_h_3, c_e, s10, s11) | (~node19(c_e_h_3, c_e, s10, s11))) <=> (node18(c_e_h_3, c_e, s10, s11) | (~node19(c_e_h_3, c_e, s10, s11)) | node17(c_e_h_3, c_e, s10))),
% 291.42/184.01 inference(rewrite,[status(thm)],[])).
% 291.42/184.01 tff(12424,plain,
% 291.42/184.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s10) | node18(c_e_h_3, c_e, s10, s11) | (~node19(c_e_h_3, c_e, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_3, c_e, s10, s11) | (~node19(c_e_h_3, c_e, s10, s11)) | node17(c_e_h_3, c_e, s10)))),
% 291.52/184.01 inference(monotonicity,[status(thm)],[12423])).
% 291.52/184.01 tff(12425,plain,
% 291.52/184.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s10) | node18(c_e_h_3, c_e, s10, s11) | (~node19(c_e_h_3, c_e, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_3, c_e, s10, s11) | (~node19(c_e_h_3, c_e, s10, s11)) | node17(c_e_h_3, c_e, s10))),
% 291.52/184.01 inference(transitivity,[status(thm)],[12424, 12422])).
% 291.52/184.01 tff(12426,plain,
% 291.52/184.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s10) | node18(c_e_h_3, c_e, s10, s11) | (~node19(c_e_h_3, c_e, s10, s11)))),
% 291.52/184.01 inference(quant_inst,[status(thm)],[])).
% 291.52/184.01 tff(12427,plain,
% 291.52/184.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_3, c_e, s10, s11) | (~node19(c_e_h_3, c_e, s10, s11)) | node17(c_e_h_3, c_e, s10)),
% 291.52/184.01 inference(modus_ponens,[status(thm)],[12426, 12425])).
% 291.52/184.01 tff(12428,plain,
% 291.52/184.01 (node18(c_e_h_3, c_e, s10, s11) | node17(c_e_h_3, c_e, s10)),
% 291.52/184.01 inference(unit_resolution,[status(thm)],[12427, 776, 12404])).
% 291.52/184.01 tff(12429,plain,
% 291.52/184.01 ($false),
% 291.52/184.01 inference(unit_resolution,[status(thm)],[12428, 12421, 12378])).
% 291.52/184.01 tff(12430,plain,((~m_c_h_element_v_out(c_e_h_3, c_e, s11)) | m_c_h_element_v_in2(c_e_h_3, c_e, s10) | m_c_h_element_v_out(c_e_h_3, c_e, s10)), inference(lemma,lemma(discharge,[]))).
% 291.52/184.01 tff(12431,plain,
% 291.52/184.01 (~m_c_h_element_v_out(c_e_h_3, c_e, s11)),
% 291.52/184.01 inference(unit_resolution,[status(thm)],[12430, 12370, 12363])).
% 291.52/184.01 tff(12432,plain,
% 291.52/184.01 (~m_and_h_gate_v_out(c_e_h_3, c_i, s11)),
% 291.52/184.01 inference(unit_resolution,[status(thm)],[11435, 11422, 11410])).
% 291.52/184.01 tff(12433,assumption,(m_c_h_element_v_in2(c_e_h_3, c_e, s11)), introduced(assumption)).
% 291.52/184.01 tff(12434,plain,
% 291.52/184.01 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s11)) | m_and_h_gate_v_out(c_e_h_3, c_i, s11))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s11)) | m_and_h_gate_v_out(c_e_h_3, c_i, s11))),
% 291.52/184.01 inference(rewrite,[status(thm)],[])).
% 291.52/184.01 tff(12435,plain,
% 291.52/184.01 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s11)) | m_and_h_gate_v_out(c_e_h_3, c_i, s11))),
% 291.52/184.01 inference(quant_inst,[status(thm)],[])).
% 291.52/184.01 tff(12436,plain,
% 291.52/184.01 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s11)) | m_and_h_gate_v_out(c_e_h_3, c_i, s11)),
% 291.52/184.01 inference(modus_ponens,[status(thm)],[12435, 12434])).
% 291.52/184.01 tff(12437,plain,
% 291.52/184.01 ($false),
% 291.52/184.01 inference(unit_resolution,[status(thm)],[12436, 164, 12433, 11447])).
% 291.52/184.01 tff(12438,plain,((~m_c_h_element_v_in2(c_e_h_3, c_e, s11)) | m_and_h_gate_v_out(c_e_h_3, c_i, s11)), inference(lemma,lemma(discharge,[]))).
% 291.52/184.01 tff(12439,plain,
% 291.52/184.01 (~m_c_h_element_v_in2(c_e_h_3, c_e, s11)),
% 291.52/184.01 inference(unit_resolution,[status(thm)],[12438, 12432])).
% 291.52/184.01 tff(12440,assumption,(~m_c_h_element_v_out(c_e_h_3, c_e, s11)), introduced(assumption)).
% 291.52/184.01 tff(12441,assumption,(node18(c_e_h_3, c_e, s11, s12)), introduced(assumption)).
% 291.52/184.01 tff(12442,plain,
% 291.52/184.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_e, s11) | (~m_c_h_element_v_out(c_e_h_3, c_e, s12)) | (~node18(c_e_h_3, c_e, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s11) | (~m_c_h_element_v_out(c_e_h_3, c_e, s12)) | (~node18(c_e_h_3, c_e, s11, s12)))),
% 291.52/184.01 inference(rewrite,[status(thm)],[])).
% 291.52/184.01 tff(12443,plain,
% 291.52/184.01 (((~m_c_h_element_v_out(c_e_h_3, c_e, s12)) | m_c_h_element_v_out(c_e_h_3, c_e, s11) | (~node18(c_e_h_3, c_e, s11, s12))) <=> (m_c_h_element_v_out(c_e_h_3, c_e, s11) | (~m_c_h_element_v_out(c_e_h_3, c_e, s12)) | (~node18(c_e_h_3, c_e, s11, s12)))),
% 291.52/184.01 inference(rewrite,[status(thm)],[])).
% 291.52/184.01 tff(12444,plain,
% 291.52/184.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s12)) | m_c_h_element_v_out(c_e_h_3, c_e, s11) | (~node18(c_e_h_3, c_e, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_e, s11) | (~m_c_h_element_v_out(c_e_h_3, c_e, s12)) | (~node18(c_e_h_3, c_e, s11, s12))))),
% 291.52/184.01 inference(monotonicity,[status(thm)],[12443])).
% 291.52/184.01 tff(12445,plain,
% 291.52/184.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s12)) | m_c_h_element_v_out(c_e_h_3, c_e, s11) | (~node18(c_e_h_3, c_e, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s11) | (~m_c_h_element_v_out(c_e_h_3, c_e, s12)) | (~node18(c_e_h_3, c_e, s11, s12)))),
% 291.52/184.01 inference(transitivity,[status(thm)],[12444, 12442])).
% 291.52/184.01 tff(12446,plain,
% 291.52/184.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s12)) | m_c_h_element_v_out(c_e_h_3, c_e, s11) | (~node18(c_e_h_3, c_e, s11, s12)))),
% 291.52/184.01 inference(quant_inst,[status(thm)],[])).
% 291.52/184.01 tff(12447,plain,
% 291.52/184.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s11) | (~m_c_h_element_v_out(c_e_h_3, c_e, s12)) | (~node18(c_e_h_3, c_e, s11, s12))),
% 291.52/184.01 inference(modus_ponens,[status(thm)],[12446, 12445])).
% 291.52/184.01 tff(12448,plain,
% 291.52/184.01 ($false),
% 291.52/184.01 inference(unit_resolution,[status(thm)],[12447, 753, 12440, 12362, 12441])).
% 291.52/184.01 tff(12449,plain,((~node18(c_e_h_3, c_e, s11, s12)) | m_c_h_element_v_out(c_e_h_3, c_e, s11) | (~m_c_h_element_v_out(c_e_h_3, c_e, s12))), inference(lemma,lemma(discharge,[]))).
% 291.52/184.01 tff(12450,plain,
% 291.52/184.01 (~node18(c_e_h_3, c_e, s11, s12)),
% 291.52/184.01 inference(unit_resolution,[status(thm)],[12449, 12440, 12362])).
% 291.52/184.01 tff(12451,plain,
% 291.52/184.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s11, s12)) | node19(c_e_h_3, c_e, s11, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s11, s12)) | node19(c_e_h_3, c_e, s11, s12))),
% 291.52/184.01 inference(rewrite,[status(thm)],[])).
% 291.52/184.01 tff(12452,plain,
% 291.52/184.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s11, s12)) | node19(c_e_h_3, c_e, s11, s12))),
% 291.52/184.01 inference(quant_inst,[status(thm)],[])).
% 291.52/184.01 tff(12453,plain,
% 291.52/184.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s11, s12)) | node19(c_e_h_3, c_e, s11, s12)),
% 291.52/184.01 inference(modus_ponens,[status(thm)],[12452, 12451])).
% 291.52/184.01 tff(12454,plain,
% 291.52/184.01 (node19(c_e_h_3, c_e, s11, s12)),
% 291.52/184.01 inference(unit_resolution,[status(thm)],[12453, 190, 11461])).
% 291.52/184.01 tff(12455,plain,
% 291.52/184.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_3, c_e, s11, s12) | node17(c_e_h_3, c_e, s11) | (~node19(c_e_h_3, c_e, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_3, c_e, s11, s12) | node17(c_e_h_3, c_e, s11) | (~node19(c_e_h_3, c_e, s11, s12)))),
% 291.52/184.01 inference(rewrite,[status(thm)],[])).
% 291.52/184.01 tff(12456,plain,
% 291.52/184.01 ((node17(c_e_h_3, c_e, s11) | node18(c_e_h_3, c_e, s11, s12) | (~node19(c_e_h_3, c_e, s11, s12))) <=> (node18(c_e_h_3, c_e, s11, s12) | node17(c_e_h_3, c_e, s11) | (~node19(c_e_h_3, c_e, s11, s12)))),
% 291.52/184.01 inference(rewrite,[status(thm)],[])).
% 291.52/184.01 tff(12457,plain,
% 291.52/184.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s11) | node18(c_e_h_3, c_e, s11, s12) | (~node19(c_e_h_3, c_e, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_3, c_e, s11, s12) | node17(c_e_h_3, c_e, s11) | (~node19(c_e_h_3, c_e, s11, s12))))),
% 291.52/184.01 inference(monotonicity,[status(thm)],[12456])).
% 291.52/184.01 tff(12458,plain,
% 291.52/184.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s11) | node18(c_e_h_3, c_e, s11, s12) | (~node19(c_e_h_3, c_e, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_3, c_e, s11, s12) | node17(c_e_h_3, c_e, s11) | (~node19(c_e_h_3, c_e, s11, s12)))),
% 291.52/184.01 inference(transitivity,[status(thm)],[12457, 12455])).
% 291.52/184.01 tff(12459,plain,
% 291.52/184.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s11) | node18(c_e_h_3, c_e, s11, s12) | (~node19(c_e_h_3, c_e, s11, s12)))),
% 291.52/184.01 inference(quant_inst,[status(thm)],[])).
% 291.52/184.01 tff(12460,plain,
% 291.52/184.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_3, c_e, s11, s12) | node17(c_e_h_3, c_e, s11) | (~node19(c_e_h_3, c_e, s11, s12))),
% 291.52/184.01 inference(modus_ponens,[status(thm)],[12459, 12458])).
% 291.52/184.01 tff(12461,plain,
% 291.52/184.01 (node18(c_e_h_3, c_e, s11, s12) | node17(c_e_h_3, c_e, s11)),
% 291.52/184.01 inference(unit_resolution,[status(thm)],[12460, 776, 12454])).
% 291.52/184.01 tff(12462,plain,
% 291.52/184.01 (node17(c_e_h_3, c_e, s11)),
% 291.52/184.01 inference(unit_resolution,[status(thm)],[12461, 12450])).
% 291.52/184.01 tff(12463,assumption,(node15(c_e_h_3, c_e, s11, s12)), introduced(assumption)).
% 291.52/184.01 tff(12464,plain,
% 291.52/184.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s12)) | (~node15(c_e_h_3, c_e, s11, s12)) | m_c_h_element_v_out(c_e_h_3, c_e, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s12)) | (~node15(c_e_h_3, c_e, s11, s12)) | m_c_h_element_v_out(c_e_h_3, c_e, s11))),
% 291.52/184.02 inference(rewrite,[status(thm)],[])).
% 291.52/184.02 tff(12465,plain,
% 291.52/184.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s12)) | (~node15(c_e_h_3, c_e, s11, s12)) | m_c_h_element_v_out(c_e_h_3, c_e, s11))),
% 291.52/184.02 inference(quant_inst,[status(thm)],[])).
% 291.52/184.02 tff(12466,plain,
% 291.52/184.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s12)) | (~node15(c_e_h_3, c_e, s11, s12)) | m_c_h_element_v_out(c_e_h_3, c_e, s11)),
% 291.52/184.02 inference(modus_ponens,[status(thm)],[12465, 12464])).
% 291.52/184.02 tff(12467,plain,
% 291.52/184.02 ($false),
% 291.52/184.02 inference(unit_resolution,[status(thm)],[12466, 147, 12440, 12362, 12463])).
% 291.52/184.02 tff(12468,plain,((~node15(c_e_h_3, c_e, s11, s12)) | m_c_h_element_v_out(c_e_h_3, c_e, s11) | (~m_c_h_element_v_out(c_e_h_3, c_e, s12))), inference(lemma,lemma(discharge,[]))).
% 291.52/184.02 tff(12469,plain,
% 291.52/184.02 (~node15(c_e_h_3, c_e, s11, s12)),
% 291.52/184.02 inference(unit_resolution,[status(thm)],[12468, 12440, 12362])).
% 291.52/184.02 tff(12470,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_e, s11)), introduced(assumption)).
% 291.52/184.02 tff(12471,assumption,(~node15(c_e_h_3, c_e, s11, s12)), introduced(assumption)).
% 291.52/184.02 tff(12472,assumption,(node17(c_e_h_3, c_e, s11)), introduced(assumption)).
% 291.52/184.02 tff(12473,plain,
% 291.52/184.02 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s11) | (~node17(c_e_h_3, c_e, s11)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_3, c_e, s11) | (~node17(c_e_h_3, c_e, s11)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s11)))),
% 291.52/184.02 inference(rewrite,[status(thm)],[])).
% 291.52/184.02 tff(12474,plain,
% 291.52/184.02 ((m_c_h_element_v_in1(c_e_h_3, c_e, s11) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s11)) | (~node17(c_e_h_3, c_e, s11))) <=> (m_c_h_element_v_in1(c_e_h_3, c_e, s11) | (~node17(c_e_h_3, c_e, s11)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s11)))),
% 291.52/184.02 inference(rewrite,[status(thm)],[])).
% 291.52/184.02 tff(12475,plain,
% 291.52/184.02 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s11) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s11)) | (~node17(c_e_h_3, c_e, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s11) | (~node17(c_e_h_3, c_e, s11)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s11))))),
% 291.52/184.02 inference(monotonicity,[status(thm)],[12474])).
% 291.52/184.02 tff(12476,plain,
% 291.52/184.02 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s11) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s11)) | (~node17(c_e_h_3, c_e, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_3, c_e, s11) | (~node17(c_e_h_3, c_e, s11)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s11)))),
% 291.52/184.02 inference(transitivity,[status(thm)],[12475, 12473])).
% 291.52/184.02 tff(12477,plain,
% 291.52/184.02 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s11) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s11)) | (~node17(c_e_h_3, c_e, s11)))),
% 291.52/184.02 inference(quant_inst,[status(thm)],[])).
% 291.52/184.02 tff(12478,plain,
% 291.52/184.02 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_3, c_e, s11) | (~node17(c_e_h_3, c_e, s11)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s11))),
% 291.52/184.02 inference(modus_ponens,[status(thm)],[12477, 12476])).
% 291.52/184.02 tff(12479,plain,
% 291.52/184.02 (m_c_h_element_v_in1(c_e_h_3, c_e, s11) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s11))),
% 291.52/184.02 inference(unit_resolution,[status(thm)],[12478, 859, 12472])).
% 291.52/184.02 tff(12480,plain,
% 291.52/184.02 (~m_c_h_element_v_in2(c_e_h_3, c_e, s11)),
% 291.52/184.02 inference(unit_resolution,[status(thm)],[12479, 12470])).
% 291.52/184.02 tff(12481,plain,
% 291.52/184.02 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_e, s11)) | m_c_h_element_v_in1(c_e_h_3, c_e, s11) | m_c_h_element_v_in2(c_e_h_3, c_e, s11))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s11)) | m_c_h_element_v_in1(c_e_h_3, c_e, s11) | m_c_h_element_v_in2(c_e_h_3, c_e, s11))),
% 291.52/184.02 inference(rewrite,[status(thm)],[])).
% 291.52/184.02 tff(12482,plain,
% 291.52/184.02 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_e, s11)) | m_c_h_element_v_in1(c_e_h_3, c_e, s11) | m_c_h_element_v_in2(c_e_h_3, c_e, s11))),
% 291.52/184.02 inference(quant_inst,[status(thm)],[])).
% 291.52/184.02 tff(12483,plain,
% 291.52/184.02 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s11)) | m_c_h_element_v_in1(c_e_h_3, c_e, s11) | m_c_h_element_v_in2(c_e_h_3, c_e, s11)),
% 291.52/184.02 inference(modus_ponens,[status(thm)],[12482, 12481])).
% 291.52/184.02 tff(12484,plain,
% 291.52/184.02 (~node16(c_e_h_3, c_e, s11)),
% 291.52/184.02 inference(unit_resolution,[status(thm)],[12483, 178, 12470, 12480])).
% 291.52/184.02 tff(12485,plain,
% 291.52/184.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_3, c_e, s11, s12) | (~node19(c_e_h_3, c_e, s11, s12)) | node14(c_e_h_3, c_e, s11, s12) | node16(c_e_h_3, c_e, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_3, c_e, s11, s12) | (~node19(c_e_h_3, c_e, s11, s12)) | node14(c_e_h_3, c_e, s11, s12) | node16(c_e_h_3, c_e, s11))),
% 291.52/184.02 inference(rewrite,[status(thm)],[])).
% 291.52/184.02 tff(12486,plain,
% 291.52/184.02 ((node16(c_e_h_3, c_e, s11) | node14(c_e_h_3, c_e, s11, s12) | node15(c_e_h_3, c_e, s11, s12) | (~node19(c_e_h_3, c_e, s11, s12))) <=> (node15(c_e_h_3, c_e, s11, s12) | (~node19(c_e_h_3, c_e, s11, s12)) | node14(c_e_h_3, c_e, s11, s12) | node16(c_e_h_3, c_e, s11))),
% 291.52/184.02 inference(rewrite,[status(thm)],[])).
% 291.52/184.02 tff(12487,plain,
% 291.52/184.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s11) | node14(c_e_h_3, c_e, s11, s12) | node15(c_e_h_3, c_e, s11, s12) | (~node19(c_e_h_3, c_e, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_3, c_e, s11, s12) | (~node19(c_e_h_3, c_e, s11, s12)) | node14(c_e_h_3, c_e, s11, s12) | node16(c_e_h_3, c_e, s11)))),
% 291.52/184.02 inference(monotonicity,[status(thm)],[12486])).
% 291.52/184.02 tff(12488,plain,
% 291.52/184.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s11) | node14(c_e_h_3, c_e, s11, s12) | node15(c_e_h_3, c_e, s11, s12) | (~node19(c_e_h_3, c_e, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_3, c_e, s11, s12) | (~node19(c_e_h_3, c_e, s11, s12)) | node14(c_e_h_3, c_e, s11, s12) | node16(c_e_h_3, c_e, s11))),
% 291.52/184.02 inference(transitivity,[status(thm)],[12487, 12485])).
% 291.52/184.02 tff(12489,plain,
% 291.52/184.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s11) | node14(c_e_h_3, c_e, s11, s12) | node15(c_e_h_3, c_e, s11, s12) | (~node19(c_e_h_3, c_e, s11, s12)))),
% 291.52/184.02 inference(quant_inst,[status(thm)],[])).
% 291.52/184.02 tff(12490,plain,
% 291.52/184.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_3, c_e, s11, s12) | (~node19(c_e_h_3, c_e, s11, s12)) | node14(c_e_h_3, c_e, s11, s12) | node16(c_e_h_3, c_e, s11)),
% 291.52/184.02 inference(modus_ponens,[status(thm)],[12489, 12488])).
% 291.52/184.02 tff(12491,plain,
% 291.52/184.02 (node15(c_e_h_3, c_e, s11, s12) | node14(c_e_h_3, c_e, s11, s12) | node16(c_e_h_3, c_e, s11)),
% 291.52/184.02 inference(unit_resolution,[status(thm)],[12490, 204, 12454])).
% 291.52/184.02 tff(12492,plain,
% 291.52/184.02 (node14(c_e_h_3, c_e, s11, s12)),
% 291.52/184.02 inference(unit_resolution,[status(thm)],[12491, 12484, 12471])).
% 291.52/184.02 tff(12493,plain,
% 291.52/184.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s12)) | m_c_h_element_v_in1(c_e_h_3, c_e, s11) | (~node14(c_e_h_3, c_e, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s12)) | m_c_h_element_v_in1(c_e_h_3, c_e, s11) | (~node14(c_e_h_3, c_e, s11, s12)))),
% 291.52/184.03 inference(rewrite,[status(thm)],[])).
% 291.52/184.03 tff(12494,plain,
% 291.52/184.03 (((~node14(c_e_h_3, c_e, s11, s12)) | m_c_h_element_v_in1(c_e_h_3, c_e, s11) | (~m_c_h_element_v_out(c_e_h_3, c_e, s12))) <=> ((~m_c_h_element_v_out(c_e_h_3, c_e, s12)) | m_c_h_element_v_in1(c_e_h_3, c_e, s11) | (~node14(c_e_h_3, c_e, s11, s12)))),
% 291.52/184.03 inference(rewrite,[status(thm)],[])).
% 291.52/184.03 tff(12495,plain,
% 291.52/184.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s11, s12)) | m_c_h_element_v_in1(c_e_h_3, c_e, s11) | (~m_c_h_element_v_out(c_e_h_3, c_e, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s12)) | m_c_h_element_v_in1(c_e_h_3, c_e, s11) | (~node14(c_e_h_3, c_e, s11, s12))))),
% 291.52/184.03 inference(monotonicity,[status(thm)],[12494])).
% 291.52/184.03 tff(12496,plain,
% 291.52/184.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s11, s12)) | m_c_h_element_v_in1(c_e_h_3, c_e, s11) | (~m_c_h_element_v_out(c_e_h_3, c_e, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s12)) | m_c_h_element_v_in1(c_e_h_3, c_e, s11) | (~node14(c_e_h_3, c_e, s11, s12)))),
% 291.52/184.03 inference(transitivity,[status(thm)],[12495, 12493])).
% 291.52/184.03 tff(12497,plain,
% 291.52/184.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s11, s12)) | m_c_h_element_v_in1(c_e_h_3, c_e, s11) | (~m_c_h_element_v_out(c_e_h_3, c_e, s12)))),
% 291.52/184.03 inference(quant_inst,[status(thm)],[])).
% 291.52/184.03 tff(12498,plain,
% 291.52/184.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s12)) | m_c_h_element_v_in1(c_e_h_3, c_e, s11) | (~node14(c_e_h_3, c_e, s11, s12))),
% 291.52/184.03 inference(modus_ponens,[status(thm)],[12497, 12496])).
% 291.52/184.03 tff(12499,plain,
% 291.52/184.03 ($false),
% 291.52/184.03 inference(unit_resolution,[status(thm)],[12498, 223, 12362, 12492, 12470])).
% 291.52/184.03 tff(12500,plain,(m_c_h_element_v_in1(c_e_h_3, c_e, s11) | (~m_c_h_element_v_out(c_e_h_3, c_e, s12)) | node15(c_e_h_3, c_e, s11, s12) | (~node17(c_e_h_3, c_e, s11))), inference(lemma,lemma(discharge,[]))).
% 291.52/184.03 tff(12501,plain,
% 291.52/184.03 (m_c_h_element_v_in1(c_e_h_3, c_e, s11)),
% 291.52/184.03 inference(unit_resolution,[status(thm)],[12500, 12469, 12362, 12462])).
% 291.52/184.03 tff(12502,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_e, s11)), introduced(assumption)).
% 291.52/184.03 tff(12503,plain,
% 291.52/184.03 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_3, c_e, s11) | (~node17(c_e_h_3, c_e, s11)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_e, s11) | (~node17(c_e_h_3, c_e, s11)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s11)))),
% 291.52/184.03 inference(rewrite,[status(thm)],[])).
% 291.52/184.03 tff(12504,plain,
% 291.52/184.03 (((~m_c_h_element_v_in1(c_e_h_3, c_e, s11)) | m_c_h_element_v_in2(c_e_h_3, c_e, s11) | (~node17(c_e_h_3, c_e, s11))) <=> (m_c_h_element_v_in2(c_e_h_3, c_e, s11) | (~node17(c_e_h_3, c_e, s11)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s11)))),
% 291.52/184.03 inference(rewrite,[status(thm)],[])).
% 291.52/184.03 tff(12505,plain,
% 291.52/184.03 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s11)) | m_c_h_element_v_in2(c_e_h_3, c_e, s11) | (~node17(c_e_h_3, c_e, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_3, c_e, s11) | (~node17(c_e_h_3, c_e, s11)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s11))))),
% 291.52/184.03 inference(monotonicity,[status(thm)],[12504])).
% 291.52/184.03 tff(12506,plain,
% 291.52/184.03 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s11)) | m_c_h_element_v_in2(c_e_h_3, c_e, s11) | (~node17(c_e_h_3, c_e, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_e, s11) | (~node17(c_e_h_3, c_e, s11)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s11)))),
% 291.52/184.03 inference(transitivity,[status(thm)],[12505, 12503])).
% 291.52/184.03 tff(12507,plain,
% 291.52/184.03 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s11)) | m_c_h_element_v_in2(c_e_h_3, c_e, s11) | (~node17(c_e_h_3, c_e, s11)))),
% 291.52/184.03 inference(quant_inst,[status(thm)],[])).
% 291.52/184.03 tff(12508,plain,
% 291.52/184.03 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_e, s11) | (~node17(c_e_h_3, c_e, s11)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s11))),
% 291.52/184.03 inference(modus_ponens,[status(thm)],[12507, 12506])).
% 291.52/184.03 tff(12509,plain,
% 291.52/184.03 ((~node17(c_e_h_3, c_e, s11)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s11))),
% 291.52/184.03 inference(unit_resolution,[status(thm)],[12508, 919, 12502])).
% 291.52/184.03 tff(12510,plain,
% 291.52/184.03 ($false),
% 291.52/184.03 inference(unit_resolution,[status(thm)],[12509, 12501, 12462])).
% 291.52/184.03 tff(12511,plain,(m_c_h_element_v_out(c_e_h_3, c_e, s11) | m_c_h_element_v_in2(c_e_h_3, c_e, s11) | (~m_c_h_element_v_out(c_e_h_3, c_e, s12))), inference(lemma,lemma(discharge,[]))).
% 291.52/184.03 tff(12512,plain,
% 291.52/184.03 ($false),
% 291.52/184.03 inference(unit_resolution,[status(thm)],[12511, 12439, 12431, 12362])).
% 291.52/184.03 tff(12513,plain,(m_and_h_gate_v_out(c_e_h_3, c_i, s10) | (~m_c_h_element_v_out(c_e_h_3, c_e, s12)) | m_c_h_element_v_out(c_e_h_3, c_e, s10) | node20(c_e_h_3, c_i, s10)), inference(lemma,lemma(discharge,[]))).
% 291.52/184.03 tff(12514,plain,
% 291.52/184.03 ((~m_c_h_element_v_out(c_e_h_3, c_e, s12)) | node20(c_e_h_3, c_i, s10)),
% 291.52/184.03 inference(unit_resolution,[status(thm)],[12513, 12361, 11409])).
% 291.52/184.03 tff(12515,plain,
% 291.52/184.03 (~m_c_h_element_v_out(c_e_h_3, c_e, s12)),
% 291.52/184.03 inference(unit_resolution,[status(thm)],[12514, 11228])).
% 291.52/184.03 tff(12516,plain,
% 291.52/184.03 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s12)) | m_c_h_element_v_out(c_e_h_3, c_e, s12))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s12)) | m_c_h_element_v_out(c_e_h_3, c_e, s12))),
% 291.52/184.03 inference(rewrite,[status(thm)],[])).
% 291.52/184.03 tff(12517,plain,
% 291.52/184.03 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s12)) | m_c_h_element_v_out(c_e_h_3, c_e, s12))),
% 291.52/184.03 inference(quant_inst,[status(thm)],[])).
% 291.52/184.03 tff(12518,plain,
% 291.52/184.03 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s12)) | m_c_h_element_v_out(c_e_h_3, c_e, s12)),
% 291.52/184.03 inference(modus_ponens,[status(thm)],[12517, 12516])).
% 291.52/184.03 tff(12519,plain,
% 291.52/184.03 (~m_and_h_gate_v_in1(c_e_h_3, c_r, s12)),
% 291.52/184.03 inference(unit_resolution,[status(thm)],[12518, 24, 12515])).
% 291.52/184.03 tff(12520,plain,
% 291.52/184.03 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s12)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s12))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s12)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s12))),
% 291.52/184.03 inference(rewrite,[status(thm)],[])).
% 291.52/184.03 tff(12521,plain,
% 291.52/184.03 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s12)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s12))),
% 291.52/184.03 inference(quant_inst,[status(thm)],[])).
% 291.52/184.03 tff(12522,plain,
% 291.52/184.03 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s12)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s12)),
% 291.52/184.03 inference(modus_ponens,[status(thm)],[12521, 12520])).
% 291.52/184.03 tff(12523,plain,
% 291.52/184.03 (~node20(c_e_h_3, c_r, s12)),
% 291.52/184.03 inference(unit_resolution,[status(thm)],[12522, 38, 12519])).
% 291.52/184.03 tff(12524,assumption,(~node20(c_e_h_3, c_r, s12)), introduced(assumption)).
% 291.52/184.03 tff(12525,assumption,(m_and_h_gate_v_out(c_e_h_3, c_r, s13)), introduced(assumption)).
% 291.52/184.03 tff(12526,assumption,(node21(c_e_h_3, c_r, s12, s13)), introduced(assumption)).
% 291.52/184.03 tff(12527,plain,
% 291.52/184.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s12) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s13)) | (~node21(c_e_h_3, c_r, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_r, s12) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s13)) | (~node21(c_e_h_3, c_r, s12, s13)))),
% 291.52/184.03 inference(rewrite,[status(thm)],[])).
% 291.52/184.03 tff(12528,plain,
% 291.52/184.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s12) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s13)) | (~node21(c_e_h_3, c_r, s12, s13)))),
% 291.52/184.03 inference(quant_inst,[status(thm)],[])).
% 291.52/184.03 tff(12529,plain,
% 291.52/184.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_r, s12) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s13)) | (~node21(c_e_h_3, c_r, s12, s13))),
% 291.52/184.03 inference(modus_ponens,[status(thm)],[12528, 12527])).
% 291.52/184.03 tff(12530,plain,
% 291.52/184.03 ($false),
% 291.52/184.03 inference(unit_resolution,[status(thm)],[12529, 52, 12525, 12526, 12524])).
% 291.52/184.03 tff(12531,plain,((~node21(c_e_h_3, c_r, s12, s13)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s13)) | node20(c_e_h_3, c_r, s12)), inference(lemma,lemma(discharge,[]))).
% 291.52/184.03 tff(12532,plain,
% 291.52/184.03 (~node21(c_e_h_3, c_r, s12, s13)),
% 291.52/184.03 inference(unit_resolution,[status(thm)],[12531, 12525, 12524])).
% 291.52/184.03 tff(12533,plain,
% 291.52/184.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s12, s13)) | node21(c_e_h_3, c_r, s12, s13) | node22(c_e_h_3, c_r, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s12, s13)) | node21(c_e_h_3, c_r, s12, s13) | node22(c_e_h_3, c_r, s12, s13))),
% 291.52/184.03 inference(rewrite,[status(thm)],[])).
% 291.52/184.03 tff(12534,plain,
% 291.52/184.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s12, s13)) | node21(c_e_h_3, c_r, s12, s13) | node22(c_e_h_3, c_r, s12, s13))),
% 291.52/184.04 inference(quant_inst,[status(thm)],[])).
% 291.52/184.04 tff(12535,plain,
% 291.52/184.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s12, s13)) | node21(c_e_h_3, c_r, s12, s13) | node22(c_e_h_3, c_r, s12, s13)),
% 291.52/184.04 inference(modus_ponens,[status(thm)],[12534, 12533])).
% 291.52/184.04 tff(12536,plain,
% 291.52/184.04 (node21(c_e_h_3, c_r, s12, s13) | node22(c_e_h_3, c_r, s12, s13)),
% 291.52/184.04 inference(unit_resolution,[status(thm)],[12535, 82, 11856])).
% 291.52/184.04 tff(12537,plain,
% 291.52/184.04 (node22(c_e_h_3, c_r, s12, s13)),
% 291.52/184.04 inference(unit_resolution,[status(thm)],[12536, 12532])).
% 291.52/184.04 tff(12538,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_r, s10)), introduced(assumption)).
% 291.52/184.04 tff(12539,plain,
% 291.52/184.04 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s10)) | m_c_h_element_v_out(c_e_h_3, c_e, s10))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s10)) | m_c_h_element_v_out(c_e_h_3, c_e, s10))),
% 291.52/184.04 inference(rewrite,[status(thm)],[])).
% 291.52/184.04 tff(12540,plain,
% 291.52/184.04 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s10)) | m_c_h_element_v_out(c_e_h_3, c_e, s10))),
% 291.52/184.04 inference(quant_inst,[status(thm)],[])).
% 291.52/184.04 tff(12541,plain,
% 291.52/184.04 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s10)) | m_c_h_element_v_out(c_e_h_3, c_e, s10)),
% 291.52/184.04 inference(modus_ponens,[status(thm)],[12540, 12539])).
% 291.52/184.04 tff(12542,plain,
% 291.52/184.04 ($false),
% 291.52/184.04 inference(unit_resolution,[status(thm)],[12541, 24, 12363, 12538])).
% 291.52/184.04 tff(12543,plain,(m_c_h_element_v_out(c_e_h_3, c_e, s10) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s10))), inference(lemma,lemma(discharge,[]))).
% 291.52/184.04 tff(12544,plain,
% 291.52/184.04 (~m_and_h_gate_v_in1(c_e_h_3, c_r, s10)),
% 291.52/184.04 inference(unit_resolution,[status(thm)],[12543, 12361])).
% 291.52/184.04 tff(12545,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_r, s10)), introduced(assumption)).
% 291.52/184.04 tff(12546,assumption,(node20(c_e_h_3, c_r, s10)), introduced(assumption)).
% 291.52/184.04 tff(12547,plain,
% 291.52/184.04 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s10)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s10))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s10)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s10))),
% 291.52/184.04 inference(rewrite,[status(thm)],[])).
% 291.52/184.04 tff(12548,plain,
% 291.52/184.04 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s10)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s10))),
% 291.52/184.04 inference(quant_inst,[status(thm)],[])).
% 291.52/184.04 tff(12549,plain,
% 291.52/184.04 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s10)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s10)),
% 291.52/184.04 inference(modus_ponens,[status(thm)],[12548, 12547])).
% 291.52/184.04 tff(12550,plain,
% 291.52/184.04 ($false),
% 291.52/184.04 inference(unit_resolution,[status(thm)],[12549, 38, 12546, 12545])).
% 291.52/184.04 tff(12551,plain,(m_and_h_gate_v_in1(c_e_h_3, c_r, s10) | (~node20(c_e_h_3, c_r, s10))), inference(lemma,lemma(discharge,[]))).
% 291.52/184.04 tff(12552,plain,
% 291.52/184.04 (~node20(c_e_h_3, c_r, s10)),
% 291.52/184.04 inference(unit_resolution,[status(thm)],[12551, 12544])).
% 291.52/184.04 tff(12553,plain,
% 291.52/184.04 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s9)) | m_c_h_element_v_out(c_e_h_3, c_e, s9))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s9)) | m_c_h_element_v_out(c_e_h_3, c_e, s9))),
% 291.52/184.04 inference(rewrite,[status(thm)],[])).
% 291.52/184.04 tff(12554,plain,
% 291.52/184.04 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s9)) | m_c_h_element_v_out(c_e_h_3, c_e, s9))),
% 291.52/184.04 inference(quant_inst,[status(thm)],[])).
% 291.52/184.04 tff(12555,plain,
% 291.52/184.04 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s9)) | m_c_h_element_v_out(c_e_h_3, c_e, s9)),
% 291.52/184.04 inference(modus_ponens,[status(thm)],[12554, 12553])).
% 291.52/184.04 tff(12556,plain,
% 291.52/184.04 (~m_and_h_gate_v_in1(c_e_h_3, c_r, s9)),
% 291.52/184.04 inference(unit_resolution,[status(thm)],[12555, 24, 12276])).
% 291.52/184.04 tff(12557,plain,
% 291.52/184.04 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s9)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s9))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s9)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s9))),
% 291.52/184.04 inference(rewrite,[status(thm)],[])).
% 291.52/184.04 tff(12558,plain,
% 291.52/184.04 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s9)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s9))),
% 291.52/184.04 inference(quant_inst,[status(thm)],[])).
% 291.52/184.04 tff(12559,plain,
% 291.52/184.04 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s9)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s9)),
% 291.52/184.04 inference(modus_ponens,[status(thm)],[12558, 12557])).
% 291.52/184.04 tff(12560,plain,
% 291.52/184.04 (~node20(c_e_h_3, c_r, s9)),
% 291.52/184.04 inference(unit_resolution,[status(thm)],[12559, 38, 12556])).
% 291.52/184.04 tff(12561,assumption,(m_and_h_gate_v_out(c_e_h_3, c_r, s9)), introduced(assumption)).
% 291.52/184.04 tff(12562,assumption,(node22(c_e_h_3, c_r, s8, s9)), introduced(assumption)).
% 291.52/184.04 tff(12563,plain,
% 291.52/184.04 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s7)) | m_c_h_element_v_out(c_e_h_3, c_e, s7))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s7)) | m_c_h_element_v_out(c_e_h_3, c_e, s7))),
% 291.52/184.04 inference(rewrite,[status(thm)],[])).
% 291.52/184.04 tff(12564,plain,
% 291.52/184.04 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s7)) | m_c_h_element_v_out(c_e_h_3, c_e, s7))),
% 291.52/184.04 inference(quant_inst,[status(thm)],[])).
% 291.52/184.04 tff(12565,plain,
% 291.52/184.04 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s7)) | m_c_h_element_v_out(c_e_h_3, c_e, s7)),
% 291.52/184.04 inference(modus_ponens,[status(thm)],[12564, 12563])).
% 291.52/184.04 tff(12566,plain,
% 291.52/184.04 (~m_and_h_gate_v_in1(c_e_h_3, c_r, s7)),
% 291.52/184.04 inference(unit_resolution,[status(thm)],[12565, 24, 12135])).
% 291.52/184.04 tff(12567,plain,
% 291.52/184.04 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s7))),
% 291.52/184.04 inference(rewrite,[status(thm)],[])).
% 291.52/184.04 tff(12568,plain,
% 291.52/184.04 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s7))),
% 291.52/184.04 inference(quant_inst,[status(thm)],[])).
% 291.52/184.04 tff(12569,plain,
% 291.52/184.04 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s7)),
% 291.52/184.04 inference(modus_ponens,[status(thm)],[12568, 12567])).
% 291.52/184.04 tff(12570,plain,
% 291.52/184.04 (~node20(c_e_h_3, c_r, s7)),
% 291.52/184.04 inference(unit_resolution,[status(thm)],[12569, 38, 12566])).
% 291.52/184.04 tff(12571,assumption,(m_and_h_gate_v_out(c_e_h_3, c_r, s8)), introduced(assumption)).
% 291.52/184.04 tff(12572,assumption,(~node20(c_e_h_3, c_r, s7)), introduced(assumption)).
% 291.52/184.04 tff(12573,assumption,(node22(c_e_h_3, c_r, s7, s8)), introduced(assumption)).
% 291.52/184.04 tff(12574,plain,
% 291.52/184.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s8)) | (~node22(c_e_h_3, c_r, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_r, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s8)) | (~node22(c_e_h_3, c_r, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_r, s7))),
% 291.52/184.04 inference(rewrite,[status(thm)],[])).
% 291.52/184.04 tff(12575,plain,
% 291.52/184.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s8)) | (~node22(c_e_h_3, c_r, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_r, s7))),
% 291.52/184.04 inference(quant_inst,[status(thm)],[])).
% 291.52/184.04 tff(12576,plain,
% 291.52/184.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s8)) | (~node22(c_e_h_3, c_r, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_r, s7)),
% 291.52/184.04 inference(modus_ponens,[status(thm)],[12575, 12574])).
% 291.52/184.04 tff(12577,plain,
% 291.52/184.04 ($false),
% 291.52/184.04 inference(unit_resolution,[status(thm)],[12576, 108, 12573, 2482, 12571])).
% 291.52/184.04 tff(12578,plain,((~node22(c_e_h_3, c_r, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_r, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s8))), inference(lemma,lemma(discharge,[]))).
% 291.52/184.04 tff(12579,plain,
% 291.52/184.04 (~node22(c_e_h_3, c_r, s7, s8)),
% 291.52/184.04 inference(unit_resolution,[status(thm)],[12578, 12571, 2482])).
% 291.52/184.04 tff(12580,plain,
% 291.52/184.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_3, c_r, s7, s8) | node22(c_e_h_3, c_r, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_3, c_r, s7, s8) | node22(c_e_h_3, c_r, s7, s8))),
% 291.52/184.04 inference(rewrite,[status(thm)],[])).
% 291.52/184.04 tff(12581,plain,
% 291.52/184.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_3, c_r, s7, s8) | node22(c_e_h_3, c_r, s7, s8))),
% 291.52/184.04 inference(quant_inst,[status(thm)],[])).
% 291.52/184.04 tff(12582,plain,
% 291.52/184.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_3, c_r, s7, s8) | node22(c_e_h_3, c_r, s7, s8)),
% 291.52/184.04 inference(modus_ponens,[status(thm)],[12581, 12580])).
% 291.52/184.04 tff(12583,plain,
% 291.52/184.04 (node21(c_e_h_3, c_r, s7, s8) | node22(c_e_h_3, c_r, s7, s8)),
% 291.52/184.04 inference(unit_resolution,[status(thm)],[12582, 82, 1938])).
% 291.52/184.04 tff(12584,plain,
% 291.52/184.04 (node21(c_e_h_3, c_r, s7, s8)),
% 291.52/184.04 inference(unit_resolution,[status(thm)],[12583, 12579])).
% 291.52/184.04 tff(12585,plain,
% 291.52/184.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s8)) | node20(c_e_h_3, c_r, s7) | (~node21(c_e_h_3, c_r, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s8)) | node20(c_e_h_3, c_r, s7) | (~node21(c_e_h_3, c_r, s7, s8)))),
% 291.52/184.04 inference(rewrite,[status(thm)],[])).
% 291.52/184.04 tff(12586,plain,
% 291.52/184.04 ((node20(c_e_h_3, c_r, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s8)) | (~node21(c_e_h_3, c_r, s7, s8))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_r, s8)) | node20(c_e_h_3, c_r, s7) | (~node21(c_e_h_3, c_r, s7, s8)))),
% 291.52/184.04 inference(rewrite,[status(thm)],[])).
% 291.52/184.04 tff(12587,plain,
% 291.52/184.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s8)) | (~node21(c_e_h_3, c_r, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s8)) | node20(c_e_h_3, c_r, s7) | (~node21(c_e_h_3, c_r, s7, s8))))),
% 291.52/184.04 inference(monotonicity,[status(thm)],[12586])).
% 291.52/184.04 tff(12588,plain,
% 291.52/184.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s8)) | (~node21(c_e_h_3, c_r, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s8)) | node20(c_e_h_3, c_r, s7) | (~node21(c_e_h_3, c_r, s7, s8)))),
% 291.52/184.05 inference(transitivity,[status(thm)],[12587, 12585])).
% 291.52/184.05 tff(12589,plain,
% 291.52/184.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s8)) | (~node21(c_e_h_3, c_r, s7, s8)))),
% 291.52/184.05 inference(quant_inst,[status(thm)],[])).
% 291.52/184.05 tff(12590,plain,
% 291.52/184.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s8)) | node20(c_e_h_3, c_r, s7) | (~node21(c_e_h_3, c_r, s7, s8))),
% 291.52/184.05 inference(modus_ponens,[status(thm)],[12589, 12588])).
% 291.52/184.05 tff(12591,plain,
% 291.52/184.05 ($false),
% 291.52/184.05 inference(unit_resolution,[status(thm)],[12590, 52, 12584, 12572, 12571])).
% 291.52/184.05 tff(12592,plain,((~m_and_h_gate_v_out(c_e_h_3, c_r, s8)) | node20(c_e_h_3, c_r, s7) | m_and_h_gate_v_out(c_e_h_3, c_r, s7)), inference(lemma,lemma(discharge,[]))).
% 291.52/184.05 tff(12593,plain,
% 291.52/184.05 (~m_and_h_gate_v_out(c_e_h_3, c_r, s8)),
% 291.52/184.05 inference(unit_resolution,[status(thm)],[12592, 12570, 2481])).
% 291.52/184.05 tff(12594,plain,
% 291.52/184.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s9)) | (~node22(c_e_h_3, c_r, s8, s9)) | m_and_h_gate_v_out(c_e_h_3, c_r, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s9)) | (~node22(c_e_h_3, c_r, s8, s9)) | m_and_h_gate_v_out(c_e_h_3, c_r, s8))),
% 291.52/184.05 inference(rewrite,[status(thm)],[])).
% 291.52/184.05 tff(12595,plain,
% 291.52/184.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s9)) | (~node22(c_e_h_3, c_r, s8, s9)) | m_and_h_gate_v_out(c_e_h_3, c_r, s8))),
% 291.52/184.05 inference(quant_inst,[status(thm)],[])).
% 291.52/184.05 tff(12596,plain,
% 291.52/184.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s9)) | (~node22(c_e_h_3, c_r, s8, s9)) | m_and_h_gate_v_out(c_e_h_3, c_r, s8)),
% 291.52/184.05 inference(modus_ponens,[status(thm)],[12595, 12594])).
% 291.52/184.05 tff(12597,plain,
% 291.52/184.05 ($false),
% 291.52/184.05 inference(unit_resolution,[status(thm)],[12596, 108, 12593, 12561, 12562])).
% 291.52/184.05 tff(12598,plain,((~node22(c_e_h_3, c_r, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s9))), inference(lemma,lemma(discharge,[]))).
% 291.52/184.05 tff(12599,plain,
% 291.52/184.05 (~node22(c_e_h_3, c_r, s8, s9)),
% 291.52/184.05 inference(unit_resolution,[status(thm)],[12598, 12561])).
% 291.52/184.05 tff(12600,plain,
% 291.52/184.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s8, s9)) | node21(c_e_h_3, c_r, s8, s9) | node22(c_e_h_3, c_r, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_3, c_r, s8, s9) | node22(c_e_h_3, c_r, s8, s9))),
% 291.52/184.05 inference(rewrite,[status(thm)],[])).
% 291.52/184.05 tff(12601,plain,
% 291.52/184.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s8, s9)) | node21(c_e_h_3, c_r, s8, s9) | node22(c_e_h_3, c_r, s8, s9))),
% 291.52/184.05 inference(quant_inst,[status(thm)],[])).
% 291.52/184.05 tff(12602,plain,
% 291.52/184.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_3, c_r, s8, s9) | node22(c_e_h_3, c_r, s8, s9)),
% 291.52/184.05 inference(modus_ponens,[status(thm)],[12601, 12600])).
% 291.52/184.05 tff(12603,plain,
% 291.52/184.05 (node21(c_e_h_3, c_r, s8, s9) | node22(c_e_h_3, c_r, s8, s9)),
% 291.52/184.05 inference(unit_resolution,[status(thm)],[12602, 82, 1993])).
% 291.52/184.05 tff(12604,plain,
% 291.52/184.05 (node21(c_e_h_3, c_r, s8, s9)),
% 291.52/184.05 inference(unit_resolution,[status(thm)],[12603, 12599])).
% 291.52/184.05 tff(12605,plain,
% 291.52/184.05 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s8)) | m_c_h_element_v_out(c_e_h_3, c_e, s8))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s8)) | m_c_h_element_v_out(c_e_h_3, c_e, s8))),
% 291.52/184.05 inference(rewrite,[status(thm)],[])).
% 291.52/184.05 tff(12606,plain,
% 291.52/184.05 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s8)) | m_c_h_element_v_out(c_e_h_3, c_e, s8))),
% 291.52/184.05 inference(quant_inst,[status(thm)],[])).
% 291.52/184.05 tff(12607,plain,
% 291.52/184.05 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s8)) | m_c_h_element_v_out(c_e_h_3, c_e, s8)),
% 291.52/184.05 inference(modus_ponens,[status(thm)],[12606, 12605])).
% 291.52/184.05 tff(12608,plain,
% 291.52/184.05 (~m_and_h_gate_v_in1(c_e_h_3, c_r, s8)),
% 291.52/184.05 inference(unit_resolution,[status(thm)],[12607, 24, 12186])).
% 291.52/184.05 tff(12609,plain,
% 291.52/184.05 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s8))),
% 291.52/184.05 inference(rewrite,[status(thm)],[])).
% 291.52/184.05 tff(12610,plain,
% 291.52/184.05 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s8))),
% 291.52/184.05 inference(quant_inst,[status(thm)],[])).
% 291.52/184.05 tff(12611,plain,
% 291.52/184.05 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s8)),
% 291.52/184.05 inference(modus_ponens,[status(thm)],[12610, 12609])).
% 291.52/184.05 tff(12612,plain,
% 291.52/184.05 (~node20(c_e_h_3, c_r, s8)),
% 291.52/184.05 inference(unit_resolution,[status(thm)],[12611, 38, 12608])).
% 291.52/184.05 tff(12613,plain,
% 291.52/184.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s9)) | (~node21(c_e_h_3, c_r, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_r, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s9)) | (~node21(c_e_h_3, c_r, s8, s9)))),
% 291.52/184.05 inference(rewrite,[status(thm)],[])).
% 291.52/184.05 tff(12614,plain,
% 291.52/184.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s9)) | (~node21(c_e_h_3, c_r, s8, s9)))),
% 291.52/184.05 inference(quant_inst,[status(thm)],[])).
% 291.52/184.05 tff(12615,plain,
% 291.52/184.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_r, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s9)) | (~node21(c_e_h_3, c_r, s8, s9))),
% 291.52/184.05 inference(modus_ponens,[status(thm)],[12614, 12613])).
% 291.52/184.05 tff(12616,plain,
% 291.52/184.05 ($false),
% 291.52/184.05 inference(unit_resolution,[status(thm)],[12615, 52, 12561, 12612, 12604])).
% 291.52/184.05 tff(12617,plain,(~m_and_h_gate_v_out(c_e_h_3, c_r, s9)), inference(lemma,lemma(discharge,[]))).
% 291.52/184.05 tff(12618,assumption,(~node20(c_e_h_3, c_r, s9)), introduced(assumption)).
% 291.52/184.05 tff(12619,assumption,(m_and_h_gate_v_out(c_e_h_3, c_r, s10)), introduced(assumption)).
% 291.52/184.05 tff(12620,assumption,(node21(c_e_h_3, c_r, s9, s10)), introduced(assumption)).
% 291.52/184.05 tff(12621,plain,
% 291.52/184.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s10)) | (~node21(c_e_h_3, c_r, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_r, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s10)) | (~node21(c_e_h_3, c_r, s9, s10)))),
% 291.52/184.05 inference(rewrite,[status(thm)],[])).
% 291.52/184.05 tff(12622,plain,
% 291.52/184.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s10)) | (~node21(c_e_h_3, c_r, s9, s10)))),
% 291.52/184.05 inference(quant_inst,[status(thm)],[])).
% 291.52/184.05 tff(12623,plain,
% 291.52/184.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_r, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s10)) | (~node21(c_e_h_3, c_r, s9, s10))),
% 291.52/184.05 inference(modus_ponens,[status(thm)],[12622, 12621])).
% 291.52/184.05 tff(12624,plain,
% 291.52/184.05 ($false),
% 291.52/184.05 inference(unit_resolution,[status(thm)],[12623, 52, 12620, 12619, 12618])).
% 291.52/184.05 tff(12625,plain,((~node21(c_e_h_3, c_r, s9, s10)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s10)) | node20(c_e_h_3, c_r, s9)), inference(lemma,lemma(discharge,[]))).
% 291.52/184.05 tff(12626,plain,
% 291.52/184.05 (~node21(c_e_h_3, c_r, s9, s10)),
% 291.52/184.05 inference(unit_resolution,[status(thm)],[12625, 12619, 12618])).
% 291.52/184.05 tff(12627,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_r, s9)), introduced(assumption)).
% 291.52/184.05 tff(12628,assumption,(node22(c_e_h_3, c_r, s9, s10)), introduced(assumption)).
% 291.52/184.05 tff(12629,plain,
% 291.52/184.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s10)) | (~node22(c_e_h_3, c_r, s9, s10)) | m_and_h_gate_v_out(c_e_h_3, c_r, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s10)) | (~node22(c_e_h_3, c_r, s9, s10)) | m_and_h_gate_v_out(c_e_h_3, c_r, s9))),
% 291.52/184.05 inference(rewrite,[status(thm)],[])).
% 291.52/184.05 tff(12630,plain,
% 291.52/184.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s10)) | (~node22(c_e_h_3, c_r, s9, s10)) | m_and_h_gate_v_out(c_e_h_3, c_r, s9))),
% 291.52/184.05 inference(quant_inst,[status(thm)],[])).
% 291.52/184.05 tff(12631,plain,
% 291.52/184.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s10)) | (~node22(c_e_h_3, c_r, s9, s10)) | m_and_h_gate_v_out(c_e_h_3, c_r, s9)),
% 291.52/184.05 inference(modus_ponens,[status(thm)],[12630, 12629])).
% 291.52/184.05 tff(12632,plain,
% 291.52/184.05 ($false),
% 291.52/184.05 inference(unit_resolution,[status(thm)],[12631, 108, 12628, 12619, 12627])).
% 291.52/184.05 tff(12633,plain,((~node22(c_e_h_3, c_r, s9, s10)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s10)) | m_and_h_gate_v_out(c_e_h_3, c_r, s9)), inference(lemma,lemma(discharge,[]))).
% 291.52/184.05 tff(12634,plain,
% 291.52/184.05 (~node22(c_e_h_3, c_r, s9, s10)),
% 291.52/184.05 inference(unit_resolution,[status(thm)],[12633, 12619, 12627])).
% 291.52/184.05 tff(12635,plain,
% 291.52/184.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s9, s10)) | node21(c_e_h_3, c_r, s9, s10) | node22(c_e_h_3, c_r, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s9, s10)) | node21(c_e_h_3, c_r, s9, s10) | node22(c_e_h_3, c_r, s9, s10))),
% 291.52/184.05 inference(rewrite,[status(thm)],[])).
% 291.52/184.05 tff(12636,plain,
% 291.52/184.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s9, s10)) | node21(c_e_h_3, c_r, s9, s10) | node22(c_e_h_3, c_r, s9, s10))),
% 291.52/184.05 inference(quant_inst,[status(thm)],[])).
% 291.52/184.05 tff(12637,plain,
% 291.52/184.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s9, s10)) | node21(c_e_h_3, c_r, s9, s10) | node22(c_e_h_3, c_r, s9, s10)),
% 291.52/184.05 inference(modus_ponens,[status(thm)],[12636, 12635])).
% 291.52/184.05 tff(12638,plain,
% 291.52/184.05 (node21(c_e_h_3, c_r, s9, s10) | node22(c_e_h_3, c_r, s9, s10)),
% 291.52/184.05 inference(unit_resolution,[status(thm)],[12637, 82, 7676])).
% 291.52/184.05 tff(12639,plain,
% 291.52/184.05 ($false),
% 291.52/184.05 inference(unit_resolution,[status(thm)],[12638, 12634, 12626])).
% 291.52/184.05 tff(12640,plain,((~m_and_h_gate_v_out(c_e_h_3, c_r, s10)) | m_and_h_gate_v_out(c_e_h_3, c_r, s9) | node20(c_e_h_3, c_r, s9)), inference(lemma,lemma(discharge,[]))).
% 291.52/184.06 tff(12641,plain,
% 291.52/184.06 ((~m_and_h_gate_v_out(c_e_h_3, c_r, s10)) | node20(c_e_h_3, c_r, s9)),
% 291.52/184.06 inference(unit_resolution,[status(thm)],[12640, 12617])).
% 291.52/184.06 tff(12642,plain,
% 291.52/184.06 (~m_and_h_gate_v_out(c_e_h_3, c_r, s10)),
% 291.52/184.06 inference(unit_resolution,[status(thm)],[12641, 12560])).
% 291.52/184.06 tff(12643,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_r, s10)), introduced(assumption)).
% 291.52/184.06 tff(12644,assumption,(~node20(c_e_h_3, c_r, s10)), introduced(assumption)).
% 291.52/184.06 tff(12645,assumption,(m_and_h_gate_v_out(c_e_h_3, c_r, s11)), introduced(assumption)).
% 291.52/184.06 tff(12646,assumption,(node21(c_e_h_3, c_r, s10, s11)), introduced(assumption)).
% 291.52/184.06 tff(12647,plain,
% 291.52/184.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s10) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s11)) | (~node21(c_e_h_3, c_r, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_r, s10) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s11)) | (~node21(c_e_h_3, c_r, s10, s11)))),
% 291.52/184.06 inference(rewrite,[status(thm)],[])).
% 291.52/184.06 tff(12648,plain,
% 291.52/184.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s10) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s11)) | (~node21(c_e_h_3, c_r, s10, s11)))),
% 291.52/184.06 inference(quant_inst,[status(thm)],[])).
% 291.52/184.06 tff(12649,plain,
% 291.52/184.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_r, s10) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s11)) | (~node21(c_e_h_3, c_r, s10, s11))),
% 291.52/184.06 inference(modus_ponens,[status(thm)],[12648, 12647])).
% 291.52/184.06 tff(12650,plain,
% 291.52/184.06 ($false),
% 291.52/184.06 inference(unit_resolution,[status(thm)],[12649, 52, 12645, 12646, 12644])).
% 291.52/184.06 tff(12651,plain,((~node21(c_e_h_3, c_r, s10, s11)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s11)) | node20(c_e_h_3, c_r, s10)), inference(lemma,lemma(discharge,[]))).
% 291.52/184.06 tff(12652,plain,
% 291.52/184.06 (~node21(c_e_h_3, c_r, s10, s11)),
% 291.52/184.06 inference(unit_resolution,[status(thm)],[12651, 12645, 12644])).
% 291.52/184.06 tff(12653,plain,
% 291.52/184.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s10, s11)) | node21(c_e_h_3, c_r, s10, s11) | node22(c_e_h_3, c_r, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s10, s11)) | node21(c_e_h_3, c_r, s10, s11) | node22(c_e_h_3, c_r, s10, s11))),
% 291.52/184.06 inference(rewrite,[status(thm)],[])).
% 291.52/184.06 tff(12654,plain,
% 291.52/184.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s10, s11)) | node21(c_e_h_3, c_r, s10, s11) | node22(c_e_h_3, c_r, s10, s11))),
% 291.52/184.06 inference(quant_inst,[status(thm)],[])).
% 291.52/184.06 tff(12655,plain,
% 291.52/184.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s10, s11)) | node21(c_e_h_3, c_r, s10, s11) | node22(c_e_h_3, c_r, s10, s11)),
% 291.52/184.06 inference(modus_ponens,[status(thm)],[12654, 12653])).
% 291.52/184.06 tff(12656,plain,
% 291.52/184.06 (node21(c_e_h_3, c_r, s10, s11) | node22(c_e_h_3, c_r, s10, s11)),
% 291.52/184.06 inference(unit_resolution,[status(thm)],[12655, 82, 7748])).
% 291.52/184.06 tff(12657,plain,
% 291.52/184.06 (node22(c_e_h_3, c_r, s10, s11)),
% 291.52/184.06 inference(unit_resolution,[status(thm)],[12656, 12652])).
% 291.52/184.06 tff(12658,plain,
% 291.52/184.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s11)) | (~node22(c_e_h_3, c_r, s10, s11)) | m_and_h_gate_v_out(c_e_h_3, c_r, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s11)) | (~node22(c_e_h_3, c_r, s10, s11)) | m_and_h_gate_v_out(c_e_h_3, c_r, s10))),
% 291.52/184.06 inference(rewrite,[status(thm)],[])).
% 291.52/184.06 tff(12659,plain,
% 291.52/184.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s11)) | (~node22(c_e_h_3, c_r, s10, s11)) | m_and_h_gate_v_out(c_e_h_3, c_r, s10))),
% 291.52/184.06 inference(quant_inst,[status(thm)],[])).
% 291.52/184.06 tff(12660,plain,
% 291.52/184.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s11)) | (~node22(c_e_h_3, c_r, s10, s11)) | m_and_h_gate_v_out(c_e_h_3, c_r, s10)),
% 291.52/184.06 inference(modus_ponens,[status(thm)],[12659, 12658])).
% 291.52/184.06 tff(12661,plain,
% 291.52/184.06 ($false),
% 291.52/184.06 inference(unit_resolution,[status(thm)],[12660, 108, 12645, 12657, 12643])).
% 291.52/184.06 tff(12662,plain,((~m_and_h_gate_v_out(c_e_h_3, c_r, s11)) | m_and_h_gate_v_out(c_e_h_3, c_r, s10) | node20(c_e_h_3, c_r, s10)), inference(lemma,lemma(discharge,[]))).
% 291.52/184.06 tff(12663,plain,
% 291.52/184.06 ((~m_and_h_gate_v_out(c_e_h_3, c_r, s11)) | node20(c_e_h_3, c_r, s10)),
% 291.52/184.06 inference(unit_resolution,[status(thm)],[12662, 12642])).
% 291.52/184.06 tff(12664,plain,
% 291.52/184.06 (~m_and_h_gate_v_out(c_e_h_3, c_r, s11)),
% 291.52/184.06 inference(unit_resolution,[status(thm)],[12663, 12552])).
% 291.52/184.06 tff(12665,plain,
% 291.52/184.06 (~m_c_h_element_v_in2(c_e_h_3, c_e, s10)),
% 291.52/184.06 inference(unit_resolution,[status(thm)],[12369, 11409])).
% 291.52/184.06 tff(12666,plain,
% 291.52/184.06 (~m_c_h_element_v_out(c_e_h_3, c_e, s11)),
% 291.52/184.06 inference(unit_resolution,[status(thm)],[12430, 12665, 12361])).
% 291.52/184.06 tff(12667,plain,
% 291.52/184.06 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s11)) | m_c_h_element_v_out(c_e_h_3, c_e, s11))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s11)) | m_c_h_element_v_out(c_e_h_3, c_e, s11))),
% 291.52/184.06 inference(rewrite,[status(thm)],[])).
% 291.52/184.06 tff(12668,plain,
% 291.52/184.06 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s11)) | m_c_h_element_v_out(c_e_h_3, c_e, s11))),
% 291.52/184.06 inference(quant_inst,[status(thm)],[])).
% 291.52/184.06 tff(12669,plain,
% 291.52/184.06 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s11)) | m_c_h_element_v_out(c_e_h_3, c_e, s11)),
% 291.52/184.06 inference(modus_ponens,[status(thm)],[12668, 12667])).
% 291.52/184.06 tff(12670,plain,
% 291.52/184.06 (~m_and_h_gate_v_in1(c_e_h_3, c_r, s11)),
% 291.52/184.06 inference(unit_resolution,[status(thm)],[12669, 24, 12666])).
% 291.52/184.06 tff(12671,plain,
% 291.52/184.06 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s11)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s11))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s11)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s11))),
% 291.52/184.06 inference(rewrite,[status(thm)],[])).
% 291.52/184.06 tff(12672,plain,
% 291.52/184.06 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s11)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s11))),
% 291.52/184.06 inference(quant_inst,[status(thm)],[])).
% 291.52/184.06 tff(12673,plain,
% 291.52/184.06 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s11)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s11)),
% 291.52/184.06 inference(modus_ponens,[status(thm)],[12672, 12671])).
% 291.52/184.06 tff(12674,plain,
% 291.52/184.06 (~node20(c_e_h_3, c_r, s11)),
% 291.52/184.06 inference(unit_resolution,[status(thm)],[12673, 38, 12670])).
% 291.52/184.06 tff(12675,assumption,(m_and_h_gate_v_out(c_e_h_3, c_r, s12)), introduced(assumption)).
% 291.52/184.06 tff(12676,assumption,(~node20(c_e_h_3, c_r, s11)), introduced(assumption)).
% 291.52/184.06 tff(12677,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_r, s11)), introduced(assumption)).
% 291.52/184.06 tff(12678,assumption,(node22(c_e_h_3, c_r, s11, s12)), introduced(assumption)).
% 291.52/184.06 tff(12679,plain,
% 291.52/184.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s12)) | (~node22(c_e_h_3, c_r, s11, s12)) | m_and_h_gate_v_out(c_e_h_3, c_r, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s12)) | (~node22(c_e_h_3, c_r, s11, s12)) | m_and_h_gate_v_out(c_e_h_3, c_r, s11))),
% 291.52/184.06 inference(rewrite,[status(thm)],[])).
% 291.52/184.06 tff(12680,plain,
% 291.52/184.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s12)) | (~node22(c_e_h_3, c_r, s11, s12)) | m_and_h_gate_v_out(c_e_h_3, c_r, s11))),
% 291.52/184.06 inference(quant_inst,[status(thm)],[])).
% 291.52/184.06 tff(12681,plain,
% 291.52/184.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s12)) | (~node22(c_e_h_3, c_r, s11, s12)) | m_and_h_gate_v_out(c_e_h_3, c_r, s11)),
% 291.52/184.06 inference(modus_ponens,[status(thm)],[12680, 12679])).
% 291.52/184.06 tff(12682,plain,
% 291.52/184.06 ($false),
% 291.52/184.06 inference(unit_resolution,[status(thm)],[12681, 108, 12678, 12677, 12675])).
% 291.52/184.06 tff(12683,plain,((~node22(c_e_h_3, c_r, s11, s12)) | m_and_h_gate_v_out(c_e_h_3, c_r, s11) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s12))), inference(lemma,lemma(discharge,[]))).
% 291.52/184.06 tff(12684,plain,
% 291.52/184.06 (~node22(c_e_h_3, c_r, s11, s12)),
% 291.52/184.06 inference(unit_resolution,[status(thm)],[12683, 12675, 12677])).
% 291.52/184.06 tff(12685,plain,
% 291.52/184.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s11, s12)) | node21(c_e_h_3, c_r, s11, s12) | node22(c_e_h_3, c_r, s11, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s11, s12)) | node21(c_e_h_3, c_r, s11, s12) | node22(c_e_h_3, c_r, s11, s12))),
% 291.52/184.06 inference(rewrite,[status(thm)],[])).
% 291.52/184.06 tff(12686,plain,
% 291.52/184.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s11, s12)) | node21(c_e_h_3, c_r, s11, s12) | node22(c_e_h_3, c_r, s11, s12))),
% 291.52/184.06 inference(quant_inst,[status(thm)],[])).
% 291.52/184.06 tff(12687,plain,
% 291.52/184.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s11, s12)) | node21(c_e_h_3, c_r, s11, s12) | node22(c_e_h_3, c_r, s11, s12)),
% 291.52/184.06 inference(modus_ponens,[status(thm)],[12686, 12685])).
% 291.52/184.06 tff(12688,plain,
% 291.52/184.06 (node21(c_e_h_3, c_r, s11, s12) | node22(c_e_h_3, c_r, s11, s12)),
% 291.52/184.06 inference(unit_resolution,[status(thm)],[12687, 82, 11461])).
% 291.52/184.06 tff(12689,plain,
% 291.52/184.06 (node21(c_e_h_3, c_r, s11, s12)),
% 291.52/184.06 inference(unit_resolution,[status(thm)],[12688, 12684])).
% 291.52/184.06 tff(12690,plain,
% 291.52/184.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s11) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s12)) | (~node21(c_e_h_3, c_r, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_r, s11) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s12)) | (~node21(c_e_h_3, c_r, s11, s12)))),
% 291.52/184.06 inference(rewrite,[status(thm)],[])).
% 291.52/184.06 tff(12691,plain,
% 291.52/184.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s11) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s12)) | (~node21(c_e_h_3, c_r, s11, s12)))),
% 291.52/184.06 inference(quant_inst,[status(thm)],[])).
% 291.52/184.06 tff(12692,plain,
% 291.52/184.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_r, s11) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s12)) | (~node21(c_e_h_3, c_r, s11, s12))),
% 291.52/184.06 inference(modus_ponens,[status(thm)],[12691, 12690])).
% 291.52/184.06 tff(12693,plain,
% 291.52/184.06 ($false),
% 291.52/184.06 inference(unit_resolution,[status(thm)],[12692, 52, 12689, 12676, 12675])).
% 291.52/184.06 tff(12694,plain,((~m_and_h_gate_v_out(c_e_h_3, c_r, s12)) | node20(c_e_h_3, c_r, s11) | m_and_h_gate_v_out(c_e_h_3, c_r, s11)), inference(lemma,lemma(discharge,[]))).
% 291.52/184.06 tff(12695,plain,
% 291.52/184.06 (~m_and_h_gate_v_out(c_e_h_3, c_r, s12)),
% 291.52/184.06 inference(unit_resolution,[status(thm)],[12694, 12674, 12664])).
% 291.52/184.07 tff(12696,plain,
% 291.52/184.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s13)) | (~node22(c_e_h_3, c_r, s12, s13)) | m_and_h_gate_v_out(c_e_h_3, c_r, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s13)) | (~node22(c_e_h_3, c_r, s12, s13)) | m_and_h_gate_v_out(c_e_h_3, c_r, s12))),
% 291.52/184.07 inference(rewrite,[status(thm)],[])).
% 291.52/184.07 tff(12697,plain,
% 291.52/184.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s13)) | (~node22(c_e_h_3, c_r, s12, s13)) | m_and_h_gate_v_out(c_e_h_3, c_r, s12))),
% 291.52/184.07 inference(quant_inst,[status(thm)],[])).
% 291.52/184.07 tff(12698,plain,
% 291.52/184.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s13)) | (~node22(c_e_h_3, c_r, s12, s13)) | m_and_h_gate_v_out(c_e_h_3, c_r, s12)),
% 291.52/184.07 inference(modus_ponens,[status(thm)],[12697, 12696])).
% 291.52/184.07 tff(12699,plain,
% 291.52/184.07 ($false),
% 291.52/184.07 inference(unit_resolution,[status(thm)],[12698, 108, 12525, 12695, 12537])).
% 291.52/184.07 tff(12700,plain,((~m_and_h_gate_v_out(c_e_h_3, c_r, s13)) | node20(c_e_h_3, c_r, s12)), inference(lemma,lemma(discharge,[]))).
% 291.52/184.07 tff(12701,plain,
% 291.52/184.07 (~m_and_h_gate_v_out(c_e_h_3, c_r, s13)),
% 291.52/184.07 inference(unit_resolution,[status(thm)],[12700, 12523])).
% 291.52/184.07 tff(12702,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_r, s13)), introduced(assumption)).
% 291.52/184.07 tff(12703,assumption,(m_user_v_ack(c_e_h_3, c_u, s13)), introduced(assumption)).
% 291.52/184.07 tff(12704,plain,
% 291.52/184.07 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_3, c_u, s13)) | m_and_h_gate_v_out(c_e_h_3, c_r, s13))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_3, c_u, s13)) | m_and_h_gate_v_out(c_e_h_3, c_r, s13))),
% 291.52/184.07 inference(rewrite,[status(thm)],[])).
% 291.52/184.07 tff(12705,plain,
% 291.52/184.07 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_3, c_u, s13)) | m_and_h_gate_v_out(c_e_h_3, c_r, s13))),
% 291.52/184.07 inference(quant_inst,[status(thm)],[])).
% 291.52/184.07 tff(12706,plain,
% 291.52/184.07 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_3, c_u, s13)) | m_and_h_gate_v_out(c_e_h_3, c_r, s13)),
% 291.52/184.07 inference(modus_ponens,[status(thm)],[12705, 12704])).
% 291.52/184.07 tff(12707,plain,
% 291.52/184.07 ($false),
% 291.52/184.07 inference(unit_resolution,[status(thm)],[12706, 268, 12703, 12702])).
% 291.52/184.07 tff(12708,plain,((~m_user_v_ack(c_e_h_3, c_u, s13)) | m_and_h_gate_v_out(c_e_h_3, c_r, s13)), inference(lemma,lemma(discharge,[]))).
% 291.52/184.07 tff(12709,plain,
% 291.52/184.07 (~m_user_v_ack(c_e_h_3, c_u, s13)),
% 291.52/184.07 inference(unit_resolution,[status(thm)],[12708, 12701])).
% 291.52/184.07 tff(12710,assumption,(m_c_h_element_v_in2(c_e_h_3, c_e, s12)), introduced(assumption)).
% 291.52/184.07 tff(12711,plain,
% 291.52/184.07 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s12)) | m_and_h_gate_v_out(c_e_h_3, c_i, s12))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s12)) | m_and_h_gate_v_out(c_e_h_3, c_i, s12))),
% 291.52/184.07 inference(rewrite,[status(thm)],[])).
% 291.52/184.07 tff(12712,plain,
% 291.52/184.07 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_e, s12)) | m_and_h_gate_v_out(c_e_h_3, c_i, s12))),
% 291.52/184.07 inference(quant_inst,[status(thm)],[])).
% 291.52/184.07 tff(12713,plain,
% 291.52/184.07 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s12)) | m_and_h_gate_v_out(c_e_h_3, c_i, s12)),
% 291.52/184.07 inference(modus_ponens,[status(thm)],[12712, 12711])).
% 291.52/184.07 tff(12714,plain,
% 291.52/184.07 ($false),
% 291.52/184.07 inference(unit_resolution,[status(thm)],[12713, 164, 12710, 11833])).
% 291.52/184.07 tff(12715,plain,((~m_c_h_element_v_in2(c_e_h_3, c_e, s12)) | m_and_h_gate_v_out(c_e_h_3, c_i, s12)), inference(lemma,lemma(discharge,[]))).
% 291.52/184.07 tff(12716,plain,
% 291.52/184.07 (~m_c_h_element_v_in2(c_e_h_3, c_e, s12)),
% 291.52/184.07 inference(unit_resolution,[status(thm)],[12715, 11468])).
% 291.52/184.07 tff(12717,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_e, s12)), introduced(assumption)).
% 291.52/184.07 tff(12718,assumption,(m_c_h_element_v_out(c_e_h_3, c_e, s13)), introduced(assumption)).
% 291.52/184.07 tff(12719,assumption,(~m_c_h_element_v_out(c_e_h_3, c_e, s12)), introduced(assumption)).
% 291.52/184.07 tff(12720,assumption,(node15(c_e_h_3, c_e, s12, s13)), introduced(assumption)).
% 291.52/184.07 tff(12721,plain,
% 291.52/184.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s13)) | (~node15(c_e_h_3, c_e, s12, s13)) | m_c_h_element_v_out(c_e_h_3, c_e, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s13)) | (~node15(c_e_h_3, c_e, s12, s13)) | m_c_h_element_v_out(c_e_h_3, c_e, s12))),
% 291.52/184.07 inference(rewrite,[status(thm)],[])).
% 291.52/184.07 tff(12722,plain,
% 291.52/184.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s13)) | (~node15(c_e_h_3, c_e, s12, s13)) | m_c_h_element_v_out(c_e_h_3, c_e, s12))),
% 291.52/184.07 inference(quant_inst,[status(thm)],[])).
% 291.52/184.07 tff(12723,plain,
% 291.52/184.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_e, s13)) | (~node15(c_e_h_3, c_e, s12, s13)) | m_c_h_element_v_out(c_e_h_3, c_e, s12)),
% 291.52/184.07 inference(modus_ponens,[status(thm)],[12722, 12721])).
% 291.52/184.07 tff(12724,plain,
% 291.52/184.07 ($false),
% 291.52/184.07 inference(unit_resolution,[status(thm)],[12723, 147, 12718, 12719, 12720])).
% 291.52/184.07 tff(12725,plain,((~node15(c_e_h_3, c_e, s12, s13)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s13)) | m_c_h_element_v_out(c_e_h_3, c_e, s12)), inference(lemma,lemma(discharge,[]))).
% 291.52/184.07 tff(12726,plain,
% 291.52/184.07 (~node15(c_e_h_3, c_e, s12, s13)),
% 291.52/184.07 inference(unit_resolution,[status(thm)],[12725, 12719, 12718])).
% 291.52/184.07 tff(12727,assumption,(node18(c_e_h_3, c_e, s12, s13)), introduced(assumption)).
% 291.52/184.07 tff(12728,plain,
% 291.52/184.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_e, s12) | (~m_c_h_element_v_out(c_e_h_3, c_e, s13)) | (~node18(c_e_h_3, c_e, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s12) | (~m_c_h_element_v_out(c_e_h_3, c_e, s13)) | (~node18(c_e_h_3, c_e, s12, s13)))),
% 291.52/184.07 inference(rewrite,[status(thm)],[])).
% 291.52/184.07 tff(12729,plain,
% 291.52/184.07 (((~m_c_h_element_v_out(c_e_h_3, c_e, s13)) | m_c_h_element_v_out(c_e_h_3, c_e, s12) | (~node18(c_e_h_3, c_e, s12, s13))) <=> (m_c_h_element_v_out(c_e_h_3, c_e, s12) | (~m_c_h_element_v_out(c_e_h_3, c_e, s13)) | (~node18(c_e_h_3, c_e, s12, s13)))),
% 291.52/184.07 inference(rewrite,[status(thm)],[])).
% 291.52/184.07 tff(12730,plain,
% 291.52/184.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s13)) | m_c_h_element_v_out(c_e_h_3, c_e, s12) | (~node18(c_e_h_3, c_e, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_e, s12) | (~m_c_h_element_v_out(c_e_h_3, c_e, s13)) | (~node18(c_e_h_3, c_e, s12, s13))))),
% 291.52/184.07 inference(monotonicity,[status(thm)],[12729])).
% 291.52/184.07 tff(12731,plain,
% 291.52/184.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s13)) | m_c_h_element_v_out(c_e_h_3, c_e, s12) | (~node18(c_e_h_3, c_e, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s12) | (~m_c_h_element_v_out(c_e_h_3, c_e, s13)) | (~node18(c_e_h_3, c_e, s12, s13)))),
% 291.52/184.07 inference(transitivity,[status(thm)],[12730, 12728])).
% 291.52/184.07 tff(12732,plain,
% 291.52/184.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_e, s13)) | m_c_h_element_v_out(c_e_h_3, c_e, s12) | (~node18(c_e_h_3, c_e, s12, s13)))),
% 291.52/184.07 inference(quant_inst,[status(thm)],[])).
% 291.52/184.07 tff(12733,plain,
% 291.52/184.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_e, s12) | (~m_c_h_element_v_out(c_e_h_3, c_e, s13)) | (~node18(c_e_h_3, c_e, s12, s13))),
% 291.52/184.07 inference(modus_ponens,[status(thm)],[12732, 12731])).
% 291.52/184.07 tff(12734,plain,
% 291.52/184.07 ($false),
% 291.52/184.07 inference(unit_resolution,[status(thm)],[12733, 753, 12718, 12719, 12727])).
% 291.52/184.07 tff(12735,plain,((~node18(c_e_h_3, c_e, s12, s13)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s13)) | m_c_h_element_v_out(c_e_h_3, c_e, s12)), inference(lemma,lemma(discharge,[]))).
% 291.52/184.07 tff(12736,plain,
% 291.52/184.07 (~node18(c_e_h_3, c_e, s12, s13)),
% 291.52/184.07 inference(unit_resolution,[status(thm)],[12735, 12719, 12718])).
% 291.52/184.07 tff(12737,plain,
% 291.52/184.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s12, s13)) | node19(c_e_h_3, c_e, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s12, s13)) | node19(c_e_h_3, c_e, s12, s13))),
% 291.52/184.07 inference(rewrite,[status(thm)],[])).
% 291.52/184.07 tff(12738,plain,
% 291.52/184.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s12, s13)) | node19(c_e_h_3, c_e, s12, s13))),
% 291.52/184.07 inference(quant_inst,[status(thm)],[])).
% 291.52/184.07 tff(12739,plain,
% 291.52/184.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s12, s13)) | node19(c_e_h_3, c_e, s12, s13)),
% 291.52/184.07 inference(modus_ponens,[status(thm)],[12738, 12737])).
% 291.52/184.07 tff(12740,plain,
% 291.52/184.07 (node19(c_e_h_3, c_e, s12, s13)),
% 291.52/184.07 inference(unit_resolution,[status(thm)],[12739, 190, 11856])).
% 291.52/184.07 tff(12741,plain,
% 291.52/184.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s12) | node18(c_e_h_3, c_e, s12, s13) | (~node19(c_e_h_3, c_e, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_e, s12) | node18(c_e_h_3, c_e, s12, s13) | (~node19(c_e_h_3, c_e, s12, s13)))),
% 291.52/184.07 inference(rewrite,[status(thm)],[])).
% 291.52/184.07 tff(12742,plain,
% 291.52/184.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_e, s12) | node18(c_e_h_3, c_e, s12, s13) | (~node19(c_e_h_3, c_e, s12, s13)))),
% 291.52/184.07 inference(quant_inst,[status(thm)],[])).
% 291.52/184.07 tff(12743,plain,
% 291.52/184.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_e, s12) | node18(c_e_h_3, c_e, s12, s13) | (~node19(c_e_h_3, c_e, s12, s13))),
% 291.52/184.07 inference(modus_ponens,[status(thm)],[12742, 12741])).
% 291.52/184.07 tff(12744,plain,
% 291.52/184.07 (node17(c_e_h_3, c_e, s12) | node18(c_e_h_3, c_e, s12, s13)),
% 291.52/184.07 inference(unit_resolution,[status(thm)],[12743, 776, 12740])).
% 291.52/184.07 tff(12745,plain,
% 291.52/184.07 (node17(c_e_h_3, c_e, s12)),
% 291.52/184.07 inference(unit_resolution,[status(thm)],[12744, 12736])).
% 291.52/184.07 tff(12746,assumption,(node17(c_e_h_3, c_e, s12)), introduced(assumption)).
% 291.52/184.07 tff(12747,plain,
% 291.52/184.07 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s12)) | m_c_h_element_v_in2(c_e_h_3, c_e, s12) | (~node17(c_e_h_3, c_e, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s12)) | m_c_h_element_v_in2(c_e_h_3, c_e, s12) | (~node17(c_e_h_3, c_e, s12)))),
% 291.52/184.08 inference(rewrite,[status(thm)],[])).
% 291.52/184.08 tff(12748,plain,
% 291.52/184.08 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s12)) | m_c_h_element_v_in2(c_e_h_3, c_e, s12) | (~node17(c_e_h_3, c_e, s12)))),
% 291.52/184.08 inference(quant_inst,[status(thm)],[])).
% 291.52/184.08 tff(12749,plain,
% 291.52/184.08 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s12)) | m_c_h_element_v_in2(c_e_h_3, c_e, s12) | (~node17(c_e_h_3, c_e, s12))),
% 291.52/184.08 inference(modus_ponens,[status(thm)],[12748, 12747])).
% 291.52/184.08 tff(12750,plain,
% 291.52/184.08 ((~m_c_h_element_v_in1(c_e_h_3, c_e, s12)) | (~node17(c_e_h_3, c_e, s12))),
% 291.52/184.08 inference(unit_resolution,[status(thm)],[12749, 919, 12717])).
% 291.52/184.08 tff(12751,plain,
% 291.52/184.08 (~m_c_h_element_v_in1(c_e_h_3, c_e, s12)),
% 291.52/184.08 inference(unit_resolution,[status(thm)],[12750, 12746])).
% 291.52/184.08 tff(12752,assumption,(~node15(c_e_h_3, c_e, s12, s13)), introduced(assumption)).
% 291.52/184.08 tff(12753,assumption,(node16(c_e_h_3, c_e, s12)), introduced(assumption)).
% 291.52/184.08 tff(12754,plain,
% 291.52/184.08 ((~m_c_h_element_v_in1(c_e_h_3, c_e, s12)) | m_c_h_element_v_in2(c_e_h_3, c_e, s12)),
% 291.52/184.08 inference(unit_resolution,[status(thm)],[12749, 919, 12746])).
% 291.52/184.08 tff(12755,plain,
% 291.52/184.08 (~m_c_h_element_v_in1(c_e_h_3, c_e, s12)),
% 291.52/184.08 inference(unit_resolution,[status(thm)],[12754, 12717])).
% 291.52/184.08 tff(12756,plain,
% 291.52/184.08 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_e, s12)) | m_c_h_element_v_in1(c_e_h_3, c_e, s12) | m_c_h_element_v_in2(c_e_h_3, c_e, s12))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s12)) | m_c_h_element_v_in1(c_e_h_3, c_e, s12) | m_c_h_element_v_in2(c_e_h_3, c_e, s12))),
% 291.52/184.08 inference(rewrite,[status(thm)],[])).
% 291.52/184.08 tff(12757,plain,
% 291.52/184.08 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_e, s12)) | m_c_h_element_v_in1(c_e_h_3, c_e, s12) | m_c_h_element_v_in2(c_e_h_3, c_e, s12))),
% 291.52/184.08 inference(quant_inst,[status(thm)],[])).
% 291.52/184.08 tff(12758,plain,
% 291.52/184.08 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_e, s12)) | m_c_h_element_v_in1(c_e_h_3, c_e, s12) | m_c_h_element_v_in2(c_e_h_3, c_e, s12)),
% 291.52/184.08 inference(modus_ponens,[status(thm)],[12757, 12756])).
% 291.52/184.08 tff(12759,plain,
% 291.52/184.08 (m_c_h_element_v_in1(c_e_h_3, c_e, s12) | m_c_h_element_v_in2(c_e_h_3, c_e, s12)),
% 291.52/184.08 inference(unit_resolution,[status(thm)],[12758, 178, 12753])).
% 291.52/184.08 tff(12760,plain,
% 291.52/184.08 ($false),
% 291.52/184.08 inference(unit_resolution,[status(thm)],[12759, 12755, 12717])).
% 291.52/184.08 tff(12761,plain,(m_c_h_element_v_in2(c_e_h_3, c_e, s12) | (~node16(c_e_h_3, c_e, s12)) | (~node17(c_e_h_3, c_e, s12))), inference(lemma,lemma(discharge,[]))).
% 291.52/184.08 tff(12762,plain,
% 291.52/184.08 (m_c_h_element_v_in2(c_e_h_3, c_e, s12)),
% 291.52/184.08 inference(unit_resolution,[status(thm)],[12761, 12753, 12746])).
% 291.52/184.08 tff(12763,plain,
% 291.52/184.08 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s12) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s12)) | (~node17(c_e_h_3, c_e, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_3, c_e, s12) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s12)) | (~node17(c_e_h_3, c_e, s12)))),
% 291.52/184.08 inference(rewrite,[status(thm)],[])).
% 291.52/184.08 tff(12764,plain,
% 291.52/184.08 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s12) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s12)) | (~node17(c_e_h_3, c_e, s12)))),
% 291.52/184.08 inference(quant_inst,[status(thm)],[])).
% 291.52/184.08 tff(12765,plain,
% 291.52/184.08 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_3, c_e, s12) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s12)) | (~node17(c_e_h_3, c_e, s12))),
% 291.52/184.08 inference(modus_ponens,[status(thm)],[12764, 12763])).
% 291.52/184.08 tff(12766,plain,
% 291.52/184.08 (m_c_h_element_v_in1(c_e_h_3, c_e, s12) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s12))),
% 291.52/184.08 inference(unit_resolution,[status(thm)],[12765, 859, 12746])).
% 291.52/184.08 tff(12767,plain,
% 291.52/184.08 (m_c_h_element_v_in1(c_e_h_3, c_e, s12)),
% 291.52/184.08 inference(unit_resolution,[status(thm)],[12766, 12762])).
% 291.52/184.08 tff(12768,plain,
% 291.52/184.08 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s12)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s12)) | (~node16(c_e_h_3, c_e, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s12)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s12)) | (~node16(c_e_h_3, c_e, s12)))),
% 291.52/184.08 inference(rewrite,[status(thm)],[])).
% 291.52/184.08 tff(12769,plain,
% 291.52/184.08 (((~node16(c_e_h_3, c_e, s12)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s12)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s12))) <=> ((~m_c_h_element_v_in1(c_e_h_3, c_e, s12)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s12)) | (~node16(c_e_h_3, c_e, s12)))),
% 291.52/184.08 inference(rewrite,[status(thm)],[])).
% 291.52/184.08 tff(12770,plain,
% 291.52/184.08 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_e, s12)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s12)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_e, s12)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s12)) | (~node16(c_e_h_3, c_e, s12))))),
% 291.52/184.08 inference(monotonicity,[status(thm)],[12769])).
% 291.52/184.08 tff(12771,plain,
% 291.52/184.08 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_e, s12)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s12)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s12)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s12)) | (~node16(c_e_h_3, c_e, s12)))),
% 291.52/184.08 inference(transitivity,[status(thm)],[12770, 12768])).
% 291.52/184.08 tff(12772,plain,
% 291.52/184.08 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_e, s12)) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s12)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s12)))),
% 291.52/184.08 inference(quant_inst,[status(thm)],[])).
% 291.52/184.08 tff(12773,plain,
% 291.52/184.08 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_e, s12)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s12)) | (~node16(c_e_h_3, c_e, s12))),
% 291.52/184.08 inference(modus_ponens,[status(thm)],[12772, 12771])).
% 291.52/184.08 tff(12774,plain,
% 291.52/184.08 ((~m_c_h_element_v_in1(c_e_h_3, c_e, s12)) | (~m_c_h_element_v_in2(c_e_h_3, c_e, s12))),
% 291.52/184.08 inference(unit_resolution,[status(thm)],[12773, 2307, 12753])).
% 291.52/184.08 tff(12775,plain,
% 291.52/184.08 ($false),
% 291.52/184.08 inference(unit_resolution,[status(thm)],[12774, 12767, 12762])).
% 291.52/184.08 tff(12776,plain,((~node16(c_e_h_3, c_e, s12)) | (~node17(c_e_h_3, c_e, s12))), inference(lemma,lemma(discharge,[]))).
% 291.52/184.08 tff(12777,plain,
% 291.52/184.08 (~node16(c_e_h_3, c_e, s12)),
% 291.52/184.08 inference(unit_resolution,[status(thm)],[12776, 12746])).
% 291.52/184.08 tff(12778,plain,
% 291.52/184.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s12) | node14(c_e_h_3, c_e, s12, s13) | node15(c_e_h_3, c_e, s12, s13) | (~node19(c_e_h_3, c_e, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_e, s12) | node14(c_e_h_3, c_e, s12, s13) | node15(c_e_h_3, c_e, s12, s13) | (~node19(c_e_h_3, c_e, s12, s13)))),
% 291.52/184.09 inference(rewrite,[status(thm)],[])).
% 291.52/184.09 tff(12779,plain,
% 291.52/184.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_e, s12) | node14(c_e_h_3, c_e, s12, s13) | node15(c_e_h_3, c_e, s12, s13) | (~node19(c_e_h_3, c_e, s12, s13)))),
% 291.52/184.09 inference(quant_inst,[status(thm)],[])).
% 291.52/184.09 tff(12780,plain,
% 291.52/184.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_e, s12) | node14(c_e_h_3, c_e, s12, s13) | node15(c_e_h_3, c_e, s12, s13) | (~node19(c_e_h_3, c_e, s12, s13))),
% 291.52/184.09 inference(modus_ponens,[status(thm)],[12779, 12778])).
% 291.52/184.09 tff(12781,plain,
% 291.52/184.09 (node16(c_e_h_3, c_e, s12) | node14(c_e_h_3, c_e, s12, s13) | node15(c_e_h_3, c_e, s12, s13)),
% 291.52/184.09 inference(unit_resolution,[status(thm)],[12780, 204, 12740])).
% 291.52/184.09 tff(12782,plain,
% 291.52/184.09 (node14(c_e_h_3, c_e, s12, s13)),
% 291.52/184.09 inference(unit_resolution,[status(thm)],[12781, 12777, 12752])).
% 291.52/184.09 tff(12783,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_e, s12)), introduced(assumption)).
% 291.52/184.09 tff(12784,assumption,(node14(c_e_h_3, c_e, s12, s13)), introduced(assumption)).
% 291.52/184.09 tff(12785,plain,
% 291.52/184.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s12) | (~m_c_h_element_v_out(c_e_h_3, c_e, s13)) | (~node14(c_e_h_3, c_e, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_e, s12) | (~m_c_h_element_v_out(c_e_h_3, c_e, s13)) | (~node14(c_e_h_3, c_e, s12, s13)))),
% 291.52/184.09 inference(rewrite,[status(thm)],[])).
% 291.52/184.09 tff(12786,plain,
% 291.52/184.09 (((~node14(c_e_h_3, c_e, s12, s13)) | m_c_h_element_v_in1(c_e_h_3, c_e, s12) | (~m_c_h_element_v_out(c_e_h_3, c_e, s13))) <=> (m_c_h_element_v_in1(c_e_h_3, c_e, s12) | (~m_c_h_element_v_out(c_e_h_3, c_e, s13)) | (~node14(c_e_h_3, c_e, s12, s13)))),
% 291.52/184.09 inference(rewrite,[status(thm)],[])).
% 291.52/184.09 tff(12787,plain,
% 291.52/184.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s12, s13)) | m_c_h_element_v_in1(c_e_h_3, c_e, s12) | (~m_c_h_element_v_out(c_e_h_3, c_e, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_e, s12) | (~m_c_h_element_v_out(c_e_h_3, c_e, s13)) | (~node14(c_e_h_3, c_e, s12, s13))))),
% 291.52/184.09 inference(monotonicity,[status(thm)],[12786])).
% 291.52/184.09 tff(12788,plain,
% 291.52/184.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s12, s13)) | m_c_h_element_v_in1(c_e_h_3, c_e, s12) | (~m_c_h_element_v_out(c_e_h_3, c_e, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_e, s12) | (~m_c_h_element_v_out(c_e_h_3, c_e, s13)) | (~node14(c_e_h_3, c_e, s12, s13)))),
% 291.52/184.09 inference(transitivity,[status(thm)],[12787, 12785])).
% 291.52/184.09 tff(12789,plain,
% 291.52/184.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_e, s12, s13)) | m_c_h_element_v_in1(c_e_h_3, c_e, s12) | (~m_c_h_element_v_out(c_e_h_3, c_e, s13)))),
% 291.52/184.09 inference(quant_inst,[status(thm)],[])).
% 291.52/184.09 tff(12790,plain,
% 291.52/184.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_e, s12) | (~m_c_h_element_v_out(c_e_h_3, c_e, s13)) | (~node14(c_e_h_3, c_e, s12, s13))),
% 291.52/184.09 inference(modus_ponens,[status(thm)],[12789, 12788])).
% 291.52/184.09 tff(12791,plain,
% 291.52/184.09 ($false),
% 291.52/184.09 inference(unit_resolution,[status(thm)],[12790, 223, 12718, 12784, 12783])).
% 291.52/184.09 tff(12792,plain,((~node14(c_e_h_3, c_e, s12, s13)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s13)) | m_c_h_element_v_in1(c_e_h_3, c_e, s12)), inference(lemma,lemma(discharge,[]))).
% 291.52/184.09 tff(12793,plain,
% 291.52/184.09 ($false),
% 291.52/184.09 inference(unit_resolution,[status(thm)],[12792, 12782, 12751, 12718])).
% 291.52/184.09 tff(12794,plain,((~node17(c_e_h_3, c_e, s12)) | (~m_c_h_element_v_out(c_e_h_3, c_e, s13)) | node15(c_e_h_3, c_e, s12, s13) | m_c_h_element_v_in2(c_e_h_3, c_e, s12)), inference(lemma,lemma(discharge,[]))).
% 291.52/184.09 tff(12795,plain,
% 291.52/184.09 ($false),
% 291.52/184.09 inference(unit_resolution,[status(thm)],[12794, 12745, 12726, 12718, 12717])).
% 291.52/184.09 tff(12796,plain,(m_c_h_element_v_out(c_e_h_3, c_e, s12) | (~m_c_h_element_v_out(c_e_h_3, c_e, s13)) | m_c_h_element_v_in2(c_e_h_3, c_e, s12)), inference(lemma,lemma(discharge,[]))).
% 291.52/184.09 tff(12797,plain,
% 291.52/184.09 (~m_c_h_element_v_out(c_e_h_3, c_e, s13)),
% 291.52/184.09 inference(unit_resolution,[status(thm)],[12796, 12716, 12515])).
% 291.52/184.09 tff(12798,plain,
% 291.52/184.09 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s13)) | m_c_h_element_v_out(c_e_h_3, c_e, s13))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s13)) | m_c_h_element_v_out(c_e_h_3, c_e, s13))),
% 291.52/184.09 inference(rewrite,[status(thm)],[])).
% 291.52/184.09 tff(12799,plain,
% 291.52/184.09 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_r, s13)) | m_c_h_element_v_out(c_e_h_3, c_e, s13))),
% 291.52/184.09 inference(quant_inst,[status(thm)],[])).
% 291.52/184.09 tff(12800,plain,
% 291.52/184.09 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_r, s13)) | m_c_h_element_v_out(c_e_h_3, c_e, s13)),
% 291.52/184.09 inference(modus_ponens,[status(thm)],[12799, 12798])).
% 291.52/184.09 tff(12801,plain,
% 291.52/184.09 (~m_and_h_gate_v_in1(c_e_h_3, c_r, s13)),
% 291.52/184.09 inference(unit_resolution,[status(thm)],[12800, 24, 12797])).
% 291.52/184.09 tff(12802,plain,
% 291.52/184.09 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s13)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s13))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s13)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s13))),
% 291.52/184.09 inference(rewrite,[status(thm)],[])).
% 291.52/184.09 tff(12803,plain,
% 291.52/184.09 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_r, s13)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s13))),
% 291.52/184.09 inference(quant_inst,[status(thm)],[])).
% 291.52/184.09 tff(12804,plain,
% 291.52/184.09 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_r, s13)) | m_and_h_gate_v_in1(c_e_h_3, c_r, s13)),
% 291.52/184.09 inference(modus_ponens,[status(thm)],[12803, 12802])).
% 291.52/184.09 tff(12805,plain,
% 291.52/184.09 (~node20(c_e_h_3, c_r, s13)),
% 291.52/184.09 inference(unit_resolution,[status(thm)],[12804, 38, 12801])).
% 291.52/184.09 tff(12806,assumption,(m_and_h_gate_v_out(c_e_h_3, c_r, s14)), introduced(assumption)).
% 291.52/184.09 tff(12807,assumption,(node22(c_e_h_3, c_r, s13, s14)), introduced(assumption)).
% 291.52/184.09 tff(12808,plain,
% 291.52/184.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s14)) | (~node22(c_e_h_3, c_r, s13, s14)) | m_and_h_gate_v_out(c_e_h_3, c_r, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s14)) | (~node22(c_e_h_3, c_r, s13, s14)) | m_and_h_gate_v_out(c_e_h_3, c_r, s13))),
% 291.52/184.09 inference(rewrite,[status(thm)],[])).
% 291.52/184.09 tff(12809,plain,
% 291.52/184.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s14)) | (~node22(c_e_h_3, c_r, s13, s14)) | m_and_h_gate_v_out(c_e_h_3, c_r, s13))),
% 291.61/184.09 inference(quant_inst,[status(thm)],[])).
% 291.61/184.09 tff(12810,plain,
% 291.61/184.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s14)) | (~node22(c_e_h_3, c_r, s13, s14)) | m_and_h_gate_v_out(c_e_h_3, c_r, s13)),
% 291.61/184.09 inference(modus_ponens,[status(thm)],[12809, 12808])).
% 291.61/184.09 tff(12811,plain,
% 291.61/184.09 ($false),
% 291.61/184.09 inference(unit_resolution,[status(thm)],[12810, 108, 12807, 12806, 12702])).
% 291.61/184.09 tff(12812,plain,((~node22(c_e_h_3, c_r, s13, s14)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s14)) | m_and_h_gate_v_out(c_e_h_3, c_r, s13)), inference(lemma,lemma(discharge,[]))).
% 291.61/184.09 tff(12813,plain,
% 291.61/184.09 (~node22(c_e_h_3, c_r, s13, s14)),
% 291.61/184.09 inference(unit_resolution,[status(thm)],[12812, 12806, 12702])).
% 291.61/184.09 tff(12814,assumption,(~node20(c_e_h_3, c_r, s13)), introduced(assumption)).
% 291.61/184.09 tff(12815,assumption,(node21(c_e_h_3, c_r, s13, s14)), introduced(assumption)).
% 291.61/184.09 tff(12816,plain,
% 291.61/184.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s14)) | node20(c_e_h_3, c_r, s13) | (~node21(c_e_h_3, c_r, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s14)) | node20(c_e_h_3, c_r, s13) | (~node21(c_e_h_3, c_r, s13, s14)))),
% 291.61/184.09 inference(rewrite,[status(thm)],[])).
% 291.61/184.09 tff(12817,plain,
% 291.61/184.09 ((node20(c_e_h_3, c_r, s13) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s14)) | (~node21(c_e_h_3, c_r, s13, s14))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_r, s14)) | node20(c_e_h_3, c_r, s13) | (~node21(c_e_h_3, c_r, s13, s14)))),
% 291.61/184.09 inference(rewrite,[status(thm)],[])).
% 291.61/184.09 tff(12818,plain,
% 291.61/184.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s13) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s14)) | (~node21(c_e_h_3, c_r, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_r, s14)) | node20(c_e_h_3, c_r, s13) | (~node21(c_e_h_3, c_r, s13, s14))))),
% 291.61/184.09 inference(monotonicity,[status(thm)],[12817])).
% 291.61/184.09 tff(12819,plain,
% 291.61/184.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s13) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s14)) | (~node21(c_e_h_3, c_r, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s14)) | node20(c_e_h_3, c_r, s13) | (~node21(c_e_h_3, c_r, s13, s14)))),
% 291.61/184.09 inference(transitivity,[status(thm)],[12818, 12816])).
% 291.61/184.09 tff(12820,plain,
% 291.61/184.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_r, s13) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s14)) | (~node21(c_e_h_3, c_r, s13, s14)))),
% 291.61/184.09 inference(quant_inst,[status(thm)],[])).
% 291.61/184.09 tff(12821,plain,
% 291.61/184.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s14)) | node20(c_e_h_3, c_r, s13) | (~node21(c_e_h_3, c_r, s13, s14))),
% 291.61/184.09 inference(modus_ponens,[status(thm)],[12820, 12819])).
% 291.61/184.09 tff(12822,plain,
% 291.61/184.09 ($false),
% 291.61/184.09 inference(unit_resolution,[status(thm)],[12821, 52, 12815, 12806, 12814])).
% 291.61/184.09 tff(12823,plain,((~node21(c_e_h_3, c_r, s13, s14)) | (~m_and_h_gate_v_out(c_e_h_3, c_r, s14)) | node20(c_e_h_3, c_r, s13)), inference(lemma,lemma(discharge,[]))).
% 291.61/184.09 tff(12824,plain,
% 291.61/184.09 (~node21(c_e_h_3, c_r, s13, s14)),
% 291.61/184.09 inference(unit_resolution,[status(thm)],[12823, 12806, 12814])).
% 291.61/184.09 tff(12825,plain,
% 291.61/184.09 (succ(s13, s14) <=> succ(s13, s14)),
% 291.61/184.09 inference(rewrite,[status(thm)],[])).
% 291.61/184.09 tff(12826,axiom,(succ(s13, s14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound14')).
% 291.61/184.10 tff(12827,plain,
% 291.61/184.10 (succ(s13, s14)),
% 291.61/184.10 inference(modus_ponens,[status(thm)],[12826, 12825])).
% 291.61/184.10 tff(12828,plain,
% 291.61/184.10 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s13, s14)) | trans(s13, s14))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s13, s14)) | trans(s13, s14))),
% 291.61/184.10 inference(rewrite,[status(thm)],[])).
% 291.61/184.10 tff(12829,plain,
% 291.61/184.10 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s13, s14)) | trans(s13, s14))),
% 291.61/184.10 inference(quant_inst,[status(thm)],[])).
% 291.61/184.10 tff(12830,plain,
% 291.61/184.10 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s13, s14)) | trans(s13, s14)),
% 291.61/184.10 inference(modus_ponens,[status(thm)],[12829, 12828])).
% 291.61/184.10 tff(12831,plain,
% 291.61/184.10 (trans(s13, s14)),
% 291.61/184.10 inference(unit_resolution,[status(thm)],[12830, 12827, 65])).
% 291.61/184.10 tff(12832,plain,
% 291.61/184.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s13, s14)) | node21(c_e_h_3, c_r, s13, s14) | node22(c_e_h_3, c_r, s13, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s13, s14)) | node21(c_e_h_3, c_r, s13, s14) | node22(c_e_h_3, c_r, s13, s14))),
% 291.61/184.10 inference(rewrite,[status(thm)],[])).
% 291.61/184.10 tff(12833,plain,
% 291.61/184.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s13, s14)) | node21(c_e_h_3, c_r, s13, s14) | node22(c_e_h_3, c_r, s13, s14))),
% 291.61/184.10 inference(quant_inst,[status(thm)],[])).
% 291.61/184.10 tff(12834,plain,
% 291.61/184.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s13, s14)) | node21(c_e_h_3, c_r, s13, s14) | node22(c_e_h_3, c_r, s13, s14)),
% 291.61/184.10 inference(modus_ponens,[status(thm)],[12833, 12832])).
% 291.61/184.10 tff(12835,plain,
% 291.61/184.10 (node21(c_e_h_3, c_r, s13, s14) | node22(c_e_h_3, c_r, s13, s14)),
% 291.61/184.10 inference(unit_resolution,[status(thm)],[12834, 82, 12831])).
% 291.61/184.10 tff(12836,plain,
% 291.61/184.10 ($false),
% 291.61/184.10 inference(unit_resolution,[status(thm)],[12835, 12824, 12813])).
% 291.61/184.10 tff(12837,plain,((~m_and_h_gate_v_out(c_e_h_3, c_r, s14)) | node20(c_e_h_3, c_r, s13) | m_and_h_gate_v_out(c_e_h_3, c_r, s13)), inference(lemma,lemma(discharge,[]))).
% 291.61/184.10 tff(12838,plain,
% 291.61/184.10 (~m_and_h_gate_v_out(c_e_h_3, c_r, s14)),
% 291.61/184.10 inference(unit_resolution,[status(thm)],[12837, 12701, 12805])).
% 291.61/184.10 tff(12839,assumption,(~m_user_v_ack(c_e_h_3, c_u, s13)), introduced(assumption)).
% 291.61/184.10 tff(12840,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_r, s14)), introduced(assumption)).
% 291.61/184.10 tff(12841,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_f, s14)), introduced(assumption)).
% 291.61/184.10 tff(12842,plain,
% 291.61/184.10 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s16) | m_c_h_element_v_out(c_e_h_3, c_f, s16))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s16) | m_c_h_element_v_out(c_e_h_3, c_f, s16))),
% 291.61/184.10 inference(rewrite,[status(thm)],[])).
% 291.61/184.10 tff(12843,plain,
% 291.61/184.10 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s16) | m_c_h_element_v_out(c_e_h_3, c_f, s16))),
% 291.61/184.10 inference(quant_inst,[status(thm)],[])).
% 291.61/184.10 tff(12844,plain,
% 291.61/184.10 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s16) | m_c_h_element_v_out(c_e_h_3, c_f, s16)),
% 291.61/184.10 inference(modus_ponens,[status(thm)],[12843, 12842])).
% 291.61/184.10 tff(12845,plain,
% 291.61/184.10 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s16) | m_c_h_element_v_out(c_e_h_3, c_f, s16)),
% 291.61/184.10 inference(unit_resolution,[status(thm)],[12844, 5689])).
% 291.61/184.10 tff(12846,plain,
% 291.61/184.10 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s16)),
% 291.61/184.10 inference(unit_resolution,[status(thm)],[12845, 11924])).
% 291.61/184.10 tff(12847,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_f, s13)), introduced(assumption)).
% 291.61/184.10 tff(12848,plain,
% 291.61/184.10 (~m_c_h_element_v_out(c_e_h_3, c_f, s13)),
% 291.61/184.10 inference(unit_resolution,[status(thm)],[11914, 11905, 11841])).
% 291.61/184.10 tff(12849,assumption,(~m_c_h_element_v_out(c_e_h_3, c_f, s13)), introduced(assumption)).
% 291.61/184.10 tff(12850,assumption,(m_c_h_element_v_out(c_e_h_3, c_f, s14)), introduced(assumption)).
% 291.61/184.10 tff(12851,assumption,(node14(c_e_h_3, c_f, s13, s14)), introduced(assumption)).
% 291.61/184.10 tff(12852,plain,
% 291.61/184.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s14)) | m_c_h_element_v_in1(c_e_h_3, c_f, s13) | (~node14(c_e_h_3, c_f, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s14)) | m_c_h_element_v_in1(c_e_h_3, c_f, s13) | (~node14(c_e_h_3, c_f, s13, s14)))),
% 291.61/184.10 inference(rewrite,[status(thm)],[])).
% 291.61/184.10 tff(12853,plain,
% 291.61/184.10 (((~node14(c_e_h_3, c_f, s13, s14)) | m_c_h_element_v_in1(c_e_h_3, c_f, s13) | (~m_c_h_element_v_out(c_e_h_3, c_f, s14))) <=> ((~m_c_h_element_v_out(c_e_h_3, c_f, s14)) | m_c_h_element_v_in1(c_e_h_3, c_f, s13) | (~node14(c_e_h_3, c_f, s13, s14)))),
% 291.61/184.10 inference(rewrite,[status(thm)],[])).
% 291.61/184.10 tff(12854,plain,
% 291.61/184.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s13, s14)) | m_c_h_element_v_in1(c_e_h_3, c_f, s13) | (~m_c_h_element_v_out(c_e_h_3, c_f, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s14)) | m_c_h_element_v_in1(c_e_h_3, c_f, s13) | (~node14(c_e_h_3, c_f, s13, s14))))),
% 291.61/184.10 inference(monotonicity,[status(thm)],[12853])).
% 291.61/184.10 tff(12855,plain,
% 291.61/184.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s13, s14)) | m_c_h_element_v_in1(c_e_h_3, c_f, s13) | (~m_c_h_element_v_out(c_e_h_3, c_f, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s14)) | m_c_h_element_v_in1(c_e_h_3, c_f, s13) | (~node14(c_e_h_3, c_f, s13, s14)))),
% 291.61/184.10 inference(transitivity,[status(thm)],[12854, 12852])).
% 291.61/184.10 tff(12856,plain,
% 291.61/184.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s13, s14)) | m_c_h_element_v_in1(c_e_h_3, c_f, s13) | (~m_c_h_element_v_out(c_e_h_3, c_f, s14)))),
% 291.61/184.10 inference(quant_inst,[status(thm)],[])).
% 291.61/184.10 tff(12857,plain,
% 291.61/184.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s14)) | m_c_h_element_v_in1(c_e_h_3, c_f, s13) | (~node14(c_e_h_3, c_f, s13, s14))),
% 291.61/184.10 inference(modus_ponens,[status(thm)],[12856, 12855])).
% 291.61/184.10 tff(12858,plain,
% 291.61/184.10 ($false),
% 291.61/184.10 inference(unit_resolution,[status(thm)],[12857, 223, 12851, 12850, 12847])).
% 291.61/184.10 tff(12859,plain,((~node14(c_e_h_3, c_f, s13, s14)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s14)) | m_c_h_element_v_in1(c_e_h_3, c_f, s13)), inference(lemma,lemma(discharge,[]))).
% 291.61/184.10 tff(12860,plain,
% 291.61/184.10 (~node14(c_e_h_3, c_f, s13, s14)),
% 291.61/184.10 inference(unit_resolution,[status(thm)],[12859, 12847, 12850])).
% 291.61/184.10 tff(12861,assumption,(node18(c_e_h_3, c_f, s13, s14)), introduced(assumption)).
% 291.61/184.10 tff(12862,plain,
% 291.61/184.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_f, s13) | (~m_c_h_element_v_out(c_e_h_3, c_f, s14)) | (~node18(c_e_h_3, c_f, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s13) | (~m_c_h_element_v_out(c_e_h_3, c_f, s14)) | (~node18(c_e_h_3, c_f, s13, s14)))),
% 291.61/184.10 inference(rewrite,[status(thm)],[])).
% 291.61/184.10 tff(12863,plain,
% 291.61/184.10 (((~m_c_h_element_v_out(c_e_h_3, c_f, s14)) | m_c_h_element_v_out(c_e_h_3, c_f, s13) | (~node18(c_e_h_3, c_f, s13, s14))) <=> (m_c_h_element_v_out(c_e_h_3, c_f, s13) | (~m_c_h_element_v_out(c_e_h_3, c_f, s14)) | (~node18(c_e_h_3, c_f, s13, s14)))),
% 291.61/184.10 inference(rewrite,[status(thm)],[])).
% 291.61/184.10 tff(12864,plain,
% 291.61/184.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s14)) | m_c_h_element_v_out(c_e_h_3, c_f, s13) | (~node18(c_e_h_3, c_f, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_f, s13) | (~m_c_h_element_v_out(c_e_h_3, c_f, s14)) | (~node18(c_e_h_3, c_f, s13, s14))))),
% 291.61/184.10 inference(monotonicity,[status(thm)],[12863])).
% 291.61/184.10 tff(12865,plain,
% 291.61/184.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s14)) | m_c_h_element_v_out(c_e_h_3, c_f, s13) | (~node18(c_e_h_3, c_f, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s13) | (~m_c_h_element_v_out(c_e_h_3, c_f, s14)) | (~node18(c_e_h_3, c_f, s13, s14)))),
% 291.61/184.10 inference(transitivity,[status(thm)],[12864, 12862])).
% 291.61/184.10 tff(12866,plain,
% 291.61/184.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s14)) | m_c_h_element_v_out(c_e_h_3, c_f, s13) | (~node18(c_e_h_3, c_f, s13, s14)))),
% 291.61/184.10 inference(quant_inst,[status(thm)],[])).
% 291.61/184.10 tff(12867,plain,
% 291.61/184.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s13) | (~m_c_h_element_v_out(c_e_h_3, c_f, s14)) | (~node18(c_e_h_3, c_f, s13, s14))),
% 291.61/184.10 inference(modus_ponens,[status(thm)],[12866, 12865])).
% 291.61/184.10 tff(12868,plain,
% 291.61/184.10 ($false),
% 291.61/184.10 inference(unit_resolution,[status(thm)],[12867, 753, 12861, 12850, 12849])).
% 291.61/184.10 tff(12869,plain,((~node18(c_e_h_3, c_f, s13, s14)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s14)) | m_c_h_element_v_out(c_e_h_3, c_f, s13)), inference(lemma,lemma(discharge,[]))).
% 291.61/184.10 tff(12870,plain,
% 291.61/184.10 (~node18(c_e_h_3, c_f, s13, s14)),
% 291.61/184.10 inference(unit_resolution,[status(thm)],[12869, 12849, 12850])).
% 291.61/184.10 tff(12871,plain,
% 291.61/184.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s13, s14)) | node19(c_e_h_3, c_f, s13, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s13, s14)) | node19(c_e_h_3, c_f, s13, s14))),
% 291.61/184.10 inference(rewrite,[status(thm)],[])).
% 291.61/184.10 tff(12872,plain,
% 291.61/184.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s13, s14)) | node19(c_e_h_3, c_f, s13, s14))),
% 291.61/184.10 inference(quant_inst,[status(thm)],[])).
% 291.61/184.10 tff(12873,plain,
% 291.61/184.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s13, s14)) | node19(c_e_h_3, c_f, s13, s14)),
% 291.61/184.10 inference(modus_ponens,[status(thm)],[12872, 12871])).
% 291.61/184.10 tff(12874,plain,
% 291.61/184.10 (node19(c_e_h_3, c_f, s13, s14)),
% 291.61/184.10 inference(unit_resolution,[status(thm)],[12873, 190, 12831])).
% 291.61/184.10 tff(12875,plain,
% 291.61/184.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_3, c_f, s13, s14) | (~node19(c_e_h_3, c_f, s13, s14)) | node17(c_e_h_3, c_f, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_3, c_f, s13, s14) | (~node19(c_e_h_3, c_f, s13, s14)) | node17(c_e_h_3, c_f, s13))),
% 291.61/184.10 inference(rewrite,[status(thm)],[])).
% 291.61/184.10 tff(12876,plain,
% 291.61/184.10 ((node17(c_e_h_3, c_f, s13) | node18(c_e_h_3, c_f, s13, s14) | (~node19(c_e_h_3, c_f, s13, s14))) <=> (node18(c_e_h_3, c_f, s13, s14) | (~node19(c_e_h_3, c_f, s13, s14)) | node17(c_e_h_3, c_f, s13))),
% 291.61/184.11 inference(rewrite,[status(thm)],[])).
% 291.61/184.11 tff(12877,plain,
% 291.61/184.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s13) | node18(c_e_h_3, c_f, s13, s14) | (~node19(c_e_h_3, c_f, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_3, c_f, s13, s14) | (~node19(c_e_h_3, c_f, s13, s14)) | node17(c_e_h_3, c_f, s13)))),
% 291.61/184.11 inference(monotonicity,[status(thm)],[12876])).
% 291.61/184.11 tff(12878,plain,
% 291.61/184.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s13) | node18(c_e_h_3, c_f, s13, s14) | (~node19(c_e_h_3, c_f, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_3, c_f, s13, s14) | (~node19(c_e_h_3, c_f, s13, s14)) | node17(c_e_h_3, c_f, s13))),
% 291.61/184.11 inference(transitivity,[status(thm)],[12877, 12875])).
% 291.61/184.11 tff(12879,plain,
% 291.61/184.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s13) | node18(c_e_h_3, c_f, s13, s14) | (~node19(c_e_h_3, c_f, s13, s14)))),
% 291.61/184.11 inference(quant_inst,[status(thm)],[])).
% 291.61/184.11 tff(12880,plain,
% 291.61/184.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_3, c_f, s13, s14) | (~node19(c_e_h_3, c_f, s13, s14)) | node17(c_e_h_3, c_f, s13)),
% 291.61/184.11 inference(modus_ponens,[status(thm)],[12879, 12878])).
% 291.61/184.11 tff(12881,plain,
% 291.61/184.11 (node18(c_e_h_3, c_f, s13, s14) | node17(c_e_h_3, c_f, s13)),
% 291.61/184.11 inference(unit_resolution,[status(thm)],[12880, 776, 12874])).
% 291.61/184.11 tff(12882,plain,
% 291.61/184.11 (node17(c_e_h_3, c_f, s13)),
% 291.61/184.11 inference(unit_resolution,[status(thm)],[12881, 12870])).
% 291.61/184.11 tff(12883,plain,
% 291.61/184.11 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s13)) | m_c_h_element_v_in1(c_e_h_3, c_f, s13) | (~node17(c_e_h_3, c_f, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s13)) | m_c_h_element_v_in1(c_e_h_3, c_f, s13) | (~node17(c_e_h_3, c_f, s13)))),
% 291.61/184.11 inference(rewrite,[status(thm)],[])).
% 291.61/184.11 tff(12884,plain,
% 291.61/184.11 ((m_c_h_element_v_in1(c_e_h_3, c_f, s13) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s13)) | (~node17(c_e_h_3, c_f, s13))) <=> ((~m_c_h_element_v_in2(c_e_h_3, c_f, s13)) | m_c_h_element_v_in1(c_e_h_3, c_f, s13) | (~node17(c_e_h_3, c_f, s13)))),
% 291.61/184.11 inference(rewrite,[status(thm)],[])).
% 291.61/184.11 tff(12885,plain,
% 291.61/184.11 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s13) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s13)) | (~node17(c_e_h_3, c_f, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s13)) | m_c_h_element_v_in1(c_e_h_3, c_f, s13) | (~node17(c_e_h_3, c_f, s13))))),
% 291.61/184.11 inference(monotonicity,[status(thm)],[12884])).
% 291.61/184.11 tff(12886,plain,
% 291.61/184.11 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s13) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s13)) | (~node17(c_e_h_3, c_f, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s13)) | m_c_h_element_v_in1(c_e_h_3, c_f, s13) | (~node17(c_e_h_3, c_f, s13)))),
% 291.61/184.11 inference(transitivity,[status(thm)],[12885, 12883])).
% 291.61/184.11 tff(12887,plain,
% 291.61/184.11 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s13) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s13)) | (~node17(c_e_h_3, c_f, s13)))),
% 291.61/184.11 inference(quant_inst,[status(thm)],[])).
% 291.61/184.11 tff(12888,plain,
% 291.61/184.11 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s13)) | m_c_h_element_v_in1(c_e_h_3, c_f, s13) | (~node17(c_e_h_3, c_f, s13))),
% 291.61/184.11 inference(modus_ponens,[status(thm)],[12887, 12886])).
% 291.61/184.11 tff(12889,plain,
% 291.61/184.11 (~m_c_h_element_v_in2(c_e_h_3, c_f, s13)),
% 291.61/184.11 inference(unit_resolution,[status(thm)],[12888, 859, 12882, 12847])).
% 291.61/184.11 tff(12890,plain,
% 291.61/184.11 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s13)) | m_c_h_element_v_in1(c_e_h_3, c_f, s13) | m_c_h_element_v_in2(c_e_h_3, c_f, s13))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s13)) | m_c_h_element_v_in1(c_e_h_3, c_f, s13) | m_c_h_element_v_in2(c_e_h_3, c_f, s13))),
% 291.61/184.11 inference(rewrite,[status(thm)],[])).
% 291.61/184.11 tff(12891,plain,
% 291.61/184.11 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s13)) | m_c_h_element_v_in1(c_e_h_3, c_f, s13) | m_c_h_element_v_in2(c_e_h_3, c_f, s13))),
% 291.61/184.11 inference(quant_inst,[status(thm)],[])).
% 291.61/184.11 tff(12892,plain,
% 291.61/184.11 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s13)) | m_c_h_element_v_in1(c_e_h_3, c_f, s13) | m_c_h_element_v_in2(c_e_h_3, c_f, s13)),
% 291.61/184.11 inference(modus_ponens,[status(thm)],[12891, 12890])).
% 291.61/184.11 tff(12893,plain,
% 291.61/184.11 (~node16(c_e_h_3, c_f, s13)),
% 291.61/184.11 inference(unit_resolution,[status(thm)],[12892, 178, 12847, 12889])).
% 291.61/184.11 tff(12894,plain,
% 291.61/184.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_f, s13, s14)) | node14(c_e_h_3, c_f, s13, s14) | node15(c_e_h_3, c_f, s13, s14) | node16(c_e_h_3, c_f, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s13, s14)) | node14(c_e_h_3, c_f, s13, s14) | node15(c_e_h_3, c_f, s13, s14) | node16(c_e_h_3, c_f, s13))),
% 291.61/184.11 inference(rewrite,[status(thm)],[])).
% 291.61/184.11 tff(12895,plain,
% 291.61/184.11 ((node16(c_e_h_3, c_f, s13) | node14(c_e_h_3, c_f, s13, s14) | node15(c_e_h_3, c_f, s13, s14) | (~node19(c_e_h_3, c_f, s13, s14))) <=> ((~node19(c_e_h_3, c_f, s13, s14)) | node14(c_e_h_3, c_f, s13, s14) | node15(c_e_h_3, c_f, s13, s14) | node16(c_e_h_3, c_f, s13))),
% 291.61/184.11 inference(rewrite,[status(thm)],[])).
% 291.61/184.11 tff(12896,plain,
% 291.61/184.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s13) | node14(c_e_h_3, c_f, s13, s14) | node15(c_e_h_3, c_f, s13, s14) | (~node19(c_e_h_3, c_f, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_f, s13, s14)) | node14(c_e_h_3, c_f, s13, s14) | node15(c_e_h_3, c_f, s13, s14) | node16(c_e_h_3, c_f, s13)))),
% 291.61/184.11 inference(monotonicity,[status(thm)],[12895])).
% 291.61/184.11 tff(12897,plain,
% 291.61/184.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s13) | node14(c_e_h_3, c_f, s13, s14) | node15(c_e_h_3, c_f, s13, s14) | (~node19(c_e_h_3, c_f, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s13, s14)) | node14(c_e_h_3, c_f, s13, s14) | node15(c_e_h_3, c_f, s13, s14) | node16(c_e_h_3, c_f, s13))),
% 291.61/184.11 inference(transitivity,[status(thm)],[12896, 12894])).
% 291.61/184.11 tff(12898,plain,
% 291.61/184.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s13) | node14(c_e_h_3, c_f, s13, s14) | node15(c_e_h_3, c_f, s13, s14) | (~node19(c_e_h_3, c_f, s13, s14)))),
% 291.61/184.11 inference(quant_inst,[status(thm)],[])).
% 291.61/184.11 tff(12899,plain,
% 291.61/184.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s13, s14)) | node14(c_e_h_3, c_f, s13, s14) | node15(c_e_h_3, c_f, s13, s14) | node16(c_e_h_3, c_f, s13)),
% 291.61/184.11 inference(modus_ponens,[status(thm)],[12898, 12897])).
% 291.61/184.11 tff(12900,plain,
% 291.61/184.11 (node14(c_e_h_3, c_f, s13, s14) | node15(c_e_h_3, c_f, s13, s14) | node16(c_e_h_3, c_f, s13)),
% 291.61/184.11 inference(unit_resolution,[status(thm)],[12899, 204, 12874])).
% 291.61/184.11 tff(12901,plain,
% 291.61/184.11 (node15(c_e_h_3, c_f, s13, s14)),
% 291.61/184.11 inference(unit_resolution,[status(thm)],[12900, 12893, 12860])).
% 291.61/184.11 tff(12902,plain,
% 291.61/184.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s14)) | (~node15(c_e_h_3, c_f, s13, s14)) | m_c_h_element_v_out(c_e_h_3, c_f, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s14)) | (~node15(c_e_h_3, c_f, s13, s14)) | m_c_h_element_v_out(c_e_h_3, c_f, s13))),
% 291.61/184.11 inference(rewrite,[status(thm)],[])).
% 291.61/184.11 tff(12903,plain,
% 291.61/184.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s14)) | (~node15(c_e_h_3, c_f, s13, s14)) | m_c_h_element_v_out(c_e_h_3, c_f, s13))),
% 291.61/184.11 inference(quant_inst,[status(thm)],[])).
% 291.61/184.11 tff(12904,plain,
% 291.61/184.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s14)) | (~node15(c_e_h_3, c_f, s13, s14)) | m_c_h_element_v_out(c_e_h_3, c_f, s13)),
% 291.61/184.12 inference(modus_ponens,[status(thm)],[12903, 12902])).
% 291.61/184.12 tff(12905,plain,
% 291.61/184.12 ($false),
% 291.61/184.12 inference(unit_resolution,[status(thm)],[12904, 147, 12901, 12850, 12849])).
% 291.61/184.12 tff(12906,plain,(m_c_h_element_v_out(c_e_h_3, c_f, s13) | (~m_c_h_element_v_out(c_e_h_3, c_f, s14)) | m_c_h_element_v_in1(c_e_h_3, c_f, s13)), inference(lemma,lemma(discharge,[]))).
% 291.61/184.12 tff(12907,plain,
% 291.61/184.12 (~m_c_h_element_v_out(c_e_h_3, c_f, s14)),
% 291.61/184.12 inference(unit_resolution,[status(thm)],[12906, 12847, 12848])).
% 291.61/184.12 tff(12908,assumption,(m_c_h_element_v_out(c_e_h_3, c_f, s15)), introduced(assumption)).
% 291.61/184.12 tff(12909,assumption,(~m_c_h_element_v_out(c_e_h_3, c_f, s14)), introduced(assumption)).
% 291.61/184.12 tff(12910,assumption,(node18(c_e_h_3, c_f, s14, s15)), introduced(assumption)).
% 291.61/184.12 tff(12911,plain,
% 291.61/184.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_f, s14) | (~node18(c_e_h_3, c_f, s14, s15)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s14) | (~node18(c_e_h_3, c_f, s14, s15)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s15)))),
% 291.61/184.12 inference(rewrite,[status(thm)],[])).
% 291.61/184.12 tff(12912,plain,
% 291.61/184.12 (((~m_c_h_element_v_out(c_e_h_3, c_f, s15)) | m_c_h_element_v_out(c_e_h_3, c_f, s14) | (~node18(c_e_h_3, c_f, s14, s15))) <=> (m_c_h_element_v_out(c_e_h_3, c_f, s14) | (~node18(c_e_h_3, c_f, s14, s15)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s15)))),
% 291.61/184.12 inference(rewrite,[status(thm)],[])).
% 291.61/184.12 tff(12913,plain,
% 291.61/184.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s15)) | m_c_h_element_v_out(c_e_h_3, c_f, s14) | (~node18(c_e_h_3, c_f, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_f, s14) | (~node18(c_e_h_3, c_f, s14, s15)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s15))))),
% 291.61/184.12 inference(monotonicity,[status(thm)],[12912])).
% 291.61/184.12 tff(12914,plain,
% 291.61/184.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s15)) | m_c_h_element_v_out(c_e_h_3, c_f, s14) | (~node18(c_e_h_3, c_f, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s14) | (~node18(c_e_h_3, c_f, s14, s15)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s15)))),
% 291.61/184.12 inference(transitivity,[status(thm)],[12913, 12911])).
% 291.61/184.12 tff(12915,plain,
% 291.61/184.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s15)) | m_c_h_element_v_out(c_e_h_3, c_f, s14) | (~node18(c_e_h_3, c_f, s14, s15)))),
% 291.61/184.12 inference(quant_inst,[status(thm)],[])).
% 291.61/184.12 tff(12916,plain,
% 291.61/184.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s14) | (~node18(c_e_h_3, c_f, s14, s15)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s15))),
% 291.61/184.12 inference(modus_ponens,[status(thm)],[12915, 12914])).
% 291.61/184.12 tff(12917,plain,
% 291.61/184.12 ($false),
% 291.61/184.12 inference(unit_resolution,[status(thm)],[12916, 753, 12910, 12909, 12908])).
% 291.61/184.12 tff(12918,plain,((~node18(c_e_h_3, c_f, s14, s15)) | m_c_h_element_v_out(c_e_h_3, c_f, s14) | (~m_c_h_element_v_out(c_e_h_3, c_f, s15))), inference(lemma,lemma(discharge,[]))).
% 291.61/184.12 tff(12919,plain,
% 291.61/184.12 (~node18(c_e_h_3, c_f, s14, s15)),
% 291.61/184.12 inference(unit_resolution,[status(thm)],[12918, 12909, 12908])).
% 291.61/184.12 tff(12920,plain,
% 291.61/184.12 (succ(s14, s15) <=> succ(s14, s15)),
% 291.61/184.12 inference(rewrite,[status(thm)],[])).
% 291.61/184.12 tff(12921,axiom,(succ(s14, s15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound15')).
% 291.61/184.12 tff(12922,plain,
% 291.61/184.12 (succ(s14, s15)),
% 291.61/184.12 inference(modus_ponens,[status(thm)],[12921, 12920])).
% 291.61/184.12 tff(12923,plain,
% 291.61/184.12 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s14, s15)) | trans(s14, s15))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s14, s15)) | trans(s14, s15))),
% 291.61/184.12 inference(rewrite,[status(thm)],[])).
% 291.61/184.12 tff(12924,plain,
% 291.61/184.12 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s14, s15)) | trans(s14, s15))),
% 291.61/184.12 inference(quant_inst,[status(thm)],[])).
% 291.61/184.12 tff(12925,plain,
% 291.61/184.12 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s14, s15)) | trans(s14, s15)),
% 291.61/184.12 inference(modus_ponens,[status(thm)],[12924, 12923])).
% 291.61/184.12 tff(12926,plain,
% 291.61/184.12 (trans(s14, s15)),
% 291.61/184.12 inference(unit_resolution,[status(thm)],[12925, 12922, 65])).
% 291.61/184.12 tff(12927,plain,
% 291.61/184.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s14, s15)) | node19(c_e_h_3, c_f, s14, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s14, s15)) | node19(c_e_h_3, c_f, s14, s15))),
% 291.61/184.12 inference(rewrite,[status(thm)],[])).
% 291.61/184.12 tff(12928,plain,
% 291.61/184.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s14, s15)) | node19(c_e_h_3, c_f, s14, s15))),
% 291.61/184.12 inference(quant_inst,[status(thm)],[])).
% 291.61/184.12 tff(12929,plain,
% 291.61/184.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s14, s15)) | node19(c_e_h_3, c_f, s14, s15)),
% 291.61/184.12 inference(modus_ponens,[status(thm)],[12928, 12927])).
% 291.61/184.12 tff(12930,plain,
% 291.61/184.12 (node19(c_e_h_3, c_f, s14, s15)),
% 291.61/184.12 inference(unit_resolution,[status(thm)],[12929, 190, 12926])).
% 291.61/184.12 tff(12931,plain,
% 291.61/184.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_f, s14, s15)) | node18(c_e_h_3, c_f, s14, s15) | node17(c_e_h_3, c_f, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s14, s15)) | node18(c_e_h_3, c_f, s14, s15) | node17(c_e_h_3, c_f, s14))),
% 291.61/184.12 inference(rewrite,[status(thm)],[])).
% 291.61/184.12 tff(12932,plain,
% 291.61/184.12 ((node17(c_e_h_3, c_f, s14) | node18(c_e_h_3, c_f, s14, s15) | (~node19(c_e_h_3, c_f, s14, s15))) <=> ((~node19(c_e_h_3, c_f, s14, s15)) | node18(c_e_h_3, c_f, s14, s15) | node17(c_e_h_3, c_f, s14))),
% 291.61/184.12 inference(rewrite,[status(thm)],[])).
% 291.61/184.12 tff(12933,plain,
% 291.61/184.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s14) | node18(c_e_h_3, c_f, s14, s15) | (~node19(c_e_h_3, c_f, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_f, s14, s15)) | node18(c_e_h_3, c_f, s14, s15) | node17(c_e_h_3, c_f, s14)))),
% 291.61/184.12 inference(monotonicity,[status(thm)],[12932])).
% 291.61/184.12 tff(12934,plain,
% 291.61/184.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s14) | node18(c_e_h_3, c_f, s14, s15) | (~node19(c_e_h_3, c_f, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s14, s15)) | node18(c_e_h_3, c_f, s14, s15) | node17(c_e_h_3, c_f, s14))),
% 291.61/184.12 inference(transitivity,[status(thm)],[12933, 12931])).
% 291.61/184.12 tff(12935,plain,
% 291.61/184.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s14) | node18(c_e_h_3, c_f, s14, s15) | (~node19(c_e_h_3, c_f, s14, s15)))),
% 291.61/184.12 inference(quant_inst,[status(thm)],[])).
% 291.61/184.12 tff(12936,plain,
% 291.61/184.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_f, s14, s15)) | node18(c_e_h_3, c_f, s14, s15) | node17(c_e_h_3, c_f, s14)),
% 291.61/184.12 inference(modus_ponens,[status(thm)],[12935, 12934])).
% 291.61/184.12 tff(12937,plain,
% 291.61/184.12 (node18(c_e_h_3, c_f, s14, s15) | node17(c_e_h_3, c_f, s14)),
% 291.61/184.12 inference(unit_resolution,[status(thm)],[12936, 776, 12930])).
% 291.61/184.12 tff(12938,plain,
% 291.61/184.12 (node17(c_e_h_3, c_f, s14)),
% 291.61/184.12 inference(unit_resolution,[status(thm)],[12937, 12919])).
% 291.61/184.12 tff(12939,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_f, s14)), introduced(assumption)).
% 291.61/184.12 tff(12940,assumption,(~node14(c_e_h_3, c_f, s14, s15)), introduced(assumption)).
% 291.61/184.12 tff(12941,assumption,(node15(c_e_h_3, c_f, s14, s15)), introduced(assumption)).
% 291.61/184.12 tff(12942,plain,
% 291.61/184.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s15)) | (~node15(c_e_h_3, c_f, s14, s15)) | m_c_h_element_v_out(c_e_h_3, c_f, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s15)) | (~node15(c_e_h_3, c_f, s14, s15)) | m_c_h_element_v_out(c_e_h_3, c_f, s14))),
% 291.61/184.12 inference(rewrite,[status(thm)],[])).
% 291.61/184.12 tff(12943,plain,
% 291.61/184.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s15)) | (~node15(c_e_h_3, c_f, s14, s15)) | m_c_h_element_v_out(c_e_h_3, c_f, s14))),
% 291.61/184.12 inference(quant_inst,[status(thm)],[])).
% 291.61/184.12 tff(12944,plain,
% 291.61/184.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s15)) | (~node15(c_e_h_3, c_f, s14, s15)) | m_c_h_element_v_out(c_e_h_3, c_f, s14)),
% 291.61/184.12 inference(modus_ponens,[status(thm)],[12943, 12942])).
% 291.61/184.12 tff(12945,plain,
% 291.61/184.12 ($false),
% 291.61/184.12 inference(unit_resolution,[status(thm)],[12944, 147, 12941, 12909, 12908])).
% 291.61/184.12 tff(12946,plain,((~node15(c_e_h_3, c_f, s14, s15)) | m_c_h_element_v_out(c_e_h_3, c_f, s14) | (~m_c_h_element_v_out(c_e_h_3, c_f, s15))), inference(lemma,lemma(discharge,[]))).
% 291.61/184.12 tff(12947,plain,
% 291.61/184.12 (~node15(c_e_h_3, c_f, s14, s15)),
% 291.61/184.12 inference(unit_resolution,[status(thm)],[12946, 12908, 12909])).
% 291.61/184.13 tff(12948,plain,
% 291.61/184.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_3, c_f, s14, s15) | node15(c_e_h_3, c_f, s14, s15) | node16(c_e_h_3, c_f, s14) | (~node19(c_e_h_3, c_f, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_f, s14, s15) | node15(c_e_h_3, c_f, s14, s15) | node16(c_e_h_3, c_f, s14) | (~node19(c_e_h_3, c_f, s14, s15)))),
% 291.61/184.13 inference(rewrite,[status(thm)],[])).
% 291.61/184.13 tff(12949,plain,
% 291.61/184.13 ((node16(c_e_h_3, c_f, s14) | node14(c_e_h_3, c_f, s14, s15) | node15(c_e_h_3, c_f, s14, s15) | (~node19(c_e_h_3, c_f, s14, s15))) <=> (node14(c_e_h_3, c_f, s14, s15) | node15(c_e_h_3, c_f, s14, s15) | node16(c_e_h_3, c_f, s14) | (~node19(c_e_h_3, c_f, s14, s15)))),
% 291.61/184.13 inference(rewrite,[status(thm)],[])).
% 291.61/184.13 tff(12950,plain,
% 291.61/184.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s14) | node14(c_e_h_3, c_f, s14, s15) | node15(c_e_h_3, c_f, s14, s15) | (~node19(c_e_h_3, c_f, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_3, c_f, s14, s15) | node15(c_e_h_3, c_f, s14, s15) | node16(c_e_h_3, c_f, s14) | (~node19(c_e_h_3, c_f, s14, s15))))),
% 291.61/184.13 inference(monotonicity,[status(thm)],[12949])).
% 291.61/184.13 tff(12951,plain,
% 291.61/184.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s14) | node14(c_e_h_3, c_f, s14, s15) | node15(c_e_h_3, c_f, s14, s15) | (~node19(c_e_h_3, c_f, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_f, s14, s15) | node15(c_e_h_3, c_f, s14, s15) | node16(c_e_h_3, c_f, s14) | (~node19(c_e_h_3, c_f, s14, s15)))),
% 291.61/184.13 inference(transitivity,[status(thm)],[12950, 12948])).
% 291.61/184.13 tff(12952,plain,
% 291.61/184.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s14) | node14(c_e_h_3, c_f, s14, s15) | node15(c_e_h_3, c_f, s14, s15) | (~node19(c_e_h_3, c_f, s14, s15)))),
% 291.61/184.13 inference(quant_inst,[status(thm)],[])).
% 291.61/184.13 tff(12953,plain,
% 291.61/184.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_3, c_f, s14, s15) | node15(c_e_h_3, c_f, s14, s15) | node16(c_e_h_3, c_f, s14) | (~node19(c_e_h_3, c_f, s14, s15))),
% 291.61/184.13 inference(modus_ponens,[status(thm)],[12952, 12951])).
% 291.61/184.13 tff(12954,plain,
% 291.61/184.13 (node14(c_e_h_3, c_f, s14, s15) | node15(c_e_h_3, c_f, s14, s15) | node16(c_e_h_3, c_f, s14)),
% 291.61/184.13 inference(unit_resolution,[status(thm)],[12953, 204, 12930])).
% 291.61/184.13 tff(12955,plain,
% 291.61/184.13 (node16(c_e_h_3, c_f, s14)),
% 291.61/184.13 inference(unit_resolution,[status(thm)],[12954, 12947, 12940])).
% 291.61/184.13 tff(12956,plain,
% 291.61/184.13 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s14)) | m_c_h_element_v_in1(c_e_h_3, c_f, s14) | m_c_h_element_v_in2(c_e_h_3, c_f, s14))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s14)) | m_c_h_element_v_in1(c_e_h_3, c_f, s14) | m_c_h_element_v_in2(c_e_h_3, c_f, s14))),
% 291.61/184.13 inference(rewrite,[status(thm)],[])).
% 291.61/184.13 tff(12957,plain,
% 291.61/184.13 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s14)) | m_c_h_element_v_in1(c_e_h_3, c_f, s14) | m_c_h_element_v_in2(c_e_h_3, c_f, s14))),
% 291.61/184.13 inference(quant_inst,[status(thm)],[])).
% 291.61/184.13 tff(12958,plain,
% 291.61/184.13 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s14)) | m_c_h_element_v_in1(c_e_h_3, c_f, s14) | m_c_h_element_v_in2(c_e_h_3, c_f, s14)),
% 291.61/184.13 inference(modus_ponens,[status(thm)],[12957, 12956])).
% 291.61/184.13 tff(12959,plain,
% 291.61/184.13 ((~node16(c_e_h_3, c_f, s14)) | m_c_h_element_v_in1(c_e_h_3, c_f, s14)),
% 291.61/184.13 inference(unit_resolution,[status(thm)],[12958, 178, 12939])).
% 291.61/184.13 tff(12960,plain,
% 291.61/184.13 (m_c_h_element_v_in1(c_e_h_3, c_f, s14)),
% 291.61/184.13 inference(unit_resolution,[status(thm)],[12959, 12955])).
% 291.61/184.13 tff(12961,plain,
% 291.61/184.13 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_f, s14)) | m_c_h_element_v_in2(c_e_h_3, c_f, s14) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s14)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_f, s14)) | m_c_h_element_v_in2(c_e_h_3, c_f, s14) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s14)))),
% 291.61/184.13 inference(rewrite,[status(thm)],[])).
% 291.61/184.13 tff(12962,plain,
% 291.61/184.13 (((~m_c_h_element_v_in1(c_e_h_3, c_f, s14)) | m_c_h_element_v_in2(c_e_h_3, c_f, s14) | (~node17(c_e_h_3, c_f, s14))) <=> ((~node17(c_e_h_3, c_f, s14)) | m_c_h_element_v_in2(c_e_h_3, c_f, s14) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s14)))),
% 291.61/184.13 inference(rewrite,[status(thm)],[])).
% 291.61/184.13 tff(12963,plain,
% 291.61/184.13 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s14)) | m_c_h_element_v_in2(c_e_h_3, c_f, s14) | (~node17(c_e_h_3, c_f, s14)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_f, s14)) | m_c_h_element_v_in2(c_e_h_3, c_f, s14) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s14))))),
% 291.61/184.13 inference(monotonicity,[status(thm)],[12962])).
% 291.61/184.13 tff(12964,plain,
% 291.61/184.13 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s14)) | m_c_h_element_v_in2(c_e_h_3, c_f, s14) | (~node17(c_e_h_3, c_f, s14)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_f, s14)) | m_c_h_element_v_in2(c_e_h_3, c_f, s14) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s14)))),
% 291.61/184.13 inference(transitivity,[status(thm)],[12963, 12961])).
% 291.61/184.13 tff(12965,plain,
% 291.61/184.13 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s14)) | m_c_h_element_v_in2(c_e_h_3, c_f, s14) | (~node17(c_e_h_3, c_f, s14)))),
% 291.61/184.13 inference(quant_inst,[status(thm)],[])).
% 291.61/184.13 tff(12966,plain,
% 291.61/184.13 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_f, s14)) | m_c_h_element_v_in2(c_e_h_3, c_f, s14) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s14))),
% 291.61/184.13 inference(modus_ponens,[status(thm)],[12965, 12964])).
% 291.61/184.13 tff(12967,plain,
% 291.61/184.13 ((~node17(c_e_h_3, c_f, s14)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s14))),
% 291.61/184.13 inference(unit_resolution,[status(thm)],[12966, 919, 12939])).
% 291.61/184.13 tff(12968,plain,
% 291.61/184.13 (~node17(c_e_h_3, c_f, s14)),
% 291.61/184.13 inference(unit_resolution,[status(thm)],[12967, 12960])).
% 291.61/184.13 tff(12969,plain,
% 291.61/184.13 (node18(c_e_h_3, c_f, s14, s15)),
% 291.61/184.13 inference(unit_resolution,[status(thm)],[12937, 12968])).
% 291.61/184.13 tff(12970,plain,
% 291.61/184.13 ($false),
% 291.61/184.13 inference(unit_resolution,[status(thm)],[12916, 753, 12969, 12909, 12908])).
% 291.61/184.13 tff(12971,plain,((~m_c_h_element_v_out(c_e_h_3, c_f, s15)) | m_c_h_element_v_out(c_e_h_3, c_f, s14) | m_c_h_element_v_in2(c_e_h_3, c_f, s14) | node14(c_e_h_3, c_f, s14, s15)), inference(lemma,lemma(discharge,[]))).
% 291.61/184.13 tff(12972,plain,
% 291.61/184.13 (node14(c_e_h_3, c_f, s14, s15)),
% 291.61/184.13 inference(unit_resolution,[status(thm)],[12971, 12909, 12908, 12939])).
% 291.61/184.13 tff(12973,assumption,(node14(c_e_h_3, c_f, s14, s15)), introduced(assumption)).
% 291.61/184.13 tff(12974,plain,
% 291.61/184.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s14) | (~node14(c_e_h_3, c_f, s14, s15)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_f, s14) | (~node14(c_e_h_3, c_f, s14, s15)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s15)))),
% 291.61/184.13 inference(rewrite,[status(thm)],[])).
% 291.61/184.13 tff(12975,plain,
% 291.61/184.13 (((~node14(c_e_h_3, c_f, s14, s15)) | m_c_h_element_v_in1(c_e_h_3, c_f, s14) | (~m_c_h_element_v_out(c_e_h_3, c_f, s15))) <=> (m_c_h_element_v_in1(c_e_h_3, c_f, s14) | (~node14(c_e_h_3, c_f, s14, s15)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s15)))),
% 291.61/184.13 inference(rewrite,[status(thm)],[])).
% 291.61/184.13 tff(12976,plain,
% 291.61/184.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s14, s15)) | m_c_h_element_v_in1(c_e_h_3, c_f, s14) | (~m_c_h_element_v_out(c_e_h_3, c_f, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s14) | (~node14(c_e_h_3, c_f, s14, s15)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s15))))),
% 291.61/184.13 inference(monotonicity,[status(thm)],[12975])).
% 291.61/184.13 tff(12977,plain,
% 291.61/184.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s14, s15)) | m_c_h_element_v_in1(c_e_h_3, c_f, s14) | (~m_c_h_element_v_out(c_e_h_3, c_f, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_f, s14) | (~node14(c_e_h_3, c_f, s14, s15)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s15)))),
% 291.61/184.13 inference(transitivity,[status(thm)],[12976, 12974])).
% 291.61/184.13 tff(12978,plain,
% 291.61/184.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s14, s15)) | m_c_h_element_v_in1(c_e_h_3, c_f, s14) | (~m_c_h_element_v_out(c_e_h_3, c_f, s15)))),
% 291.61/184.13 inference(quant_inst,[status(thm)],[])).
% 291.61/184.13 tff(12979,plain,
% 291.61/184.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_f, s14) | (~node14(c_e_h_3, c_f, s14, s15)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s15))),
% 291.61/184.13 inference(modus_ponens,[status(thm)],[12978, 12977])).
% 291.61/184.13 tff(12980,plain,
% 291.61/184.13 ($false),
% 291.61/184.13 inference(unit_resolution,[status(thm)],[12979, 223, 12973, 12841, 12908])).
% 291.61/184.13 tff(12981,plain,((~node14(c_e_h_3, c_f, s14, s15)) | m_c_h_element_v_in1(c_e_h_3, c_f, s14) | (~m_c_h_element_v_out(c_e_h_3, c_f, s15))), inference(lemma,lemma(discharge,[]))).
% 291.61/184.13 tff(12982,plain,
% 291.61/184.13 (m_c_h_element_v_in1(c_e_h_3, c_f, s14)),
% 291.61/184.13 inference(unit_resolution,[status(thm)],[12981, 12972, 12908])).
% 291.61/184.13 tff(12983,plain,
% 291.61/184.13 ($false),
% 291.61/184.13 inference(unit_resolution,[status(thm)],[12967, 12982, 12938])).
% 291.61/184.13 tff(12984,plain,(m_c_h_element_v_out(c_e_h_3, c_f, s14) | m_c_h_element_v_in2(c_e_h_3, c_f, s14) | (~m_c_h_element_v_out(c_e_h_3, c_f, s15))), inference(lemma,lemma(discharge,[]))).
% 291.61/184.13 tff(12985,plain,
% 291.61/184.13 (m_c_h_element_v_in2(c_e_h_3, c_f, s14)),
% 291.61/184.13 inference(unit_resolution,[status(thm)],[12984, 12909, 12908])).
% 291.61/184.13 tff(12986,plain,
% 291.61/184.13 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s14) | (~node17(c_e_h_3, c_f, s14)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s14)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_3, c_f, s14) | (~node17(c_e_h_3, c_f, s14)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s14)))),
% 291.61/184.13 inference(rewrite,[status(thm)],[])).
% 291.61/184.14 tff(12987,plain,
% 291.61/184.14 ((m_c_h_element_v_in1(c_e_h_3, c_f, s14) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s14)) | (~node17(c_e_h_3, c_f, s14))) <=> (m_c_h_element_v_in1(c_e_h_3, c_f, s14) | (~node17(c_e_h_3, c_f, s14)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s14)))),
% 291.61/184.14 inference(rewrite,[status(thm)],[])).
% 291.61/184.14 tff(12988,plain,
% 291.61/184.14 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s14) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s14)) | (~node17(c_e_h_3, c_f, s14)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s14) | (~node17(c_e_h_3, c_f, s14)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s14))))),
% 291.61/184.14 inference(monotonicity,[status(thm)],[12987])).
% 291.61/184.14 tff(12989,plain,
% 291.61/184.14 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s14) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s14)) | (~node17(c_e_h_3, c_f, s14)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_3, c_f, s14) | (~node17(c_e_h_3, c_f, s14)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s14)))),
% 291.61/184.14 inference(transitivity,[status(thm)],[12988, 12986])).
% 291.61/184.14 tff(12990,plain,
% 291.61/184.14 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s14) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s14)) | (~node17(c_e_h_3, c_f, s14)))),
% 291.61/184.14 inference(quant_inst,[status(thm)],[])).
% 291.61/184.14 tff(12991,plain,
% 291.61/184.14 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_3, c_f, s14) | (~node17(c_e_h_3, c_f, s14)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s14))),
% 291.61/184.14 inference(modus_ponens,[status(thm)],[12990, 12989])).
% 291.61/184.14 tff(12992,plain,
% 291.61/184.14 ((~node17(c_e_h_3, c_f, s14)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s14))),
% 291.61/184.14 inference(unit_resolution,[status(thm)],[12991, 859, 12841])).
% 291.61/184.14 tff(12993,plain,
% 291.61/184.14 ($false),
% 291.61/184.14 inference(unit_resolution,[status(thm)],[12992, 12938, 12985])).
% 291.61/184.14 tff(12994,plain,(m_c_h_element_v_out(c_e_h_3, c_f, s14) | m_c_h_element_v_in1(c_e_h_3, c_f, s14) | (~m_c_h_element_v_out(c_e_h_3, c_f, s15))), inference(lemma,lemma(discharge,[]))).
% 291.61/184.14 tff(12995,plain,
% 291.61/184.14 (~m_c_h_element_v_out(c_e_h_3, c_f, s15)),
% 291.61/184.14 inference(unit_resolution,[status(thm)],[12994, 12907, 12841])).
% 291.61/184.14 tff(12996,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s15)), introduced(assumption)).
% 291.61/184.14 tff(12997,assumption,(~m_c_h_element_v_out(c_e_h_3, c_f, s15)), introduced(assumption)).
% 291.61/184.14 tff(12998,plain,
% 291.61/184.14 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s15) | m_c_h_element_v_out(c_e_h_3, c_f, s15))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s15) | m_c_h_element_v_out(c_e_h_3, c_f, s15))),
% 291.61/184.14 inference(rewrite,[status(thm)],[])).
% 291.61/184.14 tff(12999,plain,
% 291.61/184.14 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s15) | m_c_h_element_v_out(c_e_h_3, c_f, s15))),
% 291.61/184.14 inference(quant_inst,[status(thm)],[])).
% 291.61/184.14 tff(13000,plain,
% 291.61/184.14 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s15) | m_c_h_element_v_out(c_e_h_3, c_f, s15)),
% 291.61/184.14 inference(modus_ponens,[status(thm)],[12999, 12998])).
% 291.61/184.14 tff(13001,plain,
% 291.61/184.14 ($false),
% 291.61/184.14 inference(unit_resolution,[status(thm)],[13000, 5689, 12997, 12996])).
% 291.61/184.14 tff(13002,plain,(m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s15) | m_c_h_element_v_out(c_e_h_3, c_f, s15)), inference(lemma,lemma(discharge,[]))).
% 291.61/184.14 tff(13003,plain,
% 291.61/184.14 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s15)),
% 291.61/184.14 inference(unit_resolution,[status(thm)],[13002, 12995])).
% 291.61/184.14 tff(13004,plain,
% 291.61/184.14 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s10) | m_c_h_element_v_out(c_e_h_3, c_f, s10))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s10) | m_c_h_element_v_out(c_e_h_3, c_f, s10))),
% 291.61/184.14 inference(rewrite,[status(thm)],[])).
% 291.61/184.14 tff(13005,plain,
% 291.61/184.14 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s10) | m_c_h_element_v_out(c_e_h_3, c_f, s10))),
% 291.61/184.14 inference(quant_inst,[status(thm)],[])).
% 291.61/184.14 tff(13006,plain,
% 291.61/184.14 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s10) | m_c_h_element_v_out(c_e_h_3, c_f, s10)),
% 291.61/184.14 inference(modus_ponens,[status(thm)],[13005, 13004])).
% 291.61/184.14 tff(13007,plain,
% 291.61/184.14 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s10) | m_c_h_element_v_out(c_e_h_3, c_f, s10)),
% 291.61/184.14 inference(unit_resolution,[status(thm)],[13006, 5689])).
% 291.61/184.14 tff(13008,plain,
% 291.61/184.14 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s10)),
% 291.61/184.14 inference(unit_resolution,[status(thm)],[13007, 11677])).
% 291.61/184.14 tff(13009,plain,
% 291.61/184.14 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s9) | m_c_h_element_v_out(c_e_h_3, c_f, s9))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s9) | m_c_h_element_v_out(c_e_h_3, c_f, s9))),
% 291.61/184.14 inference(rewrite,[status(thm)],[])).
% 291.61/184.14 tff(13010,plain,
% 291.61/184.14 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s9) | m_c_h_element_v_out(c_e_h_3, c_f, s9))),
% 291.61/184.14 inference(quant_inst,[status(thm)],[])).
% 291.61/184.14 tff(13011,plain,
% 291.61/184.14 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s9) | m_c_h_element_v_out(c_e_h_3, c_f, s9)),
% 291.61/184.14 inference(modus_ponens,[status(thm)],[13010, 13009])).
% 291.61/184.14 tff(13012,plain,
% 291.61/184.14 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s9) | m_c_h_element_v_out(c_e_h_3, c_f, s9)),
% 291.61/184.14 inference(unit_resolution,[status(thm)],[13011, 5689])).
% 291.61/184.14 tff(13013,plain,
% 291.61/184.14 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s9)),
% 291.61/184.14 inference(unit_resolution,[status(thm)],[13012, 11583])).
% 291.61/184.14 tff(13014,plain,
% 291.61/184.14 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8)))),
% 291.61/184.14 inference(rewrite,[status(thm)],[])).
% 291.61/184.14 tff(13015,plain,
% 291.61/184.14 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8)))),
% 291.61/184.14 inference(quant_inst,[status(thm)],[])).
% 291.61/184.14 tff(13016,plain,
% 291.61/184.14 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s8))),
% 291.61/184.14 inference(modus_ponens,[status(thm)],[13015, 13014])).
% 291.61/184.14 tff(13017,plain,
% 291.61/184.14 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s8)),
% 291.61/184.14 inference(unit_resolution,[status(thm)],[13016, 5601, 10844])).
% 291.61/184.14 tff(13018,plain,
% 291.61/184.14 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s8)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s8)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s8))),
% 291.61/184.14 inference(rewrite,[status(thm)],[])).
% 291.61/184.14 tff(13019,plain,
% 291.61/184.14 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s8)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s8))),
% 291.61/184.14 inference(quant_inst,[status(thm)],[])).
% 291.61/184.14 tff(13020,plain,
% 291.61/184.14 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s8)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s8)),
% 291.61/184.14 inference(modus_ponens,[status(thm)],[13019, 13018])).
% 291.61/184.14 tff(13021,plain,
% 291.61/184.14 (~node9(c_e_h_3, c_n, s8)),
% 291.61/184.14 inference(unit_resolution,[status(thm)],[13020, 4972, 13017])).
% 291.61/184.14 tff(13022,plain,
% 291.61/184.14 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s7)),
% 291.61/184.14 inference(unit_resolution,[status(thm)],[9260, 5601, 7149])).
% 291.61/184.14 tff(13023,plain,
% 291.61/184.14 (~node9(c_e_h_3, c_n, s7)),
% 291.61/184.14 inference(unit_resolution,[status(thm)],[9264, 4972, 13022])).
% 291.61/184.14 tff(13024,plain,
% 291.61/184.14 (~node11(c_e_h_3, c_n, s7, s8)),
% 291.61/184.14 inference(unit_resolution,[status(thm)],[9338, 9333, 9266])).
% 291.61/184.14 tff(13025,assumption,(~node9(c_e_h_3, c_n, s7)), introduced(assumption)).
% 291.61/184.14 tff(13026,assumption,(node10(c_e_h_3, c_n, s7, s8)), introduced(assumption)).
% 291.61/184.14 tff(13027,plain,
% 291.61/184.14 ($false),
% 291.61/184.14 inference(unit_resolution,[status(thm)],[9347, 4986, 9333, 13026, 13025])).
% 291.61/184.14 tff(13028,plain,((~node10(c_e_h_3, c_n, s7, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8)) | node9(c_e_h_3, c_n, s7)), inference(lemma,lemma(discharge,[]))).
% 291.61/184.14 tff(13029,plain,
% 291.61/184.14 (~node10(c_e_h_3, c_n, s7, s8)),
% 291.61/184.14 inference(unit_resolution,[status(thm)],[13028, 9333, 13025])).
% 291.61/184.14 tff(13030,plain,
% 291.61/184.14 ($false),
% 291.61/184.14 inference(unit_resolution,[status(thm)],[9343, 13029, 13024])).
% 291.61/184.14 tff(13031,plain,((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8)) | node9(c_e_h_3, c_n, s7) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)), inference(lemma,lemma(discharge,[]))).
% 291.61/184.14 tff(13032,plain,
% 291.61/184.14 ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8)) | node9(c_e_h_3, c_n, s7)),
% 291.61/184.14 inference(unit_resolution,[status(thm)],[13031, 10840])).
% 291.61/184.14 tff(13033,plain,
% 291.61/184.14 (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8)),
% 291.61/184.14 inference(unit_resolution,[status(thm)],[13032, 13023])).
% 291.61/184.14 tff(13034,assumption,(~node9(c_e_h_3, c_n, s8)), introduced(assumption)).
% 291.61/184.14 tff(13035,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9)), introduced(assumption)).
% 291.61/184.14 tff(13036,assumption,(node10(c_e_h_3, c_n, s8, s9)), introduced(assumption)).
% 291.61/184.14 tff(13037,plain,
% 291.61/184.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9)) | node9(c_e_h_3, c_n, s8) | (~node10(c_e_h_3, c_n, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9)) | node9(c_e_h_3, c_n, s8) | (~node10(c_e_h_3, c_n, s8, s9)))),
% 291.61/184.14 inference(rewrite,[status(thm)],[])).
% 291.61/184.14 tff(13038,plain,
% 291.61/184.14 ((node9(c_e_h_3, c_n, s8) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9)) | (~node10(c_e_h_3, c_n, s8, s9))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9)) | node9(c_e_h_3, c_n, s8) | (~node10(c_e_h_3, c_n, s8, s9)))),
% 291.61/184.14 inference(rewrite,[status(thm)],[])).
% 291.61/184.14 tff(13039,plain,
% 291.61/184.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s8) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9)) | (~node10(c_e_h_3, c_n, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9)) | node9(c_e_h_3, c_n, s8) | (~node10(c_e_h_3, c_n, s8, s9))))),
% 291.61/184.14 inference(monotonicity,[status(thm)],[13038])).
% 291.61/184.14 tff(13040,plain,
% 291.61/184.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s8) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9)) | (~node10(c_e_h_3, c_n, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9)) | node9(c_e_h_3, c_n, s8) | (~node10(c_e_h_3, c_n, s8, s9)))),
% 291.61/184.15 inference(transitivity,[status(thm)],[13039, 13037])).
% 291.61/184.15 tff(13041,plain,
% 291.61/184.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s8) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9)) | (~node10(c_e_h_3, c_n, s8, s9)))),
% 291.61/184.15 inference(quant_inst,[status(thm)],[])).
% 291.61/184.15 tff(13042,plain,
% 291.61/184.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9)) | node9(c_e_h_3, c_n, s8) | (~node10(c_e_h_3, c_n, s8, s9))),
% 291.61/184.15 inference(modus_ponens,[status(thm)],[13041, 13040])).
% 291.61/184.15 tff(13043,plain,
% 291.61/184.15 ($false),
% 291.61/184.15 inference(unit_resolution,[status(thm)],[13042, 4986, 13035, 13036, 13034])).
% 291.61/184.15 tff(13044,plain,((~node10(c_e_h_3, c_n, s8, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9)) | node9(c_e_h_3, c_n, s8)), inference(lemma,lemma(discharge,[]))).
% 291.61/184.15 tff(13045,plain,
% 291.61/184.15 (~node10(c_e_h_3, c_n, s8, s9)),
% 291.61/184.15 inference(unit_resolution,[status(thm)],[13044, 13035, 13034])).
% 291.61/184.15 tff(13046,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8)), introduced(assumption)).
% 291.61/184.15 tff(13047,assumption,(node11(c_e_h_3, c_n, s8, s9)), introduced(assumption)).
% 291.61/184.15 tff(13048,plain,
% 291.61/184.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9)) | (~node11(c_e_h_3, c_n, s8, s9)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9)) | (~node11(c_e_h_3, c_n, s8, s9)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8))),
% 291.61/184.15 inference(rewrite,[status(thm)],[])).
% 291.61/184.15 tff(13049,plain,
% 291.61/184.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9)) | (~node11(c_e_h_3, c_n, s8, s9)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8))),
% 291.61/184.15 inference(quant_inst,[status(thm)],[])).
% 291.61/184.15 tff(13050,plain,
% 291.61/184.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9)) | (~node11(c_e_h_3, c_n, s8, s9)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8)),
% 291.61/184.15 inference(modus_ponens,[status(thm)],[13049, 13048])).
% 291.61/184.15 tff(13051,plain,
% 291.61/184.15 ($false),
% 291.61/184.15 inference(unit_resolution,[status(thm)],[13050, 5017, 13046, 13035, 13047])).
% 291.61/184.15 tff(13052,plain,((~node11(c_e_h_3, c_n, s8, s9)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9))), inference(lemma,lemma(discharge,[]))).
% 291.61/184.15 tff(13053,plain,
% 291.61/184.15 (~node11(c_e_h_3, c_n, s8, s9)),
% 291.61/184.15 inference(unit_resolution,[status(thm)],[13052, 13035, 13046])).
% 291.61/184.15 tff(13054,plain,
% 291.61/184.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s8, s9)) | node10(c_e_h_3, c_n, s8, s9) | node11(c_e_h_3, c_n, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s8, s9)) | node10(c_e_h_3, c_n, s8, s9) | node11(c_e_h_3, c_n, s8, s9))),
% 291.61/184.15 inference(rewrite,[status(thm)],[])).
% 291.61/184.15 tff(13055,plain,
% 291.61/184.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s8, s9)) | node10(c_e_h_3, c_n, s8, s9) | node11(c_e_h_3, c_n, s8, s9))),
% 291.61/184.15 inference(quant_inst,[status(thm)],[])).
% 291.61/184.15 tff(13056,plain,
% 291.61/184.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s8, s9)) | node10(c_e_h_3, c_n, s8, s9) | node11(c_e_h_3, c_n, s8, s9)),
% 291.61/184.15 inference(modus_ponens,[status(thm)],[13055, 13054])).
% 291.61/184.15 tff(13057,plain,
% 291.61/184.15 (node10(c_e_h_3, c_n, s8, s9) | node11(c_e_h_3, c_n, s8, s9)),
% 291.61/184.15 inference(unit_resolution,[status(thm)],[13056, 5002, 1993])).
% 291.61/184.15 tff(13058,plain,
% 291.61/184.15 ($false),
% 291.61/184.15 inference(unit_resolution,[status(thm)],[13057, 13053, 13045])).
% 291.61/184.15 tff(13059,plain,((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8) | node9(c_e_h_3, c_n, s8)), inference(lemma,lemma(discharge,[]))).
% 291.61/184.15 tff(13060,plain,
% 291.61/184.15 ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9)) | node9(c_e_h_3, c_n, s8)),
% 291.61/184.15 inference(unit_resolution,[status(thm)],[13059, 13033])).
% 291.61/184.15 tff(13061,plain,
% 291.61/184.15 (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9)),
% 291.61/184.15 inference(unit_resolution,[status(thm)],[13060, 13021])).
% 291.61/184.15 tff(13062,plain,
% 291.61/184.15 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s9) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s9) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9))),
% 291.61/184.15 inference(rewrite,[status(thm)],[])).
% 291.61/184.15 tff(13063,plain,
% 291.61/184.15 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s9) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9))),
% 291.61/184.15 inference(quant_inst,[status(thm)],[])).
% 291.61/184.15 tff(13064,plain,
% 291.61/184.15 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s9) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9)),
% 291.61/184.15 inference(modus_ponens,[status(thm)],[13063, 13062])).
% 291.61/184.15 tff(13065,plain,
% 291.61/184.15 (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s9) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9)),
% 291.61/184.15 inference(unit_resolution,[status(thm)],[13064, 5704])).
% 291.61/184.15 tff(13066,plain,
% 291.61/184.15 (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s9)),
% 291.61/184.15 inference(unit_resolution,[status(thm)],[13065, 13061])).
% 291.61/184.15 tff(13067,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9)), introduced(assumption)).
% 291.61/184.15 tff(13068,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10)), introduced(assumption)).
% 291.61/184.15 tff(13069,assumption,(node11(c_e_h_3, c_m, s9, s10)), introduced(assumption)).
% 291.61/184.15 tff(13070,plain,
% 291.61/184.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9)) | (~node11(c_e_h_3, c_m, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9)) | (~node11(c_e_h_3, c_m, s9, s10)))),
% 291.61/184.15 inference(rewrite,[status(thm)],[])).
% 291.61/184.15 tff(13071,plain,
% 291.61/184.15 ((m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10) | (~node11(c_e_h_3, c_m, s9, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9))) <=> (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9)) | (~node11(c_e_h_3, c_m, s9, s10)))),
% 291.61/184.15 inference(rewrite,[status(thm)],[])).
% 291.61/184.15 tff(13072,plain,
% 291.61/184.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10) | (~node11(c_e_h_3, c_m, s9, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9)) | (~node11(c_e_h_3, c_m, s9, s10))))),
% 291.61/184.15 inference(monotonicity,[status(thm)],[13071])).
% 291.61/184.15 tff(13073,plain,
% 291.61/184.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10) | (~node11(c_e_h_3, c_m, s9, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9)) | (~node11(c_e_h_3, c_m, s9, s10)))),
% 291.61/184.15 inference(transitivity,[status(thm)],[13072, 13070])).
% 291.61/184.15 tff(13074,plain,
% 291.61/184.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10) | (~node11(c_e_h_3, c_m, s9, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9)))),
% 291.61/184.15 inference(quant_inst,[status(thm)],[])).
% 291.61/184.15 tff(13075,plain,
% 291.61/184.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9)) | (~node11(c_e_h_3, c_m, s9, s10))),
% 291.61/184.15 inference(modus_ponens,[status(thm)],[13074, 13073])).
% 291.61/184.15 tff(13076,plain,
% 291.61/184.15 ($false),
% 291.61/184.15 inference(unit_resolution,[status(thm)],[13075, 5742, 13068, 13067, 13069])).
% 291.61/184.15 tff(13077,plain,((~node11(c_e_h_3, c_m, s9, s10)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9))), inference(lemma,lemma(discharge,[]))).
% 291.61/184.15 tff(13078,plain,
% 291.61/184.15 (~node11(c_e_h_3, c_m, s9, s10)),
% 291.61/184.15 inference(unit_resolution,[status(thm)],[13077, 13068, 13067])).
% 291.61/184.15 tff(13079,plain,
% 291.61/184.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s9, s10)) | node10(c_e_h_3, c_m, s9, s10) | node11(c_e_h_3, c_m, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s9, s10)) | node10(c_e_h_3, c_m, s9, s10) | node11(c_e_h_3, c_m, s9, s10))),
% 291.61/184.15 inference(rewrite,[status(thm)],[])).
% 291.61/184.15 tff(13080,plain,
% 291.61/184.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s9, s10)) | node10(c_e_h_3, c_m, s9, s10) | node11(c_e_h_3, c_m, s9, s10))),
% 291.61/184.15 inference(quant_inst,[status(thm)],[])).
% 291.61/184.15 tff(13081,plain,
% 291.61/184.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s9, s10)) | node10(c_e_h_3, c_m, s9, s10) | node11(c_e_h_3, c_m, s9, s10)),
% 291.61/184.15 inference(modus_ponens,[status(thm)],[13080, 13079])).
% 291.61/184.15 tff(13082,plain,
% 291.61/184.15 (node10(c_e_h_3, c_m, s9, s10) | node11(c_e_h_3, c_m, s9, s10)),
% 291.61/184.15 inference(unit_resolution,[status(thm)],[13081, 5002, 7676])).
% 291.61/184.15 tff(13083,plain,
% 291.61/184.15 (node10(c_e_h_3, c_m, s9, s10)),
% 291.61/184.15 inference(unit_resolution,[status(thm)],[13082, 13078])).
% 291.61/184.15 tff(13084,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s9)), introduced(assumption)).
% 291.61/184.15 tff(13085,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s9)), introduced(assumption)).
% 291.61/184.15 tff(13086,plain,
% 291.61/184.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s9)) | (~node10(c_e_h_3, c_m, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s9)) | (~node10(c_e_h_3, c_m, s9, s10)))),
% 291.61/184.15 inference(rewrite,[status(thm)],[])).
% 291.61/184.15 tff(13087,plain,
% 291.61/184.15 (((~node10(c_e_h_3, c_m, s9, s10)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s9)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10)) <=> (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s9)) | (~node10(c_e_h_3, c_m, s9, s10)))),
% 291.61/184.16 inference(rewrite,[status(thm)],[])).
% 291.61/184.16 tff(13088,plain,
% 291.61/184.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s9, s10)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s9)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s9)) | (~node10(c_e_h_3, c_m, s9, s10))))),
% 291.61/184.16 inference(monotonicity,[status(thm)],[13087])).
% 291.61/184.16 tff(13089,plain,
% 291.61/184.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s9, s10)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s9)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s9)) | (~node10(c_e_h_3, c_m, s9, s10)))),
% 291.61/184.16 inference(transitivity,[status(thm)],[13088, 13086])).
% 291.61/184.16 tff(13090,plain,
% 291.61/184.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s9, s10)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s9)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10))),
% 291.61/184.16 inference(quant_inst,[status(thm)],[])).
% 291.61/184.16 tff(13091,plain,
% 291.61/184.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s9)) | (~node10(c_e_h_3, c_m, s9, s10))),
% 291.61/184.16 inference(modus_ponens,[status(thm)],[13090, 13089])).
% 291.61/184.16 tff(13092,plain,
% 291.61/184.16 ($false),
% 291.61/184.16 inference(unit_resolution,[status(thm)],[13091, 5718, 13068, 13085, 13084, 13083])).
% 291.61/184.16 tff(13093,plain,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9))), inference(lemma,lemma(discharge,[]))).
% 291.61/184.16 tff(13094,plain,
% 291.61/184.16 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s9))),
% 291.61/184.16 inference(unit_resolution,[status(thm)],[13093, 9445, 13066])).
% 291.61/184.16 tff(13095,plain,
% 291.61/184.16 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10)),
% 291.61/184.16 inference(unit_resolution,[status(thm)],[13094, 13013])).
% 291.61/184.16 tff(13096,plain,
% 291.61/184.16 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9)))),
% 291.61/184.16 inference(rewrite,[status(thm)],[])).
% 291.61/184.16 tff(13097,plain,
% 291.61/184.16 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9)))),
% 291.61/184.16 inference(quant_inst,[status(thm)],[])).
% 291.61/184.16 tff(13098,plain,
% 291.61/184.16 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9))),
% 291.61/184.16 inference(modus_ponens,[status(thm)],[13097, 13096])).
% 291.61/184.16 tff(13099,plain,
% 291.61/184.16 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s9)),
% 291.61/184.16 inference(unit_resolution,[status(thm)],[13098, 5601, 9445])).
% 291.61/184.16 tff(13100,plain,
% 291.61/184.16 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s9)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s9))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s9)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s9))),
% 291.61/184.16 inference(rewrite,[status(thm)],[])).
% 291.61/184.16 tff(13101,plain,
% 291.61/184.16 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s9)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s9))),
% 291.61/184.16 inference(quant_inst,[status(thm)],[])).
% 291.61/184.16 tff(13102,plain,
% 291.61/184.16 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s9)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s9)),
% 291.61/184.16 inference(modus_ponens,[status(thm)],[13101, 13100])).
% 291.61/184.16 tff(13103,plain,
% 291.61/184.16 (~node9(c_e_h_3, c_n, s9)),
% 291.61/184.16 inference(unit_resolution,[status(thm)],[13102, 4972, 13099])).
% 291.61/184.16 tff(13104,assumption,(~node9(c_e_h_3, c_n, s9)), introduced(assumption)).
% 291.61/184.16 tff(13105,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9)), introduced(assumption)).
% 291.61/184.16 tff(13106,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10)), introduced(assumption)).
% 291.61/184.16 tff(13107,assumption,(node11(c_e_h_3, c_n, s9, s10)), introduced(assumption)).
% 291.61/184.16 tff(13108,plain,
% 291.61/184.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10)) | (~node11(c_e_h_3, c_n, s9, s10)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10)) | (~node11(c_e_h_3, c_n, s9, s10)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9))),
% 291.61/184.16 inference(rewrite,[status(thm)],[])).
% 291.61/184.16 tff(13109,plain,
% 291.61/184.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10)) | (~node11(c_e_h_3, c_n, s9, s10)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9))),
% 291.61/184.16 inference(quant_inst,[status(thm)],[])).
% 291.61/184.16 tff(13110,plain,
% 291.61/184.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10)) | (~node11(c_e_h_3, c_n, s9, s10)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9)),
% 291.61/184.16 inference(modus_ponens,[status(thm)],[13109, 13108])).
% 291.61/184.16 tff(13111,plain,
% 291.61/184.16 ($false),
% 291.61/184.16 inference(unit_resolution,[status(thm)],[13110, 5017, 13105, 13106, 13107])).
% 291.61/184.16 tff(13112,plain,((~node11(c_e_h_3, c_n, s9, s10)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10))), inference(lemma,lemma(discharge,[]))).
% 291.61/184.16 tff(13113,plain,
% 291.61/184.16 (~node11(c_e_h_3, c_n, s9, s10)),
% 291.61/184.16 inference(unit_resolution,[status(thm)],[13112, 13106, 13105])).
% 291.61/184.16 tff(13114,plain,
% 291.61/184.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s9, s10)) | node10(c_e_h_3, c_n, s9, s10) | node11(c_e_h_3, c_n, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s9, s10)) | node10(c_e_h_3, c_n, s9, s10) | node11(c_e_h_3, c_n, s9, s10))),
% 291.61/184.16 inference(rewrite,[status(thm)],[])).
% 291.61/184.16 tff(13115,plain,
% 291.61/184.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s9, s10)) | node10(c_e_h_3, c_n, s9, s10) | node11(c_e_h_3, c_n, s9, s10))),
% 291.61/184.16 inference(quant_inst,[status(thm)],[])).
% 291.61/184.16 tff(13116,plain,
% 291.61/184.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s9, s10)) | node10(c_e_h_3, c_n, s9, s10) | node11(c_e_h_3, c_n, s9, s10)),
% 291.61/184.16 inference(modus_ponens,[status(thm)],[13115, 13114])).
% 291.61/184.16 tff(13117,plain,
% 291.61/184.16 (node10(c_e_h_3, c_n, s9, s10) | node11(c_e_h_3, c_n, s9, s10)),
% 291.61/184.16 inference(unit_resolution,[status(thm)],[13116, 5002, 7676])).
% 291.61/184.16 tff(13118,plain,
% 291.61/184.16 (node10(c_e_h_3, c_n, s9, s10)),
% 291.61/184.16 inference(unit_resolution,[status(thm)],[13117, 13113])).
% 291.61/184.16 tff(13119,plain,
% 291.61/184.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10)) | (~node10(c_e_h_3, c_n, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_3, c_n, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10)) | (~node10(c_e_h_3, c_n, s9, s10)))),
% 291.61/184.16 inference(rewrite,[status(thm)],[])).
% 291.61/184.16 tff(13120,plain,
% 291.61/184.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10)) | (~node10(c_e_h_3, c_n, s9, s10)))),
% 291.61/184.16 inference(quant_inst,[status(thm)],[])).
% 291.61/184.16 tff(13121,plain,
% 291.61/184.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_3, c_n, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10)) | (~node10(c_e_h_3, c_n, s9, s10))),
% 291.61/184.16 inference(modus_ponens,[status(thm)],[13120, 13119])).
% 291.61/184.16 tff(13122,plain,
% 291.61/184.16 ($false),
% 291.61/184.16 inference(unit_resolution,[status(thm)],[13121, 4986, 13106, 13118, 13104])).
% 291.61/184.16 tff(13123,plain,((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10)) | node9(c_e_h_3, c_n, s9) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9)), inference(lemma,lemma(discharge,[]))).
% 291.61/184.16 tff(13124,plain,
% 291.61/184.16 (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10)),
% 291.61/184.16 inference(unit_resolution,[status(thm)],[13123, 13103, 13061])).
% 291.61/184.16 tff(13125,plain,
% 291.61/184.16 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s10) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s10) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10))),
% 291.61/184.16 inference(rewrite,[status(thm)],[])).
% 291.61/184.16 tff(13126,plain,
% 291.61/184.16 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s10) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10))),
% 291.61/184.16 inference(quant_inst,[status(thm)],[])).
% 291.61/184.16 tff(13127,plain,
% 291.61/184.16 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s10) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10)),
% 291.61/184.16 inference(modus_ponens,[status(thm)],[13126, 13125])).
% 291.61/184.16 tff(13128,plain,
% 291.61/184.16 (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s10) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10)),
% 291.61/184.16 inference(unit_resolution,[status(thm)],[13127, 5704])).
% 291.61/184.16 tff(13129,plain,
% 291.61/184.16 (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s10)),
% 291.61/184.16 inference(unit_resolution,[status(thm)],[13128, 13124])).
% 291.61/184.16 tff(13130,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10)), introduced(assumption)).
% 291.61/184.16 tff(13131,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s11)), introduced(assumption)).
% 291.61/184.16 tff(13132,assumption,(node11(c_e_h_3, c_m, s10, s11)), introduced(assumption)).
% 291.61/184.16 tff(13133,plain,
% 291.61/184.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10)) | (~node11(c_e_h_3, c_m, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10)) | (~node11(c_e_h_3, c_m, s10, s11)))),
% 291.61/184.17 inference(rewrite,[status(thm)],[])).
% 291.61/184.17 tff(13134,plain,
% 291.61/184.17 ((m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s11) | (~node11(c_e_h_3, c_m, s10, s11)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10))) <=> (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10)) | (~node11(c_e_h_3, c_m, s10, s11)))),
% 291.61/184.17 inference(rewrite,[status(thm)],[])).
% 291.61/184.17 tff(13135,plain,
% 291.61/184.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s11) | (~node11(c_e_h_3, c_m, s10, s11)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10)) | (~node11(c_e_h_3, c_m, s10, s11))))),
% 291.61/184.17 inference(monotonicity,[status(thm)],[13134])).
% 291.61/184.17 tff(13136,plain,
% 291.61/184.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s11) | (~node11(c_e_h_3, c_m, s10, s11)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10)) | (~node11(c_e_h_3, c_m, s10, s11)))),
% 291.61/184.17 inference(transitivity,[status(thm)],[13135, 13133])).
% 291.61/184.17 tff(13137,plain,
% 291.61/184.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s11) | (~node11(c_e_h_3, c_m, s10, s11)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10)))),
% 291.61/184.17 inference(quant_inst,[status(thm)],[])).
% 291.61/184.17 tff(13138,plain,
% 291.61/184.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10)) | (~node11(c_e_h_3, c_m, s10, s11))),
% 291.61/184.17 inference(modus_ponens,[status(thm)],[13137, 13136])).
% 291.61/184.17 tff(13139,plain,
% 291.61/184.17 ($false),
% 291.61/184.17 inference(unit_resolution,[status(thm)],[13138, 5742, 13130, 13131, 13132])).
% 291.61/184.17 tff(13140,plain,((~node11(c_e_h_3, c_m, s10, s11)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s11)), inference(lemma,lemma(discharge,[]))).
% 291.61/184.17 tff(13141,plain,
% 291.61/184.17 (~node11(c_e_h_3, c_m, s10, s11)),
% 291.61/184.17 inference(unit_resolution,[status(thm)],[13140, 13131, 13130])).
% 291.61/184.17 tff(13142,plain,
% 291.61/184.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s10, s11)) | node10(c_e_h_3, c_m, s10, s11) | node11(c_e_h_3, c_m, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s10, s11)) | node10(c_e_h_3, c_m, s10, s11) | node11(c_e_h_3, c_m, s10, s11))),
% 291.61/184.17 inference(rewrite,[status(thm)],[])).
% 291.61/184.17 tff(13143,plain,
% 291.61/184.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s10, s11)) | node10(c_e_h_3, c_m, s10, s11) | node11(c_e_h_3, c_m, s10, s11))),
% 291.61/184.17 inference(quant_inst,[status(thm)],[])).
% 291.61/184.17 tff(13144,plain,
% 291.61/184.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s10, s11)) | node10(c_e_h_3, c_m, s10, s11) | node11(c_e_h_3, c_m, s10, s11)),
% 291.61/184.17 inference(modus_ponens,[status(thm)],[13143, 13142])).
% 291.61/184.17 tff(13145,plain,
% 291.61/184.17 (node10(c_e_h_3, c_m, s10, s11) | node11(c_e_h_3, c_m, s10, s11)),
% 291.61/184.17 inference(unit_resolution,[status(thm)],[13144, 5002, 7748])).
% 291.61/184.17 tff(13146,plain,
% 291.61/184.17 (node10(c_e_h_3, c_m, s10, s11)),
% 291.61/184.17 inference(unit_resolution,[status(thm)],[13145, 13141])).
% 291.61/184.17 tff(13147,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s10)), introduced(assumption)).
% 291.61/184.17 tff(13148,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s10)), introduced(assumption)).
% 291.61/184.17 tff(13149,plain,
% 291.61/184.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s11) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s10)) | (~node10(c_e_h_3, c_m, s10, s11)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s11) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s10)) | (~node10(c_e_h_3, c_m, s10, s11)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s10)))),
% 291.61/184.17 inference(rewrite,[status(thm)],[])).
% 291.61/184.17 tff(13150,plain,
% 291.61/184.17 (((~node10(c_e_h_3, c_m, s10, s11)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s10)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s10)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s11)) <=> (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s11) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s10)) | (~node10(c_e_h_3, c_m, s10, s11)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s10)))),
% 291.61/184.17 inference(rewrite,[status(thm)],[])).
% 291.61/184.17 tff(13151,plain,
% 291.61/184.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s10, s11)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s10)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s10)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s11) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s10)) | (~node10(c_e_h_3, c_m, s10, s11)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s10))))),
% 291.61/184.17 inference(monotonicity,[status(thm)],[13150])).
% 291.61/184.17 tff(13152,plain,
% 291.61/184.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s10, s11)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s10)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s10)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s11) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s10)) | (~node10(c_e_h_3, c_m, s10, s11)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s10)))),
% 291.61/184.17 inference(transitivity,[status(thm)],[13151, 13149])).
% 291.61/184.17 tff(13153,plain,
% 291.61/184.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s10, s11)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s10)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s10)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s11))),
% 291.61/184.17 inference(quant_inst,[status(thm)],[])).
% 291.61/184.17 tff(13154,plain,
% 291.61/184.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s11) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s10)) | (~node10(c_e_h_3, c_m, s10, s11)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s10))),
% 291.61/184.17 inference(modus_ponens,[status(thm)],[13153, 13152])).
% 291.61/184.17 tff(13155,plain,
% 291.61/184.17 ($false),
% 291.61/184.17 inference(unit_resolution,[status(thm)],[13154, 5718, 13148, 13131, 13147, 13146])).
% 291.61/184.17 tff(13156,plain,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s11) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s10)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10))), inference(lemma,lemma(discharge,[]))).
% 291.61/184.17 tff(13157,plain,
% 291.61/184.17 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s11) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10))),
% 291.61/184.17 inference(unit_resolution,[status(thm)],[13156, 13129])).
% 291.61/184.17 tff(13158,plain,
% 291.61/184.17 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s11) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s10))),
% 291.61/184.17 inference(unit_resolution,[status(thm)],[13157, 13095])).
% 291.61/184.17 tff(13159,plain,
% 291.61/184.17 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s11)),
% 291.61/184.17 inference(unit_resolution,[status(thm)],[13158, 13008])).
% 291.61/184.17 tff(13160,plain,
% 291.61/184.17 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s11)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s11)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s11)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s11)))),
% 291.61/184.17 inference(rewrite,[status(thm)],[])).
% 291.61/184.17 tff(13161,plain,
% 291.61/184.17 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s11)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s11)))),
% 291.61/184.17 inference(quant_inst,[status(thm)],[])).
% 291.61/184.17 tff(13162,plain,
% 291.61/184.17 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s11)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s11))),
% 291.61/184.17 inference(modus_ponens,[status(thm)],[13161, 13160])).
% 291.61/184.17 tff(13163,plain,
% 291.61/184.17 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s11)),
% 291.61/184.17 inference(unit_resolution,[status(thm)],[13162, 5601, 13159])).
% 291.61/184.17 tff(13164,plain,
% 291.61/184.17 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s11)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s11))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s11)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s11))),
% 291.61/184.17 inference(rewrite,[status(thm)],[])).
% 291.61/184.17 tff(13165,plain,
% 291.61/184.17 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s11)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s11))),
% 291.61/184.17 inference(quant_inst,[status(thm)],[])).
% 291.61/184.17 tff(13166,plain,
% 291.61/184.17 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s11)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s11)),
% 291.61/184.17 inference(modus_ponens,[status(thm)],[13165, 13164])).
% 291.61/184.17 tff(13167,plain,
% 291.61/184.17 (~node9(c_e_h_3, c_n, s11)),
% 291.61/184.17 inference(unit_resolution,[status(thm)],[13166, 4972, 13163])).
% 291.61/184.17 tff(13168,plain,
% 291.61/184.17 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10)))),
% 291.61/184.17 inference(rewrite,[status(thm)],[])).
% 291.61/184.17 tff(13169,plain,
% 291.61/184.17 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10)))),
% 291.61/184.18 inference(quant_inst,[status(thm)],[])).
% 291.61/184.18 tff(13170,plain,
% 291.61/184.18 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10))),
% 291.61/184.18 inference(modus_ponens,[status(thm)],[13169, 13168])).
% 291.61/184.18 tff(13171,plain,
% 291.61/184.18 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s10)),
% 291.61/184.18 inference(unit_resolution,[status(thm)],[13170, 5601, 13095])).
% 291.61/184.18 tff(13172,plain,
% 291.61/184.18 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s10)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s10))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s10)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s10))),
% 291.61/184.18 inference(rewrite,[status(thm)],[])).
% 291.61/184.18 tff(13173,plain,
% 291.61/184.18 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s10)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s10))),
% 291.61/184.18 inference(quant_inst,[status(thm)],[])).
% 291.61/184.18 tff(13174,plain,
% 291.61/184.18 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s10)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s10)),
% 291.61/184.18 inference(modus_ponens,[status(thm)],[13173, 13172])).
% 291.61/184.18 tff(13175,plain,
% 291.61/184.18 (~node9(c_e_h_3, c_n, s10)),
% 291.61/184.18 inference(unit_resolution,[status(thm)],[13174, 4972, 13171])).
% 291.61/184.18 tff(13176,assumption,(~node9(c_e_h_3, c_n, s10)), introduced(assumption)).
% 291.61/184.18 tff(13177,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10)), introduced(assumption)).
% 291.61/184.18 tff(13178,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11)), introduced(assumption)).
% 291.61/184.18 tff(13179,assumption,(node11(c_e_h_3, c_n, s10, s11)), introduced(assumption)).
% 291.61/184.18 tff(13180,plain,
% 291.61/184.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11)) | (~node11(c_e_h_3, c_n, s10, s11)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11)) | (~node11(c_e_h_3, c_n, s10, s11)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10))),
% 291.61/184.18 inference(rewrite,[status(thm)],[])).
% 291.61/184.18 tff(13181,plain,
% 291.61/184.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11)) | (~node11(c_e_h_3, c_n, s10, s11)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10))),
% 291.61/184.18 inference(quant_inst,[status(thm)],[])).
% 291.61/184.18 tff(13182,plain,
% 291.61/184.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11)) | (~node11(c_e_h_3, c_n, s10, s11)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10)),
% 291.61/184.18 inference(modus_ponens,[status(thm)],[13181, 13180])).
% 291.61/184.18 tff(13183,plain,
% 291.61/184.18 ($false),
% 291.61/184.18 inference(unit_resolution,[status(thm)],[13182, 5017, 13177, 13178, 13179])).
% 291.61/184.18 tff(13184,plain,((~node11(c_e_h_3, c_n, s10, s11)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11))), inference(lemma,lemma(discharge,[]))).
% 291.61/184.18 tff(13185,plain,
% 291.61/184.18 (~node11(c_e_h_3, c_n, s10, s11)),
% 291.61/184.18 inference(unit_resolution,[status(thm)],[13184, 13178, 13177])).
% 291.61/184.18 tff(13186,plain,
% 291.61/184.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s10, s11)) | node10(c_e_h_3, c_n, s10, s11) | node11(c_e_h_3, c_n, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s10, s11)) | node10(c_e_h_3, c_n, s10, s11) | node11(c_e_h_3, c_n, s10, s11))),
% 291.61/184.18 inference(rewrite,[status(thm)],[])).
% 291.61/184.18 tff(13187,plain,
% 291.61/184.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s10, s11)) | node10(c_e_h_3, c_n, s10, s11) | node11(c_e_h_3, c_n, s10, s11))),
% 291.61/184.18 inference(quant_inst,[status(thm)],[])).
% 291.61/184.18 tff(13188,plain,
% 291.61/184.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s10, s11)) | node10(c_e_h_3, c_n, s10, s11) | node11(c_e_h_3, c_n, s10, s11)),
% 291.61/184.18 inference(modus_ponens,[status(thm)],[13187, 13186])).
% 291.61/184.18 tff(13189,plain,
% 291.61/184.18 (node10(c_e_h_3, c_n, s10, s11) | node11(c_e_h_3, c_n, s10, s11)),
% 291.61/184.18 inference(unit_resolution,[status(thm)],[13188, 5002, 7748])).
% 291.61/184.18 tff(13190,plain,
% 291.61/184.18 (node10(c_e_h_3, c_n, s10, s11)),
% 291.61/184.18 inference(unit_resolution,[status(thm)],[13189, 13185])).
% 291.61/184.18 tff(13191,plain,
% 291.61/184.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11)) | (~node10(c_e_h_3, c_n, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_3, c_n, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11)) | (~node10(c_e_h_3, c_n, s10, s11)))),
% 291.61/184.18 inference(rewrite,[status(thm)],[])).
% 291.61/184.18 tff(13192,plain,
% 291.61/184.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11)) | (~node10(c_e_h_3, c_n, s10, s11)))),
% 291.61/184.18 inference(quant_inst,[status(thm)],[])).
% 291.61/184.18 tff(13193,plain,
% 291.61/184.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_3, c_n, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11)) | (~node10(c_e_h_3, c_n, s10, s11))),
% 291.61/184.18 inference(modus_ponens,[status(thm)],[13192, 13191])).
% 291.61/184.18 tff(13194,plain,
% 291.61/184.18 ($false),
% 291.61/184.18 inference(unit_resolution,[status(thm)],[13193, 4986, 13178, 13190, 13176])).
% 291.61/184.18 tff(13195,plain,((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11)) | node9(c_e_h_3, c_n, s10) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10)), inference(lemma,lemma(discharge,[]))).
% 291.61/184.18 tff(13196,plain,
% 291.61/184.18 ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11)) | node9(c_e_h_3, c_n, s10)),
% 291.61/184.18 inference(unit_resolution,[status(thm)],[13195, 13124])).
% 291.61/184.18 tff(13197,plain,
% 291.61/184.18 (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11)),
% 291.61/184.18 inference(unit_resolution,[status(thm)],[13196, 13175])).
% 291.61/184.18 tff(13198,assumption,(~node9(c_e_h_3, c_n, s11)), introduced(assumption)).
% 291.61/184.18 tff(13199,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s12)), introduced(assumption)).
% 291.61/184.18 tff(13200,assumption,(node10(c_e_h_3, c_n, s11, s12)), introduced(assumption)).
% 291.61/184.18 tff(13201,plain,
% 291.61/184.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s12)) | (~node10(c_e_h_3, c_n, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_3, c_n, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s12)) | (~node10(c_e_h_3, c_n, s11, s12)))),
% 291.61/184.18 inference(rewrite,[status(thm)],[])).
% 291.61/184.18 tff(13202,plain,
% 291.61/184.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s12)) | (~node10(c_e_h_3, c_n, s11, s12)))),
% 291.61/184.18 inference(quant_inst,[status(thm)],[])).
% 291.61/184.18 tff(13203,plain,
% 291.61/184.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_3, c_n, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s12)) | (~node10(c_e_h_3, c_n, s11, s12))),
% 291.61/184.18 inference(modus_ponens,[status(thm)],[13202, 13201])).
% 291.61/184.18 tff(13204,plain,
% 291.61/184.18 ($false),
% 291.61/184.18 inference(unit_resolution,[status(thm)],[13203, 4986, 13199, 13200, 13198])).
% 291.69/184.18 tff(13205,plain,((~node10(c_e_h_3, c_n, s11, s12)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s12)) | node9(c_e_h_3, c_n, s11)), inference(lemma,lemma(discharge,[]))).
% 291.69/184.18 tff(13206,plain,
% 291.69/184.18 (~node10(c_e_h_3, c_n, s11, s12)),
% 291.69/184.18 inference(unit_resolution,[status(thm)],[13205, 13199, 13198])).
% 291.69/184.18 tff(13207,plain,
% 291.69/184.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s11, s12)) | node10(c_e_h_3, c_n, s11, s12) | node11(c_e_h_3, c_n, s11, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s11, s12)) | node10(c_e_h_3, c_n, s11, s12) | node11(c_e_h_3, c_n, s11, s12))),
% 291.69/184.18 inference(rewrite,[status(thm)],[])).
% 291.69/184.18 tff(13208,plain,
% 291.69/184.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s11, s12)) | node10(c_e_h_3, c_n, s11, s12) | node11(c_e_h_3, c_n, s11, s12))),
% 291.69/184.18 inference(quant_inst,[status(thm)],[])).
% 291.69/184.18 tff(13209,plain,
% 291.69/184.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s11, s12)) | node10(c_e_h_3, c_n, s11, s12) | node11(c_e_h_3, c_n, s11, s12)),
% 291.69/184.18 inference(modus_ponens,[status(thm)],[13208, 13207])).
% 291.69/184.18 tff(13210,plain,
% 291.69/184.18 (node10(c_e_h_3, c_n, s11, s12) | node11(c_e_h_3, c_n, s11, s12)),
% 291.69/184.18 inference(unit_resolution,[status(thm)],[13209, 5002, 11461])).
% 291.69/184.18 tff(13211,plain,
% 291.69/184.18 (node11(c_e_h_3, c_n, s11, s12)),
% 291.69/184.18 inference(unit_resolution,[status(thm)],[13210, 13206])).
% 291.69/184.18 tff(13212,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11)), introduced(assumption)).
% 291.69/184.18 tff(13213,plain,
% 291.69/184.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s12)) | (~node11(c_e_h_3, c_n, s11, s12)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s12)) | (~node11(c_e_h_3, c_n, s11, s12)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11))),
% 291.69/184.18 inference(rewrite,[status(thm)],[])).
% 291.69/184.18 tff(13214,plain,
% 291.69/184.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s12)) | (~node11(c_e_h_3, c_n, s11, s12)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11))),
% 291.69/184.18 inference(quant_inst,[status(thm)],[])).
% 291.69/184.18 tff(13215,plain,
% 291.69/184.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s12)) | (~node11(c_e_h_3, c_n, s11, s12)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11)),
% 291.69/184.18 inference(modus_ponens,[status(thm)],[13214, 13213])).
% 291.69/184.18 tff(13216,plain,
% 291.69/184.18 ($false),
% 291.69/184.18 inference(unit_resolution,[status(thm)],[13215, 5017, 13212, 13199, 13211])).
% 291.69/184.18 tff(13217,plain,((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s12)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11) | node9(c_e_h_3, c_n, s11)), inference(lemma,lemma(discharge,[]))).
% 291.69/184.18 tff(13218,plain,
% 291.69/184.18 ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s12)) | node9(c_e_h_3, c_n, s11)),
% 291.69/184.18 inference(unit_resolution,[status(thm)],[13217, 13197])).
% 291.69/184.18 tff(13219,plain,
% 291.69/184.18 (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s12)),
% 291.69/184.18 inference(unit_resolution,[status(thm)],[13218, 13167])).
% 291.69/184.18 tff(13220,plain,
% 291.69/184.18 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s12) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s12))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s12) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s12))),
% 291.69/184.18 inference(rewrite,[status(thm)],[])).
% 291.69/184.18 tff(13221,plain,
% 291.69/184.18 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s12) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s12))),
% 291.70/184.19 inference(quant_inst,[status(thm)],[])).
% 291.70/184.19 tff(13222,plain,
% 291.70/184.19 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s12) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s12)),
% 291.70/184.19 inference(modus_ponens,[status(thm)],[13221, 13220])).
% 291.70/184.19 tff(13223,plain,
% 291.70/184.19 (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s12) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s12)),
% 291.70/184.19 inference(unit_resolution,[status(thm)],[13222, 5704])).
% 291.70/184.19 tff(13224,plain,
% 291.70/184.19 (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s12)),
% 291.70/184.19 inference(unit_resolution,[status(thm)],[13223, 13219])).
% 291.70/184.19 tff(13225,plain,
% 291.70/184.19 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s11) | m_c_h_element_v_out(c_e_h_3, c_f, s11))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s11) | m_c_h_element_v_out(c_e_h_3, c_f, s11))),
% 291.70/184.19 inference(rewrite,[status(thm)],[])).
% 291.70/184.19 tff(13226,plain,
% 291.70/184.19 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s11) | m_c_h_element_v_out(c_e_h_3, c_f, s11))),
% 291.70/184.19 inference(quant_inst,[status(thm)],[])).
% 291.70/184.19 tff(13227,plain,
% 291.70/184.19 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s11) | m_c_h_element_v_out(c_e_h_3, c_f, s11)),
% 291.70/184.19 inference(modus_ponens,[status(thm)],[13226, 13225])).
% 291.70/184.19 tff(13228,plain,
% 291.70/184.19 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s11) | m_c_h_element_v_out(c_e_h_3, c_f, s11)),
% 291.70/184.19 inference(unit_resolution,[status(thm)],[13227, 5689])).
% 291.70/184.19 tff(13229,plain,
% 291.70/184.19 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s11)),
% 291.70/184.19 inference(unit_resolution,[status(thm)],[13228, 11759])).
% 291.70/184.19 tff(13230,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12)), introduced(assumption)).
% 291.70/184.19 tff(13231,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s11)), introduced(assumption)).
% 291.70/184.19 tff(13232,plain,
% 291.70/184.19 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s9)),
% 291.70/184.19 inference(unit_resolution,[status(thm)],[13012, 11586])).
% 291.70/184.19 tff(13233,plain,
% 291.70/184.19 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s9)),
% 291.70/184.19 inference(unit_resolution,[status(thm)],[13098, 5601, 13067])).
% 291.70/184.19 tff(13234,plain,
% 291.70/184.19 (~node9(c_e_h_3, c_n, s9)),
% 291.70/184.19 inference(unit_resolution,[status(thm)],[13102, 4972, 13233])).
% 291.70/184.19 tff(13235,plain,
% 291.70/184.19 (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10)),
% 291.70/184.19 inference(unit_resolution,[status(thm)],[13123, 13105, 13234])).
% 291.70/184.19 tff(13236,plain,
% 291.70/184.19 (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s10)),
% 291.70/184.19 inference(unit_resolution,[status(thm)],[13128, 13235])).
% 291.70/184.19 tff(13237,plain,
% 291.70/184.19 (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s9)),
% 291.70/184.19 inference(unit_resolution,[status(thm)],[13065, 13105])).
% 291.70/184.19 tff(13238,plain,
% 291.70/184.19 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10)),
% 291.70/184.19 inference(unit_resolution,[status(thm)],[13093, 13237, 13084, 13067])).
% 291.70/184.19 tff(13239,plain,
% 291.70/184.19 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s11)),
% 291.70/184.19 inference(unit_resolution,[status(thm)],[13156, 13238, 13148, 13236])).
% 291.70/184.19 tff(13240,assumption,(node11(c_e_h_3, c_m, s11, s12)), introduced(assumption)).
% 291.70/184.19 tff(13241,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s11)), introduced(assumption)).
% 291.70/184.19 tff(13242,plain,
% 291.70/184.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s11)) | (~node11(c_e_h_3, c_m, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s11)) | (~node11(c_e_h_3, c_m, s11, s12)))),
% 291.70/184.19 inference(rewrite,[status(thm)],[])).
% 291.70/184.19 tff(13243,plain,
% 291.70/184.19 ((m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12) | (~node11(c_e_h_3, c_m, s11, s12)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s11))) <=> (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s11)) | (~node11(c_e_h_3, c_m, s11, s12)))),
% 291.70/184.19 inference(rewrite,[status(thm)],[])).
% 291.70/184.19 tff(13244,plain,
% 291.70/184.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12) | (~node11(c_e_h_3, c_m, s11, s12)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s11)) | (~node11(c_e_h_3, c_m, s11, s12))))),
% 291.70/184.19 inference(monotonicity,[status(thm)],[13243])).
% 291.70/184.19 tff(13245,plain,
% 291.70/184.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12) | (~node11(c_e_h_3, c_m, s11, s12)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s11)) | (~node11(c_e_h_3, c_m, s11, s12)))),
% 291.70/184.19 inference(transitivity,[status(thm)],[13244, 13242])).
% 291.70/184.19 tff(13246,plain,
% 291.70/184.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12) | (~node11(c_e_h_3, c_m, s11, s12)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s11)))),
% 291.70/184.19 inference(quant_inst,[status(thm)],[])).
% 291.70/184.19 tff(13247,plain,
% 291.70/184.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s11)) | (~node11(c_e_h_3, c_m, s11, s12))),
% 291.70/184.19 inference(modus_ponens,[status(thm)],[13246, 13245])).
% 291.70/184.19 tff(13248,plain,
% 291.70/184.19 ($false),
% 291.70/184.19 inference(unit_resolution,[status(thm)],[13247, 5742, 13230, 13241, 13240])).
% 291.70/184.19 tff(13249,plain,((~node11(c_e_h_3, c_m, s11, s12)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s11))), inference(lemma,lemma(discharge,[]))).
% 291.70/184.19 tff(13250,plain,
% 291.70/184.19 (~node11(c_e_h_3, c_m, s11, s12)),
% 291.70/184.19 inference(unit_resolution,[status(thm)],[13249, 13239, 13230])).
% 291.70/184.19 tff(13251,plain,
% 291.70/184.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s11, s12)) | node10(c_e_h_3, c_m, s11, s12) | node11(c_e_h_3, c_m, s11, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s11, s12)) | node10(c_e_h_3, c_m, s11, s12) | node11(c_e_h_3, c_m, s11, s12))),
% 291.70/184.19 inference(rewrite,[status(thm)],[])).
% 291.70/184.19 tff(13252,plain,
% 291.70/184.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s11, s12)) | node10(c_e_h_3, c_m, s11, s12) | node11(c_e_h_3, c_m, s11, s12))),
% 291.70/184.19 inference(quant_inst,[status(thm)],[])).
% 291.70/184.19 tff(13253,plain,
% 291.70/184.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s11, s12)) | node10(c_e_h_3, c_m, s11, s12) | node11(c_e_h_3, c_m, s11, s12)),
% 291.70/184.19 inference(modus_ponens,[status(thm)],[13252, 13251])).
% 291.70/184.19 tff(13254,plain,
% 291.70/184.19 (node10(c_e_h_3, c_m, s11, s12) | node11(c_e_h_3, c_m, s11, s12)),
% 291.70/184.19 inference(unit_resolution,[status(thm)],[13253, 5002, 11461])).
% 291.70/184.19 tff(13255,plain,
% 291.70/184.19 (node10(c_e_h_3, c_m, s11, s12)),
% 291.70/184.19 inference(unit_resolution,[status(thm)],[13254, 13250])).
% 291.70/184.19 tff(13256,assumption,(node10(c_e_h_3, c_m, s11, s12)), introduced(assumption)).
% 291.70/184.19 tff(13257,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s11)), introduced(assumption)).
% 291.70/184.19 tff(13258,plain,
% 291.70/184.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s11)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s11)) | (~node10(c_e_h_3, c_m, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s11)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s11)) | (~node10(c_e_h_3, c_m, s11, s12)))),
% 291.70/184.19 inference(rewrite,[status(thm)],[])).
% 291.70/184.19 tff(13259,plain,
% 291.70/184.19 (((~node10(c_e_h_3, c_m, s11, s12)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s11)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s11)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12)) <=> (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s11)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s11)) | (~node10(c_e_h_3, c_m, s11, s12)))),
% 291.70/184.19 inference(rewrite,[status(thm)],[])).
% 291.70/184.19 tff(13260,plain,
% 291.70/184.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s11, s12)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s11)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s11)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s11)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s11)) | (~node10(c_e_h_3, c_m, s11, s12))))),
% 291.70/184.19 inference(monotonicity,[status(thm)],[13259])).
% 291.70/184.19 tff(13261,plain,
% 291.70/184.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s11, s12)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s11)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s11)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s11)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s11)) | (~node10(c_e_h_3, c_m, s11, s12)))),
% 291.70/184.19 inference(transitivity,[status(thm)],[13260, 13258])).
% 291.70/184.19 tff(13262,plain,
% 291.70/184.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s11, s12)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s11)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s11)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12))),
% 291.70/184.19 inference(quant_inst,[status(thm)],[])).
% 291.70/184.19 tff(13263,plain,
% 291.70/184.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s11)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s11)) | (~node10(c_e_h_3, c_m, s11, s12))),
% 291.70/184.19 inference(modus_ponens,[status(thm)],[13262, 13261])).
% 291.70/184.19 tff(13264,plain,
% 291.70/184.19 ($false),
% 291.70/184.19 inference(unit_resolution,[status(thm)],[13263, 5718, 13230, 13231, 13257, 13256])).
% 291.70/184.19 tff(13265,plain,((~node10(c_e_h_3, c_m, s11, s12)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s11)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s11))), inference(lemma,lemma(discharge,[]))).
% 291.70/184.20 tff(13266,plain,
% 291.70/184.20 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s11)),
% 291.70/184.20 inference(unit_resolution,[status(thm)],[13265, 13255, 13231, 13230])).
% 291.70/184.20 tff(13267,plain,
% 291.70/184.20 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s11) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s11) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11))),
% 291.70/184.20 inference(rewrite,[status(thm)],[])).
% 291.70/184.20 tff(13268,plain,
% 291.70/184.20 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s11) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11))),
% 291.70/184.20 inference(quant_inst,[status(thm)],[])).
% 291.70/184.20 tff(13269,plain,
% 291.70/184.20 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s11) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11)),
% 291.70/184.20 inference(modus_ponens,[status(thm)],[13268, 13267])).
% 291.70/184.20 tff(13270,plain,
% 291.70/184.20 (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s11) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11)),
% 291.70/184.20 inference(unit_resolution,[status(thm)],[13269, 5704])).
% 291.70/184.20 tff(13271,plain,
% 291.70/184.20 (m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11)),
% 291.70/184.20 inference(unit_resolution,[status(thm)],[13270, 13266])).
% 291.70/184.20 tff(13272,plain,
% 291.70/184.20 (~node11(c_e_h_3, c_n, s10, s11)),
% 291.70/184.20 inference(unit_resolution,[status(thm)],[13184, 13271, 13235])).
% 291.70/184.20 tff(13273,plain,
% 291.70/184.20 (node10(c_e_h_3, c_n, s10, s11)),
% 291.70/184.20 inference(unit_resolution,[status(thm)],[13189, 13272])).
% 291.70/184.20 tff(13274,plain,
% 291.70/184.20 (node9(c_e_h_3, c_n, s10)),
% 291.70/184.20 inference(unit_resolution,[status(thm)],[13193, 4986, 13271, 13273])).
% 291.70/184.20 tff(13275,plain,
% 291.70/184.20 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s10)),
% 291.70/184.20 inference(unit_resolution,[status(thm)],[13170, 5601, 13238])).
% 291.70/184.20 tff(13276,plain,
% 291.70/184.20 ($false),
% 291.70/184.20 inference(unit_resolution,[status(thm)],[13174, 4972, 13275, 13274])).
% 291.70/184.20 tff(13277,plain,(m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s11)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s10)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9))), inference(lemma,lemma(discharge,[]))).
% 291.70/184.20 tff(13278,plain,
% 291.70/184.20 (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s10)),
% 291.70/184.20 inference(unit_resolution,[status(thm)],[13277, 13232, 13067, 13231, 13105, 13230])).
% 291.70/184.20 tff(13279,plain,
% 291.70/184.20 (m_c_h_element_v_out(c_e_h_3, c_f, s10)),
% 291.70/184.20 inference(unit_resolution,[status(thm)],[13007, 13278])).
% 291.70/184.20 tff(13280,plain,
% 291.70/184.20 (~node18(c_e_h_3, c_f, s9, s10)),
% 291.70/184.20 inference(unit_resolution,[status(thm)],[11625, 13279, 11586])).
% 291.70/184.20 tff(13281,plain,
% 291.70/184.20 (node17(c_e_h_3, c_f, s9)),
% 291.70/184.20 inference(unit_resolution,[status(thm)],[11633, 13280])).
% 291.70/184.20 tff(13282,plain,
% 291.70/184.20 (~node16(c_e_h_3, c_f, s9)),
% 291.70/184.20 inference(unit_resolution,[status(thm)],[11668, 13281])).
% 291.70/184.20 tff(13283,plain,
% 291.70/184.20 ((~node17(c_e_h_3, c_f, s9)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s9))),
% 291.70/184.20 inference(unit_resolution,[status(thm)],[11657, 919, 11584])).
% 291.70/184.20 tff(13284,plain,
% 291.70/184.20 (~m_c_h_element_v_in1(c_e_h_3, c_f, s9)),
% 291.70/184.20 inference(unit_resolution,[status(thm)],[13283, 13281])).
% 291.70/184.20 tff(13285,plain,
% 291.70/184.20 ($false),
% 291.70/184.20 inference(unit_resolution,[status(thm)],[11615, 13284, 13282, 13279, 11586])).
% 291.70/184.20 tff(13286,plain,(m_c_h_element_v_out(c_e_h_3, c_f, s9) | m_c_h_element_v_in2(c_e_h_3, c_f, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s11)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12)), inference(lemma,lemma(discharge,[]))).
% 291.70/184.20 tff(13287,plain,
% 291.70/184.20 (m_c_h_element_v_out(c_e_h_3, c_f, s9) | m_c_h_element_v_in2(c_e_h_3, c_f, s9) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s11)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12)),
% 291.70/184.20 inference(unit_resolution,[status(thm)],[13286, 9445, 13061])).
% 291.70/184.20 tff(13288,plain,
% 291.70/184.20 (m_c_h_element_v_in2(c_e_h_3, c_f, s9) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s11)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12)),
% 291.70/184.20 inference(unit_resolution,[status(thm)],[13287, 11583])).
% 291.70/184.20 tff(13289,plain,
% 291.70/184.20 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12)),
% 291.70/184.20 inference(unit_resolution,[status(thm)],[13288, 13229, 11482])).
% 291.70/184.20 tff(13290,plain,
% 291.70/184.20 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s12)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s12)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12)))),
% 291.70/184.20 inference(rewrite,[status(thm)],[])).
% 291.70/184.20 tff(13291,plain,
% 291.70/184.20 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s12)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12)))),
% 291.70/184.20 inference(quant_inst,[status(thm)],[])).
% 291.70/184.20 tff(13292,plain,
% 291.70/184.20 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s12)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12))),
% 291.70/184.20 inference(modus_ponens,[status(thm)],[13291, 13290])).
% 291.70/184.20 tff(13293,plain,
% 291.70/184.20 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s12)),
% 291.70/184.20 inference(unit_resolution,[status(thm)],[13292, 5601, 13289])).
% 291.70/184.20 tff(13294,plain,
% 291.70/184.20 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s12)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s12))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s12)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s12))),
% 291.70/184.20 inference(rewrite,[status(thm)],[])).
% 291.70/184.20 tff(13295,plain,
% 291.70/184.20 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s12)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s12))),
% 291.70/184.20 inference(quant_inst,[status(thm)],[])).
% 291.70/184.20 tff(13296,plain,
% 291.70/184.20 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s12)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s12)),
% 291.70/184.20 inference(modus_ponens,[status(thm)],[13295, 13294])).
% 291.70/184.20 tff(13297,plain,
% 291.70/184.20 (~node9(c_e_h_3, c_n, s12)),
% 291.70/184.20 inference(unit_resolution,[status(thm)],[13296, 4972, 13293])).
% 291.70/184.20 tff(13298,assumption,(~node9(c_e_h_3, c_n, s12)), introduced(assumption)).
% 291.70/184.20 tff(13299,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s12)), introduced(assumption)).
% 291.70/184.20 tff(13300,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s13)), introduced(assumption)).
% 291.70/184.20 tff(13301,assumption,(node11(c_e_h_3, c_n, s12, s13)), introduced(assumption)).
% 291.70/184.20 tff(13302,plain,
% 291.70/184.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s13)) | (~node11(c_e_h_3, c_n, s12, s13)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s13)) | (~node11(c_e_h_3, c_n, s12, s13)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s12))),
% 291.70/184.20 inference(rewrite,[status(thm)],[])).
% 291.70/184.20 tff(13303,plain,
% 291.70/184.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s13)) | (~node11(c_e_h_3, c_n, s12, s13)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s12))),
% 291.70/184.20 inference(quant_inst,[status(thm)],[])).
% 291.70/184.20 tff(13304,plain,
% 291.70/184.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s13)) | (~node11(c_e_h_3, c_n, s12, s13)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s12)),
% 291.71/184.20 inference(modus_ponens,[status(thm)],[13303, 13302])).
% 291.71/184.20 tff(13305,plain,
% 291.71/184.20 ($false),
% 291.71/184.20 inference(unit_resolution,[status(thm)],[13304, 5017, 13300, 13299, 13301])).
% 291.71/184.20 tff(13306,plain,((~node11(c_e_h_3, c_n, s12, s13)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s13)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s12)), inference(lemma,lemma(discharge,[]))).
% 291.71/184.20 tff(13307,plain,
% 291.71/184.20 (~node11(c_e_h_3, c_n, s12, s13)),
% 291.71/184.20 inference(unit_resolution,[status(thm)],[13306, 13300, 13299])).
% 291.71/184.20 tff(13308,plain,
% 291.71/184.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s12, s13)) | node10(c_e_h_3, c_n, s12, s13) | node11(c_e_h_3, c_n, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s12, s13)) | node10(c_e_h_3, c_n, s12, s13) | node11(c_e_h_3, c_n, s12, s13))),
% 291.71/184.20 inference(rewrite,[status(thm)],[])).
% 291.71/184.20 tff(13309,plain,
% 291.71/184.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s12, s13)) | node10(c_e_h_3, c_n, s12, s13) | node11(c_e_h_3, c_n, s12, s13))),
% 291.71/184.20 inference(quant_inst,[status(thm)],[])).
% 291.71/184.20 tff(13310,plain,
% 291.71/184.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s12, s13)) | node10(c_e_h_3, c_n, s12, s13) | node11(c_e_h_3, c_n, s12, s13)),
% 291.71/184.20 inference(modus_ponens,[status(thm)],[13309, 13308])).
% 291.71/184.20 tff(13311,plain,
% 291.71/184.20 (node10(c_e_h_3, c_n, s12, s13) | node11(c_e_h_3, c_n, s12, s13)),
% 291.71/184.20 inference(unit_resolution,[status(thm)],[13310, 5002, 11856])).
% 291.71/184.20 tff(13312,plain,
% 291.71/184.20 (node10(c_e_h_3, c_n, s12, s13)),
% 291.71/184.20 inference(unit_resolution,[status(thm)],[13311, 13307])).
% 291.71/184.20 tff(13313,plain,
% 291.71/184.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s13)) | node9(c_e_h_3, c_n, s12) | (~node10(c_e_h_3, c_n, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s13)) | node9(c_e_h_3, c_n, s12) | (~node10(c_e_h_3, c_n, s12, s13)))),
% 291.71/184.20 inference(rewrite,[status(thm)],[])).
% 291.71/184.20 tff(13314,plain,
% 291.71/184.20 ((node9(c_e_h_3, c_n, s12) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s13)) | (~node10(c_e_h_3, c_n, s12, s13))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s13)) | node9(c_e_h_3, c_n, s12) | (~node10(c_e_h_3, c_n, s12, s13)))),
% 291.71/184.20 inference(rewrite,[status(thm)],[])).
% 291.71/184.20 tff(13315,plain,
% 291.71/184.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s12) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s13)) | (~node10(c_e_h_3, c_n, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s13)) | node9(c_e_h_3, c_n, s12) | (~node10(c_e_h_3, c_n, s12, s13))))),
% 291.71/184.20 inference(monotonicity,[status(thm)],[13314])).
% 291.71/184.20 tff(13316,plain,
% 291.71/184.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s12) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s13)) | (~node10(c_e_h_3, c_n, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s13)) | node9(c_e_h_3, c_n, s12) | (~node10(c_e_h_3, c_n, s12, s13)))),
% 291.71/184.20 inference(transitivity,[status(thm)],[13315, 13313])).
% 291.71/184.20 tff(13317,plain,
% 291.71/184.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s12) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s13)) | (~node10(c_e_h_3, c_n, s12, s13)))),
% 291.71/184.21 inference(quant_inst,[status(thm)],[])).
% 291.71/184.21 tff(13318,plain,
% 291.71/184.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s13)) | node9(c_e_h_3, c_n, s12) | (~node10(c_e_h_3, c_n, s12, s13))),
% 291.71/184.21 inference(modus_ponens,[status(thm)],[13317, 13316])).
% 291.71/184.21 tff(13319,plain,
% 291.71/184.21 ($false),
% 291.71/184.21 inference(unit_resolution,[status(thm)],[13318, 4986, 13300, 13312, 13298])).
% 291.71/184.21 tff(13320,plain,((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s13)) | node9(c_e_h_3, c_n, s12) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s12)), inference(lemma,lemma(discharge,[]))).
% 291.71/184.21 tff(13321,plain,
% 291.71/184.21 (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s13)),
% 291.71/184.21 inference(unit_resolution,[status(thm)],[13320, 13297, 13219])).
% 291.71/184.21 tff(13322,plain,
% 291.71/184.21 (~m_c_h_element_v_out(c_e_h_3, c_f, s13)),
% 291.71/184.21 inference(unit_resolution,[status(thm)],[11914, 11841, 11905])).
% 291.71/184.21 tff(13323,plain,
% 291.71/184.21 (~m_c_h_element_v_out(c_e_h_3, c_f, s14)),
% 291.71/184.21 inference(unit_resolution,[status(thm)],[12906, 13322, 12847])).
% 291.71/184.21 tff(13324,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s13)), introduced(assumption)).
% 291.71/184.21 tff(13325,plain,
% 291.71/184.21 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s13) | m_c_h_element_v_out(c_e_h_3, c_f, s13))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s13) | m_c_h_element_v_out(c_e_h_3, c_f, s13))),
% 291.71/184.21 inference(rewrite,[status(thm)],[])).
% 291.71/184.21 tff(13326,plain,
% 291.71/184.21 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s13) | m_c_h_element_v_out(c_e_h_3, c_f, s13))),
% 291.71/184.21 inference(quant_inst,[status(thm)],[])).
% 291.71/184.21 tff(13327,plain,
% 291.71/184.21 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s13) | m_c_h_element_v_out(c_e_h_3, c_f, s13)),
% 291.71/184.21 inference(modus_ponens,[status(thm)],[13326, 13325])).
% 291.71/184.21 tff(13328,plain,
% 291.71/184.21 ($false),
% 291.71/184.21 inference(unit_resolution,[status(thm)],[13327, 5689, 12849, 13324])).
% 291.71/184.21 tff(13329,plain,(m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s13) | m_c_h_element_v_out(c_e_h_3, c_f, s13)), inference(lemma,lemma(discharge,[]))).
% 291.71/184.21 tff(13330,plain,
% 291.71/184.21 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s13)),
% 291.71/184.21 inference(unit_resolution,[status(thm)],[13329, 13322])).
% 291.71/184.21 tff(13331,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s15)), introduced(assumption)).
% 291.71/184.21 tff(13332,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s13)), introduced(assumption)).
% 291.71/184.21 tff(13333,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s16)), introduced(assumption)).
% 291.71/184.21 tff(13334,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s17)), introduced(assumption)).
% 291.71/184.21 tff(13335,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s12)), introduced(assumption)).
% 291.71/184.21 tff(13336,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12)), introduced(assumption)).
% 291.71/184.21 tff(13337,plain,
% 291.71/184.21 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s12) | m_c_h_element_v_out(c_e_h_3, c_f, s12))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s12) | m_c_h_element_v_out(c_e_h_3, c_f, s12))),
% 291.71/184.21 inference(rewrite,[status(thm)],[])).
% 291.71/184.21 tff(13338,plain,
% 291.71/184.21 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s12) | m_c_h_element_v_out(c_e_h_3, c_f, s12))),
% 291.71/184.21 inference(quant_inst,[status(thm)],[])).
% 291.71/184.21 tff(13339,plain,
% 291.71/184.21 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s12) | m_c_h_element_v_out(c_e_h_3, c_f, s12)),
% 291.71/184.21 inference(modus_ponens,[status(thm)],[13338, 13337])).
% 291.71/184.21 tff(13340,plain,
% 291.71/184.21 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s12) | m_c_h_element_v_out(c_e_h_3, c_f, s12)),
% 291.71/184.21 inference(unit_resolution,[status(thm)],[13339, 5689])).
% 291.71/184.21 tff(13341,plain,
% 291.71/184.21 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s12)),
% 291.71/184.21 inference(unit_resolution,[status(thm)],[13340, 11841])).
% 291.71/184.21 tff(13342,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s12)), introduced(assumption)).
% 291.71/184.21 tff(13343,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s13)), introduced(assumption)).
% 291.71/184.21 tff(13344,assumption,(node10(c_e_h_3, c_m, s12, s13)), introduced(assumption)).
% 291.71/184.21 tff(13345,plain,
% 291.71/184.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s13) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s12)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s12)) | (~node10(c_e_h_3, c_m, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s13) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s12)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s12)) | (~node10(c_e_h_3, c_m, s12, s13)))),
% 291.71/184.21 inference(rewrite,[status(thm)],[])).
% 291.71/184.21 tff(13346,plain,
% 291.71/184.21 (((~node10(c_e_h_3, c_m, s12, s13)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s12)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s13)) <=> (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s13) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s12)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s12)) | (~node10(c_e_h_3, c_m, s12, s13)))),
% 291.71/184.21 inference(rewrite,[status(thm)],[])).
% 291.71/184.21 tff(13347,plain,
% 291.71/184.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s12, s13)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s12)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s13) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s12)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s12)) | (~node10(c_e_h_3, c_m, s12, s13))))),
% 291.71/184.21 inference(monotonicity,[status(thm)],[13346])).
% 291.71/184.21 tff(13348,plain,
% 291.71/184.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s12, s13)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s12)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s13) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s12)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s12)) | (~node10(c_e_h_3, c_m, s12, s13)))),
% 291.71/184.21 inference(transitivity,[status(thm)],[13347, 13345])).
% 291.71/184.21 tff(13349,plain,
% 291.71/184.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s12, s13)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s12)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s13))),
% 291.71/184.21 inference(quant_inst,[status(thm)],[])).
% 291.71/184.21 tff(13350,plain,
% 291.71/184.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s13) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s12)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s12)) | (~node10(c_e_h_3, c_m, s12, s13))),
% 291.72/184.21 inference(modus_ponens,[status(thm)],[13349, 13348])).
% 291.72/184.21 tff(13351,plain,
% 291.72/184.21 ($false),
% 291.72/184.21 inference(unit_resolution,[status(thm)],[13350, 5718, 13343, 13342, 13335, 13344])).
% 291.72/184.21 tff(13352,plain,((~node10(c_e_h_3, c_m, s12, s13)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s13) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s12)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s12))), inference(lemma,lemma(discharge,[]))).
% 291.72/184.21 tff(13353,plain,
% 291.72/184.21 (~node10(c_e_h_3, c_m, s12, s13)),
% 291.72/184.21 inference(unit_resolution,[status(thm)],[13352, 13343, 13335, 13342])).
% 291.72/184.21 tff(13354,assumption,(node11(c_e_h_3, c_m, s12, s13)), introduced(assumption)).
% 291.72/184.21 tff(13355,plain,
% 291.72/184.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12)) | (~node11(c_e_h_3, c_m, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12)) | (~node11(c_e_h_3, c_m, s12, s13)))),
% 291.72/184.21 inference(rewrite,[status(thm)],[])).
% 291.72/184.21 tff(13356,plain,
% 291.72/184.21 ((m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s13) | (~node11(c_e_h_3, c_m, s12, s13)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12))) <=> (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12)) | (~node11(c_e_h_3, c_m, s12, s13)))),
% 291.72/184.21 inference(rewrite,[status(thm)],[])).
% 291.72/184.21 tff(13357,plain,
% 291.72/184.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s13) | (~node11(c_e_h_3, c_m, s12, s13)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12)) | (~node11(c_e_h_3, c_m, s12, s13))))),
% 291.72/184.21 inference(monotonicity,[status(thm)],[13356])).
% 291.72/184.21 tff(13358,plain,
% 291.72/184.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s13) | (~node11(c_e_h_3, c_m, s12, s13)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12)) | (~node11(c_e_h_3, c_m, s12, s13)))),
% 291.72/184.21 inference(transitivity,[status(thm)],[13357, 13355])).
% 291.72/184.21 tff(13359,plain,
% 291.72/184.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s13) | (~node11(c_e_h_3, c_m, s12, s13)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12)))),
% 291.72/184.21 inference(quant_inst,[status(thm)],[])).
% 291.72/184.21 tff(13360,plain,
% 291.72/184.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12)) | (~node11(c_e_h_3, c_m, s12, s13))),
% 291.72/184.21 inference(modus_ponens,[status(thm)],[13359, 13358])).
% 291.72/184.21 tff(13361,plain,
% 291.72/184.21 ($false),
% 291.72/184.21 inference(unit_resolution,[status(thm)],[13360, 5742, 13336, 13343, 13354])).
% 291.72/184.21 tff(13362,plain,((~node11(c_e_h_3, c_m, s12, s13)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s13)), inference(lemma,lemma(discharge,[]))).
% 291.72/184.21 tff(13363,plain,
% 291.72/184.21 (~node11(c_e_h_3, c_m, s12, s13)),
% 291.72/184.21 inference(unit_resolution,[status(thm)],[13362, 13343, 13336])).
% 291.72/184.21 tff(13364,plain,
% 291.72/184.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s12, s13)) | node10(c_e_h_3, c_m, s12, s13) | node11(c_e_h_3, c_m, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s12, s13)) | node10(c_e_h_3, c_m, s12, s13) | node11(c_e_h_3, c_m, s12, s13))),
% 291.72/184.21 inference(rewrite,[status(thm)],[])).
% 291.72/184.21 tff(13365,plain,
% 291.72/184.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s12, s13)) | node10(c_e_h_3, c_m, s12, s13) | node11(c_e_h_3, c_m, s12, s13))),
% 291.72/184.21 inference(quant_inst,[status(thm)],[])).
% 291.72/184.21 tff(13366,plain,
% 291.72/184.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s12, s13)) | node10(c_e_h_3, c_m, s12, s13) | node11(c_e_h_3, c_m, s12, s13)),
% 291.72/184.21 inference(modus_ponens,[status(thm)],[13365, 13364])).
% 291.72/184.21 tff(13367,plain,
% 291.72/184.21 (node10(c_e_h_3, c_m, s12, s13) | node11(c_e_h_3, c_m, s12, s13)),
% 291.72/184.21 inference(unit_resolution,[status(thm)],[13366, 5002, 11856])).
% 291.72/184.21 tff(13368,plain,
% 291.72/184.21 ($false),
% 291.72/184.21 inference(unit_resolution,[status(thm)],[13367, 13363, 13353])).
% 291.72/184.21 tff(13369,plain,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s12))), inference(lemma,lemma(discharge,[]))).
% 291.72/184.21 tff(13370,plain,
% 291.72/184.21 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s13)),
% 291.72/184.21 inference(unit_resolution,[status(thm)],[13369, 13341, 13336, 13335])).
% 291.72/184.21 tff(13371,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s14)), introduced(assumption)).
% 291.72/184.21 tff(13372,assumption,(~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s13)), introduced(assumption)).
% 291.72/184.21 tff(13373,plain,
% 291.72/184.21 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s13) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s13))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s13) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s13))),
% 291.72/184.21 inference(rewrite,[status(thm)],[])).
% 291.72/184.21 tff(13374,plain,
% 291.72/184.21 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s13) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s13))),
% 291.72/184.21 inference(quant_inst,[status(thm)],[])).
% 291.72/184.21 tff(13375,plain,
% 291.72/184.21 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s13) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s13)),
% 291.72/184.21 inference(modus_ponens,[status(thm)],[13374, 13373])).
% 291.72/184.21 tff(13376,plain,
% 291.72/184.21 ($false),
% 291.72/184.21 inference(unit_resolution,[status(thm)],[13375, 5704, 13372, 13332])).
% 291.72/184.21 tff(13377,plain,(m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s13) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s13)), inference(lemma,lemma(discharge,[]))).
% 291.72/184.21 tff(13378,plain,
% 291.72/184.21 (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s13)),
% 291.72/184.21 inference(unit_resolution,[status(thm)],[13377, 13332])).
% 291.72/184.21 tff(13379,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s13)), introduced(assumption)).
% 291.72/184.21 tff(13380,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s13)), introduced(assumption)).
% 291.72/184.21 tff(13381,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s13)), introduced(assumption)).
% 291.72/184.21 tff(13382,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s14)), introduced(assumption)).
% 291.72/184.21 tff(13383,assumption,(node10(c_e_h_3, c_m, s13, s14)), introduced(assumption)).
% 291.72/184.21 tff(13384,plain,
% 291.72/184.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s13, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s13)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s14) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~node10(c_e_h_3, c_m, s13, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s13)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s14) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s13)))),
% 291.72/184.22 inference(rewrite,[status(thm)],[])).
% 291.72/184.22 tff(13385,plain,
% 291.72/184.22 (((~node10(c_e_h_3, c_m, s13, s14)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s13)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s13)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s14)) <=> ((~node10(c_e_h_3, c_m, s13, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s13)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s14) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s13)))),
% 291.72/184.22 inference(rewrite,[status(thm)],[])).
% 291.72/184.22 tff(13386,plain,
% 291.72/184.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s13, s14)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s13)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s13)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s13, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s13)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s14) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s13))))),
% 291.72/184.22 inference(monotonicity,[status(thm)],[13385])).
% 291.72/184.22 tff(13387,plain,
% 291.72/184.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s13, s14)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s13)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s13)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~node10(c_e_h_3, c_m, s13, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s13)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s14) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s13)))),
% 291.72/184.22 inference(transitivity,[status(thm)],[13386, 13384])).
% 291.72/184.22 tff(13388,plain,
% 291.72/184.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s13, s14)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s13)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s13)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s14))),
% 291.72/184.22 inference(quant_inst,[status(thm)],[])).
% 291.72/184.22 tff(13389,plain,
% 291.72/184.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~node10(c_e_h_3, c_m, s13, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s13)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s14) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s13))),
% 291.72/184.22 inference(modus_ponens,[status(thm)],[13388, 13387])).
% 291.72/184.22 tff(13390,plain,
% 291.72/184.22 ($false),
% 291.72/184.22 inference(unit_resolution,[status(thm)],[13389, 5718, 13382, 13383, 13381, 13379])).
% 291.72/184.22 tff(13391,plain,((~node10(c_e_h_3, c_m, s13, s14)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s14) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s13)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s13))), inference(lemma,lemma(discharge,[]))).
% 291.72/184.22 tff(13392,plain,
% 291.72/184.22 (~node10(c_e_h_3, c_m, s13, s14)),
% 291.72/184.22 inference(unit_resolution,[status(thm)],[13391, 13382, 13381, 13379])).
% 291.72/184.22 tff(13393,plain,
% 291.72/184.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s13, s14)) | node10(c_e_h_3, c_m, s13, s14) | node11(c_e_h_3, c_m, s13, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s13, s14)) | node10(c_e_h_3, c_m, s13, s14) | node11(c_e_h_3, c_m, s13, s14))),
% 291.72/184.22 inference(rewrite,[status(thm)],[])).
% 291.72/184.22 tff(13394,plain,
% 291.72/184.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s13, s14)) | node10(c_e_h_3, c_m, s13, s14) | node11(c_e_h_3, c_m, s13, s14))),
% 291.72/184.22 inference(quant_inst,[status(thm)],[])).
% 291.72/184.22 tff(13395,plain,
% 291.72/184.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s13, s14)) | node10(c_e_h_3, c_m, s13, s14) | node11(c_e_h_3, c_m, s13, s14)),
% 291.72/184.22 inference(modus_ponens,[status(thm)],[13394, 13393])).
% 291.72/184.22 tff(13396,plain,
% 291.72/184.22 (node10(c_e_h_3, c_m, s13, s14) | node11(c_e_h_3, c_m, s13, s14)),
% 291.72/184.22 inference(unit_resolution,[status(thm)],[13395, 5002, 12831])).
% 291.72/184.22 tff(13397,plain,
% 291.72/184.22 (node11(c_e_h_3, c_m, s13, s14)),
% 291.72/184.22 inference(unit_resolution,[status(thm)],[13396, 13392])).
% 291.72/184.22 tff(13398,plain,
% 291.72/184.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s14) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s13)) | (~node11(c_e_h_3, c_m, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s14) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s13)) | (~node11(c_e_h_3, c_m, s13, s14)))),
% 291.72/184.22 inference(rewrite,[status(thm)],[])).
% 291.72/184.22 tff(13399,plain,
% 291.72/184.22 ((m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s14) | (~node11(c_e_h_3, c_m, s13, s14)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s13))) <=> (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s14) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s13)) | (~node11(c_e_h_3, c_m, s13, s14)))),
% 291.72/184.22 inference(rewrite,[status(thm)],[])).
% 291.72/184.22 tff(13400,plain,
% 291.72/184.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s14) | (~node11(c_e_h_3, c_m, s13, s14)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s14) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s13)) | (~node11(c_e_h_3, c_m, s13, s14))))),
% 291.72/184.22 inference(monotonicity,[status(thm)],[13399])).
% 291.72/184.22 tff(13401,plain,
% 291.72/184.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s14) | (~node11(c_e_h_3, c_m, s13, s14)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s14) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s13)) | (~node11(c_e_h_3, c_m, s13, s14)))),
% 291.72/184.22 inference(transitivity,[status(thm)],[13400, 13398])).
% 291.72/184.22 tff(13402,plain,
% 291.72/184.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s14) | (~node11(c_e_h_3, c_m, s13, s14)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s13)))),
% 291.72/184.22 inference(quant_inst,[status(thm)],[])).
% 291.72/184.22 tff(13403,plain,
% 291.72/184.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s14) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s13)) | (~node11(c_e_h_3, c_m, s13, s14))),
% 291.72/184.22 inference(modus_ponens,[status(thm)],[13402, 13401])).
% 291.72/184.22 tff(13404,plain,
% 291.72/184.22 ($false),
% 291.72/184.22 inference(unit_resolution,[status(thm)],[13403, 5742, 13382, 13397, 13380])).
% 291.72/184.22 tff(13405,plain,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s14) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s13)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s13)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s13))), inference(lemma,lemma(discharge,[]))).
% 291.72/184.22 tff(13406,plain,
% 291.72/184.22 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s14)),
% 291.72/184.22 inference(unit_resolution,[status(thm)],[13405, 13380, 13379, 13378])).
% 291.72/184.22 tff(13407,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s14)), introduced(assumption)).
% 291.72/184.22 tff(13408,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s14)), introduced(assumption)).
% 291.72/184.22 tff(13409,plain,
% 291.72/184.22 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s14)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s14)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s14)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s14)))),
% 291.72/184.22 inference(rewrite,[status(thm)],[])).
% 291.72/184.22 tff(13410,plain,
% 291.72/184.22 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s14)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s14)))),
% 291.72/184.22 inference(quant_inst,[status(thm)],[])).
% 291.72/184.22 tff(13411,plain,
% 291.72/184.22 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s14)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s14))),
% 291.72/184.22 inference(modus_ponens,[status(thm)],[13410, 13409])).
% 291.72/184.22 tff(13412,plain,
% 291.72/184.22 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s14)),
% 291.72/184.22 inference(unit_resolution,[status(thm)],[13411, 5601, 13408])).
% 291.72/184.22 tff(13413,plain,
% 291.72/184.22 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s14)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s14))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s14)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s14))),
% 291.72/184.22 inference(rewrite,[status(thm)],[])).
% 291.72/184.22 tff(13414,plain,
% 291.72/184.22 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s14)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s14))),
% 291.72/184.22 inference(quant_inst,[status(thm)],[])).
% 291.72/184.22 tff(13415,plain,
% 291.72/184.22 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s14)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s14)),
% 291.72/184.22 inference(modus_ponens,[status(thm)],[13414, 13413])).
% 291.72/184.22 tff(13416,plain,
% 291.72/184.22 (~node9(c_e_h_3, c_n, s14)),
% 291.72/184.22 inference(unit_resolution,[status(thm)],[13415, 4972, 13412])).
% 291.72/184.22 tff(13417,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s15)), introduced(assumption)).
% 291.72/184.22 tff(13418,assumption,(~node9(c_e_h_3, c_n, s14)), introduced(assumption)).
% 291.72/184.22 tff(13419,assumption,(node11(c_e_h_3, c_n, s14, s15)), introduced(assumption)).
% 291.72/184.22 tff(13420,plain,
% 291.72/184.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s15)) | (~node11(c_e_h_3, c_n, s14, s15)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s15)) | (~node11(c_e_h_3, c_n, s14, s15)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s14))),
% 291.72/184.22 inference(rewrite,[status(thm)],[])).
% 291.72/184.22 tff(13421,plain,
% 291.72/184.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s15)) | (~node11(c_e_h_3, c_n, s14, s15)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s14))),
% 291.72/184.23 inference(quant_inst,[status(thm)],[])).
% 291.72/184.23 tff(13422,plain,
% 291.72/184.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s15)) | (~node11(c_e_h_3, c_n, s14, s15)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s14)),
% 291.72/184.23 inference(modus_ponens,[status(thm)],[13421, 13420])).
% 291.72/184.23 tff(13423,plain,
% 291.72/184.23 ($false),
% 291.72/184.23 inference(unit_resolution,[status(thm)],[13422, 5017, 13419, 13407, 13417])).
% 291.72/184.23 tff(13424,plain,((~node11(c_e_h_3, c_n, s14, s15)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s14) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s15))), inference(lemma,lemma(discharge,[]))).
% 291.72/184.23 tff(13425,plain,
% 291.72/184.23 (~node11(c_e_h_3, c_n, s14, s15)),
% 291.72/184.23 inference(unit_resolution,[status(thm)],[13424, 13417, 13407])).
% 291.72/184.23 tff(13426,plain,
% 291.72/184.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s14, s15)) | node10(c_e_h_3, c_n, s14, s15) | node11(c_e_h_3, c_n, s14, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s14, s15)) | node10(c_e_h_3, c_n, s14, s15) | node11(c_e_h_3, c_n, s14, s15))),
% 291.72/184.23 inference(rewrite,[status(thm)],[])).
% 291.72/184.23 tff(13427,plain,
% 291.72/184.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s14, s15)) | node10(c_e_h_3, c_n, s14, s15) | node11(c_e_h_3, c_n, s14, s15))),
% 291.72/184.23 inference(quant_inst,[status(thm)],[])).
% 291.72/184.23 tff(13428,plain,
% 291.72/184.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s14, s15)) | node10(c_e_h_3, c_n, s14, s15) | node11(c_e_h_3, c_n, s14, s15)),
% 291.72/184.23 inference(modus_ponens,[status(thm)],[13427, 13426])).
% 291.72/184.23 tff(13429,plain,
% 291.72/184.23 (node10(c_e_h_3, c_n, s14, s15) | node11(c_e_h_3, c_n, s14, s15)),
% 291.72/184.23 inference(unit_resolution,[status(thm)],[13428, 5002, 12926])).
% 291.72/184.23 tff(13430,plain,
% 291.72/184.23 (node10(c_e_h_3, c_n, s14, s15)),
% 291.72/184.23 inference(unit_resolution,[status(thm)],[13429, 13425])).
% 291.72/184.23 tff(13431,plain,
% 291.72/184.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s14) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s15)) | (~node10(c_e_h_3, c_n, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_3, c_n, s14) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s15)) | (~node10(c_e_h_3, c_n, s14, s15)))),
% 291.72/184.23 inference(rewrite,[status(thm)],[])).
% 291.72/184.23 tff(13432,plain,
% 291.72/184.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s14) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s15)) | (~node10(c_e_h_3, c_n, s14, s15)))),
% 291.72/184.23 inference(quant_inst,[status(thm)],[])).
% 291.72/184.23 tff(13433,plain,
% 291.72/184.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_3, c_n, s14) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s15)) | (~node10(c_e_h_3, c_n, s14, s15))),
% 291.72/184.23 inference(modus_ponens,[status(thm)],[13432, 13431])).
% 291.72/184.23 tff(13434,plain,
% 291.72/184.23 ($false),
% 291.72/184.23 inference(unit_resolution,[status(thm)],[13433, 4986, 13430, 13418, 13417])).
% 291.72/184.23 tff(13435,plain,((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s15)) | node9(c_e_h_3, c_n, s14) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s14)), inference(lemma,lemma(discharge,[]))).
% 291.72/184.23 tff(13436,plain,
% 291.72/184.23 (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s15)),
% 291.72/184.23 inference(unit_resolution,[status(thm)],[13435, 13416, 13407])).
% 291.72/184.23 tff(13437,assumption,(~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s14)), introduced(assumption)).
% 291.72/184.23 tff(13438,plain,
% 291.72/184.23 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s14) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s14))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s14) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s14))),
% 291.72/184.23 inference(rewrite,[status(thm)],[])).
% 291.72/184.23 tff(13439,plain,
% 291.72/184.23 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s14) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s14))),
% 291.72/184.23 inference(quant_inst,[status(thm)],[])).
% 291.72/184.23 tff(13440,plain,
% 291.72/184.23 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s14) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s14)),
% 291.72/184.23 inference(modus_ponens,[status(thm)],[13439, 13438])).
% 291.72/184.23 tff(13441,plain,
% 291.72/184.23 ($false),
% 291.72/184.23 inference(unit_resolution,[status(thm)],[13440, 5704, 13407, 13437])).
% 291.72/184.23 tff(13442,plain,(m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s14) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s14)), inference(lemma,lemma(discharge,[]))).
% 291.72/184.23 tff(13443,plain,
% 291.72/184.23 (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s14)),
% 291.72/184.23 inference(unit_resolution,[status(thm)],[13442, 13407])).
% 291.72/184.23 tff(13444,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s15)), introduced(assumption)).
% 291.72/184.23 tff(13445,assumption,(node11(c_e_h_3, c_m, s14, s15)), introduced(assumption)).
% 291.72/184.23 tff(13446,plain,
% 291.72/184.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s15) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s14)) | (~node11(c_e_h_3, c_m, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s15) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s14)) | (~node11(c_e_h_3, c_m, s14, s15)))),
% 291.72/184.23 inference(rewrite,[status(thm)],[])).
% 291.72/184.23 tff(13447,plain,
% 291.72/184.23 ((m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s15) | (~node11(c_e_h_3, c_m, s14, s15)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s14))) <=> (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s15) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s14)) | (~node11(c_e_h_3, c_m, s14, s15)))),
% 291.72/184.23 inference(rewrite,[status(thm)],[])).
% 291.72/184.23 tff(13448,plain,
% 291.72/184.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s15) | (~node11(c_e_h_3, c_m, s14, s15)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s15) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s14)) | (~node11(c_e_h_3, c_m, s14, s15))))),
% 291.72/184.23 inference(monotonicity,[status(thm)],[13447])).
% 291.72/184.23 tff(13449,plain,
% 291.72/184.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s15) | (~node11(c_e_h_3, c_m, s14, s15)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s15) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s14)) | (~node11(c_e_h_3, c_m, s14, s15)))),
% 291.72/184.23 inference(transitivity,[status(thm)],[13448, 13446])).
% 291.72/184.23 tff(13450,plain,
% 291.72/184.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s15) | (~node11(c_e_h_3, c_m, s14, s15)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s14)))),
% 291.72/184.23 inference(quant_inst,[status(thm)],[])).
% 291.72/184.23 tff(13451,plain,
% 291.72/184.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s15) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s14)) | (~node11(c_e_h_3, c_m, s14, s15))),
% 291.72/184.23 inference(modus_ponens,[status(thm)],[13450, 13449])).
% 291.72/184.23 tff(13452,plain,
% 291.72/184.23 ($false),
% 291.72/184.23 inference(unit_resolution,[status(thm)],[13451, 5742, 13444, 13408, 13445])).
% 291.72/184.23 tff(13453,plain,((~node11(c_e_h_3, c_m, s14, s15)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s15) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s14))), inference(lemma,lemma(discharge,[]))).
% 291.72/184.23 tff(13454,plain,
% 291.72/184.23 (~node11(c_e_h_3, c_m, s14, s15)),
% 291.72/184.23 inference(unit_resolution,[status(thm)],[13453, 13444, 13408])).
% 291.72/184.23 tff(13455,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s14)), introduced(assumption)).
% 291.72/184.23 tff(13456,assumption,(node10(c_e_h_3, c_m, s14, s15)), introduced(assumption)).
% 291.72/184.23 tff(13457,plain,
% 291.72/184.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s14)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s15) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s14)) | (~node10(c_e_h_3, c_m, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s14)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s15) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s14)) | (~node10(c_e_h_3, c_m, s14, s15)))),
% 291.72/184.23 inference(rewrite,[status(thm)],[])).
% 291.72/184.23 tff(13458,plain,
% 291.72/184.23 (((~node10(c_e_h_3, c_m, s14, s15)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s14)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s15)) <=> ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s14)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s15) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s14)) | (~node10(c_e_h_3, c_m, s14, s15)))),
% 291.72/184.23 inference(rewrite,[status(thm)],[])).
% 291.72/184.23 tff(13459,plain,
% 291.72/184.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s14, s15)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s14)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s14)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s15) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s14)) | (~node10(c_e_h_3, c_m, s14, s15))))),
% 291.72/184.23 inference(monotonicity,[status(thm)],[13458])).
% 291.72/184.23 tff(13460,plain,
% 291.72/184.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s14, s15)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s14)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s14)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s15) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s14)) | (~node10(c_e_h_3, c_m, s14, s15)))),
% 291.72/184.23 inference(transitivity,[status(thm)],[13459, 13457])).
% 291.72/184.23 tff(13461,plain,
% 291.72/184.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s14, s15)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s14)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s15))),
% 291.72/184.24 inference(quant_inst,[status(thm)],[])).
% 291.72/184.24 tff(13462,plain,
% 291.72/184.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s14)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s15) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s14)) | (~node10(c_e_h_3, c_m, s14, s15))),
% 291.72/184.24 inference(modus_ponens,[status(thm)],[13461, 13460])).
% 291.72/184.24 tff(13463,plain,
% 291.72/184.24 ($false),
% 291.72/184.24 inference(unit_resolution,[status(thm)],[13462, 5718, 13444, 13456, 13455, 13371])).
% 291.72/184.24 tff(13464,plain,((~node10(c_e_h_3, c_m, s14, s15)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s15) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s14))), inference(lemma,lemma(discharge,[]))).
% 291.72/184.24 tff(13465,plain,
% 291.72/184.24 (~node10(c_e_h_3, c_m, s14, s15)),
% 291.72/184.24 inference(unit_resolution,[status(thm)],[13464, 13444, 13455, 13371])).
% 291.72/184.24 tff(13466,plain,
% 291.72/184.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s14, s15)) | node10(c_e_h_3, c_m, s14, s15) | node11(c_e_h_3, c_m, s14, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s14, s15)) | node10(c_e_h_3, c_m, s14, s15) | node11(c_e_h_3, c_m, s14, s15))),
% 291.72/184.24 inference(rewrite,[status(thm)],[])).
% 291.72/184.24 tff(13467,plain,
% 291.72/184.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s14, s15)) | node10(c_e_h_3, c_m, s14, s15) | node11(c_e_h_3, c_m, s14, s15))),
% 291.72/184.24 inference(quant_inst,[status(thm)],[])).
% 291.72/184.24 tff(13468,plain,
% 291.72/184.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s14, s15)) | node10(c_e_h_3, c_m, s14, s15) | node11(c_e_h_3, c_m, s14, s15)),
% 291.72/184.24 inference(modus_ponens,[status(thm)],[13467, 13466])).
% 291.72/184.24 tff(13469,plain,
% 291.72/184.24 (node10(c_e_h_3, c_m, s14, s15) | node11(c_e_h_3, c_m, s14, s15)),
% 291.72/184.24 inference(unit_resolution,[status(thm)],[13468, 5002, 12926])).
% 291.72/184.24 tff(13470,plain,
% 291.72/184.24 ($false),
% 291.72/184.24 inference(unit_resolution,[status(thm)],[13469, 13465, 13454])).
% 291.72/184.24 tff(13471,plain,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s15) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s14)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s14))), inference(lemma,lemma(discharge,[]))).
% 291.72/184.24 tff(13472,plain,
% 291.72/184.24 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s15)),
% 291.72/184.24 inference(unit_resolution,[status(thm)],[13471, 13408, 13371, 13443])).
% 291.72/184.24 tff(13473,assumption,(~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s15)), introduced(assumption)).
% 291.72/184.24 tff(13474,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s15)), introduced(assumption)).
% 291.72/184.24 tff(13475,plain,
% 291.72/184.24 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s15) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s15))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s15) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s15))),
% 291.72/184.24 inference(rewrite,[status(thm)],[])).
% 291.72/184.24 tff(13476,plain,
% 291.72/184.24 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s15) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s15))),
% 291.72/184.24 inference(quant_inst,[status(thm)],[])).
% 291.72/184.24 tff(13477,plain,
% 291.72/184.24 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s15) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s15)),
% 291.72/184.24 inference(modus_ponens,[status(thm)],[13476, 13475])).
% 291.72/184.24 tff(13478,plain,
% 291.72/184.24 ($false),
% 291.72/184.24 inference(unit_resolution,[status(thm)],[13477, 5704, 13474, 13473])).
% 291.72/184.24 tff(13479,plain,(m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s15) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s15)), inference(lemma,lemma(discharge,[]))).
% 291.72/184.24 tff(13480,plain,
% 291.72/184.24 (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s15)),
% 291.72/184.24 inference(unit_resolution,[status(thm)],[13479, 13436])).
% 291.72/184.24 tff(13481,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s15)), introduced(assumption)).
% 291.72/184.24 tff(13482,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s16)), introduced(assumption)).
% 291.72/184.24 tff(13483,assumption,(node10(c_e_h_3, c_m, s15, s16)), introduced(assumption)).
% 291.72/184.24 tff(13484,plain,
% 291.72/184.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s16) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s15)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s15)) | (~node10(c_e_h_3, c_m, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s16) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s15)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s15)) | (~node10(c_e_h_3, c_m, s15, s16)))),
% 291.72/184.24 inference(rewrite,[status(thm)],[])).
% 291.72/184.24 tff(13485,plain,
% 291.72/184.24 (((~node10(c_e_h_3, c_m, s15, s16)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s15)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s15)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s16)) <=> (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s16) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s15)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s15)) | (~node10(c_e_h_3, c_m, s15, s16)))),
% 291.72/184.24 inference(rewrite,[status(thm)],[])).
% 291.72/184.24 tff(13486,plain,
% 291.72/184.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s15, s16)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s15)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s15)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s16) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s15)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s15)) | (~node10(c_e_h_3, c_m, s15, s16))))),
% 291.72/184.24 inference(monotonicity,[status(thm)],[13485])).
% 291.72/184.24 tff(13487,plain,
% 291.72/184.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s15, s16)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s15)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s15)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s16) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s15)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s15)) | (~node10(c_e_h_3, c_m, s15, s16)))),
% 291.72/184.24 inference(transitivity,[status(thm)],[13486, 13484])).
% 291.72/184.24 tff(13488,plain,
% 291.72/184.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s15, s16)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s15)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s15)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s16))),
% 291.72/184.24 inference(quant_inst,[status(thm)],[])).
% 291.72/184.24 tff(13489,plain,
% 291.72/184.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s16) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s15)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s15)) | (~node10(c_e_h_3, c_m, s15, s16))),
% 291.72/184.24 inference(modus_ponens,[status(thm)],[13488, 13487])).
% 291.72/184.24 tff(13490,plain,
% 291.72/184.24 ($false),
% 291.72/184.24 inference(unit_resolution,[status(thm)],[13489, 5718, 13482, 13483, 13481, 13331])).
% 291.72/184.24 tff(13491,plain,((~node10(c_e_h_3, c_m, s15, s16)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s16) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s15)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s15))), inference(lemma,lemma(discharge,[]))).
% 291.72/184.24 tff(13492,plain,
% 291.72/184.24 (~node10(c_e_h_3, c_m, s15, s16)),
% 291.72/184.24 inference(unit_resolution,[status(thm)],[13491, 13482, 13481, 13331])).
% 291.72/184.24 tff(13493,plain,
% 291.72/184.24 (succ(s15, s16) <=> succ(s15, s16)),
% 291.72/184.24 inference(rewrite,[status(thm)],[])).
% 291.72/184.24 tff(13494,axiom,(succ(s15, s16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound16')).
% 291.72/184.24 tff(13495,plain,
% 291.72/184.24 (succ(s15, s16)),
% 291.72/184.24 inference(modus_ponens,[status(thm)],[13494, 13493])).
% 291.72/184.24 tff(13496,plain,
% 291.72/184.24 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s15, s16)) | trans(s15, s16))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s15, s16)) | trans(s15, s16))),
% 291.72/184.24 inference(rewrite,[status(thm)],[])).
% 291.72/184.24 tff(13497,plain,
% 291.72/184.24 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s15, s16)) | trans(s15, s16))),
% 291.72/184.24 inference(quant_inst,[status(thm)],[])).
% 291.72/184.24 tff(13498,plain,
% 291.72/184.24 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s15, s16)) | trans(s15, s16)),
% 291.72/184.24 inference(modus_ponens,[status(thm)],[13497, 13496])).
% 291.72/184.24 tff(13499,plain,
% 291.72/184.24 (trans(s15, s16)),
% 291.72/184.24 inference(unit_resolution,[status(thm)],[13498, 13495, 65])).
% 291.72/184.24 tff(13500,plain,
% 291.72/184.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s15, s16)) | node10(c_e_h_3, c_m, s15, s16) | node11(c_e_h_3, c_m, s15, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s15, s16)) | node10(c_e_h_3, c_m, s15, s16) | node11(c_e_h_3, c_m, s15, s16))),
% 291.72/184.24 inference(rewrite,[status(thm)],[])).
% 291.72/184.24 tff(13501,plain,
% 291.72/184.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s15, s16)) | node10(c_e_h_3, c_m, s15, s16) | node11(c_e_h_3, c_m, s15, s16))),
% 291.72/184.24 inference(quant_inst,[status(thm)],[])).
% 291.72/184.24 tff(13502,plain,
% 291.72/184.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s15, s16)) | node10(c_e_h_3, c_m, s15, s16) | node11(c_e_h_3, c_m, s15, s16)),
% 291.72/184.24 inference(modus_ponens,[status(thm)],[13501, 13500])).
% 291.72/184.24 tff(13503,plain,
% 291.72/184.24 (node10(c_e_h_3, c_m, s15, s16) | node11(c_e_h_3, c_m, s15, s16)),
% 291.72/184.24 inference(unit_resolution,[status(thm)],[13502, 5002, 13499])).
% 291.72/184.24 tff(13504,plain,
% 291.72/184.24 (node11(c_e_h_3, c_m, s15, s16)),
% 291.72/184.24 inference(unit_resolution,[status(thm)],[13503, 13492])).
% 291.72/184.24 tff(13505,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s15)), introduced(assumption)).
% 291.72/184.24 tff(13506,plain,
% 291.72/184.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s16) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s15)) | (~node11(c_e_h_3, c_m, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s16) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s15)) | (~node11(c_e_h_3, c_m, s15, s16)))),
% 291.72/184.24 inference(rewrite,[status(thm)],[])).
% 291.72/184.24 tff(13507,plain,
% 291.72/184.24 ((m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s16) | (~node11(c_e_h_3, c_m, s15, s16)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s15))) <=> (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s16) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s15)) | (~node11(c_e_h_3, c_m, s15, s16)))),
% 291.72/184.24 inference(rewrite,[status(thm)],[])).
% 291.72/184.24 tff(13508,plain,
% 291.72/184.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s16) | (~node11(c_e_h_3, c_m, s15, s16)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s16) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s15)) | (~node11(c_e_h_3, c_m, s15, s16))))),
% 291.72/184.25 inference(monotonicity,[status(thm)],[13507])).
% 291.72/184.25 tff(13509,plain,
% 291.72/184.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s16) | (~node11(c_e_h_3, c_m, s15, s16)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s16) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s15)) | (~node11(c_e_h_3, c_m, s15, s16)))),
% 291.72/184.25 inference(transitivity,[status(thm)],[13508, 13506])).
% 291.72/184.25 tff(13510,plain,
% 291.72/184.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s16) | (~node11(c_e_h_3, c_m, s15, s16)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s15)))),
% 291.72/184.25 inference(quant_inst,[status(thm)],[])).
% 291.72/184.25 tff(13511,plain,
% 291.72/184.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s16) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s15)) | (~node11(c_e_h_3, c_m, s15, s16))),
% 291.72/184.25 inference(modus_ponens,[status(thm)],[13510, 13509])).
% 291.72/184.25 tff(13512,plain,
% 291.72/184.25 ($false),
% 291.72/184.25 inference(unit_resolution,[status(thm)],[13511, 5742, 13505, 13482, 13504])).
% 291.72/184.25 tff(13513,plain,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s16) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s15)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s15)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s15))), inference(lemma,lemma(discharge,[]))).
% 291.72/184.25 tff(13514,plain,
% 291.72/184.25 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s16)),
% 291.72/184.25 inference(unit_resolution,[status(thm)],[13513, 13480, 13331, 13472])).
% 291.72/184.25 tff(13515,assumption,(node11(c_e_h_3, c_m, s16, s17)), introduced(assumption)).
% 291.72/184.25 tff(13516,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s16)), introduced(assumption)).
% 291.72/184.25 tff(13517,plain,
% 291.72/184.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s16)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s17) | (~node11(c_e_h_3, c_m, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s16)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s17) | (~node11(c_e_h_3, c_m, s16, s17)))),
% 291.72/184.25 inference(rewrite,[status(thm)],[])).
% 291.72/184.25 tff(13518,plain,
% 291.72/184.25 ((m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s17) | (~node11(c_e_h_3, c_m, s16, s17)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s16))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s16)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s17) | (~node11(c_e_h_3, c_m, s16, s17)))),
% 291.72/184.25 inference(rewrite,[status(thm)],[])).
% 291.72/184.25 tff(13519,plain,
% 291.72/184.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s17) | (~node11(c_e_h_3, c_m, s16, s17)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s16)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s17) | (~node11(c_e_h_3, c_m, s16, s17))))),
% 291.72/184.25 inference(monotonicity,[status(thm)],[13518])).
% 291.72/184.25 tff(13520,plain,
% 291.72/184.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s17) | (~node11(c_e_h_3, c_m, s16, s17)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s16)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s17) | (~node11(c_e_h_3, c_m, s16, s17)))),
% 291.72/184.25 inference(transitivity,[status(thm)],[13519, 13517])).
% 291.72/184.25 tff(13521,plain,
% 291.72/184.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s17) | (~node11(c_e_h_3, c_m, s16, s17)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s16)))),
% 291.72/184.25 inference(quant_inst,[status(thm)],[])).
% 291.72/184.25 tff(13522,plain,
% 291.72/184.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s16)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s17) | (~node11(c_e_h_3, c_m, s16, s17))),
% 291.72/184.25 inference(modus_ponens,[status(thm)],[13521, 13520])).
% 291.72/184.25 tff(13523,plain,
% 291.72/184.25 ($false),
% 291.72/184.25 inference(unit_resolution,[status(thm)],[13522, 5742, 13516, 13334, 13515])).
% 291.72/184.25 tff(13524,plain,((~node11(c_e_h_3, c_m, s16, s17)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s16)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s17)), inference(lemma,lemma(discharge,[]))).
% 291.72/184.25 tff(13525,plain,
% 291.72/184.25 (~node11(c_e_h_3, c_m, s16, s17)),
% 291.72/184.25 inference(unit_resolution,[status(thm)],[13524, 13514, 13334])).
% 291.72/184.25 tff(13526,plain,
% 291.72/184.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s16, s17)) | node10(c_e_h_3, c_m, s16, s17) | node11(c_e_h_3, c_m, s16, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s16, s17)) | node10(c_e_h_3, c_m, s16, s17) | node11(c_e_h_3, c_m, s16, s17))),
% 291.72/184.25 inference(rewrite,[status(thm)],[])).
% 291.72/184.25 tff(13527,plain,
% 291.72/184.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s16, s17)) | node10(c_e_h_3, c_m, s16, s17) | node11(c_e_h_3, c_m, s16, s17))),
% 291.72/184.25 inference(quant_inst,[status(thm)],[])).
% 291.72/184.25 tff(13528,plain,
% 291.72/184.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s16, s17)) | node10(c_e_h_3, c_m, s16, s17) | node11(c_e_h_3, c_m, s16, s17)),
% 291.72/184.25 inference(modus_ponens,[status(thm)],[13527, 13526])).
% 291.72/184.25 tff(13529,plain,
% 291.72/184.25 (node10(c_e_h_3, c_m, s16, s17) | node11(c_e_h_3, c_m, s16, s17)),
% 291.72/184.25 inference(unit_resolution,[status(thm)],[13528, 5002, 11967])).
% 291.72/184.25 tff(13530,plain,
% 291.72/184.25 (node10(c_e_h_3, c_m, s16, s17)),
% 291.72/184.25 inference(unit_resolution,[status(thm)],[13529, 13525])).
% 291.72/184.25 tff(13531,assumption,(node10(c_e_h_3, c_m, s16, s17)), introduced(assumption)).
% 291.72/184.25 tff(13532,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s16)), introduced(assumption)).
% 291.72/184.25 tff(13533,plain,
% 291.72/184.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s16)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s17) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s16)) | (~node10(c_e_h_3, c_m, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s16)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s17) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s16)) | (~node10(c_e_h_3, c_m, s16, s17)))),
% 291.72/184.25 inference(rewrite,[status(thm)],[])).
% 291.72/184.25 tff(13534,plain,
% 291.72/184.25 (((~node10(c_e_h_3, c_m, s16, s17)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s16)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s16)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s17)) <=> ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s16)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s17) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s16)) | (~node10(c_e_h_3, c_m, s16, s17)))),
% 291.72/184.25 inference(rewrite,[status(thm)],[])).
% 291.72/184.25 tff(13535,plain,
% 291.72/184.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s16, s17)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s16)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s16)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s16)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s17) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s16)) | (~node10(c_e_h_3, c_m, s16, s17))))),
% 291.72/184.25 inference(monotonicity,[status(thm)],[13534])).
% 291.72/184.25 tff(13536,plain,
% 291.72/184.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s16, s17)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s16)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s16)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s16)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s17) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s16)) | (~node10(c_e_h_3, c_m, s16, s17)))),
% 291.72/184.25 inference(transitivity,[status(thm)],[13535, 13533])).
% 291.72/184.25 tff(13537,plain,
% 291.72/184.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_3, c_m, s16, s17)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s16)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s16)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s17))),
% 291.72/184.25 inference(quant_inst,[status(thm)],[])).
% 291.72/184.25 tff(13538,plain,
% 291.72/184.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s16)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s17) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s16)) | (~node10(c_e_h_3, c_m, s16, s17))),
% 291.72/184.25 inference(modus_ponens,[status(thm)],[13537, 13536])).
% 291.72/184.25 tff(13539,plain,
% 291.72/184.25 ($false),
% 291.72/184.25 inference(unit_resolution,[status(thm)],[13538, 5718, 13532, 13334, 13333, 13531])).
% 291.72/184.25 tff(13540,plain,((~node10(c_e_h_3, c_m, s16, s17)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s16)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s17) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s16))), inference(lemma,lemma(discharge,[]))).
% 291.72/184.25 tff(13541,plain,
% 291.72/184.25 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s16)),
% 291.72/184.25 inference(unit_resolution,[status(thm)],[13540, 13530, 13334, 13333])).
% 291.72/184.25 tff(13542,plain,
% 291.72/184.25 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s16) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s16))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s16) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s16))),
% 291.72/184.25 inference(rewrite,[status(thm)],[])).
% 291.72/184.25 tff(13543,plain,
% 291.72/184.25 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s16) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s16))),
% 291.72/184.26 inference(quant_inst,[status(thm)],[])).
% 291.72/184.26 tff(13544,plain,
% 291.72/184.26 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s16) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s16)),
% 291.72/184.26 inference(modus_ponens,[status(thm)],[13543, 13542])).
% 291.72/184.26 tff(13545,plain,
% 291.72/184.26 (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s16) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s16)),
% 291.72/184.26 inference(unit_resolution,[status(thm)],[13544, 5704])).
% 291.72/184.26 tff(13546,plain,
% 291.72/184.26 (m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s16)),
% 291.72/184.26 inference(unit_resolution,[status(thm)],[13545, 13541])).
% 291.72/184.26 tff(13547,assumption,(node11(c_e_h_3, c_n, s15, s16)), introduced(assumption)).
% 291.72/184.26 tff(13548,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s16)), introduced(assumption)).
% 291.72/184.26 tff(13549,plain,
% 291.72/184.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s16)) | (~node11(c_e_h_3, c_n, s15, s16)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s16)) | (~node11(c_e_h_3, c_n, s15, s16)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s15))),
% 291.72/184.26 inference(rewrite,[status(thm)],[])).
% 291.72/184.26 tff(13550,plain,
% 291.72/184.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s16)) | (~node11(c_e_h_3, c_n, s15, s16)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s15))),
% 291.72/184.26 inference(quant_inst,[status(thm)],[])).
% 291.72/184.26 tff(13551,plain,
% 291.72/184.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s16)) | (~node11(c_e_h_3, c_n, s15, s16)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s15)),
% 291.72/184.26 inference(modus_ponens,[status(thm)],[13550, 13549])).
% 291.72/184.26 tff(13552,plain,
% 291.72/184.26 ($false),
% 291.72/184.26 inference(unit_resolution,[status(thm)],[13551, 5017, 13548, 13547, 13474])).
% 291.72/184.26 tff(13553,plain,((~node11(c_e_h_3, c_n, s15, s16)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s16)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s15)), inference(lemma,lemma(discharge,[]))).
% 291.72/184.26 tff(13554,plain,
% 291.72/184.26 (~node11(c_e_h_3, c_n, s15, s16)),
% 291.72/184.26 inference(unit_resolution,[status(thm)],[13553, 13546, 13436])).
% 291.72/184.26 tff(13555,plain,
% 291.72/184.26 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s15)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s15)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s15)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s15)))),
% 291.72/184.26 inference(rewrite,[status(thm)],[])).
% 291.72/184.26 tff(13556,plain,
% 291.72/184.26 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s15)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s15)))),
% 291.72/184.26 inference(quant_inst,[status(thm)],[])).
% 291.72/184.26 tff(13557,plain,
% 291.72/184.26 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s15)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s15))),
% 291.72/184.26 inference(modus_ponens,[status(thm)],[13556, 13555])).
% 291.72/184.26 tff(13558,plain,
% 291.72/184.26 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s15)),
% 291.72/184.26 inference(unit_resolution,[status(thm)],[13557, 5601, 13472])).
% 291.72/184.26 tff(13559,plain,
% 291.72/184.26 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s15)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s15))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s15)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s15))),
% 291.72/184.26 inference(rewrite,[status(thm)],[])).
% 291.72/184.26 tff(13560,plain,
% 291.72/184.26 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s15)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s15))),
% 291.72/184.26 inference(quant_inst,[status(thm)],[])).
% 291.72/184.26 tff(13561,plain,
% 291.72/184.26 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s15)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s15)),
% 291.72/184.26 inference(modus_ponens,[status(thm)],[13560, 13559])).
% 291.72/184.26 tff(13562,plain,
% 291.72/184.26 (~node9(c_e_h_3, c_n, s15)),
% 291.72/184.26 inference(unit_resolution,[status(thm)],[13561, 4972, 13558])).
% 291.72/184.26 tff(13563,assumption,(~node9(c_e_h_3, c_n, s15)), introduced(assumption)).
% 291.72/184.26 tff(13564,assumption,(node10(c_e_h_3, c_n, s15, s16)), introduced(assumption)).
% 291.72/184.26 tff(13565,plain,
% 291.72/184.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s16)) | node9(c_e_h_3, c_n, s15) | (~node10(c_e_h_3, c_n, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s16)) | node9(c_e_h_3, c_n, s15) | (~node10(c_e_h_3, c_n, s15, s16)))),
% 291.72/184.26 inference(rewrite,[status(thm)],[])).
% 291.72/184.26 tff(13566,plain,
% 291.72/184.26 ((node9(c_e_h_3, c_n, s15) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s16)) | (~node10(c_e_h_3, c_n, s15, s16))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s16)) | node9(c_e_h_3, c_n, s15) | (~node10(c_e_h_3, c_n, s15, s16)))),
% 291.72/184.26 inference(rewrite,[status(thm)],[])).
% 291.72/184.26 tff(13567,plain,
% 291.72/184.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s15) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s16)) | (~node10(c_e_h_3, c_n, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s16)) | node9(c_e_h_3, c_n, s15) | (~node10(c_e_h_3, c_n, s15, s16))))),
% 291.72/184.26 inference(monotonicity,[status(thm)],[13566])).
% 291.72/184.26 tff(13568,plain,
% 291.72/184.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s15) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s16)) | (~node10(c_e_h_3, c_n, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s16)) | node9(c_e_h_3, c_n, s15) | (~node10(c_e_h_3, c_n, s15, s16)))),
% 291.72/184.26 inference(transitivity,[status(thm)],[13567, 13565])).
% 291.72/184.26 tff(13569,plain,
% 291.72/184.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s15) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s16)) | (~node10(c_e_h_3, c_n, s15, s16)))),
% 291.72/184.26 inference(quant_inst,[status(thm)],[])).
% 291.72/184.26 tff(13570,plain,
% 291.72/184.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s16)) | node9(c_e_h_3, c_n, s15) | (~node10(c_e_h_3, c_n, s15, s16))),
% 291.72/184.26 inference(modus_ponens,[status(thm)],[13569, 13568])).
% 291.72/184.26 tff(13571,plain,
% 291.72/184.26 ($false),
% 291.72/184.26 inference(unit_resolution,[status(thm)],[13570, 4986, 13548, 13564, 13563])).
% 291.72/184.26 tff(13572,plain,((~node10(c_e_h_3, c_n, s15, s16)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s16)) | node9(c_e_h_3, c_n, s15)), inference(lemma,lemma(discharge,[]))).
% 291.72/184.26 tff(13573,plain,
% 291.72/184.26 (~node10(c_e_h_3, c_n, s15, s16)),
% 291.72/184.26 inference(unit_resolution,[status(thm)],[13572, 13546, 13562])).
% 291.72/184.26 tff(13574,plain,
% 291.72/184.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s15, s16)) | node10(c_e_h_3, c_n, s15, s16) | node11(c_e_h_3, c_n, s15, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s15, s16)) | node10(c_e_h_3, c_n, s15, s16) | node11(c_e_h_3, c_n, s15, s16))),
% 291.72/184.26 inference(rewrite,[status(thm)],[])).
% 291.72/184.26 tff(13575,plain,
% 291.72/184.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s15, s16)) | node10(c_e_h_3, c_n, s15, s16) | node11(c_e_h_3, c_n, s15, s16))),
% 291.72/184.26 inference(quant_inst,[status(thm)],[])).
% 291.72/184.26 tff(13576,plain,
% 291.72/184.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s15, s16)) | node10(c_e_h_3, c_n, s15, s16) | node11(c_e_h_3, c_n, s15, s16)),
% 291.72/184.26 inference(modus_ponens,[status(thm)],[13575, 13574])).
% 291.72/184.26 tff(13577,plain,
% 291.72/184.26 (node10(c_e_h_3, c_n, s15, s16) | node11(c_e_h_3, c_n, s15, s16)),
% 291.72/184.26 inference(unit_resolution,[status(thm)],[13576, 5002, 13499])).
% 291.72/184.26 tff(13578,plain,
% 291.72/184.26 ($false),
% 291.72/184.26 inference(unit_resolution,[status(thm)],[13577, 13573, 13554])).
% 291.72/184.26 tff(13579,plain,((~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s14)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s17) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s16)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s15)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s14) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s14))), inference(lemma,lemma(discharge,[]))).
% 291.72/184.26 tff(13580,plain,
% 291.72/184.26 (m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s14)),
% 291.72/184.26 inference(unit_resolution,[status(thm)],[13579, 13406, 13334, 13333, 13371, 13331])).
% 291.72/184.26 tff(13581,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s14)), introduced(assumption)).
% 291.72/184.26 tff(13582,assumption,(node11(c_e_h_3, c_n, s13, s14)), introduced(assumption)).
% 291.72/184.26 tff(13583,plain,
% 291.72/184.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s14)) | (~node11(c_e_h_3, c_n, s13, s14)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s14)) | (~node11(c_e_h_3, c_n, s13, s14)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s13))),
% 291.72/184.26 inference(rewrite,[status(thm)],[])).
% 291.72/184.26 tff(13584,plain,
% 291.72/184.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s14)) | (~node11(c_e_h_3, c_n, s13, s14)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s13))),
% 291.72/184.26 inference(quant_inst,[status(thm)],[])).
% 291.72/184.26 tff(13585,plain,
% 291.72/184.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s14)) | (~node11(c_e_h_3, c_n, s13, s14)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s13)),
% 291.72/184.26 inference(modus_ponens,[status(thm)],[13584, 13583])).
% 291.72/184.26 tff(13586,plain,
% 291.72/184.26 ($false),
% 291.72/184.26 inference(unit_resolution,[status(thm)],[13585, 5017, 13332, 13582, 13581])).
% 291.72/184.26 tff(13587,plain,((~node11(c_e_h_3, c_n, s13, s14)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s14))), inference(lemma,lemma(discharge,[]))).
% 291.72/184.26 tff(13588,plain,
% 291.72/184.26 (~node11(c_e_h_3, c_n, s13, s14)),
% 291.72/184.26 inference(unit_resolution,[status(thm)],[13587, 13581, 13332])).
% 291.72/184.26 tff(13589,assumption,(~node9(c_e_h_3, c_n, s13)), introduced(assumption)).
% 291.72/184.26 tff(13590,assumption,(node10(c_e_h_3, c_n, s13, s14)), introduced(assumption)).
% 291.72/184.26 tff(13591,plain,
% 291.72/184.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s13) | (~node10(c_e_h_3, c_n, s13, s14)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_3, c_n, s13) | (~node10(c_e_h_3, c_n, s13, s14)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s14)))),
% 291.72/184.27 inference(rewrite,[status(thm)],[])).
% 291.72/184.27 tff(13592,plain,
% 291.72/184.27 ((node9(c_e_h_3, c_n, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s14)) | (~node10(c_e_h_3, c_n, s13, s14))) <=> (node9(c_e_h_3, c_n, s13) | (~node10(c_e_h_3, c_n, s13, s14)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s14)))),
% 291.72/184.27 inference(rewrite,[status(thm)],[])).
% 291.72/184.27 tff(13593,plain,
% 291.72/184.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s14)) | (~node10(c_e_h_3, c_n, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s13) | (~node10(c_e_h_3, c_n, s13, s14)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s14))))),
% 291.72/184.27 inference(monotonicity,[status(thm)],[13592])).
% 291.72/184.27 tff(13594,plain,
% 291.72/184.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s14)) | (~node10(c_e_h_3, c_n, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_3, c_n, s13) | (~node10(c_e_h_3, c_n, s13, s14)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s14)))),
% 291.72/184.27 inference(transitivity,[status(thm)],[13593, 13591])).
% 291.72/184.27 tff(13595,plain,
% 291.72/184.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s14)) | (~node10(c_e_h_3, c_n, s13, s14)))),
% 291.72/184.27 inference(quant_inst,[status(thm)],[])).
% 291.72/184.27 tff(13596,plain,
% 291.72/184.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_3, c_n, s13) | (~node10(c_e_h_3, c_n, s13, s14)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s14))),
% 291.72/184.27 inference(modus_ponens,[status(thm)],[13595, 13594])).
% 291.72/184.27 tff(13597,plain,
% 291.72/184.27 ($false),
% 291.72/184.27 inference(unit_resolution,[status(thm)],[13596, 4986, 13590, 13589, 13581])).
% 291.72/184.27 tff(13598,plain,((~node10(c_e_h_3, c_n, s13, s14)) | node9(c_e_h_3, c_n, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s14))), inference(lemma,lemma(discharge,[]))).
% 291.72/184.27 tff(13599,plain,
% 291.72/184.27 (~node10(c_e_h_3, c_n, s13, s14)),
% 291.72/184.27 inference(unit_resolution,[status(thm)],[13598, 13581, 13589])).
% 291.72/184.27 tff(13600,plain,
% 291.72/184.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s13, s14)) | node10(c_e_h_3, c_n, s13, s14) | node11(c_e_h_3, c_n, s13, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s13, s14)) | node10(c_e_h_3, c_n, s13, s14) | node11(c_e_h_3, c_n, s13, s14))),
% 291.72/184.27 inference(rewrite,[status(thm)],[])).
% 291.72/184.27 tff(13601,plain,
% 291.72/184.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s13, s14)) | node10(c_e_h_3, c_n, s13, s14) | node11(c_e_h_3, c_n, s13, s14))),
% 291.72/184.27 inference(quant_inst,[status(thm)],[])).
% 291.72/184.27 tff(13602,plain,
% 291.72/184.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s13, s14)) | node10(c_e_h_3, c_n, s13, s14) | node11(c_e_h_3, c_n, s13, s14)),
% 291.72/184.27 inference(modus_ponens,[status(thm)],[13601, 13600])).
% 291.72/184.27 tff(13603,plain,
% 291.72/184.27 (node10(c_e_h_3, c_n, s13, s14) | node11(c_e_h_3, c_n, s13, s14)),
% 291.72/184.27 inference(unit_resolution,[status(thm)],[13602, 5002, 12831])).
% 291.72/184.27 tff(13604,plain,
% 291.72/184.27 ($false),
% 291.72/184.27 inference(unit_resolution,[status(thm)],[13603, 13599, 13588])).
% 291.72/184.27 tff(13605,plain,((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s14)) | node9(c_e_h_3, c_n, s13) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s13)), inference(lemma,lemma(discharge,[]))).
% 291.72/184.27 tff(13606,plain,
% 291.72/184.27 (node9(c_e_h_3, c_n, s13)),
% 291.72/184.27 inference(unit_resolution,[status(thm)],[13605, 13580, 13332])).
% 291.72/184.27 tff(13607,plain,
% 291.72/184.27 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s13)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s13)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s13)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s13)))),
% 291.72/184.27 inference(rewrite,[status(thm)],[])).
% 291.72/184.27 tff(13608,plain,
% 291.72/184.27 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s13)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s13)))),
% 291.72/184.27 inference(quant_inst,[status(thm)],[])).
% 291.72/184.27 tff(13609,plain,
% 291.72/184.27 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s13)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s13))),
% 291.72/184.27 inference(modus_ponens,[status(thm)],[13608, 13607])).
% 291.72/184.27 tff(13610,plain,
% 291.72/184.27 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s13)),
% 291.72/184.27 inference(unit_resolution,[status(thm)],[13609, 5601, 13380])).
% 291.72/184.27 tff(13611,plain,
% 291.72/184.27 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s13)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s13))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s13)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s13))),
% 291.72/184.27 inference(rewrite,[status(thm)],[])).
% 291.72/184.27 tff(13612,plain,
% 291.72/184.27 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s13)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s13))),
% 291.72/184.27 inference(quant_inst,[status(thm)],[])).
% 291.72/184.27 tff(13613,plain,
% 291.72/184.27 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s13)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s13)),
% 291.72/184.27 inference(modus_ponens,[status(thm)],[13612, 13611])).
% 291.72/184.27 tff(13614,plain,
% 291.72/184.27 ($false),
% 291.72/184.27 inference(unit_resolution,[status(thm)],[13613, 4972, 13610, 13606])).
% 291.72/184.27 tff(13615,plain,((~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s13)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s13) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s17) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s16)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s15)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s13))), inference(lemma,lemma(discharge,[]))).
% 291.72/184.27 tff(13616,plain,
% 291.72/184.27 (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s14)),
% 291.72/184.27 inference(unit_resolution,[status(thm)],[13615, 13370, 13334, 13333, 13332, 13331, 13330])).
% 291.72/184.27 tff(13617,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s14)), introduced(assumption)).
% 291.72/184.27 tff(13618,plain,
% 291.72/184.27 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s14) | m_c_h_element_v_out(c_e_h_3, c_f, s14))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s14) | m_c_h_element_v_out(c_e_h_3, c_f, s14))),
% 291.72/184.27 inference(rewrite,[status(thm)],[])).
% 291.72/184.27 tff(13619,plain,
% 291.72/184.27 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s14) | m_c_h_element_v_out(c_e_h_3, c_f, s14))),
% 291.72/184.27 inference(quant_inst,[status(thm)],[])).
% 291.72/184.27 tff(13620,plain,
% 291.72/184.27 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s14) | m_c_h_element_v_out(c_e_h_3, c_f, s14)),
% 291.72/184.27 inference(modus_ponens,[status(thm)],[13619, 13618])).
% 291.72/184.27 tff(13621,plain,
% 291.72/184.27 ($false),
% 291.72/184.27 inference(unit_resolution,[status(thm)],[13620, 5689, 12909, 13617])).
% 291.72/184.27 tff(13622,plain,(m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s14) | m_c_h_element_v_out(c_e_h_3, c_f, s14)), inference(lemma,lemma(discharge,[]))).
% 291.72/184.27 tff(13623,plain,
% 291.72/184.27 ($false),
% 291.72/184.27 inference(unit_resolution,[status(thm)],[13622, 13616, 13323])).
% 291.72/184.27 tff(13624,plain,(m_c_h_element_v_out(c_e_h_3, c_f, s12) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s17) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s16)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s13) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s15)) | m_c_h_element_v_in1(c_e_h_3, c_f, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s12)) | m_c_h_element_v_in2(c_e_h_3, c_f, s12)), inference(lemma,lemma(discharge,[]))).
% 291.72/184.27 tff(13625,plain,
% 291.72/184.27 (m_c_h_element_v_out(c_e_h_3, c_f, s12) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s17) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s16)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s15)) | m_c_h_element_v_in1(c_e_h_3, c_f, s13) | m_c_h_element_v_in2(c_e_h_3, c_f, s12)),
% 291.72/184.27 inference(unit_resolution,[status(thm)],[13624, 13289, 13321, 13224])).
% 291.72/184.27 tff(13626,plain,
% 291.72/184.27 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s17)),
% 291.72/184.27 inference(unit_resolution,[status(thm)],[13625, 13003, 11905, 11841, 12847, 12846])).
% 291.72/184.27 tff(13627,assumption,(~m_or_h_gate_v_out(c_e_h_1, c_g, s8)), introduced(assumption)).
% 291.72/184.27 tff(13628,assumption,(m_and_h_gate_v_out(c_e_h_1, c_p, s9)), introduced(assumption)).
% 291.72/184.27 tff(13629,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_c, s6)), introduced(assumption)).
% 291.72/184.27 tff(13630,assumption,(m_or_h_gate_v_out(c_e_h_1, c_g, s6)), introduced(assumption)).
% 291.72/184.27 tff(13631,assumption,(m_and_h_gate_v_out(c_e_h_2, c_p, s3)), introduced(assumption)).
% 291.72/184.27 tff(13632,assumption,(m_and_h_gate_v_out(c_e_h_2, c_k, s2)), introduced(assumption)).
% 291.72/184.27 tff(13633,assumption,(m_and_h_gate_v_out(c_e_h_2, c_k, s1)), introduced(assumption)).
% 291.72/184.27 tff(13634,plain,
% 291.72/184.27 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_k, s0)) | m_or_h_gate_v_out(c_e_h_2, c_g, s0))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_k, s0)) | m_or_h_gate_v_out(c_e_h_2, c_g, s0))),
% 291.72/184.27 inference(rewrite,[status(thm)],[])).
% 291.72/184.27 tff(13635,plain,
% 291.72/184.27 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_k, s0)) | m_or_h_gate_v_out(c_e_h_2, c_g, s0))),
% 291.72/184.27 inference(quant_inst,[status(thm)],[])).
% 291.72/184.27 tff(13636,plain,
% 291.72/184.27 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_k, s0)) | m_or_h_gate_v_out(c_e_h_2, c_g, s0)),
% 291.72/184.27 inference(modus_ponens,[status(thm)],[13635, 13634])).
% 291.72/184.27 tff(13637,plain,
% 291.72/184.27 (~m_and_h_gate_v_in1(c_e_h_2, c_k, s0)),
% 291.72/184.27 inference(unit_resolution,[status(thm)],[13636, 2048, 3839])).
% 291.72/184.27 tff(13638,plain,
% 291.72/184.27 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_k, s0)) | m_and_h_gate_v_in1(c_e_h_2, c_k, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_k, s0)) | m_and_h_gate_v_in1(c_e_h_2, c_k, s0))),
% 291.72/184.27 inference(rewrite,[status(thm)],[])).
% 291.72/184.27 tff(13639,plain,
% 291.72/184.27 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_k, s0)) | m_and_h_gate_v_in1(c_e_h_2, c_k, s0))),
% 291.72/184.27 inference(quant_inst,[status(thm)],[])).
% 291.72/184.27 tff(13640,plain,
% 291.72/184.27 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_k, s0)) | m_and_h_gate_v_in1(c_e_h_2, c_k, s0)),
% 291.72/184.27 inference(modus_ponens,[status(thm)],[13639, 13638])).
% 291.72/184.27 tff(13641,plain,
% 291.72/184.27 (~node20(c_e_h_2, c_k, s0)),
% 291.72/184.27 inference(unit_resolution,[status(thm)],[13640, 38, 13637])).
% 291.72/184.27 tff(13642,assumption,(m_and_h_gate_v_out(c_e_h_2, c_k, s0)), introduced(assumption)).
% 291.72/184.27 tff(13643,plain,
% 291.72/184.27 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_2, c_k, s0))),
% 291.72/184.27 inference(quant_inst,[status(thm)],[])).
% 291.72/184.27 tff(13644,plain,
% 291.72/184.27 ($false),
% 291.72/184.27 inference(unit_resolution,[status(thm)],[13643, 95, 13642])).
% 291.72/184.27 tff(13645,plain,(~m_and_h_gate_v_out(c_e_h_2, c_k, s0)), inference(lemma,lemma(discharge,[]))).
% 291.72/184.28 tff(13646,assumption,(node22(c_e_h_2, c_k, s0, s1)), introduced(assumption)).
% 291.72/184.28 tff(13647,plain,
% 291.72/184.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_k, s1)) | (~node22(c_e_h_2, c_k, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_k, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_k, s1)) | (~node22(c_e_h_2, c_k, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_k, s0))),
% 291.72/184.28 inference(rewrite,[status(thm)],[])).
% 291.72/184.28 tff(13648,plain,
% 291.72/184.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_k, s1)) | (~node22(c_e_h_2, c_k, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_k, s0))),
% 291.72/184.28 inference(quant_inst,[status(thm)],[])).
% 291.72/184.28 tff(13649,plain,
% 291.72/184.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_k, s1)) | (~node22(c_e_h_2, c_k, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_k, s0)),
% 291.72/184.28 inference(modus_ponens,[status(thm)],[13648, 13647])).
% 291.72/184.28 tff(13650,plain,
% 291.72/184.28 ($false),
% 291.72/184.28 inference(unit_resolution,[status(thm)],[13649, 108, 13646, 13645, 13633])).
% 291.72/184.28 tff(13651,plain,((~node22(c_e_h_2, c_k, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_2, c_k, s1))), inference(lemma,lemma(discharge,[]))).
% 291.72/184.28 tff(13652,plain,
% 291.72/184.28 (~node22(c_e_h_2, c_k, s0, s1)),
% 291.72/184.28 inference(unit_resolution,[status(thm)],[13651, 13633])).
% 291.72/184.28 tff(13653,plain,
% 291.72/184.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_2, c_k, s0, s1) | node22(c_e_h_2, c_k, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_2, c_k, s0, s1) | node22(c_e_h_2, c_k, s0, s1))),
% 291.72/184.28 inference(rewrite,[status(thm)],[])).
% 291.72/184.28 tff(13654,plain,
% 291.72/184.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_2, c_k, s0, s1) | node22(c_e_h_2, c_k, s0, s1))),
% 291.72/184.28 inference(quant_inst,[status(thm)],[])).
% 291.72/184.28 tff(13655,plain,
% 291.72/184.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_2, c_k, s0, s1) | node22(c_e_h_2, c_k, s0, s1)),
% 291.72/184.28 inference(modus_ponens,[status(thm)],[13654, 13653])).
% 291.72/184.28 tff(13656,plain,
% 291.72/184.28 (node21(c_e_h_2, c_k, s0, s1) | node22(c_e_h_2, c_k, s0, s1)),
% 291.72/184.28 inference(unit_resolution,[status(thm)],[13655, 82, 72])).
% 291.72/184.28 tff(13657,plain,
% 291.72/184.28 (node21(c_e_h_2, c_k, s0, s1)),
% 291.72/184.28 inference(unit_resolution,[status(thm)],[13656, 13652])).
% 291.72/184.28 tff(13658,plain,
% 291.72/184.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_k, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_k, s1)) | (~node21(c_e_h_2, c_k, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_k, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_k, s1)) | (~node21(c_e_h_2, c_k, s0, s1)))),
% 291.72/184.28 inference(rewrite,[status(thm)],[])).
% 291.72/184.28 tff(13659,plain,
% 291.72/184.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_k, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_k, s1)) | (~node21(c_e_h_2, c_k, s0, s1)))),
% 291.72/184.28 inference(quant_inst,[status(thm)],[])).
% 291.72/184.28 tff(13660,plain,
% 291.72/184.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_k, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_k, s1)) | (~node21(c_e_h_2, c_k, s0, s1))),
% 291.72/184.28 inference(modus_ponens,[status(thm)],[13659, 13658])).
% 291.72/184.28 tff(13661,plain,
% 291.72/184.28 ($false),
% 291.72/184.28 inference(unit_resolution,[status(thm)],[13660, 52, 13657, 13641, 13633])).
% 291.72/184.28 tff(13662,plain,(~m_and_h_gate_v_out(c_e_h_2, c_k, s1)), inference(lemma,lemma(discharge,[]))).
% 291.72/184.28 tff(13663,plain,
% 291.72/184.28 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_k, s1)) | m_or_h_gate_v_out(c_e_h_2, c_g, s1))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_k, s1)) | m_or_h_gate_v_out(c_e_h_2, c_g, s1))),
% 291.72/184.28 inference(rewrite,[status(thm)],[])).
% 291.72/184.28 tff(13664,plain,
% 291.72/184.28 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_k, s1)) | m_or_h_gate_v_out(c_e_h_2, c_g, s1))),
% 291.72/184.28 inference(quant_inst,[status(thm)],[])).
% 291.72/184.28 tff(13665,plain,
% 291.72/184.28 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_k, s1)) | m_or_h_gate_v_out(c_e_h_2, c_g, s1)),
% 291.72/184.28 inference(modus_ponens,[status(thm)],[13664, 13663])).
% 291.72/184.28 tff(13666,plain,
% 291.72/184.28 (~m_and_h_gate_v_in1(c_e_h_2, c_k, s1)),
% 291.72/184.28 inference(unit_resolution,[status(thm)],[13665, 2048, 4143])).
% 291.72/184.28 tff(13667,plain,
% 291.72/184.28 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_k, s1)) | m_and_h_gate_v_in1(c_e_h_2, c_k, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_k, s1)) | m_and_h_gate_v_in1(c_e_h_2, c_k, s1))),
% 291.72/184.28 inference(rewrite,[status(thm)],[])).
% 291.72/184.28 tff(13668,plain,
% 291.72/184.28 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_k, s1)) | m_and_h_gate_v_in1(c_e_h_2, c_k, s1))),
% 291.72/184.28 inference(quant_inst,[status(thm)],[])).
% 291.72/184.28 tff(13669,plain,
% 291.72/184.28 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_k, s1)) | m_and_h_gate_v_in1(c_e_h_2, c_k, s1)),
% 291.72/184.28 inference(modus_ponens,[status(thm)],[13668, 13667])).
% 291.72/184.28 tff(13670,plain,
% 291.72/184.28 (~node20(c_e_h_2, c_k, s1)),
% 291.72/184.28 inference(unit_resolution,[status(thm)],[13669, 38, 13666])).
% 291.72/184.28 tff(13671,assumption,(node21(c_e_h_2, c_k, s1, s2)), introduced(assumption)).
% 291.72/184.28 tff(13672,plain,
% 291.72/184.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_k, s2)) | node20(c_e_h_2, c_k, s1) | (~node21(c_e_h_2, c_k, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_k, s2)) | node20(c_e_h_2, c_k, s1) | (~node21(c_e_h_2, c_k, s1, s2)))),
% 291.72/184.28 inference(rewrite,[status(thm)],[])).
% 291.72/184.28 tff(13673,plain,
% 291.72/184.28 ((node20(c_e_h_2, c_k, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_k, s2)) | (~node21(c_e_h_2, c_k, s1, s2))) <=> ((~m_and_h_gate_v_out(c_e_h_2, c_k, s2)) | node20(c_e_h_2, c_k, s1) | (~node21(c_e_h_2, c_k, s1, s2)))),
% 291.72/184.28 inference(rewrite,[status(thm)],[])).
% 291.72/184.28 tff(13674,plain,
% 291.72/184.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_k, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_k, s2)) | (~node21(c_e_h_2, c_k, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_k, s2)) | node20(c_e_h_2, c_k, s1) | (~node21(c_e_h_2, c_k, s1, s2))))),
% 291.72/184.28 inference(monotonicity,[status(thm)],[13673])).
% 291.72/184.28 tff(13675,plain,
% 291.72/184.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_k, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_k, s2)) | (~node21(c_e_h_2, c_k, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_k, s2)) | node20(c_e_h_2, c_k, s1) | (~node21(c_e_h_2, c_k, s1, s2)))),
% 291.72/184.28 inference(transitivity,[status(thm)],[13674, 13672])).
% 291.72/184.28 tff(13676,plain,
% 291.72/184.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_k, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_k, s2)) | (~node21(c_e_h_2, c_k, s1, s2)))),
% 291.72/184.28 inference(quant_inst,[status(thm)],[])).
% 291.72/184.28 tff(13677,plain,
% 291.72/184.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_k, s2)) | node20(c_e_h_2, c_k, s1) | (~node21(c_e_h_2, c_k, s1, s2))),
% 291.72/184.28 inference(modus_ponens,[status(thm)],[13676, 13675])).
% 291.72/184.28 tff(13678,plain,
% 291.72/184.28 ($false),
% 291.72/184.28 inference(unit_resolution,[status(thm)],[13677, 52, 13671, 13670, 13632])).
% 291.72/184.28 tff(13679,plain,((~node21(c_e_h_2, c_k, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_2, c_k, s2))), inference(lemma,lemma(discharge,[]))).
% 291.72/184.28 tff(13680,plain,
% 291.72/184.28 (~node21(c_e_h_2, c_k, s1, s2)),
% 291.72/184.28 inference(unit_resolution,[status(thm)],[13679, 13632])).
% 291.72/184.28 tff(13681,plain,
% 291.72/184.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_2, c_k, s1, s2) | node22(c_e_h_2, c_k, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_2, c_k, s1, s2) | node22(c_e_h_2, c_k, s1, s2))),
% 291.72/184.28 inference(rewrite,[status(thm)],[])).
% 291.72/184.28 tff(13682,plain,
% 291.72/184.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_2, c_k, s1, s2) | node22(c_e_h_2, c_k, s1, s2))),
% 291.72/184.28 inference(quant_inst,[status(thm)],[])).
% 291.72/184.28 tff(13683,plain,
% 291.72/184.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_2, c_k, s1, s2) | node22(c_e_h_2, c_k, s1, s2)),
% 291.72/184.28 inference(modus_ponens,[status(thm)],[13682, 13681])).
% 291.72/184.28 tff(13684,plain,
% 291.72/184.28 (node21(c_e_h_2, c_k, s1, s2) | node22(c_e_h_2, c_k, s1, s2)),
% 291.72/184.28 inference(unit_resolution,[status(thm)],[13683, 82, 255])).
% 291.72/184.28 tff(13685,plain,
% 291.72/184.28 (node22(c_e_h_2, c_k, s1, s2)),
% 291.72/184.28 inference(unit_resolution,[status(thm)],[13684, 13680])).
% 291.72/184.28 tff(13686,plain,
% 291.72/184.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_k, s2)) | (~node22(c_e_h_2, c_k, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_k, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_k, s2)) | (~node22(c_e_h_2, c_k, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_k, s1))),
% 291.72/184.28 inference(rewrite,[status(thm)],[])).
% 291.72/184.28 tff(13687,plain,
% 291.72/184.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_k, s2)) | (~node22(c_e_h_2, c_k, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_k, s1))),
% 291.72/184.28 inference(quant_inst,[status(thm)],[])).
% 291.72/184.28 tff(13688,plain,
% 291.72/184.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_k, s2)) | (~node22(c_e_h_2, c_k, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_k, s1)),
% 291.72/184.28 inference(modus_ponens,[status(thm)],[13687, 13686])).
% 291.72/184.28 tff(13689,plain,
% 291.72/184.28 ($false),
% 291.72/184.28 inference(unit_resolution,[status(thm)],[13688, 108, 13685, 13662, 13632])).
% 291.72/184.28 tff(13690,plain,(~m_and_h_gate_v_out(c_e_h_2, c_k, s2)), inference(lemma,lemma(discharge,[]))).
% 291.72/184.28 tff(13691,plain,
% 291.72/184.28 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_p, s2)) | m_and_h_gate_v_out(c_e_h_2, c_k, s2))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_p, s2)) | m_and_h_gate_v_out(c_e_h_2, c_k, s2))),
% 291.72/184.28 inference(rewrite,[status(thm)],[])).
% 291.72/184.28 tff(13692,plain,
% 291.72/184.28 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_p, s2)) | m_and_h_gate_v_out(c_e_h_2, c_k, s2))),
% 291.72/184.29 inference(quant_inst,[status(thm)],[])).
% 291.72/184.29 tff(13693,plain,
% 291.72/184.29 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_p, s2)) | m_and_h_gate_v_out(c_e_h_2, c_k, s2)),
% 291.72/184.29 inference(modus_ponens,[status(thm)],[13692, 13691])).
% 291.72/184.29 tff(13694,plain,
% 291.72/184.29 (~m_and_h_gate_v_in1(c_e_h_2, c_p, s2)),
% 291.72/184.29 inference(unit_resolution,[status(thm)],[13693, 3033, 13690])).
% 291.72/184.29 tff(13695,plain,
% 291.72/184.29 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_p, s2)) | m_and_h_gate_v_in1(c_e_h_2, c_p, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_p, s2)) | m_and_h_gate_v_in1(c_e_h_2, c_p, s2))),
% 291.72/184.29 inference(rewrite,[status(thm)],[])).
% 291.72/184.29 tff(13696,plain,
% 291.72/184.29 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_p, s2)) | m_and_h_gate_v_in1(c_e_h_2, c_p, s2))),
% 291.72/184.29 inference(quant_inst,[status(thm)],[])).
% 291.72/184.29 tff(13697,plain,
% 291.72/184.29 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_p, s2)) | m_and_h_gate_v_in1(c_e_h_2, c_p, s2)),
% 291.72/184.29 inference(modus_ponens,[status(thm)],[13696, 13695])).
% 291.72/184.29 tff(13698,plain,
% 291.72/184.29 (~node20(c_e_h_2, c_p, s2)),
% 291.72/184.29 inference(unit_resolution,[status(thm)],[13697, 38, 13694])).
% 291.72/184.29 tff(13699,assumption,(node21(c_e_h_2, c_p, s2, s3)), introduced(assumption)).
% 291.72/184.29 tff(13700,plain,
% 291.72/184.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_p, s3)) | node20(c_e_h_2, c_p, s2) | (~node21(c_e_h_2, c_p, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_p, s3)) | node20(c_e_h_2, c_p, s2) | (~node21(c_e_h_2, c_p, s2, s3)))),
% 291.72/184.29 inference(rewrite,[status(thm)],[])).
% 291.72/184.29 tff(13701,plain,
% 291.72/184.29 ((node20(c_e_h_2, c_p, s2) | (~m_and_h_gate_v_out(c_e_h_2, c_p, s3)) | (~node21(c_e_h_2, c_p, s2, s3))) <=> ((~m_and_h_gate_v_out(c_e_h_2, c_p, s3)) | node20(c_e_h_2, c_p, s2) | (~node21(c_e_h_2, c_p, s2, s3)))),
% 291.72/184.29 inference(rewrite,[status(thm)],[])).
% 291.72/184.29 tff(13702,plain,
% 291.72/184.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_p, s2) | (~m_and_h_gate_v_out(c_e_h_2, c_p, s3)) | (~node21(c_e_h_2, c_p, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_p, s3)) | node20(c_e_h_2, c_p, s2) | (~node21(c_e_h_2, c_p, s2, s3))))),
% 291.72/184.29 inference(monotonicity,[status(thm)],[13701])).
% 291.72/184.29 tff(13703,plain,
% 291.72/184.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_p, s2) | (~m_and_h_gate_v_out(c_e_h_2, c_p, s3)) | (~node21(c_e_h_2, c_p, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_p, s3)) | node20(c_e_h_2, c_p, s2) | (~node21(c_e_h_2, c_p, s2, s3)))),
% 291.72/184.29 inference(transitivity,[status(thm)],[13702, 13700])).
% 291.72/184.29 tff(13704,plain,
% 291.72/184.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_p, s2) | (~m_and_h_gate_v_out(c_e_h_2, c_p, s3)) | (~node21(c_e_h_2, c_p, s2, s3)))),
% 291.72/184.29 inference(quant_inst,[status(thm)],[])).
% 291.72/184.29 tff(13705,plain,
% 291.72/184.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_p, s3)) | node20(c_e_h_2, c_p, s2) | (~node21(c_e_h_2, c_p, s2, s3))),
% 291.72/184.29 inference(modus_ponens,[status(thm)],[13704, 13703])).
% 291.72/184.29 tff(13706,plain,
% 291.72/184.29 ($false),
% 291.72/184.29 inference(unit_resolution,[status(thm)],[13705, 52, 13699, 13631, 13698])).
% 291.72/184.29 tff(13707,plain,((~node21(c_e_h_2, c_p, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_2, c_p, s3))), inference(lemma,lemma(discharge,[]))).
% 291.72/184.29 tff(13708,plain,
% 291.72/184.29 (~node21(c_e_h_2, c_p, s2, s3)),
% 291.72/184.29 inference(unit_resolution,[status(thm)],[13707, 13631])).
% 291.72/184.29 tff(13709,plain,
% 291.72/184.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_2, c_p, s2, s3) | node22(c_e_h_2, c_p, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_2, c_p, s2, s3) | node22(c_e_h_2, c_p, s2, s3))),
% 291.72/184.29 inference(rewrite,[status(thm)],[])).
% 291.72/184.29 tff(13710,plain,
% 291.72/184.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_2, c_p, s2, s3) | node22(c_e_h_2, c_p, s2, s3))),
% 291.72/184.29 inference(quant_inst,[status(thm)],[])).
% 291.72/184.29 tff(13711,plain,
% 291.72/184.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_2, c_p, s2, s3) | node22(c_e_h_2, c_p, s2, s3)),
% 291.72/184.29 inference(modus_ponens,[status(thm)],[13710, 13709])).
% 291.72/184.29 tff(13712,plain,
% 291.72/184.29 (node21(c_e_h_2, c_p, s2, s3) | node22(c_e_h_2, c_p, s2, s3)),
% 291.72/184.29 inference(unit_resolution,[status(thm)],[13711, 82, 318])).
% 291.72/184.29 tff(13713,plain,
% 291.72/184.29 (node22(c_e_h_2, c_p, s2, s3)),
% 291.72/184.29 inference(unit_resolution,[status(thm)],[13712, 13708])).
% 291.72/184.29 tff(13714,assumption,(m_and_h_gate_v_out(c_e_h_2, c_p, s2)), introduced(assumption)).
% 291.72/184.29 tff(13715,assumption,(m_and_h_gate_v_out(c_e_h_2, c_p, s0)), introduced(assumption)).
% 291.72/184.29 tff(13716,plain,
% 291.72/184.29 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_2, c_p, s0))),
% 291.72/184.29 inference(quant_inst,[status(thm)],[])).
% 291.72/184.29 tff(13717,plain,
% 291.72/184.29 ($false),
% 291.72/184.29 inference(unit_resolution,[status(thm)],[13716, 95, 13715])).
% 291.72/184.29 tff(13718,plain,(~m_and_h_gate_v_out(c_e_h_2, c_p, s0)), inference(lemma,lemma(discharge,[]))).
% 291.72/184.29 tff(13719,assumption,(m_and_h_gate_v_out(c_e_h_2, c_p, s1)), introduced(assumption)).
% 291.72/184.29 tff(13720,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_p, s0)), introduced(assumption)).
% 291.72/184.29 tff(13721,assumption,(node21(c_e_h_2, c_p, s0, s1)), introduced(assumption)).
% 291.72/184.29 tff(13722,plain,
% 291.72/184.29 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_p, s0)) | m_and_h_gate_v_out(c_e_h_2, c_k, s0))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_p, s0)) | m_and_h_gate_v_out(c_e_h_2, c_k, s0))),
% 291.72/184.29 inference(rewrite,[status(thm)],[])).
% 291.72/184.29 tff(13723,plain,
% 291.72/184.29 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_p, s0)) | m_and_h_gate_v_out(c_e_h_2, c_k, s0))),
% 291.72/184.29 inference(quant_inst,[status(thm)],[])).
% 291.72/184.29 tff(13724,plain,
% 291.72/184.29 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_p, s0)) | m_and_h_gate_v_out(c_e_h_2, c_k, s0)),
% 291.72/184.29 inference(modus_ponens,[status(thm)],[13723, 13722])).
% 291.72/184.29 tff(13725,plain,
% 291.72/184.29 (~m_and_h_gate_v_in1(c_e_h_2, c_p, s0)),
% 291.72/184.29 inference(unit_resolution,[status(thm)],[13724, 3033, 13645])).
% 291.72/184.29 tff(13726,plain,
% 291.72/184.29 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_p, s0)) | m_and_h_gate_v_in1(c_e_h_2, c_p, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_p, s0)) | m_and_h_gate_v_in1(c_e_h_2, c_p, s0))),
% 291.72/184.29 inference(rewrite,[status(thm)],[])).
% 291.72/184.29 tff(13727,plain,
% 291.72/184.29 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_p, s0)) | m_and_h_gate_v_in1(c_e_h_2, c_p, s0))),
% 291.72/184.29 inference(quant_inst,[status(thm)],[])).
% 291.72/184.29 tff(13728,plain,
% 291.72/184.29 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_p, s0)) | m_and_h_gate_v_in1(c_e_h_2, c_p, s0)),
% 291.72/184.29 inference(modus_ponens,[status(thm)],[13727, 13726])).
% 291.72/184.29 tff(13729,plain,
% 291.72/184.29 (~node20(c_e_h_2, c_p, s0)),
% 291.72/184.29 inference(unit_resolution,[status(thm)],[13728, 38, 13725])).
% 291.72/184.29 tff(13730,plain,
% 291.72/184.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_p, s1)) | node20(c_e_h_2, c_p, s0) | (~node21(c_e_h_2, c_p, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_p, s1)) | node20(c_e_h_2, c_p, s0) | (~node21(c_e_h_2, c_p, s0, s1)))),
% 291.72/184.29 inference(rewrite,[status(thm)],[])).
% 291.72/184.29 tff(13731,plain,
% 291.72/184.29 ((node20(c_e_h_2, c_p, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_p, s1)) | (~node21(c_e_h_2, c_p, s0, s1))) <=> ((~m_and_h_gate_v_out(c_e_h_2, c_p, s1)) | node20(c_e_h_2, c_p, s0) | (~node21(c_e_h_2, c_p, s0, s1)))),
% 291.72/184.29 inference(rewrite,[status(thm)],[])).
% 291.72/184.29 tff(13732,plain,
% 291.72/184.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_p, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_p, s1)) | (~node21(c_e_h_2, c_p, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_p, s1)) | node20(c_e_h_2, c_p, s0) | (~node21(c_e_h_2, c_p, s0, s1))))),
% 291.72/184.29 inference(monotonicity,[status(thm)],[13731])).
% 291.72/184.29 tff(13733,plain,
% 291.72/184.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_p, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_p, s1)) | (~node21(c_e_h_2, c_p, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_p, s1)) | node20(c_e_h_2, c_p, s0) | (~node21(c_e_h_2, c_p, s0, s1)))),
% 291.72/184.29 inference(transitivity,[status(thm)],[13732, 13730])).
% 291.72/184.29 tff(13734,plain,
% 291.72/184.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_p, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_p, s1)) | (~node21(c_e_h_2, c_p, s0, s1)))),
% 291.72/184.29 inference(quant_inst,[status(thm)],[])).
% 291.72/184.29 tff(13735,plain,
% 291.72/184.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_p, s1)) | node20(c_e_h_2, c_p, s0) | (~node21(c_e_h_2, c_p, s0, s1))),
% 291.72/184.29 inference(modus_ponens,[status(thm)],[13734, 13733])).
% 291.72/184.29 tff(13736,plain,
% 291.72/184.29 ($false),
% 291.72/184.29 inference(unit_resolution,[status(thm)],[13735, 52, 13729, 13721, 13719])).
% 291.72/184.29 tff(13737,plain,((~node21(c_e_h_2, c_p, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_2, c_p, s1))), inference(lemma,lemma(discharge,[]))).
% 291.72/184.29 tff(13738,plain,
% 291.72/184.29 (~node21(c_e_h_2, c_p, s0, s1)),
% 291.72/184.29 inference(unit_resolution,[status(thm)],[13737, 13719])).
% 291.72/184.29 tff(13739,plain,
% 291.72/184.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_2, c_p, s0, s1) | node22(c_e_h_2, c_p, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_2, c_p, s0, s1) | node22(c_e_h_2, c_p, s0, s1))),
% 291.72/184.29 inference(rewrite,[status(thm)],[])).
% 291.72/184.29 tff(13740,plain,
% 291.72/184.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_2, c_p, s0, s1) | node22(c_e_h_2, c_p, s0, s1))),
% 291.72/184.29 inference(quant_inst,[status(thm)],[])).
% 291.72/184.29 tff(13741,plain,
% 291.72/184.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_2, c_p, s0, s1) | node22(c_e_h_2, c_p, s0, s1)),
% 291.72/184.29 inference(modus_ponens,[status(thm)],[13740, 13739])).
% 291.72/184.29 tff(13742,plain,
% 291.72/184.29 (node21(c_e_h_2, c_p, s0, s1) | node22(c_e_h_2, c_p, s0, s1)),
% 291.72/184.29 inference(unit_resolution,[status(thm)],[13741, 82, 72])).
% 291.72/184.30 tff(13743,plain,
% 291.72/184.30 (node22(c_e_h_2, c_p, s0, s1)),
% 291.72/184.30 inference(unit_resolution,[status(thm)],[13742, 13738])).
% 291.72/184.30 tff(13744,plain,
% 291.72/184.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_p, s1)) | (~node22(c_e_h_2, c_p, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_p, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_p, s1)) | (~node22(c_e_h_2, c_p, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_p, s0))),
% 291.72/184.30 inference(rewrite,[status(thm)],[])).
% 291.72/184.30 tff(13745,plain,
% 291.72/184.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_p, s1)) | (~node22(c_e_h_2, c_p, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_p, s0))),
% 291.72/184.30 inference(quant_inst,[status(thm)],[])).
% 291.72/184.30 tff(13746,plain,
% 291.72/184.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_p, s1)) | (~node22(c_e_h_2, c_p, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_p, s0)),
% 291.72/184.30 inference(modus_ponens,[status(thm)],[13745, 13744])).
% 291.72/184.30 tff(13747,plain,
% 291.72/184.30 ($false),
% 291.72/184.30 inference(unit_resolution,[status(thm)],[13746, 108, 13743, 13720, 13719])).
% 291.72/184.30 tff(13748,plain,((~m_and_h_gate_v_out(c_e_h_2, c_p, s1)) | m_and_h_gate_v_out(c_e_h_2, c_p, s0)), inference(lemma,lemma(discharge,[]))).
% 291.72/184.30 tff(13749,plain,
% 291.72/184.30 (~m_and_h_gate_v_out(c_e_h_2, c_p, s1)),
% 291.72/184.30 inference(unit_resolution,[status(thm)],[13748, 13718])).
% 291.72/184.30 tff(13750,assumption,(node22(c_e_h_2, c_p, s1, s2)), introduced(assumption)).
% 291.72/184.30 tff(13751,plain,
% 291.72/184.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_p, s2)) | (~node22(c_e_h_2, c_p, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_p, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_p, s2)) | (~node22(c_e_h_2, c_p, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_p, s1))),
% 291.72/184.30 inference(rewrite,[status(thm)],[])).
% 291.72/184.30 tff(13752,plain,
% 291.72/184.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_p, s2)) | (~node22(c_e_h_2, c_p, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_p, s1))),
% 291.72/184.30 inference(quant_inst,[status(thm)],[])).
% 291.72/184.30 tff(13753,plain,
% 291.72/184.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_p, s2)) | (~node22(c_e_h_2, c_p, s1, s2)) | m_and_h_gate_v_out(c_e_h_2, c_p, s1)),
% 291.72/184.30 inference(modus_ponens,[status(thm)],[13752, 13751])).
% 291.72/184.30 tff(13754,plain,
% 291.72/184.30 ($false),
% 291.72/184.30 inference(unit_resolution,[status(thm)],[13753, 108, 13750, 13714, 13749])).
% 291.72/184.30 tff(13755,plain,((~node22(c_e_h_2, c_p, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_2, c_p, s2))), inference(lemma,lemma(discharge,[]))).
% 291.72/184.30 tff(13756,plain,
% 291.72/184.30 (~node22(c_e_h_2, c_p, s1, s2)),
% 291.72/184.30 inference(unit_resolution,[status(thm)],[13755, 13714])).
% 291.72/184.30 tff(13757,plain,
% 291.72/184.30 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_p, s1)) | m_and_h_gate_v_out(c_e_h_2, c_k, s1))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_p, s1)) | m_and_h_gate_v_out(c_e_h_2, c_k, s1))),
% 291.72/184.30 inference(rewrite,[status(thm)],[])).
% 291.72/184.30 tff(13758,plain,
% 291.72/184.30 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_p, s1)) | m_and_h_gate_v_out(c_e_h_2, c_k, s1))),
% 291.72/184.30 inference(quant_inst,[status(thm)],[])).
% 291.72/184.30 tff(13759,plain,
% 291.72/184.30 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_p, s1)) | m_and_h_gate_v_out(c_e_h_2, c_k, s1)),
% 291.72/184.30 inference(modus_ponens,[status(thm)],[13758, 13757])).
% 291.72/184.30 tff(13760,plain,
% 291.72/184.30 (~m_and_h_gate_v_in1(c_e_h_2, c_p, s1)),
% 291.72/184.30 inference(unit_resolution,[status(thm)],[13759, 3033, 13662])).
% 291.72/184.30 tff(13761,plain,
% 291.72/184.30 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_p, s1)) | m_and_h_gate_v_in1(c_e_h_2, c_p, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_p, s1)) | m_and_h_gate_v_in1(c_e_h_2, c_p, s1))),
% 291.72/184.30 inference(rewrite,[status(thm)],[])).
% 291.72/184.30 tff(13762,plain,
% 291.72/184.30 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_p, s1)) | m_and_h_gate_v_in1(c_e_h_2, c_p, s1))),
% 291.72/184.30 inference(quant_inst,[status(thm)],[])).
% 291.72/184.30 tff(13763,plain,
% 291.72/184.30 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_p, s1)) | m_and_h_gate_v_in1(c_e_h_2, c_p, s1)),
% 291.72/184.30 inference(modus_ponens,[status(thm)],[13762, 13761])).
% 291.72/184.30 tff(13764,plain,
% 291.72/184.30 (~node20(c_e_h_2, c_p, s1)),
% 291.72/184.30 inference(unit_resolution,[status(thm)],[13763, 38, 13760])).
% 291.72/184.30 tff(13765,assumption,(~node20(c_e_h_2, c_p, s1)), introduced(assumption)).
% 291.72/184.30 tff(13766,assumption,(node21(c_e_h_2, c_p, s1, s2)), introduced(assumption)).
% 291.72/184.30 tff(13767,plain,
% 291.72/184.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_p, s1) | (~node21(c_e_h_2, c_p, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_2, c_p, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_p, s1) | (~node21(c_e_h_2, c_p, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_2, c_p, s2)))),
% 291.72/184.30 inference(rewrite,[status(thm)],[])).
% 291.72/184.30 tff(13768,plain,
% 291.72/184.30 ((node20(c_e_h_2, c_p, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_p, s2)) | (~node21(c_e_h_2, c_p, s1, s2))) <=> (node20(c_e_h_2, c_p, s1) | (~node21(c_e_h_2, c_p, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_2, c_p, s2)))),
% 291.72/184.30 inference(rewrite,[status(thm)],[])).
% 291.72/184.30 tff(13769,plain,
% 291.72/184.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_p, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_p, s2)) | (~node21(c_e_h_2, c_p, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_p, s1) | (~node21(c_e_h_2, c_p, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_2, c_p, s2))))),
% 291.72/184.30 inference(monotonicity,[status(thm)],[13768])).
% 291.72/184.30 tff(13770,plain,
% 291.72/184.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_p, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_p, s2)) | (~node21(c_e_h_2, c_p, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_p, s1) | (~node21(c_e_h_2, c_p, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_2, c_p, s2)))),
% 291.72/184.30 inference(transitivity,[status(thm)],[13769, 13767])).
% 291.72/184.30 tff(13771,plain,
% 291.72/184.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_p, s1) | (~m_and_h_gate_v_out(c_e_h_2, c_p, s2)) | (~node21(c_e_h_2, c_p, s1, s2)))),
% 291.72/184.30 inference(quant_inst,[status(thm)],[])).
% 291.72/184.30 tff(13772,plain,
% 291.72/184.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_p, s1) | (~node21(c_e_h_2, c_p, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_2, c_p, s2))),
% 291.72/184.30 inference(modus_ponens,[status(thm)],[13771, 13770])).
% 291.72/184.30 tff(13773,plain,
% 291.72/184.30 ($false),
% 291.72/184.30 inference(unit_resolution,[status(thm)],[13772, 52, 13766, 13714, 13765])).
% 291.72/184.30 tff(13774,plain,((~node21(c_e_h_2, c_p, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_2, c_p, s2)) | node20(c_e_h_2, c_p, s1)), inference(lemma,lemma(discharge,[]))).
% 291.72/184.30 tff(13775,plain,
% 291.72/184.30 ((~node21(c_e_h_2, c_p, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_2, c_p, s2))),
% 291.72/184.30 inference(unit_resolution,[status(thm)],[13774, 13764])).
% 291.72/184.30 tff(13776,plain,
% 291.72/184.30 (~node21(c_e_h_2, c_p, s1, s2)),
% 291.72/184.30 inference(unit_resolution,[status(thm)],[13775, 13714])).
% 291.72/184.30 tff(13777,plain,
% 291.72/184.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_2, c_p, s1, s2) | node22(c_e_h_2, c_p, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_2, c_p, s1, s2) | node22(c_e_h_2, c_p, s1, s2))),
% 291.72/184.30 inference(rewrite,[status(thm)],[])).
% 291.72/184.30 tff(13778,plain,
% 291.72/184.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_2, c_p, s1, s2) | node22(c_e_h_2, c_p, s1, s2))),
% 291.72/184.30 inference(quant_inst,[status(thm)],[])).
% 291.72/184.30 tff(13779,plain,
% 291.72/184.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_2, c_p, s1, s2) | node22(c_e_h_2, c_p, s1, s2)),
% 291.72/184.30 inference(modus_ponens,[status(thm)],[13778, 13777])).
% 291.72/184.30 tff(13780,plain,
% 291.72/184.30 (node21(c_e_h_2, c_p, s1, s2) | node22(c_e_h_2, c_p, s1, s2)),
% 291.72/184.30 inference(unit_resolution,[status(thm)],[13779, 82, 255])).
% 291.72/184.30 tff(13781,plain,
% 291.72/184.30 ($false),
% 291.72/184.30 inference(unit_resolution,[status(thm)],[13780, 13776, 13756])).
% 291.72/184.30 tff(13782,plain,(~m_and_h_gate_v_out(c_e_h_2, c_p, s2)), inference(lemma,lemma(discharge,[]))).
% 291.72/184.30 tff(13783,plain,
% 291.72/184.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_p, s3)) | (~node22(c_e_h_2, c_p, s2, s3)) | m_and_h_gate_v_out(c_e_h_2, c_p, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_p, s3)) | (~node22(c_e_h_2, c_p, s2, s3)) | m_and_h_gate_v_out(c_e_h_2, c_p, s2))),
% 291.72/184.30 inference(rewrite,[status(thm)],[])).
% 291.72/184.30 tff(13784,plain,
% 291.72/184.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_p, s3)) | (~node22(c_e_h_2, c_p, s2, s3)) | m_and_h_gate_v_out(c_e_h_2, c_p, s2))),
% 291.72/184.30 inference(quant_inst,[status(thm)],[])).
% 291.72/184.30 tff(13785,plain,
% 291.72/184.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_p, s3)) | (~node22(c_e_h_2, c_p, s2, s3)) | m_and_h_gate_v_out(c_e_h_2, c_p, s2)),
% 291.72/184.30 inference(modus_ponens,[status(thm)],[13784, 13783])).
% 291.72/184.30 tff(13786,plain,
% 291.72/184.30 ($false),
% 291.72/184.30 inference(unit_resolution,[status(thm)],[13785, 108, 13782, 13713, 13631])).
% 291.72/184.30 tff(13787,plain,(~m_and_h_gate_v_out(c_e_h_2, c_p, s3)), inference(lemma,lemma(discharge,[]))).
% 291.72/184.30 tff(13788,plain,
% 291.72/184.30 (((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | ((~m_cell_v_req(c_e_h_2, s3)) | m_and_h_gate_v_out(c_e_h_2, c_p, s3))) <=> ((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | (~m_cell_v_req(c_e_h_2, s3)) | m_and_h_gate_v_out(c_e_h_2, c_p, s3))),
% 291.72/184.30 inference(rewrite,[status(thm)],[])).
% 291.72/184.30 tff(13789,plain,
% 291.72/184.30 ((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | ((~m_cell_v_req(c_e_h_2, s3)) | m_and_h_gate_v_out(c_e_h_2, c_p, s3))),
% 291.72/184.30 inference(quant_inst,[status(thm)],[])).
% 291.72/184.30 tff(13790,plain,
% 291.72/184.30 ((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | (~m_cell_v_req(c_e_h_2, s3)) | m_and_h_gate_v_out(c_e_h_2, c_p, s3)),
% 291.72/184.30 inference(modus_ponens,[status(thm)],[13789, 13788])).
% 291.72/184.30 tff(13791,plain,
% 291.72/184.30 (~m_cell_v_req(c_e_h_2, s3)),
% 291.72/184.30 inference(unit_resolution,[status(thm)],[13790, 2908, 13787])).
% 291.72/184.30 tff(13792,plain,
% 291.72/184.30 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node1(c_e_h_1, c_e_h_2, s3))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node1(c_e_h_1, c_e_h_2, s3))),
% 291.82/184.31 inference(rewrite,[status(thm)],[])).
% 291.82/184.31 tff(13793,plain,
% 291.82/184.31 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node1(c_e_h_1, c_e_h_2, s3))),
% 291.82/184.31 inference(quant_inst,[status(thm)],[])).
% 291.82/184.31 tff(13794,plain,
% 291.82/184.31 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node1(c_e_h_1, c_e_h_2, s3)),
% 291.82/184.31 inference(modus_ponens,[status(thm)],[13793, 13792])).
% 291.82/184.31 tff(13795,plain,
% 291.82/184.31 (node1(c_e_h_1, c_e_h_2, s3)),
% 291.82/184.31 inference(unit_resolution,[status(thm)],[13794, 4166, 2919])).
% 291.82/184.31 tff(13796,plain,
% 291.82/184.31 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~m_mutex_h_half_v_inp(c_e_h_1, c_b, s3)) | (~node1(c_e_h_1, c_e_h_2, s3)) | m_cell_v_req(c_e_h_2, s3))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | (~m_mutex_h_half_v_inp(c_e_h_1, c_b, s3)) | (~node1(c_e_h_1, c_e_h_2, s3)) | m_cell_v_req(c_e_h_2, s3))),
% 291.82/184.31 inference(rewrite,[status(thm)],[])).
% 291.82/184.31 tff(13797,plain,
% 291.82/184.31 (((~node1(c_e_h_1, c_e_h_2, s3)) | m_cell_v_req(c_e_h_2, s3) | (~m_mutex_h_half_v_inp(c_e_h_1, c_b, s3))) <=> ((~m_mutex_h_half_v_inp(c_e_h_1, c_b, s3)) | (~node1(c_e_h_1, c_e_h_2, s3)) | m_cell_v_req(c_e_h_2, s3))),
% 291.82/184.31 inference(rewrite,[status(thm)],[])).
% 291.82/184.31 tff(13798,plain,
% 291.82/184.31 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_1, c_e_h_2, s3)) | m_cell_v_req(c_e_h_2, s3) | (~m_mutex_h_half_v_inp(c_e_h_1, c_b, s3)))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~m_mutex_h_half_v_inp(c_e_h_1, c_b, s3)) | (~node1(c_e_h_1, c_e_h_2, s3)) | m_cell_v_req(c_e_h_2, s3)))),
% 291.82/184.31 inference(monotonicity,[status(thm)],[13797])).
% 291.82/184.31 tff(13799,plain,
% 291.82/184.31 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_1, c_e_h_2, s3)) | m_cell_v_req(c_e_h_2, s3) | (~m_mutex_h_half_v_inp(c_e_h_1, c_b, s3)))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | (~m_mutex_h_half_v_inp(c_e_h_1, c_b, s3)) | (~node1(c_e_h_1, c_e_h_2, s3)) | m_cell_v_req(c_e_h_2, s3))),
% 291.82/184.31 inference(transitivity,[status(thm)],[13798, 13796])).
% 291.82/184.31 tff(13800,plain,
% 291.82/184.31 ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_1, c_e_h_2, s3)) | m_cell_v_req(c_e_h_2, s3) | (~m_mutex_h_half_v_inp(c_e_h_1, c_b, s3)))),
% 291.82/184.31 inference(quant_inst,[status(thm)],[])).
% 291.82/184.31 tff(13801,plain,
% 291.82/184.31 ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | (~m_mutex_h_half_v_inp(c_e_h_1, c_b, s3)) | (~node1(c_e_h_1, c_e_h_2, s3)) | m_cell_v_req(c_e_h_2, s3)),
% 291.82/184.31 inference(modus_ponens,[status(thm)],[13800, 13799])).
% 291.82/184.31 tff(13802,plain,
% 291.82/184.31 ((~m_mutex_h_half_v_inp(c_e_h_1, c_b, s3)) | m_cell_v_req(c_e_h_2, s3)),
% 291.82/184.31 inference(unit_resolution,[status(thm)],[13801, 2936, 13795])).
% 291.82/184.31 tff(13803,plain,
% 291.82/184.31 (~m_mutex_h_half_v_inp(c_e_h_1, c_b, s3)),
% 291.82/184.31 inference(unit_resolution,[status(thm)],[13802, 13791])).
% 291.82/184.31 tff(13804,assumption,(m_mutex_h_half_v_out(c_e_h_1, c_b, s4)), introduced(assumption)).
% 291.82/184.31 tff(13805,plain,
% 291.82/184.31 (((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | ((~m_cell_v_req(c_e_h_2, s2)) | m_and_h_gate_v_out(c_e_h_2, c_p, s2))) <=> ((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | (~m_cell_v_req(c_e_h_2, s2)) | m_and_h_gate_v_out(c_e_h_2, c_p, s2))),
% 291.82/184.31 inference(rewrite,[status(thm)],[])).
% 291.82/184.31 tff(13806,plain,
% 291.82/184.31 ((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | ((~m_cell_v_req(c_e_h_2, s2)) | m_and_h_gate_v_out(c_e_h_2, c_p, s2))),
% 291.82/184.31 inference(quant_inst,[status(thm)],[])).
% 291.82/184.31 tff(13807,plain,
% 291.82/184.31 ((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | (~m_cell_v_req(c_e_h_2, s2)) | m_and_h_gate_v_out(c_e_h_2, c_p, s2)),
% 291.82/184.31 inference(modus_ponens,[status(thm)],[13806, 13805])).
% 291.82/184.31 tff(13808,plain,
% 291.82/184.31 (~m_cell_v_req(c_e_h_2, s2)),
% 291.82/184.31 inference(unit_resolution,[status(thm)],[13807, 2908, 13782])).
% 291.82/184.31 tff(13809,plain,
% 291.82/184.31 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node1(c_e_h_1, c_e_h_2, s2))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node1(c_e_h_1, c_e_h_2, s2))),
% 291.82/184.31 inference(rewrite,[status(thm)],[])).
% 291.82/184.31 tff(13810,plain,
% 291.82/184.31 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node1(c_e_h_1, c_e_h_2, s2))),
% 291.82/184.31 inference(quant_inst,[status(thm)],[])).
% 291.82/184.31 tff(13811,plain,
% 291.82/184.31 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node1(c_e_h_1, c_e_h_2, s2)),
% 291.82/184.31 inference(modus_ponens,[status(thm)],[13810, 13809])).
% 291.82/184.31 tff(13812,plain,
% 291.82/184.31 (node1(c_e_h_1, c_e_h_2, s2)),
% 291.82/184.31 inference(unit_resolution,[status(thm)],[13811, 4166, 2919])).
% 291.82/184.31 tff(13813,plain,
% 291.82/184.31 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | (m_cell_v_req(c_e_h_2, s2) | (~node1(c_e_h_1, c_e_h_2, s2)) | (~m_mutex_h_half_v_inp(c_e_h_1, c_b, s2)))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | m_cell_v_req(c_e_h_2, s2) | (~node1(c_e_h_1, c_e_h_2, s2)) | (~m_mutex_h_half_v_inp(c_e_h_1, c_b, s2)))),
% 291.82/184.31 inference(rewrite,[status(thm)],[])).
% 291.82/184.31 tff(13814,plain,
% 291.82/184.31 (((~node1(c_e_h_1, c_e_h_2, s2)) | m_cell_v_req(c_e_h_2, s2) | (~m_mutex_h_half_v_inp(c_e_h_1, c_b, s2))) <=> (m_cell_v_req(c_e_h_2, s2) | (~node1(c_e_h_1, c_e_h_2, s2)) | (~m_mutex_h_half_v_inp(c_e_h_1, c_b, s2)))),
% 291.82/184.31 inference(rewrite,[status(thm)],[])).
% 291.82/184.31 tff(13815,plain,
% 291.82/184.31 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_1, c_e_h_2, s2)) | m_cell_v_req(c_e_h_2, s2) | (~m_mutex_h_half_v_inp(c_e_h_1, c_b, s2)))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | (m_cell_v_req(c_e_h_2, s2) | (~node1(c_e_h_1, c_e_h_2, s2)) | (~m_mutex_h_half_v_inp(c_e_h_1, c_b, s2))))),
% 291.82/184.31 inference(monotonicity,[status(thm)],[13814])).
% 291.82/184.31 tff(13816,plain,
% 291.82/184.31 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_1, c_e_h_2, s2)) | m_cell_v_req(c_e_h_2, s2) | (~m_mutex_h_half_v_inp(c_e_h_1, c_b, s2)))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | m_cell_v_req(c_e_h_2, s2) | (~node1(c_e_h_1, c_e_h_2, s2)) | (~m_mutex_h_half_v_inp(c_e_h_1, c_b, s2)))),
% 291.82/184.31 inference(transitivity,[status(thm)],[13815, 13813])).
% 291.82/184.31 tff(13817,plain,
% 291.82/184.31 ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_1, c_e_h_2, s2)) | m_cell_v_req(c_e_h_2, s2) | (~m_mutex_h_half_v_inp(c_e_h_1, c_b, s2)))),
% 291.82/184.31 inference(quant_inst,[status(thm)],[])).
% 291.82/184.31 tff(13818,plain,
% 291.82/184.31 ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | m_cell_v_req(c_e_h_2, s2) | (~node1(c_e_h_1, c_e_h_2, s2)) | (~m_mutex_h_half_v_inp(c_e_h_1, c_b, s2))),
% 291.82/184.31 inference(modus_ponens,[status(thm)],[13817, 13816])).
% 291.82/184.31 tff(13819,plain,
% 291.82/184.31 (m_cell_v_req(c_e_h_2, s2) | (~m_mutex_h_half_v_inp(c_e_h_1, c_b, s2))),
% 291.82/184.31 inference(unit_resolution,[status(thm)],[13818, 2936, 13812])).
% 291.82/184.31 tff(13820,plain,
% 291.82/184.31 (~m_mutex_h_half_v_inp(c_e_h_1, c_b, s2)),
% 291.82/184.31 inference(unit_resolution,[status(thm)],[13819, 13808])).
% 291.82/184.31 tff(13821,assumption,(m_mutex_h_half_v_out(c_e_h_1, c_b, s3)), introduced(assumption)).
% 291.82/184.31 tff(13822,assumption,(m_mutex_h_half_v_out(c_e_h_1, c_b, s1)), introduced(assumption)).
% 291.82/184.31 tff(13823,assumption,(node13(c_e_h_1, c_b, s0, s1)), introduced(assumption)).
% 291.82/184.31 tff(13824,plain,
% 291.82/184.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_1, c_b, s1)) | (~node13(c_e_h_1, c_b, s0, s1)) | m_mutex_h_half_v_out(c_e_h_1, c_b, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s1)) | (~node13(c_e_h_1, c_b, s0, s1)) | m_mutex_h_half_v_out(c_e_h_1, c_b, s0))),
% 291.82/184.31 inference(rewrite,[status(thm)],[])).
% 291.82/184.31 tff(13825,plain,
% 291.82/184.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_1, c_b, s1)) | (~node13(c_e_h_1, c_b, s0, s1)) | m_mutex_h_half_v_out(c_e_h_1, c_b, s0))),
% 291.82/184.31 inference(quant_inst,[status(thm)],[])).
% 291.82/184.31 tff(13826,plain,
% 291.82/184.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s1)) | (~node13(c_e_h_1, c_b, s0, s1)) | m_mutex_h_half_v_out(c_e_h_1, c_b, s0)),
% 291.82/184.31 inference(modus_ponens,[status(thm)],[13825, 13824])).
% 291.82/184.31 tff(13827,plain,
% 291.82/184.31 ($false),
% 291.82/184.31 inference(unit_resolution,[status(thm)],[13826, 423, 13823, 9747, 13822])).
% 291.82/184.31 tff(13828,plain,((~node13(c_e_h_1, c_b, s0, s1)) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s1))), inference(lemma,lemma(discharge,[]))).
% 291.82/184.31 tff(13829,plain,
% 291.82/184.31 (~node13(c_e_h_1, c_b, s0, s1)),
% 291.82/184.31 inference(unit_resolution,[status(thm)],[13828, 13822])).
% 291.82/184.31 tff(13830,plain,
% 291.82/184.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s0, s1)) | node12(c_e_h_1, c_b, s0, s1) | node13(c_e_h_1, c_b, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s0, s1)) | node12(c_e_h_1, c_b, s0, s1) | node13(c_e_h_1, c_b, s0, s1))),
% 291.82/184.31 inference(rewrite,[status(thm)],[])).
% 291.82/184.31 tff(13831,plain,
% 291.82/184.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s0, s1)) | node12(c_e_h_1, c_b, s0, s1) | node13(c_e_h_1, c_b, s0, s1))),
% 291.82/184.31 inference(quant_inst,[status(thm)],[])).
% 291.82/184.31 tff(13832,plain,
% 291.82/184.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s0, s1)) | node12(c_e_h_1, c_b, s0, s1) | node13(c_e_h_1, c_b, s0, s1)),
% 291.82/184.31 inference(modus_ponens,[status(thm)],[13831, 13830])).
% 291.82/184.31 tff(13833,plain,
% 291.82/184.31 (node12(c_e_h_1, c_b, s0, s1) | node13(c_e_h_1, c_b, s0, s1)),
% 291.82/184.31 inference(unit_resolution,[status(thm)],[13832, 439, 72])).
% 291.82/184.31 tff(13834,plain,
% 291.82/184.31 (node12(c_e_h_1, c_b, s0, s1)),
% 291.82/184.31 inference(unit_resolution,[status(thm)],[13833, 13829])).
% 291.82/184.31 tff(13835,plain,
% 291.82/184.31 (((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | ((~m_cell_v_req(c_e_h_2, s0)) | m_and_h_gate_v_out(c_e_h_2, c_p, s0))) <=> ((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | (~m_cell_v_req(c_e_h_2, s0)) | m_and_h_gate_v_out(c_e_h_2, c_p, s0))),
% 291.82/184.31 inference(rewrite,[status(thm)],[])).
% 291.82/184.31 tff(13836,plain,
% 291.82/184.31 ((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | ((~m_cell_v_req(c_e_h_2, s0)) | m_and_h_gate_v_out(c_e_h_2, c_p, s0))),
% 291.82/184.31 inference(quant_inst,[status(thm)],[])).
% 291.82/184.31 tff(13837,plain,
% 291.82/184.31 ((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | (~m_cell_v_req(c_e_h_2, s0)) | m_and_h_gate_v_out(c_e_h_2, c_p, s0)),
% 291.82/184.31 inference(modus_ponens,[status(thm)],[13836, 13835])).
% 291.82/184.31 tff(13838,plain,
% 291.82/184.31 (~m_cell_v_req(c_e_h_2, s0)),
% 291.82/184.31 inference(unit_resolution,[status(thm)],[13837, 2908, 13718])).
% 291.82/184.31 tff(13839,plain,
% 291.82/184.31 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node1(c_e_h_1, c_e_h_2, s0))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node1(c_e_h_1, c_e_h_2, s0))),
% 291.82/184.32 inference(rewrite,[status(thm)],[])).
% 291.82/184.32 tff(13840,plain,
% 291.82/184.32 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node1(c_e_h_1, c_e_h_2, s0))),
% 291.82/184.32 inference(quant_inst,[status(thm)],[])).
% 291.82/184.32 tff(13841,plain,
% 291.82/184.32 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node1(c_e_h_1, c_e_h_2, s0)),
% 291.82/184.32 inference(modus_ponens,[status(thm)],[13840, 13839])).
% 291.82/184.32 tff(13842,plain,
% 291.82/184.32 (node1(c_e_h_1, c_e_h_2, s0)),
% 291.82/184.32 inference(unit_resolution,[status(thm)],[13841, 4166, 2919])).
% 291.82/184.32 tff(13843,plain,
% 291.82/184.32 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_1, c_e_h_2, s0)) | m_cell_v_req(c_e_h_2, s0) | (~m_mutex_h_half_v_inp(c_e_h_1, c_b, s0)))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | (~node1(c_e_h_1, c_e_h_2, s0)) | m_cell_v_req(c_e_h_2, s0) | (~m_mutex_h_half_v_inp(c_e_h_1, c_b, s0)))),
% 291.82/184.32 inference(rewrite,[status(thm)],[])).
% 291.82/184.32 tff(13844,plain,
% 291.82/184.32 ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_1, c_e_h_2, s0)) | m_cell_v_req(c_e_h_2, s0) | (~m_mutex_h_half_v_inp(c_e_h_1, c_b, s0)))),
% 291.82/184.32 inference(quant_inst,[status(thm)],[])).
% 291.82/184.32 tff(13845,plain,
% 291.82/184.32 ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | (~node1(c_e_h_1, c_e_h_2, s0)) | m_cell_v_req(c_e_h_2, s0) | (~m_mutex_h_half_v_inp(c_e_h_1, c_b, s0))),
% 291.82/184.32 inference(modus_ponens,[status(thm)],[13844, 13843])).
% 291.82/184.32 tff(13846,plain,
% 291.82/184.32 (m_cell_v_req(c_e_h_2, s0) | (~m_mutex_h_half_v_inp(c_e_h_1, c_b, s0))),
% 291.82/184.32 inference(unit_resolution,[status(thm)],[13845, 2936, 13842])).
% 291.82/184.32 tff(13847,plain,
% 291.82/184.32 (~m_mutex_h_half_v_inp(c_e_h_1, c_b, s0)),
% 291.82/184.32 inference(unit_resolution,[status(thm)],[13846, 13838])).
% 291.82/184.32 tff(13848,plain,
% 291.82/184.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_1, c_b, s0) | (~node12(c_e_h_1, c_b, s0, s1)) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_1, c_b, s0) | (~node12(c_e_h_1, c_b, s0, s1)) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s1)))),
% 291.82/184.32 inference(rewrite,[status(thm)],[])).
% 291.82/184.32 tff(13849,plain,
% 291.82/184.32 (((~node12(c_e_h_1, c_b, s0, s1)) | m_mutex_h_half_v_inp(c_e_h_1, c_b, s0) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s1))) <=> (m_mutex_h_half_v_inp(c_e_h_1, c_b, s0) | (~node12(c_e_h_1, c_b, s0, s1)) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s1)))),
% 291.82/184.32 inference(rewrite,[status(thm)],[])).
% 291.82/184.32 tff(13850,plain,
% 291.82/184.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_1, c_b, s0, s1)) | m_mutex_h_half_v_inp(c_e_h_1, c_b, s0) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_1, c_b, s0) | (~node12(c_e_h_1, c_b, s0, s1)) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s1))))),
% 291.82/184.32 inference(monotonicity,[status(thm)],[13849])).
% 291.82/184.32 tff(13851,plain,
% 291.82/184.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_1, c_b, s0, s1)) | m_mutex_h_half_v_inp(c_e_h_1, c_b, s0) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_1, c_b, s0) | (~node12(c_e_h_1, c_b, s0, s1)) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s1)))),
% 291.82/184.32 inference(transitivity,[status(thm)],[13850, 13848])).
% 291.82/184.32 tff(13852,plain,
% 291.82/184.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_1, c_b, s0, s1)) | m_mutex_h_half_v_inp(c_e_h_1, c_b, s0) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s1)))),
% 291.82/184.32 inference(quant_inst,[status(thm)],[])).
% 291.82/184.32 tff(13853,plain,
% 291.82/184.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_1, c_b, s0) | (~node12(c_e_h_1, c_b, s0, s1)) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s1))),
% 291.82/184.32 inference(modus_ponens,[status(thm)],[13852, 13851])).
% 291.82/184.32 tff(13854,plain,
% 291.82/184.32 ($false),
% 291.82/184.32 inference(unit_resolution,[status(thm)],[13853, 454, 13847, 13834, 13822])).
% 291.82/184.32 tff(13855,plain,(~m_mutex_h_half_v_out(c_e_h_1, c_b, s1)), inference(lemma,lemma(discharge,[]))).
% 291.82/184.32 tff(13856,assumption,(m_mutex_h_half_v_out(c_e_h_1, c_b, s2)), introduced(assumption)).
% 291.82/184.32 tff(13857,assumption,(~m_mutex_h_half_v_out(c_e_h_1, c_b, s1)), introduced(assumption)).
% 291.82/184.32 tff(13858,assumption,(node13(c_e_h_1, c_b, s1, s2)), introduced(assumption)).
% 291.82/184.32 tff(13859,plain,
% 291.82/184.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_1, c_b, s2)) | (~node13(c_e_h_1, c_b, s1, s2)) | m_mutex_h_half_v_out(c_e_h_1, c_b, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s2)) | (~node13(c_e_h_1, c_b, s1, s2)) | m_mutex_h_half_v_out(c_e_h_1, c_b, s1))),
% 291.82/184.32 inference(rewrite,[status(thm)],[])).
% 291.82/184.32 tff(13860,plain,
% 291.82/184.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_1, c_b, s2)) | (~node13(c_e_h_1, c_b, s1, s2)) | m_mutex_h_half_v_out(c_e_h_1, c_b, s1))),
% 291.82/184.32 inference(quant_inst,[status(thm)],[])).
% 291.82/184.32 tff(13861,plain,
% 291.82/184.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s2)) | (~node13(c_e_h_1, c_b, s1, s2)) | m_mutex_h_half_v_out(c_e_h_1, c_b, s1)),
% 291.82/184.32 inference(modus_ponens,[status(thm)],[13860, 13859])).
% 291.82/184.32 tff(13862,plain,
% 291.82/184.32 ($false),
% 291.82/184.32 inference(unit_resolution,[status(thm)],[13861, 423, 13858, 13857, 13856])).
% 291.82/184.32 tff(13863,plain,((~node13(c_e_h_1, c_b, s1, s2)) | m_mutex_h_half_v_out(c_e_h_1, c_b, s1) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s2))), inference(lemma,lemma(discharge,[]))).
% 291.82/184.32 tff(13864,plain,
% 291.82/184.32 (~node13(c_e_h_1, c_b, s1, s2)),
% 291.82/184.32 inference(unit_resolution,[status(thm)],[13863, 13856, 13857])).
% 291.82/184.32 tff(13865,plain,
% 291.82/184.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s1, s2)) | node12(c_e_h_1, c_b, s1, s2) | node13(c_e_h_1, c_b, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s1, s2)) | node12(c_e_h_1, c_b, s1, s2) | node13(c_e_h_1, c_b, s1, s2))),
% 291.82/184.32 inference(rewrite,[status(thm)],[])).
% 291.82/184.32 tff(13866,plain,
% 291.82/184.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s1, s2)) | node12(c_e_h_1, c_b, s1, s2) | node13(c_e_h_1, c_b, s1, s2))),
% 291.82/184.32 inference(quant_inst,[status(thm)],[])).
% 291.82/184.32 tff(13867,plain,
% 291.82/184.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s1, s2)) | node12(c_e_h_1, c_b, s1, s2) | node13(c_e_h_1, c_b, s1, s2)),
% 291.82/184.32 inference(modus_ponens,[status(thm)],[13866, 13865])).
% 291.82/184.32 tff(13868,plain,
% 291.82/184.32 (node12(c_e_h_1, c_b, s1, s2) | node13(c_e_h_1, c_b, s1, s2)),
% 291.82/184.32 inference(unit_resolution,[status(thm)],[13867, 439, 255])).
% 291.82/184.32 tff(13869,plain,
% 291.82/184.32 (node12(c_e_h_1, c_b, s1, s2)),
% 291.82/184.32 inference(unit_resolution,[status(thm)],[13868, 13864])).
% 291.82/184.32 tff(13870,plain,
% 291.82/184.32 (((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | ((~m_cell_v_req(c_e_h_2, s1)) | m_and_h_gate_v_out(c_e_h_2, c_p, s1))) <=> ((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | (~m_cell_v_req(c_e_h_2, s1)) | m_and_h_gate_v_out(c_e_h_2, c_p, s1))),
% 291.82/184.32 inference(rewrite,[status(thm)],[])).
% 291.82/184.32 tff(13871,plain,
% 291.82/184.32 ((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | ((~m_cell_v_req(c_e_h_2, s1)) | m_and_h_gate_v_out(c_e_h_2, c_p, s1))),
% 291.82/184.32 inference(quant_inst,[status(thm)],[])).
% 291.82/184.32 tff(13872,plain,
% 291.82/184.32 ((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | (~m_cell_v_req(c_e_h_2, s1)) | m_and_h_gate_v_out(c_e_h_2, c_p, s1)),
% 291.82/184.32 inference(modus_ponens,[status(thm)],[13871, 13870])).
% 291.82/184.32 tff(13873,plain,
% 291.82/184.32 (~m_cell_v_req(c_e_h_2, s1)),
% 291.82/184.32 inference(unit_resolution,[status(thm)],[13872, 2908, 13749])).
% 291.82/184.32 tff(13874,plain,
% 291.82/184.32 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node1(c_e_h_1, c_e_h_2, s1))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node1(c_e_h_1, c_e_h_2, s1))),
% 291.82/184.32 inference(rewrite,[status(thm)],[])).
% 291.82/184.32 tff(13875,plain,
% 291.82/184.32 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node1(c_e_h_1, c_e_h_2, s1))),
% 291.82/184.32 inference(quant_inst,[status(thm)],[])).
% 291.82/184.32 tff(13876,plain,
% 291.82/184.32 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node1(c_e_h_1, c_e_h_2, s1)),
% 291.82/184.32 inference(modus_ponens,[status(thm)],[13875, 13874])).
% 291.82/184.32 tff(13877,plain,
% 291.82/184.32 (node1(c_e_h_1, c_e_h_2, s1)),
% 291.82/184.32 inference(unit_resolution,[status(thm)],[13876, 4166, 2919])).
% 291.82/184.32 tff(13878,plain,
% 291.82/184.32 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_1, c_e_h_2, s1)) | (~m_mutex_h_half_v_inp(c_e_h_1, c_b, s1)) | m_cell_v_req(c_e_h_2, s1))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | (~node1(c_e_h_1, c_e_h_2, s1)) | (~m_mutex_h_half_v_inp(c_e_h_1, c_b, s1)) | m_cell_v_req(c_e_h_2, s1))),
% 291.82/184.32 inference(rewrite,[status(thm)],[])).
% 291.82/184.32 tff(13879,plain,
% 291.82/184.32 (((~node1(c_e_h_1, c_e_h_2, s1)) | m_cell_v_req(c_e_h_2, s1) | (~m_mutex_h_half_v_inp(c_e_h_1, c_b, s1))) <=> ((~node1(c_e_h_1, c_e_h_2, s1)) | (~m_mutex_h_half_v_inp(c_e_h_1, c_b, s1)) | m_cell_v_req(c_e_h_2, s1))),
% 291.82/184.32 inference(rewrite,[status(thm)],[])).
% 291.82/184.32 tff(13880,plain,
% 291.82/184.32 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_1, c_e_h_2, s1)) | m_cell_v_req(c_e_h_2, s1) | (~m_mutex_h_half_v_inp(c_e_h_1, c_b, s1)))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_1, c_e_h_2, s1)) | (~m_mutex_h_half_v_inp(c_e_h_1, c_b, s1)) | m_cell_v_req(c_e_h_2, s1)))),
% 291.82/184.32 inference(monotonicity,[status(thm)],[13879])).
% 291.82/184.32 tff(13881,plain,
% 291.82/184.32 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_1, c_e_h_2, s1)) | m_cell_v_req(c_e_h_2, s1) | (~m_mutex_h_half_v_inp(c_e_h_1, c_b, s1)))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | (~node1(c_e_h_1, c_e_h_2, s1)) | (~m_mutex_h_half_v_inp(c_e_h_1, c_b, s1)) | m_cell_v_req(c_e_h_2, s1))),
% 291.82/184.32 inference(transitivity,[status(thm)],[13880, 13878])).
% 291.82/184.32 tff(13882,plain,
% 291.82/184.32 ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_1, c_e_h_2, s1)) | m_cell_v_req(c_e_h_2, s1) | (~m_mutex_h_half_v_inp(c_e_h_1, c_b, s1)))),
% 291.82/184.33 inference(quant_inst,[status(thm)],[])).
% 291.82/184.33 tff(13883,plain,
% 291.82/184.33 ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | (~node1(c_e_h_1, c_e_h_2, s1)) | (~m_mutex_h_half_v_inp(c_e_h_1, c_b, s1)) | m_cell_v_req(c_e_h_2, s1)),
% 291.82/184.33 inference(modus_ponens,[status(thm)],[13882, 13881])).
% 291.82/184.33 tff(13884,plain,
% 291.82/184.33 ((~m_mutex_h_half_v_inp(c_e_h_1, c_b, s1)) | m_cell_v_req(c_e_h_2, s1)),
% 291.82/184.33 inference(unit_resolution,[status(thm)],[13883, 2936, 13877])).
% 291.82/184.33 tff(13885,plain,
% 291.82/184.33 (~m_mutex_h_half_v_inp(c_e_h_1, c_b, s1)),
% 291.82/184.33 inference(unit_resolution,[status(thm)],[13884, 13873])).
% 291.82/184.33 tff(13886,plain,
% 291.82/184.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_1, c_b, s1) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s2)) | (~node12(c_e_h_1, c_b, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_1, c_b, s1) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s2)) | (~node12(c_e_h_1, c_b, s1, s2)))),
% 291.82/184.33 inference(rewrite,[status(thm)],[])).
% 291.82/184.33 tff(13887,plain,
% 291.82/184.33 (((~node12(c_e_h_1, c_b, s1, s2)) | m_mutex_h_half_v_inp(c_e_h_1, c_b, s1) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s2))) <=> (m_mutex_h_half_v_inp(c_e_h_1, c_b, s1) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s2)) | (~node12(c_e_h_1, c_b, s1, s2)))),
% 291.82/184.33 inference(rewrite,[status(thm)],[])).
% 291.82/184.33 tff(13888,plain,
% 291.82/184.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_1, c_b, s1, s2)) | m_mutex_h_half_v_inp(c_e_h_1, c_b, s1) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_1, c_b, s1) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s2)) | (~node12(c_e_h_1, c_b, s1, s2))))),
% 291.82/184.33 inference(monotonicity,[status(thm)],[13887])).
% 291.82/184.33 tff(13889,plain,
% 291.82/184.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_1, c_b, s1, s2)) | m_mutex_h_half_v_inp(c_e_h_1, c_b, s1) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_1, c_b, s1) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s2)) | (~node12(c_e_h_1, c_b, s1, s2)))),
% 291.82/184.33 inference(transitivity,[status(thm)],[13888, 13886])).
% 291.82/184.33 tff(13890,plain,
% 291.82/184.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_1, c_b, s1, s2)) | m_mutex_h_half_v_inp(c_e_h_1, c_b, s1) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s2)))),
% 291.82/184.33 inference(quant_inst,[status(thm)],[])).
% 291.82/184.33 tff(13891,plain,
% 291.82/184.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_1, c_b, s1) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s2)) | (~node12(c_e_h_1, c_b, s1, s2))),
% 291.82/184.33 inference(modus_ponens,[status(thm)],[13890, 13889])).
% 291.82/184.33 tff(13892,plain,
% 291.82/184.33 ($false),
% 291.82/184.33 inference(unit_resolution,[status(thm)],[13891, 454, 13885, 13869, 13856])).
% 291.82/184.33 tff(13893,plain,((~m_mutex_h_half_v_out(c_e_h_1, c_b, s2)) | m_mutex_h_half_v_out(c_e_h_1, c_b, s1)), inference(lemma,lemma(discharge,[]))).
% 291.82/184.33 tff(13894,plain,
% 291.82/184.33 (~m_mutex_h_half_v_out(c_e_h_1, c_b, s2)),
% 291.82/184.33 inference(unit_resolution,[status(thm)],[13893, 13855])).
% 291.82/184.33 tff(13895,assumption,(node13(c_e_h_1, c_b, s2, s3)), introduced(assumption)).
% 291.82/184.33 tff(13896,plain,
% 291.82/184.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_1, c_b, s3)) | (~node13(c_e_h_1, c_b, s2, s3)) | m_mutex_h_half_v_out(c_e_h_1, c_b, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s3)) | (~node13(c_e_h_1, c_b, s2, s3)) | m_mutex_h_half_v_out(c_e_h_1, c_b, s2))),
% 291.82/184.33 inference(rewrite,[status(thm)],[])).
% 291.82/184.33 tff(13897,plain,
% 291.82/184.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_1, c_b, s3)) | (~node13(c_e_h_1, c_b, s2, s3)) | m_mutex_h_half_v_out(c_e_h_1, c_b, s2))),
% 291.82/184.33 inference(quant_inst,[status(thm)],[])).
% 291.82/184.33 tff(13898,plain,
% 291.82/184.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s3)) | (~node13(c_e_h_1, c_b, s2, s3)) | m_mutex_h_half_v_out(c_e_h_1, c_b, s2)),
% 291.82/184.33 inference(modus_ponens,[status(thm)],[13897, 13896])).
% 291.82/184.33 tff(13899,plain,
% 291.82/184.33 ($false),
% 291.82/184.33 inference(unit_resolution,[status(thm)],[13898, 423, 13895, 13821, 13894])).
% 291.82/184.33 tff(13900,plain,((~node13(c_e_h_1, c_b, s2, s3)) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s3))), inference(lemma,lemma(discharge,[]))).
% 291.82/184.33 tff(13901,plain,
% 291.82/184.33 (~node13(c_e_h_1, c_b, s2, s3)),
% 291.82/184.33 inference(unit_resolution,[status(thm)],[13900, 13821])).
% 291.82/184.33 tff(13902,assumption,(~m_mutex_h_half_v_inp(c_e_h_1, c_b, s2)), introduced(assumption)).
% 291.82/184.33 tff(13903,assumption,(node12(c_e_h_1, c_b, s2, s3)), introduced(assumption)).
% 291.82/184.33 tff(13904,plain,
% 291.82/184.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~m_mutex_h_half_v_out(c_e_h_1, c_b, s3)) | m_mutex_h_half_v_inp(c_e_h_1, c_b, s2) | (~node12(c_e_h_1, c_b, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s3)) | m_mutex_h_half_v_inp(c_e_h_1, c_b, s2) | (~node12(c_e_h_1, c_b, s2, s3)))),
% 291.82/184.33 inference(rewrite,[status(thm)],[])).
% 291.82/184.33 tff(13905,plain,
% 291.82/184.33 (((~node12(c_e_h_1, c_b, s2, s3)) | m_mutex_h_half_v_inp(c_e_h_1, c_b, s2) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s3))) <=> ((~m_mutex_h_half_v_out(c_e_h_1, c_b, s3)) | m_mutex_h_half_v_inp(c_e_h_1, c_b, s2) | (~node12(c_e_h_1, c_b, s2, s3)))),
% 291.82/184.33 inference(rewrite,[status(thm)],[])).
% 291.82/184.33 tff(13906,plain,
% 291.82/184.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_1, c_b, s2, s3)) | m_mutex_h_half_v_inp(c_e_h_1, c_b, s2) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~m_mutex_h_half_v_out(c_e_h_1, c_b, s3)) | m_mutex_h_half_v_inp(c_e_h_1, c_b, s2) | (~node12(c_e_h_1, c_b, s2, s3))))),
% 291.82/184.33 inference(monotonicity,[status(thm)],[13905])).
% 291.82/184.33 tff(13907,plain,
% 291.82/184.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_1, c_b, s2, s3)) | m_mutex_h_half_v_inp(c_e_h_1, c_b, s2) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s3)) | m_mutex_h_half_v_inp(c_e_h_1, c_b, s2) | (~node12(c_e_h_1, c_b, s2, s3)))),
% 291.82/184.33 inference(transitivity,[status(thm)],[13906, 13904])).
% 291.82/184.33 tff(13908,plain,
% 291.82/184.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_1, c_b, s2, s3)) | m_mutex_h_half_v_inp(c_e_h_1, c_b, s2) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s3)))),
% 291.82/184.33 inference(quant_inst,[status(thm)],[])).
% 291.82/184.33 tff(13909,plain,
% 291.82/184.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s3)) | m_mutex_h_half_v_inp(c_e_h_1, c_b, s2) | (~node12(c_e_h_1, c_b, s2, s3))),
% 291.82/184.33 inference(modus_ponens,[status(thm)],[13908, 13907])).
% 291.82/184.33 tff(13910,plain,
% 291.82/184.33 ($false),
% 291.82/184.33 inference(unit_resolution,[status(thm)],[13909, 454, 13902, 13903, 13821])).
% 291.82/184.33 tff(13911,plain,((~node12(c_e_h_1, c_b, s2, s3)) | m_mutex_h_half_v_inp(c_e_h_1, c_b, s2) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s3))), inference(lemma,lemma(discharge,[]))).
% 291.82/184.33 tff(13912,plain,
% 291.82/184.33 (~node12(c_e_h_1, c_b, s2, s3)),
% 291.82/184.33 inference(unit_resolution,[status(thm)],[13911, 13821, 13902])).
% 291.82/184.33 tff(13913,plain,
% 291.82/184.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s2, s3)) | node12(c_e_h_1, c_b, s2, s3) | node13(c_e_h_1, c_b, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s2, s3)) | node12(c_e_h_1, c_b, s2, s3) | node13(c_e_h_1, c_b, s2, s3))),
% 291.82/184.33 inference(rewrite,[status(thm)],[])).
% 291.82/184.33 tff(13914,plain,
% 291.82/184.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s2, s3)) | node12(c_e_h_1, c_b, s2, s3) | node13(c_e_h_1, c_b, s2, s3))),
% 291.82/184.33 inference(quant_inst,[status(thm)],[])).
% 291.82/184.33 tff(13915,plain,
% 291.82/184.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s2, s3)) | node12(c_e_h_1, c_b, s2, s3) | node13(c_e_h_1, c_b, s2, s3)),
% 291.82/184.33 inference(modus_ponens,[status(thm)],[13914, 13913])).
% 291.82/184.33 tff(13916,plain,
% 291.82/184.33 (node12(c_e_h_1, c_b, s2, s3) | node13(c_e_h_1, c_b, s2, s3)),
% 291.82/184.33 inference(unit_resolution,[status(thm)],[13915, 439, 318])).
% 291.82/184.33 tff(13917,plain,
% 291.82/184.33 ($false),
% 291.82/184.33 inference(unit_resolution,[status(thm)],[13916, 13912, 13901])).
% 291.82/184.33 tff(13918,plain,((~m_mutex_h_half_v_out(c_e_h_1, c_b, s3)) | m_mutex_h_half_v_inp(c_e_h_1, c_b, s2)), inference(lemma,lemma(discharge,[]))).
% 291.82/184.33 tff(13919,plain,
% 291.82/184.33 (~m_mutex_h_half_v_out(c_e_h_1, c_b, s3)),
% 291.82/184.33 inference(unit_resolution,[status(thm)],[13918, 13820])).
% 291.82/184.33 tff(13920,assumption,(~m_mutex_h_half_v_out(c_e_h_1, c_b, s3)), introduced(assumption)).
% 291.82/184.33 tff(13921,assumption,(node13(c_e_h_1, c_b, s3, s4)), introduced(assumption)).
% 291.82/184.33 tff(13922,plain,
% 291.82/184.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_1, c_b, s4)) | (~node13(c_e_h_1, c_b, s3, s4)) | m_mutex_h_half_v_out(c_e_h_1, c_b, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s4)) | (~node13(c_e_h_1, c_b, s3, s4)) | m_mutex_h_half_v_out(c_e_h_1, c_b, s3))),
% 291.82/184.33 inference(rewrite,[status(thm)],[])).
% 291.82/184.33 tff(13923,plain,
% 291.82/184.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_1, c_b, s4)) | (~node13(c_e_h_1, c_b, s3, s4)) | m_mutex_h_half_v_out(c_e_h_1, c_b, s3))),
% 291.82/184.33 inference(quant_inst,[status(thm)],[])).
% 291.82/184.33 tff(13924,plain,
% 291.82/184.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s4)) | (~node13(c_e_h_1, c_b, s3, s4)) | m_mutex_h_half_v_out(c_e_h_1, c_b, s3)),
% 291.82/184.33 inference(modus_ponens,[status(thm)],[13923, 13922])).
% 291.82/184.33 tff(13925,plain,
% 291.82/184.33 ($false),
% 291.82/184.33 inference(unit_resolution,[status(thm)],[13924, 423, 13921, 13920, 13804])).
% 291.82/184.33 tff(13926,plain,((~node13(c_e_h_1, c_b, s3, s4)) | m_mutex_h_half_v_out(c_e_h_1, c_b, s3) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s4))), inference(lemma,lemma(discharge,[]))).
% 291.82/184.33 tff(13927,plain,
% 291.82/184.33 ((~node13(c_e_h_1, c_b, s3, s4)) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s4))),
% 291.82/184.33 inference(unit_resolution,[status(thm)],[13926, 13919])).
% 291.82/184.33 tff(13928,plain,
% 291.82/184.33 (~node13(c_e_h_1, c_b, s3, s4)),
% 291.82/184.33 inference(unit_resolution,[status(thm)],[13927, 13804])).
% 291.82/184.33 tff(13929,assumption,(~m_mutex_h_half_v_inp(c_e_h_1, c_b, s3)), introduced(assumption)).
% 291.82/184.34 tff(13930,assumption,(node12(c_e_h_1, c_b, s3, s4)), introduced(assumption)).
% 291.82/184.34 tff(13931,plain,
% 291.82/184.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_1, c_b, s3) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s4)) | (~node12(c_e_h_1, c_b, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_1, c_b, s3) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s4)) | (~node12(c_e_h_1, c_b, s3, s4)))),
% 291.82/184.34 inference(rewrite,[status(thm)],[])).
% 291.82/184.34 tff(13932,plain,
% 291.82/184.34 (((~node12(c_e_h_1, c_b, s3, s4)) | m_mutex_h_half_v_inp(c_e_h_1, c_b, s3) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s4))) <=> (m_mutex_h_half_v_inp(c_e_h_1, c_b, s3) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s4)) | (~node12(c_e_h_1, c_b, s3, s4)))),
% 291.82/184.34 inference(rewrite,[status(thm)],[])).
% 291.82/184.34 tff(13933,plain,
% 291.82/184.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_1, c_b, s3, s4)) | m_mutex_h_half_v_inp(c_e_h_1, c_b, s3) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_1, c_b, s3) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s4)) | (~node12(c_e_h_1, c_b, s3, s4))))),
% 291.82/184.34 inference(monotonicity,[status(thm)],[13932])).
% 291.82/184.34 tff(13934,plain,
% 291.82/184.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_1, c_b, s3, s4)) | m_mutex_h_half_v_inp(c_e_h_1, c_b, s3) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_1, c_b, s3) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s4)) | (~node12(c_e_h_1, c_b, s3, s4)))),
% 291.82/184.34 inference(transitivity,[status(thm)],[13933, 13931])).
% 291.82/184.34 tff(13935,plain,
% 291.82/184.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_1, c_b, s3, s4)) | m_mutex_h_half_v_inp(c_e_h_1, c_b, s3) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s4)))),
% 291.82/184.34 inference(quant_inst,[status(thm)],[])).
% 291.82/184.34 tff(13936,plain,
% 291.82/184.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_1, c_b, s3) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s4)) | (~node12(c_e_h_1, c_b, s3, s4))),
% 291.82/184.34 inference(modus_ponens,[status(thm)],[13935, 13934])).
% 291.82/184.34 tff(13937,plain,
% 291.82/184.34 ($false),
% 291.82/184.34 inference(unit_resolution,[status(thm)],[13936, 454, 13930, 13929, 13804])).
% 291.82/184.34 tff(13938,plain,((~node12(c_e_h_1, c_b, s3, s4)) | m_mutex_h_half_v_inp(c_e_h_1, c_b, s3) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s4))), inference(lemma,lemma(discharge,[]))).
% 291.82/184.34 tff(13939,plain,
% 291.82/184.34 (~node12(c_e_h_1, c_b, s3, s4)),
% 291.82/184.34 inference(unit_resolution,[status(thm)],[13938, 13804, 13929])).
% 291.82/184.34 tff(13940,plain,
% 291.82/184.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s3, s4)) | node12(c_e_h_1, c_b, s3, s4) | node13(c_e_h_1, c_b, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s3, s4)) | node12(c_e_h_1, c_b, s3, s4) | node13(c_e_h_1, c_b, s3, s4))),
% 291.82/184.34 inference(rewrite,[status(thm)],[])).
% 291.82/184.34 tff(13941,plain,
% 291.82/184.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s3, s4)) | node12(c_e_h_1, c_b, s3, s4) | node13(c_e_h_1, c_b, s3, s4))),
% 291.82/184.34 inference(quant_inst,[status(thm)],[])).
% 291.82/184.34 tff(13942,plain,
% 291.82/184.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s3, s4)) | node12(c_e_h_1, c_b, s3, s4) | node13(c_e_h_1, c_b, s3, s4)),
% 291.82/184.34 inference(modus_ponens,[status(thm)],[13941, 13940])).
% 291.82/184.34 tff(13943,plain,
% 291.82/184.34 (node12(c_e_h_1, c_b, s3, s4) | node13(c_e_h_1, c_b, s3, s4)),
% 291.82/184.34 inference(unit_resolution,[status(thm)],[13942, 439, 531])).
% 291.82/184.34 tff(13944,plain,
% 291.82/184.34 ($false),
% 291.82/184.34 inference(unit_resolution,[status(thm)],[13943, 13939, 13928])).
% 291.82/184.34 tff(13945,plain,((~m_mutex_h_half_v_out(c_e_h_1, c_b, s4)) | m_mutex_h_half_v_inp(c_e_h_1, c_b, s3)), inference(lemma,lemma(discharge,[]))).
% 291.82/184.34 tff(13946,plain,
% 291.82/184.34 (~m_mutex_h_half_v_out(c_e_h_1, c_b, s4)),
% 291.82/184.34 inference(unit_resolution,[status(thm)],[13945, 13803])).
% 291.82/184.34 tff(13947,assumption,(m_and_h_gate_v_in1(c_e_h_1, c_d, s4)), introduced(assumption)).
% 291.82/184.34 tff(13948,assumption,(~m_mutex_h_half_v_out(c_e_h_1, c_b, s4)), introduced(assumption)).
% 291.82/184.34 tff(13949,plain,
% 291.82/184.34 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_d, s4)) | m_mutex_h_half_v_out(c_e_h_1, c_b, s4))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_d, s4)) | m_mutex_h_half_v_out(c_e_h_1, c_b, s4))),
% 291.82/184.34 inference(rewrite,[status(thm)],[])).
% 291.82/184.34 tff(13950,plain,
% 291.82/184.34 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_d, s4)) | m_mutex_h_half_v_out(c_e_h_1, c_b, s4))),
% 291.82/184.34 inference(quant_inst,[status(thm)],[])).
% 291.82/184.34 tff(13951,plain,
% 291.82/184.34 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_d, s4)) | m_mutex_h_half_v_out(c_e_h_1, c_b, s4)),
% 291.82/184.34 inference(modus_ponens,[status(thm)],[13950, 13949])).
% 291.82/184.34 tff(13952,plain,
% 291.82/184.34 ($false),
% 291.82/184.34 inference(unit_resolution,[status(thm)],[13951, 2808, 13948, 13947])).
% 291.82/184.34 tff(13953,plain,((~m_and_h_gate_v_in1(c_e_h_1, c_d, s4)) | m_mutex_h_half_v_out(c_e_h_1, c_b, s4)), inference(lemma,lemma(discharge,[]))).
% 291.82/184.34 tff(13954,plain,
% 291.82/184.34 (~m_and_h_gate_v_in1(c_e_h_1, c_d, s4)),
% 291.82/184.34 inference(unit_resolution,[status(thm)],[13953, 13946])).
% 291.82/184.34 tff(13955,assumption,(~m_and_h_gate_v_in1(c_e_h_1, c_d, s4)), introduced(assumption)).
% 291.82/184.34 tff(13956,assumption,(node20(c_e_h_1, c_d, s4)), introduced(assumption)).
% 291.82/184.34 tff(13957,plain,
% 291.82/184.34 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_d, s4)) | m_and_h_gate_v_in1(c_e_h_1, c_d, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_d, s4)) | m_and_h_gate_v_in1(c_e_h_1, c_d, s4))),
% 291.82/184.34 inference(rewrite,[status(thm)],[])).
% 291.82/184.34 tff(13958,plain,
% 291.82/184.34 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_d, s4)) | m_and_h_gate_v_in1(c_e_h_1, c_d, s4))),
% 291.82/184.34 inference(quant_inst,[status(thm)],[])).
% 291.82/184.34 tff(13959,plain,
% 291.82/184.34 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_d, s4)) | m_and_h_gate_v_in1(c_e_h_1, c_d, s4)),
% 291.82/184.34 inference(modus_ponens,[status(thm)],[13958, 13957])).
% 291.82/184.34 tff(13960,plain,
% 291.82/184.34 ($false),
% 291.82/184.34 inference(unit_resolution,[status(thm)],[13959, 38, 13956, 13955])).
% 291.82/184.34 tff(13961,plain,((~node20(c_e_h_1, c_d, s4)) | m_and_h_gate_v_in1(c_e_h_1, c_d, s4)), inference(lemma,lemma(discharge,[]))).
% 291.82/184.34 tff(13962,plain,
% 291.82/184.34 (~node20(c_e_h_1, c_d, s4)),
% 291.82/184.34 inference(unit_resolution,[status(thm)],[13961, 13954])).
% 291.82/184.34 tff(13963,assumption,(m_and_h_gate_v_in1(c_e_h_1, c_d, s3)), introduced(assumption)).
% 291.82/184.34 tff(13964,plain,
% 291.82/184.34 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_d, s3)) | m_mutex_h_half_v_out(c_e_h_1, c_b, s3))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_d, s3)) | m_mutex_h_half_v_out(c_e_h_1, c_b, s3))),
% 291.82/184.34 inference(rewrite,[status(thm)],[])).
% 291.82/184.34 tff(13965,plain,
% 291.82/184.34 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_d, s3)) | m_mutex_h_half_v_out(c_e_h_1, c_b, s3))),
% 291.82/184.34 inference(quant_inst,[status(thm)],[])).
% 291.82/184.34 tff(13966,plain,
% 291.82/184.34 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_d, s3)) | m_mutex_h_half_v_out(c_e_h_1, c_b, s3)),
% 291.82/184.34 inference(modus_ponens,[status(thm)],[13965, 13964])).
% 291.82/184.34 tff(13967,plain,
% 291.82/184.34 ($false),
% 291.82/184.34 inference(unit_resolution,[status(thm)],[13966, 2808, 13919, 13963])).
% 291.82/184.34 tff(13968,plain,(~m_and_h_gate_v_in1(c_e_h_1, c_d, s3)), inference(lemma,lemma(discharge,[]))).
% 291.82/184.34 tff(13969,plain,
% 291.82/184.34 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_d, s3)) | m_and_h_gate_v_in1(c_e_h_1, c_d, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_d, s3)) | m_and_h_gate_v_in1(c_e_h_1, c_d, s3))),
% 291.82/184.34 inference(rewrite,[status(thm)],[])).
% 291.82/184.34 tff(13970,plain,
% 291.82/184.34 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_d, s3)) | m_and_h_gate_v_in1(c_e_h_1, c_d, s3))),
% 291.82/184.34 inference(quant_inst,[status(thm)],[])).
% 291.82/184.34 tff(13971,plain,
% 291.82/184.34 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_d, s3)) | m_and_h_gate_v_in1(c_e_h_1, c_d, s3)),
% 291.82/184.34 inference(modus_ponens,[status(thm)],[13970, 13969])).
% 291.82/184.34 tff(13972,plain,
% 291.82/184.34 (~node20(c_e_h_1, c_d, s3)),
% 291.82/184.34 inference(unit_resolution,[status(thm)],[13971, 38, 13968])).
% 291.82/184.34 tff(13973,assumption,(m_and_h_gate_v_out(c_e_h_1, c_d, s2)), introduced(assumption)).
% 291.82/184.34 tff(13974,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_d, s1)), introduced(assumption)).
% 291.82/184.34 tff(13975,assumption,(node22(c_e_h_1, c_d, s1, s2)), introduced(assumption)).
% 291.82/184.34 tff(13976,plain,
% 291.82/184.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_d, s2)) | (~node22(c_e_h_1, c_d, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_d, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s2)) | (~node22(c_e_h_1, c_d, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_d, s1))),
% 291.82/184.34 inference(rewrite,[status(thm)],[])).
% 291.82/184.34 tff(13977,plain,
% 291.82/184.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_d, s2)) | (~node22(c_e_h_1, c_d, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_d, s1))),
% 291.82/184.34 inference(quant_inst,[status(thm)],[])).
% 291.82/184.34 tff(13978,plain,
% 291.82/184.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s2)) | (~node22(c_e_h_1, c_d, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_d, s1)),
% 291.82/184.34 inference(modus_ponens,[status(thm)],[13977, 13976])).
% 291.82/184.34 tff(13979,plain,
% 291.82/184.34 ($false),
% 291.82/184.34 inference(unit_resolution,[status(thm)],[13978, 108, 13975, 13973, 13974])).
% 291.82/184.34 tff(13980,plain,((~node22(c_e_h_1, c_d, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s2)) | m_and_h_gate_v_out(c_e_h_1, c_d, s1)), inference(lemma,lemma(discharge,[]))).
% 291.82/184.34 tff(13981,plain,
% 291.82/184.34 ((~node22(c_e_h_1, c_d, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s2))),
% 291.82/184.34 inference(unit_resolution,[status(thm)],[13980, 9773])).
% 291.82/184.34 tff(13982,plain,
% 291.82/184.34 (~node22(c_e_h_1, c_d, s1, s2)),
% 291.82/184.34 inference(unit_resolution,[status(thm)],[13981, 13973])).
% 291.82/184.34 tff(13983,assumption,(m_and_h_gate_v_in1(c_e_h_1, c_d, s1)), introduced(assumption)).
% 291.82/184.34 tff(13984,plain,
% 291.82/184.34 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_d, s1)) | m_mutex_h_half_v_out(c_e_h_1, c_b, s1))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_d, s1)) | m_mutex_h_half_v_out(c_e_h_1, c_b, s1))),
% 291.82/184.34 inference(rewrite,[status(thm)],[])).
% 291.82/184.34 tff(13985,plain,
% 291.82/184.34 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_d, s1)) | m_mutex_h_half_v_out(c_e_h_1, c_b, s1))),
% 291.82/184.35 inference(quant_inst,[status(thm)],[])).
% 291.82/184.35 tff(13986,plain,
% 291.82/184.35 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_d, s1)) | m_mutex_h_half_v_out(c_e_h_1, c_b, s1)),
% 291.82/184.35 inference(modus_ponens,[status(thm)],[13985, 13984])).
% 291.82/184.35 tff(13987,plain,
% 291.82/184.35 ($false),
% 291.82/184.35 inference(unit_resolution,[status(thm)],[13986, 2808, 13855, 13983])).
% 291.82/184.35 tff(13988,plain,(~m_and_h_gate_v_in1(c_e_h_1, c_d, s1)), inference(lemma,lemma(discharge,[]))).
% 291.82/184.35 tff(13989,plain,
% 291.82/184.35 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_d, s1)) | m_and_h_gate_v_in1(c_e_h_1, c_d, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_d, s1)) | m_and_h_gate_v_in1(c_e_h_1, c_d, s1))),
% 291.82/184.35 inference(rewrite,[status(thm)],[])).
% 291.82/184.35 tff(13990,plain,
% 291.82/184.35 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_d, s1)) | m_and_h_gate_v_in1(c_e_h_1, c_d, s1))),
% 291.82/184.35 inference(quant_inst,[status(thm)],[])).
% 291.82/184.35 tff(13991,plain,
% 291.82/184.35 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_d, s1)) | m_and_h_gate_v_in1(c_e_h_1, c_d, s1)),
% 291.82/184.35 inference(modus_ponens,[status(thm)],[13990, 13989])).
% 291.82/184.35 tff(13992,plain,
% 291.82/184.35 (~node20(c_e_h_1, c_d, s1)),
% 291.82/184.35 inference(unit_resolution,[status(thm)],[13991, 38, 13988])).
% 291.82/184.35 tff(13993,assumption,(~node20(c_e_h_1, c_d, s1)), introduced(assumption)).
% 291.82/184.35 tff(13994,assumption,(node21(c_e_h_1, c_d, s1, s2)), introduced(assumption)).
% 291.82/184.35 tff(13995,plain,
% 291.82/184.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_d, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s2)) | (~node21(c_e_h_1, c_d, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_d, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s2)) | (~node21(c_e_h_1, c_d, s1, s2)))),
% 291.82/184.35 inference(rewrite,[status(thm)],[])).
% 291.82/184.35 tff(13996,plain,
% 291.82/184.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_d, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s2)) | (~node21(c_e_h_1, c_d, s1, s2)))),
% 291.82/184.35 inference(quant_inst,[status(thm)],[])).
% 291.82/184.35 tff(13997,plain,
% 291.82/184.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_d, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s2)) | (~node21(c_e_h_1, c_d, s1, s2))),
% 291.82/184.35 inference(modus_ponens,[status(thm)],[13996, 13995])).
% 291.82/184.35 tff(13998,plain,
% 291.82/184.35 ($false),
% 291.82/184.35 inference(unit_resolution,[status(thm)],[13997, 52, 13994, 13973, 13993])).
% 291.82/184.35 tff(13999,plain,((~node21(c_e_h_1, c_d, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s2)) | node20(c_e_h_1, c_d, s1)), inference(lemma,lemma(discharge,[]))).
% 291.82/184.35 tff(14000,plain,
% 291.82/184.35 ((~node21(c_e_h_1, c_d, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s2))),
% 291.82/184.35 inference(unit_resolution,[status(thm)],[13999, 13992])).
% 291.82/184.35 tff(14001,plain,
% 291.82/184.35 (~node21(c_e_h_1, c_d, s1, s2)),
% 291.82/184.35 inference(unit_resolution,[status(thm)],[14000, 13973])).
% 291.82/184.35 tff(14002,plain,
% 291.82/184.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_1, c_d, s1, s2) | node22(c_e_h_1, c_d, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_1, c_d, s1, s2) | node22(c_e_h_1, c_d, s1, s2))),
% 291.82/184.35 inference(rewrite,[status(thm)],[])).
% 291.82/184.35 tff(14003,plain,
% 291.82/184.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_1, c_d, s1, s2) | node22(c_e_h_1, c_d, s1, s2))),
% 291.82/184.35 inference(quant_inst,[status(thm)],[])).
% 291.82/184.35 tff(14004,plain,
% 291.82/184.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_1, c_d, s1, s2) | node22(c_e_h_1, c_d, s1, s2)),
% 291.82/184.35 inference(modus_ponens,[status(thm)],[14003, 14002])).
% 291.82/184.35 tff(14005,plain,
% 291.82/184.35 (node21(c_e_h_1, c_d, s1, s2) | node22(c_e_h_1, c_d, s1, s2)),
% 291.82/184.35 inference(unit_resolution,[status(thm)],[14004, 82, 255])).
% 291.82/184.35 tff(14006,plain,
% 291.82/184.35 ($false),
% 291.82/184.35 inference(unit_resolution,[status(thm)],[14005, 14001, 13982])).
% 291.82/184.35 tff(14007,plain,(~m_and_h_gate_v_out(c_e_h_1, c_d, s2)), inference(lemma,lemma(discharge,[]))).
% 291.82/184.35 tff(14008,assumption,(m_and_h_gate_v_in1(c_e_h_1, c_d, s2)), introduced(assumption)).
% 291.82/184.35 tff(14009,plain,
% 291.82/184.35 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_d, s2)) | m_mutex_h_half_v_out(c_e_h_1, c_b, s2))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_d, s2)) | m_mutex_h_half_v_out(c_e_h_1, c_b, s2))),
% 291.82/184.35 inference(rewrite,[status(thm)],[])).
% 291.82/184.35 tff(14010,plain,
% 291.82/184.35 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_d, s2)) | m_mutex_h_half_v_out(c_e_h_1, c_b, s2))),
% 291.82/184.35 inference(quant_inst,[status(thm)],[])).
% 291.82/184.35 tff(14011,plain,
% 291.82/184.35 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_d, s2)) | m_mutex_h_half_v_out(c_e_h_1, c_b, s2)),
% 291.82/184.35 inference(modus_ponens,[status(thm)],[14010, 14009])).
% 291.82/184.35 tff(14012,plain,
% 291.82/184.35 ($false),
% 291.82/184.35 inference(unit_resolution,[status(thm)],[14011, 2808, 13894, 14008])).
% 291.82/184.35 tff(14013,plain,(~m_and_h_gate_v_in1(c_e_h_1, c_d, s2)), inference(lemma,lemma(discharge,[]))).
% 291.82/184.35 tff(14014,plain,
% 291.82/184.35 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_d, s2)) | m_and_h_gate_v_in1(c_e_h_1, c_d, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_d, s2)) | m_and_h_gate_v_in1(c_e_h_1, c_d, s2))),
% 291.82/184.35 inference(rewrite,[status(thm)],[])).
% 291.82/184.35 tff(14015,plain,
% 291.82/184.35 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_d, s2)) | m_and_h_gate_v_in1(c_e_h_1, c_d, s2))),
% 291.82/184.35 inference(quant_inst,[status(thm)],[])).
% 291.82/184.35 tff(14016,plain,
% 291.82/184.35 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_d, s2)) | m_and_h_gate_v_in1(c_e_h_1, c_d, s2)),
% 291.82/184.35 inference(modus_ponens,[status(thm)],[14015, 14014])).
% 291.82/184.35 tff(14017,plain,
% 291.82/184.35 (~node20(c_e_h_1, c_d, s2)),
% 291.82/184.35 inference(unit_resolution,[status(thm)],[14016, 38, 14013])).
% 291.82/184.35 tff(14018,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_d, s2)), introduced(assumption)).
% 291.82/184.35 tff(14019,assumption,(~node20(c_e_h_1, c_d, s2)), introduced(assumption)).
% 291.82/184.35 tff(14020,assumption,(m_and_h_gate_v_out(c_e_h_1, c_d, s3)), introduced(assumption)).
% 291.82/184.35 tff(14021,assumption,(node21(c_e_h_1, c_d, s2, s3)), introduced(assumption)).
% 291.82/184.35 tff(14022,plain,
% 291.82/184.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_d, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s3)) | (~node21(c_e_h_1, c_d, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_d, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s3)) | (~node21(c_e_h_1, c_d, s2, s3)))),
% 291.82/184.35 inference(rewrite,[status(thm)],[])).
% 291.82/184.35 tff(14023,plain,
% 291.82/184.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_d, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s3)) | (~node21(c_e_h_1, c_d, s2, s3)))),
% 291.82/184.35 inference(quant_inst,[status(thm)],[])).
% 291.82/184.35 tff(14024,plain,
% 291.82/184.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_d, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s3)) | (~node21(c_e_h_1, c_d, s2, s3))),
% 291.82/184.35 inference(modus_ponens,[status(thm)],[14023, 14022])).
% 291.82/184.35 tff(14025,plain,
% 291.82/184.35 ($false),
% 291.82/184.35 inference(unit_resolution,[status(thm)],[14024, 52, 14020, 14021, 14019])).
% 291.82/184.35 tff(14026,plain,((~node21(c_e_h_1, c_d, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s3)) | node20(c_e_h_1, c_d, s2)), inference(lemma,lemma(discharge,[]))).
% 291.82/184.35 tff(14027,plain,
% 291.82/184.35 (~node21(c_e_h_1, c_d, s2, s3)),
% 291.82/184.35 inference(unit_resolution,[status(thm)],[14026, 14020, 14019])).
% 291.82/184.35 tff(14028,plain,
% 291.82/184.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_1, c_d, s2, s3) | node22(c_e_h_1, c_d, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_1, c_d, s2, s3) | node22(c_e_h_1, c_d, s2, s3))),
% 291.82/184.35 inference(rewrite,[status(thm)],[])).
% 291.82/184.35 tff(14029,plain,
% 291.82/184.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_1, c_d, s2, s3) | node22(c_e_h_1, c_d, s2, s3))),
% 291.82/184.35 inference(quant_inst,[status(thm)],[])).
% 291.82/184.35 tff(14030,plain,
% 291.82/184.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_1, c_d, s2, s3) | node22(c_e_h_1, c_d, s2, s3)),
% 291.82/184.35 inference(modus_ponens,[status(thm)],[14029, 14028])).
% 291.82/184.35 tff(14031,plain,
% 291.82/184.35 (node21(c_e_h_1, c_d, s2, s3) | node22(c_e_h_1, c_d, s2, s3)),
% 291.82/184.35 inference(unit_resolution,[status(thm)],[14030, 82, 318])).
% 291.82/184.35 tff(14032,plain,
% 291.82/184.35 (node22(c_e_h_1, c_d, s2, s3)),
% 291.82/184.35 inference(unit_resolution,[status(thm)],[14031, 14027])).
% 291.82/184.35 tff(14033,plain,
% 291.82/184.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_d, s3)) | (~node22(c_e_h_1, c_d, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_d, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s3)) | (~node22(c_e_h_1, c_d, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_d, s2))),
% 291.82/184.35 inference(rewrite,[status(thm)],[])).
% 291.82/184.35 tff(14034,plain,
% 291.82/184.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_d, s3)) | (~node22(c_e_h_1, c_d, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_d, s2))),
% 291.82/184.35 inference(quant_inst,[status(thm)],[])).
% 291.82/184.35 tff(14035,plain,
% 291.82/184.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s3)) | (~node22(c_e_h_1, c_d, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_d, s2)),
% 291.82/184.35 inference(modus_ponens,[status(thm)],[14034, 14033])).
% 291.82/184.35 tff(14036,plain,
% 291.82/184.35 ($false),
% 291.82/184.35 inference(unit_resolution,[status(thm)],[14035, 108, 14020, 14032, 14018])).
% 291.82/184.35 tff(14037,plain,((~m_and_h_gate_v_out(c_e_h_1, c_d, s3)) | m_and_h_gate_v_out(c_e_h_1, c_d, s2) | node20(c_e_h_1, c_d, s2)), inference(lemma,lemma(discharge,[]))).
% 291.82/184.35 tff(14038,plain,
% 291.82/184.35 ((~m_and_h_gate_v_out(c_e_h_1, c_d, s3)) | m_and_h_gate_v_out(c_e_h_1, c_d, s2)),
% 291.82/184.35 inference(unit_resolution,[status(thm)],[14037, 14017])).
% 291.82/184.35 tff(14039,plain,
% 291.82/184.35 (~m_and_h_gate_v_out(c_e_h_1, c_d, s3)),
% 291.82/184.35 inference(unit_resolution,[status(thm)],[14038, 14007])).
% 291.82/184.35 tff(14040,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_d, s3)), introduced(assumption)).
% 291.82/184.35 tff(14041,assumption,(m_and_h_gate_v_out(c_e_h_1, c_d, s4)), introduced(assumption)).
% 291.82/184.35 tff(14042,assumption,(node22(c_e_h_1, c_d, s3, s4)), introduced(assumption)).
% 291.82/184.35 tff(14043,plain,
% 291.82/184.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_d, s4)) | (~node22(c_e_h_1, c_d, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_d, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s4)) | (~node22(c_e_h_1, c_d, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_d, s3))),
% 291.82/184.36 inference(rewrite,[status(thm)],[])).
% 291.82/184.36 tff(14044,plain,
% 291.82/184.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_d, s4)) | (~node22(c_e_h_1, c_d, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_d, s3))),
% 291.82/184.36 inference(quant_inst,[status(thm)],[])).
% 291.82/184.36 tff(14045,plain,
% 291.82/184.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s4)) | (~node22(c_e_h_1, c_d, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_d, s3)),
% 291.82/184.36 inference(modus_ponens,[status(thm)],[14044, 14043])).
% 291.82/184.36 tff(14046,plain,
% 291.82/184.36 ($false),
% 291.82/184.36 inference(unit_resolution,[status(thm)],[14045, 108, 14042, 14041, 14040])).
% 291.82/184.36 tff(14047,plain,((~node22(c_e_h_1, c_d, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s4)) | m_and_h_gate_v_out(c_e_h_1, c_d, s3)), inference(lemma,lemma(discharge,[]))).
% 291.82/184.36 tff(14048,plain,
% 291.82/184.36 (~node22(c_e_h_1, c_d, s3, s4)),
% 291.82/184.36 inference(unit_resolution,[status(thm)],[14047, 14041, 14040])).
% 291.82/184.36 tff(14049,assumption,(~node20(c_e_h_1, c_d, s3)), introduced(assumption)).
% 291.82/184.36 tff(14050,assumption,(node21(c_e_h_1, c_d, s3, s4)), introduced(assumption)).
% 291.82/184.36 tff(14051,plain,
% 291.82/184.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_d, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s4)) | (~node21(c_e_h_1, c_d, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_d, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s4)) | (~node21(c_e_h_1, c_d, s3, s4)))),
% 291.82/184.36 inference(rewrite,[status(thm)],[])).
% 291.82/184.36 tff(14052,plain,
% 291.82/184.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_d, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s4)) | (~node21(c_e_h_1, c_d, s3, s4)))),
% 291.82/184.36 inference(quant_inst,[status(thm)],[])).
% 291.82/184.36 tff(14053,plain,
% 291.82/184.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_d, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s4)) | (~node21(c_e_h_1, c_d, s3, s4))),
% 291.82/184.36 inference(modus_ponens,[status(thm)],[14052, 14051])).
% 291.82/184.36 tff(14054,plain,
% 291.82/184.36 ($false),
% 291.82/184.36 inference(unit_resolution,[status(thm)],[14053, 52, 14050, 14041, 14049])).
% 291.82/184.36 tff(14055,plain,((~node21(c_e_h_1, c_d, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s4)) | node20(c_e_h_1, c_d, s3)), inference(lemma,lemma(discharge,[]))).
% 291.82/184.36 tff(14056,plain,
% 291.82/184.36 (~node21(c_e_h_1, c_d, s3, s4)),
% 291.82/184.36 inference(unit_resolution,[status(thm)],[14055, 14041, 14049])).
% 291.82/184.36 tff(14057,plain,
% 291.82/184.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_1, c_d, s3, s4) | node22(c_e_h_1, c_d, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_1, c_d, s3, s4) | node22(c_e_h_1, c_d, s3, s4))),
% 291.82/184.36 inference(rewrite,[status(thm)],[])).
% 291.82/184.36 tff(14058,plain,
% 291.82/184.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_1, c_d, s3, s4) | node22(c_e_h_1, c_d, s3, s4))),
% 291.82/184.36 inference(quant_inst,[status(thm)],[])).
% 291.82/184.36 tff(14059,plain,
% 291.82/184.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_1, c_d, s3, s4) | node22(c_e_h_1, c_d, s3, s4)),
% 291.82/184.36 inference(modus_ponens,[status(thm)],[14058, 14057])).
% 291.82/184.36 tff(14060,plain,
% 291.82/184.36 (node21(c_e_h_1, c_d, s3, s4) | node22(c_e_h_1, c_d, s3, s4)),
% 291.82/184.36 inference(unit_resolution,[status(thm)],[14059, 82, 531])).
% 291.82/184.36 tff(14061,plain,
% 291.82/184.36 ($false),
% 291.82/184.36 inference(unit_resolution,[status(thm)],[14060, 14056, 14048])).
% 291.82/184.36 tff(14062,plain,((~m_and_h_gate_v_out(c_e_h_1, c_d, s4)) | node20(c_e_h_1, c_d, s3) | m_and_h_gate_v_out(c_e_h_1, c_d, s3)), inference(lemma,lemma(discharge,[]))).
% 291.82/184.36 tff(14063,plain,
% 291.82/184.36 ((~m_and_h_gate_v_out(c_e_h_1, c_d, s4)) | node20(c_e_h_1, c_d, s3)),
% 291.82/184.36 inference(unit_resolution,[status(thm)],[14062, 14039])).
% 291.82/184.36 tff(14064,plain,
% 291.82/184.36 (~m_and_h_gate_v_out(c_e_h_1, c_d, s4)),
% 291.82/184.36 inference(unit_resolution,[status(thm)],[14063, 13972])).
% 291.82/184.36 tff(14065,assumption,(~node20(c_e_h_1, c_d, s4)), introduced(assumption)).
% 291.82/184.36 tff(14066,assumption,(m_and_h_gate_v_out(c_e_h_1, c_d, s5)), introduced(assumption)).
% 291.82/184.36 tff(14067,assumption,(node21(c_e_h_1, c_d, s4, s5)), introduced(assumption)).
% 291.82/184.36 tff(14068,plain,
% 291.82/184.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_d, s5)) | node20(c_e_h_1, c_d, s4) | (~node21(c_e_h_1, c_d, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s5)) | node20(c_e_h_1, c_d, s4) | (~node21(c_e_h_1, c_d, s4, s5)))),
% 291.82/184.36 inference(rewrite,[status(thm)],[])).
% 291.82/184.36 tff(14069,plain,
% 291.82/184.36 ((node20(c_e_h_1, c_d, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s5)) | (~node21(c_e_h_1, c_d, s4, s5))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_d, s5)) | node20(c_e_h_1, c_d, s4) | (~node21(c_e_h_1, c_d, s4, s5)))),
% 291.82/184.36 inference(rewrite,[status(thm)],[])).
% 291.82/184.36 tff(14070,plain,
% 291.82/184.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_d, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s5)) | (~node21(c_e_h_1, c_d, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_d, s5)) | node20(c_e_h_1, c_d, s4) | (~node21(c_e_h_1, c_d, s4, s5))))),
% 291.82/184.36 inference(monotonicity,[status(thm)],[14069])).
% 291.82/184.36 tff(14071,plain,
% 291.82/184.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_d, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s5)) | (~node21(c_e_h_1, c_d, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s5)) | node20(c_e_h_1, c_d, s4) | (~node21(c_e_h_1, c_d, s4, s5)))),
% 291.82/184.36 inference(transitivity,[status(thm)],[14070, 14068])).
% 291.82/184.36 tff(14072,plain,
% 291.82/184.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_d, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s5)) | (~node21(c_e_h_1, c_d, s4, s5)))),
% 291.82/184.36 inference(quant_inst,[status(thm)],[])).
% 291.82/184.36 tff(14073,plain,
% 291.82/184.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s5)) | node20(c_e_h_1, c_d, s4) | (~node21(c_e_h_1, c_d, s4, s5))),
% 291.82/184.36 inference(modus_ponens,[status(thm)],[14072, 14071])).
% 291.82/184.36 tff(14074,plain,
% 291.82/184.36 ($false),
% 291.82/184.36 inference(unit_resolution,[status(thm)],[14073, 52, 14067, 14066, 14065])).
% 291.82/184.36 tff(14075,plain,((~node21(c_e_h_1, c_d, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s5)) | node20(c_e_h_1, c_d, s4)), inference(lemma,lemma(discharge,[]))).
% 291.82/184.36 tff(14076,plain,
% 291.82/184.36 (~node21(c_e_h_1, c_d, s4, s5)),
% 291.82/184.36 inference(unit_resolution,[status(thm)],[14075, 14066, 14065])).
% 291.82/184.36 tff(14077,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_d, s4)), introduced(assumption)).
% 291.82/184.36 tff(14078,assumption,(node22(c_e_h_1, c_d, s4, s5)), introduced(assumption)).
% 291.82/184.36 tff(14079,plain,
% 291.82/184.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_d, s5)) | (~node22(c_e_h_1, c_d, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_d, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s5)) | (~node22(c_e_h_1, c_d, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_d, s4))),
% 291.82/184.36 inference(rewrite,[status(thm)],[])).
% 291.82/184.36 tff(14080,plain,
% 291.82/184.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_d, s5)) | (~node22(c_e_h_1, c_d, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_d, s4))),
% 291.82/184.36 inference(quant_inst,[status(thm)],[])).
% 291.82/184.36 tff(14081,plain,
% 291.82/184.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s5)) | (~node22(c_e_h_1, c_d, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_d, s4)),
% 291.82/184.36 inference(modus_ponens,[status(thm)],[14080, 14079])).
% 291.82/184.36 tff(14082,plain,
% 291.82/184.36 ($false),
% 291.82/184.36 inference(unit_resolution,[status(thm)],[14081, 108, 14078, 14066, 14077])).
% 291.82/184.36 tff(14083,plain,((~node22(c_e_h_1, c_d, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s5)) | m_and_h_gate_v_out(c_e_h_1, c_d, s4)), inference(lemma,lemma(discharge,[]))).
% 291.82/184.36 tff(14084,plain,
% 291.82/184.36 (~node22(c_e_h_1, c_d, s4, s5)),
% 291.82/184.36 inference(unit_resolution,[status(thm)],[14083, 14066, 14077])).
% 291.82/184.36 tff(14085,plain,
% 291.82/184.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_1, c_d, s4, s5) | node22(c_e_h_1, c_d, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_1, c_d, s4, s5) | node22(c_e_h_1, c_d, s4, s5))),
% 291.82/184.36 inference(rewrite,[status(thm)],[])).
% 291.82/184.36 tff(14086,plain,
% 291.82/184.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_1, c_d, s4, s5) | node22(c_e_h_1, c_d, s4, s5))),
% 291.82/184.36 inference(quant_inst,[status(thm)],[])).
% 291.82/184.36 tff(14087,plain,
% 291.82/184.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_1, c_d, s4, s5) | node22(c_e_h_1, c_d, s4, s5)),
% 291.82/184.36 inference(modus_ponens,[status(thm)],[14086, 14085])).
% 291.82/184.36 tff(14088,plain,
% 291.82/184.36 (node21(c_e_h_1, c_d, s4, s5) | node22(c_e_h_1, c_d, s4, s5)),
% 291.82/184.36 inference(unit_resolution,[status(thm)],[14087, 82, 1028])).
% 291.82/184.36 tff(14089,plain,
% 291.82/184.36 ($false),
% 291.82/184.36 inference(unit_resolution,[status(thm)],[14088, 14084, 14076])).
% 291.82/184.36 tff(14090,plain,((~m_and_h_gate_v_out(c_e_h_1, c_d, s5)) | m_and_h_gate_v_out(c_e_h_1, c_d, s4) | node20(c_e_h_1, c_d, s4)), inference(lemma,lemma(discharge,[]))).
% 291.82/184.36 tff(14091,plain,
% 291.82/184.36 ((~m_and_h_gate_v_out(c_e_h_1, c_d, s5)) | node20(c_e_h_1, c_d, s4)),
% 291.82/184.36 inference(unit_resolution,[status(thm)],[14090, 14064])).
% 291.82/184.36 tff(14092,plain,
% 291.82/184.36 (~m_and_h_gate_v_out(c_e_h_1, c_d, s5)),
% 291.82/184.36 inference(unit_resolution,[status(thm)],[14091, 13962])).
% 291.82/184.36 tff(14093,assumption,(m_or_h_gate_v_in2(c_e_h_1, c_g, s5)), introduced(assumption)).
% 291.82/184.36 tff(14094,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_d, s5)), introduced(assumption)).
% 291.82/184.36 tff(14095,plain,
% 291.82/184.36 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_g, s5)) | m_and_h_gate_v_out(c_e_h_1, c_d, s5))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_g, s5)) | m_and_h_gate_v_out(c_e_h_1, c_d, s5))),
% 291.82/184.36 inference(rewrite,[status(thm)],[])).
% 291.82/184.36 tff(14096,plain,
% 291.82/184.36 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_g, s5)) | m_and_h_gate_v_out(c_e_h_1, c_d, s5))),
% 291.82/184.36 inference(quant_inst,[status(thm)],[])).
% 291.82/184.36 tff(14097,plain,
% 291.82/184.36 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_g, s5)) | m_and_h_gate_v_out(c_e_h_1, c_d, s5)),
% 291.82/184.36 inference(modus_ponens,[status(thm)],[14096, 14095])).
% 291.82/184.36 tff(14098,plain,
% 291.82/184.36 ($false),
% 291.82/184.36 inference(unit_resolution,[status(thm)],[14097, 2762, 14094, 14093])).
% 291.82/184.37 tff(14099,plain,((~m_or_h_gate_v_in2(c_e_h_1, c_g, s5)) | m_and_h_gate_v_out(c_e_h_1, c_d, s5)), inference(lemma,lemma(discharge,[]))).
% 291.82/184.37 tff(14100,plain,
% 291.82/184.37 (~m_or_h_gate_v_in2(c_e_h_1, c_g, s5)),
% 291.82/184.37 inference(unit_resolution,[status(thm)],[14099, 14092])).
% 291.82/184.37 tff(14101,assumption,(~m_or_h_gate_v_in2(c_e_h_1, c_g, s5)), introduced(assumption)).
% 291.82/184.37 tff(14102,assumption,(~m_mutex_h_half_v_out(c_e_h_1, c_a, s4)), introduced(assumption)).
% 291.82/184.37 tff(14103,assumption,(m_and_h_gate_v_in1(c_e_h_1, c_c, s4)), introduced(assumption)).
% 291.82/184.37 tff(14104,plain,
% 291.82/184.37 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_c, s4)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s4))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s4)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s4))),
% 291.82/184.37 inference(rewrite,[status(thm)],[])).
% 291.82/184.37 tff(14105,plain,
% 291.82/184.37 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_c, s4)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s4))),
% 291.82/184.37 inference(quant_inst,[status(thm)],[])).
% 291.82/184.37 tff(14106,plain,
% 291.82/184.37 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s4)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s4)),
% 291.82/184.37 inference(modus_ponens,[status(thm)],[14105, 14104])).
% 291.82/184.37 tff(14107,plain,
% 291.82/184.37 ($false),
% 291.82/184.37 inference(unit_resolution,[status(thm)],[14106, 567, 14102, 14103])).
% 291.82/184.37 tff(14108,plain,((~m_and_h_gate_v_in1(c_e_h_1, c_c, s4)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s4)), inference(lemma,lemma(discharge,[]))).
% 291.82/184.37 tff(14109,plain,
% 291.82/184.37 (~m_and_h_gate_v_in1(c_e_h_1, c_c, s4)),
% 291.82/184.37 inference(unit_resolution,[status(thm)],[14108, 14102])).
% 291.82/184.37 tff(14110,assumption,(~m_and_h_gate_v_in1(c_e_h_1, c_c, s4)), introduced(assumption)).
% 291.82/184.37 tff(14111,assumption,(node20(c_e_h_1, c_c, s4)), introduced(assumption)).
% 291.82/184.37 tff(14112,plain,
% 291.82/184.37 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_c, s4)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_c, s4)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s4))),
% 291.82/184.37 inference(rewrite,[status(thm)],[])).
% 291.82/184.37 tff(14113,plain,
% 291.82/184.37 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_c, s4)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s4))),
% 291.82/184.37 inference(quant_inst,[status(thm)],[])).
% 291.82/184.37 tff(14114,plain,
% 291.82/184.37 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_c, s4)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s4)),
% 291.82/184.37 inference(modus_ponens,[status(thm)],[14113, 14112])).
% 291.82/184.37 tff(14115,plain,
% 291.82/184.37 ($false),
% 291.82/184.37 inference(unit_resolution,[status(thm)],[14114, 38, 14111, 14110])).
% 291.82/184.37 tff(14116,plain,((~node20(c_e_h_1, c_c, s4)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s4)), inference(lemma,lemma(discharge,[]))).
% 291.82/184.37 tff(14117,plain,
% 291.82/184.37 (~node20(c_e_h_1, c_c, s4)),
% 291.82/184.37 inference(unit_resolution,[status(thm)],[14116, 14109])).
% 291.82/184.37 tff(14118,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_c, s4)), introduced(assumption)).
% 291.82/184.37 tff(14119,assumption,(m_or_h_gate_v_in1(c_e_h_1, c_g, s4)), introduced(assumption)).
% 291.82/184.37 tff(14120,plain,
% 291.82/184.37 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_g, s4)) | m_and_h_gate_v_out(c_e_h_1, c_c, s4))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_g, s4)) | m_and_h_gate_v_out(c_e_h_1, c_c, s4))),
% 291.82/184.37 inference(rewrite,[status(thm)],[])).
% 291.82/184.37 tff(14121,plain,
% 291.82/184.37 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_g, s4)) | m_and_h_gate_v_out(c_e_h_1, c_c, s4))),
% 291.82/184.37 inference(quant_inst,[status(thm)],[])).
% 291.82/184.37 tff(14122,plain,
% 291.82/184.37 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_g, s4)) | m_and_h_gate_v_out(c_e_h_1, c_c, s4)),
% 291.82/184.37 inference(modus_ponens,[status(thm)],[14121, 14120])).
% 291.82/184.37 tff(14123,plain,
% 291.82/184.37 ($false),
% 291.82/184.37 inference(unit_resolution,[status(thm)],[14122, 2708, 14118, 14119])).
% 291.82/184.37 tff(14124,plain,((~m_or_h_gate_v_in1(c_e_h_1, c_g, s4)) | m_and_h_gate_v_out(c_e_h_1, c_c, s4)), inference(lemma,lemma(discharge,[]))).
% 291.82/184.37 tff(14125,plain,
% 291.82/184.37 (~m_or_h_gate_v_in1(c_e_h_1, c_g, s4)),
% 291.82/184.37 inference(unit_resolution,[status(thm)],[14124, 14118])).
% 291.82/184.37 tff(14126,assumption,(m_and_h_gate_v_out(c_e_h_1, c_c, s3)), introduced(assumption)).
% 291.82/184.37 tff(14127,assumption,(node22(c_e_h_1, c_c, s3, s4)), introduced(assumption)).
% 291.82/184.37 tff(14128,plain,
% 291.82/184.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_c, s3)) | m_and_h_gate_v_out(c_e_h_1, c_c, s4) | (~node22(c_e_h_1, c_c, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s3)) | m_and_h_gate_v_out(c_e_h_1, c_c, s4) | (~node22(c_e_h_1, c_c, s3, s4)))),
% 291.82/184.37 inference(rewrite,[status(thm)],[])).
% 291.82/184.37 tff(14129,plain,
% 291.82/184.37 ((m_and_h_gate_v_out(c_e_h_1, c_c, s4) | (~node22(c_e_h_1, c_c, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s3))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_c, s3)) | m_and_h_gate_v_out(c_e_h_1, c_c, s4) | (~node22(c_e_h_1, c_c, s3, s4)))),
% 291.82/184.37 inference(rewrite,[status(thm)],[])).
% 291.82/184.37 tff(14130,plain,
% 291.82/184.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_1, c_c, s4) | (~node22(c_e_h_1, c_c, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_c, s3)) | m_and_h_gate_v_out(c_e_h_1, c_c, s4) | (~node22(c_e_h_1, c_c, s3, s4))))),
% 291.82/184.37 inference(monotonicity,[status(thm)],[14129])).
% 291.82/184.37 tff(14131,plain,
% 291.82/184.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_1, c_c, s4) | (~node22(c_e_h_1, c_c, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s3)) | m_and_h_gate_v_out(c_e_h_1, c_c, s4) | (~node22(c_e_h_1, c_c, s3, s4)))),
% 291.82/184.37 inference(transitivity,[status(thm)],[14130, 14128])).
% 291.82/184.37 tff(14132,plain,
% 291.82/184.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_1, c_c, s4) | (~node22(c_e_h_1, c_c, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s3)))),
% 291.82/184.37 inference(quant_inst,[status(thm)],[])).
% 291.82/184.37 tff(14133,plain,
% 291.82/184.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s3)) | m_and_h_gate_v_out(c_e_h_1, c_c, s4) | (~node22(c_e_h_1, c_c, s3, s4))),
% 291.82/184.37 inference(modus_ponens,[status(thm)],[14132, 14131])).
% 291.82/184.37 tff(14134,plain,
% 291.82/184.37 ($false),
% 291.82/184.37 inference(unit_resolution,[status(thm)],[14133, 5871, 14127, 14118, 14126])).
% 291.82/184.37 tff(14135,plain,((~node22(c_e_h_1, c_c, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_c, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s3))), inference(lemma,lemma(discharge,[]))).
% 291.82/184.37 tff(14136,plain,
% 291.82/184.37 (~node22(c_e_h_1, c_c, s3, s4)),
% 291.82/184.37 inference(unit_resolution,[status(thm)],[14135, 14118, 14126])).
% 291.82/184.37 tff(14137,assumption,(m_and_h_gate_v_out(c_e_h_1, c_c, s2)), introduced(assumption)).
% 291.82/184.37 tff(14138,assumption,(m_mutex_h_half_v_out(c_e_h_1, c_a, s1)), introduced(assumption)).
% 291.82/184.37 tff(14139,assumption,(node12(c_e_h_1, c_a, s0, s1)), introduced(assumption)).
% 291.82/184.37 tff(14140,assumption,(m_user_v_req(c_e_h_1, c_u, s0)), introduced(assumption)).
% 291.82/184.37 tff(14141,plain,
% 291.82/184.37 ((~![I0: $i, I1: $i] : (~m_user_v_req(I0, I1, s0))) | (~m_user_v_req(c_e_h_1, c_u, s0))),
% 291.82/184.37 inference(quant_inst,[status(thm)],[])).
% 291.82/184.37 tff(14142,plain,
% 291.82/184.37 ($false),
% 291.82/184.37 inference(unit_resolution,[status(thm)],[14141, 2642, 14140])).
% 291.82/184.37 tff(14143,plain,(~m_user_v_req(c_e_h_1, c_u, s0)), inference(lemma,lemma(discharge,[]))).
% 291.82/184.37 tff(14144,plain,
% 291.82/184.37 (((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | ((~m_mutex_h_half_v_inp(c_e_h_1, c_a, s0)) | m_user_v_req(c_e_h_1, c_u, s0))) <=> ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s0)) | m_user_v_req(c_e_h_1, c_u, s0))),
% 291.82/184.37 inference(rewrite,[status(thm)],[])).
% 291.82/184.37 tff(14145,plain,
% 291.82/184.37 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | ((~m_mutex_h_half_v_inp(c_e_h_1, c_a, s0)) | m_user_v_req(c_e_h_1, c_u, s0))),
% 291.82/184.37 inference(quant_inst,[status(thm)],[])).
% 291.82/184.37 tff(14146,plain,
% 291.82/184.37 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s0)) | m_user_v_req(c_e_h_1, c_u, s0)),
% 291.82/184.37 inference(modus_ponens,[status(thm)],[14145, 14144])).
% 291.82/184.37 tff(14147,plain,
% 291.82/184.37 (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s0)),
% 291.82/184.37 inference(unit_resolution,[status(thm)],[14146, 395, 14143])).
% 291.82/184.37 tff(14148,plain,
% 291.82/184.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_1, c_a, s0) | (~node12(c_e_h_1, c_a, s0, s1)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s0) | (~node12(c_e_h_1, c_a, s0, s1)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s1)))),
% 291.82/184.37 inference(rewrite,[status(thm)],[])).
% 291.82/184.37 tff(14149,plain,
% 291.82/184.37 (((~node12(c_e_h_1, c_a, s0, s1)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s0) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s1))) <=> (m_mutex_h_half_v_inp(c_e_h_1, c_a, s0) | (~node12(c_e_h_1, c_a, s0, s1)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s1)))),
% 291.82/184.37 inference(rewrite,[status(thm)],[])).
% 291.82/184.37 tff(14150,plain,
% 291.82/184.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_1, c_a, s0, s1)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s0) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_1, c_a, s0) | (~node12(c_e_h_1, c_a, s0, s1)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s1))))),
% 291.82/184.37 inference(monotonicity,[status(thm)],[14149])).
% 291.82/184.37 tff(14151,plain,
% 291.82/184.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_1, c_a, s0, s1)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s0) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s0) | (~node12(c_e_h_1, c_a, s0, s1)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s1)))),
% 291.82/184.37 inference(transitivity,[status(thm)],[14150, 14148])).
% 291.82/184.37 tff(14152,plain,
% 291.82/184.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_1, c_a, s0, s1)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s0) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s1)))),
% 291.82/184.37 inference(quant_inst,[status(thm)],[])).
% 291.82/184.37 tff(14153,plain,
% 291.82/184.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s0) | (~node12(c_e_h_1, c_a, s0, s1)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s1))),
% 291.82/184.38 inference(modus_ponens,[status(thm)],[14152, 14151])).
% 291.82/184.38 tff(14154,plain,
% 291.82/184.38 ($false),
% 291.82/184.38 inference(unit_resolution,[status(thm)],[14153, 454, 14147, 14139, 14138])).
% 291.82/184.38 tff(14155,plain,((~node12(c_e_h_1, c_a, s0, s1)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s1))), inference(lemma,lemma(discharge,[]))).
% 291.82/184.38 tff(14156,plain,
% 291.82/184.38 (~node12(c_e_h_1, c_a, s0, s1)),
% 291.82/184.38 inference(unit_resolution,[status(thm)],[14155, 14138])).
% 291.82/184.38 tff(14157,plain,
% 291.82/184.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s0, s1)) | node12(c_e_h_1, c_a, s0, s1) | node13(c_e_h_1, c_a, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s0, s1)) | node12(c_e_h_1, c_a, s0, s1) | node13(c_e_h_1, c_a, s0, s1))),
% 291.82/184.38 inference(rewrite,[status(thm)],[])).
% 291.82/184.38 tff(14158,plain,
% 291.82/184.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s0, s1)) | node12(c_e_h_1, c_a, s0, s1) | node13(c_e_h_1, c_a, s0, s1))),
% 291.82/184.38 inference(quant_inst,[status(thm)],[])).
% 291.82/184.38 tff(14159,plain,
% 291.82/184.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s0, s1)) | node12(c_e_h_1, c_a, s0, s1) | node13(c_e_h_1, c_a, s0, s1)),
% 291.82/184.38 inference(modus_ponens,[status(thm)],[14158, 14157])).
% 291.82/184.38 tff(14160,plain,
% 291.82/184.38 (node12(c_e_h_1, c_a, s0, s1) | node13(c_e_h_1, c_a, s0, s1)),
% 291.82/184.38 inference(unit_resolution,[status(thm)],[14159, 439, 72])).
% 291.82/184.38 tff(14161,plain,
% 291.82/184.38 (node13(c_e_h_1, c_a, s0, s1)),
% 291.82/184.38 inference(unit_resolution,[status(thm)],[14160, 14156])).
% 291.82/184.38 tff(14162,plain,
% 291.82/184.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_1, c_a, s1)) | (~node13(c_e_h_1, c_a, s0, s1)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s1)) | (~node13(c_e_h_1, c_a, s0, s1)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s0))),
% 291.82/184.38 inference(rewrite,[status(thm)],[])).
% 291.82/184.38 tff(14163,plain,
% 291.82/184.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_1, c_a, s1)) | (~node13(c_e_h_1, c_a, s0, s1)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s0))),
% 291.82/184.38 inference(quant_inst,[status(thm)],[])).
% 291.82/184.38 tff(14164,plain,
% 291.82/184.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s1)) | (~node13(c_e_h_1, c_a, s0, s1)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s0)),
% 291.82/184.38 inference(modus_ponens,[status(thm)],[14163, 14162])).
% 291.82/184.38 tff(14165,plain,
% 291.82/184.38 ($false),
% 291.82/184.38 inference(unit_resolution,[status(thm)],[14164, 423, 14161, 14138, 9782])).
% 291.82/184.38 tff(14166,plain,(~m_mutex_h_half_v_out(c_e_h_1, c_a, s1)), inference(lemma,lemma(discharge,[]))).
% 291.82/184.38 tff(14167,plain,
% 291.82/184.38 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_c, s1)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s1))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s1)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s1))),
% 291.82/184.38 inference(rewrite,[status(thm)],[])).
% 291.82/184.38 tff(14168,plain,
% 291.82/184.38 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_c, s1)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s1))),
% 291.82/184.38 inference(quant_inst,[status(thm)],[])).
% 291.82/184.38 tff(14169,plain,
% 291.82/184.38 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s1)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s1)),
% 291.82/184.38 inference(modus_ponens,[status(thm)],[14168, 14167])).
% 291.82/184.38 tff(14170,plain,
% 291.82/184.38 (~m_and_h_gate_v_in1(c_e_h_1, c_c, s1)),
% 291.82/184.38 inference(unit_resolution,[status(thm)],[14169, 567, 14166])).
% 291.82/184.38 tff(14171,plain,
% 291.82/184.38 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_c, s1)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_c, s1)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s1))),
% 291.82/184.38 inference(rewrite,[status(thm)],[])).
% 291.82/184.38 tff(14172,plain,
% 291.82/184.38 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_c, s1)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s1))),
% 291.82/184.38 inference(quant_inst,[status(thm)],[])).
% 291.82/184.38 tff(14173,plain,
% 291.82/184.38 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_c, s1)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s1)),
% 291.82/184.38 inference(modus_ponens,[status(thm)],[14172, 14171])).
% 291.82/184.38 tff(14174,plain,
% 291.82/184.38 (~node20(c_e_h_1, c_c, s1)),
% 291.82/184.38 inference(unit_resolution,[status(thm)],[14173, 38, 14170])).
% 291.82/184.38 tff(14175,assumption,(~node20(c_e_h_1, c_c, s1)), introduced(assumption)).
% 291.82/184.38 tff(14176,assumption,(node21(c_e_h_1, c_c, s1, s2)), introduced(assumption)).
% 291.82/184.38 tff(14177,plain,
% 291.82/184.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_c, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s2)) | (~node21(c_e_h_1, c_c, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_c, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s2)) | (~node21(c_e_h_1, c_c, s1, s2)))),
% 291.82/184.38 inference(rewrite,[status(thm)],[])).
% 291.82/184.38 tff(14178,plain,
% 291.82/184.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_c, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s2)) | (~node21(c_e_h_1, c_c, s1, s2)))),
% 291.82/184.38 inference(quant_inst,[status(thm)],[])).
% 291.82/184.38 tff(14179,plain,
% 291.82/184.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_c, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s2)) | (~node21(c_e_h_1, c_c, s1, s2))),
% 291.82/184.38 inference(modus_ponens,[status(thm)],[14178, 14177])).
% 291.82/184.38 tff(14180,plain,
% 291.82/184.38 ($false),
% 291.82/184.38 inference(unit_resolution,[status(thm)],[14179, 52, 14176, 14175, 14137])).
% 291.82/184.38 tff(14181,plain,((~node21(c_e_h_1, c_c, s1, s2)) | node20(c_e_h_1, c_c, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s2))), inference(lemma,lemma(discharge,[]))).
% 291.82/184.38 tff(14182,plain,
% 291.82/184.38 ((~node21(c_e_h_1, c_c, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s2))),
% 291.82/184.38 inference(unit_resolution,[status(thm)],[14181, 14174])).
% 291.82/184.38 tff(14183,plain,
% 291.82/184.38 (~node21(c_e_h_1, c_c, s1, s2)),
% 291.82/184.38 inference(unit_resolution,[status(thm)],[14182, 14137])).
% 291.82/184.38 tff(14184,plain,
% 291.82/184.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_1, c_c, s1, s2) | node22(c_e_h_1, c_c, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_1, c_c, s1, s2) | node22(c_e_h_1, c_c, s1, s2))),
% 291.82/184.38 inference(rewrite,[status(thm)],[])).
% 291.82/184.38 tff(14185,plain,
% 291.82/184.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_1, c_c, s1, s2) | node22(c_e_h_1, c_c, s1, s2))),
% 291.82/184.38 inference(quant_inst,[status(thm)],[])).
% 291.82/184.38 tff(14186,plain,
% 291.82/184.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_1, c_c, s1, s2) | node22(c_e_h_1, c_c, s1, s2)),
% 291.82/184.38 inference(modus_ponens,[status(thm)],[14185, 14184])).
% 291.82/184.38 tff(14187,plain,
% 291.82/184.38 (node21(c_e_h_1, c_c, s1, s2) | node22(c_e_h_1, c_c, s1, s2)),
% 291.82/184.38 inference(unit_resolution,[status(thm)],[14186, 82, 255])).
% 291.82/184.38 tff(14188,plain,
% 291.82/184.38 (node22(c_e_h_1, c_c, s1, s2)),
% 291.82/184.38 inference(unit_resolution,[status(thm)],[14187, 14183])).
% 291.82/184.38 tff(14189,plain,
% 291.82/184.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_c, s2)) | (~node22(c_e_h_1, c_c, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_c, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s2)) | (~node22(c_e_h_1, c_c, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_c, s1))),
% 291.82/184.38 inference(rewrite,[status(thm)],[])).
% 291.82/184.38 tff(14190,plain,
% 291.82/184.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_c, s2)) | (~node22(c_e_h_1, c_c, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_c, s1))),
% 291.82/184.38 inference(quant_inst,[status(thm)],[])).
% 291.82/184.38 tff(14191,plain,
% 291.82/184.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s2)) | (~node22(c_e_h_1, c_c, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_c, s1)),
% 291.82/184.38 inference(modus_ponens,[status(thm)],[14190, 14189])).
% 291.82/184.38 tff(14192,plain,
% 291.82/184.38 ($false),
% 291.82/184.38 inference(unit_resolution,[status(thm)],[14191, 108, 14188, 14137, 9810])).
% 291.82/184.38 tff(14193,plain,(~m_and_h_gate_v_out(c_e_h_1, c_c, s2)), inference(lemma,lemma(discharge,[]))).
% 291.82/184.38 tff(14194,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_c, s2)), introduced(assumption)).
% 291.82/184.38 tff(14195,assumption,(~node20(c_e_h_1, c_c, s2)), introduced(assumption)).
% 291.82/184.38 tff(14196,assumption,(node21(c_e_h_1, c_c, s2, s3)), introduced(assumption)).
% 291.82/184.38 tff(14197,plain,
% 291.82/184.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_c, s3)) | node20(c_e_h_1, c_c, s2) | (~node21(c_e_h_1, c_c, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s3)) | node20(c_e_h_1, c_c, s2) | (~node21(c_e_h_1, c_c, s2, s3)))),
% 291.82/184.39 inference(rewrite,[status(thm)],[])).
% 291.82/184.39 tff(14198,plain,
% 291.82/184.39 ((node20(c_e_h_1, c_c, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s3)) | (~node21(c_e_h_1, c_c, s2, s3))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_c, s3)) | node20(c_e_h_1, c_c, s2) | (~node21(c_e_h_1, c_c, s2, s3)))),
% 291.82/184.39 inference(rewrite,[status(thm)],[])).
% 291.82/184.39 tff(14199,plain,
% 291.82/184.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_c, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s3)) | (~node21(c_e_h_1, c_c, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_c, s3)) | node20(c_e_h_1, c_c, s2) | (~node21(c_e_h_1, c_c, s2, s3))))),
% 291.82/184.39 inference(monotonicity,[status(thm)],[14198])).
% 291.82/184.39 tff(14200,plain,
% 291.82/184.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_c, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s3)) | (~node21(c_e_h_1, c_c, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s3)) | node20(c_e_h_1, c_c, s2) | (~node21(c_e_h_1, c_c, s2, s3)))),
% 291.82/184.39 inference(transitivity,[status(thm)],[14199, 14197])).
% 291.82/184.39 tff(14201,plain,
% 291.82/184.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_c, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s3)) | (~node21(c_e_h_1, c_c, s2, s3)))),
% 291.82/184.39 inference(quant_inst,[status(thm)],[])).
% 291.82/184.39 tff(14202,plain,
% 291.82/184.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s3)) | node20(c_e_h_1, c_c, s2) | (~node21(c_e_h_1, c_c, s2, s3))),
% 291.82/184.39 inference(modus_ponens,[status(thm)],[14201, 14200])).
% 291.82/184.39 tff(14203,plain,
% 291.82/184.39 ($false),
% 291.82/184.39 inference(unit_resolution,[status(thm)],[14202, 52, 14126, 14196, 14195])).
% 291.82/184.39 tff(14204,plain,((~node21(c_e_h_1, c_c, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s3)) | node20(c_e_h_1, c_c, s2)), inference(lemma,lemma(discharge,[]))).
% 291.82/184.39 tff(14205,plain,
% 291.82/184.39 (~node21(c_e_h_1, c_c, s2, s3)),
% 291.82/184.39 inference(unit_resolution,[status(thm)],[14204, 14126, 14195])).
% 291.82/184.39 tff(14206,plain,
% 291.82/184.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_1, c_c, s2, s3) | node22(c_e_h_1, c_c, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_1, c_c, s2, s3) | node22(c_e_h_1, c_c, s2, s3))),
% 291.82/184.39 inference(rewrite,[status(thm)],[])).
% 291.82/184.39 tff(14207,plain,
% 291.82/184.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_1, c_c, s2, s3) | node22(c_e_h_1, c_c, s2, s3))),
% 291.82/184.39 inference(quant_inst,[status(thm)],[])).
% 291.82/184.39 tff(14208,plain,
% 291.82/184.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_1, c_c, s2, s3) | node22(c_e_h_1, c_c, s2, s3)),
% 291.82/184.39 inference(modus_ponens,[status(thm)],[14207, 14206])).
% 291.82/184.39 tff(14209,plain,
% 291.82/184.39 (node21(c_e_h_1, c_c, s2, s3) | node22(c_e_h_1, c_c, s2, s3)),
% 291.82/184.39 inference(unit_resolution,[status(thm)],[14208, 82, 318])).
% 291.82/184.39 tff(14210,plain,
% 291.82/184.39 (node22(c_e_h_1, c_c, s2, s3)),
% 291.82/184.39 inference(unit_resolution,[status(thm)],[14209, 14205])).
% 291.82/184.39 tff(14211,plain,
% 291.82/184.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_c, s3)) | (~node22(c_e_h_1, c_c, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_c, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s3)) | (~node22(c_e_h_1, c_c, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_c, s2))),
% 291.82/184.39 inference(rewrite,[status(thm)],[])).
% 291.82/184.39 tff(14212,plain,
% 291.82/184.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_c, s3)) | (~node22(c_e_h_1, c_c, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_c, s2))),
% 291.82/184.39 inference(quant_inst,[status(thm)],[])).
% 291.82/184.39 tff(14213,plain,
% 291.82/184.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s3)) | (~node22(c_e_h_1, c_c, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_c, s2)),
% 291.82/184.39 inference(modus_ponens,[status(thm)],[14212, 14211])).
% 291.82/184.39 tff(14214,plain,
% 291.82/184.39 ($false),
% 291.82/184.39 inference(unit_resolution,[status(thm)],[14213, 108, 14126, 14210, 14194])).
% 291.82/184.39 tff(14215,plain,((~m_and_h_gate_v_out(c_e_h_1, c_c, s3)) | m_and_h_gate_v_out(c_e_h_1, c_c, s2) | node20(c_e_h_1, c_c, s2)), inference(lemma,lemma(discharge,[]))).
% 291.82/184.39 tff(14216,plain,
% 291.82/184.39 ((~m_and_h_gate_v_out(c_e_h_1, c_c, s3)) | node20(c_e_h_1, c_c, s2)),
% 291.82/184.39 inference(unit_resolution,[status(thm)],[14215, 14193])).
% 291.82/184.39 tff(14217,plain,
% 291.82/184.39 (node20(c_e_h_1, c_c, s2)),
% 291.82/184.39 inference(unit_resolution,[status(thm)],[14216, 14126])).
% 291.82/184.39 tff(14218,assumption,(~m_and_h_gate_v_in1(c_e_h_1, c_c, s2)), introduced(assumption)).
% 291.82/184.39 tff(14219,assumption,(node20(c_e_h_1, c_c, s2)), introduced(assumption)).
% 291.82/184.39 tff(14220,plain,
% 291.82/184.39 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_c, s2)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_c, s2)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s2))),
% 291.82/184.39 inference(rewrite,[status(thm)],[])).
% 291.82/184.39 tff(14221,plain,
% 291.82/184.39 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_c, s2)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s2))),
% 291.82/184.39 inference(quant_inst,[status(thm)],[])).
% 291.82/184.39 tff(14222,plain,
% 291.82/184.39 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_c, s2)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s2)),
% 291.82/184.39 inference(modus_ponens,[status(thm)],[14221, 14220])).
% 291.82/184.39 tff(14223,plain,
% 291.82/184.39 ($false),
% 291.82/184.39 inference(unit_resolution,[status(thm)],[14222, 38, 14219, 14218])).
% 291.82/184.39 tff(14224,plain,((~node20(c_e_h_1, c_c, s2)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s2)), inference(lemma,lemma(discharge,[]))).
% 291.82/184.39 tff(14225,plain,
% 291.82/184.39 (m_and_h_gate_v_in1(c_e_h_1, c_c, s2)),
% 291.82/184.39 inference(unit_resolution,[status(thm)],[14224, 14217])).
% 291.82/184.39 tff(14226,assumption,(m_and_h_gate_v_in1(c_e_h_1, c_c, s2)), introduced(assumption)).
% 291.82/184.39 tff(14227,assumption,(~m_mutex_h_half_v_out(c_e_h_1, c_a, s2)), introduced(assumption)).
% 291.82/184.39 tff(14228,plain,
% 291.82/184.39 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_c, s2)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s2))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s2)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s2))),
% 291.82/184.39 inference(rewrite,[status(thm)],[])).
% 291.82/184.39 tff(14229,plain,
% 291.82/184.39 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_c, s2)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s2))),
% 291.82/184.39 inference(quant_inst,[status(thm)],[])).
% 291.82/184.39 tff(14230,plain,
% 291.82/184.39 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s2)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s2)),
% 291.82/184.39 inference(modus_ponens,[status(thm)],[14229, 14228])).
% 291.82/184.39 tff(14231,plain,
% 291.82/184.39 ($false),
% 291.82/184.39 inference(unit_resolution,[status(thm)],[14230, 567, 14227, 14226])).
% 291.82/184.39 tff(14232,plain,((~m_and_h_gate_v_in1(c_e_h_1, c_c, s2)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s2)), inference(lemma,lemma(discharge,[]))).
% 291.82/184.39 tff(14233,plain,
% 291.82/184.39 (m_mutex_h_half_v_out(c_e_h_1, c_a, s2)),
% 291.82/184.39 inference(unit_resolution,[status(thm)],[14232, 14225])).
% 291.82/184.39 tff(14234,assumption,(m_mutex_h_half_v_out(c_e_h_1, c_a, s2)), introduced(assumption)).
% 291.82/184.39 tff(14235,assumption,(node13(c_e_h_1, c_a, s1, s2)), introduced(assumption)).
% 291.82/184.39 tff(14236,plain,
% 291.82/184.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_1, c_a, s2)) | (~node13(c_e_h_1, c_a, s1, s2)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s2)) | (~node13(c_e_h_1, c_a, s1, s2)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s1))),
% 291.82/184.39 inference(rewrite,[status(thm)],[])).
% 291.82/184.39 tff(14237,plain,
% 291.82/184.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_1, c_a, s2)) | (~node13(c_e_h_1, c_a, s1, s2)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s1))),
% 291.82/184.39 inference(quant_inst,[status(thm)],[])).
% 291.82/184.39 tff(14238,plain,
% 291.82/184.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s2)) | (~node13(c_e_h_1, c_a, s1, s2)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s1)),
% 291.82/184.39 inference(modus_ponens,[status(thm)],[14237, 14236])).
% 291.82/184.39 tff(14239,plain,
% 291.82/184.39 ($false),
% 291.82/184.39 inference(unit_resolution,[status(thm)],[14238, 423, 14235, 14166, 14234])).
% 291.82/184.39 tff(14240,plain,((~node13(c_e_h_1, c_a, s1, s2)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s2))), inference(lemma,lemma(discharge,[]))).
% 291.82/184.39 tff(14241,plain,
% 291.82/184.39 (~node13(c_e_h_1, c_a, s1, s2)),
% 291.82/184.39 inference(unit_resolution,[status(thm)],[14240, 14234])).
% 291.82/184.39 tff(14242,assumption,(~m_mutex_h_half_v_inp(c_e_h_1, c_a, s1)), introduced(assumption)).
% 291.82/184.39 tff(14243,assumption,(node12(c_e_h_1, c_a, s1, s2)), introduced(assumption)).
% 291.82/184.39 tff(14244,plain,
% 291.82/184.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_1, c_a, s1) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s2)) | (~node12(c_e_h_1, c_a, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s1) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s2)) | (~node12(c_e_h_1, c_a, s1, s2)))),
% 291.82/184.40 inference(rewrite,[status(thm)],[])).
% 291.82/184.40 tff(14245,plain,
% 291.82/184.40 (((~node12(c_e_h_1, c_a, s1, s2)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s1) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s2))) <=> (m_mutex_h_half_v_inp(c_e_h_1, c_a, s1) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s2)) | (~node12(c_e_h_1, c_a, s1, s2)))),
% 291.82/184.40 inference(rewrite,[status(thm)],[])).
% 291.82/184.40 tff(14246,plain,
% 291.82/184.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_1, c_a, s1, s2)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s1) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_1, c_a, s1) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s2)) | (~node12(c_e_h_1, c_a, s1, s2))))),
% 291.82/184.40 inference(monotonicity,[status(thm)],[14245])).
% 291.82/184.40 tff(14247,plain,
% 291.82/184.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_1, c_a, s1, s2)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s1) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s1) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s2)) | (~node12(c_e_h_1, c_a, s1, s2)))),
% 291.82/184.40 inference(transitivity,[status(thm)],[14246, 14244])).
% 291.82/184.40 tff(14248,plain,
% 291.82/184.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_1, c_a, s1, s2)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s1) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s2)))),
% 291.82/184.40 inference(quant_inst,[status(thm)],[])).
% 291.82/184.40 tff(14249,plain,
% 291.82/184.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s1) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s2)) | (~node12(c_e_h_1, c_a, s1, s2))),
% 291.82/184.40 inference(modus_ponens,[status(thm)],[14248, 14247])).
% 291.82/184.40 tff(14250,plain,
% 291.82/184.40 ($false),
% 291.82/184.40 inference(unit_resolution,[status(thm)],[14249, 454, 14243, 14234, 14242])).
% 291.82/184.40 tff(14251,plain,((~node12(c_e_h_1, c_a, s1, s2)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s2)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s1)), inference(lemma,lemma(discharge,[]))).
% 291.82/184.40 tff(14252,plain,
% 291.82/184.40 (~node12(c_e_h_1, c_a, s1, s2)),
% 291.82/184.40 inference(unit_resolution,[status(thm)],[14251, 14234, 14242])).
% 291.82/184.40 tff(14253,plain,
% 291.82/184.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s1, s2)) | node12(c_e_h_1, c_a, s1, s2) | node13(c_e_h_1, c_a, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s1, s2)) | node12(c_e_h_1, c_a, s1, s2) | node13(c_e_h_1, c_a, s1, s2))),
% 291.82/184.40 inference(rewrite,[status(thm)],[])).
% 291.82/184.40 tff(14254,plain,
% 291.82/184.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s1, s2)) | node12(c_e_h_1, c_a, s1, s2) | node13(c_e_h_1, c_a, s1, s2))),
% 291.82/184.40 inference(quant_inst,[status(thm)],[])).
% 291.82/184.40 tff(14255,plain,
% 291.82/184.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s1, s2)) | node12(c_e_h_1, c_a, s1, s2) | node13(c_e_h_1, c_a, s1, s2)),
% 291.82/184.40 inference(modus_ponens,[status(thm)],[14254, 14253])).
% 291.82/184.40 tff(14256,plain,
% 291.82/184.40 (node12(c_e_h_1, c_a, s1, s2) | node13(c_e_h_1, c_a, s1, s2)),
% 291.82/184.41 inference(unit_resolution,[status(thm)],[14255, 439, 255])).
% 291.82/184.41 tff(14257,plain,
% 291.82/184.41 ($false),
% 291.82/184.41 inference(unit_resolution,[status(thm)],[14256, 14252, 14241])).
% 291.82/184.41 tff(14258,plain,((~m_mutex_h_half_v_out(c_e_h_1, c_a, s2)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s1)), inference(lemma,lemma(discharge,[]))).
% 291.82/184.41 tff(14259,plain,
% 291.82/184.41 (m_mutex_h_half_v_inp(c_e_h_1, c_a, s1)),
% 291.82/184.41 inference(unit_resolution,[status(thm)],[14258, 14234])).
% 291.82/184.41 tff(14260,plain,
% 291.82/184.41 (((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | ((~m_mutex_h_half_v_inp(c_e_h_1, c_a, s1)) | m_user_v_req(c_e_h_1, c_u, s1))) <=> ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s1)) | m_user_v_req(c_e_h_1, c_u, s1))),
% 291.82/184.41 inference(rewrite,[status(thm)],[])).
% 291.82/184.41 tff(14261,plain,
% 291.82/184.41 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | ((~m_mutex_h_half_v_inp(c_e_h_1, c_a, s1)) | m_user_v_req(c_e_h_1, c_u, s1))),
% 291.82/184.41 inference(quant_inst,[status(thm)],[])).
% 291.82/184.41 tff(14262,plain,
% 291.82/184.41 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s1)) | m_user_v_req(c_e_h_1, c_u, s1)),
% 291.82/184.41 inference(modus_ponens,[status(thm)],[14261, 14260])).
% 291.82/184.41 tff(14263,plain,
% 291.82/184.41 (m_user_v_req(c_e_h_1, c_u, s1)),
% 291.82/184.41 inference(unit_resolution,[status(thm)],[14262, 395, 14259])).
% 291.82/184.41 tff(14264,assumption,(~m_user_v_req(c_e_h_1, c_u, s2)), introduced(assumption)).
% 291.82/184.41 tff(14265,assumption,(node7(c_e_h_1, c_u, s1, s2)), introduced(assumption)).
% 291.82/184.41 tff(14266,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s1)), introduced(assumption)).
% 291.82/184.41 tff(14267,assumption,(node21(c_e_h_1, c_r, s0, s1)), introduced(assumption)).
% 291.82/184.41 tff(14268,assumption,(m_cell_v_token(c_e_h_1, s0)), introduced(assumption)).
% 291.82/184.41 tff(14269,plain,
% 291.82/184.41 (^[X: $i] : refl((~m_cell_v_token(c_e_h_1, X)) <=> (~m_cell_v_token(c_e_h_1, X)))),
% 291.82/184.41 inference(bind,[status(th)],[])).
% 291.82/184.41 tff(14270,plain,
% 291.82/184.41 (![X: $i] : (~m_cell_v_token(c_e_h_1, X)) <=> ![X: $i] : (~m_cell_v_token(c_e_h_1, X))),
% 291.82/184.41 inference(quant_intro,[status(thm)],[14269])).
% 291.82/184.41 tff(14271,plain,
% 291.82/184.41 (![X: $i] : (~m_cell_v_token(c_e_h_1, X)) <=> ![X: $i] : (~m_cell_v_token(c_e_h_1, X))),
% 291.82/184.41 inference(rewrite,[status(thm)],[])).
% 291.82/184.41 tff(14272,axiom,(![X: $i] : (~m_cell_v_token(c_e_h_1, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_3')).
% 291.82/184.41 tff(14273,plain,
% 291.82/184.41 (![X: $i] : (~m_cell_v_token(c_e_h_1, X))),
% 291.82/184.41 inference(modus_ponens,[status(thm)],[14272, 14271])).
% 291.82/184.41 tff(14274,plain,(
% 291.82/184.41 ![X: $i] : (~m_cell_v_token(c_e_h_1, X))),
% 291.82/184.41 inference(skolemize,[status(sab)],[14273])).
% 291.82/184.41 tff(14275,plain,
% 291.82/184.41 (![X: $i] : (~m_cell_v_token(c_e_h_1, X))),
% 291.82/184.41 inference(modus_ponens,[status(thm)],[14274, 14270])).
% 291.82/184.41 tff(14276,plain,
% 291.82/184.41 ((~![X: $i] : (~m_cell_v_token(c_e_h_1, X))) | (~m_cell_v_token(c_e_h_1, s0))),
% 291.82/184.41 inference(quant_inst,[status(thm)],[])).
% 291.82/184.41 tff(14277,plain,
% 291.82/184.41 ($false),
% 291.82/184.41 inference(unit_resolution,[status(thm)],[14276, 14275, 14268])).
% 291.82/184.41 tff(14278,plain,(~m_cell_v_token(c_e_h_1, s0)), inference(lemma,lemma(discharge,[]))).
% 291.82/184.41 tff(14279,plain,
% 291.82/184.41 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) | m_cell_v_token(I0, X))) | ((~m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_m, s0)) | m_cell_v_token(c_e_h_1, s0))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) | m_cell_v_token(I0, X))) | (~m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_m, s0)) | m_cell_v_token(c_e_h_1, s0))),
% 291.82/184.41 inference(rewrite,[status(thm)],[])).
% 291.82/184.41 tff(14280,plain,
% 291.82/184.41 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) | m_cell_v_token(I0, X))) | ((~m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_m, s0)) | m_cell_v_token(c_e_h_1, s0))),
% 291.82/184.41 inference(quant_inst,[status(thm)],[])).
% 291.82/184.41 tff(14281,plain,
% 291.82/184.41 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, c_m, X)) | m_cell_v_token(I0, X))) | (~m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_m, s0)) | m_cell_v_token(c_e_h_1, s0)),
% 291.82/184.41 inference(modus_ponens,[status(thm)],[14280, 14279])).
% 291.82/184.41 tff(14282,plain,
% 291.92/184.41 (~m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_m, s0)),
% 291.92/184.41 inference(unit_resolution,[status(thm)],[14281, 4527, 14278])).
% 291.92/184.41 tff(14283,plain,
% 291.92/184.41 (((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, s0)) | m_and_h_gate_h_init_v_init_h_out(I0, I1, s0))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0)) | m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_m, s0))) <=> ((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, s0)) | m_and_h_gate_h_init_v_init_h_out(I0, I1, s0))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0)) | m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_m, s0))),
% 291.92/184.41 inference(rewrite,[status(thm)],[])).
% 291.92/184.41 tff(14284,plain,
% 291.92/184.41 ((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, s0)) | m_and_h_gate_h_init_v_init_h_out(I0, I1, s0))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0)) | m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_m, s0))),
% 291.92/184.41 inference(quant_inst,[status(thm)],[])).
% 291.92/184.41 tff(14285,plain,
% 291.92/184.41 ((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, s0)) | m_and_h_gate_h_init_v_init_h_out(I0, I1, s0))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0)) | m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_m, s0)),
% 291.92/184.41 inference(modus_ponens,[status(thm)],[14284, 14283])).
% 291.92/184.41 tff(14286,plain,
% 291.92/184.41 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0)),
% 291.92/184.41 inference(unit_resolution,[status(thm)],[14285, 4538, 14282])).
% 291.92/184.41 tff(14287,plain,
% 291.92/184.41 (^[I0: $i, X: $i] : refl(((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X)) <=> ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X)))),
% 291.92/184.41 inference(bind,[status(th)],[])).
% 291.92/184.41 tff(14288,plain,
% 291.92/184.41 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))),
% 291.92/184.41 inference(quant_intro,[status(thm)],[14287])).
% 291.92/184.41 tff(14289,plain,
% 291.92/184.41 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))),
% 291.92/184.41 inference(rewrite,[status(thm)],[])).
% 291.92/184.41 tff(14290,axiom,(![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_74')).
% 291.92/184.41 tff(14291,plain,
% 291.92/184.41 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))),
% 291.92/184.41 inference(modus_ponens,[status(thm)],[14290, 14289])).
% 291.92/184.41 tff(14292,plain,(
% 291.92/184.41 ![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))),
% 291.92/184.41 inference(skolemize,[status(sab)],[14291])).
% 291.92/184.41 tff(14293,plain,
% 291.92/184.41 (![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))),
% 291.92/184.41 inference(modus_ponens,[status(thm)],[14292, 14288])).
% 291.92/184.41 tff(14294,plain,
% 291.92/184.41 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0))),
% 291.92/184.41 inference(rewrite,[status(thm)],[])).
% 291.92/184.41 tff(14295,plain,
% 291.92/184.41 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0))),
% 291.92/184.41 inference(quant_inst,[status(thm)],[])).
% 291.92/184.41 tff(14296,plain,
% 291.92/184.41 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0)),
% 291.92/184.41 inference(modus_ponens,[status(thm)],[14295, 14294])).
% 291.92/184.41 tff(14297,plain,
% 291.92/184.41 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s0)),
% 291.92/184.41 inference(unit_resolution,[status(thm)],[14296, 14293, 14286])).
% 291.92/184.41 tff(14298,plain,
% 291.92/184.41 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s0)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s0)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s0))),
% 291.92/184.41 inference(rewrite,[status(thm)],[])).
% 291.92/184.41 tff(14299,plain,
% 291.92/184.41 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s0)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s0))),
% 291.92/184.41 inference(quant_inst,[status(thm)],[])).
% 291.92/184.41 tff(14300,plain,
% 291.92/184.41 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s0)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s0)),
% 291.92/184.41 inference(modus_ponens,[status(thm)],[14299, 14298])).
% 291.92/184.41 tff(14301,plain,
% 291.92/184.41 (~node20(c_e_h_1, c_r, s0)),
% 291.92/184.41 inference(unit_resolution,[status(thm)],[14300, 4563, 14297])).
% 291.92/184.41 tff(14302,plain,
% 291.92/184.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s1)) | (~node21(c_e_h_1, c_r, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s1)) | (~node21(c_e_h_1, c_r, s0, s1)))),
% 291.92/184.41 inference(rewrite,[status(thm)],[])).
% 291.92/184.41 tff(14303,plain,
% 291.92/184.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s1)) | (~node21(c_e_h_1, c_r, s0, s1)))),
% 291.92/184.41 inference(quant_inst,[status(thm)],[])).
% 291.92/184.41 tff(14304,plain,
% 291.92/184.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s1)) | (~node21(c_e_h_1, c_r, s0, s1))),
% 291.92/184.41 inference(modus_ponens,[status(thm)],[14303, 14302])).
% 291.92/184.41 tff(14305,plain,
% 291.92/184.41 ($false),
% 291.92/184.41 inference(unit_resolution,[status(thm)],[14304, 52, 14301, 14267, 14266])).
% 291.92/184.41 tff(14306,plain,((~node21(c_e_h_1, c_r, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s1))), inference(lemma,lemma(discharge,[]))).
% 291.92/184.41 tff(14307,plain,
% 291.92/184.41 (~node21(c_e_h_1, c_r, s0, s1)),
% 291.92/184.41 inference(unit_resolution,[status(thm)],[14306, 14266])).
% 291.92/184.41 tff(14308,plain,
% 291.92/184.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_1, c_r, s0, s1) | node22(c_e_h_1, c_r, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_1, c_r, s0, s1) | node22(c_e_h_1, c_r, s0, s1))),
% 291.92/184.41 inference(rewrite,[status(thm)],[])).
% 291.92/184.41 tff(14309,plain,
% 291.92/184.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_1, c_r, s0, s1) | node22(c_e_h_1, c_r, s0, s1))),
% 291.92/184.41 inference(quant_inst,[status(thm)],[])).
% 291.92/184.41 tff(14310,plain,
% 291.92/184.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_1, c_r, s0, s1) | node22(c_e_h_1, c_r, s0, s1)),
% 291.92/184.41 inference(modus_ponens,[status(thm)],[14309, 14308])).
% 291.92/184.41 tff(14311,plain,
% 291.92/184.41 (node21(c_e_h_1, c_r, s0, s1) | node22(c_e_h_1, c_r, s0, s1)),
% 291.92/184.41 inference(unit_resolution,[status(thm)],[14310, 82, 72])).
% 291.92/184.41 tff(14312,plain,
% 291.92/184.41 (node22(c_e_h_1, c_r, s0, s1)),
% 291.92/184.41 inference(unit_resolution,[status(thm)],[14311, 14307])).
% 291.92/184.41 tff(14313,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s0)), introduced(assumption)).
% 291.92/184.41 tff(14314,plain,
% 291.92/184.41 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s0))),
% 291.92/184.41 inference(quant_inst,[status(thm)],[])).
% 291.92/184.41 tff(14315,plain,
% 291.92/184.41 ($false),
% 291.92/184.41 inference(unit_resolution,[status(thm)],[14314, 95, 14313])).
% 291.92/184.41 tff(14316,plain,(~m_and_h_gate_v_out(c_e_h_1, c_r, s0)), inference(lemma,lemma(discharge,[]))).
% 291.92/184.41 tff(14317,plain,
% 291.92/184.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s1)) | (~node22(c_e_h_1, c_r, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_r, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s1)) | (~node22(c_e_h_1, c_r, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_r, s0))),
% 291.92/184.41 inference(rewrite,[status(thm)],[])).
% 291.92/184.41 tff(14318,plain,
% 291.92/184.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s1)) | (~node22(c_e_h_1, c_r, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_r, s0))),
% 291.92/184.41 inference(quant_inst,[status(thm)],[])).
% 291.92/184.41 tff(14319,plain,
% 291.92/184.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s1)) | (~node22(c_e_h_1, c_r, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_r, s0)),
% 291.92/184.41 inference(modus_ponens,[status(thm)],[14318, 14317])).
% 291.92/184.41 tff(14320,plain,
% 291.92/184.41 ($false),
% 291.92/184.41 inference(unit_resolution,[status(thm)],[14319, 108, 14316, 14312, 14266])).
% 291.92/184.41 tff(14321,plain,(~m_and_h_gate_v_out(c_e_h_1, c_r, s1)), inference(lemma,lemma(discharge,[]))).
% 291.92/184.41 tff(14322,plain,
% 291.92/184.41 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s1)) | m_and_h_gate_v_out(c_e_h_1, c_r, s1))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s1)) | m_and_h_gate_v_out(c_e_h_1, c_r, s1))),
% 291.92/184.41 inference(rewrite,[status(thm)],[])).
% 291.92/184.41 tff(14323,plain,
% 291.92/184.41 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s1)) | m_and_h_gate_v_out(c_e_h_1, c_r, s1))),
% 291.92/184.41 inference(quant_inst,[status(thm)],[])).
% 291.92/184.41 tff(14324,plain,
% 291.92/184.41 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s1)) | m_and_h_gate_v_out(c_e_h_1, c_r, s1)),
% 291.92/184.41 inference(modus_ponens,[status(thm)],[14323, 14322])).
% 291.92/184.41 tff(14325,plain,
% 291.92/184.41 (~m_user_v_ack(c_e_h_1, c_u, s1)),
% 291.92/184.41 inference(unit_resolution,[status(thm)],[14324, 268, 14321])).
% 291.92/184.41 tff(14326,plain,
% 291.92/184.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | ((~node7(c_e_h_1, c_u, s1, s2)) | m_user_v_ack(c_e_h_1, c_u, s1) | m_user_v_req(c_e_h_1, c_u, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | (~node7(c_e_h_1, c_u, s1, s2)) | m_user_v_ack(c_e_h_1, c_u, s1) | m_user_v_req(c_e_h_1, c_u, s2))),
% 291.92/184.41 inference(rewrite,[status(thm)],[])).
% 291.92/184.41 tff(14327,plain,
% 291.92/184.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | ((~node7(c_e_h_1, c_u, s1, s2)) | m_user_v_ack(c_e_h_1, c_u, s1) | m_user_v_req(c_e_h_1, c_u, s2))),
% 291.92/184.41 inference(quant_inst,[status(thm)],[])).
% 291.92/184.41 tff(14328,plain,
% 291.92/184.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | (~node7(c_e_h_1, c_u, s1, s2)) | m_user_v_ack(c_e_h_1, c_u, s1) | m_user_v_req(c_e_h_1, c_u, s2)),
% 291.92/184.41 inference(modus_ponens,[status(thm)],[14327, 14326])).
% 291.92/184.41 tff(14329,plain,
% 291.92/184.41 ($false),
% 291.92/184.41 inference(unit_resolution,[status(thm)],[14328, 284, 14325, 14265, 14264])).
% 291.92/184.41 tff(14330,plain,((~node7(c_e_h_1, c_u, s1, s2)) | m_user_v_req(c_e_h_1, c_u, s2)), inference(lemma,lemma(discharge,[]))).
% 291.92/184.41 tff(14331,plain,
% 291.92/184.41 (~node7(c_e_h_1, c_u, s1, s2)),
% 291.92/184.41 inference(unit_resolution,[status(thm)],[14330, 14264])).
% 291.92/184.41 tff(14332,assumption,(m_user_v_req(c_e_h_1, c_u, s1)), introduced(assumption)).
% 291.92/184.41 tff(14333,assumption,(node8(c_e_h_1, c_u, s1, s2)), introduced(assumption)).
% 291.92/184.41 tff(14334,plain,
% 291.92/184.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | ((~m_user_v_req(c_e_h_1, c_u, s1)) | m_user_v_req(c_e_h_1, c_u, s2) | (~node8(c_e_h_1, c_u, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (~m_user_v_req(c_e_h_1, c_u, s1)) | m_user_v_req(c_e_h_1, c_u, s2) | (~node8(c_e_h_1, c_u, s1, s2)))),
% 291.92/184.41 inference(rewrite,[status(thm)],[])).
% 291.92/184.41 tff(14335,plain,
% 291.92/184.41 ((m_user_v_req(c_e_h_1, c_u, s2) | (~node8(c_e_h_1, c_u, s1, s2)) | (~m_user_v_req(c_e_h_1, c_u, s1))) <=> ((~m_user_v_req(c_e_h_1, c_u, s1)) | m_user_v_req(c_e_h_1, c_u, s2) | (~node8(c_e_h_1, c_u, s1, s2)))),
% 291.92/184.41 inference(rewrite,[status(thm)],[])).
% 291.92/184.41 tff(14336,plain,
% 291.92/184.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_1, c_u, s2) | (~node8(c_e_h_1, c_u, s1, s2)) | (~m_user_v_req(c_e_h_1, c_u, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | ((~m_user_v_req(c_e_h_1, c_u, s1)) | m_user_v_req(c_e_h_1, c_u, s2) | (~node8(c_e_h_1, c_u, s1, s2))))),
% 291.92/184.41 inference(monotonicity,[status(thm)],[14335])).
% 291.92/184.41 tff(14337,plain,
% 291.92/184.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_1, c_u, s2) | (~node8(c_e_h_1, c_u, s1, s2)) | (~m_user_v_req(c_e_h_1, c_u, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (~m_user_v_req(c_e_h_1, c_u, s1)) | m_user_v_req(c_e_h_1, c_u, s2) | (~node8(c_e_h_1, c_u, s1, s2)))),
% 291.92/184.41 inference(transitivity,[status(thm)],[14336, 14334])).
% 291.92/184.41 tff(14338,plain,
% 291.92/184.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_1, c_u, s2) | (~node8(c_e_h_1, c_u, s1, s2)) | (~m_user_v_req(c_e_h_1, c_u, s1)))),
% 291.92/184.41 inference(quant_inst,[status(thm)],[])).
% 291.92/184.41 tff(14339,plain,
% 291.92/184.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (~m_user_v_req(c_e_h_1, c_u, s1)) | m_user_v_req(c_e_h_1, c_u, s2) | (~node8(c_e_h_1, c_u, s1, s2))),
% 291.92/184.41 inference(modus_ponens,[status(thm)],[14338, 14337])).
% 291.92/184.41 tff(14340,plain,
% 291.92/184.41 ($false),
% 291.92/184.41 inference(unit_resolution,[status(thm)],[14339, 302, 14333, 14332, 14264])).
% 291.92/184.41 tff(14341,plain,((~node8(c_e_h_1, c_u, s1, s2)) | (~m_user_v_req(c_e_h_1, c_u, s1)) | m_user_v_req(c_e_h_1, c_u, s2)), inference(lemma,lemma(discharge,[]))).
% 291.92/184.41 tff(14342,plain,
% 291.92/184.41 (~node8(c_e_h_1, c_u, s1, s2)),
% 291.92/184.41 inference(unit_resolution,[status(thm)],[14341, 14264, 14332])).
% 291.92/184.41 tff(14343,plain,
% 291.92/184.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | ((~trans(s1, s2)) | node7(c_e_h_1, c_u, s1, s2) | node8(c_e_h_1, c_u, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | (~trans(s1, s2)) | node7(c_e_h_1, c_u, s1, s2) | node8(c_e_h_1, c_u, s1, s2))),
% 291.92/184.41 inference(rewrite,[status(thm)],[])).
% 291.92/184.41 tff(14344,plain,
% 291.92/184.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | ((~trans(s1, s2)) | node7(c_e_h_1, c_u, s1, s2) | node8(c_e_h_1, c_u, s1, s2))),
% 291.92/184.41 inference(quant_inst,[status(thm)],[])).
% 291.92/184.41 tff(14345,plain,
% 291.92/184.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | (~trans(s1, s2)) | node7(c_e_h_1, c_u, s1, s2) | node8(c_e_h_1, c_u, s1, s2)),
% 291.92/184.41 inference(modus_ponens,[status(thm)],[14344, 14343])).
% 291.92/184.41 tff(14346,plain,
% 291.92/184.41 (node7(c_e_h_1, c_u, s1, s2) | node8(c_e_h_1, c_u, s1, s2)),
% 291.92/184.41 inference(unit_resolution,[status(thm)],[14345, 328, 255])).
% 291.92/184.41 tff(14347,plain,
% 291.92/184.41 ($false),
% 291.92/184.41 inference(unit_resolution,[status(thm)],[14346, 14342, 14331])).
% 291.92/184.41 tff(14348,plain,(m_user_v_req(c_e_h_1, c_u, s2) | (~m_user_v_req(c_e_h_1, c_u, s1))), inference(lemma,lemma(discharge,[]))).
% 291.92/184.41 tff(14349,plain,
% 291.92/184.41 (m_user_v_req(c_e_h_1, c_u, s2)),
% 291.92/184.41 inference(unit_resolution,[status(thm)],[14348, 14263])).
% 291.92/184.41 tff(14350,assumption,(~m_mutex_h_half_v_inp(c_e_h_1, c_a, s2)), introduced(assumption)).
% 291.92/184.41 tff(14351,assumption,(m_user_v_req(c_e_h_1, c_u, s2)), introduced(assumption)).
% 291.92/184.41 tff(14352,plain,
% 291.92/184.41 (((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | ((~m_user_v_req(c_e_h_1, c_u, s2)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s2))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | (~m_user_v_req(c_e_h_1, c_u, s2)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s2))),
% 291.92/184.41 inference(rewrite,[status(thm)],[])).
% 291.92/184.41 tff(14353,plain,
% 291.92/184.41 ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | ((~m_user_v_req(c_e_h_1, c_u, s2)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s2))),
% 291.92/184.41 inference(quant_inst,[status(thm)],[])).
% 291.92/184.41 tff(14354,plain,
% 291.92/184.41 ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | (~m_user_v_req(c_e_h_1, c_u, s2)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s2)),
% 291.92/184.41 inference(modus_ponens,[status(thm)],[14353, 14352])).
% 291.92/184.41 tff(14355,plain,
% 291.92/184.41 ($false),
% 291.92/184.41 inference(unit_resolution,[status(thm)],[14354, 1426, 14351, 14350])).
% 291.92/184.41 tff(14356,plain,(m_mutex_h_half_v_inp(c_e_h_1, c_a, s2) | (~m_user_v_req(c_e_h_1, c_u, s2))), inference(lemma,lemma(discharge,[]))).
% 291.92/184.41 tff(14357,plain,
% 291.92/184.41 (m_mutex_h_half_v_inp(c_e_h_1, c_a, s2)),
% 291.92/184.41 inference(unit_resolution,[status(thm)],[14356, 14349])).
% 291.92/184.41 tff(14358,assumption,(~m_mutex_h_half_v_out(c_e_h_1, c_a, s3)), introduced(assumption)).
% 291.92/184.41 tff(14359,assumption,(node13(c_e_h_1, c_a, s2, s3)), introduced(assumption)).
% 291.92/184.41 tff(14360,plain,
% 291.92/184.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_1, c_a, s3) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s2)) | (~node13(c_e_h_1, c_a, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | m_mutex_h_half_v_out(c_e_h_1, c_a, s3) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s2)) | (~node13(c_e_h_1, c_a, s2, s3)))),
% 291.92/184.41 inference(rewrite,[status(thm)],[])).
% 291.92/184.41 tff(14361,plain,
% 291.92/184.41 ((m_mutex_h_half_v_out(c_e_h_1, c_a, s3) | (~node13(c_e_h_1, c_a, s2, s3)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s2))) <=> (m_mutex_h_half_v_out(c_e_h_1, c_a, s3) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s2)) | (~node13(c_e_h_1, c_a, s2, s3)))),
% 291.92/184.41 inference(rewrite,[status(thm)],[])).
% 291.92/184.41 tff(14362,plain,
% 291.92/184.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_1, c_a, s3) | (~node13(c_e_h_1, c_a, s2, s3)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_1, c_a, s3) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s2)) | (~node13(c_e_h_1, c_a, s2, s3))))),
% 291.92/184.41 inference(monotonicity,[status(thm)],[14361])).
% 291.92/184.41 tff(14363,plain,
% 291.92/184.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_1, c_a, s3) | (~node13(c_e_h_1, c_a, s2, s3)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | m_mutex_h_half_v_out(c_e_h_1, c_a, s3) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s2)) | (~node13(c_e_h_1, c_a, s2, s3)))),
% 291.92/184.41 inference(transitivity,[status(thm)],[14362, 14360])).
% 291.92/184.41 tff(14364,plain,
% 291.92/184.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_1, c_a, s3) | (~node13(c_e_h_1, c_a, s2, s3)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s2)))),
% 291.92/184.41 inference(quant_inst,[status(thm)],[])).
% 291.92/184.41 tff(14365,plain,
% 291.92/184.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | m_mutex_h_half_v_out(c_e_h_1, c_a, s3) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s2)) | (~node13(c_e_h_1, c_a, s2, s3))),
% 291.92/184.42 inference(modus_ponens,[status(thm)],[14364, 14363])).
% 291.92/184.42 tff(14366,plain,
% 291.92/184.42 ($false),
% 291.92/184.42 inference(unit_resolution,[status(thm)],[14365, 1459, 14358, 14359, 14234])).
% 291.92/184.42 tff(14367,plain,((~node13(c_e_h_1, c_a, s2, s3)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s3) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s2))), inference(lemma,lemma(discharge,[]))).
% 291.92/184.42 tff(14368,plain,
% 291.92/184.42 (~node13(c_e_h_1, c_a, s2, s3)),
% 291.92/184.42 inference(unit_resolution,[status(thm)],[14367, 14358, 14234])).
% 291.92/184.42 tff(14369,plain,
% 291.92/184.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s2, s3)) | node12(c_e_h_1, c_a, s2, s3) | node13(c_e_h_1, c_a, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s2, s3)) | node12(c_e_h_1, c_a, s2, s3) | node13(c_e_h_1, c_a, s2, s3))),
% 291.92/184.42 inference(rewrite,[status(thm)],[])).
% 291.92/184.42 tff(14370,plain,
% 291.92/184.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s2, s3)) | node12(c_e_h_1, c_a, s2, s3) | node13(c_e_h_1, c_a, s2, s3))),
% 291.92/184.42 inference(quant_inst,[status(thm)],[])).
% 291.92/184.42 tff(14371,plain,
% 291.92/184.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s2, s3)) | node12(c_e_h_1, c_a, s2, s3) | node13(c_e_h_1, c_a, s2, s3)),
% 291.92/184.42 inference(modus_ponens,[status(thm)],[14370, 14369])).
% 291.92/184.42 tff(14372,plain,
% 291.92/184.42 (node12(c_e_h_1, c_a, s2, s3) | node13(c_e_h_1, c_a, s2, s3)),
% 291.92/184.42 inference(unit_resolution,[status(thm)],[14371, 439, 318])).
% 291.92/184.42 tff(14373,plain,
% 291.92/184.42 (node12(c_e_h_1, c_a, s2, s3)),
% 291.92/184.42 inference(unit_resolution,[status(thm)],[14372, 14368])).
% 291.92/184.42 tff(14374,plain,
% 291.92/184.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (m_mutex_h_half_v_out(c_e_h_1, c_a, s3) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s2)) | (~node12(c_e_h_1, c_a, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | m_mutex_h_half_v_out(c_e_h_1, c_a, s3) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s2)) | (~node12(c_e_h_1, c_a, s2, s3)))),
% 291.92/184.42 inference(rewrite,[status(thm)],[])).
% 291.92/184.42 tff(14375,plain,
% 291.92/184.42 (((~node12(c_e_h_1, c_a, s2, s3)) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s2)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s3)) <=> (m_mutex_h_half_v_out(c_e_h_1, c_a, s3) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s2)) | (~node12(c_e_h_1, c_a, s2, s3)))),
% 291.92/184.42 inference(rewrite,[status(thm)],[])).
% 291.92/184.42 tff(14376,plain,
% 291.92/184.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_1, c_a, s2, s3)) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s2)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (m_mutex_h_half_v_out(c_e_h_1, c_a, s3) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s2)) | (~node12(c_e_h_1, c_a, s2, s3))))),
% 291.92/184.42 inference(monotonicity,[status(thm)],[14375])).
% 291.92/184.42 tff(14377,plain,
% 291.92/184.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_1, c_a, s2, s3)) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s2)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | m_mutex_h_half_v_out(c_e_h_1, c_a, s3) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s2)) | (~node12(c_e_h_1, c_a, s2, s3)))),
% 291.92/184.42 inference(transitivity,[status(thm)],[14376, 14374])).
% 291.92/184.42 tff(14378,plain,
% 291.92/184.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_1, c_a, s2, s3)) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s2)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s3))),
% 291.92/184.42 inference(quant_inst,[status(thm)],[])).
% 291.92/184.42 tff(14379,plain,
% 291.92/184.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | m_mutex_h_half_v_out(c_e_h_1, c_a, s3) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s2)) | (~node12(c_e_h_1, c_a, s2, s3))),
% 291.92/184.42 inference(modus_ponens,[status(thm)],[14378, 14377])).
% 291.92/184.42 tff(14380,plain,
% 291.92/184.42 ($false),
% 291.92/184.42 inference(unit_resolution,[status(thm)],[14379, 1483, 14358, 14373, 14357])).
% 291.92/184.42 tff(14381,plain,(m_mutex_h_half_v_out(c_e_h_1, c_a, s3) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s2))), inference(lemma,lemma(discharge,[]))).
% 291.92/184.42 tff(14382,plain,
% 291.92/184.42 (m_mutex_h_half_v_out(c_e_h_1, c_a, s3)),
% 291.92/184.42 inference(unit_resolution,[status(thm)],[14381, 14233])).
% 291.92/184.42 tff(14383,plain,
% 291.92/184.42 (((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | ((~m_mutex_h_half_v_out(c_e_h_1, c_a, s3)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s3))) <=> ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s3)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s3))),
% 291.92/184.42 inference(rewrite,[status(thm)],[])).
% 291.92/184.42 tff(14384,plain,
% 291.92/184.42 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | ((~m_mutex_h_half_v_out(c_e_h_1, c_a, s3)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s3))),
% 291.92/184.42 inference(quant_inst,[status(thm)],[])).
% 291.92/184.42 tff(14385,plain,
% 291.92/184.42 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s3)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s3)),
% 291.92/184.42 inference(modus_ponens,[status(thm)],[14384, 14383])).
% 291.92/184.42 tff(14386,plain,
% 291.92/184.42 (m_and_h_gate_v_in1(c_e_h_1, c_c, s3)),
% 291.92/184.42 inference(unit_resolution,[status(thm)],[14385, 2556, 14382])).
% 291.92/184.42 tff(14387,plain,
% 291.92/184.42 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node2(c_e_h_1, c_e_h_2, s3))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node2(c_e_h_1, c_e_h_2, s3))),
% 291.92/184.42 inference(rewrite,[status(thm)],[])).
% 291.92/184.42 tff(14388,plain,
% 291.92/184.42 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node2(c_e_h_1, c_e_h_2, s3))),
% 291.92/184.42 inference(quant_inst,[status(thm)],[])).
% 291.92/184.42 tff(14389,plain,
% 291.92/184.42 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node2(c_e_h_1, c_e_h_2, s3)),
% 291.92/184.42 inference(modus_ponens,[status(thm)],[14388, 14387])).
% 291.92/184.42 tff(14390,plain,
% 291.92/184.42 (node2(c_e_h_1, c_e_h_2, s3)),
% 291.92/184.42 inference(unit_resolution,[status(thm)],[14389, 4166, 5821])).
% 291.92/184.42 tff(14391,plain,
% 291.92/184.42 (((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | ((~node2(c_e_h_1, c_e_h_2, s3)) | m_cell_v_ack(c_e_h_2, s3) | m_and_h_gate_v_in2(c_e_h_1, c_c, s3))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | (~node2(c_e_h_1, c_e_h_2, s3)) | m_cell_v_ack(c_e_h_2, s3) | m_and_h_gate_v_in2(c_e_h_1, c_c, s3))),
% 291.92/184.42 inference(rewrite,[status(thm)],[])).
% 291.92/184.42 tff(14392,plain,
% 291.92/184.42 ((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | ((~node2(c_e_h_1, c_e_h_2, s3)) | m_cell_v_ack(c_e_h_2, s3) | m_and_h_gate_v_in2(c_e_h_1, c_c, s3))),
% 291.92/184.42 inference(quant_inst,[status(thm)],[])).
% 291.92/184.42 tff(14393,plain,
% 291.92/184.42 ((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | (~node2(c_e_h_1, c_e_h_2, s3)) | m_cell_v_ack(c_e_h_2, s3) | m_and_h_gate_v_in2(c_e_h_1, c_c, s3)),
% 291.92/184.42 inference(modus_ponens,[status(thm)],[14392, 14391])).
% 291.92/184.42 tff(14394,plain,
% 291.92/184.42 (m_cell_v_ack(c_e_h_2, s3) | m_and_h_gate_v_in2(c_e_h_1, c_c, s3)),
% 291.92/184.42 inference(unit_resolution,[status(thm)],[14393, 5835, 14390])).
% 291.92/184.42 tff(14395,plain,
% 291.92/184.42 (m_and_h_gate_v_in2(c_e_h_1, c_c, s3)),
% 291.92/184.42 inference(unit_resolution,[status(thm)],[14394, 8088])).
% 291.92/184.43 tff(14396,assumption,(m_and_h_gate_v_in1(c_e_h_1, c_c, s3)), introduced(assumption)).
% 291.92/184.43 tff(14397,assumption,(node21(c_e_h_1, c_c, s3, s4)), introduced(assumption)).
% 291.92/184.43 tff(14398,assumption,(m_and_h_gate_v_in2(c_e_h_1, c_c, s3)), introduced(assumption)).
% 291.92/184.43 tff(14399,plain,
% 291.92/184.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_c, s3)) | m_and_h_gate_v_out(c_e_h_1, c_c, s4) | (~m_and_h_gate_v_in2(c_e_h_1, c_c, s3)) | (~node21(c_e_h_1, c_c, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s3)) | m_and_h_gate_v_out(c_e_h_1, c_c, s4) | (~m_and_h_gate_v_in2(c_e_h_1, c_c, s3)) | (~node21(c_e_h_1, c_c, s3, s4)))),
% 291.92/184.43 inference(rewrite,[status(thm)],[])).
% 291.92/184.43 tff(14400,plain,
% 291.92/184.43 (((~node21(c_e_h_1, c_c, s3, s4)) | (~m_and_h_gate_v_in2(c_e_h_1, c_c, s3)) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s3)) | m_and_h_gate_v_out(c_e_h_1, c_c, s4)) <=> ((~m_and_h_gate_v_in1(c_e_h_1, c_c, s3)) | m_and_h_gate_v_out(c_e_h_1, c_c, s4) | (~m_and_h_gate_v_in2(c_e_h_1, c_c, s3)) | (~node21(c_e_h_1, c_c, s3, s4)))),
% 291.92/184.43 inference(rewrite,[status(thm)],[])).
% 291.92/184.43 tff(14401,plain,
% 291.92/184.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_1, c_c, s3, s4)) | (~m_and_h_gate_v_in2(c_e_h_1, c_c, s3)) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s3)) | m_and_h_gate_v_out(c_e_h_1, c_c, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_c, s3)) | m_and_h_gate_v_out(c_e_h_1, c_c, s4) | (~m_and_h_gate_v_in2(c_e_h_1, c_c, s3)) | (~node21(c_e_h_1, c_c, s3, s4))))),
% 291.92/184.43 inference(monotonicity,[status(thm)],[14400])).
% 291.92/184.43 tff(14402,plain,
% 291.92/184.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_1, c_c, s3, s4)) | (~m_and_h_gate_v_in2(c_e_h_1, c_c, s3)) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s3)) | m_and_h_gate_v_out(c_e_h_1, c_c, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s3)) | m_and_h_gate_v_out(c_e_h_1, c_c, s4) | (~m_and_h_gate_v_in2(c_e_h_1, c_c, s3)) | (~node21(c_e_h_1, c_c, s3, s4)))),
% 291.92/184.43 inference(transitivity,[status(thm)],[14401, 14399])).
% 291.92/184.43 tff(14403,plain,
% 291.92/184.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_1, c_c, s3, s4)) | (~m_and_h_gate_v_in2(c_e_h_1, c_c, s3)) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s3)) | m_and_h_gate_v_out(c_e_h_1, c_c, s4))),
% 291.92/184.43 inference(quant_inst,[status(thm)],[])).
% 291.92/184.43 tff(14404,plain,
% 291.92/184.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s3)) | m_and_h_gate_v_out(c_e_h_1, c_c, s4) | (~m_and_h_gate_v_in2(c_e_h_1, c_c, s3)) | (~node21(c_e_h_1, c_c, s3, s4))),
% 291.92/184.43 inference(modus_ponens,[status(thm)],[14403, 14402])).
% 291.92/184.43 tff(14405,plain,
% 291.92/184.43 ($false),
% 291.92/184.43 inference(unit_resolution,[status(thm)],[14404, 5851, 14398, 14397, 14118, 14396])).
% 291.92/184.43 tff(14406,plain,((~node21(c_e_h_1, c_c, s3, s4)) | (~m_and_h_gate_v_in2(c_e_h_1, c_c, s3)) | m_and_h_gate_v_out(c_e_h_1, c_c, s4) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s3))), inference(lemma,lemma(discharge,[]))).
% 291.92/184.43 tff(14407,plain,
% 291.92/184.43 ((~node21(c_e_h_1, c_c, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_c, s4) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s3))),
% 291.92/184.43 inference(unit_resolution,[status(thm)],[14406, 14395])).
% 291.92/184.43 tff(14408,plain,
% 291.92/184.43 (~node21(c_e_h_1, c_c, s3, s4)),
% 291.92/184.43 inference(unit_resolution,[status(thm)],[14407, 14118, 14386])).
% 291.92/184.43 tff(14409,plain,
% 291.92/184.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_1, c_c, s3, s4) | node22(c_e_h_1, c_c, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_1, c_c, s3, s4) | node22(c_e_h_1, c_c, s3, s4))),
% 291.92/184.43 inference(rewrite,[status(thm)],[])).
% 291.92/184.43 tff(14410,plain,
% 291.92/184.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_1, c_c, s3, s4) | node22(c_e_h_1, c_c, s3, s4))),
% 291.92/184.43 inference(quant_inst,[status(thm)],[])).
% 291.92/184.43 tff(14411,plain,
% 291.92/184.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_1, c_c, s3, s4) | node22(c_e_h_1, c_c, s3, s4)),
% 291.92/184.43 inference(modus_ponens,[status(thm)],[14410, 14409])).
% 291.92/184.43 tff(14412,plain,
% 291.92/184.43 (node21(c_e_h_1, c_c, s3, s4) | node22(c_e_h_1, c_c, s3, s4)),
% 291.92/184.43 inference(unit_resolution,[status(thm)],[14411, 82, 531])).
% 291.92/184.43 tff(14413,plain,
% 291.92/184.43 ($false),
% 291.92/184.43 inference(unit_resolution,[status(thm)],[14412, 14408, 14136])).
% 291.92/184.43 tff(14414,plain,(m_and_h_gate_v_out(c_e_h_1, c_c, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s3))), inference(lemma,lemma(discharge,[]))).
% 291.92/184.43 tff(14415,plain,
% 291.92/184.43 (~m_and_h_gate_v_out(c_e_h_1, c_c, s3)),
% 291.92/184.43 inference(unit_resolution,[status(thm)],[14414, 14118])).
% 291.92/184.43 tff(14416,plain,
% 291.92/184.43 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_g, s3)) | m_and_h_gate_v_out(c_e_h_1, c_c, s3))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_g, s3)) | m_and_h_gate_v_out(c_e_h_1, c_c, s3))),
% 291.92/184.43 inference(rewrite,[status(thm)],[])).
% 291.92/184.43 tff(14417,plain,
% 291.92/184.43 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_g, s3)) | m_and_h_gate_v_out(c_e_h_1, c_c, s3))),
% 291.92/184.43 inference(quant_inst,[status(thm)],[])).
% 291.92/184.43 tff(14418,plain,
% 291.92/184.43 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_g, s3)) | m_and_h_gate_v_out(c_e_h_1, c_c, s3)),
% 291.92/184.43 inference(modus_ponens,[status(thm)],[14417, 14416])).
% 291.92/184.43 tff(14419,plain,
% 291.92/184.43 (~m_or_h_gate_v_in1(c_e_h_1, c_g, s3)),
% 291.92/184.43 inference(unit_resolution,[status(thm)],[14418, 2708, 14415])).
% 291.92/184.43 tff(14420,assumption,(m_or_h_gate_v_in2(c_e_h_1, c_g, s3)), introduced(assumption)).
% 291.92/184.43 tff(14421,plain,
% 291.92/184.43 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_g, s3)) | m_and_h_gate_v_out(c_e_h_1, c_d, s3))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_g, s3)) | m_and_h_gate_v_out(c_e_h_1, c_d, s3))),
% 291.92/184.43 inference(rewrite,[status(thm)],[])).
% 291.92/184.43 tff(14422,plain,
% 291.92/184.43 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_g, s3)) | m_and_h_gate_v_out(c_e_h_1, c_d, s3))),
% 291.92/184.43 inference(quant_inst,[status(thm)],[])).
% 291.92/184.43 tff(14423,plain,
% 291.92/184.43 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_g, s3)) | m_and_h_gate_v_out(c_e_h_1, c_d, s3)),
% 291.92/184.43 inference(modus_ponens,[status(thm)],[14422, 14421])).
% 291.92/184.43 tff(14424,plain,
% 291.92/184.43 ($false),
% 291.92/184.43 inference(unit_resolution,[status(thm)],[14423, 2762, 14040, 14420])).
% 291.92/184.43 tff(14425,plain,((~m_or_h_gate_v_in2(c_e_h_1, c_g, s3)) | m_and_h_gate_v_out(c_e_h_1, c_d, s3)), inference(lemma,lemma(discharge,[]))).
% 291.92/184.43 tff(14426,plain,
% 291.92/184.43 (~m_or_h_gate_v_in2(c_e_h_1, c_g, s3)),
% 291.92/184.43 inference(unit_resolution,[status(thm)],[14425, 14039])).
% 291.92/184.43 tff(14427,assumption,(m_or_h_gate_v_in2(c_e_h_1, c_g, s2)), introduced(assumption)).
% 291.92/184.43 tff(14428,plain,
% 291.92/184.43 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_g, s2)) | m_and_h_gate_v_out(c_e_h_1, c_d, s2))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_g, s2)) | m_and_h_gate_v_out(c_e_h_1, c_d, s2))),
% 291.92/184.43 inference(rewrite,[status(thm)],[])).
% 291.92/184.43 tff(14429,plain,
% 291.92/184.43 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_g, s2)) | m_and_h_gate_v_out(c_e_h_1, c_d, s2))),
% 291.92/184.43 inference(quant_inst,[status(thm)],[])).
% 291.92/184.43 tff(14430,plain,
% 291.92/184.43 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_g, s2)) | m_and_h_gate_v_out(c_e_h_1, c_d, s2)),
% 291.92/184.43 inference(modus_ponens,[status(thm)],[14429, 14428])).
% 291.92/184.43 tff(14431,plain,
% 291.92/184.43 ($false),
% 291.92/184.43 inference(unit_resolution,[status(thm)],[14430, 2762, 14018, 14427])).
% 291.92/184.43 tff(14432,plain,((~m_or_h_gate_v_in2(c_e_h_1, c_g, s2)) | m_and_h_gate_v_out(c_e_h_1, c_d, s2)), inference(lemma,lemma(discharge,[]))).
% 291.92/184.43 tff(14433,plain,
% 291.92/184.43 (~m_or_h_gate_v_in2(c_e_h_1, c_g, s2)),
% 291.92/184.43 inference(unit_resolution,[status(thm)],[14432, 14007])).
% 291.92/184.43 tff(14434,plain,
% 291.92/184.43 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_g, s2)) | m_and_h_gate_v_out(c_e_h_1, c_c, s2))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_g, s2)) | m_and_h_gate_v_out(c_e_h_1, c_c, s2))),
% 291.92/184.43 inference(rewrite,[status(thm)],[])).
% 291.92/184.43 tff(14435,plain,
% 291.92/184.43 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_g, s2)) | m_and_h_gate_v_out(c_e_h_1, c_c, s2))),
% 291.92/184.43 inference(quant_inst,[status(thm)],[])).
% 291.92/184.43 tff(14436,plain,
% 291.92/184.43 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_g, s2)) | m_and_h_gate_v_out(c_e_h_1, c_c, s2)),
% 291.92/184.43 inference(modus_ponens,[status(thm)],[14435, 14434])).
% 291.92/184.43 tff(14437,plain,
% 291.92/184.43 (~m_or_h_gate_v_in1(c_e_h_1, c_g, s2)),
% 291.92/184.43 inference(unit_resolution,[status(thm)],[14436, 2708, 14193])).
% 291.92/184.43 tff(14438,assumption,(~m_or_h_gate_v_in1(c_e_h_1, c_g, s2)), introduced(assumption)).
% 291.92/184.43 tff(14439,assumption,(~m_or_h_gate_v_in2(c_e_h_1, c_g, s2)), introduced(assumption)).
% 291.92/184.43 tff(14440,assumption,(m_or_h_gate_v_out(c_e_h_1, c_g, s3)), introduced(assumption)).
% 291.92/184.43 tff(14441,assumption,(node6(c_e_h_1, c_g, s2, s3)), introduced(assumption)).
% 291.92/184.43 tff(14442,plain,
% 291.92/184.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_1, c_g, s3)) | (~node6(c_e_h_1, c_g, s2, s3)) | m_or_h_gate_v_out(c_e_h_1, c_g, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s3)) | (~node6(c_e_h_1, c_g, s2, s3)) | m_or_h_gate_v_out(c_e_h_1, c_g, s2))),
% 291.92/184.43 inference(rewrite,[status(thm)],[])).
% 291.92/184.43 tff(14443,plain,
% 291.92/184.43 (((~node6(c_e_h_1, c_g, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s3)) | m_or_h_gate_v_out(c_e_h_1, c_g, s2)) <=> ((~m_or_h_gate_v_out(c_e_h_1, c_g, s3)) | (~node6(c_e_h_1, c_g, s2, s3)) | m_or_h_gate_v_out(c_e_h_1, c_g, s2))),
% 291.92/184.43 inference(rewrite,[status(thm)],[])).
% 291.92/184.43 tff(14444,plain,
% 291.92/184.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_g, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s3)) | m_or_h_gate_v_out(c_e_h_1, c_g, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_1, c_g, s3)) | (~node6(c_e_h_1, c_g, s2, s3)) | m_or_h_gate_v_out(c_e_h_1, c_g, s2)))),
% 291.92/184.43 inference(monotonicity,[status(thm)],[14443])).
% 291.92/184.44 tff(14445,plain,
% 291.92/184.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_g, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s3)) | m_or_h_gate_v_out(c_e_h_1, c_g, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s3)) | (~node6(c_e_h_1, c_g, s2, s3)) | m_or_h_gate_v_out(c_e_h_1, c_g, s2))),
% 291.92/184.44 inference(transitivity,[status(thm)],[14444, 14442])).
% 291.92/184.44 tff(14446,plain,
% 291.92/184.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_g, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s3)) | m_or_h_gate_v_out(c_e_h_1, c_g, s2))),
% 291.92/184.44 inference(quant_inst,[status(thm)],[])).
% 291.92/184.44 tff(14447,plain,
% 291.92/184.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s3)) | (~node6(c_e_h_1, c_g, s2, s3)) | m_or_h_gate_v_out(c_e_h_1, c_g, s2)),
% 291.92/184.44 inference(modus_ponens,[status(thm)],[14446, 14445])).
% 291.92/184.44 tff(14448,plain,
% 291.92/184.44 ($false),
% 291.92/184.44 inference(unit_resolution,[status(thm)],[14447, 1121, 14441, 9845, 14440])).
% 291.92/184.44 tff(14449,plain,((~node6(c_e_h_1, c_g, s2, s3)) | m_or_h_gate_v_out(c_e_h_1, c_g, s2) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s3))), inference(lemma,lemma(discharge,[]))).
% 291.92/184.44 tff(14450,plain,
% 291.92/184.44 (~node6(c_e_h_1, c_g, s2, s3)),
% 291.92/184.44 inference(unit_resolution,[status(thm)],[14449, 14440, 9845])).
% 291.92/184.44 tff(14451,plain,
% 291.92/184.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s2, s3)) | node5(c_e_h_1, c_g, s2, s3) | node6(c_e_h_1, c_g, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s2, s3)) | node5(c_e_h_1, c_g, s2, s3) | node6(c_e_h_1, c_g, s2, s3))),
% 291.92/184.44 inference(rewrite,[status(thm)],[])).
% 291.92/184.44 tff(14452,plain,
% 291.92/184.44 ((node6(c_e_h_1, c_g, s2, s3) | node5(c_e_h_1, c_g, s2, s3) | (~trans(s2, s3))) <=> ((~trans(s2, s3)) | node5(c_e_h_1, c_g, s2, s3) | node6(c_e_h_1, c_g, s2, s3))),
% 291.92/184.44 inference(rewrite,[status(thm)],[])).
% 291.92/184.44 tff(14453,plain,
% 291.92/184.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_g, s2, s3) | node5(c_e_h_1, c_g, s2, s3) | (~trans(s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s2, s3)) | node5(c_e_h_1, c_g, s2, s3) | node6(c_e_h_1, c_g, s2, s3)))),
% 291.92/184.44 inference(monotonicity,[status(thm)],[14452])).
% 291.92/184.44 tff(14454,plain,
% 291.92/184.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_g, s2, s3) | node5(c_e_h_1, c_g, s2, s3) | (~trans(s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s2, s3)) | node5(c_e_h_1, c_g, s2, s3) | node6(c_e_h_1, c_g, s2, s3))),
% 291.92/184.44 inference(transitivity,[status(thm)],[14453, 14451])).
% 291.92/184.44 tff(14455,plain,
% 291.92/184.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_g, s2, s3) | node5(c_e_h_1, c_g, s2, s3) | (~trans(s2, s3)))),
% 291.92/184.44 inference(quant_inst,[status(thm)],[])).
% 291.92/184.44 tff(14456,plain,
% 291.92/184.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s2, s3)) | node5(c_e_h_1, c_g, s2, s3) | node6(c_e_h_1, c_g, s2, s3)),
% 291.92/184.44 inference(modus_ponens,[status(thm)],[14455, 14454])).
% 291.92/184.44 tff(14457,plain,
% 291.92/184.44 (node5(c_e_h_1, c_g, s2, s3) | node6(c_e_h_1, c_g, s2, s3)),
% 291.92/184.44 inference(unit_resolution,[status(thm)],[14456, 1141, 318])).
% 291.92/184.44 tff(14458,plain,
% 291.92/184.44 (node5(c_e_h_1, c_g, s2, s3)),
% 291.92/184.44 inference(unit_resolution,[status(thm)],[14457, 14450])).
% 291.92/184.44 tff(14459,plain,
% 291.92/184.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_1, c_g, s3)) | m_or_h_gate_v_in2(c_e_h_1, c_g, s2) | (~node5(c_e_h_1, c_g, s2, s3)) | m_or_h_gate_v_in1(c_e_h_1, c_g, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s3)) | m_or_h_gate_v_in2(c_e_h_1, c_g, s2) | (~node5(c_e_h_1, c_g, s2, s3)) | m_or_h_gate_v_in1(c_e_h_1, c_g, s2))),
% 291.92/184.44 inference(rewrite,[status(thm)],[])).
% 291.92/184.44 tff(14460,plain,
% 291.92/184.44 ((m_or_h_gate_v_in1(c_e_h_1, c_g, s2) | m_or_h_gate_v_in2(c_e_h_1, c_g, s2) | (~node5(c_e_h_1, c_g, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s3))) <=> ((~m_or_h_gate_v_out(c_e_h_1, c_g, s3)) | m_or_h_gate_v_in2(c_e_h_1, c_g, s2) | (~node5(c_e_h_1, c_g, s2, s3)) | m_or_h_gate_v_in1(c_e_h_1, c_g, s2))),
% 291.92/184.44 inference(rewrite,[status(thm)],[])).
% 291.92/184.44 tff(14461,plain,
% 291.92/184.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_g, s2) | m_or_h_gate_v_in2(c_e_h_1, c_g, s2) | (~node5(c_e_h_1, c_g, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_1, c_g, s3)) | m_or_h_gate_v_in2(c_e_h_1, c_g, s2) | (~node5(c_e_h_1, c_g, s2, s3)) | m_or_h_gate_v_in1(c_e_h_1, c_g, s2)))),
% 291.92/184.44 inference(monotonicity,[status(thm)],[14460])).
% 291.92/184.44 tff(14462,plain,
% 291.92/184.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_g, s2) | m_or_h_gate_v_in2(c_e_h_1, c_g, s2) | (~node5(c_e_h_1, c_g, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s3)) | m_or_h_gate_v_in2(c_e_h_1, c_g, s2) | (~node5(c_e_h_1, c_g, s2, s3)) | m_or_h_gate_v_in1(c_e_h_1, c_g, s2))),
% 291.92/184.44 inference(transitivity,[status(thm)],[14461, 14459])).
% 291.92/184.44 tff(14463,plain,
% 291.92/184.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_g, s2) | m_or_h_gate_v_in2(c_e_h_1, c_g, s2) | (~node5(c_e_h_1, c_g, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s3)))),
% 291.92/184.44 inference(quant_inst,[status(thm)],[])).
% 291.92/184.44 tff(14464,plain,
% 291.92/184.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s3)) | m_or_h_gate_v_in2(c_e_h_1, c_g, s2) | (~node5(c_e_h_1, c_g, s2, s3)) | m_or_h_gate_v_in1(c_e_h_1, c_g, s2)),
% 291.92/184.44 inference(modus_ponens,[status(thm)],[14463, 14462])).
% 291.92/184.44 tff(14465,plain,
% 291.92/184.44 ($false),
% 291.92/184.44 inference(unit_resolution,[status(thm)],[14464, 1159, 14458, 14440, 14439, 14438])).
% 291.92/184.44 tff(14466,plain,((~m_or_h_gate_v_out(c_e_h_1, c_g, s3)) | m_or_h_gate_v_in2(c_e_h_1, c_g, s2) | m_or_h_gate_v_in1(c_e_h_1, c_g, s2) | m_or_h_gate_v_out(c_e_h_1, c_g, s2)), inference(lemma,lemma(discharge,[]))).
% 291.92/184.44 tff(14467,plain,
% 291.92/184.44 ((~m_or_h_gate_v_out(c_e_h_1, c_g, s3)) | m_or_h_gate_v_in2(c_e_h_1, c_g, s2) | m_or_h_gate_v_out(c_e_h_1, c_g, s2)),
% 291.92/184.44 inference(unit_resolution,[status(thm)],[14466, 14437])).
% 291.92/184.44 tff(14468,plain,
% 291.92/184.44 ((~m_or_h_gate_v_out(c_e_h_1, c_g, s3)) | m_or_h_gate_v_in2(c_e_h_1, c_g, s2)),
% 291.92/184.44 inference(unit_resolution,[status(thm)],[14467, 9843])).
% 291.92/184.44 tff(14469,plain,
% 291.92/184.44 (~m_or_h_gate_v_out(c_e_h_1, c_g, s3)),
% 291.92/184.44 inference(unit_resolution,[status(thm)],[14468, 14433])).
% 291.92/184.44 tff(14470,assumption,(~m_or_h_gate_v_out(c_e_h_1, c_g, s3)), introduced(assumption)).
% 291.92/184.44 tff(14471,assumption,(m_or_h_gate_v_out(c_e_h_1, c_g, s4)), introduced(assumption)).
% 291.92/184.44 tff(14472,assumption,(node6(c_e_h_1, c_g, s3, s4)), introduced(assumption)).
% 291.92/184.44 tff(14473,plain,
% 291.92/184.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_1, c_g, s4)) | m_or_h_gate_v_out(c_e_h_1, c_g, s3) | (~node6(c_e_h_1, c_g, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s4)) | m_or_h_gate_v_out(c_e_h_1, c_g, s3) | (~node6(c_e_h_1, c_g, s3, s4)))),
% 291.92/184.44 inference(rewrite,[status(thm)],[])).
% 291.92/184.44 tff(14474,plain,
% 291.92/184.44 (((~node6(c_e_h_1, c_g, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s4)) | m_or_h_gate_v_out(c_e_h_1, c_g, s3)) <=> ((~m_or_h_gate_v_out(c_e_h_1, c_g, s4)) | m_or_h_gate_v_out(c_e_h_1, c_g, s3) | (~node6(c_e_h_1, c_g, s3, s4)))),
% 291.92/184.44 inference(rewrite,[status(thm)],[])).
% 291.92/184.44 tff(14475,plain,
% 291.92/184.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_g, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s4)) | m_or_h_gate_v_out(c_e_h_1, c_g, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_1, c_g, s4)) | m_or_h_gate_v_out(c_e_h_1, c_g, s3) | (~node6(c_e_h_1, c_g, s3, s4))))),
% 291.92/184.44 inference(monotonicity,[status(thm)],[14474])).
% 291.92/184.44 tff(14476,plain,
% 291.92/184.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_g, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s4)) | m_or_h_gate_v_out(c_e_h_1, c_g, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s4)) | m_or_h_gate_v_out(c_e_h_1, c_g, s3) | (~node6(c_e_h_1, c_g, s3, s4)))),
% 291.92/184.44 inference(transitivity,[status(thm)],[14475, 14473])).
% 291.92/184.44 tff(14477,plain,
% 291.92/184.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_g, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s4)) | m_or_h_gate_v_out(c_e_h_1, c_g, s3))),
% 291.92/184.44 inference(quant_inst,[status(thm)],[])).
% 291.92/184.44 tff(14478,plain,
% 291.92/184.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s4)) | m_or_h_gate_v_out(c_e_h_1, c_g, s3) | (~node6(c_e_h_1, c_g, s3, s4))),
% 291.92/184.44 inference(modus_ponens,[status(thm)],[14477, 14476])).
% 291.92/184.44 tff(14479,plain,
% 291.92/184.44 ($false),
% 291.92/184.44 inference(unit_resolution,[status(thm)],[14478, 1121, 14472, 14471, 14470])).
% 291.92/184.44 tff(14480,plain,((~node6(c_e_h_1, c_g, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s4)) | m_or_h_gate_v_out(c_e_h_1, c_g, s3)), inference(lemma,lemma(discharge,[]))).
% 291.92/184.44 tff(14481,plain,
% 291.92/184.44 (~node6(c_e_h_1, c_g, s3, s4)),
% 291.92/184.44 inference(unit_resolution,[status(thm)],[14480, 14471, 14470])).
% 291.92/184.44 tff(14482,assumption,(~m_or_h_gate_v_in1(c_e_h_1, c_g, s3)), introduced(assumption)).
% 291.92/184.44 tff(14483,assumption,(~m_or_h_gate_v_in2(c_e_h_1, c_g, s3)), introduced(assumption)).
% 291.92/184.44 tff(14484,assumption,(node5(c_e_h_1, c_g, s3, s4)), introduced(assumption)).
% 291.92/184.44 tff(14485,plain,
% 291.92/184.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~node5(c_e_h_1, c_g, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s4)) | m_or_h_gate_v_in2(c_e_h_1, c_g, s3) | m_or_h_gate_v_in1(c_e_h_1, c_g, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~node5(c_e_h_1, c_g, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s4)) | m_or_h_gate_v_in2(c_e_h_1, c_g, s3) | m_or_h_gate_v_in1(c_e_h_1, c_g, s3))),
% 291.92/184.44 inference(rewrite,[status(thm)],[])).
% 291.92/184.44 tff(14486,plain,
% 291.92/184.44 ((m_or_h_gate_v_in1(c_e_h_1, c_g, s3) | m_or_h_gate_v_in2(c_e_h_1, c_g, s3) | (~node5(c_e_h_1, c_g, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s4))) <=> ((~node5(c_e_h_1, c_g, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s4)) | m_or_h_gate_v_in2(c_e_h_1, c_g, s3) | m_or_h_gate_v_in1(c_e_h_1, c_g, s3))),
% 291.92/184.45 inference(rewrite,[status(thm)],[])).
% 291.92/184.45 tff(14487,plain,
% 291.92/184.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_g, s3) | m_or_h_gate_v_in2(c_e_h_1, c_g, s3) | (~node5(c_e_h_1, c_g, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~node5(c_e_h_1, c_g, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s4)) | m_or_h_gate_v_in2(c_e_h_1, c_g, s3) | m_or_h_gate_v_in1(c_e_h_1, c_g, s3)))),
% 291.92/184.45 inference(monotonicity,[status(thm)],[14486])).
% 291.92/184.45 tff(14488,plain,
% 291.92/184.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_g, s3) | m_or_h_gate_v_in2(c_e_h_1, c_g, s3) | (~node5(c_e_h_1, c_g, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~node5(c_e_h_1, c_g, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s4)) | m_or_h_gate_v_in2(c_e_h_1, c_g, s3) | m_or_h_gate_v_in1(c_e_h_1, c_g, s3))),
% 291.92/184.45 inference(transitivity,[status(thm)],[14487, 14485])).
% 291.92/184.45 tff(14489,plain,
% 291.92/184.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_g, s3) | m_or_h_gate_v_in2(c_e_h_1, c_g, s3) | (~node5(c_e_h_1, c_g, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s4)))),
% 291.92/184.45 inference(quant_inst,[status(thm)],[])).
% 291.92/184.45 tff(14490,plain,
% 291.92/184.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~node5(c_e_h_1, c_g, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s4)) | m_or_h_gate_v_in2(c_e_h_1, c_g, s3) | m_or_h_gate_v_in1(c_e_h_1, c_g, s3)),
% 291.92/184.45 inference(modus_ponens,[status(thm)],[14489, 14488])).
% 291.92/184.45 tff(14491,plain,
% 291.92/184.45 ($false),
% 291.92/184.45 inference(unit_resolution,[status(thm)],[14490, 1159, 14484, 14471, 14482, 14483])).
% 291.92/184.45 tff(14492,plain,((~node5(c_e_h_1, c_g, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s4)) | m_or_h_gate_v_in1(c_e_h_1, c_g, s3) | m_or_h_gate_v_in2(c_e_h_1, c_g, s3)), inference(lemma,lemma(discharge,[]))).
% 291.92/184.45 tff(14493,plain,
% 291.92/184.45 (~node5(c_e_h_1, c_g, s3, s4)),
% 291.92/184.45 inference(unit_resolution,[status(thm)],[14492, 14471, 14483, 14482])).
% 291.92/184.45 tff(14494,plain,
% 291.92/184.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s3, s4)) | node5(c_e_h_1, c_g, s3, s4) | node6(c_e_h_1, c_g, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s3, s4)) | node5(c_e_h_1, c_g, s3, s4) | node6(c_e_h_1, c_g, s3, s4))),
% 291.92/184.45 inference(rewrite,[status(thm)],[])).
% 291.92/184.45 tff(14495,plain,
% 291.92/184.45 ((node6(c_e_h_1, c_g, s3, s4) | node5(c_e_h_1, c_g, s3, s4) | (~trans(s3, s4))) <=> ((~trans(s3, s4)) | node5(c_e_h_1, c_g, s3, s4) | node6(c_e_h_1, c_g, s3, s4))),
% 291.92/184.45 inference(rewrite,[status(thm)],[])).
% 291.92/184.45 tff(14496,plain,
% 291.92/184.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_g, s3, s4) | node5(c_e_h_1, c_g, s3, s4) | (~trans(s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s3, s4)) | node5(c_e_h_1, c_g, s3, s4) | node6(c_e_h_1, c_g, s3, s4)))),
% 291.92/184.45 inference(monotonicity,[status(thm)],[14495])).
% 291.92/184.45 tff(14497,plain,
% 291.92/184.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_g, s3, s4) | node5(c_e_h_1, c_g, s3, s4) | (~trans(s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s3, s4)) | node5(c_e_h_1, c_g, s3, s4) | node6(c_e_h_1, c_g, s3, s4))),
% 291.92/184.45 inference(transitivity,[status(thm)],[14496, 14494])).
% 291.92/184.45 tff(14498,plain,
% 291.92/184.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_g, s3, s4) | node5(c_e_h_1, c_g, s3, s4) | (~trans(s3, s4)))),
% 291.92/184.45 inference(quant_inst,[status(thm)],[])).
% 291.92/184.45 tff(14499,plain,
% 291.92/184.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s3, s4)) | node5(c_e_h_1, c_g, s3, s4) | node6(c_e_h_1, c_g, s3, s4)),
% 291.92/184.45 inference(modus_ponens,[status(thm)],[14498, 14497])).
% 291.92/184.45 tff(14500,plain,
% 291.92/184.45 (node5(c_e_h_1, c_g, s3, s4) | node6(c_e_h_1, c_g, s3, s4)),
% 291.92/184.45 inference(unit_resolution,[status(thm)],[14499, 1141, 531])).
% 291.92/184.45 tff(14501,plain,
% 291.92/184.45 ($false),
% 291.92/184.45 inference(unit_resolution,[status(thm)],[14500, 14493, 14481])).
% 291.92/184.45 tff(14502,plain,((~m_or_h_gate_v_out(c_e_h_1, c_g, s4)) | m_or_h_gate_v_in2(c_e_h_1, c_g, s3) | m_or_h_gate_v_in1(c_e_h_1, c_g, s3) | m_or_h_gate_v_out(c_e_h_1, c_g, s3)), inference(lemma,lemma(discharge,[]))).
% 291.92/184.45 tff(14503,plain,
% 291.92/184.45 ((~m_or_h_gate_v_out(c_e_h_1, c_g, s4)) | m_or_h_gate_v_in1(c_e_h_1, c_g, s3)),
% 291.92/184.45 inference(unit_resolution,[status(thm)],[14502, 14469, 14426])).
% 291.92/184.45 tff(14504,plain,
% 291.92/184.45 (~m_or_h_gate_v_out(c_e_h_1, c_g, s4)),
% 291.92/184.45 inference(unit_resolution,[status(thm)],[14503, 14419])).
% 291.92/184.45 tff(14505,assumption,(~node20(c_e_h_1, c_c, s4)), introduced(assumption)).
% 291.92/184.45 tff(14506,assumption,(m_and_h_gate_v_out(c_e_h_1, c_c, s5)), introduced(assumption)).
% 291.92/184.45 tff(14507,assumption,(node22(c_e_h_1, c_c, s4, s5)), introduced(assumption)).
% 291.92/184.45 tff(14508,plain,
% 291.92/184.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_c, s5)) | (~node22(c_e_h_1, c_c, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_c, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s5)) | (~node22(c_e_h_1, c_c, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_c, s4))),
% 291.92/184.45 inference(rewrite,[status(thm)],[])).
% 291.92/184.45 tff(14509,plain,
% 291.92/184.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_c, s5)) | (~node22(c_e_h_1, c_c, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_c, s4))),
% 291.92/184.45 inference(quant_inst,[status(thm)],[])).
% 291.92/184.45 tff(14510,plain,
% 291.92/184.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s5)) | (~node22(c_e_h_1, c_c, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_c, s4)),
% 291.92/184.45 inference(modus_ponens,[status(thm)],[14509, 14508])).
% 291.92/184.45 tff(14511,plain,
% 291.92/184.45 ($false),
% 291.92/184.45 inference(unit_resolution,[status(thm)],[14510, 108, 14507, 14118, 14506])).
% 291.92/184.45 tff(14512,plain,((~node22(c_e_h_1, c_c, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_c, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s5))), inference(lemma,lemma(discharge,[]))).
% 291.92/184.45 tff(14513,plain,
% 291.92/184.45 (~node22(c_e_h_1, c_c, s4, s5)),
% 291.92/184.45 inference(unit_resolution,[status(thm)],[14512, 14506, 14118])).
% 291.92/184.45 tff(14514,assumption,(node21(c_e_h_1, c_c, s4, s5)), introduced(assumption)).
% 291.92/184.45 tff(14515,plain,
% 291.92/184.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_c, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s5)) | (~node21(c_e_h_1, c_c, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_c, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s5)) | (~node21(c_e_h_1, c_c, s4, s5)))),
% 291.92/184.45 inference(rewrite,[status(thm)],[])).
% 291.92/184.45 tff(14516,plain,
% 291.92/184.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_c, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s5)) | (~node21(c_e_h_1, c_c, s4, s5)))),
% 291.92/184.45 inference(quant_inst,[status(thm)],[])).
% 291.92/184.45 tff(14517,plain,
% 291.92/184.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_c, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s5)) | (~node21(c_e_h_1, c_c, s4, s5))),
% 291.92/184.45 inference(modus_ponens,[status(thm)],[14516, 14515])).
% 291.92/184.45 tff(14518,plain,
% 291.92/184.45 ($false),
% 291.92/184.45 inference(unit_resolution,[status(thm)],[14517, 52, 14514, 14506, 14505])).
% 291.92/184.45 tff(14519,plain,((~node21(c_e_h_1, c_c, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s5)) | node20(c_e_h_1, c_c, s4)), inference(lemma,lemma(discharge,[]))).
% 291.92/184.45 tff(14520,plain,
% 291.92/184.45 (~node21(c_e_h_1, c_c, s4, s5)),
% 291.92/184.45 inference(unit_resolution,[status(thm)],[14519, 14506, 14505])).
% 291.92/184.45 tff(14521,plain,
% 291.92/184.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_1, c_c, s4, s5) | node22(c_e_h_1, c_c, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_1, c_c, s4, s5) | node22(c_e_h_1, c_c, s4, s5))),
% 291.92/184.45 inference(rewrite,[status(thm)],[])).
% 291.92/184.45 tff(14522,plain,
% 291.92/184.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_1, c_c, s4, s5) | node22(c_e_h_1, c_c, s4, s5))),
% 291.92/184.45 inference(quant_inst,[status(thm)],[])).
% 291.92/184.45 tff(14523,plain,
% 291.92/184.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_1, c_c, s4, s5) | node22(c_e_h_1, c_c, s4, s5)),
% 291.92/184.45 inference(modus_ponens,[status(thm)],[14522, 14521])).
% 291.92/184.45 tff(14524,plain,
% 291.92/184.45 (node21(c_e_h_1, c_c, s4, s5) | node22(c_e_h_1, c_c, s4, s5)),
% 291.92/184.45 inference(unit_resolution,[status(thm)],[14523, 82, 1028])).
% 291.92/184.45 tff(14525,plain,
% 291.92/184.45 ($false),
% 291.92/184.45 inference(unit_resolution,[status(thm)],[14524, 14520, 14513])).
% 291.92/184.45 tff(14526,plain,((~m_and_h_gate_v_out(c_e_h_1, c_c, s5)) | node20(c_e_h_1, c_c, s4) | m_and_h_gate_v_out(c_e_h_1, c_c, s4)), inference(lemma,lemma(discharge,[]))).
% 291.92/184.45 tff(14527,plain,
% 291.92/184.45 (~m_and_h_gate_v_out(c_e_h_1, c_c, s5)),
% 291.92/184.45 inference(unit_resolution,[status(thm)],[14526, 14118, 14505])).
% 291.92/184.45 tff(14528,plain,
% 291.92/184.45 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_g, s5)) | m_and_h_gate_v_out(c_e_h_1, c_c, s5))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_g, s5)) | m_and_h_gate_v_out(c_e_h_1, c_c, s5))),
% 291.92/184.45 inference(rewrite,[status(thm)],[])).
% 291.92/184.45 tff(14529,plain,
% 291.92/184.45 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_g, s5)) | m_and_h_gate_v_out(c_e_h_1, c_c, s5))),
% 291.92/184.45 inference(quant_inst,[status(thm)],[])).
% 291.92/184.45 tff(14530,plain,
% 291.92/184.45 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_g, s5)) | m_and_h_gate_v_out(c_e_h_1, c_c, s5)),
% 291.92/184.45 inference(modus_ponens,[status(thm)],[14529, 14528])).
% 291.92/184.45 tff(14531,plain,
% 291.92/184.45 (~m_or_h_gate_v_in1(c_e_h_1, c_g, s5)),
% 291.92/184.45 inference(unit_resolution,[status(thm)],[14530, 2708, 14527])).
% 291.92/184.45 tff(14532,assumption,(~m_or_h_gate_v_in1(c_e_h_1, c_g, s5)), introduced(assumption)).
% 291.92/184.45 tff(14533,assumption,(node5(c_e_h_1, c_g, s5, s6)), introduced(assumption)).
% 291.92/184.45 tff(14534,plain,
% 291.92/184.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_1, c_g, s5) | m_or_h_gate_v_in1(c_e_h_1, c_g, s5) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s6)) | (~node5(c_e_h_1, c_g, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_1, c_g, s5) | m_or_h_gate_v_in1(c_e_h_1, c_g, s5) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s6)) | (~node5(c_e_h_1, c_g, s5, s6)))),
% 291.92/184.46 inference(rewrite,[status(thm)],[])).
% 291.92/184.46 tff(14535,plain,
% 291.92/184.46 ((m_or_h_gate_v_in1(c_e_h_1, c_g, s5) | m_or_h_gate_v_in2(c_e_h_1, c_g, s5) | (~node5(c_e_h_1, c_g, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s6))) <=> (m_or_h_gate_v_in2(c_e_h_1, c_g, s5) | m_or_h_gate_v_in1(c_e_h_1, c_g, s5) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s6)) | (~node5(c_e_h_1, c_g, s5, s6)))),
% 291.92/184.46 inference(rewrite,[status(thm)],[])).
% 291.92/184.46 tff(14536,plain,
% 291.92/184.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_g, s5) | m_or_h_gate_v_in2(c_e_h_1, c_g, s5) | (~node5(c_e_h_1, c_g, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_1, c_g, s5) | m_or_h_gate_v_in1(c_e_h_1, c_g, s5) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s6)) | (~node5(c_e_h_1, c_g, s5, s6))))),
% 291.92/184.46 inference(monotonicity,[status(thm)],[14535])).
% 291.92/184.46 tff(14537,plain,
% 291.92/184.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_g, s5) | m_or_h_gate_v_in2(c_e_h_1, c_g, s5) | (~node5(c_e_h_1, c_g, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_1, c_g, s5) | m_or_h_gate_v_in1(c_e_h_1, c_g, s5) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s6)) | (~node5(c_e_h_1, c_g, s5, s6)))),
% 291.92/184.46 inference(transitivity,[status(thm)],[14536, 14534])).
% 291.92/184.46 tff(14538,plain,
% 291.92/184.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_g, s5) | m_or_h_gate_v_in2(c_e_h_1, c_g, s5) | (~node5(c_e_h_1, c_g, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s6)))),
% 291.92/184.46 inference(quant_inst,[status(thm)],[])).
% 291.92/184.46 tff(14539,plain,
% 291.92/184.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_1, c_g, s5) | m_or_h_gate_v_in1(c_e_h_1, c_g, s5) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s6)) | (~node5(c_e_h_1, c_g, s5, s6))),
% 291.92/184.46 inference(modus_ponens,[status(thm)],[14538, 14537])).
% 291.92/184.46 tff(14540,plain,
% 291.92/184.46 ($false),
% 291.92/184.46 inference(unit_resolution,[status(thm)],[14539, 1159, 14533, 13630, 14532, 14101])).
% 291.92/184.46 tff(14541,plain,((~node5(c_e_h_1, c_g, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s6)) | m_or_h_gate_v_in1(c_e_h_1, c_g, s5) | m_or_h_gate_v_in2(c_e_h_1, c_g, s5)), inference(lemma,lemma(discharge,[]))).
% 291.92/184.46 tff(14542,plain,
% 291.92/184.46 (~node5(c_e_h_1, c_g, s5, s6)),
% 291.92/184.46 inference(unit_resolution,[status(thm)],[14541, 13630, 14101, 14532])).
% 291.92/184.46 tff(14543,assumption,(~m_or_h_gate_v_out(c_e_h_1, c_g, s5)), introduced(assumption)).
% 291.92/184.46 tff(14544,assumption,(node6(c_e_h_1, c_g, s5, s6)), introduced(assumption)).
% 291.92/184.46 tff(14545,plain,
% 291.92/184.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_g, s5) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s6)) | (~node6(c_e_h_1, c_g, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_g, s5) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s6)) | (~node6(c_e_h_1, c_g, s5, s6)))),
% 291.92/184.46 inference(rewrite,[status(thm)],[])).
% 291.92/184.46 tff(14546,plain,
% 291.92/184.46 (((~node6(c_e_h_1, c_g, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s6)) | m_or_h_gate_v_out(c_e_h_1, c_g, s5)) <=> (m_or_h_gate_v_out(c_e_h_1, c_g, s5) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s6)) | (~node6(c_e_h_1, c_g, s5, s6)))),
% 291.92/184.46 inference(rewrite,[status(thm)],[])).
% 291.92/184.46 tff(14547,plain,
% 291.92/184.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_g, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s6)) | m_or_h_gate_v_out(c_e_h_1, c_g, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_g, s5) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s6)) | (~node6(c_e_h_1, c_g, s5, s6))))),
% 291.92/184.46 inference(monotonicity,[status(thm)],[14546])).
% 291.92/184.46 tff(14548,plain,
% 291.92/184.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_g, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s6)) | m_or_h_gate_v_out(c_e_h_1, c_g, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_g, s5) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s6)) | (~node6(c_e_h_1, c_g, s5, s6)))),
% 291.92/184.46 inference(transitivity,[status(thm)],[14547, 14545])).
% 291.92/184.46 tff(14549,plain,
% 291.92/184.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_g, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s6)) | m_or_h_gate_v_out(c_e_h_1, c_g, s5))),
% 291.92/184.46 inference(quant_inst,[status(thm)],[])).
% 291.92/184.46 tff(14550,plain,
% 291.92/184.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_g, s5) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s6)) | (~node6(c_e_h_1, c_g, s5, s6))),
% 291.92/184.46 inference(modus_ponens,[status(thm)],[14549, 14548])).
% 291.92/184.46 tff(14551,plain,
% 291.92/184.46 ($false),
% 291.92/184.46 inference(unit_resolution,[status(thm)],[14550, 1121, 14544, 14543, 13630])).
% 291.92/184.46 tff(14552,plain,((~node6(c_e_h_1, c_g, s5, s6)) | m_or_h_gate_v_out(c_e_h_1, c_g, s5) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s6))), inference(lemma,lemma(discharge,[]))).
% 291.92/184.46 tff(14553,plain,
% 291.92/184.46 (~node6(c_e_h_1, c_g, s5, s6)),
% 291.92/184.46 inference(unit_resolution,[status(thm)],[14552, 13630, 14543])).
% 291.92/184.46 tff(14554,plain,
% 291.92/184.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s5, s6)) | node6(c_e_h_1, c_g, s5, s6) | node5(c_e_h_1, c_g, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s5, s6)) | node6(c_e_h_1, c_g, s5, s6) | node5(c_e_h_1, c_g, s5, s6))),
% 291.92/184.46 inference(rewrite,[status(thm)],[])).
% 291.92/184.46 tff(14555,plain,
% 291.92/184.46 ((node6(c_e_h_1, c_g, s5, s6) | node5(c_e_h_1, c_g, s5, s6) | (~trans(s5, s6))) <=> ((~trans(s5, s6)) | node6(c_e_h_1, c_g, s5, s6) | node5(c_e_h_1, c_g, s5, s6))),
% 291.92/184.46 inference(rewrite,[status(thm)],[])).
% 291.92/184.46 tff(14556,plain,
% 291.92/184.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_g, s5, s6) | node5(c_e_h_1, c_g, s5, s6) | (~trans(s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s5, s6)) | node6(c_e_h_1, c_g, s5, s6) | node5(c_e_h_1, c_g, s5, s6)))),
% 291.92/184.46 inference(monotonicity,[status(thm)],[14555])).
% 291.92/184.46 tff(14557,plain,
% 291.92/184.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_g, s5, s6) | node5(c_e_h_1, c_g, s5, s6) | (~trans(s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s5, s6)) | node6(c_e_h_1, c_g, s5, s6) | node5(c_e_h_1, c_g, s5, s6))),
% 291.92/184.46 inference(transitivity,[status(thm)],[14556, 14554])).
% 291.92/184.46 tff(14558,plain,
% 291.92/184.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_g, s5, s6) | node5(c_e_h_1, c_g, s5, s6) | (~trans(s5, s6)))),
% 291.92/184.47 inference(quant_inst,[status(thm)],[])).
% 291.92/184.47 tff(14559,plain,
% 291.92/184.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s5, s6)) | node6(c_e_h_1, c_g, s5, s6) | node5(c_e_h_1, c_g, s5, s6)),
% 291.92/184.47 inference(modus_ponens,[status(thm)],[14558, 14557])).
% 291.92/184.47 tff(14560,plain,
% 291.92/184.47 (node6(c_e_h_1, c_g, s5, s6) | node5(c_e_h_1, c_g, s5, s6)),
% 291.92/184.47 inference(unit_resolution,[status(thm)],[14559, 1141, 1406])).
% 291.92/184.47 tff(14561,plain,
% 291.92/184.47 ($false),
% 291.92/184.47 inference(unit_resolution,[status(thm)],[14560, 14553, 14542])).
% 291.92/184.47 tff(14562,plain,((~m_or_h_gate_v_out(c_e_h_1, c_g, s6)) | m_or_h_gate_v_out(c_e_h_1, c_g, s5) | m_or_h_gate_v_in2(c_e_h_1, c_g, s5) | m_or_h_gate_v_in1(c_e_h_1, c_g, s5)), inference(lemma,lemma(discharge,[]))).
% 291.92/184.47 tff(14563,plain,
% 291.92/184.47 (m_or_h_gate_v_out(c_e_h_1, c_g, s5)),
% 291.92/184.47 inference(unit_resolution,[status(thm)],[14562, 14531, 14101, 13630])).
% 291.92/184.47 tff(14564,assumption,(m_or_h_gate_v_in2(c_e_h_1, c_g, s4)), introduced(assumption)).
% 291.92/184.47 tff(14565,plain,
% 291.92/184.47 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_g, s4)) | m_and_h_gate_v_out(c_e_h_1, c_d, s4))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_g, s4)) | m_and_h_gate_v_out(c_e_h_1, c_d, s4))),
% 291.92/184.47 inference(rewrite,[status(thm)],[])).
% 291.92/184.47 tff(14566,plain,
% 291.92/184.47 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_g, s4)) | m_and_h_gate_v_out(c_e_h_1, c_d, s4))),
% 291.92/184.47 inference(quant_inst,[status(thm)],[])).
% 291.92/184.47 tff(14567,plain,
% 291.92/184.47 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_g, s4)) | m_and_h_gate_v_out(c_e_h_1, c_d, s4)),
% 291.92/184.47 inference(modus_ponens,[status(thm)],[14566, 14565])).
% 291.92/184.47 tff(14568,plain,
% 291.92/184.47 ($false),
% 291.92/184.47 inference(unit_resolution,[status(thm)],[14567, 2762, 14077, 14564])).
% 291.92/184.47 tff(14569,plain,(m_and_h_gate_v_out(c_e_h_1, c_d, s4) | (~m_or_h_gate_v_in2(c_e_h_1, c_g, s4))), inference(lemma,lemma(discharge,[]))).
% 291.92/184.47 tff(14570,plain,
% 291.92/184.47 (~m_or_h_gate_v_in2(c_e_h_1, c_g, s4)),
% 291.92/184.47 inference(unit_resolution,[status(thm)],[14569, 14064])).
% 291.92/184.47 tff(14571,assumption,(m_or_h_gate_v_out(c_e_h_1, c_g, s5)), introduced(assumption)).
% 291.92/184.47 tff(14572,assumption,(~m_or_h_gate_v_out(c_e_h_1, c_g, s4)), introduced(assumption)).
% 291.92/184.47 tff(14573,assumption,(~m_or_h_gate_v_in2(c_e_h_1, c_g, s4)), introduced(assumption)).
% 291.92/184.47 tff(14574,assumption,(~m_or_h_gate_v_in1(c_e_h_1, c_g, s4)), introduced(assumption)).
% 291.92/184.47 tff(14575,assumption,(node5(c_e_h_1, c_g, s4, s5)), introduced(assumption)).
% 291.92/184.47 tff(14576,plain,
% 291.92/184.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_1, c_g, s4) | m_or_h_gate_v_in1(c_e_h_1, c_g, s4) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s5)) | (~node5(c_e_h_1, c_g, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_1, c_g, s4) | m_or_h_gate_v_in1(c_e_h_1, c_g, s4) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s5)) | (~node5(c_e_h_1, c_g, s4, s5)))),
% 291.92/184.47 inference(rewrite,[status(thm)],[])).
% 291.92/184.47 tff(14577,plain,
% 291.92/184.47 ((m_or_h_gate_v_in1(c_e_h_1, c_g, s4) | m_or_h_gate_v_in2(c_e_h_1, c_g, s4) | (~node5(c_e_h_1, c_g, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s5))) <=> (m_or_h_gate_v_in2(c_e_h_1, c_g, s4) | m_or_h_gate_v_in1(c_e_h_1, c_g, s4) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s5)) | (~node5(c_e_h_1, c_g, s4, s5)))),
% 291.92/184.47 inference(rewrite,[status(thm)],[])).
% 291.92/184.47 tff(14578,plain,
% 291.92/184.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_g, s4) | m_or_h_gate_v_in2(c_e_h_1, c_g, s4) | (~node5(c_e_h_1, c_g, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_1, c_g, s4) | m_or_h_gate_v_in1(c_e_h_1, c_g, s4) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s5)) | (~node5(c_e_h_1, c_g, s4, s5))))),
% 291.92/184.47 inference(monotonicity,[status(thm)],[14577])).
% 291.92/184.47 tff(14579,plain,
% 291.92/184.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_g, s4) | m_or_h_gate_v_in2(c_e_h_1, c_g, s4) | (~node5(c_e_h_1, c_g, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_1, c_g, s4) | m_or_h_gate_v_in1(c_e_h_1, c_g, s4) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s5)) | (~node5(c_e_h_1, c_g, s4, s5)))),
% 291.92/184.47 inference(transitivity,[status(thm)],[14578, 14576])).
% 291.92/184.47 tff(14580,plain,
% 291.92/184.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_g, s4) | m_or_h_gate_v_in2(c_e_h_1, c_g, s4) | (~node5(c_e_h_1, c_g, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s5)))),
% 291.92/184.47 inference(quant_inst,[status(thm)],[])).
% 291.92/184.47 tff(14581,plain,
% 291.92/184.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_1, c_g, s4) | m_or_h_gate_v_in1(c_e_h_1, c_g, s4) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s5)) | (~node5(c_e_h_1, c_g, s4, s5))),
% 291.92/184.47 inference(modus_ponens,[status(thm)],[14580, 14579])).
% 291.92/184.47 tff(14582,plain,
% 291.92/184.47 ($false),
% 291.92/184.47 inference(unit_resolution,[status(thm)],[14581, 1159, 14575, 14571, 14574, 14573])).
% 291.92/184.47 tff(14583,plain,((~node5(c_e_h_1, c_g, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s5)) | m_or_h_gate_v_in1(c_e_h_1, c_g, s4) | m_or_h_gate_v_in2(c_e_h_1, c_g, s4)), inference(lemma,lemma(discharge,[]))).
% 291.92/184.47 tff(14584,plain,
% 291.92/184.47 (~node5(c_e_h_1, c_g, s4, s5)),
% 291.92/184.47 inference(unit_resolution,[status(thm)],[14583, 14571, 14574, 14573])).
% 291.92/184.47 tff(14585,plain,
% 291.92/184.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s4, s5)) | node6(c_e_h_1, c_g, s4, s5) | node5(c_e_h_1, c_g, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s4, s5)) | node6(c_e_h_1, c_g, s4, s5) | node5(c_e_h_1, c_g, s4, s5))),
% 291.92/184.47 inference(rewrite,[status(thm)],[])).
% 291.92/184.47 tff(14586,plain,
% 291.92/184.47 ((node6(c_e_h_1, c_g, s4, s5) | node5(c_e_h_1, c_g, s4, s5) | (~trans(s4, s5))) <=> ((~trans(s4, s5)) | node6(c_e_h_1, c_g, s4, s5) | node5(c_e_h_1, c_g, s4, s5))),
% 291.92/184.47 inference(rewrite,[status(thm)],[])).
% 291.92/184.47 tff(14587,plain,
% 291.92/184.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_g, s4, s5) | node5(c_e_h_1, c_g, s4, s5) | (~trans(s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s4, s5)) | node6(c_e_h_1, c_g, s4, s5) | node5(c_e_h_1, c_g, s4, s5)))),
% 291.92/184.47 inference(monotonicity,[status(thm)],[14586])).
% 291.92/184.47 tff(14588,plain,
% 291.92/184.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_g, s4, s5) | node5(c_e_h_1, c_g, s4, s5) | (~trans(s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s4, s5)) | node6(c_e_h_1, c_g, s4, s5) | node5(c_e_h_1, c_g, s4, s5))),
% 291.92/184.47 inference(transitivity,[status(thm)],[14587, 14585])).
% 291.92/184.47 tff(14589,plain,
% 291.92/184.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_g, s4, s5) | node5(c_e_h_1, c_g, s4, s5) | (~trans(s4, s5)))),
% 291.92/184.47 inference(quant_inst,[status(thm)],[])).
% 291.92/184.47 tff(14590,plain,
% 291.92/184.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s4, s5)) | node6(c_e_h_1, c_g, s4, s5) | node5(c_e_h_1, c_g, s4, s5)),
% 291.92/184.47 inference(modus_ponens,[status(thm)],[14589, 14588])).
% 291.92/184.47 tff(14591,plain,
% 291.92/184.47 (node6(c_e_h_1, c_g, s4, s5) | node5(c_e_h_1, c_g, s4, s5)),
% 291.92/184.47 inference(unit_resolution,[status(thm)],[14590, 1141, 1028])).
% 291.92/184.47 tff(14592,plain,
% 291.92/184.47 (node6(c_e_h_1, c_g, s4, s5)),
% 291.92/184.47 inference(unit_resolution,[status(thm)],[14591, 14584])).
% 291.92/184.47 tff(14593,plain,
% 291.92/184.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_g, s4) | (~node6(c_e_h_1, c_g, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_g, s4) | (~node6(c_e_h_1, c_g, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s5)))),
% 291.92/184.47 inference(rewrite,[status(thm)],[])).
% 291.92/184.47 tff(14594,plain,
% 291.92/184.47 (((~node6(c_e_h_1, c_g, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s5)) | m_or_h_gate_v_out(c_e_h_1, c_g, s4)) <=> (m_or_h_gate_v_out(c_e_h_1, c_g, s4) | (~node6(c_e_h_1, c_g, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s5)))),
% 291.92/184.47 inference(rewrite,[status(thm)],[])).
% 291.92/184.47 tff(14595,plain,
% 291.92/184.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_g, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s5)) | m_or_h_gate_v_out(c_e_h_1, c_g, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_g, s4) | (~node6(c_e_h_1, c_g, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s5))))),
% 291.92/184.47 inference(monotonicity,[status(thm)],[14594])).
% 291.92/184.47 tff(14596,plain,
% 291.92/184.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_g, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s5)) | m_or_h_gate_v_out(c_e_h_1, c_g, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_g, s4) | (~node6(c_e_h_1, c_g, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s5)))),
% 291.92/184.47 inference(transitivity,[status(thm)],[14595, 14593])).
% 291.92/184.47 tff(14597,plain,
% 291.92/184.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_g, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s5)) | m_or_h_gate_v_out(c_e_h_1, c_g, s4))),
% 291.92/184.47 inference(quant_inst,[status(thm)],[])).
% 291.92/184.47 tff(14598,plain,
% 291.92/184.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_g, s4) | (~node6(c_e_h_1, c_g, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s5))),
% 291.92/184.47 inference(modus_ponens,[status(thm)],[14597, 14596])).
% 291.92/184.47 tff(14599,plain,
% 291.92/184.47 ($false),
% 291.92/184.47 inference(unit_resolution,[status(thm)],[14598, 1121, 14592, 14572, 14571])).
% 291.92/184.47 tff(14600,plain,((~m_or_h_gate_v_out(c_e_h_1, c_g, s5)) | m_or_h_gate_v_out(c_e_h_1, c_g, s4) | m_or_h_gate_v_in1(c_e_h_1, c_g, s4) | m_or_h_gate_v_in2(c_e_h_1, c_g, s4)), inference(lemma,lemma(discharge,[]))).
% 291.92/184.47 tff(14601,plain,
% 291.92/184.47 ((~m_or_h_gate_v_out(c_e_h_1, c_g, s5)) | m_or_h_gate_v_out(c_e_h_1, c_g, s4) | m_or_h_gate_v_in1(c_e_h_1, c_g, s4)),
% 291.92/184.47 inference(unit_resolution,[status(thm)],[14600, 14570])).
% 291.92/184.47 tff(14602,plain,
% 291.92/184.47 ($false),
% 291.92/184.47 inference(unit_resolution,[status(thm)],[14601, 14563, 14504, 14125])).
% 291.92/184.47 tff(14603,plain,(m_and_h_gate_v_out(c_e_h_1, c_c, s4) | m_or_h_gate_v_in2(c_e_h_1, c_g, s5) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s6)) | node20(c_e_h_1, c_c, s4)), inference(lemma,lemma(discharge,[]))).
% 291.92/184.47 tff(14604,plain,
% 291.92/184.47 (m_and_h_gate_v_out(c_e_h_1, c_c, s4)),
% 291.92/184.47 inference(unit_resolution,[status(thm)],[14603, 14117, 13630, 14101])).
% 291.92/184.48 tff(14605,assumption,(m_and_h_gate_v_out(c_e_h_1, c_c, s4)), introduced(assumption)).
% 291.92/184.48 tff(14606,assumption,(m_mutex_h_half_v_out(c_e_h_1, c_a, s3)), introduced(assumption)).
% 291.92/184.48 tff(14607,plain,
% 291.92/184.48 (((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | ((~m_mutex_h_half_v_inp(c_e_h_1, c_a, s2)) | m_user_v_req(c_e_h_1, c_u, s2))) <=> ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s2)) | m_user_v_req(c_e_h_1, c_u, s2))),
% 291.92/184.48 inference(rewrite,[status(thm)],[])).
% 291.92/184.48 tff(14608,plain,
% 291.92/184.48 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | ((~m_mutex_h_half_v_inp(c_e_h_1, c_a, s2)) | m_user_v_req(c_e_h_1, c_u, s2))),
% 291.92/184.48 inference(quant_inst,[status(thm)],[])).
% 291.92/184.48 tff(14609,plain,
% 291.92/184.48 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s2)) | m_user_v_req(c_e_h_1, c_u, s2)),
% 291.92/184.48 inference(modus_ponens,[status(thm)],[14608, 14607])).
% 291.92/184.48 tff(14610,plain,
% 291.92/184.48 (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s2)),
% 291.92/184.48 inference(unit_resolution,[status(thm)],[14609, 395, 14264])).
% 291.92/184.48 tff(14611,assumption,(node12(c_e_h_1, c_a, s2, s3)), introduced(assumption)).
% 291.92/184.48 tff(14612,plain,
% 291.92/184.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~m_mutex_h_half_v_out(c_e_h_1, c_a, s3)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s2) | (~node12(c_e_h_1, c_a, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s3)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s2) | (~node12(c_e_h_1, c_a, s2, s3)))),
% 291.92/184.48 inference(rewrite,[status(thm)],[])).
% 291.92/184.48 tff(14613,plain,
% 291.92/184.48 (((~node12(c_e_h_1, c_a, s2, s3)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s2) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s3))) <=> ((~m_mutex_h_half_v_out(c_e_h_1, c_a, s3)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s2) | (~node12(c_e_h_1, c_a, s2, s3)))),
% 291.92/184.48 inference(rewrite,[status(thm)],[])).
% 291.92/184.48 tff(14614,plain,
% 291.92/184.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_1, c_a, s2, s3)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s2) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~m_mutex_h_half_v_out(c_e_h_1, c_a, s3)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s2) | (~node12(c_e_h_1, c_a, s2, s3))))),
% 291.92/184.48 inference(monotonicity,[status(thm)],[14613])).
% 291.92/184.48 tff(14615,plain,
% 291.92/184.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_1, c_a, s2, s3)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s2) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s3)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s2) | (~node12(c_e_h_1, c_a, s2, s3)))),
% 291.92/184.48 inference(transitivity,[status(thm)],[14614, 14612])).
% 291.92/184.48 tff(14616,plain,
% 291.92/184.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_1, c_a, s2, s3)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s2) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s3)))),
% 291.92/184.48 inference(quant_inst,[status(thm)],[])).
% 291.92/184.48 tff(14617,plain,
% 291.92/184.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s3)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s2) | (~node12(c_e_h_1, c_a, s2, s3))),
% 291.92/184.48 inference(modus_ponens,[status(thm)],[14616, 14615])).
% 291.92/184.48 tff(14618,plain,
% 291.92/184.48 ($false),
% 291.92/184.48 inference(unit_resolution,[status(thm)],[14617, 454, 14606, 14611, 14350])).
% 291.92/184.48 tff(14619,plain,((~node12(c_e_h_1, c_a, s2, s3)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s3)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s2)), inference(lemma,lemma(discharge,[]))).
% 291.92/184.48 tff(14620,plain,
% 291.92/184.48 (~node12(c_e_h_1, c_a, s2, s3)),
% 291.92/184.48 inference(unit_resolution,[status(thm)],[14619, 14606, 14350])).
% 291.92/184.48 tff(14621,plain,
% 291.92/184.48 (node13(c_e_h_1, c_a, s2, s3)),
% 291.92/184.48 inference(unit_resolution,[status(thm)],[14372, 14620])).
% 291.92/184.48 tff(14622,plain,
% 291.92/184.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_1, c_a, s3)) | (~node13(c_e_h_1, c_a, s2, s3)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s3)) | (~node13(c_e_h_1, c_a, s2, s3)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s2))),
% 291.92/184.48 inference(rewrite,[status(thm)],[])).
% 291.92/184.48 tff(14623,plain,
% 291.92/184.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_1, c_a, s3)) | (~node13(c_e_h_1, c_a, s2, s3)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s2))),
% 291.92/184.48 inference(quant_inst,[status(thm)],[])).
% 291.92/184.48 tff(14624,plain,
% 291.92/184.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s3)) | (~node13(c_e_h_1, c_a, s2, s3)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s2)),
% 291.92/184.48 inference(modus_ponens,[status(thm)],[14623, 14622])).
% 291.92/184.48 tff(14625,plain,
% 291.92/184.48 ($false),
% 291.92/184.48 inference(unit_resolution,[status(thm)],[14624, 423, 14606, 14621, 14227])).
% 291.92/184.48 tff(14626,plain,((~m_mutex_h_half_v_out(c_e_h_1, c_a, s3)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s2) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s2)), inference(lemma,lemma(discharge,[]))).
% 291.92/184.48 tff(14627,plain,
% 291.92/184.48 (m_mutex_h_half_v_out(c_e_h_1, c_a, s2)),
% 291.92/184.48 inference(unit_resolution,[status(thm)],[14626, 14610, 14606])).
% 291.92/184.48 tff(14628,plain,
% 291.92/184.48 (m_mutex_h_half_v_inp(c_e_h_1, c_a, s1)),
% 291.92/184.48 inference(unit_resolution,[status(thm)],[14258, 14627])).
% 291.92/184.48 tff(14629,plain,
% 291.92/184.48 (node8(c_e_h_1, c_u, s1, s2)),
% 291.92/184.48 inference(unit_resolution,[status(thm)],[14346, 14331])).
% 291.92/184.48 tff(14630,plain,
% 291.92/184.48 (~m_user_v_req(c_e_h_1, c_u, s1)),
% 291.92/184.48 inference(unit_resolution,[status(thm)],[14341, 14629, 14264])).
% 291.92/184.48 tff(14631,plain,
% 291.92/184.48 ($false),
% 291.92/184.48 inference(unit_resolution,[status(thm)],[14262, 395, 14630, 14628])).
% 291.92/184.48 tff(14632,plain,(m_user_v_req(c_e_h_1, c_u, s2) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s3))), inference(lemma,lemma(discharge,[]))).
% 291.92/184.48 tff(14633,plain,
% 291.92/184.48 (~m_mutex_h_half_v_out(c_e_h_1, c_a, s3)),
% 291.92/184.48 inference(unit_resolution,[status(thm)],[14632, 14264])).
% 291.92/184.48 tff(14634,plain,
% 291.92/184.48 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_c, s3)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s3))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s3)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s3))),
% 291.92/184.48 inference(rewrite,[status(thm)],[])).
% 291.92/184.48 tff(14635,plain,
% 291.92/184.48 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_c, s3)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s3))),
% 291.92/184.48 inference(quant_inst,[status(thm)],[])).
% 291.92/184.48 tff(14636,plain,
% 291.92/184.48 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s3)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s3)),
% 291.92/184.48 inference(modus_ponens,[status(thm)],[14635, 14634])).
% 291.92/184.48 tff(14637,plain,
% 291.92/184.48 ($false),
% 291.92/184.48 inference(unit_resolution,[status(thm)],[14636, 567, 14358, 14396])).
% 291.92/184.48 tff(14638,plain,((~m_and_h_gate_v_in1(c_e_h_1, c_c, s3)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s3)), inference(lemma,lemma(discharge,[]))).
% 291.92/184.48 tff(14639,plain,
% 291.92/184.48 (~m_and_h_gate_v_in1(c_e_h_1, c_c, s3)),
% 291.92/184.48 inference(unit_resolution,[status(thm)],[14638, 14633])).
% 291.92/184.48 tff(14640,assumption,(node20(c_e_h_1, c_c, s3)), introduced(assumption)).
% 291.92/184.48 tff(14641,assumption,(~m_and_h_gate_v_in1(c_e_h_1, c_c, s3)), introduced(assumption)).
% 291.92/184.48 tff(14642,plain,
% 291.92/184.48 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_c, s3)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_c, s3)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s3))),
% 291.92/184.48 inference(rewrite,[status(thm)],[])).
% 291.92/184.48 tff(14643,plain,
% 291.92/184.48 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_c, s3)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s3))),
% 291.92/184.48 inference(quant_inst,[status(thm)],[])).
% 291.92/184.48 tff(14644,plain,
% 291.92/184.48 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_c, s3)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s3)),
% 291.92/184.48 inference(modus_ponens,[status(thm)],[14643, 14642])).
% 291.92/184.48 tff(14645,plain,
% 291.92/184.48 ($false),
% 291.92/184.48 inference(unit_resolution,[status(thm)],[14644, 38, 14641, 14640])).
% 291.92/184.48 tff(14646,plain,((~node20(c_e_h_1, c_c, s3)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s3)), inference(lemma,lemma(discharge,[]))).
% 291.92/184.48 tff(14647,plain,
% 291.92/184.48 (~node20(c_e_h_1, c_c, s3)),
% 291.92/184.48 inference(unit_resolution,[status(thm)],[14646, 14639])).
% 291.92/184.48 tff(14648,assumption,(~node20(c_e_h_1, c_c, s3)), introduced(assumption)).
% 291.92/184.48 tff(14649,plain,
% 291.92/184.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_c, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s4)) | (~node21(c_e_h_1, c_c, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_c, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s4)) | (~node21(c_e_h_1, c_c, s3, s4)))),
% 291.92/184.48 inference(rewrite,[status(thm)],[])).
% 291.92/184.48 tff(14650,plain,
% 291.92/184.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_c, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s4)) | (~node21(c_e_h_1, c_c, s3, s4)))),
% 291.92/184.48 inference(quant_inst,[status(thm)],[])).
% 291.92/184.48 tff(14651,plain,
% 291.92/184.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_c, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s4)) | (~node21(c_e_h_1, c_c, s3, s4))),
% 291.92/184.48 inference(modus_ponens,[status(thm)],[14650, 14649])).
% 291.92/184.48 tff(14652,plain,
% 291.92/184.48 ($false),
% 291.92/184.48 inference(unit_resolution,[status(thm)],[14651, 52, 14397, 14605, 14648])).
% 291.92/184.48 tff(14653,plain,((~node21(c_e_h_1, c_c, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s4)) | node20(c_e_h_1, c_c, s3)), inference(lemma,lemma(discharge,[]))).
% 291.92/184.48 tff(14654,plain,
% 291.92/184.48 (~node21(c_e_h_1, c_c, s3, s4)),
% 291.92/184.48 inference(unit_resolution,[status(thm)],[14653, 14605, 14648])).
% 291.92/184.48 tff(14655,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_c, s3)), introduced(assumption)).
% 291.92/184.48 tff(14656,plain,
% 291.92/184.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_c, s4)) | (~node22(c_e_h_1, c_c, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_c, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s4)) | (~node22(c_e_h_1, c_c, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_c, s3))),
% 291.92/184.48 inference(rewrite,[status(thm)],[])).
% 291.92/184.48 tff(14657,plain,
% 291.92/184.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_c, s4)) | (~node22(c_e_h_1, c_c, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_c, s3))),
% 291.92/184.48 inference(quant_inst,[status(thm)],[])).
% 291.92/184.48 tff(14658,plain,
% 291.92/184.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s4)) | (~node22(c_e_h_1, c_c, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_c, s3)),
% 291.92/184.49 inference(modus_ponens,[status(thm)],[14657, 14656])).
% 291.92/184.49 tff(14659,plain,
% 291.92/184.49 ($false),
% 291.92/184.49 inference(unit_resolution,[status(thm)],[14658, 108, 14127, 14605, 14655])).
% 291.92/184.49 tff(14660,plain,((~node22(c_e_h_1, c_c, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s4)) | m_and_h_gate_v_out(c_e_h_1, c_c, s3)), inference(lemma,lemma(discharge,[]))).
% 291.92/184.49 tff(14661,plain,
% 291.92/184.49 (~node22(c_e_h_1, c_c, s3, s4)),
% 291.92/184.49 inference(unit_resolution,[status(thm)],[14660, 14605, 14655])).
% 291.92/184.49 tff(14662,plain,
% 291.92/184.49 ($false),
% 291.92/184.49 inference(unit_resolution,[status(thm)],[14412, 14661, 14654])).
% 291.92/184.49 tff(14663,plain,((~m_and_h_gate_v_out(c_e_h_1, c_c, s4)) | m_and_h_gate_v_out(c_e_h_1, c_c, s3) | node20(c_e_h_1, c_c, s3)), inference(lemma,lemma(discharge,[]))).
% 291.92/184.49 tff(14664,plain,
% 291.92/184.49 (m_and_h_gate_v_out(c_e_h_1, c_c, s3)),
% 291.92/184.49 inference(unit_resolution,[status(thm)],[14663, 14647, 14605])).
% 291.92/184.49 tff(14665,plain,
% 291.92/184.49 (node20(c_e_h_1, c_c, s2)),
% 291.92/184.49 inference(unit_resolution,[status(thm)],[14216, 14664])).
% 291.92/184.49 tff(14666,plain,
% 291.92/184.49 (m_and_h_gate_v_in1(c_e_h_1, c_c, s2)),
% 291.92/184.49 inference(unit_resolution,[status(thm)],[14224, 14665])).
% 291.92/184.49 tff(14667,plain,
% 291.92/184.49 (m_mutex_h_half_v_out(c_e_h_1, c_a, s2)),
% 291.92/184.49 inference(unit_resolution,[status(thm)],[14232, 14666])).
% 291.92/184.49 tff(14668,plain,
% 291.92/184.49 (m_mutex_h_half_v_inp(c_e_h_1, c_a, s1)),
% 291.92/184.49 inference(unit_resolution,[status(thm)],[14258, 14667])).
% 291.92/184.49 tff(14669,plain,
% 291.92/184.49 (~m_user_v_req(c_e_h_1, c_u, s1)),
% 291.92/184.49 inference(unit_resolution,[status(thm)],[14348, 14264])).
% 291.92/184.49 tff(14670,plain,
% 291.92/184.49 ($false),
% 291.92/184.49 inference(unit_resolution,[status(thm)],[14262, 395, 14669, 14668])).
% 291.92/184.49 tff(14671,plain,(m_user_v_req(c_e_h_1, c_u, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s4))), inference(lemma,lemma(discharge,[]))).
% 291.92/184.49 tff(14672,plain,
% 291.92/184.49 (m_user_v_req(c_e_h_1, c_u, s2)),
% 291.92/184.49 inference(unit_resolution,[status(thm)],[14671, 14604])).
% 291.92/184.49 tff(14673,assumption,(~m_user_v_req(c_e_h_1, c_u, s3)), introduced(assumption)).
% 291.92/184.49 tff(14674,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s2)), introduced(assumption)).
% 291.92/184.49 tff(14675,assumption,(node21(c_e_h_1, c_r, s1, s2)), introduced(assumption)).
% 291.92/184.49 tff(14676,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)), introduced(assumption)).
% 291.92/184.49 tff(14677,assumption,(node10(c_e_h_1, c_m, s0, s1)), introduced(assumption)).
% 291.92/184.49 tff(14678,plain,
% 291.92/184.49 (((~![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))) | (m_cell_v_token(c_e_h_1, s0) | m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_n, s0))) <=> ((~![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))) | m_cell_v_token(c_e_h_1, s0) | m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_n, s0))),
% 291.92/184.49 inference(rewrite,[status(thm)],[])).
% 291.92/184.49 tff(14679,plain,
% 291.92/184.49 ((~![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))) | (m_cell_v_token(c_e_h_1, s0) | m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_n, s0))),
% 291.92/184.49 inference(quant_inst,[status(thm)],[])).
% 291.92/184.49 tff(14680,plain,
% 291.92/184.49 ((~![I0: $i, X: $i] : (m_cell_v_token(I0, X) | m_and_h_gate_h_init_v_init_h_out(I0, c_n, X))) | m_cell_v_token(c_e_h_1, s0) | m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_n, s0)),
% 291.92/184.49 inference(modus_ponens,[status(thm)],[14679, 14678])).
% 291.92/184.49 tff(14681,plain,
% 291.92/184.49 (m_cell_v_token(c_e_h_1, s0) | m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_n, s0)),
% 291.92/184.49 inference(unit_resolution,[status(thm)],[14680, 4932])).
% 291.92/184.49 tff(14682,plain,
% 291.92/184.49 (m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_n, s0)),
% 291.92/184.49 inference(unit_resolution,[status(thm)],[14681, 14278])).
% 291.92/184.49 tff(14683,plain,
% 291.92/184.49 (((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0))) | ((~m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0))) <=> ((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0))) | (~m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0))),
% 291.92/184.49 inference(rewrite,[status(thm)],[])).
% 291.92/184.49 tff(14684,plain,
% 291.92/184.49 ((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0))) | ((~m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0))),
% 291.92/184.49 inference(quant_inst,[status(thm)],[])).
% 291.92/184.49 tff(14685,plain,
% 291.92/184.49 ((~![I0: $i, I1: $i] : ((~m_and_h_gate_h_init_v_init_h_out(I0, I1, s0)) | m_and_h_gate_h_init_v_out(I0, I1, s0))) | (~m_and_h_gate_h_init_v_init_h_out(c_e_h_1, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0)),
% 291.92/184.49 inference(modus_ponens,[status(thm)],[14684, 14683])).
% 291.92/184.49 tff(14686,plain,
% 291.92/184.49 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0)),
% 291.92/184.49 inference(unit_resolution,[status(thm)],[14685, 4946, 14682])).
% 291.92/184.49 tff(14687,plain,
% 291.92/184.49 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s0)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s0)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0)))),
% 291.92/184.49 inference(rewrite,[status(thm)],[])).
% 291.92/184.49 tff(14688,plain,
% 291.92/184.49 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s0)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0)))),
% 291.92/184.49 inference(quant_inst,[status(thm)],[])).
% 291.92/184.49 tff(14689,plain,
% 291.92/184.49 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s0)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0))),
% 291.92/184.49 inference(modus_ponens,[status(thm)],[14688, 14687])).
% 291.92/184.49 tff(14690,plain,
% 291.92/184.49 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s0)),
% 291.92/184.49 inference(unit_resolution,[status(thm)],[14689, 4958, 14686])).
% 291.92/184.49 tff(14691,plain,
% 291.92/184.49 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s0)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s0)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s0))),
% 291.92/184.49 inference(rewrite,[status(thm)],[])).
% 291.92/184.49 tff(14692,plain,
% 291.92/184.49 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s0)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s0))),
% 291.92/184.49 inference(quant_inst,[status(thm)],[])).
% 291.92/184.49 tff(14693,plain,
% 291.92/184.49 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s0)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s0)),
% 291.92/184.49 inference(modus_ponens,[status(thm)],[14692, 14691])).
% 291.92/184.49 tff(14694,plain,
% 291.92/184.49 (~node9(c_e_h_1, c_m, s0)),
% 291.92/184.49 inference(unit_resolution,[status(thm)],[14693, 4972, 14690])).
% 291.92/184.49 tff(14695,plain,
% 291.92/184.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s0) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)) | (~node10(c_e_h_1, c_m, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_1, c_m, s0) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)) | (~node10(c_e_h_1, c_m, s0, s1)))),
% 291.92/184.49 inference(rewrite,[status(thm)],[])).
% 291.92/184.49 tff(14696,plain,
% 291.92/184.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s0) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)) | (~node10(c_e_h_1, c_m, s0, s1)))),
% 291.92/184.49 inference(quant_inst,[status(thm)],[])).
% 291.92/184.49 tff(14697,plain,
% 291.92/184.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_1, c_m, s0) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)) | (~node10(c_e_h_1, c_m, s0, s1))),
% 291.92/184.49 inference(modus_ponens,[status(thm)],[14696, 14695])).
% 291.92/184.49 tff(14698,plain,
% 291.92/184.49 ($false),
% 291.92/184.49 inference(unit_resolution,[status(thm)],[14697, 4986, 14694, 14676, 14677])).
% 291.92/184.49 tff(14699,plain,((~node10(c_e_h_1, c_m, s0, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1))), inference(lemma,lemma(discharge,[]))).
% 291.92/184.49 tff(14700,plain,
% 291.92/184.49 (~node10(c_e_h_1, c_m, s0, s1)),
% 291.92/184.49 inference(unit_resolution,[status(thm)],[14699, 14676])).
% 291.92/184.49 tff(14701,plain,
% 291.92/184.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s0, s1)) | node10(c_e_h_1, c_m, s0, s1) | node11(c_e_h_1, c_m, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s0, s1)) | node10(c_e_h_1, c_m, s0, s1) | node11(c_e_h_1, c_m, s0, s1))),
% 291.92/184.49 inference(rewrite,[status(thm)],[])).
% 291.92/184.49 tff(14702,plain,
% 291.92/184.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s0, s1)) | node10(c_e_h_1, c_m, s0, s1) | node11(c_e_h_1, c_m, s0, s1))),
% 291.92/184.49 inference(quant_inst,[status(thm)],[])).
% 291.92/184.49 tff(14703,plain,
% 291.92/184.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s0, s1)) | node10(c_e_h_1, c_m, s0, s1) | node11(c_e_h_1, c_m, s0, s1)),
% 291.92/184.49 inference(modus_ponens,[status(thm)],[14702, 14701])).
% 291.92/184.49 tff(14704,plain,
% 291.92/184.49 (node10(c_e_h_1, c_m, s0, s1) | node11(c_e_h_1, c_m, s0, s1)),
% 291.92/184.49 inference(unit_resolution,[status(thm)],[14703, 5002, 72])).
% 291.92/184.49 tff(14705,plain,
% 291.92/184.49 (node11(c_e_h_1, c_m, s0, s1)),
% 291.92/184.49 inference(unit_resolution,[status(thm)],[14704, 14700])).
% 291.92/184.49 tff(14706,plain,
% 291.92/184.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)) | (~node11(c_e_h_1, c_m, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)) | (~node11(c_e_h_1, c_m, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0))),
% 291.92/184.49 inference(rewrite,[status(thm)],[])).
% 291.92/184.49 tff(14707,plain,
% 291.92/184.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)) | (~node11(c_e_h_1, c_m, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0))),
% 291.92/184.49 inference(quant_inst,[status(thm)],[])).
% 291.92/184.49 tff(14708,plain,
% 291.92/184.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)) | (~node11(c_e_h_1, c_m, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0)),
% 291.92/184.49 inference(modus_ponens,[status(thm)],[14707, 14706])).
% 291.92/184.49 tff(14709,plain,
% 291.92/184.49 ($false),
% 291.92/184.49 inference(unit_resolution,[status(thm)],[14708, 5017, 14286, 14676, 14705])).
% 291.92/184.49 tff(14710,plain,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)), inference(lemma,lemma(discharge,[]))).
% 291.92/184.49 tff(14711,plain,
% 291.92/184.49 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1))),
% 291.92/184.49 inference(rewrite,[status(thm)],[])).
% 291.92/184.49 tff(14712,plain,
% 291.92/184.49 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1))),
% 291.92/184.49 inference(quant_inst,[status(thm)],[])).
% 291.92/184.49 tff(14713,plain,
% 291.92/184.49 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)),
% 291.92/184.49 inference(modus_ponens,[status(thm)],[14712, 14711])).
% 292.01/184.50 tff(14714,plain,
% 292.01/184.50 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s1)),
% 292.01/184.50 inference(unit_resolution,[status(thm)],[14713, 14293, 14710])).
% 292.01/184.50 tff(14715,plain,
% 292.01/184.50 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s1)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s1)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s1))),
% 292.01/184.50 inference(rewrite,[status(thm)],[])).
% 292.01/184.50 tff(14716,plain,
% 292.01/184.50 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s1)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s1))),
% 292.01/184.50 inference(quant_inst,[status(thm)],[])).
% 292.01/184.50 tff(14717,plain,
% 292.01/184.50 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s1)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s1)),
% 292.01/184.50 inference(modus_ponens,[status(thm)],[14716, 14715])).
% 292.01/184.50 tff(14718,plain,
% 292.01/184.50 (~node20(c_e_h_1, c_r, s1)),
% 292.01/184.50 inference(unit_resolution,[status(thm)],[14717, 4563, 14714])).
% 292.01/184.50 tff(14719,plain,
% 292.01/184.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s2)) | (~node21(c_e_h_1, c_r, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s2)) | (~node21(c_e_h_1, c_r, s1, s2)))),
% 292.01/184.50 inference(rewrite,[status(thm)],[])).
% 292.01/184.50 tff(14720,plain,
% 292.01/184.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s2)) | (~node21(c_e_h_1, c_r, s1, s2)))),
% 292.01/184.50 inference(quant_inst,[status(thm)],[])).
% 292.01/184.50 tff(14721,plain,
% 292.01/184.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s2)) | (~node21(c_e_h_1, c_r, s1, s2))),
% 292.01/184.50 inference(modus_ponens,[status(thm)],[14720, 14719])).
% 292.01/184.50 tff(14722,plain,
% 292.01/184.50 ($false),
% 292.01/184.50 inference(unit_resolution,[status(thm)],[14721, 52, 14718, 14675, 14674])).
% 292.01/184.50 tff(14723,plain,((~node21(c_e_h_1, c_r, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s2))), inference(lemma,lemma(discharge,[]))).
% 292.01/184.50 tff(14724,plain,
% 292.01/184.50 (~node21(c_e_h_1, c_r, s1, s2)),
% 292.01/184.50 inference(unit_resolution,[status(thm)],[14723, 14674])).
% 292.01/184.50 tff(14725,plain,
% 292.01/184.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_1, c_r, s1, s2) | node22(c_e_h_1, c_r, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_1, c_r, s1, s2) | node22(c_e_h_1, c_r, s1, s2))),
% 292.01/184.50 inference(rewrite,[status(thm)],[])).
% 292.01/184.50 tff(14726,plain,
% 292.01/184.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_1, c_r, s1, s2) | node22(c_e_h_1, c_r, s1, s2))),
% 292.01/184.50 inference(quant_inst,[status(thm)],[])).
% 292.01/184.50 tff(14727,plain,
% 292.01/184.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_1, c_r, s1, s2) | node22(c_e_h_1, c_r, s1, s2)),
% 292.01/184.50 inference(modus_ponens,[status(thm)],[14726, 14725])).
% 292.01/184.50 tff(14728,plain,
% 292.01/184.50 (node21(c_e_h_1, c_r, s1, s2) | node22(c_e_h_1, c_r, s1, s2)),
% 292.01/184.50 inference(unit_resolution,[status(thm)],[14727, 82, 255])).
% 292.01/184.50 tff(14729,plain,
% 292.01/184.50 (node22(c_e_h_1, c_r, s1, s2)),
% 292.01/184.50 inference(unit_resolution,[status(thm)],[14728, 14724])).
% 292.01/184.50 tff(14730,plain,
% 292.01/184.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s2)) | (~node22(c_e_h_1, c_r, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_r, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s2)) | (~node22(c_e_h_1, c_r, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_r, s1))),
% 292.01/184.50 inference(rewrite,[status(thm)],[])).
% 292.01/184.50 tff(14731,plain,
% 292.01/184.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s2)) | (~node22(c_e_h_1, c_r, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_r, s1))),
% 292.01/184.50 inference(quant_inst,[status(thm)],[])).
% 292.01/184.50 tff(14732,plain,
% 292.01/184.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s2)) | (~node22(c_e_h_1, c_r, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_r, s1)),
% 292.01/184.50 inference(modus_ponens,[status(thm)],[14731, 14730])).
% 292.01/184.50 tff(14733,plain,
% 292.01/184.50 ($false),
% 292.01/184.50 inference(unit_resolution,[status(thm)],[14732, 108, 14729, 14321, 14674])).
% 292.01/184.50 tff(14734,plain,(~m_and_h_gate_v_out(c_e_h_1, c_r, s2)), inference(lemma,lemma(discharge,[]))).
% 292.01/184.50 tff(14735,plain,
% 292.01/184.50 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s2)) | m_and_h_gate_v_out(c_e_h_1, c_r, s2))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s2)) | m_and_h_gate_v_out(c_e_h_1, c_r, s2))),
% 292.01/184.50 inference(rewrite,[status(thm)],[])).
% 292.01/184.50 tff(14736,plain,
% 292.01/184.50 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s2)) | m_and_h_gate_v_out(c_e_h_1, c_r, s2))),
% 292.01/184.50 inference(quant_inst,[status(thm)],[])).
% 292.01/184.50 tff(14737,plain,
% 292.01/184.50 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s2)) | m_and_h_gate_v_out(c_e_h_1, c_r, s2)),
% 292.01/184.50 inference(modus_ponens,[status(thm)],[14736, 14735])).
% 292.01/184.50 tff(14738,plain,
% 292.01/184.50 (~m_user_v_ack(c_e_h_1, c_u, s2)),
% 292.01/184.50 inference(unit_resolution,[status(thm)],[14737, 268, 14734])).
% 292.01/184.50 tff(14739,assumption,(node7(c_e_h_1, c_u, s2, s3)), introduced(assumption)).
% 292.01/184.50 tff(14740,assumption,(~m_user_v_ack(c_e_h_1, c_u, s2)), introduced(assumption)).
% 292.01/184.50 tff(14741,plain,
% 292.01/184.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | ((~node7(c_e_h_1, c_u, s2, s3)) | m_user_v_ack(c_e_h_1, c_u, s2) | m_user_v_req(c_e_h_1, c_u, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | (~node7(c_e_h_1, c_u, s2, s3)) | m_user_v_ack(c_e_h_1, c_u, s2) | m_user_v_req(c_e_h_1, c_u, s3))),
% 292.01/184.50 inference(rewrite,[status(thm)],[])).
% 292.01/184.50 tff(14742,plain,
% 292.01/184.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | ((~node7(c_e_h_1, c_u, s2, s3)) | m_user_v_ack(c_e_h_1, c_u, s2) | m_user_v_req(c_e_h_1, c_u, s3))),
% 292.01/184.50 inference(quant_inst,[status(thm)],[])).
% 292.01/184.50 tff(14743,plain,
% 292.01/184.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | (~node7(c_e_h_1, c_u, s2, s3)) | m_user_v_ack(c_e_h_1, c_u, s2) | m_user_v_req(c_e_h_1, c_u, s3)),
% 292.01/184.50 inference(modus_ponens,[status(thm)],[14742, 14741])).
% 292.01/184.50 tff(14744,plain,
% 292.01/184.50 ($false),
% 292.01/184.50 inference(unit_resolution,[status(thm)],[14743, 284, 14740, 14739, 14673])).
% 292.01/184.50 tff(14745,plain,((~node7(c_e_h_1, c_u, s2, s3)) | m_user_v_ack(c_e_h_1, c_u, s2) | m_user_v_req(c_e_h_1, c_u, s3)), inference(lemma,lemma(discharge,[]))).
% 292.01/184.50 tff(14746,plain,
% 292.01/184.50 ((~node7(c_e_h_1, c_u, s2, s3)) | m_user_v_req(c_e_h_1, c_u, s3)),
% 292.01/184.50 inference(unit_resolution,[status(thm)],[14745, 14738])).
% 292.01/184.50 tff(14747,plain,
% 292.01/184.50 (~node7(c_e_h_1, c_u, s2, s3)),
% 292.01/184.50 inference(unit_resolution,[status(thm)],[14746, 14673])).
% 292.01/184.50 tff(14748,plain,
% 292.01/184.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | ((~trans(s2, s3)) | node7(c_e_h_1, c_u, s2, s3) | node8(c_e_h_1, c_u, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | (~trans(s2, s3)) | node7(c_e_h_1, c_u, s2, s3) | node8(c_e_h_1, c_u, s2, s3))),
% 292.01/184.51 inference(rewrite,[status(thm)],[])).
% 292.01/184.51 tff(14749,plain,
% 292.01/184.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | ((~trans(s2, s3)) | node7(c_e_h_1, c_u, s2, s3) | node8(c_e_h_1, c_u, s2, s3))),
% 292.01/184.51 inference(quant_inst,[status(thm)],[])).
% 292.01/184.51 tff(14750,plain,
% 292.01/184.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | (~trans(s2, s3)) | node7(c_e_h_1, c_u, s2, s3) | node8(c_e_h_1, c_u, s2, s3)),
% 292.01/184.51 inference(modus_ponens,[status(thm)],[14749, 14748])).
% 292.01/184.51 tff(14751,plain,
% 292.01/184.51 (node7(c_e_h_1, c_u, s2, s3) | node8(c_e_h_1, c_u, s2, s3)),
% 292.01/184.51 inference(unit_resolution,[status(thm)],[14750, 328, 318])).
% 292.01/184.51 tff(14752,plain,
% 292.01/184.51 (node8(c_e_h_1, c_u, s2, s3)),
% 292.01/184.51 inference(unit_resolution,[status(thm)],[14751, 14747])).
% 292.01/184.51 tff(14753,plain,
% 292.01/184.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | ((~m_user_v_req(c_e_h_1, c_u, s2)) | m_user_v_req(c_e_h_1, c_u, s3) | (~node8(c_e_h_1, c_u, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (~m_user_v_req(c_e_h_1, c_u, s2)) | m_user_v_req(c_e_h_1, c_u, s3) | (~node8(c_e_h_1, c_u, s2, s3)))),
% 292.01/184.51 inference(rewrite,[status(thm)],[])).
% 292.01/184.51 tff(14754,plain,
% 292.01/184.51 ((m_user_v_req(c_e_h_1, c_u, s3) | (~node8(c_e_h_1, c_u, s2, s3)) | (~m_user_v_req(c_e_h_1, c_u, s2))) <=> ((~m_user_v_req(c_e_h_1, c_u, s2)) | m_user_v_req(c_e_h_1, c_u, s3) | (~node8(c_e_h_1, c_u, s2, s3)))),
% 292.01/184.51 inference(rewrite,[status(thm)],[])).
% 292.01/184.51 tff(14755,plain,
% 292.01/184.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_1, c_u, s3) | (~node8(c_e_h_1, c_u, s2, s3)) | (~m_user_v_req(c_e_h_1, c_u, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | ((~m_user_v_req(c_e_h_1, c_u, s2)) | m_user_v_req(c_e_h_1, c_u, s3) | (~node8(c_e_h_1, c_u, s2, s3))))),
% 292.01/184.51 inference(monotonicity,[status(thm)],[14754])).
% 292.01/184.51 tff(14756,plain,
% 292.01/184.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_1, c_u, s3) | (~node8(c_e_h_1, c_u, s2, s3)) | (~m_user_v_req(c_e_h_1, c_u, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (~m_user_v_req(c_e_h_1, c_u, s2)) | m_user_v_req(c_e_h_1, c_u, s3) | (~node8(c_e_h_1, c_u, s2, s3)))),
% 292.01/184.51 inference(transitivity,[status(thm)],[14755, 14753])).
% 292.01/184.51 tff(14757,plain,
% 292.01/184.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_1, c_u, s3) | (~node8(c_e_h_1, c_u, s2, s3)) | (~m_user_v_req(c_e_h_1, c_u, s2)))),
% 292.01/184.51 inference(quant_inst,[status(thm)],[])).
% 292.01/184.51 tff(14758,plain,
% 292.01/184.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (~m_user_v_req(c_e_h_1, c_u, s2)) | m_user_v_req(c_e_h_1, c_u, s3) | (~node8(c_e_h_1, c_u, s2, s3))),
% 292.01/184.51 inference(modus_ponens,[status(thm)],[14757, 14756])).
% 292.01/184.51 tff(14759,plain,
% 292.01/184.51 ($false),
% 292.01/184.51 inference(unit_resolution,[status(thm)],[14758, 302, 14752, 14673, 14351])).
% 292.01/184.51 tff(14760,plain,(m_user_v_req(c_e_h_1, c_u, s3) | (~m_user_v_req(c_e_h_1, c_u, s2))), inference(lemma,lemma(discharge,[]))).
% 292.01/184.51 tff(14761,plain,
% 292.01/184.51 (m_user_v_req(c_e_h_1, c_u, s3)),
% 292.01/184.51 inference(unit_resolution,[status(thm)],[14760, 14672])).
% 292.01/184.51 tff(14762,assumption,(~m_mutex_h_half_v_inp(c_e_h_1, c_a, s3)), introduced(assumption)).
% 292.01/184.51 tff(14763,assumption,(m_user_v_req(c_e_h_1, c_u, s3)), introduced(assumption)).
% 292.01/184.51 tff(14764,plain,
% 292.01/184.51 (((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | ((~m_user_v_req(c_e_h_1, c_u, s3)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s3))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | (~m_user_v_req(c_e_h_1, c_u, s3)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s3))),
% 292.01/184.51 inference(rewrite,[status(thm)],[])).
% 292.01/184.51 tff(14765,plain,
% 292.01/184.51 ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | ((~m_user_v_req(c_e_h_1, c_u, s3)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s3))),
% 292.01/184.51 inference(quant_inst,[status(thm)],[])).
% 292.01/184.51 tff(14766,plain,
% 292.01/184.51 ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | (~m_user_v_req(c_e_h_1, c_u, s3)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s3)),
% 292.01/184.51 inference(modus_ponens,[status(thm)],[14765, 14764])).
% 292.01/184.51 tff(14767,plain,
% 292.01/184.51 ($false),
% 292.01/184.51 inference(unit_resolution,[status(thm)],[14766, 1426, 14763, 14762])).
% 292.01/184.51 tff(14768,plain,(m_mutex_h_half_v_inp(c_e_h_1, c_a, s3) | (~m_user_v_req(c_e_h_1, c_u, s3))), inference(lemma,lemma(discharge,[]))).
% 292.01/184.51 tff(14769,plain,
% 292.01/184.51 (m_mutex_h_half_v_inp(c_e_h_1, c_a, s3)),
% 292.01/184.51 inference(unit_resolution,[status(thm)],[14768, 14761])).
% 292.01/184.51 tff(14770,assumption,(m_mutex_h_half_v_inp(c_e_h_1, c_a, s3)), introduced(assumption)).
% 292.01/184.51 tff(14771,assumption,(node12(c_e_h_1, c_a, s3, s4)), introduced(assumption)).
% 292.01/184.51 tff(14772,plain,
% 292.01/184.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (m_mutex_h_half_v_out(c_e_h_1, c_a, s4) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s3)) | (~node12(c_e_h_1, c_a, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | m_mutex_h_half_v_out(c_e_h_1, c_a, s4) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s3)) | (~node12(c_e_h_1, c_a, s3, s4)))),
% 292.01/184.51 inference(rewrite,[status(thm)],[])).
% 292.01/184.51 tff(14773,plain,
% 292.01/184.51 (((~node12(c_e_h_1, c_a, s3, s4)) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s3)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s4)) <=> (m_mutex_h_half_v_out(c_e_h_1, c_a, s4) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s3)) | (~node12(c_e_h_1, c_a, s3, s4)))),
% 292.01/184.51 inference(rewrite,[status(thm)],[])).
% 292.01/184.51 tff(14774,plain,
% 292.01/184.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_1, c_a, s3, s4)) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s3)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (m_mutex_h_half_v_out(c_e_h_1, c_a, s4) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s3)) | (~node12(c_e_h_1, c_a, s3, s4))))),
% 292.01/184.51 inference(monotonicity,[status(thm)],[14773])).
% 292.01/184.51 tff(14775,plain,
% 292.01/184.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_1, c_a, s3, s4)) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s3)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | m_mutex_h_half_v_out(c_e_h_1, c_a, s4) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s3)) | (~node12(c_e_h_1, c_a, s3, s4)))),
% 292.01/184.51 inference(transitivity,[status(thm)],[14774, 14772])).
% 292.01/184.51 tff(14776,plain,
% 292.01/184.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_1, c_a, s3, s4)) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s3)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s4))),
% 292.01/184.51 inference(quant_inst,[status(thm)],[])).
% 292.01/184.51 tff(14777,plain,
% 292.01/184.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | m_mutex_h_half_v_out(c_e_h_1, c_a, s4) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s3)) | (~node12(c_e_h_1, c_a, s3, s4))),
% 292.01/184.51 inference(modus_ponens,[status(thm)],[14776, 14775])).
% 292.01/184.51 tff(14778,plain,
% 292.01/184.51 ($false),
% 292.01/184.51 inference(unit_resolution,[status(thm)],[14777, 1483, 14771, 14102, 14770])).
% 292.01/184.51 tff(14779,plain,((~node12(c_e_h_1, c_a, s3, s4)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s4) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s3))), inference(lemma,lemma(discharge,[]))).
% 292.01/184.51 tff(14780,plain,
% 292.01/184.51 (~node12(c_e_h_1, c_a, s3, s4)),
% 292.01/184.51 inference(unit_resolution,[status(thm)],[14779, 14102, 14770])).
% 292.01/184.51 tff(14781,assumption,(node13(c_e_h_1, c_a, s3, s4)), introduced(assumption)).
% 292.01/184.51 tff(14782,plain,
% 292.01/184.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_1, c_a, s4) | (~node13(c_e_h_1, c_a, s3, s4)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | m_mutex_h_half_v_out(c_e_h_1, c_a, s4) | (~node13(c_e_h_1, c_a, s3, s4)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s3)))),
% 292.01/184.51 inference(rewrite,[status(thm)],[])).
% 292.01/184.51 tff(14783,plain,
% 292.01/184.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_1, c_a, s4) | (~node13(c_e_h_1, c_a, s3, s4)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s3)))),
% 292.01/184.51 inference(quant_inst,[status(thm)],[])).
% 292.01/184.51 tff(14784,plain,
% 292.01/184.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | m_mutex_h_half_v_out(c_e_h_1, c_a, s4) | (~node13(c_e_h_1, c_a, s3, s4)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s3))),
% 292.01/184.51 inference(modus_ponens,[status(thm)],[14783, 14782])).
% 292.01/184.51 tff(14785,plain,
% 292.01/184.51 ($false),
% 292.01/184.51 inference(unit_resolution,[status(thm)],[14784, 1459, 14781, 14102, 14606])).
% 292.01/184.51 tff(14786,plain,((~node13(c_e_h_1, c_a, s3, s4)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s4) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s3))), inference(lemma,lemma(discharge,[]))).
% 292.01/184.51 tff(14787,plain,
% 292.01/184.51 (~node13(c_e_h_1, c_a, s3, s4)),
% 292.01/184.51 inference(unit_resolution,[status(thm)],[14786, 14102, 14606])).
% 292.01/184.51 tff(14788,plain,
% 292.01/184.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s3, s4)) | node12(c_e_h_1, c_a, s3, s4) | node13(c_e_h_1, c_a, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s3, s4)) | node12(c_e_h_1, c_a, s3, s4) | node13(c_e_h_1, c_a, s3, s4))),
% 292.01/184.51 inference(rewrite,[status(thm)],[])).
% 292.01/184.51 tff(14789,plain,
% 292.01/184.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s3, s4)) | node12(c_e_h_1, c_a, s3, s4) | node13(c_e_h_1, c_a, s3, s4))),
% 292.01/184.51 inference(quant_inst,[status(thm)],[])).
% 292.01/184.51 tff(14790,plain,
% 292.01/184.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s3, s4)) | node12(c_e_h_1, c_a, s3, s4) | node13(c_e_h_1, c_a, s3, s4)),
% 292.01/184.51 inference(modus_ponens,[status(thm)],[14789, 14788])).
% 292.01/184.51 tff(14791,plain,
% 292.01/184.51 (node12(c_e_h_1, c_a, s3, s4) | node13(c_e_h_1, c_a, s3, s4)),
% 292.01/184.51 inference(unit_resolution,[status(thm)],[14790, 439, 531])).
% 292.01/184.51 tff(14792,plain,
% 292.01/184.51 ($false),
% 292.01/184.51 inference(unit_resolution,[status(thm)],[14791, 14787, 14780])).
% 292.01/184.51 tff(14793,plain,(m_mutex_h_half_v_out(c_e_h_1, c_a, s4) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s3)) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s3))), inference(lemma,lemma(discharge,[]))).
% 292.01/184.51 tff(14794,plain,
% 292.01/184.51 (~m_mutex_h_half_v_out(c_e_h_1, c_a, s3)),
% 292.01/184.51 inference(unit_resolution,[status(thm)],[14793, 14769, 14102])).
% 292.01/184.51 tff(14795,plain,
% 292.01/184.51 (~m_and_h_gate_v_in1(c_e_h_1, c_c, s3)),
% 292.01/184.51 inference(unit_resolution,[status(thm)],[14638, 14794])).
% 292.01/184.51 tff(14796,plain,
% 292.01/184.51 (~node20(c_e_h_1, c_c, s3)),
% 292.01/184.51 inference(unit_resolution,[status(thm)],[14646, 14795])).
% 292.01/184.51 tff(14797,plain,
% 292.01/184.51 (m_and_h_gate_v_out(c_e_h_1, c_c, s3)),
% 292.01/184.51 inference(unit_resolution,[status(thm)],[14663, 14796, 14604])).
% 292.01/184.51 tff(14798,plain,
% 292.01/184.51 (~m_mutex_h_half_v_out(c_e_h_1, c_a, s2)),
% 292.01/184.51 inference(unit_resolution,[status(thm)],[14381, 14794])).
% 292.01/184.51 tff(14799,plain,
% 292.01/184.52 (~m_and_h_gate_v_in1(c_e_h_1, c_c, s2)),
% 292.01/184.52 inference(unit_resolution,[status(thm)],[14232, 14798])).
% 292.01/184.52 tff(14800,plain,
% 292.01/184.52 (~node20(c_e_h_1, c_c, s2)),
% 292.01/184.52 inference(unit_resolution,[status(thm)],[14224, 14799])).
% 292.01/184.52 tff(14801,plain,
% 292.01/184.52 ($false),
% 292.01/184.52 inference(unit_resolution,[status(thm)],[14216, 14800, 14797])).
% 292.01/184.52 tff(14802,plain,(m_mutex_h_half_v_out(c_e_h_1, c_a, s4) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s6)) | m_or_h_gate_v_in2(c_e_h_1, c_g, s5)), inference(lemma,lemma(discharge,[]))).
% 292.01/184.52 tff(14803,plain,
% 292.01/184.52 (m_mutex_h_half_v_out(c_e_h_1, c_a, s4) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s6))),
% 292.01/184.52 inference(unit_resolution,[status(thm)],[14802, 14100])).
% 292.01/184.52 tff(14804,plain,
% 292.01/184.52 (m_mutex_h_half_v_out(c_e_h_1, c_a, s4)),
% 292.01/184.52 inference(unit_resolution,[status(thm)],[14803, 13630])).
% 292.01/184.52 tff(14805,assumption,(m_mutex_h_half_v_out(c_e_h_1, c_a, s4)), introduced(assumption)).
% 292.01/184.52 tff(14806,plain,
% 292.01/184.52 (((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | ((~m_mutex_h_half_v_out(c_e_h_1, c_a, s4)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s4))) <=> ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s4)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s4))),
% 292.01/184.52 inference(rewrite,[status(thm)],[])).
% 292.01/184.52 tff(14807,plain,
% 292.01/184.52 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | ((~m_mutex_h_half_v_out(c_e_h_1, c_a, s4)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s4))),
% 292.01/184.52 inference(quant_inst,[status(thm)],[])).
% 292.01/184.52 tff(14808,plain,
% 292.01/184.52 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s4)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s4)),
% 292.01/184.52 inference(modus_ponens,[status(thm)],[14807, 14806])).
% 292.01/184.52 tff(14809,plain,
% 292.01/184.52 ($false),
% 292.01/184.52 inference(unit_resolution,[status(thm)],[14808, 2556, 14805, 14110])).
% 292.01/184.52 tff(14810,plain,(m_and_h_gate_v_in1(c_e_h_1, c_c, s4) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s4))), inference(lemma,lemma(discharge,[]))).
% 292.01/184.52 tff(14811,plain,
% 292.01/184.52 (m_and_h_gate_v_in1(c_e_h_1, c_c, s4)),
% 292.01/184.52 inference(unit_resolution,[status(thm)],[14810, 14804])).
% 292.01/184.52 tff(14812,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_c, s5)), introduced(assumption)).
% 292.01/184.52 tff(14813,plain,
% 292.01/184.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_c, s4)) | m_and_h_gate_v_out(c_e_h_1, c_c, s5) | (~node22(c_e_h_1, c_c, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s4)) | m_and_h_gate_v_out(c_e_h_1, c_c, s5) | (~node22(c_e_h_1, c_c, s4, s5)))),
% 292.01/184.52 inference(rewrite,[status(thm)],[])).
% 292.01/184.52 tff(14814,plain,
% 292.01/184.52 ((m_and_h_gate_v_out(c_e_h_1, c_c, s5) | (~node22(c_e_h_1, c_c, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s4))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_c, s4)) | m_and_h_gate_v_out(c_e_h_1, c_c, s5) | (~node22(c_e_h_1, c_c, s4, s5)))),
% 292.01/184.52 inference(rewrite,[status(thm)],[])).
% 292.01/184.52 tff(14815,plain,
% 292.01/184.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_1, c_c, s5) | (~node22(c_e_h_1, c_c, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_c, s4)) | m_and_h_gate_v_out(c_e_h_1, c_c, s5) | (~node22(c_e_h_1, c_c, s4, s5))))),
% 292.01/184.52 inference(monotonicity,[status(thm)],[14814])).
% 292.01/184.52 tff(14816,plain,
% 292.01/184.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_1, c_c, s5) | (~node22(c_e_h_1, c_c, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s4)) | m_and_h_gate_v_out(c_e_h_1, c_c, s5) | (~node22(c_e_h_1, c_c, s4, s5)))),
% 292.01/184.52 inference(transitivity,[status(thm)],[14815, 14813])).
% 292.01/184.52 tff(14817,plain,
% 292.01/184.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_1, c_c, s5) | (~node22(c_e_h_1, c_c, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s4)))),
% 292.01/184.52 inference(quant_inst,[status(thm)],[])).
% 292.01/184.52 tff(14818,plain,
% 292.01/184.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s4)) | m_and_h_gate_v_out(c_e_h_1, c_c, s5) | (~node22(c_e_h_1, c_c, s4, s5))),
% 292.01/184.52 inference(modus_ponens,[status(thm)],[14817, 14816])).
% 292.01/184.52 tff(14819,plain,
% 292.01/184.52 ($false),
% 292.01/184.52 inference(unit_resolution,[status(thm)],[14818, 5871, 14507, 14605, 14812])).
% 292.01/184.52 tff(14820,plain,((~node22(c_e_h_1, c_c, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s4)) | m_and_h_gate_v_out(c_e_h_1, c_c, s5)), inference(lemma,lemma(discharge,[]))).
% 292.01/184.52 tff(14821,plain,
% 292.01/184.52 (~node22(c_e_h_1, c_c, s4, s5)),
% 292.01/184.52 inference(unit_resolution,[status(thm)],[14820, 14812, 14605])).
% 292.01/184.52 tff(14822,plain,
% 292.01/184.52 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node2(c_e_h_1, c_e_h_2, s4))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node2(c_e_h_1, c_e_h_2, s4))),
% 292.01/184.52 inference(rewrite,[status(thm)],[])).
% 292.01/184.52 tff(14823,plain,
% 292.01/184.52 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node2(c_e_h_1, c_e_h_2, s4))),
% 292.01/184.52 inference(quant_inst,[status(thm)],[])).
% 292.01/184.52 tff(14824,plain,
% 292.01/184.52 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node2(c_e_h_1, c_e_h_2, s4)),
% 292.01/184.52 inference(modus_ponens,[status(thm)],[14823, 14822])).
% 292.01/184.52 tff(14825,plain,
% 292.01/184.52 (node2(c_e_h_1, c_e_h_2, s4)),
% 292.01/184.52 inference(unit_resolution,[status(thm)],[14824, 4166, 5821])).
% 292.01/184.52 tff(14826,plain,
% 292.01/184.52 (((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | ((~node2(c_e_h_1, c_e_h_2, s4)) | m_cell_v_ack(c_e_h_2, s4) | m_and_h_gate_v_in2(c_e_h_1, c_c, s4))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | (~node2(c_e_h_1, c_e_h_2, s4)) | m_cell_v_ack(c_e_h_2, s4) | m_and_h_gate_v_in2(c_e_h_1, c_c, s4))),
% 292.01/184.52 inference(rewrite,[status(thm)],[])).
% 292.01/184.52 tff(14827,plain,
% 292.01/184.52 ((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | ((~node2(c_e_h_1, c_e_h_2, s4)) | m_cell_v_ack(c_e_h_2, s4) | m_and_h_gate_v_in2(c_e_h_1, c_c, s4))),
% 292.01/184.52 inference(quant_inst,[status(thm)],[])).
% 292.01/184.52 tff(14828,plain,
% 292.01/184.52 ((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | (~node2(c_e_h_1, c_e_h_2, s4)) | m_cell_v_ack(c_e_h_2, s4) | m_and_h_gate_v_in2(c_e_h_1, c_c, s4)),
% 292.01/184.52 inference(modus_ponens,[status(thm)],[14827, 14826])).
% 292.01/184.52 tff(14829,plain,
% 292.01/184.52 (m_cell_v_ack(c_e_h_2, s4) | m_and_h_gate_v_in2(c_e_h_1, c_c, s4)),
% 292.01/184.52 inference(unit_resolution,[status(thm)],[14828, 5835, 14825])).
% 292.01/184.52 tff(14830,plain,
% 292.01/184.52 (m_and_h_gate_v_in2(c_e_h_1, c_c, s4)),
% 292.01/184.52 inference(unit_resolution,[status(thm)],[14829, 8573])).
% 292.01/184.52 tff(14831,assumption,(m_and_h_gate_v_in2(c_e_h_1, c_c, s4)), introduced(assumption)).
% 292.01/184.52 tff(14832,plain,
% 292.01/184.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_c, s4)) | (~m_and_h_gate_v_in2(c_e_h_1, c_c, s4)) | m_and_h_gate_v_out(c_e_h_1, c_c, s5) | (~node21(c_e_h_1, c_c, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s4)) | (~m_and_h_gate_v_in2(c_e_h_1, c_c, s4)) | m_and_h_gate_v_out(c_e_h_1, c_c, s5) | (~node21(c_e_h_1, c_c, s4, s5)))),
% 292.01/184.52 inference(rewrite,[status(thm)],[])).
% 292.01/184.52 tff(14833,plain,
% 292.01/184.52 (((~node21(c_e_h_1, c_c, s4, s5)) | (~m_and_h_gate_v_in2(c_e_h_1, c_c, s4)) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s4)) | m_and_h_gate_v_out(c_e_h_1, c_c, s5)) <=> ((~m_and_h_gate_v_in1(c_e_h_1, c_c, s4)) | (~m_and_h_gate_v_in2(c_e_h_1, c_c, s4)) | m_and_h_gate_v_out(c_e_h_1, c_c, s5) | (~node21(c_e_h_1, c_c, s4, s5)))),
% 292.01/184.52 inference(rewrite,[status(thm)],[])).
% 292.01/184.52 tff(14834,plain,
% 292.01/184.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_1, c_c, s4, s5)) | (~m_and_h_gate_v_in2(c_e_h_1, c_c, s4)) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s4)) | m_and_h_gate_v_out(c_e_h_1, c_c, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_c, s4)) | (~m_and_h_gate_v_in2(c_e_h_1, c_c, s4)) | m_and_h_gate_v_out(c_e_h_1, c_c, s5) | (~node21(c_e_h_1, c_c, s4, s5))))),
% 292.01/184.52 inference(monotonicity,[status(thm)],[14833])).
% 292.01/184.52 tff(14835,plain,
% 292.01/184.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_1, c_c, s4, s5)) | (~m_and_h_gate_v_in2(c_e_h_1, c_c, s4)) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s4)) | m_and_h_gate_v_out(c_e_h_1, c_c, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s4)) | (~m_and_h_gate_v_in2(c_e_h_1, c_c, s4)) | m_and_h_gate_v_out(c_e_h_1, c_c, s5) | (~node21(c_e_h_1, c_c, s4, s5)))),
% 292.01/184.52 inference(transitivity,[status(thm)],[14834, 14832])).
% 292.01/184.52 tff(14836,plain,
% 292.01/184.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_1, c_c, s4, s5)) | (~m_and_h_gate_v_in2(c_e_h_1, c_c, s4)) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s4)) | m_and_h_gate_v_out(c_e_h_1, c_c, s5))),
% 292.01/184.52 inference(quant_inst,[status(thm)],[])).
% 292.01/184.52 tff(14837,plain,
% 292.01/184.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s4)) | (~m_and_h_gate_v_in2(c_e_h_1, c_c, s4)) | m_and_h_gate_v_out(c_e_h_1, c_c, s5) | (~node21(c_e_h_1, c_c, s4, s5))),
% 292.01/184.52 inference(modus_ponens,[status(thm)],[14836, 14835])).
% 292.01/184.52 tff(14838,plain,
% 292.01/184.52 ($false),
% 292.01/184.52 inference(unit_resolution,[status(thm)],[14837, 5851, 14514, 14831, 14812, 14103])).
% 292.01/184.52 tff(14839,plain,((~node21(c_e_h_1, c_c, s4, s5)) | (~m_and_h_gate_v_in2(c_e_h_1, c_c, s4)) | m_and_h_gate_v_out(c_e_h_1, c_c, s5) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s4))), inference(lemma,lemma(discharge,[]))).
% 292.01/184.52 tff(14840,plain,
% 292.01/184.52 ((~node21(c_e_h_1, c_c, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_c, s5) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s4))),
% 292.01/184.52 inference(unit_resolution,[status(thm)],[14839, 14830])).
% 292.01/184.52 tff(14841,plain,
% 292.01/184.52 (~node21(c_e_h_1, c_c, s4, s5)),
% 292.01/184.52 inference(unit_resolution,[status(thm)],[14840, 14812, 14103])).
% 292.01/184.52 tff(14842,plain,
% 292.01/184.52 ($false),
% 292.01/184.52 inference(unit_resolution,[status(thm)],[14524, 14841, 14821])).
% 292.01/184.52 tff(14843,plain,(m_and_h_gate_v_out(c_e_h_1, c_c, s5) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s4)) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s4))), inference(lemma,lemma(discharge,[]))).
% 292.01/184.52 tff(14844,plain,
% 292.01/184.52 (~m_and_h_gate_v_out(c_e_h_1, c_c, s4)),
% 292.01/184.52 inference(unit_resolution,[status(thm)],[14843, 14812, 14811])).
% 292.01/184.52 tff(14845,plain,
% 292.01/184.52 (m_or_h_gate_v_out(c_e_h_1, c_g, s4)),
% 292.01/184.52 inference(unit_resolution,[status(thm)],[14601, 14125, 14571])).
% 292.01/184.52 tff(14846,plain,
% 292.01/184.52 (m_or_h_gate_v_in1(c_e_h_1, c_g, s3)),
% 292.01/184.53 inference(unit_resolution,[status(thm)],[14503, 14845])).
% 292.01/184.53 tff(14847,plain,
% 292.01/184.53 ($false),
% 292.01/184.53 inference(unit_resolution,[status(thm)],[14418, 2708, 14415, 14846])).
% 292.01/184.53 tff(14848,plain,(m_and_h_gate_v_out(c_e_h_1, c_c, s4) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s5))), inference(lemma,lemma(discharge,[]))).
% 292.01/184.53 tff(14849,plain,
% 292.01/184.53 (~m_or_h_gate_v_out(c_e_h_1, c_g, s5)),
% 292.01/184.53 inference(unit_resolution,[status(thm)],[14848, 14844])).
% 292.01/184.53 tff(14850,plain,
% 292.01/184.53 ((~m_or_h_gate_v_out(c_e_h_1, c_g, s6)) | m_or_h_gate_v_out(c_e_h_1, c_g, s5) | m_or_h_gate_v_in1(c_e_h_1, c_g, s5)),
% 292.01/184.53 inference(unit_resolution,[status(thm)],[14562, 14100])).
% 292.01/184.53 tff(14851,plain,
% 292.01/184.53 (m_or_h_gate_v_in1(c_e_h_1, c_g, s5)),
% 292.01/184.53 inference(unit_resolution,[status(thm)],[14850, 14849, 13630])).
% 292.01/184.53 tff(14852,plain,
% 292.01/184.53 ($false),
% 292.01/184.53 inference(unit_resolution,[status(thm)],[14530, 2708, 14812, 14851])).
% 292.01/184.53 tff(14853,plain,(m_and_h_gate_v_out(c_e_h_1, c_c, s5) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s6))), inference(lemma,lemma(discharge,[]))).
% 292.01/184.53 tff(14854,plain,
% 292.01/184.53 (m_and_h_gate_v_out(c_e_h_1, c_c, s5)),
% 292.01/184.53 inference(unit_resolution,[status(thm)],[14853, 13630])).
% 292.01/184.53 tff(14855,assumption,(~m_mutex_h_half_v_out(c_e_h_1, c_a, s5)), introduced(assumption)).
% 292.01/184.53 tff(14856,plain,
% 292.01/184.53 (m_user_v_req(c_e_h_1, c_u, s2)),
% 292.01/184.53 inference(unit_resolution,[status(thm)],[14671, 14605])).
% 292.01/184.53 tff(14857,plain,
% 292.01/184.53 (m_user_v_req(c_e_h_1, c_u, s3)),
% 292.01/184.53 inference(unit_resolution,[status(thm)],[14760, 14856])).
% 292.01/184.53 tff(14858,plain,
% 292.01/184.53 (m_mutex_h_half_v_inp(c_e_h_1, c_a, s3)),
% 292.01/184.53 inference(unit_resolution,[status(thm)],[14768, 14857])).
% 292.01/184.53 tff(14859,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s3)), introduced(assumption)).
% 292.01/184.53 tff(14860,assumption,(node21(c_e_h_1, c_r, s2, s3)), introduced(assumption)).
% 292.01/184.53 tff(14861,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)), introduced(assumption)).
% 292.01/184.53 tff(14862,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)), introduced(assumption)).
% 292.01/184.53 tff(14863,assumption,(node10(c_e_h_1, c_n, s0, s1)), introduced(assumption)).
% 292.01/184.53 tff(14864,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s0)), introduced(assumption)).
% 292.01/184.53 tff(14865,plain,
% 292.01/184.53 ((~![I0: $i, I1: $i] : (~m_c_h_element_v_out(I0, I1, s0))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s0))),
% 292.01/184.53 inference(quant_inst,[status(thm)],[])).
% 292.01/184.53 tff(14866,plain,
% 292.01/184.53 ($false),
% 292.01/184.53 inference(unit_resolution,[status(thm)],[14865, 14, 14864])).
% 292.01/184.53 tff(14867,plain,(~m_c_h_element_v_out(c_e_h_1, c_e, s0)), inference(lemma,lemma(discharge,[]))).
% 292.01/184.53 tff(14868,plain,
% 292.01/184.53 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0) | m_c_h_element_v_out(c_e_h_1, c_e, s0))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0) | m_c_h_element_v_out(c_e_h_1, c_e, s0))),
% 292.01/184.53 inference(rewrite,[status(thm)],[])).
% 292.01/184.53 tff(14869,plain,
% 292.01/184.53 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0) | m_c_h_element_v_out(c_e_h_1, c_e, s0))),
% 292.01/184.53 inference(quant_inst,[status(thm)],[])).
% 292.01/184.53 tff(14870,plain,
% 292.01/184.53 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0) | m_c_h_element_v_out(c_e_h_1, c_e, s0)),
% 292.01/184.53 inference(modus_ponens,[status(thm)],[14869, 14868])).
% 292.01/184.53 tff(14871,plain,
% 292.01/184.53 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0) | m_c_h_element_v_out(c_e_h_1, c_e, s0)),
% 292.01/184.53 inference(unit_resolution,[status(thm)],[14870, 7856])).
% 292.01/184.53 tff(14872,plain,
% 292.01/184.53 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0)),
% 292.01/184.53 inference(unit_resolution,[status(thm)],[14871, 14867])).
% 292.01/184.53 tff(14873,plain,
% 292.01/184.53 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0))),
% 292.01/184.53 inference(rewrite,[status(thm)],[])).
% 292.01/184.53 tff(14874,plain,
% 292.01/184.53 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0))),
% 292.01/184.53 inference(quant_inst,[status(thm)],[])).
% 292.01/184.53 tff(14875,plain,
% 292.01/184.53 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0)),
% 292.01/184.53 inference(modus_ponens,[status(thm)],[14874, 14873])).
% 292.01/184.53 tff(14876,plain,
% 292.01/184.53 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0)),
% 292.01/184.53 inference(unit_resolution,[status(thm)],[14875, 7868])).
% 292.01/184.53 tff(14877,plain,
% 292.01/184.53 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0)),
% 292.01/184.53 inference(unit_resolution,[status(thm)],[14876, 14286])).
% 292.01/184.53 tff(14878,plain,
% 292.01/184.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0)) | (~node10(c_e_h_1, c_n, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0)) | (~node10(c_e_h_1, c_n, s0, s1)))),
% 292.01/184.53 inference(rewrite,[status(thm)],[])).
% 292.01/184.53 tff(14879,plain,
% 292.01/184.53 (((~node10(c_e_h_1, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)) <=> ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0)) | (~node10(c_e_h_1, c_n, s0, s1)))),
% 292.01/184.53 inference(rewrite,[status(thm)],[])).
% 292.01/184.53 tff(14880,plain,
% 292.01/184.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0)) | (~node10(c_e_h_1, c_n, s0, s1))))),
% 292.01/184.53 inference(monotonicity,[status(thm)],[14879])).
% 292.01/184.53 tff(14881,plain,
% 292.01/184.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0)) | (~node10(c_e_h_1, c_n, s0, s1)))),
% 292.01/184.53 inference(transitivity,[status(thm)],[14880, 14878])).
% 292.01/184.53 tff(14882,plain,
% 292.01/184.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1))),
% 292.01/184.53 inference(quant_inst,[status(thm)],[])).
% 292.01/184.53 tff(14883,plain,
% 292.01/184.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s0)) | (~node10(c_e_h_1, c_n, s0, s1))),
% 292.01/184.53 inference(modus_ponens,[status(thm)],[14882, 14881])).
% 292.01/184.53 tff(14884,plain,
% 292.01/184.53 ($false),
% 292.01/184.53 inference(unit_resolution,[status(thm)],[14883, 5718, 14877, 14862, 14872, 14863])).
% 292.01/184.53 tff(14885,plain,((~node10(c_e_h_1, c_n, s0, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)), inference(lemma,lemma(discharge,[]))).
% 292.01/184.53 tff(14886,plain,
% 292.01/184.53 (~node10(c_e_h_1, c_n, s0, s1)),
% 292.01/184.53 inference(unit_resolution,[status(thm)],[14885, 14862])).
% 292.01/184.53 tff(14887,plain,
% 292.01/184.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s0, s1)) | node10(c_e_h_1, c_n, s0, s1) | node11(c_e_h_1, c_n, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s0, s1)) | node10(c_e_h_1, c_n, s0, s1) | node11(c_e_h_1, c_n, s0, s1))),
% 292.01/184.53 inference(rewrite,[status(thm)],[])).
% 292.01/184.53 tff(14888,plain,
% 292.01/184.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s0, s1)) | node10(c_e_h_1, c_n, s0, s1) | node11(c_e_h_1, c_n, s0, s1))),
% 292.01/184.53 inference(quant_inst,[status(thm)],[])).
% 292.01/184.53 tff(14889,plain,
% 292.01/184.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s0, s1)) | node10(c_e_h_1, c_n, s0, s1) | node11(c_e_h_1, c_n, s0, s1)),
% 292.01/184.53 inference(modus_ponens,[status(thm)],[14888, 14887])).
% 292.01/184.53 tff(14890,plain,
% 292.01/184.53 (node10(c_e_h_1, c_n, s0, s1) | node11(c_e_h_1, c_n, s0, s1)),
% 292.01/184.53 inference(unit_resolution,[status(thm)],[14889, 5002, 72])).
% 292.01/184.53 tff(14891,plain,
% 292.01/184.53 (node11(c_e_h_1, c_n, s0, s1)),
% 292.01/184.53 inference(unit_resolution,[status(thm)],[14890, 14886])).
% 292.01/184.53 tff(14892,plain,
% 292.01/184.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~node11(c_e_h_1, c_n, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~node11(c_e_h_1, c_n, s0, s1)))),
% 292.01/184.53 inference(rewrite,[status(thm)],[])).
% 292.01/184.53 tff(14893,plain,
% 292.01/184.53 ((m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~node11(c_e_h_1, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~node11(c_e_h_1, c_n, s0, s1)))),
% 292.01/184.53 inference(rewrite,[status(thm)],[])).
% 292.01/184.53 tff(14894,plain,
% 292.01/184.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~node11(c_e_h_1, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~node11(c_e_h_1, c_n, s0, s1))))),
% 292.01/184.53 inference(monotonicity,[status(thm)],[14893])).
% 292.01/184.53 tff(14895,plain,
% 292.01/184.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~node11(c_e_h_1, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~node11(c_e_h_1, c_n, s0, s1)))),
% 292.01/184.54 inference(transitivity,[status(thm)],[14894, 14892])).
% 292.01/184.54 tff(14896,plain,
% 292.01/184.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~node11(c_e_h_1, c_n, s0, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0)))),
% 292.01/184.54 inference(quant_inst,[status(thm)],[])).
% 292.01/184.54 tff(14897,plain,
% 292.01/184.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1) | (~node11(c_e_h_1, c_n, s0, s1))),
% 292.01/184.54 inference(modus_ponens,[status(thm)],[14896, 14895])).
% 292.01/184.54 tff(14898,plain,
% 292.01/184.54 ($false),
% 292.01/184.54 inference(unit_resolution,[status(thm)],[14897, 5742, 14686, 14862, 14891])).
% 292.01/184.54 tff(14899,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)), inference(lemma,lemma(discharge,[]))).
% 292.01/184.54 tff(14900,plain,
% 292.01/184.54 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)))),
% 292.01/184.54 inference(rewrite,[status(thm)],[])).
% 292.01/184.54 tff(14901,plain,
% 292.01/184.54 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)))),
% 292.01/184.54 inference(quant_inst,[status(thm)],[])).
% 292.01/184.54 tff(14902,plain,
% 292.01/184.54 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s1)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1))),
% 292.01/184.54 inference(modus_ponens,[status(thm)],[14901, 14900])).
% 292.01/184.54 tff(14903,plain,
% 292.01/184.54 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s1)),
% 292.01/184.54 inference(unit_resolution,[status(thm)],[14902, 4958, 14899])).
% 292.01/184.54 tff(14904,plain,
% 292.01/184.54 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s1)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s1)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s1))),
% 292.01/184.54 inference(rewrite,[status(thm)],[])).
% 292.01/184.54 tff(14905,plain,
% 292.01/184.54 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s1)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s1))),
% 292.01/184.54 inference(quant_inst,[status(thm)],[])).
% 292.01/184.54 tff(14906,plain,
% 292.01/184.54 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s1)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s1)),
% 292.01/184.54 inference(modus_ponens,[status(thm)],[14905, 14904])).
% 292.01/184.54 tff(14907,plain,
% 292.01/184.54 (~node9(c_e_h_1, c_m, s1)),
% 292.01/184.54 inference(unit_resolution,[status(thm)],[14906, 4972, 14903])).
% 292.01/184.54 tff(14908,assumption,(node10(c_e_h_1, c_m, s1, s2)), introduced(assumption)).
% 292.01/184.54 tff(14909,plain,
% 292.01/184.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s1) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)) | (~node10(c_e_h_1, c_m, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_1, c_m, s1) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)) | (~node10(c_e_h_1, c_m, s1, s2)))),
% 292.01/184.54 inference(rewrite,[status(thm)],[])).
% 292.01/184.54 tff(14910,plain,
% 292.01/184.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s1) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)) | (~node10(c_e_h_1, c_m, s1, s2)))),
% 292.01/184.54 inference(quant_inst,[status(thm)],[])).
% 292.01/184.54 tff(14911,plain,
% 292.01/184.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_1, c_m, s1) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)) | (~node10(c_e_h_1, c_m, s1, s2))),
% 292.01/184.54 inference(modus_ponens,[status(thm)],[14910, 14909])).
% 292.01/184.54 tff(14912,plain,
% 292.01/184.54 ($false),
% 292.01/184.54 inference(unit_resolution,[status(thm)],[14911, 4986, 14861, 14908, 14907])).
% 292.01/184.54 tff(14913,plain,((~node10(c_e_h_1, c_m, s1, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2))), inference(lemma,lemma(discharge,[]))).
% 292.01/184.54 tff(14914,plain,
% 292.01/184.54 (~node10(c_e_h_1, c_m, s1, s2)),
% 292.01/184.54 inference(unit_resolution,[status(thm)],[14913, 14861])).
% 292.01/184.54 tff(14915,plain,
% 292.01/184.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s1, s2)) | node10(c_e_h_1, c_m, s1, s2) | node11(c_e_h_1, c_m, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s1, s2)) | node10(c_e_h_1, c_m, s1, s2) | node11(c_e_h_1, c_m, s1, s2))),
% 292.01/184.54 inference(rewrite,[status(thm)],[])).
% 292.01/184.54 tff(14916,plain,
% 292.01/184.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s1, s2)) | node10(c_e_h_1, c_m, s1, s2) | node11(c_e_h_1, c_m, s1, s2))),
% 292.01/184.54 inference(quant_inst,[status(thm)],[])).
% 292.01/184.54 tff(14917,plain,
% 292.01/184.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s1, s2)) | node10(c_e_h_1, c_m, s1, s2) | node11(c_e_h_1, c_m, s1, s2)),
% 292.01/184.54 inference(modus_ponens,[status(thm)],[14916, 14915])).
% 292.01/184.54 tff(14918,plain,
% 292.01/184.54 (node10(c_e_h_1, c_m, s1, s2) | node11(c_e_h_1, c_m, s1, s2)),
% 292.01/184.54 inference(unit_resolution,[status(thm)],[14917, 5002, 255])).
% 292.01/184.54 tff(14919,plain,
% 292.01/184.54 (node11(c_e_h_1, c_m, s1, s2)),
% 292.01/184.54 inference(unit_resolution,[status(thm)],[14918, 14914])).
% 292.01/184.54 tff(14920,plain,
% 292.01/184.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)) | (~node11(c_e_h_1, c_m, s1, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)) | (~node11(c_e_h_1, c_m, s1, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1))),
% 292.01/184.54 inference(rewrite,[status(thm)],[])).
% 292.01/184.54 tff(14921,plain,
% 292.01/184.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)) | (~node11(c_e_h_1, c_m, s1, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1))),
% 292.01/184.54 inference(quant_inst,[status(thm)],[])).
% 292.01/184.54 tff(14922,plain,
% 292.01/184.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)) | (~node11(c_e_h_1, c_m, s1, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)),
% 292.01/184.54 inference(modus_ponens,[status(thm)],[14921, 14920])).
% 292.01/184.54 tff(14923,plain,
% 292.01/184.54 ($false),
% 292.01/184.54 inference(unit_resolution,[status(thm)],[14922, 5017, 14861, 14710, 14919])).
% 292.01/184.54 tff(14924,plain,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)), inference(lemma,lemma(discharge,[]))).
% 292.01/184.54 tff(14925,plain,
% 292.01/184.54 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2))),
% 292.01/184.54 inference(rewrite,[status(thm)],[])).
% 292.01/184.54 tff(14926,plain,
% 292.01/184.54 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2))),
% 292.01/184.54 inference(quant_inst,[status(thm)],[])).
% 292.01/184.54 tff(14927,plain,
% 292.01/184.54 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)),
% 292.01/184.54 inference(modus_ponens,[status(thm)],[14926, 14925])).
% 292.01/184.54 tff(14928,plain,
% 292.01/184.54 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s2)),
% 292.01/184.54 inference(unit_resolution,[status(thm)],[14927, 14293, 14924])).
% 292.01/184.54 tff(14929,plain,
% 292.01/184.54 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s2)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s2)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s2))),
% 292.01/184.54 inference(rewrite,[status(thm)],[])).
% 292.01/184.54 tff(14930,plain,
% 292.01/184.54 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s2)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s2))),
% 292.01/184.54 inference(quant_inst,[status(thm)],[])).
% 292.01/184.54 tff(14931,plain,
% 292.01/184.54 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s2)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s2)),
% 292.01/184.54 inference(modus_ponens,[status(thm)],[14930, 14929])).
% 292.01/184.54 tff(14932,plain,
% 292.01/184.54 (~node20(c_e_h_1, c_r, s2)),
% 292.01/184.54 inference(unit_resolution,[status(thm)],[14931, 4563, 14928])).
% 292.01/184.54 tff(14933,plain,
% 292.01/184.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | node20(c_e_h_1, c_r, s2) | (~node21(c_e_h_1, c_r, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | node20(c_e_h_1, c_r, s2) | (~node21(c_e_h_1, c_r, s2, s3)))),
% 292.01/184.54 inference(rewrite,[status(thm)],[])).
% 292.01/184.54 tff(14934,plain,
% 292.01/184.54 ((node20(c_e_h_1, c_r, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | (~node21(c_e_h_1, c_r, s2, s3))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | node20(c_e_h_1, c_r, s2) | (~node21(c_e_h_1, c_r, s2, s3)))),
% 292.01/184.54 inference(rewrite,[status(thm)],[])).
% 292.01/184.54 tff(14935,plain,
% 292.01/184.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | (~node21(c_e_h_1, c_r, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | node20(c_e_h_1, c_r, s2) | (~node21(c_e_h_1, c_r, s2, s3))))),
% 292.01/184.54 inference(monotonicity,[status(thm)],[14934])).
% 292.01/184.54 tff(14936,plain,
% 292.01/184.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | (~node21(c_e_h_1, c_r, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | node20(c_e_h_1, c_r, s2) | (~node21(c_e_h_1, c_r, s2, s3)))),
% 292.01/184.54 inference(transitivity,[status(thm)],[14935, 14933])).
% 292.01/184.54 tff(14937,plain,
% 292.01/184.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | (~node21(c_e_h_1, c_r, s2, s3)))),
% 292.01/184.54 inference(quant_inst,[status(thm)],[])).
% 292.01/184.54 tff(14938,plain,
% 292.01/184.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | node20(c_e_h_1, c_r, s2) | (~node21(c_e_h_1, c_r, s2, s3))),
% 292.01/184.54 inference(modus_ponens,[status(thm)],[14937, 14936])).
% 292.01/184.55 tff(14939,plain,
% 292.01/184.55 ($false),
% 292.01/184.55 inference(unit_resolution,[status(thm)],[14938, 52, 14859, 14932, 14860])).
% 292.01/184.55 tff(14940,plain,((~node21(c_e_h_1, c_r, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s3))), inference(lemma,lemma(discharge,[]))).
% 292.01/184.55 tff(14941,plain,
% 292.01/184.55 (~node21(c_e_h_1, c_r, s2, s3)),
% 292.01/184.55 inference(unit_resolution,[status(thm)],[14940, 14859])).
% 292.01/184.55 tff(14942,plain,
% 292.01/184.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_1, c_r, s2, s3) | node22(c_e_h_1, c_r, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_1, c_r, s2, s3) | node22(c_e_h_1, c_r, s2, s3))),
% 292.01/184.55 inference(rewrite,[status(thm)],[])).
% 292.01/184.55 tff(14943,plain,
% 292.01/184.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_1, c_r, s2, s3) | node22(c_e_h_1, c_r, s2, s3))),
% 292.01/184.55 inference(quant_inst,[status(thm)],[])).
% 292.01/184.55 tff(14944,plain,
% 292.01/184.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_1, c_r, s2, s3) | node22(c_e_h_1, c_r, s2, s3)),
% 292.01/184.55 inference(modus_ponens,[status(thm)],[14943, 14942])).
% 292.01/184.55 tff(14945,plain,
% 292.01/184.55 (node21(c_e_h_1, c_r, s2, s3) | node22(c_e_h_1, c_r, s2, s3)),
% 292.01/184.55 inference(unit_resolution,[status(thm)],[14944, 82, 318])).
% 292.01/184.55 tff(14946,plain,
% 292.01/184.55 (node22(c_e_h_1, c_r, s2, s3)),
% 292.01/184.55 inference(unit_resolution,[status(thm)],[14945, 14941])).
% 292.01/184.55 tff(14947,plain,
% 292.01/184.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | (~node22(c_e_h_1, c_r, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_r, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | (~node22(c_e_h_1, c_r, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_r, s2))),
% 292.01/184.55 inference(rewrite,[status(thm)],[])).
% 292.01/184.55 tff(14948,plain,
% 292.01/184.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | (~node22(c_e_h_1, c_r, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_r, s2))),
% 292.01/184.55 inference(quant_inst,[status(thm)],[])).
% 292.01/184.55 tff(14949,plain,
% 292.01/184.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s3)) | (~node22(c_e_h_1, c_r, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_r, s2)),
% 292.01/184.55 inference(modus_ponens,[status(thm)],[14948, 14947])).
% 292.01/184.55 tff(14950,plain,
% 292.01/184.55 ($false),
% 292.01/184.55 inference(unit_resolution,[status(thm)],[14949, 108, 14859, 14946, 14734])).
% 292.01/184.55 tff(14951,plain,(~m_and_h_gate_v_out(c_e_h_1, c_r, s3)), inference(lemma,lemma(discharge,[]))).
% 292.01/184.55 tff(14952,assumption,(m_user_v_ack(c_e_h_1, c_u, s3)), introduced(assumption)).
% 292.01/184.55 tff(14953,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s3)), introduced(assumption)).
% 292.01/184.55 tff(14954,plain,
% 292.01/184.55 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s3)) | m_and_h_gate_v_out(c_e_h_1, c_r, s3))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s3)) | m_and_h_gate_v_out(c_e_h_1, c_r, s3))),
% 292.01/184.55 inference(rewrite,[status(thm)],[])).
% 292.01/184.55 tff(14955,plain,
% 292.01/184.55 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s3)) | m_and_h_gate_v_out(c_e_h_1, c_r, s3))),
% 292.01/184.55 inference(quant_inst,[status(thm)],[])).
% 292.01/184.55 tff(14956,plain,
% 292.01/184.55 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s3)) | m_and_h_gate_v_out(c_e_h_1, c_r, s3)),
% 292.01/184.55 inference(modus_ponens,[status(thm)],[14955, 14954])).
% 292.01/184.55 tff(14957,plain,
% 292.01/184.55 ($false),
% 292.01/184.55 inference(unit_resolution,[status(thm)],[14956, 268, 14953, 14952])).
% 292.01/184.55 tff(14958,plain,((~m_user_v_ack(c_e_h_1, c_u, s3)) | m_and_h_gate_v_out(c_e_h_1, c_r, s3)), inference(lemma,lemma(discharge,[]))).
% 292.01/184.55 tff(14959,plain,
% 292.01/184.55 (~m_user_v_ack(c_e_h_1, c_u, s3)),
% 292.01/184.55 inference(unit_resolution,[status(thm)],[14958, 14951])).
% 292.01/184.55 tff(14960,assumption,(~m_user_v_req(c_e_h_1, c_u, s4)), introduced(assumption)).
% 292.01/184.55 tff(14961,assumption,(~m_user_v_ack(c_e_h_1, c_u, s3)), introduced(assumption)).
% 292.01/184.55 tff(14962,assumption,(node7(c_e_h_1, c_u, s3, s4)), introduced(assumption)).
% 292.01/184.55 tff(14963,plain,
% 292.01/184.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | ((~node7(c_e_h_1, c_u, s3, s4)) | m_user_v_ack(c_e_h_1, c_u, s3) | m_user_v_req(c_e_h_1, c_u, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | (~node7(c_e_h_1, c_u, s3, s4)) | m_user_v_ack(c_e_h_1, c_u, s3) | m_user_v_req(c_e_h_1, c_u, s4))),
% 292.01/184.55 inference(rewrite,[status(thm)],[])).
% 292.01/184.55 tff(14964,plain,
% 292.01/184.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | ((~node7(c_e_h_1, c_u, s3, s4)) | m_user_v_ack(c_e_h_1, c_u, s3) | m_user_v_req(c_e_h_1, c_u, s4))),
% 292.01/184.55 inference(quant_inst,[status(thm)],[])).
% 292.01/184.55 tff(14965,plain,
% 292.01/184.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | (~node7(c_e_h_1, c_u, s3, s4)) | m_user_v_ack(c_e_h_1, c_u, s3) | m_user_v_req(c_e_h_1, c_u, s4)),
% 292.01/184.55 inference(modus_ponens,[status(thm)],[14964, 14963])).
% 292.01/184.55 tff(14966,plain,
% 292.01/184.55 ($false),
% 292.01/184.55 inference(unit_resolution,[status(thm)],[14965, 284, 14962, 14961, 14960])).
% 292.01/184.55 tff(14967,plain,((~node7(c_e_h_1, c_u, s3, s4)) | m_user_v_ack(c_e_h_1, c_u, s3) | m_user_v_req(c_e_h_1, c_u, s4)), inference(lemma,lemma(discharge,[]))).
% 292.01/184.55 tff(14968,plain,
% 292.01/184.55 (~node7(c_e_h_1, c_u, s3, s4)),
% 292.01/184.55 inference(unit_resolution,[status(thm)],[14967, 14960, 14961])).
% 292.01/184.55 tff(14969,plain,
% 292.01/184.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | ((~trans(s3, s4)) | node7(c_e_h_1, c_u, s3, s4) | node8(c_e_h_1, c_u, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | (~trans(s3, s4)) | node7(c_e_h_1, c_u, s3, s4) | node8(c_e_h_1, c_u, s3, s4))),
% 292.01/184.55 inference(rewrite,[status(thm)],[])).
% 292.01/184.55 tff(14970,plain,
% 292.01/184.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | ((~trans(s3, s4)) | node7(c_e_h_1, c_u, s3, s4) | node8(c_e_h_1, c_u, s3, s4))),
% 292.01/184.55 inference(quant_inst,[status(thm)],[])).
% 292.01/184.55 tff(14971,plain,
% 292.01/184.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | (~trans(s3, s4)) | node7(c_e_h_1, c_u, s3, s4) | node8(c_e_h_1, c_u, s3, s4)),
% 292.01/184.55 inference(modus_ponens,[status(thm)],[14970, 14969])).
% 292.01/184.55 tff(14972,plain,
% 292.01/184.55 (node7(c_e_h_1, c_u, s3, s4) | node8(c_e_h_1, c_u, s3, s4)),
% 292.01/184.55 inference(unit_resolution,[status(thm)],[14971, 328, 531])).
% 292.01/184.55 tff(14973,plain,
% 292.01/184.55 (node8(c_e_h_1, c_u, s3, s4)),
% 292.01/184.55 inference(unit_resolution,[status(thm)],[14972, 14968])).
% 292.01/184.55 tff(14974,plain,
% 292.01/184.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_1, c_u, s4) | (~node8(c_e_h_1, c_u, s3, s4)) | (~m_user_v_req(c_e_h_1, c_u, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | m_user_v_req(c_e_h_1, c_u, s4) | (~node8(c_e_h_1, c_u, s3, s4)) | (~m_user_v_req(c_e_h_1, c_u, s3)))),
% 292.01/184.55 inference(rewrite,[status(thm)],[])).
% 292.01/184.55 tff(14975,plain,
% 292.01/184.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_1, c_u, s4) | (~node8(c_e_h_1, c_u, s3, s4)) | (~m_user_v_req(c_e_h_1, c_u, s3)))),
% 292.01/184.55 inference(quant_inst,[status(thm)],[])).
% 292.01/184.55 tff(14976,plain,
% 292.01/184.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | m_user_v_req(c_e_h_1, c_u, s4) | (~node8(c_e_h_1, c_u, s3, s4)) | (~m_user_v_req(c_e_h_1, c_u, s3))),
% 292.01/184.56 inference(modus_ponens,[status(thm)],[14975, 14974])).
% 292.01/184.56 tff(14977,plain,
% 292.01/184.56 ($false),
% 292.01/184.56 inference(unit_resolution,[status(thm)],[14976, 302, 14973, 14960, 14763])).
% 292.01/184.56 tff(14978,plain,(m_user_v_req(c_e_h_1, c_u, s4) | (~m_user_v_req(c_e_h_1, c_u, s3)) | m_user_v_ack(c_e_h_1, c_u, s3)), inference(lemma,lemma(discharge,[]))).
% 292.01/184.56 tff(14979,plain,
% 292.01/184.56 (m_user_v_req(c_e_h_1, c_u, s4) | (~m_user_v_req(c_e_h_1, c_u, s3))),
% 292.01/184.56 inference(unit_resolution,[status(thm)],[14978, 14959])).
% 292.01/184.56 tff(14980,plain,
% 292.01/184.56 (m_user_v_req(c_e_h_1, c_u, s4)),
% 292.01/184.56 inference(unit_resolution,[status(thm)],[14979, 14857])).
% 292.01/184.56 tff(14981,assumption,(~m_mutex_h_half_v_inp(c_e_h_1, c_a, s4)), introduced(assumption)).
% 292.01/184.56 tff(14982,assumption,(m_user_v_req(c_e_h_1, c_u, s4)), introduced(assumption)).
% 292.01/184.56 tff(14983,plain,
% 292.01/184.56 (((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | ((~m_user_v_req(c_e_h_1, c_u, s4)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s4))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | (~m_user_v_req(c_e_h_1, c_u, s4)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s4))),
% 292.01/184.56 inference(rewrite,[status(thm)],[])).
% 292.01/184.56 tff(14984,plain,
% 292.01/184.56 ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | ((~m_user_v_req(c_e_h_1, c_u, s4)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s4))),
% 292.01/184.56 inference(quant_inst,[status(thm)],[])).
% 292.01/184.56 tff(14985,plain,
% 292.01/184.56 ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | (~m_user_v_req(c_e_h_1, c_u, s4)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s4)),
% 292.01/184.56 inference(modus_ponens,[status(thm)],[14984, 14983])).
% 292.01/184.56 tff(14986,plain,
% 292.01/184.56 ($false),
% 292.01/184.56 inference(unit_resolution,[status(thm)],[14985, 1426, 14982, 14981])).
% 292.01/184.56 tff(14987,plain,(m_mutex_h_half_v_inp(c_e_h_1, c_a, s4) | (~m_user_v_req(c_e_h_1, c_u, s4))), inference(lemma,lemma(discharge,[]))).
% 292.01/184.56 tff(14988,plain,
% 292.01/184.56 (m_mutex_h_half_v_inp(c_e_h_1, c_a, s4)),
% 292.01/184.56 inference(unit_resolution,[status(thm)],[14987, 14980])).
% 292.01/184.56 tff(14989,assumption,(m_mutex_h_half_v_inp(c_e_h_1, c_a, s4)), introduced(assumption)).
% 292.01/184.56 tff(14990,assumption,(node12(c_e_h_1, c_a, s4, s5)), introduced(assumption)).
% 292.01/184.56 tff(14991,plain,
% 292.01/184.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~m_mutex_h_half_v_inp(c_e_h_1, c_a, s4)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s5) | (~node12(c_e_h_1, c_a, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s4)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s5) | (~node12(c_e_h_1, c_a, s4, s5)))),
% 292.01/184.56 inference(rewrite,[status(thm)],[])).
% 292.01/184.56 tff(14992,plain,
% 292.01/184.56 (((~node12(c_e_h_1, c_a, s4, s5)) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s4)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s5)) <=> ((~m_mutex_h_half_v_inp(c_e_h_1, c_a, s4)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s5) | (~node12(c_e_h_1, c_a, s4, s5)))),
% 292.01/184.56 inference(rewrite,[status(thm)],[])).
% 292.01/184.56 tff(14993,plain,
% 292.01/184.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_1, c_a, s4, s5)) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s4)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~m_mutex_h_half_v_inp(c_e_h_1, c_a, s4)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s5) | (~node12(c_e_h_1, c_a, s4, s5))))),
% 292.01/184.56 inference(monotonicity,[status(thm)],[14992])).
% 292.01/184.56 tff(14994,plain,
% 292.01/184.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_1, c_a, s4, s5)) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s4)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s4)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s5) | (~node12(c_e_h_1, c_a, s4, s5)))),
% 292.01/184.56 inference(transitivity,[status(thm)],[14993, 14991])).
% 292.01/184.56 tff(14995,plain,
% 292.01/184.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_1, c_a, s4, s5)) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s4)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s5))),
% 292.01/184.56 inference(quant_inst,[status(thm)],[])).
% 292.01/184.56 tff(14996,plain,
% 292.01/184.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s4)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s5) | (~node12(c_e_h_1, c_a, s4, s5))),
% 292.01/184.56 inference(modus_ponens,[status(thm)],[14995, 14994])).
% 292.01/184.56 tff(14997,plain,
% 292.01/184.56 ($false),
% 292.01/184.56 inference(unit_resolution,[status(thm)],[14996, 1483, 14990, 14855, 14989])).
% 292.01/184.56 tff(14998,plain,((~node12(c_e_h_1, c_a, s4, s5)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s5) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s4))), inference(lemma,lemma(discharge,[]))).
% 292.01/184.56 tff(14999,plain,
% 292.01/184.56 (~node12(c_e_h_1, c_a, s4, s5)),
% 292.01/184.56 inference(unit_resolution,[status(thm)],[14998, 14988, 14855])).
% 292.01/184.56 tff(15000,plain,
% 292.01/184.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s4, s5)) | node12(c_e_h_1, c_a, s4, s5) | node13(c_e_h_1, c_a, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s4, s5)) | node12(c_e_h_1, c_a, s4, s5) | node13(c_e_h_1, c_a, s4, s5))),
% 292.01/184.56 inference(rewrite,[status(thm)],[])).
% 292.01/184.56 tff(15001,plain,
% 292.01/184.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s4, s5)) | node12(c_e_h_1, c_a, s4, s5) | node13(c_e_h_1, c_a, s4, s5))),
% 292.01/184.56 inference(quant_inst,[status(thm)],[])).
% 292.01/184.56 tff(15002,plain,
% 292.01/184.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s4, s5)) | node12(c_e_h_1, c_a, s4, s5) | node13(c_e_h_1, c_a, s4, s5)),
% 292.01/184.56 inference(modus_ponens,[status(thm)],[15001, 15000])).
% 292.01/184.56 tff(15003,plain,
% 292.01/184.56 (node12(c_e_h_1, c_a, s4, s5) | node13(c_e_h_1, c_a, s4, s5)),
% 292.01/184.56 inference(unit_resolution,[status(thm)],[15002, 439, 1028])).
% 292.01/184.56 tff(15004,plain,
% 292.01/184.56 (node13(c_e_h_1, c_a, s4, s5)),
% 292.01/184.56 inference(unit_resolution,[status(thm)],[15003, 14999])).
% 292.01/184.56 tff(15005,assumption,(node13(c_e_h_1, c_a, s4, s5)), introduced(assumption)).
% 292.01/184.56 tff(15006,plain,
% 292.01/184.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | ((~m_mutex_h_half_v_out(c_e_h_1, c_a, s4)) | (~node13(c_e_h_1, c_a, s4, s5)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s4)) | (~node13(c_e_h_1, c_a, s4, s5)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s5))),
% 292.01/184.56 inference(rewrite,[status(thm)],[])).
% 292.01/184.56 tff(15007,plain,
% 292.01/184.56 ((m_mutex_h_half_v_out(c_e_h_1, c_a, s5) | (~node13(c_e_h_1, c_a, s4, s5)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s4))) <=> ((~m_mutex_h_half_v_out(c_e_h_1, c_a, s4)) | (~node13(c_e_h_1, c_a, s4, s5)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s5))),
% 292.01/184.56 inference(rewrite,[status(thm)],[])).
% 292.01/184.56 tff(15008,plain,
% 292.01/184.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_1, c_a, s5) | (~node13(c_e_h_1, c_a, s4, s5)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | ((~m_mutex_h_half_v_out(c_e_h_1, c_a, s4)) | (~node13(c_e_h_1, c_a, s4, s5)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s5)))),
% 292.01/184.56 inference(monotonicity,[status(thm)],[15007])).
% 292.01/184.56 tff(15009,plain,
% 292.01/184.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_1, c_a, s5) | (~node13(c_e_h_1, c_a, s4, s5)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s4)) | (~node13(c_e_h_1, c_a, s4, s5)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s5))),
% 292.01/184.56 inference(transitivity,[status(thm)],[15008, 15006])).
% 292.01/184.56 tff(15010,plain,
% 292.01/184.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_1, c_a, s5) | (~node13(c_e_h_1, c_a, s4, s5)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s4)))),
% 292.01/184.56 inference(quant_inst,[status(thm)],[])).
% 292.01/184.56 tff(15011,plain,
% 292.01/184.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s4)) | (~node13(c_e_h_1, c_a, s4, s5)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s5)),
% 292.01/184.56 inference(modus_ponens,[status(thm)],[15010, 15009])).
% 292.01/184.56 tff(15012,plain,
% 292.01/184.56 ($false),
% 292.01/184.56 inference(unit_resolution,[status(thm)],[15011, 1459, 15005, 14805, 14855])).
% 292.01/184.56 tff(15013,plain,((~node13(c_e_h_1, c_a, s4, s5)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s4)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s5)), inference(lemma,lemma(discharge,[]))).
% 292.01/184.56 tff(15014,plain,
% 292.01/184.56 (~m_mutex_h_half_v_out(c_e_h_1, c_a, s4)),
% 292.01/184.56 inference(unit_resolution,[status(thm)],[15013, 15004, 14855])).
% 292.01/184.56 tff(15015,plain,
% 292.01/184.56 (~m_mutex_h_half_v_out(c_e_h_1, c_a, s3)),
% 292.01/184.56 inference(unit_resolution,[status(thm)],[14793, 15014, 14858])).
% 292.01/184.56 tff(15016,plain,
% 292.01/184.56 (~m_and_h_gate_v_in1(c_e_h_1, c_c, s3)),
% 292.01/184.56 inference(unit_resolution,[status(thm)],[14638, 15015])).
% 292.01/184.56 tff(15017,plain,
% 292.01/184.56 (~node20(c_e_h_1, c_c, s3)),
% 292.01/184.56 inference(unit_resolution,[status(thm)],[14646, 15016])).
% 292.01/184.56 tff(15018,plain,
% 292.01/184.56 (m_and_h_gate_v_out(c_e_h_1, c_c, s3)),
% 292.01/184.56 inference(unit_resolution,[status(thm)],[14663, 15017, 14605])).
% 292.01/184.56 tff(15019,plain,
% 292.01/184.56 (~m_mutex_h_half_v_out(c_e_h_1, c_a, s2)),
% 292.01/184.56 inference(unit_resolution,[status(thm)],[14381, 15015])).
% 292.01/184.56 tff(15020,plain,
% 292.01/184.56 (~m_and_h_gate_v_in1(c_e_h_1, c_c, s2)),
% 292.01/184.56 inference(unit_resolution,[status(thm)],[14232, 15019])).
% 292.01/184.56 tff(15021,plain,
% 292.01/184.56 (~node20(c_e_h_1, c_c, s2)),
% 292.01/184.56 inference(unit_resolution,[status(thm)],[14224, 15020])).
% 292.01/184.56 tff(15022,plain,
% 292.01/184.56 ($false),
% 292.01/184.56 inference(unit_resolution,[status(thm)],[14216, 15021, 15018])).
% 292.01/184.56 tff(15023,plain,((~m_and_h_gate_v_out(c_e_h_1, c_c, s4)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s5)), inference(lemma,lemma(discharge,[]))).
% 292.01/184.56 tff(15024,plain,
% 292.01/184.56 (~m_and_h_gate_v_out(c_e_h_1, c_c, s4)),
% 292.01/184.56 inference(unit_resolution,[status(thm)],[15023, 14855])).
% 292.01/184.56 tff(15025,plain,
% 292.01/184.56 (~m_or_h_gate_v_in1(c_e_h_1, c_g, s4)),
% 292.01/184.56 inference(unit_resolution,[status(thm)],[14124, 15024])).
% 292.01/184.56 tff(15026,plain,
% 292.01/184.56 (~m_and_h_gate_v_out(c_e_h_1, c_c, s3)),
% 292.01/184.56 inference(unit_resolution,[status(thm)],[14414, 15024])).
% 292.01/184.56 tff(15027,plain,
% 292.01/184.56 (~m_or_h_gate_v_in1(c_e_h_1, c_g, s3)),
% 292.01/184.56 inference(unit_resolution,[status(thm)],[14418, 2708, 15026])).
% 292.01/184.56 tff(15028,plain,
% 292.01/184.56 (~m_or_h_gate_v_out(c_e_h_1, c_g, s4)),
% 292.01/184.56 inference(unit_resolution,[status(thm)],[14503, 15027])).
% 292.01/184.56 tff(15029,plain,
% 292.01/184.56 (~m_or_h_gate_v_out(c_e_h_1, c_g, s5)),
% 292.01/184.56 inference(unit_resolution,[status(thm)],[14601, 15028, 15025])).
% 292.01/184.56 tff(15030,plain,
% 292.01/184.56 (m_or_h_gate_v_in1(c_e_h_1, c_g, s5)),
% 292.01/184.56 inference(unit_resolution,[status(thm)],[14562, 15029, 14101, 13630])).
% 292.01/184.56 tff(15031,plain,
% 292.01/184.56 (m_and_h_gate_v_out(c_e_h_1, c_c, s5)),
% 292.01/184.56 inference(unit_resolution,[status(thm)],[14530, 2708, 15030])).
% 292.01/184.56 tff(15032,plain,
% 292.01/184.56 (node20(c_e_h_1, c_c, s4)),
% 292.01/184.56 inference(unit_resolution,[status(thm)],[14526, 15031, 15024])).
% 292.01/184.56 tff(15033,plain,
% 292.01/184.56 (m_and_h_gate_v_in1(c_e_h_1, c_c, s4)),
% 292.01/184.56 inference(unit_resolution,[status(thm)],[14116, 15032])).
% 292.01/184.56 tff(15034,plain,
% 292.01/184.56 (m_mutex_h_half_v_out(c_e_h_1, c_a, s4)),
% 292.01/184.56 inference(unit_resolution,[status(thm)],[14108, 15033])).
% 292.01/184.56 tff(15035,plain,
% 292.01/184.56 (~node13(c_e_h_1, c_a, s4, s5)),
% 292.01/184.56 inference(unit_resolution,[status(thm)],[15013, 15034, 14855])).
% 292.01/184.56 tff(15036,plain,
% 292.01/184.56 (node12(c_e_h_1, c_a, s4, s5)),
% 292.01/184.56 inference(unit_resolution,[status(thm)],[15003, 15035])).
% 292.01/184.56 tff(15037,plain,
% 292.01/184.56 (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s4)),
% 292.01/184.56 inference(unit_resolution,[status(thm)],[14998, 15036, 14855])).
% 292.01/184.56 tff(15038,plain,
% 292.01/184.56 (~m_user_v_req(c_e_h_1, c_u, s4)),
% 292.01/184.56 inference(unit_resolution,[status(thm)],[14987, 15037])).
% 292.01/184.56 tff(15039,plain,
% 292.01/184.56 (~m_user_v_req(c_e_h_1, c_u, s3)),
% 292.01/184.56 inference(unit_resolution,[status(thm)],[14979, 15038])).
% 292.01/184.56 tff(15040,plain,
% 292.01/184.56 (~m_user_v_req(c_e_h_1, c_u, s2)),
% 292.01/184.56 inference(unit_resolution,[status(thm)],[14760, 15039])).
% 292.01/184.56 tff(15041,plain,
% 292.01/184.56 (~m_mutex_h_half_v_out(c_e_h_1, c_a, s3)),
% 292.01/184.56 inference(unit_resolution,[status(thm)],[14632, 15040])).
% 292.01/184.57 tff(15042,plain,
% 292.01/184.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~m_mutex_h_half_v_out(c_e_h_1, c_a, s4)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s3) | (~node12(c_e_h_1, c_a, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s4)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s3) | (~node12(c_e_h_1, c_a, s3, s4)))),
% 292.01/184.57 inference(rewrite,[status(thm)],[])).
% 292.01/184.57 tff(15043,plain,
% 292.01/184.57 (((~node12(c_e_h_1, c_a, s3, s4)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s3) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s4))) <=> ((~m_mutex_h_half_v_out(c_e_h_1, c_a, s4)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s3) | (~node12(c_e_h_1, c_a, s3, s4)))),
% 292.01/184.57 inference(rewrite,[status(thm)],[])).
% 292.01/184.57 tff(15044,plain,
% 292.01/184.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_1, c_a, s3, s4)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s3) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~m_mutex_h_half_v_out(c_e_h_1, c_a, s4)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s3) | (~node12(c_e_h_1, c_a, s3, s4))))),
% 292.01/184.57 inference(monotonicity,[status(thm)],[15043])).
% 292.01/184.57 tff(15045,plain,
% 292.01/184.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_1, c_a, s3, s4)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s3) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s4)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s3) | (~node12(c_e_h_1, c_a, s3, s4)))),
% 292.01/184.57 inference(transitivity,[status(thm)],[15044, 15042])).
% 292.01/184.57 tff(15046,plain,
% 292.01/184.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_1, c_a, s3, s4)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s3) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s4)))),
% 292.01/184.57 inference(quant_inst,[status(thm)],[])).
% 292.01/184.57 tff(15047,plain,
% 292.01/184.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s4)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s3) | (~node12(c_e_h_1, c_a, s3, s4))),
% 292.01/184.57 inference(modus_ponens,[status(thm)],[15046, 15045])).
% 292.01/184.57 tff(15048,plain,
% 292.01/184.57 ($false),
% 292.01/184.57 inference(unit_resolution,[status(thm)],[15047, 454, 14771, 14805, 14762])).
% 292.01/184.57 tff(15049,plain,((~node12(c_e_h_1, c_a, s3, s4)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s4)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s3)), inference(lemma,lemma(discharge,[]))).
% 292.01/184.57 tff(15050,plain,
% 292.01/184.57 (~node12(c_e_h_1, c_a, s3, s4)),
% 292.01/184.57 inference(unit_resolution,[status(thm)],[15049, 14805, 14762])).
% 292.01/184.57 tff(15051,plain,
% 292.01/184.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_1, c_a, s4)) | (~node13(c_e_h_1, c_a, s3, s4)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s4)) | (~node13(c_e_h_1, c_a, s3, s4)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s3))),
% 292.01/184.57 inference(rewrite,[status(thm)],[])).
% 292.01/184.57 tff(15052,plain,
% 292.01/184.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_1, c_a, s4)) | (~node13(c_e_h_1, c_a, s3, s4)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s3))),
% 292.01/184.57 inference(quant_inst,[status(thm)],[])).
% 292.01/184.57 tff(15053,plain,
% 292.01/184.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s4)) | (~node13(c_e_h_1, c_a, s3, s4)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s3)),
% 292.01/184.57 inference(modus_ponens,[status(thm)],[15052, 15051])).
% 292.01/184.57 tff(15054,plain,
% 292.01/184.57 ($false),
% 292.01/184.57 inference(unit_resolution,[status(thm)],[15053, 423, 14781, 14805, 14358])).
% 292.01/184.57 tff(15055,plain,((~node13(c_e_h_1, c_a, s3, s4)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s4)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s3)), inference(lemma,lemma(discharge,[]))).
% 292.01/184.57 tff(15056,plain,
% 292.01/184.57 (~node13(c_e_h_1, c_a, s3, s4)),
% 292.01/184.57 inference(unit_resolution,[status(thm)],[15055, 14805, 14358])).
% 292.01/184.57 tff(15057,plain,
% 292.01/184.57 ($false),
% 292.01/184.57 inference(unit_resolution,[status(thm)],[14791, 15056, 15050])).
% 292.01/184.57 tff(15058,plain,((~m_mutex_h_half_v_out(c_e_h_1, c_a, s4)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s3) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s3)), inference(lemma,lemma(discharge,[]))).
% 292.01/184.57 tff(15059,plain,
% 292.01/184.57 (m_mutex_h_half_v_inp(c_e_h_1, c_a, s3)),
% 292.01/184.57 inference(unit_resolution,[status(thm)],[15058, 15041, 15034])).
% 292.01/184.57 tff(15060,plain,
% 292.01/184.57 (((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | ((~m_mutex_h_half_v_inp(c_e_h_1, c_a, s3)) | m_user_v_req(c_e_h_1, c_u, s3))) <=> ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s3)) | m_user_v_req(c_e_h_1, c_u, s3))),
% 292.01/184.57 inference(rewrite,[status(thm)],[])).
% 292.01/184.57 tff(15061,plain,
% 292.01/184.57 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | ((~m_mutex_h_half_v_inp(c_e_h_1, c_a, s3)) | m_user_v_req(c_e_h_1, c_u, s3))),
% 292.01/184.57 inference(quant_inst,[status(thm)],[])).
% 292.01/184.57 tff(15062,plain,
% 292.01/184.57 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s3)) | m_user_v_req(c_e_h_1, c_u, s3)),
% 292.01/184.57 inference(modus_ponens,[status(thm)],[15061, 15060])).
% 292.01/184.57 tff(15063,plain,
% 292.01/184.57 ($false),
% 292.01/184.57 inference(unit_resolution,[status(thm)],[15062, 395, 15039, 15059])).
% 292.01/184.57 tff(15064,plain,(m_mutex_h_half_v_out(c_e_h_1, c_a, s5) | m_or_h_gate_v_in2(c_e_h_1, c_g, s5) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s6))), inference(lemma,lemma(discharge,[]))).
% 292.01/184.57 tff(15065,plain,
% 292.01/184.57 (m_mutex_h_half_v_out(c_e_h_1, c_a, s5) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s6))),
% 292.01/184.57 inference(unit_resolution,[status(thm)],[15064, 14100])).
% 292.01/184.57 tff(15066,plain,
% 292.01/184.57 (m_mutex_h_half_v_out(c_e_h_1, c_a, s5)),
% 292.01/184.57 inference(unit_resolution,[status(thm)],[15065, 13630])).
% 292.01/184.57 tff(15067,assumption,(~m_and_h_gate_v_in1(c_e_h_1, c_c, s5)), introduced(assumption)).
% 292.01/184.57 tff(15068,assumption,(m_mutex_h_half_v_out(c_e_h_1, c_a, s5)), introduced(assumption)).
% 292.01/184.57 tff(15069,plain,
% 292.01/184.57 (((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | ((~m_mutex_h_half_v_out(c_e_h_1, c_a, s5)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s5))) <=> ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s5)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s5))),
% 292.01/184.57 inference(rewrite,[status(thm)],[])).
% 292.01/184.57 tff(15070,plain,
% 292.01/184.57 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | ((~m_mutex_h_half_v_out(c_e_h_1, c_a, s5)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s5))),
% 292.01/184.57 inference(quant_inst,[status(thm)],[])).
% 292.01/184.57 tff(15071,plain,
% 292.01/184.57 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s5)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s5)),
% 292.01/184.57 inference(modus_ponens,[status(thm)],[15070, 15069])).
% 292.01/184.57 tff(15072,plain,
% 292.01/184.57 ($false),
% 292.01/184.57 inference(unit_resolution,[status(thm)],[15071, 2556, 15068, 15067])).
% 292.01/184.57 tff(15073,plain,(m_and_h_gate_v_in1(c_e_h_1, c_c, s5) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s5))), inference(lemma,lemma(discharge,[]))).
% 292.01/184.57 tff(15074,plain,
% 292.01/184.57 (m_and_h_gate_v_in1(c_e_h_1, c_c, s5)),
% 292.01/184.57 inference(unit_resolution,[status(thm)],[15073, 15066])).
% 292.01/184.57 tff(15075,assumption,(m_and_h_gate_v_in1(c_e_h_1, c_c, s5)), introduced(assumption)).
% 292.01/184.57 tff(15076,assumption,(node21(c_e_h_1, c_c, s5, s6)), introduced(assumption)).
% 292.01/184.57 tff(15077,assumption,(m_c_h_element_v_out(c_e_h_1, c_f, s4)), introduced(assumption)).
% 292.01/184.57 tff(15078,assumption,(~m_c_h_element_v_out(c_e_h_1, c_f, s3)), introduced(assumption)).
% 292.01/184.57 tff(15079,assumption,(node18(c_e_h_1, c_f, s3, s4)), introduced(assumption)).
% 292.01/184.57 tff(15080,plain,
% 292.01/184.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~node18(c_e_h_1, c_f, s3, s4)) | m_c_h_element_v_out(c_e_h_1, c_f, s3) | (~m_c_h_element_v_out(c_e_h_1, c_f, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_1, c_f, s3, s4)) | m_c_h_element_v_out(c_e_h_1, c_f, s3) | (~m_c_h_element_v_out(c_e_h_1, c_f, s4)))),
% 292.01/184.57 inference(rewrite,[status(thm)],[])).
% 292.01/184.57 tff(15081,plain,
% 292.01/184.57 (((~m_c_h_element_v_out(c_e_h_1, c_f, s4)) | m_c_h_element_v_out(c_e_h_1, c_f, s3) | (~node18(c_e_h_1, c_f, s3, s4))) <=> ((~node18(c_e_h_1, c_f, s3, s4)) | m_c_h_element_v_out(c_e_h_1, c_f, s3) | (~m_c_h_element_v_out(c_e_h_1, c_f, s4)))),
% 292.01/184.57 inference(rewrite,[status(thm)],[])).
% 292.01/184.57 tff(15082,plain,
% 292.01/184.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s4)) | m_c_h_element_v_out(c_e_h_1, c_f, s3) | (~node18(c_e_h_1, c_f, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~node18(c_e_h_1, c_f, s3, s4)) | m_c_h_element_v_out(c_e_h_1, c_f, s3) | (~m_c_h_element_v_out(c_e_h_1, c_f, s4))))),
% 292.01/184.57 inference(monotonicity,[status(thm)],[15081])).
% 292.01/184.57 tff(15083,plain,
% 292.01/184.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s4)) | m_c_h_element_v_out(c_e_h_1, c_f, s3) | (~node18(c_e_h_1, c_f, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_1, c_f, s3, s4)) | m_c_h_element_v_out(c_e_h_1, c_f, s3) | (~m_c_h_element_v_out(c_e_h_1, c_f, s4)))),
% 292.01/184.57 inference(transitivity,[status(thm)],[15082, 15080])).
% 292.01/184.57 tff(15084,plain,
% 292.01/184.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s4)) | m_c_h_element_v_out(c_e_h_1, c_f, s3) | (~node18(c_e_h_1, c_f, s3, s4)))),
% 292.01/184.57 inference(quant_inst,[status(thm)],[])).
% 292.01/184.57 tff(15085,plain,
% 292.01/184.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~node18(c_e_h_1, c_f, s3, s4)) | m_c_h_element_v_out(c_e_h_1, c_f, s3) | (~m_c_h_element_v_out(c_e_h_1, c_f, s4))),
% 292.01/184.57 inference(modus_ponens,[status(thm)],[15084, 15083])).
% 292.01/184.58 tff(15086,plain,
% 292.01/184.58 ($false),
% 292.01/184.58 inference(unit_resolution,[status(thm)],[15085, 753, 15077, 15079, 15078])).
% 292.01/184.58 tff(15087,plain,((~node18(c_e_h_1, c_f, s3, s4)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s4)) | m_c_h_element_v_out(c_e_h_1, c_f, s3)), inference(lemma,lemma(discharge,[]))).
% 292.01/184.58 tff(15088,plain,
% 292.01/184.58 (~node18(c_e_h_1, c_f, s3, s4)),
% 292.01/184.58 inference(unit_resolution,[status(thm)],[15087, 15078, 15077])).
% 292.01/184.58 tff(15089,assumption,(node15(c_e_h_1, c_f, s3, s4)), introduced(assumption)).
% 292.01/184.58 tff(15090,plain,
% 292.01/184.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s4)) | (~node15(c_e_h_1, c_f, s3, s4)) | m_c_h_element_v_out(c_e_h_1, c_f, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s4)) | (~node15(c_e_h_1, c_f, s3, s4)) | m_c_h_element_v_out(c_e_h_1, c_f, s3))),
% 292.01/184.58 inference(rewrite,[status(thm)],[])).
% 292.01/184.58 tff(15091,plain,
% 292.01/184.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s4)) | (~node15(c_e_h_1, c_f, s3, s4)) | m_c_h_element_v_out(c_e_h_1, c_f, s3))),
% 292.01/184.58 inference(quant_inst,[status(thm)],[])).
% 292.01/184.58 tff(15092,plain,
% 292.01/184.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s4)) | (~node15(c_e_h_1, c_f, s3, s4)) | m_c_h_element_v_out(c_e_h_1, c_f, s3)),
% 292.01/184.58 inference(modus_ponens,[status(thm)],[15091, 15090])).
% 292.01/184.58 tff(15093,plain,
% 292.01/184.58 ($false),
% 292.01/184.58 inference(unit_resolution,[status(thm)],[15092, 147, 15077, 15089, 15078])).
% 292.01/184.58 tff(15094,plain,((~node15(c_e_h_1, c_f, s3, s4)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s4)) | m_c_h_element_v_out(c_e_h_1, c_f, s3)), inference(lemma,lemma(discharge,[]))).
% 292.01/184.58 tff(15095,plain,
% 292.01/184.58 (~node15(c_e_h_1, c_f, s3, s4)),
% 292.01/184.58 inference(unit_resolution,[status(thm)],[15094, 15078, 15077])).
% 292.01/184.58 tff(15096,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s3)), introduced(assumption)).
% 292.01/184.58 tff(15097,assumption,(m_c_h_element_v_out(c_e_h_1, c_h, s2)), introduced(assumption)).
% 292.01/184.58 tff(15098,assumption,(node18(c_e_h_1, c_h, s1, s2)), introduced(assumption)).
% 292.01/184.58 tff(15099,plain,
% 292.01/184.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_h, s1) | (~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | (~node18(c_e_h_1, c_h, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s1) | (~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | (~node18(c_e_h_1, c_h, s1, s2)))),
% 292.01/184.58 inference(rewrite,[status(thm)],[])).
% 292.01/184.58 tff(15100,plain,
% 292.01/184.58 (((~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | m_c_h_element_v_out(c_e_h_1, c_h, s1) | (~node18(c_e_h_1, c_h, s1, s2))) <=> (m_c_h_element_v_out(c_e_h_1, c_h, s1) | (~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | (~node18(c_e_h_1, c_h, s1, s2)))),
% 292.01/184.58 inference(rewrite,[status(thm)],[])).
% 292.01/184.58 tff(15101,plain,
% 292.01/184.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | m_c_h_element_v_out(c_e_h_1, c_h, s1) | (~node18(c_e_h_1, c_h, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_h, s1) | (~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | (~node18(c_e_h_1, c_h, s1, s2))))),
% 292.01/184.58 inference(monotonicity,[status(thm)],[15100])).
% 292.01/184.58 tff(15102,plain,
% 292.01/184.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | m_c_h_element_v_out(c_e_h_1, c_h, s1) | (~node18(c_e_h_1, c_h, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s1) | (~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | (~node18(c_e_h_1, c_h, s1, s2)))),
% 292.01/184.58 inference(transitivity,[status(thm)],[15101, 15099])).
% 292.01/184.58 tff(15103,plain,
% 292.01/184.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | m_c_h_element_v_out(c_e_h_1, c_h, s1) | (~node18(c_e_h_1, c_h, s1, s2)))),
% 292.01/184.58 inference(quant_inst,[status(thm)],[])).
% 292.01/184.58 tff(15104,plain,
% 292.01/184.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s1) | (~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | (~node18(c_e_h_1, c_h, s1, s2))),
% 292.01/184.58 inference(modus_ponens,[status(thm)],[15103, 15102])).
% 292.01/184.58 tff(15105,plain,
% 292.01/184.58 ($false),
% 292.01/184.58 inference(unit_resolution,[status(thm)],[15104, 753, 8451, 15097, 15098])).
% 292.01/184.58 tff(15106,plain,((~node18(c_e_h_1, c_h, s1, s2)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s2))), inference(lemma,lemma(discharge,[]))).
% 292.01/184.58 tff(15107,plain,
% 292.01/184.58 (~node18(c_e_h_1, c_h, s1, s2)),
% 292.01/184.58 inference(unit_resolution,[status(thm)],[15106, 15097])).
% 292.01/184.58 tff(15108,plain,
% 292.01/184.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s1, s2)) | node19(c_e_h_1, c_h, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s1, s2)) | node19(c_e_h_1, c_h, s1, s2))),
% 292.01/184.58 inference(rewrite,[status(thm)],[])).
% 292.01/184.58 tff(15109,plain,
% 292.01/184.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s1, s2)) | node19(c_e_h_1, c_h, s1, s2))),
% 292.01/184.58 inference(quant_inst,[status(thm)],[])).
% 292.01/184.58 tff(15110,plain,
% 292.01/184.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s1, s2)) | node19(c_e_h_1, c_h, s1, s2)),
% 292.01/184.58 inference(modus_ponens,[status(thm)],[15109, 15108])).
% 292.01/184.58 tff(15111,plain,
% 292.01/184.58 (node19(c_e_h_1, c_h, s1, s2)),
% 292.01/184.58 inference(unit_resolution,[status(thm)],[15110, 190, 255])).
% 292.01/184.58 tff(15112,plain,
% 292.01/184.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_h, s1, s2)) | node18(c_e_h_1, c_h, s1, s2) | node17(c_e_h_1, c_h, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_h, s1, s2)) | node18(c_e_h_1, c_h, s1, s2) | node17(c_e_h_1, c_h, s1))),
% 292.01/184.58 inference(rewrite,[status(thm)],[])).
% 292.01/184.58 tff(15113,plain,
% 292.01/184.58 ((node17(c_e_h_1, c_h, s1) | node18(c_e_h_1, c_h, s1, s2) | (~node19(c_e_h_1, c_h, s1, s2))) <=> ((~node19(c_e_h_1, c_h, s1, s2)) | node18(c_e_h_1, c_h, s1, s2) | node17(c_e_h_1, c_h, s1))),
% 292.01/184.58 inference(rewrite,[status(thm)],[])).
% 292.01/184.58 tff(15114,plain,
% 292.01/184.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s1) | node18(c_e_h_1, c_h, s1, s2) | (~node19(c_e_h_1, c_h, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_h, s1, s2)) | node18(c_e_h_1, c_h, s1, s2) | node17(c_e_h_1, c_h, s1)))),
% 292.01/184.58 inference(monotonicity,[status(thm)],[15113])).
% 292.01/184.58 tff(15115,plain,
% 292.01/184.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s1) | node18(c_e_h_1, c_h, s1, s2) | (~node19(c_e_h_1, c_h, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_h, s1, s2)) | node18(c_e_h_1, c_h, s1, s2) | node17(c_e_h_1, c_h, s1))),
% 292.01/184.58 inference(transitivity,[status(thm)],[15114, 15112])).
% 292.01/184.58 tff(15116,plain,
% 292.01/184.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s1) | node18(c_e_h_1, c_h, s1, s2) | (~node19(c_e_h_1, c_h, s1, s2)))),
% 292.01/184.58 inference(quant_inst,[status(thm)],[])).
% 292.01/184.58 tff(15117,plain,
% 292.01/184.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_h, s1, s2)) | node18(c_e_h_1, c_h, s1, s2) | node17(c_e_h_1, c_h, s1)),
% 292.01/184.58 inference(modus_ponens,[status(thm)],[15116, 15115])).
% 292.01/184.58 tff(15118,plain,
% 292.01/184.58 (node18(c_e_h_1, c_h, s1, s2) | node17(c_e_h_1, c_h, s1)),
% 292.01/184.58 inference(unit_resolution,[status(thm)],[15117, 776, 15111])).
% 292.01/184.58 tff(15119,plain,
% 292.01/184.58 (node17(c_e_h_1, c_h, s1)),
% 292.01/184.58 inference(unit_resolution,[status(thm)],[15118, 15107])).
% 292.01/184.58 tff(15120,assumption,(m_and_h_gate_v_out(c_e_h_1, c_l, s0)), introduced(assumption)).
% 292.01/184.58 tff(15121,plain,
% 292.01/184.58 ((~![I0: $i, I1: $i] : (~m_and_h_gate_v_out(I0, I1, s0))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s0))),
% 292.01/184.58 inference(quant_inst,[status(thm)],[])).
% 292.01/184.58 tff(15122,plain,
% 292.01/184.58 ($false),
% 292.01/184.58 inference(unit_resolution,[status(thm)],[15121, 95, 15120])).
% 292.01/184.58 tff(15123,plain,(~m_and_h_gate_v_out(c_e_h_1, c_l, s0)), inference(lemma,lemma(discharge,[]))).
% 292.01/184.58 tff(15124,plain,
% 292.01/184.58 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s0)) | m_and_h_gate_v_out(c_e_h_1, c_l, s0))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s0)) | m_and_h_gate_v_out(c_e_h_1, c_l, s0))),
% 292.01/184.58 inference(rewrite,[status(thm)],[])).
% 292.01/184.58 tff(15125,plain,
% 292.01/184.58 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s0)) | m_and_h_gate_v_out(c_e_h_1, c_l, s0))),
% 292.01/184.58 inference(quant_inst,[status(thm)],[])).
% 292.01/184.58 tff(15126,plain,
% 292.01/184.58 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s0)) | m_and_h_gate_v_out(c_e_h_1, c_l, s0)),
% 292.01/184.58 inference(modus_ponens,[status(thm)],[15125, 15124])).
% 292.01/184.58 tff(15127,plain,
% 292.01/184.58 (~m_or_h_gate_v_in1(c_e_h_1, c_j, s0)),
% 292.01/184.58 inference(unit_resolution,[status(thm)],[15126, 1100, 15123])).
% 292.01/184.58 tff(15128,assumption,(m_or_h_gate_v_out(c_e_h_1, c_j, s1)), introduced(assumption)).
% 292.01/184.58 tff(15129,assumption,(node6(c_e_h_1, c_j, s0, s1)), introduced(assumption)).
% 292.01/184.58 tff(15130,plain,
% 292.01/184.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s0) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s1)) | (~node6(c_e_h_1, c_j, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s0) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s1)) | (~node6(c_e_h_1, c_j, s0, s1)))),
% 292.01/184.58 inference(rewrite,[status(thm)],[])).
% 292.01/184.58 tff(15131,plain,
% 292.01/184.58 (((~node6(c_e_h_1, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s1)) | m_or_h_gate_v_out(c_e_h_1, c_j, s0)) <=> (m_or_h_gate_v_out(c_e_h_1, c_j, s0) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s1)) | (~node6(c_e_h_1, c_j, s0, s1)))),
% 292.01/184.58 inference(rewrite,[status(thm)],[])).
% 292.01/184.58 tff(15132,plain,
% 292.01/184.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s1)) | m_or_h_gate_v_out(c_e_h_1, c_j, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s0) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s1)) | (~node6(c_e_h_1, c_j, s0, s1))))),
% 292.01/184.58 inference(monotonicity,[status(thm)],[15131])).
% 292.01/184.58 tff(15133,plain,
% 292.01/184.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s1)) | m_or_h_gate_v_out(c_e_h_1, c_j, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s0) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s1)) | (~node6(c_e_h_1, c_j, s0, s1)))),
% 292.01/184.59 inference(transitivity,[status(thm)],[15132, 15130])).
% 292.01/184.59 tff(15134,plain,
% 292.01/184.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s1)) | m_or_h_gate_v_out(c_e_h_1, c_j, s0))),
% 292.01/184.59 inference(quant_inst,[status(thm)],[])).
% 292.01/184.59 tff(15135,plain,
% 292.01/184.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s0) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s1)) | (~node6(c_e_h_1, c_j, s0, s1))),
% 292.01/184.59 inference(modus_ponens,[status(thm)],[15134, 15133])).
% 292.01/184.59 tff(15136,plain,
% 292.01/184.59 ($false),
% 292.01/184.59 inference(unit_resolution,[status(thm)],[15135, 1121, 8421, 15128, 15129])).
% 292.01/184.59 tff(15137,plain,((~node6(c_e_h_1, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s1))), inference(lemma,lemma(discharge,[]))).
% 292.01/184.59 tff(15138,plain,
% 292.01/184.59 (~node6(c_e_h_1, c_j, s0, s1)),
% 292.01/184.59 inference(unit_resolution,[status(thm)],[15137, 15128])).
% 292.01/184.59 tff(15139,plain,
% 292.01/184.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s0, s1)) | node5(c_e_h_1, c_j, s0, s1) | node6(c_e_h_1, c_j, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s0, s1)) | node5(c_e_h_1, c_j, s0, s1) | node6(c_e_h_1, c_j, s0, s1))),
% 292.01/184.59 inference(rewrite,[status(thm)],[])).
% 292.01/184.59 tff(15140,plain,
% 292.01/184.59 ((node6(c_e_h_1, c_j, s0, s1) | node5(c_e_h_1, c_j, s0, s1) | (~trans(s0, s1))) <=> ((~trans(s0, s1)) | node5(c_e_h_1, c_j, s0, s1) | node6(c_e_h_1, c_j, s0, s1))),
% 292.01/184.59 inference(rewrite,[status(thm)],[])).
% 292.01/184.59 tff(15141,plain,
% 292.01/184.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s0, s1) | node5(c_e_h_1, c_j, s0, s1) | (~trans(s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s0, s1)) | node5(c_e_h_1, c_j, s0, s1) | node6(c_e_h_1, c_j, s0, s1)))),
% 292.01/184.59 inference(monotonicity,[status(thm)],[15140])).
% 292.01/184.59 tff(15142,plain,
% 292.01/184.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s0, s1) | node5(c_e_h_1, c_j, s0, s1) | (~trans(s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s0, s1)) | node5(c_e_h_1, c_j, s0, s1) | node6(c_e_h_1, c_j, s0, s1))),
% 292.01/184.59 inference(transitivity,[status(thm)],[15141, 15139])).
% 292.01/184.59 tff(15143,plain,
% 292.01/184.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s0, s1) | node5(c_e_h_1, c_j, s0, s1) | (~trans(s0, s1)))),
% 292.01/184.59 inference(quant_inst,[status(thm)],[])).
% 292.01/184.59 tff(15144,plain,
% 292.01/184.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s0, s1)) | node5(c_e_h_1, c_j, s0, s1) | node6(c_e_h_1, c_j, s0, s1)),
% 292.01/184.59 inference(modus_ponens,[status(thm)],[15143, 15142])).
% 292.01/184.59 tff(15145,plain,
% 292.01/184.59 (node5(c_e_h_1, c_j, s0, s1) | node6(c_e_h_1, c_j, s0, s1)),
% 292.01/184.59 inference(unit_resolution,[status(thm)],[15144, 1141, 72])).
% 292.01/184.59 tff(15146,plain,
% 292.01/184.59 (node5(c_e_h_1, c_j, s0, s1)),
% 292.01/184.59 inference(unit_resolution,[status(thm)],[15145, 15138])).
% 292.01/184.59 tff(15147,plain,
% 292.01/184.59 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s0))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s0))),
% 292.01/184.59 inference(rewrite,[status(thm)],[])).
% 292.01/184.59 tff(15148,plain,
% 292.01/184.59 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s0))),
% 292.01/184.59 inference(quant_inst,[status(thm)],[])).
% 292.01/184.59 tff(15149,plain,
% 292.01/184.59 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s0)),
% 292.01/184.59 inference(modus_ponens,[status(thm)],[15148, 15147])).
% 292.01/184.59 tff(15150,plain,
% 292.01/184.59 (node3(c_e_h_3, c_e_h_1, s0)),
% 292.01/184.59 inference(unit_resolution,[status(thm)],[15149, 2922, 1056])).
% 292.01/184.59 tff(15151,plain,
% 292.01/184.59 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s0)) | (~node3(c_e_h_3, c_e_h_1, s0)) | m_and_h_gate_v_out(c_e_h_3, c_q, s0))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s0)) | (~node3(c_e_h_3, c_e_h_1, s0)) | m_and_h_gate_v_out(c_e_h_3, c_q, s0))),
% 292.01/184.59 inference(rewrite,[status(thm)],[])).
% 292.01/184.59 tff(15152,plain,
% 292.01/184.59 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s0)) | (~node3(c_e_h_3, c_e_h_1, s0)) | m_and_h_gate_v_out(c_e_h_3, c_q, s0))),
% 292.01/184.59 inference(quant_inst,[status(thm)],[])).
% 292.01/184.59 tff(15153,plain,
% 292.01/184.59 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s0)) | (~node3(c_e_h_3, c_e_h_1, s0)) | m_and_h_gate_v_out(c_e_h_3, c_q, s0)),
% 292.01/184.59 inference(modus_ponens,[status(thm)],[15152, 15151])).
% 292.01/184.59 tff(15154,plain,
% 292.01/184.59 ((~m_cell_v_ack(c_e_h_1, s0)) | m_and_h_gate_v_out(c_e_h_3, c_q, s0)),
% 292.01/184.59 inference(unit_resolution,[status(thm)],[15153, 1073, 15150])).
% 292.01/184.59 tff(15155,plain,
% 292.01/184.59 (~m_cell_v_ack(c_e_h_1, s0)),
% 292.01/184.59 inference(unit_resolution,[status(thm)],[15154, 5646])).
% 292.01/184.59 tff(15156,plain,
% 292.01/184.59 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s0)) | m_cell_v_ack(c_e_h_1, s0))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s0)) | m_cell_v_ack(c_e_h_1, s0))),
% 292.01/184.59 inference(rewrite,[status(thm)],[])).
% 292.01/184.59 tff(15157,plain,
% 292.01/184.59 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s0)) | m_cell_v_ack(c_e_h_1, s0))),
% 292.01/184.59 inference(quant_inst,[status(thm)],[])).
% 292.01/184.59 tff(15158,plain,
% 292.01/184.59 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s0)) | m_cell_v_ack(c_e_h_1, s0)),
% 292.01/184.59 inference(modus_ponens,[status(thm)],[15157, 15156])).
% 292.01/184.59 tff(15159,plain,
% 292.01/184.59 (~m_or_h_gate_v_in2(c_e_h_1, c_j, s0)),
% 292.01/184.59 inference(unit_resolution,[status(thm)],[15158, 1085, 15155])).
% 292.01/184.59 tff(15160,plain,
% 292.01/184.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_1, c_j, s0) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s1)) | (~node5(c_e_h_1, c_j, s0, s1)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_1, c_j, s0) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s1)) | (~node5(c_e_h_1, c_j, s0, s1)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s0))),
% 292.01/184.59 inference(rewrite,[status(thm)],[])).
% 292.01/184.59 tff(15161,plain,
% 292.01/184.59 ((m_or_h_gate_v_in1(c_e_h_1, c_j, s0) | m_or_h_gate_v_in2(c_e_h_1, c_j, s0) | (~node5(c_e_h_1, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s1))) <=> (m_or_h_gate_v_in2(c_e_h_1, c_j, s0) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s1)) | (~node5(c_e_h_1, c_j, s0, s1)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s0))),
% 292.01/184.59 inference(rewrite,[status(thm)],[])).
% 292.01/184.59 tff(15162,plain,
% 292.01/184.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s0) | m_or_h_gate_v_in2(c_e_h_1, c_j, s0) | (~node5(c_e_h_1, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_1, c_j, s0) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s1)) | (~node5(c_e_h_1, c_j, s0, s1)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s0)))),
% 292.01/184.59 inference(monotonicity,[status(thm)],[15161])).
% 292.01/184.59 tff(15163,plain,
% 292.01/184.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s0) | m_or_h_gate_v_in2(c_e_h_1, c_j, s0) | (~node5(c_e_h_1, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_1, c_j, s0) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s1)) | (~node5(c_e_h_1, c_j, s0, s1)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s0))),
% 292.01/184.59 inference(transitivity,[status(thm)],[15162, 15160])).
% 292.01/184.59 tff(15164,plain,
% 292.01/184.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s0) | m_or_h_gate_v_in2(c_e_h_1, c_j, s0) | (~node5(c_e_h_1, c_j, s0, s1)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s1)))),
% 292.01/184.59 inference(quant_inst,[status(thm)],[])).
% 292.01/184.59 tff(15165,plain,
% 292.01/184.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_1, c_j, s0) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s1)) | (~node5(c_e_h_1, c_j, s0, s1)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s0)),
% 292.01/184.59 inference(modus_ponens,[status(thm)],[15164, 15163])).
% 292.01/184.59 tff(15166,plain,
% 292.01/184.59 ($false),
% 292.01/184.59 inference(unit_resolution,[status(thm)],[15165, 1159, 15159, 15128, 15146, 15127])).
% 292.01/184.59 tff(15167,plain,(~m_or_h_gate_v_out(c_e_h_1, c_j, s1)), inference(lemma,lemma(discharge,[]))).
% 292.01/184.59 tff(15168,plain,
% 292.01/184.59 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s1)) | m_or_h_gate_v_out(c_e_h_1, c_j, s1))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s1)) | m_or_h_gate_v_out(c_e_h_1, c_j, s1))),
% 292.01/184.59 inference(rewrite,[status(thm)],[])).
% 292.01/184.59 tff(15169,plain,
% 292.01/184.59 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s1)) | m_or_h_gate_v_out(c_e_h_1, c_j, s1))),
% 292.01/184.59 inference(quant_inst,[status(thm)],[])).
% 292.01/184.59 tff(15170,plain,
% 292.01/184.59 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s1)) | m_or_h_gate_v_out(c_e_h_1, c_j, s1)),
% 292.01/184.59 inference(modus_ponens,[status(thm)],[15169, 15168])).
% 292.01/184.59 tff(15171,plain,
% 292.01/184.59 (~m_c_h_element_v_in2(c_e_h_1, c_h, s1)),
% 292.01/184.59 inference(unit_resolution,[status(thm)],[15170, 1174, 15167])).
% 292.01/184.59 tff(15172,plain,
% 292.01/184.59 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s1)) | m_c_h_element_v_in2(c_e_h_1, c_h, s1) | (~node17(c_e_h_1, c_h, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s1)) | m_c_h_element_v_in2(c_e_h_1, c_h, s1) | (~node17(c_e_h_1, c_h, s1)))),
% 292.01/184.59 inference(rewrite,[status(thm)],[])).
% 292.01/184.59 tff(15173,plain,
% 292.01/184.59 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s1)) | m_c_h_element_v_in2(c_e_h_1, c_h, s1) | (~node17(c_e_h_1, c_h, s1)))),
% 292.01/184.59 inference(quant_inst,[status(thm)],[])).
% 292.01/184.59 tff(15174,plain,
% 292.01/184.59 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s1)) | m_c_h_element_v_in2(c_e_h_1, c_h, s1) | (~node17(c_e_h_1, c_h, s1))),
% 292.01/184.60 inference(modus_ponens,[status(thm)],[15173, 15172])).
% 292.01/184.60 tff(15175,plain,
% 292.01/184.60 ((~m_c_h_element_v_in1(c_e_h_1, c_h, s1)) | (~node17(c_e_h_1, c_h, s1))),
% 292.01/184.60 inference(unit_resolution,[status(thm)],[15174, 919, 15171])).
% 292.01/184.60 tff(15176,plain,
% 292.01/184.60 (~m_c_h_element_v_in1(c_e_h_1, c_h, s1)),
% 292.01/184.60 inference(unit_resolution,[status(thm)],[15175, 15119])).
% 292.01/184.60 tff(15177,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_h, s1)), introduced(assumption)).
% 292.01/184.60 tff(15178,assumption,(~node15(c_e_h_1, c_h, s1, s2)), introduced(assumption)).
% 292.01/184.60 tff(15179,plain,
% 292.01/184.60 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s1)) | m_c_h_element_v_in1(c_e_h_1, c_h, s1) | m_c_h_element_v_in2(c_e_h_1, c_h, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s1)) | m_c_h_element_v_in1(c_e_h_1, c_h, s1) | m_c_h_element_v_in2(c_e_h_1, c_h, s1))),
% 292.01/184.60 inference(rewrite,[status(thm)],[])).
% 292.01/184.60 tff(15180,plain,
% 292.01/184.60 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s1)) | m_c_h_element_v_in1(c_e_h_1, c_h, s1) | m_c_h_element_v_in2(c_e_h_1, c_h, s1))),
% 292.01/184.60 inference(quant_inst,[status(thm)],[])).
% 292.01/184.60 tff(15181,plain,
% 292.01/184.60 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s1)) | m_c_h_element_v_in1(c_e_h_1, c_h, s1) | m_c_h_element_v_in2(c_e_h_1, c_h, s1)),
% 292.01/184.60 inference(modus_ponens,[status(thm)],[15180, 15179])).
% 292.01/184.60 tff(15182,plain,
% 292.01/184.60 ((~node16(c_e_h_1, c_h, s1)) | m_c_h_element_v_in1(c_e_h_1, c_h, s1)),
% 292.01/184.60 inference(unit_resolution,[status(thm)],[15181, 178, 15171])).
% 292.01/184.60 tff(15183,plain,
% 292.01/184.60 (~node16(c_e_h_1, c_h, s1)),
% 292.01/184.60 inference(unit_resolution,[status(thm)],[15182, 15177])).
% 292.01/184.60 tff(15184,plain,
% 292.01/184.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_h, s1, s2)) | node15(c_e_h_1, c_h, s1, s2) | node14(c_e_h_1, c_h, s1, s2) | node16(c_e_h_1, c_h, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_h, s1, s2)) | node15(c_e_h_1, c_h, s1, s2) | node14(c_e_h_1, c_h, s1, s2) | node16(c_e_h_1, c_h, s1))),
% 292.01/184.60 inference(rewrite,[status(thm)],[])).
% 292.01/184.60 tff(15185,plain,
% 292.01/184.60 ((node16(c_e_h_1, c_h, s1) | node14(c_e_h_1, c_h, s1, s2) | node15(c_e_h_1, c_h, s1, s2) | (~node19(c_e_h_1, c_h, s1, s2))) <=> ((~node19(c_e_h_1, c_h, s1, s2)) | node15(c_e_h_1, c_h, s1, s2) | node14(c_e_h_1, c_h, s1, s2) | node16(c_e_h_1, c_h, s1))),
% 292.01/184.60 inference(rewrite,[status(thm)],[])).
% 292.01/184.60 tff(15186,plain,
% 292.01/184.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s1) | node14(c_e_h_1, c_h, s1, s2) | node15(c_e_h_1, c_h, s1, s2) | (~node19(c_e_h_1, c_h, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_h, s1, s2)) | node15(c_e_h_1, c_h, s1, s2) | node14(c_e_h_1, c_h, s1, s2) | node16(c_e_h_1, c_h, s1)))),
% 292.01/184.60 inference(monotonicity,[status(thm)],[15185])).
% 292.01/184.60 tff(15187,plain,
% 292.01/184.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s1) | node14(c_e_h_1, c_h, s1, s2) | node15(c_e_h_1, c_h, s1, s2) | (~node19(c_e_h_1, c_h, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_h, s1, s2)) | node15(c_e_h_1, c_h, s1, s2) | node14(c_e_h_1, c_h, s1, s2) | node16(c_e_h_1, c_h, s1))),
% 292.01/184.60 inference(transitivity,[status(thm)],[15186, 15184])).
% 292.01/184.60 tff(15188,plain,
% 292.01/184.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s1) | node14(c_e_h_1, c_h, s1, s2) | node15(c_e_h_1, c_h, s1, s2) | (~node19(c_e_h_1, c_h, s1, s2)))),
% 292.11/184.61 inference(quant_inst,[status(thm)],[])).
% 292.11/184.61 tff(15189,plain,
% 292.11/184.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_h, s1, s2)) | node15(c_e_h_1, c_h, s1, s2) | node14(c_e_h_1, c_h, s1, s2) | node16(c_e_h_1, c_h, s1)),
% 292.11/184.61 inference(modus_ponens,[status(thm)],[15188, 15187])).
% 292.11/184.61 tff(15190,plain,
% 292.11/184.61 (node15(c_e_h_1, c_h, s1, s2) | node14(c_e_h_1, c_h, s1, s2) | node16(c_e_h_1, c_h, s1)),
% 292.11/184.61 inference(unit_resolution,[status(thm)],[15189, 204, 15111])).
% 292.11/184.61 tff(15191,plain,
% 292.11/184.61 (node14(c_e_h_1, c_h, s1, s2)),
% 292.11/184.61 inference(unit_resolution,[status(thm)],[15190, 15183, 15178])).
% 292.11/184.61 tff(15192,plain,
% 292.11/184.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | m_c_h_element_v_in1(c_e_h_1, c_h, s1) | (~node14(c_e_h_1, c_h, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | m_c_h_element_v_in1(c_e_h_1, c_h, s1) | (~node14(c_e_h_1, c_h, s1, s2)))),
% 292.11/184.61 inference(rewrite,[status(thm)],[])).
% 292.11/184.61 tff(15193,plain,
% 292.11/184.61 (((~node14(c_e_h_1, c_h, s1, s2)) | m_c_h_element_v_in1(c_e_h_1, c_h, s1) | (~m_c_h_element_v_out(c_e_h_1, c_h, s2))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | m_c_h_element_v_in1(c_e_h_1, c_h, s1) | (~node14(c_e_h_1, c_h, s1, s2)))),
% 292.11/184.61 inference(rewrite,[status(thm)],[])).
% 292.11/184.61 tff(15194,plain,
% 292.11/184.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s1, s2)) | m_c_h_element_v_in1(c_e_h_1, c_h, s1) | (~m_c_h_element_v_out(c_e_h_1, c_h, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | m_c_h_element_v_in1(c_e_h_1, c_h, s1) | (~node14(c_e_h_1, c_h, s1, s2))))),
% 292.11/184.61 inference(monotonicity,[status(thm)],[15193])).
% 292.11/184.61 tff(15195,plain,
% 292.11/184.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s1, s2)) | m_c_h_element_v_in1(c_e_h_1, c_h, s1) | (~m_c_h_element_v_out(c_e_h_1, c_h, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | m_c_h_element_v_in1(c_e_h_1, c_h, s1) | (~node14(c_e_h_1, c_h, s1, s2)))),
% 292.11/184.61 inference(transitivity,[status(thm)],[15194, 15192])).
% 292.11/184.61 tff(15196,plain,
% 292.11/184.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s1, s2)) | m_c_h_element_v_in1(c_e_h_1, c_h, s1) | (~m_c_h_element_v_out(c_e_h_1, c_h, s2)))),
% 292.11/184.61 inference(quant_inst,[status(thm)],[])).
% 292.11/184.61 tff(15197,plain,
% 292.11/184.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | m_c_h_element_v_in1(c_e_h_1, c_h, s1) | (~node14(c_e_h_1, c_h, s1, s2))),
% 292.11/184.61 inference(modus_ponens,[status(thm)],[15196, 15195])).
% 292.11/184.61 tff(15198,plain,
% 292.11/184.61 ($false),
% 292.11/184.61 inference(unit_resolution,[status(thm)],[15197, 223, 15097, 15191, 15177])).
% 292.11/184.61 tff(15199,plain,(m_c_h_element_v_in1(c_e_h_1, c_h, s1) | (~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | node15(c_e_h_1, c_h, s1, s2)), inference(lemma,lemma(discharge,[]))).
% 292.11/184.61 tff(15200,plain,
% 292.11/184.61 (node15(c_e_h_1, c_h, s1, s2)),
% 292.11/184.61 inference(unit_resolution,[status(thm)],[15199, 15176, 15097])).
% 292.11/184.61 tff(15201,plain,
% 292.11/184.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | (~node15(c_e_h_1, c_h, s1, s2)) | m_c_h_element_v_out(c_e_h_1, c_h, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | (~node15(c_e_h_1, c_h, s1, s2)) | m_c_h_element_v_out(c_e_h_1, c_h, s1))),
% 292.11/184.61 inference(rewrite,[status(thm)],[])).
% 292.11/184.61 tff(15202,plain,
% 292.11/184.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | (~node15(c_e_h_1, c_h, s1, s2)) | m_c_h_element_v_out(c_e_h_1, c_h, s1))),
% 292.11/184.61 inference(quant_inst,[status(thm)],[])).
% 292.11/184.61 tff(15203,plain,
% 292.11/184.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s2)) | (~node15(c_e_h_1, c_h, s1, s2)) | m_c_h_element_v_out(c_e_h_1, c_h, s1)),
% 292.11/184.61 inference(modus_ponens,[status(thm)],[15202, 15201])).
% 292.11/184.61 tff(15204,plain,
% 292.11/184.61 ($false),
% 292.11/184.61 inference(unit_resolution,[status(thm)],[15203, 147, 8451, 15097, 15200])).
% 292.11/184.61 tff(15205,plain,(~m_c_h_element_v_out(c_e_h_1, c_h, s2)), inference(lemma,lemma(discharge,[]))).
% 292.11/184.61 tff(15206,plain,
% 292.11/184.61 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s2)) | m_c_h_element_v_out(c_e_h_1, c_h, s2))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s2)) | m_c_h_element_v_out(c_e_h_1, c_h, s2))),
% 292.11/184.61 inference(rewrite,[status(thm)],[])).
% 292.11/184.61 tff(15207,plain,
% 292.11/184.61 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s2)) | m_c_h_element_v_out(c_e_h_1, c_h, s2))),
% 292.11/184.61 inference(quant_inst,[status(thm)],[])).
% 292.11/184.61 tff(15208,plain,
% 292.11/184.61 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s2)) | m_c_h_element_v_out(c_e_h_1, c_h, s2)),
% 292.11/184.61 inference(modus_ponens,[status(thm)],[15207, 15206])).
% 292.11/184.61 tff(15209,plain,
% 292.11/184.61 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s2)),
% 292.11/184.61 inference(unit_resolution,[status(thm)],[15208, 619, 15205])).
% 292.11/184.61 tff(15210,plain,
% 292.11/184.61 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s2)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s2)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s2))),
% 292.11/184.61 inference(rewrite,[status(thm)],[])).
% 292.11/184.61 tff(15211,plain,
% 292.11/184.61 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s2)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s2))),
% 292.11/184.61 inference(quant_inst,[status(thm)],[])).
% 292.11/184.61 tff(15212,plain,
% 292.11/184.61 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s2)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s2)),
% 292.11/184.61 inference(modus_ponens,[status(thm)],[15211, 15210])).
% 292.11/184.61 tff(15213,plain,
% 292.11/184.61 (~node20(c_e_h_1, c_i, s2)),
% 292.11/184.61 inference(unit_resolution,[status(thm)],[15212, 38, 15209])).
% 292.11/184.61 tff(15214,assumption,(node21(c_e_h_1, c_i, s2, s3)), introduced(assumption)).
% 292.11/184.61 tff(15215,plain,
% 292.11/184.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s3)) | node20(c_e_h_1, c_i, s2) | (~node21(c_e_h_1, c_i, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s3)) | node20(c_e_h_1, c_i, s2) | (~node21(c_e_h_1, c_i, s2, s3)))),
% 292.11/184.61 inference(rewrite,[status(thm)],[])).
% 292.11/184.61 tff(15216,plain,
% 292.11/184.61 ((node20(c_e_h_1, c_i, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s3)) | (~node21(c_e_h_1, c_i, s2, s3))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_i, s3)) | node20(c_e_h_1, c_i, s2) | (~node21(c_e_h_1, c_i, s2, s3)))),
% 292.11/184.61 inference(rewrite,[status(thm)],[])).
% 292.11/184.61 tff(15217,plain,
% 292.11/184.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s3)) | (~node21(c_e_h_1, c_i, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s3)) | node20(c_e_h_1, c_i, s2) | (~node21(c_e_h_1, c_i, s2, s3))))),
% 292.11/184.61 inference(monotonicity,[status(thm)],[15216])).
% 292.11/184.61 tff(15218,plain,
% 292.11/184.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s3)) | (~node21(c_e_h_1, c_i, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s3)) | node20(c_e_h_1, c_i, s2) | (~node21(c_e_h_1, c_i, s2, s3)))),
% 292.11/184.61 inference(transitivity,[status(thm)],[15217, 15215])).
% 292.11/184.61 tff(15219,plain,
% 292.11/184.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s3)) | (~node21(c_e_h_1, c_i, s2, s3)))),
% 292.11/184.61 inference(quant_inst,[status(thm)],[])).
% 292.11/184.61 tff(15220,plain,
% 292.11/184.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s3)) | node20(c_e_h_1, c_i, s2) | (~node21(c_e_h_1, c_i, s2, s3))),
% 292.11/184.61 inference(modus_ponens,[status(thm)],[15219, 15218])).
% 292.11/184.61 tff(15221,plain,
% 292.11/184.61 ($false),
% 292.11/184.61 inference(unit_resolution,[status(thm)],[15220, 52, 15096, 15214, 15213])).
% 292.11/184.61 tff(15222,plain,((~node21(c_e_h_1, c_i, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s3))), inference(lemma,lemma(discharge,[]))).
% 292.11/184.61 tff(15223,plain,
% 292.11/184.61 (~node21(c_e_h_1, c_i, s2, s3)),
% 292.11/184.61 inference(unit_resolution,[status(thm)],[15222, 15096])).
% 292.11/184.61 tff(15224,plain,
% 292.11/184.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_1, c_i, s2, s3) | node22(c_e_h_1, c_i, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_1, c_i, s2, s3) | node22(c_e_h_1, c_i, s2, s3))),
% 292.11/184.61 inference(rewrite,[status(thm)],[])).
% 292.11/184.61 tff(15225,plain,
% 292.11/184.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_1, c_i, s2, s3) | node22(c_e_h_1, c_i, s2, s3))),
% 292.11/184.61 inference(quant_inst,[status(thm)],[])).
% 292.11/184.61 tff(15226,plain,
% 292.11/184.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_1, c_i, s2, s3) | node22(c_e_h_1, c_i, s2, s3)),
% 292.11/184.61 inference(modus_ponens,[status(thm)],[15225, 15224])).
% 292.11/184.61 tff(15227,plain,
% 292.11/184.61 (node21(c_e_h_1, c_i, s2, s3) | node22(c_e_h_1, c_i, s2, s3)),
% 292.11/184.61 inference(unit_resolution,[status(thm)],[15226, 82, 318])).
% 292.11/184.61 tff(15228,plain,
% 292.11/184.61 (node22(c_e_h_1, c_i, s2, s3)),
% 292.11/184.61 inference(unit_resolution,[status(thm)],[15227, 15223])).
% 292.11/184.61 tff(15229,plain,
% 292.11/184.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s3)) | (~node22(c_e_h_1, c_i, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_i, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s3)) | (~node22(c_e_h_1, c_i, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_i, s2))),
% 292.11/184.61 inference(rewrite,[status(thm)],[])).
% 292.11/184.61 tff(15230,plain,
% 292.11/184.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s3)) | (~node22(c_e_h_1, c_i, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_i, s2))),
% 292.11/184.61 inference(quant_inst,[status(thm)],[])).
% 292.11/184.61 tff(15231,plain,
% 292.11/184.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s3)) | (~node22(c_e_h_1, c_i, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_i, s2)),
% 292.11/184.61 inference(modus_ponens,[status(thm)],[15230, 15229])).
% 292.11/184.61 tff(15232,plain,
% 292.11/184.61 ($false),
% 292.11/184.61 inference(unit_resolution,[status(thm)],[15231, 108, 15096, 15228, 8477])).
% 292.11/184.61 tff(15233,plain,(~m_and_h_gate_v_out(c_e_h_1, c_i, s3)), inference(lemma,lemma(discharge,[]))).
% 292.11/184.61 tff(15234,plain,
% 292.11/184.61 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s3)) | m_and_h_gate_v_out(c_e_h_1, c_i, s3))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s3)) | m_and_h_gate_v_out(c_e_h_1, c_i, s3))),
% 292.11/184.61 inference(rewrite,[status(thm)],[])).
% 292.11/184.61 tff(15235,plain,
% 292.11/184.61 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s3)) | m_and_h_gate_v_out(c_e_h_1, c_i, s3))),
% 292.11/184.61 inference(quant_inst,[status(thm)],[])).
% 292.11/184.61 tff(15236,plain,
% 292.11/184.61 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s3)) | m_and_h_gate_v_out(c_e_h_1, c_i, s3)),
% 292.11/184.61 inference(modus_ponens,[status(thm)],[15235, 15234])).
% 292.11/184.61 tff(15237,plain,
% 292.11/184.61 (~m_c_h_element_v_in2(c_e_h_1, c_f, s3)),
% 292.11/184.61 inference(unit_resolution,[status(thm)],[15236, 2143, 15233])).
% 292.11/184.61 tff(15238,assumption,(node17(c_e_h_1, c_f, s3)), introduced(assumption)).
% 292.11/184.61 tff(15239,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_f, s3)), introduced(assumption)).
% 292.11/184.61 tff(15240,plain,
% 292.11/184.61 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s3)) | m_c_h_element_v_in2(c_e_h_1, c_f, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s3)) | m_c_h_element_v_in2(c_e_h_1, c_f, s3))),
% 292.11/184.61 inference(rewrite,[status(thm)],[])).
% 292.11/184.61 tff(15241,plain,
% 292.11/184.61 (((~m_c_h_element_v_in1(c_e_h_1, c_f, s3)) | m_c_h_element_v_in2(c_e_h_1, c_f, s3) | (~node17(c_e_h_1, c_f, s3))) <=> ((~node17(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s3)) | m_c_h_element_v_in2(c_e_h_1, c_f, s3))),
% 292.11/184.61 inference(rewrite,[status(thm)],[])).
% 292.11/184.61 tff(15242,plain,
% 292.11/184.61 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s3)) | m_c_h_element_v_in2(c_e_h_1, c_f, s3) | (~node17(c_e_h_1, c_f, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s3)) | m_c_h_element_v_in2(c_e_h_1, c_f, s3)))),
% 292.11/184.61 inference(monotonicity,[status(thm)],[15241])).
% 292.11/184.61 tff(15243,plain,
% 292.11/184.61 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s3)) | m_c_h_element_v_in2(c_e_h_1, c_f, s3) | (~node17(c_e_h_1, c_f, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s3)) | m_c_h_element_v_in2(c_e_h_1, c_f, s3))),
% 292.11/184.61 inference(transitivity,[status(thm)],[15242, 15240])).
% 292.11/184.61 tff(15244,plain,
% 292.11/184.61 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s3)) | m_c_h_element_v_in2(c_e_h_1, c_f, s3) | (~node17(c_e_h_1, c_f, s3)))),
% 292.11/184.62 inference(quant_inst,[status(thm)],[])).
% 292.11/184.62 tff(15245,plain,
% 292.11/184.62 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s3)) | m_c_h_element_v_in2(c_e_h_1, c_f, s3)),
% 292.11/184.62 inference(modus_ponens,[status(thm)],[15244, 15243])).
% 292.11/184.62 tff(15246,plain,
% 292.11/184.62 ((~node17(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s3))),
% 292.11/184.62 inference(unit_resolution,[status(thm)],[15245, 919, 15239])).
% 292.11/184.62 tff(15247,plain,
% 292.11/184.62 (~m_c_h_element_v_in1(c_e_h_1, c_f, s3)),
% 292.11/184.62 inference(unit_resolution,[status(thm)],[15246, 15238])).
% 292.11/184.62 tff(15248,assumption,(~node15(c_e_h_1, c_f, s3, s4)), introduced(assumption)).
% 292.11/184.62 tff(15249,assumption,(node16(c_e_h_1, c_f, s3)), introduced(assumption)).
% 292.11/184.62 tff(15250,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_f, s3)), introduced(assumption)).
% 292.11/184.62 tff(15251,plain,
% 292.11/184.62 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s3)) | (~node17(c_e_h_1, c_f, s3)) | m_c_h_element_v_in1(c_e_h_1, c_f, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s3)) | (~node17(c_e_h_1, c_f, s3)) | m_c_h_element_v_in1(c_e_h_1, c_f, s3))),
% 292.11/184.62 inference(rewrite,[status(thm)],[])).
% 292.11/184.62 tff(15252,plain,
% 292.11/184.62 ((m_c_h_element_v_in1(c_e_h_1, c_f, s3) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s3)) | (~node17(c_e_h_1, c_f, s3))) <=> ((~m_c_h_element_v_in2(c_e_h_1, c_f, s3)) | (~node17(c_e_h_1, c_f, s3)) | m_c_h_element_v_in1(c_e_h_1, c_f, s3))),
% 292.11/184.62 inference(rewrite,[status(thm)],[])).
% 292.11/184.62 tff(15253,plain,
% 292.11/184.62 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s3) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s3)) | (~node17(c_e_h_1, c_f, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s3)) | (~node17(c_e_h_1, c_f, s3)) | m_c_h_element_v_in1(c_e_h_1, c_f, s3)))),
% 292.11/184.62 inference(monotonicity,[status(thm)],[15252])).
% 292.11/184.62 tff(15254,plain,
% 292.11/184.62 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s3) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s3)) | (~node17(c_e_h_1, c_f, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s3)) | (~node17(c_e_h_1, c_f, s3)) | m_c_h_element_v_in1(c_e_h_1, c_f, s3))),
% 292.11/184.62 inference(transitivity,[status(thm)],[15253, 15251])).
% 292.11/184.62 tff(15255,plain,
% 292.11/184.62 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s3) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s3)) | (~node17(c_e_h_1, c_f, s3)))),
% 292.11/184.62 inference(quant_inst,[status(thm)],[])).
% 292.11/184.62 tff(15256,plain,
% 292.11/184.62 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s3)) | (~node17(c_e_h_1, c_f, s3)) | m_c_h_element_v_in1(c_e_h_1, c_f, s3)),
% 292.11/184.62 inference(modus_ponens,[status(thm)],[15255, 15254])).
% 292.11/184.62 tff(15257,plain,
% 292.11/184.62 ((~m_c_h_element_v_in2(c_e_h_1, c_f, s3)) | m_c_h_element_v_in1(c_e_h_1, c_f, s3)),
% 292.11/184.62 inference(unit_resolution,[status(thm)],[15256, 859, 15238])).
% 292.11/184.62 tff(15258,plain,
% 292.11/184.62 (~m_c_h_element_v_in2(c_e_h_1, c_f, s3)),
% 292.11/184.62 inference(unit_resolution,[status(thm)],[15257, 15250])).
% 292.11/184.62 tff(15259,plain,
% 292.11/184.62 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s3)) | m_c_h_element_v_in1(c_e_h_1, c_f, s3) | m_c_h_element_v_in2(c_e_h_1, c_f, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s3)) | m_c_h_element_v_in1(c_e_h_1, c_f, s3) | m_c_h_element_v_in2(c_e_h_1, c_f, s3))),
% 292.11/184.62 inference(rewrite,[status(thm)],[])).
% 292.11/184.62 tff(15260,plain,
% 292.11/184.62 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s3)) | m_c_h_element_v_in1(c_e_h_1, c_f, s3) | m_c_h_element_v_in2(c_e_h_1, c_f, s3))),
% 292.11/184.62 inference(quant_inst,[status(thm)],[])).
% 292.11/184.62 tff(15261,plain,
% 292.11/184.62 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s3)) | m_c_h_element_v_in1(c_e_h_1, c_f, s3) | m_c_h_element_v_in2(c_e_h_1, c_f, s3)),
% 292.11/184.62 inference(modus_ponens,[status(thm)],[15260, 15259])).
% 292.11/184.62 tff(15262,plain,
% 292.11/184.62 (m_c_h_element_v_in1(c_e_h_1, c_f, s3) | m_c_h_element_v_in2(c_e_h_1, c_f, s3)),
% 292.11/184.62 inference(unit_resolution,[status(thm)],[15261, 178, 15249])).
% 292.11/184.62 tff(15263,plain,
% 292.11/184.62 ($false),
% 292.11/184.62 inference(unit_resolution,[status(thm)],[15262, 15258, 15250])).
% 292.11/184.62 tff(15264,plain,(m_c_h_element_v_in1(c_e_h_1, c_f, s3) | (~node16(c_e_h_1, c_f, s3)) | (~node17(c_e_h_1, c_f, s3))), inference(lemma,lemma(discharge,[]))).
% 292.11/184.62 tff(15265,plain,
% 292.11/184.62 (m_c_h_element_v_in1(c_e_h_1, c_f, s3)),
% 292.11/184.62 inference(unit_resolution,[status(thm)],[15264, 15249, 15238])).
% 292.11/184.62 tff(15266,plain,
% 292.11/184.62 ((~m_c_h_element_v_in1(c_e_h_1, c_f, s3)) | m_c_h_element_v_in2(c_e_h_1, c_f, s3)),
% 292.11/184.62 inference(unit_resolution,[status(thm)],[15245, 919, 15238])).
% 292.11/184.62 tff(15267,plain,
% 292.11/184.62 (m_c_h_element_v_in2(c_e_h_1, c_f, s3)),
% 292.11/184.62 inference(unit_resolution,[status(thm)],[15266, 15265])).
% 292.11/184.62 tff(15268,plain,
% 292.11/184.62 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~node16(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s3)))),
% 292.11/184.62 inference(rewrite,[status(thm)],[])).
% 292.11/184.62 tff(15269,plain,
% 292.11/184.62 (((~node16(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s3))) <=> ((~node16(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s3)))),
% 292.11/184.62 inference(rewrite,[status(thm)],[])).
% 292.11/184.62 tff(15270,plain,
% 292.11/184.62 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s3))))),
% 292.11/184.62 inference(monotonicity,[status(thm)],[15269])).
% 292.11/184.62 tff(15271,plain,
% 292.11/184.62 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~node16(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s3)))),
% 292.11/184.62 inference(transitivity,[status(thm)],[15270, 15268])).
% 292.11/184.62 tff(15272,plain,
% 292.11/184.62 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s3)))),
% 292.11/184.62 inference(quant_inst,[status(thm)],[])).
% 292.11/184.62 tff(15273,plain,
% 292.11/184.62 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~node16(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s3))),
% 292.11/184.63 inference(modus_ponens,[status(thm)],[15272, 15271])).
% 292.11/184.63 tff(15274,plain,
% 292.11/184.63 ((~m_c_h_element_v_in2(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s3))),
% 292.11/184.63 inference(unit_resolution,[status(thm)],[15273, 2307, 15249])).
% 292.11/184.63 tff(15275,plain,
% 292.11/184.63 ($false),
% 292.11/184.63 inference(unit_resolution,[status(thm)],[15274, 15267, 15265])).
% 292.11/184.63 tff(15276,plain,((~node16(c_e_h_1, c_f, s3)) | (~node17(c_e_h_1, c_f, s3))), inference(lemma,lemma(discharge,[]))).
% 292.11/184.63 tff(15277,plain,
% 292.11/184.63 (~node16(c_e_h_1, c_f, s3)),
% 292.11/184.63 inference(unit_resolution,[status(thm)],[15276, 15238])).
% 292.11/184.63 tff(15278,plain,
% 292.11/184.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s3, s4)) | node19(c_e_h_1, c_f, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s3, s4)) | node19(c_e_h_1, c_f, s3, s4))),
% 292.11/184.63 inference(rewrite,[status(thm)],[])).
% 292.11/184.63 tff(15279,plain,
% 292.11/184.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s3, s4)) | node19(c_e_h_1, c_f, s3, s4))),
% 292.11/184.63 inference(quant_inst,[status(thm)],[])).
% 292.11/184.63 tff(15280,plain,
% 292.11/184.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s3, s4)) | node19(c_e_h_1, c_f, s3, s4)),
% 292.11/184.63 inference(modus_ponens,[status(thm)],[15279, 15278])).
% 292.11/184.63 tff(15281,plain,
% 292.11/184.63 (node19(c_e_h_1, c_f, s3, s4)),
% 292.11/184.63 inference(unit_resolution,[status(thm)],[15280, 190, 531])).
% 292.11/184.63 tff(15282,plain,
% 292.11/184.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_1, c_f, s3, s4) | node16(c_e_h_1, c_f, s3) | node14(c_e_h_1, c_f, s3, s4) | (~node19(c_e_h_1, c_f, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_f, s3, s4) | node16(c_e_h_1, c_f, s3) | node14(c_e_h_1, c_f, s3, s4) | (~node19(c_e_h_1, c_f, s3, s4)))),
% 292.11/184.63 inference(rewrite,[status(thm)],[])).
% 292.11/184.63 tff(15283,plain,
% 292.11/184.63 ((node16(c_e_h_1, c_f, s3) | node14(c_e_h_1, c_f, s3, s4) | node15(c_e_h_1, c_f, s3, s4) | (~node19(c_e_h_1, c_f, s3, s4))) <=> (node15(c_e_h_1, c_f, s3, s4) | node16(c_e_h_1, c_f, s3) | node14(c_e_h_1, c_f, s3, s4) | (~node19(c_e_h_1, c_f, s3, s4)))),
% 292.11/184.63 inference(rewrite,[status(thm)],[])).
% 292.11/184.63 tff(15284,plain,
% 292.11/184.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s3) | node14(c_e_h_1, c_f, s3, s4) | node15(c_e_h_1, c_f, s3, s4) | (~node19(c_e_h_1, c_f, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_1, c_f, s3, s4) | node16(c_e_h_1, c_f, s3) | node14(c_e_h_1, c_f, s3, s4) | (~node19(c_e_h_1, c_f, s3, s4))))),
% 292.11/184.63 inference(monotonicity,[status(thm)],[15283])).
% 292.11/184.63 tff(15285,plain,
% 292.11/184.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s3) | node14(c_e_h_1, c_f, s3, s4) | node15(c_e_h_1, c_f, s3, s4) | (~node19(c_e_h_1, c_f, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_f, s3, s4) | node16(c_e_h_1, c_f, s3) | node14(c_e_h_1, c_f, s3, s4) | (~node19(c_e_h_1, c_f, s3, s4)))),
% 292.11/184.63 inference(transitivity,[status(thm)],[15284, 15282])).
% 292.11/184.63 tff(15286,plain,
% 292.11/184.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s3) | node14(c_e_h_1, c_f, s3, s4) | node15(c_e_h_1, c_f, s3, s4) | (~node19(c_e_h_1, c_f, s3, s4)))),
% 292.11/184.63 inference(quant_inst,[status(thm)],[])).
% 292.11/184.63 tff(15287,plain,
% 292.11/184.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_f, s3, s4) | node16(c_e_h_1, c_f, s3) | node14(c_e_h_1, c_f, s3, s4) | (~node19(c_e_h_1, c_f, s3, s4))),
% 292.11/184.63 inference(modus_ponens,[status(thm)],[15286, 15285])).
% 292.11/184.63 tff(15288,plain,
% 292.11/184.63 (node15(c_e_h_1, c_f, s3, s4) | node16(c_e_h_1, c_f, s3) | node14(c_e_h_1, c_f, s3, s4)),
% 292.11/184.63 inference(unit_resolution,[status(thm)],[15287, 204, 15281])).
% 292.11/184.63 tff(15289,plain,
% 292.11/184.63 (node14(c_e_h_1, c_f, s3, s4)),
% 292.11/184.63 inference(unit_resolution,[status(thm)],[15288, 15277, 15248])).
% 292.11/184.63 tff(15290,plain,
% 292.11/184.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s4)) | m_c_h_element_v_in1(c_e_h_1, c_f, s3) | (~node14(c_e_h_1, c_f, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s4)) | m_c_h_element_v_in1(c_e_h_1, c_f, s3) | (~node14(c_e_h_1, c_f, s3, s4)))),
% 292.11/184.63 inference(rewrite,[status(thm)],[])).
% 292.11/184.63 tff(15291,plain,
% 292.11/184.63 (((~node14(c_e_h_1, c_f, s3, s4)) | m_c_h_element_v_in1(c_e_h_1, c_f, s3) | (~m_c_h_element_v_out(c_e_h_1, c_f, s4))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_f, s4)) | m_c_h_element_v_in1(c_e_h_1, c_f, s3) | (~node14(c_e_h_1, c_f, s3, s4)))),
% 292.11/184.63 inference(rewrite,[status(thm)],[])).
% 292.11/184.63 tff(15292,plain,
% 292.11/184.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s3, s4)) | m_c_h_element_v_in1(c_e_h_1, c_f, s3) | (~m_c_h_element_v_out(c_e_h_1, c_f, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s4)) | m_c_h_element_v_in1(c_e_h_1, c_f, s3) | (~node14(c_e_h_1, c_f, s3, s4))))),
% 292.11/184.63 inference(monotonicity,[status(thm)],[15291])).
% 292.11/184.63 tff(15293,plain,
% 292.11/184.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s3, s4)) | m_c_h_element_v_in1(c_e_h_1, c_f, s3) | (~m_c_h_element_v_out(c_e_h_1, c_f, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s4)) | m_c_h_element_v_in1(c_e_h_1, c_f, s3) | (~node14(c_e_h_1, c_f, s3, s4)))),
% 292.11/184.63 inference(transitivity,[status(thm)],[15292, 15290])).
% 292.11/184.63 tff(15294,plain,
% 292.11/184.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s3, s4)) | m_c_h_element_v_in1(c_e_h_1, c_f, s3) | (~m_c_h_element_v_out(c_e_h_1, c_f, s4)))),
% 292.11/184.63 inference(quant_inst,[status(thm)],[])).
% 292.11/184.63 tff(15295,plain,
% 292.11/184.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s4)) | m_c_h_element_v_in1(c_e_h_1, c_f, s3) | (~node14(c_e_h_1, c_f, s3, s4))),
% 292.11/184.63 inference(modus_ponens,[status(thm)],[15294, 15293])).
% 292.11/184.63 tff(15296,plain,
% 292.11/184.63 ($false),
% 292.11/184.63 inference(unit_resolution,[status(thm)],[15295, 223, 15077, 15289, 15247])).
% 292.11/184.63 tff(15297,plain,((~node17(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s4)) | node15(c_e_h_1, c_f, s3, s4) | m_c_h_element_v_in2(c_e_h_1, c_f, s3)), inference(lemma,lemma(discharge,[]))).
% 292.11/184.63 tff(15298,plain,
% 292.11/184.63 ((~node17(c_e_h_1, c_f, s3)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s4)) | node15(c_e_h_1, c_f, s3, s4)),
% 292.11/184.63 inference(unit_resolution,[status(thm)],[15297, 15237])).
% 292.11/184.63 tff(15299,plain,
% 292.11/184.63 (~node17(c_e_h_1, c_f, s3)),
% 292.11/184.63 inference(unit_resolution,[status(thm)],[15298, 15095, 15077])).
% 292.11/184.63 tff(15300,plain,
% 292.11/184.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s3) | node18(c_e_h_1, c_f, s3, s4) | (~node19(c_e_h_1, c_f, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_f, s3) | node18(c_e_h_1, c_f, s3, s4) | (~node19(c_e_h_1, c_f, s3, s4)))),
% 292.11/184.63 inference(rewrite,[status(thm)],[])).
% 292.11/184.63 tff(15301,plain,
% 292.11/184.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s3) | node18(c_e_h_1, c_f, s3, s4) | (~node19(c_e_h_1, c_f, s3, s4)))),
% 292.11/184.63 inference(quant_inst,[status(thm)],[])).
% 292.11/184.63 tff(15302,plain,
% 292.11/184.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_f, s3) | node18(c_e_h_1, c_f, s3, s4) | (~node19(c_e_h_1, c_f, s3, s4))),
% 292.11/184.63 inference(modus_ponens,[status(thm)],[15301, 15300])).
% 292.11/184.63 tff(15303,plain,
% 292.11/184.63 (node17(c_e_h_1, c_f, s3) | node18(c_e_h_1, c_f, s3, s4)),
% 292.11/184.63 inference(unit_resolution,[status(thm)],[15302, 776, 15281])).
% 292.11/184.63 tff(15304,plain,
% 292.11/184.63 ($false),
% 292.11/184.63 inference(unit_resolution,[status(thm)],[15303, 15299, 15088])).
% 292.11/184.63 tff(15305,plain,(m_c_h_element_v_out(c_e_h_1, c_f, s3) | (~m_c_h_element_v_out(c_e_h_1, c_f, s4))), inference(lemma,lemma(discharge,[]))).
% 292.11/184.63 tff(15306,plain,
% 292.11/184.63 (~m_c_h_element_v_out(c_e_h_1, c_f, s4)),
% 292.11/184.63 inference(unit_resolution,[status(thm)],[15305, 8532])).
% 292.11/184.63 tff(15307,plain,
% 292.11/184.63 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s4)) | m_c_h_element_v_out(c_e_h_1, c_f, s4))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s4)) | m_c_h_element_v_out(c_e_h_1, c_f, s4))),
% 292.11/184.63 inference(rewrite,[status(thm)],[])).
% 292.11/184.63 tff(15308,plain,
% 292.11/184.63 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s4)) | m_c_h_element_v_out(c_e_h_1, c_f, s4))),
% 292.11/184.63 inference(quant_inst,[status(thm)],[])).
% 292.11/184.63 tff(15309,plain,
% 292.11/184.63 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s4)) | m_c_h_element_v_out(c_e_h_1, c_f, s4)),
% 292.11/184.63 inference(modus_ponens,[status(thm)],[15308, 15307])).
% 292.11/184.63 tff(15310,plain,
% 292.11/184.63 (~m_and_h_gate_v_in1(c_e_h_1, c_q, s4)),
% 292.11/184.63 inference(unit_resolution,[status(thm)],[15309, 1586, 15306])).
% 292.11/184.63 tff(15311,assumption,(~m_and_h_gate_v_in1(c_e_h_1, c_q, s4)), introduced(assumption)).
% 292.11/184.63 tff(15312,assumption,(node20(c_e_h_1, c_q, s4)), introduced(assumption)).
% 292.11/184.63 tff(15313,plain,
% 292.11/184.63 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s4)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s4)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s4))),
% 292.11/184.63 inference(rewrite,[status(thm)],[])).
% 292.11/184.63 tff(15314,plain,
% 292.11/184.63 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s4)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s4))),
% 292.11/184.63 inference(quant_inst,[status(thm)],[])).
% 292.11/184.63 tff(15315,plain,
% 292.11/184.63 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s4)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s4)),
% 292.11/184.63 inference(modus_ponens,[status(thm)],[15314, 15313])).
% 292.11/184.63 tff(15316,plain,
% 292.11/184.63 ($false),
% 292.11/184.63 inference(unit_resolution,[status(thm)],[15315, 38, 15312, 15311])).
% 292.11/184.63 tff(15317,plain,(m_and_h_gate_v_in1(c_e_h_1, c_q, s4) | (~node20(c_e_h_1, c_q, s4))), inference(lemma,lemma(discharge,[]))).
% 292.11/184.63 tff(15318,plain,
% 292.11/184.63 (~node20(c_e_h_1, c_q, s4)),
% 292.11/184.63 inference(unit_resolution,[status(thm)],[15317, 15310])).
% 292.11/184.63 tff(15319,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_q, s4)), introduced(assumption)).
% 292.11/184.63 tff(15320,assumption,(~node20(c_e_h_1, c_q, s4)), introduced(assumption)).
% 292.11/184.63 tff(15321,assumption,(m_and_h_gate_v_out(c_e_h_1, c_q, s5)), introduced(assumption)).
% 292.11/184.63 tff(15322,assumption,(node21(c_e_h_1, c_q, s4, s5)), introduced(assumption)).
% 292.11/184.63 tff(15323,plain,
% 292.11/184.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s5)) | node20(c_e_h_1, c_q, s4) | (~node21(c_e_h_1, c_q, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s5)) | node20(c_e_h_1, c_q, s4) | (~node21(c_e_h_1, c_q, s4, s5)))),
% 292.11/184.64 inference(rewrite,[status(thm)],[])).
% 292.11/184.64 tff(15324,plain,
% 292.11/184.64 ((node20(c_e_h_1, c_q, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s5)) | (~node21(c_e_h_1, c_q, s4, s5))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_q, s5)) | node20(c_e_h_1, c_q, s4) | (~node21(c_e_h_1, c_q, s4, s5)))),
% 292.11/184.64 inference(rewrite,[status(thm)],[])).
% 292.11/184.64 tff(15325,plain,
% 292.11/184.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s5)) | (~node21(c_e_h_1, c_q, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s5)) | node20(c_e_h_1, c_q, s4) | (~node21(c_e_h_1, c_q, s4, s5))))),
% 292.11/184.64 inference(monotonicity,[status(thm)],[15324])).
% 292.11/184.64 tff(15326,plain,
% 292.11/184.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s5)) | (~node21(c_e_h_1, c_q, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s5)) | node20(c_e_h_1, c_q, s4) | (~node21(c_e_h_1, c_q, s4, s5)))),
% 292.11/184.64 inference(transitivity,[status(thm)],[15325, 15323])).
% 292.11/184.64 tff(15327,plain,
% 292.11/184.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s5)) | (~node21(c_e_h_1, c_q, s4, s5)))),
% 292.11/184.64 inference(quant_inst,[status(thm)],[])).
% 292.11/184.64 tff(15328,plain,
% 292.11/184.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s5)) | node20(c_e_h_1, c_q, s4) | (~node21(c_e_h_1, c_q, s4, s5))),
% 292.11/184.64 inference(modus_ponens,[status(thm)],[15327, 15326])).
% 292.11/184.64 tff(15329,plain,
% 292.11/184.64 ($false),
% 292.11/184.64 inference(unit_resolution,[status(thm)],[15328, 52, 15321, 15322, 15320])).
% 292.11/184.64 tff(15330,plain,((~node21(c_e_h_1, c_q, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s5)) | node20(c_e_h_1, c_q, s4)), inference(lemma,lemma(discharge,[]))).
% 292.11/184.64 tff(15331,plain,
% 292.11/184.64 (~node21(c_e_h_1, c_q, s4, s5)),
% 292.11/184.64 inference(unit_resolution,[status(thm)],[15330, 15321, 15320])).
% 292.11/184.64 tff(15332,plain,
% 292.11/184.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_1, c_q, s4, s5) | node22(c_e_h_1, c_q, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_1, c_q, s4, s5) | node22(c_e_h_1, c_q, s4, s5))),
% 292.11/184.64 inference(rewrite,[status(thm)],[])).
% 292.11/184.64 tff(15333,plain,
% 292.11/184.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_1, c_q, s4, s5) | node22(c_e_h_1, c_q, s4, s5))),
% 292.11/184.64 inference(quant_inst,[status(thm)],[])).
% 292.11/184.64 tff(15334,plain,
% 292.11/184.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_1, c_q, s4, s5) | node22(c_e_h_1, c_q, s4, s5)),
% 292.11/184.64 inference(modus_ponens,[status(thm)],[15333, 15332])).
% 292.11/184.64 tff(15335,plain,
% 292.11/184.64 (node21(c_e_h_1, c_q, s4, s5) | node22(c_e_h_1, c_q, s4, s5)),
% 292.11/184.64 inference(unit_resolution,[status(thm)],[15334, 82, 1028])).
% 292.11/184.64 tff(15336,plain,
% 292.11/184.64 (node22(c_e_h_1, c_q, s4, s5)),
% 292.11/184.64 inference(unit_resolution,[status(thm)],[15335, 15331])).
% 292.11/184.64 tff(15337,plain,
% 292.11/184.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s5)) | (~node22(c_e_h_1, c_q, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_q, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s5)) | (~node22(c_e_h_1, c_q, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_q, s4))),
% 292.11/184.64 inference(rewrite,[status(thm)],[])).
% 292.11/184.64 tff(15338,plain,
% 292.11/184.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s5)) | (~node22(c_e_h_1, c_q, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_q, s4))),
% 292.11/184.64 inference(quant_inst,[status(thm)],[])).
% 292.11/184.64 tff(15339,plain,
% 292.11/184.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s5)) | (~node22(c_e_h_1, c_q, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_q, s4)),
% 292.11/184.64 inference(modus_ponens,[status(thm)],[15338, 15337])).
% 292.11/184.64 tff(15340,plain,
% 292.11/184.64 ($false),
% 292.11/184.64 inference(unit_resolution,[status(thm)],[15339, 108, 15321, 15336, 15319])).
% 292.11/184.64 tff(15341,plain,((~m_and_h_gate_v_out(c_e_h_1, c_q, s5)) | m_and_h_gate_v_out(c_e_h_1, c_q, s4) | node20(c_e_h_1, c_q, s4)), inference(lemma,lemma(discharge,[]))).
% 292.11/184.64 tff(15342,plain,
% 292.11/184.64 (~m_and_h_gate_v_out(c_e_h_1, c_q, s5)),
% 292.11/184.64 inference(unit_resolution,[status(thm)],[15341, 8564, 15318])).
% 292.11/184.64 tff(15343,plain,
% 292.11/184.64 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s5))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s5))),
% 292.11/184.64 inference(rewrite,[status(thm)],[])).
% 292.11/184.64 tff(15344,plain,
% 292.11/184.64 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s5))),
% 292.11/184.64 inference(quant_inst,[status(thm)],[])).
% 292.11/184.64 tff(15345,plain,
% 292.11/184.64 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s5)),
% 292.11/184.64 inference(modus_ponens,[status(thm)],[15344, 15343])).
% 292.11/184.64 tff(15346,plain,
% 292.11/184.64 (node3(c_e_h_1, c_e_h_2, s5)),
% 292.11/184.64 inference(unit_resolution,[status(thm)],[15345, 4166, 1056])).
% 292.11/184.64 tff(15347,plain,
% 292.11/184.64 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s5)) | (~node3(c_e_h_1, c_e_h_2, s5)) | m_and_h_gate_v_out(c_e_h_1, c_q, s5))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s5)) | (~node3(c_e_h_1, c_e_h_2, s5)) | m_and_h_gate_v_out(c_e_h_1, c_q, s5))),
% 292.11/184.64 inference(rewrite,[status(thm)],[])).
% 292.11/184.64 tff(15348,plain,
% 292.11/184.64 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s5)) | (~node3(c_e_h_1, c_e_h_2, s5)) | m_and_h_gate_v_out(c_e_h_1, c_q, s5))),
% 292.11/184.64 inference(quant_inst,[status(thm)],[])).
% 292.11/184.64 tff(15349,plain,
% 292.11/184.64 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s5)) | (~node3(c_e_h_1, c_e_h_2, s5)) | m_and_h_gate_v_out(c_e_h_1, c_q, s5)),
% 292.11/184.64 inference(modus_ponens,[status(thm)],[15348, 15347])).
% 292.11/184.64 tff(15350,plain,
% 292.11/184.64 ((~m_cell_v_ack(c_e_h_2, s5)) | m_and_h_gate_v_out(c_e_h_1, c_q, s5)),
% 292.11/184.64 inference(unit_resolution,[status(thm)],[15349, 1073, 15346])).
% 292.11/184.64 tff(15351,plain,
% 292.11/184.64 (~m_cell_v_ack(c_e_h_2, s5)),
% 292.11/184.64 inference(unit_resolution,[status(thm)],[15350, 15342])).
% 292.11/184.64 tff(15352,plain,
% 292.11/184.64 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node2(c_e_h_1, c_e_h_2, s5))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node2(c_e_h_1, c_e_h_2, s5))),
% 292.11/184.64 inference(rewrite,[status(thm)],[])).
% 292.11/184.64 tff(15353,plain,
% 292.11/184.64 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node2(c_e_h_1, c_e_h_2, s5))),
% 292.11/184.64 inference(quant_inst,[status(thm)],[])).
% 292.11/184.64 tff(15354,plain,
% 292.11/184.64 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node2(c_e_h_1, c_e_h_2, s5)),
% 292.11/184.64 inference(modus_ponens,[status(thm)],[15353, 15352])).
% 292.11/184.64 tff(15355,plain,
% 292.11/184.64 (node2(c_e_h_1, c_e_h_2, s5)),
% 292.11/184.64 inference(unit_resolution,[status(thm)],[15354, 4166, 5821])).
% 292.11/184.64 tff(15356,plain,
% 292.11/184.64 (((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | ((~node2(c_e_h_1, c_e_h_2, s5)) | m_cell_v_ack(c_e_h_2, s5) | m_and_h_gate_v_in2(c_e_h_1, c_c, s5))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | (~node2(c_e_h_1, c_e_h_2, s5)) | m_cell_v_ack(c_e_h_2, s5) | m_and_h_gate_v_in2(c_e_h_1, c_c, s5))),
% 292.11/184.64 inference(rewrite,[status(thm)],[])).
% 292.11/184.64 tff(15357,plain,
% 292.11/184.64 ((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | ((~node2(c_e_h_1, c_e_h_2, s5)) | m_cell_v_ack(c_e_h_2, s5) | m_and_h_gate_v_in2(c_e_h_1, c_c, s5))),
% 292.11/184.64 inference(quant_inst,[status(thm)],[])).
% 292.11/184.64 tff(15358,plain,
% 292.11/184.64 ((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | (~node2(c_e_h_1, c_e_h_2, s5)) | m_cell_v_ack(c_e_h_2, s5) | m_and_h_gate_v_in2(c_e_h_1, c_c, s5)),
% 292.11/184.64 inference(modus_ponens,[status(thm)],[15357, 15356])).
% 292.11/184.64 tff(15359,plain,
% 292.11/184.64 (m_cell_v_ack(c_e_h_2, s5) | m_and_h_gate_v_in2(c_e_h_1, c_c, s5)),
% 292.11/184.64 inference(unit_resolution,[status(thm)],[15358, 5835, 15355])).
% 292.11/184.64 tff(15360,plain,
% 292.11/184.64 (m_and_h_gate_v_in2(c_e_h_1, c_c, s5)),
% 292.11/184.64 inference(unit_resolution,[status(thm)],[15359, 15351])).
% 292.11/184.64 tff(15361,plain,
% 292.11/184.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_c, s5)) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s5)) | (~node21(c_e_h_1, c_c, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_c, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in2(c_e_h_1, c_c, s5)) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s5)) | (~node21(c_e_h_1, c_c, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_c, s6))),
% 292.11/184.64 inference(rewrite,[status(thm)],[])).
% 292.11/184.64 tff(15362,plain,
% 292.11/184.64 (((~node21(c_e_h_1, c_c, s5, s6)) | (~m_and_h_gate_v_in2(c_e_h_1, c_c, s5)) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s5)) | m_and_h_gate_v_out(c_e_h_1, c_c, s6)) <=> ((~m_and_h_gate_v_in2(c_e_h_1, c_c, s5)) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s5)) | (~node21(c_e_h_1, c_c, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_c, s6))),
% 292.11/184.64 inference(rewrite,[status(thm)],[])).
% 292.11/184.64 tff(15363,plain,
% 292.11/184.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_1, c_c, s5, s6)) | (~m_and_h_gate_v_in2(c_e_h_1, c_c, s5)) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s5)) | m_and_h_gate_v_out(c_e_h_1, c_c, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_c, s5)) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s5)) | (~node21(c_e_h_1, c_c, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_c, s6)))),
% 292.11/184.64 inference(monotonicity,[status(thm)],[15362])).
% 292.11/184.64 tff(15364,plain,
% 292.11/184.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_1, c_c, s5, s6)) | (~m_and_h_gate_v_in2(c_e_h_1, c_c, s5)) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s5)) | m_and_h_gate_v_out(c_e_h_1, c_c, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in2(c_e_h_1, c_c, s5)) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s5)) | (~node21(c_e_h_1, c_c, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_c, s6))),
% 292.11/184.65 inference(transitivity,[status(thm)],[15363, 15361])).
% 292.11/184.65 tff(15365,plain,
% 292.11/184.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_1, c_c, s5, s6)) | (~m_and_h_gate_v_in2(c_e_h_1, c_c, s5)) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s5)) | m_and_h_gate_v_out(c_e_h_1, c_c, s6))),
% 292.11/184.65 inference(quant_inst,[status(thm)],[])).
% 292.11/184.65 tff(15366,plain,
% 292.11/184.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in2(c_e_h_1, c_c, s5)) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s5)) | (~node21(c_e_h_1, c_c, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_c, s6)),
% 292.11/184.65 inference(modus_ponens,[status(thm)],[15365, 15364])).
% 292.11/184.65 tff(15367,plain,
% 292.11/184.65 ($false),
% 292.11/184.65 inference(unit_resolution,[status(thm)],[15366, 5851, 15360, 15076, 13629, 15075])).
% 292.11/184.65 tff(15368,plain,((~node21(c_e_h_1, c_c, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_c, s6) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s5))), inference(lemma,lemma(discharge,[]))).
% 292.11/184.65 tff(15369,plain,
% 292.11/184.65 (~node21(c_e_h_1, c_c, s5, s6)),
% 292.11/184.65 inference(unit_resolution,[status(thm)],[15368, 13629, 15075])).
% 292.11/184.65 tff(15370,assumption,(node22(c_e_h_1, c_c, s5, s6)), introduced(assumption)).
% 292.11/184.65 tff(15371,plain,
% 292.11/184.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_c, s5)) | m_and_h_gate_v_out(c_e_h_1, c_c, s6) | (~node22(c_e_h_1, c_c, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s5)) | m_and_h_gate_v_out(c_e_h_1, c_c, s6) | (~node22(c_e_h_1, c_c, s5, s6)))),
% 292.11/184.65 inference(rewrite,[status(thm)],[])).
% 292.11/184.65 tff(15372,plain,
% 292.11/184.65 ((m_and_h_gate_v_out(c_e_h_1, c_c, s6) | (~node22(c_e_h_1, c_c, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s5))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_c, s5)) | m_and_h_gate_v_out(c_e_h_1, c_c, s6) | (~node22(c_e_h_1, c_c, s5, s6)))),
% 292.11/184.65 inference(rewrite,[status(thm)],[])).
% 292.11/184.65 tff(15373,plain,
% 292.11/184.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_1, c_c, s6) | (~node22(c_e_h_1, c_c, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_c, s5)) | m_and_h_gate_v_out(c_e_h_1, c_c, s6) | (~node22(c_e_h_1, c_c, s5, s6))))),
% 292.11/184.65 inference(monotonicity,[status(thm)],[15372])).
% 292.11/184.65 tff(15374,plain,
% 292.11/184.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_1, c_c, s6) | (~node22(c_e_h_1, c_c, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s5)) | m_and_h_gate_v_out(c_e_h_1, c_c, s6) | (~node22(c_e_h_1, c_c, s5, s6)))),
% 292.11/184.65 inference(transitivity,[status(thm)],[15373, 15371])).
% 292.11/184.65 tff(15375,plain,
% 292.11/184.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_1, c_c, s6) | (~node22(c_e_h_1, c_c, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s5)))),
% 292.11/184.65 inference(quant_inst,[status(thm)],[])).
% 292.11/184.65 tff(15376,plain,
% 292.11/184.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s5)) | m_and_h_gate_v_out(c_e_h_1, c_c, s6) | (~node22(c_e_h_1, c_c, s5, s6))),
% 292.11/184.65 inference(modus_ponens,[status(thm)],[15375, 15374])).
% 292.11/184.65 tff(15377,plain,
% 292.11/184.65 ($false),
% 292.11/184.65 inference(unit_resolution,[status(thm)],[15376, 5871, 14506, 15370, 13629])).
% 292.11/184.65 tff(15378,plain,((~node22(c_e_h_1, c_c, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s5)) | m_and_h_gate_v_out(c_e_h_1, c_c, s6)), inference(lemma,lemma(discharge,[]))).
% 292.11/184.65 tff(15379,plain,
% 292.11/184.65 (~node22(c_e_h_1, c_c, s5, s6)),
% 292.11/184.65 inference(unit_resolution,[status(thm)],[15378, 13629, 14506])).
% 292.11/184.65 tff(15380,plain,
% 292.11/184.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_1, c_c, s5, s6) | node22(c_e_h_1, c_c, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_1, c_c, s5, s6) | node22(c_e_h_1, c_c, s5, s6))),
% 292.11/184.65 inference(rewrite,[status(thm)],[])).
% 292.11/184.65 tff(15381,plain,
% 292.11/184.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_1, c_c, s5, s6) | node22(c_e_h_1, c_c, s5, s6))),
% 292.11/184.65 inference(quant_inst,[status(thm)],[])).
% 292.11/184.65 tff(15382,plain,
% 292.11/184.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_1, c_c, s5, s6) | node22(c_e_h_1, c_c, s5, s6)),
% 292.11/184.65 inference(modus_ponens,[status(thm)],[15381, 15380])).
% 292.11/184.65 tff(15383,plain,
% 292.11/184.65 (node21(c_e_h_1, c_c, s5, s6) | node22(c_e_h_1, c_c, s5, s6)),
% 292.11/184.65 inference(unit_resolution,[status(thm)],[15382, 82, 1406])).
% 292.11/184.65 tff(15384,plain,
% 292.11/184.65 ($false),
% 292.11/184.65 inference(unit_resolution,[status(thm)],[15383, 15379, 15369])).
% 292.11/184.65 tff(15385,plain,(m_and_h_gate_v_out(c_e_h_1, c_c, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s5)) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s5))), inference(lemma,lemma(discharge,[]))).
% 292.11/184.65 tff(15386,plain,
% 292.11/184.65 ($false),
% 292.11/184.65 inference(unit_resolution,[status(thm)],[15385, 15074, 14854, 13629])).
% 292.11/184.65 tff(15387,plain,((~m_or_h_gate_v_out(c_e_h_1, c_g, s6)) | m_and_h_gate_v_out(c_e_h_1, c_c, s6)), inference(lemma,lemma(discharge,[]))).
% 292.11/184.65 tff(15388,plain,
% 292.11/184.65 (~m_or_h_gate_v_out(c_e_h_1, c_g, s6)),
% 292.11/184.65 inference(unit_resolution,[status(thm)],[15387, 13629])).
% 292.11/184.65 tff(15389,assumption,(~m_or_h_gate_v_out(c_e_h_1, c_g, s6)), introduced(assumption)).
% 292.11/184.65 tff(15390,assumption,(m_and_h_gate_v_in1(c_e_h_1, c_k, s6)), introduced(assumption)).
% 292.11/184.65 tff(15391,plain,
% 292.11/184.65 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_k, s6)) | m_or_h_gate_v_out(c_e_h_1, c_g, s6))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_k, s6)) | m_or_h_gate_v_out(c_e_h_1, c_g, s6))),
% 292.11/184.65 inference(rewrite,[status(thm)],[])).
% 292.11/184.65 tff(15392,plain,
% 292.11/184.65 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_k, s6)) | m_or_h_gate_v_out(c_e_h_1, c_g, s6))),
% 292.11/184.65 inference(quant_inst,[status(thm)],[])).
% 292.11/184.65 tff(15393,plain,
% 292.11/184.65 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_k, s6)) | m_or_h_gate_v_out(c_e_h_1, c_g, s6)),
% 292.11/184.65 inference(modus_ponens,[status(thm)],[15392, 15391])).
% 292.11/184.65 tff(15394,plain,
% 292.11/184.65 ($false),
% 292.11/184.65 inference(unit_resolution,[status(thm)],[15393, 2048, 15389, 15390])).
% 292.11/184.65 tff(15395,plain,((~m_and_h_gate_v_in1(c_e_h_1, c_k, s6)) | m_or_h_gate_v_out(c_e_h_1, c_g, s6)), inference(lemma,lemma(discharge,[]))).
% 292.11/184.65 tff(15396,plain,
% 292.11/184.65 (~m_and_h_gate_v_in1(c_e_h_1, c_k, s6)),
% 292.11/184.65 inference(unit_resolution,[status(thm)],[15395, 15389])).
% 292.11/184.65 tff(15397,assumption,(~m_and_h_gate_v_in1(c_e_h_1, c_k, s6)), introduced(assumption)).
% 292.11/184.65 tff(15398,assumption,(node20(c_e_h_1, c_k, s6)), introduced(assumption)).
% 292.11/184.65 tff(15399,plain,
% 292.11/184.65 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_k, s6)) | m_and_h_gate_v_in1(c_e_h_1, c_k, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_k, s6)) | m_and_h_gate_v_in1(c_e_h_1, c_k, s6))),
% 292.11/184.65 inference(rewrite,[status(thm)],[])).
% 292.11/184.65 tff(15400,plain,
% 292.11/184.65 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_k, s6)) | m_and_h_gate_v_in1(c_e_h_1, c_k, s6))),
% 292.11/184.65 inference(quant_inst,[status(thm)],[])).
% 292.11/184.65 tff(15401,plain,
% 292.11/184.65 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_k, s6)) | m_and_h_gate_v_in1(c_e_h_1, c_k, s6)),
% 292.11/184.65 inference(modus_ponens,[status(thm)],[15400, 15399])).
% 292.11/184.65 tff(15402,plain,
% 292.11/184.65 ($false),
% 292.11/184.65 inference(unit_resolution,[status(thm)],[15401, 38, 15398, 15397])).
% 292.11/184.65 tff(15403,plain,(m_and_h_gate_v_in1(c_e_h_1, c_k, s6) | (~node20(c_e_h_1, c_k, s6))), inference(lemma,lemma(discharge,[]))).
% 292.11/184.65 tff(15404,plain,
% 292.11/184.65 (~node20(c_e_h_1, c_k, s6)),
% 292.11/184.65 inference(unit_resolution,[status(thm)],[15403, 15396])).
% 292.11/184.65 tff(15405,assumption,(m_and_h_gate_v_out(c_e_h_1, c_k, s7)), introduced(assumption)).
% 292.11/184.65 tff(15406,assumption,(~node20(c_e_h_1, c_k, s6)), introduced(assumption)).
% 292.11/184.65 tff(15407,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_k, s6)), introduced(assumption)).
% 292.11/184.65 tff(15408,assumption,(node22(c_e_h_1, c_k, s6, s7)), introduced(assumption)).
% 292.11/184.65 tff(15409,plain,
% 292.11/184.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_k, s7)) | (~node22(c_e_h_1, c_k, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_k, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s7)) | (~node22(c_e_h_1, c_k, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_k, s6))),
% 292.11/184.65 inference(rewrite,[status(thm)],[])).
% 292.11/184.65 tff(15410,plain,
% 292.11/184.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_k, s7)) | (~node22(c_e_h_1, c_k, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_k, s6))),
% 292.11/184.65 inference(quant_inst,[status(thm)],[])).
% 292.11/184.65 tff(15411,plain,
% 292.11/184.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s7)) | (~node22(c_e_h_1, c_k, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_k, s6)),
% 292.11/184.65 inference(modus_ponens,[status(thm)],[15410, 15409])).
% 292.11/184.65 tff(15412,plain,
% 292.11/184.65 ($false),
% 292.11/184.65 inference(unit_resolution,[status(thm)],[15411, 108, 15408, 15407, 15405])).
% 292.11/184.65 tff(15413,plain,((~node22(c_e_h_1, c_k, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_k, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s7))), inference(lemma,lemma(discharge,[]))).
% 292.11/184.65 tff(15414,plain,
% 292.11/184.65 (~node22(c_e_h_1, c_k, s6, s7)),
% 292.11/184.65 inference(unit_resolution,[status(thm)],[15413, 15405, 15407])).
% 292.11/184.65 tff(15415,plain,
% 292.11/184.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_1, c_k, s6, s7) | node22(c_e_h_1, c_k, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_1, c_k, s6, s7) | node22(c_e_h_1, c_k, s6, s7))),
% 292.11/184.65 inference(rewrite,[status(thm)],[])).
% 292.11/184.65 tff(15416,plain,
% 292.11/184.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_1, c_k, s6, s7) | node22(c_e_h_1, c_k, s6, s7))),
% 292.11/184.65 inference(quant_inst,[status(thm)],[])).
% 292.11/184.65 tff(15417,plain,
% 292.11/184.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_1, c_k, s6, s7) | node22(c_e_h_1, c_k, s6, s7)),
% 292.11/184.65 inference(modus_ponens,[status(thm)],[15416, 15415])).
% 292.11/184.66 tff(15418,plain,
% 292.11/184.66 (node21(c_e_h_1, c_k, s6, s7) | node22(c_e_h_1, c_k, s6, s7)),
% 292.11/184.66 inference(unit_resolution,[status(thm)],[15417, 82, 1844])).
% 292.11/184.66 tff(15419,plain,
% 292.11/184.66 (node21(c_e_h_1, c_k, s6, s7)),
% 292.11/184.66 inference(unit_resolution,[status(thm)],[15418, 15414])).
% 292.11/184.66 tff(15420,plain,
% 292.11/184.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_k, s6) | (~node21(c_e_h_1, c_k, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_k, s6) | (~node21(c_e_h_1, c_k, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s7)))),
% 292.11/184.66 inference(rewrite,[status(thm)],[])).
% 292.11/184.66 tff(15421,plain,
% 292.11/184.66 ((node20(c_e_h_1, c_k, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s7)) | (~node21(c_e_h_1, c_k, s6, s7))) <=> (node20(c_e_h_1, c_k, s6) | (~node21(c_e_h_1, c_k, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s7)))),
% 292.11/184.66 inference(rewrite,[status(thm)],[])).
% 292.11/184.66 tff(15422,plain,
% 292.11/184.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_k, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s7)) | (~node21(c_e_h_1, c_k, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_k, s6) | (~node21(c_e_h_1, c_k, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s7))))),
% 292.11/184.66 inference(monotonicity,[status(thm)],[15421])).
% 292.11/184.66 tff(15423,plain,
% 292.11/184.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_k, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s7)) | (~node21(c_e_h_1, c_k, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_k, s6) | (~node21(c_e_h_1, c_k, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s7)))),
% 292.11/184.66 inference(transitivity,[status(thm)],[15422, 15420])).
% 292.11/184.66 tff(15424,plain,
% 292.11/184.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_k, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s7)) | (~node21(c_e_h_1, c_k, s6, s7)))),
% 292.11/184.66 inference(quant_inst,[status(thm)],[])).
% 292.11/184.66 tff(15425,plain,
% 292.11/184.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_k, s6) | (~node21(c_e_h_1, c_k, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s7))),
% 292.11/184.66 inference(modus_ponens,[status(thm)],[15424, 15423])).
% 292.11/184.66 tff(15426,plain,
% 292.11/184.66 ($false),
% 292.11/184.66 inference(unit_resolution,[status(thm)],[15425, 52, 15419, 15405, 15406])).
% 292.11/184.66 tff(15427,plain,((~m_and_h_gate_v_out(c_e_h_1, c_k, s7)) | node20(c_e_h_1, c_k, s6) | m_and_h_gate_v_out(c_e_h_1, c_k, s6)), inference(lemma,lemma(discharge,[]))).
% 292.11/184.66 tff(15428,plain,
% 292.11/184.66 (m_and_h_gate_v_out(c_e_h_1, c_k, s6)),
% 292.11/184.66 inference(unit_resolution,[status(thm)],[15427, 15405, 15404])).
% 292.11/184.66 tff(15429,assumption,(m_and_h_gate_v_out(c_e_h_1, c_k, s6)), introduced(assumption)).
% 292.11/184.66 tff(15430,assumption,(m_and_h_gate_v_in1(c_e_h_1, c_k, s4)), introduced(assumption)).
% 292.11/184.66 tff(15431,plain,
% 292.11/184.66 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_k, s4)) | m_or_h_gate_v_out(c_e_h_1, c_g, s4))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_k, s4)) | m_or_h_gate_v_out(c_e_h_1, c_g, s4))),
% 292.11/184.66 inference(rewrite,[status(thm)],[])).
% 292.11/184.66 tff(15432,plain,
% 292.11/184.66 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_k, s4)) | m_or_h_gate_v_out(c_e_h_1, c_g, s4))),
% 292.11/184.66 inference(quant_inst,[status(thm)],[])).
% 292.11/184.66 tff(15433,plain,
% 292.11/184.66 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_k, s4)) | m_or_h_gate_v_out(c_e_h_1, c_g, s4)),
% 292.11/184.66 inference(modus_ponens,[status(thm)],[15432, 15431])).
% 292.11/184.66 tff(15434,plain,
% 292.11/184.66 ($false),
% 292.11/184.66 inference(unit_resolution,[status(thm)],[15433, 2048, 14572, 15430])).
% 292.11/184.66 tff(15435,plain,((~m_and_h_gate_v_in1(c_e_h_1, c_k, s4)) | m_or_h_gate_v_out(c_e_h_1, c_g, s4)), inference(lemma,lemma(discharge,[]))).
% 292.11/184.66 tff(15436,plain,
% 292.11/184.66 (~m_and_h_gate_v_in1(c_e_h_1, c_k, s4)),
% 292.11/184.66 inference(unit_resolution,[status(thm)],[15435, 14572])).
% 292.11/184.66 tff(15437,assumption,(~m_and_h_gate_v_in1(c_e_h_1, c_k, s4)), introduced(assumption)).
% 292.11/184.66 tff(15438,assumption,(node20(c_e_h_1, c_k, s4)), introduced(assumption)).
% 292.11/184.66 tff(15439,plain,
% 292.11/184.66 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_k, s4)) | m_and_h_gate_v_in1(c_e_h_1, c_k, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_k, s4)) | m_and_h_gate_v_in1(c_e_h_1, c_k, s4))),
% 292.11/184.66 inference(rewrite,[status(thm)],[])).
% 292.11/184.66 tff(15440,plain,
% 292.11/184.66 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_k, s4)) | m_and_h_gate_v_in1(c_e_h_1, c_k, s4))),
% 292.11/184.66 inference(quant_inst,[status(thm)],[])).
% 292.11/184.66 tff(15441,plain,
% 292.11/184.66 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_k, s4)) | m_and_h_gate_v_in1(c_e_h_1, c_k, s4)),
% 292.11/184.66 inference(modus_ponens,[status(thm)],[15440, 15439])).
% 292.11/184.66 tff(15442,plain,
% 292.11/184.66 ($false),
% 292.11/184.66 inference(unit_resolution,[status(thm)],[15441, 38, 15438, 15437])).
% 292.11/184.66 tff(15443,plain,((~node20(c_e_h_1, c_k, s4)) | m_and_h_gate_v_in1(c_e_h_1, c_k, s4)), inference(lemma,lemma(discharge,[]))).
% 292.11/184.66 tff(15444,plain,
% 292.11/184.66 (~node20(c_e_h_1, c_k, s4)),
% 292.11/184.66 inference(unit_resolution,[status(thm)],[15443, 15436])).
% 292.11/184.66 tff(15445,assumption,(m_and_h_gate_v_out(c_e_h_1, c_k, s5)), introduced(assumption)).
% 292.11/184.66 tff(15446,plain,
% 292.11/184.66 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_k, s3)) | m_or_h_gate_v_out(c_e_h_1, c_g, s3))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_k, s3)) | m_or_h_gate_v_out(c_e_h_1, c_g, s3))),
% 292.11/184.66 inference(rewrite,[status(thm)],[])).
% 292.11/184.66 tff(15447,plain,
% 292.11/184.66 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_k, s3)) | m_or_h_gate_v_out(c_e_h_1, c_g, s3))),
% 292.11/184.66 inference(quant_inst,[status(thm)],[])).
% 292.11/184.66 tff(15448,plain,
% 292.11/184.66 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_k, s3)) | m_or_h_gate_v_out(c_e_h_1, c_g, s3)),
% 292.11/184.66 inference(modus_ponens,[status(thm)],[15447, 15446])).
% 292.11/184.66 tff(15449,plain,
% 292.11/184.66 (~m_and_h_gate_v_in1(c_e_h_1, c_k, s3)),
% 292.11/184.66 inference(unit_resolution,[status(thm)],[15448, 2048, 14469])).
% 292.11/184.66 tff(15450,plain,
% 292.11/184.66 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_k, s3)) | m_and_h_gate_v_in1(c_e_h_1, c_k, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_k, s3)) | m_and_h_gate_v_in1(c_e_h_1, c_k, s3))),
% 292.11/184.66 inference(rewrite,[status(thm)],[])).
% 292.11/184.66 tff(15451,plain,
% 292.11/184.66 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_k, s3)) | m_and_h_gate_v_in1(c_e_h_1, c_k, s3))),
% 292.11/184.66 inference(quant_inst,[status(thm)],[])).
% 292.11/184.66 tff(15452,plain,
% 292.11/184.66 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_k, s3)) | m_and_h_gate_v_in1(c_e_h_1, c_k, s3)),
% 292.11/184.66 inference(modus_ponens,[status(thm)],[15451, 15450])).
% 292.11/184.66 tff(15453,plain,
% 292.11/184.66 (~node20(c_e_h_1, c_k, s3)),
% 292.11/184.66 inference(unit_resolution,[status(thm)],[15452, 38, 15449])).
% 292.11/184.66 tff(15454,assumption,(m_and_h_gate_v_out(c_e_h_1, c_k, s4)), introduced(assumption)).
% 292.11/184.66 tff(15455,assumption,(~node20(c_e_h_1, c_k, s3)), introduced(assumption)).
% 292.11/184.66 tff(15456,assumption,(node22(c_e_h_1, c_k, s3, s4)), introduced(assumption)).
% 292.11/184.67 tff(15457,plain,
% 292.11/184.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_k, s4)) | (~node22(c_e_h_1, c_k, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_k, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s4)) | (~node22(c_e_h_1, c_k, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_k, s3))),
% 292.11/184.67 inference(rewrite,[status(thm)],[])).
% 292.11/184.67 tff(15458,plain,
% 292.11/184.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_k, s4)) | (~node22(c_e_h_1, c_k, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_k, s3))),
% 292.11/184.67 inference(quant_inst,[status(thm)],[])).
% 292.11/184.67 tff(15459,plain,
% 292.11/184.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s4)) | (~node22(c_e_h_1, c_k, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_k, s3)),
% 292.11/184.67 inference(modus_ponens,[status(thm)],[15458, 15457])).
% 292.11/184.67 tff(15460,plain,
% 292.11/184.67 ($false),
% 292.11/184.67 inference(unit_resolution,[status(thm)],[15459, 108, 15456, 9882, 15454])).
% 292.11/184.67 tff(15461,plain,((~node22(c_e_h_1, c_k, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_k, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s4))), inference(lemma,lemma(discharge,[]))).
% 292.11/184.67 tff(15462,plain,
% 292.11/184.67 (~node22(c_e_h_1, c_k, s3, s4)),
% 292.11/184.67 inference(unit_resolution,[status(thm)],[15461, 15454, 9882])).
% 292.11/184.67 tff(15463,plain,
% 292.11/184.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_1, c_k, s3, s4) | node22(c_e_h_1, c_k, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_1, c_k, s3, s4) | node22(c_e_h_1, c_k, s3, s4))),
% 292.11/184.67 inference(rewrite,[status(thm)],[])).
% 292.11/184.67 tff(15464,plain,
% 292.11/184.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_1, c_k, s3, s4) | node22(c_e_h_1, c_k, s3, s4))),
% 292.11/184.67 inference(quant_inst,[status(thm)],[])).
% 292.11/184.67 tff(15465,plain,
% 292.11/184.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_1, c_k, s3, s4) | node22(c_e_h_1, c_k, s3, s4)),
% 292.11/184.67 inference(modus_ponens,[status(thm)],[15464, 15463])).
% 292.11/184.67 tff(15466,plain,
% 292.11/184.67 (node21(c_e_h_1, c_k, s3, s4) | node22(c_e_h_1, c_k, s3, s4)),
% 292.11/184.67 inference(unit_resolution,[status(thm)],[15465, 82, 531])).
% 292.11/184.67 tff(15467,plain,
% 292.11/184.67 (node21(c_e_h_1, c_k, s3, s4)),
% 292.11/184.67 inference(unit_resolution,[status(thm)],[15466, 15462])).
% 292.11/184.67 tff(15468,plain,
% 292.11/184.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_k, s3) | (~node21(c_e_h_1, c_k, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_k, s3) | (~node21(c_e_h_1, c_k, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s4)))),
% 292.11/184.67 inference(rewrite,[status(thm)],[])).
% 292.11/184.67 tff(15469,plain,
% 292.11/184.67 ((node20(c_e_h_1, c_k, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s4)) | (~node21(c_e_h_1, c_k, s3, s4))) <=> (node20(c_e_h_1, c_k, s3) | (~node21(c_e_h_1, c_k, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s4)))),
% 292.11/184.67 inference(rewrite,[status(thm)],[])).
% 292.11/184.67 tff(15470,plain,
% 292.11/184.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_k, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s4)) | (~node21(c_e_h_1, c_k, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_k, s3) | (~node21(c_e_h_1, c_k, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s4))))),
% 292.11/184.67 inference(monotonicity,[status(thm)],[15469])).
% 292.11/184.67 tff(15471,plain,
% 292.11/184.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_k, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s4)) | (~node21(c_e_h_1, c_k, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_k, s3) | (~node21(c_e_h_1, c_k, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s4)))),
% 292.11/184.67 inference(transitivity,[status(thm)],[15470, 15468])).
% 292.11/184.67 tff(15472,plain,
% 292.11/184.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_k, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s4)) | (~node21(c_e_h_1, c_k, s3, s4)))),
% 292.11/184.67 inference(quant_inst,[status(thm)],[])).
% 292.11/184.67 tff(15473,plain,
% 292.11/184.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_k, s3) | (~node21(c_e_h_1, c_k, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s4))),
% 292.11/184.67 inference(modus_ponens,[status(thm)],[15472, 15471])).
% 292.11/184.67 tff(15474,plain,
% 292.11/184.67 ($false),
% 292.11/184.67 inference(unit_resolution,[status(thm)],[15473, 52, 15467, 15455, 15454])).
% 292.11/184.67 tff(15475,plain,((~m_and_h_gate_v_out(c_e_h_1, c_k, s4)) | node20(c_e_h_1, c_k, s3) | m_and_h_gate_v_out(c_e_h_1, c_k, s3)), inference(lemma,lemma(discharge,[]))).
% 292.11/184.67 tff(15476,plain,
% 292.11/184.67 ((~m_and_h_gate_v_out(c_e_h_1, c_k, s4)) | m_and_h_gate_v_out(c_e_h_1, c_k, s3)),
% 292.11/184.67 inference(unit_resolution,[status(thm)],[15475, 15453])).
% 292.11/184.67 tff(15477,plain,
% 292.11/184.67 (~m_and_h_gate_v_out(c_e_h_1, c_k, s4)),
% 292.11/184.67 inference(unit_resolution,[status(thm)],[15476, 9879])).
% 292.11/184.67 tff(15478,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_k, s4)), introduced(assumption)).
% 292.11/184.67 tff(15479,assumption,(node22(c_e_h_1, c_k, s4, s5)), introduced(assumption)).
% 292.11/184.67 tff(15480,plain,
% 292.11/184.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_k, s5)) | (~node22(c_e_h_1, c_k, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_k, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s5)) | (~node22(c_e_h_1, c_k, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_k, s4))),
% 292.11/184.67 inference(rewrite,[status(thm)],[])).
% 292.11/184.67 tff(15481,plain,
% 292.11/184.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_k, s5)) | (~node22(c_e_h_1, c_k, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_k, s4))),
% 292.11/184.67 inference(quant_inst,[status(thm)],[])).
% 292.11/184.67 tff(15482,plain,
% 292.11/184.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s5)) | (~node22(c_e_h_1, c_k, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_k, s4)),
% 292.11/184.67 inference(modus_ponens,[status(thm)],[15481, 15480])).
% 292.11/184.67 tff(15483,plain,
% 292.11/184.67 ($false),
% 292.11/184.67 inference(unit_resolution,[status(thm)],[15482, 108, 15479, 15478, 15445])).
% 292.11/184.67 tff(15484,plain,((~node22(c_e_h_1, c_k, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_k, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s5))), inference(lemma,lemma(discharge,[]))).
% 292.11/184.67 tff(15485,plain,
% 292.11/184.67 ((~node22(c_e_h_1, c_k, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s5))),
% 292.11/184.67 inference(unit_resolution,[status(thm)],[15484, 15477])).
% 292.11/184.67 tff(15486,plain,
% 292.11/184.67 (~node22(c_e_h_1, c_k, s4, s5)),
% 292.11/184.67 inference(unit_resolution,[status(thm)],[15485, 15445])).
% 292.11/184.67 tff(15487,assumption,(~node20(c_e_h_1, c_k, s4)), introduced(assumption)).
% 292.11/184.67 tff(15488,assumption,(node21(c_e_h_1, c_k, s4, s5)), introduced(assumption)).
% 292.11/184.67 tff(15489,plain,
% 292.11/184.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_k, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s5)) | (~node21(c_e_h_1, c_k, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_k, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s5)) | (~node21(c_e_h_1, c_k, s4, s5)))),
% 292.11/184.67 inference(rewrite,[status(thm)],[])).
% 292.11/184.67 tff(15490,plain,
% 292.11/184.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_k, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s5)) | (~node21(c_e_h_1, c_k, s4, s5)))),
% 292.11/184.67 inference(quant_inst,[status(thm)],[])).
% 292.11/184.67 tff(15491,plain,
% 292.11/184.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_k, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s5)) | (~node21(c_e_h_1, c_k, s4, s5))),
% 292.11/184.67 inference(modus_ponens,[status(thm)],[15490, 15489])).
% 292.11/184.67 tff(15492,plain,
% 292.11/184.67 ($false),
% 292.11/184.67 inference(unit_resolution,[status(thm)],[15491, 52, 15488, 15445, 15487])).
% 292.11/184.67 tff(15493,plain,((~node21(c_e_h_1, c_k, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s5)) | node20(c_e_h_1, c_k, s4)), inference(lemma,lemma(discharge,[]))).
% 292.11/184.67 tff(15494,plain,
% 292.11/184.67 (~node21(c_e_h_1, c_k, s4, s5)),
% 292.11/184.67 inference(unit_resolution,[status(thm)],[15493, 15445, 15487])).
% 292.11/184.67 tff(15495,plain,
% 292.11/184.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_1, c_k, s4, s5) | node22(c_e_h_1, c_k, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_1, c_k, s4, s5) | node22(c_e_h_1, c_k, s4, s5))),
% 292.11/184.67 inference(rewrite,[status(thm)],[])).
% 292.11/184.67 tff(15496,plain,
% 292.11/184.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_1, c_k, s4, s5) | node22(c_e_h_1, c_k, s4, s5))),
% 292.11/184.67 inference(quant_inst,[status(thm)],[])).
% 292.11/184.67 tff(15497,plain,
% 292.11/184.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_1, c_k, s4, s5) | node22(c_e_h_1, c_k, s4, s5)),
% 292.11/184.67 inference(modus_ponens,[status(thm)],[15496, 15495])).
% 292.11/184.67 tff(15498,plain,
% 292.11/184.67 (node21(c_e_h_1, c_k, s4, s5) | node22(c_e_h_1, c_k, s4, s5)),
% 292.11/184.67 inference(unit_resolution,[status(thm)],[15497, 82, 1028])).
% 292.11/184.67 tff(15499,plain,
% 292.11/184.67 ($false),
% 292.11/184.67 inference(unit_resolution,[status(thm)],[15498, 15494, 15486])).
% 292.11/184.67 tff(15500,plain,((~m_and_h_gate_v_out(c_e_h_1, c_k, s5)) | node20(c_e_h_1, c_k, s4)), inference(lemma,lemma(discharge,[]))).
% 292.11/184.67 tff(15501,plain,
% 292.11/184.67 (~m_and_h_gate_v_out(c_e_h_1, c_k, s5)),
% 292.11/184.67 inference(unit_resolution,[status(thm)],[15500, 15444])).
% 292.11/184.67 tff(15502,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_k, s5)), introduced(assumption)).
% 292.11/184.67 tff(15503,assumption,(node22(c_e_h_1, c_k, s5, s6)), introduced(assumption)).
% 292.11/184.67 tff(15504,plain,
% 292.11/184.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_k, s6)) | (~node22(c_e_h_1, c_k, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_k, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s6)) | (~node22(c_e_h_1, c_k, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_k, s5))),
% 292.11/184.67 inference(rewrite,[status(thm)],[])).
% 292.11/184.67 tff(15505,plain,
% 292.11/184.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_k, s6)) | (~node22(c_e_h_1, c_k, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_k, s5))),
% 292.11/184.67 inference(quant_inst,[status(thm)],[])).
% 292.11/184.67 tff(15506,plain,
% 292.11/184.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s6)) | (~node22(c_e_h_1, c_k, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_k, s5)),
% 292.11/184.67 inference(modus_ponens,[status(thm)],[15505, 15504])).
% 292.11/184.68 tff(15507,plain,
% 292.11/184.68 ($false),
% 292.11/184.68 inference(unit_resolution,[status(thm)],[15506, 108, 15503, 15429, 15502])).
% 292.11/184.68 tff(15508,plain,((~node22(c_e_h_1, c_k, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s6)) | m_and_h_gate_v_out(c_e_h_1, c_k, s5)), inference(lemma,lemma(discharge,[]))).
% 292.11/184.68 tff(15509,plain,
% 292.11/184.68 (~node22(c_e_h_1, c_k, s5, s6)),
% 292.11/184.68 inference(unit_resolution,[status(thm)],[15508, 15429, 15502])).
% 292.11/184.68 tff(15510,assumption,(~node20(c_e_h_1, c_k, s5)), introduced(assumption)).
% 292.11/184.68 tff(15511,assumption,(node21(c_e_h_1, c_k, s5, s6)), introduced(assumption)).
% 292.11/184.68 tff(15512,plain,
% 292.11/184.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_k, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s6)) | (~node21(c_e_h_1, c_k, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_k, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s6)) | (~node21(c_e_h_1, c_k, s5, s6)))),
% 292.11/184.68 inference(rewrite,[status(thm)],[])).
% 292.11/184.68 tff(15513,plain,
% 292.11/184.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_k, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s6)) | (~node21(c_e_h_1, c_k, s5, s6)))),
% 292.11/184.68 inference(quant_inst,[status(thm)],[])).
% 292.11/184.68 tff(15514,plain,
% 292.11/184.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_k, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s6)) | (~node21(c_e_h_1, c_k, s5, s6))),
% 292.11/184.68 inference(modus_ponens,[status(thm)],[15513, 15512])).
% 292.11/184.68 tff(15515,plain,
% 292.11/184.68 ($false),
% 292.11/184.68 inference(unit_resolution,[status(thm)],[15514, 52, 15511, 15510, 15429])).
% 292.11/184.68 tff(15516,plain,((~node21(c_e_h_1, c_k, s5, s6)) | node20(c_e_h_1, c_k, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s6))), inference(lemma,lemma(discharge,[]))).
% 292.11/184.68 tff(15517,plain,
% 292.11/184.68 (~node21(c_e_h_1, c_k, s5, s6)),
% 292.11/184.68 inference(unit_resolution,[status(thm)],[15516, 15429, 15510])).
% 292.11/184.68 tff(15518,plain,
% 292.11/184.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_1, c_k, s5, s6) | node22(c_e_h_1, c_k, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_1, c_k, s5, s6) | node22(c_e_h_1, c_k, s5, s6))),
% 292.11/184.68 inference(rewrite,[status(thm)],[])).
% 292.11/184.68 tff(15519,plain,
% 292.11/184.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_1, c_k, s5, s6) | node22(c_e_h_1, c_k, s5, s6))),
% 292.11/184.68 inference(quant_inst,[status(thm)],[])).
% 292.11/184.68 tff(15520,plain,
% 292.11/184.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_1, c_k, s5, s6) | node22(c_e_h_1, c_k, s5, s6)),
% 292.11/184.68 inference(modus_ponens,[status(thm)],[15519, 15518])).
% 292.11/184.68 tff(15521,plain,
% 292.11/184.68 (node21(c_e_h_1, c_k, s5, s6) | node22(c_e_h_1, c_k, s5, s6)),
% 292.11/184.68 inference(unit_resolution,[status(thm)],[15520, 82, 1406])).
% 292.11/184.68 tff(15522,plain,
% 292.11/184.68 ($false),
% 292.11/184.68 inference(unit_resolution,[status(thm)],[15521, 15517, 15509])).
% 292.11/184.68 tff(15523,plain,((~m_and_h_gate_v_out(c_e_h_1, c_k, s6)) | node20(c_e_h_1, c_k, s5) | m_and_h_gate_v_out(c_e_h_1, c_k, s5)), inference(lemma,lemma(discharge,[]))).
% 292.11/184.68 tff(15524,plain,
% 292.11/184.68 (node20(c_e_h_1, c_k, s5)),
% 292.11/184.68 inference(unit_resolution,[status(thm)],[15523, 15501, 15429])).
% 292.11/184.68 tff(15525,assumption,(~m_and_h_gate_v_in1(c_e_h_1, c_k, s5)), introduced(assumption)).
% 292.11/184.68 tff(15526,assumption,(node20(c_e_h_1, c_k, s5)), introduced(assumption)).
% 292.11/184.68 tff(15527,plain,
% 292.11/184.68 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_k, s5)) | m_and_h_gate_v_in1(c_e_h_1, c_k, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_k, s5)) | m_and_h_gate_v_in1(c_e_h_1, c_k, s5))),
% 292.11/184.68 inference(rewrite,[status(thm)],[])).
% 292.11/184.68 tff(15528,plain,
% 292.11/184.68 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_k, s5)) | m_and_h_gate_v_in1(c_e_h_1, c_k, s5))),
% 292.11/184.68 inference(quant_inst,[status(thm)],[])).
% 292.11/184.68 tff(15529,plain,
% 292.11/184.68 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_k, s5)) | m_and_h_gate_v_in1(c_e_h_1, c_k, s5)),
% 292.11/184.68 inference(modus_ponens,[status(thm)],[15528, 15527])).
% 292.11/184.68 tff(15530,plain,
% 292.11/184.68 ($false),
% 292.11/184.68 inference(unit_resolution,[status(thm)],[15529, 38, 15526, 15525])).
% 292.11/184.68 tff(15531,plain,((~node20(c_e_h_1, c_k, s5)) | m_and_h_gate_v_in1(c_e_h_1, c_k, s5)), inference(lemma,lemma(discharge,[]))).
% 292.11/184.68 tff(15532,plain,
% 292.11/184.68 (m_and_h_gate_v_in1(c_e_h_1, c_k, s5)),
% 292.11/184.68 inference(unit_resolution,[status(thm)],[15531, 15524])).
% 292.11/184.68 tff(15533,assumption,(m_and_h_gate_v_in1(c_e_h_1, c_k, s5)), introduced(assumption)).
% 292.11/184.68 tff(15534,plain,
% 292.11/184.68 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_k, s5)) | m_or_h_gate_v_out(c_e_h_1, c_g, s5))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_k, s5)) | m_or_h_gate_v_out(c_e_h_1, c_g, s5))),
% 292.11/184.68 inference(rewrite,[status(thm)],[])).
% 292.11/184.68 tff(15535,plain,
% 292.11/184.68 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_k, s5)) | m_or_h_gate_v_out(c_e_h_1, c_g, s5))),
% 292.11/184.68 inference(quant_inst,[status(thm)],[])).
% 292.11/184.68 tff(15536,plain,
% 292.11/184.68 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_k, s5)) | m_or_h_gate_v_out(c_e_h_1, c_g, s5)),
% 292.11/184.68 inference(modus_ponens,[status(thm)],[15535, 15534])).
% 292.11/184.68 tff(15537,plain,
% 292.11/184.68 ($false),
% 292.11/184.68 inference(unit_resolution,[status(thm)],[15536, 2048, 14543, 15533])).
% 292.11/184.68 tff(15538,plain,((~m_and_h_gate_v_in1(c_e_h_1, c_k, s5)) | m_or_h_gate_v_out(c_e_h_1, c_g, s5)), inference(lemma,lemma(discharge,[]))).
% 292.11/184.68 tff(15539,plain,
% 292.11/184.68 (m_or_h_gate_v_out(c_e_h_1, c_g, s5)),
% 292.11/184.68 inference(unit_resolution,[status(thm)],[15538, 15532])).
% 292.11/184.68 tff(15540,plain,
% 292.11/184.68 (m_or_h_gate_v_in1(c_e_h_1, c_g, s4)),
% 292.11/184.68 inference(unit_resolution,[status(thm)],[14600, 15539, 14573, 14572])).
% 292.11/184.68 tff(15541,plain,
% 292.11/184.68 (m_and_h_gate_v_out(c_e_h_1, c_c, s4)),
% 292.11/184.68 inference(unit_resolution,[status(thm)],[14124, 15540])).
% 292.11/184.68 tff(15542,plain,
% 292.11/184.68 (m_user_v_req(c_e_h_1, c_u, s2)),
% 292.11/184.68 inference(unit_resolution,[status(thm)],[14671, 15541])).
% 292.11/184.68 tff(15543,plain,
% 292.11/184.68 (m_mutex_h_half_v_inp(c_e_h_1, c_a, s2)),
% 292.11/184.68 inference(unit_resolution,[status(thm)],[14354, 1426, 15542])).
% 292.11/184.68 tff(15544,plain,
% 292.11/184.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | ((~m_or_h_gate_v_out(c_e_h_1, c_g, s5)) | m_or_h_gate_v_out(c_e_h_1, c_g, s6) | (~node6(c_e_h_1, c_g, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s5)) | m_or_h_gate_v_out(c_e_h_1, c_g, s6) | (~node6(c_e_h_1, c_g, s5, s6)))),
% 292.11/184.68 inference(rewrite,[status(thm)],[])).
% 292.11/184.68 tff(15545,plain,
% 292.11/184.68 ((m_or_h_gate_v_out(c_e_h_1, c_g, s6) | (~node6(c_e_h_1, c_g, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s5))) <=> ((~m_or_h_gate_v_out(c_e_h_1, c_g, s5)) | m_or_h_gate_v_out(c_e_h_1, c_g, s6) | (~node6(c_e_h_1, c_g, s5, s6)))),
% 292.11/184.68 inference(rewrite,[status(thm)],[])).
% 292.11/184.68 tff(15546,plain,
% 292.11/184.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_1, c_g, s6) | (~node6(c_e_h_1, c_g, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | ((~m_or_h_gate_v_out(c_e_h_1, c_g, s5)) | m_or_h_gate_v_out(c_e_h_1, c_g, s6) | (~node6(c_e_h_1, c_g, s5, s6))))),
% 292.11/184.68 inference(monotonicity,[status(thm)],[15545])).
% 292.11/184.68 tff(15547,plain,
% 292.11/184.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_1, c_g, s6) | (~node6(c_e_h_1, c_g, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s5)) | m_or_h_gate_v_out(c_e_h_1, c_g, s6) | (~node6(c_e_h_1, c_g, s5, s6)))),
% 292.11/184.68 inference(transitivity,[status(thm)],[15546, 15544])).
% 292.11/184.68 tff(15548,plain,
% 292.11/184.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_1, c_g, s6) | (~node6(c_e_h_1, c_g, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s5)))),
% 292.11/184.68 inference(quant_inst,[status(thm)],[])).
% 292.11/184.68 tff(15549,plain,
% 292.11/184.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s5)) | m_or_h_gate_v_out(c_e_h_1, c_g, s6) | (~node6(c_e_h_1, c_g, s5, s6))),
% 292.11/184.68 inference(modus_ponens,[status(thm)],[15548, 15547])).
% 292.11/184.68 tff(15550,plain,
% 292.11/184.68 ($false),
% 292.11/184.68 inference(unit_resolution,[status(thm)],[15549, 5474, 14544, 14571, 15389])).
% 292.11/184.68 tff(15551,plain,((~node6(c_e_h_1, c_g, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s5)) | m_or_h_gate_v_out(c_e_h_1, c_g, s6)), inference(lemma,lemma(discharge,[]))).
% 292.11/184.68 tff(15552,plain,
% 292.11/184.68 (~node6(c_e_h_1, c_g, s5, s6)),
% 292.11/184.68 inference(unit_resolution,[status(thm)],[15551, 15539, 15389])).
% 292.11/184.68 tff(15553,plain,
% 292.11/184.68 (node5(c_e_h_1, c_g, s5, s6)),
% 292.11/184.68 inference(unit_resolution,[status(thm)],[14560, 15552])).
% 292.11/184.68 tff(15554,assumption,(~node4(c_e_h_1, c_g, s5)), introduced(assumption)).
% 292.11/184.68 tff(15555,plain,
% 292.11/184.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (m_or_h_gate_v_out(c_e_h_1, c_g, s6) | node4(c_e_h_1, c_g, s5) | (~node5(c_e_h_1, c_g, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | m_or_h_gate_v_out(c_e_h_1, c_g, s6) | node4(c_e_h_1, c_g, s5) | (~node5(c_e_h_1, c_g, s5, s6)))),
% 292.11/184.68 inference(rewrite,[status(thm)],[])).
% 292.11/184.68 tff(15556,plain,
% 292.11/184.68 ((node4(c_e_h_1, c_g, s5) | (~node5(c_e_h_1, c_g, s5, s6)) | m_or_h_gate_v_out(c_e_h_1, c_g, s6)) <=> (m_or_h_gate_v_out(c_e_h_1, c_g, s6) | node4(c_e_h_1, c_g, s5) | (~node5(c_e_h_1, c_g, s5, s6)))),
% 292.11/184.68 inference(rewrite,[status(thm)],[])).
% 292.11/184.68 tff(15557,plain,
% 292.11/184.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_1, c_g, s5) | (~node5(c_e_h_1, c_g, s5, s6)) | m_or_h_gate_v_out(c_e_h_1, c_g, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (m_or_h_gate_v_out(c_e_h_1, c_g, s6) | node4(c_e_h_1, c_g, s5) | (~node5(c_e_h_1, c_g, s5, s6))))),
% 292.11/184.68 inference(monotonicity,[status(thm)],[15556])).
% 292.11/184.68 tff(15558,plain,
% 292.11/184.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_1, c_g, s5) | (~node5(c_e_h_1, c_g, s5, s6)) | m_or_h_gate_v_out(c_e_h_1, c_g, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | m_or_h_gate_v_out(c_e_h_1, c_g, s6) | node4(c_e_h_1, c_g, s5) | (~node5(c_e_h_1, c_g, s5, s6)))),
% 292.11/184.68 inference(transitivity,[status(thm)],[15557, 15555])).
% 292.11/184.68 tff(15559,plain,
% 292.11/184.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_1, c_g, s5) | (~node5(c_e_h_1, c_g, s5, s6)) | m_or_h_gate_v_out(c_e_h_1, c_g, s6))),
% 292.11/184.68 inference(quant_inst,[status(thm)],[])).
% 292.11/184.68 tff(15560,plain,
% 292.11/184.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | m_or_h_gate_v_out(c_e_h_1, c_g, s6) | node4(c_e_h_1, c_g, s5) | (~node5(c_e_h_1, c_g, s5, s6))),
% 292.11/184.69 inference(modus_ponens,[status(thm)],[15559, 15558])).
% 292.11/184.69 tff(15561,plain,
% 292.11/184.69 ($false),
% 292.11/184.69 inference(unit_resolution,[status(thm)],[15560, 5498, 14533, 15389, 15554])).
% 292.11/184.69 tff(15562,plain,((~node5(c_e_h_1, c_g, s5, s6)) | m_or_h_gate_v_out(c_e_h_1, c_g, s6) | node4(c_e_h_1, c_g, s5)), inference(lemma,lemma(discharge,[]))).
% 292.11/184.69 tff(15563,plain,
% 292.11/184.69 (node4(c_e_h_1, c_g, s5)),
% 292.11/184.69 inference(unit_resolution,[status(thm)],[15562, 15553, 15389])).
% 292.11/184.69 tff(15564,plain,
% 292.11/184.69 (((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_g, s5)) | (~node4(c_e_h_1, c_g, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | (~m_or_h_gate_v_in1(c_e_h_1, c_g, s5)) | (~node4(c_e_h_1, c_g, s5)))),
% 292.11/184.69 inference(rewrite,[status(thm)],[])).
% 292.11/184.69 tff(15565,plain,
% 292.11/184.69 ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_g, s5)) | (~node4(c_e_h_1, c_g, s5)))),
% 292.11/184.69 inference(quant_inst,[status(thm)],[])).
% 292.11/184.69 tff(15566,plain,
% 292.11/184.69 ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | (~m_or_h_gate_v_in1(c_e_h_1, c_g, s5)) | (~node4(c_e_h_1, c_g, s5))),
% 292.11/184.69 inference(modus_ponens,[status(thm)],[15565, 15564])).
% 292.11/184.69 tff(15567,plain,
% 292.11/184.69 (~m_or_h_gate_v_in1(c_e_h_1, c_g, s5)),
% 292.11/184.69 inference(unit_resolution,[status(thm)],[15566, 5516, 15563])).
% 292.11/184.69 tff(15568,plain,
% 292.11/184.69 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_c, s5)) | m_or_h_gate_v_in1(c_e_h_1, c_g, s5))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s5)) | m_or_h_gate_v_in1(c_e_h_1, c_g, s5))),
% 292.11/184.69 inference(rewrite,[status(thm)],[])).
% 292.11/184.69 tff(15569,plain,
% 292.11/184.69 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_c, s5)) | m_or_h_gate_v_in1(c_e_h_1, c_g, s5))),
% 292.11/184.69 inference(quant_inst,[status(thm)],[])).
% 292.11/184.69 tff(15570,plain,
% 292.11/184.69 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s5)) | m_or_h_gate_v_in1(c_e_h_1, c_g, s5)),
% 292.11/184.69 inference(modus_ponens,[status(thm)],[15569, 15568])).
% 292.11/184.69 tff(15571,plain,
% 292.11/184.69 (~m_and_h_gate_v_out(c_e_h_1, c_c, s5)),
% 292.11/184.69 inference(unit_resolution,[status(thm)],[15570, 5896, 15567])).
% 292.11/184.69 tff(15572,plain,
% 292.11/184.69 (~node22(c_e_h_1, c_c, s4, s5)),
% 292.11/184.69 inference(unit_resolution,[status(thm)],[14820, 15571, 15541])).
% 292.11/184.69 tff(15573,plain,
% 292.11/184.69 (node21(c_e_h_1, c_c, s4, s5)),
% 292.11/184.69 inference(unit_resolution,[status(thm)],[14524, 15572])).
% 292.11/184.69 tff(15574,plain,
% 292.11/184.69 (~m_and_h_gate_v_in1(c_e_h_1, c_c, s4)),
% 292.11/184.69 inference(unit_resolution,[status(thm)],[14840, 15573, 15571])).
% 292.11/184.69 tff(15575,plain,
% 292.11/184.69 (~m_mutex_h_half_v_out(c_e_h_1, c_a, s4)),
% 292.11/184.69 inference(unit_resolution,[status(thm)],[14808, 2556, 15574])).
% 292.11/184.69 tff(15576,plain,
% 292.11/184.69 (m_user_v_req(c_e_h_1, c_u, s3)),
% 292.11/184.69 inference(unit_resolution,[status(thm)],[14760, 15542])).
% 292.11/184.69 tff(15577,plain,
% 292.11/184.69 (m_mutex_h_half_v_inp(c_e_h_1, c_a, s3)),
% 292.11/184.69 inference(unit_resolution,[status(thm)],[14768, 15576])).
% 292.11/184.69 tff(15578,plain,
% 292.11/184.69 (~node12(c_e_h_1, c_a, s3, s4)),
% 292.11/184.69 inference(unit_resolution,[status(thm)],[14779, 15575, 15577])).
% 292.11/184.69 tff(15579,plain,
% 292.11/184.69 (node13(c_e_h_1, c_a, s3, s4)),
% 292.11/184.69 inference(unit_resolution,[status(thm)],[14791, 15578])).
% 292.11/184.69 tff(15580,plain,
% 292.11/184.69 (~m_mutex_h_half_v_out(c_e_h_1, c_a, s3)),
% 292.11/184.69 inference(unit_resolution,[status(thm)],[14786, 15579, 15575])).
% 292.11/184.69 tff(15581,plain,
% 292.11/184.69 (~m_and_h_gate_v_in1(c_e_h_1, c_c, s3)),
% 292.11/184.69 inference(unit_resolution,[status(thm)],[14638, 15580])).
% 292.11/184.69 tff(15582,plain,
% 292.11/184.69 (~node20(c_e_h_1, c_c, s3)),
% 292.11/184.69 inference(unit_resolution,[status(thm)],[14646, 15581])).
% 292.11/184.69 tff(15583,plain,
% 292.11/184.69 (m_and_h_gate_v_out(c_e_h_1, c_c, s3)),
% 292.11/184.69 inference(unit_resolution,[status(thm)],[14663, 15582, 15541])).
% 292.11/184.69 tff(15584,plain,
% 292.11/184.69 (node20(c_e_h_1, c_c, s2)),
% 292.11/184.69 inference(unit_resolution,[status(thm)],[14216, 15583])).
% 292.11/184.69 tff(15585,plain,
% 292.11/184.69 (m_and_h_gate_v_in1(c_e_h_1, c_c, s2)),
% 292.11/184.69 inference(unit_resolution,[status(thm)],[14224, 15584])).
% 292.11/184.69 tff(15586,plain,
% 292.11/184.69 (m_mutex_h_half_v_out(c_e_h_1, c_a, s2)),
% 292.11/184.69 inference(unit_resolution,[status(thm)],[14232, 15585])).
% 292.11/184.69 tff(15587,plain,
% 292.11/184.69 (~node13(c_e_h_1, c_a, s2, s3)),
% 292.11/184.69 inference(unit_resolution,[status(thm)],[14367, 15586, 15580])).
% 292.11/184.69 tff(15588,plain,
% 292.11/184.69 (node12(c_e_h_1, c_a, s2, s3)),
% 292.11/184.69 inference(unit_resolution,[status(thm)],[14372, 15587])).
% 292.11/184.69 tff(15589,plain,
% 292.11/184.69 ($false),
% 292.11/184.69 inference(unit_resolution,[status(thm)],[14379, 1483, 15580, 15588, 15543])).
% 292.11/184.69 tff(15590,plain,(m_or_h_gate_v_out(c_e_h_1, c_g, s4) | m_or_h_gate_v_out(c_e_h_1, c_g, s6) | m_or_h_gate_v_in2(c_e_h_1, c_g, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s6))), inference(lemma,lemma(discharge,[]))).
% 292.11/184.69 tff(15591,plain,
% 292.11/184.69 (m_or_h_gate_v_out(c_e_h_1, c_g, s4) | m_or_h_gate_v_out(c_e_h_1, c_g, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s6))),
% 292.11/184.69 inference(unit_resolution,[status(thm)],[15590, 14570])).
% 292.11/184.69 tff(15592,plain,
% 292.11/184.69 (m_or_h_gate_v_out(c_e_h_1, c_g, s4)),
% 292.11/184.69 inference(unit_resolution,[status(thm)],[15591, 15428, 15389])).
% 292.11/184.69 tff(15593,plain,
% 292.11/184.69 (m_or_h_gate_v_in1(c_e_h_1, c_g, s3)),
% 292.11/184.69 inference(unit_resolution,[status(thm)],[14503, 14471])).
% 292.11/184.69 tff(15594,plain,
% 292.11/184.69 (m_and_h_gate_v_out(c_e_h_1, c_c, s3)),
% 292.11/184.69 inference(unit_resolution,[status(thm)],[14418, 2708, 15593])).
% 292.11/184.69 tff(15595,plain,
% 292.11/184.69 (m_and_h_gate_v_out(c_e_h_1, c_c, s4)),
% 292.11/184.69 inference(unit_resolution,[status(thm)],[14414, 15594])).
% 292.11/184.69 tff(15596,plain,
% 292.11/184.69 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_c, s4)) | m_or_h_gate_v_in1(c_e_h_1, c_g, s4))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s4)) | m_or_h_gate_v_in1(c_e_h_1, c_g, s4))),
% 292.11/184.69 inference(rewrite,[status(thm)],[])).
% 292.11/184.69 tff(15597,plain,
% 292.11/184.69 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_c, s4)) | m_or_h_gate_v_in1(c_e_h_1, c_g, s4))),
% 292.11/184.69 inference(quant_inst,[status(thm)],[])).
% 292.11/184.69 tff(15598,plain,
% 292.11/184.69 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s4)) | m_or_h_gate_v_in1(c_e_h_1, c_g, s4)),
% 292.11/184.69 inference(modus_ponens,[status(thm)],[15597, 15596])).
% 292.11/184.69 tff(15599,plain,
% 292.11/184.69 ($false),
% 292.11/184.69 inference(unit_resolution,[status(thm)],[15598, 5896, 14605, 14574])).
% 292.11/184.69 tff(15600,plain,(m_or_h_gate_v_in1(c_e_h_1, c_g, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s4))), inference(lemma,lemma(discharge,[]))).
% 292.11/184.69 tff(15601,plain,
% 292.11/184.69 (m_or_h_gate_v_in1(c_e_h_1, c_g, s4)),
% 292.11/184.69 inference(unit_resolution,[status(thm)],[15600, 15595])).
% 292.11/184.69 tff(15602,plain,
% 292.11/184.69 (((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_g, s4)) | (~node4(c_e_h_1, c_g, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | (~m_or_h_gate_v_in1(c_e_h_1, c_g, s4)) | (~node4(c_e_h_1, c_g, s4)))),
% 292.11/184.69 inference(rewrite,[status(thm)],[])).
% 292.11/184.69 tff(15603,plain,
% 292.11/184.69 ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_g, s4)) | (~node4(c_e_h_1, c_g, s4)))),
% 292.11/184.69 inference(quant_inst,[status(thm)],[])).
% 292.11/184.69 tff(15604,plain,
% 292.11/184.69 ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | (~m_or_h_gate_v_in1(c_e_h_1, c_g, s4)) | (~node4(c_e_h_1, c_g, s4))),
% 292.11/184.69 inference(modus_ponens,[status(thm)],[15603, 15602])).
% 292.11/184.69 tff(15605,plain,
% 292.11/184.69 (~node4(c_e_h_1, c_g, s4)),
% 292.11/184.69 inference(unit_resolution,[status(thm)],[15604, 5516, 15601])).
% 292.11/184.69 tff(15606,assumption,(node6(c_e_h_1, c_g, s4, s5)), introduced(assumption)).
% 292.11/184.69 tff(15607,plain,
% 292.11/184.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | ((~m_or_h_gate_v_out(c_e_h_1, c_g, s4)) | (~node6(c_e_h_1, c_g, s4, s5)) | m_or_h_gate_v_out(c_e_h_1, c_g, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s4)) | (~node6(c_e_h_1, c_g, s4, s5)) | m_or_h_gate_v_out(c_e_h_1, c_g, s5))),
% 292.21/184.69 inference(rewrite,[status(thm)],[])).
% 292.21/184.69 tff(15608,plain,
% 292.21/184.69 ((m_or_h_gate_v_out(c_e_h_1, c_g, s5) | (~node6(c_e_h_1, c_g, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s4))) <=> ((~m_or_h_gate_v_out(c_e_h_1, c_g, s4)) | (~node6(c_e_h_1, c_g, s4, s5)) | m_or_h_gate_v_out(c_e_h_1, c_g, s5))),
% 292.21/184.69 inference(rewrite,[status(thm)],[])).
% 292.21/184.69 tff(15609,plain,
% 292.21/184.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_1, c_g, s5) | (~node6(c_e_h_1, c_g, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | ((~m_or_h_gate_v_out(c_e_h_1, c_g, s4)) | (~node6(c_e_h_1, c_g, s4, s5)) | m_or_h_gate_v_out(c_e_h_1, c_g, s5)))),
% 292.21/184.69 inference(monotonicity,[status(thm)],[15608])).
% 292.21/184.69 tff(15610,plain,
% 292.21/184.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_1, c_g, s5) | (~node6(c_e_h_1, c_g, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s4)) | (~node6(c_e_h_1, c_g, s4, s5)) | m_or_h_gate_v_out(c_e_h_1, c_g, s5))),
% 292.21/184.69 inference(transitivity,[status(thm)],[15609, 15607])).
% 292.21/184.69 tff(15611,plain,
% 292.21/184.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_1, c_g, s5) | (~node6(c_e_h_1, c_g, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s4)))),
% 292.21/184.69 inference(quant_inst,[status(thm)],[])).
% 292.21/184.69 tff(15612,plain,
% 292.21/184.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s4)) | (~node6(c_e_h_1, c_g, s4, s5)) | m_or_h_gate_v_out(c_e_h_1, c_g, s5)),
% 292.21/184.69 inference(modus_ponens,[status(thm)],[15611, 15610])).
% 292.21/184.69 tff(15613,plain,
% 292.21/184.69 ($false),
% 292.21/184.69 inference(unit_resolution,[status(thm)],[15612, 5474, 15606, 14471, 14543])).
% 292.21/184.69 tff(15614,plain,((~node6(c_e_h_1, c_g, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s4)) | m_or_h_gate_v_out(c_e_h_1, c_g, s5)), inference(lemma,lemma(discharge,[]))).
% 292.21/184.69 tff(15615,plain,
% 292.21/184.69 (~node6(c_e_h_1, c_g, s4, s5)),
% 292.21/184.69 inference(unit_resolution,[status(thm)],[15614, 14543, 14471])).
% 292.21/184.69 tff(15616,plain,
% 292.21/184.69 (node5(c_e_h_1, c_g, s4, s5)),
% 292.21/184.69 inference(unit_resolution,[status(thm)],[14591, 15615])).
% 292.21/184.69 tff(15617,plain,
% 292.21/184.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (m_or_h_gate_v_out(c_e_h_1, c_g, s5) | (~node5(c_e_h_1, c_g, s4, s5)) | node4(c_e_h_1, c_g, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | m_or_h_gate_v_out(c_e_h_1, c_g, s5) | (~node5(c_e_h_1, c_g, s4, s5)) | node4(c_e_h_1, c_g, s4))),
% 292.21/184.69 inference(rewrite,[status(thm)],[])).
% 292.21/184.69 tff(15618,plain,
% 292.21/184.69 ((node4(c_e_h_1, c_g, s4) | (~node5(c_e_h_1, c_g, s4, s5)) | m_or_h_gate_v_out(c_e_h_1, c_g, s5)) <=> (m_or_h_gate_v_out(c_e_h_1, c_g, s5) | (~node5(c_e_h_1, c_g, s4, s5)) | node4(c_e_h_1, c_g, s4))),
% 292.21/184.69 inference(rewrite,[status(thm)],[])).
% 292.21/184.69 tff(15619,plain,
% 292.21/184.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_1, c_g, s4) | (~node5(c_e_h_1, c_g, s4, s5)) | m_or_h_gate_v_out(c_e_h_1, c_g, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (m_or_h_gate_v_out(c_e_h_1, c_g, s5) | (~node5(c_e_h_1, c_g, s4, s5)) | node4(c_e_h_1, c_g, s4)))),
% 292.21/184.69 inference(monotonicity,[status(thm)],[15618])).
% 292.21/184.70 tff(15620,plain,
% 292.21/184.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_1, c_g, s4) | (~node5(c_e_h_1, c_g, s4, s5)) | m_or_h_gate_v_out(c_e_h_1, c_g, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | m_or_h_gate_v_out(c_e_h_1, c_g, s5) | (~node5(c_e_h_1, c_g, s4, s5)) | node4(c_e_h_1, c_g, s4))),
% 292.21/184.70 inference(transitivity,[status(thm)],[15619, 15617])).
% 292.21/184.70 tff(15621,plain,
% 292.21/184.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_1, c_g, s4) | (~node5(c_e_h_1, c_g, s4, s5)) | m_or_h_gate_v_out(c_e_h_1, c_g, s5))),
% 292.21/184.70 inference(quant_inst,[status(thm)],[])).
% 292.21/184.70 tff(15622,plain,
% 292.21/184.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | m_or_h_gate_v_out(c_e_h_1, c_g, s5) | (~node5(c_e_h_1, c_g, s4, s5)) | node4(c_e_h_1, c_g, s4)),
% 292.21/184.70 inference(modus_ponens,[status(thm)],[15621, 15620])).
% 292.21/184.70 tff(15623,plain,
% 292.21/184.70 ($false),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[15622, 5498, 15616, 14543, 15605])).
% 292.21/184.70 tff(15624,plain,(m_or_h_gate_v_out(c_e_h_1, c_g, s5) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s4))), inference(lemma,lemma(discharge,[]))).
% 292.21/184.70 tff(15625,plain,
% 292.21/184.70 (m_or_h_gate_v_out(c_e_h_1, c_g, s5)),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[15624, 15592])).
% 292.21/184.70 tff(15626,plain,
% 292.21/184.70 (~node6(c_e_h_1, c_g, s5, s6)),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[15551, 15625, 15389])).
% 292.21/184.70 tff(15627,plain,
% 292.21/184.70 (node5(c_e_h_1, c_g, s5, s6)),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[14560, 15626])).
% 292.21/184.70 tff(15628,plain,
% 292.21/184.70 (node4(c_e_h_1, c_g, s5)),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[15562, 15627, 15389])).
% 292.21/184.70 tff(15629,plain,
% 292.21/184.70 (~m_or_h_gate_v_in1(c_e_h_1, c_g, s5)),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[15566, 5516, 15628])).
% 292.21/184.70 tff(15630,plain,
% 292.21/184.70 (m_and_h_gate_v_out(c_e_h_1, c_c, s4)),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[14848, 15625])).
% 292.21/184.70 tff(15631,plain,
% 292.21/184.70 (~m_user_v_req(c_e_h_1, c_u, s2)),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[14760, 14673])).
% 292.21/184.70 tff(15632,plain,
% 292.21/184.70 (~m_mutex_h_half_v_out(c_e_h_1, c_a, s3)),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[14632, 15631])).
% 292.21/184.70 tff(15633,plain,
% 292.21/184.70 (m_mutex_h_half_v_inp(c_e_h_1, c_a, s3)),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[15058, 15632, 14805])).
% 292.21/184.70 tff(15634,plain,
% 292.21/184.70 ($false),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[15062, 395, 14673, 15633])).
% 292.21/184.70 tff(15635,plain,(m_user_v_req(c_e_h_1, c_u, s3) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s4))), inference(lemma,lemma(discharge,[]))).
% 292.21/184.70 tff(15636,plain,
% 292.21/184.70 (~m_mutex_h_half_v_out(c_e_h_1, c_a, s4)),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[15635, 14673])).
% 292.21/184.70 tff(15637,plain,
% 292.21/184.70 (~m_or_h_gate_v_out(c_e_h_1, c_g, s6)),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[14802, 15636, 14101])).
% 292.21/184.70 tff(15638,plain,
% 292.21/184.70 (~m_and_h_gate_v_in1(c_e_h_1, c_k, s6)),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[15395, 15637])).
% 292.21/184.70 tff(15639,plain,
% 292.21/184.70 (~node20(c_e_h_1, c_k, s6)),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[15403, 15638])).
% 292.21/184.70 tff(15640,plain,
% 292.21/184.70 (m_and_h_gate_v_out(c_e_h_1, c_k, s6)),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[15427, 15639, 15405])).
% 292.21/184.70 tff(15641,plain,
% 292.21/184.70 (m_or_h_gate_v_out(c_e_h_1, c_g, s4)),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[15591, 15640, 15637])).
% 292.21/184.70 tff(15642,plain,
% 292.21/184.70 (m_or_h_gate_v_in1(c_e_h_1, c_g, s3)),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[14503, 15641])).
% 292.21/184.70 tff(15643,plain,
% 292.21/184.70 (~m_and_h_gate_v_out(c_e_h_1, c_c, s4)),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[14671, 15631])).
% 292.21/184.70 tff(15644,plain,
% 292.21/184.70 (~m_and_h_gate_v_out(c_e_h_1, c_c, s3)),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[14414, 15643])).
% 292.21/184.70 tff(15645,plain,
% 292.21/184.70 ($false),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[14418, 2708, 15644, 15642])).
% 292.21/184.70 tff(15646,plain,(m_user_v_req(c_e_h_1, c_u, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s7)) | m_or_h_gate_v_in2(c_e_h_1, c_g, s5)), inference(lemma,lemma(discharge,[]))).
% 292.21/184.70 tff(15647,plain,
% 292.21/184.70 (m_user_v_req(c_e_h_1, c_u, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s7))),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[15646, 14100])).
% 292.21/184.70 tff(15648,plain,
% 292.21/184.70 (m_user_v_req(c_e_h_1, c_u, s3)),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[15647, 15405])).
% 292.21/184.70 tff(15649,plain,
% 292.21/184.70 (m_mutex_h_half_v_inp(c_e_h_1, c_a, s3)),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[14768, 15648])).
% 292.21/184.70 tff(15650,plain,
% 292.21/184.70 (m_or_h_gate_v_in1(c_e_h_1, c_g, s3)),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[14503, 15592])).
% 292.21/184.70 tff(15651,plain,
% 292.21/184.70 (m_and_h_gate_v_out(c_e_h_1, c_c, s3)),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[14418, 2708, 15650])).
% 292.21/184.70 tff(15652,plain,
% 292.21/184.70 (node20(c_e_h_1, c_c, s2)),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[14216, 15651])).
% 292.21/184.70 tff(15653,plain,
% 292.21/184.70 (m_and_h_gate_v_in1(c_e_h_1, c_c, s2)),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[14224, 15652])).
% 292.21/184.70 tff(15654,plain,
% 292.21/184.70 (m_mutex_h_half_v_out(c_e_h_1, c_a, s2)),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[14232, 15653])).
% 292.21/184.70 tff(15655,plain,
% 292.21/184.70 (m_mutex_h_half_v_out(c_e_h_1, c_a, s3)),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[14381, 15654])).
% 292.21/184.70 tff(15656,plain,
% 292.21/184.70 (m_mutex_h_half_v_out(c_e_h_1, c_a, s4)),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[14793, 15655, 15649])).
% 292.21/184.70 tff(15657,plain,
% 292.21/184.70 (m_and_h_gate_v_in1(c_e_h_1, c_c, s4)),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[14810, 15656])).
% 292.21/184.70 tff(15658,plain,
% 292.21/184.70 (m_and_h_gate_v_out(c_e_h_1, c_c, s5)),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[14843, 15657, 15630])).
% 292.21/184.70 tff(15659,plain,
% 292.21/184.70 ($false),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[15570, 5896, 15658, 15629])).
% 292.21/184.70 tff(15660,plain,((~m_and_h_gate_v_out(c_e_h_1, c_k, s7)) | m_or_h_gate_v_out(c_e_h_1, c_g, s6)), inference(lemma,lemma(discharge,[]))).
% 292.21/184.70 tff(15661,plain,
% 292.21/184.70 (~m_and_h_gate_v_out(c_e_h_1, c_k, s7)),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[15660, 15388])).
% 292.21/184.70 tff(15662,assumption,(m_and_h_gate_v_out(c_e_h_1, c_p, s8)), introduced(assumption)).
% 292.21/184.70 tff(15663,plain,
% 292.21/184.70 (m_and_h_gate_v_out(c_e_h_1, c_c, s4)),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[14414, 14126])).
% 292.21/184.70 tff(15664,plain,
% 292.21/184.70 (m_mutex_h_half_v_out(c_e_h_1, c_a, s5)),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[15023, 15663])).
% 292.21/184.70 tff(15665,plain,
% 292.21/184.70 (m_and_h_gate_v_in1(c_e_h_1, c_c, s5)),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[15073, 15664])).
% 292.21/184.70 tff(15666,plain,
% 292.21/184.70 (~node21(c_e_h_1, c_c, s5, s6)),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[15368, 15665, 13629])).
% 292.21/184.70 tff(15667,plain,
% 292.21/184.70 (node22(c_e_h_1, c_c, s5, s6)),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[15383, 15666])).
% 292.21/184.70 tff(15668,plain,
% 292.21/184.70 (~m_and_h_gate_v_out(c_e_h_1, c_c, s5)),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[15378, 15667, 13629])).
% 292.21/184.70 tff(15669,plain,
% 292.21/184.70 (~m_and_h_gate_v_in1(c_e_h_1, c_c, s4)),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[14843, 15668, 15663])).
% 292.21/184.70 tff(15670,plain,
% 292.21/184.70 (m_user_v_req(c_e_h_1, c_u, s2)),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[14671, 15663])).
% 292.21/184.70 tff(15671,plain,
% 292.21/184.70 (m_user_v_req(c_e_h_1, c_u, s3)),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[14760, 15670])).
% 292.21/184.70 tff(15672,plain,
% 292.21/184.70 (m_mutex_h_half_v_inp(c_e_h_1, c_a, s3)),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[14768, 15671])).
% 292.21/184.70 tff(15673,plain,
% 292.21/184.70 (m_mutex_h_half_v_out(c_e_h_1, c_a, s4)),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[14793, 15672, 14382])).
% 292.21/184.70 tff(15674,plain,
% 292.21/184.70 ($false),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[14808, 2556, 15673, 15669])).
% 292.21/184.70 tff(15675,plain,((~m_and_h_gate_v_out(c_e_h_1, c_c, s3)) | m_and_h_gate_v_out(c_e_h_1, c_c, s6)), inference(lemma,lemma(discharge,[]))).
% 292.21/184.70 tff(15676,plain,
% 292.21/184.70 (~m_and_h_gate_v_out(c_e_h_1, c_c, s3)),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[15675, 13629])).
% 292.21/184.70 tff(15677,plain,
% 292.21/184.70 (~m_or_h_gate_v_in1(c_e_h_1, c_g, s3)),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[14418, 2708, 15676])).
% 292.21/184.70 tff(15678,plain,
% 292.21/184.70 (~m_or_h_gate_v_out(c_e_h_1, c_g, s4)),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[14503, 15677])).
% 292.21/184.70 tff(15679,plain,
% 292.21/184.70 (~m_and_h_gate_v_in1(c_e_h_1, c_k, s4)),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[15435, 15678])).
% 292.21/184.70 tff(15680,plain,
% 292.21/184.70 (~node20(c_e_h_1, c_k, s4)),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[15443, 15679])).
% 292.21/184.70 tff(15681,plain,
% 292.21/184.70 (~m_and_h_gate_v_out(c_e_h_1, c_k, s5)),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[15500, 15680])).
% 292.21/184.70 tff(15682,assumption,(m_and_h_gate_v_in1(c_e_h_1, c_p, s5)), introduced(assumption)).
% 292.21/184.70 tff(15683,plain,
% 292.21/184.70 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_p, s5)) | m_and_h_gate_v_out(c_e_h_1, c_k, s5))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s5)) | m_and_h_gate_v_out(c_e_h_1, c_k, s5))),
% 292.21/184.70 inference(rewrite,[status(thm)],[])).
% 292.21/184.70 tff(15684,plain,
% 292.21/184.70 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_p, s5)) | m_and_h_gate_v_out(c_e_h_1, c_k, s5))),
% 292.21/184.70 inference(quant_inst,[status(thm)],[])).
% 292.21/184.70 tff(15685,plain,
% 292.21/184.70 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s5)) | m_and_h_gate_v_out(c_e_h_1, c_k, s5)),
% 292.21/184.70 inference(modus_ponens,[status(thm)],[15684, 15683])).
% 292.21/184.70 tff(15686,plain,
% 292.21/184.70 ($false),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[15685, 3033, 15502, 15682])).
% 292.21/184.70 tff(15687,plain,((~m_and_h_gate_v_in1(c_e_h_1, c_p, s5)) | m_and_h_gate_v_out(c_e_h_1, c_k, s5)), inference(lemma,lemma(discharge,[]))).
% 292.21/184.70 tff(15688,plain,
% 292.21/184.70 (~m_and_h_gate_v_in1(c_e_h_1, c_p, s5)),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[15687, 15681])).
% 292.21/184.70 tff(15689,assumption,(~m_and_h_gate_v_in1(c_e_h_1, c_p, s5)), introduced(assumption)).
% 292.21/184.70 tff(15690,assumption,(node20(c_e_h_1, c_p, s5)), introduced(assumption)).
% 292.21/184.70 tff(15691,plain,
% 292.21/184.70 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_p, s5)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_p, s5)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s5))),
% 292.21/184.70 inference(rewrite,[status(thm)],[])).
% 292.21/184.70 tff(15692,plain,
% 292.21/184.70 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_p, s5)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s5))),
% 292.21/184.70 inference(quant_inst,[status(thm)],[])).
% 292.21/184.70 tff(15693,plain,
% 292.21/184.70 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_p, s5)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s5)),
% 292.21/184.70 inference(modus_ponens,[status(thm)],[15692, 15691])).
% 292.21/184.70 tff(15694,plain,
% 292.21/184.70 ($false),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[15693, 38, 15690, 15689])).
% 292.21/184.70 tff(15695,plain,((~node20(c_e_h_1, c_p, s5)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s5)), inference(lemma,lemma(discharge,[]))).
% 292.21/184.70 tff(15696,plain,
% 292.21/184.70 (~node20(c_e_h_1, c_p, s5)),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[15695, 15688])).
% 292.21/184.70 tff(15697,assumption,(m_and_h_gate_v_in1(c_e_h_1, c_p, s4)), introduced(assumption)).
% 292.21/184.70 tff(15698,plain,
% 292.21/184.70 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_p, s4)) | m_and_h_gate_v_out(c_e_h_1, c_k, s4))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s4)) | m_and_h_gate_v_out(c_e_h_1, c_k, s4))),
% 292.21/184.70 inference(rewrite,[status(thm)],[])).
% 292.21/184.70 tff(15699,plain,
% 292.21/184.70 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_p, s4)) | m_and_h_gate_v_out(c_e_h_1, c_k, s4))),
% 292.21/184.70 inference(quant_inst,[status(thm)],[])).
% 292.21/184.70 tff(15700,plain,
% 292.21/184.70 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s4)) | m_and_h_gate_v_out(c_e_h_1, c_k, s4)),
% 292.21/184.70 inference(modus_ponens,[status(thm)],[15699, 15698])).
% 292.21/184.70 tff(15701,plain,
% 292.21/184.70 ($false),
% 292.21/184.70 inference(unit_resolution,[status(thm)],[15700, 3033, 15477, 15697])).
% 292.21/184.70 tff(15702,plain,(~m_and_h_gate_v_in1(c_e_h_1, c_p, s4)), inference(lemma,lemma(discharge,[]))).
% 292.21/184.71 tff(15703,plain,
% 292.21/184.71 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_p, s4)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_p, s4)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s4))),
% 292.21/184.71 inference(rewrite,[status(thm)],[])).
% 292.21/184.71 tff(15704,plain,
% 292.21/184.71 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_p, s4)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s4))),
% 292.21/184.71 inference(quant_inst,[status(thm)],[])).
% 292.21/184.71 tff(15705,plain,
% 292.21/184.71 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_p, s4)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s4)),
% 292.21/184.71 inference(modus_ponens,[status(thm)],[15704, 15703])).
% 292.21/184.71 tff(15706,plain,
% 292.21/184.71 (~node20(c_e_h_1, c_p, s4)),
% 292.21/184.71 inference(unit_resolution,[status(thm)],[15705, 38, 15702])).
% 292.21/184.71 tff(15707,assumption,(m_and_h_gate_v_in1(c_e_h_1, c_p, s3)), introduced(assumption)).
% 292.21/184.71 tff(15708,plain,
% 292.21/184.71 ($false),
% 292.21/184.71 inference(unit_resolution,[status(thm)],[9885, 3033, 9879, 15707])).
% 292.21/184.71 tff(15709,plain,(~m_and_h_gate_v_in1(c_e_h_1, c_p, s3)), inference(lemma,lemma(discharge,[]))).
% 292.21/184.71 tff(15710,plain,
% 292.21/184.71 (~node20(c_e_h_1, c_p, s3)),
% 292.21/184.71 inference(unit_resolution,[status(thm)],[9889, 38, 15709])).
% 292.21/184.71 tff(15711,plain,
% 292.21/184.71 (~node22(c_e_h_1, c_p, s3, s4)),
% 292.21/184.71 inference(unit_resolution,[status(thm)],[9936, 9930, 9647])).
% 292.21/184.71 tff(15712,assumption,(node21(c_e_h_1, c_p, s3, s4)), introduced(assumption)).
% 292.21/184.71 tff(15713,plain,
% 292.21/184.71 ($false),
% 292.21/184.71 inference(unit_resolution,[status(thm)],[9948, 52, 15712, 9930, 9929])).
% 292.21/184.71 tff(15714,plain,((~node21(c_e_h_1, c_p, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s4)) | node20(c_e_h_1, c_p, s3)), inference(lemma,lemma(discharge,[]))).
% 292.21/184.71 tff(15715,plain,
% 292.21/184.71 (~node21(c_e_h_1, c_p, s3, s4)),
% 292.21/184.71 inference(unit_resolution,[status(thm)],[15714, 9930, 9929])).
% 292.21/184.71 tff(15716,plain,
% 292.21/184.71 ($false),
% 292.21/184.71 inference(unit_resolution,[status(thm)],[9941, 15715, 15711])).
% 292.21/184.71 tff(15717,plain,((~m_and_h_gate_v_out(c_e_h_1, c_p, s4)) | node20(c_e_h_1, c_p, s3) | m_and_h_gate_v_out(c_e_h_1, c_p, s3)), inference(lemma,lemma(discharge,[]))).
% 292.21/184.71 tff(15718,plain,
% 292.21/184.71 ((~m_and_h_gate_v_out(c_e_h_1, c_p, s4)) | m_and_h_gate_v_out(c_e_h_1, c_p, s3)),
% 292.21/184.71 inference(unit_resolution,[status(thm)],[15717, 15710])).
% 292.21/184.71 tff(15719,plain,
% 292.21/184.71 (~m_and_h_gate_v_out(c_e_h_1, c_p, s4)),
% 292.21/184.71 inference(unit_resolution,[status(thm)],[15718, 9646])).
% 292.21/184.71 tff(15720,assumption,(~node20(c_e_h_1, c_p, s4)), introduced(assumption)).
% 292.21/184.71 tff(15721,assumption,(m_and_h_gate_v_out(c_e_h_1, c_p, s5)), introduced(assumption)).
% 292.21/184.71 tff(15722,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_p, s4)), introduced(assumption)).
% 292.21/184.71 tff(15723,assumption,(node22(c_e_h_1, c_p, s4, s5)), introduced(assumption)).
% 292.21/184.71 tff(15724,plain,
% 292.21/184.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_p, s5)) | (~node22(c_e_h_1, c_p, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_p, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s5)) | (~node22(c_e_h_1, c_p, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_p, s4))),
% 292.21/184.71 inference(rewrite,[status(thm)],[])).
% 292.21/184.71 tff(15725,plain,
% 292.21/184.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_p, s5)) | (~node22(c_e_h_1, c_p, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_p, s4))),
% 292.21/184.71 inference(quant_inst,[status(thm)],[])).
% 292.21/184.71 tff(15726,plain,
% 292.21/184.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s5)) | (~node22(c_e_h_1, c_p, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_p, s4)),
% 292.21/184.71 inference(modus_ponens,[status(thm)],[15725, 15724])).
% 292.21/184.71 tff(15727,plain,
% 292.21/184.71 ($false),
% 292.21/184.71 inference(unit_resolution,[status(thm)],[15726, 108, 15723, 15722, 15721])).
% 292.21/184.71 tff(15728,plain,((~node22(c_e_h_1, c_p, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_p, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s5))), inference(lemma,lemma(discharge,[]))).
% 292.21/184.71 tff(15729,plain,
% 292.21/184.71 (~node22(c_e_h_1, c_p, s4, s5)),
% 292.21/184.71 inference(unit_resolution,[status(thm)],[15728, 15721, 15722])).
% 292.21/184.71 tff(15730,plain,
% 292.21/184.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_1, c_p, s4, s5) | node22(c_e_h_1, c_p, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_1, c_p, s4, s5) | node22(c_e_h_1, c_p, s4, s5))),
% 292.21/184.71 inference(rewrite,[status(thm)],[])).
% 292.21/184.71 tff(15731,plain,
% 292.21/184.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_1, c_p, s4, s5) | node22(c_e_h_1, c_p, s4, s5))),
% 292.21/184.71 inference(quant_inst,[status(thm)],[])).
% 292.21/184.71 tff(15732,plain,
% 292.21/184.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_1, c_p, s4, s5) | node22(c_e_h_1, c_p, s4, s5)),
% 292.21/184.71 inference(modus_ponens,[status(thm)],[15731, 15730])).
% 292.21/184.71 tff(15733,plain,
% 292.21/184.71 (node21(c_e_h_1, c_p, s4, s5) | node22(c_e_h_1, c_p, s4, s5)),
% 292.21/184.71 inference(unit_resolution,[status(thm)],[15732, 82, 1028])).
% 292.21/184.71 tff(15734,plain,
% 292.21/184.71 (node21(c_e_h_1, c_p, s4, s5)),
% 292.21/184.71 inference(unit_resolution,[status(thm)],[15733, 15729])).
% 292.21/184.71 tff(15735,plain,
% 292.21/184.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~node21(c_e_h_1, c_p, s4, s5)) | node20(c_e_h_1, c_p, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~node21(c_e_h_1, c_p, s4, s5)) | node20(c_e_h_1, c_p, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s5)))),
% 292.21/184.71 inference(rewrite,[status(thm)],[])).
% 292.21/184.71 tff(15736,plain,
% 292.21/184.71 ((node20(c_e_h_1, c_p, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s5)) | (~node21(c_e_h_1, c_p, s4, s5))) <=> ((~node21(c_e_h_1, c_p, s4, s5)) | node20(c_e_h_1, c_p, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s5)))),
% 292.21/184.71 inference(rewrite,[status(thm)],[])).
% 292.21/184.71 tff(15737,plain,
% 292.21/184.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_p, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s5)) | (~node21(c_e_h_1, c_p, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~node21(c_e_h_1, c_p, s4, s5)) | node20(c_e_h_1, c_p, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s5))))),
% 292.21/184.71 inference(monotonicity,[status(thm)],[15736])).
% 292.21/184.71 tff(15738,plain,
% 292.21/184.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_p, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s5)) | (~node21(c_e_h_1, c_p, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~node21(c_e_h_1, c_p, s4, s5)) | node20(c_e_h_1, c_p, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s5)))),
% 292.21/184.71 inference(transitivity,[status(thm)],[15737, 15735])).
% 292.21/184.71 tff(15739,plain,
% 292.21/184.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_p, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s5)) | (~node21(c_e_h_1, c_p, s4, s5)))),
% 292.21/184.71 inference(quant_inst,[status(thm)],[])).
% 292.21/184.71 tff(15740,plain,
% 292.21/184.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~node21(c_e_h_1, c_p, s4, s5)) | node20(c_e_h_1, c_p, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s5))),
% 292.21/184.71 inference(modus_ponens,[status(thm)],[15739, 15738])).
% 292.21/184.71 tff(15741,plain,
% 292.21/184.71 ($false),
% 292.21/184.71 inference(unit_resolution,[status(thm)],[15740, 52, 15734, 15721, 15720])).
% 292.21/184.71 tff(15742,plain,((~m_and_h_gate_v_out(c_e_h_1, c_p, s5)) | node20(c_e_h_1, c_p, s4) | m_and_h_gate_v_out(c_e_h_1, c_p, s4)), inference(lemma,lemma(discharge,[]))).
% 292.21/184.71 tff(15743,plain,
% 292.21/184.71 ((~m_and_h_gate_v_out(c_e_h_1, c_p, s5)) | node20(c_e_h_1, c_p, s4)),
% 292.21/184.71 inference(unit_resolution,[status(thm)],[15742, 15719])).
% 292.21/184.71 tff(15744,plain,
% 292.21/184.71 (~m_and_h_gate_v_out(c_e_h_1, c_p, s5)),
% 292.21/184.71 inference(unit_resolution,[status(thm)],[15743, 15706])).
% 292.21/184.71 tff(15745,assumption,(m_and_h_gate_v_out(c_e_h_1, c_p, s6)), introduced(assumption)).
% 292.21/184.71 tff(15746,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_p, s5)), introduced(assumption)).
% 292.21/184.71 tff(15747,assumption,(~node20(c_e_h_1, c_p, s5)), introduced(assumption)).
% 292.21/184.71 tff(15748,assumption,(node21(c_e_h_1, c_p, s5, s6)), introduced(assumption)).
% 292.21/184.71 tff(15749,plain,
% 292.21/184.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_p, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s6)) | (~node21(c_e_h_1, c_p, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_p, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s6)) | (~node21(c_e_h_1, c_p, s5, s6)))),
% 292.21/184.71 inference(rewrite,[status(thm)],[])).
% 292.21/184.71 tff(15750,plain,
% 292.21/184.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_p, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s6)) | (~node21(c_e_h_1, c_p, s5, s6)))),
% 292.21/184.71 inference(quant_inst,[status(thm)],[])).
% 292.21/184.71 tff(15751,plain,
% 292.21/184.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_p, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s6)) | (~node21(c_e_h_1, c_p, s5, s6))),
% 292.21/184.71 inference(modus_ponens,[status(thm)],[15750, 15749])).
% 292.21/184.71 tff(15752,plain,
% 292.21/184.71 ($false),
% 292.21/184.71 inference(unit_resolution,[status(thm)],[15751, 52, 15748, 15745, 15747])).
% 292.21/184.71 tff(15753,plain,((~node21(c_e_h_1, c_p, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s6)) | node20(c_e_h_1, c_p, s5)), inference(lemma,lemma(discharge,[]))).
% 292.21/184.71 tff(15754,plain,
% 292.21/184.71 (~node21(c_e_h_1, c_p, s5, s6)),
% 292.21/184.71 inference(unit_resolution,[status(thm)],[15753, 15745, 15747])).
% 292.21/184.71 tff(15755,plain,
% 292.21/184.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_1, c_p, s5, s6) | node22(c_e_h_1, c_p, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_1, c_p, s5, s6) | node22(c_e_h_1, c_p, s5, s6))),
% 292.21/184.71 inference(rewrite,[status(thm)],[])).
% 292.21/184.71 tff(15756,plain,
% 292.21/184.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_1, c_p, s5, s6) | node22(c_e_h_1, c_p, s5, s6))),
% 292.21/184.71 inference(quant_inst,[status(thm)],[])).
% 292.21/184.71 tff(15757,plain,
% 292.21/184.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_1, c_p, s5, s6) | node22(c_e_h_1, c_p, s5, s6)),
% 292.21/184.71 inference(modus_ponens,[status(thm)],[15756, 15755])).
% 292.21/184.71 tff(15758,plain,
% 292.21/184.71 (node21(c_e_h_1, c_p, s5, s6) | node22(c_e_h_1, c_p, s5, s6)),
% 292.21/184.71 inference(unit_resolution,[status(thm)],[15757, 82, 1406])).
% 292.21/184.71 tff(15759,plain,
% 292.21/184.71 (node22(c_e_h_1, c_p, s5, s6)),
% 292.21/184.71 inference(unit_resolution,[status(thm)],[15758, 15754])).
% 292.21/184.71 tff(15760,plain,
% 292.21/184.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_p, s6)) | (~node22(c_e_h_1, c_p, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_p, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s6)) | (~node22(c_e_h_1, c_p, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_p, s5))),
% 292.21/184.71 inference(rewrite,[status(thm)],[])).
% 292.21/184.72 tff(15761,plain,
% 292.21/184.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_p, s6)) | (~node22(c_e_h_1, c_p, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_p, s5))),
% 292.21/184.72 inference(quant_inst,[status(thm)],[])).
% 292.21/184.72 tff(15762,plain,
% 292.21/184.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s6)) | (~node22(c_e_h_1, c_p, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_p, s5)),
% 292.21/184.72 inference(modus_ponens,[status(thm)],[15761, 15760])).
% 292.21/184.72 tff(15763,plain,
% 292.21/184.72 ($false),
% 292.21/184.72 inference(unit_resolution,[status(thm)],[15762, 108, 15759, 15746, 15745])).
% 292.21/184.72 tff(15764,plain,((~m_and_h_gate_v_out(c_e_h_1, c_p, s6)) | m_and_h_gate_v_out(c_e_h_1, c_p, s5) | node20(c_e_h_1, c_p, s5)), inference(lemma,lemma(discharge,[]))).
% 292.21/184.72 tff(15765,plain,
% 292.21/184.72 ((~m_and_h_gate_v_out(c_e_h_1, c_p, s6)) | node20(c_e_h_1, c_p, s5)),
% 292.21/184.72 inference(unit_resolution,[status(thm)],[15764, 15744])).
% 292.21/184.72 tff(15766,plain,
% 292.21/184.72 (~m_and_h_gate_v_out(c_e_h_1, c_p, s6)),
% 292.21/184.72 inference(unit_resolution,[status(thm)],[15765, 15696])).
% 292.21/184.72 tff(15767,plain,
% 292.21/184.72 (~m_and_h_gate_v_in1(c_e_h_1, c_k, s5)),
% 292.21/184.72 inference(unit_resolution,[status(thm)],[15538, 14543])).
% 292.21/184.72 tff(15768,plain,
% 292.21/184.72 (~node20(c_e_h_1, c_k, s5)),
% 292.21/184.72 inference(unit_resolution,[status(thm)],[15531, 15767])).
% 292.21/184.72 tff(15769,plain,
% 292.21/184.72 (~m_and_h_gate_v_out(c_e_h_1, c_k, s6)),
% 292.21/184.72 inference(unit_resolution,[status(thm)],[15523, 15768, 15681])).
% 292.21/184.72 tff(15770,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_p, s6)), introduced(assumption)).
% 292.21/184.72 tff(15771,plain,
% 292.21/184.72 (~m_and_h_gate_v_out(c_e_h_1, c_k, s7)),
% 292.21/184.72 inference(unit_resolution,[status(thm)],[15427, 15407, 15406])).
% 292.21/184.72 tff(15772,plain,
% 292.21/184.72 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_p, s7)) | m_and_h_gate_v_out(c_e_h_1, c_k, s7))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s7)) | m_and_h_gate_v_out(c_e_h_1, c_k, s7))),
% 292.21/184.72 inference(rewrite,[status(thm)],[])).
% 292.21/184.72 tff(15773,plain,
% 292.21/184.72 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_p, s7)) | m_and_h_gate_v_out(c_e_h_1, c_k, s7))),
% 292.21/184.72 inference(quant_inst,[status(thm)],[])).
% 292.21/184.72 tff(15774,plain,
% 292.21/184.72 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s7)) | m_and_h_gate_v_out(c_e_h_1, c_k, s7)),
% 292.21/184.72 inference(modus_ponens,[status(thm)],[15773, 15772])).
% 292.21/184.72 tff(15775,plain,
% 292.21/184.72 (~m_and_h_gate_v_in1(c_e_h_1, c_p, s7)),
% 292.21/184.72 inference(unit_resolution,[status(thm)],[15774, 3033, 15771])).
% 292.21/184.72 tff(15776,plain,
% 292.21/184.72 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_p, s7)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_p, s7)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s7))),
% 292.21/184.72 inference(rewrite,[status(thm)],[])).
% 292.21/184.72 tff(15777,plain,
% 292.21/184.72 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_p, s7)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s7))),
% 292.21/184.72 inference(quant_inst,[status(thm)],[])).
% 292.21/184.72 tff(15778,plain,
% 292.21/184.72 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_p, s7)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s7)),
% 292.21/184.72 inference(modus_ponens,[status(thm)],[15777, 15776])).
% 292.21/184.72 tff(15779,plain,
% 292.21/184.72 (~node20(c_e_h_1, c_p, s7)),
% 292.21/184.72 inference(unit_resolution,[status(thm)],[15778, 38, 15775])).
% 292.21/184.72 tff(15780,assumption,(~node20(c_e_h_1, c_p, s7)), introduced(assumption)).
% 292.21/184.72 tff(15781,assumption,(node21(c_e_h_1, c_p, s7, s8)), introduced(assumption)).
% 292.21/184.72 tff(15782,plain,
% 292.21/184.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_p, s8)) | node20(c_e_h_1, c_p, s7) | (~node21(c_e_h_1, c_p, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s8)) | node20(c_e_h_1, c_p, s7) | (~node21(c_e_h_1, c_p, s7, s8)))),
% 292.21/184.72 inference(rewrite,[status(thm)],[])).
% 292.21/184.72 tff(15783,plain,
% 292.21/184.72 ((node20(c_e_h_1, c_p, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s8)) | (~node21(c_e_h_1, c_p, s7, s8))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_p, s8)) | node20(c_e_h_1, c_p, s7) | (~node21(c_e_h_1, c_p, s7, s8)))),
% 292.21/184.72 inference(rewrite,[status(thm)],[])).
% 292.21/184.72 tff(15784,plain,
% 292.21/184.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_p, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s8)) | (~node21(c_e_h_1, c_p, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_p, s8)) | node20(c_e_h_1, c_p, s7) | (~node21(c_e_h_1, c_p, s7, s8))))),
% 292.21/184.72 inference(monotonicity,[status(thm)],[15783])).
% 292.21/184.72 tff(15785,plain,
% 292.21/184.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_p, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s8)) | (~node21(c_e_h_1, c_p, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s8)) | node20(c_e_h_1, c_p, s7) | (~node21(c_e_h_1, c_p, s7, s8)))),
% 292.21/184.72 inference(transitivity,[status(thm)],[15784, 15782])).
% 292.21/184.72 tff(15786,plain,
% 292.21/184.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_p, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s8)) | (~node21(c_e_h_1, c_p, s7, s8)))),
% 292.21/184.72 inference(quant_inst,[status(thm)],[])).
% 292.21/184.72 tff(15787,plain,
% 292.21/184.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s8)) | node20(c_e_h_1, c_p, s7) | (~node21(c_e_h_1, c_p, s7, s8))),
% 292.21/184.72 inference(modus_ponens,[status(thm)],[15786, 15785])).
% 292.21/184.72 tff(15788,plain,
% 292.21/184.72 ($false),
% 292.21/184.72 inference(unit_resolution,[status(thm)],[15787, 52, 15781, 15662, 15780])).
% 292.21/184.72 tff(15789,plain,((~node21(c_e_h_1, c_p, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s8)) | node20(c_e_h_1, c_p, s7)), inference(lemma,lemma(discharge,[]))).
% 292.21/184.72 tff(15790,plain,
% 292.21/184.72 (~node21(c_e_h_1, c_p, s7, s8)),
% 292.21/184.72 inference(unit_resolution,[status(thm)],[15789, 15779, 15662])).
% 292.21/184.72 tff(15791,plain,
% 292.21/184.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_1, c_p, s7, s8) | node22(c_e_h_1, c_p, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_1, c_p, s7, s8) | node22(c_e_h_1, c_p, s7, s8))),
% 292.21/184.72 inference(rewrite,[status(thm)],[])).
% 292.21/184.72 tff(15792,plain,
% 292.21/184.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_1, c_p, s7, s8) | node22(c_e_h_1, c_p, s7, s8))),
% 292.21/184.72 inference(quant_inst,[status(thm)],[])).
% 292.21/184.72 tff(15793,plain,
% 292.21/184.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_1, c_p, s7, s8) | node22(c_e_h_1, c_p, s7, s8)),
% 292.21/184.72 inference(modus_ponens,[status(thm)],[15792, 15791])).
% 292.21/184.72 tff(15794,plain,
% 292.21/184.72 (node21(c_e_h_1, c_p, s7, s8) | node22(c_e_h_1, c_p, s7, s8)),
% 292.21/184.72 inference(unit_resolution,[status(thm)],[15793, 82, 1938])).
% 292.21/184.72 tff(15795,plain,
% 292.21/184.72 (node22(c_e_h_1, c_p, s7, s8)),
% 292.21/184.72 inference(unit_resolution,[status(thm)],[15794, 15790])).
% 292.21/184.72 tff(15796,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_p, s7)), introduced(assumption)).
% 292.21/184.72 tff(15797,assumption,(node22(c_e_h_1, c_p, s7, s8)), introduced(assumption)).
% 292.21/184.72 tff(15798,plain,
% 292.21/184.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_p, s8)) | (~node22(c_e_h_1, c_p, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_p, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s8)) | (~node22(c_e_h_1, c_p, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_p, s7))),
% 292.21/184.72 inference(rewrite,[status(thm)],[])).
% 292.21/184.72 tff(15799,plain,
% 292.21/184.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_p, s8)) | (~node22(c_e_h_1, c_p, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_p, s7))),
% 292.21/184.72 inference(quant_inst,[status(thm)],[])).
% 292.21/184.72 tff(15800,plain,
% 292.21/184.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s8)) | (~node22(c_e_h_1, c_p, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_p, s7)),
% 292.21/184.72 inference(modus_ponens,[status(thm)],[15799, 15798])).
% 292.21/184.72 tff(15801,plain,
% 292.21/184.72 ($false),
% 292.21/184.72 inference(unit_resolution,[status(thm)],[15800, 108, 15797, 15796, 15662])).
% 292.21/184.72 tff(15802,plain,((~node22(c_e_h_1, c_p, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_p, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s8))), inference(lemma,lemma(discharge,[]))).
% 292.21/184.72 tff(15803,plain,
% 292.21/184.72 (m_and_h_gate_v_out(c_e_h_1, c_p, s7)),
% 292.21/184.72 inference(unit_resolution,[status(thm)],[15802, 15795, 15662])).
% 292.21/184.72 tff(15804,assumption,(~node20(c_e_h_1, c_p, s6)), introduced(assumption)).
% 292.21/184.72 tff(15805,assumption,(m_and_h_gate_v_out(c_e_h_1, c_p, s7)), introduced(assumption)).
% 292.21/184.72 tff(15806,assumption,(node22(c_e_h_1, c_p, s6, s7)), introduced(assumption)).
% 292.21/184.72 tff(15807,plain,
% 292.21/184.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_p, s7)) | (~node22(c_e_h_1, c_p, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_p, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s7)) | (~node22(c_e_h_1, c_p, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_p, s6))),
% 292.21/184.72 inference(rewrite,[status(thm)],[])).
% 292.21/184.72 tff(15808,plain,
% 292.21/184.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_p, s7)) | (~node22(c_e_h_1, c_p, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_p, s6))),
% 292.21/184.72 inference(quant_inst,[status(thm)],[])).
% 292.21/184.72 tff(15809,plain,
% 292.21/184.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s7)) | (~node22(c_e_h_1, c_p, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_p, s6)),
% 292.21/184.72 inference(modus_ponens,[status(thm)],[15808, 15807])).
% 292.21/184.72 tff(15810,plain,
% 292.21/184.72 ($false),
% 292.21/184.72 inference(unit_resolution,[status(thm)],[15809, 108, 15806, 15770, 15805])).
% 292.21/184.72 tff(15811,plain,((~node22(c_e_h_1, c_p, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_p, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s7))), inference(lemma,lemma(discharge,[]))).
% 292.21/184.72 tff(15812,plain,
% 292.21/184.72 (~node22(c_e_h_1, c_p, s6, s7)),
% 292.21/184.72 inference(unit_resolution,[status(thm)],[15811, 15805, 15770])).
% 292.21/184.72 tff(15813,plain,
% 292.21/184.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_1, c_p, s6, s7) | node22(c_e_h_1, c_p, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_1, c_p, s6, s7) | node22(c_e_h_1, c_p, s6, s7))),
% 292.21/184.72 inference(rewrite,[status(thm)],[])).
% 292.21/184.72 tff(15814,plain,
% 292.21/184.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_1, c_p, s6, s7) | node22(c_e_h_1, c_p, s6, s7))),
% 292.21/184.73 inference(quant_inst,[status(thm)],[])).
% 292.21/184.73 tff(15815,plain,
% 292.21/184.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_1, c_p, s6, s7) | node22(c_e_h_1, c_p, s6, s7)),
% 292.21/184.73 inference(modus_ponens,[status(thm)],[15814, 15813])).
% 292.21/184.73 tff(15816,plain,
% 292.21/184.73 (node21(c_e_h_1, c_p, s6, s7) | node22(c_e_h_1, c_p, s6, s7)),
% 292.21/184.73 inference(unit_resolution,[status(thm)],[15815, 82, 1844])).
% 292.21/184.73 tff(15817,plain,
% 292.21/184.73 (node21(c_e_h_1, c_p, s6, s7)),
% 292.21/184.73 inference(unit_resolution,[status(thm)],[15816, 15812])).
% 292.21/184.73 tff(15818,plain,
% 292.21/184.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_p, s7)) | node20(c_e_h_1, c_p, s6) | (~node21(c_e_h_1, c_p, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s7)) | node20(c_e_h_1, c_p, s6) | (~node21(c_e_h_1, c_p, s6, s7)))),
% 292.21/184.73 inference(rewrite,[status(thm)],[])).
% 292.21/184.73 tff(15819,plain,
% 292.21/184.73 ((node20(c_e_h_1, c_p, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s7)) | (~node21(c_e_h_1, c_p, s6, s7))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_p, s7)) | node20(c_e_h_1, c_p, s6) | (~node21(c_e_h_1, c_p, s6, s7)))),
% 292.21/184.73 inference(rewrite,[status(thm)],[])).
% 292.21/184.73 tff(15820,plain,
% 292.21/184.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_p, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s7)) | (~node21(c_e_h_1, c_p, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_p, s7)) | node20(c_e_h_1, c_p, s6) | (~node21(c_e_h_1, c_p, s6, s7))))),
% 292.21/184.73 inference(monotonicity,[status(thm)],[15819])).
% 292.21/184.73 tff(15821,plain,
% 292.21/184.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_p, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s7)) | (~node21(c_e_h_1, c_p, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s7)) | node20(c_e_h_1, c_p, s6) | (~node21(c_e_h_1, c_p, s6, s7)))),
% 292.21/184.73 inference(transitivity,[status(thm)],[15820, 15818])).
% 292.21/184.73 tff(15822,plain,
% 292.21/184.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_p, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s7)) | (~node21(c_e_h_1, c_p, s6, s7)))),
% 292.21/184.73 inference(quant_inst,[status(thm)],[])).
% 292.21/184.73 tff(15823,plain,
% 292.21/184.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s7)) | node20(c_e_h_1, c_p, s6) | (~node21(c_e_h_1, c_p, s6, s7))),
% 292.21/184.73 inference(modus_ponens,[status(thm)],[15822, 15821])).
% 292.21/184.73 tff(15824,plain,
% 292.21/184.73 ($false),
% 292.21/184.73 inference(unit_resolution,[status(thm)],[15823, 52, 15817, 15805, 15804])).
% 292.21/184.73 tff(15825,plain,((~m_and_h_gate_v_out(c_e_h_1, c_p, s7)) | node20(c_e_h_1, c_p, s6) | m_and_h_gate_v_out(c_e_h_1, c_p, s6)), inference(lemma,lemma(discharge,[]))).
% 292.21/184.73 tff(15826,plain,
% 292.21/184.73 (node20(c_e_h_1, c_p, s6)),
% 292.21/184.73 inference(unit_resolution,[status(thm)],[15825, 15803, 15770])).
% 292.21/184.73 tff(15827,plain,
% 292.21/184.73 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_p, s6)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_p, s6)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s6))),
% 292.21/184.73 inference(rewrite,[status(thm)],[])).
% 292.21/184.73 tff(15828,plain,
% 292.21/184.73 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_p, s6)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s6))),
% 292.21/184.73 inference(quant_inst,[status(thm)],[])).
% 292.21/184.73 tff(15829,plain,
% 292.21/184.73 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_p, s6)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s6)),
% 292.21/184.73 inference(modus_ponens,[status(thm)],[15828, 15827])).
% 292.21/184.73 tff(15830,plain,
% 292.21/184.73 (m_and_h_gate_v_in1(c_e_h_1, c_p, s6)),
% 292.21/184.73 inference(unit_resolution,[status(thm)],[15829, 38, 15826])).
% 292.21/184.73 tff(15831,plain,
% 292.21/184.73 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_p, s6)) | m_and_h_gate_v_out(c_e_h_1, c_k, s6))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s6)) | m_and_h_gate_v_out(c_e_h_1, c_k, s6))),
% 292.21/184.73 inference(rewrite,[status(thm)],[])).
% 292.21/184.73 tff(15832,plain,
% 292.21/184.73 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_p, s6)) | m_and_h_gate_v_out(c_e_h_1, c_k, s6))),
% 292.21/184.73 inference(quant_inst,[status(thm)],[])).
% 292.21/184.73 tff(15833,plain,
% 292.21/184.73 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s6)) | m_and_h_gate_v_out(c_e_h_1, c_k, s6)),
% 292.21/184.73 inference(modus_ponens,[status(thm)],[15832, 15831])).
% 292.21/184.73 tff(15834,plain,
% 292.21/184.73 ($false),
% 292.21/184.73 inference(unit_resolution,[status(thm)],[15833, 3033, 15407, 15830])).
% 292.21/184.73 tff(15835,plain,(m_and_h_gate_v_out(c_e_h_1, c_k, s6) | m_and_h_gate_v_out(c_e_h_1, c_p, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s8)) | node20(c_e_h_1, c_k, s6)), inference(lemma,lemma(discharge,[]))).
% 292.21/184.73 tff(15836,plain,
% 292.21/184.73 (node20(c_e_h_1, c_k, s6)),
% 292.21/184.73 inference(unit_resolution,[status(thm)],[15835, 15769, 15662, 15766])).
% 292.21/184.73 tff(15837,plain,
% 292.21/184.73 (m_and_h_gate_v_in1(c_e_h_1, c_k, s6)),
% 292.21/184.73 inference(unit_resolution,[status(thm)],[15403, 15836])).
% 292.21/184.73 tff(15838,plain,
% 292.21/184.73 (m_or_h_gate_v_out(c_e_h_1, c_g, s6)),
% 292.21/184.73 inference(unit_resolution,[status(thm)],[15395, 15837])).
% 292.21/184.73 tff(15839,plain,
% 292.21/184.73 (m_or_h_gate_v_in1(c_e_h_1, c_g, s5)),
% 292.21/184.73 inference(unit_resolution,[status(thm)],[14850, 15838, 14543])).
% 292.21/184.73 tff(15840,plain,
% 292.21/184.73 (m_mutex_h_half_v_out(c_e_h_1, c_a, s5)),
% 292.21/184.73 inference(unit_resolution,[status(thm)],[15065, 15838])).
% 292.21/184.73 tff(15841,plain,
% 292.21/184.73 (m_and_h_gate_v_in1(c_e_h_1, c_c, s5)),
% 292.21/184.73 inference(unit_resolution,[status(thm)],[15073, 15840])).
% 292.21/184.73 tff(15842,plain,
% 292.21/184.73 (~node21(c_e_h_1, c_c, s5, s6)),
% 292.21/184.73 inference(unit_resolution,[status(thm)],[15368, 15841, 13629])).
% 292.21/184.73 tff(15843,plain,
% 292.21/184.73 (node22(c_e_h_1, c_c, s5, s6)),
% 292.21/184.73 inference(unit_resolution,[status(thm)],[15383, 15842])).
% 292.21/184.73 tff(15844,plain,
% 292.21/184.73 (~m_and_h_gate_v_out(c_e_h_1, c_c, s5)),
% 292.21/184.73 inference(unit_resolution,[status(thm)],[15378, 15843, 13629])).
% 292.21/184.73 tff(15845,plain,
% 292.21/184.73 ($false),
% 292.21/184.73 inference(unit_resolution,[status(thm)],[14530, 2708, 15844, 15839])).
% 292.21/184.73 tff(15846,plain,(m_or_h_gate_v_out(c_e_h_1, c_g, s5) | m_and_h_gate_v_out(c_e_h_1, c_c, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s8))), inference(lemma,lemma(discharge,[]))).
% 292.21/184.73 tff(15847,plain,
% 292.21/184.73 (m_or_h_gate_v_out(c_e_h_1, c_g, s5)),
% 292.21/184.73 inference(unit_resolution,[status(thm)],[15846, 13629, 15662])).
% 292.21/184.73 tff(15848,plain,
% 292.21/184.73 (m_and_h_gate_v_out(c_e_h_1, c_c, s4)),
% 292.21/184.73 inference(unit_resolution,[status(thm)],[14848, 15847])).
% 292.21/184.73 tff(15849,plain,
% 292.21/184.73 (m_mutex_h_half_v_out(c_e_h_1, c_a, s5)),
% 292.21/184.73 inference(unit_resolution,[status(thm)],[15023, 15848])).
% 292.21/184.73 tff(15850,plain,
% 292.21/184.73 (m_and_h_gate_v_in1(c_e_h_1, c_c, s5)),
% 292.21/184.73 inference(unit_resolution,[status(thm)],[15073, 15849])).
% 292.21/184.73 tff(15851,plain,
% 292.21/184.73 (~node21(c_e_h_1, c_c, s5, s6)),
% 292.21/184.73 inference(unit_resolution,[status(thm)],[15368, 15850, 13629])).
% 292.21/184.73 tff(15852,plain,
% 292.21/184.73 (node22(c_e_h_1, c_c, s5, s6)),
% 292.21/184.73 inference(unit_resolution,[status(thm)],[15383, 15851])).
% 292.21/184.73 tff(15853,plain,
% 292.21/184.73 (~m_and_h_gate_v_out(c_e_h_1, c_c, s5)),
% 292.21/184.73 inference(unit_resolution,[status(thm)],[15378, 15852, 13629])).
% 292.21/184.73 tff(15854,plain,
% 292.21/184.73 (~m_and_h_gate_v_in1(c_e_h_1, c_c, s4)),
% 292.21/184.73 inference(unit_resolution,[status(thm)],[14843, 15853, 15848])).
% 292.21/184.73 tff(15855,plain,
% 292.21/184.73 (m_user_v_req(c_e_h_1, c_u, s2)),
% 292.21/184.73 inference(unit_resolution,[status(thm)],[14671, 15848])).
% 292.21/184.73 tff(15856,plain,
% 292.21/184.73 (m_user_v_req(c_e_h_1, c_u, s3)),
% 292.21/184.73 inference(unit_resolution,[status(thm)],[14760, 15855])).
% 292.21/184.73 tff(15857,plain,
% 292.21/184.73 (m_mutex_h_half_v_inp(c_e_h_1, c_a, s3)),
% 292.21/184.73 inference(unit_resolution,[status(thm)],[14768, 15856])).
% 292.21/184.73 tff(15858,plain,
% 292.21/184.73 (node20(c_e_h_1, c_c, s3)),
% 292.21/184.73 inference(unit_resolution,[status(thm)],[14663, 15848, 15676])).
% 292.21/184.73 tff(15859,plain,
% 292.21/184.73 (m_and_h_gate_v_in1(c_e_h_1, c_c, s3)),
% 292.21/184.73 inference(unit_resolution,[status(thm)],[14646, 15858])).
% 292.21/184.73 tff(15860,plain,
% 292.21/184.73 (m_mutex_h_half_v_out(c_e_h_1, c_a, s3)),
% 292.21/184.73 inference(unit_resolution,[status(thm)],[14638, 15859])).
% 292.21/184.73 tff(15861,plain,
% 292.21/184.73 (m_mutex_h_half_v_out(c_e_h_1, c_a, s4)),
% 292.21/184.73 inference(unit_resolution,[status(thm)],[14793, 15860, 15857])).
% 292.21/184.73 tff(15862,plain,
% 292.21/184.73 ($false),
% 292.21/184.73 inference(unit_resolution,[status(thm)],[14808, 2556, 15861, 15854])).
% 292.21/184.73 tff(15863,plain,(m_and_h_gate_v_out(c_e_h_1, c_c, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s8))), inference(lemma,lemma(discharge,[]))).
% 292.21/184.73 tff(15864,plain,
% 292.21/184.73 (~m_and_h_gate_v_out(c_e_h_1, c_p, s8)),
% 292.21/184.73 inference(unit_resolution,[status(thm)],[15863, 13629])).
% 292.21/184.73 tff(15865,assumption,(~node20(c_e_h_1, c_p, s8)), introduced(assumption)).
% 292.21/184.73 tff(15866,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_p, s8)), introduced(assumption)).
% 292.21/184.73 tff(15867,assumption,(node22(c_e_h_1, c_p, s8, s9)), introduced(assumption)).
% 292.21/184.73 tff(15868,plain,
% 292.21/184.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_p, s9)) | (~node22(c_e_h_1, c_p, s8, s9)) | m_and_h_gate_v_out(c_e_h_1, c_p, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s9)) | (~node22(c_e_h_1, c_p, s8, s9)) | m_and_h_gate_v_out(c_e_h_1, c_p, s8))),
% 292.21/184.73 inference(rewrite,[status(thm)],[])).
% 292.21/184.73 tff(15869,plain,
% 292.21/184.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_p, s9)) | (~node22(c_e_h_1, c_p, s8, s9)) | m_and_h_gate_v_out(c_e_h_1, c_p, s8))),
% 292.21/184.73 inference(quant_inst,[status(thm)],[])).
% 292.21/184.73 tff(15870,plain,
% 292.21/184.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s9)) | (~node22(c_e_h_1, c_p, s8, s9)) | m_and_h_gate_v_out(c_e_h_1, c_p, s8)),
% 292.21/184.73 inference(modus_ponens,[status(thm)],[15869, 15868])).
% 292.21/184.73 tff(15871,plain,
% 292.21/184.73 ($false),
% 292.21/184.73 inference(unit_resolution,[status(thm)],[15870, 108, 15866, 13628, 15867])).
% 292.21/184.73 tff(15872,plain,((~node22(c_e_h_1, c_p, s8, s9)) | m_and_h_gate_v_out(c_e_h_1, c_p, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s9))), inference(lemma,lemma(discharge,[]))).
% 292.21/184.73 tff(15873,plain,
% 292.21/184.73 (~node22(c_e_h_1, c_p, s8, s9)),
% 292.21/184.73 inference(unit_resolution,[status(thm)],[15872, 13628, 15866])).
% 292.21/184.73 tff(15874,plain,
% 292.21/184.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s8, s9)) | node21(c_e_h_1, c_p, s8, s9) | node22(c_e_h_1, c_p, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_1, c_p, s8, s9) | node22(c_e_h_1, c_p, s8, s9))),
% 292.21/184.73 inference(rewrite,[status(thm)],[])).
% 292.21/184.73 tff(15875,plain,
% 292.21/184.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s8, s9)) | node21(c_e_h_1, c_p, s8, s9) | node22(c_e_h_1, c_p, s8, s9))),
% 292.21/184.73 inference(quant_inst,[status(thm)],[])).
% 292.21/184.73 tff(15876,plain,
% 292.21/184.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_1, c_p, s8, s9) | node22(c_e_h_1, c_p, s8, s9)),
% 292.21/184.73 inference(modus_ponens,[status(thm)],[15875, 15874])).
% 292.21/184.73 tff(15877,plain,
% 292.21/184.73 (node21(c_e_h_1, c_p, s8, s9) | node22(c_e_h_1, c_p, s8, s9)),
% 292.21/184.73 inference(unit_resolution,[status(thm)],[15876, 82, 1993])).
% 292.21/184.73 tff(15878,plain,
% 292.21/184.73 (node21(c_e_h_1, c_p, s8, s9)),
% 292.21/184.74 inference(unit_resolution,[status(thm)],[15877, 15873])).
% 292.21/184.74 tff(15879,plain,
% 292.21/184.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_p, s9)) | node20(c_e_h_1, c_p, s8) | (~node21(c_e_h_1, c_p, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s9)) | node20(c_e_h_1, c_p, s8) | (~node21(c_e_h_1, c_p, s8, s9)))),
% 292.21/184.74 inference(rewrite,[status(thm)],[])).
% 292.21/184.74 tff(15880,plain,
% 292.21/184.74 ((node20(c_e_h_1, c_p, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s9)) | (~node21(c_e_h_1, c_p, s8, s9))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_p, s9)) | node20(c_e_h_1, c_p, s8) | (~node21(c_e_h_1, c_p, s8, s9)))),
% 292.21/184.74 inference(rewrite,[status(thm)],[])).
% 292.21/184.74 tff(15881,plain,
% 292.21/184.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_p, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s9)) | (~node21(c_e_h_1, c_p, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_p, s9)) | node20(c_e_h_1, c_p, s8) | (~node21(c_e_h_1, c_p, s8, s9))))),
% 292.21/184.74 inference(monotonicity,[status(thm)],[15880])).
% 292.21/184.74 tff(15882,plain,
% 292.21/184.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_p, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s9)) | (~node21(c_e_h_1, c_p, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s9)) | node20(c_e_h_1, c_p, s8) | (~node21(c_e_h_1, c_p, s8, s9)))),
% 292.21/184.74 inference(transitivity,[status(thm)],[15881, 15879])).
% 292.21/184.74 tff(15883,plain,
% 292.21/184.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_p, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s9)) | (~node21(c_e_h_1, c_p, s8, s9)))),
% 292.21/184.74 inference(quant_inst,[status(thm)],[])).
% 292.21/184.74 tff(15884,plain,
% 292.21/184.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s9)) | node20(c_e_h_1, c_p, s8) | (~node21(c_e_h_1, c_p, s8, s9))),
% 292.21/184.74 inference(modus_ponens,[status(thm)],[15883, 15882])).
% 292.21/184.74 tff(15885,plain,
% 292.21/184.74 ($false),
% 292.21/184.74 inference(unit_resolution,[status(thm)],[15884, 52, 13628, 15878, 15865])).
% 292.21/184.74 tff(15886,plain,((~m_and_h_gate_v_out(c_e_h_1, c_p, s9)) | node20(c_e_h_1, c_p, s8) | m_and_h_gate_v_out(c_e_h_1, c_p, s8)), inference(lemma,lemma(discharge,[]))).
% 292.21/184.74 tff(15887,plain,
% 292.21/184.74 (node20(c_e_h_1, c_p, s8)),
% 292.21/184.74 inference(unit_resolution,[status(thm)],[15886, 15864, 13628])).
% 292.21/184.74 tff(15888,assumption,(node20(c_e_h_1, c_p, s8)), introduced(assumption)).
% 292.21/184.74 tff(15889,assumption,(~m_and_h_gate_v_in1(c_e_h_1, c_p, s8)), introduced(assumption)).
% 292.21/184.74 tff(15890,plain,
% 292.21/184.74 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_p, s8)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_p, s8)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s8))),
% 292.21/184.74 inference(rewrite,[status(thm)],[])).
% 292.21/184.74 tff(15891,plain,
% 292.21/184.74 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_p, s8)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s8))),
% 292.21/184.74 inference(quant_inst,[status(thm)],[])).
% 292.21/184.74 tff(15892,plain,
% 292.21/184.74 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_p, s8)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s8)),
% 292.21/184.74 inference(modus_ponens,[status(thm)],[15891, 15890])).
% 292.21/184.74 tff(15893,plain,
% 292.21/184.74 ($false),
% 292.21/184.74 inference(unit_resolution,[status(thm)],[15892, 38, 15889, 15888])).
% 292.21/184.74 tff(15894,plain,((~node20(c_e_h_1, c_p, s8)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s8)), inference(lemma,lemma(discharge,[]))).
% 292.21/184.74 tff(15895,plain,
% 292.21/184.74 (m_and_h_gate_v_in1(c_e_h_1, c_p, s8)),
% 292.21/184.74 inference(unit_resolution,[status(thm)],[15894, 15887])).
% 292.21/184.74 tff(15896,assumption,(m_and_h_gate_v_in1(c_e_h_1, c_p, s8)), introduced(assumption)).
% 292.21/184.74 tff(15897,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_k, s8)), introduced(assumption)).
% 292.21/184.74 tff(15898,plain,
% 292.21/184.74 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_p, s8)) | m_and_h_gate_v_out(c_e_h_1, c_k, s8))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s8)) | m_and_h_gate_v_out(c_e_h_1, c_k, s8))),
% 292.21/184.74 inference(rewrite,[status(thm)],[])).
% 292.21/184.74 tff(15899,plain,
% 292.21/184.74 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_p, s8)) | m_and_h_gate_v_out(c_e_h_1, c_k, s8))),
% 292.21/184.74 inference(quant_inst,[status(thm)],[])).
% 292.21/184.74 tff(15900,plain,
% 292.21/184.74 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s8)) | m_and_h_gate_v_out(c_e_h_1, c_k, s8)),
% 292.21/184.74 inference(modus_ponens,[status(thm)],[15899, 15898])).
% 292.21/184.74 tff(15901,plain,
% 292.21/184.74 ($false),
% 292.21/184.74 inference(unit_resolution,[status(thm)],[15900, 3033, 15897, 15896])).
% 292.21/184.74 tff(15902,plain,((~m_and_h_gate_v_in1(c_e_h_1, c_p, s8)) | m_and_h_gate_v_out(c_e_h_1, c_k, s8)), inference(lemma,lemma(discharge,[]))).
% 292.21/184.74 tff(15903,plain,
% 292.21/184.74 (m_and_h_gate_v_out(c_e_h_1, c_k, s8)),
% 292.21/184.74 inference(unit_resolution,[status(thm)],[15902, 15895])).
% 292.21/184.74 tff(15904,assumption,(m_and_h_gate_v_out(c_e_h_1, c_k, s8)), introduced(assumption)).
% 292.21/184.74 tff(15905,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_k, s7)), introduced(assumption)).
% 292.21/184.74 tff(15906,assumption,(~node20(c_e_h_1, c_k, s7)), introduced(assumption)).
% 292.21/184.74 tff(15907,assumption,(node21(c_e_h_1, c_k, s7, s8)), introduced(assumption)).
% 292.21/184.74 tff(15908,plain,
% 292.21/184.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_k, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s8)) | (~node21(c_e_h_1, c_k, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_k, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s8)) | (~node21(c_e_h_1, c_k, s7, s8)))),
% 292.21/184.74 inference(rewrite,[status(thm)],[])).
% 292.21/184.74 tff(15909,plain,
% 292.21/184.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_k, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s8)) | (~node21(c_e_h_1, c_k, s7, s8)))),
% 292.21/184.74 inference(quant_inst,[status(thm)],[])).
% 292.21/184.74 tff(15910,plain,
% 292.21/184.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_k, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s8)) | (~node21(c_e_h_1, c_k, s7, s8))),
% 292.21/184.74 inference(modus_ponens,[status(thm)],[15909, 15908])).
% 292.21/184.74 tff(15911,plain,
% 292.21/184.74 ($false),
% 292.21/184.74 inference(unit_resolution,[status(thm)],[15910, 52, 15907, 15906, 15904])).
% 292.21/184.74 tff(15912,plain,((~node21(c_e_h_1, c_k, s7, s8)) | node20(c_e_h_1, c_k, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s8))), inference(lemma,lemma(discharge,[]))).
% 292.21/184.74 tff(15913,plain,
% 292.21/184.74 (~node21(c_e_h_1, c_k, s7, s8)),
% 292.21/184.74 inference(unit_resolution,[status(thm)],[15912, 15904, 15906])).
% 292.21/184.74 tff(15914,plain,
% 292.21/184.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_1, c_k, s7, s8) | node22(c_e_h_1, c_k, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_1, c_k, s7, s8) | node22(c_e_h_1, c_k, s7, s8))),
% 292.21/184.74 inference(rewrite,[status(thm)],[])).
% 292.21/184.74 tff(15915,plain,
% 292.21/184.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_1, c_k, s7, s8) | node22(c_e_h_1, c_k, s7, s8))),
% 292.21/184.75 inference(quant_inst,[status(thm)],[])).
% 292.21/184.75 tff(15916,plain,
% 292.21/184.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_1, c_k, s7, s8) | node22(c_e_h_1, c_k, s7, s8)),
% 292.21/184.75 inference(modus_ponens,[status(thm)],[15915, 15914])).
% 292.21/184.75 tff(15917,plain,
% 292.21/184.75 (node21(c_e_h_1, c_k, s7, s8) | node22(c_e_h_1, c_k, s7, s8)),
% 292.21/184.75 inference(unit_resolution,[status(thm)],[15916, 82, 1938])).
% 292.21/184.75 tff(15918,plain,
% 292.21/184.75 (node22(c_e_h_1, c_k, s7, s8)),
% 292.21/184.75 inference(unit_resolution,[status(thm)],[15917, 15913])).
% 292.21/184.75 tff(15919,plain,
% 292.21/184.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_k, s8)) | (~node22(c_e_h_1, c_k, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_k, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s8)) | (~node22(c_e_h_1, c_k, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_k, s7))),
% 292.21/184.75 inference(rewrite,[status(thm)],[])).
% 292.21/184.75 tff(15920,plain,
% 292.21/184.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_k, s8)) | (~node22(c_e_h_1, c_k, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_k, s7))),
% 292.21/184.75 inference(quant_inst,[status(thm)],[])).
% 292.21/184.75 tff(15921,plain,
% 292.21/184.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s8)) | (~node22(c_e_h_1, c_k, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_k, s7)),
% 292.21/184.75 inference(modus_ponens,[status(thm)],[15920, 15919])).
% 292.21/184.75 tff(15922,plain,
% 292.21/184.75 ($false),
% 292.21/184.75 inference(unit_resolution,[status(thm)],[15921, 108, 15918, 15905, 15904])).
% 292.21/184.75 tff(15923,plain,((~m_and_h_gate_v_out(c_e_h_1, c_k, s8)) | m_and_h_gate_v_out(c_e_h_1, c_k, s7) | node20(c_e_h_1, c_k, s7)), inference(lemma,lemma(discharge,[]))).
% 292.21/184.75 tff(15924,plain,
% 292.21/184.75 (node20(c_e_h_1, c_k, s7)),
% 292.21/184.75 inference(unit_resolution,[status(thm)],[15923, 15903, 15661])).
% 292.21/184.75 tff(15925,assumption,(~m_and_h_gate_v_in1(c_e_h_1, c_k, s7)), introduced(assumption)).
% 292.21/184.75 tff(15926,assumption,(node20(c_e_h_1, c_k, s7)), introduced(assumption)).
% 292.21/184.75 tff(15927,plain,
% 292.21/184.75 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_k, s7)) | m_and_h_gate_v_in1(c_e_h_1, c_k, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_k, s7)) | m_and_h_gate_v_in1(c_e_h_1, c_k, s7))),
% 292.21/184.75 inference(rewrite,[status(thm)],[])).
% 292.21/184.75 tff(15928,plain,
% 292.21/184.75 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_k, s7)) | m_and_h_gate_v_in1(c_e_h_1, c_k, s7))),
% 292.21/184.75 inference(quant_inst,[status(thm)],[])).
% 292.21/184.75 tff(15929,plain,
% 292.21/184.75 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_k, s7)) | m_and_h_gate_v_in1(c_e_h_1, c_k, s7)),
% 292.21/184.75 inference(modus_ponens,[status(thm)],[15928, 15927])).
% 292.21/184.75 tff(15930,plain,
% 292.21/184.75 ($false),
% 292.21/184.75 inference(unit_resolution,[status(thm)],[15929, 38, 15926, 15925])).
% 292.21/184.75 tff(15931,plain,(m_and_h_gate_v_in1(c_e_h_1, c_k, s7) | (~node20(c_e_h_1, c_k, s7))), inference(lemma,lemma(discharge,[]))).
% 292.21/184.75 tff(15932,plain,
% 292.21/184.75 (m_and_h_gate_v_in1(c_e_h_1, c_k, s7)),
% 292.21/184.75 inference(unit_resolution,[status(thm)],[15931, 15924])).
% 292.21/184.75 tff(15933,assumption,(m_and_h_gate_v_in1(c_e_h_1, c_k, s7)), introduced(assumption)).
% 292.21/184.75 tff(15934,assumption,(~m_or_h_gate_v_out(c_e_h_1, c_g, s7)), introduced(assumption)).
% 292.21/184.75 tff(15935,plain,
% 292.21/184.75 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_k, s7)) | m_or_h_gate_v_out(c_e_h_1, c_g, s7))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_k, s7)) | m_or_h_gate_v_out(c_e_h_1, c_g, s7))),
% 292.21/184.75 inference(rewrite,[status(thm)],[])).
% 292.21/184.75 tff(15936,plain,
% 292.21/184.75 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_k, s7)) | m_or_h_gate_v_out(c_e_h_1, c_g, s7))),
% 292.21/184.75 inference(quant_inst,[status(thm)],[])).
% 292.21/184.75 tff(15937,plain,
% 292.21/184.75 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_k, s7)) | m_or_h_gate_v_out(c_e_h_1, c_g, s7)),
% 292.21/184.75 inference(modus_ponens,[status(thm)],[15936, 15935])).
% 292.21/184.75 tff(15938,plain,
% 292.21/184.75 ($false),
% 292.21/184.75 inference(unit_resolution,[status(thm)],[15937, 2048, 15934, 15933])).
% 292.21/184.75 tff(15939,plain,((~m_and_h_gate_v_in1(c_e_h_1, c_k, s7)) | m_or_h_gate_v_out(c_e_h_1, c_g, s7)), inference(lemma,lemma(discharge,[]))).
% 292.21/184.75 tff(15940,plain,
% 292.21/184.75 (m_or_h_gate_v_out(c_e_h_1, c_g, s7)),
% 292.21/184.75 inference(unit_resolution,[status(thm)],[15939, 15932])).
% 292.21/184.75 tff(15941,assumption,(~node4(c_e_h_1, c_g, s7)), introduced(assumption)).
% 292.21/184.75 tff(15942,assumption,(node5(c_e_h_1, c_g, s7, s8)), introduced(assumption)).
% 292.21/184.75 tff(15943,plain,
% 292.21/184.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (m_or_h_gate_v_out(c_e_h_1, c_g, s8) | (~node5(c_e_h_1, c_g, s7, s8)) | node4(c_e_h_1, c_g, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | m_or_h_gate_v_out(c_e_h_1, c_g, s8) | (~node5(c_e_h_1, c_g, s7, s8)) | node4(c_e_h_1, c_g, s7))),
% 292.21/184.75 inference(rewrite,[status(thm)],[])).
% 292.21/184.75 tff(15944,plain,
% 292.21/184.75 ((node4(c_e_h_1, c_g, s7) | (~node5(c_e_h_1, c_g, s7, s8)) | m_or_h_gate_v_out(c_e_h_1, c_g, s8)) <=> (m_or_h_gate_v_out(c_e_h_1, c_g, s8) | (~node5(c_e_h_1, c_g, s7, s8)) | node4(c_e_h_1, c_g, s7))),
% 292.21/184.75 inference(rewrite,[status(thm)],[])).
% 292.21/184.75 tff(15945,plain,
% 292.21/184.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_1, c_g, s7) | (~node5(c_e_h_1, c_g, s7, s8)) | m_or_h_gate_v_out(c_e_h_1, c_g, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (m_or_h_gate_v_out(c_e_h_1, c_g, s8) | (~node5(c_e_h_1, c_g, s7, s8)) | node4(c_e_h_1, c_g, s7)))),
% 292.21/184.75 inference(monotonicity,[status(thm)],[15944])).
% 292.21/184.75 tff(15946,plain,
% 292.21/184.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_1, c_g, s7) | (~node5(c_e_h_1, c_g, s7, s8)) | m_or_h_gate_v_out(c_e_h_1, c_g, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | m_or_h_gate_v_out(c_e_h_1, c_g, s8) | (~node5(c_e_h_1, c_g, s7, s8)) | node4(c_e_h_1, c_g, s7))),
% 292.21/184.75 inference(transitivity,[status(thm)],[15945, 15943])).
% 292.21/184.75 tff(15947,plain,
% 292.21/184.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_1, c_g, s7) | (~node5(c_e_h_1, c_g, s7, s8)) | m_or_h_gate_v_out(c_e_h_1, c_g, s8))),
% 292.21/184.75 inference(quant_inst,[status(thm)],[])).
% 292.21/184.75 tff(15948,plain,
% 292.21/184.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | m_or_h_gate_v_out(c_e_h_1, c_g, s8) | (~node5(c_e_h_1, c_g, s7, s8)) | node4(c_e_h_1, c_g, s7)),
% 292.21/184.75 inference(modus_ponens,[status(thm)],[15947, 15946])).
% 292.21/184.75 tff(15949,plain,
% 292.21/184.75 ($false),
% 292.21/184.75 inference(unit_resolution,[status(thm)],[15948, 5498, 15942, 15941, 13627])).
% 292.21/184.75 tff(15950,plain,((~node5(c_e_h_1, c_g, s7, s8)) | node4(c_e_h_1, c_g, s7) | m_or_h_gate_v_out(c_e_h_1, c_g, s8)), inference(lemma,lemma(discharge,[]))).
% 292.21/184.75 tff(15951,plain,
% 292.21/184.75 (~node5(c_e_h_1, c_g, s7, s8)),
% 292.21/184.75 inference(unit_resolution,[status(thm)],[15950, 13627, 15941])).
% 292.21/184.75 tff(15952,assumption,(m_or_h_gate_v_out(c_e_h_1, c_g, s7)), introduced(assumption)).
% 292.21/184.75 tff(15953,assumption,(node6(c_e_h_1, c_g, s7, s8)), introduced(assumption)).
% 292.21/184.75 tff(15954,plain,
% 292.21/184.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | ((~m_or_h_gate_v_out(c_e_h_1, c_g, s7)) | m_or_h_gate_v_out(c_e_h_1, c_g, s8) | (~node6(c_e_h_1, c_g, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s7)) | m_or_h_gate_v_out(c_e_h_1, c_g, s8) | (~node6(c_e_h_1, c_g, s7, s8)))),
% 292.21/184.75 inference(rewrite,[status(thm)],[])).
% 292.21/184.75 tff(15955,plain,
% 292.21/184.75 ((m_or_h_gate_v_out(c_e_h_1, c_g, s8) | (~node6(c_e_h_1, c_g, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s7))) <=> ((~m_or_h_gate_v_out(c_e_h_1, c_g, s7)) | m_or_h_gate_v_out(c_e_h_1, c_g, s8) | (~node6(c_e_h_1, c_g, s7, s8)))),
% 292.21/184.75 inference(rewrite,[status(thm)],[])).
% 292.21/184.75 tff(15956,plain,
% 292.21/184.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_1, c_g, s8) | (~node6(c_e_h_1, c_g, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | ((~m_or_h_gate_v_out(c_e_h_1, c_g, s7)) | m_or_h_gate_v_out(c_e_h_1, c_g, s8) | (~node6(c_e_h_1, c_g, s7, s8))))),
% 292.21/184.75 inference(monotonicity,[status(thm)],[15955])).
% 292.21/184.75 tff(15957,plain,
% 292.21/184.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_1, c_g, s8) | (~node6(c_e_h_1, c_g, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s7)) | m_or_h_gate_v_out(c_e_h_1, c_g, s8) | (~node6(c_e_h_1, c_g, s7, s8)))),
% 292.21/184.75 inference(transitivity,[status(thm)],[15956, 15954])).
% 292.21/184.75 tff(15958,plain,
% 292.21/184.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_1, c_g, s8) | (~node6(c_e_h_1, c_g, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s7)))),
% 292.21/184.75 inference(quant_inst,[status(thm)],[])).
% 292.21/184.75 tff(15959,plain,
% 292.21/184.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s7)) | m_or_h_gate_v_out(c_e_h_1, c_g, s8) | (~node6(c_e_h_1, c_g, s7, s8))),
% 292.21/184.75 inference(modus_ponens,[status(thm)],[15958, 15957])).
% 292.21/184.75 tff(15960,plain,
% 292.21/184.75 ($false),
% 292.21/184.75 inference(unit_resolution,[status(thm)],[15959, 5474, 15953, 13627, 15952])).
% 292.21/184.75 tff(15961,plain,((~node6(c_e_h_1, c_g, s7, s8)) | m_or_h_gate_v_out(c_e_h_1, c_g, s8) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s7))), inference(lemma,lemma(discharge,[]))).
% 292.21/184.75 tff(15962,plain,
% 292.21/184.75 (~node6(c_e_h_1, c_g, s7, s8)),
% 292.21/184.75 inference(unit_resolution,[status(thm)],[15961, 13627, 15952])).
% 292.21/184.75 tff(15963,plain,
% 292.21/184.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s7, s8)) | node6(c_e_h_1, c_g, s7, s8) | node5(c_e_h_1, c_g, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s7, s8)) | node6(c_e_h_1, c_g, s7, s8) | node5(c_e_h_1, c_g, s7, s8))),
% 292.21/184.75 inference(rewrite,[status(thm)],[])).
% 292.21/184.75 tff(15964,plain,
% 292.21/184.75 ((node6(c_e_h_1, c_g, s7, s8) | node5(c_e_h_1, c_g, s7, s8) | (~trans(s7, s8))) <=> ((~trans(s7, s8)) | node6(c_e_h_1, c_g, s7, s8) | node5(c_e_h_1, c_g, s7, s8))),
% 292.21/184.75 inference(rewrite,[status(thm)],[])).
% 292.21/184.75 tff(15965,plain,
% 292.21/184.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_g, s7, s8) | node5(c_e_h_1, c_g, s7, s8) | (~trans(s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s7, s8)) | node6(c_e_h_1, c_g, s7, s8) | node5(c_e_h_1, c_g, s7, s8)))),
% 292.21/184.75 inference(monotonicity,[status(thm)],[15964])).
% 292.21/184.75 tff(15966,plain,
% 292.21/184.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_g, s7, s8) | node5(c_e_h_1, c_g, s7, s8) | (~trans(s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s7, s8)) | node6(c_e_h_1, c_g, s7, s8) | node5(c_e_h_1, c_g, s7, s8))),
% 292.21/184.76 inference(transitivity,[status(thm)],[15965, 15963])).
% 292.21/184.76 tff(15967,plain,
% 292.21/184.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_g, s7, s8) | node5(c_e_h_1, c_g, s7, s8) | (~trans(s7, s8)))),
% 292.21/184.76 inference(quant_inst,[status(thm)],[])).
% 292.21/184.76 tff(15968,plain,
% 292.21/184.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s7, s8)) | node6(c_e_h_1, c_g, s7, s8) | node5(c_e_h_1, c_g, s7, s8)),
% 292.21/184.76 inference(modus_ponens,[status(thm)],[15967, 15966])).
% 292.21/184.76 tff(15969,plain,
% 292.21/184.76 (node6(c_e_h_1, c_g, s7, s8) | node5(c_e_h_1, c_g, s7, s8)),
% 292.21/184.76 inference(unit_resolution,[status(thm)],[15968, 1141, 1938])).
% 292.21/184.76 tff(15970,plain,
% 292.21/184.76 ($false),
% 292.21/184.76 inference(unit_resolution,[status(thm)],[15969, 15962, 15951])).
% 292.21/184.76 tff(15971,plain,(m_or_h_gate_v_out(c_e_h_1, c_g, s8) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s7)) | node4(c_e_h_1, c_g, s7)), inference(lemma,lemma(discharge,[]))).
% 292.21/184.76 tff(15972,plain,
% 292.21/184.76 (node4(c_e_h_1, c_g, s7)),
% 292.21/184.76 inference(unit_resolution,[status(thm)],[15971, 15940, 13627])).
% 292.21/184.76 tff(15973,assumption,(m_or_h_gate_v_in1(c_e_h_1, c_g, s7)), introduced(assumption)).
% 292.21/184.76 tff(15974,assumption,(node4(c_e_h_1, c_g, s7)), introduced(assumption)).
% 292.21/184.76 tff(15975,plain,
% 292.21/184.76 (((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_g, s7)) | (~node4(c_e_h_1, c_g, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | (~m_or_h_gate_v_in1(c_e_h_1, c_g, s7)) | (~node4(c_e_h_1, c_g, s7)))),
% 292.21/184.76 inference(rewrite,[status(thm)],[])).
% 292.21/184.76 tff(15976,plain,
% 292.21/184.76 ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_g, s7)) | (~node4(c_e_h_1, c_g, s7)))),
% 292.21/184.76 inference(quant_inst,[status(thm)],[])).
% 292.21/184.76 tff(15977,plain,
% 292.21/184.76 ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | (~m_or_h_gate_v_in1(c_e_h_1, c_g, s7)) | (~node4(c_e_h_1, c_g, s7))),
% 292.21/184.76 inference(modus_ponens,[status(thm)],[15976, 15975])).
% 292.21/184.76 tff(15978,plain,
% 292.21/184.76 ($false),
% 292.21/184.76 inference(unit_resolution,[status(thm)],[15977, 5516, 15974, 15973])).
% 292.21/184.76 tff(15979,plain,((~m_or_h_gate_v_in1(c_e_h_1, c_g, s7)) | (~node4(c_e_h_1, c_g, s7))), inference(lemma,lemma(discharge,[]))).
% 292.21/184.76 tff(15980,plain,
% 292.21/184.76 (~m_or_h_gate_v_in1(c_e_h_1, c_g, s7)),
% 292.21/184.76 inference(unit_resolution,[status(thm)],[15979, 15972])).
% 292.21/184.76 tff(15981,assumption,(node6(c_e_h_1, c_g, s6, s7)), introduced(assumption)).
% 292.21/184.76 tff(15982,plain,
% 292.21/184.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_1, c_g, s7)) | m_or_h_gate_v_out(c_e_h_1, c_g, s6) | (~node6(c_e_h_1, c_g, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s7)) | m_or_h_gate_v_out(c_e_h_1, c_g, s6) | (~node6(c_e_h_1, c_g, s6, s7)))),
% 292.21/184.76 inference(rewrite,[status(thm)],[])).
% 292.21/184.76 tff(15983,plain,
% 292.21/184.76 (((~node6(c_e_h_1, c_g, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s7)) | m_or_h_gate_v_out(c_e_h_1, c_g, s6)) <=> ((~m_or_h_gate_v_out(c_e_h_1, c_g, s7)) | m_or_h_gate_v_out(c_e_h_1, c_g, s6) | (~node6(c_e_h_1, c_g, s6, s7)))),
% 292.21/184.76 inference(rewrite,[status(thm)],[])).
% 292.21/184.76 tff(15984,plain,
% 292.21/184.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_g, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s7)) | m_or_h_gate_v_out(c_e_h_1, c_g, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_1, c_g, s7)) | m_or_h_gate_v_out(c_e_h_1, c_g, s6) | (~node6(c_e_h_1, c_g, s6, s7))))),
% 292.21/184.76 inference(monotonicity,[status(thm)],[15983])).
% 292.21/184.76 tff(15985,plain,
% 292.21/184.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_g, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s7)) | m_or_h_gate_v_out(c_e_h_1, c_g, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s7)) | m_or_h_gate_v_out(c_e_h_1, c_g, s6) | (~node6(c_e_h_1, c_g, s6, s7)))),
% 292.21/184.76 inference(transitivity,[status(thm)],[15984, 15982])).
% 292.21/184.76 tff(15986,plain,
% 292.21/184.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_g, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s7)) | m_or_h_gate_v_out(c_e_h_1, c_g, s6))),
% 292.21/184.76 inference(quant_inst,[status(thm)],[])).
% 292.21/184.76 tff(15987,plain,
% 292.21/184.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s7)) | m_or_h_gate_v_out(c_e_h_1, c_g, s6) | (~node6(c_e_h_1, c_g, s6, s7))),
% 292.21/184.76 inference(modus_ponens,[status(thm)],[15986, 15985])).
% 292.21/184.76 tff(15988,plain,
% 292.21/184.76 ($false),
% 292.21/184.76 inference(unit_resolution,[status(thm)],[15987, 1121, 15981, 15952, 15389])).
% 292.21/184.76 tff(15989,plain,((~node6(c_e_h_1, c_g, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s7)) | m_or_h_gate_v_out(c_e_h_1, c_g, s6)), inference(lemma,lemma(discharge,[]))).
% 292.21/184.76 tff(15990,plain,
% 292.21/184.76 (~node6(c_e_h_1, c_g, s6, s7)),
% 292.21/184.76 inference(unit_resolution,[status(thm)],[15989, 15952, 15389])).
% 292.21/184.76 tff(15991,assumption,(~m_or_h_gate_v_in1(c_e_h_1, c_g, s6)), introduced(assumption)).
% 292.21/184.76 tff(15992,assumption,(m_and_h_gate_v_out(c_e_h_2, c_p, s4)), introduced(assumption)).
% 292.21/184.76 tff(15993,assumption,(m_and_h_gate_v_out(c_e_h_2, c_k, s3)), introduced(assumption)).
% 292.21/184.76 tff(15994,assumption,(m_and_h_gate_v_out(c_e_h_2, c_d, s1)), introduced(assumption)).
% 292.21/184.76 tff(15995,assumption,(m_mutex_h_half_v_out(c_e_h_2, c_b, s0)), introduced(assumption)).
% 292.21/184.76 tff(15996,plain,
% 292.21/184.76 ((~![I0: $i, I1: $i] : (~m_mutex_h_half_v_out(I0, I1, s0))) | (~m_mutex_h_half_v_out(c_e_h_2, c_b, s0))),
% 292.21/184.76 inference(quant_inst,[status(thm)],[])).
% 292.21/184.76 tff(15997,plain,
% 292.21/184.76 ($false),
% 292.21/184.76 inference(unit_resolution,[status(thm)],[15996, 409, 15995])).
% 292.21/184.76 tff(15998,plain,(~m_mutex_h_half_v_out(c_e_h_2, c_b, s0)), inference(lemma,lemma(discharge,[]))).
% 292.21/184.76 tff(15999,plain,
% 292.21/184.76 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_d, s0)) | m_mutex_h_half_v_out(c_e_h_2, c_b, s0))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_d, s0)) | m_mutex_h_half_v_out(c_e_h_2, c_b, s0))),
% 292.21/184.76 inference(rewrite,[status(thm)],[])).
% 292.21/184.76 tff(16000,plain,
% 292.21/184.76 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_d, s0)) | m_mutex_h_half_v_out(c_e_h_2, c_b, s0))),
% 292.21/184.76 inference(quant_inst,[status(thm)],[])).
% 292.21/184.76 tff(16001,plain,
% 292.21/184.76 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_d, s0)) | m_mutex_h_half_v_out(c_e_h_2, c_b, s0)),
% 292.21/184.76 inference(modus_ponens,[status(thm)],[16000, 15999])).
% 292.21/184.76 tff(16002,plain,
% 292.21/184.76 (~m_and_h_gate_v_in1(c_e_h_2, c_d, s0)),
% 292.21/184.76 inference(unit_resolution,[status(thm)],[16001, 2808, 15998])).
% 292.21/184.76 tff(16003,plain,
% 292.21/184.76 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_d, s0)) | m_and_h_gate_v_in1(c_e_h_2, c_d, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_d, s0)) | m_and_h_gate_v_in1(c_e_h_2, c_d, s0))),
% 292.21/184.76 inference(rewrite,[status(thm)],[])).
% 292.21/184.76 tff(16004,plain,
% 292.21/184.76 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_d, s0)) | m_and_h_gate_v_in1(c_e_h_2, c_d, s0))),
% 292.21/184.76 inference(quant_inst,[status(thm)],[])).
% 292.21/184.76 tff(16005,plain,
% 292.21/184.76 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_d, s0)) | m_and_h_gate_v_in1(c_e_h_2, c_d, s0)),
% 292.21/184.76 inference(modus_ponens,[status(thm)],[16004, 16003])).
% 292.21/184.76 tff(16006,plain,
% 292.21/184.76 (~node20(c_e_h_2, c_d, s0)),
% 292.21/184.76 inference(unit_resolution,[status(thm)],[16005, 38, 16002])).
% 292.21/184.76 tff(16007,assumption,(node21(c_e_h_2, c_d, s0, s1)), introduced(assumption)).
% 292.21/184.76 tff(16008,plain,
% 292.21/184.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_d, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_d, s1)) | (~node21(c_e_h_2, c_d, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_d, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_d, s1)) | (~node21(c_e_h_2, c_d, s0, s1)))),
% 292.21/184.76 inference(rewrite,[status(thm)],[])).
% 292.21/184.76 tff(16009,plain,
% 292.21/184.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_d, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_d, s1)) | (~node21(c_e_h_2, c_d, s0, s1)))),
% 292.21/184.76 inference(quant_inst,[status(thm)],[])).
% 292.21/184.76 tff(16010,plain,
% 292.21/184.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_d, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_d, s1)) | (~node21(c_e_h_2, c_d, s0, s1))),
% 292.21/184.76 inference(modus_ponens,[status(thm)],[16009, 16008])).
% 292.21/184.76 tff(16011,plain,
% 292.21/184.76 ($false),
% 292.21/184.76 inference(unit_resolution,[status(thm)],[16010, 52, 16007, 16006, 15994])).
% 292.21/184.76 tff(16012,plain,((~node21(c_e_h_2, c_d, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_2, c_d, s1))), inference(lemma,lemma(discharge,[]))).
% 292.21/184.76 tff(16013,plain,
% 292.21/184.76 (~node21(c_e_h_2, c_d, s0, s1)),
% 292.21/184.76 inference(unit_resolution,[status(thm)],[16012, 15994])).
% 292.21/184.76 tff(16014,plain,
% 292.21/184.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_2, c_d, s0, s1) | node22(c_e_h_2, c_d, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_2, c_d, s0, s1) | node22(c_e_h_2, c_d, s0, s1))),
% 292.21/184.76 inference(rewrite,[status(thm)],[])).
% 292.21/184.76 tff(16015,plain,
% 292.21/184.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_2, c_d, s0, s1) | node22(c_e_h_2, c_d, s0, s1))),
% 292.21/184.76 inference(quant_inst,[status(thm)],[])).
% 292.21/184.76 tff(16016,plain,
% 292.21/184.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_2, c_d, s0, s1) | node22(c_e_h_2, c_d, s0, s1)),
% 292.21/184.76 inference(modus_ponens,[status(thm)],[16015, 16014])).
% 292.21/184.76 tff(16017,plain,
% 292.21/184.76 (node21(c_e_h_2, c_d, s0, s1) | node22(c_e_h_2, c_d, s0, s1)),
% 292.21/184.76 inference(unit_resolution,[status(thm)],[16016, 82, 72])).
% 292.21/184.76 tff(16018,plain,
% 292.21/184.76 (node22(c_e_h_2, c_d, s0, s1)),
% 292.21/184.76 inference(unit_resolution,[status(thm)],[16017, 16013])).
% 292.21/184.76 tff(16019,plain,
% 292.21/184.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_d, s1)) | (~node22(c_e_h_2, c_d, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_d, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_d, s1)) | (~node22(c_e_h_2, c_d, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_d, s0))),
% 292.21/184.76 inference(rewrite,[status(thm)],[])).
% 292.21/184.76 tff(16020,plain,
% 292.21/184.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_d, s1)) | (~node22(c_e_h_2, c_d, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_d, s0))),
% 292.21/184.76 inference(quant_inst,[status(thm)],[])).
% 292.21/184.77 tff(16021,plain,
% 292.21/184.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_d, s1)) | (~node22(c_e_h_2, c_d, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_d, s0)),
% 292.21/184.77 inference(modus_ponens,[status(thm)],[16020, 16019])).
% 292.21/184.77 tff(16022,plain,
% 292.21/184.77 ($false),
% 292.21/184.77 inference(unit_resolution,[status(thm)],[16021, 108, 16018, 2109, 15994])).
% 292.21/184.77 tff(16023,plain,(~m_and_h_gate_v_out(c_e_h_2, c_d, s1)), inference(lemma,lemma(discharge,[]))).
% 292.21/184.77 tff(16024,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_d, s1)), introduced(assumption)).
% 292.21/184.77 tff(16025,assumption,(m_or_h_gate_v_in2(c_e_h_2, c_g, s1)), introduced(assumption)).
% 292.21/184.77 tff(16026,plain,
% 292.21/184.77 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_g, s1)) | m_and_h_gate_v_out(c_e_h_2, c_d, s1))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_g, s1)) | m_and_h_gate_v_out(c_e_h_2, c_d, s1))),
% 292.21/184.77 inference(rewrite,[status(thm)],[])).
% 292.21/184.77 tff(16027,plain,
% 292.21/184.77 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_g, s1)) | m_and_h_gate_v_out(c_e_h_2, c_d, s1))),
% 292.21/184.77 inference(quant_inst,[status(thm)],[])).
% 292.21/184.77 tff(16028,plain,
% 292.21/184.77 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_g, s1)) | m_and_h_gate_v_out(c_e_h_2, c_d, s1)),
% 292.21/184.77 inference(modus_ponens,[status(thm)],[16027, 16026])).
% 292.21/184.77 tff(16029,plain,
% 292.21/184.77 ($false),
% 292.21/184.77 inference(unit_resolution,[status(thm)],[16028, 2762, 16025, 16024])).
% 292.21/184.77 tff(16030,plain,((~m_or_h_gate_v_in2(c_e_h_2, c_g, s1)) | m_and_h_gate_v_out(c_e_h_2, c_d, s1)), inference(lemma,lemma(discharge,[]))).
% 292.21/184.77 tff(16031,plain,
% 292.21/184.77 (~m_or_h_gate_v_in2(c_e_h_2, c_g, s1)),
% 292.21/184.77 inference(unit_resolution,[status(thm)],[16030, 16023])).
% 292.21/184.77 tff(16032,assumption,(m_and_h_gate_v_out(c_e_h_2, c_c, s1)), introduced(assumption)).
% 292.21/184.77 tff(16033,assumption,(m_mutex_h_half_v_out(c_e_h_2, c_a, s0)), introduced(assumption)).
% 292.21/184.77 tff(16034,plain,
% 292.21/184.77 ((~![I0: $i, I1: $i] : (~m_mutex_h_half_v_out(I0, I1, s0))) | (~m_mutex_h_half_v_out(c_e_h_2, c_a, s0))),
% 292.21/184.77 inference(quant_inst,[status(thm)],[])).
% 292.21/184.77 tff(16035,plain,
% 292.21/184.77 ($false),
% 292.21/184.77 inference(unit_resolution,[status(thm)],[16034, 409, 16033])).
% 292.21/184.77 tff(16036,plain,(~m_mutex_h_half_v_out(c_e_h_2, c_a, s0)), inference(lemma,lemma(discharge,[]))).
% 292.21/184.77 tff(16037,plain,
% 292.21/184.77 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_c, s0)) | m_mutex_h_half_v_out(c_e_h_2, c_a, s0))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_c, s0)) | m_mutex_h_half_v_out(c_e_h_2, c_a, s0))),
% 292.21/184.77 inference(rewrite,[status(thm)],[])).
% 292.21/184.77 tff(16038,plain,
% 292.21/184.77 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_c, s0)) | m_mutex_h_half_v_out(c_e_h_2, c_a, s0))),
% 292.21/184.77 inference(quant_inst,[status(thm)],[])).
% 292.21/184.77 tff(16039,plain,
% 292.21/184.77 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_c, s0)) | m_mutex_h_half_v_out(c_e_h_2, c_a, s0)),
% 292.21/184.77 inference(modus_ponens,[status(thm)],[16038, 16037])).
% 292.21/184.77 tff(16040,plain,
% 292.21/184.77 (~m_and_h_gate_v_in1(c_e_h_2, c_c, s0)),
% 292.21/184.77 inference(unit_resolution,[status(thm)],[16039, 567, 16036])).
% 292.21/184.77 tff(16041,plain,
% 292.21/184.77 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_c, s0)) | m_and_h_gate_v_in1(c_e_h_2, c_c, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_c, s0)) | m_and_h_gate_v_in1(c_e_h_2, c_c, s0))),
% 292.21/184.77 inference(rewrite,[status(thm)],[])).
% 292.21/184.77 tff(16042,plain,
% 292.21/184.77 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_c, s0)) | m_and_h_gate_v_in1(c_e_h_2, c_c, s0))),
% 292.21/184.77 inference(quant_inst,[status(thm)],[])).
% 292.21/184.77 tff(16043,plain,
% 292.21/184.77 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_c, s0)) | m_and_h_gate_v_in1(c_e_h_2, c_c, s0)),
% 292.21/184.77 inference(modus_ponens,[status(thm)],[16042, 16041])).
% 292.21/184.77 tff(16044,plain,
% 292.21/184.77 (~node20(c_e_h_2, c_c, s0)),
% 292.21/184.77 inference(unit_resolution,[status(thm)],[16043, 38, 16040])).
% 292.21/184.77 tff(16045,assumption,(node21(c_e_h_2, c_c, s0, s1)), introduced(assumption)).
% 292.21/184.77 tff(16046,plain,
% 292.21/184.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_c, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_c, s1)) | (~node21(c_e_h_2, c_c, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_c, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_c, s1)) | (~node21(c_e_h_2, c_c, s0, s1)))),
% 292.21/184.77 inference(rewrite,[status(thm)],[])).
% 292.21/184.77 tff(16047,plain,
% 292.21/184.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_c, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_c, s1)) | (~node21(c_e_h_2, c_c, s0, s1)))),
% 292.21/184.77 inference(quant_inst,[status(thm)],[])).
% 292.21/184.77 tff(16048,plain,
% 292.21/184.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_c, s0) | (~m_and_h_gate_v_out(c_e_h_2, c_c, s1)) | (~node21(c_e_h_2, c_c, s0, s1))),
% 292.21/184.77 inference(modus_ponens,[status(thm)],[16047, 16046])).
% 292.21/184.77 tff(16049,plain,
% 292.21/184.77 ($false),
% 292.21/184.77 inference(unit_resolution,[status(thm)],[16048, 52, 16045, 16044, 16032])).
% 292.21/184.77 tff(16050,plain,((~node21(c_e_h_2, c_c, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_2, c_c, s1))), inference(lemma,lemma(discharge,[]))).
% 292.21/184.77 tff(16051,plain,
% 292.21/184.77 (~node21(c_e_h_2, c_c, s0, s1)),
% 292.21/184.77 inference(unit_resolution,[status(thm)],[16050, 16032])).
% 292.21/184.77 tff(16052,plain,
% 292.21/184.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_2, c_c, s0, s1) | node22(c_e_h_2, c_c, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_2, c_c, s0, s1) | node22(c_e_h_2, c_c, s0, s1))),
% 292.21/184.77 inference(rewrite,[status(thm)],[])).
% 292.21/184.77 tff(16053,plain,
% 292.21/184.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_2, c_c, s0, s1) | node22(c_e_h_2, c_c, s0, s1))),
% 292.21/184.77 inference(quant_inst,[status(thm)],[])).
% 292.21/184.77 tff(16054,plain,
% 292.21/184.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_2, c_c, s0, s1) | node22(c_e_h_2, c_c, s0, s1)),
% 292.21/184.77 inference(modus_ponens,[status(thm)],[16053, 16052])).
% 292.21/184.77 tff(16055,plain,
% 292.21/184.77 (node21(c_e_h_2, c_c, s0, s1) | node22(c_e_h_2, c_c, s0, s1)),
% 292.21/184.77 inference(unit_resolution,[status(thm)],[16054, 82, 72])).
% 292.21/184.77 tff(16056,plain,
% 292.21/184.77 (node22(c_e_h_2, c_c, s0, s1)),
% 292.21/184.77 inference(unit_resolution,[status(thm)],[16055, 16051])).
% 292.21/184.77 tff(16057,plain,
% 292.21/184.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_c, s1)) | (~node22(c_e_h_2, c_c, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_c, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_c, s1)) | (~node22(c_e_h_2, c_c, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_c, s0))),
% 292.21/184.77 inference(rewrite,[status(thm)],[])).
% 292.21/184.77 tff(16058,plain,
% 292.21/184.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_c, s1)) | (~node22(c_e_h_2, c_c, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_c, s0))),
% 292.21/184.77 inference(quant_inst,[status(thm)],[])).
% 292.21/184.78 tff(16059,plain,
% 292.21/184.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_c, s1)) | (~node22(c_e_h_2, c_c, s0, s1)) | m_and_h_gate_v_out(c_e_h_2, c_c, s0)),
% 292.21/184.78 inference(modus_ponens,[status(thm)],[16058, 16057])).
% 292.21/184.78 tff(16060,plain,
% 292.21/184.78 ($false),
% 292.21/184.78 inference(unit_resolution,[status(thm)],[16059, 108, 4113, 16056, 16032])).
% 292.21/184.78 tff(16061,plain,(~m_and_h_gate_v_out(c_e_h_2, c_c, s1)), inference(lemma,lemma(discharge,[]))).
% 292.21/184.78 tff(16062,plain,
% 292.21/184.78 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_or_h_gate_v_in1(c_e_h_2, c_g, s1)) | m_and_h_gate_v_out(c_e_h_2, c_c, s1))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_g, s1)) | m_and_h_gate_v_out(c_e_h_2, c_c, s1))),
% 292.21/184.78 inference(rewrite,[status(thm)],[])).
% 292.21/184.78 tff(16063,plain,
% 292.21/184.78 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_or_h_gate_v_in1(c_e_h_2, c_g, s1)) | m_and_h_gate_v_out(c_e_h_2, c_c, s1))),
% 292.21/184.78 inference(quant_inst,[status(thm)],[])).
% 292.21/184.78 tff(16064,plain,
% 292.21/184.78 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_g, s1)) | m_and_h_gate_v_out(c_e_h_2, c_c, s1)),
% 292.21/184.78 inference(modus_ponens,[status(thm)],[16063, 16062])).
% 292.21/184.78 tff(16065,plain,
% 292.21/184.78 (~m_or_h_gate_v_in1(c_e_h_2, c_g, s1)),
% 292.21/184.78 inference(unit_resolution,[status(thm)],[16064, 2708, 16061])).
% 292.21/184.78 tff(16066,assumption,(m_or_h_gate_v_out(c_e_h_2, c_g, s2)), introduced(assumption)).
% 292.21/184.78 tff(16067,assumption,(~m_or_h_gate_v_in1(c_e_h_2, c_g, s1)), introduced(assumption)).
% 292.21/184.78 tff(16068,assumption,(~m_or_h_gate_v_in2(c_e_h_2, c_g, s1)), introduced(assumption)).
% 292.21/184.78 tff(16069,assumption,(~m_or_h_gate_v_out(c_e_h_2, c_g, s1)), introduced(assumption)).
% 292.21/184.78 tff(16070,assumption,(node6(c_e_h_2, c_g, s1, s2)), introduced(assumption)).
% 292.21/184.78 tff(16071,plain,
% 292.21/184.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_2, c_g, s1) | (~m_or_h_gate_v_out(c_e_h_2, c_g, s2)) | (~node6(c_e_h_2, c_g, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_g, s1) | (~m_or_h_gate_v_out(c_e_h_2, c_g, s2)) | (~node6(c_e_h_2, c_g, s1, s2)))),
% 292.21/184.78 inference(rewrite,[status(thm)],[])).
% 292.21/184.78 tff(16072,plain,
% 292.21/184.78 (((~node6(c_e_h_2, c_g, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_2, c_g, s2)) | m_or_h_gate_v_out(c_e_h_2, c_g, s1)) <=> (m_or_h_gate_v_out(c_e_h_2, c_g, s1) | (~m_or_h_gate_v_out(c_e_h_2, c_g, s2)) | (~node6(c_e_h_2, c_g, s1, s2)))),
% 292.21/184.78 inference(rewrite,[status(thm)],[])).
% 292.21/184.78 tff(16073,plain,
% 292.21/184.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_g, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_2, c_g, s2)) | m_or_h_gate_v_out(c_e_h_2, c_g, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_2, c_g, s1) | (~m_or_h_gate_v_out(c_e_h_2, c_g, s2)) | (~node6(c_e_h_2, c_g, s1, s2))))),
% 292.21/184.78 inference(monotonicity,[status(thm)],[16072])).
% 292.21/184.78 tff(16074,plain,
% 292.21/184.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_g, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_2, c_g, s2)) | m_or_h_gate_v_out(c_e_h_2, c_g, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_g, s1) | (~m_or_h_gate_v_out(c_e_h_2, c_g, s2)) | (~node6(c_e_h_2, c_g, s1, s2)))),
% 292.21/184.78 inference(transitivity,[status(thm)],[16073, 16071])).
% 292.21/184.78 tff(16075,plain,
% 292.21/184.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_g, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_2, c_g, s2)) | m_or_h_gate_v_out(c_e_h_2, c_g, s1))),
% 292.21/184.78 inference(quant_inst,[status(thm)],[])).
% 292.21/184.78 tff(16076,plain,
% 292.21/184.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_g, s1) | (~m_or_h_gate_v_out(c_e_h_2, c_g, s2)) | (~node6(c_e_h_2, c_g, s1, s2))),
% 292.21/184.78 inference(modus_ponens,[status(thm)],[16075, 16074])).
% 292.21/184.78 tff(16077,plain,
% 292.21/184.78 ($false),
% 292.21/184.78 inference(unit_resolution,[status(thm)],[16076, 1121, 16070, 16069, 16066])).
% 292.21/184.78 tff(16078,plain,((~node6(c_e_h_2, c_g, s1, s2)) | m_or_h_gate_v_out(c_e_h_2, c_g, s1) | (~m_or_h_gate_v_out(c_e_h_2, c_g, s2))), inference(lemma,lemma(discharge,[]))).
% 292.21/184.78 tff(16079,plain,
% 292.21/184.78 (~node6(c_e_h_2, c_g, s1, s2)),
% 292.21/184.78 inference(unit_resolution,[status(thm)],[16078, 16066, 16069])).
% 292.21/184.78 tff(16080,plain,
% 292.21/184.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s1, s2)) | node5(c_e_h_2, c_g, s1, s2) | node6(c_e_h_2, c_g, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s1, s2)) | node5(c_e_h_2, c_g, s1, s2) | node6(c_e_h_2, c_g, s1, s2))),
% 292.21/184.78 inference(rewrite,[status(thm)],[])).
% 292.21/184.78 tff(16081,plain,
% 292.21/184.78 ((node6(c_e_h_2, c_g, s1, s2) | node5(c_e_h_2, c_g, s1, s2) | (~trans(s1, s2))) <=> ((~trans(s1, s2)) | node5(c_e_h_2, c_g, s1, s2) | node6(c_e_h_2, c_g, s1, s2))),
% 292.21/184.78 inference(rewrite,[status(thm)],[])).
% 292.21/184.78 tff(16082,plain,
% 292.21/184.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_g, s1, s2) | node5(c_e_h_2, c_g, s1, s2) | (~trans(s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s1, s2)) | node5(c_e_h_2, c_g, s1, s2) | node6(c_e_h_2, c_g, s1, s2)))),
% 292.21/184.78 inference(monotonicity,[status(thm)],[16081])).
% 292.21/184.78 tff(16083,plain,
% 292.21/184.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_g, s1, s2) | node5(c_e_h_2, c_g, s1, s2) | (~trans(s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s1, s2)) | node5(c_e_h_2, c_g, s1, s2) | node6(c_e_h_2, c_g, s1, s2))),
% 292.21/184.78 inference(transitivity,[status(thm)],[16082, 16080])).
% 292.21/184.78 tff(16084,plain,
% 292.21/184.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_g, s1, s2) | node5(c_e_h_2, c_g, s1, s2) | (~trans(s1, s2)))),
% 292.21/184.78 inference(quant_inst,[status(thm)],[])).
% 292.21/184.78 tff(16085,plain,
% 292.21/184.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s1, s2)) | node5(c_e_h_2, c_g, s1, s2) | node6(c_e_h_2, c_g, s1, s2)),
% 292.21/184.78 inference(modus_ponens,[status(thm)],[16084, 16083])).
% 292.21/184.78 tff(16086,plain,
% 292.21/184.78 (node5(c_e_h_2, c_g, s1, s2) | node6(c_e_h_2, c_g, s1, s2)),
% 292.21/184.78 inference(unit_resolution,[status(thm)],[16085, 1141, 255])).
% 292.21/184.78 tff(16087,plain,
% 292.21/184.78 (node5(c_e_h_2, c_g, s1, s2)),
% 292.21/184.78 inference(unit_resolution,[status(thm)],[16086, 16079])).
% 292.21/184.78 tff(16088,plain,
% 292.21/184.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_2, c_g, s1) | (~m_or_h_gate_v_out(c_e_h_2, c_g, s2)) | m_or_h_gate_v_in1(c_e_h_2, c_g, s1) | (~node5(c_e_h_2, c_g, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_2, c_g, s1) | (~m_or_h_gate_v_out(c_e_h_2, c_g, s2)) | m_or_h_gate_v_in1(c_e_h_2, c_g, s1) | (~node5(c_e_h_2, c_g, s1, s2)))),
% 292.21/184.78 inference(rewrite,[status(thm)],[])).
% 292.21/184.78 tff(16089,plain,
% 292.21/184.78 ((m_or_h_gate_v_in1(c_e_h_2, c_g, s1) | m_or_h_gate_v_in2(c_e_h_2, c_g, s1) | (~node5(c_e_h_2, c_g, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_2, c_g, s2))) <=> (m_or_h_gate_v_in2(c_e_h_2, c_g, s1) | (~m_or_h_gate_v_out(c_e_h_2, c_g, s2)) | m_or_h_gate_v_in1(c_e_h_2, c_g, s1) | (~node5(c_e_h_2, c_g, s1, s2)))),
% 292.21/184.78 inference(rewrite,[status(thm)],[])).
% 292.21/184.78 tff(16090,plain,
% 292.21/184.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_g, s1) | m_or_h_gate_v_in2(c_e_h_2, c_g, s1) | (~node5(c_e_h_2, c_g, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_2, c_g, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_2, c_g, s1) | (~m_or_h_gate_v_out(c_e_h_2, c_g, s2)) | m_or_h_gate_v_in1(c_e_h_2, c_g, s1) | (~node5(c_e_h_2, c_g, s1, s2))))),
% 292.21/184.78 inference(monotonicity,[status(thm)],[16089])).
% 292.21/184.78 tff(16091,plain,
% 292.21/184.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_g, s1) | m_or_h_gate_v_in2(c_e_h_2, c_g, s1) | (~node5(c_e_h_2, c_g, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_2, c_g, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_2, c_g, s1) | (~m_or_h_gate_v_out(c_e_h_2, c_g, s2)) | m_or_h_gate_v_in1(c_e_h_2, c_g, s1) | (~node5(c_e_h_2, c_g, s1, s2)))),
% 292.21/184.78 inference(transitivity,[status(thm)],[16090, 16088])).
% 292.21/184.78 tff(16092,plain,
% 292.21/184.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_g, s1) | m_or_h_gate_v_in2(c_e_h_2, c_g, s1) | (~node5(c_e_h_2, c_g, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_2, c_g, s2)))),
% 292.21/184.78 inference(quant_inst,[status(thm)],[])).
% 292.21/184.78 tff(16093,plain,
% 292.21/184.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_2, c_g, s1) | (~m_or_h_gate_v_out(c_e_h_2, c_g, s2)) | m_or_h_gate_v_in1(c_e_h_2, c_g, s1) | (~node5(c_e_h_2, c_g, s1, s2))),
% 292.21/184.78 inference(modus_ponens,[status(thm)],[16092, 16091])).
% 292.21/184.78 tff(16094,plain,
% 292.21/184.78 ($false),
% 292.21/184.78 inference(unit_resolution,[status(thm)],[16093, 1159, 16087, 16068, 16067, 16066])).
% 292.21/184.78 tff(16095,plain,((~m_or_h_gate_v_out(c_e_h_2, c_g, s2)) | m_or_h_gate_v_in2(c_e_h_2, c_g, s1) | m_or_h_gate_v_in1(c_e_h_2, c_g, s1) | m_or_h_gate_v_out(c_e_h_2, c_g, s1)), inference(lemma,lemma(discharge,[]))).
% 292.21/184.78 tff(16096,plain,
% 292.21/184.78 ((~m_or_h_gate_v_out(c_e_h_2, c_g, s2)) | m_or_h_gate_v_in2(c_e_h_2, c_g, s1) | m_or_h_gate_v_out(c_e_h_2, c_g, s1)),
% 292.21/184.78 inference(unit_resolution,[status(thm)],[16095, 16065])).
% 292.21/184.78 tff(16097,plain,
% 292.21/184.78 ((~m_or_h_gate_v_out(c_e_h_2, c_g, s2)) | m_or_h_gate_v_in2(c_e_h_2, c_g, s1)),
% 292.21/184.78 inference(unit_resolution,[status(thm)],[16096, 4143])).
% 292.21/184.78 tff(16098,plain,
% 292.21/184.78 (~m_or_h_gate_v_out(c_e_h_2, c_g, s2)),
% 292.21/184.78 inference(unit_resolution,[status(thm)],[16097, 16031])).
% 292.21/184.78 tff(16099,plain,
% 292.21/184.78 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_k, s2)) | m_or_h_gate_v_out(c_e_h_2, c_g, s2))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_k, s2)) | m_or_h_gate_v_out(c_e_h_2, c_g, s2))),
% 292.21/184.78 inference(rewrite,[status(thm)],[])).
% 292.21/184.78 tff(16100,plain,
% 292.21/184.78 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_k, s2)) | m_or_h_gate_v_out(c_e_h_2, c_g, s2))),
% 292.21/184.78 inference(quant_inst,[status(thm)],[])).
% 292.21/184.78 tff(16101,plain,
% 292.21/184.78 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_k, s2)) | m_or_h_gate_v_out(c_e_h_2, c_g, s2)),
% 292.21/184.78 inference(modus_ponens,[status(thm)],[16100, 16099])).
% 292.21/184.79 tff(16102,plain,
% 292.21/184.79 (~m_and_h_gate_v_in1(c_e_h_2, c_k, s2)),
% 292.21/184.79 inference(unit_resolution,[status(thm)],[16101, 2048, 16098])).
% 292.21/184.79 tff(16103,plain,
% 292.21/184.79 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_k, s2)) | m_and_h_gate_v_in1(c_e_h_2, c_k, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_k, s2)) | m_and_h_gate_v_in1(c_e_h_2, c_k, s2))),
% 292.21/184.79 inference(rewrite,[status(thm)],[])).
% 292.21/184.79 tff(16104,plain,
% 292.21/184.79 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_k, s2)) | m_and_h_gate_v_in1(c_e_h_2, c_k, s2))),
% 292.21/184.79 inference(quant_inst,[status(thm)],[])).
% 292.21/184.79 tff(16105,plain,
% 292.21/184.79 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_k, s2)) | m_and_h_gate_v_in1(c_e_h_2, c_k, s2)),
% 292.21/184.79 inference(modus_ponens,[status(thm)],[16104, 16103])).
% 292.21/184.79 tff(16106,plain,
% 292.21/184.79 (~node20(c_e_h_2, c_k, s2)),
% 292.21/184.79 inference(unit_resolution,[status(thm)],[16105, 38, 16102])).
% 292.21/184.79 tff(16107,assumption,(node21(c_e_h_2, c_k, s2, s3)), introduced(assumption)).
% 292.21/184.79 tff(16108,plain,
% 292.21/184.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_k, s3)) | node20(c_e_h_2, c_k, s2) | (~node21(c_e_h_2, c_k, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_k, s3)) | node20(c_e_h_2, c_k, s2) | (~node21(c_e_h_2, c_k, s2, s3)))),
% 292.21/184.79 inference(rewrite,[status(thm)],[])).
% 292.21/184.79 tff(16109,plain,
% 292.21/184.79 ((node20(c_e_h_2, c_k, s2) | (~m_and_h_gate_v_out(c_e_h_2, c_k, s3)) | (~node21(c_e_h_2, c_k, s2, s3))) <=> ((~m_and_h_gate_v_out(c_e_h_2, c_k, s3)) | node20(c_e_h_2, c_k, s2) | (~node21(c_e_h_2, c_k, s2, s3)))),
% 292.21/184.79 inference(rewrite,[status(thm)],[])).
% 292.21/184.79 tff(16110,plain,
% 292.21/184.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_k, s2) | (~m_and_h_gate_v_out(c_e_h_2, c_k, s3)) | (~node21(c_e_h_2, c_k, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_k, s3)) | node20(c_e_h_2, c_k, s2) | (~node21(c_e_h_2, c_k, s2, s3))))),
% 292.21/184.79 inference(monotonicity,[status(thm)],[16109])).
% 292.21/184.79 tff(16111,plain,
% 292.21/184.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_k, s2) | (~m_and_h_gate_v_out(c_e_h_2, c_k, s3)) | (~node21(c_e_h_2, c_k, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_k, s3)) | node20(c_e_h_2, c_k, s2) | (~node21(c_e_h_2, c_k, s2, s3)))),
% 292.21/184.79 inference(transitivity,[status(thm)],[16110, 16108])).
% 292.21/184.79 tff(16112,plain,
% 292.21/184.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_k, s2) | (~m_and_h_gate_v_out(c_e_h_2, c_k, s3)) | (~node21(c_e_h_2, c_k, s2, s3)))),
% 292.21/184.79 inference(quant_inst,[status(thm)],[])).
% 292.21/184.79 tff(16113,plain,
% 292.21/184.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_k, s3)) | node20(c_e_h_2, c_k, s2) | (~node21(c_e_h_2, c_k, s2, s3))),
% 292.21/184.79 inference(modus_ponens,[status(thm)],[16112, 16111])).
% 292.21/184.79 tff(16114,plain,
% 292.21/184.79 ($false),
% 292.21/184.79 inference(unit_resolution,[status(thm)],[16113, 52, 16107, 15993, 16106])).
% 292.21/184.79 tff(16115,plain,((~node21(c_e_h_2, c_k, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_2, c_k, s3))), inference(lemma,lemma(discharge,[]))).
% 292.21/184.79 tff(16116,plain,
% 292.21/184.79 (~node21(c_e_h_2, c_k, s2, s3)),
% 292.21/184.79 inference(unit_resolution,[status(thm)],[16115, 15993])).
% 292.21/184.79 tff(16117,plain,
% 292.21/184.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_2, c_k, s2, s3) | node22(c_e_h_2, c_k, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_2, c_k, s2, s3) | node22(c_e_h_2, c_k, s2, s3))),
% 292.30/184.79 inference(rewrite,[status(thm)],[])).
% 292.30/184.79 tff(16118,plain,
% 292.30/184.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_2, c_k, s2, s3) | node22(c_e_h_2, c_k, s2, s3))),
% 292.30/184.79 inference(quant_inst,[status(thm)],[])).
% 292.30/184.79 tff(16119,plain,
% 292.30/184.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_2, c_k, s2, s3) | node22(c_e_h_2, c_k, s2, s3)),
% 292.30/184.79 inference(modus_ponens,[status(thm)],[16118, 16117])).
% 292.30/184.79 tff(16120,plain,
% 292.30/184.79 (node21(c_e_h_2, c_k, s2, s3) | node22(c_e_h_2, c_k, s2, s3)),
% 292.30/184.79 inference(unit_resolution,[status(thm)],[16119, 82, 318])).
% 292.30/184.79 tff(16121,plain,
% 292.30/184.79 (node22(c_e_h_2, c_k, s2, s3)),
% 292.30/184.79 inference(unit_resolution,[status(thm)],[16120, 16116])).
% 292.30/184.79 tff(16122,plain,
% 292.30/184.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_k, s3)) | (~node22(c_e_h_2, c_k, s2, s3)) | m_and_h_gate_v_out(c_e_h_2, c_k, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_k, s3)) | (~node22(c_e_h_2, c_k, s2, s3)) | m_and_h_gate_v_out(c_e_h_2, c_k, s2))),
% 292.30/184.79 inference(rewrite,[status(thm)],[])).
% 292.30/184.79 tff(16123,plain,
% 292.30/184.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_k, s3)) | (~node22(c_e_h_2, c_k, s2, s3)) | m_and_h_gate_v_out(c_e_h_2, c_k, s2))),
% 292.30/184.79 inference(quant_inst,[status(thm)],[])).
% 292.30/184.79 tff(16124,plain,
% 292.30/184.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_k, s3)) | (~node22(c_e_h_2, c_k, s2, s3)) | m_and_h_gate_v_out(c_e_h_2, c_k, s2)),
% 292.30/184.79 inference(modus_ponens,[status(thm)],[16123, 16122])).
% 292.30/184.79 tff(16125,plain,
% 292.30/184.79 ($false),
% 292.30/184.79 inference(unit_resolution,[status(thm)],[16124, 108, 16121, 15993, 13690])).
% 292.30/184.79 tff(16126,plain,(~m_and_h_gate_v_out(c_e_h_2, c_k, s3)), inference(lemma,lemma(discharge,[]))).
% 292.30/184.79 tff(16127,plain,
% 292.30/184.79 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_p, s3)) | m_and_h_gate_v_out(c_e_h_2, c_k, s3))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_p, s3)) | m_and_h_gate_v_out(c_e_h_2, c_k, s3))),
% 292.30/184.79 inference(rewrite,[status(thm)],[])).
% 292.30/184.79 tff(16128,plain,
% 292.30/184.79 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_p, s3)) | m_and_h_gate_v_out(c_e_h_2, c_k, s3))),
% 292.30/184.79 inference(quant_inst,[status(thm)],[])).
% 292.30/184.79 tff(16129,plain,
% 292.30/184.79 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_p, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_p, s3)) | m_and_h_gate_v_out(c_e_h_2, c_k, s3)),
% 292.30/184.79 inference(modus_ponens,[status(thm)],[16128, 16127])).
% 292.30/184.79 tff(16130,plain,
% 292.30/184.79 (~m_and_h_gate_v_in1(c_e_h_2, c_p, s3)),
% 292.30/184.79 inference(unit_resolution,[status(thm)],[16129, 3033, 16126])).
% 292.30/184.79 tff(16131,plain,
% 292.30/184.79 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_p, s3)) | m_and_h_gate_v_in1(c_e_h_2, c_p, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_p, s3)) | m_and_h_gate_v_in1(c_e_h_2, c_p, s3))),
% 292.30/184.79 inference(rewrite,[status(thm)],[])).
% 292.30/184.79 tff(16132,plain,
% 292.30/184.79 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_p, s3)) | m_and_h_gate_v_in1(c_e_h_2, c_p, s3))),
% 292.30/184.79 inference(quant_inst,[status(thm)],[])).
% 292.30/184.79 tff(16133,plain,
% 292.30/184.79 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_p, s3)) | m_and_h_gate_v_in1(c_e_h_2, c_p, s3)),
% 292.30/184.79 inference(modus_ponens,[status(thm)],[16132, 16131])).
% 292.30/184.79 tff(16134,plain,
% 292.30/184.79 (~node20(c_e_h_2, c_p, s3)),
% 292.30/184.79 inference(unit_resolution,[status(thm)],[16133, 38, 16130])).
% 292.30/184.79 tff(16135,assumption,(~node20(c_e_h_2, c_p, s3)), introduced(assumption)).
% 292.30/184.79 tff(16136,assumption,(node21(c_e_h_2, c_p, s3, s4)), introduced(assumption)).
% 292.30/184.79 tff(16137,plain,
% 292.30/184.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_p, s4)) | node20(c_e_h_2, c_p, s3) | (~node21(c_e_h_2, c_p, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_p, s4)) | node20(c_e_h_2, c_p, s3) | (~node21(c_e_h_2, c_p, s3, s4)))),
% 292.30/184.79 inference(rewrite,[status(thm)],[])).
% 292.30/184.79 tff(16138,plain,
% 292.30/184.79 ((node20(c_e_h_2, c_p, s3) | (~m_and_h_gate_v_out(c_e_h_2, c_p, s4)) | (~node21(c_e_h_2, c_p, s3, s4))) <=> ((~m_and_h_gate_v_out(c_e_h_2, c_p, s4)) | node20(c_e_h_2, c_p, s3) | (~node21(c_e_h_2, c_p, s3, s4)))),
% 292.30/184.79 inference(rewrite,[status(thm)],[])).
% 292.30/184.79 tff(16139,plain,
% 292.30/184.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_p, s3) | (~m_and_h_gate_v_out(c_e_h_2, c_p, s4)) | (~node21(c_e_h_2, c_p, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_p, s4)) | node20(c_e_h_2, c_p, s3) | (~node21(c_e_h_2, c_p, s3, s4))))),
% 292.30/184.79 inference(monotonicity,[status(thm)],[16138])).
% 292.30/184.79 tff(16140,plain,
% 292.30/184.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_p, s3) | (~m_and_h_gate_v_out(c_e_h_2, c_p, s4)) | (~node21(c_e_h_2, c_p, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_p, s4)) | node20(c_e_h_2, c_p, s3) | (~node21(c_e_h_2, c_p, s3, s4)))),
% 292.30/184.79 inference(transitivity,[status(thm)],[16139, 16137])).
% 292.30/184.79 tff(16141,plain,
% 292.30/184.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_p, s3) | (~m_and_h_gate_v_out(c_e_h_2, c_p, s4)) | (~node21(c_e_h_2, c_p, s3, s4)))),
% 292.30/184.79 inference(quant_inst,[status(thm)],[])).
% 292.30/184.79 tff(16142,plain,
% 292.30/184.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_p, s4)) | node20(c_e_h_2, c_p, s3) | (~node21(c_e_h_2, c_p, s3, s4))),
% 292.30/184.79 inference(modus_ponens,[status(thm)],[16141, 16140])).
% 292.30/184.79 tff(16143,plain,
% 292.30/184.79 ($false),
% 292.30/184.79 inference(unit_resolution,[status(thm)],[16142, 52, 16136, 15992, 16135])).
% 292.30/184.79 tff(16144,plain,((~node21(c_e_h_2, c_p, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_2, c_p, s4)) | node20(c_e_h_2, c_p, s3)), inference(lemma,lemma(discharge,[]))).
% 292.30/184.79 tff(16145,plain,
% 292.30/184.79 ((~node21(c_e_h_2, c_p, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_2, c_p, s4))),
% 292.30/184.79 inference(unit_resolution,[status(thm)],[16144, 16134])).
% 292.30/184.79 tff(16146,plain,
% 292.30/184.79 (~node21(c_e_h_2, c_p, s3, s4)),
% 292.30/184.79 inference(unit_resolution,[status(thm)],[16145, 15992])).
% 292.30/184.79 tff(16147,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_p, s3)), introduced(assumption)).
% 292.30/184.79 tff(16148,assumption,(node22(c_e_h_2, c_p, s3, s4)), introduced(assumption)).
% 292.30/184.79 tff(16149,plain,
% 292.30/184.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_p, s4)) | (~node22(c_e_h_2, c_p, s3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_p, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_p, s4)) | (~node22(c_e_h_2, c_p, s3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_p, s3))),
% 292.31/184.80 inference(rewrite,[status(thm)],[])).
% 292.31/184.80 tff(16150,plain,
% 292.31/184.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_p, s4)) | (~node22(c_e_h_2, c_p, s3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_p, s3))),
% 292.31/184.80 inference(quant_inst,[status(thm)],[])).
% 292.31/184.80 tff(16151,plain,
% 292.31/184.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_p, s4)) | (~node22(c_e_h_2, c_p, s3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_p, s3)),
% 292.31/184.80 inference(modus_ponens,[status(thm)],[16150, 16149])).
% 292.31/184.80 tff(16152,plain,
% 292.31/184.80 ($false),
% 292.31/184.80 inference(unit_resolution,[status(thm)],[16151, 108, 16148, 16147, 15992])).
% 292.31/184.80 tff(16153,plain,((~node22(c_e_h_2, c_p, s3, s4)) | m_and_h_gate_v_out(c_e_h_2, c_p, s3) | (~m_and_h_gate_v_out(c_e_h_2, c_p, s4))), inference(lemma,lemma(discharge,[]))).
% 292.31/184.80 tff(16154,plain,
% 292.31/184.80 (~node22(c_e_h_2, c_p, s3, s4)),
% 292.31/184.80 inference(unit_resolution,[status(thm)],[16153, 15992, 13787])).
% 292.31/184.80 tff(16155,plain,
% 292.31/184.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_2, c_p, s3, s4) | node22(c_e_h_2, c_p, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_2, c_p, s3, s4) | node22(c_e_h_2, c_p, s3, s4))),
% 292.31/184.80 inference(rewrite,[status(thm)],[])).
% 292.31/184.80 tff(16156,plain,
% 292.31/184.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_2, c_p, s3, s4) | node22(c_e_h_2, c_p, s3, s4))),
% 292.31/184.80 inference(quant_inst,[status(thm)],[])).
% 292.31/184.80 tff(16157,plain,
% 292.31/184.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_2, c_p, s3, s4) | node22(c_e_h_2, c_p, s3, s4)),
% 292.31/184.80 inference(modus_ponens,[status(thm)],[16156, 16155])).
% 292.31/184.80 tff(16158,plain,
% 292.31/184.80 (node21(c_e_h_2, c_p, s3, s4) | node22(c_e_h_2, c_p, s3, s4)),
% 292.31/184.80 inference(unit_resolution,[status(thm)],[16157, 82, 531])).
% 292.31/184.80 tff(16159,plain,
% 292.31/184.80 ($false),
% 292.31/184.80 inference(unit_resolution,[status(thm)],[16158, 16154, 16146])).
% 292.31/184.80 tff(16160,plain,(~m_and_h_gate_v_out(c_e_h_2, c_p, s4)), inference(lemma,lemma(discharge,[]))).
% 292.31/184.80 tff(16161,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_p, s4)), introduced(assumption)).
% 292.31/184.80 tff(16162,assumption,(m_cell_v_req(c_e_h_2, s4)), introduced(assumption)).
% 292.31/184.80 tff(16163,plain,
% 292.31/184.80 (((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | ((~m_cell_v_req(c_e_h_2, s4)) | m_and_h_gate_v_out(c_e_h_2, c_p, s4))) <=> ((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | (~m_cell_v_req(c_e_h_2, s4)) | m_and_h_gate_v_out(c_e_h_2, c_p, s4))),
% 292.31/184.80 inference(rewrite,[status(thm)],[])).
% 292.31/184.80 tff(16164,plain,
% 292.31/184.80 ((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | ((~m_cell_v_req(c_e_h_2, s4)) | m_and_h_gate_v_out(c_e_h_2, c_p, s4))),
% 292.31/184.80 inference(quant_inst,[status(thm)],[])).
% 292.31/184.80 tff(16165,plain,
% 292.31/184.80 ((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | (~m_cell_v_req(c_e_h_2, s4)) | m_and_h_gate_v_out(c_e_h_2, c_p, s4)),
% 292.31/184.80 inference(modus_ponens,[status(thm)],[16164, 16163])).
% 292.31/184.80 tff(16166,plain,
% 292.31/184.80 ($false),
% 292.31/184.80 inference(unit_resolution,[status(thm)],[16165, 2908, 16162, 16161])).
% 292.31/184.80 tff(16167,plain,((~m_cell_v_req(c_e_h_2, s4)) | m_and_h_gate_v_out(c_e_h_2, c_p, s4)), inference(lemma,lemma(discharge,[]))).
% 292.31/184.80 tff(16168,plain,
% 292.31/184.80 (~m_cell_v_req(c_e_h_2, s4)),
% 292.31/184.80 inference(unit_resolution,[status(thm)],[16167, 16160])).
% 292.31/184.80 tff(16169,plain,
% 292.31/184.80 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node1(c_e_h_1, c_e_h_2, s4))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node1(c_e_h_1, c_e_h_2, s4))),
% 292.31/184.80 inference(rewrite,[status(thm)],[])).
% 292.31/184.80 tff(16170,plain,
% 292.31/184.80 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node1(c_e_h_1, c_e_h_2, s4))),
% 292.31/184.80 inference(quant_inst,[status(thm)],[])).
% 292.31/184.80 tff(16171,plain,
% 292.31/184.80 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node1(c_e_h_1, c_e_h_2, s4)),
% 292.31/184.80 inference(modus_ponens,[status(thm)],[16170, 16169])).
% 292.31/184.80 tff(16172,plain,
% 292.31/184.80 (node1(c_e_h_1, c_e_h_2, s4)),
% 292.31/184.80 inference(unit_resolution,[status(thm)],[16171, 4166, 2919])).
% 292.31/184.80 tff(16173,plain,
% 292.31/184.80 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~m_mutex_h_half_v_inp(c_e_h_1, c_b, s4)) | m_cell_v_req(c_e_h_2, s4) | (~node1(c_e_h_1, c_e_h_2, s4)))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | (~m_mutex_h_half_v_inp(c_e_h_1, c_b, s4)) | m_cell_v_req(c_e_h_2, s4) | (~node1(c_e_h_1, c_e_h_2, s4)))),
% 292.31/184.80 inference(rewrite,[status(thm)],[])).
% 292.31/184.80 tff(16174,plain,
% 292.31/184.80 (((~node1(c_e_h_1, c_e_h_2, s4)) | m_cell_v_req(c_e_h_2, s4) | (~m_mutex_h_half_v_inp(c_e_h_1, c_b, s4))) <=> ((~m_mutex_h_half_v_inp(c_e_h_1, c_b, s4)) | m_cell_v_req(c_e_h_2, s4) | (~node1(c_e_h_1, c_e_h_2, s4)))),
% 292.31/184.80 inference(rewrite,[status(thm)],[])).
% 292.31/184.80 tff(16175,plain,
% 292.31/184.80 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_1, c_e_h_2, s4)) | m_cell_v_req(c_e_h_2, s4) | (~m_mutex_h_half_v_inp(c_e_h_1, c_b, s4)))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~m_mutex_h_half_v_inp(c_e_h_1, c_b, s4)) | m_cell_v_req(c_e_h_2, s4) | (~node1(c_e_h_1, c_e_h_2, s4))))),
% 292.31/184.80 inference(monotonicity,[status(thm)],[16174])).
% 292.31/184.80 tff(16176,plain,
% 292.31/184.80 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_1, c_e_h_2, s4)) | m_cell_v_req(c_e_h_2, s4) | (~m_mutex_h_half_v_inp(c_e_h_1, c_b, s4)))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | (~m_mutex_h_half_v_inp(c_e_h_1, c_b, s4)) | m_cell_v_req(c_e_h_2, s4) | (~node1(c_e_h_1, c_e_h_2, s4)))),
% 292.31/184.80 inference(transitivity,[status(thm)],[16175, 16173])).
% 292.31/184.80 tff(16177,plain,
% 292.31/184.80 ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_1, c_e_h_2, s4)) | m_cell_v_req(c_e_h_2, s4) | (~m_mutex_h_half_v_inp(c_e_h_1, c_b, s4)))),
% 292.31/184.80 inference(quant_inst,[status(thm)],[])).
% 292.31/184.80 tff(16178,plain,
% 292.31/184.80 ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | (~m_mutex_h_half_v_inp(c_e_h_1, c_b, s4)) | m_cell_v_req(c_e_h_2, s4) | (~node1(c_e_h_1, c_e_h_2, s4))),
% 292.31/184.80 inference(modus_ponens,[status(thm)],[16177, 16176])).
% 292.31/184.80 tff(16179,plain,
% 292.31/184.80 ((~m_mutex_h_half_v_inp(c_e_h_1, c_b, s4)) | m_cell_v_req(c_e_h_2, s4)),
% 292.31/184.80 inference(unit_resolution,[status(thm)],[16178, 2936, 16172])).
% 292.31/184.80 tff(16180,plain,
% 292.31/184.80 (~m_mutex_h_half_v_inp(c_e_h_1, c_b, s4)),
% 292.31/184.80 inference(unit_resolution,[status(thm)],[16179, 16168])).
% 292.31/184.80 tff(16181,assumption,(m_mutex_h_half_v_out(c_e_h_1, c_b, s5)), introduced(assumption)).
% 292.31/184.80 tff(16182,assumption,(~m_mutex_h_half_v_inp(c_e_h_1, c_b, s4)), introduced(assumption)).
% 292.31/184.80 tff(16183,assumption,(node12(c_e_h_1, c_b, s4, s5)), introduced(assumption)).
% 292.31/184.80 tff(16184,plain,
% 292.31/184.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_1, c_b, s4, s5)) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s5)) | m_mutex_h_half_v_inp(c_e_h_1, c_b, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (~node12(c_e_h_1, c_b, s4, s5)) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s5)) | m_mutex_h_half_v_inp(c_e_h_1, c_b, s4))),
% 292.31/184.81 inference(rewrite,[status(thm)],[])).
% 292.31/184.81 tff(16185,plain,
% 292.31/184.81 (((~node12(c_e_h_1, c_b, s4, s5)) | m_mutex_h_half_v_inp(c_e_h_1, c_b, s4) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s5))) <=> ((~node12(c_e_h_1, c_b, s4, s5)) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s5)) | m_mutex_h_half_v_inp(c_e_h_1, c_b, s4))),
% 292.31/184.81 inference(rewrite,[status(thm)],[])).
% 292.31/184.81 tff(16186,plain,
% 292.31/184.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_1, c_b, s4, s5)) | m_mutex_h_half_v_inp(c_e_h_1, c_b, s4) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_1, c_b, s4, s5)) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s5)) | m_mutex_h_half_v_inp(c_e_h_1, c_b, s4)))),
% 292.31/184.81 inference(monotonicity,[status(thm)],[16185])).
% 292.31/184.81 tff(16187,plain,
% 292.31/184.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_1, c_b, s4, s5)) | m_mutex_h_half_v_inp(c_e_h_1, c_b, s4) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (~node12(c_e_h_1, c_b, s4, s5)) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s5)) | m_mutex_h_half_v_inp(c_e_h_1, c_b, s4))),
% 292.31/184.81 inference(transitivity,[status(thm)],[16186, 16184])).
% 292.31/184.81 tff(16188,plain,
% 292.31/184.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_1, c_b, s4, s5)) | m_mutex_h_half_v_inp(c_e_h_1, c_b, s4) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s5)))),
% 292.31/184.81 inference(quant_inst,[status(thm)],[])).
% 292.31/184.81 tff(16189,plain,
% 292.31/184.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (~node12(c_e_h_1, c_b, s4, s5)) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s5)) | m_mutex_h_half_v_inp(c_e_h_1, c_b, s4)),
% 292.31/184.81 inference(modus_ponens,[status(thm)],[16188, 16187])).
% 292.31/184.81 tff(16190,plain,
% 292.31/184.81 ($false),
% 292.31/184.81 inference(unit_resolution,[status(thm)],[16189, 454, 16183, 16182, 16181])).
% 292.31/184.81 tff(16191,plain,((~node12(c_e_h_1, c_b, s4, s5)) | m_mutex_h_half_v_inp(c_e_h_1, c_b, s4) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s5))), inference(lemma,lemma(discharge,[]))).
% 292.31/184.81 tff(16192,plain,
% 292.31/184.81 (~node12(c_e_h_1, c_b, s4, s5)),
% 292.31/184.81 inference(unit_resolution,[status(thm)],[16191, 16181, 16182])).
% 292.31/184.81 tff(16193,plain,
% 292.31/184.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s4, s5)) | node12(c_e_h_1, c_b, s4, s5) | node13(c_e_h_1, c_b, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s4, s5)) | node12(c_e_h_1, c_b, s4, s5) | node13(c_e_h_1, c_b, s4, s5))),
% 292.31/184.81 inference(rewrite,[status(thm)],[])).
% 292.31/184.81 tff(16194,plain,
% 292.31/184.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s4, s5)) | node12(c_e_h_1, c_b, s4, s5) | node13(c_e_h_1, c_b, s4, s5))),
% 292.31/184.81 inference(quant_inst,[status(thm)],[])).
% 292.31/184.81 tff(16195,plain,
% 292.31/184.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s4, s5)) | node12(c_e_h_1, c_b, s4, s5) | node13(c_e_h_1, c_b, s4, s5)),
% 292.31/184.81 inference(modus_ponens,[status(thm)],[16194, 16193])).
% 292.31/184.81 tff(16196,plain,
% 292.31/184.81 (node12(c_e_h_1, c_b, s4, s5) | node13(c_e_h_1, c_b, s4, s5)),
% 292.31/184.81 inference(unit_resolution,[status(thm)],[16195, 439, 1028])).
% 292.31/184.81 tff(16197,plain,
% 292.31/184.81 (node13(c_e_h_1, c_b, s4, s5)),
% 292.31/184.81 inference(unit_resolution,[status(thm)],[16196, 16192])).
% 292.31/184.81 tff(16198,plain,
% 292.31/184.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_1, c_b, s5)) | (~node13(c_e_h_1, c_b, s4, s5)) | m_mutex_h_half_v_out(c_e_h_1, c_b, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s5)) | (~node13(c_e_h_1, c_b, s4, s5)) | m_mutex_h_half_v_out(c_e_h_1, c_b, s4))),
% 292.31/184.81 inference(rewrite,[status(thm)],[])).
% 292.31/184.81 tff(16199,plain,
% 292.31/184.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_1, c_b, s5)) | (~node13(c_e_h_1, c_b, s4, s5)) | m_mutex_h_half_v_out(c_e_h_1, c_b, s4))),
% 292.31/184.81 inference(quant_inst,[status(thm)],[])).
% 292.31/184.81 tff(16200,plain,
% 292.31/184.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_1, c_b, s5)) | (~node13(c_e_h_1, c_b, s4, s5)) | m_mutex_h_half_v_out(c_e_h_1, c_b, s4)),
% 292.31/184.81 inference(modus_ponens,[status(thm)],[16199, 16198])).
% 292.31/184.81 tff(16201,plain,
% 292.31/184.81 ($false),
% 292.31/184.81 inference(unit_resolution,[status(thm)],[16200, 423, 16197, 13948, 16181])).
% 292.31/184.81 tff(16202,plain,((~m_mutex_h_half_v_out(c_e_h_1, c_b, s5)) | m_mutex_h_half_v_out(c_e_h_1, c_b, s4) | m_mutex_h_half_v_inp(c_e_h_1, c_b, s4)), inference(lemma,lemma(discharge,[]))).
% 292.31/184.81 tff(16203,plain,
% 292.31/184.81 (~m_mutex_h_half_v_out(c_e_h_1, c_b, s5)),
% 292.31/184.81 inference(unit_resolution,[status(thm)],[16202, 16180, 13946])).
% 292.31/184.81 tff(16204,assumption,(m_and_h_gate_v_in1(c_e_h_1, c_d, s5)), introduced(assumption)).
% 292.31/184.81 tff(16205,assumption,(~m_mutex_h_half_v_out(c_e_h_1, c_b, s5)), introduced(assumption)).
% 292.31/184.81 tff(16206,plain,
% 292.31/184.81 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_d, s5)) | m_mutex_h_half_v_out(c_e_h_1, c_b, s5))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_d, s5)) | m_mutex_h_half_v_out(c_e_h_1, c_b, s5))),
% 292.31/184.81 inference(rewrite,[status(thm)],[])).
% 292.31/184.81 tff(16207,plain,
% 292.31/184.81 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_d, s5)) | m_mutex_h_half_v_out(c_e_h_1, c_b, s5))),
% 292.31/184.81 inference(quant_inst,[status(thm)],[])).
% 292.31/184.81 tff(16208,plain,
% 292.31/184.81 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_d, s5)) | m_mutex_h_half_v_out(c_e_h_1, c_b, s5)),
% 292.31/184.81 inference(modus_ponens,[status(thm)],[16207, 16206])).
% 292.31/184.81 tff(16209,plain,
% 292.31/184.81 ($false),
% 292.31/184.81 inference(unit_resolution,[status(thm)],[16208, 2808, 16205, 16204])).
% 292.31/184.81 tff(16210,plain,(m_mutex_h_half_v_out(c_e_h_1, c_b, s5) | (~m_and_h_gate_v_in1(c_e_h_1, c_d, s5))), inference(lemma,lemma(discharge,[]))).
% 292.31/184.81 tff(16211,plain,
% 292.31/184.81 (~m_and_h_gate_v_in1(c_e_h_1, c_d, s5)),
% 292.31/184.81 inference(unit_resolution,[status(thm)],[16210, 16203])).
% 292.31/184.81 tff(16212,assumption,(~m_and_h_gate_v_in1(c_e_h_1, c_d, s5)), introduced(assumption)).
% 292.31/184.81 tff(16213,assumption,(node20(c_e_h_1, c_d, s5)), introduced(assumption)).
% 292.31/184.81 tff(16214,plain,
% 292.31/184.81 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_d, s5)) | m_and_h_gate_v_in1(c_e_h_1, c_d, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_d, s5)) | m_and_h_gate_v_in1(c_e_h_1, c_d, s5))),
% 292.31/184.81 inference(rewrite,[status(thm)],[])).
% 292.31/184.81 tff(16215,plain,
% 292.31/184.81 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_d, s5)) | m_and_h_gate_v_in1(c_e_h_1, c_d, s5))),
% 292.31/184.81 inference(quant_inst,[status(thm)],[])).
% 292.31/184.81 tff(16216,plain,
% 292.31/184.81 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_d, s5)) | m_and_h_gate_v_in1(c_e_h_1, c_d, s5)),
% 292.31/184.81 inference(modus_ponens,[status(thm)],[16215, 16214])).
% 292.31/184.81 tff(16217,plain,
% 292.31/184.81 ($false),
% 292.31/184.81 inference(unit_resolution,[status(thm)],[16216, 38, 16213, 16212])).
% 292.31/184.81 tff(16218,plain,(m_and_h_gate_v_in1(c_e_h_1, c_d, s5) | (~node20(c_e_h_1, c_d, s5))), inference(lemma,lemma(discharge,[]))).
% 292.31/184.81 tff(16219,plain,
% 292.31/184.81 (~node20(c_e_h_1, c_d, s5)),
% 292.31/184.81 inference(unit_resolution,[status(thm)],[16218, 16211])).
% 292.31/184.81 tff(16220,assumption,(m_and_h_gate_v_out(c_e_h_1, c_d, s6)), introduced(assumption)).
% 292.31/184.81 tff(16221,assumption,(~node20(c_e_h_1, c_d, s5)), introduced(assumption)).
% 292.31/184.81 tff(16222,assumption,(node21(c_e_h_1, c_d, s5, s6)), introduced(assumption)).
% 292.31/184.81 tff(16223,plain,
% 292.31/184.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_d, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s6)) | (~node21(c_e_h_1, c_d, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_d, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s6)) | (~node21(c_e_h_1, c_d, s5, s6)))),
% 292.31/184.81 inference(rewrite,[status(thm)],[])).
% 292.31/184.81 tff(16224,plain,
% 292.31/184.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_d, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s6)) | (~node21(c_e_h_1, c_d, s5, s6)))),
% 292.31/184.81 inference(quant_inst,[status(thm)],[])).
% 292.31/184.81 tff(16225,plain,
% 292.31/184.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_d, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s6)) | (~node21(c_e_h_1, c_d, s5, s6))),
% 292.31/184.81 inference(modus_ponens,[status(thm)],[16224, 16223])).
% 292.31/184.81 tff(16226,plain,
% 292.31/184.81 ($false),
% 292.31/184.81 inference(unit_resolution,[status(thm)],[16225, 52, 16222, 16221, 16220])).
% 292.31/184.81 tff(16227,plain,((~node21(c_e_h_1, c_d, s5, s6)) | node20(c_e_h_1, c_d, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s6))), inference(lemma,lemma(discharge,[]))).
% 292.31/184.81 tff(16228,plain,
% 292.31/184.81 (~node21(c_e_h_1, c_d, s5, s6)),
% 292.31/184.81 inference(unit_resolution,[status(thm)],[16227, 16220, 16221])).
% 292.31/184.81 tff(16229,plain,
% 292.31/184.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_1, c_d, s5, s6) | node22(c_e_h_1, c_d, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_1, c_d, s5, s6) | node22(c_e_h_1, c_d, s5, s6))),
% 292.31/184.81 inference(rewrite,[status(thm)],[])).
% 292.31/184.81 tff(16230,plain,
% 292.31/184.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_1, c_d, s5, s6) | node22(c_e_h_1, c_d, s5, s6))),
% 292.31/184.81 inference(quant_inst,[status(thm)],[])).
% 292.31/184.81 tff(16231,plain,
% 292.31/184.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_1, c_d, s5, s6) | node22(c_e_h_1, c_d, s5, s6)),
% 292.31/184.81 inference(modus_ponens,[status(thm)],[16230, 16229])).
% 292.31/184.81 tff(16232,plain,
% 292.31/184.81 (node21(c_e_h_1, c_d, s5, s6) | node22(c_e_h_1, c_d, s5, s6)),
% 292.31/184.81 inference(unit_resolution,[status(thm)],[16231, 82, 1406])).
% 292.31/184.81 tff(16233,plain,
% 292.31/184.81 (node22(c_e_h_1, c_d, s5, s6)),
% 292.31/184.81 inference(unit_resolution,[status(thm)],[16232, 16228])).
% 292.31/184.81 tff(16234,plain,
% 292.31/184.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_d, s6)) | (~node22(c_e_h_1, c_d, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_d, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s6)) | (~node22(c_e_h_1, c_d, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_d, s5))),
% 292.31/184.81 inference(rewrite,[status(thm)],[])).
% 292.31/184.81 tff(16235,plain,
% 292.31/184.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_d, s6)) | (~node22(c_e_h_1, c_d, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_d, s5))),
% 292.31/184.82 inference(quant_inst,[status(thm)],[])).
% 292.31/184.82 tff(16236,plain,
% 292.31/184.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_d, s6)) | (~node22(c_e_h_1, c_d, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_d, s5)),
% 292.31/184.82 inference(modus_ponens,[status(thm)],[16235, 16234])).
% 292.31/184.82 tff(16237,plain,
% 292.31/184.82 ($false),
% 292.31/184.82 inference(unit_resolution,[status(thm)],[16236, 108, 16233, 14094, 16220])).
% 292.31/184.82 tff(16238,plain,((~m_and_h_gate_v_out(c_e_h_1, c_d, s6)) | m_and_h_gate_v_out(c_e_h_1, c_d, s5) | node20(c_e_h_1, c_d, s5)), inference(lemma,lemma(discharge,[]))).
% 292.31/184.82 tff(16239,plain,
% 292.31/184.82 (~m_and_h_gate_v_out(c_e_h_1, c_d, s6)),
% 292.31/184.82 inference(unit_resolution,[status(thm)],[16238, 16219, 14092])).
% 292.31/184.82 tff(16240,plain,
% 292.31/184.82 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_g, s6)) | m_and_h_gate_v_out(c_e_h_1, c_d, s6))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_g, s6)) | m_and_h_gate_v_out(c_e_h_1, c_d, s6))),
% 292.31/184.82 inference(rewrite,[status(thm)],[])).
% 292.31/184.82 tff(16241,plain,
% 292.31/184.82 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_g, s6)) | m_and_h_gate_v_out(c_e_h_1, c_d, s6))),
% 292.31/184.82 inference(quant_inst,[status(thm)],[])).
% 292.31/184.82 tff(16242,plain,
% 292.31/184.82 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_g, s6)) | m_and_h_gate_v_out(c_e_h_1, c_d, s6)),
% 292.31/184.82 inference(modus_ponens,[status(thm)],[16241, 16240])).
% 292.31/184.82 tff(16243,plain,
% 292.31/184.82 (~m_or_h_gate_v_in2(c_e_h_1, c_g, s6)),
% 292.31/184.82 inference(unit_resolution,[status(thm)],[16242, 2762, 16239])).
% 292.31/184.82 tff(16244,assumption,(~m_or_h_gate_v_in2(c_e_h_1, c_g, s6)), introduced(assumption)).
% 292.31/184.82 tff(16245,assumption,(node5(c_e_h_1, c_g, s6, s7)), introduced(assumption)).
% 292.31/184.82 tff(16246,plain,
% 292.31/184.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_1, c_g, s7)) | m_or_h_gate_v_in2(c_e_h_1, c_g, s6) | m_or_h_gate_v_in1(c_e_h_1, c_g, s6) | (~node5(c_e_h_1, c_g, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s7)) | m_or_h_gate_v_in2(c_e_h_1, c_g, s6) | m_or_h_gate_v_in1(c_e_h_1, c_g, s6) | (~node5(c_e_h_1, c_g, s6, s7)))),
% 292.31/184.82 inference(rewrite,[status(thm)],[])).
% 292.31/184.82 tff(16247,plain,
% 292.31/184.82 ((m_or_h_gate_v_in1(c_e_h_1, c_g, s6) | m_or_h_gate_v_in2(c_e_h_1, c_g, s6) | (~node5(c_e_h_1, c_g, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s7))) <=> ((~m_or_h_gate_v_out(c_e_h_1, c_g, s7)) | m_or_h_gate_v_in2(c_e_h_1, c_g, s6) | m_or_h_gate_v_in1(c_e_h_1, c_g, s6) | (~node5(c_e_h_1, c_g, s6, s7)))),
% 292.31/184.82 inference(rewrite,[status(thm)],[])).
% 292.31/184.82 tff(16248,plain,
% 292.31/184.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_g, s6) | m_or_h_gate_v_in2(c_e_h_1, c_g, s6) | (~node5(c_e_h_1, c_g, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_1, c_g, s7)) | m_or_h_gate_v_in2(c_e_h_1, c_g, s6) | m_or_h_gate_v_in1(c_e_h_1, c_g, s6) | (~node5(c_e_h_1, c_g, s6, s7))))),
% 292.31/184.82 inference(monotonicity,[status(thm)],[16247])).
% 292.31/184.82 tff(16249,plain,
% 292.31/184.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_g, s6) | m_or_h_gate_v_in2(c_e_h_1, c_g, s6) | (~node5(c_e_h_1, c_g, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s7)) | m_or_h_gate_v_in2(c_e_h_1, c_g, s6) | m_or_h_gate_v_in1(c_e_h_1, c_g, s6) | (~node5(c_e_h_1, c_g, s6, s7)))),
% 292.31/184.82 inference(transitivity,[status(thm)],[16248, 16246])).
% 292.31/184.82 tff(16250,plain,
% 292.31/184.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_g, s6) | m_or_h_gate_v_in2(c_e_h_1, c_g, s6) | (~node5(c_e_h_1, c_g, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s7)))),
% 292.31/184.82 inference(quant_inst,[status(thm)],[])).
% 292.31/184.82 tff(16251,plain,
% 292.31/184.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s7)) | m_or_h_gate_v_in2(c_e_h_1, c_g, s6) | m_or_h_gate_v_in1(c_e_h_1, c_g, s6) | (~node5(c_e_h_1, c_g, s6, s7))),
% 292.31/184.82 inference(modus_ponens,[status(thm)],[16250, 16249])).
% 292.31/184.82 tff(16252,plain,
% 292.31/184.82 ($false),
% 292.31/184.82 inference(unit_resolution,[status(thm)],[16251, 1159, 16245, 15952, 15991, 16244])).
% 292.31/184.82 tff(16253,plain,((~node5(c_e_h_1, c_g, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s7)) | m_or_h_gate_v_in1(c_e_h_1, c_g, s6) | m_or_h_gate_v_in2(c_e_h_1, c_g, s6)), inference(lemma,lemma(discharge,[]))).
% 292.31/184.82 tff(16254,plain,
% 292.31/184.82 ((~node5(c_e_h_1, c_g, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s7)) | m_or_h_gate_v_in1(c_e_h_1, c_g, s6)),
% 292.31/184.82 inference(unit_resolution,[status(thm)],[16253, 16243])).
% 292.31/184.82 tff(16255,plain,
% 292.31/184.82 (~node5(c_e_h_1, c_g, s6, s7)),
% 292.31/184.82 inference(unit_resolution,[status(thm)],[16254, 15952, 15991])).
% 292.31/184.82 tff(16256,plain,
% 292.31/184.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s6, s7)) | node5(c_e_h_1, c_g, s6, s7) | node6(c_e_h_1, c_g, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s6, s7)) | node5(c_e_h_1, c_g, s6, s7) | node6(c_e_h_1, c_g, s6, s7))),
% 292.31/184.82 inference(rewrite,[status(thm)],[])).
% 292.31/184.82 tff(16257,plain,
% 292.31/184.82 ((node6(c_e_h_1, c_g, s6, s7) | node5(c_e_h_1, c_g, s6, s7) | (~trans(s6, s7))) <=> ((~trans(s6, s7)) | node5(c_e_h_1, c_g, s6, s7) | node6(c_e_h_1, c_g, s6, s7))),
% 292.31/184.82 inference(rewrite,[status(thm)],[])).
% 292.31/184.82 tff(16258,plain,
% 292.31/184.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_g, s6, s7) | node5(c_e_h_1, c_g, s6, s7) | (~trans(s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s6, s7)) | node5(c_e_h_1, c_g, s6, s7) | node6(c_e_h_1, c_g, s6, s7)))),
% 292.31/184.82 inference(monotonicity,[status(thm)],[16257])).
% 292.31/184.82 tff(16259,plain,
% 292.31/184.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_g, s6, s7) | node5(c_e_h_1, c_g, s6, s7) | (~trans(s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s6, s7)) | node5(c_e_h_1, c_g, s6, s7) | node6(c_e_h_1, c_g, s6, s7))),
% 292.31/184.82 inference(transitivity,[status(thm)],[16258, 16256])).
% 292.31/184.82 tff(16260,plain,
% 292.31/184.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_g, s6, s7) | node5(c_e_h_1, c_g, s6, s7) | (~trans(s6, s7)))),
% 292.31/184.82 inference(quant_inst,[status(thm)],[])).
% 292.31/184.82 tff(16261,plain,
% 292.31/184.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s6, s7)) | node5(c_e_h_1, c_g, s6, s7) | node6(c_e_h_1, c_g, s6, s7)),
% 292.31/184.82 inference(modus_ponens,[status(thm)],[16260, 16259])).
% 292.31/184.82 tff(16262,plain,
% 292.31/184.82 (node5(c_e_h_1, c_g, s6, s7) | node6(c_e_h_1, c_g, s6, s7)),
% 292.31/184.82 inference(unit_resolution,[status(thm)],[16261, 1141, 1844])).
% 292.31/184.82 tff(16263,plain,
% 292.31/184.82 ($false),
% 292.31/184.82 inference(unit_resolution,[status(thm)],[16262, 16255, 15990])).
% 292.31/184.82 tff(16264,plain,((~m_or_h_gate_v_out(c_e_h_1, c_g, s7)) | m_or_h_gate_v_in1(c_e_h_1, c_g, s6) | m_or_h_gate_v_out(c_e_h_1, c_g, s6)), inference(lemma,lemma(discharge,[]))).
% 292.31/184.82 tff(16265,plain,
% 292.31/184.82 (m_or_h_gate_v_in1(c_e_h_1, c_g, s6)),
% 292.31/184.82 inference(unit_resolution,[status(thm)],[16264, 15952, 15389])).
% 292.31/184.82 tff(16266,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_c, s7)), introduced(assumption)).
% 292.31/184.82 tff(16267,assumption,(~m_user_v_req(c_e_h_1, c_u, s5)), introduced(assumption)).
% 292.31/184.82 tff(16268,assumption,(m_and_h_gate_v_out(c_e_h_1, c_c, s6)), introduced(assumption)).
% 292.31/184.82 tff(16269,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s4)), introduced(assumption)).
% 292.31/184.82 tff(16270,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)), introduced(assumption)).
% 292.31/184.82 tff(16271,assumption,(node10(c_e_h_1, c_n, s1, s2)), introduced(assumption)).
% 292.31/184.82 tff(16272,plain,
% 292.31/184.82 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1))),
% 292.31/184.82 inference(rewrite,[status(thm)],[])).
% 292.31/184.82 tff(16273,plain,
% 292.31/184.82 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1))),
% 292.31/184.82 inference(quant_inst,[status(thm)],[])).
% 292.31/184.82 tff(16274,plain,
% 292.31/184.82 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)),
% 292.31/184.82 inference(modus_ponens,[status(thm)],[16273, 16272])).
% 292.31/184.82 tff(16275,plain,
% 292.31/184.82 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)),
% 292.31/184.82 inference(unit_resolution,[status(thm)],[16274, 7868])).
% 292.31/184.82 tff(16276,plain,
% 292.31/184.82 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1)),
% 292.31/184.82 inference(unit_resolution,[status(thm)],[16275, 14710])).
% 292.31/184.82 tff(16277,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s1)), introduced(assumption)).
% 292.31/184.82 tff(16278,plain,
% 292.31/184.82 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s0)) | m_and_h_gate_v_out(c_e_h_1, c_c, s0))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s0)) | m_and_h_gate_v_out(c_e_h_1, c_c, s0))),
% 292.31/184.82 inference(rewrite,[status(thm)],[])).
% 292.31/184.82 tff(16279,plain,
% 292.31/184.82 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s0)) | m_and_h_gate_v_out(c_e_h_1, c_c, s0))),
% 292.31/184.82 inference(quant_inst,[status(thm)],[])).
% 292.31/184.82 tff(16280,plain,
% 292.31/184.82 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s0)) | m_and_h_gate_v_out(c_e_h_1, c_c, s0)),
% 292.31/184.82 inference(modus_ponens,[status(thm)],[16279, 16278])).
% 292.31/184.82 tff(16281,plain,
% 292.31/184.82 (~m_c_h_element_v_in1(c_e_h_1, c_e, s0)),
% 292.31/184.82 inference(unit_resolution,[status(thm)],[16280, 131, 9548])).
% 292.31/184.82 tff(16282,assumption,(node14(c_e_h_1, c_e, s0, s1)), introduced(assumption)).
% 292.31/184.82 tff(16283,plain,
% 292.31/184.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s1)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~node14(c_e_h_1, c_e, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~node14(c_e_h_1, c_e, s0, s1)))),
% 292.31/184.82 inference(rewrite,[status(thm)],[])).
% 292.31/184.82 tff(16284,plain,
% 292.31/184.82 (((~node14(c_e_h_1, c_e, s0, s1)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_e, s1)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~node14(c_e_h_1, c_e, s0, s1)))),
% 292.31/184.83 inference(rewrite,[status(thm)],[])).
% 292.31/184.83 tff(16285,plain,
% 292.31/184.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s0, s1)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s1)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~node14(c_e_h_1, c_e, s0, s1))))),
% 292.31/184.83 inference(monotonicity,[status(thm)],[16284])).
% 292.31/184.83 tff(16286,plain,
% 292.31/184.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s0, s1)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~node14(c_e_h_1, c_e, s0, s1)))),
% 292.31/184.83 inference(transitivity,[status(thm)],[16285, 16283])).
% 292.31/184.83 tff(16287,plain,
% 292.31/184.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s0, s1)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1)))),
% 292.31/184.83 inference(quant_inst,[status(thm)],[])).
% 292.31/184.83 tff(16288,plain,
% 292.31/184.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~node14(c_e_h_1, c_e, s0, s1))),
% 292.31/184.83 inference(modus_ponens,[status(thm)],[16287, 16286])).
% 292.31/184.83 tff(16289,plain,
% 292.31/184.83 ($false),
% 292.31/184.83 inference(unit_resolution,[status(thm)],[16288, 223, 16277, 16282, 16281])).
% 292.31/184.83 tff(16290,plain,((~node14(c_e_h_1, c_e, s0, s1)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1))), inference(lemma,lemma(discharge,[]))).
% 292.31/184.83 tff(16291,plain,
% 292.31/184.83 (~node14(c_e_h_1, c_e, s0, s1)),
% 292.31/184.83 inference(unit_resolution,[status(thm)],[16290, 16277])).
% 292.31/184.83 tff(16292,assumption,(node15(c_e_h_1, c_e, s0, s1)), introduced(assumption)).
% 292.31/184.83 tff(16293,plain,
% 292.31/184.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s1)) | (~node15(c_e_h_1, c_e, s0, s1)) | m_c_h_element_v_out(c_e_h_1, c_e, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1)) | (~node15(c_e_h_1, c_e, s0, s1)) | m_c_h_element_v_out(c_e_h_1, c_e, s0))),
% 292.31/184.83 inference(rewrite,[status(thm)],[])).
% 292.31/184.83 tff(16294,plain,
% 292.31/184.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s1)) | (~node15(c_e_h_1, c_e, s0, s1)) | m_c_h_element_v_out(c_e_h_1, c_e, s0))),
% 292.31/184.83 inference(quant_inst,[status(thm)],[])).
% 292.31/184.83 tff(16295,plain,
% 292.31/184.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1)) | (~node15(c_e_h_1, c_e, s0, s1)) | m_c_h_element_v_out(c_e_h_1, c_e, s0)),
% 292.31/184.83 inference(modus_ponens,[status(thm)],[16294, 16293])).
% 292.31/184.83 tff(16296,plain,
% 292.31/184.83 ($false),
% 292.31/184.83 inference(unit_resolution,[status(thm)],[16295, 147, 16277, 14867, 16292])).
% 292.31/184.83 tff(16297,plain,((~node15(c_e_h_1, c_e, s0, s1)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1))), inference(lemma,lemma(discharge,[]))).
% 292.31/184.83 tff(16298,plain,
% 292.31/184.83 (~node15(c_e_h_1, c_e, s0, s1)),
% 292.31/184.83 inference(unit_resolution,[status(thm)],[16297, 16277])).
% 292.31/184.83 tff(16299,plain,
% 292.31/184.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s0, s1)) | node19(c_e_h_1, c_e, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s0, s1)) | node19(c_e_h_1, c_e, s0, s1))),
% 292.31/184.83 inference(rewrite,[status(thm)],[])).
% 292.31/184.83 tff(16300,plain,
% 292.31/184.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s0, s1)) | node19(c_e_h_1, c_e, s0, s1))),
% 292.31/184.83 inference(quant_inst,[status(thm)],[])).
% 292.31/184.83 tff(16301,plain,
% 292.31/184.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s0, s1)) | node19(c_e_h_1, c_e, s0, s1)),
% 292.31/184.83 inference(modus_ponens,[status(thm)],[16300, 16299])).
% 292.31/184.83 tff(16302,plain,
% 292.31/184.83 (node19(c_e_h_1, c_e, s0, s1)),
% 292.31/184.83 inference(unit_resolution,[status(thm)],[16301, 190, 72])).
% 292.31/184.83 tff(16303,plain,
% 292.31/184.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_1, c_e, s0, s1) | (~node19(c_e_h_1, c_e, s0, s1)) | node15(c_e_h_1, c_e, s0, s1) | node16(c_e_h_1, c_e, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_e, s0, s1) | (~node19(c_e_h_1, c_e, s0, s1)) | node15(c_e_h_1, c_e, s0, s1) | node16(c_e_h_1, c_e, s0))),
% 292.31/184.83 inference(rewrite,[status(thm)],[])).
% 292.31/184.83 tff(16304,plain,
% 292.31/184.83 ((node16(c_e_h_1, c_e, s0) | node14(c_e_h_1, c_e, s0, s1) | node15(c_e_h_1, c_e, s0, s1) | (~node19(c_e_h_1, c_e, s0, s1))) <=> (node14(c_e_h_1, c_e, s0, s1) | (~node19(c_e_h_1, c_e, s0, s1)) | node15(c_e_h_1, c_e, s0, s1) | node16(c_e_h_1, c_e, s0))),
% 292.31/184.83 inference(rewrite,[status(thm)],[])).
% 292.31/184.83 tff(16305,plain,
% 292.31/184.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s0) | node14(c_e_h_1, c_e, s0, s1) | node15(c_e_h_1, c_e, s0, s1) | (~node19(c_e_h_1, c_e, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_1, c_e, s0, s1) | (~node19(c_e_h_1, c_e, s0, s1)) | node15(c_e_h_1, c_e, s0, s1) | node16(c_e_h_1, c_e, s0)))),
% 292.31/184.83 inference(monotonicity,[status(thm)],[16304])).
% 292.31/184.83 tff(16306,plain,
% 292.31/184.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s0) | node14(c_e_h_1, c_e, s0, s1) | node15(c_e_h_1, c_e, s0, s1) | (~node19(c_e_h_1, c_e, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_e, s0, s1) | (~node19(c_e_h_1, c_e, s0, s1)) | node15(c_e_h_1, c_e, s0, s1) | node16(c_e_h_1, c_e, s0))),
% 292.31/184.83 inference(transitivity,[status(thm)],[16305, 16303])).
% 292.31/184.83 tff(16307,plain,
% 292.31/184.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s0) | node14(c_e_h_1, c_e, s0, s1) | node15(c_e_h_1, c_e, s0, s1) | (~node19(c_e_h_1, c_e, s0, s1)))),
% 292.31/184.83 inference(quant_inst,[status(thm)],[])).
% 292.31/184.83 tff(16308,plain,
% 292.31/184.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_e, s0, s1) | (~node19(c_e_h_1, c_e, s0, s1)) | node15(c_e_h_1, c_e, s0, s1) | node16(c_e_h_1, c_e, s0)),
% 292.31/184.83 inference(modus_ponens,[status(thm)],[16307, 16306])).
% 292.31/184.83 tff(16309,plain,
% 292.31/184.83 (node14(c_e_h_1, c_e, s0, s1) | node15(c_e_h_1, c_e, s0, s1) | node16(c_e_h_1, c_e, s0)),
% 292.31/184.83 inference(unit_resolution,[status(thm)],[16308, 204, 16302])).
% 292.31/184.83 tff(16310,plain,
% 292.31/184.83 (node16(c_e_h_1, c_e, s0)),
% 292.31/184.83 inference(unit_resolution,[status(thm)],[16309, 16298, 16291])).
% 292.31/184.83 tff(16311,plain,
% 292.31/184.83 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s0)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | m_c_h_element_v_in2(c_e_h_1, c_e, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s0)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | m_c_h_element_v_in2(c_e_h_1, c_e, s0))),
% 292.31/184.84 inference(rewrite,[status(thm)],[])).
% 292.31/184.84 tff(16312,plain,
% 292.31/184.84 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s0)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | m_c_h_element_v_in2(c_e_h_1, c_e, s0))),
% 292.31/184.84 inference(quant_inst,[status(thm)],[])).
% 292.31/184.84 tff(16313,plain,
% 292.31/184.84 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s0)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | m_c_h_element_v_in2(c_e_h_1, c_e, s0)),
% 292.31/184.84 inference(modus_ponens,[status(thm)],[16312, 16311])).
% 292.31/184.84 tff(16314,plain,
% 292.31/184.84 ((~node16(c_e_h_1, c_e, s0)) | m_c_h_element_v_in2(c_e_h_1, c_e, s0)),
% 292.31/184.84 inference(unit_resolution,[status(thm)],[16313, 178, 16281])).
% 292.31/184.84 tff(16315,plain,
% 292.31/184.84 (m_c_h_element_v_in2(c_e_h_1, c_e, s0)),
% 292.31/184.84 inference(unit_resolution,[status(thm)],[16314, 16310])).
% 292.31/184.84 tff(16316,plain,
% 292.31/184.84 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s0)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~node17(c_e_h_1, c_e, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s0)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~node17(c_e_h_1, c_e, s0)))),
% 292.31/184.84 inference(rewrite,[status(thm)],[])).
% 292.31/184.84 tff(16317,plain,
% 292.31/184.84 ((m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s0)) | (~node17(c_e_h_1, c_e, s0))) <=> ((~m_c_h_element_v_in2(c_e_h_1, c_e, s0)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~node17(c_e_h_1, c_e, s0)))),
% 292.31/184.84 inference(rewrite,[status(thm)],[])).
% 292.31/184.84 tff(16318,plain,
% 292.31/184.84 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s0)) | (~node17(c_e_h_1, c_e, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s0)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~node17(c_e_h_1, c_e, s0))))),
% 292.31/184.84 inference(monotonicity,[status(thm)],[16317])).
% 292.31/184.84 tff(16319,plain,
% 292.31/184.84 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s0)) | (~node17(c_e_h_1, c_e, s0)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s0)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~node17(c_e_h_1, c_e, s0)))),
% 292.31/184.84 inference(transitivity,[status(thm)],[16318, 16316])).
% 292.31/184.84 tff(16320,plain,
% 292.31/184.84 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s0)) | (~node17(c_e_h_1, c_e, s0)))),
% 292.31/184.84 inference(quant_inst,[status(thm)],[])).
% 292.31/184.84 tff(16321,plain,
% 292.31/184.84 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s0)) | m_c_h_element_v_in1(c_e_h_1, c_e, s0) | (~node17(c_e_h_1, c_e, s0))),
% 292.31/184.84 inference(modus_ponens,[status(thm)],[16320, 16319])).
% 292.31/184.84 tff(16322,plain,
% 292.31/184.84 ((~m_c_h_element_v_in2(c_e_h_1, c_e, s0)) | (~node17(c_e_h_1, c_e, s0))),
% 292.31/184.84 inference(unit_resolution,[status(thm)],[16321, 859, 16281])).
% 292.31/184.84 tff(16323,plain,
% 292.31/184.84 (~node17(c_e_h_1, c_e, s0)),
% 292.31/184.84 inference(unit_resolution,[status(thm)],[16322, 16315])).
% 292.31/184.84 tff(16324,plain,
% 292.31/184.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_1, c_e, s0, s1) | (~node19(c_e_h_1, c_e, s0, s1)) | node17(c_e_h_1, c_e, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_e, s0, s1) | (~node19(c_e_h_1, c_e, s0, s1)) | node17(c_e_h_1, c_e, s0))),
% 292.31/184.84 inference(rewrite,[status(thm)],[])).
% 292.31/184.84 tff(16325,plain,
% 292.31/184.84 ((node17(c_e_h_1, c_e, s0) | node18(c_e_h_1, c_e, s0, s1) | (~node19(c_e_h_1, c_e, s0, s1))) <=> (node18(c_e_h_1, c_e, s0, s1) | (~node19(c_e_h_1, c_e, s0, s1)) | node17(c_e_h_1, c_e, s0))),
% 292.31/184.84 inference(rewrite,[status(thm)],[])).
% 292.31/184.84 tff(16326,plain,
% 292.31/184.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s0) | node18(c_e_h_1, c_e, s0, s1) | (~node19(c_e_h_1, c_e, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_1, c_e, s0, s1) | (~node19(c_e_h_1, c_e, s0, s1)) | node17(c_e_h_1, c_e, s0)))),
% 292.31/184.84 inference(monotonicity,[status(thm)],[16325])).
% 292.31/184.84 tff(16327,plain,
% 292.31/184.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s0) | node18(c_e_h_1, c_e, s0, s1) | (~node19(c_e_h_1, c_e, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_e, s0, s1) | (~node19(c_e_h_1, c_e, s0, s1)) | node17(c_e_h_1, c_e, s0))),
% 292.31/184.84 inference(transitivity,[status(thm)],[16326, 16324])).
% 292.31/184.84 tff(16328,plain,
% 292.31/184.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s0) | node18(c_e_h_1, c_e, s0, s1) | (~node19(c_e_h_1, c_e, s0, s1)))),
% 292.31/184.84 inference(quant_inst,[status(thm)],[])).
% 292.31/184.84 tff(16329,plain,
% 292.31/184.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_e, s0, s1) | (~node19(c_e_h_1, c_e, s0, s1)) | node17(c_e_h_1, c_e, s0)),
% 292.31/184.84 inference(modus_ponens,[status(thm)],[16328, 16327])).
% 292.31/184.84 tff(16330,plain,
% 292.31/184.84 (node18(c_e_h_1, c_e, s0, s1) | node17(c_e_h_1, c_e, s0)),
% 292.31/184.84 inference(unit_resolution,[status(thm)],[16329, 776, 16302])).
% 292.31/184.84 tff(16331,plain,
% 292.31/184.84 (node18(c_e_h_1, c_e, s0, s1)),
% 292.31/184.84 inference(unit_resolution,[status(thm)],[16330, 16323])).
% 292.31/184.84 tff(16332,plain,
% 292.31/184.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s1)) | m_c_h_element_v_out(c_e_h_1, c_e, s0) | (~node18(c_e_h_1, c_e, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1)) | m_c_h_element_v_out(c_e_h_1, c_e, s0) | (~node18(c_e_h_1, c_e, s0, s1)))),
% 292.31/184.84 inference(rewrite,[status(thm)],[])).
% 292.31/184.84 tff(16333,plain,
% 292.31/184.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s1)) | m_c_h_element_v_out(c_e_h_1, c_e, s0) | (~node18(c_e_h_1, c_e, s0, s1)))),
% 292.31/184.84 inference(quant_inst,[status(thm)],[])).
% 292.31/184.84 tff(16334,plain,
% 292.31/184.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s1)) | m_c_h_element_v_out(c_e_h_1, c_e, s0) | (~node18(c_e_h_1, c_e, s0, s1))),
% 292.31/184.84 inference(modus_ponens,[status(thm)],[16333, 16332])).
% 292.31/184.84 tff(16335,plain,
% 292.31/184.84 ($false),
% 292.31/184.84 inference(unit_resolution,[status(thm)],[16334, 753, 16277, 14867, 16331])).
% 292.31/184.84 tff(16336,plain,(~m_c_h_element_v_out(c_e_h_1, c_e, s1)), inference(lemma,lemma(discharge,[]))).
% 292.31/184.84 tff(16337,plain,
% 292.31/184.84 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1) | m_c_h_element_v_out(c_e_h_1, c_e, s1))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1) | m_c_h_element_v_out(c_e_h_1, c_e, s1))),
% 292.31/184.84 inference(rewrite,[status(thm)],[])).
% 292.31/184.84 tff(16338,plain,
% 292.31/184.84 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1) | m_c_h_element_v_out(c_e_h_1, c_e, s1))),
% 292.31/184.84 inference(quant_inst,[status(thm)],[])).
% 292.31/184.84 tff(16339,plain,
% 292.31/184.84 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1) | m_c_h_element_v_out(c_e_h_1, c_e, s1)),
% 292.31/184.84 inference(modus_ponens,[status(thm)],[16338, 16337])).
% 292.31/184.84 tff(16340,plain,
% 292.31/184.84 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1) | m_c_h_element_v_out(c_e_h_1, c_e, s1)),
% 292.31/184.84 inference(unit_resolution,[status(thm)],[16339, 7856])).
% 292.31/184.84 tff(16341,plain,
% 292.31/184.84 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)),
% 292.31/184.84 inference(unit_resolution,[status(thm)],[16340, 16336])).
% 292.31/184.84 tff(16342,plain,
% 292.31/184.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2) | (~node10(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2) | (~node10(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1)))),
% 292.31/184.84 inference(rewrite,[status(thm)],[])).
% 292.31/184.84 tff(16343,plain,
% 292.31/184.84 (((~node10(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)) <=> ((~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2) | (~node10(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1)))),
% 292.31/184.84 inference(rewrite,[status(thm)],[])).
% 292.31/184.84 tff(16344,plain,
% 292.31/184.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2) | (~node10(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1))))),
% 292.31/184.84 inference(monotonicity,[status(thm)],[16343])).
% 292.31/184.84 tff(16345,plain,
% 292.31/184.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2) | (~node10(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1)))),
% 292.31/184.84 inference(transitivity,[status(thm)],[16344, 16342])).
% 292.31/184.84 tff(16346,plain,
% 292.31/184.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2))),
% 292.31/184.85 inference(quant_inst,[status(thm)],[])).
% 292.31/184.85 tff(16347,plain,
% 292.31/184.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2) | (~node10(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s1))),
% 292.31/184.85 inference(modus_ponens,[status(thm)],[16346, 16345])).
% 292.31/184.85 tff(16348,plain,
% 292.31/184.85 ($false),
% 292.31/184.85 inference(unit_resolution,[status(thm)],[16347, 5718, 16341, 16270, 16276, 16271])).
% 292.31/184.85 tff(16349,plain,((~node10(c_e_h_1, c_n, s1, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)), inference(lemma,lemma(discharge,[]))).
% 292.31/184.85 tff(16350,plain,
% 292.31/184.85 (~node10(c_e_h_1, c_n, s1, s2)),
% 292.31/184.85 inference(unit_resolution,[status(thm)],[16349, 16270])).
% 292.31/184.85 tff(16351,plain,
% 292.31/184.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s1, s2)) | node10(c_e_h_1, c_n, s1, s2) | node11(c_e_h_1, c_n, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s1, s2)) | node10(c_e_h_1, c_n, s1, s2) | node11(c_e_h_1, c_n, s1, s2))),
% 292.31/184.85 inference(rewrite,[status(thm)],[])).
% 292.31/184.85 tff(16352,plain,
% 292.31/184.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s1, s2)) | node10(c_e_h_1, c_n, s1, s2) | node11(c_e_h_1, c_n, s1, s2))),
% 292.31/184.85 inference(quant_inst,[status(thm)],[])).
% 292.31/184.85 tff(16353,plain,
% 292.31/184.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s1, s2)) | node10(c_e_h_1, c_n, s1, s2) | node11(c_e_h_1, c_n, s1, s2)),
% 292.31/184.85 inference(modus_ponens,[status(thm)],[16352, 16351])).
% 292.31/184.85 tff(16354,plain,
% 292.31/184.85 (node10(c_e_h_1, c_n, s1, s2) | node11(c_e_h_1, c_n, s1, s2)),
% 292.31/184.85 inference(unit_resolution,[status(thm)],[16353, 5002, 255])).
% 292.31/184.85 tff(16355,plain,
% 292.31/184.85 (node11(c_e_h_1, c_n, s1, s2)),
% 292.31/184.85 inference(unit_resolution,[status(thm)],[16354, 16350])).
% 292.31/184.85 tff(16356,plain,
% 292.31/184.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)) | (~node11(c_e_h_1, c_n, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)) | (~node11(c_e_h_1, c_n, s1, s2)))),
% 292.31/184.85 inference(rewrite,[status(thm)],[])).
% 292.31/184.85 tff(16357,plain,
% 292.31/184.85 ((m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2) | (~node11(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1))) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)) | (~node11(c_e_h_1, c_n, s1, s2)))),
% 292.31/184.85 inference(rewrite,[status(thm)],[])).
% 292.31/184.85 tff(16358,plain,
% 292.31/184.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2) | (~node11(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)) | (~node11(c_e_h_1, c_n, s1, s2))))),
% 292.31/184.85 inference(monotonicity,[status(thm)],[16357])).
% 292.31/184.85 tff(16359,plain,
% 292.31/184.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2) | (~node11(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)) | (~node11(c_e_h_1, c_n, s1, s2)))),
% 292.31/184.85 inference(transitivity,[status(thm)],[16358, 16356])).
% 292.31/184.85 tff(16360,plain,
% 292.31/184.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2) | (~node11(c_e_h_1, c_n, s1, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)))),
% 292.31/184.85 inference(quant_inst,[status(thm)],[])).
% 292.31/184.85 tff(16361,plain,
% 292.31/184.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s1)) | (~node11(c_e_h_1, c_n, s1, s2))),
% 292.31/184.85 inference(modus_ponens,[status(thm)],[16360, 16359])).
% 292.31/184.85 tff(16362,plain,
% 292.31/184.85 ($false),
% 292.31/184.85 inference(unit_resolution,[status(thm)],[16361, 5742, 14899, 16270, 16355])).
% 292.31/184.85 tff(16363,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)), inference(lemma,lemma(discharge,[]))).
% 292.31/184.85 tff(16364,plain,
% 292.31/184.85 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)))),
% 292.31/184.85 inference(rewrite,[status(thm)],[])).
% 292.31/184.85 tff(16365,plain,
% 292.31/184.85 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)))),
% 292.31/184.85 inference(quant_inst,[status(thm)],[])).
% 292.31/184.85 tff(16366,plain,
% 292.31/184.85 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s2)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2))),
% 292.31/184.85 inference(modus_ponens,[status(thm)],[16365, 16364])).
% 292.31/184.85 tff(16367,plain,
% 292.31/184.85 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s2)),
% 292.31/184.85 inference(unit_resolution,[status(thm)],[16366, 4958, 16363])).
% 292.31/184.85 tff(16368,plain,
% 292.31/184.85 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s2)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s2)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s2))),
% 292.31/184.85 inference(rewrite,[status(thm)],[])).
% 292.31/184.85 tff(16369,plain,
% 292.31/184.85 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s2)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s2))),
% 292.31/184.85 inference(quant_inst,[status(thm)],[])).
% 292.31/184.85 tff(16370,plain,
% 292.31/184.85 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s2)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s2)),
% 292.31/184.85 inference(modus_ponens,[status(thm)],[16369, 16368])).
% 292.31/184.85 tff(16371,plain,
% 292.31/184.85 (~node9(c_e_h_1, c_m, s2)),
% 292.31/184.85 inference(unit_resolution,[status(thm)],[16370, 4972, 16367])).
% 292.31/184.85 tff(16372,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)), introduced(assumption)).
% 292.31/184.85 tff(16373,assumption,(node11(c_e_h_1, c_m, s2, s3)), introduced(assumption)).
% 292.31/184.85 tff(16374,plain,
% 292.31/184.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)) | (~node11(c_e_h_1, c_m, s2, s3)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)) | (~node11(c_e_h_1, c_m, s2, s3)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2))),
% 292.31/184.85 inference(rewrite,[status(thm)],[])).
% 292.31/184.85 tff(16375,plain,
% 292.31/184.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)) | (~node11(c_e_h_1, c_m, s2, s3)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2))),
% 292.31/184.85 inference(quant_inst,[status(thm)],[])).
% 292.31/184.85 tff(16376,plain,
% 292.31/184.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)) | (~node11(c_e_h_1, c_m, s2, s3)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)),
% 292.31/184.85 inference(modus_ponens,[status(thm)],[16375, 16374])).
% 292.31/184.85 tff(16377,plain,
% 292.31/184.85 ($false),
% 292.31/184.85 inference(unit_resolution,[status(thm)],[16376, 5017, 14924, 16372, 16373])).
% 292.31/184.85 tff(16378,plain,((~node11(c_e_h_1, c_m, s2, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3))), inference(lemma,lemma(discharge,[]))).
% 292.31/184.85 tff(16379,plain,
% 292.31/184.85 (~node11(c_e_h_1, c_m, s2, s3)),
% 292.31/184.85 inference(unit_resolution,[status(thm)],[16378, 16372])).
% 292.31/184.85 tff(16380,plain,
% 292.31/184.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s2, s3)) | node10(c_e_h_1, c_m, s2, s3) | node11(c_e_h_1, c_m, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s2, s3)) | node10(c_e_h_1, c_m, s2, s3) | node11(c_e_h_1, c_m, s2, s3))),
% 292.31/184.85 inference(rewrite,[status(thm)],[])).
% 292.31/184.85 tff(16381,plain,
% 292.31/184.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s2, s3)) | node10(c_e_h_1, c_m, s2, s3) | node11(c_e_h_1, c_m, s2, s3))),
% 292.31/184.85 inference(quant_inst,[status(thm)],[])).
% 292.31/184.85 tff(16382,plain,
% 292.31/184.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s2, s3)) | node10(c_e_h_1, c_m, s2, s3) | node11(c_e_h_1, c_m, s2, s3)),
% 292.31/184.85 inference(modus_ponens,[status(thm)],[16381, 16380])).
% 292.31/184.85 tff(16383,plain,
% 292.31/184.85 (node10(c_e_h_1, c_m, s2, s3) | node11(c_e_h_1, c_m, s2, s3)),
% 292.31/184.85 inference(unit_resolution,[status(thm)],[16382, 5002, 318])).
% 292.31/184.85 tff(16384,plain,
% 292.31/184.85 (node10(c_e_h_1, c_m, s2, s3)),
% 292.31/184.85 inference(unit_resolution,[status(thm)],[16383, 16379])).
% 292.31/184.85 tff(16385,plain,
% 292.31/184.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)) | node9(c_e_h_1, c_m, s2) | (~node10(c_e_h_1, c_m, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)) | node9(c_e_h_1, c_m, s2) | (~node10(c_e_h_1, c_m, s2, s3)))),
% 292.31/184.85 inference(rewrite,[status(thm)],[])).
% 292.31/184.85 tff(16386,plain,
% 292.31/184.85 ((node9(c_e_h_1, c_m, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)) | (~node10(c_e_h_1, c_m, s2, s3))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)) | node9(c_e_h_1, c_m, s2) | (~node10(c_e_h_1, c_m, s2, s3)))),
% 292.31/184.85 inference(rewrite,[status(thm)],[])).
% 292.31/184.85 tff(16387,plain,
% 292.31/184.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)) | (~node10(c_e_h_1, c_m, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)) | node9(c_e_h_1, c_m, s2) | (~node10(c_e_h_1, c_m, s2, s3))))),
% 292.31/184.85 inference(monotonicity,[status(thm)],[16386])).
% 292.31/184.85 tff(16388,plain,
% 292.31/184.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)) | (~node10(c_e_h_1, c_m, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)) | node9(c_e_h_1, c_m, s2) | (~node10(c_e_h_1, c_m, s2, s3)))),
% 292.31/184.86 inference(transitivity,[status(thm)],[16387, 16385])).
% 292.31/184.86 tff(16389,plain,
% 292.31/184.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s2) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)) | (~node10(c_e_h_1, c_m, s2, s3)))),
% 292.31/184.86 inference(quant_inst,[status(thm)],[])).
% 292.31/184.86 tff(16390,plain,
% 292.31/184.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)) | node9(c_e_h_1, c_m, s2) | (~node10(c_e_h_1, c_m, s2, s3))),
% 292.31/184.86 inference(modus_ponens,[status(thm)],[16389, 16388])).
% 292.31/184.86 tff(16391,plain,
% 292.31/184.86 ($false),
% 292.31/184.86 inference(unit_resolution,[status(thm)],[16390, 4986, 16372, 16384, 16371])).
% 292.31/184.86 tff(16392,plain,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)), inference(lemma,lemma(discharge,[]))).
% 292.31/184.86 tff(16393,plain,
% 292.31/184.86 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s3)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s3)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3))),
% 292.31/184.86 inference(rewrite,[status(thm)],[])).
% 292.31/184.86 tff(16394,plain,
% 292.31/184.86 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s3)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3))),
% 292.31/184.86 inference(quant_inst,[status(thm)],[])).
% 292.31/184.86 tff(16395,plain,
% 292.31/184.86 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s3)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)),
% 292.31/184.86 inference(modus_ponens,[status(thm)],[16394, 16393])).
% 292.31/184.86 tff(16396,plain,
% 292.31/184.86 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s3)),
% 292.31/184.86 inference(unit_resolution,[status(thm)],[16395, 14293, 16392])).
% 292.31/184.86 tff(16397,plain,
% 292.31/184.86 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s3)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s3)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s3))),
% 292.31/184.86 inference(rewrite,[status(thm)],[])).
% 292.31/184.86 tff(16398,plain,
% 292.31/184.86 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s3)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s3))),
% 292.31/184.86 inference(quant_inst,[status(thm)],[])).
% 292.31/184.86 tff(16399,plain,
% 292.31/184.86 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s3)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s3)),
% 292.31/184.86 inference(modus_ponens,[status(thm)],[16398, 16397])).
% 292.31/184.86 tff(16400,plain,
% 292.31/184.86 (~node20(c_e_h_1, c_r, s3)),
% 292.31/184.86 inference(unit_resolution,[status(thm)],[16399, 4563, 16396])).
% 292.31/184.86 tff(16401,assumption,(node21(c_e_h_1, c_r, s3, s4)), introduced(assumption)).
% 292.31/184.86 tff(16402,plain,
% 292.31/184.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | (~node21(c_e_h_1, c_r, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | (~node21(c_e_h_1, c_r, s3, s4)))),
% 292.31/184.86 inference(rewrite,[status(thm)],[])).
% 292.31/184.86 tff(16403,plain,
% 292.31/184.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | (~node21(c_e_h_1, c_r, s3, s4)))),
% 292.31/184.86 inference(quant_inst,[status(thm)],[])).
% 292.31/184.86 tff(16404,plain,
% 292.31/184.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | (~node21(c_e_h_1, c_r, s3, s4))),
% 292.31/184.86 inference(modus_ponens,[status(thm)],[16403, 16402])).
% 292.31/184.86 tff(16405,plain,
% 292.31/184.86 ($false),
% 292.31/184.86 inference(unit_resolution,[status(thm)],[16404, 52, 16401, 16269, 16400])).
% 292.31/184.86 tff(16406,plain,((~node21(c_e_h_1, c_r, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s4))), inference(lemma,lemma(discharge,[]))).
% 292.31/184.86 tff(16407,plain,
% 292.31/184.86 (~node21(c_e_h_1, c_r, s3, s4)),
% 292.31/184.86 inference(unit_resolution,[status(thm)],[16406, 16269])).
% 292.31/184.86 tff(16408,assumption,(node22(c_e_h_1, c_r, s3, s4)), introduced(assumption)).
% 292.31/184.86 tff(16409,plain,
% 292.31/184.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | (~node22(c_e_h_1, c_r, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_r, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | (~node22(c_e_h_1, c_r, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_r, s3))),
% 292.31/184.86 inference(rewrite,[status(thm)],[])).
% 292.31/184.86 tff(16410,plain,
% 292.31/184.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | (~node22(c_e_h_1, c_r, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_r, s3))),
% 292.31/184.86 inference(quant_inst,[status(thm)],[])).
% 292.31/184.86 tff(16411,plain,
% 292.31/184.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | (~node22(c_e_h_1, c_r, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_r, s3)),
% 292.31/184.86 inference(modus_ponens,[status(thm)],[16410, 16409])).
% 292.31/184.86 tff(16412,plain,
% 292.31/184.86 ($false),
% 292.31/184.86 inference(unit_resolution,[status(thm)],[16411, 108, 16408, 16269, 14953])).
% 292.31/184.86 tff(16413,plain,((~node22(c_e_h_1, c_r, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s4)) | m_and_h_gate_v_out(c_e_h_1, c_r, s3)), inference(lemma,lemma(discharge,[]))).
% 292.31/184.86 tff(16414,plain,
% 292.31/184.86 ((~node22(c_e_h_1, c_r, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s4))),
% 292.31/184.86 inference(unit_resolution,[status(thm)],[16413, 14951])).
% 292.31/184.86 tff(16415,plain,
% 292.31/184.86 (~node22(c_e_h_1, c_r, s3, s4)),
% 292.31/184.86 inference(unit_resolution,[status(thm)],[16414, 16269])).
% 292.31/184.86 tff(16416,plain,
% 292.31/184.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_1, c_r, s3, s4) | node22(c_e_h_1, c_r, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_1, c_r, s3, s4) | node22(c_e_h_1, c_r, s3, s4))),
% 292.31/184.86 inference(rewrite,[status(thm)],[])).
% 292.31/184.86 tff(16417,plain,
% 292.31/184.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_1, c_r, s3, s4) | node22(c_e_h_1, c_r, s3, s4))),
% 292.31/184.86 inference(quant_inst,[status(thm)],[])).
% 292.31/184.86 tff(16418,plain,
% 292.31/184.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_1, c_r, s3, s4) | node22(c_e_h_1, c_r, s3, s4)),
% 292.31/184.86 inference(modus_ponens,[status(thm)],[16417, 16416])).
% 292.31/184.86 tff(16419,plain,
% 292.31/184.86 (node21(c_e_h_1, c_r, s3, s4) | node22(c_e_h_1, c_r, s3, s4)),
% 292.31/184.86 inference(unit_resolution,[status(thm)],[16418, 82, 531])).
% 292.31/184.86 tff(16420,plain,
% 292.31/184.86 ($false),
% 292.31/184.86 inference(unit_resolution,[status(thm)],[16419, 16415, 16407])).
% 292.31/184.86 tff(16421,plain,(~m_and_h_gate_v_out(c_e_h_1, c_r, s4)), inference(lemma,lemma(discharge,[]))).
% 292.31/184.86 tff(16422,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s4)), introduced(assumption)).
% 292.31/184.86 tff(16423,assumption,(m_user_v_ack(c_e_h_1, c_u, s4)), introduced(assumption)).
% 292.31/184.86 tff(16424,plain,
% 292.31/184.86 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s4)) | m_and_h_gate_v_out(c_e_h_1, c_r, s4))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s4)) | m_and_h_gate_v_out(c_e_h_1, c_r, s4))),
% 292.31/184.86 inference(rewrite,[status(thm)],[])).
% 292.31/184.86 tff(16425,plain,
% 292.31/184.86 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s4)) | m_and_h_gate_v_out(c_e_h_1, c_r, s4))),
% 292.31/184.86 inference(quant_inst,[status(thm)],[])).
% 292.31/184.86 tff(16426,plain,
% 292.31/184.86 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s4)) | m_and_h_gate_v_out(c_e_h_1, c_r, s4)),
% 292.31/184.86 inference(modus_ponens,[status(thm)],[16425, 16424])).
% 292.31/184.86 tff(16427,plain,
% 292.31/184.86 ($false),
% 292.31/184.86 inference(unit_resolution,[status(thm)],[16426, 268, 16423, 16422])).
% 292.31/184.86 tff(16428,plain,((~m_user_v_ack(c_e_h_1, c_u, s4)) | m_and_h_gate_v_out(c_e_h_1, c_r, s4)), inference(lemma,lemma(discharge,[]))).
% 292.31/184.86 tff(16429,plain,
% 292.31/184.86 (~m_user_v_ack(c_e_h_1, c_u, s4)),
% 292.31/184.86 inference(unit_resolution,[status(thm)],[16428, 16421])).
% 292.31/184.86 tff(16430,assumption,(~m_user_v_ack(c_e_h_1, c_u, s4)), introduced(assumption)).
% 292.31/184.86 tff(16431,assumption,(node8(c_e_h_1, c_u, s4, s5)), introduced(assumption)).
% 292.31/184.86 tff(16432,plain,
% 292.31/184.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | ((~m_user_v_req(c_e_h_1, c_u, s4)) | (~node8(c_e_h_1, c_u, s4, s5)) | m_user_v_req(c_e_h_1, c_u, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (~m_user_v_req(c_e_h_1, c_u, s4)) | (~node8(c_e_h_1, c_u, s4, s5)) | m_user_v_req(c_e_h_1, c_u, s5))),
% 292.31/184.86 inference(rewrite,[status(thm)],[])).
% 292.31/184.86 tff(16433,plain,
% 292.31/184.86 ((m_user_v_req(c_e_h_1, c_u, s5) | (~node8(c_e_h_1, c_u, s4, s5)) | (~m_user_v_req(c_e_h_1, c_u, s4))) <=> ((~m_user_v_req(c_e_h_1, c_u, s4)) | (~node8(c_e_h_1, c_u, s4, s5)) | m_user_v_req(c_e_h_1, c_u, s5))),
% 292.31/184.86 inference(rewrite,[status(thm)],[])).
% 292.31/184.86 tff(16434,plain,
% 292.31/184.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_1, c_u, s5) | (~node8(c_e_h_1, c_u, s4, s5)) | (~m_user_v_req(c_e_h_1, c_u, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | ((~m_user_v_req(c_e_h_1, c_u, s4)) | (~node8(c_e_h_1, c_u, s4, s5)) | m_user_v_req(c_e_h_1, c_u, s5)))),
% 292.31/184.86 inference(monotonicity,[status(thm)],[16433])).
% 292.31/184.86 tff(16435,plain,
% 292.31/184.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_1, c_u, s5) | (~node8(c_e_h_1, c_u, s4, s5)) | (~m_user_v_req(c_e_h_1, c_u, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (~m_user_v_req(c_e_h_1, c_u, s4)) | (~node8(c_e_h_1, c_u, s4, s5)) | m_user_v_req(c_e_h_1, c_u, s5))),
% 292.31/184.86 inference(transitivity,[status(thm)],[16434, 16432])).
% 292.31/184.86 tff(16436,plain,
% 292.31/184.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_1, c_u, s5) | (~node8(c_e_h_1, c_u, s4, s5)) | (~m_user_v_req(c_e_h_1, c_u, s4)))),
% 292.31/184.86 inference(quant_inst,[status(thm)],[])).
% 292.31/184.86 tff(16437,plain,
% 292.31/184.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (~m_user_v_req(c_e_h_1, c_u, s4)) | (~node8(c_e_h_1, c_u, s4, s5)) | m_user_v_req(c_e_h_1, c_u, s5)),
% 292.31/184.86 inference(modus_ponens,[status(thm)],[16436, 16435])).
% 292.31/184.86 tff(16438,plain,
% 292.31/184.86 ($false),
% 292.31/184.86 inference(unit_resolution,[status(thm)],[16437, 302, 16431, 14982, 16267])).
% 292.31/184.86 tff(16439,plain,((~node8(c_e_h_1, c_u, s4, s5)) | (~m_user_v_req(c_e_h_1, c_u, s4)) | m_user_v_req(c_e_h_1, c_u, s5)), inference(lemma,lemma(discharge,[]))).
% 292.31/184.86 tff(16440,plain,
% 292.31/184.86 (~node8(c_e_h_1, c_u, s4, s5)),
% 292.31/184.86 inference(unit_resolution,[status(thm)],[16439, 16267, 14982])).
% 292.31/184.87 tff(16441,plain,
% 292.31/184.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | ((~trans(s4, s5)) | node7(c_e_h_1, c_u, s4, s5) | node8(c_e_h_1, c_u, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | (~trans(s4, s5)) | node7(c_e_h_1, c_u, s4, s5) | node8(c_e_h_1, c_u, s4, s5))),
% 292.31/184.87 inference(rewrite,[status(thm)],[])).
% 292.31/184.87 tff(16442,plain,
% 292.31/184.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | ((~trans(s4, s5)) | node7(c_e_h_1, c_u, s4, s5) | node8(c_e_h_1, c_u, s4, s5))),
% 292.31/184.87 inference(quant_inst,[status(thm)],[])).
% 292.31/184.87 tff(16443,plain,
% 292.31/184.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | (~trans(s4, s5)) | node7(c_e_h_1, c_u, s4, s5) | node8(c_e_h_1, c_u, s4, s5)),
% 292.31/184.87 inference(modus_ponens,[status(thm)],[16442, 16441])).
% 292.31/184.87 tff(16444,plain,
% 292.31/184.87 (node7(c_e_h_1, c_u, s4, s5) | node8(c_e_h_1, c_u, s4, s5)),
% 292.31/184.87 inference(unit_resolution,[status(thm)],[16443, 328, 1028])).
% 292.31/184.87 tff(16445,plain,
% 292.31/184.87 (node7(c_e_h_1, c_u, s4, s5)),
% 292.31/184.87 inference(unit_resolution,[status(thm)],[16444, 16440])).
% 292.31/184.87 tff(16446,plain,
% 292.31/184.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | ((~node7(c_e_h_1, c_u, s4, s5)) | m_user_v_ack(c_e_h_1, c_u, s4) | m_user_v_req(c_e_h_1, c_u, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | (~node7(c_e_h_1, c_u, s4, s5)) | m_user_v_ack(c_e_h_1, c_u, s4) | m_user_v_req(c_e_h_1, c_u, s5))),
% 292.31/184.87 inference(rewrite,[status(thm)],[])).
% 292.31/184.87 tff(16447,plain,
% 292.31/184.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | ((~node7(c_e_h_1, c_u, s4, s5)) | m_user_v_ack(c_e_h_1, c_u, s4) | m_user_v_req(c_e_h_1, c_u, s5))),
% 292.31/184.87 inference(quant_inst,[status(thm)],[])).
% 292.31/184.87 tff(16448,plain,
% 292.31/184.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | (~node7(c_e_h_1, c_u, s4, s5)) | m_user_v_ack(c_e_h_1, c_u, s4) | m_user_v_req(c_e_h_1, c_u, s5)),
% 292.31/184.87 inference(modus_ponens,[status(thm)],[16447, 16446])).
% 292.31/184.87 tff(16449,plain,
% 292.31/184.87 ($false),
% 292.31/184.87 inference(unit_resolution,[status(thm)],[16448, 284, 16445, 16430, 16267])).
% 292.31/184.87 tff(16450,plain,(m_user_v_req(c_e_h_1, c_u, s5) | m_user_v_ack(c_e_h_1, c_u, s4) | (~m_user_v_req(c_e_h_1, c_u, s4))), inference(lemma,lemma(discharge,[]))).
% 292.31/184.87 tff(16451,plain,
% 292.31/184.87 (m_user_v_req(c_e_h_1, c_u, s5) | (~m_user_v_req(c_e_h_1, c_u, s4))),
% 292.31/184.87 inference(unit_resolution,[status(thm)],[16450, 16429])).
% 292.31/184.87 tff(16452,plain,
% 292.31/184.87 (~m_user_v_req(c_e_h_1, c_u, s4)),
% 292.31/184.87 inference(unit_resolution,[status(thm)],[16451, 16267])).
% 292.31/184.87 tff(16453,plain,
% 292.31/184.87 (~m_user_v_req(c_e_h_1, c_u, s3)),
% 292.31/184.87 inference(unit_resolution,[status(thm)],[14979, 16452])).
% 292.31/184.87 tff(16454,plain,
% 292.31/184.87 (~m_user_v_req(c_e_h_1, c_u, s2)),
% 292.31/184.87 inference(unit_resolution,[status(thm)],[14760, 16453])).
% 292.31/184.87 tff(16455,plain,
% 292.31/184.87 (~m_mutex_h_half_v_out(c_e_h_1, c_a, s3)),
% 292.31/184.87 inference(unit_resolution,[status(thm)],[14632, 16454])).
% 292.31/184.87 tff(16456,plain,
% 292.31/184.87 (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s3)),
% 292.31/184.87 inference(unit_resolution,[status(thm)],[15062, 395, 16453])).
% 292.31/184.87 tff(16457,plain,
% 292.31/184.87 (~m_mutex_h_half_v_out(c_e_h_1, c_a, s4)),
% 292.31/184.87 inference(unit_resolution,[status(thm)],[15058, 16456, 16455])).
% 292.31/184.87 tff(16458,plain,
% 292.31/184.87 (((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | ((~m_mutex_h_half_v_inp(c_e_h_1, c_a, s4)) | m_user_v_req(c_e_h_1, c_u, s4))) <=> ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s4)) | m_user_v_req(c_e_h_1, c_u, s4))),
% 292.31/184.87 inference(rewrite,[status(thm)],[])).
% 292.31/184.87 tff(16459,plain,
% 292.31/184.87 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | ((~m_mutex_h_half_v_inp(c_e_h_1, c_a, s4)) | m_user_v_req(c_e_h_1, c_u, s4))),
% 292.31/184.87 inference(quant_inst,[status(thm)],[])).
% 292.31/184.87 tff(16460,plain,
% 292.31/184.87 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s4)) | m_user_v_req(c_e_h_1, c_u, s4)),
% 292.31/184.87 inference(modus_ponens,[status(thm)],[16459, 16458])).
% 292.31/184.87 tff(16461,plain,
% 292.31/184.87 (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s4)),
% 292.31/184.87 inference(unit_resolution,[status(thm)],[16460, 395, 16452])).
% 292.31/184.87 tff(16462,plain,
% 292.31/184.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_1, c_a, s4) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s5)) | (~node12(c_e_h_1, c_a, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s4) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s5)) | (~node12(c_e_h_1, c_a, s4, s5)))),
% 292.31/184.87 inference(rewrite,[status(thm)],[])).
% 292.31/184.87 tff(16463,plain,
% 292.31/184.87 (((~node12(c_e_h_1, c_a, s4, s5)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s4) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s5))) <=> (m_mutex_h_half_v_inp(c_e_h_1, c_a, s4) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s5)) | (~node12(c_e_h_1, c_a, s4, s5)))),
% 292.31/184.87 inference(rewrite,[status(thm)],[])).
% 292.31/184.87 tff(16464,plain,
% 292.31/184.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_1, c_a, s4, s5)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s4) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_1, c_a, s4) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s5)) | (~node12(c_e_h_1, c_a, s4, s5))))),
% 292.31/184.87 inference(monotonicity,[status(thm)],[16463])).
% 292.31/184.87 tff(16465,plain,
% 292.31/184.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_1, c_a, s4, s5)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s4) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s4) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s5)) | (~node12(c_e_h_1, c_a, s4, s5)))),
% 292.31/184.87 inference(transitivity,[status(thm)],[16464, 16462])).
% 292.31/184.87 tff(16466,plain,
% 292.31/184.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_1, c_a, s4, s5)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s4) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s5)))),
% 292.31/184.87 inference(quant_inst,[status(thm)],[])).
% 292.31/184.87 tff(16467,plain,
% 292.31/184.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s4) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s5)) | (~node12(c_e_h_1, c_a, s4, s5))),
% 292.31/184.87 inference(modus_ponens,[status(thm)],[16466, 16465])).
% 292.31/184.87 tff(16468,plain,
% 292.31/184.87 ($false),
% 292.31/184.87 inference(unit_resolution,[status(thm)],[16467, 454, 14990, 15068, 14981])).
% 292.31/184.87 tff(16469,plain,((~node12(c_e_h_1, c_a, s4, s5)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s5)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s4)), inference(lemma,lemma(discharge,[]))).
% 292.31/184.87 tff(16470,plain,
% 292.31/184.87 (~node12(c_e_h_1, c_a, s4, s5)),
% 292.31/184.87 inference(unit_resolution,[status(thm)],[16469, 15068, 14981])).
% 292.31/184.87 tff(16471,plain,
% 292.31/184.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_1, c_a, s5)) | (~node13(c_e_h_1, c_a, s4, s5)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s5)) | (~node13(c_e_h_1, c_a, s4, s5)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s4))),
% 292.31/184.87 inference(rewrite,[status(thm)],[])).
% 292.31/184.88 tff(16472,plain,
% 292.31/184.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_1, c_a, s5)) | (~node13(c_e_h_1, c_a, s4, s5)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s4))),
% 292.31/184.88 inference(quant_inst,[status(thm)],[])).
% 292.31/184.88 tff(16473,plain,
% 292.31/184.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s5)) | (~node13(c_e_h_1, c_a, s4, s5)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s4)),
% 292.31/184.88 inference(modus_ponens,[status(thm)],[16472, 16471])).
% 292.31/184.88 tff(16474,plain,
% 292.31/184.88 ($false),
% 292.31/184.88 inference(unit_resolution,[status(thm)],[16473, 423, 15005, 14102, 15068])).
% 292.31/184.88 tff(16475,plain,((~node13(c_e_h_1, c_a, s4, s5)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s4) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s5))), inference(lemma,lemma(discharge,[]))).
% 292.31/184.88 tff(16476,plain,
% 292.31/184.88 (~node13(c_e_h_1, c_a, s4, s5)),
% 292.31/184.88 inference(unit_resolution,[status(thm)],[16475, 15068, 14102])).
% 292.31/184.88 tff(16477,plain,
% 292.31/184.88 ($false),
% 292.31/184.88 inference(unit_resolution,[status(thm)],[15003, 16476, 16470])).
% 292.31/184.88 tff(16478,plain,((~m_mutex_h_half_v_out(c_e_h_1, c_a, s5)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s4) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s4)), inference(lemma,lemma(discharge,[]))).
% 292.31/184.88 tff(16479,plain,
% 292.31/184.88 (~m_mutex_h_half_v_out(c_e_h_1, c_a, s5)),
% 292.31/184.88 inference(unit_resolution,[status(thm)],[16478, 16461, 16457])).
% 292.31/184.88 tff(16480,assumption,(m_mutex_h_half_v_out(c_e_h_1, c_a, s6)), introduced(assumption)).
% 292.31/184.88 tff(16481,plain,
% 292.31/184.88 (((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | ((~m_mutex_h_half_v_inp(c_e_h_1, c_a, s5)) | m_user_v_req(c_e_h_1, c_u, s5))) <=> ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s5)) | m_user_v_req(c_e_h_1, c_u, s5))),
% 292.31/184.88 inference(rewrite,[status(thm)],[])).
% 292.31/184.88 tff(16482,plain,
% 292.31/184.88 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | ((~m_mutex_h_half_v_inp(c_e_h_1, c_a, s5)) | m_user_v_req(c_e_h_1, c_u, s5))),
% 292.31/184.88 inference(quant_inst,[status(thm)],[])).
% 292.31/184.88 tff(16483,plain,
% 292.31/184.88 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s5)) | m_user_v_req(c_e_h_1, c_u, s5)),
% 292.31/184.88 inference(modus_ponens,[status(thm)],[16482, 16481])).
% 292.31/184.88 tff(16484,plain,
% 292.31/184.88 (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s5)),
% 292.31/184.88 inference(unit_resolution,[status(thm)],[16483, 395, 16267])).
% 292.31/184.88 tff(16485,assumption,(~m_mutex_h_half_v_inp(c_e_h_1, c_a, s5)), introduced(assumption)).
% 292.31/184.88 tff(16486,assumption,(node12(c_e_h_1, c_a, s5, s6)), introduced(assumption)).
% 292.31/184.88 tff(16487,plain,
% 292.31/184.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_1, c_a, s5, s6)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s5) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (~node12(c_e_h_1, c_a, s5, s6)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s5) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s6)))),
% 292.31/184.88 inference(rewrite,[status(thm)],[])).
% 292.31/184.88 tff(16488,plain,
% 292.31/184.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_1, c_a, s5, s6)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s5) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s6)))),
% 292.31/184.88 inference(quant_inst,[status(thm)],[])).
% 292.31/184.88 tff(16489,plain,
% 292.31/184.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (~node12(c_e_h_1, c_a, s5, s6)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s5) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s6))),
% 292.31/184.88 inference(modus_ponens,[status(thm)],[16488, 16487])).
% 292.31/184.88 tff(16490,plain,
% 292.31/184.88 ($false),
% 292.31/184.88 inference(unit_resolution,[status(thm)],[16489, 454, 16486, 16485, 16480])).
% 292.31/184.88 tff(16491,plain,((~node12(c_e_h_1, c_a, s5, s6)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s5) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s6))), inference(lemma,lemma(discharge,[]))).
% 292.31/184.88 tff(16492,plain,
% 292.31/184.88 (~node12(c_e_h_1, c_a, s5, s6)),
% 292.31/184.88 inference(unit_resolution,[status(thm)],[16491, 16484, 16480])).
% 292.31/184.88 tff(16493,plain,
% 292.31/184.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s5, s6)) | node12(c_e_h_1, c_a, s5, s6) | node13(c_e_h_1, c_a, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s5, s6)) | node12(c_e_h_1, c_a, s5, s6) | node13(c_e_h_1, c_a, s5, s6))),
% 292.31/184.88 inference(rewrite,[status(thm)],[])).
% 292.31/184.88 tff(16494,plain,
% 292.31/184.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s5, s6)) | node12(c_e_h_1, c_a, s5, s6) | node13(c_e_h_1, c_a, s5, s6))),
% 292.31/184.88 inference(quant_inst,[status(thm)],[])).
% 292.31/184.88 tff(16495,plain,
% 292.31/184.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s5, s6)) | node12(c_e_h_1, c_a, s5, s6) | node13(c_e_h_1, c_a, s5, s6)),
% 292.31/184.88 inference(modus_ponens,[status(thm)],[16494, 16493])).
% 292.31/184.88 tff(16496,plain,
% 292.31/184.88 (node12(c_e_h_1, c_a, s5, s6) | node13(c_e_h_1, c_a, s5, s6)),
% 292.31/184.88 inference(unit_resolution,[status(thm)],[16495, 439, 1406])).
% 292.31/184.88 tff(16497,plain,
% 292.31/184.88 (node13(c_e_h_1, c_a, s5, s6)),
% 292.31/184.88 inference(unit_resolution,[status(thm)],[16496, 16492])).
% 292.31/184.88 tff(16498,plain,
% 292.31/184.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_1, c_a, s6)) | (~node13(c_e_h_1, c_a, s5, s6)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s6)) | (~node13(c_e_h_1, c_a, s5, s6)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s5))),
% 292.31/184.88 inference(rewrite,[status(thm)],[])).
% 292.31/184.88 tff(16499,plain,
% 292.31/184.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_1, c_a, s6)) | (~node13(c_e_h_1, c_a, s5, s6)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s5))),
% 292.31/184.88 inference(quant_inst,[status(thm)],[])).
% 292.31/184.88 tff(16500,plain,
% 292.31/184.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s6)) | (~node13(c_e_h_1, c_a, s5, s6)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s5)),
% 292.31/184.88 inference(modus_ponens,[status(thm)],[16499, 16498])).
% 292.31/184.88 tff(16501,plain,
% 292.31/184.88 ($false),
% 292.31/184.88 inference(unit_resolution,[status(thm)],[16500, 423, 16497, 16480, 16479])).
% 292.31/184.88 tff(16502,plain,(m_user_v_req(c_e_h_1, c_u, s5) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s6))), inference(lemma,lemma(discharge,[]))).
% 292.31/184.88 tff(16503,plain,
% 292.31/184.88 (~m_mutex_h_half_v_out(c_e_h_1, c_a, s6)),
% 292.31/184.88 inference(unit_resolution,[status(thm)],[16502, 16267])).
% 292.31/184.88 tff(16504,plain,
% 292.31/184.88 (~node7(c_e_h_1, c_u, s1, s2)),
% 292.31/184.88 inference(unit_resolution,[status(thm)],[14330, 15631])).
% 292.31/184.88 tff(16505,plain,
% 292.31/184.88 (node8(c_e_h_1, c_u, s1, s2)),
% 292.31/184.88 inference(unit_resolution,[status(thm)],[14346, 16504])).
% 292.31/184.88 tff(16506,plain,
% 292.31/184.88 (~m_user_v_req(c_e_h_1, c_u, s1)),
% 292.31/184.88 inference(unit_resolution,[status(thm)],[14341, 16505, 15631])).
% 292.31/184.88 tff(16507,plain,
% 292.31/184.88 (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s1)),
% 292.31/184.88 inference(unit_resolution,[status(thm)],[14262, 395, 16506])).
% 292.31/184.88 tff(16508,plain,
% 292.31/184.88 (~m_mutex_h_half_v_out(c_e_h_1, c_a, s2)),
% 292.31/184.88 inference(unit_resolution,[status(thm)],[14258, 16507])).
% 292.31/184.88 tff(16509,plain,
% 292.31/184.88 (~m_and_h_gate_v_in1(c_e_h_1, c_c, s2)),
% 292.31/184.88 inference(unit_resolution,[status(thm)],[14232, 16508])).
% 292.31/184.88 tff(16510,plain,
% 292.31/184.88 (~m_and_h_gate_v_in1(c_e_h_1, c_c, s3)),
% 292.31/184.88 inference(unit_resolution,[status(thm)],[14638, 15632])).
% 292.31/184.88 tff(16511,plain,
% 292.31/184.88 (~node20(c_e_h_1, c_c, s3)),
% 292.31/184.88 inference(unit_resolution,[status(thm)],[14646, 16510])).
% 292.31/184.88 tff(16512,plain,
% 292.31/184.88 (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s3)),
% 292.31/184.88 inference(unit_resolution,[status(thm)],[15062, 395, 14673])).
% 292.31/184.88 tff(16513,plain,
% 292.31/184.88 (~m_mutex_h_half_v_out(c_e_h_1, c_a, s4)),
% 292.31/184.88 inference(unit_resolution,[status(thm)],[15058, 16512, 15632])).
% 292.31/184.88 tff(16514,plain,
% 292.31/184.88 (~m_and_h_gate_v_in1(c_e_h_1, c_c, s4)),
% 292.31/184.88 inference(unit_resolution,[status(thm)],[14108, 16513])).
% 292.31/184.88 tff(16515,plain,
% 292.31/184.88 (~node20(c_e_h_1, c_c, s4)),
% 292.31/184.88 inference(unit_resolution,[status(thm)],[14116, 16514])).
% 292.31/184.88 tff(16516,assumption,(~m_mutex_h_half_v_out(c_e_h_1, c_a, s6)), introduced(assumption)).
% 292.31/184.88 tff(16517,plain,
% 292.31/184.88 (m_mutex_h_half_v_inp(c_e_h_1, c_a, s4)),
% 292.31/184.88 inference(unit_resolution,[status(thm)],[16478, 15068, 14102])).
% 292.31/184.88 tff(16518,assumption,(m_mutex_h_half_v_inp(c_e_h_1, c_a, s5)), introduced(assumption)).
% 292.31/184.88 tff(16519,plain,
% 292.31/184.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_1, c_a, s5, s6)) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s5)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (~node12(c_e_h_1, c_a, s5, s6)) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s5)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s6))),
% 292.31/184.88 inference(rewrite,[status(thm)],[])).
% 292.31/184.88 tff(16520,plain,
% 292.31/184.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_1, c_a, s5, s6)) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s5)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s6))),
% 292.31/184.88 inference(quant_inst,[status(thm)],[])).
% 292.31/184.88 tff(16521,plain,
% 292.31/184.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (~node12(c_e_h_1, c_a, s5, s6)) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s5)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s6)),
% 292.31/184.88 inference(modus_ponens,[status(thm)],[16520, 16519])).
% 292.31/184.88 tff(16522,plain,
% 292.31/184.88 ($false),
% 292.31/184.88 inference(unit_resolution,[status(thm)],[16521, 1483, 16486, 16518, 16516])).
% 292.31/184.88 tff(16523,plain,((~node12(c_e_h_1, c_a, s5, s6)) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s5)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s6)), inference(lemma,lemma(discharge,[]))).
% 292.31/184.88 tff(16524,plain,
% 292.31/184.88 (~node12(c_e_h_1, c_a, s5, s6)),
% 292.31/184.88 inference(unit_resolution,[status(thm)],[16523, 16516, 16518])).
% 292.31/184.88 tff(16525,assumption,(node13(c_e_h_1, c_a, s5, s6)), introduced(assumption)).
% 292.31/184.88 tff(16526,plain,
% 292.31/184.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | ((~m_mutex_h_half_v_out(c_e_h_1, c_a, s5)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s6) | (~node13(c_e_h_1, c_a, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s5)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s6) | (~node13(c_e_h_1, c_a, s5, s6)))),
% 292.31/184.88 inference(rewrite,[status(thm)],[])).
% 292.31/184.88 tff(16527,plain,
% 292.31/184.88 ((m_mutex_h_half_v_out(c_e_h_1, c_a, s6) | (~node13(c_e_h_1, c_a, s5, s6)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s5))) <=> ((~m_mutex_h_half_v_out(c_e_h_1, c_a, s5)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s6) | (~node13(c_e_h_1, c_a, s5, s6)))),
% 292.31/184.88 inference(rewrite,[status(thm)],[])).
% 292.31/184.88 tff(16528,plain,
% 292.31/184.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_1, c_a, s6) | (~node13(c_e_h_1, c_a, s5, s6)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | ((~m_mutex_h_half_v_out(c_e_h_1, c_a, s5)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s6) | (~node13(c_e_h_1, c_a, s5, s6))))),
% 292.31/184.88 inference(monotonicity,[status(thm)],[16527])).
% 292.31/184.88 tff(16529,plain,
% 292.31/184.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_1, c_a, s6) | (~node13(c_e_h_1, c_a, s5, s6)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s5)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s6) | (~node13(c_e_h_1, c_a, s5, s6)))),
% 292.31/184.89 inference(transitivity,[status(thm)],[16528, 16526])).
% 292.31/184.89 tff(16530,plain,
% 292.31/184.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_1, c_a, s6) | (~node13(c_e_h_1, c_a, s5, s6)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s5)))),
% 292.31/184.89 inference(quant_inst,[status(thm)],[])).
% 292.31/184.89 tff(16531,plain,
% 292.31/184.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s5)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s6) | (~node13(c_e_h_1, c_a, s5, s6))),
% 292.31/184.89 inference(modus_ponens,[status(thm)],[16530, 16529])).
% 292.31/184.89 tff(16532,plain,
% 292.31/184.89 ($false),
% 292.31/184.89 inference(unit_resolution,[status(thm)],[16531, 1459, 16525, 16516, 15068])).
% 292.31/184.89 tff(16533,plain,((~node13(c_e_h_1, c_a, s5, s6)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s6) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s5))), inference(lemma,lemma(discharge,[]))).
% 292.31/184.89 tff(16534,plain,
% 292.31/184.89 (~node13(c_e_h_1, c_a, s5, s6)),
% 292.31/184.89 inference(unit_resolution,[status(thm)],[16533, 16516, 15068])).
% 292.31/184.89 tff(16535,plain,
% 292.31/184.89 ($false),
% 292.31/184.89 inference(unit_resolution,[status(thm)],[16496, 16534, 16524])).
% 292.31/184.89 tff(16536,plain,(m_mutex_h_half_v_out(c_e_h_1, c_a, s6) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s5)) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s5))), inference(lemma,lemma(discharge,[]))).
% 292.31/184.89 tff(16537,plain,
% 292.31/184.89 (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s5)),
% 292.31/184.89 inference(unit_resolution,[status(thm)],[16536, 15068, 16516])).
% 292.31/184.89 tff(16538,assumption,(m_user_v_req(c_e_h_1, c_u, s5)), introduced(assumption)).
% 292.31/184.89 tff(16539,plain,
% 292.31/184.89 (((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | ((~m_user_v_req(c_e_h_1, c_u, s5)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s5))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | (~m_user_v_req(c_e_h_1, c_u, s5)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s5))),
% 292.31/184.89 inference(rewrite,[status(thm)],[])).
% 292.31/184.89 tff(16540,plain,
% 292.31/184.89 ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | ((~m_user_v_req(c_e_h_1, c_u, s5)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s5))),
% 292.31/184.89 inference(quant_inst,[status(thm)],[])).
% 292.31/184.89 tff(16541,plain,
% 292.31/184.89 ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | (~m_user_v_req(c_e_h_1, c_u, s5)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s5)),
% 292.31/184.89 inference(modus_ponens,[status(thm)],[16540, 16539])).
% 292.31/184.89 tff(16542,plain,
% 292.31/184.89 ($false),
% 292.31/184.89 inference(unit_resolution,[status(thm)],[16541, 1426, 16538, 16485])).
% 292.31/184.89 tff(16543,plain,(m_mutex_h_half_v_inp(c_e_h_1, c_a, s5) | (~m_user_v_req(c_e_h_1, c_u, s5))), inference(lemma,lemma(discharge,[]))).
% 292.31/184.89 tff(16544,plain,
% 292.31/184.89 (~m_user_v_req(c_e_h_1, c_u, s5)),
% 292.31/184.89 inference(unit_resolution,[status(thm)],[16543, 16537])).
% 292.31/184.89 tff(16545,plain,
% 292.31/184.89 (~m_user_v_req(c_e_h_1, c_u, s4)),
% 292.31/184.89 inference(unit_resolution,[status(thm)],[16450, 16544, 16429])).
% 292.31/184.89 tff(16546,plain,
% 292.31/184.89 ($false),
% 292.31/184.89 inference(unit_resolution,[status(thm)],[16460, 395, 16545, 16517])).
% 292.31/184.89 tff(16547,plain,((~m_mutex_h_half_v_out(c_e_h_1, c_a, s5)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s6) | m_mutex_h_half_v_out(c_e_h_1, c_a, s4)), inference(lemma,lemma(discharge,[]))).
% 292.31/184.89 tff(16548,plain,
% 292.31/184.89 (~m_mutex_h_half_v_out(c_e_h_1, c_a, s5)),
% 292.31/184.89 inference(unit_resolution,[status(thm)],[16547, 16513, 16516])).
% 292.31/184.89 tff(16549,plain,
% 292.31/184.89 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_c, s5)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s5))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s5)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s5))),
% 292.31/184.89 inference(rewrite,[status(thm)],[])).
% 292.31/184.89 tff(16550,plain,
% 292.31/184.89 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_c, s5)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s5))),
% 292.31/184.89 inference(quant_inst,[status(thm)],[])).
% 292.31/184.89 tff(16551,plain,
% 292.31/184.89 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s5)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s5)),
% 292.31/184.89 inference(modus_ponens,[status(thm)],[16550, 16549])).
% 292.31/184.89 tff(16552,plain,
% 292.31/184.89 ($false),
% 292.31/184.89 inference(unit_resolution,[status(thm)],[16551, 567, 14855, 15075])).
% 292.31/184.89 tff(16553,plain,((~m_and_h_gate_v_in1(c_e_h_1, c_c, s5)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s5)), inference(lemma,lemma(discharge,[]))).
% 292.31/184.89 tff(16554,plain,
% 292.31/184.89 (~m_and_h_gate_v_in1(c_e_h_1, c_c, s5)),
% 292.31/184.89 inference(unit_resolution,[status(thm)],[16553, 16548])).
% 292.31/184.89 tff(16555,assumption,(node20(c_e_h_1, c_c, s5)), introduced(assumption)).
% 292.31/184.89 tff(16556,plain,
% 292.31/184.89 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_c, s5)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_c, s5)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s5))),
% 292.31/184.89 inference(rewrite,[status(thm)],[])).
% 292.31/184.89 tff(16557,plain,
% 292.31/184.89 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_c, s5)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s5))),
% 292.31/184.89 inference(quant_inst,[status(thm)],[])).
% 292.31/184.89 tff(16558,plain,
% 292.31/184.89 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_c, s5)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s5)),
% 292.31/184.89 inference(modus_ponens,[status(thm)],[16557, 16556])).
% 292.31/184.89 tff(16559,plain,
% 292.31/184.89 ($false),
% 292.31/184.89 inference(unit_resolution,[status(thm)],[16558, 38, 16555, 15067])).
% 292.31/184.89 tff(16560,plain,((~node20(c_e_h_1, c_c, s5)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s5)), inference(lemma,lemma(discharge,[]))).
% 292.31/184.89 tff(16561,plain,
% 292.31/184.89 (~node20(c_e_h_1, c_c, s5)),
% 292.31/184.89 inference(unit_resolution,[status(thm)],[16560, 16554])).
% 292.31/184.89 tff(16562,plain,
% 292.31/184.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_c, s6)) | (~node22(c_e_h_1, c_c, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_c, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s6)) | (~node22(c_e_h_1, c_c, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_c, s5))),
% 292.31/184.89 inference(rewrite,[status(thm)],[])).
% 292.31/184.89 tff(16563,plain,
% 292.31/184.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_c, s6)) | (~node22(c_e_h_1, c_c, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_c, s5))),
% 292.31/184.89 inference(quant_inst,[status(thm)],[])).
% 292.31/184.89 tff(16564,plain,
% 292.31/184.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s6)) | (~node22(c_e_h_1, c_c, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_c, s5)),
% 292.31/184.89 inference(modus_ponens,[status(thm)],[16563, 16562])).
% 292.31/184.89 tff(16565,plain,
% 292.31/184.89 ($false),
% 292.31/184.89 inference(unit_resolution,[status(thm)],[16564, 108, 14812, 15370, 16268])).
% 292.31/184.89 tff(16566,plain,((~node22(c_e_h_1, c_c, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_c, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s6))), inference(lemma,lemma(discharge,[]))).
% 292.31/184.89 tff(16567,plain,
% 292.31/184.89 (~node22(c_e_h_1, c_c, s5, s6)),
% 292.31/184.89 inference(unit_resolution,[status(thm)],[16566, 16268, 14812])).
% 292.31/184.89 tff(16568,assumption,(~node20(c_e_h_1, c_c, s5)), introduced(assumption)).
% 292.31/184.89 tff(16569,plain,
% 292.31/184.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_c, s5) | (~node21(c_e_h_1, c_c, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_c, s5) | (~node21(c_e_h_1, c_c, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s6)))),
% 292.31/184.89 inference(rewrite,[status(thm)],[])).
% 292.31/184.89 tff(16570,plain,
% 292.31/184.89 ((node20(c_e_h_1, c_c, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s6)) | (~node21(c_e_h_1, c_c, s5, s6))) <=> (node20(c_e_h_1, c_c, s5) | (~node21(c_e_h_1, c_c, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s6)))),
% 292.31/184.89 inference(rewrite,[status(thm)],[])).
% 292.31/184.89 tff(16571,plain,
% 292.31/184.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_c, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s6)) | (~node21(c_e_h_1, c_c, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_c, s5) | (~node21(c_e_h_1, c_c, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s6))))),
% 292.31/184.89 inference(monotonicity,[status(thm)],[16570])).
% 292.31/184.89 tff(16572,plain,
% 292.31/184.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_c, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s6)) | (~node21(c_e_h_1, c_c, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_c, s5) | (~node21(c_e_h_1, c_c, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s6)))),
% 292.31/184.89 inference(transitivity,[status(thm)],[16571, 16569])).
% 292.31/184.89 tff(16573,plain,
% 292.31/184.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_c, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s6)) | (~node21(c_e_h_1, c_c, s5, s6)))),
% 292.31/184.89 inference(quant_inst,[status(thm)],[])).
% 292.31/184.89 tff(16574,plain,
% 292.31/184.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_c, s5) | (~node21(c_e_h_1, c_c, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s6))),
% 292.31/184.89 inference(modus_ponens,[status(thm)],[16573, 16572])).
% 292.31/184.89 tff(16575,plain,
% 292.31/184.89 ($false),
% 292.31/184.89 inference(unit_resolution,[status(thm)],[16574, 52, 15076, 16268, 16568])).
% 292.31/184.89 tff(16576,plain,((~node21(c_e_h_1, c_c, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s6)) | node20(c_e_h_1, c_c, s5)), inference(lemma,lemma(discharge,[]))).
% 292.31/184.89 tff(16577,plain,
% 292.31/184.89 (~node21(c_e_h_1, c_c, s5, s6)),
% 292.31/184.89 inference(unit_resolution,[status(thm)],[16576, 16268, 16568])).
% 292.31/184.89 tff(16578,plain,
% 292.31/184.89 ($false),
% 292.31/184.89 inference(unit_resolution,[status(thm)],[15383, 16577, 16567])).
% 292.31/184.89 tff(16579,plain,((~m_and_h_gate_v_out(c_e_h_1, c_c, s6)) | node20(c_e_h_1, c_c, s5) | m_and_h_gate_v_out(c_e_h_1, c_c, s5)), inference(lemma,lemma(discharge,[]))).
% 292.31/184.89 tff(16580,plain,
% 292.31/184.89 (m_and_h_gate_v_out(c_e_h_1, c_c, s5)),
% 292.31/184.89 inference(unit_resolution,[status(thm)],[16579, 16561, 16268])).
% 292.31/184.89 tff(16581,plain,
% 292.31/184.89 (m_and_h_gate_v_out(c_e_h_1, c_c, s4)),
% 292.31/184.89 inference(unit_resolution,[status(thm)],[14526, 16580, 16515])).
% 292.31/184.89 tff(16582,plain,
% 292.31/184.89 (m_and_h_gate_v_out(c_e_h_1, c_c, s3)),
% 292.31/184.89 inference(unit_resolution,[status(thm)],[14663, 16581, 16511])).
% 292.31/184.89 tff(16583,plain,
% 292.31/184.89 (node20(c_e_h_1, c_c, s2)),
% 292.31/184.89 inference(unit_resolution,[status(thm)],[14216, 16582])).
% 292.31/184.89 tff(16584,plain,
% 292.31/184.89 ($false),
% 292.31/184.89 inference(unit_resolution,[status(thm)],[14222, 38, 16583, 16509])).
% 292.31/184.89 tff(16585,plain,(m_user_v_req(c_e_h_1, c_u, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s6)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s6)), inference(lemma,lemma(discharge,[]))).
% 292.31/184.89 tff(16586,plain,
% 292.31/184.89 ($false),
% 292.31/184.89 inference(unit_resolution,[status(thm)],[16585, 16453, 16503, 16268])).
% 292.31/184.89 tff(16587,plain,(m_user_v_req(c_e_h_1, c_u, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s6))), inference(lemma,lemma(discharge,[]))).
% 292.31/184.89 tff(16588,plain,
% 292.31/184.89 (~m_and_h_gate_v_out(c_e_h_1, c_c, s6)),
% 292.31/184.89 inference(unit_resolution,[status(thm)],[16587, 16267])).
% 292.31/184.89 tff(16589,plain,
% 292.31/184.89 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_g, s6)) | m_and_h_gate_v_out(c_e_h_1, c_c, s6))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_g, s6)) | m_and_h_gate_v_out(c_e_h_1, c_c, s6))),
% 292.31/184.89 inference(rewrite,[status(thm)],[])).
% 292.31/184.89 tff(16590,plain,
% 292.31/184.89 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_g, s6)) | m_and_h_gate_v_out(c_e_h_1, c_c, s6))),
% 292.31/184.89 inference(quant_inst,[status(thm)],[])).
% 292.31/184.89 tff(16591,plain,
% 292.31/184.89 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_g, s6)) | m_and_h_gate_v_out(c_e_h_1, c_c, s6)),
% 292.31/184.89 inference(modus_ponens,[status(thm)],[16590, 16589])).
% 292.31/184.89 tff(16592,plain,
% 292.31/184.89 (~m_or_h_gate_v_in1(c_e_h_1, c_g, s6)),
% 292.31/184.89 inference(unit_resolution,[status(thm)],[16591, 2708, 16588])).
% 292.31/184.89 tff(16593,plain,
% 292.31/184.89 (~node5(c_e_h_1, c_g, s6, s7)),
% 292.31/184.89 inference(unit_resolution,[status(thm)],[16253, 16592, 16244, 15952])).
% 292.31/184.89 tff(16594,plain,
% 292.31/184.89 (node6(c_e_h_1, c_g, s6, s7)),
% 292.31/184.89 inference(unit_resolution,[status(thm)],[16262, 16593])).
% 292.31/184.89 tff(16595,plain,
% 292.31/184.89 (m_or_h_gate_v_out(c_e_h_1, c_g, s6)),
% 292.31/184.89 inference(unit_resolution,[status(thm)],[15989, 16594, 15952])).
% 292.31/184.89 tff(16596,plain,
% 292.31/184.89 (~m_and_h_gate_v_out(c_e_h_1, c_c, s4)),
% 292.31/184.89 inference(unit_resolution,[status(thm)],[14671, 16454])).
% 292.31/184.89 tff(16597,plain,
% 292.31/184.89 (~m_or_h_gate_v_in1(c_e_h_1, c_g, s4)),
% 292.31/184.89 inference(unit_resolution,[status(thm)],[14124, 16596])).
% 292.31/184.89 tff(16598,plain,
% 292.31/184.89 (~m_and_h_gate_v_out(c_e_h_1, c_c, s3)),
% 292.31/184.89 inference(unit_resolution,[status(thm)],[14414, 16596])).
% 292.31/184.89 tff(16599,plain,
% 292.31/184.89 (~m_or_h_gate_v_in1(c_e_h_1, c_g, s3)),
% 292.31/184.89 inference(unit_resolution,[status(thm)],[14418, 2708, 16598])).
% 292.31/184.89 tff(16600,plain,
% 292.31/184.89 (~m_or_h_gate_v_out(c_e_h_1, c_g, s4)),
% 292.31/184.89 inference(unit_resolution,[status(thm)],[14503, 16599])).
% 292.31/184.89 tff(16601,plain,
% 292.31/184.89 (~m_or_h_gate_v_out(c_e_h_1, c_g, s5)),
% 292.31/184.89 inference(unit_resolution,[status(thm)],[14601, 16600, 16597])).
% 292.31/184.89 tff(16602,plain,
% 292.31/184.89 (m_or_h_gate_v_in1(c_e_h_1, c_g, s5)),
% 292.31/184.89 inference(unit_resolution,[status(thm)],[14562, 16601, 14101, 16595])).
% 292.31/184.89 tff(16603,plain,
% 292.31/184.89 (~m_and_h_gate_v_in1(c_e_h_1, c_c, s4)),
% 292.31/184.89 inference(unit_resolution,[status(thm)],[14108, 16457])).
% 292.31/184.89 tff(16604,plain,
% 292.31/184.89 (~node20(c_e_h_1, c_c, s4)),
% 292.31/184.89 inference(unit_resolution,[status(thm)],[14116, 16603])).
% 292.31/184.89 tff(16605,plain,
% 292.31/184.89 (~m_and_h_gate_v_out(c_e_h_1, c_c, s5)),
% 292.31/184.89 inference(unit_resolution,[status(thm)],[14526, 16604, 16596])).
% 292.31/184.89 tff(16606,plain,
% 292.31/184.89 ($false),
% 292.31/184.89 inference(unit_resolution,[status(thm)],[14530, 2708, 16605, 16602])).
% 292.31/184.89 tff(16607,plain,(m_user_v_req(c_e_h_1, c_u, s5) | m_or_h_gate_v_in2(c_e_h_1, c_g, s5) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s7)) | m_or_h_gate_v_in2(c_e_h_1, c_g, s6)), inference(lemma,lemma(discharge,[]))).
% 292.31/184.89 tff(16608,plain,
% 292.31/184.89 (m_user_v_req(c_e_h_1, c_u, s5)),
% 292.31/184.89 inference(unit_resolution,[status(thm)],[16607, 15952, 16244, 14101])).
% 292.31/184.89 tff(16609,plain,
% 292.31/184.89 (m_mutex_h_half_v_inp(c_e_h_1, c_a, s5)),
% 292.31/184.89 inference(unit_resolution,[status(thm)],[16543, 16608])).
% 292.31/184.89 tff(16610,plain,
% 292.31/184.89 (~m_mutex_h_half_v_out(c_e_h_1, c_a, s5)),
% 292.31/184.89 inference(unit_resolution,[status(thm)],[16536, 16516, 16609])).
% 292.31/184.89 tff(16611,plain,
% 292.31/184.89 (~m_and_h_gate_v_out(c_e_h_1, c_c, s4)),
% 292.31/184.89 inference(unit_resolution,[status(thm)],[15023, 16610])).
% 292.31/184.89 tff(16612,plain,
% 292.31/184.89 (m_user_v_req(c_e_h_1, c_u, s3)),
% 292.31/184.89 inference(unit_resolution,[status(thm)],[16585, 16268, 16516])).
% 292.31/184.89 tff(16613,plain,
% 292.31/184.89 (m_user_v_req(c_e_h_1, c_u, s4)),
% 292.31/184.89 inference(unit_resolution,[status(thm)],[14979, 16612])).
% 292.31/184.89 tff(16614,plain,
% 292.31/184.89 (m_mutex_h_half_v_inp(c_e_h_1, c_a, s4)),
% 292.31/184.89 inference(unit_resolution,[status(thm)],[14987, 16613])).
% 292.31/184.89 tff(16615,plain,
% 292.31/184.89 (~m_and_h_gate_v_in1(c_e_h_1, c_c, s5)),
% 292.31/184.89 inference(unit_resolution,[status(thm)],[16553, 14855])).
% 292.31/184.90 tff(16616,plain,
% 292.31/184.90 (~node20(c_e_h_1, c_c, s5)),
% 292.31/184.90 inference(unit_resolution,[status(thm)],[16560, 16615])).
% 292.31/184.90 tff(16617,plain,
% 292.31/184.90 (m_and_h_gate_v_out(c_e_h_1, c_c, s5)),
% 292.31/184.90 inference(unit_resolution,[status(thm)],[16579, 16268, 16616])).
% 292.31/184.90 tff(16618,plain,
% 292.31/184.90 (m_mutex_h_half_v_inp(c_e_h_1, c_a, s3)),
% 292.31/184.90 inference(unit_resolution,[status(thm)],[14768, 16612])).
% 292.31/184.90 tff(16619,plain,
% 292.31/184.90 (m_and_h_gate_v_out(c_e_h_1, c_c, s4)),
% 292.31/184.90 inference(unit_resolution,[status(thm)],[14526, 14117, 14506])).
% 292.31/184.90 tff(16620,plain,
% 292.31/184.90 (node20(c_e_h_1, c_c, s3)),
% 292.31/184.90 inference(unit_resolution,[status(thm)],[14663, 16619, 14655])).
% 292.31/184.90 tff(16621,plain,
% 292.31/184.90 (m_and_h_gate_v_in1(c_e_h_1, c_c, s3)),
% 292.31/184.90 inference(unit_resolution,[status(thm)],[14646, 16620])).
% 292.31/184.90 tff(16622,plain,
% 292.31/184.90 (m_mutex_h_half_v_out(c_e_h_1, c_a, s3)),
% 292.31/184.90 inference(unit_resolution,[status(thm)],[14638, 16621])).
% 292.31/184.90 tff(16623,plain,
% 292.31/184.90 (~node13(c_e_h_1, c_a, s3, s4)),
% 292.31/184.90 inference(unit_resolution,[status(thm)],[14786, 16622, 14102])).
% 292.31/184.90 tff(16624,plain,
% 292.31/184.90 (node12(c_e_h_1, c_a, s3, s4)),
% 292.31/184.90 inference(unit_resolution,[status(thm)],[14791, 16623])).
% 292.31/184.90 tff(16625,plain,
% 292.31/184.90 ($false),
% 292.31/184.90 inference(unit_resolution,[status(thm)],[14777, 1483, 16624, 14102, 14770])).
% 292.31/184.90 tff(16626,plain,(m_mutex_h_half_v_out(c_e_h_1, c_a, s4) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s3)) | m_and_h_gate_v_out(c_e_h_1, c_c, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s5))), inference(lemma,lemma(discharge,[]))).
% 292.31/184.90 tff(16627,plain,
% 292.31/184.90 (m_and_h_gate_v_out(c_e_h_1, c_c, s3)),
% 292.31/184.90 inference(unit_resolution,[status(thm)],[16626, 14102, 14770, 14506])).
% 292.31/184.90 tff(16628,plain,
% 292.31/184.90 (node20(c_e_h_1, c_c, s2)),
% 292.31/184.90 inference(unit_resolution,[status(thm)],[14216, 16627])).
% 292.31/184.90 tff(16629,plain,
% 292.31/184.90 (m_and_h_gate_v_in1(c_e_h_1, c_c, s2)),
% 292.31/184.90 inference(unit_resolution,[status(thm)],[14224, 16628])).
% 292.31/184.90 tff(16630,plain,
% 292.31/184.90 (m_mutex_h_half_v_out(c_e_h_1, c_a, s2)),
% 292.31/184.90 inference(unit_resolution,[status(thm)],[14232, 16629])).
% 292.31/184.90 tff(16631,plain,
% 292.31/184.90 (node13(c_e_h_1, c_a, s3, s4)),
% 292.31/184.90 inference(unit_resolution,[status(thm)],[14791, 14780])).
% 292.31/184.90 tff(16632,plain,
% 292.31/184.90 (~m_mutex_h_half_v_out(c_e_h_1, c_a, s3)),
% 292.31/184.90 inference(unit_resolution,[status(thm)],[14786, 16631, 14102])).
% 292.31/184.90 tff(16633,plain,
% 292.31/184.90 (~node13(c_e_h_1, c_a, s2, s3)),
% 292.31/184.90 inference(unit_resolution,[status(thm)],[14367, 16632, 16630])).
% 292.31/184.90 tff(16634,plain,
% 292.31/184.90 (node12(c_e_h_1, c_a, s2, s3)),
% 292.31/184.90 inference(unit_resolution,[status(thm)],[14372, 16633])).
% 292.31/184.90 tff(16635,plain,
% 292.31/184.90 (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s2)),
% 292.31/184.90 inference(unit_resolution,[status(thm)],[14379, 1483, 16632, 16634])).
% 292.31/184.90 tff(16636,plain,
% 292.31/184.90 (m_mutex_h_half_v_inp(c_e_h_1, c_a, s1)),
% 292.31/184.90 inference(unit_resolution,[status(thm)],[14258, 16630])).
% 292.31/184.90 tff(16637,plain,
% 292.31/184.90 (m_user_v_req(c_e_h_1, c_u, s1)),
% 292.31/184.90 inference(unit_resolution,[status(thm)],[14262, 395, 16636])).
% 292.31/184.90 tff(16638,plain,
% 292.31/184.90 (m_user_v_req(c_e_h_1, c_u, s2)),
% 292.31/184.90 inference(unit_resolution,[status(thm)],[14348, 16637])).
% 292.31/184.90 tff(16639,plain,
% 292.31/184.90 ($false),
% 292.31/184.90 inference(unit_resolution,[status(thm)],[14354, 1426, 16638, 16635])).
% 292.31/184.90 tff(16640,plain,(m_mutex_h_half_v_out(c_e_h_1, c_a, s4) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s3)) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s5))), inference(lemma,lemma(discharge,[]))).
% 292.31/184.90 tff(16641,plain,
% 292.31/184.90 (m_mutex_h_half_v_out(c_e_h_1, c_a, s4)),
% 292.31/184.90 inference(unit_resolution,[status(thm)],[16640, 16618, 16617])).
% 292.31/184.90 tff(16642,plain,
% 292.31/184.90 (~node13(c_e_h_1, c_a, s4, s5)),
% 292.31/184.90 inference(unit_resolution,[status(thm)],[15013, 16641, 14855])).
% 292.31/184.90 tff(16643,plain,
% 292.31/184.90 (node12(c_e_h_1, c_a, s4, s5)),
% 292.31/184.90 inference(unit_resolution,[status(thm)],[15003, 16642])).
% 292.31/184.90 tff(16644,plain,
% 292.31/184.90 ($false),
% 292.31/184.90 inference(unit_resolution,[status(thm)],[14996, 1483, 16643, 14855, 16614])).
% 292.31/184.90 tff(16645,plain,((~m_and_h_gate_v_out(c_e_h_1, c_c, s6)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s5) | m_mutex_h_half_v_out(c_e_h_1, c_a, s6)), inference(lemma,lemma(discharge,[]))).
% 292.31/184.90 tff(16646,plain,
% 292.31/184.90 (m_mutex_h_half_v_out(c_e_h_1, c_a, s5)),
% 292.31/184.90 inference(unit_resolution,[status(thm)],[16645, 16268, 16516])).
% 292.31/184.90 tff(16647,plain,
% 292.31/184.90 (m_user_v_req(c_e_h_1, c_u, s5)),
% 292.31/184.90 inference(unit_resolution,[status(thm)],[16587, 16268])).
% 292.41/184.90 tff(16648,plain,
% 292.41/184.90 (m_mutex_h_half_v_inp(c_e_h_1, c_a, s5)),
% 292.41/184.90 inference(unit_resolution,[status(thm)],[16543, 16647])).
% 292.41/184.90 tff(16649,plain,
% 292.41/184.90 ($false),
% 292.41/184.90 inference(unit_resolution,[status(thm)],[16536, 16648, 16646, 16516])).
% 292.41/184.90 tff(16650,plain,((~m_and_h_gate_v_out(c_e_h_1, c_c, s6)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s6)), inference(lemma,lemma(discharge,[]))).
% 292.41/184.90 tff(16651,plain,
% 292.41/184.90 (~m_and_h_gate_v_out(c_e_h_1, c_c, s6)),
% 292.41/184.90 inference(unit_resolution,[status(thm)],[16650, 16516])).
% 292.41/184.90 tff(16652,plain,
% 292.41/184.90 (~m_or_h_gate_v_in1(c_e_h_1, c_g, s6)),
% 292.41/184.90 inference(unit_resolution,[status(thm)],[16591, 2708, 16651])).
% 292.41/184.90 tff(16653,plain,
% 292.41/184.90 (~node5(c_e_h_1, c_g, s6, s7)),
% 292.41/184.90 inference(unit_resolution,[status(thm)],[16253, 16652, 16244, 15952])).
% 292.41/184.90 tff(16654,plain,
% 292.41/184.90 (node6(c_e_h_1, c_g, s6, s7)),
% 292.41/184.90 inference(unit_resolution,[status(thm)],[16262, 16653])).
% 292.41/184.90 tff(16655,plain,
% 292.41/184.90 (m_or_h_gate_v_out(c_e_h_1, c_g, s6)),
% 292.41/184.90 inference(unit_resolution,[status(thm)],[15989, 16654, 15952])).
% 292.41/184.90 tff(16656,plain,
% 292.41/184.90 (~m_or_h_gate_v_in1(c_e_h_1, c_g, s4)),
% 292.41/184.90 inference(unit_resolution,[status(thm)],[14124, 16611])).
% 292.41/184.90 tff(16657,plain,
% 292.41/184.90 (~m_and_h_gate_v_out(c_e_h_1, c_c, s3)),
% 292.41/184.90 inference(unit_resolution,[status(thm)],[14414, 16611])).
% 292.41/184.90 tff(16658,plain,
% 292.41/184.90 (~m_or_h_gate_v_in1(c_e_h_1, c_g, s3)),
% 292.41/184.90 inference(unit_resolution,[status(thm)],[14418, 2708, 16657])).
% 292.41/184.90 tff(16659,plain,
% 292.41/184.90 (~m_or_h_gate_v_out(c_e_h_1, c_g, s4)),
% 292.41/184.90 inference(unit_resolution,[status(thm)],[14503, 16658])).
% 292.41/184.90 tff(16660,plain,
% 292.41/184.90 (~m_or_h_gate_v_out(c_e_h_1, c_g, s5)),
% 292.41/184.90 inference(unit_resolution,[status(thm)],[14601, 16659, 16656])).
% 292.41/184.90 tff(16661,plain,
% 292.41/184.90 (m_or_h_gate_v_in1(c_e_h_1, c_g, s5)),
% 292.41/184.90 inference(unit_resolution,[status(thm)],[14562, 16660, 14101, 16655])).
% 292.41/184.90 tff(16662,plain,
% 292.41/184.90 (m_and_h_gate_v_out(c_e_h_1, c_c, s5)),
% 292.41/184.90 inference(unit_resolution,[status(thm)],[14530, 2708, 16661])).
% 292.41/184.90 tff(16663,plain,
% 292.41/184.90 (node20(c_e_h_1, c_c, s4)),
% 292.41/184.90 inference(unit_resolution,[status(thm)],[14526, 16662, 16611])).
% 292.41/184.90 tff(16664,plain,
% 292.41/184.90 (m_and_h_gate_v_in1(c_e_h_1, c_c, s4)),
% 292.41/184.90 inference(unit_resolution,[status(thm)],[14116, 16663])).
% 292.41/184.90 tff(16665,plain,
% 292.41/184.90 (m_mutex_h_half_v_out(c_e_h_1, c_a, s4)),
% 292.41/184.90 inference(unit_resolution,[status(thm)],[14108, 16664])).
% 292.41/184.90 tff(16666,plain,
% 292.41/184.90 (~node13(c_e_h_1, c_a, s4, s5)),
% 292.41/184.90 inference(unit_resolution,[status(thm)],[15013, 16665, 16610])).
% 292.41/184.90 tff(16667,plain,
% 292.41/184.90 (node12(c_e_h_1, c_a, s4, s5)),
% 292.41/184.90 inference(unit_resolution,[status(thm)],[15003, 16666])).
% 292.41/184.90 tff(16668,plain,
% 292.41/184.90 (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s4)),
% 292.41/184.90 inference(unit_resolution,[status(thm)],[14998, 16667, 16610])).
% 292.41/184.90 tff(16669,plain,
% 292.41/184.90 (~m_user_v_req(c_e_h_1, c_u, s4)),
% 292.41/184.90 inference(unit_resolution,[status(thm)],[14987, 16668])).
% 292.41/184.90 tff(16670,plain,
% 292.41/184.90 (~m_user_v_req(c_e_h_1, c_u, s3)),
% 292.41/184.90 inference(unit_resolution,[status(thm)],[14979, 16669])).
% 292.41/184.90 tff(16671,plain,
% 292.41/184.90 (~m_user_v_req(c_e_h_1, c_u, s2)),
% 292.41/184.90 inference(unit_resolution,[status(thm)],[14760, 16670])).
% 292.41/184.90 tff(16672,plain,
% 292.41/184.90 (~m_mutex_h_half_v_out(c_e_h_1, c_a, s3)),
% 292.41/184.90 inference(unit_resolution,[status(thm)],[14632, 16671])).
% 292.41/184.90 tff(16673,plain,
% 292.41/184.90 (m_mutex_h_half_v_inp(c_e_h_1, c_a, s3)),
% 292.41/184.90 inference(unit_resolution,[status(thm)],[15058, 16672, 16665])).
% 292.41/184.90 tff(16674,plain,
% 292.41/184.90 ($false),
% 292.41/184.90 inference(unit_resolution,[status(thm)],[15062, 395, 16670, 16673])).
% 292.41/184.90 tff(16675,plain,(m_mutex_h_half_v_out(c_e_h_1, c_a, s6) | m_or_h_gate_v_in2(c_e_h_1, c_g, s5) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s7)) | m_or_h_gate_v_in2(c_e_h_1, c_g, s6)), inference(lemma,lemma(discharge,[]))).
% 292.41/184.90 tff(16676,plain,
% 292.41/184.90 (m_mutex_h_half_v_out(c_e_h_1, c_a, s6) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s7))),
% 292.41/184.90 inference(unit_resolution,[status(thm)],[16675, 16243, 14100])).
% 292.41/184.90 tff(16677,plain,
% 292.41/184.90 (m_mutex_h_half_v_out(c_e_h_1, c_a, s6)),
% 292.41/184.90 inference(unit_resolution,[status(thm)],[16676, 15952])).
% 292.41/184.90 tff(16678,assumption,(~m_and_h_gate_v_in1(c_e_h_1, c_c, s6)), introduced(assumption)).
% 292.41/184.90 tff(16679,plain,
% 292.41/184.90 (((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | ((~m_mutex_h_half_v_out(c_e_h_1, c_a, s6)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s6))) <=> ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s6)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s6))),
% 292.41/184.90 inference(rewrite,[status(thm)],[])).
% 292.41/184.90 tff(16680,plain,
% 292.41/184.90 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | ((~m_mutex_h_half_v_out(c_e_h_1, c_a, s6)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s6))),
% 292.41/184.90 inference(quant_inst,[status(thm)],[])).
% 292.41/184.90 tff(16681,plain,
% 292.41/184.90 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s6)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s6)),
% 292.41/184.90 inference(modus_ponens,[status(thm)],[16680, 16679])).
% 292.41/184.90 tff(16682,plain,
% 292.41/184.90 ($false),
% 292.41/184.90 inference(unit_resolution,[status(thm)],[16681, 2556, 16480, 16678])).
% 292.41/184.90 tff(16683,plain,(m_and_h_gate_v_in1(c_e_h_1, c_c, s6) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s6))), inference(lemma,lemma(discharge,[]))).
% 292.41/184.90 tff(16684,plain,
% 292.41/184.90 (m_and_h_gate_v_in1(c_e_h_1, c_c, s6)),
% 292.41/184.90 inference(unit_resolution,[status(thm)],[16683, 16677])).
% 292.41/184.90 tff(16685,assumption,(m_and_h_gate_v_in1(c_e_h_1, c_c, s6)), introduced(assumption)).
% 292.41/184.90 tff(16686,assumption,(node21(c_e_h_1, c_c, s6, s7)), introduced(assumption)).
% 292.41/184.90 tff(16687,assumption,(m_or_h_gate_v_out(c_e_h_1, c_j, s2)), introduced(assumption)).
% 292.41/184.90 tff(16688,assumption,(node6(c_e_h_1, c_j, s1, s2)), introduced(assumption)).
% 292.41/184.90 tff(16689,plain,
% 292.41/184.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2)) | (~node6(c_e_h_1, c_j, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2)) | (~node6(c_e_h_1, c_j, s1, s2)))),
% 292.41/184.90 inference(rewrite,[status(thm)],[])).
% 292.41/184.90 tff(16690,plain,
% 292.41/184.90 (((~node6(c_e_h_1, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2)) | m_or_h_gate_v_out(c_e_h_1, c_j, s1)) <=> (m_or_h_gate_v_out(c_e_h_1, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2)) | (~node6(c_e_h_1, c_j, s1, s2)))),
% 292.41/184.90 inference(rewrite,[status(thm)],[])).
% 292.41/184.90 tff(16691,plain,
% 292.41/184.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2)) | m_or_h_gate_v_out(c_e_h_1, c_j, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2)) | (~node6(c_e_h_1, c_j, s1, s2))))),
% 292.41/184.90 inference(monotonicity,[status(thm)],[16690])).
% 292.41/184.90 tff(16692,plain,
% 292.41/184.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2)) | m_or_h_gate_v_out(c_e_h_1, c_j, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2)) | (~node6(c_e_h_1, c_j, s1, s2)))),
% 292.41/184.90 inference(transitivity,[status(thm)],[16691, 16689])).
% 292.41/184.90 tff(16693,plain,
% 292.41/184.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2)) | m_or_h_gate_v_out(c_e_h_1, c_j, s1))),
% 292.41/184.90 inference(quant_inst,[status(thm)],[])).
% 292.41/184.90 tff(16694,plain,
% 292.41/184.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2)) | (~node6(c_e_h_1, c_j, s1, s2))),
% 292.41/184.90 inference(modus_ponens,[status(thm)],[16693, 16692])).
% 292.41/184.91 tff(16695,plain,
% 292.41/184.91 ($false),
% 292.41/184.91 inference(unit_resolution,[status(thm)],[16694, 1121, 16687, 15167, 16688])).
% 292.41/184.91 tff(16696,plain,((~node6(c_e_h_1, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2))), inference(lemma,lemma(discharge,[]))).
% 292.41/184.91 tff(16697,plain,
% 292.41/184.91 (~node6(c_e_h_1, c_j, s1, s2)),
% 292.41/184.91 inference(unit_resolution,[status(thm)],[16696, 16687])).
% 292.41/184.91 tff(16698,plain,
% 292.41/184.91 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s1))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s1))),
% 292.41/184.91 inference(rewrite,[status(thm)],[])).
% 292.41/184.91 tff(16699,plain,
% 292.41/184.91 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s1))),
% 292.41/184.91 inference(quant_inst,[status(thm)],[])).
% 292.41/184.91 tff(16700,plain,
% 292.41/184.91 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s1)),
% 292.41/184.91 inference(modus_ponens,[status(thm)],[16699, 16698])).
% 292.41/184.91 tff(16701,plain,
% 292.41/184.91 (node3(c_e_h_3, c_e_h_1, s1)),
% 292.41/184.91 inference(unit_resolution,[status(thm)],[16700, 2922, 1056])).
% 292.41/184.91 tff(16702,plain,
% 292.41/184.91 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s1)) | (~node3(c_e_h_3, c_e_h_1, s1)) | m_and_h_gate_v_out(c_e_h_3, c_q, s1))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s1)) | (~node3(c_e_h_3, c_e_h_1, s1)) | m_and_h_gate_v_out(c_e_h_3, c_q, s1))),
% 292.41/184.91 inference(rewrite,[status(thm)],[])).
% 292.41/184.91 tff(16703,plain,
% 292.41/184.91 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s1)) | (~node3(c_e_h_3, c_e_h_1, s1)) | m_and_h_gate_v_out(c_e_h_3, c_q, s1))),
% 292.41/184.91 inference(quant_inst,[status(thm)],[])).
% 292.41/184.91 tff(16704,plain,
% 292.41/184.91 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s1)) | (~node3(c_e_h_3, c_e_h_1, s1)) | m_and_h_gate_v_out(c_e_h_3, c_q, s1)),
% 292.41/184.91 inference(modus_ponens,[status(thm)],[16703, 16702])).
% 292.41/184.91 tff(16705,plain,
% 292.41/184.91 ((~m_cell_v_ack(c_e_h_1, s1)) | m_and_h_gate_v_out(c_e_h_3, c_q, s1)),
% 292.41/184.91 inference(unit_resolution,[status(thm)],[16704, 1073, 16701])).
% 292.41/184.91 tff(16706,plain,
% 292.41/184.91 (~m_cell_v_ack(c_e_h_1, s1)),
% 292.41/184.91 inference(unit_resolution,[status(thm)],[16705, 5670])).
% 292.41/184.91 tff(16707,plain,
% 292.41/184.91 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s1)) | m_cell_v_ack(c_e_h_1, s1))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s1)) | m_cell_v_ack(c_e_h_1, s1))),
% 292.41/184.91 inference(rewrite,[status(thm)],[])).
% 292.41/184.91 tff(16708,plain,
% 292.41/184.91 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s1)) | m_cell_v_ack(c_e_h_1, s1))),
% 292.41/184.91 inference(quant_inst,[status(thm)],[])).
% 292.41/184.91 tff(16709,plain,
% 292.41/184.91 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s1)) | m_cell_v_ack(c_e_h_1, s1)),
% 292.41/184.91 inference(modus_ponens,[status(thm)],[16708, 16707])).
% 292.41/184.91 tff(16710,plain,
% 292.41/184.91 (~m_or_h_gate_v_in2(c_e_h_1, c_j, s1)),
% 292.41/184.91 inference(unit_resolution,[status(thm)],[16709, 1085, 16706])).
% 292.41/184.91 tff(16711,assumption,(m_and_h_gate_v_out(c_e_h_1, c_l, s1)), introduced(assumption)).
% 292.41/184.91 tff(16712,assumption,(node21(c_e_h_1, c_l, s0, s1)), introduced(assumption)).
% 292.41/184.91 tff(16713,plain,
% 292.41/184.91 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0))),
% 292.41/184.91 inference(rewrite,[status(thm)],[])).
% 292.41/184.91 tff(16714,plain,
% 292.41/184.91 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0))),
% 292.41/184.91 inference(quant_inst,[status(thm)],[])).
% 292.41/184.91 tff(16715,plain,
% 292.41/184.91 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s0)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s0)),
% 292.41/184.91 inference(modus_ponens,[status(thm)],[16714, 16713])).
% 292.41/184.91 tff(16716,plain,
% 292.41/184.91 (~m_and_h_gate_v_in2(c_e_h_1, c_l, s0)),
% 292.41/184.91 inference(unit_resolution,[status(thm)],[16715, 4549, 14286])).
% 292.41/184.91 tff(16717,plain,
% 292.41/184.91 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s0)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s0))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s0)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s0))),
% 292.41/184.91 inference(rewrite,[status(thm)],[])).
% 292.41/184.91 tff(16718,plain,
% 292.41/184.91 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s0)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s0))),
% 292.41/184.91 inference(quant_inst,[status(thm)],[])).
% 292.41/184.91 tff(16719,plain,
% 292.41/184.91 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s0)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s0)),
% 292.41/184.91 inference(modus_ponens,[status(thm)],[16718, 16717])).
% 292.41/184.91 tff(16720,plain,
% 292.41/184.91 (~node20(c_e_h_1, c_l, s0)),
% 292.41/184.91 inference(unit_resolution,[status(thm)],[16719, 4563, 16716])).
% 292.41/184.91 tff(16721,plain,
% 292.41/184.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s1)) | (~node21(c_e_h_1, c_l, s0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s1)) | (~node21(c_e_h_1, c_l, s0, s1)))),
% 292.41/184.91 inference(rewrite,[status(thm)],[])).
% 292.41/184.91 tff(16722,plain,
% 292.41/184.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s1)) | (~node21(c_e_h_1, c_l, s0, s1)))),
% 292.41/184.91 inference(quant_inst,[status(thm)],[])).
% 292.41/184.91 tff(16723,plain,
% 292.41/184.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s0) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s1)) | (~node21(c_e_h_1, c_l, s0, s1))),
% 292.41/184.91 inference(modus_ponens,[status(thm)],[16722, 16721])).
% 292.41/184.91 tff(16724,plain,
% 292.41/184.91 ($false),
% 292.41/184.91 inference(unit_resolution,[status(thm)],[16723, 52, 16720, 16712, 16711])).
% 292.41/184.91 tff(16725,plain,((~node21(c_e_h_1, c_l, s0, s1)) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s1))), inference(lemma,lemma(discharge,[]))).
% 292.41/184.91 tff(16726,plain,
% 292.41/184.91 (~node21(c_e_h_1, c_l, s0, s1)),
% 292.41/184.91 inference(unit_resolution,[status(thm)],[16725, 16711])).
% 292.41/184.91 tff(16727,plain,
% 292.41/184.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_1, c_l, s0, s1) | node22(c_e_h_1, c_l, s0, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_1, c_l, s0, s1) | node22(c_e_h_1, c_l, s0, s1))),
% 292.41/184.91 inference(rewrite,[status(thm)],[])).
% 292.41/184.91 tff(16728,plain,
% 292.41/184.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s0, s1)) | node21(c_e_h_1, c_l, s0, s1) | node22(c_e_h_1, c_l, s0, s1))),
% 292.41/184.91 inference(quant_inst,[status(thm)],[])).
% 292.41/184.91 tff(16729,plain,
% 292.41/184.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s0, s1)) | node21(c_e_h_1, c_l, s0, s1) | node22(c_e_h_1, c_l, s0, s1)),
% 292.41/184.91 inference(modus_ponens,[status(thm)],[16728, 16727])).
% 292.41/184.91 tff(16730,plain,
% 292.41/184.91 (node21(c_e_h_1, c_l, s0, s1) | node22(c_e_h_1, c_l, s0, s1)),
% 292.41/184.91 inference(unit_resolution,[status(thm)],[16729, 82, 72])).
% 292.41/184.91 tff(16731,plain,
% 292.41/184.91 (node22(c_e_h_1, c_l, s0, s1)),
% 292.41/184.91 inference(unit_resolution,[status(thm)],[16730, 16726])).
% 292.41/184.91 tff(16732,plain,
% 292.41/184.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s1)) | (~node22(c_e_h_1, c_l, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_l, s0))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s1)) | (~node22(c_e_h_1, c_l, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_l, s0))),
% 292.41/184.91 inference(rewrite,[status(thm)],[])).
% 292.41/184.91 tff(16733,plain,
% 292.41/184.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s1)) | (~node22(c_e_h_1, c_l, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_l, s0))),
% 292.41/184.91 inference(quant_inst,[status(thm)],[])).
% 292.41/184.91 tff(16734,plain,
% 292.41/184.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s1)) | (~node22(c_e_h_1, c_l, s0, s1)) | m_and_h_gate_v_out(c_e_h_1, c_l, s0)),
% 292.41/184.91 inference(modus_ponens,[status(thm)],[16733, 16732])).
% 292.41/184.91 tff(16735,plain,
% 292.41/184.91 ($false),
% 292.41/184.91 inference(unit_resolution,[status(thm)],[16734, 108, 15123, 16731, 16711])).
% 292.41/184.91 tff(16736,plain,(~m_and_h_gate_v_out(c_e_h_1, c_l, s1)), inference(lemma,lemma(discharge,[]))).
% 292.41/184.91 tff(16737,plain,
% 292.41/184.91 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s1)) | m_and_h_gate_v_out(c_e_h_1, c_l, s1))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s1)) | m_and_h_gate_v_out(c_e_h_1, c_l, s1))),
% 292.41/184.91 inference(rewrite,[status(thm)],[])).
% 292.41/184.91 tff(16738,plain,
% 292.41/184.91 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s1)) | m_and_h_gate_v_out(c_e_h_1, c_l, s1))),
% 292.41/184.91 inference(quant_inst,[status(thm)],[])).
% 292.41/184.91 tff(16739,plain,
% 292.41/184.91 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s1)) | m_and_h_gate_v_out(c_e_h_1, c_l, s1)),
% 292.41/184.91 inference(modus_ponens,[status(thm)],[16738, 16737])).
% 292.41/184.91 tff(16740,plain,
% 292.41/184.91 (~m_or_h_gate_v_in1(c_e_h_1, c_j, s1)),
% 292.41/184.91 inference(unit_resolution,[status(thm)],[16739, 1100, 16736])).
% 292.41/184.91 tff(16741,assumption,(~m_or_h_gate_v_in2(c_e_h_1, c_j, s1)), introduced(assumption)).
% 292.41/184.91 tff(16742,assumption,(node5(c_e_h_1, c_j, s1, s2)), introduced(assumption)).
% 292.41/184.91 tff(16743,plain,
% 292.41/184.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_1, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s1) | (~node5(c_e_h_1, c_j, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_1, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s1) | (~node5(c_e_h_1, c_j, s1, s2)))),
% 292.41/184.91 inference(rewrite,[status(thm)],[])).
% 292.41/184.91 tff(16744,plain,
% 292.41/184.91 ((m_or_h_gate_v_in1(c_e_h_1, c_j, s1) | m_or_h_gate_v_in2(c_e_h_1, c_j, s1) | (~node5(c_e_h_1, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2))) <=> (m_or_h_gate_v_in2(c_e_h_1, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s1) | (~node5(c_e_h_1, c_j, s1, s2)))),
% 292.41/184.91 inference(rewrite,[status(thm)],[])).
% 292.41/184.91 tff(16745,plain,
% 292.41/184.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s1) | m_or_h_gate_v_in2(c_e_h_1, c_j, s1) | (~node5(c_e_h_1, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_1, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s1) | (~node5(c_e_h_1, c_j, s1, s2))))),
% 292.41/184.92 inference(monotonicity,[status(thm)],[16744])).
% 292.41/184.92 tff(16746,plain,
% 292.41/184.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s1) | m_or_h_gate_v_in2(c_e_h_1, c_j, s1) | (~node5(c_e_h_1, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_1, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s1) | (~node5(c_e_h_1, c_j, s1, s2)))),
% 292.41/184.92 inference(transitivity,[status(thm)],[16745, 16743])).
% 292.41/184.92 tff(16747,plain,
% 292.41/184.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s1) | m_or_h_gate_v_in2(c_e_h_1, c_j, s1) | (~node5(c_e_h_1, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2)))),
% 292.41/184.92 inference(quant_inst,[status(thm)],[])).
% 292.41/184.92 tff(16748,plain,
% 292.41/184.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_1, c_j, s1) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s1) | (~node5(c_e_h_1, c_j, s1, s2))),
% 292.41/184.92 inference(modus_ponens,[status(thm)],[16747, 16746])).
% 292.41/184.92 tff(16749,plain,
% 292.41/184.92 ($false),
% 292.41/184.92 inference(unit_resolution,[status(thm)],[16748, 1159, 16687, 16742, 16741, 16740])).
% 292.41/184.92 tff(16750,plain,((~node5(c_e_h_1, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s1)), inference(lemma,lemma(discharge,[]))).
% 292.41/184.92 tff(16751,plain,
% 292.41/184.92 ((~node5(c_e_h_1, c_j, s1, s2)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s2))),
% 292.41/184.92 inference(unit_resolution,[status(thm)],[16750, 16710])).
% 292.41/184.92 tff(16752,plain,
% 292.41/184.92 (~node5(c_e_h_1, c_j, s1, s2)),
% 292.41/184.92 inference(unit_resolution,[status(thm)],[16751, 16687])).
% 292.41/184.92 tff(16753,plain,
% 292.41/184.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s1, s2)) | node6(c_e_h_1, c_j, s1, s2) | node5(c_e_h_1, c_j, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s1, s2)) | node6(c_e_h_1, c_j, s1, s2) | node5(c_e_h_1, c_j, s1, s2))),
% 292.41/184.92 inference(rewrite,[status(thm)],[])).
% 292.41/184.92 tff(16754,plain,
% 292.41/184.92 ((node6(c_e_h_1, c_j, s1, s2) | node5(c_e_h_1, c_j, s1, s2) | (~trans(s1, s2))) <=> ((~trans(s1, s2)) | node6(c_e_h_1, c_j, s1, s2) | node5(c_e_h_1, c_j, s1, s2))),
% 292.41/184.92 inference(rewrite,[status(thm)],[])).
% 292.41/184.92 tff(16755,plain,
% 292.41/184.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s1, s2) | node5(c_e_h_1, c_j, s1, s2) | (~trans(s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s1, s2)) | node6(c_e_h_1, c_j, s1, s2) | node5(c_e_h_1, c_j, s1, s2)))),
% 292.41/184.92 inference(monotonicity,[status(thm)],[16754])).
% 292.41/184.92 tff(16756,plain,
% 292.41/184.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s1, s2) | node5(c_e_h_1, c_j, s1, s2) | (~trans(s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s1, s2)) | node6(c_e_h_1, c_j, s1, s2) | node5(c_e_h_1, c_j, s1, s2))),
% 292.41/184.92 inference(transitivity,[status(thm)],[16755, 16753])).
% 292.41/184.92 tff(16757,plain,
% 292.41/184.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s1, s2) | node5(c_e_h_1, c_j, s1, s2) | (~trans(s1, s2)))),
% 292.41/184.92 inference(quant_inst,[status(thm)],[])).
% 292.41/184.92 tff(16758,plain,
% 292.41/184.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s1, s2)) | node6(c_e_h_1, c_j, s1, s2) | node5(c_e_h_1, c_j, s1, s2)),
% 292.41/184.92 inference(modus_ponens,[status(thm)],[16757, 16756])).
% 292.41/184.92 tff(16759,plain,
% 292.41/184.92 (node6(c_e_h_1, c_j, s1, s2) | node5(c_e_h_1, c_j, s1, s2)),
% 292.41/184.92 inference(unit_resolution,[status(thm)],[16758, 1141, 255])).
% 292.41/184.92 tff(16760,plain,
% 292.41/184.92 ($false),
% 292.41/184.92 inference(unit_resolution,[status(thm)],[16759, 16752, 16697])).
% 292.41/184.92 tff(16761,plain,(~m_or_h_gate_v_out(c_e_h_1, c_j, s2)), inference(lemma,lemma(discharge,[]))).
% 292.41/184.92 tff(16762,plain,
% 292.41/184.92 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s2)) | m_or_h_gate_v_out(c_e_h_1, c_j, s2))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s2)) | m_or_h_gate_v_out(c_e_h_1, c_j, s2))),
% 292.41/184.92 inference(rewrite,[status(thm)],[])).
% 292.41/184.92 tff(16763,plain,
% 292.41/184.92 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s2)) | m_or_h_gate_v_out(c_e_h_1, c_j, s2))),
% 292.41/184.92 inference(quant_inst,[status(thm)],[])).
% 292.41/184.92 tff(16764,plain,
% 292.41/184.92 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s2)) | m_or_h_gate_v_out(c_e_h_1, c_j, s2)),
% 292.41/184.92 inference(modus_ponens,[status(thm)],[16763, 16762])).
% 292.41/184.92 tff(16765,plain,
% 292.41/184.92 (~m_c_h_element_v_in2(c_e_h_1, c_h, s2)),
% 292.41/184.92 inference(unit_resolution,[status(thm)],[16764, 1174, 16761])).
% 292.41/184.92 tff(16766,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_h, s2)), introduced(assumption)).
% 292.41/184.92 tff(16767,assumption,(m_c_h_element_v_out(c_e_h_1, c_h, s3)), introduced(assumption)).
% 292.41/184.92 tff(16768,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_h, s2)), introduced(assumption)).
% 292.41/184.92 tff(16769,assumption,(node15(c_e_h_1, c_h, s2, s3)), introduced(assumption)).
% 292.41/184.92 tff(16770,plain,
% 292.41/184.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s3)) | (~node15(c_e_h_1, c_h, s2, s3)) | m_c_h_element_v_out(c_e_h_1, c_h, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3)) | (~node15(c_e_h_1, c_h, s2, s3)) | m_c_h_element_v_out(c_e_h_1, c_h, s2))),
% 292.41/184.92 inference(rewrite,[status(thm)],[])).
% 292.41/184.92 tff(16771,plain,
% 292.41/184.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s3)) | (~node15(c_e_h_1, c_h, s2, s3)) | m_c_h_element_v_out(c_e_h_1, c_h, s2))),
% 292.41/184.92 inference(quant_inst,[status(thm)],[])).
% 292.41/184.92 tff(16772,plain,
% 292.41/184.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3)) | (~node15(c_e_h_1, c_h, s2, s3)) | m_c_h_element_v_out(c_e_h_1, c_h, s2)),
% 292.41/184.92 inference(modus_ponens,[status(thm)],[16771, 16770])).
% 292.41/184.92 tff(16773,plain,
% 292.41/184.92 ($false),
% 292.41/184.92 inference(unit_resolution,[status(thm)],[16772, 147, 16767, 15205, 16769])).
% 292.41/184.92 tff(16774,plain,((~node15(c_e_h_1, c_h, s2, s3)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3))), inference(lemma,lemma(discharge,[]))).
% 292.41/184.92 tff(16775,plain,
% 292.41/184.92 (~node15(c_e_h_1, c_h, s2, s3)),
% 292.41/184.92 inference(unit_resolution,[status(thm)],[16774, 16767])).
% 292.41/184.92 tff(16776,plain,
% 292.41/184.92 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s2)) | m_c_h_element_v_in1(c_e_h_1, c_h, s2) | m_c_h_element_v_in2(c_e_h_1, c_h, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s2)) | m_c_h_element_v_in1(c_e_h_1, c_h, s2) | m_c_h_element_v_in2(c_e_h_1, c_h, s2))),
% 292.41/184.93 inference(rewrite,[status(thm)],[])).
% 292.41/184.93 tff(16777,plain,
% 292.41/184.93 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s2)) | m_c_h_element_v_in1(c_e_h_1, c_h, s2) | m_c_h_element_v_in2(c_e_h_1, c_h, s2))),
% 292.41/184.93 inference(quant_inst,[status(thm)],[])).
% 292.41/184.93 tff(16778,plain,
% 292.41/184.93 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s2)) | m_c_h_element_v_in1(c_e_h_1, c_h, s2) | m_c_h_element_v_in2(c_e_h_1, c_h, s2)),
% 292.41/184.93 inference(modus_ponens,[status(thm)],[16777, 16776])).
% 292.41/184.93 tff(16779,plain,
% 292.41/184.93 ((~node16(c_e_h_1, c_h, s2)) | m_c_h_element_v_in1(c_e_h_1, c_h, s2)),
% 292.41/184.93 inference(unit_resolution,[status(thm)],[16778, 178, 16766])).
% 292.41/184.93 tff(16780,plain,
% 292.41/184.93 (~node16(c_e_h_1, c_h, s2)),
% 292.41/184.93 inference(unit_resolution,[status(thm)],[16779, 16768])).
% 292.41/184.93 tff(16781,plain,
% 292.41/184.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s2, s3)) | node19(c_e_h_1, c_h, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s2, s3)) | node19(c_e_h_1, c_h, s2, s3))),
% 292.41/184.93 inference(rewrite,[status(thm)],[])).
% 292.41/184.93 tff(16782,plain,
% 292.41/184.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s2, s3)) | node19(c_e_h_1, c_h, s2, s3))),
% 292.41/184.93 inference(quant_inst,[status(thm)],[])).
% 292.41/184.93 tff(16783,plain,
% 292.41/184.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s2, s3)) | node19(c_e_h_1, c_h, s2, s3)),
% 292.41/184.93 inference(modus_ponens,[status(thm)],[16782, 16781])).
% 292.41/184.93 tff(16784,plain,
% 292.41/184.93 (node19(c_e_h_1, c_h, s2, s3)),
% 292.41/184.93 inference(unit_resolution,[status(thm)],[16783, 190, 318])).
% 292.41/184.93 tff(16785,plain,
% 292.41/184.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_1, c_h, s2, s3) | node16(c_e_h_1, c_h, s2) | node15(c_e_h_1, c_h, s2, s3) | (~node19(c_e_h_1, c_h, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_h, s2, s3) | node16(c_e_h_1, c_h, s2) | node15(c_e_h_1, c_h, s2, s3) | (~node19(c_e_h_1, c_h, s2, s3)))),
% 292.41/184.93 inference(rewrite,[status(thm)],[])).
% 292.41/184.93 tff(16786,plain,
% 292.41/184.93 ((node16(c_e_h_1, c_h, s2) | node14(c_e_h_1, c_h, s2, s3) | node15(c_e_h_1, c_h, s2, s3) | (~node19(c_e_h_1, c_h, s2, s3))) <=> (node14(c_e_h_1, c_h, s2, s3) | node16(c_e_h_1, c_h, s2) | node15(c_e_h_1, c_h, s2, s3) | (~node19(c_e_h_1, c_h, s2, s3)))),
% 292.41/184.93 inference(rewrite,[status(thm)],[])).
% 292.41/184.93 tff(16787,plain,
% 292.41/184.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s2) | node14(c_e_h_1, c_h, s2, s3) | node15(c_e_h_1, c_h, s2, s3) | (~node19(c_e_h_1, c_h, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_1, c_h, s2, s3) | node16(c_e_h_1, c_h, s2) | node15(c_e_h_1, c_h, s2, s3) | (~node19(c_e_h_1, c_h, s2, s3))))),
% 292.41/184.93 inference(monotonicity,[status(thm)],[16786])).
% 292.41/184.93 tff(16788,plain,
% 292.41/184.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s2) | node14(c_e_h_1, c_h, s2, s3) | node15(c_e_h_1, c_h, s2, s3) | (~node19(c_e_h_1, c_h, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_h, s2, s3) | node16(c_e_h_1, c_h, s2) | node15(c_e_h_1, c_h, s2, s3) | (~node19(c_e_h_1, c_h, s2, s3)))),
% 292.41/184.93 inference(transitivity,[status(thm)],[16787, 16785])).
% 292.41/184.93 tff(16789,plain,
% 292.41/184.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s2) | node14(c_e_h_1, c_h, s2, s3) | node15(c_e_h_1, c_h, s2, s3) | (~node19(c_e_h_1, c_h, s2, s3)))),
% 292.41/184.93 inference(quant_inst,[status(thm)],[])).
% 292.41/184.93 tff(16790,plain,
% 292.41/184.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_h, s2, s3) | node16(c_e_h_1, c_h, s2) | node15(c_e_h_1, c_h, s2, s3) | (~node19(c_e_h_1, c_h, s2, s3))),
% 292.41/184.93 inference(modus_ponens,[status(thm)],[16789, 16788])).
% 292.41/184.93 tff(16791,plain,
% 292.41/184.93 (node14(c_e_h_1, c_h, s2, s3) | node16(c_e_h_1, c_h, s2) | node15(c_e_h_1, c_h, s2, s3)),
% 292.41/184.93 inference(unit_resolution,[status(thm)],[16790, 204, 16784])).
% 292.41/184.93 tff(16792,plain,
% 292.41/184.93 (node14(c_e_h_1, c_h, s2, s3)),
% 292.41/184.93 inference(unit_resolution,[status(thm)],[16791, 16780, 16775])).
% 292.41/184.93 tff(16793,plain,
% 292.41/184.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s3)) | m_c_h_element_v_in1(c_e_h_1, c_h, s2) | (~node14(c_e_h_1, c_h, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3)) | m_c_h_element_v_in1(c_e_h_1, c_h, s2) | (~node14(c_e_h_1, c_h, s2, s3)))),
% 292.41/184.93 inference(rewrite,[status(thm)],[])).
% 292.41/184.93 tff(16794,plain,
% 292.41/184.93 (((~node14(c_e_h_1, c_h, s2, s3)) | m_c_h_element_v_in1(c_e_h_1, c_h, s2) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_h, s3)) | m_c_h_element_v_in1(c_e_h_1, c_h, s2) | (~node14(c_e_h_1, c_h, s2, s3)))),
% 292.41/184.93 inference(rewrite,[status(thm)],[])).
% 292.41/184.93 tff(16795,plain,
% 292.41/184.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s2, s3)) | m_c_h_element_v_in1(c_e_h_1, c_h, s2) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s3)) | m_c_h_element_v_in1(c_e_h_1, c_h, s2) | (~node14(c_e_h_1, c_h, s2, s3))))),
% 292.41/184.93 inference(monotonicity,[status(thm)],[16794])).
% 292.41/184.93 tff(16796,plain,
% 292.41/184.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s2, s3)) | m_c_h_element_v_in1(c_e_h_1, c_h, s2) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3)) | m_c_h_element_v_in1(c_e_h_1, c_h, s2) | (~node14(c_e_h_1, c_h, s2, s3)))),
% 292.41/184.93 inference(transitivity,[status(thm)],[16795, 16793])).
% 292.41/184.93 tff(16797,plain,
% 292.41/184.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s2, s3)) | m_c_h_element_v_in1(c_e_h_1, c_h, s2) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3)))),
% 292.41/184.93 inference(quant_inst,[status(thm)],[])).
% 292.41/184.93 tff(16798,plain,
% 292.41/184.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3)) | m_c_h_element_v_in1(c_e_h_1, c_h, s2) | (~node14(c_e_h_1, c_h, s2, s3))),
% 292.41/184.93 inference(modus_ponens,[status(thm)],[16797, 16796])).
% 292.41/184.93 tff(16799,plain,
% 292.41/184.93 ($false),
% 292.41/184.93 inference(unit_resolution,[status(thm)],[16798, 223, 16767, 16792, 16768])).
% 292.41/184.93 tff(16800,plain,(m_c_h_element_v_in1(c_e_h_1, c_h, s2) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3)) | m_c_h_element_v_in2(c_e_h_1, c_h, s2)), inference(lemma,lemma(discharge,[]))).
% 292.41/184.93 tff(16801,plain,
% 292.41/184.93 (m_c_h_element_v_in1(c_e_h_1, c_h, s2)),
% 292.41/184.93 inference(unit_resolution,[status(thm)],[16800, 16766, 16767])).
% 292.41/184.93 tff(16802,assumption,(node18(c_e_h_1, c_h, s2, s3)), introduced(assumption)).
% 292.41/184.93 tff(16803,plain,
% 292.41/184.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s3)) | m_c_h_element_v_out(c_e_h_1, c_h, s2) | (~node18(c_e_h_1, c_h, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3)) | m_c_h_element_v_out(c_e_h_1, c_h, s2) | (~node18(c_e_h_1, c_h, s2, s3)))),
% 292.41/184.93 inference(rewrite,[status(thm)],[])).
% 292.41/184.93 tff(16804,plain,
% 292.41/184.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s3)) | m_c_h_element_v_out(c_e_h_1, c_h, s2) | (~node18(c_e_h_1, c_h, s2, s3)))),
% 292.41/184.93 inference(quant_inst,[status(thm)],[])).
% 292.41/184.93 tff(16805,plain,
% 292.41/184.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3)) | m_c_h_element_v_out(c_e_h_1, c_h, s2) | (~node18(c_e_h_1, c_h, s2, s3))),
% 292.41/184.93 inference(modus_ponens,[status(thm)],[16804, 16803])).
% 292.41/184.93 tff(16806,plain,
% 292.41/184.93 ($false),
% 292.41/184.93 inference(unit_resolution,[status(thm)],[16805, 753, 16767, 15205, 16802])).
% 292.41/184.93 tff(16807,plain,((~node18(c_e_h_1, c_h, s2, s3)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3))), inference(lemma,lemma(discharge,[]))).
% 292.41/184.93 tff(16808,plain,
% 292.41/184.93 (~node18(c_e_h_1, c_h, s2, s3)),
% 292.41/184.93 inference(unit_resolution,[status(thm)],[16807, 16767])).
% 292.41/184.93 tff(16809,plain,
% 292.41/184.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s2) | node18(c_e_h_1, c_h, s2, s3) | (~node19(c_e_h_1, c_h, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s2) | node18(c_e_h_1, c_h, s2, s3) | (~node19(c_e_h_1, c_h, s2, s3)))),
% 292.41/184.93 inference(rewrite,[status(thm)],[])).
% 292.41/184.93 tff(16810,plain,
% 292.41/184.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s2) | node18(c_e_h_1, c_h, s2, s3) | (~node19(c_e_h_1, c_h, s2, s3)))),
% 292.41/184.93 inference(quant_inst,[status(thm)],[])).
% 292.41/184.93 tff(16811,plain,
% 292.41/184.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s2) | node18(c_e_h_1, c_h, s2, s3) | (~node19(c_e_h_1, c_h, s2, s3))),
% 292.41/184.93 inference(modus_ponens,[status(thm)],[16810, 16809])).
% 292.41/184.93 tff(16812,plain,
% 292.41/184.93 (node17(c_e_h_1, c_h, s2) | node18(c_e_h_1, c_h, s2, s3)),
% 292.41/184.93 inference(unit_resolution,[status(thm)],[16811, 776, 16784])).
% 292.41/184.93 tff(16813,plain,
% 292.41/184.93 (node17(c_e_h_1, c_h, s2)),
% 292.41/184.93 inference(unit_resolution,[status(thm)],[16812, 16808])).
% 292.41/184.93 tff(16814,plain,
% 292.41/184.93 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_h, s2)) | m_c_h_element_v_in2(c_e_h_1, c_h, s2) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_h, s2)) | m_c_h_element_v_in2(c_e_h_1, c_h, s2) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s2)))),
% 292.41/184.93 inference(rewrite,[status(thm)],[])).
% 292.41/184.93 tff(16815,plain,
% 292.41/184.93 (((~m_c_h_element_v_in1(c_e_h_1, c_h, s2)) | m_c_h_element_v_in2(c_e_h_1, c_h, s2) | (~node17(c_e_h_1, c_h, s2))) <=> ((~node17(c_e_h_1, c_h, s2)) | m_c_h_element_v_in2(c_e_h_1, c_h, s2) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s2)))),
% 292.41/184.93 inference(rewrite,[status(thm)],[])).
% 292.41/184.93 tff(16816,plain,
% 292.41/184.93 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s2)) | m_c_h_element_v_in2(c_e_h_1, c_h, s2) | (~node17(c_e_h_1, c_h, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_h, s2)) | m_c_h_element_v_in2(c_e_h_1, c_h, s2) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s2))))),
% 292.41/184.94 inference(monotonicity,[status(thm)],[16815])).
% 292.41/184.94 tff(16817,plain,
% 292.41/184.94 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s2)) | m_c_h_element_v_in2(c_e_h_1, c_h, s2) | (~node17(c_e_h_1, c_h, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_h, s2)) | m_c_h_element_v_in2(c_e_h_1, c_h, s2) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s2)))),
% 292.41/184.94 inference(transitivity,[status(thm)],[16816, 16814])).
% 292.41/184.94 tff(16818,plain,
% 292.41/184.94 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s2)) | m_c_h_element_v_in2(c_e_h_1, c_h, s2) | (~node17(c_e_h_1, c_h, s2)))),
% 292.41/184.94 inference(quant_inst,[status(thm)],[])).
% 292.41/184.94 tff(16819,plain,
% 292.41/184.94 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_h, s2)) | m_c_h_element_v_in2(c_e_h_1, c_h, s2) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s2))),
% 292.41/184.94 inference(modus_ponens,[status(thm)],[16818, 16817])).
% 292.41/184.94 tff(16820,plain,
% 292.41/184.94 (m_c_h_element_v_in2(c_e_h_1, c_h, s2) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s2))),
% 292.41/184.94 inference(unit_resolution,[status(thm)],[16819, 919, 16813])).
% 292.41/184.94 tff(16821,plain,
% 292.41/184.94 ($false),
% 292.41/184.94 inference(unit_resolution,[status(thm)],[16820, 16801, 16766])).
% 292.41/184.94 tff(16822,plain,(m_c_h_element_v_in2(c_e_h_1, c_h, s2) | (~m_c_h_element_v_out(c_e_h_1, c_h, s3))), inference(lemma,lemma(discharge,[]))).
% 292.41/184.94 tff(16823,plain,
% 292.41/184.94 (~m_c_h_element_v_out(c_e_h_1, c_h, s3)),
% 292.41/184.94 inference(unit_resolution,[status(thm)],[16822, 16765])).
% 292.41/184.94 tff(16824,plain,
% 292.41/184.94 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s3)) | m_c_h_element_v_out(c_e_h_1, c_h, s3))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s3)) | m_c_h_element_v_out(c_e_h_1, c_h, s3))),
% 292.41/184.94 inference(rewrite,[status(thm)],[])).
% 292.41/184.94 tff(16825,plain,
% 292.41/184.94 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s3)) | m_c_h_element_v_out(c_e_h_1, c_h, s3))),
% 292.41/184.94 inference(quant_inst,[status(thm)],[])).
% 292.41/184.94 tff(16826,plain,
% 292.41/184.94 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s3)) | m_c_h_element_v_out(c_e_h_1, c_h, s3)),
% 292.41/184.94 inference(modus_ponens,[status(thm)],[16825, 16824])).
% 292.41/184.94 tff(16827,plain,
% 292.41/184.94 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s3)),
% 292.41/184.94 inference(unit_resolution,[status(thm)],[16826, 619, 16823])).
% 292.41/184.94 tff(16828,plain,
% 292.41/184.94 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s3)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s3)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s3))),
% 292.41/184.94 inference(rewrite,[status(thm)],[])).
% 292.41/184.94 tff(16829,plain,
% 292.41/184.94 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s3)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s3))),
% 292.41/184.94 inference(quant_inst,[status(thm)],[])).
% 292.41/184.94 tff(16830,plain,
% 292.41/184.94 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s3)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s3)),
% 292.41/184.94 inference(modus_ponens,[status(thm)],[16829, 16828])).
% 292.41/184.94 tff(16831,plain,
% 292.41/184.94 (~node20(c_e_h_1, c_i, s3)),
% 292.41/184.94 inference(unit_resolution,[status(thm)],[16830, 38, 16827])).
% 292.41/184.94 tff(16832,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s4)), introduced(assumption)).
% 292.41/184.94 tff(16833,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_i, s3)), introduced(assumption)).
% 292.41/184.94 tff(16834,assumption,(~node20(c_e_h_1, c_i, s3)), introduced(assumption)).
% 292.41/184.94 tff(16835,assumption,(node21(c_e_h_1, c_i, s3, s4)), introduced(assumption)).
% 292.41/184.94 tff(16836,plain,
% 292.41/184.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s4)) | (~node21(c_e_h_1, c_i, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s4)) | (~node21(c_e_h_1, c_i, s3, s4)))),
% 292.41/184.94 inference(rewrite,[status(thm)],[])).
% 292.41/184.94 tff(16837,plain,
% 292.41/184.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s4)) | (~node21(c_e_h_1, c_i, s3, s4)))),
% 292.41/184.94 inference(quant_inst,[status(thm)],[])).
% 292.41/184.94 tff(16838,plain,
% 292.41/184.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s4)) | (~node21(c_e_h_1, c_i, s3, s4))),
% 292.41/184.94 inference(modus_ponens,[status(thm)],[16837, 16836])).
% 292.41/184.94 tff(16839,plain,
% 292.41/184.94 ($false),
% 292.41/184.94 inference(unit_resolution,[status(thm)],[16838, 52, 16835, 16834, 16832])).
% 292.41/184.94 tff(16840,plain,((~node21(c_e_h_1, c_i, s3, s4)) | node20(c_e_h_1, c_i, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s4))), inference(lemma,lemma(discharge,[]))).
% 292.41/184.94 tff(16841,plain,
% 292.41/184.94 (~node21(c_e_h_1, c_i, s3, s4)),
% 292.41/184.94 inference(unit_resolution,[status(thm)],[16840, 16832, 16834])).
% 292.41/184.94 tff(16842,plain,
% 292.41/184.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_1, c_i, s3, s4) | node22(c_e_h_1, c_i, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_1, c_i, s3, s4) | node22(c_e_h_1, c_i, s3, s4))),
% 292.41/184.94 inference(rewrite,[status(thm)],[])).
% 292.41/184.94 tff(16843,plain,
% 292.41/184.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_1, c_i, s3, s4) | node22(c_e_h_1, c_i, s3, s4))),
% 292.41/184.94 inference(quant_inst,[status(thm)],[])).
% 292.41/184.94 tff(16844,plain,
% 292.41/184.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_1, c_i, s3, s4) | node22(c_e_h_1, c_i, s3, s4)),
% 292.41/184.94 inference(modus_ponens,[status(thm)],[16843, 16842])).
% 292.41/184.94 tff(16845,plain,
% 292.41/184.94 (node21(c_e_h_1, c_i, s3, s4) | node22(c_e_h_1, c_i, s3, s4)),
% 292.41/184.94 inference(unit_resolution,[status(thm)],[16844, 82, 531])).
% 292.41/184.94 tff(16846,plain,
% 292.41/184.94 (node22(c_e_h_1, c_i, s3, s4)),
% 292.41/184.94 inference(unit_resolution,[status(thm)],[16845, 16841])).
% 292.41/184.94 tff(16847,plain,
% 292.41/184.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s4)) | (~node22(c_e_h_1, c_i, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_i, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s4)) | (~node22(c_e_h_1, c_i, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_i, s3))),
% 292.41/184.94 inference(rewrite,[status(thm)],[])).
% 292.41/184.94 tff(16848,plain,
% 292.41/184.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s4)) | (~node22(c_e_h_1, c_i, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_i, s3))),
% 292.41/184.94 inference(quant_inst,[status(thm)],[])).
% 292.41/184.94 tff(16849,plain,
% 292.41/184.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s4)) | (~node22(c_e_h_1, c_i, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_i, s3)),
% 292.41/184.94 inference(modus_ponens,[status(thm)],[16848, 16847])).
% 292.41/184.94 tff(16850,plain,
% 292.41/184.94 ($false),
% 292.41/184.94 inference(unit_resolution,[status(thm)],[16849, 108, 16846, 16833, 16832])).
% 292.41/184.94 tff(16851,plain,((~m_and_h_gate_v_out(c_e_h_1, c_i, s4)) | m_and_h_gate_v_out(c_e_h_1, c_i, s3) | node20(c_e_h_1, c_i, s3)), inference(lemma,lemma(discharge,[]))).
% 292.41/184.94 tff(16852,plain,
% 292.41/184.94 ((~m_and_h_gate_v_out(c_e_h_1, c_i, s4)) | node20(c_e_h_1, c_i, s3)),
% 292.41/184.94 inference(unit_resolution,[status(thm)],[16851, 15233])).
% 292.41/184.94 tff(16853,plain,
% 292.41/184.94 (~m_and_h_gate_v_out(c_e_h_1, c_i, s4)),
% 292.41/184.94 inference(unit_resolution,[status(thm)],[16852, 16831])).
% 292.41/184.94 tff(16854,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_i, s4)), introduced(assumption)).
% 292.41/184.94 tff(16855,assumption,(m_c_h_element_v_in2(c_e_h_1, c_f, s4)), introduced(assumption)).
% 292.41/184.94 tff(16856,plain,
% 292.41/184.94 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s4)) | m_and_h_gate_v_out(c_e_h_1, c_i, s4))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s4)) | m_and_h_gate_v_out(c_e_h_1, c_i, s4))),
% 292.41/184.94 inference(rewrite,[status(thm)],[])).
% 292.41/184.94 tff(16857,plain,
% 292.41/184.94 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s4)) | m_and_h_gate_v_out(c_e_h_1, c_i, s4))),
% 292.41/184.94 inference(quant_inst,[status(thm)],[])).
% 292.41/184.94 tff(16858,plain,
% 292.41/184.94 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s4)) | m_and_h_gate_v_out(c_e_h_1, c_i, s4)),
% 292.41/184.94 inference(modus_ponens,[status(thm)],[16857, 16856])).
% 292.41/184.94 tff(16859,plain,
% 292.41/184.94 ($false),
% 292.41/184.94 inference(unit_resolution,[status(thm)],[16858, 2143, 16855, 16854])).
% 292.41/184.94 tff(16860,plain,((~m_c_h_element_v_in2(c_e_h_1, c_f, s4)) | m_and_h_gate_v_out(c_e_h_1, c_i, s4)), inference(lemma,lemma(discharge,[]))).
% 292.41/184.94 tff(16861,plain,
% 292.41/184.94 (~m_c_h_element_v_in2(c_e_h_1, c_f, s4)),
% 292.41/184.94 inference(unit_resolution,[status(thm)],[16860, 16853])).
% 292.41/184.94 tff(16862,assumption,(m_c_h_element_v_out(c_e_h_1, c_f, s5)), introduced(assumption)).
% 292.41/184.94 tff(16863,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_f, s4)), introduced(assumption)).
% 292.41/184.94 tff(16864,assumption,(~m_c_h_element_v_out(c_e_h_1, c_f, s4)), introduced(assumption)).
% 292.41/184.94 tff(16865,assumption,(node18(c_e_h_1, c_f, s4, s5)), introduced(assumption)).
% 292.41/184.94 tff(16866,plain,
% 292.41/184.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_f, s4) | (~m_c_h_element_v_out(c_e_h_1, c_f, s5)) | (~node18(c_e_h_1, c_f, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s4) | (~m_c_h_element_v_out(c_e_h_1, c_f, s5)) | (~node18(c_e_h_1, c_f, s4, s5)))),
% 292.41/184.94 inference(rewrite,[status(thm)],[])).
% 292.41/184.94 tff(16867,plain,
% 292.41/184.94 (((~m_c_h_element_v_out(c_e_h_1, c_f, s5)) | m_c_h_element_v_out(c_e_h_1, c_f, s4) | (~node18(c_e_h_1, c_f, s4, s5))) <=> (m_c_h_element_v_out(c_e_h_1, c_f, s4) | (~m_c_h_element_v_out(c_e_h_1, c_f, s5)) | (~node18(c_e_h_1, c_f, s4, s5)))),
% 292.41/184.94 inference(rewrite,[status(thm)],[])).
% 292.41/184.94 tff(16868,plain,
% 292.41/184.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s5)) | m_c_h_element_v_out(c_e_h_1, c_f, s4) | (~node18(c_e_h_1, c_f, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_f, s4) | (~m_c_h_element_v_out(c_e_h_1, c_f, s5)) | (~node18(c_e_h_1, c_f, s4, s5))))),
% 292.41/184.94 inference(monotonicity,[status(thm)],[16867])).
% 292.41/184.94 tff(16869,plain,
% 292.41/184.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s5)) | m_c_h_element_v_out(c_e_h_1, c_f, s4) | (~node18(c_e_h_1, c_f, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s4) | (~m_c_h_element_v_out(c_e_h_1, c_f, s5)) | (~node18(c_e_h_1, c_f, s4, s5)))),
% 292.41/184.95 inference(transitivity,[status(thm)],[16868, 16866])).
% 292.41/184.95 tff(16870,plain,
% 292.41/184.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s5)) | m_c_h_element_v_out(c_e_h_1, c_f, s4) | (~node18(c_e_h_1, c_f, s4, s5)))),
% 292.41/184.95 inference(quant_inst,[status(thm)],[])).
% 292.41/184.95 tff(16871,plain,
% 292.41/184.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s4) | (~m_c_h_element_v_out(c_e_h_1, c_f, s5)) | (~node18(c_e_h_1, c_f, s4, s5))),
% 292.41/184.95 inference(modus_ponens,[status(thm)],[16870, 16869])).
% 292.41/184.95 tff(16872,plain,
% 292.41/184.95 ($false),
% 292.41/184.95 inference(unit_resolution,[status(thm)],[16871, 753, 16864, 16865, 16862])).
% 292.41/184.95 tff(16873,plain,((~node18(c_e_h_1, c_f, s4, s5)) | m_c_h_element_v_out(c_e_h_1, c_f, s4) | (~m_c_h_element_v_out(c_e_h_1, c_f, s5))), inference(lemma,lemma(discharge,[]))).
% 292.41/184.95 tff(16874,plain,
% 292.41/184.95 (~node18(c_e_h_1, c_f, s4, s5)),
% 292.41/184.95 inference(unit_resolution,[status(thm)],[16873, 16862, 16864])).
% 292.41/184.95 tff(16875,plain,
% 292.41/184.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s4, s5)) | node19(c_e_h_1, c_f, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s4, s5)) | node19(c_e_h_1, c_f, s4, s5))),
% 292.41/184.95 inference(rewrite,[status(thm)],[])).
% 292.41/184.95 tff(16876,plain,
% 292.41/184.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s4, s5)) | node19(c_e_h_1, c_f, s4, s5))),
% 292.41/184.95 inference(quant_inst,[status(thm)],[])).
% 292.41/184.95 tff(16877,plain,
% 292.41/184.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s4, s5)) | node19(c_e_h_1, c_f, s4, s5)),
% 292.41/184.95 inference(modus_ponens,[status(thm)],[16876, 16875])).
% 292.41/184.95 tff(16878,plain,
% 292.41/184.95 (node19(c_e_h_1, c_f, s4, s5)),
% 292.41/184.95 inference(unit_resolution,[status(thm)],[16877, 190, 1028])).
% 292.41/184.95 tff(16879,plain,
% 292.41/184.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s4) | node18(c_e_h_1, c_f, s4, s5) | (~node19(c_e_h_1, c_f, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_f, s4) | node18(c_e_h_1, c_f, s4, s5) | (~node19(c_e_h_1, c_f, s4, s5)))),
% 292.41/184.95 inference(rewrite,[status(thm)],[])).
% 292.41/184.95 tff(16880,plain,
% 292.41/184.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s4) | node18(c_e_h_1, c_f, s4, s5) | (~node19(c_e_h_1, c_f, s4, s5)))),
% 292.41/184.95 inference(quant_inst,[status(thm)],[])).
% 292.41/184.95 tff(16881,plain,
% 292.41/184.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_f, s4) | node18(c_e_h_1, c_f, s4, s5) | (~node19(c_e_h_1, c_f, s4, s5))),
% 292.41/184.95 inference(modus_ponens,[status(thm)],[16880, 16879])).
% 292.41/184.95 tff(16882,plain,
% 292.41/184.95 (node17(c_e_h_1, c_f, s4) | node18(c_e_h_1, c_f, s4, s5)),
% 292.41/184.95 inference(unit_resolution,[status(thm)],[16881, 776, 16878])).
% 292.41/184.95 tff(16883,plain,
% 292.41/184.95 (node17(c_e_h_1, c_f, s4)),
% 292.41/184.95 inference(unit_resolution,[status(thm)],[16882, 16874])).
% 292.41/184.95 tff(16884,assumption,(node16(c_e_h_1, c_f, s4)), introduced(assumption)).
% 292.41/184.95 tff(16885,plain,
% 292.41/184.95 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s4)) | m_c_h_element_v_in1(c_e_h_1, c_f, s4) | m_c_h_element_v_in2(c_e_h_1, c_f, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s4)) | m_c_h_element_v_in1(c_e_h_1, c_f, s4) | m_c_h_element_v_in2(c_e_h_1, c_f, s4))),
% 292.41/184.95 inference(rewrite,[status(thm)],[])).
% 292.41/184.95 tff(16886,plain,
% 292.41/184.95 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s4)) | m_c_h_element_v_in1(c_e_h_1, c_f, s4) | m_c_h_element_v_in2(c_e_h_1, c_f, s4))),
% 292.41/184.95 inference(quant_inst,[status(thm)],[])).
% 292.41/184.95 tff(16887,plain,
% 292.41/184.95 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s4)) | m_c_h_element_v_in1(c_e_h_1, c_f, s4) | m_c_h_element_v_in2(c_e_h_1, c_f, s4)),
% 292.41/184.95 inference(modus_ponens,[status(thm)],[16886, 16885])).
% 292.41/184.95 tff(16888,plain,
% 292.41/184.95 (m_c_h_element_v_in1(c_e_h_1, c_f, s4) | m_c_h_element_v_in2(c_e_h_1, c_f, s4)),
% 292.41/184.95 inference(unit_resolution,[status(thm)],[16887, 178, 16884])).
% 292.41/184.95 tff(16889,plain,
% 292.41/184.95 (m_c_h_element_v_in1(c_e_h_1, c_f, s4)),
% 292.41/184.95 inference(unit_resolution,[status(thm)],[16888, 16863])).
% 292.41/184.95 tff(16890,assumption,(node17(c_e_h_1, c_f, s4)), introduced(assumption)).
% 292.41/184.95 tff(16891,plain,
% 292.41/184.95 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s4)) | m_c_h_element_v_in2(c_e_h_1, c_f, s4) | (~node17(c_e_h_1, c_f, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s4)) | m_c_h_element_v_in2(c_e_h_1, c_f, s4) | (~node17(c_e_h_1, c_f, s4)))),
% 292.41/184.95 inference(rewrite,[status(thm)],[])).
% 292.41/184.95 tff(16892,plain,
% 292.41/184.95 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s4)) | m_c_h_element_v_in2(c_e_h_1, c_f, s4) | (~node17(c_e_h_1, c_f, s4)))),
% 292.41/184.95 inference(quant_inst,[status(thm)],[])).
% 292.41/184.95 tff(16893,plain,
% 292.41/184.95 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s4)) | m_c_h_element_v_in2(c_e_h_1, c_f, s4) | (~node17(c_e_h_1, c_f, s4))),
% 292.41/184.95 inference(modus_ponens,[status(thm)],[16892, 16891])).
% 292.41/184.95 tff(16894,plain,
% 292.41/184.95 ((~m_c_h_element_v_in1(c_e_h_1, c_f, s4)) | m_c_h_element_v_in2(c_e_h_1, c_f, s4)),
% 292.41/184.95 inference(unit_resolution,[status(thm)],[16893, 919, 16890])).
% 292.41/184.95 tff(16895,plain,
% 292.41/184.95 ($false),
% 292.41/184.95 inference(unit_resolution,[status(thm)],[16894, 16889, 16863])).
% 292.41/184.95 tff(16896,plain,(m_c_h_element_v_in2(c_e_h_1, c_f, s4) | (~node17(c_e_h_1, c_f, s4)) | (~node16(c_e_h_1, c_f, s4))), inference(lemma,lemma(discharge,[]))).
% 292.41/184.95 tff(16897,plain,
% 292.41/184.95 (~node16(c_e_h_1, c_f, s4)),
% 292.41/184.95 inference(unit_resolution,[status(thm)],[16896, 16883, 16863])).
% 292.41/184.95 tff(16898,plain,
% 292.41/184.95 ((~m_c_h_element_v_in1(c_e_h_1, c_f, s4)) | (~node17(c_e_h_1, c_f, s4))),
% 292.41/184.95 inference(unit_resolution,[status(thm)],[16893, 919, 16863])).
% 292.41/184.95 tff(16899,plain,
% 292.41/184.95 (~m_c_h_element_v_in1(c_e_h_1, c_f, s4)),
% 292.41/184.95 inference(unit_resolution,[status(thm)],[16898, 16883])).
% 292.41/184.95 tff(16900,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_f, s4)), introduced(assumption)).
% 292.41/184.95 tff(16901,assumption,(node14(c_e_h_1, c_f, s4, s5)), introduced(assumption)).
% 292.41/184.95 tff(16902,plain,
% 292.41/184.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s4) | (~node14(c_e_h_1, c_f, s4, s5)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_f, s4) | (~node14(c_e_h_1, c_f, s4, s5)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s5)))),
% 292.41/184.95 inference(rewrite,[status(thm)],[])).
% 292.41/184.95 tff(16903,plain,
% 292.41/184.95 (((~node14(c_e_h_1, c_f, s4, s5)) | m_c_h_element_v_in1(c_e_h_1, c_f, s4) | (~m_c_h_element_v_out(c_e_h_1, c_f, s5))) <=> (m_c_h_element_v_in1(c_e_h_1, c_f, s4) | (~node14(c_e_h_1, c_f, s4, s5)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s5)))),
% 292.41/184.96 inference(rewrite,[status(thm)],[])).
% 292.41/184.96 tff(16904,plain,
% 292.41/184.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s4, s5)) | m_c_h_element_v_in1(c_e_h_1, c_f, s4) | (~m_c_h_element_v_out(c_e_h_1, c_f, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s4) | (~node14(c_e_h_1, c_f, s4, s5)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s5))))),
% 292.41/184.96 inference(monotonicity,[status(thm)],[16903])).
% 292.41/184.96 tff(16905,plain,
% 292.41/184.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s4, s5)) | m_c_h_element_v_in1(c_e_h_1, c_f, s4) | (~m_c_h_element_v_out(c_e_h_1, c_f, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_f, s4) | (~node14(c_e_h_1, c_f, s4, s5)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s5)))),
% 292.41/184.96 inference(transitivity,[status(thm)],[16904, 16902])).
% 292.41/184.96 tff(16906,plain,
% 292.41/184.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s4, s5)) | m_c_h_element_v_in1(c_e_h_1, c_f, s4) | (~m_c_h_element_v_out(c_e_h_1, c_f, s5)))),
% 292.41/184.96 inference(quant_inst,[status(thm)],[])).
% 292.41/184.96 tff(16907,plain,
% 292.41/184.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_f, s4) | (~node14(c_e_h_1, c_f, s4, s5)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s5))),
% 292.41/184.96 inference(modus_ponens,[status(thm)],[16906, 16905])).
% 292.41/184.96 tff(16908,plain,
% 292.41/184.96 ($false),
% 292.41/184.96 inference(unit_resolution,[status(thm)],[16907, 223, 16901, 16900, 16862])).
% 292.41/184.96 tff(16909,plain,((~node14(c_e_h_1, c_f, s4, s5)) | m_c_h_element_v_in1(c_e_h_1, c_f, s4) | (~m_c_h_element_v_out(c_e_h_1, c_f, s5))), inference(lemma,lemma(discharge,[]))).
% 292.41/184.96 tff(16910,plain,
% 292.41/184.96 (~node14(c_e_h_1, c_f, s4, s5)),
% 292.41/184.96 inference(unit_resolution,[status(thm)],[16909, 16899, 16862])).
% 292.41/184.96 tff(16911,plain,
% 292.41/184.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_1, c_f, s4, s5) | node16(c_e_h_1, c_f, s4) | (~node19(c_e_h_1, c_f, s4, s5)) | node14(c_e_h_1, c_f, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_f, s4, s5) | node16(c_e_h_1, c_f, s4) | (~node19(c_e_h_1, c_f, s4, s5)) | node14(c_e_h_1, c_f, s4, s5))),
% 292.41/184.96 inference(rewrite,[status(thm)],[])).
% 292.41/184.96 tff(16912,plain,
% 292.41/184.96 ((node16(c_e_h_1, c_f, s4) | node14(c_e_h_1, c_f, s4, s5) | node15(c_e_h_1, c_f, s4, s5) | (~node19(c_e_h_1, c_f, s4, s5))) <=> (node15(c_e_h_1, c_f, s4, s5) | node16(c_e_h_1, c_f, s4) | (~node19(c_e_h_1, c_f, s4, s5)) | node14(c_e_h_1, c_f, s4, s5))),
% 292.41/184.96 inference(rewrite,[status(thm)],[])).
% 292.41/184.96 tff(16913,plain,
% 292.41/184.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s4) | node14(c_e_h_1, c_f, s4, s5) | node15(c_e_h_1, c_f, s4, s5) | (~node19(c_e_h_1, c_f, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_1, c_f, s4, s5) | node16(c_e_h_1, c_f, s4) | (~node19(c_e_h_1, c_f, s4, s5)) | node14(c_e_h_1, c_f, s4, s5)))),
% 292.41/184.96 inference(monotonicity,[status(thm)],[16912])).
% 292.41/184.96 tff(16914,plain,
% 292.41/184.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s4) | node14(c_e_h_1, c_f, s4, s5) | node15(c_e_h_1, c_f, s4, s5) | (~node19(c_e_h_1, c_f, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_f, s4, s5) | node16(c_e_h_1, c_f, s4) | (~node19(c_e_h_1, c_f, s4, s5)) | node14(c_e_h_1, c_f, s4, s5))),
% 292.41/184.96 inference(transitivity,[status(thm)],[16913, 16911])).
% 292.41/184.96 tff(16915,plain,
% 292.41/184.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s4) | node14(c_e_h_1, c_f, s4, s5) | node15(c_e_h_1, c_f, s4, s5) | (~node19(c_e_h_1, c_f, s4, s5)))),
% 292.41/184.96 inference(quant_inst,[status(thm)],[])).
% 292.41/184.96 tff(16916,plain,
% 292.41/184.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_f, s4, s5) | node16(c_e_h_1, c_f, s4) | (~node19(c_e_h_1, c_f, s4, s5)) | node14(c_e_h_1, c_f, s4, s5)),
% 292.41/184.96 inference(modus_ponens,[status(thm)],[16915, 16914])).
% 292.41/184.96 tff(16917,plain,
% 292.41/184.96 (node15(c_e_h_1, c_f, s4, s5) | node16(c_e_h_1, c_f, s4) | node14(c_e_h_1, c_f, s4, s5)),
% 292.41/184.96 inference(unit_resolution,[status(thm)],[16916, 204, 16878])).
% 292.41/184.96 tff(16918,plain,
% 292.41/184.96 (node15(c_e_h_1, c_f, s4, s5)),
% 292.41/184.96 inference(unit_resolution,[status(thm)],[16917, 16910, 16897])).
% 292.41/184.96 tff(16919,plain,
% 292.41/184.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s5)) | (~node15(c_e_h_1, c_f, s4, s5)) | m_c_h_element_v_out(c_e_h_1, c_f, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s5)) | (~node15(c_e_h_1, c_f, s4, s5)) | m_c_h_element_v_out(c_e_h_1, c_f, s4))),
% 292.41/184.96 inference(rewrite,[status(thm)],[])).
% 292.41/184.96 tff(16920,plain,
% 292.41/184.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s5)) | (~node15(c_e_h_1, c_f, s4, s5)) | m_c_h_element_v_out(c_e_h_1, c_f, s4))),
% 292.41/184.96 inference(quant_inst,[status(thm)],[])).
% 292.41/184.96 tff(16921,plain,
% 292.41/184.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s5)) | (~node15(c_e_h_1, c_f, s4, s5)) | m_c_h_element_v_out(c_e_h_1, c_f, s4)),
% 292.41/184.96 inference(modus_ponens,[status(thm)],[16920, 16919])).
% 292.41/184.96 tff(16922,plain,
% 292.41/184.96 ($false),
% 292.41/184.96 inference(unit_resolution,[status(thm)],[16921, 147, 16864, 16918, 16862])).
% 292.41/184.96 tff(16923,plain,((~m_c_h_element_v_out(c_e_h_1, c_f, s5)) | m_c_h_element_v_out(c_e_h_1, c_f, s4) | m_c_h_element_v_in2(c_e_h_1, c_f, s4)), inference(lemma,lemma(discharge,[]))).
% 292.41/184.96 tff(16924,plain,
% 292.41/184.96 ((~m_c_h_element_v_out(c_e_h_1, c_f, s5)) | m_c_h_element_v_out(c_e_h_1, c_f, s4)),
% 292.41/184.96 inference(unit_resolution,[status(thm)],[16923, 16861])).
% 292.41/184.96 tff(16925,plain,
% 292.41/184.96 (~m_c_h_element_v_out(c_e_h_1, c_f, s5)),
% 292.41/184.96 inference(unit_resolution,[status(thm)],[16924, 15306])).
% 292.41/184.96 tff(16926,assumption,(m_and_h_gate_v_in1(c_e_h_1, c_q, s5)), introduced(assumption)).
% 292.41/184.96 tff(16927,assumption,(~m_c_h_element_v_out(c_e_h_1, c_f, s5)), introduced(assumption)).
% 292.41/184.96 tff(16928,plain,
% 292.41/184.96 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s5)) | m_c_h_element_v_out(c_e_h_1, c_f, s5))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s5)) | m_c_h_element_v_out(c_e_h_1, c_f, s5))),
% 292.41/184.96 inference(rewrite,[status(thm)],[])).
% 292.41/184.96 tff(16929,plain,
% 292.41/184.96 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s5)) | m_c_h_element_v_out(c_e_h_1, c_f, s5))),
% 292.41/184.96 inference(quant_inst,[status(thm)],[])).
% 292.41/184.96 tff(16930,plain,
% 292.41/184.96 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s5)) | m_c_h_element_v_out(c_e_h_1, c_f, s5)),
% 292.41/184.96 inference(modus_ponens,[status(thm)],[16929, 16928])).
% 292.41/184.96 tff(16931,plain,
% 292.41/184.96 ($false),
% 292.41/184.96 inference(unit_resolution,[status(thm)],[16930, 1586, 16927, 16926])).
% 292.41/184.96 tff(16932,plain,((~m_and_h_gate_v_in1(c_e_h_1, c_q, s5)) | m_c_h_element_v_out(c_e_h_1, c_f, s5)), inference(lemma,lemma(discharge,[]))).
% 292.41/184.96 tff(16933,plain,
% 292.41/184.96 (~m_and_h_gate_v_in1(c_e_h_1, c_q, s5)),
% 292.41/184.96 inference(unit_resolution,[status(thm)],[16932, 16925])).
% 292.41/184.96 tff(16934,assumption,(~m_and_h_gate_v_in1(c_e_h_1, c_q, s5)), introduced(assumption)).
% 292.41/184.96 tff(16935,assumption,(node20(c_e_h_1, c_q, s5)), introduced(assumption)).
% 292.41/184.96 tff(16936,plain,
% 292.41/184.96 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s5)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s5)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s5))),
% 292.41/184.96 inference(rewrite,[status(thm)],[])).
% 292.41/184.96 tff(16937,plain,
% 292.41/184.96 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s5)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s5))),
% 292.41/184.96 inference(quant_inst,[status(thm)],[])).
% 292.41/184.96 tff(16938,plain,
% 292.41/184.96 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s5)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s5)),
% 292.41/184.96 inference(modus_ponens,[status(thm)],[16937, 16936])).
% 292.41/184.96 tff(16939,plain,
% 292.41/184.96 ($false),
% 292.41/184.96 inference(unit_resolution,[status(thm)],[16938, 38, 16935, 16934])).
% 292.41/184.96 tff(16940,plain,(m_and_h_gate_v_in1(c_e_h_1, c_q, s5) | (~node20(c_e_h_1, c_q, s5))), inference(lemma,lemma(discharge,[]))).
% 292.41/184.96 tff(16941,plain,
% 292.41/184.96 (~node20(c_e_h_1, c_q, s5)),
% 292.41/184.96 inference(unit_resolution,[status(thm)],[16940, 16933])).
% 292.41/184.96 tff(16942,assumption,(~node20(c_e_h_1, c_q, s5)), introduced(assumption)).
% 292.41/184.96 tff(16943,assumption,(m_and_h_gate_v_out(c_e_h_1, c_q, s6)), introduced(assumption)).
% 292.41/184.96 tff(16944,assumption,(node21(c_e_h_1, c_q, s5, s6)), introduced(assumption)).
% 292.41/184.96 tff(16945,plain,
% 292.41/184.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s6)) | (~node21(c_e_h_1, c_q, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_q, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s6)) | (~node21(c_e_h_1, c_q, s5, s6)))),
% 292.41/184.96 inference(rewrite,[status(thm)],[])).
% 292.41/184.96 tff(16946,plain,
% 292.41/184.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s6)) | (~node21(c_e_h_1, c_q, s5, s6)))),
% 292.41/184.96 inference(quant_inst,[status(thm)],[])).
% 292.41/184.96 tff(16947,plain,
% 292.41/184.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_q, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s6)) | (~node21(c_e_h_1, c_q, s5, s6))),
% 292.41/184.96 inference(modus_ponens,[status(thm)],[16946, 16945])).
% 292.41/184.96 tff(16948,plain,
% 292.41/184.96 ($false),
% 292.41/184.96 inference(unit_resolution,[status(thm)],[16947, 52, 16943, 16944, 16942])).
% 292.41/184.96 tff(16949,plain,((~node21(c_e_h_1, c_q, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s6)) | node20(c_e_h_1, c_q, s5)), inference(lemma,lemma(discharge,[]))).
% 292.41/184.96 tff(16950,plain,
% 292.41/184.96 (~node21(c_e_h_1, c_q, s5, s6)),
% 292.41/184.96 inference(unit_resolution,[status(thm)],[16949, 16943, 16942])).
% 292.41/184.96 tff(16951,plain,
% 292.41/184.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_1, c_q, s5, s6) | node22(c_e_h_1, c_q, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_1, c_q, s5, s6) | node22(c_e_h_1, c_q, s5, s6))),
% 292.41/184.96 inference(rewrite,[status(thm)],[])).
% 292.41/184.96 tff(16952,plain,
% 292.41/184.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_1, c_q, s5, s6) | node22(c_e_h_1, c_q, s5, s6))),
% 292.41/184.97 inference(quant_inst,[status(thm)],[])).
% 292.41/184.97 tff(16953,plain,
% 292.41/184.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_1, c_q, s5, s6) | node22(c_e_h_1, c_q, s5, s6)),
% 292.41/184.97 inference(modus_ponens,[status(thm)],[16952, 16951])).
% 292.41/184.97 tff(16954,plain,
% 292.41/184.97 (node21(c_e_h_1, c_q, s5, s6) | node22(c_e_h_1, c_q, s5, s6)),
% 292.41/184.97 inference(unit_resolution,[status(thm)],[16953, 82, 1406])).
% 292.41/184.97 tff(16955,plain,
% 292.41/184.97 (node22(c_e_h_1, c_q, s5, s6)),
% 292.41/184.97 inference(unit_resolution,[status(thm)],[16954, 16950])).
% 292.41/184.97 tff(16956,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_q, s5)), introduced(assumption)).
% 292.41/184.97 tff(16957,plain,
% 292.41/184.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s6)) | (~node22(c_e_h_1, c_q, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_q, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s6)) | (~node22(c_e_h_1, c_q, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_q, s5))),
% 292.41/184.97 inference(rewrite,[status(thm)],[])).
% 292.41/184.97 tff(16958,plain,
% 292.41/184.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s6)) | (~node22(c_e_h_1, c_q, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_q, s5))),
% 292.41/184.97 inference(quant_inst,[status(thm)],[])).
% 292.41/184.97 tff(16959,plain,
% 292.41/184.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s6)) | (~node22(c_e_h_1, c_q, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_q, s5)),
% 292.41/184.97 inference(modus_ponens,[status(thm)],[16958, 16957])).
% 292.41/184.97 tff(16960,plain,
% 292.41/184.97 ($false),
% 292.41/184.97 inference(unit_resolution,[status(thm)],[16959, 108, 16956, 16943, 16955])).
% 292.41/184.97 tff(16961,plain,((~m_and_h_gate_v_out(c_e_h_1, c_q, s6)) | m_and_h_gate_v_out(c_e_h_1, c_q, s5) | node20(c_e_h_1, c_q, s5)), inference(lemma,lemma(discharge,[]))).
% 292.41/184.97 tff(16962,plain,
% 292.41/184.97 (~m_and_h_gate_v_out(c_e_h_1, c_q, s6)),
% 292.41/184.97 inference(unit_resolution,[status(thm)],[16961, 15342, 16941])).
% 292.41/184.97 tff(16963,plain,
% 292.41/184.97 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s6))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s6))),
% 292.41/184.97 inference(rewrite,[status(thm)],[])).
% 292.41/184.97 tff(16964,plain,
% 292.41/184.97 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s6))),
% 292.41/184.97 inference(quant_inst,[status(thm)],[])).
% 292.41/184.97 tff(16965,plain,
% 292.41/184.97 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s6)),
% 292.41/184.97 inference(modus_ponens,[status(thm)],[16964, 16963])).
% 292.41/184.97 tff(16966,plain,
% 292.41/184.97 (node3(c_e_h_1, c_e_h_2, s6)),
% 292.41/184.97 inference(unit_resolution,[status(thm)],[16965, 4166, 1056])).
% 292.41/184.97 tff(16967,plain,
% 292.41/184.97 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s6)) | (~node3(c_e_h_1, c_e_h_2, s6)) | m_and_h_gate_v_out(c_e_h_1, c_q, s6))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s6)) | (~node3(c_e_h_1, c_e_h_2, s6)) | m_and_h_gate_v_out(c_e_h_1, c_q, s6))),
% 292.41/184.97 inference(rewrite,[status(thm)],[])).
% 292.41/184.97 tff(16968,plain,
% 292.41/184.97 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s6)) | (~node3(c_e_h_1, c_e_h_2, s6)) | m_and_h_gate_v_out(c_e_h_1, c_q, s6))),
% 292.41/184.97 inference(quant_inst,[status(thm)],[])).
% 292.41/184.97 tff(16969,plain,
% 292.41/184.97 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s6)) | (~node3(c_e_h_1, c_e_h_2, s6)) | m_and_h_gate_v_out(c_e_h_1, c_q, s6)),
% 292.41/184.97 inference(modus_ponens,[status(thm)],[16968, 16967])).
% 292.41/184.97 tff(16970,plain,
% 292.41/184.97 ((~m_cell_v_ack(c_e_h_2, s6)) | m_and_h_gate_v_out(c_e_h_1, c_q, s6)),
% 292.41/184.97 inference(unit_resolution,[status(thm)],[16969, 1073, 16966])).
% 292.41/184.97 tff(16971,plain,
% 292.41/184.97 (~m_cell_v_ack(c_e_h_2, s6)),
% 292.41/184.97 inference(unit_resolution,[status(thm)],[16970, 16962])).
% 292.41/184.97 tff(16972,plain,
% 292.41/184.97 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node2(c_e_h_1, c_e_h_2, s6))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node2(c_e_h_1, c_e_h_2, s6))),
% 292.41/184.97 inference(rewrite,[status(thm)],[])).
% 292.41/184.97 tff(16973,plain,
% 292.41/184.97 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node2(c_e_h_1, c_e_h_2, s6))),
% 292.41/184.97 inference(quant_inst,[status(thm)],[])).
% 292.41/184.97 tff(16974,plain,
% 292.41/184.97 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node2(c_e_h_1, c_e_h_2, s6)),
% 292.41/184.97 inference(modus_ponens,[status(thm)],[16973, 16972])).
% 292.41/184.97 tff(16975,plain,
% 292.41/184.97 (node2(c_e_h_1, c_e_h_2, s6)),
% 292.41/184.97 inference(unit_resolution,[status(thm)],[16974, 4166, 5821])).
% 292.41/184.97 tff(16976,plain,
% 292.41/184.97 (((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | ((~node2(c_e_h_1, c_e_h_2, s6)) | m_cell_v_ack(c_e_h_2, s6) | m_and_h_gate_v_in2(c_e_h_1, c_c, s6))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | (~node2(c_e_h_1, c_e_h_2, s6)) | m_cell_v_ack(c_e_h_2, s6) | m_and_h_gate_v_in2(c_e_h_1, c_c, s6))),
% 292.41/184.97 inference(rewrite,[status(thm)],[])).
% 292.41/184.97 tff(16977,plain,
% 292.41/184.97 ((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | ((~node2(c_e_h_1, c_e_h_2, s6)) | m_cell_v_ack(c_e_h_2, s6) | m_and_h_gate_v_in2(c_e_h_1, c_c, s6))),
% 292.41/184.97 inference(quant_inst,[status(thm)],[])).
% 292.41/184.97 tff(16978,plain,
% 292.41/184.97 ((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | (~node2(c_e_h_1, c_e_h_2, s6)) | m_cell_v_ack(c_e_h_2, s6) | m_and_h_gate_v_in2(c_e_h_1, c_c, s6)),
% 292.41/184.97 inference(modus_ponens,[status(thm)],[16977, 16976])).
% 292.41/184.97 tff(16979,plain,
% 292.41/184.97 (m_cell_v_ack(c_e_h_2, s6) | m_and_h_gate_v_in2(c_e_h_1, c_c, s6)),
% 292.41/184.97 inference(unit_resolution,[status(thm)],[16978, 5835, 16975])).
% 292.41/184.97 tff(16980,plain,
% 292.41/184.97 (m_and_h_gate_v_in2(c_e_h_1, c_c, s6)),
% 292.41/184.97 inference(unit_resolution,[status(thm)],[16979, 16971])).
% 292.41/184.97 tff(16981,plain,
% 292.41/184.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_c, s6)) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s6)) | m_and_h_gate_v_out(c_e_h_1, c_c, s7) | (~node21(c_e_h_1, c_c, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in2(c_e_h_1, c_c, s6)) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s6)) | m_and_h_gate_v_out(c_e_h_1, c_c, s7) | (~node21(c_e_h_1, c_c, s6, s7)))),
% 292.41/184.97 inference(rewrite,[status(thm)],[])).
% 292.41/184.97 tff(16982,plain,
% 292.41/184.97 (((~node21(c_e_h_1, c_c, s6, s7)) | (~m_and_h_gate_v_in2(c_e_h_1, c_c, s6)) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s6)) | m_and_h_gate_v_out(c_e_h_1, c_c, s7)) <=> ((~m_and_h_gate_v_in2(c_e_h_1, c_c, s6)) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s6)) | m_and_h_gate_v_out(c_e_h_1, c_c, s7) | (~node21(c_e_h_1, c_c, s6, s7)))),
% 292.41/184.97 inference(rewrite,[status(thm)],[])).
% 292.41/184.97 tff(16983,plain,
% 292.41/184.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_1, c_c, s6, s7)) | (~m_and_h_gate_v_in2(c_e_h_1, c_c, s6)) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s6)) | m_and_h_gate_v_out(c_e_h_1, c_c, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_c, s6)) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s6)) | m_and_h_gate_v_out(c_e_h_1, c_c, s7) | (~node21(c_e_h_1, c_c, s6, s7))))),
% 292.41/184.97 inference(monotonicity,[status(thm)],[16982])).
% 292.41/184.97 tff(16984,plain,
% 292.41/184.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_1, c_c, s6, s7)) | (~m_and_h_gate_v_in2(c_e_h_1, c_c, s6)) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s6)) | m_and_h_gate_v_out(c_e_h_1, c_c, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in2(c_e_h_1, c_c, s6)) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s6)) | m_and_h_gate_v_out(c_e_h_1, c_c, s7) | (~node21(c_e_h_1, c_c, s6, s7)))),
% 292.41/184.97 inference(transitivity,[status(thm)],[16983, 16981])).
% 292.41/184.97 tff(16985,plain,
% 292.41/184.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_1, c_c, s6, s7)) | (~m_and_h_gate_v_in2(c_e_h_1, c_c, s6)) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s6)) | m_and_h_gate_v_out(c_e_h_1, c_c, s7))),
% 292.41/184.97 inference(quant_inst,[status(thm)],[])).
% 292.41/184.97 tff(16986,plain,
% 292.41/184.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in2(c_e_h_1, c_c, s6)) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s6)) | m_and_h_gate_v_out(c_e_h_1, c_c, s7) | (~node21(c_e_h_1, c_c, s6, s7))),
% 292.41/184.97 inference(modus_ponens,[status(thm)],[16985, 16984])).
% 292.41/184.97 tff(16987,plain,
% 292.41/184.97 ($false),
% 292.41/184.97 inference(unit_resolution,[status(thm)],[16986, 5851, 16980, 16266, 16686, 16685])).
% 292.41/184.97 tff(16988,plain,((~node21(c_e_h_1, c_c, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_c, s7) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s6))), inference(lemma,lemma(discharge,[]))).
% 292.41/184.97 tff(16989,plain,
% 292.41/184.97 (~node21(c_e_h_1, c_c, s6, s7)),
% 292.41/184.97 inference(unit_resolution,[status(thm)],[16988, 16266, 16685])).
% 292.41/184.97 tff(16990,assumption,(node22(c_e_h_1, c_c, s6, s7)), introduced(assumption)).
% 292.41/184.97 tff(16991,plain,
% 292.41/184.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_c, s6)) | m_and_h_gate_v_out(c_e_h_1, c_c, s7) | (~node22(c_e_h_1, c_c, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s6)) | m_and_h_gate_v_out(c_e_h_1, c_c, s7) | (~node22(c_e_h_1, c_c, s6, s7)))),
% 292.41/184.97 inference(rewrite,[status(thm)],[])).
% 292.41/184.97 tff(16992,plain,
% 292.41/184.97 ((m_and_h_gate_v_out(c_e_h_1, c_c, s7) | (~node22(c_e_h_1, c_c, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s6))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_c, s6)) | m_and_h_gate_v_out(c_e_h_1, c_c, s7) | (~node22(c_e_h_1, c_c, s6, s7)))),
% 292.41/184.97 inference(rewrite,[status(thm)],[])).
% 292.41/184.97 tff(16993,plain,
% 292.41/184.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_1, c_c, s7) | (~node22(c_e_h_1, c_c, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_c, s6)) | m_and_h_gate_v_out(c_e_h_1, c_c, s7) | (~node22(c_e_h_1, c_c, s6, s7))))),
% 292.41/184.97 inference(monotonicity,[status(thm)],[16992])).
% 292.41/184.97 tff(16994,plain,
% 292.41/184.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_1, c_c, s7) | (~node22(c_e_h_1, c_c, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s6)) | m_and_h_gate_v_out(c_e_h_1, c_c, s7) | (~node22(c_e_h_1, c_c, s6, s7)))),
% 292.41/184.98 inference(transitivity,[status(thm)],[16993, 16991])).
% 292.41/184.98 tff(16995,plain,
% 292.41/184.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_1, c_c, s7) | (~node22(c_e_h_1, c_c, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s6)))),
% 292.41/184.98 inference(quant_inst,[status(thm)],[])).
% 292.41/184.98 tff(16996,plain,
% 292.41/184.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s6)) | m_and_h_gate_v_out(c_e_h_1, c_c, s7) | (~node22(c_e_h_1, c_c, s6, s7))),
% 292.41/184.98 inference(modus_ponens,[status(thm)],[16995, 16994])).
% 292.41/184.98 tff(16997,plain,
% 292.41/184.98 ($false),
% 292.41/184.98 inference(unit_resolution,[status(thm)],[16996, 5871, 16266, 16268, 16990])).
% 292.41/184.98 tff(16998,plain,((~node22(c_e_h_1, c_c, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_c, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s6))), inference(lemma,lemma(discharge,[]))).
% 292.41/184.98 tff(16999,plain,
% 292.41/184.98 (~node22(c_e_h_1, c_c, s6, s7)),
% 292.41/184.98 inference(unit_resolution,[status(thm)],[16998, 16266, 16268])).
% 292.41/184.98 tff(17000,plain,
% 292.41/184.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_1, c_c, s6, s7) | node22(c_e_h_1, c_c, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_1, c_c, s6, s7) | node22(c_e_h_1, c_c, s6, s7))),
% 292.41/184.98 inference(rewrite,[status(thm)],[])).
% 292.41/184.98 tff(17001,plain,
% 292.41/184.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_1, c_c, s6, s7) | node22(c_e_h_1, c_c, s6, s7))),
% 292.41/184.98 inference(quant_inst,[status(thm)],[])).
% 292.41/184.98 tff(17002,plain,
% 292.41/184.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_1, c_c, s6, s7) | node22(c_e_h_1, c_c, s6, s7)),
% 292.41/184.98 inference(modus_ponens,[status(thm)],[17001, 17000])).
% 292.41/184.98 tff(17003,plain,
% 292.41/184.98 (node21(c_e_h_1, c_c, s6, s7) | node22(c_e_h_1, c_c, s6, s7)),
% 292.41/184.98 inference(unit_resolution,[status(thm)],[17002, 82, 1844])).
% 292.41/184.98 tff(17004,plain,
% 292.41/184.98 ($false),
% 292.41/184.98 inference(unit_resolution,[status(thm)],[17003, 16999, 16989])).
% 292.41/184.98 tff(17005,plain,(m_and_h_gate_v_out(c_e_h_1, c_c, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s6)) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s6))), inference(lemma,lemma(discharge,[]))).
% 292.41/184.98 tff(17006,plain,
% 292.41/184.98 (~m_and_h_gate_v_out(c_e_h_1, c_c, s6)),
% 292.41/184.98 inference(unit_resolution,[status(thm)],[17005, 16684, 16266])).
% 292.41/184.98 tff(17007,plain,
% 292.41/184.98 ($false),
% 292.41/184.98 inference(unit_resolution,[status(thm)],[16591, 2708, 17006, 16265])).
% 292.41/184.98 tff(17008,plain,((~m_or_h_gate_v_out(c_e_h_1, c_g, s7)) | m_and_h_gate_v_out(c_e_h_1, c_c, s7) | m_or_h_gate_v_out(c_e_h_1, c_g, s6)), inference(lemma,lemma(discharge,[]))).
% 292.41/184.98 tff(17009,plain,
% 292.41/184.98 (m_and_h_gate_v_out(c_e_h_1, c_c, s7)),
% 292.41/184.98 inference(unit_resolution,[status(thm)],[17008, 15940, 15388])).
% 292.41/184.98 tff(17010,plain,
% 292.41/184.98 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_c, s7)) | m_or_h_gate_v_in1(c_e_h_1, c_g, s7))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s7)) | m_or_h_gate_v_in1(c_e_h_1, c_g, s7))),
% 292.41/184.98 inference(rewrite,[status(thm)],[])).
% 292.41/184.98 tff(17011,plain,
% 292.41/184.98 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_c, s7)) | m_or_h_gate_v_in1(c_e_h_1, c_g, s7))),
% 292.41/184.98 inference(quant_inst,[status(thm)],[])).
% 292.41/184.98 tff(17012,plain,
% 292.41/184.98 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s7)) | m_or_h_gate_v_in1(c_e_h_1, c_g, s7)),
% 292.41/184.98 inference(modus_ponens,[status(thm)],[17011, 17010])).
% 292.41/184.98 tff(17013,plain,
% 292.41/184.98 ($false),
% 292.41/184.98 inference(unit_resolution,[status(thm)],[17012, 5896, 17009, 15980])).
% 292.41/184.98 tff(17014,plain,(m_and_h_gate_v_out(c_e_h_1, c_c, s6) | m_or_h_gate_v_out(c_e_h_1, c_g, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s9))), inference(lemma,lemma(discharge,[]))).
% 292.41/184.98 tff(17015,plain,
% 292.41/184.98 (m_and_h_gate_v_out(c_e_h_1, c_c, s6)),
% 292.41/184.98 inference(unit_resolution,[status(thm)],[17014, 13628, 13627])).
% 292.41/184.98 tff(17016,plain,
% 292.41/184.98 (m_and_h_gate_v_out(c_e_h_1, c_c, s6)),
% 292.41/184.98 inference(unit_resolution,[status(thm)],[17014, 13627, 13628])).
% 292.41/184.98 tff(17017,plain,
% 292.41/184.98 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_c, s6)) | m_or_h_gate_v_in1(c_e_h_1, c_g, s6))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s6)) | m_or_h_gate_v_in1(c_e_h_1, c_g, s6))),
% 292.41/184.98 inference(rewrite,[status(thm)],[])).
% 292.41/184.98 tff(17018,plain,
% 292.41/184.98 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_c, s6)) | m_or_h_gate_v_in1(c_e_h_1, c_g, s6))),
% 292.41/184.98 inference(quant_inst,[status(thm)],[])).
% 292.41/184.98 tff(17019,plain,
% 292.41/184.98 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s6)) | m_or_h_gate_v_in1(c_e_h_1, c_g, s6)),
% 292.41/184.98 inference(modus_ponens,[status(thm)],[17018, 17017])).
% 292.41/184.98 tff(17020,plain,
% 292.41/184.98 (m_or_h_gate_v_in1(c_e_h_1, c_g, s6)),
% 292.41/184.98 inference(unit_resolution,[status(thm)],[17019, 5896, 17016])).
% 292.41/184.98 tff(17021,assumption,(m_or_h_gate_v_in1(c_e_h_1, c_g, s6)), introduced(assumption)).
% 292.41/184.98 tff(17022,assumption,(node4(c_e_h_1, c_g, s6)), introduced(assumption)).
% 292.41/184.98 tff(17023,plain,
% 292.41/184.98 (((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_g, s6)) | (~node4(c_e_h_1, c_g, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | (~m_or_h_gate_v_in1(c_e_h_1, c_g, s6)) | (~node4(c_e_h_1, c_g, s6)))),
% 292.41/184.98 inference(rewrite,[status(thm)],[])).
% 292.41/184.98 tff(17024,plain,
% 292.41/184.98 ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_g, s6)) | (~node4(c_e_h_1, c_g, s6)))),
% 292.41/184.98 inference(quant_inst,[status(thm)],[])).
% 292.41/184.98 tff(17025,plain,
% 292.41/184.98 ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | (~m_or_h_gate_v_in1(c_e_h_1, c_g, s6)) | (~node4(c_e_h_1, c_g, s6))),
% 292.41/184.98 inference(modus_ponens,[status(thm)],[17024, 17023])).
% 292.41/184.98 tff(17026,plain,
% 292.41/184.98 ($false),
% 292.41/184.98 inference(unit_resolution,[status(thm)],[17025, 5516, 17022, 17021])).
% 292.41/184.98 tff(17027,plain,((~m_or_h_gate_v_in1(c_e_h_1, c_g, s6)) | (~node4(c_e_h_1, c_g, s6))), inference(lemma,lemma(discharge,[]))).
% 292.41/184.98 tff(17028,plain,
% 292.41/184.98 (~node4(c_e_h_1, c_g, s6)),
% 292.41/184.98 inference(unit_resolution,[status(thm)],[17027, 17020])).
% 292.41/184.98 tff(17029,plain,
% 292.41/184.98 (m_and_h_gate_v_out(c_e_h_1, c_c, s7)),
% 292.41/184.98 inference(unit_resolution,[status(thm)],[17005, 17016, 16685])).
% 292.41/184.98 tff(17030,plain,
% 292.41/184.98 (m_or_h_gate_v_in1(c_e_h_1, c_g, s7)),
% 292.41/184.98 inference(unit_resolution,[status(thm)],[17012, 5896, 17029])).
% 292.41/184.98 tff(17031,plain,
% 292.41/184.98 (~node4(c_e_h_1, c_g, s7)),
% 292.41/184.98 inference(unit_resolution,[status(thm)],[15979, 17030])).
% 292.41/184.98 tff(17032,plain,
% 292.41/184.98 (~m_or_h_gate_v_out(c_e_h_1, c_g, s7)),
% 292.41/184.98 inference(unit_resolution,[status(thm)],[15971, 17031, 13627])).
% 292.41/184.98 tff(17033,assumption,(~node4(c_e_h_1, c_g, s6)), introduced(assumption)).
% 292.41/184.98 tff(17034,plain,
% 292.41/184.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (m_or_h_gate_v_out(c_e_h_1, c_g, s7) | node4(c_e_h_1, c_g, s6) | (~node5(c_e_h_1, c_g, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | m_or_h_gate_v_out(c_e_h_1, c_g, s7) | node4(c_e_h_1, c_g, s6) | (~node5(c_e_h_1, c_g, s6, s7)))),
% 292.41/184.98 inference(rewrite,[status(thm)],[])).
% 292.41/184.98 tff(17035,plain,
% 292.41/184.98 ((node4(c_e_h_1, c_g, s6) | (~node5(c_e_h_1, c_g, s6, s7)) | m_or_h_gate_v_out(c_e_h_1, c_g, s7)) <=> (m_or_h_gate_v_out(c_e_h_1, c_g, s7) | node4(c_e_h_1, c_g, s6) | (~node5(c_e_h_1, c_g, s6, s7)))),
% 292.41/184.98 inference(rewrite,[status(thm)],[])).
% 292.41/184.98 tff(17036,plain,
% 292.41/184.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_1, c_g, s6) | (~node5(c_e_h_1, c_g, s6, s7)) | m_or_h_gate_v_out(c_e_h_1, c_g, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (m_or_h_gate_v_out(c_e_h_1, c_g, s7) | node4(c_e_h_1, c_g, s6) | (~node5(c_e_h_1, c_g, s6, s7))))),
% 292.41/184.98 inference(monotonicity,[status(thm)],[17035])).
% 292.41/184.98 tff(17037,plain,
% 292.41/184.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_1, c_g, s6) | (~node5(c_e_h_1, c_g, s6, s7)) | m_or_h_gate_v_out(c_e_h_1, c_g, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | m_or_h_gate_v_out(c_e_h_1, c_g, s7) | node4(c_e_h_1, c_g, s6) | (~node5(c_e_h_1, c_g, s6, s7)))),
% 292.41/184.98 inference(transitivity,[status(thm)],[17036, 17034])).
% 292.41/184.98 tff(17038,plain,
% 292.41/184.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_1, c_g, s6) | (~node5(c_e_h_1, c_g, s6, s7)) | m_or_h_gate_v_out(c_e_h_1, c_g, s7))),
% 292.41/184.98 inference(quant_inst,[status(thm)],[])).
% 292.41/184.98 tff(17039,plain,
% 292.41/184.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | m_or_h_gate_v_out(c_e_h_1, c_g, s7) | node4(c_e_h_1, c_g, s6) | (~node5(c_e_h_1, c_g, s6, s7))),
% 292.41/184.98 inference(modus_ponens,[status(thm)],[17038, 17037])).
% 292.41/184.98 tff(17040,plain,
% 292.41/184.98 ($false),
% 292.41/184.98 inference(unit_resolution,[status(thm)],[17039, 5498, 16245, 17033, 15934])).
% 292.41/184.98 tff(17041,plain,((~node5(c_e_h_1, c_g, s6, s7)) | node4(c_e_h_1, c_g, s6) | m_or_h_gate_v_out(c_e_h_1, c_g, s7)), inference(lemma,lemma(discharge,[]))).
% 292.41/184.98 tff(17042,plain,
% 292.41/184.98 (~node5(c_e_h_1, c_g, s6, s7)),
% 292.41/184.98 inference(unit_resolution,[status(thm)],[17041, 15934, 17033])).
% 292.41/184.98 tff(17043,plain,
% 292.41/184.98 (node6(c_e_h_1, c_g, s6, s7)),
% 292.41/184.98 inference(unit_resolution,[status(thm)],[16262, 17042])).
% 292.41/184.98 tff(17044,plain,
% 292.41/184.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_1, c_g, s7) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s6)) | (~node6(c_e_h_1, c_g, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | m_or_h_gate_v_out(c_e_h_1, c_g, s7) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s6)) | (~node6(c_e_h_1, c_g, s6, s7)))),
% 292.41/184.98 inference(rewrite,[status(thm)],[])).
% 292.41/184.98 tff(17045,plain,
% 292.41/184.98 ((m_or_h_gate_v_out(c_e_h_1, c_g, s7) | (~node6(c_e_h_1, c_g, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s6))) <=> (m_or_h_gate_v_out(c_e_h_1, c_g, s7) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s6)) | (~node6(c_e_h_1, c_g, s6, s7)))),
% 292.41/184.98 inference(rewrite,[status(thm)],[])).
% 292.41/184.98 tff(17046,plain,
% 292.41/184.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_1, c_g, s7) | (~node6(c_e_h_1, c_g, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_1, c_g, s7) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s6)) | (~node6(c_e_h_1, c_g, s6, s7))))),
% 292.41/184.98 inference(monotonicity,[status(thm)],[17045])).
% 292.41/184.98 tff(17047,plain,
% 292.41/184.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_1, c_g, s7) | (~node6(c_e_h_1, c_g, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | m_or_h_gate_v_out(c_e_h_1, c_g, s7) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s6)) | (~node6(c_e_h_1, c_g, s6, s7)))),
% 292.41/184.99 inference(transitivity,[status(thm)],[17046, 17044])).
% 292.41/184.99 tff(17048,plain,
% 292.41/184.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_1, c_g, s7) | (~node6(c_e_h_1, c_g, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s6)))),
% 292.41/184.99 inference(quant_inst,[status(thm)],[])).
% 292.41/184.99 tff(17049,plain,
% 292.41/184.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | m_or_h_gate_v_out(c_e_h_1, c_g, s7) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s6)) | (~node6(c_e_h_1, c_g, s6, s7))),
% 292.41/184.99 inference(modus_ponens,[status(thm)],[17048, 17047])).
% 292.41/184.99 tff(17050,plain,
% 292.41/184.99 ($false),
% 292.41/184.99 inference(unit_resolution,[status(thm)],[17049, 5474, 17043, 15934, 13630])).
% 292.41/184.99 tff(17051,plain,(m_or_h_gate_v_out(c_e_h_1, c_g, s7) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s6)) | node4(c_e_h_1, c_g, s6)), inference(lemma,lemma(discharge,[]))).
% 292.41/184.99 tff(17052,plain,
% 292.41/184.99 (~m_or_h_gate_v_out(c_e_h_1, c_g, s6)),
% 292.41/184.99 inference(unit_resolution,[status(thm)],[17051, 17032, 17028])).
% 292.41/184.99 tff(17053,plain,
% 292.41/184.99 (~m_and_h_gate_v_out(c_e_h_1, c_k, s7)),
% 292.41/184.99 inference(unit_resolution,[status(thm)],[15660, 17052])).
% 292.41/184.99 tff(17054,plain,
% 292.41/184.99 (~m_and_h_gate_v_in1(c_e_h_1, c_k, s7)),
% 292.41/184.99 inference(unit_resolution,[status(thm)],[15939, 17032])).
% 292.41/184.99 tff(17055,plain,
% 292.41/184.99 (~node20(c_e_h_1, c_k, s7)),
% 292.41/184.99 inference(unit_resolution,[status(thm)],[15931, 17054])).
% 292.41/184.99 tff(17056,plain,
% 292.41/184.99 (~m_and_h_gate_v_out(c_e_h_1, c_k, s8)),
% 292.41/184.99 inference(unit_resolution,[status(thm)],[15923, 17055, 17053])).
% 292.41/184.99 tff(17057,plain,
% 292.41/184.99 (~m_and_h_gate_v_in1(c_e_h_1, c_p, s8)),
% 292.41/184.99 inference(unit_resolution,[status(thm)],[15902, 17056])).
% 292.41/184.99 tff(17058,plain,
% 292.41/184.99 (~node20(c_e_h_1, c_p, s8)),
% 292.41/184.99 inference(unit_resolution,[status(thm)],[15894, 17057])).
% 292.41/184.99 tff(17059,plain,
% 292.41/184.99 (m_and_h_gate_v_out(c_e_h_1, c_p, s8)),
% 292.41/184.99 inference(unit_resolution,[status(thm)],[15886, 17058, 13628])).
% 292.41/184.99 tff(17060,plain,
% 292.41/184.99 (~m_and_h_gate_v_out(c_e_h_1, c_k, s6)),
% 292.41/184.99 inference(unit_resolution,[status(thm)],[15591, 14572, 15389])).
% 292.41/184.99 tff(17061,plain,
% 292.41/184.99 (m_and_h_gate_v_out(c_e_h_1, c_p, s6)),
% 292.41/184.99 inference(unit_resolution,[status(thm)],[15835, 17060, 15662, 15404])).
% 292.41/184.99 tff(17062,plain,
% 292.41/184.99 (node20(c_e_h_1, c_p, s5)),
% 292.41/184.99 inference(unit_resolution,[status(thm)],[15765, 17061])).
% 292.41/184.99 tff(17063,plain,
% 292.41/184.99 (~m_and_h_gate_v_in1(c_e_h_1, c_p, s5)),
% 292.41/184.99 inference(unit_resolution,[status(thm)],[15687, 15501])).
% 292.41/184.99 tff(17064,plain,
% 292.41/184.99 ($false),
% 292.41/184.99 inference(unit_resolution,[status(thm)],[15695, 17063, 17062])).
% 292.41/184.99 tff(17065,plain,(m_or_h_gate_v_out(c_e_h_1, c_g, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s8)) | m_or_h_gate_v_out(c_e_h_1, c_g, s6)), inference(lemma,lemma(discharge,[]))).
% 292.41/184.99 tff(17066,plain,
% 292.41/184.99 (m_or_h_gate_v_out(c_e_h_1, c_g, s4)),
% 292.41/184.99 inference(unit_resolution,[status(thm)],[17065, 17059, 17052])).
% 292.41/184.99 tff(17067,plain,
% 292.41/184.99 (m_or_h_gate_v_out(c_e_h_1, c_g, s5)),
% 292.41/184.99 inference(unit_resolution,[status(thm)],[15624, 17066])).
% 292.41/184.99 tff(17068,plain,
% 292.41/184.99 (~node5(c_e_h_1, c_g, s5, s6)),
% 292.41/184.99 inference(unit_resolution,[status(thm)],[15562, 15389, 15554])).
% 292.41/184.99 tff(17069,plain,
% 292.41/184.99 (~node6(c_e_h_1, c_g, s5, s6)),
% 292.41/184.99 inference(unit_resolution,[status(thm)],[15551, 15389, 14571])).
% 292.41/184.99 tff(17070,plain,
% 292.41/184.99 ($false),
% 292.41/184.99 inference(unit_resolution,[status(thm)],[14560, 17069, 17068])).
% 292.41/184.99 tff(17071,plain,(m_or_h_gate_v_out(c_e_h_1, c_g, s6) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s5)) | node4(c_e_h_1, c_g, s5)), inference(lemma,lemma(discharge,[]))).
% 292.41/184.99 tff(17072,plain,
% 292.41/184.99 (node4(c_e_h_1, c_g, s5)),
% 292.41/184.99 inference(unit_resolution,[status(thm)],[17071, 17067, 17052])).
% 292.41/184.99 tff(17073,plain,
% 292.41/184.99 (~m_or_h_gate_v_in1(c_e_h_1, c_g, s5)),
% 292.41/184.99 inference(unit_resolution,[status(thm)],[15566, 5516, 17072])).
% 292.41/184.99 tff(17074,plain,
% 292.41/184.99 (m_and_h_gate_v_out(c_e_h_1, c_c, s4)),
% 292.41/184.99 inference(unit_resolution,[status(thm)],[14848, 17067])).
% 292.41/184.99 tff(17075,plain,
% 292.41/184.99 (m_user_v_req(c_e_h_1, c_u, s2)),
% 292.41/184.99 inference(unit_resolution,[status(thm)],[14671, 17074])).
% 292.41/184.99 tff(17076,plain,
% 292.41/184.99 (m_user_v_req(c_e_h_1, c_u, s3)),
% 292.41/184.99 inference(unit_resolution,[status(thm)],[14760, 17075])).
% 292.41/184.99 tff(17077,plain,
% 292.41/184.99 (m_mutex_h_half_v_inp(c_e_h_1, c_a, s3)),
% 292.41/184.99 inference(unit_resolution,[status(thm)],[14768, 17076])).
% 292.41/184.99 tff(17078,plain,
% 292.41/184.99 (m_or_h_gate_v_in1(c_e_h_1, c_g, s3)),
% 292.41/184.99 inference(unit_resolution,[status(thm)],[14503, 17066])).
% 292.41/184.99 tff(17079,plain,
% 292.41/184.99 (m_and_h_gate_v_out(c_e_h_1, c_c, s3)),
% 292.41/184.99 inference(unit_resolution,[status(thm)],[14418, 2708, 17078])).
% 292.41/184.99 tff(17080,plain,
% 292.41/184.99 (node20(c_e_h_1, c_c, s2)),
% 292.41/184.99 inference(unit_resolution,[status(thm)],[14216, 17079])).
% 292.41/184.99 tff(17081,plain,
% 292.41/184.99 (m_and_h_gate_v_in1(c_e_h_1, c_c, s2)),
% 292.41/184.99 inference(unit_resolution,[status(thm)],[14224, 17080])).
% 292.41/184.99 tff(17082,plain,
% 292.41/184.99 (m_mutex_h_half_v_out(c_e_h_1, c_a, s2)),
% 292.41/184.99 inference(unit_resolution,[status(thm)],[14232, 17081])).
% 292.41/184.99 tff(17083,plain,
% 292.41/184.99 (m_mutex_h_half_v_out(c_e_h_1, c_a, s3)),
% 292.41/184.99 inference(unit_resolution,[status(thm)],[14381, 17082])).
% 292.41/184.99 tff(17084,plain,
% 292.41/184.99 (m_mutex_h_half_v_out(c_e_h_1, c_a, s4)),
% 292.41/184.99 inference(unit_resolution,[status(thm)],[14793, 17083, 17077])).
% 292.41/184.99 tff(17085,plain,
% 292.41/184.99 (m_and_h_gate_v_in1(c_e_h_1, c_c, s4)),
% 292.41/184.99 inference(unit_resolution,[status(thm)],[14810, 17084])).
% 292.41/184.99 tff(17086,plain,
% 292.41/184.99 (m_and_h_gate_v_out(c_e_h_1, c_c, s5)),
% 292.41/184.99 inference(unit_resolution,[status(thm)],[14843, 17085, 17074])).
% 292.41/184.99 tff(17087,plain,
% 292.41/184.99 ($false),
% 292.41/184.99 inference(unit_resolution,[status(thm)],[15570, 5896, 17086, 17073])).
% 292.41/184.99 tff(17088,plain,(m_or_h_gate_v_out(c_e_h_1, c_g, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s9)) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s6))), inference(lemma,lemma(discharge,[]))).
% 292.41/184.99 tff(17089,plain,
% 292.41/184.99 (~m_and_h_gate_v_in1(c_e_h_1, c_c, s6)),
% 292.41/184.99 inference(unit_resolution,[status(thm)],[17088, 13628, 13627])).
% 292.41/184.99 tff(17090,plain,
% 292.41/184.99 (~m_mutex_h_half_v_out(c_e_h_1, c_a, s6)),
% 292.41/184.99 inference(unit_resolution,[status(thm)],[16683, 17089])).
% 292.41/184.99 tff(17091,plain,
% 292.41/184.99 ($false),
% 292.41/184.99 inference(unit_resolution,[status(thm)],[16650, 17090, 17015])).
% 292.41/184.99 tff(17092,plain,((~m_and_h_gate_v_out(c_e_h_1, c_p, s9)) | m_or_h_gate_v_out(c_e_h_1, c_g, s8)), inference(lemma,lemma(discharge,[]))).
% 292.41/184.99 tff(17093,plain,
% 292.41/184.99 (~m_and_h_gate_v_out(c_e_h_1, c_p, s9)),
% 292.41/184.99 inference(unit_resolution,[status(thm)],[17092, 13627])).
% 292.41/184.99 tff(17094,assumption,(m_and_h_gate_v_out(c_e_h_3, c_d, s9)), introduced(assumption)).
% 292.41/184.99 tff(17095,assumption,(~m_mutex_h_half_v_out(c_e_h_3, c_b, s9)), introduced(assumption)).
% 292.41/184.99 tff(17096,assumption,(~m_mutex_h_half_v_out(c_e_h_3, c_b, s7)), introduced(assumption)).
% 292.41/184.99 tff(17097,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_d, s7)), introduced(assumption)).
% 292.41/184.99 tff(17098,plain,
% 292.41/184.99 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_d, s7)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s7))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_d, s7)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s7))),
% 292.41/184.99 inference(rewrite,[status(thm)],[])).
% 292.41/184.99 tff(17099,plain,
% 292.41/184.99 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_d, s7)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s7))),
% 292.41/184.99 inference(quant_inst,[status(thm)],[])).
% 292.41/184.99 tff(17100,plain,
% 292.41/184.99 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_d, s7)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s7)),
% 292.41/184.99 inference(modus_ponens,[status(thm)],[17099, 17098])).
% 292.41/184.99 tff(17101,plain,
% 292.41/184.99 ($false),
% 292.41/184.99 inference(unit_resolution,[status(thm)],[17100, 2808, 17096, 17097])).
% 292.41/184.99 tff(17102,plain,((~m_and_h_gate_v_in1(c_e_h_3, c_d, s7)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s7)), inference(lemma,lemma(discharge,[]))).
% 292.41/184.99 tff(17103,plain,
% 292.41/184.99 (~m_and_h_gate_v_in1(c_e_h_3, c_d, s7)),
% 292.41/184.99 inference(unit_resolution,[status(thm)],[17102, 17096])).
% 292.41/184.99 tff(17104,assumption,(node20(c_e_h_3, c_d, s7)), introduced(assumption)).
% 292.41/184.99 tff(17105,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_d, s7)), introduced(assumption)).
% 292.41/184.99 tff(17106,plain,
% 292.41/184.99 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_d, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_d, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s7))),
% 292.41/184.99 inference(rewrite,[status(thm)],[])).
% 292.41/184.99 tff(17107,plain,
% 292.41/184.99 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_d, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s7))),
% 292.41/184.99 inference(quant_inst,[status(thm)],[])).
% 292.41/184.99 tff(17108,plain,
% 292.41/184.99 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_d, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s7)),
% 292.41/184.99 inference(modus_ponens,[status(thm)],[17107, 17106])).
% 292.41/184.99 tff(17109,plain,
% 292.41/184.99 ($false),
% 292.41/184.99 inference(unit_resolution,[status(thm)],[17108, 38, 17105, 17104])).
% 292.41/184.99 tff(17110,plain,((~node20(c_e_h_3, c_d, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s7)), inference(lemma,lemma(discharge,[]))).
% 292.41/184.99 tff(17111,plain,
% 292.41/184.99 (~node20(c_e_h_3, c_d, s7)),
% 292.41/184.99 inference(unit_resolution,[status(thm)],[17110, 17103])).
% 292.41/184.99 tff(17112,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_d, s6)), introduced(assumption)).
% 292.41/184.99 tff(17113,assumption,(m_cell_v_req(c_e_h_1, s5)), introduced(assumption)).
% 292.41/184.99 tff(17114,plain,
% 292.41/184.99 (((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | ((~m_cell_v_req(c_e_h_1, s5)) | m_and_h_gate_v_out(c_e_h_1, c_p, s5))) <=> ((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | (~m_cell_v_req(c_e_h_1, s5)) | m_and_h_gate_v_out(c_e_h_1, c_p, s5))),
% 292.41/184.99 inference(rewrite,[status(thm)],[])).
% 292.41/184.99 tff(17115,plain,
% 292.41/184.99 ((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | ((~m_cell_v_req(c_e_h_1, s5)) | m_and_h_gate_v_out(c_e_h_1, c_p, s5))),
% 292.41/184.99 inference(quant_inst,[status(thm)],[])).
% 292.41/184.99 tff(17116,plain,
% 292.41/184.99 ((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | (~m_cell_v_req(c_e_h_1, s5)) | m_and_h_gate_v_out(c_e_h_1, c_p, s5)),
% 292.41/184.99 inference(modus_ponens,[status(thm)],[17115, 17114])).
% 292.41/184.99 tff(17117,plain,
% 292.41/184.99 ($false),
% 292.41/184.99 inference(unit_resolution,[status(thm)],[17116, 2908, 17113, 15746])).
% 292.41/184.99 tff(17118,plain,((~m_cell_v_req(c_e_h_1, s5)) | m_and_h_gate_v_out(c_e_h_1, c_p, s5)), inference(lemma,lemma(discharge,[]))).
% 292.41/184.99 tff(17119,plain,
% 292.41/184.99 (~m_cell_v_req(c_e_h_1, s5)),
% 292.41/184.99 inference(unit_resolution,[status(thm)],[17118, 15744])).
% 292.41/184.99 tff(17120,plain,
% 292.41/184.99 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node1(c_e_h_3, c_e_h_1, s5))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node1(c_e_h_3, c_e_h_1, s5))),
% 292.41/184.99 inference(rewrite,[status(thm)],[])).
% 292.41/184.99 tff(17121,plain,
% 292.41/184.99 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node1(c_e_h_3, c_e_h_1, s5))),
% 292.41/184.99 inference(quant_inst,[status(thm)],[])).
% 292.41/184.99 tff(17122,plain,
% 292.41/184.99 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node1(c_e_h_3, c_e_h_1, s5)),
% 292.41/184.99 inference(modus_ponens,[status(thm)],[17121, 17120])).
% 292.41/184.99 tff(17123,plain,
% 292.41/184.99 (node1(c_e_h_3, c_e_h_1, s5)),
% 292.41/184.99 inference(unit_resolution,[status(thm)],[17122, 2922, 2919])).
% 292.41/184.99 tff(17124,plain,
% 292.41/184.99 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_b, s5)) | (~node1(c_e_h_3, c_e_h_1, s5)) | m_cell_v_req(c_e_h_1, s5))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s5)) | (~node1(c_e_h_3, c_e_h_1, s5)) | m_cell_v_req(c_e_h_1, s5))),
% 292.51/185.00 inference(rewrite,[status(thm)],[])).
% 292.51/185.00 tff(17125,plain,
% 292.51/185.00 (((~node1(c_e_h_3, c_e_h_1, s5)) | m_cell_v_req(c_e_h_1, s5) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s5))) <=> ((~m_mutex_h_half_v_inp(c_e_h_3, c_b, s5)) | (~node1(c_e_h_3, c_e_h_1, s5)) | m_cell_v_req(c_e_h_1, s5))),
% 292.51/185.00 inference(rewrite,[status(thm)],[])).
% 292.51/185.00 tff(17126,plain,
% 292.51/185.00 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_3, c_e_h_1, s5)) | m_cell_v_req(c_e_h_1, s5) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s5)))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_b, s5)) | (~node1(c_e_h_3, c_e_h_1, s5)) | m_cell_v_req(c_e_h_1, s5)))),
% 292.51/185.00 inference(monotonicity,[status(thm)],[17125])).
% 292.51/185.00 tff(17127,plain,
% 292.51/185.00 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_3, c_e_h_1, s5)) | m_cell_v_req(c_e_h_1, s5) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s5)))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s5)) | (~node1(c_e_h_3, c_e_h_1, s5)) | m_cell_v_req(c_e_h_1, s5))),
% 292.51/185.00 inference(transitivity,[status(thm)],[17126, 17124])).
% 292.51/185.00 tff(17128,plain,
% 292.51/185.00 ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_3, c_e_h_1, s5)) | m_cell_v_req(c_e_h_1, s5) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s5)))),
% 292.51/185.00 inference(quant_inst,[status(thm)],[])).
% 292.51/185.00 tff(17129,plain,
% 292.51/185.00 ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s5)) | (~node1(c_e_h_3, c_e_h_1, s5)) | m_cell_v_req(c_e_h_1, s5)),
% 292.51/185.00 inference(modus_ponens,[status(thm)],[17128, 17127])).
% 292.51/185.00 tff(17130,plain,
% 292.51/185.00 ((~m_mutex_h_half_v_inp(c_e_h_3, c_b, s5)) | m_cell_v_req(c_e_h_1, s5)),
% 292.51/185.00 inference(unit_resolution,[status(thm)],[17129, 2936, 17123])).
% 292.51/185.00 tff(17131,plain,
% 292.51/185.00 (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s5)),
% 292.51/185.00 inference(unit_resolution,[status(thm)],[17130, 17119])).
% 292.51/185.00 tff(17132,assumption,(m_mutex_h_half_v_out(c_e_h_3, c_b, s6)), introduced(assumption)).
% 292.51/185.00 tff(17133,assumption,(~m_mutex_h_half_v_inp(c_e_h_3, c_b, s5)), introduced(assumption)).
% 292.51/185.00 tff(17134,assumption,(node12(c_e_h_3, c_b, s5, s6)), introduced(assumption)).
% 292.51/185.00 tff(17135,plain,
% 292.51/185.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_3, c_b, s5) | (~node12(c_e_h_3, c_b, s5, s6)) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s5) | (~node12(c_e_h_3, c_b, s5, s6)) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s6)))),
% 292.51/185.00 inference(rewrite,[status(thm)],[])).
% 292.51/185.00 tff(17136,plain,
% 292.51/185.00 (((~node12(c_e_h_3, c_b, s5, s6)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s5) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s6))) <=> (m_mutex_h_half_v_inp(c_e_h_3, c_b, s5) | (~node12(c_e_h_3, c_b, s5, s6)) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s6)))),
% 292.51/185.00 inference(rewrite,[status(thm)],[])).
% 292.51/185.00 tff(17137,plain,
% 292.51/185.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_b, s5, s6)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s5) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_3, c_b, s5) | (~node12(c_e_h_3, c_b, s5, s6)) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s6))))),
% 292.51/185.00 inference(monotonicity,[status(thm)],[17136])).
% 292.51/185.00 tff(17138,plain,
% 292.51/185.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_b, s5, s6)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s5) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s5) | (~node12(c_e_h_3, c_b, s5, s6)) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s6)))),
% 292.51/185.00 inference(transitivity,[status(thm)],[17137, 17135])).
% 292.51/185.00 tff(17139,plain,
% 292.51/185.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_b, s5, s6)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s5) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s6)))),
% 292.51/185.00 inference(quant_inst,[status(thm)],[])).
% 292.51/185.00 tff(17140,plain,
% 292.51/185.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s5) | (~node12(c_e_h_3, c_b, s5, s6)) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s6))),
% 292.51/185.00 inference(modus_ponens,[status(thm)],[17139, 17138])).
% 292.51/185.00 tff(17141,plain,
% 292.51/185.00 ($false),
% 292.51/185.00 inference(unit_resolution,[status(thm)],[17140, 454, 17133, 17134, 17132])).
% 292.51/185.00 tff(17142,plain,((~node12(c_e_h_3, c_b, s5, s6)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s5) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s6))), inference(lemma,lemma(discharge,[]))).
% 292.51/185.00 tff(17143,plain,
% 292.51/185.00 (~node12(c_e_h_3, c_b, s5, s6)),
% 292.51/185.00 inference(unit_resolution,[status(thm)],[17142, 17132, 17133])).
% 292.51/185.00 tff(17144,plain,
% 292.51/185.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s5, s6)) | node12(c_e_h_3, c_b, s5, s6) | node13(c_e_h_3, c_b, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s5, s6)) | node12(c_e_h_3, c_b, s5, s6) | node13(c_e_h_3, c_b, s5, s6))),
% 292.51/185.00 inference(rewrite,[status(thm)],[])).
% 292.51/185.00 tff(17145,plain,
% 292.51/185.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s5, s6)) | node12(c_e_h_3, c_b, s5, s6) | node13(c_e_h_3, c_b, s5, s6))),
% 292.51/185.00 inference(quant_inst,[status(thm)],[])).
% 292.51/185.00 tff(17146,plain,
% 292.51/185.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s5, s6)) | node12(c_e_h_3, c_b, s5, s6) | node13(c_e_h_3, c_b, s5, s6)),
% 292.51/185.00 inference(modus_ponens,[status(thm)],[17145, 17144])).
% 292.51/185.00 tff(17147,plain,
% 292.51/185.00 (node12(c_e_h_3, c_b, s5, s6) | node13(c_e_h_3, c_b, s5, s6)),
% 292.51/185.00 inference(unit_resolution,[status(thm)],[17146, 439, 1406])).
% 292.51/185.00 tff(17148,plain,
% 292.51/185.00 (node13(c_e_h_3, c_b, s5, s6)),
% 292.51/185.00 inference(unit_resolution,[status(thm)],[17147, 17143])).
% 292.51/185.00 tff(17149,plain,
% 292.51/185.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_b, s6)) | (~node13(c_e_h_3, c_b, s5, s6)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s6)) | (~node13(c_e_h_3, c_b, s5, s6)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s5))),
% 292.51/185.00 inference(rewrite,[status(thm)],[])).
% 292.51/185.00 tff(17150,plain,
% 292.51/185.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_b, s6)) | (~node13(c_e_h_3, c_b, s5, s6)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s5))),
% 292.51/185.00 inference(quant_inst,[status(thm)],[])).
% 292.51/185.00 tff(17151,plain,
% 292.51/185.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s6)) | (~node13(c_e_h_3, c_b, s5, s6)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s5)),
% 292.51/185.00 inference(modus_ponens,[status(thm)],[17150, 17149])).
% 292.51/185.00 tff(17152,plain,
% 292.51/185.00 ($false),
% 292.51/185.00 inference(unit_resolution,[status(thm)],[17151, 423, 17148, 9966, 17132])).
% 292.51/185.00 tff(17153,plain,((~m_mutex_h_half_v_out(c_e_h_3, c_b, s6)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s5) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s5)), inference(lemma,lemma(discharge,[]))).
% 292.51/185.00 tff(17154,plain,
% 292.51/185.00 ((~m_mutex_h_half_v_out(c_e_h_3, c_b, s6)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s5)),
% 292.51/185.00 inference(unit_resolution,[status(thm)],[17153, 17131])).
% 292.51/185.00 tff(17155,plain,
% 292.51/185.00 (~m_mutex_h_half_v_out(c_e_h_3, c_b, s6)),
% 292.51/185.00 inference(unit_resolution,[status(thm)],[17154, 9964])).
% 292.51/185.00 tff(17156,plain,
% 292.51/185.00 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_d, s6)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s6))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_d, s6)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s6))),
% 292.51/185.00 inference(rewrite,[status(thm)],[])).
% 292.51/185.00 tff(17157,plain,
% 292.51/185.00 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_d, s6)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s6))),
% 292.51/185.00 inference(quant_inst,[status(thm)],[])).
% 292.51/185.00 tff(17158,plain,
% 292.51/185.00 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_d, s6)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s6)),
% 292.51/185.00 inference(modus_ponens,[status(thm)],[17157, 17156])).
% 292.51/185.00 tff(17159,plain,
% 292.51/185.00 ($false),
% 292.51/185.00 inference(unit_resolution,[status(thm)],[17158, 2808, 17155, 17112])).
% 292.51/185.00 tff(17160,plain,(~m_and_h_gate_v_in1(c_e_h_3, c_d, s6)), inference(lemma,lemma(discharge,[]))).
% 292.51/185.00 tff(17161,plain,
% 292.51/185.00 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_d, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_d, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s6))),
% 292.51/185.00 inference(rewrite,[status(thm)],[])).
% 292.51/185.00 tff(17162,plain,
% 292.51/185.00 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_d, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s6))),
% 292.51/185.00 inference(quant_inst,[status(thm)],[])).
% 292.51/185.00 tff(17163,plain,
% 292.51/185.00 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_d, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s6)),
% 292.51/185.00 inference(modus_ponens,[status(thm)],[17162, 17161])).
% 292.51/185.00 tff(17164,plain,
% 292.51/185.00 (~node20(c_e_h_3, c_d, s6)),
% 292.51/185.00 inference(unit_resolution,[status(thm)],[17163, 38, 17160])).
% 292.51/185.00 tff(17165,assumption,(m_and_h_gate_v_out(c_e_h_3, c_d, s7)), introduced(assumption)).
% 292.51/185.00 tff(17166,assumption,(node22(c_e_h_3, c_d, s6, s7)), introduced(assumption)).
% 292.51/185.00 tff(17167,plain,
% 292.51/185.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_d, s7)) | (~node22(c_e_h_3, c_d, s6, s7)) | m_and_h_gate_v_out(c_e_h_3, c_d, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s7)) | (~node22(c_e_h_3, c_d, s6, s7)) | m_and_h_gate_v_out(c_e_h_3, c_d, s6))),
% 292.51/185.00 inference(rewrite,[status(thm)],[])).
% 292.51/185.00 tff(17168,plain,
% 292.51/185.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_d, s7)) | (~node22(c_e_h_3, c_d, s6, s7)) | m_and_h_gate_v_out(c_e_h_3, c_d, s6))),
% 292.51/185.00 inference(quant_inst,[status(thm)],[])).
% 292.51/185.00 tff(17169,plain,
% 292.51/185.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s7)) | (~node22(c_e_h_3, c_d, s6, s7)) | m_and_h_gate_v_out(c_e_h_3, c_d, s6)),
% 292.51/185.00 inference(modus_ponens,[status(thm)],[17168, 17167])).
% 292.51/185.01 tff(17170,plain,
% 292.51/185.01 ($false),
% 292.51/185.01 inference(unit_resolution,[status(thm)],[17169, 108, 10007, 17166, 17165])).
% 292.51/185.01 tff(17171,plain,((~node22(c_e_h_3, c_d, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s7))), inference(lemma,lemma(discharge,[]))).
% 292.51/185.01 tff(17172,plain,
% 292.51/185.01 (~node22(c_e_h_3, c_d, s6, s7)),
% 292.51/185.01 inference(unit_resolution,[status(thm)],[17171, 17165])).
% 292.51/185.01 tff(17173,plain,
% 292.51/185.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_3, c_d, s6, s7) | node22(c_e_h_3, c_d, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_3, c_d, s6, s7) | node22(c_e_h_3, c_d, s6, s7))),
% 292.51/185.01 inference(rewrite,[status(thm)],[])).
% 292.51/185.01 tff(17174,plain,
% 292.51/185.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_3, c_d, s6, s7) | node22(c_e_h_3, c_d, s6, s7))),
% 292.51/185.01 inference(quant_inst,[status(thm)],[])).
% 292.51/185.01 tff(17175,plain,
% 292.51/185.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_3, c_d, s6, s7) | node22(c_e_h_3, c_d, s6, s7)),
% 292.51/185.01 inference(modus_ponens,[status(thm)],[17174, 17173])).
% 292.51/185.01 tff(17176,plain,
% 292.51/185.01 (node21(c_e_h_3, c_d, s6, s7) | node22(c_e_h_3, c_d, s6, s7)),
% 292.51/185.01 inference(unit_resolution,[status(thm)],[17175, 82, 1844])).
% 292.51/185.01 tff(17177,plain,
% 292.51/185.01 (node21(c_e_h_3, c_d, s6, s7)),
% 292.51/185.01 inference(unit_resolution,[status(thm)],[17176, 17172])).
% 292.51/185.01 tff(17178,plain,
% 292.51/185.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_d, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s7)) | (~node21(c_e_h_3, c_d, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_d, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s7)) | (~node21(c_e_h_3, c_d, s6, s7)))),
% 292.51/185.01 inference(rewrite,[status(thm)],[])).
% 292.51/185.01 tff(17179,plain,
% 292.51/185.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_d, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s7)) | (~node21(c_e_h_3, c_d, s6, s7)))),
% 292.51/185.01 inference(quant_inst,[status(thm)],[])).
% 292.51/185.01 tff(17180,plain,
% 292.51/185.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_d, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s7)) | (~node21(c_e_h_3, c_d, s6, s7))),
% 292.51/185.01 inference(modus_ponens,[status(thm)],[17179, 17178])).
% 292.51/185.01 tff(17181,plain,
% 292.51/185.01 ($false),
% 292.51/185.01 inference(unit_resolution,[status(thm)],[17180, 52, 17177, 17165, 17164])).
% 292.51/185.01 tff(17182,plain,(~m_and_h_gate_v_out(c_e_h_3, c_d, s7)), inference(lemma,lemma(discharge,[]))).
% 292.51/185.01 tff(17183,assumption,(m_and_h_gate_v_out(c_e_h_3, c_d, s8)), introduced(assumption)).
% 292.51/185.01 tff(17184,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_d, s7)), introduced(assumption)).
% 292.51/185.01 tff(17185,assumption,(node22(c_e_h_3, c_d, s7, s8)), introduced(assumption)).
% 292.51/185.01 tff(17186,plain,
% 292.51/185.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_d, s8)) | (~node22(c_e_h_3, c_d, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_d, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s8)) | (~node22(c_e_h_3, c_d, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_d, s7))),
% 292.51/185.01 inference(rewrite,[status(thm)],[])).
% 292.51/185.01 tff(17187,plain,
% 292.51/185.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_d, s8)) | (~node22(c_e_h_3, c_d, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_d, s7))),
% 292.51/185.01 inference(quant_inst,[status(thm)],[])).
% 292.51/185.01 tff(17188,plain,
% 292.51/185.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s8)) | (~node22(c_e_h_3, c_d, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_d, s7)),
% 292.51/185.01 inference(modus_ponens,[status(thm)],[17187, 17186])).
% 292.51/185.01 tff(17189,plain,
% 292.51/185.01 ($false),
% 292.51/185.01 inference(unit_resolution,[status(thm)],[17188, 108, 17183, 17185, 17184])).
% 292.51/185.01 tff(17190,plain,((~node22(c_e_h_3, c_d, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s8)) | m_and_h_gate_v_out(c_e_h_3, c_d, s7)), inference(lemma,lemma(discharge,[]))).
% 292.51/185.01 tff(17191,plain,
% 292.51/185.01 (~node22(c_e_h_3, c_d, s7, s8)),
% 292.51/185.01 inference(unit_resolution,[status(thm)],[17190, 17183, 17182])).
% 292.51/185.01 tff(17192,assumption,(~node20(c_e_h_3, c_d, s7)), introduced(assumption)).
% 292.51/185.01 tff(17193,assumption,(node21(c_e_h_3, c_d, s7, s8)), introduced(assumption)).
% 292.51/185.01 tff(17194,plain,
% 292.51/185.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_d, s8)) | node20(c_e_h_3, c_d, s7) | (~node21(c_e_h_3, c_d, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s8)) | node20(c_e_h_3, c_d, s7) | (~node21(c_e_h_3, c_d, s7, s8)))),
% 292.51/185.01 inference(rewrite,[status(thm)],[])).
% 292.51/185.01 tff(17195,plain,
% 292.51/185.01 ((node20(c_e_h_3, c_d, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s8)) | (~node21(c_e_h_3, c_d, s7, s8))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_d, s8)) | node20(c_e_h_3, c_d, s7) | (~node21(c_e_h_3, c_d, s7, s8)))),
% 292.51/185.01 inference(rewrite,[status(thm)],[])).
% 292.51/185.01 tff(17196,plain,
% 292.51/185.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_d, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s8)) | (~node21(c_e_h_3, c_d, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_d, s8)) | node20(c_e_h_3, c_d, s7) | (~node21(c_e_h_3, c_d, s7, s8))))),
% 292.51/185.01 inference(monotonicity,[status(thm)],[17195])).
% 292.51/185.01 tff(17197,plain,
% 292.51/185.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_d, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s8)) | (~node21(c_e_h_3, c_d, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s8)) | node20(c_e_h_3, c_d, s7) | (~node21(c_e_h_3, c_d, s7, s8)))),
% 292.51/185.01 inference(transitivity,[status(thm)],[17196, 17194])).
% 292.51/185.01 tff(17198,plain,
% 292.51/185.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_d, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s8)) | (~node21(c_e_h_3, c_d, s7, s8)))),
% 292.51/185.01 inference(quant_inst,[status(thm)],[])).
% 292.51/185.01 tff(17199,plain,
% 292.51/185.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s8)) | node20(c_e_h_3, c_d, s7) | (~node21(c_e_h_3, c_d, s7, s8))),
% 292.51/185.01 inference(modus_ponens,[status(thm)],[17198, 17197])).
% 292.51/185.01 tff(17200,plain,
% 292.51/185.01 ($false),
% 292.51/185.01 inference(unit_resolution,[status(thm)],[17199, 52, 17183, 17193, 17192])).
% 292.51/185.01 tff(17201,plain,((~node21(c_e_h_3, c_d, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s8)) | node20(c_e_h_3, c_d, s7)), inference(lemma,lemma(discharge,[]))).
% 292.51/185.01 tff(17202,plain,
% 292.51/185.01 (~node21(c_e_h_3, c_d, s7, s8)),
% 292.51/185.01 inference(unit_resolution,[status(thm)],[17201, 17183, 17192])).
% 292.51/185.01 tff(17203,plain,
% 292.51/185.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_3, c_d, s7, s8) | node22(c_e_h_3, c_d, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_3, c_d, s7, s8) | node22(c_e_h_3, c_d, s7, s8))),
% 292.51/185.01 inference(rewrite,[status(thm)],[])).
% 292.51/185.01 tff(17204,plain,
% 292.51/185.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_3, c_d, s7, s8) | node22(c_e_h_3, c_d, s7, s8))),
% 292.51/185.01 inference(quant_inst,[status(thm)],[])).
% 292.51/185.01 tff(17205,plain,
% 292.51/185.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_3, c_d, s7, s8) | node22(c_e_h_3, c_d, s7, s8)),
% 292.51/185.01 inference(modus_ponens,[status(thm)],[17204, 17203])).
% 292.51/185.01 tff(17206,plain,
% 292.51/185.01 (node21(c_e_h_3, c_d, s7, s8) | node22(c_e_h_3, c_d, s7, s8)),
% 292.51/185.01 inference(unit_resolution,[status(thm)],[17205, 82, 1938])).
% 292.51/185.01 tff(17207,plain,
% 292.51/185.01 ($false),
% 292.51/185.01 inference(unit_resolution,[status(thm)],[17206, 17202, 17191])).
% 292.51/185.01 tff(17208,plain,((~m_and_h_gate_v_out(c_e_h_3, c_d, s8)) | node20(c_e_h_3, c_d, s7)), inference(lemma,lemma(discharge,[]))).
% 292.51/185.01 tff(17209,plain,
% 292.51/185.01 (~m_and_h_gate_v_out(c_e_h_3, c_d, s8)),
% 292.51/185.01 inference(unit_resolution,[status(thm)],[17208, 17111])).
% 292.51/185.01 tff(17210,assumption,(~node20(c_e_h_3, c_d, s8)), introduced(assumption)).
% 292.51/185.01 tff(17211,assumption,(node21(c_e_h_3, c_d, s8, s9)), introduced(assumption)).
% 292.51/185.01 tff(17212,plain,
% 292.51/185.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_d, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s9)) | (~node21(c_e_h_3, c_d, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_d, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s9)) | (~node21(c_e_h_3, c_d, s8, s9)))),
% 292.51/185.01 inference(rewrite,[status(thm)],[])).
% 292.51/185.01 tff(17213,plain,
% 292.51/185.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_d, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s9)) | (~node21(c_e_h_3, c_d, s8, s9)))),
% 292.51/185.01 inference(quant_inst,[status(thm)],[])).
% 292.51/185.01 tff(17214,plain,
% 292.51/185.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_d, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s9)) | (~node21(c_e_h_3, c_d, s8, s9))),
% 292.51/185.01 inference(modus_ponens,[status(thm)],[17213, 17212])).
% 292.51/185.01 tff(17215,plain,
% 292.51/185.01 ($false),
% 292.51/185.01 inference(unit_resolution,[status(thm)],[17214, 52, 17094, 17211, 17210])).
% 292.51/185.01 tff(17216,plain,((~node21(c_e_h_3, c_d, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s9)) | node20(c_e_h_3, c_d, s8)), inference(lemma,lemma(discharge,[]))).
% 292.51/185.01 tff(17217,plain,
% 292.51/185.01 (~node21(c_e_h_3, c_d, s8, s9)),
% 292.51/185.01 inference(unit_resolution,[status(thm)],[17216, 17094, 17210])).
% 292.51/185.01 tff(17218,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_d, s8)), introduced(assumption)).
% 292.51/185.01 tff(17219,assumption,(node22(c_e_h_3, c_d, s8, s9)), introduced(assumption)).
% 292.51/185.01 tff(17220,plain,
% 292.51/185.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_d, s9)) | (~node22(c_e_h_3, c_d, s8, s9)) | m_and_h_gate_v_out(c_e_h_3, c_d, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s9)) | (~node22(c_e_h_3, c_d, s8, s9)) | m_and_h_gate_v_out(c_e_h_3, c_d, s8))),
% 292.51/185.01 inference(rewrite,[status(thm)],[])).
% 292.51/185.01 tff(17221,plain,
% 292.51/185.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_d, s9)) | (~node22(c_e_h_3, c_d, s8, s9)) | m_and_h_gate_v_out(c_e_h_3, c_d, s8))),
% 292.51/185.01 inference(quant_inst,[status(thm)],[])).
% 292.51/185.01 tff(17222,plain,
% 292.51/185.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s9)) | (~node22(c_e_h_3, c_d, s8, s9)) | m_and_h_gate_v_out(c_e_h_3, c_d, s8)),
% 292.51/185.01 inference(modus_ponens,[status(thm)],[17221, 17220])).
% 292.51/185.01 tff(17223,plain,
% 292.51/185.01 ($false),
% 292.51/185.02 inference(unit_resolution,[status(thm)],[17222, 108, 17094, 17219, 17218])).
% 292.51/185.02 tff(17224,plain,((~node22(c_e_h_3, c_d, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s9)) | m_and_h_gate_v_out(c_e_h_3, c_d, s8)), inference(lemma,lemma(discharge,[]))).
% 292.51/185.02 tff(17225,plain,
% 292.51/185.02 (~node22(c_e_h_3, c_d, s8, s9)),
% 292.51/185.02 inference(unit_resolution,[status(thm)],[17224, 17094, 17218])).
% 292.51/185.02 tff(17226,plain,
% 292.51/185.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s8, s9)) | node21(c_e_h_3, c_d, s8, s9) | node22(c_e_h_3, c_d, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_3, c_d, s8, s9) | node22(c_e_h_3, c_d, s8, s9))),
% 292.51/185.02 inference(rewrite,[status(thm)],[])).
% 292.51/185.02 tff(17227,plain,
% 292.51/185.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s8, s9)) | node21(c_e_h_3, c_d, s8, s9) | node22(c_e_h_3, c_d, s8, s9))),
% 292.51/185.02 inference(quant_inst,[status(thm)],[])).
% 292.51/185.02 tff(17228,plain,
% 292.51/185.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_3, c_d, s8, s9) | node22(c_e_h_3, c_d, s8, s9)),
% 292.51/185.02 inference(modus_ponens,[status(thm)],[17227, 17226])).
% 292.51/185.02 tff(17229,plain,
% 292.51/185.02 (node21(c_e_h_3, c_d, s8, s9) | node22(c_e_h_3, c_d, s8, s9)),
% 292.51/185.02 inference(unit_resolution,[status(thm)],[17228, 82, 1993])).
% 292.51/185.02 tff(17230,plain,
% 292.51/185.02 ($false),
% 292.51/185.02 inference(unit_resolution,[status(thm)],[17229, 17225, 17217])).
% 292.51/185.02 tff(17231,plain,((~m_and_h_gate_v_out(c_e_h_3, c_d, s9)) | m_and_h_gate_v_out(c_e_h_3, c_d, s8) | node20(c_e_h_3, c_d, s8)), inference(lemma,lemma(discharge,[]))).
% 292.51/185.02 tff(17232,plain,
% 292.51/185.02 (node20(c_e_h_3, c_d, s8)),
% 292.51/185.02 inference(unit_resolution,[status(thm)],[17231, 17209, 17094])).
% 292.51/185.02 tff(17233,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_d, s8)), introduced(assumption)).
% 292.51/185.02 tff(17234,assumption,(node20(c_e_h_3, c_d, s8)), introduced(assumption)).
% 292.51/185.02 tff(17235,plain,
% 292.51/185.02 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_d, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_d, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s8))),
% 292.51/185.02 inference(rewrite,[status(thm)],[])).
% 292.51/185.02 tff(17236,plain,
% 292.51/185.02 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_d, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s8))),
% 292.51/185.02 inference(quant_inst,[status(thm)],[])).
% 292.51/185.02 tff(17237,plain,
% 292.51/185.02 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_d, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s8)),
% 292.51/185.02 inference(modus_ponens,[status(thm)],[17236, 17235])).
% 292.51/185.02 tff(17238,plain,
% 292.51/185.02 ($false),
% 292.51/185.02 inference(unit_resolution,[status(thm)],[17237, 38, 17234, 17233])).
% 292.51/185.02 tff(17239,plain,((~node20(c_e_h_3, c_d, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s8)), inference(lemma,lemma(discharge,[]))).
% 292.51/185.02 tff(17240,plain,
% 292.51/185.02 (m_and_h_gate_v_in1(c_e_h_3, c_d, s8)),
% 292.51/185.02 inference(unit_resolution,[status(thm)],[17239, 17232])).
% 292.51/185.02 tff(17241,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_d, s8)), introduced(assumption)).
% 292.51/185.02 tff(17242,assumption,(~m_mutex_h_half_v_out(c_e_h_3, c_b, s8)), introduced(assumption)).
% 292.51/185.02 tff(17243,plain,
% 292.51/185.02 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_d, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s8))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_d, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s8))),
% 292.51/185.02 inference(rewrite,[status(thm)],[])).
% 292.51/185.02 tff(17244,plain,
% 292.51/185.02 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_d, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s8))),
% 292.51/185.02 inference(quant_inst,[status(thm)],[])).
% 292.51/185.02 tff(17245,plain,
% 292.51/185.02 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_d, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s8)),
% 292.51/185.02 inference(modus_ponens,[status(thm)],[17244, 17243])).
% 292.51/185.02 tff(17246,plain,
% 292.51/185.02 ($false),
% 292.51/185.02 inference(unit_resolution,[status(thm)],[17245, 2808, 17242, 17241])).
% 292.51/185.02 tff(17247,plain,((~m_and_h_gate_v_in1(c_e_h_3, c_d, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s8)), inference(lemma,lemma(discharge,[]))).
% 292.51/185.02 tff(17248,plain,
% 292.51/185.02 (m_mutex_h_half_v_out(c_e_h_3, c_b, s8)),
% 292.51/185.02 inference(unit_resolution,[status(thm)],[17247, 17240])).
% 292.51/185.02 tff(17249,assumption,(m_mutex_h_half_v_out(c_e_h_3, c_b, s8)), introduced(assumption)).
% 292.51/185.02 tff(17250,assumption,(node13(c_e_h_3, c_b, s8, s9)), introduced(assumption)).
% 292.51/185.02 tff(17251,plain,
% 292.51/185.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_b, s8)) | (~node13(c_e_h_3, c_b, s8, s9)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s8)) | (~node13(c_e_h_3, c_b, s8, s9)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s9))),
% 292.51/185.02 inference(rewrite,[status(thm)],[])).
% 292.51/185.02 tff(17252,plain,
% 292.51/185.02 ((m_mutex_h_half_v_out(c_e_h_3, c_b, s9) | (~node13(c_e_h_3, c_b, s8, s9)) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s8))) <=> ((~m_mutex_h_half_v_out(c_e_h_3, c_b, s8)) | (~node13(c_e_h_3, c_b, s8, s9)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s9))),
% 292.51/185.02 inference(rewrite,[status(thm)],[])).
% 292.51/185.02 tff(17253,plain,
% 292.51/185.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_b, s9) | (~node13(c_e_h_3, c_b, s8, s9)) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_b, s8)) | (~node13(c_e_h_3, c_b, s8, s9)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s9)))),
% 292.51/185.02 inference(monotonicity,[status(thm)],[17252])).
% 292.51/185.02 tff(17254,plain,
% 292.51/185.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_b, s9) | (~node13(c_e_h_3, c_b, s8, s9)) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s8)) | (~node13(c_e_h_3, c_b, s8, s9)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s9))),
% 292.51/185.02 inference(transitivity,[status(thm)],[17253, 17251])).
% 292.51/185.02 tff(17255,plain,
% 292.51/185.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_b, s9) | (~node13(c_e_h_3, c_b, s8, s9)) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s8)))),
% 292.51/185.02 inference(quant_inst,[status(thm)],[])).
% 292.51/185.02 tff(17256,plain,
% 292.51/185.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s8)) | (~node13(c_e_h_3, c_b, s8, s9)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s9)),
% 292.51/185.02 inference(modus_ponens,[status(thm)],[17255, 17254])).
% 292.51/185.02 tff(17257,plain,
% 292.51/185.02 ($false),
% 292.51/185.02 inference(unit_resolution,[status(thm)],[17256, 1459, 17250, 17249, 17095])).
% 292.51/185.02 tff(17258,plain,((~node13(c_e_h_3, c_b, s8, s9)) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s9)), inference(lemma,lemma(discharge,[]))).
% 292.51/185.02 tff(17259,plain,
% 292.51/185.02 (~node13(c_e_h_3, c_b, s8, s9)),
% 292.51/185.02 inference(unit_resolution,[status(thm)],[17258, 17248, 17095])).
% 292.51/185.02 tff(17260,plain,
% 292.51/185.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s8, s9)) | node12(c_e_h_3, c_b, s8, s9) | node13(c_e_h_3, c_b, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s8, s9)) | node12(c_e_h_3, c_b, s8, s9) | node13(c_e_h_3, c_b, s8, s9))),
% 292.51/185.03 inference(rewrite,[status(thm)],[])).
% 292.51/185.03 tff(17261,plain,
% 292.51/185.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s8, s9)) | node12(c_e_h_3, c_b, s8, s9) | node13(c_e_h_3, c_b, s8, s9))),
% 292.51/185.03 inference(quant_inst,[status(thm)],[])).
% 292.51/185.03 tff(17262,plain,
% 292.51/185.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s8, s9)) | node12(c_e_h_3, c_b, s8, s9) | node13(c_e_h_3, c_b, s8, s9)),
% 292.51/185.03 inference(modus_ponens,[status(thm)],[17261, 17260])).
% 292.51/185.03 tff(17263,plain,
% 292.51/185.03 (node12(c_e_h_3, c_b, s8, s9) | node13(c_e_h_3, c_b, s8, s9)),
% 292.51/185.03 inference(unit_resolution,[status(thm)],[17262, 439, 1993])).
% 292.51/185.03 tff(17264,plain,
% 292.51/185.03 (node12(c_e_h_3, c_b, s8, s9)),
% 292.51/185.03 inference(unit_resolution,[status(thm)],[17263, 17259])).
% 292.51/185.03 tff(17265,plain,
% 292.51/185.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_b, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s9) | (~node12(c_e_h_3, c_b, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s9) | (~node12(c_e_h_3, c_b, s8, s9)))),
% 292.51/185.03 inference(rewrite,[status(thm)],[])).
% 292.51/185.03 tff(17266,plain,
% 292.51/185.03 (((~node12(c_e_h_3, c_b, s8, s9)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s9)) <=> ((~m_mutex_h_half_v_inp(c_e_h_3, c_b, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s9) | (~node12(c_e_h_3, c_b, s8, s9)))),
% 292.51/185.03 inference(rewrite,[status(thm)],[])).
% 292.51/185.03 tff(17267,plain,
% 292.51/185.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_3, c_b, s8, s9)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_b, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s9) | (~node12(c_e_h_3, c_b, s8, s9))))),
% 292.51/185.03 inference(monotonicity,[status(thm)],[17266])).
% 292.51/185.03 tff(17268,plain,
% 292.51/185.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_3, c_b, s8, s9)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s9) | (~node12(c_e_h_3, c_b, s8, s9)))),
% 292.51/185.03 inference(transitivity,[status(thm)],[17267, 17265])).
% 292.51/185.03 tff(17269,plain,
% 292.51/185.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_3, c_b, s8, s9)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s9))),
% 292.51/185.03 inference(quant_inst,[status(thm)],[])).
% 292.51/185.03 tff(17270,plain,
% 292.51/185.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s9) | (~node12(c_e_h_3, c_b, s8, s9))),
% 292.51/185.03 inference(modus_ponens,[status(thm)],[17269, 17268])).
% 292.51/185.03 tff(17271,plain,
% 292.51/185.03 (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s8)),
% 292.51/185.03 inference(unit_resolution,[status(thm)],[17270, 1483, 17264, 17095])).
% 292.51/185.03 tff(17272,plain,
% 292.51/185.03 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node1(c_e_h_3, c_e_h_1, s8))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node1(c_e_h_3, c_e_h_1, s8))),
% 292.51/185.03 inference(rewrite,[status(thm)],[])).
% 292.51/185.03 tff(17273,plain,
% 292.51/185.03 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node1(c_e_h_3, c_e_h_1, s8))),
% 292.51/185.03 inference(quant_inst,[status(thm)],[])).
% 292.51/185.03 tff(17274,plain,
% 292.51/185.03 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node1(c_e_h_3, c_e_h_1, s8)),
% 292.51/185.03 inference(modus_ponens,[status(thm)],[17273, 17272])).
% 292.51/185.03 tff(17275,plain,
% 292.51/185.03 (node1(c_e_h_3, c_e_h_1, s8)),
% 292.51/185.03 inference(unit_resolution,[status(thm)],[17274, 2922, 2919])).
% 292.51/185.03 tff(17276,plain,
% 292.51/185.03 (^[I0: $i, X: $i, J0: $i] : refl(((~node1(I0, J0, X)) | (~m_cell_v_req(J0, X)) | m_mutex_h_half_v_inp(I0, c_b, X)) <=> ((~node1(I0, J0, X)) | (~m_cell_v_req(J0, X)) | m_mutex_h_half_v_inp(I0, c_b, X)))),
% 292.51/185.03 inference(bind,[status(th)],[])).
% 292.51/185.03 tff(17277,plain,
% 292.51/185.03 (![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | (~m_cell_v_req(J0, X)) | m_mutex_h_half_v_inp(I0, c_b, X)) <=> ![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | (~m_cell_v_req(J0, X)) | m_mutex_h_half_v_inp(I0, c_b, X))),
% 292.51/185.03 inference(quant_intro,[status(thm)],[17276])).
% 292.51/185.03 tff(17278,plain,
% 292.51/185.03 (![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | (~m_cell_v_req(J0, X)) | m_mutex_h_half_v_inp(I0, c_b, X)) <=> ![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | (~m_cell_v_req(J0, X)) | m_mutex_h_half_v_inp(I0, c_b, X))),
% 292.51/185.03 inference(rewrite,[status(thm)],[])).
% 292.51/185.03 tff(17279,plain,
% 292.51/185.03 (^[I0: $i, X: $i, J0: $i] : trans(monotonicity(rewrite((m_mutex_h_half_v_inp(I0, c_b, X) | (~m_cell_v_req(J0, X))) <=> ((~m_cell_v_req(J0, X)) | m_mutex_h_half_v_inp(I0, c_b, X))), (((m_mutex_h_half_v_inp(I0, c_b, X) | (~m_cell_v_req(J0, X))) | (~node1(I0, J0, X))) <=> (((~m_cell_v_req(J0, X)) | m_mutex_h_half_v_inp(I0, c_b, X)) | (~node1(I0, J0, X))))), rewrite((((~m_cell_v_req(J0, X)) | m_mutex_h_half_v_inp(I0, c_b, X)) | (~node1(I0, J0, X))) <=> ((~node1(I0, J0, X)) | (~m_cell_v_req(J0, X)) | m_mutex_h_half_v_inp(I0, c_b, X))), (((m_mutex_h_half_v_inp(I0, c_b, X) | (~m_cell_v_req(J0, X))) | (~node1(I0, J0, X))) <=> ((~node1(I0, J0, X)) | (~m_cell_v_req(J0, X)) | m_mutex_h_half_v_inp(I0, c_b, X))))),
% 292.51/185.03 inference(bind,[status(th)],[])).
% 292.51/185.03 tff(17280,plain,
% 292.51/185.03 (![I0: $i, X: $i, J0: $i] : ((m_mutex_h_half_v_inp(I0, c_b, X) | (~m_cell_v_req(J0, X))) | (~node1(I0, J0, X))) <=> ![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | (~m_cell_v_req(J0, X)) | m_mutex_h_half_v_inp(I0, c_b, X))),
% 292.51/185.03 inference(quant_intro,[status(thm)],[17279])).
% 292.51/185.03 tff(17281,axiom,(![I0: $i, X: $i, J0: $i] : ((m_mutex_h_half_v_inp(I0, c_b, X) | (~m_cell_v_req(J0, X))) | (~node1(I0, J0, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_5')).
% 292.51/185.03 tff(17282,plain,
% 292.51/185.03 (![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | (~m_cell_v_req(J0, X)) | m_mutex_h_half_v_inp(I0, c_b, X))),
% 292.51/185.03 inference(modus_ponens,[status(thm)],[17281, 17280])).
% 292.51/185.03 tff(17283,plain,
% 292.51/185.03 (![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | (~m_cell_v_req(J0, X)) | m_mutex_h_half_v_inp(I0, c_b, X))),
% 292.51/185.03 inference(modus_ponens,[status(thm)],[17282, 17278])).
% 292.51/185.03 tff(17284,plain,(
% 292.51/185.03 ![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | (~m_cell_v_req(J0, X)) | m_mutex_h_half_v_inp(I0, c_b, X))),
% 292.51/185.03 inference(skolemize,[status(sab)],[17283])).
% 292.51/185.03 tff(17285,plain,
% 292.51/185.03 (![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | (~m_cell_v_req(J0, X)) | m_mutex_h_half_v_inp(I0, c_b, X))),
% 292.51/185.03 inference(modus_ponens,[status(thm)],[17284, 17277])).
% 292.51/185.03 tff(17286,plain,
% 292.51/185.03 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | (~m_cell_v_req(J0, X)) | m_mutex_h_half_v_inp(I0, c_b, X))) | ((~node1(c_e_h_3, c_e_h_1, s8)) | (~m_cell_v_req(c_e_h_1, s8)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s8))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | (~m_cell_v_req(J0, X)) | m_mutex_h_half_v_inp(I0, c_b, X))) | (~node1(c_e_h_3, c_e_h_1, s8)) | (~m_cell_v_req(c_e_h_1, s8)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s8))),
% 292.51/185.03 inference(rewrite,[status(thm)],[])).
% 292.51/185.03 tff(17287,plain,
% 292.51/185.03 ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | (~m_cell_v_req(J0, X)) | m_mutex_h_half_v_inp(I0, c_b, X))) | ((~node1(c_e_h_3, c_e_h_1, s8)) | (~m_cell_v_req(c_e_h_1, s8)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s8))),
% 292.51/185.03 inference(quant_inst,[status(thm)],[])).
% 292.51/185.03 tff(17288,plain,
% 292.51/185.03 ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | (~m_cell_v_req(J0, X)) | m_mutex_h_half_v_inp(I0, c_b, X))) | (~node1(c_e_h_3, c_e_h_1, s8)) | (~m_cell_v_req(c_e_h_1, s8)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s8)),
% 292.51/185.03 inference(modus_ponens,[status(thm)],[17287, 17286])).
% 292.51/185.03 tff(17289,plain,
% 292.51/185.03 ((~m_cell_v_req(c_e_h_1, s8)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s8)),
% 292.51/185.03 inference(unit_resolution,[status(thm)],[17288, 17285, 17275])).
% 292.51/185.03 tff(17290,plain,
% 292.51/185.03 (~m_cell_v_req(c_e_h_1, s8)),
% 292.51/185.03 inference(unit_resolution,[status(thm)],[17289, 17271])).
% 292.51/185.03 tff(17291,plain,
% 292.51/185.03 (^[I0: $i, X: $i] : refl(((~m_and_h_gate_v_out(I0, c_p, X)) | m_cell_v_req(I0, X)) <=> ((~m_and_h_gate_v_out(I0, c_p, X)) | m_cell_v_req(I0, X)))),
% 292.51/185.03 inference(bind,[status(th)],[])).
% 292.51/185.03 tff(17292,plain,
% 292.51/185.03 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_p, X)) | m_cell_v_req(I0, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_p, X)) | m_cell_v_req(I0, X))),
% 292.51/185.03 inference(quant_intro,[status(thm)],[17291])).
% 292.51/185.03 tff(17293,plain,
% 292.51/185.03 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_p, X)) | m_cell_v_req(I0, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_p, X)) | m_cell_v_req(I0, X))),
% 292.51/185.03 inference(rewrite,[status(thm)],[])).
% 292.51/185.03 tff(17294,plain,
% 292.51/185.03 (^[I0: $i, X: $i] : rewrite((m_cell_v_req(I0, X) | (~m_and_h_gate_v_out(I0, c_p, X))) <=> ((~m_and_h_gate_v_out(I0, c_p, X)) | m_cell_v_req(I0, X)))),
% 292.51/185.03 inference(bind,[status(th)],[])).
% 292.51/185.03 tff(17295,plain,
% 292.51/185.03 (![I0: $i, X: $i] : (m_cell_v_req(I0, X) | (~m_and_h_gate_v_out(I0, c_p, X))) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_p, X)) | m_cell_v_req(I0, X))),
% 292.51/185.03 inference(quant_intro,[status(thm)],[17294])).
% 292.51/185.03 tff(17296,axiom,(![I0: $i, X: $i] : (m_cell_v_req(I0, X) | (~m_and_h_gate_v_out(I0, c_p, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_75')).
% 292.51/185.03 tff(17297,plain,
% 292.51/185.03 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_p, X)) | m_cell_v_req(I0, X))),
% 292.51/185.03 inference(modus_ponens,[status(thm)],[17296, 17295])).
% 292.51/185.03 tff(17298,plain,
% 292.51/185.03 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_p, X)) | m_cell_v_req(I0, X))),
% 292.51/185.03 inference(modus_ponens,[status(thm)],[17297, 17293])).
% 292.51/185.03 tff(17299,plain,(
% 292.51/185.03 ![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_p, X)) | m_cell_v_req(I0, X))),
% 292.51/185.03 inference(skolemize,[status(sab)],[17298])).
% 292.51/185.03 tff(17300,plain,
% 292.51/185.03 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_p, X)) | m_cell_v_req(I0, X))),
% 292.51/185.03 inference(modus_ponens,[status(thm)],[17299, 17292])).
% 292.51/185.03 tff(17301,plain,
% 292.51/185.03 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_p, X)) | m_cell_v_req(I0, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_p, s8)) | m_cell_v_req(c_e_h_1, s8))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_p, X)) | m_cell_v_req(I0, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s8)) | m_cell_v_req(c_e_h_1, s8))),
% 292.51/185.03 inference(rewrite,[status(thm)],[])).
% 292.51/185.03 tff(17302,plain,
% 292.51/185.03 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_p, X)) | m_cell_v_req(I0, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_p, s8)) | m_cell_v_req(c_e_h_1, s8))),
% 292.51/185.03 inference(quant_inst,[status(thm)],[])).
% 292.51/185.03 tff(17303,plain,
% 292.51/185.03 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_p, X)) | m_cell_v_req(I0, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s8)) | m_cell_v_req(c_e_h_1, s8)),
% 292.51/185.03 inference(modus_ponens,[status(thm)],[17302, 17301])).
% 292.51/185.03 tff(17304,plain,
% 292.51/185.03 (~m_and_h_gate_v_out(c_e_h_1, c_p, s8)),
% 292.51/185.03 inference(unit_resolution,[status(thm)],[17303, 17300, 17290])).
% 292.51/185.03 tff(17305,plain,
% 292.51/185.03 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s2))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s2))),
% 292.51/185.03 inference(rewrite,[status(thm)],[])).
% 292.51/185.03 tff(17306,plain,
% 292.51/185.03 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s2))),
% 292.51/185.03 inference(quant_inst,[status(thm)],[])).
% 292.51/185.03 tff(17307,plain,
% 292.51/185.03 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s2)),
% 292.51/185.03 inference(modus_ponens,[status(thm)],[17306, 17305])).
% 292.51/185.03 tff(17308,plain,
% 292.51/185.03 (node3(c_e_h_3, c_e_h_1, s2)),
% 292.51/185.03 inference(unit_resolution,[status(thm)],[17307, 2922, 1056])).
% 292.51/185.03 tff(17309,plain,
% 292.51/185.03 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s2)) | (~node3(c_e_h_3, c_e_h_1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_q, s2))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s2)) | (~node3(c_e_h_3, c_e_h_1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_q, s2))),
% 292.51/185.03 inference(rewrite,[status(thm)],[])).
% 292.51/185.03 tff(17310,plain,
% 292.51/185.03 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s2)) | (~node3(c_e_h_3, c_e_h_1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_q, s2))),
% 292.51/185.03 inference(quant_inst,[status(thm)],[])).
% 292.51/185.03 tff(17311,plain,
% 292.51/185.03 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s2)) | (~node3(c_e_h_3, c_e_h_1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_q, s2)),
% 292.51/185.03 inference(modus_ponens,[status(thm)],[17310, 17309])).
% 292.51/185.03 tff(17312,plain,
% 292.51/185.03 ((~m_cell_v_ack(c_e_h_1, s2)) | m_and_h_gate_v_out(c_e_h_3, c_q, s2)),
% 292.51/185.03 inference(unit_resolution,[status(thm)],[17311, 1073, 17308])).
% 292.51/185.03 tff(17313,plain,
% 292.51/185.03 (~m_cell_v_ack(c_e_h_1, s2)),
% 292.51/185.03 inference(unit_resolution,[status(thm)],[17312, 5675])).
% 292.51/185.03 tff(17314,plain,
% 292.51/185.03 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s2)) | m_cell_v_ack(c_e_h_1, s2))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s2)) | m_cell_v_ack(c_e_h_1, s2))),
% 292.51/185.03 inference(rewrite,[status(thm)],[])).
% 292.51/185.03 tff(17315,plain,
% 292.51/185.03 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s2)) | m_cell_v_ack(c_e_h_1, s2))),
% 292.51/185.03 inference(quant_inst,[status(thm)],[])).
% 292.51/185.03 tff(17316,plain,
% 292.51/185.03 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s2)) | m_cell_v_ack(c_e_h_1, s2)),
% 292.51/185.03 inference(modus_ponens,[status(thm)],[17315, 17314])).
% 292.51/185.03 tff(17317,plain,
% 292.51/185.03 (~m_or_h_gate_v_in2(c_e_h_1, c_j, s2)),
% 292.51/185.03 inference(unit_resolution,[status(thm)],[17316, 1085, 17313])).
% 292.51/185.03 tff(17318,assumption,(m_or_h_gate_v_out(c_e_h_1, c_j, s3)), introduced(assumption)).
% 292.51/185.03 tff(17319,assumption,(node6(c_e_h_1, c_j, s2, s3)), introduced(assumption)).
% 292.51/185.03 tff(17320,plain,
% 292.51/185.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s2) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s3)) | (~node6(c_e_h_1, c_j, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s2) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s3)) | (~node6(c_e_h_1, c_j, s2, s3)))),
% 292.51/185.03 inference(rewrite,[status(thm)],[])).
% 292.51/185.03 tff(17321,plain,
% 292.51/185.03 (((~node6(c_e_h_1, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s3)) | m_or_h_gate_v_out(c_e_h_1, c_j, s2)) <=> (m_or_h_gate_v_out(c_e_h_1, c_j, s2) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s3)) | (~node6(c_e_h_1, c_j, s2, s3)))),
% 292.51/185.03 inference(rewrite,[status(thm)],[])).
% 292.51/185.03 tff(17322,plain,
% 292.51/185.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s3)) | m_or_h_gate_v_out(c_e_h_1, c_j, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s2) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s3)) | (~node6(c_e_h_1, c_j, s2, s3))))),
% 292.51/185.04 inference(monotonicity,[status(thm)],[17321])).
% 292.51/185.04 tff(17323,plain,
% 292.51/185.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s3)) | m_or_h_gate_v_out(c_e_h_1, c_j, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s2) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s3)) | (~node6(c_e_h_1, c_j, s2, s3)))),
% 292.51/185.04 inference(transitivity,[status(thm)],[17322, 17320])).
% 292.51/185.04 tff(17324,plain,
% 292.51/185.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s3)) | m_or_h_gate_v_out(c_e_h_1, c_j, s2))),
% 292.51/185.04 inference(quant_inst,[status(thm)],[])).
% 292.51/185.04 tff(17325,plain,
% 292.51/185.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s2) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s3)) | (~node6(c_e_h_1, c_j, s2, s3))),
% 292.51/185.04 inference(modus_ponens,[status(thm)],[17324, 17323])).
% 292.51/185.04 tff(17326,plain,
% 292.51/185.04 ($false),
% 292.51/185.04 inference(unit_resolution,[status(thm)],[17325, 1121, 16761, 17319, 17318])).
% 292.51/185.04 tff(17327,plain,((~node6(c_e_h_1, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s3))), inference(lemma,lemma(discharge,[]))).
% 292.51/185.04 tff(17328,plain,
% 292.51/185.04 (~node6(c_e_h_1, c_j, s2, s3)),
% 292.51/185.04 inference(unit_resolution,[status(thm)],[17327, 17318])).
% 292.51/185.04 tff(17329,assumption,(~m_or_h_gate_v_in2(c_e_h_1, c_j, s2)), introduced(assumption)).
% 292.51/185.04 tff(17330,assumption,(m_and_h_gate_v_out(c_e_h_1, c_l, s2)), introduced(assumption)).
% 292.51/185.04 tff(17331,assumption,(node21(c_e_h_1, c_l, s1, s2)), introduced(assumption)).
% 292.51/185.04 tff(17332,plain,
% 292.51/185.04 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1))),
% 292.51/185.04 inference(rewrite,[status(thm)],[])).
% 292.51/185.04 tff(17333,plain,
% 292.51/185.04 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1))),
% 292.51/185.04 inference(quant_inst,[status(thm)],[])).
% 292.51/185.04 tff(17334,plain,
% 292.51/185.04 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s1)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s1)),
% 292.51/185.04 inference(modus_ponens,[status(thm)],[17333, 17332])).
% 292.51/185.04 tff(17335,plain,
% 292.51/185.04 (~m_and_h_gate_v_in2(c_e_h_1, c_l, s1)),
% 292.51/185.04 inference(unit_resolution,[status(thm)],[17334, 4549, 14710])).
% 292.51/185.04 tff(17336,plain,
% 292.51/185.04 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s1)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s1)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s1))),
% 292.51/185.04 inference(rewrite,[status(thm)],[])).
% 292.51/185.04 tff(17337,plain,
% 292.51/185.04 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s1)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s1))),
% 292.51/185.04 inference(quant_inst,[status(thm)],[])).
% 292.51/185.04 tff(17338,plain,
% 292.51/185.04 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s1)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s1)),
% 292.51/185.04 inference(modus_ponens,[status(thm)],[17337, 17336])).
% 292.51/185.04 tff(17339,plain,
% 292.51/185.04 (~node20(c_e_h_1, c_l, s1)),
% 292.51/185.04 inference(unit_resolution,[status(thm)],[17338, 4563, 17335])).
% 292.51/185.04 tff(17340,plain,
% 292.51/185.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s2)) | (~node21(c_e_h_1, c_l, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s2)) | (~node21(c_e_h_1, c_l, s1, s2)))),
% 292.51/185.04 inference(rewrite,[status(thm)],[])).
% 292.51/185.04 tff(17341,plain,
% 292.51/185.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s2)) | (~node21(c_e_h_1, c_l, s1, s2)))),
% 292.51/185.04 inference(quant_inst,[status(thm)],[])).
% 292.51/185.04 tff(17342,plain,
% 292.51/185.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s1) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s2)) | (~node21(c_e_h_1, c_l, s1, s2))),
% 292.51/185.04 inference(modus_ponens,[status(thm)],[17341, 17340])).
% 292.51/185.04 tff(17343,plain,
% 292.51/185.04 ($false),
% 292.51/185.04 inference(unit_resolution,[status(thm)],[17342, 52, 17339, 17331, 17330])).
% 292.51/185.04 tff(17344,plain,((~node21(c_e_h_1, c_l, s1, s2)) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s2))), inference(lemma,lemma(discharge,[]))).
% 292.51/185.04 tff(17345,plain,
% 292.51/185.04 (~node21(c_e_h_1, c_l, s1, s2)),
% 292.51/185.04 inference(unit_resolution,[status(thm)],[17344, 17330])).
% 292.51/185.04 tff(17346,plain,
% 292.51/185.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_1, c_l, s1, s2) | node22(c_e_h_1, c_l, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_1, c_l, s1, s2) | node22(c_e_h_1, c_l, s1, s2))),
% 292.51/185.04 inference(rewrite,[status(thm)],[])).
% 292.51/185.04 tff(17347,plain,
% 292.51/185.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s1, s2)) | node21(c_e_h_1, c_l, s1, s2) | node22(c_e_h_1, c_l, s1, s2))),
% 292.51/185.04 inference(quant_inst,[status(thm)],[])).
% 292.51/185.04 tff(17348,plain,
% 292.51/185.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s1, s2)) | node21(c_e_h_1, c_l, s1, s2) | node22(c_e_h_1, c_l, s1, s2)),
% 292.51/185.04 inference(modus_ponens,[status(thm)],[17347, 17346])).
% 292.51/185.04 tff(17349,plain,
% 292.51/185.04 (node21(c_e_h_1, c_l, s1, s2) | node22(c_e_h_1, c_l, s1, s2)),
% 292.51/185.04 inference(unit_resolution,[status(thm)],[17348, 82, 255])).
% 292.51/185.04 tff(17350,plain,
% 292.51/185.04 (node22(c_e_h_1, c_l, s1, s2)),
% 292.51/185.04 inference(unit_resolution,[status(thm)],[17349, 17345])).
% 292.51/185.04 tff(17351,plain,
% 292.51/185.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s2)) | (~node22(c_e_h_1, c_l, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_l, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s2)) | (~node22(c_e_h_1, c_l, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_l, s1))),
% 292.51/185.04 inference(rewrite,[status(thm)],[])).
% 292.51/185.04 tff(17352,plain,
% 292.51/185.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s2)) | (~node22(c_e_h_1, c_l, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_l, s1))),
% 292.51/185.04 inference(quant_inst,[status(thm)],[])).
% 292.51/185.04 tff(17353,plain,
% 292.51/185.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s2)) | (~node22(c_e_h_1, c_l, s1, s2)) | m_and_h_gate_v_out(c_e_h_1, c_l, s1)),
% 292.51/185.04 inference(modus_ponens,[status(thm)],[17352, 17351])).
% 292.51/185.04 tff(17354,plain,
% 292.51/185.04 ($false),
% 292.51/185.04 inference(unit_resolution,[status(thm)],[17353, 108, 16736, 17350, 17330])).
% 292.51/185.04 tff(17355,plain,(~m_and_h_gate_v_out(c_e_h_1, c_l, s2)), inference(lemma,lemma(discharge,[]))).
% 292.51/185.04 tff(17356,plain,
% 292.51/185.04 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s2)) | m_and_h_gate_v_out(c_e_h_1, c_l, s2))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s2)) | m_and_h_gate_v_out(c_e_h_1, c_l, s2))),
% 292.51/185.04 inference(rewrite,[status(thm)],[])).
% 292.51/185.04 tff(17357,plain,
% 292.51/185.04 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s2)) | m_and_h_gate_v_out(c_e_h_1, c_l, s2))),
% 292.51/185.04 inference(quant_inst,[status(thm)],[])).
% 292.51/185.04 tff(17358,plain,
% 292.51/185.04 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s2)) | m_and_h_gate_v_out(c_e_h_1, c_l, s2)),
% 292.51/185.04 inference(modus_ponens,[status(thm)],[17357, 17356])).
% 292.51/185.04 tff(17359,plain,
% 292.51/185.04 (~m_or_h_gate_v_in1(c_e_h_1, c_j, s2)),
% 292.51/185.04 inference(unit_resolution,[status(thm)],[17358, 1100, 17355])).
% 292.51/185.04 tff(17360,assumption,(~m_or_h_gate_v_in1(c_e_h_1, c_j, s2)), introduced(assumption)).
% 292.51/185.04 tff(17361,assumption,(node5(c_e_h_1, c_j, s2, s3)), introduced(assumption)).
% 292.51/185.04 tff(17362,plain,
% 292.51/185.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_1, c_j, s3)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s2) | m_or_h_gate_v_in1(c_e_h_1, c_j, s2) | (~node5(c_e_h_1, c_j, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s3)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s2) | m_or_h_gate_v_in1(c_e_h_1, c_j, s2) | (~node5(c_e_h_1, c_j, s2, s3)))),
% 292.51/185.04 inference(rewrite,[status(thm)],[])).
% 292.51/185.04 tff(17363,plain,
% 292.51/185.04 ((m_or_h_gate_v_in1(c_e_h_1, c_j, s2) | m_or_h_gate_v_in2(c_e_h_1, c_j, s2) | (~node5(c_e_h_1, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s3))) <=> ((~m_or_h_gate_v_out(c_e_h_1, c_j, s3)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s2) | m_or_h_gate_v_in1(c_e_h_1, c_j, s2) | (~node5(c_e_h_1, c_j, s2, s3)))),
% 292.51/185.04 inference(rewrite,[status(thm)],[])).
% 292.51/185.04 tff(17364,plain,
% 292.51/185.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s2) | m_or_h_gate_v_in2(c_e_h_1, c_j, s2) | (~node5(c_e_h_1, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_1, c_j, s3)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s2) | m_or_h_gate_v_in1(c_e_h_1, c_j, s2) | (~node5(c_e_h_1, c_j, s2, s3))))),
% 292.51/185.05 inference(monotonicity,[status(thm)],[17363])).
% 292.51/185.05 tff(17365,plain,
% 292.51/185.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s2) | m_or_h_gate_v_in2(c_e_h_1, c_j, s2) | (~node5(c_e_h_1, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s3)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s2) | m_or_h_gate_v_in1(c_e_h_1, c_j, s2) | (~node5(c_e_h_1, c_j, s2, s3)))),
% 292.51/185.05 inference(transitivity,[status(thm)],[17364, 17362])).
% 292.51/185.05 tff(17366,plain,
% 292.51/185.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s2) | m_or_h_gate_v_in2(c_e_h_1, c_j, s2) | (~node5(c_e_h_1, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s3)))),
% 292.51/185.05 inference(quant_inst,[status(thm)],[])).
% 292.51/185.05 tff(17367,plain,
% 292.51/185.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s3)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s2) | m_or_h_gate_v_in1(c_e_h_1, c_j, s2) | (~node5(c_e_h_1, c_j, s2, s3))),
% 292.51/185.05 inference(modus_ponens,[status(thm)],[17366, 17365])).
% 292.51/185.05 tff(17368,plain,
% 292.51/185.05 ($false),
% 292.51/185.05 inference(unit_resolution,[status(thm)],[17367, 1159, 17361, 17318, 17329, 17360])).
% 292.51/185.05 tff(17369,plain,((~node5(c_e_h_1, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s3)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s2) | m_or_h_gate_v_in1(c_e_h_1, c_j, s2)), inference(lemma,lemma(discharge,[]))).
% 292.51/185.05 tff(17370,plain,
% 292.51/185.05 ((~node5(c_e_h_1, c_j, s2, s3)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s3)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s2)),
% 292.51/185.05 inference(unit_resolution,[status(thm)],[17369, 17359])).
% 292.51/185.05 tff(17371,plain,
% 292.51/185.05 (~node5(c_e_h_1, c_j, s2, s3)),
% 292.51/185.05 inference(unit_resolution,[status(thm)],[17370, 17318, 17329])).
% 292.51/185.05 tff(17372,plain,
% 292.51/185.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s2, s3)) | node6(c_e_h_1, c_j, s2, s3) | node5(c_e_h_1, c_j, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s2, s3)) | node6(c_e_h_1, c_j, s2, s3) | node5(c_e_h_1, c_j, s2, s3))),
% 292.51/185.05 inference(rewrite,[status(thm)],[])).
% 292.51/185.05 tff(17373,plain,
% 292.51/185.05 ((node6(c_e_h_1, c_j, s2, s3) | node5(c_e_h_1, c_j, s2, s3) | (~trans(s2, s3))) <=> ((~trans(s2, s3)) | node6(c_e_h_1, c_j, s2, s3) | node5(c_e_h_1, c_j, s2, s3))),
% 292.51/185.05 inference(rewrite,[status(thm)],[])).
% 292.51/185.05 tff(17374,plain,
% 292.51/185.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s2, s3) | node5(c_e_h_1, c_j, s2, s3) | (~trans(s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s2, s3)) | node6(c_e_h_1, c_j, s2, s3) | node5(c_e_h_1, c_j, s2, s3)))),
% 292.51/185.05 inference(monotonicity,[status(thm)],[17373])).
% 292.51/185.05 tff(17375,plain,
% 292.51/185.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s2, s3) | node5(c_e_h_1, c_j, s2, s3) | (~trans(s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s2, s3)) | node6(c_e_h_1, c_j, s2, s3) | node5(c_e_h_1, c_j, s2, s3))),
% 292.51/185.05 inference(transitivity,[status(thm)],[17374, 17372])).
% 292.51/185.05 tff(17376,plain,
% 292.51/185.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s2, s3) | node5(c_e_h_1, c_j, s2, s3) | (~trans(s2, s3)))),
% 292.51/185.05 inference(quant_inst,[status(thm)],[])).
% 292.51/185.05 tff(17377,plain,
% 292.51/185.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s2, s3)) | node6(c_e_h_1, c_j, s2, s3) | node5(c_e_h_1, c_j, s2, s3)),
% 292.51/185.05 inference(modus_ponens,[status(thm)],[17376, 17375])).
% 292.51/185.05 tff(17378,plain,
% 292.51/185.05 (node6(c_e_h_1, c_j, s2, s3) | node5(c_e_h_1, c_j, s2, s3)),
% 292.51/185.05 inference(unit_resolution,[status(thm)],[17377, 1141, 318])).
% 292.51/185.05 tff(17379,plain,
% 292.51/185.05 ($false),
% 292.51/185.05 inference(unit_resolution,[status(thm)],[17378, 17371, 17328])).
% 292.51/185.05 tff(17380,plain,((~m_or_h_gate_v_out(c_e_h_1, c_j, s3)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s2)), inference(lemma,lemma(discharge,[]))).
% 292.51/185.05 tff(17381,plain,
% 292.51/185.05 (~m_or_h_gate_v_out(c_e_h_1, c_j, s3)),
% 292.51/185.05 inference(unit_resolution,[status(thm)],[17380, 17317])).
% 292.51/185.05 tff(17382,assumption,(m_c_h_element_v_in2(c_e_h_1, c_h, s3)), introduced(assumption)).
% 292.51/185.05 tff(17383,plain,
% 292.51/185.05 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s3)) | m_or_h_gate_v_out(c_e_h_1, c_j, s3))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s3)) | m_or_h_gate_v_out(c_e_h_1, c_j, s3))),
% 292.51/185.05 inference(rewrite,[status(thm)],[])).
% 292.51/185.05 tff(17384,plain,
% 292.51/185.05 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s3)) | m_or_h_gate_v_out(c_e_h_1, c_j, s3))),
% 292.51/185.05 inference(quant_inst,[status(thm)],[])).
% 292.51/185.05 tff(17385,plain,
% 292.51/185.05 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s3)) | m_or_h_gate_v_out(c_e_h_1, c_j, s3)),
% 292.51/185.05 inference(modus_ponens,[status(thm)],[17384, 17383])).
% 292.51/185.05 tff(17386,plain,
% 292.51/185.05 ($false),
% 292.51/185.05 inference(unit_resolution,[status(thm)],[17385, 1174, 17382, 17381])).
% 292.51/185.05 tff(17387,plain,(~m_c_h_element_v_in2(c_e_h_1, c_h, s3)), inference(lemma,lemma(discharge,[]))).
% 292.51/185.05 tff(17388,assumption,(m_c_h_element_v_out(c_e_h_1, c_h, s4)), introduced(assumption)).
% 292.51/185.05 tff(17389,assumption,(~m_c_h_element_v_out(c_e_h_1, c_h, s3)), introduced(assumption)).
% 292.51/185.05 tff(17390,assumption,(node15(c_e_h_1, c_h, s3, s4)), introduced(assumption)).
% 292.51/185.05 tff(17391,plain,
% 292.51/185.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s4)) | (~node15(c_e_h_1, c_h, s3, s4)) | m_c_h_element_v_out(c_e_h_1, c_h, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4)) | (~node15(c_e_h_1, c_h, s3, s4)) | m_c_h_element_v_out(c_e_h_1, c_h, s3))),
% 292.51/185.05 inference(rewrite,[status(thm)],[])).
% 292.51/185.05 tff(17392,plain,
% 292.51/185.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s4)) | (~node15(c_e_h_1, c_h, s3, s4)) | m_c_h_element_v_out(c_e_h_1, c_h, s3))),
% 292.51/185.05 inference(quant_inst,[status(thm)],[])).
% 292.51/185.05 tff(17393,plain,
% 292.51/185.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4)) | (~node15(c_e_h_1, c_h, s3, s4)) | m_c_h_element_v_out(c_e_h_1, c_h, s3)),
% 292.51/185.05 inference(modus_ponens,[status(thm)],[17392, 17391])).
% 292.51/185.05 tff(17394,plain,
% 292.51/185.05 ($false),
% 292.51/185.05 inference(unit_resolution,[status(thm)],[17393, 147, 17389, 17390, 17388])).
% 292.51/185.05 tff(17395,plain,((~node15(c_e_h_1, c_h, s3, s4)) | m_c_h_element_v_out(c_e_h_1, c_h, s3) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4))), inference(lemma,lemma(discharge,[]))).
% 292.51/185.05 tff(17396,plain,
% 292.51/185.05 (~node15(c_e_h_1, c_h, s3, s4)),
% 292.51/185.05 inference(unit_resolution,[status(thm)],[17395, 17389, 17388])).
% 292.51/185.05 tff(17397,assumption,(node18(c_e_h_1, c_h, s3, s4)), introduced(assumption)).
% 292.51/185.05 tff(17398,plain,
% 292.51/185.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_h, s3) | (~node18(c_e_h_1, c_h, s3, s4)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s3) | (~node18(c_e_h_1, c_h, s3, s4)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4)))),
% 292.51/185.05 inference(rewrite,[status(thm)],[])).
% 292.51/185.05 tff(17399,plain,
% 292.51/185.05 (((~m_c_h_element_v_out(c_e_h_1, c_h, s4)) | m_c_h_element_v_out(c_e_h_1, c_h, s3) | (~node18(c_e_h_1, c_h, s3, s4))) <=> (m_c_h_element_v_out(c_e_h_1, c_h, s3) | (~node18(c_e_h_1, c_h, s3, s4)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4)))),
% 292.51/185.05 inference(rewrite,[status(thm)],[])).
% 292.51/185.05 tff(17400,plain,
% 292.51/185.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s4)) | m_c_h_element_v_out(c_e_h_1, c_h, s3) | (~node18(c_e_h_1, c_h, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_h, s3) | (~node18(c_e_h_1, c_h, s3, s4)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4))))),
% 292.51/185.06 inference(monotonicity,[status(thm)],[17399])).
% 292.51/185.06 tff(17401,plain,
% 292.51/185.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s4)) | m_c_h_element_v_out(c_e_h_1, c_h, s3) | (~node18(c_e_h_1, c_h, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s3) | (~node18(c_e_h_1, c_h, s3, s4)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4)))),
% 292.51/185.06 inference(transitivity,[status(thm)],[17400, 17398])).
% 292.51/185.06 tff(17402,plain,
% 292.51/185.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s4)) | m_c_h_element_v_out(c_e_h_1, c_h, s3) | (~node18(c_e_h_1, c_h, s3, s4)))),
% 292.51/185.06 inference(quant_inst,[status(thm)],[])).
% 292.51/185.06 tff(17403,plain,
% 292.51/185.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s3) | (~node18(c_e_h_1, c_h, s3, s4)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4))),
% 292.51/185.06 inference(modus_ponens,[status(thm)],[17402, 17401])).
% 292.51/185.06 tff(17404,plain,
% 292.51/185.06 ($false),
% 292.51/185.06 inference(unit_resolution,[status(thm)],[17403, 753, 17389, 17397, 17388])).
% 292.51/185.06 tff(17405,plain,((~node18(c_e_h_1, c_h, s3, s4)) | m_c_h_element_v_out(c_e_h_1, c_h, s3) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4))), inference(lemma,lemma(discharge,[]))).
% 292.51/185.06 tff(17406,plain,
% 292.51/185.06 (~node18(c_e_h_1, c_h, s3, s4)),
% 292.51/185.06 inference(unit_resolution,[status(thm)],[17405, 17389, 17388])).
% 292.51/185.06 tff(17407,plain,
% 292.51/185.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s3, s4)) | node19(c_e_h_1, c_h, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s3, s4)) | node19(c_e_h_1, c_h, s3, s4))),
% 292.51/185.06 inference(rewrite,[status(thm)],[])).
% 292.51/185.06 tff(17408,plain,
% 292.51/185.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s3, s4)) | node19(c_e_h_1, c_h, s3, s4))),
% 292.51/185.06 inference(quant_inst,[status(thm)],[])).
% 292.51/185.06 tff(17409,plain,
% 292.51/185.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s3, s4)) | node19(c_e_h_1, c_h, s3, s4)),
% 292.51/185.06 inference(modus_ponens,[status(thm)],[17408, 17407])).
% 292.51/185.06 tff(17410,plain,
% 292.51/185.06 (node19(c_e_h_1, c_h, s3, s4)),
% 292.51/185.06 inference(unit_resolution,[status(thm)],[17409, 190, 531])).
% 292.51/185.06 tff(17411,plain,
% 292.51/185.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_h, s3, s4)) | node17(c_e_h_1, c_h, s3) | node18(c_e_h_1, c_h, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_h, s3, s4)) | node17(c_e_h_1, c_h, s3) | node18(c_e_h_1, c_h, s3, s4))),
% 292.51/185.06 inference(rewrite,[status(thm)],[])).
% 292.51/185.06 tff(17412,plain,
% 292.51/185.06 ((node17(c_e_h_1, c_h, s3) | node18(c_e_h_1, c_h, s3, s4) | (~node19(c_e_h_1, c_h, s3, s4))) <=> ((~node19(c_e_h_1, c_h, s3, s4)) | node17(c_e_h_1, c_h, s3) | node18(c_e_h_1, c_h, s3, s4))),
% 292.51/185.06 inference(rewrite,[status(thm)],[])).
% 292.51/185.06 tff(17413,plain,
% 292.51/185.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s3) | node18(c_e_h_1, c_h, s3, s4) | (~node19(c_e_h_1, c_h, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_h, s3, s4)) | node17(c_e_h_1, c_h, s3) | node18(c_e_h_1, c_h, s3, s4)))),
% 292.51/185.06 inference(monotonicity,[status(thm)],[17412])).
% 292.51/185.06 tff(17414,plain,
% 292.51/185.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s3) | node18(c_e_h_1, c_h, s3, s4) | (~node19(c_e_h_1, c_h, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_h, s3, s4)) | node17(c_e_h_1, c_h, s3) | node18(c_e_h_1, c_h, s3, s4))),
% 292.51/185.06 inference(transitivity,[status(thm)],[17413, 17411])).
% 292.51/185.06 tff(17415,plain,
% 292.51/185.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s3) | node18(c_e_h_1, c_h, s3, s4) | (~node19(c_e_h_1, c_h, s3, s4)))),
% 292.51/185.06 inference(quant_inst,[status(thm)],[])).
% 292.51/185.06 tff(17416,plain,
% 292.51/185.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_h, s3, s4)) | node17(c_e_h_1, c_h, s3) | node18(c_e_h_1, c_h, s3, s4)),
% 292.51/185.06 inference(modus_ponens,[status(thm)],[17415, 17414])).
% 292.51/185.06 tff(17417,plain,
% 292.51/185.06 (node17(c_e_h_1, c_h, s3) | node18(c_e_h_1, c_h, s3, s4)),
% 292.51/185.06 inference(unit_resolution,[status(thm)],[17416, 776, 17410])).
% 292.51/185.06 tff(17418,plain,
% 292.51/185.06 (node17(c_e_h_1, c_h, s3)),
% 292.51/185.06 inference(unit_resolution,[status(thm)],[17417, 17406])).
% 292.51/185.06 tff(17419,assumption,(node17(c_e_h_1, c_h, s3)), introduced(assumption)).
% 292.51/185.06 tff(17420,assumption,(node16(c_e_h_1, c_h, s3)), introduced(assumption)).
% 292.51/185.06 tff(17421,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_h, s3)), introduced(assumption)).
% 292.51/185.06 tff(17422,plain,
% 292.51/185.06 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s3)) | (~node17(c_e_h_1, c_h, s3)) | m_c_h_element_v_in2(c_e_h_1, c_h, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s3)) | (~node17(c_e_h_1, c_h, s3)) | m_c_h_element_v_in2(c_e_h_1, c_h, s3))),
% 292.51/185.06 inference(rewrite,[status(thm)],[])).
% 292.51/185.06 tff(17423,plain,
% 292.51/185.06 (((~m_c_h_element_v_in1(c_e_h_1, c_h, s3)) | m_c_h_element_v_in2(c_e_h_1, c_h, s3) | (~node17(c_e_h_1, c_h, s3))) <=> ((~m_c_h_element_v_in1(c_e_h_1, c_h, s3)) | (~node17(c_e_h_1, c_h, s3)) | m_c_h_element_v_in2(c_e_h_1, c_h, s3))),
% 292.51/185.06 inference(rewrite,[status(thm)],[])).
% 292.51/185.06 tff(17424,plain,
% 292.51/185.06 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s3)) | m_c_h_element_v_in2(c_e_h_1, c_h, s3) | (~node17(c_e_h_1, c_h, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s3)) | (~node17(c_e_h_1, c_h, s3)) | m_c_h_element_v_in2(c_e_h_1, c_h, s3)))),
% 292.51/185.06 inference(monotonicity,[status(thm)],[17423])).
% 292.51/185.06 tff(17425,plain,
% 292.51/185.06 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s3)) | m_c_h_element_v_in2(c_e_h_1, c_h, s3) | (~node17(c_e_h_1, c_h, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s3)) | (~node17(c_e_h_1, c_h, s3)) | m_c_h_element_v_in2(c_e_h_1, c_h, s3))),
% 292.51/185.06 inference(transitivity,[status(thm)],[17424, 17422])).
% 292.51/185.06 tff(17426,plain,
% 292.51/185.06 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s3)) | m_c_h_element_v_in2(c_e_h_1, c_h, s3) | (~node17(c_e_h_1, c_h, s3)))),
% 292.51/185.06 inference(quant_inst,[status(thm)],[])).
% 292.51/185.06 tff(17427,plain,
% 292.51/185.06 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s3)) | (~node17(c_e_h_1, c_h, s3)) | m_c_h_element_v_in2(c_e_h_1, c_h, s3)),
% 292.51/185.06 inference(modus_ponens,[status(thm)],[17426, 17425])).
% 292.51/185.06 tff(17428,plain,
% 292.51/185.06 ((~m_c_h_element_v_in1(c_e_h_1, c_h, s3)) | m_c_h_element_v_in2(c_e_h_1, c_h, s3)),
% 292.51/185.06 inference(unit_resolution,[status(thm)],[17427, 919, 17419])).
% 292.51/185.06 tff(17429,plain,
% 292.51/185.06 (~m_c_h_element_v_in1(c_e_h_1, c_h, s3)),
% 292.51/185.06 inference(unit_resolution,[status(thm)],[17428, 17421])).
% 292.51/185.06 tff(17430,plain,
% 292.51/185.06 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s3)) | m_c_h_element_v_in1(c_e_h_1, c_h, s3) | m_c_h_element_v_in2(c_e_h_1, c_h, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s3)) | m_c_h_element_v_in1(c_e_h_1, c_h, s3) | m_c_h_element_v_in2(c_e_h_1, c_h, s3))),
% 292.51/185.06 inference(rewrite,[status(thm)],[])).
% 292.51/185.06 tff(17431,plain,
% 292.51/185.06 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s3)) | m_c_h_element_v_in1(c_e_h_1, c_h, s3) | m_c_h_element_v_in2(c_e_h_1, c_h, s3))),
% 292.51/185.06 inference(quant_inst,[status(thm)],[])).
% 292.51/185.06 tff(17432,plain,
% 292.51/185.06 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s3)) | m_c_h_element_v_in1(c_e_h_1, c_h, s3) | m_c_h_element_v_in2(c_e_h_1, c_h, s3)),
% 292.51/185.06 inference(modus_ponens,[status(thm)],[17431, 17430])).
% 292.51/185.06 tff(17433,plain,
% 292.51/185.06 (m_c_h_element_v_in1(c_e_h_1, c_h, s3) | m_c_h_element_v_in2(c_e_h_1, c_h, s3)),
% 292.51/185.06 inference(unit_resolution,[status(thm)],[17432, 178, 17420])).
% 292.51/185.06 tff(17434,plain,
% 292.51/185.06 ($false),
% 292.51/185.06 inference(unit_resolution,[status(thm)],[17433, 17429, 17421])).
% 292.51/185.06 tff(17435,plain,(m_c_h_element_v_in2(c_e_h_1, c_h, s3) | (~node16(c_e_h_1, c_h, s3)) | (~node17(c_e_h_1, c_h, s3))), inference(lemma,lemma(discharge,[]))).
% 292.51/185.06 tff(17436,plain,
% 292.51/185.06 (m_c_h_element_v_in2(c_e_h_1, c_h, s3)),
% 292.51/185.06 inference(unit_resolution,[status(thm)],[17435, 17420, 17419])).
% 292.51/185.06 tff(17437,plain,
% 292.51/185.06 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s3) | (~node17(c_e_h_1, c_h, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s3) | (~node17(c_e_h_1, c_h, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s3)))),
% 292.51/185.06 inference(rewrite,[status(thm)],[])).
% 292.51/185.06 tff(17438,plain,
% 292.51/185.06 ((m_c_h_element_v_in1(c_e_h_1, c_h, s3) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s3)) | (~node17(c_e_h_1, c_h, s3))) <=> (m_c_h_element_v_in1(c_e_h_1, c_h, s3) | (~node17(c_e_h_1, c_h, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s3)))),
% 292.51/185.06 inference(rewrite,[status(thm)],[])).
% 292.51/185.06 tff(17439,plain,
% 292.51/185.06 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s3) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s3)) | (~node17(c_e_h_1, c_h, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s3) | (~node17(c_e_h_1, c_h, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s3))))),
% 292.51/185.06 inference(monotonicity,[status(thm)],[17438])).
% 292.51/185.06 tff(17440,plain,
% 292.51/185.06 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s3) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s3)) | (~node17(c_e_h_1, c_h, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s3) | (~node17(c_e_h_1, c_h, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s3)))),
% 292.51/185.06 inference(transitivity,[status(thm)],[17439, 17437])).
% 292.51/185.06 tff(17441,plain,
% 292.51/185.06 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s3) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s3)) | (~node17(c_e_h_1, c_h, s3)))),
% 292.51/185.06 inference(quant_inst,[status(thm)],[])).
% 292.51/185.07 tff(17442,plain,
% 292.51/185.07 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s3) | (~node17(c_e_h_1, c_h, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s3))),
% 292.51/185.07 inference(modus_ponens,[status(thm)],[17441, 17440])).
% 292.51/185.07 tff(17443,plain,
% 292.51/185.07 (m_c_h_element_v_in1(c_e_h_1, c_h, s3) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s3))),
% 292.51/185.07 inference(unit_resolution,[status(thm)],[17442, 859, 17419])).
% 292.51/185.07 tff(17444,plain,
% 292.51/185.07 (m_c_h_element_v_in1(c_e_h_1, c_h, s3)),
% 292.51/185.07 inference(unit_resolution,[status(thm)],[17443, 17436])).
% 292.51/185.07 tff(17445,plain,
% 292.51/185.07 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s3)) | (~node16(c_e_h_1, c_h, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s3)) | (~node16(c_e_h_1, c_h, s3)))),
% 292.51/185.07 inference(rewrite,[status(thm)],[])).
% 292.51/185.07 tff(17446,plain,
% 292.51/185.07 (((~node16(c_e_h_1, c_h, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s3))) <=> ((~m_c_h_element_v_in1(c_e_h_1, c_h, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s3)) | (~node16(c_e_h_1, c_h, s3)))),
% 292.51/185.07 inference(rewrite,[status(thm)],[])).
% 292.51/185.07 tff(17447,plain,
% 292.51/185.07 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_h, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s3)) | (~node16(c_e_h_1, c_h, s3))))),
% 292.51/185.07 inference(monotonicity,[status(thm)],[17446])).
% 292.51/185.07 tff(17448,plain,
% 292.51/185.07 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_h, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s3)) | (~node16(c_e_h_1, c_h, s3)))),
% 292.51/185.07 inference(transitivity,[status(thm)],[17447, 17445])).
% 292.51/185.07 tff(17449,plain,
% 292.51/185.07 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_h, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s3)))),
% 292.51/185.07 inference(quant_inst,[status(thm)],[])).
% 292.51/185.07 tff(17450,plain,
% 292.51/185.07 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s3)) | (~node16(c_e_h_1, c_h, s3))),
% 292.51/185.07 inference(modus_ponens,[status(thm)],[17449, 17448])).
% 292.51/185.07 tff(17451,plain,
% 292.51/185.07 ((~m_c_h_element_v_in1(c_e_h_1, c_h, s3)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s3))),
% 292.51/185.07 inference(unit_resolution,[status(thm)],[17450, 2307, 17420])).
% 292.51/185.07 tff(17452,plain,
% 292.51/185.07 ($false),
% 292.51/185.07 inference(unit_resolution,[status(thm)],[17451, 17444, 17436])).
% 292.51/185.07 tff(17453,plain,((~node16(c_e_h_1, c_h, s3)) | (~node17(c_e_h_1, c_h, s3))), inference(lemma,lemma(discharge,[]))).
% 292.51/185.07 tff(17454,plain,
% 292.51/185.07 (~node16(c_e_h_1, c_h, s3)),
% 292.51/185.07 inference(unit_resolution,[status(thm)],[17453, 17418])).
% 292.51/185.07 tff(17455,plain,
% 292.51/185.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_h, s3, s4)) | node14(c_e_h_1, c_h, s3, s4) | node16(c_e_h_1, c_h, s3) | node15(c_e_h_1, c_h, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_h, s3, s4)) | node14(c_e_h_1, c_h, s3, s4) | node16(c_e_h_1, c_h, s3) | node15(c_e_h_1, c_h, s3, s4))),
% 292.51/185.07 inference(rewrite,[status(thm)],[])).
% 292.51/185.07 tff(17456,plain,
% 292.51/185.07 ((node16(c_e_h_1, c_h, s3) | node14(c_e_h_1, c_h, s3, s4) | node15(c_e_h_1, c_h, s3, s4) | (~node19(c_e_h_1, c_h, s3, s4))) <=> ((~node19(c_e_h_1, c_h, s3, s4)) | node14(c_e_h_1, c_h, s3, s4) | node16(c_e_h_1, c_h, s3) | node15(c_e_h_1, c_h, s3, s4))),
% 292.51/185.07 inference(rewrite,[status(thm)],[])).
% 292.51/185.07 tff(17457,plain,
% 292.51/185.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s3) | node14(c_e_h_1, c_h, s3, s4) | node15(c_e_h_1, c_h, s3, s4) | (~node19(c_e_h_1, c_h, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_h, s3, s4)) | node14(c_e_h_1, c_h, s3, s4) | node16(c_e_h_1, c_h, s3) | node15(c_e_h_1, c_h, s3, s4)))),
% 292.51/185.07 inference(monotonicity,[status(thm)],[17456])).
% 292.51/185.07 tff(17458,plain,
% 292.51/185.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s3) | node14(c_e_h_1, c_h, s3, s4) | node15(c_e_h_1, c_h, s3, s4) | (~node19(c_e_h_1, c_h, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_h, s3, s4)) | node14(c_e_h_1, c_h, s3, s4) | node16(c_e_h_1, c_h, s3) | node15(c_e_h_1, c_h, s3, s4))),
% 292.51/185.07 inference(transitivity,[status(thm)],[17457, 17455])).
% 292.51/185.07 tff(17459,plain,
% 292.51/185.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s3) | node14(c_e_h_1, c_h, s3, s4) | node15(c_e_h_1, c_h, s3, s4) | (~node19(c_e_h_1, c_h, s3, s4)))),
% 292.51/185.07 inference(quant_inst,[status(thm)],[])).
% 292.51/185.07 tff(17460,plain,
% 292.51/185.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_h, s3, s4)) | node14(c_e_h_1, c_h, s3, s4) | node16(c_e_h_1, c_h, s3) | node15(c_e_h_1, c_h, s3, s4)),
% 292.51/185.07 inference(modus_ponens,[status(thm)],[17459, 17458])).
% 292.51/185.07 tff(17461,plain,
% 292.51/185.07 (node14(c_e_h_1, c_h, s3, s4) | node16(c_e_h_1, c_h, s3) | node15(c_e_h_1, c_h, s3, s4)),
% 292.51/185.07 inference(unit_resolution,[status(thm)],[17460, 204, 17410])).
% 292.51/185.07 tff(17462,plain,
% 292.51/185.07 (node14(c_e_h_1, c_h, s3, s4)),
% 292.51/185.07 inference(unit_resolution,[status(thm)],[17461, 17454, 17396])).
% 292.51/185.07 tff(17463,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_h, s3)), introduced(assumption)).
% 292.51/185.07 tff(17464,assumption,(node14(c_e_h_1, c_h, s3, s4)), introduced(assumption)).
% 292.51/185.07 tff(17465,plain,
% 292.51/185.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s3) | (~node14(c_e_h_1, c_h, s3, s4)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s3) | (~node14(c_e_h_1, c_h, s3, s4)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4)))),
% 292.51/185.07 inference(rewrite,[status(thm)],[])).
% 292.51/185.07 tff(17466,plain,
% 292.51/185.07 (((~node14(c_e_h_1, c_h, s3, s4)) | m_c_h_element_v_in1(c_e_h_1, c_h, s3) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4))) <=> (m_c_h_element_v_in1(c_e_h_1, c_h, s3) | (~node14(c_e_h_1, c_h, s3, s4)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4)))),
% 292.51/185.07 inference(rewrite,[status(thm)],[])).
% 292.51/185.07 tff(17467,plain,
% 292.51/185.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s3, s4)) | m_c_h_element_v_in1(c_e_h_1, c_h, s3) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s3) | (~node14(c_e_h_1, c_h, s3, s4)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4))))),
% 292.51/185.08 inference(monotonicity,[status(thm)],[17466])).
% 292.51/185.08 tff(17468,plain,
% 292.51/185.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s3, s4)) | m_c_h_element_v_in1(c_e_h_1, c_h, s3) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s3) | (~node14(c_e_h_1, c_h, s3, s4)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4)))),
% 292.51/185.08 inference(transitivity,[status(thm)],[17467, 17465])).
% 292.51/185.08 tff(17469,plain,
% 292.51/185.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s3, s4)) | m_c_h_element_v_in1(c_e_h_1, c_h, s3) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4)))),
% 292.51/185.08 inference(quant_inst,[status(thm)],[])).
% 292.51/185.08 tff(17470,plain,
% 292.51/185.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s3) | (~node14(c_e_h_1, c_h, s3, s4)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4))),
% 292.51/185.08 inference(modus_ponens,[status(thm)],[17469, 17468])).
% 292.51/185.08 tff(17471,plain,
% 292.51/185.08 ($false),
% 292.51/185.08 inference(unit_resolution,[status(thm)],[17470, 223, 17464, 17388, 17463])).
% 292.51/185.08 tff(17472,plain,((~node14(c_e_h_1, c_h, s3, s4)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4)) | m_c_h_element_v_in1(c_e_h_1, c_h, s3)), inference(lemma,lemma(discharge,[]))).
% 292.51/185.08 tff(17473,plain,
% 292.51/185.08 (m_c_h_element_v_in1(c_e_h_1, c_h, s3)),
% 292.51/185.08 inference(unit_resolution,[status(thm)],[17472, 17462, 17388])).
% 292.51/185.08 tff(17474,plain,
% 292.51/185.08 ($false),
% 292.51/185.08 inference(unit_resolution,[status(thm)],[17427, 919, 17418, 17421, 17473])).
% 292.51/185.08 tff(17475,plain,(m_c_h_element_v_out(c_e_h_1, c_h, s3) | m_c_h_element_v_in2(c_e_h_1, c_h, s3) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4))), inference(lemma,lemma(discharge,[]))).
% 292.51/185.08 tff(17476,plain,
% 292.51/185.08 (m_c_h_element_v_in2(c_e_h_1, c_h, s3) | (~m_c_h_element_v_out(c_e_h_1, c_h, s4))),
% 292.51/185.08 inference(unit_resolution,[status(thm)],[17475, 16823])).
% 292.51/185.08 tff(17477,plain,
% 292.51/185.08 (~m_c_h_element_v_out(c_e_h_1, c_h, s4)),
% 292.51/185.08 inference(unit_resolution,[status(thm)],[17476, 17387])).
% 292.51/185.08 tff(17478,assumption,(m_and_h_gate_v_in1(c_e_h_1, c_i, s4)), introduced(assumption)).
% 292.51/185.08 tff(17479,assumption,(~m_c_h_element_v_out(c_e_h_1, c_h, s4)), introduced(assumption)).
% 292.51/185.08 tff(17480,plain,
% 292.51/185.08 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s4)) | m_c_h_element_v_out(c_e_h_1, c_h, s4))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s4)) | m_c_h_element_v_out(c_e_h_1, c_h, s4))),
% 292.51/185.08 inference(rewrite,[status(thm)],[])).
% 292.51/185.08 tff(17481,plain,
% 292.51/185.08 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s4)) | m_c_h_element_v_out(c_e_h_1, c_h, s4))),
% 292.51/185.08 inference(quant_inst,[status(thm)],[])).
% 292.51/185.08 tff(17482,plain,
% 292.51/185.08 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s4)) | m_c_h_element_v_out(c_e_h_1, c_h, s4)),
% 292.51/185.08 inference(modus_ponens,[status(thm)],[17481, 17480])).
% 292.51/185.08 tff(17483,plain,
% 292.51/185.08 ($false),
% 292.51/185.08 inference(unit_resolution,[status(thm)],[17482, 619, 17479, 17478])).
% 292.51/185.08 tff(17484,plain,((~m_and_h_gate_v_in1(c_e_h_1, c_i, s4)) | m_c_h_element_v_out(c_e_h_1, c_h, s4)), inference(lemma,lemma(discharge,[]))).
% 292.51/185.08 tff(17485,plain,
% 292.51/185.08 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s4)),
% 292.51/185.08 inference(unit_resolution,[status(thm)],[17484, 17477])).
% 292.51/185.08 tff(17486,assumption,(~m_and_h_gate_v_in1(c_e_h_1, c_i, s4)), introduced(assumption)).
% 292.51/185.08 tff(17487,assumption,(node20(c_e_h_1, c_i, s4)), introduced(assumption)).
% 292.51/185.08 tff(17488,plain,
% 292.51/185.08 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s4)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s4)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s4))),
% 292.51/185.08 inference(rewrite,[status(thm)],[])).
% 292.51/185.08 tff(17489,plain,
% 292.51/185.08 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s4)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s4))),
% 292.51/185.08 inference(quant_inst,[status(thm)],[])).
% 292.51/185.08 tff(17490,plain,
% 292.51/185.08 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s4)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s4)),
% 292.51/185.08 inference(modus_ponens,[status(thm)],[17489, 17488])).
% 292.51/185.08 tff(17491,plain,
% 292.51/185.08 ($false),
% 292.51/185.08 inference(unit_resolution,[status(thm)],[17490, 38, 17487, 17486])).
% 292.51/185.08 tff(17492,plain,((~node20(c_e_h_1, c_i, s4)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s4)), inference(lemma,lemma(discharge,[]))).
% 292.51/185.08 tff(17493,plain,
% 292.51/185.08 (~node20(c_e_h_1, c_i, s4)),
% 292.51/185.08 inference(unit_resolution,[status(thm)],[17492, 17485])).
% 292.51/185.08 tff(17494,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s5)), introduced(assumption)).
% 292.51/185.08 tff(17495,assumption,(node22(c_e_h_1, c_i, s4, s5)), introduced(assumption)).
% 292.51/185.08 tff(17496,plain,
% 292.51/185.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s5)) | (~node22(c_e_h_1, c_i, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_i, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s5)) | (~node22(c_e_h_1, c_i, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_i, s4))),
% 292.51/185.08 inference(rewrite,[status(thm)],[])).
% 292.51/185.08 tff(17497,plain,
% 292.51/185.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s5)) | (~node22(c_e_h_1, c_i, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_i, s4))),
% 292.51/185.08 inference(quant_inst,[status(thm)],[])).
% 292.51/185.08 tff(17498,plain,
% 292.51/185.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s5)) | (~node22(c_e_h_1, c_i, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_i, s4)),
% 292.51/185.08 inference(modus_ponens,[status(thm)],[17497, 17496])).
% 292.51/185.08 tff(17499,plain,
% 292.51/185.08 ($false),
% 292.51/185.08 inference(unit_resolution,[status(thm)],[17498, 108, 17495, 17494, 16854])).
% 292.51/185.08 tff(17500,plain,((~node22(c_e_h_1, c_i, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s5)) | m_and_h_gate_v_out(c_e_h_1, c_i, s4)), inference(lemma,lemma(discharge,[]))).
% 292.51/185.08 tff(17501,plain,
% 292.51/185.08 (~node22(c_e_h_1, c_i, s4, s5)),
% 292.51/185.08 inference(unit_resolution,[status(thm)],[17500, 17494, 16854])).
% 292.51/185.08 tff(17502,assumption,(~node20(c_e_h_1, c_i, s4)), introduced(assumption)).
% 292.51/185.08 tff(17503,assumption,(node21(c_e_h_1, c_i, s4, s5)), introduced(assumption)).
% 292.51/185.08 tff(17504,plain,
% 292.51/185.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s5)) | node20(c_e_h_1, c_i, s4) | (~node21(c_e_h_1, c_i, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s5)) | node20(c_e_h_1, c_i, s4) | (~node21(c_e_h_1, c_i, s4, s5)))),
% 292.51/185.08 inference(rewrite,[status(thm)],[])).
% 292.51/185.08 tff(17505,plain,
% 292.51/185.08 ((node20(c_e_h_1, c_i, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s5)) | (~node21(c_e_h_1, c_i, s4, s5))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_i, s5)) | node20(c_e_h_1, c_i, s4) | (~node21(c_e_h_1, c_i, s4, s5)))),
% 292.51/185.08 inference(rewrite,[status(thm)],[])).
% 292.51/185.08 tff(17506,plain,
% 292.51/185.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s5)) | (~node21(c_e_h_1, c_i, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s5)) | node20(c_e_h_1, c_i, s4) | (~node21(c_e_h_1, c_i, s4, s5))))),
% 292.51/185.08 inference(monotonicity,[status(thm)],[17505])).
% 292.51/185.08 tff(17507,plain,
% 292.51/185.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s5)) | (~node21(c_e_h_1, c_i, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s5)) | node20(c_e_h_1, c_i, s4) | (~node21(c_e_h_1, c_i, s4, s5)))),
% 292.51/185.08 inference(transitivity,[status(thm)],[17506, 17504])).
% 292.51/185.08 tff(17508,plain,
% 292.51/185.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s5)) | (~node21(c_e_h_1, c_i, s4, s5)))),
% 292.51/185.08 inference(quant_inst,[status(thm)],[])).
% 292.51/185.08 tff(17509,plain,
% 292.51/185.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s5)) | node20(c_e_h_1, c_i, s4) | (~node21(c_e_h_1, c_i, s4, s5))),
% 292.51/185.08 inference(modus_ponens,[status(thm)],[17508, 17507])).
% 292.51/185.08 tff(17510,plain,
% 292.51/185.08 ($false),
% 292.51/185.08 inference(unit_resolution,[status(thm)],[17509, 52, 17503, 17494, 17502])).
% 292.51/185.08 tff(17511,plain,((~node21(c_e_h_1, c_i, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s5)) | node20(c_e_h_1, c_i, s4)), inference(lemma,lemma(discharge,[]))).
% 292.51/185.08 tff(17512,plain,
% 292.51/185.08 (~node21(c_e_h_1, c_i, s4, s5)),
% 292.51/185.08 inference(unit_resolution,[status(thm)],[17511, 17494, 17502])).
% 292.51/185.08 tff(17513,plain,
% 292.51/185.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_1, c_i, s4, s5) | node22(c_e_h_1, c_i, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_1, c_i, s4, s5) | node22(c_e_h_1, c_i, s4, s5))),
% 292.51/185.08 inference(rewrite,[status(thm)],[])).
% 292.51/185.08 tff(17514,plain,
% 292.51/185.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_1, c_i, s4, s5) | node22(c_e_h_1, c_i, s4, s5))),
% 292.51/185.08 inference(quant_inst,[status(thm)],[])).
% 292.51/185.08 tff(17515,plain,
% 292.51/185.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_1, c_i, s4, s5) | node22(c_e_h_1, c_i, s4, s5)),
% 292.51/185.08 inference(modus_ponens,[status(thm)],[17514, 17513])).
% 292.51/185.08 tff(17516,plain,
% 292.51/185.08 (node21(c_e_h_1, c_i, s4, s5) | node22(c_e_h_1, c_i, s4, s5)),
% 292.51/185.08 inference(unit_resolution,[status(thm)],[17515, 82, 1028])).
% 292.51/185.08 tff(17517,plain,
% 292.51/185.08 ($false),
% 292.51/185.08 inference(unit_resolution,[status(thm)],[17516, 17512, 17501])).
% 292.51/185.08 tff(17518,plain,((~m_and_h_gate_v_out(c_e_h_1, c_i, s5)) | node20(c_e_h_1, c_i, s4) | m_and_h_gate_v_out(c_e_h_1, c_i, s4)), inference(lemma,lemma(discharge,[]))).
% 292.51/185.08 tff(17519,plain,
% 292.51/185.08 ((~m_and_h_gate_v_out(c_e_h_1, c_i, s5)) | node20(c_e_h_1, c_i, s4)),
% 292.51/185.08 inference(unit_resolution,[status(thm)],[17518, 16853])).
% 292.51/185.08 tff(17520,plain,
% 292.51/185.08 (~m_and_h_gate_v_out(c_e_h_1, c_i, s5)),
% 292.51/185.08 inference(unit_resolution,[status(thm)],[17519, 17493])).
% 292.51/185.08 tff(17521,assumption,(m_c_h_element_v_in2(c_e_h_1, c_e, s5)), introduced(assumption)).
% 292.51/185.08 tff(17522,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_i, s5)), introduced(assumption)).
% 292.51/185.08 tff(17523,plain,
% 292.51/185.08 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s5)) | m_and_h_gate_v_out(c_e_h_1, c_i, s5))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s5)) | m_and_h_gate_v_out(c_e_h_1, c_i, s5))),
% 292.51/185.08 inference(rewrite,[status(thm)],[])).
% 292.51/185.09 tff(17524,plain,
% 292.51/185.09 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s5)) | m_and_h_gate_v_out(c_e_h_1, c_i, s5))),
% 292.51/185.09 inference(quant_inst,[status(thm)],[])).
% 292.51/185.09 tff(17525,plain,
% 292.51/185.09 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s5)) | m_and_h_gate_v_out(c_e_h_1, c_i, s5)),
% 292.51/185.09 inference(modus_ponens,[status(thm)],[17524, 17523])).
% 292.51/185.09 tff(17526,plain,
% 292.51/185.09 ($false),
% 292.51/185.09 inference(unit_resolution,[status(thm)],[17525, 164, 17522, 17521])).
% 292.51/185.09 tff(17527,plain,((~m_c_h_element_v_in2(c_e_h_1, c_e, s5)) | m_and_h_gate_v_out(c_e_h_1, c_i, s5)), inference(lemma,lemma(discharge,[]))).
% 292.51/185.09 tff(17528,plain,
% 292.51/185.09 (~m_c_h_element_v_in2(c_e_h_1, c_e, s5)),
% 292.51/185.09 inference(unit_resolution,[status(thm)],[17527, 17520])).
% 292.51/185.09 tff(17529,assumption,(m_c_h_element_v_in2(c_e_h_1, c_e, s4)), introduced(assumption)).
% 292.51/185.09 tff(17530,plain,
% 292.51/185.09 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s4)) | m_and_h_gate_v_out(c_e_h_1, c_i, s4))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s4)) | m_and_h_gate_v_out(c_e_h_1, c_i, s4))),
% 292.51/185.09 inference(rewrite,[status(thm)],[])).
% 292.51/185.09 tff(17531,plain,
% 292.51/185.09 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s4)) | m_and_h_gate_v_out(c_e_h_1, c_i, s4))),
% 292.51/185.09 inference(quant_inst,[status(thm)],[])).
% 292.51/185.09 tff(17532,plain,
% 292.51/185.09 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s4)) | m_and_h_gate_v_out(c_e_h_1, c_i, s4)),
% 292.51/185.09 inference(modus_ponens,[status(thm)],[17531, 17530])).
% 292.51/185.09 tff(17533,plain,
% 292.51/185.09 ($false),
% 292.51/185.09 inference(unit_resolution,[status(thm)],[17532, 164, 16854, 17529])).
% 292.51/185.09 tff(17534,plain,((~m_c_h_element_v_in2(c_e_h_1, c_e, s4)) | m_and_h_gate_v_out(c_e_h_1, c_i, s4)), inference(lemma,lemma(discharge,[]))).
% 292.51/185.09 tff(17535,plain,
% 292.51/185.09 (~m_c_h_element_v_in2(c_e_h_1, c_e, s4)),
% 292.51/185.09 inference(unit_resolution,[status(thm)],[17534, 16853])).
% 292.51/185.09 tff(17536,plain,
% 292.51/185.09 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s2)) | m_and_h_gate_v_out(c_e_h_1, c_i, s2))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s2)) | m_and_h_gate_v_out(c_e_h_1, c_i, s2))),
% 292.51/185.09 inference(rewrite,[status(thm)],[])).
% 292.51/185.09 tff(17537,plain,
% 292.51/185.09 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s2)) | m_and_h_gate_v_out(c_e_h_1, c_i, s2))),
% 292.51/185.09 inference(quant_inst,[status(thm)],[])).
% 292.51/185.09 tff(17538,plain,
% 292.51/185.09 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s2)) | m_and_h_gate_v_out(c_e_h_1, c_i, s2)),
% 292.51/185.09 inference(modus_ponens,[status(thm)],[17537, 17536])).
% 292.51/185.09 tff(17539,plain,
% 292.51/185.09 (~m_c_h_element_v_in2(c_e_h_1, c_e, s2)),
% 292.51/185.09 inference(unit_resolution,[status(thm)],[17538, 164, 8477])).
% 292.51/185.09 tff(17540,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s3)), introduced(assumption)).
% 292.51/185.09 tff(17541,assumption,(node18(c_e_h_1, c_e, s2, s3)), introduced(assumption)).
% 292.51/185.09 tff(17542,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s2)), introduced(assumption)).
% 292.51/185.09 tff(17543,assumption,(node18(c_e_h_1, c_e, s1, s2)), introduced(assumption)).
% 292.51/185.09 tff(17544,plain,
% 292.51/185.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s1) | (~m_c_h_element_v_out(c_e_h_1, c_e, s2)) | (~node18(c_e_h_1, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s1) | (~m_c_h_element_v_out(c_e_h_1, c_e, s2)) | (~node18(c_e_h_1, c_e, s1, s2)))),
% 292.51/185.09 inference(rewrite,[status(thm)],[])).
% 292.51/185.09 tff(17545,plain,
% 292.51/185.09 (((~m_c_h_element_v_out(c_e_h_1, c_e, s2)) | m_c_h_element_v_out(c_e_h_1, c_e, s1) | (~node18(c_e_h_1, c_e, s1, s2))) <=> (m_c_h_element_v_out(c_e_h_1, c_e, s1) | (~m_c_h_element_v_out(c_e_h_1, c_e, s2)) | (~node18(c_e_h_1, c_e, s1, s2)))),
% 292.51/185.09 inference(rewrite,[status(thm)],[])).
% 292.51/185.09 tff(17546,plain,
% 292.51/185.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s2)) | m_c_h_element_v_out(c_e_h_1, c_e, s1) | (~node18(c_e_h_1, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s1) | (~m_c_h_element_v_out(c_e_h_1, c_e, s2)) | (~node18(c_e_h_1, c_e, s1, s2))))),
% 292.51/185.09 inference(monotonicity,[status(thm)],[17545])).
% 292.51/185.09 tff(17547,plain,
% 292.51/185.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s2)) | m_c_h_element_v_out(c_e_h_1, c_e, s1) | (~node18(c_e_h_1, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s1) | (~m_c_h_element_v_out(c_e_h_1, c_e, s2)) | (~node18(c_e_h_1, c_e, s1, s2)))),
% 292.51/185.09 inference(transitivity,[status(thm)],[17546, 17544])).
% 292.51/185.09 tff(17548,plain,
% 292.51/185.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s2)) | m_c_h_element_v_out(c_e_h_1, c_e, s1) | (~node18(c_e_h_1, c_e, s1, s2)))),
% 292.51/185.09 inference(quant_inst,[status(thm)],[])).
% 292.51/185.09 tff(17549,plain,
% 292.51/185.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s1) | (~m_c_h_element_v_out(c_e_h_1, c_e, s2)) | (~node18(c_e_h_1, c_e, s1, s2))),
% 292.51/185.09 inference(modus_ponens,[status(thm)],[17548, 17547])).
% 292.51/185.09 tff(17550,plain,
% 292.51/185.09 ($false),
% 292.51/185.09 inference(unit_resolution,[status(thm)],[17549, 753, 16336, 17542, 17543])).
% 292.51/185.09 tff(17551,plain,((~node18(c_e_h_1, c_e, s1, s2)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s2))), inference(lemma,lemma(discharge,[]))).
% 292.51/185.09 tff(17552,plain,
% 292.51/185.09 (~node18(c_e_h_1, c_e, s1, s2)),
% 292.51/185.09 inference(unit_resolution,[status(thm)],[17551, 17542])).
% 292.51/185.09 tff(17553,plain,
% 292.51/185.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s1, s2)) | node19(c_e_h_1, c_e, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s1, s2)) | node19(c_e_h_1, c_e, s1, s2))),
% 292.51/185.09 inference(rewrite,[status(thm)],[])).
% 292.51/185.09 tff(17554,plain,
% 292.51/185.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s1, s2)) | node19(c_e_h_1, c_e, s1, s2))),
% 292.51/185.09 inference(quant_inst,[status(thm)],[])).
% 292.51/185.09 tff(17555,plain,
% 292.51/185.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s1, s2)) | node19(c_e_h_1, c_e, s1, s2)),
% 292.51/185.09 inference(modus_ponens,[status(thm)],[17554, 17553])).
% 292.51/185.09 tff(17556,plain,
% 292.51/185.09 (node19(c_e_h_1, c_e, s1, s2)),
% 292.51/185.09 inference(unit_resolution,[status(thm)],[17555, 190, 255])).
% 292.51/185.09 tff(17557,plain,
% 292.51/185.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s1) | (~node19(c_e_h_1, c_e, s1, s2)) | node18(c_e_h_1, c_e, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_e, s1) | (~node19(c_e_h_1, c_e, s1, s2)) | node18(c_e_h_1, c_e, s1, s2))),
% 292.51/185.09 inference(rewrite,[status(thm)],[])).
% 292.51/185.09 tff(17558,plain,
% 292.51/185.09 ((node17(c_e_h_1, c_e, s1) | node18(c_e_h_1, c_e, s1, s2) | (~node19(c_e_h_1, c_e, s1, s2))) <=> (node17(c_e_h_1, c_e, s1) | (~node19(c_e_h_1, c_e, s1, s2)) | node18(c_e_h_1, c_e, s1, s2))),
% 292.51/185.09 inference(rewrite,[status(thm)],[])).
% 292.51/185.09 tff(17559,plain,
% 292.51/185.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s1) | node18(c_e_h_1, c_e, s1, s2) | (~node19(c_e_h_1, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s1) | (~node19(c_e_h_1, c_e, s1, s2)) | node18(c_e_h_1, c_e, s1, s2)))),
% 292.51/185.09 inference(monotonicity,[status(thm)],[17558])).
% 292.51/185.09 tff(17560,plain,
% 292.51/185.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s1) | node18(c_e_h_1, c_e, s1, s2) | (~node19(c_e_h_1, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_e, s1) | (~node19(c_e_h_1, c_e, s1, s2)) | node18(c_e_h_1, c_e, s1, s2))),
% 292.51/185.09 inference(transitivity,[status(thm)],[17559, 17557])).
% 292.51/185.09 tff(17561,plain,
% 292.51/185.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s1) | node18(c_e_h_1, c_e, s1, s2) | (~node19(c_e_h_1, c_e, s1, s2)))),
% 292.51/185.09 inference(quant_inst,[status(thm)],[])).
% 292.51/185.09 tff(17562,plain,
% 292.51/185.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_e, s1) | (~node19(c_e_h_1, c_e, s1, s2)) | node18(c_e_h_1, c_e, s1, s2)),
% 292.51/185.09 inference(modus_ponens,[status(thm)],[17561, 17560])).
% 292.51/185.09 tff(17563,plain,
% 292.51/185.09 (node17(c_e_h_1, c_e, s1) | node18(c_e_h_1, c_e, s1, s2)),
% 292.51/185.09 inference(unit_resolution,[status(thm)],[17562, 776, 17556])).
% 292.51/185.09 tff(17564,plain,
% 292.51/185.09 (node17(c_e_h_1, c_e, s1)),
% 292.51/185.09 inference(unit_resolution,[status(thm)],[17563, 17552])).
% 292.51/185.09 tff(17565,plain,
% 292.51/185.09 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s1)) | m_and_h_gate_v_out(c_e_h_1, c_i, s1))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s1)) | m_and_h_gate_v_out(c_e_h_1, c_i, s1))),
% 292.51/185.09 inference(rewrite,[status(thm)],[])).
% 292.51/185.09 tff(17566,plain,
% 292.51/185.09 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s1)) | m_and_h_gate_v_out(c_e_h_1, c_i, s1))),
% 292.51/185.09 inference(quant_inst,[status(thm)],[])).
% 292.51/185.09 tff(17567,plain,
% 292.51/185.09 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s1)) | m_and_h_gate_v_out(c_e_h_1, c_i, s1)),
% 292.51/185.09 inference(modus_ponens,[status(thm)],[17566, 17565])).
% 292.51/185.09 tff(17568,plain,
% 292.51/185.09 (~m_c_h_element_v_in2(c_e_h_1, c_e, s1)),
% 292.51/185.09 inference(unit_resolution,[status(thm)],[17567, 164, 7984])).
% 292.51/185.09 tff(17569,plain,
% 292.51/185.09 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_e, s1) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s1)) | (~node17(c_e_h_1, c_e, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s1) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s1)) | (~node17(c_e_h_1, c_e, s1)))),
% 292.51/185.09 inference(rewrite,[status(thm)],[])).
% 292.51/185.09 tff(17570,plain,
% 292.51/185.09 (((~m_c_h_element_v_in1(c_e_h_1, c_e, s1)) | m_c_h_element_v_in2(c_e_h_1, c_e, s1) | (~node17(c_e_h_1, c_e, s1))) <=> (m_c_h_element_v_in2(c_e_h_1, c_e, s1) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s1)) | (~node17(c_e_h_1, c_e, s1)))),
% 292.51/185.09 inference(rewrite,[status(thm)],[])).
% 292.51/185.09 tff(17571,plain,
% 292.51/185.09 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s1)) | m_c_h_element_v_in2(c_e_h_1, c_e, s1) | (~node17(c_e_h_1, c_e, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_e, s1) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s1)) | (~node17(c_e_h_1, c_e, s1))))),
% 292.51/185.10 inference(monotonicity,[status(thm)],[17570])).
% 292.51/185.10 tff(17572,plain,
% 292.51/185.10 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s1)) | m_c_h_element_v_in2(c_e_h_1, c_e, s1) | (~node17(c_e_h_1, c_e, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s1) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s1)) | (~node17(c_e_h_1, c_e, s1)))),
% 292.51/185.10 inference(transitivity,[status(thm)],[17571, 17569])).
% 292.51/185.10 tff(17573,plain,
% 292.51/185.10 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s1)) | m_c_h_element_v_in2(c_e_h_1, c_e, s1) | (~node17(c_e_h_1, c_e, s1)))),
% 292.51/185.10 inference(quant_inst,[status(thm)],[])).
% 292.51/185.10 tff(17574,plain,
% 292.51/185.10 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s1) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s1)) | (~node17(c_e_h_1, c_e, s1))),
% 292.51/185.10 inference(modus_ponens,[status(thm)],[17573, 17572])).
% 292.51/185.10 tff(17575,plain,
% 292.51/185.10 ((~m_c_h_element_v_in1(c_e_h_1, c_e, s1)) | (~node17(c_e_h_1, c_e, s1))),
% 292.51/185.10 inference(unit_resolution,[status(thm)],[17574, 919, 17568])).
% 292.51/185.10 tff(17576,plain,
% 292.51/185.10 (~m_c_h_element_v_in1(c_e_h_1, c_e, s1)),
% 292.51/185.10 inference(unit_resolution,[status(thm)],[17575, 17564])).
% 292.51/185.10 tff(17577,plain,
% 292.51/185.10 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s1)) | m_c_h_element_v_in1(c_e_h_1, c_e, s1) | m_c_h_element_v_in2(c_e_h_1, c_e, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s1)) | m_c_h_element_v_in1(c_e_h_1, c_e, s1) | m_c_h_element_v_in2(c_e_h_1, c_e, s1))),
% 292.51/185.10 inference(rewrite,[status(thm)],[])).
% 292.51/185.10 tff(17578,plain,
% 292.51/185.10 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s1)) | m_c_h_element_v_in1(c_e_h_1, c_e, s1) | m_c_h_element_v_in2(c_e_h_1, c_e, s1))),
% 292.51/185.10 inference(quant_inst,[status(thm)],[])).
% 292.51/185.10 tff(17579,plain,
% 292.51/185.10 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s1)) | m_c_h_element_v_in1(c_e_h_1, c_e, s1) | m_c_h_element_v_in2(c_e_h_1, c_e, s1)),
% 292.51/185.10 inference(modus_ponens,[status(thm)],[17578, 17577])).
% 292.51/185.10 tff(17580,plain,
% 292.51/185.10 ((~node16(c_e_h_1, c_e, s1)) | m_c_h_element_v_in1(c_e_h_1, c_e, s1)),
% 292.51/185.10 inference(unit_resolution,[status(thm)],[17579, 178, 17568])).
% 292.51/185.10 tff(17581,plain,
% 292.51/185.10 (~node16(c_e_h_1, c_e, s1)),
% 292.51/185.10 inference(unit_resolution,[status(thm)],[17580, 17576])).
% 292.51/185.10 tff(17582,assumption,(node14(c_e_h_1, c_e, s1, s2)), introduced(assumption)).
% 292.51/185.10 tff(17583,plain,
% 292.51/185.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s2)) | m_c_h_element_v_in1(c_e_h_1, c_e, s1) | (~node14(c_e_h_1, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s2)) | m_c_h_element_v_in1(c_e_h_1, c_e, s1) | (~node14(c_e_h_1, c_e, s1, s2)))),
% 292.51/185.10 inference(rewrite,[status(thm)],[])).
% 292.51/185.10 tff(17584,plain,
% 292.51/185.10 (((~node14(c_e_h_1, c_e, s1, s2)) | m_c_h_element_v_in1(c_e_h_1, c_e, s1) | (~m_c_h_element_v_out(c_e_h_1, c_e, s2))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_e, s2)) | m_c_h_element_v_in1(c_e_h_1, c_e, s1) | (~node14(c_e_h_1, c_e, s1, s2)))),
% 292.51/185.10 inference(rewrite,[status(thm)],[])).
% 292.51/185.10 tff(17585,plain,
% 292.51/185.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s1, s2)) | m_c_h_element_v_in1(c_e_h_1, c_e, s1) | (~m_c_h_element_v_out(c_e_h_1, c_e, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s2)) | m_c_h_element_v_in1(c_e_h_1, c_e, s1) | (~node14(c_e_h_1, c_e, s1, s2))))),
% 292.51/185.10 inference(monotonicity,[status(thm)],[17584])).
% 292.51/185.10 tff(17586,plain,
% 292.51/185.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s1, s2)) | m_c_h_element_v_in1(c_e_h_1, c_e, s1) | (~m_c_h_element_v_out(c_e_h_1, c_e, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s2)) | m_c_h_element_v_in1(c_e_h_1, c_e, s1) | (~node14(c_e_h_1, c_e, s1, s2)))),
% 292.51/185.10 inference(transitivity,[status(thm)],[17585, 17583])).
% 292.51/185.10 tff(17587,plain,
% 292.51/185.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s1, s2)) | m_c_h_element_v_in1(c_e_h_1, c_e, s1) | (~m_c_h_element_v_out(c_e_h_1, c_e, s2)))),
% 292.51/185.10 inference(quant_inst,[status(thm)],[])).
% 292.51/185.10 tff(17588,plain,
% 292.51/185.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s2)) | m_c_h_element_v_in1(c_e_h_1, c_e, s1) | (~node14(c_e_h_1, c_e, s1, s2))),
% 292.51/185.10 inference(modus_ponens,[status(thm)],[17587, 17586])).
% 292.51/185.10 tff(17589,plain,
% 292.51/185.10 ($false),
% 292.51/185.10 inference(unit_resolution,[status(thm)],[17588, 223, 17542, 17582, 17576])).
% 292.51/185.10 tff(17590,plain,((~node14(c_e_h_1, c_e, s1, s2)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s2))), inference(lemma,lemma(discharge,[]))).
% 292.51/185.10 tff(17591,plain,
% 292.51/185.10 (~node14(c_e_h_1, c_e, s1, s2)),
% 292.51/185.10 inference(unit_resolution,[status(thm)],[17590, 17542])).
% 292.51/185.10 tff(17592,plain,
% 292.51/185.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_1, c_e, s1, s2) | node15(c_e_h_1, c_e, s1, s2) | node16(c_e_h_1, c_e, s1) | (~node19(c_e_h_1, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_e, s1, s2) | node15(c_e_h_1, c_e, s1, s2) | node16(c_e_h_1, c_e, s1) | (~node19(c_e_h_1, c_e, s1, s2)))),
% 292.51/185.10 inference(rewrite,[status(thm)],[])).
% 292.51/185.10 tff(17593,plain,
% 292.51/185.10 ((node16(c_e_h_1, c_e, s1) | node14(c_e_h_1, c_e, s1, s2) | node15(c_e_h_1, c_e, s1, s2) | (~node19(c_e_h_1, c_e, s1, s2))) <=> (node14(c_e_h_1, c_e, s1, s2) | node15(c_e_h_1, c_e, s1, s2) | node16(c_e_h_1, c_e, s1) | (~node19(c_e_h_1, c_e, s1, s2)))),
% 292.51/185.10 inference(rewrite,[status(thm)],[])).
% 292.51/185.10 tff(17594,plain,
% 292.51/185.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s1) | node14(c_e_h_1, c_e, s1, s2) | node15(c_e_h_1, c_e, s1, s2) | (~node19(c_e_h_1, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_1, c_e, s1, s2) | node15(c_e_h_1, c_e, s1, s2) | node16(c_e_h_1, c_e, s1) | (~node19(c_e_h_1, c_e, s1, s2))))),
% 292.51/185.10 inference(monotonicity,[status(thm)],[17593])).
% 292.51/185.10 tff(17595,plain,
% 292.51/185.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s1) | node14(c_e_h_1, c_e, s1, s2) | node15(c_e_h_1, c_e, s1, s2) | (~node19(c_e_h_1, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_e, s1, s2) | node15(c_e_h_1, c_e, s1, s2) | node16(c_e_h_1, c_e, s1) | (~node19(c_e_h_1, c_e, s1, s2)))),
% 292.61/185.11 inference(transitivity,[status(thm)],[17594, 17592])).
% 292.61/185.11 tff(17596,plain,
% 292.61/185.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s1) | node14(c_e_h_1, c_e, s1, s2) | node15(c_e_h_1, c_e, s1, s2) | (~node19(c_e_h_1, c_e, s1, s2)))),
% 292.61/185.11 inference(quant_inst,[status(thm)],[])).
% 292.61/185.11 tff(17597,plain,
% 292.61/185.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_e, s1, s2) | node15(c_e_h_1, c_e, s1, s2) | node16(c_e_h_1, c_e, s1) | (~node19(c_e_h_1, c_e, s1, s2))),
% 292.61/185.11 inference(modus_ponens,[status(thm)],[17596, 17595])).
% 292.61/185.11 tff(17598,plain,
% 292.61/185.11 (node14(c_e_h_1, c_e, s1, s2) | node15(c_e_h_1, c_e, s1, s2) | node16(c_e_h_1, c_e, s1)),
% 292.61/185.11 inference(unit_resolution,[status(thm)],[17597, 204, 17556])).
% 292.61/185.11 tff(17599,plain,
% 292.61/185.11 (node15(c_e_h_1, c_e, s1, s2)),
% 292.61/185.11 inference(unit_resolution,[status(thm)],[17598, 17591, 17581])).
% 292.61/185.11 tff(17600,plain,
% 292.61/185.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s2)) | (~node15(c_e_h_1, c_e, s1, s2)) | m_c_h_element_v_out(c_e_h_1, c_e, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s2)) | (~node15(c_e_h_1, c_e, s1, s2)) | m_c_h_element_v_out(c_e_h_1, c_e, s1))),
% 292.61/185.11 inference(rewrite,[status(thm)],[])).
% 292.61/185.11 tff(17601,plain,
% 292.61/185.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s2)) | (~node15(c_e_h_1, c_e, s1, s2)) | m_c_h_element_v_out(c_e_h_1, c_e, s1))),
% 292.61/185.11 inference(quant_inst,[status(thm)],[])).
% 292.61/185.11 tff(17602,plain,
% 292.61/185.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s2)) | (~node15(c_e_h_1, c_e, s1, s2)) | m_c_h_element_v_out(c_e_h_1, c_e, s1)),
% 292.61/185.11 inference(modus_ponens,[status(thm)],[17601, 17600])).
% 292.61/185.11 tff(17603,plain,
% 292.61/185.11 ($false),
% 292.61/185.11 inference(unit_resolution,[status(thm)],[17602, 147, 16336, 17542, 17599])).
% 292.61/185.11 tff(17604,plain,(~m_c_h_element_v_out(c_e_h_1, c_e, s2)), inference(lemma,lemma(discharge,[]))).
% 292.61/185.11 tff(17605,plain,
% 292.61/185.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s3)) | m_c_h_element_v_out(c_e_h_1, c_e, s2) | (~node18(c_e_h_1, c_e, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s3)) | m_c_h_element_v_out(c_e_h_1, c_e, s2) | (~node18(c_e_h_1, c_e, s2, s3)))),
% 292.61/185.11 inference(rewrite,[status(thm)],[])).
% 292.61/185.11 tff(17606,plain,
% 292.61/185.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s3)) | m_c_h_element_v_out(c_e_h_1, c_e, s2) | (~node18(c_e_h_1, c_e, s2, s3)))),
% 292.61/185.11 inference(quant_inst,[status(thm)],[])).
% 292.61/185.11 tff(17607,plain,
% 292.61/185.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s3)) | m_c_h_element_v_out(c_e_h_1, c_e, s2) | (~node18(c_e_h_1, c_e, s2, s3))),
% 292.61/185.11 inference(modus_ponens,[status(thm)],[17606, 17605])).
% 292.61/185.11 tff(17608,plain,
% 292.61/185.11 ($false),
% 292.61/185.11 inference(unit_resolution,[status(thm)],[17607, 753, 17604, 17540, 17541])).
% 292.61/185.11 tff(17609,plain,((~node18(c_e_h_1, c_e, s2, s3)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s3))), inference(lemma,lemma(discharge,[]))).
% 292.61/185.11 tff(17610,plain,
% 292.61/185.11 (~node18(c_e_h_1, c_e, s2, s3)),
% 292.62/185.11 inference(unit_resolution,[status(thm)],[17609, 17540])).
% 292.62/185.11 tff(17611,plain,
% 292.62/185.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s2, s3)) | node19(c_e_h_1, c_e, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s2, s3)) | node19(c_e_h_1, c_e, s2, s3))),
% 292.62/185.11 inference(rewrite,[status(thm)],[])).
% 292.62/185.11 tff(17612,plain,
% 292.62/185.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s2, s3)) | node19(c_e_h_1, c_e, s2, s3))),
% 292.62/185.11 inference(quant_inst,[status(thm)],[])).
% 292.62/185.11 tff(17613,plain,
% 292.62/185.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s2, s3)) | node19(c_e_h_1, c_e, s2, s3)),
% 292.62/185.11 inference(modus_ponens,[status(thm)],[17612, 17611])).
% 292.62/185.11 tff(17614,plain,
% 292.62/185.11 (node19(c_e_h_1, c_e, s2, s3)),
% 292.62/185.11 inference(unit_resolution,[status(thm)],[17613, 190, 318])).
% 292.62/185.11 tff(17615,plain,
% 292.62/185.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_e, s2, s3)) | node17(c_e_h_1, c_e, s2) | node18(c_e_h_1, c_e, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s2, s3)) | node17(c_e_h_1, c_e, s2) | node18(c_e_h_1, c_e, s2, s3))),
% 292.62/185.11 inference(rewrite,[status(thm)],[])).
% 292.62/185.11 tff(17616,plain,
% 292.62/185.11 ((node17(c_e_h_1, c_e, s2) | node18(c_e_h_1, c_e, s2, s3) | (~node19(c_e_h_1, c_e, s2, s3))) <=> ((~node19(c_e_h_1, c_e, s2, s3)) | node17(c_e_h_1, c_e, s2) | node18(c_e_h_1, c_e, s2, s3))),
% 292.62/185.11 inference(rewrite,[status(thm)],[])).
% 292.62/185.11 tff(17617,plain,
% 292.62/185.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s2) | node18(c_e_h_1, c_e, s2, s3) | (~node19(c_e_h_1, c_e, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_e, s2, s3)) | node17(c_e_h_1, c_e, s2) | node18(c_e_h_1, c_e, s2, s3)))),
% 292.62/185.11 inference(monotonicity,[status(thm)],[17616])).
% 292.62/185.11 tff(17618,plain,
% 292.62/185.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s2) | node18(c_e_h_1, c_e, s2, s3) | (~node19(c_e_h_1, c_e, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s2, s3)) | node17(c_e_h_1, c_e, s2) | node18(c_e_h_1, c_e, s2, s3))),
% 292.62/185.11 inference(transitivity,[status(thm)],[17617, 17615])).
% 292.62/185.11 tff(17619,plain,
% 292.62/185.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s2) | node18(c_e_h_1, c_e, s2, s3) | (~node19(c_e_h_1, c_e, s2, s3)))),
% 292.62/185.11 inference(quant_inst,[status(thm)],[])).
% 292.62/185.11 tff(17620,plain,
% 292.62/185.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s2, s3)) | node17(c_e_h_1, c_e, s2) | node18(c_e_h_1, c_e, s2, s3)),
% 292.62/185.11 inference(modus_ponens,[status(thm)],[17619, 17618])).
% 292.62/185.11 tff(17621,plain,
% 292.62/185.11 (node17(c_e_h_1, c_e, s2) | node18(c_e_h_1, c_e, s2, s3)),
% 292.62/185.11 inference(unit_resolution,[status(thm)],[17620, 776, 17614])).
% 292.62/185.11 tff(17622,plain,
% 292.62/185.11 (node17(c_e_h_1, c_e, s2)),
% 292.62/185.11 inference(unit_resolution,[status(thm)],[17621, 17610])).
% 292.62/185.11 tff(17623,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_e, s2)), introduced(assumption)).
% 292.62/185.11 tff(17624,plain,
% 292.62/185.11 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_e, s2) | (~node17(c_e_h_1, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s2) | (~node17(c_e_h_1, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s2)))),
% 292.62/185.11 inference(rewrite,[status(thm)],[])).
% 292.62/185.11 tff(17625,plain,
% 292.62/185.11 (((~m_c_h_element_v_in1(c_e_h_1, c_e, s2)) | m_c_h_element_v_in2(c_e_h_1, c_e, s2) | (~node17(c_e_h_1, c_e, s2))) <=> (m_c_h_element_v_in2(c_e_h_1, c_e, s2) | (~node17(c_e_h_1, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s2)))),
% 292.62/185.11 inference(rewrite,[status(thm)],[])).
% 292.62/185.11 tff(17626,plain,
% 292.62/185.11 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s2)) | m_c_h_element_v_in2(c_e_h_1, c_e, s2) | (~node17(c_e_h_1, c_e, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_e, s2) | (~node17(c_e_h_1, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s2))))),
% 292.62/185.11 inference(monotonicity,[status(thm)],[17625])).
% 292.62/185.11 tff(17627,plain,
% 292.62/185.11 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s2)) | m_c_h_element_v_in2(c_e_h_1, c_e, s2) | (~node17(c_e_h_1, c_e, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s2) | (~node17(c_e_h_1, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s2)))),
% 292.62/185.11 inference(transitivity,[status(thm)],[17626, 17624])).
% 292.62/185.11 tff(17628,plain,
% 292.62/185.11 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s2)) | m_c_h_element_v_in2(c_e_h_1, c_e, s2) | (~node17(c_e_h_1, c_e, s2)))),
% 292.62/185.11 inference(quant_inst,[status(thm)],[])).
% 292.62/185.11 tff(17629,plain,
% 292.62/185.11 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s2) | (~node17(c_e_h_1, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s2))),
% 292.62/185.11 inference(modus_ponens,[status(thm)],[17628, 17627])).
% 292.62/185.11 tff(17630,plain,
% 292.62/185.11 ((~node17(c_e_h_1, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s2))),
% 292.62/185.11 inference(unit_resolution,[status(thm)],[17629, 919, 17623])).
% 292.62/185.11 tff(17631,plain,
% 292.62/185.11 (~m_c_h_element_v_in1(c_e_h_1, c_e, s2)),
% 292.62/185.11 inference(unit_resolution,[status(thm)],[17630, 17622])).
% 292.62/185.11 tff(17632,assumption,(node15(c_e_h_1, c_e, s2, s3)), introduced(assumption)).
% 292.62/185.11 tff(17633,plain,
% 292.62/185.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s3)) | (~node15(c_e_h_1, c_e, s2, s3)) | m_c_h_element_v_out(c_e_h_1, c_e, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s3)) | (~node15(c_e_h_1, c_e, s2, s3)) | m_c_h_element_v_out(c_e_h_1, c_e, s2))),
% 292.62/185.11 inference(rewrite,[status(thm)],[])).
% 292.62/185.11 tff(17634,plain,
% 292.62/185.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s3)) | (~node15(c_e_h_1, c_e, s2, s3)) | m_c_h_element_v_out(c_e_h_1, c_e, s2))),
% 292.62/185.11 inference(quant_inst,[status(thm)],[])).
% 292.62/185.11 tff(17635,plain,
% 292.62/185.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s3)) | (~node15(c_e_h_1, c_e, s2, s3)) | m_c_h_element_v_out(c_e_h_1, c_e, s2)),
% 292.62/185.11 inference(modus_ponens,[status(thm)],[17634, 17633])).
% 292.62/185.11 tff(17636,plain,
% 292.62/185.11 ($false),
% 292.62/185.11 inference(unit_resolution,[status(thm)],[17635, 147, 17604, 17540, 17632])).
% 292.62/185.11 tff(17637,plain,((~node15(c_e_h_1, c_e, s2, s3)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s3))), inference(lemma,lemma(discharge,[]))).
% 292.62/185.11 tff(17638,plain,
% 292.62/185.11 (~node15(c_e_h_1, c_e, s2, s3)),
% 292.62/185.11 inference(unit_resolution,[status(thm)],[17637, 17540])).
% 292.62/185.11 tff(17639,assumption,(node16(c_e_h_1, c_e, s2)), introduced(assumption)).
% 292.62/185.11 tff(17640,assumption,(node17(c_e_h_1, c_e, s2)), introduced(assumption)).
% 292.62/185.12 tff(17641,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_e, s2)), introduced(assumption)).
% 292.62/185.12 tff(17642,plain,
% 292.62/185.12 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s2)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2) | m_c_h_element_v_in2(c_e_h_1, c_e, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s2)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2) | m_c_h_element_v_in2(c_e_h_1, c_e, s2))),
% 292.62/185.12 inference(rewrite,[status(thm)],[])).
% 292.62/185.12 tff(17643,plain,
% 292.62/185.12 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s2)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2) | m_c_h_element_v_in2(c_e_h_1, c_e, s2))),
% 292.62/185.12 inference(quant_inst,[status(thm)],[])).
% 292.62/185.12 tff(17644,plain,
% 292.62/185.12 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s2)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2) | m_c_h_element_v_in2(c_e_h_1, c_e, s2)),
% 292.62/185.12 inference(modus_ponens,[status(thm)],[17643, 17642])).
% 292.62/185.12 tff(17645,plain,
% 292.62/185.12 (m_c_h_element_v_in1(c_e_h_1, c_e, s2) | m_c_h_element_v_in2(c_e_h_1, c_e, s2)),
% 292.62/185.12 inference(unit_resolution,[status(thm)],[17644, 178, 17639])).
% 292.62/185.12 tff(17646,plain,
% 292.62/185.12 (m_c_h_element_v_in2(c_e_h_1, c_e, s2)),
% 292.62/185.12 inference(unit_resolution,[status(thm)],[17645, 17641])).
% 292.62/185.12 tff(17647,plain,
% 292.62/185.12 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_e, s2)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s2)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s2)))),
% 292.62/185.12 inference(rewrite,[status(thm)],[])).
% 292.62/185.12 tff(17648,plain,
% 292.62/185.12 ((m_c_h_element_v_in1(c_e_h_1, c_e, s2) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s2)) | (~node17(c_e_h_1, c_e, s2))) <=> ((~node17(c_e_h_1, c_e, s2)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s2)))),
% 292.62/185.12 inference(rewrite,[status(thm)],[])).
% 292.62/185.12 tff(17649,plain,
% 292.62/185.12 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s2) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s2)) | (~node17(c_e_h_1, c_e, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_e, s2)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s2))))),
% 292.62/185.12 inference(monotonicity,[status(thm)],[17648])).
% 292.62/185.12 tff(17650,plain,
% 292.62/185.12 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s2) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s2)) | (~node17(c_e_h_1, c_e, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s2)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s2)))),
% 292.62/185.12 inference(transitivity,[status(thm)],[17649, 17647])).
% 292.62/185.12 tff(17651,plain,
% 292.62/185.12 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s2) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s2)) | (~node17(c_e_h_1, c_e, s2)))),
% 292.62/185.12 inference(quant_inst,[status(thm)],[])).
% 292.62/185.12 tff(17652,plain,
% 292.62/185.12 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s2)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s2))),
% 292.62/185.12 inference(modus_ponens,[status(thm)],[17651, 17650])).
% 292.62/185.12 tff(17653,plain,
% 292.62/185.12 (m_c_h_element_v_in1(c_e_h_1, c_e, s2) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s2))),
% 292.62/185.12 inference(unit_resolution,[status(thm)],[17652, 859, 17640])).
% 292.62/185.12 tff(17654,plain,
% 292.62/185.12 ($false),
% 292.62/185.12 inference(unit_resolution,[status(thm)],[17653, 17646, 17641])).
% 292.62/185.12 tff(17655,plain,(m_c_h_element_v_in1(c_e_h_1, c_e, s2) | (~node17(c_e_h_1, c_e, s2)) | (~node16(c_e_h_1, c_e, s2))), inference(lemma,lemma(discharge,[]))).
% 292.62/185.12 tff(17656,plain,
% 292.62/185.12 (m_c_h_element_v_in1(c_e_h_1, c_e, s2)),
% 292.62/185.12 inference(unit_resolution,[status(thm)],[17655, 17640, 17639])).
% 292.62/185.12 tff(17657,plain,
% 292.62/185.12 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s2)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~node16(c_e_h_1, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s2)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s2)))),
% 292.62/185.12 inference(rewrite,[status(thm)],[])).
% 292.62/185.12 tff(17658,plain,
% 292.62/185.12 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s2)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s2)))),
% 292.62/185.12 inference(quant_inst,[status(thm)],[])).
% 292.62/185.12 tff(17659,plain,
% 292.62/185.12 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~node16(c_e_h_1, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s2)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s2))),
% 292.62/185.12 inference(modus_ponens,[status(thm)],[17658, 17657])).
% 292.62/185.12 tff(17660,plain,
% 292.62/185.12 ((~m_c_h_element_v_in1(c_e_h_1, c_e, s2)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s2))),
% 292.62/185.12 inference(unit_resolution,[status(thm)],[17659, 2307, 17639])).
% 292.62/185.12 tff(17661,plain,
% 292.62/185.12 (~m_c_h_element_v_in2(c_e_h_1, c_e, s2)),
% 292.62/185.12 inference(unit_resolution,[status(thm)],[17660, 17656])).
% 292.62/185.12 tff(17662,plain,
% 292.62/185.12 (m_c_h_element_v_in2(c_e_h_1, c_e, s2) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s2))),
% 292.62/185.12 inference(unit_resolution,[status(thm)],[17629, 919, 17640])).
% 292.62/185.12 tff(17663,plain,
% 292.62/185.12 ($false),
% 292.62/185.12 inference(unit_resolution,[status(thm)],[17662, 17661, 17656])).
% 292.62/185.12 tff(17664,plain,((~node17(c_e_h_1, c_e, s2)) | (~node16(c_e_h_1, c_e, s2))), inference(lemma,lemma(discharge,[]))).
% 292.62/185.12 tff(17665,plain,
% 292.62/185.12 (~node16(c_e_h_1, c_e, s2)),
% 292.62/185.12 inference(unit_resolution,[status(thm)],[17664, 17622])).
% 292.62/185.12 tff(17666,plain,
% 292.62/185.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_e, s2, s3)) | node16(c_e_h_1, c_e, s2) | node14(c_e_h_1, c_e, s2, s3) | node15(c_e_h_1, c_e, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s2, s3)) | node16(c_e_h_1, c_e, s2) | node14(c_e_h_1, c_e, s2, s3) | node15(c_e_h_1, c_e, s2, s3))),
% 292.62/185.12 inference(rewrite,[status(thm)],[])).
% 292.62/185.12 tff(17667,plain,
% 292.62/185.12 ((node16(c_e_h_1, c_e, s2) | node14(c_e_h_1, c_e, s2, s3) | node15(c_e_h_1, c_e, s2, s3) | (~node19(c_e_h_1, c_e, s2, s3))) <=> ((~node19(c_e_h_1, c_e, s2, s3)) | node16(c_e_h_1, c_e, s2) | node14(c_e_h_1, c_e, s2, s3) | node15(c_e_h_1, c_e, s2, s3))),
% 292.62/185.12 inference(rewrite,[status(thm)],[])).
% 292.62/185.12 tff(17668,plain,
% 292.62/185.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s2) | node14(c_e_h_1, c_e, s2, s3) | node15(c_e_h_1, c_e, s2, s3) | (~node19(c_e_h_1, c_e, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_e, s2, s3)) | node16(c_e_h_1, c_e, s2) | node14(c_e_h_1, c_e, s2, s3) | node15(c_e_h_1, c_e, s2, s3)))),
% 292.62/185.12 inference(monotonicity,[status(thm)],[17667])).
% 292.62/185.12 tff(17669,plain,
% 292.62/185.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s2) | node14(c_e_h_1, c_e, s2, s3) | node15(c_e_h_1, c_e, s2, s3) | (~node19(c_e_h_1, c_e, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s2, s3)) | node16(c_e_h_1, c_e, s2) | node14(c_e_h_1, c_e, s2, s3) | node15(c_e_h_1, c_e, s2, s3))),
% 292.62/185.13 inference(transitivity,[status(thm)],[17668, 17666])).
% 292.62/185.13 tff(17670,plain,
% 292.62/185.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s2) | node14(c_e_h_1, c_e, s2, s3) | node15(c_e_h_1, c_e, s2, s3) | (~node19(c_e_h_1, c_e, s2, s3)))),
% 292.62/185.13 inference(quant_inst,[status(thm)],[])).
% 292.62/185.13 tff(17671,plain,
% 292.62/185.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s2, s3)) | node16(c_e_h_1, c_e, s2) | node14(c_e_h_1, c_e, s2, s3) | node15(c_e_h_1, c_e, s2, s3)),
% 292.62/185.13 inference(modus_ponens,[status(thm)],[17670, 17669])).
% 292.62/185.13 tff(17672,plain,
% 292.62/185.13 (node16(c_e_h_1, c_e, s2) | node14(c_e_h_1, c_e, s2, s3) | node15(c_e_h_1, c_e, s2, s3)),
% 292.62/185.13 inference(unit_resolution,[status(thm)],[17671, 204, 17614])).
% 292.62/185.13 tff(17673,plain,
% 292.62/185.13 (node14(c_e_h_1, c_e, s2, s3)),
% 292.62/185.13 inference(unit_resolution,[status(thm)],[17672, 17665, 17638])).
% 292.62/185.13 tff(17674,assumption,(node14(c_e_h_1, c_e, s2, s3)), introduced(assumption)).
% 292.62/185.13 tff(17675,plain,
% 292.62/185.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2) | (~node14(c_e_h_1, c_e, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2) | (~node14(c_e_h_1, c_e, s2, s3)))),
% 292.62/185.13 inference(rewrite,[status(thm)],[])).
% 292.62/185.13 tff(17676,plain,
% 292.62/185.13 (((~node14(c_e_h_1, c_e, s2, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2) | (~m_c_h_element_v_out(c_e_h_1, c_e, s3))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_e, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2) | (~node14(c_e_h_1, c_e, s2, s3)))),
% 292.62/185.13 inference(rewrite,[status(thm)],[])).
% 292.62/185.13 tff(17677,plain,
% 292.62/185.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s2, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2) | (~m_c_h_element_v_out(c_e_h_1, c_e, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2) | (~node14(c_e_h_1, c_e, s2, s3))))),
% 292.62/185.13 inference(monotonicity,[status(thm)],[17676])).
% 292.62/185.13 tff(17678,plain,
% 292.62/185.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s2, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2) | (~m_c_h_element_v_out(c_e_h_1, c_e, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2) | (~node14(c_e_h_1, c_e, s2, s3)))),
% 292.62/185.13 inference(transitivity,[status(thm)],[17677, 17675])).
% 292.62/185.13 tff(17679,plain,
% 292.62/185.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s2, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2) | (~m_c_h_element_v_out(c_e_h_1, c_e, s3)))),
% 292.62/185.13 inference(quant_inst,[status(thm)],[])).
% 292.62/185.13 tff(17680,plain,
% 292.62/185.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2) | (~node14(c_e_h_1, c_e, s2, s3))),
% 292.62/185.13 inference(modus_ponens,[status(thm)],[17679, 17678])).
% 292.62/185.13 tff(17681,plain,
% 292.62/185.13 ($false),
% 292.62/185.13 inference(unit_resolution,[status(thm)],[17680, 223, 17540, 17674, 17641])).
% 292.62/185.13 tff(17682,plain,((~node14(c_e_h_1, c_e, s2, s3)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s2)), inference(lemma,lemma(discharge,[]))).
% 292.62/185.13 tff(17683,plain,
% 292.62/185.13 ($false),
% 292.62/185.13 inference(unit_resolution,[status(thm)],[17682, 17673, 17631, 17540])).
% 292.62/185.13 tff(17684,plain,((~m_c_h_element_v_out(c_e_h_1, c_e, s3)) | m_c_h_element_v_in2(c_e_h_1, c_e, s2)), inference(lemma,lemma(discharge,[]))).
% 292.62/185.13 tff(17685,plain,
% 292.62/185.13 (~m_c_h_element_v_out(c_e_h_1, c_e, s3)),
% 292.62/185.13 inference(unit_resolution,[status(thm)],[17684, 17539])).
% 292.62/185.13 tff(17686,plain,
% 292.62/185.13 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s3)) | m_and_h_gate_v_out(c_e_h_1, c_i, s3))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s3)) | m_and_h_gate_v_out(c_e_h_1, c_i, s3))),
% 292.62/185.13 inference(rewrite,[status(thm)],[])).
% 292.62/185.13 tff(17687,plain,
% 292.62/185.13 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s3)) | m_and_h_gate_v_out(c_e_h_1, c_i, s3))),
% 292.62/185.13 inference(quant_inst,[status(thm)],[])).
% 292.62/185.13 tff(17688,plain,
% 292.62/185.13 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s3)) | m_and_h_gate_v_out(c_e_h_1, c_i, s3)),
% 292.62/185.13 inference(modus_ponens,[status(thm)],[17687, 17686])).
% 292.62/185.13 tff(17689,plain,
% 292.62/185.13 (~m_c_h_element_v_in2(c_e_h_1, c_e, s3)),
% 292.62/185.13 inference(unit_resolution,[status(thm)],[17688, 164, 15233])).
% 292.62/185.13 tff(17690,assumption,(~m_c_h_element_v_out(c_e_h_1, c_e, s3)), introduced(assumption)).
% 292.62/185.13 tff(17691,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s4)), introduced(assumption)).
% 292.62/185.13 tff(17692,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_e, s3)), introduced(assumption)).
% 292.62/185.13 tff(17693,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_e, s3)), introduced(assumption)).
% 292.62/185.13 tff(17694,plain,
% 292.62/185.13 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s3) | m_c_h_element_v_in2(c_e_h_1, c_e, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s3) | m_c_h_element_v_in2(c_e_h_1, c_e, s3))),
% 292.62/185.13 inference(rewrite,[status(thm)],[])).
% 292.62/185.13 tff(17695,plain,
% 292.62/185.13 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s3) | m_c_h_element_v_in2(c_e_h_1, c_e, s3))),
% 292.62/185.13 inference(quant_inst,[status(thm)],[])).
% 292.62/185.13 tff(17696,plain,
% 292.62/185.13 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s3) | m_c_h_element_v_in2(c_e_h_1, c_e, s3)),
% 292.62/185.13 inference(modus_ponens,[status(thm)],[17695, 17694])).
% 292.62/185.13 tff(17697,plain,
% 292.62/185.13 ((~node16(c_e_h_1, c_e, s3)) | m_c_h_element_v_in1(c_e_h_1, c_e, s3)),
% 292.62/185.13 inference(unit_resolution,[status(thm)],[17696, 178, 17692])).
% 292.62/185.13 tff(17698,plain,
% 292.62/185.13 (~node16(c_e_h_1, c_e, s3)),
% 292.62/185.13 inference(unit_resolution,[status(thm)],[17697, 17693])).
% 292.62/185.13 tff(17699,assumption,(~node16(c_e_h_1, c_e, s3)), introduced(assumption)).
% 292.62/185.13 tff(17700,assumption,(node15(c_e_h_1, c_e, s3, s4)), introduced(assumption)).
% 292.62/185.13 tff(17701,plain,
% 292.62/185.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s4)) | (~node15(c_e_h_1, c_e, s3, s4)) | m_c_h_element_v_out(c_e_h_1, c_e, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4)) | (~node15(c_e_h_1, c_e, s3, s4)) | m_c_h_element_v_out(c_e_h_1, c_e, s3))),
% 292.62/185.13 inference(rewrite,[status(thm)],[])).
% 292.62/185.13 tff(17702,plain,
% 292.62/185.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s4)) | (~node15(c_e_h_1, c_e, s3, s4)) | m_c_h_element_v_out(c_e_h_1, c_e, s3))),
% 292.62/185.13 inference(quant_inst,[status(thm)],[])).
% 292.62/185.13 tff(17703,plain,
% 292.62/185.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4)) | (~node15(c_e_h_1, c_e, s3, s4)) | m_c_h_element_v_out(c_e_h_1, c_e, s3)),
% 292.62/185.13 inference(modus_ponens,[status(thm)],[17702, 17701])).
% 292.62/185.13 tff(17704,plain,
% 292.62/185.13 ($false),
% 292.62/185.13 inference(unit_resolution,[status(thm)],[17703, 147, 17700, 17691, 17690])).
% 292.62/185.13 tff(17705,plain,((~node15(c_e_h_1, c_e, s3, s4)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4)) | m_c_h_element_v_out(c_e_h_1, c_e, s3)), inference(lemma,lemma(discharge,[]))).
% 292.62/185.13 tff(17706,plain,
% 292.62/185.13 (~node15(c_e_h_1, c_e, s3, s4)),
% 292.62/185.13 inference(unit_resolution,[status(thm)],[17705, 17691, 17690])).
% 292.62/185.13 tff(17707,plain,
% 292.62/185.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s3, s4)) | node19(c_e_h_1, c_e, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s3, s4)) | node19(c_e_h_1, c_e, s3, s4))),
% 292.62/185.13 inference(rewrite,[status(thm)],[])).
% 292.62/185.13 tff(17708,plain,
% 292.62/185.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s3, s4)) | node19(c_e_h_1, c_e, s3, s4))),
% 292.62/185.13 inference(quant_inst,[status(thm)],[])).
% 292.62/185.13 tff(17709,plain,
% 292.62/185.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s3, s4)) | node19(c_e_h_1, c_e, s3, s4)),
% 292.62/185.13 inference(modus_ponens,[status(thm)],[17708, 17707])).
% 292.62/185.13 tff(17710,plain,
% 292.62/185.13 (node19(c_e_h_1, c_e, s3, s4)),
% 292.62/185.13 inference(unit_resolution,[status(thm)],[17709, 190, 531])).
% 292.62/185.13 tff(17711,plain,
% 292.62/185.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s3) | node14(c_e_h_1, c_e, s3, s4) | node15(c_e_h_1, c_e, s3, s4) | (~node19(c_e_h_1, c_e, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_e, s3) | node14(c_e_h_1, c_e, s3, s4) | node15(c_e_h_1, c_e, s3, s4) | (~node19(c_e_h_1, c_e, s3, s4)))),
% 292.62/185.13 inference(rewrite,[status(thm)],[])).
% 292.62/185.13 tff(17712,plain,
% 292.62/185.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s3) | node14(c_e_h_1, c_e, s3, s4) | node15(c_e_h_1, c_e, s3, s4) | (~node19(c_e_h_1, c_e, s3, s4)))),
% 292.62/185.13 inference(quant_inst,[status(thm)],[])).
% 292.62/185.13 tff(17713,plain,
% 292.62/185.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_e, s3) | node14(c_e_h_1, c_e, s3, s4) | node15(c_e_h_1, c_e, s3, s4) | (~node19(c_e_h_1, c_e, s3, s4))),
% 292.62/185.13 inference(modus_ponens,[status(thm)],[17712, 17711])).
% 292.62/185.13 tff(17714,plain,
% 292.62/185.13 (node16(c_e_h_1, c_e, s3) | node14(c_e_h_1, c_e, s3, s4) | node15(c_e_h_1, c_e, s3, s4)),
% 292.62/185.13 inference(unit_resolution,[status(thm)],[17713, 204, 17710])).
% 292.62/185.13 tff(17715,plain,
% 292.62/185.13 (node14(c_e_h_1, c_e, s3, s4)),
% 292.62/185.13 inference(unit_resolution,[status(thm)],[17714, 17706, 17699])).
% 292.62/185.13 tff(17716,plain,
% 292.62/185.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s3) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4)) | (~node14(c_e_h_1, c_e, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s3) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4)) | (~node14(c_e_h_1, c_e, s3, s4)))),
% 292.62/185.14 inference(rewrite,[status(thm)],[])).
% 292.62/185.14 tff(17717,plain,
% 292.62/185.14 (((~node14(c_e_h_1, c_e, s3, s4)) | m_c_h_element_v_in1(c_e_h_1, c_e, s3) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4))) <=> (m_c_h_element_v_in1(c_e_h_1, c_e, s3) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4)) | (~node14(c_e_h_1, c_e, s3, s4)))),
% 292.62/185.14 inference(rewrite,[status(thm)],[])).
% 292.62/185.14 tff(17718,plain,
% 292.62/185.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s3, s4)) | m_c_h_element_v_in1(c_e_h_1, c_e, s3) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s3) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4)) | (~node14(c_e_h_1, c_e, s3, s4))))),
% 292.62/185.14 inference(monotonicity,[status(thm)],[17717])).
% 292.62/185.14 tff(17719,plain,
% 292.62/185.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s3, s4)) | m_c_h_element_v_in1(c_e_h_1, c_e, s3) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s3) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4)) | (~node14(c_e_h_1, c_e, s3, s4)))),
% 292.62/185.14 inference(transitivity,[status(thm)],[17718, 17716])).
% 292.62/185.14 tff(17720,plain,
% 292.62/185.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s3, s4)) | m_c_h_element_v_in1(c_e_h_1, c_e, s3) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4)))),
% 292.62/185.14 inference(quant_inst,[status(thm)],[])).
% 292.62/185.14 tff(17721,plain,
% 292.62/185.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s3) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4)) | (~node14(c_e_h_1, c_e, s3, s4))),
% 292.62/185.14 inference(modus_ponens,[status(thm)],[17720, 17719])).
% 292.62/185.14 tff(17722,plain,
% 292.62/185.14 ($false),
% 292.62/185.14 inference(unit_resolution,[status(thm)],[17721, 223, 17715, 17691, 17693])).
% 292.62/185.14 tff(17723,plain,((~m_c_h_element_v_out(c_e_h_1, c_e, s4)) | m_c_h_element_v_in1(c_e_h_1, c_e, s3) | node16(c_e_h_1, c_e, s3) | m_c_h_element_v_out(c_e_h_1, c_e, s3)), inference(lemma,lemma(discharge,[]))).
% 292.62/185.14 tff(17724,plain,
% 292.62/185.14 ($false),
% 292.62/185.14 inference(unit_resolution,[status(thm)],[17723, 17698, 17693, 17691, 17690])).
% 292.62/185.14 tff(17725,plain,(m_c_h_element_v_in1(c_e_h_1, c_e, s3) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4)) | m_c_h_element_v_out(c_e_h_1, c_e, s3) | m_c_h_element_v_in2(c_e_h_1, c_e, s3)), inference(lemma,lemma(discharge,[]))).
% 292.62/185.14 tff(17726,plain,
% 292.62/185.14 (m_c_h_element_v_in1(c_e_h_1, c_e, s3)),
% 292.62/185.14 inference(unit_resolution,[status(thm)],[17725, 17690, 17691, 17692])).
% 292.62/185.14 tff(17727,plain,
% 292.62/185.14 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_e, s3) | (~node17(c_e_h_1, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s3) | (~node17(c_e_h_1, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s3)))),
% 292.62/185.14 inference(rewrite,[status(thm)],[])).
% 292.62/185.14 tff(17728,plain,
% 292.62/185.14 (((~m_c_h_element_v_in1(c_e_h_1, c_e, s3)) | m_c_h_element_v_in2(c_e_h_1, c_e, s3) | (~node17(c_e_h_1, c_e, s3))) <=> (m_c_h_element_v_in2(c_e_h_1, c_e, s3) | (~node17(c_e_h_1, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s3)))),
% 292.62/185.14 inference(rewrite,[status(thm)],[])).
% 292.62/185.14 tff(17729,plain,
% 292.62/185.14 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s3)) | m_c_h_element_v_in2(c_e_h_1, c_e, s3) | (~node17(c_e_h_1, c_e, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_e, s3) | (~node17(c_e_h_1, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s3))))),
% 292.62/185.14 inference(monotonicity,[status(thm)],[17728])).
% 292.62/185.14 tff(17730,plain,
% 292.62/185.14 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s3)) | m_c_h_element_v_in2(c_e_h_1, c_e, s3) | (~node17(c_e_h_1, c_e, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s3) | (~node17(c_e_h_1, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s3)))),
% 292.62/185.14 inference(transitivity,[status(thm)],[17729, 17727])).
% 292.62/185.14 tff(17731,plain,
% 292.62/185.14 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s3)) | m_c_h_element_v_in2(c_e_h_1, c_e, s3) | (~node17(c_e_h_1, c_e, s3)))),
% 292.62/185.14 inference(quant_inst,[status(thm)],[])).
% 292.62/185.14 tff(17732,plain,
% 292.62/185.14 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s3) | (~node17(c_e_h_1, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s3))),
% 292.62/185.14 inference(modus_ponens,[status(thm)],[17731, 17730])).
% 292.62/185.14 tff(17733,plain,
% 292.62/185.14 ((~node17(c_e_h_1, c_e, s3)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s3))),
% 292.62/185.14 inference(unit_resolution,[status(thm)],[17732, 919, 17692])).
% 292.62/185.14 tff(17734,plain,
% 292.62/185.14 (~node17(c_e_h_1, c_e, s3)),
% 292.62/185.14 inference(unit_resolution,[status(thm)],[17733, 17726])).
% 292.62/185.14 tff(17735,plain,
% 292.62/185.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s3) | node18(c_e_h_1, c_e, s3, s4) | (~node19(c_e_h_1, c_e, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_e, s3) | node18(c_e_h_1, c_e, s3, s4) | (~node19(c_e_h_1, c_e, s3, s4)))),
% 292.62/185.14 inference(rewrite,[status(thm)],[])).
% 292.62/185.14 tff(17736,plain,
% 292.62/185.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s3) | node18(c_e_h_1, c_e, s3, s4) | (~node19(c_e_h_1, c_e, s3, s4)))),
% 292.62/185.14 inference(quant_inst,[status(thm)],[])).
% 292.62/185.14 tff(17737,plain,
% 292.62/185.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_e, s3) | node18(c_e_h_1, c_e, s3, s4) | (~node19(c_e_h_1, c_e, s3, s4))),
% 292.62/185.14 inference(modus_ponens,[status(thm)],[17736, 17735])).
% 292.62/185.14 tff(17738,plain,
% 292.62/185.14 (node17(c_e_h_1, c_e, s3) | node18(c_e_h_1, c_e, s3, s4)),
% 292.62/185.14 inference(unit_resolution,[status(thm)],[17737, 776, 17710])).
% 292.62/185.14 tff(17739,plain,
% 292.62/185.14 (node18(c_e_h_1, c_e, s3, s4)),
% 292.62/185.14 inference(unit_resolution,[status(thm)],[17738, 17734])).
% 292.62/185.14 tff(17740,plain,
% 292.62/185.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s4)) | m_c_h_element_v_out(c_e_h_1, c_e, s3) | (~node18(c_e_h_1, c_e, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4)) | m_c_h_element_v_out(c_e_h_1, c_e, s3) | (~node18(c_e_h_1, c_e, s3, s4)))),
% 292.62/185.14 inference(rewrite,[status(thm)],[])).
% 292.62/185.14 tff(17741,plain,
% 292.62/185.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s4)) | m_c_h_element_v_out(c_e_h_1, c_e, s3) | (~node18(c_e_h_1, c_e, s3, s4)))),
% 292.62/185.14 inference(quant_inst,[status(thm)],[])).
% 292.62/185.14 tff(17742,plain,
% 292.62/185.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4)) | m_c_h_element_v_out(c_e_h_1, c_e, s3) | (~node18(c_e_h_1, c_e, s3, s4))),
% 292.62/185.14 inference(modus_ponens,[status(thm)],[17741, 17740])).
% 292.62/185.14 tff(17743,plain,
% 292.62/185.14 ($false),
% 292.62/185.14 inference(unit_resolution,[status(thm)],[17742, 753, 17739, 17691, 17690])).
% 292.62/185.14 tff(17744,plain,(m_c_h_element_v_out(c_e_h_1, c_e, s3) | (~m_c_h_element_v_out(c_e_h_1, c_e, s4)) | m_c_h_element_v_in2(c_e_h_1, c_e, s3)), inference(lemma,lemma(discharge,[]))).
% 292.62/185.14 tff(17745,plain,
% 292.62/185.14 (~m_c_h_element_v_out(c_e_h_1, c_e, s4)),
% 292.62/185.14 inference(unit_resolution,[status(thm)],[17744, 17689, 17685])).
% 292.62/185.14 tff(17746,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_e, s4)), introduced(assumption)).
% 292.62/185.14 tff(17747,assumption,(~m_c_h_element_v_out(c_e_h_1, c_e, s4)), introduced(assumption)).
% 292.62/185.14 tff(17748,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s5)), introduced(assumption)).
% 292.62/185.15 tff(17749,assumption,(node18(c_e_h_1, c_e, s4, s5)), introduced(assumption)).
% 292.62/185.15 tff(17750,plain,
% 292.62/185.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | m_c_h_element_v_out(c_e_h_1, c_e, s4) | (~node18(c_e_h_1, c_e, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | m_c_h_element_v_out(c_e_h_1, c_e, s4) | (~node18(c_e_h_1, c_e, s4, s5)))),
% 292.62/185.15 inference(rewrite,[status(thm)],[])).
% 292.62/185.15 tff(17751,plain,
% 292.62/185.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | m_c_h_element_v_out(c_e_h_1, c_e, s4) | (~node18(c_e_h_1, c_e, s4, s5)))),
% 292.62/185.15 inference(quant_inst,[status(thm)],[])).
% 292.62/185.15 tff(17752,plain,
% 292.62/185.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | m_c_h_element_v_out(c_e_h_1, c_e, s4) | (~node18(c_e_h_1, c_e, s4, s5))),
% 292.62/185.15 inference(modus_ponens,[status(thm)],[17751, 17750])).
% 292.62/185.15 tff(17753,plain,
% 292.62/185.15 ($false),
% 292.62/185.15 inference(unit_resolution,[status(thm)],[17752, 753, 17748, 17747, 17749])).
% 292.62/185.15 tff(17754,plain,((~node18(c_e_h_1, c_e, s4, s5)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | m_c_h_element_v_out(c_e_h_1, c_e, s4)), inference(lemma,lemma(discharge,[]))).
% 292.62/185.15 tff(17755,plain,
% 292.62/185.15 (~node18(c_e_h_1, c_e, s4, s5)),
% 292.62/185.15 inference(unit_resolution,[status(thm)],[17754, 17748, 17747])).
% 292.62/185.15 tff(17756,plain,
% 292.62/185.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s4, s5)) | node19(c_e_h_1, c_e, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s4, s5)) | node19(c_e_h_1, c_e, s4, s5))),
% 292.62/185.15 inference(rewrite,[status(thm)],[])).
% 292.62/185.15 tff(17757,plain,
% 292.62/185.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s4, s5)) | node19(c_e_h_1, c_e, s4, s5))),
% 292.62/185.15 inference(quant_inst,[status(thm)],[])).
% 292.62/185.15 tff(17758,plain,
% 292.62/185.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s4, s5)) | node19(c_e_h_1, c_e, s4, s5)),
% 292.62/185.15 inference(modus_ponens,[status(thm)],[17757, 17756])).
% 292.62/185.15 tff(17759,plain,
% 292.62/185.15 (node19(c_e_h_1, c_e, s4, s5)),
% 292.62/185.15 inference(unit_resolution,[status(thm)],[17758, 190, 1028])).
% 292.62/185.15 tff(17760,plain,
% 292.62/185.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s4) | (~node19(c_e_h_1, c_e, s4, s5)) | node18(c_e_h_1, c_e, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_e, s4) | (~node19(c_e_h_1, c_e, s4, s5)) | node18(c_e_h_1, c_e, s4, s5))),
% 292.62/185.15 inference(rewrite,[status(thm)],[])).
% 292.62/185.15 tff(17761,plain,
% 292.62/185.15 ((node17(c_e_h_1, c_e, s4) | node18(c_e_h_1, c_e, s4, s5) | (~node19(c_e_h_1, c_e, s4, s5))) <=> (node17(c_e_h_1, c_e, s4) | (~node19(c_e_h_1, c_e, s4, s5)) | node18(c_e_h_1, c_e, s4, s5))),
% 292.62/185.15 inference(rewrite,[status(thm)],[])).
% 292.62/185.15 tff(17762,plain,
% 292.62/185.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s4) | node18(c_e_h_1, c_e, s4, s5) | (~node19(c_e_h_1, c_e, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s4) | (~node19(c_e_h_1, c_e, s4, s5)) | node18(c_e_h_1, c_e, s4, s5)))),
% 292.62/185.15 inference(monotonicity,[status(thm)],[17761])).
% 292.62/185.15 tff(17763,plain,
% 292.62/185.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s4) | node18(c_e_h_1, c_e, s4, s5) | (~node19(c_e_h_1, c_e, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_e, s4) | (~node19(c_e_h_1, c_e, s4, s5)) | node18(c_e_h_1, c_e, s4, s5))),
% 292.62/185.15 inference(transitivity,[status(thm)],[17762, 17760])).
% 292.62/185.15 tff(17764,plain,
% 292.62/185.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s4) | node18(c_e_h_1, c_e, s4, s5) | (~node19(c_e_h_1, c_e, s4, s5)))),
% 292.62/185.15 inference(quant_inst,[status(thm)],[])).
% 292.62/185.15 tff(17765,plain,
% 292.62/185.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_e, s4) | (~node19(c_e_h_1, c_e, s4, s5)) | node18(c_e_h_1, c_e, s4, s5)),
% 292.62/185.15 inference(modus_ponens,[status(thm)],[17764, 17763])).
% 292.62/185.15 tff(17766,plain,
% 292.62/185.15 (node17(c_e_h_1, c_e, s4) | node18(c_e_h_1, c_e, s4, s5)),
% 292.62/185.15 inference(unit_resolution,[status(thm)],[17765, 776, 17759])).
% 292.62/185.15 tff(17767,plain,
% 292.62/185.15 (node17(c_e_h_1, c_e, s4)),
% 292.62/185.15 inference(unit_resolution,[status(thm)],[17766, 17755])).
% 292.62/185.15 tff(17768,plain,
% 292.62/185.15 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_e, s4) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s4)) | (~node17(c_e_h_1, c_e, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s4) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s4)) | (~node17(c_e_h_1, c_e, s4)))),
% 292.62/185.15 inference(rewrite,[status(thm)],[])).
% 292.62/185.15 tff(17769,plain,
% 292.62/185.15 (((~m_c_h_element_v_in1(c_e_h_1, c_e, s4)) | m_c_h_element_v_in2(c_e_h_1, c_e, s4) | (~node17(c_e_h_1, c_e, s4))) <=> (m_c_h_element_v_in2(c_e_h_1, c_e, s4) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s4)) | (~node17(c_e_h_1, c_e, s4)))),
% 292.62/185.15 inference(rewrite,[status(thm)],[])).
% 292.62/185.15 tff(17770,plain,
% 292.62/185.15 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s4)) | m_c_h_element_v_in2(c_e_h_1, c_e, s4) | (~node17(c_e_h_1, c_e, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_e, s4) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s4)) | (~node17(c_e_h_1, c_e, s4))))),
% 292.62/185.15 inference(monotonicity,[status(thm)],[17769])).
% 292.62/185.15 tff(17771,plain,
% 292.62/185.15 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s4)) | m_c_h_element_v_in2(c_e_h_1, c_e, s4) | (~node17(c_e_h_1, c_e, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s4) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s4)) | (~node17(c_e_h_1, c_e, s4)))),
% 292.62/185.15 inference(transitivity,[status(thm)],[17770, 17768])).
% 292.62/185.15 tff(17772,plain,
% 292.62/185.15 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s4)) | m_c_h_element_v_in2(c_e_h_1, c_e, s4) | (~node17(c_e_h_1, c_e, s4)))),
% 292.62/185.15 inference(quant_inst,[status(thm)],[])).
% 292.62/185.15 tff(17773,plain,
% 292.62/185.15 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s4) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s4)) | (~node17(c_e_h_1, c_e, s4))),
% 292.62/185.15 inference(modus_ponens,[status(thm)],[17772, 17771])).
% 292.62/185.15 tff(17774,plain,
% 292.62/185.15 (m_c_h_element_v_in2(c_e_h_1, c_e, s4) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s4))),
% 292.62/185.15 inference(unit_resolution,[status(thm)],[17773, 919, 17767])).
% 292.62/185.15 tff(17775,plain,
% 292.62/185.15 (~m_c_h_element_v_in1(c_e_h_1, c_e, s4)),
% 292.62/185.15 inference(unit_resolution,[status(thm)],[17774, 17746])).
% 292.62/185.15 tff(17776,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_e, s4)), introduced(assumption)).
% 292.62/185.15 tff(17777,assumption,(~node16(c_e_h_1, c_e, s4)), introduced(assumption)).
% 292.62/185.15 tff(17778,assumption,(node15(c_e_h_1, c_e, s4, s5)), introduced(assumption)).
% 292.62/185.15 tff(17779,plain,
% 292.62/185.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | (~node15(c_e_h_1, c_e, s4, s5)) | m_c_h_element_v_out(c_e_h_1, c_e, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | (~node15(c_e_h_1, c_e, s4, s5)) | m_c_h_element_v_out(c_e_h_1, c_e, s4))),
% 292.62/185.15 inference(rewrite,[status(thm)],[])).
% 292.62/185.15 tff(17780,plain,
% 292.62/185.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | (~node15(c_e_h_1, c_e, s4, s5)) | m_c_h_element_v_out(c_e_h_1, c_e, s4))),
% 292.62/185.15 inference(quant_inst,[status(thm)],[])).
% 292.62/185.15 tff(17781,plain,
% 292.62/185.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | (~node15(c_e_h_1, c_e, s4, s5)) | m_c_h_element_v_out(c_e_h_1, c_e, s4)),
% 292.62/185.15 inference(modus_ponens,[status(thm)],[17780, 17779])).
% 292.62/185.15 tff(17782,plain,
% 292.62/185.15 ($false),
% 292.62/185.15 inference(unit_resolution,[status(thm)],[17781, 147, 17748, 17747, 17778])).
% 292.62/185.15 tff(17783,plain,((~node15(c_e_h_1, c_e, s4, s5)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | m_c_h_element_v_out(c_e_h_1, c_e, s4)), inference(lemma,lemma(discharge,[]))).
% 292.62/185.15 tff(17784,plain,
% 292.62/185.15 (~node15(c_e_h_1, c_e, s4, s5)),
% 292.62/185.15 inference(unit_resolution,[status(thm)],[17783, 17748, 17747])).
% 292.62/185.15 tff(17785,plain,
% 292.62/185.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s4) | node14(c_e_h_1, c_e, s4, s5) | (~node19(c_e_h_1, c_e, s4, s5)) | node15(c_e_h_1, c_e, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_e, s4) | node14(c_e_h_1, c_e, s4, s5) | (~node19(c_e_h_1, c_e, s4, s5)) | node15(c_e_h_1, c_e, s4, s5))),
% 292.62/185.15 inference(rewrite,[status(thm)],[])).
% 292.62/185.15 tff(17786,plain,
% 292.62/185.15 ((node16(c_e_h_1, c_e, s4) | node14(c_e_h_1, c_e, s4, s5) | node15(c_e_h_1, c_e, s4, s5) | (~node19(c_e_h_1, c_e, s4, s5))) <=> (node16(c_e_h_1, c_e, s4) | node14(c_e_h_1, c_e, s4, s5) | (~node19(c_e_h_1, c_e, s4, s5)) | node15(c_e_h_1, c_e, s4, s5))),
% 292.62/185.15 inference(rewrite,[status(thm)],[])).
% 292.62/185.15 tff(17787,plain,
% 292.62/185.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s4) | node14(c_e_h_1, c_e, s4, s5) | node15(c_e_h_1, c_e, s4, s5) | (~node19(c_e_h_1, c_e, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s4) | node14(c_e_h_1, c_e, s4, s5) | (~node19(c_e_h_1, c_e, s4, s5)) | node15(c_e_h_1, c_e, s4, s5)))),
% 292.62/185.16 inference(monotonicity,[status(thm)],[17786])).
% 292.62/185.16 tff(17788,plain,
% 292.62/185.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s4) | node14(c_e_h_1, c_e, s4, s5) | node15(c_e_h_1, c_e, s4, s5) | (~node19(c_e_h_1, c_e, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_e, s4) | node14(c_e_h_1, c_e, s4, s5) | (~node19(c_e_h_1, c_e, s4, s5)) | node15(c_e_h_1, c_e, s4, s5))),
% 292.62/185.16 inference(transitivity,[status(thm)],[17787, 17785])).
% 292.62/185.16 tff(17789,plain,
% 292.62/185.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s4) | node14(c_e_h_1, c_e, s4, s5) | node15(c_e_h_1, c_e, s4, s5) | (~node19(c_e_h_1, c_e, s4, s5)))),
% 292.62/185.16 inference(quant_inst,[status(thm)],[])).
% 292.62/185.16 tff(17790,plain,
% 292.62/185.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_e, s4) | node14(c_e_h_1, c_e, s4, s5) | (~node19(c_e_h_1, c_e, s4, s5)) | node15(c_e_h_1, c_e, s4, s5)),
% 292.62/185.16 inference(modus_ponens,[status(thm)],[17789, 17788])).
% 292.62/185.16 tff(17791,plain,
% 292.62/185.16 (node16(c_e_h_1, c_e, s4) | node14(c_e_h_1, c_e, s4, s5) | node15(c_e_h_1, c_e, s4, s5)),
% 292.62/185.16 inference(unit_resolution,[status(thm)],[17790, 204, 17759])).
% 292.62/185.16 tff(17792,plain,
% 292.62/185.16 (node14(c_e_h_1, c_e, s4, s5)),
% 292.62/185.16 inference(unit_resolution,[status(thm)],[17791, 17784, 17777])).
% 292.62/185.16 tff(17793,plain,
% 292.62/185.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | m_c_h_element_v_in1(c_e_h_1, c_e, s4) | (~node14(c_e_h_1, c_e, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | m_c_h_element_v_in1(c_e_h_1, c_e, s4) | (~node14(c_e_h_1, c_e, s4, s5)))),
% 292.62/185.16 inference(rewrite,[status(thm)],[])).
% 292.62/185.16 tff(17794,plain,
% 292.62/185.16 (((~node14(c_e_h_1, c_e, s4, s5)) | m_c_h_element_v_in1(c_e_h_1, c_e, s4) | (~m_c_h_element_v_out(c_e_h_1, c_e, s5))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | m_c_h_element_v_in1(c_e_h_1, c_e, s4) | (~node14(c_e_h_1, c_e, s4, s5)))),
% 292.62/185.16 inference(rewrite,[status(thm)],[])).
% 292.62/185.16 tff(17795,plain,
% 292.62/185.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s4, s5)) | m_c_h_element_v_in1(c_e_h_1, c_e, s4) | (~m_c_h_element_v_out(c_e_h_1, c_e, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | m_c_h_element_v_in1(c_e_h_1, c_e, s4) | (~node14(c_e_h_1, c_e, s4, s5))))),
% 292.62/185.16 inference(monotonicity,[status(thm)],[17794])).
% 292.62/185.16 tff(17796,plain,
% 292.62/185.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s4, s5)) | m_c_h_element_v_in1(c_e_h_1, c_e, s4) | (~m_c_h_element_v_out(c_e_h_1, c_e, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | m_c_h_element_v_in1(c_e_h_1, c_e, s4) | (~node14(c_e_h_1, c_e, s4, s5)))),
% 292.62/185.16 inference(transitivity,[status(thm)],[17795, 17793])).
% 292.62/185.16 tff(17797,plain,
% 292.62/185.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s4, s5)) | m_c_h_element_v_in1(c_e_h_1, c_e, s4) | (~m_c_h_element_v_out(c_e_h_1, c_e, s5)))),
% 292.62/185.16 inference(quant_inst,[status(thm)],[])).
% 292.62/185.16 tff(17798,plain,
% 292.62/185.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | m_c_h_element_v_in1(c_e_h_1, c_e, s4) | (~node14(c_e_h_1, c_e, s4, s5))),
% 292.62/185.16 inference(modus_ponens,[status(thm)],[17797, 17796])).
% 292.62/185.16 tff(17799,plain,
% 292.62/185.16 ($false),
% 292.62/185.16 inference(unit_resolution,[status(thm)],[17798, 223, 17748, 17792, 17776])).
% 292.62/185.16 tff(17800,plain,((~m_c_h_element_v_out(c_e_h_1, c_e, s5)) | m_c_h_element_v_in1(c_e_h_1, c_e, s4) | node16(c_e_h_1, c_e, s4) | m_c_h_element_v_out(c_e_h_1, c_e, s4)), inference(lemma,lemma(discharge,[]))).
% 292.62/185.16 tff(17801,plain,
% 292.62/185.16 (node16(c_e_h_1, c_e, s4)),
% 292.62/185.16 inference(unit_resolution,[status(thm)],[17800, 17775, 17747, 17748])).
% 292.62/185.16 tff(17802,plain,
% 292.62/185.16 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s4)) | m_c_h_element_v_in1(c_e_h_1, c_e, s4) | m_c_h_element_v_in2(c_e_h_1, c_e, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s4)) | m_c_h_element_v_in1(c_e_h_1, c_e, s4) | m_c_h_element_v_in2(c_e_h_1, c_e, s4))),
% 292.62/185.16 inference(rewrite,[status(thm)],[])).
% 292.62/185.16 tff(17803,plain,
% 292.62/185.16 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s4)) | m_c_h_element_v_in1(c_e_h_1, c_e, s4) | m_c_h_element_v_in2(c_e_h_1, c_e, s4))),
% 292.62/185.16 inference(quant_inst,[status(thm)],[])).
% 292.62/185.16 tff(17804,plain,
% 292.62/185.16 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s4)) | m_c_h_element_v_in1(c_e_h_1, c_e, s4) | m_c_h_element_v_in2(c_e_h_1, c_e, s4)),
% 292.62/185.16 inference(modus_ponens,[status(thm)],[17803, 17802])).
% 292.62/185.16 tff(17805,plain,
% 292.62/185.16 ($false),
% 292.62/185.16 inference(unit_resolution,[status(thm)],[17804, 178, 17801, 17775, 17746])).
% 292.62/185.16 tff(17806,plain,(m_c_h_element_v_in2(c_e_h_1, c_e, s4) | m_c_h_element_v_out(c_e_h_1, c_e, s4) | (~m_c_h_element_v_out(c_e_h_1, c_e, s5))), inference(lemma,lemma(discharge,[]))).
% 292.62/185.16 tff(17807,plain,
% 292.62/185.16 (m_c_h_element_v_in2(c_e_h_1, c_e, s4) | (~m_c_h_element_v_out(c_e_h_1, c_e, s5))),
% 292.62/185.16 inference(unit_resolution,[status(thm)],[17806, 17745])).
% 292.62/185.16 tff(17808,plain,
% 292.62/185.16 (~m_c_h_element_v_out(c_e_h_1, c_e, s5)),
% 292.62/185.16 inference(unit_resolution,[status(thm)],[17807, 17535])).
% 292.62/185.16 tff(17809,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_e, s5)), introduced(assumption)).
% 292.62/185.16 tff(17810,assumption,(~m_c_h_element_v_out(c_e_h_1, c_e, s5)), introduced(assumption)).
% 292.62/185.16 tff(17811,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s6)), introduced(assumption)).
% 292.62/185.16 tff(17812,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_e, s5)), introduced(assumption)).
% 292.62/185.16 tff(17813,assumption,(node18(c_e_h_1, c_e, s5, s6)), introduced(assumption)).
% 292.62/185.16 tff(17814,plain,
% 292.62/185.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s5) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | (~node18(c_e_h_1, c_e, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s5) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | (~node18(c_e_h_1, c_e, s5, s6)))),
% 292.62/185.16 inference(rewrite,[status(thm)],[])).
% 292.62/185.16 tff(17815,plain,
% 292.62/185.16 (((~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | m_c_h_element_v_out(c_e_h_1, c_e, s5) | (~node18(c_e_h_1, c_e, s5, s6))) <=> (m_c_h_element_v_out(c_e_h_1, c_e, s5) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | (~node18(c_e_h_1, c_e, s5, s6)))),
% 292.62/185.16 inference(rewrite,[status(thm)],[])).
% 292.62/185.16 tff(17816,plain,
% 292.62/185.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | m_c_h_element_v_out(c_e_h_1, c_e, s5) | (~node18(c_e_h_1, c_e, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s5) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | (~node18(c_e_h_1, c_e, s5, s6))))),
% 292.62/185.17 inference(monotonicity,[status(thm)],[17815])).
% 292.62/185.17 tff(17817,plain,
% 292.62/185.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | m_c_h_element_v_out(c_e_h_1, c_e, s5) | (~node18(c_e_h_1, c_e, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s5) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | (~node18(c_e_h_1, c_e, s5, s6)))),
% 292.62/185.17 inference(transitivity,[status(thm)],[17816, 17814])).
% 292.62/185.17 tff(17818,plain,
% 292.62/185.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | m_c_h_element_v_out(c_e_h_1, c_e, s5) | (~node18(c_e_h_1, c_e, s5, s6)))),
% 292.62/185.17 inference(quant_inst,[status(thm)],[])).
% 292.62/185.17 tff(17819,plain,
% 292.62/185.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s5) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | (~node18(c_e_h_1, c_e, s5, s6))),
% 292.62/185.17 inference(modus_ponens,[status(thm)],[17818, 17817])).
% 292.62/185.17 tff(17820,plain,
% 292.62/185.17 ($false),
% 292.62/185.17 inference(unit_resolution,[status(thm)],[17819, 753, 17810, 17811, 17813])).
% 292.62/185.17 tff(17821,plain,((~node18(c_e_h_1, c_e, s5, s6)) | m_c_h_element_v_out(c_e_h_1, c_e, s5) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6))), inference(lemma,lemma(discharge,[]))).
% 292.62/185.17 tff(17822,plain,
% 292.62/185.17 (~node18(c_e_h_1, c_e, s5, s6)),
% 292.62/185.17 inference(unit_resolution,[status(thm)],[17821, 17810, 17811])).
% 292.62/185.17 tff(17823,plain,
% 292.62/185.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s5, s6)) | node19(c_e_h_1, c_e, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s5, s6)) | node19(c_e_h_1, c_e, s5, s6))),
% 292.62/185.17 inference(rewrite,[status(thm)],[])).
% 292.62/185.17 tff(17824,plain,
% 292.62/185.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s5, s6)) | node19(c_e_h_1, c_e, s5, s6))),
% 292.62/185.17 inference(quant_inst,[status(thm)],[])).
% 292.62/185.17 tff(17825,plain,
% 292.62/185.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s5, s6)) | node19(c_e_h_1, c_e, s5, s6)),
% 292.62/185.17 inference(modus_ponens,[status(thm)],[17824, 17823])).
% 292.62/185.17 tff(17826,plain,
% 292.62/185.17 (node19(c_e_h_1, c_e, s5, s6)),
% 292.62/185.17 inference(unit_resolution,[status(thm)],[17825, 190, 1406])).
% 292.62/185.17 tff(17827,plain,
% 292.62/185.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s5) | (~node19(c_e_h_1, c_e, s5, s6)) | node18(c_e_h_1, c_e, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_e, s5) | (~node19(c_e_h_1, c_e, s5, s6)) | node18(c_e_h_1, c_e, s5, s6))),
% 292.62/185.17 inference(rewrite,[status(thm)],[])).
% 292.62/185.17 tff(17828,plain,
% 292.62/185.17 ((node17(c_e_h_1, c_e, s5) | node18(c_e_h_1, c_e, s5, s6) | (~node19(c_e_h_1, c_e, s5, s6))) <=> (node17(c_e_h_1, c_e, s5) | (~node19(c_e_h_1, c_e, s5, s6)) | node18(c_e_h_1, c_e, s5, s6))),
% 292.62/185.17 inference(rewrite,[status(thm)],[])).
% 292.62/185.17 tff(17829,plain,
% 292.62/185.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s5) | node18(c_e_h_1, c_e, s5, s6) | (~node19(c_e_h_1, c_e, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s5) | (~node19(c_e_h_1, c_e, s5, s6)) | node18(c_e_h_1, c_e, s5, s6)))),
% 292.62/185.17 inference(monotonicity,[status(thm)],[17828])).
% 292.62/185.17 tff(17830,plain,
% 292.62/185.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s5) | node18(c_e_h_1, c_e, s5, s6) | (~node19(c_e_h_1, c_e, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_e, s5) | (~node19(c_e_h_1, c_e, s5, s6)) | node18(c_e_h_1, c_e, s5, s6))),
% 292.62/185.17 inference(transitivity,[status(thm)],[17829, 17827])).
% 292.62/185.17 tff(17831,plain,
% 292.62/185.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s5) | node18(c_e_h_1, c_e, s5, s6) | (~node19(c_e_h_1, c_e, s5, s6)))),
% 292.62/185.17 inference(quant_inst,[status(thm)],[])).
% 292.62/185.17 tff(17832,plain,
% 292.62/185.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_e, s5) | (~node19(c_e_h_1, c_e, s5, s6)) | node18(c_e_h_1, c_e, s5, s6)),
% 292.62/185.17 inference(modus_ponens,[status(thm)],[17831, 17830])).
% 292.62/185.17 tff(17833,plain,
% 292.62/185.17 (node17(c_e_h_1, c_e, s5) | node18(c_e_h_1, c_e, s5, s6)),
% 292.62/185.17 inference(unit_resolution,[status(thm)],[17832, 776, 17826])).
% 292.62/185.17 tff(17834,plain,
% 292.62/185.17 (node17(c_e_h_1, c_e, s5)),
% 292.62/185.17 inference(unit_resolution,[status(thm)],[17833, 17822])).
% 292.62/185.17 tff(17835,plain,
% 292.62/185.17 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s5)) | (~node17(c_e_h_1, c_e, s5)) | m_c_h_element_v_in1(c_e_h_1, c_e, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s5)) | (~node17(c_e_h_1, c_e, s5)) | m_c_h_element_v_in1(c_e_h_1, c_e, s5))),
% 292.62/185.17 inference(rewrite,[status(thm)],[])).
% 292.62/185.17 tff(17836,plain,
% 292.62/185.17 ((m_c_h_element_v_in1(c_e_h_1, c_e, s5) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s5)) | (~node17(c_e_h_1, c_e, s5))) <=> ((~m_c_h_element_v_in2(c_e_h_1, c_e, s5)) | (~node17(c_e_h_1, c_e, s5)) | m_c_h_element_v_in1(c_e_h_1, c_e, s5))),
% 292.62/185.17 inference(rewrite,[status(thm)],[])).
% 292.62/185.17 tff(17837,plain,
% 292.62/185.17 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s5) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s5)) | (~node17(c_e_h_1, c_e, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s5)) | (~node17(c_e_h_1, c_e, s5)) | m_c_h_element_v_in1(c_e_h_1, c_e, s5)))),
% 292.62/185.17 inference(monotonicity,[status(thm)],[17836])).
% 292.62/185.17 tff(17838,plain,
% 292.62/185.17 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s5) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s5)) | (~node17(c_e_h_1, c_e, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s5)) | (~node17(c_e_h_1, c_e, s5)) | m_c_h_element_v_in1(c_e_h_1, c_e, s5))),
% 292.62/185.17 inference(transitivity,[status(thm)],[17837, 17835])).
% 292.62/185.17 tff(17839,plain,
% 292.62/185.17 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s5) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s5)) | (~node17(c_e_h_1, c_e, s5)))),
% 292.62/185.17 inference(quant_inst,[status(thm)],[])).
% 292.62/185.17 tff(17840,plain,
% 292.62/185.17 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s5)) | (~node17(c_e_h_1, c_e, s5)) | m_c_h_element_v_in1(c_e_h_1, c_e, s5)),
% 292.62/185.17 inference(modus_ponens,[status(thm)],[17839, 17838])).
% 292.62/185.17 tff(17841,plain,
% 292.62/185.17 ((~m_c_h_element_v_in2(c_e_h_1, c_e, s5)) | m_c_h_element_v_in1(c_e_h_1, c_e, s5)),
% 292.62/185.17 inference(unit_resolution,[status(thm)],[17840, 859, 17834])).
% 292.62/185.17 tff(17842,plain,
% 292.62/185.17 (~m_c_h_element_v_in2(c_e_h_1, c_e, s5)),
% 292.62/185.17 inference(unit_resolution,[status(thm)],[17841, 17812])).
% 292.62/185.17 tff(17843,assumption,(~node16(c_e_h_1, c_e, s5)), introduced(assumption)).
% 292.62/185.17 tff(17844,assumption,(node15(c_e_h_1, c_e, s5, s6)), introduced(assumption)).
% 292.62/185.17 tff(17845,plain,
% 292.62/185.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | (~node15(c_e_h_1, c_e, s5, s6)) | m_c_h_element_v_out(c_e_h_1, c_e, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | (~node15(c_e_h_1, c_e, s5, s6)) | m_c_h_element_v_out(c_e_h_1, c_e, s5))),
% 292.62/185.17 inference(rewrite,[status(thm)],[])).
% 292.62/185.17 tff(17846,plain,
% 292.62/185.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | (~node15(c_e_h_1, c_e, s5, s6)) | m_c_h_element_v_out(c_e_h_1, c_e, s5))),
% 292.62/185.17 inference(quant_inst,[status(thm)],[])).
% 292.62/185.17 tff(17847,plain,
% 292.62/185.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | (~node15(c_e_h_1, c_e, s5, s6)) | m_c_h_element_v_out(c_e_h_1, c_e, s5)),
% 292.62/185.17 inference(modus_ponens,[status(thm)],[17846, 17845])).
% 292.62/185.17 tff(17848,plain,
% 292.62/185.17 ($false),
% 292.62/185.17 inference(unit_resolution,[status(thm)],[17847, 147, 17810, 17811, 17844])).
% 292.62/185.17 tff(17849,plain,((~node15(c_e_h_1, c_e, s5, s6)) | m_c_h_element_v_out(c_e_h_1, c_e, s5) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6))), inference(lemma,lemma(discharge,[]))).
% 292.62/185.17 tff(17850,plain,
% 292.62/185.17 (~node15(c_e_h_1, c_e, s5, s6)),
% 292.62/185.17 inference(unit_resolution,[status(thm)],[17849, 17811, 17810])).
% 292.62/185.17 tff(17851,plain,
% 292.62/185.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s5) | node14(c_e_h_1, c_e, s5, s6) | (~node19(c_e_h_1, c_e, s5, s6)) | node15(c_e_h_1, c_e, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_e, s5) | node14(c_e_h_1, c_e, s5, s6) | (~node19(c_e_h_1, c_e, s5, s6)) | node15(c_e_h_1, c_e, s5, s6))),
% 292.62/185.17 inference(rewrite,[status(thm)],[])).
% 292.62/185.17 tff(17852,plain,
% 292.62/185.17 ((node16(c_e_h_1, c_e, s5) | node14(c_e_h_1, c_e, s5, s6) | node15(c_e_h_1, c_e, s5, s6) | (~node19(c_e_h_1, c_e, s5, s6))) <=> (node16(c_e_h_1, c_e, s5) | node14(c_e_h_1, c_e, s5, s6) | (~node19(c_e_h_1, c_e, s5, s6)) | node15(c_e_h_1, c_e, s5, s6))),
% 292.62/185.17 inference(rewrite,[status(thm)],[])).
% 292.62/185.17 tff(17853,plain,
% 292.62/185.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s5) | node14(c_e_h_1, c_e, s5, s6) | node15(c_e_h_1, c_e, s5, s6) | (~node19(c_e_h_1, c_e, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s5) | node14(c_e_h_1, c_e, s5, s6) | (~node19(c_e_h_1, c_e, s5, s6)) | node15(c_e_h_1, c_e, s5, s6)))),
% 292.62/185.17 inference(monotonicity,[status(thm)],[17852])).
% 292.62/185.17 tff(17854,plain,
% 292.62/185.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s5) | node14(c_e_h_1, c_e, s5, s6) | node15(c_e_h_1, c_e, s5, s6) | (~node19(c_e_h_1, c_e, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_e, s5) | node14(c_e_h_1, c_e, s5, s6) | (~node19(c_e_h_1, c_e, s5, s6)) | node15(c_e_h_1, c_e, s5, s6))),
% 292.62/185.17 inference(transitivity,[status(thm)],[17853, 17851])).
% 292.62/185.17 tff(17855,plain,
% 292.62/185.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s5) | node14(c_e_h_1, c_e, s5, s6) | node15(c_e_h_1, c_e, s5, s6) | (~node19(c_e_h_1, c_e, s5, s6)))),
% 292.62/185.17 inference(quant_inst,[status(thm)],[])).
% 292.62/185.18 tff(17856,plain,
% 292.62/185.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_e, s5) | node14(c_e_h_1, c_e, s5, s6) | (~node19(c_e_h_1, c_e, s5, s6)) | node15(c_e_h_1, c_e, s5, s6)),
% 292.62/185.18 inference(modus_ponens,[status(thm)],[17855, 17854])).
% 292.62/185.18 tff(17857,plain,
% 292.62/185.18 (node16(c_e_h_1, c_e, s5) | node14(c_e_h_1, c_e, s5, s6) | node15(c_e_h_1, c_e, s5, s6)),
% 292.62/185.18 inference(unit_resolution,[status(thm)],[17856, 204, 17826])).
% 292.62/185.18 tff(17858,plain,
% 292.62/185.18 (node14(c_e_h_1, c_e, s5, s6)),
% 292.62/185.18 inference(unit_resolution,[status(thm)],[17857, 17850, 17843])).
% 292.62/185.18 tff(17859,plain,
% 292.62/185.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s5) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | (~node14(c_e_h_1, c_e, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s5) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | (~node14(c_e_h_1, c_e, s5, s6)))),
% 292.62/185.18 inference(rewrite,[status(thm)],[])).
% 292.62/185.18 tff(17860,plain,
% 292.62/185.18 (((~node14(c_e_h_1, c_e, s5, s6)) | m_c_h_element_v_in1(c_e_h_1, c_e, s5) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6))) <=> (m_c_h_element_v_in1(c_e_h_1, c_e, s5) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | (~node14(c_e_h_1, c_e, s5, s6)))),
% 292.62/185.18 inference(rewrite,[status(thm)],[])).
% 292.62/185.18 tff(17861,plain,
% 292.62/185.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s5, s6)) | m_c_h_element_v_in1(c_e_h_1, c_e, s5) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s5) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | (~node14(c_e_h_1, c_e, s5, s6))))),
% 292.62/185.18 inference(monotonicity,[status(thm)],[17860])).
% 292.62/185.18 tff(17862,plain,
% 292.62/185.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s5, s6)) | m_c_h_element_v_in1(c_e_h_1, c_e, s5) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s5) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | (~node14(c_e_h_1, c_e, s5, s6)))),
% 292.62/185.18 inference(transitivity,[status(thm)],[17861, 17859])).
% 292.62/185.18 tff(17863,plain,
% 292.62/185.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s5, s6)) | m_c_h_element_v_in1(c_e_h_1, c_e, s5) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6)))),
% 292.62/185.18 inference(quant_inst,[status(thm)],[])).
% 292.62/185.18 tff(17864,plain,
% 292.62/185.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s5) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | (~node14(c_e_h_1, c_e, s5, s6))),
% 292.62/185.18 inference(modus_ponens,[status(thm)],[17863, 17862])).
% 292.62/185.18 tff(17865,plain,
% 292.62/185.18 ($false),
% 292.62/185.18 inference(unit_resolution,[status(thm)],[17864, 223, 17811, 17858, 17812])).
% 292.62/185.18 tff(17866,plain,((~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | m_c_h_element_v_in1(c_e_h_1, c_e, s5) | node16(c_e_h_1, c_e, s5) | m_c_h_element_v_out(c_e_h_1, c_e, s5)), inference(lemma,lemma(discharge,[]))).
% 292.62/185.18 tff(17867,plain,
% 292.62/185.18 (node16(c_e_h_1, c_e, s5)),
% 292.62/185.18 inference(unit_resolution,[status(thm)],[17866, 17812, 17811, 17810])).
% 292.62/185.18 tff(17868,plain,
% 292.62/185.18 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s5)) | m_c_h_element_v_in1(c_e_h_1, c_e, s5) | m_c_h_element_v_in2(c_e_h_1, c_e, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s5)) | m_c_h_element_v_in1(c_e_h_1, c_e, s5) | m_c_h_element_v_in2(c_e_h_1, c_e, s5))),
% 292.62/185.18 inference(rewrite,[status(thm)],[])).
% 292.62/185.18 tff(17869,plain,
% 292.62/185.18 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s5)) | m_c_h_element_v_in1(c_e_h_1, c_e, s5) | m_c_h_element_v_in2(c_e_h_1, c_e, s5))),
% 292.62/185.18 inference(quant_inst,[status(thm)],[])).
% 292.62/185.18 tff(17870,plain,
% 292.62/185.18 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s5)) | m_c_h_element_v_in1(c_e_h_1, c_e, s5) | m_c_h_element_v_in2(c_e_h_1, c_e, s5)),
% 292.62/185.18 inference(modus_ponens,[status(thm)],[17869, 17868])).
% 292.62/185.18 tff(17871,plain,
% 292.62/185.18 ($false),
% 292.62/185.18 inference(unit_resolution,[status(thm)],[17870, 178, 17867, 17812, 17842])).
% 292.62/185.18 tff(17872,plain,(m_c_h_element_v_in1(c_e_h_1, c_e, s5) | (~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | m_c_h_element_v_out(c_e_h_1, c_e, s5)), inference(lemma,lemma(discharge,[]))).
% 292.62/185.18 tff(17873,plain,
% 292.62/185.18 (m_c_h_element_v_in1(c_e_h_1, c_e, s5)),
% 292.62/185.18 inference(unit_resolution,[status(thm)],[17872, 17811, 17810])).
% 292.62/185.18 tff(17874,plain,
% 292.62/185.18 (~node18(c_e_h_1, c_e, s5, s6)),
% 292.62/185.18 inference(unit_resolution,[status(thm)],[17821, 17811, 17810])).
% 292.62/185.18 tff(17875,plain,
% 292.62/185.18 (node17(c_e_h_1, c_e, s5)),
% 292.62/185.18 inference(unit_resolution,[status(thm)],[17833, 17874])).
% 292.62/185.18 tff(17876,plain,
% 292.62/185.18 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s5)) | m_c_h_element_v_in2(c_e_h_1, c_e, s5) | (~node17(c_e_h_1, c_e, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s5)) | m_c_h_element_v_in2(c_e_h_1, c_e, s5) | (~node17(c_e_h_1, c_e, s5)))),
% 292.62/185.18 inference(rewrite,[status(thm)],[])).
% 292.62/185.18 tff(17877,plain,
% 292.62/185.18 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s5)) | m_c_h_element_v_in2(c_e_h_1, c_e, s5) | (~node17(c_e_h_1, c_e, s5)))),
% 292.62/185.18 inference(quant_inst,[status(thm)],[])).
% 292.62/185.18 tff(17878,plain,
% 292.62/185.18 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s5)) | m_c_h_element_v_in2(c_e_h_1, c_e, s5) | (~node17(c_e_h_1, c_e, s5))),
% 292.62/185.18 inference(modus_ponens,[status(thm)],[17877, 17876])).
% 292.62/185.18 tff(17879,plain,
% 292.62/185.18 ($false),
% 292.62/185.18 inference(unit_resolution,[status(thm)],[17878, 919, 17875, 17873, 17809])).
% 292.62/185.18 tff(17880,plain,((~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | m_c_h_element_v_in2(c_e_h_1, c_e, s5) | m_c_h_element_v_out(c_e_h_1, c_e, s5)), inference(lemma,lemma(discharge,[]))).
% 292.62/185.18 tff(17881,plain,
% 292.62/185.18 ((~m_c_h_element_v_out(c_e_h_1, c_e, s6)) | m_c_h_element_v_in2(c_e_h_1, c_e, s5)),
% 292.62/185.18 inference(unit_resolution,[status(thm)],[17880, 17808])).
% 292.62/185.18 tff(17882,plain,
% 292.62/185.18 (~m_c_h_element_v_out(c_e_h_1, c_e, s6)),
% 292.62/185.18 inference(unit_resolution,[status(thm)],[17881, 17528])).
% 292.62/185.18 tff(17883,plain,
% 292.62/185.18 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6) | m_c_h_element_v_out(c_e_h_1, c_e, s6))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6) | m_c_h_element_v_out(c_e_h_1, c_e, s6))),
% 292.62/185.18 inference(rewrite,[status(thm)],[])).
% 292.62/185.18 tff(17884,plain,
% 292.62/185.18 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6) | m_c_h_element_v_out(c_e_h_1, c_e, s6))),
% 292.62/185.18 inference(quant_inst,[status(thm)],[])).
% 292.62/185.18 tff(17885,plain,
% 292.62/185.18 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6) | m_c_h_element_v_out(c_e_h_1, c_e, s6)),
% 292.62/185.18 inference(modus_ponens,[status(thm)],[17884, 17883])).
% 292.62/185.18 tff(17886,plain,
% 292.62/185.18 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6) | m_c_h_element_v_out(c_e_h_1, c_e, s6)),
% 292.62/185.18 inference(unit_resolution,[status(thm)],[17885, 7856])).
% 292.62/185.18 tff(17887,plain,
% 292.62/185.18 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6)),
% 292.62/185.18 inference(unit_resolution,[status(thm)],[17886, 17882])).
% 292.62/185.18 tff(17888,plain,
% 292.62/185.18 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5) | m_c_h_element_v_out(c_e_h_1, c_e, s5))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5) | m_c_h_element_v_out(c_e_h_1, c_e, s5))),
% 292.62/185.18 inference(rewrite,[status(thm)],[])).
% 292.62/185.18 tff(17889,plain,
% 292.62/185.18 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5) | m_c_h_element_v_out(c_e_h_1, c_e, s5))),
% 292.62/185.18 inference(quant_inst,[status(thm)],[])).
% 292.62/185.18 tff(17890,plain,
% 292.62/185.18 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5) | m_c_h_element_v_out(c_e_h_1, c_e, s5)),
% 292.62/185.18 inference(modus_ponens,[status(thm)],[17889, 17888])).
% 292.62/185.18 tff(17891,plain,
% 292.62/185.18 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5) | m_c_h_element_v_out(c_e_h_1, c_e, s5)),
% 292.62/185.18 inference(unit_resolution,[status(thm)],[17890, 7856])).
% 292.62/185.18 tff(17892,plain,
% 292.62/185.18 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5)),
% 292.62/185.18 inference(unit_resolution,[status(thm)],[17891, 17808])).
% 292.62/185.18 tff(17893,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4)), introduced(assumption)).
% 292.62/185.18 tff(17894,plain,
% 292.62/185.18 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4) | m_c_h_element_v_out(c_e_h_1, c_e, s4))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4) | m_c_h_element_v_out(c_e_h_1, c_e, s4))),
% 292.62/185.18 inference(rewrite,[status(thm)],[])).
% 292.62/185.18 tff(17895,plain,
% 292.62/185.18 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4) | m_c_h_element_v_out(c_e_h_1, c_e, s4))),
% 292.62/185.18 inference(quant_inst,[status(thm)],[])).
% 292.62/185.18 tff(17896,plain,
% 292.62/185.18 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4) | m_c_h_element_v_out(c_e_h_1, c_e, s4)),
% 292.62/185.18 inference(modus_ponens,[status(thm)],[17895, 17894])).
% 292.62/185.18 tff(17897,plain,
% 292.62/185.18 ($false),
% 292.62/185.18 inference(unit_resolution,[status(thm)],[17896, 7856, 17893, 17747])).
% 292.62/185.18 tff(17898,plain,(m_c_h_element_v_out(c_e_h_1, c_e, s4) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4)), inference(lemma,lemma(discharge,[]))).
% 292.62/185.18 tff(17899,plain,
% 292.62/185.18 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4)),
% 292.62/185.18 inference(unit_resolution,[status(thm)],[17898, 17745])).
% 292.62/185.18 tff(17900,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3)), introduced(assumption)).
% 292.62/185.18 tff(17901,plain,
% 292.62/185.18 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3) | m_c_h_element_v_out(c_e_h_1, c_e, s3))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3) | m_c_h_element_v_out(c_e_h_1, c_e, s3))),
% 292.62/185.18 inference(rewrite,[status(thm)],[])).
% 292.62/185.18 tff(17902,plain,
% 292.62/185.18 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3) | m_c_h_element_v_out(c_e_h_1, c_e, s3))),
% 292.62/185.18 inference(quant_inst,[status(thm)],[])).
% 292.62/185.18 tff(17903,plain,
% 292.62/185.18 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3) | m_c_h_element_v_out(c_e_h_1, c_e, s3)),
% 292.62/185.19 inference(modus_ponens,[status(thm)],[17902, 17901])).
% 292.62/185.19 tff(17904,plain,
% 292.62/185.19 ($false),
% 292.62/185.19 inference(unit_resolution,[status(thm)],[17903, 7856, 17690, 17900])).
% 292.62/185.19 tff(17905,plain,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3) | m_c_h_element_v_out(c_e_h_1, c_e, s3)), inference(lemma,lemma(discharge,[]))).
% 292.62/185.19 tff(17906,plain,
% 292.62/185.19 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3)),
% 292.62/185.19 inference(unit_resolution,[status(thm)],[17905, 17685])).
% 292.62/185.19 tff(17907,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)), introduced(assumption)).
% 292.62/185.19 tff(17908,assumption,(node11(c_e_h_1, c_n, s3, s4)), introduced(assumption)).
% 292.62/185.19 tff(17909,plain,
% 292.62/185.19 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s2) | m_c_h_element_v_out(c_e_h_1, c_e, s2))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s2) | m_c_h_element_v_out(c_e_h_1, c_e, s2))),
% 292.62/185.19 inference(rewrite,[status(thm)],[])).
% 292.62/185.19 tff(17910,plain,
% 292.62/185.19 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s2) | m_c_h_element_v_out(c_e_h_1, c_e, s2))),
% 292.62/185.19 inference(quant_inst,[status(thm)],[])).
% 292.62/185.19 tff(17911,plain,
% 292.62/185.19 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s2) | m_c_h_element_v_out(c_e_h_1, c_e, s2)),
% 292.62/185.19 inference(modus_ponens,[status(thm)],[17910, 17909])).
% 292.62/185.19 tff(17912,plain,
% 292.62/185.19 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s2) | m_c_h_element_v_out(c_e_h_1, c_e, s2)),
% 292.62/185.19 inference(unit_resolution,[status(thm)],[17911, 7856])).
% 292.62/185.19 tff(17913,plain,
% 292.62/185.19 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s2)),
% 292.62/185.19 inference(unit_resolution,[status(thm)],[17912, 17604])).
% 292.62/185.19 tff(17914,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3)), introduced(assumption)).
% 292.62/185.19 tff(17915,assumption,(node11(c_e_h_1, c_n, s2, s3)), introduced(assumption)).
% 292.62/185.19 tff(17916,plain,
% 292.62/185.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)) | (~node11(c_e_h_1, c_n, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)) | (~node11(c_e_h_1, c_n, s2, s3)))),
% 292.62/185.19 inference(rewrite,[status(thm)],[])).
% 292.62/185.19 tff(17917,plain,
% 292.62/185.19 ((m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3) | (~node11(c_e_h_1, c_n, s2, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2))) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)) | (~node11(c_e_h_1, c_n, s2, s3)))),
% 292.62/185.19 inference(rewrite,[status(thm)],[])).
% 292.62/185.19 tff(17918,plain,
% 292.62/185.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3) | (~node11(c_e_h_1, c_n, s2, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)) | (~node11(c_e_h_1, c_n, s2, s3))))),
% 292.62/185.19 inference(monotonicity,[status(thm)],[17917])).
% 292.62/185.19 tff(17919,plain,
% 292.62/185.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3) | (~node11(c_e_h_1, c_n, s2, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)) | (~node11(c_e_h_1, c_n, s2, s3)))),
% 292.62/185.19 inference(transitivity,[status(thm)],[17918, 17916])).
% 292.62/185.19 tff(17920,plain,
% 292.62/185.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3) | (~node11(c_e_h_1, c_n, s2, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)))),
% 292.62/185.19 inference(quant_inst,[status(thm)],[])).
% 292.62/185.19 tff(17921,plain,
% 292.62/185.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s2)) | (~node11(c_e_h_1, c_n, s2, s3))),
% 292.62/185.19 inference(modus_ponens,[status(thm)],[17920, 17919])).
% 292.62/185.19 tff(17922,plain,
% 292.62/185.19 ($false),
% 292.62/185.19 inference(unit_resolution,[status(thm)],[17921, 5742, 17914, 16363, 17915])).
% 292.62/185.19 tff(17923,plain,((~node11(c_e_h_1, c_n, s2, s3)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3)), inference(lemma,lemma(discharge,[]))).
% 292.62/185.19 tff(17924,plain,
% 292.62/185.19 (~node11(c_e_h_1, c_n, s2, s3)),
% 292.62/185.19 inference(unit_resolution,[status(thm)],[17923, 17914])).
% 292.62/185.19 tff(17925,plain,
% 292.62/185.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s2, s3)) | node10(c_e_h_1, c_n, s2, s3) | node11(c_e_h_1, c_n, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s2, s3)) | node10(c_e_h_1, c_n, s2, s3) | node11(c_e_h_1, c_n, s2, s3))),
% 292.62/185.19 inference(rewrite,[status(thm)],[])).
% 292.62/185.19 tff(17926,plain,
% 292.62/185.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s2, s3)) | node10(c_e_h_1, c_n, s2, s3) | node11(c_e_h_1, c_n, s2, s3))),
% 292.62/185.19 inference(quant_inst,[status(thm)],[])).
% 292.62/185.19 tff(17927,plain,
% 292.62/185.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s2, s3)) | node10(c_e_h_1, c_n, s2, s3) | node11(c_e_h_1, c_n, s2, s3)),
% 292.62/185.19 inference(modus_ponens,[status(thm)],[17926, 17925])).
% 292.62/185.19 tff(17928,plain,
% 292.62/185.19 (node10(c_e_h_1, c_n, s2, s3) | node11(c_e_h_1, c_n, s2, s3)),
% 292.62/185.19 inference(unit_resolution,[status(thm)],[17927, 5002, 318])).
% 292.62/185.19 tff(17929,plain,
% 292.62/185.19 (node10(c_e_h_1, c_n, s2, s3)),
% 292.62/185.19 inference(unit_resolution,[status(thm)],[17928, 17924])).
% 292.62/185.19 tff(17930,plain,
% 292.62/185.19 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s2) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s2) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2))),
% 292.62/185.19 inference(rewrite,[status(thm)],[])).
% 292.62/185.19 tff(17931,plain,
% 292.62/185.19 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s2) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2))),
% 292.62/185.19 inference(quant_inst,[status(thm)],[])).
% 292.62/185.19 tff(17932,plain,
% 292.62/185.19 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s2) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)),
% 292.62/185.19 inference(modus_ponens,[status(thm)],[17931, 17930])).
% 292.62/185.19 tff(17933,plain,
% 292.62/185.19 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s2) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)),
% 292.62/185.19 inference(unit_resolution,[status(thm)],[17932, 7868])).
% 292.62/185.19 tff(17934,plain,
% 292.62/185.19 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s2)),
% 292.62/185.19 inference(unit_resolution,[status(thm)],[17933, 14924])).
% 292.62/185.19 tff(17935,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s2)), introduced(assumption)).
% 292.62/185.19 tff(17936,plain,
% 292.62/185.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s2)) | (~node10(c_e_h_1, c_n, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s2)) | (~node10(c_e_h_1, c_n, s2, s3)))),
% 292.62/185.19 inference(rewrite,[status(thm)],[])).
% 292.62/185.19 tff(17937,plain,
% 292.62/185.19 (((~node10(c_e_h_1, c_n, s2, s3)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s2)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3)) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s2)) | (~node10(c_e_h_1, c_n, s2, s3)))),
% 292.62/185.19 inference(rewrite,[status(thm)],[])).
% 292.62/185.19 tff(17938,plain,
% 292.62/185.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s2, s3)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s2)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s2)) | (~node10(c_e_h_1, c_n, s2, s3))))),
% 292.62/185.19 inference(monotonicity,[status(thm)],[17937])).
% 292.62/185.19 tff(17939,plain,
% 292.62/185.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s2, s3)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s2)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s2)) | (~node10(c_e_h_1, c_n, s2, s3)))),
% 292.62/185.19 inference(transitivity,[status(thm)],[17938, 17936])).
% 292.62/185.19 tff(17940,plain,
% 292.62/185.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s2, s3)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s2)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3))),
% 292.62/185.19 inference(quant_inst,[status(thm)],[])).
% 292.62/185.19 tff(17941,plain,
% 292.62/185.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s2)) | (~node10(c_e_h_1, c_n, s2, s3))),
% 292.62/185.19 inference(modus_ponens,[status(thm)],[17940, 17939])).
% 292.62/185.19 tff(17942,plain,
% 292.62/185.19 ($false),
% 292.62/185.19 inference(unit_resolution,[status(thm)],[17941, 5718, 17914, 17935, 17934, 17929])).
% 292.62/185.19 tff(17943,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s2))), inference(lemma,lemma(discharge,[]))).
% 292.62/185.19 tff(17944,plain,
% 292.62/185.19 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3)),
% 292.62/185.19 inference(unit_resolution,[status(thm)],[17943, 17913])).
% 292.62/185.19 tff(17945,plain,
% 292.62/185.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4) | (~node11(c_e_h_1, c_n, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4) | (~node11(c_e_h_1, c_n, s3, s4)))),
% 292.62/185.20 inference(rewrite,[status(thm)],[])).
% 292.62/185.20 tff(17946,plain,
% 292.62/185.20 ((m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4) | (~node11(c_e_h_1, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4) | (~node11(c_e_h_1, c_n, s3, s4)))),
% 292.62/185.20 inference(rewrite,[status(thm)],[])).
% 292.62/185.20 tff(17947,plain,
% 292.62/185.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4) | (~node11(c_e_h_1, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4) | (~node11(c_e_h_1, c_n, s3, s4))))),
% 292.62/185.20 inference(monotonicity,[status(thm)],[17946])).
% 292.62/185.20 tff(17948,plain,
% 292.62/185.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4) | (~node11(c_e_h_1, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4) | (~node11(c_e_h_1, c_n, s3, s4)))),
% 292.62/185.20 inference(transitivity,[status(thm)],[17947, 17945])).
% 292.62/185.20 tff(17949,plain,
% 292.62/185.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4) | (~node11(c_e_h_1, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3)))),
% 292.62/185.20 inference(quant_inst,[status(thm)],[])).
% 292.62/185.20 tff(17950,plain,
% 292.62/185.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4) | (~node11(c_e_h_1, c_n, s3, s4))),
% 292.62/185.20 inference(modus_ponens,[status(thm)],[17949, 17948])).
% 292.62/185.20 tff(17951,plain,
% 292.62/185.20 ($false),
% 292.62/185.20 inference(unit_resolution,[status(thm)],[17950, 5742, 17944, 17907, 17908])).
% 292.62/185.20 tff(17952,plain,((~node11(c_e_h_1, c_n, s3, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)), inference(lemma,lemma(discharge,[]))).
% 292.62/185.20 tff(17953,plain,
% 292.62/185.20 (~node11(c_e_h_1, c_n, s3, s4)),
% 292.62/185.20 inference(unit_resolution,[status(thm)],[17952, 17907])).
% 292.62/185.20 tff(17954,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3)), introduced(assumption)).
% 292.62/185.20 tff(17955,plain,
% 292.62/185.20 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s3) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s3) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3))),
% 292.62/185.20 inference(rewrite,[status(thm)],[])).
% 292.62/185.20 tff(17956,plain,
% 292.62/185.20 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s3) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3))),
% 292.62/185.20 inference(quant_inst,[status(thm)],[])).
% 292.62/185.20 tff(17957,plain,
% 292.62/185.20 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s3) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)),
% 292.71/185.20 inference(modus_ponens,[status(thm)],[17956, 17955])).
% 292.71/185.20 tff(17958,plain,
% 292.71/185.20 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s3) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)),
% 292.71/185.20 inference(unit_resolution,[status(thm)],[17957, 7868])).
% 292.71/185.20 tff(17959,plain,
% 292.71/185.20 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s3)),
% 292.71/185.20 inference(unit_resolution,[status(thm)],[17958, 16392])).
% 292.71/185.20 tff(17960,assumption,(node10(c_e_h_1, c_n, s3, s4)), introduced(assumption)).
% 292.71/185.20 tff(17961,plain,
% 292.71/185.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4) | (~node10(c_e_h_1, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4) | (~node10(c_e_h_1, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s3)))),
% 292.71/185.20 inference(rewrite,[status(thm)],[])).
% 292.71/185.20 tff(17962,plain,
% 292.71/185.20 (((~node10(c_e_h_1, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4) | (~node10(c_e_h_1, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s3)))),
% 292.71/185.20 inference(rewrite,[status(thm)],[])).
% 292.71/185.20 tff(17963,plain,
% 292.71/185.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4) | (~node10(c_e_h_1, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s3))))),
% 292.71/185.20 inference(monotonicity,[status(thm)],[17962])).
% 292.71/185.20 tff(17964,plain,
% 292.71/185.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4) | (~node10(c_e_h_1, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s3)))),
% 292.71/185.20 inference(transitivity,[status(thm)],[17963, 17961])).
% 292.71/185.20 tff(17965,plain,
% 292.71/185.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4))),
% 292.71/185.20 inference(quant_inst,[status(thm)],[])).
% 292.71/185.20 tff(17966,plain,
% 292.71/185.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4) | (~node10(c_e_h_1, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s3))),
% 292.71/185.21 inference(modus_ponens,[status(thm)],[17965, 17964])).
% 292.71/185.21 tff(17967,plain,
% 292.71/185.21 ($false),
% 292.71/185.21 inference(unit_resolution,[status(thm)],[17966, 5718, 17907, 17960, 17959, 17954])).
% 292.71/185.21 tff(17968,plain,((~node10(c_e_h_1, c_n, s3, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3))), inference(lemma,lemma(discharge,[]))).
% 292.71/185.21 tff(17969,plain,
% 292.71/185.21 (~node10(c_e_h_1, c_n, s3, s4)),
% 292.71/185.21 inference(unit_resolution,[status(thm)],[17968, 17907, 17954])).
% 292.71/185.21 tff(17970,plain,
% 292.71/185.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s3, s4)) | node10(c_e_h_1, c_n, s3, s4) | node11(c_e_h_1, c_n, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s3, s4)) | node10(c_e_h_1, c_n, s3, s4) | node11(c_e_h_1, c_n, s3, s4))),
% 292.71/185.21 inference(rewrite,[status(thm)],[])).
% 292.71/185.21 tff(17971,plain,
% 292.71/185.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s3, s4)) | node10(c_e_h_1, c_n, s3, s4) | node11(c_e_h_1, c_n, s3, s4))),
% 292.71/185.21 inference(quant_inst,[status(thm)],[])).
% 292.71/185.21 tff(17972,plain,
% 292.71/185.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s3, s4)) | node10(c_e_h_1, c_n, s3, s4) | node11(c_e_h_1, c_n, s3, s4)),
% 292.71/185.21 inference(modus_ponens,[status(thm)],[17971, 17970])).
% 292.71/185.21 tff(17973,plain,
% 292.71/185.21 (node10(c_e_h_1, c_n, s3, s4) | node11(c_e_h_1, c_n, s3, s4)),
% 292.71/185.21 inference(unit_resolution,[status(thm)],[17972, 5002, 531])).
% 292.71/185.21 tff(17974,plain,
% 292.71/185.21 ($false),
% 292.71/185.21 inference(unit_resolution,[status(thm)],[17973, 17969, 17953])).
% 292.71/185.21 tff(17975,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s3))), inference(lemma,lemma(discharge,[]))).
% 292.71/185.21 tff(17976,plain,
% 292.71/185.21 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)),
% 292.71/185.21 inference(unit_resolution,[status(thm)],[17975, 17906])).
% 292.71/185.21 tff(17977,plain,
% 292.71/185.21 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)))),
% 292.71/185.21 inference(rewrite,[status(thm)],[])).
% 292.71/185.21 tff(17978,plain,
% 292.71/185.21 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)))),
% 292.71/185.21 inference(quant_inst,[status(thm)],[])).
% 292.71/185.21 tff(17979,plain,
% 292.71/185.21 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4))),
% 292.71/185.21 inference(modus_ponens,[status(thm)],[17978, 17977])).
% 292.71/185.21 tff(17980,plain,
% 292.71/185.21 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s4)),
% 292.71/185.21 inference(unit_resolution,[status(thm)],[17979, 4958, 17976])).
% 292.71/185.21 tff(17981,plain,
% 292.71/185.21 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s4)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s4)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s4))),
% 292.71/185.21 inference(rewrite,[status(thm)],[])).
% 292.71/185.21 tff(17982,plain,
% 292.71/185.21 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s4)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s4))),
% 292.71/185.21 inference(quant_inst,[status(thm)],[])).
% 292.71/185.21 tff(17983,plain,
% 292.71/185.21 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s4)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s4)),
% 292.71/185.21 inference(modus_ponens,[status(thm)],[17982, 17981])).
% 292.71/185.21 tff(17984,plain,
% 292.71/185.21 (~node9(c_e_h_1, c_m, s4)),
% 292.71/185.21 inference(unit_resolution,[status(thm)],[17983, 4972, 17980])).
% 292.71/185.21 tff(17985,assumption,(~node9(c_e_h_1, c_m, s4)), introduced(assumption)).
% 292.71/185.21 tff(17986,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)), introduced(assumption)).
% 292.71/185.21 tff(17987,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)), introduced(assumption)).
% 292.71/185.21 tff(17988,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)), introduced(assumption)).
% 292.71/185.21 tff(17989,assumption,(node11(c_e_h_1, c_m, s3, s4)), introduced(assumption)).
% 292.71/185.21 tff(17990,plain,
% 292.71/185.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)) | (~node11(c_e_h_1, c_m, s3, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)) | (~node11(c_e_h_1, c_m, s3, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3))),
% 292.71/185.21 inference(rewrite,[status(thm)],[])).
% 292.71/185.21 tff(17991,plain,
% 292.71/185.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)) | (~node11(c_e_h_1, c_m, s3, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3))),
% 292.71/185.21 inference(quant_inst,[status(thm)],[])).
% 292.71/185.21 tff(17992,plain,
% 292.71/185.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)) | (~node11(c_e_h_1, c_m, s3, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)),
% 292.71/185.21 inference(modus_ponens,[status(thm)],[17991, 17990])).
% 292.71/185.21 tff(17993,plain,
% 292.71/185.21 ($false),
% 292.71/185.21 inference(unit_resolution,[status(thm)],[17992, 5017, 17989, 17987, 17988])).
% 292.71/185.21 tff(17994,plain,((~node11(c_e_h_1, c_m, s3, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)), inference(lemma,lemma(discharge,[]))).
% 292.71/185.21 tff(17995,plain,
% 292.71/185.21 ((~node11(c_e_h_1, c_m, s3, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4))),
% 292.71/185.21 inference(unit_resolution,[status(thm)],[17994, 16392])).
% 292.71/185.21 tff(17996,plain,
% 292.71/185.21 (~node11(c_e_h_1, c_m, s3, s4)),
% 292.71/185.21 inference(unit_resolution,[status(thm)],[17995, 17987])).
% 292.71/185.21 tff(17997,plain,
% 292.71/185.21 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3)))),
% 292.71/185.21 inference(rewrite,[status(thm)],[])).
% 292.71/185.21 tff(17998,plain,
% 292.71/185.21 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3)))),
% 292.71/185.21 inference(quant_inst,[status(thm)],[])).
% 292.71/185.21 tff(17999,plain,
% 292.71/185.21 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s3))),
% 292.71/185.21 inference(modus_ponens,[status(thm)],[17998, 17997])).
% 292.71/185.21 tff(18000,plain,
% 292.71/185.21 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s3)),
% 292.71/185.21 inference(unit_resolution,[status(thm)],[17999, 4958, 17944])).
% 292.71/185.21 tff(18001,plain,
% 292.71/185.21 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s3)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s3)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s3))),
% 292.71/185.21 inference(rewrite,[status(thm)],[])).
% 292.71/185.21 tff(18002,plain,
% 292.71/185.21 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s3)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s3))),
% 292.71/185.21 inference(quant_inst,[status(thm)],[])).
% 292.71/185.21 tff(18003,plain,
% 292.71/185.21 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s3)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s3)),
% 292.71/185.21 inference(modus_ponens,[status(thm)],[18002, 18001])).
% 292.71/185.21 tff(18004,plain,
% 292.71/185.21 (~node9(c_e_h_1, c_m, s3)),
% 292.71/185.21 inference(unit_resolution,[status(thm)],[18003, 4972, 18000])).
% 292.71/185.21 tff(18005,assumption,(~node9(c_e_h_1, c_m, s3)), introduced(assumption)).
% 292.71/185.21 tff(18006,assumption,(node10(c_e_h_1, c_m, s3, s4)), introduced(assumption)).
% 292.71/185.21 tff(18007,plain,
% 292.71/185.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)) | (~node10(c_e_h_1, c_m, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_1, c_m, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)) | (~node10(c_e_h_1, c_m, s3, s4)))),
% 292.71/185.21 inference(rewrite,[status(thm)],[])).
% 292.71/185.21 tff(18008,plain,
% 292.71/185.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)) | (~node10(c_e_h_1, c_m, s3, s4)))),
% 292.71/185.21 inference(quant_inst,[status(thm)],[])).
% 292.71/185.21 tff(18009,plain,
% 292.71/185.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_1, c_m, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)) | (~node10(c_e_h_1, c_m, s3, s4))),
% 292.71/185.21 inference(modus_ponens,[status(thm)],[18008, 18007])).
% 292.71/185.21 tff(18010,plain,
% 292.71/185.21 ($false),
% 292.71/185.21 inference(unit_resolution,[status(thm)],[18009, 4986, 18006, 17987, 18005])).
% 292.71/185.21 tff(18011,plain,((~node10(c_e_h_1, c_m, s3, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)) | node9(c_e_h_1, c_m, s3)), inference(lemma,lemma(discharge,[]))).
% 292.71/185.21 tff(18012,plain,
% 292.71/185.21 ((~node10(c_e_h_1, c_m, s3, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4))),
% 292.71/185.21 inference(unit_resolution,[status(thm)],[18011, 18004])).
% 292.71/185.21 tff(18013,plain,
% 292.71/185.21 (~node10(c_e_h_1, c_m, s3, s4)),
% 292.71/185.21 inference(unit_resolution,[status(thm)],[18012, 17987])).
% 292.71/185.21 tff(18014,plain,
% 292.71/185.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s3, s4)) | node10(c_e_h_1, c_m, s3, s4) | node11(c_e_h_1, c_m, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s3, s4)) | node10(c_e_h_1, c_m, s3, s4) | node11(c_e_h_1, c_m, s3, s4))),
% 292.71/185.21 inference(rewrite,[status(thm)],[])).
% 292.71/185.21 tff(18015,plain,
% 292.71/185.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s3, s4)) | node10(c_e_h_1, c_m, s3, s4) | node11(c_e_h_1, c_m, s3, s4))),
% 292.71/185.21 inference(quant_inst,[status(thm)],[])).
% 292.71/185.21 tff(18016,plain,
% 292.71/185.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s3, s4)) | node10(c_e_h_1, c_m, s3, s4) | node11(c_e_h_1, c_m, s3, s4)),
% 292.71/185.21 inference(modus_ponens,[status(thm)],[18015, 18014])).
% 292.71/185.21 tff(18017,plain,
% 292.71/185.21 (node10(c_e_h_1, c_m, s3, s4) | node11(c_e_h_1, c_m, s3, s4)),
% 292.71/185.21 inference(unit_resolution,[status(thm)],[18016, 5002, 531])).
% 292.71/185.21 tff(18018,plain,
% 292.71/185.21 ($false),
% 292.71/185.21 inference(unit_resolution,[status(thm)],[18017, 18013, 17996])).
% 292.71/185.21 tff(18019,plain,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)), inference(lemma,lemma(discharge,[]))).
% 292.71/185.21 tff(18020,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)), introduced(assumption)).
% 292.71/185.21 tff(18021,assumption,(node11(c_e_h_1, c_m, s4, s5)), introduced(assumption)).
% 292.71/185.21 tff(18022,plain,
% 292.71/185.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)) | (~node11(c_e_h_1, c_m, s4, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)) | (~node11(c_e_h_1, c_m, s4, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4))),
% 292.71/185.22 inference(rewrite,[status(thm)],[])).
% 292.71/185.22 tff(18023,plain,
% 292.71/185.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)) | (~node11(c_e_h_1, c_m, s4, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4))),
% 292.71/185.22 inference(quant_inst,[status(thm)],[])).
% 292.71/185.22 tff(18024,plain,
% 292.71/185.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)) | (~node11(c_e_h_1, c_m, s4, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)),
% 292.71/185.22 inference(modus_ponens,[status(thm)],[18023, 18022])).
% 292.71/185.22 tff(18025,plain,
% 292.71/185.22 ($false),
% 292.71/185.22 inference(unit_resolution,[status(thm)],[18024, 5017, 18021, 18020, 17986])).
% 292.71/185.22 tff(18026,plain,((~node11(c_e_h_1, c_m, s4, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5))), inference(lemma,lemma(discharge,[]))).
% 292.71/185.22 tff(18027,plain,
% 292.71/185.22 (~node11(c_e_h_1, c_m, s4, s5)),
% 292.71/185.22 inference(unit_resolution,[status(thm)],[18026, 17986, 18019])).
% 292.71/185.22 tff(18028,plain,
% 292.71/185.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s4, s5)) | node10(c_e_h_1, c_m, s4, s5) | node11(c_e_h_1, c_m, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s4, s5)) | node10(c_e_h_1, c_m, s4, s5) | node11(c_e_h_1, c_m, s4, s5))),
% 292.71/185.22 inference(rewrite,[status(thm)],[])).
% 292.71/185.22 tff(18029,plain,
% 292.71/185.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s4, s5)) | node10(c_e_h_1, c_m, s4, s5) | node11(c_e_h_1, c_m, s4, s5))),
% 292.71/185.22 inference(quant_inst,[status(thm)],[])).
% 292.71/185.22 tff(18030,plain,
% 292.71/185.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s4, s5)) | node10(c_e_h_1, c_m, s4, s5) | node11(c_e_h_1, c_m, s4, s5)),
% 292.71/185.22 inference(modus_ponens,[status(thm)],[18029, 18028])).
% 292.71/185.22 tff(18031,plain,
% 292.71/185.22 (node10(c_e_h_1, c_m, s4, s5) | node11(c_e_h_1, c_m, s4, s5)),
% 292.71/185.22 inference(unit_resolution,[status(thm)],[18030, 5002, 1028])).
% 292.71/185.22 tff(18032,plain,
% 292.71/185.22 (node10(c_e_h_1, c_m, s4, s5)),
% 292.71/185.22 inference(unit_resolution,[status(thm)],[18031, 18027])).
% 292.71/185.22 tff(18033,plain,
% 292.71/185.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)) | (~node10(c_e_h_1, c_m, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_1, c_m, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)) | (~node10(c_e_h_1, c_m, s4, s5)))),
% 292.71/185.22 inference(rewrite,[status(thm)],[])).
% 292.71/185.22 tff(18034,plain,
% 292.71/185.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)) | (~node10(c_e_h_1, c_m, s4, s5)))),
% 292.71/185.22 inference(quant_inst,[status(thm)],[])).
% 292.71/185.22 tff(18035,plain,
% 292.71/185.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_1, c_m, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)) | (~node10(c_e_h_1, c_m, s4, s5))),
% 292.71/185.22 inference(modus_ponens,[status(thm)],[18034, 18033])).
% 292.71/185.22 tff(18036,plain,
% 292.71/185.22 ($false),
% 292.71/185.22 inference(unit_resolution,[status(thm)],[18035, 4986, 18032, 17986, 17985])).
% 292.71/185.22 tff(18037,plain,((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)) | node9(c_e_h_1, c_m, s4)), inference(lemma,lemma(discharge,[]))).
% 292.71/185.22 tff(18038,plain,
% 292.71/185.22 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)),
% 292.71/185.22 inference(unit_resolution,[status(thm)],[18037, 17984])).
% 292.71/185.22 tff(18039,assumption,(~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s4)), introduced(assumption)).
% 292.71/185.22 tff(18040,plain,
% 292.71/185.22 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s4) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s4) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4))),
% 292.71/185.22 inference(rewrite,[status(thm)],[])).
% 292.71/185.22 tff(18041,plain,
% 292.71/185.22 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s4) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4))),
% 292.71/185.22 inference(quant_inst,[status(thm)],[])).
% 292.71/185.22 tff(18042,plain,
% 292.71/185.22 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s4) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)),
% 292.71/185.22 inference(modus_ponens,[status(thm)],[18041, 18040])).
% 292.71/185.22 tff(18043,plain,
% 292.71/185.22 ($false),
% 292.71/185.22 inference(unit_resolution,[status(thm)],[18042, 7868, 18020, 18039])).
% 292.71/185.22 tff(18044,plain,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s4) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)), inference(lemma,lemma(discharge,[]))).
% 292.71/185.22 tff(18045,plain,
% 292.71/185.22 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s4)),
% 292.71/185.22 inference(unit_resolution,[status(thm)],[18044, 18019])).
% 292.71/185.22 tff(18046,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)), introduced(assumption)).
% 292.71/185.22 tff(18047,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5)), introduced(assumption)).
% 292.71/185.22 tff(18048,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)), introduced(assumption)).
% 292.71/185.22 tff(18049,plain,
% 292.71/185.22 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s5) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s5) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5))),
% 292.71/185.22 inference(rewrite,[status(thm)],[])).
% 292.71/185.22 tff(18050,plain,
% 292.71/185.22 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s5) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5))),
% 292.71/185.22 inference(quant_inst,[status(thm)],[])).
% 292.71/185.22 tff(18051,plain,
% 292.71/185.22 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s5) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)),
% 292.71/185.22 inference(modus_ponens,[status(thm)],[18050, 18049])).
% 292.71/185.22 tff(18052,plain,
% 292.71/185.22 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s5)),
% 292.71/185.22 inference(unit_resolution,[status(thm)],[18051, 7868, 18048])).
% 292.71/185.22 tff(18053,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s5)), introduced(assumption)).
% 292.71/185.22 tff(18054,assumption,(node10(c_e_h_1, c_n, s5, s6)), introduced(assumption)).
% 292.71/185.22 tff(18055,plain,
% 292.71/185.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s5)) | (~node10(c_e_h_1, c_n, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s5)) | (~node10(c_e_h_1, c_n, s5, s6)))),
% 292.71/185.22 inference(rewrite,[status(thm)],[])).
% 292.71/185.22 tff(18056,plain,
% 292.71/185.22 (((~node10(c_e_h_1, c_n, s5, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)) <=> ((~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s5)) | (~node10(c_e_h_1, c_n, s5, s6)))),
% 292.71/185.22 inference(rewrite,[status(thm)],[])).
% 292.71/185.22 tff(18057,plain,
% 292.71/185.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s5, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s5)) | (~node10(c_e_h_1, c_n, s5, s6))))),
% 292.71/185.22 inference(monotonicity,[status(thm)],[18056])).
% 292.71/185.22 tff(18058,plain,
% 292.71/185.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s5, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s5)) | (~node10(c_e_h_1, c_n, s5, s6)))),
% 292.71/185.22 inference(transitivity,[status(thm)],[18057, 18055])).
% 292.71/185.22 tff(18059,plain,
% 292.71/185.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s5, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6))),
% 292.71/185.22 inference(quant_inst,[status(thm)],[])).
% 292.71/185.22 tff(18060,plain,
% 292.71/185.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s5)) | (~node10(c_e_h_1, c_n, s5, s6))),
% 292.71/185.22 inference(modus_ponens,[status(thm)],[18059, 18058])).
% 292.71/185.22 tff(18061,plain,
% 292.71/185.22 ($false),
% 292.71/185.22 inference(unit_resolution,[status(thm)],[18060, 5718, 18047, 18046, 18054, 18053])).
% 292.71/185.22 tff(18062,plain,((~node10(c_e_h_1, c_n, s5, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s5))), inference(lemma,lemma(discharge,[]))).
% 292.71/185.22 tff(18063,plain,
% 292.71/185.22 (~node10(c_e_h_1, c_n, s5, s6)),
% 292.71/185.22 inference(unit_resolution,[status(thm)],[18062, 18052, 18046, 18047])).
% 292.71/185.22 tff(18064,plain,
% 292.71/185.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s5, s6)) | node10(c_e_h_1, c_n, s5, s6) | node11(c_e_h_1, c_n, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s5, s6)) | node10(c_e_h_1, c_n, s5, s6) | node11(c_e_h_1, c_n, s5, s6))),
% 292.71/185.22 inference(rewrite,[status(thm)],[])).
% 292.71/185.22 tff(18065,plain,
% 292.71/185.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s5, s6)) | node10(c_e_h_1, c_n, s5, s6) | node11(c_e_h_1, c_n, s5, s6))),
% 292.71/185.23 inference(quant_inst,[status(thm)],[])).
% 292.71/185.23 tff(18066,plain,
% 292.71/185.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s5, s6)) | node10(c_e_h_1, c_n, s5, s6) | node11(c_e_h_1, c_n, s5, s6)),
% 292.71/185.23 inference(modus_ponens,[status(thm)],[18065, 18064])).
% 292.71/185.23 tff(18067,plain,
% 292.71/185.23 (node10(c_e_h_1, c_n, s5, s6) | node11(c_e_h_1, c_n, s5, s6)),
% 292.71/185.23 inference(unit_resolution,[status(thm)],[18066, 5002, 1406])).
% 292.71/185.23 tff(18068,plain,
% 292.71/185.23 (node11(c_e_h_1, c_n, s5, s6)),
% 292.71/185.23 inference(unit_resolution,[status(thm)],[18067, 18063])).
% 292.71/185.23 tff(18069,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)), introduced(assumption)).
% 292.71/185.23 tff(18070,assumption,(node11(c_e_h_1, c_n, s5, s6)), introduced(assumption)).
% 292.71/185.23 tff(18071,plain,
% 292.71/185.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6) | (~node11(c_e_h_1, c_n, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6) | (~node11(c_e_h_1, c_n, s5, s6)))),
% 292.71/185.23 inference(rewrite,[status(thm)],[])).
% 292.71/185.23 tff(18072,plain,
% 292.71/185.23 ((m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6) | (~node11(c_e_h_1, c_n, s5, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6) | (~node11(c_e_h_1, c_n, s5, s6)))),
% 292.71/185.23 inference(rewrite,[status(thm)],[])).
% 292.71/185.23 tff(18073,plain,
% 292.71/185.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6) | (~node11(c_e_h_1, c_n, s5, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6) | (~node11(c_e_h_1, c_n, s5, s6))))),
% 292.71/185.23 inference(monotonicity,[status(thm)],[18072])).
% 292.71/185.23 tff(18074,plain,
% 292.71/185.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6) | (~node11(c_e_h_1, c_n, s5, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6) | (~node11(c_e_h_1, c_n, s5, s6)))),
% 292.71/185.23 inference(transitivity,[status(thm)],[18073, 18071])).
% 292.71/185.23 tff(18075,plain,
% 292.71/185.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6) | (~node11(c_e_h_1, c_n, s5, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)))),
% 292.71/185.23 inference(quant_inst,[status(thm)],[])).
% 292.71/185.23 tff(18076,plain,
% 292.71/185.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6) | (~node11(c_e_h_1, c_n, s5, s6))),
% 292.71/185.23 inference(modus_ponens,[status(thm)],[18075, 18074])).
% 292.71/185.23 tff(18077,plain,
% 292.71/185.23 ($false),
% 292.71/185.23 inference(unit_resolution,[status(thm)],[18076, 5742, 18046, 18070, 18069])).
% 292.71/185.23 tff(18078,plain,((~node11(c_e_h_1, c_n, s5, s6)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5))), inference(lemma,lemma(discharge,[]))).
% 292.71/185.23 tff(18079,plain,
% 292.71/185.23 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)),
% 292.71/185.23 inference(unit_resolution,[status(thm)],[18078, 18068, 18046])).
% 292.71/185.23 tff(18080,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)), introduced(assumption)).
% 292.71/185.23 tff(18081,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4)), introduced(assumption)).
% 292.71/185.23 tff(18082,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s4)), introduced(assumption)).
% 292.71/185.23 tff(18083,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)), introduced(assumption)).
% 292.71/185.23 tff(18084,assumption,(node10(c_e_h_1, c_n, s4, s5)), introduced(assumption)).
% 292.71/185.23 tff(18085,plain,
% 292.71/185.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s4)) | (~node10(c_e_h_1, c_n, s4, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s4)) | (~node10(c_e_h_1, c_n, s4, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5))),
% 292.71/185.23 inference(rewrite,[status(thm)],[])).
% 292.71/185.23 tff(18086,plain,
% 292.71/185.23 (((~node10(c_e_h_1, c_n, s4, s5)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)) <=> ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s4)) | (~node10(c_e_h_1, c_n, s4, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5))),
% 292.71/185.23 inference(rewrite,[status(thm)],[])).
% 292.71/185.23 tff(18087,plain,
% 292.71/185.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s4, s5)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s4)) | (~node10(c_e_h_1, c_n, s4, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)))),
% 292.71/185.23 inference(monotonicity,[status(thm)],[18086])).
% 292.71/185.23 tff(18088,plain,
% 292.71/185.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s4, s5)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s4)) | (~node10(c_e_h_1, c_n, s4, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5))),
% 292.71/185.23 inference(transitivity,[status(thm)],[18087, 18085])).
% 292.71/185.23 tff(18089,plain,
% 292.71/185.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s4, s5)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5))),
% 292.71/185.23 inference(quant_inst,[status(thm)],[])).
% 292.71/185.23 tff(18090,plain,
% 292.71/185.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s4)) | (~node10(c_e_h_1, c_n, s4, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)),
% 292.71/185.23 inference(modus_ponens,[status(thm)],[18089, 18088])).
% 292.71/185.23 tff(18091,plain,
% 292.71/185.23 ($false),
% 292.71/185.23 inference(unit_resolution,[status(thm)],[18090, 5718, 18084, 18081, 18082, 18083])).
% 292.71/185.23 tff(18092,plain,((~node10(c_e_h_1, c_n, s4, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)), inference(lemma,lemma(discharge,[]))).
% 292.71/185.23 tff(18093,plain,
% 292.71/185.23 (~node10(c_e_h_1, c_n, s4, s5)),
% 292.71/185.23 inference(unit_resolution,[status(thm)],[18092, 18082, 18081, 18079])).
% 292.71/185.23 tff(18094,plain,
% 292.71/185.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s4, s5)) | node10(c_e_h_1, c_n, s4, s5) | node11(c_e_h_1, c_n, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s4, s5)) | node10(c_e_h_1, c_n, s4, s5) | node11(c_e_h_1, c_n, s4, s5))),
% 292.71/185.23 inference(rewrite,[status(thm)],[])).
% 292.71/185.23 tff(18095,plain,
% 292.71/185.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s4, s5)) | node10(c_e_h_1, c_n, s4, s5) | node11(c_e_h_1, c_n, s4, s5))),
% 292.71/185.23 inference(quant_inst,[status(thm)],[])).
% 292.71/185.23 tff(18096,plain,
% 292.71/185.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s4, s5)) | node10(c_e_h_1, c_n, s4, s5) | node11(c_e_h_1, c_n, s4, s5)),
% 292.71/185.23 inference(modus_ponens,[status(thm)],[18095, 18094])).
% 292.71/185.23 tff(18097,plain,
% 292.71/185.23 (node10(c_e_h_1, c_n, s4, s5) | node11(c_e_h_1, c_n, s4, s5)),
% 292.71/185.23 inference(unit_resolution,[status(thm)],[18096, 5002, 1028])).
% 292.71/185.23 tff(18098,plain,
% 292.71/185.23 (node11(c_e_h_1, c_n, s4, s5)),
% 292.71/185.23 inference(unit_resolution,[status(thm)],[18097, 18093])).
% 292.71/185.23 tff(18099,plain,
% 292.71/185.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5) | (~node11(c_e_h_1, c_n, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5) | (~node11(c_e_h_1, c_n, s4, s5)))),
% 292.71/185.23 inference(rewrite,[status(thm)],[])).
% 292.71/185.23 tff(18100,plain,
% 292.71/185.23 ((m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5) | (~node11(c_e_h_1, c_n, s4, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5) | (~node11(c_e_h_1, c_n, s4, s5)))),
% 292.71/185.23 inference(rewrite,[status(thm)],[])).
% 292.71/185.23 tff(18101,plain,
% 292.71/185.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5) | (~node11(c_e_h_1, c_n, s4, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5) | (~node11(c_e_h_1, c_n, s4, s5))))),
% 292.71/185.23 inference(monotonicity,[status(thm)],[18100])).
% 292.71/185.23 tff(18102,plain,
% 292.71/185.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5) | (~node11(c_e_h_1, c_n, s4, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5) | (~node11(c_e_h_1, c_n, s4, s5)))),
% 292.71/185.23 inference(transitivity,[status(thm)],[18101, 18099])).
% 292.71/185.24 tff(18103,plain,
% 292.71/185.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5) | (~node11(c_e_h_1, c_n, s4, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)))),
% 292.71/185.24 inference(quant_inst,[status(thm)],[])).
% 292.71/185.24 tff(18104,plain,
% 292.71/185.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5) | (~node11(c_e_h_1, c_n, s4, s5))),
% 292.71/185.24 inference(modus_ponens,[status(thm)],[18103, 18102])).
% 292.71/185.24 tff(18105,plain,
% 292.71/185.24 ($false),
% 292.71/185.24 inference(unit_resolution,[status(thm)],[18104, 5742, 18098, 18080, 18079])).
% 292.71/185.24 tff(18106,plain,((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)), inference(lemma,lemma(discharge,[]))).
% 292.71/185.24 tff(18107,plain,
% 292.71/185.24 ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)),
% 292.71/185.24 inference(unit_resolution,[status(thm)],[18106, 18045])).
% 292.71/185.24 tff(18108,plain,
% 292.71/185.24 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5))),
% 292.71/185.24 inference(unit_resolution,[status(thm)],[18107, 17976, 18038, 17899])).
% 292.71/185.24 tff(18109,plain,
% 292.71/185.24 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)),
% 292.71/185.24 inference(unit_resolution,[status(thm)],[18108, 17892])).
% 292.71/185.24 tff(18110,assumption,(node11(c_e_h_1, c_n, s4, s5)), introduced(assumption)).
% 292.71/185.24 tff(18111,plain,
% 292.71/185.24 ($false),
% 292.71/185.24 inference(unit_resolution,[status(thm)],[18104, 5742, 18110, 18080, 18083])).
% 292.71/185.24 tff(18112,plain,((~node11(c_e_h_1, c_n, s4, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)), inference(lemma,lemma(discharge,[]))).
% 292.71/185.24 tff(18113,plain,
% 292.71/185.24 (~node11(c_e_h_1, c_n, s4, s5)),
% 292.71/185.24 inference(unit_resolution,[status(thm)],[18112, 18083, 18080])).
% 292.71/185.24 tff(18114,plain,
% 292.71/185.24 (~node10(c_e_h_1, c_n, s4, s5)),
% 292.71/185.24 inference(unit_resolution,[status(thm)],[18092, 18083, 18045, 18081])).
% 292.71/185.24 tff(18115,plain,
% 292.71/185.24 ($false),
% 292.71/185.24 inference(unit_resolution,[status(thm)],[18097, 18114, 18113])).
% 292.71/185.24 tff(18116,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4))), inference(lemma,lemma(discharge,[]))).
% 292.71/185.24 tff(18117,plain,
% 292.71/185.24 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)),
% 292.71/185.24 inference(unit_resolution,[status(thm)],[18116, 17899, 17976])).
% 292.71/185.24 tff(18118,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s5)), introduced(assumption)).
% 292.71/185.24 tff(18119,plain,
% 292.71/185.24 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)))),
% 292.71/185.24 inference(rewrite,[status(thm)],[])).
% 292.71/185.24 tff(18120,plain,
% 292.71/185.24 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)))),
% 292.71/185.24 inference(quant_inst,[status(thm)],[])).
% 292.71/185.24 tff(18121,plain,
% 292.71/185.24 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5))),
% 292.71/185.24 inference(modus_ponens,[status(thm)],[18120, 18119])).
% 292.71/185.24 tff(18122,plain,
% 292.71/185.24 ($false),
% 292.71/185.24 inference(unit_resolution,[status(thm)],[18121, 4958, 18118, 18069])).
% 292.71/185.24 tff(18123,plain,((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5))), inference(lemma,lemma(discharge,[]))).
% 292.71/185.24 tff(18124,plain,
% 292.71/185.24 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s5)),
% 292.71/185.24 inference(unit_resolution,[status(thm)],[18123, 18117])).
% 292.71/185.24 tff(18125,assumption,(node9(c_e_h_1, c_m, s5)), introduced(assumption)).
% 292.71/185.24 tff(18126,assumption,(~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s5)), introduced(assumption)).
% 292.71/185.24 tff(18127,plain,
% 292.71/185.24 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s5)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s5)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s5))),
% 292.71/185.24 inference(rewrite,[status(thm)],[])).
% 292.71/185.24 tff(18128,plain,
% 292.71/185.24 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s5)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s5))),
% 292.71/185.24 inference(quant_inst,[status(thm)],[])).
% 292.71/185.24 tff(18129,plain,
% 292.71/185.24 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s5)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s5)),
% 292.71/185.24 inference(modus_ponens,[status(thm)],[18128, 18127])).
% 292.71/185.24 tff(18130,plain,
% 292.71/185.24 ($false),
% 292.71/185.24 inference(unit_resolution,[status(thm)],[18129, 4972, 18126, 18125])).
% 292.71/185.24 tff(18131,plain,((~node9(c_e_h_1, c_m, s5)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s5)), inference(lemma,lemma(discharge,[]))).
% 292.71/185.24 tff(18132,plain,
% 292.71/185.24 (~node9(c_e_h_1, c_m, s5)),
% 292.71/185.24 inference(unit_resolution,[status(thm)],[18131, 18124])).
% 292.71/185.24 tff(18133,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)), introduced(assumption)).
% 292.71/185.24 tff(18134,assumption,(node11(c_e_h_1, c_m, s5, s6)), introduced(assumption)).
% 292.71/185.24 tff(18135,plain,
% 292.71/185.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)) | (~node11(c_e_h_1, c_m, s5, s6)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)) | (~node11(c_e_h_1, c_m, s5, s6)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5))),
% 292.71/185.24 inference(rewrite,[status(thm)],[])).
% 292.71/185.24 tff(18136,plain,
% 292.71/185.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)) | (~node11(c_e_h_1, c_m, s5, s6)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5))),
% 292.71/185.24 inference(quant_inst,[status(thm)],[])).
% 292.71/185.24 tff(18137,plain,
% 292.71/185.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)) | (~node11(c_e_h_1, c_m, s5, s6)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)),
% 292.71/185.24 inference(modus_ponens,[status(thm)],[18136, 18135])).
% 292.71/185.24 tff(18138,plain,
% 292.71/185.24 ($false),
% 292.71/185.24 inference(unit_resolution,[status(thm)],[18137, 5017, 18133, 18134, 18048])).
% 292.71/185.24 tff(18139,plain,((~node11(c_e_h_1, c_m, s5, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)), inference(lemma,lemma(discharge,[]))).
% 292.71/185.24 tff(18140,plain,
% 292.71/185.24 (~node11(c_e_h_1, c_m, s5, s6)),
% 292.71/185.24 inference(unit_resolution,[status(thm)],[18139, 18133, 18048])).
% 292.71/185.24 tff(18141,assumption,(~node9(c_e_h_1, c_m, s5)), introduced(assumption)).
% 292.71/185.24 tff(18142,assumption,(node10(c_e_h_1, c_m, s5, s6)), introduced(assumption)).
% 292.71/185.24 tff(18143,plain,
% 292.71/185.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s5) | (~node10(c_e_h_1, c_m, s5, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_1, c_m, s5) | (~node10(c_e_h_1, c_m, s5, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)))),
% 292.71/185.24 inference(rewrite,[status(thm)],[])).
% 292.71/185.24 tff(18144,plain,
% 292.71/185.24 ((node9(c_e_h_1, c_m, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)) | (~node10(c_e_h_1, c_m, s5, s6))) <=> (node9(c_e_h_1, c_m, s5) | (~node10(c_e_h_1, c_m, s5, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)))),
% 292.71/185.24 inference(rewrite,[status(thm)],[])).
% 292.71/185.24 tff(18145,plain,
% 292.71/185.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)) | (~node10(c_e_h_1, c_m, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s5) | (~node10(c_e_h_1, c_m, s5, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6))))),
% 292.71/185.24 inference(monotonicity,[status(thm)],[18144])).
% 292.71/185.24 tff(18146,plain,
% 292.71/185.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)) | (~node10(c_e_h_1, c_m, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_1, c_m, s5) | (~node10(c_e_h_1, c_m, s5, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)))),
% 292.71/185.24 inference(transitivity,[status(thm)],[18145, 18143])).
% 292.71/185.24 tff(18147,plain,
% 292.71/185.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)) | (~node10(c_e_h_1, c_m, s5, s6)))),
% 292.71/185.24 inference(quant_inst,[status(thm)],[])).
% 292.71/185.24 tff(18148,plain,
% 292.71/185.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_1, c_m, s5) | (~node10(c_e_h_1, c_m, s5, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6))),
% 292.71/185.24 inference(modus_ponens,[status(thm)],[18147, 18146])).
% 292.71/185.24 tff(18149,plain,
% 292.71/185.24 ($false),
% 292.71/185.24 inference(unit_resolution,[status(thm)],[18148, 4986, 18133, 18142, 18141])).
% 292.71/185.24 tff(18150,plain,((~node10(c_e_h_1, c_m, s5, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)) | node9(c_e_h_1, c_m, s5)), inference(lemma,lemma(discharge,[]))).
% 292.71/185.24 tff(18151,plain,
% 292.71/185.24 (~node10(c_e_h_1, c_m, s5, s6)),
% 292.71/185.24 inference(unit_resolution,[status(thm)],[18150, 18133, 18141])).
% 292.71/185.24 tff(18152,plain,
% 292.71/185.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s5, s6)) | node10(c_e_h_1, c_m, s5, s6) | node11(c_e_h_1, c_m, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s5, s6)) | node10(c_e_h_1, c_m, s5, s6) | node11(c_e_h_1, c_m, s5, s6))),
% 292.71/185.24 inference(rewrite,[status(thm)],[])).
% 292.71/185.24 tff(18153,plain,
% 292.71/185.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s5, s6)) | node10(c_e_h_1, c_m, s5, s6) | node11(c_e_h_1, c_m, s5, s6))),
% 292.71/185.24 inference(quant_inst,[status(thm)],[])).
% 292.71/185.24 tff(18154,plain,
% 292.71/185.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s5, s6)) | node10(c_e_h_1, c_m, s5, s6) | node11(c_e_h_1, c_m, s5, s6)),
% 292.71/185.24 inference(modus_ponens,[status(thm)],[18153, 18152])).
% 292.71/185.24 tff(18155,plain,
% 292.71/185.24 (node10(c_e_h_1, c_m, s5, s6) | node11(c_e_h_1, c_m, s5, s6)),
% 292.71/185.24 inference(unit_resolution,[status(thm)],[18154, 5002, 1406])).
% 292.71/185.24 tff(18156,plain,
% 292.71/185.24 ($false),
% 292.71/185.24 inference(unit_resolution,[status(thm)],[18155, 18151, 18140])).
% 292.71/185.24 tff(18157,plain,((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)) | node9(c_e_h_1, c_m, s5) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)), inference(lemma,lemma(discharge,[]))).
% 292.71/185.24 tff(18158,plain,
% 292.71/185.24 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)),
% 292.71/185.25 inference(unit_resolution,[status(thm)],[18157, 18132, 18038])).
% 292.71/185.25 tff(18159,plain,
% 292.71/185.25 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s6) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s6) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6))),
% 292.71/185.25 inference(rewrite,[status(thm)],[])).
% 292.71/185.25 tff(18160,plain,
% 292.71/185.25 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s6) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6))),
% 292.71/185.25 inference(quant_inst,[status(thm)],[])).
% 292.71/185.25 tff(18161,plain,
% 292.71/185.25 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s6) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)),
% 292.71/185.25 inference(modus_ponens,[status(thm)],[18160, 18159])).
% 292.71/185.25 tff(18162,plain,
% 292.71/185.25 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s6) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)),
% 292.71/185.25 inference(unit_resolution,[status(thm)],[18161, 7868])).
% 292.71/185.25 tff(18163,plain,
% 292.71/185.25 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s6)),
% 292.71/185.25 inference(unit_resolution,[status(thm)],[18162, 18158])).
% 292.71/185.25 tff(18164,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s6)), introduced(assumption)).
% 292.71/185.25 tff(18165,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6)), introduced(assumption)).
% 292.71/185.25 tff(18166,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)), introduced(assumption)).
% 292.71/185.25 tff(18167,assumption,(node10(c_e_h_1, c_n, s6, s7)), introduced(assumption)).
% 292.71/185.25 tff(18168,plain,
% 292.71/185.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6)) | (~node10(c_e_h_1, c_n, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6)) | (~node10(c_e_h_1, c_n, s6, s7)))),
% 292.71/185.25 inference(rewrite,[status(thm)],[])).
% 292.71/185.25 tff(18169,plain,
% 292.71/185.25 (((~node10(c_e_h_1, c_n, s6, s7)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6)) | (~node10(c_e_h_1, c_n, s6, s7)))),
% 292.71/185.25 inference(rewrite,[status(thm)],[])).
% 292.71/185.25 tff(18170,plain,
% 292.71/185.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s6, s7)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6)) | (~node10(c_e_h_1, c_n, s6, s7))))),
% 292.71/185.25 inference(monotonicity,[status(thm)],[18169])).
% 292.71/185.25 tff(18171,plain,
% 292.71/185.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s6, s7)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6)) | (~node10(c_e_h_1, c_n, s6, s7)))),
% 292.71/185.25 inference(transitivity,[status(thm)],[18170, 18168])).
% 292.71/185.25 tff(18172,plain,
% 292.71/185.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s6, s7)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7))),
% 292.71/185.25 inference(quant_inst,[status(thm)],[])).
% 292.71/185.25 tff(18173,plain,
% 292.71/185.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6)) | (~node10(c_e_h_1, c_n, s6, s7))),
% 292.71/185.25 inference(modus_ponens,[status(thm)],[18172, 18171])).
% 292.71/185.25 tff(18174,plain,
% 292.71/185.25 ($false),
% 292.71/185.25 inference(unit_resolution,[status(thm)],[18173, 5718, 18166, 18164, 18165, 18167])).
% 292.71/185.25 tff(18175,plain,((~node10(c_e_h_1, c_n, s6, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6))), inference(lemma,lemma(discharge,[]))).
% 292.71/185.25 tff(18176,plain,
% 292.71/185.25 (~node10(c_e_h_1, c_n, s6, s7)),
% 292.71/185.25 inference(unit_resolution,[status(thm)],[18175, 18166, 18165, 18164])).
% 292.71/185.25 tff(18177,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)), introduced(assumption)).
% 292.71/185.25 tff(18178,assumption,(node11(c_e_h_1, c_n, s6, s7)), introduced(assumption)).
% 292.71/185.25 tff(18179,plain,
% 292.71/185.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)) | (~node11(c_e_h_1, c_n, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)) | (~node11(c_e_h_1, c_n, s6, s7)))),
% 292.71/185.25 inference(rewrite,[status(thm)],[])).
% 292.71/185.25 tff(18180,plain,
% 292.71/185.25 ((m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | (~node11(c_e_h_1, c_n, s6, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6))) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)) | (~node11(c_e_h_1, c_n, s6, s7)))),
% 292.71/185.25 inference(rewrite,[status(thm)],[])).
% 292.71/185.25 tff(18181,plain,
% 292.71/185.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | (~node11(c_e_h_1, c_n, s6, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)) | (~node11(c_e_h_1, c_n, s6, s7))))),
% 292.71/185.25 inference(monotonicity,[status(thm)],[18180])).
% 292.71/185.25 tff(18182,plain,
% 292.71/185.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | (~node11(c_e_h_1, c_n, s6, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)) | (~node11(c_e_h_1, c_n, s6, s7)))),
% 292.71/185.25 inference(transitivity,[status(thm)],[18181, 18179])).
% 292.71/185.25 tff(18183,plain,
% 292.71/185.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | (~node11(c_e_h_1, c_n, s6, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)))),
% 292.71/185.25 inference(quant_inst,[status(thm)],[])).
% 292.71/185.25 tff(18184,plain,
% 292.71/185.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)) | (~node11(c_e_h_1, c_n, s6, s7))),
% 292.71/185.25 inference(modus_ponens,[status(thm)],[18183, 18182])).
% 292.71/185.25 tff(18185,plain,
% 292.71/185.25 ($false),
% 292.71/185.25 inference(unit_resolution,[status(thm)],[18184, 5742, 18166, 18177, 18178])).
% 292.71/185.25 tff(18186,plain,((~node11(c_e_h_1, c_n, s6, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6))), inference(lemma,lemma(discharge,[]))).
% 292.71/185.25 tff(18187,plain,
% 292.71/185.25 (~node11(c_e_h_1, c_n, s6, s7)),
% 292.71/185.25 inference(unit_resolution,[status(thm)],[18186, 18166, 18177])).
% 292.71/185.25 tff(18188,plain,
% 292.71/185.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s6, s7)) | node10(c_e_h_1, c_n, s6, s7) | node11(c_e_h_1, c_n, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s6, s7)) | node10(c_e_h_1, c_n, s6, s7) | node11(c_e_h_1, c_n, s6, s7))),
% 292.71/185.25 inference(rewrite,[status(thm)],[])).
% 292.71/185.25 tff(18189,plain,
% 292.71/185.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s6, s7)) | node10(c_e_h_1, c_n, s6, s7) | node11(c_e_h_1, c_n, s6, s7))),
% 292.71/185.25 inference(quant_inst,[status(thm)],[])).
% 292.71/185.25 tff(18190,plain,
% 292.71/185.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s6, s7)) | node10(c_e_h_1, c_n, s6, s7) | node11(c_e_h_1, c_n, s6, s7)),
% 292.71/185.25 inference(modus_ponens,[status(thm)],[18189, 18188])).
% 292.71/185.25 tff(18191,plain,
% 292.71/185.25 (node10(c_e_h_1, c_n, s6, s7) | node11(c_e_h_1, c_n, s6, s7)),
% 292.71/185.25 inference(unit_resolution,[status(thm)],[18190, 5002, 1844])).
% 292.71/185.25 tff(18192,plain,
% 292.71/185.25 ($false),
% 292.71/185.25 inference(unit_resolution,[status(thm)],[18191, 18187, 18176])).
% 292.71/185.25 tff(18193,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s6))), inference(lemma,lemma(discharge,[]))).
% 292.71/185.25 tff(18194,plain,
% 292.71/185.25 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6))),
% 292.71/185.25 inference(unit_resolution,[status(thm)],[18193, 18163])).
% 292.71/185.25 tff(18195,plain,
% 292.71/185.25 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6))),
% 292.71/185.25 inference(unit_resolution,[status(thm)],[18194, 18109])).
% 292.71/185.25 tff(18196,plain,
% 292.71/185.25 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)),
% 292.71/185.25 inference(unit_resolution,[status(thm)],[18195, 17887])).
% 292.71/185.25 tff(18197,plain,
% 292.71/185.25 (^[I0: $i, X: $i] : refl(((~m_and_h_gate_h_init_v_out(I0, c_n, X)) | m_and_h_gate_v_in2(I0, c_p, X)) <=> ((~m_and_h_gate_h_init_v_out(I0, c_n, X)) | m_and_h_gate_v_in2(I0, c_p, X)))),
% 292.71/185.25 inference(bind,[status(th)],[])).
% 292.71/185.25 tff(18198,plain,
% 292.71/185.25 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_n, X)) | m_and_h_gate_v_in2(I0, c_p, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_n, X)) | m_and_h_gate_v_in2(I0, c_p, X))),
% 292.71/185.25 inference(quant_intro,[status(thm)],[18197])).
% 292.71/185.25 tff(18199,plain,
% 292.71/185.25 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_n, X)) | m_and_h_gate_v_in2(I0, c_p, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_n, X)) | m_and_h_gate_v_in2(I0, c_p, X))),
% 292.71/185.25 inference(rewrite,[status(thm)],[])).
% 292.71/185.25 tff(18200,plain,
% 292.71/185.25 (^[I0: $i, X: $i] : rewrite((m_and_h_gate_v_in2(I0, c_p, X) | (~m_and_h_gate_h_init_v_out(I0, c_n, X))) <=> ((~m_and_h_gate_h_init_v_out(I0, c_n, X)) | m_and_h_gate_v_in2(I0, c_p, X)))),
% 292.71/185.26 inference(bind,[status(th)],[])).
% 292.71/185.26 tff(18201,plain,
% 292.71/185.26 (![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_p, X) | (~m_and_h_gate_h_init_v_out(I0, c_n, X))) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_n, X)) | m_and_h_gate_v_in2(I0, c_p, X))),
% 292.71/185.26 inference(quant_intro,[status(thm)],[18200])).
% 292.71/185.26 tff(18202,axiom,(![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_p, X) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_65')).
% 292.71/185.26 tff(18203,plain,
% 292.71/185.26 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_n, X)) | m_and_h_gate_v_in2(I0, c_p, X))),
% 292.71/185.26 inference(modus_ponens,[status(thm)],[18202, 18201])).
% 292.71/185.26 tff(18204,plain,
% 292.71/185.26 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_n, X)) | m_and_h_gate_v_in2(I0, c_p, X))),
% 292.71/185.26 inference(modus_ponens,[status(thm)],[18203, 18199])).
% 292.71/185.26 tff(18205,plain,(
% 292.71/185.26 ![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_n, X)) | m_and_h_gate_v_in2(I0, c_p, X))),
% 292.71/185.26 inference(skolemize,[status(sab)],[18204])).
% 292.71/185.26 tff(18206,plain,
% 292.71/185.26 (![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_n, X)) | m_and_h_gate_v_in2(I0, c_p, X))),
% 292.71/185.26 inference(modus_ponens,[status(thm)],[18205, 18198])).
% 292.71/185.26 tff(18207,plain,
% 292.71/185.26 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_n, X)) | m_and_h_gate_v_in2(I0, c_p, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)) | m_and_h_gate_v_in2(c_e_h_1, c_p, s7))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_n, X)) | m_and_h_gate_v_in2(I0, c_p, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)) | m_and_h_gate_v_in2(c_e_h_1, c_p, s7))),
% 292.71/185.26 inference(rewrite,[status(thm)],[])).
% 292.71/185.26 tff(18208,plain,
% 292.71/185.26 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_n, X)) | m_and_h_gate_v_in2(I0, c_p, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)) | m_and_h_gate_v_in2(c_e_h_1, c_p, s7))),
% 292.71/185.26 inference(quant_inst,[status(thm)],[])).
% 292.71/185.26 tff(18209,plain,
% 292.71/185.26 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_n, X)) | m_and_h_gate_v_in2(I0, c_p, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)) | m_and_h_gate_v_in2(c_e_h_1, c_p, s7)),
% 292.71/185.26 inference(modus_ponens,[status(thm)],[18208, 18207])).
% 292.71/185.26 tff(18210,plain,
% 292.71/185.26 (m_and_h_gate_v_in2(c_e_h_1, c_p, s7)),
% 292.71/185.26 inference(unit_resolution,[status(thm)],[18209, 18206, 18196])).
% 292.71/185.26 tff(18211,assumption,(node13(c_e_h_3, c_b, s7, s8)), introduced(assumption)).
% 292.71/185.26 tff(18212,plain,
% 292.71/185.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_b, s8)) | (~node13(c_e_h_3, c_b, s7, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s8)) | (~node13(c_e_h_3, c_b, s7, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s7))),
% 292.71/185.26 inference(rewrite,[status(thm)],[])).
% 292.71/185.26 tff(18213,plain,
% 292.71/185.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_b, s8)) | (~node13(c_e_h_3, c_b, s7, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s7))),
% 292.71/185.26 inference(quant_inst,[status(thm)],[])).
% 292.71/185.26 tff(18214,plain,
% 292.71/185.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s8)) | (~node13(c_e_h_3, c_b, s7, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s7)),
% 292.71/185.26 inference(modus_ponens,[status(thm)],[18213, 18212])).
% 292.71/185.26 tff(18215,plain,
% 292.71/185.26 ($false),
% 292.71/185.26 inference(unit_resolution,[status(thm)],[18214, 423, 18211, 17249, 17096])).
% 292.71/185.26 tff(18216,plain,((~node13(c_e_h_3, c_b, s7, s8)) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s7)), inference(lemma,lemma(discharge,[]))).
% 292.71/185.26 tff(18217,plain,
% 292.71/185.26 (~node13(c_e_h_3, c_b, s7, s8)),
% 292.71/185.26 inference(unit_resolution,[status(thm)],[18216, 17249, 17096])).
% 292.71/185.26 tff(18218,assumption,(~m_mutex_h_half_v_inp(c_e_h_3, c_b, s7)), introduced(assumption)).
% 292.71/185.26 tff(18219,assumption,(node12(c_e_h_3, c_b, s7, s8)), introduced(assumption)).
% 292.71/185.26 tff(18220,plain,
% 292.71/185.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_3, c_b, s7) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s8)) | (~node12(c_e_h_3, c_b, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s7) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s8)) | (~node12(c_e_h_3, c_b, s7, s8)))),
% 292.71/185.26 inference(rewrite,[status(thm)],[])).
% 292.71/185.26 tff(18221,plain,
% 292.71/185.26 (((~node12(c_e_h_3, c_b, s7, s8)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s7) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s8))) <=> (m_mutex_h_half_v_inp(c_e_h_3, c_b, s7) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s8)) | (~node12(c_e_h_3, c_b, s7, s8)))),
% 292.71/185.26 inference(rewrite,[status(thm)],[])).
% 292.71/185.26 tff(18222,plain,
% 292.71/185.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_b, s7, s8)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s7) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_3, c_b, s7) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s8)) | (~node12(c_e_h_3, c_b, s7, s8))))),
% 292.71/185.26 inference(monotonicity,[status(thm)],[18221])).
% 292.71/185.26 tff(18223,plain,
% 292.71/185.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_b, s7, s8)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s7) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s7) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s8)) | (~node12(c_e_h_3, c_b, s7, s8)))),
% 292.71/185.26 inference(transitivity,[status(thm)],[18222, 18220])).
% 292.71/185.26 tff(18224,plain,
% 292.71/185.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_b, s7, s8)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s7) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s8)))),
% 292.71/185.26 inference(quant_inst,[status(thm)],[])).
% 292.71/185.26 tff(18225,plain,
% 292.71/185.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s7) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s8)) | (~node12(c_e_h_3, c_b, s7, s8))),
% 292.71/185.26 inference(modus_ponens,[status(thm)],[18224, 18223])).
% 292.71/185.26 tff(18226,plain,
% 292.71/185.26 ($false),
% 292.71/185.26 inference(unit_resolution,[status(thm)],[18225, 454, 18218, 18219, 17249])).
% 292.71/185.26 tff(18227,plain,((~node12(c_e_h_3, c_b, s7, s8)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s7) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s8))), inference(lemma,lemma(discharge,[]))).
% 292.71/185.26 tff(18228,plain,
% 292.71/185.26 (~node12(c_e_h_3, c_b, s7, s8)),
% 292.71/185.26 inference(unit_resolution,[status(thm)],[18227, 17249, 18218])).
% 292.71/185.26 tff(18229,plain,
% 292.71/185.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s7, s8)) | node12(c_e_h_3, c_b, s7, s8) | node13(c_e_h_3, c_b, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s7, s8)) | node12(c_e_h_3, c_b, s7, s8) | node13(c_e_h_3, c_b, s7, s8))),
% 292.71/185.26 inference(rewrite,[status(thm)],[])).
% 292.71/185.26 tff(18230,plain,
% 292.71/185.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s7, s8)) | node12(c_e_h_3, c_b, s7, s8) | node13(c_e_h_3, c_b, s7, s8))),
% 292.71/185.26 inference(quant_inst,[status(thm)],[])).
% 292.71/185.26 tff(18231,plain,
% 292.71/185.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s7, s8)) | node12(c_e_h_3, c_b, s7, s8) | node13(c_e_h_3, c_b, s7, s8)),
% 292.71/185.26 inference(modus_ponens,[status(thm)],[18230, 18229])).
% 292.71/185.26 tff(18232,plain,
% 292.71/185.26 (node12(c_e_h_3, c_b, s7, s8) | node13(c_e_h_3, c_b, s7, s8)),
% 292.71/185.26 inference(unit_resolution,[status(thm)],[18231, 439, 1938])).
% 292.71/185.26 tff(18233,plain,
% 292.71/185.26 ($false),
% 292.71/185.26 inference(unit_resolution,[status(thm)],[18232, 18228, 18217])).
% 292.71/185.26 tff(18234,plain,((~m_mutex_h_half_v_out(c_e_h_3, c_b, s8)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s7) | m_mutex_h_half_v_out(c_e_h_3, c_b, s7)), inference(lemma,lemma(discharge,[]))).
% 292.71/185.26 tff(18235,plain,
% 292.71/185.26 (m_mutex_h_half_v_inp(c_e_h_3, c_b, s7)),
% 292.71/185.26 inference(unit_resolution,[status(thm)],[18234, 17248, 17096])).
% 292.71/185.26 tff(18236,plain,
% 292.71/185.26 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node1(c_e_h_3, c_e_h_1, s7))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node1(c_e_h_3, c_e_h_1, s7))),
% 292.71/185.26 inference(rewrite,[status(thm)],[])).
% 292.71/185.26 tff(18237,plain,
% 292.71/185.26 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node1(c_e_h_3, c_e_h_1, s7))),
% 292.71/185.26 inference(quant_inst,[status(thm)],[])).
% 292.71/185.26 tff(18238,plain,
% 292.71/185.26 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node1(c_e_h_3, c_e_h_1, s7)),
% 292.71/185.26 inference(modus_ponens,[status(thm)],[18237, 18236])).
% 292.71/185.26 tff(18239,plain,
% 292.71/185.26 (node1(c_e_h_3, c_e_h_1, s7)),
% 292.71/185.26 inference(unit_resolution,[status(thm)],[18238, 2922, 2919])).
% 292.71/185.26 tff(18240,plain,
% 292.71/185.26 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_b, s7)) | m_cell_v_req(c_e_h_1, s7) | (~node1(c_e_h_3, c_e_h_1, s7)))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s7)) | m_cell_v_req(c_e_h_1, s7) | (~node1(c_e_h_3, c_e_h_1, s7)))),
% 292.71/185.26 inference(rewrite,[status(thm)],[])).
% 292.71/185.26 tff(18241,plain,
% 292.71/185.26 (((~node1(c_e_h_3, c_e_h_1, s7)) | m_cell_v_req(c_e_h_1, s7) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s7))) <=> ((~m_mutex_h_half_v_inp(c_e_h_3, c_b, s7)) | m_cell_v_req(c_e_h_1, s7) | (~node1(c_e_h_3, c_e_h_1, s7)))),
% 292.71/185.26 inference(rewrite,[status(thm)],[])).
% 292.71/185.26 tff(18242,plain,
% 292.71/185.26 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_3, c_e_h_1, s7)) | m_cell_v_req(c_e_h_1, s7) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s7)))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_b, s7)) | m_cell_v_req(c_e_h_1, s7) | (~node1(c_e_h_3, c_e_h_1, s7))))),
% 292.71/185.26 inference(monotonicity,[status(thm)],[18241])).
% 292.71/185.26 tff(18243,plain,
% 292.71/185.26 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_3, c_e_h_1, s7)) | m_cell_v_req(c_e_h_1, s7) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s7)))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s7)) | m_cell_v_req(c_e_h_1, s7) | (~node1(c_e_h_3, c_e_h_1, s7)))),
% 292.71/185.26 inference(transitivity,[status(thm)],[18242, 18240])).
% 292.71/185.26 tff(18244,plain,
% 292.71/185.26 ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_3, c_e_h_1, s7)) | m_cell_v_req(c_e_h_1, s7) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s7)))),
% 292.71/185.26 inference(quant_inst,[status(thm)],[])).
% 292.71/185.26 tff(18245,plain,
% 292.71/185.26 ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s7)) | m_cell_v_req(c_e_h_1, s7) | (~node1(c_e_h_3, c_e_h_1, s7))),
% 292.71/185.27 inference(modus_ponens,[status(thm)],[18244, 18243])).
% 292.71/185.27 tff(18246,plain,
% 292.71/185.27 ((~m_mutex_h_half_v_inp(c_e_h_3, c_b, s7)) | m_cell_v_req(c_e_h_1, s7)),
% 292.71/185.27 inference(unit_resolution,[status(thm)],[18245, 2936, 18239])).
% 292.71/185.27 tff(18247,plain,
% 292.71/185.27 (m_cell_v_req(c_e_h_1, s7)),
% 292.71/185.27 inference(unit_resolution,[status(thm)],[18246, 18235])).
% 292.71/185.27 tff(18248,assumption,(m_cell_v_req(c_e_h_1, s7)), introduced(assumption)).
% 292.71/185.27 tff(18249,plain,
% 292.71/185.27 (((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | ((~m_cell_v_req(c_e_h_1, s7)) | m_and_h_gate_v_out(c_e_h_1, c_p, s7))) <=> ((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | (~m_cell_v_req(c_e_h_1, s7)) | m_and_h_gate_v_out(c_e_h_1, c_p, s7))),
% 292.71/185.27 inference(rewrite,[status(thm)],[])).
% 292.71/185.27 tff(18250,plain,
% 292.71/185.27 ((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | ((~m_cell_v_req(c_e_h_1, s7)) | m_and_h_gate_v_out(c_e_h_1, c_p, s7))),
% 292.71/185.27 inference(quant_inst,[status(thm)],[])).
% 292.71/185.27 tff(18251,plain,
% 292.71/185.27 ((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | (~m_cell_v_req(c_e_h_1, s7)) | m_and_h_gate_v_out(c_e_h_1, c_p, s7)),
% 292.71/185.27 inference(modus_ponens,[status(thm)],[18250, 18249])).
% 292.71/185.27 tff(18252,plain,
% 292.71/185.27 ($false),
% 292.71/185.27 inference(unit_resolution,[status(thm)],[18251, 2908, 18248, 15796])).
% 292.71/185.27 tff(18253,plain,((~m_cell_v_req(c_e_h_1, s7)) | m_and_h_gate_v_out(c_e_h_1, c_p, s7)), inference(lemma,lemma(discharge,[]))).
% 292.71/185.27 tff(18254,plain,
% 292.71/185.27 (m_and_h_gate_v_out(c_e_h_1, c_p, s7)),
% 292.71/185.27 inference(unit_resolution,[status(thm)],[18253, 18247])).
% 292.71/185.27 tff(18255,plain,
% 292.71/185.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_p, s7)) | m_and_h_gate_v_out(c_e_h_1, c_p, s8) | (~node22(c_e_h_1, c_p, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s7)) | m_and_h_gate_v_out(c_e_h_1, c_p, s8) | (~node22(c_e_h_1, c_p, s7, s8)))),
% 292.71/185.27 inference(rewrite,[status(thm)],[])).
% 292.71/185.27 tff(18256,plain,
% 292.71/185.27 ((m_and_h_gate_v_out(c_e_h_1, c_p, s8) | (~node22(c_e_h_1, c_p, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s7))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_p, s7)) | m_and_h_gate_v_out(c_e_h_1, c_p, s8) | (~node22(c_e_h_1, c_p, s7, s8)))),
% 292.71/185.27 inference(rewrite,[status(thm)],[])).
% 292.71/185.27 tff(18257,plain,
% 292.71/185.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_1, c_p, s8) | (~node22(c_e_h_1, c_p, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_p, s7)) | m_and_h_gate_v_out(c_e_h_1, c_p, s8) | (~node22(c_e_h_1, c_p, s7, s8))))),
% 292.71/185.27 inference(monotonicity,[status(thm)],[18256])).
% 292.71/185.27 tff(18258,plain,
% 292.71/185.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_1, c_p, s8) | (~node22(c_e_h_1, c_p, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s7)) | m_and_h_gate_v_out(c_e_h_1, c_p, s8) | (~node22(c_e_h_1, c_p, s7, s8)))),
% 292.71/185.27 inference(transitivity,[status(thm)],[18257, 18255])).
% 292.71/185.27 tff(18259,plain,
% 292.71/185.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_1, c_p, s8) | (~node22(c_e_h_1, c_p, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s7)))),
% 292.71/185.27 inference(quant_inst,[status(thm)],[])).
% 292.71/185.27 tff(18260,plain,
% 292.71/185.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s7)) | m_and_h_gate_v_out(c_e_h_1, c_p, s8) | (~node22(c_e_h_1, c_p, s7, s8))),
% 292.71/185.27 inference(modus_ponens,[status(thm)],[18259, 18258])).
% 292.71/185.27 tff(18261,plain,
% 292.71/185.27 ($false),
% 292.71/185.27 inference(unit_resolution,[status(thm)],[18260, 5871, 15797, 15805, 15866])).
% 292.71/185.27 tff(18262,plain,((~node22(c_e_h_1, c_p, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s7)) | m_and_h_gate_v_out(c_e_h_1, c_p, s8)), inference(lemma,lemma(discharge,[]))).
% 292.71/185.27 tff(18263,plain,
% 292.71/185.27 (~node22(c_e_h_1, c_p, s7, s8)),
% 292.71/185.27 inference(unit_resolution,[status(thm)],[18262, 17304, 18254])).
% 292.71/185.27 tff(18264,plain,
% 292.71/185.27 (node21(c_e_h_1, c_p, s7, s8)),
% 292.71/185.27 inference(unit_resolution,[status(thm)],[15794, 18263])).
% 292.71/185.27 tff(18265,plain,
% 292.71/185.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (m_and_h_gate_v_out(c_e_h_1, c_p, s8) | (~m_and_h_gate_v_in2(c_e_h_1, c_p, s7)) | (~node21(c_e_h_1, c_p, s7, s8)) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | m_and_h_gate_v_out(c_e_h_1, c_p, s8) | (~m_and_h_gate_v_in2(c_e_h_1, c_p, s7)) | (~node21(c_e_h_1, c_p, s7, s8)) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s7)))),
% 292.71/185.27 inference(rewrite,[status(thm)],[])).
% 292.71/185.27 tff(18266,plain,
% 292.71/185.27 (((~node21(c_e_h_1, c_p, s7, s8)) | (~m_and_h_gate_v_in2(c_e_h_1, c_p, s7)) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s7)) | m_and_h_gate_v_out(c_e_h_1, c_p, s8)) <=> (m_and_h_gate_v_out(c_e_h_1, c_p, s8) | (~m_and_h_gate_v_in2(c_e_h_1, c_p, s7)) | (~node21(c_e_h_1, c_p, s7, s8)) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s7)))),
% 292.71/185.27 inference(rewrite,[status(thm)],[])).
% 292.71/185.27 tff(18267,plain,
% 292.71/185.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_1, c_p, s7, s8)) | (~m_and_h_gate_v_in2(c_e_h_1, c_p, s7)) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s7)) | m_and_h_gate_v_out(c_e_h_1, c_p, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (m_and_h_gate_v_out(c_e_h_1, c_p, s8) | (~m_and_h_gate_v_in2(c_e_h_1, c_p, s7)) | (~node21(c_e_h_1, c_p, s7, s8)) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s7))))),
% 292.71/185.27 inference(monotonicity,[status(thm)],[18266])).
% 292.71/185.27 tff(18268,plain,
% 292.71/185.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_1, c_p, s7, s8)) | (~m_and_h_gate_v_in2(c_e_h_1, c_p, s7)) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s7)) | m_and_h_gate_v_out(c_e_h_1, c_p, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | m_and_h_gate_v_out(c_e_h_1, c_p, s8) | (~m_and_h_gate_v_in2(c_e_h_1, c_p, s7)) | (~node21(c_e_h_1, c_p, s7, s8)) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s7)))),
% 292.71/185.27 inference(transitivity,[status(thm)],[18267, 18265])).
% 292.71/185.27 tff(18269,plain,
% 292.71/185.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_1, c_p, s7, s8)) | (~m_and_h_gate_v_in2(c_e_h_1, c_p, s7)) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s7)) | m_and_h_gate_v_out(c_e_h_1, c_p, s8))),
% 292.71/185.27 inference(quant_inst,[status(thm)],[])).
% 292.71/185.27 tff(18270,plain,
% 292.71/185.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | m_and_h_gate_v_out(c_e_h_1, c_p, s8) | (~m_and_h_gate_v_in2(c_e_h_1, c_p, s7)) | (~node21(c_e_h_1, c_p, s7, s8)) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s7))),
% 292.71/185.27 inference(modus_ponens,[status(thm)],[18269, 18268])).
% 292.71/185.27 tff(18271,plain,
% 292.71/185.27 (~m_and_h_gate_v_in1(c_e_h_1, c_p, s7)),
% 292.71/185.27 inference(unit_resolution,[status(thm)],[18270, 5851, 18264, 18210, 17304])).
% 292.71/185.27 tff(18272,assumption,(~m_and_h_gate_v_in1(c_e_h_1, c_p, s7)), introduced(assumption)).
% 292.71/185.27 tff(18273,plain,
% 292.71/185.27 (^[I0: $i, X: $i] : refl(((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_p, X)) <=> ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_p, X)))),
% 292.71/185.27 inference(bind,[status(th)],[])).
% 292.71/185.27 tff(18274,plain,
% 292.71/185.27 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_p, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_p, X))),
% 292.71/185.27 inference(quant_intro,[status(thm)],[18273])).
% 292.71/185.27 tff(18275,plain,
% 292.71/185.27 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_p, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_p, X))),
% 292.71/185.27 inference(rewrite,[status(thm)],[])).
% 292.71/185.27 tff(18276,plain,
% 292.71/185.27 (^[I0: $i, X: $i] : rewrite((m_and_h_gate_v_in1(I0, c_p, X) | (~m_and_h_gate_v_out(I0, c_k, X))) <=> ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_p, X)))),
% 292.71/185.27 inference(bind,[status(th)],[])).
% 292.71/185.27 tff(18277,plain,
% 292.71/185.27 (![I0: $i, X: $i] : (m_and_h_gate_v_in1(I0, c_p, X) | (~m_and_h_gate_v_out(I0, c_k, X))) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_p, X))),
% 292.71/185.27 inference(quant_intro,[status(thm)],[18276])).
% 292.71/185.27 tff(18278,axiom,(![I0: $i, X: $i] : (m_and_h_gate_v_in1(I0, c_p, X) | (~m_and_h_gate_v_out(I0, c_k, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_63')).
% 292.71/185.27 tff(18279,plain,
% 292.71/185.27 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_p, X))),
% 292.71/185.27 inference(modus_ponens,[status(thm)],[18278, 18277])).
% 292.71/185.27 tff(18280,plain,
% 292.71/185.27 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_p, X))),
% 292.71/185.27 inference(modus_ponens,[status(thm)],[18279, 18275])).
% 292.71/185.27 tff(18281,plain,(
% 292.71/185.27 ![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_p, X))),
% 292.71/185.27 inference(skolemize,[status(sab)],[18280])).
% 292.71/185.27 tff(18282,plain,
% 292.71/185.27 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_p, X))),
% 292.71/185.27 inference(modus_ponens,[status(thm)],[18281, 18274])).
% 292.71/185.27 tff(18283,plain,
% 292.71/185.27 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_p, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_k, s7)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s7))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_p, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s7)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s7))),
% 292.71/185.27 inference(rewrite,[status(thm)],[])).
% 292.71/185.27 tff(18284,plain,
% 292.71/185.27 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_p, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_k, s7)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s7))),
% 292.71/185.27 inference(quant_inst,[status(thm)],[])).
% 292.71/185.27 tff(18285,plain,
% 292.71/185.27 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_p, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s7)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s7)),
% 292.71/185.27 inference(modus_ponens,[status(thm)],[18284, 18283])).
% 292.71/185.27 tff(18286,plain,
% 292.71/185.27 ($false),
% 292.71/185.27 inference(unit_resolution,[status(thm)],[18285, 18282, 15405, 18272])).
% 292.71/185.27 tff(18287,plain,((~m_and_h_gate_v_out(c_e_h_1, c_k, s7)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s7)), inference(lemma,lemma(discharge,[]))).
% 292.71/185.27 tff(18288,plain,
% 292.71/185.27 (~m_and_h_gate_v_out(c_e_h_1, c_k, s7)),
% 292.71/185.27 inference(unit_resolution,[status(thm)],[18287, 18271])).
% 292.71/185.27 tff(18289,plain,
% 292.71/185.27 (~node20(c_e_h_1, c_p, s5)),
% 292.71/185.27 inference(unit_resolution,[status(thm)],[15695, 17063])).
% 292.71/185.27 tff(18290,plain,
% 292.71/185.27 (~m_and_h_gate_v_out(c_e_h_1, c_p, s6)),
% 292.71/185.27 inference(unit_resolution,[status(thm)],[15765, 18289])).
% 292.71/185.27 tff(18291,plain,
% 292.71/185.27 (node20(c_e_h_1, c_p, s6)),
% 292.71/185.27 inference(unit_resolution,[status(thm)],[15825, 18290, 15805])).
% 292.71/185.27 tff(18292,assumption,(~m_and_h_gate_v_in1(c_e_h_1, c_p, s6)), introduced(assumption)).
% 292.71/185.27 tff(18293,assumption,(node20(c_e_h_1, c_p, s6)), introduced(assumption)).
% 292.71/185.28 tff(18294,plain,
% 292.71/185.28 ($false),
% 292.71/185.28 inference(unit_resolution,[status(thm)],[15829, 38, 18293, 18292])).
% 292.71/185.28 tff(18295,plain,((~node20(c_e_h_1, c_p, s6)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s6)), inference(lemma,lemma(discharge,[]))).
% 292.71/185.28 tff(18296,plain,
% 292.71/185.28 (m_and_h_gate_v_in1(c_e_h_1, c_p, s6)),
% 292.71/185.28 inference(unit_resolution,[status(thm)],[18295, 18291])).
% 292.71/185.28 tff(18297,assumption,(m_and_h_gate_v_in1(c_e_h_1, c_p, s6)), introduced(assumption)).
% 292.71/185.28 tff(18298,plain,
% 292.71/185.28 ($false),
% 292.71/185.28 inference(unit_resolution,[status(thm)],[15833, 3033, 15407, 18297])).
% 292.71/185.28 tff(18299,plain,((~m_and_h_gate_v_in1(c_e_h_1, c_p, s6)) | m_and_h_gate_v_out(c_e_h_1, c_k, s6)), inference(lemma,lemma(discharge,[]))).
% 292.71/185.28 tff(18300,plain,
% 292.71/185.28 (m_and_h_gate_v_out(c_e_h_1, c_k, s6)),
% 292.71/185.28 inference(unit_resolution,[status(thm)],[18299, 18296])).
% 292.71/185.28 tff(18301,plain,
% 292.71/185.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_k, s6)) | (~node22(c_e_h_1, c_k, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_k, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s6)) | (~node22(c_e_h_1, c_k, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_k, s7))),
% 292.71/185.28 inference(rewrite,[status(thm)],[])).
% 292.71/185.28 tff(18302,plain,
% 292.71/185.28 ((m_and_h_gate_v_out(c_e_h_1, c_k, s7) | (~node22(c_e_h_1, c_k, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s6))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_k, s6)) | (~node22(c_e_h_1, c_k, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_k, s7))),
% 292.71/185.28 inference(rewrite,[status(thm)],[])).
% 292.71/185.28 tff(18303,plain,
% 292.71/185.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_1, c_k, s7) | (~node22(c_e_h_1, c_k, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_k, s6)) | (~node22(c_e_h_1, c_k, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_k, s7)))),
% 292.71/185.28 inference(monotonicity,[status(thm)],[18302])).
% 292.71/185.28 tff(18304,plain,
% 292.71/185.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_1, c_k, s7) | (~node22(c_e_h_1, c_k, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s6)) | (~node22(c_e_h_1, c_k, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_k, s7))),
% 292.71/185.28 inference(transitivity,[status(thm)],[18303, 18301])).
% 292.71/185.28 tff(18305,plain,
% 292.71/185.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_1, c_k, s7) | (~node22(c_e_h_1, c_k, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s6)))),
% 292.71/185.28 inference(quant_inst,[status(thm)],[])).
% 292.71/185.28 tff(18306,plain,
% 292.71/185.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s6)) | (~node22(c_e_h_1, c_k, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_k, s7)),
% 292.71/185.28 inference(modus_ponens,[status(thm)],[18305, 18304])).
% 292.71/185.28 tff(18307,plain,
% 292.71/185.28 ($false),
% 292.71/185.28 inference(unit_resolution,[status(thm)],[18306, 5871, 15408, 15429, 15905])).
% 292.71/185.28 tff(18308,plain,((~node22(c_e_h_1, c_k, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s6)) | m_and_h_gate_v_out(c_e_h_1, c_k, s7)), inference(lemma,lemma(discharge,[]))).
% 292.71/185.28 tff(18309,plain,
% 292.71/185.28 (~node22(c_e_h_1, c_k, s6, s7)),
% 292.71/185.28 inference(unit_resolution,[status(thm)],[18308, 18300, 15905])).
% 292.71/185.28 tff(18310,plain,
% 292.71/185.28 (node21(c_e_h_1, c_k, s6, s7)),
% 292.71/185.28 inference(unit_resolution,[status(thm)],[15418, 18309])).
% 292.71/185.28 tff(18311,assumption,(node21(c_e_h_1, c_k, s6, s7)), introduced(assumption)).
% 292.71/185.28 tff(18312,assumption,(m_c_h_element_v_in2(c_e_h_1, c_h, s5)), introduced(assumption)).
% 292.71/185.28 tff(18313,assumption,(m_or_h_gate_v_out(c_e_h_1, c_j, s5)), introduced(assumption)).
% 292.71/185.28 tff(18314,assumption,(m_or_h_gate_v_out(c_e_h_1, c_j, s4)), introduced(assumption)).
% 292.71/185.28 tff(18315,assumption,(~m_or_h_gate_v_out(c_e_h_1, c_j, s3)), introduced(assumption)).
% 292.71/185.28 tff(18316,assumption,(node6(c_e_h_1, c_j, s3, s4)), introduced(assumption)).
% 292.71/185.28 tff(18317,plain,
% 292.71/185.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s4)) | (~node6(c_e_h_1, c_j, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s4)) | (~node6(c_e_h_1, c_j, s3, s4)))),
% 292.71/185.28 inference(rewrite,[status(thm)],[])).
% 292.71/185.28 tff(18318,plain,
% 292.71/185.28 (((~node6(c_e_h_1, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s4)) | m_or_h_gate_v_out(c_e_h_1, c_j, s3)) <=> (m_or_h_gate_v_out(c_e_h_1, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s4)) | (~node6(c_e_h_1, c_j, s3, s4)))),
% 292.71/185.28 inference(rewrite,[status(thm)],[])).
% 292.71/185.28 tff(18319,plain,
% 292.71/185.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s4)) | m_or_h_gate_v_out(c_e_h_1, c_j, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s4)) | (~node6(c_e_h_1, c_j, s3, s4))))),
% 292.71/185.28 inference(monotonicity,[status(thm)],[18318])).
% 292.71/185.28 tff(18320,plain,
% 292.71/185.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s4)) | m_or_h_gate_v_out(c_e_h_1, c_j, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s4)) | (~node6(c_e_h_1, c_j, s3, s4)))),
% 292.71/185.28 inference(transitivity,[status(thm)],[18319, 18317])).
% 292.71/185.28 tff(18321,plain,
% 292.71/185.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s4)) | m_or_h_gate_v_out(c_e_h_1, c_j, s3))),
% 292.71/185.28 inference(quant_inst,[status(thm)],[])).
% 292.71/185.28 tff(18322,plain,
% 292.71/185.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s4)) | (~node6(c_e_h_1, c_j, s3, s4))),
% 292.71/185.28 inference(modus_ponens,[status(thm)],[18321, 18320])).
% 292.71/185.28 tff(18323,plain,
% 292.71/185.28 ($false),
% 292.71/185.28 inference(unit_resolution,[status(thm)],[18322, 1121, 18316, 18314, 18315])).
% 292.71/185.28 tff(18324,plain,((~node6(c_e_h_1, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s4)) | m_or_h_gate_v_out(c_e_h_1, c_j, s3)), inference(lemma,lemma(discharge,[]))).
% 292.71/185.28 tff(18325,plain,
% 292.71/185.28 ((~node6(c_e_h_1, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s4))),
% 292.71/185.28 inference(unit_resolution,[status(thm)],[18324, 17381])).
% 292.71/185.28 tff(18326,plain,
% 292.71/185.28 (~node6(c_e_h_1, c_j, s3, s4)),
% 292.71/185.28 inference(unit_resolution,[status(thm)],[18325, 18314])).
% 292.71/185.28 tff(18327,plain,
% 292.71/185.28 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s3)) | m_cell_v_ack(c_e_h_1, s3))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s3)) | m_cell_v_ack(c_e_h_1, s3))),
% 292.71/185.28 inference(rewrite,[status(thm)],[])).
% 292.71/185.28 tff(18328,plain,
% 292.71/185.28 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s3)) | m_cell_v_ack(c_e_h_1, s3))),
% 292.79/185.28 inference(quant_inst,[status(thm)],[])).
% 292.79/185.28 tff(18329,plain,
% 292.79/185.28 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s3)) | m_cell_v_ack(c_e_h_1, s3)),
% 292.79/185.28 inference(modus_ponens,[status(thm)],[18328, 18327])).
% 292.79/185.28 tff(18330,plain,
% 292.79/185.28 (~m_or_h_gate_v_in2(c_e_h_1, c_j, s3)),
% 292.79/185.28 inference(unit_resolution,[status(thm)],[18329, 1085, 5814])).
% 292.79/185.28 tff(18331,assumption,(~m_or_h_gate_v_in2(c_e_h_1, c_j, s3)), introduced(assumption)).
% 292.79/185.28 tff(18332,assumption,(m_and_h_gate_v_out(c_e_h_1, c_l, s3)), introduced(assumption)).
% 292.79/185.28 tff(18333,assumption,(node21(c_e_h_1, c_l, s2, s3)), introduced(assumption)).
% 292.79/185.28 tff(18334,plain,
% 292.79/185.28 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2))),
% 292.79/185.28 inference(rewrite,[status(thm)],[])).
% 292.79/185.28 tff(18335,plain,
% 292.79/185.28 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2))),
% 292.79/185.28 inference(quant_inst,[status(thm)],[])).
% 292.79/185.28 tff(18336,plain,
% 292.79/185.28 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s2)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s2)),
% 292.79/185.28 inference(modus_ponens,[status(thm)],[18335, 18334])).
% 292.79/185.28 tff(18337,plain,
% 292.79/185.28 (~m_and_h_gate_v_in2(c_e_h_1, c_l, s2)),
% 292.79/185.28 inference(unit_resolution,[status(thm)],[18336, 4549, 14924])).
% 292.79/185.28 tff(18338,plain,
% 292.79/185.28 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s2)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s2)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s2))),
% 292.79/185.28 inference(rewrite,[status(thm)],[])).
% 292.79/185.28 tff(18339,plain,
% 292.79/185.28 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s2)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s2))),
% 292.79/185.28 inference(quant_inst,[status(thm)],[])).
% 292.79/185.28 tff(18340,plain,
% 292.79/185.28 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s2)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s2)),
% 292.79/185.28 inference(modus_ponens,[status(thm)],[18339, 18338])).
% 292.79/185.28 tff(18341,plain,
% 292.79/185.28 (~node20(c_e_h_1, c_l, s2)),
% 292.79/185.28 inference(unit_resolution,[status(thm)],[18340, 4563, 18337])).
% 292.79/185.28 tff(18342,plain,
% 292.79/185.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s3)) | (~node21(c_e_h_1, c_l, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s3)) | (~node21(c_e_h_1, c_l, s2, s3)))),
% 292.79/185.28 inference(rewrite,[status(thm)],[])).
% 292.79/185.28 tff(18343,plain,
% 292.79/185.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s3)) | (~node21(c_e_h_1, c_l, s2, s3)))),
% 292.79/185.28 inference(quant_inst,[status(thm)],[])).
% 292.79/185.28 tff(18344,plain,
% 292.79/185.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s2) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s3)) | (~node21(c_e_h_1, c_l, s2, s3))),
% 292.79/185.28 inference(modus_ponens,[status(thm)],[18343, 18342])).
% 292.79/185.28 tff(18345,plain,
% 292.79/185.28 ($false),
% 292.79/185.28 inference(unit_resolution,[status(thm)],[18344, 52, 18341, 18333, 18332])).
% 292.79/185.28 tff(18346,plain,((~node21(c_e_h_1, c_l, s2, s3)) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s3))), inference(lemma,lemma(discharge,[]))).
% 292.79/185.29 tff(18347,plain,
% 292.79/185.29 (~node21(c_e_h_1, c_l, s2, s3)),
% 292.79/185.29 inference(unit_resolution,[status(thm)],[18346, 18332])).
% 292.79/185.29 tff(18348,plain,
% 292.79/185.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_1, c_l, s2, s3) | node22(c_e_h_1, c_l, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_1, c_l, s2, s3) | node22(c_e_h_1, c_l, s2, s3))),
% 292.79/185.29 inference(rewrite,[status(thm)],[])).
% 292.79/185.29 tff(18349,plain,
% 292.79/185.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s2, s3)) | node21(c_e_h_1, c_l, s2, s3) | node22(c_e_h_1, c_l, s2, s3))),
% 292.79/185.29 inference(quant_inst,[status(thm)],[])).
% 292.79/185.29 tff(18350,plain,
% 292.79/185.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s2, s3)) | node21(c_e_h_1, c_l, s2, s3) | node22(c_e_h_1, c_l, s2, s3)),
% 292.79/185.29 inference(modus_ponens,[status(thm)],[18349, 18348])).
% 292.79/185.29 tff(18351,plain,
% 292.79/185.29 (node21(c_e_h_1, c_l, s2, s3) | node22(c_e_h_1, c_l, s2, s3)),
% 292.79/185.29 inference(unit_resolution,[status(thm)],[18350, 82, 318])).
% 292.79/185.29 tff(18352,plain,
% 292.79/185.29 (node22(c_e_h_1, c_l, s2, s3)),
% 292.79/185.29 inference(unit_resolution,[status(thm)],[18351, 18347])).
% 292.79/185.29 tff(18353,plain,
% 292.79/185.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s3)) | (~node22(c_e_h_1, c_l, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_l, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s3)) | (~node22(c_e_h_1, c_l, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_l, s2))),
% 292.79/185.29 inference(rewrite,[status(thm)],[])).
% 292.79/185.29 tff(18354,plain,
% 292.79/185.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s3)) | (~node22(c_e_h_1, c_l, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_l, s2))),
% 292.79/185.29 inference(quant_inst,[status(thm)],[])).
% 292.79/185.29 tff(18355,plain,
% 292.79/185.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s3)) | (~node22(c_e_h_1, c_l, s2, s3)) | m_and_h_gate_v_out(c_e_h_1, c_l, s2)),
% 292.79/185.29 inference(modus_ponens,[status(thm)],[18354, 18353])).
% 292.79/185.29 tff(18356,plain,
% 292.79/185.29 ($false),
% 292.79/185.29 inference(unit_resolution,[status(thm)],[18355, 108, 18352, 17355, 18332])).
% 292.79/185.29 tff(18357,plain,(~m_and_h_gate_v_out(c_e_h_1, c_l, s3)), inference(lemma,lemma(discharge,[]))).
% 292.79/185.29 tff(18358,plain,
% 292.79/185.29 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s3)) | m_and_h_gate_v_out(c_e_h_1, c_l, s3))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s3)) | m_and_h_gate_v_out(c_e_h_1, c_l, s3))),
% 292.79/185.29 inference(rewrite,[status(thm)],[])).
% 292.79/185.29 tff(18359,plain,
% 292.79/185.29 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s3)) | m_and_h_gate_v_out(c_e_h_1, c_l, s3))),
% 292.79/185.29 inference(quant_inst,[status(thm)],[])).
% 292.79/185.29 tff(18360,plain,
% 292.79/185.29 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s3)) | m_and_h_gate_v_out(c_e_h_1, c_l, s3)),
% 292.79/185.29 inference(modus_ponens,[status(thm)],[18359, 18358])).
% 292.79/185.29 tff(18361,plain,
% 292.79/185.29 (~m_or_h_gate_v_in1(c_e_h_1, c_j, s3)),
% 292.79/185.29 inference(unit_resolution,[status(thm)],[18360, 1100, 18357])).
% 292.79/185.29 tff(18362,assumption,(node5(c_e_h_1, c_j, s3, s4)), introduced(assumption)).
% 292.79/185.29 tff(18363,plain,
% 292.79/185.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s4)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s3) | (~node5(c_e_h_1, c_j, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in1(c_e_h_1, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s4)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s3) | (~node5(c_e_h_1, c_j, s3, s4)))),
% 292.79/185.29 inference(rewrite,[status(thm)],[])).
% 292.79/185.29 tff(18364,plain,
% 292.79/185.29 ((m_or_h_gate_v_in1(c_e_h_1, c_j, s3) | m_or_h_gate_v_in2(c_e_h_1, c_j, s3) | (~node5(c_e_h_1, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s4))) <=> (m_or_h_gate_v_in1(c_e_h_1, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s4)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s3) | (~node5(c_e_h_1, c_j, s3, s4)))),
% 292.79/185.29 inference(rewrite,[status(thm)],[])).
% 292.79/185.29 tff(18365,plain,
% 292.79/185.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s3) | m_or_h_gate_v_in2(c_e_h_1, c_j, s3) | (~node5(c_e_h_1, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s4)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s3) | (~node5(c_e_h_1, c_j, s3, s4))))),
% 292.79/185.29 inference(monotonicity,[status(thm)],[18364])).
% 292.79/185.29 tff(18366,plain,
% 292.79/185.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s3) | m_or_h_gate_v_in2(c_e_h_1, c_j, s3) | (~node5(c_e_h_1, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in1(c_e_h_1, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s4)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s3) | (~node5(c_e_h_1, c_j, s3, s4)))),
% 292.79/185.29 inference(transitivity,[status(thm)],[18365, 18363])).
% 292.79/185.29 tff(18367,plain,
% 292.79/185.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s3) | m_or_h_gate_v_in2(c_e_h_1, c_j, s3) | (~node5(c_e_h_1, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s4)))),
% 292.79/185.29 inference(quant_inst,[status(thm)],[])).
% 292.79/185.29 tff(18368,plain,
% 292.79/185.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in1(c_e_h_1, c_j, s3) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s4)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s3) | (~node5(c_e_h_1, c_j, s3, s4))),
% 292.79/185.29 inference(modus_ponens,[status(thm)],[18367, 18366])).
% 292.79/185.29 tff(18369,plain,
% 292.79/185.29 ($false),
% 292.79/185.29 inference(unit_resolution,[status(thm)],[18368, 1159, 18362, 18314, 18361, 18331])).
% 292.79/185.29 tff(18370,plain,((~node5(c_e_h_1, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s4)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s3)), inference(lemma,lemma(discharge,[]))).
% 292.79/185.29 tff(18371,plain,
% 292.79/185.29 ((~node5(c_e_h_1, c_j, s3, s4)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s4))),
% 292.79/185.29 inference(unit_resolution,[status(thm)],[18370, 18330])).
% 292.79/185.29 tff(18372,plain,
% 292.79/185.29 (~node5(c_e_h_1, c_j, s3, s4)),
% 292.79/185.29 inference(unit_resolution,[status(thm)],[18371, 18314])).
% 292.79/185.29 tff(18373,plain,
% 292.79/185.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s3, s4)) | node6(c_e_h_1, c_j, s3, s4) | node5(c_e_h_1, c_j, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s3, s4)) | node6(c_e_h_1, c_j, s3, s4) | node5(c_e_h_1, c_j, s3, s4))),
% 292.79/185.29 inference(rewrite,[status(thm)],[])).
% 292.79/185.29 tff(18374,plain,
% 292.79/185.29 ((node6(c_e_h_1, c_j, s3, s4) | node5(c_e_h_1, c_j, s3, s4) | (~trans(s3, s4))) <=> ((~trans(s3, s4)) | node6(c_e_h_1, c_j, s3, s4) | node5(c_e_h_1, c_j, s3, s4))),
% 292.79/185.30 inference(rewrite,[status(thm)],[])).
% 292.79/185.30 tff(18375,plain,
% 292.79/185.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s3, s4) | node5(c_e_h_1, c_j, s3, s4) | (~trans(s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s3, s4)) | node6(c_e_h_1, c_j, s3, s4) | node5(c_e_h_1, c_j, s3, s4)))),
% 292.79/185.30 inference(monotonicity,[status(thm)],[18374])).
% 292.79/185.30 tff(18376,plain,
% 292.79/185.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s3, s4) | node5(c_e_h_1, c_j, s3, s4) | (~trans(s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s3, s4)) | node6(c_e_h_1, c_j, s3, s4) | node5(c_e_h_1, c_j, s3, s4))),
% 292.79/185.30 inference(transitivity,[status(thm)],[18375, 18373])).
% 292.79/185.30 tff(18377,plain,
% 292.79/185.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s3, s4) | node5(c_e_h_1, c_j, s3, s4) | (~trans(s3, s4)))),
% 292.79/185.30 inference(quant_inst,[status(thm)],[])).
% 292.79/185.30 tff(18378,plain,
% 292.79/185.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s3, s4)) | node6(c_e_h_1, c_j, s3, s4) | node5(c_e_h_1, c_j, s3, s4)),
% 292.79/185.30 inference(modus_ponens,[status(thm)],[18377, 18376])).
% 292.79/185.30 tff(18379,plain,
% 292.79/185.30 (node6(c_e_h_1, c_j, s3, s4) | node5(c_e_h_1, c_j, s3, s4)),
% 292.79/185.30 inference(unit_resolution,[status(thm)],[18378, 1141, 531])).
% 292.79/185.30 tff(18380,plain,
% 292.79/185.30 ($false),
% 292.79/185.30 inference(unit_resolution,[status(thm)],[18379, 18372, 18326])).
% 292.79/185.30 tff(18381,plain,(~m_or_h_gate_v_out(c_e_h_1, c_j, s4)), inference(lemma,lemma(discharge,[]))).
% 292.79/185.30 tff(18382,assumption,(~m_or_h_gate_v_out(c_e_h_1, c_j, s4)), introduced(assumption)).
% 292.79/185.30 tff(18383,assumption,(node6(c_e_h_1, c_j, s4, s5)), introduced(assumption)).
% 292.79/185.30 tff(18384,plain,
% 292.79/185.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s5)) | (~node6(c_e_h_1, c_j, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s5)) | (~node6(c_e_h_1, c_j, s4, s5)))),
% 292.79/185.30 inference(rewrite,[status(thm)],[])).
% 292.79/185.30 tff(18385,plain,
% 292.79/185.30 (((~node6(c_e_h_1, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s5)) | m_or_h_gate_v_out(c_e_h_1, c_j, s4)) <=> (m_or_h_gate_v_out(c_e_h_1, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s5)) | (~node6(c_e_h_1, c_j, s4, s5)))),
% 292.79/185.30 inference(rewrite,[status(thm)],[])).
% 292.79/185.30 tff(18386,plain,
% 292.79/185.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s5)) | m_or_h_gate_v_out(c_e_h_1, c_j, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s5)) | (~node6(c_e_h_1, c_j, s4, s5))))),
% 292.79/185.30 inference(monotonicity,[status(thm)],[18385])).
% 292.79/185.30 tff(18387,plain,
% 292.79/185.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s5)) | m_or_h_gate_v_out(c_e_h_1, c_j, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s5)) | (~node6(c_e_h_1, c_j, s4, s5)))),
% 292.79/185.30 inference(transitivity,[status(thm)],[18386, 18384])).
% 292.79/185.30 tff(18388,plain,
% 292.79/185.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s5)) | m_or_h_gate_v_out(c_e_h_1, c_j, s4))),
% 292.79/185.30 inference(quant_inst,[status(thm)],[])).
% 292.79/185.30 tff(18389,plain,
% 292.79/185.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s5)) | (~node6(c_e_h_1, c_j, s4, s5))),
% 292.79/185.30 inference(modus_ponens,[status(thm)],[18388, 18387])).
% 292.79/185.30 tff(18390,plain,
% 292.79/185.30 ($false),
% 292.79/185.30 inference(unit_resolution,[status(thm)],[18389, 1121, 18383, 18382, 18313])).
% 292.79/185.30 tff(18391,plain,((~node6(c_e_h_1, c_j, s4, s5)) | m_or_h_gate_v_out(c_e_h_1, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s5))), inference(lemma,lemma(discharge,[]))).
% 292.79/185.30 tff(18392,plain,
% 292.79/185.30 ((~node6(c_e_h_1, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s5))),
% 292.79/185.30 inference(unit_resolution,[status(thm)],[18391, 18381])).
% 292.79/185.30 tff(18393,plain,
% 292.79/185.30 (~node6(c_e_h_1, c_j, s4, s5)),
% 292.79/185.30 inference(unit_resolution,[status(thm)],[18392, 18313])).
% 292.79/185.30 tff(18394,assumption,(m_and_h_gate_v_out(c_e_h_1, c_l, s4)), introduced(assumption)).
% 292.79/185.30 tff(18395,plain,
% 292.79/185.30 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s3)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s3)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3))),
% 292.79/185.30 inference(rewrite,[status(thm)],[])).
% 292.79/185.30 tff(18396,plain,
% 292.79/185.30 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s3)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3))),
% 292.79/185.30 inference(quant_inst,[status(thm)],[])).
% 292.79/185.30 tff(18397,plain,
% 292.79/185.30 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s3)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s3)),
% 292.79/185.30 inference(modus_ponens,[status(thm)],[18396, 18395])).
% 292.79/185.30 tff(18398,plain,
% 292.79/185.30 (~m_and_h_gate_v_in2(c_e_h_1, c_l, s3)),
% 292.79/185.30 inference(unit_resolution,[status(thm)],[18397, 4549, 16392])).
% 292.79/185.30 tff(18399,plain,
% 292.79/185.30 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s3)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s3)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s3))),
% 292.79/185.30 inference(rewrite,[status(thm)],[])).
% 292.79/185.30 tff(18400,plain,
% 292.79/185.30 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s3)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s3))),
% 292.79/185.30 inference(quant_inst,[status(thm)],[])).
% 292.79/185.30 tff(18401,plain,
% 292.79/185.30 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s3)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s3)),
% 292.79/185.30 inference(modus_ponens,[status(thm)],[18400, 18399])).
% 292.79/185.30 tff(18402,plain,
% 292.79/185.30 (~node20(c_e_h_1, c_l, s3)),
% 292.79/185.30 inference(unit_resolution,[status(thm)],[18401, 4563, 18398])).
% 292.79/185.30 tff(18403,assumption,(node22(c_e_h_1, c_l, s3, s4)), introduced(assumption)).
% 292.79/185.30 tff(18404,plain,
% 292.79/185.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s4)) | (~node22(c_e_h_1, c_l, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_l, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s4)) | (~node22(c_e_h_1, c_l, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_l, s3))),
% 292.79/185.30 inference(rewrite,[status(thm)],[])).
% 292.79/185.30 tff(18405,plain,
% 292.79/185.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s4)) | (~node22(c_e_h_1, c_l, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_l, s3))),
% 292.79/185.30 inference(quant_inst,[status(thm)],[])).
% 292.79/185.30 tff(18406,plain,
% 292.79/185.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s4)) | (~node22(c_e_h_1, c_l, s3, s4)) | m_and_h_gate_v_out(c_e_h_1, c_l, s3)),
% 292.79/185.30 inference(modus_ponens,[status(thm)],[18405, 18404])).
% 292.79/185.30 tff(18407,plain,
% 292.79/185.30 ($false),
% 292.79/185.30 inference(unit_resolution,[status(thm)],[18406, 108, 18403, 18357, 18394])).
% 292.79/185.30 tff(18408,plain,((~node22(c_e_h_1, c_l, s3, s4)) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s4))), inference(lemma,lemma(discharge,[]))).
% 292.79/185.30 tff(18409,plain,
% 292.79/185.30 (~node22(c_e_h_1, c_l, s3, s4)),
% 292.79/185.30 inference(unit_resolution,[status(thm)],[18408, 18394])).
% 292.79/185.30 tff(18410,plain,
% 292.79/185.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_1, c_l, s3, s4) | node22(c_e_h_1, c_l, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_1, c_l, s3, s4) | node22(c_e_h_1, c_l, s3, s4))),
% 292.79/185.30 inference(rewrite,[status(thm)],[])).
% 292.79/185.30 tff(18411,plain,
% 292.79/185.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s3, s4)) | node21(c_e_h_1, c_l, s3, s4) | node22(c_e_h_1, c_l, s3, s4))),
% 292.79/185.30 inference(quant_inst,[status(thm)],[])).
% 292.79/185.30 tff(18412,plain,
% 292.79/185.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s3, s4)) | node21(c_e_h_1, c_l, s3, s4) | node22(c_e_h_1, c_l, s3, s4)),
% 292.79/185.30 inference(modus_ponens,[status(thm)],[18411, 18410])).
% 292.79/185.30 tff(18413,plain,
% 292.79/185.30 (node21(c_e_h_1, c_l, s3, s4) | node22(c_e_h_1, c_l, s3, s4)),
% 292.79/185.30 inference(unit_resolution,[status(thm)],[18412, 82, 531])).
% 292.79/185.30 tff(18414,plain,
% 292.79/185.30 (node21(c_e_h_1, c_l, s3, s4)),
% 292.79/185.30 inference(unit_resolution,[status(thm)],[18413, 18409])).
% 292.79/185.30 tff(18415,plain,
% 292.79/185.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s4)) | (~node21(c_e_h_1, c_l, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s4)) | (~node21(c_e_h_1, c_l, s3, s4)))),
% 292.79/185.30 inference(rewrite,[status(thm)],[])).
% 292.79/185.30 tff(18416,plain,
% 292.79/185.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s4)) | (~node21(c_e_h_1, c_l, s3, s4)))),
% 292.79/185.30 inference(quant_inst,[status(thm)],[])).
% 292.79/185.30 tff(18417,plain,
% 292.79/185.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s3) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s4)) | (~node21(c_e_h_1, c_l, s3, s4))),
% 292.79/185.30 inference(modus_ponens,[status(thm)],[18416, 18415])).
% 292.79/185.30 tff(18418,plain,
% 292.79/185.30 ($false),
% 292.79/185.30 inference(unit_resolution,[status(thm)],[18417, 52, 18414, 18402, 18394])).
% 292.79/185.30 tff(18419,plain,(~m_and_h_gate_v_out(c_e_h_1, c_l, s4)), inference(lemma,lemma(discharge,[]))).
% 292.79/185.30 tff(18420,plain,
% 292.79/185.30 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s4)) | m_and_h_gate_v_out(c_e_h_1, c_l, s4))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s4)) | m_and_h_gate_v_out(c_e_h_1, c_l, s4))),
% 292.79/185.30 inference(rewrite,[status(thm)],[])).
% 292.79/185.30 tff(18421,plain,
% 292.79/185.30 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s4)) | m_and_h_gate_v_out(c_e_h_1, c_l, s4))),
% 292.79/185.30 inference(quant_inst,[status(thm)],[])).
% 292.79/185.30 tff(18422,plain,
% 292.79/185.30 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s4)) | m_and_h_gate_v_out(c_e_h_1, c_l, s4)),
% 292.79/185.31 inference(modus_ponens,[status(thm)],[18421, 18420])).
% 292.79/185.31 tff(18423,plain,
% 292.79/185.31 (~m_or_h_gate_v_in1(c_e_h_1, c_j, s4)),
% 292.79/185.31 inference(unit_resolution,[status(thm)],[18422, 1100, 18419])).
% 292.79/185.31 tff(18424,plain,
% 292.79/185.31 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s4)) | m_cell_v_ack(c_e_h_1, s4))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s4)) | m_cell_v_ack(c_e_h_1, s4))),
% 292.79/185.31 inference(rewrite,[status(thm)],[])).
% 292.79/185.31 tff(18425,plain,
% 292.79/185.31 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s4)) | m_cell_v_ack(c_e_h_1, s4))),
% 292.79/185.31 inference(quant_inst,[status(thm)],[])).
% 292.79/185.31 tff(18426,plain,
% 292.79/185.31 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s4)) | m_cell_v_ack(c_e_h_1, s4)),
% 292.79/185.31 inference(modus_ponens,[status(thm)],[18425, 18424])).
% 292.79/185.31 tff(18427,plain,
% 292.79/185.31 (~m_or_h_gate_v_in2(c_e_h_1, c_j, s4)),
% 292.79/185.31 inference(unit_resolution,[status(thm)],[18426, 1085, 6112])).
% 292.79/185.31 tff(18428,assumption,(~m_or_h_gate_v_in1(c_e_h_1, c_j, s4)), introduced(assumption)).
% 292.79/185.31 tff(18429,assumption,(~m_or_h_gate_v_in2(c_e_h_1, c_j, s4)), introduced(assumption)).
% 292.79/185.31 tff(18430,assumption,(node5(c_e_h_1, c_j, s4, s5)), introduced(assumption)).
% 292.79/185.31 tff(18431,plain,
% 292.79/185.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s4) | m_or_h_gate_v_in2(c_e_h_1, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s5)) | (~node5(c_e_h_1, c_j, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in1(c_e_h_1, c_j, s4) | m_or_h_gate_v_in2(c_e_h_1, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s5)) | (~node5(c_e_h_1, c_j, s4, s5)))),
% 292.79/185.31 inference(rewrite,[status(thm)],[])).
% 292.79/185.31 tff(18432,plain,
% 292.79/185.31 ((m_or_h_gate_v_in1(c_e_h_1, c_j, s4) | m_or_h_gate_v_in2(c_e_h_1, c_j, s4) | (~node5(c_e_h_1, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s5))) <=> (m_or_h_gate_v_in1(c_e_h_1, c_j, s4) | m_or_h_gate_v_in2(c_e_h_1, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s5)) | (~node5(c_e_h_1, c_j, s4, s5)))),
% 292.79/185.31 inference(rewrite,[status(thm)],[])).
% 292.79/185.31 tff(18433,plain,
% 292.79/185.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s4) | m_or_h_gate_v_in2(c_e_h_1, c_j, s4) | (~node5(c_e_h_1, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s4) | m_or_h_gate_v_in2(c_e_h_1, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s5)) | (~node5(c_e_h_1, c_j, s4, s5))))),
% 292.79/185.31 inference(monotonicity,[status(thm)],[18432])).
% 292.79/185.31 tff(18434,plain,
% 292.79/185.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s4) | m_or_h_gate_v_in2(c_e_h_1, c_j, s4) | (~node5(c_e_h_1, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in1(c_e_h_1, c_j, s4) | m_or_h_gate_v_in2(c_e_h_1, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s5)) | (~node5(c_e_h_1, c_j, s4, s5)))),
% 292.79/185.31 inference(transitivity,[status(thm)],[18433, 18431])).
% 292.79/185.31 tff(18435,plain,
% 292.79/185.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s4) | m_or_h_gate_v_in2(c_e_h_1, c_j, s4) | (~node5(c_e_h_1, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s5)))),
% 292.79/185.31 inference(quant_inst,[status(thm)],[])).
% 292.79/185.31 tff(18436,plain,
% 292.79/185.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in1(c_e_h_1, c_j, s4) | m_or_h_gate_v_in2(c_e_h_1, c_j, s4) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s5)) | (~node5(c_e_h_1, c_j, s4, s5))),
% 292.79/185.31 inference(modus_ponens,[status(thm)],[18435, 18434])).
% 292.79/185.31 tff(18437,plain,
% 292.79/185.31 ($false),
% 292.79/185.31 inference(unit_resolution,[status(thm)],[18436, 1159, 18430, 18313, 18429, 18428])).
% 292.79/185.31 tff(18438,plain,((~node5(c_e_h_1, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s5)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s4) | m_or_h_gate_v_in1(c_e_h_1, c_j, s4)), inference(lemma,lemma(discharge,[]))).
% 292.79/185.31 tff(18439,plain,
% 292.79/185.31 ((~node5(c_e_h_1, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s5)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s4)),
% 292.79/185.31 inference(unit_resolution,[status(thm)],[18438, 18427])).
% 292.79/185.31 tff(18440,plain,
% 292.79/185.31 ((~node5(c_e_h_1, c_j, s4, s5)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s5))),
% 292.79/185.31 inference(unit_resolution,[status(thm)],[18439, 18423])).
% 292.79/185.31 tff(18441,plain,
% 292.79/185.31 (~node5(c_e_h_1, c_j, s4, s5)),
% 292.79/185.31 inference(unit_resolution,[status(thm)],[18440, 18313])).
% 292.79/185.31 tff(18442,plain,
% 292.79/185.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s4, s5)) | node6(c_e_h_1, c_j, s4, s5) | node5(c_e_h_1, c_j, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s4, s5)) | node6(c_e_h_1, c_j, s4, s5) | node5(c_e_h_1, c_j, s4, s5))),
% 292.79/185.31 inference(rewrite,[status(thm)],[])).
% 292.79/185.31 tff(18443,plain,
% 292.79/185.31 ((node6(c_e_h_1, c_j, s4, s5) | node5(c_e_h_1, c_j, s4, s5) | (~trans(s4, s5))) <=> ((~trans(s4, s5)) | node6(c_e_h_1, c_j, s4, s5) | node5(c_e_h_1, c_j, s4, s5))),
% 292.79/185.31 inference(rewrite,[status(thm)],[])).
% 292.79/185.31 tff(18444,plain,
% 292.79/185.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s4, s5) | node5(c_e_h_1, c_j, s4, s5) | (~trans(s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s4, s5)) | node6(c_e_h_1, c_j, s4, s5) | node5(c_e_h_1, c_j, s4, s5)))),
% 292.79/185.31 inference(monotonicity,[status(thm)],[18443])).
% 292.79/185.31 tff(18445,plain,
% 292.79/185.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s4, s5) | node5(c_e_h_1, c_j, s4, s5) | (~trans(s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s4, s5)) | node6(c_e_h_1, c_j, s4, s5) | node5(c_e_h_1, c_j, s4, s5))),
% 292.79/185.31 inference(transitivity,[status(thm)],[18444, 18442])).
% 292.79/185.31 tff(18446,plain,
% 292.79/185.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s4, s5) | node5(c_e_h_1, c_j, s4, s5) | (~trans(s4, s5)))),
% 292.79/185.31 inference(quant_inst,[status(thm)],[])).
% 292.79/185.31 tff(18447,plain,
% 292.79/185.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s4, s5)) | node6(c_e_h_1, c_j, s4, s5) | node5(c_e_h_1, c_j, s4, s5)),
% 292.79/185.31 inference(modus_ponens,[status(thm)],[18446, 18445])).
% 292.79/185.31 tff(18448,plain,
% 292.79/185.31 (node6(c_e_h_1, c_j, s4, s5) | node5(c_e_h_1, c_j, s4, s5)),
% 292.79/185.31 inference(unit_resolution,[status(thm)],[18447, 1141, 1028])).
% 292.79/185.31 tff(18449,plain,
% 292.79/185.31 ($false),
% 292.79/185.31 inference(unit_resolution,[status(thm)],[18448, 18441, 18393])).
% 292.79/185.31 tff(18450,plain,(~m_or_h_gate_v_out(c_e_h_1, c_j, s5)), inference(lemma,lemma(discharge,[]))).
% 292.79/185.31 tff(18451,plain,
% 292.79/185.31 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s5)) | m_or_h_gate_v_out(c_e_h_1, c_j, s5))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s5)) | m_or_h_gate_v_out(c_e_h_1, c_j, s5))),
% 292.79/185.32 inference(rewrite,[status(thm)],[])).
% 292.79/185.32 tff(18452,plain,
% 292.79/185.32 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s5)) | m_or_h_gate_v_out(c_e_h_1, c_j, s5))),
% 292.79/185.32 inference(quant_inst,[status(thm)],[])).
% 292.79/185.32 tff(18453,plain,
% 292.79/185.32 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s5)) | m_or_h_gate_v_out(c_e_h_1, c_j, s5)),
% 292.79/185.32 inference(modus_ponens,[status(thm)],[18452, 18451])).
% 292.79/185.32 tff(18454,plain,
% 292.79/185.32 ($false),
% 292.79/185.32 inference(unit_resolution,[status(thm)],[18453, 1174, 18450, 18312])).
% 292.79/185.32 tff(18455,plain,(~m_c_h_element_v_in2(c_e_h_1, c_h, s5)), inference(lemma,lemma(discharge,[]))).
% 292.79/185.32 tff(18456,plain,
% 292.79/185.32 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s4)) | m_or_h_gate_v_out(c_e_h_1, c_j, s4))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s4)) | m_or_h_gate_v_out(c_e_h_1, c_j, s4))),
% 292.79/185.32 inference(rewrite,[status(thm)],[])).
% 292.79/185.32 tff(18457,plain,
% 292.79/185.32 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s4)) | m_or_h_gate_v_out(c_e_h_1, c_j, s4))),
% 292.79/185.32 inference(quant_inst,[status(thm)],[])).
% 292.79/185.32 tff(18458,plain,
% 292.79/185.32 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s4)) | m_or_h_gate_v_out(c_e_h_1, c_j, s4)),
% 292.79/185.32 inference(modus_ponens,[status(thm)],[18457, 18456])).
% 292.79/185.32 tff(18459,plain,
% 292.79/185.32 (~m_c_h_element_v_in2(c_e_h_1, c_h, s4)),
% 292.79/185.32 inference(unit_resolution,[status(thm)],[18458, 1174, 18381])).
% 292.79/185.32 tff(18460,assumption,(m_c_h_element_v_out(c_e_h_1, c_h, s5)), introduced(assumption)).
% 292.79/185.32 tff(18461,assumption,(~node14(c_e_h_1, c_h, s4, s5)), introduced(assumption)).
% 292.79/185.32 tff(18462,assumption,(node15(c_e_h_1, c_h, s4, s5)), introduced(assumption)).
% 292.79/185.32 tff(18463,plain,
% 292.79/185.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s5)) | (~node15(c_e_h_1, c_h, s4, s5)) | m_c_h_element_v_out(c_e_h_1, c_h, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s5)) | (~node15(c_e_h_1, c_h, s4, s5)) | m_c_h_element_v_out(c_e_h_1, c_h, s4))),
% 292.79/185.32 inference(rewrite,[status(thm)],[])).
% 292.79/185.32 tff(18464,plain,
% 292.79/185.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s5)) | (~node15(c_e_h_1, c_h, s4, s5)) | m_c_h_element_v_out(c_e_h_1, c_h, s4))),
% 292.79/185.32 inference(quant_inst,[status(thm)],[])).
% 292.79/185.32 tff(18465,plain,
% 292.79/185.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s5)) | (~node15(c_e_h_1, c_h, s4, s5)) | m_c_h_element_v_out(c_e_h_1, c_h, s4)),
% 292.79/185.32 inference(modus_ponens,[status(thm)],[18464, 18463])).
% 292.79/185.32 tff(18466,plain,
% 292.79/185.32 ($false),
% 292.79/185.32 inference(unit_resolution,[status(thm)],[18465, 147, 18460, 18462, 17479])).
% 292.79/185.32 tff(18467,plain,((~node15(c_e_h_1, c_h, s4, s5)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s5)) | m_c_h_element_v_out(c_e_h_1, c_h, s4)), inference(lemma,lemma(discharge,[]))).
% 292.79/185.32 tff(18468,plain,
% 292.79/185.32 (~node15(c_e_h_1, c_h, s4, s5)),
% 292.79/185.32 inference(unit_resolution,[status(thm)],[18467, 17479, 18460])).
% 292.79/185.32 tff(18469,plain,
% 292.79/185.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s4, s5)) | node19(c_e_h_1, c_h, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s4, s5)) | node19(c_e_h_1, c_h, s4, s5))),
% 292.79/185.32 inference(rewrite,[status(thm)],[])).
% 292.79/185.32 tff(18470,plain,
% 292.79/185.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s4, s5)) | node19(c_e_h_1, c_h, s4, s5))),
% 292.79/185.32 inference(quant_inst,[status(thm)],[])).
% 292.79/185.32 tff(18471,plain,
% 292.79/185.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s4, s5)) | node19(c_e_h_1, c_h, s4, s5)),
% 292.79/185.32 inference(modus_ponens,[status(thm)],[18470, 18469])).
% 292.79/185.32 tff(18472,plain,
% 292.79/185.32 (node19(c_e_h_1, c_h, s4, s5)),
% 292.79/185.32 inference(unit_resolution,[status(thm)],[18471, 190, 1028])).
% 292.79/185.32 tff(18473,plain,
% 292.79/185.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s4) | node15(c_e_h_1, c_h, s4, s5) | (~node19(c_e_h_1, c_h, s4, s5)) | node14(c_e_h_1, c_h, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s4) | node15(c_e_h_1, c_h, s4, s5) | (~node19(c_e_h_1, c_h, s4, s5)) | node14(c_e_h_1, c_h, s4, s5))),
% 292.79/185.32 inference(rewrite,[status(thm)],[])).
% 292.79/185.32 tff(18474,plain,
% 292.79/185.32 ((node16(c_e_h_1, c_h, s4) | node14(c_e_h_1, c_h, s4, s5) | node15(c_e_h_1, c_h, s4, s5) | (~node19(c_e_h_1, c_h, s4, s5))) <=> (node16(c_e_h_1, c_h, s4) | node15(c_e_h_1, c_h, s4, s5) | (~node19(c_e_h_1, c_h, s4, s5)) | node14(c_e_h_1, c_h, s4, s5))),
% 292.79/185.32 inference(rewrite,[status(thm)],[])).
% 292.79/185.32 tff(18475,plain,
% 292.79/185.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s4) | node14(c_e_h_1, c_h, s4, s5) | node15(c_e_h_1, c_h, s4, s5) | (~node19(c_e_h_1, c_h, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s4) | node15(c_e_h_1, c_h, s4, s5) | (~node19(c_e_h_1, c_h, s4, s5)) | node14(c_e_h_1, c_h, s4, s5)))),
% 292.79/185.32 inference(monotonicity,[status(thm)],[18474])).
% 292.79/185.32 tff(18476,plain,
% 292.79/185.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s4) | node14(c_e_h_1, c_h, s4, s5) | node15(c_e_h_1, c_h, s4, s5) | (~node19(c_e_h_1, c_h, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s4) | node15(c_e_h_1, c_h, s4, s5) | (~node19(c_e_h_1, c_h, s4, s5)) | node14(c_e_h_1, c_h, s4, s5))),
% 292.79/185.32 inference(transitivity,[status(thm)],[18475, 18473])).
% 292.79/185.32 tff(18477,plain,
% 292.79/185.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s4) | node14(c_e_h_1, c_h, s4, s5) | node15(c_e_h_1, c_h, s4, s5) | (~node19(c_e_h_1, c_h, s4, s5)))),
% 292.79/185.32 inference(quant_inst,[status(thm)],[])).
% 292.79/185.32 tff(18478,plain,
% 292.79/185.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s4) | node15(c_e_h_1, c_h, s4, s5) | (~node19(c_e_h_1, c_h, s4, s5)) | node14(c_e_h_1, c_h, s4, s5)),
% 292.79/185.32 inference(modus_ponens,[status(thm)],[18477, 18476])).
% 292.79/185.32 tff(18479,plain,
% 292.79/185.32 (node16(c_e_h_1, c_h, s4) | node15(c_e_h_1, c_h, s4, s5) | node14(c_e_h_1, c_h, s4, s5)),
% 292.79/185.32 inference(unit_resolution,[status(thm)],[18478, 204, 18472])).
% 292.79/185.32 tff(18480,plain,
% 292.79/185.32 (node16(c_e_h_1, c_h, s4)),
% 292.79/185.32 inference(unit_resolution,[status(thm)],[18479, 18468, 18461])).
% 292.79/185.32 tff(18481,assumption,(node16(c_e_h_1, c_h, s4)), introduced(assumption)).
% 292.79/185.32 tff(18482,assumption,(node17(c_e_h_1, c_h, s4)), introduced(assumption)).
% 292.79/185.32 tff(18483,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_h, s4)), introduced(assumption)).
% 292.79/185.32 tff(18484,plain,
% 292.79/185.32 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s4)) | m_c_h_element_v_in1(c_e_h_1, c_h, s4) | m_c_h_element_v_in2(c_e_h_1, c_h, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s4)) | m_c_h_element_v_in1(c_e_h_1, c_h, s4) | m_c_h_element_v_in2(c_e_h_1, c_h, s4))),
% 292.79/185.32 inference(rewrite,[status(thm)],[])).
% 292.79/185.32 tff(18485,plain,
% 292.79/185.32 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s4)) | m_c_h_element_v_in1(c_e_h_1, c_h, s4) | m_c_h_element_v_in2(c_e_h_1, c_h, s4))),
% 292.79/185.32 inference(quant_inst,[status(thm)],[])).
% 292.79/185.32 tff(18486,plain,
% 292.79/185.32 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s4)) | m_c_h_element_v_in1(c_e_h_1, c_h, s4) | m_c_h_element_v_in2(c_e_h_1, c_h, s4)),
% 292.79/185.32 inference(modus_ponens,[status(thm)],[18485, 18484])).
% 292.79/185.32 tff(18487,plain,
% 292.79/185.32 (m_c_h_element_v_in1(c_e_h_1, c_h, s4) | m_c_h_element_v_in2(c_e_h_1, c_h, s4)),
% 292.79/185.32 inference(unit_resolution,[status(thm)],[18486, 178, 18481])).
% 292.79/185.32 tff(18488,plain,
% 292.79/185.32 (m_c_h_element_v_in1(c_e_h_1, c_h, s4)),
% 292.79/185.32 inference(unit_resolution,[status(thm)],[18487, 18483])).
% 292.79/185.32 tff(18489,plain,
% 292.79/185.32 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s4)) | m_c_h_element_v_in2(c_e_h_1, c_h, s4) | (~node17(c_e_h_1, c_h, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s4)) | m_c_h_element_v_in2(c_e_h_1, c_h, s4) | (~node17(c_e_h_1, c_h, s4)))),
% 292.79/185.32 inference(rewrite,[status(thm)],[])).
% 292.79/185.32 tff(18490,plain,
% 292.79/185.32 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s4)) | m_c_h_element_v_in2(c_e_h_1, c_h, s4) | (~node17(c_e_h_1, c_h, s4)))),
% 292.79/185.32 inference(quant_inst,[status(thm)],[])).
% 292.79/185.32 tff(18491,plain,
% 292.79/185.32 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s4)) | m_c_h_element_v_in2(c_e_h_1, c_h, s4) | (~node17(c_e_h_1, c_h, s4))),
% 292.79/185.32 inference(modus_ponens,[status(thm)],[18490, 18489])).
% 292.79/185.32 tff(18492,plain,
% 292.79/185.32 ((~m_c_h_element_v_in1(c_e_h_1, c_h, s4)) | m_c_h_element_v_in2(c_e_h_1, c_h, s4)),
% 292.79/185.32 inference(unit_resolution,[status(thm)],[18491, 919, 18482])).
% 292.79/185.32 tff(18493,plain,
% 292.79/185.32 ($false),
% 292.79/185.32 inference(unit_resolution,[status(thm)],[18492, 18488, 18483])).
% 292.79/185.32 tff(18494,plain,(m_c_h_element_v_in2(c_e_h_1, c_h, s4) | (~node17(c_e_h_1, c_h, s4)) | (~node16(c_e_h_1, c_h, s4))), inference(lemma,lemma(discharge,[]))).
% 292.79/185.32 tff(18495,plain,
% 292.79/185.32 (m_c_h_element_v_in2(c_e_h_1, c_h, s4)),
% 292.79/185.32 inference(unit_resolution,[status(thm)],[18494, 18482, 18481])).
% 292.79/185.32 tff(18496,plain,
% 292.79/185.32 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s4)) | (~node16(c_e_h_1, c_h, s4)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s4)) | (~node16(c_e_h_1, c_h, s4)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s4)))),
% 292.79/185.32 inference(rewrite,[status(thm)],[])).
% 292.79/185.32 tff(18497,plain,
% 292.79/185.32 (((~node16(c_e_h_1, c_h, s4)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s4)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s4))) <=> ((~m_c_h_element_v_in1(c_e_h_1, c_h, s4)) | (~node16(c_e_h_1, c_h, s4)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s4)))),
% 292.79/185.32 inference(rewrite,[status(thm)],[])).
% 292.79/185.32 tff(18498,plain,
% 292.79/185.32 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_h, s4)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s4)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s4)) | (~node16(c_e_h_1, c_h, s4)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s4))))),
% 292.79/185.33 inference(monotonicity,[status(thm)],[18497])).
% 292.79/185.33 tff(18499,plain,
% 292.79/185.33 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_h, s4)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s4)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s4)) | (~node16(c_e_h_1, c_h, s4)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s4)))),
% 292.79/185.33 inference(transitivity,[status(thm)],[18498, 18496])).
% 292.79/185.33 tff(18500,plain,
% 292.79/185.33 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_h, s4)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s4)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s4)))),
% 292.79/185.33 inference(quant_inst,[status(thm)],[])).
% 292.79/185.33 tff(18501,plain,
% 292.79/185.33 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s4)) | (~node16(c_e_h_1, c_h, s4)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s4))),
% 292.79/185.33 inference(modus_ponens,[status(thm)],[18500, 18499])).
% 292.79/185.33 tff(18502,plain,
% 292.79/185.33 ((~m_c_h_element_v_in1(c_e_h_1, c_h, s4)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s4))),
% 292.79/185.33 inference(unit_resolution,[status(thm)],[18501, 2307, 18481])).
% 292.79/185.33 tff(18503,plain,
% 292.79/185.33 (~m_c_h_element_v_in1(c_e_h_1, c_h, s4)),
% 292.79/185.33 inference(unit_resolution,[status(thm)],[18502, 18495])).
% 292.79/185.33 tff(18504,plain,
% 292.79/185.33 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s4) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s4)) | (~node17(c_e_h_1, c_h, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s4) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s4)) | (~node17(c_e_h_1, c_h, s4)))),
% 292.79/185.33 inference(rewrite,[status(thm)],[])).
% 292.79/185.33 tff(18505,plain,
% 292.79/185.33 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s4) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s4)) | (~node17(c_e_h_1, c_h, s4)))),
% 292.79/185.33 inference(quant_inst,[status(thm)],[])).
% 292.79/185.33 tff(18506,plain,
% 292.79/185.33 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s4) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s4)) | (~node17(c_e_h_1, c_h, s4))),
% 292.79/185.33 inference(modus_ponens,[status(thm)],[18505, 18504])).
% 292.79/185.33 tff(18507,plain,
% 292.79/185.33 (m_c_h_element_v_in1(c_e_h_1, c_h, s4) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s4))),
% 292.79/185.33 inference(unit_resolution,[status(thm)],[18506, 859, 18482])).
% 292.79/185.33 tff(18508,plain,
% 292.79/185.33 ($false),
% 292.79/185.33 inference(unit_resolution,[status(thm)],[18507, 18503, 18495])).
% 292.79/185.33 tff(18509,plain,((~node17(c_e_h_1, c_h, s4)) | (~node16(c_e_h_1, c_h, s4))), inference(lemma,lemma(discharge,[]))).
% 292.79/185.33 tff(18510,plain,
% 292.79/185.33 (~node17(c_e_h_1, c_h, s4)),
% 292.79/185.33 inference(unit_resolution,[status(thm)],[18509, 18480])).
% 292.79/185.33 tff(18511,plain,
% 292.79/185.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s4) | (~node19(c_e_h_1, c_h, s4, s5)) | node18(c_e_h_1, c_h, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s4) | (~node19(c_e_h_1, c_h, s4, s5)) | node18(c_e_h_1, c_h, s4, s5))),
% 292.79/185.33 inference(rewrite,[status(thm)],[])).
% 292.79/185.33 tff(18512,plain,
% 292.79/185.33 ((node17(c_e_h_1, c_h, s4) | node18(c_e_h_1, c_h, s4, s5) | (~node19(c_e_h_1, c_h, s4, s5))) <=> (node17(c_e_h_1, c_h, s4) | (~node19(c_e_h_1, c_h, s4, s5)) | node18(c_e_h_1, c_h, s4, s5))),
% 292.79/185.33 inference(rewrite,[status(thm)],[])).
% 292.79/185.33 tff(18513,plain,
% 292.79/185.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s4) | node18(c_e_h_1, c_h, s4, s5) | (~node19(c_e_h_1, c_h, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s4) | (~node19(c_e_h_1, c_h, s4, s5)) | node18(c_e_h_1, c_h, s4, s5)))),
% 292.79/185.33 inference(monotonicity,[status(thm)],[18512])).
% 292.79/185.33 tff(18514,plain,
% 292.79/185.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s4) | node18(c_e_h_1, c_h, s4, s5) | (~node19(c_e_h_1, c_h, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s4) | (~node19(c_e_h_1, c_h, s4, s5)) | node18(c_e_h_1, c_h, s4, s5))),
% 292.79/185.33 inference(transitivity,[status(thm)],[18513, 18511])).
% 292.79/185.33 tff(18515,plain,
% 292.79/185.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s4) | node18(c_e_h_1, c_h, s4, s5) | (~node19(c_e_h_1, c_h, s4, s5)))),
% 292.79/185.33 inference(quant_inst,[status(thm)],[])).
% 292.79/185.33 tff(18516,plain,
% 292.79/185.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s4) | (~node19(c_e_h_1, c_h, s4, s5)) | node18(c_e_h_1, c_h, s4, s5)),
% 292.79/185.33 inference(modus_ponens,[status(thm)],[18515, 18514])).
% 292.79/185.33 tff(18517,plain,
% 292.79/185.33 (node17(c_e_h_1, c_h, s4) | node18(c_e_h_1, c_h, s4, s5)),
% 292.79/185.33 inference(unit_resolution,[status(thm)],[18516, 776, 18472])).
% 292.79/185.33 tff(18518,plain,
% 292.79/185.33 (node18(c_e_h_1, c_h, s4, s5)),
% 292.79/185.33 inference(unit_resolution,[status(thm)],[18517, 18510])).
% 292.79/185.33 tff(18519,plain,
% 292.79/185.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s5)) | (~node18(c_e_h_1, c_h, s4, s5)) | m_c_h_element_v_out(c_e_h_1, c_h, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s5)) | (~node18(c_e_h_1, c_h, s4, s5)) | m_c_h_element_v_out(c_e_h_1, c_h, s4))),
% 292.79/185.33 inference(rewrite,[status(thm)],[])).
% 292.79/185.33 tff(18520,plain,
% 292.79/185.33 (((~m_c_h_element_v_out(c_e_h_1, c_h, s5)) | m_c_h_element_v_out(c_e_h_1, c_h, s4) | (~node18(c_e_h_1, c_h, s4, s5))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_h, s5)) | (~node18(c_e_h_1, c_h, s4, s5)) | m_c_h_element_v_out(c_e_h_1, c_h, s4))),
% 292.79/185.33 inference(rewrite,[status(thm)],[])).
% 292.79/185.33 tff(18521,plain,
% 292.79/185.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s5)) | m_c_h_element_v_out(c_e_h_1, c_h, s4) | (~node18(c_e_h_1, c_h, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s5)) | (~node18(c_e_h_1, c_h, s4, s5)) | m_c_h_element_v_out(c_e_h_1, c_h, s4)))),
% 292.79/185.33 inference(monotonicity,[status(thm)],[18520])).
% 292.79/185.33 tff(18522,plain,
% 292.79/185.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s5)) | m_c_h_element_v_out(c_e_h_1, c_h, s4) | (~node18(c_e_h_1, c_h, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s5)) | (~node18(c_e_h_1, c_h, s4, s5)) | m_c_h_element_v_out(c_e_h_1, c_h, s4))),
% 292.79/185.33 inference(transitivity,[status(thm)],[18521, 18519])).
% 292.79/185.33 tff(18523,plain,
% 292.79/185.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s5)) | m_c_h_element_v_out(c_e_h_1, c_h, s4) | (~node18(c_e_h_1, c_h, s4, s5)))),
% 292.79/185.33 inference(quant_inst,[status(thm)],[])).
% 292.79/185.33 tff(18524,plain,
% 292.79/185.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s5)) | (~node18(c_e_h_1, c_h, s4, s5)) | m_c_h_element_v_out(c_e_h_1, c_h, s4)),
% 292.79/185.33 inference(modus_ponens,[status(thm)],[18523, 18522])).
% 292.79/185.33 tff(18525,plain,
% 292.79/185.33 ($false),
% 292.79/185.33 inference(unit_resolution,[status(thm)],[18524, 753, 18460, 18518, 17479])).
% 292.79/185.33 tff(18526,plain,(m_c_h_element_v_out(c_e_h_1, c_h, s4) | (~m_c_h_element_v_out(c_e_h_1, c_h, s5)) | node14(c_e_h_1, c_h, s4, s5)), inference(lemma,lemma(discharge,[]))).
% 292.79/185.33 tff(18527,plain,
% 292.79/185.33 (node14(c_e_h_1, c_h, s4, s5)),
% 292.79/185.33 inference(unit_resolution,[status(thm)],[18526, 17479, 18460])).
% 292.79/185.33 tff(18528,plain,
% 292.79/185.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s4, s5)) | m_c_h_element_v_in1(c_e_h_1, c_h, s4) | (~m_c_h_element_v_out(c_e_h_1, c_h, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_1, c_h, s4, s5)) | m_c_h_element_v_in1(c_e_h_1, c_h, s4) | (~m_c_h_element_v_out(c_e_h_1, c_h, s5)))),
% 292.79/185.33 inference(rewrite,[status(thm)],[])).
% 292.79/185.33 tff(18529,plain,
% 292.79/185.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s4, s5)) | m_c_h_element_v_in1(c_e_h_1, c_h, s4) | (~m_c_h_element_v_out(c_e_h_1, c_h, s5)))),
% 292.79/185.33 inference(quant_inst,[status(thm)],[])).
% 292.79/185.33 tff(18530,plain,
% 292.79/185.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_1, c_h, s4, s5)) | m_c_h_element_v_in1(c_e_h_1, c_h, s4) | (~m_c_h_element_v_out(c_e_h_1, c_h, s5))),
% 292.79/185.33 inference(modus_ponens,[status(thm)],[18529, 18528])).
% 292.79/185.33 tff(18531,plain,
% 292.79/185.33 (m_c_h_element_v_in1(c_e_h_1, c_h, s4)),
% 292.79/185.33 inference(unit_resolution,[status(thm)],[18530, 223, 18460, 18527])).
% 292.79/185.33 tff(18532,plain,
% 292.79/185.33 ((~m_c_h_element_v_in1(c_e_h_1, c_h, s4)) | (~node17(c_e_h_1, c_h, s4))),
% 292.79/185.33 inference(unit_resolution,[status(thm)],[18491, 919, 18483])).
% 292.79/185.33 tff(18533,plain,
% 292.79/185.33 (~node17(c_e_h_1, c_h, s4)),
% 292.79/185.33 inference(unit_resolution,[status(thm)],[18532, 18531])).
% 292.79/185.33 tff(18534,plain,
% 292.79/185.33 (node18(c_e_h_1, c_h, s4, s5)),
% 292.79/185.33 inference(unit_resolution,[status(thm)],[18517, 18533])).
% 292.79/185.33 tff(18535,plain,
% 292.79/185.33 ($false),
% 292.79/185.33 inference(unit_resolution,[status(thm)],[18524, 753, 18460, 18534, 17479])).
% 292.79/185.33 tff(18536,plain,(m_c_h_element_v_out(c_e_h_1, c_h, s4) | (~m_c_h_element_v_out(c_e_h_1, c_h, s5)) | m_c_h_element_v_in2(c_e_h_1, c_h, s4)), inference(lemma,lemma(discharge,[]))).
% 292.79/185.33 tff(18537,plain,
% 292.79/185.33 ((~m_c_h_element_v_out(c_e_h_1, c_h, s5)) | m_c_h_element_v_in2(c_e_h_1, c_h, s4)),
% 292.79/185.33 inference(unit_resolution,[status(thm)],[18536, 17477])).
% 292.79/185.33 tff(18538,plain,
% 292.79/185.33 (~m_c_h_element_v_out(c_e_h_1, c_h, s5)),
% 292.79/185.33 inference(unit_resolution,[status(thm)],[18537, 18459])).
% 292.79/185.33 tff(18539,assumption,(m_c_h_element_v_out(c_e_h_1, c_h, s6)), introduced(assumption)).
% 292.79/185.33 tff(18540,assumption,(~m_c_h_element_v_out(c_e_h_1, c_h, s5)), introduced(assumption)).
% 292.79/185.33 tff(18541,assumption,(node15(c_e_h_1, c_h, s5, s6)), introduced(assumption)).
% 292.79/185.33 tff(18542,plain,
% 292.79/185.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s6)) | (~node15(c_e_h_1, c_h, s5, s6)) | m_c_h_element_v_out(c_e_h_1, c_h, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s6)) | (~node15(c_e_h_1, c_h, s5, s6)) | m_c_h_element_v_out(c_e_h_1, c_h, s5))),
% 292.79/185.33 inference(rewrite,[status(thm)],[])).
% 292.79/185.33 tff(18543,plain,
% 292.79/185.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s6)) | (~node15(c_e_h_1, c_h, s5, s6)) | m_c_h_element_v_out(c_e_h_1, c_h, s5))),
% 292.79/185.34 inference(quant_inst,[status(thm)],[])).
% 292.79/185.34 tff(18544,plain,
% 292.79/185.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s6)) | (~node15(c_e_h_1, c_h, s5, s6)) | m_c_h_element_v_out(c_e_h_1, c_h, s5)),
% 292.79/185.34 inference(modus_ponens,[status(thm)],[18543, 18542])).
% 292.79/185.34 tff(18545,plain,
% 292.79/185.34 ($false),
% 292.79/185.34 inference(unit_resolution,[status(thm)],[18544, 147, 18540, 18539, 18541])).
% 292.79/185.34 tff(18546,plain,((~node15(c_e_h_1, c_h, s5, s6)) | m_c_h_element_v_out(c_e_h_1, c_h, s5) | (~m_c_h_element_v_out(c_e_h_1, c_h, s6))), inference(lemma,lemma(discharge,[]))).
% 292.79/185.34 tff(18547,plain,
% 292.79/185.34 (~node15(c_e_h_1, c_h, s5, s6)),
% 292.79/185.34 inference(unit_resolution,[status(thm)],[18546, 18539, 18540])).
% 292.79/185.34 tff(18548,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_h, s5)), introduced(assumption)).
% 292.79/185.34 tff(18549,assumption,(node14(c_e_h_1, c_h, s5, s6)), introduced(assumption)).
% 292.79/185.34 tff(18550,plain,
% 292.79/185.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s5) | (~m_c_h_element_v_out(c_e_h_1, c_h, s6)) | (~node14(c_e_h_1, c_h, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s5) | (~m_c_h_element_v_out(c_e_h_1, c_h, s6)) | (~node14(c_e_h_1, c_h, s5, s6)))),
% 292.79/185.34 inference(rewrite,[status(thm)],[])).
% 292.79/185.34 tff(18551,plain,
% 292.79/185.34 (((~node14(c_e_h_1, c_h, s5, s6)) | m_c_h_element_v_in1(c_e_h_1, c_h, s5) | (~m_c_h_element_v_out(c_e_h_1, c_h, s6))) <=> (m_c_h_element_v_in1(c_e_h_1, c_h, s5) | (~m_c_h_element_v_out(c_e_h_1, c_h, s6)) | (~node14(c_e_h_1, c_h, s5, s6)))),
% 292.79/185.34 inference(rewrite,[status(thm)],[])).
% 292.79/185.34 tff(18552,plain,
% 292.79/185.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s5, s6)) | m_c_h_element_v_in1(c_e_h_1, c_h, s5) | (~m_c_h_element_v_out(c_e_h_1, c_h, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s5) | (~m_c_h_element_v_out(c_e_h_1, c_h, s6)) | (~node14(c_e_h_1, c_h, s5, s6))))),
% 292.79/185.34 inference(monotonicity,[status(thm)],[18551])).
% 292.79/185.34 tff(18553,plain,
% 292.79/185.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s5, s6)) | m_c_h_element_v_in1(c_e_h_1, c_h, s5) | (~m_c_h_element_v_out(c_e_h_1, c_h, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s5) | (~m_c_h_element_v_out(c_e_h_1, c_h, s6)) | (~node14(c_e_h_1, c_h, s5, s6)))),
% 292.79/185.34 inference(transitivity,[status(thm)],[18552, 18550])).
% 292.79/185.34 tff(18554,plain,
% 292.79/185.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s5, s6)) | m_c_h_element_v_in1(c_e_h_1, c_h, s5) | (~m_c_h_element_v_out(c_e_h_1, c_h, s6)))),
% 292.79/185.34 inference(quant_inst,[status(thm)],[])).
% 292.79/185.34 tff(18555,plain,
% 292.79/185.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s5) | (~m_c_h_element_v_out(c_e_h_1, c_h, s6)) | (~node14(c_e_h_1, c_h, s5, s6))),
% 292.79/185.34 inference(modus_ponens,[status(thm)],[18554, 18553])).
% 292.79/185.34 tff(18556,plain,
% 292.79/185.34 ($false),
% 292.79/185.34 inference(unit_resolution,[status(thm)],[18555, 223, 18539, 18549, 18548])).
% 292.79/185.34 tff(18557,plain,((~node14(c_e_h_1, c_h, s5, s6)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s6)) | m_c_h_element_v_in1(c_e_h_1, c_h, s5)), inference(lemma,lemma(discharge,[]))).
% 292.79/185.34 tff(18558,plain,
% 292.79/185.34 (~node14(c_e_h_1, c_h, s5, s6)),
% 292.79/185.34 inference(unit_resolution,[status(thm)],[18557, 18539, 18548])).
% 292.79/185.34 tff(18559,plain,
% 292.79/185.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s5, s6)) | node19(c_e_h_1, c_h, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s5, s6)) | node19(c_e_h_1, c_h, s5, s6))),
% 292.79/185.34 inference(rewrite,[status(thm)],[])).
% 292.79/185.34 tff(18560,plain,
% 292.79/185.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s5, s6)) | node19(c_e_h_1, c_h, s5, s6))),
% 292.79/185.34 inference(quant_inst,[status(thm)],[])).
% 292.79/185.34 tff(18561,plain,
% 292.79/185.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s5, s6)) | node19(c_e_h_1, c_h, s5, s6)),
% 292.79/185.34 inference(modus_ponens,[status(thm)],[18560, 18559])).
% 292.79/185.34 tff(18562,plain,
% 292.79/185.34 (node19(c_e_h_1, c_h, s5, s6)),
% 292.79/185.34 inference(unit_resolution,[status(thm)],[18561, 190, 1406])).
% 292.79/185.34 tff(18563,plain,
% 292.79/185.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s5) | (~node19(c_e_h_1, c_h, s5, s6)) | node15(c_e_h_1, c_h, s5, s6) | node14(c_e_h_1, c_h, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s5) | (~node19(c_e_h_1, c_h, s5, s6)) | node15(c_e_h_1, c_h, s5, s6) | node14(c_e_h_1, c_h, s5, s6))),
% 292.79/185.34 inference(rewrite,[status(thm)],[])).
% 292.79/185.34 tff(18564,plain,
% 292.79/185.34 ((node16(c_e_h_1, c_h, s5) | node14(c_e_h_1, c_h, s5, s6) | node15(c_e_h_1, c_h, s5, s6) | (~node19(c_e_h_1, c_h, s5, s6))) <=> (node16(c_e_h_1, c_h, s5) | (~node19(c_e_h_1, c_h, s5, s6)) | node15(c_e_h_1, c_h, s5, s6) | node14(c_e_h_1, c_h, s5, s6))),
% 292.79/185.34 inference(rewrite,[status(thm)],[])).
% 292.79/185.34 tff(18565,plain,
% 292.79/185.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s5) | node14(c_e_h_1, c_h, s5, s6) | node15(c_e_h_1, c_h, s5, s6) | (~node19(c_e_h_1, c_h, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s5) | (~node19(c_e_h_1, c_h, s5, s6)) | node15(c_e_h_1, c_h, s5, s6) | node14(c_e_h_1, c_h, s5, s6)))),
% 292.79/185.34 inference(monotonicity,[status(thm)],[18564])).
% 292.79/185.34 tff(18566,plain,
% 292.79/185.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s5) | node14(c_e_h_1, c_h, s5, s6) | node15(c_e_h_1, c_h, s5, s6) | (~node19(c_e_h_1, c_h, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s5) | (~node19(c_e_h_1, c_h, s5, s6)) | node15(c_e_h_1, c_h, s5, s6) | node14(c_e_h_1, c_h, s5, s6))),
% 292.79/185.34 inference(transitivity,[status(thm)],[18565, 18563])).
% 292.79/185.34 tff(18567,plain,
% 292.79/185.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s5) | node14(c_e_h_1, c_h, s5, s6) | node15(c_e_h_1, c_h, s5, s6) | (~node19(c_e_h_1, c_h, s5, s6)))),
% 292.79/185.34 inference(quant_inst,[status(thm)],[])).
% 292.79/185.34 tff(18568,plain,
% 292.79/185.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s5) | (~node19(c_e_h_1, c_h, s5, s6)) | node15(c_e_h_1, c_h, s5, s6) | node14(c_e_h_1, c_h, s5, s6)),
% 292.79/185.34 inference(modus_ponens,[status(thm)],[18567, 18566])).
% 292.79/185.34 tff(18569,plain,
% 292.79/185.34 (node16(c_e_h_1, c_h, s5) | node15(c_e_h_1, c_h, s5, s6) | node14(c_e_h_1, c_h, s5, s6)),
% 292.79/185.34 inference(unit_resolution,[status(thm)],[18568, 204, 18562])).
% 292.79/185.34 tff(18570,plain,
% 292.79/185.34 (node16(c_e_h_1, c_h, s5)),
% 292.79/185.34 inference(unit_resolution,[status(thm)],[18569, 18558, 18547])).
% 292.79/185.34 tff(18571,plain,
% 292.79/185.35 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s5)) | m_c_h_element_v_in1(c_e_h_1, c_h, s5) | m_c_h_element_v_in2(c_e_h_1, c_h, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s5)) | m_c_h_element_v_in1(c_e_h_1, c_h, s5) | m_c_h_element_v_in2(c_e_h_1, c_h, s5))),
% 292.79/185.35 inference(rewrite,[status(thm)],[])).
% 292.79/185.35 tff(18572,plain,
% 292.79/185.35 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s5)) | m_c_h_element_v_in1(c_e_h_1, c_h, s5) | m_c_h_element_v_in2(c_e_h_1, c_h, s5))),
% 292.79/185.35 inference(quant_inst,[status(thm)],[])).
% 292.79/185.35 tff(18573,plain,
% 292.79/185.35 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s5)) | m_c_h_element_v_in1(c_e_h_1, c_h, s5) | m_c_h_element_v_in2(c_e_h_1, c_h, s5)),
% 292.79/185.35 inference(modus_ponens,[status(thm)],[18572, 18571])).
% 292.79/185.35 tff(18574,plain,
% 292.79/185.35 ((~node16(c_e_h_1, c_h, s5)) | m_c_h_element_v_in2(c_e_h_1, c_h, s5)),
% 292.79/185.35 inference(unit_resolution,[status(thm)],[18573, 178, 18548])).
% 292.79/185.35 tff(18575,plain,
% 292.79/185.35 (m_c_h_element_v_in2(c_e_h_1, c_h, s5)),
% 292.79/185.35 inference(unit_resolution,[status(thm)],[18574, 18570])).
% 292.79/185.35 tff(18576,plain,
% 292.79/185.35 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_h, s5)) | m_c_h_element_v_in1(c_e_h_1, c_h, s5) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_h, s5)) | m_c_h_element_v_in1(c_e_h_1, c_h, s5) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s5)))),
% 292.79/185.35 inference(rewrite,[status(thm)],[])).
% 292.79/185.35 tff(18577,plain,
% 292.79/185.35 ((m_c_h_element_v_in1(c_e_h_1, c_h, s5) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s5)) | (~node17(c_e_h_1, c_h, s5))) <=> ((~node17(c_e_h_1, c_h, s5)) | m_c_h_element_v_in1(c_e_h_1, c_h, s5) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s5)))),
% 292.79/185.35 inference(rewrite,[status(thm)],[])).
% 292.79/185.35 tff(18578,plain,
% 292.79/185.35 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s5) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s5)) | (~node17(c_e_h_1, c_h, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_h, s5)) | m_c_h_element_v_in1(c_e_h_1, c_h, s5) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s5))))),
% 292.79/185.35 inference(monotonicity,[status(thm)],[18577])).
% 292.79/185.35 tff(18579,plain,
% 292.79/185.35 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s5) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s5)) | (~node17(c_e_h_1, c_h, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_h, s5)) | m_c_h_element_v_in1(c_e_h_1, c_h, s5) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s5)))),
% 292.79/185.35 inference(transitivity,[status(thm)],[18578, 18576])).
% 292.79/185.35 tff(18580,plain,
% 292.79/185.35 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s5) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s5)) | (~node17(c_e_h_1, c_h, s5)))),
% 292.79/185.35 inference(quant_inst,[status(thm)],[])).
% 292.79/185.35 tff(18581,plain,
% 292.79/185.35 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_h, s5)) | m_c_h_element_v_in1(c_e_h_1, c_h, s5) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s5))),
% 292.79/185.35 inference(modus_ponens,[status(thm)],[18580, 18579])).
% 292.79/185.35 tff(18582,plain,
% 292.79/185.35 ((~node17(c_e_h_1, c_h, s5)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s5))),
% 292.79/185.35 inference(unit_resolution,[status(thm)],[18581, 859, 18548])).
% 292.79/185.35 tff(18583,plain,
% 292.79/185.35 (~node17(c_e_h_1, c_h, s5)),
% 292.79/185.35 inference(unit_resolution,[status(thm)],[18582, 18575])).
% 292.79/185.35 tff(18584,plain,
% 292.79/185.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s5) | (~node19(c_e_h_1, c_h, s5, s6)) | node18(c_e_h_1, c_h, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s5) | (~node19(c_e_h_1, c_h, s5, s6)) | node18(c_e_h_1, c_h, s5, s6))),
% 292.79/185.35 inference(rewrite,[status(thm)],[])).
% 292.79/185.35 tff(18585,plain,
% 292.79/185.35 ((node17(c_e_h_1, c_h, s5) | node18(c_e_h_1, c_h, s5, s6) | (~node19(c_e_h_1, c_h, s5, s6))) <=> (node17(c_e_h_1, c_h, s5) | (~node19(c_e_h_1, c_h, s5, s6)) | node18(c_e_h_1, c_h, s5, s6))),
% 292.79/185.35 inference(rewrite,[status(thm)],[])).
% 292.79/185.35 tff(18586,plain,
% 292.79/185.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s5) | node18(c_e_h_1, c_h, s5, s6) | (~node19(c_e_h_1, c_h, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s5) | (~node19(c_e_h_1, c_h, s5, s6)) | node18(c_e_h_1, c_h, s5, s6)))),
% 292.79/185.35 inference(monotonicity,[status(thm)],[18585])).
% 292.79/185.35 tff(18587,plain,
% 292.79/185.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s5) | node18(c_e_h_1, c_h, s5, s6) | (~node19(c_e_h_1, c_h, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s5) | (~node19(c_e_h_1, c_h, s5, s6)) | node18(c_e_h_1, c_h, s5, s6))),
% 292.79/185.35 inference(transitivity,[status(thm)],[18586, 18584])).
% 292.79/185.35 tff(18588,plain,
% 292.79/185.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s5) | node18(c_e_h_1, c_h, s5, s6) | (~node19(c_e_h_1, c_h, s5, s6)))),
% 292.79/185.35 inference(quant_inst,[status(thm)],[])).
% 292.79/185.35 tff(18589,plain,
% 292.79/185.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s5) | (~node19(c_e_h_1, c_h, s5, s6)) | node18(c_e_h_1, c_h, s5, s6)),
% 292.79/185.35 inference(modus_ponens,[status(thm)],[18588, 18587])).
% 292.79/185.35 tff(18590,plain,
% 292.79/185.35 (node17(c_e_h_1, c_h, s5) | node18(c_e_h_1, c_h, s5, s6)),
% 292.79/185.35 inference(unit_resolution,[status(thm)],[18589, 776, 18562])).
% 292.79/185.35 tff(18591,plain,
% 292.79/185.35 (node18(c_e_h_1, c_h, s5, s6)),
% 292.79/185.35 inference(unit_resolution,[status(thm)],[18590, 18583])).
% 292.79/185.35 tff(18592,plain,
% 292.79/185.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_h, s5) | (~node18(c_e_h_1, c_h, s5, s6)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s5) | (~node18(c_e_h_1, c_h, s5, s6)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s6)))),
% 292.79/185.35 inference(rewrite,[status(thm)],[])).
% 292.79/185.35 tff(18593,plain,
% 292.79/185.35 (((~m_c_h_element_v_out(c_e_h_1, c_h, s6)) | m_c_h_element_v_out(c_e_h_1, c_h, s5) | (~node18(c_e_h_1, c_h, s5, s6))) <=> (m_c_h_element_v_out(c_e_h_1, c_h, s5) | (~node18(c_e_h_1, c_h, s5, s6)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s6)))),
% 292.79/185.35 inference(rewrite,[status(thm)],[])).
% 292.79/185.35 tff(18594,plain,
% 292.79/185.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s6)) | m_c_h_element_v_out(c_e_h_1, c_h, s5) | (~node18(c_e_h_1, c_h, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_h, s5) | (~node18(c_e_h_1, c_h, s5, s6)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s6))))),
% 292.79/185.35 inference(monotonicity,[status(thm)],[18593])).
% 292.79/185.35 tff(18595,plain,
% 292.79/185.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s6)) | m_c_h_element_v_out(c_e_h_1, c_h, s5) | (~node18(c_e_h_1, c_h, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s5) | (~node18(c_e_h_1, c_h, s5, s6)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s6)))),
% 292.79/185.35 inference(transitivity,[status(thm)],[18594, 18592])).
% 292.79/185.35 tff(18596,plain,
% 292.79/185.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s6)) | m_c_h_element_v_out(c_e_h_1, c_h, s5) | (~node18(c_e_h_1, c_h, s5, s6)))),
% 292.79/185.35 inference(quant_inst,[status(thm)],[])).
% 292.79/185.35 tff(18597,plain,
% 292.79/185.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s5) | (~node18(c_e_h_1, c_h, s5, s6)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s6))),
% 292.79/185.35 inference(modus_ponens,[status(thm)],[18596, 18595])).
% 292.79/185.35 tff(18598,plain,
% 292.79/185.35 ($false),
% 292.79/185.35 inference(unit_resolution,[status(thm)],[18597, 753, 18540, 18539, 18591])).
% 292.79/185.35 tff(18599,plain,((~m_c_h_element_v_out(c_e_h_1, c_h, s6)) | m_c_h_element_v_out(c_e_h_1, c_h, s5) | m_c_h_element_v_in1(c_e_h_1, c_h, s5)), inference(lemma,lemma(discharge,[]))).
% 292.79/185.35 tff(18600,plain,
% 292.79/185.35 (m_c_h_element_v_in1(c_e_h_1, c_h, s5)),
% 292.79/185.35 inference(unit_resolution,[status(thm)],[18599, 18540, 18539])).
% 292.79/185.35 tff(18601,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_h, s5)), introduced(assumption)).
% 292.79/185.35 tff(18602,plain,
% 292.79/185.35 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_h, s5)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s5)) | m_c_h_element_v_in2(c_e_h_1, c_h, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_h, s5)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s5)) | m_c_h_element_v_in2(c_e_h_1, c_h, s5))),
% 292.79/185.35 inference(rewrite,[status(thm)],[])).
% 292.79/185.35 tff(18603,plain,
% 292.79/185.35 (((~m_c_h_element_v_in1(c_e_h_1, c_h, s5)) | m_c_h_element_v_in2(c_e_h_1, c_h, s5) | (~node17(c_e_h_1, c_h, s5))) <=> ((~node17(c_e_h_1, c_h, s5)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s5)) | m_c_h_element_v_in2(c_e_h_1, c_h, s5))),
% 292.79/185.35 inference(rewrite,[status(thm)],[])).
% 292.79/185.35 tff(18604,plain,
% 292.79/185.35 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s5)) | m_c_h_element_v_in2(c_e_h_1, c_h, s5) | (~node17(c_e_h_1, c_h, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_h, s5)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s5)) | m_c_h_element_v_in2(c_e_h_1, c_h, s5)))),
% 292.79/185.35 inference(monotonicity,[status(thm)],[18603])).
% 292.79/185.35 tff(18605,plain,
% 292.79/185.35 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s5)) | m_c_h_element_v_in2(c_e_h_1, c_h, s5) | (~node17(c_e_h_1, c_h, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_h, s5)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s5)) | m_c_h_element_v_in2(c_e_h_1, c_h, s5))),
% 292.79/185.35 inference(transitivity,[status(thm)],[18604, 18602])).
% 292.79/185.35 tff(18606,plain,
% 292.79/185.35 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s5)) | m_c_h_element_v_in2(c_e_h_1, c_h, s5) | (~node17(c_e_h_1, c_h, s5)))),
% 292.79/185.35 inference(quant_inst,[status(thm)],[])).
% 292.79/185.35 tff(18607,plain,
% 292.79/185.36 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_h, s5)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s5)) | m_c_h_element_v_in2(c_e_h_1, c_h, s5)),
% 292.79/185.36 inference(modus_ponens,[status(thm)],[18606, 18605])).
% 292.79/185.36 tff(18608,plain,
% 292.79/185.36 ((~node17(c_e_h_1, c_h, s5)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s5))),
% 292.79/185.36 inference(unit_resolution,[status(thm)],[18607, 919, 18601])).
% 292.79/185.36 tff(18609,plain,
% 292.79/185.36 (~node17(c_e_h_1, c_h, s5)),
% 292.79/185.36 inference(unit_resolution,[status(thm)],[18608, 18600])).
% 292.79/185.36 tff(18610,plain,
% 292.79/185.36 (node18(c_e_h_1, c_h, s5, s6)),
% 292.79/185.36 inference(unit_resolution,[status(thm)],[18590, 18609])).
% 292.79/185.36 tff(18611,plain,
% 292.79/185.36 ($false),
% 292.79/185.36 inference(unit_resolution,[status(thm)],[18597, 753, 18540, 18539, 18610])).
% 292.79/185.36 tff(18612,plain,(m_c_h_element_v_out(c_e_h_1, c_h, s5) | (~m_c_h_element_v_out(c_e_h_1, c_h, s6)) | m_c_h_element_v_in2(c_e_h_1, c_h, s5)), inference(lemma,lemma(discharge,[]))).
% 292.79/185.36 tff(18613,plain,
% 292.79/185.36 ((~m_c_h_element_v_out(c_e_h_1, c_h, s6)) | m_c_h_element_v_in2(c_e_h_1, c_h, s5)),
% 292.79/185.36 inference(unit_resolution,[status(thm)],[18612, 18538])).
% 292.79/185.36 tff(18614,plain,
% 292.79/185.36 (~m_c_h_element_v_out(c_e_h_1, c_h, s6)),
% 292.79/185.36 inference(unit_resolution,[status(thm)],[18613, 18455])).
% 292.79/185.36 tff(18615,plain,
% 292.79/185.36 (((~![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))) | (m_and_h_gate_v_in2(c_e_h_1, c_k, s6) | m_c_h_element_v_out(c_e_h_1, c_h, s6))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))) | m_and_h_gate_v_in2(c_e_h_1, c_k, s6) | m_c_h_element_v_out(c_e_h_1, c_h, s6))),
% 292.79/185.36 inference(rewrite,[status(thm)],[])).
% 292.79/185.36 tff(18616,plain,
% 292.79/185.36 ((~![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))) | (m_and_h_gate_v_in2(c_e_h_1, c_k, s6) | m_c_h_element_v_out(c_e_h_1, c_h, s6))),
% 292.79/185.36 inference(quant_inst,[status(thm)],[])).
% 292.79/185.36 tff(18617,plain,
% 292.79/185.36 ((~![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))) | m_and_h_gate_v_in2(c_e_h_1, c_k, s6) | m_c_h_element_v_out(c_e_h_1, c_h, s6)),
% 292.79/185.36 inference(modus_ponens,[status(thm)],[18616, 18615])).
% 292.79/185.36 tff(18618,plain,
% 292.79/185.36 (m_and_h_gate_v_in2(c_e_h_1, c_k, s6) | m_c_h_element_v_out(c_e_h_1, c_h, s6)),
% 292.79/185.36 inference(unit_resolution,[status(thm)],[18617, 6420])).
% 292.79/185.36 tff(18619,plain,
% 292.79/185.36 (m_and_h_gate_v_in2(c_e_h_1, c_k, s6)),
% 292.79/185.36 inference(unit_resolution,[status(thm)],[18618, 18614])).
% 292.79/185.36 tff(18620,plain,
% 292.79/185.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_k, s6)) | (~m_and_h_gate_v_in2(c_e_h_1, c_k, s6)) | (~node21(c_e_h_1, c_k, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_k, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in1(c_e_h_1, c_k, s6)) | (~m_and_h_gate_v_in2(c_e_h_1, c_k, s6)) | (~node21(c_e_h_1, c_k, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_k, s7))),
% 292.79/185.36 inference(rewrite,[status(thm)],[])).
% 292.79/185.36 tff(18621,plain,
% 292.79/185.36 (((~node21(c_e_h_1, c_k, s6, s7)) | (~m_and_h_gate_v_in2(c_e_h_1, c_k, s6)) | (~m_and_h_gate_v_in1(c_e_h_1, c_k, s6)) | m_and_h_gate_v_out(c_e_h_1, c_k, s7)) <=> ((~m_and_h_gate_v_in1(c_e_h_1, c_k, s6)) | (~m_and_h_gate_v_in2(c_e_h_1, c_k, s6)) | (~node21(c_e_h_1, c_k, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_k, s7))),
% 292.79/185.36 inference(rewrite,[status(thm)],[])).
% 292.79/185.36 tff(18622,plain,
% 292.79/185.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_1, c_k, s6, s7)) | (~m_and_h_gate_v_in2(c_e_h_1, c_k, s6)) | (~m_and_h_gate_v_in1(c_e_h_1, c_k, s6)) | m_and_h_gate_v_out(c_e_h_1, c_k, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_k, s6)) | (~m_and_h_gate_v_in2(c_e_h_1, c_k, s6)) | (~node21(c_e_h_1, c_k, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_k, s7)))),
% 292.79/185.36 inference(monotonicity,[status(thm)],[18621])).
% 292.79/185.36 tff(18623,plain,
% 292.79/185.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_1, c_k, s6, s7)) | (~m_and_h_gate_v_in2(c_e_h_1, c_k, s6)) | (~m_and_h_gate_v_in1(c_e_h_1, c_k, s6)) | m_and_h_gate_v_out(c_e_h_1, c_k, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in1(c_e_h_1, c_k, s6)) | (~m_and_h_gate_v_in2(c_e_h_1, c_k, s6)) | (~node21(c_e_h_1, c_k, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_k, s7))),
% 292.79/185.36 inference(transitivity,[status(thm)],[18622, 18620])).
% 292.79/185.36 tff(18624,plain,
% 292.79/185.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_1, c_k, s6, s7)) | (~m_and_h_gate_v_in2(c_e_h_1, c_k, s6)) | (~m_and_h_gate_v_in1(c_e_h_1, c_k, s6)) | m_and_h_gate_v_out(c_e_h_1, c_k, s7))),
% 292.79/185.36 inference(quant_inst,[status(thm)],[])).
% 292.79/185.36 tff(18625,plain,
% 292.79/185.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in1(c_e_h_1, c_k, s6)) | (~m_and_h_gate_v_in2(c_e_h_1, c_k, s6)) | (~node21(c_e_h_1, c_k, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_k, s7)),
% 292.79/185.36 inference(modus_ponens,[status(thm)],[18624, 18623])).
% 292.79/185.36 tff(18626,plain,
% 292.79/185.36 ($false),
% 292.79/185.36 inference(unit_resolution,[status(thm)],[18625, 5851, 18619, 18311, 15905, 15390])).
% 292.79/185.36 tff(18627,plain,((~node21(c_e_h_1, c_k, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_k, s7) | (~m_and_h_gate_v_in1(c_e_h_1, c_k, s6))), inference(lemma,lemma(discharge,[]))).
% 292.79/185.36 tff(18628,plain,
% 292.79/185.36 (~m_and_h_gate_v_in1(c_e_h_1, c_k, s6)),
% 292.79/185.36 inference(unit_resolution,[status(thm)],[18627, 18310, 15905])).
% 292.79/185.36 tff(18629,plain,
% 292.79/185.36 (m_or_h_gate_v_out(c_e_h_1, c_g, s6)),
% 292.79/185.36 inference(unit_resolution,[status(thm)],[15591, 18300, 14572])).
% 292.79/185.36 tff(18630,plain,
% 292.79/185.36 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X))) | ((~m_or_h_gate_v_out(c_e_h_1, c_g, s6)) | m_and_h_gate_v_in1(c_e_h_1, c_k, s6))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X))) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s6)) | m_and_h_gate_v_in1(c_e_h_1, c_k, s6))),
% 292.79/185.36 inference(rewrite,[status(thm)],[])).
% 292.79/185.36 tff(18631,plain,
% 292.79/185.36 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X))) | ((~m_or_h_gate_v_out(c_e_h_1, c_g, s6)) | m_and_h_gate_v_in1(c_e_h_1, c_k, s6))),
% 292.79/185.36 inference(quant_inst,[status(thm)],[])).
% 292.79/185.36 tff(18632,plain,
% 292.79/185.36 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X))) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s6)) | m_and_h_gate_v_in1(c_e_h_1, c_k, s6)),
% 292.79/185.36 inference(modus_ponens,[status(thm)],[18631, 18630])).
% 292.79/185.36 tff(18633,plain,
% 292.79/185.36 ($false),
% 292.79/185.36 inference(unit_resolution,[status(thm)],[18632, 6229, 18629, 18628])).
% 292.79/185.36 tff(18634,plain,(m_or_h_gate_v_out(c_e_h_1, c_g, s4) | m_and_h_gate_v_out(c_e_h_1, c_k, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s7))), inference(lemma,lemma(discharge,[]))).
% 292.79/185.36 tff(18635,plain,
% 292.79/185.36 (m_or_h_gate_v_out(c_e_h_1, c_g, s4)),
% 292.79/185.36 inference(unit_resolution,[status(thm)],[18634, 18288, 18254])).
% 292.79/185.36 tff(18636,plain,
% 292.79/185.36 (m_or_h_gate_v_out(c_e_h_1, c_g, s5)),
% 292.79/185.36 inference(unit_resolution,[status(thm)],[15624, 18635])).
% 292.79/185.36 tff(18637,plain,
% 292.79/185.36 (m_and_h_gate_v_out(c_e_h_1, c_c, s4)),
% 292.79/185.36 inference(unit_resolution,[status(thm)],[14848, 18636])).
% 292.79/185.36 tff(18638,plain,
% 292.79/185.36 (m_user_v_req(c_e_h_1, c_u, s2)),
% 292.79/185.36 inference(unit_resolution,[status(thm)],[14671, 18637])).
% 292.79/185.36 tff(18639,plain,
% 292.79/185.36 (m_user_v_req(c_e_h_1, c_u, s3)),
% 292.79/185.36 inference(unit_resolution,[status(thm)],[14760, 18638])).
% 292.79/185.36 tff(18640,plain,
% 292.79/185.36 (m_mutex_h_half_v_inp(c_e_h_1, c_a, s3)),
% 292.79/185.36 inference(unit_resolution,[status(thm)],[14768, 18639])).
% 292.79/185.36 tff(18641,plain,
% 292.79/185.36 (m_or_h_gate_v_in1(c_e_h_1, c_g, s3)),
% 292.79/185.36 inference(unit_resolution,[status(thm)],[14503, 18635])).
% 292.79/185.36 tff(18642,plain,
% 292.79/185.36 (m_and_h_gate_v_out(c_e_h_1, c_c, s3)),
% 292.79/185.36 inference(unit_resolution,[status(thm)],[14418, 2708, 18641])).
% 292.79/185.36 tff(18643,plain,
% 292.79/185.36 (node20(c_e_h_1, c_c, s2)),
% 292.79/185.36 inference(unit_resolution,[status(thm)],[14216, 18642])).
% 292.79/185.36 tff(18644,plain,
% 292.79/185.36 (m_and_h_gate_v_in1(c_e_h_1, c_c, s2)),
% 292.79/185.36 inference(unit_resolution,[status(thm)],[14224, 18643])).
% 292.79/185.36 tff(18645,plain,
% 292.79/185.36 (m_mutex_h_half_v_out(c_e_h_1, c_a, s2)),
% 292.79/185.36 inference(unit_resolution,[status(thm)],[14232, 18644])).
% 292.79/185.36 tff(18646,plain,
% 292.79/185.36 (m_mutex_h_half_v_out(c_e_h_1, c_a, s3)),
% 292.79/185.36 inference(unit_resolution,[status(thm)],[14381, 18645])).
% 292.79/185.36 tff(18647,plain,
% 292.79/185.36 (m_mutex_h_half_v_out(c_e_h_1, c_a, s4)),
% 292.79/185.36 inference(unit_resolution,[status(thm)],[14793, 18646, 18640])).
% 292.79/185.36 tff(18648,plain,
% 292.79/185.36 (m_and_h_gate_v_in1(c_e_h_1, c_c, s4)),
% 292.79/185.36 inference(unit_resolution,[status(thm)],[14810, 18647])).
% 292.79/185.36 tff(18649,plain,
% 292.79/185.36 (m_and_h_gate_v_out(c_e_h_1, c_c, s5)),
% 292.79/185.36 inference(unit_resolution,[status(thm)],[14843, 18648, 18637])).
% 292.79/185.36 tff(18650,plain,
% 292.79/185.36 (m_or_h_gate_v_in1(c_e_h_1, c_g, s5)),
% 292.79/185.36 inference(unit_resolution,[status(thm)],[15570, 5896, 18649])).
% 292.79/185.36 tff(18651,plain,
% 292.79/185.36 (~node4(c_e_h_1, c_g, s5)),
% 292.79/185.36 inference(unit_resolution,[status(thm)],[15566, 5516, 18650])).
% 292.79/185.36 tff(18652,plain,
% 292.79/185.36 (m_or_h_gate_v_out(c_e_h_1, c_g, s6)),
% 292.79/185.36 inference(unit_resolution,[status(thm)],[17071, 18651, 18636])).
% 292.79/185.36 tff(18653,plain,
% 292.79/185.36 ($false),
% 292.79/185.36 inference(unit_resolution,[status(thm)],[18632, 6229, 13630, 15397])).
% 292.79/185.36 tff(18654,plain,(m_and_h_gate_v_in1(c_e_h_1, c_k, s6) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s6))), inference(lemma,lemma(discharge,[]))).
% 292.79/185.36 tff(18655,plain,
% 292.79/185.36 (m_and_h_gate_v_in1(c_e_h_1, c_k, s6)),
% 292.79/185.36 inference(unit_resolution,[status(thm)],[18654, 18652])).
% 292.79/185.36 tff(18656,plain,
% 292.79/185.36 (~node21(c_e_h_1, c_k, s6, s7)),
% 292.79/185.36 inference(unit_resolution,[status(thm)],[18627, 18655, 18288])).
% 292.79/185.36 tff(18657,plain,
% 292.79/185.36 (node22(c_e_h_1, c_k, s6, s7)),
% 292.79/185.36 inference(unit_resolution,[status(thm)],[15418, 18656])).
% 292.79/185.36 tff(18658,plain,
% 292.79/185.36 (~m_and_h_gate_v_out(c_e_h_1, c_k, s6)),
% 292.79/185.36 inference(unit_resolution,[status(thm)],[18308, 18657, 18288])).
% 292.79/185.36 tff(18659,plain,
% 292.79/185.36 (~m_and_h_gate_v_in1(c_e_h_1, c_p, s6)),
% 292.79/185.36 inference(unit_resolution,[status(thm)],[18299, 18658])).
% 292.79/185.36 tff(18660,plain,
% 292.79/185.36 (~node20(c_e_h_1, c_p, s6)),
% 292.79/185.36 inference(unit_resolution,[status(thm)],[18295, 18659])).
% 292.79/185.36 tff(18661,plain,
% 292.79/185.36 (m_and_h_gate_v_out(c_e_h_1, c_p, s6)),
% 292.79/185.36 inference(unit_resolution,[status(thm)],[15825, 18660, 18254])).
% 292.79/185.36 tff(18662,plain,
% 292.79/185.36 (node20(c_e_h_1, c_p, s5)),
% 292.79/185.36 inference(unit_resolution,[status(thm)],[15765, 18661])).
% 292.79/185.36 tff(18663,plain,
% 292.79/185.36 (m_and_h_gate_v_in1(c_e_h_1, c_p, s5)),
% 292.79/185.36 inference(unit_resolution,[status(thm)],[15695, 18662])).
% 292.79/185.36 tff(18664,plain,
% 292.79/185.36 (m_and_h_gate_v_out(c_e_h_1, c_k, s5)),
% 292.79/185.36 inference(unit_resolution,[status(thm)],[15687, 18663])).
% 292.79/185.36 tff(18665,plain,
% 292.79/185.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_k, s5)) | (~node22(c_e_h_1, c_k, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_k, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s5)) | (~node22(c_e_h_1, c_k, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_k, s6))),
% 292.79/185.36 inference(rewrite,[status(thm)],[])).
% 292.79/185.36 tff(18666,plain,
% 292.79/185.36 ((m_and_h_gate_v_out(c_e_h_1, c_k, s6) | (~node22(c_e_h_1, c_k, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s5))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_k, s5)) | (~node22(c_e_h_1, c_k, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_k, s6))),
% 292.79/185.36 inference(rewrite,[status(thm)],[])).
% 292.79/185.36 tff(18667,plain,
% 292.79/185.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_1, c_k, s6) | (~node22(c_e_h_1, c_k, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_k, s5)) | (~node22(c_e_h_1, c_k, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_k, s6)))),
% 292.79/185.37 inference(monotonicity,[status(thm)],[18666])).
% 292.79/185.37 tff(18668,plain,
% 292.79/185.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_1, c_k, s6) | (~node22(c_e_h_1, c_k, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s5)) | (~node22(c_e_h_1, c_k, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_k, s6))),
% 292.79/185.37 inference(transitivity,[status(thm)],[18667, 18665])).
% 292.79/185.37 tff(18669,plain,
% 292.79/185.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_1, c_k, s6) | (~node22(c_e_h_1, c_k, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s5)))),
% 292.79/185.37 inference(quant_inst,[status(thm)],[])).
% 292.79/185.37 tff(18670,plain,
% 292.79/185.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s5)) | (~node22(c_e_h_1, c_k, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_k, s6)),
% 292.79/185.37 inference(modus_ponens,[status(thm)],[18669, 18668])).
% 292.79/185.37 tff(18671,plain,
% 292.79/185.37 ($false),
% 292.79/185.37 inference(unit_resolution,[status(thm)],[18670, 5871, 15503, 15407, 15445])).
% 292.79/185.37 tff(18672,plain,((~node22(c_e_h_1, c_k, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_k, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s5))), inference(lemma,lemma(discharge,[]))).
% 292.79/185.37 tff(18673,plain,
% 292.79/185.37 (~node22(c_e_h_1, c_k, s5, s6)),
% 292.79/185.37 inference(unit_resolution,[status(thm)],[18672, 18664, 18658])).
% 292.79/185.37 tff(18674,plain,
% 292.79/185.37 (node21(c_e_h_1, c_k, s5, s6)),
% 292.79/185.37 inference(unit_resolution,[status(thm)],[15521, 18673])).
% 292.79/185.37 tff(18675,plain,
% 292.79/185.37 (((~![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))) | (m_and_h_gate_v_in2(c_e_h_1, c_k, s5) | m_c_h_element_v_out(c_e_h_1, c_h, s5))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))) | m_and_h_gate_v_in2(c_e_h_1, c_k, s5) | m_c_h_element_v_out(c_e_h_1, c_h, s5))),
% 292.79/185.37 inference(rewrite,[status(thm)],[])).
% 292.79/185.37 tff(18676,plain,
% 292.79/185.37 ((~![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))) | (m_and_h_gate_v_in2(c_e_h_1, c_k, s5) | m_c_h_element_v_out(c_e_h_1, c_h, s5))),
% 292.79/185.37 inference(quant_inst,[status(thm)],[])).
% 292.79/185.37 tff(18677,plain,
% 292.79/185.37 ((~![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))) | m_and_h_gate_v_in2(c_e_h_1, c_k, s5) | m_c_h_element_v_out(c_e_h_1, c_h, s5)),
% 292.79/185.37 inference(modus_ponens,[status(thm)],[18676, 18675])).
% 292.79/185.37 tff(18678,plain,
% 292.79/185.37 (m_and_h_gate_v_in2(c_e_h_1, c_k, s5) | m_c_h_element_v_out(c_e_h_1, c_h, s5)),
% 292.79/185.37 inference(unit_resolution,[status(thm)],[18677, 6420])).
% 292.79/185.37 tff(18679,plain,
% 292.79/185.37 (m_and_h_gate_v_in2(c_e_h_1, c_k, s5)),
% 292.79/185.37 inference(unit_resolution,[status(thm)],[18678, 18538])).
% 292.79/185.37 tff(18680,plain,
% 292.79/185.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_k, s5)) | (~m_and_h_gate_v_in1(c_e_h_1, c_k, s5)) | m_and_h_gate_v_out(c_e_h_1, c_k, s6) | (~node21(c_e_h_1, c_k, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in2(c_e_h_1, c_k, s5)) | (~m_and_h_gate_v_in1(c_e_h_1, c_k, s5)) | m_and_h_gate_v_out(c_e_h_1, c_k, s6) | (~node21(c_e_h_1, c_k, s5, s6)))),
% 292.79/185.37 inference(rewrite,[status(thm)],[])).
% 292.79/185.37 tff(18681,plain,
% 292.79/185.37 (((~node21(c_e_h_1, c_k, s5, s6)) | (~m_and_h_gate_v_in2(c_e_h_1, c_k, s5)) | (~m_and_h_gate_v_in1(c_e_h_1, c_k, s5)) | m_and_h_gate_v_out(c_e_h_1, c_k, s6)) <=> ((~m_and_h_gate_v_in2(c_e_h_1, c_k, s5)) | (~m_and_h_gate_v_in1(c_e_h_1, c_k, s5)) | m_and_h_gate_v_out(c_e_h_1, c_k, s6) | (~node21(c_e_h_1, c_k, s5, s6)))),
% 292.79/185.37 inference(rewrite,[status(thm)],[])).
% 292.79/185.37 tff(18682,plain,
% 292.79/185.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_1, c_k, s5, s6)) | (~m_and_h_gate_v_in2(c_e_h_1, c_k, s5)) | (~m_and_h_gate_v_in1(c_e_h_1, c_k, s5)) | m_and_h_gate_v_out(c_e_h_1, c_k, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_k, s5)) | (~m_and_h_gate_v_in1(c_e_h_1, c_k, s5)) | m_and_h_gate_v_out(c_e_h_1, c_k, s6) | (~node21(c_e_h_1, c_k, s5, s6))))),
% 292.79/185.37 inference(monotonicity,[status(thm)],[18681])).
% 292.79/185.37 tff(18683,plain,
% 292.79/185.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_1, c_k, s5, s6)) | (~m_and_h_gate_v_in2(c_e_h_1, c_k, s5)) | (~m_and_h_gate_v_in1(c_e_h_1, c_k, s5)) | m_and_h_gate_v_out(c_e_h_1, c_k, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in2(c_e_h_1, c_k, s5)) | (~m_and_h_gate_v_in1(c_e_h_1, c_k, s5)) | m_and_h_gate_v_out(c_e_h_1, c_k, s6) | (~node21(c_e_h_1, c_k, s5, s6)))),
% 292.79/185.37 inference(transitivity,[status(thm)],[18682, 18680])).
% 292.79/185.37 tff(18684,plain,
% 292.79/185.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_1, c_k, s5, s6)) | (~m_and_h_gate_v_in2(c_e_h_1, c_k, s5)) | (~m_and_h_gate_v_in1(c_e_h_1, c_k, s5)) | m_and_h_gate_v_out(c_e_h_1, c_k, s6))),
% 292.79/185.37 inference(quant_inst,[status(thm)],[])).
% 292.79/185.37 tff(18685,plain,
% 292.79/185.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in2(c_e_h_1, c_k, s5)) | (~m_and_h_gate_v_in1(c_e_h_1, c_k, s5)) | m_and_h_gate_v_out(c_e_h_1, c_k, s6) | (~node21(c_e_h_1, c_k, s5, s6))),
% 292.79/185.37 inference(modus_ponens,[status(thm)],[18684, 18683])).
% 292.79/185.37 tff(18686,plain,
% 292.79/185.37 ($false),
% 292.79/185.37 inference(unit_resolution,[status(thm)],[18685, 5851, 18679, 15511, 15407, 15533])).
% 292.79/185.37 tff(18687,plain,((~node21(c_e_h_1, c_k, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_k, s6) | (~m_and_h_gate_v_in1(c_e_h_1, c_k, s5))), inference(lemma,lemma(discharge,[]))).
% 292.79/185.37 tff(18688,plain,
% 292.79/185.37 (~m_and_h_gate_v_in1(c_e_h_1, c_k, s5)),
% 292.79/185.37 inference(unit_resolution,[status(thm)],[18687, 18674, 18658])).
% 292.79/185.37 tff(18689,plain,
% 292.79/185.37 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X))) | ((~m_or_h_gate_v_out(c_e_h_1, c_g, s5)) | m_and_h_gate_v_in1(c_e_h_1, c_k, s5))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X))) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s5)) | m_and_h_gate_v_in1(c_e_h_1, c_k, s5))),
% 292.79/185.37 inference(rewrite,[status(thm)],[])).
% 292.79/185.37 tff(18690,plain,
% 292.79/185.37 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X))) | ((~m_or_h_gate_v_out(c_e_h_1, c_g, s5)) | m_and_h_gate_v_in1(c_e_h_1, c_k, s5))),
% 292.79/185.37 inference(quant_inst,[status(thm)],[])).
% 292.79/185.37 tff(18691,plain,
% 292.79/185.37 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X))) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s5)) | m_and_h_gate_v_in1(c_e_h_1, c_k, s5)),
% 292.79/185.37 inference(modus_ponens,[status(thm)],[18690, 18689])).
% 292.79/185.37 tff(18692,plain,
% 292.79/185.37 ($false),
% 292.79/185.37 inference(unit_resolution,[status(thm)],[18691, 6229, 18636, 18688])).
% 292.79/185.37 tff(18693,plain,(m_mutex_h_half_v_out(c_e_h_3, c_b, s7) | m_mutex_h_half_v_out(c_e_h_3, c_b, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s9))), inference(lemma,lemma(discharge,[]))).
% 292.79/185.37 tff(18694,plain,
% 292.79/185.37 (m_mutex_h_half_v_out(c_e_h_3, c_b, s7)),
% 292.79/185.37 inference(unit_resolution,[status(thm)],[18693, 17095, 17094])).
% 292.79/185.37 tff(18695,assumption,(~m_mutex_h_half_v_inp(c_e_h_3, c_b, s6)), introduced(assumption)).
% 292.79/185.37 tff(18696,assumption,(m_mutex_h_half_v_out(c_e_h_3, c_b, s7)), introduced(assumption)).
% 292.79/185.37 tff(18697,assumption,(node12(c_e_h_3, c_b, s6, s7)), introduced(assumption)).
% 292.79/185.37 tff(18698,plain,
% 292.79/185.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_3, c_b, s6) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s7)) | (~node12(c_e_h_3, c_b, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s6) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s7)) | (~node12(c_e_h_3, c_b, s6, s7)))),
% 292.79/185.37 inference(rewrite,[status(thm)],[])).
% 292.79/185.37 tff(18699,plain,
% 292.79/185.37 (((~node12(c_e_h_3, c_b, s6, s7)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s6) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s7))) <=> (m_mutex_h_half_v_inp(c_e_h_3, c_b, s6) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s7)) | (~node12(c_e_h_3, c_b, s6, s7)))),
% 292.79/185.37 inference(rewrite,[status(thm)],[])).
% 292.79/185.37 tff(18700,plain,
% 292.79/185.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_b, s6, s7)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s6) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_3, c_b, s6) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s7)) | (~node12(c_e_h_3, c_b, s6, s7))))),
% 292.79/185.37 inference(monotonicity,[status(thm)],[18699])).
% 292.79/185.37 tff(18701,plain,
% 292.79/185.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_b, s6, s7)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s6) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s6) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s7)) | (~node12(c_e_h_3, c_b, s6, s7)))),
% 292.79/185.37 inference(transitivity,[status(thm)],[18700, 18698])).
% 292.79/185.37 tff(18702,plain,
% 292.79/185.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_b, s6, s7)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s6) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s7)))),
% 292.79/185.37 inference(quant_inst,[status(thm)],[])).
% 292.79/185.37 tff(18703,plain,
% 292.79/185.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s6) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s7)) | (~node12(c_e_h_3, c_b, s6, s7))),
% 292.79/185.37 inference(modus_ponens,[status(thm)],[18702, 18701])).
% 292.79/185.37 tff(18704,plain,
% 292.79/185.37 ($false),
% 292.79/185.37 inference(unit_resolution,[status(thm)],[18703, 454, 18695, 18697, 18696])).
% 292.79/185.37 tff(18705,plain,((~node12(c_e_h_3, c_b, s6, s7)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s6) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s7))), inference(lemma,lemma(discharge,[]))).
% 292.79/185.37 tff(18706,plain,
% 292.79/185.37 (~node12(c_e_h_3, c_b, s6, s7)),
% 292.79/185.37 inference(unit_resolution,[status(thm)],[18705, 18696, 18695])).
% 292.79/185.37 tff(18707,assumption,(~m_mutex_h_half_v_out(c_e_h_3, c_b, s6)), introduced(assumption)).
% 292.79/185.37 tff(18708,assumption,(node13(c_e_h_3, c_b, s6, s7)), introduced(assumption)).
% 292.79/185.37 tff(18709,plain,
% 292.79/185.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_b, s7)) | (~node13(c_e_h_3, c_b, s6, s7)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s7)) | (~node13(c_e_h_3, c_b, s6, s7)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s6))),
% 292.79/185.38 inference(rewrite,[status(thm)],[])).
% 292.79/185.38 tff(18710,plain,
% 292.79/185.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_b, s7)) | (~node13(c_e_h_3, c_b, s6, s7)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s6))),
% 292.79/185.38 inference(quant_inst,[status(thm)],[])).
% 292.79/185.38 tff(18711,plain,
% 292.79/185.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s7)) | (~node13(c_e_h_3, c_b, s6, s7)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s6)),
% 292.79/185.38 inference(modus_ponens,[status(thm)],[18710, 18709])).
% 292.79/185.38 tff(18712,plain,
% 292.79/185.38 ($false),
% 292.79/185.38 inference(unit_resolution,[status(thm)],[18711, 423, 18708, 18696, 18707])).
% 292.79/185.38 tff(18713,plain,((~node13(c_e_h_3, c_b, s6, s7)) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s7)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s6)), inference(lemma,lemma(discharge,[]))).
% 292.79/185.38 tff(18714,plain,
% 292.79/185.38 (~node13(c_e_h_3, c_b, s6, s7)),
% 292.79/185.38 inference(unit_resolution,[status(thm)],[18713, 18696, 18707])).
% 292.79/185.38 tff(18715,plain,
% 292.79/185.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s6, s7)) | node12(c_e_h_3, c_b, s6, s7) | node13(c_e_h_3, c_b, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s6, s7)) | node12(c_e_h_3, c_b, s6, s7) | node13(c_e_h_3, c_b, s6, s7))),
% 292.79/185.38 inference(rewrite,[status(thm)],[])).
% 292.79/185.38 tff(18716,plain,
% 292.79/185.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s6, s7)) | node12(c_e_h_3, c_b, s6, s7) | node13(c_e_h_3, c_b, s6, s7))),
% 292.79/185.38 inference(quant_inst,[status(thm)],[])).
% 292.79/185.38 tff(18717,plain,
% 292.79/185.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s6, s7)) | node12(c_e_h_3, c_b, s6, s7) | node13(c_e_h_3, c_b, s6, s7)),
% 292.79/185.38 inference(modus_ponens,[status(thm)],[18716, 18715])).
% 292.79/185.38 tff(18718,plain,
% 292.79/185.38 (node12(c_e_h_3, c_b, s6, s7) | node13(c_e_h_3, c_b, s6, s7)),
% 292.79/185.38 inference(unit_resolution,[status(thm)],[18717, 439, 1844])).
% 292.79/185.38 tff(18719,plain,
% 292.79/185.38 ($false),
% 292.79/185.38 inference(unit_resolution,[status(thm)],[18718, 18714, 18706])).
% 292.79/185.38 tff(18720,plain,((~m_mutex_h_half_v_out(c_e_h_3, c_b, s7)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s6) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s6)), inference(lemma,lemma(discharge,[]))).
% 292.79/185.38 tff(18721,plain,
% 292.79/185.38 ((~m_mutex_h_half_v_out(c_e_h_3, c_b, s7)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s6)),
% 292.79/185.38 inference(unit_resolution,[status(thm)],[18720, 17155])).
% 292.79/185.38 tff(18722,plain,
% 292.79/185.38 (m_mutex_h_half_v_inp(c_e_h_3, c_b, s6)),
% 292.79/185.38 inference(unit_resolution,[status(thm)],[18721, 18694])).
% 292.79/185.38 tff(18723,plain,
% 292.79/185.38 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node1(c_e_h_3, c_e_h_1, s6))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node1(c_e_h_3, c_e_h_1, s6))),
% 292.79/185.38 inference(rewrite,[status(thm)],[])).
% 292.79/185.38 tff(18724,plain,
% 292.79/185.38 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node1(c_e_h_3, c_e_h_1, s6))),
% 292.79/185.38 inference(quant_inst,[status(thm)],[])).
% 292.79/185.38 tff(18725,plain,
% 292.79/185.38 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node1(c_e_h_3, c_e_h_1, s6)),
% 292.79/185.38 inference(modus_ponens,[status(thm)],[18724, 18723])).
% 292.79/185.38 tff(18726,plain,
% 292.79/185.38 (node1(c_e_h_3, c_e_h_1, s6)),
% 292.79/185.38 inference(unit_resolution,[status(thm)],[18725, 2922, 2919])).
% 292.79/185.38 tff(18727,plain,
% 292.79/185.38 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | (m_cell_v_req(c_e_h_1, s6) | (~node1(c_e_h_3, c_e_h_1, s6)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s6)))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | m_cell_v_req(c_e_h_1, s6) | (~node1(c_e_h_3, c_e_h_1, s6)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s6)))),
% 292.89/185.38 inference(rewrite,[status(thm)],[])).
% 292.89/185.38 tff(18728,plain,
% 292.89/185.38 (((~node1(c_e_h_3, c_e_h_1, s6)) | m_cell_v_req(c_e_h_1, s6) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s6))) <=> (m_cell_v_req(c_e_h_1, s6) | (~node1(c_e_h_3, c_e_h_1, s6)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s6)))),
% 292.89/185.38 inference(rewrite,[status(thm)],[])).
% 292.89/185.38 tff(18729,plain,
% 292.89/185.38 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_3, c_e_h_1, s6)) | m_cell_v_req(c_e_h_1, s6) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s6)))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | (m_cell_v_req(c_e_h_1, s6) | (~node1(c_e_h_3, c_e_h_1, s6)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s6))))),
% 292.89/185.38 inference(monotonicity,[status(thm)],[18728])).
% 292.89/185.38 tff(18730,plain,
% 292.89/185.38 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_3, c_e_h_1, s6)) | m_cell_v_req(c_e_h_1, s6) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s6)))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | m_cell_v_req(c_e_h_1, s6) | (~node1(c_e_h_3, c_e_h_1, s6)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s6)))),
% 292.89/185.38 inference(transitivity,[status(thm)],[18729, 18727])).
% 292.89/185.38 tff(18731,plain,
% 292.89/185.38 ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_3, c_e_h_1, s6)) | m_cell_v_req(c_e_h_1, s6) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s6)))),
% 292.89/185.38 inference(quant_inst,[status(thm)],[])).
% 292.89/185.38 tff(18732,plain,
% 292.89/185.38 ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | m_cell_v_req(c_e_h_1, s6) | (~node1(c_e_h_3, c_e_h_1, s6)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s6))),
% 292.89/185.38 inference(modus_ponens,[status(thm)],[18731, 18730])).
% 292.89/185.38 tff(18733,plain,
% 292.89/185.38 (m_cell_v_req(c_e_h_1, s6) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s6))),
% 292.89/185.38 inference(unit_resolution,[status(thm)],[18732, 2936, 18726])).
% 292.89/185.38 tff(18734,plain,
% 292.89/185.38 (m_cell_v_req(c_e_h_1, s6)),
% 292.89/185.38 inference(unit_resolution,[status(thm)],[18733, 18722])).
% 292.89/185.38 tff(18735,assumption,(m_cell_v_req(c_e_h_1, s6)), introduced(assumption)).
% 292.89/185.38 tff(18736,plain,
% 292.89/185.38 (((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | ((~m_cell_v_req(c_e_h_1, s6)) | m_and_h_gate_v_out(c_e_h_1, c_p, s6))) <=> ((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | (~m_cell_v_req(c_e_h_1, s6)) | m_and_h_gate_v_out(c_e_h_1, c_p, s6))),
% 292.89/185.38 inference(rewrite,[status(thm)],[])).
% 292.89/185.38 tff(18737,plain,
% 292.89/185.38 ((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | ((~m_cell_v_req(c_e_h_1, s6)) | m_and_h_gate_v_out(c_e_h_1, c_p, s6))),
% 292.89/185.38 inference(quant_inst,[status(thm)],[])).
% 292.89/185.38 tff(18738,plain,
% 292.89/185.38 ((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | (~m_cell_v_req(c_e_h_1, s6)) | m_and_h_gate_v_out(c_e_h_1, c_p, s6)),
% 292.89/185.38 inference(modus_ponens,[status(thm)],[18737, 18736])).
% 292.89/185.38 tff(18739,plain,
% 292.89/185.38 ($false),
% 292.89/185.38 inference(unit_resolution,[status(thm)],[18738, 2908, 18735, 15770])).
% 292.89/185.38 tff(18740,plain,((~m_cell_v_req(c_e_h_1, s6)) | m_and_h_gate_v_out(c_e_h_1, c_p, s6)), inference(lemma,lemma(discharge,[]))).
% 292.89/185.38 tff(18741,plain,
% 292.89/185.38 (m_and_h_gate_v_out(c_e_h_1, c_p, s6)),
% 292.89/185.38 inference(unit_resolution,[status(thm)],[18740, 18734])).
% 292.89/185.38 tff(18742,plain,
% 292.89/185.38 (node20(c_e_h_1, c_p, s5)),
% 292.89/185.38 inference(unit_resolution,[status(thm)],[15765, 15745])).
% 292.89/185.38 tff(18743,plain,
% 292.89/185.38 (m_and_h_gate_v_in1(c_e_h_1, c_p, s5)),
% 292.89/185.38 inference(unit_resolution,[status(thm)],[15695, 18742])).
% 292.89/185.38 tff(18744,plain,
% 292.89/185.38 (m_and_h_gate_v_out(c_e_h_1, c_k, s5)),
% 292.89/185.38 inference(unit_resolution,[status(thm)],[15687, 18743])).
% 292.89/185.38 tff(18745,plain,
% 292.89/185.38 (~node22(c_e_h_1, c_k, s5, s6)),
% 292.89/185.38 inference(unit_resolution,[status(thm)],[18672, 15407, 15445])).
% 292.89/185.38 tff(18746,plain,
% 292.89/185.38 (node20(c_e_h_1, c_k, s4)),
% 292.89/185.38 inference(unit_resolution,[status(thm)],[15500, 15445])).
% 292.89/185.38 tff(18747,plain,
% 292.89/185.38 (m_and_h_gate_v_in1(c_e_h_1, c_k, s4)),
% 292.89/185.38 inference(unit_resolution,[status(thm)],[15443, 18746])).
% 292.89/185.38 tff(18748,plain,
% 292.89/185.38 (m_or_h_gate_v_out(c_e_h_1, c_g, s4)),
% 292.89/185.38 inference(unit_resolution,[status(thm)],[15435, 18747])).
% 292.89/185.38 tff(18749,plain,
% 292.89/185.38 (m_or_h_gate_v_out(c_e_h_1, c_g, s5)),
% 292.89/185.38 inference(unit_resolution,[status(thm)],[15624, 18748])).
% 292.89/185.38 tff(18750,plain,
% 292.89/185.38 ($false),
% 292.89/185.38 inference(unit_resolution,[status(thm)],[18691, 6229, 14571, 15525])).
% 292.89/185.38 tff(18751,plain,(m_and_h_gate_v_in1(c_e_h_1, c_k, s5) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s5))), inference(lemma,lemma(discharge,[]))).
% 292.89/185.38 tff(18752,plain,
% 292.89/185.38 (m_and_h_gate_v_in1(c_e_h_1, c_k, s5)),
% 292.89/185.38 inference(unit_resolution,[status(thm)],[18751, 18749])).
% 292.89/185.38 tff(18753,plain,
% 292.89/185.38 (~node21(c_e_h_1, c_k, s5, s6)),
% 292.89/185.38 inference(unit_resolution,[status(thm)],[18687, 15407, 18752])).
% 292.89/185.38 tff(18754,plain,
% 292.89/185.38 ($false),
% 292.89/185.38 inference(unit_resolution,[status(thm)],[15521, 18753, 18745])).
% 292.89/185.38 tff(18755,plain,(m_and_h_gate_v_out(c_e_h_1, c_k, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s5))), inference(lemma,lemma(discharge,[]))).
% 292.89/185.38 tff(18756,plain,
% 292.89/185.38 (m_and_h_gate_v_out(c_e_h_1, c_k, s6)),
% 292.89/185.38 inference(unit_resolution,[status(thm)],[18755, 18744])).
% 292.89/185.38 tff(18757,plain,
% 292.89/185.38 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_p, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_k, s6)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s6))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_p, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s6)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s6))),
% 292.89/185.38 inference(rewrite,[status(thm)],[])).
% 292.89/185.38 tff(18758,plain,
% 292.89/185.38 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_p, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_k, s6)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s6))),
% 292.89/185.38 inference(quant_inst,[status(thm)],[])).
% 292.89/185.38 tff(18759,plain,
% 292.89/185.38 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_p, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s6)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s6)),
% 292.89/185.38 inference(modus_ponens,[status(thm)],[18758, 18757])).
% 292.89/185.38 tff(18760,plain,
% 292.89/185.38 (m_and_h_gate_v_in1(c_e_h_1, c_p, s6)),
% 292.89/185.38 inference(unit_resolution,[status(thm)],[18759, 18282, 18756])).
% 292.89/185.38 tff(18761,plain,
% 292.89/185.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_1, c_p, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s6)) | (~node22(c_e_h_1, c_p, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | m_and_h_gate_v_out(c_e_h_1, c_p, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s6)) | (~node22(c_e_h_1, c_p, s6, s7)))),
% 292.89/185.38 inference(rewrite,[status(thm)],[])).
% 292.89/185.38 tff(18762,plain,
% 292.89/185.38 ((m_and_h_gate_v_out(c_e_h_1, c_p, s7) | (~node22(c_e_h_1, c_p, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s6))) <=> (m_and_h_gate_v_out(c_e_h_1, c_p, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s6)) | (~node22(c_e_h_1, c_p, s6, s7)))),
% 292.89/185.38 inference(rewrite,[status(thm)],[])).
% 292.89/185.38 tff(18763,plain,
% 292.89/185.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_1, c_p, s7) | (~node22(c_e_h_1, c_p, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_1, c_p, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s6)) | (~node22(c_e_h_1, c_p, s6, s7))))),
% 292.89/185.38 inference(monotonicity,[status(thm)],[18762])).
% 292.89/185.38 tff(18764,plain,
% 292.89/185.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_1, c_p, s7) | (~node22(c_e_h_1, c_p, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | m_and_h_gate_v_out(c_e_h_1, c_p, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s6)) | (~node22(c_e_h_1, c_p, s6, s7)))),
% 292.89/185.39 inference(transitivity,[status(thm)],[18763, 18761])).
% 292.89/185.39 tff(18765,plain,
% 292.89/185.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_1, c_p, s7) | (~node22(c_e_h_1, c_p, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s6)))),
% 292.89/185.39 inference(quant_inst,[status(thm)],[])).
% 292.89/185.39 tff(18766,plain,
% 292.89/185.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | m_and_h_gate_v_out(c_e_h_1, c_p, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s6)) | (~node22(c_e_h_1, c_p, s6, s7))),
% 292.89/185.39 inference(modus_ponens,[status(thm)],[18765, 18764])).
% 292.89/185.39 tff(18767,plain,
% 292.89/185.39 ($false),
% 292.89/185.39 inference(unit_resolution,[status(thm)],[18766, 5871, 15806, 15745, 15796])).
% 292.89/185.39 tff(18768,plain,((~node22(c_e_h_1, c_p, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s6)) | m_and_h_gate_v_out(c_e_h_1, c_p, s7)), inference(lemma,lemma(discharge,[]))).
% 292.89/185.39 tff(18769,plain,
% 292.89/185.39 (~node22(c_e_h_1, c_p, s6, s7)),
% 292.89/185.39 inference(unit_resolution,[status(thm)],[18768, 15796, 15745])).
% 292.89/185.39 tff(18770,plain,
% 292.89/185.39 (node21(c_e_h_1, c_p, s6, s7)),
% 292.89/185.39 inference(unit_resolution,[status(thm)],[15816, 18769])).
% 292.89/185.39 tff(18771,plain,
% 292.89/185.39 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_n, X)) | m_and_h_gate_v_in2(I0, c_p, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)) | m_and_h_gate_v_in2(c_e_h_1, c_p, s6))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_n, X)) | m_and_h_gate_v_in2(I0, c_p, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)) | m_and_h_gate_v_in2(c_e_h_1, c_p, s6))),
% 292.89/185.39 inference(rewrite,[status(thm)],[])).
% 292.89/185.39 tff(18772,plain,
% 292.89/185.39 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_n, X)) | m_and_h_gate_v_in2(I0, c_p, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)) | m_and_h_gate_v_in2(c_e_h_1, c_p, s6))),
% 292.89/185.39 inference(quant_inst,[status(thm)],[])).
% 292.89/185.39 tff(18773,plain,
% 292.89/185.39 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_n, X)) | m_and_h_gate_v_in2(I0, c_p, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)) | m_and_h_gate_v_in2(c_e_h_1, c_p, s6)),
% 292.89/185.39 inference(modus_ponens,[status(thm)],[18772, 18771])).
% 292.89/185.39 tff(18774,plain,
% 292.89/185.39 (m_and_h_gate_v_in2(c_e_h_1, c_p, s6)),
% 292.89/185.39 inference(unit_resolution,[status(thm)],[18773, 18206, 18109])).
% 292.89/185.39 tff(18775,plain,
% 292.89/185.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (m_and_h_gate_v_out(c_e_h_1, c_p, s7) | (~m_and_h_gate_v_in2(c_e_h_1, c_p, s6)) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s6)) | (~node21(c_e_h_1, c_p, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | m_and_h_gate_v_out(c_e_h_1, c_p, s7) | (~m_and_h_gate_v_in2(c_e_h_1, c_p, s6)) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s6)) | (~node21(c_e_h_1, c_p, s6, s7)))),
% 292.89/185.39 inference(rewrite,[status(thm)],[])).
% 292.89/185.39 tff(18776,plain,
% 292.89/185.39 (((~node21(c_e_h_1, c_p, s6, s7)) | (~m_and_h_gate_v_in2(c_e_h_1, c_p, s6)) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s6)) | m_and_h_gate_v_out(c_e_h_1, c_p, s7)) <=> (m_and_h_gate_v_out(c_e_h_1, c_p, s7) | (~m_and_h_gate_v_in2(c_e_h_1, c_p, s6)) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s6)) | (~node21(c_e_h_1, c_p, s6, s7)))),
% 292.89/185.39 inference(rewrite,[status(thm)],[])).
% 292.89/185.39 tff(18777,plain,
% 292.89/185.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_1, c_p, s6, s7)) | (~m_and_h_gate_v_in2(c_e_h_1, c_p, s6)) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s6)) | m_and_h_gate_v_out(c_e_h_1, c_p, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (m_and_h_gate_v_out(c_e_h_1, c_p, s7) | (~m_and_h_gate_v_in2(c_e_h_1, c_p, s6)) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s6)) | (~node21(c_e_h_1, c_p, s6, s7))))),
% 292.90/185.39 inference(monotonicity,[status(thm)],[18776])).
% 292.90/185.39 tff(18778,plain,
% 292.90/185.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_1, c_p, s6, s7)) | (~m_and_h_gate_v_in2(c_e_h_1, c_p, s6)) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s6)) | m_and_h_gate_v_out(c_e_h_1, c_p, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | m_and_h_gate_v_out(c_e_h_1, c_p, s7) | (~m_and_h_gate_v_in2(c_e_h_1, c_p, s6)) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s6)) | (~node21(c_e_h_1, c_p, s6, s7)))),
% 292.90/185.39 inference(transitivity,[status(thm)],[18777, 18775])).
% 292.90/185.39 tff(18779,plain,
% 292.90/185.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_1, c_p, s6, s7)) | (~m_and_h_gate_v_in2(c_e_h_1, c_p, s6)) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s6)) | m_and_h_gate_v_out(c_e_h_1, c_p, s7))),
% 292.90/185.39 inference(quant_inst,[status(thm)],[])).
% 292.90/185.39 tff(18780,plain,
% 292.90/185.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | m_and_h_gate_v_out(c_e_h_1, c_p, s7) | (~m_and_h_gate_v_in2(c_e_h_1, c_p, s6)) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s6)) | (~node21(c_e_h_1, c_p, s6, s7))),
% 292.90/185.39 inference(modus_ponens,[status(thm)],[18779, 18778])).
% 292.90/185.39 tff(18781,plain,
% 292.90/185.39 ($false),
% 292.90/185.39 inference(unit_resolution,[status(thm)],[18780, 5851, 18774, 18770, 15796, 18760])).
% 292.90/185.39 tff(18782,plain,(m_and_h_gate_v_out(c_e_h_1, c_p, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s6))), inference(lemma,lemma(discharge,[]))).
% 292.90/185.39 tff(18783,plain,
% 292.90/185.39 (m_and_h_gate_v_out(c_e_h_1, c_p, s7)),
% 292.90/185.39 inference(unit_resolution,[status(thm)],[18782, 18741])).
% 292.90/185.39 tff(18784,plain,
% 292.90/185.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_b, s8) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s7)) | (~node13(c_e_h_3, c_b, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | m_mutex_h_half_v_out(c_e_h_3, c_b, s8) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s7)) | (~node13(c_e_h_3, c_b, s7, s8)))),
% 292.90/185.39 inference(rewrite,[status(thm)],[])).
% 292.90/185.39 tff(18785,plain,
% 292.90/185.39 ((m_mutex_h_half_v_out(c_e_h_3, c_b, s8) | (~node13(c_e_h_3, c_b, s7, s8)) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s7))) <=> (m_mutex_h_half_v_out(c_e_h_3, c_b, s8) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s7)) | (~node13(c_e_h_3, c_b, s7, s8)))),
% 292.90/185.39 inference(rewrite,[status(thm)],[])).
% 292.90/185.39 tff(18786,plain,
% 292.90/185.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_b, s8) | (~node13(c_e_h_3, c_b, s7, s8)) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_b, s8) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s7)) | (~node13(c_e_h_3, c_b, s7, s8))))),
% 292.90/185.39 inference(monotonicity,[status(thm)],[18785])).
% 292.90/185.39 tff(18787,plain,
% 292.90/185.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_b, s8) | (~node13(c_e_h_3, c_b, s7, s8)) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | m_mutex_h_half_v_out(c_e_h_3, c_b, s8) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s7)) | (~node13(c_e_h_3, c_b, s7, s8)))),
% 292.90/185.39 inference(transitivity,[status(thm)],[18786, 18784])).
% 292.90/185.39 tff(18788,plain,
% 292.90/185.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_b, s8) | (~node13(c_e_h_3, c_b, s7, s8)) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s7)))),
% 292.90/185.39 inference(quant_inst,[status(thm)],[])).
% 292.90/185.39 tff(18789,plain,
% 292.90/185.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | m_mutex_h_half_v_out(c_e_h_3, c_b, s8) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s7)) | (~node13(c_e_h_3, c_b, s7, s8))),
% 292.90/185.39 inference(modus_ponens,[status(thm)],[18788, 18787])).
% 292.90/185.39 tff(18790,plain,
% 292.90/185.39 ($false),
% 292.90/185.39 inference(unit_resolution,[status(thm)],[18789, 1459, 18211, 17242, 18696])).
% 292.90/185.39 tff(18791,plain,((~node13(c_e_h_3, c_b, s7, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s8) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s7))), inference(lemma,lemma(discharge,[]))).
% 292.90/185.39 tff(18792,plain,
% 292.90/185.39 (~node13(c_e_h_3, c_b, s7, s8)),
% 292.90/185.39 inference(unit_resolution,[status(thm)],[18791, 17242, 18696])).
% 292.90/185.39 tff(18793,plain,
% 292.90/185.39 (m_mutex_h_half_v_inp(c_e_h_3, c_b, s6)),
% 292.90/185.39 inference(unit_resolution,[status(thm)],[18721, 18696])).
% 292.90/185.39 tff(18794,plain,
% 292.90/185.39 (m_cell_v_req(c_e_h_1, s6)),
% 292.90/185.39 inference(unit_resolution,[status(thm)],[18733, 18793])).
% 292.90/185.39 tff(18795,plain,
% 292.90/185.39 (m_and_h_gate_v_out(c_e_h_1, c_p, s6)),
% 292.90/185.39 inference(unit_resolution,[status(thm)],[18740, 18794])).
% 292.90/185.39 tff(18796,plain,
% 292.90/185.39 (m_and_h_gate_v_out(c_e_h_1, c_p, s7)),
% 292.90/185.39 inference(unit_resolution,[status(thm)],[18782, 18795])).
% 292.90/185.39 tff(18797,assumption,(~m_cell_v_req(c_e_h_1, s7)), introduced(assumption)).
% 292.90/185.39 tff(18798,plain,
% 292.90/185.39 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_p, X)) | m_cell_v_req(I0, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_p, s7)) | m_cell_v_req(c_e_h_1, s7))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_p, X)) | m_cell_v_req(I0, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s7)) | m_cell_v_req(c_e_h_1, s7))),
% 292.90/185.39 inference(rewrite,[status(thm)],[])).
% 292.90/185.39 tff(18799,plain,
% 292.90/185.39 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_p, X)) | m_cell_v_req(I0, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_p, s7)) | m_cell_v_req(c_e_h_1, s7))),
% 292.90/185.39 inference(quant_inst,[status(thm)],[])).
% 292.90/185.39 tff(18800,plain,
% 292.90/185.39 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_p, X)) | m_cell_v_req(I0, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s7)) | m_cell_v_req(c_e_h_1, s7)),
% 292.90/185.39 inference(modus_ponens,[status(thm)],[18799, 18798])).
% 292.90/185.39 tff(18801,plain,
% 292.90/185.39 ($false),
% 292.90/185.39 inference(unit_resolution,[status(thm)],[18800, 17300, 18797, 15805])).
% 292.90/185.39 tff(18802,plain,(m_cell_v_req(c_e_h_1, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s7))), inference(lemma,lemma(discharge,[]))).
% 292.90/185.39 tff(18803,plain,
% 292.90/185.39 (m_cell_v_req(c_e_h_1, s7)),
% 292.90/185.39 inference(unit_resolution,[status(thm)],[18802, 18796])).
% 292.90/185.39 tff(18804,plain,
% 292.90/185.39 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | (~m_cell_v_req(J0, X)) | m_mutex_h_half_v_inp(I0, c_b, X))) | (m_mutex_h_half_v_inp(c_e_h_3, c_b, s7) | (~m_cell_v_req(c_e_h_1, s7)) | (~node1(c_e_h_3, c_e_h_1, s7)))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | (~m_cell_v_req(J0, X)) | m_mutex_h_half_v_inp(I0, c_b, X))) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s7) | (~m_cell_v_req(c_e_h_1, s7)) | (~node1(c_e_h_3, c_e_h_1, s7)))),
% 292.90/185.39 inference(rewrite,[status(thm)],[])).
% 292.90/185.39 tff(18805,plain,
% 292.90/185.39 (((~node1(c_e_h_3, c_e_h_1, s7)) | (~m_cell_v_req(c_e_h_1, s7)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s7)) <=> (m_mutex_h_half_v_inp(c_e_h_3, c_b, s7) | (~m_cell_v_req(c_e_h_1, s7)) | (~node1(c_e_h_3, c_e_h_1, s7)))),
% 292.90/185.39 inference(rewrite,[status(thm)],[])).
% 292.90/185.39 tff(18806,plain,
% 292.90/185.39 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | (~m_cell_v_req(J0, X)) | m_mutex_h_half_v_inp(I0, c_b, X))) | ((~node1(c_e_h_3, c_e_h_1, s7)) | (~m_cell_v_req(c_e_h_1, s7)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s7))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | (~m_cell_v_req(J0, X)) | m_mutex_h_half_v_inp(I0, c_b, X))) | (m_mutex_h_half_v_inp(c_e_h_3, c_b, s7) | (~m_cell_v_req(c_e_h_1, s7)) | (~node1(c_e_h_3, c_e_h_1, s7))))),
% 292.90/185.40 inference(monotonicity,[status(thm)],[18805])).
% 292.90/185.40 tff(18807,plain,
% 292.90/185.40 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | (~m_cell_v_req(J0, X)) | m_mutex_h_half_v_inp(I0, c_b, X))) | ((~node1(c_e_h_3, c_e_h_1, s7)) | (~m_cell_v_req(c_e_h_1, s7)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s7))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | (~m_cell_v_req(J0, X)) | m_mutex_h_half_v_inp(I0, c_b, X))) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s7) | (~m_cell_v_req(c_e_h_1, s7)) | (~node1(c_e_h_3, c_e_h_1, s7)))),
% 292.90/185.40 inference(transitivity,[status(thm)],[18806, 18804])).
% 292.90/185.40 tff(18808,plain,
% 292.90/185.40 ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | (~m_cell_v_req(J0, X)) | m_mutex_h_half_v_inp(I0, c_b, X))) | ((~node1(c_e_h_3, c_e_h_1, s7)) | (~m_cell_v_req(c_e_h_1, s7)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s7))),
% 292.90/185.40 inference(quant_inst,[status(thm)],[])).
% 292.90/185.40 tff(18809,plain,
% 292.90/185.40 ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | (~m_cell_v_req(J0, X)) | m_mutex_h_half_v_inp(I0, c_b, X))) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s7) | (~m_cell_v_req(c_e_h_1, s7)) | (~node1(c_e_h_3, c_e_h_1, s7))),
% 292.90/185.40 inference(modus_ponens,[status(thm)],[18808, 18807])).
% 292.90/185.40 tff(18810,plain,
% 292.90/185.40 (m_mutex_h_half_v_inp(c_e_h_3, c_b, s7) | (~m_cell_v_req(c_e_h_1, s7))),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[18809, 17285, 18239])).
% 292.90/185.40 tff(18811,plain,
% 292.90/185.40 (m_mutex_h_half_v_inp(c_e_h_3, c_b, s7)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[18810, 18803])).
% 292.90/185.40 tff(18812,assumption,(m_mutex_h_half_v_inp(c_e_h_3, c_b, s7)), introduced(assumption)).
% 292.90/185.40 tff(18813,plain,
% 292.90/185.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_b, s7)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s8) | (~node12(c_e_h_3, c_b, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s7)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s8) | (~node12(c_e_h_3, c_b, s7, s8)))),
% 292.90/185.40 inference(rewrite,[status(thm)],[])).
% 292.90/185.40 tff(18814,plain,
% 292.90/185.40 (((~node12(c_e_h_3, c_b, s7, s8)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s7)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s8)) <=> ((~m_mutex_h_half_v_inp(c_e_h_3, c_b, s7)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s8) | (~node12(c_e_h_3, c_b, s7, s8)))),
% 292.90/185.40 inference(rewrite,[status(thm)],[])).
% 292.90/185.40 tff(18815,plain,
% 292.90/185.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_3, c_b, s7, s8)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s7)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_b, s7)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s8) | (~node12(c_e_h_3, c_b, s7, s8))))),
% 292.90/185.40 inference(monotonicity,[status(thm)],[18814])).
% 292.90/185.40 tff(18816,plain,
% 292.90/185.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_3, c_b, s7, s8)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s7)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s7)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s8) | (~node12(c_e_h_3, c_b, s7, s8)))),
% 292.90/185.40 inference(transitivity,[status(thm)],[18815, 18813])).
% 292.90/185.40 tff(18817,plain,
% 292.90/185.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_3, c_b, s7, s8)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s7)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s8))),
% 292.90/185.40 inference(quant_inst,[status(thm)],[])).
% 292.90/185.40 tff(18818,plain,
% 292.90/185.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s7)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s8) | (~node12(c_e_h_3, c_b, s7, s8))),
% 292.90/185.40 inference(modus_ponens,[status(thm)],[18817, 18816])).
% 292.90/185.40 tff(18819,plain,
% 292.90/185.40 ($false),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[18818, 1483, 18812, 18219, 17242])).
% 292.90/185.40 tff(18820,plain,((~node12(c_e_h_3, c_b, s7, s8)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s7)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s8)), inference(lemma,lemma(discharge,[]))).
% 292.90/185.40 tff(18821,plain,
% 292.90/185.40 (~node12(c_e_h_3, c_b, s7, s8)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[18820, 17242, 18811])).
% 292.90/185.40 tff(18822,plain,
% 292.90/185.40 ($false),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[18232, 18821, 18792])).
% 292.90/185.40 tff(18823,plain,(m_mutex_h_half_v_out(c_e_h_3, c_b, s8) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s7))), inference(lemma,lemma(discharge,[]))).
% 292.90/185.40 tff(18824,plain,
% 292.90/185.40 (m_mutex_h_half_v_out(c_e_h_3, c_b, s8)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[18823, 18694])).
% 292.90/185.40 tff(18825,plain,
% 292.90/185.40 (~node13(c_e_h_3, c_b, s8, s9)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[17258, 17095, 17249])).
% 292.90/185.40 tff(18826,assumption,(m_mutex_h_half_v_inp(c_e_h_3, c_b, s8)), introduced(assumption)).
% 292.90/185.40 tff(18827,assumption,(node12(c_e_h_3, c_b, s8, s9)), introduced(assumption)).
% 292.90/185.40 tff(18828,plain,
% 292.90/185.40 ($false),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[17270, 1483, 18826, 18827, 17095])).
% 292.90/185.40 tff(18829,plain,((~node12(c_e_h_3, c_b, s8, s9)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s9)), inference(lemma,lemma(discharge,[]))).
% 292.90/185.40 tff(18830,plain,
% 292.90/185.40 (~node12(c_e_h_3, c_b, s8, s9)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[18829, 17095, 18826])).
% 292.90/185.40 tff(18831,plain,
% 292.90/185.40 ($false),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[17263, 18830, 18825])).
% 292.90/185.40 tff(18832,plain,(m_mutex_h_half_v_out(c_e_h_3, c_b, s9) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s8)) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s8))), inference(lemma,lemma(discharge,[]))).
% 292.90/185.40 tff(18833,plain,
% 292.90/185.40 (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s8)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[18832, 18824, 17095])).
% 292.90/185.40 tff(18834,plain,
% 292.90/185.40 (~m_cell_v_req(c_e_h_1, s8)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[17289, 18833])).
% 292.90/185.40 tff(18835,assumption,(~m_cell_v_req(c_e_h_1, s8)), introduced(assumption)).
% 292.90/185.40 tff(18836,plain,
% 292.90/185.40 ($false),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[17303, 17300, 18835, 15662])).
% 292.90/185.40 tff(18837,plain,(m_cell_v_req(c_e_h_1, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s8))), inference(lemma,lemma(discharge,[]))).
% 292.90/185.40 tff(18838,plain,
% 292.90/185.40 (~m_and_h_gate_v_out(c_e_h_1, c_p, s8)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[18837, 18834])).
% 292.90/185.40 tff(18839,assumption,(m_and_h_gate_v_in1(c_e_h_1, c_p, s7)), introduced(assumption)).
% 292.90/185.40 tff(18840,plain,
% 292.90/185.40 (~node22(c_e_h_1, c_p, s7, s8)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[18262, 15866, 15805])).
% 292.90/185.40 tff(18841,plain,
% 292.90/185.40 (node21(c_e_h_1, c_p, s7, s8)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[15794, 18840])).
% 292.90/185.40 tff(18842,plain,
% 292.90/185.40 ($false),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[18270, 5851, 18841, 18210, 15866, 18839])).
% 292.90/185.40 tff(18843,plain,(m_and_h_gate_v_out(c_e_h_1, c_p, s8) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s7)) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s7))), inference(lemma,lemma(discharge,[]))).
% 292.90/185.40 tff(18844,plain,
% 292.90/185.40 (~m_and_h_gate_v_in1(c_e_h_1, c_p, s7)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[18843, 18783, 18838])).
% 292.90/185.40 tff(18845,plain,
% 292.90/185.40 (~m_and_h_gate_v_out(c_e_h_1, c_k, s7)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[18287, 18844])).
% 292.90/185.40 tff(18846,plain,
% 292.90/185.40 (m_or_h_gate_v_out(c_e_h_1, c_g, s4)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[18634, 18845, 18783])).
% 292.90/185.40 tff(18847,plain,
% 292.90/185.40 (m_or_h_gate_v_out(c_e_h_1, c_g, s5)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[15624, 18846])).
% 292.90/185.40 tff(18848,plain,
% 292.90/185.40 (node20(c_e_h_1, c_p, s5)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[15765, 18741])).
% 292.90/185.40 tff(18849,plain,
% 292.90/185.40 (m_and_h_gate_v_in1(c_e_h_1, c_p, s5)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[15695, 18848])).
% 292.90/185.40 tff(18850,plain,
% 292.90/185.40 (m_and_h_gate_v_out(c_e_h_1, c_k, s5)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[15687, 18849])).
% 292.90/185.40 tff(18851,plain,
% 292.90/185.40 (m_and_h_gate_v_out(c_e_h_1, c_k, s6)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[18755, 18850])).
% 292.90/185.40 tff(18852,plain,
% 292.90/185.40 (~node21(c_e_h_1, c_k, s6, s7)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[18627, 15905, 15390])).
% 292.90/185.40 tff(18853,plain,
% 292.90/185.40 (~node22(c_e_h_1, c_k, s6, s7)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[18308, 15905, 15429])).
% 292.90/185.40 tff(18854,plain,
% 292.90/185.40 ($false),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[15418, 18853, 18852])).
% 292.90/185.40 tff(18855,plain,(m_and_h_gate_v_out(c_e_h_1, c_k, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s6)) | (~m_and_h_gate_v_in1(c_e_h_1, c_k, s6))), inference(lemma,lemma(discharge,[]))).
% 292.90/185.40 tff(18856,plain,
% 292.90/185.40 (~m_and_h_gate_v_in1(c_e_h_1, c_k, s6)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[18855, 18851, 18845])).
% 292.90/185.40 tff(18857,plain,
% 292.90/185.40 (~m_or_h_gate_v_out(c_e_h_1, c_g, s6)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[18654, 18856])).
% 292.90/185.40 tff(18858,plain,
% 292.90/185.40 (node4(c_e_h_1, c_g, s5)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[17071, 18857, 18847])).
% 292.90/185.40 tff(18859,plain,
% 292.90/185.40 (~m_or_h_gate_v_in1(c_e_h_1, c_g, s5)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[15566, 5516, 18858])).
% 292.90/185.40 tff(18860,plain,
% 292.90/185.40 (m_and_h_gate_v_out(c_e_h_1, c_c, s4)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[14848, 18847])).
% 292.90/185.40 tff(18861,plain,
% 292.90/185.40 (m_user_v_req(c_e_h_1, c_u, s2)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[14671, 18860])).
% 292.90/185.40 tff(18862,plain,
% 292.90/185.40 (m_user_v_req(c_e_h_1, c_u, s3)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[14760, 18861])).
% 292.90/185.40 tff(18863,plain,
% 292.90/185.40 (m_mutex_h_half_v_inp(c_e_h_1, c_a, s3)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[14768, 18862])).
% 292.90/185.40 tff(18864,plain,
% 292.90/185.40 (m_or_h_gate_v_in1(c_e_h_1, c_g, s3)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[14503, 18846])).
% 292.90/185.40 tff(18865,plain,
% 292.90/185.40 (m_and_h_gate_v_out(c_e_h_1, c_c, s3)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[14418, 2708, 18864])).
% 292.90/185.40 tff(18866,plain,
% 292.90/185.40 (node20(c_e_h_1, c_c, s2)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[14216, 18865])).
% 292.90/185.40 tff(18867,plain,
% 292.90/185.40 (m_and_h_gate_v_in1(c_e_h_1, c_c, s2)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[14224, 18866])).
% 292.90/185.40 tff(18868,plain,
% 292.90/185.40 (m_mutex_h_half_v_out(c_e_h_1, c_a, s2)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[14232, 18867])).
% 292.90/185.40 tff(18869,plain,
% 292.90/185.40 (m_mutex_h_half_v_out(c_e_h_1, c_a, s3)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[14381, 18868])).
% 292.90/185.40 tff(18870,plain,
% 292.90/185.40 (m_mutex_h_half_v_out(c_e_h_1, c_a, s4)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[14793, 18869, 18863])).
% 292.90/185.40 tff(18871,plain,
% 292.90/185.40 (m_and_h_gate_v_in1(c_e_h_1, c_c, s4)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[14810, 18870])).
% 292.90/185.40 tff(18872,plain,
% 292.90/185.40 (m_and_h_gate_v_out(c_e_h_1, c_c, s5)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[14843, 18871, 18860])).
% 292.90/185.40 tff(18873,plain,
% 292.90/185.40 ($false),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[15570, 5896, 18872, 18859])).
% 292.90/185.40 tff(18874,plain,(m_mutex_h_half_v_out(c_e_h_3, c_b, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s9))), inference(lemma,lemma(discharge,[]))).
% 292.90/185.40 tff(18875,plain,
% 292.90/185.40 (m_mutex_h_half_v_out(c_e_h_3, c_b, s9)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[18874, 17094])).
% 292.90/185.40 tff(18876,assumption,(m_mutex_h_half_v_out(c_e_h_3, c_b, s9)), introduced(assumption)).
% 292.90/185.40 tff(18877,plain,
% 292.90/185.40 (~m_and_h_gate_v_out(c_e_h_1, c_k, s7)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[15660, 15389])).
% 292.90/185.40 tff(18878,plain,
% 292.90/185.40 (m_or_h_gate_v_out(c_e_h_1, c_g, s4)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[17065, 15389, 15662])).
% 292.90/185.40 tff(18879,plain,
% 292.90/185.40 (m_or_h_gate_v_out(c_e_h_1, c_g, s5)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[15624, 18878])).
% 292.90/185.40 tff(18880,plain,
% 292.90/185.40 (node4(c_e_h_1, c_g, s5)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[17071, 18879, 15389])).
% 292.90/185.40 tff(18881,plain,
% 292.90/185.40 (~m_or_h_gate_v_in1(c_e_h_1, c_g, s5)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[15566, 5516, 18880])).
% 292.90/185.40 tff(18882,plain,
% 292.90/185.40 (m_and_h_gate_v_out(c_e_h_1, c_c, s4)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[14848, 18879])).
% 292.90/185.40 tff(18883,plain,
% 292.90/185.40 (m_user_v_req(c_e_h_1, c_u, s2)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[14671, 18882])).
% 292.90/185.40 tff(18884,plain,
% 292.90/185.40 (m_user_v_req(c_e_h_1, c_u, s3)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[14760, 18883])).
% 292.90/185.40 tff(18885,plain,
% 292.90/185.40 (m_mutex_h_half_v_inp(c_e_h_1, c_a, s3)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[14768, 18884])).
% 292.90/185.40 tff(18886,plain,
% 292.90/185.40 (m_or_h_gate_v_in1(c_e_h_1, c_g, s3)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[14503, 18878])).
% 292.90/185.40 tff(18887,plain,
% 292.90/185.40 (m_and_h_gate_v_out(c_e_h_1, c_c, s3)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[14418, 2708, 18886])).
% 292.90/185.40 tff(18888,plain,
% 292.90/185.40 (node20(c_e_h_1, c_c, s2)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[14216, 18887])).
% 292.90/185.40 tff(18889,plain,
% 292.90/185.40 (m_and_h_gate_v_in1(c_e_h_1, c_c, s2)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[14224, 18888])).
% 292.90/185.40 tff(18890,plain,
% 292.90/185.40 (m_mutex_h_half_v_out(c_e_h_1, c_a, s2)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[14232, 18889])).
% 292.90/185.40 tff(18891,plain,
% 292.90/185.40 (m_mutex_h_half_v_out(c_e_h_1, c_a, s3)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[14381, 18890])).
% 292.90/185.40 tff(18892,plain,
% 292.90/185.40 (m_mutex_h_half_v_out(c_e_h_1, c_a, s4)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[14793, 18891, 18885])).
% 292.90/185.40 tff(18893,plain,
% 292.90/185.40 (m_and_h_gate_v_in1(c_e_h_1, c_c, s4)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[14810, 18892])).
% 292.90/185.40 tff(18894,plain,
% 292.90/185.40 (m_and_h_gate_v_out(c_e_h_1, c_c, s5)),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[14843, 18893, 18882])).
% 292.90/185.40 tff(18895,plain,
% 292.90/185.40 ($false),
% 292.90/185.40 inference(unit_resolution,[status(thm)],[15570, 5896, 18894, 18881])).
% 292.90/185.40 tff(18896,plain,(m_or_h_gate_v_out(c_e_h_1, c_g, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s8))), inference(lemma,lemma(discharge,[]))).
% 292.90/185.40 tff(18897,plain,
% 292.90/185.41 (~m_and_h_gate_v_out(c_e_h_1, c_p, s8)),
% 292.90/185.41 inference(unit_resolution,[status(thm)],[18896, 15389])).
% 292.90/185.41 tff(18898,assumption,(m_cell_v_req(c_e_h_1, s8)), introduced(assumption)).
% 292.90/185.41 tff(18899,plain,
% 292.90/185.41 (((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | ((~m_cell_v_req(c_e_h_1, s8)) | m_and_h_gate_v_out(c_e_h_1, c_p, s8))) <=> ((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | (~m_cell_v_req(c_e_h_1, s8)) | m_and_h_gate_v_out(c_e_h_1, c_p, s8))),
% 292.90/185.41 inference(rewrite,[status(thm)],[])).
% 292.90/185.41 tff(18900,plain,
% 292.90/185.41 ((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | ((~m_cell_v_req(c_e_h_1, s8)) | m_and_h_gate_v_out(c_e_h_1, c_p, s8))),
% 292.90/185.41 inference(quant_inst,[status(thm)],[])).
% 292.90/185.41 tff(18901,plain,
% 292.90/185.41 ((~![I0: $i, X: $i] : ((~m_cell_v_req(I0, X)) | m_and_h_gate_v_out(I0, c_p, X))) | (~m_cell_v_req(c_e_h_1, s8)) | m_and_h_gate_v_out(c_e_h_1, c_p, s8)),
% 292.90/185.41 inference(modus_ponens,[status(thm)],[18900, 18899])).
% 292.90/185.41 tff(18902,plain,
% 292.90/185.41 ($false),
% 292.90/185.41 inference(unit_resolution,[status(thm)],[18901, 2908, 18898, 15866])).
% 292.90/185.41 tff(18903,plain,((~m_cell_v_req(c_e_h_1, s8)) | m_and_h_gate_v_out(c_e_h_1, c_p, s8)), inference(lemma,lemma(discharge,[]))).
% 292.90/185.41 tff(18904,plain,
% 292.90/185.41 (~m_cell_v_req(c_e_h_1, s8)),
% 292.90/185.41 inference(unit_resolution,[status(thm)],[18903, 15866])).
% 292.90/185.41 tff(18905,plain,
% 292.90/185.41 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_3, c_e_h_1, s8)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s8)) | m_cell_v_req(c_e_h_1, s8))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | (~node1(c_e_h_3, c_e_h_1, s8)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s8)) | m_cell_v_req(c_e_h_1, s8))),
% 292.90/185.41 inference(rewrite,[status(thm)],[])).
% 292.90/185.41 tff(18906,plain,
% 292.90/185.41 (((~node1(c_e_h_3, c_e_h_1, s8)) | m_cell_v_req(c_e_h_1, s8) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s8))) <=> ((~node1(c_e_h_3, c_e_h_1, s8)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s8)) | m_cell_v_req(c_e_h_1, s8))),
% 292.92/185.41 inference(rewrite,[status(thm)],[])).
% 292.92/185.41 tff(18907,plain,
% 292.92/185.41 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_3, c_e_h_1, s8)) | m_cell_v_req(c_e_h_1, s8) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s8)))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_3, c_e_h_1, s8)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s8)) | m_cell_v_req(c_e_h_1, s8)))),
% 292.92/185.41 inference(monotonicity,[status(thm)],[18906])).
% 292.92/185.41 tff(18908,plain,
% 292.92/185.41 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_3, c_e_h_1, s8)) | m_cell_v_req(c_e_h_1, s8) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s8)))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | (~node1(c_e_h_3, c_e_h_1, s8)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s8)) | m_cell_v_req(c_e_h_1, s8))),
% 292.92/185.41 inference(transitivity,[status(thm)],[18907, 18905])).
% 292.92/185.41 tff(18909,plain,
% 292.92/185.41 ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | ((~node1(c_e_h_3, c_e_h_1, s8)) | m_cell_v_req(c_e_h_1, s8) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s8)))),
% 292.92/185.41 inference(quant_inst,[status(thm)],[])).
% 292.92/185.41 tff(18910,plain,
% 292.92/185.41 ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | m_cell_v_req(J0, X) | (~m_mutex_h_half_v_inp(I0, c_b, X)))) | (~node1(c_e_h_3, c_e_h_1, s8)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s8)) | m_cell_v_req(c_e_h_1, s8)),
% 292.92/185.41 inference(modus_ponens,[status(thm)],[18909, 18908])).
% 292.92/185.41 tff(18911,plain,
% 292.92/185.41 ((~m_mutex_h_half_v_inp(c_e_h_3, c_b, s8)) | m_cell_v_req(c_e_h_1, s8)),
% 292.92/185.41 inference(unit_resolution,[status(thm)],[18910, 2936, 17275])).
% 292.92/185.41 tff(18912,plain,
% 292.92/185.41 (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s8)),
% 292.92/185.41 inference(unit_resolution,[status(thm)],[18911, 18904])).
% 292.92/185.41 tff(18913,plain,
% 292.92/185.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_b, s9)) | (~node13(c_e_h_3, c_b, s8, s9)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s9)) | (~node13(c_e_h_3, c_b, s8, s9)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s8))),
% 292.92/185.41 inference(rewrite,[status(thm)],[])).
% 292.92/185.41 tff(18914,plain,
% 292.92/185.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_b, s9)) | (~node13(c_e_h_3, c_b, s8, s9)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s8))),
% 292.92/185.41 inference(quant_inst,[status(thm)],[])).
% 292.92/185.41 tff(18915,plain,
% 292.92/185.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s9)) | (~node13(c_e_h_3, c_b, s8, s9)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s8)),
% 292.92/185.41 inference(modus_ponens,[status(thm)],[18914, 18913])).
% 292.92/185.41 tff(18916,plain,
% 292.92/185.41 ($false),
% 292.92/185.41 inference(unit_resolution,[status(thm)],[18915, 423, 17250, 18876, 17242])).
% 292.92/185.41 tff(18917,plain,((~node13(c_e_h_3, c_b, s8, s9)) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s9)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s8)), inference(lemma,lemma(discharge,[]))).
% 292.92/185.41 tff(18918,plain,
% 292.92/185.41 (~node13(c_e_h_3, c_b, s8, s9)),
% 292.92/185.41 inference(unit_resolution,[status(thm)],[18917, 18876, 17242])).
% 292.92/185.41 tff(18919,assumption,(~m_mutex_h_half_v_inp(c_e_h_3, c_b, s8)), introduced(assumption)).
% 292.92/185.41 tff(18920,plain,
% 292.92/185.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_3, c_b, s8) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s9)) | (~node12(c_e_h_3, c_b, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s8) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s9)) | (~node12(c_e_h_3, c_b, s8, s9)))),
% 292.92/185.41 inference(rewrite,[status(thm)],[])).
% 292.92/185.41 tff(18921,plain,
% 292.92/185.41 (((~node12(c_e_h_3, c_b, s8, s9)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s8) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s9))) <=> (m_mutex_h_half_v_inp(c_e_h_3, c_b, s8) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s9)) | (~node12(c_e_h_3, c_b, s8, s9)))),
% 292.92/185.41 inference(rewrite,[status(thm)],[])).
% 292.92/185.41 tff(18922,plain,
% 292.92/185.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_b, s8, s9)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s8) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_3, c_b, s8) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s9)) | (~node12(c_e_h_3, c_b, s8, s9))))),
% 292.92/185.41 inference(monotonicity,[status(thm)],[18921])).
% 292.92/185.41 tff(18923,plain,
% 292.92/185.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_b, s8, s9)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s8) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s8) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s9)) | (~node12(c_e_h_3, c_b, s8, s9)))),
% 292.92/185.41 inference(transitivity,[status(thm)],[18922, 18920])).
% 292.92/185.41 tff(18924,plain,
% 292.92/185.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_b, s8, s9)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s8) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s9)))),
% 292.92/185.41 inference(quant_inst,[status(thm)],[])).
% 292.92/185.41 tff(18925,plain,
% 292.92/185.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s8) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s9)) | (~node12(c_e_h_3, c_b, s8, s9))),
% 292.92/185.41 inference(modus_ponens,[status(thm)],[18924, 18923])).
% 292.92/185.41 tff(18926,plain,
% 292.92/185.41 ($false),
% 292.92/185.41 inference(unit_resolution,[status(thm)],[18925, 454, 18919, 18827, 18876])).
% 292.92/185.41 tff(18927,plain,((~node12(c_e_h_3, c_b, s8, s9)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s8) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s9))), inference(lemma,lemma(discharge,[]))).
% 292.92/185.41 tff(18928,plain,
% 292.92/185.41 (~node12(c_e_h_3, c_b, s8, s9)),
% 292.92/185.41 inference(unit_resolution,[status(thm)],[18927, 18876, 18919])).
% 292.92/185.41 tff(18929,plain,
% 292.92/185.41 ($false),
% 292.92/185.41 inference(unit_resolution,[status(thm)],[17263, 18928, 18918])).
% 292.92/185.41 tff(18930,plain,((~m_mutex_h_half_v_out(c_e_h_3, c_b, s9)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s8) | m_mutex_h_half_v_out(c_e_h_3, c_b, s8)), inference(lemma,lemma(discharge,[]))).
% 292.92/185.41 tff(18931,plain,
% 292.92/185.41 (m_mutex_h_half_v_out(c_e_h_3, c_b, s8)),
% 292.92/185.41 inference(unit_resolution,[status(thm)],[18930, 18912, 18876])).
% 292.92/185.41 tff(18932,plain,
% 292.92/185.41 (~node13(c_e_h_3, c_b, s7, s8)),
% 292.92/185.41 inference(unit_resolution,[status(thm)],[18216, 18931, 17096])).
% 292.92/185.41 tff(18933,plain,
% 292.92/185.41 (node12(c_e_h_3, c_b, s7, s8)),
% 292.92/185.41 inference(unit_resolution,[status(thm)],[18232, 18932])).
% 292.92/185.41 tff(18934,plain,
% 292.92/185.41 (m_mutex_h_half_v_inp(c_e_h_3, c_b, s7)),
% 292.92/185.41 inference(unit_resolution,[status(thm)],[18227, 18933, 18931])).
% 292.92/185.41 tff(18935,plain,
% 292.92/185.41 (m_cell_v_req(c_e_h_1, s7)),
% 292.92/185.41 inference(unit_resolution,[status(thm)],[18246, 18934])).
% 292.92/185.41 tff(18936,plain,
% 292.92/185.41 (m_and_h_gate_v_out(c_e_h_1, c_p, s7)),
% 292.92/185.41 inference(unit_resolution,[status(thm)],[18253, 18935])).
% 292.92/185.41 tff(18937,plain,
% 292.92/185.41 (~node22(c_e_h_1, c_p, s7, s8)),
% 292.92/185.41 inference(unit_resolution,[status(thm)],[18262, 18936, 15866])).
% 292.92/185.41 tff(18938,plain,
% 292.92/185.41 (node21(c_e_h_1, c_p, s7, s8)),
% 292.92/185.41 inference(unit_resolution,[status(thm)],[15794, 18937])).
% 292.92/185.41 tff(18939,plain,
% 292.92/185.41 (~m_and_h_gate_v_in1(c_e_h_1, c_p, s7)),
% 292.92/185.41 inference(unit_resolution,[status(thm)],[18270, 5851, 18938, 18210, 15866])).
% 292.92/185.41 tff(18940,plain,
% 292.92/185.41 (~m_and_h_gate_v_out(c_e_h_1, c_k, s7)),
% 292.92/185.41 inference(unit_resolution,[status(thm)],[18285, 18282, 18939])).
% 292.92/185.41 tff(18941,plain,
% 292.92/185.41 (node20(c_e_h_1, c_p, s6)),
% 292.92/185.41 inference(unit_resolution,[status(thm)],[15825, 18936, 15770])).
% 292.92/185.41 tff(18942,plain,
% 292.92/185.41 (m_and_h_gate_v_in1(c_e_h_1, c_p, s6)),
% 292.92/185.41 inference(unit_resolution,[status(thm)],[15829, 38, 18941])).
% 292.92/185.41 tff(18943,plain,
% 292.92/185.41 (m_and_h_gate_v_out(c_e_h_1, c_k, s6)),
% 292.92/185.41 inference(unit_resolution,[status(thm)],[15833, 3033, 18942])).
% 292.92/185.41 tff(18944,plain,
% 292.92/185.41 (~node22(c_e_h_1, c_k, s6, s7)),
% 292.92/185.41 inference(unit_resolution,[status(thm)],[18308, 18940, 18943])).
% 292.92/185.41 tff(18945,plain,
% 292.92/185.41 (node21(c_e_h_1, c_k, s6, s7)),
% 292.92/185.41 inference(unit_resolution,[status(thm)],[15418, 18944])).
% 292.92/185.41 tff(18946,plain,
% 292.92/185.41 (~m_and_h_gate_v_in1(c_e_h_1, c_k, s6)),
% 292.92/185.41 inference(unit_resolution,[status(thm)],[18627, 18945, 18940])).
% 292.92/185.41 tff(18947,plain,
% 292.92/185.41 (~m_or_h_gate_v_out(c_e_h_1, c_g, s6)),
% 292.92/185.41 inference(unit_resolution,[status(thm)],[18632, 6229, 18946])).
% 292.92/185.41 tff(18948,plain,
% 292.92/185.41 (m_or_h_gate_v_out(c_e_h_1, c_g, s4)),
% 292.92/185.41 inference(unit_resolution,[status(thm)],[15590, 18947, 14573, 18943])).
% 292.92/185.41 tff(18949,plain,
% 292.92/185.41 (m_or_h_gate_v_in1(c_e_h_1, c_g, s3)),
% 292.92/185.41 inference(unit_resolution,[status(thm)],[14503, 18948])).
% 292.92/185.41 tff(18950,plain,
% 292.92/185.41 (m_and_h_gate_v_out(c_e_h_1, c_c, s3)),
% 292.92/185.41 inference(unit_resolution,[status(thm)],[14418, 2708, 18949])).
% 292.92/185.41 tff(18951,plain,
% 292.92/185.41 (m_and_h_gate_v_out(c_e_h_1, c_c, s4)),
% 292.92/185.41 inference(unit_resolution,[status(thm)],[14414, 18950])).
% 292.92/185.41 tff(18952,plain,
% 292.92/185.41 (node20(c_e_h_1, c_c, s2)),
% 292.92/185.41 inference(unit_resolution,[status(thm)],[14216, 18950])).
% 292.92/185.41 tff(18953,plain,
% 292.92/185.41 (m_and_h_gate_v_in1(c_e_h_1, c_c, s2)),
% 292.92/185.41 inference(unit_resolution,[status(thm)],[14224, 18952])).
% 292.92/185.41 tff(18954,plain,
% 292.92/185.41 (m_mutex_h_half_v_out(c_e_h_1, c_a, s2)),
% 292.92/185.41 inference(unit_resolution,[status(thm)],[14232, 18953])).
% 292.92/185.41 tff(18955,plain,
% 292.92/185.41 (m_mutex_h_half_v_inp(c_e_h_1, c_a, s1)),
% 292.92/185.41 inference(unit_resolution,[status(thm)],[14258, 18954])).
% 292.92/185.41 tff(18956,plain,
% 292.92/185.41 (m_user_v_req(c_e_h_1, c_u, s1)),
% 292.92/185.41 inference(unit_resolution,[status(thm)],[14262, 395, 18955])).
% 292.92/185.41 tff(18957,plain,
% 292.92/185.41 (m_user_v_req(c_e_h_1, c_u, s2)),
% 292.92/185.41 inference(unit_resolution,[status(thm)],[14348, 18956])).
% 292.92/185.41 tff(18958,plain,
% 292.92/185.41 (m_user_v_req(c_e_h_1, c_u, s3)),
% 292.92/185.41 inference(unit_resolution,[status(thm)],[14760, 18957])).
% 292.92/185.41 tff(18959,plain,
% 292.92/185.41 (m_mutex_h_half_v_inp(c_e_h_1, c_a, s3)),
% 292.92/185.41 inference(unit_resolution,[status(thm)],[14768, 18958])).
% 292.92/185.41 tff(18960,plain,
% 292.92/185.41 (m_mutex_h_half_v_out(c_e_h_1, c_a, s3)),
% 292.92/185.41 inference(unit_resolution,[status(thm)],[14381, 18954])).
% 292.92/185.41 tff(18961,plain,
% 292.92/185.41 (m_mutex_h_half_v_out(c_e_h_1, c_a, s4)),
% 292.92/185.41 inference(unit_resolution,[status(thm)],[14793, 18960, 18959])).
% 292.92/185.41 tff(18962,plain,
% 292.92/185.41 (m_and_h_gate_v_in1(c_e_h_1, c_c, s4)),
% 292.92/185.41 inference(unit_resolution,[status(thm)],[14808, 2556, 18961])).
% 292.92/185.41 tff(18963,plain,
% 292.92/185.41 (m_and_h_gate_v_out(c_e_h_1, c_c, s5)),
% 292.92/185.41 inference(unit_resolution,[status(thm)],[14843, 18962, 18951])).
% 292.92/185.41 tff(18964,plain,
% 292.92/185.41 (m_or_h_gate_v_in1(c_e_h_1, c_g, s5)),
% 292.92/185.41 inference(unit_resolution,[status(thm)],[15570, 5896, 18963])).
% 292.92/185.41 tff(18965,plain,
% 292.92/185.41 (~node4(c_e_h_1, c_g, s5)),
% 292.92/185.41 inference(unit_resolution,[status(thm)],[15566, 5516, 18964])).
% 292.92/185.41 tff(18966,plain,
% 292.92/185.41 (~node5(c_e_h_1, c_g, s5, s6)),
% 292.92/185.41 inference(unit_resolution,[status(thm)],[15562, 18965, 18947])).
% 292.92/185.41 tff(18967,plain,
% 292.92/185.41 (node6(c_e_h_1, c_g, s5, s6)),
% 292.92/185.41 inference(unit_resolution,[status(thm)],[14560, 18966])).
% 292.92/185.41 tff(18968,plain,
% 292.92/185.41 (~m_or_h_gate_v_out(c_e_h_1, c_g, s5)),
% 292.92/185.41 inference(unit_resolution,[status(thm)],[15551, 18967, 18947])).
% 292.92/185.41 tff(18969,plain,
% 292.92/185.41 (~node6(c_e_h_1, c_g, s4, s5)),
% 292.92/185.41 inference(unit_resolution,[status(thm)],[15614, 18968, 18948])).
% 292.92/185.41 tff(18970,plain,
% 292.92/185.41 (node5(c_e_h_1, c_g, s4, s5)),
% 292.92/185.41 inference(unit_resolution,[status(thm)],[14591, 18969])).
% 292.92/185.41 tff(18971,plain,
% 292.92/185.41 (node4(c_e_h_1, c_g, s4)),
% 292.92/185.41 inference(unit_resolution,[status(thm)],[15622, 5498, 18970, 18968])).
% 292.92/185.42 tff(18972,plain,
% 292.92/185.42 (~m_or_h_gate_v_in1(c_e_h_1, c_g, s4)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[15604, 5516, 18971])).
% 292.92/185.42 tff(18973,plain,
% 292.92/185.42 ($false),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[15598, 5896, 18951, 18972])).
% 292.92/185.42 tff(18974,plain,(m_and_h_gate_v_out(c_e_h_1, c_p, s8) | m_or_h_gate_v_in2(c_e_h_1, c_g, s4) | m_and_h_gate_v_out(c_e_h_1, c_p, s6) | m_mutex_h_half_v_out(c_e_h_3, c_b, s7) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s9))), inference(lemma,lemma(discharge,[]))).
% 292.92/185.42 tff(18975,plain,
% 292.92/185.42 (m_and_h_gate_v_out(c_e_h_1, c_p, s8) | m_and_h_gate_v_out(c_e_h_1, c_p, s6) | m_mutex_h_half_v_out(c_e_h_3, c_b, s7) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s9))),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[18974, 14570])).
% 292.92/185.42 tff(18976,plain,
% 292.92/185.42 (m_mutex_h_half_v_out(c_e_h_3, c_b, s7)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[18975, 15770, 18876, 15866])).
% 292.92/185.42 tff(18977,plain,
% 292.92/185.42 (~m_cell_v_req(c_e_h_1, s6)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[18740, 15770])).
% 292.92/185.42 tff(18978,plain,
% 292.92/185.42 (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s6)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[18733, 18977])).
% 292.92/185.42 tff(18979,plain,
% 292.92/185.42 ($false),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[18720, 18978, 18976, 18707])).
% 292.92/185.42 tff(18980,plain,(m_and_h_gate_v_out(c_e_h_1, c_p, s6) | m_mutex_h_half_v_out(c_e_h_3, c_b, s6) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s9)) | m_and_h_gate_v_out(c_e_h_1, c_p, s8)), inference(lemma,lemma(discharge,[]))).
% 292.92/185.42 tff(18981,plain,
% 292.92/185.42 (m_and_h_gate_v_out(c_e_h_1, c_p, s6) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s9)) | m_and_h_gate_v_out(c_e_h_1, c_p, s8)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[18980, 17155])).
% 292.92/185.42 tff(18982,plain,
% 292.92/185.42 (m_and_h_gate_v_out(c_e_h_1, c_p, s6)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[18981, 18897, 18876])).
% 292.92/185.42 tff(18983,plain,
% 292.92/185.42 (m_and_h_gate_v_out(c_e_h_1, c_p, s7)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[18782, 18982])).
% 292.92/185.42 tff(18984,plain,
% 292.92/185.42 (m_or_h_gate_v_out(c_e_h_1, c_g, s4)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[18634, 18983, 18877])).
% 292.92/185.42 tff(18985,plain,
% 292.92/185.42 (m_or_h_gate_v_out(c_e_h_1, c_g, s5)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[15624, 18984])).
% 292.92/185.42 tff(18986,plain,
% 292.92/185.42 (node4(c_e_h_1, c_g, s5)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[17071, 18985, 15389])).
% 292.92/185.42 tff(18987,plain,
% 292.92/185.42 (~m_or_h_gate_v_in1(c_e_h_1, c_g, s5)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[15566, 5516, 18986])).
% 292.92/185.42 tff(18988,plain,
% 292.92/185.42 (m_and_h_gate_v_out(c_e_h_1, c_c, s4)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[14848, 18985])).
% 292.92/185.42 tff(18989,plain,
% 292.92/185.42 (m_user_v_req(c_e_h_1, c_u, s2)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[14671, 18988])).
% 292.92/185.42 tff(18990,plain,
% 292.92/185.42 (m_user_v_req(c_e_h_1, c_u, s3)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[14760, 18989])).
% 292.92/185.42 tff(18991,plain,
% 292.92/185.42 (m_mutex_h_half_v_inp(c_e_h_1, c_a, s3)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[14768, 18990])).
% 292.92/185.42 tff(18992,plain,
% 292.92/185.42 (m_or_h_gate_v_in1(c_e_h_1, c_g, s3)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[14503, 18984])).
% 292.92/185.42 tff(18993,plain,
% 292.92/185.42 (m_and_h_gate_v_out(c_e_h_1, c_c, s3)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[14418, 2708, 18992])).
% 292.92/185.42 tff(18994,plain,
% 292.92/185.42 (node20(c_e_h_1, c_c, s2)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[14216, 18993])).
% 292.92/185.42 tff(18995,plain,
% 292.92/185.42 (m_and_h_gate_v_in1(c_e_h_1, c_c, s2)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[14224, 18994])).
% 292.92/185.42 tff(18996,plain,
% 292.92/185.42 (m_mutex_h_half_v_out(c_e_h_1, c_a, s2)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[14232, 18995])).
% 292.92/185.42 tff(18997,plain,
% 292.92/185.42 (m_mutex_h_half_v_out(c_e_h_1, c_a, s3)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[14381, 18996])).
% 292.92/185.42 tff(18998,plain,
% 292.92/185.42 (m_mutex_h_half_v_out(c_e_h_1, c_a, s4)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[14793, 18997, 18991])).
% 292.92/185.42 tff(18999,plain,
% 292.92/185.42 (m_and_h_gate_v_in1(c_e_h_1, c_c, s4)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[14810, 18998])).
% 292.92/185.42 tff(19000,plain,
% 292.92/185.42 (m_and_h_gate_v_out(c_e_h_1, c_c, s5)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[14843, 18999, 18988])).
% 292.92/185.42 tff(19001,plain,
% 292.92/185.42 ($false),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[15570, 5896, 19000, 18987])).
% 292.92/185.42 tff(19002,plain,(m_or_h_gate_v_out(c_e_h_1, c_g, s6) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s9))), inference(lemma,lemma(discharge,[]))).
% 292.92/185.42 tff(19003,plain,
% 292.92/185.42 (m_or_h_gate_v_out(c_e_h_1, c_g, s6)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[19002, 18876])).
% 292.92/185.42 tff(19004,plain,
% 292.92/185.42 (m_and_h_gate_v_in1(c_e_h_1, c_k, s6)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[18654, 19003])).
% 292.92/185.42 tff(19005,plain,
% 292.92/185.42 (node22(c_e_h_1, c_k, s6, s7)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[15418, 18852])).
% 292.92/185.42 tff(19006,plain,
% 292.92/185.42 (~m_and_h_gate_v_out(c_e_h_1, c_k, s6)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[18308, 19005, 15905])).
% 292.92/185.42 tff(19007,plain,
% 292.92/185.42 ($false),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[15774, 3033, 15905, 18839])).
% 292.92/185.42 tff(19008,plain,((~m_and_h_gate_v_in1(c_e_h_1, c_p, s7)) | m_and_h_gate_v_out(c_e_h_1, c_k, s7)), inference(lemma,lemma(discharge,[]))).
% 292.92/185.42 tff(19009,plain,
% 292.92/185.42 (~m_and_h_gate_v_in1(c_e_h_1, c_p, s7)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[19008, 15905])).
% 292.92/185.42 tff(19010,assumption,(node20(c_e_h_1, c_p, s7)), introduced(assumption)).
% 292.92/185.42 tff(19011,plain,
% 292.92/185.42 ($false),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[15778, 38, 19010, 18272])).
% 292.92/185.42 tff(19012,plain,((~node20(c_e_h_1, c_p, s7)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s7)), inference(lemma,lemma(discharge,[]))).
% 292.92/185.42 tff(19013,plain,
% 292.92/185.42 (~node20(c_e_h_1, c_p, s7)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[19012, 19009])).
% 292.92/185.42 tff(19014,plain,
% 292.92/185.42 (~node21(c_e_h_1, c_p, s7, s8)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[15789, 19013, 15662])).
% 292.92/185.42 tff(19015,plain,
% 292.92/185.42 (node22(c_e_h_1, c_p, s7, s8)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[15794, 19014])).
% 292.92/185.42 tff(19016,plain,
% 292.92/185.42 (m_and_h_gate_v_out(c_e_h_1, c_p, s7)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[15802, 19015, 15662])).
% 292.92/185.42 tff(19017,plain,
% 292.92/185.42 (~m_and_h_gate_v_in1(c_e_h_1, c_p, s6)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[18299, 19006])).
% 292.92/185.42 tff(19018,plain,
% 292.92/185.42 (~node20(c_e_h_1, c_p, s6)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[18295, 19017])).
% 292.92/185.42 tff(19019,plain,
% 292.92/185.42 (m_and_h_gate_v_out(c_e_h_1, c_p, s6)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[15825, 19018, 19016])).
% 292.92/185.42 tff(19020,plain,
% 292.92/185.42 (node20(c_e_h_1, c_p, s5)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[15765, 19019])).
% 292.92/185.42 tff(19021,plain,
% 292.92/185.42 (m_and_h_gate_v_in1(c_e_h_1, c_p, s5)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[15695, 19020])).
% 292.92/185.42 tff(19022,plain,
% 292.92/185.42 (m_and_h_gate_v_out(c_e_h_1, c_k, s5)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[15687, 19021])).
% 292.92/185.42 tff(19023,plain,
% 292.92/185.42 (~node22(c_e_h_1, c_k, s5, s6)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[18672, 19006, 19022])).
% 292.92/185.42 tff(19024,plain,
% 292.92/185.42 (node21(c_e_h_1, c_k, s5, s6)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[15521, 19023])).
% 292.92/185.42 tff(19025,plain,
% 292.92/185.42 (~m_and_h_gate_v_in1(c_e_h_1, c_k, s5)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[18687, 19024, 19006])).
% 292.92/185.42 tff(19026,plain,
% 292.92/185.42 (node20(c_e_h_1, c_k, s4)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[15500, 19022])).
% 292.92/185.42 tff(19027,plain,
% 292.92/185.42 (m_and_h_gate_v_in1(c_e_h_1, c_k, s4)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[15443, 19026])).
% 292.92/185.42 tff(19028,plain,
% 292.92/185.42 (m_or_h_gate_v_out(c_e_h_1, c_g, s4)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[15435, 19027])).
% 292.92/185.42 tff(19029,plain,
% 292.92/185.42 (m_or_h_gate_v_out(c_e_h_1, c_g, s5)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[15624, 19028])).
% 292.92/185.42 tff(19030,plain,
% 292.92/185.42 ($false),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[18691, 6229, 19029, 19025])).
% 292.92/185.42 tff(19031,plain,(m_and_h_gate_v_out(c_e_h_1, c_k, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s8)) | (~m_and_h_gate_v_in1(c_e_h_1, c_k, s6))), inference(lemma,lemma(discharge,[]))).
% 292.92/185.42 tff(19032,plain,
% 292.92/185.42 (~m_and_h_gate_v_out(c_e_h_1, c_p, s8)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[19031, 15905, 19004])).
% 292.92/185.42 tff(19033,plain,
% 292.92/185.42 (m_and_h_gate_v_out(c_e_h_1, c_p, s6)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[18981, 19032, 18876])).
% 292.92/185.42 tff(19034,plain,
% 292.92/185.42 (node20(c_e_h_1, c_p, s5)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[15765, 19033])).
% 292.92/185.42 tff(19035,plain,
% 292.92/185.42 (~m_and_h_gate_v_out(c_e_h_1, c_k, s6)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[18855, 15905, 19004])).
% 292.92/185.42 tff(19036,plain,
% 292.92/185.42 (~m_and_h_gate_v_out(c_e_h_1, c_k, s5)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[18755, 19035])).
% 292.92/185.42 tff(19037,plain,
% 292.92/185.42 (~m_and_h_gate_v_in1(c_e_h_1, c_p, s5)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[15687, 19036])).
% 292.92/185.42 tff(19038,plain,
% 292.92/185.42 ($false),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[15695, 19037, 19034])).
% 292.92/185.42 tff(19039,plain,(m_and_h_gate_v_out(c_e_h_1, c_k, s7) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s9))), inference(lemma,lemma(discharge,[]))).
% 292.92/185.42 tff(19040,plain,
% 292.92/185.42 (m_and_h_gate_v_out(c_e_h_1, c_k, s7)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[19039, 18875])).
% 292.92/185.42 tff(19041,plain,
% 292.92/185.42 (~m_cell_v_req(c_e_h_1, s6)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[18740, 15766])).
% 292.92/185.42 tff(19042,plain,
% 292.92/185.42 (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s6)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[18733, 19041])).
% 292.92/185.42 tff(19043,plain,
% 292.92/185.42 (~m_mutex_h_half_v_out(c_e_h_3, c_b, s7)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[18721, 19042])).
% 292.92/185.42 tff(19044,plain,
% 292.92/185.42 (~m_and_h_gate_v_in1(c_e_h_3, c_d, s7)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[17102, 19043])).
% 292.92/185.42 tff(19045,plain,
% 292.92/185.42 (~node20(c_e_h_3, c_d, s7)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[17110, 19044])).
% 292.92/185.42 tff(19046,plain,
% 292.92/185.42 (~m_and_h_gate_v_out(c_e_h_3, c_d, s8)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[17208, 19045])).
% 292.92/185.42 tff(19047,plain,
% 292.92/185.42 (node20(c_e_h_3, c_d, s8)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[17231, 19046, 17094])).
% 292.92/185.42 tff(19048,plain,
% 292.92/185.42 (m_and_h_gate_v_in1(c_e_h_3, c_d, s8)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[17239, 19047])).
% 292.92/185.42 tff(19049,plain,
% 292.92/185.42 (m_mutex_h_half_v_out(c_e_h_3, c_b, s8)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[17247, 19048])).
% 292.92/185.42 tff(19050,plain,
% 292.92/185.42 (m_mutex_h_half_v_inp(c_e_h_3, c_b, s7)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[18234, 19049, 19043])).
% 292.92/185.42 tff(19051,plain,
% 292.92/185.42 (m_cell_v_req(c_e_h_1, s7)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[18246, 19050])).
% 292.92/185.42 tff(19052,plain,
% 292.92/185.42 (m_and_h_gate_v_out(c_e_h_1, c_p, s7)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[18253, 19051])).
% 292.92/185.42 tff(19053,plain,
% 292.92/185.42 (node20(c_e_h_1, c_p, s6)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[15825, 19052, 15766])).
% 292.92/185.42 tff(19054,plain,
% 292.92/185.42 (m_and_h_gate_v_in1(c_e_h_1, c_p, s6)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[18295, 19053])).
% 292.92/185.42 tff(19055,plain,
% 292.92/185.42 (m_and_h_gate_v_out(c_e_h_1, c_k, s6)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[18299, 19054])).
% 292.92/185.42 tff(19056,plain,
% 292.92/185.42 (m_or_h_gate_v_out(c_e_h_1, c_g, s6)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[15591, 19055, 15678])).
% 292.92/185.42 tff(19057,plain,
% 292.92/185.42 (m_mutex_h_half_v_out(c_e_h_1, c_a, s5)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[15065, 19056])).
% 292.92/185.42 tff(19058,plain,
% 292.92/185.42 (m_and_h_gate_v_in1(c_e_h_1, c_c, s5)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[15073, 19057])).
% 292.92/185.42 tff(19059,plain,
% 292.92/185.42 (~node21(c_e_h_1, c_c, s5, s6)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[15368, 19058, 13629])).
% 292.92/185.42 tff(19060,plain,
% 292.92/185.42 (node22(c_e_h_1, c_c, s5, s6)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[15383, 19059])).
% 292.92/185.42 tff(19061,plain,
% 292.92/185.42 (m_mutex_h_half_v_out(c_e_h_1, c_a, s4)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[14803, 19056])).
% 292.92/185.42 tff(19062,plain,
% 292.92/185.42 (m_and_h_gate_v_in1(c_e_h_1, c_c, s4)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[14810, 19061])).
% 292.92/185.42 tff(19063,plain,
% 292.92/185.42 (node20(c_e_h_1, c_k, s5)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[15523, 19055, 15681])).
% 292.92/185.42 tff(19064,plain,
% 292.92/185.42 (m_and_h_gate_v_in1(c_e_h_1, c_k, s5)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[15531, 19063])).
% 292.92/185.42 tff(19065,plain,
% 292.92/185.42 (m_or_h_gate_v_out(c_e_h_1, c_g, s5)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[15538, 19064])).
% 292.92/185.42 tff(19066,plain,
% 292.92/185.42 (m_and_h_gate_v_out(c_e_h_1, c_c, s4)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[14848, 19065])).
% 292.92/185.42 tff(19067,plain,
% 292.92/185.42 (m_and_h_gate_v_out(c_e_h_1, c_c, s5)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[14843, 19066, 19062])).
% 292.92/185.42 tff(19068,plain,
% 292.92/185.42 ($false),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[15378, 19067, 19060, 13629])).
% 292.92/185.42 tff(19069,plain,(m_and_h_gate_v_out(c_e_h_1, c_c, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s9))), inference(lemma,lemma(discharge,[]))).
% 292.92/185.42 tff(19070,plain,
% 292.92/185.42 (m_and_h_gate_v_out(c_e_h_1, c_c, s6)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[19069, 17094])).
% 292.92/185.42 tff(19071,plain,
% 292.92/185.42 ($false),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[17019, 5896, 16268, 15991])).
% 292.92/185.42 tff(19072,plain,(m_or_h_gate_v_in1(c_e_h_1, c_g, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s6))), inference(lemma,lemma(discharge,[]))).
% 292.92/185.42 tff(19073,plain,
% 292.92/185.42 (m_or_h_gate_v_in1(c_e_h_1, c_g, s6)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[19072, 19070])).
% 292.92/185.42 tff(19074,plain,
% 292.92/185.42 (~node4(c_e_h_1, c_g, s6)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[17027, 19073])).
% 292.92/185.42 tff(19075,plain,
% 292.92/185.42 (m_or_h_gate_v_out(c_e_h_1, c_g, s6)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[19002, 18875])).
% 292.92/185.42 tff(19076,plain,
% 292.92/185.42 (m_or_h_gate_v_out(c_e_h_1, c_g, s7)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[17051, 19075, 19074])).
% 292.92/185.42 tff(19077,plain,
% 292.92/185.42 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X))) | ((~m_or_h_gate_v_out(c_e_h_1, c_g, s7)) | m_and_h_gate_v_in1(c_e_h_1, c_k, s7))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X))) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s7)) | m_and_h_gate_v_in1(c_e_h_1, c_k, s7))),
% 292.92/185.42 inference(rewrite,[status(thm)],[])).
% 292.92/185.42 tff(19078,plain,
% 292.92/185.42 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X))) | ((~m_or_h_gate_v_out(c_e_h_1, c_g, s7)) | m_and_h_gate_v_in1(c_e_h_1, c_k, s7))),
% 292.92/185.42 inference(quant_inst,[status(thm)],[])).
% 292.92/185.42 tff(19079,plain,
% 292.92/185.42 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_and_h_gate_v_in1(I0, c_k, X))) | (~m_or_h_gate_v_out(c_e_h_1, c_g, s7)) | m_and_h_gate_v_in1(c_e_h_1, c_k, s7)),
% 292.92/185.42 inference(modus_ponens,[status(thm)],[19078, 19077])).
% 292.92/185.42 tff(19080,plain,
% 292.92/185.42 ($false),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[19079, 6229, 15952, 15925])).
% 292.92/185.42 tff(19081,plain,((~m_or_h_gate_v_out(c_e_h_1, c_g, s7)) | m_and_h_gate_v_in1(c_e_h_1, c_k, s7)), inference(lemma,lemma(discharge,[]))).
% 292.92/185.42 tff(19082,plain,
% 292.92/185.42 (m_and_h_gate_v_in1(c_e_h_1, c_k, s7)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[19081, 19076])).
% 292.92/185.42 tff(19083,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_p, s9)), introduced(assumption)).
% 292.92/185.42 tff(19084,plain,
% 292.92/185.42 (m_and_h_gate_v_out(c_e_h_1, c_p, s6)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[18981, 15866, 18876])).
% 292.92/185.42 tff(19085,plain,
% 292.92/185.42 (m_and_h_gate_v_out(c_e_h_1, c_k, s7)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[19039, 18876])).
% 292.92/185.42 tff(19086,plain,
% 292.92/185.42 (m_and_h_gate_v_in1(c_e_h_1, c_p, s7)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[18287, 19085])).
% 292.92/185.42 tff(19087,plain,
% 292.92/185.42 (~m_and_h_gate_v_out(c_e_h_1, c_p, s7)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[18843, 15866, 19086])).
% 292.92/185.42 tff(19088,plain,
% 292.92/185.42 ($false),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[18782, 19087, 19084])).
% 292.92/185.42 tff(19089,plain,(m_and_h_gate_v_out(c_e_h_1, c_p, s8) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s9))), inference(lemma,lemma(discharge,[]))).
% 292.92/185.42 tff(19090,plain,
% 292.92/185.42 (m_and_h_gate_v_out(c_e_h_1, c_p, s8)),
% 292.92/185.42 inference(unit_resolution,[status(thm)],[19089, 18875])).
% 292.92/185.42 tff(19091,assumption,(node21(c_e_h_1, c_p, s8, s9)), introduced(assumption)).
% 292.92/185.42 tff(19092,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s6)), introduced(assumption)).
% 292.92/185.42 tff(19093,plain,
% 292.92/185.42 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s5)) | m_c_h_element_v_out(c_e_h_1, c_h, s5))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s5)) | m_c_h_element_v_out(c_e_h_1, c_h, s5))),
% 292.92/185.42 inference(rewrite,[status(thm)],[])).
% 292.92/185.42 tff(19094,plain,
% 292.92/185.42 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s5)) | m_c_h_element_v_out(c_e_h_1, c_h, s5))),
% 292.92/185.42 inference(quant_inst,[status(thm)],[])).
% 292.92/185.42 tff(19095,plain,
% 292.92/185.42 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s5)) | m_c_h_element_v_out(c_e_h_1, c_h, s5)),
% 292.92/185.43 inference(modus_ponens,[status(thm)],[19094, 19093])).
% 292.92/185.43 tff(19096,plain,
% 292.92/185.43 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s5)),
% 292.92/185.43 inference(unit_resolution,[status(thm)],[19095, 619, 18538])).
% 292.92/185.43 tff(19097,plain,
% 292.92/185.43 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s5)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s5)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s5))),
% 292.92/185.43 inference(rewrite,[status(thm)],[])).
% 292.92/185.43 tff(19098,plain,
% 292.92/185.43 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s5)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s5))),
% 292.92/185.43 inference(quant_inst,[status(thm)],[])).
% 292.92/185.43 tff(19099,plain,
% 292.92/185.43 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s5)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s5)),
% 292.92/185.43 inference(modus_ponens,[status(thm)],[19098, 19097])).
% 292.92/185.43 tff(19100,plain,
% 292.92/185.43 (~node20(c_e_h_1, c_i, s5)),
% 292.92/185.43 inference(unit_resolution,[status(thm)],[19099, 38, 19096])).
% 292.92/185.43 tff(19101,assumption,(node22(c_e_h_1, c_i, s5, s6)), introduced(assumption)).
% 292.92/185.43 tff(19102,plain,
% 292.92/185.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s6)) | (~node22(c_e_h_1, c_i, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_i, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s6)) | (~node22(c_e_h_1, c_i, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_i, s5))),
% 292.92/185.43 inference(rewrite,[status(thm)],[])).
% 292.92/185.43 tff(19103,plain,
% 292.92/185.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s6)) | (~node22(c_e_h_1, c_i, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_i, s5))),
% 292.92/185.43 inference(quant_inst,[status(thm)],[])).
% 292.92/185.43 tff(19104,plain,
% 292.92/185.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s6)) | (~node22(c_e_h_1, c_i, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_i, s5)),
% 292.92/185.43 inference(modus_ponens,[status(thm)],[19103, 19102])).
% 292.92/185.43 tff(19105,plain,
% 292.92/185.43 ($false),
% 292.92/185.43 inference(unit_resolution,[status(thm)],[19104, 108, 19101, 17520, 19092])).
% 292.92/185.43 tff(19106,plain,((~node22(c_e_h_1, c_i, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s6))), inference(lemma,lemma(discharge,[]))).
% 292.92/185.43 tff(19107,plain,
% 292.92/185.43 (~node22(c_e_h_1, c_i, s5, s6)),
% 292.92/185.43 inference(unit_resolution,[status(thm)],[19106, 19092])).
% 292.92/185.43 tff(19108,plain,
% 292.92/185.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_1, c_i, s5, s6) | node22(c_e_h_1, c_i, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_1, c_i, s5, s6) | node22(c_e_h_1, c_i, s5, s6))),
% 292.92/185.43 inference(rewrite,[status(thm)],[])).
% 292.92/185.43 tff(19109,plain,
% 292.92/185.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_1, c_i, s5, s6) | node22(c_e_h_1, c_i, s5, s6))),
% 292.92/185.43 inference(quant_inst,[status(thm)],[])).
% 292.92/185.43 tff(19110,plain,
% 292.92/185.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_1, c_i, s5, s6) | node22(c_e_h_1, c_i, s5, s6)),
% 292.92/185.43 inference(modus_ponens,[status(thm)],[19109, 19108])).
% 292.92/185.43 tff(19111,plain,
% 292.92/185.43 (node21(c_e_h_1, c_i, s5, s6) | node22(c_e_h_1, c_i, s5, s6)),
% 292.92/185.43 inference(unit_resolution,[status(thm)],[19110, 82, 1406])).
% 292.92/185.43 tff(19112,plain,
% 292.92/185.43 (node21(c_e_h_1, c_i, s5, s6)),
% 292.92/185.43 inference(unit_resolution,[status(thm)],[19111, 19107])).
% 292.92/185.43 tff(19113,plain,
% 292.92/185.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s6)) | (~node21(c_e_h_1, c_i, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s6)) | (~node21(c_e_h_1, c_i, s5, s6)))),
% 292.92/185.43 inference(rewrite,[status(thm)],[])).
% 292.92/185.43 tff(19114,plain,
% 292.92/185.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s6)) | (~node21(c_e_h_1, c_i, s5, s6)))),
% 292.92/185.43 inference(quant_inst,[status(thm)],[])).
% 292.92/185.43 tff(19115,plain,
% 292.92/185.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s6)) | (~node21(c_e_h_1, c_i, s5, s6))),
% 292.92/185.43 inference(modus_ponens,[status(thm)],[19114, 19113])).
% 292.92/185.43 tff(19116,plain,
% 292.92/185.43 ($false),
% 292.92/185.43 inference(unit_resolution,[status(thm)],[19115, 52, 19112, 19100, 19092])).
% 292.92/185.43 tff(19117,plain,(~m_and_h_gate_v_out(c_e_h_1, c_i, s6)), inference(lemma,lemma(discharge,[]))).
% 292.92/185.43 tff(19118,plain,
% 292.92/185.43 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s6)) | m_and_h_gate_v_out(c_e_h_1, c_i, s6))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s6)) | m_and_h_gate_v_out(c_e_h_1, c_i, s6))),
% 292.92/185.43 inference(rewrite,[status(thm)],[])).
% 292.92/185.43 tff(19119,plain,
% 292.92/185.43 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s6)) | m_and_h_gate_v_out(c_e_h_1, c_i, s6))),
% 292.92/185.43 inference(quant_inst,[status(thm)],[])).
% 292.92/185.43 tff(19120,plain,
% 292.92/185.43 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s6)) | m_and_h_gate_v_out(c_e_h_1, c_i, s6)),
% 292.92/185.43 inference(modus_ponens,[status(thm)],[19119, 19118])).
% 292.92/185.43 tff(19121,plain,
% 292.92/185.43 (~m_c_h_element_v_in2(c_e_h_1, c_e, s6)),
% 292.92/185.43 inference(unit_resolution,[status(thm)],[19120, 164, 19117])).
% 292.92/185.43 tff(19122,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s7)), introduced(assumption)).
% 292.92/185.43 tff(19123,assumption,(~m_c_h_element_v_out(c_e_h_1, c_e, s6)), introduced(assumption)).
% 292.92/185.43 tff(19124,assumption,(node18(c_e_h_1, c_e, s6, s7)), introduced(assumption)).
% 292.92/185.43 tff(19125,plain,
% 292.92/185.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s7)) | m_c_h_element_v_out(c_e_h_1, c_e, s6) | (~node18(c_e_h_1, c_e, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s7)) | m_c_h_element_v_out(c_e_h_1, c_e, s6) | (~node18(c_e_h_1, c_e, s6, s7)))),
% 292.92/185.43 inference(rewrite,[status(thm)],[])).
% 292.92/185.43 tff(19126,plain,
% 292.92/185.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s7)) | m_c_h_element_v_out(c_e_h_1, c_e, s6) | (~node18(c_e_h_1, c_e, s6, s7)))),
% 292.92/185.43 inference(quant_inst,[status(thm)],[])).
% 292.92/185.43 tff(19127,plain,
% 292.92/185.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s7)) | m_c_h_element_v_out(c_e_h_1, c_e, s6) | (~node18(c_e_h_1, c_e, s6, s7))),
% 292.92/185.43 inference(modus_ponens,[status(thm)],[19126, 19125])).
% 292.92/185.43 tff(19128,plain,
% 292.92/185.43 ($false),
% 292.92/185.43 inference(unit_resolution,[status(thm)],[19127, 753, 19122, 19123, 19124])).
% 292.92/185.43 tff(19129,plain,((~node18(c_e_h_1, c_e, s6, s7)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s7)) | m_c_h_element_v_out(c_e_h_1, c_e, s6)), inference(lemma,lemma(discharge,[]))).
% 292.92/185.44 tff(19130,plain,
% 292.92/185.44 (~node18(c_e_h_1, c_e, s6, s7)),
% 292.92/185.44 inference(unit_resolution,[status(thm)],[19129, 19122, 19123])).
% 292.92/185.44 tff(19131,plain,
% 292.92/185.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s6, s7)) | node19(c_e_h_1, c_e, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s6, s7)) | node19(c_e_h_1, c_e, s6, s7))),
% 292.92/185.44 inference(rewrite,[status(thm)],[])).
% 292.92/185.44 tff(19132,plain,
% 292.92/185.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s6, s7)) | node19(c_e_h_1, c_e, s6, s7))),
% 292.92/185.44 inference(quant_inst,[status(thm)],[])).
% 292.92/185.44 tff(19133,plain,
% 292.92/185.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s6, s7)) | node19(c_e_h_1, c_e, s6, s7)),
% 292.92/185.44 inference(modus_ponens,[status(thm)],[19132, 19131])).
% 292.92/185.44 tff(19134,plain,
% 292.92/185.44 (node19(c_e_h_1, c_e, s6, s7)),
% 292.92/185.44 inference(unit_resolution,[status(thm)],[19133, 190, 1844])).
% 292.92/185.44 tff(19135,plain,
% 292.92/185.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_e, s6, s7)) | node18(c_e_h_1, c_e, s6, s7) | node17(c_e_h_1, c_e, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s6, s7)) | node18(c_e_h_1, c_e, s6, s7) | node17(c_e_h_1, c_e, s6))),
% 292.92/185.44 inference(rewrite,[status(thm)],[])).
% 292.92/185.44 tff(19136,plain,
% 292.92/185.44 ((node17(c_e_h_1, c_e, s6) | node18(c_e_h_1, c_e, s6, s7) | (~node19(c_e_h_1, c_e, s6, s7))) <=> ((~node19(c_e_h_1, c_e, s6, s7)) | node18(c_e_h_1, c_e, s6, s7) | node17(c_e_h_1, c_e, s6))),
% 292.92/185.44 inference(rewrite,[status(thm)],[])).
% 292.92/185.44 tff(19137,plain,
% 292.92/185.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s6) | node18(c_e_h_1, c_e, s6, s7) | (~node19(c_e_h_1, c_e, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_e, s6, s7)) | node18(c_e_h_1, c_e, s6, s7) | node17(c_e_h_1, c_e, s6)))),
% 292.92/185.44 inference(monotonicity,[status(thm)],[19136])).
% 292.92/185.44 tff(19138,plain,
% 292.92/185.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s6) | node18(c_e_h_1, c_e, s6, s7) | (~node19(c_e_h_1, c_e, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s6, s7)) | node18(c_e_h_1, c_e, s6, s7) | node17(c_e_h_1, c_e, s6))),
% 292.92/185.44 inference(transitivity,[status(thm)],[19137, 19135])).
% 292.92/185.44 tff(19139,plain,
% 292.92/185.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s6) | node18(c_e_h_1, c_e, s6, s7) | (~node19(c_e_h_1, c_e, s6, s7)))),
% 292.92/185.44 inference(quant_inst,[status(thm)],[])).
% 292.92/185.44 tff(19140,plain,
% 292.92/185.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s6, s7)) | node18(c_e_h_1, c_e, s6, s7) | node17(c_e_h_1, c_e, s6)),
% 292.92/185.44 inference(modus_ponens,[status(thm)],[19139, 19138])).
% 292.92/185.44 tff(19141,plain,
% 292.92/185.44 (node18(c_e_h_1, c_e, s6, s7) | node17(c_e_h_1, c_e, s6)),
% 292.92/185.44 inference(unit_resolution,[status(thm)],[19140, 776, 19134])).
% 292.92/185.44 tff(19142,plain,
% 292.92/185.44 (node17(c_e_h_1, c_e, s6)),
% 292.92/185.44 inference(unit_resolution,[status(thm)],[19141, 19130])).
% 292.92/185.44 tff(19143,assumption,(node15(c_e_h_1, c_e, s6, s7)), introduced(assumption)).
% 292.92/185.44 tff(19144,plain,
% 292.92/185.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s7)) | (~node15(c_e_h_1, c_e, s6, s7)) | m_c_h_element_v_out(c_e_h_1, c_e, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s7)) | (~node15(c_e_h_1, c_e, s6, s7)) | m_c_h_element_v_out(c_e_h_1, c_e, s6))),
% 292.92/185.44 inference(rewrite,[status(thm)],[])).
% 292.92/185.44 tff(19145,plain,
% 292.92/185.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s7)) | (~node15(c_e_h_1, c_e, s6, s7)) | m_c_h_element_v_out(c_e_h_1, c_e, s6))),
% 292.92/185.44 inference(quant_inst,[status(thm)],[])).
% 292.92/185.44 tff(19146,plain,
% 292.92/185.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s7)) | (~node15(c_e_h_1, c_e, s6, s7)) | m_c_h_element_v_out(c_e_h_1, c_e, s6)),
% 292.92/185.44 inference(modus_ponens,[status(thm)],[19145, 19144])).
% 292.92/185.44 tff(19147,plain,
% 292.92/185.44 ($false),
% 292.92/185.44 inference(unit_resolution,[status(thm)],[19146, 147, 19122, 19123, 19143])).
% 292.92/185.44 tff(19148,plain,((~node15(c_e_h_1, c_e, s6, s7)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s7)) | m_c_h_element_v_out(c_e_h_1, c_e, s6)), inference(lemma,lemma(discharge,[]))).
% 292.92/185.44 tff(19149,plain,
% 292.92/185.44 (~node15(c_e_h_1, c_e, s6, s7)),
% 292.92/185.44 inference(unit_resolution,[status(thm)],[19148, 19122, 19123])).
% 292.92/185.44 tff(19150,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_e, s6)), introduced(assumption)).
% 292.92/185.44 tff(19151,assumption,(node14(c_e_h_1, c_e, s6, s7)), introduced(assumption)).
% 292.92/185.44 tff(19152,plain,
% 292.92/185.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s7)) | m_c_h_element_v_in1(c_e_h_1, c_e, s6) | (~node14(c_e_h_1, c_e, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s7)) | m_c_h_element_v_in1(c_e_h_1, c_e, s6) | (~node14(c_e_h_1, c_e, s6, s7)))),
% 292.92/185.44 inference(rewrite,[status(thm)],[])).
% 292.92/185.44 tff(19153,plain,
% 292.92/185.44 (((~node14(c_e_h_1, c_e, s6, s7)) | m_c_h_element_v_in1(c_e_h_1, c_e, s6) | (~m_c_h_element_v_out(c_e_h_1, c_e, s7))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_e, s7)) | m_c_h_element_v_in1(c_e_h_1, c_e, s6) | (~node14(c_e_h_1, c_e, s6, s7)))),
% 292.92/185.44 inference(rewrite,[status(thm)],[])).
% 292.92/185.44 tff(19154,plain,
% 292.92/185.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s6, s7)) | m_c_h_element_v_in1(c_e_h_1, c_e, s6) | (~m_c_h_element_v_out(c_e_h_1, c_e, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s7)) | m_c_h_element_v_in1(c_e_h_1, c_e, s6) | (~node14(c_e_h_1, c_e, s6, s7))))),
% 292.92/185.44 inference(monotonicity,[status(thm)],[19153])).
% 292.92/185.44 tff(19155,plain,
% 292.92/185.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s6, s7)) | m_c_h_element_v_in1(c_e_h_1, c_e, s6) | (~m_c_h_element_v_out(c_e_h_1, c_e, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s7)) | m_c_h_element_v_in1(c_e_h_1, c_e, s6) | (~node14(c_e_h_1, c_e, s6, s7)))),
% 292.92/185.44 inference(transitivity,[status(thm)],[19154, 19152])).
% 292.92/185.44 tff(19156,plain,
% 292.92/185.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s6, s7)) | m_c_h_element_v_in1(c_e_h_1, c_e, s6) | (~m_c_h_element_v_out(c_e_h_1, c_e, s7)))),
% 292.92/185.44 inference(quant_inst,[status(thm)],[])).
% 292.92/185.44 tff(19157,plain,
% 292.92/185.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s7)) | m_c_h_element_v_in1(c_e_h_1, c_e, s6) | (~node14(c_e_h_1, c_e, s6, s7))),
% 292.92/185.44 inference(modus_ponens,[status(thm)],[19156, 19155])).
% 292.92/185.44 tff(19158,plain,
% 292.92/185.44 ($false),
% 292.92/185.44 inference(unit_resolution,[status(thm)],[19157, 223, 19122, 19151, 19150])).
% 292.92/185.44 tff(19159,plain,((~node14(c_e_h_1, c_e, s6, s7)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s7)) | m_c_h_element_v_in1(c_e_h_1, c_e, s6)), inference(lemma,lemma(discharge,[]))).
% 292.92/185.44 tff(19160,plain,
% 292.92/185.44 (~node14(c_e_h_1, c_e, s6, s7)),
% 292.92/185.44 inference(unit_resolution,[status(thm)],[19159, 19122, 19150])).
% 292.92/185.44 tff(19161,plain,
% 292.92/185.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_1, c_e, s6, s7) | node15(c_e_h_1, c_e, s6, s7) | (~node19(c_e_h_1, c_e, s6, s7)) | node16(c_e_h_1, c_e, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_e, s6, s7) | node15(c_e_h_1, c_e, s6, s7) | (~node19(c_e_h_1, c_e, s6, s7)) | node16(c_e_h_1, c_e, s6))),
% 292.92/185.44 inference(rewrite,[status(thm)],[])).
% 292.92/185.44 tff(19162,plain,
% 292.92/185.44 ((node16(c_e_h_1, c_e, s6) | node14(c_e_h_1, c_e, s6, s7) | node15(c_e_h_1, c_e, s6, s7) | (~node19(c_e_h_1, c_e, s6, s7))) <=> (node14(c_e_h_1, c_e, s6, s7) | node15(c_e_h_1, c_e, s6, s7) | (~node19(c_e_h_1, c_e, s6, s7)) | node16(c_e_h_1, c_e, s6))),
% 292.92/185.44 inference(rewrite,[status(thm)],[])).
% 292.92/185.44 tff(19163,plain,
% 292.92/185.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s6) | node14(c_e_h_1, c_e, s6, s7) | node15(c_e_h_1, c_e, s6, s7) | (~node19(c_e_h_1, c_e, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_1, c_e, s6, s7) | node15(c_e_h_1, c_e, s6, s7) | (~node19(c_e_h_1, c_e, s6, s7)) | node16(c_e_h_1, c_e, s6)))),
% 292.92/185.44 inference(monotonicity,[status(thm)],[19162])).
% 292.92/185.44 tff(19164,plain,
% 292.92/185.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s6) | node14(c_e_h_1, c_e, s6, s7) | node15(c_e_h_1, c_e, s6, s7) | (~node19(c_e_h_1, c_e, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_e, s6, s7) | node15(c_e_h_1, c_e, s6, s7) | (~node19(c_e_h_1, c_e, s6, s7)) | node16(c_e_h_1, c_e, s6))),
% 292.92/185.44 inference(transitivity,[status(thm)],[19163, 19161])).
% 292.92/185.44 tff(19165,plain,
% 292.92/185.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s6) | node14(c_e_h_1, c_e, s6, s7) | node15(c_e_h_1, c_e, s6, s7) | (~node19(c_e_h_1, c_e, s6, s7)))),
% 292.92/185.44 inference(quant_inst,[status(thm)],[])).
% 292.92/185.44 tff(19166,plain,
% 292.92/185.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_e, s6, s7) | node15(c_e_h_1, c_e, s6, s7) | (~node19(c_e_h_1, c_e, s6, s7)) | node16(c_e_h_1, c_e, s6)),
% 292.92/185.44 inference(modus_ponens,[status(thm)],[19165, 19164])).
% 292.92/185.44 tff(19167,plain,
% 292.92/185.44 (node14(c_e_h_1, c_e, s6, s7) | node15(c_e_h_1, c_e, s6, s7) | node16(c_e_h_1, c_e, s6)),
% 292.92/185.44 inference(unit_resolution,[status(thm)],[19166, 204, 19134])).
% 292.92/185.44 tff(19168,plain,
% 292.92/185.44 (node16(c_e_h_1, c_e, s6)),
% 292.92/185.44 inference(unit_resolution,[status(thm)],[19167, 19160, 19149])).
% 292.92/185.44 tff(19169,assumption,(node17(c_e_h_1, c_e, s6)), introduced(assumption)).
% 292.92/185.44 tff(19170,assumption,(node16(c_e_h_1, c_e, s6)), introduced(assumption)).
% 292.92/185.44 tff(19171,plain,
% 292.92/185.44 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_e, s6)) | m_c_h_element_v_in1(c_e_h_1, c_e, s6) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s6)) | m_c_h_element_v_in1(c_e_h_1, c_e, s6) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s6)))),
% 292.92/185.44 inference(rewrite,[status(thm)],[])).
% 292.92/185.45 tff(19172,plain,
% 292.92/185.45 ((m_c_h_element_v_in1(c_e_h_1, c_e, s6) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s6)) | (~node17(c_e_h_1, c_e, s6))) <=> ((~node17(c_e_h_1, c_e, s6)) | m_c_h_element_v_in1(c_e_h_1, c_e, s6) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s6)))),
% 292.92/185.45 inference(rewrite,[status(thm)],[])).
% 292.92/185.45 tff(19173,plain,
% 292.92/185.45 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s6) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s6)) | (~node17(c_e_h_1, c_e, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_e, s6)) | m_c_h_element_v_in1(c_e_h_1, c_e, s6) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s6))))),
% 292.92/185.45 inference(monotonicity,[status(thm)],[19172])).
% 292.92/185.45 tff(19174,plain,
% 292.92/185.45 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s6) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s6)) | (~node17(c_e_h_1, c_e, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s6)) | m_c_h_element_v_in1(c_e_h_1, c_e, s6) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s6)))),
% 292.92/185.45 inference(transitivity,[status(thm)],[19173, 19171])).
% 292.92/185.45 tff(19175,plain,
% 292.92/185.45 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s6) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s6)) | (~node17(c_e_h_1, c_e, s6)))),
% 292.92/185.45 inference(quant_inst,[status(thm)],[])).
% 292.92/185.45 tff(19176,plain,
% 292.92/185.45 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s6)) | m_c_h_element_v_in1(c_e_h_1, c_e, s6) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s6))),
% 292.92/185.45 inference(modus_ponens,[status(thm)],[19175, 19174])).
% 292.92/185.45 tff(19177,plain,
% 292.92/185.45 (m_c_h_element_v_in1(c_e_h_1, c_e, s6) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s6))),
% 292.92/185.45 inference(unit_resolution,[status(thm)],[19176, 859, 19169])).
% 292.92/185.45 tff(19178,plain,
% 292.92/185.45 (~m_c_h_element_v_in2(c_e_h_1, c_e, s6)),
% 292.92/185.45 inference(unit_resolution,[status(thm)],[19177, 19150])).
% 292.92/185.45 tff(19179,plain,
% 292.92/185.45 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s6)) | m_c_h_element_v_in1(c_e_h_1, c_e, s6) | m_c_h_element_v_in2(c_e_h_1, c_e, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s6)) | m_c_h_element_v_in1(c_e_h_1, c_e, s6) | m_c_h_element_v_in2(c_e_h_1, c_e, s6))),
% 292.92/185.45 inference(rewrite,[status(thm)],[])).
% 292.92/185.45 tff(19180,plain,
% 292.92/185.45 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s6)) | m_c_h_element_v_in1(c_e_h_1, c_e, s6) | m_c_h_element_v_in2(c_e_h_1, c_e, s6))),
% 292.92/185.45 inference(quant_inst,[status(thm)],[])).
% 292.92/185.45 tff(19181,plain,
% 292.92/185.45 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s6)) | m_c_h_element_v_in1(c_e_h_1, c_e, s6) | m_c_h_element_v_in2(c_e_h_1, c_e, s6)),
% 292.92/185.45 inference(modus_ponens,[status(thm)],[19180, 19179])).
% 292.92/185.45 tff(19182,plain,
% 292.92/185.45 (m_c_h_element_v_in1(c_e_h_1, c_e, s6) | m_c_h_element_v_in2(c_e_h_1, c_e, s6)),
% 292.92/185.45 inference(unit_resolution,[status(thm)],[19181, 178, 19170])).
% 292.92/185.45 tff(19183,plain,
% 292.92/185.45 ($false),
% 292.92/185.45 inference(unit_resolution,[status(thm)],[19182, 19178, 19150])).
% 292.92/185.45 tff(19184,plain,(m_c_h_element_v_in1(c_e_h_1, c_e, s6) | (~node16(c_e_h_1, c_e, s6)) | (~node17(c_e_h_1, c_e, s6))), inference(lemma,lemma(discharge,[]))).
% 292.92/185.45 tff(19185,plain,
% 292.92/185.45 (m_c_h_element_v_in1(c_e_h_1, c_e, s6)),
% 292.92/185.45 inference(unit_resolution,[status(thm)],[19184, 19170, 19169])).
% 292.92/185.45 tff(19186,plain,
% 292.92/185.45 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_e, s6)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s6)) | m_c_h_element_v_in2(c_e_h_1, c_e, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s6)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s6)) | m_c_h_element_v_in2(c_e_h_1, c_e, s6))),
% 292.92/185.45 inference(rewrite,[status(thm)],[])).
% 292.92/185.45 tff(19187,plain,
% 292.92/185.45 (((~m_c_h_element_v_in1(c_e_h_1, c_e, s6)) | m_c_h_element_v_in2(c_e_h_1, c_e, s6) | (~node17(c_e_h_1, c_e, s6))) <=> ((~node17(c_e_h_1, c_e, s6)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s6)) | m_c_h_element_v_in2(c_e_h_1, c_e, s6))),
% 292.92/185.45 inference(rewrite,[status(thm)],[])).
% 292.92/185.45 tff(19188,plain,
% 292.92/185.45 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s6)) | m_c_h_element_v_in2(c_e_h_1, c_e, s6) | (~node17(c_e_h_1, c_e, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_e, s6)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s6)) | m_c_h_element_v_in2(c_e_h_1, c_e, s6)))),
% 292.92/185.45 inference(monotonicity,[status(thm)],[19187])).
% 292.92/185.45 tff(19189,plain,
% 292.92/185.45 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s6)) | m_c_h_element_v_in2(c_e_h_1, c_e, s6) | (~node17(c_e_h_1, c_e, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s6)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s6)) | m_c_h_element_v_in2(c_e_h_1, c_e, s6))),
% 292.92/185.45 inference(transitivity,[status(thm)],[19188, 19186])).
% 292.92/185.45 tff(19190,plain,
% 292.92/185.45 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s6)) | m_c_h_element_v_in2(c_e_h_1, c_e, s6) | (~node17(c_e_h_1, c_e, s6)))),
% 292.92/185.45 inference(quant_inst,[status(thm)],[])).
% 292.92/185.45 tff(19191,plain,
% 292.92/185.45 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s6)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s6)) | m_c_h_element_v_in2(c_e_h_1, c_e, s6)),
% 292.92/185.45 inference(modus_ponens,[status(thm)],[19190, 19189])).
% 292.92/185.45 tff(19192,plain,
% 292.92/185.45 ((~m_c_h_element_v_in1(c_e_h_1, c_e, s6)) | m_c_h_element_v_in2(c_e_h_1, c_e, s6)),
% 292.92/185.45 inference(unit_resolution,[status(thm)],[19191, 919, 19169])).
% 292.92/185.45 tff(19193,plain,
% 292.92/185.45 (m_c_h_element_v_in2(c_e_h_1, c_e, s6)),
% 292.92/185.45 inference(unit_resolution,[status(thm)],[19192, 19185])).
% 292.92/185.45 tff(19194,plain,
% 292.92/185.45 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s6)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s6)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~node16(c_e_h_1, c_e, s6)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s6)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s6)))),
% 292.92/185.45 inference(rewrite,[status(thm)],[])).
% 292.92/185.45 tff(19195,plain,
% 292.92/185.45 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s6)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s6)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s6)))),
% 292.92/185.45 inference(quant_inst,[status(thm)],[])).
% 292.92/185.45 tff(19196,plain,
% 292.92/185.45 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~node16(c_e_h_1, c_e, s6)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s6)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s6))),
% 292.92/185.45 inference(modus_ponens,[status(thm)],[19195, 19194])).
% 292.92/185.45 tff(19197,plain,
% 292.92/185.45 ((~m_c_h_element_v_in1(c_e_h_1, c_e, s6)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s6))),
% 292.92/185.45 inference(unit_resolution,[status(thm)],[19196, 2307, 19170])).
% 292.92/185.45 tff(19198,plain,
% 292.92/185.45 ($false),
% 292.92/185.45 inference(unit_resolution,[status(thm)],[19197, 19193, 19185])).
% 292.92/185.45 tff(19199,plain,((~node16(c_e_h_1, c_e, s6)) | (~node17(c_e_h_1, c_e, s6))), inference(lemma,lemma(discharge,[]))).
% 292.92/185.45 tff(19200,plain,
% 292.92/185.45 ($false),
% 292.92/185.45 inference(unit_resolution,[status(thm)],[19199, 19168, 19142])).
% 292.92/185.45 tff(19201,plain,((~m_c_h_element_v_out(c_e_h_1, c_e, s7)) | m_c_h_element_v_in1(c_e_h_1, c_e, s6) | m_c_h_element_v_out(c_e_h_1, c_e, s6)), inference(lemma,lemma(discharge,[]))).
% 292.92/185.45 tff(19202,plain,
% 292.92/185.45 ((~m_c_h_element_v_out(c_e_h_1, c_e, s7)) | m_c_h_element_v_in1(c_e_h_1, c_e, s6)),
% 292.92/185.45 inference(unit_resolution,[status(thm)],[19201, 17882])).
% 292.92/185.45 tff(19203,plain,
% 292.92/185.45 (m_c_h_element_v_in1(c_e_h_1, c_e, s6)),
% 292.92/185.45 inference(unit_resolution,[status(thm)],[19202, 19122])).
% 292.92/185.45 tff(19204,plain,
% 292.92/185.45 ((~node18(c_e_h_1, c_e, s6, s7)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s7))),
% 292.92/185.45 inference(unit_resolution,[status(thm)],[19129, 17882])).
% 292.92/185.45 tff(19205,plain,
% 292.92/185.45 (~node18(c_e_h_1, c_e, s6, s7)),
% 292.92/185.45 inference(unit_resolution,[status(thm)],[19204, 19122])).
% 292.92/185.45 tff(19206,plain,
% 292.92/185.45 (node17(c_e_h_1, c_e, s6)),
% 292.92/185.45 inference(unit_resolution,[status(thm)],[19141, 19205])).
% 292.92/185.45 tff(19207,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_e, s6)), introduced(assumption)).
% 292.92/185.45 tff(19208,plain,
% 292.92/185.45 ((~node17(c_e_h_1, c_e, s6)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s6))),
% 292.92/185.45 inference(unit_resolution,[status(thm)],[19191, 919, 19207])).
% 292.92/185.45 tff(19209,plain,
% 292.92/185.45 ($false),
% 292.92/185.45 inference(unit_resolution,[status(thm)],[19208, 19206, 19203])).
% 292.92/185.45 tff(19210,plain,((~m_c_h_element_v_out(c_e_h_1, c_e, s7)) | m_c_h_element_v_in2(c_e_h_1, c_e, s6)), inference(lemma,lemma(discharge,[]))).
% 292.92/185.45 tff(19211,plain,
% 292.92/185.45 (~m_c_h_element_v_out(c_e_h_1, c_e, s7)),
% 292.92/185.45 inference(unit_resolution,[status(thm)],[19210, 19121])).
% 292.92/185.45 tff(19212,plain,
% 292.92/185.45 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7) | m_c_h_element_v_out(c_e_h_1, c_e, s7))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7) | m_c_h_element_v_out(c_e_h_1, c_e, s7))),
% 292.92/185.45 inference(rewrite,[status(thm)],[])).
% 292.92/185.45 tff(19213,plain,
% 292.92/185.45 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7) | m_c_h_element_v_out(c_e_h_1, c_e, s7))),
% 292.92/185.45 inference(quant_inst,[status(thm)],[])).
% 292.92/185.45 tff(19214,plain,
% 292.92/185.45 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7) | m_c_h_element_v_out(c_e_h_1, c_e, s7)),
% 292.92/185.45 inference(modus_ponens,[status(thm)],[19213, 19212])).
% 292.92/185.45 tff(19215,plain,
% 292.92/185.45 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7) | m_c_h_element_v_out(c_e_h_1, c_e, s7)),
% 292.92/185.45 inference(unit_resolution,[status(thm)],[19214, 7856])).
% 292.92/185.45 tff(19216,plain,
% 292.92/185.45 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7)),
% 292.92/185.45 inference(unit_resolution,[status(thm)],[19215, 19211])).
% 292.92/185.45 tff(19217,plain,
% 292.92/185.45 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)))),
% 292.92/185.45 inference(rewrite,[status(thm)],[])).
% 292.92/185.45 tff(19218,plain,
% 292.92/185.45 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)))),
% 292.92/185.45 inference(quant_inst,[status(thm)],[])).
% 292.92/185.45 tff(19219,plain,
% 292.92/185.45 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6))),
% 292.92/185.46 inference(modus_ponens,[status(thm)],[19218, 19217])).
% 292.92/185.46 tff(19220,plain,
% 292.92/185.46 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s6)),
% 292.92/185.46 inference(unit_resolution,[status(thm)],[19219, 4958, 18109])).
% 292.92/185.46 tff(19221,plain,
% 292.92/185.46 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s6)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s6)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s6))),
% 292.92/185.46 inference(rewrite,[status(thm)],[])).
% 292.92/185.46 tff(19222,plain,
% 292.92/185.46 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s6)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s6))),
% 292.92/185.46 inference(quant_inst,[status(thm)],[])).
% 292.92/185.46 tff(19223,plain,
% 292.92/185.46 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s6)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s6)),
% 292.92/185.46 inference(modus_ponens,[status(thm)],[19222, 19221])).
% 292.92/185.46 tff(19224,plain,
% 292.92/185.46 (~node9(c_e_h_1, c_m, s6)),
% 292.92/185.46 inference(unit_resolution,[status(thm)],[19223, 4972, 19220])).
% 292.92/185.46 tff(19225,assumption,(~node9(c_e_h_1, c_m, s6)), introduced(assumption)).
% 292.92/185.46 tff(19226,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)), introduced(assumption)).
% 292.92/185.46 tff(19227,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)), introduced(assumption)).
% 292.92/185.46 tff(19228,assumption,(node11(c_e_h_1, c_m, s6, s7)), introduced(assumption)).
% 292.92/185.46 tff(19229,plain,
% 292.92/185.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)) | (~node11(c_e_h_1, c_m, s6, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)) | (~node11(c_e_h_1, c_m, s6, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6))),
% 292.92/185.46 inference(rewrite,[status(thm)],[])).
% 292.92/185.46 tff(19230,plain,
% 292.92/185.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)) | (~node11(c_e_h_1, c_m, s6, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6))),
% 292.92/185.46 inference(quant_inst,[status(thm)],[])).
% 292.92/185.46 tff(19231,plain,
% 292.92/185.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)) | (~node11(c_e_h_1, c_m, s6, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)),
% 292.92/185.46 inference(modus_ponens,[status(thm)],[19230, 19229])).
% 292.92/185.46 tff(19232,plain,
% 292.92/185.46 ($false),
% 292.92/185.46 inference(unit_resolution,[status(thm)],[19231, 5017, 19227, 19226, 19228])).
% 292.92/185.46 tff(19233,plain,((~node11(c_e_h_1, c_m, s6, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)), inference(lemma,lemma(discharge,[]))).
% 292.92/185.46 tff(19234,plain,
% 292.92/185.46 (~node11(c_e_h_1, c_m, s6, s7)),
% 292.92/185.46 inference(unit_resolution,[status(thm)],[19233, 19227, 19226])).
% 292.92/185.46 tff(19235,plain,
% 292.92/185.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s6, s7)) | node10(c_e_h_1, c_m, s6, s7) | node11(c_e_h_1, c_m, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s6, s7)) | node10(c_e_h_1, c_m, s6, s7) | node11(c_e_h_1, c_m, s6, s7))),
% 292.92/185.46 inference(rewrite,[status(thm)],[])).
% 292.92/185.46 tff(19236,plain,
% 292.92/185.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s6, s7)) | node10(c_e_h_1, c_m, s6, s7) | node11(c_e_h_1, c_m, s6, s7))),
% 292.92/185.46 inference(quant_inst,[status(thm)],[])).
% 292.92/185.46 tff(19237,plain,
% 292.92/185.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s6, s7)) | node10(c_e_h_1, c_m, s6, s7) | node11(c_e_h_1, c_m, s6, s7)),
% 292.92/185.46 inference(modus_ponens,[status(thm)],[19236, 19235])).
% 292.92/185.46 tff(19238,plain,
% 292.92/185.46 (node10(c_e_h_1, c_m, s6, s7) | node11(c_e_h_1, c_m, s6, s7)),
% 292.92/185.46 inference(unit_resolution,[status(thm)],[19237, 5002, 1844])).
% 292.92/185.46 tff(19239,plain,
% 292.92/185.46 (node10(c_e_h_1, c_m, s6, s7)),
% 292.92/185.46 inference(unit_resolution,[status(thm)],[19238, 19234])).
% 292.92/185.46 tff(19240,plain,
% 292.92/185.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)) | node9(c_e_h_1, c_m, s6) | (~node10(c_e_h_1, c_m, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)) | node9(c_e_h_1, c_m, s6) | (~node10(c_e_h_1, c_m, s6, s7)))),
% 292.92/185.46 inference(rewrite,[status(thm)],[])).
% 292.92/185.46 tff(19241,plain,
% 292.92/185.46 ((node9(c_e_h_1, c_m, s6) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)) | (~node10(c_e_h_1, c_m, s6, s7))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)) | node9(c_e_h_1, c_m, s6) | (~node10(c_e_h_1, c_m, s6, s7)))),
% 292.92/185.46 inference(rewrite,[status(thm)],[])).
% 292.92/185.46 tff(19242,plain,
% 292.92/185.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s6) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)) | (~node10(c_e_h_1, c_m, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)) | node9(c_e_h_1, c_m, s6) | (~node10(c_e_h_1, c_m, s6, s7))))),
% 292.92/185.46 inference(monotonicity,[status(thm)],[19241])).
% 292.92/185.46 tff(19243,plain,
% 292.92/185.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s6) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)) | (~node10(c_e_h_1, c_m, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)) | node9(c_e_h_1, c_m, s6) | (~node10(c_e_h_1, c_m, s6, s7)))),
% 292.92/185.46 inference(transitivity,[status(thm)],[19242, 19240])).
% 292.92/185.46 tff(19244,plain,
% 292.92/185.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s6) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)) | (~node10(c_e_h_1, c_m, s6, s7)))),
% 292.92/185.46 inference(quant_inst,[status(thm)],[])).
% 292.92/185.46 tff(19245,plain,
% 292.92/185.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)) | node9(c_e_h_1, c_m, s6) | (~node10(c_e_h_1, c_m, s6, s7))),
% 292.92/185.46 inference(modus_ponens,[status(thm)],[19244, 19243])).
% 292.92/185.46 tff(19246,plain,
% 292.92/185.46 ($false),
% 292.92/185.46 inference(unit_resolution,[status(thm)],[19245, 4986, 19227, 19239, 19225])).
% 292.92/185.46 tff(19247,plain,((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)) | node9(c_e_h_1, c_m, s6) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)), inference(lemma,lemma(discharge,[]))).
% 292.92/185.46 tff(19248,plain,
% 292.92/185.46 ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)) | node9(c_e_h_1, c_m, s6)),
% 292.92/185.46 inference(unit_resolution,[status(thm)],[19247, 18158])).
% 292.92/185.46 tff(19249,plain,
% 292.92/185.46 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)),
% 292.92/185.46 inference(unit_resolution,[status(thm)],[19248, 19224])).
% 292.92/185.46 tff(19250,plain,
% 292.92/185.46 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s7) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s7) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7))),
% 292.92/185.46 inference(rewrite,[status(thm)],[])).
% 292.92/185.46 tff(19251,plain,
% 292.92/185.46 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s7) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7))),
% 292.92/185.46 inference(quant_inst,[status(thm)],[])).
% 292.92/185.46 tff(19252,plain,
% 292.92/185.46 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s7) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)),
% 292.92/185.46 inference(modus_ponens,[status(thm)],[19251, 19250])).
% 292.92/185.46 tff(19253,plain,
% 292.92/185.46 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s7) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)),
% 292.92/185.46 inference(unit_resolution,[status(thm)],[19252, 7868])).
% 292.92/185.46 tff(19254,plain,
% 292.92/185.46 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s7)),
% 292.92/185.46 inference(unit_resolution,[status(thm)],[19253, 19249])).
% 292.92/185.46 tff(19255,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7)), introduced(assumption)).
% 292.92/185.46 tff(19256,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s7)), introduced(assumption)).
% 292.92/185.46 tff(19257,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8)), introduced(assumption)).
% 292.92/185.46 tff(19258,assumption,(node10(c_e_h_1, c_n, s7, s8)), introduced(assumption)).
% 292.92/185.46 tff(19259,plain,
% 292.92/185.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s7)) | (~node10(c_e_h_1, c_n, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s7)) | (~node10(c_e_h_1, c_n, s7, s8)))),
% 292.92/185.46 inference(rewrite,[status(thm)],[])).
% 292.92/185.46 tff(19260,plain,
% 292.92/185.46 (((~node10(c_e_h_1, c_n, s7, s8)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8)) <=> ((~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s7)) | (~node10(c_e_h_1, c_n, s7, s8)))),
% 292.92/185.46 inference(rewrite,[status(thm)],[])).
% 292.92/185.46 tff(19261,plain,
% 292.92/185.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s7, s8)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s7)) | (~node10(c_e_h_1, c_n, s7, s8))))),
% 292.92/185.46 inference(monotonicity,[status(thm)],[19260])).
% 292.92/185.46 tff(19262,plain,
% 292.92/185.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s7, s8)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s7)) | (~node10(c_e_h_1, c_n, s7, s8)))),
% 292.92/185.46 inference(transitivity,[status(thm)],[19261, 19259])).
% 292.92/185.46 tff(19263,plain,
% 292.92/185.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s7, s8)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8))),
% 292.92/185.47 inference(quant_inst,[status(thm)],[])).
% 292.92/185.47 tff(19264,plain,
% 292.92/185.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s7)) | (~node10(c_e_h_1, c_n, s7, s8))),
% 292.92/185.47 inference(modus_ponens,[status(thm)],[19263, 19262])).
% 292.92/185.47 tff(19265,plain,
% 292.92/185.47 ($false),
% 292.92/185.47 inference(unit_resolution,[status(thm)],[19264, 5718, 19255, 19256, 19257, 19258])).
% 292.92/185.47 tff(19266,plain,((~node10(c_e_h_1, c_n, s7, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8)), inference(lemma,lemma(discharge,[]))).
% 292.92/185.47 tff(19267,plain,
% 292.92/185.47 (~node10(c_e_h_1, c_n, s7, s8)),
% 292.92/185.47 inference(unit_resolution,[status(thm)],[19266, 19257, 19256, 19255])).
% 292.92/185.47 tff(19268,plain,
% 292.92/185.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s7, s8)) | node10(c_e_h_1, c_n, s7, s8) | node11(c_e_h_1, c_n, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s7, s8)) | node10(c_e_h_1, c_n, s7, s8) | node11(c_e_h_1, c_n, s7, s8))),
% 292.92/185.47 inference(rewrite,[status(thm)],[])).
% 292.92/185.47 tff(19269,plain,
% 292.92/185.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s7, s8)) | node10(c_e_h_1, c_n, s7, s8) | node11(c_e_h_1, c_n, s7, s8))),
% 292.92/185.47 inference(quant_inst,[status(thm)],[])).
% 292.92/185.47 tff(19270,plain,
% 292.92/185.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s7, s8)) | node10(c_e_h_1, c_n, s7, s8) | node11(c_e_h_1, c_n, s7, s8)),
% 292.92/185.47 inference(modus_ponens,[status(thm)],[19269, 19268])).
% 292.92/185.47 tff(19271,plain,
% 292.92/185.47 (node10(c_e_h_1, c_n, s7, s8) | node11(c_e_h_1, c_n, s7, s8)),
% 292.92/185.47 inference(unit_resolution,[status(thm)],[19270, 5002, 1938])).
% 292.92/185.47 tff(19272,plain,
% 292.92/185.47 (node11(c_e_h_1, c_n, s7, s8)),
% 292.92/185.47 inference(unit_resolution,[status(thm)],[19271, 19267])).
% 292.92/185.47 tff(19273,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)), introduced(assumption)).
% 292.92/185.47 tff(19274,plain,
% 292.92/185.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8) | (~node11(c_e_h_1, c_n, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8) | (~node11(c_e_h_1, c_n, s7, s8)))),
% 292.92/185.47 inference(rewrite,[status(thm)],[])).
% 292.92/185.47 tff(19275,plain,
% 292.92/185.47 ((m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8) | (~node11(c_e_h_1, c_n, s7, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8) | (~node11(c_e_h_1, c_n, s7, s8)))),
% 292.92/185.47 inference(rewrite,[status(thm)],[])).
% 292.92/185.47 tff(19276,plain,
% 292.92/185.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8) | (~node11(c_e_h_1, c_n, s7, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8) | (~node11(c_e_h_1, c_n, s7, s8))))),
% 292.92/185.47 inference(monotonicity,[status(thm)],[19275])).
% 292.92/185.47 tff(19277,plain,
% 292.92/185.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8) | (~node11(c_e_h_1, c_n, s7, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8) | (~node11(c_e_h_1, c_n, s7, s8)))),
% 292.92/185.47 inference(transitivity,[status(thm)],[19276, 19274])).
% 292.92/185.47 tff(19278,plain,
% 292.92/185.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8) | (~node11(c_e_h_1, c_n, s7, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)))),
% 292.92/185.47 inference(quant_inst,[status(thm)],[])).
% 292.92/185.47 tff(19279,plain,
% 292.92/185.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8) | (~node11(c_e_h_1, c_n, s7, s8))),
% 292.92/185.47 inference(modus_ponens,[status(thm)],[19278, 19277])).
% 292.92/185.47 tff(19280,plain,
% 292.92/185.47 ($false),
% 292.92/185.47 inference(unit_resolution,[status(thm)],[19279, 5742, 19273, 19257, 19272])).
% 292.92/185.47 tff(19281,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7))), inference(lemma,lemma(discharge,[]))).
% 292.92/185.47 tff(19282,plain,
% 292.92/185.47 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7))),
% 292.92/185.47 inference(unit_resolution,[status(thm)],[19281, 19254])).
% 292.92/185.47 tff(19283,plain,
% 292.92/185.47 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7))),
% 292.92/185.47 inference(unit_resolution,[status(thm)],[19282, 18196])).
% 292.92/185.47 tff(19284,plain,
% 292.92/185.47 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8)),
% 292.92/185.47 inference(unit_resolution,[status(thm)],[19283, 19216])).
% 292.92/185.47 tff(19285,plain,
% 292.92/185.47 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_n, X)) | m_and_h_gate_v_in2(I0, c_p, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8)) | m_and_h_gate_v_in2(c_e_h_1, c_p, s8))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_n, X)) | m_and_h_gate_v_in2(I0, c_p, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8)) | m_and_h_gate_v_in2(c_e_h_1, c_p, s8))),
% 292.92/185.47 inference(rewrite,[status(thm)],[])).
% 292.92/185.47 tff(19286,plain,
% 292.92/185.47 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_n, X)) | m_and_h_gate_v_in2(I0, c_p, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8)) | m_and_h_gate_v_in2(c_e_h_1, c_p, s8))),
% 292.92/185.47 inference(quant_inst,[status(thm)],[])).
% 292.92/185.47 tff(19287,plain,
% 292.92/185.47 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_out(I0, c_n, X)) | m_and_h_gate_v_in2(I0, c_p, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8)) | m_and_h_gate_v_in2(c_e_h_1, c_p, s8)),
% 292.92/185.47 inference(modus_ponens,[status(thm)],[19286, 19285])).
% 292.92/185.47 tff(19288,plain,
% 292.92/185.47 (m_and_h_gate_v_in2(c_e_h_1, c_p, s8)),
% 292.92/185.47 inference(unit_resolution,[status(thm)],[19287, 18206, 19284])).
% 292.92/185.47 tff(19289,plain,
% 292.92/185.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (m_and_h_gate_v_out(c_e_h_1, c_p, s9) | (~m_and_h_gate_v_in2(c_e_h_1, c_p, s8)) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s8)) | (~node21(c_e_h_1, c_p, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | m_and_h_gate_v_out(c_e_h_1, c_p, s9) | (~m_and_h_gate_v_in2(c_e_h_1, c_p, s8)) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s8)) | (~node21(c_e_h_1, c_p, s8, s9)))),
% 292.92/185.47 inference(rewrite,[status(thm)],[])).
% 292.92/185.47 tff(19290,plain,
% 292.92/185.47 (((~node21(c_e_h_1, c_p, s8, s9)) | (~m_and_h_gate_v_in2(c_e_h_1, c_p, s8)) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s8)) | m_and_h_gate_v_out(c_e_h_1, c_p, s9)) <=> (m_and_h_gate_v_out(c_e_h_1, c_p, s9) | (~m_and_h_gate_v_in2(c_e_h_1, c_p, s8)) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s8)) | (~node21(c_e_h_1, c_p, s8, s9)))),
% 292.92/185.47 inference(rewrite,[status(thm)],[])).
% 292.92/185.47 tff(19291,plain,
% 292.92/185.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_1, c_p, s8, s9)) | (~m_and_h_gate_v_in2(c_e_h_1, c_p, s8)) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s8)) | m_and_h_gate_v_out(c_e_h_1, c_p, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (m_and_h_gate_v_out(c_e_h_1, c_p, s9) | (~m_and_h_gate_v_in2(c_e_h_1, c_p, s8)) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s8)) | (~node21(c_e_h_1, c_p, s8, s9))))),
% 292.92/185.47 inference(monotonicity,[status(thm)],[19290])).
% 292.92/185.47 tff(19292,plain,
% 292.92/185.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_1, c_p, s8, s9)) | (~m_and_h_gate_v_in2(c_e_h_1, c_p, s8)) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s8)) | m_and_h_gate_v_out(c_e_h_1, c_p, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | m_and_h_gate_v_out(c_e_h_1, c_p, s9) | (~m_and_h_gate_v_in2(c_e_h_1, c_p, s8)) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s8)) | (~node21(c_e_h_1, c_p, s8, s9)))),
% 292.92/185.47 inference(transitivity,[status(thm)],[19291, 19289])).
% 292.92/185.47 tff(19293,plain,
% 292.92/185.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_1, c_p, s8, s9)) | (~m_and_h_gate_v_in2(c_e_h_1, c_p, s8)) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s8)) | m_and_h_gate_v_out(c_e_h_1, c_p, s9))),
% 292.92/185.47 inference(quant_inst,[status(thm)],[])).
% 292.92/185.47 tff(19294,plain,
% 292.92/185.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | m_and_h_gate_v_out(c_e_h_1, c_p, s9) | (~m_and_h_gate_v_in2(c_e_h_1, c_p, s8)) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s8)) | (~node21(c_e_h_1, c_p, s8, s9))),
% 292.92/185.47 inference(modus_ponens,[status(thm)],[19293, 19292])).
% 292.92/185.47 tff(19295,plain,
% 292.92/185.47 ($false),
% 292.92/185.47 inference(unit_resolution,[status(thm)],[19294, 5851, 19083, 19288, 19091, 15896])).
% 292.92/185.47 tff(19296,plain,((~node21(c_e_h_1, c_p, s8, s9)) | m_and_h_gate_v_out(c_e_h_1, c_p, s9) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s8))), inference(lemma,lemma(discharge,[]))).
% 292.92/185.47 tff(19297,plain,
% 292.92/185.47 (~node21(c_e_h_1, c_p, s8, s9)),
% 292.92/185.47 inference(unit_resolution,[status(thm)],[19296, 19083, 15896])).
% 292.92/185.47 tff(19298,plain,
% 292.92/185.47 (node22(c_e_h_1, c_p, s8, s9)),
% 292.92/185.47 inference(unit_resolution,[status(thm)],[15877, 19297])).
% 292.92/185.47 tff(19299,plain,
% 292.92/185.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_p, s8)) | m_and_h_gate_v_out(c_e_h_1, c_p, s9) | (~node22(c_e_h_1, c_p, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s8)) | m_and_h_gate_v_out(c_e_h_1, c_p, s9) | (~node22(c_e_h_1, c_p, s8, s9)))),
% 292.92/185.47 inference(rewrite,[status(thm)],[])).
% 292.92/185.47 tff(19300,plain,
% 292.92/185.47 ((m_and_h_gate_v_out(c_e_h_1, c_p, s9) | (~node22(c_e_h_1, c_p, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s8))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_p, s8)) | m_and_h_gate_v_out(c_e_h_1, c_p, s9) | (~node22(c_e_h_1, c_p, s8, s9)))),
% 292.92/185.48 inference(rewrite,[status(thm)],[])).
% 292.92/185.48 tff(19301,plain,
% 292.92/185.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_1, c_p, s9) | (~node22(c_e_h_1, c_p, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_p, s8)) | m_and_h_gate_v_out(c_e_h_1, c_p, s9) | (~node22(c_e_h_1, c_p, s8, s9))))),
% 292.92/185.48 inference(monotonicity,[status(thm)],[19300])).
% 292.92/185.48 tff(19302,plain,
% 292.92/185.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_1, c_p, s9) | (~node22(c_e_h_1, c_p, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s8)) | m_and_h_gate_v_out(c_e_h_1, c_p, s9) | (~node22(c_e_h_1, c_p, s8, s9)))),
% 292.92/185.48 inference(transitivity,[status(thm)],[19301, 19299])).
% 292.92/185.48 tff(19303,plain,
% 292.92/185.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_1, c_p, s9) | (~node22(c_e_h_1, c_p, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s8)))),
% 292.92/185.48 inference(quant_inst,[status(thm)],[])).
% 292.92/185.48 tff(19304,plain,
% 292.92/185.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s8)) | m_and_h_gate_v_out(c_e_h_1, c_p, s9) | (~node22(c_e_h_1, c_p, s8, s9))),
% 292.92/185.48 inference(modus_ponens,[status(thm)],[19303, 19302])).
% 292.92/185.48 tff(19305,plain,
% 292.92/185.48 ($false),
% 292.92/185.48 inference(unit_resolution,[status(thm)],[19304, 5871, 15662, 19083, 19298])).
% 292.92/185.48 tff(19306,plain,(m_and_h_gate_v_out(c_e_h_1, c_p, s9) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s8)) | (~m_and_h_gate_v_in1(c_e_h_1, c_p, s8))), inference(lemma,lemma(discharge,[]))).
% 292.92/185.48 tff(19307,plain,
% 292.92/185.48 (~m_and_h_gate_v_in1(c_e_h_1, c_p, s8)),
% 292.92/185.48 inference(unit_resolution,[status(thm)],[19306, 19090, 19083])).
% 292.92/185.48 tff(19308,plain,
% 292.92/185.48 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_p, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_k, s8)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s8))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_p, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s8)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s8))),
% 292.92/185.48 inference(rewrite,[status(thm)],[])).
% 292.92/185.48 tff(19309,plain,
% 292.92/185.48 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_p, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_k, s8)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s8))),
% 292.92/185.48 inference(quant_inst,[status(thm)],[])).
% 292.92/185.48 tff(19310,plain,
% 292.92/185.48 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_k, X)) | m_and_h_gate_v_in1(I0, c_p, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s8)) | m_and_h_gate_v_in1(c_e_h_1, c_p, s8)),
% 292.92/185.48 inference(modus_ponens,[status(thm)],[19309, 19308])).
% 292.92/185.48 tff(19311,plain,
% 292.92/185.48 ($false),
% 292.92/185.48 inference(unit_resolution,[status(thm)],[19310, 18282, 15904, 15889])).
% 292.92/185.48 tff(19312,plain,(m_and_h_gate_v_in1(c_e_h_1, c_p, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s8))), inference(lemma,lemma(discharge,[]))).
% 292.92/185.48 tff(19313,plain,
% 292.92/185.48 (~m_and_h_gate_v_out(c_e_h_1, c_k, s8)),
% 292.92/185.48 inference(unit_resolution,[status(thm)],[19312, 19307])).
% 292.92/185.48 tff(19314,assumption,(m_or_h_gate_v_out(c_e_h_1, c_j, s6)), introduced(assumption)).
% 292.92/185.48 tff(19315,assumption,(~m_or_h_gate_v_out(c_e_h_1, c_j, s5)), introduced(assumption)).
% 292.92/185.48 tff(19316,assumption,(node6(c_e_h_1, c_j, s5, s6)), introduced(assumption)).
% 292.92/185.48 tff(19317,plain,
% 292.92/185.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s6)) | (~node6(c_e_h_1, c_j, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s6)) | (~node6(c_e_h_1, c_j, s5, s6)))),
% 292.92/185.48 inference(rewrite,[status(thm)],[])).
% 292.92/185.48 tff(19318,plain,
% 292.92/185.48 (((~node6(c_e_h_1, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s6)) | m_or_h_gate_v_out(c_e_h_1, c_j, s5)) <=> (m_or_h_gate_v_out(c_e_h_1, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s6)) | (~node6(c_e_h_1, c_j, s5, s6)))),
% 292.92/185.48 inference(rewrite,[status(thm)],[])).
% 292.92/185.48 tff(19319,plain,
% 292.92/185.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s6)) | m_or_h_gate_v_out(c_e_h_1, c_j, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s6)) | (~node6(c_e_h_1, c_j, s5, s6))))),
% 292.92/185.48 inference(monotonicity,[status(thm)],[19318])).
% 292.92/185.48 tff(19320,plain,
% 292.92/185.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s6)) | m_or_h_gate_v_out(c_e_h_1, c_j, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s6)) | (~node6(c_e_h_1, c_j, s5, s6)))),
% 292.92/185.48 inference(transitivity,[status(thm)],[19319, 19317])).
% 292.92/185.48 tff(19321,plain,
% 292.92/185.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s6)) | m_or_h_gate_v_out(c_e_h_1, c_j, s5))),
% 292.92/185.48 inference(quant_inst,[status(thm)],[])).
% 292.92/185.48 tff(19322,plain,
% 292.92/185.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s6)) | (~node6(c_e_h_1, c_j, s5, s6))),
% 292.92/185.48 inference(modus_ponens,[status(thm)],[19321, 19320])).
% 292.92/185.48 tff(19323,plain,
% 292.92/185.48 ($false),
% 292.92/185.48 inference(unit_resolution,[status(thm)],[19322, 1121, 19314, 19316, 19315])).
% 292.92/185.48 tff(19324,plain,((~node6(c_e_h_1, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s6)) | m_or_h_gate_v_out(c_e_h_1, c_j, s5)), inference(lemma,lemma(discharge,[]))).
% 292.92/185.48 tff(19325,plain,
% 292.92/185.48 ((~node6(c_e_h_1, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s6))),
% 292.92/185.48 inference(unit_resolution,[status(thm)],[19324, 18450])).
% 292.92/185.48 tff(19326,plain,
% 292.92/185.48 (~node6(c_e_h_1, c_j, s5, s6)),
% 292.92/185.48 inference(unit_resolution,[status(thm)],[19325, 19314])).
% 292.92/185.48 tff(19327,assumption,(m_and_h_gate_v_out(c_e_h_1, c_l, s5)), introduced(assumption)).
% 292.92/185.48 tff(19328,assumption,(m_and_h_gate_v_in2(c_e_h_1, c_l, s4)), introduced(assumption)).
% 292.92/185.48 tff(19329,plain,
% 292.92/185.48 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4))),
% 292.92/185.48 inference(rewrite,[status(thm)],[])).
% 292.92/185.48 tff(19330,plain,
% 292.92/185.48 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4))),
% 292.92/185.48 inference(quant_inst,[status(thm)],[])).
% 292.92/185.48 tff(19331,plain,
% 292.92/185.48 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s4)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s4)),
% 292.92/185.48 inference(modus_ponens,[status(thm)],[19330, 19329])).
% 292.92/185.48 tff(19332,plain,
% 292.92/185.48 ($false),
% 292.92/185.48 inference(unit_resolution,[status(thm)],[19331, 4549, 18019, 19328])).
% 292.92/185.48 tff(19333,plain,(~m_and_h_gate_v_in2(c_e_h_1, c_l, s4)), inference(lemma,lemma(discharge,[]))).
% 292.92/185.48 tff(19334,plain,
% 292.92/185.48 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s4)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s4)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s4))),
% 292.92/185.48 inference(rewrite,[status(thm)],[])).
% 292.92/185.48 tff(19335,plain,
% 292.92/185.48 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s4)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s4))),
% 292.92/185.48 inference(quant_inst,[status(thm)],[])).
% 292.92/185.48 tff(19336,plain,
% 292.92/185.48 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s4)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s4)),
% 292.92/185.48 inference(modus_ponens,[status(thm)],[19335, 19334])).
% 292.92/185.48 tff(19337,plain,
% 292.92/185.48 (~node20(c_e_h_1, c_l, s4)),
% 292.92/185.48 inference(unit_resolution,[status(thm)],[19336, 4563, 19333])).
% 292.92/185.48 tff(19338,assumption,(node21(c_e_h_1, c_l, s4, s5)), introduced(assumption)).
% 292.92/185.48 tff(19339,plain,
% 292.92/185.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s5)) | (~node21(c_e_h_1, c_l, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s5)) | (~node21(c_e_h_1, c_l, s4, s5)))),
% 292.92/185.48 inference(rewrite,[status(thm)],[])).
% 292.92/185.48 tff(19340,plain,
% 292.92/185.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s5)) | (~node21(c_e_h_1, c_l, s4, s5)))),
% 292.92/185.48 inference(quant_inst,[status(thm)],[])).
% 292.92/185.48 tff(19341,plain,
% 292.92/185.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s5)) | (~node21(c_e_h_1, c_l, s4, s5))),
% 292.92/185.49 inference(modus_ponens,[status(thm)],[19340, 19339])).
% 292.92/185.49 tff(19342,plain,
% 292.92/185.49 ($false),
% 292.92/185.49 inference(unit_resolution,[status(thm)],[19341, 52, 19338, 19327, 19337])).
% 292.92/185.49 tff(19343,plain,((~node21(c_e_h_1, c_l, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s5))), inference(lemma,lemma(discharge,[]))).
% 292.92/185.49 tff(19344,plain,
% 292.92/185.49 (~node21(c_e_h_1, c_l, s4, s5)),
% 292.92/185.49 inference(unit_resolution,[status(thm)],[19343, 19327])).
% 292.92/185.49 tff(19345,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_l, s4)), introduced(assumption)).
% 292.92/185.49 tff(19346,assumption,(node22(c_e_h_1, c_l, s4, s5)), introduced(assumption)).
% 292.92/185.49 tff(19347,plain,
% 292.92/185.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s5)) | (~node22(c_e_h_1, c_l, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_l, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s5)) | (~node22(c_e_h_1, c_l, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_l, s4))),
% 292.92/185.49 inference(rewrite,[status(thm)],[])).
% 292.92/185.49 tff(19348,plain,
% 292.92/185.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s5)) | (~node22(c_e_h_1, c_l, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_l, s4))),
% 292.92/185.49 inference(quant_inst,[status(thm)],[])).
% 292.92/185.49 tff(19349,plain,
% 292.92/185.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s5)) | (~node22(c_e_h_1, c_l, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_l, s4)),
% 292.92/185.49 inference(modus_ponens,[status(thm)],[19348, 19347])).
% 292.92/185.49 tff(19350,plain,
% 292.92/185.49 ($false),
% 292.92/185.49 inference(unit_resolution,[status(thm)],[19349, 108, 19346, 19327, 19345])).
% 292.92/185.49 tff(19351,plain,((~node22(c_e_h_1, c_l, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s5)) | m_and_h_gate_v_out(c_e_h_1, c_l, s4)), inference(lemma,lemma(discharge,[]))).
% 292.92/185.49 tff(19352,plain,
% 292.92/185.49 ((~node22(c_e_h_1, c_l, s4, s5)) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s5))),
% 292.92/185.49 inference(unit_resolution,[status(thm)],[19351, 18419])).
% 292.92/185.49 tff(19353,plain,
% 292.92/185.49 (~node22(c_e_h_1, c_l, s4, s5)),
% 292.92/185.49 inference(unit_resolution,[status(thm)],[19352, 19327])).
% 292.92/185.49 tff(19354,plain,
% 292.92/185.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_1, c_l, s4, s5) | node22(c_e_h_1, c_l, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_1, c_l, s4, s5) | node22(c_e_h_1, c_l, s4, s5))),
% 292.92/185.49 inference(rewrite,[status(thm)],[])).
% 292.92/185.49 tff(19355,plain,
% 292.92/185.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_1, c_l, s4, s5) | node22(c_e_h_1, c_l, s4, s5))),
% 292.92/185.49 inference(quant_inst,[status(thm)],[])).
% 292.92/185.49 tff(19356,plain,
% 292.92/185.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_1, c_l, s4, s5) | node22(c_e_h_1, c_l, s4, s5)),
% 292.92/185.49 inference(modus_ponens,[status(thm)],[19355, 19354])).
% 292.92/185.49 tff(19357,plain,
% 292.92/185.49 (node21(c_e_h_1, c_l, s4, s5) | node22(c_e_h_1, c_l, s4, s5)),
% 292.92/185.49 inference(unit_resolution,[status(thm)],[19356, 82, 1028])).
% 292.92/185.49 tff(19358,plain,
% 292.92/185.49 ($false),
% 292.92/185.49 inference(unit_resolution,[status(thm)],[19357, 19353, 19344])).
% 292.92/185.49 tff(19359,plain,(~m_and_h_gate_v_out(c_e_h_1, c_l, s5)), inference(lemma,lemma(discharge,[]))).
% 292.92/185.49 tff(19360,plain,
% 292.92/185.49 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s5)) | m_and_h_gate_v_out(c_e_h_1, c_l, s5))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s5)) | m_and_h_gate_v_out(c_e_h_1, c_l, s5))),
% 292.92/185.49 inference(rewrite,[status(thm)],[])).
% 292.92/185.49 tff(19361,plain,
% 292.92/185.49 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s5)) | m_and_h_gate_v_out(c_e_h_1, c_l, s5))),
% 292.92/185.49 inference(quant_inst,[status(thm)],[])).
% 292.92/185.49 tff(19362,plain,
% 292.92/185.49 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s5)) | m_and_h_gate_v_out(c_e_h_1, c_l, s5)),
% 292.92/185.49 inference(modus_ponens,[status(thm)],[19361, 19360])).
% 292.92/185.49 tff(19363,plain,
% 292.92/185.49 (~m_or_h_gate_v_in1(c_e_h_1, c_j, s5)),
% 292.92/185.49 inference(unit_resolution,[status(thm)],[19362, 1100, 19359])).
% 292.92/185.49 tff(19364,assumption,(~m_or_h_gate_v_in1(c_e_h_1, c_j, s5)), introduced(assumption)).
% 292.92/185.49 tff(19365,plain,
% 292.92/185.49 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s5)) | m_cell_v_ack(c_e_h_1, s5))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s5)) | m_cell_v_ack(c_e_h_1, s5))),
% 292.92/185.49 inference(rewrite,[status(thm)],[])).
% 292.92/185.49 tff(19366,plain,
% 292.92/185.49 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s5)) | m_cell_v_ack(c_e_h_1, s5))),
% 292.92/185.49 inference(quant_inst,[status(thm)],[])).
% 292.92/185.49 tff(19367,plain,
% 292.92/185.49 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s5)) | m_cell_v_ack(c_e_h_1, s5)),
% 292.92/185.49 inference(modus_ponens,[status(thm)],[19366, 19365])).
% 292.92/185.49 tff(19368,plain,
% 292.92/185.49 (~m_or_h_gate_v_in2(c_e_h_1, c_j, s5)),
% 292.92/185.49 inference(unit_resolution,[status(thm)],[19367, 1085, 10351])).
% 292.92/185.49 tff(19369,assumption,(node5(c_e_h_1, c_j, s5, s6)), introduced(assumption)).
% 292.92/185.49 tff(19370,plain,
% 292.92/185.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_1, c_j, s5) | m_or_h_gate_v_in1(c_e_h_1, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s6)) | (~node5(c_e_h_1, c_j, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_1, c_j, s5) | m_or_h_gate_v_in1(c_e_h_1, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s6)) | (~node5(c_e_h_1, c_j, s5, s6)))),
% 292.92/185.49 inference(rewrite,[status(thm)],[])).
% 292.92/185.49 tff(19371,plain,
% 292.92/185.49 ((m_or_h_gate_v_in1(c_e_h_1, c_j, s5) | m_or_h_gate_v_in2(c_e_h_1, c_j, s5) | (~node5(c_e_h_1, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s6))) <=> (m_or_h_gate_v_in2(c_e_h_1, c_j, s5) | m_or_h_gate_v_in1(c_e_h_1, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s6)) | (~node5(c_e_h_1, c_j, s5, s6)))),
% 292.92/185.49 inference(rewrite,[status(thm)],[])).
% 292.92/185.49 tff(19372,plain,
% 292.92/185.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s5) | m_or_h_gate_v_in2(c_e_h_1, c_j, s5) | (~node5(c_e_h_1, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_1, c_j, s5) | m_or_h_gate_v_in1(c_e_h_1, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s6)) | (~node5(c_e_h_1, c_j, s5, s6))))),
% 292.92/185.49 inference(monotonicity,[status(thm)],[19371])).
% 292.92/185.49 tff(19373,plain,
% 292.92/185.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s5) | m_or_h_gate_v_in2(c_e_h_1, c_j, s5) | (~node5(c_e_h_1, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_1, c_j, s5) | m_or_h_gate_v_in1(c_e_h_1, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s6)) | (~node5(c_e_h_1, c_j, s5, s6)))),
% 292.92/185.49 inference(transitivity,[status(thm)],[19372, 19370])).
% 292.92/185.49 tff(19374,plain,
% 292.92/185.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s5) | m_or_h_gate_v_in2(c_e_h_1, c_j, s5) | (~node5(c_e_h_1, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s6)))),
% 292.92/185.49 inference(quant_inst,[status(thm)],[])).
% 292.92/185.49 tff(19375,plain,
% 292.92/185.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_1, c_j, s5) | m_or_h_gate_v_in1(c_e_h_1, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s6)) | (~node5(c_e_h_1, c_j, s5, s6))),
% 292.92/185.49 inference(modus_ponens,[status(thm)],[19374, 19373])).
% 292.92/185.49 tff(19376,plain,
% 292.92/185.49 ($false),
% 292.92/185.49 inference(unit_resolution,[status(thm)],[19375, 1159, 19314, 19369, 19368, 19364])).
% 292.92/185.49 tff(19377,plain,((~node5(c_e_h_1, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s6)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s5)), inference(lemma,lemma(discharge,[]))).
% 292.92/185.49 tff(19378,plain,
% 292.92/185.49 (~node5(c_e_h_1, c_j, s5, s6)),
% 292.92/185.49 inference(unit_resolution,[status(thm)],[19377, 19314, 19363])).
% 292.92/185.49 tff(19379,plain,
% 292.92/185.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s5, s6)) | node6(c_e_h_1, c_j, s5, s6) | node5(c_e_h_1, c_j, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s5, s6)) | node6(c_e_h_1, c_j, s5, s6) | node5(c_e_h_1, c_j, s5, s6))),
% 292.92/185.49 inference(rewrite,[status(thm)],[])).
% 292.92/185.49 tff(19380,plain,
% 292.92/185.49 ((node6(c_e_h_1, c_j, s5, s6) | node5(c_e_h_1, c_j, s5, s6) | (~trans(s5, s6))) <=> ((~trans(s5, s6)) | node6(c_e_h_1, c_j, s5, s6) | node5(c_e_h_1, c_j, s5, s6))),
% 292.92/185.50 inference(rewrite,[status(thm)],[])).
% 292.92/185.50 tff(19381,plain,
% 292.92/185.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s5, s6) | node5(c_e_h_1, c_j, s5, s6) | (~trans(s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s5, s6)) | node6(c_e_h_1, c_j, s5, s6) | node5(c_e_h_1, c_j, s5, s6)))),
% 292.92/185.50 inference(monotonicity,[status(thm)],[19380])).
% 292.92/185.50 tff(19382,plain,
% 292.92/185.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s5, s6) | node5(c_e_h_1, c_j, s5, s6) | (~trans(s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s5, s6)) | node6(c_e_h_1, c_j, s5, s6) | node5(c_e_h_1, c_j, s5, s6))),
% 292.92/185.50 inference(transitivity,[status(thm)],[19381, 19379])).
% 292.92/185.50 tff(19383,plain,
% 292.92/185.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s5, s6) | node5(c_e_h_1, c_j, s5, s6) | (~trans(s5, s6)))),
% 292.92/185.50 inference(quant_inst,[status(thm)],[])).
% 292.92/185.50 tff(19384,plain,
% 292.92/185.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s5, s6)) | node6(c_e_h_1, c_j, s5, s6) | node5(c_e_h_1, c_j, s5, s6)),
% 292.92/185.50 inference(modus_ponens,[status(thm)],[19383, 19382])).
% 292.92/185.50 tff(19385,plain,
% 292.92/185.50 (node6(c_e_h_1, c_j, s5, s6) | node5(c_e_h_1, c_j, s5, s6)),
% 292.92/185.50 inference(unit_resolution,[status(thm)],[19384, 1141, 1406])).
% 292.92/185.50 tff(19386,plain,
% 292.92/185.50 ($false),
% 292.92/185.50 inference(unit_resolution,[status(thm)],[19385, 19378, 19326])).
% 292.92/185.50 tff(19387,plain,(~m_or_h_gate_v_out(c_e_h_1, c_j, s6)), inference(lemma,lemma(discharge,[]))).
% 292.92/185.50 tff(19388,plain,
% 292.92/185.50 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s6)) | m_or_h_gate_v_out(c_e_h_1, c_j, s6))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s6)) | m_or_h_gate_v_out(c_e_h_1, c_j, s6))),
% 292.92/185.50 inference(rewrite,[status(thm)],[])).
% 292.92/185.50 tff(19389,plain,
% 292.92/185.50 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s6)) | m_or_h_gate_v_out(c_e_h_1, c_j, s6))),
% 292.92/185.50 inference(quant_inst,[status(thm)],[])).
% 292.92/185.50 tff(19390,plain,
% 292.92/185.50 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s6)) | m_or_h_gate_v_out(c_e_h_1, c_j, s6)),
% 292.92/185.50 inference(modus_ponens,[status(thm)],[19389, 19388])).
% 292.92/185.50 tff(19391,plain,
% 292.92/185.50 (~m_c_h_element_v_in2(c_e_h_1, c_h, s6)),
% 292.92/185.50 inference(unit_resolution,[status(thm)],[19390, 1174, 19387])).
% 292.92/185.50 tff(19392,assumption,(~m_c_h_element_v_out(c_e_h_1, c_h, s6)), introduced(assumption)).
% 292.92/185.50 tff(19393,assumption,(m_c_h_element_v_out(c_e_h_1, c_h, s7)), introduced(assumption)).
% 292.92/185.50 tff(19394,assumption,(node18(c_e_h_1, c_h, s6, s7)), introduced(assumption)).
% 292.92/185.50 tff(19395,plain,
% 292.92/185.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s7)) | m_c_h_element_v_out(c_e_h_1, c_h, s6) | (~node18(c_e_h_1, c_h, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s7)) | m_c_h_element_v_out(c_e_h_1, c_h, s6) | (~node18(c_e_h_1, c_h, s6, s7)))),
% 292.92/185.50 inference(rewrite,[status(thm)],[])).
% 292.92/185.50 tff(19396,plain,
% 292.92/185.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s7)) | m_c_h_element_v_out(c_e_h_1, c_h, s6) | (~node18(c_e_h_1, c_h, s6, s7)))),
% 292.92/185.50 inference(quant_inst,[status(thm)],[])).
% 292.92/185.50 tff(19397,plain,
% 292.92/185.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s7)) | m_c_h_element_v_out(c_e_h_1, c_h, s6) | (~node18(c_e_h_1, c_h, s6, s7))),
% 292.92/185.50 inference(modus_ponens,[status(thm)],[19396, 19395])).
% 292.92/185.50 tff(19398,plain,
% 292.92/185.50 ($false),
% 292.92/185.50 inference(unit_resolution,[status(thm)],[19397, 753, 19393, 19392, 19394])).
% 292.92/185.50 tff(19399,plain,((~node18(c_e_h_1, c_h, s6, s7)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s7)) | m_c_h_element_v_out(c_e_h_1, c_h, s6)), inference(lemma,lemma(discharge,[]))).
% 292.92/185.50 tff(19400,plain,
% 292.92/185.50 (~node18(c_e_h_1, c_h, s6, s7)),
% 292.92/185.50 inference(unit_resolution,[status(thm)],[19399, 19392, 19393])).
% 292.92/185.50 tff(19401,plain,
% 292.92/185.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s6, s7)) | node19(c_e_h_1, c_h, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s6, s7)) | node19(c_e_h_1, c_h, s6, s7))),
% 292.92/185.50 inference(rewrite,[status(thm)],[])).
% 292.92/185.50 tff(19402,plain,
% 292.92/185.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s6, s7)) | node19(c_e_h_1, c_h, s6, s7))),
% 292.92/185.50 inference(quant_inst,[status(thm)],[])).
% 292.92/185.50 tff(19403,plain,
% 292.92/185.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s6, s7)) | node19(c_e_h_1, c_h, s6, s7)),
% 292.92/185.50 inference(modus_ponens,[status(thm)],[19402, 19401])).
% 292.92/185.50 tff(19404,plain,
% 292.92/185.50 (node19(c_e_h_1, c_h, s6, s7)),
% 292.92/185.50 inference(unit_resolution,[status(thm)],[19403, 190, 1844])).
% 292.92/185.50 tff(19405,plain,
% 292.92/185.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s6) | node18(c_e_h_1, c_h, s6, s7) | (~node19(c_e_h_1, c_h, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s6) | node18(c_e_h_1, c_h, s6, s7) | (~node19(c_e_h_1, c_h, s6, s7)))),
% 292.92/185.50 inference(rewrite,[status(thm)],[])).
% 292.92/185.50 tff(19406,plain,
% 292.92/185.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s6) | node18(c_e_h_1, c_h, s6, s7) | (~node19(c_e_h_1, c_h, s6, s7)))),
% 292.92/185.50 inference(quant_inst,[status(thm)],[])).
% 292.92/185.50 tff(19407,plain,
% 292.92/185.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s6) | node18(c_e_h_1, c_h, s6, s7) | (~node19(c_e_h_1, c_h, s6, s7))),
% 292.92/185.50 inference(modus_ponens,[status(thm)],[19406, 19405])).
% 292.92/185.50 tff(19408,plain,
% 292.92/185.50 (node17(c_e_h_1, c_h, s6) | node18(c_e_h_1, c_h, s6, s7)),
% 292.92/185.50 inference(unit_resolution,[status(thm)],[19407, 776, 19404])).
% 292.92/185.50 tff(19409,plain,
% 292.92/185.50 (node17(c_e_h_1, c_h, s6)),
% 292.92/185.50 inference(unit_resolution,[status(thm)],[19408, 19400])).
% 292.92/185.50 tff(19410,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_h, s6)), introduced(assumption)).
% 292.92/185.50 tff(19411,plain,
% 292.92/185.50 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s6)) | (~node17(c_e_h_1, c_h, s6)) | m_c_h_element_v_in2(c_e_h_1, c_h, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s6)) | (~node17(c_e_h_1, c_h, s6)) | m_c_h_element_v_in2(c_e_h_1, c_h, s6))),
% 292.92/185.50 inference(rewrite,[status(thm)],[])).
% 292.92/185.50 tff(19412,plain,
% 292.92/185.50 (((~m_c_h_element_v_in1(c_e_h_1, c_h, s6)) | m_c_h_element_v_in2(c_e_h_1, c_h, s6) | (~node17(c_e_h_1, c_h, s6))) <=> ((~m_c_h_element_v_in1(c_e_h_1, c_h, s6)) | (~node17(c_e_h_1, c_h, s6)) | m_c_h_element_v_in2(c_e_h_1, c_h, s6))),
% 292.92/185.50 inference(rewrite,[status(thm)],[])).
% 292.92/185.50 tff(19413,plain,
% 292.92/185.50 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s6)) | m_c_h_element_v_in2(c_e_h_1, c_h, s6) | (~node17(c_e_h_1, c_h, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s6)) | (~node17(c_e_h_1, c_h, s6)) | m_c_h_element_v_in2(c_e_h_1, c_h, s6)))),
% 293.01/185.50 inference(monotonicity,[status(thm)],[19412])).
% 293.01/185.50 tff(19414,plain,
% 293.01/185.50 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s6)) | m_c_h_element_v_in2(c_e_h_1, c_h, s6) | (~node17(c_e_h_1, c_h, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s6)) | (~node17(c_e_h_1, c_h, s6)) | m_c_h_element_v_in2(c_e_h_1, c_h, s6))),
% 293.01/185.50 inference(transitivity,[status(thm)],[19413, 19411])).
% 293.01/185.50 tff(19415,plain,
% 293.01/185.50 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s6)) | m_c_h_element_v_in2(c_e_h_1, c_h, s6) | (~node17(c_e_h_1, c_h, s6)))),
% 293.01/185.50 inference(quant_inst,[status(thm)],[])).
% 293.01/185.50 tff(19416,plain,
% 293.01/185.50 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s6)) | (~node17(c_e_h_1, c_h, s6)) | m_c_h_element_v_in2(c_e_h_1, c_h, s6)),
% 293.01/185.50 inference(modus_ponens,[status(thm)],[19415, 19414])).
% 293.01/185.50 tff(19417,plain,
% 293.01/185.50 ((~m_c_h_element_v_in1(c_e_h_1, c_h, s6)) | (~node17(c_e_h_1, c_h, s6))),
% 293.01/185.50 inference(unit_resolution,[status(thm)],[19416, 919, 19410])).
% 293.01/185.50 tff(19418,plain,
% 293.01/185.50 (~m_c_h_element_v_in1(c_e_h_1, c_h, s6)),
% 293.01/185.50 inference(unit_resolution,[status(thm)],[19417, 19409])).
% 293.01/185.50 tff(19419,plain,
% 293.01/185.50 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s6)) | m_c_h_element_v_in1(c_e_h_1, c_h, s6) | m_c_h_element_v_in2(c_e_h_1, c_h, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s6)) | m_c_h_element_v_in1(c_e_h_1, c_h, s6) | m_c_h_element_v_in2(c_e_h_1, c_h, s6))),
% 293.01/185.50 inference(rewrite,[status(thm)],[])).
% 293.01/185.50 tff(19420,plain,
% 293.01/185.50 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s6)) | m_c_h_element_v_in1(c_e_h_1, c_h, s6) | m_c_h_element_v_in2(c_e_h_1, c_h, s6))),
% 293.01/185.50 inference(quant_inst,[status(thm)],[])).
% 293.01/185.50 tff(19421,plain,
% 293.01/185.50 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s6)) | m_c_h_element_v_in1(c_e_h_1, c_h, s6) | m_c_h_element_v_in2(c_e_h_1, c_h, s6)),
% 293.01/185.50 inference(modus_ponens,[status(thm)],[19420, 19419])).
% 293.01/185.50 tff(19422,plain,
% 293.01/185.50 ((~node16(c_e_h_1, c_h, s6)) | m_c_h_element_v_in1(c_e_h_1, c_h, s6)),
% 293.01/185.50 inference(unit_resolution,[status(thm)],[19421, 178, 19410])).
% 293.01/185.50 tff(19423,plain,
% 293.01/185.50 (~node16(c_e_h_1, c_h, s6)),
% 293.01/185.50 inference(unit_resolution,[status(thm)],[19422, 19418])).
% 293.01/185.50 tff(19424,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_h, s6)), introduced(assumption)).
% 293.01/185.50 tff(19425,assumption,(~node16(c_e_h_1, c_h, s6)), introduced(assumption)).
% 293.01/185.50 tff(19426,assumption,(node15(c_e_h_1, c_h, s6, s7)), introduced(assumption)).
% 293.01/185.50 tff(19427,plain,
% 293.01/185.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s7)) | (~node15(c_e_h_1, c_h, s6, s7)) | m_c_h_element_v_out(c_e_h_1, c_h, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s7)) | (~node15(c_e_h_1, c_h, s6, s7)) | m_c_h_element_v_out(c_e_h_1, c_h, s6))),
% 293.01/185.50 inference(rewrite,[status(thm)],[])).
% 293.01/185.50 tff(19428,plain,
% 293.01/185.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s7)) | (~node15(c_e_h_1, c_h, s6, s7)) | m_c_h_element_v_out(c_e_h_1, c_h, s6))),
% 293.01/185.51 inference(quant_inst,[status(thm)],[])).
% 293.01/185.51 tff(19429,plain,
% 293.01/185.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s7)) | (~node15(c_e_h_1, c_h, s6, s7)) | m_c_h_element_v_out(c_e_h_1, c_h, s6)),
% 293.01/185.51 inference(modus_ponens,[status(thm)],[19428, 19427])).
% 293.01/185.51 tff(19430,plain,
% 293.01/185.51 ($false),
% 293.01/185.51 inference(unit_resolution,[status(thm)],[19429, 147, 19393, 19392, 19426])).
% 293.01/185.51 tff(19431,plain,((~node15(c_e_h_1, c_h, s6, s7)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s7)) | m_c_h_element_v_out(c_e_h_1, c_h, s6)), inference(lemma,lemma(discharge,[]))).
% 293.01/185.51 tff(19432,plain,
% 293.01/185.51 (~node15(c_e_h_1, c_h, s6, s7)),
% 293.01/185.51 inference(unit_resolution,[status(thm)],[19431, 19393, 19392])).
% 293.01/185.51 tff(19433,plain,
% 293.01/185.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s6) | (~node19(c_e_h_1, c_h, s6, s7)) | node15(c_e_h_1, c_h, s6, s7) | node14(c_e_h_1, c_h, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s6) | (~node19(c_e_h_1, c_h, s6, s7)) | node15(c_e_h_1, c_h, s6, s7) | node14(c_e_h_1, c_h, s6, s7))),
% 293.01/185.51 inference(rewrite,[status(thm)],[])).
% 293.01/185.51 tff(19434,plain,
% 293.01/185.51 ((node16(c_e_h_1, c_h, s6) | node14(c_e_h_1, c_h, s6, s7) | node15(c_e_h_1, c_h, s6, s7) | (~node19(c_e_h_1, c_h, s6, s7))) <=> (node16(c_e_h_1, c_h, s6) | (~node19(c_e_h_1, c_h, s6, s7)) | node15(c_e_h_1, c_h, s6, s7) | node14(c_e_h_1, c_h, s6, s7))),
% 293.01/185.51 inference(rewrite,[status(thm)],[])).
% 293.01/185.51 tff(19435,plain,
% 293.01/185.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s6) | node14(c_e_h_1, c_h, s6, s7) | node15(c_e_h_1, c_h, s6, s7) | (~node19(c_e_h_1, c_h, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s6) | (~node19(c_e_h_1, c_h, s6, s7)) | node15(c_e_h_1, c_h, s6, s7) | node14(c_e_h_1, c_h, s6, s7)))),
% 293.01/185.51 inference(monotonicity,[status(thm)],[19434])).
% 293.01/185.51 tff(19436,plain,
% 293.01/185.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s6) | node14(c_e_h_1, c_h, s6, s7) | node15(c_e_h_1, c_h, s6, s7) | (~node19(c_e_h_1, c_h, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s6) | (~node19(c_e_h_1, c_h, s6, s7)) | node15(c_e_h_1, c_h, s6, s7) | node14(c_e_h_1, c_h, s6, s7))),
% 293.01/185.51 inference(transitivity,[status(thm)],[19435, 19433])).
% 293.01/185.51 tff(19437,plain,
% 293.01/185.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s6) | node14(c_e_h_1, c_h, s6, s7) | node15(c_e_h_1, c_h, s6, s7) | (~node19(c_e_h_1, c_h, s6, s7)))),
% 293.01/185.51 inference(quant_inst,[status(thm)],[])).
% 293.01/185.51 tff(19438,plain,
% 293.01/185.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s6) | (~node19(c_e_h_1, c_h, s6, s7)) | node15(c_e_h_1, c_h, s6, s7) | node14(c_e_h_1, c_h, s6, s7)),
% 293.01/185.51 inference(modus_ponens,[status(thm)],[19437, 19436])).
% 293.01/185.51 tff(19439,plain,
% 293.01/185.51 (node16(c_e_h_1, c_h, s6) | node15(c_e_h_1, c_h, s6, s7) | node14(c_e_h_1, c_h, s6, s7)),
% 293.01/185.51 inference(unit_resolution,[status(thm)],[19438, 204, 19404])).
% 293.01/185.51 tff(19440,plain,
% 293.01/185.51 (node14(c_e_h_1, c_h, s6, s7)),
% 293.01/185.51 inference(unit_resolution,[status(thm)],[19439, 19432, 19425])).
% 293.01/185.51 tff(19441,plain,
% 293.01/185.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s7)) | m_c_h_element_v_in1(c_e_h_1, c_h, s6) | (~node14(c_e_h_1, c_h, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s7)) | m_c_h_element_v_in1(c_e_h_1, c_h, s6) | (~node14(c_e_h_1, c_h, s6, s7)))),
% 293.01/185.51 inference(rewrite,[status(thm)],[])).
% 293.01/185.51 tff(19442,plain,
% 293.01/185.51 (((~node14(c_e_h_1, c_h, s6, s7)) | m_c_h_element_v_in1(c_e_h_1, c_h, s6) | (~m_c_h_element_v_out(c_e_h_1, c_h, s7))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_h, s7)) | m_c_h_element_v_in1(c_e_h_1, c_h, s6) | (~node14(c_e_h_1, c_h, s6, s7)))),
% 293.01/185.51 inference(rewrite,[status(thm)],[])).
% 293.01/185.51 tff(19443,plain,
% 293.01/185.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s6, s7)) | m_c_h_element_v_in1(c_e_h_1, c_h, s6) | (~m_c_h_element_v_out(c_e_h_1, c_h, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s7)) | m_c_h_element_v_in1(c_e_h_1, c_h, s6) | (~node14(c_e_h_1, c_h, s6, s7))))),
% 293.01/185.51 inference(monotonicity,[status(thm)],[19442])).
% 293.01/185.51 tff(19444,plain,
% 293.01/185.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s6, s7)) | m_c_h_element_v_in1(c_e_h_1, c_h, s6) | (~m_c_h_element_v_out(c_e_h_1, c_h, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s7)) | m_c_h_element_v_in1(c_e_h_1, c_h, s6) | (~node14(c_e_h_1, c_h, s6, s7)))),
% 293.01/185.51 inference(transitivity,[status(thm)],[19443, 19441])).
% 293.01/185.51 tff(19445,plain,
% 293.01/185.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s6, s7)) | m_c_h_element_v_in1(c_e_h_1, c_h, s6) | (~m_c_h_element_v_out(c_e_h_1, c_h, s7)))),
% 293.01/185.51 inference(quant_inst,[status(thm)],[])).
% 293.01/185.51 tff(19446,plain,
% 293.01/185.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s7)) | m_c_h_element_v_in1(c_e_h_1, c_h, s6) | (~node14(c_e_h_1, c_h, s6, s7))),
% 293.01/185.51 inference(modus_ponens,[status(thm)],[19445, 19444])).
% 293.01/185.51 tff(19447,plain,
% 293.01/185.51 ($false),
% 293.01/185.51 inference(unit_resolution,[status(thm)],[19446, 223, 19393, 19440, 19424])).
% 293.01/185.51 tff(19448,plain,((~m_c_h_element_v_out(c_e_h_1, c_h, s7)) | m_c_h_element_v_in1(c_e_h_1, c_h, s6) | node16(c_e_h_1, c_h, s6) | m_c_h_element_v_out(c_e_h_1, c_h, s6)), inference(lemma,lemma(discharge,[]))).
% 293.01/185.51 tff(19449,plain,
% 293.01/185.51 ($false),
% 293.01/185.51 inference(unit_resolution,[status(thm)],[19448, 19423, 19418, 19393, 19392])).
% 293.01/185.51 tff(19450,plain,(m_c_h_element_v_out(c_e_h_1, c_h, s6) | (~m_c_h_element_v_out(c_e_h_1, c_h, s7)) | m_c_h_element_v_in2(c_e_h_1, c_h, s6)), inference(lemma,lemma(discharge,[]))).
% 293.01/185.51 tff(19451,plain,
% 293.01/185.51 ((~m_c_h_element_v_out(c_e_h_1, c_h, s7)) | m_c_h_element_v_in2(c_e_h_1, c_h, s6)),
% 293.01/185.51 inference(unit_resolution,[status(thm)],[19450, 18614])).
% 293.01/185.51 tff(19452,plain,
% 293.01/185.51 (~m_c_h_element_v_out(c_e_h_1, c_h, s7)),
% 293.01/185.51 inference(unit_resolution,[status(thm)],[19451, 19391])).
% 293.01/185.51 tff(19453,plain,
% 293.01/185.51 (((~![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))) | (m_and_h_gate_v_in2(c_e_h_1, c_k, s7) | m_c_h_element_v_out(c_e_h_1, c_h, s7))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))) | m_and_h_gate_v_in2(c_e_h_1, c_k, s7) | m_c_h_element_v_out(c_e_h_1, c_h, s7))),
% 293.01/185.51 inference(rewrite,[status(thm)],[])).
% 293.01/185.51 tff(19454,plain,
% 293.01/185.51 ((~![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))) | (m_and_h_gate_v_in2(c_e_h_1, c_k, s7) | m_c_h_element_v_out(c_e_h_1, c_h, s7))),
% 293.01/185.51 inference(quant_inst,[status(thm)],[])).
% 293.01/185.51 tff(19455,plain,
% 293.01/185.51 ((~![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))) | m_and_h_gate_v_in2(c_e_h_1, c_k, s7) | m_c_h_element_v_out(c_e_h_1, c_h, s7)),
% 293.01/185.52 inference(modus_ponens,[status(thm)],[19454, 19453])).
% 293.01/185.52 tff(19456,plain,
% 293.01/185.52 (m_and_h_gate_v_in2(c_e_h_1, c_k, s7) | m_c_h_element_v_out(c_e_h_1, c_h, s7)),
% 293.01/185.52 inference(unit_resolution,[status(thm)],[19455, 6420])).
% 293.01/185.52 tff(19457,plain,
% 293.01/185.52 (m_and_h_gate_v_in2(c_e_h_1, c_k, s7)),
% 293.01/185.52 inference(unit_resolution,[status(thm)],[19456, 19452])).
% 293.01/185.52 tff(19458,plain,
% 293.01/185.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_k, s7)) | (~m_and_h_gate_v_in1(c_e_h_1, c_k, s7)) | (~node21(c_e_h_1, c_k, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_k, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in2(c_e_h_1, c_k, s7)) | (~m_and_h_gate_v_in1(c_e_h_1, c_k, s7)) | (~node21(c_e_h_1, c_k, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_k, s8))),
% 293.01/185.52 inference(rewrite,[status(thm)],[])).
% 293.01/185.52 tff(19459,plain,
% 293.01/185.52 (((~node21(c_e_h_1, c_k, s7, s8)) | (~m_and_h_gate_v_in2(c_e_h_1, c_k, s7)) | (~m_and_h_gate_v_in1(c_e_h_1, c_k, s7)) | m_and_h_gate_v_out(c_e_h_1, c_k, s8)) <=> ((~m_and_h_gate_v_in2(c_e_h_1, c_k, s7)) | (~m_and_h_gate_v_in1(c_e_h_1, c_k, s7)) | (~node21(c_e_h_1, c_k, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_k, s8))),
% 293.01/185.52 inference(rewrite,[status(thm)],[])).
% 293.01/185.52 tff(19460,plain,
% 293.01/185.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_1, c_k, s7, s8)) | (~m_and_h_gate_v_in2(c_e_h_1, c_k, s7)) | (~m_and_h_gate_v_in1(c_e_h_1, c_k, s7)) | m_and_h_gate_v_out(c_e_h_1, c_k, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_k, s7)) | (~m_and_h_gate_v_in1(c_e_h_1, c_k, s7)) | (~node21(c_e_h_1, c_k, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_k, s8)))),
% 293.01/185.52 inference(monotonicity,[status(thm)],[19459])).
% 293.01/185.52 tff(19461,plain,
% 293.01/185.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_1, c_k, s7, s8)) | (~m_and_h_gate_v_in2(c_e_h_1, c_k, s7)) | (~m_and_h_gate_v_in1(c_e_h_1, c_k, s7)) | m_and_h_gate_v_out(c_e_h_1, c_k, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in2(c_e_h_1, c_k, s7)) | (~m_and_h_gate_v_in1(c_e_h_1, c_k, s7)) | (~node21(c_e_h_1, c_k, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_k, s8))),
% 293.01/185.52 inference(transitivity,[status(thm)],[19460, 19458])).
% 293.01/185.52 tff(19462,plain,
% 293.01/185.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_1, c_k, s7, s8)) | (~m_and_h_gate_v_in2(c_e_h_1, c_k, s7)) | (~m_and_h_gate_v_in1(c_e_h_1, c_k, s7)) | m_and_h_gate_v_out(c_e_h_1, c_k, s8))),
% 293.01/185.52 inference(quant_inst,[status(thm)],[])).
% 293.01/185.52 tff(19463,plain,
% 293.01/185.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in2(c_e_h_1, c_k, s7)) | (~m_and_h_gate_v_in1(c_e_h_1, c_k, s7)) | (~node21(c_e_h_1, c_k, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_k, s8)),
% 293.01/185.52 inference(modus_ponens,[status(thm)],[19462, 19461])).
% 293.01/185.52 tff(19464,plain,
% 293.01/185.52 ($false),
% 293.01/185.52 inference(unit_resolution,[status(thm)],[19463, 5851, 19457, 15907, 15897, 15933])).
% 293.01/185.52 tff(19465,plain,((~node21(c_e_h_1, c_k, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_k, s8) | (~m_and_h_gate_v_in1(c_e_h_1, c_k, s7))), inference(lemma,lemma(discharge,[]))).
% 293.01/185.52 tff(19466,plain,
% 293.01/185.52 (~node21(c_e_h_1, c_k, s7, s8)),
% 293.01/185.52 inference(unit_resolution,[status(thm)],[19465, 15897, 15933])).
% 293.01/185.52 tff(19467,plain,
% 293.01/185.52 (node22(c_e_h_1, c_k, s7, s8)),
% 293.01/185.52 inference(unit_resolution,[status(thm)],[15917, 19466])).
% 293.01/185.52 tff(19468,plain,
% 293.01/185.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_1, c_k, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s7)) | (~node22(c_e_h_1, c_k, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | m_and_h_gate_v_out(c_e_h_1, c_k, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s7)) | (~node22(c_e_h_1, c_k, s7, s8)))),
% 293.01/185.52 inference(rewrite,[status(thm)],[])).
% 293.01/185.52 tff(19469,plain,
% 293.01/185.52 ((m_and_h_gate_v_out(c_e_h_1, c_k, s8) | (~node22(c_e_h_1, c_k, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s7))) <=> (m_and_h_gate_v_out(c_e_h_1, c_k, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s7)) | (~node22(c_e_h_1, c_k, s7, s8)))),
% 293.01/185.52 inference(rewrite,[status(thm)],[])).
% 293.01/185.52 tff(19470,plain,
% 293.01/185.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_1, c_k, s8) | (~node22(c_e_h_1, c_k, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_1, c_k, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s7)) | (~node22(c_e_h_1, c_k, s7, s8))))),
% 293.01/185.52 inference(monotonicity,[status(thm)],[19469])).
% 293.01/185.52 tff(19471,plain,
% 293.01/185.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_1, c_k, s8) | (~node22(c_e_h_1, c_k, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | m_and_h_gate_v_out(c_e_h_1, c_k, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s7)) | (~node22(c_e_h_1, c_k, s7, s8)))),
% 293.01/185.52 inference(transitivity,[status(thm)],[19470, 19468])).
% 293.01/185.52 tff(19472,plain,
% 293.01/185.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_1, c_k, s8) | (~node22(c_e_h_1, c_k, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s7)))),
% 293.01/185.52 inference(quant_inst,[status(thm)],[])).
% 293.01/185.52 tff(19473,plain,
% 293.01/185.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | m_and_h_gate_v_out(c_e_h_1, c_k, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s7)) | (~node22(c_e_h_1, c_k, s7, s8))),
% 293.01/185.52 inference(modus_ponens,[status(thm)],[19472, 19471])).
% 293.01/185.52 tff(19474,plain,
% 293.01/185.52 ($false),
% 293.01/185.52 inference(unit_resolution,[status(thm)],[19473, 5871, 19467, 15405, 15897])).
% 293.01/185.52 tff(19475,plain,(m_and_h_gate_v_out(c_e_h_1, c_k, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_k, s7)) | (~m_and_h_gate_v_in1(c_e_h_1, c_k, s7))), inference(lemma,lemma(discharge,[]))).
% 293.01/185.52 tff(19476,plain,
% 293.01/185.52 ($false),
% 293.01/185.52 inference(unit_resolution,[status(thm)],[19475, 19313, 19082, 19040])).
% 293.01/185.52 tff(19477,plain,((~m_and_h_gate_v_out(c_e_h_3, c_d, s9)) | m_and_h_gate_v_out(c_e_h_1, c_p, s9)), inference(lemma,lemma(discharge,[]))).
% 293.01/185.52 tff(19478,plain,
% 293.01/185.52 (~m_and_h_gate_v_out(c_e_h_3, c_d, s9)),
% 293.01/185.52 inference(unit_resolution,[status(thm)],[19477, 17093])).
% 293.01/185.52 tff(19479,assumption,(m_or_h_gate_v_in2(c_e_h_3, c_g, s9)), introduced(assumption)).
% 293.01/185.52 tff(19480,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_d, s9)), introduced(assumption)).
% 293.01/185.52 tff(19481,plain,
% 293.01/185.52 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_g, s9)) | m_and_h_gate_v_out(c_e_h_3, c_d, s9))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_g, s9)) | m_and_h_gate_v_out(c_e_h_3, c_d, s9))),
% 293.01/185.52 inference(rewrite,[status(thm)],[])).
% 293.01/185.52 tff(19482,plain,
% 293.01/185.52 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_g, s9)) | m_and_h_gate_v_out(c_e_h_3, c_d, s9))),
% 293.01/185.52 inference(quant_inst,[status(thm)],[])).
% 293.01/185.52 tff(19483,plain,
% 293.01/185.52 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_g, s9)) | m_and_h_gate_v_out(c_e_h_3, c_d, s9)),
% 293.01/185.52 inference(modus_ponens,[status(thm)],[19482, 19481])).
% 293.01/185.52 tff(19484,plain,
% 293.01/185.52 ($false),
% 293.01/185.52 inference(unit_resolution,[status(thm)],[19483, 2762, 19480, 19479])).
% 293.01/185.52 tff(19485,plain,((~m_or_h_gate_v_in2(c_e_h_3, c_g, s9)) | m_and_h_gate_v_out(c_e_h_3, c_d, s9)), inference(lemma,lemma(discharge,[]))).
% 293.01/185.52 tff(19486,plain,
% 293.01/185.52 (~m_or_h_gate_v_in2(c_e_h_3, c_g, s9)),
% 293.01/185.52 inference(unit_resolution,[status(thm)],[19485, 19478])).
% 293.01/185.52 tff(19487,plain,
% 293.01/185.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_d, s8)) | m_and_h_gate_v_out(c_e_h_3, c_d, s9) | (~node22(c_e_h_3, c_d, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s8)) | m_and_h_gate_v_out(c_e_h_3, c_d, s9) | (~node22(c_e_h_3, c_d, s8, s9)))),
% 293.01/185.52 inference(rewrite,[status(thm)],[])).
% 293.01/185.52 tff(19488,plain,
% 293.01/185.52 ((m_and_h_gate_v_out(c_e_h_3, c_d, s9) | (~node22(c_e_h_3, c_d, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s8))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_d, s8)) | m_and_h_gate_v_out(c_e_h_3, c_d, s9) | (~node22(c_e_h_3, c_d, s8, s9)))),
% 293.01/185.52 inference(rewrite,[status(thm)],[])).
% 293.01/185.52 tff(19489,plain,
% 293.01/185.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_d, s9) | (~node22(c_e_h_3, c_d, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_d, s8)) | m_and_h_gate_v_out(c_e_h_3, c_d, s9) | (~node22(c_e_h_3, c_d, s8, s9))))),
% 293.01/185.52 inference(monotonicity,[status(thm)],[19488])).
% 293.01/185.52 tff(19490,plain,
% 293.01/185.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_d, s9) | (~node22(c_e_h_3, c_d, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s8)) | m_and_h_gate_v_out(c_e_h_3, c_d, s9) | (~node22(c_e_h_3, c_d, s8, s9)))),
% 293.01/185.52 inference(transitivity,[status(thm)],[19489, 19487])).
% 293.01/185.52 tff(19491,plain,
% 293.01/185.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_d, s9) | (~node22(c_e_h_3, c_d, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s8)))),
% 293.01/185.52 inference(quant_inst,[status(thm)],[])).
% 293.01/185.52 tff(19492,plain,
% 293.01/185.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s8)) | m_and_h_gate_v_out(c_e_h_3, c_d, s9) | (~node22(c_e_h_3, c_d, s8, s9))),
% 293.01/185.52 inference(modus_ponens,[status(thm)],[19491, 19490])).
% 293.01/185.52 tff(19493,plain,
% 293.01/185.52 ($false),
% 293.01/185.52 inference(unit_resolution,[status(thm)],[19492, 5871, 19480, 17219, 17183])).
% 293.01/185.52 tff(19494,plain,((~node22(c_e_h_3, c_d, s8, s9)) | m_and_h_gate_v_out(c_e_h_3, c_d, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s8))), inference(lemma,lemma(discharge,[]))).
% 293.01/185.52 tff(19495,plain,
% 293.01/185.52 (~node22(c_e_h_3, c_d, s8, s9)),
% 293.01/185.52 inference(unit_resolution,[status(thm)],[19494, 19480, 17183])).
% 293.01/185.52 tff(19496,plain,
% 293.01/185.52 (node20(c_e_h_3, c_d, s7)),
% 293.01/185.53 inference(unit_resolution,[status(thm)],[17208, 17183])).
% 293.01/185.53 tff(19497,plain,
% 293.01/185.53 (m_and_h_gate_v_in1(c_e_h_3, c_d, s7)),
% 293.01/185.53 inference(unit_resolution,[status(thm)],[17110, 19496])).
% 293.01/185.53 tff(19498,plain,
% 293.01/185.53 (m_mutex_h_half_v_out(c_e_h_3, c_b, s7)),
% 293.01/185.53 inference(unit_resolution,[status(thm)],[17102, 19497])).
% 293.01/185.53 tff(19499,plain,
% 293.01/185.53 (m_mutex_h_half_v_out(c_e_h_3, c_b, s8)),
% 293.01/185.53 inference(unit_resolution,[status(thm)],[18823, 19498])).
% 293.01/185.53 tff(19500,plain,
% 293.01/185.53 (^[I0: $i, X: $i] : refl(((~m_mutex_h_half_v_out(I0, c_b, X)) | m_and_h_gate_v_in1(I0, c_d, X)) <=> ((~m_mutex_h_half_v_out(I0, c_b, X)) | m_and_h_gate_v_in1(I0, c_d, X)))),
% 293.01/185.53 inference(bind,[status(th)],[])).
% 293.01/185.53 tff(19501,plain,
% 293.01/185.53 (![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_b, X)) | m_and_h_gate_v_in1(I0, c_d, X)) <=> ![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_b, X)) | m_and_h_gate_v_in1(I0, c_d, X))),
% 293.01/185.53 inference(quant_intro,[status(thm)],[19500])).
% 293.01/185.53 tff(19502,plain,
% 293.01/185.53 (![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_b, X)) | m_and_h_gate_v_in1(I0, c_d, X)) <=> ![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_b, X)) | m_and_h_gate_v_in1(I0, c_d, X))),
% 293.01/185.53 inference(rewrite,[status(thm)],[])).
% 293.01/185.53 tff(19503,plain,
% 293.01/185.53 (^[I0: $i, X: $i] : rewrite((m_and_h_gate_v_in1(I0, c_d, X) | (~m_mutex_h_half_v_out(I0, c_b, X))) <=> ((~m_mutex_h_half_v_out(I0, c_b, X)) | m_and_h_gate_v_in1(I0, c_d, X)))),
% 293.01/185.53 inference(bind,[status(th)],[])).
% 293.01/185.53 tff(19504,plain,
% 293.01/185.53 (![I0: $i, X: $i] : (m_and_h_gate_v_in1(I0, c_d, X) | (~m_mutex_h_half_v_out(I0, c_b, X))) <=> ![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_b, X)) | m_and_h_gate_v_in1(I0, c_d, X))),
% 293.01/185.53 inference(quant_intro,[status(thm)],[19503])).
% 293.01/185.53 tff(19505,axiom,(![I0: $i, X: $i] : (m_and_h_gate_v_in1(I0, c_d, X) | (~m_mutex_h_half_v_out(I0, c_b, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_15')).
% 293.01/185.53 tff(19506,plain,
% 293.01/185.53 (![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_b, X)) | m_and_h_gate_v_in1(I0, c_d, X))),
% 293.01/185.53 inference(modus_ponens,[status(thm)],[19505, 19504])).
% 293.01/185.53 tff(19507,plain,
% 293.01/185.53 (![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_b, X)) | m_and_h_gate_v_in1(I0, c_d, X))),
% 293.01/185.53 inference(modus_ponens,[status(thm)],[19506, 19502])).
% 293.01/185.53 tff(19508,plain,(
% 293.01/185.53 ![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_b, X)) | m_and_h_gate_v_in1(I0, c_d, X))),
% 293.01/185.53 inference(skolemize,[status(sab)],[19507])).
% 293.01/185.53 tff(19509,plain,
% 293.01/185.53 (![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_b, X)) | m_and_h_gate_v_in1(I0, c_d, X))),
% 293.01/185.53 inference(modus_ponens,[status(thm)],[19508, 19501])).
% 293.01/185.53 tff(19510,plain,
% 293.01/185.53 (((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_b, X)) | m_and_h_gate_v_in1(I0, c_d, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_b, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s8))) <=> ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_b, X)) | m_and_h_gate_v_in1(I0, c_d, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s8))),
% 293.01/185.53 inference(rewrite,[status(thm)],[])).
% 293.01/185.53 tff(19511,plain,
% 293.01/185.53 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_b, X)) | m_and_h_gate_v_in1(I0, c_d, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_b, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s8))),
% 293.01/185.53 inference(quant_inst,[status(thm)],[])).
% 293.01/185.53 tff(19512,plain,
% 293.01/185.53 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_b, X)) | m_and_h_gate_v_in1(I0, c_d, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s8)),
% 293.01/185.53 inference(modus_ponens,[status(thm)],[19511, 19510])).
% 293.01/185.53 tff(19513,plain,
% 293.01/185.53 ($false),
% 293.01/185.53 inference(unit_resolution,[status(thm)],[19512, 19509, 17249, 17233])).
% 293.01/185.53 tff(19514,plain,(m_and_h_gate_v_in1(c_e_h_3, c_d, s8) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s8))), inference(lemma,lemma(discharge,[]))).
% 293.01/185.53 tff(19515,plain,
% 293.01/185.53 (m_and_h_gate_v_in1(c_e_h_3, c_d, s8)),
% 293.01/185.53 inference(unit_resolution,[status(thm)],[19514, 19499])).
% 293.01/185.53 tff(19516,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_r, s8)), introduced(assumption)).
% 293.01/185.53 tff(19517,assumption,(m_user_v_ack(c_e_h_3, c_u, s8)), introduced(assumption)).
% 293.01/185.53 tff(19518,plain,
% 293.01/185.53 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_3, c_u, s8)) | m_and_h_gate_v_out(c_e_h_3, c_r, s8))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_3, c_u, s8)) | m_and_h_gate_v_out(c_e_h_3, c_r, s8))),
% 293.01/185.53 inference(rewrite,[status(thm)],[])).
% 293.01/185.53 tff(19519,plain,
% 293.01/185.53 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_3, c_u, s8)) | m_and_h_gate_v_out(c_e_h_3, c_r, s8))),
% 293.01/185.53 inference(quant_inst,[status(thm)],[])).
% 293.01/185.53 tff(19520,plain,
% 293.01/185.53 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_3, c_u, s8)) | m_and_h_gate_v_out(c_e_h_3, c_r, s8)),
% 293.01/185.53 inference(modus_ponens,[status(thm)],[19519, 19518])).
% 293.01/185.53 tff(19521,plain,
% 293.01/185.53 ($false),
% 293.01/185.53 inference(unit_resolution,[status(thm)],[19520, 268, 19517, 19516])).
% 293.01/185.53 tff(19522,plain,((~m_user_v_ack(c_e_h_3, c_u, s8)) | m_and_h_gate_v_out(c_e_h_3, c_r, s8)), inference(lemma,lemma(discharge,[]))).
% 293.01/185.53 tff(19523,plain,
% 293.01/185.53 (~m_user_v_ack(c_e_h_3, c_u, s8)),
% 293.01/185.53 inference(unit_resolution,[status(thm)],[19522, 12593])).
% 293.01/185.53 tff(19524,plain,
% 293.01/185.53 (^[I0: $i, X: $i] : refl((m_and_h_gate_v_in2(I0, c_d, X) | m_user_v_ack(I0, c_u, X)) <=> (m_and_h_gate_v_in2(I0, c_d, X) | m_user_v_ack(I0, c_u, X)))),
% 293.01/185.53 inference(bind,[status(th)],[])).
% 293.01/185.53 tff(19525,plain,
% 293.01/185.53 (![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_d, X) | m_user_v_ack(I0, c_u, X)) <=> ![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_d, X) | m_user_v_ack(I0, c_u, X))),
% 293.01/185.53 inference(quant_intro,[status(thm)],[19524])).
% 293.01/185.53 tff(19526,plain,
% 293.01/185.53 (![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_d, X) | m_user_v_ack(I0, c_u, X)) <=> ![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_d, X) | m_user_v_ack(I0, c_u, X))),
% 293.01/185.53 inference(rewrite,[status(thm)],[])).
% 293.01/185.53 tff(19527,axiom,(![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_d, X) | m_user_v_ack(I0, c_u, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_17')).
% 293.01/185.53 tff(19528,plain,
% 293.01/185.53 (![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_d, X) | m_user_v_ack(I0, c_u, X))),
% 293.01/185.53 inference(modus_ponens,[status(thm)],[19527, 19526])).
% 293.01/185.53 tff(19529,plain,(
% 293.01/185.53 ![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_d, X) | m_user_v_ack(I0, c_u, X))),
% 293.01/185.53 inference(skolemize,[status(sab)],[19528])).
% 293.01/185.53 tff(19530,plain,
% 293.01/185.53 (![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_d, X) | m_user_v_ack(I0, c_u, X))),
% 293.01/185.53 inference(modus_ponens,[status(thm)],[19529, 19525])).
% 293.01/185.53 tff(19531,plain,
% 293.01/185.53 (((~![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_d, X) | m_user_v_ack(I0, c_u, X))) | (m_and_h_gate_v_in2(c_e_h_3, c_d, s8) | m_user_v_ack(c_e_h_3, c_u, s8))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_d, X) | m_user_v_ack(I0, c_u, X))) | m_and_h_gate_v_in2(c_e_h_3, c_d, s8) | m_user_v_ack(c_e_h_3, c_u, s8))),
% 293.01/185.53 inference(rewrite,[status(thm)],[])).
% 293.01/185.53 tff(19532,plain,
% 293.01/185.53 ((~![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_d, X) | m_user_v_ack(I0, c_u, X))) | (m_and_h_gate_v_in2(c_e_h_3, c_d, s8) | m_user_v_ack(c_e_h_3, c_u, s8))),
% 293.01/185.53 inference(quant_inst,[status(thm)],[])).
% 293.01/185.53 tff(19533,plain,
% 293.01/185.53 ((~![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_d, X) | m_user_v_ack(I0, c_u, X))) | m_and_h_gate_v_in2(c_e_h_3, c_d, s8) | m_user_v_ack(c_e_h_3, c_u, s8)),
% 293.01/185.53 inference(modus_ponens,[status(thm)],[19532, 19531])).
% 293.01/185.53 tff(19534,plain,
% 293.01/185.53 (m_and_h_gate_v_in2(c_e_h_3, c_d, s8) | m_user_v_ack(c_e_h_3, c_u, s8)),
% 293.01/185.53 inference(unit_resolution,[status(thm)],[19533, 19530])).
% 293.01/185.53 tff(19535,plain,
% 293.01/185.53 (m_and_h_gate_v_in2(c_e_h_3, c_d, s8)),
% 293.01/185.53 inference(unit_resolution,[status(thm)],[19534, 19523])).
% 293.01/185.53 tff(19536,plain,
% 293.01/185.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_d, s8)) | (~m_and_h_gate_v_in1(c_e_h_3, c_d, s8)) | m_and_h_gate_v_out(c_e_h_3, c_d, s9) | (~node21(c_e_h_3, c_d, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in2(c_e_h_3, c_d, s8)) | (~m_and_h_gate_v_in1(c_e_h_3, c_d, s8)) | m_and_h_gate_v_out(c_e_h_3, c_d, s9) | (~node21(c_e_h_3, c_d, s8, s9)))),
% 293.01/185.53 inference(rewrite,[status(thm)],[])).
% 293.01/185.53 tff(19537,plain,
% 293.01/185.53 (((~node21(c_e_h_3, c_d, s8, s9)) | (~m_and_h_gate_v_in2(c_e_h_3, c_d, s8)) | (~m_and_h_gate_v_in1(c_e_h_3, c_d, s8)) | m_and_h_gate_v_out(c_e_h_3, c_d, s9)) <=> ((~m_and_h_gate_v_in2(c_e_h_3, c_d, s8)) | (~m_and_h_gate_v_in1(c_e_h_3, c_d, s8)) | m_and_h_gate_v_out(c_e_h_3, c_d, s9) | (~node21(c_e_h_3, c_d, s8, s9)))),
% 293.01/185.53 inference(rewrite,[status(thm)],[])).
% 293.01/185.53 tff(19538,plain,
% 293.01/185.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_d, s8, s9)) | (~m_and_h_gate_v_in2(c_e_h_3, c_d, s8)) | (~m_and_h_gate_v_in1(c_e_h_3, c_d, s8)) | m_and_h_gate_v_out(c_e_h_3, c_d, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_d, s8)) | (~m_and_h_gate_v_in1(c_e_h_3, c_d, s8)) | m_and_h_gate_v_out(c_e_h_3, c_d, s9) | (~node21(c_e_h_3, c_d, s8, s9))))),
% 293.01/185.53 inference(monotonicity,[status(thm)],[19537])).
% 293.01/185.53 tff(19539,plain,
% 293.01/185.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_d, s8, s9)) | (~m_and_h_gate_v_in2(c_e_h_3, c_d, s8)) | (~m_and_h_gate_v_in1(c_e_h_3, c_d, s8)) | m_and_h_gate_v_out(c_e_h_3, c_d, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in2(c_e_h_3, c_d, s8)) | (~m_and_h_gate_v_in1(c_e_h_3, c_d, s8)) | m_and_h_gate_v_out(c_e_h_3, c_d, s9) | (~node21(c_e_h_3, c_d, s8, s9)))),
% 293.01/185.53 inference(transitivity,[status(thm)],[19538, 19536])).
% 293.01/185.53 tff(19540,plain,
% 293.01/185.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_d, s8, s9)) | (~m_and_h_gate_v_in2(c_e_h_3, c_d, s8)) | (~m_and_h_gate_v_in1(c_e_h_3, c_d, s8)) | m_and_h_gate_v_out(c_e_h_3, c_d, s9))),
% 293.01/185.53 inference(quant_inst,[status(thm)],[])).
% 293.01/185.53 tff(19541,plain,
% 293.01/185.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in2(c_e_h_3, c_d, s8)) | (~m_and_h_gate_v_in1(c_e_h_3, c_d, s8)) | m_and_h_gate_v_out(c_e_h_3, c_d, s9) | (~node21(c_e_h_3, c_d, s8, s9))),
% 293.01/185.53 inference(modus_ponens,[status(thm)],[19540, 19539])).
% 293.01/185.53 tff(19542,plain,
% 293.01/185.53 ($false),
% 293.01/185.53 inference(unit_resolution,[status(thm)],[19541, 5851, 19535, 19480, 17211, 17241])).
% 293.01/185.53 tff(19543,plain,((~node21(c_e_h_3, c_d, s8, s9)) | m_and_h_gate_v_out(c_e_h_3, c_d, s9) | (~m_and_h_gate_v_in1(c_e_h_3, c_d, s8))), inference(lemma,lemma(discharge,[]))).
% 293.01/185.53 tff(19544,plain,
% 293.01/185.53 (~node21(c_e_h_3, c_d, s8, s9)),
% 293.01/185.53 inference(unit_resolution,[status(thm)],[19543, 19480, 19515])).
% 293.01/185.53 tff(19545,plain,
% 293.01/185.53 ($false),
% 293.01/185.53 inference(unit_resolution,[status(thm)],[17229, 19544, 19495])).
% 293.01/185.53 tff(19546,plain,(m_and_h_gate_v_out(c_e_h_3, c_d, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s8))), inference(lemma,lemma(discharge,[]))).
% 293.01/185.53 tff(19547,plain,
% 293.01/185.53 (~m_and_h_gate_v_out(c_e_h_3, c_d, s8)),
% 293.01/185.53 inference(unit_resolution,[status(thm)],[19546, 19478])).
% 293.01/185.53 tff(19548,assumption,(m_or_h_gate_v_in2(c_e_h_3, c_g, s8)), introduced(assumption)).
% 293.01/185.53 tff(19549,plain,
% 293.01/185.53 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_g, s8)) | m_and_h_gate_v_out(c_e_h_3, c_d, s8))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_g, s8)) | m_and_h_gate_v_out(c_e_h_3, c_d, s8))),
% 293.01/185.53 inference(rewrite,[status(thm)],[])).
% 293.01/185.53 tff(19550,plain,
% 293.01/185.53 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_g, s8)) | m_and_h_gate_v_out(c_e_h_3, c_d, s8))),
% 293.01/185.53 inference(quant_inst,[status(thm)],[])).
% 293.01/185.53 tff(19551,plain,
% 293.01/185.53 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_g, s8)) | m_and_h_gate_v_out(c_e_h_3, c_d, s8)),
% 293.01/185.53 inference(modus_ponens,[status(thm)],[19550, 19549])).
% 293.01/185.53 tff(19552,plain,
% 293.01/185.53 ($false),
% 293.01/185.53 inference(unit_resolution,[status(thm)],[19551, 2762, 17218, 19548])).
% 293.01/185.53 tff(19553,plain,((~m_or_h_gate_v_in2(c_e_h_3, c_g, s8)) | m_and_h_gate_v_out(c_e_h_3, c_d, s8)), inference(lemma,lemma(discharge,[]))).
% 293.01/185.53 tff(19554,plain,
% 293.01/185.53 (~m_or_h_gate_v_in2(c_e_h_3, c_g, s8)),
% 293.01/185.53 inference(unit_resolution,[status(thm)],[19553, 19547])).
% 293.01/185.53 tff(19555,assumption,(~m_mutex_h_half_v_out(c_e_h_3, c_a, s13)), introduced(assumption)).
% 293.01/185.53 tff(19556,assumption,(m_user_v_ack(c_e_h_3, c_u, s11)), introduced(assumption)).
% 293.01/185.53 tff(19557,plain,
% 293.01/185.53 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_3, c_u, s11)) | m_and_h_gate_v_out(c_e_h_3, c_r, s11))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_3, c_u, s11)) | m_and_h_gate_v_out(c_e_h_3, c_r, s11))),
% 293.01/185.53 inference(rewrite,[status(thm)],[])).
% 293.01/185.53 tff(19558,plain,
% 293.01/185.53 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_3, c_u, s11)) | m_and_h_gate_v_out(c_e_h_3, c_r, s11))),
% 293.01/185.53 inference(quant_inst,[status(thm)],[])).
% 293.01/185.53 tff(19559,plain,
% 293.01/185.53 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_3, c_u, s11)) | m_and_h_gate_v_out(c_e_h_3, c_r, s11)),
% 293.01/185.53 inference(modus_ponens,[status(thm)],[19558, 19557])).
% 293.01/185.53 tff(19560,plain,
% 293.01/185.53 ($false),
% 293.01/185.53 inference(unit_resolution,[status(thm)],[19559, 268, 19556, 12677])).
% 293.01/185.53 tff(19561,plain,((~m_user_v_ack(c_e_h_3, c_u, s11)) | m_and_h_gate_v_out(c_e_h_3, c_r, s11)), inference(lemma,lemma(discharge,[]))).
% 293.01/185.53 tff(19562,plain,
% 293.01/185.53 (~m_user_v_ack(c_e_h_3, c_u, s11)),
% 293.01/185.53 inference(unit_resolution,[status(thm)],[19561, 12664])).
% 293.01/185.53 tff(19563,plain,
% 293.01/185.53 (~m_user_v_req(c_e_h_3, c_u, s5)),
% 293.01/185.53 inference(unit_resolution,[status(thm)],[1900, 1826])).
% 293.01/185.53 tff(19564,plain,
% 293.01/185.53 (~m_user_v_req(c_e_h_3, c_u, s4)),
% 293.01/185.53 inference(unit_resolution,[status(thm)],[1035, 19563])).
% 293.01/185.53 tff(19565,plain,
% 293.01/185.53 (~m_user_v_req(c_e_h_3, c_u, s3)),
% 293.01/185.53 inference(unit_resolution,[status(thm)],[732, 19564])).
% 293.01/185.53 tff(19566,plain,
% 293.01/185.53 (~m_user_v_req(c_e_h_3, c_u, s2)),
% 293.01/185.53 inference(unit_resolution,[status(thm)],[335, 19565])).
% 293.01/185.53 tff(19567,plain,
% 293.01/185.53 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s3)),
% 293.01/185.53 inference(unit_resolution,[status(thm)],[514, 19566])).
% 293.01/185.53 tff(19568,plain,
% 293.01/185.53 (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s3)),
% 293.01/185.53 inference(unit_resolution,[status(thm)],[548, 395, 19565])).
% 293.01/185.53 tff(19569,plain,
% 293.01/185.53 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s4)),
% 293.01/185.54 inference(unit_resolution,[status(thm)],[544, 19568, 19567])).
% 293.01/185.54 tff(19570,assumption,(m_user_v_ack(c_e_h_3, c_u, s6)), introduced(assumption)).
% 293.01/185.54 tff(19571,plain,
% 293.01/185.54 ($false),
% 293.01/185.54 inference(unit_resolution,[status(thm)],[1860, 268, 19570, 2458])).
% 293.01/185.54 tff(19572,plain,((~m_user_v_ack(c_e_h_3, c_u, s6)) | m_and_h_gate_v_out(c_e_h_3, c_r, s6)), inference(lemma,lemma(discharge,[]))).
% 293.01/185.54 tff(19573,plain,
% 293.01/185.54 (~m_user_v_ack(c_e_h_3, c_u, s6)),
% 293.01/185.54 inference(unit_resolution,[status(thm)],[19572, 2456])).
% 293.01/185.54 tff(19574,plain,
% 293.01/185.54 ((~node7(c_e_h_3, c_u, s6, s7)) | m_user_v_req(c_e_h_3, c_u, s7)),
% 293.01/185.54 inference(unit_resolution,[status(thm)],[1856, 19573])).
% 293.01/185.54 tff(19575,plain,
% 293.01/185.54 (~node7(c_e_h_3, c_u, s6, s7)),
% 293.01/185.54 inference(unit_resolution,[status(thm)],[19574, 1826])).
% 293.01/185.54 tff(19576,plain,
% 293.01/185.54 (node8(c_e_h_3, c_u, s6, s7)),
% 293.01/185.54 inference(unit_resolution,[status(thm)],[1848, 19575])).
% 293.01/185.54 tff(19577,plain,
% 293.01/185.54 (~m_user_v_req(c_e_h_3, c_u, s6)),
% 293.01/185.54 inference(unit_resolution,[status(thm)],[1836, 19576, 1826])).
% 293.01/185.54 tff(19578,plain,
% 293.01/185.54 (((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_a, s6)) | m_user_v_req(c_e_h_3, c_u, s6))) <=> ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s6)) | m_user_v_req(c_e_h_3, c_u, s6))),
% 293.01/185.54 inference(rewrite,[status(thm)],[])).
% 293.01/185.54 tff(19579,plain,
% 293.01/185.54 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_a, s6)) | m_user_v_req(c_e_h_3, c_u, s6))),
% 293.01/185.54 inference(quant_inst,[status(thm)],[])).
% 293.01/185.54 tff(19580,plain,
% 293.01/185.54 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s6)) | m_user_v_req(c_e_h_3, c_u, s6)),
% 293.01/185.54 inference(modus_ponens,[status(thm)],[19579, 19578])).
% 293.01/185.54 tff(19581,plain,
% 293.01/185.54 (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s6)),
% 293.01/185.54 inference(unit_resolution,[status(thm)],[19580, 395, 19577])).
% 293.01/185.54 tff(19582,plain,
% 293.01/185.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_3, c_a, s6) | (~node12(c_e_h_3, c_a, s6, s7)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s6) | (~node12(c_e_h_3, c_a, s6, s7)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s7)))),
% 293.01/185.54 inference(rewrite,[status(thm)],[])).
% 293.01/185.54 tff(19583,plain,
% 293.01/185.54 (((~node12(c_e_h_3, c_a, s6, s7)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s6) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s7))) <=> (m_mutex_h_half_v_inp(c_e_h_3, c_a, s6) | (~node12(c_e_h_3, c_a, s6, s7)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s7)))),
% 293.01/185.54 inference(rewrite,[status(thm)],[])).
% 293.01/185.54 tff(19584,plain,
% 293.01/185.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_a, s6, s7)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s6) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_3, c_a, s6) | (~node12(c_e_h_3, c_a, s6, s7)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s7))))),
% 293.01/185.54 inference(monotonicity,[status(thm)],[19583])).
% 293.01/185.54 tff(19585,plain,
% 293.01/185.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_a, s6, s7)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s6) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s6) | (~node12(c_e_h_3, c_a, s6, s7)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s7)))),
% 293.01/185.54 inference(transitivity,[status(thm)],[19584, 19582])).
% 293.01/185.54 tff(19586,plain,
% 293.01/185.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_a, s6, s7)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s6) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s7)))),
% 293.01/185.54 inference(quant_inst,[status(thm)],[])).
% 293.01/185.54 tff(19587,plain,
% 293.01/185.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s6) | (~node12(c_e_h_3, c_a, s6, s7)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s7))),
% 293.01/185.54 inference(modus_ponens,[status(thm)],[19586, 19585])).
% 293.01/185.54 tff(19588,plain,
% 293.01/185.54 ($false),
% 293.01/185.54 inference(unit_resolution,[status(thm)],[19587, 454, 1949, 1415, 1910])).
% 293.01/185.54 tff(19589,plain,((~node12(c_e_h_3, c_a, s6, s7)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s6) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s7))), inference(lemma,lemma(discharge,[]))).
% 293.01/185.54 tff(19590,plain,
% 293.01/185.54 (~node12(c_e_h_3, c_a, s6, s7)),
% 293.01/185.54 inference(unit_resolution,[status(thm)],[19589, 19581, 1910])).
% 293.01/185.54 tff(19591,plain,
% 293.01/185.54 (node13(c_e_h_3, c_a, s6, s7)),
% 293.01/185.54 inference(unit_resolution,[status(thm)],[1962, 19590])).
% 293.01/185.54 tff(19592,plain,
% 293.01/185.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s7)) | (~node13(c_e_h_3, c_a, s6, s7)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s7)) | (~node13(c_e_h_3, c_a, s6, s7)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s6))),
% 293.01/185.54 inference(rewrite,[status(thm)],[])).
% 293.01/185.54 tff(19593,plain,
% 293.01/185.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s7)) | (~node13(c_e_h_3, c_a, s6, s7)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s6))),
% 293.01/185.54 inference(quant_inst,[status(thm)],[])).
% 293.01/185.54 tff(19594,plain,
% 293.01/185.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s7)) | (~node13(c_e_h_3, c_a, s6, s7)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s6)),
% 293.01/185.54 inference(modus_ponens,[status(thm)],[19593, 19592])).
% 293.01/185.54 tff(19595,plain,
% 293.01/185.54 (m_mutex_h_half_v_out(c_e_h_3, c_a, s6)),
% 293.01/185.54 inference(unit_resolution,[status(thm)],[19594, 423, 19591, 1910])).
% 293.01/185.54 tff(19596,plain,
% 293.01/185.54 (((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_a, s5)) | m_user_v_req(c_e_h_3, c_u, s5))) <=> ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s5)) | m_user_v_req(c_e_h_3, c_u, s5))),
% 293.01/185.54 inference(rewrite,[status(thm)],[])).
% 293.01/185.54 tff(19597,plain,
% 293.01/185.54 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_a, s5)) | m_user_v_req(c_e_h_3, c_u, s5))),
% 293.01/185.54 inference(quant_inst,[status(thm)],[])).
% 293.01/185.54 tff(19598,plain,
% 293.01/185.54 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s5)) | m_user_v_req(c_e_h_3, c_u, s5)),
% 293.01/185.54 inference(modus_ponens,[status(thm)],[19597, 19596])).
% 293.01/185.54 tff(19599,plain,
% 293.01/185.54 (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s5)),
% 293.01/185.54 inference(unit_resolution,[status(thm)],[19598, 395, 19563])).
% 293.01/185.54 tff(19600,assumption,(node12(c_e_h_3, c_a, s5, s6)), introduced(assumption)).
% 293.01/185.54 tff(19601,plain,
% 293.01/185.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_3, c_a, s5) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s6)) | (~node12(c_e_h_3, c_a, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s5) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s6)) | (~node12(c_e_h_3, c_a, s5, s6)))),
% 293.01/185.54 inference(rewrite,[status(thm)],[])).
% 293.01/185.54 tff(19602,plain,
% 293.01/185.54 (((~node12(c_e_h_3, c_a, s5, s6)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s5) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s6))) <=> (m_mutex_h_half_v_inp(c_e_h_3, c_a, s5) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s6)) | (~node12(c_e_h_3, c_a, s5, s6)))),
% 293.01/185.54 inference(rewrite,[status(thm)],[])).
% 293.01/185.54 tff(19603,plain,
% 293.01/185.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_a, s5, s6)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s5) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_3, c_a, s5) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s6)) | (~node12(c_e_h_3, c_a, s5, s6))))),
% 293.01/185.54 inference(monotonicity,[status(thm)],[19602])).
% 293.01/185.55 tff(19604,plain,
% 293.01/185.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_a, s5, s6)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s5) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s5) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s6)) | (~node12(c_e_h_3, c_a, s5, s6)))),
% 293.01/185.55 inference(transitivity,[status(thm)],[19603, 19601])).
% 293.01/185.55 tff(19605,plain,
% 293.01/185.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_a, s5, s6)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s5) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s6)))),
% 293.01/185.55 inference(quant_inst,[status(thm)],[])).
% 293.01/185.55 tff(19606,plain,
% 293.01/185.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s5) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s6)) | (~node12(c_e_h_3, c_a, s5, s6))),
% 293.01/185.55 inference(modus_ponens,[status(thm)],[19605, 19604])).
% 293.01/185.55 tff(19607,plain,
% 293.01/185.55 ($false),
% 293.01/185.55 inference(unit_resolution,[status(thm)],[19606, 454, 19600, 1946, 1433])).
% 293.01/185.55 tff(19608,plain,((~node12(c_e_h_3, c_a, s5, s6)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s6)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s5)), inference(lemma,lemma(discharge,[]))).
% 293.01/185.55 tff(19609,plain,
% 293.01/185.55 (~node12(c_e_h_3, c_a, s5, s6)),
% 293.01/185.55 inference(unit_resolution,[status(thm)],[19608, 19595, 19599])).
% 293.01/185.55 tff(19610,plain,
% 293.01/185.55 (node13(c_e_h_3, c_a, s5, s6)),
% 293.01/185.55 inference(unit_resolution,[status(thm)],[1506, 19609])).
% 293.01/185.55 tff(19611,plain,
% 293.01/185.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s6)) | (~node13(c_e_h_3, c_a, s5, s6)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s6)) | (~node13(c_e_h_3, c_a, s5, s6)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s5))),
% 293.01/185.55 inference(rewrite,[status(thm)],[])).
% 293.01/185.55 tff(19612,plain,
% 293.01/185.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s6)) | (~node13(c_e_h_3, c_a, s5, s6)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s5))),
% 293.01/185.55 inference(quant_inst,[status(thm)],[])).
% 293.01/185.55 tff(19613,plain,
% 293.01/185.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s6)) | (~node13(c_e_h_3, c_a, s5, s6)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s5)),
% 293.01/185.55 inference(modus_ponens,[status(thm)],[19612, 19611])).
% 293.01/185.55 tff(19614,plain,
% 293.01/185.55 ($false),
% 293.01/185.55 inference(unit_resolution,[status(thm)],[19613, 423, 1493, 1448, 1946])).
% 293.01/185.55 tff(19615,plain,((~node13(c_e_h_3, c_a, s5, s6)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s5) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s6))), inference(lemma,lemma(discharge,[]))).
% 293.01/185.55 tff(19616,plain,
% 293.01/185.55 (m_mutex_h_half_v_out(c_e_h_3, c_a, s5)),
% 293.01/185.55 inference(unit_resolution,[status(thm)],[19615, 19610, 19595])).
% 293.01/185.55 tff(19617,plain,
% 293.01/185.55 (~node13(c_e_h_3, c_a, s4, s5)),
% 293.01/185.55 inference(unit_resolution,[status(thm)],[10197, 19616, 19569])).
% 293.01/185.55 tff(19618,plain,
% 293.01/185.55 (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s4)),
% 293.01/185.55 inference(unit_resolution,[status(thm)],[10214, 395, 19564])).
% 293.01/185.55 tff(19619,plain,
% 293.01/185.55 (~node12(c_e_h_3, c_a, s4, s5)),
% 293.01/185.55 inference(unit_resolution,[status(thm)],[10207, 19616, 19618])).
% 293.01/185.55 tff(19620,plain,
% 293.01/185.55 ($false),
% 293.01/185.55 inference(unit_resolution,[status(thm)],[1472, 19619, 19617])).
% 293.01/185.55 tff(19621,plain,(m_user_v_req(c_e_h_3, c_u, s7) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s7))), inference(lemma,lemma(discharge,[]))).
% 293.01/185.55 tff(19622,plain,
% 293.01/185.55 (m_user_v_req(c_e_h_3, c_u, s7)),
% 293.01/185.55 inference(unit_resolution,[status(thm)],[19621, 1910])).
% 293.01/185.55 tff(19623,plain,
% 293.01/185.55 (m_user_v_req(c_e_h_3, c_u, s8)),
% 293.01/185.55 inference(unit_resolution,[status(thm)],[2509, 19622])).
% 293.01/185.55 tff(19624,plain,
% 293.01/185.55 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s8)),
% 293.01/185.55 inference(unit_resolution,[status(thm)],[2014, 19623])).
% 293.01/185.55 tff(19625,plain,
% 293.01/185.55 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s7)),
% 293.01/185.55 inference(unit_resolution,[status(thm)],[1908, 19622])).
% 293.01/185.55 tff(19626,plain,
% 293.01/185.55 (m_mutex_h_half_v_out(c_e_h_3, c_a, s8)),
% 293.01/185.55 inference(unit_resolution,[status(thm)],[1944, 19625, 1910])).
% 293.01/185.55 tff(19627,plain,
% 293.01/185.55 ($false),
% 293.01/185.55 inference(unit_resolution,[status(thm)],[2006, 19626, 19624, 1])).
% 293.01/185.55 tff(19628,plain,((~m_mutex_h_half_v_out(c_e_h_3, c_a, s7)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s9)), inference(lemma,lemma(discharge,[]))).
% 293.01/185.55 tff(19629,plain,
% 293.01/185.55 (m_mutex_h_half_v_out(c_e_h_3, c_a, s9)),
% 293.01/185.55 inference(unit_resolution,[status(thm)],[19628, 1910])).
% 293.01/185.55 tff(19630,assumption,(~m_mutex_h_half_v_out(c_e_h_3, c_a, s10)), introduced(assumption)).
% 293.01/185.55 tff(19631,assumption,(m_mutex_h_half_v_out(c_e_h_3, c_a, s9)), introduced(assumption)).
% 293.01/185.55 tff(19632,assumption,(node13(c_e_h_3, c_a, s9, s10)), introduced(assumption)).
% 293.01/185.55 tff(19633,plain,
% 293.01/185.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | ((~node13(c_e_h_3, c_a, s9, s10)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s10) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (~node13(c_e_h_3, c_a, s9, s10)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s10) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s9)))),
% 293.01/185.55 inference(rewrite,[status(thm)],[])).
% 293.01/185.55 tff(19634,plain,
% 293.01/185.55 ((m_mutex_h_half_v_out(c_e_h_3, c_a, s10) | (~node13(c_e_h_3, c_a, s9, s10)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s9))) <=> ((~node13(c_e_h_3, c_a, s9, s10)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s10) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s9)))),
% 293.01/185.55 inference(rewrite,[status(thm)],[])).
% 293.01/185.55 tff(19635,plain,
% 293.01/185.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s10) | (~node13(c_e_h_3, c_a, s9, s10)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | ((~node13(c_e_h_3, c_a, s9, s10)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s10) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s9))))),
% 293.01/185.55 inference(monotonicity,[status(thm)],[19634])).
% 293.01/185.55 tff(19636,plain,
% 293.01/185.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s10) | (~node13(c_e_h_3, c_a, s9, s10)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (~node13(c_e_h_3, c_a, s9, s10)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s10) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s9)))),
% 293.01/185.55 inference(transitivity,[status(thm)],[19635, 19633])).
% 293.01/185.55 tff(19637,plain,
% 293.01/185.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s10) | (~node13(c_e_h_3, c_a, s9, s10)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s9)))),
% 293.01/185.55 inference(quant_inst,[status(thm)],[])).
% 293.01/185.55 tff(19638,plain,
% 293.01/185.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (~node13(c_e_h_3, c_a, s9, s10)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s10) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s9))),
% 293.01/185.55 inference(modus_ponens,[status(thm)],[19637, 19636])).
% 293.01/185.55 tff(19639,plain,
% 293.01/185.55 ($false),
% 293.01/185.55 inference(unit_resolution,[status(thm)],[19638, 1459, 19632, 19630, 19631])).
% 293.01/185.55 tff(19640,plain,((~node13(c_e_h_3, c_a, s9, s10)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s10) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s9))), inference(lemma,lemma(discharge,[]))).
% 293.01/185.55 tff(19641,plain,
% 293.01/185.55 (~node13(c_e_h_3, c_a, s9, s10)),
% 293.01/185.55 inference(unit_resolution,[status(thm)],[19640, 19631, 19630])).
% 293.01/185.55 tff(19642,plain,
% 293.01/185.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s9, s10)) | node12(c_e_h_3, c_a, s9, s10) | node13(c_e_h_3, c_a, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s9, s10)) | node12(c_e_h_3, c_a, s9, s10) | node13(c_e_h_3, c_a, s9, s10))),
% 293.01/185.55 inference(rewrite,[status(thm)],[])).
% 293.01/185.55 tff(19643,plain,
% 293.01/185.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s9, s10)) | node12(c_e_h_3, c_a, s9, s10) | node13(c_e_h_3, c_a, s9, s10))),
% 293.01/185.55 inference(quant_inst,[status(thm)],[])).
% 293.01/185.55 tff(19644,plain,
% 293.01/185.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s9, s10)) | node12(c_e_h_3, c_a, s9, s10) | node13(c_e_h_3, c_a, s9, s10)),
% 293.01/185.55 inference(modus_ponens,[status(thm)],[19643, 19642])).
% 293.01/185.55 tff(19645,plain,
% 293.01/185.55 (node12(c_e_h_3, c_a, s9, s10) | node13(c_e_h_3, c_a, s9, s10)),
% 293.01/185.55 inference(unit_resolution,[status(thm)],[19644, 439, 7676])).
% 293.01/185.55 tff(19646,plain,
% 293.01/185.55 (node12(c_e_h_3, c_a, s9, s10)),
% 293.01/185.55 inference(unit_resolution,[status(thm)],[19645, 19641])).
% 293.01/185.55 tff(19647,assumption,(m_mutex_h_half_v_inp(c_e_h_3, c_a, s9)), introduced(assumption)).
% 293.01/185.55 tff(19648,assumption,(node12(c_e_h_3, c_a, s9, s10)), introduced(assumption)).
% 293.01/185.55 tff(19649,plain,
% 293.01/185.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_a, s9)) | (~node12(c_e_h_3, c_a, s9, s10)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s9)) | (~node12(c_e_h_3, c_a, s9, s10)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s10))),
% 293.01/185.55 inference(rewrite,[status(thm)],[])).
% 293.01/185.55 tff(19650,plain,
% 293.01/185.55 (((~node12(c_e_h_3, c_a, s9, s10)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s9)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s10)) <=> ((~m_mutex_h_half_v_inp(c_e_h_3, c_a, s9)) | (~node12(c_e_h_3, c_a, s9, s10)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s10))),
% 293.01/185.55 inference(rewrite,[status(thm)],[])).
% 293.01/185.55 tff(19651,plain,
% 293.01/185.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_3, c_a, s9, s10)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s9)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_a, s9)) | (~node12(c_e_h_3, c_a, s9, s10)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s10)))),
% 293.01/185.55 inference(monotonicity,[status(thm)],[19650])).
% 293.01/185.55 tff(19652,plain,
% 293.01/185.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_3, c_a, s9, s10)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s9)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s9)) | (~node12(c_e_h_3, c_a, s9, s10)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s10))),
% 293.01/185.55 inference(transitivity,[status(thm)],[19651, 19649])).
% 293.01/185.55 tff(19653,plain,
% 293.01/185.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_3, c_a, s9, s10)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s9)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s10))),
% 293.01/185.55 inference(quant_inst,[status(thm)],[])).
% 293.01/185.56 tff(19654,plain,
% 293.01/185.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s9)) | (~node12(c_e_h_3, c_a, s9, s10)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s10)),
% 293.01/185.56 inference(modus_ponens,[status(thm)],[19653, 19652])).
% 293.01/185.56 tff(19655,plain,
% 293.01/185.56 ($false),
% 293.01/185.56 inference(unit_resolution,[status(thm)],[19654, 1483, 19648, 19630, 19647])).
% 293.01/185.56 tff(19656,plain,((~node12(c_e_h_3, c_a, s9, s10)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s10) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s9))), inference(lemma,lemma(discharge,[]))).
% 293.01/185.56 tff(19657,plain,
% 293.01/185.56 (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s9)),
% 293.01/185.56 inference(unit_resolution,[status(thm)],[19656, 19646, 19630])).
% 293.01/185.56 tff(19658,assumption,(~m_mutex_h_half_v_inp(c_e_h_3, c_a, s9)), introduced(assumption)).
% 293.01/185.56 tff(19659,assumption,(m_user_v_req(c_e_h_3, c_u, s9)), introduced(assumption)).
% 293.01/185.56 tff(19660,plain,
% 293.01/185.56 (((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | ((~m_user_v_req(c_e_h_3, c_u, s9)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s9))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | (~m_user_v_req(c_e_h_3, c_u, s9)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s9))),
% 293.01/185.56 inference(rewrite,[status(thm)],[])).
% 293.01/185.56 tff(19661,plain,
% 293.01/185.56 ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | ((~m_user_v_req(c_e_h_3, c_u, s9)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s9))),
% 293.01/185.56 inference(quant_inst,[status(thm)],[])).
% 293.01/185.56 tff(19662,plain,
% 293.01/185.56 ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | (~m_user_v_req(c_e_h_3, c_u, s9)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s9)),
% 293.01/185.56 inference(modus_ponens,[status(thm)],[19661, 19660])).
% 293.01/185.56 tff(19663,plain,
% 293.01/185.56 ($false),
% 293.01/185.56 inference(unit_resolution,[status(thm)],[19662, 1426, 19659, 19658])).
% 293.01/185.56 tff(19664,plain,((~m_user_v_req(c_e_h_3, c_u, s9)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s9)), inference(lemma,lemma(discharge,[]))).
% 293.01/185.56 tff(19665,plain,
% 293.01/185.56 (~m_user_v_req(c_e_h_3, c_u, s9)),
% 293.01/185.56 inference(unit_resolution,[status(thm)],[19664, 19657])).
% 293.01/185.56 tff(19666,assumption,(~m_user_v_ack(c_e_h_3, c_u, s8)), introduced(assumption)).
% 293.01/185.56 tff(19667,assumption,(~m_user_v_req(c_e_h_3, c_u, s9)), introduced(assumption)).
% 293.01/185.56 tff(19668,assumption,(node7(c_e_h_3, c_u, s8, s9)), introduced(assumption)).
% 293.01/185.56 tff(19669,plain,
% 293.01/185.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | ((~node7(c_e_h_3, c_u, s8, s9)) | m_user_v_ack(c_e_h_3, c_u, s8) | m_user_v_req(c_e_h_3, c_u, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | (~node7(c_e_h_3, c_u, s8, s9)) | m_user_v_ack(c_e_h_3, c_u, s8) | m_user_v_req(c_e_h_3, c_u, s9))),
% 293.01/185.56 inference(rewrite,[status(thm)],[])).
% 293.01/185.56 tff(19670,plain,
% 293.01/185.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | ((~node7(c_e_h_3, c_u, s8, s9)) | m_user_v_ack(c_e_h_3, c_u, s8) | m_user_v_req(c_e_h_3, c_u, s9))),
% 293.01/185.56 inference(quant_inst,[status(thm)],[])).
% 293.01/185.56 tff(19671,plain,
% 293.01/185.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | (~node7(c_e_h_3, c_u, s8, s9)) | m_user_v_ack(c_e_h_3, c_u, s8) | m_user_v_req(c_e_h_3, c_u, s9)),
% 293.01/185.56 inference(modus_ponens,[status(thm)],[19670, 19669])).
% 293.01/185.56 tff(19672,plain,
% 293.01/185.56 ($false),
% 293.01/185.56 inference(unit_resolution,[status(thm)],[19671, 284, 19666, 19668, 19667])).
% 293.01/185.56 tff(19673,plain,((~node7(c_e_h_3, c_u, s8, s9)) | m_user_v_ack(c_e_h_3, c_u, s8) | m_user_v_req(c_e_h_3, c_u, s9)), inference(lemma,lemma(discharge,[]))).
% 293.01/185.56 tff(19674,plain,
% 293.01/185.56 (~node7(c_e_h_3, c_u, s8, s9)),
% 293.01/185.56 inference(unit_resolution,[status(thm)],[19673, 19667, 19666])).
% 293.01/185.56 tff(19675,assumption,(node8(c_e_h_3, c_u, s8, s9)), introduced(assumption)).
% 293.01/185.56 tff(19676,plain,
% 293.01/185.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_3, c_u, s9) | (~node8(c_e_h_3, c_u, s8, s9)) | (~m_user_v_req(c_e_h_3, c_u, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | m_user_v_req(c_e_h_3, c_u, s9) | (~node8(c_e_h_3, c_u, s8, s9)) | (~m_user_v_req(c_e_h_3, c_u, s8)))),
% 293.01/185.56 inference(rewrite,[status(thm)],[])).
% 293.01/185.56 tff(19677,plain,
% 293.01/185.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_3, c_u, s9) | (~node8(c_e_h_3, c_u, s8, s9)) | (~m_user_v_req(c_e_h_3, c_u, s8)))),
% 293.01/185.56 inference(quant_inst,[status(thm)],[])).
% 293.01/185.56 tff(19678,plain,
% 293.01/185.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | m_user_v_req(c_e_h_3, c_u, s9) | (~node8(c_e_h_3, c_u, s8, s9)) | (~m_user_v_req(c_e_h_3, c_u, s8))),
% 293.01/185.56 inference(modus_ponens,[status(thm)],[19677, 19676])).
% 293.01/185.56 tff(19679,plain,
% 293.01/185.56 ($false),
% 293.01/185.56 inference(unit_resolution,[status(thm)],[19678, 302, 19675, 2009, 19667])).
% 293.01/185.56 tff(19680,plain,((~node8(c_e_h_3, c_u, s8, s9)) | (~m_user_v_req(c_e_h_3, c_u, s8)) | m_user_v_req(c_e_h_3, c_u, s9)), inference(lemma,lemma(discharge,[]))).
% 293.01/185.56 tff(19681,plain,
% 293.01/185.56 (~node8(c_e_h_3, c_u, s8, s9)),
% 293.01/185.56 inference(unit_resolution,[status(thm)],[19680, 19667, 2009])).
% 293.01/185.56 tff(19682,plain,
% 293.01/185.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | ((~trans(s8, s9)) | node7(c_e_h_3, c_u, s8, s9) | node8(c_e_h_3, c_u, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | (~trans(s8, s9)) | node7(c_e_h_3, c_u, s8, s9) | node8(c_e_h_3, c_u, s8, s9))),
% 293.01/185.56 inference(rewrite,[status(thm)],[])).
% 293.01/185.56 tff(19683,plain,
% 293.01/185.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | ((~trans(s8, s9)) | node7(c_e_h_3, c_u, s8, s9) | node8(c_e_h_3, c_u, s8, s9))),
% 293.01/185.56 inference(quant_inst,[status(thm)],[])).
% 293.01/185.56 tff(19684,plain,
% 293.01/185.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | (~trans(s8, s9)) | node7(c_e_h_3, c_u, s8, s9) | node8(c_e_h_3, c_u, s8, s9)),
% 293.01/185.56 inference(modus_ponens,[status(thm)],[19683, 19682])).
% 293.01/185.56 tff(19685,plain,
% 293.01/185.56 (node7(c_e_h_3, c_u, s8, s9) | node8(c_e_h_3, c_u, s8, s9)),
% 293.01/185.56 inference(unit_resolution,[status(thm)],[19684, 328, 1993])).
% 293.01/185.56 tff(19686,plain,
% 293.01/185.56 ($false),
% 293.01/185.56 inference(unit_resolution,[status(thm)],[19685, 19681, 19674])).
% 293.01/185.56 tff(19687,plain,(m_user_v_req(c_e_h_3, c_u, s9) | (~m_user_v_req(c_e_h_3, c_u, s8)) | m_user_v_ack(c_e_h_3, c_u, s8)), inference(lemma,lemma(discharge,[]))).
% 293.01/185.56 tff(19688,plain,
% 293.01/185.56 (m_user_v_req(c_e_h_3, c_u, s9) | (~m_user_v_req(c_e_h_3, c_u, s8))),
% 293.01/185.56 inference(unit_resolution,[status(thm)],[19687, 19523])).
% 293.01/185.56 tff(19689,plain,
% 293.01/185.56 (~m_user_v_req(c_e_h_3, c_u, s8)),
% 293.01/185.56 inference(unit_resolution,[status(thm)],[19688, 19665])).
% 293.01/185.56 tff(19690,plain,
% 293.01/185.56 (~m_user_v_req(c_e_h_3, c_u, s7)),
% 293.01/185.56 inference(unit_resolution,[status(thm)],[2509, 19689])).
% 293.01/185.56 tff(19691,plain,
% 293.01/185.56 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s7)),
% 293.01/185.56 inference(unit_resolution,[status(thm)],[19621, 19690])).
% 293.01/185.56 tff(19692,plain,
% 293.01/185.56 (((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_a, s7)) | m_user_v_req(c_e_h_3, c_u, s7))) <=> ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s7)) | m_user_v_req(c_e_h_3, c_u, s7))),
% 293.01/185.56 inference(rewrite,[status(thm)],[])).
% 293.01/185.56 tff(19693,plain,
% 293.01/185.56 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_a, s7)) | m_user_v_req(c_e_h_3, c_u, s7))),
% 293.01/185.56 inference(quant_inst,[status(thm)],[])).
% 293.01/185.56 tff(19694,plain,
% 293.01/185.56 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s7)) | m_user_v_req(c_e_h_3, c_u, s7)),
% 293.01/185.56 inference(modus_ponens,[status(thm)],[19693, 19692])).
% 293.01/185.56 tff(19695,plain,
% 293.01/185.56 (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s7)),
% 293.01/185.56 inference(unit_resolution,[status(thm)],[19694, 395, 19690])).
% 293.01/185.56 tff(19696,plain,
% 293.01/185.56 (((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_a, s8)) | m_user_v_req(c_e_h_3, c_u, s8))) <=> ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s8)) | m_user_v_req(c_e_h_3, c_u, s8))),
% 293.01/185.56 inference(rewrite,[status(thm)],[])).
% 293.01/185.56 tff(19697,plain,
% 293.01/185.56 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_a, s8)) | m_user_v_req(c_e_h_3, c_u, s8))),
% 293.01/185.56 inference(quant_inst,[status(thm)],[])).
% 293.01/185.56 tff(19698,plain,
% 293.01/185.56 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s8)) | m_user_v_req(c_e_h_3, c_u, s8)),
% 293.01/185.56 inference(modus_ponens,[status(thm)],[19697, 19696])).
% 293.01/185.56 tff(19699,plain,
% 293.01/185.56 (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s8)),
% 293.01/185.56 inference(unit_resolution,[status(thm)],[19698, 395, 19689])).
% 293.01/185.56 tff(19700,assumption,(node12(c_e_h_3, c_a, s8, s9)), introduced(assumption)).
% 293.01/185.56 tff(19701,plain,
% 293.01/185.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_3, c_a, s8) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s9)) | (~node12(c_e_h_3, c_a, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s8) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s9)) | (~node12(c_e_h_3, c_a, s8, s9)))),
% 293.01/185.56 inference(rewrite,[status(thm)],[])).
% 293.01/185.56 tff(19702,plain,
% 293.01/185.56 (((~node12(c_e_h_3, c_a, s8, s9)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s8) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s9))) <=> (m_mutex_h_half_v_inp(c_e_h_3, c_a, s8) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s9)) | (~node12(c_e_h_3, c_a, s8, s9)))),
% 293.01/185.56 inference(rewrite,[status(thm)],[])).
% 293.01/185.56 tff(19703,plain,
% 293.01/185.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_a, s8, s9)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s8) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_3, c_a, s8) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s9)) | (~node12(c_e_h_3, c_a, s8, s9))))),
% 293.01/185.56 inference(monotonicity,[status(thm)],[19702])).
% 293.01/185.56 tff(19704,plain,
% 293.01/185.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_a, s8, s9)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s8) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s8) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s9)) | (~node12(c_e_h_3, c_a, s8, s9)))),
% 293.01/185.56 inference(transitivity,[status(thm)],[19703, 19701])).
% 293.01/185.56 tff(19705,plain,
% 293.01/185.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_a, s8, s9)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s8) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s9)))),
% 293.01/185.56 inference(quant_inst,[status(thm)],[])).
% 293.01/185.56 tff(19706,plain,
% 293.01/185.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s8) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s9)) | (~node12(c_e_h_3, c_a, s8, s9))),
% 293.01/185.56 inference(modus_ponens,[status(thm)],[19705, 19704])).
% 293.01/185.56 tff(19707,plain,
% 293.01/185.56 ($false),
% 293.01/185.56 inference(unit_resolution,[status(thm)],[19706, 454, 19700, 19631, 2008])).
% 293.01/185.57 tff(19708,plain,((~node12(c_e_h_3, c_a, s8, s9)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s9)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s8)), inference(lemma,lemma(discharge,[]))).
% 293.01/185.57 tff(19709,plain,
% 293.01/185.57 (~node12(c_e_h_3, c_a, s8, s9)),
% 293.01/185.57 inference(unit_resolution,[status(thm)],[19708, 19631, 2008])).
% 293.01/185.57 tff(19710,plain,
% 293.01/185.57 (node13(c_e_h_3, c_a, s8, s9)),
% 293.01/185.57 inference(unit_resolution,[status(thm)],[1997, 19709])).
% 293.01/185.57 tff(19711,plain,
% 293.01/185.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s9)) | (~node13(c_e_h_3, c_a, s8, s9)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s9)) | (~node13(c_e_h_3, c_a, s8, s9)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s8))),
% 293.01/185.57 inference(rewrite,[status(thm)],[])).
% 293.01/185.57 tff(19712,plain,
% 293.01/185.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s9)) | (~node13(c_e_h_3, c_a, s8, s9)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s8))),
% 293.01/185.57 inference(quant_inst,[status(thm)],[])).
% 293.01/185.57 tff(19713,plain,
% 293.01/185.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s9)) | (~node13(c_e_h_3, c_a, s8, s9)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s8)),
% 293.01/185.57 inference(modus_ponens,[status(thm)],[19712, 19711])).
% 293.01/185.57 tff(19714,plain,
% 293.01/185.57 ($false),
% 293.01/185.57 inference(unit_resolution,[status(thm)],[19713, 423, 19710, 1517, 19631])).
% 293.01/185.57 tff(19715,plain,((~m_mutex_h_half_v_out(c_e_h_3, c_a, s9)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s8) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s8)), inference(lemma,lemma(discharge,[]))).
% 293.01/185.57 tff(19716,plain,
% 293.01/185.57 (m_mutex_h_half_v_out(c_e_h_3, c_a, s8)),
% 293.01/185.57 inference(unit_resolution,[status(thm)],[19715, 19699, 19631])).
% 293.01/185.57 tff(19717,plain,
% 293.01/185.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_3, c_a, s7) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s8)) | (~node12(c_e_h_3, c_a, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s7) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s8)) | (~node12(c_e_h_3, c_a, s7, s8)))),
% 293.01/185.57 inference(rewrite,[status(thm)],[])).
% 293.01/185.57 tff(19718,plain,
% 293.01/185.57 (((~node12(c_e_h_3, c_a, s7, s8)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s7) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s8))) <=> (m_mutex_h_half_v_inp(c_e_h_3, c_a, s7) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s8)) | (~node12(c_e_h_3, c_a, s7, s8)))),
% 293.01/185.57 inference(rewrite,[status(thm)],[])).
% 293.01/185.57 tff(19719,plain,
% 293.01/185.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_a, s7, s8)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s7) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_3, c_a, s7) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s8)) | (~node12(c_e_h_3, c_a, s7, s8))))),
% 293.01/185.57 inference(monotonicity,[status(thm)],[19718])).
% 293.01/185.57 tff(19720,plain,
% 293.01/185.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_a, s7, s8)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s7) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s7) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s8)) | (~node12(c_e_h_3, c_a, s7, s8)))),
% 293.01/185.57 inference(transitivity,[status(thm)],[19719, 19717])).
% 293.01/185.57 tff(19721,plain,
% 293.01/185.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_a, s7, s8)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s7) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s8)))),
% 293.01/185.57 inference(quant_inst,[status(thm)],[])).
% 293.01/185.57 tff(19722,plain,
% 293.01/185.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s7) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s8)) | (~node12(c_e_h_3, c_a, s7, s8))),
% 293.01/185.57 inference(modus_ponens,[status(thm)],[19721, 19720])).
% 293.01/185.57 tff(19723,plain,
% 293.01/185.57 ($false),
% 293.01/185.57 inference(unit_resolution,[status(thm)],[19722, 454, 1922, 1976, 1902])).
% 293.01/185.57 tff(19724,plain,((~node12(c_e_h_3, c_a, s7, s8)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s8)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s7)), inference(lemma,lemma(discharge,[]))).
% 293.01/185.57 tff(19725,plain,
% 293.01/185.57 (~node12(c_e_h_3, c_a, s7, s8)),
% 293.01/185.57 inference(unit_resolution,[status(thm)],[19724, 1976, 1902])).
% 293.01/185.57 tff(19726,plain,
% 293.01/185.57 (node13(c_e_h_3, c_a, s7, s8)),
% 293.01/185.57 inference(unit_resolution,[status(thm)],[1942, 19725])).
% 293.01/185.57 tff(19727,plain,
% 293.01/185.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s8)) | (~node13(c_e_h_3, c_a, s7, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s8)) | (~node13(c_e_h_3, c_a, s7, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s7))),
% 293.01/185.57 inference(rewrite,[status(thm)],[])).
% 293.01/185.57 tff(19728,plain,
% 293.01/185.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s8)) | (~node13(c_e_h_3, c_a, s7, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s7))),
% 293.01/185.57 inference(quant_inst,[status(thm)],[])).
% 293.01/185.57 tff(19729,plain,
% 293.01/185.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s8)) | (~node13(c_e_h_3, c_a, s7, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s7)),
% 293.01/185.57 inference(modus_ponens,[status(thm)],[19728, 19727])).
% 293.01/185.57 tff(19730,plain,
% 293.01/185.57 ($false),
% 293.01/185.57 inference(unit_resolution,[status(thm)],[19729, 423, 19726, 1976, 1947])).
% 293.01/185.57 tff(19731,plain,((~m_mutex_h_half_v_out(c_e_h_3, c_a, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s7) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s7)), inference(lemma,lemma(discharge,[]))).
% 293.01/185.57 tff(19732,plain,
% 293.01/185.57 ($false),
% 293.01/185.57 inference(unit_resolution,[status(thm)],[19731, 19716, 19695, 19691])).
% 293.01/185.57 tff(19733,plain,((~m_mutex_h_half_v_out(c_e_h_3, c_a, s9)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s10)), inference(lemma,lemma(discharge,[]))).
% 293.01/185.57 tff(19734,plain,
% 293.01/185.57 (m_mutex_h_half_v_out(c_e_h_3, c_a, s10)),
% 293.01/185.57 inference(unit_resolution,[status(thm)],[19733, 19629])).
% 293.01/185.57 tff(19735,assumption,(m_mutex_h_half_v_out(c_e_h_3, c_a, s10)), introduced(assumption)).
% 293.01/185.57 tff(19736,plain,
% 293.01/185.57 (~m_user_v_req(c_e_h_3, c_u, s8)),
% 293.01/185.57 inference(unit_resolution,[status(thm)],[19688, 19667])).
% 293.01/185.57 tff(19737,plain,
% 293.01/185.57 (~m_user_v_req(c_e_h_3, c_u, s7)),
% 293.01/185.57 inference(unit_resolution,[status(thm)],[2509, 19736])).
% 293.01/185.57 tff(19738,plain,
% 293.01/185.57 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s7)),
% 293.01/185.57 inference(unit_resolution,[status(thm)],[19621, 19737])).
% 293.01/185.57 tff(19739,plain,
% 293.01/185.57 (m_mutex_h_half_v_out(c_e_h_3, c_a, s6)),
% 293.01/185.57 inference(unit_resolution,[status(thm)],[1515, 1439, 1489])).
% 293.01/185.57 tff(19740,plain,
% 293.01/185.57 ($false),
% 293.01/185.57 inference(unit_resolution,[status(thm)],[1971, 19739, 1432, 1947])).
% 293.01/185.57 tff(19741,plain,((~m_mutex_h_half_v_out(c_e_h_3, c_a, s4)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s7)), inference(lemma,lemma(discharge,[]))).
% 293.01/185.57 tff(19742,plain,
% 293.01/185.57 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s4)),
% 293.01/185.57 inference(unit_resolution,[status(thm)],[19741, 19738])).
% 293.01/185.57 tff(19743,plain,
% 293.01/185.57 ((~node7(c_e_h_3, c_u, s8, s9)) | m_user_v_req(c_e_h_3, c_u, s9)),
% 293.01/185.57 inference(unit_resolution,[status(thm)],[19673, 19523])).
% 293.01/185.57 tff(19744,plain,
% 293.01/185.57 (~node7(c_e_h_3, c_u, s8, s9)),
% 293.01/185.57 inference(unit_resolution,[status(thm)],[19743, 19667])).
% 293.01/185.57 tff(19745,plain,
% 293.01/185.57 (node8(c_e_h_3, c_u, s8, s9)),
% 293.01/185.57 inference(unit_resolution,[status(thm)],[19685, 19744])).
% 293.01/185.57 tff(19746,plain,
% 293.01/185.57 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl(((~m_user_v_req(I0, I1, Y)) | (~node8(I0, I1, X, Y)) | m_user_v_req(I0, I1, X)) <=> ((~m_user_v_req(I0, I1, Y)) | (~node8(I0, I1, X, Y)) | m_user_v_req(I0, I1, X)))),
% 293.01/185.57 inference(bind,[status(th)],[])).
% 293.01/185.57 tff(19747,plain,
% 293.01/185.57 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_user_v_req(I0, I1, Y)) | (~node8(I0, I1, X, Y)) | m_user_v_req(I0, I1, X)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_user_v_req(I0, I1, Y)) | (~node8(I0, I1, X, Y)) | m_user_v_req(I0, I1, X))),
% 293.01/185.57 inference(quant_intro,[status(thm)],[19746])).
% 293.01/185.57 tff(19748,plain,
% 293.01/185.57 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_user_v_req(I0, I1, Y)) | (~node8(I0, I1, X, Y)) | m_user_v_req(I0, I1, X)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_user_v_req(I0, I1, Y)) | (~node8(I0, I1, X, Y)) | m_user_v_req(I0, I1, X))),
% 293.01/185.57 inference(rewrite,[status(thm)],[])).
% 293.01/185.57 tff(19749,plain,
% 293.01/185.57 (^[Y: $i, I0: $i, X: $i, I1: $i] : rewrite((((~m_user_v_req(I0, I1, Y)) | m_user_v_req(I0, I1, X)) | (~node8(I0, I1, X, Y))) <=> ((~m_user_v_req(I0, I1, Y)) | (~node8(I0, I1, X, Y)) | m_user_v_req(I0, I1, X)))),
% 293.01/185.57 inference(bind,[status(th)],[])).
% 293.01/185.57 tff(19750,plain,
% 293.01/185.57 (![Y: $i, I0: $i, X: $i, I1: $i] : (((~m_user_v_req(I0, I1, Y)) | m_user_v_req(I0, I1, X)) | (~node8(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_user_v_req(I0, I1, Y)) | (~node8(I0, I1, X, Y)) | m_user_v_req(I0, I1, X))),
% 293.01/185.57 inference(quant_intro,[status(thm)],[19749])).
% 293.01/185.57 tff(19751,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : (((~m_user_v_req(I0, I1, Y)) | m_user_v_req(I0, I1, X)) | (~node8(I0, I1, X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_user_5')).
% 293.01/185.57 tff(19752,plain,
% 293.01/185.57 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_user_v_req(I0, I1, Y)) | (~node8(I0, I1, X, Y)) | m_user_v_req(I0, I1, X))),
% 293.01/185.57 inference(modus_ponens,[status(thm)],[19751, 19750])).
% 293.01/185.57 tff(19753,plain,
% 293.01/185.57 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_user_v_req(I0, I1, Y)) | (~node8(I0, I1, X, Y)) | m_user_v_req(I0, I1, X))),
% 293.01/185.57 inference(modus_ponens,[status(thm)],[19752, 19748])).
% 293.01/185.57 tff(19754,plain,(
% 293.01/185.57 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_user_v_req(I0, I1, Y)) | (~node8(I0, I1, X, Y)) | m_user_v_req(I0, I1, X))),
% 293.01/185.57 inference(skolemize,[status(sab)],[19753])).
% 293.01/185.57 tff(19755,plain,
% 293.01/185.57 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_user_v_req(I0, I1, Y)) | (~node8(I0, I1, X, Y)) | m_user_v_req(I0, I1, X))),
% 293.01/185.57 inference(modus_ponens,[status(thm)],[19754, 19747])).
% 293.01/185.57 tff(19756,plain,
% 293.01/185.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_user_v_req(I0, I1, Y)) | (~node8(I0, I1, X, Y)) | m_user_v_req(I0, I1, X))) | ((~m_user_v_req(c_e_h_3, c_u, s9)) | (~node8(c_e_h_3, c_u, s8, s9)) | m_user_v_req(c_e_h_3, c_u, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_user_v_req(I0, I1, Y)) | (~node8(I0, I1, X, Y)) | m_user_v_req(I0, I1, X))) | (~m_user_v_req(c_e_h_3, c_u, s9)) | (~node8(c_e_h_3, c_u, s8, s9)) | m_user_v_req(c_e_h_3, c_u, s8))),
% 293.01/185.57 inference(rewrite,[status(thm)],[])).
% 293.01/185.57 tff(19757,plain,
% 293.01/185.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_user_v_req(I0, I1, Y)) | (~node8(I0, I1, X, Y)) | m_user_v_req(I0, I1, X))) | ((~m_user_v_req(c_e_h_3, c_u, s9)) | (~node8(c_e_h_3, c_u, s8, s9)) | m_user_v_req(c_e_h_3, c_u, s8))),
% 293.01/185.57 inference(quant_inst,[status(thm)],[])).
% 293.01/185.57 tff(19758,plain,
% 293.01/185.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_user_v_req(I0, I1, Y)) | (~node8(I0, I1, X, Y)) | m_user_v_req(I0, I1, X))) | (~m_user_v_req(c_e_h_3, c_u, s9)) | (~node8(c_e_h_3, c_u, s8, s9)) | m_user_v_req(c_e_h_3, c_u, s8)),
% 293.01/185.57 inference(modus_ponens,[status(thm)],[19757, 19756])).
% 293.01/185.57 tff(19759,plain,
% 293.01/185.57 ((~m_user_v_req(c_e_h_3, c_u, s9)) | m_user_v_req(c_e_h_3, c_u, s8)),
% 293.01/185.57 inference(unit_resolution,[status(thm)],[19758, 19755, 19675])).
% 293.01/185.58 tff(19760,plain,
% 293.01/185.58 (~m_user_v_req(c_e_h_3, c_u, s9)),
% 293.01/185.58 inference(unit_resolution,[status(thm)],[19759, 2490])).
% 293.01/185.58 tff(19761,plain,
% 293.01/185.58 (((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_a, s9)) | m_user_v_req(c_e_h_3, c_u, s9))) <=> ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s9)) | m_user_v_req(c_e_h_3, c_u, s9))),
% 293.01/185.58 inference(rewrite,[status(thm)],[])).
% 293.01/185.58 tff(19762,plain,
% 293.01/185.58 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_a, s9)) | m_user_v_req(c_e_h_3, c_u, s9))),
% 293.01/185.58 inference(quant_inst,[status(thm)],[])).
% 293.01/185.58 tff(19763,plain,
% 293.01/185.58 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s9)) | m_user_v_req(c_e_h_3, c_u, s9)),
% 293.01/185.58 inference(modus_ponens,[status(thm)],[19762, 19761])).
% 293.01/185.58 tff(19764,plain,
% 293.01/185.58 (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s9)),
% 293.01/185.58 inference(unit_resolution,[status(thm)],[19763, 395, 19760])).
% 293.01/185.58 tff(19765,plain,
% 293.01/185.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_3, c_a, s9) | (~node12(c_e_h_3, c_a, s9, s10)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s9) | (~node12(c_e_h_3, c_a, s9, s10)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s10)))),
% 293.01/185.58 inference(rewrite,[status(thm)],[])).
% 293.01/185.58 tff(19766,plain,
% 293.01/185.58 (((~node12(c_e_h_3, c_a, s9, s10)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s9) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s10))) <=> (m_mutex_h_half_v_inp(c_e_h_3, c_a, s9) | (~node12(c_e_h_3, c_a, s9, s10)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s10)))),
% 293.01/185.58 inference(rewrite,[status(thm)],[])).
% 293.01/185.58 tff(19767,plain,
% 293.01/185.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_a, s9, s10)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s9) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_3, c_a, s9) | (~node12(c_e_h_3, c_a, s9, s10)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s10))))),
% 293.01/185.58 inference(monotonicity,[status(thm)],[19766])).
% 293.01/185.58 tff(19768,plain,
% 293.01/185.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_a, s9, s10)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s9) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s9) | (~node12(c_e_h_3, c_a, s9, s10)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s10)))),
% 293.01/185.58 inference(transitivity,[status(thm)],[19767, 19765])).
% 293.01/185.58 tff(19769,plain,
% 293.01/185.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_3, c_a, s9, s10)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s9) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s10)))),
% 293.01/185.58 inference(quant_inst,[status(thm)],[])).
% 293.01/185.58 tff(19770,plain,
% 293.01/185.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s9) | (~node12(c_e_h_3, c_a, s9, s10)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s10))),
% 293.01/185.58 inference(modus_ponens,[status(thm)],[19769, 19768])).
% 293.01/185.58 tff(19771,plain,
% 293.01/185.58 ($false),
% 293.01/185.58 inference(unit_resolution,[status(thm)],[19770, 454, 19648, 19735, 19658])).
% 293.01/185.58 tff(19772,plain,((~node12(c_e_h_3, c_a, s9, s10)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s10)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s9)), inference(lemma,lemma(discharge,[]))).
% 293.01/185.58 tff(19773,plain,
% 293.01/185.58 (~node12(c_e_h_3, c_a, s9, s10)),
% 293.01/185.58 inference(unit_resolution,[status(thm)],[19772, 19764, 19735])).
% 293.01/185.58 tff(19774,plain,
% 293.01/185.58 (node13(c_e_h_3, c_a, s9, s10)),
% 293.01/185.58 inference(unit_resolution,[status(thm)],[19645, 19773])).
% 293.01/185.58 tff(19775,plain,
% 293.01/185.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s10)) | (~node13(c_e_h_3, c_a, s9, s10)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s10)) | (~node13(c_e_h_3, c_a, s9, s10)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s9))),
% 293.01/185.58 inference(rewrite,[status(thm)],[])).
% 293.01/185.58 tff(19776,plain,
% 293.01/185.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s10)) | (~node13(c_e_h_3, c_a, s9, s10)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s9))),
% 293.01/185.58 inference(quant_inst,[status(thm)],[])).
% 293.01/185.58 tff(19777,plain,
% 293.01/185.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s10)) | (~node13(c_e_h_3, c_a, s9, s10)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s9)),
% 293.01/185.58 inference(modus_ponens,[status(thm)],[19776, 19775])).
% 293.01/185.58 tff(19778,plain,
% 293.01/185.58 ($false),
% 293.01/185.58 inference(unit_resolution,[status(thm)],[19777, 423, 19632, 19735, 1])).
% 293.01/185.58 tff(19779,plain,((~node13(c_e_h_3, c_a, s9, s10)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s10)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s9)), inference(lemma,lemma(discharge,[]))).
% 293.01/185.58 tff(19780,plain,
% 293.01/185.58 (m_mutex_h_half_v_out(c_e_h_3, c_a, s9)),
% 293.01/185.58 inference(unit_resolution,[status(thm)],[19779, 19774, 19735])).
% 293.01/185.58 tff(19781,plain,
% 293.01/185.58 (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s8)),
% 293.01/185.58 inference(unit_resolution,[status(thm)],[19698, 395, 2490])).
% 293.01/185.58 tff(19782,plain,
% 293.01/185.58 (~node12(c_e_h_3, c_a, s8, s9)),
% 293.01/185.58 inference(unit_resolution,[status(thm)],[19708, 19780, 19781])).
% 293.01/185.58 tff(19783,plain,
% 293.01/185.58 (node13(c_e_h_3, c_a, s8, s9)),
% 293.01/185.58 inference(unit_resolution,[status(thm)],[1997, 19782])).
% 293.01/185.58 tff(19784,plain,
% 293.01/185.58 (m_mutex_h_half_v_out(c_e_h_3, c_a, s8)),
% 293.01/185.58 inference(unit_resolution,[status(thm)],[19713, 423, 19783, 19780])).
% 293.01/185.58 tff(19785,plain,
% 293.01/185.58 (~m_user_v_req(c_e_h_3, c_u, s7)),
% 293.01/185.58 inference(unit_resolution,[status(thm)],[2508, 2490, 2503])).
% 293.01/185.58 tff(19786,plain,
% 293.01/185.58 (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s7)),
% 293.01/185.58 inference(unit_resolution,[status(thm)],[19694, 395, 19785])).
% 293.01/185.58 tff(19787,plain,
% 293.01/185.58 (~node12(c_e_h_3, c_a, s7, s8)),
% 293.01/185.58 inference(unit_resolution,[status(thm)],[19724, 19784, 19786])).
% 293.01/185.58 tff(19788,plain,
% 293.01/185.58 (node13(c_e_h_3, c_a, s7, s8)),
% 293.01/185.58 inference(unit_resolution,[status(thm)],[1942, 19787])).
% 293.01/185.58 tff(19789,plain,
% 293.01/185.58 (m_mutex_h_half_v_out(c_e_h_3, c_a, s7)),
% 293.01/185.58 inference(unit_resolution,[status(thm)],[19729, 423, 19788, 19784])).
% 293.01/185.58 tff(19790,plain,
% 293.01/185.58 (~node7(c_e_h_3, c_u, s6, s7)),
% 293.01/185.58 inference(unit_resolution,[status(thm)],[19574, 19785])).
% 293.01/185.58 tff(19791,plain,
% 293.01/185.58 (node8(c_e_h_3, c_u, s6, s7)),
% 293.01/185.58 inference(unit_resolution,[status(thm)],[1848, 19790])).
% 293.01/185.58 tff(19792,plain,
% 293.01/185.58 (~m_user_v_req(c_e_h_3, c_u, s6)),
% 293.01/185.58 inference(unit_resolution,[status(thm)],[1836, 19791, 19785])).
% 293.01/185.58 tff(19793,plain,
% 293.01/185.58 (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s6)),
% 293.01/185.58 inference(unit_resolution,[status(thm)],[19580, 395, 19792])).
% 293.01/185.58 tff(19794,plain,
% 293.01/185.58 (~node12(c_e_h_3, c_a, s6, s7)),
% 293.01/185.58 inference(unit_resolution,[status(thm)],[19589, 19793, 19789])).
% 293.01/185.58 tff(19795,plain,
% 293.01/185.58 (node13(c_e_h_3, c_a, s6, s7)),
% 293.01/185.58 inference(unit_resolution,[status(thm)],[1962, 19794])).
% 293.01/185.58 tff(19796,plain,
% 293.01/185.58 (m_mutex_h_half_v_out(c_e_h_3, c_a, s6)),
% 293.01/185.58 inference(unit_resolution,[status(thm)],[19594, 423, 19795, 19789])).
% 293.01/185.58 tff(19797,plain,
% 293.01/185.58 (~m_user_v_req(c_e_h_3, c_u, s5)),
% 293.01/185.58 inference(unit_resolution,[status(thm)],[1900, 19785])).
% 293.01/185.58 tff(19798,plain,
% 293.01/185.58 (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s5)),
% 293.01/185.58 inference(unit_resolution,[status(thm)],[19598, 395, 19797])).
% 293.01/185.58 tff(19799,plain,
% 293.01/185.58 (~node13(c_e_h_3, c_a, s5, s6)),
% 293.01/185.58 inference(unit_resolution,[status(thm)],[19615, 19796, 1448])).
% 293.01/185.58 tff(19800,plain,
% 293.01/185.58 (node12(c_e_h_3, c_a, s5, s6)),
% 293.01/185.58 inference(unit_resolution,[status(thm)],[1506, 19799])).
% 293.01/185.58 tff(19801,plain,
% 293.01/185.58 ($false),
% 293.01/185.58 inference(unit_resolution,[status(thm)],[19606, 454, 19800, 19798, 19796])).
% 293.01/185.58 tff(19802,plain,(m_user_v_req(c_e_h_3, c_u, s8) | m_mutex_h_half_v_out(c_e_h_3, c_a, s5) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s10)) | (~node8(c_e_h_3, c_u, s8, s9)) | m_user_v_ack(c_e_h_3, c_u, s7)), inference(lemma,lemma(discharge,[]))).
% 293.01/185.58 tff(19803,plain,
% 293.01/185.58 (m_user_v_req(c_e_h_3, c_u, s8) | m_mutex_h_half_v_out(c_e_h_3, c_a, s5) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s10)) | (~node8(c_e_h_3, c_u, s8, s9))),
% 293.01/185.58 inference(unit_resolution,[status(thm)],[19802, 2489])).
% 293.01/185.58 tff(19804,plain,
% 293.01/185.58 (m_mutex_h_half_v_out(c_e_h_3, c_a, s5)),
% 293.01/185.58 inference(unit_resolution,[status(thm)],[19803, 19745, 19735, 19736])).
% 293.01/185.58 tff(19805,plain,
% 293.01/185.58 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s4)),
% 293.01/185.58 inference(unit_resolution,[status(thm)],[10210, 19804, 19742])).
% 293.01/185.58 tff(19806,plain,
% 293.01/185.58 (~m_user_v_req(c_e_h_3, c_u, s5)),
% 293.01/185.58 inference(unit_resolution,[status(thm)],[1900, 19737])).
% 293.01/185.58 tff(19807,plain,
% 293.01/185.58 (~m_user_v_req(c_e_h_3, c_u, s4)),
% 293.01/185.58 inference(unit_resolution,[status(thm)],[1035, 19806])).
% 293.01/185.58 tff(19808,plain,
% 293.01/185.58 ($false),
% 293.01/185.58 inference(unit_resolution,[status(thm)],[10214, 395, 19807, 19805])).
% 293.01/185.58 tff(19809,plain,(m_user_v_req(c_e_h_3, c_u, s9) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s10))), inference(lemma,lemma(discharge,[]))).
% 293.01/185.58 tff(19810,plain,
% 293.01/185.58 (m_user_v_req(c_e_h_3, c_u, s9)),
% 293.01/185.58 inference(unit_resolution,[status(thm)],[19809, 19735])).
% 293.01/185.58 tff(19811,assumption,(m_user_v_ack(c_e_h_3, c_u, s9)), introduced(assumption)).
% 293.01/185.58 tff(19812,plain,
% 293.01/185.58 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_3, c_u, s9)) | m_and_h_gate_v_out(c_e_h_3, c_r, s9))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_3, c_u, s9)) | m_and_h_gate_v_out(c_e_h_3, c_r, s9))),
% 293.01/185.58 inference(rewrite,[status(thm)],[])).
% 293.01/185.58 tff(19813,plain,
% 293.01/185.58 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_3, c_u, s9)) | m_and_h_gate_v_out(c_e_h_3, c_r, s9))),
% 293.01/185.58 inference(quant_inst,[status(thm)],[])).
% 293.01/185.58 tff(19814,plain,
% 293.01/185.58 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_3, c_u, s9)) | m_and_h_gate_v_out(c_e_h_3, c_r, s9)),
% 293.01/185.58 inference(modus_ponens,[status(thm)],[19813, 19812])).
% 293.01/185.58 tff(19815,plain,
% 293.01/185.58 ($false),
% 293.01/185.58 inference(unit_resolution,[status(thm)],[19814, 268, 19811, 12627])).
% 293.01/185.58 tff(19816,plain,((~m_user_v_ack(c_e_h_3, c_u, s9)) | m_and_h_gate_v_out(c_e_h_3, c_r, s9)), inference(lemma,lemma(discharge,[]))).
% 293.01/185.58 tff(19817,plain,
% 293.01/185.58 (~m_user_v_ack(c_e_h_3, c_u, s9)),
% 293.01/185.58 inference(unit_resolution,[status(thm)],[19816, 12617])).
% 293.01/185.58 tff(19818,assumption,(~m_user_v_ack(c_e_h_3, c_u, s9)), introduced(assumption)).
% 293.01/185.58 tff(19819,assumption,(~m_user_v_req(c_e_h_3, c_u, s11)), introduced(assumption)).
% 293.01/185.58 tff(19820,plain,
% 293.01/185.58 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_3, c_u, s10)) | m_and_h_gate_v_out(c_e_h_3, c_r, s10))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_3, c_u, s10)) | m_and_h_gate_v_out(c_e_h_3, c_r, s10))),
% 293.01/185.58 inference(rewrite,[status(thm)],[])).
% 293.01/185.58 tff(19821,plain,
% 293.01/185.58 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_3, c_u, s10)) | m_and_h_gate_v_out(c_e_h_3, c_r, s10))),
% 293.01/185.58 inference(quant_inst,[status(thm)],[])).
% 293.01/185.58 tff(19822,plain,
% 293.01/185.58 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_3, c_u, s10)) | m_and_h_gate_v_out(c_e_h_3, c_r, s10)),
% 293.09/185.59 inference(modus_ponens,[status(thm)],[19821, 19820])).
% 293.09/185.59 tff(19823,plain,
% 293.09/185.59 (~m_user_v_ack(c_e_h_3, c_u, s10)),
% 293.09/185.59 inference(unit_resolution,[status(thm)],[19822, 268, 12643])).
% 293.09/185.59 tff(19824,assumption,(m_user_v_req(c_e_h_3, c_u, s10)), introduced(assumption)).
% 293.09/185.59 tff(19825,assumption,(~m_user_v_ack(c_e_h_3, c_u, s10)), introduced(assumption)).
% 293.09/185.59 tff(19826,assumption,(node7(c_e_h_3, c_u, s10, s11)), introduced(assumption)).
% 293.09/185.59 tff(19827,plain,
% 293.09/185.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | ((~node7(c_e_h_3, c_u, s10, s11)) | m_user_v_ack(c_e_h_3, c_u, s10) | m_user_v_req(c_e_h_3, c_u, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | (~node7(c_e_h_3, c_u, s10, s11)) | m_user_v_ack(c_e_h_3, c_u, s10) | m_user_v_req(c_e_h_3, c_u, s11))),
% 293.09/185.59 inference(rewrite,[status(thm)],[])).
% 293.09/185.59 tff(19828,plain,
% 293.09/185.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | ((~node7(c_e_h_3, c_u, s10, s11)) | m_user_v_ack(c_e_h_3, c_u, s10) | m_user_v_req(c_e_h_3, c_u, s11))),
% 293.09/185.59 inference(quant_inst,[status(thm)],[])).
% 293.09/185.59 tff(19829,plain,
% 293.09/185.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | (~node7(c_e_h_3, c_u, s10, s11)) | m_user_v_ack(c_e_h_3, c_u, s10) | m_user_v_req(c_e_h_3, c_u, s11)),
% 293.09/185.59 inference(modus_ponens,[status(thm)],[19828, 19827])).
% 293.09/185.59 tff(19830,plain,
% 293.09/185.59 ($false),
% 293.09/185.59 inference(unit_resolution,[status(thm)],[19829, 284, 19825, 19826, 19819])).
% 293.09/185.59 tff(19831,plain,((~node7(c_e_h_3, c_u, s10, s11)) | m_user_v_ack(c_e_h_3, c_u, s10) | m_user_v_req(c_e_h_3, c_u, s11)), inference(lemma,lemma(discharge,[]))).
% 293.09/185.59 tff(19832,plain,
% 293.09/185.59 (~node7(c_e_h_3, c_u, s10, s11)),
% 293.09/185.59 inference(unit_resolution,[status(thm)],[19831, 19819, 19825])).
% 293.09/185.59 tff(19833,plain,
% 293.09/185.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | ((~trans(s10, s11)) | node7(c_e_h_3, c_u, s10, s11) | node8(c_e_h_3, c_u, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | (~trans(s10, s11)) | node7(c_e_h_3, c_u, s10, s11) | node8(c_e_h_3, c_u, s10, s11))),
% 293.09/185.59 inference(rewrite,[status(thm)],[])).
% 293.09/185.59 tff(19834,plain,
% 293.09/185.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | ((~trans(s10, s11)) | node7(c_e_h_3, c_u, s10, s11) | node8(c_e_h_3, c_u, s10, s11))),
% 293.09/185.59 inference(quant_inst,[status(thm)],[])).
% 293.09/185.59 tff(19835,plain,
% 293.09/185.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | (~trans(s10, s11)) | node7(c_e_h_3, c_u, s10, s11) | node8(c_e_h_3, c_u, s10, s11)),
% 293.09/185.59 inference(modus_ponens,[status(thm)],[19834, 19833])).
% 293.09/185.59 tff(19836,plain,
% 293.09/185.59 (node7(c_e_h_3, c_u, s10, s11) | node8(c_e_h_3, c_u, s10, s11)),
% 293.09/185.59 inference(unit_resolution,[status(thm)],[19835, 328, 7748])).
% 293.09/185.59 tff(19837,plain,
% 293.09/185.59 (node8(c_e_h_3, c_u, s10, s11)),
% 293.09/185.59 inference(unit_resolution,[status(thm)],[19836, 19832])).
% 293.09/185.59 tff(19838,plain,
% 293.09/185.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | ((~m_user_v_req(c_e_h_3, c_u, s10)) | m_user_v_req(c_e_h_3, c_u, s11) | (~node8(c_e_h_3, c_u, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (~m_user_v_req(c_e_h_3, c_u, s10)) | m_user_v_req(c_e_h_3, c_u, s11) | (~node8(c_e_h_3, c_u, s10, s11)))),
% 293.09/185.59 inference(rewrite,[status(thm)],[])).
% 293.09/185.59 tff(19839,plain,
% 293.09/185.59 ((m_user_v_req(c_e_h_3, c_u, s11) | (~node8(c_e_h_3, c_u, s10, s11)) | (~m_user_v_req(c_e_h_3, c_u, s10))) <=> ((~m_user_v_req(c_e_h_3, c_u, s10)) | m_user_v_req(c_e_h_3, c_u, s11) | (~node8(c_e_h_3, c_u, s10, s11)))),
% 293.09/185.59 inference(rewrite,[status(thm)],[])).
% 293.09/185.59 tff(19840,plain,
% 293.09/185.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_3, c_u, s11) | (~node8(c_e_h_3, c_u, s10, s11)) | (~m_user_v_req(c_e_h_3, c_u, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | ((~m_user_v_req(c_e_h_3, c_u, s10)) | m_user_v_req(c_e_h_3, c_u, s11) | (~node8(c_e_h_3, c_u, s10, s11))))),
% 293.09/185.59 inference(monotonicity,[status(thm)],[19839])).
% 293.09/185.59 tff(19841,plain,
% 293.09/185.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_3, c_u, s11) | (~node8(c_e_h_3, c_u, s10, s11)) | (~m_user_v_req(c_e_h_3, c_u, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (~m_user_v_req(c_e_h_3, c_u, s10)) | m_user_v_req(c_e_h_3, c_u, s11) | (~node8(c_e_h_3, c_u, s10, s11)))),
% 293.09/185.59 inference(transitivity,[status(thm)],[19840, 19838])).
% 293.09/185.59 tff(19842,plain,
% 293.09/185.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_3, c_u, s11) | (~node8(c_e_h_3, c_u, s10, s11)) | (~m_user_v_req(c_e_h_3, c_u, s10)))),
% 293.09/185.59 inference(quant_inst,[status(thm)],[])).
% 293.09/185.59 tff(19843,plain,
% 293.09/185.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (~m_user_v_req(c_e_h_3, c_u, s10)) | m_user_v_req(c_e_h_3, c_u, s11) | (~node8(c_e_h_3, c_u, s10, s11))),
% 293.09/185.59 inference(modus_ponens,[status(thm)],[19842, 19841])).
% 293.09/185.59 tff(19844,plain,
% 293.09/185.59 ($false),
% 293.09/185.59 inference(unit_resolution,[status(thm)],[19843, 302, 19837, 19824, 19819])).
% 293.09/185.59 tff(19845,plain,(m_user_v_req(c_e_h_3, c_u, s11) | (~m_user_v_req(c_e_h_3, c_u, s10)) | m_user_v_ack(c_e_h_3, c_u, s10)), inference(lemma,lemma(discharge,[]))).
% 293.09/185.59 tff(19846,plain,
% 293.09/185.59 (~m_user_v_req(c_e_h_3, c_u, s10)),
% 293.09/185.59 inference(unit_resolution,[status(thm)],[19845, 19823, 19819])).
% 293.09/185.59 tff(19847,assumption,(~m_user_v_req(c_e_h_3, c_u, s10)), introduced(assumption)).
% 293.09/185.59 tff(19848,assumption,(node7(c_e_h_3, c_u, s9, s10)), introduced(assumption)).
% 293.09/185.59 tff(19849,plain,
% 293.09/185.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | ((~node7(c_e_h_3, c_u, s9, s10)) | m_user_v_ack(c_e_h_3, c_u, s9) | m_user_v_req(c_e_h_3, c_u, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | (~node7(c_e_h_3, c_u, s9, s10)) | m_user_v_ack(c_e_h_3, c_u, s9) | m_user_v_req(c_e_h_3, c_u, s10))),
% 293.09/185.59 inference(rewrite,[status(thm)],[])).
% 293.09/185.59 tff(19850,plain,
% 293.09/185.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | ((~node7(c_e_h_3, c_u, s9, s10)) | m_user_v_ack(c_e_h_3, c_u, s9) | m_user_v_req(c_e_h_3, c_u, s10))),
% 293.09/185.59 inference(quant_inst,[status(thm)],[])).
% 293.09/185.59 tff(19851,plain,
% 293.09/185.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | (~node7(c_e_h_3, c_u, s9, s10)) | m_user_v_ack(c_e_h_3, c_u, s9) | m_user_v_req(c_e_h_3, c_u, s10)),
% 293.09/185.59 inference(modus_ponens,[status(thm)],[19850, 19849])).
% 293.09/185.59 tff(19852,plain,
% 293.09/185.59 ($false),
% 293.09/185.59 inference(unit_resolution,[status(thm)],[19851, 284, 19818, 19848, 19847])).
% 293.09/185.59 tff(19853,plain,((~node7(c_e_h_3, c_u, s9, s10)) | m_user_v_ack(c_e_h_3, c_u, s9) | m_user_v_req(c_e_h_3, c_u, s10)), inference(lemma,lemma(discharge,[]))).
% 293.09/185.59 tff(19854,plain,
% 293.09/185.59 (~node7(c_e_h_3, c_u, s9, s10)),
% 293.09/185.59 inference(unit_resolution,[status(thm)],[19853, 19846, 19818])).
% 293.09/185.59 tff(19855,assumption,(node8(c_e_h_3, c_u, s9, s10)), introduced(assumption)).
% 293.09/185.59 tff(19856,plain,
% 293.09/185.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | ((~m_user_v_req(c_e_h_3, c_u, s9)) | (~node8(c_e_h_3, c_u, s9, s10)) | m_user_v_req(c_e_h_3, c_u, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (~m_user_v_req(c_e_h_3, c_u, s9)) | (~node8(c_e_h_3, c_u, s9, s10)) | m_user_v_req(c_e_h_3, c_u, s10))),
% 293.09/185.59 inference(rewrite,[status(thm)],[])).
% 293.09/185.59 tff(19857,plain,
% 293.09/185.59 ((m_user_v_req(c_e_h_3, c_u, s10) | (~node8(c_e_h_3, c_u, s9, s10)) | (~m_user_v_req(c_e_h_3, c_u, s9))) <=> ((~m_user_v_req(c_e_h_3, c_u, s9)) | (~node8(c_e_h_3, c_u, s9, s10)) | m_user_v_req(c_e_h_3, c_u, s10))),
% 293.09/185.59 inference(rewrite,[status(thm)],[])).
% 293.09/185.59 tff(19858,plain,
% 293.09/185.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_3, c_u, s10) | (~node8(c_e_h_3, c_u, s9, s10)) | (~m_user_v_req(c_e_h_3, c_u, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | ((~m_user_v_req(c_e_h_3, c_u, s9)) | (~node8(c_e_h_3, c_u, s9, s10)) | m_user_v_req(c_e_h_3, c_u, s10)))),
% 293.09/185.59 inference(monotonicity,[status(thm)],[19857])).
% 293.09/185.59 tff(19859,plain,
% 293.09/185.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_3, c_u, s10) | (~node8(c_e_h_3, c_u, s9, s10)) | (~m_user_v_req(c_e_h_3, c_u, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (~m_user_v_req(c_e_h_3, c_u, s9)) | (~node8(c_e_h_3, c_u, s9, s10)) | m_user_v_req(c_e_h_3, c_u, s10))),
% 293.09/185.59 inference(transitivity,[status(thm)],[19858, 19856])).
% 293.09/185.59 tff(19860,plain,
% 293.09/185.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_3, c_u, s10) | (~node8(c_e_h_3, c_u, s9, s10)) | (~m_user_v_req(c_e_h_3, c_u, s9)))),
% 293.09/185.59 inference(quant_inst,[status(thm)],[])).
% 293.09/185.59 tff(19861,plain,
% 293.09/185.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (~m_user_v_req(c_e_h_3, c_u, s9)) | (~node8(c_e_h_3, c_u, s9, s10)) | m_user_v_req(c_e_h_3, c_u, s10)),
% 293.09/185.59 inference(modus_ponens,[status(thm)],[19860, 19859])).
% 293.09/185.59 tff(19862,plain,
% 293.09/185.59 ($false),
% 293.09/185.59 inference(unit_resolution,[status(thm)],[19861, 302, 19855, 19847, 19659])).
% 293.09/185.59 tff(19863,plain,((~node8(c_e_h_3, c_u, s9, s10)) | m_user_v_req(c_e_h_3, c_u, s10) | (~m_user_v_req(c_e_h_3, c_u, s9))), inference(lemma,lemma(discharge,[]))).
% 293.09/185.59 tff(19864,plain,
% 293.09/185.59 (~node8(c_e_h_3, c_u, s9, s10)),
% 293.09/185.59 inference(unit_resolution,[status(thm)],[19863, 19846, 19659])).
% 293.09/185.59 tff(19865,plain,
% 293.09/185.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | ((~trans(s9, s10)) | node7(c_e_h_3, c_u, s9, s10) | node8(c_e_h_3, c_u, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | (~trans(s9, s10)) | node7(c_e_h_3, c_u, s9, s10) | node8(c_e_h_3, c_u, s9, s10))),
% 293.09/185.59 inference(rewrite,[status(thm)],[])).
% 293.09/185.59 tff(19866,plain,
% 293.09/185.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | ((~trans(s9, s10)) | node7(c_e_h_3, c_u, s9, s10) | node8(c_e_h_3, c_u, s9, s10))),
% 293.09/185.59 inference(quant_inst,[status(thm)],[])).
% 293.09/185.59 tff(19867,plain,
% 293.09/185.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | (~trans(s9, s10)) | node7(c_e_h_3, c_u, s9, s10) | node8(c_e_h_3, c_u, s9, s10)),
% 293.09/185.59 inference(modus_ponens,[status(thm)],[19866, 19865])).
% 293.09/185.59 tff(19868,plain,
% 293.09/185.59 (node7(c_e_h_3, c_u, s9, s10) | node8(c_e_h_3, c_u, s9, s10)),
% 293.09/185.59 inference(unit_resolution,[status(thm)],[19867, 328, 7676])).
% 293.09/185.59 tff(19869,plain,
% 293.09/185.59 ($false),
% 293.09/185.59 inference(unit_resolution,[status(thm)],[19868, 19864, 19854])).
% 293.09/185.59 tff(19870,plain,(m_user_v_ack(c_e_h_3, c_u, s9) | (~m_user_v_req(c_e_h_3, c_u, s9)) | m_user_v_req(c_e_h_3, c_u, s11) | m_and_h_gate_v_out(c_e_h_3, c_r, s10)), inference(lemma,lemma(discharge,[]))).
% 293.09/185.59 tff(19871,plain,
% 293.09/185.59 ((~m_user_v_req(c_e_h_3, c_u, s9)) | m_user_v_req(c_e_h_3, c_u, s11) | m_and_h_gate_v_out(c_e_h_3, c_r, s10)),
% 293.09/185.59 inference(unit_resolution,[status(thm)],[19870, 19817])).
% 293.09/185.59 tff(19872,plain,
% 293.09/185.59 (m_user_v_req(c_e_h_3, c_u, s11)),
% 293.09/185.59 inference(unit_resolution,[status(thm)],[19871, 19810, 12643])).
% 293.09/185.60 tff(19873,assumption,(~m_mutex_h_half_v_out(c_e_h_3, c_a, s12)), introduced(assumption)).
% 293.09/185.60 tff(19874,assumption,(~m_mutex_h_half_v_out(c_e_h_3, c_a, s11)), introduced(assumption)).
% 293.09/185.60 tff(19875,assumption,(node13(c_e_h_3, c_a, s10, s11)), introduced(assumption)).
% 293.09/185.60 tff(19876,plain,
% 293.09/185.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s10)) | (~node13(c_e_h_3, c_a, s10, s11)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s10)) | (~node13(c_e_h_3, c_a, s10, s11)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s11))),
% 293.09/185.60 inference(rewrite,[status(thm)],[])).
% 293.09/185.60 tff(19877,plain,
% 293.09/185.60 ((m_mutex_h_half_v_out(c_e_h_3, c_a, s11) | (~node13(c_e_h_3, c_a, s10, s11)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s10))) <=> ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s10)) | (~node13(c_e_h_3, c_a, s10, s11)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s11))),
% 293.09/185.60 inference(rewrite,[status(thm)],[])).
% 293.09/185.60 tff(19878,plain,
% 293.09/185.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s11) | (~node13(c_e_h_3, c_a, s10, s11)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s10)) | (~node13(c_e_h_3, c_a, s10, s11)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s11)))),
% 293.09/185.60 inference(monotonicity,[status(thm)],[19877])).
% 293.09/185.60 tff(19879,plain,
% 293.09/185.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s11) | (~node13(c_e_h_3, c_a, s10, s11)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s10)) | (~node13(c_e_h_3, c_a, s10, s11)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s11))),
% 293.09/185.60 inference(transitivity,[status(thm)],[19878, 19876])).
% 293.09/185.60 tff(19880,plain,
% 293.09/185.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s11) | (~node13(c_e_h_3, c_a, s10, s11)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s10)))),
% 293.09/185.60 inference(quant_inst,[status(thm)],[])).
% 293.09/185.60 tff(19881,plain,
% 293.09/185.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s10)) | (~node13(c_e_h_3, c_a, s10, s11)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s11)),
% 293.09/185.60 inference(modus_ponens,[status(thm)],[19880, 19879])).
% 293.09/185.60 tff(19882,plain,
% 293.09/185.60 ($false),
% 293.09/185.60 inference(unit_resolution,[status(thm)],[19881, 1459, 19875, 19874, 19735])).
% 293.09/185.60 tff(19883,plain,((~node13(c_e_h_3, c_a, s10, s11)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s11) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s10))), inference(lemma,lemma(discharge,[]))).
% 293.09/185.60 tff(19884,plain,
% 293.09/185.60 (~node13(c_e_h_3, c_a, s10, s11)),
% 293.09/185.60 inference(unit_resolution,[status(thm)],[19883, 19874, 19735])).
% 293.09/185.60 tff(19885,plain,
% 293.09/185.60 (~node7(c_e_h_3, c_u, s9, s10)),
% 293.09/185.60 inference(unit_resolution,[status(thm)],[19853, 19847, 19818])).
% 293.09/185.60 tff(19886,plain,
% 293.09/185.60 (~node8(c_e_h_3, c_u, s9, s10)),
% 293.09/185.60 inference(unit_resolution,[status(thm)],[19863, 19847, 19659])).
% 293.09/185.60 tff(19887,plain,
% 293.09/185.60 ($false),
% 293.09/185.60 inference(unit_resolution,[status(thm)],[19868, 19886, 19885])).
% 293.09/185.60 tff(19888,plain,(m_user_v_req(c_e_h_3, c_u, s10) | (~m_user_v_req(c_e_h_3, c_u, s9)) | m_user_v_ack(c_e_h_3, c_u, s9)), inference(lemma,lemma(discharge,[]))).
% 293.09/185.60 tff(19889,plain,
% 293.09/185.60 (m_user_v_req(c_e_h_3, c_u, s10)),
% 293.09/185.60 inference(unit_resolution,[status(thm)],[19888, 19810, 19817])).
% 293.09/185.60 tff(19890,assumption,(~m_mutex_h_half_v_inp(c_e_h_3, c_a, s10)), introduced(assumption)).
% 293.09/185.60 tff(19891,plain,
% 293.09/185.60 (((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | ((~m_user_v_req(c_e_h_3, c_u, s10)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s10))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | (~m_user_v_req(c_e_h_3, c_u, s10)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s10))),
% 293.09/185.60 inference(rewrite,[status(thm)],[])).
% 293.09/185.60 tff(19892,plain,
% 293.09/185.60 ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | ((~m_user_v_req(c_e_h_3, c_u, s10)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s10))),
% 293.09/185.60 inference(quant_inst,[status(thm)],[])).
% 293.09/185.60 tff(19893,plain,
% 293.09/185.60 ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | (~m_user_v_req(c_e_h_3, c_u, s10)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s10)),
% 293.09/185.60 inference(modus_ponens,[status(thm)],[19892, 19891])).
% 293.09/185.60 tff(19894,plain,
% 293.09/185.60 ($false),
% 293.09/185.60 inference(unit_resolution,[status(thm)],[19893, 1426, 19824, 19890])).
% 293.09/185.60 tff(19895,plain,((~m_user_v_req(c_e_h_3, c_u, s10)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s10)), inference(lemma,lemma(discharge,[]))).
% 293.09/185.60 tff(19896,plain,
% 293.09/185.60 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s10)),
% 293.09/185.60 inference(unit_resolution,[status(thm)],[19895, 19889])).
% 293.09/185.60 tff(19897,assumption,(m_mutex_h_half_v_inp(c_e_h_3, c_a, s10)), introduced(assumption)).
% 293.09/185.60 tff(19898,assumption,(node12(c_e_h_3, c_a, s10, s11)), introduced(assumption)).
% 293.09/185.60 tff(19899,plain,
% 293.09/185.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_a, s10)) | (~node12(c_e_h_3, c_a, s10, s11)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s10)) | (~node12(c_e_h_3, c_a, s10, s11)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s11))),
% 293.09/185.60 inference(rewrite,[status(thm)],[])).
% 293.09/185.60 tff(19900,plain,
% 293.09/185.60 (((~node12(c_e_h_3, c_a, s10, s11)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s10)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s11)) <=> ((~m_mutex_h_half_v_inp(c_e_h_3, c_a, s10)) | (~node12(c_e_h_3, c_a, s10, s11)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s11))),
% 293.09/185.60 inference(rewrite,[status(thm)],[])).
% 293.09/185.60 tff(19901,plain,
% 293.09/185.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_3, c_a, s10, s11)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s10)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_a, s10)) | (~node12(c_e_h_3, c_a, s10, s11)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s11)))),
% 293.09/185.60 inference(monotonicity,[status(thm)],[19900])).
% 293.09/185.60 tff(19902,plain,
% 293.09/185.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_3, c_a, s10, s11)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s10)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s10)) | (~node12(c_e_h_3, c_a, s10, s11)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s11))),
% 293.09/185.60 inference(transitivity,[status(thm)],[19901, 19899])).
% 293.09/185.60 tff(19903,plain,
% 293.09/185.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_3, c_a, s10, s11)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s10)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s11))),
% 293.09/185.60 inference(quant_inst,[status(thm)],[])).
% 293.09/185.60 tff(19904,plain,
% 293.09/185.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s10)) | (~node12(c_e_h_3, c_a, s10, s11)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s11)),
% 293.09/185.60 inference(modus_ponens,[status(thm)],[19903, 19902])).
% 293.09/185.60 tff(19905,plain,
% 293.09/185.60 ($false),
% 293.09/185.60 inference(unit_resolution,[status(thm)],[19904, 1483, 19898, 19874, 19897])).
% 293.09/185.60 tff(19906,plain,((~node12(c_e_h_3, c_a, s10, s11)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s11) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s10))), inference(lemma,lemma(discharge,[]))).
% 293.09/185.60 tff(19907,plain,
% 293.09/185.60 (~node12(c_e_h_3, c_a, s10, s11)),
% 293.09/185.60 inference(unit_resolution,[status(thm)],[19906, 19874, 19896])).
% 293.09/185.60 tff(19908,plain,
% 293.09/185.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s10, s11)) | node12(c_e_h_3, c_a, s10, s11) | node13(c_e_h_3, c_a, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s10, s11)) | node12(c_e_h_3, c_a, s10, s11) | node13(c_e_h_3, c_a, s10, s11))),
% 293.09/185.60 inference(rewrite,[status(thm)],[])).
% 293.09/185.60 tff(19909,plain,
% 293.09/185.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s10, s11)) | node12(c_e_h_3, c_a, s10, s11) | node13(c_e_h_3, c_a, s10, s11))),
% 293.09/185.60 inference(quant_inst,[status(thm)],[])).
% 293.09/185.60 tff(19910,plain,
% 293.09/185.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s10, s11)) | node12(c_e_h_3, c_a, s10, s11) | node13(c_e_h_3, c_a, s10, s11)),
% 293.09/185.60 inference(modus_ponens,[status(thm)],[19909, 19908])).
% 293.09/185.60 tff(19911,plain,
% 293.09/185.60 (node12(c_e_h_3, c_a, s10, s11) | node13(c_e_h_3, c_a, s10, s11)),
% 293.09/185.60 inference(unit_resolution,[status(thm)],[19910, 439, 7748])).
% 293.09/185.60 tff(19912,plain,
% 293.09/185.60 ($false),
% 293.09/185.60 inference(unit_resolution,[status(thm)],[19911, 19907, 19884])).
% 293.09/185.60 tff(19913,plain,(m_mutex_h_half_v_out(c_e_h_3, c_a, s11) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s10))), inference(lemma,lemma(discharge,[]))).
% 293.09/185.60 tff(19914,plain,
% 293.09/185.60 (m_mutex_h_half_v_out(c_e_h_3, c_a, s11)),
% 293.09/185.60 inference(unit_resolution,[status(thm)],[19913, 19735])).
% 293.09/185.60 tff(19915,assumption,(m_mutex_h_half_v_out(c_e_h_3, c_a, s11)), introduced(assumption)).
% 293.09/185.60 tff(19916,assumption,(node13(c_e_h_3, c_a, s11, s12)), introduced(assumption)).
% 293.09/185.60 tff(19917,plain,
% 293.09/185.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s12) | (~node13(c_e_h_3, c_a, s11, s12)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | m_mutex_h_half_v_out(c_e_h_3, c_a, s12) | (~node13(c_e_h_3, c_a, s11, s12)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s11)))),
% 293.09/185.60 inference(rewrite,[status(thm)],[])).
% 293.09/185.60 tff(19918,plain,
% 293.09/185.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s12) | (~node13(c_e_h_3, c_a, s11, s12)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s11)))),
% 293.09/185.60 inference(quant_inst,[status(thm)],[])).
% 293.09/185.60 tff(19919,plain,
% 293.09/185.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | m_mutex_h_half_v_out(c_e_h_3, c_a, s12) | (~node13(c_e_h_3, c_a, s11, s12)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s11))),
% 293.09/185.60 inference(modus_ponens,[status(thm)],[19918, 19917])).
% 293.09/185.60 tff(19920,plain,
% 293.09/185.60 ($false),
% 293.09/185.60 inference(unit_resolution,[status(thm)],[19919, 1459, 19916, 19873, 19915])).
% 293.09/185.60 tff(19921,plain,((~node13(c_e_h_3, c_a, s11, s12)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s12) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s11))), inference(lemma,lemma(discharge,[]))).
% 293.09/185.60 tff(19922,plain,
% 293.09/185.60 (~node13(c_e_h_3, c_a, s11, s12)),
% 293.09/185.60 inference(unit_resolution,[status(thm)],[19921, 19873, 19915])).
% 293.09/185.60 tff(19923,assumption,(m_mutex_h_half_v_inp(c_e_h_3, c_a, s11)), introduced(assumption)).
% 293.09/185.61 tff(19924,assumption,(node12(c_e_h_3, c_a, s11, s12)), introduced(assumption)).
% 293.09/185.61 tff(19925,plain,
% 293.09/185.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_3, c_a, s11, s12)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s11)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (~node12(c_e_h_3, c_a, s11, s12)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s11)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s12))),
% 293.09/185.61 inference(rewrite,[status(thm)],[])).
% 293.09/185.61 tff(19926,plain,
% 293.09/185.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_3, c_a, s11, s12)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s11)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s12))),
% 293.09/185.61 inference(quant_inst,[status(thm)],[])).
% 293.09/185.61 tff(19927,plain,
% 293.09/185.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (~node12(c_e_h_3, c_a, s11, s12)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s11)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s12)),
% 293.09/185.61 inference(modus_ponens,[status(thm)],[19926, 19925])).
% 293.09/185.61 tff(19928,plain,
% 293.09/185.61 ($false),
% 293.09/185.61 inference(unit_resolution,[status(thm)],[19927, 1483, 19924, 19873, 19923])).
% 293.09/185.61 tff(19929,plain,((~node12(c_e_h_3, c_a, s11, s12)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s12) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s11))), inference(lemma,lemma(discharge,[]))).
% 293.09/185.61 tff(19930,plain,
% 293.09/185.61 (~node12(c_e_h_3, c_a, s11, s12)),
% 293.09/185.61 inference(unit_resolution,[status(thm)],[19929, 19873, 19923])).
% 293.09/185.61 tff(19931,plain,
% 293.09/185.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s11, s12)) | node12(c_e_h_3, c_a, s11, s12) | node13(c_e_h_3, c_a, s11, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s11, s12)) | node12(c_e_h_3, c_a, s11, s12) | node13(c_e_h_3, c_a, s11, s12))),
% 293.09/185.61 inference(rewrite,[status(thm)],[])).
% 293.09/185.61 tff(19932,plain,
% 293.09/185.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s11, s12)) | node12(c_e_h_3, c_a, s11, s12) | node13(c_e_h_3, c_a, s11, s12))),
% 293.09/185.61 inference(quant_inst,[status(thm)],[])).
% 293.09/185.61 tff(19933,plain,
% 293.09/185.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s11, s12)) | node12(c_e_h_3, c_a, s11, s12) | node13(c_e_h_3, c_a, s11, s12)),
% 293.09/185.61 inference(modus_ponens,[status(thm)],[19932, 19931])).
% 293.09/185.61 tff(19934,plain,
% 293.09/185.61 (node12(c_e_h_3, c_a, s11, s12) | node13(c_e_h_3, c_a, s11, s12)),
% 293.09/185.61 inference(unit_resolution,[status(thm)],[19933, 439, 11461])).
% 293.09/185.61 tff(19935,plain,
% 293.09/185.61 ($false),
% 293.09/185.61 inference(unit_resolution,[status(thm)],[19934, 19930, 19922])).
% 293.09/185.61 tff(19936,plain,(m_mutex_h_half_v_out(c_e_h_3, c_a, s12) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s11)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s11))), inference(lemma,lemma(discharge,[]))).
% 293.09/185.61 tff(19937,plain,
% 293.09/185.61 (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s11)),
% 293.09/185.61 inference(unit_resolution,[status(thm)],[19936, 19914, 19873])).
% 293.09/185.61 tff(19938,assumption,(~m_mutex_h_half_v_inp(c_e_h_3, c_a, s11)), introduced(assumption)).
% 293.09/185.61 tff(19939,assumption,(m_user_v_req(c_e_h_3, c_u, s11)), introduced(assumption)).
% 293.09/185.61 tff(19940,plain,
% 293.09/185.61 (((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | ((~m_user_v_req(c_e_h_3, c_u, s11)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s11))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | (~m_user_v_req(c_e_h_3, c_u, s11)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s11))),
% 293.09/185.61 inference(rewrite,[status(thm)],[])).
% 293.09/185.61 tff(19941,plain,
% 293.09/185.61 ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | ((~m_user_v_req(c_e_h_3, c_u, s11)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s11))),
% 293.09/185.61 inference(quant_inst,[status(thm)],[])).
% 293.09/185.61 tff(19942,plain,
% 293.09/185.61 ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | (~m_user_v_req(c_e_h_3, c_u, s11)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s11)),
% 293.09/185.61 inference(modus_ponens,[status(thm)],[19941, 19940])).
% 293.09/185.61 tff(19943,plain,
% 293.09/185.61 ($false),
% 293.09/185.61 inference(unit_resolution,[status(thm)],[19942, 1426, 19939, 19938])).
% 293.09/185.61 tff(19944,plain,(m_mutex_h_half_v_inp(c_e_h_3, c_a, s11) | (~m_user_v_req(c_e_h_3, c_u, s11))), inference(lemma,lemma(discharge,[]))).
% 293.09/185.61 tff(19945,plain,
% 293.09/185.61 ($false),
% 293.09/185.61 inference(unit_resolution,[status(thm)],[19944, 19937, 19872])).
% 293.09/185.61 tff(19946,plain,((~m_mutex_h_half_v_out(c_e_h_3, c_a, s10)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s12) | m_and_h_gate_v_out(c_e_h_3, c_r, s10)), inference(lemma,lemma(discharge,[]))).
% 293.09/185.61 tff(19947,plain,
% 293.09/185.61 (m_mutex_h_half_v_out(c_e_h_3, c_a, s12)),
% 293.09/185.61 inference(unit_resolution,[status(thm)],[19946, 19734, 12643])).
% 293.09/185.61 tff(19948,assumption,(m_mutex_h_half_v_out(c_e_h_3, c_a, s12)), introduced(assumption)).
% 293.09/185.61 tff(19949,assumption,(m_mutex_h_half_v_inp(c_e_h_3, c_a, s12)), introduced(assumption)).
% 293.09/185.61 tff(19950,assumption,(node12(c_e_h_3, c_a, s12, s13)), introduced(assumption)).
% 293.09/185.61 tff(19951,plain,
% 293.09/185.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s13) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s12)) | (~node12(c_e_h_3, c_a, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | m_mutex_h_half_v_out(c_e_h_3, c_a, s13) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s12)) | (~node12(c_e_h_3, c_a, s12, s13)))),
% 293.09/185.61 inference(rewrite,[status(thm)],[])).
% 293.09/185.61 tff(19952,plain,
% 293.09/185.61 (((~node12(c_e_h_3, c_a, s12, s13)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s12)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s13)) <=> (m_mutex_h_half_v_out(c_e_h_3, c_a, s13) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s12)) | (~node12(c_e_h_3, c_a, s12, s13)))),
% 293.09/185.61 inference(rewrite,[status(thm)],[])).
% 293.09/185.61 tff(19953,plain,
% 293.09/185.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_3, c_a, s12, s13)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s12)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s13) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s12)) | (~node12(c_e_h_3, c_a, s12, s13))))),
% 293.09/185.61 inference(monotonicity,[status(thm)],[19952])).
% 293.09/185.61 tff(19954,plain,
% 293.09/185.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_3, c_a, s12, s13)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s12)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | m_mutex_h_half_v_out(c_e_h_3, c_a, s13) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s12)) | (~node12(c_e_h_3, c_a, s12, s13)))),
% 293.09/185.61 inference(transitivity,[status(thm)],[19953, 19951])).
% 293.09/185.61 tff(19955,plain,
% 293.09/185.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_3, c_a, s12, s13)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s12)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s13))),
% 293.09/185.61 inference(quant_inst,[status(thm)],[])).
% 293.09/185.61 tff(19956,plain,
% 293.09/185.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | m_mutex_h_half_v_out(c_e_h_3, c_a, s13) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s12)) | (~node12(c_e_h_3, c_a, s12, s13))),
% 293.09/185.61 inference(modus_ponens,[status(thm)],[19955, 19954])).
% 293.09/185.61 tff(19957,plain,
% 293.09/185.61 ($false),
% 293.09/185.61 inference(unit_resolution,[status(thm)],[19956, 1483, 19555, 19950, 19949])).
% 293.09/185.62 tff(19958,plain,((~node12(c_e_h_3, c_a, s12, s13)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s13) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s12))), inference(lemma,lemma(discharge,[]))).
% 293.09/185.62 tff(19959,plain,
% 293.09/185.62 (~node12(c_e_h_3, c_a, s12, s13)),
% 293.09/185.62 inference(unit_resolution,[status(thm)],[19958, 19555, 19949])).
% 293.09/185.62 tff(19960,plain,
% 293.09/185.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s12, s13)) | node12(c_e_h_3, c_a, s12, s13) | node13(c_e_h_3, c_a, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s12, s13)) | node12(c_e_h_3, c_a, s12, s13) | node13(c_e_h_3, c_a, s12, s13))),
% 293.09/185.62 inference(rewrite,[status(thm)],[])).
% 293.09/185.62 tff(19961,plain,
% 293.09/185.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s12, s13)) | node12(c_e_h_3, c_a, s12, s13) | node13(c_e_h_3, c_a, s12, s13))),
% 293.09/185.62 inference(quant_inst,[status(thm)],[])).
% 293.09/185.62 tff(19962,plain,
% 293.09/185.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s12, s13)) | node12(c_e_h_3, c_a, s12, s13) | node13(c_e_h_3, c_a, s12, s13)),
% 293.09/185.62 inference(modus_ponens,[status(thm)],[19961, 19960])).
% 293.09/185.62 tff(19963,plain,
% 293.09/185.62 (node12(c_e_h_3, c_a, s12, s13) | node13(c_e_h_3, c_a, s12, s13)),
% 293.09/185.62 inference(unit_resolution,[status(thm)],[19962, 439, 11856])).
% 293.09/185.62 tff(19964,plain,
% 293.09/185.62 (node13(c_e_h_3, c_a, s12, s13)),
% 293.09/185.62 inference(unit_resolution,[status(thm)],[19963, 19959])).
% 293.09/185.62 tff(19965,plain,
% 293.09/185.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s13) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s12)) | (~node13(c_e_h_3, c_a, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | m_mutex_h_half_v_out(c_e_h_3, c_a, s13) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s12)) | (~node13(c_e_h_3, c_a, s12, s13)))),
% 293.09/185.62 inference(rewrite,[status(thm)],[])).
% 293.09/185.62 tff(19966,plain,
% 293.09/185.62 ((m_mutex_h_half_v_out(c_e_h_3, c_a, s13) | (~node13(c_e_h_3, c_a, s12, s13)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s12))) <=> (m_mutex_h_half_v_out(c_e_h_3, c_a, s13) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s12)) | (~node13(c_e_h_3, c_a, s12, s13)))),
% 293.09/185.62 inference(rewrite,[status(thm)],[])).
% 293.09/185.62 tff(19967,plain,
% 293.09/185.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s13) | (~node13(c_e_h_3, c_a, s12, s13)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s13) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s12)) | (~node13(c_e_h_3, c_a, s12, s13))))),
% 293.09/185.62 inference(monotonicity,[status(thm)],[19966])).
% 293.09/185.62 tff(19968,plain,
% 293.09/185.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s13) | (~node13(c_e_h_3, c_a, s12, s13)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | m_mutex_h_half_v_out(c_e_h_3, c_a, s13) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s12)) | (~node13(c_e_h_3, c_a, s12, s13)))),
% 293.09/185.62 inference(transitivity,[status(thm)],[19967, 19965])).
% 293.09/185.62 tff(19969,plain,
% 293.09/185.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_a, s13) | (~node13(c_e_h_3, c_a, s12, s13)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s12)))),
% 293.09/185.62 inference(quant_inst,[status(thm)],[])).
% 293.09/185.62 tff(19970,plain,
% 293.09/185.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | m_mutex_h_half_v_out(c_e_h_3, c_a, s13) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s12)) | (~node13(c_e_h_3, c_a, s12, s13))),
% 293.09/185.62 inference(modus_ponens,[status(thm)],[19969, 19968])).
% 293.09/185.62 tff(19971,plain,
% 293.09/185.62 ($false),
% 293.09/185.62 inference(unit_resolution,[status(thm)],[19970, 1459, 19555, 19964, 19948])).
% 293.09/185.62 tff(19972,plain,(m_mutex_h_half_v_out(c_e_h_3, c_a, s13) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s12)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s12))), inference(lemma,lemma(discharge,[]))).
% 293.09/185.62 tff(19973,plain,
% 293.09/185.62 (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s12)),
% 293.09/185.62 inference(unit_resolution,[status(thm)],[19972, 19947, 19555])).
% 293.09/185.62 tff(19974,assumption,(~m_user_v_ack(c_e_h_3, c_u, s11)), introduced(assumption)).
% 293.09/185.62 tff(19975,plain,
% 293.09/185.62 (m_user_v_req(c_e_h_3, c_u, s9)),
% 293.09/185.62 inference(unit_resolution,[status(thm)],[19688, 19623])).
% 293.09/185.62 tff(19976,plain,
% 293.09/185.62 (m_user_v_req(c_e_h_3, c_u, s11)),
% 293.09/185.62 inference(unit_resolution,[status(thm)],[19871, 19975, 12643])).
% 293.09/185.62 tff(19977,assumption,(~m_user_v_req(c_e_h_3, c_u, s12)), introduced(assumption)).
% 293.09/185.62 tff(19978,assumption,(node7(c_e_h_3, c_u, s11, s12)), introduced(assumption)).
% 293.09/185.62 tff(19979,plain,
% 293.09/185.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | ((~node7(c_e_h_3, c_u, s11, s12)) | m_user_v_ack(c_e_h_3, c_u, s11) | m_user_v_req(c_e_h_3, c_u, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | (~node7(c_e_h_3, c_u, s11, s12)) | m_user_v_ack(c_e_h_3, c_u, s11) | m_user_v_req(c_e_h_3, c_u, s12))),
% 293.09/185.62 inference(rewrite,[status(thm)],[])).
% 293.09/185.62 tff(19980,plain,
% 293.09/185.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | ((~node7(c_e_h_3, c_u, s11, s12)) | m_user_v_ack(c_e_h_3, c_u, s11) | m_user_v_req(c_e_h_3, c_u, s12))),
% 293.09/185.62 inference(quant_inst,[status(thm)],[])).
% 293.09/185.62 tff(19981,plain,
% 293.09/185.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | (~node7(c_e_h_3, c_u, s11, s12)) | m_user_v_ack(c_e_h_3, c_u, s11) | m_user_v_req(c_e_h_3, c_u, s12)),
% 293.09/185.62 inference(modus_ponens,[status(thm)],[19980, 19979])).
% 293.09/185.62 tff(19982,plain,
% 293.09/185.62 ($false),
% 293.09/185.62 inference(unit_resolution,[status(thm)],[19981, 284, 19978, 19977, 19974])).
% 293.09/185.62 tff(19983,plain,((~node7(c_e_h_3, c_u, s11, s12)) | m_user_v_req(c_e_h_3, c_u, s12) | m_user_v_ack(c_e_h_3, c_u, s11)), inference(lemma,lemma(discharge,[]))).
% 293.09/185.62 tff(19984,plain,
% 293.09/185.62 (~node7(c_e_h_3, c_u, s11, s12)),
% 293.09/185.62 inference(unit_resolution,[status(thm)],[19983, 19977, 19974])).
% 293.09/185.62 tff(19985,assumption,(node8(c_e_h_3, c_u, s11, s12)), introduced(assumption)).
% 293.09/185.62 tff(19986,plain,
% 293.09/185.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_3, c_u, s12) | (~m_user_v_req(c_e_h_3, c_u, s11)) | (~node8(c_e_h_3, c_u, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | m_user_v_req(c_e_h_3, c_u, s12) | (~m_user_v_req(c_e_h_3, c_u, s11)) | (~node8(c_e_h_3, c_u, s11, s12)))),
% 293.09/185.62 inference(rewrite,[status(thm)],[])).
% 293.09/185.62 tff(19987,plain,
% 293.09/185.62 ((m_user_v_req(c_e_h_3, c_u, s12) | (~node8(c_e_h_3, c_u, s11, s12)) | (~m_user_v_req(c_e_h_3, c_u, s11))) <=> (m_user_v_req(c_e_h_3, c_u, s12) | (~m_user_v_req(c_e_h_3, c_u, s11)) | (~node8(c_e_h_3, c_u, s11, s12)))),
% 293.09/185.62 inference(rewrite,[status(thm)],[])).
% 293.09/185.62 tff(19988,plain,
% 293.09/185.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_3, c_u, s12) | (~node8(c_e_h_3, c_u, s11, s12)) | (~m_user_v_req(c_e_h_3, c_u, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_3, c_u, s12) | (~m_user_v_req(c_e_h_3, c_u, s11)) | (~node8(c_e_h_3, c_u, s11, s12))))),
% 293.09/185.62 inference(monotonicity,[status(thm)],[19987])).
% 293.09/185.62 tff(19989,plain,
% 293.09/185.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_3, c_u, s12) | (~node8(c_e_h_3, c_u, s11, s12)) | (~m_user_v_req(c_e_h_3, c_u, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | m_user_v_req(c_e_h_3, c_u, s12) | (~m_user_v_req(c_e_h_3, c_u, s11)) | (~node8(c_e_h_3, c_u, s11, s12)))),
% 293.09/185.62 inference(transitivity,[status(thm)],[19988, 19986])).
% 293.09/185.62 tff(19990,plain,
% 293.09/185.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_3, c_u, s12) | (~node8(c_e_h_3, c_u, s11, s12)) | (~m_user_v_req(c_e_h_3, c_u, s11)))),
% 293.09/185.62 inference(quant_inst,[status(thm)],[])).
% 293.09/185.62 tff(19991,plain,
% 293.09/185.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | m_user_v_req(c_e_h_3, c_u, s12) | (~m_user_v_req(c_e_h_3, c_u, s11)) | (~node8(c_e_h_3, c_u, s11, s12))),
% 293.09/185.62 inference(modus_ponens,[status(thm)],[19990, 19989])).
% 293.09/185.62 tff(19992,plain,
% 293.09/185.62 ($false),
% 293.09/185.62 inference(unit_resolution,[status(thm)],[19991, 302, 19985, 19939, 19977])).
% 293.09/185.62 tff(19993,plain,((~node8(c_e_h_3, c_u, s11, s12)) | (~m_user_v_req(c_e_h_3, c_u, s11)) | m_user_v_req(c_e_h_3, c_u, s12)), inference(lemma,lemma(discharge,[]))).
% 293.09/185.62 tff(19994,plain,
% 293.09/185.62 (~node8(c_e_h_3, c_u, s11, s12)),
% 293.09/185.62 inference(unit_resolution,[status(thm)],[19993, 19977, 19939])).
% 293.09/185.62 tff(19995,plain,
% 293.09/185.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | ((~trans(s11, s12)) | node7(c_e_h_3, c_u, s11, s12) | node8(c_e_h_3, c_u, s11, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | (~trans(s11, s12)) | node7(c_e_h_3, c_u, s11, s12) | node8(c_e_h_3, c_u, s11, s12))),
% 293.09/185.62 inference(rewrite,[status(thm)],[])).
% 293.09/185.62 tff(19996,plain,
% 293.09/185.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | ((~trans(s11, s12)) | node7(c_e_h_3, c_u, s11, s12) | node8(c_e_h_3, c_u, s11, s12))),
% 293.09/185.62 inference(quant_inst,[status(thm)],[])).
% 293.09/185.62 tff(19997,plain,
% 293.09/185.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | (~trans(s11, s12)) | node7(c_e_h_3, c_u, s11, s12) | node8(c_e_h_3, c_u, s11, s12)),
% 293.09/185.62 inference(modus_ponens,[status(thm)],[19996, 19995])).
% 293.09/185.62 tff(19998,plain,
% 293.09/185.62 (node7(c_e_h_3, c_u, s11, s12) | node8(c_e_h_3, c_u, s11, s12)),
% 293.09/185.62 inference(unit_resolution,[status(thm)],[19997, 328, 11461])).
% 293.09/185.62 tff(19999,plain,
% 293.09/185.62 ($false),
% 293.09/185.62 inference(unit_resolution,[status(thm)],[19998, 19994, 19984])).
% 293.09/185.62 tff(20000,plain,(m_user_v_req(c_e_h_3, c_u, s12) | (~m_user_v_req(c_e_h_3, c_u, s11)) | m_user_v_ack(c_e_h_3, c_u, s11)), inference(lemma,lemma(discharge,[]))).
% 293.09/185.62 tff(20001,plain,
% 293.09/185.62 (m_user_v_req(c_e_h_3, c_u, s12)),
% 293.09/185.62 inference(unit_resolution,[status(thm)],[20000, 19976, 19974])).
% 293.09/185.62 tff(20002,assumption,(m_user_v_req(c_e_h_3, c_u, s12)), introduced(assumption)).
% 293.09/185.62 tff(20003,assumption,(~m_mutex_h_half_v_inp(c_e_h_3, c_a, s12)), introduced(assumption)).
% 293.09/185.62 tff(20004,plain,
% 293.09/185.62 (((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | ((~m_user_v_req(c_e_h_3, c_u, s12)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s12))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | (~m_user_v_req(c_e_h_3, c_u, s12)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s12))),
% 293.09/185.62 inference(rewrite,[status(thm)],[])).
% 293.09/185.62 tff(20005,plain,
% 293.09/185.62 ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | ((~m_user_v_req(c_e_h_3, c_u, s12)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s12))),
% 293.09/185.62 inference(quant_inst,[status(thm)],[])).
% 293.09/185.62 tff(20006,plain,
% 293.09/185.62 ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | (~m_user_v_req(c_e_h_3, c_u, s12)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s12)),
% 293.09/185.62 inference(modus_ponens,[status(thm)],[20005, 20004])).
% 293.09/185.62 tff(20007,plain,
% 293.09/185.63 ($false),
% 293.09/185.63 inference(unit_resolution,[status(thm)],[20006, 1426, 20003, 20002])).
% 293.09/185.63 tff(20008,plain,((~m_user_v_req(c_e_h_3, c_u, s12)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s12)), inference(lemma,lemma(discharge,[]))).
% 293.09/185.63 tff(20009,plain,
% 293.09/185.63 ($false),
% 293.09/185.63 inference(unit_resolution,[status(thm)],[20008, 20001, 19973])).
% 293.09/185.63 tff(20010,plain,((~m_mutex_h_half_v_out(c_e_h_3, c_a, s7)) | m_user_v_ack(c_e_h_3, c_u, s11) | m_mutex_h_half_v_out(c_e_h_3, c_a, s13) | m_and_h_gate_v_out(c_e_h_3, c_r, s10)), inference(lemma,lemma(discharge,[]))).
% 293.09/185.63 tff(20011,plain,
% 293.09/185.63 ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s7)) | m_user_v_ack(c_e_h_3, c_u, s11) | m_mutex_h_half_v_out(c_e_h_3, c_a, s13)),
% 293.09/185.63 inference(unit_resolution,[status(thm)],[20010, 12642])).
% 293.09/185.63 tff(20012,plain,
% 293.09/185.63 ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s7)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s13)),
% 293.09/185.63 inference(unit_resolution,[status(thm)],[20011, 19562])).
% 293.09/185.63 tff(20013,plain,
% 293.09/185.63 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s7)),
% 293.09/185.63 inference(unit_resolution,[status(thm)],[20012, 19555])).
% 293.09/185.63 tff(20014,plain,
% 293.09/185.63 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s4)),
% 293.09/185.63 inference(unit_resolution,[status(thm)],[19741, 20013])).
% 293.09/185.63 tff(20015,plain,
% 293.09/185.63 (~m_and_h_gate_v_out(c_e_h_3, c_c, s5)),
% 293.09/185.63 inference(unit_resolution,[status(thm)],[10330, 20014])).
% 293.09/185.63 tff(20016,plain,
% 293.09/185.63 (~m_and_h_gate_v_out(c_e_h_3, c_c, s4)),
% 293.09/185.63 inference(unit_resolution,[status(thm)],[6170, 20015])).
% 293.09/185.63 tff(20017,assumption,(~m_or_h_gate_v_in2(c_e_h_3, c_g, s9)), introduced(assumption)).
% 293.09/185.63 tff(20018,assumption,(~m_or_h_gate_v_in2(c_e_h_3, c_g, s8)), introduced(assumption)).
% 293.09/185.63 tff(20019,plain,
% 293.09/185.63 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s4)),
% 293.09/185.63 inference(unit_resolution,[status(thm)],[19741, 1947])).
% 293.09/185.63 tff(20020,assumption,(m_and_h_gate_v_out(c_e_h_3, c_c, s8)), introduced(assumption)).
% 293.09/185.63 tff(20021,plain,
% 293.09/185.63 (~m_and_h_gate_v_out(c_e_h_3, c_c, s5)),
% 293.09/185.63 inference(unit_resolution,[status(thm)],[10330, 20019])).
% 293.09/185.63 tff(20022,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_c, s7)), introduced(assumption)).
% 293.09/185.63 tff(20023,plain,
% 293.09/185.63 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_c, s7)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s7))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s7)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s7))),
% 293.09/185.63 inference(rewrite,[status(thm)],[])).
% 293.09/185.63 tff(20024,plain,
% 293.09/185.63 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_c, s7)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s7))),
% 293.09/185.63 inference(quant_inst,[status(thm)],[])).
% 293.09/185.63 tff(20025,plain,
% 293.09/185.63 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s7)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s7)),
% 293.09/185.63 inference(modus_ponens,[status(thm)],[20024, 20023])).
% 293.09/185.63 tff(20026,plain,
% 293.09/185.63 ($false),
% 293.09/185.63 inference(unit_resolution,[status(thm)],[20025, 567, 20022, 1947])).
% 293.09/185.63 tff(20027,plain,((~m_and_h_gate_v_in1(c_e_h_3, c_c, s7)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s7)), inference(lemma,lemma(discharge,[]))).
% 293.09/185.63 tff(20028,plain,
% 293.09/185.63 (~m_and_h_gate_v_in1(c_e_h_3, c_c, s7)),
% 293.09/185.63 inference(unit_resolution,[status(thm)],[20027, 1947])).
% 293.09/185.63 tff(20029,assumption,(node20(c_e_h_3, c_c, s7)), introduced(assumption)).
% 293.09/185.63 tff(20030,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_c, s7)), introduced(assumption)).
% 293.09/185.63 tff(20031,plain,
% 293.09/185.63 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_c, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_c, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s7))),
% 293.09/185.63 inference(rewrite,[status(thm)],[])).
% 293.09/185.63 tff(20032,plain,
% 293.09/185.63 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_c, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s7))),
% 293.09/185.63 inference(quant_inst,[status(thm)],[])).
% 293.09/185.63 tff(20033,plain,
% 293.09/185.63 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_c, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s7)),
% 293.09/185.63 inference(modus_ponens,[status(thm)],[20032, 20031])).
% 293.09/185.63 tff(20034,plain,
% 293.09/185.63 ($false),
% 293.09/185.63 inference(unit_resolution,[status(thm)],[20033, 38, 20030, 20029])).
% 293.09/185.63 tff(20035,plain,((~node20(c_e_h_3, c_c, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s7)), inference(lemma,lemma(discharge,[]))).
% 293.09/185.63 tff(20036,plain,
% 293.09/185.63 (~node20(c_e_h_3, c_c, s7)),
% 293.09/185.63 inference(unit_resolution,[status(thm)],[20035, 20028])).
% 293.09/185.63 tff(20037,assumption,(~node20(c_e_h_3, c_c, s7)), introduced(assumption)).
% 293.09/185.63 tff(20038,assumption,(node21(c_e_h_3, c_c, s7, s8)), introduced(assumption)).
% 293.09/185.63 tff(20039,plain,
% 293.09/185.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s8)) | (~node21(c_e_h_3, c_c, s7, s8)) | node20(c_e_h_3, c_c, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s8)) | (~node21(c_e_h_3, c_c, s7, s8)) | node20(c_e_h_3, c_c, s7))),
% 293.09/185.63 inference(rewrite,[status(thm)],[])).
% 293.09/185.63 tff(20040,plain,
% 293.09/185.63 ((node20(c_e_h_3, c_c, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s8)) | (~node21(c_e_h_3, c_c, s7, s8))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_c, s8)) | (~node21(c_e_h_3, c_c, s7, s8)) | node20(c_e_h_3, c_c, s7))),
% 293.09/185.63 inference(rewrite,[status(thm)],[])).
% 293.09/185.63 tff(20041,plain,
% 293.09/185.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_c, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s8)) | (~node21(c_e_h_3, c_c, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s8)) | (~node21(c_e_h_3, c_c, s7, s8)) | node20(c_e_h_3, c_c, s7)))),
% 293.09/185.63 inference(monotonicity,[status(thm)],[20040])).
% 293.09/185.63 tff(20042,plain,
% 293.09/185.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_c, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s8)) | (~node21(c_e_h_3, c_c, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s8)) | (~node21(c_e_h_3, c_c, s7, s8)) | node20(c_e_h_3, c_c, s7))),
% 293.09/185.63 inference(transitivity,[status(thm)],[20041, 20039])).
% 293.09/185.63 tff(20043,plain,
% 293.09/185.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_c, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s8)) | (~node21(c_e_h_3, c_c, s7, s8)))),
% 293.09/185.63 inference(quant_inst,[status(thm)],[])).
% 293.09/185.63 tff(20044,plain,
% 293.09/185.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s8)) | (~node21(c_e_h_3, c_c, s7, s8)) | node20(c_e_h_3, c_c, s7)),
% 293.09/185.63 inference(modus_ponens,[status(thm)],[20043, 20042])).
% 293.09/185.63 tff(20045,plain,
% 293.09/185.63 ($false),
% 293.09/185.63 inference(unit_resolution,[status(thm)],[20044, 52, 20038, 20020, 20037])).
% 293.09/185.63 tff(20046,plain,((~node21(c_e_h_3, c_c, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s8)) | node20(c_e_h_3, c_c, s7)), inference(lemma,lemma(discharge,[]))).
% 293.09/185.63 tff(20047,plain,
% 293.09/185.63 (~node21(c_e_h_3, c_c, s7, s8)),
% 293.09/185.63 inference(unit_resolution,[status(thm)],[20046, 20020, 20037])).
% 293.09/185.63 tff(20048,assumption,(node22(c_e_h_3, c_c, s7, s8)), introduced(assumption)).
% 293.09/185.63 tff(20049,plain,
% 293.09/185.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s8)) | (~node22(c_e_h_3, c_c, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_c, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s8)) | (~node22(c_e_h_3, c_c, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_c, s7))),
% 293.09/185.63 inference(rewrite,[status(thm)],[])).
% 293.09/185.63 tff(20050,plain,
% 293.09/185.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s8)) | (~node22(c_e_h_3, c_c, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_c, s7))),
% 293.09/185.63 inference(quant_inst,[status(thm)],[])).
% 293.09/185.63 tff(20051,plain,
% 293.09/185.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s8)) | (~node22(c_e_h_3, c_c, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_c, s7)),
% 293.09/185.63 inference(modus_ponens,[status(thm)],[20050, 20049])).
% 293.09/185.63 tff(20052,plain,
% 293.09/185.63 ($false),
% 293.09/185.63 inference(unit_resolution,[status(thm)],[20051, 108, 20048, 10016, 20020])).
% 293.09/185.63 tff(20053,plain,((~node22(c_e_h_3, c_c, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_c, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s8))), inference(lemma,lemma(discharge,[]))).
% 293.09/185.63 tff(20054,plain,
% 293.09/185.63 (~node22(c_e_h_3, c_c, s7, s8)),
% 293.09/185.63 inference(unit_resolution,[status(thm)],[20053, 20020, 10016])).
% 293.09/185.63 tff(20055,plain,
% 293.09/185.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_3, c_c, s7, s8) | node22(c_e_h_3, c_c, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_3, c_c, s7, s8) | node22(c_e_h_3, c_c, s7, s8))),
% 293.09/185.63 inference(rewrite,[status(thm)],[])).
% 293.09/185.63 tff(20056,plain,
% 293.09/185.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_3, c_c, s7, s8) | node22(c_e_h_3, c_c, s7, s8))),
% 293.09/185.63 inference(quant_inst,[status(thm)],[])).
% 293.09/185.63 tff(20057,plain,
% 293.09/185.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_3, c_c, s7, s8) | node22(c_e_h_3, c_c, s7, s8)),
% 293.09/185.63 inference(modus_ponens,[status(thm)],[20056, 20055])).
% 293.09/185.63 tff(20058,plain,
% 293.09/185.63 (node21(c_e_h_3, c_c, s7, s8) | node22(c_e_h_3, c_c, s7, s8)),
% 293.09/185.63 inference(unit_resolution,[status(thm)],[20057, 82, 1938])).
% 293.09/185.63 tff(20059,plain,
% 293.09/185.63 ($false),
% 293.09/185.63 inference(unit_resolution,[status(thm)],[20058, 20054, 20047])).
% 293.09/185.63 tff(20060,plain,((~m_and_h_gate_v_out(c_e_h_3, c_c, s8)) | m_and_h_gate_v_out(c_e_h_3, c_c, s7) | node20(c_e_h_3, c_c, s7)), inference(lemma,lemma(discharge,[]))).
% 293.09/185.63 tff(20061,plain,
% 293.09/185.63 (m_and_h_gate_v_out(c_e_h_3, c_c, s7)),
% 293.09/185.63 inference(unit_resolution,[status(thm)],[20060, 20036, 20020])).
% 293.09/185.63 tff(20062,plain,
% 293.09/185.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s7)) | (~node22(c_e_h_3, c_c, s6, s7)) | m_and_h_gate_v_out(c_e_h_3, c_c, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s7)) | (~node22(c_e_h_3, c_c, s6, s7)) | m_and_h_gate_v_out(c_e_h_3, c_c, s6))),
% 293.09/185.63 inference(rewrite,[status(thm)],[])).
% 293.09/185.63 tff(20063,plain,
% 293.09/185.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s7)) | (~node22(c_e_h_3, c_c, s6, s7)) | m_and_h_gate_v_out(c_e_h_3, c_c, s6))),
% 293.09/185.63 inference(quant_inst,[status(thm)],[])).
% 293.09/185.63 tff(20064,plain,
% 293.09/185.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s7)) | (~node22(c_e_h_3, c_c, s6, s7)) | m_and_h_gate_v_out(c_e_h_3, c_c, s6)),
% 293.09/185.63 inference(modus_ponens,[status(thm)],[20063, 20062])).
% 293.09/185.63 tff(20065,plain,
% 293.09/185.63 ($false),
% 293.09/185.63 inference(unit_resolution,[status(thm)],[20064, 108, 10226, 11155, 10061])).
% 293.09/185.63 tff(20066,plain,((~node22(c_e_h_3, c_c, s6, s7)) | m_and_h_gate_v_out(c_e_h_3, c_c, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s7))), inference(lemma,lemma(discharge,[]))).
% 293.09/185.64 tff(20067,plain,
% 293.09/185.64 (~node22(c_e_h_3, c_c, s6, s7)),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[20066, 11155, 10226])).
% 293.09/185.64 tff(20068,assumption,(~node20(c_e_h_3, c_c, s6)), introduced(assumption)).
% 293.09/185.64 tff(20069,plain,
% 293.09/185.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_c, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s7)) | (~node21(c_e_h_3, c_c, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_c, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s7)) | (~node21(c_e_h_3, c_c, s6, s7)))),
% 293.09/185.64 inference(rewrite,[status(thm)],[])).
% 293.09/185.64 tff(20070,plain,
% 293.09/185.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_c, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s7)) | (~node21(c_e_h_3, c_c, s6, s7)))),
% 293.09/185.64 inference(quant_inst,[status(thm)],[])).
% 293.09/185.64 tff(20071,plain,
% 293.09/185.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_c, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s7)) | (~node21(c_e_h_3, c_c, s6, s7))),
% 293.09/185.64 inference(modus_ponens,[status(thm)],[20070, 20069])).
% 293.09/185.64 tff(20072,plain,
% 293.09/185.64 ($false),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[20071, 52, 11155, 10292, 20068])).
% 293.09/185.64 tff(20073,plain,((~node21(c_e_h_3, c_c, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s7)) | node20(c_e_h_3, c_c, s6)), inference(lemma,lemma(discharge,[]))).
% 293.09/185.64 tff(20074,plain,
% 293.09/185.64 (~node21(c_e_h_3, c_c, s6, s7)),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[20073, 11155, 20068])).
% 293.09/185.64 tff(20075,plain,
% 293.09/185.64 ($false),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[10074, 20074, 20067])).
% 293.09/185.64 tff(20076,plain,((~m_and_h_gate_v_out(c_e_h_3, c_c, s7)) | node20(c_e_h_3, c_c, s6) | m_and_h_gate_v_out(c_e_h_3, c_c, s6)), inference(lemma,lemma(discharge,[]))).
% 293.09/185.64 tff(20077,plain,
% 293.09/185.64 (node20(c_e_h_3, c_c, s6)),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[20076, 20061, 10226])).
% 293.09/185.64 tff(20078,assumption,(node20(c_e_h_3, c_c, s6)), introduced(assumption)).
% 293.09/185.64 tff(20079,plain,
% 293.09/185.64 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_c, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_c, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s6))),
% 293.09/185.64 inference(rewrite,[status(thm)],[])).
% 293.09/185.64 tff(20080,plain,
% 293.09/185.64 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_c, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s6))),
% 293.09/185.64 inference(quant_inst,[status(thm)],[])).
% 293.09/185.64 tff(20081,plain,
% 293.09/185.64 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_c, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s6)),
% 293.09/185.64 inference(modus_ponens,[status(thm)],[20080, 20079])).
% 293.09/185.64 tff(20082,plain,
% 293.09/185.64 ($false),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[20081, 38, 20078, 10296])).
% 293.09/185.64 tff(20083,plain,((~node20(c_e_h_3, c_c, s6)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s6)), inference(lemma,lemma(discharge,[]))).
% 293.09/185.64 tff(20084,plain,
% 293.09/185.64 (m_and_h_gate_v_in1(c_e_h_3, c_c, s6)),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[20083, 20077])).
% 293.09/185.64 tff(20085,plain,
% 293.09/185.64 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_c, s6)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s6))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s6)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s6))),
% 293.09/185.64 inference(rewrite,[status(thm)],[])).
% 293.09/185.64 tff(20086,plain,
% 293.09/185.64 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_c, s6)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s6))),
% 293.09/185.64 inference(quant_inst,[status(thm)],[])).
% 293.09/185.64 tff(20087,plain,
% 293.09/185.64 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s6)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s6)),
% 293.09/185.64 inference(modus_ponens,[status(thm)],[20086, 20085])).
% 293.09/185.64 tff(20088,plain,
% 293.09/185.64 ($false),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[20087, 567, 1491, 10291])).
% 293.09/185.64 tff(20089,plain,((~m_and_h_gate_v_in1(c_e_h_3, c_c, s6)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s6)), inference(lemma,lemma(discharge,[]))).
% 293.09/185.64 tff(20090,plain,
% 293.09/185.64 (m_mutex_h_half_v_out(c_e_h_3, c_a, s6)),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[20089, 20084])).
% 293.09/185.64 tff(20091,plain,
% 293.09/185.64 (~node13(c_e_h_3, c_a, s5, s6)),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[19615, 20090, 1448])).
% 293.09/185.64 tff(20092,plain,
% 293.09/185.64 (node12(c_e_h_3, c_a, s5, s6)),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[1506, 20091])).
% 293.09/185.64 tff(20093,plain,
% 293.09/185.64 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s5)),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[19608, 20092, 20090])).
% 293.09/185.64 tff(20094,plain,
% 293.09/185.64 (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s6)),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[1971, 20090, 1947])).
% 293.09/185.64 tff(20095,plain,
% 293.09/185.64 (~m_user_v_req(c_e_h_3, c_u, s6)),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[1431, 20094])).
% 293.09/185.64 tff(20096,plain,
% 293.09/185.64 (~m_user_v_req(c_e_h_3, c_u, s5)),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[1413, 20095])).
% 293.09/185.64 tff(20097,plain,
% 293.09/185.64 ($false),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[19598, 395, 20096, 20093])).
% 293.09/185.64 tff(20098,plain,(m_mutex_h_half_v_out(c_e_h_3, c_a, s7) | m_mutex_h_half_v_out(c_e_h_3, c_a, s5) | m_and_h_gate_v_out(c_e_h_3, c_c, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s8))), inference(lemma,lemma(discharge,[]))).
% 293.09/185.64 tff(20099,plain,
% 293.09/185.64 (m_and_h_gate_v_out(c_e_h_3, c_c, s6)),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[20098, 1448, 20020, 1947])).
% 293.09/185.64 tff(20100,plain,
% 293.09/185.64 (~m_and_h_gate_v_in1(c_e_h_3, c_c, s5)),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[10191, 1448])).
% 293.09/185.64 tff(20101,assumption,(node20(c_e_h_3, c_c, s5)), introduced(assumption)).
% 293.09/185.64 tff(20102,plain,
% 293.09/185.64 ($false),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[10184, 38, 20101, 10336])).
% 293.09/185.64 tff(20103,plain,((~node20(c_e_h_3, c_c, s5)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s5)), inference(lemma,lemma(discharge,[]))).
% 293.09/185.64 tff(20104,plain,
% 293.09/185.64 (~node20(c_e_h_3, c_c, s5)),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[20103, 20100])).
% 293.09/185.64 tff(20105,plain,
% 293.09/185.64 ($false),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[10180, 20104, 20099, 5931])).
% 293.09/185.64 tff(20106,plain,(m_mutex_h_half_v_out(c_e_h_3, c_a, s5) | m_and_h_gate_v_out(c_e_h_3, c_c, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s7)), inference(lemma,lemma(discharge,[]))).
% 293.09/185.64 tff(20107,plain,
% 293.09/185.64 (m_mutex_h_half_v_out(c_e_h_3, c_a, s5)),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[20106, 20021, 20020, 1947])).
% 293.09/185.64 tff(20108,plain,
% 293.09/185.64 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s4)),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[10210, 20107, 20019])).
% 293.09/185.64 tff(20109,plain,
% 293.09/185.64 (m_user_v_req(c_e_h_3, c_u, s4)),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[10214, 395, 20108])).
% 293.09/185.64 tff(20110,plain,
% 293.09/185.64 (m_user_v_req(c_e_h_3, c_u, s5)),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[1035, 20109])).
% 293.09/185.64 tff(20111,plain,
% 293.09/185.64 (m_user_v_req(c_e_h_3, c_u, s6)),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[1413, 20110])).
% 293.09/185.64 tff(20112,plain,
% 293.09/185.64 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s6)),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[1431, 20111])).
% 293.09/185.64 tff(20113,plain,
% 293.09/185.64 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s5)),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[1438, 20110])).
% 293.09/185.64 tff(20114,plain,
% 293.09/185.64 (m_mutex_h_half_v_out(c_e_h_3, c_a, s6)),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[1515, 20113, 20107])).
% 293.09/185.64 tff(20115,plain,
% 293.09/185.64 ($false),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[1971, 20114, 20112, 1947])).
% 293.09/185.64 tff(20116,plain,(m_mutex_h_half_v_out(c_e_h_3, c_a, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s8))), inference(lemma,lemma(discharge,[]))).
% 293.09/185.64 tff(20117,plain,
% 293.09/185.64 (~m_and_h_gate_v_out(c_e_h_3, c_c, s8)),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[20116, 20013])).
% 293.09/185.64 tff(20118,assumption,(m_or_h_gate_v_in1(c_e_h_3, c_g, s8)), introduced(assumption)).
% 293.09/185.64 tff(20119,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_c, s8)), introduced(assumption)).
% 293.09/185.64 tff(20120,plain,
% 293.09/185.64 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_g, s8)) | m_and_h_gate_v_out(c_e_h_3, c_c, s8))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s8)) | m_and_h_gate_v_out(c_e_h_3, c_c, s8))),
% 293.09/185.64 inference(rewrite,[status(thm)],[])).
% 293.09/185.64 tff(20121,plain,
% 293.09/185.64 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_g, s8)) | m_and_h_gate_v_out(c_e_h_3, c_c, s8))),
% 293.09/185.64 inference(quant_inst,[status(thm)],[])).
% 293.09/185.64 tff(20122,plain,
% 293.09/185.64 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s8)) | m_and_h_gate_v_out(c_e_h_3, c_c, s8)),
% 293.09/185.64 inference(modus_ponens,[status(thm)],[20121, 20120])).
% 293.09/185.64 tff(20123,plain,
% 293.09/185.64 ($false),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[20122, 2708, 20119, 20118])).
% 293.09/185.64 tff(20124,plain,((~m_or_h_gate_v_in1(c_e_h_3, c_g, s8)) | m_and_h_gate_v_out(c_e_h_3, c_c, s8)), inference(lemma,lemma(discharge,[]))).
% 293.09/185.64 tff(20125,plain,
% 293.09/185.64 (~m_or_h_gate_v_in1(c_e_h_3, c_g, s8)),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[20124, 20117])).
% 293.09/185.64 tff(20126,plain,
% 293.09/185.64 (~m_user_v_req(c_e_h_3, c_u, s4)),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[1035, 1003])).
% 293.09/185.64 tff(20127,plain,
% 293.09/185.64 (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s4)),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[10214, 395, 20126])).
% 293.09/185.64 tff(20128,plain,
% 293.09/185.64 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s5)),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[10210, 20127, 2513])).
% 293.09/185.64 tff(20129,plain,
% 293.09/185.64 (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s5)),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[19598, 395, 1003])).
% 293.09/185.64 tff(20130,plain,
% 293.09/185.64 (~node13(c_e_h_3, c_a, s5, s6)),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[19615, 1946, 1448])).
% 293.09/185.64 tff(20131,plain,
% 293.09/185.64 (~node12(c_e_h_3, c_a, s5, s6)),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[19608, 1946, 1433])).
% 293.09/185.64 tff(20132,plain,
% 293.09/185.64 ($false),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[1506, 20131, 20130])).
% 293.09/185.64 tff(20133,plain,((~m_mutex_h_half_v_out(c_e_h_3, c_a, s6)) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s5) | m_mutex_h_half_v_out(c_e_h_3, c_a, s5)), inference(lemma,lemma(discharge,[]))).
% 293.09/185.64 tff(20134,plain,
% 293.09/185.64 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s6)),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[20133, 20129, 20128])).
% 293.09/185.64 tff(20135,plain,
% 293.09/185.64 (~m_and_h_gate_v_in1(c_e_h_3, c_c, s6)),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[20089, 20134])).
% 293.09/185.64 tff(20136,plain,
% 293.09/185.64 (~node20(c_e_h_3, c_c, s6)),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[20083, 20135])).
% 293.09/185.64 tff(20137,plain,
% 293.09/185.64 (~m_and_h_gate_v_in1(c_e_h_3, c_c, s5)),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[10191, 20128])).
% 293.09/185.64 tff(20138,plain,
% 293.09/185.64 (~node20(c_e_h_3, c_c, s5)),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[20103, 20137])).
% 293.09/185.64 tff(20139,plain,
% 293.09/185.64 (~m_and_h_gate_v_out(c_e_h_3, c_c, s6)),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[10180, 20138, 5931])).
% 293.09/185.64 tff(20140,plain,
% 293.09/185.64 ($false),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[20076, 20139, 20136, 11155])).
% 293.09/185.64 tff(20141,plain,(m_user_v_req(c_e_h_3, c_u, s5) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s7)) | m_and_h_gate_v_out(c_e_h_3, c_c, s5) | m_mutex_h_half_v_out(c_e_h_3, c_a, s4)), inference(lemma,lemma(discharge,[]))).
% 293.09/185.64 tff(20142,plain,
% 293.09/185.64 (m_user_v_req(c_e_h_3, c_u, s5)),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[20141, 11155, 5931, 2513])).
% 293.09/185.64 tff(20143,plain,
% 293.09/185.64 (m_user_v_req(c_e_h_3, c_u, s6)),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[1413, 20142])).
% 293.09/185.64 tff(20144,plain,
% 293.09/185.64 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s6)),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[1431, 20143])).
% 293.09/185.64 tff(20145,plain,
% 293.09/185.64 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s6)),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[1971, 20144, 1947])).
% 293.09/185.64 tff(20146,plain,
% 293.09/185.64 (~m_and_h_gate_v_in1(c_e_h_3, c_c, s6)),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[20089, 20145])).
% 293.09/185.64 tff(20147,plain,
% 293.09/185.64 (~node20(c_e_h_3, c_c, s6)),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[20083, 20146])).
% 293.09/185.64 tff(20148,plain,
% 293.09/185.64 (m_and_h_gate_v_out(c_e_h_3, c_c, s6)),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[20076, 20147, 11155])).
% 293.09/185.64 tff(20149,plain,
% 293.09/185.64 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s5)),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[1438, 20142])).
% 293.09/185.64 tff(20150,plain,
% 293.09/185.64 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s5)),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[1515, 20145, 20149])).
% 293.09/185.64 tff(20151,plain,
% 293.09/185.64 (~m_and_h_gate_v_in1(c_e_h_3, c_c, s5)),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[10191, 20150])).
% 293.09/185.64 tff(20152,plain,
% 293.09/185.64 (~node20(c_e_h_3, c_c, s5)),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[20103, 20151])).
% 293.09/185.64 tff(20153,plain,
% 293.09/185.64 ($false),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[10180, 20152, 20148, 5931])).
% 293.09/185.64 tff(20154,plain,((~m_and_h_gate_v_out(c_e_h_3, c_c, s7)) | m_and_h_gate_v_out(c_e_h_3, c_c, s5) | m_mutex_h_half_v_out(c_e_h_3, c_a, s7) | m_mutex_h_half_v_out(c_e_h_3, c_a, s4)), inference(lemma,lemma(discharge,[]))).
% 293.09/185.64 tff(20155,plain,
% 293.09/185.64 (~m_and_h_gate_v_out(c_e_h_3, c_c, s7)),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[20154, 20014, 20013, 20015])).
% 293.09/185.64 tff(20156,assumption,(~m_c_h_element_v_out(c_e_h_3, c_h, s14)), introduced(assumption)).
% 293.09/185.64 tff(20157,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_i, s14)), introduced(assumption)).
% 293.09/185.64 tff(20158,plain,
% 293.09/185.64 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_i, s14)) | m_c_h_element_v_out(c_e_h_3, c_h, s14))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s14)) | m_c_h_element_v_out(c_e_h_3, c_h, s14))),
% 293.09/185.64 inference(rewrite,[status(thm)],[])).
% 293.09/185.64 tff(20159,plain,
% 293.09/185.64 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_i, s14)) | m_c_h_element_v_out(c_e_h_3, c_h, s14))),
% 293.09/185.64 inference(quant_inst,[status(thm)],[])).
% 293.09/185.64 tff(20160,plain,
% 293.09/185.64 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s14)) | m_c_h_element_v_out(c_e_h_3, c_h, s14)),
% 293.09/185.64 inference(modus_ponens,[status(thm)],[20159, 20158])).
% 293.09/185.64 tff(20161,plain,
% 293.09/185.64 ($false),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[20160, 619, 20156, 20157])).
% 293.09/185.64 tff(20162,plain,(m_c_h_element_v_out(c_e_h_3, c_h, s14) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s14))), inference(lemma,lemma(discharge,[]))).
% 293.09/185.64 tff(20163,plain,
% 293.09/185.64 (~m_and_h_gate_v_in1(c_e_h_3, c_i, s14)),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[20162, 20156])).
% 293.09/185.64 tff(20164,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_i, s14)), introduced(assumption)).
% 293.09/185.64 tff(20165,assumption,(node20(c_e_h_3, c_i, s14)), introduced(assumption)).
% 293.09/185.64 tff(20166,plain,
% 293.09/185.64 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s14)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s14))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_i, s14)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s14))),
% 293.09/185.64 inference(rewrite,[status(thm)],[])).
% 293.09/185.64 tff(20167,plain,
% 293.09/185.64 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s14)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s14))),
% 293.09/185.64 inference(quant_inst,[status(thm)],[])).
% 293.09/185.64 tff(20168,plain,
% 293.09/185.64 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_i, s14)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s14)),
% 293.09/185.64 inference(modus_ponens,[status(thm)],[20167, 20166])).
% 293.09/185.64 tff(20169,plain,
% 293.09/185.64 ($false),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[20168, 38, 20165, 20164])).
% 293.09/185.64 tff(20170,plain,(m_and_h_gate_v_in1(c_e_h_3, c_i, s14) | (~node20(c_e_h_3, c_i, s14))), inference(lemma,lemma(discharge,[]))).
% 293.09/185.64 tff(20171,plain,
% 293.09/185.64 (~node20(c_e_h_3, c_i, s14)),
% 293.09/185.64 inference(unit_resolution,[status(thm)],[20170, 20163])).
% 293.09/185.64 tff(20172,assumption,(~m_or_h_gate_v_out(c_e_h_3, c_g, s10)), introduced(assumption)).
% 293.09/185.65 tff(20173,assumption,(m_and_h_gate_v_out(c_e_h_3, c_k, s10)), introduced(assumption)).
% 293.09/185.65 tff(20174,plain,
% 293.09/185.65 (~m_and_h_gate_v_out(c_e_h_3, c_c, s3)),
% 293.09/185.65 inference(unit_resolution,[status(thm)],[11306, 2743])).
% 293.09/185.65 tff(20175,plain,
% 293.09/185.65 (~m_or_h_gate_v_in1(c_e_h_3, c_g, s3)),
% 293.09/185.65 inference(unit_resolution,[status(thm)],[2713, 20174])).
% 293.09/185.65 tff(20176,plain,
% 293.09/185.65 (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)),
% 293.09/185.65 inference(unit_resolution,[status(thm)],[3377, 20175])).
% 293.09/185.65 tff(20177,plain,
% 293.09/185.65 (~m_and_h_gate_v_out(c_e_h_3, c_c, s5)),
% 293.09/185.65 inference(unit_resolution,[status(thm)],[11295, 10016])).
% 293.09/185.65 tff(20178,plain,
% 293.09/185.65 (~m_and_h_gate_v_out(c_e_h_3, c_c, s4)),
% 293.09/185.65 inference(unit_resolution,[status(thm)],[6170, 20177])).
% 293.09/185.65 tff(20179,plain,
% 293.09/185.65 (~m_or_h_gate_v_out(c_e_h_3, c_g, s5)),
% 293.09/185.65 inference(unit_resolution,[status(thm)],[11076, 20178])).
% 293.09/185.65 tff(20180,plain,
% 293.09/185.65 (~m_or_h_gate_v_in1(c_e_h_3, c_g, s5)),
% 293.09/185.65 inference(unit_resolution,[status(thm)],[10058, 20177])).
% 293.09/185.65 tff(20181,plain,
% 293.09/185.65 (~node6(c_e_h_3, c_g, s5, s6)),
% 293.09/185.65 inference(unit_resolution,[status(thm)],[10269, 10261, 3360])).
% 293.09/185.65 tff(20182,plain,
% 293.09/185.65 ((~node5(c_e_h_3, c_g, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s6)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s5)),
% 293.09/185.65 inference(unit_resolution,[status(thm)],[10309, 9740])).
% 293.09/185.65 tff(20183,plain,
% 293.09/185.65 (~node5(c_e_h_3, c_g, s5, s6)),
% 293.09/185.65 inference(unit_resolution,[status(thm)],[20182, 10261, 6172])).
% 293.09/185.65 tff(20184,plain,
% 293.09/185.65 ($false),
% 293.09/185.65 inference(unit_resolution,[status(thm)],[6216, 20183, 20181])).
% 293.09/185.65 tff(20185,plain,((~m_or_h_gate_v_out(c_e_h_3, c_g, s6)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s5) | m_or_h_gate_v_out(c_e_h_3, c_g, s5)), inference(lemma,lemma(discharge,[]))).
% 293.09/185.65 tff(20186,plain,
% 293.09/185.65 (~m_or_h_gate_v_out(c_e_h_3, c_g, s6)),
% 293.09/185.65 inference(unit_resolution,[status(thm)],[20185, 20180, 20179])).
% 293.09/185.65 tff(20187,assumption,(~m_or_h_gate_v_in1(c_e_h_3, c_g, s8)), introduced(assumption)).
% 293.09/185.65 tff(20188,plain,
% 293.09/185.65 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_g, s7)) | m_and_h_gate_v_out(c_e_h_3, c_c, s7))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s7)) | m_and_h_gate_v_out(c_e_h_3, c_c, s7))),
% 293.09/185.65 inference(rewrite,[status(thm)],[])).
% 293.09/185.65 tff(20189,plain,
% 293.09/185.65 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_g, s7)) | m_and_h_gate_v_out(c_e_h_3, c_c, s7))),
% 293.09/185.65 inference(quant_inst,[status(thm)],[])).
% 293.09/185.65 tff(20190,plain,
% 293.09/185.65 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s7)) | m_and_h_gate_v_out(c_e_h_3, c_c, s7)),
% 293.09/185.65 inference(modus_ponens,[status(thm)],[20189, 20188])).
% 293.09/185.65 tff(20191,plain,
% 293.09/185.65 ($false),
% 293.09/185.65 inference(unit_resolution,[status(thm)],[20190, 2708, 10016, 11277])).
% 293.09/185.65 tff(20192,plain,((~m_or_h_gate_v_in1(c_e_h_3, c_g, s7)) | m_and_h_gate_v_out(c_e_h_3, c_c, s7)), inference(lemma,lemma(discharge,[]))).
% 293.09/185.65 tff(20193,plain,
% 293.09/185.65 (~m_or_h_gate_v_in1(c_e_h_3, c_g, s7)),
% 293.09/185.65 inference(unit_resolution,[status(thm)],[20192, 10016])).
% 293.09/185.65 tff(20194,plain,
% 293.09/185.65 (~m_or_h_gate_v_out(c_e_h_3, c_g, s5)),
% 293.09/185.65 inference(unit_resolution,[status(thm)],[11076, 2743])).
% 293.09/185.65 tff(20195,plain,
% 293.09/185.65 (~m_or_h_gate_v_out(c_e_h_3, c_g, s7)),
% 293.09/185.65 inference(unit_resolution,[status(thm)],[10302, 10016, 6189, 20194, 2743])).
% 293.09/185.65 tff(20196,assumption,(node6(c_e_h_3, c_g, s7, s8)), introduced(assumption)).
% 293.09/185.65 tff(20197,plain,
% 293.09/185.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s7) | (~node6(c_e_h_3, c_g, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_g, s7) | (~node6(c_e_h_3, c_g, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s8)))),
% 293.09/185.65 inference(rewrite,[status(thm)],[])).
% 293.09/185.65 tff(20198,plain,
% 293.09/185.65 (((~node6(c_e_h_3, c_g, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s8)) | m_or_h_gate_v_out(c_e_h_3, c_g, s7)) <=> (m_or_h_gate_v_out(c_e_h_3, c_g, s7) | (~node6(c_e_h_3, c_g, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s8)))),
% 293.09/185.65 inference(rewrite,[status(thm)],[])).
% 293.09/185.65 tff(20199,plain,
% 293.09/185.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_g, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s8)) | m_or_h_gate_v_out(c_e_h_3, c_g, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s7) | (~node6(c_e_h_3, c_g, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s8))))),
% 293.09/185.65 inference(monotonicity,[status(thm)],[20198])).
% 293.09/185.65 tff(20200,plain,
% 293.09/185.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_g, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s8)) | m_or_h_gate_v_out(c_e_h_3, c_g, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_g, s7) | (~node6(c_e_h_3, c_g, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s8)))),
% 293.09/185.65 inference(transitivity,[status(thm)],[20199, 20197])).
% 293.09/185.65 tff(20201,plain,
% 293.09/185.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_g, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s8)) | m_or_h_gate_v_out(c_e_h_3, c_g, s7))),
% 293.09/185.65 inference(quant_inst,[status(thm)],[])).
% 293.09/185.65 tff(20202,plain,
% 293.09/185.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_g, s7) | (~node6(c_e_h_3, c_g, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s8))),
% 293.09/185.65 inference(modus_ponens,[status(thm)],[20201, 20200])).
% 293.09/185.65 tff(20203,plain,
% 293.09/185.65 ($false),
% 293.09/185.65 inference(unit_resolution,[status(thm)],[20202, 1121, 20196, 11161, 10390])).
% 293.09/185.65 tff(20204,plain,((~node6(c_e_h_3, c_g, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s8)) | m_or_h_gate_v_out(c_e_h_3, c_g, s7)), inference(lemma,lemma(discharge,[]))).
% 293.09/185.65 tff(20205,plain,
% 293.09/185.65 (~node6(c_e_h_3, c_g, s7, s8)),
% 293.09/185.65 inference(unit_resolution,[status(thm)],[20204, 11161, 10390])).
% 293.09/185.65 tff(20206,plain,
% 293.09/185.65 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_g, s7)) | m_and_h_gate_v_out(c_e_h_3, c_d, s7))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_g, s7)) | m_and_h_gate_v_out(c_e_h_3, c_d, s7))),
% 293.09/185.65 inference(rewrite,[status(thm)],[])).
% 293.09/185.65 tff(20207,plain,
% 293.09/185.65 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_g, s7)) | m_and_h_gate_v_out(c_e_h_3, c_d, s7))),
% 293.09/185.65 inference(quant_inst,[status(thm)],[])).
% 293.09/185.65 tff(20208,plain,
% 293.09/185.65 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_g, s7)) | m_and_h_gate_v_out(c_e_h_3, c_d, s7)),
% 293.09/185.65 inference(modus_ponens,[status(thm)],[20207, 20206])).
% 293.09/185.65 tff(20209,plain,
% 293.09/185.65 (~m_or_h_gate_v_in2(c_e_h_3, c_g, s7)),
% 293.09/185.65 inference(unit_resolution,[status(thm)],[20208, 2762, 17182])).
% 293.09/185.65 tff(20210,assumption,(~m_or_h_gate_v_in2(c_e_h_3, c_g, s7)), introduced(assumption)).
% 293.09/185.65 tff(20211,plain,
% 293.09/185.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~node5(c_e_h_3, c_g, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s8)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s7) | m_or_h_gate_v_in2(c_e_h_3, c_g, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~node5(c_e_h_3, c_g, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s8)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s7) | m_or_h_gate_v_in2(c_e_h_3, c_g, s7))),
% 293.09/185.65 inference(rewrite,[status(thm)],[])).
% 293.09/185.65 tff(20212,plain,
% 293.09/185.65 ((m_or_h_gate_v_in1(c_e_h_3, c_g, s7) | m_or_h_gate_v_in2(c_e_h_3, c_g, s7) | (~node5(c_e_h_3, c_g, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s8))) <=> ((~node5(c_e_h_3, c_g, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s8)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s7) | m_or_h_gate_v_in2(c_e_h_3, c_g, s7))),
% 293.09/185.65 inference(rewrite,[status(thm)],[])).
% 293.09/185.65 tff(20213,plain,
% 293.09/185.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_g, s7) | m_or_h_gate_v_in2(c_e_h_3, c_g, s7) | (~node5(c_e_h_3, c_g, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~node5(c_e_h_3, c_g, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s8)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s7) | m_or_h_gate_v_in2(c_e_h_3, c_g, s7)))),
% 293.09/185.65 inference(monotonicity,[status(thm)],[20212])).
% 293.09/185.65 tff(20214,plain,
% 293.09/185.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_g, s7) | m_or_h_gate_v_in2(c_e_h_3, c_g, s7) | (~node5(c_e_h_3, c_g, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~node5(c_e_h_3, c_g, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s8)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s7) | m_or_h_gate_v_in2(c_e_h_3, c_g, s7))),
% 293.09/185.65 inference(transitivity,[status(thm)],[20213, 20211])).
% 293.09/185.65 tff(20215,plain,
% 293.09/185.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_g, s7) | m_or_h_gate_v_in2(c_e_h_3, c_g, s7) | (~node5(c_e_h_3, c_g, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s8)))),
% 293.09/185.65 inference(quant_inst,[status(thm)],[])).
% 293.09/185.65 tff(20216,plain,
% 293.09/185.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~node5(c_e_h_3, c_g, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s8)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s7) | m_or_h_gate_v_in2(c_e_h_3, c_g, s7)),
% 293.09/185.65 inference(modus_ponens,[status(thm)],[20215, 20214])).
% 293.09/185.65 tff(20217,plain,
% 293.09/185.65 ($false),
% 293.09/185.65 inference(unit_resolution,[status(thm)],[20216, 1159, 9503, 11161, 11154, 20210])).
% 293.09/185.65 tff(20218,plain,((~node5(c_e_h_3, c_g, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s8)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s7) | m_or_h_gate_v_in2(c_e_h_3, c_g, s7)), inference(lemma,lemma(discharge,[]))).
% 293.09/185.65 tff(20219,plain,
% 293.09/185.65 (~node5(c_e_h_3, c_g, s7, s8)),
% 293.09/185.65 inference(unit_resolution,[status(thm)],[20218, 11161, 11154, 20209])).
% 293.09/185.65 tff(20220,plain,
% 293.09/185.65 ($false),
% 293.09/185.65 inference(unit_resolution,[status(thm)],[9519, 20219, 20205])).
% 293.09/185.65 tff(20221,plain,((~m_or_h_gate_v_out(c_e_h_3, c_g, s8)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s7) | m_or_h_gate_v_out(c_e_h_3, c_g, s7)), inference(lemma,lemma(discharge,[]))).
% 293.09/185.65 tff(20222,plain,
% 293.09/185.65 ($false),
% 293.09/185.65 inference(unit_resolution,[status(thm)],[20221, 20195, 20193, 11161])).
% 293.09/185.65 tff(20223,plain,(m_and_h_gate_v_out(c_e_h_3, c_c, s7) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s8)) | m_or_h_gate_v_out(c_e_h_3, c_g, s6) | m_and_h_gate_v_out(c_e_h_3, c_c, s4)), inference(lemma,lemma(discharge,[]))).
% 293.09/185.65 tff(20224,plain,
% 293.09/185.65 (~m_or_h_gate_v_out(c_e_h_3, c_g, s8)),
% 293.09/185.65 inference(unit_resolution,[status(thm)],[20223, 10016, 6189, 2743])).
% 293.09/185.65 tff(20225,assumption,(m_or_h_gate_v_out(c_e_h_3, c_g, s9)), introduced(assumption)).
% 293.09/185.65 tff(20226,assumption,(node5(c_e_h_3, c_g, s8, s9)), introduced(assumption)).
% 293.09/185.65 tff(20227,plain,
% 293.09/185.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_3, c_g, s9)) | (~node5(c_e_h_3, c_g, s8, s9)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s8) | m_or_h_gate_v_in2(c_e_h_3, c_g, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s9)) | (~node5(c_e_h_3, c_g, s8, s9)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s8) | m_or_h_gate_v_in2(c_e_h_3, c_g, s8))),
% 293.09/185.66 inference(rewrite,[status(thm)],[])).
% 293.09/185.66 tff(20228,plain,
% 293.09/185.66 ((m_or_h_gate_v_in1(c_e_h_3, c_g, s8) | m_or_h_gate_v_in2(c_e_h_3, c_g, s8) | (~node5(c_e_h_3, c_g, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s9))) <=> ((~m_or_h_gate_v_out(c_e_h_3, c_g, s9)) | (~node5(c_e_h_3, c_g, s8, s9)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s8) | m_or_h_gate_v_in2(c_e_h_3, c_g, s8))),
% 293.09/185.66 inference(rewrite,[status(thm)],[])).
% 293.09/185.66 tff(20229,plain,
% 293.09/185.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_g, s8) | m_or_h_gate_v_in2(c_e_h_3, c_g, s8) | (~node5(c_e_h_3, c_g, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_3, c_g, s9)) | (~node5(c_e_h_3, c_g, s8, s9)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s8) | m_or_h_gate_v_in2(c_e_h_3, c_g, s8)))),
% 293.09/185.66 inference(monotonicity,[status(thm)],[20228])).
% 293.09/185.66 tff(20230,plain,
% 293.09/185.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_g, s8) | m_or_h_gate_v_in2(c_e_h_3, c_g, s8) | (~node5(c_e_h_3, c_g, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s9)) | (~node5(c_e_h_3, c_g, s8, s9)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s8) | m_or_h_gate_v_in2(c_e_h_3, c_g, s8))),
% 293.09/185.66 inference(transitivity,[status(thm)],[20229, 20227])).
% 293.09/185.66 tff(20231,plain,
% 293.09/185.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_g, s8) | m_or_h_gate_v_in2(c_e_h_3, c_g, s8) | (~node5(c_e_h_3, c_g, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s9)))),
% 293.09/185.66 inference(quant_inst,[status(thm)],[])).
% 293.09/185.66 tff(20232,plain,
% 293.09/185.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s9)) | (~node5(c_e_h_3, c_g, s8, s9)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s8) | m_or_h_gate_v_in2(c_e_h_3, c_g, s8)),
% 293.09/185.66 inference(modus_ponens,[status(thm)],[20231, 20230])).
% 293.09/185.66 tff(20233,plain,
% 293.09/185.66 ($false),
% 293.09/185.66 inference(unit_resolution,[status(thm)],[20232, 1159, 20226, 20225, 20018, 20187])).
% 293.09/185.66 tff(20234,plain,((~node5(c_e_h_3, c_g, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s9)) | m_or_h_gate_v_in2(c_e_h_3, c_g, s8) | m_or_h_gate_v_in1(c_e_h_3, c_g, s8)), inference(lemma,lemma(discharge,[]))).
% 293.09/185.66 tff(20235,plain,
% 293.09/185.66 (~node5(c_e_h_3, c_g, s8, s9)),
% 293.09/185.66 inference(unit_resolution,[status(thm)],[20234, 20225, 20018, 20187])).
% 293.09/185.66 tff(20236,assumption,(node6(c_e_h_3, c_g, s8, s9)), introduced(assumption)).
% 293.09/185.66 tff(20237,plain,
% 293.09/185.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_3, c_g, s9)) | m_or_h_gate_v_out(c_e_h_3, c_g, s8) | (~node6(c_e_h_3, c_g, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s9)) | m_or_h_gate_v_out(c_e_h_3, c_g, s8) | (~node6(c_e_h_3, c_g, s8, s9)))),
% 293.09/185.66 inference(rewrite,[status(thm)],[])).
% 293.09/185.66 tff(20238,plain,
% 293.09/185.66 (((~node6(c_e_h_3, c_g, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s9)) | m_or_h_gate_v_out(c_e_h_3, c_g, s8)) <=> ((~m_or_h_gate_v_out(c_e_h_3, c_g, s9)) | m_or_h_gate_v_out(c_e_h_3, c_g, s8) | (~node6(c_e_h_3, c_g, s8, s9)))),
% 293.09/185.66 inference(rewrite,[status(thm)],[])).
% 293.09/185.66 tff(20239,plain,
% 293.09/185.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_g, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s9)) | m_or_h_gate_v_out(c_e_h_3, c_g, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_3, c_g, s9)) | m_or_h_gate_v_out(c_e_h_3, c_g, s8) | (~node6(c_e_h_3, c_g, s8, s9))))),
% 293.09/185.66 inference(monotonicity,[status(thm)],[20238])).
% 293.09/185.66 tff(20240,plain,
% 293.09/185.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_g, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s9)) | m_or_h_gate_v_out(c_e_h_3, c_g, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s9)) | m_or_h_gate_v_out(c_e_h_3, c_g, s8) | (~node6(c_e_h_3, c_g, s8, s9)))),
% 293.09/185.66 inference(transitivity,[status(thm)],[20239, 20237])).
% 293.09/185.66 tff(20241,plain,
% 293.09/185.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_g, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s9)) | m_or_h_gate_v_out(c_e_h_3, c_g, s8))),
% 293.09/185.66 inference(quant_inst,[status(thm)],[])).
% 293.09/185.66 tff(20242,plain,
% 293.09/185.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s9)) | m_or_h_gate_v_out(c_e_h_3, c_g, s8) | (~node6(c_e_h_3, c_g, s8, s9))),
% 293.09/185.66 inference(modus_ponens,[status(thm)],[20241, 20240])).
% 293.09/185.66 tff(20243,plain,
% 293.09/185.66 ($false),
% 293.09/185.66 inference(unit_resolution,[status(thm)],[20242, 1121, 20236, 20225, 9500])).
% 293.09/185.66 tff(20244,plain,((~node6(c_e_h_3, c_g, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s9)) | m_or_h_gate_v_out(c_e_h_3, c_g, s8)), inference(lemma,lemma(discharge,[]))).
% 293.09/185.66 tff(20245,plain,
% 293.09/185.66 (~node6(c_e_h_3, c_g, s8, s9)),
% 293.09/185.66 inference(unit_resolution,[status(thm)],[20244, 20225, 9500])).
% 293.09/185.66 tff(20246,plain,
% 293.09/185.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s8, s9)) | node5(c_e_h_3, c_g, s8, s9) | node6(c_e_h_3, c_g, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s8, s9)) | node5(c_e_h_3, c_g, s8, s9) | node6(c_e_h_3, c_g, s8, s9))),
% 293.09/185.66 inference(rewrite,[status(thm)],[])).
% 293.09/185.66 tff(20247,plain,
% 293.09/185.66 ((node6(c_e_h_3, c_g, s8, s9) | node5(c_e_h_3, c_g, s8, s9) | (~trans(s8, s9))) <=> ((~trans(s8, s9)) | node5(c_e_h_3, c_g, s8, s9) | node6(c_e_h_3, c_g, s8, s9))),
% 293.09/185.66 inference(rewrite,[status(thm)],[])).
% 293.09/185.66 tff(20248,plain,
% 293.09/185.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s8, s9) | node5(c_e_h_3, c_g, s8, s9) | (~trans(s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s8, s9)) | node5(c_e_h_3, c_g, s8, s9) | node6(c_e_h_3, c_g, s8, s9)))),
% 293.09/185.66 inference(monotonicity,[status(thm)],[20247])).
% 293.09/185.66 tff(20249,plain,
% 293.09/185.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s8, s9) | node5(c_e_h_3, c_g, s8, s9) | (~trans(s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s8, s9)) | node5(c_e_h_3, c_g, s8, s9) | node6(c_e_h_3, c_g, s8, s9))),
% 293.09/185.67 inference(transitivity,[status(thm)],[20248, 20246])).
% 293.09/185.67 tff(20250,plain,
% 293.09/185.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s8, s9) | node5(c_e_h_3, c_g, s8, s9) | (~trans(s8, s9)))),
% 293.09/185.67 inference(quant_inst,[status(thm)],[])).
% 293.09/185.67 tff(20251,plain,
% 293.09/185.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s8, s9)) | node5(c_e_h_3, c_g, s8, s9) | node6(c_e_h_3, c_g, s8, s9)),
% 293.09/185.67 inference(modus_ponens,[status(thm)],[20250, 20249])).
% 293.09/185.67 tff(20252,plain,
% 293.09/185.67 (node5(c_e_h_3, c_g, s8, s9) | node6(c_e_h_3, c_g, s8, s9)),
% 293.09/185.67 inference(unit_resolution,[status(thm)],[20251, 1141, 1993])).
% 293.09/185.67 tff(20253,plain,
% 293.09/185.67 ($false),
% 293.09/185.67 inference(unit_resolution,[status(thm)],[20252, 20245, 20235])).
% 293.09/185.67 tff(20254,plain,((~m_or_h_gate_v_out(c_e_h_3, c_g, s9)) | m_or_h_gate_v_out(c_e_h_3, c_g, s8) | m_or_h_gate_v_in2(c_e_h_3, c_g, s8) | m_or_h_gate_v_in1(c_e_h_3, c_g, s8)), inference(lemma,lemma(discharge,[]))).
% 293.09/185.67 tff(20255,plain,
% 293.09/185.67 (~m_or_h_gate_v_out(c_e_h_3, c_g, s9)),
% 293.09/185.67 inference(unit_resolution,[status(thm)],[20254, 20224, 20018, 20187])).
% 293.09/185.67 tff(20256,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_k, s9)), introduced(assumption)).
% 293.09/185.67 tff(20257,assumption,(~m_or_h_gate_v_out(c_e_h_3, c_g, s9)), introduced(assumption)).
% 293.09/185.67 tff(20258,plain,
% 293.09/185.67 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_k, s9)) | m_or_h_gate_v_out(c_e_h_3, c_g, s9))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s9)) | m_or_h_gate_v_out(c_e_h_3, c_g, s9))),
% 293.09/185.67 inference(rewrite,[status(thm)],[])).
% 293.09/185.67 tff(20259,plain,
% 293.09/185.67 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_k, s9)) | m_or_h_gate_v_out(c_e_h_3, c_g, s9))),
% 293.09/185.67 inference(quant_inst,[status(thm)],[])).
% 293.09/185.67 tff(20260,plain,
% 293.09/185.67 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s9)) | m_or_h_gate_v_out(c_e_h_3, c_g, s9)),
% 293.09/185.67 inference(modus_ponens,[status(thm)],[20259, 20258])).
% 293.09/185.67 tff(20261,plain,
% 293.09/185.67 ($false),
% 293.09/185.67 inference(unit_resolution,[status(thm)],[20260, 2048, 20257, 20256])).
% 293.09/185.67 tff(20262,plain,((~m_and_h_gate_v_in1(c_e_h_3, c_k, s9)) | m_or_h_gate_v_out(c_e_h_3, c_g, s9)), inference(lemma,lemma(discharge,[]))).
% 293.09/185.67 tff(20263,plain,
% 293.09/185.67 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s9)),
% 293.09/185.67 inference(unit_resolution,[status(thm)],[20262, 20255])).
% 293.09/185.67 tff(20264,plain,
% 293.09/185.67 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s5)),
% 293.09/185.67 inference(unit_resolution,[status(thm)],[3365, 20194])).
% 293.09/185.67 tff(20265,plain,
% 293.09/185.67 (~node20(c_e_h_3, c_k, s5)),
% 293.09/185.67 inference(unit_resolution,[status(thm)],[5458, 20264])).
% 293.09/185.67 tff(20266,plain,
% 293.09/185.67 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s4)),
% 293.09/185.67 inference(unit_resolution,[status(thm)],[3384, 20176])).
% 293.09/185.67 tff(20267,plain,
% 293.09/185.67 (~node20(c_e_h_3, c_k, s4)),
% 293.09/185.67 inference(unit_resolution,[status(thm)],[3392, 20266])).
% 293.09/185.67 tff(20268,plain,
% 293.09/185.67 (~m_and_h_gate_v_out(c_e_h_3, c_k, s5)),
% 293.09/185.67 inference(unit_resolution,[status(thm)],[7635, 20267])).
% 293.09/185.67 tff(20269,plain,
% 293.09/185.67 (~m_and_h_gate_v_out(c_e_h_3, c_k, s6)),
% 293.09/185.67 inference(unit_resolution,[status(thm)],[4467, 20268, 20265])).
% 293.09/185.67 tff(20270,plain,
% 293.09/185.67 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s6)),
% 293.09/185.67 inference(unit_resolution,[status(thm)],[10448, 2048, 6189])).
% 293.09/185.67 tff(20271,plain,
% 293.09/185.67 (~node20(c_e_h_3, c_k, s6)),
% 293.09/185.67 inference(unit_resolution,[status(thm)],[10444, 38, 20270])).
% 293.09/185.67 tff(20272,plain,
% 293.09/185.67 (~m_and_h_gate_v_out(c_e_h_3, c_k, s7)),
% 293.09/185.67 inference(unit_resolution,[status(thm)],[10440, 20271, 20269])).
% 293.09/185.67 tff(20273,plain,
% 293.09/185.67 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s7)),
% 293.09/185.67 inference(unit_resolution,[status(thm)],[10395, 20195])).
% 293.09/185.67 tff(20274,plain,
% 293.09/185.67 (~node20(c_e_h_3, c_k, s7)),
% 293.09/185.67 inference(unit_resolution,[status(thm)],[10403, 20273])).
% 293.09/185.67 tff(20275,plain,
% 293.09/185.67 (~m_and_h_gate_v_out(c_e_h_3, c_k, s8)),
% 293.09/185.67 inference(unit_resolution,[status(thm)],[10425, 20274, 20272])).
% 293.09/185.67 tff(20276,plain,
% 293.09/185.67 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_k, s8)) | m_or_h_gate_v_out(c_e_h_3, c_g, s8))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s8)) | m_or_h_gate_v_out(c_e_h_3, c_g, s8))),
% 293.09/185.67 inference(rewrite,[status(thm)],[])).
% 293.09/185.67 tff(20277,plain,
% 293.09/185.67 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_k, s8)) | m_or_h_gate_v_out(c_e_h_3, c_g, s8))),
% 293.09/185.67 inference(quant_inst,[status(thm)],[])).
% 293.09/185.67 tff(20278,plain,
% 293.09/185.67 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s8)) | m_or_h_gate_v_out(c_e_h_3, c_g, s8)),
% 293.09/185.67 inference(modus_ponens,[status(thm)],[20277, 20276])).
% 293.09/185.67 tff(20279,plain,
% 293.09/185.67 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s8)),
% 293.09/185.67 inference(unit_resolution,[status(thm)],[20278, 2048, 20224])).
% 293.09/185.67 tff(20280,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_k, s8)), introduced(assumption)).
% 293.09/185.67 tff(20281,assumption,(node20(c_e_h_3, c_k, s8)), introduced(assumption)).
% 293.09/185.67 tff(20282,plain,
% 293.09/185.67 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_k, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_k, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s8))),
% 293.09/185.67 inference(rewrite,[status(thm)],[])).
% 293.09/185.67 tff(20283,plain,
% 293.09/185.67 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_k, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s8))),
% 293.09/185.67 inference(quant_inst,[status(thm)],[])).
% 293.09/185.67 tff(20284,plain,
% 293.09/185.67 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_k, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s8)),
% 293.09/185.67 inference(modus_ponens,[status(thm)],[20283, 20282])).
% 293.09/185.67 tff(20285,plain,
% 293.09/185.67 ($false),
% 293.09/185.67 inference(unit_resolution,[status(thm)],[20284, 38, 20281, 20280])).
% 293.09/185.67 tff(20286,plain,(m_and_h_gate_v_in1(c_e_h_3, c_k, s8) | (~node20(c_e_h_3, c_k, s8))), inference(lemma,lemma(discharge,[]))).
% 293.09/185.67 tff(20287,plain,
% 293.09/185.67 (~node20(c_e_h_3, c_k, s8)),
% 293.09/185.67 inference(unit_resolution,[status(thm)],[20286, 20279])).
% 293.09/185.67 tff(20288,assumption,(~node20(c_e_h_3, c_k, s8)), introduced(assumption)).
% 293.09/185.67 tff(20289,plain,
% 293.09/185.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_k, s8) | (~node21(c_e_h_3, c_k, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_k, s8) | (~node21(c_e_h_3, c_k, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s9)))),
% 293.09/185.67 inference(rewrite,[status(thm)],[])).
% 293.09/185.67 tff(20290,plain,
% 293.09/185.67 ((node20(c_e_h_3, c_k, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s9)) | (~node21(c_e_h_3, c_k, s8, s9))) <=> (node20(c_e_h_3, c_k, s8) | (~node21(c_e_h_3, c_k, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s9)))),
% 293.09/185.67 inference(rewrite,[status(thm)],[])).
% 293.09/185.67 tff(20291,plain,
% 293.09/185.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_k, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s9)) | (~node21(c_e_h_3, c_k, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_k, s8) | (~node21(c_e_h_3, c_k, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s9))))),
% 293.09/185.67 inference(monotonicity,[status(thm)],[20290])).
% 293.09/185.67 tff(20292,plain,
% 293.09/185.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_k, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s9)) | (~node21(c_e_h_3, c_k, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_k, s8) | (~node21(c_e_h_3, c_k, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s9)))),
% 293.09/185.67 inference(transitivity,[status(thm)],[20291, 20289])).
% 293.09/185.67 tff(20293,plain,
% 293.09/185.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_k, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s9)) | (~node21(c_e_h_3, c_k, s8, s9)))),
% 293.09/185.67 inference(quant_inst,[status(thm)],[])).
% 293.09/185.67 tff(20294,plain,
% 293.09/185.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_k, s8) | (~node21(c_e_h_3, c_k, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s9))),
% 293.09/185.67 inference(modus_ponens,[status(thm)],[20293, 20292])).
% 293.09/185.67 tff(20295,plain,
% 293.09/185.67 ($false),
% 293.09/185.67 inference(unit_resolution,[status(thm)],[20294, 52, 9486, 9461, 20288])).
% 293.09/185.67 tff(20296,plain,((~node21(c_e_h_3, c_k, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s9)) | node20(c_e_h_3, c_k, s8)), inference(lemma,lemma(discharge,[]))).
% 293.09/185.67 tff(20297,plain,
% 293.09/185.67 (~node21(c_e_h_3, c_k, s8, s9)),
% 293.09/185.67 inference(unit_resolution,[status(thm)],[20296, 9461, 20288])).
% 293.09/185.67 tff(20298,plain,
% 293.09/185.67 (node22(c_e_h_3, c_k, s8, s9)),
% 293.09/185.67 inference(unit_resolution,[status(thm)],[9483, 20297])).
% 293.09/185.67 tff(20299,plain,
% 293.09/185.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s9)) | (~node22(c_e_h_3, c_k, s8, s9)) | m_and_h_gate_v_out(c_e_h_3, c_k, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s9)) | (~node22(c_e_h_3, c_k, s8, s9)) | m_and_h_gate_v_out(c_e_h_3, c_k, s8))),
% 293.09/185.67 inference(rewrite,[status(thm)],[])).
% 293.09/185.67 tff(20300,plain,
% 293.09/185.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s9)) | (~node22(c_e_h_3, c_k, s8, s9)) | m_and_h_gate_v_out(c_e_h_3, c_k, s8))),
% 293.09/185.67 inference(quant_inst,[status(thm)],[])).
% 293.09/185.67 tff(20301,plain,
% 293.09/185.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s9)) | (~node22(c_e_h_3, c_k, s8, s9)) | m_and_h_gate_v_out(c_e_h_3, c_k, s8)),
% 293.09/185.67 inference(modus_ponens,[status(thm)],[20300, 20299])).
% 293.09/185.67 tff(20302,plain,
% 293.09/185.67 ($false),
% 293.09/185.67 inference(unit_resolution,[status(thm)],[20301, 108, 20298, 10531, 9461])).
% 293.09/185.67 tff(20303,plain,((~m_and_h_gate_v_out(c_e_h_3, c_k, s9)) | m_and_h_gate_v_out(c_e_h_3, c_k, s8) | node20(c_e_h_3, c_k, s8)), inference(lemma,lemma(discharge,[]))).
% 293.09/185.67 tff(20304,plain,
% 293.09/185.67 (~m_and_h_gate_v_out(c_e_h_3, c_k, s9)),
% 293.09/185.67 inference(unit_resolution,[status(thm)],[20303, 20287, 20275])).
% 293.09/185.67 tff(20305,assumption,(node22(c_e_h_3, c_k, s9, s10)), introduced(assumption)).
% 293.09/185.67 tff(20306,plain,
% 293.09/185.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s10)) | (~node22(c_e_h_3, c_k, s9, s10)) | m_and_h_gate_v_out(c_e_h_3, c_k, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s10)) | (~node22(c_e_h_3, c_k, s9, s10)) | m_and_h_gate_v_out(c_e_h_3, c_k, s9))),
% 293.09/185.67 inference(rewrite,[status(thm)],[])).
% 293.09/185.67 tff(20307,plain,
% 293.09/185.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s10)) | (~node22(c_e_h_3, c_k, s9, s10)) | m_and_h_gate_v_out(c_e_h_3, c_k, s9))),
% 293.09/185.67 inference(quant_inst,[status(thm)],[])).
% 293.09/185.67 tff(20308,plain,
% 293.09/185.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s10)) | (~node22(c_e_h_3, c_k, s9, s10)) | m_and_h_gate_v_out(c_e_h_3, c_k, s9)),
% 293.09/185.68 inference(modus_ponens,[status(thm)],[20307, 20306])).
% 293.09/185.68 tff(20309,plain,
% 293.09/185.68 ($false),
% 293.09/185.68 inference(unit_resolution,[status(thm)],[20308, 108, 20305, 9469, 20173])).
% 293.09/185.68 tff(20310,plain,((~node22(c_e_h_3, c_k, s9, s10)) | m_and_h_gate_v_out(c_e_h_3, c_k, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s10))), inference(lemma,lemma(discharge,[]))).
% 293.09/185.68 tff(20311,plain,
% 293.09/185.68 (~node22(c_e_h_3, c_k, s9, s10)),
% 293.09/185.68 inference(unit_resolution,[status(thm)],[20310, 20173, 9469])).
% 293.09/185.68 tff(20312,assumption,(~node20(c_e_h_3, c_k, s9)), introduced(assumption)).
% 293.09/185.68 tff(20313,assumption,(node21(c_e_h_3, c_k, s9, s10)), introduced(assumption)).
% 293.09/185.68 tff(20314,plain,
% 293.09/185.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_k, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s10)) | (~node21(c_e_h_3, c_k, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_k, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s10)) | (~node21(c_e_h_3, c_k, s9, s10)))),
% 293.09/185.68 inference(rewrite,[status(thm)],[])).
% 293.09/185.68 tff(20315,plain,
% 293.09/185.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_k, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s10)) | (~node21(c_e_h_3, c_k, s9, s10)))),
% 293.09/185.68 inference(quant_inst,[status(thm)],[])).
% 293.09/185.68 tff(20316,plain,
% 293.09/185.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_k, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s10)) | (~node21(c_e_h_3, c_k, s9, s10))),
% 293.09/185.68 inference(modus_ponens,[status(thm)],[20315, 20314])).
% 293.09/185.68 tff(20317,plain,
% 293.09/185.68 ($false),
% 293.09/185.68 inference(unit_resolution,[status(thm)],[20316, 52, 20313, 20173, 20312])).
% 293.09/185.68 tff(20318,plain,((~node21(c_e_h_3, c_k, s9, s10)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s10)) | node20(c_e_h_3, c_k, s9)), inference(lemma,lemma(discharge,[]))).
% 293.09/185.68 tff(20319,plain,
% 293.09/185.68 (~node21(c_e_h_3, c_k, s9, s10)),
% 293.09/185.68 inference(unit_resolution,[status(thm)],[20318, 20173, 20312])).
% 293.09/185.68 tff(20320,plain,
% 293.09/185.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s9, s10)) | node21(c_e_h_3, c_k, s9, s10) | node22(c_e_h_3, c_k, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s9, s10)) | node21(c_e_h_3, c_k, s9, s10) | node22(c_e_h_3, c_k, s9, s10))),
% 293.09/185.68 inference(rewrite,[status(thm)],[])).
% 293.09/185.68 tff(20321,plain,
% 293.09/185.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s9, s10)) | node21(c_e_h_3, c_k, s9, s10) | node22(c_e_h_3, c_k, s9, s10))),
% 293.09/185.68 inference(quant_inst,[status(thm)],[])).
% 293.09/185.68 tff(20322,plain,
% 293.09/185.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s9, s10)) | node21(c_e_h_3, c_k, s9, s10) | node22(c_e_h_3, c_k, s9, s10)),
% 293.09/185.68 inference(modus_ponens,[status(thm)],[20321, 20320])).
% 293.09/185.68 tff(20323,plain,
% 293.09/185.68 (node21(c_e_h_3, c_k, s9, s10) | node22(c_e_h_3, c_k, s9, s10)),
% 293.09/185.68 inference(unit_resolution,[status(thm)],[20322, 82, 7676])).
% 293.09/185.68 tff(20324,plain,
% 293.09/185.68 ($false),
% 293.09/185.68 inference(unit_resolution,[status(thm)],[20323, 20319, 20311])).
% 293.09/185.68 tff(20325,plain,((~m_and_h_gate_v_out(c_e_h_3, c_k, s10)) | node20(c_e_h_3, c_k, s9) | m_and_h_gate_v_out(c_e_h_3, c_k, s9)), inference(lemma,lemma(discharge,[]))).
% 293.09/185.68 tff(20326,plain,
% 293.09/185.68 (node20(c_e_h_3, c_k, s9)),
% 293.09/185.68 inference(unit_resolution,[status(thm)],[20325, 20304, 20173])).
% 293.09/185.68 tff(20327,plain,
% 293.09/185.68 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_k, s9)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s9))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_k, s9)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s9))),
% 293.09/185.68 inference(rewrite,[status(thm)],[])).
% 293.09/185.68 tff(20328,plain,
% 293.09/185.68 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_k, s9)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s9))),
% 293.09/185.68 inference(quant_inst,[status(thm)],[])).
% 293.09/185.68 tff(20329,plain,
% 293.09/185.68 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_k, s9)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s9)),
% 293.09/185.68 inference(modus_ponens,[status(thm)],[20328, 20327])).
% 293.09/185.68 tff(20330,plain,
% 293.09/185.68 ($false),
% 293.09/185.68 inference(unit_resolution,[status(thm)],[20329, 38, 20326, 20263])).
% 293.09/185.68 tff(20331,plain,(m_and_h_gate_v_out(c_e_h_3, c_c, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s10)) | m_or_h_gate_v_in2(c_e_h_3, c_g, s8) | m_or_h_gate_v_in1(c_e_h_3, c_g, s8) | m_or_h_gate_v_out(c_e_h_3, c_g, s6) | m_and_h_gate_v_out(c_e_h_3, c_c, s4)), inference(lemma,lemma(discharge,[]))).
% 293.09/185.68 tff(20332,plain,
% 293.09/185.68 (m_or_h_gate_v_in1(c_e_h_3, c_g, s8)),
% 293.09/185.68 inference(unit_resolution,[status(thm)],[20331, 20173, 20018, 10016, 20186, 20178])).
% 293.09/185.68 tff(20333,plain,
% 293.09/185.68 (m_and_h_gate_v_out(c_e_h_3, c_c, s8)),
% 293.09/185.68 inference(unit_resolution,[status(thm)],[20124, 20332])).
% 293.09/185.68 tff(20334,plain,
% 293.09/185.68 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s4)),
% 293.09/185.68 inference(unit_resolution,[status(thm)],[550, 19565])).
% 293.09/185.68 tff(20335,plain,
% 293.09/185.68 (~m_and_h_gate_v_out(c_e_h_3, c_c, s5)),
% 293.09/185.68 inference(unit_resolution,[status(thm)],[10330, 20334])).
% 293.09/185.68 tff(20336,plain,
% 293.09/185.68 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s7)),
% 293.09/185.68 inference(unit_resolution,[status(thm)],[19621, 1826])).
% 293.09/185.68 tff(20337,plain,
% 293.09/185.68 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s5)),
% 293.09/185.68 inference(unit_resolution,[status(thm)],[10210, 19618, 20334])).
% 293.09/185.68 tff(20338,plain,
% 293.09/185.68 (m_and_h_gate_v_out(c_e_h_3, c_c, s6)),
% 293.09/185.68 inference(unit_resolution,[status(thm)],[20098, 20337, 20020, 20336])).
% 293.09/185.68 tff(20339,plain,
% 293.09/185.68 (~m_and_h_gate_v_in1(c_e_h_3, c_c, s5)),
% 293.09/185.68 inference(unit_resolution,[status(thm)],[10191, 20337])).
% 293.09/185.68 tff(20340,plain,
% 293.09/185.68 (~node20(c_e_h_3, c_c, s5)),
% 293.09/185.68 inference(unit_resolution,[status(thm)],[20103, 20339])).
% 293.09/185.68 tff(20341,plain,
% 293.09/185.68 ($false),
% 293.09/185.68 inference(unit_resolution,[status(thm)],[10180, 20340, 20338, 20335])).
% 293.09/185.68 tff(20342,plain,(m_user_v_req(c_e_h_3, c_u, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s8))), inference(lemma,lemma(discharge,[]))).
% 293.09/185.68 tff(20343,plain,
% 293.09/185.68 (m_user_v_req(c_e_h_3, c_u, s7)),
% 293.09/185.68 inference(unit_resolution,[status(thm)],[20342, 20020])).
% 293.09/185.68 tff(20344,plain,
% 293.09/185.68 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s7)),
% 293.09/185.68 inference(unit_resolution,[status(thm)],[1908, 20343])).
% 293.09/185.68 tff(20345,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_c, s9)), introduced(assumption)).
% 293.09/185.68 tff(20346,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_c, s8)), introduced(assumption)).
% 293.09/185.68 tff(20347,assumption,(node22(c_e_h_3, c_c, s8, s9)), introduced(assumption)).
% 293.09/185.68 tff(20348,plain,
% 293.09/185.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_c, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s8)) | (~node22(c_e_h_3, c_c, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | m_and_h_gate_v_out(c_e_h_3, c_c, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s8)) | (~node22(c_e_h_3, c_c, s8, s9)))),
% 293.09/185.68 inference(rewrite,[status(thm)],[])).
% 293.09/185.68 tff(20349,plain,
% 293.09/185.68 ((m_and_h_gate_v_out(c_e_h_3, c_c, s9) | (~node22(c_e_h_3, c_c, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s8))) <=> (m_and_h_gate_v_out(c_e_h_3, c_c, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s8)) | (~node22(c_e_h_3, c_c, s8, s9)))),
% 293.09/185.68 inference(rewrite,[status(thm)],[])).
% 293.09/185.68 tff(20350,plain,
% 293.09/185.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_c, s9) | (~node22(c_e_h_3, c_c, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_c, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s8)) | (~node22(c_e_h_3, c_c, s8, s9))))),
% 293.09/185.68 inference(monotonicity,[status(thm)],[20349])).
% 293.09/185.68 tff(20351,plain,
% 293.09/185.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_c, s9) | (~node22(c_e_h_3, c_c, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | m_and_h_gate_v_out(c_e_h_3, c_c, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s8)) | (~node22(c_e_h_3, c_c, s8, s9)))),
% 293.09/185.68 inference(transitivity,[status(thm)],[20350, 20348])).
% 293.09/185.68 tff(20352,plain,
% 293.09/185.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_c, s9) | (~node22(c_e_h_3, c_c, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s8)))),
% 293.09/185.68 inference(quant_inst,[status(thm)],[])).
% 293.09/185.68 tff(20353,plain,
% 293.09/185.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | m_and_h_gate_v_out(c_e_h_3, c_c, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s8)) | (~node22(c_e_h_3, c_c, s8, s9))),
% 293.09/185.68 inference(modus_ponens,[status(thm)],[20352, 20351])).
% 293.09/185.68 tff(20354,plain,
% 293.09/185.68 ($false),
% 293.09/185.68 inference(unit_resolution,[status(thm)],[20353, 5871, 20020, 20347, 20345])).
% 293.09/185.68 tff(20355,plain,((~node22(c_e_h_3, c_c, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s8)) | m_and_h_gate_v_out(c_e_h_3, c_c, s9)), inference(lemma,lemma(discharge,[]))).
% 293.09/185.68 tff(20356,plain,
% 293.09/185.68 (~node22(c_e_h_3, c_c, s8, s9)),
% 293.09/185.68 inference(unit_resolution,[status(thm)],[20355, 20345, 20020])).
% 293.09/185.68 tff(20357,plain,
% 293.09/185.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s8, s9)) | node21(c_e_h_3, c_c, s8, s9) | node22(c_e_h_3, c_c, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_3, c_c, s8, s9) | node22(c_e_h_3, c_c, s8, s9))),
% 293.09/185.68 inference(rewrite,[status(thm)],[])).
% 293.09/185.68 tff(20358,plain,
% 293.09/185.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s8, s9)) | node21(c_e_h_3, c_c, s8, s9) | node22(c_e_h_3, c_c, s8, s9))),
% 293.09/185.68 inference(quant_inst,[status(thm)],[])).
% 293.09/185.68 tff(20359,plain,
% 293.09/185.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_3, c_c, s8, s9) | node22(c_e_h_3, c_c, s8, s9)),
% 293.09/185.68 inference(modus_ponens,[status(thm)],[20358, 20357])).
% 293.09/185.68 tff(20360,plain,
% 293.09/185.68 (node21(c_e_h_3, c_c, s8, s9) | node22(c_e_h_3, c_c, s8, s9)),
% 293.09/185.68 inference(unit_resolution,[status(thm)],[20359, 82, 1993])).
% 293.09/185.68 tff(20361,plain,
% 293.09/185.68 (node21(c_e_h_3, c_c, s8, s9)),
% 293.09/185.68 inference(unit_resolution,[status(thm)],[20360, 20356])).
% 293.09/185.68 tff(20362,plain,
% 293.09/185.68 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s7)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s7)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7))),
% 293.09/185.68 inference(rewrite,[status(thm)],[])).
% 293.09/185.68 tff(20363,plain,
% 293.09/185.68 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s7)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7))),
% 293.09/185.68 inference(quant_inst,[status(thm)],[])).
% 293.09/185.68 tff(20364,plain,
% 293.09/185.68 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s7)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s7)),
% 293.09/185.68 inference(modus_ponens,[status(thm)],[20363, 20362])).
% 293.09/185.68 tff(20365,plain,
% 293.09/185.68 (~m_and_h_gate_v_in2(c_e_h_3, c_q, s7)),
% 293.09/185.68 inference(unit_resolution,[status(thm)],[20364, 5621, 10840])).
% 293.09/185.69 tff(20366,plain,
% 293.09/185.69 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s7)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s7)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s7))),
% 293.09/185.69 inference(rewrite,[status(thm)],[])).
% 293.09/185.69 tff(20367,plain,
% 293.09/185.69 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s7)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s7))),
% 293.09/185.69 inference(quant_inst,[status(thm)],[])).
% 293.09/185.69 tff(20368,plain,
% 293.09/185.69 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s7)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s7)),
% 293.09/185.69 inference(modus_ponens,[status(thm)],[20367, 20366])).
% 293.09/185.69 tff(20369,plain,
% 293.09/185.69 (~node20(c_e_h_3, c_q, s7)),
% 293.09/185.69 inference(unit_resolution,[status(thm)],[20368, 4563, 20365])).
% 293.09/185.69 tff(20370,assumption,(m_and_h_gate_v_out(c_e_h_3, c_q, s7)), introduced(assumption)).
% 293.09/185.69 tff(20371,assumption,(node21(c_e_h_3, c_q, s6, s7)), introduced(assumption)).
% 293.09/185.69 tff(20372,plain,
% 293.09/185.69 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s6)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s6)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6))),
% 293.09/185.69 inference(rewrite,[status(thm)],[])).
% 293.09/185.69 tff(20373,plain,
% 293.09/185.69 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s6)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6))),
% 293.09/185.69 inference(quant_inst,[status(thm)],[])).
% 293.09/185.69 tff(20374,plain,
% 293.09/185.69 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s6)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s6)),
% 293.09/185.69 inference(modus_ponens,[status(thm)],[20373, 20372])).
% 293.09/185.69 tff(20375,plain,
% 293.09/185.69 (~m_and_h_gate_v_in2(c_e_h_3, c_q, s6)),
% 293.09/185.69 inference(unit_resolution,[status(thm)],[20374, 5621, 7112])).
% 293.09/185.69 tff(20376,plain,
% 293.09/185.69 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s6)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s6)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s6))),
% 293.09/185.69 inference(rewrite,[status(thm)],[])).
% 293.09/185.69 tff(20377,plain,
% 293.09/185.69 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s6)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s6))),
% 293.09/185.69 inference(quant_inst,[status(thm)],[])).
% 293.09/185.69 tff(20378,plain,
% 293.09/185.69 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s6)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s6)),
% 293.09/185.69 inference(modus_ponens,[status(thm)],[20377, 20376])).
% 293.09/185.69 tff(20379,plain,
% 293.09/185.69 (~node20(c_e_h_3, c_q, s6)),
% 293.09/185.69 inference(unit_resolution,[status(thm)],[20378, 4563, 20375])).
% 293.09/185.69 tff(20380,plain,
% 293.09/185.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s7)) | node20(c_e_h_3, c_q, s6) | (~node21(c_e_h_3, c_q, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s7)) | node20(c_e_h_3, c_q, s6) | (~node21(c_e_h_3, c_q, s6, s7)))),
% 293.09/185.69 inference(rewrite,[status(thm)],[])).
% 293.09/185.69 tff(20381,plain,
% 293.09/185.69 ((node20(c_e_h_3, c_q, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s7)) | (~node21(c_e_h_3, c_q, s6, s7))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_q, s7)) | node20(c_e_h_3, c_q, s6) | (~node21(c_e_h_3, c_q, s6, s7)))),
% 293.09/185.69 inference(rewrite,[status(thm)],[])).
% 293.09/185.69 tff(20382,plain,
% 293.09/185.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s7)) | (~node21(c_e_h_3, c_q, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s7)) | node20(c_e_h_3, c_q, s6) | (~node21(c_e_h_3, c_q, s6, s7))))),
% 293.09/185.69 inference(monotonicity,[status(thm)],[20381])).
% 293.09/185.69 tff(20383,plain,
% 293.09/185.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s7)) | (~node21(c_e_h_3, c_q, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s7)) | node20(c_e_h_3, c_q, s6) | (~node21(c_e_h_3, c_q, s6, s7)))),
% 293.09/185.69 inference(transitivity,[status(thm)],[20382, 20380])).
% 293.09/185.69 tff(20384,plain,
% 293.09/185.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s6) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s7)) | (~node21(c_e_h_3, c_q, s6, s7)))),
% 293.09/185.69 inference(quant_inst,[status(thm)],[])).
% 293.09/185.69 tff(20385,plain,
% 293.09/185.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s7)) | node20(c_e_h_3, c_q, s6) | (~node21(c_e_h_3, c_q, s6, s7))),
% 293.09/185.69 inference(modus_ponens,[status(thm)],[20384, 20383])).
% 293.09/185.69 tff(20386,plain,
% 293.09/185.69 ($false),
% 293.09/185.69 inference(unit_resolution,[status(thm)],[20385, 52, 20370, 20379, 20371])).
% 293.09/185.69 tff(20387,plain,((~node21(c_e_h_3, c_q, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s7))), inference(lemma,lemma(discharge,[]))).
% 293.09/185.69 tff(20388,plain,
% 293.09/185.69 (~node21(c_e_h_3, c_q, s6, s7)),
% 293.09/185.69 inference(unit_resolution,[status(thm)],[20387, 20370])).
% 293.09/185.69 tff(20389,assumption,(node22(c_e_h_3, c_q, s6, s7)), introduced(assumption)).
% 293.09/185.69 tff(20390,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_q, s6)), introduced(assumption)).
% 293.09/185.69 tff(20391,plain,
% 293.09/185.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s7)) | (~node22(c_e_h_3, c_q, s6, s7)) | m_and_h_gate_v_out(c_e_h_3, c_q, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s7)) | (~node22(c_e_h_3, c_q, s6, s7)) | m_and_h_gate_v_out(c_e_h_3, c_q, s6))),
% 293.09/185.69 inference(rewrite,[status(thm)],[])).
% 293.09/185.69 tff(20392,plain,
% 293.09/185.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s7)) | (~node22(c_e_h_3, c_q, s6, s7)) | m_and_h_gate_v_out(c_e_h_3, c_q, s6))),
% 293.09/185.69 inference(quant_inst,[status(thm)],[])).
% 293.09/185.69 tff(20393,plain,
% 293.09/185.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s7)) | (~node22(c_e_h_3, c_q, s6, s7)) | m_and_h_gate_v_out(c_e_h_3, c_q, s6)),
% 293.09/185.69 inference(modus_ponens,[status(thm)],[20392, 20391])).
% 293.09/185.69 tff(20394,plain,
% 293.09/185.69 ($false),
% 293.09/185.69 inference(unit_resolution,[status(thm)],[20393, 108, 20370, 20390, 20389])).
% 293.09/185.69 tff(20395,plain,((~node22(c_e_h_3, c_q, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s7)) | m_and_h_gate_v_out(c_e_h_3, c_q, s6)), inference(lemma,lemma(discharge,[]))).
% 293.09/185.69 tff(20396,plain,
% 293.09/185.69 (~node22(c_e_h_3, c_q, s6, s7)),
% 293.09/185.69 inference(unit_resolution,[status(thm)],[20395, 20370, 10137])).
% 293.09/185.69 tff(20397,plain,
% 293.09/185.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_3, c_q, s6, s7) | node22(c_e_h_3, c_q, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_3, c_q, s6, s7) | node22(c_e_h_3, c_q, s6, s7))),
% 293.20/185.69 inference(rewrite,[status(thm)],[])).
% 293.20/185.69 tff(20398,plain,
% 293.20/185.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_3, c_q, s6, s7) | node22(c_e_h_3, c_q, s6, s7))),
% 293.20/185.69 inference(quant_inst,[status(thm)],[])).
% 293.20/185.69 tff(20399,plain,
% 293.20/185.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_3, c_q, s6, s7) | node22(c_e_h_3, c_q, s6, s7)),
% 293.20/185.69 inference(modus_ponens,[status(thm)],[20398, 20397])).
% 293.20/185.69 tff(20400,plain,
% 293.20/185.69 (node21(c_e_h_3, c_q, s6, s7) | node22(c_e_h_3, c_q, s6, s7)),
% 293.20/185.69 inference(unit_resolution,[status(thm)],[20399, 82, 1844])).
% 293.20/185.69 tff(20401,plain,
% 293.20/185.69 ($false),
% 293.20/185.69 inference(unit_resolution,[status(thm)],[20400, 20396, 20388])).
% 293.20/185.69 tff(20402,plain,(~m_and_h_gate_v_out(c_e_h_3, c_q, s7)), inference(lemma,lemma(discharge,[]))).
% 293.20/185.69 tff(20403,assumption,(~node20(c_e_h_3, c_q, s7)), introduced(assumption)).
% 293.20/185.69 tff(20404,assumption,(m_and_h_gate_v_out(c_e_h_3, c_q, s8)), introduced(assumption)).
% 293.20/185.69 tff(20405,assumption,(node21(c_e_h_3, c_q, s7, s8)), introduced(assumption)).
% 293.20/185.69 tff(20406,plain,
% 293.20/185.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s8)) | (~node21(c_e_h_3, c_q, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_q, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s8)) | (~node21(c_e_h_3, c_q, s7, s8)))),
% 293.20/185.69 inference(rewrite,[status(thm)],[])).
% 293.20/185.69 tff(20407,plain,
% 293.20/185.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s8)) | (~node21(c_e_h_3, c_q, s7, s8)))),
% 293.20/185.69 inference(quant_inst,[status(thm)],[])).
% 293.20/185.69 tff(20408,plain,
% 293.20/185.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_q, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s8)) | (~node21(c_e_h_3, c_q, s7, s8))),
% 293.20/185.69 inference(modus_ponens,[status(thm)],[20407, 20406])).
% 293.20/185.69 tff(20409,plain,
% 293.20/185.69 ($false),
% 293.20/185.69 inference(unit_resolution,[status(thm)],[20408, 52, 20404, 20405, 20403])).
% 293.20/185.69 tff(20410,plain,((~node21(c_e_h_3, c_q, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s8)) | node20(c_e_h_3, c_q, s7)), inference(lemma,lemma(discharge,[]))).
% 293.20/185.69 tff(20411,plain,
% 293.20/185.69 (~node21(c_e_h_3, c_q, s7, s8)),
% 293.20/185.69 inference(unit_resolution,[status(thm)],[20410, 20404, 20403])).
% 293.20/185.69 tff(20412,plain,
% 293.20/185.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_3, c_q, s7, s8) | node22(c_e_h_3, c_q, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_3, c_q, s7, s8) | node22(c_e_h_3, c_q, s7, s8))),
% 293.20/185.69 inference(rewrite,[status(thm)],[])).
% 293.20/185.69 tff(20413,plain,
% 293.20/185.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_3, c_q, s7, s8) | node22(c_e_h_3, c_q, s7, s8))),
% 293.20/185.69 inference(quant_inst,[status(thm)],[])).
% 293.20/185.69 tff(20414,plain,
% 293.20/185.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_3, c_q, s7, s8) | node22(c_e_h_3, c_q, s7, s8)),
% 293.20/185.69 inference(modus_ponens,[status(thm)],[20413, 20412])).
% 293.20/185.69 tff(20415,plain,
% 293.20/185.69 (node21(c_e_h_3, c_q, s7, s8) | node22(c_e_h_3, c_q, s7, s8)),
% 293.20/185.69 inference(unit_resolution,[status(thm)],[20414, 82, 1938])).
% 293.20/185.69 tff(20416,plain,
% 293.20/185.69 (node22(c_e_h_3, c_q, s7, s8)),
% 293.20/185.69 inference(unit_resolution,[status(thm)],[20415, 20411])).
% 293.20/185.69 tff(20417,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_q, s7)), introduced(assumption)).
% 293.20/185.69 tff(20418,plain,
% 293.20/185.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s8)) | (~node22(c_e_h_3, c_q, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_q, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s8)) | (~node22(c_e_h_3, c_q, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_q, s7))),
% 293.20/185.70 inference(rewrite,[status(thm)],[])).
% 293.20/185.70 tff(20419,plain,
% 293.20/185.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s8)) | (~node22(c_e_h_3, c_q, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_q, s7))),
% 293.20/185.70 inference(quant_inst,[status(thm)],[])).
% 293.20/185.70 tff(20420,plain,
% 293.20/185.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s8)) | (~node22(c_e_h_3, c_q, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_q, s7)),
% 293.20/185.70 inference(modus_ponens,[status(thm)],[20419, 20418])).
% 293.20/185.70 tff(20421,plain,
% 293.20/185.70 ($false),
% 293.20/185.70 inference(unit_resolution,[status(thm)],[20420, 108, 20417, 20404, 20416])).
% 293.20/185.70 tff(20422,plain,((~m_and_h_gate_v_out(c_e_h_3, c_q, s8)) | m_and_h_gate_v_out(c_e_h_3, c_q, s7) | node20(c_e_h_3, c_q, s7)), inference(lemma,lemma(discharge,[]))).
% 293.20/185.70 tff(20423,plain,
% 293.20/185.70 ((~m_and_h_gate_v_out(c_e_h_3, c_q, s8)) | node20(c_e_h_3, c_q, s7)),
% 293.20/185.70 inference(unit_resolution,[status(thm)],[20422, 20402])).
% 293.20/185.70 tff(20424,plain,
% 293.20/185.70 (~m_and_h_gate_v_out(c_e_h_3, c_q, s8)),
% 293.20/185.70 inference(unit_resolution,[status(thm)],[20423, 20369])).
% 293.20/185.70 tff(20425,plain,
% 293.20/185.70 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s8))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s8))),
% 293.20/185.70 inference(rewrite,[status(thm)],[])).
% 293.20/185.70 tff(20426,plain,
% 293.20/185.70 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s8))),
% 293.20/185.70 inference(quant_inst,[status(thm)],[])).
% 293.20/185.70 tff(20427,plain,
% 293.20/185.70 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s8)),
% 293.20/185.70 inference(modus_ponens,[status(thm)],[20426, 20425])).
% 293.20/185.70 tff(20428,plain,
% 293.20/185.70 (node3(c_e_h_3, c_e_h_1, s8)),
% 293.20/185.70 inference(unit_resolution,[status(thm)],[20427, 2922, 1056])).
% 293.20/185.70 tff(20429,plain,
% 293.20/185.70 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s8)) | (~node3(c_e_h_3, c_e_h_1, s8)) | m_and_h_gate_v_out(c_e_h_3, c_q, s8))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s8)) | (~node3(c_e_h_3, c_e_h_1, s8)) | m_and_h_gate_v_out(c_e_h_3, c_q, s8))),
% 293.20/185.70 inference(rewrite,[status(thm)],[])).
% 293.20/185.70 tff(20430,plain,
% 293.20/185.70 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s8)) | (~node3(c_e_h_3, c_e_h_1, s8)) | m_and_h_gate_v_out(c_e_h_3, c_q, s8))),
% 293.20/185.70 inference(quant_inst,[status(thm)],[])).
% 293.20/185.70 tff(20431,plain,
% 293.20/185.70 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s8)) | (~node3(c_e_h_3, c_e_h_1, s8)) | m_and_h_gate_v_out(c_e_h_3, c_q, s8)),
% 293.20/185.70 inference(modus_ponens,[status(thm)],[20430, 20429])).
% 293.20/185.70 tff(20432,plain,
% 293.20/185.70 ((~m_cell_v_ack(c_e_h_1, s8)) | m_and_h_gate_v_out(c_e_h_3, c_q, s8)),
% 293.20/185.70 inference(unit_resolution,[status(thm)],[20431, 1073, 20428])).
% 293.20/185.70 tff(20433,plain,
% 293.20/185.70 (~m_cell_v_ack(c_e_h_1, s8)),
% 293.20/185.70 inference(unit_resolution,[status(thm)],[20432, 20424])).
% 293.20/185.70 tff(20434,plain,
% 293.20/185.70 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node2(c_e_h_3, c_e_h_1, s8))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node2(c_e_h_3, c_e_h_1, s8))),
% 293.20/185.70 inference(rewrite,[status(thm)],[])).
% 293.20/185.70 tff(20435,plain,
% 293.20/185.70 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node2(c_e_h_3, c_e_h_1, s8))),
% 293.20/185.70 inference(quant_inst,[status(thm)],[])).
% 293.20/185.70 tff(20436,plain,
% 293.20/185.70 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node2(c_e_h_3, c_e_h_1, s8)),
% 293.20/185.70 inference(modus_ponens,[status(thm)],[20435, 20434])).
% 293.20/185.70 tff(20437,plain,
% 293.20/185.70 (node2(c_e_h_3, c_e_h_1, s8)),
% 293.20/185.70 inference(unit_resolution,[status(thm)],[20436, 2922, 5821])).
% 293.20/185.70 tff(20438,plain,
% 293.20/185.70 (((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | ((~node2(c_e_h_3, c_e_h_1, s8)) | m_cell_v_ack(c_e_h_1, s8) | m_and_h_gate_v_in2(c_e_h_3, c_c, s8))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | (~node2(c_e_h_3, c_e_h_1, s8)) | m_cell_v_ack(c_e_h_1, s8) | m_and_h_gate_v_in2(c_e_h_3, c_c, s8))),
% 293.20/185.70 inference(rewrite,[status(thm)],[])).
% 293.20/185.70 tff(20439,plain,
% 293.20/185.70 ((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | ((~node2(c_e_h_3, c_e_h_1, s8)) | m_cell_v_ack(c_e_h_1, s8) | m_and_h_gate_v_in2(c_e_h_3, c_c, s8))),
% 293.20/185.70 inference(quant_inst,[status(thm)],[])).
% 293.20/185.70 tff(20440,plain,
% 293.20/185.70 ((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | (~node2(c_e_h_3, c_e_h_1, s8)) | m_cell_v_ack(c_e_h_1, s8) | m_and_h_gate_v_in2(c_e_h_3, c_c, s8)),
% 293.20/185.70 inference(modus_ponens,[status(thm)],[20439, 20438])).
% 293.20/185.70 tff(20441,plain,
% 293.20/185.70 (m_cell_v_ack(c_e_h_1, s8) | m_and_h_gate_v_in2(c_e_h_3, c_c, s8)),
% 293.20/185.70 inference(unit_resolution,[status(thm)],[20440, 5835, 20437])).
% 293.20/185.70 tff(20442,plain,
% 293.20/185.70 (m_and_h_gate_v_in2(c_e_h_3, c_c, s8)),
% 293.20/185.70 inference(unit_resolution,[status(thm)],[20441, 20433])).
% 293.20/185.70 tff(20443,plain,
% 293.20/185.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_c, s8)) | m_and_h_gate_v_out(c_e_h_3, c_c, s9) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s8)) | (~node21(c_e_h_3, c_c, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s8)) | m_and_h_gate_v_out(c_e_h_3, c_c, s9) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s8)) | (~node21(c_e_h_3, c_c, s8, s9)))),
% 293.20/185.70 inference(rewrite,[status(thm)],[])).
% 293.20/185.70 tff(20444,plain,
% 293.20/185.70 (((~node21(c_e_h_3, c_c, s8, s9)) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s8)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s8)) | m_and_h_gate_v_out(c_e_h_3, c_c, s9)) <=> ((~m_and_h_gate_v_in2(c_e_h_3, c_c, s8)) | m_and_h_gate_v_out(c_e_h_3, c_c, s9) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s8)) | (~node21(c_e_h_3, c_c, s8, s9)))),
% 293.20/185.70 inference(rewrite,[status(thm)],[])).
% 293.20/185.70 tff(20445,plain,
% 293.20/185.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_c, s8, s9)) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s8)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s8)) | m_and_h_gate_v_out(c_e_h_3, c_c, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_c, s8)) | m_and_h_gate_v_out(c_e_h_3, c_c, s9) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s8)) | (~node21(c_e_h_3, c_c, s8, s9))))),
% 293.20/185.70 inference(monotonicity,[status(thm)],[20444])).
% 293.20/185.70 tff(20446,plain,
% 293.20/185.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_c, s8, s9)) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s8)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s8)) | m_and_h_gate_v_out(c_e_h_3, c_c, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s8)) | m_and_h_gate_v_out(c_e_h_3, c_c, s9) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s8)) | (~node21(c_e_h_3, c_c, s8, s9)))),
% 293.20/185.70 inference(transitivity,[status(thm)],[20445, 20443])).
% 293.20/185.70 tff(20447,plain,
% 293.20/185.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_c, s8, s9)) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s8)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s8)) | m_and_h_gate_v_out(c_e_h_3, c_c, s9))),
% 293.20/185.70 inference(quant_inst,[status(thm)],[])).
% 293.20/185.70 tff(20448,plain,
% 293.20/185.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s8)) | m_and_h_gate_v_out(c_e_h_3, c_c, s9) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s8)) | (~node21(c_e_h_3, c_c, s8, s9))),
% 293.20/185.70 inference(modus_ponens,[status(thm)],[20447, 20446])).
% 293.20/185.70 tff(20449,plain,
% 293.20/185.70 ($false),
% 293.20/185.70 inference(unit_resolution,[status(thm)],[20448, 5851, 20442, 20361, 20345, 20346])).
% 293.20/185.70 tff(20450,plain,(m_and_h_gate_v_out(c_e_h_3, c_c, s9) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s8)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s8))), inference(lemma,lemma(discharge,[]))).
% 293.20/185.70 tff(20451,plain,
% 293.20/185.70 (~m_and_h_gate_v_in1(c_e_h_3, c_c, s8)),
% 293.20/185.70 inference(unit_resolution,[status(thm)],[20450, 20020, 20345])).
% 293.20/185.70 tff(20452,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_c, s8)), introduced(assumption)).
% 293.20/185.70 tff(20453,plain,
% 293.20/185.70 (((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s8))) <=> ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s8))),
% 293.20/185.70 inference(rewrite,[status(thm)],[])).
% 293.20/185.70 tff(20454,plain,
% 293.20/185.70 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s8))),
% 293.20/185.70 inference(quant_inst,[status(thm)],[])).
% 293.20/185.70 tff(20455,plain,
% 293.20/185.70 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s8)),
% 293.20/185.70 inference(modus_ponens,[status(thm)],[20454, 20453])).
% 293.20/185.70 tff(20456,plain,
% 293.20/185.70 ($false),
% 293.20/185.70 inference(unit_resolution,[status(thm)],[20455, 2556, 1976, 20452])).
% 293.20/185.70 tff(20457,plain,(m_and_h_gate_v_in1(c_e_h_3, c_c, s8) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s8))), inference(lemma,lemma(discharge,[]))).
% 293.20/185.70 tff(20458,plain,
% 293.20/185.70 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s8)),
% 293.20/185.70 inference(unit_resolution,[status(thm)],[20457, 20451])).
% 293.20/185.70 tff(20459,plain,
% 293.20/185.70 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s7)),
% 293.20/185.70 inference(unit_resolution,[status(thm)],[1944, 20458, 20344])).
% 293.20/185.70 tff(20460,plain,
% 293.20/185.70 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s4)),
% 293.20/185.70 inference(unit_resolution,[status(thm)],[1973, 20458])).
% 293.20/185.70 tff(20461,plain,
% 293.20/185.70 (~m_and_h_gate_v_out(c_e_h_3, c_c, s5)),
% 293.20/185.70 inference(unit_resolution,[status(thm)],[10330, 20460])).
% 293.20/185.70 tff(20462,plain,
% 293.20/185.70 (m_mutex_h_half_v_out(c_e_h_3, c_a, s5)),
% 293.20/185.70 inference(unit_resolution,[status(thm)],[20106, 20459, 20020, 20461])).
% 293.20/185.70 tff(20463,plain,
% 293.20/185.70 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s4)),
% 293.20/185.70 inference(unit_resolution,[status(thm)],[10210, 20462, 20460])).
% 293.20/185.70 tff(20464,plain,
% 293.20/185.70 (m_user_v_req(c_e_h_3, c_u, s4)),
% 293.20/185.70 inference(unit_resolution,[status(thm)],[10214, 395, 20463])).
% 293.20/185.70 tff(20465,plain,
% 293.20/185.70 (m_user_v_req(c_e_h_3, c_u, s5)),
% 293.20/185.70 inference(unit_resolution,[status(thm)],[1035, 20464])).
% 293.20/185.70 tff(20466,plain,
% 293.20/185.70 (m_user_v_req(c_e_h_3, c_u, s6)),
% 293.21/185.71 inference(unit_resolution,[status(thm)],[1413, 20465])).
% 293.21/185.71 tff(20467,plain,
% 293.21/185.71 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s6)),
% 293.21/185.71 inference(unit_resolution,[status(thm)],[1431, 20466])).
% 293.21/185.71 tff(20468,plain,
% 293.21/185.71 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s5)),
% 293.21/185.71 inference(unit_resolution,[status(thm)],[1438, 20465])).
% 293.21/185.71 tff(20469,plain,
% 293.21/185.71 (m_mutex_h_half_v_out(c_e_h_3, c_a, s6)),
% 293.21/185.71 inference(unit_resolution,[status(thm)],[1515, 20468, 20462])).
% 293.21/185.71 tff(20470,plain,
% 293.21/185.71 ($false),
% 293.21/185.71 inference(unit_resolution,[status(thm)],[1971, 20469, 20467, 20459])).
% 293.21/185.71 tff(20471,plain,((~m_and_h_gate_v_out(c_e_h_3, c_c, s8)) | m_and_h_gate_v_out(c_e_h_3, c_c, s9)), inference(lemma,lemma(discharge,[]))).
% 293.21/185.71 tff(20472,plain,
% 293.21/185.71 (m_and_h_gate_v_out(c_e_h_3, c_c, s9)),
% 293.21/185.71 inference(unit_resolution,[status(thm)],[20471, 20333])).
% 293.21/185.71 tff(20473,assumption,(~m_or_h_gate_v_in1(c_e_h_3, c_g, s9)), introduced(assumption)).
% 293.21/185.71 tff(20474,assumption,(m_and_h_gate_v_out(c_e_h_3, c_c, s9)), introduced(assumption)).
% 293.21/185.71 tff(20475,plain,
% 293.21/185.71 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s9)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s9))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s9)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s9))),
% 293.21/185.71 inference(rewrite,[status(thm)],[])).
% 293.21/185.71 tff(20476,plain,
% 293.21/185.71 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s9)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s9))),
% 293.21/185.71 inference(quant_inst,[status(thm)],[])).
% 293.21/185.71 tff(20477,plain,
% 293.21/185.71 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s9)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s9)),
% 293.21/185.71 inference(modus_ponens,[status(thm)],[20476, 20475])).
% 293.21/185.71 tff(20478,plain,
% 293.21/185.71 ($false),
% 293.21/185.71 inference(unit_resolution,[status(thm)],[20477, 5896, 20474, 20473])).
% 293.21/185.71 tff(20479,plain,(m_or_h_gate_v_in1(c_e_h_3, c_g, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s9))), inference(lemma,lemma(discharge,[]))).
% 293.21/185.71 tff(20480,plain,
% 293.21/185.71 (m_or_h_gate_v_in1(c_e_h_3, c_g, s9)),
% 293.21/185.71 inference(unit_resolution,[status(thm)],[20479, 20472])).
% 293.21/185.71 tff(20481,plain,
% 293.21/185.71 (~m_or_h_gate_v_out(c_e_h_3, c_g, s7)),
% 293.21/185.71 inference(unit_resolution,[status(thm)],[10302, 20186, 10016, 20179, 20178])).
% 293.21/185.71 tff(20482,plain,
% 293.21/185.71 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s7)),
% 293.21/185.71 inference(unit_resolution,[status(thm)],[10395, 20481])).
% 293.21/185.71 tff(20483,plain,
% 293.21/185.71 (~node20(c_e_h_3, c_k, s7)),
% 293.21/185.71 inference(unit_resolution,[status(thm)],[10403, 20482])).
% 293.21/185.71 tff(20484,plain,
% 293.21/185.71 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s5)),
% 293.21/185.71 inference(unit_resolution,[status(thm)],[3365, 20179])).
% 293.21/185.71 tff(20485,plain,
% 293.21/185.71 (~node20(c_e_h_3, c_k, s5)),
% 293.21/185.71 inference(unit_resolution,[status(thm)],[5458, 20484])).
% 293.21/185.71 tff(20486,plain,
% 293.21/185.71 (~m_and_h_gate_v_out(c_e_h_3, c_c, s3)),
% 293.21/185.71 inference(unit_resolution,[status(thm)],[11306, 20178])).
% 293.21/185.71 tff(20487,plain,
% 293.21/185.71 (~m_or_h_gate_v_in1(c_e_h_3, c_g, s3)),
% 293.21/185.71 inference(unit_resolution,[status(thm)],[2713, 20486])).
% 293.21/185.71 tff(20488,plain,
% 293.21/185.71 (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)),
% 293.21/185.71 inference(unit_resolution,[status(thm)],[3377, 20487])).
% 293.21/185.71 tff(20489,plain,
% 293.21/185.71 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s4)),
% 293.21/185.71 inference(unit_resolution,[status(thm)],[3384, 20488])).
% 293.21/185.71 tff(20490,plain,
% 293.21/185.71 (~node20(c_e_h_3, c_k, s4)),
% 293.21/185.71 inference(unit_resolution,[status(thm)],[3392, 20489])).
% 293.21/185.71 tff(20491,plain,
% 293.21/185.71 (~m_and_h_gate_v_out(c_e_h_3, c_k, s5)),
% 293.21/185.71 inference(unit_resolution,[status(thm)],[7635, 20490])).
% 293.21/185.71 tff(20492,plain,
% 293.21/185.71 (~m_and_h_gate_v_out(c_e_h_3, c_k, s6)),
% 293.21/185.71 inference(unit_resolution,[status(thm)],[4467, 20491, 20485])).
% 293.21/185.71 tff(20493,plain,
% 293.21/185.71 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s6)),
% 293.21/185.71 inference(unit_resolution,[status(thm)],[10448, 2048, 20186])).
% 293.21/185.71 tff(20494,plain,
% 293.21/185.71 (~node20(c_e_h_3, c_k, s6)),
% 293.21/185.71 inference(unit_resolution,[status(thm)],[10444, 38, 20493])).
% 293.21/185.71 tff(20495,plain,
% 293.21/185.71 (~m_and_h_gate_v_out(c_e_h_3, c_k, s7)),
% 293.21/185.71 inference(unit_resolution,[status(thm)],[10440, 20494, 20492])).
% 293.21/185.71 tff(20496,plain,
% 293.21/185.71 (~m_and_h_gate_v_out(c_e_h_3, c_k, s8)),
% 293.21/185.71 inference(unit_resolution,[status(thm)],[10425, 20495, 20483])).
% 293.21/185.71 tff(20497,assumption,(node4(c_e_h_3, c_g, s8)), introduced(assumption)).
% 293.21/185.71 tff(20498,plain,
% 293.21/185.71 (((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_g, s8)) | (~node4(c_e_h_3, c_g, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s8)) | (~node4(c_e_h_3, c_g, s8)))),
% 293.21/185.71 inference(rewrite,[status(thm)],[])).
% 293.21/185.71 tff(20499,plain,
% 293.21/185.71 ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_g, s8)) | (~node4(c_e_h_3, c_g, s8)))),
% 293.21/185.71 inference(quant_inst,[status(thm)],[])).
% 293.21/185.71 tff(20500,plain,
% 293.21/185.71 ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s8)) | (~node4(c_e_h_3, c_g, s8))),
% 293.21/185.71 inference(modus_ponens,[status(thm)],[20499, 20498])).
% 293.21/185.71 tff(20501,plain,
% 293.21/185.71 ($false),
% 293.21/185.71 inference(unit_resolution,[status(thm)],[20500, 5516, 20497, 20118])).
% 293.21/185.71 tff(20502,plain,((~node4(c_e_h_3, c_g, s8)) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s8))), inference(lemma,lemma(discharge,[]))).
% 293.21/185.71 tff(20503,plain,
% 293.21/185.71 (~node4(c_e_h_3, c_g, s8)),
% 293.21/185.71 inference(unit_resolution,[status(thm)],[20502, 20332])).
% 293.21/185.71 tff(20504,plain,
% 293.21/185.71 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s9)),
% 293.21/185.71 inference(unit_resolution,[status(thm)],[20262, 20257])).
% 293.21/185.71 tff(20505,assumption,(~node4(c_e_h_3, c_g, s8)), introduced(assumption)).
% 293.21/185.71 tff(20506,plain,
% 293.21/185.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s9) | (~node5(c_e_h_3, c_g, s8, s9)) | node4(c_e_h_3, c_g, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | m_or_h_gate_v_out(c_e_h_3, c_g, s9) | (~node5(c_e_h_3, c_g, s8, s9)) | node4(c_e_h_3, c_g, s8))),
% 293.21/185.71 inference(rewrite,[status(thm)],[])).
% 293.21/185.71 tff(20507,plain,
% 293.21/185.71 ((node4(c_e_h_3, c_g, s8) | (~node5(c_e_h_3, c_g, s8, s9)) | m_or_h_gate_v_out(c_e_h_3, c_g, s9)) <=> (m_or_h_gate_v_out(c_e_h_3, c_g, s9) | (~node5(c_e_h_3, c_g, s8, s9)) | node4(c_e_h_3, c_g, s8))),
% 293.21/185.71 inference(rewrite,[status(thm)],[])).
% 293.21/185.71 tff(20508,plain,
% 293.21/185.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_3, c_g, s8) | (~node5(c_e_h_3, c_g, s8, s9)) | m_or_h_gate_v_out(c_e_h_3, c_g, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s9) | (~node5(c_e_h_3, c_g, s8, s9)) | node4(c_e_h_3, c_g, s8)))),
% 293.21/185.71 inference(monotonicity,[status(thm)],[20507])).
% 293.21/185.71 tff(20509,plain,
% 293.21/185.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_3, c_g, s8) | (~node5(c_e_h_3, c_g, s8, s9)) | m_or_h_gate_v_out(c_e_h_3, c_g, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | m_or_h_gate_v_out(c_e_h_3, c_g, s9) | (~node5(c_e_h_3, c_g, s8, s9)) | node4(c_e_h_3, c_g, s8))),
% 293.21/185.71 inference(transitivity,[status(thm)],[20508, 20506])).
% 293.21/185.71 tff(20510,plain,
% 293.21/185.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_3, c_g, s8) | (~node5(c_e_h_3, c_g, s8, s9)) | m_or_h_gate_v_out(c_e_h_3, c_g, s9))),
% 293.21/185.71 inference(quant_inst,[status(thm)],[])).
% 293.21/185.71 tff(20511,plain,
% 293.21/185.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | m_or_h_gate_v_out(c_e_h_3, c_g, s9) | (~node5(c_e_h_3, c_g, s8, s9)) | node4(c_e_h_3, c_g, s8)),
% 293.21/185.71 inference(modus_ponens,[status(thm)],[20510, 20509])).
% 293.21/185.71 tff(20512,plain,
% 293.21/185.71 ($false),
% 293.21/185.71 inference(unit_resolution,[status(thm)],[20511, 5498, 20226, 20257, 20505])).
% 293.21/185.71 tff(20513,plain,((~node5(c_e_h_3, c_g, s8, s9)) | m_or_h_gate_v_out(c_e_h_3, c_g, s9) | node4(c_e_h_3, c_g, s8)), inference(lemma,lemma(discharge,[]))).
% 293.21/185.71 tff(20514,plain,
% 293.21/185.71 (~node5(c_e_h_3, c_g, s8, s9)),
% 293.21/185.71 inference(unit_resolution,[status(thm)],[20513, 20257, 20505])).
% 293.21/185.71 tff(20515,plain,
% 293.21/185.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s9) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s8)) | (~node6(c_e_h_3, c_g, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | m_or_h_gate_v_out(c_e_h_3, c_g, s9) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s8)) | (~node6(c_e_h_3, c_g, s8, s9)))),
% 293.21/185.71 inference(rewrite,[status(thm)],[])).
% 293.21/185.71 tff(20516,plain,
% 293.21/185.71 ((m_or_h_gate_v_out(c_e_h_3, c_g, s9) | (~node6(c_e_h_3, c_g, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s8))) <=> (m_or_h_gate_v_out(c_e_h_3, c_g, s9) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s8)) | (~node6(c_e_h_3, c_g, s8, s9)))),
% 293.21/185.71 inference(rewrite,[status(thm)],[])).
% 293.21/185.71 tff(20517,plain,
% 293.21/185.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s9) | (~node6(c_e_h_3, c_g, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s9) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s8)) | (~node6(c_e_h_3, c_g, s8, s9))))),
% 293.21/185.71 inference(monotonicity,[status(thm)],[20516])).
% 293.21/185.71 tff(20518,plain,
% 293.21/185.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s9) | (~node6(c_e_h_3, c_g, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | m_or_h_gate_v_out(c_e_h_3, c_g, s9) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s8)) | (~node6(c_e_h_3, c_g, s8, s9)))),
% 293.21/185.71 inference(transitivity,[status(thm)],[20517, 20515])).
% 293.21/185.71 tff(20519,plain,
% 293.21/185.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s9) | (~node6(c_e_h_3, c_g, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s8)))),
% 293.21/185.71 inference(quant_inst,[status(thm)],[])).
% 293.21/185.71 tff(20520,plain,
% 293.21/185.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | m_or_h_gate_v_out(c_e_h_3, c_g, s9) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s8)) | (~node6(c_e_h_3, c_g, s8, s9))),
% 293.21/185.71 inference(modus_ponens,[status(thm)],[20519, 20518])).
% 293.21/185.71 tff(20521,plain,
% 293.21/185.71 ($false),
% 293.21/185.71 inference(unit_resolution,[status(thm)],[20520, 5474, 20236, 20257, 11161])).
% 293.21/185.71 tff(20522,plain,((~node6(c_e_h_3, c_g, s8, s9)) | m_or_h_gate_v_out(c_e_h_3, c_g, s9) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s8))), inference(lemma,lemma(discharge,[]))).
% 293.21/185.71 tff(20523,plain,
% 293.21/185.71 (~node6(c_e_h_3, c_g, s8, s9)),
% 293.21/185.71 inference(unit_resolution,[status(thm)],[20522, 20257, 11161])).
% 293.21/185.71 tff(20524,plain,
% 293.21/185.71 ($false),
% 293.21/185.71 inference(unit_resolution,[status(thm)],[20252, 20523, 20514])).
% 293.21/185.71 tff(20525,plain,(m_or_h_gate_v_out(c_e_h_3, c_g, s9) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s8)) | node4(c_e_h_3, c_g, s8)), inference(lemma,lemma(discharge,[]))).
% 293.21/185.71 tff(20526,plain,
% 293.21/185.71 (~m_or_h_gate_v_out(c_e_h_3, c_g, s8)),
% 293.21/185.71 inference(unit_resolution,[status(thm)],[20525, 20257, 20505])).
% 293.21/185.71 tff(20527,plain,
% 293.21/185.71 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s8)),
% 293.21/185.71 inference(unit_resolution,[status(thm)],[20278, 2048, 20526])).
% 293.21/185.71 tff(20528,plain,
% 293.21/185.71 (~node20(c_e_h_3, c_k, s8)),
% 293.21/185.71 inference(unit_resolution,[status(thm)],[20286, 20527])).
% 293.21/185.71 tff(20529,plain,
% 293.21/185.71 (~m_and_h_gate_v_out(c_e_h_3, c_k, s9)),
% 293.21/185.71 inference(unit_resolution,[status(thm)],[20303, 20528, 10531])).
% 293.21/185.71 tff(20530,plain,
% 293.21/185.71 (node20(c_e_h_3, c_k, s9)),
% 293.21/185.71 inference(unit_resolution,[status(thm)],[20325, 20529, 20173])).
% 293.21/185.72 tff(20531,plain,
% 293.21/185.72 ($false),
% 293.21/185.72 inference(unit_resolution,[status(thm)],[20329, 38, 20530, 20504])).
% 293.21/185.72 tff(20532,plain,(m_or_h_gate_v_out(c_e_h_3, c_g, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s10)) | m_and_h_gate_v_out(c_e_h_3, c_k, s8) | node4(c_e_h_3, c_g, s8)), inference(lemma,lemma(discharge,[]))).
% 293.21/185.72 tff(20533,plain,
% 293.21/185.72 (m_or_h_gate_v_out(c_e_h_3, c_g, s9)),
% 293.21/185.72 inference(unit_resolution,[status(thm)],[20532, 20503, 20496, 20173])).
% 293.21/185.72 tff(20534,assumption,(~node4(c_e_h_3, c_g, s9)), introduced(assumption)).
% 293.21/185.72 tff(20535,assumption,(node5(c_e_h_3, c_g, s9, s10)), introduced(assumption)).
% 293.21/185.72 tff(20536,plain,
% 293.21/185.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s10) | (~node5(c_e_h_3, c_g, s9, s10)) | node4(c_e_h_3, c_g, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | m_or_h_gate_v_out(c_e_h_3, c_g, s10) | (~node5(c_e_h_3, c_g, s9, s10)) | node4(c_e_h_3, c_g, s9))),
% 293.21/185.72 inference(rewrite,[status(thm)],[])).
% 293.21/185.72 tff(20537,plain,
% 293.21/185.72 ((node4(c_e_h_3, c_g, s9) | (~node5(c_e_h_3, c_g, s9, s10)) | m_or_h_gate_v_out(c_e_h_3, c_g, s10)) <=> (m_or_h_gate_v_out(c_e_h_3, c_g, s10) | (~node5(c_e_h_3, c_g, s9, s10)) | node4(c_e_h_3, c_g, s9))),
% 293.21/185.72 inference(rewrite,[status(thm)],[])).
% 293.21/185.72 tff(20538,plain,
% 293.21/185.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_3, c_g, s9) | (~node5(c_e_h_3, c_g, s9, s10)) | m_or_h_gate_v_out(c_e_h_3, c_g, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s10) | (~node5(c_e_h_3, c_g, s9, s10)) | node4(c_e_h_3, c_g, s9)))),
% 293.21/185.72 inference(monotonicity,[status(thm)],[20537])).
% 293.21/185.72 tff(20539,plain,
% 293.21/185.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_3, c_g, s9) | (~node5(c_e_h_3, c_g, s9, s10)) | m_or_h_gate_v_out(c_e_h_3, c_g, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | m_or_h_gate_v_out(c_e_h_3, c_g, s10) | (~node5(c_e_h_3, c_g, s9, s10)) | node4(c_e_h_3, c_g, s9))),
% 293.21/185.72 inference(transitivity,[status(thm)],[20538, 20536])).
% 293.21/185.72 tff(20540,plain,
% 293.21/185.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_3, c_g, s9) | (~node5(c_e_h_3, c_g, s9, s10)) | m_or_h_gate_v_out(c_e_h_3, c_g, s10))),
% 293.21/185.72 inference(quant_inst,[status(thm)],[])).
% 293.21/185.72 tff(20541,plain,
% 293.21/185.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | m_or_h_gate_v_out(c_e_h_3, c_g, s10) | (~node5(c_e_h_3, c_g, s9, s10)) | node4(c_e_h_3, c_g, s9)),
% 293.21/185.72 inference(modus_ponens,[status(thm)],[20540, 20539])).
% 293.21/185.72 tff(20542,plain,
% 293.21/185.72 ($false),
% 293.21/185.72 inference(unit_resolution,[status(thm)],[20541, 5498, 20535, 20534, 20172])).
% 293.21/185.72 tff(20543,plain,((~node5(c_e_h_3, c_g, s9, s10)) | node4(c_e_h_3, c_g, s9) | m_or_h_gate_v_out(c_e_h_3, c_g, s10)), inference(lemma,lemma(discharge,[]))).
% 293.21/185.72 tff(20544,plain,
% 293.21/185.72 (~node5(c_e_h_3, c_g, s9, s10)),
% 293.21/185.72 inference(unit_resolution,[status(thm)],[20543, 20172, 20534])).
% 293.21/185.72 tff(20545,assumption,(node6(c_e_h_3, c_g, s9, s10)), introduced(assumption)).
% 293.21/185.72 tff(20546,plain,
% 293.21/185.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | ((~m_or_h_gate_v_out(c_e_h_3, c_g, s9)) | m_or_h_gate_v_out(c_e_h_3, c_g, s10) | (~node6(c_e_h_3, c_g, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s9)) | m_or_h_gate_v_out(c_e_h_3, c_g, s10) | (~node6(c_e_h_3, c_g, s9, s10)))),
% 293.21/185.72 inference(rewrite,[status(thm)],[])).
% 293.21/185.72 tff(20547,plain,
% 293.21/185.72 ((m_or_h_gate_v_out(c_e_h_3, c_g, s10) | (~node6(c_e_h_3, c_g, s9, s10)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s9))) <=> ((~m_or_h_gate_v_out(c_e_h_3, c_g, s9)) | m_or_h_gate_v_out(c_e_h_3, c_g, s10) | (~node6(c_e_h_3, c_g, s9, s10)))),
% 293.21/185.72 inference(rewrite,[status(thm)],[])).
% 293.21/185.72 tff(20548,plain,
% 293.21/185.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s10) | (~node6(c_e_h_3, c_g, s9, s10)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | ((~m_or_h_gate_v_out(c_e_h_3, c_g, s9)) | m_or_h_gate_v_out(c_e_h_3, c_g, s10) | (~node6(c_e_h_3, c_g, s9, s10))))),
% 293.21/185.72 inference(monotonicity,[status(thm)],[20547])).
% 293.21/185.72 tff(20549,plain,
% 293.21/185.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s10) | (~node6(c_e_h_3, c_g, s9, s10)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s9)) | m_or_h_gate_v_out(c_e_h_3, c_g, s10) | (~node6(c_e_h_3, c_g, s9, s10)))),
% 293.21/185.72 inference(transitivity,[status(thm)],[20548, 20546])).
% 293.21/185.72 tff(20550,plain,
% 293.21/185.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s10) | (~node6(c_e_h_3, c_g, s9, s10)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s9)))),
% 293.21/185.72 inference(quant_inst,[status(thm)],[])).
% 293.21/185.72 tff(20551,plain,
% 293.21/185.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s9)) | m_or_h_gate_v_out(c_e_h_3, c_g, s10) | (~node6(c_e_h_3, c_g, s9, s10))),
% 293.21/185.72 inference(modus_ponens,[status(thm)],[20550, 20549])).
% 293.21/185.72 tff(20552,plain,
% 293.21/185.72 ($false),
% 293.21/185.72 inference(unit_resolution,[status(thm)],[20551, 5474, 20225, 20545, 20172])).
% 293.21/185.72 tff(20553,plain,((~node6(c_e_h_3, c_g, s9, s10)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s9)) | m_or_h_gate_v_out(c_e_h_3, c_g, s10)), inference(lemma,lemma(discharge,[]))).
% 293.21/185.72 tff(20554,plain,
% 293.21/185.72 (~node6(c_e_h_3, c_g, s9, s10)),
% 293.21/185.72 inference(unit_resolution,[status(thm)],[20553, 20172, 20225])).
% 293.21/185.72 tff(20555,plain,
% 293.21/185.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s9, s10)) | node6(c_e_h_3, c_g, s9, s10) | node5(c_e_h_3, c_g, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s9, s10)) | node6(c_e_h_3, c_g, s9, s10) | node5(c_e_h_3, c_g, s9, s10))),
% 293.21/185.72 inference(rewrite,[status(thm)],[])).
% 293.21/185.72 tff(20556,plain,
% 293.21/185.72 ((node6(c_e_h_3, c_g, s9, s10) | node5(c_e_h_3, c_g, s9, s10) | (~trans(s9, s10))) <=> ((~trans(s9, s10)) | node6(c_e_h_3, c_g, s9, s10) | node5(c_e_h_3, c_g, s9, s10))),
% 293.21/185.72 inference(rewrite,[status(thm)],[])).
% 293.21/185.72 tff(20557,plain,
% 293.21/185.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s9, s10) | node5(c_e_h_3, c_g, s9, s10) | (~trans(s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s9, s10)) | node6(c_e_h_3, c_g, s9, s10) | node5(c_e_h_3, c_g, s9, s10)))),
% 293.21/185.72 inference(monotonicity,[status(thm)],[20556])).
% 293.21/185.72 tff(20558,plain,
% 293.21/185.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s9, s10) | node5(c_e_h_3, c_g, s9, s10) | (~trans(s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s9, s10)) | node6(c_e_h_3, c_g, s9, s10) | node5(c_e_h_3, c_g, s9, s10))),
% 293.21/185.72 inference(transitivity,[status(thm)],[20557, 20555])).
% 293.21/185.72 tff(20559,plain,
% 293.21/185.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s9, s10) | node5(c_e_h_3, c_g, s9, s10) | (~trans(s9, s10)))),
% 293.23/185.73 inference(quant_inst,[status(thm)],[])).
% 293.23/185.73 tff(20560,plain,
% 293.23/185.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s9, s10)) | node6(c_e_h_3, c_g, s9, s10) | node5(c_e_h_3, c_g, s9, s10)),
% 293.23/185.73 inference(modus_ponens,[status(thm)],[20559, 20558])).
% 293.23/185.73 tff(20561,plain,
% 293.23/185.73 (node6(c_e_h_3, c_g, s9, s10) | node5(c_e_h_3, c_g, s9, s10)),
% 293.23/185.73 inference(unit_resolution,[status(thm)],[20560, 1141, 7676])).
% 293.23/185.73 tff(20562,plain,
% 293.23/185.73 ($false),
% 293.23/185.73 inference(unit_resolution,[status(thm)],[20561, 20554, 20544])).
% 293.23/185.73 tff(20563,plain,(m_or_h_gate_v_out(c_e_h_3, c_g, s10) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s9)) | node4(c_e_h_3, c_g, s9)), inference(lemma,lemma(discharge,[]))).
% 293.23/185.73 tff(20564,plain,
% 293.23/185.73 (node4(c_e_h_3, c_g, s9)),
% 293.23/185.73 inference(unit_resolution,[status(thm)],[20563, 20533, 20172])).
% 293.23/185.73 tff(20565,assumption,(m_or_h_gate_v_in1(c_e_h_3, c_g, s9)), introduced(assumption)).
% 293.23/185.73 tff(20566,assumption,(node4(c_e_h_3, c_g, s9)), introduced(assumption)).
% 293.23/185.73 tff(20567,plain,
% 293.23/185.73 (((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_g, s9)) | (~node4(c_e_h_3, c_g, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s9)) | (~node4(c_e_h_3, c_g, s9)))),
% 293.23/185.73 inference(rewrite,[status(thm)],[])).
% 293.23/185.73 tff(20568,plain,
% 293.23/185.73 ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_g, s9)) | (~node4(c_e_h_3, c_g, s9)))),
% 293.23/185.73 inference(quant_inst,[status(thm)],[])).
% 293.23/185.73 tff(20569,plain,
% 293.23/185.73 ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s9)) | (~node4(c_e_h_3, c_g, s9))),
% 293.23/185.73 inference(modus_ponens,[status(thm)],[20568, 20567])).
% 293.23/185.73 tff(20570,plain,
% 293.23/185.73 ($false),
% 293.23/185.73 inference(unit_resolution,[status(thm)],[20569, 5516, 20566, 20565])).
% 293.23/185.73 tff(20571,plain,((~node4(c_e_h_3, c_g, s9)) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s9))), inference(lemma,lemma(discharge,[]))).
% 293.23/185.73 tff(20572,plain,
% 293.23/185.73 ($false),
% 293.23/185.73 inference(unit_resolution,[status(thm)],[20571, 20564, 20480])).
% 293.23/185.73 tff(20573,plain,((~m_and_h_gate_v_out(c_e_h_3, c_k, s10)) | m_or_h_gate_v_out(c_e_h_3, c_g, s10) | m_or_h_gate_v_in2(c_e_h_3, c_g, s8) | m_and_h_gate_v_out(c_e_h_3, c_c, s7)), inference(lemma,lemma(discharge,[]))).
% 293.23/185.73 tff(20574,plain,
% 293.23/185.73 (m_and_h_gate_v_out(c_e_h_3, c_c, s7)),
% 293.23/185.73 inference(unit_resolution,[status(thm)],[20573, 20173, 20172, 20018])).
% 293.23/185.73 tff(20575,plain,
% 293.23/185.73 (m_mutex_h_half_v_out(c_e_h_3, c_a, s7)),
% 293.23/185.73 inference(unit_resolution,[status(thm)],[19741, 11283])).
% 293.23/185.73 tff(20576,plain,
% 293.23/185.73 (((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s7))) <=> ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s7))),
% 293.23/185.73 inference(rewrite,[status(thm)],[])).
% 293.23/185.73 tff(20577,plain,
% 293.23/185.73 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s7))),
% 293.23/185.73 inference(quant_inst,[status(thm)],[])).
% 293.23/185.73 tff(20578,plain,
% 293.23/185.73 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s7)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s7)),
% 293.23/185.73 inference(modus_ponens,[status(thm)],[20577, 20576])).
% 293.23/185.73 tff(20579,plain,
% 293.23/185.73 ($false),
% 293.23/185.73 inference(unit_resolution,[status(thm)],[20578, 2556, 20030, 1910])).
% 293.23/185.73 tff(20580,plain,(m_and_h_gate_v_in1(c_e_h_3, c_c, s7) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s7))), inference(lemma,lemma(discharge,[]))).
% 293.23/185.73 tff(20581,plain,
% 293.23/185.73 (m_and_h_gate_v_in1(c_e_h_3, c_c, s7)),
% 293.23/185.73 inference(unit_resolution,[status(thm)],[20580, 20575])).
% 293.23/185.73 tff(20582,plain,
% 293.23/185.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_c, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s7)) | (~node22(c_e_h_3, c_c, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | m_and_h_gate_v_out(c_e_h_3, c_c, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s7)) | (~node22(c_e_h_3, c_c, s7, s8)))),
% 293.23/185.73 inference(rewrite,[status(thm)],[])).
% 293.23/185.73 tff(20583,plain,
% 293.23/185.73 ((m_and_h_gate_v_out(c_e_h_3, c_c, s8) | (~node22(c_e_h_3, c_c, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s7))) <=> (m_and_h_gate_v_out(c_e_h_3, c_c, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s7)) | (~node22(c_e_h_3, c_c, s7, s8)))),
% 293.23/185.73 inference(rewrite,[status(thm)],[])).
% 293.23/185.73 tff(20584,plain,
% 293.23/185.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_c, s8) | (~node22(c_e_h_3, c_c, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_c, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s7)) | (~node22(c_e_h_3, c_c, s7, s8))))),
% 293.23/185.73 inference(monotonicity,[status(thm)],[20583])).
% 293.23/185.73 tff(20585,plain,
% 293.23/185.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_c, s8) | (~node22(c_e_h_3, c_c, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | m_and_h_gate_v_out(c_e_h_3, c_c, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s7)) | (~node22(c_e_h_3, c_c, s7, s8)))),
% 293.23/185.73 inference(transitivity,[status(thm)],[20584, 20582])).
% 293.23/185.73 tff(20586,plain,
% 293.23/185.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_c, s8) | (~node22(c_e_h_3, c_c, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s7)))),
% 293.23/185.73 inference(quant_inst,[status(thm)],[])).
% 293.23/185.73 tff(20587,plain,
% 293.23/185.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | m_and_h_gate_v_out(c_e_h_3, c_c, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s7)) | (~node22(c_e_h_3, c_c, s7, s8))),
% 293.23/185.73 inference(modus_ponens,[status(thm)],[20586, 20585])).
% 293.23/185.73 tff(20588,plain,
% 293.23/185.73 ($false),
% 293.23/185.73 inference(unit_resolution,[status(thm)],[20587, 5871, 20048, 11155, 20119])).
% 293.23/185.73 tff(20589,plain,((~node22(c_e_h_3, c_c, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s7)) | m_and_h_gate_v_out(c_e_h_3, c_c, s8)), inference(lemma,lemma(discharge,[]))).
% 293.23/185.73 tff(20590,plain,
% 293.23/185.73 (~node22(c_e_h_3, c_c, s7, s8)),
% 293.23/185.73 inference(unit_resolution,[status(thm)],[20589, 20119, 11155])).
% 293.23/185.73 tff(20591,plain,
% 293.23/185.73 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s7))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s7))),
% 293.23/185.73 inference(rewrite,[status(thm)],[])).
% 293.23/185.73 tff(20592,plain,
% 293.23/185.73 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s7))),
% 293.23/185.73 inference(quant_inst,[status(thm)],[])).
% 293.23/185.73 tff(20593,plain,
% 293.23/185.73 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s7)),
% 293.23/185.73 inference(modus_ponens,[status(thm)],[20592, 20591])).
% 293.23/185.73 tff(20594,plain,
% 293.23/185.73 (node3(c_e_h_3, c_e_h_1, s7)),
% 293.23/185.73 inference(unit_resolution,[status(thm)],[20593, 2922, 1056])).
% 293.23/185.73 tff(20595,plain,
% 293.23/185.73 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s7)) | (~node3(c_e_h_3, c_e_h_1, s7)) | m_and_h_gate_v_out(c_e_h_3, c_q, s7))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s7)) | (~node3(c_e_h_3, c_e_h_1, s7)) | m_and_h_gate_v_out(c_e_h_3, c_q, s7))),
% 293.23/185.73 inference(rewrite,[status(thm)],[])).
% 293.23/185.73 tff(20596,plain,
% 293.23/185.73 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s7)) | (~node3(c_e_h_3, c_e_h_1, s7)) | m_and_h_gate_v_out(c_e_h_3, c_q, s7))),
% 293.23/185.73 inference(quant_inst,[status(thm)],[])).
% 293.23/185.73 tff(20597,plain,
% 293.23/185.73 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s7)) | (~node3(c_e_h_3, c_e_h_1, s7)) | m_and_h_gate_v_out(c_e_h_3, c_q, s7)),
% 293.23/185.73 inference(modus_ponens,[status(thm)],[20596, 20595])).
% 293.23/185.73 tff(20598,plain,
% 293.23/185.73 ((~m_cell_v_ack(c_e_h_1, s7)) | m_and_h_gate_v_out(c_e_h_3, c_q, s7)),
% 293.23/185.73 inference(unit_resolution,[status(thm)],[20597, 1073, 20594])).
% 293.23/185.73 tff(20599,plain,
% 293.23/185.73 (~m_cell_v_ack(c_e_h_1, s7)),
% 293.23/185.73 inference(unit_resolution,[status(thm)],[20598, 20402])).
% 293.23/185.73 tff(20600,plain,
% 293.23/185.73 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node2(c_e_h_3, c_e_h_1, s7))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node2(c_e_h_3, c_e_h_1, s7))),
% 293.23/185.73 inference(rewrite,[status(thm)],[])).
% 293.23/185.73 tff(20601,plain,
% 293.23/185.73 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node2(c_e_h_3, c_e_h_1, s7))),
% 293.23/185.73 inference(quant_inst,[status(thm)],[])).
% 293.23/185.73 tff(20602,plain,
% 293.23/185.73 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node2(c_e_h_3, c_e_h_1, s7)),
% 293.23/185.73 inference(modus_ponens,[status(thm)],[20601, 20600])).
% 293.23/185.73 tff(20603,plain,
% 293.23/185.73 (node2(c_e_h_3, c_e_h_1, s7)),
% 293.23/185.73 inference(unit_resolution,[status(thm)],[20602, 2922, 5821])).
% 293.23/185.73 tff(20604,plain,
% 293.23/185.73 (((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | ((~node2(c_e_h_3, c_e_h_1, s7)) | m_cell_v_ack(c_e_h_1, s7) | m_and_h_gate_v_in2(c_e_h_3, c_c, s7))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | (~node2(c_e_h_3, c_e_h_1, s7)) | m_cell_v_ack(c_e_h_1, s7) | m_and_h_gate_v_in2(c_e_h_3, c_c, s7))),
% 293.23/185.73 inference(rewrite,[status(thm)],[])).
% 293.23/185.73 tff(20605,plain,
% 293.23/185.73 ((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | ((~node2(c_e_h_3, c_e_h_1, s7)) | m_cell_v_ack(c_e_h_1, s7) | m_and_h_gate_v_in2(c_e_h_3, c_c, s7))),
% 293.23/185.73 inference(quant_inst,[status(thm)],[])).
% 293.23/185.73 tff(20606,plain,
% 293.23/185.73 ((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | (~node2(c_e_h_3, c_e_h_1, s7)) | m_cell_v_ack(c_e_h_1, s7) | m_and_h_gate_v_in2(c_e_h_3, c_c, s7)),
% 293.23/185.73 inference(modus_ponens,[status(thm)],[20605, 20604])).
% 293.23/185.73 tff(20607,plain,
% 293.23/185.73 (m_cell_v_ack(c_e_h_1, s7) | m_and_h_gate_v_in2(c_e_h_3, c_c, s7)),
% 293.23/185.73 inference(unit_resolution,[status(thm)],[20606, 5835, 20603])).
% 293.23/185.73 tff(20608,plain,
% 293.23/185.73 (m_and_h_gate_v_in2(c_e_h_3, c_c, s7)),
% 293.23/185.73 inference(unit_resolution,[status(thm)],[20607, 20599])).
% 293.23/185.73 tff(20609,assumption,(m_and_h_gate_v_in2(c_e_h_3, c_c, s7)), introduced(assumption)).
% 293.23/185.73 tff(20610,plain,
% 293.23/185.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_c, s7)) | m_and_h_gate_v_out(c_e_h_3, c_c, s8) | (~node21(c_e_h_3, c_c, s7, s8)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s7)) | m_and_h_gate_v_out(c_e_h_3, c_c, s8) | (~node21(c_e_h_3, c_c, s7, s8)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s7)))),
% 293.23/185.74 inference(rewrite,[status(thm)],[])).
% 293.23/185.74 tff(20611,plain,
% 293.23/185.74 (((~node21(c_e_h_3, c_c, s7, s8)) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s7)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s7)) | m_and_h_gate_v_out(c_e_h_3, c_c, s8)) <=> ((~m_and_h_gate_v_in2(c_e_h_3, c_c, s7)) | m_and_h_gate_v_out(c_e_h_3, c_c, s8) | (~node21(c_e_h_3, c_c, s7, s8)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s7)))),
% 293.23/185.74 inference(rewrite,[status(thm)],[])).
% 293.23/185.74 tff(20612,plain,
% 293.23/185.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_c, s7, s8)) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s7)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s7)) | m_and_h_gate_v_out(c_e_h_3, c_c, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_c, s7)) | m_and_h_gate_v_out(c_e_h_3, c_c, s8) | (~node21(c_e_h_3, c_c, s7, s8)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s7))))),
% 293.23/185.74 inference(monotonicity,[status(thm)],[20611])).
% 293.23/185.74 tff(20613,plain,
% 293.23/185.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_c, s7, s8)) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s7)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s7)) | m_and_h_gate_v_out(c_e_h_3, c_c, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s7)) | m_and_h_gate_v_out(c_e_h_3, c_c, s8) | (~node21(c_e_h_3, c_c, s7, s8)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s7)))),
% 293.23/185.74 inference(transitivity,[status(thm)],[20612, 20610])).
% 293.23/185.74 tff(20614,plain,
% 293.23/185.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_c, s7, s8)) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s7)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s7)) | m_and_h_gate_v_out(c_e_h_3, c_c, s8))),
% 293.23/185.74 inference(quant_inst,[status(thm)],[])).
% 293.23/185.74 tff(20615,plain,
% 293.23/185.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s7)) | m_and_h_gate_v_out(c_e_h_3, c_c, s8) | (~node21(c_e_h_3, c_c, s7, s8)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s7))),
% 293.23/185.74 inference(modus_ponens,[status(thm)],[20614, 20613])).
% 293.23/185.74 tff(20616,plain,
% 293.23/185.74 ($false),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[20615, 5851, 20609, 20038, 20119, 20022])).
% 293.23/185.74 tff(20617,plain,((~node21(c_e_h_3, c_c, s7, s8)) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s7)) | m_and_h_gate_v_out(c_e_h_3, c_c, s8) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s7))), inference(lemma,lemma(discharge,[]))).
% 293.23/185.74 tff(20618,plain,
% 293.23/185.74 ((~node21(c_e_h_3, c_c, s7, s8)) | m_and_h_gate_v_out(c_e_h_3, c_c, s8) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s7))),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[20617, 20608])).
% 293.23/185.74 tff(20619,plain,
% 293.23/185.74 (~node21(c_e_h_3, c_c, s7, s8)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[20618, 20119, 20022])).
% 293.23/185.74 tff(20620,plain,
% 293.23/185.74 ($false),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[20058, 20619, 20590])).
% 293.23/185.74 tff(20621,plain,(m_and_h_gate_v_out(c_e_h_3, c_c, s8) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s7)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s7))), inference(lemma,lemma(discharge,[]))).
% 293.23/185.74 tff(20622,plain,
% 293.23/185.74 (~m_and_h_gate_v_out(c_e_h_3, c_c, s7)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[20621, 20581, 20119])).
% 293.23/185.74 tff(20623,plain,
% 293.23/185.74 (m_mutex_h_half_v_out(c_e_h_3, c_a, s6)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[1515, 11291, 11287])).
% 293.23/185.74 tff(20624,plain,
% 293.23/185.74 (m_and_h_gate_v_in1(c_e_h_3, c_c, s6)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[10298, 20623])).
% 293.23/185.74 tff(20625,plain,
% 293.23/185.74 ($false),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[10938, 11289, 20624, 20622])).
% 293.23/185.74 tff(20626,plain,((~m_and_h_gate_v_out(c_e_h_3, c_c, s5)) | m_and_h_gate_v_out(c_e_h_3, c_c, s8)), inference(lemma,lemma(discharge,[]))).
% 293.23/185.74 tff(20627,plain,
% 293.23/185.74 (~m_and_h_gate_v_out(c_e_h_3, c_c, s5)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[20626, 20119])).
% 293.23/185.74 tff(20628,plain,
% 293.23/185.74 (~m_and_h_gate_v_in1(c_e_h_3, c_c, s7)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[20621, 20119, 11155])).
% 293.23/185.74 tff(20629,plain,
% 293.23/185.74 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s7)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[20580, 20628])).
% 293.23/185.74 tff(20630,plain,
% 293.23/185.74 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s4)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[19741, 20629])).
% 293.23/185.74 tff(20631,plain,
% 293.23/185.74 ($false),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[20154, 20630, 20629, 11155, 20627])).
% 293.23/185.74 tff(20632,plain,(m_and_h_gate_v_out(c_e_h_3, c_c, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s7))), inference(lemma,lemma(discharge,[]))).
% 293.23/185.74 tff(20633,plain,
% 293.23/185.74 (m_and_h_gate_v_out(c_e_h_3, c_c, s8)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[20632, 20574])).
% 293.23/185.74 tff(20634,plain,
% 293.23/185.74 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s8)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s8))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s8)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s8))),
% 293.23/185.74 inference(rewrite,[status(thm)],[])).
% 293.23/185.74 tff(20635,plain,
% 293.23/185.74 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s8)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s8))),
% 293.23/185.74 inference(quant_inst,[status(thm)],[])).
% 293.23/185.74 tff(20636,plain,
% 293.23/185.74 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s8)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s8)),
% 293.23/185.74 inference(modus_ponens,[status(thm)],[20635, 20634])).
% 293.23/185.74 tff(20637,plain,
% 293.23/185.74 ($false),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[20636, 5896, 20020, 20187])).
% 293.23/185.74 tff(20638,plain,(m_or_h_gate_v_in1(c_e_h_3, c_g, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s8))), inference(lemma,lemma(discharge,[]))).
% 293.23/185.74 tff(20639,plain,
% 293.23/185.74 (m_or_h_gate_v_in1(c_e_h_3, c_g, s8)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[20638, 20633])).
% 293.23/185.74 tff(20640,plain,
% 293.23/185.74 (~node4(c_e_h_3, c_g, s8)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[20502, 20639])).
% 293.23/185.74 tff(20641,plain,
% 293.23/185.74 (m_and_h_gate_v_out(c_e_h_3, c_c, s9)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[20471, 20633])).
% 293.23/185.74 tff(20642,plain,
% 293.23/185.74 (m_or_h_gate_v_in1(c_e_h_3, c_g, s9)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[20479, 20641])).
% 293.23/185.74 tff(20643,plain,
% 293.23/185.74 (~node4(c_e_h_3, c_g, s9)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[20571, 20642])).
% 293.23/185.74 tff(20644,plain,
% 293.23/185.74 (~m_or_h_gate_v_out(c_e_h_3, c_g, s9)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[20563, 20643, 20172])).
% 293.23/185.74 tff(20645,plain,
% 293.23/185.74 (~m_or_h_gate_v_out(c_e_h_3, c_g, s8)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[20525, 20644, 20640])).
% 293.23/185.74 tff(20646,plain,
% 293.23/185.74 (m_and_h_gate_v_out(c_e_h_3, c_k, s8)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[20532, 20644, 20173, 20640])).
% 293.23/185.74 tff(20647,plain,
% 293.23/185.74 (m_or_h_gate_v_in1(c_e_h_3, c_g, s5)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[6178, 6173])).
% 293.23/185.74 tff(20648,plain,
% 293.23/185.74 (~node4(c_e_h_3, c_g, s5)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[6186, 20647])).
% 293.23/185.74 tff(20649,plain,
% 293.23/185.74 (m_or_h_gate_v_in1(c_e_h_3, c_g, s6)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[10996, 11289])).
% 293.23/185.74 tff(20650,plain,
% 293.23/185.74 (~node4(c_e_h_3, c_g, s6)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[11092, 20649])).
% 293.23/185.74 tff(20651,plain,
% 293.23/185.74 (~m_or_h_gate_v_out(c_e_h_3, c_g, s6)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[10485, 10390, 10466])).
% 293.23/185.74 tff(20652,plain,
% 293.23/185.74 (~m_or_h_gate_v_out(c_e_h_3, c_g, s5)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[6218, 20651, 6188])).
% 293.23/185.74 tff(20653,plain,
% 293.23/185.74 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s5)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[3365, 20652])).
% 293.23/185.74 tff(20654,plain,
% 293.23/185.74 (~node20(c_e_h_3, c_k, s5)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[5458, 20653])).
% 293.23/185.74 tff(20655,plain,
% 293.23/185.74 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s7)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[10395, 10390])).
% 293.23/185.74 tff(20656,plain,
% 293.23/185.74 (~node20(c_e_h_3, c_k, s7)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[10403, 20655])).
% 293.23/185.74 tff(20657,plain,
% 293.23/185.74 (m_and_h_gate_v_out(c_e_h_3, c_k, s7)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[10425, 20656, 9468])).
% 293.23/185.74 tff(20658,plain,
% 293.23/185.74 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s6)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[10448, 2048, 20651])).
% 293.23/185.74 tff(20659,plain,
% 293.23/185.74 (~node20(c_e_h_3, c_k, s6)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[10444, 38, 20658])).
% 293.23/185.74 tff(20660,plain,
% 293.23/185.74 (m_and_h_gate_v_out(c_e_h_3, c_k, s6)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[10440, 20659, 20657])).
% 293.23/185.74 tff(20661,plain,
% 293.23/185.74 (m_and_h_gate_v_out(c_e_h_3, c_k, s5)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[4467, 20660, 20654])).
% 293.23/185.74 tff(20662,plain,
% 293.23/185.74 (node20(c_e_h_3, c_k, s4)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[7635, 20661])).
% 293.23/185.74 tff(20663,plain,
% 293.23/185.74 (m_and_h_gate_v_in1(c_e_h_3, c_k, s4)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[3392, 20662])).
% 293.23/185.74 tff(20664,plain,
% 293.23/185.74 (m_or_h_gate_v_out(c_e_h_3, c_g, s4)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[3384, 20663])).
% 293.23/185.74 tff(20665,plain,
% 293.23/185.74 (node4(c_e_h_3, c_g, s4)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[5922, 20664, 20652])).
% 293.23/185.74 tff(20666,plain,
% 293.23/185.74 (~m_or_h_gate_v_in1(c_e_h_3, c_g, s4)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[5903, 5516, 20665])).
% 293.23/185.74 tff(20667,plain,
% 293.23/185.74 (m_or_h_gate_v_in1(c_e_h_3, c_g, s3)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[3377, 20664])).
% 293.23/185.74 tff(20668,plain,
% 293.23/185.74 (m_and_h_gate_v_out(c_e_h_3, c_c, s3)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[2713, 20667])).
% 293.23/185.74 tff(20669,plain,
% 293.23/185.74 (m_and_h_gate_v_out(c_e_h_3, c_c, s4)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[11306, 20668])).
% 293.23/185.74 tff(20670,plain,
% 293.23/185.74 ($false),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[5899, 5896, 20669, 20666])).
% 293.23/185.74 tff(20671,plain,(m_or_h_gate_v_out(c_e_h_3, c_g, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s8)) | node4(c_e_h_3, c_g, s5) | node4(c_e_h_3, c_g, s6)), inference(lemma,lemma(discharge,[]))).
% 293.23/185.74 tff(20672,plain,
% 293.23/185.74 (m_or_h_gate_v_out(c_e_h_3, c_g, s7)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[20671, 20650, 9468, 20648])).
% 293.23/185.74 tff(20673,plain,
% 293.23/185.74 (m_and_h_gate_v_out(c_e_h_3, c_c, s7)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[10938, 11289, 20624])).
% 293.23/185.74 tff(20674,plain,
% 293.23/185.74 (m_or_h_gate_v_in1(c_e_h_3, c_g, s7)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[11157, 20673])).
% 293.23/185.74 tff(20675,plain,
% 293.23/185.74 (~node4(c_e_h_3, c_g, s7)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[11280, 20674])).
% 293.23/185.74 tff(20676,plain,
% 293.23/185.74 ($false),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[9528, 20675, 20672, 9500])).
% 293.23/185.74 tff(20677,plain,((~m_and_h_gate_v_out(c_e_h_3, c_c, s5)) | m_or_h_gate_v_out(c_e_h_3, c_g, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s8))), inference(lemma,lemma(discharge,[]))).
% 293.23/185.74 tff(20678,plain,
% 293.23/185.74 (~m_and_h_gate_v_out(c_e_h_3, c_c, s5)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[20677, 20646, 20645])).
% 293.23/185.74 tff(20679,plain,
% 293.23/185.74 (~m_or_h_gate_v_out(c_e_h_3, c_g, s6)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[10319, 20678, 20176])).
% 293.23/185.74 tff(20680,plain,
% 293.23/185.74 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s6)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[10448, 2048, 20679])).
% 293.23/185.74 tff(20681,plain,
% 293.23/185.74 (~m_or_h_gate_v_out(c_e_h_3, c_g, s7)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[10387, 20645, 20176, 2743, 20194])).
% 293.23/185.74 tff(20682,plain,
% 293.23/185.74 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s7)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[10395, 20681])).
% 293.23/185.74 tff(20683,plain,
% 293.23/185.74 (~node20(c_e_h_3, c_k, s7)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[10403, 20682])).
% 293.23/185.74 tff(20684,plain,
% 293.23/185.74 (m_and_h_gate_v_out(c_e_h_3, c_k, s7)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[10425, 20683, 20646])).
% 293.23/185.74 tff(20685,plain,
% 293.23/185.74 (node20(c_e_h_3, c_k, s6)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[10440, 20684, 20269])).
% 293.23/185.74 tff(20686,plain,
% 293.23/185.74 ($false),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[10444, 38, 20685, 20680])).
% 293.23/185.74 tff(20687,plain,((~m_and_h_gate_v_out(c_e_h_3, c_k, s10)) | m_and_h_gate_v_out(c_e_h_3, c_c, s4) | m_or_h_gate_v_out(c_e_h_3, c_g, s10) | m_or_h_gate_v_in2(c_e_h_3, c_g, s8)), inference(lemma,lemma(discharge,[]))).
% 293.23/185.74 tff(20688,plain,
% 293.23/185.74 (m_or_h_gate_v_in2(c_e_h_3, c_g, s8)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[20687, 20173, 20172, 2743])).
% 293.23/185.74 tff(20689,plain,
% 293.23/185.74 (^[I0: $i, X: $i, I1: $i] : refl(((~m_or_h_gate_v_in2(I0, I1, X)) | (~node4(I0, I1, X))) <=> ((~m_or_h_gate_v_in2(I0, I1, X)) | (~node4(I0, I1, X))))),
% 293.23/185.74 inference(bind,[status(th)],[])).
% 293.23/185.74 tff(20690,plain,
% 293.23/185.74 (![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in2(I0, I1, X)) | (~node4(I0, I1, X))) <=> ![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in2(I0, I1, X)) | (~node4(I0, I1, X)))),
% 293.23/185.74 inference(quant_intro,[status(thm)],[20689])).
% 293.23/185.74 tff(20691,plain,
% 293.23/185.74 (![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in2(I0, I1, X)) | (~node4(I0, I1, X))) <=> ![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in2(I0, I1, X)) | (~node4(I0, I1, X)))),
% 293.23/185.74 inference(rewrite,[status(thm)],[])).
% 293.23/185.74 tff(20692,axiom,(![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in2(I0, I1, X)) | (~node4(I0, I1, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_or_h_gate_3')).
% 293.23/185.74 tff(20693,plain,
% 293.23/185.74 (![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in2(I0, I1, X)) | (~node4(I0, I1, X)))),
% 293.23/185.74 inference(modus_ponens,[status(thm)],[20692, 20691])).
% 293.23/185.74 tff(20694,plain,(
% 293.23/185.74 ![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in2(I0, I1, X)) | (~node4(I0, I1, X)))),
% 293.23/185.74 inference(skolemize,[status(sab)],[20693])).
% 293.23/185.74 tff(20695,plain,
% 293.23/185.74 (![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in2(I0, I1, X)) | (~node4(I0, I1, X)))),
% 293.23/185.74 inference(modus_ponens,[status(thm)],[20694, 20690])).
% 293.23/185.74 tff(20696,plain,
% 293.23/185.74 (((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in2(I0, I1, X)) | (~node4(I0, I1, X)))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_g, s8)) | (~node4(c_e_h_3, c_g, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in2(I0, I1, X)) | (~node4(I0, I1, X)))) | (~m_or_h_gate_v_in2(c_e_h_3, c_g, s8)) | (~node4(c_e_h_3, c_g, s8)))),
% 293.23/185.74 inference(rewrite,[status(thm)],[])).
% 293.23/185.74 tff(20697,plain,
% 293.23/185.74 ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in2(I0, I1, X)) | (~node4(I0, I1, X)))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_g, s8)) | (~node4(c_e_h_3, c_g, s8)))),
% 293.23/185.74 inference(quant_inst,[status(thm)],[])).
% 293.23/185.74 tff(20698,plain,
% 293.23/185.74 ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in2(I0, I1, X)) | (~node4(I0, I1, X)))) | (~m_or_h_gate_v_in2(c_e_h_3, c_g, s8)) | (~node4(c_e_h_3, c_g, s8))),
% 293.23/185.74 inference(modus_ponens,[status(thm)],[20697, 20696])).
% 293.23/185.74 tff(20699,plain,
% 293.23/185.74 (~node4(c_e_h_3, c_g, s8)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[20698, 20695, 20688])).
% 293.23/185.74 tff(20700,plain,
% 293.23/185.74 (m_and_h_gate_v_out(c_e_h_3, c_d, s8)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[19553, 20688])).
% 293.23/185.74 tff(20701,plain,
% 293.23/185.74 (m_and_h_gate_v_out(c_e_h_3, c_d, s9)),
% 293.23/185.74 inference(unit_resolution,[status(thm)],[19546, 20700])).
% 293.23/185.74 tff(20702,plain,
% 293.23/185.74 (^[I0: $i, X: $i] : refl(((~m_and_h_gate_v_out(I0, c_d, X)) | m_or_h_gate_v_in2(I0, c_g, X)) <=> ((~m_and_h_gate_v_out(I0, c_d, X)) | m_or_h_gate_v_in2(I0, c_g, X)))),
% 293.23/185.74 inference(bind,[status(th)],[])).
% 293.23/185.74 tff(20703,plain,
% 293.23/185.74 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_d, X)) | m_or_h_gate_v_in2(I0, c_g, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_d, X)) | m_or_h_gate_v_in2(I0, c_g, X))),
% 293.23/185.74 inference(quant_intro,[status(thm)],[20702])).
% 293.23/185.74 tff(20704,plain,
% 293.23/185.74 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_d, X)) | m_or_h_gate_v_in2(I0, c_g, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_d, X)) | m_or_h_gate_v_in2(I0, c_g, X))),
% 293.23/185.74 inference(rewrite,[status(thm)],[])).
% 293.23/185.74 tff(20705,plain,
% 293.23/185.74 (^[I0: $i, X: $i] : rewrite((m_or_h_gate_v_in2(I0, c_g, X) | (~m_and_h_gate_v_out(I0, c_d, X))) <=> ((~m_and_h_gate_v_out(I0, c_d, X)) | m_or_h_gate_v_in2(I0, c_g, X)))),
% 293.23/185.74 inference(bind,[status(th)],[])).
% 293.23/185.74 tff(20706,plain,
% 293.23/185.74 (![I0: $i, X: $i] : (m_or_h_gate_v_in2(I0, c_g, X) | (~m_and_h_gate_v_out(I0, c_d, X))) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_d, X)) | m_or_h_gate_v_in2(I0, c_g, X))),
% 293.23/185.75 inference(quant_intro,[status(thm)],[20705])).
% 293.23/185.75 tff(20707,axiom,(![I0: $i, X: $i] : (m_or_h_gate_v_in2(I0, c_g, X) | (~m_and_h_gate_v_out(I0, c_d, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_29')).
% 293.23/185.75 tff(20708,plain,
% 293.23/185.75 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_d, X)) | m_or_h_gate_v_in2(I0, c_g, X))),
% 293.23/185.75 inference(modus_ponens,[status(thm)],[20707, 20706])).
% 293.23/185.75 tff(20709,plain,
% 293.23/185.75 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_d, X)) | m_or_h_gate_v_in2(I0, c_g, X))),
% 293.23/185.75 inference(modus_ponens,[status(thm)],[20708, 20704])).
% 293.23/185.75 tff(20710,plain,(
% 293.23/185.75 ![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_d, X)) | m_or_h_gate_v_in2(I0, c_g, X))),
% 293.23/185.75 inference(skolemize,[status(sab)],[20709])).
% 293.23/185.75 tff(20711,plain,
% 293.23/185.75 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_d, X)) | m_or_h_gate_v_in2(I0, c_g, X))),
% 293.23/185.75 inference(modus_ponens,[status(thm)],[20710, 20703])).
% 293.23/185.75 tff(20712,plain,
% 293.23/185.75 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_d, X)) | m_or_h_gate_v_in2(I0, c_g, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_d, s9)) | m_or_h_gate_v_in2(c_e_h_3, c_g, s9))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_d, X)) | m_or_h_gate_v_in2(I0, c_g, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s9)) | m_or_h_gate_v_in2(c_e_h_3, c_g, s9))),
% 293.23/185.75 inference(rewrite,[status(thm)],[])).
% 293.23/185.75 tff(20713,plain,
% 293.23/185.75 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_d, X)) | m_or_h_gate_v_in2(I0, c_g, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_d, s9)) | m_or_h_gate_v_in2(c_e_h_3, c_g, s9))),
% 293.23/185.75 inference(quant_inst,[status(thm)],[])).
% 293.23/185.75 tff(20714,plain,
% 293.23/185.75 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_d, X)) | m_or_h_gate_v_in2(I0, c_g, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s9)) | m_or_h_gate_v_in2(c_e_h_3, c_g, s9)),
% 293.23/185.75 inference(modus_ponens,[status(thm)],[20713, 20712])).
% 293.23/185.75 tff(20715,plain,
% 293.23/185.75 ($false),
% 293.23/185.75 inference(unit_resolution,[status(thm)],[20714, 20711, 17094, 20017])).
% 293.23/185.75 tff(20716,plain,((~m_and_h_gate_v_out(c_e_h_3, c_d, s9)) | m_or_h_gate_v_in2(c_e_h_3, c_g, s9)), inference(lemma,lemma(discharge,[]))).
% 293.23/185.75 tff(20717,plain,
% 293.23/185.75 (m_or_h_gate_v_in2(c_e_h_3, c_g, s9)),
% 293.23/185.75 inference(unit_resolution,[status(thm)],[20716, 20701])).
% 293.23/185.75 tff(20718,plain,
% 293.23/185.75 (((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in2(I0, I1, X)) | (~node4(I0, I1, X)))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_g, s9)) | (~node4(c_e_h_3, c_g, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in2(I0, I1, X)) | (~node4(I0, I1, X)))) | (~m_or_h_gate_v_in2(c_e_h_3, c_g, s9)) | (~node4(c_e_h_3, c_g, s9)))),
% 293.23/185.75 inference(rewrite,[status(thm)],[])).
% 293.23/185.75 tff(20719,plain,
% 293.23/185.75 ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in2(I0, I1, X)) | (~node4(I0, I1, X)))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_g, s9)) | (~node4(c_e_h_3, c_g, s9)))),
% 293.23/185.75 inference(quant_inst,[status(thm)],[])).
% 293.23/185.75 tff(20720,plain,
% 293.23/185.75 ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in2(I0, I1, X)) | (~node4(I0, I1, X)))) | (~m_or_h_gate_v_in2(c_e_h_3, c_g, s9)) | (~node4(c_e_h_3, c_g, s9))),
% 293.23/185.75 inference(modus_ponens,[status(thm)],[20719, 20718])).
% 293.23/185.75 tff(20721,plain,
% 293.23/185.75 (~node4(c_e_h_3, c_g, s9)),
% 293.23/185.75 inference(unit_resolution,[status(thm)],[20720, 20695, 20717])).
% 293.23/185.75 tff(20722,plain,
% 293.23/185.75 (~m_or_h_gate_v_out(c_e_h_3, c_g, s9)),
% 293.23/185.75 inference(unit_resolution,[status(thm)],[20563, 20721, 20172])).
% 293.23/185.75 tff(20723,plain,
% 293.23/185.75 (m_mutex_h_half_v_out(c_e_h_3, c_b, s9)),
% 293.23/185.75 inference(unit_resolution,[status(thm)],[18874, 20701])).
% 293.23/185.75 tff(20724,assumption,(m_mutex_h_half_v_other_h_out(c_e_h_3, c_b, s9)), introduced(assumption)).
% 293.23/185.75 tff(20725,plain,
% 293.23/185.75 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl(((~trans(X, Y)) | (~m_mutex_h_half_v_out(I0, I1, Y)) | (~m_mutex_h_half_v_other_h_out(I0, I1, Y))) <=> ((~trans(X, Y)) | (~m_mutex_h_half_v_out(I0, I1, Y)) | (~m_mutex_h_half_v_other_h_out(I0, I1, Y))))),
% 293.23/185.75 inference(bind,[status(th)],[])).
% 293.23/185.75 tff(20726,plain,
% 293.23/185.75 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | (~m_mutex_h_half_v_out(I0, I1, Y)) | (~m_mutex_h_half_v_other_h_out(I0, I1, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | (~m_mutex_h_half_v_out(I0, I1, Y)) | (~m_mutex_h_half_v_other_h_out(I0, I1, Y)))),
% 293.23/185.75 inference(quant_intro,[status(thm)],[20725])).
% 293.23/185.75 tff(20727,plain,
% 293.23/185.75 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | (~m_mutex_h_half_v_out(I0, I1, Y)) | (~m_mutex_h_half_v_other_h_out(I0, I1, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | (~m_mutex_h_half_v_out(I0, I1, Y)) | (~m_mutex_h_half_v_other_h_out(I0, I1, Y)))),
% 293.23/185.75 inference(rewrite,[status(thm)],[])).
% 293.23/185.75 tff(20728,plain,
% 293.23/185.75 (^[Y: $i, I0: $i, X: $i, I1: $i] : trans(monotonicity(rewrite((((~trans(X, Y)) | (~trans(X, Y))) | (~m_mutex_h_half_v_out(I0, I1, Y))) <=> ((~trans(X, Y)) | (~m_mutex_h_half_v_out(I0, I1, Y)))), (((((~trans(X, Y)) | (~trans(X, Y))) | (~m_mutex_h_half_v_out(I0, I1, Y))) | (~m_mutex_h_half_v_other_h_out(I0, I1, Y))) <=> (((~trans(X, Y)) | (~m_mutex_h_half_v_out(I0, I1, Y))) | (~m_mutex_h_half_v_other_h_out(I0, I1, Y))))), rewrite((((~trans(X, Y)) | (~m_mutex_h_half_v_out(I0, I1, Y))) | (~m_mutex_h_half_v_other_h_out(I0, I1, Y))) <=> ((~trans(X, Y)) | (~m_mutex_h_half_v_out(I0, I1, Y)) | (~m_mutex_h_half_v_other_h_out(I0, I1, Y)))), (((((~trans(X, Y)) | (~trans(X, Y))) | (~m_mutex_h_half_v_out(I0, I1, Y))) | (~m_mutex_h_half_v_other_h_out(I0, I1, Y))) <=> ((~trans(X, Y)) | (~m_mutex_h_half_v_out(I0, I1, Y)) | (~m_mutex_h_half_v_other_h_out(I0, I1, Y)))))),
% 293.23/185.75 inference(bind,[status(th)],[])).
% 293.23/185.75 tff(20729,plain,
% 293.23/185.75 (![Y: $i, I0: $i, X: $i, I1: $i] : ((((~trans(X, Y)) | (~trans(X, Y))) | (~m_mutex_h_half_v_out(I0, I1, Y))) | (~m_mutex_h_half_v_other_h_out(I0, I1, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | (~m_mutex_h_half_v_out(I0, I1, Y)) | (~m_mutex_h_half_v_other_h_out(I0, I1, Y)))),
% 293.23/185.75 inference(quant_intro,[status(thm)],[20728])).
% 293.23/185.75 tff(20730,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : ((((~trans(X, Y)) | (~trans(X, Y))) | (~m_mutex_h_half_v_out(I0, I1, Y))) | (~m_mutex_h_half_v_other_h_out(I0, I1, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_mutex_h_half_7')).
% 293.23/185.75 tff(20731,plain,
% 293.23/185.75 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | (~m_mutex_h_half_v_out(I0, I1, Y)) | (~m_mutex_h_half_v_other_h_out(I0, I1, Y)))),
% 293.23/185.75 inference(modus_ponens,[status(thm)],[20730, 20729])).
% 293.23/185.75 tff(20732,plain,
% 293.23/185.75 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | (~m_mutex_h_half_v_out(I0, I1, Y)) | (~m_mutex_h_half_v_other_h_out(I0, I1, Y)))),
% 293.23/185.75 inference(modus_ponens,[status(thm)],[20731, 20727])).
% 293.23/185.75 tff(20733,plain,(
% 293.23/185.75 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | (~m_mutex_h_half_v_out(I0, I1, Y)) | (~m_mutex_h_half_v_other_h_out(I0, I1, Y)))),
% 293.23/185.75 inference(skolemize,[status(sab)],[20732])).
% 293.23/185.75 tff(20734,plain,
% 293.23/185.75 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | (~m_mutex_h_half_v_out(I0, I1, Y)) | (~m_mutex_h_half_v_other_h_out(I0, I1, Y)))),
% 293.23/185.75 inference(modus_ponens,[status(thm)],[20733, 20726])).
% 293.23/185.75 tff(20735,plain,
% 293.23/185.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | (~m_mutex_h_half_v_out(I0, I1, Y)) | (~m_mutex_h_half_v_other_h_out(I0, I1, Y)))) | ((~trans(s8, s9)) | (~m_mutex_h_half_v_other_h_out(c_e_h_3, c_b, s9)) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | (~m_mutex_h_half_v_out(I0, I1, Y)) | (~m_mutex_h_half_v_other_h_out(I0, I1, Y)))) | (~trans(s8, s9)) | (~m_mutex_h_half_v_other_h_out(c_e_h_3, c_b, s9)) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s9)))),
% 293.23/185.75 inference(rewrite,[status(thm)],[])).
% 293.23/185.75 tff(20736,plain,
% 293.23/185.75 (((~trans(s8, s9)) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s9)) | (~m_mutex_h_half_v_other_h_out(c_e_h_3, c_b, s9))) <=> ((~trans(s8, s9)) | (~m_mutex_h_half_v_other_h_out(c_e_h_3, c_b, s9)) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s9)))),
% 293.23/185.75 inference(rewrite,[status(thm)],[])).
% 293.23/185.75 tff(20737,plain,
% 293.23/185.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | (~m_mutex_h_half_v_out(I0, I1, Y)) | (~m_mutex_h_half_v_other_h_out(I0, I1, Y)))) | ((~trans(s8, s9)) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s9)) | (~m_mutex_h_half_v_other_h_out(c_e_h_3, c_b, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | (~m_mutex_h_half_v_out(I0, I1, Y)) | (~m_mutex_h_half_v_other_h_out(I0, I1, Y)))) | ((~trans(s8, s9)) | (~m_mutex_h_half_v_other_h_out(c_e_h_3, c_b, s9)) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s9))))),
% 293.23/185.75 inference(monotonicity,[status(thm)],[20736])).
% 293.23/185.75 tff(20738,plain,
% 293.23/185.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | (~m_mutex_h_half_v_out(I0, I1, Y)) | (~m_mutex_h_half_v_other_h_out(I0, I1, Y)))) | ((~trans(s8, s9)) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s9)) | (~m_mutex_h_half_v_other_h_out(c_e_h_3, c_b, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | (~m_mutex_h_half_v_out(I0, I1, Y)) | (~m_mutex_h_half_v_other_h_out(I0, I1, Y)))) | (~trans(s8, s9)) | (~m_mutex_h_half_v_other_h_out(c_e_h_3, c_b, s9)) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s9)))),
% 293.23/185.75 inference(transitivity,[status(thm)],[20737, 20735])).
% 293.23/185.75 tff(20739,plain,
% 293.23/185.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | (~m_mutex_h_half_v_out(I0, I1, Y)) | (~m_mutex_h_half_v_other_h_out(I0, I1, Y)))) | ((~trans(s8, s9)) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s9)) | (~m_mutex_h_half_v_other_h_out(c_e_h_3, c_b, s9)))),
% 293.23/185.75 inference(quant_inst,[status(thm)],[])).
% 293.23/185.75 tff(20740,plain,
% 293.23/185.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | (~m_mutex_h_half_v_out(I0, I1, Y)) | (~m_mutex_h_half_v_other_h_out(I0, I1, Y)))) | (~trans(s8, s9)) | (~m_mutex_h_half_v_other_h_out(c_e_h_3, c_b, s9)) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s9))),
% 293.23/185.75 inference(modus_ponens,[status(thm)],[20739, 20738])).
% 293.23/185.75 tff(20741,plain,
% 293.23/185.75 ($false),
% 293.23/185.75 inference(unit_resolution,[status(thm)],[20740, 20734, 1993, 18876, 20724])).
% 293.23/185.75 tff(20742,plain,((~m_mutex_h_half_v_out(c_e_h_3, c_b, s9)) | (~m_mutex_h_half_v_other_h_out(c_e_h_3, c_b, s9))), inference(lemma,lemma(discharge,[]))).
% 293.23/185.75 tff(20743,plain,
% 293.23/185.75 (~m_mutex_h_half_v_other_h_out(c_e_h_3, c_b, s9)),
% 293.23/185.75 inference(unit_resolution,[status(thm)],[20742, 20723])).
% 293.23/185.75 tff(20744,assumption,(~m_mutex_h_half_v_other_h_out(c_e_h_3, c_b, s9)), introduced(assumption)).
% 293.23/185.75 tff(20745,plain,
% 293.23/185.75 (^[I0: $i, X: $i] : refl(((~m_mutex_h_half_v_out(I0, c_a, X)) | m_mutex_h_half_v_other_h_out(I0, c_b, X)) <=> ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_mutex_h_half_v_other_h_out(I0, c_b, X)))),
% 293.23/185.75 inference(bind,[status(th)],[])).
% 293.23/185.75 tff(20746,plain,
% 293.23/185.75 (![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_mutex_h_half_v_other_h_out(I0, c_b, X)) <=> ![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_mutex_h_half_v_other_h_out(I0, c_b, X))),
% 293.23/185.75 inference(quant_intro,[status(thm)],[20745])).
% 293.23/185.75 tff(20747,plain,
% 293.23/185.75 (![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_mutex_h_half_v_other_h_out(I0, c_b, X)) <=> ![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_mutex_h_half_v_other_h_out(I0, c_b, X))),
% 293.23/185.75 inference(rewrite,[status(thm)],[])).
% 293.23/185.75 tff(20748,plain,
% 293.23/185.75 (^[I0: $i, X: $i] : rewrite((m_mutex_h_half_v_other_h_out(I0, c_b, X) | (~m_mutex_h_half_v_out(I0, c_a, X))) <=> ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_mutex_h_half_v_other_h_out(I0, c_b, X)))),
% 293.23/185.75 inference(bind,[status(th)],[])).
% 293.23/185.75 tff(20749,plain,
% 293.23/185.75 (![I0: $i, X: $i] : (m_mutex_h_half_v_other_h_out(I0, c_b, X) | (~m_mutex_h_half_v_out(I0, c_a, X))) <=> ![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_mutex_h_half_v_other_h_out(I0, c_b, X))),
% 293.23/185.75 inference(quant_intro,[status(thm)],[20748])).
% 293.23/185.75 tff(20750,axiom,(![I0: $i, X: $i] : (m_mutex_h_half_v_other_h_out(I0, c_b, X) | (~m_mutex_h_half_v_out(I0, c_a, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_8')).
% 293.23/185.75 tff(20751,plain,
% 293.23/185.75 (![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_mutex_h_half_v_other_h_out(I0, c_b, X))),
% 293.23/185.75 inference(modus_ponens,[status(thm)],[20750, 20749])).
% 293.23/185.75 tff(20752,plain,
% 293.23/185.75 (![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_mutex_h_half_v_other_h_out(I0, c_b, X))),
% 293.23/185.75 inference(modus_ponens,[status(thm)],[20751, 20747])).
% 293.23/185.75 tff(20753,plain,(
% 293.23/185.75 ![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_mutex_h_half_v_other_h_out(I0, c_b, X))),
% 293.23/185.75 inference(skolemize,[status(sab)],[20752])).
% 293.23/185.75 tff(20754,plain,
% 293.23/185.75 (![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_mutex_h_half_v_other_h_out(I0, c_b, X))),
% 293.23/185.75 inference(modus_ponens,[status(thm)],[20753, 20746])).
% 293.23/185.75 tff(20755,plain,
% 293.23/185.75 (((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_mutex_h_half_v_other_h_out(I0, c_b, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s9)) | m_mutex_h_half_v_other_h_out(c_e_h_3, c_b, s9))) <=> ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_mutex_h_half_v_other_h_out(I0, c_b, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s9)) | m_mutex_h_half_v_other_h_out(c_e_h_3, c_b, s9))),
% 293.23/185.75 inference(rewrite,[status(thm)],[])).
% 293.23/185.75 tff(20756,plain,
% 293.23/185.75 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_mutex_h_half_v_other_h_out(I0, c_b, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s9)) | m_mutex_h_half_v_other_h_out(c_e_h_3, c_b, s9))),
% 293.23/185.75 inference(quant_inst,[status(thm)],[])).
% 293.23/185.75 tff(20757,plain,
% 293.23/185.75 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_mutex_h_half_v_other_h_out(I0, c_b, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s9)) | m_mutex_h_half_v_other_h_out(c_e_h_3, c_b, s9)),
% 293.23/185.75 inference(modus_ponens,[status(thm)],[20756, 20755])).
% 293.23/185.75 tff(20758,plain,
% 293.23/185.75 ($false),
% 293.23/185.75 inference(unit_resolution,[status(thm)],[20757, 20754, 19631, 20744])).
% 293.23/185.75 tff(20759,plain,(m_mutex_h_half_v_other_h_out(c_e_h_3, c_b, s9) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s9))), inference(lemma,lemma(discharge,[]))).
% 293.23/185.75 tff(20760,plain,
% 293.23/185.75 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s9)),
% 293.23/185.75 inference(unit_resolution,[status(thm)],[20759, 20743])).
% 293.23/185.75 tff(20761,plain,
% 293.23/185.75 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s7)),
% 293.23/185.75 inference(unit_resolution,[status(thm)],[19628, 1])).
% 293.23/185.75 tff(20762,plain,
% 293.23/185.75 (m_and_h_gate_v_out(c_e_h_3, c_c, s5)),
% 293.23/185.75 inference(unit_resolution,[status(thm)],[20154, 20761, 11155, 2512])).
% 293.23/185.75 tff(20763,plain,
% 293.23/185.75 ($false),
% 293.23/185.75 inference(unit_resolution,[status(thm)],[10330, 20762, 2512])).
% 293.23/185.75 tff(20764,plain,(m_mutex_h_half_v_out(c_e_h_3, c_a, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s7))), inference(lemma,lemma(discharge,[]))).
% 293.23/185.75 tff(20765,plain,
% 293.23/185.75 (~m_and_h_gate_v_out(c_e_h_3, c_c, s7)),
% 293.23/185.75 inference(unit_resolution,[status(thm)],[20764, 20760])).
% 293.23/185.75 tff(20766,plain,
% 293.23/185.75 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s4)),
% 293.23/185.75 inference(unit_resolution,[status(thm)],[2511, 20760])).
% 293.23/185.75 tff(20767,plain,
% 293.23/185.75 (~m_and_h_gate_v_out(c_e_h_3, c_c, s5)),
% 293.23/185.75 inference(unit_resolution,[status(thm)],[10330, 20766])).
% 293.23/185.75 tff(20768,plain,
% 293.23/185.75 (~m_or_h_gate_v_out(c_e_h_3, c_g, s6)),
% 293.23/185.75 inference(unit_resolution,[status(thm)],[10319, 20767, 20176])).
% 293.23/185.75 tff(20769,plain,
% 293.23/185.75 (~m_or_h_gate_v_out(c_e_h_3, c_g, s7)),
% 293.23/185.75 inference(unit_resolution,[status(thm)],[10302, 20768, 20765, 20194, 2743])).
% 293.23/185.75 tff(20770,plain,
% 293.23/185.75 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s7)),
% 293.23/185.75 inference(unit_resolution,[status(thm)],[10395, 20769])).
% 293.23/185.75 tff(20771,plain,
% 293.23/185.75 (~node20(c_e_h_3, c_k, s7)),
% 293.23/185.75 inference(unit_resolution,[status(thm)],[10403, 20770])).
% 293.23/185.75 tff(20772,plain,
% 293.23/185.75 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s6)),
% 293.23/185.75 inference(unit_resolution,[status(thm)],[10448, 2048, 20768])).
% 293.23/185.75 tff(20773,plain,
% 293.23/185.75 (~node20(c_e_h_3, c_k, s6)),
% 293.23/185.75 inference(unit_resolution,[status(thm)],[10444, 38, 20772])).
% 293.23/185.75 tff(20774,plain,
% 293.23/185.75 (~m_and_h_gate_v_out(c_e_h_3, c_k, s7)),
% 293.23/185.75 inference(unit_resolution,[status(thm)],[10440, 20773, 20269])).
% 293.23/185.75 tff(20775,plain,
% 293.23/185.75 (~m_and_h_gate_v_out(c_e_h_3, c_k, s8)),
% 293.23/185.75 inference(unit_resolution,[status(thm)],[10425, 20774, 20771])).
% 293.23/185.75 tff(20776,plain,
% 293.23/185.75 ($false),
% 293.23/185.75 inference(unit_resolution,[status(thm)],[20532, 20775, 20722, 20173, 20699])).
% 293.23/185.75 tff(20777,plain,((~m_and_h_gate_v_out(c_e_h_3, c_k, s10)) | m_or_h_gate_v_out(c_e_h_3, c_g, s10) | m_and_h_gate_v_out(c_e_h_3, c_c, s4)), inference(lemma,lemma(discharge,[]))).
% 293.23/185.75 tff(20778,plain,
% 293.23/185.75 (~m_and_h_gate_v_out(c_e_h_3, c_k, s10)),
% 293.23/185.75 inference(unit_resolution,[status(thm)],[20777, 2743, 20172])).
% 293.23/185.75 tff(20779,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_l, s10)), introduced(assumption)).
% 293.23/185.75 tff(20780,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_k, s10)), introduced(assumption)).
% 293.23/185.75 tff(20781,plain,
% 293.23/185.75 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_l, s10)) | m_and_h_gate_v_out(c_e_h_3, c_k, s10))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s10)) | m_and_h_gate_v_out(c_e_h_3, c_k, s10))),
% 293.23/185.76 inference(rewrite,[status(thm)],[])).
% 293.23/185.76 tff(20782,plain,
% 293.23/185.76 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_l, s10)) | m_and_h_gate_v_out(c_e_h_3, c_k, s10))),
% 293.23/185.76 inference(quant_inst,[status(thm)],[])).
% 293.23/185.76 tff(20783,plain,
% 293.23/185.76 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s10)) | m_and_h_gate_v_out(c_e_h_3, c_k, s10)),
% 293.23/185.76 inference(modus_ponens,[status(thm)],[20782, 20781])).
% 293.23/185.76 tff(20784,plain,
% 293.23/185.76 ($false),
% 293.23/185.76 inference(unit_resolution,[status(thm)],[20783, 1529, 20780, 20779])).
% 293.23/185.76 tff(20785,plain,((~m_and_h_gate_v_in1(c_e_h_3, c_l, s10)) | m_and_h_gate_v_out(c_e_h_3, c_k, s10)), inference(lemma,lemma(discharge,[]))).
% 293.23/185.76 tff(20786,plain,
% 293.23/185.76 (~m_and_h_gate_v_in1(c_e_h_3, c_l, s10)),
% 293.23/185.76 inference(unit_resolution,[status(thm)],[20785, 20778])).
% 293.23/185.76 tff(20787,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_l, s10)), introduced(assumption)).
% 293.23/185.76 tff(20788,assumption,(node20(c_e_h_3, c_l, s10)), introduced(assumption)).
% 293.23/185.76 tff(20789,plain,
% 293.23/185.76 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_l, s10)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s10))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_l, s10)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s10))),
% 293.23/185.76 inference(rewrite,[status(thm)],[])).
% 293.23/185.76 tff(20790,plain,
% 293.23/185.76 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_l, s10)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s10))),
% 293.23/185.76 inference(quant_inst,[status(thm)],[])).
% 293.23/185.76 tff(20791,plain,
% 293.23/185.76 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_l, s10)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s10)),
% 293.23/185.76 inference(modus_ponens,[status(thm)],[20790, 20789])).
% 293.23/185.76 tff(20792,plain,
% 293.23/185.76 ($false),
% 293.23/185.76 inference(unit_resolution,[status(thm)],[20791, 38, 20788, 20787])).
% 293.23/185.76 tff(20793,plain,((~node20(c_e_h_3, c_l, s10)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s10)), inference(lemma,lemma(discharge,[]))).
% 293.23/185.76 tff(20794,plain,
% 293.23/185.76 (~node20(c_e_h_3, c_l, s10)),
% 293.23/185.76 inference(unit_resolution,[status(thm)],[20793, 20786])).
% 293.23/185.76 tff(20795,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_k, s10)), introduced(assumption)).
% 293.23/185.76 tff(20796,plain,
% 293.23/185.76 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_k, s10)) | m_or_h_gate_v_out(c_e_h_3, c_g, s10))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s10)) | m_or_h_gate_v_out(c_e_h_3, c_g, s10))),
% 293.23/185.76 inference(rewrite,[status(thm)],[])).
% 293.23/185.76 tff(20797,plain,
% 293.23/185.76 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_k, s10)) | m_or_h_gate_v_out(c_e_h_3, c_g, s10))),
% 293.23/185.76 inference(quant_inst,[status(thm)],[])).
% 293.23/185.76 tff(20798,plain,
% 293.23/185.76 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_k, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_k, s10)) | m_or_h_gate_v_out(c_e_h_3, c_g, s10)),
% 293.23/185.76 inference(modus_ponens,[status(thm)],[20797, 20796])).
% 293.23/185.76 tff(20799,plain,
% 293.23/185.76 ($false),
% 293.23/185.76 inference(unit_resolution,[status(thm)],[20798, 2048, 20172, 20795])).
% 293.23/185.76 tff(20800,plain,((~m_and_h_gate_v_in1(c_e_h_3, c_k, s10)) | m_or_h_gate_v_out(c_e_h_3, c_g, s10)), inference(lemma,lemma(discharge,[]))).
% 293.23/185.76 tff(20801,plain,
% 293.23/185.76 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s10)),
% 293.23/185.76 inference(unit_resolution,[status(thm)],[20800, 20172])).
% 293.23/185.76 tff(20802,assumption,(node20(c_e_h_3, c_k, s10)), introduced(assumption)).
% 293.23/185.76 tff(20803,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_k, s10)), introduced(assumption)).
% 293.23/185.76 tff(20804,plain,
% 293.23/185.76 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_k, s10)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s10))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_k, s10)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s10))),
% 293.23/185.76 inference(rewrite,[status(thm)],[])).
% 293.23/185.76 tff(20805,plain,
% 293.23/185.76 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_k, s10)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s10))),
% 293.23/185.76 inference(quant_inst,[status(thm)],[])).
% 293.23/185.76 tff(20806,plain,
% 293.23/185.76 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_k, s10)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s10)),
% 293.23/185.76 inference(modus_ponens,[status(thm)],[20805, 20804])).
% 293.23/185.76 tff(20807,plain,
% 293.23/185.76 ($false),
% 293.23/185.76 inference(unit_resolution,[status(thm)],[20806, 38, 20803, 20802])).
% 293.23/185.76 tff(20808,plain,((~node20(c_e_h_3, c_k, s10)) | m_and_h_gate_v_in1(c_e_h_3, c_k, s10)), inference(lemma,lemma(discharge,[]))).
% 293.23/185.76 tff(20809,plain,
% 293.23/185.76 (~node20(c_e_h_3, c_k, s10)),
% 293.23/185.76 inference(unit_resolution,[status(thm)],[20808, 20801])).
% 293.23/185.76 tff(20810,assumption,(m_or_h_gate_v_out(c_e_h_3, c_j, s13)), introduced(assumption)).
% 293.23/185.76 tff(20811,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_h, s13)), introduced(assumption)).
% 293.23/185.76 tff(20812,plain,
% 293.23/185.76 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_j, X)) | m_c_h_element_v_in2(I0, c_h, X))) | ((~m_or_h_gate_v_out(c_e_h_3, c_j, s13)) | m_c_h_element_v_in2(c_e_h_3, c_h, s13))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_j, X)) | m_c_h_element_v_in2(I0, c_h, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s13)) | m_c_h_element_v_in2(c_e_h_3, c_h, s13))),
% 293.23/185.76 inference(rewrite,[status(thm)],[])).
% 293.23/185.76 tff(20813,plain,
% 293.23/185.76 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_j, X)) | m_c_h_element_v_in2(I0, c_h, X))) | ((~m_or_h_gate_v_out(c_e_h_3, c_j, s13)) | m_c_h_element_v_in2(c_e_h_3, c_h, s13))),
% 293.23/185.76 inference(quant_inst,[status(thm)],[])).
% 293.23/185.76 tff(20814,plain,
% 293.23/185.76 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_j, X)) | m_c_h_element_v_in2(I0, c_h, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s13)) | m_c_h_element_v_in2(c_e_h_3, c_h, s13)),
% 293.23/185.76 inference(modus_ponens,[status(thm)],[20813, 20812])).
% 293.23/185.76 tff(20815,plain,
% 293.23/185.76 ($false),
% 293.23/185.76 inference(unit_resolution,[status(thm)],[20814, 7385, 20810, 20811])).
% 293.23/185.76 tff(20816,plain,((~m_or_h_gate_v_out(c_e_h_3, c_j, s13)) | m_c_h_element_v_in2(c_e_h_3, c_h, s13)), inference(lemma,lemma(discharge,[]))).
% 293.23/185.76 tff(20817,plain,
% 293.23/185.76 (m_c_h_element_v_in2(c_e_h_3, c_h, s13)),
% 293.23/185.76 inference(unit_resolution,[status(thm)],[20816, 20810])).
% 293.23/185.76 tff(20818,assumption,(m_c_h_element_v_out(c_e_h_3, c_h, s13)), introduced(assumption)).
% 293.23/185.76 tff(20819,assumption,(node15(c_e_h_3, c_h, s13, s14)), introduced(assumption)).
% 293.23/185.76 tff(20820,plain,
% 293.23/185.76 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl((m_c_h_element_v_out(I0, I1, Y) | (~node15(I0, I1, X, Y)) | (~m_c_h_element_v_out(I0, I1, X))) <=> (m_c_h_element_v_out(I0, I1, Y) | (~node15(I0, I1, X, Y)) | (~m_c_h_element_v_out(I0, I1, X))))),
% 293.23/185.76 inference(bind,[status(th)],[])).
% 293.23/185.76 tff(20821,plain,
% 293.23/185.76 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~node15(I0, I1, X, Y)) | (~m_c_h_element_v_out(I0, I1, X))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~node15(I0, I1, X, Y)) | (~m_c_h_element_v_out(I0, I1, X)))),
% 293.23/185.76 inference(quant_intro,[status(thm)],[20820])).
% 293.23/185.76 tff(20822,plain,
% 293.23/185.76 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~node15(I0, I1, X, Y)) | (~m_c_h_element_v_out(I0, I1, X))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~node15(I0, I1, X, Y)) | (~m_c_h_element_v_out(I0, I1, X)))),
% 293.23/185.76 inference(rewrite,[status(thm)],[])).
% 293.23/185.76 tff(20823,plain,
% 293.23/185.76 (^[Y: $i, I0: $i, X: $i, I1: $i] : trans(monotonicity(rewrite((m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_out(I0, I1, X))) <=> (m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_out(I0, I1, X)))), (((m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_out(I0, I1, X))) | (~node15(I0, I1, X, Y))) <=> ((m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_out(I0, I1, X))) | (~node15(I0, I1, X, Y))))), rewrite(((m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_out(I0, I1, X))) | (~node15(I0, I1, X, Y))) <=> (m_c_h_element_v_out(I0, I1, Y) | (~node15(I0, I1, X, Y)) | (~m_c_h_element_v_out(I0, I1, X)))), (((m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_out(I0, I1, X))) | (~node15(I0, I1, X, Y))) <=> (m_c_h_element_v_out(I0, I1, Y) | (~node15(I0, I1, X, Y)) | (~m_c_h_element_v_out(I0, I1, X)))))),
% 293.23/185.76 inference(bind,[status(th)],[])).
% 293.23/185.76 tff(20824,plain,
% 293.23/185.76 (![Y: $i, I0: $i, X: $i, I1: $i] : ((m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_out(I0, I1, X))) | (~node15(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~node15(I0, I1, X, Y)) | (~m_c_h_element_v_out(I0, I1, X)))),
% 293.23/185.76 inference(quant_intro,[status(thm)],[20823])).
% 293.23/185.76 tff(20825,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : ((m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_out(I0, I1, X))) | (~node15(I0, I1, X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_c_h_element_4')).
% 293.23/185.76 tff(20826,plain,
% 293.23/185.76 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~node15(I0, I1, X, Y)) | (~m_c_h_element_v_out(I0, I1, X)))),
% 293.23/185.76 inference(modus_ponens,[status(thm)],[20825, 20824])).
% 293.23/185.76 tff(20827,plain,
% 293.23/185.76 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~node15(I0, I1, X, Y)) | (~m_c_h_element_v_out(I0, I1, X)))),
% 293.23/185.76 inference(modus_ponens,[status(thm)],[20826, 20822])).
% 293.23/185.76 tff(20828,plain,(
% 293.23/185.76 ![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~node15(I0, I1, X, Y)) | (~m_c_h_element_v_out(I0, I1, X)))),
% 293.23/185.76 inference(skolemize,[status(sab)],[20827])).
% 293.23/185.76 tff(20829,plain,
% 293.23/185.76 (![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~node15(I0, I1, X, Y)) | (~m_c_h_element_v_out(I0, I1, X)))),
% 293.23/185.76 inference(modus_ponens,[status(thm)],[20828, 20821])).
% 293.23/185.76 tff(20830,plain,
% 293.23/185.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~node15(I0, I1, X, Y)) | (~m_c_h_element_v_out(I0, I1, X)))) | (m_c_h_element_v_out(c_e_h_3, c_h, s14) | (~m_c_h_element_v_out(c_e_h_3, c_h, s13)) | (~node15(c_e_h_3, c_h, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~node15(I0, I1, X, Y)) | (~m_c_h_element_v_out(I0, I1, X)))) | m_c_h_element_v_out(c_e_h_3, c_h, s14) | (~m_c_h_element_v_out(c_e_h_3, c_h, s13)) | (~node15(c_e_h_3, c_h, s13, s14)))),
% 293.23/185.76 inference(rewrite,[status(thm)],[])).
% 293.23/185.76 tff(20831,plain,
% 293.23/185.76 ((m_c_h_element_v_out(c_e_h_3, c_h, s14) | (~node15(c_e_h_3, c_h, s13, s14)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s13))) <=> (m_c_h_element_v_out(c_e_h_3, c_h, s14) | (~m_c_h_element_v_out(c_e_h_3, c_h, s13)) | (~node15(c_e_h_3, c_h, s13, s14)))),
% 293.23/185.76 inference(rewrite,[status(thm)],[])).
% 293.23/185.76 tff(20832,plain,
% 293.23/185.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~node15(I0, I1, X, Y)) | (~m_c_h_element_v_out(I0, I1, X)))) | (m_c_h_element_v_out(c_e_h_3, c_h, s14) | (~node15(c_e_h_3, c_h, s13, s14)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~node15(I0, I1, X, Y)) | (~m_c_h_element_v_out(I0, I1, X)))) | (m_c_h_element_v_out(c_e_h_3, c_h, s14) | (~m_c_h_element_v_out(c_e_h_3, c_h, s13)) | (~node15(c_e_h_3, c_h, s13, s14))))),
% 293.23/185.76 inference(monotonicity,[status(thm)],[20831])).
% 293.23/185.76 tff(20833,plain,
% 293.23/185.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~node15(I0, I1, X, Y)) | (~m_c_h_element_v_out(I0, I1, X)))) | (m_c_h_element_v_out(c_e_h_3, c_h, s14) | (~node15(c_e_h_3, c_h, s13, s14)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~node15(I0, I1, X, Y)) | (~m_c_h_element_v_out(I0, I1, X)))) | m_c_h_element_v_out(c_e_h_3, c_h, s14) | (~m_c_h_element_v_out(c_e_h_3, c_h, s13)) | (~node15(c_e_h_3, c_h, s13, s14)))),
% 293.23/185.76 inference(transitivity,[status(thm)],[20832, 20830])).
% 293.23/185.76 tff(20834,plain,
% 293.23/185.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~node15(I0, I1, X, Y)) | (~m_c_h_element_v_out(I0, I1, X)))) | (m_c_h_element_v_out(c_e_h_3, c_h, s14) | (~node15(c_e_h_3, c_h, s13, s14)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s13)))),
% 293.23/185.76 inference(quant_inst,[status(thm)],[])).
% 293.23/185.76 tff(20835,plain,
% 293.23/185.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~node15(I0, I1, X, Y)) | (~m_c_h_element_v_out(I0, I1, X)))) | m_c_h_element_v_out(c_e_h_3, c_h, s14) | (~m_c_h_element_v_out(c_e_h_3, c_h, s13)) | (~node15(c_e_h_3, c_h, s13, s14))),
% 293.23/185.76 inference(modus_ponens,[status(thm)],[20834, 20833])).
% 293.23/185.76 tff(20836,plain,
% 293.23/185.76 ($false),
% 293.23/185.76 inference(unit_resolution,[status(thm)],[20835, 20829, 20156, 20818, 20819])).
% 293.23/185.76 tff(20837,plain,((~node15(c_e_h_3, c_h, s13, s14)) | m_c_h_element_v_out(c_e_h_3, c_h, s14) | (~m_c_h_element_v_out(c_e_h_3, c_h, s13))), inference(lemma,lemma(discharge,[]))).
% 293.23/185.76 tff(20838,plain,
% 293.23/185.76 (~node15(c_e_h_3, c_h, s13, s14)),
% 293.23/185.76 inference(unit_resolution,[status(thm)],[20837, 20156, 20818])).
% 293.23/185.76 tff(20839,assumption,(node18(c_e_h_3, c_h, s13, s14)), introduced(assumption)).
% 293.23/185.76 tff(20840,plain,
% 293.23/185.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_out(I0, I1, X)) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_h, s14) | (~m_c_h_element_v_out(c_e_h_3, c_h, s13)) | (~node18(c_e_h_3, c_h, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_out(I0, I1, X)) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s14) | (~m_c_h_element_v_out(c_e_h_3, c_h, s13)) | (~node18(c_e_h_3, c_h, s13, s14)))),
% 293.23/185.76 inference(rewrite,[status(thm)],[])).
% 293.23/185.76 tff(20841,plain,
% 293.23/185.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_out(I0, I1, X)) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_h, s14) | (~m_c_h_element_v_out(c_e_h_3, c_h, s13)) | (~node18(c_e_h_3, c_h, s13, s14)))),
% 293.23/185.76 inference(quant_inst,[status(thm)],[])).
% 293.23/185.76 tff(20842,plain,
% 293.23/185.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_out(I0, I1, X)) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s14) | (~m_c_h_element_v_out(c_e_h_3, c_h, s13)) | (~node18(c_e_h_3, c_h, s13, s14))),
% 293.23/185.76 inference(modus_ponens,[status(thm)],[20841, 20840])).
% 293.23/185.76 tff(20843,plain,
% 293.23/185.76 ($false),
% 293.23/185.76 inference(unit_resolution,[status(thm)],[20842, 11191, 20156, 20818, 20839])).
% 293.23/185.76 tff(20844,plain,((~node18(c_e_h_3, c_h, s13, s14)) | m_c_h_element_v_out(c_e_h_3, c_h, s14) | (~m_c_h_element_v_out(c_e_h_3, c_h, s13))), inference(lemma,lemma(discharge,[]))).
% 293.23/185.76 tff(20845,plain,
% 293.23/185.76 (~node18(c_e_h_3, c_h, s13, s14)),
% 293.23/185.76 inference(unit_resolution,[status(thm)],[20844, 20156, 20818])).
% 293.23/185.76 tff(20846,plain,
% 293.23/185.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s13, s14)) | node19(c_e_h_3, c_h, s13, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s13, s14)) | node19(c_e_h_3, c_h, s13, s14))),
% 293.23/185.76 inference(rewrite,[status(thm)],[])).
% 293.23/185.76 tff(20847,plain,
% 293.23/185.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s13, s14)) | node19(c_e_h_3, c_h, s13, s14))),
% 293.23/185.76 inference(quant_inst,[status(thm)],[])).
% 293.23/185.76 tff(20848,plain,
% 293.23/185.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s13, s14)) | node19(c_e_h_3, c_h, s13, s14)),
% 293.23/185.76 inference(modus_ponens,[status(thm)],[20847, 20846])).
% 293.23/185.76 tff(20849,plain,
% 293.23/185.76 (node19(c_e_h_3, c_h, s13, s14)),
% 293.23/185.76 inference(unit_resolution,[status(thm)],[20848, 190, 12831])).
% 293.23/185.76 tff(20850,plain,
% 293.23/185.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_h, s13, s14)) | node17(c_e_h_3, c_h, s13) | node18(c_e_h_3, c_h, s13, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_h, s13, s14)) | node17(c_e_h_3, c_h, s13) | node18(c_e_h_3, c_h, s13, s14))),
% 293.23/185.77 inference(rewrite,[status(thm)],[])).
% 293.23/185.77 tff(20851,plain,
% 293.23/185.77 ((node17(c_e_h_3, c_h, s13) | node18(c_e_h_3, c_h, s13, s14) | (~node19(c_e_h_3, c_h, s13, s14))) <=> ((~node19(c_e_h_3, c_h, s13, s14)) | node17(c_e_h_3, c_h, s13) | node18(c_e_h_3, c_h, s13, s14))),
% 293.23/185.77 inference(rewrite,[status(thm)],[])).
% 293.23/185.77 tff(20852,plain,
% 293.23/185.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s13) | node18(c_e_h_3, c_h, s13, s14) | (~node19(c_e_h_3, c_h, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_h, s13, s14)) | node17(c_e_h_3, c_h, s13) | node18(c_e_h_3, c_h, s13, s14)))),
% 293.23/185.77 inference(monotonicity,[status(thm)],[20851])).
% 293.23/185.77 tff(20853,plain,
% 293.23/185.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s13) | node18(c_e_h_3, c_h, s13, s14) | (~node19(c_e_h_3, c_h, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_h, s13, s14)) | node17(c_e_h_3, c_h, s13) | node18(c_e_h_3, c_h, s13, s14))),
% 293.23/185.77 inference(transitivity,[status(thm)],[20852, 20850])).
% 293.23/185.77 tff(20854,plain,
% 293.23/185.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s13) | node18(c_e_h_3, c_h, s13, s14) | (~node19(c_e_h_3, c_h, s13, s14)))),
% 293.23/185.77 inference(quant_inst,[status(thm)],[])).
% 293.23/185.77 tff(20855,plain,
% 293.23/185.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_h, s13, s14)) | node17(c_e_h_3, c_h, s13) | node18(c_e_h_3, c_h, s13, s14)),
% 293.23/185.77 inference(modus_ponens,[status(thm)],[20854, 20853])).
% 293.23/185.77 tff(20856,plain,
% 293.23/185.77 (node17(c_e_h_3, c_h, s13) | node18(c_e_h_3, c_h, s13, s14)),
% 293.23/185.77 inference(unit_resolution,[status(thm)],[20855, 776, 20849])).
% 293.23/185.77 tff(20857,plain,
% 293.23/185.77 (node17(c_e_h_3, c_h, s13)),
% 293.23/185.77 inference(unit_resolution,[status(thm)],[20856, 20845])).
% 293.23/185.77 tff(20858,assumption,(m_c_h_element_v_in2(c_e_h_3, c_h, s13)), introduced(assumption)).
% 293.23/185.77 tff(20859,plain,
% 293.23/185.77 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s13) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s13)) | (~node17(c_e_h_3, c_h, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_3, c_h, s13) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s13)) | (~node17(c_e_h_3, c_h, s13)))),
% 293.23/185.77 inference(rewrite,[status(thm)],[])).
% 293.23/185.77 tff(20860,plain,
% 293.23/185.77 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s13) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s13)) | (~node17(c_e_h_3, c_h, s13)))),
% 293.23/185.77 inference(quant_inst,[status(thm)],[])).
% 293.23/185.77 tff(20861,plain,
% 293.23/185.77 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_3, c_h, s13) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s13)) | (~node17(c_e_h_3, c_h, s13))),
% 293.23/185.77 inference(modus_ponens,[status(thm)],[20860, 20859])).
% 293.23/185.77 tff(20862,plain,
% 293.23/185.77 (m_c_h_element_v_in1(c_e_h_3, c_h, s13) | (~node17(c_e_h_3, c_h, s13))),
% 293.23/185.77 inference(unit_resolution,[status(thm)],[20861, 859, 20858])).
% 293.23/185.77 tff(20863,plain,
% 293.23/185.77 (m_c_h_element_v_in1(c_e_h_3, c_h, s13)),
% 293.23/185.77 inference(unit_resolution,[status(thm)],[20862, 20857])).
% 293.23/185.77 tff(20864,assumption,(m_c_h_element_v_in1(c_e_h_3, c_h, s13)), introduced(assumption)).
% 293.23/185.77 tff(20865,assumption,(node14(c_e_h_3, c_h, s13, s14)), introduced(assumption)).
% 293.23/185.77 tff(20866,plain,
% 293.23/185.77 (^[Y: $i, I0: $i, X: $i, I1: $i] : refl(((~node14(I0, I1, X, Y)) | (~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_out(I0, I1, Y)) <=> ((~node14(I0, I1, X, Y)) | (~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_out(I0, I1, Y)))),
% 293.23/185.77 inference(bind,[status(th)],[])).
% 293.23/185.77 tff(20867,plain,
% 293.23/185.77 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | (~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_out(I0, I1, Y)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | (~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_out(I0, I1, Y))),
% 293.23/185.77 inference(quant_intro,[status(thm)],[20866])).
% 293.23/185.77 tff(20868,plain,
% 293.23/185.77 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | (~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_out(I0, I1, Y)) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | (~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_out(I0, I1, Y))),
% 293.23/185.77 inference(rewrite,[status(thm)],[])).
% 293.23/185.77 tff(20869,plain,
% 293.23/185.77 (^[Y: $i, I0: $i, X: $i, I1: $i] : trans(monotonicity(rewrite((m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_in1(I0, I1, X))) <=> ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_out(I0, I1, Y))), (((m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_in1(I0, I1, X))) | (~node14(I0, I1, X, Y))) <=> (((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_out(I0, I1, Y)) | (~node14(I0, I1, X, Y))))), rewrite((((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_out(I0, I1, Y)) | (~node14(I0, I1, X, Y))) <=> ((~node14(I0, I1, X, Y)) | (~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_out(I0, I1, Y))), (((m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_in1(I0, I1, X))) | (~node14(I0, I1, X, Y))) <=> ((~node14(I0, I1, X, Y)) | (~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_out(I0, I1, Y))))),
% 293.23/185.77 inference(bind,[status(th)],[])).
% 293.23/185.77 tff(20870,plain,
% 293.23/185.77 (![Y: $i, I0: $i, X: $i, I1: $i] : ((m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_in1(I0, I1, X))) | (~node14(I0, I1, X, Y))) <=> ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | (~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_out(I0, I1, Y))),
% 293.23/185.77 inference(quant_intro,[status(thm)],[20869])).
% 293.23/185.77 tff(20871,axiom,(![Y: $i, I0: $i, X: $i, I1: $i] : ((m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_in1(I0, I1, X))) | (~node14(I0, I1, X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_c_h_element_2')).
% 293.23/185.77 tff(20872,plain,
% 293.23/185.77 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | (~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_out(I0, I1, Y))),
% 293.23/185.77 inference(modus_ponens,[status(thm)],[20871, 20870])).
% 293.23/185.77 tff(20873,plain,
% 293.23/185.77 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | (~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_out(I0, I1, Y))),
% 293.23/185.77 inference(modus_ponens,[status(thm)],[20872, 20868])).
% 293.23/185.77 tff(20874,plain,(
% 293.23/185.77 ![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | (~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_out(I0, I1, Y))),
% 293.23/185.77 inference(skolemize,[status(sab)],[20873])).
% 293.23/185.77 tff(20875,plain,
% 293.23/185.77 (![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | (~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_out(I0, I1, Y))),
% 293.23/185.77 inference(modus_ponens,[status(thm)],[20874, 20867])).
% 293.23/185.77 tff(20876,plain,
% 293.23/185.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | (~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_out(I0, I1, Y))) | (m_c_h_element_v_out(c_e_h_3, c_h, s14) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s13)) | (~node14(c_e_h_3, c_h, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | (~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_out(I0, I1, Y))) | m_c_h_element_v_out(c_e_h_3, c_h, s14) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s13)) | (~node14(c_e_h_3, c_h, s13, s14)))),
% 293.23/185.77 inference(rewrite,[status(thm)],[])).
% 293.23/185.77 tff(20877,plain,
% 293.23/185.77 (((~node14(c_e_h_3, c_h, s13, s14)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s13)) | m_c_h_element_v_out(c_e_h_3, c_h, s14)) <=> (m_c_h_element_v_out(c_e_h_3, c_h, s14) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s13)) | (~node14(c_e_h_3, c_h, s13, s14)))),
% 293.23/185.77 inference(rewrite,[status(thm)],[])).
% 293.23/185.77 tff(20878,plain,
% 293.23/185.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | (~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_out(I0, I1, Y))) | ((~node14(c_e_h_3, c_h, s13, s14)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s13)) | m_c_h_element_v_out(c_e_h_3, c_h, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | (~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_out(I0, I1, Y))) | (m_c_h_element_v_out(c_e_h_3, c_h, s14) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s13)) | (~node14(c_e_h_3, c_h, s13, s14))))),
% 293.23/185.77 inference(monotonicity,[status(thm)],[20877])).
% 293.23/185.77 tff(20879,plain,
% 293.23/185.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | (~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_out(I0, I1, Y))) | ((~node14(c_e_h_3, c_h, s13, s14)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s13)) | m_c_h_element_v_out(c_e_h_3, c_h, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | (~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_out(I0, I1, Y))) | m_c_h_element_v_out(c_e_h_3, c_h, s14) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s13)) | (~node14(c_e_h_3, c_h, s13, s14)))),
% 293.23/185.77 inference(transitivity,[status(thm)],[20878, 20876])).
% 293.23/185.77 tff(20880,plain,
% 293.23/185.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | (~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_out(I0, I1, Y))) | ((~node14(c_e_h_3, c_h, s13, s14)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s13)) | m_c_h_element_v_out(c_e_h_3, c_h, s14))),
% 293.23/185.77 inference(quant_inst,[status(thm)],[])).
% 293.23/185.77 tff(20881,plain,
% 293.23/185.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | (~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_out(I0, I1, Y))) | m_c_h_element_v_out(c_e_h_3, c_h, s14) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s13)) | (~node14(c_e_h_3, c_h, s13, s14))),
% 293.23/185.77 inference(modus_ponens,[status(thm)],[20880, 20879])).
% 293.23/185.77 tff(20882,plain,
% 293.23/185.77 ($false),
% 293.23/185.77 inference(unit_resolution,[status(thm)],[20881, 20875, 20156, 20865, 20864])).
% 293.23/185.77 tff(20883,plain,((~node14(c_e_h_3, c_h, s13, s14)) | m_c_h_element_v_out(c_e_h_3, c_h, s14) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s13))), inference(lemma,lemma(discharge,[]))).
% 293.23/185.77 tff(20884,plain,
% 293.23/185.77 (~node14(c_e_h_3, c_h, s13, s14)),
% 293.23/185.77 inference(unit_resolution,[status(thm)],[20883, 20863, 20156])).
% 293.23/185.77 tff(20885,plain,
% 293.23/185.77 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s13)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s13)) | (~node16(c_e_h_3, c_h, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s13)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s13)) | (~node16(c_e_h_3, c_h, s13)))),
% 293.23/185.77 inference(rewrite,[status(thm)],[])).
% 293.23/185.77 tff(20886,plain,
% 293.23/185.77 (((~node16(c_e_h_3, c_h, s13)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s13)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s13))) <=> ((~m_c_h_element_v_in1(c_e_h_3, c_h, s13)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s13)) | (~node16(c_e_h_3, c_h, s13)))),
% 293.23/185.77 inference(rewrite,[status(thm)],[])).
% 293.23/185.77 tff(20887,plain,
% 293.23/185.77 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_h, s13)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s13)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s13)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s13)) | (~node16(c_e_h_3, c_h, s13))))),
% 293.23/185.77 inference(monotonicity,[status(thm)],[20886])).
% 293.23/185.77 tff(20888,plain,
% 293.23/185.77 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_h, s13)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s13)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s13)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s13)) | (~node16(c_e_h_3, c_h, s13)))),
% 293.23/185.77 inference(transitivity,[status(thm)],[20887, 20885])).
% 293.23/185.78 tff(20889,plain,
% 293.23/185.78 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_h, s13)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s13)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s13)))),
% 293.23/185.78 inference(quant_inst,[status(thm)],[])).
% 293.23/185.78 tff(20890,plain,
% 293.23/185.78 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s13)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s13)) | (~node16(c_e_h_3, c_h, s13))),
% 293.23/185.78 inference(modus_ponens,[status(thm)],[20889, 20888])).
% 293.23/185.78 tff(20891,plain,
% 293.23/185.78 ((~m_c_h_element_v_in1(c_e_h_3, c_h, s13)) | (~node16(c_e_h_3, c_h, s13))),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[20890, 2307, 20858])).
% 293.23/185.78 tff(20892,plain,
% 293.23/185.78 (~node16(c_e_h_3, c_h, s13)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[20891, 20863])).
% 293.23/185.78 tff(20893,plain,
% 293.23/185.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_3, c_h, s13, s14) | node14(c_e_h_3, c_h, s13, s14) | (~node19(c_e_h_3, c_h, s13, s14)) | node16(c_e_h_3, c_h, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_3, c_h, s13, s14) | node14(c_e_h_3, c_h, s13, s14) | (~node19(c_e_h_3, c_h, s13, s14)) | node16(c_e_h_3, c_h, s13))),
% 293.23/185.78 inference(rewrite,[status(thm)],[])).
% 293.23/185.78 tff(20894,plain,
% 293.23/185.78 ((node16(c_e_h_3, c_h, s13) | node14(c_e_h_3, c_h, s13, s14) | node15(c_e_h_3, c_h, s13, s14) | (~node19(c_e_h_3, c_h, s13, s14))) <=> (node15(c_e_h_3, c_h, s13, s14) | node14(c_e_h_3, c_h, s13, s14) | (~node19(c_e_h_3, c_h, s13, s14)) | node16(c_e_h_3, c_h, s13))),
% 293.23/185.78 inference(rewrite,[status(thm)],[])).
% 293.23/185.78 tff(20895,plain,
% 293.23/185.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s13) | node14(c_e_h_3, c_h, s13, s14) | node15(c_e_h_3, c_h, s13, s14) | (~node19(c_e_h_3, c_h, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_3, c_h, s13, s14) | node14(c_e_h_3, c_h, s13, s14) | (~node19(c_e_h_3, c_h, s13, s14)) | node16(c_e_h_3, c_h, s13)))),
% 293.23/185.78 inference(monotonicity,[status(thm)],[20894])).
% 293.23/185.78 tff(20896,plain,
% 293.23/185.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s13) | node14(c_e_h_3, c_h, s13, s14) | node15(c_e_h_3, c_h, s13, s14) | (~node19(c_e_h_3, c_h, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_3, c_h, s13, s14) | node14(c_e_h_3, c_h, s13, s14) | (~node19(c_e_h_3, c_h, s13, s14)) | node16(c_e_h_3, c_h, s13))),
% 293.23/185.78 inference(transitivity,[status(thm)],[20895, 20893])).
% 293.23/185.78 tff(20897,plain,
% 293.23/185.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s13) | node14(c_e_h_3, c_h, s13, s14) | node15(c_e_h_3, c_h, s13, s14) | (~node19(c_e_h_3, c_h, s13, s14)))),
% 293.23/185.78 inference(quant_inst,[status(thm)],[])).
% 293.23/185.78 tff(20898,plain,
% 293.23/185.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_3, c_h, s13, s14) | node14(c_e_h_3, c_h, s13, s14) | (~node19(c_e_h_3, c_h, s13, s14)) | node16(c_e_h_3, c_h, s13)),
% 293.23/185.78 inference(modus_ponens,[status(thm)],[20897, 20896])).
% 293.23/185.78 tff(20899,plain,
% 293.23/185.78 (node15(c_e_h_3, c_h, s13, s14) | node14(c_e_h_3, c_h, s13, s14) | node16(c_e_h_3, c_h, s13)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[20898, 204, 20849])).
% 293.23/185.78 tff(20900,plain,
% 293.23/185.78 ($false),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[20899, 20892, 20884, 20838])).
% 293.23/185.78 tff(20901,plain,(m_c_h_element_v_out(c_e_h_3, c_h, s14) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s13)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s13))), inference(lemma,lemma(discharge,[]))).
% 293.23/185.78 tff(20902,plain,
% 293.23/185.78 (~m_c_h_element_v_out(c_e_h_3, c_h, s13)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[20901, 20817, 20156])).
% 293.23/185.78 tff(20903,plain,
% 293.23/185.78 (~m_and_h_gate_v_out(c_e_h_3, c_c, s5)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[10330, 2513])).
% 293.23/185.78 tff(20904,plain,
% 293.23/185.78 (~m_and_h_gate_v_out(c_e_h_3, c_c, s4)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[6170, 20903])).
% 293.23/185.78 tff(20905,plain,
% 293.23/185.78 (~m_or_h_gate_v_out(c_e_h_3, c_g, s5)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[11076, 20904])).
% 293.23/185.78 tff(20906,plain,
% 293.23/185.78 (~m_and_h_gate_v_out(c_e_h_3, c_c, s3)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[2698, 10324])).
% 293.23/185.78 tff(20907,plain,
% 293.23/185.78 (~m_or_h_gate_v_in1(c_e_h_3, c_g, s3)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[2713, 20906])).
% 293.23/185.78 tff(20908,plain,
% 293.23/185.78 (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[3377, 20907])).
% 293.23/185.78 tff(20909,plain,
% 293.23/185.78 (~m_or_h_gate_v_out(c_e_h_3, c_g, s6)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[10319, 20908, 20903])).
% 293.23/185.78 tff(20910,plain,
% 293.23/185.78 (~m_or_h_gate_v_out(c_e_h_3, c_j, s8)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[5460, 10325])).
% 293.23/185.78 tff(20911,plain,
% 293.23/185.78 (~m_c_h_element_v_out(c_e_h_3, c_h, s8)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[7551, 20907])).
% 293.23/185.78 tff(20912,plain,
% 293.23/185.78 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s4)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[3384, 20908])).
% 293.23/185.78 tff(20913,plain,
% 293.23/185.78 (~node20(c_e_h_3, c_k, s4)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[3392, 20912])).
% 293.23/185.78 tff(20914,plain,
% 293.23/185.78 (~m_and_h_gate_v_out(c_e_h_3, c_l, s6)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[7633, 20913])).
% 293.23/185.78 tff(20915,plain,
% 293.23/185.78 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s5)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[3365, 20905])).
% 293.23/185.78 tff(20916,plain,
% 293.23/185.78 (~node20(c_e_h_3, c_k, s5)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[5458, 20915])).
% 293.23/185.78 tff(20917,plain,
% 293.23/185.78 (~m_and_h_gate_v_out(c_e_h_3, c_k, s5)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[7635, 20913])).
% 293.23/185.78 tff(20918,plain,
% 293.23/185.78 (~m_and_h_gate_v_out(c_e_h_3, c_k, s6)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[4467, 20917, 20916])).
% 293.23/185.78 tff(20919,plain,
% 293.23/185.78 (~m_and_h_gate_v_in1(c_e_h_3, c_l, s6)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[4475, 20918])).
% 293.23/185.78 tff(20920,plain,
% 293.23/185.78 (~node20(c_e_h_3, c_l, s6)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[4483, 20919])).
% 293.23/185.78 tff(20921,plain,
% 293.23/185.78 (~m_and_h_gate_v_out(c_e_h_3, c_l, s7)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[5441, 20920, 20914])).
% 293.23/185.78 tff(20922,plain,
% 293.23/185.78 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s6)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[10448, 2048, 20909])).
% 293.23/185.78 tff(20923,plain,
% 293.23/185.78 (~node20(c_e_h_3, c_k, s6)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[10444, 38, 20922])).
% 293.23/185.78 tff(20924,plain,
% 293.23/185.78 (~m_and_h_gate_v_out(c_e_h_3, c_k, s7)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[10440, 20923, 20918])).
% 293.23/185.78 tff(20925,plain,
% 293.23/185.78 (node20(c_e_h_3, c_k, s7)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[10982, 20924, 7626, 20921, 20911, 20910])).
% 293.23/185.78 tff(20926,plain,
% 293.23/185.78 (m_and_h_gate_v_in1(c_e_h_3, c_k, s7)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[10403, 20925])).
% 293.23/185.78 tff(20927,plain,
% 293.23/185.78 (m_or_h_gate_v_out(c_e_h_3, c_g, s7)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[10395, 20926])).
% 293.23/185.78 tff(20928,plain,
% 293.23/185.78 (m_and_h_gate_v_out(c_e_h_3, c_c, s7)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[10302, 20927, 20909, 20905, 20904])).
% 293.23/185.78 tff(20929,plain,
% 293.23/185.78 (~m_and_h_gate_v_in1(c_e_h_3, c_c, s7)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[20621, 20928, 20119])).
% 293.23/185.78 tff(20930,plain,
% 293.23/185.78 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s7)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[20580, 20929])).
% 293.23/185.78 tff(20931,plain,
% 293.23/185.78 ((~m_or_h_gate_v_out(c_e_h_3, c_g, s7)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s6) | m_or_h_gate_v_out(c_e_h_3, c_g, s6)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[10259, 10015])).
% 293.23/185.78 tff(20932,plain,
% 293.23/185.78 (m_or_h_gate_v_in1(c_e_h_3, c_g, s6)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[20931, 20927, 20909])).
% 293.23/185.78 tff(20933,plain,
% 293.23/185.78 (m_and_h_gate_v_out(c_e_h_3, c_c, s6)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[10231, 20932])).
% 293.23/185.78 tff(20934,plain,
% 293.23/185.78 (node20(c_e_h_3, c_c, s5)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[10180, 20933, 20903])).
% 293.23/185.78 tff(20935,plain,
% 293.23/185.78 (m_and_h_gate_v_in1(c_e_h_3, c_c, s5)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[20103, 20934])).
% 293.23/185.78 tff(20936,plain,
% 293.23/185.78 (m_mutex_h_half_v_out(c_e_h_3, c_a, s5)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[10191, 20935])).
% 293.23/185.78 tff(20937,plain,
% 293.23/185.78 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s4)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[10210, 20936, 2513])).
% 293.23/185.78 tff(20938,plain,
% 293.23/185.78 (m_user_v_req(c_e_h_3, c_u, s4)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[10214, 395, 20937])).
% 293.23/185.78 tff(20939,plain,
% 293.23/185.78 (m_user_v_req(c_e_h_3, c_u, s5)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[1035, 20938])).
% 293.23/185.78 tff(20940,plain,
% 293.23/185.78 (m_user_v_req(c_e_h_3, c_u, s6)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[1413, 20939])).
% 293.23/185.78 tff(20941,plain,
% 293.23/185.78 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s6)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[1431, 20940])).
% 293.23/185.78 tff(20942,plain,
% 293.23/185.78 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s5)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[1438, 20939])).
% 293.23/185.78 tff(20943,plain,
% 293.23/185.78 (m_mutex_h_half_v_out(c_e_h_3, c_a, s6)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[1515, 20942, 20936])).
% 293.23/185.78 tff(20944,plain,
% 293.23/185.78 ($false),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[1971, 20943, 20941, 20930])).
% 293.23/185.78 tff(20945,plain,(m_mutex_h_half_v_out(c_e_h_3, c_a, s4) | m_and_h_gate_v_out(c_e_h_3, c_c, s8) | (~m_c_h_element_v_out(c_e_h_3, c_h, s11))), inference(lemma,lemma(discharge,[]))).
% 293.23/185.78 tff(20946,plain,
% 293.23/185.78 (m_mutex_h_half_v_out(c_e_h_3, c_a, s4)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[20945, 7626, 20119])).
% 293.23/185.78 tff(20947,plain,
% 293.23/185.78 (m_user_v_req(c_e_h_3, c_u, s3)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[550, 20946])).
% 293.23/185.78 tff(20948,plain,
% 293.23/185.78 (m_user_v_req(c_e_h_3, c_u, s4)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[732, 20947])).
% 293.23/185.78 tff(20949,plain,
% 293.23/185.78 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s4)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[1445, 20948])).
% 293.23/185.78 tff(20950,plain,
% 293.23/185.78 (m_mutex_h_half_v_out(c_e_h_3, c_a, s5)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[1488, 20949, 20946])).
% 293.23/185.78 tff(20951,plain,
% 293.23/185.78 (m_and_h_gate_v_in1(c_e_h_3, c_c, s5)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[10341, 20950])).
% 293.23/185.78 tff(20952,plain,
% 293.23/185.78 (m_user_v_req(c_e_h_3, c_u, s5)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[1035, 20948])).
% 293.23/185.78 tff(20953,plain,
% 293.23/185.78 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s5)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[1438, 20952])).
% 293.23/185.78 tff(20954,plain,
% 293.23/185.78 (m_mutex_h_half_v_out(c_e_h_3, c_a, s6)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[1515, 20953, 20950])).
% 293.23/185.78 tff(20955,plain,
% 293.23/185.78 (m_and_h_gate_v_in1(c_e_h_3, c_c, s6)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[10298, 20954])).
% 293.23/185.78 tff(20956,plain,
% 293.23/185.78 (m_user_v_req(c_e_h_3, c_u, s6)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[1413, 20952])).
% 293.23/185.78 tff(20957,plain,
% 293.23/185.78 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s6)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[1431, 20956])).
% 293.23/185.78 tff(20958,plain,
% 293.23/185.78 (m_mutex_h_half_v_out(c_e_h_3, c_a, s7)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[1971, 20954, 20957])).
% 293.23/185.78 tff(20959,plain,
% 293.23/185.78 (m_and_h_gate_v_in1(c_e_h_3, c_c, s7)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[20580, 20958])).
% 293.23/185.78 tff(20960,plain,
% 293.23/185.78 (~m_and_h_gate_v_out(c_e_h_3, c_c, s7)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[20621, 20959, 20119])).
% 293.23/185.78 tff(20961,plain,
% 293.23/185.78 (~m_and_h_gate_v_out(c_e_h_3, c_c, s6)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[10938, 20960, 20955])).
% 293.23/185.78 tff(20962,plain,
% 293.23/185.78 (~m_and_h_gate_v_out(c_e_h_3, c_c, s5)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[10378, 20961, 20951])).
% 293.23/185.78 tff(20963,plain,
% 293.23/185.78 (~m_and_h_gate_v_out(c_e_h_3, c_c, s4)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[6170, 20962])).
% 293.23/185.78 tff(20964,plain,
% 293.23/185.78 (~m_and_h_gate_v_out(c_e_h_3, c_c, s3)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[11306, 20963])).
% 293.23/185.78 tff(20965,plain,
% 293.23/185.78 (~m_or_h_gate_v_in1(c_e_h_3, c_g, s3)),
% 293.23/185.78 inference(unit_resolution,[status(thm)],[2713, 20964])).
% 293.23/185.79 tff(20966,plain,
% 293.23/185.79 (~m_or_h_gate_v_out(c_e_h_3, c_g, s4)),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[3377, 20965])).
% 293.23/185.79 tff(20967,plain,
% 293.23/185.79 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s4)),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[3384, 20966])).
% 293.23/185.79 tff(20968,plain,
% 293.23/185.79 (~node20(c_e_h_3, c_k, s4)),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[3392, 20967])).
% 293.23/185.79 tff(20969,plain,
% 293.23/185.79 (~m_and_h_gate_v_out(c_e_h_3, c_l, s6)),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[7633, 20968])).
% 293.23/185.79 tff(20970,plain,
% 293.23/185.79 (~m_or_h_gate_v_out(c_e_h_3, c_g, s5)),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[11076, 20963])).
% 293.23/185.79 tff(20971,plain,
% 293.23/185.79 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s5)),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[3365, 20970])).
% 293.23/185.79 tff(20972,plain,
% 293.23/185.79 (~node20(c_e_h_3, c_k, s5)),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[5458, 20971])).
% 293.23/185.79 tff(20973,plain,
% 293.23/185.79 (~m_and_h_gate_v_out(c_e_h_3, c_k, s5)),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[7635, 20968])).
% 293.23/185.79 tff(20974,plain,
% 293.23/185.79 (~m_and_h_gate_v_out(c_e_h_3, c_k, s6)),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[4467, 20973, 20972])).
% 293.23/185.79 tff(20975,plain,
% 293.23/185.79 (~m_and_h_gate_v_in1(c_e_h_3, c_l, s6)),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[4475, 20974])).
% 293.23/185.79 tff(20976,plain,
% 293.23/185.79 (~node20(c_e_h_3, c_l, s6)),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[4483, 20975])).
% 293.23/185.79 tff(20977,plain,
% 293.23/185.79 (~m_or_h_gate_v_out(c_e_h_3, c_j, s8)),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[5885, 20963])).
% 293.23/185.79 tff(20978,plain,
% 293.23/185.79 (~m_or_h_gate_v_in1(c_e_h_3, c_g, s5)),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[10058, 20962])).
% 293.23/185.79 tff(20979,plain,
% 293.23/185.79 (~m_or_h_gate_v_out(c_e_h_3, c_g, s6)),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[20185, 20978, 20970])).
% 293.23/185.79 tff(20980,plain,
% 293.23/185.79 (~m_or_h_gate_v_out(c_e_h_3, c_g, s7)),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[10302, 20979, 20960, 20970, 20963])).
% 293.23/185.79 tff(20981,plain,
% 293.23/185.79 (~m_c_h_element_v_in1(c_e_h_3, c_h, s7)),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[11270, 20980])).
% 293.23/185.79 tff(20982,plain,
% 293.23/185.79 (~m_c_h_element_v_out(c_e_h_3, c_h, s8)),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[11263, 20981])).
% 293.23/185.79 tff(20983,plain,
% 293.23/185.79 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s7)),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[10395, 20980])).
% 293.23/185.79 tff(20984,plain,
% 293.23/185.79 (~node20(c_e_h_3, c_k, s7)),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[10403, 20983])).
% 293.23/185.79 tff(20985,plain,
% 293.23/185.79 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s6)),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[10448, 2048, 20979])).
% 293.23/185.79 tff(20986,plain,
% 293.23/185.79 (~node20(c_e_h_3, c_k, s6)),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[10444, 38, 20985])).
% 293.23/185.79 tff(20987,plain,
% 293.23/185.79 (~m_and_h_gate_v_out(c_e_h_3, c_k, s7)),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[10440, 20974, 20986])).
% 293.23/185.79 tff(20988,plain,
% 293.23/185.79 (m_and_h_gate_v_out(c_e_h_3, c_l, s7)),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[10982, 20987, 7626, 20984, 20982, 20977])).
% 293.23/185.79 tff(20989,plain,
% 293.23/185.79 ($false),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[5441, 20988, 20976, 20969])).
% 293.23/185.79 tff(20990,plain,((~m_c_h_element_v_out(c_e_h_3, c_h, s11)) | m_and_h_gate_v_out(c_e_h_3, c_c, s8)), inference(lemma,lemma(discharge,[]))).
% 293.23/185.79 tff(20991,plain,
% 293.23/185.79 (m_and_h_gate_v_out(c_e_h_3, c_c, s8)),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[20990, 7626])).
% 293.23/185.79 tff(20992,plain,
% 293.23/185.79 (m_and_h_gate_v_out(c_e_h_3, c_c, s9)),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[20471, 20991])).
% 293.23/185.79 tff(20993,plain,
% 293.23/185.79 (~m_or_h_gate_v_out(c_e_h_3, c_g, s9)),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[20563, 20172, 20534])).
% 293.23/185.79 tff(20994,assumption,(m_c_h_element_v_in1(c_e_h_3, c_h, s10)), introduced(assumption)).
% 293.23/185.79 tff(20995,plain,
% 293.23/185.79 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s10)) | m_or_h_gate_v_out(c_e_h_3, c_g, s10))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s10)) | m_or_h_gate_v_out(c_e_h_3, c_g, s10))),
% 293.23/185.79 inference(rewrite,[status(thm)],[])).
% 293.23/185.79 tff(20996,plain,
% 293.23/185.79 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s10)) | m_or_h_gate_v_out(c_e_h_3, c_g, s10))),
% 293.23/185.79 inference(quant_inst,[status(thm)],[])).
% 293.23/185.79 tff(20997,plain,
% 293.23/185.79 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s10)) | m_or_h_gate_v_out(c_e_h_3, c_g, s10)),
% 293.23/185.79 inference(modus_ponens,[status(thm)],[20996, 20995])).
% 293.23/185.79 tff(20998,plain,
% 293.23/185.79 ($false),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[20997, 811, 20172, 20994])).
% 293.23/185.79 tff(20999,plain,((~m_c_h_element_v_in1(c_e_h_3, c_h, s10)) | m_or_h_gate_v_out(c_e_h_3, c_g, s10)), inference(lemma,lemma(discharge,[]))).
% 293.23/185.79 tff(21000,plain,
% 293.23/185.79 (~m_c_h_element_v_in1(c_e_h_3, c_h, s10)),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[20999, 20172])).
% 293.23/185.79 tff(21001,plain,
% 293.23/185.79 (m_c_h_element_v_out(c_e_h_3, c_h, s10)),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[7795, 21000, 7626])).
% 293.23/185.79 tff(21002,plain,
% 293.23/185.79 (~m_or_h_gate_v_out(c_e_h_3, c_g, s8)),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[20525, 20993, 20505])).
% 293.23/185.79 tff(21003,assumption,(m_c_h_element_v_in1(c_e_h_3, c_h, s9)), introduced(assumption)).
% 293.23/185.79 tff(21004,plain,
% 293.23/185.79 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s9)) | m_or_h_gate_v_out(c_e_h_3, c_g, s9))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s9)) | m_or_h_gate_v_out(c_e_h_3, c_g, s9))),
% 293.23/185.79 inference(rewrite,[status(thm)],[])).
% 293.23/185.79 tff(21005,plain,
% 293.23/185.79 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s9)) | m_or_h_gate_v_out(c_e_h_3, c_g, s9))),
% 293.23/185.79 inference(quant_inst,[status(thm)],[])).
% 293.23/185.79 tff(21006,plain,
% 293.23/185.79 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s9)) | m_or_h_gate_v_out(c_e_h_3, c_g, s9)),
% 293.23/185.79 inference(modus_ponens,[status(thm)],[21005, 21004])).
% 293.23/185.79 tff(21007,plain,
% 293.23/185.79 ($false),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[21006, 811, 20257, 21003])).
% 293.23/185.79 tff(21008,plain,(m_or_h_gate_v_out(c_e_h_3, c_g, s9) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s9))), inference(lemma,lemma(discharge,[]))).
% 293.23/185.79 tff(21009,plain,
% 293.23/185.79 (~m_c_h_element_v_in1(c_e_h_3, c_h, s9)),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[21008, 20257])).
% 293.23/185.79 tff(21010,plain,
% 293.23/185.79 (m_c_h_element_v_in2(c_e_h_3, c_h, s9)),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[7721, 7649, 7655])).
% 293.23/185.79 tff(21011,plain,
% 293.23/185.79 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_h, s9)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s9)) | m_c_h_element_v_in1(c_e_h_3, c_h, s9))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_h, s9)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s9)) | m_c_h_element_v_in1(c_e_h_3, c_h, s9))),
% 293.23/185.79 inference(rewrite,[status(thm)],[])).
% 293.23/185.79 tff(21012,plain,
% 293.23/185.79 ((m_c_h_element_v_in1(c_e_h_3, c_h, s9) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s9)) | (~node17(c_e_h_3, c_h, s9))) <=> ((~node17(c_e_h_3, c_h, s9)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s9)) | m_c_h_element_v_in1(c_e_h_3, c_h, s9))),
% 293.23/185.79 inference(rewrite,[status(thm)],[])).
% 293.23/185.79 tff(21013,plain,
% 293.23/185.79 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s9) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s9)) | (~node17(c_e_h_3, c_h, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_3, c_h, s9)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s9)) | m_c_h_element_v_in1(c_e_h_3, c_h, s9)))),
% 293.23/185.79 inference(monotonicity,[status(thm)],[21012])).
% 293.23/185.79 tff(21014,plain,
% 293.23/185.79 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s9) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s9)) | (~node17(c_e_h_3, c_h, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_h, s9)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s9)) | m_c_h_element_v_in1(c_e_h_3, c_h, s9))),
% 293.23/185.79 inference(transitivity,[status(thm)],[21013, 21011])).
% 293.23/185.79 tff(21015,plain,
% 293.23/185.79 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s9) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s9)) | (~node17(c_e_h_3, c_h, s9)))),
% 293.23/185.79 inference(quant_inst,[status(thm)],[])).
% 293.23/185.79 tff(21016,plain,
% 293.23/185.79 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_3, c_h, s9)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s9)) | m_c_h_element_v_in1(c_e_h_3, c_h, s9)),
% 293.23/185.79 inference(modus_ponens,[status(thm)],[21015, 21014])).
% 293.23/185.79 tff(21017,plain,
% 293.23/185.79 ((~node17(c_e_h_3, c_h, s9)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s9))),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[21016, 859, 7664])).
% 293.23/185.79 tff(21018,plain,
% 293.23/185.79 (~node17(c_e_h_3, c_h, s9)),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[21017, 21010])).
% 293.23/185.79 tff(21019,plain,
% 293.23/185.79 (node18(c_e_h_3, c_h, s9, s10)),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[7712, 21018])).
% 293.23/185.79 tff(21020,plain,
% 293.23/185.79 ($false),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[7719, 753, 7655, 7649, 21019])).
% 293.23/185.79 tff(21021,plain,(m_c_h_element_v_out(c_e_h_3, c_h, s9) | (~m_c_h_element_v_out(c_e_h_3, c_h, s10)) | m_c_h_element_v_in1(c_e_h_3, c_h, s9)), inference(lemma,lemma(discharge,[]))).
% 293.23/185.79 tff(21022,plain,
% 293.23/185.79 (m_c_h_element_v_out(c_e_h_3, c_h, s9)),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[21021, 21009, 7655])).
% 293.23/185.79 tff(21023,assumption,(m_c_h_element_v_in1(c_e_h_3, c_h, s8)), introduced(assumption)).
% 293.23/185.79 tff(21024,plain,
% 293.23/185.79 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s8)) | m_or_h_gate_v_out(c_e_h_3, c_g, s8))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s8)) | m_or_h_gate_v_out(c_e_h_3, c_g, s8))),
% 293.23/185.79 inference(rewrite,[status(thm)],[])).
% 293.23/185.79 tff(21025,plain,
% 293.23/185.79 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s8)) | m_or_h_gate_v_out(c_e_h_3, c_g, s8))),
% 293.23/185.79 inference(quant_inst,[status(thm)],[])).
% 293.23/185.79 tff(21026,plain,
% 293.23/185.79 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s8)) | m_or_h_gate_v_out(c_e_h_3, c_g, s8)),
% 293.23/185.79 inference(modus_ponens,[status(thm)],[21025, 21024])).
% 293.23/185.79 tff(21027,plain,
% 293.23/185.79 ($false),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[21026, 811, 9500, 21023])).
% 293.23/185.79 tff(21028,plain,((~m_c_h_element_v_in1(c_e_h_3, c_h, s8)) | m_or_h_gate_v_out(c_e_h_3, c_g, s8)), inference(lemma,lemma(discharge,[]))).
% 293.23/185.79 tff(21029,plain,
% 293.23/185.79 (~m_c_h_element_v_in1(c_e_h_3, c_h, s8)),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[21028, 20526])).
% 293.23/185.79 tff(21030,plain,
% 293.23/185.79 (m_c_h_element_v_in2(c_e_h_3, c_h, s8)),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[7358, 7305, 7300])).
% 293.23/185.79 tff(21031,plain,
% 293.23/185.79 (~node18(c_e_h_3, c_h, s8, s9)),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[7318, 7305, 7300])).
% 293.23/185.79 tff(21032,plain,
% 293.23/185.79 (node17(c_e_h_3, c_h, s8)),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[7330, 21031])).
% 293.23/185.79 tff(21033,plain,
% 293.23/185.79 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s8)) | (~node17(c_e_h_3, c_h, s8)) | m_c_h_element_v_in1(c_e_h_3, c_h, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s8)) | (~node17(c_e_h_3, c_h, s8)) | m_c_h_element_v_in1(c_e_h_3, c_h, s8))),
% 293.23/185.79 inference(rewrite,[status(thm)],[])).
% 293.23/185.79 tff(21034,plain,
% 293.23/185.79 ((m_c_h_element_v_in1(c_e_h_3, c_h, s8) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s8)) | (~node17(c_e_h_3, c_h, s8))) <=> ((~m_c_h_element_v_in2(c_e_h_3, c_h, s8)) | (~node17(c_e_h_3, c_h, s8)) | m_c_h_element_v_in1(c_e_h_3, c_h, s8))),
% 293.23/185.79 inference(rewrite,[status(thm)],[])).
% 293.23/185.79 tff(21035,plain,
% 293.23/185.79 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s8) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s8)) | (~node17(c_e_h_3, c_h, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s8)) | (~node17(c_e_h_3, c_h, s8)) | m_c_h_element_v_in1(c_e_h_3, c_h, s8)))),
% 293.23/185.79 inference(monotonicity,[status(thm)],[21034])).
% 293.23/185.79 tff(21036,plain,
% 293.23/185.79 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s8) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s8)) | (~node17(c_e_h_3, c_h, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s8)) | (~node17(c_e_h_3, c_h, s8)) | m_c_h_element_v_in1(c_e_h_3, c_h, s8))),
% 293.23/185.79 inference(transitivity,[status(thm)],[21035, 21033])).
% 293.23/185.79 tff(21037,plain,
% 293.23/185.79 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s8) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s8)) | (~node17(c_e_h_3, c_h, s8)))),
% 293.23/185.79 inference(quant_inst,[status(thm)],[])).
% 293.23/185.79 tff(21038,plain,
% 293.23/185.79 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s8)) | (~node17(c_e_h_3, c_h, s8)) | m_c_h_element_v_in1(c_e_h_3, c_h, s8)),
% 293.23/185.79 inference(modus_ponens,[status(thm)],[21037, 21036])).
% 293.23/185.79 tff(21039,plain,
% 293.23/185.79 ((~m_c_h_element_v_in2(c_e_h_3, c_h, s8)) | (~node17(c_e_h_3, c_h, s8))),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[21038, 859, 11162])).
% 293.23/185.79 tff(21040,plain,
% 293.23/185.79 ($false),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[21039, 21032, 21030])).
% 293.23/185.79 tff(21041,plain,(m_c_h_element_v_out(c_e_h_3, c_h, s8) | m_c_h_element_v_in1(c_e_h_3, c_h, s8) | (~m_c_h_element_v_out(c_e_h_3, c_h, s9))), inference(lemma,lemma(discharge,[]))).
% 293.23/185.79 tff(21042,plain,
% 293.23/185.79 ($false),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[21041, 21029, 21022, 7305])).
% 293.23/185.79 tff(21043,plain,(m_or_h_gate_v_out(c_e_h_3, c_g, s9) | m_c_h_element_v_out(c_e_h_3, c_h, s8) | (~m_c_h_element_v_out(c_e_h_3, c_h, s10)) | node4(c_e_h_3, c_g, s8)), inference(lemma,lemma(discharge,[]))).
% 293.23/185.79 tff(21044,plain,
% 293.23/185.79 (m_c_h_element_v_out(c_e_h_3, c_h, s8)),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[21043, 7655, 20257, 20505])).
% 293.23/185.79 tff(21045,plain,
% 293.23/185.79 (m_c_h_element_v_in1(c_e_h_3, c_h, s7)),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[11263, 21044])).
% 293.23/185.79 tff(21046,plain,
% 293.23/185.79 (m_or_h_gate_v_out(c_e_h_3, c_g, s7)),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[11270, 21045])).
% 293.23/185.79 tff(21047,plain,
% 293.23/185.79 (node4(c_e_h_3, c_g, s7)),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[9528, 21046, 9500])).
% 293.23/185.79 tff(21048,plain,
% 293.23/185.79 (~m_or_h_gate_v_in1(c_e_h_3, c_g, s7)),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[11280, 21047])).
% 293.23/185.79 tff(21049,plain,
% 293.23/185.79 (~m_and_h_gate_v_out(c_e_h_3, c_c, s7)),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[11157, 21048])).
% 293.23/185.79 tff(21050,plain,
% 293.23/185.79 (m_c_h_element_v_out(c_e_h_3, c_h, s9)),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[21021, 7655, 21009])).
% 293.23/185.79 tff(21051,plain,
% 293.23/185.79 (m_or_h_gate_v_out(c_e_h_3, c_j, s8)),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[7624, 21050])).
% 293.23/185.79 tff(21052,plain,
% 293.23/185.79 (m_and_h_gate_v_out(c_e_h_3, c_c, s4)),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[5885, 21051])).
% 293.23/185.79 tff(21053,plain,
% 293.23/185.79 (m_and_h_gate_v_out(c_e_h_3, c_c, s5)),
% 293.23/185.79 inference(unit_resolution,[status(thm)],[6170, 21052])).
% 293.23/185.79 tff(21054,plain,
% 293.23/185.79 (m_and_h_gate_v_in1(c_e_h_3, c_c, s3)),
% 293.23/185.80 inference(unit_resolution,[status(thm)],[5460, 21051])).
% 293.23/185.80 tff(21055,plain,
% 293.23/185.80 (m_mutex_h_half_v_out(c_e_h_3, c_a, s3)),
% 293.23/185.80 inference(unit_resolution,[status(thm)],[2544, 21054])).
% 293.23/185.80 tff(21056,plain,
% 293.23/185.80 (m_mutex_h_half_v_out(c_e_h_3, c_a, s4)),
% 293.23/185.80 inference(unit_resolution,[status(thm)],[2537, 21055])).
% 293.23/185.80 tff(21057,plain,
% 293.23/185.80 (m_user_v_req(c_e_h_3, c_u, s2)),
% 293.23/185.80 inference(unit_resolution,[status(thm)],[514, 21055])).
% 293.23/185.80 tff(21058,plain,
% 293.23/185.80 (m_user_v_req(c_e_h_3, c_u, s3)),
% 293.23/185.80 inference(unit_resolution,[status(thm)],[335, 21057])).
% 293.23/185.80 tff(21059,plain,
% 293.23/185.80 (m_user_v_req(c_e_h_3, c_u, s4)),
% 293.23/185.80 inference(unit_resolution,[status(thm)],[732, 21058])).
% 293.23/185.80 tff(21060,plain,
% 293.23/185.80 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s4)),
% 293.23/185.80 inference(unit_resolution,[status(thm)],[1445, 21059])).
% 293.23/185.80 tff(21061,plain,
% 293.23/185.80 (m_mutex_h_half_v_out(c_e_h_3, c_a, s5)),
% 293.23/185.80 inference(unit_resolution,[status(thm)],[1488, 21060, 21056])).
% 293.23/185.80 tff(21062,plain,
% 293.23/185.80 (m_and_h_gate_v_in1(c_e_h_3, c_c, s5)),
% 293.23/185.80 inference(unit_resolution,[status(thm)],[10341, 21061])).
% 293.23/185.80 tff(21063,plain,
% 293.23/185.80 (m_and_h_gate_v_out(c_e_h_3, c_c, s6)),
% 293.23/185.80 inference(unit_resolution,[status(thm)],[10378, 21062, 21053])).
% 293.23/185.80 tff(21064,plain,
% 293.23/185.80 (m_user_v_req(c_e_h_3, c_u, s5)),
% 293.23/185.80 inference(unit_resolution,[status(thm)],[1035, 21059])).
% 293.23/185.80 tff(21065,plain,
% 293.23/185.80 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s5)),
% 293.23/185.80 inference(unit_resolution,[status(thm)],[1438, 21064])).
% 293.23/185.80 tff(21066,plain,
% 293.23/185.80 (m_mutex_h_half_v_out(c_e_h_3, c_a, s6)),
% 293.23/185.80 inference(unit_resolution,[status(thm)],[1515, 21061, 21065])).
% 293.23/185.80 tff(21067,plain,
% 293.23/185.80 (m_and_h_gate_v_in1(c_e_h_3, c_c, s6)),
% 293.23/185.80 inference(unit_resolution,[status(thm)],[10298, 21066])).
% 293.23/185.80 tff(21068,plain,
% 293.23/185.80 ($false),
% 293.23/185.80 inference(unit_resolution,[status(thm)],[10938, 21067, 21063, 21049])).
% 293.23/185.80 tff(21069,plain,((~m_c_h_element_v_out(c_e_h_3, c_h, s10)) | m_or_h_gate_v_out(c_e_h_3, c_g, s8) | m_or_h_gate_v_out(c_e_h_3, c_g, s9) | node4(c_e_h_3, c_g, s8)), inference(lemma,lemma(discharge,[]))).
% 293.23/185.80 tff(21070,plain,
% 293.23/185.80 ($false),
% 293.23/185.80 inference(unit_resolution,[status(thm)],[21069, 21002, 21001, 20505, 20993])).
% 293.23/185.80 tff(21071,plain,(m_or_h_gate_v_out(c_e_h_3, c_g, s10) | node4(c_e_h_3, c_g, s8) | (~m_c_h_element_v_out(c_e_h_3, c_h, s11)) | node4(c_e_h_3, c_g, s9)), inference(lemma,lemma(discharge,[]))).
% 293.23/185.80 tff(21072,plain,
% 293.23/185.80 (node4(c_e_h_3, c_g, s9)),
% 293.23/185.80 inference(unit_resolution,[status(thm)],[21071, 7626, 20505, 20172])).
% 293.23/185.80 tff(21073,plain,
% 293.23/185.80 (~m_or_h_gate_v_in1(c_e_h_3, c_g, s9)),
% 293.23/185.80 inference(unit_resolution,[status(thm)],[20571, 21072])).
% 293.23/185.80 tff(21074,plain,
% 293.23/185.80 ($false),
% 293.23/185.80 inference(unit_resolution,[status(thm)],[20479, 21073, 20992])).
% 293.23/185.80 tff(21075,plain,((~m_c_h_element_v_out(c_e_h_3, c_h, s11)) | node4(c_e_h_3, c_g, s8) | m_or_h_gate_v_out(c_e_h_3, c_g, s10)), inference(lemma,lemma(discharge,[]))).
% 293.23/185.80 tff(21076,plain,
% 293.23/185.80 (node4(c_e_h_3, c_g, s8)),
% 293.23/185.80 inference(unit_resolution,[status(thm)],[21075, 7626, 20172])).
% 293.23/185.80 tff(21077,plain,
% 293.23/185.80 (m_or_h_gate_v_in1(c_e_h_3, c_g, s8)),
% 293.23/185.80 inference(unit_resolution,[status(thm)],[20638, 20991])).
% 293.23/185.80 tff(21078,plain,
% 293.23/185.80 ($false),
% 293.23/185.80 inference(unit_resolution,[status(thm)],[20502, 21077, 21076])).
% 293.23/185.80 tff(21079,plain,((~m_c_h_element_v_out(c_e_h_3, c_h, s11)) | m_or_h_gate_v_out(c_e_h_3, c_g, s10)), inference(lemma,lemma(discharge,[]))).
% 293.23/185.80 tff(21080,plain,
% 293.23/185.80 (~m_c_h_element_v_out(c_e_h_3, c_h, s11)),
% 293.23/185.80 inference(unit_resolution,[status(thm)],[21079, 20172])).
% 293.23/185.80 tff(21081,assumption,(m_c_h_element_v_out(c_e_h_3, c_h, s12)), introduced(assumption)).
% 293.23/185.80 tff(21082,assumption,(~m_c_h_element_v_out(c_e_h_3, c_h, s11)), introduced(assumption)).
% 293.23/185.80 tff(21083,assumption,(node18(c_e_h_3, c_h, s11, s12)), introduced(assumption)).
% 293.23/185.80 tff(21084,plain,
% 293.23/185.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_h, s11) | (~m_c_h_element_v_out(c_e_h_3, c_h, s12)) | (~node18(c_e_h_3, c_h, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s11) | (~m_c_h_element_v_out(c_e_h_3, c_h, s12)) | (~node18(c_e_h_3, c_h, s11, s12)))),
% 293.23/185.80 inference(rewrite,[status(thm)],[])).
% 293.23/185.80 tff(21085,plain,
% 293.23/185.80 (((~m_c_h_element_v_out(c_e_h_3, c_h, s12)) | m_c_h_element_v_out(c_e_h_3, c_h, s11) | (~node18(c_e_h_3, c_h, s11, s12))) <=> (m_c_h_element_v_out(c_e_h_3, c_h, s11) | (~m_c_h_element_v_out(c_e_h_3, c_h, s12)) | (~node18(c_e_h_3, c_h, s11, s12)))),
% 293.23/185.80 inference(rewrite,[status(thm)],[])).
% 293.23/185.80 tff(21086,plain,
% 293.23/185.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s12)) | m_c_h_element_v_out(c_e_h_3, c_h, s11) | (~node18(c_e_h_3, c_h, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_h, s11) | (~m_c_h_element_v_out(c_e_h_3, c_h, s12)) | (~node18(c_e_h_3, c_h, s11, s12))))),
% 293.23/185.80 inference(monotonicity,[status(thm)],[21085])).
% 293.23/185.80 tff(21087,plain,
% 293.23/185.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s12)) | m_c_h_element_v_out(c_e_h_3, c_h, s11) | (~node18(c_e_h_3, c_h, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s11) | (~m_c_h_element_v_out(c_e_h_3, c_h, s12)) | (~node18(c_e_h_3, c_h, s11, s12)))),
% 293.23/185.80 inference(transitivity,[status(thm)],[21086, 21084])).
% 293.23/185.80 tff(21088,plain,
% 293.23/185.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s12)) | m_c_h_element_v_out(c_e_h_3, c_h, s11) | (~node18(c_e_h_3, c_h, s11, s12)))),
% 293.23/185.80 inference(quant_inst,[status(thm)],[])).
% 293.23/185.80 tff(21089,plain,
% 293.23/185.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s11) | (~m_c_h_element_v_out(c_e_h_3, c_h, s12)) | (~node18(c_e_h_3, c_h, s11, s12))),
% 293.23/185.80 inference(modus_ponens,[status(thm)],[21088, 21087])).
% 293.23/185.80 tff(21090,plain,
% 293.23/185.80 ($false),
% 293.23/185.80 inference(unit_resolution,[status(thm)],[21089, 753, 21082, 21081, 21083])).
% 293.23/185.80 tff(21091,plain,((~node18(c_e_h_3, c_h, s11, s12)) | m_c_h_element_v_out(c_e_h_3, c_h, s11) | (~m_c_h_element_v_out(c_e_h_3, c_h, s12))), inference(lemma,lemma(discharge,[]))).
% 293.23/185.80 tff(21092,plain,
% 293.23/185.80 (~node18(c_e_h_3, c_h, s11, s12)),
% 293.23/185.80 inference(unit_resolution,[status(thm)],[21091, 21082, 21081])).
% 293.23/185.80 tff(21093,plain,
% 293.23/185.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s11, s12)) | node19(c_e_h_3, c_h, s11, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s11, s12)) | node19(c_e_h_3, c_h, s11, s12))),
% 293.23/185.80 inference(rewrite,[status(thm)],[])).
% 293.23/185.80 tff(21094,plain,
% 293.23/185.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s11, s12)) | node19(c_e_h_3, c_h, s11, s12))),
% 293.23/185.80 inference(quant_inst,[status(thm)],[])).
% 293.23/185.80 tff(21095,plain,
% 293.23/185.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s11, s12)) | node19(c_e_h_3, c_h, s11, s12)),
% 293.23/185.80 inference(modus_ponens,[status(thm)],[21094, 21093])).
% 293.23/185.80 tff(21096,plain,
% 293.23/185.80 (node19(c_e_h_3, c_h, s11, s12)),
% 293.23/185.80 inference(unit_resolution,[status(thm)],[21095, 190, 11461])).
% 293.23/185.80 tff(21097,plain,
% 293.23/185.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_3, c_h, s11, s12) | node17(c_e_h_3, c_h, s11) | (~node19(c_e_h_3, c_h, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_3, c_h, s11, s12) | node17(c_e_h_3, c_h, s11) | (~node19(c_e_h_3, c_h, s11, s12)))),
% 293.23/185.80 inference(rewrite,[status(thm)],[])).
% 293.23/185.81 tff(21098,plain,
% 293.23/185.81 ((node17(c_e_h_3, c_h, s11) | node18(c_e_h_3, c_h, s11, s12) | (~node19(c_e_h_3, c_h, s11, s12))) <=> (node18(c_e_h_3, c_h, s11, s12) | node17(c_e_h_3, c_h, s11) | (~node19(c_e_h_3, c_h, s11, s12)))),
% 293.23/185.81 inference(rewrite,[status(thm)],[])).
% 293.23/185.81 tff(21099,plain,
% 293.23/185.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s11) | node18(c_e_h_3, c_h, s11, s12) | (~node19(c_e_h_3, c_h, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_3, c_h, s11, s12) | node17(c_e_h_3, c_h, s11) | (~node19(c_e_h_3, c_h, s11, s12))))),
% 293.23/185.81 inference(monotonicity,[status(thm)],[21098])).
% 293.23/185.81 tff(21100,plain,
% 293.23/185.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s11) | node18(c_e_h_3, c_h, s11, s12) | (~node19(c_e_h_3, c_h, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_3, c_h, s11, s12) | node17(c_e_h_3, c_h, s11) | (~node19(c_e_h_3, c_h, s11, s12)))),
% 293.23/185.81 inference(transitivity,[status(thm)],[21099, 21097])).
% 293.23/185.81 tff(21101,plain,
% 293.23/185.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s11) | node18(c_e_h_3, c_h, s11, s12) | (~node19(c_e_h_3, c_h, s11, s12)))),
% 293.23/185.81 inference(quant_inst,[status(thm)],[])).
% 293.23/185.81 tff(21102,plain,
% 293.23/185.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_3, c_h, s11, s12) | node17(c_e_h_3, c_h, s11) | (~node19(c_e_h_3, c_h, s11, s12))),
% 293.23/185.81 inference(modus_ponens,[status(thm)],[21101, 21100])).
% 293.23/185.81 tff(21103,plain,
% 293.23/185.81 (node18(c_e_h_3, c_h, s11, s12) | node17(c_e_h_3, c_h, s11)),
% 293.23/185.81 inference(unit_resolution,[status(thm)],[21102, 776, 21096])).
% 293.23/185.81 tff(21104,plain,
% 293.23/185.81 (node17(c_e_h_3, c_h, s11)),
% 293.23/185.81 inference(unit_resolution,[status(thm)],[21103, 21092])).
% 293.23/185.81 tff(21105,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_h, s11)), introduced(assumption)).
% 293.23/185.81 tff(21106,assumption,(node14(c_e_h_3, c_h, s11, s12)), introduced(assumption)).
% 293.23/185.81 tff(21107,plain,
% 293.23/185.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s11) | (~m_c_h_element_v_out(c_e_h_3, c_h, s12)) | (~node14(c_e_h_3, c_h, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_h, s11) | (~m_c_h_element_v_out(c_e_h_3, c_h, s12)) | (~node14(c_e_h_3, c_h, s11, s12)))),
% 293.23/185.81 inference(rewrite,[status(thm)],[])).
% 293.23/185.81 tff(21108,plain,
% 293.23/185.81 (((~node14(c_e_h_3, c_h, s11, s12)) | m_c_h_element_v_in1(c_e_h_3, c_h, s11) | (~m_c_h_element_v_out(c_e_h_3, c_h, s12))) <=> (m_c_h_element_v_in1(c_e_h_3, c_h, s11) | (~m_c_h_element_v_out(c_e_h_3, c_h, s12)) | (~node14(c_e_h_3, c_h, s11, s12)))),
% 293.23/185.81 inference(rewrite,[status(thm)],[])).
% 293.23/185.81 tff(21109,plain,
% 293.23/185.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s11, s12)) | m_c_h_element_v_in1(c_e_h_3, c_h, s11) | (~m_c_h_element_v_out(c_e_h_3, c_h, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s11) | (~m_c_h_element_v_out(c_e_h_3, c_h, s12)) | (~node14(c_e_h_3, c_h, s11, s12))))),
% 293.23/185.81 inference(monotonicity,[status(thm)],[21108])).
% 293.23/185.81 tff(21110,plain,
% 293.23/185.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s11, s12)) | m_c_h_element_v_in1(c_e_h_3, c_h, s11) | (~m_c_h_element_v_out(c_e_h_3, c_h, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_h, s11) | (~m_c_h_element_v_out(c_e_h_3, c_h, s12)) | (~node14(c_e_h_3, c_h, s11, s12)))),
% 293.23/185.81 inference(transitivity,[status(thm)],[21109, 21107])).
% 293.23/185.81 tff(21111,plain,
% 293.23/185.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s11, s12)) | m_c_h_element_v_in1(c_e_h_3, c_h, s11) | (~m_c_h_element_v_out(c_e_h_3, c_h, s12)))),
% 293.23/185.81 inference(quant_inst,[status(thm)],[])).
% 293.23/185.81 tff(21112,plain,
% 293.23/185.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_h, s11) | (~m_c_h_element_v_out(c_e_h_3, c_h, s12)) | (~node14(c_e_h_3, c_h, s11, s12))),
% 293.23/185.81 inference(modus_ponens,[status(thm)],[21111, 21110])).
% 293.23/185.81 tff(21113,plain,
% 293.23/185.81 ($false),
% 293.23/185.81 inference(unit_resolution,[status(thm)],[21112, 223, 21081, 21106, 21105])).
% 293.23/185.81 tff(21114,plain,((~node14(c_e_h_3, c_h, s11, s12)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s12)) | m_c_h_element_v_in1(c_e_h_3, c_h, s11)), inference(lemma,lemma(discharge,[]))).
% 293.23/185.81 tff(21115,plain,
% 293.23/185.81 (~node14(c_e_h_3, c_h, s11, s12)),
% 293.23/185.81 inference(unit_resolution,[status(thm)],[21114, 21105, 21081])).
% 293.23/185.81 tff(21116,assumption,(node15(c_e_h_3, c_h, s11, s12)), introduced(assumption)).
% 293.23/185.81 tff(21117,plain,
% 293.23/185.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s12)) | (~node15(c_e_h_3, c_h, s11, s12)) | m_c_h_element_v_out(c_e_h_3, c_h, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s12)) | (~node15(c_e_h_3, c_h, s11, s12)) | m_c_h_element_v_out(c_e_h_3, c_h, s11))),
% 293.23/185.81 inference(rewrite,[status(thm)],[])).
% 293.23/185.81 tff(21118,plain,
% 293.23/185.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s12)) | (~node15(c_e_h_3, c_h, s11, s12)) | m_c_h_element_v_out(c_e_h_3, c_h, s11))),
% 293.23/185.81 inference(quant_inst,[status(thm)],[])).
% 293.23/185.81 tff(21119,plain,
% 293.23/185.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s12)) | (~node15(c_e_h_3, c_h, s11, s12)) | m_c_h_element_v_out(c_e_h_3, c_h, s11)),
% 293.23/185.81 inference(modus_ponens,[status(thm)],[21118, 21117])).
% 293.23/185.81 tff(21120,plain,
% 293.23/185.81 ($false),
% 293.23/185.81 inference(unit_resolution,[status(thm)],[21119, 147, 21082, 21081, 21116])).
% 293.23/185.81 tff(21121,plain,((~node15(c_e_h_3, c_h, s11, s12)) | m_c_h_element_v_out(c_e_h_3, c_h, s11) | (~m_c_h_element_v_out(c_e_h_3, c_h, s12))), inference(lemma,lemma(discharge,[]))).
% 293.23/185.81 tff(21122,plain,
% 293.23/185.81 (~node15(c_e_h_3, c_h, s11, s12)),
% 293.23/185.81 inference(unit_resolution,[status(thm)],[21121, 21082, 21081])).
% 293.23/185.81 tff(21123,plain,
% 293.23/185.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_h, s11, s12)) | node14(c_e_h_3, c_h, s11, s12) | node15(c_e_h_3, c_h, s11, s12) | node16(c_e_h_3, c_h, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_h, s11, s12)) | node14(c_e_h_3, c_h, s11, s12) | node15(c_e_h_3, c_h, s11, s12) | node16(c_e_h_3, c_h, s11))),
% 293.23/185.81 inference(rewrite,[status(thm)],[])).
% 293.23/185.81 tff(21124,plain,
% 293.23/185.81 ((node16(c_e_h_3, c_h, s11) | node14(c_e_h_3, c_h, s11, s12) | node15(c_e_h_3, c_h, s11, s12) | (~node19(c_e_h_3, c_h, s11, s12))) <=> ((~node19(c_e_h_3, c_h, s11, s12)) | node14(c_e_h_3, c_h, s11, s12) | node15(c_e_h_3, c_h, s11, s12) | node16(c_e_h_3, c_h, s11))),
% 293.23/185.81 inference(rewrite,[status(thm)],[])).
% 293.23/185.81 tff(21125,plain,
% 293.23/185.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s11) | node14(c_e_h_3, c_h, s11, s12) | node15(c_e_h_3, c_h, s11, s12) | (~node19(c_e_h_3, c_h, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_3, c_h, s11, s12)) | node14(c_e_h_3, c_h, s11, s12) | node15(c_e_h_3, c_h, s11, s12) | node16(c_e_h_3, c_h, s11)))),
% 293.32/185.81 inference(monotonicity,[status(thm)],[21124])).
% 293.32/185.81 tff(21126,plain,
% 293.32/185.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s11) | node14(c_e_h_3, c_h, s11, s12) | node15(c_e_h_3, c_h, s11, s12) | (~node19(c_e_h_3, c_h, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_h, s11, s12)) | node14(c_e_h_3, c_h, s11, s12) | node15(c_e_h_3, c_h, s11, s12) | node16(c_e_h_3, c_h, s11))),
% 293.32/185.81 inference(transitivity,[status(thm)],[21125, 21123])).
% 293.32/185.81 tff(21127,plain,
% 293.32/185.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s11) | node14(c_e_h_3, c_h, s11, s12) | node15(c_e_h_3, c_h, s11, s12) | (~node19(c_e_h_3, c_h, s11, s12)))),
% 293.32/185.81 inference(quant_inst,[status(thm)],[])).
% 293.32/185.81 tff(21128,plain,
% 293.32/185.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_3, c_h, s11, s12)) | node14(c_e_h_3, c_h, s11, s12) | node15(c_e_h_3, c_h, s11, s12) | node16(c_e_h_3, c_h, s11)),
% 293.32/185.81 inference(modus_ponens,[status(thm)],[21127, 21126])).
% 293.32/185.81 tff(21129,plain,
% 293.32/185.81 (node14(c_e_h_3, c_h, s11, s12) | node15(c_e_h_3, c_h, s11, s12) | node16(c_e_h_3, c_h, s11)),
% 293.32/185.81 inference(unit_resolution,[status(thm)],[21128, 204, 21096])).
% 293.32/185.81 tff(21130,plain,
% 293.32/185.81 (node16(c_e_h_3, c_h, s11)),
% 293.32/185.81 inference(unit_resolution,[status(thm)],[21129, 21122, 21115])).
% 293.32/185.81 tff(21131,plain,
% 293.32/185.81 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_h, s11)) | m_c_h_element_v_in1(c_e_h_3, c_h, s11) | m_c_h_element_v_in2(c_e_h_3, c_h, s11))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_h, s11)) | m_c_h_element_v_in1(c_e_h_3, c_h, s11) | m_c_h_element_v_in2(c_e_h_3, c_h, s11))),
% 293.32/185.81 inference(rewrite,[status(thm)],[])).
% 293.32/185.81 tff(21132,plain,
% 293.32/185.81 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_h, s11)) | m_c_h_element_v_in1(c_e_h_3, c_h, s11) | m_c_h_element_v_in2(c_e_h_3, c_h, s11))),
% 293.32/185.81 inference(quant_inst,[status(thm)],[])).
% 293.32/185.81 tff(21133,plain,
% 293.32/185.81 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_h, s11)) | m_c_h_element_v_in1(c_e_h_3, c_h, s11) | m_c_h_element_v_in2(c_e_h_3, c_h, s11)),
% 293.32/185.81 inference(modus_ponens,[status(thm)],[21132, 21131])).
% 293.32/185.81 tff(21134,plain,
% 293.32/185.81 ((~node16(c_e_h_3, c_h, s11)) | m_c_h_element_v_in2(c_e_h_3, c_h, s11)),
% 293.32/185.81 inference(unit_resolution,[status(thm)],[21133, 178, 21105])).
% 293.32/185.81 tff(21135,plain,
% 293.32/185.81 (m_c_h_element_v_in2(c_e_h_3, c_h, s11)),
% 293.32/185.81 inference(unit_resolution,[status(thm)],[21134, 21130])).
% 293.32/185.81 tff(21136,plain,
% 293.32/185.81 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s11) | (~node17(c_e_h_3, c_h, s11)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_3, c_h, s11) | (~node17(c_e_h_3, c_h, s11)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s11)))),
% 293.32/185.81 inference(rewrite,[status(thm)],[])).
% 293.32/185.81 tff(21137,plain,
% 293.32/185.81 ((m_c_h_element_v_in1(c_e_h_3, c_h, s11) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s11)) | (~node17(c_e_h_3, c_h, s11))) <=> (m_c_h_element_v_in1(c_e_h_3, c_h, s11) | (~node17(c_e_h_3, c_h, s11)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s11)))),
% 293.32/185.82 inference(rewrite,[status(thm)],[])).
% 293.32/185.82 tff(21138,plain,
% 293.32/185.82 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s11) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s11)) | (~node17(c_e_h_3, c_h, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s11) | (~node17(c_e_h_3, c_h, s11)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s11))))),
% 293.32/185.82 inference(monotonicity,[status(thm)],[21137])).
% 293.32/185.82 tff(21139,plain,
% 293.32/185.82 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s11) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s11)) | (~node17(c_e_h_3, c_h, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_3, c_h, s11) | (~node17(c_e_h_3, c_h, s11)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s11)))),
% 293.32/185.82 inference(transitivity,[status(thm)],[21138, 21136])).
% 293.32/185.82 tff(21140,plain,
% 293.32/185.82 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s11) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s11)) | (~node17(c_e_h_3, c_h, s11)))),
% 293.32/185.82 inference(quant_inst,[status(thm)],[])).
% 293.32/185.82 tff(21141,plain,
% 293.32/185.82 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_3, c_h, s11) | (~node17(c_e_h_3, c_h, s11)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s11))),
% 293.32/185.82 inference(modus_ponens,[status(thm)],[21140, 21139])).
% 293.32/185.82 tff(21142,plain,
% 293.32/185.82 ((~node17(c_e_h_3, c_h, s11)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s11))),
% 293.32/185.82 inference(unit_resolution,[status(thm)],[21141, 859, 21105])).
% 293.32/185.82 tff(21143,plain,
% 293.32/185.82 ($false),
% 293.32/185.82 inference(unit_resolution,[status(thm)],[21142, 21135, 21104])).
% 293.32/185.82 tff(21144,plain,(m_c_h_element_v_out(c_e_h_3, c_h, s11) | m_c_h_element_v_in1(c_e_h_3, c_h, s11) | (~m_c_h_element_v_out(c_e_h_3, c_h, s12))), inference(lemma,lemma(discharge,[]))).
% 293.32/185.82 tff(21145,plain,
% 293.32/185.82 (m_c_h_element_v_in1(c_e_h_3, c_h, s11)),
% 293.32/185.82 inference(unit_resolution,[status(thm)],[21144, 21081, 21080])).
% 293.32/185.82 tff(21146,assumption,(m_c_h_element_v_in1(c_e_h_3, c_h, s11)), introduced(assumption)).
% 293.32/185.82 tff(21147,assumption,(~m_or_h_gate_v_out(c_e_h_3, c_g, s11)), introduced(assumption)).
% 293.32/185.82 tff(21148,plain,
% 293.32/185.82 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s11)) | m_or_h_gate_v_out(c_e_h_3, c_g, s11))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s11)) | m_or_h_gate_v_out(c_e_h_3, c_g, s11))),
% 293.32/185.82 inference(rewrite,[status(thm)],[])).
% 293.32/185.82 tff(21149,plain,
% 293.32/185.82 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s11)) | m_or_h_gate_v_out(c_e_h_3, c_g, s11))),
% 293.32/185.82 inference(quant_inst,[status(thm)],[])).
% 293.32/185.82 tff(21150,plain,
% 293.32/185.82 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_g, X))) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s11)) | m_or_h_gate_v_out(c_e_h_3, c_g, s11)),
% 293.32/185.82 inference(modus_ponens,[status(thm)],[21149, 21148])).
% 293.32/185.82 tff(21151,plain,
% 293.32/185.82 ($false),
% 293.32/185.82 inference(unit_resolution,[status(thm)],[21150, 811, 21147, 21146])).
% 293.32/185.82 tff(21152,plain,((~m_c_h_element_v_in1(c_e_h_3, c_h, s11)) | m_or_h_gate_v_out(c_e_h_3, c_g, s11)), inference(lemma,lemma(discharge,[]))).
% 293.32/185.82 tff(21153,plain,
% 293.32/185.82 (m_or_h_gate_v_out(c_e_h_3, c_g, s11)),
% 293.32/185.82 inference(unit_resolution,[status(thm)],[21152, 21145])).
% 293.32/185.82 tff(21154,assumption,(~m_c_h_element_v_out(c_e_h_3, c_h, s13)), introduced(assumption)).
% 293.32/185.82 tff(21155,assumption,(node15(c_e_h_3, c_h, s12, s13)), introduced(assumption)).
% 293.32/185.82 tff(21156,plain,
% 293.32/185.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~node15(I0, I1, X, Y)) | (~m_c_h_element_v_out(I0, I1, X)))) | (m_c_h_element_v_out(c_e_h_3, c_h, s13) | (~m_c_h_element_v_out(c_e_h_3, c_h, s12)) | (~node15(c_e_h_3, c_h, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~node15(I0, I1, X, Y)) | (~m_c_h_element_v_out(I0, I1, X)))) | m_c_h_element_v_out(c_e_h_3, c_h, s13) | (~m_c_h_element_v_out(c_e_h_3, c_h, s12)) | (~node15(c_e_h_3, c_h, s12, s13)))),
% 293.32/185.82 inference(rewrite,[status(thm)],[])).
% 293.32/185.82 tff(21157,plain,
% 293.32/185.82 ((m_c_h_element_v_out(c_e_h_3, c_h, s13) | (~node15(c_e_h_3, c_h, s12, s13)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s12))) <=> (m_c_h_element_v_out(c_e_h_3, c_h, s13) | (~m_c_h_element_v_out(c_e_h_3, c_h, s12)) | (~node15(c_e_h_3, c_h, s12, s13)))),
% 293.32/185.82 inference(rewrite,[status(thm)],[])).
% 293.32/185.82 tff(21158,plain,
% 293.32/185.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~node15(I0, I1, X, Y)) | (~m_c_h_element_v_out(I0, I1, X)))) | (m_c_h_element_v_out(c_e_h_3, c_h, s13) | (~node15(c_e_h_3, c_h, s12, s13)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~node15(I0, I1, X, Y)) | (~m_c_h_element_v_out(I0, I1, X)))) | (m_c_h_element_v_out(c_e_h_3, c_h, s13) | (~m_c_h_element_v_out(c_e_h_3, c_h, s12)) | (~node15(c_e_h_3, c_h, s12, s13))))),
% 293.32/185.82 inference(monotonicity,[status(thm)],[21157])).
% 293.32/185.82 tff(21159,plain,
% 293.32/185.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~node15(I0, I1, X, Y)) | (~m_c_h_element_v_out(I0, I1, X)))) | (m_c_h_element_v_out(c_e_h_3, c_h, s13) | (~node15(c_e_h_3, c_h, s12, s13)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~node15(I0, I1, X, Y)) | (~m_c_h_element_v_out(I0, I1, X)))) | m_c_h_element_v_out(c_e_h_3, c_h, s13) | (~m_c_h_element_v_out(c_e_h_3, c_h, s12)) | (~node15(c_e_h_3, c_h, s12, s13)))),
% 293.32/185.82 inference(transitivity,[status(thm)],[21158, 21156])).
% 293.32/185.82 tff(21160,plain,
% 293.32/185.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~node15(I0, I1, X, Y)) | (~m_c_h_element_v_out(I0, I1, X)))) | (m_c_h_element_v_out(c_e_h_3, c_h, s13) | (~node15(c_e_h_3, c_h, s12, s13)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s12)))),
% 293.32/185.82 inference(quant_inst,[status(thm)],[])).
% 293.32/185.82 tff(21161,plain,
% 293.32/185.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~node15(I0, I1, X, Y)) | (~m_c_h_element_v_out(I0, I1, X)))) | m_c_h_element_v_out(c_e_h_3, c_h, s13) | (~m_c_h_element_v_out(c_e_h_3, c_h, s12)) | (~node15(c_e_h_3, c_h, s12, s13))),
% 293.32/185.82 inference(modus_ponens,[status(thm)],[21160, 21159])).
% 293.32/185.82 tff(21162,plain,
% 293.32/185.82 ($false),
% 293.32/185.82 inference(unit_resolution,[status(thm)],[21161, 20829, 21154, 21081, 21155])).
% 293.32/185.82 tff(21163,plain,((~node15(c_e_h_3, c_h, s12, s13)) | m_c_h_element_v_out(c_e_h_3, c_h, s13) | (~m_c_h_element_v_out(c_e_h_3, c_h, s12))), inference(lemma,lemma(discharge,[]))).
% 293.32/185.82 tff(21164,plain,
% 293.32/185.82 (~node15(c_e_h_3, c_h, s12, s13)),
% 293.32/185.82 inference(unit_resolution,[status(thm)],[21163, 21154, 21081])).
% 293.32/185.82 tff(21165,assumption,(m_c_h_element_v_in1(c_e_h_3, c_h, s12)), introduced(assumption)).
% 293.32/185.82 tff(21166,assumption,(node14(c_e_h_3, c_h, s12, s13)), introduced(assumption)).
% 293.32/185.82 tff(21167,plain,
% 293.32/185.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | (~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_out(I0, I1, Y))) | (m_c_h_element_v_out(c_e_h_3, c_h, s13) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s12)) | (~node14(c_e_h_3, c_h, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | (~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_out(I0, I1, Y))) | m_c_h_element_v_out(c_e_h_3, c_h, s13) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s12)) | (~node14(c_e_h_3, c_h, s12, s13)))),
% 293.32/185.82 inference(rewrite,[status(thm)],[])).
% 293.32/185.82 tff(21168,plain,
% 293.32/185.82 (((~node14(c_e_h_3, c_h, s12, s13)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s12)) | m_c_h_element_v_out(c_e_h_3, c_h, s13)) <=> (m_c_h_element_v_out(c_e_h_3, c_h, s13) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s12)) | (~node14(c_e_h_3, c_h, s12, s13)))),
% 293.32/185.82 inference(rewrite,[status(thm)],[])).
% 293.32/185.82 tff(21169,plain,
% 293.32/185.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | (~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_out(I0, I1, Y))) | ((~node14(c_e_h_3, c_h, s12, s13)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s12)) | m_c_h_element_v_out(c_e_h_3, c_h, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | (~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_out(I0, I1, Y))) | (m_c_h_element_v_out(c_e_h_3, c_h, s13) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s12)) | (~node14(c_e_h_3, c_h, s12, s13))))),
% 293.32/185.82 inference(monotonicity,[status(thm)],[21168])).
% 293.32/185.82 tff(21170,plain,
% 293.32/185.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | (~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_out(I0, I1, Y))) | ((~node14(c_e_h_3, c_h, s12, s13)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s12)) | m_c_h_element_v_out(c_e_h_3, c_h, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | (~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_out(I0, I1, Y))) | m_c_h_element_v_out(c_e_h_3, c_h, s13) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s12)) | (~node14(c_e_h_3, c_h, s12, s13)))),
% 293.32/185.82 inference(transitivity,[status(thm)],[21169, 21167])).
% 293.32/185.82 tff(21171,plain,
% 293.32/185.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | (~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_out(I0, I1, Y))) | ((~node14(c_e_h_3, c_h, s12, s13)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s12)) | m_c_h_element_v_out(c_e_h_3, c_h, s13))),
% 293.32/185.82 inference(quant_inst,[status(thm)],[])).
% 293.32/185.82 tff(21172,plain,
% 293.32/185.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | (~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_out(I0, I1, Y))) | m_c_h_element_v_out(c_e_h_3, c_h, s13) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s12)) | (~node14(c_e_h_3, c_h, s12, s13))),
% 293.32/185.82 inference(modus_ponens,[status(thm)],[21171, 21170])).
% 293.32/185.82 tff(21173,plain,
% 293.32/185.82 ($false),
% 293.32/185.82 inference(unit_resolution,[status(thm)],[21172, 20875, 21154, 21166, 21165])).
% 293.32/185.82 tff(21174,plain,((~node14(c_e_h_3, c_h, s12, s13)) | m_c_h_element_v_out(c_e_h_3, c_h, s13) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s12))), inference(lemma,lemma(discharge,[]))).
% 293.32/185.82 tff(21175,plain,
% 293.32/185.82 (~node14(c_e_h_3, c_h, s12, s13)),
% 293.32/185.82 inference(unit_resolution,[status(thm)],[21174, 21154, 21165])).
% 293.32/185.82 tff(21176,plain,
% 293.32/185.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s12, s13)) | node19(c_e_h_3, c_h, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s12, s13)) | node19(c_e_h_3, c_h, s12, s13))),
% 293.32/185.82 inference(rewrite,[status(thm)],[])).
% 293.32/185.82 tff(21177,plain,
% 293.32/185.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s12, s13)) | node19(c_e_h_3, c_h, s12, s13))),
% 293.32/185.82 inference(quant_inst,[status(thm)],[])).
% 293.32/185.82 tff(21178,plain,
% 293.32/185.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s12, s13)) | node19(c_e_h_3, c_h, s12, s13)),
% 293.32/185.82 inference(modus_ponens,[status(thm)],[21177, 21176])).
% 293.32/185.82 tff(21179,plain,
% 293.32/185.82 (node19(c_e_h_3, c_h, s12, s13)),
% 293.32/185.82 inference(unit_resolution,[status(thm)],[21178, 190, 11856])).
% 293.32/185.82 tff(21180,plain,
% 293.32/185.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s12) | node15(c_e_h_3, c_h, s12, s13) | (~node19(c_e_h_3, c_h, s12, s13)) | node14(c_e_h_3, c_h, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_h, s12) | node15(c_e_h_3, c_h, s12, s13) | (~node19(c_e_h_3, c_h, s12, s13)) | node14(c_e_h_3, c_h, s12, s13))),
% 293.32/185.82 inference(rewrite,[status(thm)],[])).
% 293.32/185.82 tff(21181,plain,
% 293.32/185.82 ((node16(c_e_h_3, c_h, s12) | node14(c_e_h_3, c_h, s12, s13) | node15(c_e_h_3, c_h, s12, s13) | (~node19(c_e_h_3, c_h, s12, s13))) <=> (node16(c_e_h_3, c_h, s12) | node15(c_e_h_3, c_h, s12, s13) | (~node19(c_e_h_3, c_h, s12, s13)) | node14(c_e_h_3, c_h, s12, s13))),
% 293.32/185.83 inference(rewrite,[status(thm)],[])).
% 293.32/185.83 tff(21182,plain,
% 293.32/185.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s12) | node14(c_e_h_3, c_h, s12, s13) | node15(c_e_h_3, c_h, s12, s13) | (~node19(c_e_h_3, c_h, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s12) | node15(c_e_h_3, c_h, s12, s13) | (~node19(c_e_h_3, c_h, s12, s13)) | node14(c_e_h_3, c_h, s12, s13)))),
% 293.32/185.83 inference(monotonicity,[status(thm)],[21181])).
% 293.32/185.83 tff(21183,plain,
% 293.32/185.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s12) | node14(c_e_h_3, c_h, s12, s13) | node15(c_e_h_3, c_h, s12, s13) | (~node19(c_e_h_3, c_h, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_h, s12) | node15(c_e_h_3, c_h, s12, s13) | (~node19(c_e_h_3, c_h, s12, s13)) | node14(c_e_h_3, c_h, s12, s13))),
% 293.32/185.83 inference(transitivity,[status(thm)],[21182, 21180])).
% 293.32/185.83 tff(21184,plain,
% 293.32/185.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_h, s12) | node14(c_e_h_3, c_h, s12, s13) | node15(c_e_h_3, c_h, s12, s13) | (~node19(c_e_h_3, c_h, s12, s13)))),
% 293.32/185.83 inference(quant_inst,[status(thm)],[])).
% 293.32/185.83 tff(21185,plain,
% 293.32/185.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_3, c_h, s12) | node15(c_e_h_3, c_h, s12, s13) | (~node19(c_e_h_3, c_h, s12, s13)) | node14(c_e_h_3, c_h, s12, s13)),
% 293.32/185.83 inference(modus_ponens,[status(thm)],[21184, 21183])).
% 293.32/185.83 tff(21186,plain,
% 293.32/185.83 (node16(c_e_h_3, c_h, s12) | node15(c_e_h_3, c_h, s12, s13) | node14(c_e_h_3, c_h, s12, s13)),
% 293.32/185.83 inference(unit_resolution,[status(thm)],[21185, 204, 21179])).
% 293.32/185.83 tff(21187,plain,
% 293.32/185.83 (node16(c_e_h_3, c_h, s12)),
% 293.32/185.83 inference(unit_resolution,[status(thm)],[21186, 21175, 21164])).
% 293.32/185.83 tff(21188,assumption,(node18(c_e_h_3, c_h, s12, s13)), introduced(assumption)).
% 293.32/185.83 tff(21189,plain,
% 293.32/185.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_out(I0, I1, X)) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_h, s13) | (~m_c_h_element_v_out(c_e_h_3, c_h, s12)) | (~node18(c_e_h_3, c_h, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_out(I0, I1, X)) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s13) | (~m_c_h_element_v_out(c_e_h_3, c_h, s12)) | (~node18(c_e_h_3, c_h, s12, s13)))),
% 293.32/185.83 inference(rewrite,[status(thm)],[])).
% 293.32/185.83 tff(21190,plain,
% 293.32/185.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_out(I0, I1, X)) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_h, s13) | (~m_c_h_element_v_out(c_e_h_3, c_h, s12)) | (~node18(c_e_h_3, c_h, s12, s13)))),
% 293.32/185.83 inference(quant_inst,[status(thm)],[])).
% 293.32/185.83 tff(21191,plain,
% 293.32/185.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_out(I0, I1, X)) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s13) | (~m_c_h_element_v_out(c_e_h_3, c_h, s12)) | (~node18(c_e_h_3, c_h, s12, s13))),
% 293.32/185.83 inference(modus_ponens,[status(thm)],[21190, 21189])).
% 293.32/185.83 tff(21192,plain,
% 293.32/185.83 ($false),
% 293.32/185.83 inference(unit_resolution,[status(thm)],[21191, 11191, 21154, 21081, 21188])).
% 293.32/185.83 tff(21193,plain,((~node18(c_e_h_3, c_h, s12, s13)) | m_c_h_element_v_out(c_e_h_3, c_h, s13) | (~m_c_h_element_v_out(c_e_h_3, c_h, s12))), inference(lemma,lemma(discharge,[]))).
% 293.32/185.83 tff(21194,plain,
% 293.32/185.83 (~node18(c_e_h_3, c_h, s12, s13)),
% 293.32/185.83 inference(unit_resolution,[status(thm)],[21193, 21154, 21081])).
% 293.32/185.83 tff(21195,plain,
% 293.32/185.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s12) | (~node19(c_e_h_3, c_h, s12, s13)) | node18(c_e_h_3, c_h, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_h, s12) | (~node19(c_e_h_3, c_h, s12, s13)) | node18(c_e_h_3, c_h, s12, s13))),
% 293.32/185.83 inference(rewrite,[status(thm)],[])).
% 293.32/185.83 tff(21196,plain,
% 293.32/185.83 ((node17(c_e_h_3, c_h, s12) | node18(c_e_h_3, c_h, s12, s13) | (~node19(c_e_h_3, c_h, s12, s13))) <=> (node17(c_e_h_3, c_h, s12) | (~node19(c_e_h_3, c_h, s12, s13)) | node18(c_e_h_3, c_h, s12, s13))),
% 293.32/185.83 inference(rewrite,[status(thm)],[])).
% 293.32/185.83 tff(21197,plain,
% 293.32/185.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s12) | node18(c_e_h_3, c_h, s12, s13) | (~node19(c_e_h_3, c_h, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s12) | (~node19(c_e_h_3, c_h, s12, s13)) | node18(c_e_h_3, c_h, s12, s13)))),
% 293.32/185.83 inference(monotonicity,[status(thm)],[21196])).
% 293.32/185.83 tff(21198,plain,
% 293.32/185.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s12) | node18(c_e_h_3, c_h, s12, s13) | (~node19(c_e_h_3, c_h, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_h, s12) | (~node19(c_e_h_3, c_h, s12, s13)) | node18(c_e_h_3, c_h, s12, s13))),
% 293.32/185.83 inference(transitivity,[status(thm)],[21197, 21195])).
% 293.32/185.83 tff(21199,plain,
% 293.32/185.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_h, s12) | node18(c_e_h_3, c_h, s12, s13) | (~node19(c_e_h_3, c_h, s12, s13)))),
% 293.32/185.83 inference(quant_inst,[status(thm)],[])).
% 293.32/185.83 tff(21200,plain,
% 293.32/185.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_3, c_h, s12) | (~node19(c_e_h_3, c_h, s12, s13)) | node18(c_e_h_3, c_h, s12, s13)),
% 293.32/185.83 inference(modus_ponens,[status(thm)],[21199, 21198])).
% 293.32/185.83 tff(21201,plain,
% 293.32/185.83 (node17(c_e_h_3, c_h, s12) | node18(c_e_h_3, c_h, s12, s13)),
% 293.32/185.83 inference(unit_resolution,[status(thm)],[21200, 776, 21179])).
% 293.32/185.83 tff(21202,plain,
% 293.32/185.83 (node17(c_e_h_3, c_h, s12)),
% 293.32/185.83 inference(unit_resolution,[status(thm)],[21201, 21194])).
% 293.32/185.83 tff(21203,assumption,(node16(c_e_h_3, c_h, s12)), introduced(assumption)).
% 293.32/185.83 tff(21204,assumption,(node17(c_e_h_3, c_h, s12)), introduced(assumption)).
% 293.32/185.83 tff(21205,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_h, s12)), introduced(assumption)).
% 293.32/185.83 tff(21206,plain,
% 293.32/185.83 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_h, s12)) | m_c_h_element_v_in1(c_e_h_3, c_h, s12) | m_c_h_element_v_in2(c_e_h_3, c_h, s12))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_h, s12)) | m_c_h_element_v_in1(c_e_h_3, c_h, s12) | m_c_h_element_v_in2(c_e_h_3, c_h, s12))),
% 293.32/185.83 inference(rewrite,[status(thm)],[])).
% 293.32/185.83 tff(21207,plain,
% 293.32/185.83 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_h, s12)) | m_c_h_element_v_in1(c_e_h_3, c_h, s12) | m_c_h_element_v_in2(c_e_h_3, c_h, s12))),
% 293.32/185.83 inference(quant_inst,[status(thm)],[])).
% 293.32/185.83 tff(21208,plain,
% 293.32/185.83 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_h, s12)) | m_c_h_element_v_in1(c_e_h_3, c_h, s12) | m_c_h_element_v_in2(c_e_h_3, c_h, s12)),
% 293.32/185.83 inference(modus_ponens,[status(thm)],[21207, 21206])).
% 293.32/185.83 tff(21209,plain,
% 293.32/185.83 (m_c_h_element_v_in1(c_e_h_3, c_h, s12) | m_c_h_element_v_in2(c_e_h_3, c_h, s12)),
% 293.32/185.84 inference(unit_resolution,[status(thm)],[21208, 178, 21203])).
% 293.32/185.84 tff(21210,plain,
% 293.32/185.84 (m_c_h_element_v_in2(c_e_h_3, c_h, s12)),
% 293.32/185.84 inference(unit_resolution,[status(thm)],[21209, 21205])).
% 293.32/185.84 tff(21211,plain,
% 293.32/185.84 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s12)) | m_c_h_element_v_in1(c_e_h_3, c_h, s12) | (~node17(c_e_h_3, c_h, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s12)) | m_c_h_element_v_in1(c_e_h_3, c_h, s12) | (~node17(c_e_h_3, c_h, s12)))),
% 293.32/185.84 inference(rewrite,[status(thm)],[])).
% 293.32/185.84 tff(21212,plain,
% 293.32/185.84 ((m_c_h_element_v_in1(c_e_h_3, c_h, s12) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s12)) | (~node17(c_e_h_3, c_h, s12))) <=> ((~m_c_h_element_v_in2(c_e_h_3, c_h, s12)) | m_c_h_element_v_in1(c_e_h_3, c_h, s12) | (~node17(c_e_h_3, c_h, s12)))),
% 293.32/185.84 inference(rewrite,[status(thm)],[])).
% 293.32/185.84 tff(21213,plain,
% 293.32/185.84 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s12) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s12)) | (~node17(c_e_h_3, c_h, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s12)) | m_c_h_element_v_in1(c_e_h_3, c_h, s12) | (~node17(c_e_h_3, c_h, s12))))),
% 293.32/185.84 inference(monotonicity,[status(thm)],[21212])).
% 293.32/185.84 tff(21214,plain,
% 293.32/185.84 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s12) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s12)) | (~node17(c_e_h_3, c_h, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s12)) | m_c_h_element_v_in1(c_e_h_3, c_h, s12) | (~node17(c_e_h_3, c_h, s12)))),
% 293.32/185.84 inference(transitivity,[status(thm)],[21213, 21211])).
% 293.32/185.84 tff(21215,plain,
% 293.32/185.84 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_h, s12) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s12)) | (~node17(c_e_h_3, c_h, s12)))),
% 293.32/185.84 inference(quant_inst,[status(thm)],[])).
% 293.32/185.84 tff(21216,plain,
% 293.32/185.84 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s12)) | m_c_h_element_v_in1(c_e_h_3, c_h, s12) | (~node17(c_e_h_3, c_h, s12))),
% 293.32/185.84 inference(modus_ponens,[status(thm)],[21215, 21214])).
% 293.32/185.84 tff(21217,plain,
% 293.32/185.84 ((~m_c_h_element_v_in2(c_e_h_3, c_h, s12)) | m_c_h_element_v_in1(c_e_h_3, c_h, s12)),
% 293.32/185.84 inference(unit_resolution,[status(thm)],[21216, 859, 21204])).
% 293.32/185.84 tff(21218,plain,
% 293.32/185.84 ($false),
% 293.32/185.84 inference(unit_resolution,[status(thm)],[21217, 21210, 21205])).
% 293.32/185.84 tff(21219,plain,(m_c_h_element_v_in1(c_e_h_3, c_h, s12) | (~node17(c_e_h_3, c_h, s12)) | (~node16(c_e_h_3, c_h, s12))), inference(lemma,lemma(discharge,[]))).
% 293.32/185.84 tff(21220,plain,
% 293.32/185.84 (m_c_h_element_v_in1(c_e_h_3, c_h, s12)),
% 293.32/185.84 inference(unit_resolution,[status(thm)],[21219, 21204, 21203])).
% 293.32/185.84 tff(21221,plain,
% 293.32/185.84 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s12)) | (~node16(c_e_h_3, c_h, s12)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s12)) | (~node16(c_e_h_3, c_h, s12)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s12)))),
% 293.32/185.84 inference(rewrite,[status(thm)],[])).
% 293.32/185.84 tff(21222,plain,
% 293.32/185.84 (((~node16(c_e_h_3, c_h, s12)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s12)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s12))) <=> ((~m_c_h_element_v_in2(c_e_h_3, c_h, s12)) | (~node16(c_e_h_3, c_h, s12)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s12)))),
% 293.32/185.84 inference(rewrite,[status(thm)],[])).
% 293.32/185.84 tff(21223,plain,
% 293.32/185.84 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_h, s12)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s12)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s12)) | (~node16(c_e_h_3, c_h, s12)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s12))))),
% 293.32/185.84 inference(monotonicity,[status(thm)],[21222])).
% 293.32/185.84 tff(21224,plain,
% 293.32/185.84 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_h, s12)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s12)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s12)) | (~node16(c_e_h_3, c_h, s12)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s12)))),
% 293.32/185.84 inference(transitivity,[status(thm)],[21223, 21221])).
% 293.32/185.84 tff(21225,plain,
% 293.32/185.84 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_h, s12)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s12)) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s12)))),
% 293.32/185.84 inference(quant_inst,[status(thm)],[])).
% 293.32/185.84 tff(21226,plain,
% 293.32/185.84 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s12)) | (~node16(c_e_h_3, c_h, s12)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s12))),
% 293.32/185.84 inference(modus_ponens,[status(thm)],[21225, 21224])).
% 293.32/185.84 tff(21227,plain,
% 293.32/185.84 ((~m_c_h_element_v_in2(c_e_h_3, c_h, s12)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s12))),
% 293.32/185.84 inference(unit_resolution,[status(thm)],[21226, 2307, 21203])).
% 293.32/185.84 tff(21228,plain,
% 293.32/185.84 (~m_c_h_element_v_in2(c_e_h_3, c_h, s12)),
% 293.32/185.84 inference(unit_resolution,[status(thm)],[21227, 21220])).
% 293.32/185.84 tff(21229,plain,
% 293.32/185.84 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_3, c_h, s12) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s12)) | (~node17(c_e_h_3, c_h, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_h, s12) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s12)) | (~node17(c_e_h_3, c_h, s12)))),
% 293.32/185.84 inference(rewrite,[status(thm)],[])).
% 293.32/185.84 tff(21230,plain,
% 293.32/185.84 (((~m_c_h_element_v_in1(c_e_h_3, c_h, s12)) | m_c_h_element_v_in2(c_e_h_3, c_h, s12) | (~node17(c_e_h_3, c_h, s12))) <=> (m_c_h_element_v_in2(c_e_h_3, c_h, s12) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s12)) | (~node17(c_e_h_3, c_h, s12)))),
% 293.32/185.84 inference(rewrite,[status(thm)],[])).
% 293.32/185.84 tff(21231,plain,
% 293.32/185.84 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s12)) | m_c_h_element_v_in2(c_e_h_3, c_h, s12) | (~node17(c_e_h_3, c_h, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_3, c_h, s12) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s12)) | (~node17(c_e_h_3, c_h, s12))))),
% 293.32/185.84 inference(monotonicity,[status(thm)],[21230])).
% 293.32/185.84 tff(21232,plain,
% 293.32/185.84 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s12)) | m_c_h_element_v_in2(c_e_h_3, c_h, s12) | (~node17(c_e_h_3, c_h, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_h, s12) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s12)) | (~node17(c_e_h_3, c_h, s12)))),
% 293.32/185.84 inference(transitivity,[status(thm)],[21231, 21229])).
% 293.32/185.84 tff(21233,plain,
% 293.32/185.84 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_h, s12)) | m_c_h_element_v_in2(c_e_h_3, c_h, s12) | (~node17(c_e_h_3, c_h, s12)))),
% 293.32/185.84 inference(quant_inst,[status(thm)],[])).
% 293.32/185.84 tff(21234,plain,
% 293.32/185.84 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_h, s12) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s12)) | (~node17(c_e_h_3, c_h, s12))),
% 293.32/185.84 inference(modus_ponens,[status(thm)],[21233, 21232])).
% 293.32/185.84 tff(21235,plain,
% 293.32/185.84 (m_c_h_element_v_in2(c_e_h_3, c_h, s12) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s12))),
% 293.32/185.84 inference(unit_resolution,[status(thm)],[21234, 919, 21204])).
% 293.32/185.84 tff(21236,plain,
% 293.32/185.84 ($false),
% 293.32/185.84 inference(unit_resolution,[status(thm)],[21235, 21228, 21220])).
% 293.32/185.84 tff(21237,plain,((~node17(c_e_h_3, c_h, s12)) | (~node16(c_e_h_3, c_h, s12))), inference(lemma,lemma(discharge,[]))).
% 293.32/185.84 tff(21238,plain,
% 293.32/185.84 ($false),
% 293.32/185.84 inference(unit_resolution,[status(thm)],[21237, 21202, 21187])).
% 293.32/185.84 tff(21239,plain,(m_c_h_element_v_out(c_e_h_3, c_h, s13) | (~m_c_h_element_v_out(c_e_h_3, c_h, s12)) | (~m_c_h_element_v_in1(c_e_h_3, c_h, s12))), inference(lemma,lemma(discharge,[]))).
% 293.32/185.84 tff(21240,plain,
% 293.32/185.84 (~m_c_h_element_v_in1(c_e_h_3, c_h, s12)),
% 293.32/185.84 inference(unit_resolution,[status(thm)],[21239, 21081, 21154])).
% 293.32/185.84 tff(21241,assumption,(m_or_h_gate_v_out(c_e_h_3, c_g, s12)), introduced(assumption)).
% 293.32/185.84 tff(21242,plain,
% 293.32/185.84 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_c_h_element_v_in1(I0, c_h, X))) | ((~m_or_h_gate_v_out(c_e_h_3, c_g, s12)) | m_c_h_element_v_in1(c_e_h_3, c_h, s12))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_c_h_element_v_in1(I0, c_h, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s12)) | m_c_h_element_v_in1(c_e_h_3, c_h, s12))),
% 293.32/185.84 inference(rewrite,[status(thm)],[])).
% 293.32/185.84 tff(21243,plain,
% 293.32/185.84 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_c_h_element_v_in1(I0, c_h, X))) | ((~m_or_h_gate_v_out(c_e_h_3, c_g, s12)) | m_c_h_element_v_in1(c_e_h_3, c_h, s12))),
% 293.32/185.84 inference(quant_inst,[status(thm)],[])).
% 293.32/185.84 tff(21244,plain,
% 293.32/185.84 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_c_h_element_v_in1(I0, c_h, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s12)) | m_c_h_element_v_in1(c_e_h_3, c_h, s12)),
% 293.32/185.84 inference(modus_ponens,[status(thm)],[21243, 21242])).
% 293.32/185.84 tff(21245,plain,
% 293.32/185.84 ($false),
% 293.32/185.84 inference(unit_resolution,[status(thm)],[21244, 11172, 21241, 21205])).
% 293.32/185.84 tff(21246,plain,(m_c_h_element_v_in1(c_e_h_3, c_h, s12) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s12))), inference(lemma,lemma(discharge,[]))).
% 293.32/185.84 tff(21247,plain,
% 293.32/185.84 (~m_or_h_gate_v_out(c_e_h_3, c_g, s12)),
% 293.32/185.84 inference(unit_resolution,[status(thm)],[21246, 21240])).
% 293.32/185.84 tff(21248,assumption,(~m_or_h_gate_v_out(c_e_h_3, c_g, s12)), introduced(assumption)).
% 293.32/185.84 tff(21249,assumption,(m_or_h_gate_v_out(c_e_h_3, c_g, s11)), introduced(assumption)).
% 293.32/185.84 tff(21250,assumption,(~m_or_h_gate_v_in2(c_e_h_3, c_g, s10)), introduced(assumption)).
% 293.32/185.84 tff(21251,assumption,(node6(c_e_h_3, c_g, s10, s11)), introduced(assumption)).
% 293.32/185.84 tff(21252,plain,
% 293.32/185.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s10) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s11)) | (~node6(c_e_h_3, c_g, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_g, s10) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s11)) | (~node6(c_e_h_3, c_g, s10, s11)))),
% 293.32/185.84 inference(rewrite,[status(thm)],[])).
% 293.32/185.84 tff(21253,plain,
% 293.32/185.84 (((~node6(c_e_h_3, c_g, s10, s11)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s11)) | m_or_h_gate_v_out(c_e_h_3, c_g, s10)) <=> (m_or_h_gate_v_out(c_e_h_3, c_g, s10) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s11)) | (~node6(c_e_h_3, c_g, s10, s11)))),
% 293.32/185.85 inference(rewrite,[status(thm)],[])).
% 293.32/185.85 tff(21254,plain,
% 293.32/185.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_g, s10, s11)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s11)) | m_or_h_gate_v_out(c_e_h_3, c_g, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s10) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s11)) | (~node6(c_e_h_3, c_g, s10, s11))))),
% 293.32/185.85 inference(monotonicity,[status(thm)],[21253])).
% 293.32/185.85 tff(21255,plain,
% 293.32/185.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_g, s10, s11)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s11)) | m_or_h_gate_v_out(c_e_h_3, c_g, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_g, s10) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s11)) | (~node6(c_e_h_3, c_g, s10, s11)))),
% 293.32/185.85 inference(transitivity,[status(thm)],[21254, 21252])).
% 293.32/185.85 tff(21256,plain,
% 293.32/185.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_g, s10, s11)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s11)) | m_or_h_gate_v_out(c_e_h_3, c_g, s10))),
% 293.32/185.85 inference(quant_inst,[status(thm)],[])).
% 293.32/185.85 tff(21257,plain,
% 293.32/185.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_g, s10) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s11)) | (~node6(c_e_h_3, c_g, s10, s11))),
% 293.32/185.85 inference(modus_ponens,[status(thm)],[21256, 21255])).
% 293.32/185.85 tff(21258,plain,
% 293.32/185.85 ($false),
% 293.32/185.85 inference(unit_resolution,[status(thm)],[21257, 1121, 21251, 21249, 20172])).
% 293.32/185.85 tff(21259,plain,((~node6(c_e_h_3, c_g, s10, s11)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s11)) | m_or_h_gate_v_out(c_e_h_3, c_g, s10)), inference(lemma,lemma(discharge,[]))).
% 293.32/185.85 tff(21260,plain,
% 293.32/185.85 (~node6(c_e_h_3, c_g, s10, s11)),
% 293.32/185.85 inference(unit_resolution,[status(thm)],[21259, 21249, 20172])).
% 293.32/185.85 tff(21261,assumption,(~m_or_h_gate_v_in1(c_e_h_3, c_g, s10)), introduced(assumption)).
% 293.32/185.85 tff(21262,assumption,(node5(c_e_h_3, c_g, s10, s11)), introduced(assumption)).
% 293.32/185.85 tff(21263,plain,
% 293.32/185.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_3, c_g, s11)) | m_or_h_gate_v_in2(c_e_h_3, c_g, s10) | (~node5(c_e_h_3, c_g, s10, s11)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s11)) | m_or_h_gate_v_in2(c_e_h_3, c_g, s10) | (~node5(c_e_h_3, c_g, s10, s11)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s10))),
% 293.32/185.85 inference(rewrite,[status(thm)],[])).
% 293.32/185.85 tff(21264,plain,
% 293.32/185.85 ((m_or_h_gate_v_in1(c_e_h_3, c_g, s10) | m_or_h_gate_v_in2(c_e_h_3, c_g, s10) | (~node5(c_e_h_3, c_g, s10, s11)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s11))) <=> ((~m_or_h_gate_v_out(c_e_h_3, c_g, s11)) | m_or_h_gate_v_in2(c_e_h_3, c_g, s10) | (~node5(c_e_h_3, c_g, s10, s11)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s10))),
% 293.32/185.85 inference(rewrite,[status(thm)],[])).
% 293.32/185.85 tff(21265,plain,
% 293.32/185.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_g, s10) | m_or_h_gate_v_in2(c_e_h_3, c_g, s10) | (~node5(c_e_h_3, c_g, s10, s11)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_3, c_g, s11)) | m_or_h_gate_v_in2(c_e_h_3, c_g, s10) | (~node5(c_e_h_3, c_g, s10, s11)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s10)))),
% 293.32/185.85 inference(monotonicity,[status(thm)],[21264])).
% 293.32/185.85 tff(21266,plain,
% 293.32/185.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_g, s10) | m_or_h_gate_v_in2(c_e_h_3, c_g, s10) | (~node5(c_e_h_3, c_g, s10, s11)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s11)) | m_or_h_gate_v_in2(c_e_h_3, c_g, s10) | (~node5(c_e_h_3, c_g, s10, s11)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s10))),
% 293.32/185.85 inference(transitivity,[status(thm)],[21265, 21263])).
% 293.32/185.85 tff(21267,plain,
% 293.32/185.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_g, s10) | m_or_h_gate_v_in2(c_e_h_3, c_g, s10) | (~node5(c_e_h_3, c_g, s10, s11)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s11)))),
% 293.32/185.85 inference(quant_inst,[status(thm)],[])).
% 293.32/185.85 tff(21268,plain,
% 293.32/185.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s11)) | m_or_h_gate_v_in2(c_e_h_3, c_g, s10) | (~node5(c_e_h_3, c_g, s10, s11)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s10)),
% 293.32/185.85 inference(modus_ponens,[status(thm)],[21267, 21266])).
% 293.32/185.85 tff(21269,plain,
% 293.32/185.85 ($false),
% 293.32/185.85 inference(unit_resolution,[status(thm)],[21268, 1159, 21262, 21249, 21250, 21261])).
% 293.32/185.85 tff(21270,plain,((~node5(c_e_h_3, c_g, s10, s11)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s11)) | m_or_h_gate_v_in2(c_e_h_3, c_g, s10) | m_or_h_gate_v_in1(c_e_h_3, c_g, s10)), inference(lemma,lemma(discharge,[]))).
% 293.32/185.85 tff(21271,plain,
% 293.32/185.85 (~node5(c_e_h_3, c_g, s10, s11)),
% 293.32/185.85 inference(unit_resolution,[status(thm)],[21270, 21249, 21261, 21250])).
% 293.32/185.85 tff(21272,plain,
% 293.32/185.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s10, s11)) | node5(c_e_h_3, c_g, s10, s11) | node6(c_e_h_3, c_g, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s10, s11)) | node5(c_e_h_3, c_g, s10, s11) | node6(c_e_h_3, c_g, s10, s11))),
% 293.32/185.85 inference(rewrite,[status(thm)],[])).
% 293.32/185.85 tff(21273,plain,
% 293.32/185.85 ((node6(c_e_h_3, c_g, s10, s11) | node5(c_e_h_3, c_g, s10, s11) | (~trans(s10, s11))) <=> ((~trans(s10, s11)) | node5(c_e_h_3, c_g, s10, s11) | node6(c_e_h_3, c_g, s10, s11))),
% 293.32/185.85 inference(rewrite,[status(thm)],[])).
% 293.32/185.85 tff(21274,plain,
% 293.32/185.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s10, s11) | node5(c_e_h_3, c_g, s10, s11) | (~trans(s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s10, s11)) | node5(c_e_h_3, c_g, s10, s11) | node6(c_e_h_3, c_g, s10, s11)))),
% 293.32/185.85 inference(monotonicity,[status(thm)],[21273])).
% 293.32/185.85 tff(21275,plain,
% 293.32/185.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s10, s11) | node5(c_e_h_3, c_g, s10, s11) | (~trans(s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s10, s11)) | node5(c_e_h_3, c_g, s10, s11) | node6(c_e_h_3, c_g, s10, s11))),
% 293.32/185.85 inference(transitivity,[status(thm)],[21274, 21272])).
% 293.32/185.85 tff(21276,plain,
% 293.32/185.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s10, s11) | node5(c_e_h_3, c_g, s10, s11) | (~trans(s10, s11)))),
% 293.32/185.85 inference(quant_inst,[status(thm)],[])).
% 293.32/185.85 tff(21277,plain,
% 293.32/185.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s10, s11)) | node5(c_e_h_3, c_g, s10, s11) | node6(c_e_h_3, c_g, s10, s11)),
% 293.32/185.85 inference(modus_ponens,[status(thm)],[21276, 21275])).
% 293.32/185.85 tff(21278,plain,
% 293.32/185.85 (node5(c_e_h_3, c_g, s10, s11) | node6(c_e_h_3, c_g, s10, s11)),
% 293.32/185.85 inference(unit_resolution,[status(thm)],[21277, 1141, 7748])).
% 293.32/185.85 tff(21279,plain,
% 293.32/185.85 ($false),
% 293.32/185.85 inference(unit_resolution,[status(thm)],[21278, 21271, 21260])).
% 293.32/185.85 tff(21280,plain,((~m_or_h_gate_v_out(c_e_h_3, c_g, s11)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s10) | m_or_h_gate_v_in2(c_e_h_3, c_g, s10) | m_or_h_gate_v_out(c_e_h_3, c_g, s10)), inference(lemma,lemma(discharge,[]))).
% 293.32/185.85 tff(21281,plain,
% 293.32/185.85 (m_or_h_gate_v_in1(c_e_h_3, c_g, s10)),
% 293.32/185.85 inference(unit_resolution,[status(thm)],[21280, 21249, 21250, 20172])).
% 293.32/185.85 tff(21282,assumption,(m_or_h_gate_v_in1(c_e_h_3, c_g, s10)), introduced(assumption)).
% 293.32/185.85 tff(21283,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_c, s10)), introduced(assumption)).
% 293.32/185.85 tff(21284,plain,
% 293.32/185.85 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_g, s10)) | m_and_h_gate_v_out(c_e_h_3, c_c, s10))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s10)) | m_and_h_gate_v_out(c_e_h_3, c_c, s10))),
% 293.32/185.85 inference(rewrite,[status(thm)],[])).
% 293.32/185.85 tff(21285,plain,
% 293.32/185.85 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_g, s10)) | m_and_h_gate_v_out(c_e_h_3, c_c, s10))),
% 293.32/185.85 inference(quant_inst,[status(thm)],[])).
% 293.32/185.85 tff(21286,plain,
% 293.32/185.85 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s10)) | m_and_h_gate_v_out(c_e_h_3, c_c, s10)),
% 293.32/185.85 inference(modus_ponens,[status(thm)],[21285, 21284])).
% 293.32/185.85 tff(21287,plain,
% 293.32/185.85 ($false),
% 293.32/185.85 inference(unit_resolution,[status(thm)],[21286, 2708, 21283, 21282])).
% 293.32/185.85 tff(21288,plain,((~m_or_h_gate_v_in1(c_e_h_3, c_g, s10)) | m_and_h_gate_v_out(c_e_h_3, c_c, s10)), inference(lemma,lemma(discharge,[]))).
% 293.32/185.85 tff(21289,plain,
% 293.32/185.85 (m_and_h_gate_v_out(c_e_h_3, c_c, s10)),
% 293.32/185.85 inference(unit_resolution,[status(thm)],[21288, 21281])).
% 293.32/185.85 tff(21290,assumption,(~node4(c_e_h_3, c_g, s11)), introduced(assumption)).
% 293.32/185.85 tff(21291,assumption,(node5(c_e_h_3, c_g, s11, s12)), introduced(assumption)).
% 293.32/185.85 tff(21292,plain,
% 293.32/185.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s12) | (~node5(c_e_h_3, c_g, s11, s12)) | node4(c_e_h_3, c_g, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | m_or_h_gate_v_out(c_e_h_3, c_g, s12) | (~node5(c_e_h_3, c_g, s11, s12)) | node4(c_e_h_3, c_g, s11))),
% 293.32/185.85 inference(rewrite,[status(thm)],[])).
% 293.32/185.85 tff(21293,plain,
% 293.32/185.85 ((node4(c_e_h_3, c_g, s11) | (~node5(c_e_h_3, c_g, s11, s12)) | m_or_h_gate_v_out(c_e_h_3, c_g, s12)) <=> (m_or_h_gate_v_out(c_e_h_3, c_g, s12) | (~node5(c_e_h_3, c_g, s11, s12)) | node4(c_e_h_3, c_g, s11))),
% 293.32/185.85 inference(rewrite,[status(thm)],[])).
% 293.32/185.85 tff(21294,plain,
% 293.32/185.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_3, c_g, s11) | (~node5(c_e_h_3, c_g, s11, s12)) | m_or_h_gate_v_out(c_e_h_3, c_g, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s12) | (~node5(c_e_h_3, c_g, s11, s12)) | node4(c_e_h_3, c_g, s11)))),
% 293.32/185.85 inference(monotonicity,[status(thm)],[21293])).
% 293.32/185.85 tff(21295,plain,
% 293.32/185.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_3, c_g, s11) | (~node5(c_e_h_3, c_g, s11, s12)) | m_or_h_gate_v_out(c_e_h_3, c_g, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | m_or_h_gate_v_out(c_e_h_3, c_g, s12) | (~node5(c_e_h_3, c_g, s11, s12)) | node4(c_e_h_3, c_g, s11))),
% 293.32/185.86 inference(transitivity,[status(thm)],[21294, 21292])).
% 293.32/185.86 tff(21296,plain,
% 293.32/185.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | (node4(c_e_h_3, c_g, s11) | (~node5(c_e_h_3, c_g, s11, s12)) | m_or_h_gate_v_out(c_e_h_3, c_g, s12))),
% 293.32/185.86 inference(quant_inst,[status(thm)],[])).
% 293.32/185.86 tff(21297,plain,
% 293.32/185.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node4(I0, I1, X) | (~node5(I0, I1, X, Y)) | m_or_h_gate_v_out(I0, I1, Y))) | m_or_h_gate_v_out(c_e_h_3, c_g, s12) | (~node5(c_e_h_3, c_g, s11, s12)) | node4(c_e_h_3, c_g, s11)),
% 293.32/185.86 inference(modus_ponens,[status(thm)],[21296, 21295])).
% 293.32/185.86 tff(21298,plain,
% 293.32/185.86 ($false),
% 293.32/185.86 inference(unit_resolution,[status(thm)],[21297, 5498, 21291, 21248, 21290])).
% 293.32/185.86 tff(21299,plain,((~node5(c_e_h_3, c_g, s11, s12)) | m_or_h_gate_v_out(c_e_h_3, c_g, s12) | node4(c_e_h_3, c_g, s11)), inference(lemma,lemma(discharge,[]))).
% 293.32/185.86 tff(21300,plain,
% 293.32/185.86 (~node5(c_e_h_3, c_g, s11, s12)),
% 293.32/185.86 inference(unit_resolution,[status(thm)],[21299, 21248, 21290])).
% 293.32/185.86 tff(21301,assumption,(node6(c_e_h_3, c_g, s11, s12)), introduced(assumption)).
% 293.32/185.86 tff(21302,plain,
% 293.32/185.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s12) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s11)) | (~node6(c_e_h_3, c_g, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | m_or_h_gate_v_out(c_e_h_3, c_g, s12) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s11)) | (~node6(c_e_h_3, c_g, s11, s12)))),
% 293.32/185.86 inference(rewrite,[status(thm)],[])).
% 293.32/185.86 tff(21303,plain,
% 293.32/185.86 ((m_or_h_gate_v_out(c_e_h_3, c_g, s12) | (~node6(c_e_h_3, c_g, s11, s12)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s11))) <=> (m_or_h_gate_v_out(c_e_h_3, c_g, s12) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s11)) | (~node6(c_e_h_3, c_g, s11, s12)))),
% 293.32/185.86 inference(rewrite,[status(thm)],[])).
% 293.32/185.86 tff(21304,plain,
% 293.32/185.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s12) | (~node6(c_e_h_3, c_g, s11, s12)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s12) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s11)) | (~node6(c_e_h_3, c_g, s11, s12))))),
% 293.32/185.86 inference(monotonicity,[status(thm)],[21303])).
% 293.32/185.86 tff(21305,plain,
% 293.32/185.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s12) | (~node6(c_e_h_3, c_g, s11, s12)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | m_or_h_gate_v_out(c_e_h_3, c_g, s12) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s11)) | (~node6(c_e_h_3, c_g, s11, s12)))),
% 293.32/185.86 inference(transitivity,[status(thm)],[21304, 21302])).
% 293.32/185.86 tff(21306,plain,
% 293.32/185.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | (m_or_h_gate_v_out(c_e_h_3, c_g, s12) | (~node6(c_e_h_3, c_g, s11, s12)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s11)))),
% 293.32/185.86 inference(quant_inst,[status(thm)],[])).
% 293.32/185.86 tff(21307,plain,
% 293.32/185.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_out(I0, I1, Y) | (~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, X)))) | m_or_h_gate_v_out(c_e_h_3, c_g, s12) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s11)) | (~node6(c_e_h_3, c_g, s11, s12))),
% 293.32/185.86 inference(modus_ponens,[status(thm)],[21306, 21305])).
% 293.32/185.86 tff(21308,plain,
% 293.32/185.86 ($false),
% 293.32/185.86 inference(unit_resolution,[status(thm)],[21307, 5474, 21301, 21249, 21248])).
% 293.32/185.86 tff(21309,plain,((~node6(c_e_h_3, c_g, s11, s12)) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s11)) | m_or_h_gate_v_out(c_e_h_3, c_g, s12)), inference(lemma,lemma(discharge,[]))).
% 293.32/185.86 tff(21310,plain,
% 293.32/185.86 (~node6(c_e_h_3, c_g, s11, s12)),
% 293.32/185.86 inference(unit_resolution,[status(thm)],[21309, 21248, 21249])).
% 293.32/185.86 tff(21311,plain,
% 293.32/185.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s11, s12)) | node6(c_e_h_3, c_g, s11, s12) | node5(c_e_h_3, c_g, s11, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s11, s12)) | node6(c_e_h_3, c_g, s11, s12) | node5(c_e_h_3, c_g, s11, s12))),
% 293.32/185.86 inference(rewrite,[status(thm)],[])).
% 293.32/185.86 tff(21312,plain,
% 293.32/185.86 ((node6(c_e_h_3, c_g, s11, s12) | node5(c_e_h_3, c_g, s11, s12) | (~trans(s11, s12))) <=> ((~trans(s11, s12)) | node6(c_e_h_3, c_g, s11, s12) | node5(c_e_h_3, c_g, s11, s12))),
% 293.32/185.86 inference(rewrite,[status(thm)],[])).
% 293.32/185.86 tff(21313,plain,
% 293.32/185.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s11, s12) | node5(c_e_h_3, c_g, s11, s12) | (~trans(s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s11, s12)) | node6(c_e_h_3, c_g, s11, s12) | node5(c_e_h_3, c_g, s11, s12)))),
% 293.32/185.86 inference(monotonicity,[status(thm)],[21312])).
% 293.32/185.86 tff(21314,plain,
% 293.32/185.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s11, s12) | node5(c_e_h_3, c_g, s11, s12) | (~trans(s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s11, s12)) | node6(c_e_h_3, c_g, s11, s12) | node5(c_e_h_3, c_g, s11, s12))),
% 293.32/185.86 inference(transitivity,[status(thm)],[21313, 21311])).
% 293.32/185.86 tff(21315,plain,
% 293.32/185.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_g, s11, s12) | node5(c_e_h_3, c_g, s11, s12) | (~trans(s11, s12)))),
% 293.32/185.86 inference(quant_inst,[status(thm)],[])).
% 293.32/185.86 tff(21316,plain,
% 293.32/185.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s11, s12)) | node6(c_e_h_3, c_g, s11, s12) | node5(c_e_h_3, c_g, s11, s12)),
% 293.32/185.86 inference(modus_ponens,[status(thm)],[21315, 21314])).
% 293.32/185.86 tff(21317,plain,
% 293.32/185.86 (node6(c_e_h_3, c_g, s11, s12) | node5(c_e_h_3, c_g, s11, s12)),
% 293.32/185.86 inference(unit_resolution,[status(thm)],[21316, 1141, 11461])).
% 293.32/185.86 tff(21318,plain,
% 293.32/185.86 ($false),
% 293.32/185.86 inference(unit_resolution,[status(thm)],[21317, 21310, 21300])).
% 293.32/185.86 tff(21319,plain,(m_or_h_gate_v_out(c_e_h_3, c_g, s12) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s11)) | node4(c_e_h_3, c_g, s11)), inference(lemma,lemma(discharge,[]))).
% 293.32/185.86 tff(21320,plain,
% 293.32/185.86 (node4(c_e_h_3, c_g, s11)),
% 293.32/185.86 inference(unit_resolution,[status(thm)],[21319, 21249, 21248])).
% 293.32/185.86 tff(21321,assumption,(m_or_h_gate_v_in1(c_e_h_3, c_g, s11)), introduced(assumption)).
% 293.32/185.86 tff(21322,assumption,(node4(c_e_h_3, c_g, s11)), introduced(assumption)).
% 293.32/185.86 tff(21323,plain,
% 293.32/185.86 (((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_g, s11)) | (~node4(c_e_h_3, c_g, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s11)) | (~node4(c_e_h_3, c_g, s11)))),
% 293.32/185.86 inference(rewrite,[status(thm)],[])).
% 293.32/185.86 tff(21324,plain,
% 293.32/185.86 ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_g, s11)) | (~node4(c_e_h_3, c_g, s11)))),
% 293.32/185.86 inference(quant_inst,[status(thm)],[])).
% 293.32/185.86 tff(21325,plain,
% 293.32/185.86 ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in1(I0, I1, X)) | (~node4(I0, I1, X)))) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s11)) | (~node4(c_e_h_3, c_g, s11))),
% 293.32/185.86 inference(modus_ponens,[status(thm)],[21324, 21323])).
% 293.32/185.86 tff(21326,plain,
% 293.32/185.86 ($false),
% 293.32/185.86 inference(unit_resolution,[status(thm)],[21325, 5516, 21322, 21321])).
% 293.32/185.86 tff(21327,plain,((~node4(c_e_h_3, c_g, s11)) | (~m_or_h_gate_v_in1(c_e_h_3, c_g, s11))), inference(lemma,lemma(discharge,[]))).
% 293.32/185.86 tff(21328,plain,
% 293.32/185.86 (~m_or_h_gate_v_in1(c_e_h_3, c_g, s11)),
% 293.32/185.86 inference(unit_resolution,[status(thm)],[21327, 21320])).
% 293.32/185.86 tff(21329,assumption,(~m_or_h_gate_v_in1(c_e_h_3, c_g, s11)), introduced(assumption)).
% 293.32/185.86 tff(21330,assumption,(m_and_h_gate_v_out(c_e_h_3, c_c, s11)), introduced(assumption)).
% 293.32/185.86 tff(21331,plain,
% 293.32/185.86 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s11)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s11))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s11)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s11))),
% 293.32/185.86 inference(rewrite,[status(thm)],[])).
% 293.32/185.86 tff(21332,plain,
% 293.32/185.86 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s11)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s11))),
% 293.32/185.86 inference(quant_inst,[status(thm)],[])).
% 293.32/185.86 tff(21333,plain,
% 293.32/185.86 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_or_h_gate_v_in1(I0, c_g, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s11)) | m_or_h_gate_v_in1(c_e_h_3, c_g, s11)),
% 293.32/185.86 inference(modus_ponens,[status(thm)],[21332, 21331])).
% 293.32/185.86 tff(21334,plain,
% 293.32/185.86 ($false),
% 293.32/185.86 inference(unit_resolution,[status(thm)],[21333, 5896, 21330, 21329])).
% 293.32/185.86 tff(21335,plain,(m_or_h_gate_v_in1(c_e_h_3, c_g, s11) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s11))), inference(lemma,lemma(discharge,[]))).
% 293.32/185.86 tff(21336,plain,
% 293.32/185.86 (~m_and_h_gate_v_out(c_e_h_3, c_c, s11)),
% 293.32/185.86 inference(unit_resolution,[status(thm)],[21335, 21328])).
% 293.32/185.86 tff(21337,assumption,(m_and_h_gate_v_out(c_e_h_3, c_c, s10)), introduced(assumption)).
% 293.32/185.86 tff(21338,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_c, s11)), introduced(assumption)).
% 293.32/185.86 tff(21339,assumption,(m_and_h_gate_v_out(c_e_h_3, c_q, s9)), introduced(assumption)).
% 293.32/185.86 tff(21340,assumption,(node22(c_e_h_3, c_q, s8, s9)), introduced(assumption)).
% 293.32/185.86 tff(21341,plain,
% 293.32/185.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s9)) | (~node22(c_e_h_3, c_q, s8, s9)) | m_and_h_gate_v_out(c_e_h_3, c_q, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s9)) | (~node22(c_e_h_3, c_q, s8, s9)) | m_and_h_gate_v_out(c_e_h_3, c_q, s8))),
% 293.32/185.86 inference(rewrite,[status(thm)],[])).
% 293.32/185.86 tff(21342,plain,
% 293.32/185.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s9)) | (~node22(c_e_h_3, c_q, s8, s9)) | m_and_h_gate_v_out(c_e_h_3, c_q, s8))),
% 293.32/185.86 inference(quant_inst,[status(thm)],[])).
% 293.32/185.86 tff(21343,plain,
% 293.32/185.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s9)) | (~node22(c_e_h_3, c_q, s8, s9)) | m_and_h_gate_v_out(c_e_h_3, c_q, s8)),
% 293.32/185.86 inference(modus_ponens,[status(thm)],[21342, 21341])).
% 293.32/185.86 tff(21344,plain,
% 293.32/185.86 ($false),
% 293.32/185.86 inference(unit_resolution,[status(thm)],[21343, 108, 21339, 20424, 21340])).
% 293.32/185.86 tff(21345,plain,((~node22(c_e_h_3, c_q, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s9))), inference(lemma,lemma(discharge,[]))).
% 293.32/185.86 tff(21346,plain,
% 293.32/185.86 (~node22(c_e_h_3, c_q, s8, s9)),
% 293.32/185.86 inference(unit_resolution,[status(thm)],[21345, 21339])).
% 293.32/185.86 tff(21347,plain,
% 293.32/185.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s8, s9)) | node21(c_e_h_3, c_q, s8, s9) | node22(c_e_h_3, c_q, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_3, c_q, s8, s9) | node22(c_e_h_3, c_q, s8, s9))),
% 293.32/185.86 inference(rewrite,[status(thm)],[])).
% 293.32/185.86 tff(21348,plain,
% 293.32/185.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s8, s9)) | node21(c_e_h_3, c_q, s8, s9) | node22(c_e_h_3, c_q, s8, s9))),
% 293.32/185.86 inference(quant_inst,[status(thm)],[])).
% 293.32/185.87 tff(21349,plain,
% 293.32/185.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_3, c_q, s8, s9) | node22(c_e_h_3, c_q, s8, s9)),
% 293.32/185.87 inference(modus_ponens,[status(thm)],[21348, 21347])).
% 293.32/185.87 tff(21350,plain,
% 293.32/185.87 (node21(c_e_h_3, c_q, s8, s9) | node22(c_e_h_3, c_q, s8, s9)),
% 293.32/185.87 inference(unit_resolution,[status(thm)],[21349, 82, 1993])).
% 293.32/185.87 tff(21351,plain,
% 293.32/185.87 (node21(c_e_h_3, c_q, s8, s9)),
% 293.32/185.87 inference(unit_resolution,[status(thm)],[21350, 21346])).
% 293.32/185.87 tff(21352,plain,
% 293.32/185.87 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s8)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s8)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8))),
% 293.32/185.87 inference(rewrite,[status(thm)],[])).
% 293.32/185.87 tff(21353,plain,
% 293.32/185.87 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s8)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8))),
% 293.32/185.87 inference(quant_inst,[status(thm)],[])).
% 293.32/185.87 tff(21354,plain,
% 293.32/185.87 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s8)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s8)),
% 293.32/185.87 inference(modus_ponens,[status(thm)],[21353, 21352])).
% 293.32/185.87 tff(21355,plain,
% 293.32/185.87 (~m_and_h_gate_v_in2(c_e_h_3, c_q, s8)),
% 293.32/185.87 inference(unit_resolution,[status(thm)],[21354, 5621, 13033])).
% 293.32/185.87 tff(21356,plain,
% 293.32/185.87 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s8)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s8)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s8))),
% 293.32/185.87 inference(rewrite,[status(thm)],[])).
% 293.32/185.87 tff(21357,plain,
% 293.32/185.87 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s8)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s8))),
% 293.32/185.87 inference(quant_inst,[status(thm)],[])).
% 293.32/185.87 tff(21358,plain,
% 293.32/185.87 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s8)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s8)),
% 293.32/185.87 inference(modus_ponens,[status(thm)],[21357, 21356])).
% 293.32/185.87 tff(21359,plain,
% 293.32/185.87 (~node20(c_e_h_3, c_q, s8)),
% 293.32/185.87 inference(unit_resolution,[status(thm)],[21358, 4563, 21355])).
% 293.32/185.87 tff(21360,plain,
% 293.32/185.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s9)) | node20(c_e_h_3, c_q, s8) | (~node21(c_e_h_3, c_q, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s9)) | node20(c_e_h_3, c_q, s8) | (~node21(c_e_h_3, c_q, s8, s9)))),
% 293.32/185.87 inference(rewrite,[status(thm)],[])).
% 293.32/185.87 tff(21361,plain,
% 293.32/185.87 ((node20(c_e_h_3, c_q, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s9)) | (~node21(c_e_h_3, c_q, s8, s9))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_q, s9)) | node20(c_e_h_3, c_q, s8) | (~node21(c_e_h_3, c_q, s8, s9)))),
% 293.32/185.87 inference(rewrite,[status(thm)],[])).
% 293.32/185.87 tff(21362,plain,
% 293.32/185.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s9)) | (~node21(c_e_h_3, c_q, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s9)) | node20(c_e_h_3, c_q, s8) | (~node21(c_e_h_3, c_q, s8, s9))))),
% 293.32/185.87 inference(monotonicity,[status(thm)],[21361])).
% 293.32/185.87 tff(21363,plain,
% 293.32/185.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s9)) | (~node21(c_e_h_3, c_q, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s9)) | node20(c_e_h_3, c_q, s8) | (~node21(c_e_h_3, c_q, s8, s9)))),
% 293.32/185.87 inference(transitivity,[status(thm)],[21362, 21360])).
% 293.32/185.87 tff(21364,plain,
% 293.32/185.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s9)) | (~node21(c_e_h_3, c_q, s8, s9)))),
% 293.32/185.87 inference(quant_inst,[status(thm)],[])).
% 293.32/185.87 tff(21365,plain,
% 293.32/185.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s9)) | node20(c_e_h_3, c_q, s8) | (~node21(c_e_h_3, c_q, s8, s9))),
% 293.32/185.87 inference(modus_ponens,[status(thm)],[21364, 21363])).
% 293.32/185.87 tff(21366,plain,
% 293.32/185.87 ($false),
% 293.32/185.87 inference(unit_resolution,[status(thm)],[21365, 52, 21339, 21359, 21351])).
% 293.32/185.87 tff(21367,plain,(~m_and_h_gate_v_out(c_e_h_3, c_q, s9)), inference(lemma,lemma(discharge,[]))).
% 293.32/185.87 tff(21368,plain,
% 293.32/185.87 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s9)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s9)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9))),
% 293.32/185.87 inference(rewrite,[status(thm)],[])).
% 293.32/185.87 tff(21369,plain,
% 293.32/185.87 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s9)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9))),
% 293.32/185.87 inference(quant_inst,[status(thm)],[])).
% 293.32/185.87 tff(21370,plain,
% 293.32/185.87 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s9)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s9)),
% 293.32/185.87 inference(modus_ponens,[status(thm)],[21369, 21368])).
% 293.32/185.87 tff(21371,plain,
% 293.32/185.87 (~m_and_h_gate_v_in2(c_e_h_3, c_q, s9)),
% 293.32/185.87 inference(unit_resolution,[status(thm)],[21370, 5621, 13061])).
% 293.32/185.87 tff(21372,plain,
% 293.32/185.87 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s9)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s9))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s9)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s9))),
% 293.32/185.87 inference(rewrite,[status(thm)],[])).
% 293.32/185.87 tff(21373,plain,
% 293.32/185.87 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s9)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s9))),
% 293.32/185.87 inference(quant_inst,[status(thm)],[])).
% 293.32/185.87 tff(21374,plain,
% 293.32/185.87 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s9)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s9)),
% 293.32/185.87 inference(modus_ponens,[status(thm)],[21373, 21372])).
% 293.32/185.87 tff(21375,plain,
% 293.32/185.87 (~node20(c_e_h_3, c_q, s9)),
% 293.32/185.87 inference(unit_resolution,[status(thm)],[21374, 4563, 21371])).
% 293.32/185.87 tff(21376,assumption,(~node20(c_e_h_3, c_q, s9)), introduced(assumption)).
% 293.32/185.87 tff(21377,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_q, s9)), introduced(assumption)).
% 293.32/185.87 tff(21378,assumption,(m_and_h_gate_v_out(c_e_h_3, c_q, s10)), introduced(assumption)).
% 293.32/185.87 tff(21379,assumption,(node22(c_e_h_3, c_q, s9, s10)), introduced(assumption)).
% 293.32/185.87 tff(21380,plain,
% 293.32/185.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s10)) | (~node22(c_e_h_3, c_q, s9, s10)) | m_and_h_gate_v_out(c_e_h_3, c_q, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s10)) | (~node22(c_e_h_3, c_q, s9, s10)) | m_and_h_gate_v_out(c_e_h_3, c_q, s9))),
% 293.32/185.88 inference(rewrite,[status(thm)],[])).
% 293.32/185.88 tff(21381,plain,
% 293.32/185.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s10)) | (~node22(c_e_h_3, c_q, s9, s10)) | m_and_h_gate_v_out(c_e_h_3, c_q, s9))),
% 293.32/185.88 inference(quant_inst,[status(thm)],[])).
% 293.32/185.88 tff(21382,plain,
% 293.32/185.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s10)) | (~node22(c_e_h_3, c_q, s9, s10)) | m_and_h_gate_v_out(c_e_h_3, c_q, s9)),
% 293.32/185.88 inference(modus_ponens,[status(thm)],[21381, 21380])).
% 293.32/185.88 tff(21383,plain,
% 293.32/185.88 ($false),
% 293.32/185.88 inference(unit_resolution,[status(thm)],[21382, 108, 21377, 21378, 21379])).
% 293.32/185.88 tff(21384,plain,((~node22(c_e_h_3, c_q, s9, s10)) | m_and_h_gate_v_out(c_e_h_3, c_q, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s10))), inference(lemma,lemma(discharge,[]))).
% 293.32/185.88 tff(21385,plain,
% 293.32/185.88 (~node22(c_e_h_3, c_q, s9, s10)),
% 293.32/185.88 inference(unit_resolution,[status(thm)],[21384, 21378, 21377])).
% 293.32/185.88 tff(21386,plain,
% 293.32/185.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s9, s10)) | node21(c_e_h_3, c_q, s9, s10) | node22(c_e_h_3, c_q, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s9, s10)) | node21(c_e_h_3, c_q, s9, s10) | node22(c_e_h_3, c_q, s9, s10))),
% 293.32/185.88 inference(rewrite,[status(thm)],[])).
% 293.32/185.88 tff(21387,plain,
% 293.32/185.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s9, s10)) | node21(c_e_h_3, c_q, s9, s10) | node22(c_e_h_3, c_q, s9, s10))),
% 293.32/185.88 inference(quant_inst,[status(thm)],[])).
% 293.32/185.88 tff(21388,plain,
% 293.32/185.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s9, s10)) | node21(c_e_h_3, c_q, s9, s10) | node22(c_e_h_3, c_q, s9, s10)),
% 293.32/185.88 inference(modus_ponens,[status(thm)],[21387, 21386])).
% 293.32/185.88 tff(21389,plain,
% 293.32/185.88 (node21(c_e_h_3, c_q, s9, s10) | node22(c_e_h_3, c_q, s9, s10)),
% 293.32/185.88 inference(unit_resolution,[status(thm)],[21388, 82, 7676])).
% 293.32/185.88 tff(21390,plain,
% 293.32/185.88 (node21(c_e_h_3, c_q, s9, s10)),
% 293.32/185.88 inference(unit_resolution,[status(thm)],[21389, 21385])).
% 293.32/185.88 tff(21391,plain,
% 293.32/185.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s10)) | node20(c_e_h_3, c_q, s9) | (~node21(c_e_h_3, c_q, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s10)) | node20(c_e_h_3, c_q, s9) | (~node21(c_e_h_3, c_q, s9, s10)))),
% 293.32/185.88 inference(rewrite,[status(thm)],[])).
% 293.32/185.88 tff(21392,plain,
% 293.32/185.88 ((node20(c_e_h_3, c_q, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s10)) | (~node21(c_e_h_3, c_q, s9, s10))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_q, s10)) | node20(c_e_h_3, c_q, s9) | (~node21(c_e_h_3, c_q, s9, s10)))),
% 293.32/185.88 inference(rewrite,[status(thm)],[])).
% 293.32/185.88 tff(21393,plain,
% 293.32/185.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s10)) | (~node21(c_e_h_3, c_q, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s10)) | node20(c_e_h_3, c_q, s9) | (~node21(c_e_h_3, c_q, s9, s10))))),
% 293.32/185.88 inference(monotonicity,[status(thm)],[21392])).
% 293.32/185.88 tff(21394,plain,
% 293.32/185.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s10)) | (~node21(c_e_h_3, c_q, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s10)) | node20(c_e_h_3, c_q, s9) | (~node21(c_e_h_3, c_q, s9, s10)))),
% 293.32/185.88 inference(transitivity,[status(thm)],[21393, 21391])).
% 293.32/185.88 tff(21395,plain,
% 293.32/185.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s10)) | (~node21(c_e_h_3, c_q, s9, s10)))),
% 293.32/185.88 inference(quant_inst,[status(thm)],[])).
% 293.32/185.88 tff(21396,plain,
% 293.32/185.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s10)) | node20(c_e_h_3, c_q, s9) | (~node21(c_e_h_3, c_q, s9, s10))),
% 293.32/185.88 inference(modus_ponens,[status(thm)],[21395, 21394])).
% 293.32/185.88 tff(21397,plain,
% 293.32/185.88 ($false),
% 293.32/185.88 inference(unit_resolution,[status(thm)],[21396, 52, 21378, 21390, 21376])).
% 293.32/185.88 tff(21398,plain,((~m_and_h_gate_v_out(c_e_h_3, c_q, s10)) | node20(c_e_h_3, c_q, s9) | m_and_h_gate_v_out(c_e_h_3, c_q, s9)), inference(lemma,lemma(discharge,[]))).
% 293.32/185.88 tff(21399,plain,
% 293.32/185.88 ((~m_and_h_gate_v_out(c_e_h_3, c_q, s10)) | m_and_h_gate_v_out(c_e_h_3, c_q, s9)),
% 293.32/185.88 inference(unit_resolution,[status(thm)],[21398, 21375])).
% 293.32/185.88 tff(21400,plain,
% 293.32/185.88 (~m_and_h_gate_v_out(c_e_h_3, c_q, s10)),
% 293.32/185.88 inference(unit_resolution,[status(thm)],[21399, 21367])).
% 293.32/185.88 tff(21401,plain,
% 293.32/185.88 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s10))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s10))),
% 293.32/185.88 inference(rewrite,[status(thm)],[])).
% 293.32/185.88 tff(21402,plain,
% 293.32/185.88 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s10))),
% 293.32/185.88 inference(quant_inst,[status(thm)],[])).
% 293.32/185.88 tff(21403,plain,
% 293.32/185.88 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s10)),
% 293.32/185.88 inference(modus_ponens,[status(thm)],[21402, 21401])).
% 293.32/185.88 tff(21404,plain,
% 293.32/185.88 (node3(c_e_h_3, c_e_h_1, s10)),
% 293.32/185.88 inference(unit_resolution,[status(thm)],[21403, 2922, 1056])).
% 293.32/185.88 tff(21405,plain,
% 293.32/185.88 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s10)) | (~node3(c_e_h_3, c_e_h_1, s10)) | m_and_h_gate_v_out(c_e_h_3, c_q, s10))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s10)) | (~node3(c_e_h_3, c_e_h_1, s10)) | m_and_h_gate_v_out(c_e_h_3, c_q, s10))),
% 293.32/185.88 inference(rewrite,[status(thm)],[])).
% 293.32/185.88 tff(21406,plain,
% 293.32/185.88 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s10)) | (~node3(c_e_h_3, c_e_h_1, s10)) | m_and_h_gate_v_out(c_e_h_3, c_q, s10))),
% 293.32/185.88 inference(quant_inst,[status(thm)],[])).
% 293.32/185.88 tff(21407,plain,
% 293.32/185.88 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s10)) | (~node3(c_e_h_3, c_e_h_1, s10)) | m_and_h_gate_v_out(c_e_h_3, c_q, s10)),
% 293.32/185.88 inference(modus_ponens,[status(thm)],[21406, 21405])).
% 293.32/185.88 tff(21408,plain,
% 293.32/185.88 ((~m_cell_v_ack(c_e_h_1, s10)) | m_and_h_gate_v_out(c_e_h_3, c_q, s10)),
% 293.32/185.88 inference(unit_resolution,[status(thm)],[21407, 1073, 21404])).
% 293.32/185.88 tff(21409,plain,
% 293.32/185.88 (~m_cell_v_ack(c_e_h_1, s10)),
% 293.32/185.88 inference(unit_resolution,[status(thm)],[21408, 21400])).
% 293.32/185.88 tff(21410,plain,
% 293.32/185.88 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node2(c_e_h_3, c_e_h_1, s10))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node2(c_e_h_3, c_e_h_1, s10))),
% 293.32/185.88 inference(rewrite,[status(thm)],[])).
% 293.32/185.88 tff(21411,plain,
% 293.32/185.88 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node2(c_e_h_3, c_e_h_1, s10))),
% 293.32/185.88 inference(quant_inst,[status(thm)],[])).
% 293.32/185.88 tff(21412,plain,
% 293.32/185.88 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node2(c_e_h_3, c_e_h_1, s10)),
% 293.32/185.88 inference(modus_ponens,[status(thm)],[21411, 21410])).
% 293.32/185.88 tff(21413,plain,
% 293.32/185.88 (node2(c_e_h_3, c_e_h_1, s10)),
% 293.32/185.88 inference(unit_resolution,[status(thm)],[21412, 2922, 5821])).
% 293.32/185.88 tff(21414,plain,
% 293.32/185.88 (((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | ((~node2(c_e_h_3, c_e_h_1, s10)) | m_cell_v_ack(c_e_h_1, s10) | m_and_h_gate_v_in2(c_e_h_3, c_c, s10))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | (~node2(c_e_h_3, c_e_h_1, s10)) | m_cell_v_ack(c_e_h_1, s10) | m_and_h_gate_v_in2(c_e_h_3, c_c, s10))),
% 293.32/185.88 inference(rewrite,[status(thm)],[])).
% 293.32/185.88 tff(21415,plain,
% 293.32/185.88 ((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | ((~node2(c_e_h_3, c_e_h_1, s10)) | m_cell_v_ack(c_e_h_1, s10) | m_and_h_gate_v_in2(c_e_h_3, c_c, s10))),
% 293.32/185.88 inference(quant_inst,[status(thm)],[])).
% 293.32/185.88 tff(21416,plain,
% 293.32/185.88 ((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | (~node2(c_e_h_3, c_e_h_1, s10)) | m_cell_v_ack(c_e_h_1, s10) | m_and_h_gate_v_in2(c_e_h_3, c_c, s10)),
% 293.32/185.88 inference(modus_ponens,[status(thm)],[21415, 21414])).
% 293.32/185.88 tff(21417,plain,
% 293.32/185.88 (m_cell_v_ack(c_e_h_1, s10) | m_and_h_gate_v_in2(c_e_h_3, c_c, s10)),
% 293.32/185.88 inference(unit_resolution,[status(thm)],[21416, 5835, 21413])).
% 293.32/185.88 tff(21418,plain,
% 293.32/185.88 (m_and_h_gate_v_in2(c_e_h_3, c_c, s10)),
% 293.32/185.88 inference(unit_resolution,[status(thm)],[21417, 21409])).
% 293.32/185.88 tff(21419,assumption,(node22(c_e_h_3, c_c, s10, s11)), introduced(assumption)).
% 293.32/185.88 tff(21420,plain,
% 293.32/185.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_c, s11) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s10)) | (~node22(c_e_h_3, c_c, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | m_and_h_gate_v_out(c_e_h_3, c_c, s11) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s10)) | (~node22(c_e_h_3, c_c, s10, s11)))),
% 293.32/185.88 inference(rewrite,[status(thm)],[])).
% 293.32/185.88 tff(21421,plain,
% 293.32/185.88 ((m_and_h_gate_v_out(c_e_h_3, c_c, s11) | (~node22(c_e_h_3, c_c, s10, s11)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s10))) <=> (m_and_h_gate_v_out(c_e_h_3, c_c, s11) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s10)) | (~node22(c_e_h_3, c_c, s10, s11)))),
% 293.32/185.88 inference(rewrite,[status(thm)],[])).
% 293.32/185.88 tff(21422,plain,
% 293.32/185.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_c, s11) | (~node22(c_e_h_3, c_c, s10, s11)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_c, s11) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s10)) | (~node22(c_e_h_3, c_c, s10, s11))))),
% 293.32/185.88 inference(monotonicity,[status(thm)],[21421])).
% 293.32/185.88 tff(21423,plain,
% 293.32/185.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_c, s11) | (~node22(c_e_h_3, c_c, s10, s11)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | m_and_h_gate_v_out(c_e_h_3, c_c, s11) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s10)) | (~node22(c_e_h_3, c_c, s10, s11)))),
% 293.32/185.88 inference(transitivity,[status(thm)],[21422, 21420])).
% 293.32/185.88 tff(21424,plain,
% 293.32/185.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_c, s11) | (~node22(c_e_h_3, c_c, s10, s11)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s10)))),
% 293.39/185.89 inference(quant_inst,[status(thm)],[])).
% 293.39/185.89 tff(21425,plain,
% 293.39/185.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | m_and_h_gate_v_out(c_e_h_3, c_c, s11) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s10)) | (~node22(c_e_h_3, c_c, s10, s11))),
% 293.39/185.89 inference(modus_ponens,[status(thm)],[21424, 21423])).
% 293.39/185.89 tff(21426,plain,
% 293.39/185.89 ($false),
% 293.39/185.89 inference(unit_resolution,[status(thm)],[21425, 5871, 21337, 21338, 21419])).
% 293.39/185.89 tff(21427,plain,((~node22(c_e_h_3, c_c, s10, s11)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s10)) | m_and_h_gate_v_out(c_e_h_3, c_c, s11)), inference(lemma,lemma(discharge,[]))).
% 293.39/185.89 tff(21428,plain,
% 293.39/185.89 (~node22(c_e_h_3, c_c, s10, s11)),
% 293.39/185.89 inference(unit_resolution,[status(thm)],[21427, 21338, 21337])).
% 293.39/185.89 tff(21429,assumption,(m_and_h_gate_v_in2(c_e_h_3, c_c, s10)), introduced(assumption)).
% 293.39/185.89 tff(21430,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_c, s10)), introduced(assumption)).
% 293.39/185.89 tff(21431,assumption,(node21(c_e_h_3, c_c, s10, s11)), introduced(assumption)).
% 293.39/185.89 tff(21432,plain,
% 293.39/185.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_c, s10)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s10)) | m_and_h_gate_v_out(c_e_h_3, c_c, s11) | (~node21(c_e_h_3, c_c, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s10)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s10)) | m_and_h_gate_v_out(c_e_h_3, c_c, s11) | (~node21(c_e_h_3, c_c, s10, s11)))),
% 293.39/185.89 inference(rewrite,[status(thm)],[])).
% 293.39/185.89 tff(21433,plain,
% 293.39/185.89 (((~node21(c_e_h_3, c_c, s10, s11)) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s10)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s10)) | m_and_h_gate_v_out(c_e_h_3, c_c, s11)) <=> ((~m_and_h_gate_v_in2(c_e_h_3, c_c, s10)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s10)) | m_and_h_gate_v_out(c_e_h_3, c_c, s11) | (~node21(c_e_h_3, c_c, s10, s11)))),
% 293.39/185.89 inference(rewrite,[status(thm)],[])).
% 293.39/185.89 tff(21434,plain,
% 293.39/185.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_c, s10, s11)) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s10)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s10)) | m_and_h_gate_v_out(c_e_h_3, c_c, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_c, s10)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s10)) | m_and_h_gate_v_out(c_e_h_3, c_c, s11) | (~node21(c_e_h_3, c_c, s10, s11))))),
% 293.39/185.89 inference(monotonicity,[status(thm)],[21433])).
% 293.39/185.89 tff(21435,plain,
% 293.39/185.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_c, s10, s11)) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s10)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s10)) | m_and_h_gate_v_out(c_e_h_3, c_c, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s10)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s10)) | m_and_h_gate_v_out(c_e_h_3, c_c, s11) | (~node21(c_e_h_3, c_c, s10, s11)))),
% 293.39/185.89 inference(transitivity,[status(thm)],[21434, 21432])).
% 293.39/185.89 tff(21436,plain,
% 293.39/185.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_c, s10, s11)) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s10)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s10)) | m_and_h_gate_v_out(c_e_h_3, c_c, s11))),
% 293.39/185.89 inference(quant_inst,[status(thm)],[])).
% 293.39/185.89 tff(21437,plain,
% 293.39/185.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s10)) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s10)) | m_and_h_gate_v_out(c_e_h_3, c_c, s11) | (~node21(c_e_h_3, c_c, s10, s11))),
% 293.39/185.89 inference(modus_ponens,[status(thm)],[21436, 21435])).
% 293.39/185.89 tff(21438,plain,
% 293.39/185.89 ($false),
% 293.39/185.89 inference(unit_resolution,[status(thm)],[21437, 5851, 21429, 21338, 21431, 21430])).
% 293.39/185.89 tff(21439,plain,((~node21(c_e_h_3, c_c, s10, s11)) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s10)) | m_and_h_gate_v_out(c_e_h_3, c_c, s11) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s10))), inference(lemma,lemma(discharge,[]))).
% 293.39/185.89 tff(21440,plain,
% 293.39/185.89 (~node21(c_e_h_3, c_c, s10, s11)),
% 293.39/185.89 inference(unit_resolution,[status(thm)],[21439, 21338, 21430, 21429])).
% 293.39/185.89 tff(21441,plain,
% 293.39/185.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s10, s11)) | node21(c_e_h_3, c_c, s10, s11) | node22(c_e_h_3, c_c, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s10, s11)) | node21(c_e_h_3, c_c, s10, s11) | node22(c_e_h_3, c_c, s10, s11))),
% 293.39/185.89 inference(rewrite,[status(thm)],[])).
% 293.39/185.89 tff(21442,plain,
% 293.39/185.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s10, s11)) | node21(c_e_h_3, c_c, s10, s11) | node22(c_e_h_3, c_c, s10, s11))),
% 293.39/185.89 inference(quant_inst,[status(thm)],[])).
% 293.39/185.89 tff(21443,plain,
% 293.39/185.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s10, s11)) | node21(c_e_h_3, c_c, s10, s11) | node22(c_e_h_3, c_c, s10, s11)),
% 293.39/185.89 inference(modus_ponens,[status(thm)],[21442, 21441])).
% 293.39/185.89 tff(21444,plain,
% 293.39/185.89 (node21(c_e_h_3, c_c, s10, s11) | node22(c_e_h_3, c_c, s10, s11)),
% 293.39/185.89 inference(unit_resolution,[status(thm)],[21443, 82, 7748])).
% 293.39/185.89 tff(21445,plain,
% 293.39/185.89 ($false),
% 293.39/185.89 inference(unit_resolution,[status(thm)],[21444, 21440, 21428])).
% 293.39/185.89 tff(21446,plain,(m_and_h_gate_v_out(c_e_h_3, c_c, s11) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s10)) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s10)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s10))), inference(lemma,lemma(discharge,[]))).
% 293.39/185.89 tff(21447,plain,
% 293.39/185.89 (m_and_h_gate_v_out(c_e_h_3, c_c, s11) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s10)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s10))),
% 293.39/185.89 inference(unit_resolution,[status(thm)],[21446, 21418])).
% 293.39/185.89 tff(21448,plain,
% 293.39/185.89 (~m_and_h_gate_v_in1(c_e_h_3, c_c, s10)),
% 293.39/185.89 inference(unit_resolution,[status(thm)],[21447, 21338, 21337])).
% 293.39/185.89 tff(21449,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_c, s10)), introduced(assumption)).
% 293.39/185.89 tff(21450,plain,
% 293.39/185.89 (((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s10)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s10))) <=> ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s10)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s10))),
% 293.39/185.89 inference(rewrite,[status(thm)],[])).
% 293.39/185.89 tff(21451,plain,
% 293.39/185.89 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s10)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s10))),
% 293.39/185.89 inference(quant_inst,[status(thm)],[])).
% 293.39/185.89 tff(21452,plain,
% 293.39/185.89 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s10)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s10)),
% 293.39/185.89 inference(modus_ponens,[status(thm)],[21451, 21450])).
% 293.39/185.89 tff(21453,plain,
% 293.39/185.89 ($false),
% 293.39/185.89 inference(unit_resolution,[status(thm)],[21452, 2556, 19735, 21449])).
% 293.39/185.89 tff(21454,plain,(m_and_h_gate_v_in1(c_e_h_3, c_c, s10) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s10))), inference(lemma,lemma(discharge,[]))).
% 293.39/185.89 tff(21455,plain,
% 293.39/185.89 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s10)),
% 293.39/185.89 inference(unit_resolution,[status(thm)],[21454, 21448])).
% 293.39/185.89 tff(21456,assumption,(~node20(c_e_h_3, c_c, s9)), introduced(assumption)).
% 293.39/185.89 tff(21457,assumption,(node21(c_e_h_3, c_c, s9, s10)), introduced(assumption)).
% 293.39/185.89 tff(21458,plain,
% 293.39/185.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_c, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s10)) | (~node21(c_e_h_3, c_c, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_c, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s10)) | (~node21(c_e_h_3, c_c, s9, s10)))),
% 293.39/185.89 inference(rewrite,[status(thm)],[])).
% 293.39/185.89 tff(21459,plain,
% 293.39/185.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_c, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s10)) | (~node21(c_e_h_3, c_c, s9, s10)))),
% 293.39/185.89 inference(quant_inst,[status(thm)],[])).
% 293.39/185.89 tff(21460,plain,
% 293.39/185.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_c, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s10)) | (~node21(c_e_h_3, c_c, s9, s10))),
% 293.39/185.89 inference(modus_ponens,[status(thm)],[21459, 21458])).
% 293.39/185.89 tff(21461,plain,
% 293.39/185.89 ($false),
% 293.39/185.89 inference(unit_resolution,[status(thm)],[21460, 52, 21457, 21456, 21337])).
% 293.39/185.89 tff(21462,plain,((~node21(c_e_h_3, c_c, s9, s10)) | node20(c_e_h_3, c_c, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s10))), inference(lemma,lemma(discharge,[]))).
% 293.39/185.89 tff(21463,plain,
% 293.39/185.89 (~node21(c_e_h_3, c_c, s9, s10)),
% 293.39/185.89 inference(unit_resolution,[status(thm)],[21462, 21337, 21456])).
% 293.39/185.89 tff(21464,plain,
% 293.39/185.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s9, s10)) | node21(c_e_h_3, c_c, s9, s10) | node22(c_e_h_3, c_c, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s9, s10)) | node21(c_e_h_3, c_c, s9, s10) | node22(c_e_h_3, c_c, s9, s10))),
% 293.39/185.89 inference(rewrite,[status(thm)],[])).
% 293.39/185.89 tff(21465,plain,
% 293.39/185.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s9, s10)) | node21(c_e_h_3, c_c, s9, s10) | node22(c_e_h_3, c_c, s9, s10))),
% 293.39/185.89 inference(quant_inst,[status(thm)],[])).
% 293.39/185.89 tff(21466,plain,
% 293.39/185.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s9, s10)) | node21(c_e_h_3, c_c, s9, s10) | node22(c_e_h_3, c_c, s9, s10)),
% 293.39/185.89 inference(modus_ponens,[status(thm)],[21465, 21464])).
% 293.39/185.89 tff(21467,plain,
% 293.39/185.89 (node21(c_e_h_3, c_c, s9, s10) | node22(c_e_h_3, c_c, s9, s10)),
% 293.39/185.89 inference(unit_resolution,[status(thm)],[21466, 82, 7676])).
% 293.39/185.89 tff(21468,plain,
% 293.39/185.89 (node22(c_e_h_3, c_c, s9, s10)),
% 293.39/185.89 inference(unit_resolution,[status(thm)],[21467, 21463])).
% 293.39/185.89 tff(21469,assumption,(node22(c_e_h_3, c_c, s9, s10)), introduced(assumption)).
% 293.39/185.89 tff(21470,plain,
% 293.39/185.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s10)) | (~node22(c_e_h_3, c_c, s9, s10)) | m_and_h_gate_v_out(c_e_h_3, c_c, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s10)) | (~node22(c_e_h_3, c_c, s9, s10)) | m_and_h_gate_v_out(c_e_h_3, c_c, s9))),
% 293.39/185.89 inference(rewrite,[status(thm)],[])).
% 293.39/185.89 tff(21471,plain,
% 293.39/185.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s10)) | (~node22(c_e_h_3, c_c, s9, s10)) | m_and_h_gate_v_out(c_e_h_3, c_c, s9))),
% 293.39/185.89 inference(quant_inst,[status(thm)],[])).
% 293.39/185.89 tff(21472,plain,
% 293.39/185.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s10)) | (~node22(c_e_h_3, c_c, s9, s10)) | m_and_h_gate_v_out(c_e_h_3, c_c, s9)),
% 293.39/185.90 inference(modus_ponens,[status(thm)],[21471, 21470])).
% 293.39/185.90 tff(21473,plain,
% 293.39/185.90 ($false),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[21472, 108, 21469, 21337, 20345])).
% 293.39/185.90 tff(21474,plain,((~node22(c_e_h_3, c_c, s9, s10)) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s10)) | m_and_h_gate_v_out(c_e_h_3, c_c, s9)), inference(lemma,lemma(discharge,[]))).
% 293.39/185.90 tff(21475,plain,
% 293.39/185.90 (m_and_h_gate_v_out(c_e_h_3, c_c, s9)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[21474, 21468, 21337])).
% 293.39/185.90 tff(21476,plain,
% 293.39/185.90 (~m_and_h_gate_v_in1(c_e_h_3, c_c, s10)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[21446, 21337, 21429, 21338])).
% 293.39/185.90 tff(21477,plain,
% 293.39/185.90 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s10)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[21454, 21476])).
% 293.39/185.90 tff(21478,plain,
% 293.39/185.90 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s9)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[19733, 21477])).
% 293.39/185.90 tff(21479,plain,
% 293.39/185.90 (~m_and_h_gate_v_out(c_e_h_3, c_c, s5)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[10330, 2512])).
% 293.39/185.90 tff(21480,plain,
% 293.39/185.90 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s5)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[10210, 1440, 2512])).
% 293.39/185.90 tff(21481,assumption,(~node20(c_e_h_3, c_c, s8)), introduced(assumption)).
% 293.39/185.90 tff(21482,plain,
% 293.39/185.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s9)) | (~node22(c_e_h_3, c_c, s8, s9)) | m_and_h_gate_v_out(c_e_h_3, c_c, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s9)) | (~node22(c_e_h_3, c_c, s8, s9)) | m_and_h_gate_v_out(c_e_h_3, c_c, s8))),
% 293.39/185.90 inference(rewrite,[status(thm)],[])).
% 293.39/185.90 tff(21483,plain,
% 293.39/185.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_c, s9)) | (~node22(c_e_h_3, c_c, s8, s9)) | m_and_h_gate_v_out(c_e_h_3, c_c, s8))),
% 293.39/185.90 inference(quant_inst,[status(thm)],[])).
% 293.39/185.90 tff(21484,plain,
% 293.39/185.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s9)) | (~node22(c_e_h_3, c_c, s8, s9)) | m_and_h_gate_v_out(c_e_h_3, c_c, s8)),
% 293.39/185.90 inference(modus_ponens,[status(thm)],[21483, 21482])).
% 293.39/185.90 tff(21485,plain,
% 293.39/185.90 ($false),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[21484, 108, 20119, 20347, 20474])).
% 293.39/185.90 tff(21486,plain,((~node22(c_e_h_3, c_c, s8, s9)) | m_and_h_gate_v_out(c_e_h_3, c_c, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s9))), inference(lemma,lemma(discharge,[]))).
% 293.39/185.90 tff(21487,plain,
% 293.39/185.90 (~node22(c_e_h_3, c_c, s8, s9)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[21486, 20474, 20119])).
% 293.39/185.90 tff(21488,plain,
% 293.39/185.90 (node21(c_e_h_3, c_c, s8, s9)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[20360, 21487])).
% 293.39/185.90 tff(21489,plain,
% 293.39/185.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_c, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s9)) | (~node21(c_e_h_3, c_c, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_c, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s9)) | (~node21(c_e_h_3, c_c, s8, s9)))),
% 293.39/185.90 inference(rewrite,[status(thm)],[])).
% 293.39/185.90 tff(21490,plain,
% 293.39/185.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_c, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s9)) | (~node21(c_e_h_3, c_c, s8, s9)))),
% 293.39/185.90 inference(quant_inst,[status(thm)],[])).
% 293.39/185.90 tff(21491,plain,
% 293.39/185.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_c, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s9)) | (~node21(c_e_h_3, c_c, s8, s9))),
% 293.39/185.90 inference(modus_ponens,[status(thm)],[21490, 21489])).
% 293.39/185.90 tff(21492,plain,
% 293.39/185.90 ($false),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[21491, 52, 21488, 20474, 21481])).
% 293.39/185.90 tff(21493,plain,((~m_and_h_gate_v_out(c_e_h_3, c_c, s9)) | node20(c_e_h_3, c_c, s8) | m_and_h_gate_v_out(c_e_h_3, c_c, s8)), inference(lemma,lemma(discharge,[]))).
% 293.39/185.90 tff(21494,plain,
% 293.39/185.90 (node20(c_e_h_3, c_c, s8)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[21493, 20474, 20119])).
% 293.39/185.90 tff(21495,assumption,(node20(c_e_h_3, c_c, s8)), introduced(assumption)).
% 293.39/185.90 tff(21496,plain,
% 293.39/185.90 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_c, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_c, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s8))),
% 293.39/185.90 inference(rewrite,[status(thm)],[])).
% 293.39/185.90 tff(21497,plain,
% 293.39/185.90 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_c, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s8))),
% 293.39/185.90 inference(quant_inst,[status(thm)],[])).
% 293.39/185.90 tff(21498,plain,
% 293.39/185.90 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_c, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s8)),
% 293.39/185.90 inference(modus_ponens,[status(thm)],[21497, 21496])).
% 293.39/185.90 tff(21499,plain,
% 293.39/185.90 ($false),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[21498, 38, 21495, 20452])).
% 293.39/185.90 tff(21500,plain,((~node20(c_e_h_3, c_c, s8)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s8)), inference(lemma,lemma(discharge,[]))).
% 293.39/185.90 tff(21501,plain,
% 293.39/185.90 (m_and_h_gate_v_in1(c_e_h_3, c_c, s8)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[21500, 21494])).
% 293.39/185.90 tff(21502,plain,
% 293.39/185.90 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_c, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s8))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s8))),
% 293.39/185.90 inference(rewrite,[status(thm)],[])).
% 293.39/185.90 tff(21503,plain,
% 293.39/185.90 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_c, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s8))),
% 293.39/185.90 inference(quant_inst,[status(thm)],[])).
% 293.39/185.90 tff(21504,plain,
% 293.39/185.90 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s8)),
% 293.39/185.90 inference(modus_ponens,[status(thm)],[21503, 21502])).
% 293.39/185.90 tff(21505,plain,
% 293.39/185.90 ($false),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[21504, 567, 1517, 20346])).
% 293.39/185.90 tff(21506,plain,((~m_and_h_gate_v_in1(c_e_h_3, c_c, s8)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s8)), inference(lemma,lemma(discharge,[]))).
% 293.39/185.90 tff(21507,plain,
% 293.39/185.90 (m_mutex_h_half_v_out(c_e_h_3, c_a, s8)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[21506, 21501])).
% 293.39/185.90 tff(21508,plain,
% 293.39/185.90 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s5)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[10210, 20334, 1440])).
% 293.39/185.90 tff(21509,plain,
% 293.39/185.90 (~m_mutex_h_half_v_inp(c_e_h_3, c_a, s7)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[19694, 395, 1826])).
% 293.39/185.90 tff(21510,plain,
% 293.39/185.90 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s8)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[19731, 21509, 20336])).
% 293.39/185.90 tff(21511,plain,
% 293.39/185.90 (~m_and_h_gate_v_in1(c_e_h_3, c_c, s8)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[21506, 21510])).
% 293.39/185.90 tff(21512,plain,
% 293.39/185.90 (~node20(c_e_h_3, c_c, s8)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[21500, 21511])).
% 293.39/185.90 tff(21513,plain,
% 293.39/185.90 (m_and_h_gate_v_out(c_e_h_3, c_c, s8)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[21493, 21512, 20474])).
% 293.39/185.90 tff(21514,plain,
% 293.39/185.90 (~m_and_h_gate_v_in1(c_e_h_3, c_c, s7)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[20027, 20336])).
% 293.39/185.90 tff(21515,plain,
% 293.39/185.90 (~node20(c_e_h_3, c_c, s7)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[20033, 38, 21514])).
% 293.39/185.90 tff(21516,plain,
% 293.39/185.90 (~node21(c_e_h_3, c_c, s7, s8)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[20046, 21515, 21513])).
% 293.39/185.90 tff(21517,plain,
% 293.39/185.90 (node22(c_e_h_3, c_c, s7, s8)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[20058, 21516])).
% 293.39/185.90 tff(21518,plain,
% 293.39/185.90 (m_and_h_gate_v_out(c_e_h_3, c_c, s7)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[20053, 21517, 21513])).
% 293.39/185.90 tff(21519,plain,
% 293.39/185.90 (~m_and_h_gate_v_in1(c_e_h_3, c_c, s5)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[10189, 567, 21508])).
% 293.39/185.90 tff(21520,plain,
% 293.39/185.90 (~node20(c_e_h_3, c_c, s5)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[10184, 38, 21519])).
% 293.39/185.90 tff(21521,plain,
% 293.39/185.90 (~m_and_h_gate_v_out(c_e_h_3, c_c, s6)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[10180, 21520, 5931])).
% 293.39/185.90 tff(21522,plain,
% 293.39/185.90 (~node22(c_e_h_3, c_c, s6, s7)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[20066, 21518, 21521])).
% 293.39/185.90 tff(21523,plain,
% 293.39/185.90 (node21(c_e_h_3, c_c, s6, s7)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[10074, 21522])).
% 293.39/185.90 tff(21524,plain,
% 293.39/185.90 (node20(c_e_h_3, c_c, s6)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[20073, 21523, 21518])).
% 293.39/185.90 tff(21525,plain,
% 293.39/185.90 (m_and_h_gate_v_in1(c_e_h_3, c_c, s6)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[20081, 38, 21524])).
% 293.39/185.90 tff(21526,plain,
% 293.39/185.90 (m_mutex_h_half_v_out(c_e_h_3, c_a, s6)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[20087, 567, 21525])).
% 293.39/185.90 tff(21527,plain,
% 293.39/185.90 (~node13(c_e_h_3, c_a, s5, s6)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[19615, 21526, 21508])).
% 293.39/185.90 tff(21528,plain,
% 293.39/185.90 (~node12(c_e_h_3, c_a, s5, s6)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[19608, 21526, 19599])).
% 293.39/185.90 tff(21529,plain,
% 293.39/185.90 ($false),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[1506, 21528, 21527])).
% 293.39/185.90 tff(21530,plain,(m_user_v_req(c_e_h_3, c_u, s7) | m_and_h_gate_v_out(c_e_h_3, c_c, s5) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s9))), inference(lemma,lemma(discharge,[]))).
% 293.39/185.90 tff(21531,plain,
% 293.39/185.90 (m_user_v_req(c_e_h_3, c_u, s7)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[21530, 20474, 1440, 5931])).
% 293.39/185.90 tff(21532,plain,
% 293.39/185.90 (m_user_v_req(c_e_h_3, c_u, s8)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[2509, 21531])).
% 293.39/185.90 tff(21533,plain,
% 293.39/185.90 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s8)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[2014, 21532])).
% 293.39/185.90 tff(21534,plain,
% 293.39/185.90 ($false),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[2006, 21533, 21507, 1])).
% 293.39/185.90 tff(21535,plain,((~m_and_h_gate_v_out(c_e_h_3, c_c, s9)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s9) | m_mutex_h_half_v_inp(c_e_h_3, c_a, s4) | m_and_h_gate_v_out(c_e_h_3, c_c, s5) | m_and_h_gate_v_out(c_e_h_3, c_c, s8)), inference(lemma,lemma(discharge,[]))).
% 293.39/185.90 tff(21536,plain,
% 293.39/185.90 (m_and_h_gate_v_out(c_e_h_3, c_c, s8)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[21535, 1440, 20474, 1, 21479])).
% 293.39/185.90 tff(21537,plain,
% 293.39/185.90 (m_and_h_gate_v_out(c_e_h_3, c_c, s6)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[20098, 21536, 20761, 21480])).
% 293.39/185.90 tff(21538,plain,
% 293.39/185.90 (~m_and_h_gate_v_in1(c_e_h_3, c_c, s5)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[10191, 21480])).
% 293.39/185.90 tff(21539,plain,
% 293.39/185.90 (~node20(c_e_h_3, c_c, s5)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[20103, 21538])).
% 293.39/185.90 tff(21540,plain,
% 293.39/185.90 ($false),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[10180, 21539, 21537, 21479])).
% 293.39/185.90 tff(21541,plain,(m_mutex_h_half_v_inp(c_e_h_3, c_a, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s9)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s9)), inference(lemma,lemma(discharge,[]))).
% 293.39/185.90 tff(21542,plain,
% 293.39/185.90 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s4)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[21541, 1, 20474])).
% 293.39/185.90 tff(21543,plain,
% 293.39/185.90 (m_user_v_req(c_e_h_3, c_u, s4)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[10214, 395, 21542])).
% 293.39/185.90 tff(21544,plain,
% 293.39/185.90 (m_user_v_req(c_e_h_3, c_u, s5)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[1035, 21543])).
% 293.39/185.90 tff(21545,plain,
% 293.39/185.90 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s5)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[1438, 21544])).
% 293.39/185.90 tff(21546,plain,
% 293.39/185.90 (m_user_v_req(c_e_h_3, c_u, s6)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[1413, 21544])).
% 293.39/185.90 tff(21547,plain,
% 293.39/185.90 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s6)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[1431, 21546])).
% 293.39/185.90 tff(21548,plain,
% 293.39/185.90 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s6)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[1971, 21547, 20761])).
% 293.39/185.90 tff(21549,plain,
% 293.39/185.90 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s5)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[1515, 21548, 21545])).
% 293.39/185.90 tff(21550,plain,
% 293.39/185.90 (~m_and_h_gate_v_in1(c_e_h_3, c_c, s5)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[10191, 21549])).
% 293.39/185.90 tff(21551,plain,
% 293.39/185.90 (~node20(c_e_h_3, c_c, s5)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[20103, 21550])).
% 293.39/185.90 tff(21552,plain,
% 293.39/185.90 (~m_and_h_gate_v_out(c_e_h_3, c_c, s6)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[10180, 21551, 21479])).
% 293.39/185.90 tff(21553,plain,
% 293.39/185.90 (m_user_v_req(c_e_h_3, c_u, s7)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[1900, 21544])).
% 293.39/185.90 tff(21554,plain,
% 293.39/185.90 (m_user_v_req(c_e_h_3, c_u, s8)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[2509, 21553])).
% 293.39/185.90 tff(21555,plain,
% 293.39/185.90 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s8)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[2014, 21554])).
% 293.39/185.90 tff(21556,plain,
% 293.39/185.90 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s8)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[2006, 21555, 1])).
% 293.39/185.90 tff(21557,plain,
% 293.39/185.90 (~m_and_h_gate_v_in1(c_e_h_3, c_c, s8)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[21506, 21556])).
% 293.39/185.90 tff(21558,plain,
% 293.39/185.90 (~node20(c_e_h_3, c_c, s8)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[21500, 21557])).
% 293.39/185.90 tff(21559,plain,
% 293.39/185.90 (m_and_h_gate_v_out(c_e_h_3, c_c, s8)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[21493, 21558, 20474])).
% 293.39/185.90 tff(21560,plain,
% 293.39/185.90 ($false),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[20098, 21559, 21552, 20761, 21549])).
% 293.39/185.90 tff(21561,plain,(m_mutex_h_half_v_out(c_e_h_3, c_a, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s9))), inference(lemma,lemma(discharge,[]))).
% 293.39/185.90 tff(21562,plain,
% 293.39/185.90 ($false),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[21561, 21478, 21475])).
% 293.39/185.90 tff(21563,plain,((~m_and_h_gate_v_out(c_e_h_3, c_c, s10)) | (~m_and_h_gate_v_in2(c_e_h_3, c_c, s10)) | m_and_h_gate_v_out(c_e_h_3, c_c, s11) | node20(c_e_h_3, c_c, s9)), inference(lemma,lemma(discharge,[]))).
% 293.39/185.90 tff(21564,plain,
% 293.39/185.90 ((~m_and_h_gate_v_out(c_e_h_3, c_c, s10)) | m_and_h_gate_v_out(c_e_h_3, c_c, s11) | node20(c_e_h_3, c_c, s9)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[21563, 21418])).
% 293.39/185.90 tff(21565,plain,
% 293.39/185.90 (node20(c_e_h_3, c_c, s9)),
% 293.39/185.90 inference(unit_resolution,[status(thm)],[21564, 21338, 21337])).
% 293.39/185.90 tff(21566,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_c, s9)), introduced(assumption)).
% 293.39/185.90 tff(21567,assumption,(node20(c_e_h_3, c_c, s9)), introduced(assumption)).
% 293.39/185.90 tff(21568,plain,
% 293.39/185.90 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_c, s9)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s9))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_c, s9)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s9))),
% 293.39/185.90 inference(rewrite,[status(thm)],[])).
% 293.39/185.90 tff(21569,plain,
% 293.39/185.90 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_c, s9)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s9))),
% 293.39/185.90 inference(quant_inst,[status(thm)],[])).
% 293.39/185.91 tff(21570,plain,
% 293.39/185.91 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_c, s9)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s9)),
% 293.39/185.91 inference(modus_ponens,[status(thm)],[21569, 21568])).
% 293.39/185.91 tff(21571,plain,
% 293.39/185.91 ($false),
% 293.39/185.91 inference(unit_resolution,[status(thm)],[21570, 38, 21567, 21566])).
% 293.39/185.91 tff(21572,plain,((~node20(c_e_h_3, c_c, s9)) | m_and_h_gate_v_in1(c_e_h_3, c_c, s9)), inference(lemma,lemma(discharge,[]))).
% 293.39/185.91 tff(21573,plain,
% 293.39/185.91 (m_and_h_gate_v_in1(c_e_h_3, c_c, s9)),
% 293.39/185.91 inference(unit_resolution,[status(thm)],[21572, 21565])).
% 293.39/185.91 tff(21574,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_c, s9)), introduced(assumption)).
% 293.39/185.91 tff(21575,plain,
% 293.39/185.91 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_c, s9)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s9))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s9)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s9))),
% 293.39/185.91 inference(rewrite,[status(thm)],[])).
% 293.39/185.91 tff(21576,plain,
% 293.39/185.91 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_c, s9)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s9))),
% 293.39/185.91 inference(quant_inst,[status(thm)],[])).
% 293.39/185.91 tff(21577,plain,
% 293.39/185.91 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_c, s9)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s9)),
% 293.39/185.91 inference(modus_ponens,[status(thm)],[21576, 21575])).
% 293.39/185.91 tff(21578,plain,
% 293.39/185.91 ($false),
% 293.39/185.91 inference(unit_resolution,[status(thm)],[21577, 567, 1, 21574])).
% 293.39/185.91 tff(21579,plain,((~m_and_h_gate_v_in1(c_e_h_3, c_c, s9)) | m_mutex_h_half_v_out(c_e_h_3, c_a, s9)), inference(lemma,lemma(discharge,[]))).
% 293.39/185.91 tff(21580,plain,
% 293.39/185.91 (m_mutex_h_half_v_out(c_e_h_3, c_a, s9)),
% 293.39/185.91 inference(unit_resolution,[status(thm)],[21579, 21573])).
% 293.39/185.91 tff(21581,plain,
% 293.39/185.91 ($false),
% 293.39/185.91 inference(unit_resolution,[status(thm)],[19733, 21580, 21455])).
% 293.39/185.91 tff(21582,plain,(m_and_h_gate_v_out(c_e_h_3, c_c, s11) | (~m_and_h_gate_v_out(c_e_h_3, c_c, s10))), inference(lemma,lemma(discharge,[]))).
% 293.39/185.91 tff(21583,plain,
% 293.39/185.91 ($false),
% 293.39/185.91 inference(unit_resolution,[status(thm)],[21582, 21336, 21289])).
% 293.39/185.91 tff(21584,plain,((~m_or_h_gate_v_out(c_e_h_3, c_g, s11)) | m_or_h_gate_v_in2(c_e_h_3, c_g, s10) | m_or_h_gate_v_out(c_e_h_3, c_g, s10) | m_or_h_gate_v_out(c_e_h_3, c_g, s12)), inference(lemma,lemma(discharge,[]))).
% 293.39/185.91 tff(21585,plain,
% 293.39/185.91 (m_or_h_gate_v_in2(c_e_h_3, c_g, s10)),
% 293.39/185.91 inference(unit_resolution,[status(thm)],[21584, 21249, 20172, 21248])).
% 293.39/185.91 tff(21586,assumption,(m_or_h_gate_v_in2(c_e_h_3, c_g, s10)), introduced(assumption)).
% 293.39/185.91 tff(21587,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_d, s10)), introduced(assumption)).
% 293.39/185.91 tff(21588,plain,
% 293.39/185.91 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_g, s10)) | m_and_h_gate_v_out(c_e_h_3, c_d, s10))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_g, s10)) | m_and_h_gate_v_out(c_e_h_3, c_d, s10))),
% 293.39/185.91 inference(rewrite,[status(thm)],[])).
% 293.39/185.91 tff(21589,plain,
% 293.39/185.91 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_g, s10)) | m_and_h_gate_v_out(c_e_h_3, c_d, s10))),
% 293.39/185.91 inference(quant_inst,[status(thm)],[])).
% 293.39/185.91 tff(21590,plain,
% 293.39/185.91 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_g, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_g, s10)) | m_and_h_gate_v_out(c_e_h_3, c_d, s10)),
% 293.39/185.91 inference(modus_ponens,[status(thm)],[21589, 21588])).
% 293.39/185.91 tff(21591,plain,
% 293.39/185.91 ($false),
% 293.39/185.91 inference(unit_resolution,[status(thm)],[21590, 2762, 21587, 21586])).
% 293.39/185.91 tff(21592,plain,((~m_or_h_gate_v_in2(c_e_h_3, c_g, s10)) | m_and_h_gate_v_out(c_e_h_3, c_d, s10)), inference(lemma,lemma(discharge,[]))).
% 293.39/185.91 tff(21593,plain,
% 293.39/185.91 (m_and_h_gate_v_out(c_e_h_3, c_d, s10)),
% 293.39/185.91 inference(unit_resolution,[status(thm)],[21592, 21585])).
% 293.39/185.91 tff(21594,assumption,(m_and_h_gate_v_out(c_e_h_3, c_d, s10)), introduced(assumption)).
% 293.39/185.91 tff(21595,plain,
% 293.39/185.91 (~m_and_h_gate_v_out(c_e_h_3, c_d, s9)),
% 293.39/185.91 inference(unit_resolution,[status(thm)],[18874, 17095])).
% 293.39/185.91 tff(21596,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_d, s9)), introduced(assumption)).
% 293.39/185.91 tff(21597,plain,
% 293.39/185.91 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_d, s9)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s9))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_d, s9)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s9))),
% 293.39/185.91 inference(rewrite,[status(thm)],[])).
% 293.39/185.91 tff(21598,plain,
% 293.39/185.91 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_d, s9)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s9))),
% 293.39/185.91 inference(quant_inst,[status(thm)],[])).
% 293.39/185.91 tff(21599,plain,
% 293.39/185.91 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_d, s9)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s9)),
% 293.39/185.91 inference(modus_ponens,[status(thm)],[21598, 21597])).
% 293.39/185.91 tff(21600,plain,
% 293.39/185.91 ($false),
% 293.39/185.91 inference(unit_resolution,[status(thm)],[21599, 2808, 17095, 21596])).
% 293.39/185.91 tff(21601,plain,((~m_and_h_gate_v_in1(c_e_h_3, c_d, s9)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s9)), inference(lemma,lemma(discharge,[]))).
% 293.39/185.91 tff(21602,plain,
% 293.39/185.91 (~m_and_h_gate_v_in1(c_e_h_3, c_d, s9)),
% 293.39/185.91 inference(unit_resolution,[status(thm)],[21601, 17095])).
% 293.39/185.91 tff(21603,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_d, s9)), introduced(assumption)).
% 293.39/185.91 tff(21604,assumption,(node20(c_e_h_3, c_d, s9)), introduced(assumption)).
% 293.39/185.91 tff(21605,plain,
% 293.39/185.91 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_d, s9)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s9))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_d, s9)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s9))),
% 293.39/185.91 inference(rewrite,[status(thm)],[])).
% 293.39/185.91 tff(21606,plain,
% 293.39/185.91 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_d, s9)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s9))),
% 293.39/185.91 inference(quant_inst,[status(thm)],[])).
% 293.39/185.91 tff(21607,plain,
% 293.39/185.91 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_d, s9)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s9)),
% 293.39/185.91 inference(modus_ponens,[status(thm)],[21606, 21605])).
% 293.39/185.91 tff(21608,plain,
% 293.39/185.91 ($false),
% 293.39/185.91 inference(unit_resolution,[status(thm)],[21607, 38, 21604, 21603])).
% 293.39/185.91 tff(21609,plain,((~node20(c_e_h_3, c_d, s9)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s9)), inference(lemma,lemma(discharge,[]))).
% 293.39/185.91 tff(21610,plain,
% 293.39/185.91 (~node20(c_e_h_3, c_d, s9)),
% 293.39/185.91 inference(unit_resolution,[status(thm)],[21609, 21602])).
% 293.39/185.91 tff(21611,assumption,(node22(c_e_h_3, c_d, s9, s10)), introduced(assumption)).
% 293.39/185.91 tff(21612,plain,
% 293.39/185.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_d, s10)) | (~node22(c_e_h_3, c_d, s9, s10)) | m_and_h_gate_v_out(c_e_h_3, c_d, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s10)) | (~node22(c_e_h_3, c_d, s9, s10)) | m_and_h_gate_v_out(c_e_h_3, c_d, s9))),
% 293.39/185.91 inference(rewrite,[status(thm)],[])).
% 293.39/185.91 tff(21613,plain,
% 293.39/185.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_d, s10)) | (~node22(c_e_h_3, c_d, s9, s10)) | m_and_h_gate_v_out(c_e_h_3, c_d, s9))),
% 293.39/185.91 inference(quant_inst,[status(thm)],[])).
% 293.39/185.91 tff(21614,plain,
% 293.39/185.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s10)) | (~node22(c_e_h_3, c_d, s9, s10)) | m_and_h_gate_v_out(c_e_h_3, c_d, s9)),
% 293.39/185.91 inference(modus_ponens,[status(thm)],[21613, 21612])).
% 293.39/185.91 tff(21615,plain,
% 293.39/185.91 ($false),
% 293.39/185.91 inference(unit_resolution,[status(thm)],[21614, 108, 21611, 19480, 21594])).
% 293.39/185.91 tff(21616,plain,((~node22(c_e_h_3, c_d, s9, s10)) | m_and_h_gate_v_out(c_e_h_3, c_d, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s10))), inference(lemma,lemma(discharge,[]))).
% 293.39/185.91 tff(21617,plain,
% 293.39/185.91 (~node22(c_e_h_3, c_d, s9, s10)),
% 293.39/185.91 inference(unit_resolution,[status(thm)],[21616, 21594, 19480])).
% 293.39/185.91 tff(21618,assumption,(~node20(c_e_h_3, c_d, s9)), introduced(assumption)).
% 293.39/185.91 tff(21619,assumption,(node21(c_e_h_3, c_d, s9, s10)), introduced(assumption)).
% 293.39/185.91 tff(21620,plain,
% 293.39/185.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_d, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s10)) | (~node21(c_e_h_3, c_d, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_d, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s10)) | (~node21(c_e_h_3, c_d, s9, s10)))),
% 293.39/185.91 inference(rewrite,[status(thm)],[])).
% 293.39/185.91 tff(21621,plain,
% 293.39/185.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_d, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s10)) | (~node21(c_e_h_3, c_d, s9, s10)))),
% 293.39/185.91 inference(quant_inst,[status(thm)],[])).
% 293.39/185.91 tff(21622,plain,
% 293.39/185.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_d, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s10)) | (~node21(c_e_h_3, c_d, s9, s10))),
% 293.39/185.91 inference(modus_ponens,[status(thm)],[21621, 21620])).
% 293.39/185.91 tff(21623,plain,
% 293.39/185.91 ($false),
% 293.39/185.91 inference(unit_resolution,[status(thm)],[21622, 52, 21619, 21594, 21618])).
% 293.39/185.91 tff(21624,plain,((~node21(c_e_h_3, c_d, s9, s10)) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s10)) | node20(c_e_h_3, c_d, s9)), inference(lemma,lemma(discharge,[]))).
% 293.39/185.91 tff(21625,plain,
% 293.39/185.91 (~node21(c_e_h_3, c_d, s9, s10)),
% 293.39/185.91 inference(unit_resolution,[status(thm)],[21624, 21594, 21618])).
% 293.39/185.91 tff(21626,plain,
% 293.39/185.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s9, s10)) | node21(c_e_h_3, c_d, s9, s10) | node22(c_e_h_3, c_d, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s9, s10)) | node21(c_e_h_3, c_d, s9, s10) | node22(c_e_h_3, c_d, s9, s10))),
% 293.39/185.91 inference(rewrite,[status(thm)],[])).
% 293.39/185.91 tff(21627,plain,
% 293.39/185.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s9, s10)) | node21(c_e_h_3, c_d, s9, s10) | node22(c_e_h_3, c_d, s9, s10))),
% 293.39/185.91 inference(quant_inst,[status(thm)],[])).
% 293.39/185.91 tff(21628,plain,
% 293.39/185.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s9, s10)) | node21(c_e_h_3, c_d, s9, s10) | node22(c_e_h_3, c_d, s9, s10)),
% 293.39/185.91 inference(modus_ponens,[status(thm)],[21627, 21626])).
% 293.39/185.91 tff(21629,plain,
% 293.39/185.91 (node21(c_e_h_3, c_d, s9, s10) | node22(c_e_h_3, c_d, s9, s10)),
% 293.39/185.91 inference(unit_resolution,[status(thm)],[21628, 82, 7676])).
% 293.39/185.91 tff(21630,plain,
% 293.39/185.91 ($false),
% 293.39/185.91 inference(unit_resolution,[status(thm)],[21629, 21625, 21617])).
% 293.39/185.91 tff(21631,plain,((~m_and_h_gate_v_out(c_e_h_3, c_d, s10)) | node20(c_e_h_3, c_d, s9) | m_and_h_gate_v_out(c_e_h_3, c_d, s9)), inference(lemma,lemma(discharge,[]))).
% 293.39/185.91 tff(21632,plain,
% 293.39/185.91 ($false),
% 293.39/185.91 inference(unit_resolution,[status(thm)],[21631, 21610, 21595, 21594])).
% 293.39/185.91 tff(21633,plain,(m_mutex_h_half_v_out(c_e_h_3, c_b, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s10))), inference(lemma,lemma(discharge,[]))).
% 293.39/185.91 tff(21634,plain,
% 293.39/185.91 (m_mutex_h_half_v_out(c_e_h_3, c_b, s9)),
% 293.39/185.91 inference(unit_resolution,[status(thm)],[21633, 21593])).
% 293.39/185.91 tff(21635,plain,
% 293.39/185.91 (m_and_h_gate_v_out(c_e_h_1, c_k, s7)),
% 293.39/185.91 inference(unit_resolution,[status(thm)],[19039, 21634])).
% 293.39/185.91 tff(21636,plain,
% 293.39/185.91 (m_or_h_gate_v_out(c_e_h_1, c_g, s6)),
% 293.39/185.91 inference(unit_resolution,[status(thm)],[19002, 21634])).
% 293.39/185.91 tff(21637,plain,
% 293.39/185.91 (m_and_h_gate_v_out(c_e_h_1, c_p, s6)),
% 293.39/185.91 inference(unit_resolution,[status(thm)],[18981, 15864, 18876])).
% 293.39/185.91 tff(21638,plain,
% 293.39/185.91 (node20(c_e_h_1, c_p, s5)),
% 293.39/185.91 inference(unit_resolution,[status(thm)],[15765, 21637])).
% 293.39/185.91 tff(21639,plain,
% 293.39/185.91 (m_and_h_gate_v_in1(c_e_h_1, c_p, s5)),
% 293.39/185.91 inference(unit_resolution,[status(thm)],[15695, 21638])).
% 293.39/185.91 tff(21640,plain,
% 293.39/185.91 (m_and_h_gate_v_out(c_e_h_1, c_k, s5)),
% 293.39/185.91 inference(unit_resolution,[status(thm)],[15687, 21639])).
% 293.39/185.91 tff(21641,plain,
% 293.39/185.91 (node20(c_e_h_1, c_k, s4)),
% 293.39/185.91 inference(unit_resolution,[status(thm)],[15500, 21640])).
% 293.39/185.91 tff(21642,plain,
% 293.39/185.91 (m_and_h_gate_v_in1(c_e_h_1, c_k, s4)),
% 293.39/185.91 inference(unit_resolution,[status(thm)],[15443, 21641])).
% 293.39/185.91 tff(21643,plain,
% 293.39/185.91 (m_or_h_gate_v_out(c_e_h_1, c_g, s4)),
% 293.39/185.91 inference(unit_resolution,[status(thm)],[15435, 21642])).
% 293.39/185.92 tff(21644,plain,
% 293.39/185.92 (m_or_h_gate_v_out(c_e_h_1, c_g, s5)),
% 293.39/185.92 inference(unit_resolution,[status(thm)],[15624, 21643])).
% 293.39/185.92 tff(21645,plain,
% 293.39/185.92 (m_and_h_gate_v_out(c_e_h_1, c_c, s4)),
% 293.39/185.92 inference(unit_resolution,[status(thm)],[14848, 21644])).
% 293.39/185.92 tff(21646,plain,
% 293.39/185.92 (m_mutex_h_half_v_out(c_e_h_1, c_a, s5)),
% 293.39/185.92 inference(unit_resolution,[status(thm)],[15023, 21645])).
% 293.39/185.92 tff(21647,plain,
% 293.39/185.92 (m_and_h_gate_v_in1(c_e_h_1, c_c, s5)),
% 293.39/185.92 inference(unit_resolution,[status(thm)],[15073, 21646])).
% 293.39/185.92 tff(21648,plain,
% 293.39/185.92 (~node21(c_e_h_1, c_c, s5, s6)),
% 293.39/185.92 inference(unit_resolution,[status(thm)],[15368, 21647, 13629])).
% 293.39/185.92 tff(21649,plain,
% 293.39/185.92 (node22(c_e_h_1, c_c, s5, s6)),
% 293.39/185.92 inference(unit_resolution,[status(thm)],[15383, 21648])).
% 293.39/185.92 tff(21650,plain,
% 293.39/185.92 (~m_and_h_gate_v_out(c_e_h_1, c_c, s5)),
% 293.39/185.92 inference(unit_resolution,[status(thm)],[15378, 21649, 13629])).
% 293.39/185.92 tff(21651,plain,
% 293.39/185.92 (m_user_v_req(c_e_h_1, c_u, s2)),
% 293.39/185.92 inference(unit_resolution,[status(thm)],[14671, 21645])).
% 293.39/185.92 tff(21652,plain,
% 293.39/185.92 (m_user_v_req(c_e_h_1, c_u, s3)),
% 293.39/185.92 inference(unit_resolution,[status(thm)],[14760, 21651])).
% 293.39/185.92 tff(21653,plain,
% 293.39/185.92 (m_mutex_h_half_v_inp(c_e_h_1, c_a, s3)),
% 293.39/185.92 inference(unit_resolution,[status(thm)],[14768, 21652])).
% 293.39/185.92 tff(21654,plain,
% 293.39/185.92 (node20(c_e_h_1, c_c, s3)),
% 293.39/185.92 inference(unit_resolution,[status(thm)],[14663, 21645, 15676])).
% 293.39/185.92 tff(21655,plain,
% 293.39/185.92 (m_and_h_gate_v_in1(c_e_h_1, c_c, s3)),
% 293.39/185.92 inference(unit_resolution,[status(thm)],[14646, 21654])).
% 293.39/185.92 tff(21656,plain,
% 293.39/185.92 (m_mutex_h_half_v_out(c_e_h_1, c_a, s3)),
% 293.39/185.92 inference(unit_resolution,[status(thm)],[14638, 21655])).
% 293.39/185.92 tff(21657,plain,
% 293.39/185.92 (m_mutex_h_half_v_out(c_e_h_1, c_a, s4)),
% 293.39/185.92 inference(unit_resolution,[status(thm)],[14793, 21656, 21653])).
% 293.39/185.92 tff(21658,plain,
% 293.39/185.92 (m_and_h_gate_v_in1(c_e_h_1, c_c, s4)),
% 293.39/185.92 inference(unit_resolution,[status(thm)],[14810, 21657])).
% 293.39/185.92 tff(21659,plain,
% 293.39/185.92 ($false),
% 293.39/185.92 inference(unit_resolution,[status(thm)],[14843, 21658, 21650, 21645])).
% 293.39/185.92 tff(21660,plain,(m_and_h_gate_v_out(c_e_h_1, c_c, s6) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s9))), inference(lemma,lemma(discharge,[]))).
% 293.39/185.92 tff(21661,plain,
% 293.39/185.92 (m_and_h_gate_v_out(c_e_h_1, c_c, s6)),
% 293.39/185.92 inference(unit_resolution,[status(thm)],[21660, 21634])).
% 293.39/185.92 tff(21662,plain,
% 293.39/185.92 (m_or_h_gate_v_in1(c_e_h_1, c_g, s6)),
% 293.39/185.92 inference(unit_resolution,[status(thm)],[19072, 21661])).
% 293.39/185.92 tff(21663,plain,
% 293.39/185.92 (~node4(c_e_h_1, c_g, s6)),
% 293.39/185.92 inference(unit_resolution,[status(thm)],[17027, 21662])).
% 293.39/185.92 tff(21664,plain,
% 293.39/185.92 (m_or_h_gate_v_out(c_e_h_1, c_g, s7)),
% 293.39/185.92 inference(unit_resolution,[status(thm)],[17051, 21663, 21636])).
% 293.39/185.92 tff(21665,plain,
% 293.39/185.92 (m_and_h_gate_v_in1(c_e_h_1, c_k, s7)),
% 293.39/185.92 inference(unit_resolution,[status(thm)],[19081, 21664])).
% 293.39/185.92 tff(21666,plain,
% 293.39/185.92 (m_and_h_gate_v_out(c_e_h_1, c_k, s8)),
% 293.39/185.92 inference(unit_resolution,[status(thm)],[19475, 21665, 21635])).
% 293.39/185.92 tff(21667,plain,
% 293.39/185.92 (m_and_h_gate_v_out(c_e_h_1, c_p, s8)),
% 293.39/185.92 inference(unit_resolution,[status(thm)],[19089, 21634])).
% 293.39/185.92 tff(21668,assumption,(m_or_h_gate_v_in2(c_e_h_3, c_g, s11)), introduced(assumption)).
% 293.39/185.92 tff(21669,plain,
% 293.39/185.92 (((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in2(I0, I1, X)) | (~node4(I0, I1, X)))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_g, s11)) | (~node4(c_e_h_3, c_g, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in2(I0, I1, X)) | (~node4(I0, I1, X)))) | (~m_or_h_gate_v_in2(c_e_h_3, c_g, s11)) | (~node4(c_e_h_3, c_g, s11)))),
% 293.39/185.92 inference(rewrite,[status(thm)],[])).
% 293.39/185.92 tff(21670,plain,
% 293.39/185.92 ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in2(I0, I1, X)) | (~node4(I0, I1, X)))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_g, s11)) | (~node4(c_e_h_3, c_g, s11)))),
% 293.39/185.92 inference(quant_inst,[status(thm)],[])).
% 293.39/185.92 tff(21671,plain,
% 293.39/185.92 ((~![I0: $i, X: $i, I1: $i] : ((~m_or_h_gate_v_in2(I0, I1, X)) | (~node4(I0, I1, X)))) | (~m_or_h_gate_v_in2(c_e_h_3, c_g, s11)) | (~node4(c_e_h_3, c_g, s11))),
% 293.39/185.92 inference(modus_ponens,[status(thm)],[21670, 21669])).
% 293.39/185.92 tff(21672,plain,
% 293.39/185.92 ($false),
% 293.39/185.92 inference(unit_resolution,[status(thm)],[21671, 20695, 21322, 21668])).
% 293.39/185.92 tff(21673,plain,((~node4(c_e_h_3, c_g, s11)) | (~m_or_h_gate_v_in2(c_e_h_3, c_g, s11))), inference(lemma,lemma(discharge,[]))).
% 293.39/185.92 tff(21674,plain,
% 293.39/185.92 (~m_or_h_gate_v_in2(c_e_h_3, c_g, s11)),
% 293.39/185.92 inference(unit_resolution,[status(thm)],[21673, 21320])).
% 293.39/185.92 tff(21675,assumption,(~m_or_h_gate_v_in2(c_e_h_3, c_g, s11)), introduced(assumption)).
% 293.39/185.92 tff(21676,assumption,(m_and_h_gate_v_out(c_e_h_3, c_d, s11)), introduced(assumption)).
% 293.39/185.92 tff(21677,plain,
% 293.39/185.92 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_d, X)) | m_or_h_gate_v_in2(I0, c_g, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_d, s11)) | m_or_h_gate_v_in2(c_e_h_3, c_g, s11))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_d, X)) | m_or_h_gate_v_in2(I0, c_g, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s11)) | m_or_h_gate_v_in2(c_e_h_3, c_g, s11))),
% 293.39/185.92 inference(rewrite,[status(thm)],[])).
% 293.39/185.92 tff(21678,plain,
% 293.39/185.92 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_d, X)) | m_or_h_gate_v_in2(I0, c_g, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_d, s11)) | m_or_h_gate_v_in2(c_e_h_3, c_g, s11))),
% 293.39/185.92 inference(quant_inst,[status(thm)],[])).
% 293.39/185.92 tff(21679,plain,
% 293.39/185.92 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_d, X)) | m_or_h_gate_v_in2(I0, c_g, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s11)) | m_or_h_gate_v_in2(c_e_h_3, c_g, s11)),
% 293.39/185.92 inference(modus_ponens,[status(thm)],[21678, 21677])).
% 293.39/185.92 tff(21680,plain,
% 293.39/185.92 ($false),
% 293.39/185.92 inference(unit_resolution,[status(thm)],[21679, 20711, 21676, 21675])).
% 293.39/185.92 tff(21681,plain,((~m_and_h_gate_v_out(c_e_h_3, c_d, s11)) | m_or_h_gate_v_in2(c_e_h_3, c_g, s11)), inference(lemma,lemma(discharge,[]))).
% 293.39/185.92 tff(21682,plain,
% 293.39/185.92 (~m_and_h_gate_v_out(c_e_h_3, c_d, s11)),
% 293.39/185.92 inference(unit_resolution,[status(thm)],[21681, 21674])).
% 293.39/185.92 tff(21683,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_d, s10)), introduced(assumption)).
% 293.39/185.92 tff(21684,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_d, s11)), introduced(assumption)).
% 293.39/185.92 tff(21685,assumption,(node22(c_e_h_3, c_d, s10, s11)), introduced(assumption)).
% 293.39/185.92 tff(21686,plain,
% 293.39/185.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_d, s11) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s10)) | (~node22(c_e_h_3, c_d, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | m_and_h_gate_v_out(c_e_h_3, c_d, s11) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s10)) | (~node22(c_e_h_3, c_d, s10, s11)))),
% 293.39/185.92 inference(rewrite,[status(thm)],[])).
% 293.39/185.92 tff(21687,plain,
% 293.39/185.92 ((m_and_h_gate_v_out(c_e_h_3, c_d, s11) | (~node22(c_e_h_3, c_d, s10, s11)) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s10))) <=> (m_and_h_gate_v_out(c_e_h_3, c_d, s11) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s10)) | (~node22(c_e_h_3, c_d, s10, s11)))),
% 293.39/185.92 inference(rewrite,[status(thm)],[])).
% 293.39/185.92 tff(21688,plain,
% 293.39/185.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_d, s11) | (~node22(c_e_h_3, c_d, s10, s11)) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_d, s11) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s10)) | (~node22(c_e_h_3, c_d, s10, s11))))),
% 293.39/185.92 inference(monotonicity,[status(thm)],[21687])).
% 293.39/185.92 tff(21689,plain,
% 293.39/185.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_d, s11) | (~node22(c_e_h_3, c_d, s10, s11)) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | m_and_h_gate_v_out(c_e_h_3, c_d, s11) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s10)) | (~node22(c_e_h_3, c_d, s10, s11)))),
% 293.39/185.92 inference(transitivity,[status(thm)],[21688, 21686])).
% 293.39/185.92 tff(21690,plain,
% 293.39/185.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_3, c_d, s11) | (~node22(c_e_h_3, c_d, s10, s11)) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s10)))),
% 293.39/185.92 inference(quant_inst,[status(thm)],[])).
% 293.39/185.92 tff(21691,plain,
% 293.39/185.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | m_and_h_gate_v_out(c_e_h_3, c_d, s11) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s10)) | (~node22(c_e_h_3, c_d, s10, s11))),
% 293.39/185.92 inference(modus_ponens,[status(thm)],[21690, 21689])).
% 293.39/185.92 tff(21692,plain,
% 293.39/185.92 ($false),
% 293.39/185.92 inference(unit_resolution,[status(thm)],[21691, 5871, 21594, 21685, 21684])).
% 293.39/185.92 tff(21693,plain,((~node22(c_e_h_3, c_d, s10, s11)) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s10)) | m_and_h_gate_v_out(c_e_h_3, c_d, s11)), inference(lemma,lemma(discharge,[]))).
% 293.39/185.92 tff(21694,plain,
% 293.39/185.92 (~node22(c_e_h_3, c_d, s10, s11)),
% 293.39/185.92 inference(unit_resolution,[status(thm)],[21693, 21684, 21594])).
% 293.39/185.92 tff(21695,plain,
% 293.39/185.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s10, s11)) | node21(c_e_h_3, c_d, s10, s11) | node22(c_e_h_3, c_d, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s10, s11)) | node21(c_e_h_3, c_d, s10, s11) | node22(c_e_h_3, c_d, s10, s11))),
% 293.39/185.92 inference(rewrite,[status(thm)],[])).
% 293.39/185.92 tff(21696,plain,
% 293.39/185.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s10, s11)) | node21(c_e_h_3, c_d, s10, s11) | node22(c_e_h_3, c_d, s10, s11))),
% 293.39/185.92 inference(quant_inst,[status(thm)],[])).
% 293.39/185.92 tff(21697,plain,
% 293.39/185.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s10, s11)) | node21(c_e_h_3, c_d, s10, s11) | node22(c_e_h_3, c_d, s10, s11)),
% 293.39/185.92 inference(modus_ponens,[status(thm)],[21696, 21695])).
% 293.39/185.92 tff(21698,plain,
% 293.39/185.92 (node21(c_e_h_3, c_d, s10, s11) | node22(c_e_h_3, c_d, s10, s11)),
% 293.39/185.92 inference(unit_resolution,[status(thm)],[21697, 82, 7748])).
% 293.39/185.92 tff(21699,plain,
% 293.39/185.92 (node21(c_e_h_3, c_d, s10, s11)),
% 293.39/185.92 inference(unit_resolution,[status(thm)],[21698, 21694])).
% 293.39/185.92 tff(21700,assumption,(m_user_v_ack(c_e_h_3, c_u, s10)), introduced(assumption)).
% 293.39/185.92 tff(21701,plain,
% 293.39/185.92 ($false),
% 293.39/185.92 inference(unit_resolution,[status(thm)],[19822, 268, 21700, 12643])).
% 293.39/185.92 tff(21702,plain,((~m_user_v_ack(c_e_h_3, c_u, s10)) | m_and_h_gate_v_out(c_e_h_3, c_r, s10)), inference(lemma,lemma(discharge,[]))).
% 293.39/185.92 tff(21703,plain,
% 293.39/185.92 (~m_user_v_ack(c_e_h_3, c_u, s10)),
% 293.39/185.92 inference(unit_resolution,[status(thm)],[21702, 12642])).
% 293.39/185.92 tff(21704,plain,
% 293.39/185.92 (((~![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_d, X) | m_user_v_ack(I0, c_u, X))) | (m_and_h_gate_v_in2(c_e_h_3, c_d, s10) | m_user_v_ack(c_e_h_3, c_u, s10))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_d, X) | m_user_v_ack(I0, c_u, X))) | m_and_h_gate_v_in2(c_e_h_3, c_d, s10) | m_user_v_ack(c_e_h_3, c_u, s10))),
% 293.39/185.92 inference(rewrite,[status(thm)],[])).
% 293.39/185.92 tff(21705,plain,
% 293.39/185.92 ((~![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_d, X) | m_user_v_ack(I0, c_u, X))) | (m_and_h_gate_v_in2(c_e_h_3, c_d, s10) | m_user_v_ack(c_e_h_3, c_u, s10))),
% 293.39/185.92 inference(quant_inst,[status(thm)],[])).
% 293.39/185.92 tff(21706,plain,
% 293.39/185.92 ((~![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_d, X) | m_user_v_ack(I0, c_u, X))) | m_and_h_gate_v_in2(c_e_h_3, c_d, s10) | m_user_v_ack(c_e_h_3, c_u, s10)),
% 293.39/185.92 inference(modus_ponens,[status(thm)],[21705, 21704])).
% 293.39/185.92 tff(21707,plain,
% 293.39/185.92 (m_and_h_gate_v_in2(c_e_h_3, c_d, s10) | m_user_v_ack(c_e_h_3, c_u, s10)),
% 293.39/185.92 inference(unit_resolution,[status(thm)],[21706, 19530])).
% 293.39/185.92 tff(21708,plain,
% 293.39/185.92 (m_and_h_gate_v_in2(c_e_h_3, c_d, s10)),
% 293.39/185.92 inference(unit_resolution,[status(thm)],[21707, 21703])).
% 293.39/185.92 tff(21709,plain,
% 293.39/185.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_d, s10)) | m_and_h_gate_v_out(c_e_h_3, c_d, s11) | (~m_and_h_gate_v_in1(c_e_h_3, c_d, s10)) | (~node21(c_e_h_3, c_d, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in2(c_e_h_3, c_d, s10)) | m_and_h_gate_v_out(c_e_h_3, c_d, s11) | (~m_and_h_gate_v_in1(c_e_h_3, c_d, s10)) | (~node21(c_e_h_3, c_d, s10, s11)))),
% 293.39/185.93 inference(rewrite,[status(thm)],[])).
% 293.39/185.93 tff(21710,plain,
% 293.39/185.93 (((~node21(c_e_h_3, c_d, s10, s11)) | (~m_and_h_gate_v_in2(c_e_h_3, c_d, s10)) | (~m_and_h_gate_v_in1(c_e_h_3, c_d, s10)) | m_and_h_gate_v_out(c_e_h_3, c_d, s11)) <=> ((~m_and_h_gate_v_in2(c_e_h_3, c_d, s10)) | m_and_h_gate_v_out(c_e_h_3, c_d, s11) | (~m_and_h_gate_v_in1(c_e_h_3, c_d, s10)) | (~node21(c_e_h_3, c_d, s10, s11)))),
% 293.39/185.93 inference(rewrite,[status(thm)],[])).
% 293.39/185.93 tff(21711,plain,
% 293.39/185.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_d, s10, s11)) | (~m_and_h_gate_v_in2(c_e_h_3, c_d, s10)) | (~m_and_h_gate_v_in1(c_e_h_3, c_d, s10)) | m_and_h_gate_v_out(c_e_h_3, c_d, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_d, s10)) | m_and_h_gate_v_out(c_e_h_3, c_d, s11) | (~m_and_h_gate_v_in1(c_e_h_3, c_d, s10)) | (~node21(c_e_h_3, c_d, s10, s11))))),
% 293.39/185.93 inference(monotonicity,[status(thm)],[21710])).
% 293.39/185.93 tff(21712,plain,
% 293.39/185.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_d, s10, s11)) | (~m_and_h_gate_v_in2(c_e_h_3, c_d, s10)) | (~m_and_h_gate_v_in1(c_e_h_3, c_d, s10)) | m_and_h_gate_v_out(c_e_h_3, c_d, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in2(c_e_h_3, c_d, s10)) | m_and_h_gate_v_out(c_e_h_3, c_d, s11) | (~m_and_h_gate_v_in1(c_e_h_3, c_d, s10)) | (~node21(c_e_h_3, c_d, s10, s11)))),
% 293.39/185.93 inference(transitivity,[status(thm)],[21711, 21709])).
% 293.39/185.93 tff(21713,plain,
% 293.39/185.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_3, c_d, s10, s11)) | (~m_and_h_gate_v_in2(c_e_h_3, c_d, s10)) | (~m_and_h_gate_v_in1(c_e_h_3, c_d, s10)) | m_and_h_gate_v_out(c_e_h_3, c_d, s11))),
% 293.39/185.93 inference(quant_inst,[status(thm)],[])).
% 293.39/185.93 tff(21714,plain,
% 293.39/185.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in2(c_e_h_3, c_d, s10)) | m_and_h_gate_v_out(c_e_h_3, c_d, s11) | (~m_and_h_gate_v_in1(c_e_h_3, c_d, s10)) | (~node21(c_e_h_3, c_d, s10, s11))),
% 293.39/185.93 inference(modus_ponens,[status(thm)],[21713, 21712])).
% 293.39/185.93 tff(21715,plain,
% 293.39/185.93 ($false),
% 293.39/185.93 inference(unit_resolution,[status(thm)],[21714, 5851, 21708, 21699, 21684, 21683])).
% 293.39/185.93 tff(21716,plain,(m_and_h_gate_v_out(c_e_h_3, c_d, s11) | (~m_and_h_gate_v_in1(c_e_h_3, c_d, s10)) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s10))), inference(lemma,lemma(discharge,[]))).
% 293.39/185.93 tff(21717,plain,
% 293.39/185.93 (~m_and_h_gate_v_in1(c_e_h_3, c_d, s10)),
% 293.39/185.93 inference(unit_resolution,[status(thm)],[21716, 21682, 21593])).
% 293.39/185.93 tff(21718,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_d, s10)), introduced(assumption)).
% 293.39/185.93 tff(21719,assumption,(m_mutex_h_half_v_out(c_e_h_3, c_b, s10)), introduced(assumption)).
% 293.39/185.93 tff(21720,plain,
% 293.39/185.93 (((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_b, X)) | m_and_h_gate_v_in1(I0, c_d, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_b, s10)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s10))) <=> ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_b, X)) | m_and_h_gate_v_in1(I0, c_d, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s10)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s10))),
% 293.39/185.93 inference(rewrite,[status(thm)],[])).
% 293.39/185.93 tff(21721,plain,
% 293.39/185.93 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_b, X)) | m_and_h_gate_v_in1(I0, c_d, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_b, s10)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s10))),
% 293.39/185.93 inference(quant_inst,[status(thm)],[])).
% 293.39/185.93 tff(21722,plain,
% 293.39/185.93 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_b, X)) | m_and_h_gate_v_in1(I0, c_d, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s10)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s10)),
% 293.39/185.93 inference(modus_ponens,[status(thm)],[21721, 21720])).
% 293.39/185.93 tff(21723,plain,
% 293.39/185.93 ($false),
% 293.39/185.93 inference(unit_resolution,[status(thm)],[21722, 19509, 21719, 21718])).
% 293.39/185.93 tff(21724,plain,(m_and_h_gate_v_in1(c_e_h_3, c_d, s10) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s10))), inference(lemma,lemma(discharge,[]))).
% 293.39/185.93 tff(21725,plain,
% 293.39/185.93 (~m_mutex_h_half_v_out(c_e_h_3, c_b, s10)),
% 293.39/185.93 inference(unit_resolution,[status(thm)],[21724, 21717])).
% 293.39/185.93 tff(21726,assumption,(~m_mutex_h_half_v_out(c_e_h_3, c_b, s10)), introduced(assumption)).
% 293.39/185.93 tff(21727,assumption,(node13(c_e_h_3, c_b, s9, s10)), introduced(assumption)).
% 293.39/185.93 tff(21728,plain,
% 293.39/185.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_b, s10) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s9)) | (~node13(c_e_h_3, c_b, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | m_mutex_h_half_v_out(c_e_h_3, c_b, s10) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s9)) | (~node13(c_e_h_3, c_b, s9, s10)))),
% 293.39/185.93 inference(rewrite,[status(thm)],[])).
% 293.39/185.93 tff(21729,plain,
% 293.39/185.93 ((m_mutex_h_half_v_out(c_e_h_3, c_b, s10) | (~node13(c_e_h_3, c_b, s9, s10)) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s9))) <=> (m_mutex_h_half_v_out(c_e_h_3, c_b, s10) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s9)) | (~node13(c_e_h_3, c_b, s9, s10)))),
% 293.39/185.93 inference(rewrite,[status(thm)],[])).
% 293.39/185.93 tff(21730,plain,
% 293.39/185.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_b, s10) | (~node13(c_e_h_3, c_b, s9, s10)) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_b, s10) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s9)) | (~node13(c_e_h_3, c_b, s9, s10))))),
% 293.39/185.93 inference(monotonicity,[status(thm)],[21729])).
% 293.39/185.93 tff(21731,plain,
% 293.39/185.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_b, s10) | (~node13(c_e_h_3, c_b, s9, s10)) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | m_mutex_h_half_v_out(c_e_h_3, c_b, s10) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s9)) | (~node13(c_e_h_3, c_b, s9, s10)))),
% 293.39/185.93 inference(transitivity,[status(thm)],[21730, 21728])).
% 293.39/185.93 tff(21732,plain,
% 293.39/185.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_3, c_b, s10) | (~node13(c_e_h_3, c_b, s9, s10)) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s9)))),
% 293.39/185.93 inference(quant_inst,[status(thm)],[])).
% 293.39/185.93 tff(21733,plain,
% 293.39/185.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | m_mutex_h_half_v_out(c_e_h_3, c_b, s10) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s9)) | (~node13(c_e_h_3, c_b, s9, s10))),
% 293.39/185.93 inference(modus_ponens,[status(thm)],[21732, 21731])).
% 293.39/185.93 tff(21734,plain,
% 293.39/185.93 ($false),
% 293.39/185.93 inference(unit_resolution,[status(thm)],[21733, 1459, 21727, 18876, 21726])).
% 293.39/185.93 tff(21735,plain,((~node13(c_e_h_3, c_b, s9, s10)) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s9)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s10)), inference(lemma,lemma(discharge,[]))).
% 293.39/185.93 tff(21736,plain,
% 293.39/185.93 (~node13(c_e_h_3, c_b, s9, s10)),
% 293.39/185.93 inference(unit_resolution,[status(thm)],[21735, 21726, 18876])).
% 293.39/185.93 tff(21737,assumption,(m_mutex_h_half_v_inp(c_e_h_3, c_b, s9)), introduced(assumption)).
% 293.39/185.93 tff(21738,assumption,(node12(c_e_h_3, c_b, s9, s10)), introduced(assumption)).
% 293.39/185.93 tff(21739,plain,
% 293.39/185.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_b, s9)) | (~node12(c_e_h_3, c_b, s9, s10)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s9)) | (~node12(c_e_h_3, c_b, s9, s10)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s10))),
% 293.39/185.93 inference(rewrite,[status(thm)],[])).
% 293.39/185.93 tff(21740,plain,
% 293.39/185.93 (((~node12(c_e_h_3, c_b, s9, s10)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s9)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s10)) <=> ((~m_mutex_h_half_v_inp(c_e_h_3, c_b, s9)) | (~node12(c_e_h_3, c_b, s9, s10)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s10))),
% 293.39/185.93 inference(rewrite,[status(thm)],[])).
% 293.39/185.93 tff(21741,plain,
% 293.39/185.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_3, c_b, s9, s10)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s9)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~m_mutex_h_half_v_inp(c_e_h_3, c_b, s9)) | (~node12(c_e_h_3, c_b, s9, s10)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s10)))),
% 293.39/185.93 inference(monotonicity,[status(thm)],[21740])).
% 293.39/185.93 tff(21742,plain,
% 293.39/185.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_3, c_b, s9, s10)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s9)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s9)) | (~node12(c_e_h_3, c_b, s9, s10)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s10))),
% 293.39/185.93 inference(transitivity,[status(thm)],[21741, 21739])).
% 293.39/185.93 tff(21743,plain,
% 293.39/185.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_3, c_b, s9, s10)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s9)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s10))),
% 293.39/185.93 inference(quant_inst,[status(thm)],[])).
% 293.39/185.93 tff(21744,plain,
% 293.39/185.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s9)) | (~node12(c_e_h_3, c_b, s9, s10)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s10)),
% 293.39/185.93 inference(modus_ponens,[status(thm)],[21743, 21742])).
% 293.39/185.93 tff(21745,plain,
% 293.39/185.93 ($false),
% 293.39/185.93 inference(unit_resolution,[status(thm)],[21744, 1483, 21737, 21738, 21726])).
% 293.39/185.93 tff(21746,plain,((~node12(c_e_h_3, c_b, s9, s10)) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s9)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s10)), inference(lemma,lemma(discharge,[]))).
% 293.39/185.93 tff(21747,plain,
% 293.39/185.93 (~node12(c_e_h_3, c_b, s9, s10)),
% 293.39/185.93 inference(unit_resolution,[status(thm)],[21746, 21726, 21737])).
% 293.39/185.93 tff(21748,plain,
% 293.39/185.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s9, s10)) | node12(c_e_h_3, c_b, s9, s10) | node13(c_e_h_3, c_b, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s9, s10)) | node12(c_e_h_3, c_b, s9, s10) | node13(c_e_h_3, c_b, s9, s10))),
% 293.39/185.93 inference(rewrite,[status(thm)],[])).
% 293.39/185.93 tff(21749,plain,
% 293.39/185.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s9, s10)) | node12(c_e_h_3, c_b, s9, s10) | node13(c_e_h_3, c_b, s9, s10))),
% 293.39/185.94 inference(quant_inst,[status(thm)],[])).
% 293.39/185.94 tff(21750,plain,
% 293.39/185.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s9, s10)) | node12(c_e_h_3, c_b, s9, s10) | node13(c_e_h_3, c_b, s9, s10)),
% 293.39/185.94 inference(modus_ponens,[status(thm)],[21749, 21748])).
% 293.39/185.94 tff(21751,plain,
% 293.39/185.94 (node12(c_e_h_3, c_b, s9, s10) | node13(c_e_h_3, c_b, s9, s10)),
% 293.39/185.94 inference(unit_resolution,[status(thm)],[21750, 439, 7676])).
% 293.39/185.94 tff(21752,plain,
% 293.39/185.94 ($false),
% 293.39/185.94 inference(unit_resolution,[status(thm)],[21751, 21747, 21736])).
% 293.39/185.94 tff(21753,plain,(m_mutex_h_half_v_out(c_e_h_3, c_b, s10) | (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s9)) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s9))), inference(lemma,lemma(discharge,[]))).
% 293.39/185.94 tff(21754,plain,
% 293.39/185.94 (~m_mutex_h_half_v_inp(c_e_h_3, c_b, s9)),
% 293.39/185.94 inference(unit_resolution,[status(thm)],[21753, 21725, 21634])).
% 293.39/185.94 tff(21755,plain,
% 293.39/185.94 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node1(c_e_h_3, c_e_h_1, s9))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node1(c_e_h_3, c_e_h_1, s9))),
% 293.39/185.94 inference(rewrite,[status(thm)],[])).
% 293.39/185.94 tff(21756,plain,
% 293.39/185.94 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node1(c_e_h_3, c_e_h_1, s9))),
% 293.39/185.94 inference(quant_inst,[status(thm)],[])).
% 293.39/185.94 tff(21757,plain,
% 293.39/185.94 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node1(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node1(c_e_h_3, c_e_h_1, s9)),
% 293.39/185.94 inference(modus_ponens,[status(thm)],[21756, 21755])).
% 293.39/185.94 tff(21758,plain,
% 293.39/185.94 (node1(c_e_h_3, c_e_h_1, s9)),
% 293.39/185.94 inference(unit_resolution,[status(thm)],[21757, 2922, 2919])).
% 293.39/185.94 tff(21759,plain,
% 293.39/185.94 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | (~m_cell_v_req(J0, X)) | m_mutex_h_half_v_inp(I0, c_b, X))) | (m_mutex_h_half_v_inp(c_e_h_3, c_b, s9) | (~node1(c_e_h_3, c_e_h_1, s9)) | (~m_cell_v_req(c_e_h_1, s9)))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | (~m_cell_v_req(J0, X)) | m_mutex_h_half_v_inp(I0, c_b, X))) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s9) | (~node1(c_e_h_3, c_e_h_1, s9)) | (~m_cell_v_req(c_e_h_1, s9)))),
% 293.39/185.94 inference(rewrite,[status(thm)],[])).
% 293.39/185.94 tff(21760,plain,
% 293.39/185.94 (((~node1(c_e_h_3, c_e_h_1, s9)) | (~m_cell_v_req(c_e_h_1, s9)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s9)) <=> (m_mutex_h_half_v_inp(c_e_h_3, c_b, s9) | (~node1(c_e_h_3, c_e_h_1, s9)) | (~m_cell_v_req(c_e_h_1, s9)))),
% 293.39/185.94 inference(rewrite,[status(thm)],[])).
% 293.39/185.94 tff(21761,plain,
% 293.39/185.94 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | (~m_cell_v_req(J0, X)) | m_mutex_h_half_v_inp(I0, c_b, X))) | ((~node1(c_e_h_3, c_e_h_1, s9)) | (~m_cell_v_req(c_e_h_1, s9)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s9))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | (~m_cell_v_req(J0, X)) | m_mutex_h_half_v_inp(I0, c_b, X))) | (m_mutex_h_half_v_inp(c_e_h_3, c_b, s9) | (~node1(c_e_h_3, c_e_h_1, s9)) | (~m_cell_v_req(c_e_h_1, s9))))),
% 293.39/185.94 inference(monotonicity,[status(thm)],[21760])).
% 293.39/185.94 tff(21762,plain,
% 293.39/185.94 (((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | (~m_cell_v_req(J0, X)) | m_mutex_h_half_v_inp(I0, c_b, X))) | ((~node1(c_e_h_3, c_e_h_1, s9)) | (~m_cell_v_req(c_e_h_1, s9)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s9))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | (~m_cell_v_req(J0, X)) | m_mutex_h_half_v_inp(I0, c_b, X))) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s9) | (~node1(c_e_h_3, c_e_h_1, s9)) | (~m_cell_v_req(c_e_h_1, s9)))),
% 293.39/185.94 inference(transitivity,[status(thm)],[21761, 21759])).
% 293.39/185.94 tff(21763,plain,
% 293.39/185.94 ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | (~m_cell_v_req(J0, X)) | m_mutex_h_half_v_inp(I0, c_b, X))) | ((~node1(c_e_h_3, c_e_h_1, s9)) | (~m_cell_v_req(c_e_h_1, s9)) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s9))),
% 293.39/185.94 inference(quant_inst,[status(thm)],[])).
% 293.39/185.94 tff(21764,plain,
% 293.39/185.94 ((~![I0: $i, X: $i, J0: $i] : ((~node1(I0, J0, X)) | (~m_cell_v_req(J0, X)) | m_mutex_h_half_v_inp(I0, c_b, X))) | m_mutex_h_half_v_inp(c_e_h_3, c_b, s9) | (~node1(c_e_h_3, c_e_h_1, s9)) | (~m_cell_v_req(c_e_h_1, s9))),
% 293.39/185.94 inference(modus_ponens,[status(thm)],[21763, 21762])).
% 293.39/185.94 tff(21765,plain,
% 293.39/185.94 (m_mutex_h_half_v_inp(c_e_h_3, c_b, s9) | (~m_cell_v_req(c_e_h_1, s9))),
% 293.39/185.94 inference(unit_resolution,[status(thm)],[21764, 17285, 21758])).
% 293.39/185.94 tff(21766,plain,
% 293.39/185.94 (~m_cell_v_req(c_e_h_1, s9)),
% 293.39/185.94 inference(unit_resolution,[status(thm)],[21765, 21754])).
% 293.39/185.94 tff(21767,assumption,(~m_cell_v_req(c_e_h_1, s9)), introduced(assumption)).
% 293.39/185.94 tff(21768,plain,
% 293.39/185.94 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_p, X)) | m_cell_v_req(I0, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_p, s9)) | m_cell_v_req(c_e_h_1, s9))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_p, X)) | m_cell_v_req(I0, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s9)) | m_cell_v_req(c_e_h_1, s9))),
% 293.39/185.94 inference(rewrite,[status(thm)],[])).
% 293.39/185.94 tff(21769,plain,
% 293.39/185.94 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_p, X)) | m_cell_v_req(I0, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_p, s9)) | m_cell_v_req(c_e_h_1, s9))),
% 293.39/185.94 inference(quant_inst,[status(thm)],[])).
% 293.39/185.94 tff(21770,plain,
% 293.39/185.94 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_p, X)) | m_cell_v_req(I0, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s9)) | m_cell_v_req(c_e_h_1, s9)),
% 293.39/185.94 inference(modus_ponens,[status(thm)],[21769, 21768])).
% 293.39/185.94 tff(21771,plain,
% 293.39/185.94 ($false),
% 293.39/185.94 inference(unit_resolution,[status(thm)],[21770, 17300, 21767, 13628])).
% 293.39/185.94 tff(21772,plain,(m_cell_v_req(c_e_h_1, s9) | (~m_and_h_gate_v_out(c_e_h_1, c_p, s9))), inference(lemma,lemma(discharge,[]))).
% 293.39/185.94 tff(21773,plain,
% 293.39/185.94 (~m_and_h_gate_v_out(c_e_h_1, c_p, s9)),
% 293.39/185.94 inference(unit_resolution,[status(thm)],[21772, 21766])).
% 293.39/185.94 tff(21774,plain,
% 293.39/185.94 (~m_and_h_gate_v_in1(c_e_h_1, c_p, s8)),
% 293.39/185.94 inference(unit_resolution,[status(thm)],[19306, 21773, 21667])).
% 293.39/185.94 tff(21775,plain,
% 293.39/185.94 ($false),
% 293.39/185.94 inference(unit_resolution,[status(thm)],[19312, 21774, 21666])).
% 293.39/185.94 tff(21776,plain,((~m_or_h_gate_v_out(c_e_h_3, c_g, s11)) | m_or_h_gate_v_out(c_e_h_3, c_g, s12) | m_or_h_gate_v_out(c_e_h_3, c_g, s10)), inference(lemma,lemma(discharge,[]))).
% 293.39/185.94 tff(21777,plain,
% 293.39/185.94 ($false),
% 293.39/185.94 inference(unit_resolution,[status(thm)],[21776, 21247, 21153, 20172])).
% 293.39/185.94 tff(21778,plain,((~m_c_h_element_v_out(c_e_h_3, c_h, s12)) | m_or_h_gate_v_out(c_e_h_3, c_g, s10) | m_c_h_element_v_out(c_e_h_3, c_h, s13)), inference(lemma,lemma(discharge,[]))).
% 293.39/185.94 tff(21779,plain,
% 293.39/185.94 (~m_c_h_element_v_out(c_e_h_3, c_h, s12)),
% 293.39/185.94 inference(unit_resolution,[status(thm)],[21778, 20902, 20172])).
% 293.39/185.94 tff(21780,assumption,(m_and_h_gate_v_out(c_e_h_3, c_k, s11)), introduced(assumption)).
% 293.39/185.94 tff(21781,assumption,(node22(c_e_h_3, c_k, s10, s11)), introduced(assumption)).
% 293.39/185.94 tff(21782,plain,
% 293.39/185.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s11)) | (~node22(c_e_h_3, c_k, s10, s11)) | m_and_h_gate_v_out(c_e_h_3, c_k, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s11)) | (~node22(c_e_h_3, c_k, s10, s11)) | m_and_h_gate_v_out(c_e_h_3, c_k, s10))),
% 293.39/185.94 inference(rewrite,[status(thm)],[])).
% 293.39/185.94 tff(21783,plain,
% 293.39/185.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_k, s11)) | (~node22(c_e_h_3, c_k, s10, s11)) | m_and_h_gate_v_out(c_e_h_3, c_k, s10))),
% 293.39/185.94 inference(quant_inst,[status(thm)],[])).
% 293.39/185.94 tff(21784,plain,
% 293.39/185.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s11)) | (~node22(c_e_h_3, c_k, s10, s11)) | m_and_h_gate_v_out(c_e_h_3, c_k, s10)),
% 293.39/185.94 inference(modus_ponens,[status(thm)],[21783, 21782])).
% 293.39/185.94 tff(21785,plain,
% 293.39/185.94 ($false),
% 293.39/185.94 inference(unit_resolution,[status(thm)],[21784, 108, 21781, 21780, 20780])).
% 293.39/185.94 tff(21786,plain,((~node22(c_e_h_3, c_k, s10, s11)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s11)) | m_and_h_gate_v_out(c_e_h_3, c_k, s10)), inference(lemma,lemma(discharge,[]))).
% 293.39/185.94 tff(21787,plain,
% 293.39/185.94 (~node22(c_e_h_3, c_k, s10, s11)),
% 293.39/185.94 inference(unit_resolution,[status(thm)],[21786, 21780, 20780])).
% 293.39/185.94 tff(21788,assumption,(~node20(c_e_h_3, c_k, s10)), introduced(assumption)).
% 293.39/185.94 tff(21789,assumption,(node21(c_e_h_3, c_k, s10, s11)), introduced(assumption)).
% 293.39/185.94 tff(21790,plain,
% 293.39/185.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_k, s10) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s11)) | (~node21(c_e_h_3, c_k, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_k, s10) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s11)) | (~node21(c_e_h_3, c_k, s10, s11)))),
% 293.39/185.94 inference(rewrite,[status(thm)],[])).
% 293.39/185.94 tff(21791,plain,
% 293.39/185.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_k, s10) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s11)) | (~node21(c_e_h_3, c_k, s10, s11)))),
% 293.39/185.94 inference(quant_inst,[status(thm)],[])).
% 293.39/185.94 tff(21792,plain,
% 293.39/185.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_k, s10) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s11)) | (~node21(c_e_h_3, c_k, s10, s11))),
% 293.39/185.94 inference(modus_ponens,[status(thm)],[21791, 21790])).
% 293.39/185.94 tff(21793,plain,
% 293.39/185.94 ($false),
% 293.39/185.94 inference(unit_resolution,[status(thm)],[21792, 52, 21789, 21780, 21788])).
% 293.39/185.94 tff(21794,plain,((~node21(c_e_h_3, c_k, s10, s11)) | (~m_and_h_gate_v_out(c_e_h_3, c_k, s11)) | node20(c_e_h_3, c_k, s10)), inference(lemma,lemma(discharge,[]))).
% 293.39/185.94 tff(21795,plain,
% 293.39/185.94 (~node21(c_e_h_3, c_k, s10, s11)),
% 293.39/185.94 inference(unit_resolution,[status(thm)],[21794, 21780, 21788])).
% 293.39/185.94 tff(21796,plain,
% 293.39/185.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s10, s11)) | node21(c_e_h_3, c_k, s10, s11) | node22(c_e_h_3, c_k, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s10, s11)) | node21(c_e_h_3, c_k, s10, s11) | node22(c_e_h_3, c_k, s10, s11))),
% 293.39/185.94 inference(rewrite,[status(thm)],[])).
% 293.39/185.94 tff(21797,plain,
% 293.39/185.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s10, s11)) | node21(c_e_h_3, c_k, s10, s11) | node22(c_e_h_3, c_k, s10, s11))),
% 293.39/185.94 inference(quant_inst,[status(thm)],[])).
% 293.39/185.94 tff(21798,plain,
% 293.39/185.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s10, s11)) | node21(c_e_h_3, c_k, s10, s11) | node22(c_e_h_3, c_k, s10, s11)),
% 293.39/185.94 inference(modus_ponens,[status(thm)],[21797, 21796])).
% 293.39/185.94 tff(21799,plain,
% 293.39/185.94 (node21(c_e_h_3, c_k, s10, s11) | node22(c_e_h_3, c_k, s10, s11)),
% 293.39/185.94 inference(unit_resolution,[status(thm)],[21798, 82, 7748])).
% 293.39/185.94 tff(21800,plain,
% 293.39/185.94 ($false),
% 293.39/185.94 inference(unit_resolution,[status(thm)],[21799, 21795, 21787])).
% 293.39/185.94 tff(21801,plain,((~m_and_h_gate_v_out(c_e_h_3, c_k, s11)) | node20(c_e_h_3, c_k, s10) | m_and_h_gate_v_out(c_e_h_3, c_k, s10)), inference(lemma,lemma(discharge,[]))).
% 293.39/185.94 tff(21802,plain,
% 293.39/185.94 (~m_and_h_gate_v_out(c_e_h_3, c_k, s11)),
% 293.39/185.94 inference(unit_resolution,[status(thm)],[21801, 20778, 20809])).
% 293.39/185.94 tff(21803,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_l, s11)), introduced(assumption)).
% 293.39/185.94 tff(21804,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_k, s11)), introduced(assumption)).
% 293.39/185.94 tff(21805,plain,
% 293.39/185.94 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_l, s11)) | m_and_h_gate_v_out(c_e_h_3, c_k, s11))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s11)) | m_and_h_gate_v_out(c_e_h_3, c_k, s11))),
% 293.39/185.94 inference(rewrite,[status(thm)],[])).
% 293.39/185.94 tff(21806,plain,
% 293.39/185.94 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_l, s11)) | m_and_h_gate_v_out(c_e_h_3, c_k, s11))),
% 293.39/185.95 inference(quant_inst,[status(thm)],[])).
% 293.39/185.95 tff(21807,plain,
% 293.39/185.95 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s11)) | m_and_h_gate_v_out(c_e_h_3, c_k, s11)),
% 293.39/185.95 inference(modus_ponens,[status(thm)],[21806, 21805])).
% 293.39/185.95 tff(21808,plain,
% 293.39/185.95 ($false),
% 293.39/185.95 inference(unit_resolution,[status(thm)],[21807, 1529, 21804, 21803])).
% 293.39/185.95 tff(21809,plain,(m_and_h_gate_v_out(c_e_h_3, c_k, s11) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s11))), inference(lemma,lemma(discharge,[]))).
% 293.39/185.95 tff(21810,plain,
% 293.39/185.95 (~m_and_h_gate_v_in1(c_e_h_3, c_l, s11)),
% 293.39/185.95 inference(unit_resolution,[status(thm)],[21809, 21802])).
% 293.39/185.95 tff(21811,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_l, s11)), introduced(assumption)).
% 293.39/185.95 tff(21812,assumption,(node20(c_e_h_3, c_l, s11)), introduced(assumption)).
% 293.39/185.95 tff(21813,plain,
% 293.39/185.95 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_l, s11)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s11))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_l, s11)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s11))),
% 293.39/185.95 inference(rewrite,[status(thm)],[])).
% 293.39/185.95 tff(21814,plain,
% 293.39/185.95 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_l, s11)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s11))),
% 293.39/185.95 inference(quant_inst,[status(thm)],[])).
% 293.39/185.95 tff(21815,plain,
% 293.39/185.95 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_l, s11)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s11)),
% 293.39/185.95 inference(modus_ponens,[status(thm)],[21814, 21813])).
% 293.39/185.95 tff(21816,plain,
% 293.39/185.95 ($false),
% 293.39/185.95 inference(unit_resolution,[status(thm)],[21815, 38, 21812, 21811])).
% 293.39/185.95 tff(21817,plain,(m_and_h_gate_v_in1(c_e_h_3, c_l, s11) | (~node20(c_e_h_3, c_l, s11))), inference(lemma,lemma(discharge,[]))).
% 293.39/185.95 tff(21818,plain,
% 293.39/185.95 (~node20(c_e_h_3, c_l, s11)),
% 293.39/185.95 inference(unit_resolution,[status(thm)],[21817, 21810])).
% 293.39/185.95 tff(21819,plain,
% 293.39/185.95 (~m_or_h_gate_v_out(c_e_h_3, c_g, s6)),
% 293.39/185.95 inference(unit_resolution,[status(thm)],[10319, 20177, 20176])).
% 293.39/185.95 tff(21820,plain,
% 293.39/185.95 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s6)),
% 293.39/185.95 inference(unit_resolution,[status(thm)],[10448, 2048, 21819])).
% 293.39/185.95 tff(21821,plain,
% 293.39/185.95 (~m_or_h_gate_v_out(c_e_h_3, c_g, s7)),
% 293.39/185.95 inference(unit_resolution,[status(thm)],[10302, 21819, 10016, 20194, 2743])).
% 293.39/185.95 tff(21822,plain,
% 293.39/185.95 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s7)),
% 293.39/185.95 inference(unit_resolution,[status(thm)],[10395, 21821])).
% 293.39/185.95 tff(21823,plain,
% 293.39/185.95 (~node20(c_e_h_3, c_k, s7)),
% 293.39/185.95 inference(unit_resolution,[status(thm)],[10403, 21822])).
% 293.39/185.95 tff(21824,plain,
% 293.39/185.95 (~m_or_h_gate_v_out(c_e_h_3, c_g, s8)),
% 293.39/185.95 inference(unit_resolution,[status(thm)],[20223, 21819, 10016, 2743])).
% 293.39/185.95 tff(21825,plain,
% 293.39/185.95 (~m_and_h_gate_v_out(c_e_h_3, c_k, s7)),
% 293.39/185.95 inference(unit_resolution,[status(thm)],[10440, 7637, 10427])).
% 293.39/185.95 tff(21826,plain,
% 293.39/185.95 (~m_and_h_gate_v_in1(c_e_h_3, c_l, s7)),
% 293.39/185.95 inference(unit_resolution,[status(thm)],[10601, 21825])).
% 293.39/185.95 tff(21827,plain,
% 293.39/185.95 (~node20(c_e_h_3, c_l, s7)),
% 293.39/185.95 inference(unit_resolution,[status(thm)],[10595, 21826])).
% 293.39/185.95 tff(21828,plain,
% 293.39/185.95 ($false),
% 293.39/185.95 inference(unit_resolution,[status(thm)],[10588, 21827, 7640, 5524])).
% 293.39/185.95 tff(21829,plain,(node20(c_e_h_3, c_k, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s8)) | node20(c_e_h_3, c_k, s6) | node20(c_e_h_3, c_k, s5)), inference(lemma,lemma(discharge,[]))).
% 293.39/185.95 tff(21830,plain,
% 293.39/185.95 (node20(c_e_h_3, c_k, s6)),
% 293.39/185.95 inference(unit_resolution,[status(thm)],[21829, 20267, 5524, 5926])).
% 293.39/185.95 tff(21831,plain,
% 293.39/185.95 (m_and_h_gate_v_in1(c_e_h_3, c_k, s6)),
% 293.39/185.95 inference(unit_resolution,[status(thm)],[10444, 38, 21830])).
% 293.39/185.95 tff(21832,plain,
% 293.39/185.95 (m_or_h_gate_v_out(c_e_h_3, c_g, s6)),
% 293.39/185.95 inference(unit_resolution,[status(thm)],[10448, 2048, 21831])).
% 293.39/185.95 tff(21833,plain,
% 293.39/185.95 (m_and_h_gate_v_out(c_e_h_3, c_c, s5)),
% 293.39/185.95 inference(unit_resolution,[status(thm)],[10319, 21832, 20176])).
% 293.39/185.95 tff(21834,plain,
% 293.39/185.95 (m_mutex_h_half_v_out(c_e_h_3, c_a, s4)),
% 293.39/185.95 inference(unit_resolution,[status(thm)],[10330, 21833])).
% 293.39/185.95 tff(21835,plain,
% 293.39/185.95 (m_user_v_req(c_e_h_3, c_u, s3)),
% 293.39/185.95 inference(unit_resolution,[status(thm)],[550, 21834])).
% 293.39/185.95 tff(21836,plain,
% 293.39/185.95 (m_user_v_req(c_e_h_3, c_u, s4)),
% 293.39/185.95 inference(unit_resolution,[status(thm)],[732, 21835])).
% 293.39/185.95 tff(21837,plain,
% 293.39/185.95 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s4)),
% 293.39/185.95 inference(unit_resolution,[status(thm)],[1445, 21836])).
% 293.39/185.95 tff(21838,plain,
% 293.39/185.95 (~m_or_h_gate_v_out(c_e_h_3, c_g, s7)),
% 293.39/185.95 inference(unit_resolution,[status(thm)],[10387, 20176, 9500, 2743, 3360])).
% 293.39/185.95 tff(21839,plain,
% 293.39/185.95 (node4(c_e_h_3, c_g, s6)),
% 293.39/185.95 inference(unit_resolution,[status(thm)],[10485, 21832, 21838])).
% 293.39/185.95 tff(21840,plain,
% 293.39/185.95 (~m_or_h_gate_v_in1(c_e_h_3, c_g, s6)),
% 293.39/185.95 inference(unit_resolution,[status(thm)],[11092, 21839])).
% 293.39/185.95 tff(21841,plain,
% 293.39/185.95 (~m_and_h_gate_v_out(c_e_h_3, c_c, s6)),
% 293.39/185.95 inference(unit_resolution,[status(thm)],[10996, 21840])).
% 293.39/185.95 tff(21842,plain,
% 293.39/185.95 (~m_and_h_gate_v_in1(c_e_h_3, c_c, s5)),
% 293.39/185.95 inference(unit_resolution,[status(thm)],[10378, 21841, 21833])).
% 293.39/185.95 tff(21843,plain,
% 293.39/185.95 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s5)),
% 293.39/185.95 inference(unit_resolution,[status(thm)],[10341, 21842])).
% 293.39/185.95 tff(21844,plain,
% 293.39/185.95 ($false),
% 293.39/185.95 inference(unit_resolution,[status(thm)],[1488, 21843, 21837, 21834])).
% 293.39/185.95 tff(21845,plain,(m_and_h_gate_v_out(c_e_h_3, c_c, s4) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s8)) | m_or_h_gate_v_out(c_e_h_3, c_g, s8) | m_or_h_gate_v_out(c_e_h_3, c_g, s5)), inference(lemma,lemma(discharge,[]))).
% 293.39/185.95 tff(21846,plain,
% 293.39/185.95 (~m_and_h_gate_v_out(c_e_h_3, c_l, s8)),
% 293.39/185.95 inference(unit_resolution,[status(thm)],[21845, 21824, 2743, 20194])).
% 293.39/185.95 tff(21847,plain,
% 293.39/185.95 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_l, s9)) | m_and_h_gate_v_out(c_e_h_3, c_k, s9))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s9)) | m_and_h_gate_v_out(c_e_h_3, c_k, s9))),
% 293.39/185.95 inference(rewrite,[status(thm)],[])).
% 293.39/185.95 tff(21848,plain,
% 293.39/185.95 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_l, s9)) | m_and_h_gate_v_out(c_e_h_3, c_k, s9))),
% 293.39/185.95 inference(quant_inst,[status(thm)],[])).
% 293.39/185.95 tff(21849,plain,
% 293.39/185.95 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s9)) | m_and_h_gate_v_out(c_e_h_3, c_k, s9)),
% 293.39/185.95 inference(modus_ponens,[status(thm)],[21848, 21847])).
% 293.39/185.95 tff(21850,plain,
% 293.39/185.95 ($false),
% 293.39/185.95 inference(unit_resolution,[status(thm)],[21849, 1529, 9469, 9036])).
% 293.39/185.95 tff(21851,plain,(m_and_h_gate_v_out(c_e_h_3, c_k, s9) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s9))), inference(lemma,lemma(discharge,[]))).
% 293.39/185.95 tff(21852,plain,
% 293.39/185.95 (~m_and_h_gate_v_in1(c_e_h_3, c_l, s9)),
% 293.39/185.95 inference(unit_resolution,[status(thm)],[21851, 9469])).
% 293.39/185.95 tff(21853,assumption,(node20(c_e_h_3, c_l, s9)), introduced(assumption)).
% 293.39/185.95 tff(21854,plain,
% 293.39/185.95 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_l, s9)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s9))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_l, s9)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s9))),
% 293.39/185.95 inference(rewrite,[status(thm)],[])).
% 293.39/185.95 tff(21855,plain,
% 293.39/185.95 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_l, s9)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s9))),
% 293.39/185.95 inference(quant_inst,[status(thm)],[])).
% 293.39/185.95 tff(21856,plain,
% 293.39/185.95 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_l, s9)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s9)),
% 293.39/185.95 inference(modus_ponens,[status(thm)],[21855, 21854])).
% 293.39/185.95 tff(21857,plain,
% 293.39/185.95 ($false),
% 293.39/185.95 inference(unit_resolution,[status(thm)],[21856, 38, 21853, 9460])).
% 293.39/185.95 tff(21858,plain,(m_and_h_gate_v_in1(c_e_h_3, c_l, s9) | (~node20(c_e_h_3, c_l, s9))), inference(lemma,lemma(discharge,[]))).
% 293.39/185.95 tff(21859,plain,
% 293.39/185.95 (~node20(c_e_h_3, c_l, s9)),
% 293.39/185.95 inference(unit_resolution,[status(thm)],[21858, 21852])).
% 293.39/185.95 tff(21860,assumption,(~node20(c_e_h_3, c_l, s9)), introduced(assumption)).
% 293.39/185.95 tff(21861,plain,
% 293.39/185.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s10)) | node20(c_e_h_3, c_l, s9) | (~node21(c_e_h_3, c_l, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s10)) | node20(c_e_h_3, c_l, s9) | (~node21(c_e_h_3, c_l, s9, s10)))),
% 293.39/185.95 inference(rewrite,[status(thm)],[])).
% 293.39/185.95 tff(21862,plain,
% 293.39/185.95 ((node20(c_e_h_3, c_l, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s10)) | (~node21(c_e_h_3, c_l, s9, s10))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_l, s10)) | node20(c_e_h_3, c_l, s9) | (~node21(c_e_h_3, c_l, s9, s10)))),
% 293.39/185.95 inference(rewrite,[status(thm)],[])).
% 293.39/185.95 tff(21863,plain,
% 293.39/185.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s10)) | (~node21(c_e_h_3, c_l, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s10)) | node20(c_e_h_3, c_l, s9) | (~node21(c_e_h_3, c_l, s9, s10))))),
% 293.39/185.95 inference(monotonicity,[status(thm)],[21862])).
% 293.39/185.95 tff(21864,plain,
% 293.39/185.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s10)) | (~node21(c_e_h_3, c_l, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s10)) | node20(c_e_h_3, c_l, s9) | (~node21(c_e_h_3, c_l, s9, s10)))),
% 293.39/185.95 inference(transitivity,[status(thm)],[21863, 21861])).
% 293.39/185.95 tff(21865,plain,
% 293.39/185.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s9) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s10)) | (~node21(c_e_h_3, c_l, s9, s10)))),
% 293.39/185.95 inference(quant_inst,[status(thm)],[])).
% 293.39/185.95 tff(21866,plain,
% 293.39/185.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s10)) | node20(c_e_h_3, c_l, s9) | (~node21(c_e_h_3, c_l, s9, s10))),
% 293.39/185.95 inference(modus_ponens,[status(thm)],[21865, 21864])).
% 293.39/185.95 tff(21867,plain,
% 293.39/185.95 ($false),
% 293.39/185.95 inference(unit_resolution,[status(thm)],[21866, 52, 9450, 11031, 21860])).
% 293.39/185.95 tff(21868,plain,((~node21(c_e_h_3, c_l, s9, s10)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s10)) | node20(c_e_h_3, c_l, s9)), inference(lemma,lemma(discharge,[]))).
% 293.39/185.95 tff(21869,plain,
% 293.39/185.95 (~node21(c_e_h_3, c_l, s9, s10)),
% 293.39/185.95 inference(unit_resolution,[status(thm)],[21868, 11031, 21860])).
% 293.39/185.95 tff(21870,plain,
% 293.39/185.95 (node22(c_e_h_3, c_l, s9, s10)),
% 293.39/185.95 inference(unit_resolution,[status(thm)],[9034, 21869])).
% 293.39/185.95 tff(21871,plain,
% 293.39/185.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s10)) | (~node22(c_e_h_3, c_l, s9, s10)) | m_and_h_gate_v_out(c_e_h_3, c_l, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s10)) | (~node22(c_e_h_3, c_l, s9, s10)) | m_and_h_gate_v_out(c_e_h_3, c_l, s9))),
% 293.39/185.95 inference(rewrite,[status(thm)],[])).
% 293.39/185.95 tff(21872,plain,
% 293.39/185.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s10)) | (~node22(c_e_h_3, c_l, s9, s10)) | m_and_h_gate_v_out(c_e_h_3, c_l, s9))),
% 293.39/185.96 inference(quant_inst,[status(thm)],[])).
% 293.39/185.96 tff(21873,plain,
% 293.39/185.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s10)) | (~node22(c_e_h_3, c_l, s9, s10)) | m_and_h_gate_v_out(c_e_h_3, c_l, s9)),
% 293.39/185.96 inference(modus_ponens,[status(thm)],[21872, 21871])).
% 293.39/185.96 tff(21874,plain,
% 293.39/185.96 ($false),
% 293.39/185.96 inference(unit_resolution,[status(thm)],[21873, 108, 21870, 11031, 8974])).
% 293.39/185.96 tff(21875,plain,((~m_and_h_gate_v_out(c_e_h_3, c_l, s10)) | m_and_h_gate_v_out(c_e_h_3, c_l, s9) | node20(c_e_h_3, c_l, s9)), inference(lemma,lemma(discharge,[]))).
% 293.39/185.96 tff(21876,plain,
% 293.39/185.96 (m_and_h_gate_v_out(c_e_h_3, c_l, s9)),
% 293.39/185.96 inference(unit_resolution,[status(thm)],[21875, 21859, 11031])).
% 293.39/185.96 tff(21877,plain,
% 293.39/185.96 (~m_c_h_element_v_out(c_e_h_3, c_h, s8)),
% 293.39/185.96 inference(unit_resolution,[status(thm)],[7551, 20175])).
% 293.39/185.96 tff(21878,plain,
% 293.39/185.96 (m_and_h_gate_v_in2(c_e_h_3, c_k, s8)),
% 293.39/185.96 inference(unit_resolution,[status(thm)],[7644, 21877])).
% 293.39/185.96 tff(21879,plain,
% 293.39/185.96 (~m_and_h_gate_v_out(c_e_h_3, c_k, s8)),
% 293.39/185.96 inference(unit_resolution,[status(thm)],[10528, 9469, 20269, 2743, 20176, 20194, 21878, 20268])).
% 293.39/185.96 tff(21880,plain,
% 293.39/185.96 (~m_and_h_gate_v_in1(c_e_h_3, c_l, s8)),
% 293.39/185.96 inference(unit_resolution,[status(thm)],[10536, 21879])).
% 293.39/185.96 tff(21881,plain,
% 293.39/185.96 (~node20(c_e_h_3, c_l, s8)),
% 293.39/185.96 inference(unit_resolution,[status(thm)],[10544, 21880])).
% 293.39/185.96 tff(21882,plain,
% 293.39/185.96 ($false),
% 293.39/185.96 inference(unit_resolution,[status(thm)],[10569, 21881, 21876, 6450])).
% 293.39/185.96 tff(21883,plain,(m_and_h_gate_v_out(c_e_h_3, c_k, s9) | m_and_h_gate_v_out(c_e_h_3, c_l, s8) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s10)) | m_and_h_gate_v_out(c_e_h_3, c_c, s4)), inference(lemma,lemma(discharge,[]))).
% 293.39/185.96 tff(21884,plain,
% 293.39/185.96 (m_and_h_gate_v_out(c_e_h_3, c_k, s9)),
% 293.39/185.96 inference(unit_resolution,[status(thm)],[21883, 21846, 11031, 2743])).
% 293.39/185.96 tff(21885,plain,
% 293.39/185.96 (~m_and_h_gate_v_in1(c_e_h_3, c_k, s8)),
% 293.39/185.96 inference(unit_resolution,[status(thm)],[20278, 2048, 21824])).
% 293.39/185.96 tff(21886,plain,
% 293.39/185.96 (~node20(c_e_h_3, c_k, s8)),
% 293.39/185.96 inference(unit_resolution,[status(thm)],[20286, 21885])).
% 293.39/185.96 tff(21887,plain,
% 293.39/185.96 (m_and_h_gate_v_out(c_e_h_3, c_k, s8)),
% 293.39/185.96 inference(unit_resolution,[status(thm)],[20303, 21886, 21884])).
% 293.39/185.96 tff(21888,plain,
% 293.39/185.96 (m_and_h_gate_v_out(c_e_h_3, c_k, s7)),
% 293.39/185.96 inference(unit_resolution,[status(thm)],[10425, 21887, 21823])).
% 293.39/185.96 tff(21889,plain,
% 293.39/185.96 (node20(c_e_h_3, c_k, s6)),
% 293.39/185.96 inference(unit_resolution,[status(thm)],[10440, 21888, 20269])).
% 293.39/185.96 tff(21890,plain,
% 293.39/185.96 ($false),
% 293.39/185.96 inference(unit_resolution,[status(thm)],[10444, 38, 21889, 21820])).
% 293.39/185.96 tff(21891,plain,(m_and_h_gate_v_out(c_e_h_3, c_c, s7) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s10)) | m_and_h_gate_v_out(c_e_h_3, c_c, s4)), inference(lemma,lemma(discharge,[]))).
% 293.39/185.96 tff(21892,plain,
% 293.39/185.96 (~m_and_h_gate_v_out(c_e_h_3, c_l, s10)),
% 293.39/185.96 inference(unit_resolution,[status(thm)],[21891, 10016, 2743])).
% 293.39/185.96 tff(21893,assumption,(~node20(c_e_h_3, c_l, s10)), introduced(assumption)).
% 293.39/185.96 tff(21894,assumption,(~m_c_h_element_v_out(c_e_h_3, c_h, s12)), introduced(assumption)).
% 293.39/185.96 tff(21895,assumption,(~node20(c_e_h_3, c_l, s11)), introduced(assumption)).
% 293.39/185.96 tff(21896,assumption,(m_and_h_gate_v_out(c_e_h_3, c_l, s11)), introduced(assumption)).
% 293.39/185.96 tff(21897,assumption,(node22(c_e_h_3, c_l, s10, s11)), introduced(assumption)).
% 293.39/185.96 tff(21898,plain,
% 293.39/185.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s11)) | (~node22(c_e_h_3, c_l, s10, s11)) | m_and_h_gate_v_out(c_e_h_3, c_l, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s11)) | (~node22(c_e_h_3, c_l, s10, s11)) | m_and_h_gate_v_out(c_e_h_3, c_l, s10))),
% 293.39/185.96 inference(rewrite,[status(thm)],[])).
% 293.39/185.96 tff(21899,plain,
% 293.39/185.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s11)) | (~node22(c_e_h_3, c_l, s10, s11)) | m_and_h_gate_v_out(c_e_h_3, c_l, s10))),
% 293.39/185.96 inference(quant_inst,[status(thm)],[])).
% 293.39/185.96 tff(21900,plain,
% 293.39/185.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s11)) | (~node22(c_e_h_3, c_l, s10, s11)) | m_and_h_gate_v_out(c_e_h_3, c_l, s10)),
% 293.39/185.96 inference(modus_ponens,[status(thm)],[21899, 21898])).
% 293.39/185.96 tff(21901,plain,
% 293.39/185.96 ($false),
% 293.39/185.96 inference(unit_resolution,[status(thm)],[21900, 108, 21897, 9020, 21896])).
% 293.39/185.96 tff(21902,plain,((~node22(c_e_h_3, c_l, s10, s11)) | m_and_h_gate_v_out(c_e_h_3, c_l, s10) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s11))), inference(lemma,lemma(discharge,[]))).
% 293.39/185.96 tff(21903,plain,
% 293.39/185.96 (~node22(c_e_h_3, c_l, s10, s11)),
% 293.39/185.96 inference(unit_resolution,[status(thm)],[21902, 21896, 9020])).
% 293.39/185.96 tff(21904,assumption,(node21(c_e_h_3, c_l, s10, s11)), introduced(assumption)).
% 293.39/185.96 tff(21905,plain,
% 293.39/185.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s10) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s11)) | (~node21(c_e_h_3, c_l, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_l, s10) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s11)) | (~node21(c_e_h_3, c_l, s10, s11)))),
% 293.39/185.96 inference(rewrite,[status(thm)],[])).
% 293.39/185.96 tff(21906,plain,
% 293.39/185.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s10) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s11)) | (~node21(c_e_h_3, c_l, s10, s11)))),
% 293.39/185.96 inference(quant_inst,[status(thm)],[])).
% 293.39/185.96 tff(21907,plain,
% 293.39/185.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_l, s10) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s11)) | (~node21(c_e_h_3, c_l, s10, s11))),
% 293.39/185.96 inference(modus_ponens,[status(thm)],[21906, 21905])).
% 293.39/185.96 tff(21908,plain,
% 293.39/185.96 ($false),
% 293.39/185.96 inference(unit_resolution,[status(thm)],[21907, 52, 21904, 21896, 21893])).
% 293.39/185.96 tff(21909,plain,((~node21(c_e_h_3, c_l, s10, s11)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s11)) | node20(c_e_h_3, c_l, s10)), inference(lemma,lemma(discharge,[]))).
% 293.39/185.96 tff(21910,plain,
% 293.39/185.96 (~node21(c_e_h_3, c_l, s10, s11)),
% 293.39/185.96 inference(unit_resolution,[status(thm)],[21909, 21896, 21893])).
% 293.39/185.96 tff(21911,plain,
% 293.39/185.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s10, s11)) | node21(c_e_h_3, c_l, s10, s11) | node22(c_e_h_3, c_l, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s10, s11)) | node21(c_e_h_3, c_l, s10, s11) | node22(c_e_h_3, c_l, s10, s11))),
% 293.39/185.96 inference(rewrite,[status(thm)],[])).
% 293.39/185.96 tff(21912,plain,
% 293.39/185.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s10, s11)) | node21(c_e_h_3, c_l, s10, s11) | node22(c_e_h_3, c_l, s10, s11))),
% 293.39/185.96 inference(quant_inst,[status(thm)],[])).
% 293.39/185.96 tff(21913,plain,
% 293.39/185.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s10, s11)) | node21(c_e_h_3, c_l, s10, s11) | node22(c_e_h_3, c_l, s10, s11)),
% 293.39/185.96 inference(modus_ponens,[status(thm)],[21912, 21911])).
% 293.39/185.96 tff(21914,plain,
% 293.39/185.96 (node21(c_e_h_3, c_l, s10, s11) | node22(c_e_h_3, c_l, s10, s11)),
% 293.39/185.96 inference(unit_resolution,[status(thm)],[21913, 82, 7748])).
% 293.39/185.96 tff(21915,plain,
% 293.39/185.96 ($false),
% 293.39/185.96 inference(unit_resolution,[status(thm)],[21914, 21910, 21903])).
% 293.39/185.96 tff(21916,plain,((~m_and_h_gate_v_out(c_e_h_3, c_l, s11)) | node20(c_e_h_3, c_l, s10) | m_and_h_gate_v_out(c_e_h_3, c_l, s10)), inference(lemma,lemma(discharge,[]))).
% 293.39/185.96 tff(21917,plain,
% 293.39/185.96 (~m_and_h_gate_v_out(c_e_h_3, c_l, s11)),
% 293.39/185.96 inference(unit_resolution,[status(thm)],[21916, 21892, 21893])).
% 293.39/185.96 tff(21918,assumption,(m_and_h_gate_v_out(c_e_h_3, c_l, s12)), introduced(assumption)).
% 293.39/185.96 tff(21919,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_l, s11)), introduced(assumption)).
% 293.39/185.96 tff(21920,assumption,(node21(c_e_h_3, c_l, s11, s12)), introduced(assumption)).
% 293.39/185.96 tff(21921,plain,
% 293.39/185.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s11) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s12)) | (~node21(c_e_h_3, c_l, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_l, s11) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s12)) | (~node21(c_e_h_3, c_l, s11, s12)))),
% 293.39/185.96 inference(rewrite,[status(thm)],[])).
% 293.39/185.96 tff(21922,plain,
% 293.39/185.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s11) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s12)) | (~node21(c_e_h_3, c_l, s11, s12)))),
% 293.39/185.96 inference(quant_inst,[status(thm)],[])).
% 293.39/185.96 tff(21923,plain,
% 293.39/185.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_l, s11) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s12)) | (~node21(c_e_h_3, c_l, s11, s12))),
% 293.39/185.96 inference(modus_ponens,[status(thm)],[21922, 21921])).
% 293.39/185.96 tff(21924,plain,
% 293.39/185.96 ($false),
% 293.39/185.96 inference(unit_resolution,[status(thm)],[21923, 52, 21920, 21895, 21918])).
% 293.39/185.96 tff(21925,plain,((~node21(c_e_h_3, c_l, s11, s12)) | node20(c_e_h_3, c_l, s11) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s12))), inference(lemma,lemma(discharge,[]))).
% 293.39/185.96 tff(21926,plain,
% 293.39/185.96 (~node21(c_e_h_3, c_l, s11, s12)),
% 293.39/185.96 inference(unit_resolution,[status(thm)],[21925, 21918, 21895])).
% 293.39/185.96 tff(21927,plain,
% 293.39/185.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s11, s12)) | node21(c_e_h_3, c_l, s11, s12) | node22(c_e_h_3, c_l, s11, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s11, s12)) | node21(c_e_h_3, c_l, s11, s12) | node22(c_e_h_3, c_l, s11, s12))),
% 293.39/185.96 inference(rewrite,[status(thm)],[])).
% 293.39/185.96 tff(21928,plain,
% 293.39/185.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s11, s12)) | node21(c_e_h_3, c_l, s11, s12) | node22(c_e_h_3, c_l, s11, s12))),
% 293.39/185.96 inference(quant_inst,[status(thm)],[])).
% 293.39/185.96 tff(21929,plain,
% 293.39/185.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s11, s12)) | node21(c_e_h_3, c_l, s11, s12) | node22(c_e_h_3, c_l, s11, s12)),
% 293.39/185.96 inference(modus_ponens,[status(thm)],[21928, 21927])).
% 293.39/185.96 tff(21930,plain,
% 293.39/185.96 (node21(c_e_h_3, c_l, s11, s12) | node22(c_e_h_3, c_l, s11, s12)),
% 293.39/185.96 inference(unit_resolution,[status(thm)],[21929, 82, 11461])).
% 293.39/185.96 tff(21931,plain,
% 293.39/185.96 (node22(c_e_h_3, c_l, s11, s12)),
% 293.39/185.96 inference(unit_resolution,[status(thm)],[21930, 21926])).
% 293.39/185.96 tff(21932,plain,
% 293.39/185.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s12)) | (~node22(c_e_h_3, c_l, s11, s12)) | m_and_h_gate_v_out(c_e_h_3, c_l, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s12)) | (~node22(c_e_h_3, c_l, s11, s12)) | m_and_h_gate_v_out(c_e_h_3, c_l, s11))),
% 293.39/185.96 inference(rewrite,[status(thm)],[])).
% 293.39/185.96 tff(21933,plain,
% 293.39/185.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s12)) | (~node22(c_e_h_3, c_l, s11, s12)) | m_and_h_gate_v_out(c_e_h_3, c_l, s11))),
% 293.39/185.96 inference(quant_inst,[status(thm)],[])).
% 293.39/185.96 tff(21934,plain,
% 293.39/185.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s12)) | (~node22(c_e_h_3, c_l, s11, s12)) | m_and_h_gate_v_out(c_e_h_3, c_l, s11)),
% 293.39/185.97 inference(modus_ponens,[status(thm)],[21933, 21932])).
% 293.39/185.97 tff(21935,plain,
% 293.39/185.97 ($false),
% 293.39/185.97 inference(unit_resolution,[status(thm)],[21934, 108, 21931, 21919, 21918])).
% 293.39/185.97 tff(21936,plain,((~m_and_h_gate_v_out(c_e_h_3, c_l, s12)) | m_and_h_gate_v_out(c_e_h_3, c_l, s11) | node20(c_e_h_3, c_l, s11)), inference(lemma,lemma(discharge,[]))).
% 293.39/185.97 tff(21937,plain,
% 293.39/185.97 (~m_and_h_gate_v_out(c_e_h_3, c_l, s12)),
% 293.39/185.97 inference(unit_resolution,[status(thm)],[21936, 21917, 21895])).
% 293.39/185.97 tff(21938,plain,
% 293.39/185.97 (~m_and_h_gate_v_in1(c_e_h_3, c_i, s8)),
% 293.39/185.97 inference(unit_resolution,[status(thm)],[11251, 619, 21877])).
% 293.39/185.97 tff(21939,plain,
% 293.39/185.97 (~node20(c_e_h_3, c_i, s8)),
% 293.39/185.97 inference(unit_resolution,[status(thm)],[11233, 38, 21938])).
% 293.39/185.97 tff(21940,plain,
% 293.39/185.97 (~m_and_h_gate_v_out(c_e_h_3, c_i, s9)),
% 293.39/185.97 inference(unit_resolution,[status(thm)],[11363, 21939])).
% 293.39/185.97 tff(21941,plain,
% 293.39/185.97 (~m_c_h_element_v_in2(c_e_h_3, c_f, s9)),
% 293.39/185.97 inference(unit_resolution,[status(thm)],[11481, 21940])).
% 293.39/185.97 tff(21942,plain,
% 293.39/185.97 (~m_c_h_element_v_out(c_e_h_3, c_f, s10)),
% 293.39/185.97 inference(unit_resolution,[status(thm)],[11676, 21941])).
% 293.39/185.97 tff(21943,plain,
% 293.39/185.97 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s10)),
% 293.39/185.97 inference(unit_resolution,[status(thm)],[13007, 21942])).
% 293.39/185.97 tff(21944,plain,
% 293.39/185.97 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s11)),
% 293.39/185.97 inference(unit_resolution,[status(thm)],[13158, 21943])).
% 293.39/185.97 tff(21945,plain,
% 293.39/185.97 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s11)),
% 293.39/185.97 inference(unit_resolution,[status(thm)],[13162, 5601, 21944])).
% 293.39/185.97 tff(21946,plain,
% 293.39/185.97 (~node9(c_e_h_3, c_n, s11)),
% 293.39/185.97 inference(unit_resolution,[status(thm)],[13166, 4972, 21945])).
% 293.39/185.97 tff(21947,plain,
% 293.39/185.97 (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s12)),
% 293.39/185.97 inference(unit_resolution,[status(thm)],[13218, 21946])).
% 293.39/185.97 tff(21948,plain,
% 293.39/185.97 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s12)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s12))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s12)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s12))),
% 293.39/185.97 inference(rewrite,[status(thm)],[])).
% 293.39/185.97 tff(21949,plain,
% 293.39/185.97 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s12)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s12))),
% 293.39/185.97 inference(quant_inst,[status(thm)],[])).
% 293.39/185.97 tff(21950,plain,
% 293.39/185.97 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s12)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s12)),
% 293.39/185.97 inference(modus_ponens,[status(thm)],[21949, 21948])).
% 293.39/185.97 tff(21951,plain,
% 293.39/185.97 (~m_and_h_gate_v_in2(c_e_h_3, c_q, s12)),
% 293.39/185.97 inference(unit_resolution,[status(thm)],[21950, 5621, 21947])).
% 293.39/185.97 tff(21952,plain,
% 293.39/185.97 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s12)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s12))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s12)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s12))),
% 293.39/185.97 inference(rewrite,[status(thm)],[])).
% 293.39/185.97 tff(21953,plain,
% 293.39/185.97 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s12)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s12))),
% 293.39/185.97 inference(quant_inst,[status(thm)],[])).
% 293.39/185.97 tff(21954,plain,
% 293.39/185.97 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s12)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s12)),
% 293.39/185.97 inference(modus_ponens,[status(thm)],[21953, 21952])).
% 293.39/185.97 tff(21955,plain,
% 293.39/185.97 (~node20(c_e_h_3, c_q, s12)),
% 293.39/185.97 inference(unit_resolution,[status(thm)],[21954, 4563, 21951])).
% 293.39/185.97 tff(21956,plain,
% 293.39/185.97 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s11)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s11)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11))),
% 293.47/185.97 inference(rewrite,[status(thm)],[])).
% 293.47/185.97 tff(21957,plain,
% 293.47/185.97 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s11)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11))),
% 293.47/185.97 inference(quant_inst,[status(thm)],[])).
% 293.47/185.97 tff(21958,plain,
% 293.47/185.97 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s11)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11)),
% 293.47/185.97 inference(modus_ponens,[status(thm)],[21957, 21956])).
% 293.47/185.97 tff(21959,plain,
% 293.47/185.97 (~m_and_h_gate_v_in2(c_e_h_3, c_q, s11)),
% 293.47/185.97 inference(unit_resolution,[status(thm)],[21958, 5621, 13197])).
% 293.47/185.97 tff(21960,plain,
% 293.47/185.97 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s11)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s11))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s11)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s11))),
% 293.47/185.97 inference(rewrite,[status(thm)],[])).
% 293.47/185.97 tff(21961,plain,
% 293.47/185.97 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s11)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s11))),
% 293.47/185.97 inference(quant_inst,[status(thm)],[])).
% 293.47/185.97 tff(21962,plain,
% 293.47/185.97 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s11)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s11)),
% 293.47/185.97 inference(modus_ponens,[status(thm)],[21961, 21960])).
% 293.47/185.97 tff(21963,plain,
% 293.47/185.97 (~node20(c_e_h_3, c_q, s11)),
% 293.47/185.97 inference(unit_resolution,[status(thm)],[21962, 4563, 21959])).
% 293.47/185.97 tff(21964,assumption,(m_and_h_gate_v_out(c_e_h_3, c_q, s11)), introduced(assumption)).
% 293.47/185.97 tff(21965,plain,
% 293.47/185.97 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s10)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s10)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10))),
% 293.47/185.97 inference(rewrite,[status(thm)],[])).
% 293.47/185.97 tff(21966,plain,
% 293.47/185.97 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s10)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10))),
% 293.47/185.97 inference(quant_inst,[status(thm)],[])).
% 293.47/185.97 tff(21967,plain,
% 293.47/185.97 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s10)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s10)),
% 293.47/185.97 inference(modus_ponens,[status(thm)],[21966, 21965])).
% 293.47/185.97 tff(21968,plain,
% 293.47/185.97 (~m_and_h_gate_v_in2(c_e_h_3, c_q, s10)),
% 293.47/185.97 inference(unit_resolution,[status(thm)],[21967, 5621, 13124])).
% 293.47/185.97 tff(21969,plain,
% 293.47/185.97 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s10)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s10))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s10)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s10))),
% 293.47/185.97 inference(rewrite,[status(thm)],[])).
% 293.47/185.97 tff(21970,plain,
% 293.47/185.97 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s10)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s10))),
% 293.47/185.97 inference(quant_inst,[status(thm)],[])).
% 293.47/185.97 tff(21971,plain,
% 293.47/185.97 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s10)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s10)),
% 293.47/185.97 inference(modus_ponens,[status(thm)],[21970, 21969])).
% 293.47/185.97 tff(21972,plain,
% 293.47/185.97 (~node20(c_e_h_3, c_q, s10)),
% 293.47/185.97 inference(unit_resolution,[status(thm)],[21971, 4563, 21968])).
% 293.47/185.97 tff(21973,assumption,(node21(c_e_h_3, c_q, s10, s11)), introduced(assumption)).
% 293.47/185.97 tff(21974,plain,
% 293.47/185.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s11)) | node20(c_e_h_3, c_q, s10) | (~node21(c_e_h_3, c_q, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s11)) | node20(c_e_h_3, c_q, s10) | (~node21(c_e_h_3, c_q, s10, s11)))),
% 293.47/185.97 inference(rewrite,[status(thm)],[])).
% 293.47/185.97 tff(21975,plain,
% 293.47/185.97 ((node20(c_e_h_3, c_q, s10) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s11)) | (~node21(c_e_h_3, c_q, s10, s11))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_q, s11)) | node20(c_e_h_3, c_q, s10) | (~node21(c_e_h_3, c_q, s10, s11)))),
% 293.47/185.97 inference(rewrite,[status(thm)],[])).
% 293.47/185.97 tff(21976,plain,
% 293.47/185.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s10) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s11)) | (~node21(c_e_h_3, c_q, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s11)) | node20(c_e_h_3, c_q, s10) | (~node21(c_e_h_3, c_q, s10, s11))))),
% 293.47/185.97 inference(monotonicity,[status(thm)],[21975])).
% 293.47/185.97 tff(21977,plain,
% 293.47/185.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s10) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s11)) | (~node21(c_e_h_3, c_q, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s11)) | node20(c_e_h_3, c_q, s10) | (~node21(c_e_h_3, c_q, s10, s11)))),
% 293.47/185.97 inference(transitivity,[status(thm)],[21976, 21974])).
% 293.47/185.97 tff(21978,plain,
% 293.47/185.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s10) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s11)) | (~node21(c_e_h_3, c_q, s10, s11)))),
% 293.47/185.97 inference(quant_inst,[status(thm)],[])).
% 293.47/185.97 tff(21979,plain,
% 293.47/185.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s11)) | node20(c_e_h_3, c_q, s10) | (~node21(c_e_h_3, c_q, s10, s11))),
% 293.47/185.97 inference(modus_ponens,[status(thm)],[21978, 21977])).
% 293.47/185.97 tff(21980,plain,
% 293.47/185.97 ($false),
% 293.47/185.97 inference(unit_resolution,[status(thm)],[21979, 52, 21964, 21973, 21972])).
% 293.47/185.97 tff(21981,plain,((~node21(c_e_h_3, c_q, s10, s11)) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s11))), inference(lemma,lemma(discharge,[]))).
% 293.47/185.97 tff(21982,plain,
% 293.47/185.97 (~node21(c_e_h_3, c_q, s10, s11)),
% 293.47/185.97 inference(unit_resolution,[status(thm)],[21981, 21964])).
% 293.47/185.97 tff(21983,plain,
% 293.47/185.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s10, s11)) | node21(c_e_h_3, c_q, s10, s11) | node22(c_e_h_3, c_q, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s10, s11)) | node21(c_e_h_3, c_q, s10, s11) | node22(c_e_h_3, c_q, s10, s11))),
% 293.47/185.97 inference(rewrite,[status(thm)],[])).
% 293.47/185.97 tff(21984,plain,
% 293.47/185.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s10, s11)) | node21(c_e_h_3, c_q, s10, s11) | node22(c_e_h_3, c_q, s10, s11))),
% 293.47/185.97 inference(quant_inst,[status(thm)],[])).
% 293.47/185.97 tff(21985,plain,
% 293.47/185.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s10, s11)) | node21(c_e_h_3, c_q, s10, s11) | node22(c_e_h_3, c_q, s10, s11)),
% 293.47/185.97 inference(modus_ponens,[status(thm)],[21984, 21983])).
% 293.47/185.97 tff(21986,plain,
% 293.47/185.97 (node21(c_e_h_3, c_q, s10, s11) | node22(c_e_h_3, c_q, s10, s11)),
% 293.47/185.97 inference(unit_resolution,[status(thm)],[21985, 82, 7748])).
% 293.47/185.97 tff(21987,plain,
% 293.47/185.97 (node22(c_e_h_3, c_q, s10, s11)),
% 293.47/185.97 inference(unit_resolution,[status(thm)],[21986, 21982])).
% 293.47/185.97 tff(21988,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_q, s10)), introduced(assumption)).
% 293.47/185.98 tff(21989,plain,
% 293.47/185.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s11)) | (~node22(c_e_h_3, c_q, s10, s11)) | m_and_h_gate_v_out(c_e_h_3, c_q, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s11)) | (~node22(c_e_h_3, c_q, s10, s11)) | m_and_h_gate_v_out(c_e_h_3, c_q, s10))),
% 293.47/185.98 inference(rewrite,[status(thm)],[])).
% 293.47/185.98 tff(21990,plain,
% 293.47/185.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s11)) | (~node22(c_e_h_3, c_q, s10, s11)) | m_and_h_gate_v_out(c_e_h_3, c_q, s10))),
% 293.47/185.98 inference(quant_inst,[status(thm)],[])).
% 293.47/185.98 tff(21991,plain,
% 293.47/185.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s11)) | (~node22(c_e_h_3, c_q, s10, s11)) | m_and_h_gate_v_out(c_e_h_3, c_q, s10)),
% 293.47/185.98 inference(modus_ponens,[status(thm)],[21990, 21989])).
% 293.47/185.98 tff(21992,plain,
% 293.47/185.98 ($false),
% 293.47/185.98 inference(unit_resolution,[status(thm)],[21991, 108, 21964, 21988, 21987])).
% 293.47/185.98 tff(21993,plain,((~m_and_h_gate_v_out(c_e_h_3, c_q, s11)) | m_and_h_gate_v_out(c_e_h_3, c_q, s10)), inference(lemma,lemma(discharge,[]))).
% 293.47/185.98 tff(21994,plain,
% 293.47/185.98 (~m_and_h_gate_v_out(c_e_h_3, c_q, s11)),
% 293.47/185.98 inference(unit_resolution,[status(thm)],[21993, 21400])).
% 293.47/185.98 tff(21995,assumption,(~node20(c_e_h_3, c_q, s11)), introduced(assumption)).
% 293.47/185.98 tff(21996,assumption,(m_and_h_gate_v_out(c_e_h_3, c_q, s12)), introduced(assumption)).
% 293.47/185.98 tff(21997,assumption,(node21(c_e_h_3, c_q, s11, s12)), introduced(assumption)).
% 293.47/185.98 tff(21998,plain,
% 293.47/185.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s12)) | node20(c_e_h_3, c_q, s11) | (~node21(c_e_h_3, c_q, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s12)) | node20(c_e_h_3, c_q, s11) | (~node21(c_e_h_3, c_q, s11, s12)))),
% 293.48/185.98 inference(rewrite,[status(thm)],[])).
% 293.48/185.98 tff(21999,plain,
% 293.48/185.98 ((node20(c_e_h_3, c_q, s11) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s12)) | (~node21(c_e_h_3, c_q, s11, s12))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_q, s12)) | node20(c_e_h_3, c_q, s11) | (~node21(c_e_h_3, c_q, s11, s12)))),
% 293.48/185.98 inference(rewrite,[status(thm)],[])).
% 293.48/185.98 tff(22000,plain,
% 293.48/185.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s11) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s12)) | (~node21(c_e_h_3, c_q, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s12)) | node20(c_e_h_3, c_q, s11) | (~node21(c_e_h_3, c_q, s11, s12))))),
% 293.48/185.98 inference(monotonicity,[status(thm)],[21999])).
% 293.48/185.98 tff(22001,plain,
% 293.48/185.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s11) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s12)) | (~node21(c_e_h_3, c_q, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s12)) | node20(c_e_h_3, c_q, s11) | (~node21(c_e_h_3, c_q, s11, s12)))),
% 293.48/185.98 inference(transitivity,[status(thm)],[22000, 21998])).
% 293.48/185.98 tff(22002,plain,
% 293.48/185.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s11) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s12)) | (~node21(c_e_h_3, c_q, s11, s12)))),
% 293.48/185.98 inference(quant_inst,[status(thm)],[])).
% 293.48/185.98 tff(22003,plain,
% 293.48/185.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s12)) | node20(c_e_h_3, c_q, s11) | (~node21(c_e_h_3, c_q, s11, s12))),
% 293.48/185.98 inference(modus_ponens,[status(thm)],[22002, 22001])).
% 293.48/185.98 tff(22004,plain,
% 293.48/185.98 ($false),
% 293.48/185.98 inference(unit_resolution,[status(thm)],[22003, 52, 21996, 21997, 21995])).
% 293.48/185.98 tff(22005,plain,((~node21(c_e_h_3, c_q, s11, s12)) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s12)) | node20(c_e_h_3, c_q, s11)), inference(lemma,lemma(discharge,[]))).
% 293.48/185.98 tff(22006,plain,
% 293.48/185.98 (~node21(c_e_h_3, c_q, s11, s12)),
% 293.48/185.98 inference(unit_resolution,[status(thm)],[22005, 21996, 21995])).
% 293.48/185.98 tff(22007,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_q, s11)), introduced(assumption)).
% 293.48/185.98 tff(22008,assumption,(node22(c_e_h_3, c_q, s11, s12)), introduced(assumption)).
% 293.48/185.98 tff(22009,plain,
% 293.48/185.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s12)) | (~node22(c_e_h_3, c_q, s11, s12)) | m_and_h_gate_v_out(c_e_h_3, c_q, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s12)) | (~node22(c_e_h_3, c_q, s11, s12)) | m_and_h_gate_v_out(c_e_h_3, c_q, s11))),
% 293.48/185.98 inference(rewrite,[status(thm)],[])).
% 293.48/185.98 tff(22010,plain,
% 293.48/185.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s12)) | (~node22(c_e_h_3, c_q, s11, s12)) | m_and_h_gate_v_out(c_e_h_3, c_q, s11))),
% 293.48/185.98 inference(quant_inst,[status(thm)],[])).
% 293.48/185.98 tff(22011,plain,
% 293.48/185.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s12)) | (~node22(c_e_h_3, c_q, s11, s12)) | m_and_h_gate_v_out(c_e_h_3, c_q, s11)),
% 293.48/185.98 inference(modus_ponens,[status(thm)],[22010, 22009])).
% 293.48/185.98 tff(22012,plain,
% 293.48/185.98 ($false),
% 293.48/185.98 inference(unit_resolution,[status(thm)],[22011, 108, 22007, 21996, 22008])).
% 293.48/185.98 tff(22013,plain,((~node22(c_e_h_3, c_q, s11, s12)) | m_and_h_gate_v_out(c_e_h_3, c_q, s11) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s12))), inference(lemma,lemma(discharge,[]))).
% 293.48/185.98 tff(22014,plain,
% 293.48/185.98 (~node22(c_e_h_3, c_q, s11, s12)),
% 293.48/185.98 inference(unit_resolution,[status(thm)],[22013, 21996, 22007])).
% 293.48/185.98 tff(22015,plain,
% 293.48/185.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s11, s12)) | node21(c_e_h_3, c_q, s11, s12) | node22(c_e_h_3, c_q, s11, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s11, s12)) | node21(c_e_h_3, c_q, s11, s12) | node22(c_e_h_3, c_q, s11, s12))),
% 293.48/185.98 inference(rewrite,[status(thm)],[])).
% 293.48/185.98 tff(22016,plain,
% 293.48/185.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s11, s12)) | node21(c_e_h_3, c_q, s11, s12) | node22(c_e_h_3, c_q, s11, s12))),
% 293.48/185.98 inference(quant_inst,[status(thm)],[])).
% 293.48/185.98 tff(22017,plain,
% 293.48/185.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s11, s12)) | node21(c_e_h_3, c_q, s11, s12) | node22(c_e_h_3, c_q, s11, s12)),
% 293.48/185.98 inference(modus_ponens,[status(thm)],[22016, 22015])).
% 293.48/185.98 tff(22018,plain,
% 293.48/185.98 (node21(c_e_h_3, c_q, s11, s12) | node22(c_e_h_3, c_q, s11, s12)),
% 293.48/185.98 inference(unit_resolution,[status(thm)],[22017, 82, 11461])).
% 293.48/185.98 tff(22019,plain,
% 293.48/185.98 ($false),
% 293.48/185.98 inference(unit_resolution,[status(thm)],[22018, 22014, 22006])).
% 293.48/185.98 tff(22020,plain,((~m_and_h_gate_v_out(c_e_h_3, c_q, s12)) | m_and_h_gate_v_out(c_e_h_3, c_q, s11) | node20(c_e_h_3, c_q, s11)), inference(lemma,lemma(discharge,[]))).
% 293.48/185.98 tff(22021,plain,
% 293.48/185.98 ((~m_and_h_gate_v_out(c_e_h_3, c_q, s12)) | node20(c_e_h_3, c_q, s11)),
% 293.48/185.98 inference(unit_resolution,[status(thm)],[22020, 21994])).
% 293.48/185.98 tff(22022,plain,
% 293.48/185.99 (~m_and_h_gate_v_out(c_e_h_3, c_q, s12)),
% 293.48/185.99 inference(unit_resolution,[status(thm)],[22021, 21963])).
% 293.48/185.99 tff(22023,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_q, s12)), introduced(assumption)).
% 293.48/185.99 tff(22024,assumption,(m_and_h_gate_v_out(c_e_h_3, c_q, s13)), introduced(assumption)).
% 293.48/185.99 tff(22025,assumption,(node22(c_e_h_3, c_q, s12, s13)), introduced(assumption)).
% 293.48/185.99 tff(22026,plain,
% 293.48/185.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s13)) | (~node22(c_e_h_3, c_q, s12, s13)) | m_and_h_gate_v_out(c_e_h_3, c_q, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s13)) | (~node22(c_e_h_3, c_q, s12, s13)) | m_and_h_gate_v_out(c_e_h_3, c_q, s12))),
% 293.48/185.99 inference(rewrite,[status(thm)],[])).
% 293.48/185.99 tff(22027,plain,
% 293.48/185.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s13)) | (~node22(c_e_h_3, c_q, s12, s13)) | m_and_h_gate_v_out(c_e_h_3, c_q, s12))),
% 293.48/185.99 inference(quant_inst,[status(thm)],[])).
% 293.48/185.99 tff(22028,plain,
% 293.48/185.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s13)) | (~node22(c_e_h_3, c_q, s12, s13)) | m_and_h_gate_v_out(c_e_h_3, c_q, s12)),
% 293.48/185.99 inference(modus_ponens,[status(thm)],[22027, 22026])).
% 293.48/185.99 tff(22029,plain,
% 293.48/185.99 ($false),
% 293.48/185.99 inference(unit_resolution,[status(thm)],[22028, 108, 22024, 22023, 22025])).
% 293.48/185.99 tff(22030,plain,((~node22(c_e_h_3, c_q, s12, s13)) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s13)) | m_and_h_gate_v_out(c_e_h_3, c_q, s12)), inference(lemma,lemma(discharge,[]))).
% 293.48/185.99 tff(22031,plain,
% 293.48/185.99 (~node22(c_e_h_3, c_q, s12, s13)),
% 293.48/185.99 inference(unit_resolution,[status(thm)],[22030, 22024, 22023])).
% 293.48/185.99 tff(22032,assumption,(~node20(c_e_h_3, c_q, s12)), introduced(assumption)).
% 293.48/185.99 tff(22033,assumption,(node21(c_e_h_3, c_q, s12, s13)), introduced(assumption)).
% 293.48/185.99 tff(22034,plain,
% 293.48/185.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s13)) | node20(c_e_h_3, c_q, s12) | (~node21(c_e_h_3, c_q, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s13)) | node20(c_e_h_3, c_q, s12) | (~node21(c_e_h_3, c_q, s12, s13)))),
% 293.48/185.99 inference(rewrite,[status(thm)],[])).
% 293.48/185.99 tff(22035,plain,
% 293.48/185.99 ((node20(c_e_h_3, c_q, s12) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s13)) | (~node21(c_e_h_3, c_q, s12, s13))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_q, s13)) | node20(c_e_h_3, c_q, s12) | (~node21(c_e_h_3, c_q, s12, s13)))),
% 293.48/185.99 inference(rewrite,[status(thm)],[])).
% 293.48/185.99 tff(22036,plain,
% 293.48/185.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s12) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s13)) | (~node21(c_e_h_3, c_q, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s13)) | node20(c_e_h_3, c_q, s12) | (~node21(c_e_h_3, c_q, s12, s13))))),
% 293.48/185.99 inference(monotonicity,[status(thm)],[22035])).
% 293.48/185.99 tff(22037,plain,
% 293.48/185.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s12) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s13)) | (~node21(c_e_h_3, c_q, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s13)) | node20(c_e_h_3, c_q, s12) | (~node21(c_e_h_3, c_q, s12, s13)))),
% 293.48/185.99 inference(transitivity,[status(thm)],[22036, 22034])).
% 293.48/185.99 tff(22038,plain,
% 293.48/185.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s12) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s13)) | (~node21(c_e_h_3, c_q, s12, s13)))),
% 293.48/185.99 inference(quant_inst,[status(thm)],[])).
% 293.48/185.99 tff(22039,plain,
% 293.48/185.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s13)) | node20(c_e_h_3, c_q, s12) | (~node21(c_e_h_3, c_q, s12, s13))),
% 293.48/185.99 inference(modus_ponens,[status(thm)],[22038, 22037])).
% 293.48/185.99 tff(22040,plain,
% 293.48/185.99 ($false),
% 293.48/185.99 inference(unit_resolution,[status(thm)],[22039, 52, 22024, 22033, 22032])).
% 293.48/185.99 tff(22041,plain,((~node21(c_e_h_3, c_q, s12, s13)) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s13)) | node20(c_e_h_3, c_q, s12)), inference(lemma,lemma(discharge,[]))).
% 293.48/185.99 tff(22042,plain,
% 293.48/185.99 (~node21(c_e_h_3, c_q, s12, s13)),
% 293.48/185.99 inference(unit_resolution,[status(thm)],[22041, 22024, 22032])).
% 293.48/185.99 tff(22043,plain,
% 293.48/185.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s12, s13)) | node21(c_e_h_3, c_q, s12, s13) | node22(c_e_h_3, c_q, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s12, s13)) | node21(c_e_h_3, c_q, s12, s13) | node22(c_e_h_3, c_q, s12, s13))),
% 293.48/185.99 inference(rewrite,[status(thm)],[])).
% 293.48/185.99 tff(22044,plain,
% 293.48/185.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s12, s13)) | node21(c_e_h_3, c_q, s12, s13) | node22(c_e_h_3, c_q, s12, s13))),
% 293.48/185.99 inference(quant_inst,[status(thm)],[])).
% 293.48/185.99 tff(22045,plain,
% 293.48/185.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s12, s13)) | node21(c_e_h_3, c_q, s12, s13) | node22(c_e_h_3, c_q, s12, s13)),
% 293.48/185.99 inference(modus_ponens,[status(thm)],[22044, 22043])).
% 293.48/185.99 tff(22046,plain,
% 293.48/185.99 (node21(c_e_h_3, c_q, s12, s13) | node22(c_e_h_3, c_q, s12, s13)),
% 293.48/185.99 inference(unit_resolution,[status(thm)],[22045, 82, 11856])).
% 293.48/185.99 tff(22047,plain,
% 293.48/185.99 ($false),
% 293.48/185.99 inference(unit_resolution,[status(thm)],[22046, 22042, 22031])).
% 293.48/185.99 tff(22048,plain,((~m_and_h_gate_v_out(c_e_h_3, c_q, s13)) | node20(c_e_h_3, c_q, s12) | m_and_h_gate_v_out(c_e_h_3, c_q, s12)), inference(lemma,lemma(discharge,[]))).
% 293.48/185.99 tff(22049,plain,
% 293.48/185.99 ((~m_and_h_gate_v_out(c_e_h_3, c_q, s13)) | node20(c_e_h_3, c_q, s12)),
% 293.48/185.99 inference(unit_resolution,[status(thm)],[22048, 22022])).
% 293.48/185.99 tff(22050,plain,
% 293.48/185.99 (~m_and_h_gate_v_out(c_e_h_3, c_q, s13)),
% 293.48/185.99 inference(unit_resolution,[status(thm)],[22049, 21955])).
% 293.48/185.99 tff(22051,plain,
% 293.48/185.99 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s13))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s13))),
% 293.48/185.99 inference(rewrite,[status(thm)],[])).
% 293.48/185.99 tff(22052,plain,
% 293.48/185.99 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s13))),
% 293.48/185.99 inference(quant_inst,[status(thm)],[])).
% 293.48/185.99 tff(22053,plain,
% 293.48/185.99 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s13)),
% 293.48/185.99 inference(modus_ponens,[status(thm)],[22052, 22051])).
% 293.48/185.99 tff(22054,plain,
% 293.48/185.99 (node3(c_e_h_3, c_e_h_1, s13)),
% 293.48/185.99 inference(unit_resolution,[status(thm)],[22053, 2922, 1056])).
% 293.48/185.99 tff(22055,plain,
% 293.48/185.99 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s13)) | (~node3(c_e_h_3, c_e_h_1, s13)) | m_and_h_gate_v_out(c_e_h_3, c_q, s13))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s13)) | (~node3(c_e_h_3, c_e_h_1, s13)) | m_and_h_gate_v_out(c_e_h_3, c_q, s13))),
% 293.48/185.99 inference(rewrite,[status(thm)],[])).
% 293.48/185.99 tff(22056,plain,
% 293.48/185.99 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s13)) | (~node3(c_e_h_3, c_e_h_1, s13)) | m_and_h_gate_v_out(c_e_h_3, c_q, s13))),
% 293.48/185.99 inference(quant_inst,[status(thm)],[])).
% 293.48/185.99 tff(22057,plain,
% 293.48/185.99 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s13)) | (~node3(c_e_h_3, c_e_h_1, s13)) | m_and_h_gate_v_out(c_e_h_3, c_q, s13)),
% 293.48/185.99 inference(modus_ponens,[status(thm)],[22056, 22055])).
% 293.48/185.99 tff(22058,plain,
% 293.48/185.99 ((~m_cell_v_ack(c_e_h_1, s13)) | m_and_h_gate_v_out(c_e_h_3, c_q, s13)),
% 293.48/185.99 inference(unit_resolution,[status(thm)],[22057, 1073, 22054])).
% 293.48/185.99 tff(22059,plain,
% 293.48/185.99 (~m_cell_v_ack(c_e_h_1, s13)),
% 293.48/185.99 inference(unit_resolution,[status(thm)],[22058, 22050])).
% 293.48/185.99 tff(22060,plain,
% 293.48/185.99 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s13)) | m_cell_v_ack(c_e_h_1, s13))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s13)) | m_cell_v_ack(c_e_h_1, s13))),
% 293.48/185.99 inference(rewrite,[status(thm)],[])).
% 293.48/185.99 tff(22061,plain,
% 293.48/185.99 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s13)) | m_cell_v_ack(c_e_h_1, s13))),
% 293.48/185.99 inference(quant_inst,[status(thm)],[])).
% 293.48/185.99 tff(22062,plain,
% 293.48/185.99 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s13)) | m_cell_v_ack(c_e_h_1, s13)),
% 293.48/185.99 inference(modus_ponens,[status(thm)],[22061, 22060])).
% 293.48/185.99 tff(22063,plain,
% 293.48/185.99 (~m_or_h_gate_v_in2(c_e_h_1, c_j, s13)),
% 293.48/185.99 inference(unit_resolution,[status(thm)],[22062, 1085, 22059])).
% 293.48/185.99 tff(22064,plain,
% 293.48/185.99 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s12))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s12))),
% 293.48/185.99 inference(rewrite,[status(thm)],[])).
% 293.48/185.99 tff(22065,plain,
% 293.48/185.99 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s12))),
% 293.48/185.99 inference(quant_inst,[status(thm)],[])).
% 293.48/185.99 tff(22066,plain,
% 293.48/185.99 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s12)),
% 293.48/185.99 inference(modus_ponens,[status(thm)],[22065, 22064])).
% 293.48/185.99 tff(22067,plain,
% 293.48/185.99 (node3(c_e_h_3, c_e_h_1, s12)),
% 293.48/185.99 inference(unit_resolution,[status(thm)],[22066, 2922, 1056])).
% 293.48/185.99 tff(22068,plain,
% 293.48/185.99 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s12)) | (~node3(c_e_h_3, c_e_h_1, s12)) | m_and_h_gate_v_out(c_e_h_3, c_q, s12))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s12)) | (~node3(c_e_h_3, c_e_h_1, s12)) | m_and_h_gate_v_out(c_e_h_3, c_q, s12))),
% 293.48/185.99 inference(rewrite,[status(thm)],[])).
% 293.48/185.99 tff(22069,plain,
% 293.48/185.99 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s12)) | (~node3(c_e_h_3, c_e_h_1, s12)) | m_and_h_gate_v_out(c_e_h_3, c_q, s12))),
% 293.48/185.99 inference(quant_inst,[status(thm)],[])).
% 293.48/185.99 tff(22070,plain,
% 293.48/185.99 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s12)) | (~node3(c_e_h_3, c_e_h_1, s12)) | m_and_h_gate_v_out(c_e_h_3, c_q, s12)),
% 293.48/185.99 inference(modus_ponens,[status(thm)],[22069, 22068])).
% 293.48/185.99 tff(22071,plain,
% 293.48/185.99 ((~m_cell_v_ack(c_e_h_1, s12)) | m_and_h_gate_v_out(c_e_h_3, c_q, s12)),
% 293.48/185.99 inference(unit_resolution,[status(thm)],[22070, 1073, 22067])).
% 293.48/185.99 tff(22072,plain,
% 293.48/185.99 (~m_cell_v_ack(c_e_h_1, s12)),
% 293.48/185.99 inference(unit_resolution,[status(thm)],[22071, 22022])).
% 293.48/186.00 tff(22073,plain,
% 293.48/186.00 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s12)) | m_cell_v_ack(c_e_h_1, s12))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s12)) | m_cell_v_ack(c_e_h_1, s12))),
% 293.48/186.00 inference(rewrite,[status(thm)],[])).
% 293.48/186.00 tff(22074,plain,
% 293.48/186.00 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s12)) | m_cell_v_ack(c_e_h_1, s12))),
% 293.48/186.00 inference(quant_inst,[status(thm)],[])).
% 293.48/186.00 tff(22075,plain,
% 293.48/186.00 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s12)) | m_cell_v_ack(c_e_h_1, s12)),
% 293.48/186.00 inference(modus_ponens,[status(thm)],[22074, 22073])).
% 293.48/186.00 tff(22076,plain,
% 293.48/186.00 (~m_or_h_gate_v_in2(c_e_h_1, c_j, s12)),
% 293.48/186.00 inference(unit_resolution,[status(thm)],[22075, 1085, 22072])).
% 293.48/186.00 tff(22077,plain,
% 293.48/186.00 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s9))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s9))),
% 293.48/186.00 inference(rewrite,[status(thm)],[])).
% 293.48/186.00 tff(22078,plain,
% 293.48/186.00 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s9))),
% 293.48/186.00 inference(quant_inst,[status(thm)],[])).
% 293.48/186.00 tff(22079,plain,
% 293.48/186.00 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s9)),
% 293.48/186.00 inference(modus_ponens,[status(thm)],[22078, 22077])).
% 293.48/186.00 tff(22080,plain,
% 293.48/186.00 (node3(c_e_h_3, c_e_h_1, s9)),
% 293.48/186.00 inference(unit_resolution,[status(thm)],[22079, 2922, 1056])).
% 293.48/186.00 tff(22081,plain,
% 293.48/186.00 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s9)) | (~node3(c_e_h_3, c_e_h_1, s9)) | m_and_h_gate_v_out(c_e_h_3, c_q, s9))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s9)) | (~node3(c_e_h_3, c_e_h_1, s9)) | m_and_h_gate_v_out(c_e_h_3, c_q, s9))),
% 293.48/186.00 inference(rewrite,[status(thm)],[])).
% 293.48/186.00 tff(22082,plain,
% 293.48/186.00 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s9)) | (~node3(c_e_h_3, c_e_h_1, s9)) | m_and_h_gate_v_out(c_e_h_3, c_q, s9))),
% 293.48/186.00 inference(quant_inst,[status(thm)],[])).
% 293.48/186.00 tff(22083,plain,
% 293.48/186.00 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s9)) | (~node3(c_e_h_3, c_e_h_1, s9)) | m_and_h_gate_v_out(c_e_h_3, c_q, s9)),
% 293.48/186.00 inference(modus_ponens,[status(thm)],[22082, 22081])).
% 293.48/186.00 tff(22084,plain,
% 293.48/186.00 ((~m_cell_v_ack(c_e_h_1, s9)) | m_and_h_gate_v_out(c_e_h_3, c_q, s9)),
% 293.48/186.00 inference(unit_resolution,[status(thm)],[22083, 1073, 22080])).
% 293.48/186.00 tff(22085,plain,
% 293.48/186.00 (~m_cell_v_ack(c_e_h_1, s9)),
% 293.48/186.00 inference(unit_resolution,[status(thm)],[22084, 21367])).
% 293.48/186.00 tff(22086,assumption,(m_or_h_gate_v_in2(c_e_h_1, c_j, s9)), introduced(assumption)).
% 293.48/186.00 tff(22087,assumption,(~m_cell_v_ack(c_e_h_1, s9)), introduced(assumption)).
% 293.48/186.00 tff(22088,plain,
% 293.48/186.00 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s9)) | m_cell_v_ack(c_e_h_1, s9))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s9)) | m_cell_v_ack(c_e_h_1, s9))),
% 293.48/186.00 inference(rewrite,[status(thm)],[])).
% 293.48/186.00 tff(22089,plain,
% 293.48/186.00 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s9)) | m_cell_v_ack(c_e_h_1, s9))),
% 293.48/186.00 inference(quant_inst,[status(thm)],[])).
% 293.48/186.00 tff(22090,plain,
% 293.48/186.00 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s9)) | m_cell_v_ack(c_e_h_1, s9)),
% 293.48/186.00 inference(modus_ponens,[status(thm)],[22089, 22088])).
% 293.48/186.00 tff(22091,plain,
% 293.48/186.00 ($false),
% 293.48/186.00 inference(unit_resolution,[status(thm)],[22090, 1085, 22087, 22086])).
% 293.48/186.00 tff(22092,plain,(m_cell_v_ack(c_e_h_1, s9) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s9))), inference(lemma,lemma(discharge,[]))).
% 293.48/186.00 tff(22093,plain,
% 293.48/186.00 (~m_or_h_gate_v_in2(c_e_h_1, c_j, s9)),
% 293.48/186.00 inference(unit_resolution,[status(thm)],[22092, 22085])).
% 293.48/186.00 tff(22094,assumption,(m_or_h_gate_v_out(c_e_h_1, c_j, s12)), introduced(assumption)).
% 293.48/186.00 tff(22095,assumption,(~m_or_h_gate_v_in2(c_e_h_1, c_j, s9)), introduced(assumption)).
% 293.48/186.00 tff(22096,assumption,(m_or_h_gate_v_out(c_e_h_1, c_j, s10)), introduced(assumption)).
% 293.48/186.00 tff(22097,assumption,(m_or_h_gate_v_out(c_e_h_1, c_j, s7)), introduced(assumption)).
% 293.48/186.00 tff(22098,assumption,(m_and_h_gate_v_out(c_e_h_1, c_l, s6)), introduced(assumption)).
% 293.48/186.00 tff(22099,plain,
% 293.48/186.00 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5))),
% 293.48/186.00 inference(rewrite,[status(thm)],[])).
% 293.48/186.00 tff(22100,plain,
% 293.48/186.00 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5))),
% 293.48/186.00 inference(quant_inst,[status(thm)],[])).
% 293.48/186.00 tff(22101,plain,
% 293.48/186.00 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s5)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)),
% 293.48/186.00 inference(modus_ponens,[status(thm)],[22100, 22099])).
% 293.48/186.00 tff(22102,plain,
% 293.48/186.00 (~m_and_h_gate_v_in2(c_e_h_1, c_l, s5)),
% 293.48/186.00 inference(unit_resolution,[status(thm)],[22101, 4549, 18038])).
% 293.48/186.00 tff(22103,plain,
% 293.48/186.00 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s5)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s5)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s5))),
% 293.48/186.00 inference(rewrite,[status(thm)],[])).
% 293.48/186.00 tff(22104,plain,
% 293.48/186.00 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s5)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s5))),
% 293.48/186.00 inference(quant_inst,[status(thm)],[])).
% 293.48/186.00 tff(22105,plain,
% 293.48/186.00 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s5)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s5)),
% 293.48/186.00 inference(modus_ponens,[status(thm)],[22104, 22103])).
% 293.48/186.00 tff(22106,plain,
% 293.48/186.00 (~node20(c_e_h_1, c_l, s5)),
% 293.48/186.00 inference(unit_resolution,[status(thm)],[22105, 4563, 22102])).
% 293.48/186.00 tff(22107,assumption,(node21(c_e_h_1, c_l, s5, s6)), introduced(assumption)).
% 293.48/186.00 tff(22108,plain,
% 293.48/186.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s6)) | (~node21(c_e_h_1, c_l, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s6)) | (~node21(c_e_h_1, c_l, s5, s6)))),
% 293.48/186.00 inference(rewrite,[status(thm)],[])).
% 293.48/186.00 tff(22109,plain,
% 293.48/186.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s6)) | (~node21(c_e_h_1, c_l, s5, s6)))),
% 293.48/186.00 inference(quant_inst,[status(thm)],[])).
% 293.48/186.00 tff(22110,plain,
% 293.48/186.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s6)) | (~node21(c_e_h_1, c_l, s5, s6))),
% 293.48/186.00 inference(modus_ponens,[status(thm)],[22109, 22108])).
% 293.48/186.00 tff(22111,plain,
% 293.48/186.00 ($false),
% 293.48/186.00 inference(unit_resolution,[status(thm)],[22110, 52, 22107, 22098, 22106])).
% 293.48/186.00 tff(22112,plain,((~node21(c_e_h_1, c_l, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s6))), inference(lemma,lemma(discharge,[]))).
% 293.48/186.00 tff(22113,plain,
% 293.48/186.00 (~node21(c_e_h_1, c_l, s5, s6)),
% 293.48/186.00 inference(unit_resolution,[status(thm)],[22112, 22098])).
% 293.48/186.00 tff(22114,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_l, s5)), introduced(assumption)).
% 293.48/186.00 tff(22115,assumption,(node22(c_e_h_1, c_l, s5, s6)), introduced(assumption)).
% 293.48/186.00 tff(22116,plain,
% 293.48/186.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s6)) | (~node22(c_e_h_1, c_l, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_l, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s6)) | (~node22(c_e_h_1, c_l, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_l, s5))),
% 293.48/186.00 inference(rewrite,[status(thm)],[])).
% 293.48/186.00 tff(22117,plain,
% 293.48/186.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s6)) | (~node22(c_e_h_1, c_l, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_l, s5))),
% 293.48/186.00 inference(quant_inst,[status(thm)],[])).
% 293.48/186.00 tff(22118,plain,
% 293.48/186.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s6)) | (~node22(c_e_h_1, c_l, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_l, s5)),
% 293.48/186.00 inference(modus_ponens,[status(thm)],[22117, 22116])).
% 293.48/186.00 tff(22119,plain,
% 293.48/186.00 ($false),
% 293.48/186.00 inference(unit_resolution,[status(thm)],[22118, 108, 22115, 22098, 22114])).
% 293.48/186.00 tff(22120,plain,((~node22(c_e_h_1, c_l, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s6)) | m_and_h_gate_v_out(c_e_h_1, c_l, s5)), inference(lemma,lemma(discharge,[]))).
% 293.48/186.00 tff(22121,plain,
% 293.48/186.00 ((~node22(c_e_h_1, c_l, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s6))),
% 293.48/186.00 inference(unit_resolution,[status(thm)],[22120, 19359])).
% 293.48/186.00 tff(22122,plain,
% 293.48/186.00 (~node22(c_e_h_1, c_l, s5, s6)),
% 293.48/186.00 inference(unit_resolution,[status(thm)],[22121, 22098])).
% 293.48/186.00 tff(22123,plain,
% 293.48/186.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_1, c_l, s5, s6) | node22(c_e_h_1, c_l, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_1, c_l, s5, s6) | node22(c_e_h_1, c_l, s5, s6))),
% 293.48/186.00 inference(rewrite,[status(thm)],[])).
% 293.48/186.00 tff(22124,plain,
% 293.48/186.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_1, c_l, s5, s6) | node22(c_e_h_1, c_l, s5, s6))),
% 293.48/186.00 inference(quant_inst,[status(thm)],[])).
% 293.48/186.00 tff(22125,plain,
% 293.48/186.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_1, c_l, s5, s6) | node22(c_e_h_1, c_l, s5, s6)),
% 293.48/186.00 inference(modus_ponens,[status(thm)],[22124, 22123])).
% 293.48/186.00 tff(22126,plain,
% 293.48/186.00 (node21(c_e_h_1, c_l, s5, s6) | node22(c_e_h_1, c_l, s5, s6)),
% 293.48/186.00 inference(unit_resolution,[status(thm)],[22125, 82, 1406])).
% 293.48/186.00 tff(22127,plain,
% 293.48/186.00 ($false),
% 293.48/186.00 inference(unit_resolution,[status(thm)],[22126, 22122, 22113])).
% 293.48/186.00 tff(22128,plain,(~m_and_h_gate_v_out(c_e_h_1, c_l, s6)), inference(lemma,lemma(discharge,[]))).
% 293.48/186.00 tff(22129,plain,
% 293.48/186.00 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s6)) | m_and_h_gate_v_out(c_e_h_1, c_l, s6))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s6)) | m_and_h_gate_v_out(c_e_h_1, c_l, s6))),
% 293.48/186.00 inference(rewrite,[status(thm)],[])).
% 293.48/186.00 tff(22130,plain,
% 293.48/186.01 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s6)) | m_and_h_gate_v_out(c_e_h_1, c_l, s6))),
% 293.48/186.01 inference(quant_inst,[status(thm)],[])).
% 293.48/186.01 tff(22131,plain,
% 293.48/186.01 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s6)) | m_and_h_gate_v_out(c_e_h_1, c_l, s6)),
% 293.48/186.01 inference(modus_ponens,[status(thm)],[22130, 22129])).
% 293.48/186.01 tff(22132,plain,
% 293.48/186.01 (~m_or_h_gate_v_in1(c_e_h_1, c_j, s6)),
% 293.48/186.01 inference(unit_resolution,[status(thm)],[22131, 1100, 22128])).
% 293.48/186.01 tff(22133,assumption,(~m_or_h_gate_v_in1(c_e_h_1, c_j, s6)), introduced(assumption)).
% 293.48/186.01 tff(22134,plain,
% 293.48/186.01 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s6)) | m_cell_v_ack(c_e_h_1, s6))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s6)) | m_cell_v_ack(c_e_h_1, s6))),
% 293.48/186.01 inference(rewrite,[status(thm)],[])).
% 293.48/186.01 tff(22135,plain,
% 293.48/186.01 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s6)) | m_cell_v_ack(c_e_h_1, s6))),
% 293.48/186.01 inference(quant_inst,[status(thm)],[])).
% 293.48/186.01 tff(22136,plain,
% 293.48/186.01 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s6)) | m_cell_v_ack(c_e_h_1, s6)),
% 293.48/186.01 inference(modus_ponens,[status(thm)],[22135, 22134])).
% 293.48/186.01 tff(22137,plain,
% 293.48/186.01 (~m_or_h_gate_v_in2(c_e_h_1, c_j, s6)),
% 293.48/186.01 inference(unit_resolution,[status(thm)],[22136, 1085, 10146])).
% 293.48/186.01 tff(22138,assumption,(node5(c_e_h_1, c_j, s6, s7)), introduced(assumption)).
% 293.48/186.01 tff(22139,plain,
% 293.48/186.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_1, c_j, s7)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s6) | m_or_h_gate_v_in1(c_e_h_1, c_j, s6) | (~node5(c_e_h_1, c_j, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s7)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s6) | m_or_h_gate_v_in1(c_e_h_1, c_j, s6) | (~node5(c_e_h_1, c_j, s6, s7)))),
% 293.48/186.01 inference(rewrite,[status(thm)],[])).
% 293.48/186.01 tff(22140,plain,
% 293.48/186.01 ((m_or_h_gate_v_in1(c_e_h_1, c_j, s6) | m_or_h_gate_v_in2(c_e_h_1, c_j, s6) | (~node5(c_e_h_1, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s7))) <=> ((~m_or_h_gate_v_out(c_e_h_1, c_j, s7)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s6) | m_or_h_gate_v_in1(c_e_h_1, c_j, s6) | (~node5(c_e_h_1, c_j, s6, s7)))),
% 293.48/186.01 inference(rewrite,[status(thm)],[])).
% 293.48/186.01 tff(22141,plain,
% 293.48/186.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s6) | m_or_h_gate_v_in2(c_e_h_1, c_j, s6) | (~node5(c_e_h_1, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_1, c_j, s7)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s6) | m_or_h_gate_v_in1(c_e_h_1, c_j, s6) | (~node5(c_e_h_1, c_j, s6, s7))))),
% 293.48/186.01 inference(monotonicity,[status(thm)],[22140])).
% 293.48/186.01 tff(22142,plain,
% 293.48/186.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s6) | m_or_h_gate_v_in2(c_e_h_1, c_j, s6) | (~node5(c_e_h_1, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s7)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s6) | m_or_h_gate_v_in1(c_e_h_1, c_j, s6) | (~node5(c_e_h_1, c_j, s6, s7)))),
% 293.51/186.01 inference(transitivity,[status(thm)],[22141, 22139])).
% 293.51/186.01 tff(22143,plain,
% 293.51/186.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s6) | m_or_h_gate_v_in2(c_e_h_1, c_j, s6) | (~node5(c_e_h_1, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s7)))),
% 293.51/186.01 inference(quant_inst,[status(thm)],[])).
% 293.51/186.01 tff(22144,plain,
% 293.51/186.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s7)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s6) | m_or_h_gate_v_in1(c_e_h_1, c_j, s6) | (~node5(c_e_h_1, c_j, s6, s7))),
% 293.51/186.01 inference(modus_ponens,[status(thm)],[22143, 22142])).
% 293.51/186.01 tff(22145,plain,
% 293.51/186.01 ($false),
% 293.51/186.01 inference(unit_resolution,[status(thm)],[22144, 1159, 22097, 22138, 22137, 22133])).
% 293.51/186.01 tff(22146,plain,((~node5(c_e_h_1, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s7)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s6)), inference(lemma,lemma(discharge,[]))).
% 293.51/186.01 tff(22147,plain,
% 293.51/186.01 ((~node5(c_e_h_1, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s7))),
% 293.51/186.01 inference(unit_resolution,[status(thm)],[22146, 22132])).
% 293.51/186.01 tff(22148,plain,
% 293.51/186.01 (~node5(c_e_h_1, c_j, s6, s7)),
% 293.51/186.01 inference(unit_resolution,[status(thm)],[22147, 22097])).
% 293.51/186.01 tff(22149,assumption,(node6(c_e_h_1, c_j, s6, s7)), introduced(assumption)).
% 293.51/186.01 tff(22150,assumption,(~m_or_h_gate_v_out(c_e_h_1, c_j, s6)), introduced(assumption)).
% 293.51/186.01 tff(22151,plain,
% 293.51/186.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_1, c_j, s7)) | m_or_h_gate_v_out(c_e_h_1, c_j, s6) | (~node6(c_e_h_1, c_j, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s7)) | m_or_h_gate_v_out(c_e_h_1, c_j, s6) | (~node6(c_e_h_1, c_j, s6, s7)))),
% 293.51/186.01 inference(rewrite,[status(thm)],[])).
% 293.51/186.01 tff(22152,plain,
% 293.51/186.01 (((~node6(c_e_h_1, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s7)) | m_or_h_gate_v_out(c_e_h_1, c_j, s6)) <=> ((~m_or_h_gate_v_out(c_e_h_1, c_j, s7)) | m_or_h_gate_v_out(c_e_h_1, c_j, s6) | (~node6(c_e_h_1, c_j, s6, s7)))),
% 293.51/186.01 inference(rewrite,[status(thm)],[])).
% 293.51/186.01 tff(22153,plain,
% 293.51/186.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s7)) | m_or_h_gate_v_out(c_e_h_1, c_j, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_1, c_j, s7)) | m_or_h_gate_v_out(c_e_h_1, c_j, s6) | (~node6(c_e_h_1, c_j, s6, s7))))),
% 293.51/186.01 inference(monotonicity,[status(thm)],[22152])).
% 293.51/186.01 tff(22154,plain,
% 293.51/186.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s7)) | m_or_h_gate_v_out(c_e_h_1, c_j, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s7)) | m_or_h_gate_v_out(c_e_h_1, c_j, s6) | (~node6(c_e_h_1, c_j, s6, s7)))),
% 293.51/186.01 inference(transitivity,[status(thm)],[22153, 22151])).
% 293.51/186.01 tff(22155,plain,
% 293.51/186.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s7)) | m_or_h_gate_v_out(c_e_h_1, c_j, s6))),
% 293.51/186.01 inference(quant_inst,[status(thm)],[])).
% 293.51/186.01 tff(22156,plain,
% 293.51/186.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s7)) | m_or_h_gate_v_out(c_e_h_1, c_j, s6) | (~node6(c_e_h_1, c_j, s6, s7))),
% 293.51/186.01 inference(modus_ponens,[status(thm)],[22155, 22154])).
% 293.51/186.01 tff(22157,plain,
% 293.51/186.01 ($false),
% 293.51/186.01 inference(unit_resolution,[status(thm)],[22156, 1121, 22097, 22150, 22149])).
% 293.51/186.01 tff(22158,plain,((~node6(c_e_h_1, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s7)) | m_or_h_gate_v_out(c_e_h_1, c_j, s6)), inference(lemma,lemma(discharge,[]))).
% 293.51/186.01 tff(22159,plain,
% 293.51/186.01 ((~node6(c_e_h_1, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s7))),
% 293.51/186.01 inference(unit_resolution,[status(thm)],[22158, 19387])).
% 293.51/186.01 tff(22160,plain,
% 293.51/186.01 (~node6(c_e_h_1, c_j, s6, s7)),
% 293.51/186.01 inference(unit_resolution,[status(thm)],[22159, 22097])).
% 293.51/186.01 tff(22161,plain,
% 293.51/186.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s6, s7)) | node5(c_e_h_1, c_j, s6, s7) | node6(c_e_h_1, c_j, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s6, s7)) | node5(c_e_h_1, c_j, s6, s7) | node6(c_e_h_1, c_j, s6, s7))),
% 293.51/186.01 inference(rewrite,[status(thm)],[])).
% 293.51/186.01 tff(22162,plain,
% 293.51/186.01 ((node6(c_e_h_1, c_j, s6, s7) | node5(c_e_h_1, c_j, s6, s7) | (~trans(s6, s7))) <=> ((~trans(s6, s7)) | node5(c_e_h_1, c_j, s6, s7) | node6(c_e_h_1, c_j, s6, s7))),
% 293.51/186.01 inference(rewrite,[status(thm)],[])).
% 293.51/186.01 tff(22163,plain,
% 293.51/186.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s6, s7) | node5(c_e_h_1, c_j, s6, s7) | (~trans(s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s6, s7)) | node5(c_e_h_1, c_j, s6, s7) | node6(c_e_h_1, c_j, s6, s7)))),
% 293.51/186.01 inference(monotonicity,[status(thm)],[22162])).
% 293.51/186.01 tff(22164,plain,
% 293.51/186.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s6, s7) | node5(c_e_h_1, c_j, s6, s7) | (~trans(s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s6, s7)) | node5(c_e_h_1, c_j, s6, s7) | node6(c_e_h_1, c_j, s6, s7))),
% 293.51/186.01 inference(transitivity,[status(thm)],[22163, 22161])).
% 293.51/186.01 tff(22165,plain,
% 293.51/186.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s6, s7) | node5(c_e_h_1, c_j, s6, s7) | (~trans(s6, s7)))),
% 293.51/186.01 inference(quant_inst,[status(thm)],[])).
% 293.51/186.01 tff(22166,plain,
% 293.51/186.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s6, s7)) | node5(c_e_h_1, c_j, s6, s7) | node6(c_e_h_1, c_j, s6, s7)),
% 293.51/186.01 inference(modus_ponens,[status(thm)],[22165, 22164])).
% 293.51/186.01 tff(22167,plain,
% 293.51/186.01 (node5(c_e_h_1, c_j, s6, s7) | node6(c_e_h_1, c_j, s6, s7)),
% 293.51/186.01 inference(unit_resolution,[status(thm)],[22166, 1141, 1844])).
% 293.51/186.01 tff(22168,plain,
% 293.51/186.01 ($false),
% 293.51/186.01 inference(unit_resolution,[status(thm)],[22167, 22160, 22148])).
% 293.51/186.01 tff(22169,plain,(~m_or_h_gate_v_out(c_e_h_1, c_j, s7)), inference(lemma,lemma(discharge,[]))).
% 293.51/186.01 tff(22170,assumption,(m_and_h_gate_v_out(c_e_h_1, c_l, s7)), introduced(assumption)).
% 293.51/186.01 tff(22171,assumption,(node21(c_e_h_1, c_l, s6, s7)), introduced(assumption)).
% 293.51/186.01 tff(22172,plain,
% 293.51/186.01 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s6)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s6)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6))),
% 293.51/186.01 inference(rewrite,[status(thm)],[])).
% 293.51/186.01 tff(22173,plain,
% 293.51/186.01 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s6)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6))),
% 293.51/186.01 inference(quant_inst,[status(thm)],[])).
% 293.51/186.01 tff(22174,plain,
% 293.51/186.01 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s6)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)),
% 293.51/186.02 inference(modus_ponens,[status(thm)],[22173, 22172])).
% 293.51/186.02 tff(22175,plain,
% 293.51/186.02 (~m_and_h_gate_v_in2(c_e_h_1, c_l, s6)),
% 293.51/186.02 inference(unit_resolution,[status(thm)],[22174, 4549, 18158])).
% 293.51/186.02 tff(22176,plain,
% 293.51/186.02 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s6)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s6)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s6))),
% 293.51/186.02 inference(rewrite,[status(thm)],[])).
% 293.51/186.02 tff(22177,plain,
% 293.51/186.02 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s6)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s6))),
% 293.51/186.02 inference(quant_inst,[status(thm)],[])).
% 293.51/186.02 tff(22178,plain,
% 293.51/186.02 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s6)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s6)),
% 293.51/186.02 inference(modus_ponens,[status(thm)],[22177, 22176])).
% 293.51/186.02 tff(22179,plain,
% 293.51/186.02 (~node20(c_e_h_1, c_l, s6)),
% 293.51/186.02 inference(unit_resolution,[status(thm)],[22178, 4563, 22175])).
% 293.51/186.02 tff(22180,plain,
% 293.51/186.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s7)) | (~node21(c_e_h_1, c_l, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s7)) | (~node21(c_e_h_1, c_l, s6, s7)))),
% 293.51/186.02 inference(rewrite,[status(thm)],[])).
% 293.51/186.02 tff(22181,plain,
% 293.51/186.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s7)) | (~node21(c_e_h_1, c_l, s6, s7)))),
% 293.51/186.02 inference(quant_inst,[status(thm)],[])).
% 293.51/186.02 tff(22182,plain,
% 293.51/186.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s7)) | (~node21(c_e_h_1, c_l, s6, s7))),
% 293.51/186.02 inference(modus_ponens,[status(thm)],[22181, 22180])).
% 293.51/186.02 tff(22183,plain,
% 293.51/186.02 ($false),
% 293.51/186.02 inference(unit_resolution,[status(thm)],[22182, 52, 22179, 22171, 22170])).
% 293.51/186.02 tff(22184,plain,((~node21(c_e_h_1, c_l, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s7))), inference(lemma,lemma(discharge,[]))).
% 293.51/186.02 tff(22185,plain,
% 293.51/186.02 (~node21(c_e_h_1, c_l, s6, s7)),
% 293.51/186.02 inference(unit_resolution,[status(thm)],[22184, 22170])).
% 293.51/186.02 tff(22186,plain,
% 293.51/186.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_1, c_l, s6, s7) | node22(c_e_h_1, c_l, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_1, c_l, s6, s7) | node22(c_e_h_1, c_l, s6, s7))),
% 293.51/186.02 inference(rewrite,[status(thm)],[])).
% 293.51/186.02 tff(22187,plain,
% 293.51/186.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_1, c_l, s6, s7) | node22(c_e_h_1, c_l, s6, s7))),
% 293.51/186.02 inference(quant_inst,[status(thm)],[])).
% 293.51/186.02 tff(22188,plain,
% 293.51/186.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_1, c_l, s6, s7) | node22(c_e_h_1, c_l, s6, s7)),
% 293.51/186.02 inference(modus_ponens,[status(thm)],[22187, 22186])).
% 293.51/186.02 tff(22189,plain,
% 293.51/186.02 (node21(c_e_h_1, c_l, s6, s7) | node22(c_e_h_1, c_l, s6, s7)),
% 293.51/186.02 inference(unit_resolution,[status(thm)],[22188, 82, 1844])).
% 293.51/186.02 tff(22190,plain,
% 293.51/186.02 (node22(c_e_h_1, c_l, s6, s7)),
% 293.51/186.02 inference(unit_resolution,[status(thm)],[22189, 22185])).
% 293.51/186.02 tff(22191,plain,
% 293.51/186.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s7)) | (~node22(c_e_h_1, c_l, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_l, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s7)) | (~node22(c_e_h_1, c_l, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_l, s6))),
% 293.51/186.02 inference(rewrite,[status(thm)],[])).
% 293.51/186.02 tff(22192,plain,
% 293.51/186.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s7)) | (~node22(c_e_h_1, c_l, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_l, s6))),
% 293.51/186.02 inference(quant_inst,[status(thm)],[])).
% 293.51/186.02 tff(22193,plain,
% 293.51/186.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s7)) | (~node22(c_e_h_1, c_l, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_l, s6)),
% 293.51/186.02 inference(modus_ponens,[status(thm)],[22192, 22191])).
% 293.51/186.02 tff(22194,plain,
% 293.51/186.02 ($false),
% 293.51/186.02 inference(unit_resolution,[status(thm)],[22193, 108, 22190, 22170, 22128])).
% 293.51/186.02 tff(22195,plain,(~m_and_h_gate_v_out(c_e_h_1, c_l, s7)), inference(lemma,lemma(discharge,[]))).
% 293.51/186.02 tff(22196,plain,
% 293.51/186.02 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s7)) | m_and_h_gate_v_out(c_e_h_1, c_l, s7))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s7)) | m_and_h_gate_v_out(c_e_h_1, c_l, s7))),
% 293.51/186.02 inference(rewrite,[status(thm)],[])).
% 293.51/186.02 tff(22197,plain,
% 293.51/186.02 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s7)) | m_and_h_gate_v_out(c_e_h_1, c_l, s7))),
% 293.51/186.02 inference(quant_inst,[status(thm)],[])).
% 293.51/186.02 tff(22198,plain,
% 293.51/186.02 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s7)) | m_and_h_gate_v_out(c_e_h_1, c_l, s7)),
% 293.51/186.02 inference(modus_ponens,[status(thm)],[22197, 22196])).
% 293.51/186.02 tff(22199,plain,
% 293.51/186.02 (~m_or_h_gate_v_in1(c_e_h_1, c_j, s7)),
% 293.51/186.02 inference(unit_resolution,[status(thm)],[22198, 1100, 22195])).
% 293.51/186.02 tff(22200,plain,
% 293.51/186.02 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s7)) | m_cell_v_ack(c_e_h_1, s7))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s7)) | m_cell_v_ack(c_e_h_1, s7))),
% 293.51/186.02 inference(rewrite,[status(thm)],[])).
% 293.51/186.02 tff(22201,plain,
% 293.51/186.02 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s7)) | m_cell_v_ack(c_e_h_1, s7))),
% 293.51/186.02 inference(quant_inst,[status(thm)],[])).
% 293.51/186.02 tff(22202,plain,
% 293.51/186.02 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s7)) | m_cell_v_ack(c_e_h_1, s7)),
% 293.51/186.02 inference(modus_ponens,[status(thm)],[22201, 22200])).
% 293.51/186.02 tff(22203,plain,
% 293.51/186.02 (~m_or_h_gate_v_in2(c_e_h_1, c_j, s7)),
% 293.51/186.02 inference(unit_resolution,[status(thm)],[22202, 1085, 20599])).
% 293.51/186.02 tff(22204,assumption,(~m_or_h_gate_v_out(c_e_h_1, c_j, s7)), introduced(assumption)).
% 293.51/186.02 tff(22205,assumption,(m_or_h_gate_v_out(c_e_h_1, c_j, s8)), introduced(assumption)).
% 293.51/186.02 tff(22206,assumption,(node6(c_e_h_1, c_j, s7, s8)), introduced(assumption)).
% 293.51/186.02 tff(22207,plain,
% 293.51/186.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s7) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s8)) | (~node6(c_e_h_1, c_j, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s7) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s8)) | (~node6(c_e_h_1, c_j, s7, s8)))),
% 293.51/186.02 inference(rewrite,[status(thm)],[])).
% 293.51/186.02 tff(22208,plain,
% 293.51/186.02 (((~node6(c_e_h_1, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s8)) | m_or_h_gate_v_out(c_e_h_1, c_j, s7)) <=> (m_or_h_gate_v_out(c_e_h_1, c_j, s7) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s8)) | (~node6(c_e_h_1, c_j, s7, s8)))),
% 293.53/186.02 inference(rewrite,[status(thm)],[])).
% 293.53/186.02 tff(22209,plain,
% 293.53/186.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s8)) | m_or_h_gate_v_out(c_e_h_1, c_j, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s7) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s8)) | (~node6(c_e_h_1, c_j, s7, s8))))),
% 293.53/186.02 inference(monotonicity,[status(thm)],[22208])).
% 293.53/186.02 tff(22210,plain,
% 293.53/186.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s8)) | m_or_h_gate_v_out(c_e_h_1, c_j, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s7) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s8)) | (~node6(c_e_h_1, c_j, s7, s8)))),
% 293.53/186.02 inference(transitivity,[status(thm)],[22209, 22207])).
% 293.53/186.02 tff(22211,plain,
% 293.53/186.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s8)) | m_or_h_gate_v_out(c_e_h_1, c_j, s7))),
% 293.53/186.02 inference(quant_inst,[status(thm)],[])).
% 293.53/186.02 tff(22212,plain,
% 293.53/186.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s7) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s8)) | (~node6(c_e_h_1, c_j, s7, s8))),
% 293.53/186.02 inference(modus_ponens,[status(thm)],[22211, 22210])).
% 293.53/186.02 tff(22213,plain,
% 293.53/186.02 ($false),
% 293.53/186.02 inference(unit_resolution,[status(thm)],[22212, 1121, 22204, 22205, 22206])).
% 293.53/186.02 tff(22214,plain,((~node6(c_e_h_1, c_j, s7, s8)) | m_or_h_gate_v_out(c_e_h_1, c_j, s7) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s8))), inference(lemma,lemma(discharge,[]))).
% 293.53/186.02 tff(22215,plain,
% 293.53/186.02 (~node6(c_e_h_1, c_j, s7, s8)),
% 293.53/186.02 inference(unit_resolution,[status(thm)],[22214, 22205, 22204])).
% 293.53/186.02 tff(22216,plain,
% 293.53/186.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s7, s8)) | node6(c_e_h_1, c_j, s7, s8) | node5(c_e_h_1, c_j, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s7, s8)) | node6(c_e_h_1, c_j, s7, s8) | node5(c_e_h_1, c_j, s7, s8))),
% 293.53/186.02 inference(rewrite,[status(thm)],[])).
% 293.53/186.02 tff(22217,plain,
% 293.53/186.02 ((node6(c_e_h_1, c_j, s7, s8) | node5(c_e_h_1, c_j, s7, s8) | (~trans(s7, s8))) <=> ((~trans(s7, s8)) | node6(c_e_h_1, c_j, s7, s8) | node5(c_e_h_1, c_j, s7, s8))),
% 293.53/186.02 inference(rewrite,[status(thm)],[])).
% 293.53/186.02 tff(22218,plain,
% 293.53/186.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s7, s8) | node5(c_e_h_1, c_j, s7, s8) | (~trans(s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s7, s8)) | node6(c_e_h_1, c_j, s7, s8) | node5(c_e_h_1, c_j, s7, s8)))),
% 293.53/186.02 inference(monotonicity,[status(thm)],[22217])).
% 293.53/186.02 tff(22219,plain,
% 293.53/186.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s7, s8) | node5(c_e_h_1, c_j, s7, s8) | (~trans(s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s7, s8)) | node6(c_e_h_1, c_j, s7, s8) | node5(c_e_h_1, c_j, s7, s8))),
% 293.53/186.02 inference(transitivity,[status(thm)],[22218, 22216])).
% 293.53/186.02 tff(22220,plain,
% 293.53/186.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s7, s8) | node5(c_e_h_1, c_j, s7, s8) | (~trans(s7, s8)))),
% 293.53/186.03 inference(quant_inst,[status(thm)],[])).
% 293.53/186.03 tff(22221,plain,
% 293.53/186.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s7, s8)) | node6(c_e_h_1, c_j, s7, s8) | node5(c_e_h_1, c_j, s7, s8)),
% 293.53/186.03 inference(modus_ponens,[status(thm)],[22220, 22219])).
% 293.53/186.03 tff(22222,plain,
% 293.53/186.03 (node6(c_e_h_1, c_j, s7, s8) | node5(c_e_h_1, c_j, s7, s8)),
% 293.53/186.03 inference(unit_resolution,[status(thm)],[22221, 1141, 1938])).
% 293.53/186.03 tff(22223,plain,
% 293.53/186.03 (node5(c_e_h_1, c_j, s7, s8)),
% 293.53/186.03 inference(unit_resolution,[status(thm)],[22222, 22215])).
% 293.53/186.03 tff(22224,plain,
% 293.53/186.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_1, c_j, s7) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s8)) | (~node5(c_e_h_1, c_j, s7, s8)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_1, c_j, s7) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s8)) | (~node5(c_e_h_1, c_j, s7, s8)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s7))),
% 293.53/186.03 inference(rewrite,[status(thm)],[])).
% 293.53/186.03 tff(22225,plain,
% 293.53/186.03 ((m_or_h_gate_v_in1(c_e_h_1, c_j, s7) | m_or_h_gate_v_in2(c_e_h_1, c_j, s7) | (~node5(c_e_h_1, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s8))) <=> (m_or_h_gate_v_in2(c_e_h_1, c_j, s7) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s8)) | (~node5(c_e_h_1, c_j, s7, s8)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s7))),
% 293.53/186.03 inference(rewrite,[status(thm)],[])).
% 293.53/186.03 tff(22226,plain,
% 293.53/186.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s7) | m_or_h_gate_v_in2(c_e_h_1, c_j, s7) | (~node5(c_e_h_1, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_1, c_j, s7) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s8)) | (~node5(c_e_h_1, c_j, s7, s8)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s7)))),
% 293.53/186.03 inference(monotonicity,[status(thm)],[22225])).
% 293.53/186.03 tff(22227,plain,
% 293.53/186.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s7) | m_or_h_gate_v_in2(c_e_h_1, c_j, s7) | (~node5(c_e_h_1, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_1, c_j, s7) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s8)) | (~node5(c_e_h_1, c_j, s7, s8)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s7))),
% 293.53/186.03 inference(transitivity,[status(thm)],[22226, 22224])).
% 293.53/186.03 tff(22228,plain,
% 293.53/186.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s7) | m_or_h_gate_v_in2(c_e_h_1, c_j, s7) | (~node5(c_e_h_1, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s8)))),
% 293.53/186.03 inference(quant_inst,[status(thm)],[])).
% 293.53/186.03 tff(22229,plain,
% 293.53/186.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_1, c_j, s7) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s8)) | (~node5(c_e_h_1, c_j, s7, s8)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s7)),
% 293.53/186.03 inference(modus_ponens,[status(thm)],[22228, 22227])).
% 293.53/186.03 tff(22230,plain,
% 293.53/186.03 ($false),
% 293.53/186.03 inference(unit_resolution,[status(thm)],[22229, 1159, 22205, 22223, 22203, 22199])).
% 293.53/186.03 tff(22231,plain,((~m_or_h_gate_v_out(c_e_h_1, c_j, s8)) | m_or_h_gate_v_out(c_e_h_1, c_j, s7)), inference(lemma,lemma(discharge,[]))).
% 293.53/186.03 tff(22232,plain,
% 293.53/186.03 (~m_or_h_gate_v_out(c_e_h_1, c_j, s8)),
% 293.53/186.03 inference(unit_resolution,[status(thm)],[22231, 22169])).
% 293.53/186.03 tff(22233,assumption,(m_and_h_gate_v_out(c_e_h_1, c_l, s8)), introduced(assumption)).
% 293.53/186.03 tff(22234,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_l, s7)), introduced(assumption)).
% 293.53/186.03 tff(22235,assumption,(node22(c_e_h_1, c_l, s7, s8)), introduced(assumption)).
% 293.53/186.03 tff(22236,plain,
% 293.53/186.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s8)) | (~node22(c_e_h_1, c_l, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_l, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s8)) | (~node22(c_e_h_1, c_l, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_l, s7))),
% 293.53/186.03 inference(rewrite,[status(thm)],[])).
% 293.53/186.03 tff(22237,plain,
% 293.53/186.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s8)) | (~node22(c_e_h_1, c_l, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_l, s7))),
% 293.53/186.03 inference(quant_inst,[status(thm)],[])).
% 293.53/186.03 tff(22238,plain,
% 293.53/186.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s8)) | (~node22(c_e_h_1, c_l, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_l, s7)),
% 293.53/186.03 inference(modus_ponens,[status(thm)],[22237, 22236])).
% 293.53/186.03 tff(22239,plain,
% 293.53/186.03 ($false),
% 293.53/186.03 inference(unit_resolution,[status(thm)],[22238, 108, 22235, 22234, 22233])).
% 293.53/186.03 tff(22240,plain,((~node22(c_e_h_1, c_l, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_l, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s8))), inference(lemma,lemma(discharge,[]))).
% 293.53/186.03 tff(22241,plain,
% 293.53/186.03 (~node22(c_e_h_1, c_l, s7, s8)),
% 293.53/186.03 inference(unit_resolution,[status(thm)],[22240, 22233, 22234])).
% 293.53/186.03 tff(22242,plain,
% 293.53/186.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_1, c_l, s7, s8) | node22(c_e_h_1, c_l, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_1, c_l, s7, s8) | node22(c_e_h_1, c_l, s7, s8))),
% 293.53/186.03 inference(rewrite,[status(thm)],[])).
% 293.53/186.03 tff(22243,plain,
% 293.53/186.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_1, c_l, s7, s8) | node22(c_e_h_1, c_l, s7, s8))),
% 293.53/186.03 inference(quant_inst,[status(thm)],[])).
% 293.53/186.03 tff(22244,plain,
% 293.53/186.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_1, c_l, s7, s8) | node22(c_e_h_1, c_l, s7, s8)),
% 293.53/186.03 inference(modus_ponens,[status(thm)],[22243, 22242])).
% 293.53/186.03 tff(22245,plain,
% 293.53/186.03 (node21(c_e_h_1, c_l, s7, s8) | node22(c_e_h_1, c_l, s7, s8)),
% 293.53/186.03 inference(unit_resolution,[status(thm)],[22244, 82, 1938])).
% 293.53/186.03 tff(22246,plain,
% 293.53/186.03 (node21(c_e_h_1, c_l, s7, s8)),
% 293.53/186.03 inference(unit_resolution,[status(thm)],[22245, 22241])).
% 293.53/186.03 tff(22247,plain,
% 293.53/186.03 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7))),
% 293.53/186.03 inference(rewrite,[status(thm)],[])).
% 293.53/186.03 tff(22248,plain,
% 293.53/186.03 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7))),
% 293.53/186.03 inference(quant_inst,[status(thm)],[])).
% 293.53/186.03 tff(22249,plain,
% 293.53/186.03 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)),
% 293.53/186.04 inference(modus_ponens,[status(thm)],[22248, 22247])).
% 293.53/186.04 tff(22250,plain,
% 293.53/186.04 (~m_and_h_gate_v_in2(c_e_h_1, c_l, s7)),
% 293.53/186.04 inference(unit_resolution,[status(thm)],[22249, 4549, 19249])).
% 293.53/186.04 tff(22251,plain,
% 293.53/186.04 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s7)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s7)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s7))),
% 293.53/186.04 inference(rewrite,[status(thm)],[])).
% 293.53/186.04 tff(22252,plain,
% 293.53/186.04 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s7)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s7))),
% 293.53/186.04 inference(quant_inst,[status(thm)],[])).
% 293.53/186.04 tff(22253,plain,
% 293.53/186.04 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s7)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s7)),
% 293.53/186.04 inference(modus_ponens,[status(thm)],[22252, 22251])).
% 293.53/186.04 tff(22254,plain,
% 293.53/186.04 (~node20(c_e_h_1, c_l, s7)),
% 293.53/186.04 inference(unit_resolution,[status(thm)],[22253, 4563, 22250])).
% 293.53/186.04 tff(22255,plain,
% 293.53/186.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s8)) | (~node21(c_e_h_1, c_l, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s8)) | (~node21(c_e_h_1, c_l, s7, s8)))),
% 293.53/186.04 inference(rewrite,[status(thm)],[])).
% 293.53/186.04 tff(22256,plain,
% 293.53/186.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s8)) | (~node21(c_e_h_1, c_l, s7, s8)))),
% 293.53/186.04 inference(quant_inst,[status(thm)],[])).
% 293.53/186.04 tff(22257,plain,
% 293.53/186.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s8)) | (~node21(c_e_h_1, c_l, s7, s8))),
% 293.53/186.04 inference(modus_ponens,[status(thm)],[22256, 22255])).
% 293.53/186.04 tff(22258,plain,
% 293.53/186.04 ($false),
% 293.53/186.04 inference(unit_resolution,[status(thm)],[22257, 52, 22254, 22246, 22233])).
% 293.53/186.04 tff(22259,plain,((~m_and_h_gate_v_out(c_e_h_1, c_l, s8)) | m_and_h_gate_v_out(c_e_h_1, c_l, s7)), inference(lemma,lemma(discharge,[]))).
% 293.53/186.04 tff(22260,plain,
% 293.53/186.04 (~m_and_h_gate_v_out(c_e_h_1, c_l, s8)),
% 293.53/186.04 inference(unit_resolution,[status(thm)],[22259, 22195])).
% 293.53/186.04 tff(22261,plain,
% 293.53/186.04 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s8)) | m_and_h_gate_v_out(c_e_h_1, c_l, s8))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s8)) | m_and_h_gate_v_out(c_e_h_1, c_l, s8))),
% 293.53/186.04 inference(rewrite,[status(thm)],[])).
% 293.53/186.04 tff(22262,plain,
% 293.53/186.04 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s8)) | m_and_h_gate_v_out(c_e_h_1, c_l, s8))),
% 293.53/186.04 inference(quant_inst,[status(thm)],[])).
% 293.53/186.04 tff(22263,plain,
% 293.53/186.04 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s8)) | m_and_h_gate_v_out(c_e_h_1, c_l, s8)),
% 293.53/186.04 inference(modus_ponens,[status(thm)],[22262, 22261])).
% 293.53/186.04 tff(22264,plain,
% 293.53/186.04 (~m_or_h_gate_v_in1(c_e_h_1, c_j, s8)),
% 293.53/186.04 inference(unit_resolution,[status(thm)],[22263, 1100, 22260])).
% 293.53/186.04 tff(22265,assumption,(m_or_h_gate_v_out(c_e_h_1, c_j, s9)), introduced(assumption)).
% 293.53/186.04 tff(22266,plain,
% 293.53/186.04 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s8)) | m_cell_v_ack(c_e_h_1, s8))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s8)) | m_cell_v_ack(c_e_h_1, s8))),
% 293.53/186.04 inference(rewrite,[status(thm)],[])).
% 293.53/186.04 tff(22267,plain,
% 293.53/186.04 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s8)) | m_cell_v_ack(c_e_h_1, s8))),
% 293.53/186.04 inference(quant_inst,[status(thm)],[])).
% 293.53/186.04 tff(22268,plain,
% 293.53/186.04 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s8)) | m_cell_v_ack(c_e_h_1, s8)),
% 293.53/186.04 inference(modus_ponens,[status(thm)],[22267, 22266])).
% 293.53/186.04 tff(22269,plain,
% 293.53/186.04 (~m_or_h_gate_v_in2(c_e_h_1, c_j, s8)),
% 293.53/186.04 inference(unit_resolution,[status(thm)],[22268, 1085, 20433])).
% 293.53/186.04 tff(22270,assumption,(~m_or_h_gate_v_in1(c_e_h_1, c_j, s8)), introduced(assumption)).
% 293.53/186.04 tff(22271,assumption,(~m_or_h_gate_v_in2(c_e_h_1, c_j, s8)), introduced(assumption)).
% 293.53/186.04 tff(22272,assumption,(node5(c_e_h_1, c_j, s8, s9)), introduced(assumption)).
% 293.53/186.04 tff(22273,plain,
% 293.53/186.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_1, c_j, s9)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s8) | m_or_h_gate_v_in1(c_e_h_1, c_j, s8) | (~node5(c_e_h_1, c_j, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s9)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s8) | m_or_h_gate_v_in1(c_e_h_1, c_j, s8) | (~node5(c_e_h_1, c_j, s8, s9)))),
% 293.53/186.04 inference(rewrite,[status(thm)],[])).
% 293.53/186.04 tff(22274,plain,
% 293.53/186.04 ((m_or_h_gate_v_in1(c_e_h_1, c_j, s8) | m_or_h_gate_v_in2(c_e_h_1, c_j, s8) | (~node5(c_e_h_1, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s9))) <=> ((~m_or_h_gate_v_out(c_e_h_1, c_j, s9)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s8) | m_or_h_gate_v_in1(c_e_h_1, c_j, s8) | (~node5(c_e_h_1, c_j, s8, s9)))),
% 293.53/186.04 inference(rewrite,[status(thm)],[])).
% 293.53/186.04 tff(22275,plain,
% 293.53/186.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s8) | m_or_h_gate_v_in2(c_e_h_1, c_j, s8) | (~node5(c_e_h_1, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_1, c_j, s9)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s8) | m_or_h_gate_v_in1(c_e_h_1, c_j, s8) | (~node5(c_e_h_1, c_j, s8, s9))))),
% 293.53/186.04 inference(monotonicity,[status(thm)],[22274])).
% 293.53/186.04 tff(22276,plain,
% 293.53/186.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s8) | m_or_h_gate_v_in2(c_e_h_1, c_j, s8) | (~node5(c_e_h_1, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s9)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s8) | m_or_h_gate_v_in1(c_e_h_1, c_j, s8) | (~node5(c_e_h_1, c_j, s8, s9)))),
% 293.53/186.04 inference(transitivity,[status(thm)],[22275, 22273])).
% 293.53/186.04 tff(22277,plain,
% 293.53/186.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s8) | m_or_h_gate_v_in2(c_e_h_1, c_j, s8) | (~node5(c_e_h_1, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s9)))),
% 293.53/186.04 inference(quant_inst,[status(thm)],[])).
% 293.53/186.04 tff(22278,plain,
% 293.53/186.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s9)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s8) | m_or_h_gate_v_in1(c_e_h_1, c_j, s8) | (~node5(c_e_h_1, c_j, s8, s9))),
% 293.53/186.04 inference(modus_ponens,[status(thm)],[22277, 22276])).
% 293.53/186.04 tff(22279,plain,
% 293.53/186.04 ($false),
% 293.53/186.04 inference(unit_resolution,[status(thm)],[22278, 1159, 22265, 22272, 22271, 22270])).
% 293.53/186.04 tff(22280,plain,((~node5(c_e_h_1, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s9)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s8) | m_or_h_gate_v_in1(c_e_h_1, c_j, s8)), inference(lemma,lemma(discharge,[]))).
% 293.53/186.04 tff(22281,plain,
% 293.53/186.04 ((~node5(c_e_h_1, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s9)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s8)),
% 293.53/186.04 inference(unit_resolution,[status(thm)],[22280, 22269])).
% 293.53/186.04 tff(22282,plain,
% 293.53/186.04 (~node5(c_e_h_1, c_j, s8, s9)),
% 293.53/186.04 inference(unit_resolution,[status(thm)],[22281, 22265, 22264])).
% 293.53/186.04 tff(22283,plain,
% 293.53/186.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s8, s9)) | node6(c_e_h_1, c_j, s8, s9) | node5(c_e_h_1, c_j, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s8, s9)) | node6(c_e_h_1, c_j, s8, s9) | node5(c_e_h_1, c_j, s8, s9))),
% 293.53/186.04 inference(rewrite,[status(thm)],[])).
% 293.53/186.04 tff(22284,plain,
% 293.53/186.04 ((node6(c_e_h_1, c_j, s8, s9) | node5(c_e_h_1, c_j, s8, s9) | (~trans(s8, s9))) <=> ((~trans(s8, s9)) | node6(c_e_h_1, c_j, s8, s9) | node5(c_e_h_1, c_j, s8, s9))),
% 293.53/186.04 inference(rewrite,[status(thm)],[])).
% 293.53/186.04 tff(22285,plain,
% 293.53/186.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s8, s9) | node5(c_e_h_1, c_j, s8, s9) | (~trans(s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s8, s9)) | node6(c_e_h_1, c_j, s8, s9) | node5(c_e_h_1, c_j, s8, s9)))),
% 293.53/186.04 inference(monotonicity,[status(thm)],[22284])).
% 293.53/186.04 tff(22286,plain,
% 293.53/186.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s8, s9) | node5(c_e_h_1, c_j, s8, s9) | (~trans(s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s8, s9)) | node6(c_e_h_1, c_j, s8, s9) | node5(c_e_h_1, c_j, s8, s9))),
% 293.53/186.04 inference(transitivity,[status(thm)],[22285, 22283])).
% 293.53/186.04 tff(22287,plain,
% 293.53/186.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s8, s9) | node5(c_e_h_1, c_j, s8, s9) | (~trans(s8, s9)))),
% 293.53/186.04 inference(quant_inst,[status(thm)],[])).
% 293.53/186.04 tff(22288,plain,
% 293.53/186.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s8, s9)) | node6(c_e_h_1, c_j, s8, s9) | node5(c_e_h_1, c_j, s8, s9)),
% 293.53/186.04 inference(modus_ponens,[status(thm)],[22287, 22286])).
% 293.53/186.04 tff(22289,plain,
% 293.53/186.04 (node6(c_e_h_1, c_j, s8, s9) | node5(c_e_h_1, c_j, s8, s9)),
% 293.53/186.04 inference(unit_resolution,[status(thm)],[22288, 1141, 1993])).
% 293.53/186.04 tff(22290,plain,
% 293.53/186.04 (node6(c_e_h_1, c_j, s8, s9)),
% 293.53/186.04 inference(unit_resolution,[status(thm)],[22289, 22282])).
% 293.53/186.04 tff(22291,assumption,(~m_or_h_gate_v_out(c_e_h_1, c_j, s8)), introduced(assumption)).
% 293.53/186.04 tff(22292,plain,
% 293.53/186.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_1, c_j, s9)) | m_or_h_gate_v_out(c_e_h_1, c_j, s8) | (~node6(c_e_h_1, c_j, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s9)) | m_or_h_gate_v_out(c_e_h_1, c_j, s8) | (~node6(c_e_h_1, c_j, s8, s9)))),
% 293.53/186.04 inference(rewrite,[status(thm)],[])).
% 293.53/186.04 tff(22293,plain,
% 293.53/186.04 (((~node6(c_e_h_1, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s9)) | m_or_h_gate_v_out(c_e_h_1, c_j, s8)) <=> ((~m_or_h_gate_v_out(c_e_h_1, c_j, s9)) | m_or_h_gate_v_out(c_e_h_1, c_j, s8) | (~node6(c_e_h_1, c_j, s8, s9)))),
% 293.53/186.04 inference(rewrite,[status(thm)],[])).
% 293.53/186.04 tff(22294,plain,
% 293.53/186.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s9)) | m_or_h_gate_v_out(c_e_h_1, c_j, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_1, c_j, s9)) | m_or_h_gate_v_out(c_e_h_1, c_j, s8) | (~node6(c_e_h_1, c_j, s8, s9))))),
% 293.53/186.05 inference(monotonicity,[status(thm)],[22293])).
% 293.53/186.05 tff(22295,plain,
% 293.53/186.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s9)) | m_or_h_gate_v_out(c_e_h_1, c_j, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s9)) | m_or_h_gate_v_out(c_e_h_1, c_j, s8) | (~node6(c_e_h_1, c_j, s8, s9)))),
% 293.53/186.05 inference(transitivity,[status(thm)],[22294, 22292])).
% 293.53/186.05 tff(22296,plain,
% 293.53/186.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s9)) | m_or_h_gate_v_out(c_e_h_1, c_j, s8))),
% 293.53/186.05 inference(quant_inst,[status(thm)],[])).
% 293.53/186.05 tff(22297,plain,
% 293.53/186.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s9)) | m_or_h_gate_v_out(c_e_h_1, c_j, s8) | (~node6(c_e_h_1, c_j, s8, s9))),
% 293.53/186.05 inference(modus_ponens,[status(thm)],[22296, 22295])).
% 293.53/186.05 tff(22298,plain,
% 293.53/186.05 ($false),
% 293.53/186.05 inference(unit_resolution,[status(thm)],[22297, 1121, 22265, 22291, 22290])).
% 293.53/186.05 tff(22299,plain,((~m_or_h_gate_v_out(c_e_h_1, c_j, s9)) | m_or_h_gate_v_out(c_e_h_1, c_j, s8)), inference(lemma,lemma(discharge,[]))).
% 293.53/186.05 tff(22300,plain,
% 293.53/186.05 (~m_or_h_gate_v_out(c_e_h_1, c_j, s9)),
% 293.53/186.05 inference(unit_resolution,[status(thm)],[22299, 22232])).
% 293.53/186.05 tff(22301,assumption,(node6(c_e_h_1, c_j, s9, s10)), introduced(assumption)).
% 293.53/186.05 tff(22302,assumption,(~m_or_h_gate_v_out(c_e_h_1, c_j, s9)), introduced(assumption)).
% 293.53/186.05 tff(22303,plain,
% 293.53/186.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s9) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s10)) | (~node6(c_e_h_1, c_j, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s9) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s10)) | (~node6(c_e_h_1, c_j, s9, s10)))),
% 293.53/186.05 inference(rewrite,[status(thm)],[])).
% 293.53/186.05 tff(22304,plain,
% 293.53/186.05 (((~node6(c_e_h_1, c_j, s9, s10)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s10)) | m_or_h_gate_v_out(c_e_h_1, c_j, s9)) <=> (m_or_h_gate_v_out(c_e_h_1, c_j, s9) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s10)) | (~node6(c_e_h_1, c_j, s9, s10)))),
% 293.53/186.05 inference(rewrite,[status(thm)],[])).
% 293.53/186.05 tff(22305,plain,
% 293.53/186.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s9, s10)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s10)) | m_or_h_gate_v_out(c_e_h_1, c_j, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s9) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s10)) | (~node6(c_e_h_1, c_j, s9, s10))))),
% 293.53/186.05 inference(monotonicity,[status(thm)],[22304])).
% 293.53/186.05 tff(22306,plain,
% 293.53/186.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s9, s10)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s10)) | m_or_h_gate_v_out(c_e_h_1, c_j, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s9) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s10)) | (~node6(c_e_h_1, c_j, s9, s10)))),
% 293.53/186.05 inference(transitivity,[status(thm)],[22305, 22303])).
% 293.53/186.05 tff(22307,plain,
% 293.53/186.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s9, s10)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s10)) | m_or_h_gate_v_out(c_e_h_1, c_j, s9))),
% 293.53/186.05 inference(quant_inst,[status(thm)],[])).
% 293.53/186.05 tff(22308,plain,
% 293.53/186.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s9) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s10)) | (~node6(c_e_h_1, c_j, s9, s10))),
% 293.53/186.05 inference(modus_ponens,[status(thm)],[22307, 22306])).
% 293.53/186.05 tff(22309,plain,
% 293.53/186.05 ($false),
% 293.53/186.05 inference(unit_resolution,[status(thm)],[22308, 1121, 22302, 22096, 22301])).
% 293.53/186.05 tff(22310,plain,((~node6(c_e_h_1, c_j, s9, s10)) | m_or_h_gate_v_out(c_e_h_1, c_j, s9) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s10))), inference(lemma,lemma(discharge,[]))).
% 293.53/186.05 tff(22311,plain,
% 293.53/186.05 ((~node6(c_e_h_1, c_j, s9, s10)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s10))),
% 293.53/186.05 inference(unit_resolution,[status(thm)],[22310, 22300])).
% 293.53/186.05 tff(22312,plain,
% 293.53/186.05 (~node6(c_e_h_1, c_j, s9, s10)),
% 293.53/186.05 inference(unit_resolution,[status(thm)],[22311, 22096])).
% 293.53/186.05 tff(22313,assumption,(m_and_h_gate_v_out(c_e_h_1, c_l, s9)), introduced(assumption)).
% 293.53/186.05 tff(22314,assumption,(node21(c_e_h_1, c_l, s8, s9)), introduced(assumption)).
% 293.53/186.05 tff(22315,plain,
% 293.53/186.05 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s5)),
% 293.53/186.05 inference(unit_resolution,[status(thm)],[18116, 18081, 18080])).
% 293.53/186.05 tff(22316,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)), introduced(assumption)).
% 293.53/186.05 tff(22317,plain,
% 293.53/186.05 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s4)),
% 293.53/186.05 inference(unit_resolution,[status(thm)],[17979, 4958, 18080])).
% 293.53/186.05 tff(22318,plain,
% 293.53/186.05 (~node9(c_e_h_1, c_m, s4)),
% 293.53/186.05 inference(unit_resolution,[status(thm)],[17983, 4972, 22317])).
% 293.53/186.05 tff(22319,plain,
% 293.53/186.05 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s5)),
% 293.53/186.05 inference(unit_resolution,[status(thm)],[18037, 22318])).
% 293.53/186.05 tff(22320,plain,
% 293.53/186.05 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6)),
% 293.53/186.05 inference(unit_resolution,[status(thm)],[18107, 18081, 22319, 18047, 18080])).
% 293.53/186.05 tff(22321,plain,
% 293.53/186.05 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s6)),
% 293.53/186.05 inference(unit_resolution,[status(thm)],[19219, 4958, 18177])).
% 293.53/186.05 tff(22322,plain,
% 293.53/186.05 (~node9(c_e_h_1, c_m, s6)),
% 293.53/186.05 inference(unit_resolution,[status(thm)],[19223, 4972, 22321])).
% 293.53/186.05 tff(22323,plain,
% 293.53/186.05 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)),
% 293.53/186.05 inference(unit_resolution,[status(thm)],[19247, 19226, 22322])).
% 293.53/186.05 tff(22324,assumption,(node11(c_e_h_1, c_m, s7, s8)), introduced(assumption)).
% 293.53/186.05 tff(22325,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)), introduced(assumption)).
% 293.53/186.05 tff(22326,plain,
% 293.53/186.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)) | (~node11(c_e_h_1, c_m, s7, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)) | (~node11(c_e_h_1, c_m, s7, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7))),
% 293.53/186.05 inference(rewrite,[status(thm)],[])).
% 293.53/186.05 tff(22327,plain,
% 293.53/186.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)) | (~node11(c_e_h_1, c_m, s7, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7))),
% 293.53/186.05 inference(quant_inst,[status(thm)],[])).
% 293.53/186.05 tff(22328,plain,
% 293.53/186.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)) | (~node11(c_e_h_1, c_m, s7, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)),
% 293.53/186.05 inference(modus_ponens,[status(thm)],[22327, 22326])).
% 293.53/186.05 tff(22329,plain,
% 293.53/186.05 ($false),
% 293.53/186.05 inference(unit_resolution,[status(thm)],[22328, 5017, 22325, 22316, 22324])).
% 293.53/186.05 tff(22330,plain,((~node11(c_e_h_1, c_m, s7, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8))), inference(lemma,lemma(discharge,[]))).
% 293.53/186.05 tff(22331,plain,
% 293.53/186.05 (~node11(c_e_h_1, c_m, s7, s8)),
% 293.53/186.05 inference(unit_resolution,[status(thm)],[22330, 22323, 22316])).
% 293.53/186.05 tff(22332,plain,
% 293.53/186.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s7, s8)) | node10(c_e_h_1, c_m, s7, s8) | node11(c_e_h_1, c_m, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s7, s8)) | node10(c_e_h_1, c_m, s7, s8) | node11(c_e_h_1, c_m, s7, s8))),
% 293.53/186.05 inference(rewrite,[status(thm)],[])).
% 293.53/186.05 tff(22333,plain,
% 293.53/186.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s7, s8)) | node10(c_e_h_1, c_m, s7, s8) | node11(c_e_h_1, c_m, s7, s8))),
% 293.53/186.05 inference(quant_inst,[status(thm)],[])).
% 293.53/186.05 tff(22334,plain,
% 293.53/186.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s7, s8)) | node10(c_e_h_1, c_m, s7, s8) | node11(c_e_h_1, c_m, s7, s8)),
% 293.53/186.05 inference(modus_ponens,[status(thm)],[22333, 22332])).
% 293.53/186.05 tff(22335,plain,
% 293.53/186.05 (node10(c_e_h_1, c_m, s7, s8) | node11(c_e_h_1, c_m, s7, s8)),
% 293.53/186.05 inference(unit_resolution,[status(thm)],[22334, 5002, 1938])).
% 293.53/186.05 tff(22336,plain,
% 293.53/186.05 (node10(c_e_h_1, c_m, s7, s8)),
% 293.53/186.05 inference(unit_resolution,[status(thm)],[22335, 22331])).
% 293.53/186.05 tff(22337,assumption,(~node9(c_e_h_1, c_m, s7)), introduced(assumption)).
% 293.53/186.05 tff(22338,assumption,(node10(c_e_h_1, c_m, s7, s8)), introduced(assumption)).
% 293.53/186.05 tff(22339,plain,
% 293.53/186.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)) | node9(c_e_h_1, c_m, s7) | (~node10(c_e_h_1, c_m, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)) | node9(c_e_h_1, c_m, s7) | (~node10(c_e_h_1, c_m, s7, s8)))),
% 293.53/186.05 inference(rewrite,[status(thm)],[])).
% 293.53/186.05 tff(22340,plain,
% 293.53/186.05 ((node9(c_e_h_1, c_m, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)) | (~node10(c_e_h_1, c_m, s7, s8))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)) | node9(c_e_h_1, c_m, s7) | (~node10(c_e_h_1, c_m, s7, s8)))),
% 293.53/186.05 inference(rewrite,[status(thm)],[])).
% 293.53/186.05 tff(22341,plain,
% 293.53/186.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)) | (~node10(c_e_h_1, c_m, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)) | node9(c_e_h_1, c_m, s7) | (~node10(c_e_h_1, c_m, s7, s8))))),
% 293.53/186.05 inference(monotonicity,[status(thm)],[22340])).
% 293.53/186.05 tff(22342,plain,
% 293.53/186.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)) | (~node10(c_e_h_1, c_m, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)) | node9(c_e_h_1, c_m, s7) | (~node10(c_e_h_1, c_m, s7, s8)))),
% 293.53/186.05 inference(transitivity,[status(thm)],[22341, 22339])).
% 293.53/186.05 tff(22343,plain,
% 293.53/186.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s7) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)) | (~node10(c_e_h_1, c_m, s7, s8)))),
% 293.53/186.05 inference(quant_inst,[status(thm)],[])).
% 293.53/186.05 tff(22344,plain,
% 293.53/186.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)) | node9(c_e_h_1, c_m, s7) | (~node10(c_e_h_1, c_m, s7, s8))),
% 293.53/186.06 inference(modus_ponens,[status(thm)],[22343, 22342])).
% 293.53/186.06 tff(22345,plain,
% 293.53/186.06 ($false),
% 293.53/186.06 inference(unit_resolution,[status(thm)],[22344, 4986, 22316, 22338, 22337])).
% 293.53/186.06 tff(22346,plain,((~node10(c_e_h_1, c_m, s7, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)) | node9(c_e_h_1, c_m, s7)), inference(lemma,lemma(discharge,[]))).
% 293.53/186.06 tff(22347,plain,
% 293.53/186.06 (node9(c_e_h_1, c_m, s7)),
% 293.53/186.06 inference(unit_resolution,[status(thm)],[22346, 22336, 22316])).
% 293.53/186.06 tff(22348,plain,
% 293.53/186.06 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s6)),
% 293.53/186.06 inference(unit_resolution,[status(thm)],[18162, 19226])).
% 293.53/186.06 tff(22349,plain,
% 293.53/186.06 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)),
% 293.53/186.06 inference(unit_resolution,[status(thm)],[18193, 22348, 18165, 18177])).
% 293.53/186.06 tff(22350,plain,
% 293.53/186.06 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)))),
% 293.53/186.06 inference(rewrite,[status(thm)],[])).
% 293.53/186.06 tff(22351,plain,
% 293.53/186.06 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)))),
% 293.53/186.06 inference(quant_inst,[status(thm)],[])).
% 293.53/186.06 tff(22352,plain,
% 293.53/186.06 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7))),
% 293.53/186.06 inference(modus_ponens,[status(thm)],[22351, 22350])).
% 293.53/186.06 tff(22353,plain,
% 293.53/186.06 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s7)),
% 293.53/186.06 inference(unit_resolution,[status(thm)],[22352, 4958, 22349])).
% 293.53/186.06 tff(22354,plain,
% 293.53/186.06 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s7)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s7)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s7))),
% 293.53/186.06 inference(rewrite,[status(thm)],[])).
% 293.53/186.06 tff(22355,plain,
% 293.53/186.06 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s7)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s7))),
% 293.53/186.06 inference(quant_inst,[status(thm)],[])).
% 293.53/186.06 tff(22356,plain,
% 293.53/186.06 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s7)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s7)),
% 293.53/186.06 inference(modus_ponens,[status(thm)],[22355, 22354])).
% 293.53/186.06 tff(22357,plain,
% 293.53/186.06 ($false),
% 293.53/186.06 inference(unit_resolution,[status(thm)],[22356, 4972, 22353, 22347])).
% 293.53/186.06 tff(22358,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s6))), inference(lemma,lemma(discharge,[]))).
% 293.53/186.06 tff(22359,plain,
% 293.53/186.06 (m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)),
% 293.53/186.06 inference(unit_resolution,[status(thm)],[22358, 22320, 18165, 22316])).
% 293.53/186.06 tff(22360,plain,
% 293.53/186.06 (~node11(c_e_h_1, c_m, s5, s6)),
% 293.53/186.06 inference(unit_resolution,[status(thm)],[18139, 22359, 22319])).
% 293.53/186.06 tff(22361,plain,
% 293.53/186.06 (node10(c_e_h_1, c_m, s5, s6)),
% 293.53/186.06 inference(unit_resolution,[status(thm)],[18155, 22360])).
% 293.53/186.06 tff(22362,plain,
% 293.53/186.06 (node9(c_e_h_1, c_m, s5)),
% 293.53/186.06 inference(unit_resolution,[status(thm)],[18150, 22361, 22359])).
% 293.53/186.06 tff(22363,plain,
% 293.53/186.06 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s5)),
% 293.53/186.06 inference(unit_resolution,[status(thm)],[18129, 4972, 22362])).
% 293.53/186.06 tff(22364,plain,
% 293.53/186.06 ($false),
% 293.53/186.06 inference(unit_resolution,[status(thm)],[18121, 4958, 22363, 22315])).
% 293.53/186.06 tff(22365,plain,((~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s4))), inference(lemma,lemma(discharge,[]))).
% 293.53/186.06 tff(22366,plain,
% 293.53/186.06 ((~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s5))),
% 293.53/186.06 inference(unit_resolution,[status(thm)],[22365, 17976, 17899])).
% 293.53/186.06 tff(22367,plain,
% 293.53/186.06 ((~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8))),
% 293.53/186.06 inference(unit_resolution,[status(thm)],[22366, 17892])).
% 293.53/186.06 tff(22368,plain,
% 293.53/186.06 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)),
% 293.53/186.06 inference(unit_resolution,[status(thm)],[22367, 17887])).
% 293.53/186.06 tff(22369,plain,
% 293.53/186.06 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8))),
% 293.53/186.06 inference(rewrite,[status(thm)],[])).
% 293.53/186.06 tff(22370,plain,
% 293.53/186.06 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8))),
% 293.53/186.06 inference(quant_inst,[status(thm)],[])).
% 293.53/186.06 tff(22371,plain,
% 293.53/186.06 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)),
% 293.53/186.06 inference(modus_ponens,[status(thm)],[22370, 22369])).
% 293.53/186.06 tff(22372,plain,
% 293.53/186.06 (~m_and_h_gate_v_in2(c_e_h_1, c_l, s8)),
% 293.53/186.06 inference(unit_resolution,[status(thm)],[22371, 4549, 22368])).
% 293.53/186.06 tff(22373,plain,
% 293.53/186.06 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s8)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s8)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s8))),
% 293.53/186.06 inference(rewrite,[status(thm)],[])).
% 293.53/186.06 tff(22374,plain,
% 293.53/186.06 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s8)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s8))),
% 293.53/186.06 inference(quant_inst,[status(thm)],[])).
% 293.53/186.06 tff(22375,plain,
% 293.53/186.06 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s8)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s8)),
% 293.53/186.06 inference(modus_ponens,[status(thm)],[22374, 22373])).
% 293.53/186.06 tff(22376,plain,
% 293.53/186.06 (~node20(c_e_h_1, c_l, s8)),
% 293.53/186.06 inference(unit_resolution,[status(thm)],[22375, 4563, 22372])).
% 293.53/186.06 tff(22377,plain,
% 293.53/186.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s9)) | (~node21(c_e_h_1, c_l, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s9)) | (~node21(c_e_h_1, c_l, s8, s9)))),
% 293.53/186.06 inference(rewrite,[status(thm)],[])).
% 293.53/186.06 tff(22378,plain,
% 293.53/186.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s9)) | (~node21(c_e_h_1, c_l, s8, s9)))),
% 293.53/186.06 inference(quant_inst,[status(thm)],[])).
% 293.53/186.06 tff(22379,plain,
% 293.53/186.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s9)) | (~node21(c_e_h_1, c_l, s8, s9))),
% 293.53/186.06 inference(modus_ponens,[status(thm)],[22378, 22377])).
% 293.53/186.06 tff(22380,plain,
% 293.53/186.06 ($false),
% 293.53/186.06 inference(unit_resolution,[status(thm)],[22379, 52, 22376, 22314, 22313])).
% 293.53/186.06 tff(22381,plain,((~node21(c_e_h_1, c_l, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s9))), inference(lemma,lemma(discharge,[]))).
% 293.53/186.06 tff(22382,plain,
% 293.53/186.06 (~node21(c_e_h_1, c_l, s8, s9)),
% 293.53/186.06 inference(unit_resolution,[status(thm)],[22381, 22313])).
% 293.53/186.06 tff(22383,plain,
% 293.53/186.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s8, s9)) | node21(c_e_h_1, c_l, s8, s9) | node22(c_e_h_1, c_l, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_1, c_l, s8, s9) | node22(c_e_h_1, c_l, s8, s9))),
% 293.53/186.06 inference(rewrite,[status(thm)],[])).
% 293.53/186.06 tff(22384,plain,
% 293.53/186.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s8, s9)) | node21(c_e_h_1, c_l, s8, s9) | node22(c_e_h_1, c_l, s8, s9))),
% 293.53/186.06 inference(quant_inst,[status(thm)],[])).
% 293.53/186.06 tff(22385,plain,
% 293.53/186.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_1, c_l, s8, s9) | node22(c_e_h_1, c_l, s8, s9)),
% 293.53/186.06 inference(modus_ponens,[status(thm)],[22384, 22383])).
% 293.53/186.06 tff(22386,plain,
% 293.53/186.06 (node21(c_e_h_1, c_l, s8, s9) | node22(c_e_h_1, c_l, s8, s9)),
% 293.53/186.06 inference(unit_resolution,[status(thm)],[22385, 82, 1993])).
% 293.53/186.06 tff(22387,plain,
% 293.53/186.06 (node22(c_e_h_1, c_l, s8, s9)),
% 293.53/186.06 inference(unit_resolution,[status(thm)],[22386, 22382])).
% 293.53/186.06 tff(22388,plain,
% 293.53/186.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s9)) | (~node22(c_e_h_1, c_l, s8, s9)) | m_and_h_gate_v_out(c_e_h_1, c_l, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s9)) | (~node22(c_e_h_1, c_l, s8, s9)) | m_and_h_gate_v_out(c_e_h_1, c_l, s8))),
% 293.53/186.06 inference(rewrite,[status(thm)],[])).
% 293.53/186.06 tff(22389,plain,
% 293.53/186.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s9)) | (~node22(c_e_h_1, c_l, s8, s9)) | m_and_h_gate_v_out(c_e_h_1, c_l, s8))),
% 293.53/186.06 inference(quant_inst,[status(thm)],[])).
% 293.53/186.06 tff(22390,plain,
% 293.53/186.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s9)) | (~node22(c_e_h_1, c_l, s8, s9)) | m_and_h_gate_v_out(c_e_h_1, c_l, s8)),
% 293.53/186.06 inference(modus_ponens,[status(thm)],[22389, 22388])).
% 293.53/186.06 tff(22391,plain,
% 293.53/186.06 ($false),
% 293.53/186.06 inference(unit_resolution,[status(thm)],[22390, 108, 22260, 22387, 22313])).
% 293.53/186.06 tff(22392,plain,(~m_and_h_gate_v_out(c_e_h_1, c_l, s9)), inference(lemma,lemma(discharge,[]))).
% 293.53/186.06 tff(22393,plain,
% 293.53/186.06 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s9)) | m_and_h_gate_v_out(c_e_h_1, c_l, s9))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s9)) | m_and_h_gate_v_out(c_e_h_1, c_l, s9))),
% 293.53/186.06 inference(rewrite,[status(thm)],[])).
% 293.53/186.06 tff(22394,plain,
% 293.53/186.06 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s9)) | m_and_h_gate_v_out(c_e_h_1, c_l, s9))),
% 293.53/186.06 inference(quant_inst,[status(thm)],[])).
% 293.53/186.06 tff(22395,plain,
% 293.53/186.06 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s9)) | m_and_h_gate_v_out(c_e_h_1, c_l, s9)),
% 293.53/186.06 inference(modus_ponens,[status(thm)],[22394, 22393])).
% 293.53/186.06 tff(22396,plain,
% 293.53/186.06 (~m_or_h_gate_v_in1(c_e_h_1, c_j, s9)),
% 293.53/186.06 inference(unit_resolution,[status(thm)],[22395, 1100, 22392])).
% 293.53/186.06 tff(22397,assumption,(~m_or_h_gate_v_in1(c_e_h_1, c_j, s9)), introduced(assumption)).
% 293.53/186.06 tff(22398,assumption,(node5(c_e_h_1, c_j, s9, s10)), introduced(assumption)).
% 293.53/186.07 tff(22399,plain,
% 293.53/186.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_1, c_j, s10)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s9) | m_or_h_gate_v_in1(c_e_h_1, c_j, s9) | (~node5(c_e_h_1, c_j, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s10)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s9) | m_or_h_gate_v_in1(c_e_h_1, c_j, s9) | (~node5(c_e_h_1, c_j, s9, s10)))),
% 293.53/186.07 inference(rewrite,[status(thm)],[])).
% 293.53/186.07 tff(22400,plain,
% 293.53/186.07 ((m_or_h_gate_v_in1(c_e_h_1, c_j, s9) | m_or_h_gate_v_in2(c_e_h_1, c_j, s9) | (~node5(c_e_h_1, c_j, s9, s10)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s10))) <=> ((~m_or_h_gate_v_out(c_e_h_1, c_j, s10)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s9) | m_or_h_gate_v_in1(c_e_h_1, c_j, s9) | (~node5(c_e_h_1, c_j, s9, s10)))),
% 293.53/186.07 inference(rewrite,[status(thm)],[])).
% 293.53/186.07 tff(22401,plain,
% 293.53/186.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s9) | m_or_h_gate_v_in2(c_e_h_1, c_j, s9) | (~node5(c_e_h_1, c_j, s9, s10)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_1, c_j, s10)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s9) | m_or_h_gate_v_in1(c_e_h_1, c_j, s9) | (~node5(c_e_h_1, c_j, s9, s10))))),
% 293.53/186.07 inference(monotonicity,[status(thm)],[22400])).
% 293.53/186.07 tff(22402,plain,
% 293.53/186.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s9) | m_or_h_gate_v_in2(c_e_h_1, c_j, s9) | (~node5(c_e_h_1, c_j, s9, s10)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s10)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s9) | m_or_h_gate_v_in1(c_e_h_1, c_j, s9) | (~node5(c_e_h_1, c_j, s9, s10)))),
% 293.53/186.07 inference(transitivity,[status(thm)],[22401, 22399])).
% 293.53/186.07 tff(22403,plain,
% 293.53/186.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s9) | m_or_h_gate_v_in2(c_e_h_1, c_j, s9) | (~node5(c_e_h_1, c_j, s9, s10)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s10)))),
% 293.53/186.07 inference(quant_inst,[status(thm)],[])).
% 293.53/186.07 tff(22404,plain,
% 293.53/186.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s10)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s9) | m_or_h_gate_v_in1(c_e_h_1, c_j, s9) | (~node5(c_e_h_1, c_j, s9, s10))),
% 293.53/186.07 inference(modus_ponens,[status(thm)],[22403, 22402])).
% 293.53/186.07 tff(22405,plain,
% 293.53/186.07 ($false),
% 293.53/186.07 inference(unit_resolution,[status(thm)],[22404, 1159, 22096, 22398, 22095, 22397])).
% 293.53/186.07 tff(22406,plain,((~node5(c_e_h_1, c_j, s9, s10)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s10)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s9) | m_or_h_gate_v_in1(c_e_h_1, c_j, s9)), inference(lemma,lemma(discharge,[]))).
% 293.53/186.07 tff(22407,plain,
% 293.53/186.07 ((~node5(c_e_h_1, c_j, s9, s10)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s10)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s9)),
% 293.53/186.07 inference(unit_resolution,[status(thm)],[22406, 22396])).
% 293.53/186.07 tff(22408,plain,
% 293.53/186.07 (~node5(c_e_h_1, c_j, s9, s10)),
% 293.53/186.07 inference(unit_resolution,[status(thm)],[22407, 22096, 22095])).
% 293.53/186.07 tff(22409,plain,
% 293.53/186.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s9, s10)) | node6(c_e_h_1, c_j, s9, s10) | node5(c_e_h_1, c_j, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s9, s10)) | node6(c_e_h_1, c_j, s9, s10) | node5(c_e_h_1, c_j, s9, s10))),
% 293.53/186.07 inference(rewrite,[status(thm)],[])).
% 293.53/186.07 tff(22410,plain,
% 293.53/186.07 ((node6(c_e_h_1, c_j, s9, s10) | node5(c_e_h_1, c_j, s9, s10) | (~trans(s9, s10))) <=> ((~trans(s9, s10)) | node6(c_e_h_1, c_j, s9, s10) | node5(c_e_h_1, c_j, s9, s10))),
% 293.53/186.07 inference(rewrite,[status(thm)],[])).
% 293.53/186.07 tff(22411,plain,
% 293.53/186.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s9, s10) | node5(c_e_h_1, c_j, s9, s10) | (~trans(s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s9, s10)) | node6(c_e_h_1, c_j, s9, s10) | node5(c_e_h_1, c_j, s9, s10)))),
% 293.53/186.07 inference(monotonicity,[status(thm)],[22410])).
% 293.53/186.07 tff(22412,plain,
% 293.53/186.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s9, s10) | node5(c_e_h_1, c_j, s9, s10) | (~trans(s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s9, s10)) | node6(c_e_h_1, c_j, s9, s10) | node5(c_e_h_1, c_j, s9, s10))),
% 293.53/186.07 inference(transitivity,[status(thm)],[22411, 22409])).
% 293.53/186.07 tff(22413,plain,
% 293.53/186.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s9, s10) | node5(c_e_h_1, c_j, s9, s10) | (~trans(s9, s10)))),
% 293.53/186.07 inference(quant_inst,[status(thm)],[])).
% 293.53/186.07 tff(22414,plain,
% 293.53/186.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s9, s10)) | node6(c_e_h_1, c_j, s9, s10) | node5(c_e_h_1, c_j, s9, s10)),
% 293.53/186.07 inference(modus_ponens,[status(thm)],[22413, 22412])).
% 293.53/186.07 tff(22415,plain,
% 293.53/186.07 (node6(c_e_h_1, c_j, s9, s10) | node5(c_e_h_1, c_j, s9, s10)),
% 293.53/186.07 inference(unit_resolution,[status(thm)],[22414, 1141, 7676])).
% 293.53/186.07 tff(22416,plain,
% 293.53/186.07 ($false),
% 293.53/186.07 inference(unit_resolution,[status(thm)],[22415, 22408, 22312])).
% 293.53/186.07 tff(22417,plain,((~m_or_h_gate_v_out(c_e_h_1, c_j, s10)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s9)), inference(lemma,lemma(discharge,[]))).
% 293.53/186.07 tff(22418,plain,
% 293.53/186.07 (~m_or_h_gate_v_out(c_e_h_1, c_j, s10)),
% 293.53/186.07 inference(unit_resolution,[status(thm)],[22417, 22095])).
% 293.53/186.07 tff(22419,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s8)), introduced(assumption)).
% 293.53/186.07 tff(22420,assumption,(node18(c_e_h_1, c_e, s7, s8)), introduced(assumption)).
% 293.53/186.07 tff(22421,assumption,(~m_c_h_element_v_out(c_e_h_1, c_e, s7)), introduced(assumption)).
% 293.53/186.07 tff(22422,plain,
% 293.53/186.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s7) | (~m_c_h_element_v_out(c_e_h_1, c_e, s8)) | (~node18(c_e_h_1, c_e, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s7) | (~m_c_h_element_v_out(c_e_h_1, c_e, s8)) | (~node18(c_e_h_1, c_e, s7, s8)))),
% 293.53/186.07 inference(rewrite,[status(thm)],[])).
% 293.53/186.07 tff(22423,plain,
% 293.53/186.07 (((~m_c_h_element_v_out(c_e_h_1, c_e, s8)) | m_c_h_element_v_out(c_e_h_1, c_e, s7) | (~node18(c_e_h_1, c_e, s7, s8))) <=> (m_c_h_element_v_out(c_e_h_1, c_e, s7) | (~m_c_h_element_v_out(c_e_h_1, c_e, s8)) | (~node18(c_e_h_1, c_e, s7, s8)))),
% 293.53/186.07 inference(rewrite,[status(thm)],[])).
% 293.53/186.07 tff(22424,plain,
% 293.53/186.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s8)) | m_c_h_element_v_out(c_e_h_1, c_e, s7) | (~node18(c_e_h_1, c_e, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s7) | (~m_c_h_element_v_out(c_e_h_1, c_e, s8)) | (~node18(c_e_h_1, c_e, s7, s8))))),
% 293.53/186.07 inference(monotonicity,[status(thm)],[22423])).
% 293.53/186.07 tff(22425,plain,
% 293.53/186.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s8)) | m_c_h_element_v_out(c_e_h_1, c_e, s7) | (~node18(c_e_h_1, c_e, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s7) | (~m_c_h_element_v_out(c_e_h_1, c_e, s8)) | (~node18(c_e_h_1, c_e, s7, s8)))),
% 293.53/186.07 inference(transitivity,[status(thm)],[22424, 22422])).
% 293.53/186.07 tff(22426,plain,
% 293.53/186.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s8)) | m_c_h_element_v_out(c_e_h_1, c_e, s7) | (~node18(c_e_h_1, c_e, s7, s8)))),
% 293.53/186.07 inference(quant_inst,[status(thm)],[])).
% 293.53/186.07 tff(22427,plain,
% 293.53/186.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s7) | (~m_c_h_element_v_out(c_e_h_1, c_e, s8)) | (~node18(c_e_h_1, c_e, s7, s8))),
% 293.53/186.07 inference(modus_ponens,[status(thm)],[22426, 22425])).
% 293.53/186.07 tff(22428,plain,
% 293.53/186.07 ($false),
% 293.53/186.07 inference(unit_resolution,[status(thm)],[22427, 753, 22421, 22419, 22420])).
% 293.53/186.07 tff(22429,plain,((~node18(c_e_h_1, c_e, s7, s8)) | m_c_h_element_v_out(c_e_h_1, c_e, s7) | (~m_c_h_element_v_out(c_e_h_1, c_e, s8))), inference(lemma,lemma(discharge,[]))).
% 293.53/186.07 tff(22430,plain,
% 293.53/186.07 ((~node18(c_e_h_1, c_e, s7, s8)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s8))),
% 293.53/186.07 inference(unit_resolution,[status(thm)],[22429, 19211])).
% 293.53/186.07 tff(22431,plain,
% 293.53/186.07 (~node18(c_e_h_1, c_e, s7, s8)),
% 293.53/186.07 inference(unit_resolution,[status(thm)],[22430, 22419])).
% 293.53/186.07 tff(22432,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_e, s7)), introduced(assumption)).
% 293.53/186.07 tff(22433,assumption,(~node14(c_e_h_1, c_e, s7, s8)), introduced(assumption)).
% 293.53/186.07 tff(22434,assumption,(node15(c_e_h_1, c_e, s7, s8)), introduced(assumption)).
% 293.53/186.07 tff(22435,plain,
% 293.53/186.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s8)) | (~node15(c_e_h_1, c_e, s7, s8)) | m_c_h_element_v_out(c_e_h_1, c_e, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s8)) | (~node15(c_e_h_1, c_e, s7, s8)) | m_c_h_element_v_out(c_e_h_1, c_e, s7))),
% 293.53/186.07 inference(rewrite,[status(thm)],[])).
% 293.53/186.07 tff(22436,plain,
% 293.53/186.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s8)) | (~node15(c_e_h_1, c_e, s7, s8)) | m_c_h_element_v_out(c_e_h_1, c_e, s7))),
% 293.53/186.07 inference(quant_inst,[status(thm)],[])).
% 293.53/186.07 tff(22437,plain,
% 293.53/186.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s8)) | (~node15(c_e_h_1, c_e, s7, s8)) | m_c_h_element_v_out(c_e_h_1, c_e, s7)),
% 293.53/186.07 inference(modus_ponens,[status(thm)],[22436, 22435])).
% 293.53/186.07 tff(22438,plain,
% 293.53/186.07 ($false),
% 293.53/186.07 inference(unit_resolution,[status(thm)],[22437, 147, 22421, 22419, 22434])).
% 293.53/186.07 tff(22439,plain,((~node15(c_e_h_1, c_e, s7, s8)) | m_c_h_element_v_out(c_e_h_1, c_e, s7) | (~m_c_h_element_v_out(c_e_h_1, c_e, s8))), inference(lemma,lemma(discharge,[]))).
% 293.53/186.07 tff(22440,plain,
% 293.53/186.07 (~node15(c_e_h_1, c_e, s7, s8)),
% 293.53/186.07 inference(unit_resolution,[status(thm)],[22439, 22421, 22419])).
% 293.53/186.07 tff(22441,plain,
% 293.53/186.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s7, s8)) | node19(c_e_h_1, c_e, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s7, s8)) | node19(c_e_h_1, c_e, s7, s8))),
% 293.53/186.07 inference(rewrite,[status(thm)],[])).
% 293.53/186.07 tff(22442,plain,
% 293.53/186.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s7, s8)) | node19(c_e_h_1, c_e, s7, s8))),
% 293.53/186.08 inference(quant_inst,[status(thm)],[])).
% 293.53/186.08 tff(22443,plain,
% 293.53/186.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s7, s8)) | node19(c_e_h_1, c_e, s7, s8)),
% 293.53/186.08 inference(modus_ponens,[status(thm)],[22442, 22441])).
% 293.53/186.08 tff(22444,plain,
% 293.53/186.08 (node19(c_e_h_1, c_e, s7, s8)),
% 293.53/186.08 inference(unit_resolution,[status(thm)],[22443, 190, 1938])).
% 293.53/186.08 tff(22445,plain,
% 293.53/186.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_e, s7, s8)) | node15(c_e_h_1, c_e, s7, s8) | node14(c_e_h_1, c_e, s7, s8) | node16(c_e_h_1, c_e, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s7, s8)) | node15(c_e_h_1, c_e, s7, s8) | node14(c_e_h_1, c_e, s7, s8) | node16(c_e_h_1, c_e, s7))),
% 293.53/186.08 inference(rewrite,[status(thm)],[])).
% 293.53/186.08 tff(22446,plain,
% 293.53/186.08 ((node16(c_e_h_1, c_e, s7) | node14(c_e_h_1, c_e, s7, s8) | node15(c_e_h_1, c_e, s7, s8) | (~node19(c_e_h_1, c_e, s7, s8))) <=> ((~node19(c_e_h_1, c_e, s7, s8)) | node15(c_e_h_1, c_e, s7, s8) | node14(c_e_h_1, c_e, s7, s8) | node16(c_e_h_1, c_e, s7))),
% 293.53/186.08 inference(rewrite,[status(thm)],[])).
% 293.53/186.08 tff(22447,plain,
% 293.53/186.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s7) | node14(c_e_h_1, c_e, s7, s8) | node15(c_e_h_1, c_e, s7, s8) | (~node19(c_e_h_1, c_e, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_e, s7, s8)) | node15(c_e_h_1, c_e, s7, s8) | node14(c_e_h_1, c_e, s7, s8) | node16(c_e_h_1, c_e, s7)))),
% 293.53/186.08 inference(monotonicity,[status(thm)],[22446])).
% 293.53/186.08 tff(22448,plain,
% 293.53/186.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s7) | node14(c_e_h_1, c_e, s7, s8) | node15(c_e_h_1, c_e, s7, s8) | (~node19(c_e_h_1, c_e, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s7, s8)) | node15(c_e_h_1, c_e, s7, s8) | node14(c_e_h_1, c_e, s7, s8) | node16(c_e_h_1, c_e, s7))),
% 293.53/186.08 inference(transitivity,[status(thm)],[22447, 22445])).
% 293.53/186.08 tff(22449,plain,
% 293.53/186.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s7) | node14(c_e_h_1, c_e, s7, s8) | node15(c_e_h_1, c_e, s7, s8) | (~node19(c_e_h_1, c_e, s7, s8)))),
% 293.53/186.08 inference(quant_inst,[status(thm)],[])).
% 293.53/186.08 tff(22450,plain,
% 293.53/186.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s7, s8)) | node15(c_e_h_1, c_e, s7, s8) | node14(c_e_h_1, c_e, s7, s8) | node16(c_e_h_1, c_e, s7)),
% 293.53/186.08 inference(modus_ponens,[status(thm)],[22449, 22448])).
% 293.53/186.08 tff(22451,plain,
% 293.53/186.08 (node15(c_e_h_1, c_e, s7, s8) | node14(c_e_h_1, c_e, s7, s8) | node16(c_e_h_1, c_e, s7)),
% 293.53/186.08 inference(unit_resolution,[status(thm)],[22450, 204, 22444])).
% 293.53/186.08 tff(22452,plain,
% 293.53/186.08 (node16(c_e_h_1, c_e, s7)),
% 293.53/186.08 inference(unit_resolution,[status(thm)],[22451, 22440, 22433])).
% 293.53/186.08 tff(22453,assumption,(m_c_h_element_v_in1(c_e_h_1, c_e, s7)), introduced(assumption)).
% 293.53/186.08 tff(22454,plain,
% 293.53/186.08 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s7)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s7)) | (~node16(c_e_h_1, c_e, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s7)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s7)) | (~node16(c_e_h_1, c_e, s7)))),
% 293.53/186.08 inference(rewrite,[status(thm)],[])).
% 293.53/186.08 tff(22455,plain,
% 293.53/186.08 (((~node16(c_e_h_1, c_e, s7)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s7)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s7))) <=> ((~m_c_h_element_v_in1(c_e_h_1, c_e, s7)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s7)) | (~node16(c_e_h_1, c_e, s7)))),
% 293.53/186.08 inference(rewrite,[status(thm)],[])).
% 293.53/186.08 tff(22456,plain,
% 293.53/186.08 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s7)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s7)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s7)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s7)) | (~node16(c_e_h_1, c_e, s7))))),
% 293.53/186.08 inference(monotonicity,[status(thm)],[22455])).
% 293.53/186.08 tff(22457,plain,
% 293.53/186.08 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s7)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s7)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s7)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s7)) | (~node16(c_e_h_1, c_e, s7)))),
% 293.53/186.08 inference(transitivity,[status(thm)],[22456, 22454])).
% 293.53/186.08 tff(22458,plain,
% 293.53/186.08 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s7)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s7)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s7)))),
% 293.53/186.08 inference(quant_inst,[status(thm)],[])).
% 293.53/186.08 tff(22459,plain,
% 293.53/186.08 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s7)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s7)) | (~node16(c_e_h_1, c_e, s7))),
% 293.53/186.08 inference(modus_ponens,[status(thm)],[22458, 22457])).
% 293.53/186.08 tff(22460,plain,
% 293.53/186.08 ((~m_c_h_element_v_in2(c_e_h_1, c_e, s7)) | (~node16(c_e_h_1, c_e, s7))),
% 293.53/186.08 inference(unit_resolution,[status(thm)],[22459, 2307, 22453])).
% 293.53/186.08 tff(22461,plain,
% 293.53/186.08 (~m_c_h_element_v_in2(c_e_h_1, c_e, s7)),
% 293.53/186.08 inference(unit_resolution,[status(thm)],[22460, 22452])).
% 293.53/186.08 tff(22462,plain,
% 293.53/186.08 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s7)) | m_c_h_element_v_in2(c_e_h_1, c_e, s7) | (~node17(c_e_h_1, c_e, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s7)) | m_c_h_element_v_in2(c_e_h_1, c_e, s7) | (~node17(c_e_h_1, c_e, s7)))),
% 293.53/186.08 inference(rewrite,[status(thm)],[])).
% 293.53/186.08 tff(22463,plain,
% 293.53/186.08 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s7)) | m_c_h_element_v_in2(c_e_h_1, c_e, s7) | (~node17(c_e_h_1, c_e, s7)))),
% 293.53/186.08 inference(quant_inst,[status(thm)],[])).
% 293.53/186.08 tff(22464,plain,
% 293.53/186.08 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s7)) | m_c_h_element_v_in2(c_e_h_1, c_e, s7) | (~node17(c_e_h_1, c_e, s7))),
% 293.53/186.08 inference(modus_ponens,[status(thm)],[22463, 22462])).
% 293.53/186.08 tff(22465,plain,
% 293.53/186.08 (m_c_h_element_v_in2(c_e_h_1, c_e, s7) | (~node17(c_e_h_1, c_e, s7))),
% 293.53/186.08 inference(unit_resolution,[status(thm)],[22464, 919, 22453])).
% 293.53/186.08 tff(22466,plain,
% 293.53/186.08 (~node17(c_e_h_1, c_e, s7)),
% 293.53/186.08 inference(unit_resolution,[status(thm)],[22465, 22461])).
% 293.53/186.08 tff(22467,plain,
% 293.53/186.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_1, c_e, s7, s8) | (~node19(c_e_h_1, c_e, s7, s8)) | node17(c_e_h_1, c_e, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_e, s7, s8) | (~node19(c_e_h_1, c_e, s7, s8)) | node17(c_e_h_1, c_e, s7))),
% 293.53/186.08 inference(rewrite,[status(thm)],[])).
% 293.53/186.08 tff(22468,plain,
% 293.53/186.08 ((node17(c_e_h_1, c_e, s7) | node18(c_e_h_1, c_e, s7, s8) | (~node19(c_e_h_1, c_e, s7, s8))) <=> (node18(c_e_h_1, c_e, s7, s8) | (~node19(c_e_h_1, c_e, s7, s8)) | node17(c_e_h_1, c_e, s7))),
% 293.53/186.08 inference(rewrite,[status(thm)],[])).
% 293.53/186.08 tff(22469,plain,
% 293.53/186.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s7) | node18(c_e_h_1, c_e, s7, s8) | (~node19(c_e_h_1, c_e, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_1, c_e, s7, s8) | (~node19(c_e_h_1, c_e, s7, s8)) | node17(c_e_h_1, c_e, s7)))),
% 293.53/186.08 inference(monotonicity,[status(thm)],[22468])).
% 293.53/186.08 tff(22470,plain,
% 293.53/186.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s7) | node18(c_e_h_1, c_e, s7, s8) | (~node19(c_e_h_1, c_e, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_e, s7, s8) | (~node19(c_e_h_1, c_e, s7, s8)) | node17(c_e_h_1, c_e, s7))),
% 293.53/186.08 inference(transitivity,[status(thm)],[22469, 22467])).
% 293.53/186.08 tff(22471,plain,
% 293.53/186.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s7) | node18(c_e_h_1, c_e, s7, s8) | (~node19(c_e_h_1, c_e, s7, s8)))),
% 293.53/186.08 inference(quant_inst,[status(thm)],[])).
% 293.53/186.08 tff(22472,plain,
% 293.53/186.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_e, s7, s8) | (~node19(c_e_h_1, c_e, s7, s8)) | node17(c_e_h_1, c_e, s7)),
% 293.53/186.08 inference(modus_ponens,[status(thm)],[22471, 22470])).
% 293.53/186.08 tff(22473,plain,
% 293.53/186.08 (node18(c_e_h_1, c_e, s7, s8) | node17(c_e_h_1, c_e, s7)),
% 293.53/186.08 inference(unit_resolution,[status(thm)],[22472, 776, 22444])).
% 293.53/186.08 tff(22474,plain,
% 293.53/186.08 (node18(c_e_h_1, c_e, s7, s8)),
% 293.53/186.08 inference(unit_resolution,[status(thm)],[22473, 22466])).
% 293.53/186.08 tff(22475,plain,
% 293.53/186.08 ($false),
% 293.53/186.08 inference(unit_resolution,[status(thm)],[22427, 753, 22421, 22419, 22474])).
% 293.53/186.08 tff(22476,plain,(m_c_h_element_v_out(c_e_h_1, c_e, s7) | (~m_c_h_element_v_out(c_e_h_1, c_e, s8)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s7)) | node14(c_e_h_1, c_e, s7, s8)), inference(lemma,lemma(discharge,[]))).
% 293.53/186.08 tff(22477,plain,
% 293.53/186.08 (~m_c_h_element_v_in1(c_e_h_1, c_e, s7)),
% 293.53/186.08 inference(unit_resolution,[status(thm)],[22476, 22433, 22419, 22421])).
% 293.53/186.08 tff(22478,plain,
% 293.53/186.08 (~node18(c_e_h_1, c_e, s7, s8)),
% 293.53/186.08 inference(unit_resolution,[status(thm)],[22429, 22421, 22419])).
% 293.53/186.08 tff(22479,plain,
% 293.53/186.08 (node17(c_e_h_1, c_e, s7)),
% 293.53/186.08 inference(unit_resolution,[status(thm)],[22473, 22478])).
% 293.53/186.08 tff(22480,plain,
% 293.53/186.08 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s7) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s7)) | (~node17(c_e_h_1, c_e, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s7) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s7)) | (~node17(c_e_h_1, c_e, s7)))),
% 293.53/186.08 inference(rewrite,[status(thm)],[])).
% 293.53/186.08 tff(22481,plain,
% 293.53/186.08 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s7) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s7)) | (~node17(c_e_h_1, c_e, s7)))),
% 293.53/186.08 inference(quant_inst,[status(thm)],[])).
% 293.53/186.08 tff(22482,plain,
% 293.53/186.08 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s7) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s7)) | (~node17(c_e_h_1, c_e, s7))),
% 293.53/186.09 inference(modus_ponens,[status(thm)],[22481, 22480])).
% 293.53/186.09 tff(22483,plain,
% 293.53/186.09 (m_c_h_element_v_in1(c_e_h_1, c_e, s7) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s7))),
% 293.53/186.09 inference(unit_resolution,[status(thm)],[22482, 859, 22479])).
% 293.53/186.09 tff(22484,plain,
% 293.53/186.09 (~m_c_h_element_v_in2(c_e_h_1, c_e, s7)),
% 293.53/186.09 inference(unit_resolution,[status(thm)],[22483, 22477])).
% 293.53/186.09 tff(22485,plain,
% 293.53/186.09 (node16(c_e_h_1, c_e, s7)),
% 293.53/186.09 inference(unit_resolution,[status(thm)],[22451, 22433, 22440])).
% 293.53/186.09 tff(22486,plain,
% 293.53/186.09 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s7)) | m_c_h_element_v_in1(c_e_h_1, c_e, s7) | m_c_h_element_v_in2(c_e_h_1, c_e, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s7)) | m_c_h_element_v_in1(c_e_h_1, c_e, s7) | m_c_h_element_v_in2(c_e_h_1, c_e, s7))),
% 293.53/186.09 inference(rewrite,[status(thm)],[])).
% 293.53/186.09 tff(22487,plain,
% 293.53/186.09 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s7)) | m_c_h_element_v_in1(c_e_h_1, c_e, s7) | m_c_h_element_v_in2(c_e_h_1, c_e, s7))),
% 293.53/186.09 inference(quant_inst,[status(thm)],[])).
% 293.53/186.09 tff(22488,plain,
% 293.53/186.09 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s7)) | m_c_h_element_v_in1(c_e_h_1, c_e, s7) | m_c_h_element_v_in2(c_e_h_1, c_e, s7)),
% 293.53/186.09 inference(modus_ponens,[status(thm)],[22487, 22486])).
% 293.53/186.09 tff(22489,plain,
% 293.53/186.09 ($false),
% 293.53/186.09 inference(unit_resolution,[status(thm)],[22488, 178, 22485, 22477, 22484])).
% 293.53/186.09 tff(22490,plain,(node14(c_e_h_1, c_e, s7, s8) | (~m_c_h_element_v_out(c_e_h_1, c_e, s8)) | m_c_h_element_v_out(c_e_h_1, c_e, s7)), inference(lemma,lemma(discharge,[]))).
% 293.53/186.09 tff(22491,plain,
% 293.53/186.09 (node14(c_e_h_1, c_e, s7, s8)),
% 293.53/186.09 inference(unit_resolution,[status(thm)],[22490, 22419, 22421])).
% 293.53/186.09 tff(22492,assumption,(node14(c_e_h_1, c_e, s7, s8)), introduced(assumption)).
% 293.53/186.09 tff(22493,plain,
% 293.53/186.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s8)) | m_c_h_element_v_in1(c_e_h_1, c_e, s7) | (~node14(c_e_h_1, c_e, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s8)) | m_c_h_element_v_in1(c_e_h_1, c_e, s7) | (~node14(c_e_h_1, c_e, s7, s8)))),
% 293.53/186.09 inference(rewrite,[status(thm)],[])).
% 293.53/186.09 tff(22494,plain,
% 293.53/186.09 (((~node14(c_e_h_1, c_e, s7, s8)) | m_c_h_element_v_in1(c_e_h_1, c_e, s7) | (~m_c_h_element_v_out(c_e_h_1, c_e, s8))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_e, s8)) | m_c_h_element_v_in1(c_e_h_1, c_e, s7) | (~node14(c_e_h_1, c_e, s7, s8)))),
% 293.53/186.09 inference(rewrite,[status(thm)],[])).
% 293.53/186.09 tff(22495,plain,
% 293.53/186.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s7, s8)) | m_c_h_element_v_in1(c_e_h_1, c_e, s7) | (~m_c_h_element_v_out(c_e_h_1, c_e, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s8)) | m_c_h_element_v_in1(c_e_h_1, c_e, s7) | (~node14(c_e_h_1, c_e, s7, s8))))),
% 293.53/186.09 inference(monotonicity,[status(thm)],[22494])).
% 293.53/186.09 tff(22496,plain,
% 293.53/186.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s7, s8)) | m_c_h_element_v_in1(c_e_h_1, c_e, s7) | (~m_c_h_element_v_out(c_e_h_1, c_e, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s8)) | m_c_h_element_v_in1(c_e_h_1, c_e, s7) | (~node14(c_e_h_1, c_e, s7, s8)))),
% 293.53/186.09 inference(transitivity,[status(thm)],[22495, 22493])).
% 293.53/186.09 tff(22497,plain,
% 293.53/186.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s7, s8)) | m_c_h_element_v_in1(c_e_h_1, c_e, s7) | (~m_c_h_element_v_out(c_e_h_1, c_e, s8)))),
% 293.53/186.09 inference(quant_inst,[status(thm)],[])).
% 293.53/186.09 tff(22498,plain,
% 293.53/186.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s8)) | m_c_h_element_v_in1(c_e_h_1, c_e, s7) | (~node14(c_e_h_1, c_e, s7, s8))),
% 293.53/186.09 inference(modus_ponens,[status(thm)],[22497, 22496])).
% 293.53/186.09 tff(22499,plain,
% 293.53/186.09 ($false),
% 293.53/186.09 inference(unit_resolution,[status(thm)],[22498, 223, 22419, 22492, 22432])).
% 293.53/186.09 tff(22500,plain,((~node14(c_e_h_1, c_e, s7, s8)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s8)) | m_c_h_element_v_in1(c_e_h_1, c_e, s7)), inference(lemma,lemma(discharge,[]))).
% 293.53/186.09 tff(22501,plain,
% 293.53/186.09 ($false),
% 293.53/186.09 inference(unit_resolution,[status(thm)],[22500, 22491, 22419, 22432])).
% 293.53/186.09 tff(22502,plain,((~m_c_h_element_v_out(c_e_h_1, c_e, s8)) | m_c_h_element_v_in1(c_e_h_1, c_e, s7) | m_c_h_element_v_out(c_e_h_1, c_e, s7)), inference(lemma,lemma(discharge,[]))).
% 293.53/186.09 tff(22503,plain,
% 293.53/186.09 ((~m_c_h_element_v_out(c_e_h_1, c_e, s8)) | m_c_h_element_v_in1(c_e_h_1, c_e, s7)),
% 293.53/186.09 inference(unit_resolution,[status(thm)],[22502, 19211])).
% 293.53/186.09 tff(22504,plain,
% 293.53/186.09 (m_c_h_element_v_in1(c_e_h_1, c_e, s7)),
% 293.53/186.09 inference(unit_resolution,[status(thm)],[22503, 22419])).
% 293.53/186.09 tff(22505,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s7)), introduced(assumption)).
% 293.53/186.09 tff(22506,plain,
% 293.53/186.09 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s6)) | m_c_h_element_v_out(c_e_h_1, c_h, s6))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s6)) | m_c_h_element_v_out(c_e_h_1, c_h, s6))),
% 293.53/186.09 inference(rewrite,[status(thm)],[])).
% 293.53/186.09 tff(22507,plain,
% 293.53/186.09 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s6)) | m_c_h_element_v_out(c_e_h_1, c_h, s6))),
% 293.53/186.09 inference(quant_inst,[status(thm)],[])).
% 293.53/186.09 tff(22508,plain,
% 293.53/186.09 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s6)) | m_c_h_element_v_out(c_e_h_1, c_h, s6)),
% 293.53/186.09 inference(modus_ponens,[status(thm)],[22507, 22506])).
% 293.53/186.09 tff(22509,plain,
% 293.53/186.09 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s6)),
% 293.53/186.09 inference(unit_resolution,[status(thm)],[22508, 619, 18614])).
% 293.53/186.09 tff(22510,plain,
% 293.53/186.09 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s6)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s6)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s6))),
% 293.53/186.09 inference(rewrite,[status(thm)],[])).
% 293.53/186.09 tff(22511,plain,
% 293.53/186.09 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s6)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s6))),
% 293.53/186.09 inference(quant_inst,[status(thm)],[])).
% 293.53/186.09 tff(22512,plain,
% 293.53/186.09 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s6)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s6)),
% 293.53/186.09 inference(modus_ponens,[status(thm)],[22511, 22510])).
% 293.53/186.09 tff(22513,plain,
% 293.53/186.09 (~node20(c_e_h_1, c_i, s6)),
% 293.53/186.09 inference(unit_resolution,[status(thm)],[22512, 38, 22509])).
% 293.53/186.09 tff(22514,assumption,(~node20(c_e_h_1, c_i, s6)), introduced(assumption)).
% 293.53/186.09 tff(22515,assumption,(node21(c_e_h_1, c_i, s6, s7)), introduced(assumption)).
% 293.53/186.09 tff(22516,plain,
% 293.53/186.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s7)) | (~node21(c_e_h_1, c_i, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s7)) | (~node21(c_e_h_1, c_i, s6, s7)))),
% 293.53/186.09 inference(rewrite,[status(thm)],[])).
% 293.53/186.09 tff(22517,plain,
% 293.53/186.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s7)) | (~node21(c_e_h_1, c_i, s6, s7)))),
% 293.53/186.09 inference(quant_inst,[status(thm)],[])).
% 293.53/186.09 tff(22518,plain,
% 293.53/186.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s7)) | (~node21(c_e_h_1, c_i, s6, s7))),
% 293.53/186.09 inference(modus_ponens,[status(thm)],[22517, 22516])).
% 293.53/186.09 tff(22519,plain,
% 293.53/186.09 ($false),
% 293.53/186.09 inference(unit_resolution,[status(thm)],[22518, 52, 22515, 22505, 22514])).
% 293.53/186.09 tff(22520,plain,((~node21(c_e_h_1, c_i, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s7)) | node20(c_e_h_1, c_i, s6)), inference(lemma,lemma(discharge,[]))).
% 293.53/186.09 tff(22521,plain,
% 293.53/186.09 ((~node21(c_e_h_1, c_i, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s7))),
% 293.53/186.09 inference(unit_resolution,[status(thm)],[22520, 22513])).
% 293.53/186.09 tff(22522,plain,
% 293.53/186.09 (~node21(c_e_h_1, c_i, s6, s7)),
% 293.53/186.09 inference(unit_resolution,[status(thm)],[22521, 22505])).
% 293.53/186.09 tff(22523,plain,
% 293.53/186.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_1, c_i, s6, s7) | node22(c_e_h_1, c_i, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_1, c_i, s6, s7) | node22(c_e_h_1, c_i, s6, s7))),
% 293.53/186.09 inference(rewrite,[status(thm)],[])).
% 293.53/186.09 tff(22524,plain,
% 293.53/186.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_1, c_i, s6, s7) | node22(c_e_h_1, c_i, s6, s7))),
% 293.53/186.09 inference(quant_inst,[status(thm)],[])).
% 293.53/186.09 tff(22525,plain,
% 293.53/186.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_1, c_i, s6, s7) | node22(c_e_h_1, c_i, s6, s7)),
% 293.53/186.09 inference(modus_ponens,[status(thm)],[22524, 22523])).
% 293.53/186.09 tff(22526,plain,
% 293.53/186.09 (node21(c_e_h_1, c_i, s6, s7) | node22(c_e_h_1, c_i, s6, s7)),
% 293.53/186.09 inference(unit_resolution,[status(thm)],[22525, 82, 1844])).
% 293.53/186.09 tff(22527,plain,
% 293.53/186.09 (node22(c_e_h_1, c_i, s6, s7)),
% 293.53/186.09 inference(unit_resolution,[status(thm)],[22526, 22522])).
% 293.53/186.09 tff(22528,plain,
% 293.53/186.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s7)) | (~node22(c_e_h_1, c_i, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_i, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s7)) | (~node22(c_e_h_1, c_i, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_i, s6))),
% 293.53/186.09 inference(rewrite,[status(thm)],[])).
% 293.53/186.09 tff(22529,plain,
% 293.53/186.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s7)) | (~node22(c_e_h_1, c_i, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_i, s6))),
% 293.53/186.09 inference(quant_inst,[status(thm)],[])).
% 293.53/186.09 tff(22530,plain,
% 293.53/186.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s7)) | (~node22(c_e_h_1, c_i, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_i, s6)),
% 293.53/186.09 inference(modus_ponens,[status(thm)],[22529, 22528])).
% 293.53/186.09 tff(22531,plain,
% 293.53/186.09 ($false),
% 293.53/186.09 inference(unit_resolution,[status(thm)],[22530, 108, 22527, 22505, 19117])).
% 293.53/186.09 tff(22532,plain,(~m_and_h_gate_v_out(c_e_h_1, c_i, s7)), inference(lemma,lemma(discharge,[]))).
% 293.53/186.09 tff(22533,plain,
% 293.53/186.09 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s7)) | m_and_h_gate_v_out(c_e_h_1, c_i, s7))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s7)) | m_and_h_gate_v_out(c_e_h_1, c_i, s7))),
% 293.53/186.10 inference(rewrite,[status(thm)],[])).
% 293.53/186.10 tff(22534,plain,
% 293.53/186.10 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s7)) | m_and_h_gate_v_out(c_e_h_1, c_i, s7))),
% 293.53/186.10 inference(quant_inst,[status(thm)],[])).
% 293.53/186.10 tff(22535,plain,
% 293.53/186.10 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s7)) | m_and_h_gate_v_out(c_e_h_1, c_i, s7)),
% 293.53/186.10 inference(modus_ponens,[status(thm)],[22534, 22533])).
% 293.53/186.10 tff(22536,plain,
% 293.53/186.10 (~m_c_h_element_v_in2(c_e_h_1, c_e, s7)),
% 293.53/186.10 inference(unit_resolution,[status(thm)],[22535, 164, 22532])).
% 293.53/186.10 tff(22537,plain,
% 293.53/186.10 ((~m_c_h_element_v_in1(c_e_h_1, c_e, s7)) | (~node17(c_e_h_1, c_e, s7))),
% 293.53/186.10 inference(unit_resolution,[status(thm)],[22464, 919, 22536])).
% 293.53/186.10 tff(22538,plain,
% 293.53/186.10 (~node17(c_e_h_1, c_e, s7)),
% 293.53/186.10 inference(unit_resolution,[status(thm)],[22537, 22504])).
% 293.53/186.10 tff(22539,plain,
% 293.53/186.10 ($false),
% 293.53/186.10 inference(unit_resolution,[status(thm)],[22473, 22538, 22431])).
% 293.53/186.10 tff(22540,plain,(~m_c_h_element_v_out(c_e_h_1, c_e, s8)), inference(lemma,lemma(discharge,[]))).
% 293.53/186.10 tff(22541,plain,
% 293.53/186.10 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s8) | m_c_h_element_v_out(c_e_h_1, c_e, s8))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s8) | m_c_h_element_v_out(c_e_h_1, c_e, s8))),
% 293.53/186.10 inference(rewrite,[status(thm)],[])).
% 293.53/186.10 tff(22542,plain,
% 293.53/186.10 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s8) | m_c_h_element_v_out(c_e_h_1, c_e, s8))),
% 293.53/186.10 inference(quant_inst,[status(thm)],[])).
% 293.53/186.10 tff(22543,plain,
% 293.53/186.10 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s8) | m_c_h_element_v_out(c_e_h_1, c_e, s8)),
% 293.53/186.10 inference(modus_ponens,[status(thm)],[22542, 22541])).
% 293.53/186.10 tff(22544,plain,
% 293.53/186.10 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s8) | m_c_h_element_v_out(c_e_h_1, c_e, s8)),
% 293.53/186.10 inference(unit_resolution,[status(thm)],[22543, 7856])).
% 293.53/186.10 tff(22545,plain,
% 293.53/186.10 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s8)),
% 293.53/186.10 inference(unit_resolution,[status(thm)],[22544, 22540])).
% 293.53/186.10 tff(22546,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)), introduced(assumption)).
% 293.53/186.10 tff(22547,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s8)), introduced(assumption)).
% 293.53/186.10 tff(22548,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9)), introduced(assumption)).
% 293.53/186.10 tff(22549,plain,
% 293.53/186.10 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s7)),
% 293.53/186.10 inference(unit_resolution,[status(thm)],[18195, 18165])).
% 293.53/186.10 tff(22550,plain,
% 293.53/186.10 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8)),
% 293.53/186.10 inference(unit_resolution,[status(thm)],[19282, 22549, 19255])).
% 293.53/186.10 tff(22551,plain,
% 293.53/186.10 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)),
% 293.53/186.10 inference(unit_resolution,[status(thm)],[22367, 18165])).
% 293.53/186.10 tff(22552,plain,
% 293.53/186.10 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s8) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s8) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8))),
% 293.53/186.10 inference(rewrite,[status(thm)],[])).
% 293.53/186.10 tff(22553,plain,
% 293.53/186.10 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s8) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8))),
% 293.53/186.10 inference(quant_inst,[status(thm)],[])).
% 293.53/186.10 tff(22554,plain,
% 293.53/186.10 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s8) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)),
% 293.53/186.10 inference(modus_ponens,[status(thm)],[22553, 22552])).
% 293.53/186.10 tff(22555,plain,
% 293.53/186.10 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s8) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)),
% 293.53/186.10 inference(unit_resolution,[status(thm)],[22554, 7868])).
% 293.53/186.10 tff(22556,plain,
% 293.53/186.10 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s8)),
% 293.53/186.10 inference(unit_resolution,[status(thm)],[22555, 22551])).
% 293.53/186.10 tff(22557,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s8)), introduced(assumption)).
% 293.53/186.10 tff(22558,assumption,(node10(c_e_h_1, c_n, s8, s9)), introduced(assumption)).
% 293.53/186.10 tff(22559,plain,
% 293.53/186.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s8)) | (~node10(c_e_h_1, c_n, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s8)) | (~node10(c_e_h_1, c_n, s8, s9)))),
% 293.53/186.10 inference(rewrite,[status(thm)],[])).
% 293.53/186.10 tff(22560,plain,
% 293.53/186.10 (((~node10(c_e_h_1, c_n, s8, s9)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9)) <=> ((~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s8)) | (~node10(c_e_h_1, c_n, s8, s9)))),
% 293.53/186.10 inference(rewrite,[status(thm)],[])).
% 293.53/186.10 tff(22561,plain,
% 293.53/186.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s8, s9)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s8)) | (~node10(c_e_h_1, c_n, s8, s9))))),
% 293.53/186.10 inference(monotonicity,[status(thm)],[22560])).
% 293.53/186.10 tff(22562,plain,
% 293.53/186.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s8, s9)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s8)) | (~node10(c_e_h_1, c_n, s8, s9)))),
% 293.53/186.10 inference(transitivity,[status(thm)],[22561, 22559])).
% 293.53/186.10 tff(22563,plain,
% 293.53/186.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s8, s9)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9))),
% 293.53/186.10 inference(quant_inst,[status(thm)],[])).
% 293.53/186.10 tff(22564,plain,
% 293.53/186.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s8)) | (~node10(c_e_h_1, c_n, s8, s9))),
% 293.53/186.10 inference(modus_ponens,[status(thm)],[22563, 22562])).
% 293.53/186.10 tff(22565,plain,
% 293.53/186.10 ($false),
% 293.53/186.10 inference(unit_resolution,[status(thm)],[22564, 5718, 22547, 22548, 22557, 22558])).
% 293.53/186.10 tff(22566,plain,((~node10(c_e_h_1, c_n, s8, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s8))), inference(lemma,lemma(discharge,[]))).
% 293.53/186.10 tff(22567,plain,
% 293.53/186.10 (~node10(c_e_h_1, c_n, s8, s9)),
% 293.53/186.10 inference(unit_resolution,[status(thm)],[22566, 22548, 22557, 22547])).
% 293.53/186.10 tff(22568,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8)), introduced(assumption)).
% 293.53/186.10 tff(22569,assumption,(node11(c_e_h_1, c_n, s8, s9)), introduced(assumption)).
% 293.53/186.10 tff(22570,plain,
% 293.53/186.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9) | (~node11(c_e_h_1, c_n, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9) | (~node11(c_e_h_1, c_n, s8, s9)))),
% 293.53/186.10 inference(rewrite,[status(thm)],[])).
% 293.53/186.10 tff(22571,plain,
% 293.53/186.10 ((m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9) | (~node11(c_e_h_1, c_n, s8, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9) | (~node11(c_e_h_1, c_n, s8, s9)))),
% 293.53/186.10 inference(rewrite,[status(thm)],[])).
% 293.53/186.10 tff(22572,plain,
% 293.53/186.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9) | (~node11(c_e_h_1, c_n, s8, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9) | (~node11(c_e_h_1, c_n, s8, s9))))),
% 293.53/186.10 inference(monotonicity,[status(thm)],[22571])).
% 293.53/186.10 tff(22573,plain,
% 293.53/186.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9) | (~node11(c_e_h_1, c_n, s8, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9) | (~node11(c_e_h_1, c_n, s8, s9)))),
% 293.53/186.10 inference(transitivity,[status(thm)],[22572, 22570])).
% 293.53/186.10 tff(22574,plain,
% 293.53/186.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9) | (~node11(c_e_h_1, c_n, s8, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8)))),
% 293.53/186.10 inference(quant_inst,[status(thm)],[])).
% 293.53/186.10 tff(22575,plain,
% 293.53/186.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9) | (~node11(c_e_h_1, c_n, s8, s9))),
% 293.53/186.10 inference(modus_ponens,[status(thm)],[22574, 22573])).
% 293.53/186.10 tff(22576,plain,
% 293.53/186.10 ($false),
% 293.53/186.10 inference(unit_resolution,[status(thm)],[22575, 5742, 22568, 22548, 22569])).
% 293.53/186.11 tff(22577,plain,((~node11(c_e_h_1, c_n, s8, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9)), inference(lemma,lemma(discharge,[]))).
% 293.53/186.11 tff(22578,plain,
% 293.53/186.11 (~node11(c_e_h_1, c_n, s8, s9)),
% 293.53/186.11 inference(unit_resolution,[status(thm)],[22577, 22548, 22568])).
% 293.53/186.11 tff(22579,plain,
% 293.53/186.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s8, s9)) | node10(c_e_h_1, c_n, s8, s9) | node11(c_e_h_1, c_n, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s8, s9)) | node10(c_e_h_1, c_n, s8, s9) | node11(c_e_h_1, c_n, s8, s9))),
% 293.53/186.11 inference(rewrite,[status(thm)],[])).
% 293.53/186.11 tff(22580,plain,
% 293.53/186.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s8, s9)) | node10(c_e_h_1, c_n, s8, s9) | node11(c_e_h_1, c_n, s8, s9))),
% 293.53/186.11 inference(quant_inst,[status(thm)],[])).
% 293.53/186.11 tff(22581,plain,
% 293.53/186.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s8, s9)) | node10(c_e_h_1, c_n, s8, s9) | node11(c_e_h_1, c_n, s8, s9)),
% 293.53/186.11 inference(modus_ponens,[status(thm)],[22580, 22579])).
% 293.53/186.11 tff(22582,plain,
% 293.53/186.11 (node10(c_e_h_1, c_n, s8, s9) | node11(c_e_h_1, c_n, s8, s9)),
% 293.53/186.11 inference(unit_resolution,[status(thm)],[22581, 5002, 1993])).
% 293.53/186.11 tff(22583,plain,
% 293.53/186.11 ($false),
% 293.53/186.11 inference(unit_resolution,[status(thm)],[22582, 22578, 22567])).
% 293.53/186.11 tff(22584,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s8))), inference(lemma,lemma(discharge,[]))).
% 293.53/186.11 tff(22585,plain,
% 293.53/186.11 ($false),
% 293.53/186.11 inference(unit_resolution,[status(thm)],[22584, 22556, 22550, 22547, 22548])).
% 293.53/186.11 tff(22586,plain,((~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7))), inference(lemma,lemma(discharge,[]))).
% 293.53/186.11 tff(22587,plain,
% 293.53/186.11 ((~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7))),
% 293.53/186.11 inference(unit_resolution,[status(thm)],[22586, 17887])).
% 293.53/186.11 tff(22588,plain,
% 293.53/186.11 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9)),
% 293.53/186.11 inference(unit_resolution,[status(thm)],[22587, 19255, 22547])).
% 293.53/186.11 tff(22589,plain,
% 293.53/186.11 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9)))),
% 293.53/186.11 inference(rewrite,[status(thm)],[])).
% 293.53/186.11 tff(22590,plain,
% 293.53/186.11 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9)))),
% 293.53/186.11 inference(quant_inst,[status(thm)],[])).
% 293.53/186.11 tff(22591,plain,
% 293.53/186.11 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9))),
% 293.53/186.11 inference(modus_ponens,[status(thm)],[22590, 22589])).
% 293.53/186.11 tff(22592,plain,
% 293.53/186.11 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s9)),
% 293.53/186.11 inference(unit_resolution,[status(thm)],[22591, 4958, 22588])).
% 293.53/186.11 tff(22593,plain,
% 293.53/186.11 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s9)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s9))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s9)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s9))),
% 293.53/186.11 inference(rewrite,[status(thm)],[])).
% 293.53/186.11 tff(22594,plain,
% 293.53/186.11 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s9)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s9))),
% 293.53/186.11 inference(quant_inst,[status(thm)],[])).
% 293.53/186.11 tff(22595,plain,
% 293.53/186.11 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s9)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s9)),
% 293.53/186.11 inference(modus_ponens,[status(thm)],[22594, 22593])).
% 293.53/186.11 tff(22596,plain,
% 293.53/186.11 (~node9(c_e_h_1, c_m, s9)),
% 293.53/186.11 inference(unit_resolution,[status(thm)],[22595, 4972, 22592])).
% 293.53/186.11 tff(22597,plain,
% 293.53/186.11 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8)),
% 293.53/186.11 inference(unit_resolution,[status(thm)],[19283, 19255])).
% 293.53/186.11 tff(22598,plain,
% 293.53/186.11 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8)))),
% 293.53/186.11 inference(rewrite,[status(thm)],[])).
% 293.53/186.11 tff(22599,plain,
% 293.53/186.11 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8)))),
% 293.53/186.11 inference(quant_inst,[status(thm)],[])).
% 293.53/186.11 tff(22600,plain,
% 293.53/186.11 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s8)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8))),
% 293.53/186.11 inference(modus_ponens,[status(thm)],[22599, 22598])).
% 293.53/186.11 tff(22601,plain,
% 293.53/186.11 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s8)),
% 293.53/186.11 inference(unit_resolution,[status(thm)],[22600, 4958, 22597])).
% 293.53/186.11 tff(22602,plain,
% 293.53/186.11 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s8)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s8)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s8))),
% 293.53/186.11 inference(rewrite,[status(thm)],[])).
% 293.53/186.11 tff(22603,plain,
% 293.53/186.11 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s8)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s8))),
% 293.53/186.11 inference(quant_inst,[status(thm)],[])).
% 293.53/186.11 tff(22604,plain,
% 293.53/186.11 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s8)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s8)),
% 293.53/186.11 inference(modus_ponens,[status(thm)],[22603, 22602])).
% 293.53/186.11 tff(22605,plain,
% 293.53/186.11 (~node9(c_e_h_1, c_m, s8)),
% 293.53/186.11 inference(unit_resolution,[status(thm)],[22604, 4972, 22601])).
% 293.53/186.11 tff(22606,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)), introduced(assumption)).
% 293.53/186.11 tff(22607,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)), introduced(assumption)).
% 293.53/186.11 tff(22608,assumption,(node11(c_e_h_1, c_m, s8, s9)), introduced(assumption)).
% 293.53/186.11 tff(22609,plain,
% 293.53/186.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)) | (~node11(c_e_h_1, c_m, s8, s9)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)) | (~node11(c_e_h_1, c_m, s8, s9)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8))),
% 293.53/186.11 inference(rewrite,[status(thm)],[])).
% 293.53/186.11 tff(22610,plain,
% 293.53/186.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)) | (~node11(c_e_h_1, c_m, s8, s9)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8))),
% 293.53/186.11 inference(quant_inst,[status(thm)],[])).
% 293.53/186.11 tff(22611,plain,
% 293.53/186.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)) | (~node11(c_e_h_1, c_m, s8, s9)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)),
% 293.53/186.11 inference(modus_ponens,[status(thm)],[22610, 22609])).
% 293.53/186.11 tff(22612,plain,
% 293.53/186.11 ($false),
% 293.53/186.11 inference(unit_resolution,[status(thm)],[22611, 5017, 22607, 22606, 22608])).
% 293.53/186.11 tff(22613,plain,((~node11(c_e_h_1, c_m, s8, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)), inference(lemma,lemma(discharge,[]))).
% 293.53/186.11 tff(22614,plain,
% 293.53/186.11 (~node11(c_e_h_1, c_m, s8, s9)),
% 293.53/186.11 inference(unit_resolution,[status(thm)],[22613, 22607, 22606])).
% 293.53/186.11 tff(22615,assumption,(~node9(c_e_h_1, c_m, s8)), introduced(assumption)).
% 293.53/186.11 tff(22616,assumption,(node10(c_e_h_1, c_m, s8, s9)), introduced(assumption)).
% 293.53/186.11 tff(22617,plain,
% 293.53/186.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)) | node9(c_e_h_1, c_m, s8) | (~node10(c_e_h_1, c_m, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)) | node9(c_e_h_1, c_m, s8) | (~node10(c_e_h_1, c_m, s8, s9)))),
% 293.53/186.11 inference(rewrite,[status(thm)],[])).
% 293.53/186.11 tff(22618,plain,
% 293.53/186.11 ((node9(c_e_h_1, c_m, s8) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)) | (~node10(c_e_h_1, c_m, s8, s9))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)) | node9(c_e_h_1, c_m, s8) | (~node10(c_e_h_1, c_m, s8, s9)))),
% 293.53/186.11 inference(rewrite,[status(thm)],[])).
% 293.53/186.11 tff(22619,plain,
% 293.53/186.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s8) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)) | (~node10(c_e_h_1, c_m, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)) | node9(c_e_h_1, c_m, s8) | (~node10(c_e_h_1, c_m, s8, s9))))),
% 293.53/186.11 inference(monotonicity,[status(thm)],[22618])).
% 293.53/186.11 tff(22620,plain,
% 293.53/186.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s8) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)) | (~node10(c_e_h_1, c_m, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)) | node9(c_e_h_1, c_m, s8) | (~node10(c_e_h_1, c_m, s8, s9)))),
% 293.53/186.11 inference(transitivity,[status(thm)],[22619, 22617])).
% 293.53/186.11 tff(22621,plain,
% 293.53/186.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s8) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)) | (~node10(c_e_h_1, c_m, s8, s9)))),
% 293.53/186.11 inference(quant_inst,[status(thm)],[])).
% 293.53/186.11 tff(22622,plain,
% 293.53/186.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)) | node9(c_e_h_1, c_m, s8) | (~node10(c_e_h_1, c_m, s8, s9))),
% 293.53/186.11 inference(modus_ponens,[status(thm)],[22621, 22620])).
% 293.53/186.11 tff(22623,plain,
% 293.53/186.11 ($false),
% 293.53/186.11 inference(unit_resolution,[status(thm)],[22622, 4986, 22607, 22616, 22615])).
% 293.53/186.11 tff(22624,plain,((~node10(c_e_h_1, c_m, s8, s9)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)) | node9(c_e_h_1, c_m, s8)), inference(lemma,lemma(discharge,[]))).
% 293.53/186.11 tff(22625,plain,
% 293.53/186.11 (~node10(c_e_h_1, c_m, s8, s9)),
% 293.53/186.11 inference(unit_resolution,[status(thm)],[22624, 22607, 22615])).
% 293.53/186.11 tff(22626,plain,
% 293.53/186.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s8, s9)) | node10(c_e_h_1, c_m, s8, s9) | node11(c_e_h_1, c_m, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s8, s9)) | node10(c_e_h_1, c_m, s8, s9) | node11(c_e_h_1, c_m, s8, s9))),
% 293.62/186.12 inference(rewrite,[status(thm)],[])).
% 293.62/186.12 tff(22627,plain,
% 293.62/186.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s8, s9)) | node10(c_e_h_1, c_m, s8, s9) | node11(c_e_h_1, c_m, s8, s9))),
% 293.62/186.12 inference(quant_inst,[status(thm)],[])).
% 293.62/186.12 tff(22628,plain,
% 293.62/186.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s8, s9)) | node10(c_e_h_1, c_m, s8, s9) | node11(c_e_h_1, c_m, s8, s9)),
% 293.62/186.12 inference(modus_ponens,[status(thm)],[22627, 22626])).
% 293.62/186.12 tff(22629,plain,
% 293.62/186.12 (node10(c_e_h_1, c_m, s8, s9) | node11(c_e_h_1, c_m, s8, s9)),
% 293.62/186.12 inference(unit_resolution,[status(thm)],[22628, 5002, 1993])).
% 293.62/186.12 tff(22630,plain,
% 293.62/186.12 ($false),
% 293.62/186.12 inference(unit_resolution,[status(thm)],[22629, 22625, 22614])).
% 293.62/186.12 tff(22631,plain,((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)) | node9(c_e_h_1, c_m, s8) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)), inference(lemma,lemma(discharge,[]))).
% 293.62/186.12 tff(22632,plain,
% 293.62/186.12 ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)) | node9(c_e_h_1, c_m, s8)),
% 293.62/186.12 inference(unit_resolution,[status(thm)],[22631, 22368])).
% 293.62/186.12 tff(22633,plain,
% 293.62/186.12 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)),
% 293.62/186.12 inference(unit_resolution,[status(thm)],[22632, 22605])).
% 293.62/186.12 tff(22634,assumption,(~node9(c_e_h_1, c_m, s9)), introduced(assumption)).
% 293.62/186.12 tff(22635,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)), introduced(assumption)).
% 293.62/186.12 tff(22636,assumption,(node11(c_e_h_1, c_m, s9, s10)), introduced(assumption)).
% 293.62/186.12 tff(22637,plain,
% 293.62/186.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)) | (~node11(c_e_h_1, c_m, s9, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)) | (~node11(c_e_h_1, c_m, s9, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9))),
% 293.62/186.12 inference(rewrite,[status(thm)],[])).
% 293.62/186.12 tff(22638,plain,
% 293.62/186.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)) | (~node11(c_e_h_1, c_m, s9, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9))),
% 293.62/186.12 inference(quant_inst,[status(thm)],[])).
% 293.62/186.12 tff(22639,plain,
% 293.62/186.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)) | (~node11(c_e_h_1, c_m, s9, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)),
% 293.62/186.12 inference(modus_ponens,[status(thm)],[22638, 22637])).
% 293.62/186.12 tff(22640,plain,
% 293.62/186.12 ($false),
% 293.62/186.12 inference(unit_resolution,[status(thm)],[22639, 5017, 22635, 22546, 22636])).
% 293.62/186.12 tff(22641,plain,((~node11(c_e_h_1, c_m, s9, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10))), inference(lemma,lemma(discharge,[]))).
% 293.62/186.12 tff(22642,plain,
% 293.62/186.12 (~node11(c_e_h_1, c_m, s9, s10)),
% 293.62/186.12 inference(unit_resolution,[status(thm)],[22641, 22546, 22635])).
% 293.62/186.12 tff(22643,plain,
% 293.62/186.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s9, s10)) | node10(c_e_h_1, c_m, s9, s10) | node11(c_e_h_1, c_m, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s9, s10)) | node10(c_e_h_1, c_m, s9, s10) | node11(c_e_h_1, c_m, s9, s10))),
% 293.62/186.12 inference(rewrite,[status(thm)],[])).
% 293.62/186.12 tff(22644,plain,
% 293.62/186.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s9, s10)) | node10(c_e_h_1, c_m, s9, s10) | node11(c_e_h_1, c_m, s9, s10))),
% 293.62/186.12 inference(quant_inst,[status(thm)],[])).
% 293.62/186.12 tff(22645,plain,
% 293.62/186.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s9, s10)) | node10(c_e_h_1, c_m, s9, s10) | node11(c_e_h_1, c_m, s9, s10)),
% 293.62/186.12 inference(modus_ponens,[status(thm)],[22644, 22643])).
% 293.62/186.12 tff(22646,plain,
% 293.62/186.12 (node10(c_e_h_1, c_m, s9, s10) | node11(c_e_h_1, c_m, s9, s10)),
% 293.62/186.12 inference(unit_resolution,[status(thm)],[22645, 5002, 7676])).
% 293.62/186.12 tff(22647,plain,
% 293.62/186.12 (node10(c_e_h_1, c_m, s9, s10)),
% 293.62/186.12 inference(unit_resolution,[status(thm)],[22646, 22642])).
% 293.62/186.12 tff(22648,plain,
% 293.62/186.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)) | node9(c_e_h_1, c_m, s9) | (~node10(c_e_h_1, c_m, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)) | node9(c_e_h_1, c_m, s9) | (~node10(c_e_h_1, c_m, s9, s10)))),
% 293.62/186.12 inference(rewrite,[status(thm)],[])).
% 293.62/186.12 tff(22649,plain,
% 293.62/186.12 ((node9(c_e_h_1, c_m, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)) | (~node10(c_e_h_1, c_m, s9, s10))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)) | node9(c_e_h_1, c_m, s9) | (~node10(c_e_h_1, c_m, s9, s10)))),
% 293.62/186.12 inference(rewrite,[status(thm)],[])).
% 293.62/186.12 tff(22650,plain,
% 293.62/186.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)) | (~node10(c_e_h_1, c_m, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)) | node9(c_e_h_1, c_m, s9) | (~node10(c_e_h_1, c_m, s9, s10))))),
% 293.62/186.12 inference(monotonicity,[status(thm)],[22649])).
% 293.62/186.12 tff(22651,plain,
% 293.62/186.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)) | (~node10(c_e_h_1, c_m, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)) | node9(c_e_h_1, c_m, s9) | (~node10(c_e_h_1, c_m, s9, s10)))),
% 293.62/186.12 inference(transitivity,[status(thm)],[22650, 22648])).
% 293.62/186.12 tff(22652,plain,
% 293.62/186.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s9) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)) | (~node10(c_e_h_1, c_m, s9, s10)))),
% 293.62/186.12 inference(quant_inst,[status(thm)],[])).
% 293.62/186.12 tff(22653,plain,
% 293.62/186.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)) | node9(c_e_h_1, c_m, s9) | (~node10(c_e_h_1, c_m, s9, s10))),
% 293.62/186.12 inference(modus_ponens,[status(thm)],[22652, 22651])).
% 293.62/186.12 tff(22654,plain,
% 293.62/186.12 ($false),
% 293.62/186.12 inference(unit_resolution,[status(thm)],[22653, 4986, 22546, 22647, 22634])).
% 293.62/186.12 tff(22655,plain,((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)) | node9(c_e_h_1, c_m, s9) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)), inference(lemma,lemma(discharge,[]))).
% 293.62/186.12 tff(22656,plain,
% 293.62/186.12 ($false),
% 293.62/186.12 inference(unit_resolution,[status(thm)],[22655, 22633, 22596, 22546])).
% 293.62/186.12 tff(22657,plain,((~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s8))), inference(lemma,lemma(discharge,[]))).
% 293.62/186.12 tff(22658,plain,
% 293.62/186.12 ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s8))),
% 293.62/186.12 inference(unit_resolution,[status(thm)],[22657, 19216])).
% 293.62/186.12 tff(22659,plain,
% 293.62/186.12 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)),
% 293.62/186.12 inference(unit_resolution,[status(thm)],[22658, 22545])).
% 293.62/186.12 tff(22660,plain,
% 293.62/186.12 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10))),
% 293.62/186.12 inference(rewrite,[status(thm)],[])).
% 293.62/186.12 tff(22661,plain,
% 293.62/186.12 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10))),
% 293.62/186.12 inference(quant_inst,[status(thm)],[])).
% 293.62/186.12 tff(22662,plain,
% 293.62/186.12 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)),
% 293.62/186.12 inference(modus_ponens,[status(thm)],[22661, 22660])).
% 293.62/186.12 tff(22663,plain,
% 293.62/186.12 (~m_and_h_gate_v_in2(c_e_h_1, c_l, s10)),
% 293.62/186.12 inference(unit_resolution,[status(thm)],[22662, 4549, 22659])).
% 293.62/186.12 tff(22664,plain,
% 293.62/186.12 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s10)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s10))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s10)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s10))),
% 293.62/186.12 inference(rewrite,[status(thm)],[])).
% 293.62/186.12 tff(22665,plain,
% 293.62/186.12 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s10)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s10))),
% 293.62/186.12 inference(quant_inst,[status(thm)],[])).
% 293.62/186.12 tff(22666,plain,
% 293.62/186.12 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s10)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s10)),
% 293.62/186.12 inference(modus_ponens,[status(thm)],[22665, 22664])).
% 293.62/186.12 tff(22667,plain,
% 293.62/186.12 (~node20(c_e_h_1, c_l, s10)),
% 293.62/186.12 inference(unit_resolution,[status(thm)],[22666, 4563, 22663])).
% 293.62/186.12 tff(22668,plain,
% 293.62/186.12 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s8)),
% 293.62/186.12 inference(unit_resolution,[status(thm)],[22600, 4958, 19284])).
% 293.62/186.12 tff(22669,plain,
% 293.62/186.12 (~node9(c_e_h_1, c_m, s8)),
% 293.62/186.12 inference(unit_resolution,[status(thm)],[22604, 4972, 22668])).
% 293.62/186.12 tff(22670,plain,
% 293.62/186.12 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)),
% 293.62/186.12 inference(unit_resolution,[status(thm)],[22632, 22669])).
% 293.62/186.12 tff(22671,plain,
% 293.62/186.12 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s9)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s9)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9))),
% 293.62/186.12 inference(rewrite,[status(thm)],[])).
% 293.62/186.12 tff(22672,plain,
% 293.62/186.12 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s9)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9))),
% 293.62/186.12 inference(quant_inst,[status(thm)],[])).
% 293.62/186.12 tff(22673,plain,
% 293.62/186.12 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s9)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)),
% 293.62/186.12 inference(modus_ponens,[status(thm)],[22672, 22671])).
% 293.62/186.12 tff(22674,plain,
% 293.62/186.12 (~m_and_h_gate_v_in2(c_e_h_1, c_l, s9)),
% 293.62/186.12 inference(unit_resolution,[status(thm)],[22673, 4549, 22670])).
% 293.62/186.12 tff(22675,plain,
% 293.62/186.12 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s9)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s9))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s9)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s9))),
% 293.62/186.12 inference(rewrite,[status(thm)],[])).
% 293.62/186.13 tff(22676,plain,
% 293.62/186.13 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s9)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s9))),
% 293.62/186.13 inference(quant_inst,[status(thm)],[])).
% 293.62/186.13 tff(22677,plain,
% 293.62/186.13 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s9)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s9)),
% 293.62/186.13 inference(modus_ponens,[status(thm)],[22676, 22675])).
% 293.62/186.13 tff(22678,plain,
% 293.62/186.13 (~node20(c_e_h_1, c_l, s9)),
% 293.62/186.13 inference(unit_resolution,[status(thm)],[22677, 4563, 22674])).
% 293.62/186.13 tff(22679,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_l, s9)), introduced(assumption)).
% 293.62/186.13 tff(22680,assumption,(m_and_h_gate_v_out(c_e_h_1, c_l, s10)), introduced(assumption)).
% 293.62/186.13 tff(22681,assumption,(~node20(c_e_h_1, c_l, s9)), introduced(assumption)).
% 293.62/186.13 tff(22682,assumption,(node21(c_e_h_1, c_l, s9, s10)), introduced(assumption)).
% 293.62/186.13 tff(22683,plain,
% 293.62/186.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s9) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s10)) | (~node21(c_e_h_1, c_l, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s9) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s10)) | (~node21(c_e_h_1, c_l, s9, s10)))),
% 293.62/186.13 inference(rewrite,[status(thm)],[])).
% 293.62/186.13 tff(22684,plain,
% 293.62/186.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s9) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s10)) | (~node21(c_e_h_1, c_l, s9, s10)))),
% 293.62/186.13 inference(quant_inst,[status(thm)],[])).
% 293.62/186.13 tff(22685,plain,
% 293.62/186.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s9) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s10)) | (~node21(c_e_h_1, c_l, s9, s10))),
% 293.62/186.13 inference(modus_ponens,[status(thm)],[22684, 22683])).
% 293.62/186.13 tff(22686,plain,
% 293.62/186.13 ($false),
% 293.62/186.13 inference(unit_resolution,[status(thm)],[22685, 52, 22682, 22681, 22680])).
% 293.62/186.13 tff(22687,plain,((~node21(c_e_h_1, c_l, s9, s10)) | node20(c_e_h_1, c_l, s9) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s10))), inference(lemma,lemma(discharge,[]))).
% 293.62/186.13 tff(22688,plain,
% 293.62/186.13 (~node21(c_e_h_1, c_l, s9, s10)),
% 293.62/186.13 inference(unit_resolution,[status(thm)],[22687, 22680, 22681])).
% 293.62/186.13 tff(22689,plain,
% 293.62/186.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s9, s10)) | node21(c_e_h_1, c_l, s9, s10) | node22(c_e_h_1, c_l, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s9, s10)) | node21(c_e_h_1, c_l, s9, s10) | node22(c_e_h_1, c_l, s9, s10))),
% 293.62/186.13 inference(rewrite,[status(thm)],[])).
% 293.62/186.13 tff(22690,plain,
% 293.62/186.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s9, s10)) | node21(c_e_h_1, c_l, s9, s10) | node22(c_e_h_1, c_l, s9, s10))),
% 293.62/186.13 inference(quant_inst,[status(thm)],[])).
% 293.62/186.13 tff(22691,plain,
% 293.62/186.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s9, s10)) | node21(c_e_h_1, c_l, s9, s10) | node22(c_e_h_1, c_l, s9, s10)),
% 293.62/186.13 inference(modus_ponens,[status(thm)],[22690, 22689])).
% 293.62/186.13 tff(22692,plain,
% 293.62/186.13 (node21(c_e_h_1, c_l, s9, s10) | node22(c_e_h_1, c_l, s9, s10)),
% 293.62/186.13 inference(unit_resolution,[status(thm)],[22691, 82, 7676])).
% 293.62/186.13 tff(22693,plain,
% 293.62/186.13 (node22(c_e_h_1, c_l, s9, s10)),
% 293.62/186.13 inference(unit_resolution,[status(thm)],[22692, 22688])).
% 293.62/186.13 tff(22694,plain,
% 293.62/186.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s10)) | (~node22(c_e_h_1, c_l, s9, s10)) | m_and_h_gate_v_out(c_e_h_1, c_l, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s10)) | (~node22(c_e_h_1, c_l, s9, s10)) | m_and_h_gate_v_out(c_e_h_1, c_l, s9))),
% 293.62/186.13 inference(rewrite,[status(thm)],[])).
% 293.62/186.13 tff(22695,plain,
% 293.62/186.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s10)) | (~node22(c_e_h_1, c_l, s9, s10)) | m_and_h_gate_v_out(c_e_h_1, c_l, s9))),
% 293.62/186.13 inference(quant_inst,[status(thm)],[])).
% 293.62/186.13 tff(22696,plain,
% 293.62/186.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s10)) | (~node22(c_e_h_1, c_l, s9, s10)) | m_and_h_gate_v_out(c_e_h_1, c_l, s9)),
% 293.62/186.13 inference(modus_ponens,[status(thm)],[22695, 22694])).
% 293.62/186.13 tff(22697,plain,
% 293.62/186.13 ($false),
% 293.62/186.13 inference(unit_resolution,[status(thm)],[22696, 108, 22693, 22680, 22679])).
% 293.62/186.13 tff(22698,plain,((~m_and_h_gate_v_out(c_e_h_1, c_l, s10)) | m_and_h_gate_v_out(c_e_h_1, c_l, s9) | node20(c_e_h_1, c_l, s9)), inference(lemma,lemma(discharge,[]))).
% 293.62/186.13 tff(22699,plain,
% 293.62/186.13 ((~m_and_h_gate_v_out(c_e_h_1, c_l, s10)) | node20(c_e_h_1, c_l, s9)),
% 293.62/186.13 inference(unit_resolution,[status(thm)],[22698, 22392])).
% 293.62/186.13 tff(22700,plain,
% 293.62/186.13 (~m_and_h_gate_v_out(c_e_h_1, c_l, s10)),
% 293.62/186.13 inference(unit_resolution,[status(thm)],[22699, 22678])).
% 293.62/186.13 tff(22701,assumption,(m_and_h_gate_v_out(c_e_h_1, c_l, s11)), introduced(assumption)).
% 293.62/186.13 tff(22702,assumption,(~node20(c_e_h_1, c_l, s10)), introduced(assumption)).
% 293.62/186.13 tff(22703,assumption,(node21(c_e_h_1, c_l, s10, s11)), introduced(assumption)).
% 293.62/186.13 tff(22704,plain,
% 293.62/186.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s10) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s11)) | (~node21(c_e_h_1, c_l, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s10) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s11)) | (~node21(c_e_h_1, c_l, s10, s11)))),
% 293.62/186.13 inference(rewrite,[status(thm)],[])).
% 293.62/186.13 tff(22705,plain,
% 293.62/186.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s10) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s11)) | (~node21(c_e_h_1, c_l, s10, s11)))),
% 293.62/186.13 inference(quant_inst,[status(thm)],[])).
% 293.62/186.13 tff(22706,plain,
% 293.62/186.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s10) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s11)) | (~node21(c_e_h_1, c_l, s10, s11))),
% 293.62/186.13 inference(modus_ponens,[status(thm)],[22705, 22704])).
% 293.62/186.13 tff(22707,plain,
% 293.62/186.13 ($false),
% 293.62/186.13 inference(unit_resolution,[status(thm)],[22706, 52, 22703, 22702, 22701])).
% 293.62/186.13 tff(22708,plain,((~node21(c_e_h_1, c_l, s10, s11)) | node20(c_e_h_1, c_l, s10) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s11))), inference(lemma,lemma(discharge,[]))).
% 293.62/186.13 tff(22709,plain,
% 293.62/186.13 (~node21(c_e_h_1, c_l, s10, s11)),
% 293.62/186.13 inference(unit_resolution,[status(thm)],[22708, 22701, 22702])).
% 293.62/186.13 tff(22710,plain,
% 293.62/186.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s10, s11)) | node21(c_e_h_1, c_l, s10, s11) | node22(c_e_h_1, c_l, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s10, s11)) | node21(c_e_h_1, c_l, s10, s11) | node22(c_e_h_1, c_l, s10, s11))),
% 293.62/186.13 inference(rewrite,[status(thm)],[])).
% 293.62/186.13 tff(22711,plain,
% 293.62/186.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s10, s11)) | node21(c_e_h_1, c_l, s10, s11) | node22(c_e_h_1, c_l, s10, s11))),
% 293.62/186.13 inference(quant_inst,[status(thm)],[])).
% 293.62/186.13 tff(22712,plain,
% 293.62/186.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s10, s11)) | node21(c_e_h_1, c_l, s10, s11) | node22(c_e_h_1, c_l, s10, s11)),
% 293.62/186.13 inference(modus_ponens,[status(thm)],[22711, 22710])).
% 293.62/186.13 tff(22713,plain,
% 293.62/186.13 (node21(c_e_h_1, c_l, s10, s11) | node22(c_e_h_1, c_l, s10, s11)),
% 293.62/186.13 inference(unit_resolution,[status(thm)],[22712, 82, 7748])).
% 293.62/186.13 tff(22714,plain,
% 293.62/186.13 (node22(c_e_h_1, c_l, s10, s11)),
% 293.62/186.13 inference(unit_resolution,[status(thm)],[22713, 22709])).
% 293.62/186.13 tff(22715,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_l, s10)), introduced(assumption)).
% 293.62/186.13 tff(22716,plain,
% 293.62/186.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s11)) | (~node22(c_e_h_1, c_l, s10, s11)) | m_and_h_gate_v_out(c_e_h_1, c_l, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s11)) | (~node22(c_e_h_1, c_l, s10, s11)) | m_and_h_gate_v_out(c_e_h_1, c_l, s10))),
% 293.62/186.13 inference(rewrite,[status(thm)],[])).
% 293.62/186.13 tff(22717,plain,
% 293.62/186.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s11)) | (~node22(c_e_h_1, c_l, s10, s11)) | m_and_h_gate_v_out(c_e_h_1, c_l, s10))),
% 293.62/186.13 inference(quant_inst,[status(thm)],[])).
% 293.62/186.13 tff(22718,plain,
% 293.62/186.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s11)) | (~node22(c_e_h_1, c_l, s10, s11)) | m_and_h_gate_v_out(c_e_h_1, c_l, s10)),
% 293.62/186.13 inference(modus_ponens,[status(thm)],[22717, 22716])).
% 293.62/186.13 tff(22719,plain,
% 293.62/186.13 ($false),
% 293.62/186.13 inference(unit_resolution,[status(thm)],[22718, 108, 22715, 22714, 22701])).
% 293.62/186.13 tff(22720,plain,((~m_and_h_gate_v_out(c_e_h_1, c_l, s11)) | m_and_h_gate_v_out(c_e_h_1, c_l, s10) | node20(c_e_h_1, c_l, s10)), inference(lemma,lemma(discharge,[]))).
% 293.62/186.13 tff(22721,plain,
% 293.62/186.13 ((~m_and_h_gate_v_out(c_e_h_1, c_l, s11)) | node20(c_e_h_1, c_l, s10)),
% 293.62/186.13 inference(unit_resolution,[status(thm)],[22720, 22700])).
% 293.62/186.13 tff(22722,plain,
% 293.62/186.13 (~m_and_h_gate_v_out(c_e_h_1, c_l, s11)),
% 293.62/186.13 inference(unit_resolution,[status(thm)],[22721, 22667])).
% 293.62/186.13 tff(22723,assumption,(m_or_h_gate_v_in1(c_e_h_1, c_j, s11)), introduced(assumption)).
% 293.62/186.13 tff(22724,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_l, s11)), introduced(assumption)).
% 293.62/186.13 tff(22725,plain,
% 293.62/186.13 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s11)) | m_and_h_gate_v_out(c_e_h_1, c_l, s11))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s11)) | m_and_h_gate_v_out(c_e_h_1, c_l, s11))),
% 293.62/186.13 inference(rewrite,[status(thm)],[])).
% 293.62/186.13 tff(22726,plain,
% 293.62/186.13 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s11)) | m_and_h_gate_v_out(c_e_h_1, c_l, s11))),
% 293.62/186.13 inference(quant_inst,[status(thm)],[])).
% 293.62/186.13 tff(22727,plain,
% 293.62/186.13 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s11)) | m_and_h_gate_v_out(c_e_h_1, c_l, s11)),
% 293.62/186.13 inference(modus_ponens,[status(thm)],[22726, 22725])).
% 293.62/186.13 tff(22728,plain,
% 293.62/186.13 ($false),
% 293.62/186.13 inference(unit_resolution,[status(thm)],[22727, 1100, 22724, 22723])).
% 293.62/186.13 tff(22729,plain,((~m_or_h_gate_v_in1(c_e_h_1, c_j, s11)) | m_and_h_gate_v_out(c_e_h_1, c_l, s11)), inference(lemma,lemma(discharge,[]))).
% 293.62/186.13 tff(22730,plain,
% 293.62/186.13 (~m_or_h_gate_v_in1(c_e_h_1, c_j, s11)),
% 293.62/186.13 inference(unit_resolution,[status(thm)],[22729, 22722])).
% 293.62/186.13 tff(22731,assumption,(~m_or_h_gate_v_in1(c_e_h_1, c_j, s11)), introduced(assumption)).
% 293.62/186.13 tff(22732,assumption,(~m_or_h_gate_v_out(c_e_h_1, c_j, s10)), introduced(assumption)).
% 293.62/186.13 tff(22733,plain,
% 293.62/186.13 (~m_cell_v_ack(c_e_h_1, s10)),
% 293.62/186.13 inference(unit_resolution,[status(thm)],[21408, 21988])).
% 293.62/186.13 tff(22734,plain,
% 293.62/186.13 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s10)) | m_cell_v_ack(c_e_h_1, s10))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s10)) | m_cell_v_ack(c_e_h_1, s10))),
% 293.62/186.14 inference(rewrite,[status(thm)],[])).
% 293.62/186.14 tff(22735,plain,
% 293.62/186.14 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s10)) | m_cell_v_ack(c_e_h_1, s10))),
% 293.62/186.14 inference(quant_inst,[status(thm)],[])).
% 293.62/186.14 tff(22736,plain,
% 293.62/186.14 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s10)) | m_cell_v_ack(c_e_h_1, s10)),
% 293.62/186.14 inference(modus_ponens,[status(thm)],[22735, 22734])).
% 293.62/186.14 tff(22737,plain,
% 293.62/186.14 (~m_or_h_gate_v_in2(c_e_h_1, c_j, s10)),
% 293.62/186.14 inference(unit_resolution,[status(thm)],[22736, 1085, 22733])).
% 293.62/186.14 tff(22738,assumption,(m_or_h_gate_v_in1(c_e_h_1, c_j, s10)), introduced(assumption)).
% 293.62/186.14 tff(22739,plain,
% 293.62/186.14 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s10)) | m_and_h_gate_v_out(c_e_h_1, c_l, s10))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s10)) | m_and_h_gate_v_out(c_e_h_1, c_l, s10))),
% 293.62/186.14 inference(rewrite,[status(thm)],[])).
% 293.62/186.14 tff(22740,plain,
% 293.62/186.14 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s10)) | m_and_h_gate_v_out(c_e_h_1, c_l, s10))),
% 293.62/186.14 inference(quant_inst,[status(thm)],[])).
% 293.62/186.14 tff(22741,plain,
% 293.62/186.14 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s10)) | m_and_h_gate_v_out(c_e_h_1, c_l, s10)),
% 293.62/186.14 inference(modus_ponens,[status(thm)],[22740, 22739])).
% 293.62/186.14 tff(22742,plain,
% 293.62/186.14 ($false),
% 293.62/186.14 inference(unit_resolution,[status(thm)],[22741, 1100, 22715, 22738])).
% 293.62/186.14 tff(22743,plain,((~m_or_h_gate_v_in1(c_e_h_1, c_j, s10)) | m_and_h_gate_v_out(c_e_h_1, c_l, s10)), inference(lemma,lemma(discharge,[]))).
% 293.62/186.14 tff(22744,plain,
% 293.62/186.14 (~m_or_h_gate_v_in1(c_e_h_1, c_j, s10)),
% 293.62/186.14 inference(unit_resolution,[status(thm)],[22743, 22700])).
% 293.62/186.14 tff(22745,assumption,(m_or_h_gate_v_out(c_e_h_1, c_j, s11)), introduced(assumption)).
% 293.62/186.14 tff(22746,assumption,(node6(c_e_h_1, c_j, s10, s11)), introduced(assumption)).
% 293.62/186.14 tff(22747,plain,
% 293.62/186.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s10) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s11)) | (~node6(c_e_h_1, c_j, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s10) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s11)) | (~node6(c_e_h_1, c_j, s10, s11)))),
% 293.62/186.14 inference(rewrite,[status(thm)],[])).
% 293.62/186.14 tff(22748,plain,
% 293.62/186.14 (((~node6(c_e_h_1, c_j, s10, s11)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s11)) | m_or_h_gate_v_out(c_e_h_1, c_j, s10)) <=> (m_or_h_gate_v_out(c_e_h_1, c_j, s10) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s11)) | (~node6(c_e_h_1, c_j, s10, s11)))),
% 293.62/186.14 inference(rewrite,[status(thm)],[])).
% 293.62/186.14 tff(22749,plain,
% 293.62/186.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s10, s11)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s11)) | m_or_h_gate_v_out(c_e_h_1, c_j, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s10) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s11)) | (~node6(c_e_h_1, c_j, s10, s11))))),
% 293.62/186.14 inference(monotonicity,[status(thm)],[22748])).
% 293.62/186.14 tff(22750,plain,
% 293.62/186.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s10, s11)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s11)) | m_or_h_gate_v_out(c_e_h_1, c_j, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s10) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s11)) | (~node6(c_e_h_1, c_j, s10, s11)))),
% 293.62/186.14 inference(transitivity,[status(thm)],[22749, 22747])).
% 293.62/186.14 tff(22751,plain,
% 293.62/186.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s10, s11)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s11)) | m_or_h_gate_v_out(c_e_h_1, c_j, s10))),
% 293.62/186.14 inference(quant_inst,[status(thm)],[])).
% 293.62/186.14 tff(22752,plain,
% 293.62/186.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s10) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s11)) | (~node6(c_e_h_1, c_j, s10, s11))),
% 293.62/186.14 inference(modus_ponens,[status(thm)],[22751, 22750])).
% 293.62/186.14 tff(22753,plain,
% 293.62/186.14 ($false),
% 293.62/186.14 inference(unit_resolution,[status(thm)],[22752, 1121, 22732, 22745, 22746])).
% 293.62/186.14 tff(22754,plain,((~node6(c_e_h_1, c_j, s10, s11)) | m_or_h_gate_v_out(c_e_h_1, c_j, s10) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s11))), inference(lemma,lemma(discharge,[]))).
% 293.62/186.14 tff(22755,plain,
% 293.62/186.14 (~node6(c_e_h_1, c_j, s10, s11)),
% 293.62/186.14 inference(unit_resolution,[status(thm)],[22754, 22745, 22732])).
% 293.62/186.14 tff(22756,assumption,(~m_or_h_gate_v_in2(c_e_h_1, c_j, s10)), introduced(assumption)).
% 293.62/186.14 tff(22757,assumption,(~m_or_h_gate_v_in1(c_e_h_1, c_j, s10)), introduced(assumption)).
% 293.62/186.14 tff(22758,assumption,(node5(c_e_h_1, c_j, s10, s11)), introduced(assumption)).
% 293.62/186.14 tff(22759,plain,
% 293.62/186.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_1, c_j, s10) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s11)) | (~node5(c_e_h_1, c_j, s10, s11)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_1, c_j, s10) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s11)) | (~node5(c_e_h_1, c_j, s10, s11)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s10))),
% 293.62/186.14 inference(rewrite,[status(thm)],[])).
% 293.62/186.14 tff(22760,plain,
% 293.62/186.14 ((m_or_h_gate_v_in1(c_e_h_1, c_j, s10) | m_or_h_gate_v_in2(c_e_h_1, c_j, s10) | (~node5(c_e_h_1, c_j, s10, s11)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s11))) <=> (m_or_h_gate_v_in2(c_e_h_1, c_j, s10) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s11)) | (~node5(c_e_h_1, c_j, s10, s11)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s10))),
% 293.62/186.14 inference(rewrite,[status(thm)],[])).
% 293.62/186.14 tff(22761,plain,
% 293.62/186.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s10) | m_or_h_gate_v_in2(c_e_h_1, c_j, s10) | (~node5(c_e_h_1, c_j, s10, s11)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_1, c_j, s10) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s11)) | (~node5(c_e_h_1, c_j, s10, s11)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s10)))),
% 293.62/186.14 inference(monotonicity,[status(thm)],[22760])).
% 293.62/186.14 tff(22762,plain,
% 293.62/186.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s10) | m_or_h_gate_v_in2(c_e_h_1, c_j, s10) | (~node5(c_e_h_1, c_j, s10, s11)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_1, c_j, s10) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s11)) | (~node5(c_e_h_1, c_j, s10, s11)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s10))),
% 293.62/186.14 inference(transitivity,[status(thm)],[22761, 22759])).
% 293.62/186.14 tff(22763,plain,
% 293.62/186.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s10) | m_or_h_gate_v_in2(c_e_h_1, c_j, s10) | (~node5(c_e_h_1, c_j, s10, s11)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s11)))),
% 293.62/186.14 inference(quant_inst,[status(thm)],[])).
% 293.62/186.14 tff(22764,plain,
% 293.62/186.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_1, c_j, s10) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s11)) | (~node5(c_e_h_1, c_j, s10, s11)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s10)),
% 293.62/186.14 inference(modus_ponens,[status(thm)],[22763, 22762])).
% 293.62/186.14 tff(22765,plain,
% 293.62/186.14 ($false),
% 293.62/186.14 inference(unit_resolution,[status(thm)],[22764, 1159, 22745, 22758, 22756, 22757])).
% 293.62/186.14 tff(22766,plain,((~node5(c_e_h_1, c_j, s10, s11)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s11)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s10) | m_or_h_gate_v_in1(c_e_h_1, c_j, s10)), inference(lemma,lemma(discharge,[]))).
% 293.62/186.14 tff(22767,plain,
% 293.62/186.14 (~node5(c_e_h_1, c_j, s10, s11)),
% 293.62/186.14 inference(unit_resolution,[status(thm)],[22766, 22745, 22757, 22756])).
% 293.62/186.14 tff(22768,plain,
% 293.62/186.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s10, s11)) | node6(c_e_h_1, c_j, s10, s11) | node5(c_e_h_1, c_j, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s10, s11)) | node6(c_e_h_1, c_j, s10, s11) | node5(c_e_h_1, c_j, s10, s11))),
% 293.62/186.14 inference(rewrite,[status(thm)],[])).
% 293.62/186.14 tff(22769,plain,
% 293.62/186.14 ((node6(c_e_h_1, c_j, s10, s11) | node5(c_e_h_1, c_j, s10, s11) | (~trans(s10, s11))) <=> ((~trans(s10, s11)) | node6(c_e_h_1, c_j, s10, s11) | node5(c_e_h_1, c_j, s10, s11))),
% 293.62/186.14 inference(rewrite,[status(thm)],[])).
% 293.62/186.14 tff(22770,plain,
% 293.62/186.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s10, s11) | node5(c_e_h_1, c_j, s10, s11) | (~trans(s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s10, s11)) | node6(c_e_h_1, c_j, s10, s11) | node5(c_e_h_1, c_j, s10, s11)))),
% 293.62/186.14 inference(monotonicity,[status(thm)],[22769])).
% 293.62/186.14 tff(22771,plain,
% 293.62/186.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s10, s11) | node5(c_e_h_1, c_j, s10, s11) | (~trans(s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s10, s11)) | node6(c_e_h_1, c_j, s10, s11) | node5(c_e_h_1, c_j, s10, s11))),
% 293.62/186.14 inference(transitivity,[status(thm)],[22770, 22768])).
% 293.62/186.14 tff(22772,plain,
% 293.62/186.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s10, s11) | node5(c_e_h_1, c_j, s10, s11) | (~trans(s10, s11)))),
% 293.62/186.14 inference(quant_inst,[status(thm)],[])).
% 293.62/186.14 tff(22773,plain,
% 293.62/186.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s10, s11)) | node6(c_e_h_1, c_j, s10, s11) | node5(c_e_h_1, c_j, s10, s11)),
% 293.62/186.14 inference(modus_ponens,[status(thm)],[22772, 22771])).
% 293.62/186.14 tff(22774,plain,
% 293.62/186.14 (node6(c_e_h_1, c_j, s10, s11) | node5(c_e_h_1, c_j, s10, s11)),
% 293.62/186.14 inference(unit_resolution,[status(thm)],[22773, 1141, 7748])).
% 293.62/186.14 tff(22775,plain,
% 293.62/186.14 ($false),
% 293.62/186.14 inference(unit_resolution,[status(thm)],[22774, 22767, 22755])).
% 293.62/186.14 tff(22776,plain,((~m_or_h_gate_v_out(c_e_h_1, c_j, s11)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s10) | m_or_h_gate_v_in2(c_e_h_1, c_j, s10) | m_or_h_gate_v_out(c_e_h_1, c_j, s10)), inference(lemma,lemma(discharge,[]))).
% 293.62/186.14 tff(22777,plain,
% 293.62/186.14 ((~m_or_h_gate_v_out(c_e_h_1, c_j, s11)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s10) | m_or_h_gate_v_out(c_e_h_1, c_j, s10)),
% 293.62/186.14 inference(unit_resolution,[status(thm)],[22776, 22744])).
% 293.62/186.14 tff(22778,plain,
% 293.62/186.14 (~m_or_h_gate_v_out(c_e_h_1, c_j, s11)),
% 293.62/186.14 inference(unit_resolution,[status(thm)],[22777, 22737, 22732])).
% 293.62/186.14 tff(22779,assumption,(~m_or_h_gate_v_in2(c_e_h_1, c_j, s11)), introduced(assumption)).
% 293.62/186.15 tff(22780,assumption,(node5(c_e_h_1, c_j, s11, s12)), introduced(assumption)).
% 293.62/186.15 tff(22781,plain,
% 293.62/186.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_1, c_j, s11) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s12)) | (~node5(c_e_h_1, c_j, s11, s12)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_1, c_j, s11) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s12)) | (~node5(c_e_h_1, c_j, s11, s12)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s11))),
% 293.62/186.15 inference(rewrite,[status(thm)],[])).
% 293.62/186.15 tff(22782,plain,
% 293.62/186.15 ((m_or_h_gate_v_in1(c_e_h_1, c_j, s11) | m_or_h_gate_v_in2(c_e_h_1, c_j, s11) | (~node5(c_e_h_1, c_j, s11, s12)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s12))) <=> (m_or_h_gate_v_in2(c_e_h_1, c_j, s11) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s12)) | (~node5(c_e_h_1, c_j, s11, s12)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s11))),
% 293.62/186.15 inference(rewrite,[status(thm)],[])).
% 293.62/186.15 tff(22783,plain,
% 293.62/186.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s11) | m_or_h_gate_v_in2(c_e_h_1, c_j, s11) | (~node5(c_e_h_1, c_j, s11, s12)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_1, c_j, s11) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s12)) | (~node5(c_e_h_1, c_j, s11, s12)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s11)))),
% 293.62/186.15 inference(monotonicity,[status(thm)],[22782])).
% 293.62/186.15 tff(22784,plain,
% 293.62/186.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s11) | m_or_h_gate_v_in2(c_e_h_1, c_j, s11) | (~node5(c_e_h_1, c_j, s11, s12)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_1, c_j, s11) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s12)) | (~node5(c_e_h_1, c_j, s11, s12)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s11))),
% 293.62/186.15 inference(transitivity,[status(thm)],[22783, 22781])).
% 293.62/186.15 tff(22785,plain,
% 293.62/186.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s11) | m_or_h_gate_v_in2(c_e_h_1, c_j, s11) | (~node5(c_e_h_1, c_j, s11, s12)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s12)))),
% 293.62/186.15 inference(quant_inst,[status(thm)],[])).
% 293.62/186.15 tff(22786,plain,
% 293.62/186.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_1, c_j, s11) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s12)) | (~node5(c_e_h_1, c_j, s11, s12)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s11)),
% 293.62/186.15 inference(modus_ponens,[status(thm)],[22785, 22784])).
% 293.62/186.15 tff(22787,plain,
% 293.62/186.15 ($false),
% 293.62/186.15 inference(unit_resolution,[status(thm)],[22786, 1159, 22094, 22780, 22779, 22731])).
% 293.62/186.15 tff(22788,plain,((~node5(c_e_h_1, c_j, s11, s12)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s12)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s11) | m_or_h_gate_v_in1(c_e_h_1, c_j, s11)), inference(lemma,lemma(discharge,[]))).
% 293.62/186.15 tff(22789,plain,
% 293.62/186.15 (~node5(c_e_h_1, c_j, s11, s12)),
% 293.62/186.15 inference(unit_resolution,[status(thm)],[22788, 22094, 22779, 22731])).
% 293.62/186.15 tff(22790,assumption,(~m_or_h_gate_v_out(c_e_h_1, c_j, s11)), introduced(assumption)).
% 293.62/186.15 tff(22791,assumption,(node6(c_e_h_1, c_j, s11, s12)), introduced(assumption)).
% 293.62/186.15 tff(22792,plain,
% 293.62/186.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s11) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s12)) | (~node6(c_e_h_1, c_j, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s11) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s12)) | (~node6(c_e_h_1, c_j, s11, s12)))),
% 293.62/186.15 inference(rewrite,[status(thm)],[])).
% 293.62/186.15 tff(22793,plain,
% 293.62/186.15 (((~node6(c_e_h_1, c_j, s11, s12)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s12)) | m_or_h_gate_v_out(c_e_h_1, c_j, s11)) <=> (m_or_h_gate_v_out(c_e_h_1, c_j, s11) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s12)) | (~node6(c_e_h_1, c_j, s11, s12)))),
% 293.62/186.15 inference(rewrite,[status(thm)],[])).
% 293.62/186.15 tff(22794,plain,
% 293.62/186.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s11, s12)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s12)) | m_or_h_gate_v_out(c_e_h_1, c_j, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s11) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s12)) | (~node6(c_e_h_1, c_j, s11, s12))))),
% 293.62/186.15 inference(monotonicity,[status(thm)],[22793])).
% 293.62/186.15 tff(22795,plain,
% 293.62/186.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s11, s12)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s12)) | m_or_h_gate_v_out(c_e_h_1, c_j, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s11) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s12)) | (~node6(c_e_h_1, c_j, s11, s12)))),
% 293.62/186.15 inference(transitivity,[status(thm)],[22794, 22792])).
% 293.62/186.15 tff(22796,plain,
% 293.62/186.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s11, s12)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s12)) | m_or_h_gate_v_out(c_e_h_1, c_j, s11))),
% 293.62/186.15 inference(quant_inst,[status(thm)],[])).
% 293.62/186.15 tff(22797,plain,
% 293.62/186.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s11) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s12)) | (~node6(c_e_h_1, c_j, s11, s12))),
% 293.62/186.15 inference(modus_ponens,[status(thm)],[22796, 22795])).
% 293.62/186.15 tff(22798,plain,
% 293.62/186.15 ($false),
% 293.62/186.15 inference(unit_resolution,[status(thm)],[22797, 1121, 22094, 22790, 22791])).
% 293.62/186.15 tff(22799,plain,((~node6(c_e_h_1, c_j, s11, s12)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s12)) | m_or_h_gate_v_out(c_e_h_1, c_j, s11)), inference(lemma,lemma(discharge,[]))).
% 293.62/186.15 tff(22800,plain,
% 293.62/186.15 (~node6(c_e_h_1, c_j, s11, s12)),
% 293.62/186.15 inference(unit_resolution,[status(thm)],[22799, 22094, 22790])).
% 293.62/186.15 tff(22801,plain,
% 293.62/186.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s11, s12)) | node5(c_e_h_1, c_j, s11, s12) | node6(c_e_h_1, c_j, s11, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s11, s12)) | node5(c_e_h_1, c_j, s11, s12) | node6(c_e_h_1, c_j, s11, s12))),
% 293.62/186.15 inference(rewrite,[status(thm)],[])).
% 293.62/186.15 tff(22802,plain,
% 293.62/186.15 ((node6(c_e_h_1, c_j, s11, s12) | node5(c_e_h_1, c_j, s11, s12) | (~trans(s11, s12))) <=> ((~trans(s11, s12)) | node5(c_e_h_1, c_j, s11, s12) | node6(c_e_h_1, c_j, s11, s12))),
% 293.62/186.15 inference(rewrite,[status(thm)],[])).
% 293.62/186.15 tff(22803,plain,
% 293.62/186.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s11, s12) | node5(c_e_h_1, c_j, s11, s12) | (~trans(s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s11, s12)) | node5(c_e_h_1, c_j, s11, s12) | node6(c_e_h_1, c_j, s11, s12)))),
% 293.62/186.15 inference(monotonicity,[status(thm)],[22802])).
% 293.62/186.15 tff(22804,plain,
% 293.62/186.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s11, s12) | node5(c_e_h_1, c_j, s11, s12) | (~trans(s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s11, s12)) | node5(c_e_h_1, c_j, s11, s12) | node6(c_e_h_1, c_j, s11, s12))),
% 293.62/186.15 inference(transitivity,[status(thm)],[22803, 22801])).
% 293.62/186.15 tff(22805,plain,
% 293.62/186.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s11, s12) | node5(c_e_h_1, c_j, s11, s12) | (~trans(s11, s12)))),
% 293.62/186.15 inference(quant_inst,[status(thm)],[])).
% 293.62/186.15 tff(22806,plain,
% 293.62/186.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s11, s12)) | node5(c_e_h_1, c_j, s11, s12) | node6(c_e_h_1, c_j, s11, s12)),
% 293.62/186.15 inference(modus_ponens,[status(thm)],[22805, 22804])).
% 293.62/186.15 tff(22807,plain,
% 293.62/186.15 (node5(c_e_h_1, c_j, s11, s12) | node6(c_e_h_1, c_j, s11, s12)),
% 293.62/186.15 inference(unit_resolution,[status(thm)],[22806, 1141, 11461])).
% 293.62/186.15 tff(22808,plain,
% 293.62/186.15 ($false),
% 293.62/186.15 inference(unit_resolution,[status(thm)],[22807, 22800, 22789])).
% 293.62/186.15 tff(22809,plain,((~m_or_h_gate_v_out(c_e_h_1, c_j, s12)) | m_or_h_gate_v_out(c_e_h_1, c_j, s11) | m_or_h_gate_v_in2(c_e_h_1, c_j, s11) | m_or_h_gate_v_in1(c_e_h_1, c_j, s11)), inference(lemma,lemma(discharge,[]))).
% 293.62/186.15 tff(22810,plain,
% 293.62/186.15 (m_or_h_gate_v_in2(c_e_h_1, c_j, s11)),
% 293.62/186.15 inference(unit_resolution,[status(thm)],[22809, 22778, 22731, 22094])).
% 293.62/186.15 tff(22811,plain,
% 293.62/186.15 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s11)) | m_cell_v_ack(c_e_h_1, s11))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s11)) | m_cell_v_ack(c_e_h_1, s11))),
% 293.62/186.15 inference(rewrite,[status(thm)],[])).
% 293.62/186.15 tff(22812,plain,
% 293.62/186.15 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s11)) | m_cell_v_ack(c_e_h_1, s11))),
% 293.62/186.15 inference(quant_inst,[status(thm)],[])).
% 293.62/186.15 tff(22813,plain,
% 293.62/186.15 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s11)) | m_cell_v_ack(c_e_h_1, s11)),
% 293.62/186.15 inference(modus_ponens,[status(thm)],[22812, 22811])).
% 293.62/186.15 tff(22814,plain,
% 293.62/186.15 (m_cell_v_ack(c_e_h_1, s11)),
% 293.62/186.15 inference(unit_resolution,[status(thm)],[22813, 1085, 22810])).
% 293.62/186.15 tff(22815,plain,
% 293.62/186.15 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s11))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s11))),
% 293.62/186.15 inference(rewrite,[status(thm)],[])).
% 293.62/186.15 tff(22816,plain,
% 293.62/186.15 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s11))),
% 293.62/186.15 inference(quant_inst,[status(thm)],[])).
% 293.62/186.15 tff(22817,plain,
% 293.62/186.15 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s11)),
% 293.62/186.15 inference(modus_ponens,[status(thm)],[22816, 22815])).
% 293.62/186.15 tff(22818,plain,
% 293.62/186.15 (node3(c_e_h_3, c_e_h_1, s11)),
% 293.62/186.15 inference(unit_resolution,[status(thm)],[22817, 2922, 1056])).
% 293.62/186.15 tff(22819,plain,
% 293.62/186.15 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s11)) | (~node3(c_e_h_3, c_e_h_1, s11)) | m_and_h_gate_v_out(c_e_h_3, c_q, s11))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s11)) | (~node3(c_e_h_3, c_e_h_1, s11)) | m_and_h_gate_v_out(c_e_h_3, c_q, s11))),
% 293.62/186.15 inference(rewrite,[status(thm)],[])).
% 293.62/186.15 tff(22820,plain,
% 293.62/186.15 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s11)) | (~node3(c_e_h_3, c_e_h_1, s11)) | m_and_h_gate_v_out(c_e_h_3, c_q, s11))),
% 293.62/186.16 inference(quant_inst,[status(thm)],[])).
% 293.62/186.16 tff(22821,plain,
% 293.62/186.16 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s11)) | (~node3(c_e_h_3, c_e_h_1, s11)) | m_and_h_gate_v_out(c_e_h_3, c_q, s11)),
% 293.62/186.16 inference(modus_ponens,[status(thm)],[22820, 22819])).
% 293.62/186.16 tff(22822,plain,
% 293.62/186.16 ((~m_cell_v_ack(c_e_h_1, s11)) | m_and_h_gate_v_out(c_e_h_3, c_q, s11)),
% 293.62/186.16 inference(unit_resolution,[status(thm)],[22821, 1073, 22818])).
% 293.62/186.16 tff(22823,plain,
% 293.62/186.16 (m_and_h_gate_v_out(c_e_h_3, c_q, s11)),
% 293.62/186.16 inference(unit_resolution,[status(thm)],[22822, 22814])).
% 293.62/186.16 tff(22824,plain,
% 293.62/186.16 (~node21(c_e_h_3, c_q, s10, s11)),
% 293.62/186.16 inference(unit_resolution,[status(thm)],[21981, 22823])).
% 293.62/186.16 tff(22825,plain,
% 293.62/186.16 (node22(c_e_h_3, c_q, s10, s11)),
% 293.62/186.16 inference(unit_resolution,[status(thm)],[21986, 22824])).
% 293.62/186.16 tff(22826,plain,
% 293.62/186.16 ($false),
% 293.62/186.16 inference(unit_resolution,[status(thm)],[21991, 108, 22823, 21988, 22825])).
% 293.62/186.16 tff(22827,plain,(m_and_h_gate_v_out(c_e_h_3, c_q, s10) | m_or_h_gate_v_in1(c_e_h_1, c_j, s11) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s12)) | m_or_h_gate_v_out(c_e_h_1, c_j, s10)), inference(lemma,lemma(discharge,[]))).
% 293.62/186.16 tff(22828,plain,
% 293.62/186.16 (m_and_h_gate_v_out(c_e_h_3, c_q, s10) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s12)) | m_or_h_gate_v_out(c_e_h_1, c_j, s10)),
% 293.62/186.16 inference(unit_resolution,[status(thm)],[22827, 22730])).
% 293.62/186.16 tff(22829,plain,
% 293.62/186.16 (m_and_h_gate_v_out(c_e_h_3, c_q, s10)),
% 293.62/186.16 inference(unit_resolution,[status(thm)],[22828, 22418, 22094])).
% 293.62/186.16 tff(22830,assumption,(m_cell_v_ack(c_e_h_1, s9)), introduced(assumption)).
% 293.62/186.16 tff(22831,plain,
% 293.62/186.16 (^[I0: $i, X: $i] : refl(((~m_cell_v_ack(I0, X)) | m_or_h_gate_v_in2(I0, c_j, X)) <=> ((~m_cell_v_ack(I0, X)) | m_or_h_gate_v_in2(I0, c_j, X)))),
% 293.62/186.16 inference(bind,[status(th)],[])).
% 293.62/186.16 tff(22832,plain,
% 293.62/186.16 (![I0: $i, X: $i] : ((~m_cell_v_ack(I0, X)) | m_or_h_gate_v_in2(I0, c_j, X)) <=> ![I0: $i, X: $i] : ((~m_cell_v_ack(I0, X)) | m_or_h_gate_v_in2(I0, c_j, X))),
% 293.62/186.16 inference(quant_intro,[status(thm)],[22831])).
% 293.62/186.16 tff(22833,plain,
% 293.62/186.16 (![I0: $i, X: $i] : ((~m_cell_v_ack(I0, X)) | m_or_h_gate_v_in2(I0, c_j, X)) <=> ![I0: $i, X: $i] : ((~m_cell_v_ack(I0, X)) | m_or_h_gate_v_in2(I0, c_j, X))),
% 293.62/186.16 inference(rewrite,[status(thm)],[])).
% 293.62/186.16 tff(22834,plain,
% 293.62/186.16 (^[I0: $i, X: $i] : rewrite((m_or_h_gate_v_in2(I0, c_j, X) | (~m_cell_v_ack(I0, X))) <=> ((~m_cell_v_ack(I0, X)) | m_or_h_gate_v_in2(I0, c_j, X)))),
% 293.62/186.16 inference(bind,[status(th)],[])).
% 293.62/186.16 tff(22835,plain,
% 293.62/186.16 (![I0: $i, X: $i] : (m_or_h_gate_v_in2(I0, c_j, X) | (~m_cell_v_ack(I0, X))) <=> ![I0: $i, X: $i] : ((~m_cell_v_ack(I0, X)) | m_or_h_gate_v_in2(I0, c_j, X))),
% 293.62/186.16 inference(quant_intro,[status(thm)],[22834])).
% 293.62/186.16 tff(22836,axiom,(![I0: $i, X: $i] : (m_or_h_gate_v_in2(I0, c_j, X) | (~m_cell_v_ack(I0, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_41')).
% 293.62/186.16 tff(22837,plain,
% 293.62/186.16 (![I0: $i, X: $i] : ((~m_cell_v_ack(I0, X)) | m_or_h_gate_v_in2(I0, c_j, X))),
% 293.62/186.16 inference(modus_ponens,[status(thm)],[22836, 22835])).
% 293.62/186.16 tff(22838,plain,
% 293.62/186.16 (![I0: $i, X: $i] : ((~m_cell_v_ack(I0, X)) | m_or_h_gate_v_in2(I0, c_j, X))),
% 293.62/186.16 inference(modus_ponens,[status(thm)],[22837, 22833])).
% 293.62/186.16 tff(22839,plain,(
% 293.62/186.16 ![I0: $i, X: $i] : ((~m_cell_v_ack(I0, X)) | m_or_h_gate_v_in2(I0, c_j, X))),
% 293.62/186.16 inference(skolemize,[status(sab)],[22838])).
% 293.62/186.16 tff(22840,plain,
% 293.62/186.16 (![I0: $i, X: $i] : ((~m_cell_v_ack(I0, X)) | m_or_h_gate_v_in2(I0, c_j, X))),
% 293.62/186.16 inference(modus_ponens,[status(thm)],[22839, 22832])).
% 293.62/186.16 tff(22841,plain,
% 293.62/186.16 (((~![I0: $i, X: $i] : ((~m_cell_v_ack(I0, X)) | m_or_h_gate_v_in2(I0, c_j, X))) | ((~m_cell_v_ack(c_e_h_1, s9)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s9))) <=> ((~![I0: $i, X: $i] : ((~m_cell_v_ack(I0, X)) | m_or_h_gate_v_in2(I0, c_j, X))) | (~m_cell_v_ack(c_e_h_1, s9)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s9))),
% 293.62/186.16 inference(rewrite,[status(thm)],[])).
% 293.62/186.16 tff(22842,plain,
% 293.62/186.16 ((~![I0: $i, X: $i] : ((~m_cell_v_ack(I0, X)) | m_or_h_gate_v_in2(I0, c_j, X))) | ((~m_cell_v_ack(c_e_h_1, s9)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s9))),
% 293.62/186.16 inference(quant_inst,[status(thm)],[])).
% 293.62/186.16 tff(22843,plain,
% 293.62/186.16 ((~![I0: $i, X: $i] : ((~m_cell_v_ack(I0, X)) | m_or_h_gate_v_in2(I0, c_j, X))) | (~m_cell_v_ack(c_e_h_1, s9)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s9)),
% 293.62/186.16 inference(modus_ponens,[status(thm)],[22842, 22841])).
% 293.62/186.16 tff(22844,plain,
% 293.62/186.16 ($false),
% 293.62/186.16 inference(unit_resolution,[status(thm)],[22843, 22840, 22830, 22095])).
% 293.62/186.16 tff(22845,plain,((~m_cell_v_ack(c_e_h_1, s9)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s9)), inference(lemma,lemma(discharge,[]))).
% 293.62/186.16 tff(22846,plain,
% 293.62/186.16 (~m_cell_v_ack(c_e_h_1, s9)),
% 293.62/186.16 inference(unit_resolution,[status(thm)],[22845, 22095])).
% 293.62/186.16 tff(22847,plain,
% 293.62/186.16 (^[I0: $i, X: $i, J0: $i] : refl((m_cell_v_ack(J0, X) | (~node3(I0, J0, X)) | (~m_and_h_gate_v_out(I0, c_q, X))) <=> (m_cell_v_ack(J0, X) | (~node3(I0, J0, X)) | (~m_and_h_gate_v_out(I0, c_q, X))))),
% 293.62/186.16 inference(bind,[status(th)],[])).
% 293.62/186.16 tff(22848,plain,
% 293.62/186.16 (![I0: $i, X: $i, J0: $i] : (m_cell_v_ack(J0, X) | (~node3(I0, J0, X)) | (~m_and_h_gate_v_out(I0, c_q, X))) <=> ![I0: $i, X: $i, J0: $i] : (m_cell_v_ack(J0, X) | (~node3(I0, J0, X)) | (~m_and_h_gate_v_out(I0, c_q, X)))),
% 293.62/186.16 inference(quant_intro,[status(thm)],[22847])).
% 293.62/186.16 tff(22849,plain,
% 293.62/186.16 (![I0: $i, X: $i, J0: $i] : (m_cell_v_ack(J0, X) | (~node3(I0, J0, X)) | (~m_and_h_gate_v_out(I0, c_q, X))) <=> ![I0: $i, X: $i, J0: $i] : (m_cell_v_ack(J0, X) | (~node3(I0, J0, X)) | (~m_and_h_gate_v_out(I0, c_q, X)))),
% 293.62/186.16 inference(rewrite,[status(thm)],[])).
% 293.62/186.16 tff(22850,plain,
% 293.62/186.16 (^[I0: $i, X: $i, J0: $i] : trans(monotonicity(rewrite((m_cell_v_ack(J0, X) | (~m_and_h_gate_v_out(I0, c_q, X))) <=> (m_cell_v_ack(J0, X) | (~m_and_h_gate_v_out(I0, c_q, X)))), (((m_cell_v_ack(J0, X) | (~m_and_h_gate_v_out(I0, c_q, X))) | (~node3(I0, J0, X))) <=> ((m_cell_v_ack(J0, X) | (~m_and_h_gate_v_out(I0, c_q, X))) | (~node3(I0, J0, X))))), rewrite(((m_cell_v_ack(J0, X) | (~m_and_h_gate_v_out(I0, c_q, X))) | (~node3(I0, J0, X))) <=> (m_cell_v_ack(J0, X) | (~node3(I0, J0, X)) | (~m_and_h_gate_v_out(I0, c_q, X)))), (((m_cell_v_ack(J0, X) | (~m_and_h_gate_v_out(I0, c_q, X))) | (~node3(I0, J0, X))) <=> (m_cell_v_ack(J0, X) | (~node3(I0, J0, X)) | (~m_and_h_gate_v_out(I0, c_q, X)))))),
% 293.62/186.16 inference(bind,[status(th)],[])).
% 293.62/186.16 tff(22851,plain,
% 293.62/186.16 (![I0: $i, X: $i, J0: $i] : ((m_cell_v_ack(J0, X) | (~m_and_h_gate_v_out(I0, c_q, X))) | (~node3(I0, J0, X))) <=> ![I0: $i, X: $i, J0: $i] : (m_cell_v_ack(J0, X) | (~node3(I0, J0, X)) | (~m_and_h_gate_v_out(I0, c_q, X)))),
% 293.62/186.16 inference(quant_intro,[status(thm)],[22850])).
% 293.62/186.16 tff(22852,axiom,(![I0: $i, X: $i, J0: $i] : ((m_cell_v_ack(J0, X) | (~m_and_h_gate_v_out(I0, c_q, X))) | (~node3(I0, J0, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_77')).
% 293.62/186.16 tff(22853,plain,
% 293.62/186.16 (![I0: $i, X: $i, J0: $i] : (m_cell_v_ack(J0, X) | (~node3(I0, J0, X)) | (~m_and_h_gate_v_out(I0, c_q, X)))),
% 293.62/186.16 inference(modus_ponens,[status(thm)],[22852, 22851])).
% 293.62/186.16 tff(22854,plain,
% 293.62/186.16 (![I0: $i, X: $i, J0: $i] : (m_cell_v_ack(J0, X) | (~node3(I0, J0, X)) | (~m_and_h_gate_v_out(I0, c_q, X)))),
% 293.62/186.16 inference(modus_ponens,[status(thm)],[22853, 22849])).
% 293.62/186.16 tff(22855,plain,(
% 293.62/186.16 ![I0: $i, X: $i, J0: $i] : (m_cell_v_ack(J0, X) | (~node3(I0, J0, X)) | (~m_and_h_gate_v_out(I0, c_q, X)))),
% 293.62/186.16 inference(skolemize,[status(sab)],[22854])).
% 293.62/186.16 tff(22856,plain,
% 293.62/186.16 (![I0: $i, X: $i, J0: $i] : (m_cell_v_ack(J0, X) | (~node3(I0, J0, X)) | (~m_and_h_gate_v_out(I0, c_q, X)))),
% 293.62/186.16 inference(modus_ponens,[status(thm)],[22855, 22848])).
% 293.62/186.16 tff(22857,plain,
% 293.62/186.16 (((~![I0: $i, X: $i, J0: $i] : (m_cell_v_ack(J0, X) | (~node3(I0, J0, X)) | (~m_and_h_gate_v_out(I0, c_q, X)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s9)) | m_cell_v_ack(c_e_h_1, s9) | (~node3(c_e_h_3, c_e_h_1, s9)))) <=> ((~![I0: $i, X: $i, J0: $i] : (m_cell_v_ack(J0, X) | (~node3(I0, J0, X)) | (~m_and_h_gate_v_out(I0, c_q, X)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s9)) | m_cell_v_ack(c_e_h_1, s9) | (~node3(c_e_h_3, c_e_h_1, s9)))),
% 293.62/186.16 inference(rewrite,[status(thm)],[])).
% 293.62/186.16 tff(22858,plain,
% 293.62/186.16 ((m_cell_v_ack(c_e_h_1, s9) | (~node3(c_e_h_3, c_e_h_1, s9)) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s9))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_q, s9)) | m_cell_v_ack(c_e_h_1, s9) | (~node3(c_e_h_3, c_e_h_1, s9)))),
% 293.62/186.16 inference(rewrite,[status(thm)],[])).
% 293.62/186.16 tff(22859,plain,
% 293.62/186.16 (((~![I0: $i, X: $i, J0: $i] : (m_cell_v_ack(J0, X) | (~node3(I0, J0, X)) | (~m_and_h_gate_v_out(I0, c_q, X)))) | (m_cell_v_ack(c_e_h_1, s9) | (~node3(c_e_h_3, c_e_h_1, s9)) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s9)))) <=> ((~![I0: $i, X: $i, J0: $i] : (m_cell_v_ack(J0, X) | (~node3(I0, J0, X)) | (~m_and_h_gate_v_out(I0, c_q, X)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s9)) | m_cell_v_ack(c_e_h_1, s9) | (~node3(c_e_h_3, c_e_h_1, s9))))),
% 293.62/186.16 inference(monotonicity,[status(thm)],[22858])).
% 293.62/186.16 tff(22860,plain,
% 293.62/186.16 (((~![I0: $i, X: $i, J0: $i] : (m_cell_v_ack(J0, X) | (~node3(I0, J0, X)) | (~m_and_h_gate_v_out(I0, c_q, X)))) | (m_cell_v_ack(c_e_h_1, s9) | (~node3(c_e_h_3, c_e_h_1, s9)) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s9)))) <=> ((~![I0: $i, X: $i, J0: $i] : (m_cell_v_ack(J0, X) | (~node3(I0, J0, X)) | (~m_and_h_gate_v_out(I0, c_q, X)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s9)) | m_cell_v_ack(c_e_h_1, s9) | (~node3(c_e_h_3, c_e_h_1, s9)))),
% 293.62/186.16 inference(transitivity,[status(thm)],[22859, 22857])).
% 293.62/186.16 tff(22861,plain,
% 293.62/186.16 ((~![I0: $i, X: $i, J0: $i] : (m_cell_v_ack(J0, X) | (~node3(I0, J0, X)) | (~m_and_h_gate_v_out(I0, c_q, X)))) | (m_cell_v_ack(c_e_h_1, s9) | (~node3(c_e_h_3, c_e_h_1, s9)) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s9)))),
% 293.62/186.16 inference(quant_inst,[status(thm)],[])).
% 293.62/186.16 tff(22862,plain,
% 293.62/186.16 ((~![I0: $i, X: $i, J0: $i] : (m_cell_v_ack(J0, X) | (~node3(I0, J0, X)) | (~m_and_h_gate_v_out(I0, c_q, X)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s9)) | m_cell_v_ack(c_e_h_1, s9) | (~node3(c_e_h_3, c_e_h_1, s9))),
% 293.62/186.16 inference(modus_ponens,[status(thm)],[22861, 22860])).
% 293.62/186.16 tff(22863,plain,
% 293.62/186.16 ((~m_and_h_gate_v_out(c_e_h_3, c_q, s9)) | m_cell_v_ack(c_e_h_1, s9)),
% 293.62/186.16 inference(unit_resolution,[status(thm)],[22862, 22856, 22080])).
% 293.62/186.16 tff(22864,plain,
% 293.62/186.16 (~m_and_h_gate_v_out(c_e_h_3, c_q, s9)),
% 293.62/186.16 inference(unit_resolution,[status(thm)],[22863, 22846])).
% 293.62/186.16 tff(22865,plain,
% 293.62/186.16 ($false),
% 293.62/186.16 inference(unit_resolution,[status(thm)],[21399, 22864, 22829])).
% 293.62/186.16 tff(22866,plain,(m_or_h_gate_v_in2(c_e_h_1, c_j, s9) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s12))), inference(lemma,lemma(discharge,[]))).
% 293.62/186.16 tff(22867,plain,
% 293.62/186.16 (~m_or_h_gate_v_out(c_e_h_1, c_j, s12)),
% 293.62/186.16 inference(unit_resolution,[status(thm)],[22866, 22093])).
% 293.62/186.16 tff(22868,assumption,(~m_or_h_gate_v_out(c_e_h_1, c_j, s12)), introduced(assumption)).
% 293.62/186.16 tff(22869,assumption,(m_or_h_gate_v_out(c_e_h_1, c_j, s13)), introduced(assumption)).
% 293.62/186.16 tff(22870,assumption,(node6(c_e_h_1, c_j, s12, s13)), introduced(assumption)).
% 293.62/186.16 tff(22871,plain,
% 293.62/186.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s12) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s13)) | (~node6(c_e_h_1, c_j, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s12) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s13)) | (~node6(c_e_h_1, c_j, s12, s13)))),
% 293.62/186.16 inference(rewrite,[status(thm)],[])).
% 293.62/186.16 tff(22872,plain,
% 293.62/186.16 (((~node6(c_e_h_1, c_j, s12, s13)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s13)) | m_or_h_gate_v_out(c_e_h_1, c_j, s12)) <=> (m_or_h_gate_v_out(c_e_h_1, c_j, s12) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s13)) | (~node6(c_e_h_1, c_j, s12, s13)))),
% 293.62/186.16 inference(rewrite,[status(thm)],[])).
% 293.62/186.16 tff(22873,plain,
% 293.62/186.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s12, s13)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s13)) | m_or_h_gate_v_out(c_e_h_1, c_j, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s12) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s13)) | (~node6(c_e_h_1, c_j, s12, s13))))),
% 293.62/186.17 inference(monotonicity,[status(thm)],[22872])).
% 293.62/186.17 tff(22874,plain,
% 293.62/186.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s12, s13)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s13)) | m_or_h_gate_v_out(c_e_h_1, c_j, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s12) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s13)) | (~node6(c_e_h_1, c_j, s12, s13)))),
% 293.62/186.17 inference(transitivity,[status(thm)],[22873, 22871])).
% 293.62/186.17 tff(22875,plain,
% 293.62/186.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s12, s13)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s13)) | m_or_h_gate_v_out(c_e_h_1, c_j, s12))),
% 293.62/186.17 inference(quant_inst,[status(thm)],[])).
% 293.62/186.17 tff(22876,plain,
% 293.62/186.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s12) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s13)) | (~node6(c_e_h_1, c_j, s12, s13))),
% 293.62/186.17 inference(modus_ponens,[status(thm)],[22875, 22874])).
% 293.62/186.17 tff(22877,plain,
% 293.62/186.17 ($false),
% 293.62/186.17 inference(unit_resolution,[status(thm)],[22876, 1121, 22869, 22868, 22870])).
% 293.62/186.17 tff(22878,plain,((~node6(c_e_h_1, c_j, s12, s13)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s13)) | m_or_h_gate_v_out(c_e_h_1, c_j, s12)), inference(lemma,lemma(discharge,[]))).
% 293.62/186.17 tff(22879,plain,
% 293.62/186.17 (~node6(c_e_h_1, c_j, s12, s13)),
% 293.62/186.17 inference(unit_resolution,[status(thm)],[22878, 22869, 22868])).
% 293.62/186.17 tff(22880,assumption,(~m_or_h_gate_v_in2(c_e_h_1, c_j, s12)), introduced(assumption)).
% 293.62/186.17 tff(22881,assumption,(m_and_h_gate_v_out(c_e_h_1, c_l, s12)), introduced(assumption)).
% 293.62/186.17 tff(22882,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s8)), introduced(assumption)).
% 293.62/186.17 tff(22883,plain,
% 293.62/186.17 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s7)) | m_c_h_element_v_out(c_e_h_1, c_h, s7))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s7)) | m_c_h_element_v_out(c_e_h_1, c_h, s7))),
% 293.62/186.17 inference(rewrite,[status(thm)],[])).
% 293.62/186.17 tff(22884,plain,
% 293.62/186.17 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s7)) | m_c_h_element_v_out(c_e_h_1, c_h, s7))),
% 293.62/186.17 inference(quant_inst,[status(thm)],[])).
% 293.62/186.17 tff(22885,plain,
% 293.62/186.17 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s7)) | m_c_h_element_v_out(c_e_h_1, c_h, s7)),
% 293.62/186.17 inference(modus_ponens,[status(thm)],[22884, 22883])).
% 293.62/186.17 tff(22886,plain,
% 293.62/186.17 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s7)),
% 293.62/186.17 inference(unit_resolution,[status(thm)],[22885, 619, 19452])).
% 293.62/186.17 tff(22887,plain,
% 293.62/186.17 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s7)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s7)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s7))),
% 293.62/186.17 inference(rewrite,[status(thm)],[])).
% 293.62/186.17 tff(22888,plain,
% 293.62/186.17 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s7)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s7))),
% 293.62/186.17 inference(quant_inst,[status(thm)],[])).
% 293.62/186.17 tff(22889,plain,
% 293.62/186.17 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s7)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s7)),
% 293.62/186.17 inference(modus_ponens,[status(thm)],[22888, 22887])).
% 293.62/186.17 tff(22890,plain,
% 293.62/186.17 (~node20(c_e_h_1, c_i, s7)),
% 293.62/186.17 inference(unit_resolution,[status(thm)],[22889, 38, 22886])).
% 293.62/186.17 tff(22891,assumption,(~node20(c_e_h_1, c_i, s7)), introduced(assumption)).
% 293.62/186.17 tff(22892,assumption,(node21(c_e_h_1, c_i, s7, s8)), introduced(assumption)).
% 293.62/186.17 tff(22893,plain,
% 293.62/186.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s8)) | node20(c_e_h_1, c_i, s7) | (~node21(c_e_h_1, c_i, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s8)) | node20(c_e_h_1, c_i, s7) | (~node21(c_e_h_1, c_i, s7, s8)))),
% 293.62/186.17 inference(rewrite,[status(thm)],[])).
% 293.62/186.17 tff(22894,plain,
% 293.62/186.17 ((node20(c_e_h_1, c_i, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s8)) | (~node21(c_e_h_1, c_i, s7, s8))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_i, s8)) | node20(c_e_h_1, c_i, s7) | (~node21(c_e_h_1, c_i, s7, s8)))),
% 293.62/186.17 inference(rewrite,[status(thm)],[])).
% 293.62/186.17 tff(22895,plain,
% 293.62/186.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s8)) | (~node21(c_e_h_1, c_i, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s8)) | node20(c_e_h_1, c_i, s7) | (~node21(c_e_h_1, c_i, s7, s8))))),
% 293.62/186.17 inference(monotonicity,[status(thm)],[22894])).
% 293.62/186.17 tff(22896,plain,
% 293.62/186.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s8)) | (~node21(c_e_h_1, c_i, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s8)) | node20(c_e_h_1, c_i, s7) | (~node21(c_e_h_1, c_i, s7, s8)))),
% 293.62/186.17 inference(transitivity,[status(thm)],[22895, 22893])).
% 293.62/186.17 tff(22897,plain,
% 293.62/186.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s8)) | (~node21(c_e_h_1, c_i, s7, s8)))),
% 293.62/186.17 inference(quant_inst,[status(thm)],[])).
% 293.62/186.17 tff(22898,plain,
% 293.62/186.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s8)) | node20(c_e_h_1, c_i, s7) | (~node21(c_e_h_1, c_i, s7, s8))),
% 293.62/186.17 inference(modus_ponens,[status(thm)],[22897, 22896])).
% 293.62/186.17 tff(22899,plain,
% 293.62/186.17 ($false),
% 293.62/186.17 inference(unit_resolution,[status(thm)],[22898, 52, 22882, 22892, 22891])).
% 293.62/186.17 tff(22900,plain,((~node21(c_e_h_1, c_i, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s8)) | node20(c_e_h_1, c_i, s7)), inference(lemma,lemma(discharge,[]))).
% 293.62/186.17 tff(22901,plain,
% 293.62/186.17 ((~node21(c_e_h_1, c_i, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s8))),
% 293.62/186.17 inference(unit_resolution,[status(thm)],[22900, 22890])).
% 293.62/186.17 tff(22902,plain,
% 293.62/186.17 (~node21(c_e_h_1, c_i, s7, s8)),
% 293.62/186.17 inference(unit_resolution,[status(thm)],[22901, 22882])).
% 293.62/186.17 tff(22903,assumption,(node22(c_e_h_1, c_i, s7, s8)), introduced(assumption)).
% 293.62/186.17 tff(22904,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_i, s7)), introduced(assumption)).
% 293.62/186.17 tff(22905,plain,
% 293.62/186.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s8)) | (~node22(c_e_h_1, c_i, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_i, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s8)) | (~node22(c_e_h_1, c_i, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_i, s7))),
% 293.62/186.17 inference(rewrite,[status(thm)],[])).
% 293.62/186.17 tff(22906,plain,
% 293.62/186.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s8)) | (~node22(c_e_h_1, c_i, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_i, s7))),
% 293.62/186.17 inference(quant_inst,[status(thm)],[])).
% 293.62/186.17 tff(22907,plain,
% 293.62/186.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s8)) | (~node22(c_e_h_1, c_i, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_i, s7)),
% 293.62/186.17 inference(modus_ponens,[status(thm)],[22906, 22905])).
% 293.62/186.17 tff(22908,plain,
% 293.62/186.17 ($false),
% 293.62/186.17 inference(unit_resolution,[status(thm)],[22907, 108, 22882, 22904, 22903])).
% 293.62/186.17 tff(22909,plain,((~node22(c_e_h_1, c_i, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s8)) | m_and_h_gate_v_out(c_e_h_1, c_i, s7)), inference(lemma,lemma(discharge,[]))).
% 293.62/186.17 tff(22910,plain,
% 293.62/186.17 ((~node22(c_e_h_1, c_i, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s8))),
% 293.62/186.17 inference(unit_resolution,[status(thm)],[22909, 22532])).
% 293.62/186.17 tff(22911,plain,
% 293.62/186.17 (~node22(c_e_h_1, c_i, s7, s8)),
% 293.62/186.17 inference(unit_resolution,[status(thm)],[22910, 22882])).
% 293.62/186.17 tff(22912,plain,
% 293.62/186.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_1, c_i, s7, s8) | node22(c_e_h_1, c_i, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_1, c_i, s7, s8) | node22(c_e_h_1, c_i, s7, s8))),
% 293.62/186.17 inference(rewrite,[status(thm)],[])).
% 293.62/186.17 tff(22913,plain,
% 293.62/186.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_1, c_i, s7, s8) | node22(c_e_h_1, c_i, s7, s8))),
% 293.62/186.17 inference(quant_inst,[status(thm)],[])).
% 293.62/186.17 tff(22914,plain,
% 293.62/186.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_1, c_i, s7, s8) | node22(c_e_h_1, c_i, s7, s8)),
% 293.62/186.17 inference(modus_ponens,[status(thm)],[22913, 22912])).
% 293.62/186.17 tff(22915,plain,
% 293.62/186.17 (node21(c_e_h_1, c_i, s7, s8) | node22(c_e_h_1, c_i, s7, s8)),
% 293.62/186.17 inference(unit_resolution,[status(thm)],[22914, 82, 1938])).
% 293.62/186.17 tff(22916,plain,
% 293.62/186.17 ($false),
% 293.62/186.17 inference(unit_resolution,[status(thm)],[22915, 22911, 22902])).
% 293.62/186.17 tff(22917,plain,(~m_and_h_gate_v_out(c_e_h_1, c_i, s8)), inference(lemma,lemma(discharge,[]))).
% 293.62/186.17 tff(22918,plain,
% 293.62/186.17 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s8)) | m_and_h_gate_v_out(c_e_h_1, c_i, s8))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s8)) | m_and_h_gate_v_out(c_e_h_1, c_i, s8))),
% 293.62/186.17 inference(rewrite,[status(thm)],[])).
% 293.62/186.17 tff(22919,plain,
% 293.62/186.17 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s8)) | m_and_h_gate_v_out(c_e_h_1, c_i, s8))),
% 293.62/186.17 inference(quant_inst,[status(thm)],[])).
% 293.62/186.17 tff(22920,plain,
% 293.62/186.17 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s8)) | m_and_h_gate_v_out(c_e_h_1, c_i, s8)),
% 293.62/186.17 inference(modus_ponens,[status(thm)],[22919, 22918])).
% 293.62/186.17 tff(22921,plain,
% 293.62/186.17 (~m_c_h_element_v_in2(c_e_h_1, c_e, s8)),
% 293.62/186.17 inference(unit_resolution,[status(thm)],[22920, 164, 22917])).
% 293.62/186.17 tff(22922,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_e, s8)), introduced(assumption)).
% 293.62/186.17 tff(22923,assumption,(~m_c_h_element_v_out(c_e_h_1, c_e, s8)), introduced(assumption)).
% 293.62/186.17 tff(22924,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s9)), introduced(assumption)).
% 293.62/186.17 tff(22925,assumption,(node15(c_e_h_1, c_e, s8, s9)), introduced(assumption)).
% 293.62/186.17 tff(22926,plain,
% 293.62/186.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s9)) | (~node15(c_e_h_1, c_e, s8, s9)) | m_c_h_element_v_out(c_e_h_1, c_e, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s9)) | (~node15(c_e_h_1, c_e, s8, s9)) | m_c_h_element_v_out(c_e_h_1, c_e, s8))),
% 293.62/186.18 inference(rewrite,[status(thm)],[])).
% 293.62/186.18 tff(22927,plain,
% 293.62/186.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s9)) | (~node15(c_e_h_1, c_e, s8, s9)) | m_c_h_element_v_out(c_e_h_1, c_e, s8))),
% 293.62/186.18 inference(quant_inst,[status(thm)],[])).
% 293.62/186.18 tff(22928,plain,
% 293.62/186.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s9)) | (~node15(c_e_h_1, c_e, s8, s9)) | m_c_h_element_v_out(c_e_h_1, c_e, s8)),
% 293.62/186.18 inference(modus_ponens,[status(thm)],[22927, 22926])).
% 293.62/186.18 tff(22929,plain,
% 293.62/186.18 ($false),
% 293.62/186.18 inference(unit_resolution,[status(thm)],[22928, 147, 22923, 22925, 22924])).
% 293.62/186.18 tff(22930,plain,((~node15(c_e_h_1, c_e, s8, s9)) | m_c_h_element_v_out(c_e_h_1, c_e, s8) | (~m_c_h_element_v_out(c_e_h_1, c_e, s9))), inference(lemma,lemma(discharge,[]))).
% 293.62/186.18 tff(22931,plain,
% 293.62/186.18 (~node15(c_e_h_1, c_e, s8, s9)),
% 293.62/186.18 inference(unit_resolution,[status(thm)],[22930, 22924, 22923])).
% 293.62/186.18 tff(22932,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_e, s8)), introduced(assumption)).
% 293.62/186.18 tff(22933,assumption,(node14(c_e_h_1, c_e, s8, s9)), introduced(assumption)).
% 293.62/186.18 tff(22934,plain,
% 293.62/186.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s9)) | (~node14(c_e_h_1, c_e, s8, s9)) | m_c_h_element_v_in1(c_e_h_1, c_e, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s9)) | (~node14(c_e_h_1, c_e, s8, s9)) | m_c_h_element_v_in1(c_e_h_1, c_e, s8))),
% 293.62/186.18 inference(rewrite,[status(thm)],[])).
% 293.62/186.18 tff(22935,plain,
% 293.62/186.18 (((~node14(c_e_h_1, c_e, s8, s9)) | m_c_h_element_v_in1(c_e_h_1, c_e, s8) | (~m_c_h_element_v_out(c_e_h_1, c_e, s9))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_e, s9)) | (~node14(c_e_h_1, c_e, s8, s9)) | m_c_h_element_v_in1(c_e_h_1, c_e, s8))),
% 293.62/186.18 inference(rewrite,[status(thm)],[])).
% 293.62/186.18 tff(22936,plain,
% 293.62/186.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s8, s9)) | m_c_h_element_v_in1(c_e_h_1, c_e, s8) | (~m_c_h_element_v_out(c_e_h_1, c_e, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s9)) | (~node14(c_e_h_1, c_e, s8, s9)) | m_c_h_element_v_in1(c_e_h_1, c_e, s8)))),
% 293.62/186.18 inference(monotonicity,[status(thm)],[22935])).
% 293.62/186.18 tff(22937,plain,
% 293.62/186.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s8, s9)) | m_c_h_element_v_in1(c_e_h_1, c_e, s8) | (~m_c_h_element_v_out(c_e_h_1, c_e, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s9)) | (~node14(c_e_h_1, c_e, s8, s9)) | m_c_h_element_v_in1(c_e_h_1, c_e, s8))),
% 293.62/186.18 inference(transitivity,[status(thm)],[22936, 22934])).
% 293.62/186.18 tff(22938,plain,
% 293.62/186.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s8, s9)) | m_c_h_element_v_in1(c_e_h_1, c_e, s8) | (~m_c_h_element_v_out(c_e_h_1, c_e, s9)))),
% 293.62/186.18 inference(quant_inst,[status(thm)],[])).
% 293.62/186.18 tff(22939,plain,
% 293.62/186.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s9)) | (~node14(c_e_h_1, c_e, s8, s9)) | m_c_h_element_v_in1(c_e_h_1, c_e, s8)),
% 293.62/186.18 inference(modus_ponens,[status(thm)],[22938, 22937])).
% 293.62/186.18 tff(22940,plain,
% 293.62/186.18 ($false),
% 293.62/186.18 inference(unit_resolution,[status(thm)],[22939, 223, 22933, 22924, 22932])).
% 293.62/186.18 tff(22941,plain,((~node14(c_e_h_1, c_e, s8, s9)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s9)) | m_c_h_element_v_in1(c_e_h_1, c_e, s8)), inference(lemma,lemma(discharge,[]))).
% 293.62/186.18 tff(22942,plain,
% 293.62/186.18 (~node14(c_e_h_1, c_e, s8, s9)),
% 293.62/186.18 inference(unit_resolution,[status(thm)],[22941, 22924, 22932])).
% 293.62/186.18 tff(22943,plain,
% 293.62/186.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s8, s9)) | node19(c_e_h_1, c_e, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s8, s9)) | node19(c_e_h_1, c_e, s8, s9))),
% 293.62/186.18 inference(rewrite,[status(thm)],[])).
% 293.62/186.18 tff(22944,plain,
% 293.62/186.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s8, s9)) | node19(c_e_h_1, c_e, s8, s9))),
% 293.62/186.18 inference(quant_inst,[status(thm)],[])).
% 293.62/186.18 tff(22945,plain,
% 293.62/186.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s8, s9)) | node19(c_e_h_1, c_e, s8, s9)),
% 293.62/186.18 inference(modus_ponens,[status(thm)],[22944, 22943])).
% 293.62/186.18 tff(22946,plain,
% 293.62/186.18 (node19(c_e_h_1, c_e, s8, s9)),
% 293.62/186.18 inference(unit_resolution,[status(thm)],[22945, 190, 1993])).
% 293.62/186.18 tff(22947,plain,
% 293.62/186.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s8) | node15(c_e_h_1, c_e, s8, s9) | node14(c_e_h_1, c_e, s8, s9) | (~node19(c_e_h_1, c_e, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_e, s8) | node15(c_e_h_1, c_e, s8, s9) | node14(c_e_h_1, c_e, s8, s9) | (~node19(c_e_h_1, c_e, s8, s9)))),
% 293.62/186.18 inference(rewrite,[status(thm)],[])).
% 293.62/186.18 tff(22948,plain,
% 293.62/186.18 ((node16(c_e_h_1, c_e, s8) | node14(c_e_h_1, c_e, s8, s9) | node15(c_e_h_1, c_e, s8, s9) | (~node19(c_e_h_1, c_e, s8, s9))) <=> (node16(c_e_h_1, c_e, s8) | node15(c_e_h_1, c_e, s8, s9) | node14(c_e_h_1, c_e, s8, s9) | (~node19(c_e_h_1, c_e, s8, s9)))),
% 293.62/186.18 inference(rewrite,[status(thm)],[])).
% 293.62/186.18 tff(22949,plain,
% 293.62/186.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s8) | node14(c_e_h_1, c_e, s8, s9) | node15(c_e_h_1, c_e, s8, s9) | (~node19(c_e_h_1, c_e, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s8) | node15(c_e_h_1, c_e, s8, s9) | node14(c_e_h_1, c_e, s8, s9) | (~node19(c_e_h_1, c_e, s8, s9))))),
% 293.62/186.18 inference(monotonicity,[status(thm)],[22948])).
% 293.62/186.18 tff(22950,plain,
% 293.62/186.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s8) | node14(c_e_h_1, c_e, s8, s9) | node15(c_e_h_1, c_e, s8, s9) | (~node19(c_e_h_1, c_e, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_e, s8) | node15(c_e_h_1, c_e, s8, s9) | node14(c_e_h_1, c_e, s8, s9) | (~node19(c_e_h_1, c_e, s8, s9)))),
% 293.62/186.18 inference(transitivity,[status(thm)],[22949, 22947])).
% 293.62/186.18 tff(22951,plain,
% 293.62/186.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s8) | node14(c_e_h_1, c_e, s8, s9) | node15(c_e_h_1, c_e, s8, s9) | (~node19(c_e_h_1, c_e, s8, s9)))),
% 293.62/186.18 inference(quant_inst,[status(thm)],[])).
% 293.62/186.18 tff(22952,plain,
% 293.62/186.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_e, s8) | node15(c_e_h_1, c_e, s8, s9) | node14(c_e_h_1, c_e, s8, s9) | (~node19(c_e_h_1, c_e, s8, s9))),
% 293.62/186.18 inference(modus_ponens,[status(thm)],[22951, 22950])).
% 293.62/186.18 tff(22953,plain,
% 293.62/186.18 (node16(c_e_h_1, c_e, s8) | node15(c_e_h_1, c_e, s8, s9) | node14(c_e_h_1, c_e, s8, s9)),
% 293.62/186.18 inference(unit_resolution,[status(thm)],[22952, 204, 22946])).
% 293.62/186.18 tff(22954,plain,
% 293.62/186.18 (node16(c_e_h_1, c_e, s8)),
% 293.62/186.18 inference(unit_resolution,[status(thm)],[22953, 22942, 22931])).
% 293.62/186.18 tff(22955,assumption,(node18(c_e_h_1, c_e, s8, s9)), introduced(assumption)).
% 293.62/186.18 tff(22956,plain,
% 293.62/186.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s8) | (~m_c_h_element_v_out(c_e_h_1, c_e, s9)) | (~node18(c_e_h_1, c_e, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s8) | (~m_c_h_element_v_out(c_e_h_1, c_e, s9)) | (~node18(c_e_h_1, c_e, s8, s9)))),
% 293.62/186.18 inference(rewrite,[status(thm)],[])).
% 293.62/186.18 tff(22957,plain,
% 293.62/186.18 (((~m_c_h_element_v_out(c_e_h_1, c_e, s9)) | m_c_h_element_v_out(c_e_h_1, c_e, s8) | (~node18(c_e_h_1, c_e, s8, s9))) <=> (m_c_h_element_v_out(c_e_h_1, c_e, s8) | (~m_c_h_element_v_out(c_e_h_1, c_e, s9)) | (~node18(c_e_h_1, c_e, s8, s9)))),
% 293.62/186.18 inference(rewrite,[status(thm)],[])).
% 293.62/186.18 tff(22958,plain,
% 293.62/186.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s9)) | m_c_h_element_v_out(c_e_h_1, c_e, s8) | (~node18(c_e_h_1, c_e, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s8) | (~m_c_h_element_v_out(c_e_h_1, c_e, s9)) | (~node18(c_e_h_1, c_e, s8, s9))))),
% 293.62/186.18 inference(monotonicity,[status(thm)],[22957])).
% 293.62/186.18 tff(22959,plain,
% 293.62/186.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s9)) | m_c_h_element_v_out(c_e_h_1, c_e, s8) | (~node18(c_e_h_1, c_e, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s8) | (~m_c_h_element_v_out(c_e_h_1, c_e, s9)) | (~node18(c_e_h_1, c_e, s8, s9)))),
% 293.62/186.18 inference(transitivity,[status(thm)],[22958, 22956])).
% 293.62/186.18 tff(22960,plain,
% 293.62/186.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s9)) | m_c_h_element_v_out(c_e_h_1, c_e, s8) | (~node18(c_e_h_1, c_e, s8, s9)))),
% 293.62/186.18 inference(quant_inst,[status(thm)],[])).
% 293.62/186.18 tff(22961,plain,
% 293.62/186.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s8) | (~m_c_h_element_v_out(c_e_h_1, c_e, s9)) | (~node18(c_e_h_1, c_e, s8, s9))),
% 293.62/186.18 inference(modus_ponens,[status(thm)],[22960, 22959])).
% 293.62/186.18 tff(22962,plain,
% 293.62/186.18 ($false),
% 293.62/186.18 inference(unit_resolution,[status(thm)],[22961, 753, 22923, 22955, 22924])).
% 293.62/186.18 tff(22963,plain,((~node18(c_e_h_1, c_e, s8, s9)) | m_c_h_element_v_out(c_e_h_1, c_e, s8) | (~m_c_h_element_v_out(c_e_h_1, c_e, s9))), inference(lemma,lemma(discharge,[]))).
% 293.62/186.18 tff(22964,plain,
% 293.62/186.18 (~node18(c_e_h_1, c_e, s8, s9)),
% 293.62/186.18 inference(unit_resolution,[status(thm)],[22963, 22924, 22923])).
% 293.62/186.18 tff(22965,plain,
% 293.62/186.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_1, c_e, s8, s9) | node17(c_e_h_1, c_e, s8) | (~node19(c_e_h_1, c_e, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_e, s8, s9) | node17(c_e_h_1, c_e, s8) | (~node19(c_e_h_1, c_e, s8, s9)))),
% 293.62/186.18 inference(rewrite,[status(thm)],[])).
% 293.62/186.18 tff(22966,plain,
% 293.62/186.18 ((node17(c_e_h_1, c_e, s8) | node18(c_e_h_1, c_e, s8, s9) | (~node19(c_e_h_1, c_e, s8, s9))) <=> (node18(c_e_h_1, c_e, s8, s9) | node17(c_e_h_1, c_e, s8) | (~node19(c_e_h_1, c_e, s8, s9)))),
% 293.62/186.18 inference(rewrite,[status(thm)],[])).
% 293.62/186.18 tff(22967,plain,
% 293.69/186.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s8) | node18(c_e_h_1, c_e, s8, s9) | (~node19(c_e_h_1, c_e, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_1, c_e, s8, s9) | node17(c_e_h_1, c_e, s8) | (~node19(c_e_h_1, c_e, s8, s9))))),
% 293.69/186.19 inference(monotonicity,[status(thm)],[22966])).
% 293.69/186.19 tff(22968,plain,
% 293.69/186.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s8) | node18(c_e_h_1, c_e, s8, s9) | (~node19(c_e_h_1, c_e, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_e, s8, s9) | node17(c_e_h_1, c_e, s8) | (~node19(c_e_h_1, c_e, s8, s9)))),
% 293.69/186.19 inference(transitivity,[status(thm)],[22967, 22965])).
% 293.69/186.19 tff(22969,plain,
% 293.69/186.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s8) | node18(c_e_h_1, c_e, s8, s9) | (~node19(c_e_h_1, c_e, s8, s9)))),
% 293.69/186.19 inference(quant_inst,[status(thm)],[])).
% 293.69/186.19 tff(22970,plain,
% 293.69/186.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_e, s8, s9) | node17(c_e_h_1, c_e, s8) | (~node19(c_e_h_1, c_e, s8, s9))),
% 293.69/186.19 inference(modus_ponens,[status(thm)],[22969, 22968])).
% 293.69/186.19 tff(22971,plain,
% 293.69/186.19 (node18(c_e_h_1, c_e, s8, s9) | node17(c_e_h_1, c_e, s8)),
% 293.69/186.19 inference(unit_resolution,[status(thm)],[22970, 776, 22946])).
% 293.69/186.19 tff(22972,plain,
% 293.69/186.19 (node17(c_e_h_1, c_e, s8)),
% 293.69/186.19 inference(unit_resolution,[status(thm)],[22971, 22964])).
% 293.69/186.19 tff(22973,assumption,(node17(c_e_h_1, c_e, s8)), introduced(assumption)).
% 293.69/186.19 tff(22974,assumption,(node16(c_e_h_1, c_e, s8)), introduced(assumption)).
% 293.69/186.19 tff(22975,plain,
% 293.69/186.19 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s8) | (~node17(c_e_h_1, c_e, s8)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s8) | (~node17(c_e_h_1, c_e, s8)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s8)))),
% 293.69/186.19 inference(rewrite,[status(thm)],[])).
% 293.69/186.19 tff(22976,plain,
% 293.69/186.19 ((m_c_h_element_v_in1(c_e_h_1, c_e, s8) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s8)) | (~node17(c_e_h_1, c_e, s8))) <=> (m_c_h_element_v_in1(c_e_h_1, c_e, s8) | (~node17(c_e_h_1, c_e, s8)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s8)))),
% 293.69/186.19 inference(rewrite,[status(thm)],[])).
% 293.69/186.19 tff(22977,plain,
% 293.69/186.19 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s8) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s8)) | (~node17(c_e_h_1, c_e, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s8) | (~node17(c_e_h_1, c_e, s8)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s8))))),
% 293.69/186.19 inference(monotonicity,[status(thm)],[22976])).
% 293.69/186.19 tff(22978,plain,
% 293.69/186.19 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s8) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s8)) | (~node17(c_e_h_1, c_e, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s8) | (~node17(c_e_h_1, c_e, s8)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s8)))),
% 293.69/186.19 inference(transitivity,[status(thm)],[22977, 22975])).
% 293.69/186.19 tff(22979,plain,
% 293.69/186.19 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s8) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s8)) | (~node17(c_e_h_1, c_e, s8)))),
% 293.69/186.19 inference(quant_inst,[status(thm)],[])).
% 293.69/186.19 tff(22980,plain,
% 293.69/186.19 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s8) | (~node17(c_e_h_1, c_e, s8)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s8))),
% 293.69/186.19 inference(modus_ponens,[status(thm)],[22979, 22978])).
% 293.69/186.19 tff(22981,plain,
% 293.69/186.19 (m_c_h_element_v_in1(c_e_h_1, c_e, s8) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s8))),
% 293.69/186.19 inference(unit_resolution,[status(thm)],[22980, 859, 22973])).
% 293.69/186.19 tff(22982,plain,
% 293.69/186.19 (~m_c_h_element_v_in2(c_e_h_1, c_e, s8)),
% 293.69/186.19 inference(unit_resolution,[status(thm)],[22981, 22932])).
% 293.69/186.19 tff(22983,plain,
% 293.69/186.19 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s8)) | m_c_h_element_v_in1(c_e_h_1, c_e, s8) | m_c_h_element_v_in2(c_e_h_1, c_e, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s8)) | m_c_h_element_v_in1(c_e_h_1, c_e, s8) | m_c_h_element_v_in2(c_e_h_1, c_e, s8))),
% 293.69/186.19 inference(rewrite,[status(thm)],[])).
% 293.69/186.19 tff(22984,plain,
% 293.69/186.19 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s8)) | m_c_h_element_v_in1(c_e_h_1, c_e, s8) | m_c_h_element_v_in2(c_e_h_1, c_e, s8))),
% 293.69/186.19 inference(quant_inst,[status(thm)],[])).
% 293.69/186.19 tff(22985,plain,
% 293.69/186.19 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s8)) | m_c_h_element_v_in1(c_e_h_1, c_e, s8) | m_c_h_element_v_in2(c_e_h_1, c_e, s8)),
% 293.69/186.19 inference(modus_ponens,[status(thm)],[22984, 22983])).
% 293.69/186.19 tff(22986,plain,
% 293.69/186.19 (m_c_h_element_v_in1(c_e_h_1, c_e, s8) | m_c_h_element_v_in2(c_e_h_1, c_e, s8)),
% 293.69/186.19 inference(unit_resolution,[status(thm)],[22985, 178, 22974])).
% 293.69/186.19 tff(22987,plain,
% 293.69/186.19 ($false),
% 293.69/186.19 inference(unit_resolution,[status(thm)],[22986, 22982, 22932])).
% 293.69/186.19 tff(22988,plain,(m_c_h_element_v_in1(c_e_h_1, c_e, s8) | (~node16(c_e_h_1, c_e, s8)) | (~node17(c_e_h_1, c_e, s8))), inference(lemma,lemma(discharge,[]))).
% 293.69/186.19 tff(22989,plain,
% 293.69/186.19 (m_c_h_element_v_in1(c_e_h_1, c_e, s8)),
% 293.69/186.19 inference(unit_resolution,[status(thm)],[22988, 22974, 22973])).
% 293.69/186.19 tff(22990,plain,
% 293.69/186.19 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s8)) | (~node17(c_e_h_1, c_e, s8)) | m_c_h_element_v_in2(c_e_h_1, c_e, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s8)) | (~node17(c_e_h_1, c_e, s8)) | m_c_h_element_v_in2(c_e_h_1, c_e, s8))),
% 293.69/186.19 inference(rewrite,[status(thm)],[])).
% 293.69/186.19 tff(22991,plain,
% 293.69/186.19 (((~m_c_h_element_v_in1(c_e_h_1, c_e, s8)) | m_c_h_element_v_in2(c_e_h_1, c_e, s8) | (~node17(c_e_h_1, c_e, s8))) <=> ((~m_c_h_element_v_in1(c_e_h_1, c_e, s8)) | (~node17(c_e_h_1, c_e, s8)) | m_c_h_element_v_in2(c_e_h_1, c_e, s8))),
% 293.69/186.19 inference(rewrite,[status(thm)],[])).
% 293.69/186.19 tff(22992,plain,
% 293.69/186.19 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s8)) | m_c_h_element_v_in2(c_e_h_1, c_e, s8) | (~node17(c_e_h_1, c_e, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s8)) | (~node17(c_e_h_1, c_e, s8)) | m_c_h_element_v_in2(c_e_h_1, c_e, s8)))),
% 293.69/186.19 inference(monotonicity,[status(thm)],[22991])).
% 293.69/186.19 tff(22993,plain,
% 293.69/186.19 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s8)) | m_c_h_element_v_in2(c_e_h_1, c_e, s8) | (~node17(c_e_h_1, c_e, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s8)) | (~node17(c_e_h_1, c_e, s8)) | m_c_h_element_v_in2(c_e_h_1, c_e, s8))),
% 293.69/186.19 inference(transitivity,[status(thm)],[22992, 22990])).
% 293.69/186.19 tff(22994,plain,
% 293.69/186.19 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s8)) | m_c_h_element_v_in2(c_e_h_1, c_e, s8) | (~node17(c_e_h_1, c_e, s8)))),
% 293.69/186.19 inference(quant_inst,[status(thm)],[])).
% 293.69/186.19 tff(22995,plain,
% 293.69/186.19 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s8)) | (~node17(c_e_h_1, c_e, s8)) | m_c_h_element_v_in2(c_e_h_1, c_e, s8)),
% 293.69/186.19 inference(modus_ponens,[status(thm)],[22994, 22993])).
% 293.69/186.19 tff(22996,plain,
% 293.69/186.19 ((~m_c_h_element_v_in1(c_e_h_1, c_e, s8)) | m_c_h_element_v_in2(c_e_h_1, c_e, s8)),
% 293.69/186.19 inference(unit_resolution,[status(thm)],[22995, 919, 22973])).
% 293.69/186.19 tff(22997,plain,
% 293.69/186.19 (m_c_h_element_v_in2(c_e_h_1, c_e, s8)),
% 293.69/186.19 inference(unit_resolution,[status(thm)],[22996, 22989])).
% 293.69/186.19 tff(22998,plain,
% 293.69/186.19 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s8)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s8)) | (~node16(c_e_h_1, c_e, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s8)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s8)) | (~node16(c_e_h_1, c_e, s8)))),
% 293.69/186.19 inference(rewrite,[status(thm)],[])).
% 293.69/186.19 tff(22999,plain,
% 293.69/186.19 (((~node16(c_e_h_1, c_e, s8)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s8)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s8))) <=> ((~m_c_h_element_v_in1(c_e_h_1, c_e, s8)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s8)) | (~node16(c_e_h_1, c_e, s8)))),
% 293.69/186.19 inference(rewrite,[status(thm)],[])).
% 293.69/186.19 tff(23000,plain,
% 293.69/186.19 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s8)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s8)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s8)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s8)) | (~node16(c_e_h_1, c_e, s8))))),
% 293.69/186.19 inference(monotonicity,[status(thm)],[22999])).
% 293.69/186.19 tff(23001,plain,
% 293.69/186.19 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s8)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s8)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s8)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s8)) | (~node16(c_e_h_1, c_e, s8)))),
% 293.69/186.19 inference(transitivity,[status(thm)],[23000, 22998])).
% 293.69/186.19 tff(23002,plain,
% 293.69/186.19 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s8)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s8)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s8)))),
% 293.69/186.19 inference(quant_inst,[status(thm)],[])).
% 293.69/186.19 tff(23003,plain,
% 293.69/186.19 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s8)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s8)) | (~node16(c_e_h_1, c_e, s8))),
% 293.69/186.19 inference(modus_ponens,[status(thm)],[23002, 23001])).
% 293.69/186.19 tff(23004,plain,
% 293.69/186.19 ((~m_c_h_element_v_in1(c_e_h_1, c_e, s8)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s8))),
% 293.69/186.19 inference(unit_resolution,[status(thm)],[23003, 2307, 22974])).
% 293.69/186.19 tff(23005,plain,
% 293.69/186.19 ($false),
% 293.69/186.19 inference(unit_resolution,[status(thm)],[23004, 22997, 22989])).
% 293.69/186.20 tff(23006,plain,((~node16(c_e_h_1, c_e, s8)) | (~node17(c_e_h_1, c_e, s8))), inference(lemma,lemma(discharge,[]))).
% 293.69/186.20 tff(23007,plain,
% 293.69/186.20 ($false),
% 293.69/186.20 inference(unit_resolution,[status(thm)],[23006, 22972, 22954])).
% 293.69/186.20 tff(23008,plain,((~m_c_h_element_v_out(c_e_h_1, c_e, s9)) | m_c_h_element_v_out(c_e_h_1, c_e, s8) | m_c_h_element_v_in1(c_e_h_1, c_e, s8)), inference(lemma,lemma(discharge,[]))).
% 293.69/186.20 tff(23009,plain,
% 293.69/186.20 (m_c_h_element_v_in1(c_e_h_1, c_e, s8)),
% 293.69/186.20 inference(unit_resolution,[status(thm)],[23008, 22924, 22923])).
% 293.69/186.20 tff(23010,plain,
% 293.69/186.20 ($false),
% 293.69/186.20 inference(unit_resolution,[status(thm)],[22995, 919, 22972, 23009, 22922])).
% 293.69/186.20 tff(23011,plain,((~m_c_h_element_v_out(c_e_h_1, c_e, s9)) | m_c_h_element_v_in2(c_e_h_1, c_e, s8) | m_c_h_element_v_out(c_e_h_1, c_e, s8)), inference(lemma,lemma(discharge,[]))).
% 293.69/186.20 tff(23012,plain,
% 293.69/186.20 ((~m_c_h_element_v_out(c_e_h_1, c_e, s9)) | m_c_h_element_v_out(c_e_h_1, c_e, s8)),
% 293.69/186.20 inference(unit_resolution,[status(thm)],[23011, 22921])).
% 293.69/186.20 tff(23013,plain,
% 293.69/186.20 (~m_c_h_element_v_out(c_e_h_1, c_e, s9)),
% 293.69/186.20 inference(unit_resolution,[status(thm)],[23012, 22540])).
% 293.69/186.20 tff(23014,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s9)), introduced(assumption)).
% 293.69/186.20 tff(23015,assumption,(~m_c_h_element_v_out(c_e_h_1, c_e, s9)), introduced(assumption)).
% 293.69/186.20 tff(23016,plain,
% 293.69/186.20 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s9) | m_c_h_element_v_out(c_e_h_1, c_e, s9))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s9) | m_c_h_element_v_out(c_e_h_1, c_e, s9))),
% 293.69/186.20 inference(rewrite,[status(thm)],[])).
% 293.69/186.20 tff(23017,plain,
% 293.69/186.20 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s9) | m_c_h_element_v_out(c_e_h_1, c_e, s9))),
% 293.69/186.20 inference(quant_inst,[status(thm)],[])).
% 293.69/186.20 tff(23018,plain,
% 293.69/186.20 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s9) | m_c_h_element_v_out(c_e_h_1, c_e, s9)),
% 293.69/186.20 inference(modus_ponens,[status(thm)],[23017, 23016])).
% 293.69/186.20 tff(23019,plain,
% 293.69/186.20 ($false),
% 293.69/186.20 inference(unit_resolution,[status(thm)],[23018, 7856, 23015, 23014])).
% 293.69/186.20 tff(23020,plain,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s9) | m_c_h_element_v_out(c_e_h_1, c_e, s9)), inference(lemma,lemma(discharge,[]))).
% 293.69/186.20 tff(23021,plain,
% 293.69/186.20 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s9)),
% 293.69/186.20 inference(unit_resolution,[status(thm)],[23020, 23013])).
% 293.69/186.20 tff(23022,plain,
% 293.69/186.20 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9)),
% 293.69/186.20 inference(unit_resolution,[status(thm)],[22586, 19255, 18165, 22547])).
% 293.69/186.20 tff(23023,plain,
% 293.69/186.20 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s9)),
% 293.69/186.20 inference(unit_resolution,[status(thm)],[22591, 4958, 23022])).
% 293.69/186.20 tff(23024,plain,
% 293.69/186.20 (~node9(c_e_h_1, c_m, s9)),
% 293.69/186.20 inference(unit_resolution,[status(thm)],[22595, 4972, 23023])).
% 293.69/186.20 tff(23025,plain,
% 293.69/186.20 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s8)),
% 293.69/186.20 inference(unit_resolution,[status(thm)],[19282, 19255, 22549])).
% 293.69/186.20 tff(23026,plain,
% 293.69/186.20 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s8)),
% 293.69/186.20 inference(unit_resolution,[status(thm)],[22600, 4958, 23025])).
% 293.69/186.20 tff(23027,plain,
% 293.69/186.20 (~node9(c_e_h_1, c_m, s8)),
% 293.69/186.20 inference(unit_resolution,[status(thm)],[22604, 4972, 23026])).
% 293.69/186.20 tff(23028,plain,
% 293.69/186.20 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)),
% 293.69/186.20 inference(unit_resolution,[status(thm)],[22631, 23027, 22551])).
% 293.69/186.20 tff(23029,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)), introduced(assumption)).
% 293.69/186.20 tff(23030,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s9)), introduced(assumption)).
% 293.69/186.20 tff(23031,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10)), introduced(assumption)).
% 293.69/186.20 tff(23032,plain,
% 293.69/186.20 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9)),
% 293.69/186.20 inference(unit_resolution,[status(thm)],[22586, 18165, 22547, 19255])).
% 293.69/186.20 tff(23033,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s9)), introduced(assumption)).
% 293.69/186.20 tff(23034,assumption,(node10(c_e_h_1, c_n, s9, s10)), introduced(assumption)).
% 293.69/186.20 tff(23035,plain,
% 293.69/186.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s9)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s9)) | (~node10(c_e_h_1, c_n, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s9)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s9)) | (~node10(c_e_h_1, c_n, s9, s10)))),
% 293.69/186.20 inference(rewrite,[status(thm)],[])).
% 293.69/186.20 tff(23036,plain,
% 293.69/186.20 (((~node10(c_e_h_1, c_n, s9, s10)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s9)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10)) <=> ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s9)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s9)) | (~node10(c_e_h_1, c_n, s9, s10)))),
% 293.69/186.20 inference(rewrite,[status(thm)],[])).
% 293.69/186.20 tff(23037,plain,
% 293.69/186.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s9, s10)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s9)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s9)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s9)) | (~node10(c_e_h_1, c_n, s9, s10))))),
% 293.69/186.20 inference(monotonicity,[status(thm)],[23036])).
% 293.69/186.20 tff(23038,plain,
% 293.69/186.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s9, s10)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s9)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s9)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s9)) | (~node10(c_e_h_1, c_n, s9, s10)))),
% 293.69/186.20 inference(transitivity,[status(thm)],[23037, 23035])).
% 293.69/186.20 tff(23039,plain,
% 293.69/186.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s9, s10)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s9)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10))),
% 293.69/186.20 inference(quant_inst,[status(thm)],[])).
% 293.69/186.20 tff(23040,plain,
% 293.69/186.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s9)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s9)) | (~node10(c_e_h_1, c_n, s9, s10))),
% 293.69/186.20 inference(modus_ponens,[status(thm)],[23039, 23038])).
% 293.69/186.20 tff(23041,plain,
% 293.69/186.20 ($false),
% 293.69/186.20 inference(unit_resolution,[status(thm)],[23040, 5718, 23033, 23031, 23034, 23030])).
% 293.69/186.20 tff(23042,plain,((~node10(c_e_h_1, c_n, s9, s10)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s9)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s9))), inference(lemma,lemma(discharge,[]))).
% 293.69/186.20 tff(23043,plain,
% 293.69/186.20 (~node10(c_e_h_1, c_n, s9, s10)),
% 293.69/186.20 inference(unit_resolution,[status(thm)],[23042, 23031, 23033, 23030])).
% 293.69/186.20 tff(23044,plain,
% 293.69/186.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s9, s10)) | node10(c_e_h_1, c_n, s9, s10) | node11(c_e_h_1, c_n, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s9, s10)) | node10(c_e_h_1, c_n, s9, s10) | node11(c_e_h_1, c_n, s9, s10))),
% 293.69/186.20 inference(rewrite,[status(thm)],[])).
% 293.69/186.20 tff(23045,plain,
% 293.69/186.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s9, s10)) | node10(c_e_h_1, c_n, s9, s10) | node11(c_e_h_1, c_n, s9, s10))),
% 293.69/186.20 inference(quant_inst,[status(thm)],[])).
% 293.69/186.20 tff(23046,plain,
% 293.69/186.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s9, s10)) | node10(c_e_h_1, c_n, s9, s10) | node11(c_e_h_1, c_n, s9, s10)),
% 293.69/186.20 inference(modus_ponens,[status(thm)],[23045, 23044])).
% 293.69/186.20 tff(23047,plain,
% 293.69/186.20 (node10(c_e_h_1, c_n, s9, s10) | node11(c_e_h_1, c_n, s9, s10)),
% 293.69/186.20 inference(unit_resolution,[status(thm)],[23046, 5002, 7676])).
% 293.69/186.20 tff(23048,plain,
% 293.69/186.20 (node11(c_e_h_1, c_n, s9, s10)),
% 293.69/186.20 inference(unit_resolution,[status(thm)],[23047, 23043])).
% 293.69/186.20 tff(23049,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9)), introduced(assumption)).
% 293.69/186.20 tff(23050,plain,
% 293.69/186.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9)) | (~node11(c_e_h_1, c_n, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9)) | (~node11(c_e_h_1, c_n, s9, s10)))),
% 293.69/186.20 inference(rewrite,[status(thm)],[])).
% 293.69/186.20 tff(23051,plain,
% 293.69/186.20 ((m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10) | (~node11(c_e_h_1, c_n, s9, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9))) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9)) | (~node11(c_e_h_1, c_n, s9, s10)))),
% 293.69/186.20 inference(rewrite,[status(thm)],[])).
% 293.69/186.20 tff(23052,plain,
% 293.69/186.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10) | (~node11(c_e_h_1, c_n, s9, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9)) | (~node11(c_e_h_1, c_n, s9, s10))))),
% 293.69/186.20 inference(monotonicity,[status(thm)],[23051])).
% 293.69/186.20 tff(23053,plain,
% 293.69/186.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10) | (~node11(c_e_h_1, c_n, s9, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9)) | (~node11(c_e_h_1, c_n, s9, s10)))),
% 293.69/186.20 inference(transitivity,[status(thm)],[23052, 23050])).
% 293.69/186.20 tff(23054,plain,
% 293.69/186.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10) | (~node11(c_e_h_1, c_n, s9, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9)))),
% 293.69/186.21 inference(quant_inst,[status(thm)],[])).
% 293.69/186.21 tff(23055,plain,
% 293.69/186.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9)) | (~node11(c_e_h_1, c_n, s9, s10))),
% 293.69/186.21 inference(modus_ponens,[status(thm)],[23054, 23053])).
% 293.69/186.21 tff(23056,plain,
% 293.69/186.21 ($false),
% 293.69/186.21 inference(unit_resolution,[status(thm)],[23055, 5742, 23049, 23031, 23048])).
% 293.69/186.21 tff(23057,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s9)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s9))), inference(lemma,lemma(discharge,[]))).
% 293.69/186.21 tff(23058,plain,
% 293.69/186.21 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s9)),
% 293.69/186.21 inference(unit_resolution,[status(thm)],[23057, 23032, 23031, 23030])).
% 293.69/186.21 tff(23059,plain,
% 293.69/186.21 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s9) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s9) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9))),
% 293.69/186.21 inference(rewrite,[status(thm)],[])).
% 293.69/186.21 tff(23060,plain,
% 293.69/186.21 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s9) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9))),
% 293.69/186.21 inference(quant_inst,[status(thm)],[])).
% 293.69/186.21 tff(23061,plain,
% 293.69/186.21 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s9) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)),
% 293.69/186.21 inference(modus_ponens,[status(thm)],[23060, 23059])).
% 293.69/186.21 tff(23062,plain,
% 293.69/186.21 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s9) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)),
% 293.69/186.21 inference(unit_resolution,[status(thm)],[23061, 7868])).
% 293.69/186.21 tff(23063,plain,
% 293.69/186.21 (m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)),
% 293.69/186.21 inference(unit_resolution,[status(thm)],[23062, 23058])).
% 293.69/186.21 tff(23064,plain,
% 293.69/186.21 (node9(c_e_h_1, c_m, s8)),
% 293.69/186.21 inference(unit_resolution,[status(thm)],[22631, 23063, 22551])).
% 293.69/186.21 tff(23065,plain,
% 293.69/186.21 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s8)),
% 293.69/186.21 inference(unit_resolution,[status(thm)],[22600, 4958, 22550])).
% 293.69/186.21 tff(23066,plain,
% 293.69/186.21 ($false),
% 293.69/186.21 inference(unit_resolution,[status(thm)],[22604, 4972, 23065, 23064])).
% 293.69/186.21 tff(23067,plain,((~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s8))), inference(lemma,lemma(discharge,[]))).
% 293.69/186.21 tff(23068,plain,
% 293.69/186.21 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10)),
% 293.69/186.21 inference(unit_resolution,[status(thm)],[23067, 19255, 18165, 22547, 23030])).
% 293.69/186.21 tff(23069,plain,
% 293.69/186.21 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10)))),
% 293.69/186.21 inference(rewrite,[status(thm)],[])).
% 293.69/186.21 tff(23070,plain,
% 293.69/186.21 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10)))),
% 293.69/186.21 inference(quant_inst,[status(thm)],[])).
% 293.69/186.21 tff(23071,plain,
% 293.69/186.21 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10))),
% 293.69/186.21 inference(modus_ponens,[status(thm)],[23070, 23069])).
% 293.69/186.21 tff(23072,plain,
% 293.69/186.21 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s10)),
% 293.69/186.21 inference(unit_resolution,[status(thm)],[23071, 4958, 23068])).
% 293.69/186.21 tff(23073,plain,
% 293.69/186.21 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s10)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s10))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s10)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s10))),
% 293.69/186.21 inference(rewrite,[status(thm)],[])).
% 293.69/186.21 tff(23074,plain,
% 293.69/186.21 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s10)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s10))),
% 293.69/186.21 inference(quant_inst,[status(thm)],[])).
% 293.69/186.21 tff(23075,plain,
% 293.69/186.21 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s10)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s10)),
% 293.69/186.21 inference(modus_ponens,[status(thm)],[23074, 23073])).
% 293.69/186.21 tff(23076,plain,
% 293.69/186.21 (~node9(c_e_h_1, c_m, s10)),
% 293.69/186.21 inference(unit_resolution,[status(thm)],[23075, 4972, 23072])).
% 293.69/186.21 tff(23077,assumption,(~node9(c_e_h_1, c_m, s10)), introduced(assumption)).
% 293.69/186.21 tff(23078,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)), introduced(assumption)).
% 293.69/186.21 tff(23079,assumption,(node11(c_e_h_1, c_m, s10, s11)), introduced(assumption)).
% 293.69/186.21 tff(23080,plain,
% 293.69/186.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)) | (~node11(c_e_h_1, c_m, s10, s11)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)) | (~node11(c_e_h_1, c_m, s10, s11)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10))),
% 293.69/186.21 inference(rewrite,[status(thm)],[])).
% 293.69/186.21 tff(23081,plain,
% 293.69/186.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)) | (~node11(c_e_h_1, c_m, s10, s11)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10))),
% 293.69/186.21 inference(quant_inst,[status(thm)],[])).
% 293.69/186.21 tff(23082,plain,
% 293.69/186.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)) | (~node11(c_e_h_1, c_m, s10, s11)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)),
% 293.69/186.21 inference(modus_ponens,[status(thm)],[23081, 23080])).
% 293.69/186.21 tff(23083,plain,
% 293.69/186.21 ($false),
% 293.69/186.21 inference(unit_resolution,[status(thm)],[23082, 5017, 23078, 23029, 23079])).
% 293.69/186.21 tff(23084,plain,((~node11(c_e_h_1, c_m, s10, s11)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11))), inference(lemma,lemma(discharge,[]))).
% 293.69/186.21 tff(23085,plain,
% 293.69/186.21 (~node11(c_e_h_1, c_m, s10, s11)),
% 293.69/186.21 inference(unit_resolution,[status(thm)],[23084, 23029, 23078])).
% 293.69/186.21 tff(23086,plain,
% 293.69/186.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s10, s11)) | node10(c_e_h_1, c_m, s10, s11) | node11(c_e_h_1, c_m, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s10, s11)) | node10(c_e_h_1, c_m, s10, s11) | node11(c_e_h_1, c_m, s10, s11))),
% 293.69/186.21 inference(rewrite,[status(thm)],[])).
% 293.69/186.21 tff(23087,plain,
% 293.69/186.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s10, s11)) | node10(c_e_h_1, c_m, s10, s11) | node11(c_e_h_1, c_m, s10, s11))),
% 293.69/186.21 inference(quant_inst,[status(thm)],[])).
% 293.69/186.21 tff(23088,plain,
% 293.69/186.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s10, s11)) | node10(c_e_h_1, c_m, s10, s11) | node11(c_e_h_1, c_m, s10, s11)),
% 293.69/186.21 inference(modus_ponens,[status(thm)],[23087, 23086])).
% 293.69/186.21 tff(23089,plain,
% 293.69/186.21 (node10(c_e_h_1, c_m, s10, s11) | node11(c_e_h_1, c_m, s10, s11)),
% 293.69/186.21 inference(unit_resolution,[status(thm)],[23088, 5002, 7748])).
% 293.69/186.21 tff(23090,plain,
% 293.69/186.21 (node10(c_e_h_1, c_m, s10, s11)),
% 293.69/186.21 inference(unit_resolution,[status(thm)],[23089, 23085])).
% 293.69/186.21 tff(23091,plain,
% 293.69/186.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~node10(c_e_h_1, c_m, s10, s11)) | node9(c_e_h_1, c_m, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~node10(c_e_h_1, c_m, s10, s11)) | node9(c_e_h_1, c_m, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)))),
% 293.69/186.21 inference(rewrite,[status(thm)],[])).
% 293.69/186.21 tff(23092,plain,
% 293.69/186.21 ((node9(c_e_h_1, c_m, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)) | (~node10(c_e_h_1, c_m, s10, s11))) <=> ((~node10(c_e_h_1, c_m, s10, s11)) | node9(c_e_h_1, c_m, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)))),
% 293.69/186.21 inference(rewrite,[status(thm)],[])).
% 293.69/186.21 tff(23093,plain,
% 293.69/186.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)) | (~node10(c_e_h_1, c_m, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~node10(c_e_h_1, c_m, s10, s11)) | node9(c_e_h_1, c_m, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11))))),
% 293.69/186.21 inference(monotonicity,[status(thm)],[23092])).
% 293.69/186.21 tff(23094,plain,
% 293.69/186.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)) | (~node10(c_e_h_1, c_m, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~node10(c_e_h_1, c_m, s10, s11)) | node9(c_e_h_1, c_m, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)))),
% 293.69/186.21 inference(transitivity,[status(thm)],[23093, 23091])).
% 293.69/186.21 tff(23095,plain,
% 293.69/186.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)) | (~node10(c_e_h_1, c_m, s10, s11)))),
% 293.69/186.21 inference(quant_inst,[status(thm)],[])).
% 293.69/186.21 tff(23096,plain,
% 293.69/186.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~node10(c_e_h_1, c_m, s10, s11)) | node9(c_e_h_1, c_m, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11))),
% 293.69/186.21 inference(modus_ponens,[status(thm)],[23095, 23094])).
% 293.69/186.21 tff(23097,plain,
% 293.69/186.21 ($false),
% 293.69/186.21 inference(unit_resolution,[status(thm)],[23096, 4986, 23029, 23090, 23077])).
% 293.69/186.21 tff(23098,plain,((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)) | node9(c_e_h_1, c_m, s10) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)), inference(lemma,lemma(discharge,[]))).
% 293.69/186.21 tff(23099,plain,
% 293.69/186.21 (m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)),
% 293.69/186.21 inference(unit_resolution,[status(thm)],[23098, 23076, 23029])).
% 293.69/186.21 tff(23100,plain,
% 293.69/186.21 (~node11(c_e_h_1, c_m, s9, s10)),
% 293.69/186.21 inference(unit_resolution,[status(thm)],[22641, 23099, 23028])).
% 293.69/186.21 tff(23101,plain,
% 293.69/186.21 (node10(c_e_h_1, c_m, s9, s10)),
% 293.69/186.21 inference(unit_resolution,[status(thm)],[22646, 23100])).
% 293.69/186.21 tff(23102,plain,
% 293.69/186.21 ($false),
% 293.69/186.21 inference(unit_resolution,[status(thm)],[22653, 4986, 23099, 23101, 23024])).
% 293.69/186.21 tff(23103,plain,((~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s6)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s9))), inference(lemma,lemma(discharge,[]))).
% 293.69/186.21 tff(23104,plain,
% 293.69/186.21 ((~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s9))),
% 293.69/186.22 inference(unit_resolution,[status(thm)],[23103, 17887])).
% 293.69/186.22 tff(23105,plain,
% 293.69/186.22 ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s8)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s9))),
% 293.69/186.22 inference(unit_resolution,[status(thm)],[23104, 19216])).
% 293.69/186.22 tff(23106,plain,
% 293.69/186.22 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)),
% 293.69/186.22 inference(unit_resolution,[status(thm)],[23105, 23021, 22545])).
% 293.69/186.22 tff(23107,plain,
% 293.69/186.22 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s11)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s11)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11))),
% 293.69/186.22 inference(rewrite,[status(thm)],[])).
% 293.69/186.22 tff(23108,plain,
% 293.69/186.22 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s11)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11))),
% 293.69/186.22 inference(quant_inst,[status(thm)],[])).
% 293.69/186.22 tff(23109,plain,
% 293.69/186.22 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s11)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)),
% 293.69/186.22 inference(modus_ponens,[status(thm)],[23108, 23107])).
% 293.69/186.22 tff(23110,plain,
% 293.69/186.22 (~m_and_h_gate_v_in2(c_e_h_1, c_l, s11)),
% 293.69/186.22 inference(unit_resolution,[status(thm)],[23109, 4549, 23106])).
% 293.69/186.22 tff(23111,plain,
% 293.69/186.22 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s11)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s11))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s11)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s11))),
% 293.69/186.22 inference(rewrite,[status(thm)],[])).
% 293.69/186.22 tff(23112,plain,
% 293.69/186.22 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s11)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s11))),
% 293.69/186.22 inference(quant_inst,[status(thm)],[])).
% 293.69/186.22 tff(23113,plain,
% 293.69/186.22 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s11)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s11)),
% 293.69/186.22 inference(modus_ponens,[status(thm)],[23112, 23111])).
% 293.69/186.22 tff(23114,plain,
% 293.69/186.22 (~node20(c_e_h_1, c_l, s11)),
% 293.69/186.22 inference(unit_resolution,[status(thm)],[23113, 4563, 23110])).
% 293.69/186.22 tff(23115,assumption,(node21(c_e_h_1, c_l, s11, s12)), introduced(assumption)).
% 293.69/186.22 tff(23116,plain,
% 293.69/186.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s11) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s12)) | (~node21(c_e_h_1, c_l, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s11) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s12)) | (~node21(c_e_h_1, c_l, s11, s12)))),
% 293.69/186.22 inference(rewrite,[status(thm)],[])).
% 293.69/186.22 tff(23117,plain,
% 293.69/186.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s11) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s12)) | (~node21(c_e_h_1, c_l, s11, s12)))),
% 293.69/186.22 inference(quant_inst,[status(thm)],[])).
% 293.69/186.22 tff(23118,plain,
% 293.69/186.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s11) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s12)) | (~node21(c_e_h_1, c_l, s11, s12))),
% 293.69/186.22 inference(modus_ponens,[status(thm)],[23117, 23116])).
% 293.69/186.22 tff(23119,plain,
% 293.69/186.22 ($false),
% 293.69/186.22 inference(unit_resolution,[status(thm)],[23118, 52, 23115, 23114, 22881])).
% 293.69/186.22 tff(23120,plain,((~node21(c_e_h_1, c_l, s11, s12)) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s12))), inference(lemma,lemma(discharge,[]))).
% 293.69/186.22 tff(23121,plain,
% 293.69/186.22 (~node21(c_e_h_1, c_l, s11, s12)),
% 293.69/186.22 inference(unit_resolution,[status(thm)],[23120, 22881])).
% 293.69/186.22 tff(23122,plain,
% 293.69/186.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s11, s12)) | node21(c_e_h_1, c_l, s11, s12) | node22(c_e_h_1, c_l, s11, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s11, s12)) | node21(c_e_h_1, c_l, s11, s12) | node22(c_e_h_1, c_l, s11, s12))),
% 293.69/186.22 inference(rewrite,[status(thm)],[])).
% 293.69/186.22 tff(23123,plain,
% 293.69/186.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s11, s12)) | node21(c_e_h_1, c_l, s11, s12) | node22(c_e_h_1, c_l, s11, s12))),
% 293.69/186.22 inference(quant_inst,[status(thm)],[])).
% 293.69/186.22 tff(23124,plain,
% 293.69/186.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s11, s12)) | node21(c_e_h_1, c_l, s11, s12) | node22(c_e_h_1, c_l, s11, s12)),
% 293.69/186.22 inference(modus_ponens,[status(thm)],[23123, 23122])).
% 293.69/186.22 tff(23125,plain,
% 293.69/186.22 (node21(c_e_h_1, c_l, s11, s12) | node22(c_e_h_1, c_l, s11, s12)),
% 293.69/186.22 inference(unit_resolution,[status(thm)],[23124, 82, 11461])).
% 293.69/186.22 tff(23126,plain,
% 293.69/186.22 (node22(c_e_h_1, c_l, s11, s12)),
% 293.69/186.22 inference(unit_resolution,[status(thm)],[23125, 23121])).
% 293.69/186.22 tff(23127,plain,
% 293.69/186.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s12)) | (~node22(c_e_h_1, c_l, s11, s12)) | m_and_h_gate_v_out(c_e_h_1, c_l, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s12)) | (~node22(c_e_h_1, c_l, s11, s12)) | m_and_h_gate_v_out(c_e_h_1, c_l, s11))),
% 293.69/186.22 inference(rewrite,[status(thm)],[])).
% 293.69/186.22 tff(23128,plain,
% 293.69/186.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s12)) | (~node22(c_e_h_1, c_l, s11, s12)) | m_and_h_gate_v_out(c_e_h_1, c_l, s11))),
% 293.69/186.22 inference(quant_inst,[status(thm)],[])).
% 293.69/186.22 tff(23129,plain,
% 293.69/186.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s12)) | (~node22(c_e_h_1, c_l, s11, s12)) | m_and_h_gate_v_out(c_e_h_1, c_l, s11)),
% 293.69/186.22 inference(modus_ponens,[status(thm)],[23128, 23127])).
% 293.69/186.22 tff(23130,plain,
% 293.69/186.22 ($false),
% 293.69/186.22 inference(unit_resolution,[status(thm)],[23129, 108, 23126, 22722, 22881])).
% 293.69/186.22 tff(23131,plain,(~m_and_h_gate_v_out(c_e_h_1, c_l, s12)), inference(lemma,lemma(discharge,[]))).
% 293.69/186.22 tff(23132,plain,
% 293.69/186.22 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s12)) | m_and_h_gate_v_out(c_e_h_1, c_l, s12))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s12)) | m_and_h_gate_v_out(c_e_h_1, c_l, s12))),
% 293.69/186.22 inference(rewrite,[status(thm)],[])).
% 293.69/186.22 tff(23133,plain,
% 293.69/186.22 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s12)) | m_and_h_gate_v_out(c_e_h_1, c_l, s12))),
% 293.69/186.22 inference(quant_inst,[status(thm)],[])).
% 293.69/186.22 tff(23134,plain,
% 293.69/186.22 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s12)) | m_and_h_gate_v_out(c_e_h_1, c_l, s12)),
% 293.69/186.22 inference(modus_ponens,[status(thm)],[23133, 23132])).
% 293.69/186.22 tff(23135,plain,
% 293.69/186.22 (~m_or_h_gate_v_in1(c_e_h_1, c_j, s12)),
% 293.69/186.22 inference(unit_resolution,[status(thm)],[23134, 1100, 23131])).
% 293.69/186.22 tff(23136,assumption,(node5(c_e_h_1, c_j, s12, s13)), introduced(assumption)).
% 293.69/186.22 tff(23137,plain,
% 293.69/186.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_1, c_j, s13)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s12) | (~node5(c_e_h_1, c_j, s12, s13)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s13)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s12) | (~node5(c_e_h_1, c_j, s12, s13)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s12))),
% 293.69/186.22 inference(rewrite,[status(thm)],[])).
% 293.69/186.22 tff(23138,plain,
% 293.69/186.22 ((m_or_h_gate_v_in1(c_e_h_1, c_j, s12) | m_or_h_gate_v_in2(c_e_h_1, c_j, s12) | (~node5(c_e_h_1, c_j, s12, s13)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s13))) <=> ((~m_or_h_gate_v_out(c_e_h_1, c_j, s13)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s12) | (~node5(c_e_h_1, c_j, s12, s13)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s12))),
% 293.69/186.22 inference(rewrite,[status(thm)],[])).
% 293.69/186.22 tff(23139,plain,
% 293.69/186.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s12) | m_or_h_gate_v_in2(c_e_h_1, c_j, s12) | (~node5(c_e_h_1, c_j, s12, s13)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_1, c_j, s13)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s12) | (~node5(c_e_h_1, c_j, s12, s13)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s12)))),
% 293.69/186.22 inference(monotonicity,[status(thm)],[23138])).
% 293.69/186.22 tff(23140,plain,
% 293.69/186.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s12) | m_or_h_gate_v_in2(c_e_h_1, c_j, s12) | (~node5(c_e_h_1, c_j, s12, s13)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s13)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s12) | (~node5(c_e_h_1, c_j, s12, s13)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s12))),
% 293.69/186.22 inference(transitivity,[status(thm)],[23139, 23137])).
% 293.69/186.22 tff(23141,plain,
% 293.69/186.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s12) | m_or_h_gate_v_in2(c_e_h_1, c_j, s12) | (~node5(c_e_h_1, c_j, s12, s13)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s13)))),
% 293.69/186.22 inference(quant_inst,[status(thm)],[])).
% 293.69/186.22 tff(23142,plain,
% 293.69/186.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s13)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s12) | (~node5(c_e_h_1, c_j, s12, s13)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s12)),
% 293.69/186.22 inference(modus_ponens,[status(thm)],[23141, 23140])).
% 293.69/186.22 tff(23143,plain,
% 293.69/186.22 ($false),
% 293.69/186.22 inference(unit_resolution,[status(thm)],[23142, 1159, 22869, 23136, 23135, 22880])).
% 293.69/186.22 tff(23144,plain,((~node5(c_e_h_1, c_j, s12, s13)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s13)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s12)), inference(lemma,lemma(discharge,[]))).
% 293.69/186.22 tff(23145,plain,
% 293.69/186.22 (~node5(c_e_h_1, c_j, s12, s13)),
% 293.69/186.22 inference(unit_resolution,[status(thm)],[23144, 22869, 22880])).
% 293.69/186.22 tff(23146,plain,
% 293.69/186.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s12, s13)) | node5(c_e_h_1, c_j, s12, s13) | node6(c_e_h_1, c_j, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s12, s13)) | node5(c_e_h_1, c_j, s12, s13) | node6(c_e_h_1, c_j, s12, s13))),
% 293.69/186.22 inference(rewrite,[status(thm)],[])).
% 293.69/186.22 tff(23147,plain,
% 293.69/186.22 ((node6(c_e_h_1, c_j, s12, s13) | node5(c_e_h_1, c_j, s12, s13) | (~trans(s12, s13))) <=> ((~trans(s12, s13)) | node5(c_e_h_1, c_j, s12, s13) | node6(c_e_h_1, c_j, s12, s13))),
% 293.69/186.23 inference(rewrite,[status(thm)],[])).
% 293.69/186.23 tff(23148,plain,
% 293.69/186.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s12, s13) | node5(c_e_h_1, c_j, s12, s13) | (~trans(s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s12, s13)) | node5(c_e_h_1, c_j, s12, s13) | node6(c_e_h_1, c_j, s12, s13)))),
% 293.69/186.23 inference(monotonicity,[status(thm)],[23147])).
% 293.69/186.23 tff(23149,plain,
% 293.69/186.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s12, s13) | node5(c_e_h_1, c_j, s12, s13) | (~trans(s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s12, s13)) | node5(c_e_h_1, c_j, s12, s13) | node6(c_e_h_1, c_j, s12, s13))),
% 293.69/186.23 inference(transitivity,[status(thm)],[23148, 23146])).
% 293.69/186.23 tff(23150,plain,
% 293.69/186.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s12, s13) | node5(c_e_h_1, c_j, s12, s13) | (~trans(s12, s13)))),
% 293.69/186.23 inference(quant_inst,[status(thm)],[])).
% 293.69/186.23 tff(23151,plain,
% 293.69/186.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s12, s13)) | node5(c_e_h_1, c_j, s12, s13) | node6(c_e_h_1, c_j, s12, s13)),
% 293.69/186.23 inference(modus_ponens,[status(thm)],[23150, 23149])).
% 293.69/186.23 tff(23152,plain,
% 293.69/186.23 (node5(c_e_h_1, c_j, s12, s13) | node6(c_e_h_1, c_j, s12, s13)),
% 293.69/186.23 inference(unit_resolution,[status(thm)],[23151, 1141, 11856])).
% 293.69/186.23 tff(23153,plain,
% 293.69/186.23 ($false),
% 293.69/186.23 inference(unit_resolution,[status(thm)],[23152, 23145, 22879])).
% 293.69/186.23 tff(23154,plain,((~m_or_h_gate_v_out(c_e_h_1, c_j, s13)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s12) | m_or_h_gate_v_out(c_e_h_1, c_j, s12)), inference(lemma,lemma(discharge,[]))).
% 293.69/186.23 tff(23155,plain,
% 293.69/186.23 ((~m_or_h_gate_v_out(c_e_h_1, c_j, s13)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s12)),
% 293.69/186.23 inference(unit_resolution,[status(thm)],[23154, 22867])).
% 293.69/186.23 tff(23156,plain,
% 293.69/186.23 (~m_or_h_gate_v_out(c_e_h_1, c_j, s13)),
% 293.69/186.23 inference(unit_resolution,[status(thm)],[23155, 22076])).
% 293.69/186.23 tff(23157,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s9)), introduced(assumption)).
% 293.69/186.23 tff(23158,assumption,(node21(c_e_h_1, c_i, s8, s9)), introduced(assumption)).
% 293.69/186.23 tff(23159,plain,
% 293.69/186.23 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s7)) | m_or_h_gate_v_out(c_e_h_1, c_j, s7))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s7)) | m_or_h_gate_v_out(c_e_h_1, c_j, s7))),
% 293.69/186.23 inference(rewrite,[status(thm)],[])).
% 293.69/186.23 tff(23160,plain,
% 293.69/186.23 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s7)) | m_or_h_gate_v_out(c_e_h_1, c_j, s7))),
% 293.69/186.23 inference(quant_inst,[status(thm)],[])).
% 293.69/186.23 tff(23161,plain,
% 293.69/186.23 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s7)) | m_or_h_gate_v_out(c_e_h_1, c_j, s7)),
% 293.69/186.23 inference(modus_ponens,[status(thm)],[23160, 23159])).
% 293.69/186.23 tff(23162,plain,
% 293.69/186.23 (~m_c_h_element_v_in2(c_e_h_1, c_h, s7)),
% 293.69/186.23 inference(unit_resolution,[status(thm)],[23161, 1174, 22169])).
% 293.69/186.23 tff(23163,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_h, s7)), introduced(assumption)).
% 293.69/186.23 tff(23164,assumption,(m_c_h_element_v_out(c_e_h_1, c_h, s8)), introduced(assumption)).
% 293.69/186.23 tff(23165,assumption,(~m_c_h_element_v_out(c_e_h_1, c_h, s7)), introduced(assumption)).
% 293.69/186.23 tff(23166,assumption,(node15(c_e_h_1, c_h, s7, s8)), introduced(assumption)).
% 293.69/186.23 tff(23167,plain,
% 293.69/186.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s8)) | (~node15(c_e_h_1, c_h, s7, s8)) | m_c_h_element_v_out(c_e_h_1, c_h, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s8)) | (~node15(c_e_h_1, c_h, s7, s8)) | m_c_h_element_v_out(c_e_h_1, c_h, s7))),
% 293.69/186.23 inference(rewrite,[status(thm)],[])).
% 293.69/186.23 tff(23168,plain,
% 293.69/186.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s8)) | (~node15(c_e_h_1, c_h, s7, s8)) | m_c_h_element_v_out(c_e_h_1, c_h, s7))),
% 293.69/186.23 inference(quant_inst,[status(thm)],[])).
% 293.69/186.23 tff(23169,plain,
% 293.69/186.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s8)) | (~node15(c_e_h_1, c_h, s7, s8)) | m_c_h_element_v_out(c_e_h_1, c_h, s7)),
% 293.69/186.23 inference(modus_ponens,[status(thm)],[23168, 23167])).
% 293.69/186.23 tff(23170,plain,
% 293.69/186.23 ($false),
% 293.69/186.23 inference(unit_resolution,[status(thm)],[23169, 147, 23165, 23164, 23166])).
% 293.69/186.23 tff(23171,plain,((~node15(c_e_h_1, c_h, s7, s8)) | m_c_h_element_v_out(c_e_h_1, c_h, s7) | (~m_c_h_element_v_out(c_e_h_1, c_h, s8))), inference(lemma,lemma(discharge,[]))).
% 293.69/186.23 tff(23172,plain,
% 293.69/186.23 (~node15(c_e_h_1, c_h, s7, s8)),
% 293.69/186.23 inference(unit_resolution,[status(thm)],[23171, 23165, 23164])).
% 293.69/186.23 tff(23173,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_h, s7)), introduced(assumption)).
% 293.69/186.23 tff(23174,assumption,(~node15(c_e_h_1, c_h, s7, s8)), introduced(assumption)).
% 293.69/186.23 tff(23175,plain,
% 293.69/186.23 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s7)) | m_c_h_element_v_in1(c_e_h_1, c_h, s7) | m_c_h_element_v_in2(c_e_h_1, c_h, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s7)) | m_c_h_element_v_in1(c_e_h_1, c_h, s7) | m_c_h_element_v_in2(c_e_h_1, c_h, s7))),
% 293.69/186.23 inference(rewrite,[status(thm)],[])).
% 293.69/186.23 tff(23176,plain,
% 293.69/186.23 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s7)) | m_c_h_element_v_in1(c_e_h_1, c_h, s7) | m_c_h_element_v_in2(c_e_h_1, c_h, s7))),
% 293.69/186.23 inference(quant_inst,[status(thm)],[])).
% 293.69/186.23 tff(23177,plain,
% 293.69/186.23 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s7)) | m_c_h_element_v_in1(c_e_h_1, c_h, s7) | m_c_h_element_v_in2(c_e_h_1, c_h, s7)),
% 293.69/186.23 inference(modus_ponens,[status(thm)],[23176, 23175])).
% 293.69/186.23 tff(23178,plain,
% 293.69/186.23 ((~node16(c_e_h_1, c_h, s7)) | m_c_h_element_v_in1(c_e_h_1, c_h, s7)),
% 293.69/186.23 inference(unit_resolution,[status(thm)],[23177, 178, 23163])).
% 293.69/186.23 tff(23179,plain,
% 293.69/186.23 (~node16(c_e_h_1, c_h, s7)),
% 293.69/186.23 inference(unit_resolution,[status(thm)],[23178, 23173])).
% 293.69/186.23 tff(23180,plain,
% 293.69/186.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s7, s8)) | node19(c_e_h_1, c_h, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s7, s8)) | node19(c_e_h_1, c_h, s7, s8))),
% 293.69/186.23 inference(rewrite,[status(thm)],[])).
% 293.69/186.23 tff(23181,plain,
% 293.69/186.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s7, s8)) | node19(c_e_h_1, c_h, s7, s8))),
% 293.69/186.23 inference(quant_inst,[status(thm)],[])).
% 293.69/186.23 tff(23182,plain,
% 293.69/186.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s7, s8)) | node19(c_e_h_1, c_h, s7, s8)),
% 293.69/186.23 inference(modus_ponens,[status(thm)],[23181, 23180])).
% 293.69/186.23 tff(23183,plain,
% 293.69/186.23 (node19(c_e_h_1, c_h, s7, s8)),
% 293.69/186.23 inference(unit_resolution,[status(thm)],[23182, 190, 1938])).
% 293.69/186.23 tff(23184,plain,
% 293.69/186.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s7) | node14(c_e_h_1, c_h, s7, s8) | (~node19(c_e_h_1, c_h, s7, s8)) | node15(c_e_h_1, c_h, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s7) | node14(c_e_h_1, c_h, s7, s8) | (~node19(c_e_h_1, c_h, s7, s8)) | node15(c_e_h_1, c_h, s7, s8))),
% 293.69/186.23 inference(rewrite,[status(thm)],[])).
% 293.69/186.23 tff(23185,plain,
% 293.69/186.23 ((node16(c_e_h_1, c_h, s7) | node14(c_e_h_1, c_h, s7, s8) | node15(c_e_h_1, c_h, s7, s8) | (~node19(c_e_h_1, c_h, s7, s8))) <=> (node16(c_e_h_1, c_h, s7) | node14(c_e_h_1, c_h, s7, s8) | (~node19(c_e_h_1, c_h, s7, s8)) | node15(c_e_h_1, c_h, s7, s8))),
% 293.69/186.23 inference(rewrite,[status(thm)],[])).
% 293.69/186.23 tff(23186,plain,
% 293.69/186.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s7) | node14(c_e_h_1, c_h, s7, s8) | node15(c_e_h_1, c_h, s7, s8) | (~node19(c_e_h_1, c_h, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s7) | node14(c_e_h_1, c_h, s7, s8) | (~node19(c_e_h_1, c_h, s7, s8)) | node15(c_e_h_1, c_h, s7, s8)))),
% 293.69/186.23 inference(monotonicity,[status(thm)],[23185])).
% 293.69/186.23 tff(23187,plain,
% 293.69/186.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s7) | node14(c_e_h_1, c_h, s7, s8) | node15(c_e_h_1, c_h, s7, s8) | (~node19(c_e_h_1, c_h, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s7) | node14(c_e_h_1, c_h, s7, s8) | (~node19(c_e_h_1, c_h, s7, s8)) | node15(c_e_h_1, c_h, s7, s8))),
% 293.69/186.23 inference(transitivity,[status(thm)],[23186, 23184])).
% 293.69/186.23 tff(23188,plain,
% 293.69/186.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s7) | node14(c_e_h_1, c_h, s7, s8) | node15(c_e_h_1, c_h, s7, s8) | (~node19(c_e_h_1, c_h, s7, s8)))),
% 293.69/186.23 inference(quant_inst,[status(thm)],[])).
% 293.69/186.23 tff(23189,plain,
% 293.69/186.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s7) | node14(c_e_h_1, c_h, s7, s8) | (~node19(c_e_h_1, c_h, s7, s8)) | node15(c_e_h_1, c_h, s7, s8)),
% 293.69/186.23 inference(modus_ponens,[status(thm)],[23188, 23187])).
% 293.69/186.23 tff(23190,plain,
% 293.69/186.23 (node16(c_e_h_1, c_h, s7) | node14(c_e_h_1, c_h, s7, s8) | node15(c_e_h_1, c_h, s7, s8)),
% 293.69/186.23 inference(unit_resolution,[status(thm)],[23189, 204, 23183])).
% 293.69/186.23 tff(23191,plain,
% 293.69/186.23 (node14(c_e_h_1, c_h, s7, s8)),
% 293.69/186.23 inference(unit_resolution,[status(thm)],[23190, 23179, 23174])).
% 293.69/186.23 tff(23192,plain,
% 293.69/186.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s7) | (~m_c_h_element_v_out(c_e_h_1, c_h, s8)) | (~node14(c_e_h_1, c_h, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s7) | (~m_c_h_element_v_out(c_e_h_1, c_h, s8)) | (~node14(c_e_h_1, c_h, s7, s8)))),
% 293.69/186.23 inference(rewrite,[status(thm)],[])).
% 293.69/186.23 tff(23193,plain,
% 293.69/186.23 (((~node14(c_e_h_1, c_h, s7, s8)) | m_c_h_element_v_in1(c_e_h_1, c_h, s7) | (~m_c_h_element_v_out(c_e_h_1, c_h, s8))) <=> (m_c_h_element_v_in1(c_e_h_1, c_h, s7) | (~m_c_h_element_v_out(c_e_h_1, c_h, s8)) | (~node14(c_e_h_1, c_h, s7, s8)))),
% 293.69/186.23 inference(rewrite,[status(thm)],[])).
% 293.69/186.23 tff(23194,plain,
% 293.69/186.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s7, s8)) | m_c_h_element_v_in1(c_e_h_1, c_h, s7) | (~m_c_h_element_v_out(c_e_h_1, c_h, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s7) | (~m_c_h_element_v_out(c_e_h_1, c_h, s8)) | (~node14(c_e_h_1, c_h, s7, s8))))),
% 293.69/186.24 inference(monotonicity,[status(thm)],[23193])).
% 293.69/186.24 tff(23195,plain,
% 293.69/186.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s7, s8)) | m_c_h_element_v_in1(c_e_h_1, c_h, s7) | (~m_c_h_element_v_out(c_e_h_1, c_h, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s7) | (~m_c_h_element_v_out(c_e_h_1, c_h, s8)) | (~node14(c_e_h_1, c_h, s7, s8)))),
% 293.69/186.24 inference(transitivity,[status(thm)],[23194, 23192])).
% 293.69/186.24 tff(23196,plain,
% 293.69/186.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s7, s8)) | m_c_h_element_v_in1(c_e_h_1, c_h, s7) | (~m_c_h_element_v_out(c_e_h_1, c_h, s8)))),
% 293.69/186.24 inference(quant_inst,[status(thm)],[])).
% 293.69/186.24 tff(23197,plain,
% 293.69/186.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s7) | (~m_c_h_element_v_out(c_e_h_1, c_h, s8)) | (~node14(c_e_h_1, c_h, s7, s8))),
% 293.69/186.24 inference(modus_ponens,[status(thm)],[23196, 23195])).
% 293.69/186.24 tff(23198,plain,
% 293.69/186.24 ($false),
% 293.69/186.24 inference(unit_resolution,[status(thm)],[23197, 223, 23164, 23191, 23173])).
% 293.69/186.24 tff(23199,plain,(m_c_h_element_v_in1(c_e_h_1, c_h, s7) | (~m_c_h_element_v_out(c_e_h_1, c_h, s8)) | node15(c_e_h_1, c_h, s7, s8) | m_c_h_element_v_in2(c_e_h_1, c_h, s7)), inference(lemma,lemma(discharge,[]))).
% 293.69/186.24 tff(23200,plain,
% 293.69/186.24 (m_c_h_element_v_in1(c_e_h_1, c_h, s7)),
% 293.69/186.24 inference(unit_resolution,[status(thm)],[23199, 23172, 23164, 23163])).
% 293.69/186.24 tff(23201,plain,
% 293.69/186.24 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_h, s7) | (~node17(c_e_h_1, c_h, s7)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_h, s7) | (~node17(c_e_h_1, c_h, s7)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s7)))),
% 293.69/186.24 inference(rewrite,[status(thm)],[])).
% 293.69/186.24 tff(23202,plain,
% 293.69/186.24 (((~m_c_h_element_v_in1(c_e_h_1, c_h, s7)) | m_c_h_element_v_in2(c_e_h_1, c_h, s7) | (~node17(c_e_h_1, c_h, s7))) <=> (m_c_h_element_v_in2(c_e_h_1, c_h, s7) | (~node17(c_e_h_1, c_h, s7)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s7)))),
% 293.69/186.24 inference(rewrite,[status(thm)],[])).
% 293.69/186.24 tff(23203,plain,
% 293.69/186.24 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s7)) | m_c_h_element_v_in2(c_e_h_1, c_h, s7) | (~node17(c_e_h_1, c_h, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_h, s7) | (~node17(c_e_h_1, c_h, s7)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s7))))),
% 293.69/186.24 inference(monotonicity,[status(thm)],[23202])).
% 293.69/186.24 tff(23204,plain,
% 293.69/186.24 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s7)) | m_c_h_element_v_in2(c_e_h_1, c_h, s7) | (~node17(c_e_h_1, c_h, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_h, s7) | (~node17(c_e_h_1, c_h, s7)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s7)))),
% 293.69/186.24 inference(transitivity,[status(thm)],[23203, 23201])).
% 293.69/186.24 tff(23205,plain,
% 293.69/186.24 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s7)) | m_c_h_element_v_in2(c_e_h_1, c_h, s7) | (~node17(c_e_h_1, c_h, s7)))),
% 293.69/186.24 inference(quant_inst,[status(thm)],[])).
% 293.69/186.24 tff(23206,plain,
% 293.69/186.24 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_h, s7) | (~node17(c_e_h_1, c_h, s7)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s7))),
% 293.69/186.24 inference(modus_ponens,[status(thm)],[23205, 23204])).
% 293.69/186.24 tff(23207,plain,
% 293.69/186.24 ((~node17(c_e_h_1, c_h, s7)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s7))),
% 293.69/186.24 inference(unit_resolution,[status(thm)],[23206, 919, 23163])).
% 293.69/186.24 tff(23208,plain,
% 293.69/186.24 (~node17(c_e_h_1, c_h, s7)),
% 293.69/186.24 inference(unit_resolution,[status(thm)],[23207, 23200])).
% 293.69/186.24 tff(23209,plain,
% 293.69/186.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s7) | (~node19(c_e_h_1, c_h, s7, s8)) | node18(c_e_h_1, c_h, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s7) | (~node19(c_e_h_1, c_h, s7, s8)) | node18(c_e_h_1, c_h, s7, s8))),
% 293.69/186.24 inference(rewrite,[status(thm)],[])).
% 293.69/186.24 tff(23210,plain,
% 293.69/186.24 ((node17(c_e_h_1, c_h, s7) | node18(c_e_h_1, c_h, s7, s8) | (~node19(c_e_h_1, c_h, s7, s8))) <=> (node17(c_e_h_1, c_h, s7) | (~node19(c_e_h_1, c_h, s7, s8)) | node18(c_e_h_1, c_h, s7, s8))),
% 293.69/186.24 inference(rewrite,[status(thm)],[])).
% 293.69/186.24 tff(23211,plain,
% 293.69/186.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s7) | node18(c_e_h_1, c_h, s7, s8) | (~node19(c_e_h_1, c_h, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s7) | (~node19(c_e_h_1, c_h, s7, s8)) | node18(c_e_h_1, c_h, s7, s8)))),
% 293.69/186.24 inference(monotonicity,[status(thm)],[23210])).
% 293.69/186.24 tff(23212,plain,
% 293.69/186.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s7) | node18(c_e_h_1, c_h, s7, s8) | (~node19(c_e_h_1, c_h, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s7) | (~node19(c_e_h_1, c_h, s7, s8)) | node18(c_e_h_1, c_h, s7, s8))),
% 293.69/186.24 inference(transitivity,[status(thm)],[23211, 23209])).
% 293.69/186.24 tff(23213,plain,
% 293.69/186.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s7) | node18(c_e_h_1, c_h, s7, s8) | (~node19(c_e_h_1, c_h, s7, s8)))),
% 293.69/186.24 inference(quant_inst,[status(thm)],[])).
% 293.69/186.24 tff(23214,plain,
% 293.69/186.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s7) | (~node19(c_e_h_1, c_h, s7, s8)) | node18(c_e_h_1, c_h, s7, s8)),
% 293.69/186.24 inference(modus_ponens,[status(thm)],[23213, 23212])).
% 293.69/186.24 tff(23215,plain,
% 293.69/186.24 (node17(c_e_h_1, c_h, s7) | node18(c_e_h_1, c_h, s7, s8)),
% 293.69/186.24 inference(unit_resolution,[status(thm)],[23214, 776, 23183])).
% 293.69/186.24 tff(23216,plain,
% 293.69/186.24 (node18(c_e_h_1, c_h, s7, s8)),
% 293.69/186.24 inference(unit_resolution,[status(thm)],[23215, 23208])).
% 293.69/186.24 tff(23217,plain,
% 293.69/186.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_h, s7) | (~m_c_h_element_v_out(c_e_h_1, c_h, s8)) | (~node18(c_e_h_1, c_h, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s7) | (~m_c_h_element_v_out(c_e_h_1, c_h, s8)) | (~node18(c_e_h_1, c_h, s7, s8)))),
% 293.69/186.24 inference(rewrite,[status(thm)],[])).
% 293.69/186.24 tff(23218,plain,
% 293.69/186.24 (((~m_c_h_element_v_out(c_e_h_1, c_h, s8)) | m_c_h_element_v_out(c_e_h_1, c_h, s7) | (~node18(c_e_h_1, c_h, s7, s8))) <=> (m_c_h_element_v_out(c_e_h_1, c_h, s7) | (~m_c_h_element_v_out(c_e_h_1, c_h, s8)) | (~node18(c_e_h_1, c_h, s7, s8)))),
% 293.69/186.24 inference(rewrite,[status(thm)],[])).
% 293.69/186.24 tff(23219,plain,
% 293.69/186.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s8)) | m_c_h_element_v_out(c_e_h_1, c_h, s7) | (~node18(c_e_h_1, c_h, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_h, s7) | (~m_c_h_element_v_out(c_e_h_1, c_h, s8)) | (~node18(c_e_h_1, c_h, s7, s8))))),
% 293.69/186.24 inference(monotonicity,[status(thm)],[23218])).
% 293.69/186.24 tff(23220,plain,
% 293.69/186.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s8)) | m_c_h_element_v_out(c_e_h_1, c_h, s7) | (~node18(c_e_h_1, c_h, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s7) | (~m_c_h_element_v_out(c_e_h_1, c_h, s8)) | (~node18(c_e_h_1, c_h, s7, s8)))),
% 293.69/186.24 inference(transitivity,[status(thm)],[23219, 23217])).
% 293.69/186.24 tff(23221,plain,
% 293.69/186.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s8)) | m_c_h_element_v_out(c_e_h_1, c_h, s7) | (~node18(c_e_h_1, c_h, s7, s8)))),
% 293.69/186.24 inference(quant_inst,[status(thm)],[])).
% 293.69/186.24 tff(23222,plain,
% 293.69/186.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s7) | (~m_c_h_element_v_out(c_e_h_1, c_h, s8)) | (~node18(c_e_h_1, c_h, s7, s8))),
% 293.69/186.24 inference(modus_ponens,[status(thm)],[23221, 23220])).
% 293.69/186.24 tff(23223,plain,
% 293.69/186.24 ($false),
% 293.69/186.24 inference(unit_resolution,[status(thm)],[23222, 753, 23165, 23164, 23216])).
% 293.69/186.24 tff(23224,plain,(m_c_h_element_v_out(c_e_h_1, c_h, s7) | (~m_c_h_element_v_out(c_e_h_1, c_h, s8)) | m_c_h_element_v_in2(c_e_h_1, c_h, s7)), inference(lemma,lemma(discharge,[]))).
% 293.69/186.24 tff(23225,plain,
% 293.69/186.24 ((~m_c_h_element_v_out(c_e_h_1, c_h, s8)) | m_c_h_element_v_in2(c_e_h_1, c_h, s7)),
% 293.69/186.24 inference(unit_resolution,[status(thm)],[23224, 19452])).
% 293.69/186.24 tff(23226,plain,
% 293.69/186.24 (~m_c_h_element_v_out(c_e_h_1, c_h, s8)),
% 293.69/186.24 inference(unit_resolution,[status(thm)],[23225, 23162])).
% 293.69/186.24 tff(23227,plain,
% 293.69/186.24 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s8)) | m_c_h_element_v_out(c_e_h_1, c_h, s8))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s8)) | m_c_h_element_v_out(c_e_h_1, c_h, s8))),
% 293.69/186.24 inference(rewrite,[status(thm)],[])).
% 293.69/186.24 tff(23228,plain,
% 293.69/186.24 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s8)) | m_c_h_element_v_out(c_e_h_1, c_h, s8))),
% 293.69/186.24 inference(quant_inst,[status(thm)],[])).
% 293.69/186.24 tff(23229,plain,
% 293.69/186.24 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s8)) | m_c_h_element_v_out(c_e_h_1, c_h, s8)),
% 293.69/186.24 inference(modus_ponens,[status(thm)],[23228, 23227])).
% 293.69/186.24 tff(23230,plain,
% 293.69/186.24 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s8)),
% 293.69/186.24 inference(unit_resolution,[status(thm)],[23229, 619, 23226])).
% 293.69/186.24 tff(23231,plain,
% 293.69/186.24 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s8)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s8)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s8))),
% 293.69/186.24 inference(rewrite,[status(thm)],[])).
% 293.69/186.24 tff(23232,plain,
% 293.69/186.24 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s8)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s8))),
% 293.69/186.24 inference(quant_inst,[status(thm)],[])).
% 293.69/186.24 tff(23233,plain,
% 293.69/186.24 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s8)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s8)),
% 293.69/186.25 inference(modus_ponens,[status(thm)],[23232, 23231])).
% 293.69/186.25 tff(23234,plain,
% 293.69/186.25 (~node20(c_e_h_1, c_i, s8)),
% 293.69/186.25 inference(unit_resolution,[status(thm)],[23233, 38, 23230])).
% 293.69/186.25 tff(23235,plain,
% 293.69/186.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s9)) | (~node21(c_e_h_1, c_i, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s9)) | (~node21(c_e_h_1, c_i, s8, s9)))),
% 293.69/186.25 inference(rewrite,[status(thm)],[])).
% 293.69/186.25 tff(23236,plain,
% 293.69/186.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s9)) | (~node21(c_e_h_1, c_i, s8, s9)))),
% 293.69/186.25 inference(quant_inst,[status(thm)],[])).
% 293.69/186.25 tff(23237,plain,
% 293.69/186.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s9)) | (~node21(c_e_h_1, c_i, s8, s9))),
% 293.69/186.25 inference(modus_ponens,[status(thm)],[23236, 23235])).
% 293.69/186.25 tff(23238,plain,
% 293.69/186.25 ($false),
% 293.69/186.25 inference(unit_resolution,[status(thm)],[23237, 52, 23157, 23234, 23158])).
% 293.69/186.25 tff(23239,plain,((~node21(c_e_h_1, c_i, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s9))), inference(lemma,lemma(discharge,[]))).
% 293.69/186.25 tff(23240,plain,
% 293.69/186.25 (~node21(c_e_h_1, c_i, s8, s9)),
% 293.69/186.25 inference(unit_resolution,[status(thm)],[23239, 23157])).
% 293.69/186.25 tff(23241,plain,
% 293.69/186.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s8, s9)) | node21(c_e_h_1, c_i, s8, s9) | node22(c_e_h_1, c_i, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_1, c_i, s8, s9) | node22(c_e_h_1, c_i, s8, s9))),
% 293.69/186.25 inference(rewrite,[status(thm)],[])).
% 293.69/186.25 tff(23242,plain,
% 293.69/186.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s8, s9)) | node21(c_e_h_1, c_i, s8, s9) | node22(c_e_h_1, c_i, s8, s9))),
% 293.69/186.25 inference(quant_inst,[status(thm)],[])).
% 293.69/186.25 tff(23243,plain,
% 293.69/186.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_1, c_i, s8, s9) | node22(c_e_h_1, c_i, s8, s9)),
% 293.69/186.25 inference(modus_ponens,[status(thm)],[23242, 23241])).
% 293.69/186.25 tff(23244,plain,
% 293.69/186.25 (node21(c_e_h_1, c_i, s8, s9) | node22(c_e_h_1, c_i, s8, s9)),
% 293.69/186.25 inference(unit_resolution,[status(thm)],[23243, 82, 1993])).
% 293.69/186.25 tff(23245,plain,
% 293.69/186.25 (node22(c_e_h_1, c_i, s8, s9)),
% 293.69/186.25 inference(unit_resolution,[status(thm)],[23244, 23240])).
% 293.69/186.25 tff(23246,plain,
% 293.69/186.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s9)) | (~node22(c_e_h_1, c_i, s8, s9)) | m_and_h_gate_v_out(c_e_h_1, c_i, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s9)) | (~node22(c_e_h_1, c_i, s8, s9)) | m_and_h_gate_v_out(c_e_h_1, c_i, s8))),
% 293.69/186.25 inference(rewrite,[status(thm)],[])).
% 293.69/186.25 tff(23247,plain,
% 293.69/186.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s9)) | (~node22(c_e_h_1, c_i, s8, s9)) | m_and_h_gate_v_out(c_e_h_1, c_i, s8))),
% 293.69/186.25 inference(quant_inst,[status(thm)],[])).
% 293.69/186.25 tff(23248,plain,
% 293.69/186.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s9)) | (~node22(c_e_h_1, c_i, s8, s9)) | m_and_h_gate_v_out(c_e_h_1, c_i, s8)),
% 293.69/186.25 inference(modus_ponens,[status(thm)],[23247, 23246])).
% 293.69/186.25 tff(23249,plain,
% 293.69/186.25 ($false),
% 293.69/186.25 inference(unit_resolution,[status(thm)],[23248, 108, 22917, 23157, 23245])).
% 293.69/186.25 tff(23250,plain,(~m_and_h_gate_v_out(c_e_h_1, c_i, s9)), inference(lemma,lemma(discharge,[]))).
% 293.69/186.25 tff(23251,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_i, s9)), introduced(assumption)).
% 293.69/186.25 tff(23252,assumption,(m_c_h_element_v_in2(c_e_h_1, c_e, s9)), introduced(assumption)).
% 293.69/186.25 tff(23253,plain,
% 293.69/186.25 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s9)) | m_and_h_gate_v_out(c_e_h_1, c_i, s9))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s9)) | m_and_h_gate_v_out(c_e_h_1, c_i, s9))),
% 293.69/186.25 inference(rewrite,[status(thm)],[])).
% 293.69/186.25 tff(23254,plain,
% 293.69/186.25 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s9)) | m_and_h_gate_v_out(c_e_h_1, c_i, s9))),
% 293.69/186.25 inference(quant_inst,[status(thm)],[])).
% 293.69/186.25 tff(23255,plain,
% 293.69/186.25 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s9)) | m_and_h_gate_v_out(c_e_h_1, c_i, s9)),
% 293.69/186.25 inference(modus_ponens,[status(thm)],[23254, 23253])).
% 293.69/186.25 tff(23256,plain,
% 293.69/186.25 ($false),
% 293.69/186.25 inference(unit_resolution,[status(thm)],[23255, 164, 23252, 23251])).
% 293.69/186.25 tff(23257,plain,((~m_c_h_element_v_in2(c_e_h_1, c_e, s9)) | m_and_h_gate_v_out(c_e_h_1, c_i, s9)), inference(lemma,lemma(discharge,[]))).
% 293.69/186.25 tff(23258,plain,
% 293.69/186.25 (~m_c_h_element_v_in2(c_e_h_1, c_e, s9)),
% 293.69/186.25 inference(unit_resolution,[status(thm)],[23257, 23250])).
% 293.69/186.25 tff(23259,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_e, s9)), introduced(assumption)).
% 293.69/186.25 tff(23260,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s10)), introduced(assumption)).
% 293.69/186.25 tff(23261,assumption,(node15(c_e_h_1, c_e, s9, s10)), introduced(assumption)).
% 293.69/186.25 tff(23262,plain,
% 293.69/186.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | (~node15(c_e_h_1, c_e, s9, s10)) | m_c_h_element_v_out(c_e_h_1, c_e, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | (~node15(c_e_h_1, c_e, s9, s10)) | m_c_h_element_v_out(c_e_h_1, c_e, s9))),
% 293.69/186.25 inference(rewrite,[status(thm)],[])).
% 293.69/186.25 tff(23263,plain,
% 293.69/186.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | (~node15(c_e_h_1, c_e, s9, s10)) | m_c_h_element_v_out(c_e_h_1, c_e, s9))),
% 293.69/186.25 inference(quant_inst,[status(thm)],[])).
% 293.69/186.25 tff(23264,plain,
% 293.69/186.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | (~node15(c_e_h_1, c_e, s9, s10)) | m_c_h_element_v_out(c_e_h_1, c_e, s9)),
% 293.69/186.25 inference(modus_ponens,[status(thm)],[23263, 23262])).
% 293.69/186.25 tff(23265,plain,
% 293.69/186.25 ($false),
% 293.69/186.25 inference(unit_resolution,[status(thm)],[23264, 147, 23260, 23015, 23261])).
% 293.69/186.25 tff(23266,plain,((~node15(c_e_h_1, c_e, s9, s10)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | m_c_h_element_v_out(c_e_h_1, c_e, s9)), inference(lemma,lemma(discharge,[]))).
% 293.69/186.25 tff(23267,plain,
% 293.69/186.25 (~node15(c_e_h_1, c_e, s9, s10)),
% 293.69/186.25 inference(unit_resolution,[status(thm)],[23266, 23015, 23260])).
% 293.69/186.25 tff(23268,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_e, s9)), introduced(assumption)).
% 293.69/186.25 tff(23269,assumption,(~node15(c_e_h_1, c_e, s9, s10)), introduced(assumption)).
% 293.69/186.25 tff(23270,plain,
% 293.69/186.25 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s9)) | m_c_h_element_v_in1(c_e_h_1, c_e, s9) | m_c_h_element_v_in2(c_e_h_1, c_e, s9))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s9)) | m_c_h_element_v_in1(c_e_h_1, c_e, s9) | m_c_h_element_v_in2(c_e_h_1, c_e, s9))),
% 293.69/186.26 inference(rewrite,[status(thm)],[])).
% 293.69/186.26 tff(23271,plain,
% 293.69/186.26 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s9)) | m_c_h_element_v_in1(c_e_h_1, c_e, s9) | m_c_h_element_v_in2(c_e_h_1, c_e, s9))),
% 293.69/186.26 inference(quant_inst,[status(thm)],[])).
% 293.69/186.26 tff(23272,plain,
% 293.69/186.26 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s9)) | m_c_h_element_v_in1(c_e_h_1, c_e, s9) | m_c_h_element_v_in2(c_e_h_1, c_e, s9)),
% 293.69/186.26 inference(modus_ponens,[status(thm)],[23271, 23270])).
% 293.69/186.26 tff(23273,plain,
% 293.69/186.26 ((~node16(c_e_h_1, c_e, s9)) | m_c_h_element_v_in1(c_e_h_1, c_e, s9)),
% 293.69/186.26 inference(unit_resolution,[status(thm)],[23272, 178, 23259])).
% 293.69/186.26 tff(23274,plain,
% 293.69/186.26 (~node16(c_e_h_1, c_e, s9)),
% 293.69/186.26 inference(unit_resolution,[status(thm)],[23273, 23268])).
% 293.69/186.26 tff(23275,plain,
% 293.69/186.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s9, s10)) | node19(c_e_h_1, c_e, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s9, s10)) | node19(c_e_h_1, c_e, s9, s10))),
% 293.69/186.26 inference(rewrite,[status(thm)],[])).
% 293.69/186.26 tff(23276,plain,
% 293.69/186.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s9, s10)) | node19(c_e_h_1, c_e, s9, s10))),
% 293.69/186.26 inference(quant_inst,[status(thm)],[])).
% 293.69/186.26 tff(23277,plain,
% 293.69/186.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s9, s10)) | node19(c_e_h_1, c_e, s9, s10)),
% 293.69/186.26 inference(modus_ponens,[status(thm)],[23276, 23275])).
% 293.69/186.26 tff(23278,plain,
% 293.69/186.26 (node19(c_e_h_1, c_e, s9, s10)),
% 293.69/186.26 inference(unit_resolution,[status(thm)],[23277, 190, 7676])).
% 293.69/186.26 tff(23279,plain,
% 293.69/186.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_1, c_e, s9, s10) | (~node19(c_e_h_1, c_e, s9, s10)) | node16(c_e_h_1, c_e, s9) | node15(c_e_h_1, c_e, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_e, s9, s10) | (~node19(c_e_h_1, c_e, s9, s10)) | node16(c_e_h_1, c_e, s9) | node15(c_e_h_1, c_e, s9, s10))),
% 293.69/186.26 inference(rewrite,[status(thm)],[])).
% 293.69/186.26 tff(23280,plain,
% 293.69/186.26 ((node16(c_e_h_1, c_e, s9) | node14(c_e_h_1, c_e, s9, s10) | node15(c_e_h_1, c_e, s9, s10) | (~node19(c_e_h_1, c_e, s9, s10))) <=> (node14(c_e_h_1, c_e, s9, s10) | (~node19(c_e_h_1, c_e, s9, s10)) | node16(c_e_h_1, c_e, s9) | node15(c_e_h_1, c_e, s9, s10))),
% 293.69/186.26 inference(rewrite,[status(thm)],[])).
% 293.69/186.26 tff(23281,plain,
% 293.69/186.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s9) | node14(c_e_h_1, c_e, s9, s10) | node15(c_e_h_1, c_e, s9, s10) | (~node19(c_e_h_1, c_e, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_1, c_e, s9, s10) | (~node19(c_e_h_1, c_e, s9, s10)) | node16(c_e_h_1, c_e, s9) | node15(c_e_h_1, c_e, s9, s10)))),
% 293.69/186.26 inference(monotonicity,[status(thm)],[23280])).
% 293.69/186.26 tff(23282,plain,
% 293.69/186.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s9) | node14(c_e_h_1, c_e, s9, s10) | node15(c_e_h_1, c_e, s9, s10) | (~node19(c_e_h_1, c_e, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_e, s9, s10) | (~node19(c_e_h_1, c_e, s9, s10)) | node16(c_e_h_1, c_e, s9) | node15(c_e_h_1, c_e, s9, s10))),
% 293.69/186.26 inference(transitivity,[status(thm)],[23281, 23279])).
% 293.69/186.26 tff(23283,plain,
% 293.69/186.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s9) | node14(c_e_h_1, c_e, s9, s10) | node15(c_e_h_1, c_e, s9, s10) | (~node19(c_e_h_1, c_e, s9, s10)))),
% 293.69/186.26 inference(quant_inst,[status(thm)],[])).
% 293.69/186.26 tff(23284,plain,
% 293.69/186.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_e, s9, s10) | (~node19(c_e_h_1, c_e, s9, s10)) | node16(c_e_h_1, c_e, s9) | node15(c_e_h_1, c_e, s9, s10)),
% 293.69/186.26 inference(modus_ponens,[status(thm)],[23283, 23282])).
% 293.69/186.26 tff(23285,plain,
% 293.69/186.26 (node14(c_e_h_1, c_e, s9, s10) | node16(c_e_h_1, c_e, s9) | node15(c_e_h_1, c_e, s9, s10)),
% 293.69/186.26 inference(unit_resolution,[status(thm)],[23284, 204, 23278])).
% 293.69/186.26 tff(23286,plain,
% 293.69/186.26 (node14(c_e_h_1, c_e, s9, s10)),
% 293.69/186.26 inference(unit_resolution,[status(thm)],[23285, 23274, 23269])).
% 293.69/186.26 tff(23287,plain,
% 293.69/186.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | m_c_h_element_v_in1(c_e_h_1, c_e, s9) | (~node14(c_e_h_1, c_e, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | m_c_h_element_v_in1(c_e_h_1, c_e, s9) | (~node14(c_e_h_1, c_e, s9, s10)))),
% 293.69/186.26 inference(rewrite,[status(thm)],[])).
% 293.69/186.26 tff(23288,plain,
% 293.69/186.26 (((~node14(c_e_h_1, c_e, s9, s10)) | m_c_h_element_v_in1(c_e_h_1, c_e, s9) | (~m_c_h_element_v_out(c_e_h_1, c_e, s10))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | m_c_h_element_v_in1(c_e_h_1, c_e, s9) | (~node14(c_e_h_1, c_e, s9, s10)))),
% 293.69/186.26 inference(rewrite,[status(thm)],[])).
% 293.69/186.26 tff(23289,plain,
% 293.69/186.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s9, s10)) | m_c_h_element_v_in1(c_e_h_1, c_e, s9) | (~m_c_h_element_v_out(c_e_h_1, c_e, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | m_c_h_element_v_in1(c_e_h_1, c_e, s9) | (~node14(c_e_h_1, c_e, s9, s10))))),
% 293.69/186.26 inference(monotonicity,[status(thm)],[23288])).
% 293.69/186.26 tff(23290,plain,
% 293.69/186.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s9, s10)) | m_c_h_element_v_in1(c_e_h_1, c_e, s9) | (~m_c_h_element_v_out(c_e_h_1, c_e, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | m_c_h_element_v_in1(c_e_h_1, c_e, s9) | (~node14(c_e_h_1, c_e, s9, s10)))),
% 293.69/186.26 inference(transitivity,[status(thm)],[23289, 23287])).
% 293.69/186.26 tff(23291,plain,
% 293.69/186.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s9, s10)) | m_c_h_element_v_in1(c_e_h_1, c_e, s9) | (~m_c_h_element_v_out(c_e_h_1, c_e, s10)))),
% 293.69/186.26 inference(quant_inst,[status(thm)],[])).
% 293.69/186.26 tff(23292,plain,
% 293.69/186.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | m_c_h_element_v_in1(c_e_h_1, c_e, s9) | (~node14(c_e_h_1, c_e, s9, s10))),
% 293.69/186.26 inference(modus_ponens,[status(thm)],[23291, 23290])).
% 293.69/186.26 tff(23293,plain,
% 293.69/186.26 ($false),
% 293.69/186.26 inference(unit_resolution,[status(thm)],[23292, 223, 23260, 23286, 23268])).
% 293.69/186.26 tff(23294,plain,(m_c_h_element_v_in1(c_e_h_1, c_e, s9) | (~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | node15(c_e_h_1, c_e, s9, s10) | m_c_h_element_v_in2(c_e_h_1, c_e, s9)), inference(lemma,lemma(discharge,[]))).
% 293.69/186.26 tff(23295,plain,
% 293.69/186.26 (m_c_h_element_v_in1(c_e_h_1, c_e, s9)),
% 293.69/186.26 inference(unit_resolution,[status(thm)],[23294, 23267, 23260, 23259])).
% 293.69/186.26 tff(23296,assumption,(node18(c_e_h_1, c_e, s9, s10)), introduced(assumption)).
% 293.69/186.26 tff(23297,plain,
% 293.69/186.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | m_c_h_element_v_out(c_e_h_1, c_e, s9) | (~node18(c_e_h_1, c_e, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | m_c_h_element_v_out(c_e_h_1, c_e, s9) | (~node18(c_e_h_1, c_e, s9, s10)))),
% 293.69/186.26 inference(rewrite,[status(thm)],[])).
% 293.69/186.26 tff(23298,plain,
% 293.69/186.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | m_c_h_element_v_out(c_e_h_1, c_e, s9) | (~node18(c_e_h_1, c_e, s9, s10)))),
% 293.69/186.26 inference(quant_inst,[status(thm)],[])).
% 293.69/186.26 tff(23299,plain,
% 293.69/186.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | m_c_h_element_v_out(c_e_h_1, c_e, s9) | (~node18(c_e_h_1, c_e, s9, s10))),
% 293.69/186.26 inference(modus_ponens,[status(thm)],[23298, 23297])).
% 293.69/186.26 tff(23300,plain,
% 293.69/186.26 ($false),
% 293.69/186.26 inference(unit_resolution,[status(thm)],[23299, 753, 23260, 23015, 23296])).
% 293.69/186.26 tff(23301,plain,((~node18(c_e_h_1, c_e, s9, s10)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | m_c_h_element_v_out(c_e_h_1, c_e, s9)), inference(lemma,lemma(discharge,[]))).
% 293.69/186.26 tff(23302,plain,
% 293.69/186.26 (~node18(c_e_h_1, c_e, s9, s10)),
% 293.69/186.26 inference(unit_resolution,[status(thm)],[23301, 23015, 23260])).
% 293.69/186.26 tff(23303,plain,
% 293.69/186.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_e, s9, s10)) | node17(c_e_h_1, c_e, s9) | node18(c_e_h_1, c_e, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s9, s10)) | node17(c_e_h_1, c_e, s9) | node18(c_e_h_1, c_e, s9, s10))),
% 293.69/186.26 inference(rewrite,[status(thm)],[])).
% 293.69/186.26 tff(23304,plain,
% 293.69/186.26 ((node17(c_e_h_1, c_e, s9) | node18(c_e_h_1, c_e, s9, s10) | (~node19(c_e_h_1, c_e, s9, s10))) <=> ((~node19(c_e_h_1, c_e, s9, s10)) | node17(c_e_h_1, c_e, s9) | node18(c_e_h_1, c_e, s9, s10))),
% 293.69/186.26 inference(rewrite,[status(thm)],[])).
% 293.69/186.26 tff(23305,plain,
% 293.69/186.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s9) | node18(c_e_h_1, c_e, s9, s10) | (~node19(c_e_h_1, c_e, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_e, s9, s10)) | node17(c_e_h_1, c_e, s9) | node18(c_e_h_1, c_e, s9, s10)))),
% 293.69/186.26 inference(monotonicity,[status(thm)],[23304])).
% 293.69/186.26 tff(23306,plain,
% 293.69/186.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s9) | node18(c_e_h_1, c_e, s9, s10) | (~node19(c_e_h_1, c_e, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s9, s10)) | node17(c_e_h_1, c_e, s9) | node18(c_e_h_1, c_e, s9, s10))),
% 293.69/186.26 inference(transitivity,[status(thm)],[23305, 23303])).
% 293.69/186.26 tff(23307,plain,
% 293.69/186.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s9) | node18(c_e_h_1, c_e, s9, s10) | (~node19(c_e_h_1, c_e, s9, s10)))),
% 293.69/186.26 inference(quant_inst,[status(thm)],[])).
% 293.69/186.26 tff(23308,plain,
% 293.69/186.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s9, s10)) | node17(c_e_h_1, c_e, s9) | node18(c_e_h_1, c_e, s9, s10)),
% 293.69/186.26 inference(modus_ponens,[status(thm)],[23307, 23306])).
% 293.69/186.26 tff(23309,plain,
% 293.69/186.26 (node17(c_e_h_1, c_e, s9) | node18(c_e_h_1, c_e, s9, s10)),
% 293.69/186.27 inference(unit_resolution,[status(thm)],[23308, 776, 23278])).
% 293.69/186.27 tff(23310,plain,
% 293.69/186.27 (node17(c_e_h_1, c_e, s9)),
% 293.69/186.27 inference(unit_resolution,[status(thm)],[23309, 23302])).
% 293.69/186.27 tff(23311,plain,
% 293.69/186.27 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_e, s9)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s9)) | m_c_h_element_v_in2(c_e_h_1, c_e, s9))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s9)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s9)) | m_c_h_element_v_in2(c_e_h_1, c_e, s9))),
% 293.69/186.27 inference(rewrite,[status(thm)],[])).
% 293.69/186.27 tff(23312,plain,
% 293.69/186.27 (((~m_c_h_element_v_in1(c_e_h_1, c_e, s9)) | m_c_h_element_v_in2(c_e_h_1, c_e, s9) | (~node17(c_e_h_1, c_e, s9))) <=> ((~node17(c_e_h_1, c_e, s9)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s9)) | m_c_h_element_v_in2(c_e_h_1, c_e, s9))),
% 293.69/186.27 inference(rewrite,[status(thm)],[])).
% 293.69/186.27 tff(23313,plain,
% 293.69/186.27 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s9)) | m_c_h_element_v_in2(c_e_h_1, c_e, s9) | (~node17(c_e_h_1, c_e, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_e, s9)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s9)) | m_c_h_element_v_in2(c_e_h_1, c_e, s9)))),
% 293.69/186.27 inference(monotonicity,[status(thm)],[23312])).
% 293.69/186.27 tff(23314,plain,
% 293.69/186.27 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s9)) | m_c_h_element_v_in2(c_e_h_1, c_e, s9) | (~node17(c_e_h_1, c_e, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s9)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s9)) | m_c_h_element_v_in2(c_e_h_1, c_e, s9))),
% 293.69/186.27 inference(transitivity,[status(thm)],[23313, 23311])).
% 293.69/186.27 tff(23315,plain,
% 293.69/186.27 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s9)) | m_c_h_element_v_in2(c_e_h_1, c_e, s9) | (~node17(c_e_h_1, c_e, s9)))),
% 293.69/186.27 inference(quant_inst,[status(thm)],[])).
% 293.69/186.27 tff(23316,plain,
% 293.69/186.27 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s9)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s9)) | m_c_h_element_v_in2(c_e_h_1, c_e, s9)),
% 293.69/186.27 inference(modus_ponens,[status(thm)],[23315, 23314])).
% 293.69/186.27 tff(23317,plain,
% 293.69/186.27 ((~node17(c_e_h_1, c_e, s9)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s9))),
% 293.69/186.27 inference(unit_resolution,[status(thm)],[23316, 919, 23259])).
% 293.69/186.27 tff(23318,plain,
% 293.69/186.27 ($false),
% 293.69/186.27 inference(unit_resolution,[status(thm)],[23317, 23310, 23295])).
% 293.69/186.27 tff(23319,plain,(m_c_h_element_v_out(c_e_h_1, c_e, s9) | m_c_h_element_v_in2(c_e_h_1, c_e, s9) | (~m_c_h_element_v_out(c_e_h_1, c_e, s10))), inference(lemma,lemma(discharge,[]))).
% 293.69/186.27 tff(23320,plain,
% 293.69/186.27 (m_c_h_element_v_in2(c_e_h_1, c_e, s9) | (~m_c_h_element_v_out(c_e_h_1, c_e, s10))),
% 293.69/186.27 inference(unit_resolution,[status(thm)],[23319, 23013])).
% 293.69/186.27 tff(23321,plain,
% 293.69/186.27 (~m_c_h_element_v_out(c_e_h_1, c_e, s10)),
% 293.69/186.27 inference(unit_resolution,[status(thm)],[23320, 23258])).
% 293.69/186.27 tff(23322,plain,
% 293.69/186.27 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s10) | m_c_h_element_v_out(c_e_h_1, c_e, s10))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s10) | m_c_h_element_v_out(c_e_h_1, c_e, s10))),
% 293.69/186.27 inference(rewrite,[status(thm)],[])).
% 293.69/186.27 tff(23323,plain,
% 293.69/186.27 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s10) | m_c_h_element_v_out(c_e_h_1, c_e, s10))),
% 293.69/186.27 inference(quant_inst,[status(thm)],[])).
% 293.69/186.27 tff(23324,plain,
% 293.69/186.27 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s10) | m_c_h_element_v_out(c_e_h_1, c_e, s10)),
% 293.69/186.27 inference(modus_ponens,[status(thm)],[23323, 23322])).
% 293.69/186.27 tff(23325,plain,
% 293.69/186.27 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s10) | m_c_h_element_v_out(c_e_h_1, c_e, s10)),
% 293.69/186.27 inference(unit_resolution,[status(thm)],[23324, 7856])).
% 293.69/186.27 tff(23326,plain,
% 293.69/186.27 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s10)),
% 293.69/186.27 inference(unit_resolution,[status(thm)],[23325, 23321])).
% 293.69/186.27 tff(23327,plain,
% 293.69/186.27 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s7)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s8))),
% 293.69/186.27 inference(unit_resolution,[status(thm)],[23067, 17887])).
% 293.69/186.27 tff(23328,plain,
% 293.69/186.27 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s9)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s8))),
% 293.69/186.27 inference(unit_resolution,[status(thm)],[23327, 19216])).
% 293.69/186.27 tff(23329,plain,
% 293.69/186.27 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10)),
% 293.69/186.27 inference(unit_resolution,[status(thm)],[23328, 23021, 22545])).
% 293.69/186.27 tff(23330,plain,
% 293.69/186.27 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s10) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s10) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10))),
% 293.69/186.27 inference(rewrite,[status(thm)],[])).
% 293.69/186.27 tff(23331,plain,
% 293.69/186.27 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s10) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10))),
% 293.69/186.27 inference(quant_inst,[status(thm)],[])).
% 293.69/186.27 tff(23332,plain,
% 293.69/186.27 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s10) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)),
% 293.69/186.27 inference(modus_ponens,[status(thm)],[23331, 23330])).
% 293.69/186.27 tff(23333,plain,
% 293.69/186.27 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s10) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)),
% 293.69/186.27 inference(unit_resolution,[status(thm)],[23332, 7868])).
% 293.69/186.27 tff(23334,plain,
% 293.69/186.27 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s10)),
% 293.69/186.27 inference(unit_resolution,[status(thm)],[23333, 22659])).
% 293.69/186.27 tff(23335,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10)), introduced(assumption)).
% 293.69/186.27 tff(23336,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11)), introduced(assumption)).
% 293.69/186.27 tff(23337,assumption,(node11(c_e_h_1, c_n, s10, s11)), introduced(assumption)).
% 293.69/186.27 tff(23338,plain,
% 293.69/186.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10)) | (~node11(c_e_h_1, c_n, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10)) | (~node11(c_e_h_1, c_n, s10, s11)))),
% 293.69/186.27 inference(rewrite,[status(thm)],[])).
% 293.69/186.27 tff(23339,plain,
% 293.69/186.27 ((m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11) | (~node11(c_e_h_1, c_n, s10, s11)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10))) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10)) | (~node11(c_e_h_1, c_n, s10, s11)))),
% 293.69/186.27 inference(rewrite,[status(thm)],[])).
% 293.69/186.27 tff(23340,plain,
% 293.69/186.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11) | (~node11(c_e_h_1, c_n, s10, s11)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10)) | (~node11(c_e_h_1, c_n, s10, s11))))),
% 293.69/186.27 inference(monotonicity,[status(thm)],[23339])).
% 293.69/186.27 tff(23341,plain,
% 293.69/186.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11) | (~node11(c_e_h_1, c_n, s10, s11)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10)) | (~node11(c_e_h_1, c_n, s10, s11)))),
% 293.69/186.27 inference(transitivity,[status(thm)],[23340, 23338])).
% 293.69/186.27 tff(23342,plain,
% 293.69/186.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11) | (~node11(c_e_h_1, c_n, s10, s11)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10)))),
% 293.69/186.27 inference(quant_inst,[status(thm)],[])).
% 293.69/186.27 tff(23343,plain,
% 293.69/186.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10)) | (~node11(c_e_h_1, c_n, s10, s11))),
% 293.69/186.27 inference(modus_ponens,[status(thm)],[23342, 23341])).
% 293.69/186.27 tff(23344,plain,
% 293.69/186.27 ($false),
% 293.69/186.27 inference(unit_resolution,[status(thm)],[23343, 5742, 23336, 23335, 23337])).
% 293.69/186.27 tff(23345,plain,((~node11(c_e_h_1, c_n, s10, s11)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10))), inference(lemma,lemma(discharge,[]))).
% 293.69/186.27 tff(23346,plain,
% 293.69/186.27 (~node11(c_e_h_1, c_n, s10, s11)),
% 293.69/186.27 inference(unit_resolution,[status(thm)],[23345, 23336, 23335])).
% 293.69/186.27 tff(23347,plain,
% 293.69/186.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s10, s11)) | node10(c_e_h_1, c_n, s10, s11) | node11(c_e_h_1, c_n, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s10, s11)) | node10(c_e_h_1, c_n, s10, s11) | node11(c_e_h_1, c_n, s10, s11))),
% 293.69/186.27 inference(rewrite,[status(thm)],[])).
% 293.69/186.27 tff(23348,plain,
% 293.69/186.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s10, s11)) | node10(c_e_h_1, c_n, s10, s11) | node11(c_e_h_1, c_n, s10, s11))),
% 293.69/186.27 inference(quant_inst,[status(thm)],[])).
% 293.69/186.27 tff(23349,plain,
% 293.69/186.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s10, s11)) | node10(c_e_h_1, c_n, s10, s11) | node11(c_e_h_1, c_n, s10, s11)),
% 293.69/186.27 inference(modus_ponens,[status(thm)],[23348, 23347])).
% 293.69/186.27 tff(23350,plain,
% 293.69/186.27 (node10(c_e_h_1, c_n, s10, s11) | node11(c_e_h_1, c_n, s10, s11)),
% 293.69/186.27 inference(unit_resolution,[status(thm)],[23349, 5002, 7748])).
% 293.69/186.27 tff(23351,plain,
% 293.69/186.27 (node10(c_e_h_1, c_n, s10, s11)),
% 293.69/186.27 inference(unit_resolution,[status(thm)],[23350, 23346])).
% 293.69/186.27 tff(23352,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s10)), introduced(assumption)).
% 293.69/186.27 tff(23353,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s10)), introduced(assumption)).
% 293.69/186.27 tff(23354,plain,
% 293.69/186.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s10)) | (~node10(c_e_h_1, c_n, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s10)) | (~node10(c_e_h_1, c_n, s10, s11)))),
% 293.69/186.28 inference(rewrite,[status(thm)],[])).
% 293.69/186.28 tff(23355,plain,
% 293.69/186.28 (((~node10(c_e_h_1, c_n, s10, s11)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s10)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11)) <=> ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s10)) | (~node10(c_e_h_1, c_n, s10, s11)))),
% 293.69/186.28 inference(rewrite,[status(thm)],[])).
% 293.69/186.28 tff(23356,plain,
% 293.69/186.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s10, s11)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s10)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s10)) | (~node10(c_e_h_1, c_n, s10, s11))))),
% 293.69/186.28 inference(monotonicity,[status(thm)],[23355])).
% 293.69/186.28 tff(23357,plain,
% 293.69/186.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s10, s11)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s10)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s10)) | (~node10(c_e_h_1, c_n, s10, s11)))),
% 293.69/186.28 inference(transitivity,[status(thm)],[23356, 23354])).
% 293.69/186.28 tff(23358,plain,
% 293.69/186.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s10, s11)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s10)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11))),
% 293.69/186.28 inference(quant_inst,[status(thm)],[])).
% 293.69/186.28 tff(23359,plain,
% 293.69/186.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s10)) | (~node10(c_e_h_1, c_n, s10, s11))),
% 293.69/186.28 inference(modus_ponens,[status(thm)],[23358, 23357])).
% 293.69/186.28 tff(23360,plain,
% 293.69/186.28 ($false),
% 293.69/186.28 inference(unit_resolution,[status(thm)],[23359, 5718, 23353, 23352, 23336, 23351])).
% 293.69/186.28 tff(23361,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s10)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s10)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s10))), inference(lemma,lemma(discharge,[]))).
% 293.69/186.28 tff(23362,plain,
% 293.69/186.28 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s10))),
% 293.69/186.28 inference(unit_resolution,[status(thm)],[23361, 23334, 23329])).
% 293.69/186.28 tff(23363,plain,
% 293.69/186.28 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11)),
% 293.69/186.28 inference(unit_resolution,[status(thm)],[23362, 23326])).
% 293.69/186.28 tff(23364,plain,
% 293.69/186.28 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s11)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s11)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11)))),
% 293.69/186.28 inference(rewrite,[status(thm)],[])).
% 293.69/186.28 tff(23365,plain,
% 293.69/186.28 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s11)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11)))),
% 293.69/186.28 inference(quant_inst,[status(thm)],[])).
% 293.69/186.28 tff(23366,plain,
% 293.69/186.28 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s11)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11))),
% 293.69/186.28 inference(modus_ponens,[status(thm)],[23365, 23364])).
% 293.69/186.28 tff(23367,plain,
% 293.69/186.28 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s11)),
% 293.69/186.28 inference(unit_resolution,[status(thm)],[23366, 4958, 23363])).
% 293.69/186.28 tff(23368,plain,
% 293.69/186.28 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s11)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s11))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s11)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s11))),
% 293.69/186.28 inference(rewrite,[status(thm)],[])).
% 293.69/186.28 tff(23369,plain,
% 293.69/186.28 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s11)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s11))),
% 293.69/186.28 inference(quant_inst,[status(thm)],[])).
% 293.69/186.28 tff(23370,plain,
% 293.69/186.28 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s11)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s11)),
% 293.69/186.28 inference(modus_ponens,[status(thm)],[23369, 23368])).
% 293.69/186.28 tff(23371,plain,
% 293.69/186.28 (~node9(c_e_h_1, c_m, s11)),
% 293.69/186.28 inference(unit_resolution,[status(thm)],[23370, 4972, 23367])).
% 293.69/186.28 tff(23372,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)), introduced(assumption)).
% 293.69/186.28 tff(23373,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)), introduced(assumption)).
% 293.69/186.28 tff(23374,assumption,(node11(c_e_h_1, c_m, s11, s12)), introduced(assumption)).
% 293.69/186.28 tff(23375,plain,
% 293.69/186.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)) | (~node11(c_e_h_1, c_m, s11, s12)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)) | (~node11(c_e_h_1, c_m, s11, s12)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11))),
% 293.69/186.28 inference(rewrite,[status(thm)],[])).
% 293.69/186.28 tff(23376,plain,
% 293.69/186.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)) | (~node11(c_e_h_1, c_m, s11, s12)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11))),
% 293.69/186.28 inference(quant_inst,[status(thm)],[])).
% 293.69/186.28 tff(23377,plain,
% 293.69/186.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)) | (~node11(c_e_h_1, c_m, s11, s12)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)),
% 293.69/186.28 inference(modus_ponens,[status(thm)],[23376, 23375])).
% 293.69/186.28 tff(23378,plain,
% 293.69/186.28 ($false),
% 293.69/186.28 inference(unit_resolution,[status(thm)],[23377, 5017, 23372, 23373, 23374])).
% 293.69/186.28 tff(23379,plain,((~node11(c_e_h_1, c_m, s11, s12)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12))), inference(lemma,lemma(discharge,[]))).
% 293.69/186.28 tff(23380,plain,
% 293.69/186.28 (~node11(c_e_h_1, c_m, s11, s12)),
% 293.69/186.28 inference(unit_resolution,[status(thm)],[23379, 23373, 23372])).
% 293.69/186.28 tff(23381,assumption,(~node9(c_e_h_1, c_m, s11)), introduced(assumption)).
% 293.69/186.28 tff(23382,assumption,(node10(c_e_h_1, c_m, s11, s12)), introduced(assumption)).
% 293.69/186.28 tff(23383,plain,
% 293.69/186.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~node10(c_e_h_1, c_m, s11, s12)) | node9(c_e_h_1, c_m, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~node10(c_e_h_1, c_m, s11, s12)) | node9(c_e_h_1, c_m, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)))),
% 293.69/186.28 inference(rewrite,[status(thm)],[])).
% 293.69/186.28 tff(23384,plain,
% 293.69/186.28 ((node9(c_e_h_1, c_m, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)) | (~node10(c_e_h_1, c_m, s11, s12))) <=> ((~node10(c_e_h_1, c_m, s11, s12)) | node9(c_e_h_1, c_m, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)))),
% 293.69/186.28 inference(rewrite,[status(thm)],[])).
% 293.69/186.28 tff(23385,plain,
% 293.69/186.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)) | (~node10(c_e_h_1, c_m, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~node10(c_e_h_1, c_m, s11, s12)) | node9(c_e_h_1, c_m, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12))))),
% 293.69/186.28 inference(monotonicity,[status(thm)],[23384])).
% 293.69/186.28 tff(23386,plain,
% 293.69/186.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)) | (~node10(c_e_h_1, c_m, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~node10(c_e_h_1, c_m, s11, s12)) | node9(c_e_h_1, c_m, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)))),
% 293.69/186.28 inference(transitivity,[status(thm)],[23385, 23383])).
% 293.69/186.28 tff(23387,plain,
% 293.69/186.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)) | (~node10(c_e_h_1, c_m, s11, s12)))),
% 293.69/186.28 inference(quant_inst,[status(thm)],[])).
% 293.69/186.28 tff(23388,plain,
% 293.69/186.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~node10(c_e_h_1, c_m, s11, s12)) | node9(c_e_h_1, c_m, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12))),
% 293.69/186.28 inference(modus_ponens,[status(thm)],[23387, 23386])).
% 293.69/186.28 tff(23389,plain,
% 293.69/186.28 ($false),
% 293.69/186.28 inference(unit_resolution,[status(thm)],[23388, 4986, 23373, 23382, 23381])).
% 293.69/186.28 tff(23390,plain,((~node10(c_e_h_1, c_m, s11, s12)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)) | node9(c_e_h_1, c_m, s11)), inference(lemma,lemma(discharge,[]))).
% 293.69/186.28 tff(23391,plain,
% 293.69/186.28 (~node10(c_e_h_1, c_m, s11, s12)),
% 293.69/186.28 inference(unit_resolution,[status(thm)],[23390, 23373, 23381])).
% 293.69/186.28 tff(23392,plain,
% 293.69/186.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s11, s12)) | node10(c_e_h_1, c_m, s11, s12) | node11(c_e_h_1, c_m, s11, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s11, s12)) | node10(c_e_h_1, c_m, s11, s12) | node11(c_e_h_1, c_m, s11, s12))),
% 293.69/186.28 inference(rewrite,[status(thm)],[])).
% 293.69/186.28 tff(23393,plain,
% 293.69/186.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s11, s12)) | node10(c_e_h_1, c_m, s11, s12) | node11(c_e_h_1, c_m, s11, s12))),
% 293.69/186.28 inference(quant_inst,[status(thm)],[])).
% 293.69/186.28 tff(23394,plain,
% 293.69/186.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s11, s12)) | node10(c_e_h_1, c_m, s11, s12) | node11(c_e_h_1, c_m, s11, s12)),
% 293.79/186.28 inference(modus_ponens,[status(thm)],[23393, 23392])).
% 293.79/186.28 tff(23395,plain,
% 293.79/186.28 (node10(c_e_h_1, c_m, s11, s12) | node11(c_e_h_1, c_m, s11, s12)),
% 293.79/186.28 inference(unit_resolution,[status(thm)],[23394, 5002, 11461])).
% 293.79/186.28 tff(23396,plain,
% 293.79/186.28 ($false),
% 293.79/186.28 inference(unit_resolution,[status(thm)],[23395, 23391, 23380])).
% 293.79/186.28 tff(23397,plain,((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)) | node9(c_e_h_1, c_m, s11) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)), inference(lemma,lemma(discharge,[]))).
% 293.79/186.28 tff(23398,plain,
% 293.79/186.28 ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)) | node9(c_e_h_1, c_m, s11)),
% 293.79/186.28 inference(unit_resolution,[status(thm)],[23397, 23106])).
% 293.79/186.28 tff(23399,plain,
% 293.79/186.28 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)),
% 293.79/186.28 inference(unit_resolution,[status(thm)],[23398, 23371])).
% 293.79/186.28 tff(23400,plain,
% 293.79/186.28 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s12)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s12)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12))),
% 293.79/186.28 inference(rewrite,[status(thm)],[])).
% 293.79/186.28 tff(23401,plain,
% 293.79/186.28 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s12)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12))),
% 293.79/186.28 inference(quant_inst,[status(thm)],[])).
% 293.79/186.28 tff(23402,plain,
% 293.79/186.28 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s12)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)),
% 293.79/186.28 inference(modus_ponens,[status(thm)],[23401, 23400])).
% 293.79/186.28 tff(23403,plain,
% 293.79/186.28 (~m_and_h_gate_v_in2(c_e_h_1, c_l, s12)),
% 293.79/186.28 inference(unit_resolution,[status(thm)],[23402, 4549, 23399])).
% 293.79/186.28 tff(23404,assumption,(~m_and_h_gate_v_in2(c_e_h_1, c_l, s12)), introduced(assumption)).
% 293.79/186.28 tff(23405,assumption,(node20(c_e_h_1, c_l, s12)), introduced(assumption)).
% 293.79/186.28 tff(23406,plain,
% 293.79/186.28 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s12)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s12))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s12)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s12))),
% 293.79/186.28 inference(rewrite,[status(thm)],[])).
% 293.79/186.28 tff(23407,plain,
% 293.79/186.28 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s12)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s12))),
% 293.79/186.28 inference(quant_inst,[status(thm)],[])).
% 293.79/186.28 tff(23408,plain,
% 293.79/186.28 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s12)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s12)),
% 293.79/186.28 inference(modus_ponens,[status(thm)],[23407, 23406])).
% 293.79/186.28 tff(23409,plain,
% 293.79/186.28 ($false),
% 293.79/186.28 inference(unit_resolution,[status(thm)],[23408, 4563, 23405, 23404])).
% 293.79/186.28 tff(23410,plain,(m_and_h_gate_v_in2(c_e_h_1, c_l, s12) | (~node20(c_e_h_1, c_l, s12))), inference(lemma,lemma(discharge,[]))).
% 293.79/186.28 tff(23411,plain,
% 293.79/186.28 (~node20(c_e_h_1, c_l, s12)),
% 293.79/186.28 inference(unit_resolution,[status(thm)],[23410, 23403])).
% 293.79/186.28 tff(23412,assumption,(~node20(c_e_h_1, c_l, s12)), introduced(assumption)).
% 293.79/186.28 tff(23413,assumption,(m_and_h_gate_v_out(c_e_h_1, c_l, s13)), introduced(assumption)).
% 293.79/186.28 tff(23414,assumption,(node21(c_e_h_1, c_l, s12, s13)), introduced(assumption)).
% 293.79/186.28 tff(23415,plain,
% 293.79/186.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s13)) | node20(c_e_h_1, c_l, s12) | (~node21(c_e_h_1, c_l, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s13)) | node20(c_e_h_1, c_l, s12) | (~node21(c_e_h_1, c_l, s12, s13)))),
% 293.79/186.29 inference(rewrite,[status(thm)],[])).
% 293.79/186.29 tff(23416,plain,
% 293.79/186.29 ((node20(c_e_h_1, c_l, s12) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s13)) | (~node21(c_e_h_1, c_l, s12, s13))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_l, s13)) | node20(c_e_h_1, c_l, s12) | (~node21(c_e_h_1, c_l, s12, s13)))),
% 293.79/186.29 inference(rewrite,[status(thm)],[])).
% 293.79/186.29 tff(23417,plain,
% 293.79/186.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s12) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s13)) | (~node21(c_e_h_1, c_l, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s13)) | node20(c_e_h_1, c_l, s12) | (~node21(c_e_h_1, c_l, s12, s13))))),
% 293.79/186.29 inference(monotonicity,[status(thm)],[23416])).
% 293.79/186.29 tff(23418,plain,
% 293.79/186.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s12) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s13)) | (~node21(c_e_h_1, c_l, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s13)) | node20(c_e_h_1, c_l, s12) | (~node21(c_e_h_1, c_l, s12, s13)))),
% 293.79/186.29 inference(transitivity,[status(thm)],[23417, 23415])).
% 293.79/186.29 tff(23419,plain,
% 293.79/186.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s12) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s13)) | (~node21(c_e_h_1, c_l, s12, s13)))),
% 293.79/186.29 inference(quant_inst,[status(thm)],[])).
% 293.79/186.29 tff(23420,plain,
% 293.79/186.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s13)) | node20(c_e_h_1, c_l, s12) | (~node21(c_e_h_1, c_l, s12, s13))),
% 293.79/186.29 inference(modus_ponens,[status(thm)],[23419, 23418])).
% 293.79/186.29 tff(23421,plain,
% 293.79/186.29 ($false),
% 293.79/186.29 inference(unit_resolution,[status(thm)],[23420, 52, 23413, 23414, 23412])).
% 293.79/186.29 tff(23422,plain,((~node21(c_e_h_1, c_l, s12, s13)) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s13)) | node20(c_e_h_1, c_l, s12)), inference(lemma,lemma(discharge,[]))).
% 293.79/186.29 tff(23423,plain,
% 293.79/186.29 (~node21(c_e_h_1, c_l, s12, s13)),
% 293.79/186.29 inference(unit_resolution,[status(thm)],[23422, 23413, 23412])).
% 293.79/186.29 tff(23424,plain,
% 293.79/186.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s12, s13)) | node21(c_e_h_1, c_l, s12, s13) | node22(c_e_h_1, c_l, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s12, s13)) | node21(c_e_h_1, c_l, s12, s13) | node22(c_e_h_1, c_l, s12, s13))),
% 293.79/186.29 inference(rewrite,[status(thm)],[])).
% 293.79/186.29 tff(23425,plain,
% 293.79/186.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s12, s13)) | node21(c_e_h_1, c_l, s12, s13) | node22(c_e_h_1, c_l, s12, s13))),
% 293.79/186.29 inference(quant_inst,[status(thm)],[])).
% 293.79/186.29 tff(23426,plain,
% 293.79/186.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s12, s13)) | node21(c_e_h_1, c_l, s12, s13) | node22(c_e_h_1, c_l, s12, s13)),
% 293.79/186.29 inference(modus_ponens,[status(thm)],[23425, 23424])).
% 293.79/186.29 tff(23427,plain,
% 293.79/186.29 (node21(c_e_h_1, c_l, s12, s13) | node22(c_e_h_1, c_l, s12, s13)),
% 293.79/186.29 inference(unit_resolution,[status(thm)],[23426, 82, 11856])).
% 293.79/186.29 tff(23428,plain,
% 293.79/186.29 (node22(c_e_h_1, c_l, s12, s13)),
% 293.79/186.29 inference(unit_resolution,[status(thm)],[23427, 23423])).
% 293.79/186.29 tff(23429,plain,
% 293.79/186.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s13)) | (~node22(c_e_h_1, c_l, s12, s13)) | m_and_h_gate_v_out(c_e_h_1, c_l, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s13)) | (~node22(c_e_h_1, c_l, s12, s13)) | m_and_h_gate_v_out(c_e_h_1, c_l, s12))),
% 293.79/186.29 inference(rewrite,[status(thm)],[])).
% 293.79/186.29 tff(23430,plain,
% 293.79/186.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s13)) | (~node22(c_e_h_1, c_l, s12, s13)) | m_and_h_gate_v_out(c_e_h_1, c_l, s12))),
% 293.79/186.29 inference(quant_inst,[status(thm)],[])).
% 293.79/186.29 tff(23431,plain,
% 293.79/186.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s13)) | (~node22(c_e_h_1, c_l, s12, s13)) | m_and_h_gate_v_out(c_e_h_1, c_l, s12)),
% 293.79/186.29 inference(modus_ponens,[status(thm)],[23430, 23429])).
% 293.79/186.29 tff(23432,plain,
% 293.79/186.29 ($false),
% 293.79/186.29 inference(unit_resolution,[status(thm)],[23431, 108, 23413, 23428, 23131])).
% 293.79/186.29 tff(23433,plain,((~m_and_h_gate_v_out(c_e_h_1, c_l, s13)) | node20(c_e_h_1, c_l, s12)), inference(lemma,lemma(discharge,[]))).
% 293.79/186.29 tff(23434,plain,
% 293.79/186.29 (~m_and_h_gate_v_out(c_e_h_1, c_l, s13)),
% 293.79/186.29 inference(unit_resolution,[status(thm)],[23433, 23411])).
% 293.79/186.29 tff(23435,assumption,(m_or_h_gate_v_in1(c_e_h_1, c_j, s13)), introduced(assumption)).
% 293.79/186.29 tff(23436,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_l, s13)), introduced(assumption)).
% 293.79/186.29 tff(23437,plain,
% 293.79/186.29 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s13)) | m_and_h_gate_v_out(c_e_h_1, c_l, s13))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s13)) | m_and_h_gate_v_out(c_e_h_1, c_l, s13))),
% 293.79/186.29 inference(rewrite,[status(thm)],[])).
% 293.79/186.29 tff(23438,plain,
% 293.79/186.29 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s13)) | m_and_h_gate_v_out(c_e_h_1, c_l, s13))),
% 293.79/186.29 inference(quant_inst,[status(thm)],[])).
% 293.79/186.29 tff(23439,plain,
% 293.79/186.29 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s13)) | m_and_h_gate_v_out(c_e_h_1, c_l, s13)),
% 293.79/186.29 inference(modus_ponens,[status(thm)],[23438, 23437])).
% 293.79/186.29 tff(23440,plain,
% 293.79/186.29 ($false),
% 293.79/186.29 inference(unit_resolution,[status(thm)],[23439, 1100, 23436, 23435])).
% 293.79/186.29 tff(23441,plain,((~m_or_h_gate_v_in1(c_e_h_1, c_j, s13)) | m_and_h_gate_v_out(c_e_h_1, c_l, s13)), inference(lemma,lemma(discharge,[]))).
% 293.79/186.29 tff(23442,plain,
% 293.79/186.29 (~m_or_h_gate_v_in1(c_e_h_1, c_j, s13)),
% 293.79/186.29 inference(unit_resolution,[status(thm)],[23441, 23434])).
% 293.79/186.29 tff(23443,assumption,(~m_or_h_gate_v_out(c_e_h_1, c_j, s13)), introduced(assumption)).
% 293.79/186.29 tff(23444,assumption,(m_or_h_gate_v_out(c_e_h_1, c_j, s14)), introduced(assumption)).
% 293.79/186.29 tff(23445,assumption,(node6(c_e_h_1, c_j, s13, s14)), introduced(assumption)).
% 293.79/186.29 tff(23446,plain,
% 293.79/186.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s13) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s14)) | (~node6(c_e_h_1, c_j, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s13) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s14)) | (~node6(c_e_h_1, c_j, s13, s14)))),
% 293.79/186.29 inference(rewrite,[status(thm)],[])).
% 293.79/186.29 tff(23447,plain,
% 293.79/186.29 (((~node6(c_e_h_1, c_j, s13, s14)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s14)) | m_or_h_gate_v_out(c_e_h_1, c_j, s13)) <=> (m_or_h_gate_v_out(c_e_h_1, c_j, s13) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s14)) | (~node6(c_e_h_1, c_j, s13, s14)))),
% 293.79/186.29 inference(rewrite,[status(thm)],[])).
% 293.79/186.29 tff(23448,plain,
% 293.79/186.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s13, s14)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s14)) | m_or_h_gate_v_out(c_e_h_1, c_j, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s13) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s14)) | (~node6(c_e_h_1, c_j, s13, s14))))),
% 293.80/186.30 inference(monotonicity,[status(thm)],[23447])).
% 293.80/186.30 tff(23449,plain,
% 293.80/186.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s13, s14)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s14)) | m_or_h_gate_v_out(c_e_h_1, c_j, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s13) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s14)) | (~node6(c_e_h_1, c_j, s13, s14)))),
% 293.80/186.30 inference(transitivity,[status(thm)],[23448, 23446])).
% 293.80/186.30 tff(23450,plain,
% 293.80/186.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s13, s14)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s14)) | m_or_h_gate_v_out(c_e_h_1, c_j, s13))),
% 293.80/186.30 inference(quant_inst,[status(thm)],[])).
% 293.80/186.30 tff(23451,plain,
% 293.80/186.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s13) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s14)) | (~node6(c_e_h_1, c_j, s13, s14))),
% 293.80/186.30 inference(modus_ponens,[status(thm)],[23450, 23449])).
% 293.80/186.30 tff(23452,plain,
% 293.80/186.30 ($false),
% 293.80/186.30 inference(unit_resolution,[status(thm)],[23451, 1121, 23443, 23445, 23444])).
% 293.80/186.30 tff(23453,plain,((~node6(c_e_h_1, c_j, s13, s14)) | m_or_h_gate_v_out(c_e_h_1, c_j, s13) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s14))), inference(lemma,lemma(discharge,[]))).
% 293.80/186.30 tff(23454,plain,
% 293.80/186.30 (~node6(c_e_h_1, c_j, s13, s14)),
% 293.80/186.30 inference(unit_resolution,[status(thm)],[23453, 23444, 23443])).
% 293.80/186.30 tff(23455,assumption,(~m_or_h_gate_v_in1(c_e_h_1, c_j, s13)), introduced(assumption)).
% 293.80/186.30 tff(23456,assumption,(~m_or_h_gate_v_in2(c_e_h_1, c_j, s13)), introduced(assumption)).
% 293.80/186.30 tff(23457,assumption,(node5(c_e_h_1, c_j, s13, s14)), introduced(assumption)).
% 293.80/186.30 tff(23458,plain,
% 293.80/186.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~node5(c_e_h_1, c_j, s13, s14)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s13) | m_or_h_gate_v_in2(c_e_h_1, c_j, s13) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~node5(c_e_h_1, c_j, s13, s14)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s13) | m_or_h_gate_v_in2(c_e_h_1, c_j, s13) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s14)))),
% 293.80/186.30 inference(rewrite,[status(thm)],[])).
% 293.80/186.30 tff(23459,plain,
% 293.80/186.30 ((m_or_h_gate_v_in1(c_e_h_1, c_j, s13) | m_or_h_gate_v_in2(c_e_h_1, c_j, s13) | (~node5(c_e_h_1, c_j, s13, s14)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s14))) <=> ((~node5(c_e_h_1, c_j, s13, s14)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s13) | m_or_h_gate_v_in2(c_e_h_1, c_j, s13) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s14)))),
% 293.80/186.30 inference(rewrite,[status(thm)],[])).
% 293.80/186.30 tff(23460,plain,
% 293.80/186.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s13) | m_or_h_gate_v_in2(c_e_h_1, c_j, s13) | (~node5(c_e_h_1, c_j, s13, s14)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~node5(c_e_h_1, c_j, s13, s14)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s13) | m_or_h_gate_v_in2(c_e_h_1, c_j, s13) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s14))))),
% 293.80/186.30 inference(monotonicity,[status(thm)],[23459])).
% 293.80/186.30 tff(23461,plain,
% 293.80/186.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s13) | m_or_h_gate_v_in2(c_e_h_1, c_j, s13) | (~node5(c_e_h_1, c_j, s13, s14)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~node5(c_e_h_1, c_j, s13, s14)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s13) | m_or_h_gate_v_in2(c_e_h_1, c_j, s13) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s14)))),
% 293.80/186.30 inference(transitivity,[status(thm)],[23460, 23458])).
% 293.80/186.30 tff(23462,plain,
% 293.80/186.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s13) | m_or_h_gate_v_in2(c_e_h_1, c_j, s13) | (~node5(c_e_h_1, c_j, s13, s14)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s14)))),
% 293.80/186.30 inference(quant_inst,[status(thm)],[])).
% 293.80/186.30 tff(23463,plain,
% 293.80/186.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~node5(c_e_h_1, c_j, s13, s14)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s13) | m_or_h_gate_v_in2(c_e_h_1, c_j, s13) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s14))),
% 293.80/186.30 inference(modus_ponens,[status(thm)],[23462, 23461])).
% 293.80/186.30 tff(23464,plain,
% 293.80/186.30 ($false),
% 293.80/186.30 inference(unit_resolution,[status(thm)],[23463, 1159, 23457, 23444, 23455, 23456])).
% 293.80/186.30 tff(23465,plain,((~node5(c_e_h_1, c_j, s13, s14)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s14)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s13) | m_or_h_gate_v_in2(c_e_h_1, c_j, s13)), inference(lemma,lemma(discharge,[]))).
% 293.80/186.30 tff(23466,plain,
% 293.80/186.30 (~node5(c_e_h_1, c_j, s13, s14)),
% 293.80/186.30 inference(unit_resolution,[status(thm)],[23465, 23444, 23456, 23455])).
% 293.80/186.30 tff(23467,plain,
% 293.80/186.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s13, s14)) | node6(c_e_h_1, c_j, s13, s14) | node5(c_e_h_1, c_j, s13, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s13, s14)) | node6(c_e_h_1, c_j, s13, s14) | node5(c_e_h_1, c_j, s13, s14))),
% 293.80/186.30 inference(rewrite,[status(thm)],[])).
% 293.80/186.30 tff(23468,plain,
% 293.80/186.30 ((node6(c_e_h_1, c_j, s13, s14) | node5(c_e_h_1, c_j, s13, s14) | (~trans(s13, s14))) <=> ((~trans(s13, s14)) | node6(c_e_h_1, c_j, s13, s14) | node5(c_e_h_1, c_j, s13, s14))),
% 293.80/186.30 inference(rewrite,[status(thm)],[])).
% 293.80/186.30 tff(23469,plain,
% 293.80/186.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s13, s14) | node5(c_e_h_1, c_j, s13, s14) | (~trans(s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s13, s14)) | node6(c_e_h_1, c_j, s13, s14) | node5(c_e_h_1, c_j, s13, s14)))),
% 293.80/186.30 inference(monotonicity,[status(thm)],[23468])).
% 293.80/186.30 tff(23470,plain,
% 293.80/186.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s13, s14) | node5(c_e_h_1, c_j, s13, s14) | (~trans(s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s13, s14)) | node6(c_e_h_1, c_j, s13, s14) | node5(c_e_h_1, c_j, s13, s14))),
% 293.80/186.30 inference(transitivity,[status(thm)],[23469, 23467])).
% 293.80/186.30 tff(23471,plain,
% 293.80/186.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s13, s14) | node5(c_e_h_1, c_j, s13, s14) | (~trans(s13, s14)))),
% 293.80/186.30 inference(quant_inst,[status(thm)],[])).
% 293.80/186.30 tff(23472,plain,
% 293.80/186.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s13, s14)) | node6(c_e_h_1, c_j, s13, s14) | node5(c_e_h_1, c_j, s13, s14)),
% 293.80/186.30 inference(modus_ponens,[status(thm)],[23471, 23470])).
% 293.80/186.30 tff(23473,plain,
% 293.80/186.30 (node6(c_e_h_1, c_j, s13, s14) | node5(c_e_h_1, c_j, s13, s14)),
% 293.80/186.30 inference(unit_resolution,[status(thm)],[23472, 1141, 12831])).
% 293.80/186.30 tff(23474,plain,
% 293.80/186.30 ($false),
% 293.80/186.30 inference(unit_resolution,[status(thm)],[23473, 23466, 23454])).
% 293.80/186.30 tff(23475,plain,((~m_or_h_gate_v_out(c_e_h_1, c_j, s14)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s13) | m_or_h_gate_v_in1(c_e_h_1, c_j, s13) | m_or_h_gate_v_out(c_e_h_1, c_j, s13)), inference(lemma,lemma(discharge,[]))).
% 293.80/186.30 tff(23476,plain,
% 293.80/186.30 ((~m_or_h_gate_v_out(c_e_h_1, c_j, s14)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s13) | m_or_h_gate_v_out(c_e_h_1, c_j, s13)),
% 293.80/186.30 inference(unit_resolution,[status(thm)],[23475, 23442])).
% 293.80/186.30 tff(23477,plain,
% 293.80/186.30 ((~m_or_h_gate_v_out(c_e_h_1, c_j, s14)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s13)),
% 293.80/186.30 inference(unit_resolution,[status(thm)],[23476, 23156])).
% 293.80/186.30 tff(23478,plain,
% 293.80/186.30 (~m_or_h_gate_v_out(c_e_h_1, c_j, s14)),
% 293.80/186.30 inference(unit_resolution,[status(thm)],[23477, 22063])).
% 293.80/186.30 tff(23479,assumption,(m_c_h_element_v_in2(c_e_h_1, c_h, s14)), introduced(assumption)).
% 293.80/186.30 tff(23480,assumption,(~m_or_h_gate_v_out(c_e_h_1, c_j, s14)), introduced(assumption)).
% 293.80/186.30 tff(23481,plain,
% 293.80/186.30 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s14)) | m_or_h_gate_v_out(c_e_h_1, c_j, s14))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s14)) | m_or_h_gate_v_out(c_e_h_1, c_j, s14))),
% 293.80/186.30 inference(rewrite,[status(thm)],[])).
% 293.80/186.30 tff(23482,plain,
% 293.80/186.30 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s14)) | m_or_h_gate_v_out(c_e_h_1, c_j, s14))),
% 293.80/186.30 inference(quant_inst,[status(thm)],[])).
% 293.80/186.30 tff(23483,plain,
% 293.80/186.30 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s14)) | m_or_h_gate_v_out(c_e_h_1, c_j, s14)),
% 293.80/186.30 inference(modus_ponens,[status(thm)],[23482, 23481])).
% 293.80/186.30 tff(23484,plain,
% 293.80/186.30 ($false),
% 293.80/186.30 inference(unit_resolution,[status(thm)],[23483, 1174, 23480, 23479])).
% 293.80/186.30 tff(23485,plain,((~m_c_h_element_v_in2(c_e_h_1, c_h, s14)) | m_or_h_gate_v_out(c_e_h_1, c_j, s14)), inference(lemma,lemma(discharge,[]))).
% 293.80/186.30 tff(23486,plain,
% 293.80/186.30 (~m_c_h_element_v_in2(c_e_h_1, c_h, s14)),
% 293.80/186.30 inference(unit_resolution,[status(thm)],[23485, 23478])).
% 293.80/186.30 tff(23487,plain,
% 293.80/186.30 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s13)) | m_or_h_gate_v_out(c_e_h_1, c_j, s13))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s13)) | m_or_h_gate_v_out(c_e_h_1, c_j, s13))),
% 293.80/186.30 inference(rewrite,[status(thm)],[])).
% 293.80/186.30 tff(23488,plain,
% 293.80/186.30 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s13)) | m_or_h_gate_v_out(c_e_h_1, c_j, s13))),
% 293.80/186.30 inference(quant_inst,[status(thm)],[])).
% 293.80/186.30 tff(23489,plain,
% 293.80/186.30 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s13)) | m_or_h_gate_v_out(c_e_h_1, c_j, s13)),
% 293.80/186.30 inference(modus_ponens,[status(thm)],[23488, 23487])).
% 293.80/186.30 tff(23490,plain,
% 293.80/186.30 (~m_c_h_element_v_in2(c_e_h_1, c_h, s13)),
% 293.80/186.30 inference(unit_resolution,[status(thm)],[23489, 1174, 23156])).
% 293.80/186.30 tff(23491,plain,
% 293.80/186.30 (~m_or_h_gate_v_out(c_e_h_1, c_j, s10)),
% 293.80/186.30 inference(unit_resolution,[status(thm)],[22417, 22093])).
% 293.80/186.30 tff(23492,plain,
% 293.80/186.30 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s10)) | m_or_h_gate_v_out(c_e_h_1, c_j, s10))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s10)) | m_or_h_gate_v_out(c_e_h_1, c_j, s10))),
% 293.80/186.30 inference(rewrite,[status(thm)],[])).
% 293.80/186.30 tff(23493,plain,
% 293.80/186.30 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s10)) | m_or_h_gate_v_out(c_e_h_1, c_j, s10))),
% 293.80/186.30 inference(quant_inst,[status(thm)],[])).
% 293.80/186.30 tff(23494,plain,
% 293.80/186.30 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s10)) | m_or_h_gate_v_out(c_e_h_1, c_j, s10)),
% 293.80/186.31 inference(modus_ponens,[status(thm)],[23493, 23492])).
% 293.80/186.31 tff(23495,plain,
% 293.80/186.31 (~m_c_h_element_v_in2(c_e_h_1, c_h, s10)),
% 293.80/186.31 inference(unit_resolution,[status(thm)],[23494, 1174, 23491])).
% 293.80/186.31 tff(23496,plain,
% 293.80/186.31 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s9)) | m_or_h_gate_v_out(c_e_h_1, c_j, s9))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s9)) | m_or_h_gate_v_out(c_e_h_1, c_j, s9))),
% 293.80/186.31 inference(rewrite,[status(thm)],[])).
% 293.80/186.31 tff(23497,plain,
% 293.80/186.31 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s9)) | m_or_h_gate_v_out(c_e_h_1, c_j, s9))),
% 293.80/186.31 inference(quant_inst,[status(thm)],[])).
% 293.80/186.31 tff(23498,plain,
% 293.80/186.31 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s9)) | m_or_h_gate_v_out(c_e_h_1, c_j, s9)),
% 293.80/186.31 inference(modus_ponens,[status(thm)],[23497, 23496])).
% 293.80/186.31 tff(23499,plain,
% 293.80/186.31 (~m_c_h_element_v_in2(c_e_h_1, c_h, s9)),
% 293.80/186.31 inference(unit_resolution,[status(thm)],[23498, 1174, 22300])).
% 293.80/186.31 tff(23500,plain,
% 293.80/186.31 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s8)) | m_or_h_gate_v_out(c_e_h_1, c_j, s8))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s8)) | m_or_h_gate_v_out(c_e_h_1, c_j, s8))),
% 293.80/186.31 inference(rewrite,[status(thm)],[])).
% 293.80/186.31 tff(23501,plain,
% 293.80/186.31 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s8)) | m_or_h_gate_v_out(c_e_h_1, c_j, s8))),
% 293.80/186.31 inference(quant_inst,[status(thm)],[])).
% 293.80/186.31 tff(23502,plain,
% 293.80/186.31 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s8)) | m_or_h_gate_v_out(c_e_h_1, c_j, s8)),
% 293.80/186.31 inference(modus_ponens,[status(thm)],[23501, 23500])).
% 293.80/186.31 tff(23503,plain,
% 293.80/186.31 (~m_c_h_element_v_in2(c_e_h_1, c_h, s8)),
% 293.80/186.31 inference(unit_resolution,[status(thm)],[23502, 1174, 22232])).
% 293.80/186.31 tff(23504,assumption,(m_c_h_element_v_out(c_e_h_1, c_h, s9)), introduced(assumption)).
% 293.80/186.31 tff(23505,assumption,(~m_c_h_element_v_out(c_e_h_1, c_h, s8)), introduced(assumption)).
% 293.80/186.31 tff(23506,assumption,(node15(c_e_h_1, c_h, s8, s9)), introduced(assumption)).
% 293.80/186.31 tff(23507,plain,
% 293.80/186.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s9)) | (~node15(c_e_h_1, c_h, s8, s9)) | m_c_h_element_v_out(c_e_h_1, c_h, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s9)) | (~node15(c_e_h_1, c_h, s8, s9)) | m_c_h_element_v_out(c_e_h_1, c_h, s8))),
% 293.80/186.31 inference(rewrite,[status(thm)],[])).
% 293.80/186.31 tff(23508,plain,
% 293.80/186.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s9)) | (~node15(c_e_h_1, c_h, s8, s9)) | m_c_h_element_v_out(c_e_h_1, c_h, s8))),
% 293.80/186.31 inference(quant_inst,[status(thm)],[])).
% 293.80/186.31 tff(23509,plain,
% 293.80/186.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s9)) | (~node15(c_e_h_1, c_h, s8, s9)) | m_c_h_element_v_out(c_e_h_1, c_h, s8)),
% 293.80/186.31 inference(modus_ponens,[status(thm)],[23508, 23507])).
% 293.80/186.31 tff(23510,plain,
% 293.80/186.31 ($false),
% 293.80/186.31 inference(unit_resolution,[status(thm)],[23509, 147, 23505, 23504, 23506])).
% 293.80/186.31 tff(23511,plain,((~node15(c_e_h_1, c_h, s8, s9)) | m_c_h_element_v_out(c_e_h_1, c_h, s8) | (~m_c_h_element_v_out(c_e_h_1, c_h, s9))), inference(lemma,lemma(discharge,[]))).
% 293.80/186.31 tff(23512,plain,
% 293.80/186.31 (~node15(c_e_h_1, c_h, s8, s9)),
% 293.80/186.31 inference(unit_resolution,[status(thm)],[23511, 23505, 23504])).
% 293.80/186.31 tff(23513,assumption,(node18(c_e_h_1, c_h, s8, s9)), introduced(assumption)).
% 293.80/186.31 tff(23514,plain,
% 293.80/186.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_h, s8) | (~m_c_h_element_v_out(c_e_h_1, c_h, s9)) | (~node18(c_e_h_1, c_h, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s8) | (~m_c_h_element_v_out(c_e_h_1, c_h, s9)) | (~node18(c_e_h_1, c_h, s8, s9)))),
% 293.80/186.31 inference(rewrite,[status(thm)],[])).
% 293.80/186.31 tff(23515,plain,
% 293.80/186.31 (((~m_c_h_element_v_out(c_e_h_1, c_h, s9)) | m_c_h_element_v_out(c_e_h_1, c_h, s8) | (~node18(c_e_h_1, c_h, s8, s9))) <=> (m_c_h_element_v_out(c_e_h_1, c_h, s8) | (~m_c_h_element_v_out(c_e_h_1, c_h, s9)) | (~node18(c_e_h_1, c_h, s8, s9)))),
% 293.80/186.31 inference(rewrite,[status(thm)],[])).
% 293.80/186.31 tff(23516,plain,
% 293.80/186.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s9)) | m_c_h_element_v_out(c_e_h_1, c_h, s8) | (~node18(c_e_h_1, c_h, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_h, s8) | (~m_c_h_element_v_out(c_e_h_1, c_h, s9)) | (~node18(c_e_h_1, c_h, s8, s9))))),
% 293.80/186.31 inference(monotonicity,[status(thm)],[23515])).
% 293.80/186.31 tff(23517,plain,
% 293.80/186.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s9)) | m_c_h_element_v_out(c_e_h_1, c_h, s8) | (~node18(c_e_h_1, c_h, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s8) | (~m_c_h_element_v_out(c_e_h_1, c_h, s9)) | (~node18(c_e_h_1, c_h, s8, s9)))),
% 293.80/186.31 inference(transitivity,[status(thm)],[23516, 23514])).
% 293.80/186.31 tff(23518,plain,
% 293.80/186.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s9)) | m_c_h_element_v_out(c_e_h_1, c_h, s8) | (~node18(c_e_h_1, c_h, s8, s9)))),
% 293.80/186.31 inference(quant_inst,[status(thm)],[])).
% 293.80/186.31 tff(23519,plain,
% 293.80/186.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s8) | (~m_c_h_element_v_out(c_e_h_1, c_h, s9)) | (~node18(c_e_h_1, c_h, s8, s9))),
% 293.80/186.31 inference(modus_ponens,[status(thm)],[23518, 23517])).
% 293.80/186.31 tff(23520,plain,
% 293.80/186.31 ($false),
% 293.80/186.31 inference(unit_resolution,[status(thm)],[23519, 753, 23505, 23504, 23513])).
% 293.80/186.31 tff(23521,plain,((~node18(c_e_h_1, c_h, s8, s9)) | m_c_h_element_v_out(c_e_h_1, c_h, s8) | (~m_c_h_element_v_out(c_e_h_1, c_h, s9))), inference(lemma,lemma(discharge,[]))).
% 293.80/186.31 tff(23522,plain,
% 293.80/186.31 (~node18(c_e_h_1, c_h, s8, s9)),
% 293.80/186.31 inference(unit_resolution,[status(thm)],[23521, 23505, 23504])).
% 293.80/186.31 tff(23523,plain,
% 293.80/186.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s8, s9)) | node19(c_e_h_1, c_h, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s8, s9)) | node19(c_e_h_1, c_h, s8, s9))),
% 293.80/186.31 inference(rewrite,[status(thm)],[])).
% 293.80/186.31 tff(23524,plain,
% 293.80/186.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s8, s9)) | node19(c_e_h_1, c_h, s8, s9))),
% 293.80/186.31 inference(quant_inst,[status(thm)],[])).
% 293.80/186.31 tff(23525,plain,
% 293.80/186.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s8, s9)) | node19(c_e_h_1, c_h, s8, s9)),
% 293.80/186.31 inference(modus_ponens,[status(thm)],[23524, 23523])).
% 293.80/186.31 tff(23526,plain,
% 293.80/186.31 (node19(c_e_h_1, c_h, s8, s9)),
% 293.80/186.31 inference(unit_resolution,[status(thm)],[23525, 190, 1993])).
% 293.80/186.31 tff(23527,plain,
% 293.80/186.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s8) | (~node19(c_e_h_1, c_h, s8, s9)) | node18(c_e_h_1, c_h, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s8) | (~node19(c_e_h_1, c_h, s8, s9)) | node18(c_e_h_1, c_h, s8, s9))),
% 293.80/186.31 inference(rewrite,[status(thm)],[])).
% 293.80/186.31 tff(23528,plain,
% 293.80/186.31 ((node17(c_e_h_1, c_h, s8) | node18(c_e_h_1, c_h, s8, s9) | (~node19(c_e_h_1, c_h, s8, s9))) <=> (node17(c_e_h_1, c_h, s8) | (~node19(c_e_h_1, c_h, s8, s9)) | node18(c_e_h_1, c_h, s8, s9))),
% 293.80/186.31 inference(rewrite,[status(thm)],[])).
% 293.80/186.31 tff(23529,plain,
% 293.80/186.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s8) | node18(c_e_h_1, c_h, s8, s9) | (~node19(c_e_h_1, c_h, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s8) | (~node19(c_e_h_1, c_h, s8, s9)) | node18(c_e_h_1, c_h, s8, s9)))),
% 293.80/186.31 inference(monotonicity,[status(thm)],[23528])).
% 293.80/186.31 tff(23530,plain,
% 293.80/186.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s8) | node18(c_e_h_1, c_h, s8, s9) | (~node19(c_e_h_1, c_h, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s8) | (~node19(c_e_h_1, c_h, s8, s9)) | node18(c_e_h_1, c_h, s8, s9))),
% 293.80/186.31 inference(transitivity,[status(thm)],[23529, 23527])).
% 293.80/186.31 tff(23531,plain,
% 293.80/186.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s8) | node18(c_e_h_1, c_h, s8, s9) | (~node19(c_e_h_1, c_h, s8, s9)))),
% 293.80/186.31 inference(quant_inst,[status(thm)],[])).
% 293.80/186.31 tff(23532,plain,
% 293.80/186.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s8) | (~node19(c_e_h_1, c_h, s8, s9)) | node18(c_e_h_1, c_h, s8, s9)),
% 293.80/186.31 inference(modus_ponens,[status(thm)],[23531, 23530])).
% 293.80/186.31 tff(23533,plain,
% 293.80/186.31 (node17(c_e_h_1, c_h, s8) | node18(c_e_h_1, c_h, s8, s9)),
% 293.80/186.31 inference(unit_resolution,[status(thm)],[23532, 776, 23526])).
% 293.80/186.31 tff(23534,plain,
% 293.80/186.31 (node17(c_e_h_1, c_h, s8)),
% 293.80/186.31 inference(unit_resolution,[status(thm)],[23533, 23522])).
% 293.80/186.31 tff(23535,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_h, s8)), introduced(assumption)).
% 293.80/186.31 tff(23536,plain,
% 293.80/186.31 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_h, s8) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s8)) | (~node17(c_e_h_1, c_h, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_h, s8) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s8)) | (~node17(c_e_h_1, c_h, s8)))),
% 293.80/186.31 inference(rewrite,[status(thm)],[])).
% 293.80/186.31 tff(23537,plain,
% 293.80/186.31 (((~m_c_h_element_v_in1(c_e_h_1, c_h, s8)) | m_c_h_element_v_in2(c_e_h_1, c_h, s8) | (~node17(c_e_h_1, c_h, s8))) <=> (m_c_h_element_v_in2(c_e_h_1, c_h, s8) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s8)) | (~node17(c_e_h_1, c_h, s8)))),
% 293.80/186.31 inference(rewrite,[status(thm)],[])).
% 293.80/186.31 tff(23538,plain,
% 293.80/186.31 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s8)) | m_c_h_element_v_in2(c_e_h_1, c_h, s8) | (~node17(c_e_h_1, c_h, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_h, s8) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s8)) | (~node17(c_e_h_1, c_h, s8))))),
% 293.80/186.32 inference(monotonicity,[status(thm)],[23537])).
% 293.80/186.32 tff(23539,plain,
% 293.80/186.32 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s8)) | m_c_h_element_v_in2(c_e_h_1, c_h, s8) | (~node17(c_e_h_1, c_h, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_h, s8) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s8)) | (~node17(c_e_h_1, c_h, s8)))),
% 293.80/186.32 inference(transitivity,[status(thm)],[23538, 23536])).
% 293.80/186.32 tff(23540,plain,
% 293.80/186.32 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s8)) | m_c_h_element_v_in2(c_e_h_1, c_h, s8) | (~node17(c_e_h_1, c_h, s8)))),
% 293.80/186.32 inference(quant_inst,[status(thm)],[])).
% 293.80/186.32 tff(23541,plain,
% 293.80/186.32 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_h, s8) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s8)) | (~node17(c_e_h_1, c_h, s8))),
% 293.80/186.32 inference(modus_ponens,[status(thm)],[23540, 23539])).
% 293.80/186.32 tff(23542,plain,
% 293.80/186.32 ((~m_c_h_element_v_in1(c_e_h_1, c_h, s8)) | (~node17(c_e_h_1, c_h, s8))),
% 293.80/186.32 inference(unit_resolution,[status(thm)],[23541, 919, 23535])).
% 293.80/186.32 tff(23543,plain,
% 293.80/186.32 (~m_c_h_element_v_in1(c_e_h_1, c_h, s8)),
% 293.80/186.32 inference(unit_resolution,[status(thm)],[23542, 23534])).
% 293.80/186.32 tff(23544,plain,
% 293.80/186.32 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s8)) | m_c_h_element_v_in1(c_e_h_1, c_h, s8) | m_c_h_element_v_in2(c_e_h_1, c_h, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s8)) | m_c_h_element_v_in1(c_e_h_1, c_h, s8) | m_c_h_element_v_in2(c_e_h_1, c_h, s8))),
% 293.80/186.32 inference(rewrite,[status(thm)],[])).
% 293.80/186.32 tff(23545,plain,
% 293.80/186.32 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s8)) | m_c_h_element_v_in1(c_e_h_1, c_h, s8) | m_c_h_element_v_in2(c_e_h_1, c_h, s8))),
% 293.80/186.32 inference(quant_inst,[status(thm)],[])).
% 293.80/186.32 tff(23546,plain,
% 293.80/186.32 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s8)) | m_c_h_element_v_in1(c_e_h_1, c_h, s8) | m_c_h_element_v_in2(c_e_h_1, c_h, s8)),
% 293.80/186.32 inference(modus_ponens,[status(thm)],[23545, 23544])).
% 293.80/186.32 tff(23547,plain,
% 293.80/186.32 ((~node16(c_e_h_1, c_h, s8)) | m_c_h_element_v_in1(c_e_h_1, c_h, s8)),
% 293.80/186.32 inference(unit_resolution,[status(thm)],[23546, 178, 23535])).
% 293.80/186.32 tff(23548,plain,
% 293.80/186.32 (~node16(c_e_h_1, c_h, s8)),
% 293.80/186.32 inference(unit_resolution,[status(thm)],[23547, 23543])).
% 293.80/186.32 tff(23549,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_h, s8)), introduced(assumption)).
% 293.80/186.32 tff(23550,assumption,(node14(c_e_h_1, c_h, s8, s9)), introduced(assumption)).
% 293.80/186.32 tff(23551,plain,
% 293.80/186.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s9)) | m_c_h_element_v_in1(c_e_h_1, c_h, s8) | (~node14(c_e_h_1, c_h, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s9)) | m_c_h_element_v_in1(c_e_h_1, c_h, s8) | (~node14(c_e_h_1, c_h, s8, s9)))),
% 293.80/186.32 inference(rewrite,[status(thm)],[])).
% 293.80/186.32 tff(23552,plain,
% 293.80/186.32 (((~node14(c_e_h_1, c_h, s8, s9)) | m_c_h_element_v_in1(c_e_h_1, c_h, s8) | (~m_c_h_element_v_out(c_e_h_1, c_h, s9))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_h, s9)) | m_c_h_element_v_in1(c_e_h_1, c_h, s8) | (~node14(c_e_h_1, c_h, s8, s9)))),
% 293.80/186.32 inference(rewrite,[status(thm)],[])).
% 293.80/186.32 tff(23553,plain,
% 293.80/186.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s8, s9)) | m_c_h_element_v_in1(c_e_h_1, c_h, s8) | (~m_c_h_element_v_out(c_e_h_1, c_h, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s9)) | m_c_h_element_v_in1(c_e_h_1, c_h, s8) | (~node14(c_e_h_1, c_h, s8, s9))))),
% 293.80/186.32 inference(monotonicity,[status(thm)],[23552])).
% 293.80/186.32 tff(23554,plain,
% 293.80/186.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s8, s9)) | m_c_h_element_v_in1(c_e_h_1, c_h, s8) | (~m_c_h_element_v_out(c_e_h_1, c_h, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s9)) | m_c_h_element_v_in1(c_e_h_1, c_h, s8) | (~node14(c_e_h_1, c_h, s8, s9)))),
% 293.80/186.32 inference(transitivity,[status(thm)],[23553, 23551])).
% 293.80/186.32 tff(23555,plain,
% 293.80/186.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s8, s9)) | m_c_h_element_v_in1(c_e_h_1, c_h, s8) | (~m_c_h_element_v_out(c_e_h_1, c_h, s9)))),
% 293.80/186.32 inference(quant_inst,[status(thm)],[])).
% 293.80/186.32 tff(23556,plain,
% 293.80/186.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s9)) | m_c_h_element_v_in1(c_e_h_1, c_h, s8) | (~node14(c_e_h_1, c_h, s8, s9))),
% 293.80/186.32 inference(modus_ponens,[status(thm)],[23555, 23554])).
% 293.80/186.32 tff(23557,plain,
% 293.80/186.32 ($false),
% 293.80/186.32 inference(unit_resolution,[status(thm)],[23556, 223, 23504, 23550, 23549])).
% 293.80/186.32 tff(23558,plain,((~node14(c_e_h_1, c_h, s8, s9)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s9)) | m_c_h_element_v_in1(c_e_h_1, c_h, s8)), inference(lemma,lemma(discharge,[]))).
% 293.80/186.32 tff(23559,plain,
% 293.80/186.32 (~node14(c_e_h_1, c_h, s8, s9)),
% 293.80/186.32 inference(unit_resolution,[status(thm)],[23558, 23543, 23504])).
% 293.80/186.32 tff(23560,plain,
% 293.80/186.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_1, c_h, s8, s9) | node16(c_e_h_1, c_h, s8) | node15(c_e_h_1, c_h, s8, s9) | (~node19(c_e_h_1, c_h, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_h, s8, s9) | node16(c_e_h_1, c_h, s8) | node15(c_e_h_1, c_h, s8, s9) | (~node19(c_e_h_1, c_h, s8, s9)))),
% 293.80/186.32 inference(rewrite,[status(thm)],[])).
% 293.80/186.32 tff(23561,plain,
% 293.80/186.32 ((node16(c_e_h_1, c_h, s8) | node14(c_e_h_1, c_h, s8, s9) | node15(c_e_h_1, c_h, s8, s9) | (~node19(c_e_h_1, c_h, s8, s9))) <=> (node14(c_e_h_1, c_h, s8, s9) | node16(c_e_h_1, c_h, s8) | node15(c_e_h_1, c_h, s8, s9) | (~node19(c_e_h_1, c_h, s8, s9)))),
% 293.80/186.32 inference(rewrite,[status(thm)],[])).
% 293.80/186.32 tff(23562,plain,
% 293.80/186.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s8) | node14(c_e_h_1, c_h, s8, s9) | node15(c_e_h_1, c_h, s8, s9) | (~node19(c_e_h_1, c_h, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_1, c_h, s8, s9) | node16(c_e_h_1, c_h, s8) | node15(c_e_h_1, c_h, s8, s9) | (~node19(c_e_h_1, c_h, s8, s9))))),
% 293.80/186.32 inference(monotonicity,[status(thm)],[23561])).
% 293.80/186.32 tff(23563,plain,
% 293.80/186.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s8) | node14(c_e_h_1, c_h, s8, s9) | node15(c_e_h_1, c_h, s8, s9) | (~node19(c_e_h_1, c_h, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_h, s8, s9) | node16(c_e_h_1, c_h, s8) | node15(c_e_h_1, c_h, s8, s9) | (~node19(c_e_h_1, c_h, s8, s9)))),
% 293.83/186.33 inference(transitivity,[status(thm)],[23562, 23560])).
% 293.83/186.33 tff(23564,plain,
% 293.83/186.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s8) | node14(c_e_h_1, c_h, s8, s9) | node15(c_e_h_1, c_h, s8, s9) | (~node19(c_e_h_1, c_h, s8, s9)))),
% 293.83/186.33 inference(quant_inst,[status(thm)],[])).
% 293.83/186.33 tff(23565,plain,
% 293.83/186.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_h, s8, s9) | node16(c_e_h_1, c_h, s8) | node15(c_e_h_1, c_h, s8, s9) | (~node19(c_e_h_1, c_h, s8, s9))),
% 293.83/186.33 inference(modus_ponens,[status(thm)],[23564, 23563])).
% 293.83/186.33 tff(23566,plain,
% 293.83/186.33 (node14(c_e_h_1, c_h, s8, s9) | node16(c_e_h_1, c_h, s8) | node15(c_e_h_1, c_h, s8, s9)),
% 293.83/186.33 inference(unit_resolution,[status(thm)],[23565, 204, 23526])).
% 293.83/186.33 tff(23567,plain,
% 293.83/186.33 ($false),
% 293.83/186.33 inference(unit_resolution,[status(thm)],[23566, 23559, 23548, 23512])).
% 293.83/186.33 tff(23568,plain,(m_c_h_element_v_out(c_e_h_1, c_h, s8) | (~m_c_h_element_v_out(c_e_h_1, c_h, s9)) | m_c_h_element_v_in2(c_e_h_1, c_h, s8)), inference(lemma,lemma(discharge,[]))).
% 293.83/186.33 tff(23569,plain,
% 293.83/186.33 (~m_c_h_element_v_out(c_e_h_1, c_h, s9)),
% 293.83/186.33 inference(unit_resolution,[status(thm)],[23568, 23503, 23226])).
% 293.83/186.33 tff(23570,assumption,(m_c_h_element_v_out(c_e_h_1, c_h, s10)), introduced(assumption)).
% 293.83/186.33 tff(23571,assumption,(~m_c_h_element_v_out(c_e_h_1, c_h, s9)), introduced(assumption)).
% 293.83/186.33 tff(23572,assumption,(node18(c_e_h_1, c_h, s9, s10)), introduced(assumption)).
% 293.83/186.33 tff(23573,plain,
% 293.83/186.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_h, s9) | (~m_c_h_element_v_out(c_e_h_1, c_h, s10)) | (~node18(c_e_h_1, c_h, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s9) | (~m_c_h_element_v_out(c_e_h_1, c_h, s10)) | (~node18(c_e_h_1, c_h, s9, s10)))),
% 293.83/186.33 inference(rewrite,[status(thm)],[])).
% 293.83/186.33 tff(23574,plain,
% 293.83/186.33 (((~m_c_h_element_v_out(c_e_h_1, c_h, s10)) | m_c_h_element_v_out(c_e_h_1, c_h, s9) | (~node18(c_e_h_1, c_h, s9, s10))) <=> (m_c_h_element_v_out(c_e_h_1, c_h, s9) | (~m_c_h_element_v_out(c_e_h_1, c_h, s10)) | (~node18(c_e_h_1, c_h, s9, s10)))),
% 293.83/186.33 inference(rewrite,[status(thm)],[])).
% 293.83/186.33 tff(23575,plain,
% 293.83/186.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s10)) | m_c_h_element_v_out(c_e_h_1, c_h, s9) | (~node18(c_e_h_1, c_h, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_h, s9) | (~m_c_h_element_v_out(c_e_h_1, c_h, s10)) | (~node18(c_e_h_1, c_h, s9, s10))))),
% 293.83/186.33 inference(monotonicity,[status(thm)],[23574])).
% 293.83/186.33 tff(23576,plain,
% 293.83/186.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s10)) | m_c_h_element_v_out(c_e_h_1, c_h, s9) | (~node18(c_e_h_1, c_h, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s9) | (~m_c_h_element_v_out(c_e_h_1, c_h, s10)) | (~node18(c_e_h_1, c_h, s9, s10)))),
% 293.83/186.33 inference(transitivity,[status(thm)],[23575, 23573])).
% 293.83/186.33 tff(23577,plain,
% 293.83/186.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s10)) | m_c_h_element_v_out(c_e_h_1, c_h, s9) | (~node18(c_e_h_1, c_h, s9, s10)))),
% 293.83/186.33 inference(quant_inst,[status(thm)],[])).
% 293.83/186.33 tff(23578,plain,
% 293.83/186.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s9) | (~m_c_h_element_v_out(c_e_h_1, c_h, s10)) | (~node18(c_e_h_1, c_h, s9, s10))),
% 293.83/186.33 inference(modus_ponens,[status(thm)],[23577, 23576])).
% 293.83/186.33 tff(23579,plain,
% 293.83/186.33 ($false),
% 293.83/186.33 inference(unit_resolution,[status(thm)],[23578, 753, 23571, 23570, 23572])).
% 293.83/186.33 tff(23580,plain,((~node18(c_e_h_1, c_h, s9, s10)) | m_c_h_element_v_out(c_e_h_1, c_h, s9) | (~m_c_h_element_v_out(c_e_h_1, c_h, s10))), inference(lemma,lemma(discharge,[]))).
% 293.83/186.33 tff(23581,plain,
% 293.83/186.33 (~node18(c_e_h_1, c_h, s9, s10)),
% 293.83/186.33 inference(unit_resolution,[status(thm)],[23580, 23571, 23570])).
% 293.83/186.33 tff(23582,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_h, s9)), introduced(assumption)).
% 293.83/186.33 tff(23583,plain,
% 293.83/186.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s9, s10)) | node19(c_e_h_1, c_h, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s9, s10)) | node19(c_e_h_1, c_h, s9, s10))),
% 293.83/186.33 inference(rewrite,[status(thm)],[])).
% 293.83/186.33 tff(23584,plain,
% 293.83/186.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s9, s10)) | node19(c_e_h_1, c_h, s9, s10))),
% 293.83/186.33 inference(quant_inst,[status(thm)],[])).
% 293.83/186.33 tff(23585,plain,
% 293.83/186.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s9, s10)) | node19(c_e_h_1, c_h, s9, s10)),
% 293.83/186.33 inference(modus_ponens,[status(thm)],[23584, 23583])).
% 293.83/186.33 tff(23586,plain,
% 293.83/186.33 (node19(c_e_h_1, c_h, s9, s10)),
% 293.83/186.33 inference(unit_resolution,[status(thm)],[23585, 190, 7676])).
% 293.83/186.33 tff(23587,plain,
% 293.83/186.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s9) | node18(c_e_h_1, c_h, s9, s10) | (~node19(c_e_h_1, c_h, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s9) | node18(c_e_h_1, c_h, s9, s10) | (~node19(c_e_h_1, c_h, s9, s10)))),
% 293.83/186.33 inference(rewrite,[status(thm)],[])).
% 293.83/186.33 tff(23588,plain,
% 293.83/186.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s9) | node18(c_e_h_1, c_h, s9, s10) | (~node19(c_e_h_1, c_h, s9, s10)))),
% 293.83/186.33 inference(quant_inst,[status(thm)],[])).
% 293.83/186.33 tff(23589,plain,
% 293.83/186.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s9) | node18(c_e_h_1, c_h, s9, s10) | (~node19(c_e_h_1, c_h, s9, s10))),
% 293.83/186.33 inference(modus_ponens,[status(thm)],[23588, 23587])).
% 293.83/186.33 tff(23590,plain,
% 293.83/186.33 (node17(c_e_h_1, c_h, s9) | node18(c_e_h_1, c_h, s9, s10)),
% 293.83/186.33 inference(unit_resolution,[status(thm)],[23589, 776, 23586])).
% 293.83/186.33 tff(23591,plain,
% 293.83/186.33 (node17(c_e_h_1, c_h, s9)),
% 293.83/186.33 inference(unit_resolution,[status(thm)],[23590, 23581])).
% 293.83/186.33 tff(23592,assumption,(~node14(c_e_h_1, c_h, s9, s10)), introduced(assumption)).
% 293.83/186.33 tff(23593,assumption,(node15(c_e_h_1, c_h, s9, s10)), introduced(assumption)).
% 293.83/186.33 tff(23594,plain,
% 293.83/186.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s10)) | (~node15(c_e_h_1, c_h, s9, s10)) | m_c_h_element_v_out(c_e_h_1, c_h, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s10)) | (~node15(c_e_h_1, c_h, s9, s10)) | m_c_h_element_v_out(c_e_h_1, c_h, s9))),
% 293.83/186.33 inference(rewrite,[status(thm)],[])).
% 293.83/186.33 tff(23595,plain,
% 293.83/186.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s10)) | (~node15(c_e_h_1, c_h, s9, s10)) | m_c_h_element_v_out(c_e_h_1, c_h, s9))),
% 293.83/186.33 inference(quant_inst,[status(thm)],[])).
% 293.83/186.33 tff(23596,plain,
% 293.83/186.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s10)) | (~node15(c_e_h_1, c_h, s9, s10)) | m_c_h_element_v_out(c_e_h_1, c_h, s9)),
% 293.83/186.33 inference(modus_ponens,[status(thm)],[23595, 23594])).
% 293.83/186.33 tff(23597,plain,
% 293.83/186.33 ($false),
% 293.83/186.33 inference(unit_resolution,[status(thm)],[23596, 147, 23571, 23570, 23593])).
% 293.83/186.33 tff(23598,plain,((~node15(c_e_h_1, c_h, s9, s10)) | m_c_h_element_v_out(c_e_h_1, c_h, s9) | (~m_c_h_element_v_out(c_e_h_1, c_h, s10))), inference(lemma,lemma(discharge,[]))).
% 293.83/186.33 tff(23599,plain,
% 293.83/186.33 (~node15(c_e_h_1, c_h, s9, s10)),
% 293.83/186.33 inference(unit_resolution,[status(thm)],[23598, 23571, 23570])).
% 293.83/186.33 tff(23600,plain,
% 293.83/186.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s9) | node14(c_e_h_1, c_h, s9, s10) | node15(c_e_h_1, c_h, s9, s10) | (~node19(c_e_h_1, c_h, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s9) | node14(c_e_h_1, c_h, s9, s10) | node15(c_e_h_1, c_h, s9, s10) | (~node19(c_e_h_1, c_h, s9, s10)))),
% 293.83/186.33 inference(rewrite,[status(thm)],[])).
% 293.83/186.33 tff(23601,plain,
% 293.83/186.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s9) | node14(c_e_h_1, c_h, s9, s10) | node15(c_e_h_1, c_h, s9, s10) | (~node19(c_e_h_1, c_h, s9, s10)))),
% 293.83/186.33 inference(quant_inst,[status(thm)],[])).
% 293.83/186.33 tff(23602,plain,
% 293.83/186.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s9) | node14(c_e_h_1, c_h, s9, s10) | node15(c_e_h_1, c_h, s9, s10) | (~node19(c_e_h_1, c_h, s9, s10))),
% 293.83/186.33 inference(modus_ponens,[status(thm)],[23601, 23600])).
% 293.83/186.33 tff(23603,plain,
% 293.83/186.33 (node16(c_e_h_1, c_h, s9) | node14(c_e_h_1, c_h, s9, s10) | node15(c_e_h_1, c_h, s9, s10)),
% 293.83/186.33 inference(unit_resolution,[status(thm)],[23602, 204, 23586])).
% 293.83/186.33 tff(23604,plain,
% 293.83/186.33 (node16(c_e_h_1, c_h, s9)),
% 293.83/186.33 inference(unit_resolution,[status(thm)],[23603, 23599, 23592])).
% 293.83/186.33 tff(23605,assumption,(node17(c_e_h_1, c_h, s9)), introduced(assumption)).
% 293.83/186.33 tff(23606,assumption,(node16(c_e_h_1, c_h, s9)), introduced(assumption)).
% 293.83/186.33 tff(23607,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_h, s9)), introduced(assumption)).
% 293.83/186.33 tff(23608,plain,
% 293.83/186.33 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_h, s9)) | m_c_h_element_v_in2(c_e_h_1, c_h, s9) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_h, s9)) | m_c_h_element_v_in2(c_e_h_1, c_h, s9) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s9)))),
% 293.83/186.33 inference(rewrite,[status(thm)],[])).
% 293.83/186.33 tff(23609,plain,
% 293.83/186.33 (((~m_c_h_element_v_in1(c_e_h_1, c_h, s9)) | m_c_h_element_v_in2(c_e_h_1, c_h, s9) | (~node17(c_e_h_1, c_h, s9))) <=> ((~node17(c_e_h_1, c_h, s9)) | m_c_h_element_v_in2(c_e_h_1, c_h, s9) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s9)))),
% 293.83/186.33 inference(rewrite,[status(thm)],[])).
% 293.83/186.33 tff(23610,plain,
% 293.83/186.33 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s9)) | m_c_h_element_v_in2(c_e_h_1, c_h, s9) | (~node17(c_e_h_1, c_h, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_h, s9)) | m_c_h_element_v_in2(c_e_h_1, c_h, s9) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s9))))),
% 293.83/186.33 inference(monotonicity,[status(thm)],[23609])).
% 293.83/186.33 tff(23611,plain,
% 293.83/186.33 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s9)) | m_c_h_element_v_in2(c_e_h_1, c_h, s9) | (~node17(c_e_h_1, c_h, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_h, s9)) | m_c_h_element_v_in2(c_e_h_1, c_h, s9) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s9)))),
% 293.83/186.34 inference(transitivity,[status(thm)],[23610, 23608])).
% 293.83/186.34 tff(23612,plain,
% 293.83/186.34 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s9)) | m_c_h_element_v_in2(c_e_h_1, c_h, s9) | (~node17(c_e_h_1, c_h, s9)))),
% 293.83/186.34 inference(quant_inst,[status(thm)],[])).
% 293.83/186.34 tff(23613,plain,
% 293.83/186.34 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_h, s9)) | m_c_h_element_v_in2(c_e_h_1, c_h, s9) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s9))),
% 293.83/186.34 inference(modus_ponens,[status(thm)],[23612, 23611])).
% 293.83/186.34 tff(23614,plain,
% 293.83/186.34 (m_c_h_element_v_in2(c_e_h_1, c_h, s9) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s9))),
% 293.83/186.34 inference(unit_resolution,[status(thm)],[23613, 919, 23605])).
% 293.83/186.34 tff(23615,plain,
% 293.83/186.34 (~m_c_h_element_v_in1(c_e_h_1, c_h, s9)),
% 293.83/186.34 inference(unit_resolution,[status(thm)],[23614, 23607])).
% 293.83/186.34 tff(23616,plain,
% 293.83/186.34 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s9)) | m_c_h_element_v_in1(c_e_h_1, c_h, s9) | m_c_h_element_v_in2(c_e_h_1, c_h, s9))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s9)) | m_c_h_element_v_in1(c_e_h_1, c_h, s9) | m_c_h_element_v_in2(c_e_h_1, c_h, s9))),
% 293.83/186.34 inference(rewrite,[status(thm)],[])).
% 293.83/186.34 tff(23617,plain,
% 293.83/186.34 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s9)) | m_c_h_element_v_in1(c_e_h_1, c_h, s9) | m_c_h_element_v_in2(c_e_h_1, c_h, s9))),
% 293.83/186.34 inference(quant_inst,[status(thm)],[])).
% 293.83/186.34 tff(23618,plain,
% 293.83/186.34 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s9)) | m_c_h_element_v_in1(c_e_h_1, c_h, s9) | m_c_h_element_v_in2(c_e_h_1, c_h, s9)),
% 293.83/186.34 inference(modus_ponens,[status(thm)],[23617, 23616])).
% 293.83/186.34 tff(23619,plain,
% 293.83/186.34 (m_c_h_element_v_in1(c_e_h_1, c_h, s9) | m_c_h_element_v_in2(c_e_h_1, c_h, s9)),
% 293.83/186.34 inference(unit_resolution,[status(thm)],[23618, 178, 23606])).
% 293.83/186.34 tff(23620,plain,
% 293.83/186.34 ($false),
% 293.83/186.34 inference(unit_resolution,[status(thm)],[23619, 23615, 23607])).
% 293.83/186.34 tff(23621,plain,(m_c_h_element_v_in2(c_e_h_1, c_h, s9) | (~node16(c_e_h_1, c_h, s9)) | (~node17(c_e_h_1, c_h, s9))), inference(lemma,lemma(discharge,[]))).
% 293.83/186.34 tff(23622,plain,
% 293.83/186.34 (m_c_h_element_v_in2(c_e_h_1, c_h, s9)),
% 293.83/186.34 inference(unit_resolution,[status(thm)],[23621, 23606, 23605])).
% 293.83/186.34 tff(23623,plain,
% 293.83/186.34 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_h, s9)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s9)) | m_c_h_element_v_in1(c_e_h_1, c_h, s9))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_h, s9)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s9)) | m_c_h_element_v_in1(c_e_h_1, c_h, s9))),
% 293.83/186.34 inference(rewrite,[status(thm)],[])).
% 293.83/186.34 tff(23624,plain,
% 293.83/186.34 ((m_c_h_element_v_in1(c_e_h_1, c_h, s9) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s9)) | (~node17(c_e_h_1, c_h, s9))) <=> ((~node17(c_e_h_1, c_h, s9)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s9)) | m_c_h_element_v_in1(c_e_h_1, c_h, s9))),
% 293.83/186.34 inference(rewrite,[status(thm)],[])).
% 293.83/186.34 tff(23625,plain,
% 293.83/186.34 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s9) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s9)) | (~node17(c_e_h_1, c_h, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_h, s9)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s9)) | m_c_h_element_v_in1(c_e_h_1, c_h, s9)))),
% 293.83/186.34 inference(monotonicity,[status(thm)],[23624])).
% 293.83/186.34 tff(23626,plain,
% 293.83/186.34 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s9) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s9)) | (~node17(c_e_h_1, c_h, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_h, s9)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s9)) | m_c_h_element_v_in1(c_e_h_1, c_h, s9))),
% 293.83/186.34 inference(transitivity,[status(thm)],[23625, 23623])).
% 293.83/186.34 tff(23627,plain,
% 293.83/186.34 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s9) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s9)) | (~node17(c_e_h_1, c_h, s9)))),
% 293.83/186.34 inference(quant_inst,[status(thm)],[])).
% 293.83/186.34 tff(23628,plain,
% 293.83/186.34 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_h, s9)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s9)) | m_c_h_element_v_in1(c_e_h_1, c_h, s9)),
% 293.83/186.34 inference(modus_ponens,[status(thm)],[23627, 23626])).
% 293.83/186.34 tff(23629,plain,
% 293.83/186.34 ((~m_c_h_element_v_in2(c_e_h_1, c_h, s9)) | m_c_h_element_v_in1(c_e_h_1, c_h, s9)),
% 293.83/186.34 inference(unit_resolution,[status(thm)],[23628, 859, 23605])).
% 293.83/186.34 tff(23630,plain,
% 293.83/186.34 (m_c_h_element_v_in1(c_e_h_1, c_h, s9)),
% 293.83/186.34 inference(unit_resolution,[status(thm)],[23629, 23622])).
% 293.83/186.34 tff(23631,plain,
% 293.83/186.34 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_h, s9)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s9)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~node16(c_e_h_1, c_h, s9)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s9)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s9)))),
% 293.83/186.34 inference(rewrite,[status(thm)],[])).
% 293.83/186.34 tff(23632,plain,
% 293.83/186.34 (((~node16(c_e_h_1, c_h, s9)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s9)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s9))) <=> ((~node16(c_e_h_1, c_h, s9)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s9)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s9)))),
% 293.83/186.34 inference(rewrite,[status(thm)],[])).
% 293.83/186.34 tff(23633,plain,
% 293.83/186.34 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_h, s9)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s9)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_h, s9)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s9)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s9))))),
% 293.83/186.34 inference(monotonicity,[status(thm)],[23632])).
% 293.83/186.34 tff(23634,plain,
% 293.83/186.34 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_h, s9)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s9)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~node16(c_e_h_1, c_h, s9)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s9)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s9)))),
% 293.83/186.34 inference(transitivity,[status(thm)],[23633, 23631])).
% 293.83/186.34 tff(23635,plain,
% 293.83/186.34 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_h, s9)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s9)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s9)))),
% 293.83/186.34 inference(quant_inst,[status(thm)],[])).
% 293.83/186.34 tff(23636,plain,
% 293.83/186.34 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~node16(c_e_h_1, c_h, s9)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s9)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s9))),
% 293.83/186.34 inference(modus_ponens,[status(thm)],[23635, 23634])).
% 293.83/186.34 tff(23637,plain,
% 293.83/186.34 ((~m_c_h_element_v_in2(c_e_h_1, c_h, s9)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s9))),
% 293.83/186.34 inference(unit_resolution,[status(thm)],[23636, 2307, 23606])).
% 293.83/186.34 tff(23638,plain,
% 293.83/186.34 ($false),
% 293.83/186.34 inference(unit_resolution,[status(thm)],[23637, 23630, 23622])).
% 293.83/186.34 tff(23639,plain,((~node16(c_e_h_1, c_h, s9)) | (~node17(c_e_h_1, c_h, s9))), inference(lemma,lemma(discharge,[]))).
% 293.83/186.34 tff(23640,plain,
% 293.83/186.34 ($false),
% 293.83/186.34 inference(unit_resolution,[status(thm)],[23639, 23604, 23591])).
% 293.83/186.34 tff(23641,plain,(m_c_h_element_v_out(c_e_h_1, c_h, s9) | node14(c_e_h_1, c_h, s9, s10) | (~m_c_h_element_v_out(c_e_h_1, c_h, s10))), inference(lemma,lemma(discharge,[]))).
% 293.83/186.34 tff(23642,plain,
% 293.83/186.34 (node14(c_e_h_1, c_h, s9, s10)),
% 293.83/186.34 inference(unit_resolution,[status(thm)],[23641, 23570, 23571])).
% 293.83/186.34 tff(23643,assumption,(node14(c_e_h_1, c_h, s9, s10)), introduced(assumption)).
% 293.83/186.34 tff(23644,plain,
% 293.83/186.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s9) | (~m_c_h_element_v_out(c_e_h_1, c_h, s10)) | (~node14(c_e_h_1, c_h, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s9) | (~m_c_h_element_v_out(c_e_h_1, c_h, s10)) | (~node14(c_e_h_1, c_h, s9, s10)))),
% 293.83/186.34 inference(rewrite,[status(thm)],[])).
% 293.83/186.34 tff(23645,plain,
% 293.83/186.34 (((~node14(c_e_h_1, c_h, s9, s10)) | m_c_h_element_v_in1(c_e_h_1, c_h, s9) | (~m_c_h_element_v_out(c_e_h_1, c_h, s10))) <=> (m_c_h_element_v_in1(c_e_h_1, c_h, s9) | (~m_c_h_element_v_out(c_e_h_1, c_h, s10)) | (~node14(c_e_h_1, c_h, s9, s10)))),
% 293.83/186.34 inference(rewrite,[status(thm)],[])).
% 293.83/186.34 tff(23646,plain,
% 293.83/186.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s9, s10)) | m_c_h_element_v_in1(c_e_h_1, c_h, s9) | (~m_c_h_element_v_out(c_e_h_1, c_h, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s9) | (~m_c_h_element_v_out(c_e_h_1, c_h, s10)) | (~node14(c_e_h_1, c_h, s9, s10))))),
% 293.83/186.34 inference(monotonicity,[status(thm)],[23645])).
% 293.83/186.34 tff(23647,plain,
% 293.83/186.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s9, s10)) | m_c_h_element_v_in1(c_e_h_1, c_h, s9) | (~m_c_h_element_v_out(c_e_h_1, c_h, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s9) | (~m_c_h_element_v_out(c_e_h_1, c_h, s10)) | (~node14(c_e_h_1, c_h, s9, s10)))),
% 293.83/186.34 inference(transitivity,[status(thm)],[23646, 23644])).
% 293.83/186.34 tff(23648,plain,
% 293.83/186.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s9, s10)) | m_c_h_element_v_in1(c_e_h_1, c_h, s9) | (~m_c_h_element_v_out(c_e_h_1, c_h, s10)))),
% 293.83/186.34 inference(quant_inst,[status(thm)],[])).
% 293.83/186.34 tff(23649,plain,
% 293.83/186.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s9) | (~m_c_h_element_v_out(c_e_h_1, c_h, s10)) | (~node14(c_e_h_1, c_h, s9, s10))),
% 293.83/186.34 inference(modus_ponens,[status(thm)],[23648, 23647])).
% 293.83/186.34 tff(23650,plain,
% 293.83/186.34 ($false),
% 293.83/186.34 inference(unit_resolution,[status(thm)],[23649, 223, 23570, 23643, 23582])).
% 293.83/186.34 tff(23651,plain,((~node14(c_e_h_1, c_h, s9, s10)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s10)) | m_c_h_element_v_in1(c_e_h_1, c_h, s9)), inference(lemma,lemma(discharge,[]))).
% 293.83/186.35 tff(23652,plain,
% 293.83/186.35 ($false),
% 293.83/186.35 inference(unit_resolution,[status(thm)],[23651, 23642, 23570, 23582])).
% 293.83/186.35 tff(23653,plain,((~m_c_h_element_v_out(c_e_h_1, c_h, s10)) | m_c_h_element_v_in1(c_e_h_1, c_h, s9) | m_c_h_element_v_out(c_e_h_1, c_h, s9)), inference(lemma,lemma(discharge,[]))).
% 293.83/186.35 tff(23654,plain,
% 293.83/186.35 (m_c_h_element_v_in1(c_e_h_1, c_h, s9)),
% 293.83/186.35 inference(unit_resolution,[status(thm)],[23653, 23571, 23570])).
% 293.83/186.35 tff(23655,plain,
% 293.83/186.35 ((~node17(c_e_h_1, c_h, s9)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s9))),
% 293.83/186.35 inference(unit_resolution,[status(thm)],[23613, 919, 23607])).
% 293.83/186.35 tff(23656,plain,
% 293.83/186.35 (~node17(c_e_h_1, c_h, s9)),
% 293.83/186.35 inference(unit_resolution,[status(thm)],[23655, 23654])).
% 293.83/186.35 tff(23657,plain,
% 293.83/186.35 ($false),
% 293.83/186.35 inference(unit_resolution,[status(thm)],[23590, 23656, 23581])).
% 293.83/186.35 tff(23658,plain,(m_c_h_element_v_out(c_e_h_1, c_h, s9) | m_c_h_element_v_in2(c_e_h_1, c_h, s9) | (~m_c_h_element_v_out(c_e_h_1, c_h, s10))), inference(lemma,lemma(discharge,[]))).
% 293.83/186.35 tff(23659,plain,
% 293.83/186.35 (~m_c_h_element_v_out(c_e_h_1, c_h, s10)),
% 293.83/186.35 inference(unit_resolution,[status(thm)],[23658, 23569, 23499])).
% 293.83/186.35 tff(23660,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_h, s10)), introduced(assumption)).
% 293.83/186.35 tff(23661,assumption,(m_c_h_element_v_out(c_e_h_1, c_h, s11)), introduced(assumption)).
% 293.83/186.35 tff(23662,assumption,(~m_c_h_element_v_out(c_e_h_1, c_h, s10)), introduced(assumption)).
% 293.83/186.35 tff(23663,assumption,(node15(c_e_h_1, c_h, s10, s11)), introduced(assumption)).
% 293.83/186.35 tff(23664,plain,
% 293.83/186.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s11)) | (~node15(c_e_h_1, c_h, s10, s11)) | m_c_h_element_v_out(c_e_h_1, c_h, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s11)) | (~node15(c_e_h_1, c_h, s10, s11)) | m_c_h_element_v_out(c_e_h_1, c_h, s10))),
% 293.83/186.35 inference(rewrite,[status(thm)],[])).
% 293.83/186.35 tff(23665,plain,
% 293.83/186.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s11)) | (~node15(c_e_h_1, c_h, s10, s11)) | m_c_h_element_v_out(c_e_h_1, c_h, s10))),
% 293.83/186.35 inference(quant_inst,[status(thm)],[])).
% 293.83/186.35 tff(23666,plain,
% 293.83/186.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s11)) | (~node15(c_e_h_1, c_h, s10, s11)) | m_c_h_element_v_out(c_e_h_1, c_h, s10)),
% 293.83/186.35 inference(modus_ponens,[status(thm)],[23665, 23664])).
% 293.83/186.35 tff(23667,plain,
% 293.83/186.35 ($false),
% 293.83/186.35 inference(unit_resolution,[status(thm)],[23666, 147, 23661, 23662, 23663])).
% 293.83/186.35 tff(23668,plain,((~node15(c_e_h_1, c_h, s10, s11)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s11)) | m_c_h_element_v_out(c_e_h_1, c_h, s10)), inference(lemma,lemma(discharge,[]))).
% 293.83/186.35 tff(23669,plain,
% 293.83/186.35 (~node15(c_e_h_1, c_h, s10, s11)),
% 293.83/186.35 inference(unit_resolution,[status(thm)],[23668, 23662, 23661])).
% 293.83/186.35 tff(23670,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_h, s10)), introduced(assumption)).
% 293.83/186.35 tff(23671,assumption,(~node15(c_e_h_1, c_h, s10, s11)), introduced(assumption)).
% 293.83/186.35 tff(23672,plain,
% 293.83/186.35 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s10)) | m_c_h_element_v_in1(c_e_h_1, c_h, s10) | m_c_h_element_v_in2(c_e_h_1, c_h, s10))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s10)) | m_c_h_element_v_in1(c_e_h_1, c_h, s10) | m_c_h_element_v_in2(c_e_h_1, c_h, s10))),
% 293.83/186.35 inference(rewrite,[status(thm)],[])).
% 293.83/186.35 tff(23673,plain,
% 293.83/186.35 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s10)) | m_c_h_element_v_in1(c_e_h_1, c_h, s10) | m_c_h_element_v_in2(c_e_h_1, c_h, s10))),
% 293.83/186.35 inference(quant_inst,[status(thm)],[])).
% 293.83/186.35 tff(23674,plain,
% 293.83/186.35 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s10)) | m_c_h_element_v_in1(c_e_h_1, c_h, s10) | m_c_h_element_v_in2(c_e_h_1, c_h, s10)),
% 293.83/186.35 inference(modus_ponens,[status(thm)],[23673, 23672])).
% 293.83/186.35 tff(23675,plain,
% 293.83/186.35 ((~node16(c_e_h_1, c_h, s10)) | m_c_h_element_v_in1(c_e_h_1, c_h, s10)),
% 293.83/186.35 inference(unit_resolution,[status(thm)],[23674, 178, 23660])).
% 293.83/186.35 tff(23676,plain,
% 293.83/186.35 (~node16(c_e_h_1, c_h, s10)),
% 293.83/186.35 inference(unit_resolution,[status(thm)],[23675, 23670])).
% 293.83/186.35 tff(23677,plain,
% 293.83/186.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s10, s11)) | node19(c_e_h_1, c_h, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s10, s11)) | node19(c_e_h_1, c_h, s10, s11))),
% 293.83/186.35 inference(rewrite,[status(thm)],[])).
% 293.83/186.35 tff(23678,plain,
% 293.83/186.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s10, s11)) | node19(c_e_h_1, c_h, s10, s11))),
% 293.83/186.35 inference(quant_inst,[status(thm)],[])).
% 293.83/186.35 tff(23679,plain,
% 293.83/186.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s10, s11)) | node19(c_e_h_1, c_h, s10, s11)),
% 293.83/186.35 inference(modus_ponens,[status(thm)],[23678, 23677])).
% 293.83/186.35 tff(23680,plain,
% 293.83/186.35 (node19(c_e_h_1, c_h, s10, s11)),
% 293.83/186.35 inference(unit_resolution,[status(thm)],[23679, 190, 7748])).
% 293.83/186.35 tff(23681,plain,
% 293.83/186.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s10) | node14(c_e_h_1, c_h, s10, s11) | (~node19(c_e_h_1, c_h, s10, s11)) | node15(c_e_h_1, c_h, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s10) | node14(c_e_h_1, c_h, s10, s11) | (~node19(c_e_h_1, c_h, s10, s11)) | node15(c_e_h_1, c_h, s10, s11))),
% 293.83/186.35 inference(rewrite,[status(thm)],[])).
% 293.83/186.35 tff(23682,plain,
% 293.83/186.35 ((node16(c_e_h_1, c_h, s10) | node14(c_e_h_1, c_h, s10, s11) | node15(c_e_h_1, c_h, s10, s11) | (~node19(c_e_h_1, c_h, s10, s11))) <=> (node16(c_e_h_1, c_h, s10) | node14(c_e_h_1, c_h, s10, s11) | (~node19(c_e_h_1, c_h, s10, s11)) | node15(c_e_h_1, c_h, s10, s11))),
% 293.83/186.35 inference(rewrite,[status(thm)],[])).
% 293.83/186.35 tff(23683,plain,
% 293.83/186.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s10) | node14(c_e_h_1, c_h, s10, s11) | node15(c_e_h_1, c_h, s10, s11) | (~node19(c_e_h_1, c_h, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s10) | node14(c_e_h_1, c_h, s10, s11) | (~node19(c_e_h_1, c_h, s10, s11)) | node15(c_e_h_1, c_h, s10, s11)))),
% 293.83/186.35 inference(monotonicity,[status(thm)],[23682])).
% 293.83/186.35 tff(23684,plain,
% 293.83/186.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s10) | node14(c_e_h_1, c_h, s10, s11) | node15(c_e_h_1, c_h, s10, s11) | (~node19(c_e_h_1, c_h, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s10) | node14(c_e_h_1, c_h, s10, s11) | (~node19(c_e_h_1, c_h, s10, s11)) | node15(c_e_h_1, c_h, s10, s11))),
% 293.83/186.35 inference(transitivity,[status(thm)],[23683, 23681])).
% 293.83/186.35 tff(23685,plain,
% 293.83/186.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s10) | node14(c_e_h_1, c_h, s10, s11) | node15(c_e_h_1, c_h, s10, s11) | (~node19(c_e_h_1, c_h, s10, s11)))),
% 293.83/186.35 inference(quant_inst,[status(thm)],[])).
% 293.83/186.35 tff(23686,plain,
% 293.83/186.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s10) | node14(c_e_h_1, c_h, s10, s11) | (~node19(c_e_h_1, c_h, s10, s11)) | node15(c_e_h_1, c_h, s10, s11)),
% 293.83/186.35 inference(modus_ponens,[status(thm)],[23685, 23684])).
% 293.83/186.35 tff(23687,plain,
% 293.83/186.35 (node16(c_e_h_1, c_h, s10) | node14(c_e_h_1, c_h, s10, s11) | node15(c_e_h_1, c_h, s10, s11)),
% 293.83/186.35 inference(unit_resolution,[status(thm)],[23686, 204, 23680])).
% 293.83/186.35 tff(23688,plain,
% 293.83/186.35 (node14(c_e_h_1, c_h, s10, s11)),
% 293.83/186.35 inference(unit_resolution,[status(thm)],[23687, 23676, 23671])).
% 293.83/186.35 tff(23689,plain,
% 293.83/186.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s10) | (~m_c_h_element_v_out(c_e_h_1, c_h, s11)) | (~node14(c_e_h_1, c_h, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s10) | (~m_c_h_element_v_out(c_e_h_1, c_h, s11)) | (~node14(c_e_h_1, c_h, s10, s11)))),
% 293.83/186.35 inference(rewrite,[status(thm)],[])).
% 293.83/186.35 tff(23690,plain,
% 293.83/186.35 (((~node14(c_e_h_1, c_h, s10, s11)) | m_c_h_element_v_in1(c_e_h_1, c_h, s10) | (~m_c_h_element_v_out(c_e_h_1, c_h, s11))) <=> (m_c_h_element_v_in1(c_e_h_1, c_h, s10) | (~m_c_h_element_v_out(c_e_h_1, c_h, s11)) | (~node14(c_e_h_1, c_h, s10, s11)))),
% 293.83/186.35 inference(rewrite,[status(thm)],[])).
% 293.83/186.35 tff(23691,plain,
% 293.83/186.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s10, s11)) | m_c_h_element_v_in1(c_e_h_1, c_h, s10) | (~m_c_h_element_v_out(c_e_h_1, c_h, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s10) | (~m_c_h_element_v_out(c_e_h_1, c_h, s11)) | (~node14(c_e_h_1, c_h, s10, s11))))),
% 293.83/186.35 inference(monotonicity,[status(thm)],[23690])).
% 293.83/186.35 tff(23692,plain,
% 293.83/186.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s10, s11)) | m_c_h_element_v_in1(c_e_h_1, c_h, s10) | (~m_c_h_element_v_out(c_e_h_1, c_h, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s10) | (~m_c_h_element_v_out(c_e_h_1, c_h, s11)) | (~node14(c_e_h_1, c_h, s10, s11)))),
% 293.83/186.35 inference(transitivity,[status(thm)],[23691, 23689])).
% 293.83/186.35 tff(23693,plain,
% 293.83/186.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s10, s11)) | m_c_h_element_v_in1(c_e_h_1, c_h, s10) | (~m_c_h_element_v_out(c_e_h_1, c_h, s11)))),
% 293.83/186.35 inference(quant_inst,[status(thm)],[])).
% 293.83/186.35 tff(23694,plain,
% 293.83/186.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s10) | (~m_c_h_element_v_out(c_e_h_1, c_h, s11)) | (~node14(c_e_h_1, c_h, s10, s11))),
% 293.83/186.35 inference(modus_ponens,[status(thm)],[23693, 23692])).
% 293.83/186.35 tff(23695,plain,
% 293.83/186.35 ($false),
% 293.83/186.35 inference(unit_resolution,[status(thm)],[23694, 223, 23661, 23688, 23670])).
% 293.83/186.35 tff(23696,plain,(m_c_h_element_v_in1(c_e_h_1, c_h, s10) | (~m_c_h_element_v_out(c_e_h_1, c_h, s11)) | node15(c_e_h_1, c_h, s10, s11) | m_c_h_element_v_in2(c_e_h_1, c_h, s10)), inference(lemma,lemma(discharge,[]))).
% 293.83/186.35 tff(23697,plain,
% 293.83/186.35 (m_c_h_element_v_in1(c_e_h_1, c_h, s10)),
% 293.83/186.35 inference(unit_resolution,[status(thm)],[23696, 23669, 23661, 23660])).
% 293.83/186.35 tff(23698,plain,
% 293.83/186.35 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_h, s10) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s10)) | (~node17(c_e_h_1, c_h, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_h, s10) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s10)) | (~node17(c_e_h_1, c_h, s10)))),
% 293.83/186.36 inference(rewrite,[status(thm)],[])).
% 293.83/186.36 tff(23699,plain,
% 293.83/186.36 (((~m_c_h_element_v_in1(c_e_h_1, c_h, s10)) | m_c_h_element_v_in2(c_e_h_1, c_h, s10) | (~node17(c_e_h_1, c_h, s10))) <=> (m_c_h_element_v_in2(c_e_h_1, c_h, s10) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s10)) | (~node17(c_e_h_1, c_h, s10)))),
% 293.83/186.36 inference(rewrite,[status(thm)],[])).
% 293.83/186.36 tff(23700,plain,
% 293.83/186.36 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s10)) | m_c_h_element_v_in2(c_e_h_1, c_h, s10) | (~node17(c_e_h_1, c_h, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_h, s10) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s10)) | (~node17(c_e_h_1, c_h, s10))))),
% 293.83/186.36 inference(monotonicity,[status(thm)],[23699])).
% 293.83/186.36 tff(23701,plain,
% 293.83/186.36 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s10)) | m_c_h_element_v_in2(c_e_h_1, c_h, s10) | (~node17(c_e_h_1, c_h, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_h, s10) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s10)) | (~node17(c_e_h_1, c_h, s10)))),
% 293.83/186.36 inference(transitivity,[status(thm)],[23700, 23698])).
% 293.83/186.36 tff(23702,plain,
% 293.83/186.36 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s10)) | m_c_h_element_v_in2(c_e_h_1, c_h, s10) | (~node17(c_e_h_1, c_h, s10)))),
% 293.83/186.36 inference(quant_inst,[status(thm)],[])).
% 293.83/186.36 tff(23703,plain,
% 293.83/186.36 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_h, s10) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s10)) | (~node17(c_e_h_1, c_h, s10))),
% 293.83/186.36 inference(modus_ponens,[status(thm)],[23702, 23701])).
% 293.83/186.36 tff(23704,plain,
% 293.83/186.36 ((~m_c_h_element_v_in1(c_e_h_1, c_h, s10)) | (~node17(c_e_h_1, c_h, s10))),
% 293.83/186.36 inference(unit_resolution,[status(thm)],[23703, 919, 23660])).
% 293.83/186.36 tff(23705,plain,
% 293.83/186.36 (~node17(c_e_h_1, c_h, s10)),
% 293.83/186.36 inference(unit_resolution,[status(thm)],[23704, 23697])).
% 293.83/186.36 tff(23706,plain,
% 293.83/186.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s10) | (~node19(c_e_h_1, c_h, s10, s11)) | node18(c_e_h_1, c_h, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s10) | (~node19(c_e_h_1, c_h, s10, s11)) | node18(c_e_h_1, c_h, s10, s11))),
% 293.83/186.36 inference(rewrite,[status(thm)],[])).
% 293.83/186.36 tff(23707,plain,
% 293.83/186.36 ((node17(c_e_h_1, c_h, s10) | node18(c_e_h_1, c_h, s10, s11) | (~node19(c_e_h_1, c_h, s10, s11))) <=> (node17(c_e_h_1, c_h, s10) | (~node19(c_e_h_1, c_h, s10, s11)) | node18(c_e_h_1, c_h, s10, s11))),
% 293.83/186.36 inference(rewrite,[status(thm)],[])).
% 293.83/186.36 tff(23708,plain,
% 293.83/186.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s10) | node18(c_e_h_1, c_h, s10, s11) | (~node19(c_e_h_1, c_h, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s10) | (~node19(c_e_h_1, c_h, s10, s11)) | node18(c_e_h_1, c_h, s10, s11)))),
% 293.83/186.36 inference(monotonicity,[status(thm)],[23707])).
% 293.83/186.36 tff(23709,plain,
% 293.83/186.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s10) | node18(c_e_h_1, c_h, s10, s11) | (~node19(c_e_h_1, c_h, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s10) | (~node19(c_e_h_1, c_h, s10, s11)) | node18(c_e_h_1, c_h, s10, s11))),
% 293.83/186.36 inference(transitivity,[status(thm)],[23708, 23706])).
% 293.83/186.36 tff(23710,plain,
% 293.83/186.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s10) | node18(c_e_h_1, c_h, s10, s11) | (~node19(c_e_h_1, c_h, s10, s11)))),
% 293.83/186.36 inference(quant_inst,[status(thm)],[])).
% 293.83/186.36 tff(23711,plain,
% 293.83/186.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s10) | (~node19(c_e_h_1, c_h, s10, s11)) | node18(c_e_h_1, c_h, s10, s11)),
% 293.83/186.36 inference(modus_ponens,[status(thm)],[23710, 23709])).
% 293.83/186.36 tff(23712,plain,
% 293.83/186.36 (node17(c_e_h_1, c_h, s10) | node18(c_e_h_1, c_h, s10, s11)),
% 293.83/186.36 inference(unit_resolution,[status(thm)],[23711, 776, 23680])).
% 293.83/186.36 tff(23713,plain,
% 293.83/186.36 (node18(c_e_h_1, c_h, s10, s11)),
% 293.83/186.36 inference(unit_resolution,[status(thm)],[23712, 23705])).
% 293.83/186.36 tff(23714,plain,
% 293.83/186.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_h, s10) | (~m_c_h_element_v_out(c_e_h_1, c_h, s11)) | (~node18(c_e_h_1, c_h, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s10) | (~m_c_h_element_v_out(c_e_h_1, c_h, s11)) | (~node18(c_e_h_1, c_h, s10, s11)))),
% 293.83/186.36 inference(rewrite,[status(thm)],[])).
% 293.83/186.36 tff(23715,plain,
% 293.83/186.36 (((~m_c_h_element_v_out(c_e_h_1, c_h, s11)) | m_c_h_element_v_out(c_e_h_1, c_h, s10) | (~node18(c_e_h_1, c_h, s10, s11))) <=> (m_c_h_element_v_out(c_e_h_1, c_h, s10) | (~m_c_h_element_v_out(c_e_h_1, c_h, s11)) | (~node18(c_e_h_1, c_h, s10, s11)))),
% 293.83/186.36 inference(rewrite,[status(thm)],[])).
% 293.83/186.36 tff(23716,plain,
% 293.83/186.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s11)) | m_c_h_element_v_out(c_e_h_1, c_h, s10) | (~node18(c_e_h_1, c_h, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_h, s10) | (~m_c_h_element_v_out(c_e_h_1, c_h, s11)) | (~node18(c_e_h_1, c_h, s10, s11))))),
% 293.83/186.36 inference(monotonicity,[status(thm)],[23715])).
% 293.83/186.36 tff(23717,plain,
% 293.83/186.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s11)) | m_c_h_element_v_out(c_e_h_1, c_h, s10) | (~node18(c_e_h_1, c_h, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s10) | (~m_c_h_element_v_out(c_e_h_1, c_h, s11)) | (~node18(c_e_h_1, c_h, s10, s11)))),
% 293.83/186.36 inference(transitivity,[status(thm)],[23716, 23714])).
% 293.83/186.36 tff(23718,plain,
% 293.83/186.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s11)) | m_c_h_element_v_out(c_e_h_1, c_h, s10) | (~node18(c_e_h_1, c_h, s10, s11)))),
% 293.83/186.36 inference(quant_inst,[status(thm)],[])).
% 293.83/186.36 tff(23719,plain,
% 293.83/186.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s10) | (~m_c_h_element_v_out(c_e_h_1, c_h, s11)) | (~node18(c_e_h_1, c_h, s10, s11))),
% 293.83/186.36 inference(modus_ponens,[status(thm)],[23718, 23717])).
% 293.83/186.36 tff(23720,plain,
% 293.83/186.36 ($false),
% 293.83/186.36 inference(unit_resolution,[status(thm)],[23719, 753, 23661, 23662, 23713])).
% 293.83/186.36 tff(23721,plain,(m_c_h_element_v_out(c_e_h_1, c_h, s10) | (~m_c_h_element_v_out(c_e_h_1, c_h, s11)) | m_c_h_element_v_in2(c_e_h_1, c_h, s10)), inference(lemma,lemma(discharge,[]))).
% 293.83/186.36 tff(23722,plain,
% 293.83/186.37 ((~m_c_h_element_v_out(c_e_h_1, c_h, s11)) | m_c_h_element_v_in2(c_e_h_1, c_h, s10)),
% 293.83/186.37 inference(unit_resolution,[status(thm)],[23721, 23659])).
% 293.83/186.37 tff(23723,plain,
% 293.83/186.37 (~m_c_h_element_v_out(c_e_h_1, c_h, s11)),
% 293.83/186.37 inference(unit_resolution,[status(thm)],[23722, 23495])).
% 293.83/186.37 tff(23724,plain,
% 293.83/186.37 (m_or_h_gate_v_in2(c_e_h_1, c_j, s10)),
% 293.83/186.37 inference(unit_resolution,[status(thm)],[22777, 22418, 22745])).
% 293.83/186.37 tff(23725,plain,
% 293.83/186.37 (~m_and_h_gate_v_out(c_e_h_3, c_q, s10)),
% 293.83/186.37 inference(unit_resolution,[status(thm)],[21399, 22864])).
% 293.83/186.37 tff(23726,plain,
% 293.83/186.37 (~m_cell_v_ack(c_e_h_1, s10)),
% 293.83/186.37 inference(unit_resolution,[status(thm)],[21408, 23725])).
% 293.83/186.37 tff(23727,plain,
% 293.83/186.37 ($false),
% 293.83/186.37 inference(unit_resolution,[status(thm)],[22736, 1085, 23726, 23724])).
% 293.83/186.37 tff(23728,plain,(m_or_h_gate_v_in2(c_e_h_1, c_j, s9) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s11))), inference(lemma,lemma(discharge,[]))).
% 293.83/186.37 tff(23729,plain,
% 293.83/186.37 (~m_or_h_gate_v_out(c_e_h_1, c_j, s11)),
% 293.83/186.37 inference(unit_resolution,[status(thm)],[23728, 22093])).
% 293.83/186.37 tff(23730,plain,
% 293.83/186.37 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s11)) | m_or_h_gate_v_out(c_e_h_1, c_j, s11))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s11)) | m_or_h_gate_v_out(c_e_h_1, c_j, s11))),
% 293.83/186.37 inference(rewrite,[status(thm)],[])).
% 293.83/186.37 tff(23731,plain,
% 293.83/186.37 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s11)) | m_or_h_gate_v_out(c_e_h_1, c_j, s11))),
% 293.83/186.37 inference(quant_inst,[status(thm)],[])).
% 293.83/186.37 tff(23732,plain,
% 293.83/186.37 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s11)) | m_or_h_gate_v_out(c_e_h_1, c_j, s11)),
% 293.83/186.37 inference(modus_ponens,[status(thm)],[23731, 23730])).
% 293.83/186.37 tff(23733,plain,
% 293.83/186.37 (~m_c_h_element_v_in2(c_e_h_1, c_h, s11)),
% 293.83/186.37 inference(unit_resolution,[status(thm)],[23732, 1174, 23729])).
% 293.83/186.37 tff(23734,assumption,(m_c_h_element_v_out(c_e_h_1, c_h, s12)), introduced(assumption)).
% 293.83/186.37 tff(23735,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_h, s11)), introduced(assumption)).
% 293.83/186.37 tff(23736,assumption,(~m_c_h_element_v_out(c_e_h_1, c_h, s11)), introduced(assumption)).
% 293.83/186.37 tff(23737,assumption,(node15(c_e_h_1, c_h, s11, s12)), introduced(assumption)).
% 293.83/186.37 tff(23738,plain,
% 293.83/186.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s12)) | (~node15(c_e_h_1, c_h, s11, s12)) | m_c_h_element_v_out(c_e_h_1, c_h, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s12)) | (~node15(c_e_h_1, c_h, s11, s12)) | m_c_h_element_v_out(c_e_h_1, c_h, s11))),
% 293.83/186.37 inference(rewrite,[status(thm)],[])).
% 293.83/186.37 tff(23739,plain,
% 293.83/186.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s12)) | (~node15(c_e_h_1, c_h, s11, s12)) | m_c_h_element_v_out(c_e_h_1, c_h, s11))),
% 293.83/186.37 inference(quant_inst,[status(thm)],[])).
% 293.83/186.37 tff(23740,plain,
% 293.83/186.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s12)) | (~node15(c_e_h_1, c_h, s11, s12)) | m_c_h_element_v_out(c_e_h_1, c_h, s11)),
% 293.83/186.37 inference(modus_ponens,[status(thm)],[23739, 23738])).
% 293.83/186.37 tff(23741,plain,
% 293.83/186.37 ($false),
% 293.83/186.37 inference(unit_resolution,[status(thm)],[23740, 147, 23736, 23734, 23737])).
% 293.83/186.37 tff(23742,plain,((~node15(c_e_h_1, c_h, s11, s12)) | m_c_h_element_v_out(c_e_h_1, c_h, s11) | (~m_c_h_element_v_out(c_e_h_1, c_h, s12))), inference(lemma,lemma(discharge,[]))).
% 293.83/186.37 tff(23743,plain,
% 293.83/186.37 (~node15(c_e_h_1, c_h, s11, s12)),
% 293.83/186.37 inference(unit_resolution,[status(thm)],[23742, 23734, 23736])).
% 293.83/186.37 tff(23744,assumption,(~node15(c_e_h_1, c_h, s11, s12)), introduced(assumption)).
% 293.83/186.37 tff(23745,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_h, s11)), introduced(assumption)).
% 293.83/186.37 tff(23746,plain,
% 293.83/186.37 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s11)) | m_c_h_element_v_in1(c_e_h_1, c_h, s11) | m_c_h_element_v_in2(c_e_h_1, c_h, s11))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s11)) | m_c_h_element_v_in1(c_e_h_1, c_h, s11) | m_c_h_element_v_in2(c_e_h_1, c_h, s11))),
% 293.83/186.37 inference(rewrite,[status(thm)],[])).
% 293.83/186.37 tff(23747,plain,
% 293.83/186.37 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s11)) | m_c_h_element_v_in1(c_e_h_1, c_h, s11) | m_c_h_element_v_in2(c_e_h_1, c_h, s11))),
% 293.83/186.37 inference(quant_inst,[status(thm)],[])).
% 293.83/186.37 tff(23748,plain,
% 293.83/186.37 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s11)) | m_c_h_element_v_in1(c_e_h_1, c_h, s11) | m_c_h_element_v_in2(c_e_h_1, c_h, s11)),
% 293.83/186.37 inference(modus_ponens,[status(thm)],[23747, 23746])).
% 293.83/186.37 tff(23749,plain,
% 293.83/186.37 ((~node16(c_e_h_1, c_h, s11)) | m_c_h_element_v_in1(c_e_h_1, c_h, s11)),
% 293.83/186.37 inference(unit_resolution,[status(thm)],[23748, 178, 23735])).
% 293.83/186.37 tff(23750,plain,
% 293.83/186.37 (~node16(c_e_h_1, c_h, s11)),
% 293.83/186.37 inference(unit_resolution,[status(thm)],[23749, 23745])).
% 293.83/186.37 tff(23751,assumption,(node14(c_e_h_1, c_h, s11, s12)), introduced(assumption)).
% 293.83/186.37 tff(23752,plain,
% 293.83/186.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s11) | (~m_c_h_element_v_out(c_e_h_1, c_h, s12)) | (~node14(c_e_h_1, c_h, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s11) | (~m_c_h_element_v_out(c_e_h_1, c_h, s12)) | (~node14(c_e_h_1, c_h, s11, s12)))),
% 293.83/186.37 inference(rewrite,[status(thm)],[])).
% 293.83/186.37 tff(23753,plain,
% 293.83/186.37 (((~node14(c_e_h_1, c_h, s11, s12)) | m_c_h_element_v_in1(c_e_h_1, c_h, s11) | (~m_c_h_element_v_out(c_e_h_1, c_h, s12))) <=> (m_c_h_element_v_in1(c_e_h_1, c_h, s11) | (~m_c_h_element_v_out(c_e_h_1, c_h, s12)) | (~node14(c_e_h_1, c_h, s11, s12)))),
% 293.83/186.37 inference(rewrite,[status(thm)],[])).
% 293.83/186.37 tff(23754,plain,
% 293.83/186.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s11, s12)) | m_c_h_element_v_in1(c_e_h_1, c_h, s11) | (~m_c_h_element_v_out(c_e_h_1, c_h, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s11) | (~m_c_h_element_v_out(c_e_h_1, c_h, s12)) | (~node14(c_e_h_1, c_h, s11, s12))))),
% 293.83/186.37 inference(monotonicity,[status(thm)],[23753])).
% 293.83/186.37 tff(23755,plain,
% 293.83/186.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s11, s12)) | m_c_h_element_v_in1(c_e_h_1, c_h, s11) | (~m_c_h_element_v_out(c_e_h_1, c_h, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s11) | (~m_c_h_element_v_out(c_e_h_1, c_h, s12)) | (~node14(c_e_h_1, c_h, s11, s12)))),
% 293.83/186.37 inference(transitivity,[status(thm)],[23754, 23752])).
% 293.83/186.37 tff(23756,plain,
% 293.83/186.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s11, s12)) | m_c_h_element_v_in1(c_e_h_1, c_h, s11) | (~m_c_h_element_v_out(c_e_h_1, c_h, s12)))),
% 293.83/186.37 inference(quant_inst,[status(thm)],[])).
% 293.83/186.37 tff(23757,plain,
% 293.83/186.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s11) | (~m_c_h_element_v_out(c_e_h_1, c_h, s12)) | (~node14(c_e_h_1, c_h, s11, s12))),
% 293.83/186.37 inference(modus_ponens,[status(thm)],[23756, 23755])).
% 293.83/186.37 tff(23758,plain,
% 293.83/186.37 ($false),
% 293.83/186.37 inference(unit_resolution,[status(thm)],[23757, 223, 23734, 23751, 23745])).
% 293.83/186.37 tff(23759,plain,((~node14(c_e_h_1, c_h, s11, s12)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s12)) | m_c_h_element_v_in1(c_e_h_1, c_h, s11)), inference(lemma,lemma(discharge,[]))).
% 293.83/186.37 tff(23760,plain,
% 293.83/186.37 (~node14(c_e_h_1, c_h, s11, s12)),
% 293.83/186.37 inference(unit_resolution,[status(thm)],[23759, 23745, 23734])).
% 293.83/186.37 tff(23761,plain,
% 293.83/186.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s11, s12)) | node19(c_e_h_1, c_h, s11, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s11, s12)) | node19(c_e_h_1, c_h, s11, s12))),
% 293.83/186.37 inference(rewrite,[status(thm)],[])).
% 293.83/186.37 tff(23762,plain,
% 293.83/186.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s11, s12)) | node19(c_e_h_1, c_h, s11, s12))),
% 293.83/186.37 inference(quant_inst,[status(thm)],[])).
% 293.83/186.37 tff(23763,plain,
% 293.83/186.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s11, s12)) | node19(c_e_h_1, c_h, s11, s12)),
% 293.83/186.37 inference(modus_ponens,[status(thm)],[23762, 23761])).
% 293.83/186.37 tff(23764,plain,
% 293.83/186.37 (node19(c_e_h_1, c_h, s11, s12)),
% 293.83/186.37 inference(unit_resolution,[status(thm)],[23763, 190, 11461])).
% 293.83/186.37 tff(23765,plain,
% 293.83/186.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_1, c_h, s11, s12) | node15(c_e_h_1, c_h, s11, s12) | (~node19(c_e_h_1, c_h, s11, s12)) | node16(c_e_h_1, c_h, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_h, s11, s12) | node15(c_e_h_1, c_h, s11, s12) | (~node19(c_e_h_1, c_h, s11, s12)) | node16(c_e_h_1, c_h, s11))),
% 293.83/186.37 inference(rewrite,[status(thm)],[])).
% 293.83/186.37 tff(23766,plain,
% 293.83/186.37 ((node16(c_e_h_1, c_h, s11) | node14(c_e_h_1, c_h, s11, s12) | node15(c_e_h_1, c_h, s11, s12) | (~node19(c_e_h_1, c_h, s11, s12))) <=> (node14(c_e_h_1, c_h, s11, s12) | node15(c_e_h_1, c_h, s11, s12) | (~node19(c_e_h_1, c_h, s11, s12)) | node16(c_e_h_1, c_h, s11))),
% 293.83/186.37 inference(rewrite,[status(thm)],[])).
% 293.83/186.37 tff(23767,plain,
% 293.83/186.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s11) | node14(c_e_h_1, c_h, s11, s12) | node15(c_e_h_1, c_h, s11, s12) | (~node19(c_e_h_1, c_h, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_1, c_h, s11, s12) | node15(c_e_h_1, c_h, s11, s12) | (~node19(c_e_h_1, c_h, s11, s12)) | node16(c_e_h_1, c_h, s11)))),
% 293.83/186.37 inference(monotonicity,[status(thm)],[23766])).
% 293.83/186.37 tff(23768,plain,
% 293.83/186.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s11) | node14(c_e_h_1, c_h, s11, s12) | node15(c_e_h_1, c_h, s11, s12) | (~node19(c_e_h_1, c_h, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_h, s11, s12) | node15(c_e_h_1, c_h, s11, s12) | (~node19(c_e_h_1, c_h, s11, s12)) | node16(c_e_h_1, c_h, s11))),
% 293.83/186.37 inference(transitivity,[status(thm)],[23767, 23765])).
% 293.83/186.37 tff(23769,plain,
% 293.83/186.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s11) | node14(c_e_h_1, c_h, s11, s12) | node15(c_e_h_1, c_h, s11, s12) | (~node19(c_e_h_1, c_h, s11, s12)))),
% 293.83/186.37 inference(quant_inst,[status(thm)],[])).
% 293.83/186.37 tff(23770,plain,
% 293.83/186.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_h, s11, s12) | node15(c_e_h_1, c_h, s11, s12) | (~node19(c_e_h_1, c_h, s11, s12)) | node16(c_e_h_1, c_h, s11)),
% 293.83/186.38 inference(modus_ponens,[status(thm)],[23769, 23768])).
% 293.83/186.38 tff(23771,plain,
% 293.83/186.38 (node14(c_e_h_1, c_h, s11, s12) | node15(c_e_h_1, c_h, s11, s12) | node16(c_e_h_1, c_h, s11)),
% 293.83/186.38 inference(unit_resolution,[status(thm)],[23770, 204, 23764])).
% 293.83/186.38 tff(23772,plain,
% 293.83/186.38 ($false),
% 293.83/186.38 inference(unit_resolution,[status(thm)],[23771, 23760, 23750, 23744])).
% 293.83/186.38 tff(23773,plain,(m_c_h_element_v_in1(c_e_h_1, c_h, s11) | node15(c_e_h_1, c_h, s11, s12) | (~m_c_h_element_v_out(c_e_h_1, c_h, s12)) | m_c_h_element_v_in2(c_e_h_1, c_h, s11)), inference(lemma,lemma(discharge,[]))).
% 293.83/186.38 tff(23774,plain,
% 293.83/186.38 (m_c_h_element_v_in1(c_e_h_1, c_h, s11)),
% 293.83/186.38 inference(unit_resolution,[status(thm)],[23773, 23743, 23735, 23734])).
% 293.83/186.38 tff(23775,plain,
% 293.83/186.38 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s11)) | m_c_h_element_v_in2(c_e_h_1, c_h, s11) | (~node17(c_e_h_1, c_h, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s11)) | m_c_h_element_v_in2(c_e_h_1, c_h, s11) | (~node17(c_e_h_1, c_h, s11)))),
% 293.83/186.38 inference(rewrite,[status(thm)],[])).
% 293.83/186.38 tff(23776,plain,
% 293.83/186.38 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s11)) | m_c_h_element_v_in2(c_e_h_1, c_h, s11) | (~node17(c_e_h_1, c_h, s11)))),
% 293.83/186.38 inference(quant_inst,[status(thm)],[])).
% 293.83/186.38 tff(23777,plain,
% 293.83/186.38 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s11)) | m_c_h_element_v_in2(c_e_h_1, c_h, s11) | (~node17(c_e_h_1, c_h, s11))),
% 293.83/186.38 inference(modus_ponens,[status(thm)],[23776, 23775])).
% 293.83/186.38 tff(23778,plain,
% 293.83/186.38 ((~m_c_h_element_v_in1(c_e_h_1, c_h, s11)) | (~node17(c_e_h_1, c_h, s11))),
% 293.83/186.38 inference(unit_resolution,[status(thm)],[23777, 919, 23735])).
% 293.83/186.38 tff(23779,plain,
% 293.83/186.38 (~node17(c_e_h_1, c_h, s11)),
% 293.83/186.38 inference(unit_resolution,[status(thm)],[23778, 23774])).
% 293.83/186.38 tff(23780,plain,
% 293.83/186.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_1, c_h, s11, s12) | (~node19(c_e_h_1, c_h, s11, s12)) | node17(c_e_h_1, c_h, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_h, s11, s12) | (~node19(c_e_h_1, c_h, s11, s12)) | node17(c_e_h_1, c_h, s11))),
% 293.83/186.38 inference(rewrite,[status(thm)],[])).
% 293.83/186.38 tff(23781,plain,
% 293.83/186.38 ((node17(c_e_h_1, c_h, s11) | node18(c_e_h_1, c_h, s11, s12) | (~node19(c_e_h_1, c_h, s11, s12))) <=> (node18(c_e_h_1, c_h, s11, s12) | (~node19(c_e_h_1, c_h, s11, s12)) | node17(c_e_h_1, c_h, s11))),
% 293.83/186.38 inference(rewrite,[status(thm)],[])).
% 293.83/186.38 tff(23782,plain,
% 293.83/186.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s11) | node18(c_e_h_1, c_h, s11, s12) | (~node19(c_e_h_1, c_h, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_1, c_h, s11, s12) | (~node19(c_e_h_1, c_h, s11, s12)) | node17(c_e_h_1, c_h, s11)))),
% 293.83/186.38 inference(monotonicity,[status(thm)],[23781])).
% 293.83/186.38 tff(23783,plain,
% 293.83/186.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s11) | node18(c_e_h_1, c_h, s11, s12) | (~node19(c_e_h_1, c_h, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_h, s11, s12) | (~node19(c_e_h_1, c_h, s11, s12)) | node17(c_e_h_1, c_h, s11))),
% 293.83/186.38 inference(transitivity,[status(thm)],[23782, 23780])).
% 293.83/186.38 tff(23784,plain,
% 293.83/186.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s11) | node18(c_e_h_1, c_h, s11, s12) | (~node19(c_e_h_1, c_h, s11, s12)))),
% 293.83/186.38 inference(quant_inst,[status(thm)],[])).
% 293.83/186.38 tff(23785,plain,
% 293.83/186.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_h, s11, s12) | (~node19(c_e_h_1, c_h, s11, s12)) | node17(c_e_h_1, c_h, s11)),
% 293.83/186.38 inference(modus_ponens,[status(thm)],[23784, 23783])).
% 293.83/186.38 tff(23786,plain,
% 293.83/186.38 (node18(c_e_h_1, c_h, s11, s12) | node17(c_e_h_1, c_h, s11)),
% 293.83/186.38 inference(unit_resolution,[status(thm)],[23785, 776, 23764])).
% 293.83/186.38 tff(23787,plain,
% 293.83/186.38 (node18(c_e_h_1, c_h, s11, s12)),
% 293.83/186.38 inference(unit_resolution,[status(thm)],[23786, 23779])).
% 293.83/186.38 tff(23788,plain,
% 293.83/186.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_h, s11) | (~m_c_h_element_v_out(c_e_h_1, c_h, s12)) | (~node18(c_e_h_1, c_h, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s11) | (~m_c_h_element_v_out(c_e_h_1, c_h, s12)) | (~node18(c_e_h_1, c_h, s11, s12)))),
% 293.83/186.38 inference(rewrite,[status(thm)],[])).
% 293.83/186.38 tff(23789,plain,
% 293.83/186.38 (((~m_c_h_element_v_out(c_e_h_1, c_h, s12)) | m_c_h_element_v_out(c_e_h_1, c_h, s11) | (~node18(c_e_h_1, c_h, s11, s12))) <=> (m_c_h_element_v_out(c_e_h_1, c_h, s11) | (~m_c_h_element_v_out(c_e_h_1, c_h, s12)) | (~node18(c_e_h_1, c_h, s11, s12)))),
% 293.83/186.38 inference(rewrite,[status(thm)],[])).
% 293.83/186.38 tff(23790,plain,
% 293.83/186.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s12)) | m_c_h_element_v_out(c_e_h_1, c_h, s11) | (~node18(c_e_h_1, c_h, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_h, s11) | (~m_c_h_element_v_out(c_e_h_1, c_h, s12)) | (~node18(c_e_h_1, c_h, s11, s12))))),
% 293.83/186.38 inference(monotonicity,[status(thm)],[23789])).
% 293.83/186.38 tff(23791,plain,
% 293.83/186.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s12)) | m_c_h_element_v_out(c_e_h_1, c_h, s11) | (~node18(c_e_h_1, c_h, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s11) | (~m_c_h_element_v_out(c_e_h_1, c_h, s12)) | (~node18(c_e_h_1, c_h, s11, s12)))),
% 293.83/186.38 inference(transitivity,[status(thm)],[23790, 23788])).
% 293.83/186.38 tff(23792,plain,
% 293.83/186.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s12)) | m_c_h_element_v_out(c_e_h_1, c_h, s11) | (~node18(c_e_h_1, c_h, s11, s12)))),
% 293.83/186.38 inference(quant_inst,[status(thm)],[])).
% 293.83/186.38 tff(23793,plain,
% 293.83/186.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s11) | (~m_c_h_element_v_out(c_e_h_1, c_h, s12)) | (~node18(c_e_h_1, c_h, s11, s12))),
% 293.83/186.38 inference(modus_ponens,[status(thm)],[23792, 23791])).
% 293.83/186.38 tff(23794,plain,
% 293.83/186.38 ($false),
% 293.83/186.38 inference(unit_resolution,[status(thm)],[23793, 753, 23736, 23734, 23787])).
% 293.83/186.38 tff(23795,plain,((~m_c_h_element_v_out(c_e_h_1, c_h, s12)) | m_c_h_element_v_out(c_e_h_1, c_h, s11) | m_c_h_element_v_in2(c_e_h_1, c_h, s11)), inference(lemma,lemma(discharge,[]))).
% 293.83/186.38 tff(23796,plain,
% 293.83/186.38 (~m_c_h_element_v_out(c_e_h_1, c_h, s12)),
% 293.83/186.38 inference(unit_resolution,[status(thm)],[23795, 23733, 23723])).
% 293.83/186.38 tff(23797,plain,
% 293.83/186.38 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s12)) | m_or_h_gate_v_out(c_e_h_1, c_j, s12))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s12)) | m_or_h_gate_v_out(c_e_h_1, c_j, s12))),
% 293.83/186.38 inference(rewrite,[status(thm)],[])).
% 293.83/186.38 tff(23798,plain,
% 293.83/186.38 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s12)) | m_or_h_gate_v_out(c_e_h_1, c_j, s12))),
% 293.83/186.38 inference(quant_inst,[status(thm)],[])).
% 293.83/186.38 tff(23799,plain,
% 293.83/186.38 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s12)) | m_or_h_gate_v_out(c_e_h_1, c_j, s12)),
% 293.83/186.38 inference(modus_ponens,[status(thm)],[23798, 23797])).
% 293.83/186.38 tff(23800,plain,
% 293.83/186.38 (~m_c_h_element_v_in2(c_e_h_1, c_h, s12)),
% 293.83/186.38 inference(unit_resolution,[status(thm)],[23799, 1174, 22867])).
% 293.83/186.38 tff(23801,assumption,(m_c_h_element_v_out(c_e_h_1, c_h, s13)), introduced(assumption)).
% 293.83/186.38 tff(23802,assumption,(~m_c_h_element_v_out(c_e_h_1, c_h, s12)), introduced(assumption)).
% 293.83/186.38 tff(23803,assumption,(node18(c_e_h_1, c_h, s12, s13)), introduced(assumption)).
% 293.83/186.38 tff(23804,plain,
% 293.83/186.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s13)) | m_c_h_element_v_out(c_e_h_1, c_h, s12) | (~node18(c_e_h_1, c_h, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s13)) | m_c_h_element_v_out(c_e_h_1, c_h, s12) | (~node18(c_e_h_1, c_h, s12, s13)))),
% 293.83/186.38 inference(rewrite,[status(thm)],[])).
% 293.83/186.38 tff(23805,plain,
% 293.83/186.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s13)) | m_c_h_element_v_out(c_e_h_1, c_h, s12) | (~node18(c_e_h_1, c_h, s12, s13)))),
% 293.83/186.38 inference(quant_inst,[status(thm)],[])).
% 293.83/186.38 tff(23806,plain,
% 293.83/186.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s13)) | m_c_h_element_v_out(c_e_h_1, c_h, s12) | (~node18(c_e_h_1, c_h, s12, s13))),
% 293.83/186.38 inference(modus_ponens,[status(thm)],[23805, 23804])).
% 293.83/186.38 tff(23807,plain,
% 293.83/186.38 ($false),
% 293.83/186.38 inference(unit_resolution,[status(thm)],[23806, 753, 23801, 23802, 23803])).
% 293.83/186.38 tff(23808,plain,((~node18(c_e_h_1, c_h, s12, s13)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s13)) | m_c_h_element_v_out(c_e_h_1, c_h, s12)), inference(lemma,lemma(discharge,[]))).
% 293.83/186.38 tff(23809,plain,
% 293.83/186.38 (~node18(c_e_h_1, c_h, s12, s13)),
% 293.83/186.38 inference(unit_resolution,[status(thm)],[23808, 23802, 23801])).
% 293.83/186.38 tff(23810,assumption,(node15(c_e_h_1, c_h, s12, s13)), introduced(assumption)).
% 293.83/186.38 tff(23811,plain,
% 293.83/186.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s13)) | (~node15(c_e_h_1, c_h, s12, s13)) | m_c_h_element_v_out(c_e_h_1, c_h, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s13)) | (~node15(c_e_h_1, c_h, s12, s13)) | m_c_h_element_v_out(c_e_h_1, c_h, s12))),
% 293.83/186.38 inference(rewrite,[status(thm)],[])).
% 293.83/186.38 tff(23812,plain,
% 293.83/186.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s13)) | (~node15(c_e_h_1, c_h, s12, s13)) | m_c_h_element_v_out(c_e_h_1, c_h, s12))),
% 293.83/186.38 inference(quant_inst,[status(thm)],[])).
% 293.83/186.38 tff(23813,plain,
% 293.83/186.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s13)) | (~node15(c_e_h_1, c_h, s12, s13)) | m_c_h_element_v_out(c_e_h_1, c_h, s12)),
% 293.83/186.39 inference(modus_ponens,[status(thm)],[23812, 23811])).
% 293.83/186.39 tff(23814,plain,
% 293.83/186.39 ($false),
% 293.83/186.39 inference(unit_resolution,[status(thm)],[23813, 147, 23801, 23802, 23810])).
% 293.83/186.39 tff(23815,plain,((~node15(c_e_h_1, c_h, s12, s13)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s13)) | m_c_h_element_v_out(c_e_h_1, c_h, s12)), inference(lemma,lemma(discharge,[]))).
% 293.83/186.39 tff(23816,plain,
% 293.83/186.39 (~node15(c_e_h_1, c_h, s12, s13)),
% 293.83/186.39 inference(unit_resolution,[status(thm)],[23815, 23801, 23802])).
% 293.83/186.39 tff(23817,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_h, s12)), introduced(assumption)).
% 293.83/186.39 tff(23818,assumption,(node14(c_e_h_1, c_h, s12, s13)), introduced(assumption)).
% 293.83/186.39 tff(23819,plain,
% 293.83/186.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s13)) | m_c_h_element_v_in1(c_e_h_1, c_h, s12) | (~node14(c_e_h_1, c_h, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s13)) | m_c_h_element_v_in1(c_e_h_1, c_h, s12) | (~node14(c_e_h_1, c_h, s12, s13)))),
% 293.83/186.39 inference(rewrite,[status(thm)],[])).
% 293.83/186.39 tff(23820,plain,
% 293.83/186.39 (((~node14(c_e_h_1, c_h, s12, s13)) | m_c_h_element_v_in1(c_e_h_1, c_h, s12) | (~m_c_h_element_v_out(c_e_h_1, c_h, s13))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_h, s13)) | m_c_h_element_v_in1(c_e_h_1, c_h, s12) | (~node14(c_e_h_1, c_h, s12, s13)))),
% 293.83/186.39 inference(rewrite,[status(thm)],[])).
% 293.83/186.39 tff(23821,plain,
% 293.83/186.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s12, s13)) | m_c_h_element_v_in1(c_e_h_1, c_h, s12) | (~m_c_h_element_v_out(c_e_h_1, c_h, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s13)) | m_c_h_element_v_in1(c_e_h_1, c_h, s12) | (~node14(c_e_h_1, c_h, s12, s13))))),
% 293.83/186.39 inference(monotonicity,[status(thm)],[23820])).
% 293.83/186.39 tff(23822,plain,
% 293.83/186.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s12, s13)) | m_c_h_element_v_in1(c_e_h_1, c_h, s12) | (~m_c_h_element_v_out(c_e_h_1, c_h, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s13)) | m_c_h_element_v_in1(c_e_h_1, c_h, s12) | (~node14(c_e_h_1, c_h, s12, s13)))),
% 293.83/186.39 inference(transitivity,[status(thm)],[23821, 23819])).
% 293.83/186.39 tff(23823,plain,
% 293.83/186.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s12, s13)) | m_c_h_element_v_in1(c_e_h_1, c_h, s12) | (~m_c_h_element_v_out(c_e_h_1, c_h, s13)))),
% 293.83/186.39 inference(quant_inst,[status(thm)],[])).
% 293.83/186.39 tff(23824,plain,
% 293.83/186.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s13)) | m_c_h_element_v_in1(c_e_h_1, c_h, s12) | (~node14(c_e_h_1, c_h, s12, s13))),
% 293.83/186.39 inference(modus_ponens,[status(thm)],[23823, 23822])).
% 293.83/186.39 tff(23825,plain,
% 293.83/186.39 ($false),
% 293.83/186.39 inference(unit_resolution,[status(thm)],[23824, 223, 23801, 23818, 23817])).
% 293.83/186.39 tff(23826,plain,((~node14(c_e_h_1, c_h, s12, s13)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s13)) | m_c_h_element_v_in1(c_e_h_1, c_h, s12)), inference(lemma,lemma(discharge,[]))).
% 293.83/186.39 tff(23827,plain,
% 293.83/186.39 (~node14(c_e_h_1, c_h, s12, s13)),
% 293.83/186.39 inference(unit_resolution,[status(thm)],[23826, 23801, 23817])).
% 293.83/186.39 tff(23828,plain,
% 293.83/186.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s12, s13)) | node19(c_e_h_1, c_h, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s12, s13)) | node19(c_e_h_1, c_h, s12, s13))),
% 293.83/186.39 inference(rewrite,[status(thm)],[])).
% 293.83/186.39 tff(23829,plain,
% 293.83/186.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s12, s13)) | node19(c_e_h_1, c_h, s12, s13))),
% 293.83/186.39 inference(quant_inst,[status(thm)],[])).
% 293.83/186.39 tff(23830,plain,
% 293.83/186.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s12, s13)) | node19(c_e_h_1, c_h, s12, s13)),
% 293.83/186.39 inference(modus_ponens,[status(thm)],[23829, 23828])).
% 293.83/186.39 tff(23831,plain,
% 293.83/186.39 (node19(c_e_h_1, c_h, s12, s13)),
% 293.83/186.39 inference(unit_resolution,[status(thm)],[23830, 190, 11856])).
% 293.83/186.39 tff(23832,plain,
% 293.83/186.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s12) | node15(c_e_h_1, c_h, s12, s13) | (~node19(c_e_h_1, c_h, s12, s13)) | node14(c_e_h_1, c_h, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s12) | node15(c_e_h_1, c_h, s12, s13) | (~node19(c_e_h_1, c_h, s12, s13)) | node14(c_e_h_1, c_h, s12, s13))),
% 293.83/186.39 inference(rewrite,[status(thm)],[])).
% 293.83/186.39 tff(23833,plain,
% 293.83/186.39 ((node16(c_e_h_1, c_h, s12) | node14(c_e_h_1, c_h, s12, s13) | node15(c_e_h_1, c_h, s12, s13) | (~node19(c_e_h_1, c_h, s12, s13))) <=> (node16(c_e_h_1, c_h, s12) | node15(c_e_h_1, c_h, s12, s13) | (~node19(c_e_h_1, c_h, s12, s13)) | node14(c_e_h_1, c_h, s12, s13))),
% 293.83/186.39 inference(rewrite,[status(thm)],[])).
% 293.83/186.39 tff(23834,plain,
% 293.83/186.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s12) | node14(c_e_h_1, c_h, s12, s13) | node15(c_e_h_1, c_h, s12, s13) | (~node19(c_e_h_1, c_h, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s12) | node15(c_e_h_1, c_h, s12, s13) | (~node19(c_e_h_1, c_h, s12, s13)) | node14(c_e_h_1, c_h, s12, s13)))),
% 293.83/186.39 inference(monotonicity,[status(thm)],[23833])).
% 293.83/186.39 tff(23835,plain,
% 293.83/186.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s12) | node14(c_e_h_1, c_h, s12, s13) | node15(c_e_h_1, c_h, s12, s13) | (~node19(c_e_h_1, c_h, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s12) | node15(c_e_h_1, c_h, s12, s13) | (~node19(c_e_h_1, c_h, s12, s13)) | node14(c_e_h_1, c_h, s12, s13))),
% 293.83/186.39 inference(transitivity,[status(thm)],[23834, 23832])).
% 293.83/186.39 tff(23836,plain,
% 293.83/186.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s12) | node14(c_e_h_1, c_h, s12, s13) | node15(c_e_h_1, c_h, s12, s13) | (~node19(c_e_h_1, c_h, s12, s13)))),
% 293.83/186.39 inference(quant_inst,[status(thm)],[])).
% 293.83/186.39 tff(23837,plain,
% 293.83/186.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s12) | node15(c_e_h_1, c_h, s12, s13) | (~node19(c_e_h_1, c_h, s12, s13)) | node14(c_e_h_1, c_h, s12, s13)),
% 293.83/186.39 inference(modus_ponens,[status(thm)],[23836, 23835])).
% 293.83/186.39 tff(23838,plain,
% 293.83/186.39 (node16(c_e_h_1, c_h, s12) | node15(c_e_h_1, c_h, s12, s13) | node14(c_e_h_1, c_h, s12, s13)),
% 293.83/186.39 inference(unit_resolution,[status(thm)],[23837, 204, 23831])).
% 293.83/186.39 tff(23839,plain,
% 293.83/186.39 (node16(c_e_h_1, c_h, s12)),
% 293.83/186.39 inference(unit_resolution,[status(thm)],[23838, 23827, 23816])).
% 293.83/186.39 tff(23840,plain,
% 293.83/186.39 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s12)) | m_c_h_element_v_in1(c_e_h_1, c_h, s12) | m_c_h_element_v_in2(c_e_h_1, c_h, s12))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s12)) | m_c_h_element_v_in1(c_e_h_1, c_h, s12) | m_c_h_element_v_in2(c_e_h_1, c_h, s12))),
% 293.83/186.40 inference(rewrite,[status(thm)],[])).
% 293.83/186.40 tff(23841,plain,
% 293.83/186.40 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s12)) | m_c_h_element_v_in1(c_e_h_1, c_h, s12) | m_c_h_element_v_in2(c_e_h_1, c_h, s12))),
% 293.83/186.40 inference(quant_inst,[status(thm)],[])).
% 293.83/186.40 tff(23842,plain,
% 293.83/186.40 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s12)) | m_c_h_element_v_in1(c_e_h_1, c_h, s12) | m_c_h_element_v_in2(c_e_h_1, c_h, s12)),
% 293.83/186.40 inference(modus_ponens,[status(thm)],[23841, 23840])).
% 293.83/186.40 tff(23843,plain,
% 293.83/186.40 ((~node16(c_e_h_1, c_h, s12)) | m_c_h_element_v_in2(c_e_h_1, c_h, s12)),
% 293.83/186.40 inference(unit_resolution,[status(thm)],[23842, 178, 23817])).
% 293.83/186.40 tff(23844,plain,
% 293.83/186.40 (m_c_h_element_v_in2(c_e_h_1, c_h, s12)),
% 293.83/186.40 inference(unit_resolution,[status(thm)],[23843, 23839])).
% 293.83/186.40 tff(23845,plain,
% 293.83/186.40 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s12) | (~node17(c_e_h_1, c_h, s12)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s12) | (~node17(c_e_h_1, c_h, s12)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s12)))),
% 293.83/186.40 inference(rewrite,[status(thm)],[])).
% 293.83/186.40 tff(23846,plain,
% 293.83/186.40 ((m_c_h_element_v_in1(c_e_h_1, c_h, s12) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s12)) | (~node17(c_e_h_1, c_h, s12))) <=> (m_c_h_element_v_in1(c_e_h_1, c_h, s12) | (~node17(c_e_h_1, c_h, s12)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s12)))),
% 293.83/186.40 inference(rewrite,[status(thm)],[])).
% 293.83/186.40 tff(23847,plain,
% 293.83/186.40 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s12) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s12)) | (~node17(c_e_h_1, c_h, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s12) | (~node17(c_e_h_1, c_h, s12)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s12))))),
% 293.83/186.40 inference(monotonicity,[status(thm)],[23846])).
% 293.83/186.40 tff(23848,plain,
% 293.83/186.40 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s12) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s12)) | (~node17(c_e_h_1, c_h, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s12) | (~node17(c_e_h_1, c_h, s12)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s12)))),
% 293.83/186.40 inference(transitivity,[status(thm)],[23847, 23845])).
% 293.83/186.40 tff(23849,plain,
% 293.83/186.40 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s12) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s12)) | (~node17(c_e_h_1, c_h, s12)))),
% 293.83/186.40 inference(quant_inst,[status(thm)],[])).
% 293.83/186.40 tff(23850,plain,
% 293.83/186.40 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s12) | (~node17(c_e_h_1, c_h, s12)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s12))),
% 293.83/186.40 inference(modus_ponens,[status(thm)],[23849, 23848])).
% 293.83/186.40 tff(23851,plain,
% 293.83/186.40 ((~node17(c_e_h_1, c_h, s12)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s12))),
% 293.83/186.40 inference(unit_resolution,[status(thm)],[23850, 859, 23817])).
% 293.83/186.40 tff(23852,plain,
% 293.83/186.40 (~node17(c_e_h_1, c_h, s12)),
% 293.83/186.40 inference(unit_resolution,[status(thm)],[23851, 23844])).
% 293.83/186.40 tff(23853,plain,
% 293.83/186.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s12) | (~node19(c_e_h_1, c_h, s12, s13)) | node18(c_e_h_1, c_h, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s12) | (~node19(c_e_h_1, c_h, s12, s13)) | node18(c_e_h_1, c_h, s12, s13))),
% 293.90/186.40 inference(rewrite,[status(thm)],[])).
% 293.90/186.40 tff(23854,plain,
% 293.90/186.40 ((node17(c_e_h_1, c_h, s12) | node18(c_e_h_1, c_h, s12, s13) | (~node19(c_e_h_1, c_h, s12, s13))) <=> (node17(c_e_h_1, c_h, s12) | (~node19(c_e_h_1, c_h, s12, s13)) | node18(c_e_h_1, c_h, s12, s13))),
% 293.90/186.40 inference(rewrite,[status(thm)],[])).
% 293.90/186.40 tff(23855,plain,
% 293.90/186.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s12) | node18(c_e_h_1, c_h, s12, s13) | (~node19(c_e_h_1, c_h, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s12) | (~node19(c_e_h_1, c_h, s12, s13)) | node18(c_e_h_1, c_h, s12, s13)))),
% 293.90/186.40 inference(monotonicity,[status(thm)],[23854])).
% 293.90/186.40 tff(23856,plain,
% 293.90/186.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s12) | node18(c_e_h_1, c_h, s12, s13) | (~node19(c_e_h_1, c_h, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s12) | (~node19(c_e_h_1, c_h, s12, s13)) | node18(c_e_h_1, c_h, s12, s13))),
% 293.90/186.40 inference(transitivity,[status(thm)],[23855, 23853])).
% 293.90/186.40 tff(23857,plain,
% 293.90/186.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s12) | node18(c_e_h_1, c_h, s12, s13) | (~node19(c_e_h_1, c_h, s12, s13)))),
% 293.90/186.40 inference(quant_inst,[status(thm)],[])).
% 293.90/186.40 tff(23858,plain,
% 293.90/186.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s12) | (~node19(c_e_h_1, c_h, s12, s13)) | node18(c_e_h_1, c_h, s12, s13)),
% 293.90/186.40 inference(modus_ponens,[status(thm)],[23857, 23856])).
% 293.90/186.40 tff(23859,plain,
% 293.90/186.40 (node17(c_e_h_1, c_h, s12) | node18(c_e_h_1, c_h, s12, s13)),
% 293.90/186.40 inference(unit_resolution,[status(thm)],[23858, 776, 23831])).
% 293.90/186.40 tff(23860,plain,
% 293.90/186.40 (node18(c_e_h_1, c_h, s12, s13)),
% 293.90/186.40 inference(unit_resolution,[status(thm)],[23859, 23852])).
% 293.90/186.40 tff(23861,plain,
% 293.90/186.40 ($false),
% 293.90/186.40 inference(unit_resolution,[status(thm)],[23806, 753, 23801, 23802, 23860])).
% 293.90/186.40 tff(23862,plain,((~m_c_h_element_v_out(c_e_h_1, c_h, s13)) | m_c_h_element_v_out(c_e_h_1, c_h, s12) | m_c_h_element_v_in1(c_e_h_1, c_h, s12)), inference(lemma,lemma(discharge,[]))).
% 293.90/186.40 tff(23863,plain,
% 293.90/186.40 (m_c_h_element_v_in1(c_e_h_1, c_h, s12)),
% 293.90/186.40 inference(unit_resolution,[status(thm)],[23862, 23802, 23801])).
% 293.90/186.40 tff(23864,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_h, s12)), introduced(assumption)).
% 293.90/186.40 tff(23865,plain,
% 293.90/186.40 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_h, s12) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s12)) | (~node17(c_e_h_1, c_h, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_h, s12) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s12)) | (~node17(c_e_h_1, c_h, s12)))),
% 293.90/186.40 inference(rewrite,[status(thm)],[])).
% 293.90/186.40 tff(23866,plain,
% 293.90/186.40 (((~m_c_h_element_v_in1(c_e_h_1, c_h, s12)) | m_c_h_element_v_in2(c_e_h_1, c_h, s12) | (~node17(c_e_h_1, c_h, s12))) <=> (m_c_h_element_v_in2(c_e_h_1, c_h, s12) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s12)) | (~node17(c_e_h_1, c_h, s12)))),
% 293.90/186.40 inference(rewrite,[status(thm)],[])).
% 293.90/186.40 tff(23867,plain,
% 293.90/186.40 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s12)) | m_c_h_element_v_in2(c_e_h_1, c_h, s12) | (~node17(c_e_h_1, c_h, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_h, s12) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s12)) | (~node17(c_e_h_1, c_h, s12))))),
% 293.90/186.40 inference(monotonicity,[status(thm)],[23866])).
% 293.90/186.40 tff(23868,plain,
% 293.90/186.40 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s12)) | m_c_h_element_v_in2(c_e_h_1, c_h, s12) | (~node17(c_e_h_1, c_h, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_h, s12) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s12)) | (~node17(c_e_h_1, c_h, s12)))),
% 293.90/186.40 inference(transitivity,[status(thm)],[23867, 23865])).
% 293.90/186.40 tff(23869,plain,
% 293.90/186.40 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s12)) | m_c_h_element_v_in2(c_e_h_1, c_h, s12) | (~node17(c_e_h_1, c_h, s12)))),
% 293.90/186.40 inference(quant_inst,[status(thm)],[])).
% 293.90/186.40 tff(23870,plain,
% 293.90/186.40 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_h, s12) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s12)) | (~node17(c_e_h_1, c_h, s12))),
% 293.90/186.40 inference(modus_ponens,[status(thm)],[23869, 23868])).
% 293.90/186.40 tff(23871,plain,
% 293.90/186.40 ((~m_c_h_element_v_in1(c_e_h_1, c_h, s12)) | (~node17(c_e_h_1, c_h, s12))),
% 293.90/186.40 inference(unit_resolution,[status(thm)],[23870, 919, 23864])).
% 293.90/186.40 tff(23872,plain,
% 293.90/186.40 (~node17(c_e_h_1, c_h, s12)),
% 293.90/186.40 inference(unit_resolution,[status(thm)],[23871, 23863])).
% 293.90/186.40 tff(23873,plain,
% 293.90/186.40 ($false),
% 293.90/186.40 inference(unit_resolution,[status(thm)],[23859, 23872, 23809])).
% 293.90/186.40 tff(23874,plain,(m_c_h_element_v_out(c_e_h_1, c_h, s12) | m_c_h_element_v_in2(c_e_h_1, c_h, s12) | (~m_c_h_element_v_out(c_e_h_1, c_h, s13))), inference(lemma,lemma(discharge,[]))).
% 293.90/186.40 tff(23875,plain,
% 293.90/186.40 (~m_c_h_element_v_out(c_e_h_1, c_h, s13)),
% 293.90/186.40 inference(unit_resolution,[status(thm)],[23874, 23800, 23796])).
% 293.90/186.40 tff(23876,assumption,(m_c_h_element_v_out(c_e_h_1, c_h, s14)), introduced(assumption)).
% 293.90/186.40 tff(23877,assumption,(~m_c_h_element_v_out(c_e_h_1, c_h, s13)), introduced(assumption)).
% 293.90/186.40 tff(23878,assumption,(node18(c_e_h_1, c_h, s13, s14)), introduced(assumption)).
% 293.90/186.40 tff(23879,plain,
% 293.90/186.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_h, s13) | (~m_c_h_element_v_out(c_e_h_1, c_h, s14)) | (~node18(c_e_h_1, c_h, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s13) | (~m_c_h_element_v_out(c_e_h_1, c_h, s14)) | (~node18(c_e_h_1, c_h, s13, s14)))),
% 293.90/186.40 inference(rewrite,[status(thm)],[])).
% 293.90/186.40 tff(23880,plain,
% 293.90/186.40 (((~m_c_h_element_v_out(c_e_h_1, c_h, s14)) | m_c_h_element_v_out(c_e_h_1, c_h, s13) | (~node18(c_e_h_1, c_h, s13, s14))) <=> (m_c_h_element_v_out(c_e_h_1, c_h, s13) | (~m_c_h_element_v_out(c_e_h_1, c_h, s14)) | (~node18(c_e_h_1, c_h, s13, s14)))),
% 293.90/186.40 inference(rewrite,[status(thm)],[])).
% 293.90/186.40 tff(23881,plain,
% 293.90/186.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s14)) | m_c_h_element_v_out(c_e_h_1, c_h, s13) | (~node18(c_e_h_1, c_h, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_h, s13) | (~m_c_h_element_v_out(c_e_h_1, c_h, s14)) | (~node18(c_e_h_1, c_h, s13, s14))))),
% 293.90/186.40 inference(monotonicity,[status(thm)],[23880])).
% 293.90/186.40 tff(23882,plain,
% 293.90/186.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s14)) | m_c_h_element_v_out(c_e_h_1, c_h, s13) | (~node18(c_e_h_1, c_h, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s13) | (~m_c_h_element_v_out(c_e_h_1, c_h, s14)) | (~node18(c_e_h_1, c_h, s13, s14)))),
% 293.90/186.41 inference(transitivity,[status(thm)],[23881, 23879])).
% 293.90/186.41 tff(23883,plain,
% 293.90/186.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s14)) | m_c_h_element_v_out(c_e_h_1, c_h, s13) | (~node18(c_e_h_1, c_h, s13, s14)))),
% 293.90/186.41 inference(quant_inst,[status(thm)],[])).
% 293.90/186.41 tff(23884,plain,
% 293.90/186.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s13) | (~m_c_h_element_v_out(c_e_h_1, c_h, s14)) | (~node18(c_e_h_1, c_h, s13, s14))),
% 293.90/186.41 inference(modus_ponens,[status(thm)],[23883, 23882])).
% 293.90/186.41 tff(23885,plain,
% 293.90/186.41 ($false),
% 293.90/186.41 inference(unit_resolution,[status(thm)],[23884, 753, 23877, 23876, 23878])).
% 293.90/186.41 tff(23886,plain,((~node18(c_e_h_1, c_h, s13, s14)) | m_c_h_element_v_out(c_e_h_1, c_h, s13) | (~m_c_h_element_v_out(c_e_h_1, c_h, s14))), inference(lemma,lemma(discharge,[]))).
% 293.90/186.41 tff(23887,plain,
% 293.90/186.41 (~node18(c_e_h_1, c_h, s13, s14)),
% 293.90/186.41 inference(unit_resolution,[status(thm)],[23886, 23876, 23877])).
% 293.90/186.41 tff(23888,assumption,(node15(c_e_h_1, c_h, s13, s14)), introduced(assumption)).
% 293.90/186.41 tff(23889,plain,
% 293.90/186.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s14)) | (~node15(c_e_h_1, c_h, s13, s14)) | m_c_h_element_v_out(c_e_h_1, c_h, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s14)) | (~node15(c_e_h_1, c_h, s13, s14)) | m_c_h_element_v_out(c_e_h_1, c_h, s13))),
% 293.90/186.41 inference(rewrite,[status(thm)],[])).
% 293.90/186.41 tff(23890,plain,
% 293.90/186.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s14)) | (~node15(c_e_h_1, c_h, s13, s14)) | m_c_h_element_v_out(c_e_h_1, c_h, s13))),
% 293.90/186.41 inference(quant_inst,[status(thm)],[])).
% 293.90/186.41 tff(23891,plain,
% 293.90/186.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s14)) | (~node15(c_e_h_1, c_h, s13, s14)) | m_c_h_element_v_out(c_e_h_1, c_h, s13)),
% 293.90/186.41 inference(modus_ponens,[status(thm)],[23890, 23889])).
% 293.90/186.41 tff(23892,plain,
% 293.90/186.41 ($false),
% 293.90/186.41 inference(unit_resolution,[status(thm)],[23891, 147, 23877, 23876, 23888])).
% 293.90/186.41 tff(23893,plain,((~node15(c_e_h_1, c_h, s13, s14)) | m_c_h_element_v_out(c_e_h_1, c_h, s13) | (~m_c_h_element_v_out(c_e_h_1, c_h, s14))), inference(lemma,lemma(discharge,[]))).
% 293.90/186.41 tff(23894,plain,
% 293.90/186.41 (~node15(c_e_h_1, c_h, s13, s14)),
% 293.90/186.41 inference(unit_resolution,[status(thm)],[23893, 23876, 23877])).
% 293.90/186.41 tff(23895,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_h, s13)), introduced(assumption)).
% 293.90/186.41 tff(23896,assumption,(node17(c_e_h_1, c_h, s13)), introduced(assumption)).
% 293.90/186.41 tff(23897,plain,
% 293.90/186.41 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s13)) | m_c_h_element_v_in1(c_e_h_1, c_h, s13) | (~node17(c_e_h_1, c_h, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s13)) | m_c_h_element_v_in1(c_e_h_1, c_h, s13) | (~node17(c_e_h_1, c_h, s13)))),
% 293.90/186.41 inference(rewrite,[status(thm)],[])).
% 293.90/186.41 tff(23898,plain,
% 293.90/186.41 ((m_c_h_element_v_in1(c_e_h_1, c_h, s13) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s13)) | (~node17(c_e_h_1, c_h, s13))) <=> ((~m_c_h_element_v_in2(c_e_h_1, c_h, s13)) | m_c_h_element_v_in1(c_e_h_1, c_h, s13) | (~node17(c_e_h_1, c_h, s13)))),
% 293.90/186.41 inference(rewrite,[status(thm)],[])).
% 293.90/186.41 tff(23899,plain,
% 293.90/186.41 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s13) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s13)) | (~node17(c_e_h_1, c_h, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s13)) | m_c_h_element_v_in1(c_e_h_1, c_h, s13) | (~node17(c_e_h_1, c_h, s13))))),
% 293.90/186.41 inference(monotonicity,[status(thm)],[23898])).
% 293.90/186.41 tff(23900,plain,
% 293.90/186.41 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s13) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s13)) | (~node17(c_e_h_1, c_h, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s13)) | m_c_h_element_v_in1(c_e_h_1, c_h, s13) | (~node17(c_e_h_1, c_h, s13)))),
% 293.90/186.41 inference(transitivity,[status(thm)],[23899, 23897])).
% 293.90/186.41 tff(23901,plain,
% 293.90/186.41 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s13) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s13)) | (~node17(c_e_h_1, c_h, s13)))),
% 293.90/186.41 inference(quant_inst,[status(thm)],[])).
% 293.90/186.41 tff(23902,plain,
% 293.90/186.41 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s13)) | m_c_h_element_v_in1(c_e_h_1, c_h, s13) | (~node17(c_e_h_1, c_h, s13))),
% 293.90/186.41 inference(modus_ponens,[status(thm)],[23901, 23900])).
% 293.90/186.41 tff(23903,plain,
% 293.90/186.41 ((~m_c_h_element_v_in2(c_e_h_1, c_h, s13)) | m_c_h_element_v_in1(c_e_h_1, c_h, s13)),
% 293.90/186.41 inference(unit_resolution,[status(thm)],[23902, 859, 23896])).
% 293.90/186.41 tff(23904,plain,
% 293.90/186.41 (~m_c_h_element_v_in2(c_e_h_1, c_h, s13)),
% 293.90/186.41 inference(unit_resolution,[status(thm)],[23903, 23895])).
% 293.90/186.41 tff(23905,assumption,(~node15(c_e_h_1, c_h, s13, s14)), introduced(assumption)).
% 293.90/186.41 tff(23906,assumption,(node14(c_e_h_1, c_h, s13, s14)), introduced(assumption)).
% 293.90/186.41 tff(23907,plain,
% 293.90/186.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s14)) | m_c_h_element_v_in1(c_e_h_1, c_h, s13) | (~node14(c_e_h_1, c_h, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s14)) | m_c_h_element_v_in1(c_e_h_1, c_h, s13) | (~node14(c_e_h_1, c_h, s13, s14)))),
% 293.90/186.41 inference(rewrite,[status(thm)],[])).
% 293.90/186.41 tff(23908,plain,
% 293.90/186.41 (((~node14(c_e_h_1, c_h, s13, s14)) | m_c_h_element_v_in1(c_e_h_1, c_h, s13) | (~m_c_h_element_v_out(c_e_h_1, c_h, s14))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_h, s14)) | m_c_h_element_v_in1(c_e_h_1, c_h, s13) | (~node14(c_e_h_1, c_h, s13, s14)))),
% 293.90/186.41 inference(rewrite,[status(thm)],[])).
% 293.90/186.41 tff(23909,plain,
% 293.90/186.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s13, s14)) | m_c_h_element_v_in1(c_e_h_1, c_h, s13) | (~m_c_h_element_v_out(c_e_h_1, c_h, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s14)) | m_c_h_element_v_in1(c_e_h_1, c_h, s13) | (~node14(c_e_h_1, c_h, s13, s14))))),
% 293.90/186.41 inference(monotonicity,[status(thm)],[23908])).
% 293.90/186.41 tff(23910,plain,
% 293.90/186.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s13, s14)) | m_c_h_element_v_in1(c_e_h_1, c_h, s13) | (~m_c_h_element_v_out(c_e_h_1, c_h, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s14)) | m_c_h_element_v_in1(c_e_h_1, c_h, s13) | (~node14(c_e_h_1, c_h, s13, s14)))),
% 293.90/186.41 inference(transitivity,[status(thm)],[23909, 23907])).
% 293.90/186.41 tff(23911,plain,
% 293.90/186.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s13, s14)) | m_c_h_element_v_in1(c_e_h_1, c_h, s13) | (~m_c_h_element_v_out(c_e_h_1, c_h, s14)))),
% 293.90/186.41 inference(quant_inst,[status(thm)],[])).
% 293.90/186.41 tff(23912,plain,
% 293.90/186.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s14)) | m_c_h_element_v_in1(c_e_h_1, c_h, s13) | (~node14(c_e_h_1, c_h, s13, s14))),
% 293.90/186.41 inference(modus_ponens,[status(thm)],[23911, 23910])).
% 293.90/186.41 tff(23913,plain,
% 293.90/186.41 ($false),
% 293.90/186.41 inference(unit_resolution,[status(thm)],[23912, 223, 23876, 23906, 23895])).
% 293.90/186.41 tff(23914,plain,((~node14(c_e_h_1, c_h, s13, s14)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s14)) | m_c_h_element_v_in1(c_e_h_1, c_h, s13)), inference(lemma,lemma(discharge,[]))).
% 293.90/186.41 tff(23915,plain,
% 293.90/186.41 (~node14(c_e_h_1, c_h, s13, s14)),
% 293.90/186.41 inference(unit_resolution,[status(thm)],[23914, 23895, 23876])).
% 293.90/186.41 tff(23916,plain,
% 293.90/186.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s13, s14)) | node19(c_e_h_1, c_h, s13, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s13, s14)) | node19(c_e_h_1, c_h, s13, s14))),
% 293.90/186.41 inference(rewrite,[status(thm)],[])).
% 293.90/186.41 tff(23917,plain,
% 293.90/186.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s13, s14)) | node19(c_e_h_1, c_h, s13, s14))),
% 293.90/186.41 inference(quant_inst,[status(thm)],[])).
% 293.90/186.42 tff(23918,plain,
% 293.90/186.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s13, s14)) | node19(c_e_h_1, c_h, s13, s14)),
% 293.90/186.42 inference(modus_ponens,[status(thm)],[23917, 23916])).
% 293.90/186.42 tff(23919,plain,
% 293.90/186.42 (node19(c_e_h_1, c_h, s13, s14)),
% 293.90/186.42 inference(unit_resolution,[status(thm)],[23918, 190, 12831])).
% 293.90/186.42 tff(23920,plain,
% 293.90/186.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s13) | node15(c_e_h_1, c_h, s13, s14) | (~node19(c_e_h_1, c_h, s13, s14)) | node14(c_e_h_1, c_h, s13, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s13) | node15(c_e_h_1, c_h, s13, s14) | (~node19(c_e_h_1, c_h, s13, s14)) | node14(c_e_h_1, c_h, s13, s14))),
% 293.90/186.42 inference(rewrite,[status(thm)],[])).
% 293.90/186.42 tff(23921,plain,
% 293.90/186.42 ((node16(c_e_h_1, c_h, s13) | node14(c_e_h_1, c_h, s13, s14) | node15(c_e_h_1, c_h, s13, s14) | (~node19(c_e_h_1, c_h, s13, s14))) <=> (node16(c_e_h_1, c_h, s13) | node15(c_e_h_1, c_h, s13, s14) | (~node19(c_e_h_1, c_h, s13, s14)) | node14(c_e_h_1, c_h, s13, s14))),
% 293.90/186.42 inference(rewrite,[status(thm)],[])).
% 293.90/186.42 tff(23922,plain,
% 293.90/186.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s13) | node14(c_e_h_1, c_h, s13, s14) | node15(c_e_h_1, c_h, s13, s14) | (~node19(c_e_h_1, c_h, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s13) | node15(c_e_h_1, c_h, s13, s14) | (~node19(c_e_h_1, c_h, s13, s14)) | node14(c_e_h_1, c_h, s13, s14)))),
% 293.90/186.42 inference(monotonicity,[status(thm)],[23921])).
% 293.90/186.42 tff(23923,plain,
% 293.90/186.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s13) | node14(c_e_h_1, c_h, s13, s14) | node15(c_e_h_1, c_h, s13, s14) | (~node19(c_e_h_1, c_h, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s13) | node15(c_e_h_1, c_h, s13, s14) | (~node19(c_e_h_1, c_h, s13, s14)) | node14(c_e_h_1, c_h, s13, s14))),
% 293.90/186.42 inference(transitivity,[status(thm)],[23922, 23920])).
% 293.90/186.42 tff(23924,plain,
% 293.90/186.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s13) | node14(c_e_h_1, c_h, s13, s14) | node15(c_e_h_1, c_h, s13, s14) | (~node19(c_e_h_1, c_h, s13, s14)))),
% 293.90/186.42 inference(quant_inst,[status(thm)],[])).
% 293.90/186.42 tff(23925,plain,
% 293.90/186.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s13) | node15(c_e_h_1, c_h, s13, s14) | (~node19(c_e_h_1, c_h, s13, s14)) | node14(c_e_h_1, c_h, s13, s14)),
% 293.90/186.42 inference(modus_ponens,[status(thm)],[23924, 23923])).
% 293.90/186.42 tff(23926,plain,
% 293.90/186.42 (node16(c_e_h_1, c_h, s13) | node15(c_e_h_1, c_h, s13, s14) | node14(c_e_h_1, c_h, s13, s14)),
% 293.90/186.42 inference(unit_resolution,[status(thm)],[23925, 204, 23919])).
% 293.90/186.42 tff(23927,plain,
% 293.90/186.42 (node16(c_e_h_1, c_h, s13)),
% 293.90/186.42 inference(unit_resolution,[status(thm)],[23926, 23915, 23905])).
% 293.90/186.42 tff(23928,plain,
% 293.90/186.42 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s13)) | m_c_h_element_v_in1(c_e_h_1, c_h, s13) | m_c_h_element_v_in2(c_e_h_1, c_h, s13))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s13)) | m_c_h_element_v_in1(c_e_h_1, c_h, s13) | m_c_h_element_v_in2(c_e_h_1, c_h, s13))),
% 293.90/186.42 inference(rewrite,[status(thm)],[])).
% 293.90/186.42 tff(23929,plain,
% 293.90/186.42 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s13)) | m_c_h_element_v_in1(c_e_h_1, c_h, s13) | m_c_h_element_v_in2(c_e_h_1, c_h, s13))),
% 293.90/186.42 inference(quant_inst,[status(thm)],[])).
% 293.90/186.42 tff(23930,plain,
% 293.90/186.42 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s13)) | m_c_h_element_v_in1(c_e_h_1, c_h, s13) | m_c_h_element_v_in2(c_e_h_1, c_h, s13)),
% 293.90/186.42 inference(modus_ponens,[status(thm)],[23929, 23928])).
% 293.90/186.42 tff(23931,plain,
% 293.90/186.42 ($false),
% 293.90/186.42 inference(unit_resolution,[status(thm)],[23930, 178, 23927, 23895, 23904])).
% 293.90/186.42 tff(23932,plain,(m_c_h_element_v_in1(c_e_h_1, c_h, s13) | node15(c_e_h_1, c_h, s13, s14) | (~node17(c_e_h_1, c_h, s13)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s14))), inference(lemma,lemma(discharge,[]))).
% 293.90/186.42 tff(23933,plain,
% 293.90/186.42 (~node17(c_e_h_1, c_h, s13)),
% 293.90/186.42 inference(unit_resolution,[status(thm)],[23932, 23876, 23895, 23894])).
% 293.90/186.42 tff(23934,plain,
% 293.90/186.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_1, c_h, s13, s14) | (~node19(c_e_h_1, c_h, s13, s14)) | node17(c_e_h_1, c_h, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_h, s13, s14) | (~node19(c_e_h_1, c_h, s13, s14)) | node17(c_e_h_1, c_h, s13))),
% 293.90/186.42 inference(rewrite,[status(thm)],[])).
% 293.90/186.42 tff(23935,plain,
% 293.90/186.42 ((node17(c_e_h_1, c_h, s13) | node18(c_e_h_1, c_h, s13, s14) | (~node19(c_e_h_1, c_h, s13, s14))) <=> (node18(c_e_h_1, c_h, s13, s14) | (~node19(c_e_h_1, c_h, s13, s14)) | node17(c_e_h_1, c_h, s13))),
% 293.90/186.42 inference(rewrite,[status(thm)],[])).
% 293.90/186.42 tff(23936,plain,
% 293.90/186.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s13) | node18(c_e_h_1, c_h, s13, s14) | (~node19(c_e_h_1, c_h, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_1, c_h, s13, s14) | (~node19(c_e_h_1, c_h, s13, s14)) | node17(c_e_h_1, c_h, s13)))),
% 293.90/186.42 inference(monotonicity,[status(thm)],[23935])).
% 293.90/186.42 tff(23937,plain,
% 293.90/186.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s13) | node18(c_e_h_1, c_h, s13, s14) | (~node19(c_e_h_1, c_h, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_h, s13, s14) | (~node19(c_e_h_1, c_h, s13, s14)) | node17(c_e_h_1, c_h, s13))),
% 293.90/186.42 inference(transitivity,[status(thm)],[23936, 23934])).
% 293.90/186.42 tff(23938,plain,
% 293.90/186.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s13) | node18(c_e_h_1, c_h, s13, s14) | (~node19(c_e_h_1, c_h, s13, s14)))),
% 293.90/186.42 inference(quant_inst,[status(thm)],[])).
% 293.90/186.42 tff(23939,plain,
% 293.90/186.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_h, s13, s14) | (~node19(c_e_h_1, c_h, s13, s14)) | node17(c_e_h_1, c_h, s13)),
% 293.90/186.42 inference(modus_ponens,[status(thm)],[23938, 23937])).
% 293.90/186.42 tff(23940,plain,
% 293.90/186.42 (node18(c_e_h_1, c_h, s13, s14) | node17(c_e_h_1, c_h, s13)),
% 293.90/186.42 inference(unit_resolution,[status(thm)],[23939, 776, 23919])).
% 293.90/186.42 tff(23941,plain,
% 293.90/186.42 ($false),
% 293.90/186.42 inference(unit_resolution,[status(thm)],[23940, 23933, 23887])).
% 293.90/186.42 tff(23942,plain,((~m_c_h_element_v_out(c_e_h_1, c_h, s14)) | m_c_h_element_v_in1(c_e_h_1, c_h, s13) | m_c_h_element_v_out(c_e_h_1, c_h, s13)), inference(lemma,lemma(discharge,[]))).
% 293.90/186.42 tff(23943,plain,
% 293.90/186.42 (m_c_h_element_v_in1(c_e_h_1, c_h, s13)),
% 293.90/186.42 inference(unit_resolution,[status(thm)],[23942, 23877, 23876])).
% 293.90/186.42 tff(23944,plain,
% 293.90/186.42 (~node18(c_e_h_1, c_h, s13, s14)),
% 293.90/186.42 inference(unit_resolution,[status(thm)],[23886, 23877, 23876])).
% 293.90/186.42 tff(23945,plain,
% 293.90/186.42 (node17(c_e_h_1, c_h, s13)),
% 293.90/186.42 inference(unit_resolution,[status(thm)],[23940, 23944])).
% 293.90/186.42 tff(23946,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_h, s13)), introduced(assumption)).
% 293.90/186.42 tff(23947,plain,
% 293.90/186.42 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_h, s13) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s13)) | (~node17(c_e_h_1, c_h, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_h, s13) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s13)) | (~node17(c_e_h_1, c_h, s13)))),
% 293.90/186.42 inference(rewrite,[status(thm)],[])).
% 293.90/186.42 tff(23948,plain,
% 293.90/186.42 (((~m_c_h_element_v_in1(c_e_h_1, c_h, s13)) | m_c_h_element_v_in2(c_e_h_1, c_h, s13) | (~node17(c_e_h_1, c_h, s13))) <=> (m_c_h_element_v_in2(c_e_h_1, c_h, s13) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s13)) | (~node17(c_e_h_1, c_h, s13)))),
% 293.90/186.42 inference(rewrite,[status(thm)],[])).
% 293.90/186.42 tff(23949,plain,
% 293.90/186.42 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s13)) | m_c_h_element_v_in2(c_e_h_1, c_h, s13) | (~node17(c_e_h_1, c_h, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_h, s13) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s13)) | (~node17(c_e_h_1, c_h, s13))))),
% 293.90/186.42 inference(monotonicity,[status(thm)],[23948])).
% 293.90/186.42 tff(23950,plain,
% 293.90/186.42 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s13)) | m_c_h_element_v_in2(c_e_h_1, c_h, s13) | (~node17(c_e_h_1, c_h, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_h, s13) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s13)) | (~node17(c_e_h_1, c_h, s13)))),
% 293.90/186.42 inference(transitivity,[status(thm)],[23949, 23947])).
% 293.90/186.43 tff(23951,plain,
% 293.90/186.43 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s13)) | m_c_h_element_v_in2(c_e_h_1, c_h, s13) | (~node17(c_e_h_1, c_h, s13)))),
% 293.90/186.43 inference(quant_inst,[status(thm)],[])).
% 293.90/186.43 tff(23952,plain,
% 293.90/186.43 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_h, s13) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s13)) | (~node17(c_e_h_1, c_h, s13))),
% 293.90/186.43 inference(modus_ponens,[status(thm)],[23951, 23950])).
% 293.90/186.43 tff(23953,plain,
% 293.90/186.43 ((~m_c_h_element_v_in1(c_e_h_1, c_h, s13)) | (~node17(c_e_h_1, c_h, s13))),
% 293.90/186.43 inference(unit_resolution,[status(thm)],[23952, 919, 23946])).
% 293.90/186.43 tff(23954,plain,
% 293.90/186.43 ($false),
% 293.90/186.43 inference(unit_resolution,[status(thm)],[23953, 23945, 23943])).
% 293.90/186.43 tff(23955,plain,(m_c_h_element_v_out(c_e_h_1, c_h, s13) | m_c_h_element_v_in2(c_e_h_1, c_h, s13) | (~m_c_h_element_v_out(c_e_h_1, c_h, s14))), inference(lemma,lemma(discharge,[]))).
% 293.90/186.43 tff(23956,plain,
% 293.90/186.43 (m_c_h_element_v_in2(c_e_h_1, c_h, s13) | (~m_c_h_element_v_out(c_e_h_1, c_h, s14))),
% 293.90/186.43 inference(unit_resolution,[status(thm)],[23955, 23875])).
% 293.90/186.43 tff(23957,plain,
% 293.90/186.43 (~m_c_h_element_v_out(c_e_h_1, c_h, s14)),
% 293.90/186.43 inference(unit_resolution,[status(thm)],[23956, 23490])).
% 293.90/186.43 tff(23958,assumption,(m_c_h_element_v_out(c_e_h_1, c_h, s15)), introduced(assumption)).
% 293.90/186.43 tff(23959,assumption,(~m_c_h_element_v_out(c_e_h_1, c_h, s14)), introduced(assumption)).
% 293.90/186.43 tff(23960,assumption,(node18(c_e_h_1, c_h, s14, s15)), introduced(assumption)).
% 293.90/186.43 tff(23961,plain,
% 293.90/186.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_h, s14) | (~node18(c_e_h_1, c_h, s14, s15)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s14) | (~node18(c_e_h_1, c_h, s14, s15)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s15)))),
% 293.90/186.43 inference(rewrite,[status(thm)],[])).
% 293.90/186.43 tff(23962,plain,
% 293.90/186.43 (((~m_c_h_element_v_out(c_e_h_1, c_h, s15)) | m_c_h_element_v_out(c_e_h_1, c_h, s14) | (~node18(c_e_h_1, c_h, s14, s15))) <=> (m_c_h_element_v_out(c_e_h_1, c_h, s14) | (~node18(c_e_h_1, c_h, s14, s15)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s15)))),
% 293.90/186.43 inference(rewrite,[status(thm)],[])).
% 293.90/186.43 tff(23963,plain,
% 293.90/186.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s15)) | m_c_h_element_v_out(c_e_h_1, c_h, s14) | (~node18(c_e_h_1, c_h, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_h, s14) | (~node18(c_e_h_1, c_h, s14, s15)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s15))))),
% 293.90/186.43 inference(monotonicity,[status(thm)],[23962])).
% 293.90/186.43 tff(23964,plain,
% 293.90/186.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s15)) | m_c_h_element_v_out(c_e_h_1, c_h, s14) | (~node18(c_e_h_1, c_h, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s14) | (~node18(c_e_h_1, c_h, s14, s15)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s15)))),
% 293.90/186.43 inference(transitivity,[status(thm)],[23963, 23961])).
% 293.90/186.43 tff(23965,plain,
% 293.90/186.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s15)) | m_c_h_element_v_out(c_e_h_1, c_h, s14) | (~node18(c_e_h_1, c_h, s14, s15)))),
% 293.90/186.43 inference(quant_inst,[status(thm)],[])).
% 293.90/186.43 tff(23966,plain,
% 293.90/186.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s14) | (~node18(c_e_h_1, c_h, s14, s15)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s15))),
% 293.90/186.43 inference(modus_ponens,[status(thm)],[23965, 23964])).
% 293.90/186.43 tff(23967,plain,
% 293.90/186.43 ($false),
% 293.90/186.43 inference(unit_resolution,[status(thm)],[23966, 753, 23959, 23958, 23960])).
% 293.90/186.43 tff(23968,plain,((~node18(c_e_h_1, c_h, s14, s15)) | m_c_h_element_v_out(c_e_h_1, c_h, s14) | (~m_c_h_element_v_out(c_e_h_1, c_h, s15))), inference(lemma,lemma(discharge,[]))).
% 293.90/186.43 tff(23969,plain,
% 293.90/186.43 (~node18(c_e_h_1, c_h, s14, s15)),
% 293.90/186.43 inference(unit_resolution,[status(thm)],[23968, 23959, 23958])).
% 293.90/186.43 tff(23970,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_h, s14)), introduced(assumption)).
% 293.90/186.43 tff(23971,assumption,(node14(c_e_h_1, c_h, s14, s15)), introduced(assumption)).
% 293.90/186.43 tff(23972,plain,
% 293.90/186.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s14) | (~m_c_h_element_v_out(c_e_h_1, c_h, s15)) | (~node14(c_e_h_1, c_h, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s14) | (~m_c_h_element_v_out(c_e_h_1, c_h, s15)) | (~node14(c_e_h_1, c_h, s14, s15)))),
% 293.90/186.43 inference(rewrite,[status(thm)],[])).
% 293.90/186.43 tff(23973,plain,
% 293.90/186.43 (((~node14(c_e_h_1, c_h, s14, s15)) | m_c_h_element_v_in1(c_e_h_1, c_h, s14) | (~m_c_h_element_v_out(c_e_h_1, c_h, s15))) <=> (m_c_h_element_v_in1(c_e_h_1, c_h, s14) | (~m_c_h_element_v_out(c_e_h_1, c_h, s15)) | (~node14(c_e_h_1, c_h, s14, s15)))),
% 293.90/186.43 inference(rewrite,[status(thm)],[])).
% 293.90/186.43 tff(23974,plain,
% 293.90/186.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s14, s15)) | m_c_h_element_v_in1(c_e_h_1, c_h, s14) | (~m_c_h_element_v_out(c_e_h_1, c_h, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s14) | (~m_c_h_element_v_out(c_e_h_1, c_h, s15)) | (~node14(c_e_h_1, c_h, s14, s15))))),
% 293.90/186.43 inference(monotonicity,[status(thm)],[23973])).
% 293.90/186.43 tff(23975,plain,
% 293.90/186.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s14, s15)) | m_c_h_element_v_in1(c_e_h_1, c_h, s14) | (~m_c_h_element_v_out(c_e_h_1, c_h, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s14) | (~m_c_h_element_v_out(c_e_h_1, c_h, s15)) | (~node14(c_e_h_1, c_h, s14, s15)))),
% 293.90/186.43 inference(transitivity,[status(thm)],[23974, 23972])).
% 293.90/186.43 tff(23976,plain,
% 293.90/186.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s14, s15)) | m_c_h_element_v_in1(c_e_h_1, c_h, s14) | (~m_c_h_element_v_out(c_e_h_1, c_h, s15)))),
% 293.90/186.43 inference(quant_inst,[status(thm)],[])).
% 293.90/186.43 tff(23977,plain,
% 293.90/186.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s14) | (~m_c_h_element_v_out(c_e_h_1, c_h, s15)) | (~node14(c_e_h_1, c_h, s14, s15))),
% 293.90/186.43 inference(modus_ponens,[status(thm)],[23976, 23975])).
% 293.90/186.43 tff(23978,plain,
% 293.90/186.43 ($false),
% 293.90/186.43 inference(unit_resolution,[status(thm)],[23977, 223, 23958, 23971, 23970])).
% 293.90/186.43 tff(23979,plain,((~node14(c_e_h_1, c_h, s14, s15)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s15)) | m_c_h_element_v_in1(c_e_h_1, c_h, s14)), inference(lemma,lemma(discharge,[]))).
% 293.90/186.43 tff(23980,plain,
% 293.90/186.43 (~node14(c_e_h_1, c_h, s14, s15)),
% 293.90/186.43 inference(unit_resolution,[status(thm)],[23979, 23958, 23970])).
% 293.90/186.43 tff(23981,assumption,(node15(c_e_h_1, c_h, s14, s15)), introduced(assumption)).
% 293.90/186.43 tff(23982,plain,
% 293.90/186.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s15)) | (~node15(c_e_h_1, c_h, s14, s15)) | m_c_h_element_v_out(c_e_h_1, c_h, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s15)) | (~node15(c_e_h_1, c_h, s14, s15)) | m_c_h_element_v_out(c_e_h_1, c_h, s14))),
% 293.90/186.43 inference(rewrite,[status(thm)],[])).
% 293.90/186.43 tff(23983,plain,
% 293.90/186.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s15)) | (~node15(c_e_h_1, c_h, s14, s15)) | m_c_h_element_v_out(c_e_h_1, c_h, s14))),
% 293.90/186.43 inference(quant_inst,[status(thm)],[])).
% 293.90/186.43 tff(23984,plain,
% 293.90/186.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s15)) | (~node15(c_e_h_1, c_h, s14, s15)) | m_c_h_element_v_out(c_e_h_1, c_h, s14)),
% 293.90/186.43 inference(modus_ponens,[status(thm)],[23983, 23982])).
% 293.90/186.43 tff(23985,plain,
% 293.90/186.43 ($false),
% 293.90/186.43 inference(unit_resolution,[status(thm)],[23984, 147, 23959, 23958, 23981])).
% 293.90/186.43 tff(23986,plain,((~node15(c_e_h_1, c_h, s14, s15)) | m_c_h_element_v_out(c_e_h_1, c_h, s14) | (~m_c_h_element_v_out(c_e_h_1, c_h, s15))), inference(lemma,lemma(discharge,[]))).
% 293.90/186.43 tff(23987,plain,
% 293.90/186.43 (~node15(c_e_h_1, c_h, s14, s15)),
% 293.90/186.43 inference(unit_resolution,[status(thm)],[23986, 23959, 23958])).
% 293.90/186.43 tff(23988,plain,
% 293.90/186.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s14, s15)) | node19(c_e_h_1, c_h, s14, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s14, s15)) | node19(c_e_h_1, c_h, s14, s15))),
% 293.90/186.43 inference(rewrite,[status(thm)],[])).
% 293.90/186.43 tff(23989,plain,
% 293.90/186.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s14, s15)) | node19(c_e_h_1, c_h, s14, s15))),
% 293.90/186.43 inference(quant_inst,[status(thm)],[])).
% 293.90/186.43 tff(23990,plain,
% 293.90/186.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s14, s15)) | node19(c_e_h_1, c_h, s14, s15)),
% 293.90/186.43 inference(modus_ponens,[status(thm)],[23989, 23988])).
% 293.90/186.43 tff(23991,plain,
% 293.90/186.43 (node19(c_e_h_1, c_h, s14, s15)),
% 293.90/186.43 inference(unit_resolution,[status(thm)],[23990, 190, 12926])).
% 293.90/186.43 tff(23992,plain,
% 293.90/186.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_h, s14, s15)) | node14(c_e_h_1, c_h, s14, s15) | node15(c_e_h_1, c_h, s14, s15) | node16(c_e_h_1, c_h, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_h, s14, s15)) | node14(c_e_h_1, c_h, s14, s15) | node15(c_e_h_1, c_h, s14, s15) | node16(c_e_h_1, c_h, s14))),
% 293.90/186.43 inference(rewrite,[status(thm)],[])).
% 293.90/186.43 tff(23993,plain,
% 293.90/186.43 ((node16(c_e_h_1, c_h, s14) | node14(c_e_h_1, c_h, s14, s15) | node15(c_e_h_1, c_h, s14, s15) | (~node19(c_e_h_1, c_h, s14, s15))) <=> ((~node19(c_e_h_1, c_h, s14, s15)) | node14(c_e_h_1, c_h, s14, s15) | node15(c_e_h_1, c_h, s14, s15) | node16(c_e_h_1, c_h, s14))),
% 293.90/186.43 inference(rewrite,[status(thm)],[])).
% 293.90/186.43 tff(23994,plain,
% 293.90/186.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s14) | node14(c_e_h_1, c_h, s14, s15) | node15(c_e_h_1, c_h, s14, s15) | (~node19(c_e_h_1, c_h, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_h, s14, s15)) | node14(c_e_h_1, c_h, s14, s15) | node15(c_e_h_1, c_h, s14, s15) | node16(c_e_h_1, c_h, s14)))),
% 293.90/186.43 inference(monotonicity,[status(thm)],[23993])).
% 293.90/186.43 tff(23995,plain,
% 293.90/186.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s14) | node14(c_e_h_1, c_h, s14, s15) | node15(c_e_h_1, c_h, s14, s15) | (~node19(c_e_h_1, c_h, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_h, s14, s15)) | node14(c_e_h_1, c_h, s14, s15) | node15(c_e_h_1, c_h, s14, s15) | node16(c_e_h_1, c_h, s14))),
% 293.90/186.44 inference(transitivity,[status(thm)],[23994, 23992])).
% 293.90/186.44 tff(23996,plain,
% 293.90/186.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s14) | node14(c_e_h_1, c_h, s14, s15) | node15(c_e_h_1, c_h, s14, s15) | (~node19(c_e_h_1, c_h, s14, s15)))),
% 293.90/186.44 inference(quant_inst,[status(thm)],[])).
% 293.90/186.44 tff(23997,plain,
% 293.90/186.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_h, s14, s15)) | node14(c_e_h_1, c_h, s14, s15) | node15(c_e_h_1, c_h, s14, s15) | node16(c_e_h_1, c_h, s14)),
% 293.90/186.44 inference(modus_ponens,[status(thm)],[23996, 23995])).
% 293.90/186.44 tff(23998,plain,
% 293.90/186.44 (node14(c_e_h_1, c_h, s14, s15) | node15(c_e_h_1, c_h, s14, s15) | node16(c_e_h_1, c_h, s14)),
% 293.90/186.44 inference(unit_resolution,[status(thm)],[23997, 204, 23991])).
% 293.90/186.44 tff(23999,plain,
% 293.90/186.44 (node16(c_e_h_1, c_h, s14)),
% 293.90/186.44 inference(unit_resolution,[status(thm)],[23998, 23987, 23980])).
% 293.90/186.44 tff(24000,plain,
% 293.90/186.44 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s14)) | m_c_h_element_v_in1(c_e_h_1, c_h, s14) | m_c_h_element_v_in2(c_e_h_1, c_h, s14))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s14)) | m_c_h_element_v_in1(c_e_h_1, c_h, s14) | m_c_h_element_v_in2(c_e_h_1, c_h, s14))),
% 293.90/186.44 inference(rewrite,[status(thm)],[])).
% 293.90/186.44 tff(24001,plain,
% 293.90/186.44 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s14)) | m_c_h_element_v_in1(c_e_h_1, c_h, s14) | m_c_h_element_v_in2(c_e_h_1, c_h, s14))),
% 293.90/186.44 inference(quant_inst,[status(thm)],[])).
% 293.90/186.44 tff(24002,plain,
% 293.90/186.44 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s14)) | m_c_h_element_v_in1(c_e_h_1, c_h, s14) | m_c_h_element_v_in2(c_e_h_1, c_h, s14)),
% 293.90/186.44 inference(modus_ponens,[status(thm)],[24001, 24000])).
% 293.90/186.44 tff(24003,plain,
% 293.90/186.44 ((~node16(c_e_h_1, c_h, s14)) | m_c_h_element_v_in2(c_e_h_1, c_h, s14)),
% 293.90/186.44 inference(unit_resolution,[status(thm)],[24002, 178, 23970])).
% 293.90/186.44 tff(24004,plain,
% 293.90/186.44 (m_c_h_element_v_in2(c_e_h_1, c_h, s14)),
% 293.90/186.44 inference(unit_resolution,[status(thm)],[24003, 23999])).
% 293.90/186.44 tff(24005,plain,
% 293.90/186.44 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s14) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s14)) | (~node17(c_e_h_1, c_h, s14)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s14) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s14)) | (~node17(c_e_h_1, c_h, s14)))),
% 293.90/186.44 inference(rewrite,[status(thm)],[])).
% 293.90/186.44 tff(24006,plain,
% 293.90/186.44 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s14) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s14)) | (~node17(c_e_h_1, c_h, s14)))),
% 293.90/186.44 inference(quant_inst,[status(thm)],[])).
% 293.90/186.44 tff(24007,plain,
% 293.90/186.44 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s14) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s14)) | (~node17(c_e_h_1, c_h, s14))),
% 293.90/186.44 inference(modus_ponens,[status(thm)],[24006, 24005])).
% 293.90/186.44 tff(24008,plain,
% 293.90/186.44 ((~m_c_h_element_v_in2(c_e_h_1, c_h, s14)) | (~node17(c_e_h_1, c_h, s14))),
% 293.90/186.44 inference(unit_resolution,[status(thm)],[24007, 859, 23970])).
% 293.90/186.44 tff(24009,plain,
% 293.90/186.44 (~node17(c_e_h_1, c_h, s14)),
% 293.90/186.44 inference(unit_resolution,[status(thm)],[24008, 24004])).
% 293.90/186.44 tff(24010,plain,
% 293.90/186.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_h, s14, s15)) | node18(c_e_h_1, c_h, s14, s15) | node17(c_e_h_1, c_h, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_h, s14, s15)) | node18(c_e_h_1, c_h, s14, s15) | node17(c_e_h_1, c_h, s14))),
% 293.90/186.44 inference(rewrite,[status(thm)],[])).
% 293.90/186.44 tff(24011,plain,
% 293.90/186.44 ((node17(c_e_h_1, c_h, s14) | node18(c_e_h_1, c_h, s14, s15) | (~node19(c_e_h_1, c_h, s14, s15))) <=> ((~node19(c_e_h_1, c_h, s14, s15)) | node18(c_e_h_1, c_h, s14, s15) | node17(c_e_h_1, c_h, s14))),
% 293.90/186.44 inference(rewrite,[status(thm)],[])).
% 293.90/186.44 tff(24012,plain,
% 293.90/186.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s14) | node18(c_e_h_1, c_h, s14, s15) | (~node19(c_e_h_1, c_h, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_h, s14, s15)) | node18(c_e_h_1, c_h, s14, s15) | node17(c_e_h_1, c_h, s14)))),
% 293.90/186.44 inference(monotonicity,[status(thm)],[24011])).
% 293.90/186.44 tff(24013,plain,
% 293.90/186.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s14) | node18(c_e_h_1, c_h, s14, s15) | (~node19(c_e_h_1, c_h, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_h, s14, s15)) | node18(c_e_h_1, c_h, s14, s15) | node17(c_e_h_1, c_h, s14))),
% 293.90/186.44 inference(transitivity,[status(thm)],[24012, 24010])).
% 293.90/186.44 tff(24014,plain,
% 293.90/186.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s14) | node18(c_e_h_1, c_h, s14, s15) | (~node19(c_e_h_1, c_h, s14, s15)))),
% 293.90/186.44 inference(quant_inst,[status(thm)],[])).
% 293.90/186.44 tff(24015,plain,
% 293.90/186.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_h, s14, s15)) | node18(c_e_h_1, c_h, s14, s15) | node17(c_e_h_1, c_h, s14)),
% 293.90/186.44 inference(modus_ponens,[status(thm)],[24014, 24013])).
% 293.90/186.44 tff(24016,plain,
% 293.90/186.44 (node18(c_e_h_1, c_h, s14, s15) | node17(c_e_h_1, c_h, s14)),
% 293.90/186.44 inference(unit_resolution,[status(thm)],[24015, 776, 23991])).
% 293.90/186.44 tff(24017,plain,
% 293.90/186.44 (node18(c_e_h_1, c_h, s14, s15)),
% 293.90/186.44 inference(unit_resolution,[status(thm)],[24016, 24009])).
% 293.90/186.44 tff(24018,plain,
% 293.90/186.44 ($false),
% 293.90/186.44 inference(unit_resolution,[status(thm)],[23966, 753, 23959, 23958, 24017])).
% 293.90/186.44 tff(24019,plain,(m_c_h_element_v_out(c_e_h_1, c_h, s14) | (~m_c_h_element_v_out(c_e_h_1, c_h, s15)) | m_c_h_element_v_in1(c_e_h_1, c_h, s14)), inference(lemma,lemma(discharge,[]))).
% 293.90/186.44 tff(24020,plain,
% 293.90/186.44 (m_c_h_element_v_in1(c_e_h_1, c_h, s14)),
% 293.90/186.44 inference(unit_resolution,[status(thm)],[24019, 23959, 23958])).
% 293.90/186.44 tff(24021,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_h, s14)), introduced(assumption)).
% 293.90/186.44 tff(24022,plain,
% 293.90/186.44 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_h, s14) | (~node17(c_e_h_1, c_h, s14)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s14)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_h, s14) | (~node17(c_e_h_1, c_h, s14)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s14)))),
% 293.90/186.44 inference(rewrite,[status(thm)],[])).
% 293.90/186.44 tff(24023,plain,
% 293.90/186.44 (((~m_c_h_element_v_in1(c_e_h_1, c_h, s14)) | m_c_h_element_v_in2(c_e_h_1, c_h, s14) | (~node17(c_e_h_1, c_h, s14))) <=> (m_c_h_element_v_in2(c_e_h_1, c_h, s14) | (~node17(c_e_h_1, c_h, s14)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s14)))),
% 293.90/186.44 inference(rewrite,[status(thm)],[])).
% 293.90/186.44 tff(24024,plain,
% 293.90/186.44 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s14)) | m_c_h_element_v_in2(c_e_h_1, c_h, s14) | (~node17(c_e_h_1, c_h, s14)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_h, s14) | (~node17(c_e_h_1, c_h, s14)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s14))))),
% 293.90/186.44 inference(monotonicity,[status(thm)],[24023])).
% 293.90/186.44 tff(24025,plain,
% 293.90/186.44 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s14)) | m_c_h_element_v_in2(c_e_h_1, c_h, s14) | (~node17(c_e_h_1, c_h, s14)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_h, s14) | (~node17(c_e_h_1, c_h, s14)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s14)))),
% 293.90/186.44 inference(transitivity,[status(thm)],[24024, 24022])).
% 293.90/186.44 tff(24026,plain,
% 293.90/186.44 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s14)) | m_c_h_element_v_in2(c_e_h_1, c_h, s14) | (~node17(c_e_h_1, c_h, s14)))),
% 293.90/186.44 inference(quant_inst,[status(thm)],[])).
% 293.90/186.44 tff(24027,plain,
% 293.90/186.44 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_h, s14) | (~node17(c_e_h_1, c_h, s14)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s14))),
% 293.90/186.44 inference(modus_ponens,[status(thm)],[24026, 24025])).
% 293.90/186.44 tff(24028,plain,
% 293.90/186.44 ((~node17(c_e_h_1, c_h, s14)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s14))),
% 293.90/186.44 inference(unit_resolution,[status(thm)],[24027, 919, 24021])).
% 293.90/186.44 tff(24029,plain,
% 293.90/186.44 (~node17(c_e_h_1, c_h, s14)),
% 293.90/186.44 inference(unit_resolution,[status(thm)],[24028, 24020])).
% 293.90/186.44 tff(24030,plain,
% 293.90/186.44 ($false),
% 293.90/186.44 inference(unit_resolution,[status(thm)],[24016, 24029, 23969])).
% 293.90/186.44 tff(24031,plain,(m_c_h_element_v_out(c_e_h_1, c_h, s14) | m_c_h_element_v_in2(c_e_h_1, c_h, s14) | (~m_c_h_element_v_out(c_e_h_1, c_h, s15))), inference(lemma,lemma(discharge,[]))).
% 293.90/186.44 tff(24032,plain,
% 293.90/186.44 (m_c_h_element_v_in2(c_e_h_1, c_h, s14) | (~m_c_h_element_v_out(c_e_h_1, c_h, s15))),
% 293.90/186.44 inference(unit_resolution,[status(thm)],[24031, 23957])).
% 293.90/186.44 tff(24033,plain,
% 293.90/186.44 (~m_c_h_element_v_out(c_e_h_1, c_h, s15)),
% 293.90/186.44 inference(unit_resolution,[status(thm)],[24032, 23486])).
% 293.90/186.44 tff(24034,plain,
% 293.90/186.44 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s15)) | m_c_h_element_v_out(c_e_h_1, c_h, s15))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s15)) | m_c_h_element_v_out(c_e_h_1, c_h, s15))),
% 293.90/186.44 inference(rewrite,[status(thm)],[])).
% 293.90/186.44 tff(24035,plain,
% 293.90/186.44 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s15)) | m_c_h_element_v_out(c_e_h_1, c_h, s15))),
% 293.90/186.44 inference(quant_inst,[status(thm)],[])).
% 293.90/186.44 tff(24036,plain,
% 293.90/186.44 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s15)) | m_c_h_element_v_out(c_e_h_1, c_h, s15)),
% 293.90/186.44 inference(modus_ponens,[status(thm)],[24035, 24034])).
% 293.90/186.44 tff(24037,plain,
% 293.90/186.44 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s15)),
% 293.90/186.44 inference(unit_resolution,[status(thm)],[24036, 619, 24033])).
% 293.90/186.44 tff(24038,plain,
% 293.90/186.44 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s15)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s15))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s15)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s15))),
% 293.90/186.45 inference(rewrite,[status(thm)],[])).
% 293.90/186.45 tff(24039,plain,
% 293.90/186.45 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s15)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s15))),
% 293.90/186.45 inference(quant_inst,[status(thm)],[])).
% 293.90/186.45 tff(24040,plain,
% 293.90/186.45 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s15)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s15)),
% 293.90/186.45 inference(modus_ponens,[status(thm)],[24039, 24038])).
% 293.90/186.45 tff(24041,plain,
% 293.90/186.45 (~node20(c_e_h_1, c_i, s15)),
% 293.90/186.45 inference(unit_resolution,[status(thm)],[24040, 38, 24037])).
% 293.90/186.45 tff(24042,plain,
% 293.90/186.45 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s14)) | m_c_h_element_v_out(c_e_h_1, c_h, s14))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s14)) | m_c_h_element_v_out(c_e_h_1, c_h, s14))),
% 293.90/186.45 inference(rewrite,[status(thm)],[])).
% 293.90/186.45 tff(24043,plain,
% 293.90/186.45 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s14)) | m_c_h_element_v_out(c_e_h_1, c_h, s14))),
% 293.90/186.45 inference(quant_inst,[status(thm)],[])).
% 293.90/186.45 tff(24044,plain,
% 293.90/186.45 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s14)) | m_c_h_element_v_out(c_e_h_1, c_h, s14)),
% 293.90/186.45 inference(modus_ponens,[status(thm)],[24043, 24042])).
% 293.90/186.45 tff(24045,plain,
% 293.90/186.45 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s14)),
% 293.90/186.45 inference(unit_resolution,[status(thm)],[24044, 619, 23957])).
% 293.90/186.45 tff(24046,plain,
% 293.90/186.45 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s14)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s14))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s14)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s14))),
% 293.90/186.45 inference(rewrite,[status(thm)],[])).
% 293.90/186.45 tff(24047,plain,
% 293.90/186.45 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s14)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s14))),
% 293.90/186.45 inference(quant_inst,[status(thm)],[])).
% 293.90/186.45 tff(24048,plain,
% 293.90/186.45 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s14)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s14)),
% 293.90/186.45 inference(modus_ponens,[status(thm)],[24047, 24046])).
% 293.90/186.45 tff(24049,plain,
% 293.90/186.45 (~node20(c_e_h_1, c_i, s14)),
% 293.90/186.45 inference(unit_resolution,[status(thm)],[24048, 38, 24045])).
% 293.90/186.45 tff(24050,assumption,(m_and_h_gate_v_in1(c_e_h_1, c_i, s11)), introduced(assumption)).
% 293.90/186.45 tff(24051,plain,
% 293.90/186.45 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s11)) | m_c_h_element_v_out(c_e_h_1, c_h, s11))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s11)) | m_c_h_element_v_out(c_e_h_1, c_h, s11))),
% 293.90/186.45 inference(rewrite,[status(thm)],[])).
% 293.90/186.45 tff(24052,plain,
% 293.90/186.45 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s11)) | m_c_h_element_v_out(c_e_h_1, c_h, s11))),
% 293.90/186.45 inference(quant_inst,[status(thm)],[])).
% 293.90/186.45 tff(24053,plain,
% 293.90/186.45 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s11)) | m_c_h_element_v_out(c_e_h_1, c_h, s11)),
% 293.90/186.45 inference(modus_ponens,[status(thm)],[24052, 24051])).
% 293.90/186.45 tff(24054,plain,
% 293.90/186.45 ($false),
% 293.90/186.45 inference(unit_resolution,[status(thm)],[24053, 619, 23736, 24050])).
% 293.90/186.45 tff(24055,plain,(m_c_h_element_v_out(c_e_h_1, c_h, s11) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s11))), inference(lemma,lemma(discharge,[]))).
% 293.90/186.45 tff(24056,plain,
% 293.90/186.45 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s11)),
% 293.90/186.45 inference(unit_resolution,[status(thm)],[24055, 23723])).
% 293.90/186.45 tff(24057,assumption,(~m_and_h_gate_v_in1(c_e_h_1, c_i, s11)), introduced(assumption)).
% 293.90/186.45 tff(24058,assumption,(node20(c_e_h_1, c_i, s11)), introduced(assumption)).
% 293.90/186.45 tff(24059,plain,
% 293.90/186.45 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s11)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s11))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s11)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s11))),
% 293.90/186.45 inference(rewrite,[status(thm)],[])).
% 293.90/186.45 tff(24060,plain,
% 293.90/186.45 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s11)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s11))),
% 293.90/186.45 inference(quant_inst,[status(thm)],[])).
% 293.90/186.45 tff(24061,plain,
% 293.90/186.45 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s11)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s11)),
% 293.90/186.45 inference(modus_ponens,[status(thm)],[24060, 24059])).
% 293.90/186.45 tff(24062,plain,
% 293.90/186.45 ($false),
% 293.90/186.45 inference(unit_resolution,[status(thm)],[24061, 38, 24058, 24057])).
% 293.90/186.45 tff(24063,plain,(m_and_h_gate_v_in1(c_e_h_1, c_i, s11) | (~node20(c_e_h_1, c_i, s11))), inference(lemma,lemma(discharge,[]))).
% 293.90/186.45 tff(24064,plain,
% 293.90/186.45 (~node20(c_e_h_1, c_i, s11)),
% 293.90/186.45 inference(unit_resolution,[status(thm)],[24063, 24056])).
% 293.90/186.45 tff(24065,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s10)), introduced(assumption)).
% 293.90/186.45 tff(24066,assumption,(node21(c_e_h_1, c_i, s9, s10)), introduced(assumption)).
% 293.90/186.45 tff(24067,plain,
% 293.90/186.45 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s9)) | m_c_h_element_v_out(c_e_h_1, c_h, s9))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s9)) | m_c_h_element_v_out(c_e_h_1, c_h, s9))),
% 293.90/186.45 inference(rewrite,[status(thm)],[])).
% 293.90/186.45 tff(24068,plain,
% 293.90/186.45 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s9)) | m_c_h_element_v_out(c_e_h_1, c_h, s9))),
% 293.90/186.45 inference(quant_inst,[status(thm)],[])).
% 293.90/186.45 tff(24069,plain,
% 293.90/186.45 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s9)) | m_c_h_element_v_out(c_e_h_1, c_h, s9)),
% 293.90/186.45 inference(modus_ponens,[status(thm)],[24068, 24067])).
% 293.90/186.45 tff(24070,plain,
% 293.90/186.45 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s9)),
% 293.90/186.45 inference(unit_resolution,[status(thm)],[24069, 619, 23569])).
% 293.90/186.45 tff(24071,plain,
% 293.90/186.45 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s9)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s9))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s9)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s9))),
% 293.90/186.45 inference(rewrite,[status(thm)],[])).
% 293.90/186.45 tff(24072,plain,
% 293.90/186.45 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s9)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s9))),
% 293.90/186.45 inference(quant_inst,[status(thm)],[])).
% 293.90/186.45 tff(24073,plain,
% 293.90/186.45 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s9)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s9)),
% 293.90/186.45 inference(modus_ponens,[status(thm)],[24072, 24071])).
% 293.90/186.45 tff(24074,plain,
% 293.90/186.45 (~node20(c_e_h_1, c_i, s9)),
% 293.90/186.45 inference(unit_resolution,[status(thm)],[24073, 38, 24070])).
% 293.90/186.45 tff(24075,plain,
% 293.90/186.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s9) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s10)) | (~node21(c_e_h_1, c_i, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s9) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s10)) | (~node21(c_e_h_1, c_i, s9, s10)))),
% 293.90/186.46 inference(rewrite,[status(thm)],[])).
% 293.90/186.46 tff(24076,plain,
% 293.90/186.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s9) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s10)) | (~node21(c_e_h_1, c_i, s9, s10)))),
% 293.90/186.46 inference(quant_inst,[status(thm)],[])).
% 293.90/186.46 tff(24077,plain,
% 293.90/186.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s9) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s10)) | (~node21(c_e_h_1, c_i, s9, s10))),
% 293.90/186.46 inference(modus_ponens,[status(thm)],[24076, 24075])).
% 293.90/186.46 tff(24078,plain,
% 293.90/186.46 ($false),
% 293.90/186.46 inference(unit_resolution,[status(thm)],[24077, 52, 24065, 24074, 24066])).
% 293.90/186.46 tff(24079,plain,((~node21(c_e_h_1, c_i, s9, s10)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s10))), inference(lemma,lemma(discharge,[]))).
% 293.90/186.46 tff(24080,plain,
% 293.90/186.46 (~node21(c_e_h_1, c_i, s9, s10)),
% 293.90/186.46 inference(unit_resolution,[status(thm)],[24079, 24065])).
% 293.90/186.46 tff(24081,plain,
% 293.90/186.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s9, s10)) | node21(c_e_h_1, c_i, s9, s10) | node22(c_e_h_1, c_i, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s9, s10)) | node21(c_e_h_1, c_i, s9, s10) | node22(c_e_h_1, c_i, s9, s10))),
% 293.90/186.46 inference(rewrite,[status(thm)],[])).
% 293.90/186.46 tff(24082,plain,
% 293.90/186.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s9, s10)) | node21(c_e_h_1, c_i, s9, s10) | node22(c_e_h_1, c_i, s9, s10))),
% 293.90/186.46 inference(quant_inst,[status(thm)],[])).
% 293.90/186.46 tff(24083,plain,
% 293.90/186.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s9, s10)) | node21(c_e_h_1, c_i, s9, s10) | node22(c_e_h_1, c_i, s9, s10)),
% 293.90/186.46 inference(modus_ponens,[status(thm)],[24082, 24081])).
% 293.90/186.46 tff(24084,plain,
% 293.90/186.46 (node21(c_e_h_1, c_i, s9, s10) | node22(c_e_h_1, c_i, s9, s10)),
% 293.90/186.46 inference(unit_resolution,[status(thm)],[24083, 82, 7676])).
% 293.90/186.46 tff(24085,plain,
% 293.90/186.46 (node22(c_e_h_1, c_i, s9, s10)),
% 293.90/186.46 inference(unit_resolution,[status(thm)],[24084, 24080])).
% 293.90/186.46 tff(24086,plain,
% 293.90/186.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s10)) | (~node22(c_e_h_1, c_i, s9, s10)) | m_and_h_gate_v_out(c_e_h_1, c_i, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s10)) | (~node22(c_e_h_1, c_i, s9, s10)) | m_and_h_gate_v_out(c_e_h_1, c_i, s9))),
% 293.90/186.46 inference(rewrite,[status(thm)],[])).
% 293.90/186.46 tff(24087,plain,
% 293.90/186.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s10)) | (~node22(c_e_h_1, c_i, s9, s10)) | m_and_h_gate_v_out(c_e_h_1, c_i, s9))),
% 293.90/186.46 inference(quant_inst,[status(thm)],[])).
% 293.90/186.46 tff(24088,plain,
% 293.90/186.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s10)) | (~node22(c_e_h_1, c_i, s9, s10)) | m_and_h_gate_v_out(c_e_h_1, c_i, s9)),
% 293.90/186.46 inference(modus_ponens,[status(thm)],[24087, 24086])).
% 293.90/186.46 tff(24089,plain,
% 293.90/186.46 ($false),
% 293.90/186.46 inference(unit_resolution,[status(thm)],[24088, 108, 23251, 24065, 24085])).
% 293.90/186.46 tff(24090,plain,((~m_and_h_gate_v_out(c_e_h_1, c_i, s10)) | m_and_h_gate_v_out(c_e_h_1, c_i, s9)), inference(lemma,lemma(discharge,[]))).
% 293.90/186.46 tff(24091,plain,
% 293.90/186.46 (~m_and_h_gate_v_out(c_e_h_1, c_i, s10)),
% 293.90/186.46 inference(unit_resolution,[status(thm)],[24090, 23250])).
% 293.90/186.46 tff(24092,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s11)), introduced(assumption)).
% 293.90/186.46 tff(24093,plain,
% 293.90/186.46 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s10)) | m_c_h_element_v_out(c_e_h_1, c_h, s10))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s10)) | m_c_h_element_v_out(c_e_h_1, c_h, s10))),
% 293.90/186.46 inference(rewrite,[status(thm)],[])).
% 293.90/186.46 tff(24094,plain,
% 293.90/186.46 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s10)) | m_c_h_element_v_out(c_e_h_1, c_h, s10))),
% 293.90/186.46 inference(quant_inst,[status(thm)],[])).
% 293.90/186.46 tff(24095,plain,
% 293.90/186.46 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s10)) | m_c_h_element_v_out(c_e_h_1, c_h, s10)),
% 293.90/186.46 inference(modus_ponens,[status(thm)],[24094, 24093])).
% 293.90/186.46 tff(24096,plain,
% 293.90/186.46 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s10)),
% 293.90/186.46 inference(unit_resolution,[status(thm)],[24095, 619, 23659])).
% 293.90/186.46 tff(24097,plain,
% 293.90/186.46 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s10)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s10))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s10)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s10))),
% 293.90/186.46 inference(rewrite,[status(thm)],[])).
% 293.90/186.46 tff(24098,plain,
% 293.90/186.46 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s10)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s10))),
% 293.90/186.46 inference(quant_inst,[status(thm)],[])).
% 293.90/186.46 tff(24099,plain,
% 293.90/186.46 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s10)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s10)),
% 293.90/186.46 inference(modus_ponens,[status(thm)],[24098, 24097])).
% 293.90/186.46 tff(24100,plain,
% 293.90/186.46 (~node20(c_e_h_1, c_i, s10)),
% 293.90/186.46 inference(unit_resolution,[status(thm)],[24099, 38, 24096])).
% 293.90/186.46 tff(24101,assumption,(~node20(c_e_h_1, c_i, s10)), introduced(assumption)).
% 293.90/186.46 tff(24102,assumption,(node21(c_e_h_1, c_i, s10, s11)), introduced(assumption)).
% 293.90/186.46 tff(24103,plain,
% 293.90/186.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s10) | (~node21(c_e_h_1, c_i, s10, s11)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s10) | (~node21(c_e_h_1, c_i, s10, s11)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s11)))),
% 293.90/186.46 inference(rewrite,[status(thm)],[])).
% 293.90/186.46 tff(24104,plain,
% 293.90/186.46 ((node20(c_e_h_1, c_i, s10) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s11)) | (~node21(c_e_h_1, c_i, s10, s11))) <=> (node20(c_e_h_1, c_i, s10) | (~node21(c_e_h_1, c_i, s10, s11)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s11)))),
% 293.90/186.46 inference(rewrite,[status(thm)],[])).
% 293.90/186.46 tff(24105,plain,
% 293.90/186.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s10) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s11)) | (~node21(c_e_h_1, c_i, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s10) | (~node21(c_e_h_1, c_i, s10, s11)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s11))))),
% 293.90/186.46 inference(monotonicity,[status(thm)],[24104])).
% 293.90/186.46 tff(24106,plain,
% 293.90/186.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s10) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s11)) | (~node21(c_e_h_1, c_i, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s10) | (~node21(c_e_h_1, c_i, s10, s11)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s11)))),
% 293.90/186.46 inference(transitivity,[status(thm)],[24105, 24103])).
% 293.90/186.46 tff(24107,plain,
% 293.90/186.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s10) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s11)) | (~node21(c_e_h_1, c_i, s10, s11)))),
% 293.90/186.46 inference(quant_inst,[status(thm)],[])).
% 293.90/186.46 tff(24108,plain,
% 293.90/186.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s10) | (~node21(c_e_h_1, c_i, s10, s11)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s11))),
% 293.90/186.46 inference(modus_ponens,[status(thm)],[24107, 24106])).
% 293.90/186.46 tff(24109,plain,
% 293.90/186.46 ($false),
% 293.90/186.46 inference(unit_resolution,[status(thm)],[24108, 52, 24102, 24092, 24101])).
% 293.90/186.46 tff(24110,plain,((~node21(c_e_h_1, c_i, s10, s11)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s11)) | node20(c_e_h_1, c_i, s10)), inference(lemma,lemma(discharge,[]))).
% 293.90/186.46 tff(24111,plain,
% 293.90/186.46 ((~node21(c_e_h_1, c_i, s10, s11)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s11))),
% 293.90/186.46 inference(unit_resolution,[status(thm)],[24110, 24100])).
% 293.90/186.46 tff(24112,plain,
% 293.90/186.46 (~node21(c_e_h_1, c_i, s10, s11)),
% 293.90/186.46 inference(unit_resolution,[status(thm)],[24111, 24092])).
% 293.90/186.46 tff(24113,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_i, s10)), introduced(assumption)).
% 293.90/186.46 tff(24114,assumption,(node22(c_e_h_1, c_i, s10, s11)), introduced(assumption)).
% 293.90/186.46 tff(24115,plain,
% 293.90/186.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s11)) | (~node22(c_e_h_1, c_i, s10, s11)) | m_and_h_gate_v_out(c_e_h_1, c_i, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s11)) | (~node22(c_e_h_1, c_i, s10, s11)) | m_and_h_gate_v_out(c_e_h_1, c_i, s10))),
% 293.90/186.46 inference(rewrite,[status(thm)],[])).
% 293.90/186.46 tff(24116,plain,
% 293.90/186.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s11)) | (~node22(c_e_h_1, c_i, s10, s11)) | m_and_h_gate_v_out(c_e_h_1, c_i, s10))),
% 293.90/186.46 inference(quant_inst,[status(thm)],[])).
% 293.90/186.46 tff(24117,plain,
% 293.90/186.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s11)) | (~node22(c_e_h_1, c_i, s10, s11)) | m_and_h_gate_v_out(c_e_h_1, c_i, s10)),
% 293.90/186.46 inference(modus_ponens,[status(thm)],[24116, 24115])).
% 293.90/186.46 tff(24118,plain,
% 293.90/186.46 ($false),
% 293.90/186.46 inference(unit_resolution,[status(thm)],[24117, 108, 24114, 24113, 24092])).
% 293.90/186.46 tff(24119,plain,((~node22(c_e_h_1, c_i, s10, s11)) | m_and_h_gate_v_out(c_e_h_1, c_i, s10) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s11))), inference(lemma,lemma(discharge,[]))).
% 293.90/186.46 tff(24120,plain,
% 293.90/186.46 (~node22(c_e_h_1, c_i, s10, s11)),
% 293.90/186.46 inference(unit_resolution,[status(thm)],[24119, 24092, 24113])).
% 293.90/186.46 tff(24121,plain,
% 293.90/186.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s10, s11)) | node21(c_e_h_1, c_i, s10, s11) | node22(c_e_h_1, c_i, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s10, s11)) | node21(c_e_h_1, c_i, s10, s11) | node22(c_e_h_1, c_i, s10, s11))),
% 293.90/186.46 inference(rewrite,[status(thm)],[])).
% 293.90/186.46 tff(24122,plain,
% 293.90/186.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s10, s11)) | node21(c_e_h_1, c_i, s10, s11) | node22(c_e_h_1, c_i, s10, s11))),
% 293.90/186.46 inference(quant_inst,[status(thm)],[])).
% 293.90/186.46 tff(24123,plain,
% 293.90/186.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s10, s11)) | node21(c_e_h_1, c_i, s10, s11) | node22(c_e_h_1, c_i, s10, s11)),
% 293.90/186.46 inference(modus_ponens,[status(thm)],[24122, 24121])).
% 293.90/186.46 tff(24124,plain,
% 293.90/186.46 (node21(c_e_h_1, c_i, s10, s11) | node22(c_e_h_1, c_i, s10, s11)),
% 293.90/186.46 inference(unit_resolution,[status(thm)],[24123, 82, 7748])).
% 293.90/186.46 tff(24125,plain,
% 293.90/186.46 ($false),
% 293.90/186.46 inference(unit_resolution,[status(thm)],[24124, 24120, 24112])).
% 293.90/186.46 tff(24126,plain,((~m_and_h_gate_v_out(c_e_h_1, c_i, s11)) | m_and_h_gate_v_out(c_e_h_1, c_i, s10)), inference(lemma,lemma(discharge,[]))).
% 293.90/186.47 tff(24127,plain,
% 293.90/186.47 (~m_and_h_gate_v_out(c_e_h_1, c_i, s11)),
% 293.90/186.47 inference(unit_resolution,[status(thm)],[24126, 24091])).
% 293.90/186.47 tff(24128,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s12)), introduced(assumption)).
% 293.90/186.47 tff(24129,assumption,(~node20(c_e_h_1, c_i, s11)), introduced(assumption)).
% 293.90/186.47 tff(24130,assumption,(node21(c_e_h_1, c_i, s11, s12)), introduced(assumption)).
% 293.90/186.47 tff(24131,plain,
% 293.90/186.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s11) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s12)) | (~node21(c_e_h_1, c_i, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s11) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s12)) | (~node21(c_e_h_1, c_i, s11, s12)))),
% 293.90/186.47 inference(rewrite,[status(thm)],[])).
% 293.90/186.47 tff(24132,plain,
% 293.90/186.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s11) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s12)) | (~node21(c_e_h_1, c_i, s11, s12)))),
% 293.90/186.47 inference(quant_inst,[status(thm)],[])).
% 293.90/186.47 tff(24133,plain,
% 293.90/186.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s11) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s12)) | (~node21(c_e_h_1, c_i, s11, s12))),
% 293.90/186.47 inference(modus_ponens,[status(thm)],[24132, 24131])).
% 293.90/186.47 tff(24134,plain,
% 293.90/186.47 ($false),
% 293.90/186.47 inference(unit_resolution,[status(thm)],[24133, 52, 24130, 24129, 24128])).
% 293.90/186.47 tff(24135,plain,((~node21(c_e_h_1, c_i, s11, s12)) | node20(c_e_h_1, c_i, s11) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s12))), inference(lemma,lemma(discharge,[]))).
% 293.90/186.47 tff(24136,plain,
% 293.90/186.47 (~node21(c_e_h_1, c_i, s11, s12)),
% 293.90/186.47 inference(unit_resolution,[status(thm)],[24135, 24128, 24129])).
% 293.90/186.47 tff(24137,plain,
% 293.90/186.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s11, s12)) | node21(c_e_h_1, c_i, s11, s12) | node22(c_e_h_1, c_i, s11, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s11, s12)) | node21(c_e_h_1, c_i, s11, s12) | node22(c_e_h_1, c_i, s11, s12))),
% 293.90/186.47 inference(rewrite,[status(thm)],[])).
% 293.90/186.47 tff(24138,plain,
% 293.90/186.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s11, s12)) | node21(c_e_h_1, c_i, s11, s12) | node22(c_e_h_1, c_i, s11, s12))),
% 293.90/186.47 inference(quant_inst,[status(thm)],[])).
% 293.90/186.47 tff(24139,plain,
% 293.90/186.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s11, s12)) | node21(c_e_h_1, c_i, s11, s12) | node22(c_e_h_1, c_i, s11, s12)),
% 293.90/186.47 inference(modus_ponens,[status(thm)],[24138, 24137])).
% 293.90/186.47 tff(24140,plain,
% 293.90/186.47 (node21(c_e_h_1, c_i, s11, s12) | node22(c_e_h_1, c_i, s11, s12)),
% 293.90/186.47 inference(unit_resolution,[status(thm)],[24139, 82, 11461])).
% 293.90/186.47 tff(24141,plain,
% 293.90/186.47 (node22(c_e_h_1, c_i, s11, s12)),
% 293.90/186.47 inference(unit_resolution,[status(thm)],[24140, 24136])).
% 293.90/186.47 tff(24142,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_i, s11)), introduced(assumption)).
% 293.90/186.47 tff(24143,plain,
% 293.90/186.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s12)) | (~node22(c_e_h_1, c_i, s11, s12)) | m_and_h_gate_v_out(c_e_h_1, c_i, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s12)) | (~node22(c_e_h_1, c_i, s11, s12)) | m_and_h_gate_v_out(c_e_h_1, c_i, s11))),
% 293.90/186.47 inference(rewrite,[status(thm)],[])).
% 293.90/186.47 tff(24144,plain,
% 293.90/186.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s12)) | (~node22(c_e_h_1, c_i, s11, s12)) | m_and_h_gate_v_out(c_e_h_1, c_i, s11))),
% 293.98/186.47 inference(quant_inst,[status(thm)],[])).
% 293.98/186.47 tff(24145,plain,
% 293.98/186.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s12)) | (~node22(c_e_h_1, c_i, s11, s12)) | m_and_h_gate_v_out(c_e_h_1, c_i, s11)),
% 293.98/186.47 inference(modus_ponens,[status(thm)],[24144, 24143])).
% 293.98/186.47 tff(24146,plain,
% 293.98/186.47 ($false),
% 293.98/186.47 inference(unit_resolution,[status(thm)],[24145, 108, 24142, 24141, 24128])).
% 293.98/186.47 tff(24147,plain,((~m_and_h_gate_v_out(c_e_h_1, c_i, s12)) | m_and_h_gate_v_out(c_e_h_1, c_i, s11) | node20(c_e_h_1, c_i, s11)), inference(lemma,lemma(discharge,[]))).
% 293.98/186.47 tff(24148,plain,
% 293.98/186.47 ((~m_and_h_gate_v_out(c_e_h_1, c_i, s12)) | node20(c_e_h_1, c_i, s11)),
% 293.98/186.47 inference(unit_resolution,[status(thm)],[24147, 24127])).
% 293.98/186.47 tff(24149,plain,
% 293.98/186.47 (~m_and_h_gate_v_out(c_e_h_1, c_i, s12)),
% 293.98/186.47 inference(unit_resolution,[status(thm)],[24148, 24064])).
% 293.98/186.47 tff(24150,plain,
% 293.98/186.47 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s12)) | m_c_h_element_v_out(c_e_h_1, c_h, s12))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s12)) | m_c_h_element_v_out(c_e_h_1, c_h, s12))),
% 293.98/186.47 inference(rewrite,[status(thm)],[])).
% 293.98/186.47 tff(24151,plain,
% 293.98/186.47 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s12)) | m_c_h_element_v_out(c_e_h_1, c_h, s12))),
% 293.98/186.47 inference(quant_inst,[status(thm)],[])).
% 293.98/186.47 tff(24152,plain,
% 293.98/186.47 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s12)) | m_c_h_element_v_out(c_e_h_1, c_h, s12)),
% 293.98/186.47 inference(modus_ponens,[status(thm)],[24151, 24150])).
% 293.98/186.47 tff(24153,plain,
% 293.98/186.47 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s12)),
% 293.98/186.47 inference(unit_resolution,[status(thm)],[24152, 619, 23796])).
% 293.98/186.47 tff(24154,plain,
% 293.98/186.47 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s12)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s12))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s12)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s12))),
% 293.98/186.47 inference(rewrite,[status(thm)],[])).
% 293.98/186.47 tff(24155,plain,
% 293.98/186.47 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s12)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s12))),
% 293.98/186.47 inference(quant_inst,[status(thm)],[])).
% 293.98/186.47 tff(24156,plain,
% 293.98/186.47 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s12)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s12)),
% 293.98/186.47 inference(modus_ponens,[status(thm)],[24155, 24154])).
% 293.98/186.47 tff(24157,plain,
% 293.98/186.47 (~node20(c_e_h_1, c_i, s12)),
% 293.98/186.47 inference(unit_resolution,[status(thm)],[24156, 38, 24153])).
% 293.98/186.47 tff(24158,assumption,(~node20(c_e_h_1, c_i, s12)), introduced(assumption)).
% 293.98/186.47 tff(24159,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_i, s12)), introduced(assumption)).
% 293.98/186.47 tff(24160,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s13)), introduced(assumption)).
% 293.98/186.47 tff(24161,assumption,(node22(c_e_h_1, c_i, s12, s13)), introduced(assumption)).
% 293.98/186.47 tff(24162,plain,
% 293.98/186.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s13)) | (~node22(c_e_h_1, c_i, s12, s13)) | m_and_h_gate_v_out(c_e_h_1, c_i, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s13)) | (~node22(c_e_h_1, c_i, s12, s13)) | m_and_h_gate_v_out(c_e_h_1, c_i, s12))),
% 293.98/186.47 inference(rewrite,[status(thm)],[])).
% 293.98/186.47 tff(24163,plain,
% 293.98/186.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s13)) | (~node22(c_e_h_1, c_i, s12, s13)) | m_and_h_gate_v_out(c_e_h_1, c_i, s12))),
% 293.98/186.47 inference(quant_inst,[status(thm)],[])).
% 293.98/186.47 tff(24164,plain,
% 293.98/186.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s13)) | (~node22(c_e_h_1, c_i, s12, s13)) | m_and_h_gate_v_out(c_e_h_1, c_i, s12)),
% 293.98/186.47 inference(modus_ponens,[status(thm)],[24163, 24162])).
% 293.98/186.47 tff(24165,plain,
% 293.98/186.47 ($false),
% 293.98/186.47 inference(unit_resolution,[status(thm)],[24164, 108, 24160, 24159, 24161])).
% 293.98/186.47 tff(24166,plain,((~node22(c_e_h_1, c_i, s12, s13)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s13)) | m_and_h_gate_v_out(c_e_h_1, c_i, s12)), inference(lemma,lemma(discharge,[]))).
% 293.98/186.47 tff(24167,plain,
% 293.98/186.47 (~node22(c_e_h_1, c_i, s12, s13)),
% 293.98/186.47 inference(unit_resolution,[status(thm)],[24166, 24160, 24159])).
% 293.98/186.47 tff(24168,plain,
% 293.98/186.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s12, s13)) | node21(c_e_h_1, c_i, s12, s13) | node22(c_e_h_1, c_i, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s12, s13)) | node21(c_e_h_1, c_i, s12, s13) | node22(c_e_h_1, c_i, s12, s13))),
% 293.98/186.47 inference(rewrite,[status(thm)],[])).
% 293.98/186.47 tff(24169,plain,
% 293.98/186.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s12, s13)) | node21(c_e_h_1, c_i, s12, s13) | node22(c_e_h_1, c_i, s12, s13))),
% 293.98/186.47 inference(quant_inst,[status(thm)],[])).
% 293.98/186.47 tff(24170,plain,
% 293.98/186.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s12, s13)) | node21(c_e_h_1, c_i, s12, s13) | node22(c_e_h_1, c_i, s12, s13)),
% 293.98/186.47 inference(modus_ponens,[status(thm)],[24169, 24168])).
% 293.98/186.47 tff(24171,plain,
% 293.98/186.47 (node21(c_e_h_1, c_i, s12, s13) | node22(c_e_h_1, c_i, s12, s13)),
% 293.98/186.47 inference(unit_resolution,[status(thm)],[24170, 82, 11856])).
% 293.98/186.47 tff(24172,plain,
% 293.98/186.47 (node21(c_e_h_1, c_i, s12, s13)),
% 293.98/186.47 inference(unit_resolution,[status(thm)],[24171, 24167])).
% 293.98/186.47 tff(24173,plain,
% 293.98/186.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s13)) | node20(c_e_h_1, c_i, s12) | (~node21(c_e_h_1, c_i, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s13)) | node20(c_e_h_1, c_i, s12) | (~node21(c_e_h_1, c_i, s12, s13)))),
% 293.98/186.47 inference(rewrite,[status(thm)],[])).
% 293.98/186.47 tff(24174,plain,
% 293.98/186.47 ((node20(c_e_h_1, c_i, s12) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s13)) | (~node21(c_e_h_1, c_i, s12, s13))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_i, s13)) | node20(c_e_h_1, c_i, s12) | (~node21(c_e_h_1, c_i, s12, s13)))),
% 293.98/186.47 inference(rewrite,[status(thm)],[])).
% 293.98/186.47 tff(24175,plain,
% 293.98/186.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s12) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s13)) | (~node21(c_e_h_1, c_i, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s13)) | node20(c_e_h_1, c_i, s12) | (~node21(c_e_h_1, c_i, s12, s13))))),
% 293.98/186.47 inference(monotonicity,[status(thm)],[24174])).
% 293.98/186.47 tff(24176,plain,
% 293.98/186.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s12) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s13)) | (~node21(c_e_h_1, c_i, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s13)) | node20(c_e_h_1, c_i, s12) | (~node21(c_e_h_1, c_i, s12, s13)))),
% 293.98/186.47 inference(transitivity,[status(thm)],[24175, 24173])).
% 293.98/186.47 tff(24177,plain,
% 293.98/186.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s12) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s13)) | (~node21(c_e_h_1, c_i, s12, s13)))),
% 293.98/186.48 inference(quant_inst,[status(thm)],[])).
% 293.98/186.48 tff(24178,plain,
% 293.98/186.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s13)) | node20(c_e_h_1, c_i, s12) | (~node21(c_e_h_1, c_i, s12, s13))),
% 293.98/186.48 inference(modus_ponens,[status(thm)],[24177, 24176])).
% 293.98/186.48 tff(24179,plain,
% 293.98/186.48 ($false),
% 293.98/186.48 inference(unit_resolution,[status(thm)],[24178, 52, 24160, 24172, 24158])).
% 293.98/186.48 tff(24180,plain,((~m_and_h_gate_v_out(c_e_h_1, c_i, s13)) | node20(c_e_h_1, c_i, s12) | m_and_h_gate_v_out(c_e_h_1, c_i, s12)), inference(lemma,lemma(discharge,[]))).
% 293.98/186.48 tff(24181,plain,
% 293.98/186.48 (~m_and_h_gate_v_out(c_e_h_1, c_i, s13)),
% 293.98/186.48 inference(unit_resolution,[status(thm)],[24180, 24157, 24149])).
% 293.98/186.48 tff(24182,plain,
% 293.98/186.48 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s13)) | m_c_h_element_v_out(c_e_h_1, c_h, s13))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s13)) | m_c_h_element_v_out(c_e_h_1, c_h, s13))),
% 293.98/186.48 inference(rewrite,[status(thm)],[])).
% 293.98/186.48 tff(24183,plain,
% 293.98/186.48 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s13)) | m_c_h_element_v_out(c_e_h_1, c_h, s13))),
% 293.98/186.48 inference(quant_inst,[status(thm)],[])).
% 293.98/186.48 tff(24184,plain,
% 293.98/186.48 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s13)) | m_c_h_element_v_out(c_e_h_1, c_h, s13)),
% 293.98/186.48 inference(modus_ponens,[status(thm)],[24183, 24182])).
% 293.98/186.48 tff(24185,plain,
% 293.98/186.48 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s13)),
% 293.98/186.48 inference(unit_resolution,[status(thm)],[24184, 619, 23875])).
% 293.98/186.48 tff(24186,plain,
% 293.98/186.48 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s13)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s13))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s13)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s13))),
% 293.98/186.48 inference(rewrite,[status(thm)],[])).
% 293.98/186.48 tff(24187,plain,
% 293.98/186.48 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s13)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s13))),
% 293.98/186.48 inference(quant_inst,[status(thm)],[])).
% 293.98/186.48 tff(24188,plain,
% 293.98/186.48 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s13)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s13)),
% 293.98/186.48 inference(modus_ponens,[status(thm)],[24187, 24186])).
% 293.98/186.48 tff(24189,plain,
% 293.98/186.48 (~node20(c_e_h_1, c_i, s13)),
% 293.98/186.48 inference(unit_resolution,[status(thm)],[24188, 38, 24185])).
% 293.98/186.48 tff(24190,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_i, s13)), introduced(assumption)).
% 293.98/186.48 tff(24191,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s14)), introduced(assumption)).
% 293.98/186.48 tff(24192,assumption,(node22(c_e_h_1, c_i, s13, s14)), introduced(assumption)).
% 293.98/186.48 tff(24193,plain,
% 293.98/186.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s14)) | (~node22(c_e_h_1, c_i, s13, s14)) | m_and_h_gate_v_out(c_e_h_1, c_i, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s14)) | (~node22(c_e_h_1, c_i, s13, s14)) | m_and_h_gate_v_out(c_e_h_1, c_i, s13))),
% 293.98/186.48 inference(rewrite,[status(thm)],[])).
% 293.98/186.48 tff(24194,plain,
% 293.98/186.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s14)) | (~node22(c_e_h_1, c_i, s13, s14)) | m_and_h_gate_v_out(c_e_h_1, c_i, s13))),
% 293.98/186.48 inference(quant_inst,[status(thm)],[])).
% 293.98/186.48 tff(24195,plain,
% 293.98/186.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s14)) | (~node22(c_e_h_1, c_i, s13, s14)) | m_and_h_gate_v_out(c_e_h_1, c_i, s13)),
% 293.98/186.48 inference(modus_ponens,[status(thm)],[24194, 24193])).
% 293.98/186.48 tff(24196,plain,
% 293.98/186.48 ($false),
% 293.98/186.48 inference(unit_resolution,[status(thm)],[24195, 108, 24192, 24191, 24190])).
% 293.98/186.48 tff(24197,plain,((~node22(c_e_h_1, c_i, s13, s14)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s14)) | m_and_h_gate_v_out(c_e_h_1, c_i, s13)), inference(lemma,lemma(discharge,[]))).
% 293.98/186.48 tff(24198,plain,
% 293.98/186.48 (~node22(c_e_h_1, c_i, s13, s14)),
% 293.98/186.48 inference(unit_resolution,[status(thm)],[24197, 24191, 24190])).
% 293.98/186.48 tff(24199,assumption,(~node20(c_e_h_1, c_i, s13)), introduced(assumption)).
% 293.98/186.48 tff(24200,assumption,(node21(c_e_h_1, c_i, s13, s14)), introduced(assumption)).
% 293.98/186.48 tff(24201,plain,
% 293.98/186.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s14)) | node20(c_e_h_1, c_i, s13) | (~node21(c_e_h_1, c_i, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s14)) | node20(c_e_h_1, c_i, s13) | (~node21(c_e_h_1, c_i, s13, s14)))),
% 293.98/186.48 inference(rewrite,[status(thm)],[])).
% 293.98/186.48 tff(24202,plain,
% 293.98/186.48 ((node20(c_e_h_1, c_i, s13) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s14)) | (~node21(c_e_h_1, c_i, s13, s14))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_i, s14)) | node20(c_e_h_1, c_i, s13) | (~node21(c_e_h_1, c_i, s13, s14)))),
% 293.98/186.48 inference(rewrite,[status(thm)],[])).
% 293.98/186.48 tff(24203,plain,
% 293.98/186.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s13) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s14)) | (~node21(c_e_h_1, c_i, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s14)) | node20(c_e_h_1, c_i, s13) | (~node21(c_e_h_1, c_i, s13, s14))))),
% 293.98/186.48 inference(monotonicity,[status(thm)],[24202])).
% 293.98/186.48 tff(24204,plain,
% 293.98/186.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s13) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s14)) | (~node21(c_e_h_1, c_i, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s14)) | node20(c_e_h_1, c_i, s13) | (~node21(c_e_h_1, c_i, s13, s14)))),
% 293.98/186.48 inference(transitivity,[status(thm)],[24203, 24201])).
% 293.98/186.48 tff(24205,plain,
% 293.98/186.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s13) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s14)) | (~node21(c_e_h_1, c_i, s13, s14)))),
% 293.98/186.48 inference(quant_inst,[status(thm)],[])).
% 293.98/186.48 tff(24206,plain,
% 293.98/186.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s14)) | node20(c_e_h_1, c_i, s13) | (~node21(c_e_h_1, c_i, s13, s14))),
% 293.98/186.48 inference(modus_ponens,[status(thm)],[24205, 24204])).
% 293.98/186.48 tff(24207,plain,
% 293.98/186.48 ($false),
% 293.98/186.48 inference(unit_resolution,[status(thm)],[24206, 52, 24200, 24199, 24191])).
% 293.98/186.48 tff(24208,plain,((~node21(c_e_h_1, c_i, s13, s14)) | node20(c_e_h_1, c_i, s13) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s14))), inference(lemma,lemma(discharge,[]))).
% 293.98/186.48 tff(24209,plain,
% 293.98/186.48 (~node21(c_e_h_1, c_i, s13, s14)),
% 293.98/186.48 inference(unit_resolution,[status(thm)],[24208, 24191, 24199])).
% 293.98/186.48 tff(24210,plain,
% 293.98/186.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s13, s14)) | node21(c_e_h_1, c_i, s13, s14) | node22(c_e_h_1, c_i, s13, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s13, s14)) | node21(c_e_h_1, c_i, s13, s14) | node22(c_e_h_1, c_i, s13, s14))),
% 293.98/186.48 inference(rewrite,[status(thm)],[])).
% 293.98/186.48 tff(24211,plain,
% 293.98/186.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s13, s14)) | node21(c_e_h_1, c_i, s13, s14) | node22(c_e_h_1, c_i, s13, s14))),
% 293.98/186.48 inference(quant_inst,[status(thm)],[])).
% 293.98/186.48 tff(24212,plain,
% 293.98/186.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s13, s14)) | node21(c_e_h_1, c_i, s13, s14) | node22(c_e_h_1, c_i, s13, s14)),
% 293.98/186.48 inference(modus_ponens,[status(thm)],[24211, 24210])).
% 293.98/186.48 tff(24213,plain,
% 293.98/186.48 (node21(c_e_h_1, c_i, s13, s14) | node22(c_e_h_1, c_i, s13, s14)),
% 293.98/186.48 inference(unit_resolution,[status(thm)],[24212, 82, 12831])).
% 293.98/186.48 tff(24214,plain,
% 293.98/186.48 ($false),
% 293.98/186.48 inference(unit_resolution,[status(thm)],[24213, 24209, 24198])).
% 293.98/186.48 tff(24215,plain,((~m_and_h_gate_v_out(c_e_h_1, c_i, s14)) | node20(c_e_h_1, c_i, s13) | m_and_h_gate_v_out(c_e_h_1, c_i, s13)), inference(lemma,lemma(discharge,[]))).
% 293.98/186.48 tff(24216,plain,
% 293.98/186.48 (~m_and_h_gate_v_out(c_e_h_1, c_i, s14)),
% 293.98/186.48 inference(unit_resolution,[status(thm)],[24215, 24189, 24181])).
% 293.98/186.48 tff(24217,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_i, s14)), introduced(assumption)).
% 293.98/186.48 tff(24218,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s15)), introduced(assumption)).
% 293.98/186.48 tff(24219,assumption,(node22(c_e_h_1, c_i, s14, s15)), introduced(assumption)).
% 293.98/186.48 tff(24220,plain,
% 293.98/186.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s15)) | (~node22(c_e_h_1, c_i, s14, s15)) | m_and_h_gate_v_out(c_e_h_1, c_i, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s15)) | (~node22(c_e_h_1, c_i, s14, s15)) | m_and_h_gate_v_out(c_e_h_1, c_i, s14))),
% 293.98/186.48 inference(rewrite,[status(thm)],[])).
% 293.98/186.48 tff(24221,plain,
% 293.98/186.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s15)) | (~node22(c_e_h_1, c_i, s14, s15)) | m_and_h_gate_v_out(c_e_h_1, c_i, s14))),
% 293.98/186.48 inference(quant_inst,[status(thm)],[])).
% 293.98/186.48 tff(24222,plain,
% 293.98/186.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s15)) | (~node22(c_e_h_1, c_i, s14, s15)) | m_and_h_gate_v_out(c_e_h_1, c_i, s14)),
% 293.98/186.48 inference(modus_ponens,[status(thm)],[24221, 24220])).
% 293.98/186.48 tff(24223,plain,
% 293.98/186.48 ($false),
% 293.98/186.48 inference(unit_resolution,[status(thm)],[24222, 108, 24217, 24219, 24218])).
% 293.98/186.48 tff(24224,plain,((~node22(c_e_h_1, c_i, s14, s15)) | m_and_h_gate_v_out(c_e_h_1, c_i, s14) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s15))), inference(lemma,lemma(discharge,[]))).
% 293.98/186.48 tff(24225,plain,
% 293.98/186.48 (~node22(c_e_h_1, c_i, s14, s15)),
% 293.98/186.48 inference(unit_resolution,[status(thm)],[24224, 24218, 24217])).
% 293.98/186.48 tff(24226,assumption,(~node20(c_e_h_1, c_i, s14)), introduced(assumption)).
% 293.98/186.48 tff(24227,assumption,(node21(c_e_h_1, c_i, s14, s15)), introduced(assumption)).
% 293.98/186.48 tff(24228,plain,
% 293.98/186.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s14) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s15)) | (~node21(c_e_h_1, c_i, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s14) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s15)) | (~node21(c_e_h_1, c_i, s14, s15)))),
% 293.98/186.48 inference(rewrite,[status(thm)],[])).
% 293.98/186.48 tff(24229,plain,
% 293.98/186.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s14) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s15)) | (~node21(c_e_h_1, c_i, s14, s15)))),
% 293.98/186.49 inference(quant_inst,[status(thm)],[])).
% 293.98/186.49 tff(24230,plain,
% 293.98/186.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s14) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s15)) | (~node21(c_e_h_1, c_i, s14, s15))),
% 293.98/186.49 inference(modus_ponens,[status(thm)],[24229, 24228])).
% 293.98/186.49 tff(24231,plain,
% 293.98/186.49 ($false),
% 293.98/186.49 inference(unit_resolution,[status(thm)],[24230, 52, 24227, 24218, 24226])).
% 293.98/186.49 tff(24232,plain,((~node21(c_e_h_1, c_i, s14, s15)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s15)) | node20(c_e_h_1, c_i, s14)), inference(lemma,lemma(discharge,[]))).
% 293.98/186.49 tff(24233,plain,
% 293.98/186.49 (~node21(c_e_h_1, c_i, s14, s15)),
% 293.98/186.49 inference(unit_resolution,[status(thm)],[24232, 24218, 24226])).
% 293.98/186.49 tff(24234,plain,
% 293.98/186.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s14, s15)) | node21(c_e_h_1, c_i, s14, s15) | node22(c_e_h_1, c_i, s14, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s14, s15)) | node21(c_e_h_1, c_i, s14, s15) | node22(c_e_h_1, c_i, s14, s15))),
% 293.98/186.49 inference(rewrite,[status(thm)],[])).
% 293.98/186.49 tff(24235,plain,
% 293.98/186.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s14, s15)) | node21(c_e_h_1, c_i, s14, s15) | node22(c_e_h_1, c_i, s14, s15))),
% 293.98/186.49 inference(quant_inst,[status(thm)],[])).
% 293.98/186.49 tff(24236,plain,
% 293.98/186.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s14, s15)) | node21(c_e_h_1, c_i, s14, s15) | node22(c_e_h_1, c_i, s14, s15)),
% 293.98/186.49 inference(modus_ponens,[status(thm)],[24235, 24234])).
% 293.98/186.49 tff(24237,plain,
% 293.98/186.49 (node21(c_e_h_1, c_i, s14, s15) | node22(c_e_h_1, c_i, s14, s15)),
% 293.98/186.49 inference(unit_resolution,[status(thm)],[24236, 82, 12926])).
% 293.98/186.49 tff(24238,plain,
% 293.98/186.49 ($false),
% 293.98/186.49 inference(unit_resolution,[status(thm)],[24237, 24233, 24225])).
% 293.98/186.49 tff(24239,plain,((~m_and_h_gate_v_out(c_e_h_1, c_i, s15)) | node20(c_e_h_1, c_i, s14) | m_and_h_gate_v_out(c_e_h_1, c_i, s14)), inference(lemma,lemma(discharge,[]))).
% 293.98/186.49 tff(24240,plain,
% 293.98/186.49 ((~m_and_h_gate_v_out(c_e_h_1, c_i, s15)) | node20(c_e_h_1, c_i, s14)),
% 293.98/186.49 inference(unit_resolution,[status(thm)],[24239, 24216])).
% 293.98/186.49 tff(24241,plain,
% 293.98/186.49 (~m_and_h_gate_v_out(c_e_h_1, c_i, s15)),
% 293.98/186.49 inference(unit_resolution,[status(thm)],[24240, 24049])).
% 293.98/186.49 tff(24242,assumption,(~node20(c_e_h_1, c_i, s15)), introduced(assumption)).
% 293.98/186.49 tff(24243,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s16)), introduced(assumption)).
% 293.98/186.49 tff(24244,assumption,(node21(c_e_h_1, c_i, s15, s16)), introduced(assumption)).
% 293.98/186.49 tff(24245,plain,
% 293.98/186.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s15) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s16)) | (~node21(c_e_h_1, c_i, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s15) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s16)) | (~node21(c_e_h_1, c_i, s15, s16)))),
% 293.98/186.49 inference(rewrite,[status(thm)],[])).
% 293.98/186.49 tff(24246,plain,
% 293.98/186.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s15) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s16)) | (~node21(c_e_h_1, c_i, s15, s16)))),
% 293.98/186.49 inference(quant_inst,[status(thm)],[])).
% 293.98/186.49 tff(24247,plain,
% 293.98/186.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s15) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s16)) | (~node21(c_e_h_1, c_i, s15, s16))),
% 293.98/186.49 inference(modus_ponens,[status(thm)],[24246, 24245])).
% 293.98/186.49 tff(24248,plain,
% 293.98/186.49 ($false),
% 293.98/186.49 inference(unit_resolution,[status(thm)],[24247, 52, 24243, 24244, 24242])).
% 293.98/186.49 tff(24249,plain,((~node21(c_e_h_1, c_i, s15, s16)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s16)) | node20(c_e_h_1, c_i, s15)), inference(lemma,lemma(discharge,[]))).
% 293.98/186.49 tff(24250,plain,
% 293.98/186.49 (~node21(c_e_h_1, c_i, s15, s16)),
% 293.98/186.49 inference(unit_resolution,[status(thm)],[24249, 24243, 24242])).
% 293.98/186.49 tff(24251,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_i, s15)), introduced(assumption)).
% 293.98/186.49 tff(24252,assumption,(node22(c_e_h_1, c_i, s15, s16)), introduced(assumption)).
% 293.98/186.49 tff(24253,plain,
% 293.98/186.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s16)) | (~node22(c_e_h_1, c_i, s15, s16)) | m_and_h_gate_v_out(c_e_h_1, c_i, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s16)) | (~node22(c_e_h_1, c_i, s15, s16)) | m_and_h_gate_v_out(c_e_h_1, c_i, s15))),
% 293.98/186.49 inference(rewrite,[status(thm)],[])).
% 293.98/186.49 tff(24254,plain,
% 293.98/186.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s16)) | (~node22(c_e_h_1, c_i, s15, s16)) | m_and_h_gate_v_out(c_e_h_1, c_i, s15))),
% 293.98/186.49 inference(quant_inst,[status(thm)],[])).
% 293.98/186.49 tff(24255,plain,
% 293.98/186.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s16)) | (~node22(c_e_h_1, c_i, s15, s16)) | m_and_h_gate_v_out(c_e_h_1, c_i, s15)),
% 293.98/186.49 inference(modus_ponens,[status(thm)],[24254, 24253])).
% 293.98/186.49 tff(24256,plain,
% 293.98/186.49 ($false),
% 293.98/186.49 inference(unit_resolution,[status(thm)],[24255, 108, 24251, 24243, 24252])).
% 293.98/186.49 tff(24257,plain,((~node22(c_e_h_1, c_i, s15, s16)) | m_and_h_gate_v_out(c_e_h_1, c_i, s15) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s16))), inference(lemma,lemma(discharge,[]))).
% 293.98/186.49 tff(24258,plain,
% 293.98/186.49 (~node22(c_e_h_1, c_i, s15, s16)),
% 293.98/186.49 inference(unit_resolution,[status(thm)],[24257, 24243, 24251])).
% 293.98/186.49 tff(24259,plain,
% 293.98/186.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s15, s16)) | node21(c_e_h_1, c_i, s15, s16) | node22(c_e_h_1, c_i, s15, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s15, s16)) | node21(c_e_h_1, c_i, s15, s16) | node22(c_e_h_1, c_i, s15, s16))),
% 293.98/186.49 inference(rewrite,[status(thm)],[])).
% 293.98/186.49 tff(24260,plain,
% 293.98/186.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s15, s16)) | node21(c_e_h_1, c_i, s15, s16) | node22(c_e_h_1, c_i, s15, s16))),
% 293.98/186.49 inference(quant_inst,[status(thm)],[])).
% 293.98/186.49 tff(24261,plain,
% 293.98/186.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s15, s16)) | node21(c_e_h_1, c_i, s15, s16) | node22(c_e_h_1, c_i, s15, s16)),
% 293.98/186.49 inference(modus_ponens,[status(thm)],[24260, 24259])).
% 293.98/186.49 tff(24262,plain,
% 293.98/186.49 (node21(c_e_h_1, c_i, s15, s16) | node22(c_e_h_1, c_i, s15, s16)),
% 293.98/186.49 inference(unit_resolution,[status(thm)],[24261, 82, 13499])).
% 293.98/186.49 tff(24263,plain,
% 293.98/186.49 ($false),
% 293.98/186.49 inference(unit_resolution,[status(thm)],[24262, 24258, 24250])).
% 293.98/186.49 tff(24264,plain,((~m_and_h_gate_v_out(c_e_h_1, c_i, s16)) | m_and_h_gate_v_out(c_e_h_1, c_i, s15) | node20(c_e_h_1, c_i, s15)), inference(lemma,lemma(discharge,[]))).
% 293.98/186.49 tff(24265,plain,
% 293.98/186.49 ((~m_and_h_gate_v_out(c_e_h_1, c_i, s16)) | node20(c_e_h_1, c_i, s15)),
% 293.98/186.49 inference(unit_resolution,[status(thm)],[24264, 24241])).
% 293.98/186.49 tff(24266,plain,
% 293.98/186.49 (~m_and_h_gate_v_out(c_e_h_1, c_i, s16)),
% 293.98/186.49 inference(unit_resolution,[status(thm)],[24265, 24041])).
% 293.98/186.49 tff(24267,plain,
% 293.98/186.49 (~m_or_h_gate_v_out(c_e_h_3, c_j, s8)),
% 293.98/186.49 inference(unit_resolution,[status(thm)],[5885, 2743])).
% 293.98/186.49 tff(24268,plain,
% 293.98/186.49 (~m_c_h_element_v_out(c_e_h_3, c_h, s9)),
% 293.98/186.49 inference(unit_resolution,[status(thm)],[7624, 24267])).
% 293.98/186.49 tff(24269,plain,
% 293.98/186.49 (~m_and_h_gate_v_in1(c_e_h_3, c_i, s9)),
% 293.98/186.49 inference(unit_resolution,[status(thm)],[11380, 619, 24268])).
% 293.98/186.49 tff(24270,plain,
% 293.98/186.49 (~node20(c_e_h_3, c_i, s9)),
% 293.98/186.49 inference(unit_resolution,[status(thm)],[11376, 38, 24269])).
% 293.98/186.49 tff(24271,plain,
% 293.98/186.49 (~m_and_h_gate_v_out(c_e_h_3, c_i, s10)),
% 293.98/186.49 inference(unit_resolution,[status(thm)],[11407, 21940, 24270])).
% 293.98/186.49 tff(24272,plain,
% 293.98/186.49 (~m_c_h_element_v_in2(c_e_h_3, c_f, s10)),
% 293.98/186.49 inference(unit_resolution,[status(thm)],[11683, 24271])).
% 293.98/186.49 tff(24273,plain,
% 293.98/186.49 (~m_c_h_element_v_out(c_e_h_3, c_f, s11)),
% 293.98/186.49 inference(unit_resolution,[status(thm)],[11758, 24272, 21942])).
% 293.98/186.49 tff(24274,plain,
% 293.98/186.49 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s11)),
% 293.98/186.49 inference(unit_resolution,[status(thm)],[13228, 24273])).
% 293.98/186.49 tff(24275,plain,
% 293.98/186.49 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12)),
% 293.98/186.49 inference(unit_resolution,[status(thm)],[13288, 24274, 21941])).
% 293.98/186.49 tff(24276,plain,
% 293.98/186.49 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s12)),
% 293.98/186.49 inference(unit_resolution,[status(thm)],[13292, 5601, 24275])).
% 293.98/186.49 tff(24277,plain,
% 293.98/186.49 (~node9(c_e_h_3, c_n, s12)),
% 293.98/186.49 inference(unit_resolution,[status(thm)],[13296, 4972, 24276])).
% 293.98/186.49 tff(24278,plain,
% 293.98/186.49 (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s13)),
% 293.98/186.49 inference(unit_resolution,[status(thm)],[13320, 24277, 21947])).
% 293.98/186.49 tff(24279,plain,
% 293.98/186.49 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s13)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s13))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s13)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s13))),
% 293.98/186.49 inference(rewrite,[status(thm)],[])).
% 293.98/186.49 tff(24280,plain,
% 293.98/186.49 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s13)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s13))),
% 293.98/186.49 inference(quant_inst,[status(thm)],[])).
% 293.98/186.49 tff(24281,plain,
% 293.98/186.49 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s13)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s13)),
% 293.98/186.49 inference(modus_ponens,[status(thm)],[24280, 24279])).
% 293.98/186.49 tff(24282,plain,
% 293.98/186.49 (~m_and_h_gate_v_in2(c_e_h_3, c_q, s13)),
% 293.98/186.49 inference(unit_resolution,[status(thm)],[24281, 5621, 24278])).
% 293.98/186.49 tff(24283,plain,
% 293.98/186.49 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s13)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s13))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s13)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s13))),
% 293.98/186.49 inference(rewrite,[status(thm)],[])).
% 293.98/186.49 tff(24284,plain,
% 293.98/186.49 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s13)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s13))),
% 293.98/186.49 inference(quant_inst,[status(thm)],[])).
% 293.98/186.49 tff(24285,plain,
% 293.98/186.49 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s13)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s13)),
% 293.98/186.49 inference(modus_ponens,[status(thm)],[24284, 24283])).
% 293.98/186.49 tff(24286,plain,
% 293.98/186.49 (~node20(c_e_h_3, c_q, s13)),
% 293.98/186.49 inference(unit_resolution,[status(thm)],[24285, 4563, 24282])).
% 293.98/186.49 tff(24287,assumption,(~node20(c_e_h_3, c_q, s13)), introduced(assumption)).
% 293.98/186.49 tff(24288,assumption,(m_and_h_gate_v_out(c_e_h_3, c_q, s14)), introduced(assumption)).
% 293.98/186.49 tff(24289,assumption,(node21(c_e_h_3, c_q, s13, s14)), introduced(assumption)).
% 293.98/186.49 tff(24290,plain,
% 293.98/186.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s13) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s14)) | (~node21(c_e_h_3, c_q, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_q, s13) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s14)) | (~node21(c_e_h_3, c_q, s13, s14)))),
% 293.98/186.49 inference(rewrite,[status(thm)],[])).
% 293.98/186.49 tff(24291,plain,
% 293.98/186.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s13) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s14)) | (~node21(c_e_h_3, c_q, s13, s14)))),
% 293.98/186.50 inference(quant_inst,[status(thm)],[])).
% 293.98/186.50 tff(24292,plain,
% 293.98/186.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_q, s13) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s14)) | (~node21(c_e_h_3, c_q, s13, s14))),
% 293.98/186.50 inference(modus_ponens,[status(thm)],[24291, 24290])).
% 293.98/186.50 tff(24293,plain,
% 293.98/186.50 ($false),
% 293.98/186.50 inference(unit_resolution,[status(thm)],[24292, 52, 24288, 24289, 24287])).
% 293.98/186.50 tff(24294,plain,((~node21(c_e_h_3, c_q, s13, s14)) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s14)) | node20(c_e_h_3, c_q, s13)), inference(lemma,lemma(discharge,[]))).
% 293.98/186.50 tff(24295,plain,
% 293.98/186.50 (~node21(c_e_h_3, c_q, s13, s14)),
% 293.98/186.50 inference(unit_resolution,[status(thm)],[24294, 24288, 24287])).
% 293.98/186.50 tff(24296,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_q, s13)), introduced(assumption)).
% 293.98/186.50 tff(24297,assumption,(node22(c_e_h_3, c_q, s13, s14)), introduced(assumption)).
% 293.98/186.50 tff(24298,plain,
% 293.98/186.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s14)) | (~node22(c_e_h_3, c_q, s13, s14)) | m_and_h_gate_v_out(c_e_h_3, c_q, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s14)) | (~node22(c_e_h_3, c_q, s13, s14)) | m_and_h_gate_v_out(c_e_h_3, c_q, s13))),
% 293.98/186.50 inference(rewrite,[status(thm)],[])).
% 293.98/186.50 tff(24299,plain,
% 293.98/186.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s14)) | (~node22(c_e_h_3, c_q, s13, s14)) | m_and_h_gate_v_out(c_e_h_3, c_q, s13))),
% 293.98/186.50 inference(quant_inst,[status(thm)],[])).
% 293.98/186.50 tff(24300,plain,
% 293.98/186.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s14)) | (~node22(c_e_h_3, c_q, s13, s14)) | m_and_h_gate_v_out(c_e_h_3, c_q, s13)),
% 293.98/186.50 inference(modus_ponens,[status(thm)],[24299, 24298])).
% 293.98/186.50 tff(24301,plain,
% 293.98/186.50 ($false),
% 293.98/186.50 inference(unit_resolution,[status(thm)],[24300, 108, 24288, 24296, 24297])).
% 293.98/186.50 tff(24302,plain,((~node22(c_e_h_3, c_q, s13, s14)) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s14)) | m_and_h_gate_v_out(c_e_h_3, c_q, s13)), inference(lemma,lemma(discharge,[]))).
% 293.98/186.50 tff(24303,plain,
% 293.98/186.50 (~node22(c_e_h_3, c_q, s13, s14)),
% 293.98/186.50 inference(unit_resolution,[status(thm)],[24302, 24288, 24296])).
% 293.98/186.50 tff(24304,plain,
% 293.98/186.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s13, s14)) | node21(c_e_h_3, c_q, s13, s14) | node22(c_e_h_3, c_q, s13, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s13, s14)) | node21(c_e_h_3, c_q, s13, s14) | node22(c_e_h_3, c_q, s13, s14))),
% 293.98/186.50 inference(rewrite,[status(thm)],[])).
% 293.98/186.50 tff(24305,plain,
% 293.98/186.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s13, s14)) | node21(c_e_h_3, c_q, s13, s14) | node22(c_e_h_3, c_q, s13, s14))),
% 293.98/186.50 inference(quant_inst,[status(thm)],[])).
% 293.98/186.50 tff(24306,plain,
% 293.98/186.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s13, s14)) | node21(c_e_h_3, c_q, s13, s14) | node22(c_e_h_3, c_q, s13, s14)),
% 293.98/186.50 inference(modus_ponens,[status(thm)],[24305, 24304])).
% 293.98/186.50 tff(24307,plain,
% 293.98/186.50 (node21(c_e_h_3, c_q, s13, s14) | node22(c_e_h_3, c_q, s13, s14)),
% 293.98/186.50 inference(unit_resolution,[status(thm)],[24306, 82, 12831])).
% 293.98/186.50 tff(24308,plain,
% 293.98/186.50 ($false),
% 293.98/186.50 inference(unit_resolution,[status(thm)],[24307, 24303, 24295])).
% 293.98/186.50 tff(24309,plain,((~m_and_h_gate_v_out(c_e_h_3, c_q, s14)) | m_and_h_gate_v_out(c_e_h_3, c_q, s13) | node20(c_e_h_3, c_q, s13)), inference(lemma,lemma(discharge,[]))).
% 293.98/186.50 tff(24310,plain,
% 293.98/186.50 (~m_and_h_gate_v_out(c_e_h_3, c_q, s14)),
% 293.98/186.50 inference(unit_resolution,[status(thm)],[24309, 24286, 22050])).
% 293.98/186.50 tff(24311,plain,
% 293.98/186.50 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s14))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s14))),
% 293.98/186.50 inference(rewrite,[status(thm)],[])).
% 293.98/186.50 tff(24312,plain,
% 293.98/186.50 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s14))),
% 293.98/186.50 inference(quant_inst,[status(thm)],[])).
% 293.98/186.50 tff(24313,plain,
% 293.98/186.50 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s14)),
% 293.98/186.50 inference(modus_ponens,[status(thm)],[24312, 24311])).
% 293.98/186.50 tff(24314,plain,
% 293.98/186.50 (node3(c_e_h_3, c_e_h_1, s14)),
% 293.98/186.50 inference(unit_resolution,[status(thm)],[24313, 2922, 1056])).
% 293.98/186.50 tff(24315,plain,
% 293.98/186.50 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s14)) | (~node3(c_e_h_3, c_e_h_1, s14)) | m_and_h_gate_v_out(c_e_h_3, c_q, s14))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s14)) | (~node3(c_e_h_3, c_e_h_1, s14)) | m_and_h_gate_v_out(c_e_h_3, c_q, s14))),
% 293.98/186.50 inference(rewrite,[status(thm)],[])).
% 293.98/186.50 tff(24316,plain,
% 293.98/186.50 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s14)) | (~node3(c_e_h_3, c_e_h_1, s14)) | m_and_h_gate_v_out(c_e_h_3, c_q, s14))),
% 293.98/186.50 inference(quant_inst,[status(thm)],[])).
% 293.98/186.50 tff(24317,plain,
% 293.98/186.50 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s14)) | (~node3(c_e_h_3, c_e_h_1, s14)) | m_and_h_gate_v_out(c_e_h_3, c_q, s14)),
% 293.98/186.50 inference(modus_ponens,[status(thm)],[24316, 24315])).
% 293.98/186.50 tff(24318,plain,
% 293.98/186.50 ((~m_cell_v_ack(c_e_h_1, s14)) | m_and_h_gate_v_out(c_e_h_3, c_q, s14)),
% 293.98/186.50 inference(unit_resolution,[status(thm)],[24317, 1073, 24314])).
% 293.98/186.50 tff(24319,plain,
% 293.98/186.50 (~m_cell_v_ack(c_e_h_1, s14)),
% 293.98/186.50 inference(unit_resolution,[status(thm)],[24318, 24310])).
% 293.98/186.50 tff(24320,plain,
% 293.98/186.50 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s14)) | m_cell_v_ack(c_e_h_1, s14))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s14)) | m_cell_v_ack(c_e_h_1, s14))),
% 293.98/186.50 inference(rewrite,[status(thm)],[])).
% 293.98/186.50 tff(24321,plain,
% 293.98/186.50 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s14)) | m_cell_v_ack(c_e_h_1, s14))),
% 293.98/186.50 inference(quant_inst,[status(thm)],[])).
% 293.98/186.50 tff(24322,plain,
% 293.98/186.50 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s14)) | m_cell_v_ack(c_e_h_1, s14)),
% 293.98/186.50 inference(modus_ponens,[status(thm)],[24321, 24320])).
% 293.98/186.50 tff(24323,plain,
% 293.98/186.50 (~m_or_h_gate_v_in2(c_e_h_1, c_j, s14)),
% 293.98/186.50 inference(unit_resolution,[status(thm)],[24322, 1085, 24319])).
% 293.98/186.50 tff(24324,assumption,(m_c_h_element_v_in2(c_e_h_1, c_e, s10)), introduced(assumption)).
% 293.98/186.50 tff(24325,plain,
% 293.98/186.50 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s10)) | m_and_h_gate_v_out(c_e_h_1, c_i, s10))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s10)) | m_and_h_gate_v_out(c_e_h_1, c_i, s10))),
% 293.98/186.50 inference(rewrite,[status(thm)],[])).
% 293.98/186.50 tff(24326,plain,
% 293.98/186.50 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s10)) | m_and_h_gate_v_out(c_e_h_1, c_i, s10))),
% 293.98/186.50 inference(quant_inst,[status(thm)],[])).
% 293.98/186.50 tff(24327,plain,
% 293.98/186.50 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s10)) | m_and_h_gate_v_out(c_e_h_1, c_i, s10)),
% 293.98/186.50 inference(modus_ponens,[status(thm)],[24326, 24325])).
% 293.98/186.50 tff(24328,plain,
% 293.98/186.50 ($false),
% 293.98/186.50 inference(unit_resolution,[status(thm)],[24327, 164, 24113, 24324])).
% 293.98/186.50 tff(24329,plain,((~m_c_h_element_v_in2(c_e_h_1, c_e, s10)) | m_and_h_gate_v_out(c_e_h_1, c_i, s10)), inference(lemma,lemma(discharge,[]))).
% 293.98/186.50 tff(24330,plain,
% 293.98/186.50 (~m_c_h_element_v_in2(c_e_h_1, c_e, s10)),
% 293.98/186.50 inference(unit_resolution,[status(thm)],[24329, 24091])).
% 293.98/186.50 tff(24331,assumption,(~m_c_h_element_v_out(c_e_h_1, c_e, s10)), introduced(assumption)).
% 293.98/186.50 tff(24332,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s11)), introduced(assumption)).
% 293.98/186.50 tff(24333,assumption,(node18(c_e_h_1, c_e, s10, s11)), introduced(assumption)).
% 293.98/186.50 tff(24334,plain,
% 293.98/186.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s11)) | m_c_h_element_v_out(c_e_h_1, c_e, s10) | (~node18(c_e_h_1, c_e, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s11)) | m_c_h_element_v_out(c_e_h_1, c_e, s10) | (~node18(c_e_h_1, c_e, s10, s11)))),
% 293.98/186.50 inference(rewrite,[status(thm)],[])).
% 293.98/186.50 tff(24335,plain,
% 293.98/186.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s11)) | m_c_h_element_v_out(c_e_h_1, c_e, s10) | (~node18(c_e_h_1, c_e, s10, s11)))),
% 293.98/186.50 inference(quant_inst,[status(thm)],[])).
% 293.98/186.50 tff(24336,plain,
% 293.98/186.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s11)) | m_c_h_element_v_out(c_e_h_1, c_e, s10) | (~node18(c_e_h_1, c_e, s10, s11))),
% 293.98/186.50 inference(modus_ponens,[status(thm)],[24335, 24334])).
% 293.98/186.50 tff(24337,plain,
% 293.98/186.50 ($false),
% 293.98/186.50 inference(unit_resolution,[status(thm)],[24336, 753, 24332, 24331, 24333])).
% 293.98/186.50 tff(24338,plain,((~node18(c_e_h_1, c_e, s10, s11)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s11)) | m_c_h_element_v_out(c_e_h_1, c_e, s10)), inference(lemma,lemma(discharge,[]))).
% 293.98/186.50 tff(24339,plain,
% 293.98/186.50 (~node18(c_e_h_1, c_e, s10, s11)),
% 293.98/186.50 inference(unit_resolution,[status(thm)],[24338, 24332, 24331])).
% 293.98/186.50 tff(24340,assumption,(node15(c_e_h_1, c_e, s10, s11)), introduced(assumption)).
% 293.98/186.50 tff(24341,plain,
% 293.98/186.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s11)) | (~node15(c_e_h_1, c_e, s10, s11)) | m_c_h_element_v_out(c_e_h_1, c_e, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s11)) | (~node15(c_e_h_1, c_e, s10, s11)) | m_c_h_element_v_out(c_e_h_1, c_e, s10))),
% 293.98/186.50 inference(rewrite,[status(thm)],[])).
% 293.98/186.50 tff(24342,plain,
% 293.98/186.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s11)) | (~node15(c_e_h_1, c_e, s10, s11)) | m_c_h_element_v_out(c_e_h_1, c_e, s10))),
% 293.98/186.50 inference(quant_inst,[status(thm)],[])).
% 293.98/186.50 tff(24343,plain,
% 293.98/186.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s11)) | (~node15(c_e_h_1, c_e, s10, s11)) | m_c_h_element_v_out(c_e_h_1, c_e, s10)),
% 293.98/186.50 inference(modus_ponens,[status(thm)],[24342, 24341])).
% 293.98/186.50 tff(24344,plain,
% 293.98/186.50 ($false),
% 293.98/186.50 inference(unit_resolution,[status(thm)],[24343, 147, 24332, 24331, 24340])).
% 293.98/186.50 tff(24345,plain,((~node15(c_e_h_1, c_e, s10, s11)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s11)) | m_c_h_element_v_out(c_e_h_1, c_e, s10)), inference(lemma,lemma(discharge,[]))).
% 293.98/186.51 tff(24346,plain,
% 293.98/186.51 (~node15(c_e_h_1, c_e, s10, s11)),
% 293.98/186.51 inference(unit_resolution,[status(thm)],[24345, 24332, 24331])).
% 293.98/186.51 tff(24347,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_e, s10)), introduced(assumption)).
% 293.98/186.51 tff(24348,assumption,(~node15(c_e_h_1, c_e, s10, s11)), introduced(assumption)).
% 293.98/186.51 tff(24349,assumption,(node17(c_e_h_1, c_e, s10)), introduced(assumption)).
% 293.98/186.51 tff(24350,plain,
% 293.98/186.51 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s10) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s10)) | (~node17(c_e_h_1, c_e, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s10) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s10)) | (~node17(c_e_h_1, c_e, s10)))),
% 293.98/186.51 inference(rewrite,[status(thm)],[])).
% 293.98/186.51 tff(24351,plain,
% 293.98/186.51 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s10) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s10)) | (~node17(c_e_h_1, c_e, s10)))),
% 293.98/186.51 inference(quant_inst,[status(thm)],[])).
% 293.98/186.51 tff(24352,plain,
% 293.98/186.51 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s10) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s10)) | (~node17(c_e_h_1, c_e, s10))),
% 293.98/186.51 inference(modus_ponens,[status(thm)],[24351, 24350])).
% 293.98/186.51 tff(24353,plain,
% 293.98/186.51 (m_c_h_element_v_in1(c_e_h_1, c_e, s10) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s10))),
% 293.98/186.51 inference(unit_resolution,[status(thm)],[24352, 859, 24349])).
% 293.98/186.51 tff(24354,plain,
% 293.98/186.51 (~m_c_h_element_v_in2(c_e_h_1, c_e, s10)),
% 293.98/186.51 inference(unit_resolution,[status(thm)],[24353, 24347])).
% 293.98/186.51 tff(24355,plain,
% 293.98/186.51 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s10)) | m_c_h_element_v_in1(c_e_h_1, c_e, s10) | m_c_h_element_v_in2(c_e_h_1, c_e, s10))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s10)) | m_c_h_element_v_in1(c_e_h_1, c_e, s10) | m_c_h_element_v_in2(c_e_h_1, c_e, s10))),
% 293.98/186.51 inference(rewrite,[status(thm)],[])).
% 293.98/186.51 tff(24356,plain,
% 293.98/186.51 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s10)) | m_c_h_element_v_in1(c_e_h_1, c_e, s10) | m_c_h_element_v_in2(c_e_h_1, c_e, s10))),
% 293.98/186.51 inference(quant_inst,[status(thm)],[])).
% 293.98/186.51 tff(24357,plain,
% 293.98/186.51 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s10)) | m_c_h_element_v_in1(c_e_h_1, c_e, s10) | m_c_h_element_v_in2(c_e_h_1, c_e, s10)),
% 293.98/186.51 inference(modus_ponens,[status(thm)],[24356, 24355])).
% 293.98/186.51 tff(24358,plain,
% 293.98/186.51 (~node16(c_e_h_1, c_e, s10)),
% 293.98/186.51 inference(unit_resolution,[status(thm)],[24357, 178, 24347, 24354])).
% 293.98/186.51 tff(24359,plain,
% 293.98/186.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s10, s11)) | node19(c_e_h_1, c_e, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s10, s11)) | node19(c_e_h_1, c_e, s10, s11))),
% 293.98/186.51 inference(rewrite,[status(thm)],[])).
% 293.98/186.51 tff(24360,plain,
% 293.98/186.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s10, s11)) | node19(c_e_h_1, c_e, s10, s11))),
% 293.98/186.51 inference(quant_inst,[status(thm)],[])).
% 293.98/186.51 tff(24361,plain,
% 293.98/186.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s10, s11)) | node19(c_e_h_1, c_e, s10, s11)),
% 293.98/186.51 inference(modus_ponens,[status(thm)],[24360, 24359])).
% 293.98/186.51 tff(24362,plain,
% 293.98/186.51 (node19(c_e_h_1, c_e, s10, s11)),
% 293.98/186.51 inference(unit_resolution,[status(thm)],[24361, 190, 7748])).
% 293.98/186.51 tff(24363,plain,
% 293.98/186.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_1, c_e, s10, s11) | node15(c_e_h_1, c_e, s10, s11) | (~node19(c_e_h_1, c_e, s10, s11)) | node16(c_e_h_1, c_e, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_e, s10, s11) | node15(c_e_h_1, c_e, s10, s11) | (~node19(c_e_h_1, c_e, s10, s11)) | node16(c_e_h_1, c_e, s10))),
% 293.98/186.51 inference(rewrite,[status(thm)],[])).
% 293.98/186.51 tff(24364,plain,
% 293.98/186.51 ((node16(c_e_h_1, c_e, s10) | node14(c_e_h_1, c_e, s10, s11) | node15(c_e_h_1, c_e, s10, s11) | (~node19(c_e_h_1, c_e, s10, s11))) <=> (node14(c_e_h_1, c_e, s10, s11) | node15(c_e_h_1, c_e, s10, s11) | (~node19(c_e_h_1, c_e, s10, s11)) | node16(c_e_h_1, c_e, s10))),
% 293.98/186.51 inference(rewrite,[status(thm)],[])).
% 293.98/186.51 tff(24365,plain,
% 293.98/186.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s10) | node14(c_e_h_1, c_e, s10, s11) | node15(c_e_h_1, c_e, s10, s11) | (~node19(c_e_h_1, c_e, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_1, c_e, s10, s11) | node15(c_e_h_1, c_e, s10, s11) | (~node19(c_e_h_1, c_e, s10, s11)) | node16(c_e_h_1, c_e, s10)))),
% 293.98/186.51 inference(monotonicity,[status(thm)],[24364])).
% 293.98/186.51 tff(24366,plain,
% 293.98/186.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s10) | node14(c_e_h_1, c_e, s10, s11) | node15(c_e_h_1, c_e, s10, s11) | (~node19(c_e_h_1, c_e, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_e, s10, s11) | node15(c_e_h_1, c_e, s10, s11) | (~node19(c_e_h_1, c_e, s10, s11)) | node16(c_e_h_1, c_e, s10))),
% 293.98/186.51 inference(transitivity,[status(thm)],[24365, 24363])).
% 293.98/186.51 tff(24367,plain,
% 293.98/186.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s10) | node14(c_e_h_1, c_e, s10, s11) | node15(c_e_h_1, c_e, s10, s11) | (~node19(c_e_h_1, c_e, s10, s11)))),
% 293.98/186.51 inference(quant_inst,[status(thm)],[])).
% 293.98/186.51 tff(24368,plain,
% 293.98/186.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_e, s10, s11) | node15(c_e_h_1, c_e, s10, s11) | (~node19(c_e_h_1, c_e, s10, s11)) | node16(c_e_h_1, c_e, s10)),
% 293.98/186.51 inference(modus_ponens,[status(thm)],[24367, 24366])).
% 293.98/186.51 tff(24369,plain,
% 293.98/186.51 (node14(c_e_h_1, c_e, s10, s11) | node15(c_e_h_1, c_e, s10, s11) | node16(c_e_h_1, c_e, s10)),
% 293.98/186.51 inference(unit_resolution,[status(thm)],[24368, 204, 24362])).
% 293.98/186.51 tff(24370,plain,
% 293.98/186.51 (node14(c_e_h_1, c_e, s10, s11)),
% 293.98/186.51 inference(unit_resolution,[status(thm)],[24369, 24358, 24348])).
% 293.98/186.51 tff(24371,plain,
% 293.98/186.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s11)) | m_c_h_element_v_in1(c_e_h_1, c_e, s10) | (~node14(c_e_h_1, c_e, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s11)) | m_c_h_element_v_in1(c_e_h_1, c_e, s10) | (~node14(c_e_h_1, c_e, s10, s11)))),
% 293.98/186.51 inference(rewrite,[status(thm)],[])).
% 293.98/186.51 tff(24372,plain,
% 293.98/186.51 (((~node14(c_e_h_1, c_e, s10, s11)) | m_c_h_element_v_in1(c_e_h_1, c_e, s10) | (~m_c_h_element_v_out(c_e_h_1, c_e, s11))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_e, s11)) | m_c_h_element_v_in1(c_e_h_1, c_e, s10) | (~node14(c_e_h_1, c_e, s10, s11)))),
% 293.98/186.51 inference(rewrite,[status(thm)],[])).
% 293.98/186.51 tff(24373,plain,
% 293.98/186.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s10, s11)) | m_c_h_element_v_in1(c_e_h_1, c_e, s10) | (~m_c_h_element_v_out(c_e_h_1, c_e, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s11)) | m_c_h_element_v_in1(c_e_h_1, c_e, s10) | (~node14(c_e_h_1, c_e, s10, s11))))),
% 293.98/186.52 inference(monotonicity,[status(thm)],[24372])).
% 293.98/186.52 tff(24374,plain,
% 293.98/186.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s10, s11)) | m_c_h_element_v_in1(c_e_h_1, c_e, s10) | (~m_c_h_element_v_out(c_e_h_1, c_e, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s11)) | m_c_h_element_v_in1(c_e_h_1, c_e, s10) | (~node14(c_e_h_1, c_e, s10, s11)))),
% 293.98/186.52 inference(transitivity,[status(thm)],[24373, 24371])).
% 293.98/186.52 tff(24375,plain,
% 293.98/186.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s10, s11)) | m_c_h_element_v_in1(c_e_h_1, c_e, s10) | (~m_c_h_element_v_out(c_e_h_1, c_e, s11)))),
% 293.98/186.52 inference(quant_inst,[status(thm)],[])).
% 293.98/186.52 tff(24376,plain,
% 293.98/186.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s11)) | m_c_h_element_v_in1(c_e_h_1, c_e, s10) | (~node14(c_e_h_1, c_e, s10, s11))),
% 293.98/186.52 inference(modus_ponens,[status(thm)],[24375, 24374])).
% 293.98/186.52 tff(24377,plain,
% 293.98/186.52 ($false),
% 293.98/186.52 inference(unit_resolution,[status(thm)],[24376, 223, 24332, 24370, 24347])).
% 293.98/186.52 tff(24378,plain,(m_c_h_element_v_in1(c_e_h_1, c_e, s10) | (~m_c_h_element_v_out(c_e_h_1, c_e, s11)) | node15(c_e_h_1, c_e, s10, s11) | (~node17(c_e_h_1, c_e, s10))), inference(lemma,lemma(discharge,[]))).
% 293.98/186.52 tff(24379,plain,
% 293.98/186.52 (~node17(c_e_h_1, c_e, s10)),
% 293.98/186.52 inference(unit_resolution,[status(thm)],[24378, 24332, 24347, 24346])).
% 293.98/186.52 tff(24380,plain,
% 293.98/186.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_1, c_e, s10, s11) | node17(c_e_h_1, c_e, s10) | (~node19(c_e_h_1, c_e, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_e, s10, s11) | node17(c_e_h_1, c_e, s10) | (~node19(c_e_h_1, c_e, s10, s11)))),
% 293.98/186.52 inference(rewrite,[status(thm)],[])).
% 293.98/186.52 tff(24381,plain,
% 293.98/186.52 ((node17(c_e_h_1, c_e, s10) | node18(c_e_h_1, c_e, s10, s11) | (~node19(c_e_h_1, c_e, s10, s11))) <=> (node18(c_e_h_1, c_e, s10, s11) | node17(c_e_h_1, c_e, s10) | (~node19(c_e_h_1, c_e, s10, s11)))),
% 293.98/186.52 inference(rewrite,[status(thm)],[])).
% 293.98/186.52 tff(24382,plain,
% 293.98/186.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s10) | node18(c_e_h_1, c_e, s10, s11) | (~node19(c_e_h_1, c_e, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_1, c_e, s10, s11) | node17(c_e_h_1, c_e, s10) | (~node19(c_e_h_1, c_e, s10, s11))))),
% 293.98/186.52 inference(monotonicity,[status(thm)],[24381])).
% 293.98/186.52 tff(24383,plain,
% 293.98/186.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s10) | node18(c_e_h_1, c_e, s10, s11) | (~node19(c_e_h_1, c_e, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_e, s10, s11) | node17(c_e_h_1, c_e, s10) | (~node19(c_e_h_1, c_e, s10, s11)))),
% 293.98/186.52 inference(transitivity,[status(thm)],[24382, 24380])).
% 293.98/186.52 tff(24384,plain,
% 293.98/186.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s10) | node18(c_e_h_1, c_e, s10, s11) | (~node19(c_e_h_1, c_e, s10, s11)))),
% 293.98/186.52 inference(quant_inst,[status(thm)],[])).
% 293.98/186.52 tff(24385,plain,
% 293.98/186.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_e, s10, s11) | node17(c_e_h_1, c_e, s10) | (~node19(c_e_h_1, c_e, s10, s11))),
% 293.98/186.52 inference(modus_ponens,[status(thm)],[24384, 24383])).
% 293.98/186.52 tff(24386,plain,
% 293.98/186.52 (node18(c_e_h_1, c_e, s10, s11) | node17(c_e_h_1, c_e, s10)),
% 293.98/186.52 inference(unit_resolution,[status(thm)],[24385, 776, 24362])).
% 293.98/186.52 tff(24387,plain,
% 293.98/186.52 ($false),
% 293.98/186.52 inference(unit_resolution,[status(thm)],[24386, 24379, 24339])).
% 293.98/186.52 tff(24388,plain,((~m_c_h_element_v_out(c_e_h_1, c_e, s11)) | m_c_h_element_v_in1(c_e_h_1, c_e, s10) | m_c_h_element_v_out(c_e_h_1, c_e, s10)), inference(lemma,lemma(discharge,[]))).
% 293.98/186.52 tff(24389,plain,
% 293.98/186.52 (m_c_h_element_v_in1(c_e_h_1, c_e, s10)),
% 293.98/186.52 inference(unit_resolution,[status(thm)],[24388, 24332, 24331])).
% 293.98/186.52 tff(24390,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_e, s10)), introduced(assumption)).
% 293.98/186.52 tff(24391,plain,
% 293.98/186.52 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_e, s10) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s10)) | (~node17(c_e_h_1, c_e, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s10) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s10)) | (~node17(c_e_h_1, c_e, s10)))),
% 293.98/186.52 inference(rewrite,[status(thm)],[])).
% 293.98/186.52 tff(24392,plain,
% 293.98/186.52 (((~m_c_h_element_v_in1(c_e_h_1, c_e, s10)) | m_c_h_element_v_in2(c_e_h_1, c_e, s10) | (~node17(c_e_h_1, c_e, s10))) <=> (m_c_h_element_v_in2(c_e_h_1, c_e, s10) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s10)) | (~node17(c_e_h_1, c_e, s10)))),
% 293.98/186.52 inference(rewrite,[status(thm)],[])).
% 293.98/186.52 tff(24393,plain,
% 293.98/186.52 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s10)) | m_c_h_element_v_in2(c_e_h_1, c_e, s10) | (~node17(c_e_h_1, c_e, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_e, s10) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s10)) | (~node17(c_e_h_1, c_e, s10))))),
% 293.98/186.52 inference(monotonicity,[status(thm)],[24392])).
% 293.98/186.52 tff(24394,plain,
% 293.98/186.52 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s10)) | m_c_h_element_v_in2(c_e_h_1, c_e, s10) | (~node17(c_e_h_1, c_e, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s10) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s10)) | (~node17(c_e_h_1, c_e, s10)))),
% 293.98/186.52 inference(transitivity,[status(thm)],[24393, 24391])).
% 293.98/186.52 tff(24395,plain,
% 293.98/186.52 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s10)) | m_c_h_element_v_in2(c_e_h_1, c_e, s10) | (~node17(c_e_h_1, c_e, s10)))),
% 293.98/186.52 inference(quant_inst,[status(thm)],[])).
% 293.98/186.52 tff(24396,plain,
% 293.98/186.52 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s10) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s10)) | (~node17(c_e_h_1, c_e, s10))),
% 293.98/186.52 inference(modus_ponens,[status(thm)],[24395, 24394])).
% 293.98/186.52 tff(24397,plain,
% 293.98/186.52 ((~m_c_h_element_v_in1(c_e_h_1, c_e, s10)) | (~node17(c_e_h_1, c_e, s10))),
% 293.98/186.52 inference(unit_resolution,[status(thm)],[24396, 919, 24390])).
% 293.98/186.52 tff(24398,plain,
% 293.98/186.52 (~node17(c_e_h_1, c_e, s10)),
% 293.98/186.52 inference(unit_resolution,[status(thm)],[24397, 24389])).
% 293.98/186.52 tff(24399,plain,
% 293.98/186.52 ($false),
% 293.98/186.52 inference(unit_resolution,[status(thm)],[24386, 24398, 24339])).
% 293.98/186.52 tff(24400,plain,((~m_c_h_element_v_out(c_e_h_1, c_e, s11)) | m_c_h_element_v_in2(c_e_h_1, c_e, s10) | m_c_h_element_v_out(c_e_h_1, c_e, s10)), inference(lemma,lemma(discharge,[]))).
% 293.98/186.52 tff(24401,plain,
% 293.98/186.52 (~m_c_h_element_v_out(c_e_h_1, c_e, s11)),
% 293.98/186.52 inference(unit_resolution,[status(thm)],[24400, 24330, 23321])).
% 293.98/186.52 tff(24402,assumption,(~m_c_h_element_v_out(c_e_h_1, c_e, s11)), introduced(assumption)).
% 293.98/186.52 tff(24403,plain,
% 293.98/186.52 (m_c_h_element_v_in2(c_e_h_1, c_e, s9)),
% 293.98/186.52 inference(unit_resolution,[status(thm)],[23319, 23260, 23015])).
% 293.98/186.52 tff(24404,plain,
% 293.98/186.52 (~node18(c_e_h_1, c_e, s9, s10)),
% 293.98/186.52 inference(unit_resolution,[status(thm)],[23301, 23260, 23015])).
% 293.98/186.52 tff(24405,plain,
% 293.98/186.52 (node17(c_e_h_1, c_e, s9)),
% 293.98/186.52 inference(unit_resolution,[status(thm)],[23309, 24404])).
% 293.98/186.52 tff(24406,plain,
% 293.98/186.52 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_e, s9)) | m_c_h_element_v_in1(c_e_h_1, c_e, s9) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s9)) | m_c_h_element_v_in1(c_e_h_1, c_e, s9) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s9)))),
% 293.98/186.52 inference(rewrite,[status(thm)],[])).
% 293.98/186.52 tff(24407,plain,
% 293.98/186.52 ((m_c_h_element_v_in1(c_e_h_1, c_e, s9) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s9)) | (~node17(c_e_h_1, c_e, s9))) <=> ((~node17(c_e_h_1, c_e, s9)) | m_c_h_element_v_in1(c_e_h_1, c_e, s9) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s9)))),
% 293.98/186.52 inference(rewrite,[status(thm)],[])).
% 293.98/186.52 tff(24408,plain,
% 293.98/186.52 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s9) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s9)) | (~node17(c_e_h_1, c_e, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_e, s9)) | m_c_h_element_v_in1(c_e_h_1, c_e, s9) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s9))))),
% 293.98/186.52 inference(monotonicity,[status(thm)],[24407])).
% 293.98/186.52 tff(24409,plain,
% 293.98/186.52 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s9) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s9)) | (~node17(c_e_h_1, c_e, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s9)) | m_c_h_element_v_in1(c_e_h_1, c_e, s9) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s9)))),
% 293.98/186.52 inference(transitivity,[status(thm)],[24408, 24406])).
% 293.98/186.52 tff(24410,plain,
% 293.98/186.52 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s9) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s9)) | (~node17(c_e_h_1, c_e, s9)))),
% 293.98/186.52 inference(quant_inst,[status(thm)],[])).
% 293.98/186.52 tff(24411,plain,
% 293.98/186.52 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s9)) | m_c_h_element_v_in1(c_e_h_1, c_e, s9) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s9))),
% 293.98/186.52 inference(modus_ponens,[status(thm)],[24410, 24409])).
% 293.98/186.52 tff(24412,plain,
% 293.98/186.52 ((~node17(c_e_h_1, c_e, s9)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s9))),
% 293.98/186.52 inference(unit_resolution,[status(thm)],[24411, 859, 23268])).
% 293.98/186.52 tff(24413,plain,
% 293.98/186.52 ($false),
% 293.98/186.52 inference(unit_resolution,[status(thm)],[24412, 24405, 24403])).
% 293.98/186.52 tff(24414,plain,((~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | m_c_h_element_v_in1(c_e_h_1, c_e, s9) | m_c_h_element_v_out(c_e_h_1, c_e, s9)), inference(lemma,lemma(discharge,[]))).
% 293.98/186.52 tff(24415,plain,
% 293.98/186.52 ((~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | m_c_h_element_v_in1(c_e_h_1, c_e, s9)),
% 293.98/186.52 inference(unit_resolution,[status(thm)],[24414, 23013])).
% 293.98/186.52 tff(24416,plain,
% 293.98/186.52 (m_c_h_element_v_in1(c_e_h_1, c_e, s9)),
% 293.98/186.52 inference(unit_resolution,[status(thm)],[24415, 23260])).
% 293.98/186.52 tff(24417,assumption,(m_c_h_element_v_in1(c_e_h_1, c_e, s9)), introduced(assumption)).
% 293.98/186.52 tff(24418,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_c, s9)), introduced(assumption)).
% 293.98/186.53 tff(24419,plain,
% 293.98/186.53 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s9)) | m_and_h_gate_v_out(c_e_h_1, c_c, s9))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s9)) | m_and_h_gate_v_out(c_e_h_1, c_c, s9))),
% 293.98/186.53 inference(rewrite,[status(thm)],[])).
% 293.98/186.53 tff(24420,plain,
% 293.98/186.53 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s9)) | m_and_h_gate_v_out(c_e_h_1, c_c, s9))),
% 293.98/186.53 inference(quant_inst,[status(thm)],[])).
% 293.98/186.53 tff(24421,plain,
% 293.98/186.53 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s9)) | m_and_h_gate_v_out(c_e_h_1, c_c, s9)),
% 293.98/186.53 inference(modus_ponens,[status(thm)],[24420, 24419])).
% 293.98/186.53 tff(24422,plain,
% 293.98/186.53 ($false),
% 293.98/186.53 inference(unit_resolution,[status(thm)],[24421, 131, 24418, 24417])).
% 293.98/186.53 tff(24423,plain,((~m_c_h_element_v_in1(c_e_h_1, c_e, s9)) | m_and_h_gate_v_out(c_e_h_1, c_c, s9)), inference(lemma,lemma(discharge,[]))).
% 293.98/186.53 tff(24424,plain,
% 293.98/186.53 (m_and_h_gate_v_out(c_e_h_1, c_c, s9)),
% 293.98/186.53 inference(unit_resolution,[status(thm)],[24423, 24416])).
% 293.98/186.53 tff(24425,assumption,(m_and_h_gate_v_out(c_e_h_1, c_c, s9)), introduced(assumption)).
% 293.98/186.53 tff(24426,assumption,(~m_mutex_h_half_v_out(c_e_h_1, c_a, s8)), introduced(assumption)).
% 293.98/186.53 tff(24427,assumption,(m_and_h_gate_v_in1(c_e_h_1, c_c, s8)), introduced(assumption)).
% 293.98/186.53 tff(24428,plain,
% 293.98/186.53 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_c, s8)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s8))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s8)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s8))),
% 293.98/186.53 inference(rewrite,[status(thm)],[])).
% 293.98/186.53 tff(24429,plain,
% 293.98/186.53 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_c, s8)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s8))),
% 293.98/186.53 inference(quant_inst,[status(thm)],[])).
% 293.98/186.53 tff(24430,plain,
% 293.98/186.53 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s8)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s8)),
% 293.98/186.53 inference(modus_ponens,[status(thm)],[24429, 24428])).
% 293.98/186.53 tff(24431,plain,
% 293.98/186.53 ($false),
% 293.98/186.53 inference(unit_resolution,[status(thm)],[24430, 567, 24426, 24427])).
% 293.98/186.53 tff(24432,plain,((~m_and_h_gate_v_in1(c_e_h_1, c_c, s8)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s8)), inference(lemma,lemma(discharge,[]))).
% 293.98/186.53 tff(24433,plain,
% 293.98/186.53 (~m_and_h_gate_v_in1(c_e_h_1, c_c, s8)),
% 293.98/186.53 inference(unit_resolution,[status(thm)],[24432, 24426])).
% 293.98/186.53 tff(24434,assumption,(~m_and_h_gate_v_in1(c_e_h_1, c_c, s8)), introduced(assumption)).
% 293.98/186.53 tff(24435,assumption,(node20(c_e_h_1, c_c, s8)), introduced(assumption)).
% 293.98/186.53 tff(24436,plain,
% 293.98/186.53 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_c, s8)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_c, s8)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s8))),
% 293.98/186.53 inference(rewrite,[status(thm)],[])).
% 293.98/186.53 tff(24437,plain,
% 293.98/186.53 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_c, s8)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s8))),
% 293.98/186.53 inference(quant_inst,[status(thm)],[])).
% 293.98/186.53 tff(24438,plain,
% 293.98/186.53 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_c, s8)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s8)),
% 293.98/186.53 inference(modus_ponens,[status(thm)],[24437, 24436])).
% 293.98/186.53 tff(24439,plain,
% 293.98/186.53 ($false),
% 293.98/186.53 inference(unit_resolution,[status(thm)],[24438, 38, 24435, 24434])).
% 293.98/186.53 tff(24440,plain,(m_and_h_gate_v_in1(c_e_h_1, c_c, s8) | (~node20(c_e_h_1, c_c, s8))), inference(lemma,lemma(discharge,[]))).
% 293.98/186.53 tff(24441,plain,
% 293.98/186.53 (~node20(c_e_h_1, c_c, s8)),
% 293.98/186.53 inference(unit_resolution,[status(thm)],[24440, 24433])).
% 293.98/186.53 tff(24442,assumption,(~node20(c_e_h_1, c_c, s8)), introduced(assumption)).
% 293.98/186.53 tff(24443,assumption,(node21(c_e_h_1, c_c, s8, s9)), introduced(assumption)).
% 293.98/186.53 tff(24444,plain,
% 293.98/186.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_c, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s9)) | (~node21(c_e_h_1, c_c, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_c, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s9)) | (~node21(c_e_h_1, c_c, s8, s9)))),
% 293.98/186.53 inference(rewrite,[status(thm)],[])).
% 293.98/186.53 tff(24445,plain,
% 293.98/186.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_c, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s9)) | (~node21(c_e_h_1, c_c, s8, s9)))),
% 293.98/186.53 inference(quant_inst,[status(thm)],[])).
% 293.98/186.53 tff(24446,plain,
% 293.98/186.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_c, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s9)) | (~node21(c_e_h_1, c_c, s8, s9))),
% 293.98/186.53 inference(modus_ponens,[status(thm)],[24445, 24444])).
% 293.98/186.53 tff(24447,plain,
% 293.98/186.53 ($false),
% 293.98/186.53 inference(unit_resolution,[status(thm)],[24446, 52, 24425, 24443, 24442])).
% 293.98/186.53 tff(24448,plain,((~node21(c_e_h_1, c_c, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s9)) | node20(c_e_h_1, c_c, s8)), inference(lemma,lemma(discharge,[]))).
% 293.98/186.53 tff(24449,plain,
% 293.98/186.53 (~node21(c_e_h_1, c_c, s8, s9)),
% 293.98/186.53 inference(unit_resolution,[status(thm)],[24448, 24425, 24442])).
% 293.98/186.53 tff(24450,plain,
% 293.98/186.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s8, s9)) | node21(c_e_h_1, c_c, s8, s9) | node22(c_e_h_1, c_c, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_1, c_c, s8, s9) | node22(c_e_h_1, c_c, s8, s9))),
% 293.98/186.53 inference(rewrite,[status(thm)],[])).
% 293.98/186.53 tff(24451,plain,
% 293.98/186.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s8, s9)) | node21(c_e_h_1, c_c, s8, s9) | node22(c_e_h_1, c_c, s8, s9))),
% 293.98/186.53 inference(quant_inst,[status(thm)],[])).
% 293.98/186.53 tff(24452,plain,
% 293.98/186.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_1, c_c, s8, s9) | node22(c_e_h_1, c_c, s8, s9)),
% 293.98/186.53 inference(modus_ponens,[status(thm)],[24451, 24450])).
% 293.98/186.53 tff(24453,plain,
% 293.98/186.53 (node21(c_e_h_1, c_c, s8, s9) | node22(c_e_h_1, c_c, s8, s9)),
% 293.98/186.53 inference(unit_resolution,[status(thm)],[24452, 82, 1993])).
% 293.98/186.53 tff(24454,plain,
% 293.98/186.53 (node22(c_e_h_1, c_c, s8, s9)),
% 293.98/186.53 inference(unit_resolution,[status(thm)],[24453, 24449])).
% 293.98/186.53 tff(24455,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_c, s8)), introduced(assumption)).
% 293.98/186.53 tff(24456,plain,
% 293.98/186.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_c, s9)) | (~node22(c_e_h_1, c_c, s8, s9)) | m_and_h_gate_v_out(c_e_h_1, c_c, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s9)) | (~node22(c_e_h_1, c_c, s8, s9)) | m_and_h_gate_v_out(c_e_h_1, c_c, s8))),
% 293.98/186.53 inference(rewrite,[status(thm)],[])).
% 293.98/186.53 tff(24457,plain,
% 293.98/186.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_c, s9)) | (~node22(c_e_h_1, c_c, s8, s9)) | m_and_h_gate_v_out(c_e_h_1, c_c, s8))),
% 293.98/186.53 inference(quant_inst,[status(thm)],[])).
% 293.98/186.53 tff(24458,plain,
% 293.98/186.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s9)) | (~node22(c_e_h_1, c_c, s8, s9)) | m_and_h_gate_v_out(c_e_h_1, c_c, s8)),
% 293.98/186.53 inference(modus_ponens,[status(thm)],[24457, 24456])).
% 293.98/186.53 tff(24459,plain,
% 293.98/186.53 ($false),
% 293.98/186.53 inference(unit_resolution,[status(thm)],[24458, 108, 24455, 24425, 24454])).
% 293.98/186.53 tff(24460,plain,((~m_and_h_gate_v_out(c_e_h_1, c_c, s9)) | m_and_h_gate_v_out(c_e_h_1, c_c, s8) | node20(c_e_h_1, c_c, s8)), inference(lemma,lemma(discharge,[]))).
% 293.98/186.53 tff(24461,plain,
% 293.98/186.53 (m_and_h_gate_v_out(c_e_h_1, c_c, s8)),
% 293.98/186.53 inference(unit_resolution,[status(thm)],[24460, 24441, 24425])).
% 293.98/186.53 tff(24462,assumption,(m_mutex_h_half_v_out(c_e_h_1, c_a, s7)), introduced(assumption)).
% 293.98/186.53 tff(24463,assumption,(node13(c_e_h_1, c_a, s7, s8)), introduced(assumption)).
% 293.98/186.53 tff(24464,plain,
% 293.98/186.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | ((~node13(c_e_h_1, c_a, s7, s8)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s7)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (~node13(c_e_h_1, c_a, s7, s8)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s7)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s8))),
% 293.98/186.53 inference(rewrite,[status(thm)],[])).
% 293.98/186.53 tff(24465,plain,
% 293.98/186.53 ((m_mutex_h_half_v_out(c_e_h_1, c_a, s8) | (~node13(c_e_h_1, c_a, s7, s8)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s7))) <=> ((~node13(c_e_h_1, c_a, s7, s8)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s7)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s8))),
% 293.98/186.53 inference(rewrite,[status(thm)],[])).
% 293.98/186.53 tff(24466,plain,
% 293.98/186.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_1, c_a, s8) | (~node13(c_e_h_1, c_a, s7, s8)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | ((~node13(c_e_h_1, c_a, s7, s8)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s7)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s8)))),
% 293.98/186.53 inference(monotonicity,[status(thm)],[24465])).
% 293.98/186.53 tff(24467,plain,
% 293.98/186.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_1, c_a, s8) | (~node13(c_e_h_1, c_a, s7, s8)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (~node13(c_e_h_1, c_a, s7, s8)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s7)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s8))),
% 293.98/186.53 inference(transitivity,[status(thm)],[24466, 24464])).
% 293.98/186.53 tff(24468,plain,
% 293.98/186.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_1, c_a, s8) | (~node13(c_e_h_1, c_a, s7, s8)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s7)))),
% 293.98/186.53 inference(quant_inst,[status(thm)],[])).
% 293.98/186.53 tff(24469,plain,
% 293.98/186.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (~node13(c_e_h_1, c_a, s7, s8)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s7)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s8)),
% 293.98/186.53 inference(modus_ponens,[status(thm)],[24468, 24467])).
% 293.98/186.53 tff(24470,plain,
% 293.98/186.53 ($false),
% 293.98/186.53 inference(unit_resolution,[status(thm)],[24469, 1459, 24463, 24462, 24426])).
% 293.98/186.53 tff(24471,plain,((~node13(c_e_h_1, c_a, s7, s8)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s7)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s8)), inference(lemma,lemma(discharge,[]))).
% 293.98/186.53 tff(24472,plain,
% 293.98/186.53 (~node13(c_e_h_1, c_a, s7, s8)),
% 293.98/186.53 inference(unit_resolution,[status(thm)],[24471, 24426, 24462])).
% 293.98/186.53 tff(24473,assumption,(m_mutex_h_half_v_inp(c_e_h_1, c_a, s7)), introduced(assumption)).
% 293.98/186.53 tff(24474,assumption,(node12(c_e_h_1, c_a, s7, s8)), introduced(assumption)).
% 293.98/186.54 tff(24475,plain,
% 293.98/186.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~m_mutex_h_half_v_inp(c_e_h_1, c_a, s7)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s8) | (~node12(c_e_h_1, c_a, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s7)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s8) | (~node12(c_e_h_1, c_a, s7, s8)))),
% 293.98/186.54 inference(rewrite,[status(thm)],[])).
% 293.98/186.54 tff(24476,plain,
% 293.98/186.54 (((~node12(c_e_h_1, c_a, s7, s8)) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s7)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s8)) <=> ((~m_mutex_h_half_v_inp(c_e_h_1, c_a, s7)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s8) | (~node12(c_e_h_1, c_a, s7, s8)))),
% 293.98/186.54 inference(rewrite,[status(thm)],[])).
% 293.98/186.54 tff(24477,plain,
% 293.98/186.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_1, c_a, s7, s8)) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s7)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~m_mutex_h_half_v_inp(c_e_h_1, c_a, s7)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s8) | (~node12(c_e_h_1, c_a, s7, s8))))),
% 293.98/186.54 inference(monotonicity,[status(thm)],[24476])).
% 293.98/186.54 tff(24478,plain,
% 293.98/186.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_1, c_a, s7, s8)) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s7)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s7)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s8) | (~node12(c_e_h_1, c_a, s7, s8)))),
% 293.98/186.54 inference(transitivity,[status(thm)],[24477, 24475])).
% 293.98/186.54 tff(24479,plain,
% 293.98/186.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_1, c_a, s7, s8)) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s7)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s8))),
% 293.98/186.54 inference(quant_inst,[status(thm)],[])).
% 293.98/186.54 tff(24480,plain,
% 293.98/186.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s7)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s8) | (~node12(c_e_h_1, c_a, s7, s8))),
% 293.98/186.54 inference(modus_ponens,[status(thm)],[24479, 24478])).
% 293.98/186.54 tff(24481,plain,
% 293.98/186.54 ($false),
% 293.98/186.54 inference(unit_resolution,[status(thm)],[24480, 1483, 24474, 24426, 24473])).
% 293.98/186.54 tff(24482,plain,((~node12(c_e_h_1, c_a, s7, s8)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s8) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s7))), inference(lemma,lemma(discharge,[]))).
% 293.98/186.54 tff(24483,plain,
% 293.98/186.54 (~node12(c_e_h_1, c_a, s7, s8)),
% 293.98/186.54 inference(unit_resolution,[status(thm)],[24482, 24426, 24473])).
% 293.98/186.54 tff(24484,plain,
% 293.98/186.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s7, s8)) | node12(c_e_h_1, c_a, s7, s8) | node13(c_e_h_1, c_a, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s7, s8)) | node12(c_e_h_1, c_a, s7, s8) | node13(c_e_h_1, c_a, s7, s8))),
% 293.98/186.54 inference(rewrite,[status(thm)],[])).
% 293.98/186.54 tff(24485,plain,
% 293.98/186.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s7, s8)) | node12(c_e_h_1, c_a, s7, s8) | node13(c_e_h_1, c_a, s7, s8))),
% 293.98/186.54 inference(quant_inst,[status(thm)],[])).
% 293.98/186.54 tff(24486,plain,
% 293.98/186.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s7, s8)) | node12(c_e_h_1, c_a, s7, s8) | node13(c_e_h_1, c_a, s7, s8)),
% 293.98/186.54 inference(modus_ponens,[status(thm)],[24485, 24484])).
% 293.98/186.54 tff(24487,plain,
% 293.98/186.54 (node12(c_e_h_1, c_a, s7, s8) | node13(c_e_h_1, c_a, s7, s8)),
% 293.98/186.54 inference(unit_resolution,[status(thm)],[24486, 439, 1938])).
% 293.98/186.54 tff(24488,plain,
% 293.98/186.54 ($false),
% 293.98/186.54 inference(unit_resolution,[status(thm)],[24487, 24483, 24472])).
% 293.98/186.54 tff(24489,plain,(m_mutex_h_half_v_out(c_e_h_1, c_a, s8) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s7)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s7))), inference(lemma,lemma(discharge,[]))).
% 293.98/186.54 tff(24490,plain,
% 293.98/186.54 (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s7)),
% 293.98/186.54 inference(unit_resolution,[status(thm)],[24489, 24462, 24426])).
% 293.98/186.54 tff(24491,assumption,(m_user_v_req(c_e_h_1, c_u, s7)), introduced(assumption)).
% 293.98/186.54 tff(24492,assumption,(~m_mutex_h_half_v_inp(c_e_h_1, c_a, s7)), introduced(assumption)).
% 293.98/186.54 tff(24493,plain,
% 293.98/186.54 (((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | ((~m_user_v_req(c_e_h_1, c_u, s7)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s7))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | (~m_user_v_req(c_e_h_1, c_u, s7)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s7))),
% 293.98/186.54 inference(rewrite,[status(thm)],[])).
% 293.98/186.54 tff(24494,plain,
% 293.98/186.54 ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | ((~m_user_v_req(c_e_h_1, c_u, s7)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s7))),
% 293.98/186.54 inference(quant_inst,[status(thm)],[])).
% 293.98/186.54 tff(24495,plain,
% 293.98/186.54 ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | (~m_user_v_req(c_e_h_1, c_u, s7)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s7)),
% 293.98/186.54 inference(modus_ponens,[status(thm)],[24494, 24493])).
% 293.98/186.54 tff(24496,plain,
% 293.98/186.54 ($false),
% 293.98/186.54 inference(unit_resolution,[status(thm)],[24495, 1426, 24492, 24491])).
% 293.98/186.54 tff(24497,plain,(m_mutex_h_half_v_inp(c_e_h_1, c_a, s7) | (~m_user_v_req(c_e_h_1, c_u, s7))), inference(lemma,lemma(discharge,[]))).
% 293.98/186.54 tff(24498,plain,
% 293.98/186.54 (~m_user_v_req(c_e_h_1, c_u, s7)),
% 293.98/186.54 inference(unit_resolution,[status(thm)],[24497, 24490])).
% 293.98/186.54 tff(24499,assumption,(m_and_h_gate_v_in1(c_e_h_1, c_r, s4)), introduced(assumption)).
% 293.98/186.54 tff(24500,plain,
% 293.98/186.54 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_r, s4)) | m_c_h_element_v_out(c_e_h_1, c_e, s4))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_r, s4)) | m_c_h_element_v_out(c_e_h_1, c_e, s4))),
% 293.98/186.54 inference(rewrite,[status(thm)],[])).
% 293.98/186.54 tff(24501,plain,
% 293.98/186.54 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_r, s4)) | m_c_h_element_v_out(c_e_h_1, c_e, s4))),
% 293.98/186.54 inference(quant_inst,[status(thm)],[])).
% 293.98/186.54 tff(24502,plain,
% 293.98/186.54 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_r, s4)) | m_c_h_element_v_out(c_e_h_1, c_e, s4)),
% 293.98/186.54 inference(modus_ponens,[status(thm)],[24501, 24500])).
% 293.98/186.54 tff(24503,plain,
% 293.98/186.54 ($false),
% 293.98/186.54 inference(unit_resolution,[status(thm)],[24502, 24, 17745, 24499])).
% 293.98/186.54 tff(24504,plain,(~m_and_h_gate_v_in1(c_e_h_1, c_r, s4)), inference(lemma,lemma(discharge,[]))).
% 293.98/186.54 tff(24505,plain,
% 293.98/186.54 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s4)) | m_and_h_gate_v_in1(c_e_h_1, c_r, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_r, s4)) | m_and_h_gate_v_in1(c_e_h_1, c_r, s4))),
% 293.98/186.54 inference(rewrite,[status(thm)],[])).
% 293.98/186.54 tff(24506,plain,
% 293.98/186.54 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s4)) | m_and_h_gate_v_in1(c_e_h_1, c_r, s4))),
% 293.98/186.54 inference(quant_inst,[status(thm)],[])).
% 293.98/186.54 tff(24507,plain,
% 293.98/186.54 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_r, s4)) | m_and_h_gate_v_in1(c_e_h_1, c_r, s4)),
% 293.98/186.54 inference(modus_ponens,[status(thm)],[24506, 24505])).
% 293.98/186.54 tff(24508,plain,
% 293.98/186.54 (~node20(c_e_h_1, c_r, s4)),
% 293.98/186.54 inference(unit_resolution,[status(thm)],[24507, 38, 24504])).
% 293.98/186.54 tff(24509,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s5)), introduced(assumption)).
% 293.98/186.54 tff(24510,assumption,(~node20(c_e_h_1, c_r, s4)), introduced(assumption)).
% 293.98/186.54 tff(24511,assumption,(node22(c_e_h_1, c_r, s4, s5)), introduced(assumption)).
% 293.98/186.54 tff(24512,plain,
% 293.98/186.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s5)) | (~node22(c_e_h_1, c_r, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_r, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s5)) | (~node22(c_e_h_1, c_r, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_r, s4))),
% 293.98/186.54 inference(rewrite,[status(thm)],[])).
% 293.98/186.54 tff(24513,plain,
% 293.98/186.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s5)) | (~node22(c_e_h_1, c_r, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_r, s4))),
% 293.98/186.54 inference(quant_inst,[status(thm)],[])).
% 293.98/186.54 tff(24514,plain,
% 293.98/186.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s5)) | (~node22(c_e_h_1, c_r, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_r, s4)),
% 293.98/186.54 inference(modus_ponens,[status(thm)],[24513, 24512])).
% 293.98/186.54 tff(24515,plain,
% 293.98/186.54 ($false),
% 293.98/186.54 inference(unit_resolution,[status(thm)],[24514, 108, 24511, 16422, 24509])).
% 293.98/186.54 tff(24516,plain,((~node22(c_e_h_1, c_r, s4, s5)) | m_and_h_gate_v_out(c_e_h_1, c_r, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s5))), inference(lemma,lemma(discharge,[]))).
% 293.98/186.54 tff(24517,plain,
% 293.98/186.54 (~node22(c_e_h_1, c_r, s4, s5)),
% 293.98/186.54 inference(unit_resolution,[status(thm)],[24516, 24509, 16422])).
% 293.98/186.54 tff(24518,plain,
% 293.98/186.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_1, c_r, s4, s5) | node22(c_e_h_1, c_r, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_1, c_r, s4, s5) | node22(c_e_h_1, c_r, s4, s5))),
% 293.98/186.54 inference(rewrite,[status(thm)],[])).
% 293.98/186.54 tff(24519,plain,
% 293.98/186.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_1, c_r, s4, s5) | node22(c_e_h_1, c_r, s4, s5))),
% 293.98/186.54 inference(quant_inst,[status(thm)],[])).
% 293.98/186.54 tff(24520,plain,
% 293.98/186.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_1, c_r, s4, s5) | node22(c_e_h_1, c_r, s4, s5)),
% 293.98/186.54 inference(modus_ponens,[status(thm)],[24519, 24518])).
% 293.98/186.54 tff(24521,plain,
% 293.98/186.54 (node21(c_e_h_1, c_r, s4, s5) | node22(c_e_h_1, c_r, s4, s5)),
% 293.98/186.54 inference(unit_resolution,[status(thm)],[24520, 82, 1028])).
% 293.98/186.54 tff(24522,plain,
% 293.98/186.54 (node21(c_e_h_1, c_r, s4, s5)),
% 293.98/186.54 inference(unit_resolution,[status(thm)],[24521, 24517])).
% 293.98/186.54 tff(24523,plain,
% 293.98/186.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s5)) | (~node21(c_e_h_1, c_r, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s5)) | (~node21(c_e_h_1, c_r, s4, s5)))),
% 293.98/186.54 inference(rewrite,[status(thm)],[])).
% 293.98/186.54 tff(24524,plain,
% 293.98/186.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s5)) | (~node21(c_e_h_1, c_r, s4, s5)))),
% 293.98/186.54 inference(quant_inst,[status(thm)],[])).
% 293.98/186.54 tff(24525,plain,
% 293.98/186.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s4) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s5)) | (~node21(c_e_h_1, c_r, s4, s5))),
% 293.98/186.55 inference(modus_ponens,[status(thm)],[24524, 24523])).
% 293.98/186.55 tff(24526,plain,
% 293.98/186.55 ($false),
% 293.98/186.55 inference(unit_resolution,[status(thm)],[24525, 52, 24522, 24510, 24509])).
% 293.98/186.55 tff(24527,plain,((~m_and_h_gate_v_out(c_e_h_1, c_r, s5)) | node20(c_e_h_1, c_r, s4) | m_and_h_gate_v_out(c_e_h_1, c_r, s4)), inference(lemma,lemma(discharge,[]))).
% 293.98/186.55 tff(24528,plain,
% 293.98/186.55 ((~m_and_h_gate_v_out(c_e_h_1, c_r, s5)) | m_and_h_gate_v_out(c_e_h_1, c_r, s4)),
% 293.98/186.55 inference(unit_resolution,[status(thm)],[24527, 24508])).
% 293.98/186.55 tff(24529,plain,
% 293.98/186.55 (~m_and_h_gate_v_out(c_e_h_1, c_r, s5)),
% 293.98/186.55 inference(unit_resolution,[status(thm)],[24528, 16421])).
% 293.98/186.55 tff(24530,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s6)), introduced(assumption)).
% 293.98/186.55 tff(24531,plain,
% 293.98/186.55 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_r, s5)) | m_c_h_element_v_out(c_e_h_1, c_e, s5))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_r, s5)) | m_c_h_element_v_out(c_e_h_1, c_e, s5))),
% 293.98/186.55 inference(rewrite,[status(thm)],[])).
% 293.98/186.55 tff(24532,plain,
% 293.98/186.55 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_r, s5)) | m_c_h_element_v_out(c_e_h_1, c_e, s5))),
% 293.98/186.55 inference(quant_inst,[status(thm)],[])).
% 293.98/186.55 tff(24533,plain,
% 293.98/186.55 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_r, s5)) | m_c_h_element_v_out(c_e_h_1, c_e, s5)),
% 293.98/186.55 inference(modus_ponens,[status(thm)],[24532, 24531])).
% 293.98/186.55 tff(24534,plain,
% 293.98/186.55 (~m_and_h_gate_v_in1(c_e_h_1, c_r, s5)),
% 293.98/186.55 inference(unit_resolution,[status(thm)],[24533, 24, 17808])).
% 293.98/186.55 tff(24535,plain,
% 293.98/186.55 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s5)) | m_and_h_gate_v_in1(c_e_h_1, c_r, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_r, s5)) | m_and_h_gate_v_in1(c_e_h_1, c_r, s5))),
% 293.98/186.55 inference(rewrite,[status(thm)],[])).
% 293.98/186.55 tff(24536,plain,
% 293.98/186.55 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s5)) | m_and_h_gate_v_in1(c_e_h_1, c_r, s5))),
% 293.98/186.55 inference(quant_inst,[status(thm)],[])).
% 293.98/186.55 tff(24537,plain,
% 293.98/186.55 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_r, s5)) | m_and_h_gate_v_in1(c_e_h_1, c_r, s5)),
% 293.98/186.55 inference(modus_ponens,[status(thm)],[24536, 24535])).
% 293.98/186.55 tff(24538,plain,
% 293.98/186.55 (~node20(c_e_h_1, c_r, s5)),
% 293.98/186.55 inference(unit_resolution,[status(thm)],[24537, 38, 24534])).
% 293.98/186.55 tff(24539,assumption,(~node20(c_e_h_1, c_r, s5)), introduced(assumption)).
% 293.98/186.55 tff(24540,assumption,(node21(c_e_h_1, c_r, s5, s6)), introduced(assumption)).
% 293.98/186.55 tff(24541,plain,
% 293.98/186.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s6)) | (~node21(c_e_h_1, c_r, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s6)) | (~node21(c_e_h_1, c_r, s5, s6)))),
% 293.98/186.55 inference(rewrite,[status(thm)],[])).
% 293.98/186.55 tff(24542,plain,
% 293.98/186.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s6)) | (~node21(c_e_h_1, c_r, s5, s6)))),
% 293.98/186.55 inference(quant_inst,[status(thm)],[])).
% 293.98/186.55 tff(24543,plain,
% 293.98/186.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s6)) | (~node21(c_e_h_1, c_r, s5, s6))),
% 293.98/186.55 inference(modus_ponens,[status(thm)],[24542, 24541])).
% 293.98/186.55 tff(24544,plain,
% 293.98/186.55 ($false),
% 293.98/186.55 inference(unit_resolution,[status(thm)],[24543, 52, 24540, 24539, 24530])).
% 293.98/186.55 tff(24545,plain,((~node21(c_e_h_1, c_r, s5, s6)) | node20(c_e_h_1, c_r, s5) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s6))), inference(lemma,lemma(discharge,[]))).
% 293.98/186.55 tff(24546,plain,
% 293.98/186.55 ((~node21(c_e_h_1, c_r, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s6))),
% 293.98/186.55 inference(unit_resolution,[status(thm)],[24545, 24538])).
% 293.98/186.55 tff(24547,plain,
% 293.98/186.55 (~node21(c_e_h_1, c_r, s5, s6)),
% 293.98/186.55 inference(unit_resolution,[status(thm)],[24546, 24530])).
% 293.98/186.55 tff(24548,plain,
% 293.98/186.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_1, c_r, s5, s6) | node22(c_e_h_1, c_r, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_1, c_r, s5, s6) | node22(c_e_h_1, c_r, s5, s6))),
% 293.98/186.55 inference(rewrite,[status(thm)],[])).
% 293.98/186.55 tff(24549,plain,
% 293.98/186.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_1, c_r, s5, s6) | node22(c_e_h_1, c_r, s5, s6))),
% 293.98/186.55 inference(quant_inst,[status(thm)],[])).
% 293.98/186.55 tff(24550,plain,
% 293.98/186.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_1, c_r, s5, s6) | node22(c_e_h_1, c_r, s5, s6)),
% 293.98/186.55 inference(modus_ponens,[status(thm)],[24549, 24548])).
% 293.98/186.55 tff(24551,plain,
% 293.98/186.55 (node21(c_e_h_1, c_r, s5, s6) | node22(c_e_h_1, c_r, s5, s6)),
% 293.98/186.55 inference(unit_resolution,[status(thm)],[24550, 82, 1406])).
% 293.98/186.55 tff(24552,plain,
% 293.98/186.55 (node22(c_e_h_1, c_r, s5, s6)),
% 293.98/186.55 inference(unit_resolution,[status(thm)],[24551, 24547])).
% 293.98/186.55 tff(24553,plain,
% 293.98/186.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s6)) | (~node22(c_e_h_1, c_r, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_r, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s6)) | (~node22(c_e_h_1, c_r, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_r, s5))),
% 293.98/186.55 inference(rewrite,[status(thm)],[])).
% 293.98/186.55 tff(24554,plain,
% 293.98/186.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s6)) | (~node22(c_e_h_1, c_r, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_r, s5))),
% 293.98/186.55 inference(quant_inst,[status(thm)],[])).
% 293.98/186.55 tff(24555,plain,
% 293.98/186.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s6)) | (~node22(c_e_h_1, c_r, s5, s6)) | m_and_h_gate_v_out(c_e_h_1, c_r, s5)),
% 293.98/186.55 inference(modus_ponens,[status(thm)],[24554, 24553])).
% 293.98/186.55 tff(24556,plain,
% 293.98/186.55 ($false),
% 293.98/186.55 inference(unit_resolution,[status(thm)],[24555, 108, 24552, 24530, 24529])).
% 293.98/186.55 tff(24557,plain,(~m_and_h_gate_v_out(c_e_h_1, c_r, s6)), inference(lemma,lemma(discharge,[]))).
% 293.98/186.55 tff(24558,plain,
% 293.98/186.55 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s6)) | m_and_h_gate_v_out(c_e_h_1, c_r, s6))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s6)) | m_and_h_gate_v_out(c_e_h_1, c_r, s6))),
% 293.98/186.55 inference(rewrite,[status(thm)],[])).
% 293.98/186.55 tff(24559,plain,
% 293.98/186.55 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s6)) | m_and_h_gate_v_out(c_e_h_1, c_r, s6))),
% 293.98/186.55 inference(quant_inst,[status(thm)],[])).
% 293.98/186.55 tff(24560,plain,
% 293.98/186.55 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s6)) | m_and_h_gate_v_out(c_e_h_1, c_r, s6)),
% 293.98/186.55 inference(modus_ponens,[status(thm)],[24559, 24558])).
% 293.98/186.56 tff(24561,plain,
% 293.98/186.56 (~m_user_v_ack(c_e_h_1, c_u, s6)),
% 293.98/186.56 inference(unit_resolution,[status(thm)],[24560, 268, 24557])).
% 293.98/186.56 tff(24562,assumption,(~m_user_v_req(c_e_h_1, c_u, s7)), introduced(assumption)).
% 293.98/186.56 tff(24563,assumption,(m_user_v_req(c_e_h_1, c_u, s6)), introduced(assumption)).
% 293.98/186.56 tff(24564,assumption,(~m_user_v_ack(c_e_h_1, c_u, s6)), introduced(assumption)).
% 293.98/186.56 tff(24565,assumption,(node7(c_e_h_1, c_u, s6, s7)), introduced(assumption)).
% 293.98/186.56 tff(24566,plain,
% 293.98/186.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | ((~node7(c_e_h_1, c_u, s6, s7)) | m_user_v_ack(c_e_h_1, c_u, s6) | m_user_v_req(c_e_h_1, c_u, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | (~node7(c_e_h_1, c_u, s6, s7)) | m_user_v_ack(c_e_h_1, c_u, s6) | m_user_v_req(c_e_h_1, c_u, s7))),
% 293.98/186.56 inference(rewrite,[status(thm)],[])).
% 293.98/186.56 tff(24567,plain,
% 293.98/186.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | ((~node7(c_e_h_1, c_u, s6, s7)) | m_user_v_ack(c_e_h_1, c_u, s6) | m_user_v_req(c_e_h_1, c_u, s7))),
% 293.98/186.56 inference(quant_inst,[status(thm)],[])).
% 293.98/186.56 tff(24568,plain,
% 293.98/186.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | (~node7(c_e_h_1, c_u, s6, s7)) | m_user_v_ack(c_e_h_1, c_u, s6) | m_user_v_req(c_e_h_1, c_u, s7)),
% 293.98/186.56 inference(modus_ponens,[status(thm)],[24567, 24566])).
% 293.98/186.56 tff(24569,plain,
% 293.98/186.56 ($false),
% 293.98/186.56 inference(unit_resolution,[status(thm)],[24568, 284, 24564, 24565, 24562])).
% 293.98/186.56 tff(24570,plain,((~node7(c_e_h_1, c_u, s6, s7)) | m_user_v_ack(c_e_h_1, c_u, s6) | m_user_v_req(c_e_h_1, c_u, s7)), inference(lemma,lemma(discharge,[]))).
% 293.98/186.56 tff(24571,plain,
% 293.98/186.56 (~node7(c_e_h_1, c_u, s6, s7)),
% 293.98/186.56 inference(unit_resolution,[status(thm)],[24570, 24562, 24564])).
% 293.98/186.56 tff(24572,plain,
% 293.98/186.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | ((~trans(s6, s7)) | node7(c_e_h_1, c_u, s6, s7) | node8(c_e_h_1, c_u, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | (~trans(s6, s7)) | node7(c_e_h_1, c_u, s6, s7) | node8(c_e_h_1, c_u, s6, s7))),
% 293.98/186.56 inference(rewrite,[status(thm)],[])).
% 293.98/186.56 tff(24573,plain,
% 293.98/186.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | ((~trans(s6, s7)) | node7(c_e_h_1, c_u, s6, s7) | node8(c_e_h_1, c_u, s6, s7))),
% 293.98/186.56 inference(quant_inst,[status(thm)],[])).
% 293.98/186.56 tff(24574,plain,
% 293.98/186.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | (~trans(s6, s7)) | node7(c_e_h_1, c_u, s6, s7) | node8(c_e_h_1, c_u, s6, s7)),
% 293.98/186.56 inference(modus_ponens,[status(thm)],[24573, 24572])).
% 293.98/186.56 tff(24575,plain,
% 293.98/186.56 (node7(c_e_h_1, c_u, s6, s7) | node8(c_e_h_1, c_u, s6, s7)),
% 293.98/186.56 inference(unit_resolution,[status(thm)],[24574, 328, 1844])).
% 293.98/186.56 tff(24576,plain,
% 293.98/186.56 (node8(c_e_h_1, c_u, s6, s7)),
% 293.98/186.56 inference(unit_resolution,[status(thm)],[24575, 24571])).
% 293.98/186.56 tff(24577,plain,
% 293.98/186.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | ((~m_user_v_req(c_e_h_1, c_u, s6)) | m_user_v_req(c_e_h_1, c_u, s7) | (~node8(c_e_h_1, c_u, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (~m_user_v_req(c_e_h_1, c_u, s6)) | m_user_v_req(c_e_h_1, c_u, s7) | (~node8(c_e_h_1, c_u, s6, s7)))),
% 293.98/186.56 inference(rewrite,[status(thm)],[])).
% 293.98/186.56 tff(24578,plain,
% 293.98/186.56 ((m_user_v_req(c_e_h_1, c_u, s7) | (~node8(c_e_h_1, c_u, s6, s7)) | (~m_user_v_req(c_e_h_1, c_u, s6))) <=> ((~m_user_v_req(c_e_h_1, c_u, s6)) | m_user_v_req(c_e_h_1, c_u, s7) | (~node8(c_e_h_1, c_u, s6, s7)))),
% 293.98/186.56 inference(rewrite,[status(thm)],[])).
% 293.98/186.56 tff(24579,plain,
% 293.98/186.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_1, c_u, s7) | (~node8(c_e_h_1, c_u, s6, s7)) | (~m_user_v_req(c_e_h_1, c_u, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | ((~m_user_v_req(c_e_h_1, c_u, s6)) | m_user_v_req(c_e_h_1, c_u, s7) | (~node8(c_e_h_1, c_u, s6, s7))))),
% 293.98/186.56 inference(monotonicity,[status(thm)],[24578])).
% 293.98/186.56 tff(24580,plain,
% 293.98/186.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_1, c_u, s7) | (~node8(c_e_h_1, c_u, s6, s7)) | (~m_user_v_req(c_e_h_1, c_u, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (~m_user_v_req(c_e_h_1, c_u, s6)) | m_user_v_req(c_e_h_1, c_u, s7) | (~node8(c_e_h_1, c_u, s6, s7)))),
% 293.98/186.56 inference(transitivity,[status(thm)],[24579, 24577])).
% 293.98/186.56 tff(24581,plain,
% 293.98/186.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_1, c_u, s7) | (~node8(c_e_h_1, c_u, s6, s7)) | (~m_user_v_req(c_e_h_1, c_u, s6)))),
% 293.98/186.56 inference(quant_inst,[status(thm)],[])).
% 293.98/186.56 tff(24582,plain,
% 293.98/186.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (~m_user_v_req(c_e_h_1, c_u, s6)) | m_user_v_req(c_e_h_1, c_u, s7) | (~node8(c_e_h_1, c_u, s6, s7))),
% 293.98/186.56 inference(modus_ponens,[status(thm)],[24581, 24580])).
% 293.98/186.56 tff(24583,plain,
% 293.98/186.56 ($false),
% 293.98/186.56 inference(unit_resolution,[status(thm)],[24582, 302, 24576, 24563, 24562])).
% 293.98/186.56 tff(24584,plain,(m_user_v_req(c_e_h_1, c_u, s7) | (~m_user_v_req(c_e_h_1, c_u, s6)) | m_user_v_ack(c_e_h_1, c_u, s6)), inference(lemma,lemma(discharge,[]))).
% 293.98/186.56 tff(24585,plain,
% 293.98/186.56 (m_user_v_req(c_e_h_1, c_u, s7) | (~m_user_v_req(c_e_h_1, c_u, s6))),
% 293.98/186.56 inference(unit_resolution,[status(thm)],[24584, 24561])).
% 293.98/186.56 tff(24586,plain,
% 293.98/186.56 (~m_user_v_req(c_e_h_1, c_u, s6)),
% 293.98/186.56 inference(unit_resolution,[status(thm)],[24585, 24498])).
% 293.98/186.56 tff(24587,assumption,(~m_user_v_req(c_e_h_1, c_u, s6)), introduced(assumption)).
% 293.98/186.56 tff(24588,assumption,(m_user_v_ack(c_e_h_1, c_u, s5)), introduced(assumption)).
% 293.98/186.56 tff(24589,plain,
% 293.98/186.56 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s5)) | m_and_h_gate_v_out(c_e_h_1, c_r, s5))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s5)) | m_and_h_gate_v_out(c_e_h_1, c_r, s5))),
% 293.98/186.56 inference(rewrite,[status(thm)],[])).
% 293.98/186.56 tff(24590,plain,
% 293.98/186.56 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s5)) | m_and_h_gate_v_out(c_e_h_1, c_r, s5))),
% 293.98/186.56 inference(quant_inst,[status(thm)],[])).
% 293.98/186.56 tff(24591,plain,
% 293.98/186.56 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s5)) | m_and_h_gate_v_out(c_e_h_1, c_r, s5)),
% 293.98/186.56 inference(modus_ponens,[status(thm)],[24590, 24589])).
% 293.98/186.56 tff(24592,plain,
% 293.98/186.56 ($false),
% 293.98/186.56 inference(unit_resolution,[status(thm)],[24591, 268, 24529, 24588])).
% 293.98/186.56 tff(24593,plain,(~m_user_v_ack(c_e_h_1, c_u, s5)), inference(lemma,lemma(discharge,[]))).
% 293.98/186.56 tff(24594,assumption,(~m_user_v_ack(c_e_h_1, c_u, s5)), introduced(assumption)).
% 293.98/186.56 tff(24595,assumption,(node7(c_e_h_1, c_u, s5, s6)), introduced(assumption)).
% 293.98/186.56 tff(24596,plain,
% 293.98/186.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | ((~node7(c_e_h_1, c_u, s5, s6)) | m_user_v_ack(c_e_h_1, c_u, s5) | m_user_v_req(c_e_h_1, c_u, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | (~node7(c_e_h_1, c_u, s5, s6)) | m_user_v_ack(c_e_h_1, c_u, s5) | m_user_v_req(c_e_h_1, c_u, s6))),
% 293.98/186.56 inference(rewrite,[status(thm)],[])).
% 293.98/186.56 tff(24597,plain,
% 293.98/186.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | ((~node7(c_e_h_1, c_u, s5, s6)) | m_user_v_ack(c_e_h_1, c_u, s5) | m_user_v_req(c_e_h_1, c_u, s6))),
% 293.98/186.56 inference(quant_inst,[status(thm)],[])).
% 293.98/186.56 tff(24598,plain,
% 293.98/186.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | (~node7(c_e_h_1, c_u, s5, s6)) | m_user_v_ack(c_e_h_1, c_u, s5) | m_user_v_req(c_e_h_1, c_u, s6)),
% 293.98/186.56 inference(modus_ponens,[status(thm)],[24597, 24596])).
% 293.98/186.56 tff(24599,plain,
% 293.98/186.56 ($false),
% 293.98/186.56 inference(unit_resolution,[status(thm)],[24598, 284, 24595, 24594, 24587])).
% 293.98/186.56 tff(24600,plain,((~node7(c_e_h_1, c_u, s5, s6)) | m_user_v_ack(c_e_h_1, c_u, s5) | m_user_v_req(c_e_h_1, c_u, s6)), inference(lemma,lemma(discharge,[]))).
% 293.98/186.56 tff(24601,plain,
% 293.98/186.56 ((~node7(c_e_h_1, c_u, s5, s6)) | m_user_v_req(c_e_h_1, c_u, s6)),
% 293.98/186.56 inference(unit_resolution,[status(thm)],[24600, 24593])).
% 293.98/186.56 tff(24602,plain,
% 293.98/186.56 (~node7(c_e_h_1, c_u, s5, s6)),
% 293.98/186.56 inference(unit_resolution,[status(thm)],[24601, 24587])).
% 293.98/186.56 tff(24603,plain,
% 293.98/186.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | ((~trans(s5, s6)) | node7(c_e_h_1, c_u, s5, s6) | node8(c_e_h_1, c_u, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | (~trans(s5, s6)) | node7(c_e_h_1, c_u, s5, s6) | node8(c_e_h_1, c_u, s5, s6))),
% 293.98/186.56 inference(rewrite,[status(thm)],[])).
% 293.98/186.56 tff(24604,plain,
% 293.98/186.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | ((~trans(s5, s6)) | node7(c_e_h_1, c_u, s5, s6) | node8(c_e_h_1, c_u, s5, s6))),
% 293.98/186.56 inference(quant_inst,[status(thm)],[])).
% 293.98/186.56 tff(24605,plain,
% 293.98/186.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | (~trans(s5, s6)) | node7(c_e_h_1, c_u, s5, s6) | node8(c_e_h_1, c_u, s5, s6)),
% 293.98/186.56 inference(modus_ponens,[status(thm)],[24604, 24603])).
% 293.98/186.56 tff(24606,plain,
% 293.98/186.56 (node7(c_e_h_1, c_u, s5, s6) | node8(c_e_h_1, c_u, s5, s6)),
% 293.98/186.56 inference(unit_resolution,[status(thm)],[24605, 328, 1406])).
% 293.98/186.56 tff(24607,plain,
% 293.98/186.56 (node8(c_e_h_1, c_u, s5, s6)),
% 293.98/186.56 inference(unit_resolution,[status(thm)],[24606, 24602])).
% 293.98/186.56 tff(24608,plain,
% 293.98/186.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | ((~m_user_v_req(c_e_h_1, c_u, s5)) | m_user_v_req(c_e_h_1, c_u, s6) | (~node8(c_e_h_1, c_u, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (~m_user_v_req(c_e_h_1, c_u, s5)) | m_user_v_req(c_e_h_1, c_u, s6) | (~node8(c_e_h_1, c_u, s5, s6)))),
% 293.98/186.56 inference(rewrite,[status(thm)],[])).
% 293.98/186.56 tff(24609,plain,
% 293.98/186.56 ((m_user_v_req(c_e_h_1, c_u, s6) | (~node8(c_e_h_1, c_u, s5, s6)) | (~m_user_v_req(c_e_h_1, c_u, s5))) <=> ((~m_user_v_req(c_e_h_1, c_u, s5)) | m_user_v_req(c_e_h_1, c_u, s6) | (~node8(c_e_h_1, c_u, s5, s6)))),
% 293.98/186.56 inference(rewrite,[status(thm)],[])).
% 293.98/186.56 tff(24610,plain,
% 293.98/186.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_1, c_u, s6) | (~node8(c_e_h_1, c_u, s5, s6)) | (~m_user_v_req(c_e_h_1, c_u, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | ((~m_user_v_req(c_e_h_1, c_u, s5)) | m_user_v_req(c_e_h_1, c_u, s6) | (~node8(c_e_h_1, c_u, s5, s6))))),
% 293.98/186.56 inference(monotonicity,[status(thm)],[24609])).
% 293.98/186.56 tff(24611,plain,
% 293.98/186.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_1, c_u, s6) | (~node8(c_e_h_1, c_u, s5, s6)) | (~m_user_v_req(c_e_h_1, c_u, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (~m_user_v_req(c_e_h_1, c_u, s5)) | m_user_v_req(c_e_h_1, c_u, s6) | (~node8(c_e_h_1, c_u, s5, s6)))),
% 293.98/186.56 inference(transitivity,[status(thm)],[24610, 24608])).
% 293.98/186.56 tff(24612,plain,
% 293.98/186.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_1, c_u, s6) | (~node8(c_e_h_1, c_u, s5, s6)) | (~m_user_v_req(c_e_h_1, c_u, s5)))),
% 293.98/186.57 inference(quant_inst,[status(thm)],[])).
% 293.98/186.57 tff(24613,plain,
% 293.98/186.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (~m_user_v_req(c_e_h_1, c_u, s5)) | m_user_v_req(c_e_h_1, c_u, s6) | (~node8(c_e_h_1, c_u, s5, s6))),
% 293.98/186.57 inference(modus_ponens,[status(thm)],[24612, 24611])).
% 293.98/186.57 tff(24614,plain,
% 293.98/186.57 ($false),
% 293.98/186.57 inference(unit_resolution,[status(thm)],[24613, 302, 24607, 16538, 24587])).
% 293.98/186.57 tff(24615,plain,(m_user_v_req(c_e_h_1, c_u, s6) | (~m_user_v_req(c_e_h_1, c_u, s5))), inference(lemma,lemma(discharge,[]))).
% 293.98/186.57 tff(24616,plain,
% 293.98/186.57 (~m_user_v_req(c_e_h_1, c_u, s5)),
% 293.98/186.57 inference(unit_resolution,[status(thm)],[24615, 24586])).
% 293.98/186.57 tff(24617,plain,
% 293.98/186.57 (~m_mutex_h_half_v_out(c_e_h_1, c_a, s6)),
% 293.98/186.57 inference(unit_resolution,[status(thm)],[16502, 24616])).
% 293.98/186.57 tff(24618,assumption,(~m_mutex_h_half_v_inp(c_e_h_1, c_a, s6)), introduced(assumption)).
% 293.98/186.57 tff(24619,assumption,(node13(c_e_h_1, c_a, s6, s7)), introduced(assumption)).
% 293.98/186.57 tff(24620,plain,
% 293.98/186.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_1, c_a, s7)) | (~node13(c_e_h_1, c_a, s6, s7)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s7)) | (~node13(c_e_h_1, c_a, s6, s7)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s6))),
% 293.98/186.57 inference(rewrite,[status(thm)],[])).
% 293.98/186.57 tff(24621,plain,
% 293.98/186.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_1, c_a, s7)) | (~node13(c_e_h_1, c_a, s6, s7)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s6))),
% 293.98/186.57 inference(quant_inst,[status(thm)],[])).
% 293.98/186.57 tff(24622,plain,
% 293.98/186.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s7)) | (~node13(c_e_h_1, c_a, s6, s7)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s6)),
% 293.98/186.57 inference(modus_ponens,[status(thm)],[24621, 24620])).
% 293.98/186.57 tff(24623,plain,
% 293.98/186.57 ($false),
% 293.98/186.57 inference(unit_resolution,[status(thm)],[24622, 423, 24619, 16516, 24462])).
% 293.98/186.57 tff(24624,plain,((~node13(c_e_h_1, c_a, s6, s7)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s6) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s7))), inference(lemma,lemma(discharge,[]))).
% 293.98/186.57 tff(24625,plain,
% 293.98/186.57 (~node13(c_e_h_1, c_a, s6, s7)),
% 293.98/186.57 inference(unit_resolution,[status(thm)],[24624, 24462, 16516])).
% 293.98/186.57 tff(24626,plain,
% 293.98/186.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s6, s7)) | node12(c_e_h_1, c_a, s6, s7) | node13(c_e_h_1, c_a, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s6, s7)) | node12(c_e_h_1, c_a, s6, s7) | node13(c_e_h_1, c_a, s6, s7))),
% 293.98/186.57 inference(rewrite,[status(thm)],[])).
% 293.98/186.57 tff(24627,plain,
% 293.98/186.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s6, s7)) | node12(c_e_h_1, c_a, s6, s7) | node13(c_e_h_1, c_a, s6, s7))),
% 293.98/186.57 inference(quant_inst,[status(thm)],[])).
% 293.98/186.57 tff(24628,plain,
% 293.98/186.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s6, s7)) | node12(c_e_h_1, c_a, s6, s7) | node13(c_e_h_1, c_a, s6, s7)),
% 293.98/186.57 inference(modus_ponens,[status(thm)],[24627, 24626])).
% 293.98/186.57 tff(24629,plain,
% 293.98/186.57 (node12(c_e_h_1, c_a, s6, s7) | node13(c_e_h_1, c_a, s6, s7)),
% 293.98/186.57 inference(unit_resolution,[status(thm)],[24628, 439, 1844])).
% 293.98/186.57 tff(24630,plain,
% 293.98/186.57 (node12(c_e_h_1, c_a, s6, s7)),
% 293.98/186.57 inference(unit_resolution,[status(thm)],[24629, 24625])).
% 293.98/186.57 tff(24631,plain,
% 293.98/186.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_1, c_a, s6) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s7)) | (~node12(c_e_h_1, c_a, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s6) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s7)) | (~node12(c_e_h_1, c_a, s6, s7)))),
% 294.07/186.57 inference(rewrite,[status(thm)],[])).
% 294.07/186.57 tff(24632,plain,
% 294.07/186.57 (((~node12(c_e_h_1, c_a, s6, s7)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s6) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s7))) <=> (m_mutex_h_half_v_inp(c_e_h_1, c_a, s6) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s7)) | (~node12(c_e_h_1, c_a, s6, s7)))),
% 294.07/186.57 inference(rewrite,[status(thm)],[])).
% 294.07/186.57 tff(24633,plain,
% 294.07/186.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_1, c_a, s6, s7)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s6) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_1, c_a, s6) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s7)) | (~node12(c_e_h_1, c_a, s6, s7))))),
% 294.07/186.57 inference(monotonicity,[status(thm)],[24632])).
% 294.07/186.57 tff(24634,plain,
% 294.07/186.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_1, c_a, s6, s7)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s6) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s6) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s7)) | (~node12(c_e_h_1, c_a, s6, s7)))),
% 294.07/186.57 inference(transitivity,[status(thm)],[24633, 24631])).
% 294.07/186.57 tff(24635,plain,
% 294.07/186.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_1, c_a, s6, s7)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s6) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s7)))),
% 294.07/186.57 inference(quant_inst,[status(thm)],[])).
% 294.07/186.57 tff(24636,plain,
% 294.07/186.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s6) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s7)) | (~node12(c_e_h_1, c_a, s6, s7))),
% 294.07/186.57 inference(modus_ponens,[status(thm)],[24635, 24634])).
% 294.07/186.57 tff(24637,plain,
% 294.07/186.57 ($false),
% 294.07/186.57 inference(unit_resolution,[status(thm)],[24636, 454, 24630, 24462, 24618])).
% 294.07/186.57 tff(24638,plain,((~m_mutex_h_half_v_out(c_e_h_1, c_a, s7)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s6) | m_mutex_h_half_v_out(c_e_h_1, c_a, s6)), inference(lemma,lemma(discharge,[]))).
% 294.07/186.57 tff(24639,plain,
% 294.07/186.57 (m_mutex_h_half_v_inp(c_e_h_1, c_a, s6)),
% 294.07/186.57 inference(unit_resolution,[status(thm)],[24638, 24617, 24462])).
% 294.07/186.57 tff(24640,plain,
% 294.07/186.57 (((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | ((~m_mutex_h_half_v_inp(c_e_h_1, c_a, s6)) | m_user_v_req(c_e_h_1, c_u, s6))) <=> ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s6)) | m_user_v_req(c_e_h_1, c_u, s6))),
% 294.07/186.57 inference(rewrite,[status(thm)],[])).
% 294.07/186.57 tff(24641,plain,
% 294.07/186.57 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | ((~m_mutex_h_half_v_inp(c_e_h_1, c_a, s6)) | m_user_v_req(c_e_h_1, c_u, s6))),
% 294.07/186.57 inference(quant_inst,[status(thm)],[])).
% 294.07/186.57 tff(24642,plain,
% 294.07/186.57 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s6)) | m_user_v_req(c_e_h_1, c_u, s6)),
% 294.07/186.57 inference(modus_ponens,[status(thm)],[24641, 24640])).
% 294.07/186.57 tff(24643,plain,
% 294.07/186.57 ($false),
% 294.07/186.57 inference(unit_resolution,[status(thm)],[24642, 395, 24586, 24639])).
% 294.07/186.57 tff(24644,plain,((~m_mutex_h_half_v_out(c_e_h_1, c_a, s7)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s8)), inference(lemma,lemma(discharge,[]))).
% 294.07/186.57 tff(24645,plain,
% 294.07/186.57 (~m_mutex_h_half_v_out(c_e_h_1, c_a, s7)),
% 294.07/186.57 inference(unit_resolution,[status(thm)],[24644, 24426])).
% 294.07/186.57 tff(24646,assumption,(m_and_h_gate_v_in1(c_e_h_1, c_c, s7)), introduced(assumption)).
% 294.07/186.57 tff(24647,assumption,(~m_mutex_h_half_v_out(c_e_h_1, c_a, s7)), introduced(assumption)).
% 294.07/186.57 tff(24648,plain,
% 294.07/186.57 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_c, s7)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s7))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s7)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s7))),
% 294.07/186.57 inference(rewrite,[status(thm)],[])).
% 294.07/186.57 tff(24649,plain,
% 294.07/186.57 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_c, s7)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s7))),
% 294.07/186.57 inference(quant_inst,[status(thm)],[])).
% 294.07/186.57 tff(24650,plain,
% 294.07/186.57 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s7)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s7)),
% 294.07/186.57 inference(modus_ponens,[status(thm)],[24649, 24648])).
% 294.07/186.57 tff(24651,plain,
% 294.07/186.57 ($false),
% 294.07/186.57 inference(unit_resolution,[status(thm)],[24650, 567, 24647, 24646])).
% 294.07/186.57 tff(24652,plain,((~m_and_h_gate_v_in1(c_e_h_1, c_c, s7)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s7)), inference(lemma,lemma(discharge,[]))).
% 294.07/186.57 tff(24653,plain,
% 294.07/186.57 (~m_and_h_gate_v_in1(c_e_h_1, c_c, s7)),
% 294.07/186.57 inference(unit_resolution,[status(thm)],[24652, 24645])).
% 294.07/186.57 tff(24654,assumption,(~m_and_h_gate_v_in1(c_e_h_1, c_c, s7)), introduced(assumption)).
% 294.07/186.57 tff(24655,assumption,(node20(c_e_h_1, c_c, s7)), introduced(assumption)).
% 294.07/186.57 tff(24656,plain,
% 294.07/186.57 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_c, s7)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_c, s7)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s7))),
% 294.07/186.57 inference(rewrite,[status(thm)],[])).
% 294.07/186.57 tff(24657,plain,
% 294.07/186.57 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_c, s7)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s7))),
% 294.07/186.57 inference(quant_inst,[status(thm)],[])).
% 294.07/186.57 tff(24658,plain,
% 294.07/186.57 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_c, s7)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s7)),
% 294.07/186.57 inference(modus_ponens,[status(thm)],[24657, 24656])).
% 294.07/186.57 tff(24659,plain,
% 294.07/186.57 ($false),
% 294.07/186.57 inference(unit_resolution,[status(thm)],[24658, 38, 24655, 24654])).
% 294.07/186.57 tff(24660,plain,((~node20(c_e_h_1, c_c, s7)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s7)), inference(lemma,lemma(discharge,[]))).
% 294.07/186.57 tff(24661,plain,
% 294.07/186.57 (~node20(c_e_h_1, c_c, s7)),
% 294.07/186.57 inference(unit_resolution,[status(thm)],[24660, 24653])).
% 294.07/186.57 tff(24662,assumption,(m_and_h_gate_v_out(c_e_h_1, c_c, s8)), introduced(assumption)).
% 294.07/186.57 tff(24663,assumption,(node22(c_e_h_1, c_c, s7, s8)), introduced(assumption)).
% 294.07/186.57 tff(24664,plain,
% 294.07/186.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_c, s8)) | (~node22(c_e_h_1, c_c, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_c, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s8)) | (~node22(c_e_h_1, c_c, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_c, s7))),
% 294.07/186.57 inference(rewrite,[status(thm)],[])).
% 294.07/186.57 tff(24665,plain,
% 294.07/186.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_c, s8)) | (~node22(c_e_h_1, c_c, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_c, s7))),
% 294.07/186.57 inference(quant_inst,[status(thm)],[])).
% 294.07/186.57 tff(24666,plain,
% 294.07/186.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s8)) | (~node22(c_e_h_1, c_c, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_c, s7)),
% 294.07/186.58 inference(modus_ponens,[status(thm)],[24665, 24664])).
% 294.07/186.58 tff(24667,plain,
% 294.07/186.58 ($false),
% 294.07/186.58 inference(unit_resolution,[status(thm)],[24666, 108, 24663, 24662, 16266])).
% 294.07/186.58 tff(24668,plain,((~node22(c_e_h_1, c_c, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s8)) | m_and_h_gate_v_out(c_e_h_1, c_c, s7)), inference(lemma,lemma(discharge,[]))).
% 294.07/186.58 tff(24669,plain,
% 294.07/186.58 (~node22(c_e_h_1, c_c, s7, s8)),
% 294.07/186.58 inference(unit_resolution,[status(thm)],[24668, 24662, 16266])).
% 294.07/186.58 tff(24670,assumption,(~node20(c_e_h_1, c_c, s7)), introduced(assumption)).
% 294.07/186.58 tff(24671,assumption,(node21(c_e_h_1, c_c, s7, s8)), introduced(assumption)).
% 294.07/186.58 tff(24672,plain,
% 294.07/186.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_c, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s8)) | (~node21(c_e_h_1, c_c, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_c, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s8)) | (~node21(c_e_h_1, c_c, s7, s8)))),
% 294.07/186.58 inference(rewrite,[status(thm)],[])).
% 294.07/186.58 tff(24673,plain,
% 294.07/186.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_c, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s8)) | (~node21(c_e_h_1, c_c, s7, s8)))),
% 294.07/186.58 inference(quant_inst,[status(thm)],[])).
% 294.07/186.58 tff(24674,plain,
% 294.07/186.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_c, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s8)) | (~node21(c_e_h_1, c_c, s7, s8))),
% 294.07/186.58 inference(modus_ponens,[status(thm)],[24673, 24672])).
% 294.07/186.58 tff(24675,plain,
% 294.07/186.58 ($false),
% 294.07/186.58 inference(unit_resolution,[status(thm)],[24674, 52, 24671, 24662, 24670])).
% 294.07/186.58 tff(24676,plain,((~node21(c_e_h_1, c_c, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s8)) | node20(c_e_h_1, c_c, s7)), inference(lemma,lemma(discharge,[]))).
% 294.07/186.58 tff(24677,plain,
% 294.07/186.58 (~node21(c_e_h_1, c_c, s7, s8)),
% 294.07/186.58 inference(unit_resolution,[status(thm)],[24676, 24662, 24670])).
% 294.07/186.58 tff(24678,plain,
% 294.07/186.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_1, c_c, s7, s8) | node22(c_e_h_1, c_c, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_1, c_c, s7, s8) | node22(c_e_h_1, c_c, s7, s8))),
% 294.07/186.58 inference(rewrite,[status(thm)],[])).
% 294.07/186.58 tff(24679,plain,
% 294.07/186.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_1, c_c, s7, s8) | node22(c_e_h_1, c_c, s7, s8))),
% 294.07/186.58 inference(quant_inst,[status(thm)],[])).
% 294.07/186.58 tff(24680,plain,
% 294.07/186.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_1, c_c, s7, s8) | node22(c_e_h_1, c_c, s7, s8)),
% 294.07/186.58 inference(modus_ponens,[status(thm)],[24679, 24678])).
% 294.07/186.58 tff(24681,plain,
% 294.07/186.58 (node21(c_e_h_1, c_c, s7, s8) | node22(c_e_h_1, c_c, s7, s8)),
% 294.07/186.58 inference(unit_resolution,[status(thm)],[24680, 82, 1938])).
% 294.07/186.58 tff(24682,plain,
% 294.07/186.58 ($false),
% 294.07/186.58 inference(unit_resolution,[status(thm)],[24681, 24677, 24669])).
% 294.07/186.58 tff(24683,plain,((~m_and_h_gate_v_out(c_e_h_1, c_c, s8)) | node20(c_e_h_1, c_c, s7) | m_and_h_gate_v_out(c_e_h_1, c_c, s7)), inference(lemma,lemma(discharge,[]))).
% 294.07/186.58 tff(24684,plain,
% 294.07/186.58 ($false),
% 294.07/186.58 inference(unit_resolution,[status(thm)],[24683, 24661, 24461, 16266])).
% 294.07/186.58 tff(24685,plain,(m_mutex_h_half_v_out(c_e_h_1, c_a, s8) | m_and_h_gate_v_out(c_e_h_1, c_c, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s9))), inference(lemma,lemma(discharge,[]))).
% 294.07/186.58 tff(24686,plain,
% 294.07/186.58 (m_and_h_gate_v_out(c_e_h_1, c_c, s7)),
% 294.07/186.58 inference(unit_resolution,[status(thm)],[24685, 24426, 24425])).
% 294.07/186.58 tff(24687,plain,
% 294.07/186.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | ((~m_mutex_h_half_v_out(c_e_h_1, c_a, s6)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s7) | (~node13(c_e_h_1, c_a, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s6)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s7) | (~node13(c_e_h_1, c_a, s6, s7)))),
% 294.07/186.58 inference(rewrite,[status(thm)],[])).
% 294.07/186.58 tff(24688,plain,
% 294.07/186.58 ((m_mutex_h_half_v_out(c_e_h_1, c_a, s7) | (~node13(c_e_h_1, c_a, s6, s7)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s6))) <=> ((~m_mutex_h_half_v_out(c_e_h_1, c_a, s6)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s7) | (~node13(c_e_h_1, c_a, s6, s7)))),
% 294.07/186.58 inference(rewrite,[status(thm)],[])).
% 294.07/186.58 tff(24689,plain,
% 294.07/186.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_1, c_a, s7) | (~node13(c_e_h_1, c_a, s6, s7)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | ((~m_mutex_h_half_v_out(c_e_h_1, c_a, s6)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s7) | (~node13(c_e_h_1, c_a, s6, s7))))),
% 294.07/186.58 inference(monotonicity,[status(thm)],[24688])).
% 294.07/186.58 tff(24690,plain,
% 294.07/186.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_1, c_a, s7) | (~node13(c_e_h_1, c_a, s6, s7)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s6)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s7) | (~node13(c_e_h_1, c_a, s6, s7)))),
% 294.07/186.58 inference(transitivity,[status(thm)],[24689, 24687])).
% 294.07/186.58 tff(24691,plain,
% 294.07/186.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_1, c_a, s7) | (~node13(c_e_h_1, c_a, s6, s7)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s6)))),
% 294.07/186.58 inference(quant_inst,[status(thm)],[])).
% 294.07/186.58 tff(24692,plain,
% 294.07/186.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s6)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s7) | (~node13(c_e_h_1, c_a, s6, s7))),
% 294.07/186.58 inference(modus_ponens,[status(thm)],[24691, 24690])).
% 294.07/186.58 tff(24693,plain,
% 294.07/186.58 ($false),
% 294.07/186.58 inference(unit_resolution,[status(thm)],[24692, 1459, 24619, 16480, 24647])).
% 294.07/186.58 tff(24694,plain,((~node13(c_e_h_1, c_a, s6, s7)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s6)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s7)), inference(lemma,lemma(discharge,[]))).
% 294.07/186.58 tff(24695,plain,
% 294.07/186.58 (~node13(c_e_h_1, c_a, s6, s7)),
% 294.07/186.58 inference(unit_resolution,[status(thm)],[24694, 24647, 16480])).
% 294.07/186.58 tff(24696,plain,
% 294.07/186.58 (m_user_v_req(c_e_h_1, c_u, s5)),
% 294.07/186.58 inference(unit_resolution,[status(thm)],[16502, 16480])).
% 294.07/186.58 tff(24697,plain,
% 294.07/186.58 (m_user_v_req(c_e_h_1, c_u, s6)),
% 294.07/186.58 inference(unit_resolution,[status(thm)],[24615, 24696])).
% 294.07/186.58 tff(24698,plain,
% 294.07/186.58 (((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | ((~m_user_v_req(c_e_h_1, c_u, s6)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s6))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | (~m_user_v_req(c_e_h_1, c_u, s6)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s6))),
% 294.07/186.58 inference(rewrite,[status(thm)],[])).
% 294.07/186.58 tff(24699,plain,
% 294.07/186.58 ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | ((~m_user_v_req(c_e_h_1, c_u, s6)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s6))),
% 294.07/186.58 inference(quant_inst,[status(thm)],[])).
% 294.07/186.58 tff(24700,plain,
% 294.07/186.58 ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | (~m_user_v_req(c_e_h_1, c_u, s6)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s6)),
% 294.07/186.58 inference(modus_ponens,[status(thm)],[24699, 24698])).
% 294.07/186.58 tff(24701,plain,
% 294.07/186.58 (m_mutex_h_half_v_inp(c_e_h_1, c_a, s6)),
% 294.07/186.58 inference(unit_resolution,[status(thm)],[24700, 1426, 24697])).
% 294.07/186.58 tff(24702,assumption,(m_mutex_h_half_v_inp(c_e_h_1, c_a, s6)), introduced(assumption)).
% 294.07/186.58 tff(24703,assumption,(node12(c_e_h_1, c_a, s6, s7)), introduced(assumption)).
% 294.07/186.58 tff(24704,plain,
% 294.07/186.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~m_mutex_h_half_v_inp(c_e_h_1, c_a, s6)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s7) | (~node12(c_e_h_1, c_a, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s6)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s7) | (~node12(c_e_h_1, c_a, s6, s7)))),
% 294.07/186.58 inference(rewrite,[status(thm)],[])).
% 294.07/186.58 tff(24705,plain,
% 294.07/186.58 (((~node12(c_e_h_1, c_a, s6, s7)) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s6)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s7)) <=> ((~m_mutex_h_half_v_inp(c_e_h_1, c_a, s6)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s7) | (~node12(c_e_h_1, c_a, s6, s7)))),
% 294.07/186.58 inference(rewrite,[status(thm)],[])).
% 294.07/186.58 tff(24706,plain,
% 294.07/186.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_1, c_a, s6, s7)) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s6)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~m_mutex_h_half_v_inp(c_e_h_1, c_a, s6)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s7) | (~node12(c_e_h_1, c_a, s6, s7))))),
% 294.07/186.58 inference(monotonicity,[status(thm)],[24705])).
% 294.07/186.58 tff(24707,plain,
% 294.07/186.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_1, c_a, s6, s7)) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s6)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s6)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s7) | (~node12(c_e_h_1, c_a, s6, s7)))),
% 294.07/186.58 inference(transitivity,[status(thm)],[24706, 24704])).
% 294.07/186.58 tff(24708,plain,
% 294.07/186.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_1, c_a, s6, s7)) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s6)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s7))),
% 294.07/186.58 inference(quant_inst,[status(thm)],[])).
% 294.07/186.58 tff(24709,plain,
% 294.07/186.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s6)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s7) | (~node12(c_e_h_1, c_a, s6, s7))),
% 294.07/186.58 inference(modus_ponens,[status(thm)],[24708, 24707])).
% 294.07/186.58 tff(24710,plain,
% 294.07/186.58 ($false),
% 294.07/186.58 inference(unit_resolution,[status(thm)],[24709, 1483, 24703, 24647, 24702])).
% 294.07/186.58 tff(24711,plain,((~node12(c_e_h_1, c_a, s6, s7)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s7) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s6))), inference(lemma,lemma(discharge,[]))).
% 294.07/186.58 tff(24712,plain,
% 294.07/186.58 (~node12(c_e_h_1, c_a, s6, s7)),
% 294.07/186.58 inference(unit_resolution,[status(thm)],[24711, 24647, 24701])).
% 294.07/186.58 tff(24713,plain,
% 294.07/186.58 ($false),
% 294.07/186.58 inference(unit_resolution,[status(thm)],[24629, 24712, 24695])).
% 294.07/186.58 tff(24714,plain,(m_mutex_h_half_v_out(c_e_h_1, c_a, s7) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s6))), inference(lemma,lemma(discharge,[]))).
% 294.07/186.58 tff(24715,plain,
% 294.07/186.58 (~m_mutex_h_half_v_out(c_e_h_1, c_a, s6)),
% 294.07/186.58 inference(unit_resolution,[status(thm)],[24714, 24645])).
% 294.07/186.58 tff(24716,assumption,(m_and_h_gate_v_out(c_e_h_1, c_c, s7)), introduced(assumption)).
% 294.07/186.59 tff(24717,plain,
% 294.07/186.59 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_c, s6)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s6))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s6)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s6))),
% 294.07/186.59 inference(rewrite,[status(thm)],[])).
% 294.07/186.59 tff(24718,plain,
% 294.07/186.59 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_c, s6)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s6))),
% 294.07/186.59 inference(quant_inst,[status(thm)],[])).
% 294.07/186.59 tff(24719,plain,
% 294.07/186.59 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_c, X)) | m_mutex_h_half_v_out(I0, c_a, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s6)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s6)),
% 294.07/186.59 inference(modus_ponens,[status(thm)],[24718, 24717])).
% 294.07/186.59 tff(24720,plain,
% 294.07/186.59 ($false),
% 294.07/186.59 inference(unit_resolution,[status(thm)],[24719, 567, 16516, 16685])).
% 294.07/186.59 tff(24721,plain,((~m_and_h_gate_v_in1(c_e_h_1, c_c, s6)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s6)), inference(lemma,lemma(discharge,[]))).
% 294.07/186.59 tff(24722,plain,
% 294.07/186.59 (~m_and_h_gate_v_in1(c_e_h_1, c_c, s6)),
% 294.07/186.59 inference(unit_resolution,[status(thm)],[24721, 16516])).
% 294.07/186.59 tff(24723,assumption,(node20(c_e_h_1, c_c, s6)), introduced(assumption)).
% 294.07/186.59 tff(24724,plain,
% 294.07/186.59 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_c, s6)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_c, s6)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s6))),
% 294.07/186.59 inference(rewrite,[status(thm)],[])).
% 294.07/186.59 tff(24725,plain,
% 294.07/186.59 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_c, s6)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s6))),
% 294.07/186.59 inference(quant_inst,[status(thm)],[])).
% 294.07/186.59 tff(24726,plain,
% 294.07/186.59 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_c, s6)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s6)),
% 294.07/186.59 inference(modus_ponens,[status(thm)],[24725, 24724])).
% 294.07/186.59 tff(24727,plain,
% 294.07/186.59 ($false),
% 294.07/186.59 inference(unit_resolution,[status(thm)],[24726, 38, 16678, 24723])).
% 294.07/186.59 tff(24728,plain,((~node20(c_e_h_1, c_c, s6)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s6)), inference(lemma,lemma(discharge,[]))).
% 294.07/186.59 tff(24729,plain,
% 294.07/186.59 (~node20(c_e_h_1, c_c, s6)),
% 294.07/186.59 inference(unit_resolution,[status(thm)],[24728, 24722])).
% 294.07/186.59 tff(24730,assumption,(~node20(c_e_h_1, c_c, s6)), introduced(assumption)).
% 294.07/186.59 tff(24731,plain,
% 294.07/186.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_c, s7)) | (~node22(c_e_h_1, c_c, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_c, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s7)) | (~node22(c_e_h_1, c_c, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_c, s6))),
% 294.07/186.59 inference(rewrite,[status(thm)],[])).
% 294.07/186.59 tff(24732,plain,
% 294.07/186.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_c, s7)) | (~node22(c_e_h_1, c_c, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_c, s6))),
% 294.07/186.59 inference(quant_inst,[status(thm)],[])).
% 294.07/186.59 tff(24733,plain,
% 294.07/186.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s7)) | (~node22(c_e_h_1, c_c, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_c, s6)),
% 294.07/186.59 inference(modus_ponens,[status(thm)],[24732, 24731])).
% 294.07/186.59 tff(24734,plain,
% 294.07/186.59 ($false),
% 294.07/186.59 inference(unit_resolution,[status(thm)],[24733, 108, 24716, 13629, 16990])).
% 294.07/186.59 tff(24735,plain,((~node22(c_e_h_1, c_c, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s7)) | m_and_h_gate_v_out(c_e_h_1, c_c, s6)), inference(lemma,lemma(discharge,[]))).
% 294.07/186.59 tff(24736,plain,
% 294.07/186.59 (~node22(c_e_h_1, c_c, s6, s7)),
% 294.07/186.59 inference(unit_resolution,[status(thm)],[24735, 24716, 13629])).
% 294.07/186.59 tff(24737,plain,
% 294.07/186.59 (node21(c_e_h_1, c_c, s6, s7)),
% 294.07/186.59 inference(unit_resolution,[status(thm)],[17003, 24736])).
% 294.07/186.59 tff(24738,plain,
% 294.07/186.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_c, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s7)) | (~node21(c_e_h_1, c_c, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_c, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s7)) | (~node21(c_e_h_1, c_c, s6, s7)))),
% 294.07/186.59 inference(rewrite,[status(thm)],[])).
% 294.07/186.59 tff(24739,plain,
% 294.07/186.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_c, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s7)) | (~node21(c_e_h_1, c_c, s6, s7)))),
% 294.07/186.59 inference(quant_inst,[status(thm)],[])).
% 294.07/186.59 tff(24740,plain,
% 294.07/186.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_c, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s7)) | (~node21(c_e_h_1, c_c, s6, s7))),
% 294.07/186.59 inference(modus_ponens,[status(thm)],[24739, 24738])).
% 294.07/186.59 tff(24741,plain,
% 294.07/186.59 ($false),
% 294.07/186.59 inference(unit_resolution,[status(thm)],[24740, 52, 24716, 24737, 24730])).
% 294.07/186.59 tff(24742,plain,((~m_and_h_gate_v_out(c_e_h_1, c_c, s7)) | node20(c_e_h_1, c_c, s6) | m_and_h_gate_v_out(c_e_h_1, c_c, s6)), inference(lemma,lemma(discharge,[]))).
% 294.07/186.59 tff(24743,plain,
% 294.07/186.59 (m_and_h_gate_v_out(c_e_h_1, c_c, s6)),
% 294.07/186.59 inference(unit_resolution,[status(thm)],[24742, 24729, 24716])).
% 294.07/186.59 tff(24744,plain,
% 294.07/186.59 (m_mutex_h_half_v_out(c_e_h_1, c_a, s5)),
% 294.07/186.59 inference(unit_resolution,[status(thm)],[16645, 24743, 16516])).
% 294.07/186.59 tff(24745,plain,
% 294.07/186.59 (m_user_v_req(c_e_h_1, c_u, s5)),
% 294.07/186.59 inference(unit_resolution,[status(thm)],[16587, 24743])).
% 294.07/186.59 tff(24746,plain,
% 294.07/186.59 (m_mutex_h_half_v_inp(c_e_h_1, c_a, s5)),
% 294.07/186.59 inference(unit_resolution,[status(thm)],[16543, 24745])).
% 294.07/186.59 tff(24747,plain,
% 294.07/186.59 ($false),
% 294.07/186.59 inference(unit_resolution,[status(thm)],[16536, 24746, 24744, 16516])).
% 294.07/186.59 tff(24748,plain,(m_mutex_h_half_v_out(c_e_h_1, c_a, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s7))), inference(lemma,lemma(discharge,[]))).
% 294.07/186.59 tff(24749,plain,
% 294.07/186.59 ($false),
% 294.07/186.59 inference(unit_resolution,[status(thm)],[24748, 24715, 24686])).
% 294.07/186.59 tff(24750,plain,(m_mutex_h_half_v_out(c_e_h_1, c_a, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s9))), inference(lemma,lemma(discharge,[]))).
% 294.07/186.59 tff(24751,plain,
% 294.07/186.59 (m_mutex_h_half_v_out(c_e_h_1, c_a, s8)),
% 294.07/186.59 inference(unit_resolution,[status(thm)],[24750, 24424])).
% 294.07/186.59 tff(24752,assumption,(m_mutex_h_half_v_out(c_e_h_1, c_a, s8)), introduced(assumption)).
% 294.07/186.59 tff(24753,assumption,(~m_mutex_h_half_v_out(c_e_h_1, c_a, s9)), introduced(assumption)).
% 294.07/186.59 tff(24754,assumption,(node13(c_e_h_1, c_a, s8, s9)), introduced(assumption)).
% 294.07/186.59 tff(24755,plain,
% 294.07/186.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_1, c_a, s9) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s8)) | (~node13(c_e_h_1, c_a, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | m_mutex_h_half_v_out(c_e_h_1, c_a, s9) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s8)) | (~node13(c_e_h_1, c_a, s8, s9)))),
% 294.07/186.59 inference(rewrite,[status(thm)],[])).
% 294.07/186.59 tff(24756,plain,
% 294.07/186.59 ((m_mutex_h_half_v_out(c_e_h_1, c_a, s9) | (~node13(c_e_h_1, c_a, s8, s9)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s8))) <=> (m_mutex_h_half_v_out(c_e_h_1, c_a, s9) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s8)) | (~node13(c_e_h_1, c_a, s8, s9)))),
% 294.07/186.59 inference(rewrite,[status(thm)],[])).
% 294.07/186.59 tff(24757,plain,
% 294.07/186.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_1, c_a, s9) | (~node13(c_e_h_1, c_a, s8, s9)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_1, c_a, s9) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s8)) | (~node13(c_e_h_1, c_a, s8, s9))))),
% 294.10/186.59 inference(monotonicity,[status(thm)],[24756])).
% 294.10/186.59 tff(24758,plain,
% 294.10/186.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_1, c_a, s9) | (~node13(c_e_h_1, c_a, s8, s9)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | m_mutex_h_half_v_out(c_e_h_1, c_a, s9) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s8)) | (~node13(c_e_h_1, c_a, s8, s9)))),
% 294.10/186.59 inference(transitivity,[status(thm)],[24757, 24755])).
% 294.10/186.59 tff(24759,plain,
% 294.10/186.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | (m_mutex_h_half_v_out(c_e_h_1, c_a, s9) | (~node13(c_e_h_1, c_a, s8, s9)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s8)))),
% 294.10/186.59 inference(quant_inst,[status(thm)],[])).
% 294.10/186.59 tff(24760,plain,
% 294.10/186.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_mutex_h_half_v_out(I0, I1, Y) | (~node13(I0, I1, X, Y)) | (~m_mutex_h_half_v_out(I0, I1, X)))) | m_mutex_h_half_v_out(c_e_h_1, c_a, s9) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s8)) | (~node13(c_e_h_1, c_a, s8, s9))),
% 294.10/186.59 inference(modus_ponens,[status(thm)],[24759, 24758])).
% 294.10/186.59 tff(24761,plain,
% 294.10/186.59 ($false),
% 294.10/186.59 inference(unit_resolution,[status(thm)],[24760, 1459, 24754, 24753, 24752])).
% 294.10/186.59 tff(24762,plain,((~node13(c_e_h_1, c_a, s8, s9)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s9) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s8))), inference(lemma,lemma(discharge,[]))).
% 294.10/186.59 tff(24763,plain,
% 294.10/186.59 (~node13(c_e_h_1, c_a, s8, s9)),
% 294.10/186.59 inference(unit_resolution,[status(thm)],[24762, 24753, 24752])).
% 294.10/186.59 tff(24764,plain,
% 294.10/186.59 (~m_user_v_req(c_e_h_1, c_u, s6)),
% 294.10/186.59 inference(unit_resolution,[status(thm)],[24585, 24562])).
% 294.10/186.59 tff(24765,plain,
% 294.10/186.59 (~m_user_v_req(c_e_h_1, c_u, s5)),
% 294.10/186.59 inference(unit_resolution,[status(thm)],[24615, 24764])).
% 294.10/186.59 tff(24766,plain,
% 294.10/186.59 (~m_mutex_h_half_v_out(c_e_h_1, c_a, s6)),
% 294.10/186.59 inference(unit_resolution,[status(thm)],[16502, 24765])).
% 294.10/186.59 tff(24767,plain,
% 294.10/186.59 (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s6)),
% 294.10/186.59 inference(unit_resolution,[status(thm)],[24642, 395, 24764])).
% 294.10/186.59 tff(24768,plain,
% 294.10/186.59 (((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | ((~m_mutex_h_half_v_inp(c_e_h_1, c_a, s7)) | m_user_v_req(c_e_h_1, c_u, s7))) <=> ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s7)) | m_user_v_req(c_e_h_1, c_u, s7))),
% 294.10/186.59 inference(rewrite,[status(thm)],[])).
% 294.10/186.59 tff(24769,plain,
% 294.10/186.59 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | ((~m_mutex_h_half_v_inp(c_e_h_1, c_a, s7)) | m_user_v_req(c_e_h_1, c_u, s7))),
% 294.10/186.59 inference(quant_inst,[status(thm)],[])).
% 294.10/186.59 tff(24770,plain,
% 294.10/186.59 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_inp(I0, c_a, X)) | m_user_v_req(I0, c_u, X))) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s7)) | m_user_v_req(c_e_h_1, c_u, s7)),
% 294.10/186.59 inference(modus_ponens,[status(thm)],[24769, 24768])).
% 294.10/186.59 tff(24771,plain,
% 294.10/186.59 (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s7)),
% 294.10/186.59 inference(unit_resolution,[status(thm)],[24770, 395, 24562])).
% 294.10/186.59 tff(24772,plain,
% 294.10/186.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_1, c_a, s7) | (~node12(c_e_h_1, c_a, s7, s8)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s7) | (~node12(c_e_h_1, c_a, s7, s8)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s8)))),
% 294.10/186.60 inference(rewrite,[status(thm)],[])).
% 294.10/186.60 tff(24773,plain,
% 294.10/186.60 (((~node12(c_e_h_1, c_a, s7, s8)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s7) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s8))) <=> (m_mutex_h_half_v_inp(c_e_h_1, c_a, s7) | (~node12(c_e_h_1, c_a, s7, s8)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s8)))),
% 294.10/186.60 inference(rewrite,[status(thm)],[])).
% 294.10/186.60 tff(24774,plain,
% 294.10/186.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_1, c_a, s7, s8)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s7) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | (m_mutex_h_half_v_inp(c_e_h_1, c_a, s7) | (~node12(c_e_h_1, c_a, s7, s8)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s8))))),
% 294.10/186.60 inference(monotonicity,[status(thm)],[24773])).
% 294.10/186.60 tff(24775,plain,
% 294.10/186.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_1, c_a, s7, s8)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s7) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s7) | (~node12(c_e_h_1, c_a, s7, s8)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s8)))),
% 294.10/186.60 inference(transitivity,[status(thm)],[24774, 24772])).
% 294.10/186.60 tff(24776,plain,
% 294.10/186.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | ((~node12(c_e_h_1, c_a, s7, s8)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s7) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s8)))),
% 294.10/186.60 inference(quant_inst,[status(thm)],[])).
% 294.10/186.60 tff(24777,plain,
% 294.10/186.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | m_mutex_h_half_v_inp(I0, I1, X) | (~m_mutex_h_half_v_out(I0, I1, Y)))) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s7) | (~node12(c_e_h_1, c_a, s7, s8)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s8))),
% 294.10/186.60 inference(modus_ponens,[status(thm)],[24776, 24775])).
% 294.10/186.60 tff(24778,plain,
% 294.10/186.60 ($false),
% 294.10/186.60 inference(unit_resolution,[status(thm)],[24777, 454, 24474, 24752, 24492])).
% 294.10/186.60 tff(24779,plain,((~node12(c_e_h_1, c_a, s7, s8)) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s8)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s7)), inference(lemma,lemma(discharge,[]))).
% 294.10/186.60 tff(24780,plain,
% 294.10/186.60 (~node12(c_e_h_1, c_a, s7, s8)),
% 294.10/186.60 inference(unit_resolution,[status(thm)],[24779, 24752, 24492])).
% 294.10/186.60 tff(24781,plain,
% 294.10/186.60 (node13(c_e_h_1, c_a, s7, s8)),
% 294.10/186.60 inference(unit_resolution,[status(thm)],[24487, 24780])).
% 294.10/186.60 tff(24782,plain,
% 294.10/186.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_1, c_a, s8)) | (~node13(c_e_h_1, c_a, s7, s8)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s8)) | (~node13(c_e_h_1, c_a, s7, s8)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s7))),
% 294.10/186.60 inference(rewrite,[status(thm)],[])).
% 294.10/186.60 tff(24783,plain,
% 294.10/186.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | ((~m_mutex_h_half_v_out(c_e_h_1, c_a, s8)) | (~node13(c_e_h_1, c_a, s7, s8)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s7))),
% 294.10/186.60 inference(quant_inst,[status(thm)],[])).
% 294.10/186.60 tff(24784,plain,
% 294.10/186.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_mutex_h_half_v_out(I0, I1, Y)) | (~node13(I0, I1, X, Y)) | m_mutex_h_half_v_out(I0, I1, X))) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s8)) | (~node13(c_e_h_1, c_a, s7, s8)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s7)),
% 294.10/186.60 inference(modus_ponens,[status(thm)],[24783, 24782])).
% 294.10/186.60 tff(24785,plain,
% 294.10/186.60 ($false),
% 294.10/186.60 inference(unit_resolution,[status(thm)],[24784, 423, 24781, 24647, 24752])).
% 294.10/186.60 tff(24786,plain,((~m_mutex_h_half_v_out(c_e_h_1, c_a, s8)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s7) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s7)), inference(lemma,lemma(discharge,[]))).
% 294.10/186.60 tff(24787,plain,
% 294.10/186.60 (m_mutex_h_half_v_out(c_e_h_1, c_a, s7)),
% 294.10/186.60 inference(unit_resolution,[status(thm)],[24786, 24771, 24752])).
% 294.10/186.60 tff(24788,plain,
% 294.10/186.60 ($false),
% 294.10/186.60 inference(unit_resolution,[status(thm)],[24638, 24787, 24767, 24766])).
% 294.10/186.60 tff(24789,plain,(m_user_v_req(c_e_h_1, c_u, s7) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s8))), inference(lemma,lemma(discharge,[]))).
% 294.10/186.60 tff(24790,plain,
% 294.10/186.60 (m_user_v_req(c_e_h_1, c_u, s7)),
% 294.10/186.60 inference(unit_resolution,[status(thm)],[24789, 24752])).
% 294.10/186.60 tff(24791,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s7)), introduced(assumption)).
% 294.10/186.60 tff(24792,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s6)), introduced(assumption)).
% 294.10/186.60 tff(24793,assumption,(node22(c_e_h_1, c_r, s6, s7)), introduced(assumption)).
% 294.10/186.60 tff(24794,plain,
% 294.10/186.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s7)) | (~node22(c_e_h_1, c_r, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_r, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s7)) | (~node22(c_e_h_1, c_r, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_r, s6))),
% 294.10/186.60 inference(rewrite,[status(thm)],[])).
% 294.10/186.60 tff(24795,plain,
% 294.10/186.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s7)) | (~node22(c_e_h_1, c_r, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_r, s6))),
% 294.10/186.60 inference(quant_inst,[status(thm)],[])).
% 294.10/186.60 tff(24796,plain,
% 294.10/186.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s7)) | (~node22(c_e_h_1, c_r, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_r, s6)),
% 294.10/186.60 inference(modus_ponens,[status(thm)],[24795, 24794])).
% 294.10/186.60 tff(24797,plain,
% 294.10/186.60 ($false),
% 294.10/186.60 inference(unit_resolution,[status(thm)],[24796, 108, 24792, 24793, 24791])).
% 294.10/186.60 tff(24798,plain,((~node22(c_e_h_1, c_r, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_r, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s7))), inference(lemma,lemma(discharge,[]))).
% 294.10/186.60 tff(24799,plain,
% 294.10/186.60 (~node22(c_e_h_1, c_r, s6, s7)),
% 294.10/186.60 inference(unit_resolution,[status(thm)],[24798, 24791, 24792])).
% 294.10/186.60 tff(24800,plain,
% 294.10/186.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_1, c_r, s6, s7) | node22(c_e_h_1, c_r, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_1, c_r, s6, s7) | node22(c_e_h_1, c_r, s6, s7))),
% 294.10/186.60 inference(rewrite,[status(thm)],[])).
% 294.10/186.60 tff(24801,plain,
% 294.10/186.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_1, c_r, s6, s7) | node22(c_e_h_1, c_r, s6, s7))),
% 294.10/186.60 inference(quant_inst,[status(thm)],[])).
% 294.10/186.60 tff(24802,plain,
% 294.10/186.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_1, c_r, s6, s7) | node22(c_e_h_1, c_r, s6, s7)),
% 294.10/186.60 inference(modus_ponens,[status(thm)],[24801, 24800])).
% 294.10/186.60 tff(24803,plain,
% 294.10/186.60 (node21(c_e_h_1, c_r, s6, s7) | node22(c_e_h_1, c_r, s6, s7)),
% 294.10/186.60 inference(unit_resolution,[status(thm)],[24802, 82, 1844])).
% 294.10/186.60 tff(24804,plain,
% 294.10/186.60 (node21(c_e_h_1, c_r, s6, s7)),
% 294.10/186.60 inference(unit_resolution,[status(thm)],[24803, 24799])).
% 294.10/186.60 tff(24805,plain,
% 294.10/186.60 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s6)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s6)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6))),
% 294.10/186.61 inference(rewrite,[status(thm)],[])).
% 294.10/186.61 tff(24806,plain,
% 294.10/186.61 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s6)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6))),
% 294.10/186.61 inference(quant_inst,[status(thm)],[])).
% 294.10/186.61 tff(24807,plain,
% 294.10/186.61 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s6)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s6)),
% 294.10/186.61 inference(modus_ponens,[status(thm)],[24806, 24805])).
% 294.10/186.61 tff(24808,plain,
% 294.10/186.61 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s6)),
% 294.10/186.61 inference(unit_resolution,[status(thm)],[24807, 14293, 18158])).
% 294.10/186.61 tff(24809,plain,
% 294.10/186.61 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s6)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s6)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s6))),
% 294.10/186.61 inference(rewrite,[status(thm)],[])).
% 294.10/186.61 tff(24810,plain,
% 294.10/186.61 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s6)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s6))),
% 294.10/186.61 inference(quant_inst,[status(thm)],[])).
% 294.10/186.61 tff(24811,plain,
% 294.10/186.61 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s6)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s6)),
% 294.10/186.61 inference(modus_ponens,[status(thm)],[24810, 24809])).
% 294.10/186.61 tff(24812,plain,
% 294.10/186.61 (~node20(c_e_h_1, c_r, s6)),
% 294.10/186.61 inference(unit_resolution,[status(thm)],[24811, 4563, 24808])).
% 294.10/186.61 tff(24813,plain,
% 294.10/186.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s7)) | node20(c_e_h_1, c_r, s6) | (~node21(c_e_h_1, c_r, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s7)) | node20(c_e_h_1, c_r, s6) | (~node21(c_e_h_1, c_r, s6, s7)))),
% 294.10/186.61 inference(rewrite,[status(thm)],[])).
% 294.10/186.61 tff(24814,plain,
% 294.10/186.61 ((node20(c_e_h_1, c_r, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s7)) | (~node21(c_e_h_1, c_r, s6, s7))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_r, s7)) | node20(c_e_h_1, c_r, s6) | (~node21(c_e_h_1, c_r, s6, s7)))),
% 294.10/186.61 inference(rewrite,[status(thm)],[])).
% 294.10/186.61 tff(24815,plain,
% 294.10/186.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s7)) | (~node21(c_e_h_1, c_r, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s7)) | node20(c_e_h_1, c_r, s6) | (~node21(c_e_h_1, c_r, s6, s7))))),
% 294.10/186.61 inference(monotonicity,[status(thm)],[24814])).
% 294.10/186.61 tff(24816,plain,
% 294.10/186.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s7)) | (~node21(c_e_h_1, c_r, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s7)) | node20(c_e_h_1, c_r, s6) | (~node21(c_e_h_1, c_r, s6, s7)))),
% 294.10/186.61 inference(transitivity,[status(thm)],[24815, 24813])).
% 294.10/186.61 tff(24817,plain,
% 294.10/186.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s7)) | (~node21(c_e_h_1, c_r, s6, s7)))),
% 294.10/186.61 inference(quant_inst,[status(thm)],[])).
% 294.10/186.61 tff(24818,plain,
% 294.10/186.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s7)) | node20(c_e_h_1, c_r, s6) | (~node21(c_e_h_1, c_r, s6, s7))),
% 294.10/186.61 inference(modus_ponens,[status(thm)],[24817, 24816])).
% 294.10/186.61 tff(24819,plain,
% 294.10/186.61 ($false),
% 294.10/186.61 inference(unit_resolution,[status(thm)],[24818, 52, 24812, 24804, 24791])).
% 294.10/186.61 tff(24820,plain,((~m_and_h_gate_v_out(c_e_h_1, c_r, s7)) | m_and_h_gate_v_out(c_e_h_1, c_r, s6)), inference(lemma,lemma(discharge,[]))).
% 294.10/186.61 tff(24821,plain,
% 294.10/186.61 (~m_and_h_gate_v_out(c_e_h_1, c_r, s7)),
% 294.10/186.61 inference(unit_resolution,[status(thm)],[24820, 24557])).
% 294.10/186.61 tff(24822,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s7)), introduced(assumption)).
% 294.10/186.61 tff(24823,assumption,(m_user_v_ack(c_e_h_1, c_u, s7)), introduced(assumption)).
% 294.10/186.61 tff(24824,plain,
% 294.10/186.61 (((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s7)) | m_and_h_gate_v_out(c_e_h_1, c_r, s7))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s7)) | m_and_h_gate_v_out(c_e_h_1, c_r, s7))),
% 294.10/186.61 inference(rewrite,[status(thm)],[])).
% 294.10/186.61 tff(24825,plain,
% 294.10/186.61 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | ((~m_user_v_ack(c_e_h_1, c_u, s7)) | m_and_h_gate_v_out(c_e_h_1, c_r, s7))),
% 294.10/186.61 inference(quant_inst,[status(thm)],[])).
% 294.10/186.61 tff(24826,plain,
% 294.10/186.61 ((~![I0: $i, X: $i] : ((~m_user_v_ack(I0, c_u, X)) | m_and_h_gate_v_out(I0, c_r, X))) | (~m_user_v_ack(c_e_h_1, c_u, s7)) | m_and_h_gate_v_out(c_e_h_1, c_r, s7)),
% 294.10/186.61 inference(modus_ponens,[status(thm)],[24825, 24824])).
% 294.10/186.61 tff(24827,plain,
% 294.10/186.61 ($false),
% 294.10/186.61 inference(unit_resolution,[status(thm)],[24826, 268, 24823, 24822])).
% 294.10/186.61 tff(24828,plain,((~m_user_v_ack(c_e_h_1, c_u, s7)) | m_and_h_gate_v_out(c_e_h_1, c_r, s7)), inference(lemma,lemma(discharge,[]))).
% 294.10/186.61 tff(24829,plain,
% 294.10/186.61 (~m_user_v_ack(c_e_h_1, c_u, s7)),
% 294.10/186.61 inference(unit_resolution,[status(thm)],[24828, 24821])).
% 294.10/186.61 tff(24830,assumption,(~m_user_v_ack(c_e_h_1, c_u, s7)), introduced(assumption)).
% 294.10/186.61 tff(24831,assumption,(~m_user_v_req(c_e_h_1, c_u, s8)), introduced(assumption)).
% 294.10/186.61 tff(24832,assumption,(node7(c_e_h_1, c_u, s7, s8)), introduced(assumption)).
% 294.10/186.61 tff(24833,plain,
% 294.10/186.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | ((~node7(c_e_h_1, c_u, s7, s8)) | m_user_v_ack(c_e_h_1, c_u, s7) | m_user_v_req(c_e_h_1, c_u, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | (~node7(c_e_h_1, c_u, s7, s8)) | m_user_v_ack(c_e_h_1, c_u, s7) | m_user_v_req(c_e_h_1, c_u, s8))),
% 294.10/186.61 inference(rewrite,[status(thm)],[])).
% 294.10/186.61 tff(24834,plain,
% 294.10/186.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | ((~node7(c_e_h_1, c_u, s7, s8)) | m_user_v_ack(c_e_h_1, c_u, s7) | m_user_v_req(c_e_h_1, c_u, s8))),
% 294.10/186.61 inference(quant_inst,[status(thm)],[])).
% 294.10/186.61 tff(24835,plain,
% 294.10/186.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node7(I0, I1, X, Y)) | m_user_v_ack(I0, I1, X) | m_user_v_req(I0, I1, Y))) | (~node7(c_e_h_1, c_u, s7, s8)) | m_user_v_ack(c_e_h_1, c_u, s7) | m_user_v_req(c_e_h_1, c_u, s8)),
% 294.10/186.61 inference(modus_ponens,[status(thm)],[24834, 24833])).
% 294.10/186.61 tff(24836,plain,
% 294.10/186.61 ($false),
% 294.10/186.61 inference(unit_resolution,[status(thm)],[24835, 284, 24830, 24832, 24831])).
% 294.10/186.61 tff(24837,plain,((~node7(c_e_h_1, c_u, s7, s8)) | m_user_v_ack(c_e_h_1, c_u, s7) | m_user_v_req(c_e_h_1, c_u, s8)), inference(lemma,lemma(discharge,[]))).
% 294.10/186.61 tff(24838,plain,
% 294.10/186.61 (~node7(c_e_h_1, c_u, s7, s8)),
% 294.10/186.61 inference(unit_resolution,[status(thm)],[24837, 24831, 24830])).
% 294.10/186.61 tff(24839,assumption,(node8(c_e_h_1, c_u, s7, s8)), introduced(assumption)).
% 294.10/186.61 tff(24840,plain,
% 294.10/186.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_1, c_u, s8) | (~m_user_v_req(c_e_h_1, c_u, s7)) | (~node8(c_e_h_1, c_u, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | m_user_v_req(c_e_h_1, c_u, s8) | (~m_user_v_req(c_e_h_1, c_u, s7)) | (~node8(c_e_h_1, c_u, s7, s8)))),
% 294.10/186.61 inference(rewrite,[status(thm)],[])).
% 294.10/186.61 tff(24841,plain,
% 294.10/186.61 ((m_user_v_req(c_e_h_1, c_u, s8) | (~node8(c_e_h_1, c_u, s7, s8)) | (~m_user_v_req(c_e_h_1, c_u, s7))) <=> (m_user_v_req(c_e_h_1, c_u, s8) | (~m_user_v_req(c_e_h_1, c_u, s7)) | (~node8(c_e_h_1, c_u, s7, s8)))),
% 294.10/186.61 inference(rewrite,[status(thm)],[])).
% 294.10/186.61 tff(24842,plain,
% 294.10/186.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_1, c_u, s8) | (~node8(c_e_h_1, c_u, s7, s8)) | (~m_user_v_req(c_e_h_1, c_u, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_1, c_u, s8) | (~m_user_v_req(c_e_h_1, c_u, s7)) | (~node8(c_e_h_1, c_u, s7, s8))))),
% 294.10/186.61 inference(monotonicity,[status(thm)],[24841])).
% 294.10/186.61 tff(24843,plain,
% 294.10/186.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_1, c_u, s8) | (~node8(c_e_h_1, c_u, s7, s8)) | (~m_user_v_req(c_e_h_1, c_u, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | m_user_v_req(c_e_h_1, c_u, s8) | (~m_user_v_req(c_e_h_1, c_u, s7)) | (~node8(c_e_h_1, c_u, s7, s8)))),
% 294.10/186.61 inference(transitivity,[status(thm)],[24842, 24840])).
% 294.10/186.61 tff(24844,plain,
% 294.10/186.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | (m_user_v_req(c_e_h_1, c_u, s8) | (~node8(c_e_h_1, c_u, s7, s8)) | (~m_user_v_req(c_e_h_1, c_u, s7)))),
% 294.10/186.61 inference(quant_inst,[status(thm)],[])).
% 294.10/186.61 tff(24845,plain,
% 294.10/186.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_user_v_req(I0, I1, Y) | (~node8(I0, I1, X, Y)) | (~m_user_v_req(I0, I1, X)))) | m_user_v_req(c_e_h_1, c_u, s8) | (~m_user_v_req(c_e_h_1, c_u, s7)) | (~node8(c_e_h_1, c_u, s7, s8))),
% 294.10/186.61 inference(modus_ponens,[status(thm)],[24844, 24843])).
% 294.10/186.61 tff(24846,plain,
% 294.10/186.61 ($false),
% 294.10/186.61 inference(unit_resolution,[status(thm)],[24845, 302, 24839, 24491, 24831])).
% 294.10/186.61 tff(24847,plain,((~node8(c_e_h_1, c_u, s7, s8)) | (~m_user_v_req(c_e_h_1, c_u, s7)) | m_user_v_req(c_e_h_1, c_u, s8)), inference(lemma,lemma(discharge,[]))).
% 294.10/186.61 tff(24848,plain,
% 294.10/186.61 (~node8(c_e_h_1, c_u, s7, s8)),
% 294.10/186.61 inference(unit_resolution,[status(thm)],[24847, 24831, 24491])).
% 294.10/186.61 tff(24849,plain,
% 294.10/186.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | ((~trans(s7, s8)) | node7(c_e_h_1, c_u, s7, s8) | node8(c_e_h_1, c_u, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | (~trans(s7, s8)) | node7(c_e_h_1, c_u, s7, s8) | node8(c_e_h_1, c_u, s7, s8))),
% 294.10/186.61 inference(rewrite,[status(thm)],[])).
% 294.10/186.61 tff(24850,plain,
% 294.10/186.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | ((~trans(s7, s8)) | node7(c_e_h_1, c_u, s7, s8) | node8(c_e_h_1, c_u, s7, s8))),
% 294.10/186.61 inference(quant_inst,[status(thm)],[])).
% 294.10/186.61 tff(24851,plain,
% 294.10/186.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node7(I0, I1, X, Y) | node8(I0, I1, X, Y))) | (~trans(s7, s8)) | node7(c_e_h_1, c_u, s7, s8) | node8(c_e_h_1, c_u, s7, s8)),
% 294.10/186.61 inference(modus_ponens,[status(thm)],[24850, 24849])).
% 294.10/186.61 tff(24852,plain,
% 294.10/186.61 (node7(c_e_h_1, c_u, s7, s8) | node8(c_e_h_1, c_u, s7, s8)),
% 294.10/186.61 inference(unit_resolution,[status(thm)],[24851, 328, 1938])).
% 294.10/186.61 tff(24853,plain,
% 294.10/186.61 ($false),
% 294.10/186.61 inference(unit_resolution,[status(thm)],[24852, 24848, 24838])).
% 294.10/186.61 tff(24854,plain,(m_user_v_req(c_e_h_1, c_u, s8) | (~m_user_v_req(c_e_h_1, c_u, s7)) | m_user_v_ack(c_e_h_1, c_u, s7)), inference(lemma,lemma(discharge,[]))).
% 294.10/186.61 tff(24855,plain,
% 294.10/186.61 (m_user_v_req(c_e_h_1, c_u, s8) | (~m_user_v_req(c_e_h_1, c_u, s7))),
% 294.10/186.61 inference(unit_resolution,[status(thm)],[24854, 24829])).
% 294.10/186.61 tff(24856,plain,
% 294.10/186.61 (m_user_v_req(c_e_h_1, c_u, s8)),
% 294.10/186.61 inference(unit_resolution,[status(thm)],[24855, 24790])).
% 294.10/186.61 tff(24857,assumption,(m_user_v_req(c_e_h_1, c_u, s8)), introduced(assumption)).
% 294.10/186.62 tff(24858,assumption,(~m_mutex_h_half_v_inp(c_e_h_1, c_a, s8)), introduced(assumption)).
% 294.10/186.62 tff(24859,plain,
% 294.10/186.62 (((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | ((~m_user_v_req(c_e_h_1, c_u, s8)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s8))) <=> ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | (~m_user_v_req(c_e_h_1, c_u, s8)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s8))),
% 294.10/186.62 inference(rewrite,[status(thm)],[])).
% 294.10/186.62 tff(24860,plain,
% 294.10/186.62 ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | ((~m_user_v_req(c_e_h_1, c_u, s8)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s8))),
% 294.10/186.62 inference(quant_inst,[status(thm)],[])).
% 294.10/186.62 tff(24861,plain,
% 294.10/186.62 ((~![I0: $i, X: $i] : ((~m_user_v_req(I0, c_u, X)) | m_mutex_h_half_v_inp(I0, c_a, X))) | (~m_user_v_req(c_e_h_1, c_u, s8)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s8)),
% 294.10/186.62 inference(modus_ponens,[status(thm)],[24860, 24859])).
% 294.10/186.62 tff(24862,plain,
% 294.10/186.62 ($false),
% 294.10/186.62 inference(unit_resolution,[status(thm)],[24861, 1426, 24858, 24857])).
% 294.10/186.62 tff(24863,plain,((~m_user_v_req(c_e_h_1, c_u, s8)) | m_mutex_h_half_v_inp(c_e_h_1, c_a, s8)), inference(lemma,lemma(discharge,[]))).
% 294.10/186.62 tff(24864,plain,
% 294.10/186.62 (m_mutex_h_half_v_inp(c_e_h_1, c_a, s8)),
% 294.10/186.62 inference(unit_resolution,[status(thm)],[24863, 24856])).
% 294.10/186.62 tff(24865,assumption,(m_mutex_h_half_v_inp(c_e_h_1, c_a, s8)), introduced(assumption)).
% 294.10/186.62 tff(24866,assumption,(node12(c_e_h_1, c_a, s8, s9)), introduced(assumption)).
% 294.10/186.62 tff(24867,plain,
% 294.10/186.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~m_mutex_h_half_v_inp(c_e_h_1, c_a, s8)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s9) | (~node12(c_e_h_1, c_a, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s8)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s9) | (~node12(c_e_h_1, c_a, s8, s9)))),
% 294.10/186.62 inference(rewrite,[status(thm)],[])).
% 294.10/186.62 tff(24868,plain,
% 294.10/186.62 (((~node12(c_e_h_1, c_a, s8, s9)) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s8)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s9)) <=> ((~m_mutex_h_half_v_inp(c_e_h_1, c_a, s8)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s9) | (~node12(c_e_h_1, c_a, s8, s9)))),
% 294.10/186.62 inference(rewrite,[status(thm)],[])).
% 294.10/186.62 tff(24869,plain,
% 294.10/186.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_1, c_a, s8, s9)) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s8)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~m_mutex_h_half_v_inp(c_e_h_1, c_a, s8)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s9) | (~node12(c_e_h_1, c_a, s8, s9))))),
% 294.10/186.62 inference(monotonicity,[status(thm)],[24868])).
% 294.10/186.62 tff(24870,plain,
% 294.10/186.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_1, c_a, s8, s9)) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s8)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s8)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s9) | (~node12(c_e_h_1, c_a, s8, s9)))),
% 294.10/186.62 inference(transitivity,[status(thm)],[24869, 24867])).
% 294.10/186.62 tff(24871,plain,
% 294.10/186.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | ((~node12(c_e_h_1, c_a, s8, s9)) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s8)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s9))),
% 294.10/186.62 inference(quant_inst,[status(thm)],[])).
% 294.10/186.62 tff(24872,plain,
% 294.10/186.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node12(I0, I1, X, Y)) | (~m_mutex_h_half_v_inp(I0, I1, X)) | m_mutex_h_half_v_out(I0, I1, Y))) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s8)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s9) | (~node12(c_e_h_1, c_a, s8, s9))),
% 294.10/186.62 inference(modus_ponens,[status(thm)],[24871, 24870])).
% 294.10/186.62 tff(24873,plain,
% 294.10/186.62 ($false),
% 294.10/186.62 inference(unit_resolution,[status(thm)],[24872, 1483, 24866, 24753, 24865])).
% 294.10/186.62 tff(24874,plain,((~node12(c_e_h_1, c_a, s8, s9)) | m_mutex_h_half_v_out(c_e_h_1, c_a, s9) | (~m_mutex_h_half_v_inp(c_e_h_1, c_a, s8))), inference(lemma,lemma(discharge,[]))).
% 294.10/186.62 tff(24875,plain,
% 294.10/186.62 (~node12(c_e_h_1, c_a, s8, s9)),
% 294.10/186.62 inference(unit_resolution,[status(thm)],[24874, 24753, 24864])).
% 294.10/186.62 tff(24876,plain,
% 294.10/186.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s8, s9)) | node12(c_e_h_1, c_a, s8, s9) | node13(c_e_h_1, c_a, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s8, s9)) | node12(c_e_h_1, c_a, s8, s9) | node13(c_e_h_1, c_a, s8, s9))),
% 294.10/186.62 inference(rewrite,[status(thm)],[])).
% 294.10/186.62 tff(24877,plain,
% 294.10/186.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | ((~trans(s8, s9)) | node12(c_e_h_1, c_a, s8, s9) | node13(c_e_h_1, c_a, s8, s9))),
% 294.10/186.62 inference(quant_inst,[status(thm)],[])).
% 294.10/186.62 tff(24878,plain,
% 294.10/186.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node12(I0, I1, X, Y) | node13(I0, I1, X, Y))) | (~trans(s8, s9)) | node12(c_e_h_1, c_a, s8, s9) | node13(c_e_h_1, c_a, s8, s9)),
% 294.10/186.62 inference(modus_ponens,[status(thm)],[24877, 24876])).
% 294.10/186.62 tff(24879,plain,
% 294.10/186.62 (node12(c_e_h_1, c_a, s8, s9) | node13(c_e_h_1, c_a, s8, s9)),
% 294.10/186.62 inference(unit_resolution,[status(thm)],[24878, 439, 1993])).
% 294.10/186.62 tff(24880,plain,
% 294.10/186.62 ($false),
% 294.10/186.62 inference(unit_resolution,[status(thm)],[24879, 24875, 24763])).
% 294.10/186.62 tff(24881,plain,(m_mutex_h_half_v_out(c_e_h_1, c_a, s9) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s8))), inference(lemma,lemma(discharge,[]))).
% 294.10/186.62 tff(24882,plain,
% 294.10/186.62 (m_mutex_h_half_v_out(c_e_h_1, c_a, s9)),
% 294.10/186.62 inference(unit_resolution,[status(thm)],[24881, 24751])).
% 294.10/186.62 tff(24883,assumption,(~m_and_h_gate_v_in1(c_e_h_1, c_c, s9)), introduced(assumption)).
% 294.10/186.62 tff(24884,assumption,(m_mutex_h_half_v_out(c_e_h_1, c_a, s9)), introduced(assumption)).
% 294.10/186.62 tff(24885,plain,
% 294.10/186.62 (((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | ((~m_mutex_h_half_v_out(c_e_h_1, c_a, s9)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s9))) <=> ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s9)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s9))),
% 294.10/186.62 inference(rewrite,[status(thm)],[])).
% 294.10/186.62 tff(24886,plain,
% 294.10/186.62 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | ((~m_mutex_h_half_v_out(c_e_h_1, c_a, s9)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s9))),
% 294.10/186.62 inference(quant_inst,[status(thm)],[])).
% 294.10/186.62 tff(24887,plain,
% 294.10/186.62 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_and_h_gate_v_in1(I0, c_c, X))) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s9)) | m_and_h_gate_v_in1(c_e_h_1, c_c, s9)),
% 294.10/186.62 inference(modus_ponens,[status(thm)],[24886, 24885])).
% 294.10/186.62 tff(24888,plain,
% 294.10/186.62 ($false),
% 294.10/186.62 inference(unit_resolution,[status(thm)],[24887, 2556, 24884, 24883])).
% 294.10/186.62 tff(24889,plain,(m_and_h_gate_v_in1(c_e_h_1, c_c, s9) | (~m_mutex_h_half_v_out(c_e_h_1, c_a, s9))), inference(lemma,lemma(discharge,[]))).
% 294.10/186.62 tff(24890,plain,
% 294.10/186.62 (m_and_h_gate_v_in1(c_e_h_1, c_c, s9)),
% 294.10/186.62 inference(unit_resolution,[status(thm)],[24889, 24882])).
% 294.10/186.62 tff(24891,plain,
% 294.10/186.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~node15(I0, I1, X, Y)) | (~m_c_h_element_v_out(I0, I1, X)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s11) | (~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | (~node15(c_e_h_1, c_e, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~node15(I0, I1, X, Y)) | (~m_c_h_element_v_out(I0, I1, X)))) | m_c_h_element_v_out(c_e_h_1, c_e, s11) | (~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | (~node15(c_e_h_1, c_e, s10, s11)))),
% 294.13/186.62 inference(rewrite,[status(thm)],[])).
% 294.13/186.62 tff(24892,plain,
% 294.13/186.62 ((m_c_h_element_v_out(c_e_h_1, c_e, s11) | (~node15(c_e_h_1, c_e, s10, s11)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s10))) <=> (m_c_h_element_v_out(c_e_h_1, c_e, s11) | (~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | (~node15(c_e_h_1, c_e, s10, s11)))),
% 294.13/186.62 inference(rewrite,[status(thm)],[])).
% 294.13/186.62 tff(24893,plain,
% 294.13/186.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~node15(I0, I1, X, Y)) | (~m_c_h_element_v_out(I0, I1, X)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s11) | (~node15(c_e_h_1, c_e, s10, s11)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~node15(I0, I1, X, Y)) | (~m_c_h_element_v_out(I0, I1, X)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s11) | (~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | (~node15(c_e_h_1, c_e, s10, s11))))),
% 294.13/186.62 inference(monotonicity,[status(thm)],[24892])).
% 294.13/186.62 tff(24894,plain,
% 294.13/186.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~node15(I0, I1, X, Y)) | (~m_c_h_element_v_out(I0, I1, X)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s11) | (~node15(c_e_h_1, c_e, s10, s11)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~node15(I0, I1, X, Y)) | (~m_c_h_element_v_out(I0, I1, X)))) | m_c_h_element_v_out(c_e_h_1, c_e, s11) | (~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | (~node15(c_e_h_1, c_e, s10, s11)))),
% 294.13/186.62 inference(transitivity,[status(thm)],[24893, 24891])).
% 294.13/186.62 tff(24895,plain,
% 294.13/186.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~node15(I0, I1, X, Y)) | (~m_c_h_element_v_out(I0, I1, X)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s11) | (~node15(c_e_h_1, c_e, s10, s11)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s10)))),
% 294.13/186.62 inference(quant_inst,[status(thm)],[])).
% 294.13/186.62 tff(24896,plain,
% 294.13/186.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~node15(I0, I1, X, Y)) | (~m_c_h_element_v_out(I0, I1, X)))) | m_c_h_element_v_out(c_e_h_1, c_e, s11) | (~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | (~node15(c_e_h_1, c_e, s10, s11))),
% 294.13/186.62 inference(modus_ponens,[status(thm)],[24895, 24894])).
% 294.13/186.62 tff(24897,plain,
% 294.13/186.62 ($false),
% 294.13/186.62 inference(unit_resolution,[status(thm)],[24896, 20829, 24402, 23260, 24340])).
% 294.13/186.62 tff(24898,plain,((~node15(c_e_h_1, c_e, s10, s11)) | m_c_h_element_v_out(c_e_h_1, c_e, s11) | (~m_c_h_element_v_out(c_e_h_1, c_e, s10))), inference(lemma,lemma(discharge,[]))).
% 294.13/186.62 tff(24899,plain,
% 294.13/186.62 (~node15(c_e_h_1, c_e, s10, s11)),
% 294.13/186.62 inference(unit_resolution,[status(thm)],[24898, 23260, 24402])).
% 294.13/186.62 tff(24900,plain,
% 294.13/186.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_out(I0, I1, X)) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s11) | (~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | (~node18(c_e_h_1, c_e, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_out(I0, I1, X)) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s11) | (~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | (~node18(c_e_h_1, c_e, s10, s11)))),
% 294.13/186.62 inference(rewrite,[status(thm)],[])).
% 294.13/186.62 tff(24901,plain,
% 294.13/186.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_out(I0, I1, X)) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s11) | (~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | (~node18(c_e_h_1, c_e, s10, s11)))),
% 294.13/186.62 inference(quant_inst,[status(thm)],[])).
% 294.13/186.62 tff(24902,plain,
% 294.13/186.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_out(I0, I1, X)) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s11) | (~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | (~node18(c_e_h_1, c_e, s10, s11))),
% 294.13/186.62 inference(modus_ponens,[status(thm)],[24901, 24900])).
% 294.13/186.62 tff(24903,plain,
% 294.13/186.62 ($false),
% 294.13/186.62 inference(unit_resolution,[status(thm)],[24902, 11191, 24402, 23260, 24333])).
% 294.13/186.62 tff(24904,plain,((~node18(c_e_h_1, c_e, s10, s11)) | m_c_h_element_v_out(c_e_h_1, c_e, s11) | (~m_c_h_element_v_out(c_e_h_1, c_e, s10))), inference(lemma,lemma(discharge,[]))).
% 294.13/186.63 tff(24905,plain,
% 294.13/186.63 (~node18(c_e_h_1, c_e, s10, s11)),
% 294.13/186.63 inference(unit_resolution,[status(thm)],[24904, 23260, 24402])).
% 294.13/186.63 tff(24906,plain,
% 294.13/186.63 (node17(c_e_h_1, c_e, s10)),
% 294.13/186.63 inference(unit_resolution,[status(thm)],[24386, 24905])).
% 294.13/186.63 tff(24907,plain,
% 294.13/186.63 (m_c_h_element_v_in1(c_e_h_1, c_e, s10)),
% 294.13/186.63 inference(unit_resolution,[status(thm)],[24353, 24324])).
% 294.13/186.63 tff(24908,assumption,(m_c_h_element_v_in1(c_e_h_1, c_e, s10)), introduced(assumption)).
% 294.13/186.63 tff(24909,assumption,(node14(c_e_h_1, c_e, s10, s11)), introduced(assumption)).
% 294.13/186.63 tff(24910,plain,
% 294.13/186.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | (~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_out(I0, I1, Y))) | (m_c_h_element_v_out(c_e_h_1, c_e, s11) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s10)) | (~node14(c_e_h_1, c_e, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | (~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_out(I0, I1, Y))) | m_c_h_element_v_out(c_e_h_1, c_e, s11) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s10)) | (~node14(c_e_h_1, c_e, s10, s11)))),
% 294.13/186.63 inference(rewrite,[status(thm)],[])).
% 294.13/186.63 tff(24911,plain,
% 294.13/186.63 (((~node14(c_e_h_1, c_e, s10, s11)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s10)) | m_c_h_element_v_out(c_e_h_1, c_e, s11)) <=> (m_c_h_element_v_out(c_e_h_1, c_e, s11) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s10)) | (~node14(c_e_h_1, c_e, s10, s11)))),
% 294.13/186.63 inference(rewrite,[status(thm)],[])).
% 294.13/186.63 tff(24912,plain,
% 294.13/186.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | (~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_out(I0, I1, Y))) | ((~node14(c_e_h_1, c_e, s10, s11)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s10)) | m_c_h_element_v_out(c_e_h_1, c_e, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | (~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_out(I0, I1, Y))) | (m_c_h_element_v_out(c_e_h_1, c_e, s11) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s10)) | (~node14(c_e_h_1, c_e, s10, s11))))),
% 294.13/186.63 inference(monotonicity,[status(thm)],[24911])).
% 294.13/186.63 tff(24913,plain,
% 294.13/186.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | (~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_out(I0, I1, Y))) | ((~node14(c_e_h_1, c_e, s10, s11)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s10)) | m_c_h_element_v_out(c_e_h_1, c_e, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | (~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_out(I0, I1, Y))) | m_c_h_element_v_out(c_e_h_1, c_e, s11) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s10)) | (~node14(c_e_h_1, c_e, s10, s11)))),
% 294.13/186.63 inference(transitivity,[status(thm)],[24912, 24910])).
% 294.13/186.63 tff(24914,plain,
% 294.13/186.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | (~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_out(I0, I1, Y))) | ((~node14(c_e_h_1, c_e, s10, s11)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s10)) | m_c_h_element_v_out(c_e_h_1, c_e, s11))),
% 294.13/186.63 inference(quant_inst,[status(thm)],[])).
% 294.13/186.63 tff(24915,plain,
% 294.13/186.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | (~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_out(I0, I1, Y))) | m_c_h_element_v_out(c_e_h_1, c_e, s11) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s10)) | (~node14(c_e_h_1, c_e, s10, s11))),
% 294.13/186.63 inference(modus_ponens,[status(thm)],[24914, 24913])).
% 294.13/186.63 tff(24916,plain,
% 294.13/186.63 ($false),
% 294.13/186.63 inference(unit_resolution,[status(thm)],[24915, 20875, 24402, 24909, 24908])).
% 294.13/186.63 tff(24917,plain,((~node14(c_e_h_1, c_e, s10, s11)) | m_c_h_element_v_out(c_e_h_1, c_e, s11) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s10))), inference(lemma,lemma(discharge,[]))).
% 294.13/186.63 tff(24918,plain,
% 294.13/186.63 (~node14(c_e_h_1, c_e, s10, s11)),
% 294.13/186.63 inference(unit_resolution,[status(thm)],[24917, 24907, 24402])).
% 294.13/186.63 tff(24919,plain,
% 294.13/186.63 (node16(c_e_h_1, c_e, s10)),
% 294.13/186.63 inference(unit_resolution,[status(thm)],[24369, 24918, 24348])).
% 294.13/186.63 tff(24920,plain,
% 294.13/186.63 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s10)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s10)) | (~node16(c_e_h_1, c_e, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s10)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s10)) | (~node16(c_e_h_1, c_e, s10)))),
% 294.13/186.63 inference(rewrite,[status(thm)],[])).
% 294.13/186.63 tff(24921,plain,
% 294.13/186.63 (((~node16(c_e_h_1, c_e, s10)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s10)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s10))) <=> ((~m_c_h_element_v_in1(c_e_h_1, c_e, s10)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s10)) | (~node16(c_e_h_1, c_e, s10)))),
% 294.13/186.63 inference(rewrite,[status(thm)],[])).
% 294.13/186.63 tff(24922,plain,
% 294.13/186.63 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s10)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s10)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s10)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s10)) | (~node16(c_e_h_1, c_e, s10))))),
% 294.13/186.63 inference(monotonicity,[status(thm)],[24921])).
% 294.13/186.63 tff(24923,plain,
% 294.13/186.63 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s10)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s10)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s10)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s10)) | (~node16(c_e_h_1, c_e, s10)))),
% 294.13/186.63 inference(transitivity,[status(thm)],[24922, 24920])).
% 294.13/186.63 tff(24924,plain,
% 294.13/186.63 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s10)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s10)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s10)))),
% 294.13/186.63 inference(quant_inst,[status(thm)],[])).
% 294.13/186.63 tff(24925,plain,
% 294.13/186.63 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s10)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s10)) | (~node16(c_e_h_1, c_e, s10))),
% 294.13/186.63 inference(modus_ponens,[status(thm)],[24924, 24923])).
% 294.13/186.63 tff(24926,plain,
% 294.13/186.63 ($false),
% 294.13/186.63 inference(unit_resolution,[status(thm)],[24925, 2307, 24919, 24907, 24324])).
% 294.13/186.63 tff(24927,plain,((~m_c_h_element_v_in2(c_e_h_1, c_e, s10)) | node15(c_e_h_1, c_e, s10, s11) | m_c_h_element_v_out(c_e_h_1, c_e, s11) | (~node17(c_e_h_1, c_e, s10))), inference(lemma,lemma(discharge,[]))).
% 294.13/186.63 tff(24928,plain,
% 294.13/186.63 (~m_c_h_element_v_in2(c_e_h_1, c_e, s10)),
% 294.13/186.63 inference(unit_resolution,[status(thm)],[24927, 24906, 24402, 24899])).
% 294.13/186.63 tff(24929,assumption,(~node14(c_e_h_1, c_e, s10, s11)), introduced(assumption)).
% 294.13/186.63 tff(24930,plain,
% 294.13/186.63 ((~m_c_h_element_v_in2(c_e_h_1, c_e, s10)) | (~node17(c_e_h_1, c_e, s10))),
% 294.13/186.63 inference(unit_resolution,[status(thm)],[24352, 859, 24347])).
% 294.13/186.63 tff(24931,plain,
% 294.13/186.63 (~m_c_h_element_v_in2(c_e_h_1, c_e, s10)),
% 294.13/186.63 inference(unit_resolution,[status(thm)],[24930, 24906])).
% 294.13/186.63 tff(24932,plain,
% 294.13/186.63 ((~node16(c_e_h_1, c_e, s10)) | m_c_h_element_v_in2(c_e_h_1, c_e, s10)),
% 294.13/186.63 inference(unit_resolution,[status(thm)],[24357, 178, 24347])).
% 294.13/186.63 tff(24933,plain,
% 294.13/186.63 (~node16(c_e_h_1, c_e, s10)),
% 294.13/186.63 inference(unit_resolution,[status(thm)],[24932, 24931])).
% 294.13/186.63 tff(24934,plain,
% 294.13/186.63 (node15(c_e_h_1, c_e, s10, s11)),
% 294.13/186.63 inference(unit_resolution,[status(thm)],[24369, 24933, 24929])).
% 294.13/186.63 tff(24935,plain,
% 294.13/186.63 ($false),
% 294.13/186.63 inference(unit_resolution,[status(thm)],[24896, 20829, 24402, 23260, 24934])).
% 294.13/186.63 tff(24936,plain,((~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | m_c_h_element_v_out(c_e_h_1, c_e, s11) | node14(c_e_h_1, c_e, s10, s11) | m_c_h_element_v_in1(c_e_h_1, c_e, s10)), inference(lemma,lemma(discharge,[]))).
% 294.13/186.63 tff(24937,plain,
% 294.13/186.63 (m_c_h_element_v_in1(c_e_h_1, c_e, s10)),
% 294.13/186.63 inference(unit_resolution,[status(thm)],[24936, 23260, 24929, 24402])).
% 294.13/186.63 tff(24938,plain,
% 294.13/186.63 ($false),
% 294.13/186.63 inference(unit_resolution,[status(thm)],[24397, 24906, 24937])).
% 294.13/186.63 tff(24939,plain,((~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | m_c_h_element_v_in2(c_e_h_1, c_e, s10) | node14(c_e_h_1, c_e, s10, s11) | m_c_h_element_v_out(c_e_h_1, c_e, s11)), inference(lemma,lemma(discharge,[]))).
% 294.13/186.63 tff(24940,plain,
% 294.13/186.63 (node14(c_e_h_1, c_e, s10, s11)),
% 294.13/186.63 inference(unit_resolution,[status(thm)],[24939, 24928, 24402, 23260])).
% 294.13/186.63 tff(24941,plain,
% 294.13/186.63 (~m_c_h_element_v_in1(c_e_h_1, c_e, s10)),
% 294.13/186.63 inference(unit_resolution,[status(thm)],[24917, 24940, 24402])).
% 294.13/186.63 tff(24942,assumption,(m_and_h_gate_v_out(c_e_h_1, c_c, s10)), introduced(assumption)).
% 294.13/186.63 tff(24943,plain,
% 294.13/186.63 (^[I0: $i, X: $i] : refl(((~m_and_h_gate_v_out(I0, c_c, X)) | m_c_h_element_v_in1(I0, c_e, X)) <=> ((~m_and_h_gate_v_out(I0, c_c, X)) | m_c_h_element_v_in1(I0, c_e, X)))),
% 294.13/186.63 inference(bind,[status(th)],[])).
% 294.13/186.63 tff(24944,plain,
% 294.13/186.63 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_c_h_element_v_in1(I0, c_e, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_c_h_element_v_in1(I0, c_e, X))),
% 294.13/186.63 inference(quant_intro,[status(thm)],[24943])).
% 294.13/186.63 tff(24945,plain,
% 294.13/186.63 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_c_h_element_v_in1(I0, c_e, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_c_h_element_v_in1(I0, c_e, X))),
% 294.13/186.63 inference(rewrite,[status(thm)],[])).
% 294.13/186.63 tff(24946,plain,
% 294.13/186.63 (^[I0: $i, X: $i] : rewrite((m_c_h_element_v_in1(I0, c_e, X) | (~m_and_h_gate_v_out(I0, c_c, X))) <=> ((~m_and_h_gate_v_out(I0, c_c, X)) | m_c_h_element_v_in1(I0, c_e, X)))),
% 294.13/186.63 inference(bind,[status(th)],[])).
% 294.13/186.63 tff(24947,plain,
% 294.13/186.63 (![I0: $i, X: $i] : (m_c_h_element_v_in1(I0, c_e, X) | (~m_and_h_gate_v_out(I0, c_c, X))) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_c_h_element_v_in1(I0, c_e, X))),
% 294.13/186.63 inference(quant_intro,[status(thm)],[24946])).
% 294.13/186.63 tff(24948,axiom,(![I0: $i, X: $i] : (m_c_h_element_v_in1(I0, c_e, X) | (~m_and_h_gate_v_out(I0, c_c, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_19')).
% 294.13/186.63 tff(24949,plain,
% 294.13/186.63 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_c_h_element_v_in1(I0, c_e, X))),
% 294.13/186.63 inference(modus_ponens,[status(thm)],[24948, 24947])).
% 294.13/186.63 tff(24950,plain,
% 294.13/186.63 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_c_h_element_v_in1(I0, c_e, X))),
% 294.13/186.63 inference(modus_ponens,[status(thm)],[24949, 24945])).
% 294.13/186.63 tff(24951,plain,(
% 294.13/186.63 ![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_c_h_element_v_in1(I0, c_e, X))),
% 294.13/186.63 inference(skolemize,[status(sab)],[24950])).
% 294.13/186.63 tff(24952,plain,
% 294.13/186.63 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_c_h_element_v_in1(I0, c_e, X))),
% 294.13/186.63 inference(modus_ponens,[status(thm)],[24951, 24944])).
% 294.13/186.63 tff(24953,plain,
% 294.13/186.63 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_c_h_element_v_in1(I0, c_e, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_c, s10)) | m_c_h_element_v_in1(c_e_h_1, c_e, s10))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_c_h_element_v_in1(I0, c_e, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s10)) | m_c_h_element_v_in1(c_e_h_1, c_e, s10))),
% 294.13/186.63 inference(rewrite,[status(thm)],[])).
% 294.13/186.63 tff(24954,plain,
% 294.13/186.63 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_c_h_element_v_in1(I0, c_e, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_c, s10)) | m_c_h_element_v_in1(c_e_h_1, c_e, s10))),
% 294.13/186.63 inference(quant_inst,[status(thm)],[])).
% 294.13/186.63 tff(24955,plain,
% 294.13/186.63 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_c, X)) | m_c_h_element_v_in1(I0, c_e, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s10)) | m_c_h_element_v_in1(c_e_h_1, c_e, s10)),
% 294.13/186.63 inference(modus_ponens,[status(thm)],[24954, 24953])).
% 294.13/186.63 tff(24956,plain,
% 294.13/186.63 ($false),
% 294.13/186.63 inference(unit_resolution,[status(thm)],[24955, 24952, 24942, 24347])).
% 294.13/186.63 tff(24957,plain,((~m_and_h_gate_v_out(c_e_h_1, c_c, s10)) | m_c_h_element_v_in1(c_e_h_1, c_e, s10)), inference(lemma,lemma(discharge,[]))).
% 294.13/186.63 tff(24958,plain,
% 294.13/186.63 (~m_and_h_gate_v_out(c_e_h_1, c_c, s10)),
% 294.13/186.63 inference(unit_resolution,[status(thm)],[24957, 24941])).
% 294.13/186.64 tff(24959,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_c, s10)), introduced(assumption)).
% 294.13/186.64 tff(24960,assumption,(node22(c_e_h_1, c_c, s9, s10)), introduced(assumption)).
% 294.13/186.64 tff(24961,plain,
% 294.13/186.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_c, s9)) | m_and_h_gate_v_out(c_e_h_1, c_c, s10) | (~node22(c_e_h_1, c_c, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s9)) | m_and_h_gate_v_out(c_e_h_1, c_c, s10) | (~node22(c_e_h_1, c_c, s9, s10)))),
% 294.13/186.64 inference(rewrite,[status(thm)],[])).
% 294.13/186.64 tff(24962,plain,
% 294.13/186.64 ((m_and_h_gate_v_out(c_e_h_1, c_c, s10) | (~node22(c_e_h_1, c_c, s9, s10)) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s9))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_c, s9)) | m_and_h_gate_v_out(c_e_h_1, c_c, s10) | (~node22(c_e_h_1, c_c, s9, s10)))),
% 294.13/186.64 inference(rewrite,[status(thm)],[])).
% 294.13/186.64 tff(24963,plain,
% 294.13/186.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_1, c_c, s10) | (~node22(c_e_h_1, c_c, s9, s10)) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_c, s9)) | m_and_h_gate_v_out(c_e_h_1, c_c, s10) | (~node22(c_e_h_1, c_c, s9, s10))))),
% 294.13/186.64 inference(monotonicity,[status(thm)],[24962])).
% 294.13/186.64 tff(24964,plain,
% 294.13/186.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_1, c_c, s10) | (~node22(c_e_h_1, c_c, s9, s10)) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s9)) | m_and_h_gate_v_out(c_e_h_1, c_c, s10) | (~node22(c_e_h_1, c_c, s9, s10)))),
% 294.13/186.64 inference(transitivity,[status(thm)],[24963, 24961])).
% 294.13/186.64 tff(24965,plain,
% 294.13/186.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (m_and_h_gate_v_out(c_e_h_1, c_c, s10) | (~node22(c_e_h_1, c_c, s9, s10)) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s9)))),
% 294.13/186.64 inference(quant_inst,[status(thm)],[])).
% 294.13/186.64 tff(24966,plain,
% 294.13/186.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_v_out(I0, I1, Y) | (~node22(I0, I1, X, Y)) | (~m_and_h_gate_v_out(I0, I1, X)))) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s9)) | m_and_h_gate_v_out(c_e_h_1, c_c, s10) | (~node22(c_e_h_1, c_c, s9, s10))),
% 294.13/186.64 inference(modus_ponens,[status(thm)],[24965, 24964])).
% 294.13/186.64 tff(24967,plain,
% 294.13/186.64 ($false),
% 294.13/186.64 inference(unit_resolution,[status(thm)],[24966, 5871, 24960, 24425, 24959])).
% 294.13/186.64 tff(24968,plain,((~node22(c_e_h_1, c_c, s9, s10)) | (~m_and_h_gate_v_out(c_e_h_1, c_c, s9)) | m_and_h_gate_v_out(c_e_h_1, c_c, s10)), inference(lemma,lemma(discharge,[]))).
% 294.13/186.64 tff(24969,plain,
% 294.13/186.64 (~node22(c_e_h_1, c_c, s9, s10)),
% 294.13/186.64 inference(unit_resolution,[status(thm)],[24968, 24958, 24424])).
% 294.13/186.64 tff(24970,plain,
% 294.13/186.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s9, s10)) | node21(c_e_h_1, c_c, s9, s10) | node22(c_e_h_1, c_c, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s9, s10)) | node21(c_e_h_1, c_c, s9, s10) | node22(c_e_h_1, c_c, s9, s10))),
% 294.13/186.64 inference(rewrite,[status(thm)],[])).
% 294.13/186.64 tff(24971,plain,
% 294.13/186.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s9, s10)) | node21(c_e_h_1, c_c, s9, s10) | node22(c_e_h_1, c_c, s9, s10))),
% 294.13/186.64 inference(quant_inst,[status(thm)],[])).
% 294.13/186.64 tff(24972,plain,
% 294.13/186.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s9, s10)) | node21(c_e_h_1, c_c, s9, s10) | node22(c_e_h_1, c_c, s9, s10)),
% 294.13/186.64 inference(modus_ponens,[status(thm)],[24971, 24970])).
% 294.13/186.64 tff(24973,plain,
% 294.13/186.64 (node21(c_e_h_1, c_c, s9, s10) | node22(c_e_h_1, c_c, s9, s10)),
% 294.13/186.64 inference(unit_resolution,[status(thm)],[24972, 82, 7676])).
% 294.13/186.64 tff(24974,plain,
% 294.13/186.64 (node21(c_e_h_1, c_c, s9, s10)),
% 294.13/186.64 inference(unit_resolution,[status(thm)],[24973, 24969])).
% 294.13/186.64 tff(24975,assumption,(m_and_h_gate_v_out(c_e_h_1, c_q, s9)), introduced(assumption)).
% 294.13/186.64 tff(24976,assumption,(m_c_h_element_v_out(c_e_h_1, c_f, s8)), introduced(assumption)).
% 294.13/186.64 tff(24977,assumption,(node15(c_e_h_1, c_f, s7, s8)), introduced(assumption)).
% 294.13/186.64 tff(24978,assumption,(m_c_h_element_v_out(c_e_h_1, c_f, s7)), introduced(assumption)).
% 294.13/186.64 tff(24979,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_f, s6)), introduced(assumption)).
% 294.13/186.64 tff(24980,assumption,(~node16(c_e_h_1, c_f, s6)), introduced(assumption)).
% 294.13/186.64 tff(24981,assumption,(node15(c_e_h_1, c_f, s6, s7)), introduced(assumption)).
% 294.13/186.64 tff(24982,assumption,(m_c_h_element_v_in2(c_e_h_1, c_f, s5)), introduced(assumption)).
% 294.13/186.64 tff(24983,plain,
% 294.13/186.64 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s5)) | m_and_h_gate_v_out(c_e_h_1, c_i, s5))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s5)) | m_and_h_gate_v_out(c_e_h_1, c_i, s5))),
% 294.13/186.64 inference(rewrite,[status(thm)],[])).
% 294.13/186.64 tff(24984,plain,
% 294.13/186.64 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s5)) | m_and_h_gate_v_out(c_e_h_1, c_i, s5))),
% 294.13/186.64 inference(quant_inst,[status(thm)],[])).
% 294.13/186.64 tff(24985,plain,
% 294.13/186.64 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s5)) | m_and_h_gate_v_out(c_e_h_1, c_i, s5)),
% 294.13/186.64 inference(modus_ponens,[status(thm)],[24984, 24983])).
% 294.13/186.64 tff(24986,plain,
% 294.13/186.64 ($false),
% 294.13/186.64 inference(unit_resolution,[status(thm)],[24985, 2143, 17520, 24982])).
% 294.13/186.64 tff(24987,plain,(~m_c_h_element_v_in2(c_e_h_1, c_f, s5)), inference(lemma,lemma(discharge,[]))).
% 294.13/186.64 tff(24988,assumption,(m_c_h_element_v_out(c_e_h_1, c_f, s6)), introduced(assumption)).
% 294.13/186.64 tff(24989,assumption,(node18(c_e_h_1, c_f, s5, s6)), introduced(assumption)).
% 294.13/186.64 tff(24990,plain,
% 294.13/186.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_f, s5) | (~m_c_h_element_v_out(c_e_h_1, c_f, s6)) | (~node18(c_e_h_1, c_f, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s5) | (~m_c_h_element_v_out(c_e_h_1, c_f, s6)) | (~node18(c_e_h_1, c_f, s5, s6)))),
% 294.13/186.64 inference(rewrite,[status(thm)],[])).
% 294.13/186.64 tff(24991,plain,
% 294.13/186.64 (((~m_c_h_element_v_out(c_e_h_1, c_f, s6)) | m_c_h_element_v_out(c_e_h_1, c_f, s5) | (~node18(c_e_h_1, c_f, s5, s6))) <=> (m_c_h_element_v_out(c_e_h_1, c_f, s5) | (~m_c_h_element_v_out(c_e_h_1, c_f, s6)) | (~node18(c_e_h_1, c_f, s5, s6)))),
% 294.13/186.64 inference(rewrite,[status(thm)],[])).
% 294.13/186.64 tff(24992,plain,
% 294.13/186.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s6)) | m_c_h_element_v_out(c_e_h_1, c_f, s5) | (~node18(c_e_h_1, c_f, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_f, s5) | (~m_c_h_element_v_out(c_e_h_1, c_f, s6)) | (~node18(c_e_h_1, c_f, s5, s6))))),
% 294.13/186.64 inference(monotonicity,[status(thm)],[24991])).
% 294.13/186.64 tff(24993,plain,
% 294.13/186.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s6)) | m_c_h_element_v_out(c_e_h_1, c_f, s5) | (~node18(c_e_h_1, c_f, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s5) | (~m_c_h_element_v_out(c_e_h_1, c_f, s6)) | (~node18(c_e_h_1, c_f, s5, s6)))),
% 294.13/186.64 inference(transitivity,[status(thm)],[24992, 24990])).
% 294.13/186.64 tff(24994,plain,
% 294.13/186.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s6)) | m_c_h_element_v_out(c_e_h_1, c_f, s5) | (~node18(c_e_h_1, c_f, s5, s6)))),
% 294.13/186.64 inference(quant_inst,[status(thm)],[])).
% 294.13/186.64 tff(24995,plain,
% 294.13/186.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s5) | (~m_c_h_element_v_out(c_e_h_1, c_f, s6)) | (~node18(c_e_h_1, c_f, s5, s6))),
% 294.13/186.64 inference(modus_ponens,[status(thm)],[24994, 24993])).
% 294.13/186.64 tff(24996,plain,
% 294.13/186.64 ($false),
% 294.13/186.64 inference(unit_resolution,[status(thm)],[24995, 753, 16927, 24988, 24989])).
% 294.13/186.64 tff(24997,plain,((~node18(c_e_h_1, c_f, s5, s6)) | m_c_h_element_v_out(c_e_h_1, c_f, s5) | (~m_c_h_element_v_out(c_e_h_1, c_f, s6))), inference(lemma,lemma(discharge,[]))).
% 294.13/186.64 tff(24998,plain,
% 294.13/186.64 (~node18(c_e_h_1, c_f, s5, s6)),
% 294.13/186.64 inference(unit_resolution,[status(thm)],[24997, 24988, 16927])).
% 294.13/186.64 tff(24999,plain,
% 294.13/186.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s5, s6)) | node19(c_e_h_1, c_f, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s5, s6)) | node19(c_e_h_1, c_f, s5, s6))),
% 294.13/186.64 inference(rewrite,[status(thm)],[])).
% 294.13/186.64 tff(25000,plain,
% 294.13/186.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s5, s6)) | node19(c_e_h_1, c_f, s5, s6))),
% 294.13/186.64 inference(quant_inst,[status(thm)],[])).
% 294.13/186.64 tff(25001,plain,
% 294.13/186.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s5, s6)) | node19(c_e_h_1, c_f, s5, s6)),
% 294.13/186.64 inference(modus_ponens,[status(thm)],[25000, 24999])).
% 294.13/186.64 tff(25002,plain,
% 294.13/186.64 (node19(c_e_h_1, c_f, s5, s6)),
% 294.13/186.64 inference(unit_resolution,[status(thm)],[25001, 190, 1406])).
% 294.13/186.64 tff(25003,plain,
% 294.13/186.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_1, c_f, s5, s6) | node17(c_e_h_1, c_f, s5) | (~node19(c_e_h_1, c_f, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_f, s5, s6) | node17(c_e_h_1, c_f, s5) | (~node19(c_e_h_1, c_f, s5, s6)))),
% 294.13/186.64 inference(rewrite,[status(thm)],[])).
% 294.13/186.64 tff(25004,plain,
% 294.13/186.64 ((node17(c_e_h_1, c_f, s5) | node18(c_e_h_1, c_f, s5, s6) | (~node19(c_e_h_1, c_f, s5, s6))) <=> (node18(c_e_h_1, c_f, s5, s6) | node17(c_e_h_1, c_f, s5) | (~node19(c_e_h_1, c_f, s5, s6)))),
% 294.13/186.64 inference(rewrite,[status(thm)],[])).
% 294.13/186.64 tff(25005,plain,
% 294.13/186.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s5) | node18(c_e_h_1, c_f, s5, s6) | (~node19(c_e_h_1, c_f, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_1, c_f, s5, s6) | node17(c_e_h_1, c_f, s5) | (~node19(c_e_h_1, c_f, s5, s6))))),
% 294.13/186.64 inference(monotonicity,[status(thm)],[25004])).
% 294.13/186.64 tff(25006,plain,
% 294.13/186.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s5) | node18(c_e_h_1, c_f, s5, s6) | (~node19(c_e_h_1, c_f, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_f, s5, s6) | node17(c_e_h_1, c_f, s5) | (~node19(c_e_h_1, c_f, s5, s6)))),
% 294.13/186.64 inference(transitivity,[status(thm)],[25005, 25003])).
% 294.13/186.64 tff(25007,plain,
% 294.13/186.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s5) | node18(c_e_h_1, c_f, s5, s6) | (~node19(c_e_h_1, c_f, s5, s6)))),
% 294.13/186.65 inference(quant_inst,[status(thm)],[])).
% 294.13/186.65 tff(25008,plain,
% 294.13/186.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_f, s5, s6) | node17(c_e_h_1, c_f, s5) | (~node19(c_e_h_1, c_f, s5, s6))),
% 294.13/186.65 inference(modus_ponens,[status(thm)],[25007, 25006])).
% 294.13/186.65 tff(25009,plain,
% 294.13/186.65 (node18(c_e_h_1, c_f, s5, s6) | node17(c_e_h_1, c_f, s5)),
% 294.13/186.65 inference(unit_resolution,[status(thm)],[25008, 776, 25002])).
% 294.13/186.65 tff(25010,plain,
% 294.13/186.65 (node17(c_e_h_1, c_f, s5)),
% 294.13/186.65 inference(unit_resolution,[status(thm)],[25009, 24998])).
% 294.13/186.65 tff(25011,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_f, s5)), introduced(assumption)).
% 294.13/186.65 tff(25012,plain,
% 294.13/186.65 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_f, s5) | (~node17(c_e_h_1, c_f, s5)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_f, s5) | (~node17(c_e_h_1, c_f, s5)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s5)))),
% 294.13/186.65 inference(rewrite,[status(thm)],[])).
% 294.13/186.65 tff(25013,plain,
% 294.13/186.65 (((~m_c_h_element_v_in1(c_e_h_1, c_f, s5)) | m_c_h_element_v_in2(c_e_h_1, c_f, s5) | (~node17(c_e_h_1, c_f, s5))) <=> (m_c_h_element_v_in2(c_e_h_1, c_f, s5) | (~node17(c_e_h_1, c_f, s5)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s5)))),
% 294.13/186.65 inference(rewrite,[status(thm)],[])).
% 294.13/186.65 tff(25014,plain,
% 294.13/186.65 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s5)) | m_c_h_element_v_in2(c_e_h_1, c_f, s5) | (~node17(c_e_h_1, c_f, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_f, s5) | (~node17(c_e_h_1, c_f, s5)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s5))))),
% 294.13/186.65 inference(monotonicity,[status(thm)],[25013])).
% 294.13/186.65 tff(25015,plain,
% 294.13/186.65 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s5)) | m_c_h_element_v_in2(c_e_h_1, c_f, s5) | (~node17(c_e_h_1, c_f, s5)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_f, s5) | (~node17(c_e_h_1, c_f, s5)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s5)))),
% 294.13/186.65 inference(transitivity,[status(thm)],[25014, 25012])).
% 294.13/186.65 tff(25016,plain,
% 294.13/186.65 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s5)) | m_c_h_element_v_in2(c_e_h_1, c_f, s5) | (~node17(c_e_h_1, c_f, s5)))),
% 294.13/186.65 inference(quant_inst,[status(thm)],[])).
% 294.13/186.65 tff(25017,plain,
% 294.13/186.65 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_f, s5) | (~node17(c_e_h_1, c_f, s5)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s5))),
% 294.13/186.65 inference(modus_ponens,[status(thm)],[25016, 25015])).
% 294.13/186.65 tff(25018,plain,
% 294.13/186.65 ((~node17(c_e_h_1, c_f, s5)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s5))),
% 294.13/186.65 inference(unit_resolution,[status(thm)],[25017, 919, 25011])).
% 294.13/186.65 tff(25019,plain,
% 294.13/186.65 (~m_c_h_element_v_in1(c_e_h_1, c_f, s5)),
% 294.13/186.65 inference(unit_resolution,[status(thm)],[25018, 25010])).
% 294.13/186.65 tff(25020,plain,
% 294.13/186.65 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s5)) | m_c_h_element_v_in1(c_e_h_1, c_f, s5) | m_c_h_element_v_in2(c_e_h_1, c_f, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s5)) | m_c_h_element_v_in1(c_e_h_1, c_f, s5) | m_c_h_element_v_in2(c_e_h_1, c_f, s5))),
% 294.13/186.65 inference(rewrite,[status(thm)],[])).
% 294.13/186.65 tff(25021,plain,
% 294.13/186.65 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s5)) | m_c_h_element_v_in1(c_e_h_1, c_f, s5) | m_c_h_element_v_in2(c_e_h_1, c_f, s5))),
% 294.13/186.65 inference(quant_inst,[status(thm)],[])).
% 294.13/186.65 tff(25022,plain,
% 294.13/186.65 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s5)) | m_c_h_element_v_in1(c_e_h_1, c_f, s5) | m_c_h_element_v_in2(c_e_h_1, c_f, s5)),
% 294.13/186.65 inference(modus_ponens,[status(thm)],[25021, 25020])).
% 294.13/186.65 tff(25023,plain,
% 294.13/186.65 ((~node16(c_e_h_1, c_f, s5)) | m_c_h_element_v_in1(c_e_h_1, c_f, s5)),
% 294.13/186.65 inference(unit_resolution,[status(thm)],[25022, 178, 25011])).
% 294.13/186.65 tff(25024,plain,
% 294.13/186.65 (~node16(c_e_h_1, c_f, s5)),
% 294.13/186.65 inference(unit_resolution,[status(thm)],[25023, 25019])).
% 294.13/186.65 tff(25025,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_f, s5)), introduced(assumption)).
% 294.13/186.65 tff(25026,assumption,(node14(c_e_h_1, c_f, s5, s6)), introduced(assumption)).
% 294.13/186.65 tff(25027,plain,
% 294.13/186.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s5) | (~m_c_h_element_v_out(c_e_h_1, c_f, s6)) | (~node14(c_e_h_1, c_f, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_f, s5) | (~m_c_h_element_v_out(c_e_h_1, c_f, s6)) | (~node14(c_e_h_1, c_f, s5, s6)))),
% 294.13/186.65 inference(rewrite,[status(thm)],[])).
% 294.13/186.65 tff(25028,plain,
% 294.13/186.65 (((~node14(c_e_h_1, c_f, s5, s6)) | m_c_h_element_v_in1(c_e_h_1, c_f, s5) | (~m_c_h_element_v_out(c_e_h_1, c_f, s6))) <=> (m_c_h_element_v_in1(c_e_h_1, c_f, s5) | (~m_c_h_element_v_out(c_e_h_1, c_f, s6)) | (~node14(c_e_h_1, c_f, s5, s6)))),
% 294.13/186.65 inference(rewrite,[status(thm)],[])).
% 294.13/186.65 tff(25029,plain,
% 294.13/186.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s5, s6)) | m_c_h_element_v_in1(c_e_h_1, c_f, s5) | (~m_c_h_element_v_out(c_e_h_1, c_f, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s5) | (~m_c_h_element_v_out(c_e_h_1, c_f, s6)) | (~node14(c_e_h_1, c_f, s5, s6))))),
% 294.13/186.65 inference(monotonicity,[status(thm)],[25028])).
% 294.13/186.65 tff(25030,plain,
% 294.13/186.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s5, s6)) | m_c_h_element_v_in1(c_e_h_1, c_f, s5) | (~m_c_h_element_v_out(c_e_h_1, c_f, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_f, s5) | (~m_c_h_element_v_out(c_e_h_1, c_f, s6)) | (~node14(c_e_h_1, c_f, s5, s6)))),
% 294.13/186.65 inference(transitivity,[status(thm)],[25029, 25027])).
% 294.13/186.65 tff(25031,plain,
% 294.13/186.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s5, s6)) | m_c_h_element_v_in1(c_e_h_1, c_f, s5) | (~m_c_h_element_v_out(c_e_h_1, c_f, s6)))),
% 294.13/186.65 inference(quant_inst,[status(thm)],[])).
% 294.13/186.65 tff(25032,plain,
% 294.13/186.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_f, s5) | (~m_c_h_element_v_out(c_e_h_1, c_f, s6)) | (~node14(c_e_h_1, c_f, s5, s6))),
% 294.13/186.65 inference(modus_ponens,[status(thm)],[25031, 25030])).
% 294.13/186.65 tff(25033,plain,
% 294.13/186.65 ($false),
% 294.13/186.65 inference(unit_resolution,[status(thm)],[25032, 223, 24988, 25026, 25025])).
% 294.13/186.65 tff(25034,plain,((~node14(c_e_h_1, c_f, s5, s6)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s6)) | m_c_h_element_v_in1(c_e_h_1, c_f, s5)), inference(lemma,lemma(discharge,[]))).
% 294.13/186.66 tff(25035,plain,
% 294.13/186.66 (~node14(c_e_h_1, c_f, s5, s6)),
% 294.13/186.66 inference(unit_resolution,[status(thm)],[25034, 24988, 25019])).
% 294.13/186.66 tff(25036,plain,
% 294.13/186.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s5) | (~node19(c_e_h_1, c_f, s5, s6)) | node14(c_e_h_1, c_f, s5, s6) | node15(c_e_h_1, c_f, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_f, s5) | (~node19(c_e_h_1, c_f, s5, s6)) | node14(c_e_h_1, c_f, s5, s6) | node15(c_e_h_1, c_f, s5, s6))),
% 294.13/186.66 inference(rewrite,[status(thm)],[])).
% 294.13/186.66 tff(25037,plain,
% 294.13/186.66 ((node16(c_e_h_1, c_f, s5) | node14(c_e_h_1, c_f, s5, s6) | node15(c_e_h_1, c_f, s5, s6) | (~node19(c_e_h_1, c_f, s5, s6))) <=> (node16(c_e_h_1, c_f, s5) | (~node19(c_e_h_1, c_f, s5, s6)) | node14(c_e_h_1, c_f, s5, s6) | node15(c_e_h_1, c_f, s5, s6))),
% 294.13/186.66 inference(rewrite,[status(thm)],[])).
% 294.13/186.66 tff(25038,plain,
% 294.13/186.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s5) | node14(c_e_h_1, c_f, s5, s6) | node15(c_e_h_1, c_f, s5, s6) | (~node19(c_e_h_1, c_f, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s5) | (~node19(c_e_h_1, c_f, s5, s6)) | node14(c_e_h_1, c_f, s5, s6) | node15(c_e_h_1, c_f, s5, s6)))),
% 294.13/186.66 inference(monotonicity,[status(thm)],[25037])).
% 294.13/186.66 tff(25039,plain,
% 294.13/186.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s5) | node14(c_e_h_1, c_f, s5, s6) | node15(c_e_h_1, c_f, s5, s6) | (~node19(c_e_h_1, c_f, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_f, s5) | (~node19(c_e_h_1, c_f, s5, s6)) | node14(c_e_h_1, c_f, s5, s6) | node15(c_e_h_1, c_f, s5, s6))),
% 294.13/186.66 inference(transitivity,[status(thm)],[25038, 25036])).
% 294.13/186.66 tff(25040,plain,
% 294.13/186.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s5) | node14(c_e_h_1, c_f, s5, s6) | node15(c_e_h_1, c_f, s5, s6) | (~node19(c_e_h_1, c_f, s5, s6)))),
% 294.13/186.66 inference(quant_inst,[status(thm)],[])).
% 294.13/186.66 tff(25041,plain,
% 294.13/186.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_f, s5) | (~node19(c_e_h_1, c_f, s5, s6)) | node14(c_e_h_1, c_f, s5, s6) | node15(c_e_h_1, c_f, s5, s6)),
% 294.13/186.66 inference(modus_ponens,[status(thm)],[25040, 25039])).
% 294.13/186.66 tff(25042,plain,
% 294.13/186.66 (node16(c_e_h_1, c_f, s5) | node14(c_e_h_1, c_f, s5, s6) | node15(c_e_h_1, c_f, s5, s6)),
% 294.13/186.66 inference(unit_resolution,[status(thm)],[25041, 204, 25002])).
% 294.13/186.66 tff(25043,plain,
% 294.13/186.66 (node15(c_e_h_1, c_f, s5, s6)),
% 294.13/186.66 inference(unit_resolution,[status(thm)],[25042, 25035, 25024])).
% 294.13/186.66 tff(25044,plain,
% 294.13/186.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s6)) | (~node15(c_e_h_1, c_f, s5, s6)) | m_c_h_element_v_out(c_e_h_1, c_f, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s6)) | (~node15(c_e_h_1, c_f, s5, s6)) | m_c_h_element_v_out(c_e_h_1, c_f, s5))),
% 294.13/186.66 inference(rewrite,[status(thm)],[])).
% 294.13/186.66 tff(25045,plain,
% 294.13/186.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s6)) | (~node15(c_e_h_1, c_f, s5, s6)) | m_c_h_element_v_out(c_e_h_1, c_f, s5))),
% 294.13/186.66 inference(quant_inst,[status(thm)],[])).
% 294.13/186.66 tff(25046,plain,
% 294.13/186.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s6)) | (~node15(c_e_h_1, c_f, s5, s6)) | m_c_h_element_v_out(c_e_h_1, c_f, s5)),
% 294.13/186.66 inference(modus_ponens,[status(thm)],[25045, 25044])).
% 294.13/186.66 tff(25047,plain,
% 294.13/186.66 ($false),
% 294.13/186.66 inference(unit_resolution,[status(thm)],[25046, 147, 16927, 24988, 25043])).
% 294.13/186.66 tff(25048,plain,((~m_c_h_element_v_out(c_e_h_1, c_f, s6)) | m_c_h_element_v_out(c_e_h_1, c_f, s5) | m_c_h_element_v_in2(c_e_h_1, c_f, s5)), inference(lemma,lemma(discharge,[]))).
% 294.13/186.66 tff(25049,plain,
% 294.13/186.66 ((~m_c_h_element_v_out(c_e_h_1, c_f, s6)) | m_c_h_element_v_out(c_e_h_1, c_f, s5)),
% 294.13/186.66 inference(unit_resolution,[status(thm)],[25048, 24987])).
% 294.13/186.66 tff(25050,plain,
% 294.13/186.66 (~m_c_h_element_v_out(c_e_h_1, c_f, s6)),
% 294.13/186.66 inference(unit_resolution,[status(thm)],[25049, 16925])).
% 294.13/186.66 tff(25051,plain,
% 294.13/186.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s7)) | (~node15(c_e_h_1, c_f, s6, s7)) | m_c_h_element_v_out(c_e_h_1, c_f, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s7)) | (~node15(c_e_h_1, c_f, s6, s7)) | m_c_h_element_v_out(c_e_h_1, c_f, s6))),
% 294.13/186.66 inference(rewrite,[status(thm)],[])).
% 294.13/186.66 tff(25052,plain,
% 294.13/186.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s7)) | (~node15(c_e_h_1, c_f, s6, s7)) | m_c_h_element_v_out(c_e_h_1, c_f, s6))),
% 294.13/186.66 inference(quant_inst,[status(thm)],[])).
% 294.13/186.66 tff(25053,plain,
% 294.13/186.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s7)) | (~node15(c_e_h_1, c_f, s6, s7)) | m_c_h_element_v_out(c_e_h_1, c_f, s6)),
% 294.13/186.66 inference(modus_ponens,[status(thm)],[25052, 25051])).
% 294.13/186.66 tff(25054,plain,
% 294.13/186.66 ($false),
% 294.13/186.66 inference(unit_resolution,[status(thm)],[25053, 147, 24978, 25050, 24981])).
% 294.13/186.66 tff(25055,plain,((~node15(c_e_h_1, c_f, s6, s7)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s7))), inference(lemma,lemma(discharge,[]))).
% 294.13/186.66 tff(25056,plain,
% 294.13/186.66 (~node15(c_e_h_1, c_f, s6, s7)),
% 294.13/186.66 inference(unit_resolution,[status(thm)],[25055, 24978])).
% 294.13/186.66 tff(25057,plain,
% 294.13/186.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s6, s7)) | node19(c_e_h_1, c_f, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s6, s7)) | node19(c_e_h_1, c_f, s6, s7))),
% 294.13/186.66 inference(rewrite,[status(thm)],[])).
% 294.13/186.66 tff(25058,plain,
% 294.13/186.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s6, s7)) | node19(c_e_h_1, c_f, s6, s7))),
% 294.13/186.66 inference(quant_inst,[status(thm)],[])).
% 294.13/186.66 tff(25059,plain,
% 294.13/186.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s6, s7)) | node19(c_e_h_1, c_f, s6, s7)),
% 294.13/186.66 inference(modus_ponens,[status(thm)],[25058, 25057])).
% 294.13/186.66 tff(25060,plain,
% 294.13/186.66 (node19(c_e_h_1, c_f, s6, s7)),
% 294.13/186.66 inference(unit_resolution,[status(thm)],[25059, 190, 1844])).
% 294.13/186.66 tff(25061,plain,
% 294.13/186.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_f, s6, s7)) | node15(c_e_h_1, c_f, s6, s7) | node14(c_e_h_1, c_f, s6, s7) | node16(c_e_h_1, c_f, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s6, s7)) | node15(c_e_h_1, c_f, s6, s7) | node14(c_e_h_1, c_f, s6, s7) | node16(c_e_h_1, c_f, s6))),
% 294.13/186.66 inference(rewrite,[status(thm)],[])).
% 294.13/186.66 tff(25062,plain,
% 294.13/186.66 ((node16(c_e_h_1, c_f, s6) | node14(c_e_h_1, c_f, s6, s7) | node15(c_e_h_1, c_f, s6, s7) | (~node19(c_e_h_1, c_f, s6, s7))) <=> ((~node19(c_e_h_1, c_f, s6, s7)) | node15(c_e_h_1, c_f, s6, s7) | node14(c_e_h_1, c_f, s6, s7) | node16(c_e_h_1, c_f, s6))),
% 294.13/186.66 inference(rewrite,[status(thm)],[])).
% 294.13/186.66 tff(25063,plain,
% 294.13/186.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s6) | node14(c_e_h_1, c_f, s6, s7) | node15(c_e_h_1, c_f, s6, s7) | (~node19(c_e_h_1, c_f, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_f, s6, s7)) | node15(c_e_h_1, c_f, s6, s7) | node14(c_e_h_1, c_f, s6, s7) | node16(c_e_h_1, c_f, s6)))),
% 294.13/186.66 inference(monotonicity,[status(thm)],[25062])).
% 294.13/186.66 tff(25064,plain,
% 294.13/186.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s6) | node14(c_e_h_1, c_f, s6, s7) | node15(c_e_h_1, c_f, s6, s7) | (~node19(c_e_h_1, c_f, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s6, s7)) | node15(c_e_h_1, c_f, s6, s7) | node14(c_e_h_1, c_f, s6, s7) | node16(c_e_h_1, c_f, s6))),
% 294.13/186.66 inference(transitivity,[status(thm)],[25063, 25061])).
% 294.13/186.66 tff(25065,plain,
% 294.13/186.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s6) | node14(c_e_h_1, c_f, s6, s7) | node15(c_e_h_1, c_f, s6, s7) | (~node19(c_e_h_1, c_f, s6, s7)))),
% 294.13/186.66 inference(quant_inst,[status(thm)],[])).
% 294.13/186.66 tff(25066,plain,
% 294.13/186.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s6, s7)) | node15(c_e_h_1, c_f, s6, s7) | node14(c_e_h_1, c_f, s6, s7) | node16(c_e_h_1, c_f, s6)),
% 294.13/186.66 inference(modus_ponens,[status(thm)],[25065, 25064])).
% 294.13/186.66 tff(25067,plain,
% 294.13/186.66 (node15(c_e_h_1, c_f, s6, s7) | node14(c_e_h_1, c_f, s6, s7) | node16(c_e_h_1, c_f, s6)),
% 294.13/186.66 inference(unit_resolution,[status(thm)],[25066, 204, 25060])).
% 294.13/186.66 tff(25068,plain,
% 294.13/186.66 (node14(c_e_h_1, c_f, s6, s7)),
% 294.13/186.66 inference(unit_resolution,[status(thm)],[25067, 25056, 24980])).
% 294.13/186.66 tff(25069,plain,
% 294.13/186.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s7)) | m_c_h_element_v_in1(c_e_h_1, c_f, s6) | (~node14(c_e_h_1, c_f, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s7)) | m_c_h_element_v_in1(c_e_h_1, c_f, s6) | (~node14(c_e_h_1, c_f, s6, s7)))),
% 294.13/186.66 inference(rewrite,[status(thm)],[])).
% 294.13/186.66 tff(25070,plain,
% 294.13/186.66 (((~node14(c_e_h_1, c_f, s6, s7)) | m_c_h_element_v_in1(c_e_h_1, c_f, s6) | (~m_c_h_element_v_out(c_e_h_1, c_f, s7))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_f, s7)) | m_c_h_element_v_in1(c_e_h_1, c_f, s6) | (~node14(c_e_h_1, c_f, s6, s7)))),
% 294.13/186.66 inference(rewrite,[status(thm)],[])).
% 294.13/186.66 tff(25071,plain,
% 294.13/186.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s6, s7)) | m_c_h_element_v_in1(c_e_h_1, c_f, s6) | (~m_c_h_element_v_out(c_e_h_1, c_f, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s7)) | m_c_h_element_v_in1(c_e_h_1, c_f, s6) | (~node14(c_e_h_1, c_f, s6, s7))))),
% 294.13/186.66 inference(monotonicity,[status(thm)],[25070])).
% 294.13/186.66 tff(25072,plain,
% 294.13/186.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s6, s7)) | m_c_h_element_v_in1(c_e_h_1, c_f, s6) | (~m_c_h_element_v_out(c_e_h_1, c_f, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s7)) | m_c_h_element_v_in1(c_e_h_1, c_f, s6) | (~node14(c_e_h_1, c_f, s6, s7)))),
% 294.13/186.67 inference(transitivity,[status(thm)],[25071, 25069])).
% 294.13/186.67 tff(25073,plain,
% 294.13/186.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s6, s7)) | m_c_h_element_v_in1(c_e_h_1, c_f, s6) | (~m_c_h_element_v_out(c_e_h_1, c_f, s7)))),
% 294.13/186.67 inference(quant_inst,[status(thm)],[])).
% 294.13/186.67 tff(25074,plain,
% 294.13/186.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s7)) | m_c_h_element_v_in1(c_e_h_1, c_f, s6) | (~node14(c_e_h_1, c_f, s6, s7))),
% 294.13/186.67 inference(modus_ponens,[status(thm)],[25073, 25072])).
% 294.13/186.67 tff(25075,plain,
% 294.13/186.67 ($false),
% 294.13/186.67 inference(unit_resolution,[status(thm)],[25074, 223, 24978, 25068, 24979])).
% 294.13/186.67 tff(25076,plain,((~m_c_h_element_v_out(c_e_h_1, c_f, s7)) | m_c_h_element_v_in1(c_e_h_1, c_f, s6) | node16(c_e_h_1, c_f, s6)), inference(lemma,lemma(discharge,[]))).
% 294.13/186.67 tff(25077,plain,
% 294.13/186.67 (node16(c_e_h_1, c_f, s6)),
% 294.13/186.67 inference(unit_resolution,[status(thm)],[25076, 24978, 24979])).
% 294.13/186.67 tff(25078,plain,
% 294.13/186.67 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s6)) | m_c_h_element_v_in1(c_e_h_1, c_f, s6) | m_c_h_element_v_in2(c_e_h_1, c_f, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s6)) | m_c_h_element_v_in1(c_e_h_1, c_f, s6) | m_c_h_element_v_in2(c_e_h_1, c_f, s6))),
% 294.13/186.67 inference(rewrite,[status(thm)],[])).
% 294.13/186.67 tff(25079,plain,
% 294.13/186.67 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s6)) | m_c_h_element_v_in1(c_e_h_1, c_f, s6) | m_c_h_element_v_in2(c_e_h_1, c_f, s6))),
% 294.13/186.67 inference(quant_inst,[status(thm)],[])).
% 294.13/186.67 tff(25080,plain,
% 294.13/186.67 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s6)) | m_c_h_element_v_in1(c_e_h_1, c_f, s6) | m_c_h_element_v_in2(c_e_h_1, c_f, s6)),
% 294.13/186.67 inference(modus_ponens,[status(thm)],[25079, 25078])).
% 294.13/186.67 tff(25081,plain,
% 294.13/186.67 ((~node16(c_e_h_1, c_f, s6)) | m_c_h_element_v_in2(c_e_h_1, c_f, s6)),
% 294.13/186.67 inference(unit_resolution,[status(thm)],[25080, 178, 24979])).
% 294.13/186.67 tff(25082,plain,
% 294.13/186.67 (m_c_h_element_v_in2(c_e_h_1, c_f, s6)),
% 294.13/186.67 inference(unit_resolution,[status(thm)],[25081, 25077])).
% 294.13/186.67 tff(25083,plain,
% 294.13/186.67 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_f, s6)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s6)) | m_c_h_element_v_in1(c_e_h_1, c_f, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_f, s6)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s6)) | m_c_h_element_v_in1(c_e_h_1, c_f, s6))),
% 294.13/186.67 inference(rewrite,[status(thm)],[])).
% 294.13/186.67 tff(25084,plain,
% 294.13/186.67 ((m_c_h_element_v_in1(c_e_h_1, c_f, s6) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s6)) | (~node17(c_e_h_1, c_f, s6))) <=> ((~node17(c_e_h_1, c_f, s6)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s6)) | m_c_h_element_v_in1(c_e_h_1, c_f, s6))),
% 294.13/186.67 inference(rewrite,[status(thm)],[])).
% 294.13/186.67 tff(25085,plain,
% 294.13/186.67 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s6) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s6)) | (~node17(c_e_h_1, c_f, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_f, s6)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s6)) | m_c_h_element_v_in1(c_e_h_1, c_f, s6)))),
% 294.13/186.67 inference(monotonicity,[status(thm)],[25084])).
% 294.13/186.67 tff(25086,plain,
% 294.13/186.67 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s6) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s6)) | (~node17(c_e_h_1, c_f, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_f, s6)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s6)) | m_c_h_element_v_in1(c_e_h_1, c_f, s6))),
% 294.13/186.67 inference(transitivity,[status(thm)],[25085, 25083])).
% 294.13/186.67 tff(25087,plain,
% 294.13/186.67 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s6) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s6)) | (~node17(c_e_h_1, c_f, s6)))),
% 294.13/186.67 inference(quant_inst,[status(thm)],[])).
% 294.13/186.67 tff(25088,plain,
% 294.13/186.67 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_f, s6)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s6)) | m_c_h_element_v_in1(c_e_h_1, c_f, s6)),
% 294.13/186.67 inference(modus_ponens,[status(thm)],[25087, 25086])).
% 294.13/186.67 tff(25089,plain,
% 294.13/186.67 ((~node17(c_e_h_1, c_f, s6)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s6))),
% 294.13/186.67 inference(unit_resolution,[status(thm)],[25088, 859, 24979])).
% 294.13/186.67 tff(25090,plain,
% 294.13/186.67 (~node17(c_e_h_1, c_f, s6)),
% 294.13/186.67 inference(unit_resolution,[status(thm)],[25089, 25082])).
% 294.13/186.67 tff(25091,plain,
% 294.13/186.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_1, c_f, s6, s7) | (~node19(c_e_h_1, c_f, s6, s7)) | node17(c_e_h_1, c_f, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_f, s6, s7) | (~node19(c_e_h_1, c_f, s6, s7)) | node17(c_e_h_1, c_f, s6))),
% 294.13/186.67 inference(rewrite,[status(thm)],[])).
% 294.13/186.67 tff(25092,plain,
% 294.13/186.67 ((node17(c_e_h_1, c_f, s6) | node18(c_e_h_1, c_f, s6, s7) | (~node19(c_e_h_1, c_f, s6, s7))) <=> (node18(c_e_h_1, c_f, s6, s7) | (~node19(c_e_h_1, c_f, s6, s7)) | node17(c_e_h_1, c_f, s6))),
% 294.13/186.67 inference(rewrite,[status(thm)],[])).
% 294.13/186.67 tff(25093,plain,
% 294.13/186.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s6) | node18(c_e_h_1, c_f, s6, s7) | (~node19(c_e_h_1, c_f, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_1, c_f, s6, s7) | (~node19(c_e_h_1, c_f, s6, s7)) | node17(c_e_h_1, c_f, s6)))),
% 294.13/186.67 inference(monotonicity,[status(thm)],[25092])).
% 294.13/186.67 tff(25094,plain,
% 294.13/186.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s6) | node18(c_e_h_1, c_f, s6, s7) | (~node19(c_e_h_1, c_f, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_f, s6, s7) | (~node19(c_e_h_1, c_f, s6, s7)) | node17(c_e_h_1, c_f, s6))),
% 294.13/186.67 inference(transitivity,[status(thm)],[25093, 25091])).
% 294.13/186.67 tff(25095,plain,
% 294.13/186.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s6) | node18(c_e_h_1, c_f, s6, s7) | (~node19(c_e_h_1, c_f, s6, s7)))),
% 294.13/186.67 inference(quant_inst,[status(thm)],[])).
% 294.13/186.67 tff(25096,plain,
% 294.13/186.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_f, s6, s7) | (~node19(c_e_h_1, c_f, s6, s7)) | node17(c_e_h_1, c_f, s6)),
% 294.13/186.67 inference(modus_ponens,[status(thm)],[25095, 25094])).
% 294.13/186.67 tff(25097,plain,
% 294.13/186.67 (node18(c_e_h_1, c_f, s6, s7) | node17(c_e_h_1, c_f, s6)),
% 294.13/186.67 inference(unit_resolution,[status(thm)],[25096, 776, 25060])).
% 294.13/186.67 tff(25098,plain,
% 294.13/186.67 (node18(c_e_h_1, c_f, s6, s7)),
% 294.13/186.67 inference(unit_resolution,[status(thm)],[25097, 25090])).
% 294.13/186.67 tff(25099,plain,
% 294.13/186.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_f, s6) | (~m_c_h_element_v_out(c_e_h_1, c_f, s7)) | (~node18(c_e_h_1, c_f, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s6) | (~m_c_h_element_v_out(c_e_h_1, c_f, s7)) | (~node18(c_e_h_1, c_f, s6, s7)))),
% 294.13/186.68 inference(rewrite,[status(thm)],[])).
% 294.13/186.68 tff(25100,plain,
% 294.13/186.68 (((~m_c_h_element_v_out(c_e_h_1, c_f, s7)) | m_c_h_element_v_out(c_e_h_1, c_f, s6) | (~node18(c_e_h_1, c_f, s6, s7))) <=> (m_c_h_element_v_out(c_e_h_1, c_f, s6) | (~m_c_h_element_v_out(c_e_h_1, c_f, s7)) | (~node18(c_e_h_1, c_f, s6, s7)))),
% 294.13/186.68 inference(rewrite,[status(thm)],[])).
% 294.13/186.68 tff(25101,plain,
% 294.13/186.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s7)) | m_c_h_element_v_out(c_e_h_1, c_f, s6) | (~node18(c_e_h_1, c_f, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_f, s6) | (~m_c_h_element_v_out(c_e_h_1, c_f, s7)) | (~node18(c_e_h_1, c_f, s6, s7))))),
% 294.13/186.68 inference(monotonicity,[status(thm)],[25100])).
% 294.13/186.68 tff(25102,plain,
% 294.13/186.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s7)) | m_c_h_element_v_out(c_e_h_1, c_f, s6) | (~node18(c_e_h_1, c_f, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s6) | (~m_c_h_element_v_out(c_e_h_1, c_f, s7)) | (~node18(c_e_h_1, c_f, s6, s7)))),
% 294.13/186.68 inference(transitivity,[status(thm)],[25101, 25099])).
% 294.13/186.68 tff(25103,plain,
% 294.13/186.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s7)) | m_c_h_element_v_out(c_e_h_1, c_f, s6) | (~node18(c_e_h_1, c_f, s6, s7)))),
% 294.13/186.68 inference(quant_inst,[status(thm)],[])).
% 294.13/186.68 tff(25104,plain,
% 294.13/186.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s6) | (~m_c_h_element_v_out(c_e_h_1, c_f, s7)) | (~node18(c_e_h_1, c_f, s6, s7))),
% 294.13/186.68 inference(modus_ponens,[status(thm)],[25103, 25102])).
% 294.13/186.68 tff(25105,plain,
% 294.13/186.68 ($false),
% 294.13/186.68 inference(unit_resolution,[status(thm)],[25104, 753, 24978, 25050, 25098])).
% 294.13/186.68 tff(25106,plain,((~m_c_h_element_v_out(c_e_h_1, c_f, s7)) | m_c_h_element_v_in1(c_e_h_1, c_f, s6)), inference(lemma,lemma(discharge,[]))).
% 294.13/186.68 tff(25107,plain,
% 294.13/186.68 (m_c_h_element_v_in1(c_e_h_1, c_f, s6)),
% 294.13/186.68 inference(unit_resolution,[status(thm)],[25106, 24978])).
% 294.13/186.68 tff(25108,plain,
% 294.13/186.68 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s6)) | m_and_h_gate_v_out(c_e_h_1, c_i, s6))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s6)) | m_and_h_gate_v_out(c_e_h_1, c_i, s6))),
% 294.13/186.68 inference(rewrite,[status(thm)],[])).
% 294.13/186.68 tff(25109,plain,
% 294.13/186.68 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s6)) | m_and_h_gate_v_out(c_e_h_1, c_i, s6))),
% 294.13/186.68 inference(quant_inst,[status(thm)],[])).
% 294.13/186.68 tff(25110,plain,
% 294.13/186.68 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s6)) | m_and_h_gate_v_out(c_e_h_1, c_i, s6)),
% 294.13/186.68 inference(modus_ponens,[status(thm)],[25109, 25108])).
% 294.13/186.68 tff(25111,plain,
% 294.13/186.68 (~m_c_h_element_v_in2(c_e_h_1, c_f, s6)),
% 294.13/186.68 inference(unit_resolution,[status(thm)],[25110, 2143, 19117])).
% 294.13/186.68 tff(25112,plain,
% 294.13/186.68 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_f, s6)) | m_c_h_element_v_in2(c_e_h_1, c_f, s6) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_f, s6)) | m_c_h_element_v_in2(c_e_h_1, c_f, s6) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s6)))),
% 294.13/186.68 inference(rewrite,[status(thm)],[])).
% 294.13/186.68 tff(25113,plain,
% 294.13/186.68 (((~m_c_h_element_v_in1(c_e_h_1, c_f, s6)) | m_c_h_element_v_in2(c_e_h_1, c_f, s6) | (~node17(c_e_h_1, c_f, s6))) <=> ((~node17(c_e_h_1, c_f, s6)) | m_c_h_element_v_in2(c_e_h_1, c_f, s6) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s6)))),
% 294.13/186.68 inference(rewrite,[status(thm)],[])).
% 294.13/186.68 tff(25114,plain,
% 294.13/186.68 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s6)) | m_c_h_element_v_in2(c_e_h_1, c_f, s6) | (~node17(c_e_h_1, c_f, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_f, s6)) | m_c_h_element_v_in2(c_e_h_1, c_f, s6) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s6))))),
% 294.13/186.68 inference(monotonicity,[status(thm)],[25113])).
% 294.13/186.68 tff(25115,plain,
% 294.13/186.68 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s6)) | m_c_h_element_v_in2(c_e_h_1, c_f, s6) | (~node17(c_e_h_1, c_f, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_f, s6)) | m_c_h_element_v_in2(c_e_h_1, c_f, s6) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s6)))),
% 294.13/186.68 inference(transitivity,[status(thm)],[25114, 25112])).
% 294.13/186.68 tff(25116,plain,
% 294.13/186.68 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s6)) | m_c_h_element_v_in2(c_e_h_1, c_f, s6) | (~node17(c_e_h_1, c_f, s6)))),
% 294.13/186.68 inference(quant_inst,[status(thm)],[])).
% 294.13/186.68 tff(25117,plain,
% 294.13/186.68 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_f, s6)) | m_c_h_element_v_in2(c_e_h_1, c_f, s6) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s6))),
% 294.13/186.68 inference(modus_ponens,[status(thm)],[25116, 25115])).
% 294.13/186.68 tff(25118,plain,
% 294.13/186.68 ((~node17(c_e_h_1, c_f, s6)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s6))),
% 294.13/186.68 inference(unit_resolution,[status(thm)],[25117, 919, 25111])).
% 294.13/186.68 tff(25119,plain,
% 294.13/186.68 (~node17(c_e_h_1, c_f, s6)),
% 294.13/186.68 inference(unit_resolution,[status(thm)],[25118, 25107])).
% 294.13/186.68 tff(25120,plain,
% 294.13/186.68 (node18(c_e_h_1, c_f, s6, s7)),
% 294.13/186.68 inference(unit_resolution,[status(thm)],[25097, 25119])).
% 294.13/186.68 tff(25121,plain,
% 294.13/186.68 ($false),
% 294.13/186.68 inference(unit_resolution,[status(thm)],[25104, 753, 24978, 25050, 25120])).
% 294.13/186.68 tff(25122,plain,(~m_c_h_element_v_out(c_e_h_1, c_f, s7)), inference(lemma,lemma(discharge,[]))).
% 294.13/186.68 tff(25123,plain,
% 294.13/186.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s8)) | (~node15(c_e_h_1, c_f, s7, s8)) | m_c_h_element_v_out(c_e_h_1, c_f, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s8)) | (~node15(c_e_h_1, c_f, s7, s8)) | m_c_h_element_v_out(c_e_h_1, c_f, s7))),
% 294.13/186.68 inference(rewrite,[status(thm)],[])).
% 294.13/186.68 tff(25124,plain,
% 294.13/186.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s8)) | (~node15(c_e_h_1, c_f, s7, s8)) | m_c_h_element_v_out(c_e_h_1, c_f, s7))),
% 294.13/186.68 inference(quant_inst,[status(thm)],[])).
% 294.13/186.68 tff(25125,plain,
% 294.13/186.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s8)) | (~node15(c_e_h_1, c_f, s7, s8)) | m_c_h_element_v_out(c_e_h_1, c_f, s7)),
% 294.13/186.68 inference(modus_ponens,[status(thm)],[25124, 25123])).
% 294.13/186.68 tff(25126,plain,
% 294.13/186.68 ($false),
% 294.13/186.68 inference(unit_resolution,[status(thm)],[25125, 147, 25122, 24977, 24976])).
% 294.13/186.68 tff(25127,plain,((~node15(c_e_h_1, c_f, s7, s8)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s8))), inference(lemma,lemma(discharge,[]))).
% 294.13/186.68 tff(25128,plain,
% 294.13/186.68 (~node15(c_e_h_1, c_f, s7, s8)),
% 294.13/186.68 inference(unit_resolution,[status(thm)],[25127, 24976])).
% 294.13/186.68 tff(25129,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_f, s7)), introduced(assumption)).
% 294.13/186.68 tff(25130,assumption,(m_c_h_element_v_in2(c_e_h_1, c_f, s7)), introduced(assumption)).
% 294.13/186.68 tff(25131,plain,
% 294.13/186.68 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s7)) | m_and_h_gate_v_out(c_e_h_1, c_i, s7))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s7)) | m_and_h_gate_v_out(c_e_h_1, c_i, s7))),
% 294.13/186.68 inference(rewrite,[status(thm)],[])).
% 294.13/186.68 tff(25132,plain,
% 294.13/186.68 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s7)) | m_and_h_gate_v_out(c_e_h_1, c_i, s7))),
% 294.13/186.68 inference(quant_inst,[status(thm)],[])).
% 294.13/186.68 tff(25133,plain,
% 294.13/186.68 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s7)) | m_and_h_gate_v_out(c_e_h_1, c_i, s7)),
% 294.13/186.68 inference(modus_ponens,[status(thm)],[25132, 25131])).
% 294.13/186.68 tff(25134,plain,
% 294.13/186.68 ($false),
% 294.13/186.68 inference(unit_resolution,[status(thm)],[25133, 2143, 22904, 25130])).
% 294.13/186.68 tff(25135,plain,((~m_c_h_element_v_in2(c_e_h_1, c_f, s7)) | m_and_h_gate_v_out(c_e_h_1, c_i, s7)), inference(lemma,lemma(discharge,[]))).
% 294.13/186.68 tff(25136,plain,
% 294.13/186.68 (~m_c_h_element_v_in2(c_e_h_1, c_f, s7)),
% 294.13/186.68 inference(unit_resolution,[status(thm)],[25135, 22532])).
% 294.13/186.68 tff(25137,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_f, s7)), introduced(assumption)).
% 294.13/186.68 tff(25138,assumption,(node16(c_e_h_1, c_f, s7)), introduced(assumption)).
% 294.13/186.68 tff(25139,plain,
% 294.13/186.68 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s7)) | m_c_h_element_v_in1(c_e_h_1, c_f, s7) | m_c_h_element_v_in2(c_e_h_1, c_f, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s7)) | m_c_h_element_v_in1(c_e_h_1, c_f, s7) | m_c_h_element_v_in2(c_e_h_1, c_f, s7))),
% 294.13/186.68 inference(rewrite,[status(thm)],[])).
% 294.13/186.68 tff(25140,plain,
% 294.13/186.68 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s7)) | m_c_h_element_v_in1(c_e_h_1, c_f, s7) | m_c_h_element_v_in2(c_e_h_1, c_f, s7))),
% 294.13/186.68 inference(quant_inst,[status(thm)],[])).
% 294.13/186.68 tff(25141,plain,
% 294.13/186.68 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s7)) | m_c_h_element_v_in1(c_e_h_1, c_f, s7) | m_c_h_element_v_in2(c_e_h_1, c_f, s7)),
% 294.13/186.68 inference(modus_ponens,[status(thm)],[25140, 25139])).
% 294.13/186.68 tff(25142,plain,
% 294.13/186.68 ($false),
% 294.13/186.68 inference(unit_resolution,[status(thm)],[25141, 178, 25138, 25129, 25137])).
% 294.13/186.68 tff(25143,plain,((~node16(c_e_h_1, c_f, s7)) | m_c_h_element_v_in1(c_e_h_1, c_f, s7) | m_c_h_element_v_in2(c_e_h_1, c_f, s7)), inference(lemma,lemma(discharge,[]))).
% 294.13/186.68 tff(25144,plain,
% 294.13/186.68 ((~node16(c_e_h_1, c_f, s7)) | m_c_h_element_v_in1(c_e_h_1, c_f, s7)),
% 294.13/186.68 inference(unit_resolution,[status(thm)],[25143, 25136])).
% 294.13/186.68 tff(25145,plain,
% 294.13/186.68 (~node16(c_e_h_1, c_f, s7)),
% 294.13/186.68 inference(unit_resolution,[status(thm)],[25144, 25129])).
% 294.13/186.68 tff(25146,assumption,(node14(c_e_h_1, c_f, s7, s8)), introduced(assumption)).
% 294.13/186.68 tff(25147,plain,
% 294.13/186.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s8)) | m_c_h_element_v_in1(c_e_h_1, c_f, s7) | (~node14(c_e_h_1, c_f, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s8)) | m_c_h_element_v_in1(c_e_h_1, c_f, s7) | (~node14(c_e_h_1, c_f, s7, s8)))),
% 294.13/186.69 inference(rewrite,[status(thm)],[])).
% 294.13/186.69 tff(25148,plain,
% 294.13/186.69 (((~node14(c_e_h_1, c_f, s7, s8)) | m_c_h_element_v_in1(c_e_h_1, c_f, s7) | (~m_c_h_element_v_out(c_e_h_1, c_f, s8))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_f, s8)) | m_c_h_element_v_in1(c_e_h_1, c_f, s7) | (~node14(c_e_h_1, c_f, s7, s8)))),
% 294.13/186.69 inference(rewrite,[status(thm)],[])).
% 294.13/186.69 tff(25149,plain,
% 294.13/186.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s7, s8)) | m_c_h_element_v_in1(c_e_h_1, c_f, s7) | (~m_c_h_element_v_out(c_e_h_1, c_f, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s8)) | m_c_h_element_v_in1(c_e_h_1, c_f, s7) | (~node14(c_e_h_1, c_f, s7, s8))))),
% 294.13/186.69 inference(monotonicity,[status(thm)],[25148])).
% 294.13/186.69 tff(25150,plain,
% 294.13/186.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s7, s8)) | m_c_h_element_v_in1(c_e_h_1, c_f, s7) | (~m_c_h_element_v_out(c_e_h_1, c_f, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s8)) | m_c_h_element_v_in1(c_e_h_1, c_f, s7) | (~node14(c_e_h_1, c_f, s7, s8)))),
% 294.13/186.69 inference(transitivity,[status(thm)],[25149, 25147])).
% 294.13/186.69 tff(25151,plain,
% 294.13/186.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s7, s8)) | m_c_h_element_v_in1(c_e_h_1, c_f, s7) | (~m_c_h_element_v_out(c_e_h_1, c_f, s8)))),
% 294.13/186.69 inference(quant_inst,[status(thm)],[])).
% 294.13/186.69 tff(25152,plain,
% 294.13/186.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s8)) | m_c_h_element_v_in1(c_e_h_1, c_f, s7) | (~node14(c_e_h_1, c_f, s7, s8))),
% 294.13/186.69 inference(modus_ponens,[status(thm)],[25151, 25150])).
% 294.13/186.69 tff(25153,plain,
% 294.13/186.69 ($false),
% 294.13/186.69 inference(unit_resolution,[status(thm)],[25152, 223, 25146, 24976, 25129])).
% 294.13/186.69 tff(25154,plain,((~node14(c_e_h_1, c_f, s7, s8)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s8)) | m_c_h_element_v_in1(c_e_h_1, c_f, s7)), inference(lemma,lemma(discharge,[]))).
% 294.13/186.69 tff(25155,plain,
% 294.13/186.69 (~node14(c_e_h_1, c_f, s7, s8)),
% 294.13/186.69 inference(unit_resolution,[status(thm)],[25154, 25129, 24976])).
% 294.13/186.69 tff(25156,plain,
% 294.13/186.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s7, s8)) | node19(c_e_h_1, c_f, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s7, s8)) | node19(c_e_h_1, c_f, s7, s8))),
% 294.13/186.69 inference(rewrite,[status(thm)],[])).
% 294.13/186.69 tff(25157,plain,
% 294.13/186.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s7, s8)) | node19(c_e_h_1, c_f, s7, s8))),
% 294.13/186.69 inference(quant_inst,[status(thm)],[])).
% 294.13/186.69 tff(25158,plain,
% 294.13/186.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s7, s8)) | node19(c_e_h_1, c_f, s7, s8)),
% 294.13/186.69 inference(modus_ponens,[status(thm)],[25157, 25156])).
% 294.13/186.69 tff(25159,plain,
% 294.13/186.69 (node19(c_e_h_1, c_f, s7, s8)),
% 294.13/186.69 inference(unit_resolution,[status(thm)],[25158, 190, 1938])).
% 294.13/186.69 tff(25160,plain,
% 294.13/186.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_1, c_f, s7, s8) | node15(c_e_h_1, c_f, s7, s8) | (~node19(c_e_h_1, c_f, s7, s8)) | node16(c_e_h_1, c_f, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_f, s7, s8) | node15(c_e_h_1, c_f, s7, s8) | (~node19(c_e_h_1, c_f, s7, s8)) | node16(c_e_h_1, c_f, s7))),
% 294.13/186.69 inference(rewrite,[status(thm)],[])).
% 294.13/186.69 tff(25161,plain,
% 294.13/186.69 ((node16(c_e_h_1, c_f, s7) | node14(c_e_h_1, c_f, s7, s8) | node15(c_e_h_1, c_f, s7, s8) | (~node19(c_e_h_1, c_f, s7, s8))) <=> (node14(c_e_h_1, c_f, s7, s8) | node15(c_e_h_1, c_f, s7, s8) | (~node19(c_e_h_1, c_f, s7, s8)) | node16(c_e_h_1, c_f, s7))),
% 294.13/186.69 inference(rewrite,[status(thm)],[])).
% 294.13/186.69 tff(25162,plain,
% 294.13/186.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s7) | node14(c_e_h_1, c_f, s7, s8) | node15(c_e_h_1, c_f, s7, s8) | (~node19(c_e_h_1, c_f, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_1, c_f, s7, s8) | node15(c_e_h_1, c_f, s7, s8) | (~node19(c_e_h_1, c_f, s7, s8)) | node16(c_e_h_1, c_f, s7)))),
% 294.13/186.69 inference(monotonicity,[status(thm)],[25161])).
% 294.13/186.69 tff(25163,plain,
% 294.13/186.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s7) | node14(c_e_h_1, c_f, s7, s8) | node15(c_e_h_1, c_f, s7, s8) | (~node19(c_e_h_1, c_f, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_f, s7, s8) | node15(c_e_h_1, c_f, s7, s8) | (~node19(c_e_h_1, c_f, s7, s8)) | node16(c_e_h_1, c_f, s7))),
% 294.13/186.69 inference(transitivity,[status(thm)],[25162, 25160])).
% 294.13/186.69 tff(25164,plain,
% 294.13/186.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s7) | node14(c_e_h_1, c_f, s7, s8) | node15(c_e_h_1, c_f, s7, s8) | (~node19(c_e_h_1, c_f, s7, s8)))),
% 294.13/186.69 inference(quant_inst,[status(thm)],[])).
% 294.13/186.69 tff(25165,plain,
% 294.13/186.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_f, s7, s8) | node15(c_e_h_1, c_f, s7, s8) | (~node19(c_e_h_1, c_f, s7, s8)) | node16(c_e_h_1, c_f, s7)),
% 294.13/186.69 inference(modus_ponens,[status(thm)],[25164, 25163])).
% 294.13/186.69 tff(25166,plain,
% 294.13/186.69 (node14(c_e_h_1, c_f, s7, s8) | node15(c_e_h_1, c_f, s7, s8) | node16(c_e_h_1, c_f, s7)),
% 294.13/186.69 inference(unit_resolution,[status(thm)],[25165, 204, 25159])).
% 294.13/186.69 tff(25167,plain,
% 294.13/186.69 ($false),
% 294.13/186.69 inference(unit_resolution,[status(thm)],[25166, 25155, 25145, 25128])).
% 294.13/186.69 tff(25168,plain,(m_c_h_element_v_in1(c_e_h_1, c_f, s7) | (~m_c_h_element_v_out(c_e_h_1, c_f, s8))), inference(lemma,lemma(discharge,[]))).
% 294.13/186.69 tff(25169,plain,
% 294.13/186.69 (m_c_h_element_v_in1(c_e_h_1, c_f, s7)),
% 294.13/186.69 inference(unit_resolution,[status(thm)],[25168, 24976])).
% 294.13/186.69 tff(25170,plain,
% 294.13/186.69 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_f, s7) | (~node17(c_e_h_1, c_f, s7)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_f, s7) | (~node17(c_e_h_1, c_f, s7)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s7)))),
% 294.13/186.69 inference(rewrite,[status(thm)],[])).
% 294.13/186.69 tff(25171,plain,
% 294.13/186.69 (((~m_c_h_element_v_in1(c_e_h_1, c_f, s7)) | m_c_h_element_v_in2(c_e_h_1, c_f, s7) | (~node17(c_e_h_1, c_f, s7))) <=> (m_c_h_element_v_in2(c_e_h_1, c_f, s7) | (~node17(c_e_h_1, c_f, s7)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s7)))),
% 294.13/186.69 inference(rewrite,[status(thm)],[])).
% 294.13/186.69 tff(25172,plain,
% 294.13/186.69 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s7)) | m_c_h_element_v_in2(c_e_h_1, c_f, s7) | (~node17(c_e_h_1, c_f, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_f, s7) | (~node17(c_e_h_1, c_f, s7)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s7))))),
% 294.13/186.69 inference(monotonicity,[status(thm)],[25171])).
% 294.13/186.69 tff(25173,plain,
% 294.13/186.69 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s7)) | m_c_h_element_v_in2(c_e_h_1, c_f, s7) | (~node17(c_e_h_1, c_f, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_f, s7) | (~node17(c_e_h_1, c_f, s7)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s7)))),
% 294.13/186.69 inference(transitivity,[status(thm)],[25172, 25170])).
% 294.13/186.69 tff(25174,plain,
% 294.13/186.69 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s7)) | m_c_h_element_v_in2(c_e_h_1, c_f, s7) | (~node17(c_e_h_1, c_f, s7)))),
% 294.13/186.69 inference(quant_inst,[status(thm)],[])).
% 294.13/186.69 tff(25175,plain,
% 294.13/186.69 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_f, s7) | (~node17(c_e_h_1, c_f, s7)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s7))),
% 294.13/186.69 inference(modus_ponens,[status(thm)],[25174, 25173])).
% 294.13/186.69 tff(25176,plain,
% 294.13/186.69 ((~node17(c_e_h_1, c_f, s7)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s7))),
% 294.13/186.69 inference(unit_resolution,[status(thm)],[25175, 919, 25136])).
% 294.13/186.69 tff(25177,plain,
% 294.13/186.69 (~node17(c_e_h_1, c_f, s7)),
% 294.13/186.69 inference(unit_resolution,[status(thm)],[25176, 25169])).
% 294.13/186.69 tff(25178,plain,
% 294.13/186.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_f, s7, s8)) | node18(c_e_h_1, c_f, s7, s8) | node17(c_e_h_1, c_f, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s7, s8)) | node18(c_e_h_1, c_f, s7, s8) | node17(c_e_h_1, c_f, s7))),
% 294.13/186.69 inference(rewrite,[status(thm)],[])).
% 294.13/186.69 tff(25179,plain,
% 294.13/186.69 ((node17(c_e_h_1, c_f, s7) | node18(c_e_h_1, c_f, s7, s8) | (~node19(c_e_h_1, c_f, s7, s8))) <=> ((~node19(c_e_h_1, c_f, s7, s8)) | node18(c_e_h_1, c_f, s7, s8) | node17(c_e_h_1, c_f, s7))),
% 294.13/186.69 inference(rewrite,[status(thm)],[])).
% 294.13/186.69 tff(25180,plain,
% 294.13/186.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s7) | node18(c_e_h_1, c_f, s7, s8) | (~node19(c_e_h_1, c_f, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_f, s7, s8)) | node18(c_e_h_1, c_f, s7, s8) | node17(c_e_h_1, c_f, s7)))),
% 294.13/186.69 inference(monotonicity,[status(thm)],[25179])).
% 294.13/186.69 tff(25181,plain,
% 294.13/186.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s7) | node18(c_e_h_1, c_f, s7, s8) | (~node19(c_e_h_1, c_f, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s7, s8)) | node18(c_e_h_1, c_f, s7, s8) | node17(c_e_h_1, c_f, s7))),
% 294.13/186.69 inference(transitivity,[status(thm)],[25180, 25178])).
% 294.13/186.69 tff(25182,plain,
% 294.13/186.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s7) | node18(c_e_h_1, c_f, s7, s8) | (~node19(c_e_h_1, c_f, s7, s8)))),
% 294.13/186.69 inference(quant_inst,[status(thm)],[])).
% 294.13/186.69 tff(25183,plain,
% 294.13/186.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s7, s8)) | node18(c_e_h_1, c_f, s7, s8) | node17(c_e_h_1, c_f, s7)),
% 294.13/186.69 inference(modus_ponens,[status(thm)],[25182, 25181])).
% 294.20/186.70 tff(25184,plain,
% 294.20/186.70 (node18(c_e_h_1, c_f, s7, s8) | node17(c_e_h_1, c_f, s7)),
% 294.20/186.70 inference(unit_resolution,[status(thm)],[25183, 776, 25159])).
% 294.20/186.70 tff(25185,plain,
% 294.20/186.70 (node18(c_e_h_1, c_f, s7, s8)),
% 294.20/186.70 inference(unit_resolution,[status(thm)],[25184, 25177])).
% 294.20/186.70 tff(25186,plain,
% 294.20/186.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_f, s7) | (~m_c_h_element_v_out(c_e_h_1, c_f, s8)) | (~node18(c_e_h_1, c_f, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s7) | (~m_c_h_element_v_out(c_e_h_1, c_f, s8)) | (~node18(c_e_h_1, c_f, s7, s8)))),
% 294.20/186.70 inference(rewrite,[status(thm)],[])).
% 294.20/186.70 tff(25187,plain,
% 294.20/186.70 (((~m_c_h_element_v_out(c_e_h_1, c_f, s8)) | m_c_h_element_v_out(c_e_h_1, c_f, s7) | (~node18(c_e_h_1, c_f, s7, s8))) <=> (m_c_h_element_v_out(c_e_h_1, c_f, s7) | (~m_c_h_element_v_out(c_e_h_1, c_f, s8)) | (~node18(c_e_h_1, c_f, s7, s8)))),
% 294.20/186.70 inference(rewrite,[status(thm)],[])).
% 294.20/186.70 tff(25188,plain,
% 294.20/186.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s8)) | m_c_h_element_v_out(c_e_h_1, c_f, s7) | (~node18(c_e_h_1, c_f, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_f, s7) | (~m_c_h_element_v_out(c_e_h_1, c_f, s8)) | (~node18(c_e_h_1, c_f, s7, s8))))),
% 294.20/186.70 inference(monotonicity,[status(thm)],[25187])).
% 294.20/186.70 tff(25189,plain,
% 294.20/186.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s8)) | m_c_h_element_v_out(c_e_h_1, c_f, s7) | (~node18(c_e_h_1, c_f, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s7) | (~m_c_h_element_v_out(c_e_h_1, c_f, s8)) | (~node18(c_e_h_1, c_f, s7, s8)))),
% 294.20/186.70 inference(transitivity,[status(thm)],[25188, 25186])).
% 294.20/186.70 tff(25190,plain,
% 294.20/186.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s8)) | m_c_h_element_v_out(c_e_h_1, c_f, s7) | (~node18(c_e_h_1, c_f, s7, s8)))),
% 294.20/186.70 inference(quant_inst,[status(thm)],[])).
% 294.20/186.70 tff(25191,plain,
% 294.20/186.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s7) | (~m_c_h_element_v_out(c_e_h_1, c_f, s8)) | (~node18(c_e_h_1, c_f, s7, s8))),
% 294.20/186.70 inference(modus_ponens,[status(thm)],[25190, 25189])).
% 294.20/186.70 tff(25192,plain,
% 294.20/186.70 ($false),
% 294.20/186.70 inference(unit_resolution,[status(thm)],[25191, 753, 25122, 25185, 24976])).
% 294.20/186.70 tff(25193,plain,(~m_c_h_element_v_out(c_e_h_1, c_f, s8)), inference(lemma,lemma(discharge,[]))).
% 294.20/186.70 tff(25194,plain,
% 294.20/186.70 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s8)) | m_c_h_element_v_out(c_e_h_1, c_f, s8))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s8)) | m_c_h_element_v_out(c_e_h_1, c_f, s8))),
% 294.20/186.70 inference(rewrite,[status(thm)],[])).
% 294.20/186.70 tff(25195,plain,
% 294.20/186.70 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s8)) | m_c_h_element_v_out(c_e_h_1, c_f, s8))),
% 294.20/186.70 inference(quant_inst,[status(thm)],[])).
% 294.20/186.70 tff(25196,plain,
% 294.20/186.70 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s8)) | m_c_h_element_v_out(c_e_h_1, c_f, s8)),
% 294.20/186.70 inference(modus_ponens,[status(thm)],[25195, 25194])).
% 294.20/186.70 tff(25197,plain,
% 294.20/186.70 (~m_and_h_gate_v_in1(c_e_h_1, c_q, s8)),
% 294.20/186.70 inference(unit_resolution,[status(thm)],[25196, 1586, 25193])).
% 294.20/186.70 tff(25198,plain,
% 294.20/186.70 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s8)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s8)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s8))),
% 294.20/186.70 inference(rewrite,[status(thm)],[])).
% 294.20/186.70 tff(25199,plain,
% 294.20/186.70 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s8)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s8))),
% 294.20/186.70 inference(quant_inst,[status(thm)],[])).
% 294.20/186.70 tff(25200,plain,
% 294.20/186.70 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s8)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s8)),
% 294.20/186.70 inference(modus_ponens,[status(thm)],[25199, 25198])).
% 294.20/186.70 tff(25201,plain,
% 294.20/186.70 (~node20(c_e_h_1, c_q, s8)),
% 294.20/186.70 inference(unit_resolution,[status(thm)],[25200, 38, 25197])).
% 294.20/186.70 tff(25202,assumption,(node21(c_e_h_1, c_q, s8, s9)), introduced(assumption)).
% 294.20/186.70 tff(25203,plain,
% 294.20/186.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s9)) | node20(c_e_h_1, c_q, s8) | (~node21(c_e_h_1, c_q, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s9)) | node20(c_e_h_1, c_q, s8) | (~node21(c_e_h_1, c_q, s8, s9)))),
% 294.20/186.70 inference(rewrite,[status(thm)],[])).
% 294.20/186.70 tff(25204,plain,
% 294.20/186.70 ((node20(c_e_h_1, c_q, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s9)) | (~node21(c_e_h_1, c_q, s8, s9))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_q, s9)) | node20(c_e_h_1, c_q, s8) | (~node21(c_e_h_1, c_q, s8, s9)))),
% 294.20/186.70 inference(rewrite,[status(thm)],[])).
% 294.20/186.70 tff(25205,plain,
% 294.20/186.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s9)) | (~node21(c_e_h_1, c_q, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s9)) | node20(c_e_h_1, c_q, s8) | (~node21(c_e_h_1, c_q, s8, s9))))),
% 294.20/186.70 inference(monotonicity,[status(thm)],[25204])).
% 294.20/186.70 tff(25206,plain,
% 294.20/186.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s9)) | (~node21(c_e_h_1, c_q, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s9)) | node20(c_e_h_1, c_q, s8) | (~node21(c_e_h_1, c_q, s8, s9)))),
% 294.20/186.70 inference(transitivity,[status(thm)],[25205, 25203])).
% 294.20/186.70 tff(25207,plain,
% 294.20/186.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s9)) | (~node21(c_e_h_1, c_q, s8, s9)))),
% 294.20/186.70 inference(quant_inst,[status(thm)],[])).
% 294.20/186.70 tff(25208,plain,
% 294.20/186.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s9)) | node20(c_e_h_1, c_q, s8) | (~node21(c_e_h_1, c_q, s8, s9))),
% 294.20/186.70 inference(modus_ponens,[status(thm)],[25207, 25206])).
% 294.20/186.70 tff(25209,plain,
% 294.20/186.70 ($false),
% 294.20/186.70 inference(unit_resolution,[status(thm)],[25208, 52, 24975, 25202, 25201])).
% 294.20/186.70 tff(25210,plain,((~node21(c_e_h_1, c_q, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s9))), inference(lemma,lemma(discharge,[]))).
% 294.20/186.70 tff(25211,plain,
% 294.20/186.70 (~node21(c_e_h_1, c_q, s8, s9)),
% 294.20/186.70 inference(unit_resolution,[status(thm)],[25210, 24975])).
% 294.20/186.70 tff(25212,plain,
% 294.20/186.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s8, s9)) | node21(c_e_h_1, c_q, s8, s9) | node22(c_e_h_1, c_q, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_1, c_q, s8, s9) | node22(c_e_h_1, c_q, s8, s9))),
% 294.20/186.71 inference(rewrite,[status(thm)],[])).
% 294.20/186.71 tff(25213,plain,
% 294.20/186.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s8, s9)) | node21(c_e_h_1, c_q, s8, s9) | node22(c_e_h_1, c_q, s8, s9))),
% 294.20/186.71 inference(quant_inst,[status(thm)],[])).
% 294.20/186.71 tff(25214,plain,
% 294.20/186.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_1, c_q, s8, s9) | node22(c_e_h_1, c_q, s8, s9)),
% 294.20/186.71 inference(modus_ponens,[status(thm)],[25213, 25212])).
% 294.20/186.71 tff(25215,plain,
% 294.20/186.71 (node21(c_e_h_1, c_q, s8, s9) | node22(c_e_h_1, c_q, s8, s9)),
% 294.20/186.71 inference(unit_resolution,[status(thm)],[25214, 82, 1993])).
% 294.20/186.71 tff(25216,plain,
% 294.20/186.71 (node22(c_e_h_1, c_q, s8, s9)),
% 294.20/186.71 inference(unit_resolution,[status(thm)],[25215, 25211])).
% 294.20/186.71 tff(25217,plain,
% 294.20/186.71 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s7)) | m_c_h_element_v_out(c_e_h_1, c_f, s7))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s7)) | m_c_h_element_v_out(c_e_h_1, c_f, s7))),
% 294.20/186.71 inference(rewrite,[status(thm)],[])).
% 294.20/186.71 tff(25218,plain,
% 294.20/186.71 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s7)) | m_c_h_element_v_out(c_e_h_1, c_f, s7))),
% 294.20/186.71 inference(quant_inst,[status(thm)],[])).
% 294.20/186.71 tff(25219,plain,
% 294.20/186.71 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s7)) | m_c_h_element_v_out(c_e_h_1, c_f, s7)),
% 294.20/186.71 inference(modus_ponens,[status(thm)],[25218, 25217])).
% 294.20/186.71 tff(25220,plain,
% 294.20/186.71 (~m_and_h_gate_v_in1(c_e_h_1, c_q, s7)),
% 294.20/186.71 inference(unit_resolution,[status(thm)],[25219, 1586, 25122])).
% 294.20/186.71 tff(25221,plain,
% 294.20/186.71 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s7)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s7)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s7))),
% 294.20/186.71 inference(rewrite,[status(thm)],[])).
% 294.20/186.71 tff(25222,plain,
% 294.20/186.71 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s7)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s7))),
% 294.20/186.71 inference(quant_inst,[status(thm)],[])).
% 294.20/186.71 tff(25223,plain,
% 294.20/186.71 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s7)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s7)),
% 294.20/186.71 inference(modus_ponens,[status(thm)],[25222, 25221])).
% 294.20/186.71 tff(25224,plain,
% 294.20/186.71 (~node20(c_e_h_1, c_q, s7)),
% 294.20/186.71 inference(unit_resolution,[status(thm)],[25223, 38, 25220])).
% 294.20/186.71 tff(25225,assumption,(m_and_h_gate_v_out(c_e_h_1, c_q, s8)), introduced(assumption)).
% 294.20/186.71 tff(25226,assumption,(node22(c_e_h_1, c_q, s7, s8)), introduced(assumption)).
% 294.20/186.71 tff(25227,assumption,(m_and_h_gate_v_out(c_e_h_1, c_q, s7)), introduced(assumption)).
% 294.20/186.71 tff(25228,assumption,(node22(c_e_h_1, c_q, s6, s7)), introduced(assumption)).
% 294.20/186.71 tff(25229,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_q, s6)), introduced(assumption)).
% 294.20/186.71 tff(25230,plain,
% 294.20/186.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s7)) | (~node22(c_e_h_1, c_q, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_q, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s7)) | (~node22(c_e_h_1, c_q, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_q, s6))),
% 294.20/186.71 inference(rewrite,[status(thm)],[])).
% 294.20/186.71 tff(25231,plain,
% 294.20/186.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s7)) | (~node22(c_e_h_1, c_q, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_q, s6))),
% 294.20/186.71 inference(quant_inst,[status(thm)],[])).
% 294.20/186.71 tff(25232,plain,
% 294.20/186.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s7)) | (~node22(c_e_h_1, c_q, s6, s7)) | m_and_h_gate_v_out(c_e_h_1, c_q, s6)),
% 294.20/186.71 inference(modus_ponens,[status(thm)],[25231, 25230])).
% 294.20/186.71 tff(25233,plain,
% 294.20/186.71 ($false),
% 294.20/186.71 inference(unit_resolution,[status(thm)],[25232, 108, 25227, 25229, 25228])).
% 294.20/186.71 tff(25234,plain,((~node22(c_e_h_1, c_q, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s7)) | m_and_h_gate_v_out(c_e_h_1, c_q, s6)), inference(lemma,lemma(discharge,[]))).
% 294.20/186.71 tff(25235,plain,
% 294.20/186.71 ((~node22(c_e_h_1, c_q, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s7))),
% 294.20/186.71 inference(unit_resolution,[status(thm)],[25234, 16962])).
% 294.20/186.71 tff(25236,plain,
% 294.20/186.71 (~node22(c_e_h_1, c_q, s6, s7)),
% 294.20/186.71 inference(unit_resolution,[status(thm)],[25235, 25227])).
% 294.20/186.71 tff(25237,plain,
% 294.20/186.71 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s6)) | m_c_h_element_v_out(c_e_h_1, c_f, s6))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s6)) | m_c_h_element_v_out(c_e_h_1, c_f, s6))),
% 294.20/186.71 inference(rewrite,[status(thm)],[])).
% 294.20/186.71 tff(25238,plain,
% 294.20/186.71 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s6)) | m_c_h_element_v_out(c_e_h_1, c_f, s6))),
% 294.20/186.71 inference(quant_inst,[status(thm)],[])).
% 294.20/186.71 tff(25239,plain,
% 294.20/186.71 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s6)) | m_c_h_element_v_out(c_e_h_1, c_f, s6)),
% 294.20/186.71 inference(modus_ponens,[status(thm)],[25238, 25237])).
% 294.20/186.71 tff(25240,plain,
% 294.20/186.71 (~m_and_h_gate_v_in1(c_e_h_1, c_q, s6)),
% 294.20/186.71 inference(unit_resolution,[status(thm)],[25239, 1586, 25050])).
% 294.20/186.71 tff(25241,plain,
% 294.20/186.71 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s6)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s6)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s6))),
% 294.20/186.71 inference(rewrite,[status(thm)],[])).
% 294.20/186.71 tff(25242,plain,
% 294.20/186.71 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s6)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s6))),
% 294.20/186.71 inference(quant_inst,[status(thm)],[])).
% 294.20/186.71 tff(25243,plain,
% 294.20/186.71 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s6)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s6)),
% 294.20/186.71 inference(modus_ponens,[status(thm)],[25242, 25241])).
% 294.20/186.71 tff(25244,plain,
% 294.20/186.71 (~node20(c_e_h_1, c_q, s6)),
% 294.20/186.71 inference(unit_resolution,[status(thm)],[25243, 38, 25240])).
% 294.20/186.71 tff(25245,assumption,(~node20(c_e_h_1, c_q, s6)), introduced(assumption)).
% 294.20/186.71 tff(25246,assumption,(node21(c_e_h_1, c_q, s6, s7)), introduced(assumption)).
% 294.20/186.71 tff(25247,plain,
% 294.20/186.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s7)) | node20(c_e_h_1, c_q, s6) | (~node21(c_e_h_1, c_q, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s7)) | node20(c_e_h_1, c_q, s6) | (~node21(c_e_h_1, c_q, s6, s7)))),
% 294.20/186.71 inference(rewrite,[status(thm)],[])).
% 294.20/186.71 tff(25248,plain,
% 294.20/186.71 ((node20(c_e_h_1, c_q, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s7)) | (~node21(c_e_h_1, c_q, s6, s7))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_q, s7)) | node20(c_e_h_1, c_q, s6) | (~node21(c_e_h_1, c_q, s6, s7)))),
% 294.20/186.71 inference(rewrite,[status(thm)],[])).
% 294.20/186.71 tff(25249,plain,
% 294.20/186.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s7)) | (~node21(c_e_h_1, c_q, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s7)) | node20(c_e_h_1, c_q, s6) | (~node21(c_e_h_1, c_q, s6, s7))))),
% 294.20/186.71 inference(monotonicity,[status(thm)],[25248])).
% 294.20/186.71 tff(25250,plain,
% 294.20/186.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s7)) | (~node21(c_e_h_1, c_q, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s7)) | node20(c_e_h_1, c_q, s6) | (~node21(c_e_h_1, c_q, s6, s7)))),
% 294.20/186.71 inference(transitivity,[status(thm)],[25249, 25247])).
% 294.20/186.71 tff(25251,plain,
% 294.20/186.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s6) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s7)) | (~node21(c_e_h_1, c_q, s6, s7)))),
% 294.20/186.71 inference(quant_inst,[status(thm)],[])).
% 294.20/186.71 tff(25252,plain,
% 294.20/186.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s7)) | node20(c_e_h_1, c_q, s6) | (~node21(c_e_h_1, c_q, s6, s7))),
% 294.20/186.71 inference(modus_ponens,[status(thm)],[25251, 25250])).
% 294.20/186.71 tff(25253,plain,
% 294.20/186.71 ($false),
% 294.20/186.71 inference(unit_resolution,[status(thm)],[25252, 52, 25227, 25246, 25245])).
% 294.20/186.71 tff(25254,plain,((~node21(c_e_h_1, c_q, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s7)) | node20(c_e_h_1, c_q, s6)), inference(lemma,lemma(discharge,[]))).
% 294.20/186.71 tff(25255,plain,
% 294.20/186.71 ((~node21(c_e_h_1, c_q, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s7))),
% 294.20/186.71 inference(unit_resolution,[status(thm)],[25254, 25244])).
% 294.20/186.71 tff(25256,plain,
% 294.20/186.71 (~node21(c_e_h_1, c_q, s6, s7)),
% 294.20/186.71 inference(unit_resolution,[status(thm)],[25255, 25227])).
% 294.20/186.71 tff(25257,plain,
% 294.20/186.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_1, c_q, s6, s7) | node22(c_e_h_1, c_q, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_1, c_q, s6, s7) | node22(c_e_h_1, c_q, s6, s7))),
% 294.20/186.71 inference(rewrite,[status(thm)],[])).
% 294.20/186.71 tff(25258,plain,
% 294.20/186.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_1, c_q, s6, s7) | node22(c_e_h_1, c_q, s6, s7))),
% 294.20/186.71 inference(quant_inst,[status(thm)],[])).
% 294.20/186.71 tff(25259,plain,
% 294.20/186.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_1, c_q, s6, s7) | node22(c_e_h_1, c_q, s6, s7)),
% 294.20/186.71 inference(modus_ponens,[status(thm)],[25258, 25257])).
% 294.20/186.71 tff(25260,plain,
% 294.20/186.71 (node21(c_e_h_1, c_q, s6, s7) | node22(c_e_h_1, c_q, s6, s7)),
% 294.20/186.71 inference(unit_resolution,[status(thm)],[25259, 82, 1844])).
% 294.20/186.71 tff(25261,plain,
% 294.20/186.71 ($false),
% 294.20/186.71 inference(unit_resolution,[status(thm)],[25260, 25256, 25236])).
% 294.20/186.71 tff(25262,plain,(~m_and_h_gate_v_out(c_e_h_1, c_q, s7)), inference(lemma,lemma(discharge,[]))).
% 294.20/186.71 tff(25263,plain,
% 294.20/186.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s8)) | (~node22(c_e_h_1, c_q, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_q, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s8)) | (~node22(c_e_h_1, c_q, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_q, s7))),
% 294.20/186.72 inference(rewrite,[status(thm)],[])).
% 294.20/186.72 tff(25264,plain,
% 294.20/186.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s8)) | (~node22(c_e_h_1, c_q, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_q, s7))),
% 294.20/186.72 inference(quant_inst,[status(thm)],[])).
% 294.20/186.72 tff(25265,plain,
% 294.20/186.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s8)) | (~node22(c_e_h_1, c_q, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_q, s7)),
% 294.20/186.72 inference(modus_ponens,[status(thm)],[25264, 25263])).
% 294.20/186.72 tff(25266,plain,
% 294.20/186.72 ($false),
% 294.20/186.72 inference(unit_resolution,[status(thm)],[25265, 108, 25262, 25225, 25226])).
% 294.20/186.72 tff(25267,plain,((~node22(c_e_h_1, c_q, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s8))), inference(lemma,lemma(discharge,[]))).
% 294.20/186.72 tff(25268,plain,
% 294.20/186.72 (~node22(c_e_h_1, c_q, s7, s8)),
% 294.20/186.72 inference(unit_resolution,[status(thm)],[25267, 25225])).
% 294.20/186.72 tff(25269,assumption,(~node20(c_e_h_1, c_q, s7)), introduced(assumption)).
% 294.20/186.72 tff(25270,assumption,(node21(c_e_h_1, c_q, s7, s8)), introduced(assumption)).
% 294.20/186.72 tff(25271,plain,
% 294.20/186.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s8)) | (~node21(c_e_h_1, c_q, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_q, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s8)) | (~node21(c_e_h_1, c_q, s7, s8)))),
% 294.20/186.72 inference(rewrite,[status(thm)],[])).
% 294.20/186.72 tff(25272,plain,
% 294.20/186.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s8)) | (~node21(c_e_h_1, c_q, s7, s8)))),
% 294.20/186.72 inference(quant_inst,[status(thm)],[])).
% 294.20/186.72 tff(25273,plain,
% 294.20/186.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_q, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s8)) | (~node21(c_e_h_1, c_q, s7, s8))),
% 294.20/186.72 inference(modus_ponens,[status(thm)],[25272, 25271])).
% 294.20/186.72 tff(25274,plain,
% 294.20/186.72 ($false),
% 294.20/186.72 inference(unit_resolution,[status(thm)],[25273, 52, 25225, 25270, 25269])).
% 294.20/186.72 tff(25275,plain,((~node21(c_e_h_1, c_q, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s8)) | node20(c_e_h_1, c_q, s7)), inference(lemma,lemma(discharge,[]))).
% 294.20/186.72 tff(25276,plain,
% 294.20/186.72 (~node21(c_e_h_1, c_q, s7, s8)),
% 294.20/186.72 inference(unit_resolution,[status(thm)],[25275, 25225, 25269])).
% 294.20/186.72 tff(25277,plain,
% 294.20/186.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_1, c_q, s7, s8) | node22(c_e_h_1, c_q, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_1, c_q, s7, s8) | node22(c_e_h_1, c_q, s7, s8))),
% 294.20/186.72 inference(rewrite,[status(thm)],[])).
% 294.20/186.72 tff(25278,plain,
% 294.20/186.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_1, c_q, s7, s8) | node22(c_e_h_1, c_q, s7, s8))),
% 294.20/186.72 inference(quant_inst,[status(thm)],[])).
% 294.20/186.72 tff(25279,plain,
% 294.20/186.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_1, c_q, s7, s8) | node22(c_e_h_1, c_q, s7, s8)),
% 294.20/186.72 inference(modus_ponens,[status(thm)],[25278, 25277])).
% 294.20/186.72 tff(25280,plain,
% 294.20/186.72 (node21(c_e_h_1, c_q, s7, s8) | node22(c_e_h_1, c_q, s7, s8)),
% 294.20/186.72 inference(unit_resolution,[status(thm)],[25279, 82, 1938])).
% 294.20/186.72 tff(25281,plain,
% 294.20/186.72 ($false),
% 294.20/186.72 inference(unit_resolution,[status(thm)],[25280, 25276, 25268])).
% 294.20/186.72 tff(25282,plain,((~m_and_h_gate_v_out(c_e_h_1, c_q, s8)) | node20(c_e_h_1, c_q, s7)), inference(lemma,lemma(discharge,[]))).
% 294.20/186.72 tff(25283,plain,
% 294.20/186.72 (~m_and_h_gate_v_out(c_e_h_1, c_q, s8)),
% 294.20/186.72 inference(unit_resolution,[status(thm)],[25282, 25224])).
% 294.20/186.72 tff(25284,plain,
% 294.20/186.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s9)) | (~node22(c_e_h_1, c_q, s8, s9)) | m_and_h_gate_v_out(c_e_h_1, c_q, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s9)) | (~node22(c_e_h_1, c_q, s8, s9)) | m_and_h_gate_v_out(c_e_h_1, c_q, s8))),
% 294.20/186.72 inference(rewrite,[status(thm)],[])).
% 294.20/186.72 tff(25285,plain,
% 294.20/186.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s9)) | (~node22(c_e_h_1, c_q, s8, s9)) | m_and_h_gate_v_out(c_e_h_1, c_q, s8))),
% 294.20/186.72 inference(quant_inst,[status(thm)],[])).
% 294.20/186.72 tff(25286,plain,
% 294.20/186.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s9)) | (~node22(c_e_h_1, c_q, s8, s9)) | m_and_h_gate_v_out(c_e_h_1, c_q, s8)),
% 294.20/186.72 inference(modus_ponens,[status(thm)],[25285, 25284])).
% 294.20/186.72 tff(25287,plain,
% 294.20/186.72 ($false),
% 294.20/186.72 inference(unit_resolution,[status(thm)],[25286, 108, 24975, 25283, 25216])).
% 294.20/186.72 tff(25288,plain,(~m_and_h_gate_v_out(c_e_h_1, c_q, s9)), inference(lemma,lemma(discharge,[]))).
% 294.20/186.72 tff(25289,plain,
% 294.20/186.72 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s9))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s9))),
% 294.20/186.72 inference(rewrite,[status(thm)],[])).
% 294.20/186.72 tff(25290,plain,
% 294.20/186.72 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s9))),
% 294.20/186.72 inference(quant_inst,[status(thm)],[])).
% 294.20/186.72 tff(25291,plain,
% 294.20/186.72 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s9)),
% 294.20/186.72 inference(modus_ponens,[status(thm)],[25290, 25289])).
% 294.20/186.72 tff(25292,plain,
% 294.20/186.72 (node3(c_e_h_1, c_e_h_2, s9)),
% 294.20/186.72 inference(unit_resolution,[status(thm)],[25291, 4166, 1056])).
% 294.20/186.72 tff(25293,plain,
% 294.20/186.72 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s9)) | (~node3(c_e_h_1, c_e_h_2, s9)) | m_and_h_gate_v_out(c_e_h_1, c_q, s9))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s9)) | (~node3(c_e_h_1, c_e_h_2, s9)) | m_and_h_gate_v_out(c_e_h_1, c_q, s9))),
% 294.20/186.72 inference(rewrite,[status(thm)],[])).
% 294.20/186.72 tff(25294,plain,
% 294.20/186.72 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s9)) | (~node3(c_e_h_1, c_e_h_2, s9)) | m_and_h_gate_v_out(c_e_h_1, c_q, s9))),
% 294.20/186.72 inference(quant_inst,[status(thm)],[])).
% 294.20/186.72 tff(25295,plain,
% 294.20/186.72 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s9)) | (~node3(c_e_h_1, c_e_h_2, s9)) | m_and_h_gate_v_out(c_e_h_1, c_q, s9)),
% 294.20/186.72 inference(modus_ponens,[status(thm)],[25294, 25293])).
% 294.20/186.72 tff(25296,plain,
% 294.20/186.72 ((~m_cell_v_ack(c_e_h_2, s9)) | m_and_h_gate_v_out(c_e_h_1, c_q, s9)),
% 294.20/186.72 inference(unit_resolution,[status(thm)],[25295, 1073, 25292])).
% 294.20/186.72 tff(25297,plain,
% 294.20/186.72 (~m_cell_v_ack(c_e_h_2, s9)),
% 294.20/186.72 inference(unit_resolution,[status(thm)],[25296, 25288])).
% 294.20/186.72 tff(25298,plain,
% 294.20/186.72 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node2(c_e_h_1, c_e_h_2, s9))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node2(c_e_h_1, c_e_h_2, s9))),
% 294.20/186.72 inference(rewrite,[status(thm)],[])).
% 294.20/186.72 tff(25299,plain,
% 294.20/186.72 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node2(c_e_h_1, c_e_h_2, s9))),
% 294.20/186.72 inference(quant_inst,[status(thm)],[])).
% 294.20/186.72 tff(25300,plain,
% 294.20/186.72 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node2(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node2(c_e_h_1, c_e_h_2, s9)),
% 294.20/186.72 inference(modus_ponens,[status(thm)],[25299, 25298])).
% 294.20/186.72 tff(25301,plain,
% 294.20/186.72 (node2(c_e_h_1, c_e_h_2, s9)),
% 294.20/186.72 inference(unit_resolution,[status(thm)],[25300, 4166, 5821])).
% 294.20/186.72 tff(25302,plain,
% 294.20/186.72 (((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | ((~node2(c_e_h_1, c_e_h_2, s9)) | m_cell_v_ack(c_e_h_2, s9) | m_and_h_gate_v_in2(c_e_h_1, c_c, s9))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | (~node2(c_e_h_1, c_e_h_2, s9)) | m_cell_v_ack(c_e_h_2, s9) | m_and_h_gate_v_in2(c_e_h_1, c_c, s9))),
% 294.20/186.72 inference(rewrite,[status(thm)],[])).
% 294.20/186.72 tff(25303,plain,
% 294.20/186.72 ((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | ((~node2(c_e_h_1, c_e_h_2, s9)) | m_cell_v_ack(c_e_h_2, s9) | m_and_h_gate_v_in2(c_e_h_1, c_c, s9))),
% 294.20/186.72 inference(quant_inst,[status(thm)],[])).
% 294.20/186.72 tff(25304,plain,
% 294.20/186.72 ((~![I0: $i, X: $i, J0: $i] : ((~node2(I0, J0, X)) | m_cell_v_ack(J0, X) | m_and_h_gate_v_in2(I0, c_c, X))) | (~node2(c_e_h_1, c_e_h_2, s9)) | m_cell_v_ack(c_e_h_2, s9) | m_and_h_gate_v_in2(c_e_h_1, c_c, s9)),
% 294.20/186.72 inference(modus_ponens,[status(thm)],[25303, 25302])).
% 294.20/186.72 tff(25305,plain,
% 294.20/186.72 (m_cell_v_ack(c_e_h_2, s9) | m_and_h_gate_v_in2(c_e_h_1, c_c, s9)),
% 294.20/186.72 inference(unit_resolution,[status(thm)],[25304, 5835, 25301])).
% 294.20/186.72 tff(25306,plain,
% 294.20/186.72 (m_and_h_gate_v_in2(c_e_h_1, c_c, s9)),
% 294.20/186.72 inference(unit_resolution,[status(thm)],[25305, 25297])).
% 294.20/186.72 tff(25307,plain,
% 294.20/186.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_c, s9)) | m_and_h_gate_v_out(c_e_h_1, c_c, s10) | (~node21(c_e_h_1, c_c, s9, s10)) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in2(c_e_h_1, c_c, s9)) | m_and_h_gate_v_out(c_e_h_1, c_c, s10) | (~node21(c_e_h_1, c_c, s9, s10)) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s9)))),
% 294.20/186.72 inference(rewrite,[status(thm)],[])).
% 294.20/186.72 tff(25308,plain,
% 294.20/186.72 (((~node21(c_e_h_1, c_c, s9, s10)) | (~m_and_h_gate_v_in2(c_e_h_1, c_c, s9)) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s9)) | m_and_h_gate_v_out(c_e_h_1, c_c, s10)) <=> ((~m_and_h_gate_v_in2(c_e_h_1, c_c, s9)) | m_and_h_gate_v_out(c_e_h_1, c_c, s10) | (~node21(c_e_h_1, c_c, s9, s10)) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s9)))),
% 294.20/186.72 inference(rewrite,[status(thm)],[])).
% 294.20/186.72 tff(25309,plain,
% 294.20/186.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_1, c_c, s9, s10)) | (~m_and_h_gate_v_in2(c_e_h_1, c_c, s9)) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s9)) | m_and_h_gate_v_out(c_e_h_1, c_c, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_c, s9)) | m_and_h_gate_v_out(c_e_h_1, c_c, s10) | (~node21(c_e_h_1, c_c, s9, s10)) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s9))))),
% 294.20/186.72 inference(monotonicity,[status(thm)],[25308])).
% 294.20/186.72 tff(25310,plain,
% 294.20/186.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_1, c_c, s9, s10)) | (~m_and_h_gate_v_in2(c_e_h_1, c_c, s9)) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s9)) | m_and_h_gate_v_out(c_e_h_1, c_c, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in2(c_e_h_1, c_c, s9)) | m_and_h_gate_v_out(c_e_h_1, c_c, s10) | (~node21(c_e_h_1, c_c, s9, s10)) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s9)))),
% 294.20/186.73 inference(transitivity,[status(thm)],[25309, 25307])).
% 294.20/186.73 tff(25311,plain,
% 294.20/186.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | ((~node21(c_e_h_1, c_c, s9, s10)) | (~m_and_h_gate_v_in2(c_e_h_1, c_c, s9)) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s9)) | m_and_h_gate_v_out(c_e_h_1, c_c, s10))),
% 294.20/186.73 inference(quant_inst,[status(thm)],[])).
% 294.20/186.73 tff(25312,plain,
% 294.20/186.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node21(I0, I1, X, Y)) | (~m_and_h_gate_v_in2(I0, I1, X)) | (~m_and_h_gate_v_in1(I0, I1, X)) | m_and_h_gate_v_out(I0, I1, Y))) | (~m_and_h_gate_v_in2(c_e_h_1, c_c, s9)) | m_and_h_gate_v_out(c_e_h_1, c_c, s10) | (~node21(c_e_h_1, c_c, s9, s10)) | (~m_and_h_gate_v_in1(c_e_h_1, c_c, s9))),
% 294.20/186.73 inference(modus_ponens,[status(thm)],[25311, 25310])).
% 294.20/186.73 tff(25313,plain,
% 294.20/186.73 ($false),
% 294.20/186.73 inference(unit_resolution,[status(thm)],[25312, 5851, 25306, 24974, 24958, 24890])).
% 294.20/186.73 tff(25314,plain,((~m_c_h_element_v_out(c_e_h_1, c_e, s10)) | m_c_h_element_v_out(c_e_h_1, c_e, s11)), inference(lemma,lemma(discharge,[]))).
% 294.20/186.73 tff(25315,plain,
% 294.20/186.73 (~m_c_h_element_v_out(c_e_h_1, c_e, s10)),
% 294.20/186.73 inference(unit_resolution,[status(thm)],[25314, 24402])).
% 294.20/186.73 tff(25316,plain,
% 294.20/186.73 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s10)),
% 294.20/186.73 inference(unit_resolution,[status(thm)],[23325, 25315])).
% 294.20/186.73 tff(25317,plain,
% 294.20/186.73 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11)),
% 294.20/186.73 inference(unit_resolution,[status(thm)],[23362, 25316])).
% 294.20/186.73 tff(25318,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)), introduced(assumption)).
% 294.20/186.73 tff(25319,plain,
% 294.20/186.73 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11) | m_c_h_element_v_out(c_e_h_1, c_e, s11))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11) | m_c_h_element_v_out(c_e_h_1, c_e, s11))),
% 294.20/186.73 inference(rewrite,[status(thm)],[])).
% 294.20/186.73 tff(25320,plain,
% 294.20/186.73 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11) | m_c_h_element_v_out(c_e_h_1, c_e, s11))),
% 294.20/186.73 inference(quant_inst,[status(thm)],[])).
% 294.20/186.73 tff(25321,plain,
% 294.20/186.73 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11) | m_c_h_element_v_out(c_e_h_1, c_e, s11)),
% 294.20/186.73 inference(modus_ponens,[status(thm)],[25320, 25319])).
% 294.20/186.73 tff(25322,plain,
% 294.20/186.73 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11) | m_c_h_element_v_out(c_e_h_1, c_e, s11)),
% 294.20/186.73 inference(unit_resolution,[status(thm)],[25321, 7856])).
% 294.20/186.73 tff(25323,plain,
% 294.20/186.73 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11)),
% 294.20/186.73 inference(unit_resolution,[status(thm)],[25322, 24402])).
% 294.20/186.73 tff(25324,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11)), introduced(assumption)).
% 294.20/186.73 tff(25325,plain,
% 294.20/186.73 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s11) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s11) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11))),
% 294.20/186.73 inference(rewrite,[status(thm)],[])).
% 294.20/186.73 tff(25326,plain,
% 294.20/186.73 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s11) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11))),
% 294.20/186.73 inference(quant_inst,[status(thm)],[])).
% 294.20/186.73 tff(25327,plain,
% 294.20/186.73 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s11) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)),
% 294.20/186.73 inference(modus_ponens,[status(thm)],[25326, 25325])).
% 294.20/186.73 tff(25328,plain,
% 294.20/186.73 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s11) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)),
% 294.20/186.73 inference(unit_resolution,[status(thm)],[25327, 7868])).
% 294.20/186.73 tff(25329,plain,
% 294.20/186.73 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s11)),
% 294.20/186.73 inference(unit_resolution,[status(thm)],[25328, 23372])).
% 294.20/186.73 tff(25330,assumption,(~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s11)), introduced(assumption)).
% 294.20/186.73 tff(25331,plain,
% 294.20/186.73 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s11) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s11) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11))),
% 294.20/186.73 inference(rewrite,[status(thm)],[])).
% 294.20/186.73 tff(25332,plain,
% 294.20/186.73 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s11) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11))),
% 294.20/186.73 inference(quant_inst,[status(thm)],[])).
% 294.20/186.73 tff(25333,plain,
% 294.20/186.73 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s11) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11)),
% 294.20/186.73 inference(modus_ponens,[status(thm)],[25332, 25331])).
% 294.20/186.73 tff(25334,plain,
% 294.20/186.73 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s11) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11)),
% 294.20/186.73 inference(unit_resolution,[status(thm)],[25333, 5704])).
% 294.20/186.73 tff(25335,plain,
% 294.20/186.73 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11)),
% 294.20/186.73 inference(unit_resolution,[status(thm)],[25334, 25330])).
% 294.20/186.73 tff(25336,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11)), introduced(assumption)).
% 294.20/186.73 tff(25337,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12)), introduced(assumption)).
% 294.20/186.73 tff(25338,assumption,(node11(c_e_h_1, c_n, s11, s12)), introduced(assumption)).
% 294.20/186.73 tff(25339,plain,
% 294.20/186.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11)) | (~node11(c_e_h_1, c_n, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11)) | (~node11(c_e_h_1, c_n, s11, s12)))),
% 294.20/186.73 inference(rewrite,[status(thm)],[])).
% 294.20/186.73 tff(25340,plain,
% 294.20/186.73 ((m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12) | (~node11(c_e_h_1, c_n, s11, s12)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11))) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11)) | (~node11(c_e_h_1, c_n, s11, s12)))),
% 294.20/186.73 inference(rewrite,[status(thm)],[])).
% 294.20/186.73 tff(25341,plain,
% 294.20/186.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12) | (~node11(c_e_h_1, c_n, s11, s12)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11)) | (~node11(c_e_h_1, c_n, s11, s12))))),
% 294.20/186.73 inference(monotonicity,[status(thm)],[25340])).
% 294.20/186.73 tff(25342,plain,
% 294.20/186.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12) | (~node11(c_e_h_1, c_n, s11, s12)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11)) | (~node11(c_e_h_1, c_n, s11, s12)))),
% 294.20/186.73 inference(transitivity,[status(thm)],[25341, 25339])).
% 294.20/186.73 tff(25343,plain,
% 294.20/186.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12) | (~node11(c_e_h_1, c_n, s11, s12)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11)))),
% 294.20/186.73 inference(quant_inst,[status(thm)],[])).
% 294.20/186.73 tff(25344,plain,
% 294.20/186.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11)) | (~node11(c_e_h_1, c_n, s11, s12))),
% 294.20/186.73 inference(modus_ponens,[status(thm)],[25343, 25342])).
% 294.20/186.73 tff(25345,plain,
% 294.20/186.73 ($false),
% 294.20/186.73 inference(unit_resolution,[status(thm)],[25344, 5742, 25336, 25337, 25338])).
% 294.20/186.73 tff(25346,plain,((~node11(c_e_h_1, c_n, s11, s12)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12)), inference(lemma,lemma(discharge,[]))).
% 294.20/186.73 tff(25347,plain,
% 294.20/186.73 (~node11(c_e_h_1, c_n, s11, s12)),
% 294.20/186.73 inference(unit_resolution,[status(thm)],[25346, 25337, 25336])).
% 294.20/186.73 tff(25348,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s11)), introduced(assumption)).
% 294.20/186.73 tff(25349,assumption,(node10(c_e_h_1, c_n, s11, s12)), introduced(assumption)).
% 294.20/186.73 tff(25350,plain,
% 294.20/186.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s11)) | (~node10(c_e_h_1, c_n, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s11)) | (~node10(c_e_h_1, c_n, s11, s12)))),
% 294.20/186.73 inference(rewrite,[status(thm)],[])).
% 294.20/186.73 tff(25351,plain,
% 294.20/186.73 (((~node10(c_e_h_1, c_n, s11, s12)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s11)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12)) <=> ((~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s11)) | (~node10(c_e_h_1, c_n, s11, s12)))),
% 294.20/186.73 inference(rewrite,[status(thm)],[])).
% 294.20/186.73 tff(25352,plain,
% 294.20/186.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s11, s12)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s11)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s11)) | (~node10(c_e_h_1, c_n, s11, s12))))),
% 294.20/186.73 inference(monotonicity,[status(thm)],[25351])).
% 294.20/186.73 tff(25353,plain,
% 294.20/186.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s11, s12)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s11)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s11)) | (~node10(c_e_h_1, c_n, s11, s12)))),
% 294.20/186.74 inference(transitivity,[status(thm)],[25352, 25350])).
% 294.20/186.74 tff(25354,plain,
% 294.20/186.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s11, s12)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s11)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12))),
% 294.20/186.74 inference(quant_inst,[status(thm)],[])).
% 294.20/186.74 tff(25355,plain,
% 294.20/186.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s11)) | (~node10(c_e_h_1, c_n, s11, s12))),
% 294.20/186.74 inference(modus_ponens,[status(thm)],[25354, 25353])).
% 294.20/186.74 tff(25356,plain,
% 294.20/186.74 ($false),
% 294.20/186.74 inference(unit_resolution,[status(thm)],[25355, 5718, 25324, 25348, 25337, 25349])).
% 294.20/186.74 tff(25357,plain,((~node10(c_e_h_1, c_n, s11, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s11)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12)), inference(lemma,lemma(discharge,[]))).
% 294.20/186.74 tff(25358,plain,
% 294.20/186.74 (~node10(c_e_h_1, c_n, s11, s12)),
% 294.20/186.74 inference(unit_resolution,[status(thm)],[25357, 25337, 25324, 25348])).
% 294.20/186.74 tff(25359,plain,
% 294.20/186.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s11, s12)) | node10(c_e_h_1, c_n, s11, s12) | node11(c_e_h_1, c_n, s11, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s11, s12)) | node10(c_e_h_1, c_n, s11, s12) | node11(c_e_h_1, c_n, s11, s12))),
% 294.20/186.74 inference(rewrite,[status(thm)],[])).
% 294.20/186.74 tff(25360,plain,
% 294.20/186.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s11, s12)) | node10(c_e_h_1, c_n, s11, s12) | node11(c_e_h_1, c_n, s11, s12))),
% 294.20/186.74 inference(quant_inst,[status(thm)],[])).
% 294.20/186.74 tff(25361,plain,
% 294.20/186.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s11, s12)) | node10(c_e_h_1, c_n, s11, s12) | node11(c_e_h_1, c_n, s11, s12)),
% 294.20/186.74 inference(modus_ponens,[status(thm)],[25360, 25359])).
% 294.20/186.74 tff(25362,plain,
% 294.20/186.74 (node10(c_e_h_1, c_n, s11, s12) | node11(c_e_h_1, c_n, s11, s12)),
% 294.20/186.74 inference(unit_resolution,[status(thm)],[25361, 5002, 11461])).
% 294.20/186.74 tff(25363,plain,
% 294.20/186.74 ($false),
% 294.20/186.74 inference(unit_resolution,[status(thm)],[25362, 25358, 25347])).
% 294.20/186.74 tff(25364,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s11)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11))), inference(lemma,lemma(discharge,[]))).
% 294.20/186.74 tff(25365,plain,
% 294.20/186.74 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12)),
% 294.20/186.74 inference(unit_resolution,[status(thm)],[25364, 25335, 25329, 25324])).
% 294.20/186.74 tff(25366,plain,
% 294.20/186.74 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s12)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s12)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12)))),
% 294.20/186.74 inference(rewrite,[status(thm)],[])).
% 294.20/186.74 tff(25367,plain,
% 294.20/186.74 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s12)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12)))),
% 294.20/186.74 inference(quant_inst,[status(thm)],[])).
% 294.20/186.74 tff(25368,plain,
% 294.20/186.74 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s12)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12))),
% 294.20/186.74 inference(modus_ponens,[status(thm)],[25367, 25366])).
% 294.20/186.74 tff(25369,plain,
% 294.20/186.74 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s12)),
% 294.20/186.74 inference(unit_resolution,[status(thm)],[25368, 4958, 25365])).
% 294.20/186.74 tff(25370,plain,
% 294.20/186.74 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s12)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s12))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s12)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s12))),
% 294.20/186.74 inference(rewrite,[status(thm)],[])).
% 294.20/186.74 tff(25371,plain,
% 294.20/186.74 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s12)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s12))),
% 294.20/186.74 inference(quant_inst,[status(thm)],[])).
% 294.20/186.74 tff(25372,plain,
% 294.20/186.74 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s12)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s12)),
% 294.20/186.74 inference(modus_ponens,[status(thm)],[25371, 25370])).
% 294.20/186.74 tff(25373,plain,
% 294.20/186.74 (~node9(c_e_h_1, c_m, s12)),
% 294.20/186.74 inference(unit_resolution,[status(thm)],[25372, 4972, 25369])).
% 294.20/186.74 tff(25374,plain,
% 294.20/186.74 (~node9(c_e_h_1, c_m, s11)),
% 294.20/186.74 inference(unit_resolution,[status(thm)],[23370, 4972, 25330])).
% 294.20/186.74 tff(25375,plain,
% 294.20/186.74 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)),
% 294.20/186.74 inference(unit_resolution,[status(thm)],[23397, 25374, 23372])).
% 294.20/186.74 tff(25376,assumption,(~node9(c_e_h_1, c_m, s12)), introduced(assumption)).
% 294.20/186.74 tff(25377,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)), introduced(assumption)).
% 294.20/186.74 tff(25378,assumption,(node11(c_e_h_1, c_m, s12, s13)), introduced(assumption)).
% 294.20/186.74 tff(25379,plain,
% 294.20/186.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)) | (~node11(c_e_h_1, c_m, s12, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)) | (~node11(c_e_h_1, c_m, s12, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12))),
% 294.20/186.74 inference(rewrite,[status(thm)],[])).
% 294.20/186.74 tff(25380,plain,
% 294.20/186.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)) | (~node11(c_e_h_1, c_m, s12, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12))),
% 294.20/186.74 inference(quant_inst,[status(thm)],[])).
% 294.20/186.74 tff(25381,plain,
% 294.20/186.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)) | (~node11(c_e_h_1, c_m, s12, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)),
% 294.20/186.74 inference(modus_ponens,[status(thm)],[25380, 25379])).
% 294.20/186.74 tff(25382,plain,
% 294.20/186.74 ($false),
% 294.20/186.74 inference(unit_resolution,[status(thm)],[25381, 5017, 25377, 25378, 25318])).
% 294.20/186.74 tff(25383,plain,((~node11(c_e_h_1, c_m, s12, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13))), inference(lemma,lemma(discharge,[]))).
% 294.20/186.74 tff(25384,plain,
% 294.20/186.74 (~node11(c_e_h_1, c_m, s12, s13)),
% 294.20/186.74 inference(unit_resolution,[status(thm)],[25383, 25318, 25377])).
% 294.20/186.74 tff(25385,plain,
% 294.20/186.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s12, s13)) | node10(c_e_h_1, c_m, s12, s13) | node11(c_e_h_1, c_m, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s12, s13)) | node10(c_e_h_1, c_m, s12, s13) | node11(c_e_h_1, c_m, s12, s13))),
% 294.20/186.74 inference(rewrite,[status(thm)],[])).
% 294.20/186.74 tff(25386,plain,
% 294.20/186.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s12, s13)) | node10(c_e_h_1, c_m, s12, s13) | node11(c_e_h_1, c_m, s12, s13))),
% 294.20/186.74 inference(quant_inst,[status(thm)],[])).
% 294.20/186.74 tff(25387,plain,
% 294.20/186.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s12, s13)) | node10(c_e_h_1, c_m, s12, s13) | node11(c_e_h_1, c_m, s12, s13)),
% 294.20/186.74 inference(modus_ponens,[status(thm)],[25386, 25385])).
% 294.20/186.74 tff(25388,plain,
% 294.20/186.74 (node10(c_e_h_1, c_m, s12, s13) | node11(c_e_h_1, c_m, s12, s13)),
% 294.20/186.74 inference(unit_resolution,[status(thm)],[25387, 5002, 11856])).
% 294.20/186.74 tff(25389,plain,
% 294.20/186.74 (node10(c_e_h_1, c_m, s12, s13)),
% 294.20/186.74 inference(unit_resolution,[status(thm)],[25388, 25384])).
% 294.20/186.74 tff(25390,plain,
% 294.20/186.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s12) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)) | (~node10(c_e_h_1, c_m, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_1, c_m, s12) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)) | (~node10(c_e_h_1, c_m, s12, s13)))),
% 294.20/186.74 inference(rewrite,[status(thm)],[])).
% 294.20/186.74 tff(25391,plain,
% 294.20/186.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s12) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)) | (~node10(c_e_h_1, c_m, s12, s13)))),
% 294.20/186.74 inference(quant_inst,[status(thm)],[])).
% 294.20/186.74 tff(25392,plain,
% 294.20/186.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_1, c_m, s12) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)) | (~node10(c_e_h_1, c_m, s12, s13))),
% 294.20/186.74 inference(modus_ponens,[status(thm)],[25391, 25390])).
% 294.20/186.74 tff(25393,plain,
% 294.20/186.74 ($false),
% 294.20/186.74 inference(unit_resolution,[status(thm)],[25392, 4986, 25389, 25318, 25376])).
% 294.20/186.74 tff(25394,plain,((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)) | node9(c_e_h_1, c_m, s12) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)), inference(lemma,lemma(discharge,[]))).
% 294.20/186.74 tff(25395,plain,
% 294.20/186.74 ($false),
% 294.20/186.74 inference(unit_resolution,[status(thm)],[25394, 25375, 25373, 25318])).
% 294.20/186.74 tff(25396,plain,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11))), inference(lemma,lemma(discharge,[]))).
% 294.20/186.74 tff(25397,plain,
% 294.20/186.74 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11))),
% 294.20/186.74 inference(unit_resolution,[status(thm)],[25396, 23106])).
% 294.20/186.74 tff(25398,plain,
% 294.20/186.74 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s11)),
% 294.20/186.74 inference(unit_resolution,[status(thm)],[25397, 25323, 25318])).
% 294.20/186.74 tff(25399,plain,
% 294.20/186.74 ($false),
% 294.20/186.74 inference(unit_resolution,[status(thm)],[23366, 4958, 25398, 25317])).
% 294.20/186.74 tff(25400,plain,(m_c_h_element_v_out(c_e_h_1, c_e, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13))), inference(lemma,lemma(discharge,[]))).
% 294.20/186.74 tff(25401,plain,
% 294.20/186.74 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)),
% 294.20/186.74 inference(unit_resolution,[status(thm)],[25400, 24401])).
% 294.20/186.74 tff(25402,assumption,(m_and_h_gate_v_in2(c_e_h_1, c_l, s13)), introduced(assumption)).
% 294.20/186.74 tff(25403,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)), introduced(assumption)).
% 294.20/186.74 tff(25404,plain,
% 294.20/186.74 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13))),
% 294.20/186.75 inference(rewrite,[status(thm)],[])).
% 294.20/186.75 tff(25405,plain,
% 294.20/186.75 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13))),
% 294.20/186.75 inference(quant_inst,[status(thm)],[])).
% 294.20/186.75 tff(25406,plain,
% 294.20/186.75 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)),
% 294.20/186.75 inference(modus_ponens,[status(thm)],[25405, 25404])).
% 294.20/186.75 tff(25407,plain,
% 294.20/186.75 ($false),
% 294.20/186.75 inference(unit_resolution,[status(thm)],[25406, 4549, 25403, 25402])).
% 294.20/186.75 tff(25408,plain,((~m_and_h_gate_v_in2(c_e_h_1, c_l, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)), inference(lemma,lemma(discharge,[]))).
% 294.20/186.75 tff(25409,plain,
% 294.20/186.75 (~m_and_h_gate_v_in2(c_e_h_1, c_l, s13)),
% 294.20/186.75 inference(unit_resolution,[status(thm)],[25408, 25401])).
% 294.20/186.75 tff(25410,assumption,(~m_and_h_gate_v_in2(c_e_h_1, c_l, s13)), introduced(assumption)).
% 294.20/186.75 tff(25411,assumption,(node20(c_e_h_1, c_l, s13)), introduced(assumption)).
% 294.20/186.75 tff(25412,plain,
% 294.20/186.75 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s13)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s13))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s13)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s13))),
% 294.20/186.75 inference(rewrite,[status(thm)],[])).
% 294.20/186.75 tff(25413,plain,
% 294.20/186.75 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s13)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s13))),
% 294.20/186.75 inference(quant_inst,[status(thm)],[])).
% 294.20/186.75 tff(25414,plain,
% 294.20/186.75 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s13)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s13)),
% 294.20/186.75 inference(modus_ponens,[status(thm)],[25413, 25412])).
% 294.20/186.75 tff(25415,plain,
% 294.20/186.75 ($false),
% 294.20/186.75 inference(unit_resolution,[status(thm)],[25414, 4563, 25411, 25410])).
% 294.20/186.75 tff(25416,plain,((~node20(c_e_h_1, c_l, s13)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s13)), inference(lemma,lemma(discharge,[]))).
% 294.20/186.75 tff(25417,plain,
% 294.20/186.75 (~node20(c_e_h_1, c_l, s13)),
% 294.20/186.75 inference(unit_resolution,[status(thm)],[25416, 25409])).
% 294.20/186.75 tff(25418,assumption,(~node20(c_e_h_1, c_l, s13)), introduced(assumption)).
% 294.20/186.75 tff(25419,assumption,(m_and_h_gate_v_out(c_e_h_1, c_l, s14)), introduced(assumption)).
% 294.20/186.75 tff(25420,assumption,(node21(c_e_h_1, c_l, s13, s14)), introduced(assumption)).
% 294.20/186.75 tff(25421,plain,
% 294.20/186.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s13) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s14)) | (~node21(c_e_h_1, c_l, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s13) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s14)) | (~node21(c_e_h_1, c_l, s13, s14)))),
% 294.20/186.75 inference(rewrite,[status(thm)],[])).
% 294.20/186.75 tff(25422,plain,
% 294.20/186.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s13) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s14)) | (~node21(c_e_h_1, c_l, s13, s14)))),
% 294.20/186.75 inference(quant_inst,[status(thm)],[])).
% 294.20/186.75 tff(25423,plain,
% 294.20/186.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s13) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s14)) | (~node21(c_e_h_1, c_l, s13, s14))),
% 294.20/186.75 inference(modus_ponens,[status(thm)],[25422, 25421])).
% 294.20/186.75 tff(25424,plain,
% 294.20/186.75 ($false),
% 294.20/186.75 inference(unit_resolution,[status(thm)],[25423, 52, 25420, 25419, 25418])).
% 294.20/186.75 tff(25425,plain,((~node21(c_e_h_1, c_l, s13, s14)) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s14)) | node20(c_e_h_1, c_l, s13)), inference(lemma,lemma(discharge,[]))).
% 294.20/186.75 tff(25426,plain,
% 294.20/186.75 (~node21(c_e_h_1, c_l, s13, s14)),
% 294.20/186.75 inference(unit_resolution,[status(thm)],[25425, 25419, 25418])).
% 294.20/186.75 tff(25427,assumption,(node22(c_e_h_1, c_l, s13, s14)), introduced(assumption)).
% 294.20/186.75 tff(25428,plain,
% 294.20/186.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s14)) | (~node22(c_e_h_1, c_l, s13, s14)) | m_and_h_gate_v_out(c_e_h_1, c_l, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s14)) | (~node22(c_e_h_1, c_l, s13, s14)) | m_and_h_gate_v_out(c_e_h_1, c_l, s13))),
% 294.20/186.75 inference(rewrite,[status(thm)],[])).
% 294.20/186.75 tff(25429,plain,
% 294.20/186.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s14)) | (~node22(c_e_h_1, c_l, s13, s14)) | m_and_h_gate_v_out(c_e_h_1, c_l, s13))),
% 294.20/186.75 inference(quant_inst,[status(thm)],[])).
% 294.20/186.75 tff(25430,plain,
% 294.20/186.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s14)) | (~node22(c_e_h_1, c_l, s13, s14)) | m_and_h_gate_v_out(c_e_h_1, c_l, s13)),
% 294.20/186.75 inference(modus_ponens,[status(thm)],[25429, 25428])).
% 294.20/186.75 tff(25431,plain,
% 294.20/186.75 ($false),
% 294.20/186.75 inference(unit_resolution,[status(thm)],[25430, 108, 25427, 25419, 23436])).
% 294.20/186.75 tff(25432,plain,((~node22(c_e_h_1, c_l, s13, s14)) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s14)) | m_and_h_gate_v_out(c_e_h_1, c_l, s13)), inference(lemma,lemma(discharge,[]))).
% 294.20/186.75 tff(25433,plain,
% 294.20/186.75 (~node22(c_e_h_1, c_l, s13, s14)),
% 294.20/186.75 inference(unit_resolution,[status(thm)],[25432, 25419, 23436])).
% 294.20/186.75 tff(25434,plain,
% 294.20/186.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s13, s14)) | node21(c_e_h_1, c_l, s13, s14) | node22(c_e_h_1, c_l, s13, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s13, s14)) | node21(c_e_h_1, c_l, s13, s14) | node22(c_e_h_1, c_l, s13, s14))),
% 294.20/186.75 inference(rewrite,[status(thm)],[])).
% 294.20/186.75 tff(25435,plain,
% 294.20/186.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s13, s14)) | node21(c_e_h_1, c_l, s13, s14) | node22(c_e_h_1, c_l, s13, s14))),
% 294.20/186.75 inference(quant_inst,[status(thm)],[])).
% 294.20/186.75 tff(25436,plain,
% 294.20/186.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s13, s14)) | node21(c_e_h_1, c_l, s13, s14) | node22(c_e_h_1, c_l, s13, s14)),
% 294.20/186.75 inference(modus_ponens,[status(thm)],[25435, 25434])).
% 294.20/186.75 tff(25437,plain,
% 294.20/186.75 (node21(c_e_h_1, c_l, s13, s14) | node22(c_e_h_1, c_l, s13, s14)),
% 294.20/186.75 inference(unit_resolution,[status(thm)],[25436, 82, 12831])).
% 294.20/186.75 tff(25438,plain,
% 294.20/186.75 ($false),
% 294.20/186.75 inference(unit_resolution,[status(thm)],[25437, 25433, 25426])).
% 294.20/186.75 tff(25439,plain,((~m_and_h_gate_v_out(c_e_h_1, c_l, s14)) | m_and_h_gate_v_out(c_e_h_1, c_l, s13) | node20(c_e_h_1, c_l, s13)), inference(lemma,lemma(discharge,[]))).
% 294.20/186.75 tff(25440,plain,
% 294.20/186.75 (~m_and_h_gate_v_out(c_e_h_1, c_l, s14)),
% 294.20/186.75 inference(unit_resolution,[status(thm)],[25439, 23434, 25417])).
% 294.20/186.75 tff(25441,assumption,(m_or_h_gate_v_in1(c_e_h_1, c_j, s14)), introduced(assumption)).
% 294.20/186.75 tff(25442,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_l, s14)), introduced(assumption)).
% 294.20/186.75 tff(25443,plain,
% 294.20/186.75 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s14)) | m_and_h_gate_v_out(c_e_h_1, c_l, s14))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s14)) | m_and_h_gate_v_out(c_e_h_1, c_l, s14))),
% 294.20/186.75 inference(rewrite,[status(thm)],[])).
% 294.20/186.75 tff(25444,plain,
% 294.20/186.75 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s14)) | m_and_h_gate_v_out(c_e_h_1, c_l, s14))),
% 294.20/186.75 inference(quant_inst,[status(thm)],[])).
% 294.20/186.75 tff(25445,plain,
% 294.20/186.75 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s14)) | m_and_h_gate_v_out(c_e_h_1, c_l, s14)),
% 294.20/186.75 inference(modus_ponens,[status(thm)],[25444, 25443])).
% 294.20/186.75 tff(25446,plain,
% 294.20/186.75 ($false),
% 294.20/186.75 inference(unit_resolution,[status(thm)],[25445, 1100, 25442, 25441])).
% 294.20/186.75 tff(25447,plain,((~m_or_h_gate_v_in1(c_e_h_1, c_j, s14)) | m_and_h_gate_v_out(c_e_h_1, c_l, s14)), inference(lemma,lemma(discharge,[]))).
% 294.20/186.75 tff(25448,plain,
% 294.20/186.75 (~m_or_h_gate_v_in1(c_e_h_1, c_j, s14)),
% 294.20/186.75 inference(unit_resolution,[status(thm)],[25447, 25440])).
% 294.20/186.75 tff(25449,assumption,(m_or_h_gate_v_out(c_e_h_1, c_j, s15)), introduced(assumption)).
% 294.20/186.75 tff(25450,assumption,(node6(c_e_h_1, c_j, s14, s15)), introduced(assumption)).
% 294.20/186.75 tff(25451,plain,
% 294.20/186.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s14) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s15)) | (~node6(c_e_h_1, c_j, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s14) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s15)) | (~node6(c_e_h_1, c_j, s14, s15)))),
% 294.20/186.75 inference(rewrite,[status(thm)],[])).
% 294.20/186.75 tff(25452,plain,
% 294.20/186.75 (((~node6(c_e_h_1, c_j, s14, s15)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s15)) | m_or_h_gate_v_out(c_e_h_1, c_j, s14)) <=> (m_or_h_gate_v_out(c_e_h_1, c_j, s14) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s15)) | (~node6(c_e_h_1, c_j, s14, s15)))),
% 294.20/186.75 inference(rewrite,[status(thm)],[])).
% 294.20/186.75 tff(25453,plain,
% 294.20/186.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s14, s15)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s15)) | m_or_h_gate_v_out(c_e_h_1, c_j, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s14) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s15)) | (~node6(c_e_h_1, c_j, s14, s15))))),
% 294.20/186.75 inference(monotonicity,[status(thm)],[25452])).
% 294.20/186.75 tff(25454,plain,
% 294.20/186.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s14, s15)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s15)) | m_or_h_gate_v_out(c_e_h_1, c_j, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s14) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s15)) | (~node6(c_e_h_1, c_j, s14, s15)))),
% 294.20/186.75 inference(transitivity,[status(thm)],[25453, 25451])).
% 294.20/186.75 tff(25455,plain,
% 294.20/186.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s14, s15)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s15)) | m_or_h_gate_v_out(c_e_h_1, c_j, s14))),
% 294.20/186.75 inference(quant_inst,[status(thm)],[])).
% 294.20/186.75 tff(25456,plain,
% 294.20/186.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s14) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s15)) | (~node6(c_e_h_1, c_j, s14, s15))),
% 294.20/186.75 inference(modus_ponens,[status(thm)],[25455, 25454])).
% 294.20/186.75 tff(25457,plain,
% 294.20/186.75 ($false),
% 294.20/186.75 inference(unit_resolution,[status(thm)],[25456, 1121, 25450, 23480, 25449])).
% 294.20/186.75 tff(25458,plain,((~node6(c_e_h_1, c_j, s14, s15)) | m_or_h_gate_v_out(c_e_h_1, c_j, s14) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s15))), inference(lemma,lemma(discharge,[]))).
% 294.20/186.75 tff(25459,plain,
% 294.20/186.75 (~node6(c_e_h_1, c_j, s14, s15)),
% 294.20/186.75 inference(unit_resolution,[status(thm)],[25458, 25449, 23480])).
% 294.20/186.75 tff(25460,assumption,(~m_or_h_gate_v_in2(c_e_h_1, c_j, s14)), introduced(assumption)).
% 294.20/186.76 tff(25461,assumption,(~m_or_h_gate_v_in1(c_e_h_1, c_j, s14)), introduced(assumption)).
% 294.20/186.76 tff(25462,assumption,(node5(c_e_h_1, c_j, s14, s15)), introduced(assumption)).
% 294.20/186.76 tff(25463,plain,
% 294.20/186.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_1, c_j, s14) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s15)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s14) | (~node5(c_e_h_1, c_j, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_1, c_j, s14) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s15)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s14) | (~node5(c_e_h_1, c_j, s14, s15)))),
% 294.20/186.76 inference(rewrite,[status(thm)],[])).
% 294.20/186.76 tff(25464,plain,
% 294.20/186.76 ((m_or_h_gate_v_in1(c_e_h_1, c_j, s14) | m_or_h_gate_v_in2(c_e_h_1, c_j, s14) | (~node5(c_e_h_1, c_j, s14, s15)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s15))) <=> (m_or_h_gate_v_in2(c_e_h_1, c_j, s14) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s15)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s14) | (~node5(c_e_h_1, c_j, s14, s15)))),
% 294.20/186.76 inference(rewrite,[status(thm)],[])).
% 294.20/186.76 tff(25465,plain,
% 294.20/186.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s14) | m_or_h_gate_v_in2(c_e_h_1, c_j, s14) | (~node5(c_e_h_1, c_j, s14, s15)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_1, c_j, s14) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s15)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s14) | (~node5(c_e_h_1, c_j, s14, s15))))),
% 294.20/186.76 inference(monotonicity,[status(thm)],[25464])).
% 294.20/186.76 tff(25466,plain,
% 294.20/186.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s14) | m_or_h_gate_v_in2(c_e_h_1, c_j, s14) | (~node5(c_e_h_1, c_j, s14, s15)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_1, c_j, s14) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s15)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s14) | (~node5(c_e_h_1, c_j, s14, s15)))),
% 294.20/186.76 inference(transitivity,[status(thm)],[25465, 25463])).
% 294.20/186.76 tff(25467,plain,
% 294.20/186.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s14) | m_or_h_gate_v_in2(c_e_h_1, c_j, s14) | (~node5(c_e_h_1, c_j, s14, s15)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s15)))),
% 294.20/186.76 inference(quant_inst,[status(thm)],[])).
% 294.20/186.76 tff(25468,plain,
% 294.20/186.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_1, c_j, s14) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s15)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s14) | (~node5(c_e_h_1, c_j, s14, s15))),
% 294.20/186.76 inference(modus_ponens,[status(thm)],[25467, 25466])).
% 294.20/186.76 tff(25469,plain,
% 294.20/186.76 ($false),
% 294.20/186.76 inference(unit_resolution,[status(thm)],[25468, 1159, 25462, 25449, 25461, 25460])).
% 294.20/186.76 tff(25470,plain,((~node5(c_e_h_1, c_j, s14, s15)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s15)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s14) | m_or_h_gate_v_in2(c_e_h_1, c_j, s14)), inference(lemma,lemma(discharge,[]))).
% 294.20/186.76 tff(25471,plain,
% 294.20/186.76 (~node5(c_e_h_1, c_j, s14, s15)),
% 294.20/186.76 inference(unit_resolution,[status(thm)],[25470, 25449, 25461, 25460])).
% 294.20/186.76 tff(25472,plain,
% 294.20/186.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s14, s15)) | node6(c_e_h_1, c_j, s14, s15) | node5(c_e_h_1, c_j, s14, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s14, s15)) | node6(c_e_h_1, c_j, s14, s15) | node5(c_e_h_1, c_j, s14, s15))),
% 294.20/186.76 inference(rewrite,[status(thm)],[])).
% 294.20/186.76 tff(25473,plain,
% 294.20/186.76 ((node6(c_e_h_1, c_j, s14, s15) | node5(c_e_h_1, c_j, s14, s15) | (~trans(s14, s15))) <=> ((~trans(s14, s15)) | node6(c_e_h_1, c_j, s14, s15) | node5(c_e_h_1, c_j, s14, s15))),
% 294.20/186.76 inference(rewrite,[status(thm)],[])).
% 294.20/186.76 tff(25474,plain,
% 294.20/186.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s14, s15) | node5(c_e_h_1, c_j, s14, s15) | (~trans(s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s14, s15)) | node6(c_e_h_1, c_j, s14, s15) | node5(c_e_h_1, c_j, s14, s15)))),
% 294.20/186.76 inference(monotonicity,[status(thm)],[25473])).
% 294.20/186.76 tff(25475,plain,
% 294.20/186.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s14, s15) | node5(c_e_h_1, c_j, s14, s15) | (~trans(s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s14, s15)) | node6(c_e_h_1, c_j, s14, s15) | node5(c_e_h_1, c_j, s14, s15))),
% 294.20/186.76 inference(transitivity,[status(thm)],[25474, 25472])).
% 294.20/186.76 tff(25476,plain,
% 294.20/186.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s14, s15) | node5(c_e_h_1, c_j, s14, s15) | (~trans(s14, s15)))),
% 294.20/186.76 inference(quant_inst,[status(thm)],[])).
% 294.20/186.76 tff(25477,plain,
% 294.20/186.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s14, s15)) | node6(c_e_h_1, c_j, s14, s15) | node5(c_e_h_1, c_j, s14, s15)),
% 294.20/186.76 inference(modus_ponens,[status(thm)],[25476, 25475])).
% 294.20/186.76 tff(25478,plain,
% 294.20/186.76 (node6(c_e_h_1, c_j, s14, s15) | node5(c_e_h_1, c_j, s14, s15)),
% 294.20/186.76 inference(unit_resolution,[status(thm)],[25477, 1141, 12926])).
% 294.20/186.76 tff(25479,plain,
% 294.20/186.76 ($false),
% 294.20/186.76 inference(unit_resolution,[status(thm)],[25478, 25471, 25459])).
% 294.20/186.76 tff(25480,plain,((~m_or_h_gate_v_out(c_e_h_1, c_j, s15)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s14) | m_or_h_gate_v_in2(c_e_h_1, c_j, s14) | m_or_h_gate_v_out(c_e_h_1, c_j, s14)), inference(lemma,lemma(discharge,[]))).
% 294.20/186.76 tff(25481,plain,
% 294.20/186.76 ((~m_or_h_gate_v_out(c_e_h_1, c_j, s15)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s14) | m_or_h_gate_v_out(c_e_h_1, c_j, s14)),
% 294.20/186.76 inference(unit_resolution,[status(thm)],[25480, 25448])).
% 294.20/186.76 tff(25482,plain,
% 294.20/186.76 (~m_or_h_gate_v_out(c_e_h_1, c_j, s15)),
% 294.20/186.76 inference(unit_resolution,[status(thm)],[25481, 24323, 23478])).
% 294.20/186.76 tff(25483,assumption,(m_c_h_element_v_in2(c_e_h_1, c_h, s15)), introduced(assumption)).
% 294.20/186.76 tff(25484,assumption,(~m_or_h_gate_v_out(c_e_h_1, c_j, s15)), introduced(assumption)).
% 294.20/186.76 tff(25485,plain,
% 294.20/186.76 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s15)) | m_or_h_gate_v_out(c_e_h_1, c_j, s15))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s15)) | m_or_h_gate_v_out(c_e_h_1, c_j, s15))),
% 294.20/186.76 inference(rewrite,[status(thm)],[])).
% 294.20/186.76 tff(25486,plain,
% 294.20/186.76 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s15)) | m_or_h_gate_v_out(c_e_h_1, c_j, s15))),
% 294.20/186.76 inference(quant_inst,[status(thm)],[])).
% 294.20/186.76 tff(25487,plain,
% 294.20/186.76 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s15)) | m_or_h_gate_v_out(c_e_h_1, c_j, s15)),
% 294.20/186.76 inference(modus_ponens,[status(thm)],[25486, 25485])).
% 294.20/186.76 tff(25488,plain,
% 294.20/186.76 ($false),
% 294.20/186.76 inference(unit_resolution,[status(thm)],[25487, 1174, 25484, 25483])).
% 294.20/186.76 tff(25489,plain,((~m_c_h_element_v_in2(c_e_h_1, c_h, s15)) | m_or_h_gate_v_out(c_e_h_1, c_j, s15)), inference(lemma,lemma(discharge,[]))).
% 294.20/186.76 tff(25490,plain,
% 294.20/186.77 (~m_c_h_element_v_in2(c_e_h_1, c_h, s15)),
% 294.20/186.77 inference(unit_resolution,[status(thm)],[25489, 25482])).
% 294.20/186.77 tff(25491,assumption,(m_c_h_element_v_out(c_e_h_1, c_h, s16)), introduced(assumption)).
% 294.20/186.77 tff(25492,assumption,(~m_c_h_element_v_out(c_e_h_1, c_h, s15)), introduced(assumption)).
% 294.20/186.77 tff(25493,assumption,(node18(c_e_h_1, c_h, s15, s16)), introduced(assumption)).
% 294.20/186.77 tff(25494,plain,
% 294.20/186.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_h, s15) | (~m_c_h_element_v_out(c_e_h_1, c_h, s16)) | (~node18(c_e_h_1, c_h, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s15) | (~m_c_h_element_v_out(c_e_h_1, c_h, s16)) | (~node18(c_e_h_1, c_h, s15, s16)))),
% 294.20/186.77 inference(rewrite,[status(thm)],[])).
% 294.20/186.77 tff(25495,plain,
% 294.20/186.77 (((~m_c_h_element_v_out(c_e_h_1, c_h, s16)) | m_c_h_element_v_out(c_e_h_1, c_h, s15) | (~node18(c_e_h_1, c_h, s15, s16))) <=> (m_c_h_element_v_out(c_e_h_1, c_h, s15) | (~m_c_h_element_v_out(c_e_h_1, c_h, s16)) | (~node18(c_e_h_1, c_h, s15, s16)))),
% 294.20/186.77 inference(rewrite,[status(thm)],[])).
% 294.20/186.77 tff(25496,plain,
% 294.20/186.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s16)) | m_c_h_element_v_out(c_e_h_1, c_h, s15) | (~node18(c_e_h_1, c_h, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_h, s15) | (~m_c_h_element_v_out(c_e_h_1, c_h, s16)) | (~node18(c_e_h_1, c_h, s15, s16))))),
% 294.20/186.77 inference(monotonicity,[status(thm)],[25495])).
% 294.20/186.77 tff(25497,plain,
% 294.20/186.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s16)) | m_c_h_element_v_out(c_e_h_1, c_h, s15) | (~node18(c_e_h_1, c_h, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s15) | (~m_c_h_element_v_out(c_e_h_1, c_h, s16)) | (~node18(c_e_h_1, c_h, s15, s16)))),
% 294.20/186.77 inference(transitivity,[status(thm)],[25496, 25494])).
% 294.20/186.77 tff(25498,plain,
% 294.20/186.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s16)) | m_c_h_element_v_out(c_e_h_1, c_h, s15) | (~node18(c_e_h_1, c_h, s15, s16)))),
% 294.20/186.77 inference(quant_inst,[status(thm)],[])).
% 294.20/186.77 tff(25499,plain,
% 294.20/186.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s15) | (~m_c_h_element_v_out(c_e_h_1, c_h, s16)) | (~node18(c_e_h_1, c_h, s15, s16))),
% 294.20/186.77 inference(modus_ponens,[status(thm)],[25498, 25497])).
% 294.20/186.77 tff(25500,plain,
% 294.20/186.77 ($false),
% 294.20/186.77 inference(unit_resolution,[status(thm)],[25499, 753, 25492, 25491, 25493])).
% 294.20/186.77 tff(25501,plain,((~node18(c_e_h_1, c_h, s15, s16)) | m_c_h_element_v_out(c_e_h_1, c_h, s15) | (~m_c_h_element_v_out(c_e_h_1, c_h, s16))), inference(lemma,lemma(discharge,[]))).
% 294.20/186.77 tff(25502,plain,
% 294.20/186.77 (~node18(c_e_h_1, c_h, s15, s16)),
% 294.20/186.77 inference(unit_resolution,[status(thm)],[25501, 25492, 25491])).
% 294.20/186.77 tff(25503,plain,
% 294.20/186.77 (~node18(c_e_h_1, c_h, s15, s16)),
% 294.20/186.77 inference(unit_resolution,[status(thm)],[25501, 25491, 25492])).
% 294.20/186.77 tff(25504,plain,
% 294.20/186.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s15, s16)) | node19(c_e_h_1, c_h, s15, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s15, s16)) | node19(c_e_h_1, c_h, s15, s16))),
% 294.20/186.77 inference(rewrite,[status(thm)],[])).
% 294.20/186.77 tff(25505,plain,
% 294.20/186.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s15, s16)) | node19(c_e_h_1, c_h, s15, s16))),
% 294.20/186.77 inference(quant_inst,[status(thm)],[])).
% 294.20/186.77 tff(25506,plain,
% 294.20/186.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s15, s16)) | node19(c_e_h_1, c_h, s15, s16)),
% 294.20/186.77 inference(modus_ponens,[status(thm)],[25505, 25504])).
% 294.20/186.77 tff(25507,plain,
% 294.20/186.77 (node19(c_e_h_1, c_h, s15, s16)),
% 294.20/186.77 inference(unit_resolution,[status(thm)],[25506, 190, 13499])).
% 294.20/186.77 tff(25508,plain,
% 294.20/186.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s15) | (~node19(c_e_h_1, c_h, s15, s16)) | node18(c_e_h_1, c_h, s15, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s15) | (~node19(c_e_h_1, c_h, s15, s16)) | node18(c_e_h_1, c_h, s15, s16))),
% 294.20/186.77 inference(rewrite,[status(thm)],[])).
% 294.20/186.77 tff(25509,plain,
% 294.20/186.77 ((node17(c_e_h_1, c_h, s15) | node18(c_e_h_1, c_h, s15, s16) | (~node19(c_e_h_1, c_h, s15, s16))) <=> (node17(c_e_h_1, c_h, s15) | (~node19(c_e_h_1, c_h, s15, s16)) | node18(c_e_h_1, c_h, s15, s16))),
% 294.20/186.77 inference(rewrite,[status(thm)],[])).
% 294.20/186.77 tff(25510,plain,
% 294.20/186.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s15) | node18(c_e_h_1, c_h, s15, s16) | (~node19(c_e_h_1, c_h, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s15) | (~node19(c_e_h_1, c_h, s15, s16)) | node18(c_e_h_1, c_h, s15, s16)))),
% 294.20/186.77 inference(monotonicity,[status(thm)],[25509])).
% 294.20/186.77 tff(25511,plain,
% 294.20/186.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s15) | node18(c_e_h_1, c_h, s15, s16) | (~node19(c_e_h_1, c_h, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s15) | (~node19(c_e_h_1, c_h, s15, s16)) | node18(c_e_h_1, c_h, s15, s16))),
% 294.20/186.77 inference(transitivity,[status(thm)],[25510, 25508])).
% 294.20/186.77 tff(25512,plain,
% 294.20/186.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s15) | node18(c_e_h_1, c_h, s15, s16) | (~node19(c_e_h_1, c_h, s15, s16)))),
% 294.20/186.77 inference(quant_inst,[status(thm)],[])).
% 294.20/186.77 tff(25513,plain,
% 294.20/186.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s15) | (~node19(c_e_h_1, c_h, s15, s16)) | node18(c_e_h_1, c_h, s15, s16)),
% 294.20/186.77 inference(modus_ponens,[status(thm)],[25512, 25511])).
% 294.20/186.77 tff(25514,plain,
% 294.20/186.77 (node17(c_e_h_1, c_h, s15) | node18(c_e_h_1, c_h, s15, s16)),
% 294.20/186.77 inference(unit_resolution,[status(thm)],[25513, 776, 25507])).
% 294.20/186.77 tff(25515,plain,
% 294.20/186.77 (node17(c_e_h_1, c_h, s15)),
% 294.20/186.77 inference(unit_resolution,[status(thm)],[25514, 25503])).
% 294.20/186.77 tff(25516,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_h, s15)), introduced(assumption)).
% 294.20/186.77 tff(25517,plain,
% 294.20/186.77 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s15)) | (~node17(c_e_h_1, c_h, s15)) | m_c_h_element_v_in1(c_e_h_1, c_h, s15))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s15)) | (~node17(c_e_h_1, c_h, s15)) | m_c_h_element_v_in1(c_e_h_1, c_h, s15))),
% 294.20/186.77 inference(rewrite,[status(thm)],[])).
% 294.20/186.77 tff(25518,plain,
% 294.20/186.77 ((m_c_h_element_v_in1(c_e_h_1, c_h, s15) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s15)) | (~node17(c_e_h_1, c_h, s15))) <=> ((~m_c_h_element_v_in2(c_e_h_1, c_h, s15)) | (~node17(c_e_h_1, c_h, s15)) | m_c_h_element_v_in1(c_e_h_1, c_h, s15))),
% 294.20/186.77 inference(rewrite,[status(thm)],[])).
% 294.20/186.77 tff(25519,plain,
% 294.20/186.77 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s15) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s15)) | (~node17(c_e_h_1, c_h, s15)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s15)) | (~node17(c_e_h_1, c_h, s15)) | m_c_h_element_v_in1(c_e_h_1, c_h, s15)))),
% 294.20/186.77 inference(monotonicity,[status(thm)],[25518])).
% 294.20/186.77 tff(25520,plain,
% 294.20/186.77 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s15) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s15)) | (~node17(c_e_h_1, c_h, s15)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s15)) | (~node17(c_e_h_1, c_h, s15)) | m_c_h_element_v_in1(c_e_h_1, c_h, s15))),
% 294.20/186.77 inference(transitivity,[status(thm)],[25519, 25517])).
% 294.20/186.77 tff(25521,plain,
% 294.20/186.77 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s15) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s15)) | (~node17(c_e_h_1, c_h, s15)))),
% 294.20/186.77 inference(quant_inst,[status(thm)],[])).
% 294.20/186.77 tff(25522,plain,
% 294.20/186.77 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s15)) | (~node17(c_e_h_1, c_h, s15)) | m_c_h_element_v_in1(c_e_h_1, c_h, s15)),
% 294.20/186.77 inference(modus_ponens,[status(thm)],[25521, 25520])).
% 294.20/186.77 tff(25523,plain,
% 294.20/186.77 ((~m_c_h_element_v_in2(c_e_h_1, c_h, s15)) | (~node17(c_e_h_1, c_h, s15))),
% 294.20/186.77 inference(unit_resolution,[status(thm)],[25522, 859, 25516])).
% 294.20/186.77 tff(25524,plain,
% 294.20/186.77 (~m_c_h_element_v_in2(c_e_h_1, c_h, s15)),
% 294.20/186.77 inference(unit_resolution,[status(thm)],[25523, 25515])).
% 294.20/186.77 tff(25525,plain,
% 294.20/186.77 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s15)) | m_c_h_element_v_in1(c_e_h_1, c_h, s15) | m_c_h_element_v_in2(c_e_h_1, c_h, s15))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s15)) | m_c_h_element_v_in1(c_e_h_1, c_h, s15) | m_c_h_element_v_in2(c_e_h_1, c_h, s15))),
% 294.20/186.77 inference(rewrite,[status(thm)],[])).
% 294.20/186.77 tff(25526,plain,
% 294.20/186.77 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s15)) | m_c_h_element_v_in1(c_e_h_1, c_h, s15) | m_c_h_element_v_in2(c_e_h_1, c_h, s15))),
% 294.20/186.77 inference(quant_inst,[status(thm)],[])).
% 294.20/186.77 tff(25527,plain,
% 294.20/186.77 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s15)) | m_c_h_element_v_in1(c_e_h_1, c_h, s15) | m_c_h_element_v_in2(c_e_h_1, c_h, s15)),
% 294.20/186.77 inference(modus_ponens,[status(thm)],[25526, 25525])).
% 294.20/186.77 tff(25528,plain,
% 294.20/186.77 ((~node16(c_e_h_1, c_h, s15)) | m_c_h_element_v_in2(c_e_h_1, c_h, s15)),
% 294.20/186.77 inference(unit_resolution,[status(thm)],[25527, 178, 25516])).
% 294.20/186.77 tff(25529,plain,
% 294.20/186.77 (~node16(c_e_h_1, c_h, s15)),
% 294.20/186.77 inference(unit_resolution,[status(thm)],[25528, 25524])).
% 294.20/186.77 tff(25530,assumption,(node14(c_e_h_1, c_h, s15, s16)), introduced(assumption)).
% 294.20/186.77 tff(25531,plain,
% 294.20/186.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s16)) | m_c_h_element_v_in1(c_e_h_1, c_h, s15) | (~node14(c_e_h_1, c_h, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s16)) | m_c_h_element_v_in1(c_e_h_1, c_h, s15) | (~node14(c_e_h_1, c_h, s15, s16)))),
% 294.20/186.77 inference(rewrite,[status(thm)],[])).
% 294.20/186.77 tff(25532,plain,
% 294.20/186.77 (((~node14(c_e_h_1, c_h, s15, s16)) | m_c_h_element_v_in1(c_e_h_1, c_h, s15) | (~m_c_h_element_v_out(c_e_h_1, c_h, s16))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_h, s16)) | m_c_h_element_v_in1(c_e_h_1, c_h, s15) | (~node14(c_e_h_1, c_h, s15, s16)))),
% 294.20/186.78 inference(rewrite,[status(thm)],[])).
% 294.20/186.78 tff(25533,plain,
% 294.20/186.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s15, s16)) | m_c_h_element_v_in1(c_e_h_1, c_h, s15) | (~m_c_h_element_v_out(c_e_h_1, c_h, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s16)) | m_c_h_element_v_in1(c_e_h_1, c_h, s15) | (~node14(c_e_h_1, c_h, s15, s16))))),
% 294.20/186.78 inference(monotonicity,[status(thm)],[25532])).
% 294.20/186.78 tff(25534,plain,
% 294.20/186.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s15, s16)) | m_c_h_element_v_in1(c_e_h_1, c_h, s15) | (~m_c_h_element_v_out(c_e_h_1, c_h, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s16)) | m_c_h_element_v_in1(c_e_h_1, c_h, s15) | (~node14(c_e_h_1, c_h, s15, s16)))),
% 294.20/186.78 inference(transitivity,[status(thm)],[25533, 25531])).
% 294.20/186.78 tff(25535,plain,
% 294.20/186.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s15, s16)) | m_c_h_element_v_in1(c_e_h_1, c_h, s15) | (~m_c_h_element_v_out(c_e_h_1, c_h, s16)))),
% 294.20/186.78 inference(quant_inst,[status(thm)],[])).
% 294.20/186.78 tff(25536,plain,
% 294.20/186.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s16)) | m_c_h_element_v_in1(c_e_h_1, c_h, s15) | (~node14(c_e_h_1, c_h, s15, s16))),
% 294.20/186.78 inference(modus_ponens,[status(thm)],[25535, 25534])).
% 294.20/186.78 tff(25537,plain,
% 294.20/186.78 ($false),
% 294.20/186.78 inference(unit_resolution,[status(thm)],[25536, 223, 25491, 25530, 25516])).
% 294.20/186.78 tff(25538,plain,((~node14(c_e_h_1, c_h, s15, s16)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s16)) | m_c_h_element_v_in1(c_e_h_1, c_h, s15)), inference(lemma,lemma(discharge,[]))).
% 294.20/186.78 tff(25539,plain,
% 294.20/186.78 (~node14(c_e_h_1, c_h, s15, s16)),
% 294.20/186.78 inference(unit_resolution,[status(thm)],[25538, 25491, 25516])).
% 294.20/186.78 tff(25540,plain,
% 294.20/186.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s15) | node15(c_e_h_1, c_h, s15, s16) | (~node19(c_e_h_1, c_h, s15, s16)) | node14(c_e_h_1, c_h, s15, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s15) | node15(c_e_h_1, c_h, s15, s16) | (~node19(c_e_h_1, c_h, s15, s16)) | node14(c_e_h_1, c_h, s15, s16))),
% 294.20/186.78 inference(rewrite,[status(thm)],[])).
% 294.20/186.78 tff(25541,plain,
% 294.20/186.78 ((node16(c_e_h_1, c_h, s15) | node14(c_e_h_1, c_h, s15, s16) | node15(c_e_h_1, c_h, s15, s16) | (~node19(c_e_h_1, c_h, s15, s16))) <=> (node16(c_e_h_1, c_h, s15) | node15(c_e_h_1, c_h, s15, s16) | (~node19(c_e_h_1, c_h, s15, s16)) | node14(c_e_h_1, c_h, s15, s16))),
% 294.20/186.78 inference(rewrite,[status(thm)],[])).
% 294.20/186.78 tff(25542,plain,
% 294.20/186.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s15) | node14(c_e_h_1, c_h, s15, s16) | node15(c_e_h_1, c_h, s15, s16) | (~node19(c_e_h_1, c_h, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s15) | node15(c_e_h_1, c_h, s15, s16) | (~node19(c_e_h_1, c_h, s15, s16)) | node14(c_e_h_1, c_h, s15, s16)))),
% 294.20/186.78 inference(monotonicity,[status(thm)],[25541])).
% 294.20/186.78 tff(25543,plain,
% 294.20/186.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s15) | node14(c_e_h_1, c_h, s15, s16) | node15(c_e_h_1, c_h, s15, s16) | (~node19(c_e_h_1, c_h, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s15) | node15(c_e_h_1, c_h, s15, s16) | (~node19(c_e_h_1, c_h, s15, s16)) | node14(c_e_h_1, c_h, s15, s16))),
% 294.20/186.78 inference(transitivity,[status(thm)],[25542, 25540])).
% 294.20/186.78 tff(25544,plain,
% 294.20/186.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s15) | node14(c_e_h_1, c_h, s15, s16) | node15(c_e_h_1, c_h, s15, s16) | (~node19(c_e_h_1, c_h, s15, s16)))),
% 294.20/186.78 inference(quant_inst,[status(thm)],[])).
% 294.20/186.78 tff(25545,plain,
% 294.20/186.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s15) | node15(c_e_h_1, c_h, s15, s16) | (~node19(c_e_h_1, c_h, s15, s16)) | node14(c_e_h_1, c_h, s15, s16)),
% 294.20/186.78 inference(modus_ponens,[status(thm)],[25544, 25543])).
% 294.20/186.78 tff(25546,plain,
% 294.20/186.78 (node16(c_e_h_1, c_h, s15) | node15(c_e_h_1, c_h, s15, s16) | node14(c_e_h_1, c_h, s15, s16)),
% 294.20/186.78 inference(unit_resolution,[status(thm)],[25545, 204, 25507])).
% 294.20/186.78 tff(25547,plain,
% 294.20/186.78 (node15(c_e_h_1, c_h, s15, s16)),
% 294.20/186.78 inference(unit_resolution,[status(thm)],[25546, 25539, 25529])).
% 294.20/186.78 tff(25548,plain,
% 294.20/186.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s16)) | (~node15(c_e_h_1, c_h, s15, s16)) | m_c_h_element_v_out(c_e_h_1, c_h, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s16)) | (~node15(c_e_h_1, c_h, s15, s16)) | m_c_h_element_v_out(c_e_h_1, c_h, s15))),
% 294.20/186.78 inference(rewrite,[status(thm)],[])).
% 294.20/186.78 tff(25549,plain,
% 294.20/186.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s16)) | (~node15(c_e_h_1, c_h, s15, s16)) | m_c_h_element_v_out(c_e_h_1, c_h, s15))),
% 294.20/186.78 inference(quant_inst,[status(thm)],[])).
% 294.20/186.78 tff(25550,plain,
% 294.20/186.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s16)) | (~node15(c_e_h_1, c_h, s15, s16)) | m_c_h_element_v_out(c_e_h_1, c_h, s15)),
% 294.20/186.78 inference(modus_ponens,[status(thm)],[25549, 25548])).
% 294.20/186.78 tff(25551,plain,
% 294.20/186.78 ($false),
% 294.20/186.78 inference(unit_resolution,[status(thm)],[25550, 147, 25492, 25491, 25547])).
% 294.20/186.78 tff(25552,plain,((~m_c_h_element_v_out(c_e_h_1, c_h, s16)) | m_c_h_element_v_out(c_e_h_1, c_h, s15) | m_c_h_element_v_in1(c_e_h_1, c_h, s15)), inference(lemma,lemma(discharge,[]))).
% 294.20/186.78 tff(25553,plain,
% 294.20/186.78 (m_c_h_element_v_in1(c_e_h_1, c_h, s15)),
% 294.20/186.78 inference(unit_resolution,[status(thm)],[25552, 25492, 25491])).
% 294.20/186.78 tff(25554,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_h, s15)), introduced(assumption)).
% 294.20/186.78 tff(25555,plain,
% 294.20/186.78 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_h, s15) | (~node17(c_e_h_1, c_h, s15)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s15)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_h, s15) | (~node17(c_e_h_1, c_h, s15)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s15)))),
% 294.20/186.78 inference(rewrite,[status(thm)],[])).
% 294.20/186.78 tff(25556,plain,
% 294.20/186.78 (((~m_c_h_element_v_in1(c_e_h_1, c_h, s15)) | m_c_h_element_v_in2(c_e_h_1, c_h, s15) | (~node17(c_e_h_1, c_h, s15))) <=> (m_c_h_element_v_in2(c_e_h_1, c_h, s15) | (~node17(c_e_h_1, c_h, s15)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s15)))),
% 294.20/186.78 inference(rewrite,[status(thm)],[])).
% 294.20/186.78 tff(25557,plain,
% 294.20/186.78 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s15)) | m_c_h_element_v_in2(c_e_h_1, c_h, s15) | (~node17(c_e_h_1, c_h, s15)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_h, s15) | (~node17(c_e_h_1, c_h, s15)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s15))))),
% 294.20/186.78 inference(monotonicity,[status(thm)],[25556])).
% 294.20/186.78 tff(25558,plain,
% 294.20/186.78 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s15)) | m_c_h_element_v_in2(c_e_h_1, c_h, s15) | (~node17(c_e_h_1, c_h, s15)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_h, s15) | (~node17(c_e_h_1, c_h, s15)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s15)))),
% 294.20/186.78 inference(transitivity,[status(thm)],[25557, 25555])).
% 294.20/186.78 tff(25559,plain,
% 294.20/186.78 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s15)) | m_c_h_element_v_in2(c_e_h_1, c_h, s15) | (~node17(c_e_h_1, c_h, s15)))),
% 294.20/186.78 inference(quant_inst,[status(thm)],[])).
% 294.20/186.78 tff(25560,plain,
% 294.20/186.78 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_h, s15) | (~node17(c_e_h_1, c_h, s15)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s15))),
% 294.20/186.78 inference(modus_ponens,[status(thm)],[25559, 25558])).
% 294.20/186.78 tff(25561,plain,
% 294.20/186.78 ((~node17(c_e_h_1, c_h, s15)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s15))),
% 294.20/186.78 inference(unit_resolution,[status(thm)],[25560, 919, 25554])).
% 294.20/186.78 tff(25562,plain,
% 294.20/186.78 (~node17(c_e_h_1, c_h, s15)),
% 294.20/186.78 inference(unit_resolution,[status(thm)],[25561, 25553])).
% 294.20/186.78 tff(25563,plain,
% 294.20/186.78 ($false),
% 294.20/186.78 inference(unit_resolution,[status(thm)],[25514, 25562, 25502])).
% 294.20/186.78 tff(25564,plain,(m_c_h_element_v_out(c_e_h_1, c_h, s15) | m_c_h_element_v_in2(c_e_h_1, c_h, s15) | (~m_c_h_element_v_out(c_e_h_1, c_h, s16))), inference(lemma,lemma(discharge,[]))).
% 294.20/186.78 tff(25565,plain,
% 294.20/186.78 (~m_c_h_element_v_out(c_e_h_1, c_h, s16)),
% 294.20/186.78 inference(unit_resolution,[status(thm)],[25564, 25490, 24033])).
% 294.20/186.78 tff(25566,plain,
% 294.20/186.78 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s16)) | m_c_h_element_v_out(c_e_h_1, c_h, s16))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s16)) | m_c_h_element_v_out(c_e_h_1, c_h, s16))),
% 294.20/186.78 inference(rewrite,[status(thm)],[])).
% 294.20/186.78 tff(25567,plain,
% 294.20/186.78 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s16)) | m_c_h_element_v_out(c_e_h_1, c_h, s16))),
% 294.20/186.78 inference(quant_inst,[status(thm)],[])).
% 294.20/186.78 tff(25568,plain,
% 294.20/186.78 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s16)) | m_c_h_element_v_out(c_e_h_1, c_h, s16)),
% 294.20/186.78 inference(modus_ponens,[status(thm)],[25567, 25566])).
% 294.20/186.78 tff(25569,plain,
% 294.20/186.78 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s16)),
% 294.20/186.78 inference(unit_resolution,[status(thm)],[25568, 619, 25565])).
% 294.20/186.78 tff(25570,plain,
% 294.20/186.78 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s16)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s16))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s16)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s16))),
% 294.20/186.78 inference(rewrite,[status(thm)],[])).
% 294.20/186.78 tff(25571,plain,
% 294.20/186.78 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s16)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s16))),
% 294.29/186.79 inference(quant_inst,[status(thm)],[])).
% 294.29/186.79 tff(25572,plain,
% 294.29/186.79 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s16)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s16)),
% 294.29/186.79 inference(modus_ponens,[status(thm)],[25571, 25570])).
% 294.29/186.79 tff(25573,plain,
% 294.29/186.79 (~node20(c_e_h_1, c_i, s16)),
% 294.29/186.79 inference(unit_resolution,[status(thm)],[25572, 38, 25569])).
% 294.29/186.79 tff(25574,assumption,(m_c_h_element_v_in2(c_e_h_1, c_e, s15)), introduced(assumption)).
% 294.29/186.79 tff(25575,plain,
% 294.29/186.79 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s15)) | m_and_h_gate_v_out(c_e_h_1, c_i, s15))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s15)) | m_and_h_gate_v_out(c_e_h_1, c_i, s15))),
% 294.29/186.79 inference(rewrite,[status(thm)],[])).
% 294.29/186.79 tff(25576,plain,
% 294.29/186.79 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s15)) | m_and_h_gate_v_out(c_e_h_1, c_i, s15))),
% 294.29/186.79 inference(quant_inst,[status(thm)],[])).
% 294.29/186.79 tff(25577,plain,
% 294.29/186.79 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s15)) | m_and_h_gate_v_out(c_e_h_1, c_i, s15)),
% 294.29/186.79 inference(modus_ponens,[status(thm)],[25576, 25575])).
% 294.29/186.79 tff(25578,plain,
% 294.29/186.79 ($false),
% 294.29/186.79 inference(unit_resolution,[status(thm)],[25577, 164, 24251, 25574])).
% 294.29/186.79 tff(25579,plain,((~m_c_h_element_v_in2(c_e_h_1, c_e, s15)) | m_and_h_gate_v_out(c_e_h_1, c_i, s15)), inference(lemma,lemma(discharge,[]))).
% 294.29/186.79 tff(25580,plain,
% 294.29/186.79 (~m_c_h_element_v_in2(c_e_h_1, c_e, s15)),
% 294.29/186.79 inference(unit_resolution,[status(thm)],[25579, 24241])).
% 294.29/186.79 tff(25581,assumption,(m_c_h_element_v_in2(c_e_h_1, c_e, s12)), introduced(assumption)).
% 294.29/186.79 tff(25582,plain,
% 294.29/186.79 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s12)) | m_and_h_gate_v_out(c_e_h_1, c_i, s12))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s12)) | m_and_h_gate_v_out(c_e_h_1, c_i, s12))),
% 294.29/186.79 inference(rewrite,[status(thm)],[])).
% 294.29/186.79 tff(25583,plain,
% 294.29/186.79 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s12)) | m_and_h_gate_v_out(c_e_h_1, c_i, s12))),
% 294.29/186.79 inference(quant_inst,[status(thm)],[])).
% 294.29/186.79 tff(25584,plain,
% 294.29/186.79 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s12)) | m_and_h_gate_v_out(c_e_h_1, c_i, s12)),
% 294.29/186.79 inference(modus_ponens,[status(thm)],[25583, 25582])).
% 294.29/186.79 tff(25585,plain,
% 294.29/186.79 ($false),
% 294.29/186.79 inference(unit_resolution,[status(thm)],[25584, 164, 24159, 25581])).
% 294.29/186.79 tff(25586,plain,((~m_c_h_element_v_in2(c_e_h_1, c_e, s12)) | m_and_h_gate_v_out(c_e_h_1, c_i, s12)), inference(lemma,lemma(discharge,[]))).
% 294.29/186.79 tff(25587,plain,
% 294.29/186.79 (~m_c_h_element_v_in2(c_e_h_1, c_e, s12)),
% 294.29/186.79 inference(unit_resolution,[status(thm)],[25586, 24149])).
% 294.29/186.79 tff(25588,assumption,(m_c_h_element_v_in2(c_e_h_1, c_e, s11)), introduced(assumption)).
% 294.29/186.79 tff(25589,plain,
% 294.29/186.79 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s11)) | m_and_h_gate_v_out(c_e_h_1, c_i, s11))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s11)) | m_and_h_gate_v_out(c_e_h_1, c_i, s11))),
% 294.29/186.79 inference(rewrite,[status(thm)],[])).
% 294.29/186.79 tff(25590,plain,
% 294.29/186.79 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s11)) | m_and_h_gate_v_out(c_e_h_1, c_i, s11))),
% 294.29/186.79 inference(quant_inst,[status(thm)],[])).
% 294.29/186.79 tff(25591,plain,
% 294.29/186.79 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s11)) | m_and_h_gate_v_out(c_e_h_1, c_i, s11)),
% 294.29/186.79 inference(modus_ponens,[status(thm)],[25590, 25589])).
% 294.29/186.79 tff(25592,plain,
% 294.29/186.79 ($false),
% 294.29/186.79 inference(unit_resolution,[status(thm)],[25591, 164, 24142, 25588])).
% 294.29/186.79 tff(25593,plain,((~m_c_h_element_v_in2(c_e_h_1, c_e, s11)) | m_and_h_gate_v_out(c_e_h_1, c_i, s11)), inference(lemma,lemma(discharge,[]))).
% 294.29/186.79 tff(25594,plain,
% 294.29/186.79 (~m_c_h_element_v_in2(c_e_h_1, c_e, s11)),
% 294.29/186.79 inference(unit_resolution,[status(thm)],[25593, 24127])).
% 294.29/186.79 tff(25595,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s12)), introduced(assumption)).
% 294.29/186.79 tff(25596,assumption,(node18(c_e_h_1, c_e, s11, s12)), introduced(assumption)).
% 294.29/186.79 tff(25597,plain,
% 294.29/186.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s11) | (~m_c_h_element_v_out(c_e_h_1, c_e, s12)) | (~node18(c_e_h_1, c_e, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s11) | (~m_c_h_element_v_out(c_e_h_1, c_e, s12)) | (~node18(c_e_h_1, c_e, s11, s12)))),
% 294.29/186.79 inference(rewrite,[status(thm)],[])).
% 294.29/186.79 tff(25598,plain,
% 294.29/186.79 (((~m_c_h_element_v_out(c_e_h_1, c_e, s12)) | m_c_h_element_v_out(c_e_h_1, c_e, s11) | (~node18(c_e_h_1, c_e, s11, s12))) <=> (m_c_h_element_v_out(c_e_h_1, c_e, s11) | (~m_c_h_element_v_out(c_e_h_1, c_e, s12)) | (~node18(c_e_h_1, c_e, s11, s12)))),
% 294.29/186.79 inference(rewrite,[status(thm)],[])).
% 294.29/186.79 tff(25599,plain,
% 294.29/186.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s12)) | m_c_h_element_v_out(c_e_h_1, c_e, s11) | (~node18(c_e_h_1, c_e, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s11) | (~m_c_h_element_v_out(c_e_h_1, c_e, s12)) | (~node18(c_e_h_1, c_e, s11, s12))))),
% 294.29/186.79 inference(monotonicity,[status(thm)],[25598])).
% 294.29/186.79 tff(25600,plain,
% 294.29/186.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s12)) | m_c_h_element_v_out(c_e_h_1, c_e, s11) | (~node18(c_e_h_1, c_e, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s11) | (~m_c_h_element_v_out(c_e_h_1, c_e, s12)) | (~node18(c_e_h_1, c_e, s11, s12)))),
% 294.29/186.79 inference(transitivity,[status(thm)],[25599, 25597])).
% 294.29/186.79 tff(25601,plain,
% 294.29/186.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s12)) | m_c_h_element_v_out(c_e_h_1, c_e, s11) | (~node18(c_e_h_1, c_e, s11, s12)))),
% 294.29/186.79 inference(quant_inst,[status(thm)],[])).
% 294.29/186.79 tff(25602,plain,
% 294.29/186.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s11) | (~m_c_h_element_v_out(c_e_h_1, c_e, s12)) | (~node18(c_e_h_1, c_e, s11, s12))),
% 294.29/186.79 inference(modus_ponens,[status(thm)],[25601, 25600])).
% 294.29/186.79 tff(25603,plain,
% 294.29/186.79 ($false),
% 294.29/186.79 inference(unit_resolution,[status(thm)],[25602, 753, 24402, 25595, 25596])).
% 294.29/186.79 tff(25604,plain,((~node18(c_e_h_1, c_e, s11, s12)) | m_c_h_element_v_out(c_e_h_1, c_e, s11) | (~m_c_h_element_v_out(c_e_h_1, c_e, s12))), inference(lemma,lemma(discharge,[]))).
% 294.29/186.79 tff(25605,plain,
% 294.29/186.79 (~node18(c_e_h_1, c_e, s11, s12)),
% 294.29/186.79 inference(unit_resolution,[status(thm)],[25604, 25595, 24402])).
% 294.29/186.79 tff(25606,plain,
% 294.29/186.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s11, s12)) | node19(c_e_h_1, c_e, s11, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s11, s12)) | node19(c_e_h_1, c_e, s11, s12))),
% 294.29/186.80 inference(rewrite,[status(thm)],[])).
% 294.29/186.80 tff(25607,plain,
% 294.29/186.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s11, s12)) | node19(c_e_h_1, c_e, s11, s12))),
% 294.29/186.80 inference(quant_inst,[status(thm)],[])).
% 294.29/186.80 tff(25608,plain,
% 294.29/186.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s11, s12)) | node19(c_e_h_1, c_e, s11, s12)),
% 294.29/186.80 inference(modus_ponens,[status(thm)],[25607, 25606])).
% 294.29/186.80 tff(25609,plain,
% 294.29/186.80 (node19(c_e_h_1, c_e, s11, s12)),
% 294.29/186.80 inference(unit_resolution,[status(thm)],[25608, 190, 11461])).
% 294.29/186.80 tff(25610,plain,
% 294.29/186.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_1, c_e, s11, s12) | (~node19(c_e_h_1, c_e, s11, s12)) | node17(c_e_h_1, c_e, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_e, s11, s12) | (~node19(c_e_h_1, c_e, s11, s12)) | node17(c_e_h_1, c_e, s11))),
% 294.29/186.80 inference(rewrite,[status(thm)],[])).
% 294.29/186.80 tff(25611,plain,
% 294.29/186.80 ((node17(c_e_h_1, c_e, s11) | node18(c_e_h_1, c_e, s11, s12) | (~node19(c_e_h_1, c_e, s11, s12))) <=> (node18(c_e_h_1, c_e, s11, s12) | (~node19(c_e_h_1, c_e, s11, s12)) | node17(c_e_h_1, c_e, s11))),
% 294.29/186.80 inference(rewrite,[status(thm)],[])).
% 294.29/186.80 tff(25612,plain,
% 294.29/186.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s11) | node18(c_e_h_1, c_e, s11, s12) | (~node19(c_e_h_1, c_e, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_1, c_e, s11, s12) | (~node19(c_e_h_1, c_e, s11, s12)) | node17(c_e_h_1, c_e, s11)))),
% 294.29/186.80 inference(monotonicity,[status(thm)],[25611])).
% 294.29/186.80 tff(25613,plain,
% 294.29/186.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s11) | node18(c_e_h_1, c_e, s11, s12) | (~node19(c_e_h_1, c_e, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_e, s11, s12) | (~node19(c_e_h_1, c_e, s11, s12)) | node17(c_e_h_1, c_e, s11))),
% 294.29/186.80 inference(transitivity,[status(thm)],[25612, 25610])).
% 294.29/186.80 tff(25614,plain,
% 294.29/186.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s11) | node18(c_e_h_1, c_e, s11, s12) | (~node19(c_e_h_1, c_e, s11, s12)))),
% 294.29/186.80 inference(quant_inst,[status(thm)],[])).
% 294.29/186.80 tff(25615,plain,
% 294.29/186.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_e, s11, s12) | (~node19(c_e_h_1, c_e, s11, s12)) | node17(c_e_h_1, c_e, s11)),
% 294.29/186.80 inference(modus_ponens,[status(thm)],[25614, 25613])).
% 294.29/186.80 tff(25616,plain,
% 294.29/186.80 (node18(c_e_h_1, c_e, s11, s12) | node17(c_e_h_1, c_e, s11)),
% 294.29/186.80 inference(unit_resolution,[status(thm)],[25615, 776, 25609])).
% 294.29/186.80 tff(25617,plain,
% 294.29/186.80 (node17(c_e_h_1, c_e, s11)),
% 294.29/186.80 inference(unit_resolution,[status(thm)],[25616, 25605])).
% 294.29/186.80 tff(25618,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_e, s11)), introduced(assumption)).
% 294.29/186.80 tff(25619,assumption,(node14(c_e_h_1, c_e, s11, s12)), introduced(assumption)).
% 294.29/186.80 tff(25620,plain,
% 294.29/186.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s11, s12)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s12)) | m_c_h_element_v_in1(c_e_h_1, c_e, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_1, c_e, s11, s12)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s12)) | m_c_h_element_v_in1(c_e_h_1, c_e, s11))),
% 294.29/186.80 inference(rewrite,[status(thm)],[])).
% 294.29/186.80 tff(25621,plain,
% 294.29/186.80 (((~node14(c_e_h_1, c_e, s11, s12)) | m_c_h_element_v_in1(c_e_h_1, c_e, s11) | (~m_c_h_element_v_out(c_e_h_1, c_e, s12))) <=> ((~node14(c_e_h_1, c_e, s11, s12)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s12)) | m_c_h_element_v_in1(c_e_h_1, c_e, s11))),
% 294.29/186.80 inference(rewrite,[status(thm)],[])).
% 294.29/186.80 tff(25622,plain,
% 294.29/186.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s11, s12)) | m_c_h_element_v_in1(c_e_h_1, c_e, s11) | (~m_c_h_element_v_out(c_e_h_1, c_e, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s11, s12)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s12)) | m_c_h_element_v_in1(c_e_h_1, c_e, s11)))),
% 294.29/186.80 inference(monotonicity,[status(thm)],[25621])).
% 294.29/186.80 tff(25623,plain,
% 294.29/186.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s11, s12)) | m_c_h_element_v_in1(c_e_h_1, c_e, s11) | (~m_c_h_element_v_out(c_e_h_1, c_e, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_1, c_e, s11, s12)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s12)) | m_c_h_element_v_in1(c_e_h_1, c_e, s11))),
% 294.29/186.80 inference(transitivity,[status(thm)],[25622, 25620])).
% 294.29/186.80 tff(25624,plain,
% 294.29/186.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s11, s12)) | m_c_h_element_v_in1(c_e_h_1, c_e, s11) | (~m_c_h_element_v_out(c_e_h_1, c_e, s12)))),
% 294.29/186.80 inference(quant_inst,[status(thm)],[])).
% 294.29/186.80 tff(25625,plain,
% 294.29/186.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_1, c_e, s11, s12)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s12)) | m_c_h_element_v_in1(c_e_h_1, c_e, s11)),
% 294.29/186.80 inference(modus_ponens,[status(thm)],[25624, 25623])).
% 294.29/186.80 tff(25626,plain,
% 294.29/186.80 ($false),
% 294.29/186.80 inference(unit_resolution,[status(thm)],[25625, 223, 25595, 25619, 25618])).
% 294.29/186.80 tff(25627,plain,((~node14(c_e_h_1, c_e, s11, s12)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s12)) | m_c_h_element_v_in1(c_e_h_1, c_e, s11)), inference(lemma,lemma(discharge,[]))).
% 294.29/186.80 tff(25628,plain,
% 294.29/186.80 (~node14(c_e_h_1, c_e, s11, s12)),
% 294.29/186.80 inference(unit_resolution,[status(thm)],[25627, 25595, 25618])).
% 294.29/186.80 tff(25629,assumption,(node15(c_e_h_1, c_e, s11, s12)), introduced(assumption)).
% 294.29/186.80 tff(25630,plain,
% 294.29/186.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s12)) | (~node15(c_e_h_1, c_e, s11, s12)) | m_c_h_element_v_out(c_e_h_1, c_e, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s12)) | (~node15(c_e_h_1, c_e, s11, s12)) | m_c_h_element_v_out(c_e_h_1, c_e, s11))),
% 294.29/186.80 inference(rewrite,[status(thm)],[])).
% 294.29/186.80 tff(25631,plain,
% 294.29/186.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s12)) | (~node15(c_e_h_1, c_e, s11, s12)) | m_c_h_element_v_out(c_e_h_1, c_e, s11))),
% 294.29/186.80 inference(quant_inst,[status(thm)],[])).
% 294.29/186.80 tff(25632,plain,
% 294.29/186.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s12)) | (~node15(c_e_h_1, c_e, s11, s12)) | m_c_h_element_v_out(c_e_h_1, c_e, s11)),
% 294.29/186.80 inference(modus_ponens,[status(thm)],[25631, 25630])).
% 294.29/186.80 tff(25633,plain,
% 294.29/186.80 ($false),
% 294.29/186.80 inference(unit_resolution,[status(thm)],[25632, 147, 24402, 25595, 25629])).
% 294.29/186.80 tff(25634,plain,((~node15(c_e_h_1, c_e, s11, s12)) | m_c_h_element_v_out(c_e_h_1, c_e, s11) | (~m_c_h_element_v_out(c_e_h_1, c_e, s12))), inference(lemma,lemma(discharge,[]))).
% 294.29/186.80 tff(25635,plain,
% 294.29/186.80 (~node15(c_e_h_1, c_e, s11, s12)),
% 294.29/186.80 inference(unit_resolution,[status(thm)],[25634, 25595, 24402])).
% 294.29/186.80 tff(25636,plain,
% 294.29/186.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_1, c_e, s11, s12) | (~node19(c_e_h_1, c_e, s11, s12)) | node14(c_e_h_1, c_e, s11, s12) | node16(c_e_h_1, c_e, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_e, s11, s12) | (~node19(c_e_h_1, c_e, s11, s12)) | node14(c_e_h_1, c_e, s11, s12) | node16(c_e_h_1, c_e, s11))),
% 294.29/186.80 inference(rewrite,[status(thm)],[])).
% 294.29/186.80 tff(25637,plain,
% 294.29/186.80 ((node16(c_e_h_1, c_e, s11) | node14(c_e_h_1, c_e, s11, s12) | node15(c_e_h_1, c_e, s11, s12) | (~node19(c_e_h_1, c_e, s11, s12))) <=> (node15(c_e_h_1, c_e, s11, s12) | (~node19(c_e_h_1, c_e, s11, s12)) | node14(c_e_h_1, c_e, s11, s12) | node16(c_e_h_1, c_e, s11))),
% 294.29/186.80 inference(rewrite,[status(thm)],[])).
% 294.29/186.80 tff(25638,plain,
% 294.29/186.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s11) | node14(c_e_h_1, c_e, s11, s12) | node15(c_e_h_1, c_e, s11, s12) | (~node19(c_e_h_1, c_e, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_1, c_e, s11, s12) | (~node19(c_e_h_1, c_e, s11, s12)) | node14(c_e_h_1, c_e, s11, s12) | node16(c_e_h_1, c_e, s11)))),
% 294.29/186.80 inference(monotonicity,[status(thm)],[25637])).
% 294.29/186.80 tff(25639,plain,
% 294.29/186.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s11) | node14(c_e_h_1, c_e, s11, s12) | node15(c_e_h_1, c_e, s11, s12) | (~node19(c_e_h_1, c_e, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_e, s11, s12) | (~node19(c_e_h_1, c_e, s11, s12)) | node14(c_e_h_1, c_e, s11, s12) | node16(c_e_h_1, c_e, s11))),
% 294.29/186.80 inference(transitivity,[status(thm)],[25638, 25636])).
% 294.29/186.80 tff(25640,plain,
% 294.29/186.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s11) | node14(c_e_h_1, c_e, s11, s12) | node15(c_e_h_1, c_e, s11, s12) | (~node19(c_e_h_1, c_e, s11, s12)))),
% 294.29/186.80 inference(quant_inst,[status(thm)],[])).
% 294.29/186.80 tff(25641,plain,
% 294.29/186.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_e, s11, s12) | (~node19(c_e_h_1, c_e, s11, s12)) | node14(c_e_h_1, c_e, s11, s12) | node16(c_e_h_1, c_e, s11)),
% 294.29/186.80 inference(modus_ponens,[status(thm)],[25640, 25639])).
% 294.29/186.80 tff(25642,plain,
% 294.29/186.80 (node15(c_e_h_1, c_e, s11, s12) | node14(c_e_h_1, c_e, s11, s12) | node16(c_e_h_1, c_e, s11)),
% 294.29/186.80 inference(unit_resolution,[status(thm)],[25641, 204, 25609])).
% 294.29/186.80 tff(25643,plain,
% 294.29/186.80 (node16(c_e_h_1, c_e, s11)),
% 294.29/186.80 inference(unit_resolution,[status(thm)],[25642, 25635, 25628])).
% 294.29/186.80 tff(25644,assumption,(node17(c_e_h_1, c_e, s11)), introduced(assumption)).
% 294.29/186.80 tff(25645,assumption,(node16(c_e_h_1, c_e, s11)), introduced(assumption)).
% 294.29/186.80 tff(25646,plain,
% 294.29/186.80 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_e, s11)) | m_c_h_element_v_in1(c_e_h_1, c_e, s11) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s11)) | m_c_h_element_v_in1(c_e_h_1, c_e, s11) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s11)))),
% 294.29/186.80 inference(rewrite,[status(thm)],[])).
% 294.29/186.80 tff(25647,plain,
% 294.29/186.80 ((m_c_h_element_v_in1(c_e_h_1, c_e, s11) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s11)) | (~node17(c_e_h_1, c_e, s11))) <=> ((~node17(c_e_h_1, c_e, s11)) | m_c_h_element_v_in1(c_e_h_1, c_e, s11) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s11)))),
% 294.29/186.81 inference(rewrite,[status(thm)],[])).
% 294.29/186.81 tff(25648,plain,
% 294.29/186.81 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s11) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s11)) | (~node17(c_e_h_1, c_e, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_e, s11)) | m_c_h_element_v_in1(c_e_h_1, c_e, s11) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s11))))),
% 294.29/186.81 inference(monotonicity,[status(thm)],[25647])).
% 294.29/186.81 tff(25649,plain,
% 294.29/186.81 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s11) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s11)) | (~node17(c_e_h_1, c_e, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s11)) | m_c_h_element_v_in1(c_e_h_1, c_e, s11) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s11)))),
% 294.29/186.81 inference(transitivity,[status(thm)],[25648, 25646])).
% 294.29/186.81 tff(25650,plain,
% 294.29/186.81 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s11) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s11)) | (~node17(c_e_h_1, c_e, s11)))),
% 294.29/186.81 inference(quant_inst,[status(thm)],[])).
% 294.29/186.81 tff(25651,plain,
% 294.29/186.81 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s11)) | m_c_h_element_v_in1(c_e_h_1, c_e, s11) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s11))),
% 294.29/186.81 inference(modus_ponens,[status(thm)],[25650, 25649])).
% 294.29/186.81 tff(25652,plain,
% 294.29/186.81 (m_c_h_element_v_in1(c_e_h_1, c_e, s11) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s11))),
% 294.29/186.81 inference(unit_resolution,[status(thm)],[25651, 859, 25644])).
% 294.29/186.81 tff(25653,plain,
% 294.29/186.81 (~m_c_h_element_v_in2(c_e_h_1, c_e, s11)),
% 294.29/186.81 inference(unit_resolution,[status(thm)],[25652, 25618])).
% 294.29/186.81 tff(25654,plain,
% 294.29/186.81 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s11)) | m_c_h_element_v_in1(c_e_h_1, c_e, s11) | m_c_h_element_v_in2(c_e_h_1, c_e, s11))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s11)) | m_c_h_element_v_in1(c_e_h_1, c_e, s11) | m_c_h_element_v_in2(c_e_h_1, c_e, s11))),
% 294.29/186.81 inference(rewrite,[status(thm)],[])).
% 294.29/186.81 tff(25655,plain,
% 294.29/186.81 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s11)) | m_c_h_element_v_in1(c_e_h_1, c_e, s11) | m_c_h_element_v_in2(c_e_h_1, c_e, s11))),
% 294.29/186.81 inference(quant_inst,[status(thm)],[])).
% 294.29/186.81 tff(25656,plain,
% 294.29/186.81 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s11)) | m_c_h_element_v_in1(c_e_h_1, c_e, s11) | m_c_h_element_v_in2(c_e_h_1, c_e, s11)),
% 294.29/186.81 inference(modus_ponens,[status(thm)],[25655, 25654])).
% 294.29/186.81 tff(25657,plain,
% 294.29/186.81 (m_c_h_element_v_in1(c_e_h_1, c_e, s11) | m_c_h_element_v_in2(c_e_h_1, c_e, s11)),
% 294.29/186.81 inference(unit_resolution,[status(thm)],[25656, 178, 25645])).
% 294.29/186.81 tff(25658,plain,
% 294.29/186.81 ($false),
% 294.29/186.81 inference(unit_resolution,[status(thm)],[25657, 25653, 25618])).
% 294.29/186.81 tff(25659,plain,(m_c_h_element_v_in1(c_e_h_1, c_e, s11) | (~node16(c_e_h_1, c_e, s11)) | (~node17(c_e_h_1, c_e, s11))), inference(lemma,lemma(discharge,[]))).
% 294.29/186.81 tff(25660,plain,
% 294.29/186.81 (m_c_h_element_v_in1(c_e_h_1, c_e, s11)),
% 294.29/186.81 inference(unit_resolution,[status(thm)],[25659, 25645, 25644])).
% 294.29/186.81 tff(25661,plain,
% 294.29/186.81 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_e, s11)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s11)) | m_c_h_element_v_in2(c_e_h_1, c_e, s11))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s11)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s11)) | m_c_h_element_v_in2(c_e_h_1, c_e, s11))),
% 294.29/186.81 inference(rewrite,[status(thm)],[])).
% 294.29/186.81 tff(25662,plain,
% 294.29/186.81 (((~m_c_h_element_v_in1(c_e_h_1, c_e, s11)) | m_c_h_element_v_in2(c_e_h_1, c_e, s11) | (~node17(c_e_h_1, c_e, s11))) <=> ((~node17(c_e_h_1, c_e, s11)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s11)) | m_c_h_element_v_in2(c_e_h_1, c_e, s11))),
% 294.29/186.81 inference(rewrite,[status(thm)],[])).
% 294.29/186.81 tff(25663,plain,
% 294.29/186.81 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s11)) | m_c_h_element_v_in2(c_e_h_1, c_e, s11) | (~node17(c_e_h_1, c_e, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_e, s11)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s11)) | m_c_h_element_v_in2(c_e_h_1, c_e, s11)))),
% 294.29/186.81 inference(monotonicity,[status(thm)],[25662])).
% 294.29/186.81 tff(25664,plain,
% 294.29/186.81 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s11)) | m_c_h_element_v_in2(c_e_h_1, c_e, s11) | (~node17(c_e_h_1, c_e, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s11)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s11)) | m_c_h_element_v_in2(c_e_h_1, c_e, s11))),
% 294.29/186.81 inference(transitivity,[status(thm)],[25663, 25661])).
% 294.29/186.81 tff(25665,plain,
% 294.29/186.81 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s11)) | m_c_h_element_v_in2(c_e_h_1, c_e, s11) | (~node17(c_e_h_1, c_e, s11)))),
% 294.29/186.81 inference(quant_inst,[status(thm)],[])).
% 294.29/186.81 tff(25666,plain,
% 294.29/186.81 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s11)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s11)) | m_c_h_element_v_in2(c_e_h_1, c_e, s11)),
% 294.29/186.81 inference(modus_ponens,[status(thm)],[25665, 25664])).
% 294.29/186.81 tff(25667,plain,
% 294.29/186.81 ((~m_c_h_element_v_in1(c_e_h_1, c_e, s11)) | m_c_h_element_v_in2(c_e_h_1, c_e, s11)),
% 294.29/186.81 inference(unit_resolution,[status(thm)],[25666, 919, 25644])).
% 294.29/186.81 tff(25668,plain,
% 294.29/186.81 (m_c_h_element_v_in2(c_e_h_1, c_e, s11)),
% 294.29/186.81 inference(unit_resolution,[status(thm)],[25667, 25660])).
% 294.29/186.81 tff(25669,plain,
% 294.29/186.81 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s11)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s11)) | (~node16(c_e_h_1, c_e, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s11)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s11)) | (~node16(c_e_h_1, c_e, s11)))),
% 294.29/186.81 inference(rewrite,[status(thm)],[])).
% 294.29/186.81 tff(25670,plain,
% 294.29/186.81 (((~node16(c_e_h_1, c_e, s11)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s11)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s11))) <=> ((~m_c_h_element_v_in1(c_e_h_1, c_e, s11)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s11)) | (~node16(c_e_h_1, c_e, s11)))),
% 294.29/186.81 inference(rewrite,[status(thm)],[])).
% 294.29/186.81 tff(25671,plain,
% 294.29/186.81 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s11)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s11)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s11)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s11)) | (~node16(c_e_h_1, c_e, s11))))),
% 294.29/186.81 inference(monotonicity,[status(thm)],[25670])).
% 294.29/186.81 tff(25672,plain,
% 294.29/186.81 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s11)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s11)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s11)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s11)) | (~node16(c_e_h_1, c_e, s11)))),
% 294.29/186.81 inference(transitivity,[status(thm)],[25671, 25669])).
% 294.29/186.81 tff(25673,plain,
% 294.29/186.81 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s11)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s11)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s11)))),
% 294.29/186.81 inference(quant_inst,[status(thm)],[])).
% 294.29/186.81 tff(25674,plain,
% 294.29/186.81 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s11)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s11)) | (~node16(c_e_h_1, c_e, s11))),
% 294.29/186.81 inference(modus_ponens,[status(thm)],[25673, 25672])).
% 294.29/186.81 tff(25675,plain,
% 294.29/186.81 ((~m_c_h_element_v_in1(c_e_h_1, c_e, s11)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s11))),
% 294.29/186.81 inference(unit_resolution,[status(thm)],[25674, 2307, 25645])).
% 294.29/186.81 tff(25676,plain,
% 294.29/186.81 ($false),
% 294.29/186.81 inference(unit_resolution,[status(thm)],[25675, 25668, 25660])).
% 294.29/186.81 tff(25677,plain,((~node16(c_e_h_1, c_e, s11)) | (~node17(c_e_h_1, c_e, s11))), inference(lemma,lemma(discharge,[]))).
% 294.29/186.81 tff(25678,plain,
% 294.29/186.81 ($false),
% 294.29/186.81 inference(unit_resolution,[status(thm)],[25677, 25643, 25617])).
% 294.29/186.81 tff(25679,plain,((~m_c_h_element_v_out(c_e_h_1, c_e, s12)) | m_c_h_element_v_out(c_e_h_1, c_e, s11) | m_c_h_element_v_in1(c_e_h_1, c_e, s11)), inference(lemma,lemma(discharge,[]))).
% 294.29/186.81 tff(25680,plain,
% 294.29/186.81 (m_c_h_element_v_in1(c_e_h_1, c_e, s11)),
% 294.29/186.81 inference(unit_resolution,[status(thm)],[25679, 25595, 24402])).
% 294.29/186.81 tff(25681,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_e, s11)), introduced(assumption)).
% 294.29/186.81 tff(25682,plain,
% 294.29/186.81 ((~node17(c_e_h_1, c_e, s11)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s11))),
% 294.29/186.81 inference(unit_resolution,[status(thm)],[25666, 919, 25681])).
% 294.29/186.81 tff(25683,plain,
% 294.29/186.81 ($false),
% 294.29/186.81 inference(unit_resolution,[status(thm)],[25682, 25617, 25680])).
% 294.29/186.81 tff(25684,plain,((~m_c_h_element_v_out(c_e_h_1, c_e, s12)) | m_c_h_element_v_in2(c_e_h_1, c_e, s11) | m_c_h_element_v_out(c_e_h_1, c_e, s11)), inference(lemma,lemma(discharge,[]))).
% 294.29/186.81 tff(25685,plain,
% 294.29/186.81 (~m_c_h_element_v_out(c_e_h_1, c_e, s12)),
% 294.29/186.81 inference(unit_resolution,[status(thm)],[25684, 25594, 24401])).
% 294.29/186.81 tff(25686,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_e, s12)), introduced(assumption)).
% 294.29/186.81 tff(25687,assumption,(~m_c_h_element_v_out(c_e_h_1, c_e, s12)), introduced(assumption)).
% 294.29/186.81 tff(25688,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s13)), introduced(assumption)).
% 294.29/186.81 tff(25689,assumption,(node18(c_e_h_1, c_e, s12, s13)), introduced(assumption)).
% 294.29/186.81 tff(25690,plain,
% 294.29/186.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s13)) | m_c_h_element_v_out(c_e_h_1, c_e, s12) | (~node18(c_e_h_1, c_e, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s13)) | m_c_h_element_v_out(c_e_h_1, c_e, s12) | (~node18(c_e_h_1, c_e, s12, s13)))),
% 294.29/186.81 inference(rewrite,[status(thm)],[])).
% 294.29/186.81 tff(25691,plain,
% 294.29/186.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s13)) | m_c_h_element_v_out(c_e_h_1, c_e, s12) | (~node18(c_e_h_1, c_e, s12, s13)))),
% 294.29/186.81 inference(quant_inst,[status(thm)],[])).
% 294.29/186.81 tff(25692,plain,
% 294.29/186.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s13)) | m_c_h_element_v_out(c_e_h_1, c_e, s12) | (~node18(c_e_h_1, c_e, s12, s13))),
% 294.29/186.82 inference(modus_ponens,[status(thm)],[25691, 25690])).
% 294.29/186.82 tff(25693,plain,
% 294.29/186.82 ($false),
% 294.29/186.82 inference(unit_resolution,[status(thm)],[25692, 753, 25688, 25687, 25689])).
% 294.29/186.82 tff(25694,plain,((~node18(c_e_h_1, c_e, s12, s13)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s13)) | m_c_h_element_v_out(c_e_h_1, c_e, s12)), inference(lemma,lemma(discharge,[]))).
% 294.29/186.82 tff(25695,plain,
% 294.29/186.82 (~node18(c_e_h_1, c_e, s12, s13)),
% 294.29/186.82 inference(unit_resolution,[status(thm)],[25694, 25688, 25687])).
% 294.29/186.82 tff(25696,assumption,(node15(c_e_h_1, c_e, s12, s13)), introduced(assumption)).
% 294.29/186.82 tff(25697,plain,
% 294.29/186.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s13)) | (~node15(c_e_h_1, c_e, s12, s13)) | m_c_h_element_v_out(c_e_h_1, c_e, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s13)) | (~node15(c_e_h_1, c_e, s12, s13)) | m_c_h_element_v_out(c_e_h_1, c_e, s12))),
% 294.29/186.82 inference(rewrite,[status(thm)],[])).
% 294.29/186.82 tff(25698,plain,
% 294.29/186.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s13)) | (~node15(c_e_h_1, c_e, s12, s13)) | m_c_h_element_v_out(c_e_h_1, c_e, s12))),
% 294.29/186.82 inference(quant_inst,[status(thm)],[])).
% 294.29/186.82 tff(25699,plain,
% 294.29/186.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s13)) | (~node15(c_e_h_1, c_e, s12, s13)) | m_c_h_element_v_out(c_e_h_1, c_e, s12)),
% 294.29/186.82 inference(modus_ponens,[status(thm)],[25698, 25697])).
% 294.29/186.82 tff(25700,plain,
% 294.29/186.82 ($false),
% 294.29/186.82 inference(unit_resolution,[status(thm)],[25699, 147, 25688, 25687, 25696])).
% 294.29/186.82 tff(25701,plain,((~node15(c_e_h_1, c_e, s12, s13)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s13)) | m_c_h_element_v_out(c_e_h_1, c_e, s12)), inference(lemma,lemma(discharge,[]))).
% 294.29/186.82 tff(25702,plain,
% 294.29/186.82 (~node15(c_e_h_1, c_e, s12, s13)),
% 294.29/186.82 inference(unit_resolution,[status(thm)],[25701, 25688, 25687])).
% 294.29/186.82 tff(25703,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_e, s12)), introduced(assumption)).
% 294.29/186.82 tff(25704,assumption,(node17(c_e_h_1, c_e, s12)), introduced(assumption)).
% 294.29/186.82 tff(25705,plain,
% 294.29/186.82 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s12) | (~node17(c_e_h_1, c_e, s12)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s12) | (~node17(c_e_h_1, c_e, s12)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s12)))),
% 294.29/186.82 inference(rewrite,[status(thm)],[])).
% 294.29/186.82 tff(25706,plain,
% 294.29/186.82 ((m_c_h_element_v_in1(c_e_h_1, c_e, s12) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s12)) | (~node17(c_e_h_1, c_e, s12))) <=> (m_c_h_element_v_in1(c_e_h_1, c_e, s12) | (~node17(c_e_h_1, c_e, s12)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s12)))),
% 294.29/186.82 inference(rewrite,[status(thm)],[])).
% 294.29/186.82 tff(25707,plain,
% 294.29/186.82 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s12) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s12)) | (~node17(c_e_h_1, c_e, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s12) | (~node17(c_e_h_1, c_e, s12)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s12))))),
% 294.29/186.82 inference(monotonicity,[status(thm)],[25706])).
% 294.29/186.82 tff(25708,plain,
% 294.29/186.82 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s12) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s12)) | (~node17(c_e_h_1, c_e, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s12) | (~node17(c_e_h_1, c_e, s12)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s12)))),
% 294.29/186.82 inference(transitivity,[status(thm)],[25707, 25705])).
% 294.29/186.82 tff(25709,plain,
% 294.29/186.82 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s12) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s12)) | (~node17(c_e_h_1, c_e, s12)))),
% 294.29/186.82 inference(quant_inst,[status(thm)],[])).
% 294.29/186.82 tff(25710,plain,
% 294.29/186.82 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s12) | (~node17(c_e_h_1, c_e, s12)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s12))),
% 294.29/186.82 inference(modus_ponens,[status(thm)],[25709, 25708])).
% 294.29/186.82 tff(25711,plain,
% 294.29/186.82 (m_c_h_element_v_in1(c_e_h_1, c_e, s12) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s12))),
% 294.29/186.82 inference(unit_resolution,[status(thm)],[25710, 859, 25704])).
% 294.29/186.82 tff(25712,plain,
% 294.29/186.82 (~m_c_h_element_v_in2(c_e_h_1, c_e, s12)),
% 294.29/186.82 inference(unit_resolution,[status(thm)],[25711, 25703])).
% 294.29/186.82 tff(25713,assumption,(~node15(c_e_h_1, c_e, s12, s13)), introduced(assumption)).
% 294.29/186.82 tff(25714,assumption,(node14(c_e_h_1, c_e, s12, s13)), introduced(assumption)).
% 294.29/186.82 tff(25715,plain,
% 294.29/186.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s13)) | m_c_h_element_v_in1(c_e_h_1, c_e, s12) | (~node14(c_e_h_1, c_e, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s13)) | m_c_h_element_v_in1(c_e_h_1, c_e, s12) | (~node14(c_e_h_1, c_e, s12, s13)))),
% 294.29/186.82 inference(rewrite,[status(thm)],[])).
% 294.29/186.82 tff(25716,plain,
% 294.29/186.82 (((~node14(c_e_h_1, c_e, s12, s13)) | m_c_h_element_v_in1(c_e_h_1, c_e, s12) | (~m_c_h_element_v_out(c_e_h_1, c_e, s13))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_e, s13)) | m_c_h_element_v_in1(c_e_h_1, c_e, s12) | (~node14(c_e_h_1, c_e, s12, s13)))),
% 294.29/186.82 inference(rewrite,[status(thm)],[])).
% 294.29/186.82 tff(25717,plain,
% 294.29/186.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s12, s13)) | m_c_h_element_v_in1(c_e_h_1, c_e, s12) | (~m_c_h_element_v_out(c_e_h_1, c_e, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s13)) | m_c_h_element_v_in1(c_e_h_1, c_e, s12) | (~node14(c_e_h_1, c_e, s12, s13))))),
% 294.29/186.82 inference(monotonicity,[status(thm)],[25716])).
% 294.29/186.82 tff(25718,plain,
% 294.29/186.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s12, s13)) | m_c_h_element_v_in1(c_e_h_1, c_e, s12) | (~m_c_h_element_v_out(c_e_h_1, c_e, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s13)) | m_c_h_element_v_in1(c_e_h_1, c_e, s12) | (~node14(c_e_h_1, c_e, s12, s13)))),
% 294.29/186.82 inference(transitivity,[status(thm)],[25717, 25715])).
% 294.29/186.82 tff(25719,plain,
% 294.29/186.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s12, s13)) | m_c_h_element_v_in1(c_e_h_1, c_e, s12) | (~m_c_h_element_v_out(c_e_h_1, c_e, s13)))),
% 294.29/186.82 inference(quant_inst,[status(thm)],[])).
% 294.29/186.82 tff(25720,plain,
% 294.29/186.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s13)) | m_c_h_element_v_in1(c_e_h_1, c_e, s12) | (~node14(c_e_h_1, c_e, s12, s13))),
% 294.29/186.82 inference(modus_ponens,[status(thm)],[25719, 25718])).
% 294.29/186.82 tff(25721,plain,
% 294.29/186.82 ($false),
% 294.29/186.82 inference(unit_resolution,[status(thm)],[25720, 223, 25688, 25714, 25703])).
% 294.29/186.82 tff(25722,plain,((~node14(c_e_h_1, c_e, s12, s13)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s13)) | m_c_h_element_v_in1(c_e_h_1, c_e, s12)), inference(lemma,lemma(discharge,[]))).
% 294.29/186.82 tff(25723,plain,
% 294.29/186.82 (~node14(c_e_h_1, c_e, s12, s13)),
% 294.29/186.82 inference(unit_resolution,[status(thm)],[25722, 25703, 25688])).
% 294.29/186.82 tff(25724,plain,
% 294.29/186.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s12, s13)) | node19(c_e_h_1, c_e, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s12, s13)) | node19(c_e_h_1, c_e, s12, s13))),
% 294.29/186.82 inference(rewrite,[status(thm)],[])).
% 294.29/186.82 tff(25725,plain,
% 294.29/186.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s12, s13)) | node19(c_e_h_1, c_e, s12, s13))),
% 294.29/186.82 inference(quant_inst,[status(thm)],[])).
% 294.29/186.82 tff(25726,plain,
% 294.29/186.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s12, s13)) | node19(c_e_h_1, c_e, s12, s13)),
% 294.29/186.82 inference(modus_ponens,[status(thm)],[25725, 25724])).
% 294.29/186.82 tff(25727,plain,
% 294.29/186.82 (node19(c_e_h_1, c_e, s12, s13)),
% 294.29/186.82 inference(unit_resolution,[status(thm)],[25726, 190, 11856])).
% 294.29/186.82 tff(25728,plain,
% 294.29/186.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_1, c_e, s12, s13) | node15(c_e_h_1, c_e, s12, s13) | (~node19(c_e_h_1, c_e, s12, s13)) | node16(c_e_h_1, c_e, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_e, s12, s13) | node15(c_e_h_1, c_e, s12, s13) | (~node19(c_e_h_1, c_e, s12, s13)) | node16(c_e_h_1, c_e, s12))),
% 294.29/186.82 inference(rewrite,[status(thm)],[])).
% 294.29/186.82 tff(25729,plain,
% 294.29/186.82 ((node16(c_e_h_1, c_e, s12) | node14(c_e_h_1, c_e, s12, s13) | node15(c_e_h_1, c_e, s12, s13) | (~node19(c_e_h_1, c_e, s12, s13))) <=> (node14(c_e_h_1, c_e, s12, s13) | node15(c_e_h_1, c_e, s12, s13) | (~node19(c_e_h_1, c_e, s12, s13)) | node16(c_e_h_1, c_e, s12))),
% 294.29/186.82 inference(rewrite,[status(thm)],[])).
% 294.29/186.82 tff(25730,plain,
% 294.29/186.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s12) | node14(c_e_h_1, c_e, s12, s13) | node15(c_e_h_1, c_e, s12, s13) | (~node19(c_e_h_1, c_e, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_1, c_e, s12, s13) | node15(c_e_h_1, c_e, s12, s13) | (~node19(c_e_h_1, c_e, s12, s13)) | node16(c_e_h_1, c_e, s12)))),
% 294.29/186.82 inference(monotonicity,[status(thm)],[25729])).
% 294.29/186.82 tff(25731,plain,
% 294.29/186.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s12) | node14(c_e_h_1, c_e, s12, s13) | node15(c_e_h_1, c_e, s12, s13) | (~node19(c_e_h_1, c_e, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_e, s12, s13) | node15(c_e_h_1, c_e, s12, s13) | (~node19(c_e_h_1, c_e, s12, s13)) | node16(c_e_h_1, c_e, s12))),
% 294.29/186.82 inference(transitivity,[status(thm)],[25730, 25728])).
% 294.29/186.82 tff(25732,plain,
% 294.29/186.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s12) | node14(c_e_h_1, c_e, s12, s13) | node15(c_e_h_1, c_e, s12, s13) | (~node19(c_e_h_1, c_e, s12, s13)))),
% 294.29/186.82 inference(quant_inst,[status(thm)],[])).
% 294.29/186.82 tff(25733,plain,
% 294.29/186.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_e, s12, s13) | node15(c_e_h_1, c_e, s12, s13) | (~node19(c_e_h_1, c_e, s12, s13)) | node16(c_e_h_1, c_e, s12)),
% 294.29/186.83 inference(modus_ponens,[status(thm)],[25732, 25731])).
% 294.29/186.83 tff(25734,plain,
% 294.29/186.83 (node14(c_e_h_1, c_e, s12, s13) | node15(c_e_h_1, c_e, s12, s13) | node16(c_e_h_1, c_e, s12)),
% 294.29/186.83 inference(unit_resolution,[status(thm)],[25733, 204, 25727])).
% 294.29/186.83 tff(25735,plain,
% 294.29/186.83 (node16(c_e_h_1, c_e, s12)),
% 294.29/186.83 inference(unit_resolution,[status(thm)],[25734, 25723, 25713])).
% 294.29/186.83 tff(25736,plain,
% 294.29/186.83 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s12)) | m_c_h_element_v_in1(c_e_h_1, c_e, s12) | m_c_h_element_v_in2(c_e_h_1, c_e, s12))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s12)) | m_c_h_element_v_in1(c_e_h_1, c_e, s12) | m_c_h_element_v_in2(c_e_h_1, c_e, s12))),
% 294.29/186.83 inference(rewrite,[status(thm)],[])).
% 294.29/186.83 tff(25737,plain,
% 294.29/186.83 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s12)) | m_c_h_element_v_in1(c_e_h_1, c_e, s12) | m_c_h_element_v_in2(c_e_h_1, c_e, s12))),
% 294.29/186.83 inference(quant_inst,[status(thm)],[])).
% 294.29/186.83 tff(25738,plain,
% 294.29/186.83 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s12)) | m_c_h_element_v_in1(c_e_h_1, c_e, s12) | m_c_h_element_v_in2(c_e_h_1, c_e, s12)),
% 294.29/186.83 inference(modus_ponens,[status(thm)],[25737, 25736])).
% 294.29/186.83 tff(25739,plain,
% 294.29/186.83 ($false),
% 294.29/186.83 inference(unit_resolution,[status(thm)],[25738, 178, 25735, 25703, 25712])).
% 294.29/186.83 tff(25740,plain,(m_c_h_element_v_in1(c_e_h_1, c_e, s12) | node15(c_e_h_1, c_e, s12, s13) | (~node17(c_e_h_1, c_e, s12)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s13))), inference(lemma,lemma(discharge,[]))).
% 294.29/186.83 tff(25741,plain,
% 294.29/186.83 (~node17(c_e_h_1, c_e, s12)),
% 294.29/186.83 inference(unit_resolution,[status(thm)],[25740, 25688, 25703, 25702])).
% 294.29/186.83 tff(25742,plain,
% 294.29/186.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_1, c_e, s12, s13) | (~node19(c_e_h_1, c_e, s12, s13)) | node17(c_e_h_1, c_e, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_e, s12, s13) | (~node19(c_e_h_1, c_e, s12, s13)) | node17(c_e_h_1, c_e, s12))),
% 294.29/186.83 inference(rewrite,[status(thm)],[])).
% 294.29/186.83 tff(25743,plain,
% 294.29/186.83 ((node17(c_e_h_1, c_e, s12) | node18(c_e_h_1, c_e, s12, s13) | (~node19(c_e_h_1, c_e, s12, s13))) <=> (node18(c_e_h_1, c_e, s12, s13) | (~node19(c_e_h_1, c_e, s12, s13)) | node17(c_e_h_1, c_e, s12))),
% 294.29/186.83 inference(rewrite,[status(thm)],[])).
% 294.29/186.83 tff(25744,plain,
% 294.29/186.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s12) | node18(c_e_h_1, c_e, s12, s13) | (~node19(c_e_h_1, c_e, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_1, c_e, s12, s13) | (~node19(c_e_h_1, c_e, s12, s13)) | node17(c_e_h_1, c_e, s12)))),
% 294.29/186.83 inference(monotonicity,[status(thm)],[25743])).
% 294.29/186.83 tff(25745,plain,
% 294.29/186.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s12) | node18(c_e_h_1, c_e, s12, s13) | (~node19(c_e_h_1, c_e, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_e, s12, s13) | (~node19(c_e_h_1, c_e, s12, s13)) | node17(c_e_h_1, c_e, s12))),
% 294.29/186.83 inference(transitivity,[status(thm)],[25744, 25742])).
% 294.29/186.83 tff(25746,plain,
% 294.29/186.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s12) | node18(c_e_h_1, c_e, s12, s13) | (~node19(c_e_h_1, c_e, s12, s13)))),
% 294.29/186.83 inference(quant_inst,[status(thm)],[])).
% 294.29/186.83 tff(25747,plain,
% 294.29/186.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_e, s12, s13) | (~node19(c_e_h_1, c_e, s12, s13)) | node17(c_e_h_1, c_e, s12)),
% 294.29/186.83 inference(modus_ponens,[status(thm)],[25746, 25745])).
% 294.29/186.83 tff(25748,plain,
% 294.29/186.83 (node18(c_e_h_1, c_e, s12, s13) | node17(c_e_h_1, c_e, s12)),
% 294.29/186.83 inference(unit_resolution,[status(thm)],[25747, 776, 25727])).
% 294.29/186.83 tff(25749,plain,
% 294.29/186.83 ($false),
% 294.29/186.83 inference(unit_resolution,[status(thm)],[25748, 25741, 25695])).
% 294.29/186.83 tff(25750,plain,((~m_c_h_element_v_out(c_e_h_1, c_e, s13)) | m_c_h_element_v_in1(c_e_h_1, c_e, s12) | m_c_h_element_v_out(c_e_h_1, c_e, s12)), inference(lemma,lemma(discharge,[]))).
% 294.29/186.83 tff(25751,plain,
% 294.29/186.83 (m_c_h_element_v_in1(c_e_h_1, c_e, s12)),
% 294.29/186.83 inference(unit_resolution,[status(thm)],[25750, 25688, 25687])).
% 294.29/186.83 tff(25752,plain,
% 294.29/186.83 (node17(c_e_h_1, c_e, s12)),
% 294.29/186.83 inference(unit_resolution,[status(thm)],[25748, 25695])).
% 294.29/186.83 tff(25753,plain,
% 294.29/186.83 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_e, s12) | (~node17(c_e_h_1, c_e, s12)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s12) | (~node17(c_e_h_1, c_e, s12)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s12)))),
% 294.29/186.83 inference(rewrite,[status(thm)],[])).
% 294.29/186.83 tff(25754,plain,
% 294.29/186.83 (((~m_c_h_element_v_in1(c_e_h_1, c_e, s12)) | m_c_h_element_v_in2(c_e_h_1, c_e, s12) | (~node17(c_e_h_1, c_e, s12))) <=> (m_c_h_element_v_in2(c_e_h_1, c_e, s12) | (~node17(c_e_h_1, c_e, s12)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s12)))),
% 294.29/186.83 inference(rewrite,[status(thm)],[])).
% 294.29/186.83 tff(25755,plain,
% 294.29/186.83 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s12)) | m_c_h_element_v_in2(c_e_h_1, c_e, s12) | (~node17(c_e_h_1, c_e, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_e, s12) | (~node17(c_e_h_1, c_e, s12)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s12))))),
% 294.29/186.83 inference(monotonicity,[status(thm)],[25754])).
% 294.29/186.83 tff(25756,plain,
% 294.29/186.83 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s12)) | m_c_h_element_v_in2(c_e_h_1, c_e, s12) | (~node17(c_e_h_1, c_e, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s12) | (~node17(c_e_h_1, c_e, s12)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s12)))),
% 294.29/186.83 inference(transitivity,[status(thm)],[25755, 25753])).
% 294.29/186.83 tff(25757,plain,
% 294.29/186.83 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s12)) | m_c_h_element_v_in2(c_e_h_1, c_e, s12) | (~node17(c_e_h_1, c_e, s12)))),
% 294.29/186.83 inference(quant_inst,[status(thm)],[])).
% 294.29/186.83 tff(25758,plain,
% 294.29/186.83 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s12) | (~node17(c_e_h_1, c_e, s12)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s12))),
% 294.29/186.83 inference(modus_ponens,[status(thm)],[25757, 25756])).
% 294.29/186.83 tff(25759,plain,
% 294.29/186.83 ($false),
% 294.29/186.83 inference(unit_resolution,[status(thm)],[25758, 919, 25752, 25751, 25686])).
% 294.29/186.83 tff(25760,plain,((~m_c_h_element_v_out(c_e_h_1, c_e, s13)) | m_c_h_element_v_in2(c_e_h_1, c_e, s12) | m_c_h_element_v_out(c_e_h_1, c_e, s12)), inference(lemma,lemma(discharge,[]))).
% 294.29/186.83 tff(25761,plain,
% 294.29/186.83 ((~m_c_h_element_v_out(c_e_h_1, c_e, s13)) | m_c_h_element_v_in2(c_e_h_1, c_e, s12)),
% 294.29/186.83 inference(unit_resolution,[status(thm)],[25760, 25685])).
% 294.29/186.83 tff(25762,plain,
% 294.29/186.83 (~m_c_h_element_v_out(c_e_h_1, c_e, s13)),
% 294.29/186.83 inference(unit_resolution,[status(thm)],[25761, 25587])).
% 294.29/186.83 tff(25763,assumption,(m_c_h_element_v_in2(c_e_h_1, c_e, s13)), introduced(assumption)).
% 294.29/186.83 tff(25764,plain,
% 294.29/186.83 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s13)) | m_and_h_gate_v_out(c_e_h_1, c_i, s13))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s13)) | m_and_h_gate_v_out(c_e_h_1, c_i, s13))),
% 294.29/186.83 inference(rewrite,[status(thm)],[])).
% 294.29/186.83 tff(25765,plain,
% 294.29/186.83 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s13)) | m_and_h_gate_v_out(c_e_h_1, c_i, s13))),
% 294.29/186.83 inference(quant_inst,[status(thm)],[])).
% 294.29/186.83 tff(25766,plain,
% 294.29/186.83 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s13)) | m_and_h_gate_v_out(c_e_h_1, c_i, s13)),
% 294.29/186.83 inference(modus_ponens,[status(thm)],[25765, 25764])).
% 294.29/186.83 tff(25767,plain,
% 294.29/186.83 ($false),
% 294.29/186.83 inference(unit_resolution,[status(thm)],[25766, 164, 25763, 24190])).
% 294.29/186.83 tff(25768,plain,((~m_c_h_element_v_in2(c_e_h_1, c_e, s13)) | m_and_h_gate_v_out(c_e_h_1, c_i, s13)), inference(lemma,lemma(discharge,[]))).
% 294.29/186.83 tff(25769,plain,
% 294.29/186.83 (~m_c_h_element_v_in2(c_e_h_1, c_e, s13)),
% 294.29/186.83 inference(unit_resolution,[status(thm)],[25768, 24181])).
% 294.29/186.83 tff(25770,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_e, s13)), introduced(assumption)).
% 294.29/186.83 tff(25771,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s14)), introduced(assumption)).
% 294.29/186.83 tff(25772,assumption,(~m_c_h_element_v_out(c_e_h_1, c_e, s13)), introduced(assumption)).
% 294.29/186.83 tff(25773,assumption,(node18(c_e_h_1, c_e, s13, s14)), introduced(assumption)).
% 294.29/186.83 tff(25774,plain,
% 294.29/186.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s14)) | m_c_h_element_v_out(c_e_h_1, c_e, s13) | (~node18(c_e_h_1, c_e, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s14)) | m_c_h_element_v_out(c_e_h_1, c_e, s13) | (~node18(c_e_h_1, c_e, s13, s14)))),
% 294.29/186.83 inference(rewrite,[status(thm)],[])).
% 294.29/186.83 tff(25775,plain,
% 294.29/186.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s14)) | m_c_h_element_v_out(c_e_h_1, c_e, s13) | (~node18(c_e_h_1, c_e, s13, s14)))),
% 294.29/186.83 inference(quant_inst,[status(thm)],[])).
% 294.29/186.83 tff(25776,plain,
% 294.29/186.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s14)) | m_c_h_element_v_out(c_e_h_1, c_e, s13) | (~node18(c_e_h_1, c_e, s13, s14))),
% 294.29/186.83 inference(modus_ponens,[status(thm)],[25775, 25774])).
% 294.29/186.83 tff(25777,plain,
% 294.29/186.83 ($false),
% 294.29/186.83 inference(unit_resolution,[status(thm)],[25776, 753, 25771, 25772, 25773])).
% 294.29/186.83 tff(25778,plain,((~node18(c_e_h_1, c_e, s13, s14)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s14)) | m_c_h_element_v_out(c_e_h_1, c_e, s13)), inference(lemma,lemma(discharge,[]))).
% 294.29/186.83 tff(25779,plain,
% 294.29/186.83 (~node18(c_e_h_1, c_e, s13, s14)),
% 294.29/186.83 inference(unit_resolution,[status(thm)],[25778, 25771, 25772])).
% 294.29/186.83 tff(25780,plain,
% 294.29/186.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s13, s14)) | node19(c_e_h_1, c_e, s13, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s13, s14)) | node19(c_e_h_1, c_e, s13, s14))),
% 294.29/186.83 inference(rewrite,[status(thm)],[])).
% 294.29/186.83 tff(25781,plain,
% 294.29/186.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s13, s14)) | node19(c_e_h_1, c_e, s13, s14))),
% 294.29/186.83 inference(quant_inst,[status(thm)],[])).
% 294.29/186.83 tff(25782,plain,
% 294.29/186.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s13, s14)) | node19(c_e_h_1, c_e, s13, s14)),
% 294.29/186.84 inference(modus_ponens,[status(thm)],[25781, 25780])).
% 294.29/186.84 tff(25783,plain,
% 294.29/186.84 (node19(c_e_h_1, c_e, s13, s14)),
% 294.29/186.84 inference(unit_resolution,[status(thm)],[25782, 190, 12831])).
% 294.29/186.84 tff(25784,plain,
% 294.29/186.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_e, s13, s14)) | node18(c_e_h_1, c_e, s13, s14) | node17(c_e_h_1, c_e, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s13, s14)) | node18(c_e_h_1, c_e, s13, s14) | node17(c_e_h_1, c_e, s13))),
% 294.29/186.84 inference(rewrite,[status(thm)],[])).
% 294.29/186.84 tff(25785,plain,
% 294.29/186.84 ((node17(c_e_h_1, c_e, s13) | node18(c_e_h_1, c_e, s13, s14) | (~node19(c_e_h_1, c_e, s13, s14))) <=> ((~node19(c_e_h_1, c_e, s13, s14)) | node18(c_e_h_1, c_e, s13, s14) | node17(c_e_h_1, c_e, s13))),
% 294.29/186.84 inference(rewrite,[status(thm)],[])).
% 294.29/186.84 tff(25786,plain,
% 294.29/186.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s13) | node18(c_e_h_1, c_e, s13, s14) | (~node19(c_e_h_1, c_e, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_e, s13, s14)) | node18(c_e_h_1, c_e, s13, s14) | node17(c_e_h_1, c_e, s13)))),
% 294.29/186.84 inference(monotonicity,[status(thm)],[25785])).
% 294.29/186.84 tff(25787,plain,
% 294.29/186.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s13) | node18(c_e_h_1, c_e, s13, s14) | (~node19(c_e_h_1, c_e, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s13, s14)) | node18(c_e_h_1, c_e, s13, s14) | node17(c_e_h_1, c_e, s13))),
% 294.29/186.84 inference(transitivity,[status(thm)],[25786, 25784])).
% 294.29/186.84 tff(25788,plain,
% 294.29/186.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s13) | node18(c_e_h_1, c_e, s13, s14) | (~node19(c_e_h_1, c_e, s13, s14)))),
% 294.29/186.84 inference(quant_inst,[status(thm)],[])).
% 294.29/186.84 tff(25789,plain,
% 294.29/186.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s13, s14)) | node18(c_e_h_1, c_e, s13, s14) | node17(c_e_h_1, c_e, s13)),
% 294.29/186.84 inference(modus_ponens,[status(thm)],[25788, 25787])).
% 294.29/186.84 tff(25790,plain,
% 294.29/186.84 (node18(c_e_h_1, c_e, s13, s14) | node17(c_e_h_1, c_e, s13)),
% 294.29/186.84 inference(unit_resolution,[status(thm)],[25789, 776, 25783])).
% 294.29/186.84 tff(25791,plain,
% 294.29/186.84 (node17(c_e_h_1, c_e, s13)),
% 294.29/186.84 inference(unit_resolution,[status(thm)],[25790, 25779])).
% 294.29/186.84 tff(25792,assumption,(node17(c_e_h_1, c_e, s13)), introduced(assumption)).
% 294.29/186.84 tff(25793,plain,
% 294.29/186.84 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s13)) | (~node17(c_e_h_1, c_e, s13)) | m_c_h_element_v_in2(c_e_h_1, c_e, s13))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s13)) | (~node17(c_e_h_1, c_e, s13)) | m_c_h_element_v_in2(c_e_h_1, c_e, s13))),
% 294.29/186.84 inference(rewrite,[status(thm)],[])).
% 294.29/186.84 tff(25794,plain,
% 294.29/186.84 (((~m_c_h_element_v_in1(c_e_h_1, c_e, s13)) | m_c_h_element_v_in2(c_e_h_1, c_e, s13) | (~node17(c_e_h_1, c_e, s13))) <=> ((~m_c_h_element_v_in1(c_e_h_1, c_e, s13)) | (~node17(c_e_h_1, c_e, s13)) | m_c_h_element_v_in2(c_e_h_1, c_e, s13))),
% 294.29/186.84 inference(rewrite,[status(thm)],[])).
% 294.29/186.84 tff(25795,plain,
% 294.29/186.84 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s13)) | m_c_h_element_v_in2(c_e_h_1, c_e, s13) | (~node17(c_e_h_1, c_e, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s13)) | (~node17(c_e_h_1, c_e, s13)) | m_c_h_element_v_in2(c_e_h_1, c_e, s13)))),
% 294.29/186.84 inference(monotonicity,[status(thm)],[25794])).
% 294.29/186.84 tff(25796,plain,
% 294.29/186.84 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s13)) | m_c_h_element_v_in2(c_e_h_1, c_e, s13) | (~node17(c_e_h_1, c_e, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s13)) | (~node17(c_e_h_1, c_e, s13)) | m_c_h_element_v_in2(c_e_h_1, c_e, s13))),
% 294.29/186.84 inference(transitivity,[status(thm)],[25795, 25793])).
% 294.29/186.84 tff(25797,plain,
% 294.29/186.84 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s13)) | m_c_h_element_v_in2(c_e_h_1, c_e, s13) | (~node17(c_e_h_1, c_e, s13)))),
% 294.29/186.84 inference(quant_inst,[status(thm)],[])).
% 294.29/186.84 tff(25798,plain,
% 294.29/186.84 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s13)) | (~node17(c_e_h_1, c_e, s13)) | m_c_h_element_v_in2(c_e_h_1, c_e, s13)),
% 294.29/186.84 inference(modus_ponens,[status(thm)],[25797, 25796])).
% 294.29/186.84 tff(25799,plain,
% 294.29/186.84 ((~m_c_h_element_v_in1(c_e_h_1, c_e, s13)) | (~node17(c_e_h_1, c_e, s13))),
% 294.29/186.84 inference(unit_resolution,[status(thm)],[25798, 919, 25770])).
% 294.29/186.84 tff(25800,plain,
% 294.29/186.84 (~m_c_h_element_v_in1(c_e_h_1, c_e, s13)),
% 294.29/186.84 inference(unit_resolution,[status(thm)],[25799, 25792])).
% 294.29/186.84 tff(25801,assumption,(~node15(c_e_h_1, c_e, s13, s14)), introduced(assumption)).
% 294.29/186.84 tff(25802,assumption,(node16(c_e_h_1, c_e, s13)), introduced(assumption)).
% 294.29/186.84 tff(25803,plain,
% 294.29/186.84 ((~m_c_h_element_v_in1(c_e_h_1, c_e, s13)) | m_c_h_element_v_in2(c_e_h_1, c_e, s13)),
% 294.29/186.84 inference(unit_resolution,[status(thm)],[25798, 919, 25792])).
% 294.29/186.84 tff(25804,plain,
% 294.29/186.84 (~m_c_h_element_v_in1(c_e_h_1, c_e, s13)),
% 294.29/186.84 inference(unit_resolution,[status(thm)],[25803, 25770])).
% 294.29/186.84 tff(25805,plain,
% 294.29/186.84 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s13)) | m_c_h_element_v_in1(c_e_h_1, c_e, s13) | m_c_h_element_v_in2(c_e_h_1, c_e, s13))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s13)) | m_c_h_element_v_in1(c_e_h_1, c_e, s13) | m_c_h_element_v_in2(c_e_h_1, c_e, s13))),
% 294.29/186.84 inference(rewrite,[status(thm)],[])).
% 294.29/186.84 tff(25806,plain,
% 294.29/186.84 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s13)) | m_c_h_element_v_in1(c_e_h_1, c_e, s13) | m_c_h_element_v_in2(c_e_h_1, c_e, s13))),
% 294.29/186.84 inference(quant_inst,[status(thm)],[])).
% 294.29/186.84 tff(25807,plain,
% 294.29/186.84 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s13)) | m_c_h_element_v_in1(c_e_h_1, c_e, s13) | m_c_h_element_v_in2(c_e_h_1, c_e, s13)),
% 294.29/186.84 inference(modus_ponens,[status(thm)],[25806, 25805])).
% 294.29/186.84 tff(25808,plain,
% 294.29/186.84 (m_c_h_element_v_in1(c_e_h_1, c_e, s13) | m_c_h_element_v_in2(c_e_h_1, c_e, s13)),
% 294.29/186.84 inference(unit_resolution,[status(thm)],[25807, 178, 25802])).
% 294.29/186.84 tff(25809,plain,
% 294.29/186.84 ($false),
% 294.29/186.84 inference(unit_resolution,[status(thm)],[25808, 25804, 25770])).
% 294.29/186.84 tff(25810,plain,(m_c_h_element_v_in2(c_e_h_1, c_e, s13) | (~node16(c_e_h_1, c_e, s13)) | (~node17(c_e_h_1, c_e, s13))), inference(lemma,lemma(discharge,[]))).
% 294.29/186.84 tff(25811,plain,
% 294.29/186.84 (m_c_h_element_v_in2(c_e_h_1, c_e, s13)),
% 294.29/186.84 inference(unit_resolution,[status(thm)],[25810, 25802, 25792])).
% 294.29/186.84 tff(25812,plain,
% 294.29/186.84 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s13) | (~node17(c_e_h_1, c_e, s13)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s13) | (~node17(c_e_h_1, c_e, s13)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s13)))),
% 294.29/186.85 inference(rewrite,[status(thm)],[])).
% 294.29/186.85 tff(25813,plain,
% 294.29/186.85 ((m_c_h_element_v_in1(c_e_h_1, c_e, s13) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s13)) | (~node17(c_e_h_1, c_e, s13))) <=> (m_c_h_element_v_in1(c_e_h_1, c_e, s13) | (~node17(c_e_h_1, c_e, s13)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s13)))),
% 294.29/186.85 inference(rewrite,[status(thm)],[])).
% 294.29/186.85 tff(25814,plain,
% 294.29/186.85 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s13) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s13)) | (~node17(c_e_h_1, c_e, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s13) | (~node17(c_e_h_1, c_e, s13)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s13))))),
% 294.29/186.85 inference(monotonicity,[status(thm)],[25813])).
% 294.29/186.85 tff(25815,plain,
% 294.29/186.85 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s13) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s13)) | (~node17(c_e_h_1, c_e, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s13) | (~node17(c_e_h_1, c_e, s13)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s13)))),
% 294.29/186.85 inference(transitivity,[status(thm)],[25814, 25812])).
% 294.29/186.85 tff(25816,plain,
% 294.29/186.85 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s13) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s13)) | (~node17(c_e_h_1, c_e, s13)))),
% 294.29/186.85 inference(quant_inst,[status(thm)],[])).
% 294.29/186.85 tff(25817,plain,
% 294.29/186.85 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s13) | (~node17(c_e_h_1, c_e, s13)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s13))),
% 294.29/186.85 inference(modus_ponens,[status(thm)],[25816, 25815])).
% 294.29/186.85 tff(25818,plain,
% 294.29/186.85 (m_c_h_element_v_in1(c_e_h_1, c_e, s13) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s13))),
% 294.29/186.85 inference(unit_resolution,[status(thm)],[25817, 859, 25792])).
% 294.29/186.85 tff(25819,plain,
% 294.29/186.85 (m_c_h_element_v_in1(c_e_h_1, c_e, s13)),
% 294.29/186.85 inference(unit_resolution,[status(thm)],[25818, 25811])).
% 294.29/186.85 tff(25820,plain,
% 294.29/186.85 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s13)) | (~node16(c_e_h_1, c_e, s13)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s13)) | (~node16(c_e_h_1, c_e, s13)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s13)))),
% 294.29/186.85 inference(rewrite,[status(thm)],[])).
% 294.29/186.85 tff(25821,plain,
% 294.29/186.85 (((~node16(c_e_h_1, c_e, s13)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s13)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s13))) <=> ((~m_c_h_element_v_in1(c_e_h_1, c_e, s13)) | (~node16(c_e_h_1, c_e, s13)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s13)))),
% 294.29/186.85 inference(rewrite,[status(thm)],[])).
% 294.29/186.85 tff(25822,plain,
% 294.29/186.85 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s13)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s13)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s13)) | (~node16(c_e_h_1, c_e, s13)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s13))))),
% 294.29/186.85 inference(monotonicity,[status(thm)],[25821])).
% 294.29/186.85 tff(25823,plain,
% 294.29/186.85 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s13)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s13)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s13)) | (~node16(c_e_h_1, c_e, s13)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s13)))),
% 294.29/186.85 inference(transitivity,[status(thm)],[25822, 25820])).
% 294.29/186.85 tff(25824,plain,
% 294.29/186.85 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s13)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s13)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s13)))),
% 294.29/186.85 inference(quant_inst,[status(thm)],[])).
% 294.29/186.85 tff(25825,plain,
% 294.29/186.85 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s13)) | (~node16(c_e_h_1, c_e, s13)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s13))),
% 294.29/186.85 inference(modus_ponens,[status(thm)],[25824, 25823])).
% 294.29/186.85 tff(25826,plain,
% 294.29/186.85 ((~m_c_h_element_v_in1(c_e_h_1, c_e, s13)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s13))),
% 294.29/186.85 inference(unit_resolution,[status(thm)],[25825, 2307, 25802])).
% 294.29/186.85 tff(25827,plain,
% 294.29/186.85 ($false),
% 294.29/186.85 inference(unit_resolution,[status(thm)],[25826, 25819, 25811])).
% 294.29/186.85 tff(25828,plain,((~node16(c_e_h_1, c_e, s13)) | (~node17(c_e_h_1, c_e, s13))), inference(lemma,lemma(discharge,[]))).
% 294.29/186.85 tff(25829,plain,
% 294.29/186.85 (~node16(c_e_h_1, c_e, s13)),
% 294.29/186.85 inference(unit_resolution,[status(thm)],[25828, 25792])).
% 294.29/186.85 tff(25830,plain,
% 294.29/186.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_e, s13, s14)) | node15(c_e_h_1, c_e, s13, s14) | node14(c_e_h_1, c_e, s13, s14) | node16(c_e_h_1, c_e, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s13, s14)) | node15(c_e_h_1, c_e, s13, s14) | node14(c_e_h_1, c_e, s13, s14) | node16(c_e_h_1, c_e, s13))),
% 294.29/186.85 inference(rewrite,[status(thm)],[])).
% 294.29/186.85 tff(25831,plain,
% 294.29/186.85 ((node16(c_e_h_1, c_e, s13) | node14(c_e_h_1, c_e, s13, s14) | node15(c_e_h_1, c_e, s13, s14) | (~node19(c_e_h_1, c_e, s13, s14))) <=> ((~node19(c_e_h_1, c_e, s13, s14)) | node15(c_e_h_1, c_e, s13, s14) | node14(c_e_h_1, c_e, s13, s14) | node16(c_e_h_1, c_e, s13))),
% 294.29/186.85 inference(rewrite,[status(thm)],[])).
% 294.29/186.85 tff(25832,plain,
% 294.29/186.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s13) | node14(c_e_h_1, c_e, s13, s14) | node15(c_e_h_1, c_e, s13, s14) | (~node19(c_e_h_1, c_e, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_e, s13, s14)) | node15(c_e_h_1, c_e, s13, s14) | node14(c_e_h_1, c_e, s13, s14) | node16(c_e_h_1, c_e, s13)))),
% 294.29/186.85 inference(monotonicity,[status(thm)],[25831])).
% 294.29/186.85 tff(25833,plain,
% 294.29/186.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s13) | node14(c_e_h_1, c_e, s13, s14) | node15(c_e_h_1, c_e, s13, s14) | (~node19(c_e_h_1, c_e, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s13, s14)) | node15(c_e_h_1, c_e, s13, s14) | node14(c_e_h_1, c_e, s13, s14) | node16(c_e_h_1, c_e, s13))),
% 294.29/186.85 inference(transitivity,[status(thm)],[25832, 25830])).
% 294.29/186.85 tff(25834,plain,
% 294.29/186.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s13) | node14(c_e_h_1, c_e, s13, s14) | node15(c_e_h_1, c_e, s13, s14) | (~node19(c_e_h_1, c_e, s13, s14)))),
% 294.29/186.85 inference(quant_inst,[status(thm)],[])).
% 294.29/186.85 tff(25835,plain,
% 294.29/186.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s13, s14)) | node15(c_e_h_1, c_e, s13, s14) | node14(c_e_h_1, c_e, s13, s14) | node16(c_e_h_1, c_e, s13)),
% 294.29/186.85 inference(modus_ponens,[status(thm)],[25834, 25833])).
% 294.29/186.85 tff(25836,plain,
% 294.29/186.85 (node15(c_e_h_1, c_e, s13, s14) | node14(c_e_h_1, c_e, s13, s14) | node16(c_e_h_1, c_e, s13)),
% 294.29/186.85 inference(unit_resolution,[status(thm)],[25835, 204, 25783])).
% 294.29/186.85 tff(25837,plain,
% 294.29/186.85 (node14(c_e_h_1, c_e, s13, s14)),
% 294.29/186.85 inference(unit_resolution,[status(thm)],[25836, 25829, 25801])).
% 294.29/186.85 tff(25838,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_e, s13)), introduced(assumption)).
% 294.29/186.85 tff(25839,assumption,(node14(c_e_h_1, c_e, s13, s14)), introduced(assumption)).
% 294.29/186.85 tff(25840,plain,
% 294.29/186.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s14)) | m_c_h_element_v_in1(c_e_h_1, c_e, s13) | (~node14(c_e_h_1, c_e, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s14)) | m_c_h_element_v_in1(c_e_h_1, c_e, s13) | (~node14(c_e_h_1, c_e, s13, s14)))),
% 294.29/186.85 inference(rewrite,[status(thm)],[])).
% 294.29/186.85 tff(25841,plain,
% 294.29/186.85 (((~node14(c_e_h_1, c_e, s13, s14)) | m_c_h_element_v_in1(c_e_h_1, c_e, s13) | (~m_c_h_element_v_out(c_e_h_1, c_e, s14))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_e, s14)) | m_c_h_element_v_in1(c_e_h_1, c_e, s13) | (~node14(c_e_h_1, c_e, s13, s14)))),
% 294.29/186.85 inference(rewrite,[status(thm)],[])).
% 294.29/186.85 tff(25842,plain,
% 294.29/186.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s13, s14)) | m_c_h_element_v_in1(c_e_h_1, c_e, s13) | (~m_c_h_element_v_out(c_e_h_1, c_e, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s14)) | m_c_h_element_v_in1(c_e_h_1, c_e, s13) | (~node14(c_e_h_1, c_e, s13, s14))))),
% 294.29/186.85 inference(monotonicity,[status(thm)],[25841])).
% 294.29/186.85 tff(25843,plain,
% 294.29/186.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s13, s14)) | m_c_h_element_v_in1(c_e_h_1, c_e, s13) | (~m_c_h_element_v_out(c_e_h_1, c_e, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s14)) | m_c_h_element_v_in1(c_e_h_1, c_e, s13) | (~node14(c_e_h_1, c_e, s13, s14)))),
% 294.29/186.85 inference(transitivity,[status(thm)],[25842, 25840])).
% 294.29/186.85 tff(25844,plain,
% 294.29/186.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s13, s14)) | m_c_h_element_v_in1(c_e_h_1, c_e, s13) | (~m_c_h_element_v_out(c_e_h_1, c_e, s14)))),
% 294.29/186.85 inference(quant_inst,[status(thm)],[])).
% 294.29/186.85 tff(25845,plain,
% 294.29/186.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s14)) | m_c_h_element_v_in1(c_e_h_1, c_e, s13) | (~node14(c_e_h_1, c_e, s13, s14))),
% 294.29/186.85 inference(modus_ponens,[status(thm)],[25844, 25843])).
% 294.29/186.85 tff(25846,plain,
% 294.29/186.85 ($false),
% 294.29/186.85 inference(unit_resolution,[status(thm)],[25845, 223, 25771, 25839, 25838])).
% 294.29/186.85 tff(25847,plain,((~node14(c_e_h_1, c_e, s13, s14)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s14)) | m_c_h_element_v_in1(c_e_h_1, c_e, s13)), inference(lemma,lemma(discharge,[]))).
% 294.29/186.85 tff(25848,plain,
% 294.29/186.85 ($false),
% 294.29/186.85 inference(unit_resolution,[status(thm)],[25847, 25837, 25800, 25771])).
% 294.29/186.86 tff(25849,plain,((~node17(c_e_h_1, c_e, s13)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s14)) | node15(c_e_h_1, c_e, s13, s14) | m_c_h_element_v_in2(c_e_h_1, c_e, s13)), inference(lemma,lemma(discharge,[]))).
% 294.29/186.86 tff(25850,plain,
% 294.29/186.86 (node15(c_e_h_1, c_e, s13, s14)),
% 294.29/186.86 inference(unit_resolution,[status(thm)],[25849, 25791, 25771, 25770])).
% 294.29/186.86 tff(25851,plain,
% 294.29/186.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s14)) | (~node15(c_e_h_1, c_e, s13, s14)) | m_c_h_element_v_out(c_e_h_1, c_e, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s14)) | (~node15(c_e_h_1, c_e, s13, s14)) | m_c_h_element_v_out(c_e_h_1, c_e, s13))),
% 294.29/186.86 inference(rewrite,[status(thm)],[])).
% 294.29/186.86 tff(25852,plain,
% 294.29/186.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s14)) | (~node15(c_e_h_1, c_e, s13, s14)) | m_c_h_element_v_out(c_e_h_1, c_e, s13))),
% 294.29/186.86 inference(quant_inst,[status(thm)],[])).
% 294.29/186.86 tff(25853,plain,
% 294.29/186.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s14)) | (~node15(c_e_h_1, c_e, s13, s14)) | m_c_h_element_v_out(c_e_h_1, c_e, s13)),
% 294.29/186.86 inference(modus_ponens,[status(thm)],[25852, 25851])).
% 294.29/186.86 tff(25854,plain,
% 294.29/186.86 ($false),
% 294.29/186.86 inference(unit_resolution,[status(thm)],[25853, 147, 25771, 25772, 25850])).
% 294.29/186.86 tff(25855,plain,((~m_c_h_element_v_out(c_e_h_1, c_e, s14)) | m_c_h_element_v_out(c_e_h_1, c_e, s13) | m_c_h_element_v_in2(c_e_h_1, c_e, s13)), inference(lemma,lemma(discharge,[]))).
% 294.29/186.86 tff(25856,plain,
% 294.29/186.86 (~m_c_h_element_v_out(c_e_h_1, c_e, s14)),
% 294.29/186.86 inference(unit_resolution,[status(thm)],[25855, 25769, 25762])).
% 294.29/186.86 tff(25857,assumption,(m_c_h_element_v_in2(c_e_h_1, c_e, s14)), introduced(assumption)).
% 294.29/186.86 tff(25858,plain,
% 294.29/186.86 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s14)) | m_and_h_gate_v_out(c_e_h_1, c_i, s14))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s14)) | m_and_h_gate_v_out(c_e_h_1, c_i, s14))),
% 294.29/186.86 inference(rewrite,[status(thm)],[])).
% 294.29/186.86 tff(25859,plain,
% 294.29/186.86 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s14)) | m_and_h_gate_v_out(c_e_h_1, c_i, s14))),
% 294.29/186.86 inference(quant_inst,[status(thm)],[])).
% 294.29/186.86 tff(25860,plain,
% 294.29/186.86 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s14)) | m_and_h_gate_v_out(c_e_h_1, c_i, s14)),
% 294.29/186.86 inference(modus_ponens,[status(thm)],[25859, 25858])).
% 294.29/186.86 tff(25861,plain,
% 294.29/186.86 ($false),
% 294.29/186.86 inference(unit_resolution,[status(thm)],[25860, 164, 25857, 24217])).
% 294.29/186.86 tff(25862,plain,((~m_c_h_element_v_in2(c_e_h_1, c_e, s14)) | m_and_h_gate_v_out(c_e_h_1, c_i, s14)), inference(lemma,lemma(discharge,[]))).
% 294.29/186.86 tff(25863,plain,
% 294.29/186.86 (~m_c_h_element_v_in2(c_e_h_1, c_e, s14)),
% 294.29/186.86 inference(unit_resolution,[status(thm)],[25862, 24216])).
% 294.29/186.86 tff(25864,assumption,(~m_c_h_element_v_out(c_e_h_1, c_e, s14)), introduced(assumption)).
% 294.29/186.86 tff(25865,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s15)), introduced(assumption)).
% 294.29/186.86 tff(25866,assumption,(node18(c_e_h_1, c_e, s14, s15)), introduced(assumption)).
% 294.29/186.86 tff(25867,plain,
% 294.29/186.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s14) | (~m_c_h_element_v_out(c_e_h_1, c_e, s15)) | (~node18(c_e_h_1, c_e, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s14) | (~m_c_h_element_v_out(c_e_h_1, c_e, s15)) | (~node18(c_e_h_1, c_e, s14, s15)))),
% 294.29/186.86 inference(rewrite,[status(thm)],[])).
% 294.29/186.86 tff(25868,plain,
% 294.29/186.86 (((~m_c_h_element_v_out(c_e_h_1, c_e, s15)) | m_c_h_element_v_out(c_e_h_1, c_e, s14) | (~node18(c_e_h_1, c_e, s14, s15))) <=> (m_c_h_element_v_out(c_e_h_1, c_e, s14) | (~m_c_h_element_v_out(c_e_h_1, c_e, s15)) | (~node18(c_e_h_1, c_e, s14, s15)))),
% 294.29/186.86 inference(rewrite,[status(thm)],[])).
% 294.29/186.86 tff(25869,plain,
% 294.29/186.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s15)) | m_c_h_element_v_out(c_e_h_1, c_e, s14) | (~node18(c_e_h_1, c_e, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s14) | (~m_c_h_element_v_out(c_e_h_1, c_e, s15)) | (~node18(c_e_h_1, c_e, s14, s15))))),
% 294.29/186.86 inference(monotonicity,[status(thm)],[25868])).
% 294.29/186.86 tff(25870,plain,
% 294.29/186.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s15)) | m_c_h_element_v_out(c_e_h_1, c_e, s14) | (~node18(c_e_h_1, c_e, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s14) | (~m_c_h_element_v_out(c_e_h_1, c_e, s15)) | (~node18(c_e_h_1, c_e, s14, s15)))),
% 294.29/186.86 inference(transitivity,[status(thm)],[25869, 25867])).
% 294.29/186.86 tff(25871,plain,
% 294.29/186.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s15)) | m_c_h_element_v_out(c_e_h_1, c_e, s14) | (~node18(c_e_h_1, c_e, s14, s15)))),
% 294.29/186.86 inference(quant_inst,[status(thm)],[])).
% 294.29/186.86 tff(25872,plain,
% 294.29/186.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s14) | (~m_c_h_element_v_out(c_e_h_1, c_e, s15)) | (~node18(c_e_h_1, c_e, s14, s15))),
% 294.29/186.86 inference(modus_ponens,[status(thm)],[25871, 25870])).
% 294.29/186.86 tff(25873,plain,
% 294.29/186.86 ($false),
% 294.29/186.86 inference(unit_resolution,[status(thm)],[25872, 753, 25864, 25865, 25866])).
% 294.29/186.86 tff(25874,plain,((~node18(c_e_h_1, c_e, s14, s15)) | m_c_h_element_v_out(c_e_h_1, c_e, s14) | (~m_c_h_element_v_out(c_e_h_1, c_e, s15))), inference(lemma,lemma(discharge,[]))).
% 294.29/186.86 tff(25875,plain,
% 294.29/186.86 (~node18(c_e_h_1, c_e, s14, s15)),
% 294.29/186.86 inference(unit_resolution,[status(thm)],[25874, 25865, 25864])).
% 294.29/186.86 tff(25876,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_e, s14)), introduced(assumption)).
% 294.29/186.86 tff(25877,assumption,(node15(c_e_h_1, c_e, s14, s15)), introduced(assumption)).
% 294.29/186.86 tff(25878,plain,
% 294.29/186.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s15)) | (~node15(c_e_h_1, c_e, s14, s15)) | m_c_h_element_v_out(c_e_h_1, c_e, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s15)) | (~node15(c_e_h_1, c_e, s14, s15)) | m_c_h_element_v_out(c_e_h_1, c_e, s14))),
% 294.29/186.86 inference(rewrite,[status(thm)],[])).
% 294.29/186.86 tff(25879,plain,
% 294.29/186.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s15)) | (~node15(c_e_h_1, c_e, s14, s15)) | m_c_h_element_v_out(c_e_h_1, c_e, s14))),
% 294.29/186.86 inference(quant_inst,[status(thm)],[])).
% 294.29/186.86 tff(25880,plain,
% 294.29/186.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s15)) | (~node15(c_e_h_1, c_e, s14, s15)) | m_c_h_element_v_out(c_e_h_1, c_e, s14)),
% 294.29/186.86 inference(modus_ponens,[status(thm)],[25879, 25878])).
% 294.29/186.86 tff(25881,plain,
% 294.29/186.86 ($false),
% 294.29/186.86 inference(unit_resolution,[status(thm)],[25880, 147, 25864, 25865, 25877])).
% 294.29/186.86 tff(25882,plain,((~node15(c_e_h_1, c_e, s14, s15)) | m_c_h_element_v_out(c_e_h_1, c_e, s14) | (~m_c_h_element_v_out(c_e_h_1, c_e, s15))), inference(lemma,lemma(discharge,[]))).
% 294.29/186.86 tff(25883,plain,
% 294.29/186.86 (~node15(c_e_h_1, c_e, s14, s15)),
% 294.29/186.86 inference(unit_resolution,[status(thm)],[25882, 25865, 25864])).
% 294.29/186.86 tff(25884,assumption,(node17(c_e_h_1, c_e, s14)), introduced(assumption)).
% 294.29/186.86 tff(25885,plain,
% 294.29/186.86 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_e, s14) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s14)) | (~node17(c_e_h_1, c_e, s14)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s14) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s14)) | (~node17(c_e_h_1, c_e, s14)))),
% 294.29/186.86 inference(rewrite,[status(thm)],[])).
% 294.29/186.86 tff(25886,plain,
% 294.29/186.86 (((~m_c_h_element_v_in1(c_e_h_1, c_e, s14)) | m_c_h_element_v_in2(c_e_h_1, c_e, s14) | (~node17(c_e_h_1, c_e, s14))) <=> (m_c_h_element_v_in2(c_e_h_1, c_e, s14) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s14)) | (~node17(c_e_h_1, c_e, s14)))),
% 294.29/186.86 inference(rewrite,[status(thm)],[])).
% 294.29/186.86 tff(25887,plain,
% 294.29/186.86 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s14)) | m_c_h_element_v_in2(c_e_h_1, c_e, s14) | (~node17(c_e_h_1, c_e, s14)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_e, s14) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s14)) | (~node17(c_e_h_1, c_e, s14))))),
% 294.29/186.86 inference(monotonicity,[status(thm)],[25886])).
% 294.29/186.86 tff(25888,plain,
% 294.29/186.86 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s14)) | m_c_h_element_v_in2(c_e_h_1, c_e, s14) | (~node17(c_e_h_1, c_e, s14)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s14) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s14)) | (~node17(c_e_h_1, c_e, s14)))),
% 294.29/186.86 inference(transitivity,[status(thm)],[25887, 25885])).
% 294.29/186.86 tff(25889,plain,
% 294.29/186.86 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s14)) | m_c_h_element_v_in2(c_e_h_1, c_e, s14) | (~node17(c_e_h_1, c_e, s14)))),
% 294.29/186.86 inference(quant_inst,[status(thm)],[])).
% 294.29/186.86 tff(25890,plain,
% 294.29/186.86 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s14) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s14)) | (~node17(c_e_h_1, c_e, s14))),
% 294.29/186.86 inference(modus_ponens,[status(thm)],[25889, 25888])).
% 294.29/186.86 tff(25891,plain,
% 294.29/186.86 (m_c_h_element_v_in2(c_e_h_1, c_e, s14) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s14))),
% 294.29/186.86 inference(unit_resolution,[status(thm)],[25890, 919, 25884])).
% 294.29/186.86 tff(25892,plain,
% 294.29/186.86 (~m_c_h_element_v_in1(c_e_h_1, c_e, s14)),
% 294.29/186.86 inference(unit_resolution,[status(thm)],[25891, 25876])).
% 294.29/186.86 tff(25893,assumption,(~node15(c_e_h_1, c_e, s14, s15)), introduced(assumption)).
% 294.29/186.86 tff(25894,plain,
% 294.29/186.86 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s14)) | m_c_h_element_v_in1(c_e_h_1, c_e, s14) | m_c_h_element_v_in2(c_e_h_1, c_e, s14))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s14)) | m_c_h_element_v_in1(c_e_h_1, c_e, s14) | m_c_h_element_v_in2(c_e_h_1, c_e, s14))),
% 294.29/186.86 inference(rewrite,[status(thm)],[])).
% 294.29/186.86 tff(25895,plain,
% 294.29/186.86 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s14)) | m_c_h_element_v_in1(c_e_h_1, c_e, s14) | m_c_h_element_v_in2(c_e_h_1, c_e, s14))),
% 294.29/186.87 inference(quant_inst,[status(thm)],[])).
% 294.29/186.87 tff(25896,plain,
% 294.29/186.87 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s14)) | m_c_h_element_v_in1(c_e_h_1, c_e, s14) | m_c_h_element_v_in2(c_e_h_1, c_e, s14)),
% 294.29/186.87 inference(modus_ponens,[status(thm)],[25895, 25894])).
% 294.29/186.87 tff(25897,plain,
% 294.29/186.87 (~node16(c_e_h_1, c_e, s14)),
% 294.29/186.87 inference(unit_resolution,[status(thm)],[25896, 178, 25892, 25876])).
% 294.29/186.87 tff(25898,plain,
% 294.29/186.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s14, s15)) | node19(c_e_h_1, c_e, s14, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s14, s15)) | node19(c_e_h_1, c_e, s14, s15))),
% 294.29/186.87 inference(rewrite,[status(thm)],[])).
% 294.29/186.87 tff(25899,plain,
% 294.29/186.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s14, s15)) | node19(c_e_h_1, c_e, s14, s15))),
% 294.29/186.87 inference(quant_inst,[status(thm)],[])).
% 294.29/186.87 tff(25900,plain,
% 294.29/186.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s14, s15)) | node19(c_e_h_1, c_e, s14, s15)),
% 294.29/186.87 inference(modus_ponens,[status(thm)],[25899, 25898])).
% 294.29/186.87 tff(25901,plain,
% 294.29/186.87 (node19(c_e_h_1, c_e, s14, s15)),
% 294.29/186.87 inference(unit_resolution,[status(thm)],[25900, 190, 12926])).
% 294.29/186.87 tff(25902,plain,
% 294.29/186.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s14) | (~node19(c_e_h_1, c_e, s14, s15)) | node15(c_e_h_1, c_e, s14, s15) | node14(c_e_h_1, c_e, s14, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_e, s14) | (~node19(c_e_h_1, c_e, s14, s15)) | node15(c_e_h_1, c_e, s14, s15) | node14(c_e_h_1, c_e, s14, s15))),
% 294.29/186.87 inference(rewrite,[status(thm)],[])).
% 294.29/186.87 tff(25903,plain,
% 294.29/186.87 ((node16(c_e_h_1, c_e, s14) | node14(c_e_h_1, c_e, s14, s15) | node15(c_e_h_1, c_e, s14, s15) | (~node19(c_e_h_1, c_e, s14, s15))) <=> (node16(c_e_h_1, c_e, s14) | (~node19(c_e_h_1, c_e, s14, s15)) | node15(c_e_h_1, c_e, s14, s15) | node14(c_e_h_1, c_e, s14, s15))),
% 294.29/186.87 inference(rewrite,[status(thm)],[])).
% 294.29/186.87 tff(25904,plain,
% 294.29/186.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s14) | node14(c_e_h_1, c_e, s14, s15) | node15(c_e_h_1, c_e, s14, s15) | (~node19(c_e_h_1, c_e, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s14) | (~node19(c_e_h_1, c_e, s14, s15)) | node15(c_e_h_1, c_e, s14, s15) | node14(c_e_h_1, c_e, s14, s15)))),
% 294.29/186.87 inference(monotonicity,[status(thm)],[25903])).
% 294.29/186.87 tff(25905,plain,
% 294.29/186.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s14) | node14(c_e_h_1, c_e, s14, s15) | node15(c_e_h_1, c_e, s14, s15) | (~node19(c_e_h_1, c_e, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_e, s14) | (~node19(c_e_h_1, c_e, s14, s15)) | node15(c_e_h_1, c_e, s14, s15) | node14(c_e_h_1, c_e, s14, s15))),
% 294.29/186.87 inference(transitivity,[status(thm)],[25904, 25902])).
% 294.29/186.87 tff(25906,plain,
% 294.29/186.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s14) | node14(c_e_h_1, c_e, s14, s15) | node15(c_e_h_1, c_e, s14, s15) | (~node19(c_e_h_1, c_e, s14, s15)))),
% 294.29/186.87 inference(quant_inst,[status(thm)],[])).
% 294.29/186.87 tff(25907,plain,
% 294.29/186.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_e, s14) | (~node19(c_e_h_1, c_e, s14, s15)) | node15(c_e_h_1, c_e, s14, s15) | node14(c_e_h_1, c_e, s14, s15)),
% 294.29/186.87 inference(modus_ponens,[status(thm)],[25906, 25905])).
% 294.29/186.87 tff(25908,plain,
% 294.29/186.87 (node16(c_e_h_1, c_e, s14) | node15(c_e_h_1, c_e, s14, s15) | node14(c_e_h_1, c_e, s14, s15)),
% 294.29/186.87 inference(unit_resolution,[status(thm)],[25907, 204, 25901])).
% 294.29/186.87 tff(25909,plain,
% 294.29/186.87 (node14(c_e_h_1, c_e, s14, s15)),
% 294.29/186.87 inference(unit_resolution,[status(thm)],[25908, 25897, 25893])).
% 294.29/186.87 tff(25910,plain,
% 294.29/186.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s14) | (~m_c_h_element_v_out(c_e_h_1, c_e, s15)) | (~node14(c_e_h_1, c_e, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s14) | (~m_c_h_element_v_out(c_e_h_1, c_e, s15)) | (~node14(c_e_h_1, c_e, s14, s15)))),
% 294.29/186.87 inference(rewrite,[status(thm)],[])).
% 294.29/186.87 tff(25911,plain,
% 294.29/186.87 (((~node14(c_e_h_1, c_e, s14, s15)) | m_c_h_element_v_in1(c_e_h_1, c_e, s14) | (~m_c_h_element_v_out(c_e_h_1, c_e, s15))) <=> (m_c_h_element_v_in1(c_e_h_1, c_e, s14) | (~m_c_h_element_v_out(c_e_h_1, c_e, s15)) | (~node14(c_e_h_1, c_e, s14, s15)))),
% 294.29/186.87 inference(rewrite,[status(thm)],[])).
% 294.29/186.87 tff(25912,plain,
% 294.29/186.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s14, s15)) | m_c_h_element_v_in1(c_e_h_1, c_e, s14) | (~m_c_h_element_v_out(c_e_h_1, c_e, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s14) | (~m_c_h_element_v_out(c_e_h_1, c_e, s15)) | (~node14(c_e_h_1, c_e, s14, s15))))),
% 294.29/186.87 inference(monotonicity,[status(thm)],[25911])).
% 294.29/186.87 tff(25913,plain,
% 294.29/186.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s14, s15)) | m_c_h_element_v_in1(c_e_h_1, c_e, s14) | (~m_c_h_element_v_out(c_e_h_1, c_e, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s14) | (~m_c_h_element_v_out(c_e_h_1, c_e, s15)) | (~node14(c_e_h_1, c_e, s14, s15)))),
% 294.29/186.87 inference(transitivity,[status(thm)],[25912, 25910])).
% 294.29/186.87 tff(25914,plain,
% 294.29/186.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s14, s15)) | m_c_h_element_v_in1(c_e_h_1, c_e, s14) | (~m_c_h_element_v_out(c_e_h_1, c_e, s15)))),
% 294.29/186.87 inference(quant_inst,[status(thm)],[])).
% 294.29/186.87 tff(25915,plain,
% 294.29/186.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s14) | (~m_c_h_element_v_out(c_e_h_1, c_e, s15)) | (~node14(c_e_h_1, c_e, s14, s15))),
% 294.29/186.87 inference(modus_ponens,[status(thm)],[25914, 25913])).
% 294.29/186.87 tff(25916,plain,
% 294.29/186.87 ($false),
% 294.29/186.87 inference(unit_resolution,[status(thm)],[25915, 223, 25865, 25909, 25892])).
% 294.29/186.87 tff(25917,plain,(m_c_h_element_v_in2(c_e_h_1, c_e, s14) | (~m_c_h_element_v_out(c_e_h_1, c_e, s15)) | node15(c_e_h_1, c_e, s14, s15) | (~node17(c_e_h_1, c_e, s14))), inference(lemma,lemma(discharge,[]))).
% 294.29/186.87 tff(25918,plain,
% 294.29/186.87 (~node17(c_e_h_1, c_e, s14)),
% 294.29/186.87 inference(unit_resolution,[status(thm)],[25917, 25883, 25865, 25876])).
% 294.29/186.87 tff(25919,plain,
% 294.29/186.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s14) | (~node19(c_e_h_1, c_e, s14, s15)) | node18(c_e_h_1, c_e, s14, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_e, s14) | (~node19(c_e_h_1, c_e, s14, s15)) | node18(c_e_h_1, c_e, s14, s15))),
% 294.29/186.88 inference(rewrite,[status(thm)],[])).
% 294.29/186.88 tff(25920,plain,
% 294.29/186.88 ((node17(c_e_h_1, c_e, s14) | node18(c_e_h_1, c_e, s14, s15) | (~node19(c_e_h_1, c_e, s14, s15))) <=> (node17(c_e_h_1, c_e, s14) | (~node19(c_e_h_1, c_e, s14, s15)) | node18(c_e_h_1, c_e, s14, s15))),
% 294.29/186.88 inference(rewrite,[status(thm)],[])).
% 294.29/186.88 tff(25921,plain,
% 294.29/186.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s14) | node18(c_e_h_1, c_e, s14, s15) | (~node19(c_e_h_1, c_e, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s14) | (~node19(c_e_h_1, c_e, s14, s15)) | node18(c_e_h_1, c_e, s14, s15)))),
% 294.29/186.88 inference(monotonicity,[status(thm)],[25920])).
% 294.29/186.88 tff(25922,plain,
% 294.29/186.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s14) | node18(c_e_h_1, c_e, s14, s15) | (~node19(c_e_h_1, c_e, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_e, s14) | (~node19(c_e_h_1, c_e, s14, s15)) | node18(c_e_h_1, c_e, s14, s15))),
% 294.29/186.88 inference(transitivity,[status(thm)],[25921, 25919])).
% 294.29/186.88 tff(25923,plain,
% 294.29/186.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s14) | node18(c_e_h_1, c_e, s14, s15) | (~node19(c_e_h_1, c_e, s14, s15)))),
% 294.29/186.88 inference(quant_inst,[status(thm)],[])).
% 294.29/186.88 tff(25924,plain,
% 294.29/186.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_e, s14) | (~node19(c_e_h_1, c_e, s14, s15)) | node18(c_e_h_1, c_e, s14, s15)),
% 294.29/186.88 inference(modus_ponens,[status(thm)],[25923, 25922])).
% 294.29/186.88 tff(25925,plain,
% 294.29/186.88 (node17(c_e_h_1, c_e, s14) | node18(c_e_h_1, c_e, s14, s15)),
% 294.29/186.88 inference(unit_resolution,[status(thm)],[25924, 776, 25901])).
% 294.29/186.88 tff(25926,plain,
% 294.29/186.88 ($false),
% 294.29/186.88 inference(unit_resolution,[status(thm)],[25925, 25918, 25875])).
% 294.29/186.88 tff(25927,plain,((~m_c_h_element_v_out(c_e_h_1, c_e, s15)) | m_c_h_element_v_in2(c_e_h_1, c_e, s14) | m_c_h_element_v_out(c_e_h_1, c_e, s14)), inference(lemma,lemma(discharge,[]))).
% 294.29/186.88 tff(25928,plain,
% 294.29/186.88 (~m_c_h_element_v_out(c_e_h_1, c_e, s15)),
% 294.29/186.88 inference(unit_resolution,[status(thm)],[25927, 25863, 25856])).
% 294.29/186.88 tff(25929,assumption,(~m_c_h_element_v_out(c_e_h_1, c_e, s15)), introduced(assumption)).
% 294.29/186.88 tff(25930,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s16)), introduced(assumption)).
% 294.29/186.88 tff(25931,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_e, s15)), introduced(assumption)).
% 294.29/186.88 tff(25932,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_e, s15)), introduced(assumption)).
% 294.29/186.88 tff(25933,assumption,(node15(c_e_h_1, c_e, s15, s16)), introduced(assumption)).
% 294.29/186.88 tff(25934,plain,
% 294.29/186.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s16)) | (~node15(c_e_h_1, c_e, s15, s16)) | m_c_h_element_v_out(c_e_h_1, c_e, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s16)) | (~node15(c_e_h_1, c_e, s15, s16)) | m_c_h_element_v_out(c_e_h_1, c_e, s15))),
% 294.29/186.88 inference(rewrite,[status(thm)],[])).
% 294.29/186.88 tff(25935,plain,
% 294.29/186.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s16)) | (~node15(c_e_h_1, c_e, s15, s16)) | m_c_h_element_v_out(c_e_h_1, c_e, s15))),
% 294.29/186.88 inference(quant_inst,[status(thm)],[])).
% 294.29/186.88 tff(25936,plain,
% 294.29/186.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s16)) | (~node15(c_e_h_1, c_e, s15, s16)) | m_c_h_element_v_out(c_e_h_1, c_e, s15)),
% 294.29/186.88 inference(modus_ponens,[status(thm)],[25935, 25934])).
% 294.29/186.88 tff(25937,plain,
% 294.29/186.88 ($false),
% 294.29/186.88 inference(unit_resolution,[status(thm)],[25936, 147, 25930, 25929, 25933])).
% 294.29/186.88 tff(25938,plain,((~node15(c_e_h_1, c_e, s15, s16)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s16)) | m_c_h_element_v_out(c_e_h_1, c_e, s15)), inference(lemma,lemma(discharge,[]))).
% 294.29/186.88 tff(25939,plain,
% 294.29/186.88 (~node15(c_e_h_1, c_e, s15, s16)),
% 294.29/186.88 inference(unit_resolution,[status(thm)],[25938, 25930, 25929])).
% 294.29/186.88 tff(25940,assumption,(~node15(c_e_h_1, c_e, s15, s16)), introduced(assumption)).
% 294.29/186.88 tff(25941,plain,
% 294.29/186.88 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s15)) | m_c_h_element_v_in1(c_e_h_1, c_e, s15) | m_c_h_element_v_in2(c_e_h_1, c_e, s15))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s15)) | m_c_h_element_v_in1(c_e_h_1, c_e, s15) | m_c_h_element_v_in2(c_e_h_1, c_e, s15))),
% 294.29/186.88 inference(rewrite,[status(thm)],[])).
% 294.29/186.88 tff(25942,plain,
% 294.29/186.88 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s15)) | m_c_h_element_v_in1(c_e_h_1, c_e, s15) | m_c_h_element_v_in2(c_e_h_1, c_e, s15))),
% 294.29/186.88 inference(quant_inst,[status(thm)],[])).
% 294.29/186.88 tff(25943,plain,
% 294.29/186.88 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s15)) | m_c_h_element_v_in1(c_e_h_1, c_e, s15) | m_c_h_element_v_in2(c_e_h_1, c_e, s15)),
% 294.29/186.88 inference(modus_ponens,[status(thm)],[25942, 25941])).
% 294.29/186.88 tff(25944,plain,
% 294.29/186.88 ((~node16(c_e_h_1, c_e, s15)) | m_c_h_element_v_in1(c_e_h_1, c_e, s15)),
% 294.29/186.88 inference(unit_resolution,[status(thm)],[25943, 178, 25932])).
% 294.29/186.88 tff(25945,plain,
% 294.29/186.88 (~node16(c_e_h_1, c_e, s15)),
% 294.29/186.88 inference(unit_resolution,[status(thm)],[25944, 25931])).
% 294.29/186.88 tff(25946,plain,
% 294.29/186.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s15, s16)) | node19(c_e_h_1, c_e, s15, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s15, s16)) | node19(c_e_h_1, c_e, s15, s16))),
% 294.29/186.88 inference(rewrite,[status(thm)],[])).
% 294.29/186.88 tff(25947,plain,
% 294.29/186.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s15, s16)) | node19(c_e_h_1, c_e, s15, s16))),
% 294.29/186.88 inference(quant_inst,[status(thm)],[])).
% 294.29/186.88 tff(25948,plain,
% 294.29/186.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s15, s16)) | node19(c_e_h_1, c_e, s15, s16)),
% 294.29/186.88 inference(modus_ponens,[status(thm)],[25947, 25946])).
% 294.29/186.88 tff(25949,plain,
% 294.29/186.88 (node19(c_e_h_1, c_e, s15, s16)),
% 294.29/186.88 inference(unit_resolution,[status(thm)],[25948, 190, 13499])).
% 294.29/186.88 tff(25950,plain,
% 294.29/186.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s15) | node14(c_e_h_1, c_e, s15, s16) | (~node19(c_e_h_1, c_e, s15, s16)) | node15(c_e_h_1, c_e, s15, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_e, s15) | node14(c_e_h_1, c_e, s15, s16) | (~node19(c_e_h_1, c_e, s15, s16)) | node15(c_e_h_1, c_e, s15, s16))),
% 294.29/186.88 inference(rewrite,[status(thm)],[])).
% 294.29/186.88 tff(25951,plain,
% 294.29/186.88 ((node16(c_e_h_1, c_e, s15) | node14(c_e_h_1, c_e, s15, s16) | node15(c_e_h_1, c_e, s15, s16) | (~node19(c_e_h_1, c_e, s15, s16))) <=> (node16(c_e_h_1, c_e, s15) | node14(c_e_h_1, c_e, s15, s16) | (~node19(c_e_h_1, c_e, s15, s16)) | node15(c_e_h_1, c_e, s15, s16))),
% 294.29/186.88 inference(rewrite,[status(thm)],[])).
% 294.29/186.88 tff(25952,plain,
% 294.29/186.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s15) | node14(c_e_h_1, c_e, s15, s16) | node15(c_e_h_1, c_e, s15, s16) | (~node19(c_e_h_1, c_e, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s15) | node14(c_e_h_1, c_e, s15, s16) | (~node19(c_e_h_1, c_e, s15, s16)) | node15(c_e_h_1, c_e, s15, s16)))),
% 294.29/186.88 inference(monotonicity,[status(thm)],[25951])).
% 294.29/186.88 tff(25953,plain,
% 294.29/186.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s15) | node14(c_e_h_1, c_e, s15, s16) | node15(c_e_h_1, c_e, s15, s16) | (~node19(c_e_h_1, c_e, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_e, s15) | node14(c_e_h_1, c_e, s15, s16) | (~node19(c_e_h_1, c_e, s15, s16)) | node15(c_e_h_1, c_e, s15, s16))),
% 294.29/186.88 inference(transitivity,[status(thm)],[25952, 25950])).
% 294.29/186.88 tff(25954,plain,
% 294.29/186.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s15) | node14(c_e_h_1, c_e, s15, s16) | node15(c_e_h_1, c_e, s15, s16) | (~node19(c_e_h_1, c_e, s15, s16)))),
% 294.29/186.88 inference(quant_inst,[status(thm)],[])).
% 294.29/186.88 tff(25955,plain,
% 294.29/186.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_e, s15) | node14(c_e_h_1, c_e, s15, s16) | (~node19(c_e_h_1, c_e, s15, s16)) | node15(c_e_h_1, c_e, s15, s16)),
% 294.29/186.88 inference(modus_ponens,[status(thm)],[25954, 25953])).
% 294.29/186.88 tff(25956,plain,
% 294.29/186.88 (node16(c_e_h_1, c_e, s15) | node14(c_e_h_1, c_e, s15, s16) | node15(c_e_h_1, c_e, s15, s16)),
% 294.29/186.88 inference(unit_resolution,[status(thm)],[25955, 204, 25949])).
% 294.29/186.88 tff(25957,plain,
% 294.29/186.88 (node14(c_e_h_1, c_e, s15, s16)),
% 294.29/186.88 inference(unit_resolution,[status(thm)],[25956, 25945, 25940])).
% 294.29/186.88 tff(25958,plain,
% 294.29/186.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s16)) | (~node14(c_e_h_1, c_e, s15, s16)) | m_c_h_element_v_in1(c_e_h_1, c_e, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s16)) | (~node14(c_e_h_1, c_e, s15, s16)) | m_c_h_element_v_in1(c_e_h_1, c_e, s15))),
% 294.29/186.88 inference(rewrite,[status(thm)],[])).
% 294.29/186.88 tff(25959,plain,
% 294.29/186.88 (((~node14(c_e_h_1, c_e, s15, s16)) | m_c_h_element_v_in1(c_e_h_1, c_e, s15) | (~m_c_h_element_v_out(c_e_h_1, c_e, s16))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_e, s16)) | (~node14(c_e_h_1, c_e, s15, s16)) | m_c_h_element_v_in1(c_e_h_1, c_e, s15))),
% 294.29/186.88 inference(rewrite,[status(thm)],[])).
% 294.29/186.88 tff(25960,plain,
% 294.29/186.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s15, s16)) | m_c_h_element_v_in1(c_e_h_1, c_e, s15) | (~m_c_h_element_v_out(c_e_h_1, c_e, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s16)) | (~node14(c_e_h_1, c_e, s15, s16)) | m_c_h_element_v_in1(c_e_h_1, c_e, s15)))),
% 294.29/186.88 inference(monotonicity,[status(thm)],[25959])).
% 294.29/186.88 tff(25961,plain,
% 294.29/186.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s15, s16)) | m_c_h_element_v_in1(c_e_h_1, c_e, s15) | (~m_c_h_element_v_out(c_e_h_1, c_e, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s16)) | (~node14(c_e_h_1, c_e, s15, s16)) | m_c_h_element_v_in1(c_e_h_1, c_e, s15))),
% 294.29/186.88 inference(transitivity,[status(thm)],[25960, 25958])).
% 294.29/186.88 tff(25962,plain,
% 294.29/186.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s15, s16)) | m_c_h_element_v_in1(c_e_h_1, c_e, s15) | (~m_c_h_element_v_out(c_e_h_1, c_e, s16)))),
% 294.39/186.89 inference(quant_inst,[status(thm)],[])).
% 294.39/186.89 tff(25963,plain,
% 294.39/186.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s16)) | (~node14(c_e_h_1, c_e, s15, s16)) | m_c_h_element_v_in1(c_e_h_1, c_e, s15)),
% 294.39/186.89 inference(modus_ponens,[status(thm)],[25962, 25961])).
% 294.39/186.89 tff(25964,plain,
% 294.39/186.89 ($false),
% 294.39/186.89 inference(unit_resolution,[status(thm)],[25963, 223, 25930, 25957, 25931])).
% 294.39/186.89 tff(25965,plain,(m_c_h_element_v_in1(c_e_h_1, c_e, s15) | (~m_c_h_element_v_out(c_e_h_1, c_e, s16)) | node15(c_e_h_1, c_e, s15, s16) | m_c_h_element_v_in2(c_e_h_1, c_e, s15)), inference(lemma,lemma(discharge,[]))).
% 294.39/186.89 tff(25966,plain,
% 294.39/186.89 ($false),
% 294.39/186.89 inference(unit_resolution,[status(thm)],[25965, 25939, 25930, 25932, 25931])).
% 294.39/186.89 tff(25967,plain,((~m_c_h_element_v_out(c_e_h_1, c_e, s16)) | m_c_h_element_v_in2(c_e_h_1, c_e, s15) | m_c_h_element_v_in1(c_e_h_1, c_e, s15) | m_c_h_element_v_out(c_e_h_1, c_e, s15)), inference(lemma,lemma(discharge,[]))).
% 294.39/186.89 tff(25968,plain,
% 294.39/186.89 (m_c_h_element_v_in2(c_e_h_1, c_e, s15)),
% 294.39/186.89 inference(unit_resolution,[status(thm)],[25967, 25931, 25929, 25930])).
% 294.39/186.89 tff(25969,assumption,(node18(c_e_h_1, c_e, s15, s16)), introduced(assumption)).
% 294.39/186.89 tff(25970,plain,
% 294.39/186.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s16)) | m_c_h_element_v_out(c_e_h_1, c_e, s15) | (~node18(c_e_h_1, c_e, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s16)) | m_c_h_element_v_out(c_e_h_1, c_e, s15) | (~node18(c_e_h_1, c_e, s15, s16)))),
% 294.39/186.89 inference(rewrite,[status(thm)],[])).
% 294.39/186.89 tff(25971,plain,
% 294.39/186.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s16)) | m_c_h_element_v_out(c_e_h_1, c_e, s15) | (~node18(c_e_h_1, c_e, s15, s16)))),
% 294.39/186.89 inference(quant_inst,[status(thm)],[])).
% 294.39/186.89 tff(25972,plain,
% 294.39/186.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s16)) | m_c_h_element_v_out(c_e_h_1, c_e, s15) | (~node18(c_e_h_1, c_e, s15, s16))),
% 294.39/186.89 inference(modus_ponens,[status(thm)],[25971, 25970])).
% 294.39/186.89 tff(25973,plain,
% 294.39/186.89 ($false),
% 294.39/186.89 inference(unit_resolution,[status(thm)],[25972, 753, 25930, 25929, 25969])).
% 294.39/186.89 tff(25974,plain,((~node18(c_e_h_1, c_e, s15, s16)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s16)) | m_c_h_element_v_out(c_e_h_1, c_e, s15)), inference(lemma,lemma(discharge,[]))).
% 294.39/186.89 tff(25975,plain,
% 294.39/186.89 (~node18(c_e_h_1, c_e, s15, s16)),
% 294.39/186.89 inference(unit_resolution,[status(thm)],[25974, 25930, 25929])).
% 294.39/186.89 tff(25976,plain,
% 294.39/186.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s15) | (~node19(c_e_h_1, c_e, s15, s16)) | node18(c_e_h_1, c_e, s15, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_e, s15) | (~node19(c_e_h_1, c_e, s15, s16)) | node18(c_e_h_1, c_e, s15, s16))),
% 294.39/186.89 inference(rewrite,[status(thm)],[])).
% 294.39/186.89 tff(25977,plain,
% 294.39/186.89 ((node17(c_e_h_1, c_e, s15) | node18(c_e_h_1, c_e, s15, s16) | (~node19(c_e_h_1, c_e, s15, s16))) <=> (node17(c_e_h_1, c_e, s15) | (~node19(c_e_h_1, c_e, s15, s16)) | node18(c_e_h_1, c_e, s15, s16))),
% 294.39/186.89 inference(rewrite,[status(thm)],[])).
% 294.39/186.89 tff(25978,plain,
% 294.39/186.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s15) | node18(c_e_h_1, c_e, s15, s16) | (~node19(c_e_h_1, c_e, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s15) | (~node19(c_e_h_1, c_e, s15, s16)) | node18(c_e_h_1, c_e, s15, s16)))),
% 294.39/186.89 inference(monotonicity,[status(thm)],[25977])).
% 294.39/186.89 tff(25979,plain,
% 294.39/186.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s15) | node18(c_e_h_1, c_e, s15, s16) | (~node19(c_e_h_1, c_e, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_e, s15) | (~node19(c_e_h_1, c_e, s15, s16)) | node18(c_e_h_1, c_e, s15, s16))),
% 294.39/186.89 inference(transitivity,[status(thm)],[25978, 25976])).
% 294.39/186.89 tff(25980,plain,
% 294.39/186.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s15) | node18(c_e_h_1, c_e, s15, s16) | (~node19(c_e_h_1, c_e, s15, s16)))),
% 294.39/186.89 inference(quant_inst,[status(thm)],[])).
% 294.39/186.89 tff(25981,plain,
% 294.39/186.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_e, s15) | (~node19(c_e_h_1, c_e, s15, s16)) | node18(c_e_h_1, c_e, s15, s16)),
% 294.39/186.89 inference(modus_ponens,[status(thm)],[25980, 25979])).
% 294.39/186.89 tff(25982,plain,
% 294.39/186.89 (node17(c_e_h_1, c_e, s15) | node18(c_e_h_1, c_e, s15, s16)),
% 294.39/186.89 inference(unit_resolution,[status(thm)],[25981, 776, 25949])).
% 294.39/186.89 tff(25983,plain,
% 294.39/186.89 (node17(c_e_h_1, c_e, s15)),
% 294.39/186.89 inference(unit_resolution,[status(thm)],[25982, 25975])).
% 294.39/186.89 tff(25984,plain,
% 294.39/186.89 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_e, s15)) | m_c_h_element_v_in1(c_e_h_1, c_e, s15) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s15)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s15)) | m_c_h_element_v_in1(c_e_h_1, c_e, s15) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s15)))),
% 294.39/186.89 inference(rewrite,[status(thm)],[])).
% 294.39/186.89 tff(25985,plain,
% 294.39/186.89 ((m_c_h_element_v_in1(c_e_h_1, c_e, s15) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s15)) | (~node17(c_e_h_1, c_e, s15))) <=> ((~node17(c_e_h_1, c_e, s15)) | m_c_h_element_v_in1(c_e_h_1, c_e, s15) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s15)))),
% 294.39/186.89 inference(rewrite,[status(thm)],[])).
% 294.39/186.89 tff(25986,plain,
% 294.39/186.89 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s15) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s15)) | (~node17(c_e_h_1, c_e, s15)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_e, s15)) | m_c_h_element_v_in1(c_e_h_1, c_e, s15) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s15))))),
% 294.39/186.89 inference(monotonicity,[status(thm)],[25985])).
% 294.39/186.89 tff(25987,plain,
% 294.39/186.89 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s15) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s15)) | (~node17(c_e_h_1, c_e, s15)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s15)) | m_c_h_element_v_in1(c_e_h_1, c_e, s15) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s15)))),
% 294.39/186.89 inference(transitivity,[status(thm)],[25986, 25984])).
% 294.39/186.89 tff(25988,plain,
% 294.39/186.89 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s15) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s15)) | (~node17(c_e_h_1, c_e, s15)))),
% 294.39/186.89 inference(quant_inst,[status(thm)],[])).
% 294.39/186.89 tff(25989,plain,
% 294.39/186.89 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s15)) | m_c_h_element_v_in1(c_e_h_1, c_e, s15) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s15))),
% 294.39/186.89 inference(modus_ponens,[status(thm)],[25988, 25987])).
% 294.39/186.89 tff(25990,plain,
% 294.39/186.89 (m_c_h_element_v_in1(c_e_h_1, c_e, s15) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s15))),
% 294.39/186.89 inference(unit_resolution,[status(thm)],[25989, 859, 25983])).
% 294.39/186.89 tff(25991,plain,
% 294.39/186.89 ($false),
% 294.39/186.89 inference(unit_resolution,[status(thm)],[25990, 25968, 25931])).
% 294.39/186.89 tff(25992,plain,(m_c_h_element_v_in1(c_e_h_1, c_e, s15) | m_c_h_element_v_out(c_e_h_1, c_e, s15) | (~m_c_h_element_v_out(c_e_h_1, c_e, s16))), inference(lemma,lemma(discharge,[]))).
% 294.39/186.89 tff(25993,plain,
% 294.39/186.89 (m_c_h_element_v_in1(c_e_h_1, c_e, s15)),
% 294.39/186.89 inference(unit_resolution,[status(thm)],[25992, 25930, 25929])).
% 294.39/186.89 tff(25994,plain,
% 294.39/186.89 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_e, s15) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s15)) | (~node17(c_e_h_1, c_e, s15)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s15) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s15)) | (~node17(c_e_h_1, c_e, s15)))),
% 294.39/186.89 inference(rewrite,[status(thm)],[])).
% 294.39/186.89 tff(25995,plain,
% 294.39/186.89 (((~m_c_h_element_v_in1(c_e_h_1, c_e, s15)) | m_c_h_element_v_in2(c_e_h_1, c_e, s15) | (~node17(c_e_h_1, c_e, s15))) <=> (m_c_h_element_v_in2(c_e_h_1, c_e, s15) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s15)) | (~node17(c_e_h_1, c_e, s15)))),
% 294.39/186.89 inference(rewrite,[status(thm)],[])).
% 294.39/186.89 tff(25996,plain,
% 294.39/186.89 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s15)) | m_c_h_element_v_in2(c_e_h_1, c_e, s15) | (~node17(c_e_h_1, c_e, s15)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_e, s15) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s15)) | (~node17(c_e_h_1, c_e, s15))))),
% 294.39/186.89 inference(monotonicity,[status(thm)],[25995])).
% 294.39/186.89 tff(25997,plain,
% 294.39/186.89 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s15)) | m_c_h_element_v_in2(c_e_h_1, c_e, s15) | (~node17(c_e_h_1, c_e, s15)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s15) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s15)) | (~node17(c_e_h_1, c_e, s15)))),
% 294.39/186.89 inference(transitivity,[status(thm)],[25996, 25994])).
% 294.39/186.89 tff(25998,plain,
% 294.39/186.89 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s15)) | m_c_h_element_v_in2(c_e_h_1, c_e, s15) | (~node17(c_e_h_1, c_e, s15)))),
% 294.39/186.89 inference(quant_inst,[status(thm)],[])).
% 294.39/186.89 tff(25999,plain,
% 294.39/186.89 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s15) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s15)) | (~node17(c_e_h_1, c_e, s15))),
% 294.39/186.89 inference(modus_ponens,[status(thm)],[25998, 25997])).
% 294.39/186.89 tff(26000,plain,
% 294.39/186.89 ((~m_c_h_element_v_in1(c_e_h_1, c_e, s15)) | (~node17(c_e_h_1, c_e, s15))),
% 294.39/186.89 inference(unit_resolution,[status(thm)],[25999, 919, 25932])).
% 294.39/186.89 tff(26001,plain,
% 294.39/186.89 ($false),
% 294.39/186.89 inference(unit_resolution,[status(thm)],[26000, 25983, 25993])).
% 294.39/186.89 tff(26002,plain,((~m_c_h_element_v_out(c_e_h_1, c_e, s16)) | m_c_h_element_v_in2(c_e_h_1, c_e, s15) | m_c_h_element_v_out(c_e_h_1, c_e, s15)), inference(lemma,lemma(discharge,[]))).
% 294.39/186.89 tff(26003,plain,
% 294.39/186.89 ((~m_c_h_element_v_out(c_e_h_1, c_e, s16)) | m_c_h_element_v_in2(c_e_h_1, c_e, s15)),
% 294.39/186.89 inference(unit_resolution,[status(thm)],[26002, 25928])).
% 294.39/186.89 tff(26004,plain,
% 294.39/186.89 (~m_c_h_element_v_out(c_e_h_1, c_e, s16)),
% 294.39/186.89 inference(unit_resolution,[status(thm)],[26003, 25580])).
% 294.39/186.90 tff(26005,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s18)), introduced(assumption)).
% 294.39/186.90 tff(26006,assumption,(~m_c_h_element_v_out(c_e_h_1, c_e, s16)), introduced(assumption)).
% 294.39/186.90 tff(26007,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_i, s16)), introduced(assumption)).
% 294.39/186.90 tff(26008,assumption,(m_c_h_element_v_in2(c_e_h_1, c_e, s16)), introduced(assumption)).
% 294.39/186.90 tff(26009,plain,
% 294.39/186.90 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s16)) | m_and_h_gate_v_out(c_e_h_1, c_i, s16))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s16)) | m_and_h_gate_v_out(c_e_h_1, c_i, s16))),
% 294.39/186.90 inference(rewrite,[status(thm)],[])).
% 294.39/186.90 tff(26010,plain,
% 294.39/186.90 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s16)) | m_and_h_gate_v_out(c_e_h_1, c_i, s16))),
% 294.39/186.90 inference(quant_inst,[status(thm)],[])).
% 294.39/186.90 tff(26011,plain,
% 294.39/186.90 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s16)) | m_and_h_gate_v_out(c_e_h_1, c_i, s16)),
% 294.39/186.90 inference(modus_ponens,[status(thm)],[26010, 26009])).
% 294.39/186.90 tff(26012,plain,
% 294.39/186.90 ($false),
% 294.39/186.90 inference(unit_resolution,[status(thm)],[26011, 164, 26007, 26008])).
% 294.39/186.90 tff(26013,plain,((~m_c_h_element_v_in2(c_e_h_1, c_e, s16)) | m_and_h_gate_v_out(c_e_h_1, c_i, s16)), inference(lemma,lemma(discharge,[]))).
% 294.39/186.90 tff(26014,plain,
% 294.39/186.90 (~m_c_h_element_v_in2(c_e_h_1, c_e, s16)),
% 294.39/186.90 inference(unit_resolution,[status(thm)],[26013, 26007])).
% 294.39/186.90 tff(26015,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_e, s16)), introduced(assumption)).
% 294.39/186.90 tff(26016,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s17)), introduced(assumption)).
% 294.39/186.90 tff(26017,assumption,(node15(c_e_h_1, c_e, s16, s17)), introduced(assumption)).
% 294.39/186.90 tff(26018,plain,
% 294.39/186.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s17)) | (~node15(c_e_h_1, c_e, s16, s17)) | m_c_h_element_v_out(c_e_h_1, c_e, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s17)) | (~node15(c_e_h_1, c_e, s16, s17)) | m_c_h_element_v_out(c_e_h_1, c_e, s16))),
% 294.39/186.90 inference(rewrite,[status(thm)],[])).
% 294.39/186.90 tff(26019,plain,
% 294.39/186.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s17)) | (~node15(c_e_h_1, c_e, s16, s17)) | m_c_h_element_v_out(c_e_h_1, c_e, s16))),
% 294.39/186.90 inference(quant_inst,[status(thm)],[])).
% 294.39/186.90 tff(26020,plain,
% 294.39/186.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s17)) | (~node15(c_e_h_1, c_e, s16, s17)) | m_c_h_element_v_out(c_e_h_1, c_e, s16)),
% 294.39/186.90 inference(modus_ponens,[status(thm)],[26019, 26018])).
% 294.39/186.90 tff(26021,plain,
% 294.39/186.90 ($false),
% 294.39/186.90 inference(unit_resolution,[status(thm)],[26020, 147, 26006, 26016, 26017])).
% 294.39/186.90 tff(26022,plain,((~node15(c_e_h_1, c_e, s16, s17)) | m_c_h_element_v_out(c_e_h_1, c_e, s16) | (~m_c_h_element_v_out(c_e_h_1, c_e, s17))), inference(lemma,lemma(discharge,[]))).
% 294.39/186.90 tff(26023,plain,
% 294.39/186.90 (~node15(c_e_h_1, c_e, s16, s17)),
% 294.39/186.90 inference(unit_resolution,[status(thm)],[26022, 26006, 26016])).
% 294.39/186.90 tff(26024,assumption,(node18(c_e_h_1, c_e, s16, s17)), introduced(assumption)).
% 294.39/186.90 tff(26025,plain,
% 294.39/186.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s16) | (~m_c_h_element_v_out(c_e_h_1, c_e, s17)) | (~node18(c_e_h_1, c_e, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s16) | (~m_c_h_element_v_out(c_e_h_1, c_e, s17)) | (~node18(c_e_h_1, c_e, s16, s17)))),
% 294.39/186.90 inference(rewrite,[status(thm)],[])).
% 294.39/186.90 tff(26026,plain,
% 294.39/186.90 (((~m_c_h_element_v_out(c_e_h_1, c_e, s17)) | m_c_h_element_v_out(c_e_h_1, c_e, s16) | (~node18(c_e_h_1, c_e, s16, s17))) <=> (m_c_h_element_v_out(c_e_h_1, c_e, s16) | (~m_c_h_element_v_out(c_e_h_1, c_e, s17)) | (~node18(c_e_h_1, c_e, s16, s17)))),
% 294.39/186.90 inference(rewrite,[status(thm)],[])).
% 294.39/186.90 tff(26027,plain,
% 294.39/186.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s17)) | m_c_h_element_v_out(c_e_h_1, c_e, s16) | (~node18(c_e_h_1, c_e, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s16) | (~m_c_h_element_v_out(c_e_h_1, c_e, s17)) | (~node18(c_e_h_1, c_e, s16, s17))))),
% 294.39/186.90 inference(monotonicity,[status(thm)],[26026])).
% 294.39/186.90 tff(26028,plain,
% 294.39/186.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s17)) | m_c_h_element_v_out(c_e_h_1, c_e, s16) | (~node18(c_e_h_1, c_e, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s16) | (~m_c_h_element_v_out(c_e_h_1, c_e, s17)) | (~node18(c_e_h_1, c_e, s16, s17)))),
% 294.39/186.90 inference(transitivity,[status(thm)],[26027, 26025])).
% 294.39/186.90 tff(26029,plain,
% 294.39/186.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s17)) | m_c_h_element_v_out(c_e_h_1, c_e, s16) | (~node18(c_e_h_1, c_e, s16, s17)))),
% 294.39/186.90 inference(quant_inst,[status(thm)],[])).
% 294.39/186.90 tff(26030,plain,
% 294.39/186.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s16) | (~m_c_h_element_v_out(c_e_h_1, c_e, s17)) | (~node18(c_e_h_1, c_e, s16, s17))),
% 294.39/186.90 inference(modus_ponens,[status(thm)],[26029, 26028])).
% 294.39/186.90 tff(26031,plain,
% 294.39/186.90 ($false),
% 294.39/186.90 inference(unit_resolution,[status(thm)],[26030, 753, 26006, 26016, 26024])).
% 294.39/186.90 tff(26032,plain,((~node18(c_e_h_1, c_e, s16, s17)) | m_c_h_element_v_out(c_e_h_1, c_e, s16) | (~m_c_h_element_v_out(c_e_h_1, c_e, s17))), inference(lemma,lemma(discharge,[]))).
% 294.39/186.90 tff(26033,plain,
% 294.39/186.90 (~node18(c_e_h_1, c_e, s16, s17)),
% 294.39/186.90 inference(unit_resolution,[status(thm)],[26032, 26006, 26016])).
% 294.39/186.90 tff(26034,plain,
% 294.39/186.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s16, s17)) | node19(c_e_h_1, c_e, s16, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s16, s17)) | node19(c_e_h_1, c_e, s16, s17))),
% 294.39/186.90 inference(rewrite,[status(thm)],[])).
% 294.39/186.90 tff(26035,plain,
% 294.39/186.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s16, s17)) | node19(c_e_h_1, c_e, s16, s17))),
% 294.39/186.90 inference(quant_inst,[status(thm)],[])).
% 294.39/186.90 tff(26036,plain,
% 294.39/186.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s16, s17)) | node19(c_e_h_1, c_e, s16, s17)),
% 294.39/186.90 inference(modus_ponens,[status(thm)],[26035, 26034])).
% 294.39/186.90 tff(26037,plain,
% 294.39/186.90 (node19(c_e_h_1, c_e, s16, s17)),
% 294.39/186.90 inference(unit_resolution,[status(thm)],[26036, 190, 11967])).
% 294.39/186.90 tff(26038,plain,
% 294.39/186.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_e, s16, s17)) | node18(c_e_h_1, c_e, s16, s17) | node17(c_e_h_1, c_e, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s16, s17)) | node18(c_e_h_1, c_e, s16, s17) | node17(c_e_h_1, c_e, s16))),
% 294.39/186.90 inference(rewrite,[status(thm)],[])).
% 294.39/186.90 tff(26039,plain,
% 294.39/186.91 ((node17(c_e_h_1, c_e, s16) | node18(c_e_h_1, c_e, s16, s17) | (~node19(c_e_h_1, c_e, s16, s17))) <=> ((~node19(c_e_h_1, c_e, s16, s17)) | node18(c_e_h_1, c_e, s16, s17) | node17(c_e_h_1, c_e, s16))),
% 294.39/186.91 inference(rewrite,[status(thm)],[])).
% 294.39/186.91 tff(26040,plain,
% 294.39/186.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s16) | node18(c_e_h_1, c_e, s16, s17) | (~node19(c_e_h_1, c_e, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_e, s16, s17)) | node18(c_e_h_1, c_e, s16, s17) | node17(c_e_h_1, c_e, s16)))),
% 294.39/186.91 inference(monotonicity,[status(thm)],[26039])).
% 294.39/186.91 tff(26041,plain,
% 294.39/186.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s16) | node18(c_e_h_1, c_e, s16, s17) | (~node19(c_e_h_1, c_e, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s16, s17)) | node18(c_e_h_1, c_e, s16, s17) | node17(c_e_h_1, c_e, s16))),
% 294.39/186.91 inference(transitivity,[status(thm)],[26040, 26038])).
% 294.39/186.91 tff(26042,plain,
% 294.39/186.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s16) | node18(c_e_h_1, c_e, s16, s17) | (~node19(c_e_h_1, c_e, s16, s17)))),
% 294.39/186.91 inference(quant_inst,[status(thm)],[])).
% 294.39/186.91 tff(26043,plain,
% 294.39/186.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s16, s17)) | node18(c_e_h_1, c_e, s16, s17) | node17(c_e_h_1, c_e, s16)),
% 294.39/186.91 inference(modus_ponens,[status(thm)],[26042, 26041])).
% 294.39/186.91 tff(26044,plain,
% 294.39/186.91 (node18(c_e_h_1, c_e, s16, s17) | node17(c_e_h_1, c_e, s16)),
% 294.39/186.91 inference(unit_resolution,[status(thm)],[26043, 776, 26037])).
% 294.39/186.91 tff(26045,plain,
% 294.39/186.91 (node17(c_e_h_1, c_e, s16)),
% 294.39/186.91 inference(unit_resolution,[status(thm)],[26044, 26033])).
% 294.39/186.91 tff(26046,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_e, s16)), introduced(assumption)).
% 294.39/186.91 tff(26047,assumption,(~node15(c_e_h_1, c_e, s16, s17)), introduced(assumption)).
% 294.39/186.91 tff(26048,assumption,(node17(c_e_h_1, c_e, s16)), introduced(assumption)).
% 294.39/186.91 tff(26049,plain,
% 294.39/186.91 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s16)) | m_c_h_element_v_in1(c_e_h_1, c_e, s16) | (~node17(c_e_h_1, c_e, s16)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s16)) | m_c_h_element_v_in1(c_e_h_1, c_e, s16) | (~node17(c_e_h_1, c_e, s16)))),
% 294.39/186.91 inference(rewrite,[status(thm)],[])).
% 294.39/186.91 tff(26050,plain,
% 294.39/186.91 ((m_c_h_element_v_in1(c_e_h_1, c_e, s16) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s16)) | (~node17(c_e_h_1, c_e, s16))) <=> ((~m_c_h_element_v_in2(c_e_h_1, c_e, s16)) | m_c_h_element_v_in1(c_e_h_1, c_e, s16) | (~node17(c_e_h_1, c_e, s16)))),
% 294.39/186.91 inference(rewrite,[status(thm)],[])).
% 294.39/186.91 tff(26051,plain,
% 294.39/186.91 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s16) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s16)) | (~node17(c_e_h_1, c_e, s16)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s16)) | m_c_h_element_v_in1(c_e_h_1, c_e, s16) | (~node17(c_e_h_1, c_e, s16))))),
% 294.39/186.91 inference(monotonicity,[status(thm)],[26050])).
% 294.39/186.91 tff(26052,plain,
% 294.39/186.91 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s16) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s16)) | (~node17(c_e_h_1, c_e, s16)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s16)) | m_c_h_element_v_in1(c_e_h_1, c_e, s16) | (~node17(c_e_h_1, c_e, s16)))),
% 294.39/186.91 inference(transitivity,[status(thm)],[26051, 26049])).
% 294.39/186.91 tff(26053,plain,
% 294.39/186.91 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s16) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s16)) | (~node17(c_e_h_1, c_e, s16)))),
% 294.39/186.91 inference(quant_inst,[status(thm)],[])).
% 294.39/186.91 tff(26054,plain,
% 294.39/186.91 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s16)) | m_c_h_element_v_in1(c_e_h_1, c_e, s16) | (~node17(c_e_h_1, c_e, s16))),
% 294.39/186.91 inference(modus_ponens,[status(thm)],[26053, 26052])).
% 294.39/186.91 tff(26055,plain,
% 294.39/186.91 ((~m_c_h_element_v_in2(c_e_h_1, c_e, s16)) | m_c_h_element_v_in1(c_e_h_1, c_e, s16)),
% 294.39/186.91 inference(unit_resolution,[status(thm)],[26054, 859, 26048])).
% 294.39/186.91 tff(26056,plain,
% 294.39/186.91 (~m_c_h_element_v_in2(c_e_h_1, c_e, s16)),
% 294.39/186.91 inference(unit_resolution,[status(thm)],[26055, 26046])).
% 294.39/186.91 tff(26057,plain,
% 294.39/186.91 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s16)) | m_c_h_element_v_in1(c_e_h_1, c_e, s16) | m_c_h_element_v_in2(c_e_h_1, c_e, s16))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s16)) | m_c_h_element_v_in1(c_e_h_1, c_e, s16) | m_c_h_element_v_in2(c_e_h_1, c_e, s16))),
% 294.39/186.91 inference(rewrite,[status(thm)],[])).
% 294.39/186.91 tff(26058,plain,
% 294.39/186.91 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s16)) | m_c_h_element_v_in1(c_e_h_1, c_e, s16) | m_c_h_element_v_in2(c_e_h_1, c_e, s16))),
% 294.39/186.91 inference(quant_inst,[status(thm)],[])).
% 294.39/186.91 tff(26059,plain,
% 294.39/186.91 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s16)) | m_c_h_element_v_in1(c_e_h_1, c_e, s16) | m_c_h_element_v_in2(c_e_h_1, c_e, s16)),
% 294.39/186.91 inference(modus_ponens,[status(thm)],[26058, 26057])).
% 294.39/186.91 tff(26060,plain,
% 294.39/186.91 (~node16(c_e_h_1, c_e, s16)),
% 294.39/186.91 inference(unit_resolution,[status(thm)],[26059, 178, 26046, 26056])).
% 294.39/186.91 tff(26061,plain,
% 294.39/186.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_e, s16, s17)) | node14(c_e_h_1, c_e, s16, s17) | node15(c_e_h_1, c_e, s16, s17) | node16(c_e_h_1, c_e, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s16, s17)) | node14(c_e_h_1, c_e, s16, s17) | node15(c_e_h_1, c_e, s16, s17) | node16(c_e_h_1, c_e, s16))),
% 294.39/186.91 inference(rewrite,[status(thm)],[])).
% 294.39/186.91 tff(26062,plain,
% 294.39/186.91 ((node16(c_e_h_1, c_e, s16) | node14(c_e_h_1, c_e, s16, s17) | node15(c_e_h_1, c_e, s16, s17) | (~node19(c_e_h_1, c_e, s16, s17))) <=> ((~node19(c_e_h_1, c_e, s16, s17)) | node14(c_e_h_1, c_e, s16, s17) | node15(c_e_h_1, c_e, s16, s17) | node16(c_e_h_1, c_e, s16))),
% 294.39/186.91 inference(rewrite,[status(thm)],[])).
% 294.39/186.91 tff(26063,plain,
% 294.39/186.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s16) | node14(c_e_h_1, c_e, s16, s17) | node15(c_e_h_1, c_e, s16, s17) | (~node19(c_e_h_1, c_e, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_e, s16, s17)) | node14(c_e_h_1, c_e, s16, s17) | node15(c_e_h_1, c_e, s16, s17) | node16(c_e_h_1, c_e, s16)))),
% 294.39/186.91 inference(monotonicity,[status(thm)],[26062])).
% 294.39/186.91 tff(26064,plain,
% 294.39/186.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s16) | node14(c_e_h_1, c_e, s16, s17) | node15(c_e_h_1, c_e, s16, s17) | (~node19(c_e_h_1, c_e, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s16, s17)) | node14(c_e_h_1, c_e, s16, s17) | node15(c_e_h_1, c_e, s16, s17) | node16(c_e_h_1, c_e, s16))),
% 294.42/186.91 inference(transitivity,[status(thm)],[26063, 26061])).
% 294.42/186.91 tff(26065,plain,
% 294.42/186.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s16) | node14(c_e_h_1, c_e, s16, s17) | node15(c_e_h_1, c_e, s16, s17) | (~node19(c_e_h_1, c_e, s16, s17)))),
% 294.42/186.91 inference(quant_inst,[status(thm)],[])).
% 294.42/186.91 tff(26066,plain,
% 294.42/186.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s16, s17)) | node14(c_e_h_1, c_e, s16, s17) | node15(c_e_h_1, c_e, s16, s17) | node16(c_e_h_1, c_e, s16)),
% 294.42/186.91 inference(modus_ponens,[status(thm)],[26065, 26064])).
% 294.42/186.91 tff(26067,plain,
% 294.42/186.91 (node14(c_e_h_1, c_e, s16, s17) | node15(c_e_h_1, c_e, s16, s17) | node16(c_e_h_1, c_e, s16)),
% 294.42/186.91 inference(unit_resolution,[status(thm)],[26066, 204, 26037])).
% 294.42/186.91 tff(26068,plain,
% 294.42/186.91 (node14(c_e_h_1, c_e, s16, s17)),
% 294.42/186.91 inference(unit_resolution,[status(thm)],[26067, 26060, 26047])).
% 294.42/186.91 tff(26069,plain,
% 294.42/186.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s17)) | m_c_h_element_v_in1(c_e_h_1, c_e, s16) | (~node14(c_e_h_1, c_e, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s17)) | m_c_h_element_v_in1(c_e_h_1, c_e, s16) | (~node14(c_e_h_1, c_e, s16, s17)))),
% 294.42/186.91 inference(rewrite,[status(thm)],[])).
% 294.42/186.91 tff(26070,plain,
% 294.42/186.91 (((~node14(c_e_h_1, c_e, s16, s17)) | m_c_h_element_v_in1(c_e_h_1, c_e, s16) | (~m_c_h_element_v_out(c_e_h_1, c_e, s17))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_e, s17)) | m_c_h_element_v_in1(c_e_h_1, c_e, s16) | (~node14(c_e_h_1, c_e, s16, s17)))),
% 294.42/186.91 inference(rewrite,[status(thm)],[])).
% 294.42/186.91 tff(26071,plain,
% 294.42/186.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s16, s17)) | m_c_h_element_v_in1(c_e_h_1, c_e, s16) | (~m_c_h_element_v_out(c_e_h_1, c_e, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s17)) | m_c_h_element_v_in1(c_e_h_1, c_e, s16) | (~node14(c_e_h_1, c_e, s16, s17))))),
% 294.42/186.91 inference(monotonicity,[status(thm)],[26070])).
% 294.42/186.91 tff(26072,plain,
% 294.42/186.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s16, s17)) | m_c_h_element_v_in1(c_e_h_1, c_e, s16) | (~m_c_h_element_v_out(c_e_h_1, c_e, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s17)) | m_c_h_element_v_in1(c_e_h_1, c_e, s16) | (~node14(c_e_h_1, c_e, s16, s17)))),
% 294.42/186.91 inference(transitivity,[status(thm)],[26071, 26069])).
% 294.42/186.91 tff(26073,plain,
% 294.42/186.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s16, s17)) | m_c_h_element_v_in1(c_e_h_1, c_e, s16) | (~m_c_h_element_v_out(c_e_h_1, c_e, s17)))),
% 294.42/186.91 inference(quant_inst,[status(thm)],[])).
% 294.42/186.91 tff(26074,plain,
% 294.42/186.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s17)) | m_c_h_element_v_in1(c_e_h_1, c_e, s16) | (~node14(c_e_h_1, c_e, s16, s17))),
% 294.42/186.92 inference(modus_ponens,[status(thm)],[26073, 26072])).
% 294.42/186.92 tff(26075,plain,
% 294.42/186.92 ($false),
% 294.42/186.92 inference(unit_resolution,[status(thm)],[26074, 223, 26016, 26068, 26046])).
% 294.42/186.92 tff(26076,plain,(m_c_h_element_v_in1(c_e_h_1, c_e, s16) | (~m_c_h_element_v_out(c_e_h_1, c_e, s17)) | node15(c_e_h_1, c_e, s16, s17) | (~node17(c_e_h_1, c_e, s16))), inference(lemma,lemma(discharge,[]))).
% 294.42/186.92 tff(26077,plain,
% 294.42/186.92 (m_c_h_element_v_in1(c_e_h_1, c_e, s16)),
% 294.42/186.92 inference(unit_resolution,[status(thm)],[26076, 26045, 26016, 26023])).
% 294.42/186.92 tff(26078,plain,
% 294.42/186.92 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_e, s16)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s16)) | m_c_h_element_v_in2(c_e_h_1, c_e, s16))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s16)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s16)) | m_c_h_element_v_in2(c_e_h_1, c_e, s16))),
% 294.42/186.92 inference(rewrite,[status(thm)],[])).
% 294.42/186.92 tff(26079,plain,
% 294.42/186.92 (((~m_c_h_element_v_in1(c_e_h_1, c_e, s16)) | m_c_h_element_v_in2(c_e_h_1, c_e, s16) | (~node17(c_e_h_1, c_e, s16))) <=> ((~node17(c_e_h_1, c_e, s16)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s16)) | m_c_h_element_v_in2(c_e_h_1, c_e, s16))),
% 294.42/186.92 inference(rewrite,[status(thm)],[])).
% 294.42/186.92 tff(26080,plain,
% 294.42/186.92 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s16)) | m_c_h_element_v_in2(c_e_h_1, c_e, s16) | (~node17(c_e_h_1, c_e, s16)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_e, s16)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s16)) | m_c_h_element_v_in2(c_e_h_1, c_e, s16)))),
% 294.42/186.92 inference(monotonicity,[status(thm)],[26079])).
% 294.42/186.92 tff(26081,plain,
% 294.42/186.92 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s16)) | m_c_h_element_v_in2(c_e_h_1, c_e, s16) | (~node17(c_e_h_1, c_e, s16)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s16)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s16)) | m_c_h_element_v_in2(c_e_h_1, c_e, s16))),
% 294.42/186.92 inference(transitivity,[status(thm)],[26080, 26078])).
% 294.42/186.92 tff(26082,plain,
% 294.42/186.92 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s16)) | m_c_h_element_v_in2(c_e_h_1, c_e, s16) | (~node17(c_e_h_1, c_e, s16)))),
% 294.42/186.92 inference(quant_inst,[status(thm)],[])).
% 294.42/186.92 tff(26083,plain,
% 294.42/186.92 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s16)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s16)) | m_c_h_element_v_in2(c_e_h_1, c_e, s16)),
% 294.42/186.92 inference(modus_ponens,[status(thm)],[26082, 26081])).
% 294.42/186.92 tff(26084,plain,
% 294.42/186.92 ($false),
% 294.42/186.92 inference(unit_resolution,[status(thm)],[26083, 919, 26045, 26077, 26015])).
% 294.42/186.92 tff(26085,plain,(m_c_h_element_v_out(c_e_h_1, c_e, s16) | m_c_h_element_v_in2(c_e_h_1, c_e, s16) | (~m_c_h_element_v_out(c_e_h_1, c_e, s17))), inference(lemma,lemma(discharge,[]))).
% 294.42/186.92 tff(26086,plain,
% 294.42/186.92 (~m_c_h_element_v_out(c_e_h_1, c_e, s17)),
% 294.42/186.92 inference(unit_resolution,[status(thm)],[26085, 26014, 26006])).
% 294.42/186.92 tff(26087,assumption,(~node20(c_e_h_1, c_i, s16)), introduced(assumption)).
% 294.42/186.92 tff(26088,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s17)), introduced(assumption)).
% 294.42/186.92 tff(26089,assumption,(node22(c_e_h_1, c_i, s16, s17)), introduced(assumption)).
% 294.42/186.92 tff(26090,plain,
% 294.42/186.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s17)) | (~node22(c_e_h_1, c_i, s16, s17)) | m_and_h_gate_v_out(c_e_h_1, c_i, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s17)) | (~node22(c_e_h_1, c_i, s16, s17)) | m_and_h_gate_v_out(c_e_h_1, c_i, s16))),
% 294.42/186.92 inference(rewrite,[status(thm)],[])).
% 294.42/186.92 tff(26091,plain,
% 294.42/186.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s17)) | (~node22(c_e_h_1, c_i, s16, s17)) | m_and_h_gate_v_out(c_e_h_1, c_i, s16))),
% 294.42/186.92 inference(quant_inst,[status(thm)],[])).
% 294.42/186.92 tff(26092,plain,
% 294.42/186.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s17)) | (~node22(c_e_h_1, c_i, s16, s17)) | m_and_h_gate_v_out(c_e_h_1, c_i, s16)),
% 294.42/186.92 inference(modus_ponens,[status(thm)],[26091, 26090])).
% 294.42/186.92 tff(26093,plain,
% 294.42/186.92 ($false),
% 294.42/186.92 inference(unit_resolution,[status(thm)],[26092, 108, 26007, 26089, 26088])).
% 294.42/186.92 tff(26094,plain,((~node22(c_e_h_1, c_i, s16, s17)) | m_and_h_gate_v_out(c_e_h_1, c_i, s16) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s17))), inference(lemma,lemma(discharge,[]))).
% 294.42/186.92 tff(26095,plain,
% 294.42/186.92 (~node22(c_e_h_1, c_i, s16, s17)),
% 294.42/186.92 inference(unit_resolution,[status(thm)],[26094, 26088, 26007])).
% 294.42/186.92 tff(26096,assumption,(node21(c_e_h_1, c_i, s16, s17)), introduced(assumption)).
% 294.42/186.92 tff(26097,plain,
% 294.42/186.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s16) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s17)) | (~node21(c_e_h_1, c_i, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s16) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s17)) | (~node21(c_e_h_1, c_i, s16, s17)))),
% 294.42/186.92 inference(rewrite,[status(thm)],[])).
% 294.42/186.92 tff(26098,plain,
% 294.42/186.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s16) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s17)) | (~node21(c_e_h_1, c_i, s16, s17)))),
% 294.42/186.92 inference(quant_inst,[status(thm)],[])).
% 294.42/186.92 tff(26099,plain,
% 294.42/186.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s16) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s17)) | (~node21(c_e_h_1, c_i, s16, s17))),
% 294.42/186.92 inference(modus_ponens,[status(thm)],[26098, 26097])).
% 294.42/186.92 tff(26100,plain,
% 294.42/186.92 ($false),
% 294.42/186.92 inference(unit_resolution,[status(thm)],[26099, 52, 26096, 26088, 26087])).
% 294.42/186.92 tff(26101,plain,((~node21(c_e_h_1, c_i, s16, s17)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s17)) | node20(c_e_h_1, c_i, s16)), inference(lemma,lemma(discharge,[]))).
% 294.42/186.92 tff(26102,plain,
% 294.42/186.92 (~node21(c_e_h_1, c_i, s16, s17)),
% 294.42/186.92 inference(unit_resolution,[status(thm)],[26101, 26088, 26087])).
% 294.42/186.92 tff(26103,plain,
% 294.42/186.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s16, s17)) | node21(c_e_h_1, c_i, s16, s17) | node22(c_e_h_1, c_i, s16, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s16, s17)) | node21(c_e_h_1, c_i, s16, s17) | node22(c_e_h_1, c_i, s16, s17))),
% 294.42/186.92 inference(rewrite,[status(thm)],[])).
% 294.42/186.92 tff(26104,plain,
% 294.42/186.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s16, s17)) | node21(c_e_h_1, c_i, s16, s17) | node22(c_e_h_1, c_i, s16, s17))),
% 294.42/186.92 inference(quant_inst,[status(thm)],[])).
% 294.42/186.92 tff(26105,plain,
% 294.42/186.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s16, s17)) | node21(c_e_h_1, c_i, s16, s17) | node22(c_e_h_1, c_i, s16, s17)),
% 294.42/186.92 inference(modus_ponens,[status(thm)],[26104, 26103])).
% 294.42/186.92 tff(26106,plain,
% 294.42/186.92 (node21(c_e_h_1, c_i, s16, s17) | node22(c_e_h_1, c_i, s16, s17)),
% 294.42/186.92 inference(unit_resolution,[status(thm)],[26105, 82, 11967])).
% 294.43/186.92 tff(26107,plain,
% 294.43/186.92 ($false),
% 294.43/186.92 inference(unit_resolution,[status(thm)],[26106, 26102, 26095])).
% 294.43/186.92 tff(26108,plain,((~m_and_h_gate_v_out(c_e_h_1, c_i, s17)) | node20(c_e_h_1, c_i, s16) | m_and_h_gate_v_out(c_e_h_1, c_i, s16)), inference(lemma,lemma(discharge,[]))).
% 294.43/186.92 tff(26109,plain,
% 294.43/186.92 (~m_and_h_gate_v_out(c_e_h_1, c_i, s17)),
% 294.43/186.92 inference(unit_resolution,[status(thm)],[26108, 26007, 26087])).
% 294.43/186.92 tff(26110,assumption,(m_c_h_element_v_in2(c_e_h_1, c_e, s17)), introduced(assumption)).
% 294.43/186.92 tff(26111,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_i, s17)), introduced(assumption)).
% 294.43/186.92 tff(26112,plain,
% 294.43/186.92 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s17)) | m_and_h_gate_v_out(c_e_h_1, c_i, s17))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s17)) | m_and_h_gate_v_out(c_e_h_1, c_i, s17))),
% 294.43/186.92 inference(rewrite,[status(thm)],[])).
% 294.43/186.92 tff(26113,plain,
% 294.43/186.92 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s17)) | m_and_h_gate_v_out(c_e_h_1, c_i, s17))),
% 294.43/186.92 inference(quant_inst,[status(thm)],[])).
% 294.43/186.92 tff(26114,plain,
% 294.43/186.92 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s17)) | m_and_h_gate_v_out(c_e_h_1, c_i, s17)),
% 294.43/186.92 inference(modus_ponens,[status(thm)],[26113, 26112])).
% 294.43/186.92 tff(26115,plain,
% 294.43/186.92 ($false),
% 294.43/186.92 inference(unit_resolution,[status(thm)],[26114, 164, 26111, 26110])).
% 294.43/186.92 tff(26116,plain,((~m_c_h_element_v_in2(c_e_h_1, c_e, s17)) | m_and_h_gate_v_out(c_e_h_1, c_i, s17)), inference(lemma,lemma(discharge,[]))).
% 294.43/186.92 tff(26117,plain,
% 294.43/186.92 (~m_c_h_element_v_in2(c_e_h_1, c_e, s17)),
% 294.43/186.92 inference(unit_resolution,[status(thm)],[26116, 26109])).
% 294.43/186.92 tff(26118,assumption,(~m_c_h_element_v_out(c_e_h_1, c_e, s17)), introduced(assumption)).
% 294.43/186.92 tff(26119,assumption,(node18(c_e_h_1, c_e, s17, s18)), introduced(assumption)).
% 294.43/186.92 tff(26120,plain,
% 294.43/186.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s17) | (~m_c_h_element_v_out(c_e_h_1, c_e, s18)) | (~node18(c_e_h_1, c_e, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s17) | (~m_c_h_element_v_out(c_e_h_1, c_e, s18)) | (~node18(c_e_h_1, c_e, s17, s18)))),
% 294.43/186.92 inference(rewrite,[status(thm)],[])).
% 294.43/186.92 tff(26121,plain,
% 294.43/186.92 (((~m_c_h_element_v_out(c_e_h_1, c_e, s18)) | m_c_h_element_v_out(c_e_h_1, c_e, s17) | (~node18(c_e_h_1, c_e, s17, s18))) <=> (m_c_h_element_v_out(c_e_h_1, c_e, s17) | (~m_c_h_element_v_out(c_e_h_1, c_e, s18)) | (~node18(c_e_h_1, c_e, s17, s18)))),
% 294.43/186.92 inference(rewrite,[status(thm)],[])).
% 294.43/186.92 tff(26122,plain,
% 294.43/186.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s18)) | m_c_h_element_v_out(c_e_h_1, c_e, s17) | (~node18(c_e_h_1, c_e, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s17) | (~m_c_h_element_v_out(c_e_h_1, c_e, s18)) | (~node18(c_e_h_1, c_e, s17, s18))))),
% 294.43/186.92 inference(monotonicity,[status(thm)],[26121])).
% 294.43/186.92 tff(26123,plain,
% 294.43/186.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s18)) | m_c_h_element_v_out(c_e_h_1, c_e, s17) | (~node18(c_e_h_1, c_e, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s17) | (~m_c_h_element_v_out(c_e_h_1, c_e, s18)) | (~node18(c_e_h_1, c_e, s17, s18)))),
% 294.43/186.92 inference(transitivity,[status(thm)],[26122, 26120])).
% 294.43/186.93 tff(26124,plain,
% 294.43/186.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s18)) | m_c_h_element_v_out(c_e_h_1, c_e, s17) | (~node18(c_e_h_1, c_e, s17, s18)))),
% 294.43/186.93 inference(quant_inst,[status(thm)],[])).
% 294.43/186.93 tff(26125,plain,
% 294.43/186.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s17) | (~m_c_h_element_v_out(c_e_h_1, c_e, s18)) | (~node18(c_e_h_1, c_e, s17, s18))),
% 294.43/186.93 inference(modus_ponens,[status(thm)],[26124, 26123])).
% 294.43/186.93 tff(26126,plain,
% 294.43/186.93 ($false),
% 294.43/186.93 inference(unit_resolution,[status(thm)],[26125, 753, 26005, 26118, 26119])).
% 294.43/186.93 tff(26127,plain,((~node18(c_e_h_1, c_e, s17, s18)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s18)) | m_c_h_element_v_out(c_e_h_1, c_e, s17)), inference(lemma,lemma(discharge,[]))).
% 294.43/186.93 tff(26128,plain,
% 294.43/186.93 (~node18(c_e_h_1, c_e, s17, s18)),
% 294.43/186.93 inference(unit_resolution,[status(thm)],[26127, 26118, 26005])).
% 294.43/186.93 tff(26129,plain,
% 294.43/186.93 (succ(s17, s18) <=> succ(s17, s18)),
% 294.43/186.93 inference(rewrite,[status(thm)],[])).
% 294.43/186.93 tff(26130,axiom,(succ(s17, s18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound18')).
% 294.43/186.93 tff(26131,plain,
% 294.43/186.93 (succ(s17, s18)),
% 294.43/186.93 inference(modus_ponens,[status(thm)],[26130, 26129])).
% 294.43/186.93 tff(26132,plain,
% 294.43/186.93 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s17, s18)) | trans(s17, s18))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s17, s18)) | trans(s17, s18))),
% 294.43/186.93 inference(rewrite,[status(thm)],[])).
% 294.43/186.93 tff(26133,plain,
% 294.43/186.93 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s17, s18)) | trans(s17, s18))),
% 294.43/186.93 inference(quant_inst,[status(thm)],[])).
% 294.43/186.93 tff(26134,plain,
% 294.43/186.93 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s17, s18)) | trans(s17, s18)),
% 294.43/186.93 inference(modus_ponens,[status(thm)],[26133, 26132])).
% 294.43/186.93 tff(26135,plain,
% 294.43/186.93 (trans(s17, s18)),
% 294.43/186.93 inference(unit_resolution,[status(thm)],[26134, 26131, 65])).
% 294.43/186.93 tff(26136,plain,
% 294.43/186.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s17, s18)) | node19(c_e_h_1, c_e, s17, s18))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s17, s18)) | node19(c_e_h_1, c_e, s17, s18))),
% 294.43/186.93 inference(rewrite,[status(thm)],[])).
% 294.43/186.93 tff(26137,plain,
% 294.43/186.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s17, s18)) | node19(c_e_h_1, c_e, s17, s18))),
% 294.43/186.93 inference(quant_inst,[status(thm)],[])).
% 294.43/186.93 tff(26138,plain,
% 294.43/186.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s17, s18)) | node19(c_e_h_1, c_e, s17, s18)),
% 294.43/186.93 inference(modus_ponens,[status(thm)],[26137, 26136])).
% 294.43/186.93 tff(26139,plain,
% 294.43/186.93 (node19(c_e_h_1, c_e, s17, s18)),
% 294.43/186.93 inference(unit_resolution,[status(thm)],[26138, 190, 26135])).
% 294.43/186.93 tff(26140,plain,
% 294.43/186.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_1, c_e, s17, s18) | (~node19(c_e_h_1, c_e, s17, s18)) | node17(c_e_h_1, c_e, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_e, s17, s18) | (~node19(c_e_h_1, c_e, s17, s18)) | node17(c_e_h_1, c_e, s17))),
% 294.43/186.93 inference(rewrite,[status(thm)],[])).
% 294.43/186.93 tff(26141,plain,
% 294.43/186.93 ((node17(c_e_h_1, c_e, s17) | node18(c_e_h_1, c_e, s17, s18) | (~node19(c_e_h_1, c_e, s17, s18))) <=> (node18(c_e_h_1, c_e, s17, s18) | (~node19(c_e_h_1, c_e, s17, s18)) | node17(c_e_h_1, c_e, s17))),
% 294.43/186.93 inference(rewrite,[status(thm)],[])).
% 294.43/186.93 tff(26142,plain,
% 294.43/186.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s17) | node18(c_e_h_1, c_e, s17, s18) | (~node19(c_e_h_1, c_e, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_1, c_e, s17, s18) | (~node19(c_e_h_1, c_e, s17, s18)) | node17(c_e_h_1, c_e, s17)))),
% 294.43/186.93 inference(monotonicity,[status(thm)],[26141])).
% 294.43/186.93 tff(26143,plain,
% 294.43/186.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s17) | node18(c_e_h_1, c_e, s17, s18) | (~node19(c_e_h_1, c_e, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_e, s17, s18) | (~node19(c_e_h_1, c_e, s17, s18)) | node17(c_e_h_1, c_e, s17))),
% 294.43/186.93 inference(transitivity,[status(thm)],[26142, 26140])).
% 294.43/186.93 tff(26144,plain,
% 294.43/186.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s17) | node18(c_e_h_1, c_e, s17, s18) | (~node19(c_e_h_1, c_e, s17, s18)))),
% 294.43/186.93 inference(quant_inst,[status(thm)],[])).
% 294.43/186.93 tff(26145,plain,
% 294.43/186.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_e, s17, s18) | (~node19(c_e_h_1, c_e, s17, s18)) | node17(c_e_h_1, c_e, s17)),
% 294.43/186.93 inference(modus_ponens,[status(thm)],[26144, 26143])).
% 294.43/186.93 tff(26146,plain,
% 294.43/186.93 (node18(c_e_h_1, c_e, s17, s18) | node17(c_e_h_1, c_e, s17)),
% 294.43/186.93 inference(unit_resolution,[status(thm)],[26145, 776, 26139])).
% 294.43/186.93 tff(26147,plain,
% 294.43/186.93 (node17(c_e_h_1, c_e, s17)),
% 294.43/186.93 inference(unit_resolution,[status(thm)],[26146, 26128])).
% 294.43/186.93 tff(26148,assumption,(node15(c_e_h_1, c_e, s17, s18)), introduced(assumption)).
% 294.43/186.93 tff(26149,plain,
% 294.43/186.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s18)) | (~node15(c_e_h_1, c_e, s17, s18)) | m_c_h_element_v_out(c_e_h_1, c_e, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s18)) | (~node15(c_e_h_1, c_e, s17, s18)) | m_c_h_element_v_out(c_e_h_1, c_e, s17))),
% 294.43/186.93 inference(rewrite,[status(thm)],[])).
% 294.43/186.93 tff(26150,plain,
% 294.43/186.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s18)) | (~node15(c_e_h_1, c_e, s17, s18)) | m_c_h_element_v_out(c_e_h_1, c_e, s17))),
% 294.43/186.93 inference(quant_inst,[status(thm)],[])).
% 294.43/186.93 tff(26151,plain,
% 294.43/186.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s18)) | (~node15(c_e_h_1, c_e, s17, s18)) | m_c_h_element_v_out(c_e_h_1, c_e, s17)),
% 294.43/186.93 inference(modus_ponens,[status(thm)],[26150, 26149])).
% 294.43/186.93 tff(26152,plain,
% 294.43/186.93 ($false),
% 294.43/186.93 inference(unit_resolution,[status(thm)],[26151, 147, 26005, 26118, 26148])).
% 294.43/186.93 tff(26153,plain,((~node15(c_e_h_1, c_e, s17, s18)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s18)) | m_c_h_element_v_out(c_e_h_1, c_e, s17)), inference(lemma,lemma(discharge,[]))).
% 294.43/186.93 tff(26154,plain,
% 294.43/186.93 (~node15(c_e_h_1, c_e, s17, s18)),
% 294.43/186.93 inference(unit_resolution,[status(thm)],[26153, 26118, 26005])).
% 294.43/186.93 tff(26155,assumption,(~node15(c_e_h_1, c_e, s17, s18)), introduced(assumption)).
% 294.43/186.93 tff(26156,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_e, s17)), introduced(assumption)).
% 294.43/186.93 tff(26157,assumption,(node14(c_e_h_1, c_e, s17, s18)), introduced(assumption)).
% 294.43/186.93 tff(26158,plain,
% 294.43/186.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s18)) | m_c_h_element_v_in1(c_e_h_1, c_e, s17) | (~node14(c_e_h_1, c_e, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s18)) | m_c_h_element_v_in1(c_e_h_1, c_e, s17) | (~node14(c_e_h_1, c_e, s17, s18)))),
% 294.43/186.93 inference(rewrite,[status(thm)],[])).
% 294.43/186.93 tff(26159,plain,
% 294.43/186.93 (((~node14(c_e_h_1, c_e, s17, s18)) | m_c_h_element_v_in1(c_e_h_1, c_e, s17) | (~m_c_h_element_v_out(c_e_h_1, c_e, s18))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_e, s18)) | m_c_h_element_v_in1(c_e_h_1, c_e, s17) | (~node14(c_e_h_1, c_e, s17, s18)))),
% 294.43/186.94 inference(rewrite,[status(thm)],[])).
% 294.43/186.94 tff(26160,plain,
% 294.43/186.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s17, s18)) | m_c_h_element_v_in1(c_e_h_1, c_e, s17) | (~m_c_h_element_v_out(c_e_h_1, c_e, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s18)) | m_c_h_element_v_in1(c_e_h_1, c_e, s17) | (~node14(c_e_h_1, c_e, s17, s18))))),
% 294.43/186.94 inference(monotonicity,[status(thm)],[26159])).
% 294.43/186.94 tff(26161,plain,
% 294.43/186.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s17, s18)) | m_c_h_element_v_in1(c_e_h_1, c_e, s17) | (~m_c_h_element_v_out(c_e_h_1, c_e, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s18)) | m_c_h_element_v_in1(c_e_h_1, c_e, s17) | (~node14(c_e_h_1, c_e, s17, s18)))),
% 294.43/186.94 inference(transitivity,[status(thm)],[26160, 26158])).
% 294.43/186.94 tff(26162,plain,
% 294.43/186.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s17, s18)) | m_c_h_element_v_in1(c_e_h_1, c_e, s17) | (~m_c_h_element_v_out(c_e_h_1, c_e, s18)))),
% 294.43/186.94 inference(quant_inst,[status(thm)],[])).
% 294.43/186.94 tff(26163,plain,
% 294.43/186.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s18)) | m_c_h_element_v_in1(c_e_h_1, c_e, s17) | (~node14(c_e_h_1, c_e, s17, s18))),
% 294.43/186.94 inference(modus_ponens,[status(thm)],[26162, 26161])).
% 294.43/186.94 tff(26164,plain,
% 294.43/186.94 ($false),
% 294.43/186.94 inference(unit_resolution,[status(thm)],[26163, 223, 26005, 26157, 26156])).
% 294.43/186.94 tff(26165,plain,((~node14(c_e_h_1, c_e, s17, s18)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s18)) | m_c_h_element_v_in1(c_e_h_1, c_e, s17)), inference(lemma,lemma(discharge,[]))).
% 294.43/186.94 tff(26166,plain,
% 294.43/186.94 (~node14(c_e_h_1, c_e, s17, s18)),
% 294.43/186.94 inference(unit_resolution,[status(thm)],[26165, 26156, 26005])).
% 294.43/186.94 tff(26167,assumption,(node17(c_e_h_1, c_e, s17)), introduced(assumption)).
% 294.43/186.94 tff(26168,plain,
% 294.43/186.94 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s17)) | m_c_h_element_v_in1(c_e_h_1, c_e, s17) | (~node17(c_e_h_1, c_e, s17)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s17)) | m_c_h_element_v_in1(c_e_h_1, c_e, s17) | (~node17(c_e_h_1, c_e, s17)))),
% 294.43/186.94 inference(rewrite,[status(thm)],[])).
% 294.43/186.94 tff(26169,plain,
% 294.43/186.94 ((m_c_h_element_v_in1(c_e_h_1, c_e, s17) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s17)) | (~node17(c_e_h_1, c_e, s17))) <=> ((~m_c_h_element_v_in2(c_e_h_1, c_e, s17)) | m_c_h_element_v_in1(c_e_h_1, c_e, s17) | (~node17(c_e_h_1, c_e, s17)))),
% 294.43/186.94 inference(rewrite,[status(thm)],[])).
% 294.43/186.94 tff(26170,plain,
% 294.43/186.94 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s17) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s17)) | (~node17(c_e_h_1, c_e, s17)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s17)) | m_c_h_element_v_in1(c_e_h_1, c_e, s17) | (~node17(c_e_h_1, c_e, s17))))),
% 294.43/186.94 inference(monotonicity,[status(thm)],[26169])).
% 294.43/186.94 tff(26171,plain,
% 294.43/186.94 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s17) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s17)) | (~node17(c_e_h_1, c_e, s17)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s17)) | m_c_h_element_v_in1(c_e_h_1, c_e, s17) | (~node17(c_e_h_1, c_e, s17)))),
% 294.43/186.94 inference(transitivity,[status(thm)],[26170, 26168])).
% 294.43/186.94 tff(26172,plain,
% 294.43/186.94 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s17) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s17)) | (~node17(c_e_h_1, c_e, s17)))),
% 294.43/186.94 inference(quant_inst,[status(thm)],[])).
% 294.43/186.94 tff(26173,plain,
% 294.43/186.94 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s17)) | m_c_h_element_v_in1(c_e_h_1, c_e, s17) | (~node17(c_e_h_1, c_e, s17))),
% 294.43/186.94 inference(modus_ponens,[status(thm)],[26172, 26171])).
% 294.43/186.94 tff(26174,plain,
% 294.43/186.94 ((~m_c_h_element_v_in2(c_e_h_1, c_e, s17)) | m_c_h_element_v_in1(c_e_h_1, c_e, s17)),
% 294.43/186.94 inference(unit_resolution,[status(thm)],[26173, 859, 26167])).
% 294.43/186.94 tff(26175,plain,
% 294.43/186.94 (~m_c_h_element_v_in2(c_e_h_1, c_e, s17)),
% 294.43/186.94 inference(unit_resolution,[status(thm)],[26174, 26156])).
% 294.43/186.94 tff(26176,assumption,(node16(c_e_h_1, c_e, s17)), introduced(assumption)).
% 294.43/186.94 tff(26177,plain,
% 294.43/186.94 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s17)) | m_c_h_element_v_in1(c_e_h_1, c_e, s17) | m_c_h_element_v_in2(c_e_h_1, c_e, s17))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s17)) | m_c_h_element_v_in1(c_e_h_1, c_e, s17) | m_c_h_element_v_in2(c_e_h_1, c_e, s17))),
% 294.43/186.94 inference(rewrite,[status(thm)],[])).
% 294.43/186.94 tff(26178,plain,
% 294.43/186.94 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s17)) | m_c_h_element_v_in1(c_e_h_1, c_e, s17) | m_c_h_element_v_in2(c_e_h_1, c_e, s17))),
% 294.43/186.94 inference(quant_inst,[status(thm)],[])).
% 294.43/186.94 tff(26179,plain,
% 294.43/186.94 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s17)) | m_c_h_element_v_in1(c_e_h_1, c_e, s17) | m_c_h_element_v_in2(c_e_h_1, c_e, s17)),
% 294.43/186.94 inference(modus_ponens,[status(thm)],[26178, 26177])).
% 294.43/186.94 tff(26180,plain,
% 294.43/186.94 (m_c_h_element_v_in1(c_e_h_1, c_e, s17) | m_c_h_element_v_in2(c_e_h_1, c_e, s17)),
% 294.43/186.94 inference(unit_resolution,[status(thm)],[26179, 178, 26176])).
% 294.43/186.94 tff(26181,plain,
% 294.43/186.94 ($false),
% 294.43/186.94 inference(unit_resolution,[status(thm)],[26180, 26175, 26156])).
% 294.43/186.94 tff(26182,plain,(m_c_h_element_v_in1(c_e_h_1, c_e, s17) | (~node16(c_e_h_1, c_e, s17)) | (~node17(c_e_h_1, c_e, s17))), inference(lemma,lemma(discharge,[]))).
% 294.43/186.94 tff(26183,plain,
% 294.43/186.94 (~node16(c_e_h_1, c_e, s17)),
% 294.43/186.94 inference(unit_resolution,[status(thm)],[26182, 26156, 26167])).
% 294.43/186.94 tff(26184,plain,
% 294.43/186.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_1, c_e, s17, s18) | node15(c_e_h_1, c_e, s17, s18) | (~node19(c_e_h_1, c_e, s17, s18)) | node16(c_e_h_1, c_e, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_e, s17, s18) | node15(c_e_h_1, c_e, s17, s18) | (~node19(c_e_h_1, c_e, s17, s18)) | node16(c_e_h_1, c_e, s17))),
% 294.43/186.94 inference(rewrite,[status(thm)],[])).
% 294.43/186.94 tff(26185,plain,
% 294.43/186.94 ((node16(c_e_h_1, c_e, s17) | node14(c_e_h_1, c_e, s17, s18) | node15(c_e_h_1, c_e, s17, s18) | (~node19(c_e_h_1, c_e, s17, s18))) <=> (node14(c_e_h_1, c_e, s17, s18) | node15(c_e_h_1, c_e, s17, s18) | (~node19(c_e_h_1, c_e, s17, s18)) | node16(c_e_h_1, c_e, s17))),
% 294.43/186.94 inference(rewrite,[status(thm)],[])).
% 294.43/186.94 tff(26186,plain,
% 294.43/186.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s17) | node14(c_e_h_1, c_e, s17, s18) | node15(c_e_h_1, c_e, s17, s18) | (~node19(c_e_h_1, c_e, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_1, c_e, s17, s18) | node15(c_e_h_1, c_e, s17, s18) | (~node19(c_e_h_1, c_e, s17, s18)) | node16(c_e_h_1, c_e, s17)))),
% 294.43/186.94 inference(monotonicity,[status(thm)],[26185])).
% 294.43/186.94 tff(26187,plain,
% 294.43/186.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s17) | node14(c_e_h_1, c_e, s17, s18) | node15(c_e_h_1, c_e, s17, s18) | (~node19(c_e_h_1, c_e, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_e, s17, s18) | node15(c_e_h_1, c_e, s17, s18) | (~node19(c_e_h_1, c_e, s17, s18)) | node16(c_e_h_1, c_e, s17))),
% 294.43/186.94 inference(transitivity,[status(thm)],[26186, 26184])).
% 294.43/186.94 tff(26188,plain,
% 294.43/186.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s17) | node14(c_e_h_1, c_e, s17, s18) | node15(c_e_h_1, c_e, s17, s18) | (~node19(c_e_h_1, c_e, s17, s18)))),
% 294.43/186.94 inference(quant_inst,[status(thm)],[])).
% 294.43/186.94 tff(26189,plain,
% 294.43/186.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_e, s17, s18) | node15(c_e_h_1, c_e, s17, s18) | (~node19(c_e_h_1, c_e, s17, s18)) | node16(c_e_h_1, c_e, s17)),
% 294.43/186.94 inference(modus_ponens,[status(thm)],[26188, 26187])).
% 294.43/186.94 tff(26190,plain,
% 294.43/186.94 (node14(c_e_h_1, c_e, s17, s18) | node15(c_e_h_1, c_e, s17, s18) | node16(c_e_h_1, c_e, s17)),
% 294.43/186.94 inference(unit_resolution,[status(thm)],[26189, 204, 26139])).
% 294.43/186.94 tff(26191,plain,
% 294.43/186.94 ($false),
% 294.43/186.94 inference(unit_resolution,[status(thm)],[26190, 26183, 26166, 26155])).
% 294.43/186.94 tff(26192,plain,(m_c_h_element_v_in1(c_e_h_1, c_e, s17) | node15(c_e_h_1, c_e, s17, s18) | (~node17(c_e_h_1, c_e, s17)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s18))), inference(lemma,lemma(discharge,[]))).
% 294.43/186.94 tff(26193,plain,
% 294.43/186.94 (m_c_h_element_v_in1(c_e_h_1, c_e, s17)),
% 294.43/186.94 inference(unit_resolution,[status(thm)],[26192, 26147, 26005, 26154])).
% 294.43/186.94 tff(26194,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_e, s17)), introduced(assumption)).
% 294.43/186.94 tff(26195,plain,
% 294.43/186.94 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_e, s17)) | m_c_h_element_v_in2(c_e_h_1, c_e, s17) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s17)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s17)) | m_c_h_element_v_in2(c_e_h_1, c_e, s17) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s17)))),
% 294.43/186.94 inference(rewrite,[status(thm)],[])).
% 294.43/186.94 tff(26196,plain,
% 294.43/186.94 (((~m_c_h_element_v_in1(c_e_h_1, c_e, s17)) | m_c_h_element_v_in2(c_e_h_1, c_e, s17) | (~node17(c_e_h_1, c_e, s17))) <=> ((~node17(c_e_h_1, c_e, s17)) | m_c_h_element_v_in2(c_e_h_1, c_e, s17) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s17)))),
% 294.43/186.94 inference(rewrite,[status(thm)],[])).
% 294.43/186.94 tff(26197,plain,
% 294.43/186.94 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s17)) | m_c_h_element_v_in2(c_e_h_1, c_e, s17) | (~node17(c_e_h_1, c_e, s17)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_e, s17)) | m_c_h_element_v_in2(c_e_h_1, c_e, s17) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s17))))),
% 294.43/186.94 inference(monotonicity,[status(thm)],[26196])).
% 294.43/186.94 tff(26198,plain,
% 294.43/186.94 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s17)) | m_c_h_element_v_in2(c_e_h_1, c_e, s17) | (~node17(c_e_h_1, c_e, s17)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s17)) | m_c_h_element_v_in2(c_e_h_1, c_e, s17) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s17)))),
% 294.43/186.95 inference(transitivity,[status(thm)],[26197, 26195])).
% 294.43/186.95 tff(26199,plain,
% 294.43/186.95 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s17)) | m_c_h_element_v_in2(c_e_h_1, c_e, s17) | (~node17(c_e_h_1, c_e, s17)))),
% 294.43/186.95 inference(quant_inst,[status(thm)],[])).
% 294.43/186.95 tff(26200,plain,
% 294.43/186.95 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s17)) | m_c_h_element_v_in2(c_e_h_1, c_e, s17) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s17))),
% 294.43/186.95 inference(modus_ponens,[status(thm)],[26199, 26198])).
% 294.43/186.95 tff(26201,plain,
% 294.43/186.95 ((~node17(c_e_h_1, c_e, s17)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s17))),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[26200, 919, 26194])).
% 294.43/186.95 tff(26202,plain,
% 294.43/186.95 ($false),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[26201, 26193, 26147])).
% 294.43/186.95 tff(26203,plain,(m_c_h_element_v_out(c_e_h_1, c_e, s17) | m_c_h_element_v_in2(c_e_h_1, c_e, s17) | (~m_c_h_element_v_out(c_e_h_1, c_e, s18))), inference(lemma,lemma(discharge,[]))).
% 294.43/186.95 tff(26204,plain,
% 294.43/186.95 ($false),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[26203, 26117, 26086, 26005])).
% 294.43/186.95 tff(26205,plain,(m_and_h_gate_v_out(c_e_h_1, c_i, s16) | (~m_c_h_element_v_out(c_e_h_1, c_e, s18)) | m_c_h_element_v_out(c_e_h_1, c_e, s16) | node20(c_e_h_1, c_i, s16)), inference(lemma,lemma(discharge,[]))).
% 294.43/186.95 tff(26206,plain,
% 294.43/186.95 (m_and_h_gate_v_out(c_e_h_1, c_i, s16) | (~m_c_h_element_v_out(c_e_h_1, c_e, s18)) | node20(c_e_h_1, c_i, s16)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[26205, 26004])).
% 294.43/186.95 tff(26207,plain,
% 294.43/186.95 (~m_c_h_element_v_out(c_e_h_1, c_e, s18)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[26206, 25573, 24266])).
% 294.43/186.95 tff(26208,plain,
% 294.43/186.95 (~m_c_h_element_v_in2(c_e_h_3, c_f, s10)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[11683, 11422])).
% 294.43/186.95 tff(26209,plain,
% 294.43/186.95 (~m_c_h_element_v_out(c_e_h_3, c_f, s10)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[11675, 11584, 11586])).
% 294.43/186.95 tff(26210,plain,
% 294.43/186.95 (~m_c_h_element_v_out(c_e_h_3, c_f, s11)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[11758, 26209, 11751])).
% 294.43/186.95 tff(26211,plain,
% 294.43/186.95 (~m_c_h_element_v_out(c_e_h_3, c_f, s12)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[11830, 26210, 11784])).
% 294.43/186.95 tff(26212,plain,
% 294.43/186.95 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s10)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[13007, 26209])).
% 294.43/186.95 tff(26213,plain,
% 294.43/186.95 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s11)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[13228, 26210])).
% 294.43/186.95 tff(26214,plain,
% 294.43/186.95 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[13287, 11586, 11584, 13231])).
% 294.43/186.95 tff(26215,plain,
% 294.43/186.95 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s12)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[13369, 26214, 13342, 13343])).
% 294.43/186.95 tff(26216,plain,
% 294.43/186.95 (m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s12)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[13223, 26215])).
% 294.43/186.95 tff(26217,plain,
% 294.43/186.95 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[13094, 13232])).
% 294.43/186.95 tff(26218,plain,
% 294.43/186.95 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s11)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[13157, 26217, 13148])).
% 294.43/186.95 tff(26219,plain,
% 294.43/186.95 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s11)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[13162, 5601, 26218])).
% 294.43/186.95 tff(26220,plain,
% 294.43/186.95 (~node9(c_e_h_3, c_n, s11)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[13166, 4972, 26219])).
% 294.43/186.95 tff(26221,plain,
% 294.43/186.95 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s10)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[13170, 5601, 26217])).
% 294.43/186.95 tff(26222,plain,
% 294.43/186.95 (~node9(c_e_h_3, c_n, s10)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[13174, 4972, 26221])).
% 294.43/186.95 tff(26223,plain,
% 294.43/186.95 (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[13196, 26222])).
% 294.43/186.95 tff(26224,plain,
% 294.43/186.95 ($false),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[13217, 26223, 26220, 26216])).
% 294.43/186.95 tff(26225,plain,(m_c_h_element_v_out(c_e_h_3, c_f, s9) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s10)) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s12)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s13) | m_c_h_element_v_in2(c_e_h_3, c_f, s9) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s11))), inference(lemma,lemma(discharge,[]))).
% 294.43/186.95 tff(26226,plain,
% 294.43/186.95 (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s12)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[26225, 26213, 11586, 13343, 11584, 26212])).
% 294.43/186.95 tff(26227,plain,
% 294.43/186.95 ($false),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[13340, 26226, 26211])).
% 294.43/186.95 tff(26228,plain,(m_c_h_element_v_in2(c_e_h_3, c_f, s9) | m_c_h_element_v_out(c_e_h_3, c_f, s9) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s13) | m_c_h_element_v_in2(c_e_h_3, c_f, s11) | m_c_h_element_v_in2(c_e_h_3, c_f, s10)), inference(lemma,lemma(discharge,[]))).
% 294.43/186.95 tff(26229,plain,
% 294.43/186.95 (m_c_h_element_v_in2(c_e_h_3, c_f, s9) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s13) | m_c_h_element_v_in2(c_e_h_3, c_f, s11) | m_c_h_element_v_in2(c_e_h_3, c_f, s10)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[26228, 11583])).
% 294.43/186.95 tff(26230,plain,
% 294.43/186.95 (m_c_h_element_v_in2(c_e_h_3, c_f, s11)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[26229, 13343, 11584, 26208])).
% 294.43/186.95 tff(26231,plain,
% 294.43/186.95 (m_and_h_gate_v_out(c_e_h_3, c_i, s11)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[11474, 26230])).
% 294.43/186.95 tff(26232,plain,
% 294.43/186.95 (node20(c_e_h_3, c_i, s10)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[11435, 26231, 11422])).
% 294.43/186.95 tff(26233,plain,
% 294.43/186.95 (m_and_h_gate_v_in1(c_e_h_3, c_i, s10)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[11227, 38, 26232])).
% 294.43/186.95 tff(26234,plain,
% 294.43/186.95 (m_c_h_element_v_out(c_e_h_3, c_h, s10)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[11223, 619, 26233])).
% 294.43/186.95 tff(26235,plain,
% 294.43/186.95 (~m_or_h_gate_v_out(c_e_h_3, c_g, s8)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[20223, 20186, 10016, 20178])).
% 294.43/186.95 tff(26236,plain,
% 294.43/186.95 (~m_and_h_gate_v_out(c_e_h_3, c_l, s8)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[21845, 26235, 20178, 20179])).
% 294.43/186.95 tff(26237,plain,
% 294.43/186.95 (~m_or_h_gate_v_out(c_e_h_3, c_j, s8)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[5885, 20178])).
% 294.43/186.95 tff(26238,plain,
% 294.43/186.95 (~m_c_h_element_v_out(c_e_h_3, c_h, s8)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[7551, 20487])).
% 294.43/186.95 tff(26239,plain,
% 294.43/186.95 (m_or_h_gate_v_in1(c_e_h_3, c_j, s8)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[10952, 26238, 7655, 26237])).
% 294.43/186.95 tff(26240,plain,
% 294.43/186.95 ($false),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[10682, 26239, 26236])).
% 294.43/186.95 tff(26241,plain,(m_and_h_gate_v_out(c_e_h_3, c_c, s7) | (~m_c_h_element_v_out(c_e_h_3, c_h, s10))), inference(lemma,lemma(discharge,[]))).
% 294.43/186.95 tff(26242,plain,
% 294.43/186.95 (m_and_h_gate_v_out(c_e_h_3, c_c, s7)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[26241, 26234])).
% 294.43/186.95 tff(26243,plain,
% 294.43/186.95 (m_mutex_h_half_v_out(c_e_h_3, c_a, s9)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[20764, 26242])).
% 294.43/186.95 tff(26244,plain,
% 294.43/186.95 (m_mutex_h_half_v_other_h_out(c_e_h_3, c_b, s9)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[20759, 26243])).
% 294.43/186.95 tff(26245,plain,
% 294.43/186.95 (~m_mutex_h_half_v_out(c_e_h_3, c_b, s9)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[20742, 26244])).
% 294.43/186.95 tff(26246,plain,
% 294.43/186.95 (~m_and_h_gate_v_in1(c_e_h_3, c_d, s9)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[21601, 26245])).
% 294.43/186.95 tff(26247,plain,
% 294.43/186.95 (~node20(c_e_h_3, c_d, s9)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[21609, 26246])).
% 294.43/186.95 tff(26248,plain,
% 294.43/186.95 (~m_c_h_element_v_out(c_e_h_3, c_f, s10)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[11676, 11584])).
% 294.43/186.95 tff(26249,plain,
% 294.43/186.95 (~m_c_h_element_v_out(c_e_h_3, c_f, s11)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[11758, 26248, 26208])).
% 294.43/186.95 tff(26250,plain,
% 294.43/186.95 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s10)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[13007, 26248])).
% 294.43/186.95 tff(26251,plain,
% 294.43/186.95 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s11)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[13158, 26250])).
% 294.43/186.95 tff(26252,plain,
% 294.43/186.95 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s11)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[13162, 5601, 26251])).
% 294.43/186.95 tff(26253,plain,
% 294.43/186.95 (~node9(c_e_h_3, c_n, s11)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[13166, 4972, 26252])).
% 294.43/186.95 tff(26254,plain,
% 294.43/186.95 (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s12)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[13218, 26253])).
% 294.43/186.95 tff(26255,plain,
% 294.43/186.95 (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s12)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[13223, 26254])).
% 294.43/186.95 tff(26256,plain,
% 294.43/186.95 (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s11)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[13270, 13197])).
% 294.43/186.95 tff(26257,plain,
% 294.43/186.95 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s11)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[13228, 11761])).
% 294.43/186.95 tff(26258,plain,
% 294.43/186.95 (~node11(c_e_h_3, c_m, s11, s12)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[13249, 13230, 13241])).
% 294.43/186.95 tff(26259,plain,
% 294.43/186.95 (~node10(c_e_h_3, c_m, s11, s12)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[13265, 13230, 13231, 13257])).
% 294.43/186.95 tff(26260,plain,
% 294.43/186.95 ($false),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[13254, 26259, 26258])).
% 294.43/186.95 tff(26261,plain,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s11)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s11)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s11))), inference(lemma,lemma(discharge,[]))).
% 294.43/186.95 tff(26262,plain,
% 294.43/186.95 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[26261, 26257, 13241, 13257])).
% 294.43/186.95 tff(26263,plain,
% 294.43/186.95 (m_c_h_element_v_in2(c_e_h_3, c_f, s11)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[11830, 11760, 11761])).
% 294.43/186.95 tff(26264,plain,
% 294.43/186.95 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s11) | (~node17(c_e_h_3, c_f, s11)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_3, c_f, s11) | (~node17(c_e_h_3, c_f, s11)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s11)))),
% 294.43/186.95 inference(rewrite,[status(thm)],[])).
% 294.43/186.95 tff(26265,plain,
% 294.43/186.95 ((m_c_h_element_v_in1(c_e_h_3, c_f, s11) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s11)) | (~node17(c_e_h_3, c_f, s11))) <=> (m_c_h_element_v_in1(c_e_h_3, c_f, s11) | (~node17(c_e_h_3, c_f, s11)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s11)))),
% 294.43/186.95 inference(rewrite,[status(thm)],[])).
% 294.43/186.95 tff(26266,plain,
% 294.43/186.95 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s11) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s11)) | (~node17(c_e_h_3, c_f, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s11) | (~node17(c_e_h_3, c_f, s11)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s11))))),
% 294.43/186.95 inference(monotonicity,[status(thm)],[26265])).
% 294.43/186.95 tff(26267,plain,
% 294.43/186.95 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s11) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s11)) | (~node17(c_e_h_3, c_f, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_3, c_f, s11) | (~node17(c_e_h_3, c_f, s11)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s11)))),
% 294.43/186.95 inference(transitivity,[status(thm)],[26266, 26264])).
% 294.43/186.95 tff(26268,plain,
% 294.43/186.95 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s11) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s11)) | (~node17(c_e_h_3, c_f, s11)))),
% 294.43/186.95 inference(quant_inst,[status(thm)],[])).
% 294.43/186.95 tff(26269,plain,
% 294.43/186.95 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_3, c_f, s11) | (~node17(c_e_h_3, c_f, s11)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s11))),
% 294.43/186.95 inference(modus_ponens,[status(thm)],[26268, 26267])).
% 294.43/186.95 tff(26270,plain,
% 294.43/186.95 ((~node17(c_e_h_3, c_f, s11)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s11))),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[26269, 859, 11805])).
% 294.43/186.95 tff(26271,plain,
% 294.43/186.95 (~node17(c_e_h_3, c_f, s11)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[26270, 26263])).
% 294.43/186.95 tff(26272,plain,
% 294.43/186.95 ($false),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[11782, 26271, 11771])).
% 294.43/186.95 tff(26273,plain,((~m_c_h_element_v_out(c_e_h_3, c_f, s12)) | m_c_h_element_v_in1(c_e_h_3, c_f, s11) | m_c_h_element_v_out(c_e_h_3, c_f, s11)), inference(lemma,lemma(discharge,[]))).
% 294.43/186.95 tff(26274,plain,
% 294.43/186.95 (~m_c_h_element_v_out(c_e_h_3, c_f, s12)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[26273, 11761, 11805])).
% 294.43/186.95 tff(26275,plain,
% 294.43/186.95 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s12)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[13340, 26274])).
% 294.43/186.95 tff(26276,plain,
% 294.43/186.95 ($false),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[13369, 26275, 26262, 13335, 13343])).
% 294.43/186.95 tff(26277,plain,(m_c_h_element_v_out(c_e_h_3, c_f, s11) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s12)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s11)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s11)) | m_c_h_element_v_in1(c_e_h_3, c_f, s11)), inference(lemma,lemma(discharge,[]))).
% 294.43/186.95 tff(26278,plain,
% 294.43/186.95 (m_c_h_element_v_out(c_e_h_3, c_f, s11) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s12)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s11)) | m_c_h_element_v_in1(c_e_h_3, c_f, s11)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[26277, 26256])).
% 294.43/186.95 tff(26279,plain,
% 294.43/186.95 (m_c_h_element_v_in1(c_e_h_3, c_f, s11)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[26278, 13343, 26251, 26255, 26249])).
% 294.43/186.95 tff(26280,assumption,(m_c_h_element_v_in1(c_e_h_3, c_f, s11)), introduced(assumption)).
% 294.43/186.95 tff(26281,plain,
% 294.43/186.95 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s11)) | m_and_h_gate_v_out(c_e_h_3, c_d, s11))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s11)) | m_and_h_gate_v_out(c_e_h_3, c_d, s11))),
% 294.43/186.95 inference(rewrite,[status(thm)],[])).
% 294.43/186.95 tff(26282,plain,
% 294.43/186.95 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_d, X))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s11)) | m_and_h_gate_v_out(c_e_h_3, c_d, s11))),
% 294.43/186.95 inference(quant_inst,[status(thm)],[])).
% 294.43/186.95 tff(26283,plain,
% 294.43/186.95 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_d, X))) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s11)) | m_and_h_gate_v_out(c_e_h_3, c_d, s11)),
% 294.43/186.95 inference(modus_ponens,[status(thm)],[26282, 26281])).
% 294.43/186.95 tff(26284,plain,
% 294.43/186.95 ($false),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[26283, 2116, 26280, 21684])).
% 294.43/186.95 tff(26285,plain,((~m_c_h_element_v_in1(c_e_h_3, c_f, s11)) | m_and_h_gate_v_out(c_e_h_3, c_d, s11)), inference(lemma,lemma(discharge,[]))).
% 294.43/186.95 tff(26286,plain,
% 294.43/186.95 (m_and_h_gate_v_out(c_e_h_3, c_d, s11)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[26285, 26279])).
% 294.43/186.95 tff(26287,plain,
% 294.43/186.95 (m_mutex_h_half_v_out(c_e_h_3, c_a, s10)),
% 294.43/186.95 inference(unit_resolution,[status(thm)],[19733, 26243])).
% 294.43/186.95 tff(26288,assumption,(~m_mutex_h_half_v_other_h_out(c_e_h_3, c_b, s10)), introduced(assumption)).
% 294.43/186.95 tff(26289,plain,
% 294.43/186.95 (((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_mutex_h_half_v_other_h_out(I0, c_b, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s10)) | m_mutex_h_half_v_other_h_out(c_e_h_3, c_b, s10))) <=> ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_mutex_h_half_v_other_h_out(I0, c_b, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s10)) | m_mutex_h_half_v_other_h_out(c_e_h_3, c_b, s10))),
% 294.43/186.96 inference(rewrite,[status(thm)],[])).
% 294.43/186.96 tff(26290,plain,
% 294.43/186.96 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_mutex_h_half_v_other_h_out(I0, c_b, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s10)) | m_mutex_h_half_v_other_h_out(c_e_h_3, c_b, s10))),
% 294.43/186.96 inference(quant_inst,[status(thm)],[])).
% 294.43/186.96 tff(26291,plain,
% 294.43/186.96 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_mutex_h_half_v_other_h_out(I0, c_b, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s10)) | m_mutex_h_half_v_other_h_out(c_e_h_3, c_b, s10)),
% 294.43/186.96 inference(modus_ponens,[status(thm)],[26290, 26289])).
% 294.43/186.96 tff(26292,plain,
% 294.43/186.96 ($false),
% 294.43/186.96 inference(unit_resolution,[status(thm)],[26291, 20754, 19735, 26288])).
% 294.43/186.96 tff(26293,plain,(m_mutex_h_half_v_other_h_out(c_e_h_3, c_b, s10) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s10))), inference(lemma,lemma(discharge,[]))).
% 294.43/186.96 tff(26294,plain,
% 294.43/186.96 (m_mutex_h_half_v_other_h_out(c_e_h_3, c_b, s10)),
% 294.43/186.96 inference(unit_resolution,[status(thm)],[26293, 26287])).
% 294.43/186.96 tff(26295,assumption,(m_mutex_h_half_v_other_h_out(c_e_h_3, c_b, s10)), introduced(assumption)).
% 294.43/186.96 tff(26296,plain,
% 294.43/186.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | (~m_mutex_h_half_v_out(I0, I1, Y)) | (~m_mutex_h_half_v_other_h_out(I0, I1, Y)))) | ((~trans(s9, s10)) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s10)) | (~m_mutex_h_half_v_other_h_out(c_e_h_3, c_b, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | (~m_mutex_h_half_v_out(I0, I1, Y)) | (~m_mutex_h_half_v_other_h_out(I0, I1, Y)))) | (~trans(s9, s10)) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s10)) | (~m_mutex_h_half_v_other_h_out(c_e_h_3, c_b, s10)))),
% 294.43/186.96 inference(rewrite,[status(thm)],[])).
% 294.43/186.96 tff(26297,plain,
% 294.43/186.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | (~m_mutex_h_half_v_out(I0, I1, Y)) | (~m_mutex_h_half_v_other_h_out(I0, I1, Y)))) | ((~trans(s9, s10)) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s10)) | (~m_mutex_h_half_v_other_h_out(c_e_h_3, c_b, s10)))),
% 294.43/186.96 inference(quant_inst,[status(thm)],[])).
% 294.43/186.96 tff(26298,plain,
% 294.43/186.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | (~m_mutex_h_half_v_out(I0, I1, Y)) | (~m_mutex_h_half_v_other_h_out(I0, I1, Y)))) | (~trans(s9, s10)) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s10)) | (~m_mutex_h_half_v_other_h_out(c_e_h_3, c_b, s10))),
% 294.43/186.96 inference(modus_ponens,[status(thm)],[26297, 26296])).
% 294.43/186.96 tff(26299,plain,
% 294.43/186.96 ($false),
% 294.43/186.96 inference(unit_resolution,[status(thm)],[26298, 20734, 7676, 21719, 26295])).
% 294.43/186.96 tff(26300,plain,((~m_mutex_h_half_v_out(c_e_h_3, c_b, s10)) | (~m_mutex_h_half_v_other_h_out(c_e_h_3, c_b, s10))), inference(lemma,lemma(discharge,[]))).
% 294.43/186.96 tff(26301,plain,
% 294.43/186.96 (~m_mutex_h_half_v_out(c_e_h_3, c_b, s10)),
% 294.43/186.96 inference(unit_resolution,[status(thm)],[26300, 26294])).
% 294.43/186.96 tff(26302,plain,
% 294.43/186.96 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_d, s10)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s10))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_d, s10)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s10))),
% 294.43/186.96 inference(rewrite,[status(thm)],[])).
% 294.43/186.96 tff(26303,plain,
% 294.43/186.96 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_d, s10)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s10))),
% 294.43/186.96 inference(quant_inst,[status(thm)],[])).
% 294.43/186.96 tff(26304,plain,
% 294.43/186.96 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_d, X)) | m_mutex_h_half_v_out(I0, c_b, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_d, s10)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s10)),
% 294.43/186.96 inference(modus_ponens,[status(thm)],[26303, 26302])).
% 294.43/186.96 tff(26305,plain,
% 294.43/186.96 ($false),
% 294.43/186.96 inference(unit_resolution,[status(thm)],[26304, 2808, 21726, 21683])).
% 294.43/186.96 tff(26306,plain,((~m_and_h_gate_v_in1(c_e_h_3, c_d, s10)) | m_mutex_h_half_v_out(c_e_h_3, c_b, s10)), inference(lemma,lemma(discharge,[]))).
% 294.43/186.96 tff(26307,plain,
% 294.43/186.96 (~m_and_h_gate_v_in1(c_e_h_3, c_d, s10)),
% 294.43/186.96 inference(unit_resolution,[status(thm)],[26306, 26301])).
% 294.43/186.96 tff(26308,assumption,(node20(c_e_h_3, c_d, s10)), introduced(assumption)).
% 294.43/186.96 tff(26309,plain,
% 294.43/186.96 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_d, s10)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s10))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_d, s10)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s10))),
% 294.43/186.96 inference(rewrite,[status(thm)],[])).
% 294.43/186.96 tff(26310,plain,
% 294.43/186.96 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_d, s10)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s10))),
% 294.43/186.96 inference(quant_inst,[status(thm)],[])).
% 294.43/186.96 tff(26311,plain,
% 294.43/186.96 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_d, s10)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s10)),
% 294.43/186.96 inference(modus_ponens,[status(thm)],[26310, 26309])).
% 294.43/186.96 tff(26312,plain,
% 294.43/186.96 ($false),
% 294.43/186.96 inference(unit_resolution,[status(thm)],[26311, 38, 26308, 21718])).
% 294.43/186.96 tff(26313,plain,((~node20(c_e_h_3, c_d, s10)) | m_and_h_gate_v_in1(c_e_h_3, c_d, s10)), inference(lemma,lemma(discharge,[]))).
% 294.43/186.96 tff(26314,plain,
% 294.43/186.96 (~node20(c_e_h_3, c_d, s10)),
% 294.43/186.96 inference(unit_resolution,[status(thm)],[26313, 26307])).
% 294.43/186.96 tff(26315,plain,
% 294.43/186.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_d, s11)) | (~node22(c_e_h_3, c_d, s10, s11)) | m_and_h_gate_v_out(c_e_h_3, c_d, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s11)) | (~node22(c_e_h_3, c_d, s10, s11)) | m_and_h_gate_v_out(c_e_h_3, c_d, s10))),
% 294.43/186.96 inference(rewrite,[status(thm)],[])).
% 294.43/186.96 tff(26316,plain,
% 294.43/186.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_d, s11)) | (~node22(c_e_h_3, c_d, s10, s11)) | m_and_h_gate_v_out(c_e_h_3, c_d, s10))),
% 294.43/186.96 inference(quant_inst,[status(thm)],[])).
% 294.43/186.96 tff(26317,plain,
% 294.43/186.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s11)) | (~node22(c_e_h_3, c_d, s10, s11)) | m_and_h_gate_v_out(c_e_h_3, c_d, s10)),
% 294.43/186.96 inference(modus_ponens,[status(thm)],[26316, 26315])).
% 294.43/186.96 tff(26318,plain,
% 294.43/186.96 ($false),
% 294.43/186.96 inference(unit_resolution,[status(thm)],[26317, 108, 21587, 21685, 21676])).
% 294.43/186.96 tff(26319,plain,((~node22(c_e_h_3, c_d, s10, s11)) | m_and_h_gate_v_out(c_e_h_3, c_d, s10) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s11))), inference(lemma,lemma(discharge,[]))).
% 294.43/186.96 tff(26320,plain,
% 294.43/186.96 (~node22(c_e_h_3, c_d, s10, s11)),
% 294.43/186.96 inference(unit_resolution,[status(thm)],[26319, 21676, 21587])).
% 294.43/186.96 tff(26321,assumption,(~node20(c_e_h_3, c_d, s10)), introduced(assumption)).
% 294.43/186.96 tff(26322,assumption,(node21(c_e_h_3, c_d, s10, s11)), introduced(assumption)).
% 294.43/186.96 tff(26323,plain,
% 294.43/186.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_d, s10) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s11)) | (~node21(c_e_h_3, c_d, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_d, s10) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s11)) | (~node21(c_e_h_3, c_d, s10, s11)))),
% 294.43/186.96 inference(rewrite,[status(thm)],[])).
% 294.43/186.96 tff(26324,plain,
% 294.43/186.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_d, s10) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s11)) | (~node21(c_e_h_3, c_d, s10, s11)))),
% 294.43/186.96 inference(quant_inst,[status(thm)],[])).
% 294.43/186.96 tff(26325,plain,
% 294.43/186.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_d, s10) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s11)) | (~node21(c_e_h_3, c_d, s10, s11))),
% 294.43/186.96 inference(modus_ponens,[status(thm)],[26324, 26323])).
% 294.43/186.96 tff(26326,plain,
% 294.43/186.96 ($false),
% 294.43/186.96 inference(unit_resolution,[status(thm)],[26325, 52, 26322, 21676, 26321])).
% 294.43/186.96 tff(26327,plain,((~node21(c_e_h_3, c_d, s10, s11)) | (~m_and_h_gate_v_out(c_e_h_3, c_d, s11)) | node20(c_e_h_3, c_d, s10)), inference(lemma,lemma(discharge,[]))).
% 294.43/186.96 tff(26328,plain,
% 294.43/186.96 (~node21(c_e_h_3, c_d, s10, s11)),
% 294.43/186.96 inference(unit_resolution,[status(thm)],[26327, 21676, 26321])).
% 294.43/186.96 tff(26329,plain,
% 294.43/186.96 ($false),
% 294.43/186.96 inference(unit_resolution,[status(thm)],[21698, 26328, 26320])).
% 294.43/186.96 tff(26330,plain,((~m_and_h_gate_v_out(c_e_h_3, c_d, s11)) | node20(c_e_h_3, c_d, s10) | m_and_h_gate_v_out(c_e_h_3, c_d, s10)), inference(lemma,lemma(discharge,[]))).
% 294.43/186.96 tff(26331,plain,
% 294.43/186.96 (m_and_h_gate_v_out(c_e_h_3, c_d, s10)),
% 294.43/186.96 inference(unit_resolution,[status(thm)],[26330, 26314, 26286])).
% 294.43/186.96 tff(26332,plain,
% 294.43/186.96 (m_and_h_gate_v_out(c_e_h_3, c_d, s9)),
% 294.43/186.96 inference(unit_resolution,[status(thm)],[21631, 26331, 26247])).
% 294.43/186.96 tff(26333,plain,
% 294.43/186.96 (m_or_h_gate_v_in2(c_e_h_3, c_g, s9)),
% 294.43/186.96 inference(unit_resolution,[status(thm)],[20716, 26332])).
% 294.43/186.96 tff(26334,plain,
% 294.43/186.96 (~node4(c_e_h_3, c_g, s9)),
% 294.43/186.96 inference(unit_resolution,[status(thm)],[20720, 20695, 26333])).
% 294.43/186.96 tff(26335,plain,
% 294.43/186.96 (m_or_h_gate_v_out(c_e_h_3, c_j, s8)),
% 294.43/186.96 inference(unit_resolution,[status(thm)],[7624, 21022])).
% 294.43/186.96 tff(26336,plain,
% 294.43/186.96 (m_and_h_gate_v_out(c_e_h_3, c_c, s4)),
% 294.43/186.96 inference(unit_resolution,[status(thm)],[5885, 26335])).
% 294.43/186.96 tff(26337,plain,
% 294.43/186.96 (m_and_h_gate_v_out(c_e_h_3, c_c, s5)),
% 294.43/186.96 inference(unit_resolution,[status(thm)],[6170, 26336])).
% 294.43/186.96 tff(26338,plain,
% 294.43/186.96 (m_and_h_gate_v_out(c_e_h_3, c_c, s8)),
% 294.43/186.96 inference(unit_resolution,[status(thm)],[20626, 26337])).
% 294.43/186.96 tff(26339,plain,
% 294.43/186.96 (m_or_h_gate_v_in1(c_e_h_3, c_g, s8)),
% 294.43/186.96 inference(unit_resolution,[status(thm)],[20638, 26338])).
% 294.43/186.96 tff(26340,plain,
% 294.43/186.96 (~node4(c_e_h_3, c_g, s8)),
% 294.43/186.96 inference(unit_resolution,[status(thm)],[20502, 26339])).
% 294.43/186.96 tff(26341,plain,
% 294.43/186.96 (m_or_h_gate_v_out(c_e_h_3, c_g, s8)),
% 294.43/186.96 inference(unit_resolution,[status(thm)],[21069, 26340, 7655, 20257])).
% 294.43/186.96 tff(26342,plain,
% 294.43/186.96 ($false),
% 294.43/186.96 inference(unit_resolution,[status(thm)],[20525, 26341, 26340, 20257])).
% 294.43/186.96 tff(26343,plain,(m_or_h_gate_v_out(c_e_h_3, c_g, s9) | (~m_c_h_element_v_out(c_e_h_3, c_h, s10))), inference(lemma,lemma(discharge,[]))).
% 294.43/186.96 tff(26344,plain,
% 294.43/186.96 (m_or_h_gate_v_out(c_e_h_3, c_g, s9)),
% 294.43/186.96 inference(unit_resolution,[status(thm)],[26343, 26234])).
% 294.43/186.96 tff(26345,plain,
% 294.43/186.96 (m_or_h_gate_v_out(c_e_h_3, c_g, s10)),
% 294.43/186.96 inference(unit_resolution,[status(thm)],[20563, 26344, 26334])).
% 294.43/186.96 tff(26346,assumption,(m_or_h_gate_v_out(c_e_h_3, c_g, s10)), introduced(assumption)).
% 294.43/186.96 tff(26347,plain,
% 294.43/186.96 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_c_h_element_v_in1(I0, c_h, X))) | ((~m_or_h_gate_v_out(c_e_h_3, c_g, s10)) | m_c_h_element_v_in1(c_e_h_3, c_h, s10))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_c_h_element_v_in1(I0, c_h, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s10)) | m_c_h_element_v_in1(c_e_h_3, c_h, s10))),
% 294.43/186.96 inference(rewrite,[status(thm)],[])).
% 294.43/186.96 tff(26348,plain,
% 294.43/186.96 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_c_h_element_v_in1(I0, c_h, X))) | ((~m_or_h_gate_v_out(c_e_h_3, c_g, s10)) | m_c_h_element_v_in1(c_e_h_3, c_h, s10))),
% 294.43/186.96 inference(quant_inst,[status(thm)],[])).
% 294.43/186.96 tff(26349,plain,
% 294.43/186.96 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_out(I0, c_g, X)) | m_c_h_element_v_in1(I0, c_h, X))) | (~m_or_h_gate_v_out(c_e_h_3, c_g, s10)) | m_c_h_element_v_in1(c_e_h_3, c_h, s10)),
% 294.43/186.96 inference(modus_ponens,[status(thm)],[26348, 26347])).
% 294.43/186.96 tff(26350,plain,
% 294.43/186.96 ($false),
% 294.43/186.96 inference(unit_resolution,[status(thm)],[26349, 11172, 7724, 26346])).
% 294.43/186.96 tff(26351,plain,((~m_or_h_gate_v_out(c_e_h_3, c_g, s10)) | m_c_h_element_v_in1(c_e_h_3, c_h, s10)), inference(lemma,lemma(discharge,[]))).
% 294.43/186.96 tff(26352,plain,
% 294.43/186.96 (m_c_h_element_v_in1(c_e_h_3, c_h, s10)),
% 294.43/186.96 inference(unit_resolution,[status(thm)],[26351, 26345])).
% 294.43/186.96 tff(26353,plain,
% 294.43/186.96 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s10)) | m_and_h_gate_v_in2(c_e_h_3, c_i, s10))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_i, s10)) | m_and_h_gate_v_in2(c_e_h_3, c_i, s10))),
% 294.43/186.97 inference(rewrite,[status(thm)],[])).
% 294.43/186.97 tff(26354,plain,
% 294.43/186.97 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s10)) | m_and_h_gate_v_in2(c_e_h_3, c_i, s10))),
% 294.43/186.97 inference(quant_inst,[status(thm)],[])).
% 294.43/186.97 tff(26355,plain,
% 294.43/186.97 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_i, s10)) | m_and_h_gate_v_in2(c_e_h_3, c_i, s10)),
% 294.43/186.97 inference(modus_ponens,[status(thm)],[26354, 26353])).
% 294.43/186.97 tff(26356,plain,
% 294.43/186.97 (m_and_h_gate_v_in2(c_e_h_3, c_i, s10)),
% 294.43/186.97 inference(unit_resolution,[status(thm)],[26355, 4563, 26232])).
% 294.43/186.97 tff(26357,plain,
% 294.43/186.97 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_i, X)) | (~m_or_h_gate_v_out(I0, c_j, X)))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_i, s10)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s10)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_i, X)) | (~m_or_h_gate_v_out(I0, c_j, X)))) | (~m_and_h_gate_v_in2(c_e_h_3, c_i, s10)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s10)))),
% 294.43/186.97 inference(rewrite,[status(thm)],[])).
% 294.43/186.97 tff(26358,plain,
% 294.43/186.97 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_i, X)) | (~m_or_h_gate_v_out(I0, c_j, X)))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_i, s10)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s10)))),
% 294.43/186.97 inference(quant_inst,[status(thm)],[])).
% 294.43/186.97 tff(26359,plain,
% 294.43/186.97 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_i, X)) | (~m_or_h_gate_v_out(I0, c_j, X)))) | (~m_and_h_gate_v_in2(c_e_h_3, c_i, s10)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s10))),
% 294.43/186.97 inference(modus_ponens,[status(thm)],[26358, 26357])).
% 294.43/186.97 tff(26360,plain,
% 294.43/186.97 (~m_or_h_gate_v_out(c_e_h_3, c_j, s10)),
% 294.43/186.97 inference(unit_resolution,[status(thm)],[26359, 7295, 26356])).
% 294.43/186.97 tff(26361,plain,
% 294.43/186.97 (~m_c_h_element_v_in2(c_e_h_3, c_h, s10)),
% 294.43/186.97 inference(unit_resolution,[status(thm)],[7810, 1174, 26360])).
% 294.43/186.97 tff(26362,plain,
% 294.43/186.97 ((~m_c_h_element_v_in1(c_e_h_3, c_h, s10)) | (~node17(c_e_h_3, c_h, s10))),
% 294.43/186.97 inference(unit_resolution,[status(thm)],[7803, 919, 26361])).
% 294.43/186.97 tff(26363,plain,
% 294.43/186.97 (~node17(c_e_h_3, c_h, s10)),
% 294.43/186.97 inference(unit_resolution,[status(thm)],[26362, 26352])).
% 294.43/186.97 tff(26364,plain,
% 294.43/186.97 (node18(c_e_h_3, c_h, s10, s11)),
% 294.43/186.97 inference(unit_resolution,[status(thm)],[7759, 26363])).
% 294.43/186.97 tff(26365,plain,
% 294.43/186.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_out(I0, I1, X)) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_h, s11) | (~m_c_h_element_v_out(c_e_h_3, c_h, s10)) | (~node18(c_e_h_3, c_h, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_out(I0, I1, X)) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s11) | (~m_c_h_element_v_out(c_e_h_3, c_h, s10)) | (~node18(c_e_h_3, c_h, s10, s11)))),
% 294.43/186.97 inference(rewrite,[status(thm)],[])).
% 294.43/186.97 tff(26366,plain,
% 294.43/186.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_out(I0, I1, X)) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_h, s11) | (~m_c_h_element_v_out(c_e_h_3, c_h, s10)) | (~node18(c_e_h_3, c_h, s10, s11)))),
% 294.43/186.97 inference(quant_inst,[status(thm)],[])).
% 294.43/186.97 tff(26367,plain,
% 294.43/186.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_c_h_element_v_out(I0, I1, Y) | (~m_c_h_element_v_out(I0, I1, X)) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_h, s11) | (~m_c_h_element_v_out(c_e_h_3, c_h, s10)) | (~node18(c_e_h_3, c_h, s10, s11))),
% 294.43/186.97 inference(modus_ponens,[status(thm)],[26366, 26365])).
% 294.43/186.97 tff(26368,plain,
% 294.43/186.97 ($false),
% 294.43/186.97 inference(unit_resolution,[status(thm)],[26367, 11191, 21082, 7655, 7732])).
% 294.43/186.97 tff(26369,plain,((~node18(c_e_h_3, c_h, s10, s11)) | m_c_h_element_v_out(c_e_h_3, c_h, s11) | (~m_c_h_element_v_out(c_e_h_3, c_h, s10))), inference(lemma,lemma(discharge,[]))).
% 294.43/186.97 tff(26370,plain,
% 294.43/186.97 (m_c_h_element_v_out(c_e_h_3, c_h, s11)),
% 294.43/186.97 inference(unit_resolution,[status(thm)],[26369, 26364, 26234])).
% 294.43/186.97 tff(26371,plain,
% 294.43/186.97 (m_and_h_gate_v_out(c_e_h_3, c_c, s8)),
% 294.43/186.97 inference(unit_resolution,[status(thm)],[20990, 26370])).
% 294.43/186.97 tff(26372,plain,
% 294.43/186.97 (m_mutex_h_half_v_out(c_e_h_3, c_a, s7)),
% 294.43/186.97 inference(unit_resolution,[status(thm)],[20116, 26371])).
% 294.43/186.97 tff(26373,plain,
% 294.43/186.97 (m_user_v_req(c_e_h_3, c_u, s7)),
% 294.43/186.97 inference(unit_resolution,[status(thm)],[20342, 26371])).
% 294.43/186.97 tff(26374,plain,
% 294.43/186.97 (m_mutex_h_half_v_inp(c_e_h_3, c_a, s7)),
% 294.43/186.97 inference(unit_resolution,[status(thm)],[1908, 26373])).
% 294.43/186.97 tff(26375,plain,
% 294.43/186.97 (m_mutex_h_half_v_out(c_e_h_3, c_a, s8)),
% 294.43/186.97 inference(unit_resolution,[status(thm)],[1944, 26374, 26372])).
% 294.43/186.97 tff(26376,plain,
% 294.43/186.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | (~m_mutex_h_half_v_out(I0, I1, Y)) | (~m_mutex_h_half_v_other_h_out(I0, I1, Y)))) | ((~trans(s7, s8)) | (~m_mutex_h_half_v_other_h_out(c_e_h_3, c_a, s8)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | (~m_mutex_h_half_v_out(I0, I1, Y)) | (~m_mutex_h_half_v_other_h_out(I0, I1, Y)))) | (~trans(s7, s8)) | (~m_mutex_h_half_v_other_h_out(c_e_h_3, c_a, s8)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s8)))),
% 294.43/186.97 inference(rewrite,[status(thm)],[])).
% 294.43/186.97 tff(26377,plain,
% 294.43/186.97 (((~trans(s7, s8)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s8)) | (~m_mutex_h_half_v_other_h_out(c_e_h_3, c_a, s8))) <=> ((~trans(s7, s8)) | (~m_mutex_h_half_v_other_h_out(c_e_h_3, c_a, s8)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s8)))),
% 294.43/186.97 inference(rewrite,[status(thm)],[])).
% 294.43/186.97 tff(26378,plain,
% 294.43/186.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | (~m_mutex_h_half_v_out(I0, I1, Y)) | (~m_mutex_h_half_v_other_h_out(I0, I1, Y)))) | ((~trans(s7, s8)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s8)) | (~m_mutex_h_half_v_other_h_out(c_e_h_3, c_a, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | (~m_mutex_h_half_v_out(I0, I1, Y)) | (~m_mutex_h_half_v_other_h_out(I0, I1, Y)))) | ((~trans(s7, s8)) | (~m_mutex_h_half_v_other_h_out(c_e_h_3, c_a, s8)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s8))))),
% 294.43/186.97 inference(monotonicity,[status(thm)],[26377])).
% 294.43/186.97 tff(26379,plain,
% 294.43/186.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | (~m_mutex_h_half_v_out(I0, I1, Y)) | (~m_mutex_h_half_v_other_h_out(I0, I1, Y)))) | ((~trans(s7, s8)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s8)) | (~m_mutex_h_half_v_other_h_out(c_e_h_3, c_a, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | (~m_mutex_h_half_v_out(I0, I1, Y)) | (~m_mutex_h_half_v_other_h_out(I0, I1, Y)))) | (~trans(s7, s8)) | (~m_mutex_h_half_v_other_h_out(c_e_h_3, c_a, s8)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s8)))),
% 294.43/186.97 inference(transitivity,[status(thm)],[26378, 26376])).
% 294.43/186.97 tff(26380,plain,
% 294.43/186.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | (~m_mutex_h_half_v_out(I0, I1, Y)) | (~m_mutex_h_half_v_other_h_out(I0, I1, Y)))) | ((~trans(s7, s8)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s8)) | (~m_mutex_h_half_v_other_h_out(c_e_h_3, c_a, s8)))),
% 294.43/186.97 inference(quant_inst,[status(thm)],[])).
% 294.43/186.97 tff(26381,plain,
% 294.43/186.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | (~m_mutex_h_half_v_out(I0, I1, Y)) | (~m_mutex_h_half_v_other_h_out(I0, I1, Y)))) | (~trans(s7, s8)) | (~m_mutex_h_half_v_other_h_out(c_e_h_3, c_a, s8)) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s8))),
% 294.43/186.97 inference(modus_ponens,[status(thm)],[26380, 26379])).
% 294.43/186.97 tff(26382,plain,
% 294.43/186.97 (~m_mutex_h_half_v_other_h_out(c_e_h_3, c_a, s8)),
% 294.43/186.97 inference(unit_resolution,[status(thm)],[26381, 20734, 1938, 26375])).
% 294.43/186.97 tff(26383,plain,
% 294.43/186.97 (^[I0: $i, X: $i] : refl(((~m_mutex_h_half_v_out(I0, c_b, X)) | m_mutex_h_half_v_other_h_out(I0, c_a, X)) <=> ((~m_mutex_h_half_v_out(I0, c_b, X)) | m_mutex_h_half_v_other_h_out(I0, c_a, X)))),
% 294.43/186.97 inference(bind,[status(th)],[])).
% 294.43/186.97 tff(26384,plain,
% 294.43/186.97 (![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_b, X)) | m_mutex_h_half_v_other_h_out(I0, c_a, X)) <=> ![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_b, X)) | m_mutex_h_half_v_other_h_out(I0, c_a, X))),
% 294.43/186.97 inference(quant_intro,[status(thm)],[26383])).
% 294.43/186.97 tff(26385,plain,
% 294.43/186.97 (![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_b, X)) | m_mutex_h_half_v_other_h_out(I0, c_a, X)) <=> ![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_b, X)) | m_mutex_h_half_v_other_h_out(I0, c_a, X))),
% 294.43/186.97 inference(rewrite,[status(thm)],[])).
% 294.43/186.97 tff(26386,plain,
% 294.43/186.97 (^[I0: $i, X: $i] : rewrite((m_mutex_h_half_v_other_h_out(I0, c_a, X) | (~m_mutex_h_half_v_out(I0, c_b, X))) <=> ((~m_mutex_h_half_v_out(I0, c_b, X)) | m_mutex_h_half_v_other_h_out(I0, c_a, X)))),
% 294.43/186.97 inference(bind,[status(th)],[])).
% 294.43/186.97 tff(26387,plain,
% 294.43/186.97 (![I0: $i, X: $i] : (m_mutex_h_half_v_other_h_out(I0, c_a, X) | (~m_mutex_h_half_v_out(I0, c_b, X))) <=> ![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_b, X)) | m_mutex_h_half_v_other_h_out(I0, c_a, X))),
% 294.43/186.97 inference(quant_intro,[status(thm)],[26386])).
% 294.43/186.97 tff(26388,axiom,(![I0: $i, X: $i] : (m_mutex_h_half_v_other_h_out(I0, c_a, X) | (~m_mutex_h_half_v_out(I0, c_b, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_3')).
% 294.43/186.97 tff(26389,plain,
% 294.43/186.97 (![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_b, X)) | m_mutex_h_half_v_other_h_out(I0, c_a, X))),
% 294.43/186.97 inference(modus_ponens,[status(thm)],[26388, 26387])).
% 294.43/186.97 tff(26390,plain,
% 294.43/186.97 (![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_b, X)) | m_mutex_h_half_v_other_h_out(I0, c_a, X))),
% 294.43/186.97 inference(modus_ponens,[status(thm)],[26389, 26385])).
% 294.43/186.97 tff(26391,plain,(
% 294.43/186.97 ![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_b, X)) | m_mutex_h_half_v_other_h_out(I0, c_a, X))),
% 294.43/186.97 inference(skolemize,[status(sab)],[26390])).
% 294.43/186.97 tff(26392,plain,
% 294.43/186.97 (![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_b, X)) | m_mutex_h_half_v_other_h_out(I0, c_a, X))),
% 294.43/186.97 inference(modus_ponens,[status(thm)],[26391, 26384])).
% 294.43/186.97 tff(26393,plain,
% 294.43/186.97 (((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_b, X)) | m_mutex_h_half_v_other_h_out(I0, c_a, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_b, s8)) | m_mutex_h_half_v_other_h_out(c_e_h_3, c_a, s8))) <=> ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_b, X)) | m_mutex_h_half_v_other_h_out(I0, c_a, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s8)) | m_mutex_h_half_v_other_h_out(c_e_h_3, c_a, s8))),
% 294.43/186.97 inference(rewrite,[status(thm)],[])).
% 294.43/186.97 tff(26394,plain,
% 294.43/186.97 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_b, X)) | m_mutex_h_half_v_other_h_out(I0, c_a, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_b, s8)) | m_mutex_h_half_v_other_h_out(c_e_h_3, c_a, s8))),
% 294.43/186.97 inference(quant_inst,[status(thm)],[])).
% 294.43/186.97 tff(26395,plain,
% 294.43/186.97 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_b, X)) | m_mutex_h_half_v_other_h_out(I0, c_a, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s8)) | m_mutex_h_half_v_other_h_out(c_e_h_3, c_a, s8)),
% 294.43/186.97 inference(modus_ponens,[status(thm)],[26394, 26393])).
% 294.43/186.97 tff(26396,plain,
% 294.43/186.97 (~m_mutex_h_half_v_out(c_e_h_3, c_b, s8)),
% 294.43/186.97 inference(unit_resolution,[status(thm)],[26395, 26392, 26382])).
% 294.43/186.97 tff(26397,plain,
% 294.43/186.97 (~m_and_h_gate_v_in1(c_e_h_3, c_d, s8)),
% 294.43/186.97 inference(unit_resolution,[status(thm)],[17247, 26396])).
% 294.43/186.97 tff(26398,plain,
% 294.43/186.97 (~node20(c_e_h_3, c_d, s8)),
% 294.43/186.97 inference(unit_resolution,[status(thm)],[17239, 26397])).
% 294.43/186.97 tff(26399,plain,
% 294.43/186.97 (m_and_h_gate_v_out(c_e_h_3, c_d, s8)),
% 294.43/186.97 inference(unit_resolution,[status(thm)],[17231, 26398, 26332])).
% 294.43/186.97 tff(26400,plain,
% 294.43/186.97 (node20(c_e_h_3, c_d, s7)),
% 294.43/186.97 inference(unit_resolution,[status(thm)],[17208, 26399])).
% 294.43/186.97 tff(26401,plain,
% 294.43/186.97 (m_and_h_gate_v_in1(c_e_h_3, c_d, s7)),
% 294.43/186.97 inference(unit_resolution,[status(thm)],[17110, 26400])).
% 294.43/186.97 tff(26402,plain,
% 294.43/186.97 (m_mutex_h_half_v_out(c_e_h_3, c_b, s7)),
% 294.43/186.97 inference(unit_resolution,[status(thm)],[17102, 26401])).
% 294.43/186.97 tff(26403,plain,
% 294.43/186.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | (~m_mutex_h_half_v_out(I0, I1, Y)) | (~m_mutex_h_half_v_other_h_out(I0, I1, Y)))) | ((~trans(s6, s7)) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s7)) | (~m_mutex_h_half_v_other_h_out(c_e_h_3, c_b, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | (~m_mutex_h_half_v_out(I0, I1, Y)) | (~m_mutex_h_half_v_other_h_out(I0, I1, Y)))) | (~trans(s6, s7)) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s7)) | (~m_mutex_h_half_v_other_h_out(c_e_h_3, c_b, s7)))),
% 294.43/186.97 inference(rewrite,[status(thm)],[])).
% 294.43/186.97 tff(26404,plain,
% 294.43/186.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | (~m_mutex_h_half_v_out(I0, I1, Y)) | (~m_mutex_h_half_v_other_h_out(I0, I1, Y)))) | ((~trans(s6, s7)) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s7)) | (~m_mutex_h_half_v_other_h_out(c_e_h_3, c_b, s7)))),
% 294.43/186.97 inference(quant_inst,[status(thm)],[])).
% 294.43/186.97 tff(26405,plain,
% 294.43/186.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | (~m_mutex_h_half_v_out(I0, I1, Y)) | (~m_mutex_h_half_v_other_h_out(I0, I1, Y)))) | (~trans(s6, s7)) | (~m_mutex_h_half_v_out(c_e_h_3, c_b, s7)) | (~m_mutex_h_half_v_other_h_out(c_e_h_3, c_b, s7))),
% 294.43/186.97 inference(modus_ponens,[status(thm)],[26404, 26403])).
% 294.43/186.97 tff(26406,plain,
% 294.43/186.97 (~m_mutex_h_half_v_other_h_out(c_e_h_3, c_b, s7)),
% 294.43/186.97 inference(unit_resolution,[status(thm)],[26405, 20734, 1844, 26402])).
% 294.43/186.97 tff(26407,plain,
% 294.43/186.97 (((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_mutex_h_half_v_other_h_out(I0, c_b, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s7)) | m_mutex_h_half_v_other_h_out(c_e_h_3, c_b, s7))) <=> ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_mutex_h_half_v_other_h_out(I0, c_b, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s7)) | m_mutex_h_half_v_other_h_out(c_e_h_3, c_b, s7))),
% 294.43/186.97 inference(rewrite,[status(thm)],[])).
% 294.43/186.97 tff(26408,plain,
% 294.43/186.97 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_mutex_h_half_v_other_h_out(I0, c_b, X))) | ((~m_mutex_h_half_v_out(c_e_h_3, c_a, s7)) | m_mutex_h_half_v_other_h_out(c_e_h_3, c_b, s7))),
% 294.43/186.97 inference(quant_inst,[status(thm)],[])).
% 294.43/186.97 tff(26409,plain,
% 294.43/186.97 ((~![I0: $i, X: $i] : ((~m_mutex_h_half_v_out(I0, c_a, X)) | m_mutex_h_half_v_other_h_out(I0, c_b, X))) | (~m_mutex_h_half_v_out(c_e_h_3, c_a, s7)) | m_mutex_h_half_v_other_h_out(c_e_h_3, c_b, s7)),
% 294.43/186.97 inference(modus_ponens,[status(thm)],[26408, 26407])).
% 294.43/186.97 tff(26410,plain,
% 294.43/186.97 ($false),
% 294.43/186.97 inference(unit_resolution,[status(thm)],[26409, 20754, 26372, 26406])).
% 294.43/186.97 tff(26411,plain,(m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s13) | m_and_h_gate_v_out(c_e_h_3, c_i, s10) | m_c_h_element_v_in2(c_e_h_3, c_f, s9)), inference(lemma,lemma(discharge,[]))).
% 294.43/186.97 tff(26412,plain,
% 294.43/186.97 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s13)),
% 294.43/186.97 inference(unit_resolution,[status(thm)],[26411, 24271, 21941])).
% 294.43/186.97 tff(26413,plain,
% 294.43/186.97 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s13)),
% 294.43/186.97 inference(unit_resolution,[status(thm)],[13609, 5601, 26412])).
% 294.43/186.97 tff(26414,plain,
% 294.43/186.97 (~node9(c_e_h_3, c_n, s13)),
% 294.43/186.97 inference(unit_resolution,[status(thm)],[13613, 4972, 26413])).
% 294.43/186.97 tff(26415,plain,
% 294.43/186.97 (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s14)),
% 294.43/186.97 inference(unit_resolution,[status(thm)],[13605, 24278, 26414])).
% 294.43/186.97 tff(26416,assumption,(m_and_h_gate_v_in2(c_e_h_3, c_q, s14)), introduced(assumption)).
% 294.43/186.97 tff(26417,plain,
% 294.43/186.97 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s14)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s14))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s14)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s14))),
% 294.43/186.97 inference(rewrite,[status(thm)],[])).
% 294.43/186.97 tff(26418,plain,
% 294.43/186.97 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s14)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s14))),
% 294.43/186.97 inference(quant_inst,[status(thm)],[])).
% 294.43/186.97 tff(26419,plain,
% 294.43/186.97 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s14)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s14)),
% 294.43/186.97 inference(modus_ponens,[status(thm)],[26418, 26417])).
% 294.43/186.97 tff(26420,plain,
% 294.43/186.97 ($false),
% 294.43/186.97 inference(unit_resolution,[status(thm)],[26419, 5621, 13407, 26416])).
% 294.43/186.97 tff(26421,plain,((~m_and_h_gate_v_in2(c_e_h_3, c_q, s14)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s14)), inference(lemma,lemma(discharge,[]))).
% 294.43/186.97 tff(26422,plain,
% 294.43/186.97 (~m_and_h_gate_v_in2(c_e_h_3, c_q, s14)),
% 294.43/186.97 inference(unit_resolution,[status(thm)],[26421, 26415])).
% 294.43/186.98 tff(26423,assumption,(~m_and_h_gate_v_in2(c_e_h_3, c_q, s14)), introduced(assumption)).
% 294.43/186.98 tff(26424,assumption,(node20(c_e_h_3, c_q, s14)), introduced(assumption)).
% 294.43/186.98 tff(26425,plain,
% 294.43/186.98 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s14)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s14))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s14)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s14))),
% 294.43/186.98 inference(rewrite,[status(thm)],[])).
% 294.43/186.98 tff(26426,plain,
% 294.43/186.98 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s14)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s14))),
% 294.43/186.98 inference(quant_inst,[status(thm)],[])).
% 294.43/186.98 tff(26427,plain,
% 294.43/186.98 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s14)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s14)),
% 294.43/186.98 inference(modus_ponens,[status(thm)],[26426, 26425])).
% 294.43/186.98 tff(26428,plain,
% 294.43/186.98 ($false),
% 294.43/186.98 inference(unit_resolution,[status(thm)],[26427, 4563, 26424, 26423])).
% 294.43/186.98 tff(26429,plain,((~node20(c_e_h_3, c_q, s14)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s14)), inference(lemma,lemma(discharge,[]))).
% 294.43/186.98 tff(26430,plain,
% 294.43/186.98 (~node20(c_e_h_3, c_q, s14)),
% 294.43/186.98 inference(unit_resolution,[status(thm)],[26429, 26422])).
% 294.43/186.98 tff(26431,plain,
% 294.43/186.98 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11)),
% 294.43/186.98 inference(unit_resolution,[status(thm)],[25322, 24401])).
% 294.43/186.98 tff(26432,plain,
% 294.43/186.98 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12) | m_c_h_element_v_out(c_e_h_1, c_e, s12))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12) | m_c_h_element_v_out(c_e_h_1, c_e, s12))),
% 294.43/186.98 inference(rewrite,[status(thm)],[])).
% 294.43/186.98 tff(26433,plain,
% 294.43/186.98 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12) | m_c_h_element_v_out(c_e_h_1, c_e, s12))),
% 294.43/186.98 inference(quant_inst,[status(thm)],[])).
% 294.43/186.98 tff(26434,plain,
% 294.43/186.98 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12) | m_c_h_element_v_out(c_e_h_1, c_e, s12)),
% 294.43/186.98 inference(modus_ponens,[status(thm)],[26433, 26432])).
% 294.43/186.98 tff(26435,plain,
% 294.43/186.98 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12) | m_c_h_element_v_out(c_e_h_1, c_e, s12)),
% 294.43/186.98 inference(unit_resolution,[status(thm)],[26434, 7856])).
% 294.43/186.98 tff(26436,plain,
% 294.43/186.98 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12)),
% 294.43/186.98 inference(unit_resolution,[status(thm)],[26435, 25685])).
% 294.43/186.98 tff(26437,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12)), introduced(assumption)).
% 294.43/186.98 tff(26438,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13)), introduced(assumption)).
% 294.43/186.98 tff(26439,plain,
% 294.43/186.98 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s11)),
% 294.43/186.98 inference(unit_resolution,[status(thm)],[25328, 23106])).
% 294.43/186.98 tff(26440,plain,
% 294.43/186.98 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11))),
% 294.43/186.98 inference(unit_resolution,[status(thm)],[25364, 26439])).
% 294.43/186.98 tff(26441,plain,
% 294.43/186.98 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12)),
% 294.43/186.98 inference(unit_resolution,[status(thm)],[26440, 25336, 25324])).
% 294.43/186.98 tff(26442,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s12)), introduced(assumption)).
% 294.43/186.98 tff(26443,assumption,(node10(c_e_h_1, c_n, s12, s13)), introduced(assumption)).
% 294.43/186.98 tff(26444,plain,
% 294.43/186.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12)) | (~node10(c_e_h_1, c_n, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12)) | (~node10(c_e_h_1, c_n, s12, s13)))),
% 294.43/186.98 inference(rewrite,[status(thm)],[])).
% 294.43/186.98 tff(26445,plain,
% 294.43/186.98 (((~node10(c_e_h_1, c_n, s12, s13)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13)) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12)) | (~node10(c_e_h_1, c_n, s12, s13)))),
% 294.43/186.98 inference(rewrite,[status(thm)],[])).
% 294.43/186.98 tff(26446,plain,
% 294.43/186.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s12, s13)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12)) | (~node10(c_e_h_1, c_n, s12, s13))))),
% 294.43/186.98 inference(monotonicity,[status(thm)],[26445])).
% 294.43/186.98 tff(26447,plain,
% 294.43/186.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s12, s13)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12)) | (~node10(c_e_h_1, c_n, s12, s13)))),
% 294.43/186.98 inference(transitivity,[status(thm)],[26446, 26444])).
% 294.43/186.98 tff(26448,plain,
% 294.43/186.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s12, s13)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13))),
% 294.43/186.98 inference(quant_inst,[status(thm)],[])).
% 294.43/186.98 tff(26449,plain,
% 294.43/186.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12)) | (~node10(c_e_h_1, c_n, s12, s13))),
% 294.43/186.98 inference(modus_ponens,[status(thm)],[26448, 26447])).
% 294.43/186.98 tff(26450,plain,
% 294.43/186.98 ($false),
% 294.43/186.98 inference(unit_resolution,[status(thm)],[26449, 5718, 26438, 26442, 26437, 26443])).
% 294.43/186.98 tff(26451,plain,((~node10(c_e_h_1, c_n, s12, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12))), inference(lemma,lemma(discharge,[]))).
% 294.43/186.98 tff(26452,plain,
% 294.43/186.98 (~node10(c_e_h_1, c_n, s12, s13)),
% 294.43/186.98 inference(unit_resolution,[status(thm)],[26451, 26438, 26437, 26442])).
% 294.43/186.98 tff(26453,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12)), introduced(assumption)).
% 294.43/186.98 tff(26454,assumption,(node11(c_e_h_1, c_n, s12, s13)), introduced(assumption)).
% 294.43/186.98 tff(26455,plain,
% 294.43/186.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12)) | (~node11(c_e_h_1, c_n, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12)) | (~node11(c_e_h_1, c_n, s12, s13)))),
% 294.43/186.98 inference(rewrite,[status(thm)],[])).
% 294.43/186.98 tff(26456,plain,
% 294.43/186.98 ((m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13) | (~node11(c_e_h_1, c_n, s12, s13)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12))) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12)) | (~node11(c_e_h_1, c_n, s12, s13)))),
% 294.43/186.98 inference(rewrite,[status(thm)],[])).
% 294.43/186.98 tff(26457,plain,
% 294.43/186.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13) | (~node11(c_e_h_1, c_n, s12, s13)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12)) | (~node11(c_e_h_1, c_n, s12, s13))))),
% 294.43/186.98 inference(monotonicity,[status(thm)],[26456])).
% 294.43/186.98 tff(26458,plain,
% 294.43/186.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13) | (~node11(c_e_h_1, c_n, s12, s13)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12)) | (~node11(c_e_h_1, c_n, s12, s13)))),
% 294.43/186.98 inference(transitivity,[status(thm)],[26457, 26455])).
% 294.43/186.98 tff(26459,plain,
% 294.43/186.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13) | (~node11(c_e_h_1, c_n, s12, s13)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12)))),
% 294.43/186.98 inference(quant_inst,[status(thm)],[])).
% 294.43/186.98 tff(26460,plain,
% 294.43/186.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12)) | (~node11(c_e_h_1, c_n, s12, s13))),
% 294.43/186.98 inference(modus_ponens,[status(thm)],[26459, 26458])).
% 294.43/186.98 tff(26461,plain,
% 294.43/186.98 ($false),
% 294.43/186.98 inference(unit_resolution,[status(thm)],[26460, 5742, 26438, 26453, 26454])).
% 294.43/186.98 tff(26462,plain,((~node11(c_e_h_1, c_n, s12, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12))), inference(lemma,lemma(discharge,[]))).
% 294.43/186.98 tff(26463,plain,
% 294.43/186.98 (~node11(c_e_h_1, c_n, s12, s13)),
% 294.43/186.98 inference(unit_resolution,[status(thm)],[26462, 26438, 26453])).
% 294.43/186.98 tff(26464,plain,
% 294.43/186.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s12, s13)) | node10(c_e_h_1, c_n, s12, s13) | node11(c_e_h_1, c_n, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s12, s13)) | node10(c_e_h_1, c_n, s12, s13) | node11(c_e_h_1, c_n, s12, s13))),
% 294.43/186.98 inference(rewrite,[status(thm)],[])).
% 294.43/186.98 tff(26465,plain,
% 294.43/186.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s12, s13)) | node10(c_e_h_1, c_n, s12, s13) | node11(c_e_h_1, c_n, s12, s13))),
% 294.43/186.98 inference(quant_inst,[status(thm)],[])).
% 294.43/186.98 tff(26466,plain,
% 294.43/186.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s12, s13)) | node10(c_e_h_1, c_n, s12, s13) | node11(c_e_h_1, c_n, s12, s13)),
% 294.43/186.99 inference(modus_ponens,[status(thm)],[26465, 26464])).
% 294.43/186.99 tff(26467,plain,
% 294.43/186.99 (node10(c_e_h_1, c_n, s12, s13) | node11(c_e_h_1, c_n, s12, s13)),
% 294.43/186.99 inference(unit_resolution,[status(thm)],[26466, 5002, 11856])).
% 294.43/186.99 tff(26468,plain,
% 294.43/186.99 ($false),
% 294.43/186.99 inference(unit_resolution,[status(thm)],[26467, 26463, 26452])).
% 294.43/186.99 tff(26469,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s12))), inference(lemma,lemma(discharge,[]))).
% 294.43/186.99 tff(26470,plain,
% 294.43/186.99 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s12)),
% 294.43/186.99 inference(unit_resolution,[status(thm)],[26469, 26441, 26438, 26437])).
% 294.43/186.99 tff(26471,plain,
% 294.43/186.99 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s12) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s12) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12))),
% 294.43/186.99 inference(rewrite,[status(thm)],[])).
% 294.43/186.99 tff(26472,plain,
% 294.43/186.99 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s12) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12))),
% 294.43/186.99 inference(quant_inst,[status(thm)],[])).
% 294.43/186.99 tff(26473,plain,
% 294.43/186.99 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s12) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)),
% 294.43/186.99 inference(modus_ponens,[status(thm)],[26472, 26471])).
% 294.43/186.99 tff(26474,plain,
% 294.43/186.99 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s12) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)),
% 294.43/186.99 inference(unit_resolution,[status(thm)],[26473, 7868])).
% 294.43/186.99 tff(26475,plain,
% 294.43/186.99 (m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)),
% 294.43/186.99 inference(unit_resolution,[status(thm)],[26474, 26470])).
% 294.43/186.99 tff(26476,plain,
% 294.43/186.99 (node9(c_e_h_1, c_m, s11)),
% 294.43/186.99 inference(unit_resolution,[status(thm)],[23398, 26475])).
% 294.43/186.99 tff(26477,plain,
% 294.43/186.99 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s11)),
% 294.43/186.99 inference(unit_resolution,[status(thm)],[23366, 4958, 25336])).
% 294.43/186.99 tff(26478,plain,
% 294.43/186.99 ($false),
% 294.43/186.99 inference(unit_resolution,[status(thm)],[23370, 4972, 26477, 26476])).
% 294.43/186.99 tff(26479,plain,((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s11)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11))), inference(lemma,lemma(discharge,[]))).
% 294.43/186.99 tff(26480,plain,
% 294.43/186.99 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13)),
% 294.43/186.99 inference(unit_resolution,[status(thm)],[26479, 26436, 23363, 26431])).
% 294.43/186.99 tff(26481,plain,
% 294.43/186.99 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s13)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s13)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13)))),
% 294.43/186.99 inference(rewrite,[status(thm)],[])).
% 294.43/186.99 tff(26482,plain,
% 294.43/186.99 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s13)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13)))),
% 294.43/186.99 inference(quant_inst,[status(thm)],[])).
% 294.43/186.99 tff(26483,plain,
% 294.43/186.99 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s13)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13))),
% 294.43/186.99 inference(modus_ponens,[status(thm)],[26482, 26481])).
% 294.43/186.99 tff(26484,plain,
% 294.43/186.99 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s13)),
% 294.43/186.99 inference(unit_resolution,[status(thm)],[26483, 4958, 26480])).
% 294.43/186.99 tff(26485,plain,
% 294.43/186.99 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s13)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s13))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s13)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s13))),
% 294.43/186.99 inference(rewrite,[status(thm)],[])).
% 294.43/186.99 tff(26486,plain,
% 294.43/186.99 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s13)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s13))),
% 294.43/186.99 inference(quant_inst,[status(thm)],[])).
% 294.43/186.99 tff(26487,plain,
% 294.43/186.99 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s13)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s13)),
% 294.43/186.99 inference(modus_ponens,[status(thm)],[26486, 26485])).
% 294.43/186.99 tff(26488,plain,
% 294.43/186.99 (~node9(c_e_h_1, c_m, s13)),
% 294.43/186.99 inference(unit_resolution,[status(thm)],[26487, 4972, 26484])).
% 294.43/186.99 tff(26489,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)), introduced(assumption)).
% 294.43/186.99 tff(26490,assumption,(node11(c_e_h_1, c_m, s13, s14)), introduced(assumption)).
% 294.43/186.99 tff(26491,plain,
% 294.43/186.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)) | (~node11(c_e_h_1, c_m, s13, s14)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)) | (~node11(c_e_h_1, c_m, s13, s14)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13))),
% 294.43/186.99 inference(rewrite,[status(thm)],[])).
% 294.43/186.99 tff(26492,plain,
% 294.43/186.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)) | (~node11(c_e_h_1, c_m, s13, s14)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13))),
% 294.43/186.99 inference(quant_inst,[status(thm)],[])).
% 294.43/186.99 tff(26493,plain,
% 294.43/186.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)) | (~node11(c_e_h_1, c_m, s13, s14)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)),
% 294.43/186.99 inference(modus_ponens,[status(thm)],[26492, 26491])).
% 294.43/186.99 tff(26494,plain,
% 294.43/186.99 ($false),
% 294.43/186.99 inference(unit_resolution,[status(thm)],[26493, 5017, 26490, 26489, 25403])).
% 294.43/186.99 tff(26495,plain,((~node11(c_e_h_1, c_m, s13, s14)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)), inference(lemma,lemma(discharge,[]))).
% 294.43/186.99 tff(26496,plain,
% 294.43/186.99 (~node11(c_e_h_1, c_m, s13, s14)),
% 294.43/186.99 inference(unit_resolution,[status(thm)],[26495, 26489, 25403])).
% 294.43/186.99 tff(26497,assumption,(~node9(c_e_h_1, c_m, s13)), introduced(assumption)).
% 294.43/186.99 tff(26498,assumption,(node10(c_e_h_1, c_m, s13, s14)), introduced(assumption)).
% 294.43/186.99 tff(26499,plain,
% 294.43/186.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)) | node9(c_e_h_1, c_m, s13) | (~node10(c_e_h_1, c_m, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)) | node9(c_e_h_1, c_m, s13) | (~node10(c_e_h_1, c_m, s13, s14)))),
% 294.43/186.99 inference(rewrite,[status(thm)],[])).
% 294.43/186.99 tff(26500,plain,
% 294.43/186.99 ((node9(c_e_h_1, c_m, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)) | (~node10(c_e_h_1, c_m, s13, s14))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)) | node9(c_e_h_1, c_m, s13) | (~node10(c_e_h_1, c_m, s13, s14)))),
% 294.43/186.99 inference(rewrite,[status(thm)],[])).
% 294.43/186.99 tff(26501,plain,
% 294.43/186.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)) | (~node10(c_e_h_1, c_m, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)) | node9(c_e_h_1, c_m, s13) | (~node10(c_e_h_1, c_m, s13, s14))))),
% 294.43/186.99 inference(monotonicity,[status(thm)],[26500])).
% 294.43/186.99 tff(26502,plain,
% 294.43/186.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)) | (~node10(c_e_h_1, c_m, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)) | node9(c_e_h_1, c_m, s13) | (~node10(c_e_h_1, c_m, s13, s14)))),
% 294.43/186.99 inference(transitivity,[status(thm)],[26501, 26499])).
% 294.43/186.99 tff(26503,plain,
% 294.43/186.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)) | (~node10(c_e_h_1, c_m, s13, s14)))),
% 294.43/186.99 inference(quant_inst,[status(thm)],[])).
% 294.43/186.99 tff(26504,plain,
% 294.43/186.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)) | node9(c_e_h_1, c_m, s13) | (~node10(c_e_h_1, c_m, s13, s14))),
% 294.43/186.99 inference(modus_ponens,[status(thm)],[26503, 26502])).
% 294.43/186.99 tff(26505,plain,
% 294.43/186.99 ($false),
% 294.43/186.99 inference(unit_resolution,[status(thm)],[26504, 4986, 26498, 26489, 26497])).
% 294.43/186.99 tff(26506,plain,((~node10(c_e_h_1, c_m, s13, s14)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)) | node9(c_e_h_1, c_m, s13)), inference(lemma,lemma(discharge,[]))).
% 294.43/186.99 tff(26507,plain,
% 294.43/186.99 (~node10(c_e_h_1, c_m, s13, s14)),
% 294.43/186.99 inference(unit_resolution,[status(thm)],[26506, 26489, 26497])).
% 294.43/186.99 tff(26508,plain,
% 294.43/186.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s13, s14)) | node10(c_e_h_1, c_m, s13, s14) | node11(c_e_h_1, c_m, s13, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s13, s14)) | node10(c_e_h_1, c_m, s13, s14) | node11(c_e_h_1, c_m, s13, s14))),
% 294.43/186.99 inference(rewrite,[status(thm)],[])).
% 294.43/186.99 tff(26509,plain,
% 294.43/186.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s13, s14)) | node10(c_e_h_1, c_m, s13, s14) | node11(c_e_h_1, c_m, s13, s14))),
% 294.43/186.99 inference(quant_inst,[status(thm)],[])).
% 294.43/186.99 tff(26510,plain,
% 294.43/186.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s13, s14)) | node10(c_e_h_1, c_m, s13, s14) | node11(c_e_h_1, c_m, s13, s14)),
% 294.43/186.99 inference(modus_ponens,[status(thm)],[26509, 26508])).
% 294.43/186.99 tff(26511,plain,
% 294.43/186.99 (node10(c_e_h_1, c_m, s13, s14) | node11(c_e_h_1, c_m, s13, s14)),
% 294.43/186.99 inference(unit_resolution,[status(thm)],[26510, 5002, 12831])).
% 294.43/186.99 tff(26512,plain,
% 294.43/186.99 ($false),
% 294.43/186.99 inference(unit_resolution,[status(thm)],[26511, 26507, 26496])).
% 294.43/186.99 tff(26513,plain,((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)) | node9(c_e_h_1, c_m, s13) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)), inference(lemma,lemma(discharge,[]))).
% 294.43/186.99 tff(26514,plain,
% 294.43/186.99 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)),
% 294.43/186.99 inference(unit_resolution,[status(thm)],[26513, 26488, 25401])).
% 294.43/186.99 tff(26515,assumption,(m_and_h_gate_v_in2(c_e_h_1, c_l, s14)), introduced(assumption)).
% 294.43/186.99 tff(26516,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)), introduced(assumption)).
% 294.43/186.99 tff(26517,plain,
% 294.43/186.99 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s14)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s14)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14))),
% 294.43/187.00 inference(rewrite,[status(thm)],[])).
% 294.43/187.00 tff(26518,plain,
% 294.43/187.00 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s14)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14))),
% 294.43/187.00 inference(quant_inst,[status(thm)],[])).
% 294.43/187.00 tff(26519,plain,
% 294.43/187.00 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s14)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)),
% 294.43/187.00 inference(modus_ponens,[status(thm)],[26518, 26517])).
% 294.43/187.00 tff(26520,plain,
% 294.43/187.00 ($false),
% 294.43/187.00 inference(unit_resolution,[status(thm)],[26519, 4549, 26516, 26515])).
% 294.43/187.00 tff(26521,plain,((~m_and_h_gate_v_in2(c_e_h_1, c_l, s14)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)), inference(lemma,lemma(discharge,[]))).
% 294.43/187.00 tff(26522,plain,
% 294.43/187.00 (~m_and_h_gate_v_in2(c_e_h_1, c_l, s14)),
% 294.43/187.00 inference(unit_resolution,[status(thm)],[26521, 26514])).
% 294.43/187.00 tff(26523,assumption,(~m_and_h_gate_v_in2(c_e_h_1, c_l, s14)), introduced(assumption)).
% 294.43/187.00 tff(26524,assumption,(node20(c_e_h_1, c_l, s14)), introduced(assumption)).
% 294.43/187.00 tff(26525,plain,
% 294.43/187.00 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s14)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s14))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s14)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s14))),
% 294.43/187.00 inference(rewrite,[status(thm)],[])).
% 294.43/187.00 tff(26526,plain,
% 294.43/187.00 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s14)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s14))),
% 294.43/187.00 inference(quant_inst,[status(thm)],[])).
% 294.43/187.00 tff(26527,plain,
% 294.43/187.00 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s14)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s14)),
% 294.43/187.00 inference(modus_ponens,[status(thm)],[26526, 26525])).
% 294.43/187.00 tff(26528,plain,
% 294.43/187.00 ($false),
% 294.43/187.00 inference(unit_resolution,[status(thm)],[26527, 4563, 26524, 26523])).
% 294.43/187.00 tff(26529,plain,(m_and_h_gate_v_in2(c_e_h_1, c_l, s14) | (~node20(c_e_h_1, c_l, s14))), inference(lemma,lemma(discharge,[]))).
% 294.43/187.00 tff(26530,plain,
% 294.43/187.00 (~node20(c_e_h_1, c_l, s14)),
% 294.43/187.00 inference(unit_resolution,[status(thm)],[26529, 26522])).
% 294.43/187.00 tff(26531,assumption,(m_and_h_gate_v_out(c_e_h_1, c_l, s15)), introduced(assumption)).
% 294.43/187.00 tff(26532,assumption,(~node20(c_e_h_1, c_l, s14)), introduced(assumption)).
% 294.43/187.00 tff(26533,assumption,(node21(c_e_h_1, c_l, s14, s15)), introduced(assumption)).
% 294.43/187.00 tff(26534,plain,
% 294.43/187.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s14) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s15)) | (~node21(c_e_h_1, c_l, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s14) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s15)) | (~node21(c_e_h_1, c_l, s14, s15)))),
% 294.43/187.00 inference(rewrite,[status(thm)],[])).
% 294.43/187.00 tff(26535,plain,
% 294.43/187.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s14) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s15)) | (~node21(c_e_h_1, c_l, s14, s15)))),
% 294.43/187.00 inference(quant_inst,[status(thm)],[])).
% 294.43/187.00 tff(26536,plain,
% 294.43/187.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s14) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s15)) | (~node21(c_e_h_1, c_l, s14, s15))),
% 294.43/187.00 inference(modus_ponens,[status(thm)],[26535, 26534])).
% 294.43/187.00 tff(26537,plain,
% 294.43/187.00 ($false),
% 294.43/187.00 inference(unit_resolution,[status(thm)],[26536, 52, 26533, 26532, 26531])).
% 294.43/187.00 tff(26538,plain,((~node21(c_e_h_1, c_l, s14, s15)) | node20(c_e_h_1, c_l, s14) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s15))), inference(lemma,lemma(discharge,[]))).
% 294.43/187.00 tff(26539,plain,
% 294.43/187.00 (~node21(c_e_h_1, c_l, s14, s15)),
% 294.43/187.00 inference(unit_resolution,[status(thm)],[26538, 26531, 26532])).
% 294.43/187.00 tff(26540,plain,
% 294.43/187.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s14, s15)) | node21(c_e_h_1, c_l, s14, s15) | node22(c_e_h_1, c_l, s14, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s14, s15)) | node21(c_e_h_1, c_l, s14, s15) | node22(c_e_h_1, c_l, s14, s15))),
% 294.43/187.00 inference(rewrite,[status(thm)],[])).
% 294.43/187.00 tff(26541,plain,
% 294.43/187.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s14, s15)) | node21(c_e_h_1, c_l, s14, s15) | node22(c_e_h_1, c_l, s14, s15))),
% 294.43/187.00 inference(quant_inst,[status(thm)],[])).
% 294.43/187.00 tff(26542,plain,
% 294.43/187.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s14, s15)) | node21(c_e_h_1, c_l, s14, s15) | node22(c_e_h_1, c_l, s14, s15)),
% 294.43/187.00 inference(modus_ponens,[status(thm)],[26541, 26540])).
% 294.43/187.00 tff(26543,plain,
% 294.43/187.00 (node21(c_e_h_1, c_l, s14, s15) | node22(c_e_h_1, c_l, s14, s15)),
% 294.43/187.00 inference(unit_resolution,[status(thm)],[26542, 82, 12926])).
% 294.43/187.00 tff(26544,plain,
% 294.43/187.00 (node22(c_e_h_1, c_l, s14, s15)),
% 294.43/187.00 inference(unit_resolution,[status(thm)],[26543, 26539])).
% 294.43/187.00 tff(26545,plain,
% 294.43/187.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s15)) | (~node22(c_e_h_1, c_l, s14, s15)) | m_and_h_gate_v_out(c_e_h_1, c_l, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s15)) | (~node22(c_e_h_1, c_l, s14, s15)) | m_and_h_gate_v_out(c_e_h_1, c_l, s14))),
% 294.43/187.00 inference(rewrite,[status(thm)],[])).
% 294.43/187.00 tff(26546,plain,
% 294.43/187.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s15)) | (~node22(c_e_h_1, c_l, s14, s15)) | m_and_h_gate_v_out(c_e_h_1, c_l, s14))),
% 294.43/187.00 inference(quant_inst,[status(thm)],[])).
% 294.43/187.00 tff(26547,plain,
% 294.43/187.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s15)) | (~node22(c_e_h_1, c_l, s14, s15)) | m_and_h_gate_v_out(c_e_h_1, c_l, s14)),
% 294.43/187.00 inference(modus_ponens,[status(thm)],[26546, 26545])).
% 294.43/187.00 tff(26548,plain,
% 294.43/187.00 ($false),
% 294.43/187.00 inference(unit_resolution,[status(thm)],[26547, 108, 26544, 25442, 26531])).
% 294.43/187.00 tff(26549,plain,((~m_and_h_gate_v_out(c_e_h_1, c_l, s15)) | m_and_h_gate_v_out(c_e_h_1, c_l, s14) | node20(c_e_h_1, c_l, s14)), inference(lemma,lemma(discharge,[]))).
% 294.43/187.00 tff(26550,plain,
% 294.43/187.00 (~m_and_h_gate_v_out(c_e_h_1, c_l, s15)),
% 294.43/187.00 inference(unit_resolution,[status(thm)],[26549, 25440, 26530])).
% 294.43/187.00 tff(26551,assumption,(m_or_h_gate_v_in1(c_e_h_1, c_j, s15)), introduced(assumption)).
% 294.43/187.00 tff(26552,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_l, s15)), introduced(assumption)).
% 294.43/187.00 tff(26553,plain,
% 294.43/187.00 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s15)) | m_and_h_gate_v_out(c_e_h_1, c_l, s15))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s15)) | m_and_h_gate_v_out(c_e_h_1, c_l, s15))),
% 294.43/187.00 inference(rewrite,[status(thm)],[])).
% 294.43/187.00 tff(26554,plain,
% 294.43/187.00 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s15)) | m_and_h_gate_v_out(c_e_h_1, c_l, s15))),
% 294.43/187.00 inference(quant_inst,[status(thm)],[])).
% 294.43/187.00 tff(26555,plain,
% 294.43/187.00 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s15)) | m_and_h_gate_v_out(c_e_h_1, c_l, s15)),
% 294.43/187.00 inference(modus_ponens,[status(thm)],[26554, 26553])).
% 294.43/187.00 tff(26556,plain,
% 294.43/187.00 ($false),
% 294.43/187.00 inference(unit_resolution,[status(thm)],[26555, 1100, 26552, 26551])).
% 294.43/187.00 tff(26557,plain,((~m_or_h_gate_v_in1(c_e_h_1, c_j, s15)) | m_and_h_gate_v_out(c_e_h_1, c_l, s15)), inference(lemma,lemma(discharge,[]))).
% 294.43/187.00 tff(26558,plain,
% 294.43/187.00 (~m_or_h_gate_v_in1(c_e_h_1, c_j, s15)),
% 294.43/187.00 inference(unit_resolution,[status(thm)],[26557, 26550])).
% 294.43/187.00 tff(26559,assumption,(m_c_h_element_v_out(c_e_h_1, c_h, s17)), introduced(assumption)).
% 294.43/187.00 tff(26560,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_q, s14)), introduced(assumption)).
% 294.43/187.00 tff(26561,plain,
% 294.43/187.00 (~m_cell_v_ack(c_e_h_1, s14)),
% 294.43/187.00 inference(unit_resolution,[status(thm)],[24318, 26560])).
% 294.43/187.00 tff(26562,plain,
% 294.43/187.00 (~m_or_h_gate_v_in2(c_e_h_1, c_j, s14)),
% 294.43/187.00 inference(unit_resolution,[status(thm)],[24322, 1085, 26561])).
% 294.43/187.00 tff(26563,plain,
% 294.43/187.00 (~m_or_h_gate_v_out(c_e_h_1, c_j, s15)),
% 294.43/187.00 inference(unit_resolution,[status(thm)],[25480, 26562, 25461, 23480])).
% 294.43/187.00 tff(26564,plain,
% 294.43/187.00 (~m_c_h_element_v_in2(c_e_h_1, c_h, s15)),
% 294.43/187.00 inference(unit_resolution,[status(thm)],[25489, 26563])).
% 294.43/187.00 tff(26565,plain,
% 294.43/187.00 (~m_c_h_element_v_out(c_e_h_1, c_h, s16)),
% 294.43/187.00 inference(unit_resolution,[status(thm)],[25564, 26564, 25492])).
% 294.43/187.00 tff(26566,assumption,(~m_c_h_element_v_out(c_e_h_1, c_h, s16)), introduced(assumption)).
% 294.43/187.00 tff(26567,assumption,(node18(c_e_h_1, c_h, s16, s17)), introduced(assumption)).
% 294.43/187.00 tff(26568,plain,
% 294.43/187.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s17)) | m_c_h_element_v_out(c_e_h_1, c_h, s16) | (~node18(c_e_h_1, c_h, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s17)) | m_c_h_element_v_out(c_e_h_1, c_h, s16) | (~node18(c_e_h_1, c_h, s16, s17)))),
% 294.43/187.00 inference(rewrite,[status(thm)],[])).
% 294.43/187.00 tff(26569,plain,
% 294.43/187.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s17)) | m_c_h_element_v_out(c_e_h_1, c_h, s16) | (~node18(c_e_h_1, c_h, s16, s17)))),
% 294.43/187.00 inference(quant_inst,[status(thm)],[])).
% 294.43/187.00 tff(26570,plain,
% 294.43/187.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s17)) | m_c_h_element_v_out(c_e_h_1, c_h, s16) | (~node18(c_e_h_1, c_h, s16, s17))),
% 294.43/187.00 inference(modus_ponens,[status(thm)],[26569, 26568])).
% 294.43/187.00 tff(26571,plain,
% 294.43/187.00 ($false),
% 294.43/187.00 inference(unit_resolution,[status(thm)],[26570, 753, 26559, 26566, 26567])).
% 294.43/187.00 tff(26572,plain,((~node18(c_e_h_1, c_h, s16, s17)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s17)) | m_c_h_element_v_out(c_e_h_1, c_h, s16)), inference(lemma,lemma(discharge,[]))).
% 294.43/187.00 tff(26573,plain,
% 294.43/187.00 (~node18(c_e_h_1, c_h, s16, s17)),
% 294.43/187.00 inference(unit_resolution,[status(thm)],[26572, 26566, 26559])).
% 294.43/187.00 tff(26574,plain,
% 294.43/187.00 (~node18(c_e_h_1, c_h, s16, s17)),
% 294.43/187.00 inference(unit_resolution,[status(thm)],[26572, 26559, 26566])).
% 294.43/187.00 tff(26575,plain,
% 294.43/187.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s16, s17)) | node19(c_e_h_1, c_h, s16, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s16, s17)) | node19(c_e_h_1, c_h, s16, s17))),
% 294.43/187.00 inference(rewrite,[status(thm)],[])).
% 294.43/187.00 tff(26576,plain,
% 294.43/187.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s16, s17)) | node19(c_e_h_1, c_h, s16, s17))),
% 294.43/187.00 inference(quant_inst,[status(thm)],[])).
% 294.43/187.00 tff(26577,plain,
% 294.43/187.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s16, s17)) | node19(c_e_h_1, c_h, s16, s17)),
% 294.43/187.00 inference(modus_ponens,[status(thm)],[26576, 26575])).
% 294.43/187.00 tff(26578,plain,
% 294.43/187.00 (node19(c_e_h_1, c_h, s16, s17)),
% 294.43/187.00 inference(unit_resolution,[status(thm)],[26577, 190, 11967])).
% 294.43/187.00 tff(26579,plain,
% 294.43/187.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s16) | (~node19(c_e_h_1, c_h, s16, s17)) | node18(c_e_h_1, c_h, s16, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s16) | (~node19(c_e_h_1, c_h, s16, s17)) | node18(c_e_h_1, c_h, s16, s17))),
% 294.51/187.01 inference(rewrite,[status(thm)],[])).
% 294.51/187.01 tff(26580,plain,
% 294.51/187.01 ((node17(c_e_h_1, c_h, s16) | node18(c_e_h_1, c_h, s16, s17) | (~node19(c_e_h_1, c_h, s16, s17))) <=> (node17(c_e_h_1, c_h, s16) | (~node19(c_e_h_1, c_h, s16, s17)) | node18(c_e_h_1, c_h, s16, s17))),
% 294.51/187.01 inference(rewrite,[status(thm)],[])).
% 294.51/187.01 tff(26581,plain,
% 294.51/187.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s16) | node18(c_e_h_1, c_h, s16, s17) | (~node19(c_e_h_1, c_h, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s16) | (~node19(c_e_h_1, c_h, s16, s17)) | node18(c_e_h_1, c_h, s16, s17)))),
% 294.51/187.01 inference(monotonicity,[status(thm)],[26580])).
% 294.51/187.01 tff(26582,plain,
% 294.51/187.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s16) | node18(c_e_h_1, c_h, s16, s17) | (~node19(c_e_h_1, c_h, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s16) | (~node19(c_e_h_1, c_h, s16, s17)) | node18(c_e_h_1, c_h, s16, s17))),
% 294.51/187.01 inference(transitivity,[status(thm)],[26581, 26579])).
% 294.51/187.01 tff(26583,plain,
% 294.51/187.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s16) | node18(c_e_h_1, c_h, s16, s17) | (~node19(c_e_h_1, c_h, s16, s17)))),
% 294.51/187.01 inference(quant_inst,[status(thm)],[])).
% 294.51/187.01 tff(26584,plain,
% 294.51/187.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s16) | (~node19(c_e_h_1, c_h, s16, s17)) | node18(c_e_h_1, c_h, s16, s17)),
% 294.51/187.01 inference(modus_ponens,[status(thm)],[26583, 26582])).
% 294.51/187.01 tff(26585,plain,
% 294.51/187.01 (node17(c_e_h_1, c_h, s16) | node18(c_e_h_1, c_h, s16, s17)),
% 294.51/187.01 inference(unit_resolution,[status(thm)],[26584, 776, 26578])).
% 294.51/187.01 tff(26586,plain,
% 294.51/187.01 (node17(c_e_h_1, c_h, s16)),
% 294.51/187.01 inference(unit_resolution,[status(thm)],[26585, 26574])).
% 294.51/187.01 tff(26587,assumption,(node15(c_e_h_1, c_h, s16, s17)), introduced(assumption)).
% 294.51/187.01 tff(26588,plain,
% 294.51/187.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s17)) | (~node15(c_e_h_1, c_h, s16, s17)) | m_c_h_element_v_out(c_e_h_1, c_h, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s17)) | (~node15(c_e_h_1, c_h, s16, s17)) | m_c_h_element_v_out(c_e_h_1, c_h, s16))),
% 294.51/187.01 inference(rewrite,[status(thm)],[])).
% 294.51/187.01 tff(26589,plain,
% 294.51/187.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s17)) | (~node15(c_e_h_1, c_h, s16, s17)) | m_c_h_element_v_out(c_e_h_1, c_h, s16))),
% 294.51/187.01 inference(quant_inst,[status(thm)],[])).
% 294.51/187.01 tff(26590,plain,
% 294.51/187.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s17)) | (~node15(c_e_h_1, c_h, s16, s17)) | m_c_h_element_v_out(c_e_h_1, c_h, s16)),
% 294.51/187.01 inference(modus_ponens,[status(thm)],[26589, 26588])).
% 294.51/187.01 tff(26591,plain,
% 294.51/187.01 ($false),
% 294.51/187.01 inference(unit_resolution,[status(thm)],[26590, 147, 26559, 26566, 26587])).
% 294.51/187.01 tff(26592,plain,((~node15(c_e_h_1, c_h, s16, s17)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s17)) | m_c_h_element_v_out(c_e_h_1, c_h, s16)), inference(lemma,lemma(discharge,[]))).
% 294.51/187.01 tff(26593,plain,
% 294.51/187.01 (~node15(c_e_h_1, c_h, s16, s17)),
% 294.51/187.01 inference(unit_resolution,[status(thm)],[26592, 26559, 26566])).
% 294.51/187.01 tff(26594,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_h, s16)), introduced(assumption)).
% 294.51/187.01 tff(26595,assumption,(node14(c_e_h_1, c_h, s16, s17)), introduced(assumption)).
% 294.51/187.01 tff(26596,plain,
% 294.51/187.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s17)) | m_c_h_element_v_in1(c_e_h_1, c_h, s16) | (~node14(c_e_h_1, c_h, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s17)) | m_c_h_element_v_in1(c_e_h_1, c_h, s16) | (~node14(c_e_h_1, c_h, s16, s17)))),
% 294.51/187.01 inference(rewrite,[status(thm)],[])).
% 294.51/187.01 tff(26597,plain,
% 294.51/187.01 (((~node14(c_e_h_1, c_h, s16, s17)) | m_c_h_element_v_in1(c_e_h_1, c_h, s16) | (~m_c_h_element_v_out(c_e_h_1, c_h, s17))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_h, s17)) | m_c_h_element_v_in1(c_e_h_1, c_h, s16) | (~node14(c_e_h_1, c_h, s16, s17)))),
% 294.51/187.01 inference(rewrite,[status(thm)],[])).
% 294.51/187.01 tff(26598,plain,
% 294.51/187.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s16, s17)) | m_c_h_element_v_in1(c_e_h_1, c_h, s16) | (~m_c_h_element_v_out(c_e_h_1, c_h, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s17)) | m_c_h_element_v_in1(c_e_h_1, c_h, s16) | (~node14(c_e_h_1, c_h, s16, s17))))),
% 294.51/187.01 inference(monotonicity,[status(thm)],[26597])).
% 294.51/187.01 tff(26599,plain,
% 294.51/187.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s16, s17)) | m_c_h_element_v_in1(c_e_h_1, c_h, s16) | (~m_c_h_element_v_out(c_e_h_1, c_h, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s17)) | m_c_h_element_v_in1(c_e_h_1, c_h, s16) | (~node14(c_e_h_1, c_h, s16, s17)))),
% 294.51/187.01 inference(transitivity,[status(thm)],[26598, 26596])).
% 294.51/187.01 tff(26600,plain,
% 294.51/187.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s16, s17)) | m_c_h_element_v_in1(c_e_h_1, c_h, s16) | (~m_c_h_element_v_out(c_e_h_1, c_h, s17)))),
% 294.51/187.01 inference(quant_inst,[status(thm)],[])).
% 294.51/187.01 tff(26601,plain,
% 294.51/187.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s17)) | m_c_h_element_v_in1(c_e_h_1, c_h, s16) | (~node14(c_e_h_1, c_h, s16, s17))),
% 294.51/187.01 inference(modus_ponens,[status(thm)],[26600, 26599])).
% 294.51/187.01 tff(26602,plain,
% 294.51/187.01 ($false),
% 294.51/187.01 inference(unit_resolution,[status(thm)],[26601, 223, 26559, 26595, 26594])).
% 294.51/187.01 tff(26603,plain,((~node14(c_e_h_1, c_h, s16, s17)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s17)) | m_c_h_element_v_in1(c_e_h_1, c_h, s16)), inference(lemma,lemma(discharge,[]))).
% 294.51/187.01 tff(26604,plain,
% 294.51/187.01 (~node14(c_e_h_1, c_h, s16, s17)),
% 294.51/187.01 inference(unit_resolution,[status(thm)],[26603, 26559, 26594])).
% 294.51/187.01 tff(26605,plain,
% 294.51/187.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s16) | (~node19(c_e_h_1, c_h, s16, s17)) | node15(c_e_h_1, c_h, s16, s17) | node14(c_e_h_1, c_h, s16, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s16) | (~node19(c_e_h_1, c_h, s16, s17)) | node15(c_e_h_1, c_h, s16, s17) | node14(c_e_h_1, c_h, s16, s17))),
% 294.51/187.01 inference(rewrite,[status(thm)],[])).
% 294.51/187.01 tff(26606,plain,
% 294.51/187.01 ((node16(c_e_h_1, c_h, s16) | node14(c_e_h_1, c_h, s16, s17) | node15(c_e_h_1, c_h, s16, s17) | (~node19(c_e_h_1, c_h, s16, s17))) <=> (node16(c_e_h_1, c_h, s16) | (~node19(c_e_h_1, c_h, s16, s17)) | node15(c_e_h_1, c_h, s16, s17) | node14(c_e_h_1, c_h, s16, s17))),
% 294.51/187.02 inference(rewrite,[status(thm)],[])).
% 294.51/187.02 tff(26607,plain,
% 294.51/187.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s16) | node14(c_e_h_1, c_h, s16, s17) | node15(c_e_h_1, c_h, s16, s17) | (~node19(c_e_h_1, c_h, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s16) | (~node19(c_e_h_1, c_h, s16, s17)) | node15(c_e_h_1, c_h, s16, s17) | node14(c_e_h_1, c_h, s16, s17)))),
% 294.51/187.02 inference(monotonicity,[status(thm)],[26606])).
% 294.51/187.02 tff(26608,plain,
% 294.51/187.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s16) | node14(c_e_h_1, c_h, s16, s17) | node15(c_e_h_1, c_h, s16, s17) | (~node19(c_e_h_1, c_h, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s16) | (~node19(c_e_h_1, c_h, s16, s17)) | node15(c_e_h_1, c_h, s16, s17) | node14(c_e_h_1, c_h, s16, s17))),
% 294.51/187.02 inference(transitivity,[status(thm)],[26607, 26605])).
% 294.51/187.02 tff(26609,plain,
% 294.51/187.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s16) | node14(c_e_h_1, c_h, s16, s17) | node15(c_e_h_1, c_h, s16, s17) | (~node19(c_e_h_1, c_h, s16, s17)))),
% 294.51/187.02 inference(quant_inst,[status(thm)],[])).
% 294.51/187.02 tff(26610,plain,
% 294.51/187.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s16) | (~node19(c_e_h_1, c_h, s16, s17)) | node15(c_e_h_1, c_h, s16, s17) | node14(c_e_h_1, c_h, s16, s17)),
% 294.51/187.02 inference(modus_ponens,[status(thm)],[26609, 26608])).
% 294.51/187.02 tff(26611,plain,
% 294.51/187.02 (node16(c_e_h_1, c_h, s16) | node15(c_e_h_1, c_h, s16, s17) | node14(c_e_h_1, c_h, s16, s17)),
% 294.51/187.02 inference(unit_resolution,[status(thm)],[26610, 204, 26578])).
% 294.51/187.02 tff(26612,plain,
% 294.51/187.02 (node16(c_e_h_1, c_h, s16)),
% 294.51/187.02 inference(unit_resolution,[status(thm)],[26611, 26604, 26593])).
% 294.51/187.02 tff(26613,assumption,(node17(c_e_h_1, c_h, s16)), introduced(assumption)).
% 294.51/187.02 tff(26614,assumption,(node16(c_e_h_1, c_h, s16)), introduced(assumption)).
% 294.51/187.02 tff(26615,plain,
% 294.51/187.02 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s16) | (~node17(c_e_h_1, c_h, s16)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s16)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s16) | (~node17(c_e_h_1, c_h, s16)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s16)))),
% 294.51/187.02 inference(rewrite,[status(thm)],[])).
% 294.51/187.02 tff(26616,plain,
% 294.51/187.02 ((m_c_h_element_v_in1(c_e_h_1, c_h, s16) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s16)) | (~node17(c_e_h_1, c_h, s16))) <=> (m_c_h_element_v_in1(c_e_h_1, c_h, s16) | (~node17(c_e_h_1, c_h, s16)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s16)))),
% 294.51/187.02 inference(rewrite,[status(thm)],[])).
% 294.51/187.02 tff(26617,plain,
% 294.51/187.02 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s16) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s16)) | (~node17(c_e_h_1, c_h, s16)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s16) | (~node17(c_e_h_1, c_h, s16)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s16))))),
% 294.51/187.02 inference(monotonicity,[status(thm)],[26616])).
% 294.51/187.02 tff(26618,plain,
% 294.51/187.02 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s16) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s16)) | (~node17(c_e_h_1, c_h, s16)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s16) | (~node17(c_e_h_1, c_h, s16)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s16)))),
% 294.51/187.02 inference(transitivity,[status(thm)],[26617, 26615])).
% 294.51/187.02 tff(26619,plain,
% 294.51/187.02 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s16) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s16)) | (~node17(c_e_h_1, c_h, s16)))),
% 294.51/187.02 inference(quant_inst,[status(thm)],[])).
% 294.51/187.02 tff(26620,plain,
% 294.51/187.02 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s16) | (~node17(c_e_h_1, c_h, s16)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s16))),
% 294.51/187.02 inference(modus_ponens,[status(thm)],[26619, 26618])).
% 294.51/187.02 tff(26621,plain,
% 294.51/187.02 (m_c_h_element_v_in1(c_e_h_1, c_h, s16) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s16))),
% 294.51/187.02 inference(unit_resolution,[status(thm)],[26620, 859, 26613])).
% 294.51/187.02 tff(26622,plain,
% 294.51/187.02 (~m_c_h_element_v_in2(c_e_h_1, c_h, s16)),
% 294.51/187.02 inference(unit_resolution,[status(thm)],[26621, 26594])).
% 294.51/187.02 tff(26623,plain,
% 294.51/187.02 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s16)) | m_c_h_element_v_in1(c_e_h_1, c_h, s16) | m_c_h_element_v_in2(c_e_h_1, c_h, s16))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s16)) | m_c_h_element_v_in1(c_e_h_1, c_h, s16) | m_c_h_element_v_in2(c_e_h_1, c_h, s16))),
% 294.51/187.02 inference(rewrite,[status(thm)],[])).
% 294.51/187.02 tff(26624,plain,
% 294.51/187.02 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s16)) | m_c_h_element_v_in1(c_e_h_1, c_h, s16) | m_c_h_element_v_in2(c_e_h_1, c_h, s16))),
% 294.51/187.02 inference(quant_inst,[status(thm)],[])).
% 294.51/187.02 tff(26625,plain,
% 294.51/187.02 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s16)) | m_c_h_element_v_in1(c_e_h_1, c_h, s16) | m_c_h_element_v_in2(c_e_h_1, c_h, s16)),
% 294.51/187.02 inference(modus_ponens,[status(thm)],[26624, 26623])).
% 294.51/187.02 tff(26626,plain,
% 294.51/187.02 (m_c_h_element_v_in1(c_e_h_1, c_h, s16) | m_c_h_element_v_in2(c_e_h_1, c_h, s16)),
% 294.51/187.02 inference(unit_resolution,[status(thm)],[26625, 178, 26614])).
% 294.51/187.02 tff(26627,plain,
% 294.51/187.02 ($false),
% 294.51/187.02 inference(unit_resolution,[status(thm)],[26626, 26622, 26594])).
% 294.51/187.02 tff(26628,plain,(m_c_h_element_v_in1(c_e_h_1, c_h, s16) | (~node16(c_e_h_1, c_h, s16)) | (~node17(c_e_h_1, c_h, s16))), inference(lemma,lemma(discharge,[]))).
% 294.51/187.02 tff(26629,plain,
% 294.51/187.02 (m_c_h_element_v_in1(c_e_h_1, c_h, s16)),
% 294.51/187.02 inference(unit_resolution,[status(thm)],[26628, 26614, 26613])).
% 294.51/187.02 tff(26630,plain,
% 294.51/187.02 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s16)) | (~node17(c_e_h_1, c_h, s16)) | m_c_h_element_v_in2(c_e_h_1, c_h, s16))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s16)) | (~node17(c_e_h_1, c_h, s16)) | m_c_h_element_v_in2(c_e_h_1, c_h, s16))),
% 294.51/187.02 inference(rewrite,[status(thm)],[])).
% 294.51/187.02 tff(26631,plain,
% 294.51/187.02 (((~m_c_h_element_v_in1(c_e_h_1, c_h, s16)) | m_c_h_element_v_in2(c_e_h_1, c_h, s16) | (~node17(c_e_h_1, c_h, s16))) <=> ((~m_c_h_element_v_in1(c_e_h_1, c_h, s16)) | (~node17(c_e_h_1, c_h, s16)) | m_c_h_element_v_in2(c_e_h_1, c_h, s16))),
% 294.51/187.02 inference(rewrite,[status(thm)],[])).
% 294.51/187.02 tff(26632,plain,
% 294.51/187.02 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s16)) | m_c_h_element_v_in2(c_e_h_1, c_h, s16) | (~node17(c_e_h_1, c_h, s16)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s16)) | (~node17(c_e_h_1, c_h, s16)) | m_c_h_element_v_in2(c_e_h_1, c_h, s16)))),
% 294.51/187.02 inference(monotonicity,[status(thm)],[26631])).
% 294.51/187.02 tff(26633,plain,
% 294.51/187.02 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s16)) | m_c_h_element_v_in2(c_e_h_1, c_h, s16) | (~node17(c_e_h_1, c_h, s16)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s16)) | (~node17(c_e_h_1, c_h, s16)) | m_c_h_element_v_in2(c_e_h_1, c_h, s16))),
% 294.51/187.02 inference(transitivity,[status(thm)],[26632, 26630])).
% 294.51/187.02 tff(26634,plain,
% 294.51/187.02 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s16)) | m_c_h_element_v_in2(c_e_h_1, c_h, s16) | (~node17(c_e_h_1, c_h, s16)))),
% 294.51/187.02 inference(quant_inst,[status(thm)],[])).
% 294.51/187.02 tff(26635,plain,
% 294.51/187.02 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s16)) | (~node17(c_e_h_1, c_h, s16)) | m_c_h_element_v_in2(c_e_h_1, c_h, s16)),
% 294.51/187.02 inference(modus_ponens,[status(thm)],[26634, 26633])).
% 294.51/187.02 tff(26636,plain,
% 294.51/187.02 ((~m_c_h_element_v_in1(c_e_h_1, c_h, s16)) | m_c_h_element_v_in2(c_e_h_1, c_h, s16)),
% 294.51/187.02 inference(unit_resolution,[status(thm)],[26635, 919, 26613])).
% 294.51/187.02 tff(26637,plain,
% 294.51/187.02 (m_c_h_element_v_in2(c_e_h_1, c_h, s16)),
% 294.51/187.02 inference(unit_resolution,[status(thm)],[26636, 26629])).
% 294.51/187.02 tff(26638,plain,
% 294.51/187.02 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s16)) | (~node16(c_e_h_1, c_h, s16)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s16)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s16)) | (~node16(c_e_h_1, c_h, s16)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s16)))),
% 294.51/187.02 inference(rewrite,[status(thm)],[])).
% 294.51/187.02 tff(26639,plain,
% 294.51/187.02 (((~node16(c_e_h_1, c_h, s16)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s16)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s16))) <=> ((~m_c_h_element_v_in1(c_e_h_1, c_h, s16)) | (~node16(c_e_h_1, c_h, s16)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s16)))),
% 294.51/187.02 inference(rewrite,[status(thm)],[])).
% 294.51/187.02 tff(26640,plain,
% 294.51/187.02 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_h, s16)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s16)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s16)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s16)) | (~node16(c_e_h_1, c_h, s16)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s16))))),
% 294.51/187.02 inference(monotonicity,[status(thm)],[26639])).
% 294.51/187.02 tff(26641,plain,
% 294.51/187.02 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_h, s16)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s16)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s16)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s16)) | (~node16(c_e_h_1, c_h, s16)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s16)))),
% 294.51/187.02 inference(transitivity,[status(thm)],[26640, 26638])).
% 294.51/187.02 tff(26642,plain,
% 294.51/187.02 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_h, s16)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s16)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s16)))),
% 294.51/187.03 inference(quant_inst,[status(thm)],[])).
% 294.51/187.03 tff(26643,plain,
% 294.51/187.03 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s16)) | (~node16(c_e_h_1, c_h, s16)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s16))),
% 294.51/187.03 inference(modus_ponens,[status(thm)],[26642, 26641])).
% 294.51/187.03 tff(26644,plain,
% 294.51/187.03 ((~m_c_h_element_v_in1(c_e_h_1, c_h, s16)) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s16))),
% 294.51/187.03 inference(unit_resolution,[status(thm)],[26643, 2307, 26614])).
% 294.51/187.03 tff(26645,plain,
% 294.51/187.03 ($false),
% 294.51/187.03 inference(unit_resolution,[status(thm)],[26644, 26637, 26629])).
% 294.51/187.03 tff(26646,plain,((~node16(c_e_h_1, c_h, s16)) | (~node17(c_e_h_1, c_h, s16))), inference(lemma,lemma(discharge,[]))).
% 294.51/187.03 tff(26647,plain,
% 294.51/187.03 ($false),
% 294.51/187.03 inference(unit_resolution,[status(thm)],[26646, 26612, 26586])).
% 294.51/187.03 tff(26648,plain,((~m_c_h_element_v_out(c_e_h_1, c_h, s17)) | m_c_h_element_v_in1(c_e_h_1, c_h, s16) | m_c_h_element_v_out(c_e_h_1, c_h, s16)), inference(lemma,lemma(discharge,[]))).
% 294.51/187.03 tff(26649,plain,
% 294.51/187.03 (m_c_h_element_v_in1(c_e_h_1, c_h, s16)),
% 294.51/187.03 inference(unit_resolution,[status(thm)],[26648, 26566, 26559])).
% 294.51/187.03 tff(26650,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_h, s16)), introduced(assumption)).
% 294.51/187.03 tff(26651,plain,
% 294.51/187.03 ((~m_c_h_element_v_in1(c_e_h_1, c_h, s16)) | (~node17(c_e_h_1, c_h, s16))),
% 294.51/187.03 inference(unit_resolution,[status(thm)],[26635, 919, 26650])).
% 294.51/187.03 tff(26652,plain,
% 294.51/187.03 (~node17(c_e_h_1, c_h, s16)),
% 294.51/187.03 inference(unit_resolution,[status(thm)],[26651, 26649])).
% 294.51/187.03 tff(26653,plain,
% 294.51/187.03 ($false),
% 294.51/187.03 inference(unit_resolution,[status(thm)],[26585, 26652, 26573])).
% 294.51/187.03 tff(26654,plain,(m_c_h_element_v_out(c_e_h_1, c_h, s16) | m_c_h_element_v_in2(c_e_h_1, c_h, s16) | (~m_c_h_element_v_out(c_e_h_1, c_h, s17))), inference(lemma,lemma(discharge,[]))).
% 294.51/187.03 tff(26655,plain,
% 294.51/187.03 (m_c_h_element_v_in2(c_e_h_1, c_h, s16)),
% 294.51/187.03 inference(unit_resolution,[status(thm)],[26654, 26565, 26559])).
% 294.51/187.03 tff(26656,assumption,(~m_or_h_gate_v_in1(c_e_h_1, c_j, s15)), introduced(assumption)).
% 294.51/187.03 tff(26657,assumption,(~node20(c_e_h_3, c_q, s14)), introduced(assumption)).
% 294.51/187.03 tff(26658,assumption,(m_and_h_gate_v_out(c_e_h_3, c_q, s15)), introduced(assumption)).
% 294.51/187.03 tff(26659,assumption,(node22(c_e_h_3, c_q, s14, s15)), introduced(assumption)).
% 294.51/187.03 tff(26660,plain,
% 294.51/187.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s15)) | (~node22(c_e_h_3, c_q, s14, s15)) | m_and_h_gate_v_out(c_e_h_3, c_q, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s15)) | (~node22(c_e_h_3, c_q, s14, s15)) | m_and_h_gate_v_out(c_e_h_3, c_q, s14))),
% 294.51/187.03 inference(rewrite,[status(thm)],[])).
% 294.51/187.03 tff(26661,plain,
% 294.51/187.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s15)) | (~node22(c_e_h_3, c_q, s14, s15)) | m_and_h_gate_v_out(c_e_h_3, c_q, s14))),
% 294.51/187.03 inference(quant_inst,[status(thm)],[])).
% 294.51/187.03 tff(26662,plain,
% 294.51/187.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s15)) | (~node22(c_e_h_3, c_q, s14, s15)) | m_and_h_gate_v_out(c_e_h_3, c_q, s14)),
% 294.51/187.03 inference(modus_ponens,[status(thm)],[26661, 26660])).
% 294.51/187.03 tff(26663,plain,
% 294.51/187.03 ($false),
% 294.51/187.03 inference(unit_resolution,[status(thm)],[26662, 108, 26560, 26658, 26659])).
% 294.51/187.03 tff(26664,plain,((~node22(c_e_h_3, c_q, s14, s15)) | m_and_h_gate_v_out(c_e_h_3, c_q, s14) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s15))), inference(lemma,lemma(discharge,[]))).
% 294.51/187.03 tff(26665,plain,
% 294.51/187.03 (~node22(c_e_h_3, c_q, s14, s15)),
% 294.51/187.03 inference(unit_resolution,[status(thm)],[26664, 26658, 26560])).
% 294.51/187.03 tff(26666,plain,
% 294.51/187.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s14, s15)) | node21(c_e_h_3, c_q, s14, s15) | node22(c_e_h_3, c_q, s14, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s14, s15)) | node21(c_e_h_3, c_q, s14, s15) | node22(c_e_h_3, c_q, s14, s15))),
% 294.51/187.03 inference(rewrite,[status(thm)],[])).
% 294.51/187.03 tff(26667,plain,
% 294.51/187.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s14, s15)) | node21(c_e_h_3, c_q, s14, s15) | node22(c_e_h_3, c_q, s14, s15))),
% 294.51/187.03 inference(quant_inst,[status(thm)],[])).
% 294.51/187.03 tff(26668,plain,
% 294.51/187.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s14, s15)) | node21(c_e_h_3, c_q, s14, s15) | node22(c_e_h_3, c_q, s14, s15)),
% 294.51/187.03 inference(modus_ponens,[status(thm)],[26667, 26666])).
% 294.51/187.03 tff(26669,plain,
% 294.51/187.03 (node21(c_e_h_3, c_q, s14, s15) | node22(c_e_h_3, c_q, s14, s15)),
% 294.51/187.03 inference(unit_resolution,[status(thm)],[26668, 82, 12926])).
% 294.51/187.03 tff(26670,plain,
% 294.51/187.03 (node21(c_e_h_3, c_q, s14, s15)),
% 294.51/187.03 inference(unit_resolution,[status(thm)],[26669, 26665])).
% 294.51/187.03 tff(26671,plain,
% 294.51/187.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s15)) | node20(c_e_h_3, c_q, s14) | (~node21(c_e_h_3, c_q, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s15)) | node20(c_e_h_3, c_q, s14) | (~node21(c_e_h_3, c_q, s14, s15)))),
% 294.51/187.03 inference(rewrite,[status(thm)],[])).
% 294.51/187.03 tff(26672,plain,
% 294.51/187.03 ((node20(c_e_h_3, c_q, s14) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s15)) | (~node21(c_e_h_3, c_q, s14, s15))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_q, s15)) | node20(c_e_h_3, c_q, s14) | (~node21(c_e_h_3, c_q, s14, s15)))),
% 294.51/187.03 inference(rewrite,[status(thm)],[])).
% 294.51/187.03 tff(26673,plain,
% 294.51/187.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s14) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s15)) | (~node21(c_e_h_3, c_q, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s15)) | node20(c_e_h_3, c_q, s14) | (~node21(c_e_h_3, c_q, s14, s15))))),
% 294.51/187.03 inference(monotonicity,[status(thm)],[26672])).
% 294.51/187.03 tff(26674,plain,
% 294.51/187.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s14) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s15)) | (~node21(c_e_h_3, c_q, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s15)) | node20(c_e_h_3, c_q, s14) | (~node21(c_e_h_3, c_q, s14, s15)))),
% 294.51/187.03 inference(transitivity,[status(thm)],[26673, 26671])).
% 294.51/187.03 tff(26675,plain,
% 294.51/187.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s14) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s15)) | (~node21(c_e_h_3, c_q, s14, s15)))),
% 294.51/187.03 inference(quant_inst,[status(thm)],[])).
% 294.51/187.03 tff(26676,plain,
% 294.51/187.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s15)) | node20(c_e_h_3, c_q, s14) | (~node21(c_e_h_3, c_q, s14, s15))),
% 294.51/187.03 inference(modus_ponens,[status(thm)],[26675, 26674])).
% 294.51/187.03 tff(26677,plain,
% 294.51/187.03 ($false),
% 294.51/187.03 inference(unit_resolution,[status(thm)],[26676, 52, 26658, 26670, 26657])).
% 294.51/187.03 tff(26678,plain,((~m_and_h_gate_v_out(c_e_h_3, c_q, s15)) | node20(c_e_h_3, c_q, s14) | m_and_h_gate_v_out(c_e_h_3, c_q, s14)), inference(lemma,lemma(discharge,[]))).
% 294.51/187.03 tff(26679,plain,
% 294.51/187.03 (~m_and_h_gate_v_out(c_e_h_3, c_q, s15)),
% 294.51/187.03 inference(unit_resolution,[status(thm)],[26678, 26560, 26657])).
% 294.51/187.03 tff(26680,plain,
% 294.51/187.03 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s15))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s15))),
% 294.51/187.03 inference(rewrite,[status(thm)],[])).
% 294.51/187.03 tff(26681,plain,
% 294.51/187.03 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s15))),
% 294.51/187.03 inference(quant_inst,[status(thm)],[])).
% 294.51/187.03 tff(26682,plain,
% 294.51/187.03 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s15)),
% 294.51/187.03 inference(modus_ponens,[status(thm)],[26681, 26680])).
% 294.51/187.03 tff(26683,plain,
% 294.51/187.03 (node3(c_e_h_3, c_e_h_1, s15)),
% 294.51/187.03 inference(unit_resolution,[status(thm)],[26682, 2922, 1056])).
% 294.51/187.03 tff(26684,plain,
% 294.51/187.03 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s15)) | (~node3(c_e_h_3, c_e_h_1, s15)) | m_and_h_gate_v_out(c_e_h_3, c_q, s15))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s15)) | (~node3(c_e_h_3, c_e_h_1, s15)) | m_and_h_gate_v_out(c_e_h_3, c_q, s15))),
% 294.51/187.03 inference(rewrite,[status(thm)],[])).
% 294.51/187.03 tff(26685,plain,
% 294.51/187.03 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s15)) | (~node3(c_e_h_3, c_e_h_1, s15)) | m_and_h_gate_v_out(c_e_h_3, c_q, s15))),
% 294.51/187.03 inference(quant_inst,[status(thm)],[])).
% 294.51/187.03 tff(26686,plain,
% 294.51/187.03 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s15)) | (~node3(c_e_h_3, c_e_h_1, s15)) | m_and_h_gate_v_out(c_e_h_3, c_q, s15)),
% 294.51/187.03 inference(modus_ponens,[status(thm)],[26685, 26684])).
% 294.51/187.03 tff(26687,plain,
% 294.51/187.03 ((~m_cell_v_ack(c_e_h_1, s15)) | m_and_h_gate_v_out(c_e_h_3, c_q, s15)),
% 294.51/187.03 inference(unit_resolution,[status(thm)],[26686, 1073, 26683])).
% 294.51/187.03 tff(26688,plain,
% 294.51/187.03 (~m_cell_v_ack(c_e_h_1, s15)),
% 294.51/187.03 inference(unit_resolution,[status(thm)],[26687, 26679])).
% 294.51/187.03 tff(26689,plain,
% 294.51/187.03 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s15)) | m_cell_v_ack(c_e_h_1, s15))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s15)) | m_cell_v_ack(c_e_h_1, s15))),
% 294.51/187.03 inference(rewrite,[status(thm)],[])).
% 294.51/187.03 tff(26690,plain,
% 294.51/187.03 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s15)) | m_cell_v_ack(c_e_h_1, s15))),
% 294.51/187.03 inference(quant_inst,[status(thm)],[])).
% 294.51/187.03 tff(26691,plain,
% 294.51/187.03 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s15)) | m_cell_v_ack(c_e_h_1, s15)),
% 294.51/187.03 inference(modus_ponens,[status(thm)],[26690, 26689])).
% 294.51/187.03 tff(26692,plain,
% 294.51/187.03 (~m_or_h_gate_v_in2(c_e_h_1, c_j, s15)),
% 294.51/187.03 inference(unit_resolution,[status(thm)],[26691, 1085, 26688])).
% 294.51/187.03 tff(26693,assumption,(m_or_h_gate_v_out(c_e_h_1, c_j, s16)), introduced(assumption)).
% 294.51/187.03 tff(26694,assumption,(node6(c_e_h_1, c_j, s15, s16)), introduced(assumption)).
% 294.51/187.03 tff(26695,plain,
% 294.51/187.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s15) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s16)) | (~node6(c_e_h_1, c_j, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s15) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s16)) | (~node6(c_e_h_1, c_j, s15, s16)))),
% 294.51/187.03 inference(rewrite,[status(thm)],[])).
% 294.51/187.03 tff(26696,plain,
% 294.51/187.03 (((~node6(c_e_h_1, c_j, s15, s16)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s16)) | m_or_h_gate_v_out(c_e_h_1, c_j, s15)) <=> (m_or_h_gate_v_out(c_e_h_1, c_j, s15) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s16)) | (~node6(c_e_h_1, c_j, s15, s16)))),
% 294.51/187.04 inference(rewrite,[status(thm)],[])).
% 294.51/187.04 tff(26697,plain,
% 294.51/187.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s15, s16)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s16)) | m_or_h_gate_v_out(c_e_h_1, c_j, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s15) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s16)) | (~node6(c_e_h_1, c_j, s15, s16))))),
% 294.51/187.04 inference(monotonicity,[status(thm)],[26696])).
% 294.51/187.04 tff(26698,plain,
% 294.51/187.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s15, s16)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s16)) | m_or_h_gate_v_out(c_e_h_1, c_j, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s15) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s16)) | (~node6(c_e_h_1, c_j, s15, s16)))),
% 294.51/187.04 inference(transitivity,[status(thm)],[26697, 26695])).
% 294.51/187.04 tff(26699,plain,
% 294.51/187.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s15, s16)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s16)) | m_or_h_gate_v_out(c_e_h_1, c_j, s15))),
% 294.51/187.04 inference(quant_inst,[status(thm)],[])).
% 294.51/187.04 tff(26700,plain,
% 294.51/187.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s15) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s16)) | (~node6(c_e_h_1, c_j, s15, s16))),
% 294.51/187.04 inference(modus_ponens,[status(thm)],[26699, 26698])).
% 294.51/187.04 tff(26701,plain,
% 294.51/187.04 ($false),
% 294.51/187.04 inference(unit_resolution,[status(thm)],[26700, 1121, 26693, 25484, 26694])).
% 294.51/187.04 tff(26702,plain,((~node6(c_e_h_1, c_j, s15, s16)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s16)) | m_or_h_gate_v_out(c_e_h_1, c_j, s15)), inference(lemma,lemma(discharge,[]))).
% 294.51/187.04 tff(26703,plain,
% 294.51/187.04 (~node6(c_e_h_1, c_j, s15, s16)),
% 294.51/187.04 inference(unit_resolution,[status(thm)],[26702, 26693, 25484])).
% 294.51/187.04 tff(26704,assumption,(~m_or_h_gate_v_in2(c_e_h_1, c_j, s15)), introduced(assumption)).
% 294.51/187.04 tff(26705,assumption,(node5(c_e_h_1, c_j, s15, s16)), introduced(assumption)).
% 294.51/187.04 tff(26706,plain,
% 294.51/187.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_1, c_j, s15) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s16)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s15) | (~node5(c_e_h_1, c_j, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_1, c_j, s15) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s16)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s15) | (~node5(c_e_h_1, c_j, s15, s16)))),
% 294.51/187.04 inference(rewrite,[status(thm)],[])).
% 294.51/187.04 tff(26707,plain,
% 294.51/187.04 ((m_or_h_gate_v_in1(c_e_h_1, c_j, s15) | m_or_h_gate_v_in2(c_e_h_1, c_j, s15) | (~node5(c_e_h_1, c_j, s15, s16)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s16))) <=> (m_or_h_gate_v_in2(c_e_h_1, c_j, s15) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s16)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s15) | (~node5(c_e_h_1, c_j, s15, s16)))),
% 294.51/187.04 inference(rewrite,[status(thm)],[])).
% 294.51/187.04 tff(26708,plain,
% 294.51/187.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s15) | m_or_h_gate_v_in2(c_e_h_1, c_j, s15) | (~node5(c_e_h_1, c_j, s15, s16)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_1, c_j, s15) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s16)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s15) | (~node5(c_e_h_1, c_j, s15, s16))))),
% 294.51/187.04 inference(monotonicity,[status(thm)],[26707])).
% 294.51/187.04 tff(26709,plain,
% 294.51/187.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s15) | m_or_h_gate_v_in2(c_e_h_1, c_j, s15) | (~node5(c_e_h_1, c_j, s15, s16)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_1, c_j, s15) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s16)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s15) | (~node5(c_e_h_1, c_j, s15, s16)))),
% 294.51/187.04 inference(transitivity,[status(thm)],[26708, 26706])).
% 294.51/187.04 tff(26710,plain,
% 294.51/187.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s15) | m_or_h_gate_v_in2(c_e_h_1, c_j, s15) | (~node5(c_e_h_1, c_j, s15, s16)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s16)))),
% 294.51/187.04 inference(quant_inst,[status(thm)],[])).
% 294.51/187.04 tff(26711,plain,
% 294.51/187.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_1, c_j, s15) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s16)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s15) | (~node5(c_e_h_1, c_j, s15, s16))),
% 294.51/187.04 inference(modus_ponens,[status(thm)],[26710, 26709])).
% 294.51/187.04 tff(26712,plain,
% 294.51/187.04 ($false),
% 294.51/187.04 inference(unit_resolution,[status(thm)],[26711, 1159, 26693, 26705, 26704, 26656])).
% 294.51/187.04 tff(26713,plain,((~node5(c_e_h_1, c_j, s15, s16)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s16)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s15) | m_or_h_gate_v_in1(c_e_h_1, c_j, s15)), inference(lemma,lemma(discharge,[]))).
% 294.51/187.04 tff(26714,plain,
% 294.51/187.04 (~node5(c_e_h_1, c_j, s15, s16)),
% 294.51/187.04 inference(unit_resolution,[status(thm)],[26713, 26693, 26656, 26704])).
% 294.51/187.04 tff(26715,plain,
% 294.51/187.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s15, s16)) | node6(c_e_h_1, c_j, s15, s16) | node5(c_e_h_1, c_j, s15, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s15, s16)) | node6(c_e_h_1, c_j, s15, s16) | node5(c_e_h_1, c_j, s15, s16))),
% 294.51/187.04 inference(rewrite,[status(thm)],[])).
% 294.51/187.04 tff(26716,plain,
% 294.51/187.04 ((node6(c_e_h_1, c_j, s15, s16) | node5(c_e_h_1, c_j, s15, s16) | (~trans(s15, s16))) <=> ((~trans(s15, s16)) | node6(c_e_h_1, c_j, s15, s16) | node5(c_e_h_1, c_j, s15, s16))),
% 294.51/187.04 inference(rewrite,[status(thm)],[])).
% 294.51/187.04 tff(26717,plain,
% 294.51/187.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s15, s16) | node5(c_e_h_1, c_j, s15, s16) | (~trans(s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s15, s16)) | node6(c_e_h_1, c_j, s15, s16) | node5(c_e_h_1, c_j, s15, s16)))),
% 294.51/187.04 inference(monotonicity,[status(thm)],[26716])).
% 294.51/187.04 tff(26718,plain,
% 294.51/187.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s15, s16) | node5(c_e_h_1, c_j, s15, s16) | (~trans(s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s15, s16)) | node6(c_e_h_1, c_j, s15, s16) | node5(c_e_h_1, c_j, s15, s16))),
% 294.51/187.04 inference(transitivity,[status(thm)],[26717, 26715])).
% 294.51/187.04 tff(26719,plain,
% 294.51/187.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s15, s16) | node5(c_e_h_1, c_j, s15, s16) | (~trans(s15, s16)))),
% 294.51/187.04 inference(quant_inst,[status(thm)],[])).
% 294.51/187.05 tff(26720,plain,
% 294.51/187.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s15, s16)) | node6(c_e_h_1, c_j, s15, s16) | node5(c_e_h_1, c_j, s15, s16)),
% 294.51/187.05 inference(modus_ponens,[status(thm)],[26719, 26718])).
% 294.51/187.05 tff(26721,plain,
% 294.51/187.05 (node6(c_e_h_1, c_j, s15, s16) | node5(c_e_h_1, c_j, s15, s16)),
% 294.51/187.05 inference(unit_resolution,[status(thm)],[26720, 1141, 13499])).
% 294.51/187.05 tff(26722,plain,
% 294.51/187.05 ($false),
% 294.51/187.05 inference(unit_resolution,[status(thm)],[26721, 26714, 26703])).
% 294.51/187.05 tff(26723,plain,((~m_or_h_gate_v_out(c_e_h_1, c_j, s16)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s15) | m_or_h_gate_v_in2(c_e_h_1, c_j, s15) | m_or_h_gate_v_out(c_e_h_1, c_j, s15)), inference(lemma,lemma(discharge,[]))).
% 294.51/187.05 tff(26724,plain,
% 294.51/187.05 (~m_or_h_gate_v_out(c_e_h_1, c_j, s16)),
% 294.51/187.05 inference(unit_resolution,[status(thm)],[26723, 26692, 26656, 26563])).
% 294.51/187.05 tff(26725,plain,
% 294.51/187.05 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s16)) | m_or_h_gate_v_out(c_e_h_1, c_j, s16))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s16)) | m_or_h_gate_v_out(c_e_h_1, c_j, s16))),
% 294.51/187.05 inference(rewrite,[status(thm)],[])).
% 294.51/187.05 tff(26726,plain,
% 294.51/187.05 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s16)) | m_or_h_gate_v_out(c_e_h_1, c_j, s16))),
% 294.51/187.05 inference(quant_inst,[status(thm)],[])).
% 294.51/187.05 tff(26727,plain,
% 294.51/187.05 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s16)) | m_or_h_gate_v_out(c_e_h_1, c_j, s16)),
% 294.51/187.05 inference(modus_ponens,[status(thm)],[26726, 26725])).
% 294.51/187.05 tff(26728,plain,
% 294.51/187.05 ($false),
% 294.51/187.05 inference(unit_resolution,[status(thm)],[26727, 1174, 26724, 26655])).
% 294.51/187.05 tff(26729,plain,(m_and_h_gate_v_out(c_e_h_3, c_q, s14) | (~m_c_h_element_v_out(c_e_h_1, c_h, s17)) | m_c_h_element_v_out(c_e_h_1, c_h, s15) | m_or_h_gate_v_in1(c_e_h_1, c_j, s15) | m_or_h_gate_v_in1(c_e_h_1, c_j, s14) | m_or_h_gate_v_out(c_e_h_1, c_j, s14) | node20(c_e_h_3, c_q, s14)), inference(lemma,lemma(discharge,[]))).
% 294.51/187.05 tff(26730,plain,
% 294.51/187.05 (m_and_h_gate_v_out(c_e_h_3, c_q, s14) | (~m_c_h_element_v_out(c_e_h_1, c_h, s17)) | m_c_h_element_v_out(c_e_h_1, c_h, s15) | m_or_h_gate_v_out(c_e_h_1, c_j, s14) | node20(c_e_h_3, c_q, s14)),
% 294.51/187.05 inference(unit_resolution,[status(thm)],[26729, 26558, 25448])).
% 294.51/187.05 tff(26731,plain,
% 294.51/187.05 (~m_c_h_element_v_out(c_e_h_1, c_h, s17)),
% 294.51/187.05 inference(unit_resolution,[status(thm)],[26730, 24310, 26430, 24033, 23478])).
% 294.51/187.05 tff(26732,plain,
% 294.51/187.05 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s17)) | m_c_h_element_v_out(c_e_h_1, c_h, s17))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s17)) | m_c_h_element_v_out(c_e_h_1, c_h, s17))),
% 294.51/187.05 inference(rewrite,[status(thm)],[])).
% 294.51/187.05 tff(26733,plain,
% 294.51/187.05 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s17)) | m_c_h_element_v_out(c_e_h_1, c_h, s17))),
% 294.51/187.05 inference(quant_inst,[status(thm)],[])).
% 294.51/187.05 tff(26734,plain,
% 294.51/187.05 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s17)) | m_c_h_element_v_out(c_e_h_1, c_h, s17)),
% 294.51/187.05 inference(modus_ponens,[status(thm)],[26733, 26732])).
% 294.51/187.05 tff(26735,plain,
% 294.51/187.05 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s17)),
% 294.51/187.05 inference(unit_resolution,[status(thm)],[26734, 619, 26731])).
% 294.51/187.05 tff(26736,plain,
% 294.51/187.05 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s17)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s17))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s17)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s17))),
% 294.51/187.05 inference(rewrite,[status(thm)],[])).
% 294.51/187.05 tff(26737,plain,
% 294.51/187.05 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s17)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s17))),
% 294.51/187.05 inference(quant_inst,[status(thm)],[])).
% 294.51/187.05 tff(26738,plain,
% 294.51/187.05 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s17)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s17)),
% 294.51/187.05 inference(modus_ponens,[status(thm)],[26737, 26736])).
% 294.51/187.05 tff(26739,plain,
% 294.51/187.05 (~node20(c_e_h_1, c_i, s17)),
% 294.51/187.05 inference(unit_resolution,[status(thm)],[26738, 38, 26735])).
% 294.51/187.05 tff(26740,plain,
% 294.51/187.05 (~m_and_h_gate_v_out(c_e_h_1, c_i, s17)),
% 294.51/187.05 inference(unit_resolution,[status(thm)],[26108, 25573, 24266])).
% 294.51/187.05 tff(26741,assumption,(~node20(c_e_h_1, c_i, s17)), introduced(assumption)).
% 294.51/187.05 tff(26742,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s18)), introduced(assumption)).
% 294.51/187.05 tff(26743,assumption,(node22(c_e_h_1, c_i, s17, s18)), introduced(assumption)).
% 294.51/187.05 tff(26744,plain,
% 294.51/187.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s18)) | (~node22(c_e_h_1, c_i, s17, s18)) | m_and_h_gate_v_out(c_e_h_1, c_i, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s18)) | (~node22(c_e_h_1, c_i, s17, s18)) | m_and_h_gate_v_out(c_e_h_1, c_i, s17))),
% 294.51/187.05 inference(rewrite,[status(thm)],[])).
% 294.51/187.05 tff(26745,plain,
% 294.51/187.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s18)) | (~node22(c_e_h_1, c_i, s17, s18)) | m_and_h_gate_v_out(c_e_h_1, c_i, s17))),
% 294.51/187.05 inference(quant_inst,[status(thm)],[])).
% 294.51/187.05 tff(26746,plain,
% 294.51/187.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s18)) | (~node22(c_e_h_1, c_i, s17, s18)) | m_and_h_gate_v_out(c_e_h_1, c_i, s17)),
% 294.51/187.05 inference(modus_ponens,[status(thm)],[26745, 26744])).
% 294.51/187.05 tff(26747,plain,
% 294.51/187.05 ($false),
% 294.51/187.05 inference(unit_resolution,[status(thm)],[26746, 108, 26743, 26111, 26742])).
% 294.51/187.05 tff(26748,plain,((~node22(c_e_h_1, c_i, s17, s18)) | m_and_h_gate_v_out(c_e_h_1, c_i, s17) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s18))), inference(lemma,lemma(discharge,[]))).
% 294.51/187.05 tff(26749,plain,
% 294.51/187.05 (~node22(c_e_h_1, c_i, s17, s18)),
% 294.51/187.05 inference(unit_resolution,[status(thm)],[26748, 26742, 26111])).
% 294.51/187.05 tff(26750,plain,
% 294.51/187.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s17, s18)) | node21(c_e_h_1, c_i, s17, s18) | node22(c_e_h_1, c_i, s17, s18))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s17, s18)) | node21(c_e_h_1, c_i, s17, s18) | node22(c_e_h_1, c_i, s17, s18))),
% 294.51/187.05 inference(rewrite,[status(thm)],[])).
% 294.51/187.05 tff(26751,plain,
% 294.51/187.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s17, s18)) | node21(c_e_h_1, c_i, s17, s18) | node22(c_e_h_1, c_i, s17, s18))),
% 294.51/187.05 inference(quant_inst,[status(thm)],[])).
% 294.51/187.05 tff(26752,plain,
% 294.51/187.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s17, s18)) | node21(c_e_h_1, c_i, s17, s18) | node22(c_e_h_1, c_i, s17, s18)),
% 294.51/187.05 inference(modus_ponens,[status(thm)],[26751, 26750])).
% 294.51/187.05 tff(26753,plain,
% 294.51/187.05 (node21(c_e_h_1, c_i, s17, s18) | node22(c_e_h_1, c_i, s17, s18)),
% 294.51/187.05 inference(unit_resolution,[status(thm)],[26752, 82, 26135])).
% 294.51/187.05 tff(26754,plain,
% 294.51/187.05 (node21(c_e_h_1, c_i, s17, s18)),
% 294.51/187.05 inference(unit_resolution,[status(thm)],[26753, 26749])).
% 294.51/187.05 tff(26755,plain,
% 294.51/187.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s17) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s18)) | (~node21(c_e_h_1, c_i, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s17) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s18)) | (~node21(c_e_h_1, c_i, s17, s18)))),
% 294.51/187.05 inference(rewrite,[status(thm)],[])).
% 294.51/187.05 tff(26756,plain,
% 294.51/187.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s17) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s18)) | (~node21(c_e_h_1, c_i, s17, s18)))),
% 294.51/187.05 inference(quant_inst,[status(thm)],[])).
% 294.51/187.05 tff(26757,plain,
% 294.51/187.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s17) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s18)) | (~node21(c_e_h_1, c_i, s17, s18))),
% 294.51/187.05 inference(modus_ponens,[status(thm)],[26756, 26755])).
% 294.51/187.05 tff(26758,plain,
% 294.51/187.05 ($false),
% 294.51/187.05 inference(unit_resolution,[status(thm)],[26757, 52, 26754, 26742, 26741])).
% 294.51/187.05 tff(26759,plain,((~m_and_h_gate_v_out(c_e_h_1, c_i, s18)) | node20(c_e_h_1, c_i, s17) | m_and_h_gate_v_out(c_e_h_1, c_i, s17)), inference(lemma,lemma(discharge,[]))).
% 294.51/187.05 tff(26760,plain,
% 294.51/187.05 (~m_and_h_gate_v_out(c_e_h_1, c_i, s18)),
% 294.51/187.05 inference(unit_resolution,[status(thm)],[26759, 26740, 26739])).
% 294.51/187.05 tff(26761,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_i, s18)), introduced(assumption)).
% 294.51/187.05 tff(26762,assumption,(m_c_h_element_v_in2(c_e_h_1, c_e, s18)), introduced(assumption)).
% 294.51/187.05 tff(26763,plain,
% 294.51/187.05 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s18)) | m_and_h_gate_v_out(c_e_h_1, c_i, s18))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s18)) | m_and_h_gate_v_out(c_e_h_1, c_i, s18))),
% 294.51/187.05 inference(rewrite,[status(thm)],[])).
% 294.51/187.05 tff(26764,plain,
% 294.51/187.05 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s18)) | m_and_h_gate_v_out(c_e_h_1, c_i, s18))),
% 294.51/187.05 inference(quant_inst,[status(thm)],[])).
% 294.51/187.05 tff(26765,plain,
% 294.51/187.05 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s18)) | m_and_h_gate_v_out(c_e_h_1, c_i, s18)),
% 294.51/187.05 inference(modus_ponens,[status(thm)],[26764, 26763])).
% 294.51/187.05 tff(26766,plain,
% 294.51/187.05 ($false),
% 294.51/187.05 inference(unit_resolution,[status(thm)],[26765, 164, 26762, 26761])).
% 294.51/187.05 tff(26767,plain,((~m_c_h_element_v_in2(c_e_h_1, c_e, s18)) | m_and_h_gate_v_out(c_e_h_1, c_i, s18)), inference(lemma,lemma(discharge,[]))).
% 294.51/187.05 tff(26768,plain,
% 294.51/187.05 (~m_c_h_element_v_in2(c_e_h_1, c_e, s18)),
% 294.51/187.05 inference(unit_resolution,[status(thm)],[26767, 26760])).
% 294.51/187.05 tff(26769,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s19)), introduced(assumption)).
% 294.51/187.05 tff(26770,assumption,(~m_c_h_element_v_out(c_e_h_1, c_e, s18)), introduced(assumption)).
% 294.51/187.05 tff(26771,assumption,(node18(c_e_h_1, c_e, s18, s19)), introduced(assumption)).
% 294.51/187.05 tff(26772,plain,
% 294.51/187.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s18) | (~node18(c_e_h_1, c_e, s18, s19)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s18) | (~node18(c_e_h_1, c_e, s18, s19)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s19)))),
% 294.51/187.05 inference(rewrite,[status(thm)],[])).
% 294.51/187.05 tff(26773,plain,
% 294.51/187.05 (((~m_c_h_element_v_out(c_e_h_1, c_e, s19)) | m_c_h_element_v_out(c_e_h_1, c_e, s18) | (~node18(c_e_h_1, c_e, s18, s19))) <=> (m_c_h_element_v_out(c_e_h_1, c_e, s18) | (~node18(c_e_h_1, c_e, s18, s19)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s19)))),
% 294.51/187.05 inference(rewrite,[status(thm)],[])).
% 294.51/187.05 tff(26774,plain,
% 294.51/187.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s19)) | m_c_h_element_v_out(c_e_h_1, c_e, s18) | (~node18(c_e_h_1, c_e, s18, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s18) | (~node18(c_e_h_1, c_e, s18, s19)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s19))))),
% 294.51/187.06 inference(monotonicity,[status(thm)],[26773])).
% 294.51/187.06 tff(26775,plain,
% 294.51/187.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s19)) | m_c_h_element_v_out(c_e_h_1, c_e, s18) | (~node18(c_e_h_1, c_e, s18, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s18) | (~node18(c_e_h_1, c_e, s18, s19)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s19)))),
% 294.51/187.06 inference(transitivity,[status(thm)],[26774, 26772])).
% 294.51/187.06 tff(26776,plain,
% 294.51/187.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s19)) | m_c_h_element_v_out(c_e_h_1, c_e, s18) | (~node18(c_e_h_1, c_e, s18, s19)))),
% 294.51/187.06 inference(quant_inst,[status(thm)],[])).
% 294.51/187.06 tff(26777,plain,
% 294.51/187.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s18) | (~node18(c_e_h_1, c_e, s18, s19)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s19))),
% 294.51/187.06 inference(modus_ponens,[status(thm)],[26776, 26775])).
% 294.51/187.06 tff(26778,plain,
% 294.51/187.06 ($false),
% 294.51/187.06 inference(unit_resolution,[status(thm)],[26777, 753, 26770, 26769, 26771])).
% 294.51/187.06 tff(26779,plain,((~node18(c_e_h_1, c_e, s18, s19)) | m_c_h_element_v_out(c_e_h_1, c_e, s18) | (~m_c_h_element_v_out(c_e_h_1, c_e, s19))), inference(lemma,lemma(discharge,[]))).
% 294.51/187.06 tff(26780,plain,
% 294.51/187.06 (~node18(c_e_h_1, c_e, s18, s19)),
% 294.51/187.06 inference(unit_resolution,[status(thm)],[26779, 26769, 26770])).
% 294.51/187.06 tff(26781,plain,
% 294.51/187.06 (succ(s18, s19) <=> succ(s18, s19)),
% 294.51/187.06 inference(rewrite,[status(thm)],[])).
% 294.51/187.06 tff(26782,axiom,(succ(s18, s19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound19')).
% 294.51/187.06 tff(26783,plain,
% 294.51/187.06 (succ(s18, s19)),
% 294.51/187.06 inference(modus_ponens,[status(thm)],[26782, 26781])).
% 294.51/187.06 tff(26784,plain,
% 294.51/187.06 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s18, s19)) | trans(s18, s19))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s18, s19)) | trans(s18, s19))),
% 294.51/187.06 inference(rewrite,[status(thm)],[])).
% 294.51/187.06 tff(26785,plain,
% 294.51/187.06 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s18, s19)) | trans(s18, s19))),
% 294.51/187.06 inference(quant_inst,[status(thm)],[])).
% 294.51/187.06 tff(26786,plain,
% 294.51/187.06 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s18, s19)) | trans(s18, s19)),
% 294.51/187.06 inference(modus_ponens,[status(thm)],[26785, 26784])).
% 294.51/187.06 tff(26787,plain,
% 294.51/187.06 (trans(s18, s19)),
% 294.51/187.06 inference(unit_resolution,[status(thm)],[26786, 26783, 65])).
% 294.51/187.06 tff(26788,plain,
% 294.51/187.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s18, s19)) | node19(c_e_h_1, c_e, s18, s19))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s18, s19)) | node19(c_e_h_1, c_e, s18, s19))),
% 294.51/187.06 inference(rewrite,[status(thm)],[])).
% 294.51/187.06 tff(26789,plain,
% 294.51/187.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s18, s19)) | node19(c_e_h_1, c_e, s18, s19))),
% 294.51/187.06 inference(quant_inst,[status(thm)],[])).
% 294.51/187.06 tff(26790,plain,
% 294.51/187.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s18, s19)) | node19(c_e_h_1, c_e, s18, s19)),
% 294.51/187.06 inference(modus_ponens,[status(thm)],[26789, 26788])).
% 294.51/187.06 tff(26791,plain,
% 294.51/187.06 (node19(c_e_h_1, c_e, s18, s19)),
% 294.51/187.06 inference(unit_resolution,[status(thm)],[26790, 190, 26787])).
% 294.51/187.06 tff(26792,plain,
% 294.51/187.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_1, c_e, s18, s19) | (~node19(c_e_h_1, c_e, s18, s19)) | node17(c_e_h_1, c_e, s18))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_e, s18, s19) | (~node19(c_e_h_1, c_e, s18, s19)) | node17(c_e_h_1, c_e, s18))),
% 294.51/187.06 inference(rewrite,[status(thm)],[])).
% 294.51/187.06 tff(26793,plain,
% 294.51/187.06 ((node17(c_e_h_1, c_e, s18) | node18(c_e_h_1, c_e, s18, s19) | (~node19(c_e_h_1, c_e, s18, s19))) <=> (node18(c_e_h_1, c_e, s18, s19) | (~node19(c_e_h_1, c_e, s18, s19)) | node17(c_e_h_1, c_e, s18))),
% 294.51/187.06 inference(rewrite,[status(thm)],[])).
% 294.51/187.06 tff(26794,plain,
% 294.51/187.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s18) | node18(c_e_h_1, c_e, s18, s19) | (~node19(c_e_h_1, c_e, s18, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_1, c_e, s18, s19) | (~node19(c_e_h_1, c_e, s18, s19)) | node17(c_e_h_1, c_e, s18)))),
% 294.51/187.06 inference(monotonicity,[status(thm)],[26793])).
% 294.51/187.06 tff(26795,plain,
% 294.51/187.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s18) | node18(c_e_h_1, c_e, s18, s19) | (~node19(c_e_h_1, c_e, s18, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_e, s18, s19) | (~node19(c_e_h_1, c_e, s18, s19)) | node17(c_e_h_1, c_e, s18))),
% 294.51/187.06 inference(transitivity,[status(thm)],[26794, 26792])).
% 294.51/187.06 tff(26796,plain,
% 294.51/187.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s18) | node18(c_e_h_1, c_e, s18, s19) | (~node19(c_e_h_1, c_e, s18, s19)))),
% 294.51/187.06 inference(quant_inst,[status(thm)],[])).
% 294.51/187.06 tff(26797,plain,
% 294.51/187.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_e, s18, s19) | (~node19(c_e_h_1, c_e, s18, s19)) | node17(c_e_h_1, c_e, s18)),
% 294.51/187.06 inference(modus_ponens,[status(thm)],[26796, 26795])).
% 294.51/187.06 tff(26798,plain,
% 294.51/187.06 (node18(c_e_h_1, c_e, s18, s19) | node17(c_e_h_1, c_e, s18)),
% 294.51/187.06 inference(unit_resolution,[status(thm)],[26797, 776, 26791])).
% 294.51/187.06 tff(26799,plain,
% 294.51/187.06 (node17(c_e_h_1, c_e, s18)),
% 294.51/187.06 inference(unit_resolution,[status(thm)],[26798, 26780])).
% 294.51/187.06 tff(26800,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_e, s18)), introduced(assumption)).
% 294.51/187.06 tff(26801,plain,
% 294.51/187.06 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_e, s18)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s18)) | m_c_h_element_v_in2(c_e_h_1, c_e, s18))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s18)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s18)) | m_c_h_element_v_in2(c_e_h_1, c_e, s18))),
% 294.51/187.06 inference(rewrite,[status(thm)],[])).
% 294.51/187.06 tff(26802,plain,
% 294.51/187.06 (((~m_c_h_element_v_in1(c_e_h_1, c_e, s18)) | m_c_h_element_v_in2(c_e_h_1, c_e, s18) | (~node17(c_e_h_1, c_e, s18))) <=> ((~node17(c_e_h_1, c_e, s18)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s18)) | m_c_h_element_v_in2(c_e_h_1, c_e, s18))),
% 294.51/187.06 inference(rewrite,[status(thm)],[])).
% 294.51/187.06 tff(26803,plain,
% 294.51/187.06 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s18)) | m_c_h_element_v_in2(c_e_h_1, c_e, s18) | (~node17(c_e_h_1, c_e, s18)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_e, s18)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s18)) | m_c_h_element_v_in2(c_e_h_1, c_e, s18)))),
% 294.51/187.06 inference(monotonicity,[status(thm)],[26802])).
% 294.51/187.06 tff(26804,plain,
% 294.51/187.06 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s18)) | m_c_h_element_v_in2(c_e_h_1, c_e, s18) | (~node17(c_e_h_1, c_e, s18)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s18)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s18)) | m_c_h_element_v_in2(c_e_h_1, c_e, s18))),
% 294.51/187.06 inference(transitivity,[status(thm)],[26803, 26801])).
% 294.51/187.06 tff(26805,plain,
% 294.51/187.06 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s18)) | m_c_h_element_v_in2(c_e_h_1, c_e, s18) | (~node17(c_e_h_1, c_e, s18)))),
% 294.51/187.06 inference(quant_inst,[status(thm)],[])).
% 294.51/187.06 tff(26806,plain,
% 294.51/187.06 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s18)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s18)) | m_c_h_element_v_in2(c_e_h_1, c_e, s18)),
% 294.51/187.06 inference(modus_ponens,[status(thm)],[26805, 26804])).
% 294.51/187.06 tff(26807,plain,
% 294.51/187.06 ((~node17(c_e_h_1, c_e, s18)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s18))),
% 294.51/187.06 inference(unit_resolution,[status(thm)],[26806, 919, 26800])).
% 294.51/187.06 tff(26808,plain,
% 294.51/187.06 (~m_c_h_element_v_in1(c_e_h_1, c_e, s18)),
% 294.51/187.06 inference(unit_resolution,[status(thm)],[26807, 26799])).
% 294.51/187.06 tff(26809,assumption,(node15(c_e_h_1, c_e, s18, s19)), introduced(assumption)).
% 294.51/187.06 tff(26810,plain,
% 294.51/187.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s19)) | (~node15(c_e_h_1, c_e, s18, s19)) | m_c_h_element_v_out(c_e_h_1, c_e, s18))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s19)) | (~node15(c_e_h_1, c_e, s18, s19)) | m_c_h_element_v_out(c_e_h_1, c_e, s18))),
% 294.51/187.06 inference(rewrite,[status(thm)],[])).
% 294.51/187.06 tff(26811,plain,
% 294.51/187.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s19)) | (~node15(c_e_h_1, c_e, s18, s19)) | m_c_h_element_v_out(c_e_h_1, c_e, s18))),
% 294.51/187.06 inference(quant_inst,[status(thm)],[])).
% 294.51/187.06 tff(26812,plain,
% 294.51/187.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s19)) | (~node15(c_e_h_1, c_e, s18, s19)) | m_c_h_element_v_out(c_e_h_1, c_e, s18)),
% 294.51/187.06 inference(modus_ponens,[status(thm)],[26811, 26810])).
% 294.51/187.06 tff(26813,plain,
% 294.51/187.06 ($false),
% 294.51/187.06 inference(unit_resolution,[status(thm)],[26812, 147, 26770, 26769, 26809])).
% 294.51/187.06 tff(26814,plain,((~node15(c_e_h_1, c_e, s18, s19)) | m_c_h_element_v_out(c_e_h_1, c_e, s18) | (~m_c_h_element_v_out(c_e_h_1, c_e, s19))), inference(lemma,lemma(discharge,[]))).
% 294.51/187.06 tff(26815,plain,
% 294.51/187.06 (~node15(c_e_h_1, c_e, s18, s19)),
% 294.51/187.06 inference(unit_resolution,[status(thm)],[26814, 26769, 26770])).
% 294.51/187.06 tff(26816,assumption,(node17(c_e_h_1, c_e, s18)), introduced(assumption)).
% 294.51/187.06 tff(26817,assumption,(node16(c_e_h_1, c_e, s18)), introduced(assumption)).
% 294.51/187.06 tff(26818,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_e, s18)), introduced(assumption)).
% 294.51/187.06 tff(26819,plain,
% 294.51/187.06 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_e, s18)) | m_c_h_element_v_in1(c_e_h_1, c_e, s18) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s18)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s18)) | m_c_h_element_v_in1(c_e_h_1, c_e, s18) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s18)))),
% 294.51/187.06 inference(rewrite,[status(thm)],[])).
% 294.51/187.06 tff(26820,plain,
% 294.51/187.06 ((m_c_h_element_v_in1(c_e_h_1, c_e, s18) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s18)) | (~node17(c_e_h_1, c_e, s18))) <=> ((~node17(c_e_h_1, c_e, s18)) | m_c_h_element_v_in1(c_e_h_1, c_e, s18) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s18)))),
% 294.51/187.07 inference(rewrite,[status(thm)],[])).
% 294.51/187.07 tff(26821,plain,
% 294.51/187.07 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s18) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s18)) | (~node17(c_e_h_1, c_e, s18)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_e, s18)) | m_c_h_element_v_in1(c_e_h_1, c_e, s18) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s18))))),
% 294.51/187.07 inference(monotonicity,[status(thm)],[26820])).
% 294.51/187.07 tff(26822,plain,
% 294.51/187.07 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s18) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s18)) | (~node17(c_e_h_1, c_e, s18)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s18)) | m_c_h_element_v_in1(c_e_h_1, c_e, s18) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s18)))),
% 294.51/187.07 inference(transitivity,[status(thm)],[26821, 26819])).
% 294.51/187.07 tff(26823,plain,
% 294.51/187.07 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s18) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s18)) | (~node17(c_e_h_1, c_e, s18)))),
% 294.51/187.07 inference(quant_inst,[status(thm)],[])).
% 294.51/187.07 tff(26824,plain,
% 294.51/187.07 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s18)) | m_c_h_element_v_in1(c_e_h_1, c_e, s18) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s18))),
% 294.51/187.07 inference(modus_ponens,[status(thm)],[26823, 26822])).
% 294.51/187.07 tff(26825,plain,
% 294.51/187.07 (m_c_h_element_v_in1(c_e_h_1, c_e, s18) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s18))),
% 294.51/187.07 inference(unit_resolution,[status(thm)],[26824, 859, 26816])).
% 294.51/187.07 tff(26826,plain,
% 294.51/187.07 (~m_c_h_element_v_in2(c_e_h_1, c_e, s18)),
% 294.51/187.07 inference(unit_resolution,[status(thm)],[26825, 26818])).
% 294.51/187.07 tff(26827,plain,
% 294.51/187.07 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s18)) | m_c_h_element_v_in1(c_e_h_1, c_e, s18) | m_c_h_element_v_in2(c_e_h_1, c_e, s18))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s18)) | m_c_h_element_v_in1(c_e_h_1, c_e, s18) | m_c_h_element_v_in2(c_e_h_1, c_e, s18))),
% 294.51/187.07 inference(rewrite,[status(thm)],[])).
% 294.51/187.07 tff(26828,plain,
% 294.51/187.07 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s18)) | m_c_h_element_v_in1(c_e_h_1, c_e, s18) | m_c_h_element_v_in2(c_e_h_1, c_e, s18))),
% 294.51/187.07 inference(quant_inst,[status(thm)],[])).
% 294.51/187.07 tff(26829,plain,
% 294.51/187.07 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s18)) | m_c_h_element_v_in1(c_e_h_1, c_e, s18) | m_c_h_element_v_in2(c_e_h_1, c_e, s18)),
% 294.51/187.07 inference(modus_ponens,[status(thm)],[26828, 26827])).
% 294.51/187.07 tff(26830,plain,
% 294.51/187.07 (m_c_h_element_v_in1(c_e_h_1, c_e, s18) | m_c_h_element_v_in2(c_e_h_1, c_e, s18)),
% 294.51/187.07 inference(unit_resolution,[status(thm)],[26829, 178, 26817])).
% 294.51/187.07 tff(26831,plain,
% 294.51/187.07 ($false),
% 294.51/187.07 inference(unit_resolution,[status(thm)],[26830, 26826, 26818])).
% 294.51/187.07 tff(26832,plain,(m_c_h_element_v_in1(c_e_h_1, c_e, s18) | (~node16(c_e_h_1, c_e, s18)) | (~node17(c_e_h_1, c_e, s18))), inference(lemma,lemma(discharge,[]))).
% 294.51/187.07 tff(26833,plain,
% 294.51/187.07 (m_c_h_element_v_in1(c_e_h_1, c_e, s18)),
% 294.51/187.07 inference(unit_resolution,[status(thm)],[26832, 26817, 26816])).
% 294.51/187.07 tff(26834,plain,
% 294.51/187.07 ((~m_c_h_element_v_in1(c_e_h_1, c_e, s18)) | m_c_h_element_v_in2(c_e_h_1, c_e, s18)),
% 294.51/187.07 inference(unit_resolution,[status(thm)],[26806, 919, 26816])).
% 294.51/187.07 tff(26835,plain,
% 294.51/187.07 (m_c_h_element_v_in2(c_e_h_1, c_e, s18)),
% 294.51/187.07 inference(unit_resolution,[status(thm)],[26834, 26833])).
% 294.51/187.07 tff(26836,plain,
% 294.51/187.07 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s18)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s18)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s18)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~node16(c_e_h_1, c_e, s18)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s18)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s18)))),
% 294.51/187.07 inference(rewrite,[status(thm)],[])).
% 294.51/187.07 tff(26837,plain,
% 294.51/187.07 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s18)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s18)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s18)))),
% 294.51/187.07 inference(quant_inst,[status(thm)],[])).
% 294.51/187.07 tff(26838,plain,
% 294.51/187.07 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~node16(c_e_h_1, c_e, s18)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s18)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s18))),
% 294.51/187.07 inference(modus_ponens,[status(thm)],[26837, 26836])).
% 294.51/187.07 tff(26839,plain,
% 294.51/187.07 ((~m_c_h_element_v_in1(c_e_h_1, c_e, s18)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s18))),
% 294.51/187.07 inference(unit_resolution,[status(thm)],[26838, 2307, 26817])).
% 294.51/187.07 tff(26840,plain,
% 294.51/187.07 ($false),
% 294.51/187.07 inference(unit_resolution,[status(thm)],[26839, 26835, 26833])).
% 294.51/187.07 tff(26841,plain,((~node16(c_e_h_1, c_e, s18)) | (~node17(c_e_h_1, c_e, s18))), inference(lemma,lemma(discharge,[]))).
% 294.51/187.07 tff(26842,plain,
% 294.51/187.07 (~node16(c_e_h_1, c_e, s18)),
% 294.51/187.07 inference(unit_resolution,[status(thm)],[26841, 26799])).
% 294.51/187.07 tff(26843,plain,
% 294.51/187.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_1, c_e, s18, s19) | (~node19(c_e_h_1, c_e, s18, s19)) | node16(c_e_h_1, c_e, s18) | node14(c_e_h_1, c_e, s18, s19))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_e, s18, s19) | (~node19(c_e_h_1, c_e, s18, s19)) | node16(c_e_h_1, c_e, s18) | node14(c_e_h_1, c_e, s18, s19))),
% 294.51/187.07 inference(rewrite,[status(thm)],[])).
% 294.51/187.07 tff(26844,plain,
% 294.51/187.07 ((node16(c_e_h_1, c_e, s18) | node14(c_e_h_1, c_e, s18, s19) | node15(c_e_h_1, c_e, s18, s19) | (~node19(c_e_h_1, c_e, s18, s19))) <=> (node15(c_e_h_1, c_e, s18, s19) | (~node19(c_e_h_1, c_e, s18, s19)) | node16(c_e_h_1, c_e, s18) | node14(c_e_h_1, c_e, s18, s19))),
% 294.51/187.07 inference(rewrite,[status(thm)],[])).
% 294.51/187.07 tff(26845,plain,
% 294.51/187.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s18) | node14(c_e_h_1, c_e, s18, s19) | node15(c_e_h_1, c_e, s18, s19) | (~node19(c_e_h_1, c_e, s18, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_1, c_e, s18, s19) | (~node19(c_e_h_1, c_e, s18, s19)) | node16(c_e_h_1, c_e, s18) | node14(c_e_h_1, c_e, s18, s19)))),
% 294.51/187.07 inference(monotonicity,[status(thm)],[26844])).
% 294.51/187.07 tff(26846,plain,
% 294.51/187.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s18) | node14(c_e_h_1, c_e, s18, s19) | node15(c_e_h_1, c_e, s18, s19) | (~node19(c_e_h_1, c_e, s18, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_e, s18, s19) | (~node19(c_e_h_1, c_e, s18, s19)) | node16(c_e_h_1, c_e, s18) | node14(c_e_h_1, c_e, s18, s19))),
% 294.51/187.07 inference(transitivity,[status(thm)],[26845, 26843])).
% 294.51/187.07 tff(26847,plain,
% 294.51/187.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s18) | node14(c_e_h_1, c_e, s18, s19) | node15(c_e_h_1, c_e, s18, s19) | (~node19(c_e_h_1, c_e, s18, s19)))),
% 294.51/187.07 inference(quant_inst,[status(thm)],[])).
% 294.51/187.07 tff(26848,plain,
% 294.51/187.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_e, s18, s19) | (~node19(c_e_h_1, c_e, s18, s19)) | node16(c_e_h_1, c_e, s18) | node14(c_e_h_1, c_e, s18, s19)),
% 294.51/187.07 inference(modus_ponens,[status(thm)],[26847, 26846])).
% 294.51/187.07 tff(26849,plain,
% 294.51/187.07 (node15(c_e_h_1, c_e, s18, s19) | node16(c_e_h_1, c_e, s18) | node14(c_e_h_1, c_e, s18, s19)),
% 294.51/187.07 inference(unit_resolution,[status(thm)],[26848, 204, 26791])).
% 294.51/187.07 tff(26850,plain,
% 294.51/187.07 (node14(c_e_h_1, c_e, s18, s19)),
% 294.51/187.07 inference(unit_resolution,[status(thm)],[26849, 26842, 26815])).
% 294.51/187.07 tff(26851,assumption,(node14(c_e_h_1, c_e, s18, s19)), introduced(assumption)).
% 294.51/187.07 tff(26852,plain,
% 294.51/187.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s19)) | (~node14(c_e_h_1, c_e, s18, s19)) | m_c_h_element_v_in1(c_e_h_1, c_e, s18))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s19)) | (~node14(c_e_h_1, c_e, s18, s19)) | m_c_h_element_v_in1(c_e_h_1, c_e, s18))),
% 294.51/187.07 inference(rewrite,[status(thm)],[])).
% 294.51/187.07 tff(26853,plain,
% 294.51/187.07 (((~node14(c_e_h_1, c_e, s18, s19)) | m_c_h_element_v_in1(c_e_h_1, c_e, s18) | (~m_c_h_element_v_out(c_e_h_1, c_e, s19))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_e, s19)) | (~node14(c_e_h_1, c_e, s18, s19)) | m_c_h_element_v_in1(c_e_h_1, c_e, s18))),
% 294.51/187.07 inference(rewrite,[status(thm)],[])).
% 294.51/187.07 tff(26854,plain,
% 294.51/187.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s18, s19)) | m_c_h_element_v_in1(c_e_h_1, c_e, s18) | (~m_c_h_element_v_out(c_e_h_1, c_e, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s19)) | (~node14(c_e_h_1, c_e, s18, s19)) | m_c_h_element_v_in1(c_e_h_1, c_e, s18)))),
% 294.51/187.07 inference(monotonicity,[status(thm)],[26853])).
% 294.51/187.07 tff(26855,plain,
% 294.51/187.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s18, s19)) | m_c_h_element_v_in1(c_e_h_1, c_e, s18) | (~m_c_h_element_v_out(c_e_h_1, c_e, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s19)) | (~node14(c_e_h_1, c_e, s18, s19)) | m_c_h_element_v_in1(c_e_h_1, c_e, s18))),
% 294.51/187.07 inference(transitivity,[status(thm)],[26854, 26852])).
% 294.51/187.07 tff(26856,plain,
% 294.51/187.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s18, s19)) | m_c_h_element_v_in1(c_e_h_1, c_e, s18) | (~m_c_h_element_v_out(c_e_h_1, c_e, s19)))),
% 294.51/187.07 inference(quant_inst,[status(thm)],[])).
% 294.51/187.07 tff(26857,plain,
% 294.51/187.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s19)) | (~node14(c_e_h_1, c_e, s18, s19)) | m_c_h_element_v_in1(c_e_h_1, c_e, s18)),
% 294.51/187.07 inference(modus_ponens,[status(thm)],[26856, 26855])).
% 294.51/187.07 tff(26858,plain,
% 294.51/187.07 ($false),
% 294.51/187.07 inference(unit_resolution,[status(thm)],[26857, 223, 26769, 26851, 26818])).
% 294.51/187.07 tff(26859,plain,((~node14(c_e_h_1, c_e, s18, s19)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s19)) | m_c_h_element_v_in1(c_e_h_1, c_e, s18)), inference(lemma,lemma(discharge,[]))).
% 294.51/187.07 tff(26860,plain,
% 294.51/187.07 ($false),
% 294.51/187.07 inference(unit_resolution,[status(thm)],[26859, 26850, 26808, 26769])).
% 294.51/187.07 tff(26861,plain,((~m_c_h_element_v_out(c_e_h_1, c_e, s19)) | m_c_h_element_v_in2(c_e_h_1, c_e, s18) | m_c_h_element_v_out(c_e_h_1, c_e, s18)), inference(lemma,lemma(discharge,[]))).
% 294.51/187.08 tff(26862,plain,
% 294.51/187.08 (~m_c_h_element_v_out(c_e_h_1, c_e, s19)),
% 294.51/187.08 inference(unit_resolution,[status(thm)],[26861, 26768, 26207])).
% 294.51/187.08 tff(26863,plain,
% 294.51/187.08 (~m_and_h_gate_v_out(c_e_h_3, c_q, s15)),
% 294.51/187.08 inference(unit_resolution,[status(thm)],[26678, 24310, 26430])).
% 294.51/187.08 tff(26864,plain,
% 294.51/187.08 (~m_cell_v_ack(c_e_h_1, s15)),
% 294.51/187.08 inference(unit_resolution,[status(thm)],[26687, 26863])).
% 294.51/187.08 tff(26865,plain,
% 294.51/187.08 (~m_or_h_gate_v_in2(c_e_h_1, c_j, s15)),
% 294.51/187.08 inference(unit_resolution,[status(thm)],[26691, 1085, 26864])).
% 294.51/187.08 tff(26866,plain,
% 294.51/187.08 ((~m_or_h_gate_v_out(c_e_h_1, c_j, s16)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s15) | m_or_h_gate_v_out(c_e_h_1, c_j, s15)),
% 294.51/187.08 inference(unit_resolution,[status(thm)],[26723, 26558])).
% 294.51/187.08 tff(26867,plain,
% 294.51/187.08 (~m_or_h_gate_v_out(c_e_h_1, c_j, s16)),
% 294.51/187.08 inference(unit_resolution,[status(thm)],[26866, 26865, 25482])).
% 294.51/187.08 tff(26868,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_i, s12)), introduced(assumption)).
% 294.51/187.08 tff(26869,plain,
% 294.51/187.08 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_i, s12)) | m_c_h_element_v_out(c_e_h_3, c_h, s12))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s12)) | m_c_h_element_v_out(c_e_h_3, c_h, s12))),
% 294.51/187.08 inference(rewrite,[status(thm)],[])).
% 294.51/187.08 tff(26870,plain,
% 294.51/187.08 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_i, s12)) | m_c_h_element_v_out(c_e_h_3, c_h, s12))),
% 294.51/187.08 inference(quant_inst,[status(thm)],[])).
% 294.51/187.08 tff(26871,plain,
% 294.51/187.08 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s12)) | m_c_h_element_v_out(c_e_h_3, c_h, s12)),
% 294.51/187.08 inference(modus_ponens,[status(thm)],[26870, 26869])).
% 294.51/187.08 tff(26872,plain,
% 294.51/187.08 ($false),
% 294.51/187.08 inference(unit_resolution,[status(thm)],[26871, 619, 21894, 26868])).
% 294.51/187.08 tff(26873,plain,(m_c_h_element_v_out(c_e_h_3, c_h, s12) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s12))), inference(lemma,lemma(discharge,[]))).
% 294.51/187.08 tff(26874,plain,
% 294.51/187.08 (~m_and_h_gate_v_in1(c_e_h_3, c_i, s12)),
% 294.51/187.08 inference(unit_resolution,[status(thm)],[26873, 21894])).
% 294.51/187.08 tff(26875,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_i, s12)), introduced(assumption)).
% 294.51/187.08 tff(26876,assumption,(node20(c_e_h_3, c_i, s12)), introduced(assumption)).
% 294.51/187.08 tff(26877,plain,
% 294.51/187.08 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s12)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s12))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_i, s12)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s12))),
% 294.51/187.08 inference(rewrite,[status(thm)],[])).
% 294.51/187.08 tff(26878,plain,
% 294.51/187.08 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s12)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s12))),
% 294.51/187.08 inference(quant_inst,[status(thm)],[])).
% 294.51/187.08 tff(26879,plain,
% 294.51/187.08 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_i, s12)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s12)),
% 294.51/187.08 inference(modus_ponens,[status(thm)],[26878, 26877])).
% 294.51/187.08 tff(26880,plain,
% 294.51/187.08 ($false),
% 294.51/187.08 inference(unit_resolution,[status(thm)],[26879, 38, 26876, 26875])).
% 294.51/187.08 tff(26881,plain,(m_and_h_gate_v_in1(c_e_h_3, c_i, s12) | (~node20(c_e_h_3, c_i, s12))), inference(lemma,lemma(discharge,[]))).
% 294.51/187.08 tff(26882,plain,
% 294.51/187.08 (~node20(c_e_h_3, c_i, s12)),
% 294.51/187.08 inference(unit_resolution,[status(thm)],[26881, 26874])).
% 294.51/187.08 tff(26883,plain,
% 294.51/187.08 (~node20(c_e_h_3, c_i, s11)),
% 294.51/187.08 inference(unit_resolution,[status(thm)],[11217, 24267])).
% 294.51/187.08 tff(26884,assumption,(~m_or_h_gate_v_out(c_e_h_3, c_j, s12)), introduced(assumption)).
% 294.51/187.08 tff(26885,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_l, s12)), introduced(assumption)).
% 294.51/187.08 tff(26886,plain,
% 294.51/187.08 (~m_and_h_gate_v_out(c_e_h_3, c_k, s10)),
% 294.51/187.08 inference(unit_resolution,[status(thm)],[20777, 20172, 2743])).
% 294.51/187.08 tff(26887,plain,
% 294.51/187.08 (~m_and_h_gate_v_out(c_e_h_3, c_k, s11)),
% 294.51/187.08 inference(unit_resolution,[status(thm)],[21801, 26886, 20809])).
% 294.51/187.08 tff(26888,assumption,(m_or_h_gate_v_in1(c_e_h_3, c_j, s12)), introduced(assumption)).
% 294.51/187.08 tff(26889,plain,
% 294.51/187.08 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_j, s12)) | m_and_h_gate_v_out(c_e_h_3, c_l, s12))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s12)) | m_and_h_gate_v_out(c_e_h_3, c_l, s12))),
% 294.51/187.08 inference(rewrite,[status(thm)],[])).
% 294.51/187.08 tff(26890,plain,
% 294.51/187.08 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_3, c_j, s12)) | m_and_h_gate_v_out(c_e_h_3, c_l, s12))),
% 294.51/187.08 inference(quant_inst,[status(thm)],[])).
% 294.51/187.08 tff(26891,plain,
% 294.51/187.08 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_3, c_j, s12)) | m_and_h_gate_v_out(c_e_h_3, c_l, s12)),
% 294.51/187.08 inference(modus_ponens,[status(thm)],[26890, 26889])).
% 294.51/187.08 tff(26892,plain,
% 294.51/187.08 ($false),
% 294.51/187.08 inference(unit_resolution,[status(thm)],[26891, 1100, 26885, 26888])).
% 294.51/187.08 tff(26893,plain,((~m_or_h_gate_v_in1(c_e_h_3, c_j, s12)) | m_and_h_gate_v_out(c_e_h_3, c_l, s12)), inference(lemma,lemma(discharge,[]))).
% 294.51/187.08 tff(26894,plain,
% 294.51/187.08 (~m_or_h_gate_v_in1(c_e_h_3, c_j, s12)),
% 294.51/187.08 inference(unit_resolution,[status(thm)],[26893, 26885])).
% 294.51/187.08 tff(26895,assumption,(m_c_h_element_v_out(c_e_h_2, c_h, s9)), introduced(assumption)).
% 294.51/187.08 tff(26896,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_h, s8)), introduced(assumption)).
% 294.51/187.08 tff(26897,assumption,(node18(c_e_h_2, c_h, s8, s9)), introduced(assumption)).
% 294.51/187.08 tff(26898,plain,
% 294.51/187.08 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s5)) | m_cell_v_ack(c_e_h_2, s5))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s5)) | m_cell_v_ack(c_e_h_2, s5))),
% 294.51/187.08 inference(rewrite,[status(thm)],[])).
% 294.51/187.08 tff(26899,plain,
% 294.51/187.08 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s5)) | m_cell_v_ack(c_e_h_2, s5))),
% 294.51/187.08 inference(quant_inst,[status(thm)],[])).
% 294.51/187.08 tff(26900,plain,
% 294.51/187.08 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s5)) | m_cell_v_ack(c_e_h_2, s5)),
% 294.51/187.08 inference(modus_ponens,[status(thm)],[26899, 26898])).
% 294.51/187.08 tff(26901,plain,
% 294.51/187.08 (~m_or_h_gate_v_in2(c_e_h_2, c_j, s5)),
% 294.51/187.08 inference(unit_resolution,[status(thm)],[26900, 1085, 15351])).
% 294.51/187.08 tff(26902,assumption,(m_c_h_element_v_out(c_e_h_2, c_e, s2)), introduced(assumption)).
% 294.51/187.08 tff(26903,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_e, s1)), introduced(assumption)).
% 294.51/187.08 tff(26904,assumption,(node18(c_e_h_2, c_e, s1, s2)), introduced(assumption)).
% 294.51/187.08 tff(26905,plain,
% 294.51/187.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_e, s1) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | (~node18(c_e_h_2, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_e, s1) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | (~node18(c_e_h_2, c_e, s1, s2)))),
% 294.51/187.08 inference(rewrite,[status(thm)],[])).
% 294.51/187.08 tff(26906,plain,
% 294.51/187.08 (((~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | m_c_h_element_v_out(c_e_h_2, c_e, s1) | (~node18(c_e_h_2, c_e, s1, s2))) <=> (m_c_h_element_v_out(c_e_h_2, c_e, s1) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | (~node18(c_e_h_2, c_e, s1, s2)))),
% 294.51/187.08 inference(rewrite,[status(thm)],[])).
% 294.51/187.08 tff(26907,plain,
% 294.51/187.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | m_c_h_element_v_out(c_e_h_2, c_e, s1) | (~node18(c_e_h_2, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_e, s1) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | (~node18(c_e_h_2, c_e, s1, s2))))),
% 294.59/187.08 inference(monotonicity,[status(thm)],[26906])).
% 294.59/187.08 tff(26908,plain,
% 294.59/187.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | m_c_h_element_v_out(c_e_h_2, c_e, s1) | (~node18(c_e_h_2, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_e, s1) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | (~node18(c_e_h_2, c_e, s1, s2)))),
% 294.59/187.08 inference(transitivity,[status(thm)],[26907, 26905])).
% 294.59/187.08 tff(26909,plain,
% 294.59/187.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | m_c_h_element_v_out(c_e_h_2, c_e, s1) | (~node18(c_e_h_2, c_e, s1, s2)))),
% 294.59/187.08 inference(quant_inst,[status(thm)],[])).
% 294.59/187.08 tff(26910,plain,
% 294.59/187.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_e, s1) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | (~node18(c_e_h_2, c_e, s1, s2))),
% 294.59/187.08 inference(modus_ponens,[status(thm)],[26909, 26908])).
% 294.59/187.08 tff(26911,plain,
% 294.59/187.08 ($false),
% 294.59/187.08 inference(unit_resolution,[status(thm)],[26910, 753, 8304, 26902, 26904])).
% 294.59/187.08 tff(26912,plain,((~node18(c_e_h_2, c_e, s1, s2)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2))), inference(lemma,lemma(discharge,[]))).
% 294.59/187.08 tff(26913,plain,
% 294.59/187.08 (~node18(c_e_h_2, c_e, s1, s2)),
% 294.59/187.08 inference(unit_resolution,[status(thm)],[26912, 26902])).
% 294.59/187.08 tff(26914,plain,
% 294.59/187.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s1, s2)) | node19(c_e_h_2, c_e, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s1, s2)) | node19(c_e_h_2, c_e, s1, s2))),
% 294.59/187.08 inference(rewrite,[status(thm)],[])).
% 294.59/187.08 tff(26915,plain,
% 294.59/187.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s1, s2)) | node19(c_e_h_2, c_e, s1, s2))),
% 294.59/187.08 inference(quant_inst,[status(thm)],[])).
% 294.59/187.08 tff(26916,plain,
% 294.59/187.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s1, s2)) | node19(c_e_h_2, c_e, s1, s2)),
% 294.59/187.08 inference(modus_ponens,[status(thm)],[26915, 26914])).
% 294.59/187.08 tff(26917,plain,
% 294.59/187.08 (node19(c_e_h_2, c_e, s1, s2)),
% 294.59/187.08 inference(unit_resolution,[status(thm)],[26916, 190, 255])).
% 294.59/187.08 tff(26918,plain,
% 294.59/187.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_2, c_e, s1, s2) | node17(c_e_h_2, c_e, s1) | (~node19(c_e_h_2, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_2, c_e, s1, s2) | node17(c_e_h_2, c_e, s1) | (~node19(c_e_h_2, c_e, s1, s2)))),
% 294.59/187.08 inference(rewrite,[status(thm)],[])).
% 294.59/187.08 tff(26919,plain,
% 294.59/187.08 ((node17(c_e_h_2, c_e, s1) | node18(c_e_h_2, c_e, s1, s2) | (~node19(c_e_h_2, c_e, s1, s2))) <=> (node18(c_e_h_2, c_e, s1, s2) | node17(c_e_h_2, c_e, s1) | (~node19(c_e_h_2, c_e, s1, s2)))),
% 294.59/187.08 inference(rewrite,[status(thm)],[])).
% 294.59/187.08 tff(26920,plain,
% 294.59/187.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s1) | node18(c_e_h_2, c_e, s1, s2) | (~node19(c_e_h_2, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_2, c_e, s1, s2) | node17(c_e_h_2, c_e, s1) | (~node19(c_e_h_2, c_e, s1, s2))))),
% 294.59/187.08 inference(monotonicity,[status(thm)],[26919])).
% 294.59/187.08 tff(26921,plain,
% 294.59/187.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s1) | node18(c_e_h_2, c_e, s1, s2) | (~node19(c_e_h_2, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_2, c_e, s1, s2) | node17(c_e_h_2, c_e, s1) | (~node19(c_e_h_2, c_e, s1, s2)))),
% 294.59/187.09 inference(transitivity,[status(thm)],[26920, 26918])).
% 294.59/187.09 tff(26922,plain,
% 294.59/187.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s1) | node18(c_e_h_2, c_e, s1, s2) | (~node19(c_e_h_2, c_e, s1, s2)))),
% 294.59/187.09 inference(quant_inst,[status(thm)],[])).
% 294.59/187.09 tff(26923,plain,
% 294.59/187.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_2, c_e, s1, s2) | node17(c_e_h_2, c_e, s1) | (~node19(c_e_h_2, c_e, s1, s2))),
% 294.59/187.09 inference(modus_ponens,[status(thm)],[26922, 26921])).
% 294.59/187.09 tff(26924,plain,
% 294.59/187.09 (node18(c_e_h_2, c_e, s1, s2) | node17(c_e_h_2, c_e, s1)),
% 294.59/187.09 inference(unit_resolution,[status(thm)],[26923, 776, 26917])).
% 294.59/187.09 tff(26925,plain,
% 294.59/187.09 (node17(c_e_h_2, c_e, s1)),
% 294.59/187.09 inference(unit_resolution,[status(thm)],[26924, 26913])).
% 294.59/187.09 tff(26926,plain,
% 294.59/187.09 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s1)) | (~node17(c_e_h_2, c_e, s1)) | m_c_h_element_v_in2(c_e_h_2, c_e, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s1)) | (~node17(c_e_h_2, c_e, s1)) | m_c_h_element_v_in2(c_e_h_2, c_e, s1))),
% 294.59/187.09 inference(rewrite,[status(thm)],[])).
% 294.59/187.09 tff(26927,plain,
% 294.59/187.09 (((~m_c_h_element_v_in1(c_e_h_2, c_e, s1)) | m_c_h_element_v_in2(c_e_h_2, c_e, s1) | (~node17(c_e_h_2, c_e, s1))) <=> ((~m_c_h_element_v_in1(c_e_h_2, c_e, s1)) | (~node17(c_e_h_2, c_e, s1)) | m_c_h_element_v_in2(c_e_h_2, c_e, s1))),
% 294.59/187.09 inference(rewrite,[status(thm)],[])).
% 294.59/187.09 tff(26928,plain,
% 294.59/187.09 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s1)) | m_c_h_element_v_in2(c_e_h_2, c_e, s1) | (~node17(c_e_h_2, c_e, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s1)) | (~node17(c_e_h_2, c_e, s1)) | m_c_h_element_v_in2(c_e_h_2, c_e, s1)))),
% 294.59/187.09 inference(monotonicity,[status(thm)],[26927])).
% 294.59/187.09 tff(26929,plain,
% 294.59/187.09 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s1)) | m_c_h_element_v_in2(c_e_h_2, c_e, s1) | (~node17(c_e_h_2, c_e, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s1)) | (~node17(c_e_h_2, c_e, s1)) | m_c_h_element_v_in2(c_e_h_2, c_e, s1))),
% 294.59/187.09 inference(transitivity,[status(thm)],[26928, 26926])).
% 294.59/187.09 tff(26930,plain,
% 294.59/187.09 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s1)) | m_c_h_element_v_in2(c_e_h_2, c_e, s1) | (~node17(c_e_h_2, c_e, s1)))),
% 294.59/187.09 inference(quant_inst,[status(thm)],[])).
% 294.59/187.09 tff(26931,plain,
% 294.59/187.09 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s1)) | (~node17(c_e_h_2, c_e, s1)) | m_c_h_element_v_in2(c_e_h_2, c_e, s1)),
% 294.59/187.09 inference(modus_ponens,[status(thm)],[26930, 26929])).
% 294.59/187.09 tff(26932,plain,
% 294.59/187.09 ((~m_c_h_element_v_in1(c_e_h_2, c_e, s1)) | m_c_h_element_v_in2(c_e_h_2, c_e, s1)),
% 294.59/187.09 inference(unit_resolution,[status(thm)],[26931, 919, 26925])).
% 294.59/187.09 tff(26933,plain,
% 294.59/187.09 (~m_c_h_element_v_in1(c_e_h_2, c_e, s1)),
% 294.59/187.09 inference(unit_resolution,[status(thm)],[26932, 26903])).
% 294.59/187.09 tff(26934,assumption,(node15(c_e_h_2, c_e, s1, s2)), introduced(assumption)).
% 294.59/187.09 tff(26935,plain,
% 294.59/187.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | (~node15(c_e_h_2, c_e, s1, s2)) | m_c_h_element_v_out(c_e_h_2, c_e, s1))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | (~node15(c_e_h_2, c_e, s1, s2)) | m_c_h_element_v_out(c_e_h_2, c_e, s1))),
% 294.59/187.09 inference(rewrite,[status(thm)],[])).
% 294.59/187.09 tff(26936,plain,
% 294.59/187.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | (~node15(c_e_h_2, c_e, s1, s2)) | m_c_h_element_v_out(c_e_h_2, c_e, s1))),
% 294.59/187.09 inference(quant_inst,[status(thm)],[])).
% 294.59/187.09 tff(26937,plain,
% 294.59/187.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | (~node15(c_e_h_2, c_e, s1, s2)) | m_c_h_element_v_out(c_e_h_2, c_e, s1)),
% 294.59/187.09 inference(modus_ponens,[status(thm)],[26936, 26935])).
% 294.59/187.09 tff(26938,plain,
% 294.59/187.09 ($false),
% 294.59/187.09 inference(unit_resolution,[status(thm)],[26937, 147, 8304, 26902, 26934])).
% 294.59/187.09 tff(26939,plain,((~node15(c_e_h_2, c_e, s1, s2)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2))), inference(lemma,lemma(discharge,[]))).
% 294.59/187.09 tff(26940,plain,
% 294.59/187.09 (~node15(c_e_h_2, c_e, s1, s2)),
% 294.59/187.09 inference(unit_resolution,[status(thm)],[26939, 26902])).
% 294.59/187.09 tff(26941,plain,
% 294.59/187.09 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_e, s1)) | m_c_h_element_v_in1(c_e_h_2, c_e, s1) | m_c_h_element_v_in2(c_e_h_2, c_e, s1))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s1)) | m_c_h_element_v_in1(c_e_h_2, c_e, s1) | m_c_h_element_v_in2(c_e_h_2, c_e, s1))),
% 294.59/187.09 inference(rewrite,[status(thm)],[])).
% 294.59/187.09 tff(26942,plain,
% 294.59/187.09 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_e, s1)) | m_c_h_element_v_in1(c_e_h_2, c_e, s1) | m_c_h_element_v_in2(c_e_h_2, c_e, s1))),
% 294.59/187.09 inference(quant_inst,[status(thm)],[])).
% 294.59/187.09 tff(26943,plain,
% 294.59/187.09 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s1)) | m_c_h_element_v_in1(c_e_h_2, c_e, s1) | m_c_h_element_v_in2(c_e_h_2, c_e, s1)),
% 294.59/187.09 inference(modus_ponens,[status(thm)],[26942, 26941])).
% 294.59/187.09 tff(26944,plain,
% 294.59/187.09 (~node16(c_e_h_2, c_e, s1)),
% 294.59/187.09 inference(unit_resolution,[status(thm)],[26943, 178, 26933, 26903])).
% 294.59/187.09 tff(26945,plain,
% 294.59/187.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s1) | node15(c_e_h_2, c_e, s1, s2) | (~node19(c_e_h_2, c_e, s1, s2)) | node14(c_e_h_2, c_e, s1, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_e, s1) | node15(c_e_h_2, c_e, s1, s2) | (~node19(c_e_h_2, c_e, s1, s2)) | node14(c_e_h_2, c_e, s1, s2))),
% 294.59/187.09 inference(rewrite,[status(thm)],[])).
% 294.59/187.09 tff(26946,plain,
% 294.59/187.09 ((node16(c_e_h_2, c_e, s1) | node14(c_e_h_2, c_e, s1, s2) | node15(c_e_h_2, c_e, s1, s2) | (~node19(c_e_h_2, c_e, s1, s2))) <=> (node16(c_e_h_2, c_e, s1) | node15(c_e_h_2, c_e, s1, s2) | (~node19(c_e_h_2, c_e, s1, s2)) | node14(c_e_h_2, c_e, s1, s2))),
% 294.59/187.09 inference(rewrite,[status(thm)],[])).
% 294.59/187.09 tff(26947,plain,
% 294.59/187.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s1) | node14(c_e_h_2, c_e, s1, s2) | node15(c_e_h_2, c_e, s1, s2) | (~node19(c_e_h_2, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s1) | node15(c_e_h_2, c_e, s1, s2) | (~node19(c_e_h_2, c_e, s1, s2)) | node14(c_e_h_2, c_e, s1, s2)))),
% 294.59/187.10 inference(monotonicity,[status(thm)],[26946])).
% 294.59/187.10 tff(26948,plain,
% 294.59/187.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s1) | node14(c_e_h_2, c_e, s1, s2) | node15(c_e_h_2, c_e, s1, s2) | (~node19(c_e_h_2, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_e, s1) | node15(c_e_h_2, c_e, s1, s2) | (~node19(c_e_h_2, c_e, s1, s2)) | node14(c_e_h_2, c_e, s1, s2))),
% 294.59/187.10 inference(transitivity,[status(thm)],[26947, 26945])).
% 294.59/187.10 tff(26949,plain,
% 294.59/187.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s1) | node14(c_e_h_2, c_e, s1, s2) | node15(c_e_h_2, c_e, s1, s2) | (~node19(c_e_h_2, c_e, s1, s2)))),
% 294.59/187.10 inference(quant_inst,[status(thm)],[])).
% 294.59/187.10 tff(26950,plain,
% 294.59/187.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_e, s1) | node15(c_e_h_2, c_e, s1, s2) | (~node19(c_e_h_2, c_e, s1, s2)) | node14(c_e_h_2, c_e, s1, s2)),
% 294.59/187.10 inference(modus_ponens,[status(thm)],[26949, 26948])).
% 294.59/187.10 tff(26951,plain,
% 294.59/187.10 (node16(c_e_h_2, c_e, s1) | node15(c_e_h_2, c_e, s1, s2) | node14(c_e_h_2, c_e, s1, s2)),
% 294.59/187.10 inference(unit_resolution,[status(thm)],[26950, 204, 26917])).
% 294.59/187.10 tff(26952,plain,
% 294.59/187.10 (node14(c_e_h_2, c_e, s1, s2)),
% 294.59/187.10 inference(unit_resolution,[status(thm)],[26951, 26944, 26940])).
% 294.59/187.10 tff(26953,plain,
% 294.59/187.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | m_c_h_element_v_in1(c_e_h_2, c_e, s1) | (~node14(c_e_h_2, c_e, s1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | m_c_h_element_v_in1(c_e_h_2, c_e, s1) | (~node14(c_e_h_2, c_e, s1, s2)))),
% 294.59/187.10 inference(rewrite,[status(thm)],[])).
% 294.59/187.10 tff(26954,plain,
% 294.59/187.10 (((~node14(c_e_h_2, c_e, s1, s2)) | m_c_h_element_v_in1(c_e_h_2, c_e, s1) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2))) <=> ((~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | m_c_h_element_v_in1(c_e_h_2, c_e, s1) | (~node14(c_e_h_2, c_e, s1, s2)))),
% 294.59/187.10 inference(rewrite,[status(thm)],[])).
% 294.59/187.10 tff(26955,plain,
% 294.59/187.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s1, s2)) | m_c_h_element_v_in1(c_e_h_2, c_e, s1) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | m_c_h_element_v_in1(c_e_h_2, c_e, s1) | (~node14(c_e_h_2, c_e, s1, s2))))),
% 294.59/187.10 inference(monotonicity,[status(thm)],[26954])).
% 294.59/187.10 tff(26956,plain,
% 294.59/187.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s1, s2)) | m_c_h_element_v_in1(c_e_h_2, c_e, s1) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | m_c_h_element_v_in1(c_e_h_2, c_e, s1) | (~node14(c_e_h_2, c_e, s1, s2)))),
% 294.59/187.10 inference(transitivity,[status(thm)],[26955, 26953])).
% 294.59/187.10 tff(26957,plain,
% 294.59/187.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s1, s2)) | m_c_h_element_v_in1(c_e_h_2, c_e, s1) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2)))),
% 294.59/187.10 inference(quant_inst,[status(thm)],[])).
% 294.59/187.10 tff(26958,plain,
% 294.59/187.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2)) | m_c_h_element_v_in1(c_e_h_2, c_e, s1) | (~node14(c_e_h_2, c_e, s1, s2))),
% 294.59/187.10 inference(modus_ponens,[status(thm)],[26957, 26956])).
% 294.59/187.10 tff(26959,plain,
% 294.59/187.10 ($false),
% 294.59/187.10 inference(unit_resolution,[status(thm)],[26958, 223, 26902, 26952, 26933])).
% 294.59/187.10 tff(26960,plain,(m_c_h_element_v_in2(c_e_h_2, c_e, s1) | (~m_c_h_element_v_out(c_e_h_2, c_e, s2))), inference(lemma,lemma(discharge,[]))).
% 294.59/187.10 tff(26961,plain,
% 294.59/187.10 (m_c_h_element_v_in2(c_e_h_2, c_e, s1)),
% 294.59/187.10 inference(unit_resolution,[status(thm)],[26960, 26902])).
% 294.59/187.10 tff(26962,plain,
% 294.59/187.10 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s1)) | m_and_h_gate_v_out(c_e_h_2, c_c, s1))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s1)) | m_and_h_gate_v_out(c_e_h_2, c_c, s1))),
% 294.59/187.10 inference(rewrite,[status(thm)],[])).
% 294.59/187.10 tff(26963,plain,
% 294.59/187.10 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s1)) | m_and_h_gate_v_out(c_e_h_2, c_c, s1))),
% 294.59/187.10 inference(quant_inst,[status(thm)],[])).
% 294.59/187.10 tff(26964,plain,
% 294.59/187.10 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in1(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_c, X))) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s1)) | m_and_h_gate_v_out(c_e_h_2, c_c, s1)),
% 294.59/187.10 inference(modus_ponens,[status(thm)],[26963, 26962])).
% 294.59/187.10 tff(26965,plain,
% 294.59/187.10 (~m_c_h_element_v_in1(c_e_h_2, c_e, s1)),
% 294.59/187.10 inference(unit_resolution,[status(thm)],[26964, 131, 16061])).
% 294.59/187.10 tff(26966,plain,
% 294.59/187.10 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s1) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s1)) | (~node17(c_e_h_2, c_e, s1)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s1) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s1)) | (~node17(c_e_h_2, c_e, s1)))),
% 294.59/187.10 inference(rewrite,[status(thm)],[])).
% 294.59/187.10 tff(26967,plain,
% 294.59/187.10 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s1) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s1)) | (~node17(c_e_h_2, c_e, s1)))),
% 294.59/187.10 inference(quant_inst,[status(thm)],[])).
% 294.59/187.10 tff(26968,plain,
% 294.59/187.10 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s1) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s1)) | (~node17(c_e_h_2, c_e, s1))),
% 294.59/187.10 inference(modus_ponens,[status(thm)],[26967, 26966])).
% 294.59/187.10 tff(26969,plain,
% 294.59/187.10 ((~m_c_h_element_v_in2(c_e_h_2, c_e, s1)) | (~node17(c_e_h_2, c_e, s1))),
% 294.59/187.10 inference(unit_resolution,[status(thm)],[26968, 859, 26965])).
% 294.59/187.10 tff(26970,plain,
% 294.59/187.10 ($false),
% 294.59/187.10 inference(unit_resolution,[status(thm)],[26969, 26925, 26961])).
% 294.59/187.10 tff(26971,plain,(~m_c_h_element_v_out(c_e_h_2, c_e, s2)), inference(lemma,lemma(discharge,[]))).
% 294.59/187.10 tff(26972,plain,
% 294.59/187.10 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s2) | m_c_h_element_v_out(c_e_h_2, c_e, s2))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s2) | m_c_h_element_v_out(c_e_h_2, c_e, s2))),
% 294.59/187.10 inference(rewrite,[status(thm)],[])).
% 294.59/187.10 tff(26973,plain,
% 294.59/187.10 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s2) | m_c_h_element_v_out(c_e_h_2, c_e, s2))),
% 294.59/187.10 inference(quant_inst,[status(thm)],[])).
% 294.59/187.10 tff(26974,plain,
% 294.59/187.10 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s2) | m_c_h_element_v_out(c_e_h_2, c_e, s2)),
% 294.59/187.10 inference(modus_ponens,[status(thm)],[26973, 26972])).
% 294.59/187.10 tff(26975,plain,
% 294.59/187.10 (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s2) | m_c_h_element_v_out(c_e_h_2, c_e, s2)),
% 294.59/187.10 inference(unit_resolution,[status(thm)],[26974, 7856])).
% 294.59/187.10 tff(26976,plain,
% 294.59/187.10 (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s2)),
% 294.59/187.10 inference(unit_resolution,[status(thm)],[26975, 26971])).
% 294.59/187.10 tff(26977,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3)), introduced(assumption)).
% 294.59/187.10 tff(26978,assumption,(node11(c_e_h_2, c_n, s2, s3)), introduced(assumption)).
% 294.59/187.10 tff(26979,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2)), introduced(assumption)).
% 294.59/187.10 tff(26980,plain,
% 294.59/187.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2)) | (~node11(c_e_h_2, c_n, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2)) | (~node11(c_e_h_2, c_n, s2, s3)))),
% 294.59/187.10 inference(rewrite,[status(thm)],[])).
% 294.59/187.10 tff(26981,plain,
% 294.59/187.10 ((m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3) | (~node11(c_e_h_2, c_n, s2, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2))) <=> (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2)) | (~node11(c_e_h_2, c_n, s2, s3)))),
% 294.59/187.10 inference(rewrite,[status(thm)],[])).
% 294.59/187.10 tff(26982,plain,
% 294.59/187.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3) | (~node11(c_e_h_2, c_n, s2, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2)) | (~node11(c_e_h_2, c_n, s2, s3))))),
% 294.59/187.10 inference(monotonicity,[status(thm)],[26981])).
% 294.59/187.10 tff(26983,plain,
% 294.59/187.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3) | (~node11(c_e_h_2, c_n, s2, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2)) | (~node11(c_e_h_2, c_n, s2, s3)))),
% 294.59/187.10 inference(transitivity,[status(thm)],[26982, 26980])).
% 294.59/187.10 tff(26984,plain,
% 294.59/187.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3) | (~node11(c_e_h_2, c_n, s2, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2)))),
% 294.59/187.10 inference(quant_inst,[status(thm)],[])).
% 294.59/187.10 tff(26985,plain,
% 294.59/187.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2)) | (~node11(c_e_h_2, c_n, s2, s3))),
% 294.59/187.10 inference(modus_ponens,[status(thm)],[26984, 26983])).
% 294.59/187.10 tff(26986,plain,
% 294.59/187.10 ($false),
% 294.59/187.10 inference(unit_resolution,[status(thm)],[26985, 5742, 26977, 26979, 26978])).
% 294.59/187.10 tff(26987,plain,((~node11(c_e_h_2, c_n, s2, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s2))), inference(lemma,lemma(discharge,[]))).
% 294.59/187.11 tff(26988,plain,
% 294.59/187.11 ((~node11(c_e_h_2, c_n, s2, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3)),
% 294.59/187.11 inference(unit_resolution,[status(thm)],[26987, 8344])).
% 294.59/187.11 tff(26989,plain,
% 294.59/187.11 (~node11(c_e_h_2, c_n, s2, s3)),
% 294.59/187.11 inference(unit_resolution,[status(thm)],[26988, 26977])).
% 294.59/187.11 tff(26990,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s2)), introduced(assumption)).
% 294.59/187.11 tff(26991,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)), introduced(assumption)).
% 294.59/187.11 tff(26992,assumption,(~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s2)), introduced(assumption)).
% 294.59/187.11 tff(26993,plain,
% 294.59/187.11 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s2) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s2) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2))),
% 294.59/187.11 inference(rewrite,[status(thm)],[])).
% 294.59/187.11 tff(26994,plain,
% 294.59/187.11 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s2) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2))),
% 294.59/187.11 inference(quant_inst,[status(thm)],[])).
% 294.59/187.11 tff(26995,plain,
% 294.59/187.11 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s2) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2)),
% 294.59/187.11 inference(modus_ponens,[status(thm)],[26994, 26993])).
% 294.59/187.11 tff(26996,plain,
% 294.59/187.11 ($false),
% 294.59/187.11 inference(unit_resolution,[status(thm)],[26995, 7868, 26992, 26991])).
% 294.59/187.11 tff(26997,plain,(m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s2) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s2)), inference(lemma,lemma(discharge,[]))).
% 294.59/187.11 tff(26998,plain,
% 294.59/187.11 (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s2)),
% 294.59/187.11 inference(unit_resolution,[status(thm)],[26997, 7909])).
% 294.59/187.11 tff(26999,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s2)), introduced(assumption)).
% 294.59/187.11 tff(27000,assumption,(node10(c_e_h_2, c_n, s2, s3)), introduced(assumption)).
% 294.59/187.11 tff(27001,plain,
% 294.59/187.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3) | (~node10(c_e_h_2, c_n, s2, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s2)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3) | (~node10(c_e_h_2, c_n, s2, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s2)))),
% 294.59/187.11 inference(rewrite,[status(thm)],[])).
% 294.59/187.11 tff(27002,plain,
% 294.59/187.11 (((~node10(c_e_h_2, c_n, s2, s3)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s2)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s2)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3)) <=> (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3) | (~node10(c_e_h_2, c_n, s2, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s2)))),
% 294.59/187.11 inference(rewrite,[status(thm)],[])).
% 294.59/187.11 tff(27003,plain,
% 294.59/187.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s2, s3)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s2)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s2)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3) | (~node10(c_e_h_2, c_n, s2, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s2))))),
% 294.59/187.11 inference(monotonicity,[status(thm)],[27002])).
% 294.59/187.11 tff(27004,plain,
% 294.59/187.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s2, s3)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s2)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s2)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3) | (~node10(c_e_h_2, c_n, s2, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s2)))),
% 294.59/187.11 inference(transitivity,[status(thm)],[27003, 27001])).
% 294.59/187.11 tff(27005,plain,
% 294.59/187.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s2, s3)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s2)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s2)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3))),
% 294.59/187.11 inference(quant_inst,[status(thm)],[])).
% 294.59/187.11 tff(27006,plain,
% 294.59/187.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3) | (~node10(c_e_h_2, c_n, s2, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s2))),
% 294.59/187.11 inference(modus_ponens,[status(thm)],[27005, 27004])).
% 294.59/187.11 tff(27007,plain,
% 294.59/187.11 ($false),
% 294.59/187.11 inference(unit_resolution,[status(thm)],[27006, 5718, 26977, 26990, 27000, 26999])).
% 294.59/187.11 tff(27008,plain,((~node10(c_e_h_2, c_n, s2, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s2)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s2))), inference(lemma,lemma(discharge,[]))).
% 294.59/187.11 tff(27009,plain,
% 294.59/187.11 ((~node10(c_e_h_2, c_n, s2, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s2))),
% 294.59/187.11 inference(unit_resolution,[status(thm)],[27008, 26998])).
% 294.59/187.11 tff(27010,plain,
% 294.59/187.11 (~node10(c_e_h_2, c_n, s2, s3)),
% 294.59/187.11 inference(unit_resolution,[status(thm)],[27009, 26977, 26990])).
% 294.59/187.11 tff(27011,plain,
% 294.59/187.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s2, s3)) | node10(c_e_h_2, c_n, s2, s3) | node11(c_e_h_2, c_n, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s2, s3)) | node10(c_e_h_2, c_n, s2, s3) | node11(c_e_h_2, c_n, s2, s3))),
% 294.59/187.11 inference(rewrite,[status(thm)],[])).
% 294.59/187.11 tff(27012,plain,
% 294.59/187.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s2, s3)) | node10(c_e_h_2, c_n, s2, s3) | node11(c_e_h_2, c_n, s2, s3))),
% 294.59/187.11 inference(quant_inst,[status(thm)],[])).
% 294.59/187.11 tff(27013,plain,
% 294.59/187.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s2, s3)) | node10(c_e_h_2, c_n, s2, s3) | node11(c_e_h_2, c_n, s2, s3)),
% 294.59/187.11 inference(modus_ponens,[status(thm)],[27012, 27011])).
% 294.59/187.11 tff(27014,plain,
% 294.59/187.11 (node10(c_e_h_2, c_n, s2, s3) | node11(c_e_h_2, c_n, s2, s3)),
% 294.59/187.11 inference(unit_resolution,[status(thm)],[27013, 5002, 318])).
% 294.59/187.11 tff(27015,plain,
% 294.59/187.11 ($false),
% 294.59/187.11 inference(unit_resolution,[status(thm)],[27014, 27010, 26989])).
% 294.59/187.11 tff(27016,plain,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s2))), inference(lemma,lemma(discharge,[]))).
% 294.59/187.11 tff(27017,plain,
% 294.59/187.11 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3)),
% 294.59/187.11 inference(unit_resolution,[status(thm)],[27016, 26976])).
% 294.59/187.11 tff(27018,plain,
% 294.59/187.11 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3)))),
% 294.59/187.11 inference(rewrite,[status(thm)],[])).
% 294.59/187.11 tff(27019,plain,
% 294.59/187.11 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3)))),
% 294.59/187.11 inference(quant_inst,[status(thm)],[])).
% 294.59/187.11 tff(27020,plain,
% 294.59/187.11 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3))),
% 294.59/187.11 inference(modus_ponens,[status(thm)],[27019, 27018])).
% 294.59/187.11 tff(27021,plain,
% 294.59/187.11 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s3)),
% 294.59/187.11 inference(unit_resolution,[status(thm)],[27020, 4958, 27017])).
% 294.59/187.11 tff(27022,plain,
% 294.59/187.11 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s3)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s3)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s3))),
% 294.59/187.11 inference(rewrite,[status(thm)],[])).
% 294.59/187.11 tff(27023,plain,
% 294.59/187.11 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s3)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s3))),
% 294.59/187.11 inference(quant_inst,[status(thm)],[])).
% 294.59/187.11 tff(27024,plain,
% 294.59/187.11 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s3)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s3)),
% 294.59/187.11 inference(modus_ponens,[status(thm)],[27023, 27022])).
% 294.59/187.11 tff(27025,plain,
% 294.59/187.11 (~node9(c_e_h_2, c_m, s3)),
% 294.59/187.11 inference(unit_resolution,[status(thm)],[27024, 4972, 27021])).
% 294.59/187.11 tff(27026,assumption,(~node9(c_e_h_2, c_m, s3)), introduced(assumption)).
% 294.59/187.11 tff(27027,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)), introduced(assumption)).
% 294.59/187.11 tff(27028,assumption,(node11(c_e_h_2, c_m, s3, s4)), introduced(assumption)).
% 294.59/187.11 tff(27029,plain,
% 294.59/187.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)) | (~node11(c_e_h_2, c_m, s3, s4)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)) | (~node11(c_e_h_2, c_m, s3, s4)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3))),
% 294.59/187.11 inference(rewrite,[status(thm)],[])).
% 294.59/187.11 tff(27030,plain,
% 294.59/187.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)) | (~node11(c_e_h_2, c_m, s3, s4)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3))),
% 294.59/187.11 inference(quant_inst,[status(thm)],[])).
% 294.59/187.11 tff(27031,plain,
% 294.59/187.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)) | (~node11(c_e_h_2, c_m, s3, s4)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)),
% 294.59/187.11 inference(modus_ponens,[status(thm)],[27030, 27029])).
% 294.59/187.11 tff(27032,plain,
% 294.59/187.11 ($false),
% 294.59/187.11 inference(unit_resolution,[status(thm)],[27031, 5017, 27027, 27028, 8360])).
% 294.59/187.11 tff(27033,plain,((~node11(c_e_h_2, c_m, s3, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4))), inference(lemma,lemma(discharge,[]))).
% 294.59/187.11 tff(27034,plain,
% 294.59/187.11 (~node11(c_e_h_2, c_m, s3, s4)),
% 294.59/187.11 inference(unit_resolution,[status(thm)],[27033, 27027])).
% 294.59/187.11 tff(27035,plain,
% 294.59/187.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s3, s4)) | node10(c_e_h_2, c_m, s3, s4) | node11(c_e_h_2, c_m, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s3, s4)) | node10(c_e_h_2, c_m, s3, s4) | node11(c_e_h_2, c_m, s3, s4))),
% 294.59/187.12 inference(rewrite,[status(thm)],[])).
% 294.59/187.12 tff(27036,plain,
% 294.59/187.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s3, s4)) | node10(c_e_h_2, c_m, s3, s4) | node11(c_e_h_2, c_m, s3, s4))),
% 294.59/187.12 inference(quant_inst,[status(thm)],[])).
% 294.59/187.12 tff(27037,plain,
% 294.59/187.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s3, s4)) | node10(c_e_h_2, c_m, s3, s4) | node11(c_e_h_2, c_m, s3, s4)),
% 294.59/187.12 inference(modus_ponens,[status(thm)],[27036, 27035])).
% 294.59/187.12 tff(27038,plain,
% 294.59/187.12 (node10(c_e_h_2, c_m, s3, s4) | node11(c_e_h_2, c_m, s3, s4)),
% 294.59/187.12 inference(unit_resolution,[status(thm)],[27037, 5002, 531])).
% 294.59/187.12 tff(27039,plain,
% 294.59/187.12 (node10(c_e_h_2, c_m, s3, s4)),
% 294.59/187.12 inference(unit_resolution,[status(thm)],[27038, 27034])).
% 294.59/187.12 tff(27040,plain,
% 294.59/187.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)) | (~node10(c_e_h_2, c_m, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_2, c_m, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)) | (~node10(c_e_h_2, c_m, s3, s4)))),
% 294.59/187.12 inference(rewrite,[status(thm)],[])).
% 294.59/187.12 tff(27041,plain,
% 294.59/187.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)) | (~node10(c_e_h_2, c_m, s3, s4)))),
% 294.59/187.12 inference(quant_inst,[status(thm)],[])).
% 294.59/187.12 tff(27042,plain,
% 294.59/187.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_2, c_m, s3) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)) | (~node10(c_e_h_2, c_m, s3, s4))),
% 294.59/187.12 inference(modus_ponens,[status(thm)],[27041, 27040])).
% 294.59/187.12 tff(27043,plain,
% 294.59/187.12 ($false),
% 294.59/187.12 inference(unit_resolution,[status(thm)],[27042, 4986, 27027, 27039, 27026])).
% 294.59/187.12 tff(27044,plain,((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)) | node9(c_e_h_2, c_m, s3)), inference(lemma,lemma(discharge,[]))).
% 294.59/187.12 tff(27045,plain,
% 294.59/187.12 (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)),
% 294.59/187.12 inference(unit_resolution,[status(thm)],[27044, 27025])).
% 294.59/187.12 tff(27046,plain,
% 294.59/187.12 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_l, s4)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_l, s4)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4))),
% 294.59/187.12 inference(rewrite,[status(thm)],[])).
% 294.59/187.12 tff(27047,plain,
% 294.59/187.12 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_l, s4)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4))),
% 294.59/187.12 inference(quant_inst,[status(thm)],[])).
% 294.59/187.12 tff(27048,plain,
% 294.59/187.12 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_l, s4)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)),
% 294.59/187.12 inference(modus_ponens,[status(thm)],[27047, 27046])).
% 294.59/187.12 tff(27049,plain,
% 294.59/187.12 (~m_and_h_gate_v_in2(c_e_h_2, c_l, s4)),
% 294.59/187.12 inference(unit_resolution,[status(thm)],[27048, 4549, 27045])).
% 294.59/187.12 tff(27050,plain,
% 294.59/187.12 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_l, s4)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_l, s4)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s4))),
% 294.59/187.12 inference(rewrite,[status(thm)],[])).
% 294.59/187.12 tff(27051,plain,
% 294.59/187.12 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_l, s4)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s4))),
% 294.59/187.12 inference(quant_inst,[status(thm)],[])).
% 294.59/187.12 tff(27052,plain,
% 294.59/187.12 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_l, s4)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s4)),
% 294.59/187.12 inference(modus_ponens,[status(thm)],[27051, 27050])).
% 294.59/187.12 tff(27053,plain,
% 294.59/187.12 (~node20(c_e_h_2, c_l, s4)),
% 294.59/187.12 inference(unit_resolution,[status(thm)],[27052, 4563, 27049])).
% 294.59/187.12 tff(27054,assumption,(m_or_h_gate_v_out(c_e_h_2, c_j, s6)), introduced(assumption)).
% 294.59/187.12 tff(27055,plain,
% 294.59/187.12 (~m_or_h_gate_v_in1(c_e_h_2, c_j, s4)),
% 294.59/187.12 inference(unit_resolution,[status(thm)],[8395, 8389])).
% 294.59/187.12 tff(27056,plain,
% 294.59/187.12 (~m_or_h_gate_v_out(c_e_h_2, c_j, s5)),
% 294.59/187.12 inference(unit_resolution,[status(thm)],[8610, 27055, 8590, 8578])).
% 294.59/187.12 tff(27057,assumption,(node6(c_e_h_2, c_j, s5, s6)), introduced(assumption)).
% 294.59/187.12 tff(27058,plain,
% 294.59/187.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_2, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s6)) | (~node6(c_e_h_2, c_j, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s6)) | (~node6(c_e_h_2, c_j, s5, s6)))),
% 294.59/187.12 inference(rewrite,[status(thm)],[])).
% 294.59/187.12 tff(27059,plain,
% 294.59/187.12 (((~node6(c_e_h_2, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s6)) | m_or_h_gate_v_out(c_e_h_2, c_j, s5)) <=> (m_or_h_gate_v_out(c_e_h_2, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s6)) | (~node6(c_e_h_2, c_j, s5, s6)))),
% 294.59/187.12 inference(rewrite,[status(thm)],[])).
% 294.59/187.12 tff(27060,plain,
% 294.59/187.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s6)) | m_or_h_gate_v_out(c_e_h_2, c_j, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_2, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s6)) | (~node6(c_e_h_2, c_j, s5, s6))))),
% 294.59/187.12 inference(monotonicity,[status(thm)],[27059])).
% 294.59/187.12 tff(27061,plain,
% 294.59/187.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s6)) | m_or_h_gate_v_out(c_e_h_2, c_j, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s6)) | (~node6(c_e_h_2, c_j, s5, s6)))),
% 294.59/187.12 inference(transitivity,[status(thm)],[27060, 27058])).
% 294.59/187.12 tff(27062,plain,
% 294.59/187.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s6)) | m_or_h_gate_v_out(c_e_h_2, c_j, s5))),
% 294.59/187.12 inference(quant_inst,[status(thm)],[])).
% 294.59/187.12 tff(27063,plain,
% 294.59/187.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s6)) | (~node6(c_e_h_2, c_j, s5, s6))),
% 294.59/187.12 inference(modus_ponens,[status(thm)],[27062, 27061])).
% 294.59/187.12 tff(27064,plain,
% 294.59/187.12 ($false),
% 294.59/187.12 inference(unit_resolution,[status(thm)],[27063, 1121, 8615, 27057, 27054])).
% 294.59/187.12 tff(27065,plain,((~node6(c_e_h_2, c_j, s5, s6)) | m_or_h_gate_v_out(c_e_h_2, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s6))), inference(lemma,lemma(discharge,[]))).
% 294.59/187.12 tff(27066,plain,
% 294.59/187.12 (~node6(c_e_h_2, c_j, s5, s6)),
% 294.59/187.12 inference(unit_resolution,[status(thm)],[27065, 27056, 27054])).
% 294.59/187.12 tff(27067,assumption,(~m_or_h_gate_v_in2(c_e_h_2, c_j, s5)), introduced(assumption)).
% 294.59/187.12 tff(27068,assumption,(~node20(c_e_h_2, c_l, s4)), introduced(assumption)).
% 294.59/187.12 tff(27069,assumption,(m_and_h_gate_v_out(c_e_h_2, c_l, s5)), introduced(assumption)).
% 294.59/187.12 tff(27070,assumption,(node22(c_e_h_2, c_l, s4, s5)), introduced(assumption)).
% 294.59/187.12 tff(27071,plain,
% 294.59/187.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s5)) | (~node22(c_e_h_2, c_l, s4, s5)) | m_and_h_gate_v_out(c_e_h_2, c_l, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s5)) | (~node22(c_e_h_2, c_l, s4, s5)) | m_and_h_gate_v_out(c_e_h_2, c_l, s4))),
% 294.59/187.12 inference(rewrite,[status(thm)],[])).
% 294.59/187.12 tff(27072,plain,
% 294.59/187.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s5)) | (~node22(c_e_h_2, c_l, s4, s5)) | m_and_h_gate_v_out(c_e_h_2, c_l, s4))),
% 294.59/187.12 inference(quant_inst,[status(thm)],[])).
% 294.59/187.12 tff(27073,plain,
% 294.59/187.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s5)) | (~node22(c_e_h_2, c_l, s4, s5)) | m_and_h_gate_v_out(c_e_h_2, c_l, s4)),
% 294.59/187.12 inference(modus_ponens,[status(thm)],[27072, 27071])).
% 294.59/187.12 tff(27074,plain,
% 294.59/187.12 ($false),
% 294.59/187.12 inference(unit_resolution,[status(thm)],[27073, 108, 8389, 27070, 27069])).
% 294.59/187.12 tff(27075,plain,((~node22(c_e_h_2, c_l, s4, s5)) | m_and_h_gate_v_out(c_e_h_2, c_l, s4) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s5))), inference(lemma,lemma(discharge,[]))).
% 294.59/187.12 tff(27076,plain,
% 294.59/187.12 (~node22(c_e_h_2, c_l, s4, s5)),
% 294.59/187.12 inference(unit_resolution,[status(thm)],[27075, 27069, 8389])).
% 294.59/187.12 tff(27077,plain,
% 294.59/187.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_2, c_l, s4, s5) | node22(c_e_h_2, c_l, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_2, c_l, s4, s5) | node22(c_e_h_2, c_l, s4, s5))),
% 294.59/187.12 inference(rewrite,[status(thm)],[])).
% 294.59/187.12 tff(27078,plain,
% 294.59/187.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s4, s5)) | node21(c_e_h_2, c_l, s4, s5) | node22(c_e_h_2, c_l, s4, s5))),
% 294.59/187.12 inference(quant_inst,[status(thm)],[])).
% 294.59/187.12 tff(27079,plain,
% 294.59/187.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s4, s5)) | node21(c_e_h_2, c_l, s4, s5) | node22(c_e_h_2, c_l, s4, s5)),
% 294.59/187.12 inference(modus_ponens,[status(thm)],[27078, 27077])).
% 294.59/187.12 tff(27080,plain,
% 294.59/187.12 (node21(c_e_h_2, c_l, s4, s5) | node22(c_e_h_2, c_l, s4, s5)),
% 294.59/187.12 inference(unit_resolution,[status(thm)],[27079, 82, 1028])).
% 294.59/187.12 tff(27081,plain,
% 294.59/187.12 (node21(c_e_h_2, c_l, s4, s5)),
% 294.59/187.12 inference(unit_resolution,[status(thm)],[27080, 27076])).
% 294.59/187.12 tff(27082,plain,
% 294.59/187.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_l, s4) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s5)) | (~node21(c_e_h_2, c_l, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_l, s4) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s5)) | (~node21(c_e_h_2, c_l, s4, s5)))),
% 294.59/187.12 inference(rewrite,[status(thm)],[])).
% 294.59/187.12 tff(27083,plain,
% 294.59/187.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_l, s4) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s5)) | (~node21(c_e_h_2, c_l, s4, s5)))),
% 294.59/187.12 inference(quant_inst,[status(thm)],[])).
% 294.59/187.12 tff(27084,plain,
% 294.59/187.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_l, s4) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s5)) | (~node21(c_e_h_2, c_l, s4, s5))),
% 294.59/187.13 inference(modus_ponens,[status(thm)],[27083, 27082])).
% 294.59/187.13 tff(27085,plain,
% 294.59/187.13 ($false),
% 294.59/187.13 inference(unit_resolution,[status(thm)],[27084, 52, 27081, 27068, 27069])).
% 294.59/187.13 tff(27086,plain,((~m_and_h_gate_v_out(c_e_h_2, c_l, s5)) | node20(c_e_h_2, c_l, s4) | m_and_h_gate_v_out(c_e_h_2, c_l, s4)), inference(lemma,lemma(discharge,[]))).
% 294.59/187.13 tff(27087,plain,
% 294.59/187.13 (~m_and_h_gate_v_out(c_e_h_2, c_l, s5)),
% 294.59/187.13 inference(unit_resolution,[status(thm)],[27086, 8389, 27068])).
% 294.59/187.13 tff(27088,assumption,(m_or_h_gate_v_in1(c_e_h_2, c_j, s5)), introduced(assumption)).
% 294.59/187.13 tff(27089,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_l, s5)), introduced(assumption)).
% 294.59/187.13 tff(27090,plain,
% 294.59/187.13 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_2, c_j, s5)) | m_and_h_gate_v_out(c_e_h_2, c_l, s5))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_j, s5)) | m_and_h_gate_v_out(c_e_h_2, c_l, s5))),
% 294.59/187.13 inference(rewrite,[status(thm)],[])).
% 294.59/187.13 tff(27091,plain,
% 294.59/187.13 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_2, c_j, s5)) | m_and_h_gate_v_out(c_e_h_2, c_l, s5))),
% 294.59/187.13 inference(quant_inst,[status(thm)],[])).
% 294.59/187.13 tff(27092,plain,
% 294.59/187.13 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_j, s5)) | m_and_h_gate_v_out(c_e_h_2, c_l, s5)),
% 294.59/187.13 inference(modus_ponens,[status(thm)],[27091, 27090])).
% 294.59/187.13 tff(27093,plain,
% 294.59/187.13 ($false),
% 294.59/187.13 inference(unit_resolution,[status(thm)],[27092, 1100, 27089, 27088])).
% 294.59/187.13 tff(27094,plain,((~m_or_h_gate_v_in1(c_e_h_2, c_j, s5)) | m_and_h_gate_v_out(c_e_h_2, c_l, s5)), inference(lemma,lemma(discharge,[]))).
% 294.59/187.13 tff(27095,plain,
% 294.59/187.13 (~m_or_h_gate_v_in1(c_e_h_2, c_j, s5)),
% 294.59/187.13 inference(unit_resolution,[status(thm)],[27094, 27087])).
% 294.59/187.13 tff(27096,assumption,(~m_or_h_gate_v_in1(c_e_h_2, c_j, s5)), introduced(assumption)).
% 294.59/187.13 tff(27097,assumption,(node5(c_e_h_2, c_j, s5, s6)), introduced(assumption)).
% 294.59/187.13 tff(27098,plain,
% 294.59/187.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_2, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s6)) | (~node5(c_e_h_2, c_j, s5, s6)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_2, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s6)) | (~node5(c_e_h_2, c_j, s5, s6)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s5))),
% 294.59/187.13 inference(rewrite,[status(thm)],[])).
% 294.59/187.13 tff(27099,plain,
% 294.59/187.13 ((m_or_h_gate_v_in1(c_e_h_2, c_j, s5) | m_or_h_gate_v_in2(c_e_h_2, c_j, s5) | (~node5(c_e_h_2, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s6))) <=> (m_or_h_gate_v_in2(c_e_h_2, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s6)) | (~node5(c_e_h_2, c_j, s5, s6)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s5))),
% 294.59/187.13 inference(rewrite,[status(thm)],[])).
% 294.59/187.13 tff(27100,plain,
% 294.59/187.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s5) | m_or_h_gate_v_in2(c_e_h_2, c_j, s5) | (~node5(c_e_h_2, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_2, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s6)) | (~node5(c_e_h_2, c_j, s5, s6)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s5)))),
% 294.59/187.13 inference(monotonicity,[status(thm)],[27099])).
% 294.59/187.13 tff(27101,plain,
% 294.59/187.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s5) | m_or_h_gate_v_in2(c_e_h_2, c_j, s5) | (~node5(c_e_h_2, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_2, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s6)) | (~node5(c_e_h_2, c_j, s5, s6)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s5))),
% 294.59/187.13 inference(transitivity,[status(thm)],[27100, 27098])).
% 294.59/187.13 tff(27102,plain,
% 294.59/187.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s5) | m_or_h_gate_v_in2(c_e_h_2, c_j, s5) | (~node5(c_e_h_2, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s6)))),
% 294.59/187.13 inference(quant_inst,[status(thm)],[])).
% 294.59/187.13 tff(27103,plain,
% 294.59/187.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_2, c_j, s5) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s6)) | (~node5(c_e_h_2, c_j, s5, s6)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s5)),
% 294.59/187.13 inference(modus_ponens,[status(thm)],[27102, 27101])).
% 294.59/187.13 tff(27104,plain,
% 294.59/187.13 ($false),
% 294.59/187.13 inference(unit_resolution,[status(thm)],[27103, 1159, 27097, 27054, 27096, 27067])).
% 294.59/187.13 tff(27105,plain,((~node5(c_e_h_2, c_j, s5, s6)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s6)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s5) | m_or_h_gate_v_in2(c_e_h_2, c_j, s5)), inference(lemma,lemma(discharge,[]))).
% 294.59/187.13 tff(27106,plain,
% 294.59/187.13 (~node5(c_e_h_2, c_j, s5, s6)),
% 294.59/187.13 inference(unit_resolution,[status(thm)],[27105, 27095, 27054, 27067])).
% 294.59/187.13 tff(27107,plain,
% 294.59/187.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s5, s6)) | node6(c_e_h_2, c_j, s5, s6) | node5(c_e_h_2, c_j, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s5, s6)) | node6(c_e_h_2, c_j, s5, s6) | node5(c_e_h_2, c_j, s5, s6))),
% 294.59/187.13 inference(rewrite,[status(thm)],[])).
% 294.59/187.13 tff(27108,plain,
% 294.59/187.13 ((node6(c_e_h_2, c_j, s5, s6) | node5(c_e_h_2, c_j, s5, s6) | (~trans(s5, s6))) <=> ((~trans(s5, s6)) | node6(c_e_h_2, c_j, s5, s6) | node5(c_e_h_2, c_j, s5, s6))),
% 294.59/187.13 inference(rewrite,[status(thm)],[])).
% 294.59/187.13 tff(27109,plain,
% 294.59/187.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s5, s6) | node5(c_e_h_2, c_j, s5, s6) | (~trans(s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s5, s6)) | node6(c_e_h_2, c_j, s5, s6) | node5(c_e_h_2, c_j, s5, s6)))),
% 294.59/187.13 inference(monotonicity,[status(thm)],[27108])).
% 294.59/187.13 tff(27110,plain,
% 294.59/187.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s5, s6) | node5(c_e_h_2, c_j, s5, s6) | (~trans(s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s5, s6)) | node6(c_e_h_2, c_j, s5, s6) | node5(c_e_h_2, c_j, s5, s6))),
% 294.59/187.13 inference(transitivity,[status(thm)],[27109, 27107])).
% 294.59/187.13 tff(27111,plain,
% 294.59/187.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s5, s6) | node5(c_e_h_2, c_j, s5, s6) | (~trans(s5, s6)))),
% 294.59/187.13 inference(quant_inst,[status(thm)],[])).
% 294.59/187.13 tff(27112,plain,
% 294.59/187.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s5, s6)) | node6(c_e_h_2, c_j, s5, s6) | node5(c_e_h_2, c_j, s5, s6)),
% 294.59/187.13 inference(modus_ponens,[status(thm)],[27111, 27110])).
% 294.59/187.13 tff(27113,plain,
% 294.59/187.13 (node6(c_e_h_2, c_j, s5, s6) | node5(c_e_h_2, c_j, s5, s6)),
% 294.59/187.13 inference(unit_resolution,[status(thm)],[27112, 1141, 1406])).
% 294.59/187.13 tff(27114,plain,
% 294.59/187.13 ($false),
% 294.59/187.13 inference(unit_resolution,[status(thm)],[27113, 27106, 27066])).
% 294.59/187.14 tff(27115,plain,(m_and_h_gate_v_out(c_e_h_2, c_l, s4) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s6)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s5) | m_or_h_gate_v_in2(c_e_h_2, c_j, s4) | m_or_h_gate_v_out(c_e_h_2, c_j, s4) | node20(c_e_h_2, c_l, s4)), inference(lemma,lemma(discharge,[]))).
% 294.59/187.14 tff(27116,plain,
% 294.59/187.14 (m_and_h_gate_v_out(c_e_h_2, c_l, s4) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s6)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s5) | m_or_h_gate_v_in2(c_e_h_2, c_j, s4) | m_or_h_gate_v_out(c_e_h_2, c_j, s4)),
% 294.59/187.14 inference(unit_resolution,[status(thm)],[27115, 27053])).
% 294.59/187.14 tff(27117,plain,
% 294.59/187.14 (m_and_h_gate_v_out(c_e_h_2, c_l, s4) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s6)) | m_or_h_gate_v_out(c_e_h_2, c_j, s4)),
% 294.59/187.14 inference(unit_resolution,[status(thm)],[27116, 8577, 26901])).
% 294.59/187.14 tff(27118,plain,
% 294.59/187.14 ((~m_or_h_gate_v_out(c_e_h_2, c_j, s6)) | m_or_h_gate_v_out(c_e_h_2, c_j, s4)),
% 294.59/187.14 inference(unit_resolution,[status(thm)],[27117, 8388])).
% 294.59/187.14 tff(27119,plain,
% 294.59/187.14 (~m_or_h_gate_v_out(c_e_h_2, c_j, s6)),
% 294.59/187.14 inference(unit_resolution,[status(thm)],[27118, 8115])).
% 294.59/187.14 tff(27120,assumption,(m_c_h_element_v_in2(c_e_h_2, c_h, s6)), introduced(assumption)).
% 294.59/187.14 tff(27121,assumption,(~m_or_h_gate_v_out(c_e_h_2, c_j, s6)), introduced(assumption)).
% 294.59/187.14 tff(27122,plain,
% 294.59/187.14 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s6)) | m_or_h_gate_v_out(c_e_h_2, c_j, s6))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s6)) | m_or_h_gate_v_out(c_e_h_2, c_j, s6))),
% 294.59/187.14 inference(rewrite,[status(thm)],[])).
% 294.59/187.14 tff(27123,plain,
% 294.59/187.14 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s6)) | m_or_h_gate_v_out(c_e_h_2, c_j, s6))),
% 294.59/187.14 inference(quant_inst,[status(thm)],[])).
% 294.59/187.14 tff(27124,plain,
% 294.59/187.14 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s6)) | m_or_h_gate_v_out(c_e_h_2, c_j, s6)),
% 294.59/187.14 inference(modus_ponens,[status(thm)],[27123, 27122])).
% 294.59/187.14 tff(27125,plain,
% 294.59/187.14 ($false),
% 294.59/187.14 inference(unit_resolution,[status(thm)],[27124, 1174, 27121, 27120])).
% 294.59/187.14 tff(27126,plain,((~m_c_h_element_v_in2(c_e_h_2, c_h, s6)) | m_or_h_gate_v_out(c_e_h_2, c_j, s6)), inference(lemma,lemma(discharge,[]))).
% 294.59/187.14 tff(27127,plain,
% 294.59/187.14 (~m_c_h_element_v_in2(c_e_h_2, c_h, s6)),
% 294.59/187.14 inference(unit_resolution,[status(thm)],[27126, 27119])).
% 294.59/187.14 tff(27128,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_h, s6)), introduced(assumption)).
% 294.59/187.14 tff(27129,assumption,(~m_c_h_element_v_out(c_e_h_2, c_h, s6)), introduced(assumption)).
% 294.59/187.14 tff(27130,assumption,(m_c_h_element_v_out(c_e_h_2, c_h, s7)), introduced(assumption)).
% 294.59/187.14 tff(27131,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_h, s6)), introduced(assumption)).
% 294.59/187.14 tff(27132,assumption,(node14(c_e_h_2, c_h, s6, s7)), introduced(assumption)).
% 294.59/187.14 tff(27133,plain,
% 294.59/187.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s7)) | m_c_h_element_v_in1(c_e_h_2, c_h, s6) | (~node14(c_e_h_2, c_h, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s7)) | m_c_h_element_v_in1(c_e_h_2, c_h, s6) | (~node14(c_e_h_2, c_h, s6, s7)))),
% 294.59/187.14 inference(rewrite,[status(thm)],[])).
% 294.59/187.14 tff(27134,plain,
% 294.59/187.14 (((~node14(c_e_h_2, c_h, s6, s7)) | m_c_h_element_v_in1(c_e_h_2, c_h, s6) | (~m_c_h_element_v_out(c_e_h_2, c_h, s7))) <=> ((~m_c_h_element_v_out(c_e_h_2, c_h, s7)) | m_c_h_element_v_in1(c_e_h_2, c_h, s6) | (~node14(c_e_h_2, c_h, s6, s7)))),
% 294.59/187.14 inference(rewrite,[status(thm)],[])).
% 294.59/187.14 tff(27135,plain,
% 294.59/187.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s6, s7)) | m_c_h_element_v_in1(c_e_h_2, c_h, s6) | (~m_c_h_element_v_out(c_e_h_2, c_h, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s7)) | m_c_h_element_v_in1(c_e_h_2, c_h, s6) | (~node14(c_e_h_2, c_h, s6, s7))))),
% 294.59/187.14 inference(monotonicity,[status(thm)],[27134])).
% 294.59/187.14 tff(27136,plain,
% 294.59/187.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s6, s7)) | m_c_h_element_v_in1(c_e_h_2, c_h, s6) | (~m_c_h_element_v_out(c_e_h_2, c_h, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s7)) | m_c_h_element_v_in1(c_e_h_2, c_h, s6) | (~node14(c_e_h_2, c_h, s6, s7)))),
% 294.59/187.14 inference(transitivity,[status(thm)],[27135, 27133])).
% 294.59/187.14 tff(27137,plain,
% 294.59/187.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s6, s7)) | m_c_h_element_v_in1(c_e_h_2, c_h, s6) | (~m_c_h_element_v_out(c_e_h_2, c_h, s7)))),
% 294.59/187.14 inference(quant_inst,[status(thm)],[])).
% 294.59/187.14 tff(27138,plain,
% 294.59/187.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s7)) | m_c_h_element_v_in1(c_e_h_2, c_h, s6) | (~node14(c_e_h_2, c_h, s6, s7))),
% 294.59/187.14 inference(modus_ponens,[status(thm)],[27137, 27136])).
% 294.59/187.14 tff(27139,plain,
% 294.59/187.14 ($false),
% 294.59/187.14 inference(unit_resolution,[status(thm)],[27138, 223, 27130, 27132, 27131])).
% 294.59/187.14 tff(27140,plain,((~node14(c_e_h_2, c_h, s6, s7)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s7)) | m_c_h_element_v_in1(c_e_h_2, c_h, s6)), inference(lemma,lemma(discharge,[]))).
% 294.59/187.14 tff(27141,plain,
% 294.59/187.14 (~node14(c_e_h_2, c_h, s6, s7)),
% 294.59/187.14 inference(unit_resolution,[status(thm)],[27140, 27131, 27130])).
% 294.59/187.14 tff(27142,assumption,(~node14(c_e_h_2, c_h, s6, s7)), introduced(assumption)).
% 294.59/187.14 tff(27143,assumption,(node15(c_e_h_2, c_h, s6, s7)), introduced(assumption)).
% 294.59/187.14 tff(27144,plain,
% 294.59/187.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s7)) | (~node15(c_e_h_2, c_h, s6, s7)) | m_c_h_element_v_out(c_e_h_2, c_h, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s7)) | (~node15(c_e_h_2, c_h, s6, s7)) | m_c_h_element_v_out(c_e_h_2, c_h, s6))),
% 294.59/187.14 inference(rewrite,[status(thm)],[])).
% 294.59/187.14 tff(27145,plain,
% 294.59/187.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s7)) | (~node15(c_e_h_2, c_h, s6, s7)) | m_c_h_element_v_out(c_e_h_2, c_h, s6))),
% 294.59/187.14 inference(quant_inst,[status(thm)],[])).
% 294.59/187.14 tff(27146,plain,
% 294.59/187.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s7)) | (~node15(c_e_h_2, c_h, s6, s7)) | m_c_h_element_v_out(c_e_h_2, c_h, s6)),
% 294.59/187.14 inference(modus_ponens,[status(thm)],[27145, 27144])).
% 294.59/187.14 tff(27147,plain,
% 294.59/187.14 ($false),
% 294.59/187.14 inference(unit_resolution,[status(thm)],[27146, 147, 27130, 27129, 27143])).
% 294.59/187.14 tff(27148,plain,((~node15(c_e_h_2, c_h, s6, s7)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s7)) | m_c_h_element_v_out(c_e_h_2, c_h, s6)), inference(lemma,lemma(discharge,[]))).
% 294.59/187.14 tff(27149,plain,
% 294.59/187.14 (~node15(c_e_h_2, c_h, s6, s7)),
% 294.59/187.14 inference(unit_resolution,[status(thm)],[27148, 27129, 27130])).
% 294.59/187.14 tff(27150,plain,
% 294.59/187.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s6, s7)) | node19(c_e_h_2, c_h, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s6, s7)) | node19(c_e_h_2, c_h, s6, s7))),
% 294.59/187.14 inference(rewrite,[status(thm)],[])).
% 294.59/187.14 tff(27151,plain,
% 294.59/187.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s6, s7)) | node19(c_e_h_2, c_h, s6, s7))),
% 294.59/187.14 inference(quant_inst,[status(thm)],[])).
% 294.59/187.14 tff(27152,plain,
% 294.59/187.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s6, s7)) | node19(c_e_h_2, c_h, s6, s7)),
% 294.59/187.14 inference(modus_ponens,[status(thm)],[27151, 27150])).
% 294.59/187.14 tff(27153,plain,
% 294.59/187.14 (node19(c_e_h_2, c_h, s6, s7)),
% 294.59/187.14 inference(unit_resolution,[status(thm)],[27152, 190, 1844])).
% 294.59/187.14 tff(27154,plain,
% 294.59/187.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s6) | node14(c_e_h_2, c_h, s6, s7) | (~node19(c_e_h_2, c_h, s6, s7)) | node15(c_e_h_2, c_h, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s6) | node14(c_e_h_2, c_h, s6, s7) | (~node19(c_e_h_2, c_h, s6, s7)) | node15(c_e_h_2, c_h, s6, s7))),
% 294.59/187.14 inference(rewrite,[status(thm)],[])).
% 294.59/187.14 tff(27155,plain,
% 294.59/187.14 ((node16(c_e_h_2, c_h, s6) | node14(c_e_h_2, c_h, s6, s7) | node15(c_e_h_2, c_h, s6, s7) | (~node19(c_e_h_2, c_h, s6, s7))) <=> (node16(c_e_h_2, c_h, s6) | node14(c_e_h_2, c_h, s6, s7) | (~node19(c_e_h_2, c_h, s6, s7)) | node15(c_e_h_2, c_h, s6, s7))),
% 294.59/187.14 inference(rewrite,[status(thm)],[])).
% 294.59/187.14 tff(27156,plain,
% 294.59/187.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s6) | node14(c_e_h_2, c_h, s6, s7) | node15(c_e_h_2, c_h, s6, s7) | (~node19(c_e_h_2, c_h, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s6) | node14(c_e_h_2, c_h, s6, s7) | (~node19(c_e_h_2, c_h, s6, s7)) | node15(c_e_h_2, c_h, s6, s7)))),
% 294.59/187.14 inference(monotonicity,[status(thm)],[27155])).
% 294.59/187.14 tff(27157,plain,
% 294.59/187.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s6) | node14(c_e_h_2, c_h, s6, s7) | node15(c_e_h_2, c_h, s6, s7) | (~node19(c_e_h_2, c_h, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s6) | node14(c_e_h_2, c_h, s6, s7) | (~node19(c_e_h_2, c_h, s6, s7)) | node15(c_e_h_2, c_h, s6, s7))),
% 294.59/187.14 inference(transitivity,[status(thm)],[27156, 27154])).
% 294.59/187.14 tff(27158,plain,
% 294.59/187.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s6) | node14(c_e_h_2, c_h, s6, s7) | node15(c_e_h_2, c_h, s6, s7) | (~node19(c_e_h_2, c_h, s6, s7)))),
% 294.59/187.14 inference(quant_inst,[status(thm)],[])).
% 294.59/187.14 tff(27159,plain,
% 294.59/187.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s6) | node14(c_e_h_2, c_h, s6, s7) | (~node19(c_e_h_2, c_h, s6, s7)) | node15(c_e_h_2, c_h, s6, s7)),
% 294.59/187.14 inference(modus_ponens,[status(thm)],[27158, 27157])).
% 294.59/187.14 tff(27160,plain,
% 294.59/187.14 (node16(c_e_h_2, c_h, s6) | node14(c_e_h_2, c_h, s6, s7) | node15(c_e_h_2, c_h, s6, s7)),
% 294.59/187.14 inference(unit_resolution,[status(thm)],[27159, 204, 27153])).
% 294.59/187.14 tff(27161,plain,
% 294.59/187.14 (node16(c_e_h_2, c_h, s6)),
% 294.59/187.14 inference(unit_resolution,[status(thm)],[27160, 27149, 27142])).
% 294.59/187.14 tff(27162,plain,
% 294.59/187.14 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_h, s6)) | m_c_h_element_v_in1(c_e_h_2, c_h, s6) | m_c_h_element_v_in2(c_e_h_2, c_h, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_h, s6)) | m_c_h_element_v_in1(c_e_h_2, c_h, s6) | m_c_h_element_v_in2(c_e_h_2, c_h, s6))),
% 294.59/187.14 inference(rewrite,[status(thm)],[])).
% 294.59/187.15 tff(27163,plain,
% 294.59/187.15 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_h, s6)) | m_c_h_element_v_in1(c_e_h_2, c_h, s6) | m_c_h_element_v_in2(c_e_h_2, c_h, s6))),
% 294.59/187.15 inference(quant_inst,[status(thm)],[])).
% 294.59/187.15 tff(27164,plain,
% 294.59/187.15 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_h, s6)) | m_c_h_element_v_in1(c_e_h_2, c_h, s6) | m_c_h_element_v_in2(c_e_h_2, c_h, s6)),
% 294.59/187.15 inference(modus_ponens,[status(thm)],[27163, 27162])).
% 294.59/187.15 tff(27165,plain,
% 294.59/187.15 ((~node16(c_e_h_2, c_h, s6)) | m_c_h_element_v_in2(c_e_h_2, c_h, s6)),
% 294.59/187.15 inference(unit_resolution,[status(thm)],[27164, 178, 27131])).
% 294.59/187.15 tff(27166,plain,
% 294.59/187.15 (m_c_h_element_v_in2(c_e_h_2, c_h, s6)),
% 294.59/187.15 inference(unit_resolution,[status(thm)],[27165, 27161])).
% 294.59/187.15 tff(27167,plain,
% 294.59/187.15 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_h, s6)) | m_c_h_element_v_in1(c_e_h_2, c_h, s6) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_h, s6)) | m_c_h_element_v_in1(c_e_h_2, c_h, s6) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s6)))),
% 294.59/187.15 inference(rewrite,[status(thm)],[])).
% 294.59/187.15 tff(27168,plain,
% 294.59/187.15 ((m_c_h_element_v_in1(c_e_h_2, c_h, s6) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s6)) | (~node17(c_e_h_2, c_h, s6))) <=> ((~node17(c_e_h_2, c_h, s6)) | m_c_h_element_v_in1(c_e_h_2, c_h, s6) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s6)))),
% 294.59/187.15 inference(rewrite,[status(thm)],[])).
% 294.59/187.15 tff(27169,plain,
% 294.59/187.15 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s6) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s6)) | (~node17(c_e_h_2, c_h, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_h, s6)) | m_c_h_element_v_in1(c_e_h_2, c_h, s6) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s6))))),
% 294.59/187.15 inference(monotonicity,[status(thm)],[27168])).
% 294.59/187.15 tff(27170,plain,
% 294.59/187.15 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s6) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s6)) | (~node17(c_e_h_2, c_h, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_h, s6)) | m_c_h_element_v_in1(c_e_h_2, c_h, s6) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s6)))),
% 294.59/187.15 inference(transitivity,[status(thm)],[27169, 27167])).
% 294.59/187.15 tff(27171,plain,
% 294.59/187.15 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s6) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s6)) | (~node17(c_e_h_2, c_h, s6)))),
% 294.59/187.15 inference(quant_inst,[status(thm)],[])).
% 294.59/187.15 tff(27172,plain,
% 294.59/187.15 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_h, s6)) | m_c_h_element_v_in1(c_e_h_2, c_h, s6) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s6))),
% 294.59/187.15 inference(modus_ponens,[status(thm)],[27171, 27170])).
% 294.59/187.15 tff(27173,plain,
% 294.59/187.15 ((~node17(c_e_h_2, c_h, s6)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s6))),
% 294.59/187.15 inference(unit_resolution,[status(thm)],[27172, 859, 27131])).
% 294.59/187.15 tff(27174,plain,
% 294.59/187.15 (~node17(c_e_h_2, c_h, s6)),
% 294.59/187.15 inference(unit_resolution,[status(thm)],[27173, 27166])).
% 294.59/187.15 tff(27175,plain,
% 294.59/187.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_2, c_h, s6, s7) | node17(c_e_h_2, c_h, s6) | (~node19(c_e_h_2, c_h, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_2, c_h, s6, s7) | node17(c_e_h_2, c_h, s6) | (~node19(c_e_h_2, c_h, s6, s7)))),
% 294.59/187.15 inference(rewrite,[status(thm)],[])).
% 294.59/187.15 tff(27176,plain,
% 294.59/187.15 ((node17(c_e_h_2, c_h, s6) | node18(c_e_h_2, c_h, s6, s7) | (~node19(c_e_h_2, c_h, s6, s7))) <=> (node18(c_e_h_2, c_h, s6, s7) | node17(c_e_h_2, c_h, s6) | (~node19(c_e_h_2, c_h, s6, s7)))),
% 294.59/187.15 inference(rewrite,[status(thm)],[])).
% 294.59/187.15 tff(27177,plain,
% 294.59/187.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s6) | node18(c_e_h_2, c_h, s6, s7) | (~node19(c_e_h_2, c_h, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_2, c_h, s6, s7) | node17(c_e_h_2, c_h, s6) | (~node19(c_e_h_2, c_h, s6, s7))))),
% 294.59/187.15 inference(monotonicity,[status(thm)],[27176])).
% 294.59/187.15 tff(27178,plain,
% 294.59/187.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s6) | node18(c_e_h_2, c_h, s6, s7) | (~node19(c_e_h_2, c_h, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_2, c_h, s6, s7) | node17(c_e_h_2, c_h, s6) | (~node19(c_e_h_2, c_h, s6, s7)))),
% 294.59/187.15 inference(transitivity,[status(thm)],[27177, 27175])).
% 294.59/187.15 tff(27179,plain,
% 294.59/187.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s6) | node18(c_e_h_2, c_h, s6, s7) | (~node19(c_e_h_2, c_h, s6, s7)))),
% 294.59/187.15 inference(quant_inst,[status(thm)],[])).
% 294.59/187.15 tff(27180,plain,
% 294.59/187.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_2, c_h, s6, s7) | node17(c_e_h_2, c_h, s6) | (~node19(c_e_h_2, c_h, s6, s7))),
% 294.59/187.15 inference(modus_ponens,[status(thm)],[27179, 27178])).
% 294.59/187.15 tff(27181,plain,
% 294.59/187.15 (node18(c_e_h_2, c_h, s6, s7) | node17(c_e_h_2, c_h, s6)),
% 294.59/187.15 inference(unit_resolution,[status(thm)],[27180, 776, 27153])).
% 294.59/187.15 tff(27182,plain,
% 294.59/187.15 (node18(c_e_h_2, c_h, s6, s7)),
% 294.59/187.15 inference(unit_resolution,[status(thm)],[27181, 27174])).
% 294.59/187.15 tff(27183,plain,
% 294.59/187.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_h, s6) | (~m_c_h_element_v_out(c_e_h_2, c_h, s7)) | (~node18(c_e_h_2, c_h, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s6) | (~m_c_h_element_v_out(c_e_h_2, c_h, s7)) | (~node18(c_e_h_2, c_h, s6, s7)))),
% 294.59/187.15 inference(rewrite,[status(thm)],[])).
% 294.59/187.15 tff(27184,plain,
% 294.59/187.15 (((~m_c_h_element_v_out(c_e_h_2, c_h, s7)) | m_c_h_element_v_out(c_e_h_2, c_h, s6) | (~node18(c_e_h_2, c_h, s6, s7))) <=> (m_c_h_element_v_out(c_e_h_2, c_h, s6) | (~m_c_h_element_v_out(c_e_h_2, c_h, s7)) | (~node18(c_e_h_2, c_h, s6, s7)))),
% 294.59/187.15 inference(rewrite,[status(thm)],[])).
% 294.59/187.15 tff(27185,plain,
% 294.59/187.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s7)) | m_c_h_element_v_out(c_e_h_2, c_h, s6) | (~node18(c_e_h_2, c_h, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_h, s6) | (~m_c_h_element_v_out(c_e_h_2, c_h, s7)) | (~node18(c_e_h_2, c_h, s6, s7))))),
% 294.59/187.15 inference(monotonicity,[status(thm)],[27184])).
% 294.59/187.15 tff(27186,plain,
% 294.59/187.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s7)) | m_c_h_element_v_out(c_e_h_2, c_h, s6) | (~node18(c_e_h_2, c_h, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s6) | (~m_c_h_element_v_out(c_e_h_2, c_h, s7)) | (~node18(c_e_h_2, c_h, s6, s7)))),
% 294.59/187.15 inference(transitivity,[status(thm)],[27185, 27183])).
% 294.59/187.15 tff(27187,plain,
% 294.59/187.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s7)) | m_c_h_element_v_out(c_e_h_2, c_h, s6) | (~node18(c_e_h_2, c_h, s6, s7)))),
% 294.59/187.15 inference(quant_inst,[status(thm)],[])).
% 294.59/187.15 tff(27188,plain,
% 294.59/187.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s6) | (~m_c_h_element_v_out(c_e_h_2, c_h, s7)) | (~node18(c_e_h_2, c_h, s6, s7))),
% 294.59/187.15 inference(modus_ponens,[status(thm)],[27187, 27186])).
% 294.59/187.15 tff(27189,plain,
% 294.59/187.15 ($false),
% 294.59/187.15 inference(unit_resolution,[status(thm)],[27188, 753, 27130, 27129, 27182])).
% 294.59/187.15 tff(27190,plain,(m_c_h_element_v_out(c_e_h_2, c_h, s6) | (~m_c_h_element_v_out(c_e_h_2, c_h, s7)) | m_c_h_element_v_in1(c_e_h_2, c_h, s6) | node14(c_e_h_2, c_h, s6, s7)), inference(lemma,lemma(discharge,[]))).
% 294.59/187.15 tff(27191,plain,
% 294.59/187.15 ($false),
% 294.59/187.15 inference(unit_resolution,[status(thm)],[27190, 27141, 27131, 27130, 27129])).
% 294.59/187.15 tff(27192,plain,(m_c_h_element_v_in1(c_e_h_2, c_h, s6) | (~m_c_h_element_v_out(c_e_h_2, c_h, s7)) | m_c_h_element_v_out(c_e_h_2, c_h, s6)), inference(lemma,lemma(discharge,[]))).
% 294.59/187.15 tff(27193,plain,
% 294.59/187.15 (m_c_h_element_v_in1(c_e_h_2, c_h, s6)),
% 294.59/187.15 inference(unit_resolution,[status(thm)],[27192, 27130, 27129])).
% 294.59/187.15 tff(27194,plain,
% 294.59/187.15 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_h, s6)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s6)) | m_c_h_element_v_in2(c_e_h_2, c_h, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_h, s6)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s6)) | m_c_h_element_v_in2(c_e_h_2, c_h, s6))),
% 294.59/187.15 inference(rewrite,[status(thm)],[])).
% 294.59/187.15 tff(27195,plain,
% 294.59/187.15 (((~m_c_h_element_v_in1(c_e_h_2, c_h, s6)) | m_c_h_element_v_in2(c_e_h_2, c_h, s6) | (~node17(c_e_h_2, c_h, s6))) <=> ((~node17(c_e_h_2, c_h, s6)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s6)) | m_c_h_element_v_in2(c_e_h_2, c_h, s6))),
% 294.59/187.15 inference(rewrite,[status(thm)],[])).
% 294.59/187.15 tff(27196,plain,
% 294.59/187.15 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s6)) | m_c_h_element_v_in2(c_e_h_2, c_h, s6) | (~node17(c_e_h_2, c_h, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_h, s6)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s6)) | m_c_h_element_v_in2(c_e_h_2, c_h, s6)))),
% 294.59/187.15 inference(monotonicity,[status(thm)],[27195])).
% 294.59/187.15 tff(27197,plain,
% 294.59/187.15 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s6)) | m_c_h_element_v_in2(c_e_h_2, c_h, s6) | (~node17(c_e_h_2, c_h, s6)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_h, s6)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s6)) | m_c_h_element_v_in2(c_e_h_2, c_h, s6))),
% 294.59/187.15 inference(transitivity,[status(thm)],[27196, 27194])).
% 294.59/187.15 tff(27198,plain,
% 294.59/187.15 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s6)) | m_c_h_element_v_in2(c_e_h_2, c_h, s6) | (~node17(c_e_h_2, c_h, s6)))),
% 294.59/187.15 inference(quant_inst,[status(thm)],[])).
% 294.59/187.15 tff(27199,plain,
% 294.59/187.15 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_h, s6)) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s6)) | m_c_h_element_v_in2(c_e_h_2, c_h, s6)),
% 294.59/187.15 inference(modus_ponens,[status(thm)],[27198, 27197])).
% 294.59/187.16 tff(27200,plain,
% 294.59/187.16 (~node17(c_e_h_2, c_h, s6)),
% 294.59/187.16 inference(unit_resolution,[status(thm)],[27199, 919, 27193, 27128])).
% 294.59/187.16 tff(27201,plain,
% 294.59/187.16 (node18(c_e_h_2, c_h, s6, s7)),
% 294.59/187.16 inference(unit_resolution,[status(thm)],[27181, 27200])).
% 294.59/187.16 tff(27202,plain,
% 294.59/187.16 ($false),
% 294.59/187.16 inference(unit_resolution,[status(thm)],[27188, 753, 27130, 27129, 27201])).
% 294.59/187.16 tff(27203,plain,((~m_c_h_element_v_out(c_e_h_2, c_h, s7)) | m_c_h_element_v_out(c_e_h_2, c_h, s6) | m_c_h_element_v_in2(c_e_h_2, c_h, s6)), inference(lemma,lemma(discharge,[]))).
% 294.59/187.16 tff(27204,plain,
% 294.59/187.16 ((~m_c_h_element_v_out(c_e_h_2, c_h, s7)) | m_c_h_element_v_out(c_e_h_2, c_h, s6)),
% 294.59/187.16 inference(unit_resolution,[status(thm)],[27203, 27127])).
% 294.59/187.16 tff(27205,plain,
% 294.59/187.16 (~m_c_h_element_v_out(c_e_h_2, c_h, s7)),
% 294.59/187.16 inference(unit_resolution,[status(thm)],[27204, 8700])).
% 294.59/187.16 tff(27206,assumption,(~m_c_h_element_v_out(c_e_h_2, c_h, s7)), introduced(assumption)).
% 294.59/187.16 tff(27207,assumption,(m_c_h_element_v_out(c_e_h_2, c_h, s8)), introduced(assumption)).
% 294.59/187.16 tff(27208,assumption,(node18(c_e_h_2, c_h, s7, s8)), introduced(assumption)).
% 294.59/187.16 tff(27209,plain,
% 294.59/187.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_h, s7) | (~m_c_h_element_v_out(c_e_h_2, c_h, s8)) | (~node18(c_e_h_2, c_h, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s7) | (~m_c_h_element_v_out(c_e_h_2, c_h, s8)) | (~node18(c_e_h_2, c_h, s7, s8)))),
% 294.59/187.16 inference(rewrite,[status(thm)],[])).
% 294.59/187.16 tff(27210,plain,
% 294.59/187.16 (((~m_c_h_element_v_out(c_e_h_2, c_h, s8)) | m_c_h_element_v_out(c_e_h_2, c_h, s7) | (~node18(c_e_h_2, c_h, s7, s8))) <=> (m_c_h_element_v_out(c_e_h_2, c_h, s7) | (~m_c_h_element_v_out(c_e_h_2, c_h, s8)) | (~node18(c_e_h_2, c_h, s7, s8)))),
% 294.59/187.16 inference(rewrite,[status(thm)],[])).
% 294.59/187.16 tff(27211,plain,
% 294.59/187.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s8)) | m_c_h_element_v_out(c_e_h_2, c_h, s7) | (~node18(c_e_h_2, c_h, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_h, s7) | (~m_c_h_element_v_out(c_e_h_2, c_h, s8)) | (~node18(c_e_h_2, c_h, s7, s8))))),
% 294.59/187.16 inference(monotonicity,[status(thm)],[27210])).
% 294.59/187.16 tff(27212,plain,
% 294.59/187.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s8)) | m_c_h_element_v_out(c_e_h_2, c_h, s7) | (~node18(c_e_h_2, c_h, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s7) | (~m_c_h_element_v_out(c_e_h_2, c_h, s8)) | (~node18(c_e_h_2, c_h, s7, s8)))),
% 294.59/187.16 inference(transitivity,[status(thm)],[27211, 27209])).
% 294.59/187.16 tff(27213,plain,
% 294.59/187.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s8)) | m_c_h_element_v_out(c_e_h_2, c_h, s7) | (~node18(c_e_h_2, c_h, s7, s8)))),
% 294.59/187.16 inference(quant_inst,[status(thm)],[])).
% 294.59/187.16 tff(27214,plain,
% 294.59/187.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s7) | (~m_c_h_element_v_out(c_e_h_2, c_h, s8)) | (~node18(c_e_h_2, c_h, s7, s8))),
% 294.59/187.16 inference(modus_ponens,[status(thm)],[27213, 27212])).
% 294.59/187.16 tff(27215,plain,
% 294.59/187.16 ($false),
% 294.59/187.16 inference(unit_resolution,[status(thm)],[27214, 753, 27206, 27207, 27208])).
% 294.59/187.16 tff(27216,plain,((~node18(c_e_h_2, c_h, s7, s8)) | m_c_h_element_v_out(c_e_h_2, c_h, s7) | (~m_c_h_element_v_out(c_e_h_2, c_h, s8))), inference(lemma,lemma(discharge,[]))).
% 294.59/187.16 tff(27217,plain,
% 294.59/187.16 (~node18(c_e_h_2, c_h, s7, s8)),
% 294.59/187.16 inference(unit_resolution,[status(thm)],[27216, 27207, 27206])).
% 294.59/187.16 tff(27218,plain,
% 294.59/187.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s7, s8)) | node19(c_e_h_2, c_h, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s7, s8)) | node19(c_e_h_2, c_h, s7, s8))),
% 294.59/187.16 inference(rewrite,[status(thm)],[])).
% 294.59/187.16 tff(27219,plain,
% 294.59/187.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s7, s8)) | node19(c_e_h_2, c_h, s7, s8))),
% 294.59/187.16 inference(quant_inst,[status(thm)],[])).
% 294.59/187.16 tff(27220,plain,
% 294.59/187.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s7, s8)) | node19(c_e_h_2, c_h, s7, s8)),
% 294.59/187.16 inference(modus_ponens,[status(thm)],[27219, 27218])).
% 294.59/187.16 tff(27221,plain,
% 294.59/187.16 (node19(c_e_h_2, c_h, s7, s8)),
% 294.59/187.16 inference(unit_resolution,[status(thm)],[27220, 190, 1938])).
% 294.59/187.16 tff(27222,plain,
% 294.59/187.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s7) | (~node19(c_e_h_2, c_h, s7, s8)) | node18(c_e_h_2, c_h, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_h, s7) | (~node19(c_e_h_2, c_h, s7, s8)) | node18(c_e_h_2, c_h, s7, s8))),
% 294.59/187.16 inference(rewrite,[status(thm)],[])).
% 294.59/187.16 tff(27223,plain,
% 294.59/187.16 ((node17(c_e_h_2, c_h, s7) | node18(c_e_h_2, c_h, s7, s8) | (~node19(c_e_h_2, c_h, s7, s8))) <=> (node17(c_e_h_2, c_h, s7) | (~node19(c_e_h_2, c_h, s7, s8)) | node18(c_e_h_2, c_h, s7, s8))),
% 294.59/187.16 inference(rewrite,[status(thm)],[])).
% 294.59/187.16 tff(27224,plain,
% 294.59/187.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s7) | node18(c_e_h_2, c_h, s7, s8) | (~node19(c_e_h_2, c_h, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s7) | (~node19(c_e_h_2, c_h, s7, s8)) | node18(c_e_h_2, c_h, s7, s8)))),
% 294.59/187.16 inference(monotonicity,[status(thm)],[27223])).
% 294.59/187.16 tff(27225,plain,
% 294.59/187.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s7) | node18(c_e_h_2, c_h, s7, s8) | (~node19(c_e_h_2, c_h, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_h, s7) | (~node19(c_e_h_2, c_h, s7, s8)) | node18(c_e_h_2, c_h, s7, s8))),
% 294.59/187.16 inference(transitivity,[status(thm)],[27224, 27222])).
% 294.59/187.16 tff(27226,plain,
% 294.59/187.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s7) | node18(c_e_h_2, c_h, s7, s8) | (~node19(c_e_h_2, c_h, s7, s8)))),
% 294.59/187.16 inference(quant_inst,[status(thm)],[])).
% 294.59/187.16 tff(27227,plain,
% 294.59/187.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_h, s7) | (~node19(c_e_h_2, c_h, s7, s8)) | node18(c_e_h_2, c_h, s7, s8)),
% 294.59/187.16 inference(modus_ponens,[status(thm)],[27226, 27225])).
% 294.59/187.16 tff(27228,plain,
% 294.59/187.16 (node17(c_e_h_2, c_h, s7) | node18(c_e_h_2, c_h, s7, s8)),
% 294.59/187.16 inference(unit_resolution,[status(thm)],[27227, 776, 27221])).
% 294.59/187.16 tff(27229,plain,
% 294.59/187.16 (node17(c_e_h_2, c_h, s7)),
% 294.59/187.16 inference(unit_resolution,[status(thm)],[27228, 27217])).
% 294.59/187.16 tff(27230,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_h, s7)), introduced(assumption)).
% 294.59/187.16 tff(27231,plain,
% 294.59/187.16 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s7) | (~node17(c_e_h_2, c_h, s7)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s7) | (~node17(c_e_h_2, c_h, s7)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s7)))),
% 294.59/187.16 inference(rewrite,[status(thm)],[])).
% 294.59/187.17 tff(27232,plain,
% 294.59/187.17 ((m_c_h_element_v_in1(c_e_h_2, c_h, s7) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s7)) | (~node17(c_e_h_2, c_h, s7))) <=> (m_c_h_element_v_in1(c_e_h_2, c_h, s7) | (~node17(c_e_h_2, c_h, s7)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s7)))),
% 294.59/187.17 inference(rewrite,[status(thm)],[])).
% 294.59/187.17 tff(27233,plain,
% 294.59/187.17 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s7) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s7)) | (~node17(c_e_h_2, c_h, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s7) | (~node17(c_e_h_2, c_h, s7)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s7))))),
% 294.59/187.17 inference(monotonicity,[status(thm)],[27232])).
% 294.59/187.17 tff(27234,plain,
% 294.59/187.17 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s7) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s7)) | (~node17(c_e_h_2, c_h, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s7) | (~node17(c_e_h_2, c_h, s7)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s7)))),
% 294.59/187.17 inference(transitivity,[status(thm)],[27233, 27231])).
% 294.59/187.17 tff(27235,plain,
% 294.59/187.17 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s7) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s7)) | (~node17(c_e_h_2, c_h, s7)))),
% 294.59/187.17 inference(quant_inst,[status(thm)],[])).
% 294.59/187.17 tff(27236,plain,
% 294.59/187.17 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s7) | (~node17(c_e_h_2, c_h, s7)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s7))),
% 294.59/187.17 inference(modus_ponens,[status(thm)],[27235, 27234])).
% 294.59/187.17 tff(27237,plain,
% 294.59/187.17 ((~node17(c_e_h_2, c_h, s7)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s7))),
% 294.59/187.17 inference(unit_resolution,[status(thm)],[27236, 859, 27230])).
% 294.59/187.17 tff(27238,plain,
% 294.59/187.17 (~m_c_h_element_v_in2(c_e_h_2, c_h, s7)),
% 294.59/187.17 inference(unit_resolution,[status(thm)],[27237, 27229])).
% 294.59/187.17 tff(27239,plain,
% 294.59/187.17 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_h, s7)) | m_c_h_element_v_in1(c_e_h_2, c_h, s7) | m_c_h_element_v_in2(c_e_h_2, c_h, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_h, s7)) | m_c_h_element_v_in1(c_e_h_2, c_h, s7) | m_c_h_element_v_in2(c_e_h_2, c_h, s7))),
% 294.59/187.17 inference(rewrite,[status(thm)],[])).
% 294.59/187.17 tff(27240,plain,
% 294.59/187.17 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_h, s7)) | m_c_h_element_v_in1(c_e_h_2, c_h, s7) | m_c_h_element_v_in2(c_e_h_2, c_h, s7))),
% 294.59/187.17 inference(quant_inst,[status(thm)],[])).
% 294.59/187.17 tff(27241,plain,
% 294.59/187.17 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_h, s7)) | m_c_h_element_v_in1(c_e_h_2, c_h, s7) | m_c_h_element_v_in2(c_e_h_2, c_h, s7)),
% 294.59/187.17 inference(modus_ponens,[status(thm)],[27240, 27239])).
% 294.59/187.17 tff(27242,plain,
% 294.59/187.17 ((~node16(c_e_h_2, c_h, s7)) | m_c_h_element_v_in2(c_e_h_2, c_h, s7)),
% 294.59/187.17 inference(unit_resolution,[status(thm)],[27241, 178, 27230])).
% 294.59/187.17 tff(27243,plain,
% 294.59/187.17 (~node16(c_e_h_2, c_h, s7)),
% 294.59/187.17 inference(unit_resolution,[status(thm)],[27242, 27238])).
% 294.59/187.17 tff(27244,assumption,(node14(c_e_h_2, c_h, s7, s8)), introduced(assumption)).
% 294.59/187.17 tff(27245,plain,
% 294.59/187.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s7) | (~m_c_h_element_v_out(c_e_h_2, c_h, s8)) | (~node14(c_e_h_2, c_h, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s7) | (~m_c_h_element_v_out(c_e_h_2, c_h, s8)) | (~node14(c_e_h_2, c_h, s7, s8)))),
% 294.68/187.17 inference(rewrite,[status(thm)],[])).
% 294.68/187.17 tff(27246,plain,
% 294.68/187.17 (((~node14(c_e_h_2, c_h, s7, s8)) | m_c_h_element_v_in1(c_e_h_2, c_h, s7) | (~m_c_h_element_v_out(c_e_h_2, c_h, s8))) <=> (m_c_h_element_v_in1(c_e_h_2, c_h, s7) | (~m_c_h_element_v_out(c_e_h_2, c_h, s8)) | (~node14(c_e_h_2, c_h, s7, s8)))),
% 294.68/187.17 inference(rewrite,[status(thm)],[])).
% 294.68/187.17 tff(27247,plain,
% 294.68/187.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s7, s8)) | m_c_h_element_v_in1(c_e_h_2, c_h, s7) | (~m_c_h_element_v_out(c_e_h_2, c_h, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s7) | (~m_c_h_element_v_out(c_e_h_2, c_h, s8)) | (~node14(c_e_h_2, c_h, s7, s8))))),
% 294.68/187.17 inference(monotonicity,[status(thm)],[27246])).
% 294.68/187.17 tff(27248,plain,
% 294.68/187.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s7, s8)) | m_c_h_element_v_in1(c_e_h_2, c_h, s7) | (~m_c_h_element_v_out(c_e_h_2, c_h, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s7) | (~m_c_h_element_v_out(c_e_h_2, c_h, s8)) | (~node14(c_e_h_2, c_h, s7, s8)))),
% 294.68/187.17 inference(transitivity,[status(thm)],[27247, 27245])).
% 294.68/187.17 tff(27249,plain,
% 294.68/187.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s7, s8)) | m_c_h_element_v_in1(c_e_h_2, c_h, s7) | (~m_c_h_element_v_out(c_e_h_2, c_h, s8)))),
% 294.68/187.17 inference(quant_inst,[status(thm)],[])).
% 294.68/187.17 tff(27250,plain,
% 294.68/187.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s7) | (~m_c_h_element_v_out(c_e_h_2, c_h, s8)) | (~node14(c_e_h_2, c_h, s7, s8))),
% 294.68/187.17 inference(modus_ponens,[status(thm)],[27249, 27248])).
% 294.68/187.17 tff(27251,plain,
% 294.68/187.17 ($false),
% 294.68/187.17 inference(unit_resolution,[status(thm)],[27250, 223, 27207, 27244, 27230])).
% 294.68/187.17 tff(27252,plain,((~node14(c_e_h_2, c_h, s7, s8)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s8)) | m_c_h_element_v_in1(c_e_h_2, c_h, s7)), inference(lemma,lemma(discharge,[]))).
% 294.68/187.17 tff(27253,plain,
% 294.68/187.17 (~node14(c_e_h_2, c_h, s7, s8)),
% 294.68/187.17 inference(unit_resolution,[status(thm)],[27252, 27207, 27230])).
% 294.68/187.17 tff(27254,plain,
% 294.68/187.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s7) | (~node19(c_e_h_2, c_h, s7, s8)) | node15(c_e_h_2, c_h, s7, s8) | node14(c_e_h_2, c_h, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s7) | (~node19(c_e_h_2, c_h, s7, s8)) | node15(c_e_h_2, c_h, s7, s8) | node14(c_e_h_2, c_h, s7, s8))),
% 294.68/187.17 inference(rewrite,[status(thm)],[])).
% 294.68/187.17 tff(27255,plain,
% 294.68/187.17 ((node16(c_e_h_2, c_h, s7) | node14(c_e_h_2, c_h, s7, s8) | node15(c_e_h_2, c_h, s7, s8) | (~node19(c_e_h_2, c_h, s7, s8))) <=> (node16(c_e_h_2, c_h, s7) | (~node19(c_e_h_2, c_h, s7, s8)) | node15(c_e_h_2, c_h, s7, s8) | node14(c_e_h_2, c_h, s7, s8))),
% 294.68/187.17 inference(rewrite,[status(thm)],[])).
% 294.68/187.17 tff(27256,plain,
% 294.68/187.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s7) | node14(c_e_h_2, c_h, s7, s8) | node15(c_e_h_2, c_h, s7, s8) | (~node19(c_e_h_2, c_h, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s7) | (~node19(c_e_h_2, c_h, s7, s8)) | node15(c_e_h_2, c_h, s7, s8) | node14(c_e_h_2, c_h, s7, s8)))),
% 294.68/187.17 inference(monotonicity,[status(thm)],[27255])).
% 294.68/187.17 tff(27257,plain,
% 294.68/187.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s7) | node14(c_e_h_2, c_h, s7, s8) | node15(c_e_h_2, c_h, s7, s8) | (~node19(c_e_h_2, c_h, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s7) | (~node19(c_e_h_2, c_h, s7, s8)) | node15(c_e_h_2, c_h, s7, s8) | node14(c_e_h_2, c_h, s7, s8))),
% 294.68/187.17 inference(transitivity,[status(thm)],[27256, 27254])).
% 294.68/187.17 tff(27258,plain,
% 294.68/187.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s7) | node14(c_e_h_2, c_h, s7, s8) | node15(c_e_h_2, c_h, s7, s8) | (~node19(c_e_h_2, c_h, s7, s8)))),
% 294.68/187.17 inference(quant_inst,[status(thm)],[])).
% 294.68/187.17 tff(27259,plain,
% 294.68/187.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s7) | (~node19(c_e_h_2, c_h, s7, s8)) | node15(c_e_h_2, c_h, s7, s8) | node14(c_e_h_2, c_h, s7, s8)),
% 294.68/187.17 inference(modus_ponens,[status(thm)],[27258, 27257])).
% 294.68/187.17 tff(27260,plain,
% 294.68/187.17 (node16(c_e_h_2, c_h, s7) | node15(c_e_h_2, c_h, s7, s8) | node14(c_e_h_2, c_h, s7, s8)),
% 294.68/187.17 inference(unit_resolution,[status(thm)],[27259, 204, 27221])).
% 294.68/187.17 tff(27261,plain,
% 294.68/187.17 (node15(c_e_h_2, c_h, s7, s8)),
% 294.68/187.17 inference(unit_resolution,[status(thm)],[27260, 27253, 27243])).
% 294.68/187.17 tff(27262,plain,
% 294.68/187.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s8)) | (~node15(c_e_h_2, c_h, s7, s8)) | m_c_h_element_v_out(c_e_h_2, c_h, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s8)) | (~node15(c_e_h_2, c_h, s7, s8)) | m_c_h_element_v_out(c_e_h_2, c_h, s7))),
% 294.68/187.17 inference(rewrite,[status(thm)],[])).
% 294.68/187.17 tff(27263,plain,
% 294.68/187.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s8)) | (~node15(c_e_h_2, c_h, s7, s8)) | m_c_h_element_v_out(c_e_h_2, c_h, s7))),
% 294.68/187.17 inference(quant_inst,[status(thm)],[])).
% 294.68/187.17 tff(27264,plain,
% 294.68/187.17 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s8)) | (~node15(c_e_h_2, c_h, s7, s8)) | m_c_h_element_v_out(c_e_h_2, c_h, s7)),
% 294.68/187.17 inference(modus_ponens,[status(thm)],[27263, 27262])).
% 294.68/187.17 tff(27265,plain,
% 294.68/187.17 ($false),
% 294.68/187.17 inference(unit_resolution,[status(thm)],[27264, 147, 27206, 27207, 27261])).
% 294.68/187.17 tff(27266,plain,((~m_c_h_element_v_out(c_e_h_2, c_h, s8)) | m_c_h_element_v_out(c_e_h_2, c_h, s7) | m_c_h_element_v_in1(c_e_h_2, c_h, s7)), inference(lemma,lemma(discharge,[]))).
% 294.68/187.17 tff(27267,plain,
% 294.68/187.17 (m_c_h_element_v_in1(c_e_h_2, c_h, s7)),
% 294.68/187.17 inference(unit_resolution,[status(thm)],[27266, 27207, 27206])).
% 294.68/187.17 tff(27268,assumption,(m_or_h_gate_v_out(c_e_h_2, c_j, s7)), introduced(assumption)).
% 294.68/187.17 tff(27269,assumption,(node6(c_e_h_2, c_j, s6, s7)), introduced(assumption)).
% 294.68/187.17 tff(27270,plain,
% 294.68/187.17 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_2, c_j, s7)) | m_or_h_gate_v_out(c_e_h_2, c_j, s6) | (~node6(c_e_h_2, c_j, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s7)) | m_or_h_gate_v_out(c_e_h_2, c_j, s6) | (~node6(c_e_h_2, c_j, s6, s7)))),
% 294.68/187.18 inference(rewrite,[status(thm)],[])).
% 294.68/187.18 tff(27271,plain,
% 294.68/187.18 (((~node6(c_e_h_2, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s7)) | m_or_h_gate_v_out(c_e_h_2, c_j, s6)) <=> ((~m_or_h_gate_v_out(c_e_h_2, c_j, s7)) | m_or_h_gate_v_out(c_e_h_2, c_j, s6) | (~node6(c_e_h_2, c_j, s6, s7)))),
% 294.68/187.18 inference(rewrite,[status(thm)],[])).
% 294.68/187.18 tff(27272,plain,
% 294.68/187.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s7)) | m_or_h_gate_v_out(c_e_h_2, c_j, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_2, c_j, s7)) | m_or_h_gate_v_out(c_e_h_2, c_j, s6) | (~node6(c_e_h_2, c_j, s6, s7))))),
% 294.68/187.18 inference(monotonicity,[status(thm)],[27271])).
% 294.68/187.18 tff(27273,plain,
% 294.68/187.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s7)) | m_or_h_gate_v_out(c_e_h_2, c_j, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s7)) | m_or_h_gate_v_out(c_e_h_2, c_j, s6) | (~node6(c_e_h_2, c_j, s6, s7)))),
% 294.68/187.18 inference(transitivity,[status(thm)],[27272, 27270])).
% 294.68/187.18 tff(27274,plain,
% 294.68/187.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s7)) | m_or_h_gate_v_out(c_e_h_2, c_j, s6))),
% 294.68/187.18 inference(quant_inst,[status(thm)],[])).
% 294.68/187.18 tff(27275,plain,
% 294.68/187.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s7)) | m_or_h_gate_v_out(c_e_h_2, c_j, s6) | (~node6(c_e_h_2, c_j, s6, s7))),
% 294.68/187.18 inference(modus_ponens,[status(thm)],[27274, 27273])).
% 294.68/187.18 tff(27276,plain,
% 294.68/187.18 ($false),
% 294.68/187.18 inference(unit_resolution,[status(thm)],[27275, 1121, 27268, 27121, 27269])).
% 294.68/187.18 tff(27277,plain,((~node6(c_e_h_2, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s7)) | m_or_h_gate_v_out(c_e_h_2, c_j, s6)), inference(lemma,lemma(discharge,[]))).
% 294.68/187.18 tff(27278,plain,
% 294.68/187.18 ((~node6(c_e_h_2, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s7))),
% 294.68/187.18 inference(unit_resolution,[status(thm)],[27277, 27119])).
% 294.68/187.18 tff(27279,plain,
% 294.68/187.18 (~node6(c_e_h_2, c_j, s6, s7)),
% 294.68/187.18 inference(unit_resolution,[status(thm)],[27278, 27268])).
% 294.68/187.18 tff(27280,plain,
% 294.68/187.18 ((~m_and_h_gate_v_out(c_e_h_2, c_l, s5)) | m_and_h_gate_v_out(c_e_h_2, c_l, s4)),
% 294.68/187.18 inference(unit_resolution,[status(thm)],[27086, 27053])).
% 294.68/187.18 tff(27281,plain,
% 294.68/187.18 (~m_and_h_gate_v_out(c_e_h_2, c_l, s5)),
% 294.68/187.18 inference(unit_resolution,[status(thm)],[27280, 8388])).
% 294.68/187.18 tff(27282,assumption,(m_and_h_gate_v_out(c_e_h_2, c_l, s6)), introduced(assumption)).
% 294.68/187.18 tff(27283,plain,
% 294.68/187.18 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s2)) | m_and_h_gate_v_out(c_e_h_2, c_i, s2))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s2)) | m_and_h_gate_v_out(c_e_h_2, c_i, s2))),
% 294.68/187.18 inference(rewrite,[status(thm)],[])).
% 294.68/187.18 tff(27284,plain,
% 294.68/187.18 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s2)) | m_and_h_gate_v_out(c_e_h_2, c_i, s2))),
% 294.68/187.18 inference(quant_inst,[status(thm)],[])).
% 294.68/187.18 tff(27285,plain,
% 294.68/187.18 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s2)) | m_and_h_gate_v_out(c_e_h_2, c_i, s2)),
% 294.68/187.18 inference(modus_ponens,[status(thm)],[27284, 27283])).
% 294.68/187.18 tff(27286,plain,
% 294.68/187.18 (~m_c_h_element_v_in2(c_e_h_2, c_e, s2)),
% 294.68/187.18 inference(unit_resolution,[status(thm)],[27285, 164, 3902])).
% 294.68/187.18 tff(27287,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4)), introduced(assumption)).
% 294.68/187.18 tff(27288,assumption,(~m_c_h_element_v_out(c_e_h_2, c_e, s2)), introduced(assumption)).
% 294.68/187.18 tff(27289,assumption,(node18(c_e_h_2, c_e, s2, s3)), introduced(assumption)).
% 294.68/187.18 tff(27290,plain,
% 294.68/187.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s3)) | m_c_h_element_v_out(c_e_h_2, c_e, s2) | (~node18(c_e_h_2, c_e, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s3)) | m_c_h_element_v_out(c_e_h_2, c_e, s2) | (~node18(c_e_h_2, c_e, s2, s3)))),
% 294.68/187.18 inference(rewrite,[status(thm)],[])).
% 294.68/187.18 tff(27291,plain,
% 294.68/187.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s3)) | m_c_h_element_v_out(c_e_h_2, c_e, s2) | (~node18(c_e_h_2, c_e, s2, s3)))),
% 294.68/187.18 inference(quant_inst,[status(thm)],[])).
% 294.68/187.18 tff(27292,plain,
% 294.68/187.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s3)) | m_c_h_element_v_out(c_e_h_2, c_e, s2) | (~node18(c_e_h_2, c_e, s2, s3))),
% 294.68/187.18 inference(modus_ponens,[status(thm)],[27291, 27290])).
% 294.68/187.18 tff(27293,plain,
% 294.68/187.18 ((~m_c_h_element_v_out(c_e_h_2, c_e, s3)) | m_c_h_element_v_out(c_e_h_2, c_e, s2)),
% 294.68/187.18 inference(unit_resolution,[status(thm)],[27292, 753, 27289])).
% 294.68/187.18 tff(27294,plain,
% 294.68/187.18 (~m_c_h_element_v_out(c_e_h_2, c_e, s3)),
% 294.68/187.18 inference(unit_resolution,[status(thm)],[27293, 27288])).
% 294.68/187.18 tff(27295,plain,
% 294.68/187.18 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3) | m_c_h_element_v_out(c_e_h_2, c_e, s3))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3) | m_c_h_element_v_out(c_e_h_2, c_e, s3))),
% 294.68/187.18 inference(rewrite,[status(thm)],[])).
% 294.68/187.18 tff(27296,plain,
% 294.68/187.18 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3) | m_c_h_element_v_out(c_e_h_2, c_e, s3))),
% 294.68/187.18 inference(quant_inst,[status(thm)],[])).
% 294.68/187.18 tff(27297,plain,
% 294.68/187.18 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3) | m_c_h_element_v_out(c_e_h_2, c_e, s3)),
% 294.68/187.18 inference(modus_ponens,[status(thm)],[27296, 27295])).
% 294.68/187.18 tff(27298,plain,
% 294.68/187.18 (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3)),
% 294.68/187.18 inference(unit_resolution,[status(thm)],[27297, 7856, 27294])).
% 294.68/187.18 tff(27299,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3)), introduced(assumption)).
% 294.68/187.18 tff(27300,plain,
% 294.68/187.18 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s3) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s3) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3))),
% 294.68/187.18 inference(rewrite,[status(thm)],[])).
% 294.68/187.18 tff(27301,plain,
% 294.68/187.18 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s3) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3))),
% 294.68/187.18 inference(quant_inst,[status(thm)],[])).
% 294.68/187.18 tff(27302,plain,
% 294.68/187.18 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s3) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s3)),
% 294.68/187.18 inference(modus_ponens,[status(thm)],[27301, 27300])).
% 294.68/187.18 tff(27303,plain,
% 294.68/187.18 (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s3)),
% 294.68/187.18 inference(unit_resolution,[status(thm)],[27302, 7868, 8360])).
% 294.69/187.18 tff(27304,assumption,(node10(c_e_h_2, c_n, s3, s4)), introduced(assumption)).
% 294.69/187.18 tff(27305,plain,
% 294.69/187.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3)) | (~node10(c_e_h_2, c_n, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3)) | (~node10(c_e_h_2, c_n, s3, s4)))),
% 294.69/187.18 inference(rewrite,[status(thm)],[])).
% 294.69/187.18 tff(27306,plain,
% 294.69/187.18 (((~node10(c_e_h_2, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4)) <=> (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3)) | (~node10(c_e_h_2, c_n, s3, s4)))),
% 294.69/187.18 inference(rewrite,[status(thm)],[])).
% 294.69/187.18 tff(27307,plain,
% 294.69/187.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3)) | (~node10(c_e_h_2, c_n, s3, s4))))),
% 294.69/187.18 inference(monotonicity,[status(thm)],[27306])).
% 294.69/187.18 tff(27308,plain,
% 294.69/187.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3)) | (~node10(c_e_h_2, c_n, s3, s4)))),
% 294.69/187.18 inference(transitivity,[status(thm)],[27307, 27305])).
% 294.69/187.18 tff(27309,plain,
% 294.69/187.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4))),
% 294.69/187.18 inference(quant_inst,[status(thm)],[])).
% 294.69/187.18 tff(27310,plain,
% 294.69/187.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s3)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3)) | (~node10(c_e_h_2, c_n, s3, s4))),
% 294.69/187.18 inference(modus_ponens,[status(thm)],[27309, 27308])).
% 294.69/187.18 tff(27311,plain,
% 294.69/187.18 ($false),
% 294.69/187.18 inference(unit_resolution,[status(thm)],[27310, 5718, 27287, 27304, 27303, 27299])).
% 294.69/187.18 tff(27312,plain,((~node10(c_e_h_2, c_n, s3, s4)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3))), inference(lemma,lemma(discharge,[]))).
% 294.69/187.19 tff(27313,plain,
% 294.69/187.19 (~node10(c_e_h_2, c_n, s3, s4)),
% 294.69/187.19 inference(unit_resolution,[status(thm)],[27312, 27298, 27287])).
% 294.69/187.19 tff(27314,plain,
% 294.69/187.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s3, s4)) | node10(c_e_h_2, c_n, s3, s4) | node11(c_e_h_2, c_n, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s3, s4)) | node10(c_e_h_2, c_n, s3, s4) | node11(c_e_h_2, c_n, s3, s4))),
% 294.69/187.19 inference(rewrite,[status(thm)],[])).
% 294.69/187.19 tff(27315,plain,
% 294.69/187.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s3, s4)) | node10(c_e_h_2, c_n, s3, s4) | node11(c_e_h_2, c_n, s3, s4))),
% 294.69/187.19 inference(quant_inst,[status(thm)],[])).
% 294.69/187.19 tff(27316,plain,
% 294.69/187.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s3, s4)) | node10(c_e_h_2, c_n, s3, s4) | node11(c_e_h_2, c_n, s3, s4)),
% 294.69/187.19 inference(modus_ponens,[status(thm)],[27315, 27314])).
% 294.69/187.19 tff(27317,plain,
% 294.69/187.19 (node10(c_e_h_2, c_n, s3, s4) | node11(c_e_h_2, c_n, s3, s4)),
% 294.69/187.19 inference(unit_resolution,[status(thm)],[27316, 5002, 531])).
% 294.69/187.19 tff(27318,plain,
% 294.69/187.19 (node11(c_e_h_2, c_n, s3, s4)),
% 294.69/187.19 inference(unit_resolution,[status(thm)],[27317, 27313])).
% 294.69/187.19 tff(27319,assumption,(node11(c_e_h_2, c_n, s3, s4)), introduced(assumption)).
% 294.69/187.19 tff(27320,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3)), introduced(assumption)).
% 294.69/187.19 tff(27321,plain,
% 294.69/187.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4) | (~node11(c_e_h_2, c_n, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4) | (~node11(c_e_h_2, c_n, s3, s4)))),
% 294.69/187.19 inference(rewrite,[status(thm)],[])).
% 294.69/187.19 tff(27322,plain,
% 294.69/187.19 ((m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4) | (~node11(c_e_h_2, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4) | (~node11(c_e_h_2, c_n, s3, s4)))),
% 294.69/187.19 inference(rewrite,[status(thm)],[])).
% 294.69/187.19 tff(27323,plain,
% 294.69/187.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4) | (~node11(c_e_h_2, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4) | (~node11(c_e_h_2, c_n, s3, s4))))),
% 294.69/187.19 inference(monotonicity,[status(thm)],[27322])).
% 294.69/187.19 tff(27324,plain,
% 294.69/187.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4) | (~node11(c_e_h_2, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4) | (~node11(c_e_h_2, c_n, s3, s4)))),
% 294.69/187.19 inference(transitivity,[status(thm)],[27323, 27321])).
% 294.69/187.19 tff(27325,plain,
% 294.69/187.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4) | (~node11(c_e_h_2, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3)))),
% 294.69/187.19 inference(quant_inst,[status(thm)],[])).
% 294.69/187.19 tff(27326,plain,
% 294.69/187.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4) | (~node11(c_e_h_2, c_n, s3, s4))),
% 294.69/187.19 inference(modus_ponens,[status(thm)],[27325, 27324])).
% 294.69/187.19 tff(27327,plain,
% 294.69/187.19 ($false),
% 294.69/187.19 inference(unit_resolution,[status(thm)],[27326, 5742, 27320, 27287, 27319])).
% 294.69/187.19 tff(27328,plain,((~node11(c_e_h_2, c_n, s3, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4)), inference(lemma,lemma(discharge,[]))).
% 294.69/187.19 tff(27329,plain,
% 294.69/187.19 (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3)),
% 294.69/187.19 inference(unit_resolution,[status(thm)],[27328, 27318, 27287])).
% 294.69/187.19 tff(27330,plain,
% 294.69/187.19 (~node11(c_e_h_2, c_n, s2, s3)),
% 294.69/187.19 inference(unit_resolution,[status(thm)],[26988, 27329])).
% 294.69/187.19 tff(27331,plain,
% 294.69/187.19 (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s2)),
% 294.69/187.19 inference(unit_resolution,[status(thm)],[26975, 27288])).
% 294.69/187.19 tff(27332,plain,
% 294.69/187.19 (~node10(c_e_h_2, c_n, s2, s3)),
% 294.69/187.19 inference(unit_resolution,[status(thm)],[27009, 27329, 27331])).
% 294.69/187.19 tff(27333,plain,
% 294.69/187.19 ($false),
% 294.69/187.19 inference(unit_resolution,[status(thm)],[27014, 27332, 27330])).
% 294.69/187.19 tff(27334,plain,(m_c_h_element_v_out(c_e_h_2, c_e, s2) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4) | (~node18(c_e_h_2, c_e, s2, s3))), inference(lemma,lemma(discharge,[]))).
% 294.69/187.19 tff(27335,plain,
% 294.69/187.19 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4) | (~node18(c_e_h_2, c_e, s2, s3))),
% 294.69/187.19 inference(unit_resolution,[status(thm)],[27334, 26971])).
% 294.69/187.19 tff(27336,plain,
% 294.69/187.19 (~node18(c_e_h_2, c_e, s2, s3)),
% 294.69/187.19 inference(unit_resolution,[status(thm)],[27335, 27287])).
% 294.69/187.19 tff(27337,plain,
% 294.69/187.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s2, s3)) | node19(c_e_h_2, c_e, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s2, s3)) | node19(c_e_h_2, c_e, s2, s3))),
% 294.69/187.19 inference(rewrite,[status(thm)],[])).
% 294.69/187.19 tff(27338,plain,
% 294.69/187.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s2, s3)) | node19(c_e_h_2, c_e, s2, s3))),
% 294.69/187.19 inference(quant_inst,[status(thm)],[])).
% 294.69/187.19 tff(27339,plain,
% 294.69/187.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s2, s3)) | node19(c_e_h_2, c_e, s2, s3)),
% 294.69/187.19 inference(modus_ponens,[status(thm)],[27338, 27337])).
% 294.69/187.19 tff(27340,plain,
% 294.69/187.19 (node19(c_e_h_2, c_e, s2, s3)),
% 294.69/187.19 inference(unit_resolution,[status(thm)],[27339, 190, 318])).
% 294.69/187.19 tff(27341,plain,
% 294.69/187.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s2) | (~node19(c_e_h_2, c_e, s2, s3)) | node18(c_e_h_2, c_e, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_e, s2) | (~node19(c_e_h_2, c_e, s2, s3)) | node18(c_e_h_2, c_e, s2, s3))),
% 294.69/187.19 inference(rewrite,[status(thm)],[])).
% 294.69/187.19 tff(27342,plain,
% 294.69/187.19 ((node17(c_e_h_2, c_e, s2) | node18(c_e_h_2, c_e, s2, s3) | (~node19(c_e_h_2, c_e, s2, s3))) <=> (node17(c_e_h_2, c_e, s2) | (~node19(c_e_h_2, c_e, s2, s3)) | node18(c_e_h_2, c_e, s2, s3))),
% 294.69/187.19 inference(rewrite,[status(thm)],[])).
% 294.69/187.19 tff(27343,plain,
% 294.69/187.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s2) | node18(c_e_h_2, c_e, s2, s3) | (~node19(c_e_h_2, c_e, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s2) | (~node19(c_e_h_2, c_e, s2, s3)) | node18(c_e_h_2, c_e, s2, s3)))),
% 294.69/187.19 inference(monotonicity,[status(thm)],[27342])).
% 294.69/187.19 tff(27344,plain,
% 294.69/187.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s2) | node18(c_e_h_2, c_e, s2, s3) | (~node19(c_e_h_2, c_e, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_e, s2) | (~node19(c_e_h_2, c_e, s2, s3)) | node18(c_e_h_2, c_e, s2, s3))),
% 294.69/187.20 inference(transitivity,[status(thm)],[27343, 27341])).
% 294.69/187.20 tff(27345,plain,
% 294.69/187.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s2) | node18(c_e_h_2, c_e, s2, s3) | (~node19(c_e_h_2, c_e, s2, s3)))),
% 294.69/187.20 inference(quant_inst,[status(thm)],[])).
% 294.69/187.20 tff(27346,plain,
% 294.69/187.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_e, s2) | (~node19(c_e_h_2, c_e, s2, s3)) | node18(c_e_h_2, c_e, s2, s3)),
% 294.69/187.20 inference(modus_ponens,[status(thm)],[27345, 27344])).
% 294.69/187.20 tff(27347,plain,
% 294.69/187.20 (node17(c_e_h_2, c_e, s2) | node18(c_e_h_2, c_e, s2, s3)),
% 294.69/187.20 inference(unit_resolution,[status(thm)],[27346, 776, 27340])).
% 294.69/187.20 tff(27348,plain,
% 294.69/187.20 (node17(c_e_h_2, c_e, s2)),
% 294.69/187.20 inference(unit_resolution,[status(thm)],[27347, 27336])).
% 294.69/187.20 tff(27349,plain,
% 294.69/187.20 (~node11(c_e_h_2, c_n, s3, s4)),
% 294.69/187.20 inference(unit_resolution,[status(thm)],[27328, 27287, 27320])).
% 294.69/187.20 tff(27350,plain,
% 294.69/187.20 (~node10(c_e_h_2, c_n, s3, s4)),
% 294.69/187.20 inference(unit_resolution,[status(thm)],[27312, 27287, 27299])).
% 294.69/187.20 tff(27351,plain,
% 294.69/187.20 ($false),
% 294.69/187.20 inference(unit_resolution,[status(thm)],[27317, 27350, 27349])).
% 294.69/187.20 tff(27352,plain,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s3))), inference(lemma,lemma(discharge,[]))).
% 294.69/187.20 tff(27353,plain,
% 294.69/187.20 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3))),
% 294.69/187.20 inference(unit_resolution,[status(thm)],[27352, 27017])).
% 294.69/187.20 tff(27354,plain,
% 294.69/187.20 (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3)),
% 294.69/187.20 inference(unit_resolution,[status(thm)],[27353, 27287])).
% 294.69/187.20 tff(27355,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3)), introduced(assumption)).
% 294.69/187.20 tff(27356,assumption,(~m_c_h_element_v_out(c_e_h_2, c_e, s3)), introduced(assumption)).
% 294.69/187.20 tff(27357,plain,
% 294.69/187.20 ($false),
% 294.69/187.20 inference(unit_resolution,[status(thm)],[27297, 7856, 27356, 27355])).
% 294.69/187.20 tff(27358,plain,(m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s3) | m_c_h_element_v_out(c_e_h_2, c_e, s3)), inference(lemma,lemma(discharge,[]))).
% 294.69/187.20 tff(27359,plain,
% 294.69/187.20 (m_c_h_element_v_out(c_e_h_2, c_e, s3)),
% 294.69/187.20 inference(unit_resolution,[status(thm)],[27358, 27354])).
% 294.69/187.20 tff(27360,assumption,(m_c_h_element_v_out(c_e_h_2, c_e, s3)), introduced(assumption)).
% 294.69/187.20 tff(27361,assumption,(node17(c_e_h_2, c_e, s2)), introduced(assumption)).
% 294.69/187.20 tff(27362,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_e, s2)), introduced(assumption)).
% 294.69/187.20 tff(27363,plain,
% 294.69/187.20 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s2)) | m_c_h_element_v_in2(c_e_h_2, c_e, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s2)) | m_c_h_element_v_in2(c_e_h_2, c_e, s2))),
% 294.69/187.20 inference(rewrite,[status(thm)],[])).
% 294.69/187.20 tff(27364,plain,
% 294.69/187.20 (((~m_c_h_element_v_in1(c_e_h_2, c_e, s2)) | m_c_h_element_v_in2(c_e_h_2, c_e, s2) | (~node17(c_e_h_2, c_e, s2))) <=> ((~node17(c_e_h_2, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s2)) | m_c_h_element_v_in2(c_e_h_2, c_e, s2))),
% 294.69/187.20 inference(rewrite,[status(thm)],[])).
% 294.69/187.20 tff(27365,plain,
% 294.69/187.20 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s2)) | m_c_h_element_v_in2(c_e_h_2, c_e, s2) | (~node17(c_e_h_2, c_e, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s2)) | m_c_h_element_v_in2(c_e_h_2, c_e, s2)))),
% 294.69/187.20 inference(monotonicity,[status(thm)],[27364])).
% 294.69/187.20 tff(27366,plain,
% 294.69/187.20 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s2)) | m_c_h_element_v_in2(c_e_h_2, c_e, s2) | (~node17(c_e_h_2, c_e, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s2)) | m_c_h_element_v_in2(c_e_h_2, c_e, s2))),
% 294.69/187.20 inference(transitivity,[status(thm)],[27365, 27363])).
% 294.69/187.20 tff(27367,plain,
% 294.69/187.20 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s2)) | m_c_h_element_v_in2(c_e_h_2, c_e, s2) | (~node17(c_e_h_2, c_e, s2)))),
% 294.69/187.20 inference(quant_inst,[status(thm)],[])).
% 294.69/187.20 tff(27368,plain,
% 294.69/187.20 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s2)) | m_c_h_element_v_in2(c_e_h_2, c_e, s2)),
% 294.69/187.20 inference(modus_ponens,[status(thm)],[27367, 27366])).
% 294.69/187.20 tff(27369,plain,
% 294.69/187.20 ((~node17(c_e_h_2, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s2))),
% 294.69/187.20 inference(unit_resolution,[status(thm)],[27368, 919, 27362])).
% 294.69/187.20 tff(27370,plain,
% 294.69/187.20 (~m_c_h_element_v_in1(c_e_h_2, c_e, s2)),
% 294.69/187.20 inference(unit_resolution,[status(thm)],[27369, 27361])).
% 294.69/187.20 tff(27371,assumption,(node15(c_e_h_2, c_e, s2, s3)), introduced(assumption)).
% 294.69/187.20 tff(27372,plain,
% 294.69/187.20 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s3)) | (~node15(c_e_h_2, c_e, s2, s3)) | m_c_h_element_v_out(c_e_h_2, c_e, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s3)) | (~node15(c_e_h_2, c_e, s2, s3)) | m_c_h_element_v_out(c_e_h_2, c_e, s2))),
% 294.69/187.20 inference(rewrite,[status(thm)],[])).
% 294.69/187.20 tff(27373,plain,
% 294.69/187.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s3)) | (~node15(c_e_h_2, c_e, s2, s3)) | m_c_h_element_v_out(c_e_h_2, c_e, s2))),
% 294.69/187.20 inference(quant_inst,[status(thm)],[])).
% 294.69/187.20 tff(27374,plain,
% 294.69/187.20 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s3)) | (~node15(c_e_h_2, c_e, s2, s3)) | m_c_h_element_v_out(c_e_h_2, c_e, s2)),
% 294.69/187.20 inference(modus_ponens,[status(thm)],[27373, 27372])).
% 294.69/187.20 tff(27375,plain,
% 294.69/187.20 ($false),
% 294.69/187.20 inference(unit_resolution,[status(thm)],[27374, 147, 27288, 27371, 27360])).
% 294.69/187.20 tff(27376,plain,((~node15(c_e_h_2, c_e, s2, s3)) | m_c_h_element_v_out(c_e_h_2, c_e, s2) | (~m_c_h_element_v_out(c_e_h_2, c_e, s3))), inference(lemma,lemma(discharge,[]))).
% 294.69/187.20 tff(27377,plain,
% 294.69/187.20 (~node15(c_e_h_2, c_e, s2, s3)),
% 294.69/187.20 inference(unit_resolution,[status(thm)],[27376, 27360, 26971])).
% 294.69/187.20 tff(27378,assumption,(node16(c_e_h_2, c_e, s2)), introduced(assumption)).
% 294.69/187.20 tff(27379,plain,
% 294.69/187.20 ((~m_c_h_element_v_in1(c_e_h_2, c_e, s2)) | m_c_h_element_v_in2(c_e_h_2, c_e, s2)),
% 294.69/187.20 inference(unit_resolution,[status(thm)],[27368, 919, 27361])).
% 294.69/187.20 tff(27380,plain,
% 294.69/187.20 (~m_c_h_element_v_in1(c_e_h_2, c_e, s2)),
% 294.69/187.20 inference(unit_resolution,[status(thm)],[27379, 27362])).
% 294.69/187.20 tff(27381,plain,
% 294.69/187.20 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_e, s2)) | m_c_h_element_v_in1(c_e_h_2, c_e, s2) | m_c_h_element_v_in2(c_e_h_2, c_e, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s2)) | m_c_h_element_v_in1(c_e_h_2, c_e, s2) | m_c_h_element_v_in2(c_e_h_2, c_e, s2))),
% 294.69/187.20 inference(rewrite,[status(thm)],[])).
% 294.69/187.20 tff(27382,plain,
% 294.69/187.20 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_e, s2)) | m_c_h_element_v_in1(c_e_h_2, c_e, s2) | m_c_h_element_v_in2(c_e_h_2, c_e, s2))),
% 294.69/187.20 inference(quant_inst,[status(thm)],[])).
% 294.69/187.20 tff(27383,plain,
% 294.69/187.20 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s2)) | m_c_h_element_v_in1(c_e_h_2, c_e, s2) | m_c_h_element_v_in2(c_e_h_2, c_e, s2)),
% 294.69/187.20 inference(modus_ponens,[status(thm)],[27382, 27381])).
% 294.69/187.20 tff(27384,plain,
% 294.69/187.20 (m_c_h_element_v_in1(c_e_h_2, c_e, s2) | m_c_h_element_v_in2(c_e_h_2, c_e, s2)),
% 294.69/187.20 inference(unit_resolution,[status(thm)],[27383, 178, 27378])).
% 294.69/187.20 tff(27385,plain,
% 294.69/187.20 ($false),
% 294.69/187.20 inference(unit_resolution,[status(thm)],[27384, 27380, 27362])).
% 294.69/187.20 tff(27386,plain,(m_c_h_element_v_in2(c_e_h_2, c_e, s2) | (~node16(c_e_h_2, c_e, s2)) | (~node17(c_e_h_2, c_e, s2))), inference(lemma,lemma(discharge,[]))).
% 294.69/187.20 tff(27387,plain,
% 294.69/187.20 (m_c_h_element_v_in2(c_e_h_2, c_e, s2)),
% 294.69/187.20 inference(unit_resolution,[status(thm)],[27386, 27378, 27361])).
% 294.69/187.20 tff(27388,plain,
% 294.69/187.20 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s2)) | (~node17(c_e_h_2, c_e, s2)) | m_c_h_element_v_in1(c_e_h_2, c_e, s2))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s2)) | (~node17(c_e_h_2, c_e, s2)) | m_c_h_element_v_in1(c_e_h_2, c_e, s2))),
% 294.69/187.20 inference(rewrite,[status(thm)],[])).
% 294.69/187.20 tff(27389,plain,
% 294.69/187.20 ((m_c_h_element_v_in1(c_e_h_2, c_e, s2) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s2)) | (~node17(c_e_h_2, c_e, s2))) <=> ((~m_c_h_element_v_in2(c_e_h_2, c_e, s2)) | (~node17(c_e_h_2, c_e, s2)) | m_c_h_element_v_in1(c_e_h_2, c_e, s2))),
% 294.69/187.20 inference(rewrite,[status(thm)],[])).
% 294.69/187.20 tff(27390,plain,
% 294.69/187.20 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s2) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s2)) | (~node17(c_e_h_2, c_e, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s2)) | (~node17(c_e_h_2, c_e, s2)) | m_c_h_element_v_in1(c_e_h_2, c_e, s2)))),
% 294.69/187.20 inference(monotonicity,[status(thm)],[27389])).
% 294.69/187.20 tff(27391,plain,
% 294.69/187.20 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s2) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s2)) | (~node17(c_e_h_2, c_e, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s2)) | (~node17(c_e_h_2, c_e, s2)) | m_c_h_element_v_in1(c_e_h_2, c_e, s2))),
% 294.69/187.20 inference(transitivity,[status(thm)],[27390, 27388])).
% 294.69/187.20 tff(27392,plain,
% 294.69/187.20 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s2) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s2)) | (~node17(c_e_h_2, c_e, s2)))),
% 294.69/187.20 inference(quant_inst,[status(thm)],[])).
% 294.69/187.20 tff(27393,plain,
% 294.69/187.20 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s2)) | (~node17(c_e_h_2, c_e, s2)) | m_c_h_element_v_in1(c_e_h_2, c_e, s2)),
% 294.69/187.20 inference(modus_ponens,[status(thm)],[27392, 27391])).
% 294.69/187.20 tff(27394,plain,
% 294.69/187.20 ((~m_c_h_element_v_in2(c_e_h_2, c_e, s2)) | m_c_h_element_v_in1(c_e_h_2, c_e, s2)),
% 294.69/187.20 inference(unit_resolution,[status(thm)],[27393, 859, 27361])).
% 294.69/187.20 tff(27395,plain,
% 294.69/187.20 (m_c_h_element_v_in1(c_e_h_2, c_e, s2)),
% 294.69/187.20 inference(unit_resolution,[status(thm)],[27394, 27387])).
% 294.69/187.20 tff(27396,plain,
% 294.69/187.20 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s2)) | (~node16(c_e_h_2, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s2)) | (~node16(c_e_h_2, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s2)))),
% 294.69/187.21 inference(rewrite,[status(thm)],[])).
% 294.69/187.21 tff(27397,plain,
% 294.69/187.21 (((~node16(c_e_h_2, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s2)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s2))) <=> ((~m_c_h_element_v_in2(c_e_h_2, c_e, s2)) | (~node16(c_e_h_2, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s2)))),
% 294.69/187.21 inference(rewrite,[status(thm)],[])).
% 294.69/187.21 tff(27398,plain,
% 294.69/187.21 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_2, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s2)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s2)) | (~node16(c_e_h_2, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s2))))),
% 294.69/187.21 inference(monotonicity,[status(thm)],[27397])).
% 294.69/187.21 tff(27399,plain,
% 294.69/187.21 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_2, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s2)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s2)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s2)) | (~node16(c_e_h_2, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s2)))),
% 294.69/187.21 inference(transitivity,[status(thm)],[27398, 27396])).
% 294.69/187.21 tff(27400,plain,
% 294.69/187.21 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_2, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s2)) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s2)))),
% 294.69/187.21 inference(quant_inst,[status(thm)],[])).
% 294.69/187.21 tff(27401,plain,
% 294.69/187.21 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s2)) | (~node16(c_e_h_2, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s2))),
% 294.69/187.21 inference(modus_ponens,[status(thm)],[27400, 27399])).
% 294.69/187.21 tff(27402,plain,
% 294.69/187.21 ((~m_c_h_element_v_in2(c_e_h_2, c_e, s2)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s2))),
% 294.69/187.21 inference(unit_resolution,[status(thm)],[27401, 2307, 27378])).
% 294.69/187.21 tff(27403,plain,
% 294.69/187.21 ($false),
% 294.69/187.21 inference(unit_resolution,[status(thm)],[27402, 27395, 27387])).
% 294.69/187.21 tff(27404,plain,((~node16(c_e_h_2, c_e, s2)) | (~node17(c_e_h_2, c_e, s2))), inference(lemma,lemma(discharge,[]))).
% 294.69/187.21 tff(27405,plain,
% 294.69/187.21 (~node16(c_e_h_2, c_e, s2)),
% 294.69/187.21 inference(unit_resolution,[status(thm)],[27404, 27361])).
% 294.69/187.21 tff(27406,plain,
% 294.69/187.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_2, c_e, s2, s3) | (~node19(c_e_h_2, c_e, s2, s3)) | node16(c_e_h_2, c_e, s2) | node15(c_e_h_2, c_e, s2, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_2, c_e, s2, s3) | (~node19(c_e_h_2, c_e, s2, s3)) | node16(c_e_h_2, c_e, s2) | node15(c_e_h_2, c_e, s2, s3))),
% 294.69/187.21 inference(rewrite,[status(thm)],[])).
% 294.69/187.21 tff(27407,plain,
% 294.69/187.21 ((node16(c_e_h_2, c_e, s2) | node14(c_e_h_2, c_e, s2, s3) | node15(c_e_h_2, c_e, s2, s3) | (~node19(c_e_h_2, c_e, s2, s3))) <=> (node14(c_e_h_2, c_e, s2, s3) | (~node19(c_e_h_2, c_e, s2, s3)) | node16(c_e_h_2, c_e, s2) | node15(c_e_h_2, c_e, s2, s3))),
% 294.69/187.21 inference(rewrite,[status(thm)],[])).
% 294.69/187.21 tff(27408,plain,
% 294.69/187.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s2) | node14(c_e_h_2, c_e, s2, s3) | node15(c_e_h_2, c_e, s2, s3) | (~node19(c_e_h_2, c_e, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_2, c_e, s2, s3) | (~node19(c_e_h_2, c_e, s2, s3)) | node16(c_e_h_2, c_e, s2) | node15(c_e_h_2, c_e, s2, s3)))),
% 294.69/187.21 inference(monotonicity,[status(thm)],[27407])).
% 294.69/187.21 tff(27409,plain,
% 294.69/187.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s2) | node14(c_e_h_2, c_e, s2, s3) | node15(c_e_h_2, c_e, s2, s3) | (~node19(c_e_h_2, c_e, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_2, c_e, s2, s3) | (~node19(c_e_h_2, c_e, s2, s3)) | node16(c_e_h_2, c_e, s2) | node15(c_e_h_2, c_e, s2, s3))),
% 294.69/187.21 inference(transitivity,[status(thm)],[27408, 27406])).
% 294.69/187.21 tff(27410,plain,
% 294.69/187.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s2) | node14(c_e_h_2, c_e, s2, s3) | node15(c_e_h_2, c_e, s2, s3) | (~node19(c_e_h_2, c_e, s2, s3)))),
% 294.69/187.21 inference(quant_inst,[status(thm)],[])).
% 294.69/187.21 tff(27411,plain,
% 294.69/187.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_2, c_e, s2, s3) | (~node19(c_e_h_2, c_e, s2, s3)) | node16(c_e_h_2, c_e, s2) | node15(c_e_h_2, c_e, s2, s3)),
% 294.69/187.21 inference(modus_ponens,[status(thm)],[27410, 27409])).
% 294.69/187.21 tff(27412,plain,
% 294.69/187.21 (node14(c_e_h_2, c_e, s2, s3) | node16(c_e_h_2, c_e, s2) | node15(c_e_h_2, c_e, s2, s3)),
% 294.69/187.21 inference(unit_resolution,[status(thm)],[27411, 204, 27340])).
% 294.69/187.21 tff(27413,plain,
% 294.69/187.21 (node14(c_e_h_2, c_e, s2, s3)),
% 294.69/187.21 inference(unit_resolution,[status(thm)],[27412, 27405, 27377])).
% 294.69/187.21 tff(27414,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_e, s2)), introduced(assumption)).
% 294.69/187.21 tff(27415,assumption,(node14(c_e_h_2, c_e, s2, s3)), introduced(assumption)).
% 294.69/187.21 tff(27416,plain,
% 294.69/187.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s3)) | (~node14(c_e_h_2, c_e, s2, s3)) | m_c_h_element_v_in1(c_e_h_2, c_e, s2))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s3)) | (~node14(c_e_h_2, c_e, s2, s3)) | m_c_h_element_v_in1(c_e_h_2, c_e, s2))),
% 294.69/187.21 inference(rewrite,[status(thm)],[])).
% 294.69/187.21 tff(27417,plain,
% 294.69/187.21 (((~node14(c_e_h_2, c_e, s2, s3)) | m_c_h_element_v_in1(c_e_h_2, c_e, s2) | (~m_c_h_element_v_out(c_e_h_2, c_e, s3))) <=> ((~m_c_h_element_v_out(c_e_h_2, c_e, s3)) | (~node14(c_e_h_2, c_e, s2, s3)) | m_c_h_element_v_in1(c_e_h_2, c_e, s2))),
% 294.69/187.21 inference(rewrite,[status(thm)],[])).
% 294.69/187.21 tff(27418,plain,
% 294.69/187.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s2, s3)) | m_c_h_element_v_in1(c_e_h_2, c_e, s2) | (~m_c_h_element_v_out(c_e_h_2, c_e, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s3)) | (~node14(c_e_h_2, c_e, s2, s3)) | m_c_h_element_v_in1(c_e_h_2, c_e, s2)))),
% 294.69/187.21 inference(monotonicity,[status(thm)],[27417])).
% 294.69/187.21 tff(27419,plain,
% 294.69/187.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s2, s3)) | m_c_h_element_v_in1(c_e_h_2, c_e, s2) | (~m_c_h_element_v_out(c_e_h_2, c_e, s3)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s3)) | (~node14(c_e_h_2, c_e, s2, s3)) | m_c_h_element_v_in1(c_e_h_2, c_e, s2))),
% 294.72/187.21 inference(transitivity,[status(thm)],[27418, 27416])).
% 294.72/187.21 tff(27420,plain,
% 294.72/187.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s2, s3)) | m_c_h_element_v_in1(c_e_h_2, c_e, s2) | (~m_c_h_element_v_out(c_e_h_2, c_e, s3)))),
% 294.72/187.21 inference(quant_inst,[status(thm)],[])).
% 294.72/187.21 tff(27421,plain,
% 294.72/187.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s3)) | (~node14(c_e_h_2, c_e, s2, s3)) | m_c_h_element_v_in1(c_e_h_2, c_e, s2)),
% 294.72/187.21 inference(modus_ponens,[status(thm)],[27420, 27419])).
% 294.72/187.21 tff(27422,plain,
% 294.72/187.21 ($false),
% 294.72/187.21 inference(unit_resolution,[status(thm)],[27421, 223, 27415, 27360, 27414])).
% 294.72/187.21 tff(27423,plain,((~node14(c_e_h_2, c_e, s2, s3)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s3)) | m_c_h_element_v_in1(c_e_h_2, c_e, s2)), inference(lemma,lemma(discharge,[]))).
% 294.72/187.21 tff(27424,plain,
% 294.72/187.21 ($false),
% 294.72/187.21 inference(unit_resolution,[status(thm)],[27423, 27413, 27370, 27360])).
% 294.72/187.21 tff(27425,plain,((~node17(c_e_h_2, c_e, s2)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s3)) | m_c_h_element_v_in2(c_e_h_2, c_e, s2)), inference(lemma,lemma(discharge,[]))).
% 294.72/187.21 tff(27426,plain,
% 294.72/187.21 ($false),
% 294.72/187.21 inference(unit_resolution,[status(thm)],[27425, 27359, 27348, 27286])).
% 294.72/187.21 tff(27427,plain,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4)), inference(lemma,lemma(discharge,[]))).
% 294.72/187.21 tff(27428,plain,
% 294.72/187.21 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4)))),
% 294.72/187.21 inference(rewrite,[status(thm)],[])).
% 294.72/187.21 tff(27429,plain,
% 294.72/187.21 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4)))),
% 294.72/187.21 inference(quant_inst,[status(thm)],[])).
% 294.72/187.21 tff(27430,plain,
% 294.72/187.21 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s4)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4))),
% 294.72/187.21 inference(modus_ponens,[status(thm)],[27429, 27428])).
% 294.72/187.21 tff(27431,plain,
% 294.72/187.21 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s4)),
% 294.72/187.21 inference(unit_resolution,[status(thm)],[27430, 4958, 27427])).
% 294.72/187.21 tff(27432,plain,
% 294.72/187.21 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s4)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s4)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s4))),
% 294.72/187.21 inference(rewrite,[status(thm)],[])).
% 294.72/187.21 tff(27433,plain,
% 294.72/187.21 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s4)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s4))),
% 294.72/187.21 inference(quant_inst,[status(thm)],[])).
% 294.72/187.21 tff(27434,plain,
% 294.72/187.21 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s4)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s4)),
% 294.72/187.21 inference(modus_ponens,[status(thm)],[27433, 27432])).
% 294.72/187.21 tff(27435,plain,
% 294.72/187.21 (~node9(c_e_h_2, c_m, s4)),
% 294.72/187.21 inference(unit_resolution,[status(thm)],[27434, 4972, 27431])).
% 294.72/187.21 tff(27436,assumption,(~node9(c_e_h_2, c_m, s4)), introduced(assumption)).
% 294.72/187.21 tff(27437,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)), introduced(assumption)).
% 294.72/187.21 tff(27438,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)), introduced(assumption)).
% 294.72/187.21 tff(27439,assumption,(node11(c_e_h_2, c_m, s4, s5)), introduced(assumption)).
% 294.72/187.22 tff(27440,plain,
% 294.72/187.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)) | (~node11(c_e_h_2, c_m, s4, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)) | (~node11(c_e_h_2, c_m, s4, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4))),
% 294.72/187.22 inference(rewrite,[status(thm)],[])).
% 294.72/187.22 tff(27441,plain,
% 294.72/187.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)) | (~node11(c_e_h_2, c_m, s4, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4))),
% 294.72/187.22 inference(quant_inst,[status(thm)],[])).
% 294.72/187.22 tff(27442,plain,
% 294.72/187.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)) | (~node11(c_e_h_2, c_m, s4, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)),
% 294.72/187.22 inference(modus_ponens,[status(thm)],[27441, 27440])).
% 294.72/187.22 tff(27443,plain,
% 294.72/187.22 ($false),
% 294.72/187.22 inference(unit_resolution,[status(thm)],[27442, 5017, 27437, 27438, 27439])).
% 294.72/187.22 tff(27444,plain,((~node11(c_e_h_2, c_m, s4, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5))), inference(lemma,lemma(discharge,[]))).
% 294.72/187.22 tff(27445,plain,
% 294.72/187.22 (~node11(c_e_h_2, c_m, s4, s5)),
% 294.72/187.22 inference(unit_resolution,[status(thm)],[27444, 27438, 27437])).
% 294.72/187.22 tff(27446,plain,
% 294.72/187.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s4, s5)) | node10(c_e_h_2, c_m, s4, s5) | node11(c_e_h_2, c_m, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s4, s5)) | node10(c_e_h_2, c_m, s4, s5) | node11(c_e_h_2, c_m, s4, s5))),
% 294.72/187.22 inference(rewrite,[status(thm)],[])).
% 294.72/187.22 tff(27447,plain,
% 294.72/187.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s4, s5)) | node10(c_e_h_2, c_m, s4, s5) | node11(c_e_h_2, c_m, s4, s5))),
% 294.72/187.22 inference(quant_inst,[status(thm)],[])).
% 294.72/187.22 tff(27448,plain,
% 294.72/187.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s4, s5)) | node10(c_e_h_2, c_m, s4, s5) | node11(c_e_h_2, c_m, s4, s5)),
% 294.72/187.22 inference(modus_ponens,[status(thm)],[27447, 27446])).
% 294.72/187.22 tff(27449,plain,
% 294.72/187.22 (node10(c_e_h_2, c_m, s4, s5) | node11(c_e_h_2, c_m, s4, s5)),
% 294.72/187.22 inference(unit_resolution,[status(thm)],[27448, 5002, 1028])).
% 294.72/187.22 tff(27450,plain,
% 294.72/187.22 (node10(c_e_h_2, c_m, s4, s5)),
% 294.72/187.22 inference(unit_resolution,[status(thm)],[27449, 27445])).
% 294.72/187.22 tff(27451,plain,
% 294.72/187.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)) | (~node10(c_e_h_2, c_m, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_2, c_m, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)) | (~node10(c_e_h_2, c_m, s4, s5)))),
% 294.72/187.22 inference(rewrite,[status(thm)],[])).
% 294.72/187.22 tff(27452,plain,
% 294.72/187.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)) | (~node10(c_e_h_2, c_m, s4, s5)))),
% 294.72/187.22 inference(quant_inst,[status(thm)],[])).
% 294.72/187.22 tff(27453,plain,
% 294.72/187.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_2, c_m, s4) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)) | (~node10(c_e_h_2, c_m, s4, s5))),
% 294.72/187.22 inference(modus_ponens,[status(thm)],[27452, 27451])).
% 294.72/187.22 tff(27454,plain,
% 294.72/187.22 ($false),
% 294.72/187.22 inference(unit_resolution,[status(thm)],[27453, 4986, 27438, 27450, 27436])).
% 294.72/187.22 tff(27455,plain,((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)) | node9(c_e_h_2, c_m, s4) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)), inference(lemma,lemma(discharge,[]))).
% 294.72/187.22 tff(27456,plain,
% 294.72/187.22 ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)) | node9(c_e_h_2, c_m, s4)),
% 294.72/187.22 inference(unit_resolution,[status(thm)],[27455, 27045])).
% 294.72/187.22 tff(27457,plain,
% 294.72/187.22 (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)),
% 294.72/187.22 inference(unit_resolution,[status(thm)],[27456, 27435])).
% 294.72/187.22 tff(27458,plain,
% 294.72/187.22 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_l, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_l, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5))),
% 294.72/187.22 inference(rewrite,[status(thm)],[])).
% 294.72/187.22 tff(27459,plain,
% 294.72/187.22 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_l, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5))),
% 294.72/187.22 inference(quant_inst,[status(thm)],[])).
% 294.72/187.22 tff(27460,plain,
% 294.72/187.22 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_l, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)),
% 294.72/187.22 inference(modus_ponens,[status(thm)],[27459, 27458])).
% 294.72/187.22 tff(27461,plain,
% 294.72/187.22 (~m_and_h_gate_v_in2(c_e_h_2, c_l, s5)),
% 294.72/187.22 inference(unit_resolution,[status(thm)],[27460, 4549, 27457])).
% 294.72/187.22 tff(27462,plain,
% 294.72/187.22 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_l, s5)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_l, s5)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s5))),
% 294.72/187.22 inference(rewrite,[status(thm)],[])).
% 294.72/187.22 tff(27463,plain,
% 294.72/187.22 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_l, s5)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s5))),
% 294.72/187.22 inference(quant_inst,[status(thm)],[])).
% 294.72/187.22 tff(27464,plain,
% 294.72/187.22 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_l, s5)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s5)),
% 294.72/187.22 inference(modus_ponens,[status(thm)],[27463, 27462])).
% 294.72/187.22 tff(27465,plain,
% 294.72/187.22 (~node20(c_e_h_2, c_l, s5)),
% 294.72/187.22 inference(unit_resolution,[status(thm)],[27464, 4563, 27461])).
% 294.72/187.22 tff(27466,assumption,(node21(c_e_h_2, c_l, s5, s6)), introduced(assumption)).
% 294.72/187.22 tff(27467,plain,
% 294.72/187.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_l, s5) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s6)) | (~node21(c_e_h_2, c_l, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_l, s5) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s6)) | (~node21(c_e_h_2, c_l, s5, s6)))),
% 294.72/187.22 inference(rewrite,[status(thm)],[])).
% 294.72/187.22 tff(27468,plain,
% 294.72/187.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_l, s5) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s6)) | (~node21(c_e_h_2, c_l, s5, s6)))),
% 294.72/187.22 inference(quant_inst,[status(thm)],[])).
% 294.72/187.22 tff(27469,plain,
% 294.72/187.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_l, s5) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s6)) | (~node21(c_e_h_2, c_l, s5, s6))),
% 294.72/187.22 inference(modus_ponens,[status(thm)],[27468, 27467])).
% 294.72/187.22 tff(27470,plain,
% 294.72/187.22 ($false),
% 294.72/187.22 inference(unit_resolution,[status(thm)],[27469, 52, 27466, 27465, 27282])).
% 294.72/187.22 tff(27471,plain,((~node21(c_e_h_2, c_l, s5, s6)) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s6))), inference(lemma,lemma(discharge,[]))).
% 294.73/187.22 tff(27472,plain,
% 294.73/187.22 (~node21(c_e_h_2, c_l, s5, s6)),
% 294.73/187.22 inference(unit_resolution,[status(thm)],[27471, 27282])).
% 294.73/187.22 tff(27473,plain,
% 294.73/187.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_2, c_l, s5, s6) | node22(c_e_h_2, c_l, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_2, c_l, s5, s6) | node22(c_e_h_2, c_l, s5, s6))),
% 294.73/187.22 inference(rewrite,[status(thm)],[])).
% 294.73/187.22 tff(27474,plain,
% 294.73/187.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s5, s6)) | node21(c_e_h_2, c_l, s5, s6) | node22(c_e_h_2, c_l, s5, s6))),
% 294.73/187.22 inference(quant_inst,[status(thm)],[])).
% 294.73/187.22 tff(27475,plain,
% 294.73/187.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s5, s6)) | node21(c_e_h_2, c_l, s5, s6) | node22(c_e_h_2, c_l, s5, s6)),
% 294.73/187.22 inference(modus_ponens,[status(thm)],[27474, 27473])).
% 294.73/187.22 tff(27476,plain,
% 294.73/187.22 (node21(c_e_h_2, c_l, s5, s6) | node22(c_e_h_2, c_l, s5, s6)),
% 294.73/187.22 inference(unit_resolution,[status(thm)],[27475, 82, 1406])).
% 294.73/187.22 tff(27477,plain,
% 294.73/187.22 (node22(c_e_h_2, c_l, s5, s6)),
% 294.73/187.22 inference(unit_resolution,[status(thm)],[27476, 27472])).
% 294.73/187.22 tff(27478,plain,
% 294.73/187.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s6)) | (~node22(c_e_h_2, c_l, s5, s6)) | m_and_h_gate_v_out(c_e_h_2, c_l, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s6)) | (~node22(c_e_h_2, c_l, s5, s6)) | m_and_h_gate_v_out(c_e_h_2, c_l, s5))),
% 294.73/187.22 inference(rewrite,[status(thm)],[])).
% 294.73/187.22 tff(27479,plain,
% 294.73/187.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s6)) | (~node22(c_e_h_2, c_l, s5, s6)) | m_and_h_gate_v_out(c_e_h_2, c_l, s5))),
% 294.73/187.22 inference(quant_inst,[status(thm)],[])).
% 294.73/187.22 tff(27480,plain,
% 294.73/187.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s6)) | (~node22(c_e_h_2, c_l, s5, s6)) | m_and_h_gate_v_out(c_e_h_2, c_l, s5)),
% 294.73/187.22 inference(modus_ponens,[status(thm)],[27479, 27478])).
% 294.73/187.22 tff(27481,plain,
% 294.73/187.22 ($false),
% 294.73/187.22 inference(unit_resolution,[status(thm)],[27480, 108, 27089, 27477, 27282])).
% 294.73/187.22 tff(27482,plain,((~m_and_h_gate_v_out(c_e_h_2, c_l, s6)) | m_and_h_gate_v_out(c_e_h_2, c_l, s5)), inference(lemma,lemma(discharge,[]))).
% 294.73/187.22 tff(27483,plain,
% 294.73/187.22 (~m_and_h_gate_v_out(c_e_h_2, c_l, s6)),
% 294.73/187.22 inference(unit_resolution,[status(thm)],[27482, 27281])).
% 294.73/187.22 tff(27484,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_l, s6)), introduced(assumption)).
% 294.73/187.22 tff(27485,assumption,(m_or_h_gate_v_in1(c_e_h_2, c_j, s6)), introduced(assumption)).
% 294.73/187.22 tff(27486,plain,
% 294.73/187.22 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_2, c_j, s6)) | m_and_h_gate_v_out(c_e_h_2, c_l, s6))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_j, s6)) | m_and_h_gate_v_out(c_e_h_2, c_l, s6))),
% 294.73/187.22 inference(rewrite,[status(thm)],[])).
% 294.73/187.22 tff(27487,plain,
% 294.73/187.22 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_2, c_j, s6)) | m_and_h_gate_v_out(c_e_h_2, c_l, s6))),
% 294.73/187.22 inference(quant_inst,[status(thm)],[])).
% 294.73/187.22 tff(27488,plain,
% 294.73/187.22 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_j, s6)) | m_and_h_gate_v_out(c_e_h_2, c_l, s6)),
% 294.73/187.22 inference(modus_ponens,[status(thm)],[27487, 27486])).
% 294.73/187.22 tff(27489,plain,
% 294.73/187.22 ($false),
% 294.73/187.22 inference(unit_resolution,[status(thm)],[27488, 1100, 27485, 27484])).
% 294.73/187.23 tff(27490,plain,((~m_or_h_gate_v_in1(c_e_h_2, c_j, s6)) | m_and_h_gate_v_out(c_e_h_2, c_l, s6)), inference(lemma,lemma(discharge,[]))).
% 294.73/187.23 tff(27491,plain,
% 294.73/187.23 (~m_or_h_gate_v_in1(c_e_h_2, c_j, s6)),
% 294.73/187.23 inference(unit_resolution,[status(thm)],[27490, 27483])).
% 294.73/187.23 tff(27492,plain,
% 294.73/187.23 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s6)) | m_cell_v_ack(c_e_h_2, s6))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s6)) | m_cell_v_ack(c_e_h_2, s6))),
% 294.73/187.23 inference(rewrite,[status(thm)],[])).
% 294.73/187.23 tff(27493,plain,
% 294.73/187.23 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s6)) | m_cell_v_ack(c_e_h_2, s6))),
% 294.73/187.23 inference(quant_inst,[status(thm)],[])).
% 294.73/187.23 tff(27494,plain,
% 294.73/187.23 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s6)) | m_cell_v_ack(c_e_h_2, s6)),
% 294.73/187.23 inference(modus_ponens,[status(thm)],[27493, 27492])).
% 294.73/187.23 tff(27495,plain,
% 294.73/187.23 (~m_or_h_gate_v_in2(c_e_h_2, c_j, s6)),
% 294.73/187.23 inference(unit_resolution,[status(thm)],[27494, 1085, 16971])).
% 294.73/187.23 tff(27496,assumption,(~m_or_h_gate_v_in1(c_e_h_2, c_j, s6)), introduced(assumption)).
% 294.73/187.23 tff(27497,assumption,(~m_or_h_gate_v_in2(c_e_h_2, c_j, s6)), introduced(assumption)).
% 294.73/187.23 tff(27498,assumption,(node5(c_e_h_2, c_j, s6, s7)), introduced(assumption)).
% 294.73/187.23 tff(27499,plain,
% 294.73/187.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_2, c_j, s7)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s6) | m_or_h_gate_v_in1(c_e_h_2, c_j, s6) | (~node5(c_e_h_2, c_j, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s7)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s6) | m_or_h_gate_v_in1(c_e_h_2, c_j, s6) | (~node5(c_e_h_2, c_j, s6, s7)))),
% 294.73/187.23 inference(rewrite,[status(thm)],[])).
% 294.73/187.23 tff(27500,plain,
% 294.73/187.23 ((m_or_h_gate_v_in1(c_e_h_2, c_j, s6) | m_or_h_gate_v_in2(c_e_h_2, c_j, s6) | (~node5(c_e_h_2, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s7))) <=> ((~m_or_h_gate_v_out(c_e_h_2, c_j, s7)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s6) | m_or_h_gate_v_in1(c_e_h_2, c_j, s6) | (~node5(c_e_h_2, c_j, s6, s7)))),
% 294.73/187.23 inference(rewrite,[status(thm)],[])).
% 294.73/187.23 tff(27501,plain,
% 294.73/187.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s6) | m_or_h_gate_v_in2(c_e_h_2, c_j, s6) | (~node5(c_e_h_2, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_2, c_j, s7)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s6) | m_or_h_gate_v_in1(c_e_h_2, c_j, s6) | (~node5(c_e_h_2, c_j, s6, s7))))),
% 294.73/187.23 inference(monotonicity,[status(thm)],[27500])).
% 294.73/187.23 tff(27502,plain,
% 294.73/187.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s6) | m_or_h_gate_v_in2(c_e_h_2, c_j, s6) | (~node5(c_e_h_2, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s7)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s6) | m_or_h_gate_v_in1(c_e_h_2, c_j, s6) | (~node5(c_e_h_2, c_j, s6, s7)))),
% 294.73/187.23 inference(transitivity,[status(thm)],[27501, 27499])).
% 294.73/187.23 tff(27503,plain,
% 294.73/187.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s6) | m_or_h_gate_v_in2(c_e_h_2, c_j, s6) | (~node5(c_e_h_2, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s7)))),
% 294.73/187.23 inference(quant_inst,[status(thm)],[])).
% 294.73/187.23 tff(27504,plain,
% 294.73/187.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s7)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s6) | m_or_h_gate_v_in1(c_e_h_2, c_j, s6) | (~node5(c_e_h_2, c_j, s6, s7))),
% 294.73/187.23 inference(modus_ponens,[status(thm)],[27503, 27502])).
% 294.73/187.23 tff(27505,plain,
% 294.73/187.23 ($false),
% 294.73/187.23 inference(unit_resolution,[status(thm)],[27504, 1159, 27268, 27498, 27497, 27496])).
% 294.73/187.23 tff(27506,plain,((~node5(c_e_h_2, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s7)) | m_or_h_gate_v_in2(c_e_h_2, c_j, s6) | m_or_h_gate_v_in1(c_e_h_2, c_j, s6)), inference(lemma,lemma(discharge,[]))).
% 294.73/187.23 tff(27507,plain,
% 294.73/187.23 ((~node5(c_e_h_2, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s7)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s6)),
% 294.73/187.23 inference(unit_resolution,[status(thm)],[27506, 27495])).
% 294.73/187.23 tff(27508,plain,
% 294.73/187.23 ((~node5(c_e_h_2, c_j, s6, s7)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s7))),
% 294.73/187.23 inference(unit_resolution,[status(thm)],[27507, 27491])).
% 294.73/187.23 tff(27509,plain,
% 294.73/187.23 (~node5(c_e_h_2, c_j, s6, s7)),
% 294.73/187.23 inference(unit_resolution,[status(thm)],[27508, 27268])).
% 294.73/187.23 tff(27510,plain,
% 294.73/187.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s6, s7)) | node5(c_e_h_2, c_j, s6, s7) | node6(c_e_h_2, c_j, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s6, s7)) | node5(c_e_h_2, c_j, s6, s7) | node6(c_e_h_2, c_j, s6, s7))),
% 294.73/187.23 inference(rewrite,[status(thm)],[])).
% 294.73/187.23 tff(27511,plain,
% 294.73/187.23 ((node6(c_e_h_2, c_j, s6, s7) | node5(c_e_h_2, c_j, s6, s7) | (~trans(s6, s7))) <=> ((~trans(s6, s7)) | node5(c_e_h_2, c_j, s6, s7) | node6(c_e_h_2, c_j, s6, s7))),
% 294.73/187.23 inference(rewrite,[status(thm)],[])).
% 294.73/187.23 tff(27512,plain,
% 294.73/187.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s6, s7) | node5(c_e_h_2, c_j, s6, s7) | (~trans(s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s6, s7)) | node5(c_e_h_2, c_j, s6, s7) | node6(c_e_h_2, c_j, s6, s7)))),
% 294.73/187.23 inference(monotonicity,[status(thm)],[27511])).
% 294.73/187.23 tff(27513,plain,
% 294.73/187.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s6, s7) | node5(c_e_h_2, c_j, s6, s7) | (~trans(s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s6, s7)) | node5(c_e_h_2, c_j, s6, s7) | node6(c_e_h_2, c_j, s6, s7))),
% 294.73/187.23 inference(transitivity,[status(thm)],[27512, 27510])).
% 294.73/187.23 tff(27514,plain,
% 294.73/187.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s6, s7) | node5(c_e_h_2, c_j, s6, s7) | (~trans(s6, s7)))),
% 294.73/187.23 inference(quant_inst,[status(thm)],[])).
% 294.73/187.23 tff(27515,plain,
% 294.73/187.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s6, s7)) | node5(c_e_h_2, c_j, s6, s7) | node6(c_e_h_2, c_j, s6, s7)),
% 294.73/187.23 inference(modus_ponens,[status(thm)],[27514, 27513])).
% 294.73/187.23 tff(27516,plain,
% 294.73/187.23 (node5(c_e_h_2, c_j, s6, s7) | node6(c_e_h_2, c_j, s6, s7)),
% 294.73/187.23 inference(unit_resolution,[status(thm)],[27515, 1141, 1844])).
% 294.73/187.23 tff(27517,plain,
% 294.73/187.23 ($false),
% 294.73/187.23 inference(unit_resolution,[status(thm)],[27516, 27509, 27279])).
% 294.73/187.23 tff(27518,plain,(~m_or_h_gate_v_out(c_e_h_2, c_j, s7)), inference(lemma,lemma(discharge,[]))).
% 294.73/187.23 tff(27519,plain,
% 294.73/187.23 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s7)) | m_or_h_gate_v_out(c_e_h_2, c_j, s7))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s7)) | m_or_h_gate_v_out(c_e_h_2, c_j, s7))),
% 294.73/187.24 inference(rewrite,[status(thm)],[])).
% 294.73/187.24 tff(27520,plain,
% 294.73/187.24 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s7)) | m_or_h_gate_v_out(c_e_h_2, c_j, s7))),
% 294.73/187.24 inference(quant_inst,[status(thm)],[])).
% 294.73/187.24 tff(27521,plain,
% 294.73/187.24 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s7)) | m_or_h_gate_v_out(c_e_h_2, c_j, s7)),
% 294.73/187.24 inference(modus_ponens,[status(thm)],[27520, 27519])).
% 294.73/187.24 tff(27522,plain,
% 294.73/187.24 (~m_c_h_element_v_in2(c_e_h_2, c_h, s7)),
% 294.73/187.24 inference(unit_resolution,[status(thm)],[27521, 1174, 27518])).
% 294.73/187.24 tff(27523,plain,
% 294.73/187.24 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s7)) | (~node17(c_e_h_2, c_h, s7)) | m_c_h_element_v_in2(c_e_h_2, c_h, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s7)) | (~node17(c_e_h_2, c_h, s7)) | m_c_h_element_v_in2(c_e_h_2, c_h, s7))),
% 294.73/187.24 inference(rewrite,[status(thm)],[])).
% 294.73/187.24 tff(27524,plain,
% 294.73/187.24 (((~m_c_h_element_v_in1(c_e_h_2, c_h, s7)) | m_c_h_element_v_in2(c_e_h_2, c_h, s7) | (~node17(c_e_h_2, c_h, s7))) <=> ((~m_c_h_element_v_in1(c_e_h_2, c_h, s7)) | (~node17(c_e_h_2, c_h, s7)) | m_c_h_element_v_in2(c_e_h_2, c_h, s7))),
% 294.73/187.24 inference(rewrite,[status(thm)],[])).
% 294.73/187.24 tff(27525,plain,
% 294.73/187.24 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s7)) | m_c_h_element_v_in2(c_e_h_2, c_h, s7) | (~node17(c_e_h_2, c_h, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s7)) | (~node17(c_e_h_2, c_h, s7)) | m_c_h_element_v_in2(c_e_h_2, c_h, s7)))),
% 294.73/187.24 inference(monotonicity,[status(thm)],[27524])).
% 294.73/187.24 tff(27526,plain,
% 294.73/187.24 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s7)) | m_c_h_element_v_in2(c_e_h_2, c_h, s7) | (~node17(c_e_h_2, c_h, s7)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s7)) | (~node17(c_e_h_2, c_h, s7)) | m_c_h_element_v_in2(c_e_h_2, c_h, s7))),
% 294.73/187.24 inference(transitivity,[status(thm)],[27525, 27523])).
% 294.73/187.24 tff(27527,plain,
% 294.73/187.24 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s7)) | m_c_h_element_v_in2(c_e_h_2, c_h, s7) | (~node17(c_e_h_2, c_h, s7)))),
% 294.73/187.24 inference(quant_inst,[status(thm)],[])).
% 294.73/187.24 tff(27528,plain,
% 294.73/187.24 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s7)) | (~node17(c_e_h_2, c_h, s7)) | m_c_h_element_v_in2(c_e_h_2, c_h, s7)),
% 294.73/187.24 inference(modus_ponens,[status(thm)],[27527, 27526])).
% 294.73/187.24 tff(27529,plain,
% 294.73/187.24 ((~m_c_h_element_v_in1(c_e_h_2, c_h, s7)) | (~node17(c_e_h_2, c_h, s7))),
% 294.73/187.24 inference(unit_resolution,[status(thm)],[27528, 919, 27522])).
% 294.73/187.24 tff(27530,plain,
% 294.73/187.24 ($false),
% 294.73/187.24 inference(unit_resolution,[status(thm)],[27529, 27229, 27267])).
% 294.73/187.24 tff(27531,plain,((~m_c_h_element_v_out(c_e_h_2, c_h, s8)) | m_c_h_element_v_out(c_e_h_2, c_h, s7)), inference(lemma,lemma(discharge,[]))).
% 294.73/187.24 tff(27532,plain,
% 294.73/187.24 (~m_c_h_element_v_out(c_e_h_2, c_h, s8)),
% 294.73/187.24 inference(unit_resolution,[status(thm)],[27531, 27205])).
% 294.73/187.24 tff(27533,plain,
% 294.73/187.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_h, s8) | (~m_c_h_element_v_out(c_e_h_2, c_h, s9)) | (~node18(c_e_h_2, c_h, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s8) | (~m_c_h_element_v_out(c_e_h_2, c_h, s9)) | (~node18(c_e_h_2, c_h, s8, s9)))),
% 294.73/187.24 inference(rewrite,[status(thm)],[])).
% 294.73/187.24 tff(27534,plain,
% 294.73/187.24 (((~m_c_h_element_v_out(c_e_h_2, c_h, s9)) | m_c_h_element_v_out(c_e_h_2, c_h, s8) | (~node18(c_e_h_2, c_h, s8, s9))) <=> (m_c_h_element_v_out(c_e_h_2, c_h, s8) | (~m_c_h_element_v_out(c_e_h_2, c_h, s9)) | (~node18(c_e_h_2, c_h, s8, s9)))),
% 294.73/187.24 inference(rewrite,[status(thm)],[])).
% 294.73/187.24 tff(27535,plain,
% 294.73/187.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s9)) | m_c_h_element_v_out(c_e_h_2, c_h, s8) | (~node18(c_e_h_2, c_h, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_h, s8) | (~m_c_h_element_v_out(c_e_h_2, c_h, s9)) | (~node18(c_e_h_2, c_h, s8, s9))))),
% 294.73/187.24 inference(monotonicity,[status(thm)],[27534])).
% 294.73/187.24 tff(27536,plain,
% 294.73/187.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s9)) | m_c_h_element_v_out(c_e_h_2, c_h, s8) | (~node18(c_e_h_2, c_h, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s8) | (~m_c_h_element_v_out(c_e_h_2, c_h, s9)) | (~node18(c_e_h_2, c_h, s8, s9)))),
% 294.73/187.24 inference(transitivity,[status(thm)],[27535, 27533])).
% 294.73/187.24 tff(27537,plain,
% 294.73/187.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s9)) | m_c_h_element_v_out(c_e_h_2, c_h, s8) | (~node18(c_e_h_2, c_h, s8, s9)))),
% 294.73/187.24 inference(quant_inst,[status(thm)],[])).
% 294.73/187.24 tff(27538,plain,
% 294.73/187.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_h, s8) | (~m_c_h_element_v_out(c_e_h_2, c_h, s9)) | (~node18(c_e_h_2, c_h, s8, s9))),
% 294.73/187.24 inference(modus_ponens,[status(thm)],[27537, 27536])).
% 294.73/187.24 tff(27539,plain,
% 294.73/187.24 ($false),
% 294.73/187.24 inference(unit_resolution,[status(thm)],[27538, 753, 27532, 26895, 26897])).
% 294.73/187.24 tff(27540,plain,((~node18(c_e_h_2, c_h, s8, s9)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s9))), inference(lemma,lemma(discharge,[]))).
% 294.73/187.24 tff(27541,plain,
% 294.73/187.24 (~node18(c_e_h_2, c_h, s8, s9)),
% 294.73/187.24 inference(unit_resolution,[status(thm)],[27540, 26895])).
% 294.73/187.24 tff(27542,plain,
% 294.73/187.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s8, s9)) | node19(c_e_h_2, c_h, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s8, s9)) | node19(c_e_h_2, c_h, s8, s9))),
% 294.73/187.24 inference(rewrite,[status(thm)],[])).
% 294.73/187.24 tff(27543,plain,
% 294.73/187.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s8, s9)) | node19(c_e_h_2, c_h, s8, s9))),
% 294.73/187.24 inference(quant_inst,[status(thm)],[])).
% 294.73/187.24 tff(27544,plain,
% 294.73/187.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s8, s9)) | node19(c_e_h_2, c_h, s8, s9)),
% 294.73/187.24 inference(modus_ponens,[status(thm)],[27543, 27542])).
% 294.73/187.24 tff(27545,plain,
% 294.73/187.24 (node19(c_e_h_2, c_h, s8, s9)),
% 294.73/187.24 inference(unit_resolution,[status(thm)],[27544, 190, 1993])).
% 294.73/187.24 tff(27546,plain,
% 294.73/187.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s8) | node18(c_e_h_2, c_h, s8, s9) | (~node19(c_e_h_2, c_h, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_h, s8) | node18(c_e_h_2, c_h, s8, s9) | (~node19(c_e_h_2, c_h, s8, s9)))),
% 294.73/187.24 inference(rewrite,[status(thm)],[])).
% 294.73/187.24 tff(27547,plain,
% 294.73/187.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_h, s8) | node18(c_e_h_2, c_h, s8, s9) | (~node19(c_e_h_2, c_h, s8, s9)))),
% 294.73/187.24 inference(quant_inst,[status(thm)],[])).
% 294.73/187.24 tff(27548,plain,
% 294.73/187.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_h, s8) | node18(c_e_h_2, c_h, s8, s9) | (~node19(c_e_h_2, c_h, s8, s9))),
% 294.73/187.24 inference(modus_ponens,[status(thm)],[27547, 27546])).
% 294.73/187.24 tff(27549,plain,
% 294.73/187.24 (node17(c_e_h_2, c_h, s8) | node18(c_e_h_2, c_h, s8, s9)),
% 294.73/187.24 inference(unit_resolution,[status(thm)],[27548, 776, 27545])).
% 294.73/187.24 tff(27550,plain,
% 294.73/187.24 (node17(c_e_h_2, c_h, s8)),
% 294.73/187.24 inference(unit_resolution,[status(thm)],[27549, 27541])).
% 294.73/187.24 tff(27551,plain,
% 294.73/187.24 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_h, s8)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s8)) | m_c_h_element_v_in1(c_e_h_2, c_h, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_h, s8)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s8)) | m_c_h_element_v_in1(c_e_h_2, c_h, s8))),
% 294.73/187.24 inference(rewrite,[status(thm)],[])).
% 294.73/187.24 tff(27552,plain,
% 294.73/187.24 ((m_c_h_element_v_in1(c_e_h_2, c_h, s8) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s8)) | (~node17(c_e_h_2, c_h, s8))) <=> ((~node17(c_e_h_2, c_h, s8)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s8)) | m_c_h_element_v_in1(c_e_h_2, c_h, s8))),
% 294.73/187.24 inference(rewrite,[status(thm)],[])).
% 294.73/187.24 tff(27553,plain,
% 294.73/187.24 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s8) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s8)) | (~node17(c_e_h_2, c_h, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_h, s8)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s8)) | m_c_h_element_v_in1(c_e_h_2, c_h, s8)))),
% 294.73/187.24 inference(monotonicity,[status(thm)],[27552])).
% 294.73/187.24 tff(27554,plain,
% 294.73/187.24 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s8) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s8)) | (~node17(c_e_h_2, c_h, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_h, s8)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s8)) | m_c_h_element_v_in1(c_e_h_2, c_h, s8))),
% 294.73/187.24 inference(transitivity,[status(thm)],[27553, 27551])).
% 294.73/187.24 tff(27555,plain,
% 294.73/187.24 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s8) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s8)) | (~node17(c_e_h_2, c_h, s8)))),
% 294.73/187.24 inference(quant_inst,[status(thm)],[])).
% 294.73/187.24 tff(27556,plain,
% 294.73/187.24 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_h, s8)) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s8)) | m_c_h_element_v_in1(c_e_h_2, c_h, s8)),
% 294.73/187.24 inference(modus_ponens,[status(thm)],[27555, 27554])).
% 294.73/187.24 tff(27557,plain,
% 294.73/187.24 ((~m_c_h_element_v_in2(c_e_h_2, c_h, s8)) | m_c_h_element_v_in1(c_e_h_2, c_h, s8)),
% 294.73/187.24 inference(unit_resolution,[status(thm)],[27556, 859, 27550])).
% 294.73/187.24 tff(27558,plain,
% 294.73/187.24 (~m_c_h_element_v_in2(c_e_h_2, c_h, s8)),
% 294.73/187.24 inference(unit_resolution,[status(thm)],[27557, 26896])).
% 294.73/187.24 tff(27559,assumption,(~node16(c_e_h_2, c_h, s8)), introduced(assumption)).
% 294.73/187.24 tff(27560,assumption,(node14(c_e_h_2, c_h, s8, s9)), introduced(assumption)).
% 294.73/187.24 tff(27561,plain,
% 294.73/187.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s8) | (~m_c_h_element_v_out(c_e_h_2, c_h, s9)) | (~node14(c_e_h_2, c_h, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s8) | (~m_c_h_element_v_out(c_e_h_2, c_h, s9)) | (~node14(c_e_h_2, c_h, s8, s9)))),
% 294.73/187.25 inference(rewrite,[status(thm)],[])).
% 294.73/187.25 tff(27562,plain,
% 294.73/187.25 (((~node14(c_e_h_2, c_h, s8, s9)) | m_c_h_element_v_in1(c_e_h_2, c_h, s8) | (~m_c_h_element_v_out(c_e_h_2, c_h, s9))) <=> (m_c_h_element_v_in1(c_e_h_2, c_h, s8) | (~m_c_h_element_v_out(c_e_h_2, c_h, s9)) | (~node14(c_e_h_2, c_h, s8, s9)))),
% 294.73/187.25 inference(rewrite,[status(thm)],[])).
% 294.73/187.25 tff(27563,plain,
% 294.73/187.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s8, s9)) | m_c_h_element_v_in1(c_e_h_2, c_h, s8) | (~m_c_h_element_v_out(c_e_h_2, c_h, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_h, s8) | (~m_c_h_element_v_out(c_e_h_2, c_h, s9)) | (~node14(c_e_h_2, c_h, s8, s9))))),
% 294.73/187.25 inference(monotonicity,[status(thm)],[27562])).
% 294.73/187.25 tff(27564,plain,
% 294.73/187.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s8, s9)) | m_c_h_element_v_in1(c_e_h_2, c_h, s8) | (~m_c_h_element_v_out(c_e_h_2, c_h, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s8) | (~m_c_h_element_v_out(c_e_h_2, c_h, s9)) | (~node14(c_e_h_2, c_h, s8, s9)))),
% 294.73/187.25 inference(transitivity,[status(thm)],[27563, 27561])).
% 294.73/187.25 tff(27565,plain,
% 294.73/187.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_h, s8, s9)) | m_c_h_element_v_in1(c_e_h_2, c_h, s8) | (~m_c_h_element_v_out(c_e_h_2, c_h, s9)))),
% 294.73/187.25 inference(quant_inst,[status(thm)],[])).
% 294.73/187.25 tff(27566,plain,
% 294.73/187.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_h, s8) | (~m_c_h_element_v_out(c_e_h_2, c_h, s9)) | (~node14(c_e_h_2, c_h, s8, s9))),
% 294.73/187.25 inference(modus_ponens,[status(thm)],[27565, 27564])).
% 294.73/187.25 tff(27567,plain,
% 294.73/187.25 ($false),
% 294.73/187.25 inference(unit_resolution,[status(thm)],[27566, 223, 26895, 27560, 26896])).
% 294.73/187.25 tff(27568,plain,((~node14(c_e_h_2, c_h, s8, s9)) | (~m_c_h_element_v_out(c_e_h_2, c_h, s9)) | m_c_h_element_v_in1(c_e_h_2, c_h, s8)), inference(lemma,lemma(discharge,[]))).
% 294.73/187.25 tff(27569,plain,
% 294.73/187.25 (~node14(c_e_h_2, c_h, s8, s9)),
% 294.73/187.25 inference(unit_resolution,[status(thm)],[27568, 26895, 26896])).
% 294.73/187.25 tff(27570,plain,
% 294.73/187.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s8) | node14(c_e_h_2, c_h, s8, s9) | (~node19(c_e_h_2, c_h, s8, s9)) | node15(c_e_h_2, c_h, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s8) | node14(c_e_h_2, c_h, s8, s9) | (~node19(c_e_h_2, c_h, s8, s9)) | node15(c_e_h_2, c_h, s8, s9))),
% 294.73/187.25 inference(rewrite,[status(thm)],[])).
% 294.73/187.25 tff(27571,plain,
% 294.73/187.25 ((node16(c_e_h_2, c_h, s8) | node14(c_e_h_2, c_h, s8, s9) | node15(c_e_h_2, c_h, s8, s9) | (~node19(c_e_h_2, c_h, s8, s9))) <=> (node16(c_e_h_2, c_h, s8) | node14(c_e_h_2, c_h, s8, s9) | (~node19(c_e_h_2, c_h, s8, s9)) | node15(c_e_h_2, c_h, s8, s9))),
% 294.73/187.25 inference(rewrite,[status(thm)],[])).
% 294.73/187.25 tff(27572,plain,
% 294.73/187.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s8) | node14(c_e_h_2, c_h, s8, s9) | node15(c_e_h_2, c_h, s8, s9) | (~node19(c_e_h_2, c_h, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s8) | node14(c_e_h_2, c_h, s8, s9) | (~node19(c_e_h_2, c_h, s8, s9)) | node15(c_e_h_2, c_h, s8, s9)))),
% 294.73/187.25 inference(monotonicity,[status(thm)],[27571])).
% 294.73/187.25 tff(27573,plain,
% 294.73/187.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s8) | node14(c_e_h_2, c_h, s8, s9) | node15(c_e_h_2, c_h, s8, s9) | (~node19(c_e_h_2, c_h, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s8) | node14(c_e_h_2, c_h, s8, s9) | (~node19(c_e_h_2, c_h, s8, s9)) | node15(c_e_h_2, c_h, s8, s9))),
% 294.73/187.25 inference(transitivity,[status(thm)],[27572, 27570])).
% 294.73/187.25 tff(27574,plain,
% 294.73/187.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_h, s8) | node14(c_e_h_2, c_h, s8, s9) | node15(c_e_h_2, c_h, s8, s9) | (~node19(c_e_h_2, c_h, s8, s9)))),
% 294.73/187.25 inference(quant_inst,[status(thm)],[])).
% 294.73/187.25 tff(27575,plain,
% 294.73/187.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_h, s8) | node14(c_e_h_2, c_h, s8, s9) | (~node19(c_e_h_2, c_h, s8, s9)) | node15(c_e_h_2, c_h, s8, s9)),
% 294.73/187.25 inference(modus_ponens,[status(thm)],[27574, 27573])).
% 294.73/187.25 tff(27576,plain,
% 294.73/187.25 (node16(c_e_h_2, c_h, s8) | node14(c_e_h_2, c_h, s8, s9) | node15(c_e_h_2, c_h, s8, s9)),
% 294.73/187.25 inference(unit_resolution,[status(thm)],[27575, 204, 27545])).
% 294.73/187.25 tff(27577,plain,
% 294.73/187.25 (node15(c_e_h_2, c_h, s8, s9)),
% 294.73/187.25 inference(unit_resolution,[status(thm)],[27576, 27569, 27559])).
% 294.73/187.25 tff(27578,assumption,(~m_c_h_element_v_out(c_e_h_2, c_h, s8)), introduced(assumption)).
% 294.73/187.25 tff(27579,plain,
% 294.73/187.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s9)) | (~node15(c_e_h_2, c_h, s8, s9)) | m_c_h_element_v_out(c_e_h_2, c_h, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s9)) | (~node15(c_e_h_2, c_h, s8, s9)) | m_c_h_element_v_out(c_e_h_2, c_h, s8))),
% 294.73/187.25 inference(rewrite,[status(thm)],[])).
% 294.73/187.25 tff(27580,plain,
% 294.73/187.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_h, s9)) | (~node15(c_e_h_2, c_h, s8, s9)) | m_c_h_element_v_out(c_e_h_2, c_h, s8))),
% 294.73/187.25 inference(quant_inst,[status(thm)],[])).
% 294.73/187.25 tff(27581,plain,
% 294.73/187.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_h, s9)) | (~node15(c_e_h_2, c_h, s8, s9)) | m_c_h_element_v_out(c_e_h_2, c_h, s8)),
% 294.73/187.25 inference(modus_ponens,[status(thm)],[27580, 27579])).
% 294.73/187.25 tff(27582,plain,
% 294.73/187.25 ($false),
% 294.73/187.25 inference(unit_resolution,[status(thm)],[27581, 147, 27578, 26895, 27577])).
% 294.73/187.25 tff(27583,plain,((~m_c_h_element_v_out(c_e_h_2, c_h, s9)) | m_c_h_element_v_out(c_e_h_2, c_h, s8) | node16(c_e_h_2, c_h, s8) | m_c_h_element_v_in1(c_e_h_2, c_h, s8)), inference(lemma,lemma(discharge,[]))).
% 294.73/187.25 tff(27584,plain,
% 294.73/187.25 ((~m_c_h_element_v_out(c_e_h_2, c_h, s9)) | node16(c_e_h_2, c_h, s8) | m_c_h_element_v_in1(c_e_h_2, c_h, s8)),
% 294.73/187.25 inference(unit_resolution,[status(thm)],[27583, 27532])).
% 294.73/187.25 tff(27585,plain,
% 294.73/187.25 (node16(c_e_h_2, c_h, s8)),
% 294.73/187.25 inference(unit_resolution,[status(thm)],[27584, 26896, 26895])).
% 294.73/187.25 tff(27586,plain,
% 294.73/187.25 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_h, s8)) | m_c_h_element_v_in1(c_e_h_2, c_h, s8) | m_c_h_element_v_in2(c_e_h_2, c_h, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_h, s8)) | m_c_h_element_v_in1(c_e_h_2, c_h, s8) | m_c_h_element_v_in2(c_e_h_2, c_h, s8))),
% 294.73/187.25 inference(rewrite,[status(thm)],[])).
% 294.73/187.25 tff(27587,plain,
% 294.73/187.25 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_h, s8)) | m_c_h_element_v_in1(c_e_h_2, c_h, s8) | m_c_h_element_v_in2(c_e_h_2, c_h, s8))),
% 294.73/187.25 inference(quant_inst,[status(thm)],[])).
% 294.73/187.25 tff(27588,plain,
% 294.73/187.25 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_h, s8)) | m_c_h_element_v_in1(c_e_h_2, c_h, s8) | m_c_h_element_v_in2(c_e_h_2, c_h, s8)),
% 294.73/187.25 inference(modus_ponens,[status(thm)],[27587, 27586])).
% 294.73/187.25 tff(27589,plain,
% 294.73/187.25 ($false),
% 294.73/187.25 inference(unit_resolution,[status(thm)],[27588, 178, 27585, 26896, 27558])).
% 294.73/187.25 tff(27590,plain,(m_c_h_element_v_in1(c_e_h_2, c_h, s8) | (~m_c_h_element_v_out(c_e_h_2, c_h, s9))), inference(lemma,lemma(discharge,[]))).
% 294.73/187.25 tff(27591,plain,
% 294.73/187.25 (m_c_h_element_v_in1(c_e_h_2, c_h, s8)),
% 294.73/187.25 inference(unit_resolution,[status(thm)],[27590, 26895])).
% 294.73/187.25 tff(27592,assumption,(m_or_h_gate_v_in1(c_e_h_2, c_j, s7)), introduced(assumption)).
% 294.73/187.25 tff(27593,assumption,(m_and_h_gate_v_out(c_e_h_2, c_l, s7)), introduced(assumption)).
% 294.73/187.25 tff(27594,assumption,(node21(c_e_h_2, c_l, s6, s7)), introduced(assumption)).
% 294.73/187.25 tff(27595,assumption,(m_c_h_element_v_in2(c_e_h_2, c_e, s3)), introduced(assumption)).
% 294.73/187.25 tff(27596,plain,
% 294.73/187.25 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s3)) | m_and_h_gate_v_out(c_e_h_2, c_i, s3))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s3)) | m_and_h_gate_v_out(c_e_h_2, c_i, s3))),
% 294.73/187.25 inference(rewrite,[status(thm)],[])).
% 294.73/187.25 tff(27597,plain,
% 294.73/187.25 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s3)) | m_and_h_gate_v_out(c_e_h_2, c_i, s3))),
% 294.73/187.25 inference(quant_inst,[status(thm)],[])).
% 294.73/187.25 tff(27598,plain,
% 294.73/187.25 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s3)) | m_and_h_gate_v_out(c_e_h_2, c_i, s3)),
% 294.73/187.25 inference(modus_ponens,[status(thm)],[27597, 27596])).
% 294.73/187.25 tff(27599,plain,
% 294.73/187.25 ($false),
% 294.73/187.25 inference(unit_resolution,[status(thm)],[27598, 164, 27595, 4740])).
% 294.73/187.25 tff(27600,plain,((~m_c_h_element_v_in2(c_e_h_2, c_e, s3)) | m_and_h_gate_v_out(c_e_h_2, c_i, s3)), inference(lemma,lemma(discharge,[]))).
% 294.73/187.25 tff(27601,plain,
% 294.73/187.25 (~m_c_h_element_v_in2(c_e_h_2, c_e, s3)),
% 294.73/187.25 inference(unit_resolution,[status(thm)],[27600, 4257])).
% 294.73/187.25 tff(27602,plain,
% 294.73/187.25 ($false),
% 294.73/187.25 inference(unit_resolution,[status(thm)],[27292, 753, 26971, 27289, 27360])).
% 294.73/187.25 tff(27603,plain,((~node18(c_e_h_2, c_e, s2, s3)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s3))), inference(lemma,lemma(discharge,[]))).
% 294.73/187.25 tff(27604,plain,
% 294.73/187.25 (~node18(c_e_h_2, c_e, s2, s3)),
% 294.73/187.25 inference(unit_resolution,[status(thm)],[27603, 27360])).
% 294.73/187.25 tff(27605,plain,
% 294.73/187.25 ((~node17(c_e_h_2, c_e, s2)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s3))),
% 294.73/187.25 inference(unit_resolution,[status(thm)],[27425, 27286])).
% 294.73/187.25 tff(27606,plain,
% 294.73/187.25 (~node17(c_e_h_2, c_e, s2)),
% 294.73/187.25 inference(unit_resolution,[status(thm)],[27605, 27360])).
% 294.73/187.25 tff(27607,plain,
% 294.73/187.25 ($false),
% 294.73/187.25 inference(unit_resolution,[status(thm)],[27347, 27606, 27604])).
% 294.73/187.25 tff(27608,plain,(~m_c_h_element_v_out(c_e_h_2, c_e, s3)), inference(lemma,lemma(discharge,[]))).
% 294.73/187.25 tff(27609,assumption,(m_c_h_element_v_out(c_e_h_2, c_e, s4)), introduced(assumption)).
% 294.73/187.25 tff(27610,assumption,(node18(c_e_h_2, c_e, s3, s4)), introduced(assumption)).
% 294.73/187.25 tff(27611,plain,
% 294.73/187.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_e, s3) | (~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | (~node18(c_e_h_2, c_e, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_e, s3) | (~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | (~node18(c_e_h_2, c_e, s3, s4)))),
% 294.73/187.26 inference(rewrite,[status(thm)],[])).
% 294.73/187.26 tff(27612,plain,
% 294.73/187.26 (((~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | m_c_h_element_v_out(c_e_h_2, c_e, s3) | (~node18(c_e_h_2, c_e, s3, s4))) <=> (m_c_h_element_v_out(c_e_h_2, c_e, s3) | (~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | (~node18(c_e_h_2, c_e, s3, s4)))),
% 294.73/187.26 inference(rewrite,[status(thm)],[])).
% 294.73/187.26 tff(27613,plain,
% 294.73/187.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | m_c_h_element_v_out(c_e_h_2, c_e, s3) | (~node18(c_e_h_2, c_e, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_e, s3) | (~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | (~node18(c_e_h_2, c_e, s3, s4))))),
% 294.73/187.26 inference(monotonicity,[status(thm)],[27612])).
% 294.73/187.26 tff(27614,plain,
% 294.73/187.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | m_c_h_element_v_out(c_e_h_2, c_e, s3) | (~node18(c_e_h_2, c_e, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_e, s3) | (~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | (~node18(c_e_h_2, c_e, s3, s4)))),
% 294.73/187.26 inference(transitivity,[status(thm)],[27613, 27611])).
% 294.73/187.26 tff(27615,plain,
% 294.73/187.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | m_c_h_element_v_out(c_e_h_2, c_e, s3) | (~node18(c_e_h_2, c_e, s3, s4)))),
% 294.73/187.26 inference(quant_inst,[status(thm)],[])).
% 294.73/187.26 tff(27616,plain,
% 294.73/187.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_e, s3) | (~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | (~node18(c_e_h_2, c_e, s3, s4))),
% 294.73/187.26 inference(modus_ponens,[status(thm)],[27615, 27614])).
% 294.73/187.26 tff(27617,plain,
% 294.73/187.26 ($false),
% 294.73/187.26 inference(unit_resolution,[status(thm)],[27616, 753, 27610, 27609, 27356])).
% 294.73/187.26 tff(27618,plain,((~node18(c_e_h_2, c_e, s3, s4)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | m_c_h_element_v_out(c_e_h_2, c_e, s3)), inference(lemma,lemma(discharge,[]))).
% 294.73/187.26 tff(27619,plain,
% 294.73/187.26 (~node18(c_e_h_2, c_e, s3, s4)),
% 294.73/187.26 inference(unit_resolution,[status(thm)],[27618, 27609, 27356])).
% 294.73/187.26 tff(27620,assumption,(node15(c_e_h_2, c_e, s3, s4)), introduced(assumption)).
% 294.73/187.26 tff(27621,plain,
% 294.73/187.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | (~node15(c_e_h_2, c_e, s3, s4)) | m_c_h_element_v_out(c_e_h_2, c_e, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | (~node15(c_e_h_2, c_e, s3, s4)) | m_c_h_element_v_out(c_e_h_2, c_e, s3))),
% 294.73/187.26 inference(rewrite,[status(thm)],[])).
% 294.73/187.26 tff(27622,plain,
% 294.73/187.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | (~node15(c_e_h_2, c_e, s3, s4)) | m_c_h_element_v_out(c_e_h_2, c_e, s3))),
% 294.73/187.26 inference(quant_inst,[status(thm)],[])).
% 294.73/187.26 tff(27623,plain,
% 294.73/187.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | (~node15(c_e_h_2, c_e, s3, s4)) | m_c_h_element_v_out(c_e_h_2, c_e, s3)),
% 294.73/187.26 inference(modus_ponens,[status(thm)],[27622, 27621])).
% 294.73/187.26 tff(27624,plain,
% 294.73/187.26 ($false),
% 294.73/187.26 inference(unit_resolution,[status(thm)],[27623, 147, 27620, 27609, 27356])).
% 294.73/187.26 tff(27625,plain,((~node15(c_e_h_2, c_e, s3, s4)) | (~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | m_c_h_element_v_out(c_e_h_2, c_e, s3)), inference(lemma,lemma(discharge,[]))).
% 294.73/187.26 tff(27626,plain,
% 294.73/187.26 (~node15(c_e_h_2, c_e, s3, s4)),
% 294.73/187.26 inference(unit_resolution,[status(thm)],[27625, 27609, 27356])).
% 294.73/187.26 tff(27627,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_e, s3)), introduced(assumption)).
% 294.73/187.26 tff(27628,assumption,(~node15(c_e_h_2, c_e, s3, s4)), introduced(assumption)).
% 294.73/187.26 tff(27629,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_e, s3)), introduced(assumption)).
% 294.73/187.26 tff(27630,plain,
% 294.73/187.26 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_e, s3)) | m_c_h_element_v_in1(c_e_h_2, c_e, s3) | m_c_h_element_v_in2(c_e_h_2, c_e, s3))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s3)) | m_c_h_element_v_in1(c_e_h_2, c_e, s3) | m_c_h_element_v_in2(c_e_h_2, c_e, s3))),
% 294.73/187.26 inference(rewrite,[status(thm)],[])).
% 294.73/187.26 tff(27631,plain,
% 294.73/187.26 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_e, s3)) | m_c_h_element_v_in1(c_e_h_2, c_e, s3) | m_c_h_element_v_in2(c_e_h_2, c_e, s3))),
% 294.73/187.26 inference(quant_inst,[status(thm)],[])).
% 294.73/187.26 tff(27632,plain,
% 294.73/187.26 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s3)) | m_c_h_element_v_in1(c_e_h_2, c_e, s3) | m_c_h_element_v_in2(c_e_h_2, c_e, s3)),
% 294.73/187.26 inference(modus_ponens,[status(thm)],[27631, 27630])).
% 294.73/187.26 tff(27633,plain,
% 294.73/187.26 ((~node16(c_e_h_2, c_e, s3)) | m_c_h_element_v_in1(c_e_h_2, c_e, s3)),
% 294.73/187.26 inference(unit_resolution,[status(thm)],[27632, 178, 27627])).
% 294.73/187.26 tff(27634,plain,
% 294.73/187.26 (~node16(c_e_h_2, c_e, s3)),
% 294.73/187.26 inference(unit_resolution,[status(thm)],[27633, 27629])).
% 294.73/187.26 tff(27635,plain,
% 294.73/187.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s3, s4)) | node19(c_e_h_2, c_e, s3, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s3, s4)) | node19(c_e_h_2, c_e, s3, s4))),
% 294.73/187.26 inference(rewrite,[status(thm)],[])).
% 294.73/187.26 tff(27636,plain,
% 294.73/187.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s3, s4)) | node19(c_e_h_2, c_e, s3, s4))),
% 294.73/187.26 inference(quant_inst,[status(thm)],[])).
% 294.73/187.26 tff(27637,plain,
% 294.73/187.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s3, s4)) | node19(c_e_h_2, c_e, s3, s4)),
% 294.73/187.26 inference(modus_ponens,[status(thm)],[27636, 27635])).
% 294.73/187.26 tff(27638,plain,
% 294.73/187.26 (node19(c_e_h_2, c_e, s3, s4)),
% 294.73/187.26 inference(unit_resolution,[status(thm)],[27637, 190, 531])).
% 294.73/187.26 tff(27639,plain,
% 294.73/187.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_2, c_e, s3, s4) | node14(c_e_h_2, c_e, s3, s4) | (~node19(c_e_h_2, c_e, s3, s4)) | node16(c_e_h_2, c_e, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_2, c_e, s3, s4) | node14(c_e_h_2, c_e, s3, s4) | (~node19(c_e_h_2, c_e, s3, s4)) | node16(c_e_h_2, c_e, s3))),
% 294.73/187.26 inference(rewrite,[status(thm)],[])).
% 294.73/187.26 tff(27640,plain,
% 294.73/187.26 ((node16(c_e_h_2, c_e, s3) | node14(c_e_h_2, c_e, s3, s4) | node15(c_e_h_2, c_e, s3, s4) | (~node19(c_e_h_2, c_e, s3, s4))) <=> (node15(c_e_h_2, c_e, s3, s4) | node14(c_e_h_2, c_e, s3, s4) | (~node19(c_e_h_2, c_e, s3, s4)) | node16(c_e_h_2, c_e, s3))),
% 294.73/187.26 inference(rewrite,[status(thm)],[])).
% 294.73/187.26 tff(27641,plain,
% 294.73/187.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s3) | node14(c_e_h_2, c_e, s3, s4) | node15(c_e_h_2, c_e, s3, s4) | (~node19(c_e_h_2, c_e, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_2, c_e, s3, s4) | node14(c_e_h_2, c_e, s3, s4) | (~node19(c_e_h_2, c_e, s3, s4)) | node16(c_e_h_2, c_e, s3)))),
% 294.73/187.27 inference(monotonicity,[status(thm)],[27640])).
% 294.73/187.27 tff(27642,plain,
% 294.73/187.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s3) | node14(c_e_h_2, c_e, s3, s4) | node15(c_e_h_2, c_e, s3, s4) | (~node19(c_e_h_2, c_e, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_2, c_e, s3, s4) | node14(c_e_h_2, c_e, s3, s4) | (~node19(c_e_h_2, c_e, s3, s4)) | node16(c_e_h_2, c_e, s3))),
% 294.73/187.27 inference(transitivity,[status(thm)],[27641, 27639])).
% 294.73/187.27 tff(27643,plain,
% 294.73/187.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s3) | node14(c_e_h_2, c_e, s3, s4) | node15(c_e_h_2, c_e, s3, s4) | (~node19(c_e_h_2, c_e, s3, s4)))),
% 294.73/187.27 inference(quant_inst,[status(thm)],[])).
% 294.73/187.27 tff(27644,plain,
% 294.73/187.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_2, c_e, s3, s4) | node14(c_e_h_2, c_e, s3, s4) | (~node19(c_e_h_2, c_e, s3, s4)) | node16(c_e_h_2, c_e, s3)),
% 294.73/187.27 inference(modus_ponens,[status(thm)],[27643, 27642])).
% 294.73/187.27 tff(27645,plain,
% 294.73/187.27 (node15(c_e_h_2, c_e, s3, s4) | node14(c_e_h_2, c_e, s3, s4) | node16(c_e_h_2, c_e, s3)),
% 294.73/187.27 inference(unit_resolution,[status(thm)],[27644, 204, 27638])).
% 294.73/187.27 tff(27646,plain,
% 294.73/187.27 (node14(c_e_h_2, c_e, s3, s4)),
% 294.73/187.27 inference(unit_resolution,[status(thm)],[27645, 27634, 27628])).
% 294.73/187.27 tff(27647,plain,
% 294.73/187.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s3) | (~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | (~node14(c_e_h_2, c_e, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s3) | (~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | (~node14(c_e_h_2, c_e, s3, s4)))),
% 294.73/187.27 inference(rewrite,[status(thm)],[])).
% 294.73/187.27 tff(27648,plain,
% 294.73/187.27 (((~node14(c_e_h_2, c_e, s3, s4)) | m_c_h_element_v_in1(c_e_h_2, c_e, s3) | (~m_c_h_element_v_out(c_e_h_2, c_e, s4))) <=> (m_c_h_element_v_in1(c_e_h_2, c_e, s3) | (~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | (~node14(c_e_h_2, c_e, s3, s4)))),
% 294.73/187.27 inference(rewrite,[status(thm)],[])).
% 294.73/187.27 tff(27649,plain,
% 294.73/187.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s3, s4)) | m_c_h_element_v_in1(c_e_h_2, c_e, s3) | (~m_c_h_element_v_out(c_e_h_2, c_e, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s3) | (~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | (~node14(c_e_h_2, c_e, s3, s4))))),
% 294.73/187.27 inference(monotonicity,[status(thm)],[27648])).
% 294.73/187.27 tff(27650,plain,
% 294.73/187.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s3, s4)) | m_c_h_element_v_in1(c_e_h_2, c_e, s3) | (~m_c_h_element_v_out(c_e_h_2, c_e, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s3) | (~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | (~node14(c_e_h_2, c_e, s3, s4)))),
% 294.73/187.27 inference(transitivity,[status(thm)],[27649, 27647])).
% 294.73/187.27 tff(27651,plain,
% 294.73/187.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s3, s4)) | m_c_h_element_v_in1(c_e_h_2, c_e, s3) | (~m_c_h_element_v_out(c_e_h_2, c_e, s4)))),
% 294.73/187.27 inference(quant_inst,[status(thm)],[])).
% 294.73/187.27 tff(27652,plain,
% 294.73/187.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s3) | (~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | (~node14(c_e_h_2, c_e, s3, s4))),
% 294.73/187.27 inference(modus_ponens,[status(thm)],[27651, 27650])).
% 294.73/187.27 tff(27653,plain,
% 294.73/187.27 ($false),
% 294.73/187.27 inference(unit_resolution,[status(thm)],[27652, 223, 27646, 27609, 27629])).
% 294.73/187.27 tff(27654,plain,(m_c_h_element_v_in1(c_e_h_2, c_e, s3) | (~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | node15(c_e_h_2, c_e, s3, s4) | m_c_h_element_v_in2(c_e_h_2, c_e, s3)), inference(lemma,lemma(discharge,[]))).
% 294.73/187.27 tff(27655,plain,
% 294.73/187.27 (m_c_h_element_v_in1(c_e_h_2, c_e, s3)),
% 294.73/187.27 inference(unit_resolution,[status(thm)],[27654, 27627, 27628, 27609])).
% 294.73/187.27 tff(27656,assumption,(node17(c_e_h_2, c_e, s3)), introduced(assumption)).
% 294.73/187.27 tff(27657,plain,
% 294.73/187.27 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_e, s3)) | m_c_h_element_v_in2(c_e_h_2, c_e, s3) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_e, s3)) | m_c_h_element_v_in2(c_e_h_2, c_e, s3) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s3)))),
% 294.73/187.27 inference(rewrite,[status(thm)],[])).
% 294.73/187.27 tff(27658,plain,
% 294.73/187.27 (((~m_c_h_element_v_in1(c_e_h_2, c_e, s3)) | m_c_h_element_v_in2(c_e_h_2, c_e, s3) | (~node17(c_e_h_2, c_e, s3))) <=> ((~node17(c_e_h_2, c_e, s3)) | m_c_h_element_v_in2(c_e_h_2, c_e, s3) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s3)))),
% 294.73/187.27 inference(rewrite,[status(thm)],[])).
% 294.73/187.27 tff(27659,plain,
% 294.73/187.27 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s3)) | m_c_h_element_v_in2(c_e_h_2, c_e, s3) | (~node17(c_e_h_2, c_e, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_e, s3)) | m_c_h_element_v_in2(c_e_h_2, c_e, s3) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s3))))),
% 294.73/187.27 inference(monotonicity,[status(thm)],[27658])).
% 294.73/187.27 tff(27660,plain,
% 294.73/187.27 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s3)) | m_c_h_element_v_in2(c_e_h_2, c_e, s3) | (~node17(c_e_h_2, c_e, s3)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_e, s3)) | m_c_h_element_v_in2(c_e_h_2, c_e, s3) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s3)))),
% 294.73/187.27 inference(transitivity,[status(thm)],[27659, 27657])).
% 294.73/187.27 tff(27661,plain,
% 294.73/187.27 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s3)) | m_c_h_element_v_in2(c_e_h_2, c_e, s3) | (~node17(c_e_h_2, c_e, s3)))),
% 294.73/187.27 inference(quant_inst,[status(thm)],[])).
% 294.73/187.27 tff(27662,plain,
% 294.73/187.27 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_e, s3)) | m_c_h_element_v_in2(c_e_h_2, c_e, s3) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s3))),
% 294.73/187.27 inference(modus_ponens,[status(thm)],[27661, 27660])).
% 294.73/187.27 tff(27663,plain,
% 294.73/187.27 (m_c_h_element_v_in2(c_e_h_2, c_e, s3) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s3))),
% 294.73/187.27 inference(unit_resolution,[status(thm)],[27662, 919, 27656])).
% 294.73/187.27 tff(27664,plain,
% 294.73/187.27 ($false),
% 294.73/187.27 inference(unit_resolution,[status(thm)],[27663, 27655, 27627])).
% 294.73/187.27 tff(27665,plain,(m_c_h_element_v_in2(c_e_h_2, c_e, s3) | (~node17(c_e_h_2, c_e, s3)) | node15(c_e_h_2, c_e, s3, s4) | (~m_c_h_element_v_out(c_e_h_2, c_e, s4))), inference(lemma,lemma(discharge,[]))).
% 294.73/187.27 tff(27666,plain,
% 294.73/187.27 (~node17(c_e_h_2, c_e, s3)),
% 294.73/187.27 inference(unit_resolution,[status(thm)],[27665, 27609, 27627, 27626])).
% 294.73/187.27 tff(27667,plain,
% 294.73/187.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_2, c_e, s3, s4) | (~node19(c_e_h_2, c_e, s3, s4)) | node17(c_e_h_2, c_e, s3))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_2, c_e, s3, s4) | (~node19(c_e_h_2, c_e, s3, s4)) | node17(c_e_h_2, c_e, s3))),
% 294.73/187.27 inference(rewrite,[status(thm)],[])).
% 294.73/187.27 tff(27668,plain,
% 294.73/187.27 ((node17(c_e_h_2, c_e, s3) | node18(c_e_h_2, c_e, s3, s4) | (~node19(c_e_h_2, c_e, s3, s4))) <=> (node18(c_e_h_2, c_e, s3, s4) | (~node19(c_e_h_2, c_e, s3, s4)) | node17(c_e_h_2, c_e, s3))),
% 294.73/187.27 inference(rewrite,[status(thm)],[])).
% 294.73/187.27 tff(27669,plain,
% 294.73/187.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s3) | node18(c_e_h_2, c_e, s3, s4) | (~node19(c_e_h_2, c_e, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_2, c_e, s3, s4) | (~node19(c_e_h_2, c_e, s3, s4)) | node17(c_e_h_2, c_e, s3)))),
% 294.73/187.27 inference(monotonicity,[status(thm)],[27668])).
% 294.73/187.27 tff(27670,plain,
% 294.73/187.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s3) | node18(c_e_h_2, c_e, s3, s4) | (~node19(c_e_h_2, c_e, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_2, c_e, s3, s4) | (~node19(c_e_h_2, c_e, s3, s4)) | node17(c_e_h_2, c_e, s3))),
% 294.73/187.27 inference(transitivity,[status(thm)],[27669, 27667])).
% 294.73/187.27 tff(27671,plain,
% 294.73/187.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s3) | node18(c_e_h_2, c_e, s3, s4) | (~node19(c_e_h_2, c_e, s3, s4)))),
% 294.73/187.27 inference(quant_inst,[status(thm)],[])).
% 294.73/187.27 tff(27672,plain,
% 294.73/187.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_2, c_e, s3, s4) | (~node19(c_e_h_2, c_e, s3, s4)) | node17(c_e_h_2, c_e, s3)),
% 294.73/187.27 inference(modus_ponens,[status(thm)],[27671, 27670])).
% 294.73/187.27 tff(27673,plain,
% 294.73/187.27 (node18(c_e_h_2, c_e, s3, s4) | node17(c_e_h_2, c_e, s3)),
% 294.73/187.27 inference(unit_resolution,[status(thm)],[27672, 776, 27638])).
% 294.73/187.27 tff(27674,plain,
% 294.73/187.27 ($false),
% 294.73/187.27 inference(unit_resolution,[status(thm)],[27673, 27666, 27619])).
% 294.73/187.27 tff(27675,plain,((~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | m_c_h_element_v_in2(c_e_h_2, c_e, s3) | m_c_h_element_v_out(c_e_h_2, c_e, s3)), inference(lemma,lemma(discharge,[]))).
% 294.73/187.27 tff(27676,plain,
% 294.73/187.27 ((~m_c_h_element_v_out(c_e_h_2, c_e, s4)) | m_c_h_element_v_in2(c_e_h_2, c_e, s3)),
% 294.73/187.27 inference(unit_resolution,[status(thm)],[27675, 27608])).
% 294.73/187.27 tff(27677,plain,
% 294.73/187.27 (~m_c_h_element_v_out(c_e_h_2, c_e, s4)),
% 294.73/187.27 inference(unit_resolution,[status(thm)],[27676, 27601])).
% 294.73/187.27 tff(27678,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s4)), introduced(assumption)).
% 294.73/187.27 tff(27679,assumption,(~m_c_h_element_v_out(c_e_h_2, c_e, s4)), introduced(assumption)).
% 294.73/187.27 tff(27680,plain,
% 294.73/187.27 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s4) | m_c_h_element_v_out(c_e_h_2, c_e, s4))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s4) | m_c_h_element_v_out(c_e_h_2, c_e, s4))),
% 294.73/187.27 inference(rewrite,[status(thm)],[])).
% 294.73/187.27 tff(27681,plain,
% 294.73/187.27 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s4) | m_c_h_element_v_out(c_e_h_2, c_e, s4))),
% 294.73/187.27 inference(quant_inst,[status(thm)],[])).
% 294.73/187.28 tff(27682,plain,
% 294.73/187.28 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s4) | m_c_h_element_v_out(c_e_h_2, c_e, s4)),
% 294.73/187.28 inference(modus_ponens,[status(thm)],[27681, 27680])).
% 294.73/187.28 tff(27683,plain,
% 294.73/187.28 ($false),
% 294.73/187.28 inference(unit_resolution,[status(thm)],[27682, 7856, 27679, 27678])).
% 294.73/187.28 tff(27684,plain,(m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s4) | m_c_h_element_v_out(c_e_h_2, c_e, s4)), inference(lemma,lemma(discharge,[]))).
% 294.73/187.28 tff(27685,plain,
% 294.73/187.28 (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s4)),
% 294.73/187.28 inference(unit_resolution,[status(thm)],[27684, 27677])).
% 294.73/187.28 tff(27686,plain,
% 294.73/187.28 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s4) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s4) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4))),
% 294.73/187.28 inference(rewrite,[status(thm)],[])).
% 294.73/187.28 tff(27687,plain,
% 294.73/187.28 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s4) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4))),
% 294.73/187.28 inference(quant_inst,[status(thm)],[])).
% 294.73/187.28 tff(27688,plain,
% 294.73/187.28 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s4) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)),
% 294.73/187.28 inference(modus_ponens,[status(thm)],[27687, 27686])).
% 294.73/187.28 tff(27689,plain,
% 294.73/187.28 (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s4) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s4)),
% 294.73/187.28 inference(unit_resolution,[status(thm)],[27688, 7868])).
% 294.73/187.28 tff(27690,plain,
% 294.73/187.28 (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s4)),
% 294.73/187.28 inference(unit_resolution,[status(thm)],[27689, 27045])).
% 294.73/187.28 tff(27691,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s4)), introduced(assumption)).
% 294.73/187.28 tff(27692,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s4)), introduced(assumption)).
% 294.73/187.28 tff(27693,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5)), introduced(assumption)).
% 294.73/187.28 tff(27694,assumption,(node10(c_e_h_2, c_n, s4, s5)), introduced(assumption)).
% 294.73/187.28 tff(27695,plain,
% 294.73/187.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s4)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s4)) | (~node10(c_e_h_2, c_n, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s4)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s4)) | (~node10(c_e_h_2, c_n, s4, s5)))),
% 294.73/187.28 inference(rewrite,[status(thm)],[])).
% 294.73/187.28 tff(27696,plain,
% 294.73/187.28 (((~node10(c_e_h_2, c_n, s4, s5)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s4)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5)) <=> ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s4)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s4)) | (~node10(c_e_h_2, c_n, s4, s5)))),
% 294.73/187.28 inference(rewrite,[status(thm)],[])).
% 294.73/187.28 tff(27697,plain,
% 294.73/187.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s4, s5)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s4)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s4)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s4)) | (~node10(c_e_h_2, c_n, s4, s5))))),
% 294.73/187.28 inference(monotonicity,[status(thm)],[27696])).
% 294.73/187.28 tff(27698,plain,
% 294.73/187.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s4, s5)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s4)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s4)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s4)) | (~node10(c_e_h_2, c_n, s4, s5)))),
% 294.73/187.28 inference(transitivity,[status(thm)],[27697, 27695])).
% 294.73/187.28 tff(27699,plain,
% 294.73/187.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s4, s5)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s4)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5))),
% 294.73/187.28 inference(quant_inst,[status(thm)],[])).
% 294.73/187.28 tff(27700,plain,
% 294.73/187.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s4)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s4)) | (~node10(c_e_h_2, c_n, s4, s5))),
% 294.73/187.28 inference(modus_ponens,[status(thm)],[27699, 27698])).
% 294.73/187.28 tff(27701,plain,
% 294.73/187.28 ($false),
% 294.73/187.28 inference(unit_resolution,[status(thm)],[27700, 5718, 27691, 27693, 27694, 27692])).
% 294.73/187.28 tff(27702,plain,((~node10(c_e_h_2, c_n, s4, s5)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s4)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s4))), inference(lemma,lemma(discharge,[]))).
% 294.73/187.28 tff(27703,plain,
% 294.73/187.28 (~node10(c_e_h_2, c_n, s4, s5)),
% 294.73/187.28 inference(unit_resolution,[status(thm)],[27702, 27693, 27692, 27691])).
% 294.73/187.28 tff(27704,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4)), introduced(assumption)).
% 294.73/187.28 tff(27705,assumption,(node11(c_e_h_2, c_n, s4, s5)), introduced(assumption)).
% 294.73/187.28 tff(27706,plain,
% 294.73/187.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5) | (~node11(c_e_h_2, c_n, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5) | (~node11(c_e_h_2, c_n, s4, s5)))),
% 294.73/187.28 inference(rewrite,[status(thm)],[])).
% 294.73/187.28 tff(27707,plain,
% 294.73/187.28 ((m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5) | (~node11(c_e_h_2, c_n, s4, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5) | (~node11(c_e_h_2, c_n, s4, s5)))),
% 294.73/187.28 inference(rewrite,[status(thm)],[])).
% 294.73/187.28 tff(27708,plain,
% 294.73/187.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5) | (~node11(c_e_h_2, c_n, s4, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5) | (~node11(c_e_h_2, c_n, s4, s5))))),
% 294.73/187.28 inference(monotonicity,[status(thm)],[27707])).
% 294.73/187.28 tff(27709,plain,
% 294.73/187.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5) | (~node11(c_e_h_2, c_n, s4, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5) | (~node11(c_e_h_2, c_n, s4, s5)))),
% 294.73/187.28 inference(transitivity,[status(thm)],[27708, 27706])).
% 294.73/187.28 tff(27710,plain,
% 294.73/187.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5) | (~node11(c_e_h_2, c_n, s4, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4)))),
% 294.73/187.28 inference(quant_inst,[status(thm)],[])).
% 294.73/187.28 tff(27711,plain,
% 294.73/187.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5) | (~node11(c_e_h_2, c_n, s4, s5))),
% 294.73/187.28 inference(modus_ponens,[status(thm)],[27710, 27709])).
% 294.73/187.28 tff(27712,plain,
% 294.73/187.28 ($false),
% 294.73/187.28 inference(unit_resolution,[status(thm)],[27711, 5742, 27704, 27693, 27705])).
% 294.73/187.28 tff(27713,plain,((~node11(c_e_h_2, c_n, s4, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5)), inference(lemma,lemma(discharge,[]))).
% 294.73/187.28 tff(27714,plain,
% 294.73/187.28 (~node11(c_e_h_2, c_n, s4, s5)),
% 294.73/187.28 inference(unit_resolution,[status(thm)],[27713, 27693, 27704])).
% 294.73/187.28 tff(27715,plain,
% 294.73/187.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s4, s5)) | node10(c_e_h_2, c_n, s4, s5) | node11(c_e_h_2, c_n, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s4, s5)) | node10(c_e_h_2, c_n, s4, s5) | node11(c_e_h_2, c_n, s4, s5))),
% 294.73/187.28 inference(rewrite,[status(thm)],[])).
% 294.73/187.28 tff(27716,plain,
% 294.73/187.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s4, s5)) | node10(c_e_h_2, c_n, s4, s5) | node11(c_e_h_2, c_n, s4, s5))),
% 294.73/187.28 inference(quant_inst,[status(thm)],[])).
% 294.73/187.28 tff(27717,plain,
% 294.73/187.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s4, s5)) | node10(c_e_h_2, c_n, s4, s5) | node11(c_e_h_2, c_n, s4, s5)),
% 294.73/187.28 inference(modus_ponens,[status(thm)],[27716, 27715])).
% 294.73/187.28 tff(27718,plain,
% 294.73/187.28 (node10(c_e_h_2, c_n, s4, s5) | node11(c_e_h_2, c_n, s4, s5)),
% 294.73/187.28 inference(unit_resolution,[status(thm)],[27717, 5002, 1028])).
% 294.73/187.28 tff(27719,plain,
% 294.73/187.28 ($false),
% 294.73/187.28 inference(unit_resolution,[status(thm)],[27718, 27714, 27703])).
% 294.73/187.28 tff(27720,plain,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s4)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s4))), inference(lemma,lemma(discharge,[]))).
% 294.73/187.28 tff(27721,plain,
% 294.73/187.28 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s4)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s4))),
% 294.73/187.28 inference(unit_resolution,[status(thm)],[27720, 27690])).
% 294.73/187.28 tff(27722,plain,
% 294.73/187.28 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s4))),
% 294.73/187.28 inference(unit_resolution,[status(thm)],[27721, 27427])).
% 294.73/187.28 tff(27723,plain,
% 294.73/187.28 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5)),
% 294.73/187.28 inference(unit_resolution,[status(thm)],[27722, 27685])).
% 294.73/187.28 tff(27724,plain,
% 294.73/187.28 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5)))),
% 294.73/187.29 inference(rewrite,[status(thm)],[])).
% 294.73/187.29 tff(27725,plain,
% 294.73/187.29 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5)))),
% 294.73/187.29 inference(quant_inst,[status(thm)],[])).
% 294.73/187.29 tff(27726,plain,
% 294.73/187.29 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5))),
% 294.73/187.29 inference(modus_ponens,[status(thm)],[27725, 27724])).
% 294.73/187.29 tff(27727,plain,
% 294.73/187.29 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s5)),
% 294.73/187.29 inference(unit_resolution,[status(thm)],[27726, 4958, 27723])).
% 294.73/187.29 tff(27728,plain,
% 294.73/187.29 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s5)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s5))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s5)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s5))),
% 294.73/187.29 inference(rewrite,[status(thm)],[])).
% 294.73/187.29 tff(27729,plain,
% 294.73/187.29 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s5)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s5))),
% 294.73/187.29 inference(quant_inst,[status(thm)],[])).
% 294.73/187.29 tff(27730,plain,
% 294.73/187.29 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s5)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s5)),
% 294.73/187.29 inference(modus_ponens,[status(thm)],[27729, 27728])).
% 294.73/187.29 tff(27731,plain,
% 294.73/187.29 (~node9(c_e_h_2, c_m, s5)),
% 294.73/187.29 inference(unit_resolution,[status(thm)],[27730, 4972, 27727])).
% 294.73/187.29 tff(27732,assumption,(~node9(c_e_h_2, c_m, s5)), introduced(assumption)).
% 294.73/187.29 tff(27733,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)), introduced(assumption)).
% 294.73/187.29 tff(27734,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)), introduced(assumption)).
% 294.73/187.29 tff(27735,assumption,(node11(c_e_h_2, c_m, s5, s6)), introduced(assumption)).
% 294.73/187.29 tff(27736,plain,
% 294.73/187.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)) | (~node11(c_e_h_2, c_m, s5, s6)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)) | (~node11(c_e_h_2, c_m, s5, s6)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5))),
% 294.73/187.29 inference(rewrite,[status(thm)],[])).
% 294.73/187.29 tff(27737,plain,
% 294.73/187.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)) | (~node11(c_e_h_2, c_m, s5, s6)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5))),
% 294.73/187.29 inference(quant_inst,[status(thm)],[])).
% 294.73/187.29 tff(27738,plain,
% 294.73/187.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)) | (~node11(c_e_h_2, c_m, s5, s6)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)),
% 294.73/187.29 inference(modus_ponens,[status(thm)],[27737, 27736])).
% 294.73/187.29 tff(27739,plain,
% 294.73/187.29 ($false),
% 294.73/187.29 inference(unit_resolution,[status(thm)],[27738, 5017, 27733, 27734, 27735])).
% 294.73/187.29 tff(27740,plain,((~node11(c_e_h_2, c_m, s5, s6)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6))), inference(lemma,lemma(discharge,[]))).
% 294.73/187.29 tff(27741,plain,
% 294.73/187.29 (~node11(c_e_h_2, c_m, s5, s6)),
% 294.73/187.29 inference(unit_resolution,[status(thm)],[27740, 27734, 27733])).
% 294.73/187.29 tff(27742,plain,
% 294.73/187.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s5, s6)) | node10(c_e_h_2, c_m, s5, s6) | node11(c_e_h_2, c_m, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s5, s6)) | node10(c_e_h_2, c_m, s5, s6) | node11(c_e_h_2, c_m, s5, s6))),
% 294.73/187.29 inference(rewrite,[status(thm)],[])).
% 294.73/187.29 tff(27743,plain,
% 294.73/187.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s5, s6)) | node10(c_e_h_2, c_m, s5, s6) | node11(c_e_h_2, c_m, s5, s6))),
% 294.73/187.29 inference(quant_inst,[status(thm)],[])).
% 294.73/187.29 tff(27744,plain,
% 294.73/187.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s5, s6)) | node10(c_e_h_2, c_m, s5, s6) | node11(c_e_h_2, c_m, s5, s6)),
% 294.73/187.29 inference(modus_ponens,[status(thm)],[27743, 27742])).
% 294.73/187.29 tff(27745,plain,
% 294.73/187.29 (node10(c_e_h_2, c_m, s5, s6) | node11(c_e_h_2, c_m, s5, s6)),
% 294.73/187.29 inference(unit_resolution,[status(thm)],[27744, 5002, 1406])).
% 294.73/187.29 tff(27746,plain,
% 294.73/187.29 (node10(c_e_h_2, c_m, s5, s6)),
% 294.73/187.29 inference(unit_resolution,[status(thm)],[27745, 27741])).
% 294.73/187.29 tff(27747,plain,
% 294.73/187.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)) | (~node10(c_e_h_2, c_m, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_2, c_m, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)) | (~node10(c_e_h_2, c_m, s5, s6)))),
% 294.73/187.29 inference(rewrite,[status(thm)],[])).
% 294.73/187.29 tff(27748,plain,
% 294.73/187.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_2, c_m, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)) | (~node10(c_e_h_2, c_m, s5, s6)))),
% 294.73/187.29 inference(quant_inst,[status(thm)],[])).
% 294.73/187.29 tff(27749,plain,
% 294.73/187.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_2, c_m, s5) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)) | (~node10(c_e_h_2, c_m, s5, s6))),
% 294.73/187.29 inference(modus_ponens,[status(thm)],[27748, 27747])).
% 294.73/187.29 tff(27750,plain,
% 294.73/187.29 ($false),
% 294.73/187.29 inference(unit_resolution,[status(thm)],[27749, 4986, 27734, 27746, 27732])).
% 294.73/187.29 tff(27751,plain,((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)) | node9(c_e_h_2, c_m, s5) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)), inference(lemma,lemma(discharge,[]))).
% 294.73/187.29 tff(27752,plain,
% 294.73/187.29 ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)) | node9(c_e_h_2, c_m, s5)),
% 294.73/187.29 inference(unit_resolution,[status(thm)],[27751, 27457])).
% 294.73/187.29 tff(27753,plain,
% 294.73/187.29 (~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)),
% 294.73/187.29 inference(unit_resolution,[status(thm)],[27752, 27731])).
% 294.73/187.29 tff(27754,plain,
% 294.73/187.29 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_l, s6)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_l, s6)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6))),
% 294.73/187.29 inference(rewrite,[status(thm)],[])).
% 294.73/187.29 tff(27755,plain,
% 294.73/187.29 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_2, c_l, s6)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6))),
% 294.73/187.29 inference(quant_inst,[status(thm)],[])).
% 294.73/187.29 tff(27756,plain,
% 294.73/187.29 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_2, c_l, s6)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)),
% 294.73/187.29 inference(modus_ponens,[status(thm)],[27755, 27754])).
% 294.73/187.29 tff(27757,plain,
% 294.73/187.29 (~m_and_h_gate_v_in2(c_e_h_2, c_l, s6)),
% 294.73/187.29 inference(unit_resolution,[status(thm)],[27756, 4549, 27753])).
% 294.73/187.29 tff(27758,plain,
% 294.73/187.29 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_l, s6)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_l, s6)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s6))),
% 294.73/187.29 inference(rewrite,[status(thm)],[])).
% 294.73/187.29 tff(27759,plain,
% 294.73/187.29 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_2, c_l, s6)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s6))),
% 294.73/187.29 inference(quant_inst,[status(thm)],[])).
% 294.73/187.29 tff(27760,plain,
% 294.73/187.29 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_2, c_l, s6)) | m_and_h_gate_v_in2(c_e_h_2, c_l, s6)),
% 294.73/187.29 inference(modus_ponens,[status(thm)],[27759, 27758])).
% 294.73/187.29 tff(27761,plain,
% 294.73/187.29 (~node20(c_e_h_2, c_l, s6)),
% 294.73/187.29 inference(unit_resolution,[status(thm)],[27760, 4563, 27757])).
% 294.73/187.29 tff(27762,plain,
% 294.73/187.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_l, s6) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s7)) | (~node21(c_e_h_2, c_l, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_l, s6) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s7)) | (~node21(c_e_h_2, c_l, s6, s7)))),
% 294.73/187.29 inference(rewrite,[status(thm)],[])).
% 294.73/187.29 tff(27763,plain,
% 294.73/187.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_l, s6) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s7)) | (~node21(c_e_h_2, c_l, s6, s7)))),
% 294.73/187.29 inference(quant_inst,[status(thm)],[])).
% 294.73/187.29 tff(27764,plain,
% 294.73/187.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_l, s6) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s7)) | (~node21(c_e_h_2, c_l, s6, s7))),
% 294.73/187.29 inference(modus_ponens,[status(thm)],[27763, 27762])).
% 294.73/187.29 tff(27765,plain,
% 294.73/187.29 ($false),
% 294.73/187.29 inference(unit_resolution,[status(thm)],[27764, 52, 27761, 27594, 27593])).
% 294.73/187.29 tff(27766,plain,((~node21(c_e_h_2, c_l, s6, s7)) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s7))), inference(lemma,lemma(discharge,[]))).
% 294.73/187.29 tff(27767,plain,
% 294.73/187.29 (~node21(c_e_h_2, c_l, s6, s7)),
% 294.73/187.29 inference(unit_resolution,[status(thm)],[27766, 27593])).
% 294.73/187.29 tff(27768,plain,
% 294.73/187.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_2, c_l, s6, s7) | node22(c_e_h_2, c_l, s6, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_2, c_l, s6, s7) | node22(c_e_h_2, c_l, s6, s7))),
% 294.73/187.29 inference(rewrite,[status(thm)],[])).
% 294.73/187.29 tff(27769,plain,
% 294.73/187.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s6, s7)) | node21(c_e_h_2, c_l, s6, s7) | node22(c_e_h_2, c_l, s6, s7))),
% 294.73/187.29 inference(quant_inst,[status(thm)],[])).
% 294.73/187.29 tff(27770,plain,
% 294.73/187.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s6, s7)) | node21(c_e_h_2, c_l, s6, s7) | node22(c_e_h_2, c_l, s6, s7)),
% 294.73/187.29 inference(modus_ponens,[status(thm)],[27769, 27768])).
% 294.73/187.29 tff(27771,plain,
% 294.73/187.29 (node21(c_e_h_2, c_l, s6, s7) | node22(c_e_h_2, c_l, s6, s7)),
% 294.73/187.29 inference(unit_resolution,[status(thm)],[27770, 82, 1844])).
% 294.73/187.29 tff(27772,plain,
% 294.73/187.29 (node22(c_e_h_2, c_l, s6, s7)),
% 294.73/187.29 inference(unit_resolution,[status(thm)],[27771, 27767])).
% 294.73/187.29 tff(27773,plain,
% 294.73/187.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s7)) | (~node22(c_e_h_2, c_l, s6, s7)) | m_and_h_gate_v_out(c_e_h_2, c_l, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s7)) | (~node22(c_e_h_2, c_l, s6, s7)) | m_and_h_gate_v_out(c_e_h_2, c_l, s6))),
% 294.73/187.30 inference(rewrite,[status(thm)],[])).
% 294.73/187.30 tff(27774,plain,
% 294.73/187.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_l, s7)) | (~node22(c_e_h_2, c_l, s6, s7)) | m_and_h_gate_v_out(c_e_h_2, c_l, s6))),
% 294.73/187.30 inference(quant_inst,[status(thm)],[])).
% 294.73/187.30 tff(27775,plain,
% 294.73/187.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_l, s7)) | (~node22(c_e_h_2, c_l, s6, s7)) | m_and_h_gate_v_out(c_e_h_2, c_l, s6)),
% 294.73/187.30 inference(modus_ponens,[status(thm)],[27774, 27773])).
% 294.73/187.30 tff(27776,plain,
% 294.73/187.30 ($false),
% 294.73/187.30 inference(unit_resolution,[status(thm)],[27775, 108, 27772, 27484, 27593])).
% 294.73/187.30 tff(27777,plain,((~m_and_h_gate_v_out(c_e_h_2, c_l, s7)) | m_and_h_gate_v_out(c_e_h_2, c_l, s6)), inference(lemma,lemma(discharge,[]))).
% 294.73/187.30 tff(27778,plain,
% 294.73/187.30 (~m_and_h_gate_v_out(c_e_h_2, c_l, s7)),
% 294.73/187.30 inference(unit_resolution,[status(thm)],[27777, 27483])).
% 294.73/187.30 tff(27779,plain,
% 294.73/187.30 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_2, c_j, s7)) | m_and_h_gate_v_out(c_e_h_2, c_l, s7))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_j, s7)) | m_and_h_gate_v_out(c_e_h_2, c_l, s7))),
% 294.73/187.30 inference(rewrite,[status(thm)],[])).
% 294.73/187.30 tff(27780,plain,
% 294.73/187.30 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_2, c_j, s7)) | m_and_h_gate_v_out(c_e_h_2, c_l, s7))),
% 294.73/187.30 inference(quant_inst,[status(thm)],[])).
% 294.73/187.30 tff(27781,plain,
% 294.73/187.30 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_2, c_j, s7)) | m_and_h_gate_v_out(c_e_h_2, c_l, s7)),
% 294.73/187.30 inference(modus_ponens,[status(thm)],[27780, 27779])).
% 294.73/187.30 tff(27782,plain,
% 294.73/187.30 ($false),
% 294.73/187.30 inference(unit_resolution,[status(thm)],[27781, 1100, 27778, 27592])).
% 294.73/187.30 tff(27783,plain,(~m_or_h_gate_v_in1(c_e_h_2, c_j, s7)), inference(lemma,lemma(discharge,[]))).
% 294.73/187.30 tff(27784,assumption,(~m_or_h_gate_v_in1(c_e_h_2, c_j, s7)), introduced(assumption)).
% 294.73/187.30 tff(27785,assumption,(m_or_h_gate_v_out(c_e_h_2, c_j, s8)), introduced(assumption)).
% 294.73/187.30 tff(27786,plain,
% 294.73/187.30 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s7))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s7))),
% 294.73/187.30 inference(rewrite,[status(thm)],[])).
% 294.73/187.30 tff(27787,plain,
% 294.73/187.30 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s7))),
% 294.73/187.30 inference(quant_inst,[status(thm)],[])).
% 294.73/187.30 tff(27788,plain,
% 294.73/187.30 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s7)),
% 294.73/187.30 inference(modus_ponens,[status(thm)],[27787, 27786])).
% 294.73/187.30 tff(27789,plain,
% 294.73/187.30 (node3(c_e_h_1, c_e_h_2, s7)),
% 294.73/187.30 inference(unit_resolution,[status(thm)],[27788, 4166, 1056])).
% 294.73/187.30 tff(27790,plain,
% 294.73/187.30 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s7)) | (~node3(c_e_h_1, c_e_h_2, s7)) | m_and_h_gate_v_out(c_e_h_1, c_q, s7))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s7)) | (~node3(c_e_h_1, c_e_h_2, s7)) | m_and_h_gate_v_out(c_e_h_1, c_q, s7))),
% 294.73/187.30 inference(rewrite,[status(thm)],[])).
% 294.73/187.30 tff(27791,plain,
% 294.73/187.30 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s7)) | (~node3(c_e_h_1, c_e_h_2, s7)) | m_and_h_gate_v_out(c_e_h_1, c_q, s7))),
% 294.73/187.30 inference(quant_inst,[status(thm)],[])).
% 294.73/187.30 tff(27792,plain,
% 294.73/187.30 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s7)) | (~node3(c_e_h_1, c_e_h_2, s7)) | m_and_h_gate_v_out(c_e_h_1, c_q, s7)),
% 294.73/187.30 inference(modus_ponens,[status(thm)],[27791, 27790])).
% 294.73/187.30 tff(27793,plain,
% 294.73/187.30 ((~m_cell_v_ack(c_e_h_2, s7)) | m_and_h_gate_v_out(c_e_h_1, c_q, s7)),
% 294.73/187.30 inference(unit_resolution,[status(thm)],[27792, 1073, 27789])).
% 294.73/187.30 tff(27794,plain,
% 294.73/187.30 (~m_cell_v_ack(c_e_h_2, s7)),
% 294.73/187.30 inference(unit_resolution,[status(thm)],[27793, 25262])).
% 294.73/187.30 tff(27795,plain,
% 294.73/187.30 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s7)) | m_cell_v_ack(c_e_h_2, s7))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s7)) | m_cell_v_ack(c_e_h_2, s7))),
% 294.73/187.30 inference(rewrite,[status(thm)],[])).
% 294.73/187.30 tff(27796,plain,
% 294.73/187.30 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s7)) | m_cell_v_ack(c_e_h_2, s7))),
% 294.73/187.30 inference(quant_inst,[status(thm)],[])).
% 294.73/187.30 tff(27797,plain,
% 294.73/187.30 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s7)) | m_cell_v_ack(c_e_h_2, s7)),
% 294.73/187.30 inference(modus_ponens,[status(thm)],[27796, 27795])).
% 294.73/187.30 tff(27798,plain,
% 294.73/187.30 (~m_or_h_gate_v_in2(c_e_h_2, c_j, s7)),
% 294.73/187.30 inference(unit_resolution,[status(thm)],[27797, 1085, 27794])).
% 294.73/187.30 tff(27799,assumption,(node5(c_e_h_2, c_j, s7, s8)), introduced(assumption)).
% 294.73/187.30 tff(27800,plain,
% 294.73/187.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_2, c_j, s7) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s8)) | (~node5(c_e_h_2, c_j, s7, s8)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_2, c_j, s7) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s8)) | (~node5(c_e_h_2, c_j, s7, s8)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s7))),
% 294.73/187.30 inference(rewrite,[status(thm)],[])).
% 294.73/187.30 tff(27801,plain,
% 294.73/187.30 ((m_or_h_gate_v_in1(c_e_h_2, c_j, s7) | m_or_h_gate_v_in2(c_e_h_2, c_j, s7) | (~node5(c_e_h_2, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s8))) <=> (m_or_h_gate_v_in2(c_e_h_2, c_j, s7) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s8)) | (~node5(c_e_h_2, c_j, s7, s8)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s7))),
% 294.73/187.30 inference(rewrite,[status(thm)],[])).
% 294.73/187.30 tff(27802,plain,
% 294.73/187.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s7) | m_or_h_gate_v_in2(c_e_h_2, c_j, s7) | (~node5(c_e_h_2, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_2, c_j, s7) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s8)) | (~node5(c_e_h_2, c_j, s7, s8)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s7)))),
% 294.73/187.30 inference(monotonicity,[status(thm)],[27801])).
% 294.73/187.30 tff(27803,plain,
% 294.73/187.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s7) | m_or_h_gate_v_in2(c_e_h_2, c_j, s7) | (~node5(c_e_h_2, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_2, c_j, s7) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s8)) | (~node5(c_e_h_2, c_j, s7, s8)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s7))),
% 294.73/187.30 inference(transitivity,[status(thm)],[27802, 27800])).
% 294.73/187.30 tff(27804,plain,
% 294.73/187.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_2, c_j, s7) | m_or_h_gate_v_in2(c_e_h_2, c_j, s7) | (~node5(c_e_h_2, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s8)))),
% 294.73/187.30 inference(quant_inst,[status(thm)],[])).
% 294.73/187.30 tff(27805,plain,
% 294.73/187.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_2, c_j, s7) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s8)) | (~node5(c_e_h_2, c_j, s7, s8)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s7)),
% 294.73/187.30 inference(modus_ponens,[status(thm)],[27804, 27803])).
% 294.73/187.30 tff(27806,plain,
% 294.73/187.30 ($false),
% 294.73/187.30 inference(unit_resolution,[status(thm)],[27805, 1159, 27785, 27799, 27798, 27784])).
% 294.73/187.30 tff(27807,plain,((~node5(c_e_h_2, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s8)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s7)), inference(lemma,lemma(discharge,[]))).
% 294.73/187.30 tff(27808,plain,
% 294.73/187.31 (~node5(c_e_h_2, c_j, s7, s8)),
% 294.73/187.31 inference(unit_resolution,[status(thm)],[27807, 27785, 27784])).
% 294.73/187.31 tff(27809,plain,
% 294.73/187.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s7, s8)) | node5(c_e_h_2, c_j, s7, s8) | node6(c_e_h_2, c_j, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s7, s8)) | node5(c_e_h_2, c_j, s7, s8) | node6(c_e_h_2, c_j, s7, s8))),
% 294.73/187.31 inference(rewrite,[status(thm)],[])).
% 294.73/187.31 tff(27810,plain,
% 294.73/187.31 ((node6(c_e_h_2, c_j, s7, s8) | node5(c_e_h_2, c_j, s7, s8) | (~trans(s7, s8))) <=> ((~trans(s7, s8)) | node5(c_e_h_2, c_j, s7, s8) | node6(c_e_h_2, c_j, s7, s8))),
% 294.73/187.31 inference(rewrite,[status(thm)],[])).
% 294.73/187.31 tff(27811,plain,
% 294.73/187.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s7, s8) | node5(c_e_h_2, c_j, s7, s8) | (~trans(s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s7, s8)) | node5(c_e_h_2, c_j, s7, s8) | node6(c_e_h_2, c_j, s7, s8)))),
% 294.73/187.31 inference(monotonicity,[status(thm)],[27810])).
% 294.73/187.31 tff(27812,plain,
% 294.73/187.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s7, s8) | node5(c_e_h_2, c_j, s7, s8) | (~trans(s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s7, s8)) | node5(c_e_h_2, c_j, s7, s8) | node6(c_e_h_2, c_j, s7, s8))),
% 294.73/187.31 inference(transitivity,[status(thm)],[27811, 27809])).
% 294.73/187.31 tff(27813,plain,
% 294.73/187.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_2, c_j, s7, s8) | node5(c_e_h_2, c_j, s7, s8) | (~trans(s7, s8)))),
% 294.73/187.31 inference(quant_inst,[status(thm)],[])).
% 294.73/187.31 tff(27814,plain,
% 294.73/187.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s7, s8)) | node5(c_e_h_2, c_j, s7, s8) | node6(c_e_h_2, c_j, s7, s8)),
% 294.73/187.31 inference(modus_ponens,[status(thm)],[27813, 27812])).
% 294.73/187.31 tff(27815,plain,
% 294.73/187.31 (node5(c_e_h_2, c_j, s7, s8) | node6(c_e_h_2, c_j, s7, s8)),
% 294.73/187.31 inference(unit_resolution,[status(thm)],[27814, 1141, 1938])).
% 294.73/187.31 tff(27816,plain,
% 294.73/187.31 (node6(c_e_h_2, c_j, s7, s8)),
% 294.73/187.31 inference(unit_resolution,[status(thm)],[27815, 27808])).
% 294.73/187.31 tff(27817,assumption,(~m_or_h_gate_v_out(c_e_h_2, c_j, s7)), introduced(assumption)).
% 294.73/187.31 tff(27818,plain,
% 294.73/187.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_2, c_j, s7) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s8)) | (~node6(c_e_h_2, c_j, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s7) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s8)) | (~node6(c_e_h_2, c_j, s7, s8)))),
% 294.73/187.31 inference(rewrite,[status(thm)],[])).
% 294.81/187.31 tff(27819,plain,
% 294.81/187.31 (((~node6(c_e_h_2, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s8)) | m_or_h_gate_v_out(c_e_h_2, c_j, s7)) <=> (m_or_h_gate_v_out(c_e_h_2, c_j, s7) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s8)) | (~node6(c_e_h_2, c_j, s7, s8)))),
% 294.81/187.31 inference(rewrite,[status(thm)],[])).
% 294.81/187.31 tff(27820,plain,
% 294.81/187.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s8)) | m_or_h_gate_v_out(c_e_h_2, c_j, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_2, c_j, s7) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s8)) | (~node6(c_e_h_2, c_j, s7, s8))))),
% 294.81/187.31 inference(monotonicity,[status(thm)],[27819])).
% 294.81/187.31 tff(27821,plain,
% 294.81/187.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s8)) | m_or_h_gate_v_out(c_e_h_2, c_j, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s7) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s8)) | (~node6(c_e_h_2, c_j, s7, s8)))),
% 294.81/187.31 inference(transitivity,[status(thm)],[27820, 27818])).
% 294.81/187.31 tff(27822,plain,
% 294.81/187.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s7, s8)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s8)) | m_or_h_gate_v_out(c_e_h_2, c_j, s7))),
% 294.81/187.31 inference(quant_inst,[status(thm)],[])).
% 294.81/187.31 tff(27823,plain,
% 294.81/187.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_2, c_j, s7) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s8)) | (~node6(c_e_h_2, c_j, s7, s8))),
% 294.81/187.31 inference(modus_ponens,[status(thm)],[27822, 27821])).
% 294.81/187.31 tff(27824,plain,
% 294.81/187.31 ($false),
% 294.81/187.31 inference(unit_resolution,[status(thm)],[27823, 1121, 27817, 27785, 27816])).
% 294.81/187.31 tff(27825,plain,((~m_or_h_gate_v_out(c_e_h_2, c_j, s8)) | m_or_h_gate_v_out(c_e_h_2, c_j, s7) | m_or_h_gate_v_in1(c_e_h_2, c_j, s7)), inference(lemma,lemma(discharge,[]))).
% 294.81/187.31 tff(27826,plain,
% 294.81/187.31 ((~m_or_h_gate_v_out(c_e_h_2, c_j, s8)) | m_or_h_gate_v_in1(c_e_h_2, c_j, s7)),
% 294.81/187.31 inference(unit_resolution,[status(thm)],[27825, 27518])).
% 294.81/187.31 tff(27827,plain,
% 294.81/187.31 (~m_or_h_gate_v_out(c_e_h_2, c_j, s8)),
% 294.81/187.31 inference(unit_resolution,[status(thm)],[27826, 27783])).
% 294.81/187.31 tff(27828,plain,
% 294.81/187.31 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s8)) | m_or_h_gate_v_out(c_e_h_2, c_j, s8))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s8)) | m_or_h_gate_v_out(c_e_h_2, c_j, s8))),
% 294.81/187.31 inference(rewrite,[status(thm)],[])).
% 294.81/187.31 tff(27829,plain,
% 294.81/187.31 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_h, s8)) | m_or_h_gate_v_out(c_e_h_2, c_j, s8))),
% 294.81/187.31 inference(quant_inst,[status(thm)],[])).
% 294.81/187.31 tff(27830,plain,
% 294.81/187.31 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_h, s8)) | m_or_h_gate_v_out(c_e_h_2, c_j, s8)),
% 294.81/187.31 inference(modus_ponens,[status(thm)],[27829, 27828])).
% 294.81/187.31 tff(27831,plain,
% 294.81/187.31 (~m_c_h_element_v_in2(c_e_h_2, c_h, s8)),
% 294.81/187.31 inference(unit_resolution,[status(thm)],[27830, 1174, 27827])).
% 294.81/187.31 tff(27832,plain,
% 294.81/187.31 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s8)) | m_c_h_element_v_in2(c_e_h_2, c_h, s8) | (~node17(c_e_h_2, c_h, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s8)) | m_c_h_element_v_in2(c_e_h_2, c_h, s8) | (~node17(c_e_h_2, c_h, s8)))),
% 294.81/187.31 inference(rewrite,[status(thm)],[])).
% 294.81/187.31 tff(27833,plain,
% 294.81/187.31 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_h, s8)) | m_c_h_element_v_in2(c_e_h_2, c_h, s8) | (~node17(c_e_h_2, c_h, s8)))),
% 294.81/187.31 inference(quant_inst,[status(thm)],[])).
% 294.81/187.31 tff(27834,plain,
% 294.81/187.31 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_h, s8)) | m_c_h_element_v_in2(c_e_h_2, c_h, s8) | (~node17(c_e_h_2, c_h, s8))),
% 294.81/187.31 inference(modus_ponens,[status(thm)],[27833, 27832])).
% 294.81/187.31 tff(27835,plain,
% 294.81/187.31 ((~m_c_h_element_v_in1(c_e_h_2, c_h, s8)) | (~node17(c_e_h_2, c_h, s8))),
% 294.81/187.31 inference(unit_resolution,[status(thm)],[27834, 919, 27831])).
% 294.81/187.31 tff(27836,plain,
% 294.81/187.31 ($false),
% 294.81/187.31 inference(unit_resolution,[status(thm)],[27835, 27550, 27591])).
% 294.81/187.31 tff(27837,plain,(~m_c_h_element_v_out(c_e_h_2, c_h, s9)), inference(lemma,lemma(discharge,[]))).
% 294.81/187.31 tff(27838,plain,
% 294.81/187.31 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s9)) | m_c_h_element_v_out(c_e_h_2, c_h, s9))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s9)) | m_c_h_element_v_out(c_e_h_2, c_h, s9))),
% 294.81/187.31 inference(rewrite,[status(thm)],[])).
% 294.81/187.31 tff(27839,plain,
% 294.81/187.31 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s9)) | m_c_h_element_v_out(c_e_h_2, c_h, s9))),
% 294.81/187.31 inference(quant_inst,[status(thm)],[])).
% 294.81/187.31 tff(27840,plain,
% 294.81/187.31 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s9)) | m_c_h_element_v_out(c_e_h_2, c_h, s9)),
% 294.81/187.31 inference(modus_ponens,[status(thm)],[27839, 27838])).
% 294.81/187.31 tff(27841,plain,
% 294.81/187.31 (~m_and_h_gate_v_in1(c_e_h_2, c_i, s9)),
% 294.81/187.31 inference(unit_resolution,[status(thm)],[27840, 619, 27837])).
% 294.81/187.31 tff(27842,plain,
% 294.81/187.31 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s9)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s9))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s9)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s9))),
% 294.81/187.31 inference(rewrite,[status(thm)],[])).
% 294.81/187.31 tff(27843,plain,
% 294.81/187.31 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s9)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s9))),
% 294.81/187.31 inference(quant_inst,[status(thm)],[])).
% 294.81/187.31 tff(27844,plain,
% 294.81/187.31 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s9)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s9)),
% 294.81/187.31 inference(modus_ponens,[status(thm)],[27843, 27842])).
% 294.81/187.31 tff(27845,plain,
% 294.81/187.31 (~node20(c_e_h_2, c_i, s9)),
% 294.81/187.31 inference(unit_resolution,[status(thm)],[27844, 38, 27841])).
% 294.81/187.31 tff(27846,assumption,(m_and_h_gate_v_out(c_e_h_2, c_i, s10)), introduced(assumption)).
% 294.81/187.31 tff(27847,assumption,(node22(c_e_h_2, c_i, s9, s10)), introduced(assumption)).
% 294.81/187.31 tff(27848,plain,
% 294.81/187.31 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s8)) | m_c_h_element_v_out(c_e_h_2, c_h, s8))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s8)) | m_c_h_element_v_out(c_e_h_2, c_h, s8))),
% 294.81/187.31 inference(rewrite,[status(thm)],[])).
% 294.81/187.31 tff(27849,plain,
% 294.81/187.31 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s8)) | m_c_h_element_v_out(c_e_h_2, c_h, s8))),
% 294.81/187.31 inference(quant_inst,[status(thm)],[])).
% 294.81/187.31 tff(27850,plain,
% 294.81/187.31 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s8)) | m_c_h_element_v_out(c_e_h_2, c_h, s8)),
% 294.81/187.32 inference(modus_ponens,[status(thm)],[27849, 27848])).
% 294.81/187.32 tff(27851,plain,
% 294.81/187.32 (~m_and_h_gate_v_in1(c_e_h_2, c_i, s8)),
% 294.81/187.32 inference(unit_resolution,[status(thm)],[27850, 619, 27532])).
% 294.81/187.32 tff(27852,plain,
% 294.81/187.32 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s8)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s8)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s8))),
% 294.81/187.32 inference(rewrite,[status(thm)],[])).
% 294.81/187.32 tff(27853,plain,
% 294.81/187.32 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s8)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s8))),
% 294.81/187.32 inference(quant_inst,[status(thm)],[])).
% 294.81/187.32 tff(27854,plain,
% 294.81/187.32 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s8)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s8)),
% 294.81/187.32 inference(modus_ponens,[status(thm)],[27853, 27852])).
% 294.81/187.32 tff(27855,plain,
% 294.81/187.32 (~node20(c_e_h_2, c_i, s8)),
% 294.81/187.32 inference(unit_resolution,[status(thm)],[27854, 38, 27851])).
% 294.81/187.32 tff(27856,assumption,(m_and_h_gate_v_out(c_e_h_2, c_i, s9)), introduced(assumption)).
% 294.81/187.32 tff(27857,plain,
% 294.81/187.32 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s7)) | m_c_h_element_v_out(c_e_h_2, c_h, s7))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s7)) | m_c_h_element_v_out(c_e_h_2, c_h, s7))),
% 294.81/187.32 inference(rewrite,[status(thm)],[])).
% 294.81/187.32 tff(27858,plain,
% 294.81/187.32 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_i, s7)) | m_c_h_element_v_out(c_e_h_2, c_h, s7))),
% 294.81/187.32 inference(quant_inst,[status(thm)],[])).
% 294.81/187.32 tff(27859,plain,
% 294.81/187.32 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_i, s7)) | m_c_h_element_v_out(c_e_h_2, c_h, s7)),
% 294.81/187.32 inference(modus_ponens,[status(thm)],[27858, 27857])).
% 294.81/187.32 tff(27860,plain,
% 294.81/187.32 (~m_and_h_gate_v_in1(c_e_h_2, c_i, s7)),
% 294.81/187.32 inference(unit_resolution,[status(thm)],[27859, 619, 27205])).
% 294.81/187.32 tff(27861,plain,
% 294.81/187.32 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s7)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s7)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s7))),
% 294.81/187.32 inference(rewrite,[status(thm)],[])).
% 294.81/187.32 tff(27862,plain,
% 294.81/187.32 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_i, s7)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s7))),
% 294.81/187.32 inference(quant_inst,[status(thm)],[])).
% 294.81/187.32 tff(27863,plain,
% 294.81/187.32 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_i, s7)) | m_and_h_gate_v_in1(c_e_h_2, c_i, s7)),
% 294.81/187.32 inference(modus_ponens,[status(thm)],[27862, 27861])).
% 294.81/187.32 tff(27864,plain,
% 294.81/187.32 (~node20(c_e_h_2, c_i, s7)),
% 294.81/187.32 inference(unit_resolution,[status(thm)],[27863, 38, 27860])).
% 294.81/187.32 tff(27865,assumption,(~node20(c_e_h_2, c_i, s7)), introduced(assumption)).
% 294.81/187.32 tff(27866,assumption,(m_and_h_gate_v_out(c_e_h_2, c_i, s8)), introduced(assumption)).
% 294.81/187.32 tff(27867,assumption,(node21(c_e_h_2, c_i, s7, s8)), introduced(assumption)).
% 294.81/187.32 tff(27868,plain,
% 294.81/187.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s8)) | node20(c_e_h_2, c_i, s7) | (~node21(c_e_h_2, c_i, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s8)) | node20(c_e_h_2, c_i, s7) | (~node21(c_e_h_2, c_i, s7, s8)))),
% 294.81/187.32 inference(rewrite,[status(thm)],[])).
% 294.81/187.32 tff(27869,plain,
% 294.81/187.32 ((node20(c_e_h_2, c_i, s7) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s8)) | (~node21(c_e_h_2, c_i, s7, s8))) <=> ((~m_and_h_gate_v_out(c_e_h_2, c_i, s8)) | node20(c_e_h_2, c_i, s7) | (~node21(c_e_h_2, c_i, s7, s8)))),
% 294.81/187.32 inference(rewrite,[status(thm)],[])).
% 294.81/187.32 tff(27870,plain,
% 294.81/187.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s7) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s8)) | (~node21(c_e_h_2, c_i, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s8)) | node20(c_e_h_2, c_i, s7) | (~node21(c_e_h_2, c_i, s7, s8))))),
% 294.81/187.32 inference(monotonicity,[status(thm)],[27869])).
% 294.81/187.32 tff(27871,plain,
% 294.81/187.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s7) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s8)) | (~node21(c_e_h_2, c_i, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s8)) | node20(c_e_h_2, c_i, s7) | (~node21(c_e_h_2, c_i, s7, s8)))),
% 294.81/187.32 inference(transitivity,[status(thm)],[27870, 27868])).
% 294.81/187.32 tff(27872,plain,
% 294.81/187.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s7) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s8)) | (~node21(c_e_h_2, c_i, s7, s8)))),
% 294.81/187.32 inference(quant_inst,[status(thm)],[])).
% 294.81/187.32 tff(27873,plain,
% 294.81/187.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s8)) | node20(c_e_h_2, c_i, s7) | (~node21(c_e_h_2, c_i, s7, s8))),
% 294.81/187.32 inference(modus_ponens,[status(thm)],[27872, 27871])).
% 294.81/187.32 tff(27874,plain,
% 294.81/187.32 ($false),
% 294.81/187.32 inference(unit_resolution,[status(thm)],[27873, 52, 27867, 27865, 27866])).
% 294.81/187.32 tff(27875,plain,((~node21(c_e_h_2, c_i, s7, s8)) | node20(c_e_h_2, c_i, s7) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s8))), inference(lemma,lemma(discharge,[]))).
% 294.81/187.32 tff(27876,plain,
% 294.81/187.32 (~node21(c_e_h_2, c_i, s7, s8)),
% 294.81/187.32 inference(unit_resolution,[status(thm)],[27875, 27866, 27865])).
% 294.81/187.32 tff(27877,assumption,(node22(c_e_h_2, c_i, s7, s8)), introduced(assumption)).
% 294.81/187.32 tff(27878,plain,
% 294.81/187.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s8)) | (~node22(c_e_h_2, c_i, s7, s8)) | m_and_h_gate_v_out(c_e_h_2, c_i, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s8)) | (~node22(c_e_h_2, c_i, s7, s8)) | m_and_h_gate_v_out(c_e_h_2, c_i, s7))),
% 294.81/187.32 inference(rewrite,[status(thm)],[])).
% 294.81/187.32 tff(27879,plain,
% 294.81/187.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s8)) | (~node22(c_e_h_2, c_i, s7, s8)) | m_and_h_gate_v_out(c_e_h_2, c_i, s7))),
% 294.81/187.32 inference(quant_inst,[status(thm)],[])).
% 294.81/187.32 tff(27880,plain,
% 294.81/187.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s8)) | (~node22(c_e_h_2, c_i, s7, s8)) | m_and_h_gate_v_out(c_e_h_2, c_i, s7)),
% 294.81/187.32 inference(modus_ponens,[status(thm)],[27879, 27878])).
% 294.81/187.32 tff(27881,plain,
% 294.81/187.32 ($false),
% 294.81/187.32 inference(unit_resolution,[status(thm)],[27880, 108, 27877, 27866, 8727])).
% 294.81/187.32 tff(27882,plain,((~node22(c_e_h_2, c_i, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s8)) | m_and_h_gate_v_out(c_e_h_2, c_i, s7)), inference(lemma,lemma(discharge,[]))).
% 294.81/187.32 tff(27883,plain,
% 294.81/187.32 (~node22(c_e_h_2, c_i, s7, s8)),
% 294.81/187.32 inference(unit_resolution,[status(thm)],[27882, 27866, 8727])).
% 294.81/187.32 tff(27884,plain,
% 294.81/187.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_2, c_i, s7, s8) | node22(c_e_h_2, c_i, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_2, c_i, s7, s8) | node22(c_e_h_2, c_i, s7, s8))),
% 294.81/187.32 inference(rewrite,[status(thm)],[])).
% 294.81/187.32 tff(27885,plain,
% 294.81/187.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_2, c_i, s7, s8) | node22(c_e_h_2, c_i, s7, s8))),
% 294.81/187.32 inference(quant_inst,[status(thm)],[])).
% 294.81/187.32 tff(27886,plain,
% 294.81/187.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_2, c_i, s7, s8) | node22(c_e_h_2, c_i, s7, s8)),
% 294.81/187.32 inference(modus_ponens,[status(thm)],[27885, 27884])).
% 294.81/187.32 tff(27887,plain,
% 294.81/187.32 (node21(c_e_h_2, c_i, s7, s8) | node22(c_e_h_2, c_i, s7, s8)),
% 294.81/187.32 inference(unit_resolution,[status(thm)],[27886, 82, 1938])).
% 294.81/187.32 tff(27888,plain,
% 294.81/187.32 ($false),
% 294.81/187.32 inference(unit_resolution,[status(thm)],[27887, 27883, 27876])).
% 294.81/187.32 tff(27889,plain,((~m_and_h_gate_v_out(c_e_h_2, c_i, s8)) | m_and_h_gate_v_out(c_e_h_2, c_i, s7) | node20(c_e_h_2, c_i, s7)), inference(lemma,lemma(discharge,[]))).
% 294.81/187.32 tff(27890,plain,
% 294.81/187.32 (~m_and_h_gate_v_out(c_e_h_2, c_i, s8)),
% 294.81/187.32 inference(unit_resolution,[status(thm)],[27889, 8725, 27864])).
% 294.81/187.32 tff(27891,assumption,(node22(c_e_h_2, c_i, s8, s9)), introduced(assumption)).
% 294.81/187.32 tff(27892,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_i, s8)), introduced(assumption)).
% 294.81/187.32 tff(27893,plain,
% 294.81/187.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s9)) | (~node22(c_e_h_2, c_i, s8, s9)) | m_and_h_gate_v_out(c_e_h_2, c_i, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s9)) | (~node22(c_e_h_2, c_i, s8, s9)) | m_and_h_gate_v_out(c_e_h_2, c_i, s8))),
% 294.81/187.32 inference(rewrite,[status(thm)],[])).
% 294.81/187.32 tff(27894,plain,
% 294.81/187.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s9)) | (~node22(c_e_h_2, c_i, s8, s9)) | m_and_h_gate_v_out(c_e_h_2, c_i, s8))),
% 294.81/187.32 inference(quant_inst,[status(thm)],[])).
% 294.81/187.32 tff(27895,plain,
% 294.81/187.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s9)) | (~node22(c_e_h_2, c_i, s8, s9)) | m_and_h_gate_v_out(c_e_h_2, c_i, s8)),
% 294.81/187.32 inference(modus_ponens,[status(thm)],[27894, 27893])).
% 294.81/187.32 tff(27896,plain,
% 294.81/187.32 ($false),
% 294.81/187.32 inference(unit_resolution,[status(thm)],[27895, 108, 27856, 27892, 27891])).
% 294.81/187.32 tff(27897,plain,((~node22(c_e_h_2, c_i, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s9)) | m_and_h_gate_v_out(c_e_h_2, c_i, s8)), inference(lemma,lemma(discharge,[]))).
% 294.81/187.32 tff(27898,plain,
% 294.81/187.32 ((~node22(c_e_h_2, c_i, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s9))),
% 294.81/187.32 inference(unit_resolution,[status(thm)],[27897, 27890])).
% 294.81/187.32 tff(27899,plain,
% 294.81/187.32 (~node22(c_e_h_2, c_i, s8, s9)),
% 294.81/187.32 inference(unit_resolution,[status(thm)],[27898, 27856])).
% 294.81/187.32 tff(27900,plain,
% 294.81/187.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s8, s9)) | node21(c_e_h_2, c_i, s8, s9) | node22(c_e_h_2, c_i, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_2, c_i, s8, s9) | node22(c_e_h_2, c_i, s8, s9))),
% 294.81/187.32 inference(rewrite,[status(thm)],[])).
% 294.81/187.32 tff(27901,plain,
% 294.81/187.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s8, s9)) | node21(c_e_h_2, c_i, s8, s9) | node22(c_e_h_2, c_i, s8, s9))),
% 294.81/187.32 inference(quant_inst,[status(thm)],[])).
% 294.81/187.32 tff(27902,plain,
% 294.81/187.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_2, c_i, s8, s9) | node22(c_e_h_2, c_i, s8, s9)),
% 294.81/187.33 inference(modus_ponens,[status(thm)],[27901, 27900])).
% 294.81/187.33 tff(27903,plain,
% 294.81/187.33 (node21(c_e_h_2, c_i, s8, s9) | node22(c_e_h_2, c_i, s8, s9)),
% 294.81/187.33 inference(unit_resolution,[status(thm)],[27902, 82, 1993])).
% 294.81/187.33 tff(27904,plain,
% 294.81/187.33 (node21(c_e_h_2, c_i, s8, s9)),
% 294.81/187.33 inference(unit_resolution,[status(thm)],[27903, 27899])).
% 294.81/187.33 tff(27905,plain,
% 294.81/187.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s8) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s9)) | (~node21(c_e_h_2, c_i, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s8) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s9)) | (~node21(c_e_h_2, c_i, s8, s9)))),
% 294.81/187.33 inference(rewrite,[status(thm)],[])).
% 294.81/187.33 tff(27906,plain,
% 294.81/187.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s8) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s9)) | (~node21(c_e_h_2, c_i, s8, s9)))),
% 294.81/187.33 inference(quant_inst,[status(thm)],[])).
% 294.81/187.33 tff(27907,plain,
% 294.81/187.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s8) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s9)) | (~node21(c_e_h_2, c_i, s8, s9))),
% 294.81/187.33 inference(modus_ponens,[status(thm)],[27906, 27905])).
% 294.81/187.33 tff(27908,plain,
% 294.81/187.33 ($false),
% 294.81/187.33 inference(unit_resolution,[status(thm)],[27907, 52, 27856, 27904, 27855])).
% 294.81/187.33 tff(27909,plain,(~m_and_h_gate_v_out(c_e_h_2, c_i, s9)), inference(lemma,lemma(discharge,[]))).
% 294.81/187.33 tff(27910,plain,
% 294.81/187.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s10)) | (~node22(c_e_h_2, c_i, s9, s10)) | m_and_h_gate_v_out(c_e_h_2, c_i, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s10)) | (~node22(c_e_h_2, c_i, s9, s10)) | m_and_h_gate_v_out(c_e_h_2, c_i, s9))),
% 294.81/187.33 inference(rewrite,[status(thm)],[])).
% 294.81/187.33 tff(27911,plain,
% 294.81/187.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_i, s10)) | (~node22(c_e_h_2, c_i, s9, s10)) | m_and_h_gate_v_out(c_e_h_2, c_i, s9))),
% 294.81/187.33 inference(quant_inst,[status(thm)],[])).
% 294.81/187.33 tff(27912,plain,
% 294.81/187.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s10)) | (~node22(c_e_h_2, c_i, s9, s10)) | m_and_h_gate_v_out(c_e_h_2, c_i, s9)),
% 294.81/187.33 inference(modus_ponens,[status(thm)],[27911, 27910])).
% 294.81/187.33 tff(27913,plain,
% 294.81/187.33 ($false),
% 294.81/187.33 inference(unit_resolution,[status(thm)],[27912, 108, 27909, 27847, 27846])).
% 294.81/187.33 tff(27914,plain,((~node22(c_e_h_2, c_i, s9, s10)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s10))), inference(lemma,lemma(discharge,[]))).
% 294.81/187.33 tff(27915,plain,
% 294.81/187.33 (~node22(c_e_h_2, c_i, s9, s10)),
% 294.81/187.33 inference(unit_resolution,[status(thm)],[27914, 27846])).
% 294.81/187.33 tff(27916,assumption,(~node20(c_e_h_2, c_i, s9)), introduced(assumption)).
% 294.81/187.33 tff(27917,assumption,(node21(c_e_h_2, c_i, s9, s10)), introduced(assumption)).
% 294.81/187.33 tff(27918,plain,
% 294.81/187.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s9) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s10)) | (~node21(c_e_h_2, c_i, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s9) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s10)) | (~node21(c_e_h_2, c_i, s9, s10)))),
% 294.81/187.33 inference(rewrite,[status(thm)],[])).
% 294.81/187.33 tff(27919,plain,
% 294.81/187.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_i, s9) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s10)) | (~node21(c_e_h_2, c_i, s9, s10)))),
% 294.81/187.33 inference(quant_inst,[status(thm)],[])).
% 294.81/187.33 tff(27920,plain,
% 294.81/187.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_i, s9) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s10)) | (~node21(c_e_h_2, c_i, s9, s10))),
% 294.81/187.33 inference(modus_ponens,[status(thm)],[27919, 27918])).
% 294.81/187.33 tff(27921,plain,
% 294.81/187.33 ($false),
% 294.81/187.33 inference(unit_resolution,[status(thm)],[27920, 52, 27917, 27846, 27916])).
% 294.81/187.33 tff(27922,plain,((~node21(c_e_h_2, c_i, s9, s10)) | (~m_and_h_gate_v_out(c_e_h_2, c_i, s10)) | node20(c_e_h_2, c_i, s9)), inference(lemma,lemma(discharge,[]))).
% 294.81/187.33 tff(27923,plain,
% 294.81/187.33 (~node21(c_e_h_2, c_i, s9, s10)),
% 294.81/187.33 inference(unit_resolution,[status(thm)],[27922, 27846, 27916])).
% 294.81/187.33 tff(27924,plain,
% 294.81/187.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s9, s10)) | node21(c_e_h_2, c_i, s9, s10) | node22(c_e_h_2, c_i, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s9, s10)) | node21(c_e_h_2, c_i, s9, s10) | node22(c_e_h_2, c_i, s9, s10))),
% 294.81/187.33 inference(rewrite,[status(thm)],[])).
% 294.81/187.33 tff(27925,plain,
% 294.81/187.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s9, s10)) | node21(c_e_h_2, c_i, s9, s10) | node22(c_e_h_2, c_i, s9, s10))),
% 294.81/187.33 inference(quant_inst,[status(thm)],[])).
% 294.81/187.33 tff(27926,plain,
% 294.81/187.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s9, s10)) | node21(c_e_h_2, c_i, s9, s10) | node22(c_e_h_2, c_i, s9, s10)),
% 294.81/187.33 inference(modus_ponens,[status(thm)],[27925, 27924])).
% 294.81/187.33 tff(27927,plain,
% 294.81/187.33 (node21(c_e_h_2, c_i, s9, s10) | node22(c_e_h_2, c_i, s9, s10)),
% 294.81/187.33 inference(unit_resolution,[status(thm)],[27926, 82, 7676])).
% 294.81/187.33 tff(27928,plain,
% 294.81/187.33 ($false),
% 294.81/187.33 inference(unit_resolution,[status(thm)],[27927, 27923, 27915])).
% 294.81/187.33 tff(27929,plain,((~m_and_h_gate_v_out(c_e_h_2, c_i, s10)) | node20(c_e_h_2, c_i, s9)), inference(lemma,lemma(discharge,[]))).
% 294.81/187.33 tff(27930,plain,
% 294.81/187.33 (~m_and_h_gate_v_out(c_e_h_2, c_i, s10)),
% 294.81/187.33 inference(unit_resolution,[status(thm)],[27929, 27845])).
% 294.81/187.33 tff(27931,assumption,(m_c_h_element_v_in2(c_e_h_2, c_f, s10)), introduced(assumption)).
% 294.81/187.33 tff(27932,plain,
% 294.81/187.33 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_f, s10)) | m_and_h_gate_v_out(c_e_h_2, c_i, s10))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s10)) | m_and_h_gate_v_out(c_e_h_2, c_i, s10))),
% 294.81/187.33 inference(rewrite,[status(thm)],[])).
% 294.81/187.33 tff(27933,plain,
% 294.81/187.33 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_f, s10)) | m_and_h_gate_v_out(c_e_h_2, c_i, s10))),
% 294.81/187.33 inference(quant_inst,[status(thm)],[])).
% 294.81/187.33 tff(27934,plain,
% 294.81/187.33 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s10)) | m_and_h_gate_v_out(c_e_h_2, c_i, s10)),
% 294.81/187.33 inference(modus_ponens,[status(thm)],[27933, 27932])).
% 294.81/187.33 tff(27935,plain,
% 294.81/187.33 ($false),
% 294.81/187.33 inference(unit_resolution,[status(thm)],[27934, 2143, 27931, 27930])).
% 294.81/187.33 tff(27936,plain,(~m_c_h_element_v_in2(c_e_h_2, c_f, s10)), inference(lemma,lemma(discharge,[]))).
% 294.81/187.33 tff(27937,assumption,(m_c_h_element_v_in2(c_e_h_2, c_f, s8)), introduced(assumption)).
% 294.81/187.33 tff(27938,plain,
% 294.81/187.33 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_f, s8)) | m_and_h_gate_v_out(c_e_h_2, c_i, s8))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s8)) | m_and_h_gate_v_out(c_e_h_2, c_i, s8))),
% 294.81/187.33 inference(rewrite,[status(thm)],[])).
% 294.81/187.33 tff(27939,plain,
% 294.81/187.33 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_f, s8)) | m_and_h_gate_v_out(c_e_h_2, c_i, s8))),
% 294.81/187.33 inference(quant_inst,[status(thm)],[])).
% 294.81/187.33 tff(27940,plain,
% 294.81/187.33 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s8)) | m_and_h_gate_v_out(c_e_h_2, c_i, s8)),
% 294.81/187.33 inference(modus_ponens,[status(thm)],[27939, 27938])).
% 294.81/187.33 tff(27941,plain,
% 294.81/187.33 ($false),
% 294.81/187.33 inference(unit_resolution,[status(thm)],[27940, 2143, 27890, 27937])).
% 294.81/187.33 tff(27942,plain,(~m_c_h_element_v_in2(c_e_h_2, c_f, s8)), inference(lemma,lemma(discharge,[]))).
% 294.81/187.33 tff(27943,assumption,(~m_c_h_element_v_out(c_e_h_2, c_f, s8)), introduced(assumption)).
% 294.81/187.33 tff(27944,assumption,(m_c_h_element_v_out(c_e_h_2, c_f, s9)), introduced(assumption)).
% 294.81/187.33 tff(27945,assumption,(node15(c_e_h_2, c_f, s8, s9)), introduced(assumption)).
% 294.81/187.33 tff(27946,plain,
% 294.81/187.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s9)) | (~node15(c_e_h_2, c_f, s8, s9)) | m_c_h_element_v_out(c_e_h_2, c_f, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s9)) | (~node15(c_e_h_2, c_f, s8, s9)) | m_c_h_element_v_out(c_e_h_2, c_f, s8))),
% 294.81/187.33 inference(rewrite,[status(thm)],[])).
% 294.81/187.33 tff(27947,plain,
% 294.81/187.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s9)) | (~node15(c_e_h_2, c_f, s8, s9)) | m_c_h_element_v_out(c_e_h_2, c_f, s8))),
% 294.81/187.33 inference(quant_inst,[status(thm)],[])).
% 294.81/187.33 tff(27948,plain,
% 294.81/187.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s9)) | (~node15(c_e_h_2, c_f, s8, s9)) | m_c_h_element_v_out(c_e_h_2, c_f, s8)),
% 294.81/187.33 inference(modus_ponens,[status(thm)],[27947, 27946])).
% 294.81/187.33 tff(27949,plain,
% 294.81/187.33 ($false),
% 294.81/187.33 inference(unit_resolution,[status(thm)],[27948, 147, 27943, 27944, 27945])).
% 294.81/187.33 tff(27950,plain,((~node15(c_e_h_2, c_f, s8, s9)) | m_c_h_element_v_out(c_e_h_2, c_f, s8) | (~m_c_h_element_v_out(c_e_h_2, c_f, s9))), inference(lemma,lemma(discharge,[]))).
% 294.81/187.33 tff(27951,plain,
% 294.81/187.33 (~node15(c_e_h_2, c_f, s8, s9)),
% 294.81/187.33 inference(unit_resolution,[status(thm)],[27950, 27944, 27943])).
% 294.81/187.33 tff(27952,assumption,(node18(c_e_h_2, c_f, s8, s9)), introduced(assumption)).
% 294.81/187.33 tff(27953,plain,
% 294.81/187.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_f, s8) | (~m_c_h_element_v_out(c_e_h_2, c_f, s9)) | (~node18(c_e_h_2, c_f, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_f, s8) | (~m_c_h_element_v_out(c_e_h_2, c_f, s9)) | (~node18(c_e_h_2, c_f, s8, s9)))),
% 294.81/187.33 inference(rewrite,[status(thm)],[])).
% 294.81/187.33 tff(27954,plain,
% 294.81/187.33 (((~m_c_h_element_v_out(c_e_h_2, c_f, s9)) | m_c_h_element_v_out(c_e_h_2, c_f, s8) | (~node18(c_e_h_2, c_f, s8, s9))) <=> (m_c_h_element_v_out(c_e_h_2, c_f, s8) | (~m_c_h_element_v_out(c_e_h_2, c_f, s9)) | (~node18(c_e_h_2, c_f, s8, s9)))),
% 294.81/187.33 inference(rewrite,[status(thm)],[])).
% 294.81/187.33 tff(27955,plain,
% 294.81/187.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s9)) | m_c_h_element_v_out(c_e_h_2, c_f, s8) | (~node18(c_e_h_2, c_f, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_f, s8) | (~m_c_h_element_v_out(c_e_h_2, c_f, s9)) | (~node18(c_e_h_2, c_f, s8, s9))))),
% 294.81/187.34 inference(monotonicity,[status(thm)],[27954])).
% 294.81/187.34 tff(27956,plain,
% 294.81/187.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s9)) | m_c_h_element_v_out(c_e_h_2, c_f, s8) | (~node18(c_e_h_2, c_f, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_f, s8) | (~m_c_h_element_v_out(c_e_h_2, c_f, s9)) | (~node18(c_e_h_2, c_f, s8, s9)))),
% 294.81/187.34 inference(transitivity,[status(thm)],[27955, 27953])).
% 294.81/187.34 tff(27957,plain,
% 294.81/187.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s9)) | m_c_h_element_v_out(c_e_h_2, c_f, s8) | (~node18(c_e_h_2, c_f, s8, s9)))),
% 294.81/187.34 inference(quant_inst,[status(thm)],[])).
% 294.81/187.34 tff(27958,plain,
% 294.81/187.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_f, s8) | (~m_c_h_element_v_out(c_e_h_2, c_f, s9)) | (~node18(c_e_h_2, c_f, s8, s9))),
% 294.81/187.34 inference(modus_ponens,[status(thm)],[27957, 27956])).
% 294.81/187.34 tff(27959,plain,
% 294.81/187.34 ($false),
% 294.81/187.34 inference(unit_resolution,[status(thm)],[27958, 753, 27943, 27944, 27952])).
% 294.81/187.34 tff(27960,plain,((~node18(c_e_h_2, c_f, s8, s9)) | m_c_h_element_v_out(c_e_h_2, c_f, s8) | (~m_c_h_element_v_out(c_e_h_2, c_f, s9))), inference(lemma,lemma(discharge,[]))).
% 294.81/187.34 tff(27961,plain,
% 294.81/187.34 (~node18(c_e_h_2, c_f, s8, s9)),
% 294.81/187.34 inference(unit_resolution,[status(thm)],[27960, 27944, 27943])).
% 294.81/187.34 tff(27962,plain,
% 294.81/187.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s8, s9)) | node19(c_e_h_2, c_f, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s8, s9)) | node19(c_e_h_2, c_f, s8, s9))),
% 294.81/187.34 inference(rewrite,[status(thm)],[])).
% 294.81/187.34 tff(27963,plain,
% 294.81/187.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s8, s9)) | node19(c_e_h_2, c_f, s8, s9))),
% 294.81/187.34 inference(quant_inst,[status(thm)],[])).
% 294.81/187.34 tff(27964,plain,
% 294.81/187.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s8, s9)) | node19(c_e_h_2, c_f, s8, s9)),
% 294.81/187.34 inference(modus_ponens,[status(thm)],[27963, 27962])).
% 294.81/187.34 tff(27965,plain,
% 294.81/187.34 (node19(c_e_h_2, c_f, s8, s9)),
% 294.81/187.34 inference(unit_resolution,[status(thm)],[27964, 190, 1993])).
% 294.81/187.34 tff(27966,plain,
% 294.81/187.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_f, s8, s9)) | node17(c_e_h_2, c_f, s8) | node18(c_e_h_2, c_f, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_f, s8, s9)) | node17(c_e_h_2, c_f, s8) | node18(c_e_h_2, c_f, s8, s9))),
% 294.81/187.34 inference(rewrite,[status(thm)],[])).
% 294.81/187.34 tff(27967,plain,
% 294.81/187.34 ((node17(c_e_h_2, c_f, s8) | node18(c_e_h_2, c_f, s8, s9) | (~node19(c_e_h_2, c_f, s8, s9))) <=> ((~node19(c_e_h_2, c_f, s8, s9)) | node17(c_e_h_2, c_f, s8) | node18(c_e_h_2, c_f, s8, s9))),
% 294.81/187.34 inference(rewrite,[status(thm)],[])).
% 294.81/187.34 tff(27968,plain,
% 294.81/187.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s8) | node18(c_e_h_2, c_f, s8, s9) | (~node19(c_e_h_2, c_f, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_f, s8, s9)) | node17(c_e_h_2, c_f, s8) | node18(c_e_h_2, c_f, s8, s9)))),
% 294.81/187.34 inference(monotonicity,[status(thm)],[27967])).
% 294.81/187.34 tff(27969,plain,
% 294.81/187.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s8) | node18(c_e_h_2, c_f, s8, s9) | (~node19(c_e_h_2, c_f, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_f, s8, s9)) | node17(c_e_h_2, c_f, s8) | node18(c_e_h_2, c_f, s8, s9))),
% 294.81/187.34 inference(transitivity,[status(thm)],[27968, 27966])).
% 294.81/187.34 tff(27970,plain,
% 294.81/187.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s8) | node18(c_e_h_2, c_f, s8, s9) | (~node19(c_e_h_2, c_f, s8, s9)))),
% 294.81/187.34 inference(quant_inst,[status(thm)],[])).
% 294.81/187.34 tff(27971,plain,
% 294.81/187.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_f, s8, s9)) | node17(c_e_h_2, c_f, s8) | node18(c_e_h_2, c_f, s8, s9)),
% 294.81/187.34 inference(modus_ponens,[status(thm)],[27970, 27969])).
% 294.81/187.34 tff(27972,plain,
% 294.81/187.34 (node17(c_e_h_2, c_f, s8) | node18(c_e_h_2, c_f, s8, s9)),
% 294.81/187.34 inference(unit_resolution,[status(thm)],[27971, 776, 27965])).
% 294.81/187.34 tff(27973,plain,
% 294.81/187.34 (node17(c_e_h_2, c_f, s8)),
% 294.81/187.34 inference(unit_resolution,[status(thm)],[27972, 27961])).
% 294.81/187.34 tff(27974,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_f, s8)), introduced(assumption)).
% 294.81/187.34 tff(27975,plain,
% 294.81/187.34 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s8)) | m_c_h_element_v_in2(c_e_h_2, c_f, s8) | (~node17(c_e_h_2, c_f, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s8)) | m_c_h_element_v_in2(c_e_h_2, c_f, s8) | (~node17(c_e_h_2, c_f, s8)))),
% 294.81/187.34 inference(rewrite,[status(thm)],[])).
% 294.81/187.34 tff(27976,plain,
% 294.81/187.34 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s8)) | m_c_h_element_v_in2(c_e_h_2, c_f, s8) | (~node17(c_e_h_2, c_f, s8)))),
% 294.81/187.34 inference(quant_inst,[status(thm)],[])).
% 294.81/187.34 tff(27977,plain,
% 294.81/187.34 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s8)) | m_c_h_element_v_in2(c_e_h_2, c_f, s8) | (~node17(c_e_h_2, c_f, s8))),
% 294.81/187.34 inference(modus_ponens,[status(thm)],[27976, 27975])).
% 294.81/187.34 tff(27978,plain,
% 294.81/187.34 ((~m_c_h_element_v_in1(c_e_h_2, c_f, s8)) | (~node17(c_e_h_2, c_f, s8))),
% 294.81/187.34 inference(unit_resolution,[status(thm)],[27977, 919, 27974])).
% 294.81/187.34 tff(27979,plain,
% 294.81/187.34 (~m_c_h_element_v_in1(c_e_h_2, c_f, s8)),
% 294.81/187.34 inference(unit_resolution,[status(thm)],[27978, 27973])).
% 294.81/187.34 tff(27980,plain,
% 294.81/187.34 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_f, s8)) | m_c_h_element_v_in1(c_e_h_2, c_f, s8) | m_c_h_element_v_in2(c_e_h_2, c_f, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_f, s8)) | m_c_h_element_v_in1(c_e_h_2, c_f, s8) | m_c_h_element_v_in2(c_e_h_2, c_f, s8))),
% 294.81/187.34 inference(rewrite,[status(thm)],[])).
% 294.81/187.34 tff(27981,plain,
% 294.81/187.34 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_f, s8)) | m_c_h_element_v_in1(c_e_h_2, c_f, s8) | m_c_h_element_v_in2(c_e_h_2, c_f, s8))),
% 294.81/187.34 inference(quant_inst,[status(thm)],[])).
% 294.81/187.34 tff(27982,plain,
% 294.81/187.34 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_f, s8)) | m_c_h_element_v_in1(c_e_h_2, c_f, s8) | m_c_h_element_v_in2(c_e_h_2, c_f, s8)),
% 294.81/187.34 inference(modus_ponens,[status(thm)],[27981, 27980])).
% 294.81/187.34 tff(27983,plain,
% 294.81/187.34 ((~node16(c_e_h_2, c_f, s8)) | m_c_h_element_v_in1(c_e_h_2, c_f, s8)),
% 294.81/187.34 inference(unit_resolution,[status(thm)],[27982, 178, 27974])).
% 294.81/187.34 tff(27984,plain,
% 294.81/187.34 (~node16(c_e_h_2, c_f, s8)),
% 294.81/187.34 inference(unit_resolution,[status(thm)],[27983, 27979])).
% 294.81/187.34 tff(27985,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_f, s8)), introduced(assumption)).
% 294.81/187.34 tff(27986,assumption,(node14(c_e_h_2, c_f, s8, s9)), introduced(assumption)).
% 294.81/187.35 tff(27987,plain,
% 294.81/187.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_f, s8) | (~m_c_h_element_v_out(c_e_h_2, c_f, s9)) | (~node14(c_e_h_2, c_f, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_f, s8) | (~m_c_h_element_v_out(c_e_h_2, c_f, s9)) | (~node14(c_e_h_2, c_f, s8, s9)))),
% 294.81/187.35 inference(rewrite,[status(thm)],[])).
% 294.81/187.35 tff(27988,plain,
% 294.81/187.35 (((~node14(c_e_h_2, c_f, s8, s9)) | m_c_h_element_v_in1(c_e_h_2, c_f, s8) | (~m_c_h_element_v_out(c_e_h_2, c_f, s9))) <=> (m_c_h_element_v_in1(c_e_h_2, c_f, s8) | (~m_c_h_element_v_out(c_e_h_2, c_f, s9)) | (~node14(c_e_h_2, c_f, s8, s9)))),
% 294.81/187.35 inference(rewrite,[status(thm)],[])).
% 294.81/187.35 tff(27989,plain,
% 294.81/187.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_f, s8, s9)) | m_c_h_element_v_in1(c_e_h_2, c_f, s8) | (~m_c_h_element_v_out(c_e_h_2, c_f, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_f, s8) | (~m_c_h_element_v_out(c_e_h_2, c_f, s9)) | (~node14(c_e_h_2, c_f, s8, s9))))),
% 294.81/187.35 inference(monotonicity,[status(thm)],[27988])).
% 294.81/187.35 tff(27990,plain,
% 294.81/187.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_f, s8, s9)) | m_c_h_element_v_in1(c_e_h_2, c_f, s8) | (~m_c_h_element_v_out(c_e_h_2, c_f, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_f, s8) | (~m_c_h_element_v_out(c_e_h_2, c_f, s9)) | (~node14(c_e_h_2, c_f, s8, s9)))),
% 294.81/187.35 inference(transitivity,[status(thm)],[27989, 27987])).
% 294.81/187.35 tff(27991,plain,
% 294.81/187.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_f, s8, s9)) | m_c_h_element_v_in1(c_e_h_2, c_f, s8) | (~m_c_h_element_v_out(c_e_h_2, c_f, s9)))),
% 294.81/187.35 inference(quant_inst,[status(thm)],[])).
% 294.81/187.35 tff(27992,plain,
% 294.81/187.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_f, s8) | (~m_c_h_element_v_out(c_e_h_2, c_f, s9)) | (~node14(c_e_h_2, c_f, s8, s9))),
% 294.81/187.35 inference(modus_ponens,[status(thm)],[27991, 27990])).
% 294.81/187.35 tff(27993,plain,
% 294.81/187.35 ($false),
% 294.81/187.35 inference(unit_resolution,[status(thm)],[27992, 223, 27944, 27986, 27985])).
% 294.81/187.35 tff(27994,plain,((~node14(c_e_h_2, c_f, s8, s9)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s9)) | m_c_h_element_v_in1(c_e_h_2, c_f, s8)), inference(lemma,lemma(discharge,[]))).
% 294.81/187.35 tff(27995,plain,
% 294.81/187.35 (~node14(c_e_h_2, c_f, s8, s9)),
% 294.81/187.35 inference(unit_resolution,[status(thm)],[27994, 27979, 27944])).
% 294.81/187.35 tff(27996,plain,
% 294.81/187.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_f, s8, s9)) | node16(c_e_h_2, c_f, s8) | node15(c_e_h_2, c_f, s8, s9) | node14(c_e_h_2, c_f, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_f, s8, s9)) | node16(c_e_h_2, c_f, s8) | node15(c_e_h_2, c_f, s8, s9) | node14(c_e_h_2, c_f, s8, s9))),
% 294.81/187.35 inference(rewrite,[status(thm)],[])).
% 294.81/187.35 tff(27997,plain,
% 294.81/187.35 ((node16(c_e_h_2, c_f, s8) | node14(c_e_h_2, c_f, s8, s9) | node15(c_e_h_2, c_f, s8, s9) | (~node19(c_e_h_2, c_f, s8, s9))) <=> ((~node19(c_e_h_2, c_f, s8, s9)) | node16(c_e_h_2, c_f, s8) | node15(c_e_h_2, c_f, s8, s9) | node14(c_e_h_2, c_f, s8, s9))),
% 294.81/187.35 inference(rewrite,[status(thm)],[])).
% 294.81/187.35 tff(27998,plain,
% 294.81/187.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s8) | node14(c_e_h_2, c_f, s8, s9) | node15(c_e_h_2, c_f, s8, s9) | (~node19(c_e_h_2, c_f, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_f, s8, s9)) | node16(c_e_h_2, c_f, s8) | node15(c_e_h_2, c_f, s8, s9) | node14(c_e_h_2, c_f, s8, s9)))),
% 294.81/187.35 inference(monotonicity,[status(thm)],[27997])).
% 294.81/187.35 tff(27999,plain,
% 294.81/187.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s8) | node14(c_e_h_2, c_f, s8, s9) | node15(c_e_h_2, c_f, s8, s9) | (~node19(c_e_h_2, c_f, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_f, s8, s9)) | node16(c_e_h_2, c_f, s8) | node15(c_e_h_2, c_f, s8, s9) | node14(c_e_h_2, c_f, s8, s9))),
% 294.81/187.35 inference(transitivity,[status(thm)],[27998, 27996])).
% 294.81/187.35 tff(28000,plain,
% 294.81/187.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s8) | node14(c_e_h_2, c_f, s8, s9) | node15(c_e_h_2, c_f, s8, s9) | (~node19(c_e_h_2, c_f, s8, s9)))),
% 294.81/187.35 inference(quant_inst,[status(thm)],[])).
% 294.81/187.35 tff(28001,plain,
% 294.81/187.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_f, s8, s9)) | node16(c_e_h_2, c_f, s8) | node15(c_e_h_2, c_f, s8, s9) | node14(c_e_h_2, c_f, s8, s9)),
% 294.81/187.35 inference(modus_ponens,[status(thm)],[28000, 27999])).
% 294.81/187.35 tff(28002,plain,
% 294.81/187.35 (node16(c_e_h_2, c_f, s8) | node15(c_e_h_2, c_f, s8, s9) | node14(c_e_h_2, c_f, s8, s9)),
% 294.81/187.35 inference(unit_resolution,[status(thm)],[28001, 204, 27965])).
% 294.81/187.35 tff(28003,plain,
% 294.81/187.35 ($false),
% 294.81/187.35 inference(unit_resolution,[status(thm)],[28002, 27995, 27984, 27951])).
% 294.81/187.35 tff(28004,plain,((~m_c_h_element_v_out(c_e_h_2, c_f, s9)) | m_c_h_element_v_in2(c_e_h_2, c_f, s8) | m_c_h_element_v_out(c_e_h_2, c_f, s8)), inference(lemma,lemma(discharge,[]))).
% 294.81/187.35 tff(28005,plain,
% 294.81/187.35 ((~m_c_h_element_v_out(c_e_h_2, c_f, s9)) | m_c_h_element_v_in2(c_e_h_2, c_f, s8)),
% 294.81/187.35 inference(unit_resolution,[status(thm)],[28004, 8863])).
% 294.81/187.35 tff(28006,plain,
% 294.81/187.35 (~m_c_h_element_v_out(c_e_h_2, c_f, s9)),
% 294.81/187.35 inference(unit_resolution,[status(thm)],[28005, 27942])).
% 294.81/187.35 tff(28007,assumption,(m_c_h_element_v_in2(c_e_h_2, c_f, s9)), introduced(assumption)).
% 294.81/187.35 tff(28008,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_i, s9)), introduced(assumption)).
% 294.81/187.35 tff(28009,plain,
% 294.81/187.35 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_f, s9)) | m_and_h_gate_v_out(c_e_h_2, c_i, s9))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s9)) | m_and_h_gate_v_out(c_e_h_2, c_i, s9))),
% 294.81/187.35 inference(rewrite,[status(thm)],[])).
% 294.81/187.35 tff(28010,plain,
% 294.81/187.35 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_f, s9)) | m_and_h_gate_v_out(c_e_h_2, c_i, s9))),
% 294.81/187.35 inference(quant_inst,[status(thm)],[])).
% 294.81/187.35 tff(28011,plain,
% 294.81/187.35 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s9)) | m_and_h_gate_v_out(c_e_h_2, c_i, s9)),
% 294.81/187.35 inference(modus_ponens,[status(thm)],[28010, 28009])).
% 294.81/187.35 tff(28012,plain,
% 294.81/187.35 ($false),
% 294.81/187.35 inference(unit_resolution,[status(thm)],[28011, 2143, 28008, 28007])).
% 294.81/187.35 tff(28013,plain,((~m_c_h_element_v_in2(c_e_h_2, c_f, s9)) | m_and_h_gate_v_out(c_e_h_2, c_i, s9)), inference(lemma,lemma(discharge,[]))).
% 294.81/187.35 tff(28014,plain,
% 294.81/187.35 (~m_c_h_element_v_in2(c_e_h_2, c_f, s9)),
% 294.81/187.35 inference(unit_resolution,[status(thm)],[28013, 27909])).
% 294.81/187.35 tff(28015,assumption,(m_c_h_element_v_out(c_e_h_2, c_f, s10)), introduced(assumption)).
% 294.81/187.35 tff(28016,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_f, s9)), introduced(assumption)).
% 294.81/187.35 tff(28017,assumption,(~m_c_h_element_v_out(c_e_h_2, c_f, s9)), introduced(assumption)).
% 294.81/187.35 tff(28018,assumption,(node15(c_e_h_2, c_f, s9, s10)), introduced(assumption)).
% 294.81/187.35 tff(28019,plain,
% 294.81/187.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s10)) | (~node15(c_e_h_2, c_f, s9, s10)) | m_c_h_element_v_out(c_e_h_2, c_f, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s10)) | (~node15(c_e_h_2, c_f, s9, s10)) | m_c_h_element_v_out(c_e_h_2, c_f, s9))),
% 294.81/187.35 inference(rewrite,[status(thm)],[])).
% 294.81/187.35 tff(28020,plain,
% 294.81/187.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s10)) | (~node15(c_e_h_2, c_f, s9, s10)) | m_c_h_element_v_out(c_e_h_2, c_f, s9))),
% 294.81/187.35 inference(quant_inst,[status(thm)],[])).
% 294.81/187.35 tff(28021,plain,
% 294.81/187.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s10)) | (~node15(c_e_h_2, c_f, s9, s10)) | m_c_h_element_v_out(c_e_h_2, c_f, s9)),
% 294.81/187.35 inference(modus_ponens,[status(thm)],[28020, 28019])).
% 294.81/187.35 tff(28022,plain,
% 294.81/187.35 ($false),
% 294.81/187.35 inference(unit_resolution,[status(thm)],[28021, 147, 28015, 28017, 28018])).
% 294.81/187.35 tff(28023,plain,((~node15(c_e_h_2, c_f, s9, s10)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s10)) | m_c_h_element_v_out(c_e_h_2, c_f, s9)), inference(lemma,lemma(discharge,[]))).
% 294.81/187.35 tff(28024,plain,
% 294.81/187.35 (~node15(c_e_h_2, c_f, s9, s10)),
% 294.81/187.35 inference(unit_resolution,[status(thm)],[28023, 28015, 28017])).
% 294.81/187.35 tff(28025,assumption,(node18(c_e_h_2, c_f, s9, s10)), introduced(assumption)).
% 294.81/187.35 tff(28026,plain,
% 294.81/187.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s10)) | m_c_h_element_v_out(c_e_h_2, c_f, s9) | (~node18(c_e_h_2, c_f, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s10)) | m_c_h_element_v_out(c_e_h_2, c_f, s9) | (~node18(c_e_h_2, c_f, s9, s10)))),
% 294.81/187.35 inference(rewrite,[status(thm)],[])).
% 294.81/187.35 tff(28027,plain,
% 294.81/187.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s10)) | m_c_h_element_v_out(c_e_h_2, c_f, s9) | (~node18(c_e_h_2, c_f, s9, s10)))),
% 294.81/187.35 inference(quant_inst,[status(thm)],[])).
% 294.81/187.35 tff(28028,plain,
% 294.81/187.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s10)) | m_c_h_element_v_out(c_e_h_2, c_f, s9) | (~node18(c_e_h_2, c_f, s9, s10))),
% 294.81/187.35 inference(modus_ponens,[status(thm)],[28027, 28026])).
% 294.81/187.35 tff(28029,plain,
% 294.81/187.35 ($false),
% 294.81/187.35 inference(unit_resolution,[status(thm)],[28028, 753, 28015, 28017, 28025])).
% 294.81/187.35 tff(28030,plain,((~node18(c_e_h_2, c_f, s9, s10)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s10)) | m_c_h_element_v_out(c_e_h_2, c_f, s9)), inference(lemma,lemma(discharge,[]))).
% 294.81/187.35 tff(28031,plain,
% 294.81/187.35 (~node18(c_e_h_2, c_f, s9, s10)),
% 294.81/187.35 inference(unit_resolution,[status(thm)],[28030, 28015, 28017])).
% 294.81/187.35 tff(28032,plain,
% 294.81/187.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s9, s10)) | node19(c_e_h_2, c_f, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s9, s10)) | node19(c_e_h_2, c_f, s9, s10))),
% 294.81/187.35 inference(rewrite,[status(thm)],[])).
% 294.81/187.35 tff(28033,plain,
% 294.81/187.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s9, s10)) | node19(c_e_h_2, c_f, s9, s10))),
% 294.81/187.36 inference(quant_inst,[status(thm)],[])).
% 294.81/187.36 tff(28034,plain,
% 294.81/187.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s9, s10)) | node19(c_e_h_2, c_f, s9, s10)),
% 294.81/187.36 inference(modus_ponens,[status(thm)],[28033, 28032])).
% 294.81/187.36 tff(28035,plain,
% 294.81/187.36 (node19(c_e_h_2, c_f, s9, s10)),
% 294.81/187.36 inference(unit_resolution,[status(thm)],[28034, 190, 7676])).
% 294.81/187.36 tff(28036,plain,
% 294.81/187.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_2, c_f, s9, s10) | (~node19(c_e_h_2, c_f, s9, s10)) | node17(c_e_h_2, c_f, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_2, c_f, s9, s10) | (~node19(c_e_h_2, c_f, s9, s10)) | node17(c_e_h_2, c_f, s9))),
% 294.81/187.36 inference(rewrite,[status(thm)],[])).
% 294.81/187.36 tff(28037,plain,
% 294.81/187.36 ((node17(c_e_h_2, c_f, s9) | node18(c_e_h_2, c_f, s9, s10) | (~node19(c_e_h_2, c_f, s9, s10))) <=> (node18(c_e_h_2, c_f, s9, s10) | (~node19(c_e_h_2, c_f, s9, s10)) | node17(c_e_h_2, c_f, s9))),
% 294.81/187.36 inference(rewrite,[status(thm)],[])).
% 294.81/187.36 tff(28038,plain,
% 294.81/187.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s9) | node18(c_e_h_2, c_f, s9, s10) | (~node19(c_e_h_2, c_f, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_2, c_f, s9, s10) | (~node19(c_e_h_2, c_f, s9, s10)) | node17(c_e_h_2, c_f, s9)))),
% 294.81/187.36 inference(monotonicity,[status(thm)],[28037])).
% 294.81/187.36 tff(28039,plain,
% 294.81/187.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s9) | node18(c_e_h_2, c_f, s9, s10) | (~node19(c_e_h_2, c_f, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_2, c_f, s9, s10) | (~node19(c_e_h_2, c_f, s9, s10)) | node17(c_e_h_2, c_f, s9))),
% 294.81/187.36 inference(transitivity,[status(thm)],[28038, 28036])).
% 294.81/187.36 tff(28040,plain,
% 294.81/187.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s9) | node18(c_e_h_2, c_f, s9, s10) | (~node19(c_e_h_2, c_f, s9, s10)))),
% 294.81/187.36 inference(quant_inst,[status(thm)],[])).
% 294.81/187.36 tff(28041,plain,
% 294.81/187.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_2, c_f, s9, s10) | (~node19(c_e_h_2, c_f, s9, s10)) | node17(c_e_h_2, c_f, s9)),
% 294.81/187.36 inference(modus_ponens,[status(thm)],[28040, 28039])).
% 294.81/187.36 tff(28042,plain,
% 294.81/187.36 (node18(c_e_h_2, c_f, s9, s10) | node17(c_e_h_2, c_f, s9)),
% 294.81/187.36 inference(unit_resolution,[status(thm)],[28041, 776, 28035])).
% 294.81/187.36 tff(28043,plain,
% 294.81/187.36 (node17(c_e_h_2, c_f, s9)),
% 294.81/187.36 inference(unit_resolution,[status(thm)],[28042, 28031])).
% 294.81/187.36 tff(28044,assumption,(node17(c_e_h_2, c_f, s9)), introduced(assumption)).
% 294.81/187.36 tff(28045,plain,
% 294.81/187.36 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_2, c_f, s9) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s9)) | (~node17(c_e_h_2, c_f, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_f, s9) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s9)) | (~node17(c_e_h_2, c_f, s9)))),
% 294.81/187.36 inference(rewrite,[status(thm)],[])).
% 294.81/187.36 tff(28046,plain,
% 294.81/187.36 (((~m_c_h_element_v_in1(c_e_h_2, c_f, s9)) | m_c_h_element_v_in2(c_e_h_2, c_f, s9) | (~node17(c_e_h_2, c_f, s9))) <=> (m_c_h_element_v_in2(c_e_h_2, c_f, s9) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s9)) | (~node17(c_e_h_2, c_f, s9)))),
% 294.81/187.36 inference(rewrite,[status(thm)],[])).
% 294.81/187.36 tff(28047,plain,
% 294.81/187.36 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s9)) | m_c_h_element_v_in2(c_e_h_2, c_f, s9) | (~node17(c_e_h_2, c_f, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_2, c_f, s9) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s9)) | (~node17(c_e_h_2, c_f, s9))))),
% 294.81/187.36 inference(monotonicity,[status(thm)],[28046])).
% 294.81/187.36 tff(28048,plain,
% 294.81/187.36 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s9)) | m_c_h_element_v_in2(c_e_h_2, c_f, s9) | (~node17(c_e_h_2, c_f, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_f, s9) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s9)) | (~node17(c_e_h_2, c_f, s9)))),
% 294.81/187.36 inference(transitivity,[status(thm)],[28047, 28045])).
% 294.81/187.36 tff(28049,plain,
% 294.81/187.36 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s9)) | m_c_h_element_v_in2(c_e_h_2, c_f, s9) | (~node17(c_e_h_2, c_f, s9)))),
% 294.81/187.36 inference(quant_inst,[status(thm)],[])).
% 294.81/187.36 tff(28050,plain,
% 294.81/187.36 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_f, s9) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s9)) | (~node17(c_e_h_2, c_f, s9))),
% 294.81/187.36 inference(modus_ponens,[status(thm)],[28049, 28048])).
% 294.81/187.36 tff(28051,plain,
% 294.81/187.36 (m_c_h_element_v_in2(c_e_h_2, c_f, s9) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s9))),
% 294.81/187.36 inference(unit_resolution,[status(thm)],[28050, 919, 28044])).
% 294.81/187.36 tff(28052,plain,
% 294.81/187.36 (~m_c_h_element_v_in1(c_e_h_2, c_f, s9)),
% 294.81/187.36 inference(unit_resolution,[status(thm)],[28051, 28016])).
% 294.81/187.36 tff(28053,assumption,(~node15(c_e_h_2, c_f, s9, s10)), introduced(assumption)).
% 294.81/187.36 tff(28054,plain,
% 294.81/187.36 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_f, s9)) | m_c_h_element_v_in1(c_e_h_2, c_f, s9) | m_c_h_element_v_in2(c_e_h_2, c_f, s9))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_f, s9)) | m_c_h_element_v_in1(c_e_h_2, c_f, s9) | m_c_h_element_v_in2(c_e_h_2, c_f, s9))),
% 294.81/187.36 inference(rewrite,[status(thm)],[])).
% 294.81/187.36 tff(28055,plain,
% 294.81/187.36 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_f, s9)) | m_c_h_element_v_in1(c_e_h_2, c_f, s9) | m_c_h_element_v_in2(c_e_h_2, c_f, s9))),
% 294.81/187.36 inference(quant_inst,[status(thm)],[])).
% 294.81/187.36 tff(28056,plain,
% 294.81/187.36 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_f, s9)) | m_c_h_element_v_in1(c_e_h_2, c_f, s9) | m_c_h_element_v_in2(c_e_h_2, c_f, s9)),
% 294.81/187.36 inference(modus_ponens,[status(thm)],[28055, 28054])).
% 294.81/187.36 tff(28057,plain,
% 294.81/187.36 (~node16(c_e_h_2, c_f, s9)),
% 294.81/187.36 inference(unit_resolution,[status(thm)],[28056, 178, 28016, 28052])).
% 294.81/187.36 tff(28058,plain,
% 294.81/187.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_f, s9, s10)) | node14(c_e_h_2, c_f, s9, s10) | node15(c_e_h_2, c_f, s9, s10) | node16(c_e_h_2, c_f, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_f, s9, s10)) | node14(c_e_h_2, c_f, s9, s10) | node15(c_e_h_2, c_f, s9, s10) | node16(c_e_h_2, c_f, s9))),
% 294.81/187.36 inference(rewrite,[status(thm)],[])).
% 294.81/187.36 tff(28059,plain,
% 294.81/187.36 ((node16(c_e_h_2, c_f, s9) | node14(c_e_h_2, c_f, s9, s10) | node15(c_e_h_2, c_f, s9, s10) | (~node19(c_e_h_2, c_f, s9, s10))) <=> ((~node19(c_e_h_2, c_f, s9, s10)) | node14(c_e_h_2, c_f, s9, s10) | node15(c_e_h_2, c_f, s9, s10) | node16(c_e_h_2, c_f, s9))),
% 294.81/187.36 inference(rewrite,[status(thm)],[])).
% 294.81/187.36 tff(28060,plain,
% 294.81/187.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s9) | node14(c_e_h_2, c_f, s9, s10) | node15(c_e_h_2, c_f, s9, s10) | (~node19(c_e_h_2, c_f, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_2, c_f, s9, s10)) | node14(c_e_h_2, c_f, s9, s10) | node15(c_e_h_2, c_f, s9, s10) | node16(c_e_h_2, c_f, s9)))),
% 294.81/187.36 inference(monotonicity,[status(thm)],[28059])).
% 294.81/187.36 tff(28061,plain,
% 294.81/187.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s9) | node14(c_e_h_2, c_f, s9, s10) | node15(c_e_h_2, c_f, s9, s10) | (~node19(c_e_h_2, c_f, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_f, s9, s10)) | node14(c_e_h_2, c_f, s9, s10) | node15(c_e_h_2, c_f, s9, s10) | node16(c_e_h_2, c_f, s9))),
% 294.81/187.36 inference(transitivity,[status(thm)],[28060, 28058])).
% 294.81/187.36 tff(28062,plain,
% 294.81/187.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s9) | node14(c_e_h_2, c_f, s9, s10) | node15(c_e_h_2, c_f, s9, s10) | (~node19(c_e_h_2, c_f, s9, s10)))),
% 294.81/187.36 inference(quant_inst,[status(thm)],[])).
% 294.81/187.36 tff(28063,plain,
% 294.81/187.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_2, c_f, s9, s10)) | node14(c_e_h_2, c_f, s9, s10) | node15(c_e_h_2, c_f, s9, s10) | node16(c_e_h_2, c_f, s9)),
% 294.81/187.36 inference(modus_ponens,[status(thm)],[28062, 28061])).
% 294.81/187.36 tff(28064,plain,
% 294.81/187.36 (node14(c_e_h_2, c_f, s9, s10) | node15(c_e_h_2, c_f, s9, s10) | node16(c_e_h_2, c_f, s9)),
% 294.81/187.36 inference(unit_resolution,[status(thm)],[28063, 204, 28035])).
% 294.81/187.36 tff(28065,plain,
% 294.81/187.36 (node14(c_e_h_2, c_f, s9, s10)),
% 294.81/187.36 inference(unit_resolution,[status(thm)],[28064, 28057, 28053])).
% 294.81/187.36 tff(28066,plain,
% 294.81/187.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s10)) | m_c_h_element_v_in1(c_e_h_2, c_f, s9) | (~node14(c_e_h_2, c_f, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s10)) | m_c_h_element_v_in1(c_e_h_2, c_f, s9) | (~node14(c_e_h_2, c_f, s9, s10)))),
% 294.81/187.36 inference(rewrite,[status(thm)],[])).
% 294.81/187.36 tff(28067,plain,
% 294.81/187.36 (((~node14(c_e_h_2, c_f, s9, s10)) | m_c_h_element_v_in1(c_e_h_2, c_f, s9) | (~m_c_h_element_v_out(c_e_h_2, c_f, s10))) <=> ((~m_c_h_element_v_out(c_e_h_2, c_f, s10)) | m_c_h_element_v_in1(c_e_h_2, c_f, s9) | (~node14(c_e_h_2, c_f, s9, s10)))),
% 294.81/187.36 inference(rewrite,[status(thm)],[])).
% 294.81/187.36 tff(28068,plain,
% 294.81/187.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_f, s9, s10)) | m_c_h_element_v_in1(c_e_h_2, c_f, s9) | (~m_c_h_element_v_out(c_e_h_2, c_f, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s10)) | m_c_h_element_v_in1(c_e_h_2, c_f, s9) | (~node14(c_e_h_2, c_f, s9, s10))))),
% 294.81/187.36 inference(monotonicity,[status(thm)],[28067])).
% 294.81/187.36 tff(28069,plain,
% 294.81/187.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_f, s9, s10)) | m_c_h_element_v_in1(c_e_h_2, c_f, s9) | (~m_c_h_element_v_out(c_e_h_2, c_f, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s10)) | m_c_h_element_v_in1(c_e_h_2, c_f, s9) | (~node14(c_e_h_2, c_f, s9, s10)))),
% 294.81/187.37 inference(transitivity,[status(thm)],[28068, 28066])).
% 294.81/187.37 tff(28070,plain,
% 294.81/187.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_f, s9, s10)) | m_c_h_element_v_in1(c_e_h_2, c_f, s9) | (~m_c_h_element_v_out(c_e_h_2, c_f, s10)))),
% 294.81/187.37 inference(quant_inst,[status(thm)],[])).
% 294.81/187.37 tff(28071,plain,
% 294.81/187.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s10)) | m_c_h_element_v_in1(c_e_h_2, c_f, s9) | (~node14(c_e_h_2, c_f, s9, s10))),
% 294.81/187.37 inference(modus_ponens,[status(thm)],[28070, 28069])).
% 294.81/187.37 tff(28072,plain,
% 294.81/187.37 ($false),
% 294.81/187.37 inference(unit_resolution,[status(thm)],[28071, 223, 28015, 28065, 28052])).
% 294.81/187.37 tff(28073,plain,(m_c_h_element_v_in2(c_e_h_2, c_f, s9) | (~m_c_h_element_v_out(c_e_h_2, c_f, s10)) | node15(c_e_h_2, c_f, s9, s10) | (~node17(c_e_h_2, c_f, s9))), inference(lemma,lemma(discharge,[]))).
% 294.81/187.37 tff(28074,plain,
% 294.81/187.37 ($false),
% 294.81/187.37 inference(unit_resolution,[status(thm)],[28073, 28043, 28024, 28016, 28015])).
% 294.81/187.37 tff(28075,plain,((~m_c_h_element_v_out(c_e_h_2, c_f, s10)) | m_c_h_element_v_in2(c_e_h_2, c_f, s9) | m_c_h_element_v_out(c_e_h_2, c_f, s9)), inference(lemma,lemma(discharge,[]))).
% 294.81/187.37 tff(28076,plain,
% 294.81/187.37 ((~m_c_h_element_v_out(c_e_h_2, c_f, s10)) | m_c_h_element_v_out(c_e_h_2, c_f, s9)),
% 294.81/187.37 inference(unit_resolution,[status(thm)],[28075, 28014])).
% 294.81/187.37 tff(28077,plain,
% 294.81/187.37 (~m_c_h_element_v_out(c_e_h_2, c_f, s10)),
% 294.81/187.37 inference(unit_resolution,[status(thm)],[28076, 28006])).
% 294.81/187.37 tff(28078,assumption,(m_c_h_element_v_out(c_e_h_2, c_f, s11)), introduced(assumption)).
% 294.81/187.37 tff(28079,assumption,(~m_c_h_element_v_out(c_e_h_2, c_f, s10)), introduced(assumption)).
% 294.81/187.37 tff(28080,assumption,(node18(c_e_h_2, c_f, s10, s11)), introduced(assumption)).
% 294.81/187.37 tff(28081,plain,
% 294.81/187.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_f, s10) | (~m_c_h_element_v_out(c_e_h_2, c_f, s11)) | (~node18(c_e_h_2, c_f, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_f, s10) | (~m_c_h_element_v_out(c_e_h_2, c_f, s11)) | (~node18(c_e_h_2, c_f, s10, s11)))),
% 294.81/187.37 inference(rewrite,[status(thm)],[])).
% 294.81/187.37 tff(28082,plain,
% 294.81/187.37 (((~m_c_h_element_v_out(c_e_h_2, c_f, s11)) | m_c_h_element_v_out(c_e_h_2, c_f, s10) | (~node18(c_e_h_2, c_f, s10, s11))) <=> (m_c_h_element_v_out(c_e_h_2, c_f, s10) | (~m_c_h_element_v_out(c_e_h_2, c_f, s11)) | (~node18(c_e_h_2, c_f, s10, s11)))),
% 294.81/187.37 inference(rewrite,[status(thm)],[])).
% 294.81/187.37 tff(28083,plain,
% 294.81/187.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s11)) | m_c_h_element_v_out(c_e_h_2, c_f, s10) | (~node18(c_e_h_2, c_f, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_f, s10) | (~m_c_h_element_v_out(c_e_h_2, c_f, s11)) | (~node18(c_e_h_2, c_f, s10, s11))))),
% 294.81/187.37 inference(monotonicity,[status(thm)],[28082])).
% 294.81/187.37 tff(28084,plain,
% 294.81/187.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s11)) | m_c_h_element_v_out(c_e_h_2, c_f, s10) | (~node18(c_e_h_2, c_f, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_f, s10) | (~m_c_h_element_v_out(c_e_h_2, c_f, s11)) | (~node18(c_e_h_2, c_f, s10, s11)))),
% 294.81/187.37 inference(transitivity,[status(thm)],[28083, 28081])).
% 294.81/187.37 tff(28085,plain,
% 294.81/187.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s11)) | m_c_h_element_v_out(c_e_h_2, c_f, s10) | (~node18(c_e_h_2, c_f, s10, s11)))),
% 294.81/187.37 inference(quant_inst,[status(thm)],[])).
% 294.81/187.37 tff(28086,plain,
% 294.81/187.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_f, s10) | (~m_c_h_element_v_out(c_e_h_2, c_f, s11)) | (~node18(c_e_h_2, c_f, s10, s11))),
% 294.81/187.37 inference(modus_ponens,[status(thm)],[28085, 28084])).
% 294.81/187.37 tff(28087,plain,
% 294.81/187.37 ($false),
% 294.81/187.37 inference(unit_resolution,[status(thm)],[28086, 753, 28078, 28079, 28080])).
% 294.81/187.37 tff(28088,plain,((~node18(c_e_h_2, c_f, s10, s11)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s11)) | m_c_h_element_v_out(c_e_h_2, c_f, s10)), inference(lemma,lemma(discharge,[]))).
% 294.81/187.37 tff(28089,plain,
% 294.81/187.37 (~node18(c_e_h_2, c_f, s10, s11)),
% 294.81/187.37 inference(unit_resolution,[status(thm)],[28088, 28079, 28078])).
% 294.81/187.37 tff(28090,plain,
% 294.81/187.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s10, s11)) | node19(c_e_h_2, c_f, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s10, s11)) | node19(c_e_h_2, c_f, s10, s11))),
% 294.81/187.37 inference(rewrite,[status(thm)],[])).
% 294.81/187.37 tff(28091,plain,
% 294.81/187.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s10, s11)) | node19(c_e_h_2, c_f, s10, s11))),
% 294.81/187.37 inference(quant_inst,[status(thm)],[])).
% 294.81/187.37 tff(28092,plain,
% 294.81/187.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s10, s11)) | node19(c_e_h_2, c_f, s10, s11)),
% 294.81/187.37 inference(modus_ponens,[status(thm)],[28091, 28090])).
% 294.81/187.37 tff(28093,plain,
% 294.81/187.37 (node19(c_e_h_2, c_f, s10, s11)),
% 294.81/187.37 inference(unit_resolution,[status(thm)],[28092, 190, 7748])).
% 294.81/187.37 tff(28094,plain,
% 294.81/187.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_2, c_f, s10, s11) | (~node19(c_e_h_2, c_f, s10, s11)) | node17(c_e_h_2, c_f, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_2, c_f, s10, s11) | (~node19(c_e_h_2, c_f, s10, s11)) | node17(c_e_h_2, c_f, s10))),
% 294.81/187.37 inference(rewrite,[status(thm)],[])).
% 294.81/187.37 tff(28095,plain,
% 294.81/187.37 ((node17(c_e_h_2, c_f, s10) | node18(c_e_h_2, c_f, s10, s11) | (~node19(c_e_h_2, c_f, s10, s11))) <=> (node18(c_e_h_2, c_f, s10, s11) | (~node19(c_e_h_2, c_f, s10, s11)) | node17(c_e_h_2, c_f, s10))),
% 294.81/187.37 inference(rewrite,[status(thm)],[])).
% 294.81/187.37 tff(28096,plain,
% 294.81/187.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s10) | node18(c_e_h_2, c_f, s10, s11) | (~node19(c_e_h_2, c_f, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_2, c_f, s10, s11) | (~node19(c_e_h_2, c_f, s10, s11)) | node17(c_e_h_2, c_f, s10)))),
% 294.81/187.37 inference(monotonicity,[status(thm)],[28095])).
% 294.81/187.37 tff(28097,plain,
% 294.81/187.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s10) | node18(c_e_h_2, c_f, s10, s11) | (~node19(c_e_h_2, c_f, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_2, c_f, s10, s11) | (~node19(c_e_h_2, c_f, s10, s11)) | node17(c_e_h_2, c_f, s10))),
% 294.81/187.37 inference(transitivity,[status(thm)],[28096, 28094])).
% 294.81/187.37 tff(28098,plain,
% 294.81/187.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_f, s10) | node18(c_e_h_2, c_f, s10, s11) | (~node19(c_e_h_2, c_f, s10, s11)))),
% 294.81/187.37 inference(quant_inst,[status(thm)],[])).
% 294.81/187.37 tff(28099,plain,
% 294.81/187.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_2, c_f, s10, s11) | (~node19(c_e_h_2, c_f, s10, s11)) | node17(c_e_h_2, c_f, s10)),
% 294.81/187.38 inference(modus_ponens,[status(thm)],[28098, 28097])).
% 294.81/187.38 tff(28100,plain,
% 294.81/187.38 (node18(c_e_h_2, c_f, s10, s11) | node17(c_e_h_2, c_f, s10)),
% 294.81/187.38 inference(unit_resolution,[status(thm)],[28099, 776, 28093])).
% 294.81/187.38 tff(28101,plain,
% 294.81/187.38 (node17(c_e_h_2, c_f, s10)),
% 294.81/187.38 inference(unit_resolution,[status(thm)],[28100, 28089])).
% 294.81/187.38 tff(28102,assumption,(node15(c_e_h_2, c_f, s10, s11)), introduced(assumption)).
% 294.81/187.38 tff(28103,plain,
% 294.81/187.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s11)) | (~node15(c_e_h_2, c_f, s10, s11)) | m_c_h_element_v_out(c_e_h_2, c_f, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s11)) | (~node15(c_e_h_2, c_f, s10, s11)) | m_c_h_element_v_out(c_e_h_2, c_f, s10))),
% 294.81/187.38 inference(rewrite,[status(thm)],[])).
% 294.81/187.38 tff(28104,plain,
% 294.81/187.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s11)) | (~node15(c_e_h_2, c_f, s10, s11)) | m_c_h_element_v_out(c_e_h_2, c_f, s10))),
% 294.81/187.38 inference(quant_inst,[status(thm)],[])).
% 294.81/187.38 tff(28105,plain,
% 294.81/187.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s11)) | (~node15(c_e_h_2, c_f, s10, s11)) | m_c_h_element_v_out(c_e_h_2, c_f, s10)),
% 294.81/187.38 inference(modus_ponens,[status(thm)],[28104, 28103])).
% 294.81/187.38 tff(28106,plain,
% 294.81/187.38 ($false),
% 294.81/187.38 inference(unit_resolution,[status(thm)],[28105, 147, 28078, 28079, 28102])).
% 294.81/187.38 tff(28107,plain,((~node15(c_e_h_2, c_f, s10, s11)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s11)) | m_c_h_element_v_out(c_e_h_2, c_f, s10)), inference(lemma,lemma(discharge,[]))).
% 294.81/187.38 tff(28108,plain,
% 294.81/187.38 (~node15(c_e_h_2, c_f, s10, s11)),
% 294.81/187.38 inference(unit_resolution,[status(thm)],[28107, 28079, 28078])).
% 294.81/187.38 tff(28109,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_f, s10)), introduced(assumption)).
% 294.81/187.38 tff(28110,assumption,(node17(c_e_h_2, c_f, s10)), introduced(assumption)).
% 294.81/187.38 tff(28111,plain,
% 294.81/187.38 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_f, s10) | (~node17(c_e_h_2, c_f, s10)) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_f, s10) | (~node17(c_e_h_2, c_f, s10)) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s10)))),
% 294.81/187.38 inference(rewrite,[status(thm)],[])).
% 294.81/187.38 tff(28112,plain,
% 294.81/187.38 ((m_c_h_element_v_in1(c_e_h_2, c_f, s10) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s10)) | (~node17(c_e_h_2, c_f, s10))) <=> (m_c_h_element_v_in1(c_e_h_2, c_f, s10) | (~node17(c_e_h_2, c_f, s10)) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s10)))),
% 294.81/187.38 inference(rewrite,[status(thm)],[])).
% 294.81/187.38 tff(28113,plain,
% 294.81/187.38 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_f, s10) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s10)) | (~node17(c_e_h_2, c_f, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_f, s10) | (~node17(c_e_h_2, c_f, s10)) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s10))))),
% 294.81/187.38 inference(monotonicity,[status(thm)],[28112])).
% 294.81/187.38 tff(28114,plain,
% 294.81/187.38 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_f, s10) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s10)) | (~node17(c_e_h_2, c_f, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_f, s10) | (~node17(c_e_h_2, c_f, s10)) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s10)))),
% 294.81/187.38 inference(transitivity,[status(thm)],[28113, 28111])).
% 294.81/187.38 tff(28115,plain,
% 294.81/187.38 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_2, c_f, s10) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s10)) | (~node17(c_e_h_2, c_f, s10)))),
% 294.81/187.38 inference(quant_inst,[status(thm)],[])).
% 294.81/187.38 tff(28116,plain,
% 294.81/187.38 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_2, c_f, s10) | (~node17(c_e_h_2, c_f, s10)) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s10))),
% 294.81/187.38 inference(modus_ponens,[status(thm)],[28115, 28114])).
% 294.81/187.38 tff(28117,plain,
% 294.81/187.38 (m_c_h_element_v_in1(c_e_h_2, c_f, s10) | (~m_c_h_element_v_in2(c_e_h_2, c_f, s10))),
% 294.81/187.38 inference(unit_resolution,[status(thm)],[28116, 859, 28110])).
% 294.81/187.38 tff(28118,plain,
% 294.81/187.38 (~m_c_h_element_v_in2(c_e_h_2, c_f, s10)),
% 294.81/187.38 inference(unit_resolution,[status(thm)],[28117, 28109])).
% 294.81/187.38 tff(28119,assumption,(~node15(c_e_h_2, c_f, s10, s11)), introduced(assumption)).
% 294.81/187.38 tff(28120,assumption,(node14(c_e_h_2, c_f, s10, s11)), introduced(assumption)).
% 294.81/187.38 tff(28121,plain,
% 294.81/187.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s11)) | m_c_h_element_v_in1(c_e_h_2, c_f, s10) | (~node14(c_e_h_2, c_f, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s11)) | m_c_h_element_v_in1(c_e_h_2, c_f, s10) | (~node14(c_e_h_2, c_f, s10, s11)))),
% 294.81/187.38 inference(rewrite,[status(thm)],[])).
% 294.81/187.38 tff(28122,plain,
% 294.81/187.38 (((~node14(c_e_h_2, c_f, s10, s11)) | m_c_h_element_v_in1(c_e_h_2, c_f, s10) | (~m_c_h_element_v_out(c_e_h_2, c_f, s11))) <=> ((~m_c_h_element_v_out(c_e_h_2, c_f, s11)) | m_c_h_element_v_in1(c_e_h_2, c_f, s10) | (~node14(c_e_h_2, c_f, s10, s11)))),
% 294.81/187.38 inference(rewrite,[status(thm)],[])).
% 294.81/187.38 tff(28123,plain,
% 294.81/187.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_f, s10, s11)) | m_c_h_element_v_in1(c_e_h_2, c_f, s10) | (~m_c_h_element_v_out(c_e_h_2, c_f, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_f, s11)) | m_c_h_element_v_in1(c_e_h_2, c_f, s10) | (~node14(c_e_h_2, c_f, s10, s11))))),
% 294.81/187.38 inference(monotonicity,[status(thm)],[28122])).
% 294.81/187.38 tff(28124,plain,
% 294.81/187.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_f, s10, s11)) | m_c_h_element_v_in1(c_e_h_2, c_f, s10) | (~m_c_h_element_v_out(c_e_h_2, c_f, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s11)) | m_c_h_element_v_in1(c_e_h_2, c_f, s10) | (~node14(c_e_h_2, c_f, s10, s11)))),
% 294.81/187.38 inference(transitivity,[status(thm)],[28123, 28121])).
% 294.81/187.38 tff(28125,plain,
% 294.81/187.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_f, s10, s11)) | m_c_h_element_v_in1(c_e_h_2, c_f, s10) | (~m_c_h_element_v_out(c_e_h_2, c_f, s11)))),
% 294.81/187.38 inference(quant_inst,[status(thm)],[])).
% 294.81/187.38 tff(28126,plain,
% 294.81/187.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_2, c_f, s11)) | m_c_h_element_v_in1(c_e_h_2, c_f, s10) | (~node14(c_e_h_2, c_f, s10, s11))),
% 294.81/187.38 inference(modus_ponens,[status(thm)],[28125, 28124])).
% 294.81/187.38 tff(28127,plain,
% 294.81/187.38 ($false),
% 294.81/187.38 inference(unit_resolution,[status(thm)],[28126, 223, 28078, 28120, 28109])).
% 294.81/187.38 tff(28128,plain,((~node14(c_e_h_2, c_f, s10, s11)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s11)) | m_c_h_element_v_in1(c_e_h_2, c_f, s10)), inference(lemma,lemma(discharge,[]))).
% 294.81/187.38 tff(28129,plain,
% 294.81/187.38 (~node14(c_e_h_2, c_f, s10, s11)),
% 294.81/187.38 inference(unit_resolution,[status(thm)],[28128, 28109, 28078])).
% 294.81/187.38 tff(28130,plain,
% 294.81/187.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_2, c_f, s10, s11) | node14(c_e_h_2, c_f, s10, s11) | (~node19(c_e_h_2, c_f, s10, s11)) | node16(c_e_h_2, c_f, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_2, c_f, s10, s11) | node14(c_e_h_2, c_f, s10, s11) | (~node19(c_e_h_2, c_f, s10, s11)) | node16(c_e_h_2, c_f, s10))),
% 294.81/187.38 inference(rewrite,[status(thm)],[])).
% 294.81/187.38 tff(28131,plain,
% 294.81/187.38 ((node16(c_e_h_2, c_f, s10) | node14(c_e_h_2, c_f, s10, s11) | node15(c_e_h_2, c_f, s10, s11) | (~node19(c_e_h_2, c_f, s10, s11))) <=> (node15(c_e_h_2, c_f, s10, s11) | node14(c_e_h_2, c_f, s10, s11) | (~node19(c_e_h_2, c_f, s10, s11)) | node16(c_e_h_2, c_f, s10))),
% 294.81/187.38 inference(rewrite,[status(thm)],[])).
% 294.81/187.38 tff(28132,plain,
% 294.81/187.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s10) | node14(c_e_h_2, c_f, s10, s11) | node15(c_e_h_2, c_f, s10, s11) | (~node19(c_e_h_2, c_f, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_2, c_f, s10, s11) | node14(c_e_h_2, c_f, s10, s11) | (~node19(c_e_h_2, c_f, s10, s11)) | node16(c_e_h_2, c_f, s10)))),
% 294.81/187.38 inference(monotonicity,[status(thm)],[28131])).
% 294.81/187.38 tff(28133,plain,
% 294.81/187.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s10) | node14(c_e_h_2, c_f, s10, s11) | node15(c_e_h_2, c_f, s10, s11) | (~node19(c_e_h_2, c_f, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_2, c_f, s10, s11) | node14(c_e_h_2, c_f, s10, s11) | (~node19(c_e_h_2, c_f, s10, s11)) | node16(c_e_h_2, c_f, s10))),
% 294.81/187.38 inference(transitivity,[status(thm)],[28132, 28130])).
% 294.81/187.38 tff(28134,plain,
% 294.81/187.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_f, s10) | node14(c_e_h_2, c_f, s10, s11) | node15(c_e_h_2, c_f, s10, s11) | (~node19(c_e_h_2, c_f, s10, s11)))),
% 294.81/187.38 inference(quant_inst,[status(thm)],[])).
% 294.81/187.38 tff(28135,plain,
% 294.81/187.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_2, c_f, s10, s11) | node14(c_e_h_2, c_f, s10, s11) | (~node19(c_e_h_2, c_f, s10, s11)) | node16(c_e_h_2, c_f, s10)),
% 294.81/187.38 inference(modus_ponens,[status(thm)],[28134, 28133])).
% 294.81/187.38 tff(28136,plain,
% 294.81/187.38 (node15(c_e_h_2, c_f, s10, s11) | node14(c_e_h_2, c_f, s10, s11) | node16(c_e_h_2, c_f, s10)),
% 294.81/187.38 inference(unit_resolution,[status(thm)],[28135, 204, 28093])).
% 294.81/187.38 tff(28137,plain,
% 294.81/187.38 (node16(c_e_h_2, c_f, s10)),
% 294.81/187.38 inference(unit_resolution,[status(thm)],[28136, 28129, 28119])).
% 294.81/187.38 tff(28138,plain,
% 294.81/187.38 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_f, s10)) | m_c_h_element_v_in1(c_e_h_2, c_f, s10) | m_c_h_element_v_in2(c_e_h_2, c_f, s10))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_f, s10)) | m_c_h_element_v_in1(c_e_h_2, c_f, s10) | m_c_h_element_v_in2(c_e_h_2, c_f, s10))),
% 294.81/187.38 inference(rewrite,[status(thm)],[])).
% 294.81/187.38 tff(28139,plain,
% 294.81/187.38 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_f, s10)) | m_c_h_element_v_in1(c_e_h_2, c_f, s10) | m_c_h_element_v_in2(c_e_h_2, c_f, s10))),
% 294.81/187.39 inference(quant_inst,[status(thm)],[])).
% 294.81/187.39 tff(28140,plain,
% 294.81/187.39 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_f, s10)) | m_c_h_element_v_in1(c_e_h_2, c_f, s10) | m_c_h_element_v_in2(c_e_h_2, c_f, s10)),
% 294.81/187.39 inference(modus_ponens,[status(thm)],[28139, 28138])).
% 294.81/187.39 tff(28141,plain,
% 294.81/187.39 ($false),
% 294.81/187.39 inference(unit_resolution,[status(thm)],[28140, 178, 28137, 28109, 28118])).
% 294.81/187.39 tff(28142,plain,(m_c_h_element_v_in1(c_e_h_2, c_f, s10) | node15(c_e_h_2, c_f, s10, s11) | (~node17(c_e_h_2, c_f, s10)) | (~m_c_h_element_v_out(c_e_h_2, c_f, s11))), inference(lemma,lemma(discharge,[]))).
% 294.81/187.39 tff(28143,plain,
% 294.81/187.39 (m_c_h_element_v_in1(c_e_h_2, c_f, s10)),
% 294.81/187.39 inference(unit_resolution,[status(thm)],[28142, 28101, 28078, 28108])).
% 294.81/187.39 tff(28144,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_f, s10)), introduced(assumption)).
% 294.81/187.39 tff(28145,plain,
% 294.81/187.39 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_2, c_f, s10) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s10)) | (~node17(c_e_h_2, c_f, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_f, s10) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s10)) | (~node17(c_e_h_2, c_f, s10)))),
% 294.81/187.39 inference(rewrite,[status(thm)],[])).
% 294.81/187.39 tff(28146,plain,
% 294.81/187.39 (((~m_c_h_element_v_in1(c_e_h_2, c_f, s10)) | m_c_h_element_v_in2(c_e_h_2, c_f, s10) | (~node17(c_e_h_2, c_f, s10))) <=> (m_c_h_element_v_in2(c_e_h_2, c_f, s10) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s10)) | (~node17(c_e_h_2, c_f, s10)))),
% 294.81/187.39 inference(rewrite,[status(thm)],[])).
% 294.81/187.39 tff(28147,plain,
% 294.81/187.39 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s10)) | m_c_h_element_v_in2(c_e_h_2, c_f, s10) | (~node17(c_e_h_2, c_f, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_2, c_f, s10) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s10)) | (~node17(c_e_h_2, c_f, s10))))),
% 294.81/187.39 inference(monotonicity,[status(thm)],[28146])).
% 294.81/187.39 tff(28148,plain,
% 294.81/187.39 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s10)) | m_c_h_element_v_in2(c_e_h_2, c_f, s10) | (~node17(c_e_h_2, c_f, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_f, s10) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s10)) | (~node17(c_e_h_2, c_f, s10)))),
% 294.81/187.39 inference(transitivity,[status(thm)],[28147, 28145])).
% 294.81/187.39 tff(28149,plain,
% 294.81/187.39 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_f, s10)) | m_c_h_element_v_in2(c_e_h_2, c_f, s10) | (~node17(c_e_h_2, c_f, s10)))),
% 294.81/187.39 inference(quant_inst,[status(thm)],[])).
% 294.81/187.39 tff(28150,plain,
% 294.81/187.39 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_2, c_f, s10) | (~m_c_h_element_v_in1(c_e_h_2, c_f, s10)) | (~node17(c_e_h_2, c_f, s10))),
% 294.81/187.39 inference(modus_ponens,[status(thm)],[28149, 28148])).
% 294.81/187.39 tff(28151,plain,
% 294.81/187.39 ((~m_c_h_element_v_in1(c_e_h_2, c_f, s10)) | (~node17(c_e_h_2, c_f, s10))),
% 294.81/187.39 inference(unit_resolution,[status(thm)],[28150, 919, 28144])).
% 294.81/187.39 tff(28152,plain,
% 294.81/187.39 ($false),
% 294.81/187.39 inference(unit_resolution,[status(thm)],[28151, 28143, 28101])).
% 294.81/187.39 tff(28153,plain,(m_c_h_element_v_out(c_e_h_2, c_f, s10) | m_c_h_element_v_in2(c_e_h_2, c_f, s10) | (~m_c_h_element_v_out(c_e_h_2, c_f, s11))), inference(lemma,lemma(discharge,[]))).
% 294.81/187.39 tff(28154,plain,
% 294.81/187.39 (m_c_h_element_v_in2(c_e_h_2, c_f, s10) | (~m_c_h_element_v_out(c_e_h_2, c_f, s11))),
% 294.81/187.39 inference(unit_resolution,[status(thm)],[28153, 28077])).
% 294.81/187.39 tff(28155,plain,
% 294.81/187.39 (~m_c_h_element_v_out(c_e_h_2, c_f, s11)),
% 294.81/187.39 inference(unit_resolution,[status(thm)],[28154, 27936])).
% 294.81/187.39 tff(28156,plain,
% 294.81/187.39 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_q, s11)) | m_c_h_element_v_out(c_e_h_2, c_f, s11))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_q, s11)) | m_c_h_element_v_out(c_e_h_2, c_f, s11))),
% 294.81/187.39 inference(rewrite,[status(thm)],[])).
% 294.81/187.39 tff(28157,plain,
% 294.81/187.39 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_q, s11)) | m_c_h_element_v_out(c_e_h_2, c_f, s11))),
% 294.81/187.39 inference(quant_inst,[status(thm)],[])).
% 294.81/187.39 tff(28158,plain,
% 294.81/187.39 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_q, s11)) | m_c_h_element_v_out(c_e_h_2, c_f, s11)),
% 294.81/187.39 inference(modus_ponens,[status(thm)],[28157, 28156])).
% 294.81/187.39 tff(28159,plain,
% 294.81/187.39 (~m_and_h_gate_v_in1(c_e_h_2, c_q, s11)),
% 294.81/187.39 inference(unit_resolution,[status(thm)],[28158, 1586, 28155])).
% 294.81/187.39 tff(28160,plain,
% 294.81/187.39 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_q, s11)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s11))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_q, s11)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s11))),
% 294.81/187.39 inference(rewrite,[status(thm)],[])).
% 294.81/187.39 tff(28161,plain,
% 294.81/187.39 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_q, s11)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s11))),
% 294.81/187.39 inference(quant_inst,[status(thm)],[])).
% 294.81/187.39 tff(28162,plain,
% 294.81/187.39 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_q, s11)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s11)),
% 294.81/187.39 inference(modus_ponens,[status(thm)],[28161, 28160])).
% 294.81/187.39 tff(28163,plain,
% 294.81/187.39 (~node20(c_e_h_2, c_q, s11)),
% 294.81/187.39 inference(unit_resolution,[status(thm)],[28162, 38, 28159])).
% 294.81/187.39 tff(28164,assumption,(m_and_h_gate_v_out(c_e_h_2, c_q, s12)), introduced(assumption)).
% 294.81/187.39 tff(28165,assumption,(node22(c_e_h_2, c_q, s11, s12)), introduced(assumption)).
% 294.81/187.39 tff(28166,assumption,(m_and_h_gate_v_out(c_e_h_2, c_q, s11)), introduced(assumption)).
% 294.81/187.39 tff(28167,plain,
% 294.81/187.39 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_q, s10)) | m_c_h_element_v_out(c_e_h_2, c_f, s10))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_q, s10)) | m_c_h_element_v_out(c_e_h_2, c_f, s10))),
% 294.81/187.39 inference(rewrite,[status(thm)],[])).
% 294.81/187.39 tff(28168,plain,
% 294.81/187.39 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_q, s10)) | m_c_h_element_v_out(c_e_h_2, c_f, s10))),
% 294.81/187.39 inference(quant_inst,[status(thm)],[])).
% 294.81/187.39 tff(28169,plain,
% 294.81/187.39 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_q, s10)) | m_c_h_element_v_out(c_e_h_2, c_f, s10)),
% 294.81/187.39 inference(modus_ponens,[status(thm)],[28168, 28167])).
% 294.81/187.39 tff(28170,plain,
% 294.81/187.39 (~m_and_h_gate_v_in1(c_e_h_2, c_q, s10)),
% 294.81/187.39 inference(unit_resolution,[status(thm)],[28169, 1586, 28077])).
% 294.81/187.39 tff(28171,plain,
% 294.81/187.39 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_q, s10)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s10))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_q, s10)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s10))),
% 294.81/187.39 inference(rewrite,[status(thm)],[])).
% 294.81/187.39 tff(28172,plain,
% 294.81/187.39 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_q, s10)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s10))),
% 294.81/187.39 inference(quant_inst,[status(thm)],[])).
% 294.81/187.39 tff(28173,plain,
% 294.81/187.39 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_q, s10)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s10)),
% 294.81/187.39 inference(modus_ponens,[status(thm)],[28172, 28171])).
% 294.81/187.39 tff(28174,plain,
% 294.81/187.39 (~node20(c_e_h_2, c_q, s10)),
% 294.81/187.39 inference(unit_resolution,[status(thm)],[28173, 38, 28170])).
% 294.81/187.39 tff(28175,assumption,(node21(c_e_h_2, c_q, s10, s11)), introduced(assumption)).
% 294.81/187.39 tff(28176,plain,
% 294.81/187.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_q, s10) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s11)) | (~node21(c_e_h_2, c_q, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_q, s10) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s11)) | (~node21(c_e_h_2, c_q, s10, s11)))),
% 294.81/187.39 inference(rewrite,[status(thm)],[])).
% 294.81/187.39 tff(28177,plain,
% 294.81/187.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_q, s10) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s11)) | (~node21(c_e_h_2, c_q, s10, s11)))),
% 294.81/187.39 inference(quant_inst,[status(thm)],[])).
% 294.81/187.39 tff(28178,plain,
% 294.81/187.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_q, s10) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s11)) | (~node21(c_e_h_2, c_q, s10, s11))),
% 294.81/187.39 inference(modus_ponens,[status(thm)],[28177, 28176])).
% 294.81/187.39 tff(28179,plain,
% 294.81/187.39 ($false),
% 294.81/187.39 inference(unit_resolution,[status(thm)],[28178, 52, 28166, 28175, 28174])).
% 294.81/187.39 tff(28180,plain,((~node21(c_e_h_2, c_q, s10, s11)) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s11))), inference(lemma,lemma(discharge,[]))).
% 294.81/187.39 tff(28181,plain,
% 294.81/187.39 (~node21(c_e_h_2, c_q, s10, s11)),
% 294.81/187.39 inference(unit_resolution,[status(thm)],[28180, 28166])).
% 294.81/187.39 tff(28182,assumption,(m_and_h_gate_v_out(c_e_h_2, c_q, s10)), introduced(assumption)).
% 294.81/187.39 tff(28183,plain,
% 294.81/187.39 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_q, s9)) | m_c_h_element_v_out(c_e_h_2, c_f, s9))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_q, s9)) | m_c_h_element_v_out(c_e_h_2, c_f, s9))),
% 294.81/187.39 inference(rewrite,[status(thm)],[])).
% 294.81/187.39 tff(28184,plain,
% 294.81/187.39 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_2, c_q, s9)) | m_c_h_element_v_out(c_e_h_2, c_f, s9))),
% 294.81/187.39 inference(quant_inst,[status(thm)],[])).
% 294.81/187.39 tff(28185,plain,
% 294.81/187.39 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_2, c_q, s9)) | m_c_h_element_v_out(c_e_h_2, c_f, s9)),
% 294.81/187.39 inference(modus_ponens,[status(thm)],[28184, 28183])).
% 294.81/187.39 tff(28186,plain,
% 294.81/187.39 (~m_and_h_gate_v_in1(c_e_h_2, c_q, s9)),
% 294.81/187.39 inference(unit_resolution,[status(thm)],[28185, 1586, 28006])).
% 294.81/187.39 tff(28187,plain,
% 294.81/187.39 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_q, s9)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s9))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_q, s9)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s9))),
% 294.81/187.39 inference(rewrite,[status(thm)],[])).
% 294.81/187.39 tff(28188,plain,
% 294.81/187.39 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_2, c_q, s9)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s9))),
% 294.81/187.39 inference(quant_inst,[status(thm)],[])).
% 294.81/187.39 tff(28189,plain,
% 294.81/187.39 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_2, c_q, s9)) | m_and_h_gate_v_in1(c_e_h_2, c_q, s9)),
% 294.81/187.39 inference(modus_ponens,[status(thm)],[28188, 28187])).
% 294.81/187.39 tff(28190,plain,
% 294.81/187.39 (~node20(c_e_h_2, c_q, s9)),
% 294.90/187.40 inference(unit_resolution,[status(thm)],[28189, 38, 28186])).
% 294.90/187.40 tff(28191,assumption,(node21(c_e_h_2, c_q, s9, s10)), introduced(assumption)).
% 294.90/187.40 tff(28192,plain,
% 294.90/187.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_q, s9) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s10)) | (~node21(c_e_h_2, c_q, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_q, s9) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s10)) | (~node21(c_e_h_2, c_q, s9, s10)))),
% 294.90/187.40 inference(rewrite,[status(thm)],[])).
% 294.90/187.40 tff(28193,plain,
% 294.90/187.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_q, s9) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s10)) | (~node21(c_e_h_2, c_q, s9, s10)))),
% 294.90/187.40 inference(quant_inst,[status(thm)],[])).
% 294.90/187.40 tff(28194,plain,
% 294.90/187.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_q, s9) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s10)) | (~node21(c_e_h_2, c_q, s9, s10))),
% 294.90/187.40 inference(modus_ponens,[status(thm)],[28193, 28192])).
% 294.90/187.40 tff(28195,plain,
% 294.90/187.40 ($false),
% 294.90/187.40 inference(unit_resolution,[status(thm)],[28194, 52, 28182, 28191, 28190])).
% 294.90/187.40 tff(28196,plain,((~node21(c_e_h_2, c_q, s9, s10)) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s10))), inference(lemma,lemma(discharge,[]))).
% 294.90/187.40 tff(28197,plain,
% 294.90/187.40 (~node21(c_e_h_2, c_q, s9, s10)),
% 294.90/187.40 inference(unit_resolution,[status(thm)],[28196, 28182])).
% 294.90/187.40 tff(28198,plain,
% 294.90/187.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s9, s10)) | node21(c_e_h_2, c_q, s9, s10) | node22(c_e_h_2, c_q, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s9, s10)) | node21(c_e_h_2, c_q, s9, s10) | node22(c_e_h_2, c_q, s9, s10))),
% 294.90/187.40 inference(rewrite,[status(thm)],[])).
% 294.90/187.40 tff(28199,plain,
% 294.90/187.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s9, s10)) | node21(c_e_h_2, c_q, s9, s10) | node22(c_e_h_2, c_q, s9, s10))),
% 294.90/187.40 inference(quant_inst,[status(thm)],[])).
% 294.90/187.40 tff(28200,plain,
% 294.90/187.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s9, s10)) | node21(c_e_h_2, c_q, s9, s10) | node22(c_e_h_2, c_q, s9, s10)),
% 294.90/187.40 inference(modus_ponens,[status(thm)],[28199, 28198])).
% 294.90/187.40 tff(28201,plain,
% 294.90/187.40 (node21(c_e_h_2, c_q, s9, s10) | node22(c_e_h_2, c_q, s9, s10)),
% 294.90/187.40 inference(unit_resolution,[status(thm)],[28200, 82, 7676])).
% 294.90/187.40 tff(28202,plain,
% 294.90/187.40 (node22(c_e_h_2, c_q, s9, s10)),
% 294.90/187.40 inference(unit_resolution,[status(thm)],[28201, 28197])).
% 294.90/187.40 tff(28203,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_q, s9)), introduced(assumption)).
% 294.90/187.40 tff(28204,plain,
% 294.90/187.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s10)) | (~node22(c_e_h_2, c_q, s9, s10)) | m_and_h_gate_v_out(c_e_h_2, c_q, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s10)) | (~node22(c_e_h_2, c_q, s9, s10)) | m_and_h_gate_v_out(c_e_h_2, c_q, s9))),
% 294.90/187.40 inference(rewrite,[status(thm)],[])).
% 294.90/187.40 tff(28205,plain,
% 294.90/187.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s10)) | (~node22(c_e_h_2, c_q, s9, s10)) | m_and_h_gate_v_out(c_e_h_2, c_q, s9))),
% 294.90/187.40 inference(quant_inst,[status(thm)],[])).
% 294.90/187.40 tff(28206,plain,
% 294.90/187.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s10)) | (~node22(c_e_h_2, c_q, s9, s10)) | m_and_h_gate_v_out(c_e_h_2, c_q, s9)),
% 294.90/187.40 inference(modus_ponens,[status(thm)],[28205, 28204])).
% 294.90/187.40 tff(28207,plain,
% 294.90/187.40 ($false),
% 294.90/187.40 inference(unit_resolution,[status(thm)],[28206, 108, 28203, 28182, 28202])).
% 294.90/187.40 tff(28208,plain,((~m_and_h_gate_v_out(c_e_h_2, c_q, s10)) | m_and_h_gate_v_out(c_e_h_2, c_q, s9)), inference(lemma,lemma(discharge,[]))).
% 294.90/187.40 tff(28209,plain,
% 294.90/187.40 (~m_and_h_gate_v_out(c_e_h_2, c_q, s10)),
% 294.90/187.40 inference(unit_resolution,[status(thm)],[28208, 8925])).
% 294.90/187.40 tff(28210,assumption,(node22(c_e_h_2, c_q, s10, s11)), introduced(assumption)).
% 294.90/187.40 tff(28211,assumption,(~m_and_h_gate_v_out(c_e_h_2, c_q, s10)), introduced(assumption)).
% 294.90/187.40 tff(28212,plain,
% 294.90/187.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s11)) | (~node22(c_e_h_2, c_q, s10, s11)) | m_and_h_gate_v_out(c_e_h_2, c_q, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s11)) | (~node22(c_e_h_2, c_q, s10, s11)) | m_and_h_gate_v_out(c_e_h_2, c_q, s10))),
% 294.90/187.40 inference(rewrite,[status(thm)],[])).
% 294.90/187.40 tff(28213,plain,
% 294.90/187.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s11)) | (~node22(c_e_h_2, c_q, s10, s11)) | m_and_h_gate_v_out(c_e_h_2, c_q, s10))),
% 294.90/187.40 inference(quant_inst,[status(thm)],[])).
% 294.90/187.40 tff(28214,plain,
% 294.90/187.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s11)) | (~node22(c_e_h_2, c_q, s10, s11)) | m_and_h_gate_v_out(c_e_h_2, c_q, s10)),
% 294.90/187.40 inference(modus_ponens,[status(thm)],[28213, 28212])).
% 294.90/187.40 tff(28215,plain,
% 294.90/187.40 ($false),
% 294.90/187.40 inference(unit_resolution,[status(thm)],[28214, 108, 28166, 28211, 28210])).
% 294.90/187.40 tff(28216,plain,((~node22(c_e_h_2, c_q, s10, s11)) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s11)) | m_and_h_gate_v_out(c_e_h_2, c_q, s10)), inference(lemma,lemma(discharge,[]))).
% 294.90/187.40 tff(28217,plain,
% 294.90/187.40 ((~node22(c_e_h_2, c_q, s10, s11)) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s11))),
% 294.90/187.40 inference(unit_resolution,[status(thm)],[28216, 28209])).
% 294.90/187.40 tff(28218,plain,
% 294.90/187.40 (~node22(c_e_h_2, c_q, s10, s11)),
% 294.90/187.40 inference(unit_resolution,[status(thm)],[28217, 28166])).
% 294.90/187.40 tff(28219,plain,
% 294.90/187.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s10, s11)) | node21(c_e_h_2, c_q, s10, s11) | node22(c_e_h_2, c_q, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s10, s11)) | node21(c_e_h_2, c_q, s10, s11) | node22(c_e_h_2, c_q, s10, s11))),
% 294.90/187.40 inference(rewrite,[status(thm)],[])).
% 294.90/187.40 tff(28220,plain,
% 294.90/187.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s10, s11)) | node21(c_e_h_2, c_q, s10, s11) | node22(c_e_h_2, c_q, s10, s11))),
% 294.90/187.40 inference(quant_inst,[status(thm)],[])).
% 294.90/187.40 tff(28221,plain,
% 294.90/187.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s10, s11)) | node21(c_e_h_2, c_q, s10, s11) | node22(c_e_h_2, c_q, s10, s11)),
% 294.90/187.40 inference(modus_ponens,[status(thm)],[28220, 28219])).
% 294.90/187.40 tff(28222,plain,
% 294.90/187.40 (node21(c_e_h_2, c_q, s10, s11) | node22(c_e_h_2, c_q, s10, s11)),
% 294.90/187.40 inference(unit_resolution,[status(thm)],[28221, 82, 7748])).
% 294.90/187.40 tff(28223,plain,
% 294.90/187.40 ($false),
% 294.90/187.40 inference(unit_resolution,[status(thm)],[28222, 28218, 28181])).
% 294.90/187.40 tff(28224,plain,(~m_and_h_gate_v_out(c_e_h_2, c_q, s11)), inference(lemma,lemma(discharge,[]))).
% 294.90/187.40 tff(28225,plain,
% 294.90/187.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s12)) | (~node22(c_e_h_2, c_q, s11, s12)) | m_and_h_gate_v_out(c_e_h_2, c_q, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s12)) | (~node22(c_e_h_2, c_q, s11, s12)) | m_and_h_gate_v_out(c_e_h_2, c_q, s11))),
% 294.90/187.40 inference(rewrite,[status(thm)],[])).
% 294.90/187.40 tff(28226,plain,
% 294.90/187.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_2, c_q, s12)) | (~node22(c_e_h_2, c_q, s11, s12)) | m_and_h_gate_v_out(c_e_h_2, c_q, s11))),
% 294.90/187.40 inference(quant_inst,[status(thm)],[])).
% 294.90/187.40 tff(28227,plain,
% 294.90/187.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s12)) | (~node22(c_e_h_2, c_q, s11, s12)) | m_and_h_gate_v_out(c_e_h_2, c_q, s11)),
% 294.90/187.40 inference(modus_ponens,[status(thm)],[28226, 28225])).
% 294.90/187.40 tff(28228,plain,
% 294.90/187.40 ($false),
% 294.90/187.40 inference(unit_resolution,[status(thm)],[28227, 108, 28224, 28164, 28165])).
% 294.90/187.40 tff(28229,plain,((~node22(c_e_h_2, c_q, s11, s12)) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s12))), inference(lemma,lemma(discharge,[]))).
% 294.90/187.40 tff(28230,plain,
% 294.90/187.40 (~node22(c_e_h_2, c_q, s11, s12)),
% 294.90/187.40 inference(unit_resolution,[status(thm)],[28229, 28164])).
% 294.90/187.40 tff(28231,plain,
% 294.90/187.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s11, s12)) | node21(c_e_h_2, c_q, s11, s12) | node22(c_e_h_2, c_q, s11, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s11, s12)) | node21(c_e_h_2, c_q, s11, s12) | node22(c_e_h_2, c_q, s11, s12))),
% 294.90/187.40 inference(rewrite,[status(thm)],[])).
% 294.90/187.40 tff(28232,plain,
% 294.90/187.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s11, s12)) | node21(c_e_h_2, c_q, s11, s12) | node22(c_e_h_2, c_q, s11, s12))),
% 294.90/187.40 inference(quant_inst,[status(thm)],[])).
% 294.90/187.40 tff(28233,plain,
% 294.90/187.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s11, s12)) | node21(c_e_h_2, c_q, s11, s12) | node22(c_e_h_2, c_q, s11, s12)),
% 294.90/187.40 inference(modus_ponens,[status(thm)],[28232, 28231])).
% 294.90/187.40 tff(28234,plain,
% 294.90/187.40 (node21(c_e_h_2, c_q, s11, s12) | node22(c_e_h_2, c_q, s11, s12)),
% 294.90/187.40 inference(unit_resolution,[status(thm)],[28233, 82, 11461])).
% 294.90/187.40 tff(28235,plain,
% 294.90/187.40 (node21(c_e_h_2, c_q, s11, s12)),
% 294.90/187.40 inference(unit_resolution,[status(thm)],[28234, 28230])).
% 294.90/187.40 tff(28236,plain,
% 294.90/187.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_q, s11) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s12)) | (~node21(c_e_h_2, c_q, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_q, s11) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s12)) | (~node21(c_e_h_2, c_q, s11, s12)))),
% 294.90/187.40 inference(rewrite,[status(thm)],[])).
% 294.90/187.40 tff(28237,plain,
% 294.90/187.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_2, c_q, s11) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s12)) | (~node21(c_e_h_2, c_q, s11, s12)))),
% 294.90/187.40 inference(quant_inst,[status(thm)],[])).
% 294.90/187.40 tff(28238,plain,
% 294.90/187.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_2, c_q, s11) | (~m_and_h_gate_v_out(c_e_h_2, c_q, s12)) | (~node21(c_e_h_2, c_q, s11, s12))),
% 294.90/187.40 inference(modus_ponens,[status(thm)],[28237, 28236])).
% 294.90/187.40 tff(28239,plain,
% 294.90/187.40 ($false),
% 294.90/187.40 inference(unit_resolution,[status(thm)],[28238, 52, 28164, 28235, 28163])).
% 294.90/187.40 tff(28240,plain,(~m_and_h_gate_v_out(c_e_h_2, c_q, s12)), inference(lemma,lemma(discharge,[]))).
% 294.90/187.40 tff(28241,plain,
% 294.90/187.40 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s12))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s12))),
% 294.90/187.41 inference(rewrite,[status(thm)],[])).
% 294.90/187.41 tff(28242,plain,
% 294.90/187.41 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s12))),
% 294.90/187.41 inference(quant_inst,[status(thm)],[])).
% 294.90/187.41 tff(28243,plain,
% 294.90/187.41 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_2, c_e_h_3)) | node3(c_e_h_2, c_e_h_3, s12)),
% 294.90/187.41 inference(modus_ponens,[status(thm)],[28242, 28241])).
% 294.90/187.41 tff(28244,plain,
% 294.90/187.41 (node3(c_e_h_2, c_e_h_3, s12)),
% 294.90/187.41 inference(unit_resolution,[status(thm)],[28243, 1059, 1056])).
% 294.90/187.41 tff(28245,plain,
% 294.90/187.41 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_3, s12)) | (~node3(c_e_h_2, c_e_h_3, s12)) | m_and_h_gate_v_out(c_e_h_2, c_q, s12))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_3, s12)) | (~node3(c_e_h_2, c_e_h_3, s12)) | m_and_h_gate_v_out(c_e_h_2, c_q, s12))),
% 294.90/187.41 inference(rewrite,[status(thm)],[])).
% 294.90/187.41 tff(28246,plain,
% 294.90/187.41 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_3, s12)) | (~node3(c_e_h_2, c_e_h_3, s12)) | m_and_h_gate_v_out(c_e_h_2, c_q, s12))),
% 294.90/187.41 inference(quant_inst,[status(thm)],[])).
% 294.90/187.41 tff(28247,plain,
% 294.90/187.41 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_3, s12)) | (~node3(c_e_h_2, c_e_h_3, s12)) | m_and_h_gate_v_out(c_e_h_2, c_q, s12)),
% 294.90/187.41 inference(modus_ponens,[status(thm)],[28246, 28245])).
% 294.90/187.41 tff(28248,plain,
% 294.90/187.41 ((~m_cell_v_ack(c_e_h_3, s12)) | m_and_h_gate_v_out(c_e_h_2, c_q, s12)),
% 294.90/187.41 inference(unit_resolution,[status(thm)],[28247, 1073, 28244])).
% 294.90/187.41 tff(28249,plain,
% 294.90/187.41 (~m_cell_v_ack(c_e_h_3, s12)),
% 294.90/187.41 inference(unit_resolution,[status(thm)],[28248, 28240])).
% 294.90/187.41 tff(28250,plain,
% 294.90/187.41 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_j, s12)) | m_cell_v_ack(c_e_h_3, s12))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_j, s12)) | m_cell_v_ack(c_e_h_3, s12))),
% 294.90/187.41 inference(rewrite,[status(thm)],[])).
% 294.90/187.41 tff(28251,plain,
% 294.90/187.41 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_3, c_j, s12)) | m_cell_v_ack(c_e_h_3, s12))),
% 294.90/187.41 inference(quant_inst,[status(thm)],[])).
% 294.90/187.41 tff(28252,plain,
% 294.90/187.41 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_3, c_j, s12)) | m_cell_v_ack(c_e_h_3, s12)),
% 294.90/187.41 inference(modus_ponens,[status(thm)],[28251, 28250])).
% 294.90/187.41 tff(28253,plain,
% 294.90/187.41 (~m_or_h_gate_v_in2(c_e_h_3, c_j, s12)),
% 294.90/187.41 inference(unit_resolution,[status(thm)],[28252, 1085, 28249])).
% 294.90/187.41 tff(28254,assumption,(node6(c_e_h_3, c_j, s12, s13)), introduced(assumption)).
% 294.90/187.41 tff(28255,plain,
% 294.90/187.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_3, c_j, s12) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s13)) | (~node6(c_e_h_3, c_j, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_j, s12) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s13)) | (~node6(c_e_h_3, c_j, s12, s13)))),
% 294.90/187.41 inference(rewrite,[status(thm)],[])).
% 294.90/187.41 tff(28256,plain,
% 294.90/187.41 (((~node6(c_e_h_3, c_j, s12, s13)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s13)) | m_or_h_gate_v_out(c_e_h_3, c_j, s12)) <=> (m_or_h_gate_v_out(c_e_h_3, c_j, s12) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s13)) | (~node6(c_e_h_3, c_j, s12, s13)))),
% 294.90/187.41 inference(rewrite,[status(thm)],[])).
% 294.90/187.41 tff(28257,plain,
% 294.90/187.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s12, s13)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s13)) | m_or_h_gate_v_out(c_e_h_3, c_j, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_3, c_j, s12) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s13)) | (~node6(c_e_h_3, c_j, s12, s13))))),
% 294.90/187.41 inference(monotonicity,[status(thm)],[28256])).
% 294.90/187.41 tff(28258,plain,
% 294.90/187.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s12, s13)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s13)) | m_or_h_gate_v_out(c_e_h_3, c_j, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_j, s12) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s13)) | (~node6(c_e_h_3, c_j, s12, s13)))),
% 294.90/187.41 inference(transitivity,[status(thm)],[28257, 28255])).
% 294.90/187.41 tff(28259,plain,
% 294.90/187.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_3, c_j, s12, s13)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s13)) | m_or_h_gate_v_out(c_e_h_3, c_j, s12))),
% 294.90/187.41 inference(quant_inst,[status(thm)],[])).
% 294.90/187.41 tff(28260,plain,
% 294.90/187.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_3, c_j, s12) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s13)) | (~node6(c_e_h_3, c_j, s12, s13))),
% 294.90/187.41 inference(modus_ponens,[status(thm)],[28259, 28258])).
% 294.90/187.41 tff(28261,plain,
% 294.90/187.41 ($false),
% 294.90/187.41 inference(unit_resolution,[status(thm)],[28260, 1121, 26884, 20810, 28254])).
% 294.90/187.41 tff(28262,plain,((~node6(c_e_h_3, c_j, s12, s13)) | m_or_h_gate_v_out(c_e_h_3, c_j, s12) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s13))), inference(lemma,lemma(discharge,[]))).
% 294.90/187.41 tff(28263,plain,
% 294.90/187.41 (~node6(c_e_h_3, c_j, s12, s13)),
% 294.90/187.41 inference(unit_resolution,[status(thm)],[28262, 20810, 26884])).
% 294.90/187.41 tff(28264,assumption,(~m_or_h_gate_v_in1(c_e_h_3, c_j, s12)), introduced(assumption)).
% 294.90/187.41 tff(28265,assumption,(~m_or_h_gate_v_in2(c_e_h_3, c_j, s12)), introduced(assumption)).
% 294.90/187.41 tff(28266,assumption,(node5(c_e_h_3, c_j, s12, s13)), introduced(assumption)).
% 294.90/187.41 tff(28267,plain,
% 294.90/187.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_3, c_j, s13)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s12) | (~node5(c_e_h_3, c_j, s12, s13)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s13)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s12) | (~node5(c_e_h_3, c_j, s12, s13)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s12))),
% 294.90/187.41 inference(rewrite,[status(thm)],[])).
% 294.90/187.41 tff(28268,plain,
% 294.90/187.41 ((m_or_h_gate_v_in1(c_e_h_3, c_j, s12) | m_or_h_gate_v_in2(c_e_h_3, c_j, s12) | (~node5(c_e_h_3, c_j, s12, s13)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s13))) <=> ((~m_or_h_gate_v_out(c_e_h_3, c_j, s13)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s12) | (~node5(c_e_h_3, c_j, s12, s13)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s12))),
% 294.90/187.41 inference(rewrite,[status(thm)],[])).
% 294.90/187.41 tff(28269,plain,
% 294.90/187.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s12) | m_or_h_gate_v_in2(c_e_h_3, c_j, s12) | (~node5(c_e_h_3, c_j, s12, s13)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_3, c_j, s13)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s12) | (~node5(c_e_h_3, c_j, s12, s13)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s12)))),
% 294.90/187.41 inference(monotonicity,[status(thm)],[28268])).
% 294.90/187.41 tff(28270,plain,
% 294.90/187.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s12) | m_or_h_gate_v_in2(c_e_h_3, c_j, s12) | (~node5(c_e_h_3, c_j, s12, s13)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s13)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s12) | (~node5(c_e_h_3, c_j, s12, s13)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s12))),
% 294.90/187.42 inference(transitivity,[status(thm)],[28269, 28267])).
% 294.90/187.42 tff(28271,plain,
% 294.90/187.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_3, c_j, s12) | m_or_h_gate_v_in2(c_e_h_3, c_j, s12) | (~node5(c_e_h_3, c_j, s12, s13)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s13)))),
% 294.90/187.42 inference(quant_inst,[status(thm)],[])).
% 294.90/187.42 tff(28272,plain,
% 294.90/187.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s13)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s12) | (~node5(c_e_h_3, c_j, s12, s13)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s12)),
% 294.90/187.42 inference(modus_ponens,[status(thm)],[28271, 28270])).
% 294.90/187.42 tff(28273,plain,
% 294.90/187.42 ($false),
% 294.90/187.42 inference(unit_resolution,[status(thm)],[28272, 1159, 20810, 28266, 28264, 28265])).
% 294.90/187.42 tff(28274,plain,((~node5(c_e_h_3, c_j, s12, s13)) | (~m_or_h_gate_v_out(c_e_h_3, c_j, s13)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s12) | m_or_h_gate_v_in2(c_e_h_3, c_j, s12)), inference(lemma,lemma(discharge,[]))).
% 294.90/187.42 tff(28275,plain,
% 294.90/187.42 (~node5(c_e_h_3, c_j, s12, s13)),
% 294.90/187.42 inference(unit_resolution,[status(thm)],[28274, 20810, 28265, 28264])).
% 294.90/187.42 tff(28276,plain,
% 294.90/187.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s12, s13)) | node6(c_e_h_3, c_j, s12, s13) | node5(c_e_h_3, c_j, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s12, s13)) | node6(c_e_h_3, c_j, s12, s13) | node5(c_e_h_3, c_j, s12, s13))),
% 294.90/187.42 inference(rewrite,[status(thm)],[])).
% 294.90/187.42 tff(28277,plain,
% 294.90/187.42 ((node6(c_e_h_3, c_j, s12, s13) | node5(c_e_h_3, c_j, s12, s13) | (~trans(s12, s13))) <=> ((~trans(s12, s13)) | node6(c_e_h_3, c_j, s12, s13) | node5(c_e_h_3, c_j, s12, s13))),
% 294.90/187.42 inference(rewrite,[status(thm)],[])).
% 294.90/187.42 tff(28278,plain,
% 294.90/187.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s12, s13) | node5(c_e_h_3, c_j, s12, s13) | (~trans(s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s12, s13)) | node6(c_e_h_3, c_j, s12, s13) | node5(c_e_h_3, c_j, s12, s13)))),
% 294.90/187.42 inference(monotonicity,[status(thm)],[28277])).
% 294.90/187.42 tff(28279,plain,
% 294.90/187.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s12, s13) | node5(c_e_h_3, c_j, s12, s13) | (~trans(s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s12, s13)) | node6(c_e_h_3, c_j, s12, s13) | node5(c_e_h_3, c_j, s12, s13))),
% 294.90/187.42 inference(transitivity,[status(thm)],[28278, 28276])).
% 294.90/187.42 tff(28280,plain,
% 294.90/187.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_3, c_j, s12, s13) | node5(c_e_h_3, c_j, s12, s13) | (~trans(s12, s13)))),
% 294.90/187.42 inference(quant_inst,[status(thm)],[])).
% 294.90/187.42 tff(28281,plain,
% 294.90/187.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s12, s13)) | node6(c_e_h_3, c_j, s12, s13) | node5(c_e_h_3, c_j, s12, s13)),
% 294.90/187.42 inference(modus_ponens,[status(thm)],[28280, 28279])).
% 294.90/187.42 tff(28282,plain,
% 294.90/187.42 (node6(c_e_h_3, c_j, s12, s13) | node5(c_e_h_3, c_j, s12, s13)),
% 294.90/187.42 inference(unit_resolution,[status(thm)],[28281, 1141, 11856])).
% 294.90/187.42 tff(28283,plain,
% 294.90/187.42 ($false),
% 294.90/187.42 inference(unit_resolution,[status(thm)],[28282, 28275, 28263])).
% 294.90/187.42 tff(28284,plain,((~m_or_h_gate_v_out(c_e_h_3, c_j, s13)) | m_or_h_gate_v_in2(c_e_h_3, c_j, s12) | m_or_h_gate_v_in1(c_e_h_3, c_j, s12) | m_or_h_gate_v_out(c_e_h_3, c_j, s12)), inference(lemma,lemma(discharge,[]))).
% 294.90/187.42 tff(28285,plain,
% 294.90/187.42 ((~m_or_h_gate_v_out(c_e_h_3, c_j, s13)) | m_or_h_gate_v_in1(c_e_h_3, c_j, s12) | m_or_h_gate_v_out(c_e_h_3, c_j, s12)),
% 294.90/187.42 inference(unit_resolution,[status(thm)],[28284, 28253])).
% 294.90/187.42 tff(28286,plain,
% 294.90/187.42 (~m_or_h_gate_v_out(c_e_h_3, c_j, s13)),
% 294.90/187.42 inference(unit_resolution,[status(thm)],[28285, 26894, 26884])).
% 294.90/187.42 tff(28287,plain,
% 294.90/187.42 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s12)) | m_or_h_gate_v_out(c_e_h_3, c_j, s12))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s12)) | m_or_h_gate_v_out(c_e_h_3, c_j, s12))),
% 294.90/187.42 inference(rewrite,[status(thm)],[])).
% 294.90/187.42 tff(28288,plain,
% 294.90/187.42 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_h, s12)) | m_or_h_gate_v_out(c_e_h_3, c_j, s12))),
% 294.90/187.42 inference(quant_inst,[status(thm)],[])).
% 294.90/187.42 tff(28289,plain,
% 294.90/187.42 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_h, s12)) | m_or_h_gate_v_out(c_e_h_3, c_j, s12)),
% 294.90/187.42 inference(modus_ponens,[status(thm)],[28288, 28287])).
% 294.90/187.42 tff(28290,plain,
% 294.90/187.42 (~m_c_h_element_v_in2(c_e_h_3, c_h, s12)),
% 294.90/187.42 inference(unit_resolution,[status(thm)],[28289, 1174, 26884])).
% 294.90/187.42 tff(28291,plain,
% 294.90/187.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s13)) | m_c_h_element_v_out(c_e_h_3, c_h, s12) | (~node18(c_e_h_3, c_h, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s13)) | m_c_h_element_v_out(c_e_h_3, c_h, s12) | (~node18(c_e_h_3, c_h, s12, s13)))),
% 294.90/187.42 inference(rewrite,[status(thm)],[])).
% 294.90/187.42 tff(28292,plain,
% 294.90/187.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s13)) | m_c_h_element_v_out(c_e_h_3, c_h, s12) | (~node18(c_e_h_3, c_h, s12, s13)))),
% 294.90/187.42 inference(quant_inst,[status(thm)],[])).
% 294.90/187.42 tff(28293,plain,
% 294.90/187.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s13)) | m_c_h_element_v_out(c_e_h_3, c_h, s12) | (~node18(c_e_h_3, c_h, s12, s13))),
% 294.90/187.42 inference(modus_ponens,[status(thm)],[28292, 28291])).
% 294.90/187.42 tff(28294,plain,
% 294.90/187.42 ($false),
% 294.90/187.42 inference(unit_resolution,[status(thm)],[28293, 753, 20818, 21894, 21188])).
% 294.90/187.42 tff(28295,plain,((~node18(c_e_h_3, c_h, s12, s13)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s13)) | m_c_h_element_v_out(c_e_h_3, c_h, s12)), inference(lemma,lemma(discharge,[]))).
% 294.90/187.42 tff(28296,plain,
% 294.90/187.42 (~node18(c_e_h_3, c_h, s12, s13)),
% 294.90/187.42 inference(unit_resolution,[status(thm)],[28295, 21894, 20818])).
% 294.90/187.42 tff(28297,plain,
% 294.90/187.42 (node17(c_e_h_3, c_h, s12)),
% 294.90/187.42 inference(unit_resolution,[status(thm)],[21201, 28296])).
% 294.90/187.42 tff(28298,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_h, s12)), introduced(assumption)).
% 294.90/187.42 tff(28299,plain,
% 294.90/187.42 ((~m_c_h_element_v_in1(c_e_h_3, c_h, s12)) | (~node17(c_e_h_3, c_h, s12))),
% 294.90/187.42 inference(unit_resolution,[status(thm)],[21234, 919, 28298])).
% 294.90/187.42 tff(28300,plain,
% 294.90/187.42 (~m_c_h_element_v_in1(c_e_h_3, c_h, s12)),
% 294.90/187.42 inference(unit_resolution,[status(thm)],[28299, 28297])).
% 294.90/187.42 tff(28301,plain,
% 294.90/187.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s13)) | (~node15(c_e_h_3, c_h, s12, s13)) | m_c_h_element_v_out(c_e_h_3, c_h, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s13)) | (~node15(c_e_h_3, c_h, s12, s13)) | m_c_h_element_v_out(c_e_h_3, c_h, s12))),
% 294.90/187.42 inference(rewrite,[status(thm)],[])).
% 294.90/187.42 tff(28302,plain,
% 294.90/187.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s13)) | (~node15(c_e_h_3, c_h, s12, s13)) | m_c_h_element_v_out(c_e_h_3, c_h, s12))),
% 294.90/187.42 inference(quant_inst,[status(thm)],[])).
% 294.90/187.42 tff(28303,plain,
% 294.90/187.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s13)) | (~node15(c_e_h_3, c_h, s12, s13)) | m_c_h_element_v_out(c_e_h_3, c_h, s12)),
% 294.90/187.42 inference(modus_ponens,[status(thm)],[28302, 28301])).
% 294.90/187.42 tff(28304,plain,
% 294.90/187.42 ($false),
% 294.90/187.42 inference(unit_resolution,[status(thm)],[28303, 147, 20818, 21894, 21155])).
% 294.90/187.42 tff(28305,plain,((~node15(c_e_h_3, c_h, s12, s13)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s13)) | m_c_h_element_v_out(c_e_h_3, c_h, s12)), inference(lemma,lemma(discharge,[]))).
% 294.90/187.42 tff(28306,plain,
% 294.90/187.42 (~node15(c_e_h_3, c_h, s12, s13)),
% 294.90/187.42 inference(unit_resolution,[status(thm)],[28305, 21894, 20818])).
% 294.90/187.42 tff(28307,plain,
% 294.90/187.42 (~node16(c_e_h_3, c_h, s12)),
% 294.90/187.42 inference(unit_resolution,[status(thm)],[21237, 28297])).
% 294.90/187.42 tff(28308,plain,
% 294.90/187.42 (node14(c_e_h_3, c_h, s12, s13)),
% 294.90/187.42 inference(unit_resolution,[status(thm)],[21186, 28307, 28306])).
% 294.90/187.42 tff(28309,plain,
% 294.90/187.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s13)) | m_c_h_element_v_in1(c_e_h_3, c_h, s12) | (~node14(c_e_h_3, c_h, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s13)) | m_c_h_element_v_in1(c_e_h_3, c_h, s12) | (~node14(c_e_h_3, c_h, s12, s13)))),
% 294.90/187.42 inference(rewrite,[status(thm)],[])).
% 294.90/187.42 tff(28310,plain,
% 294.90/187.42 (((~node14(c_e_h_3, c_h, s12, s13)) | m_c_h_element_v_in1(c_e_h_3, c_h, s12) | (~m_c_h_element_v_out(c_e_h_3, c_h, s13))) <=> ((~m_c_h_element_v_out(c_e_h_3, c_h, s13)) | m_c_h_element_v_in1(c_e_h_3, c_h, s12) | (~node14(c_e_h_3, c_h, s12, s13)))),
% 294.90/187.42 inference(rewrite,[status(thm)],[])).
% 294.90/187.42 tff(28311,plain,
% 294.90/187.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s12, s13)) | m_c_h_element_v_in1(c_e_h_3, c_h, s12) | (~m_c_h_element_v_out(c_e_h_3, c_h, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_h, s13)) | m_c_h_element_v_in1(c_e_h_3, c_h, s12) | (~node14(c_e_h_3, c_h, s12, s13))))),
% 294.90/187.42 inference(monotonicity,[status(thm)],[28310])).
% 294.90/187.42 tff(28312,plain,
% 294.90/187.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s12, s13)) | m_c_h_element_v_in1(c_e_h_3, c_h, s12) | (~m_c_h_element_v_out(c_e_h_3, c_h, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s13)) | m_c_h_element_v_in1(c_e_h_3, c_h, s12) | (~node14(c_e_h_3, c_h, s12, s13)))),
% 294.90/187.42 inference(transitivity,[status(thm)],[28311, 28309])).
% 294.90/187.42 tff(28313,plain,
% 294.90/187.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_h, s12, s13)) | m_c_h_element_v_in1(c_e_h_3, c_h, s12) | (~m_c_h_element_v_out(c_e_h_3, c_h, s13)))),
% 294.90/187.43 inference(quant_inst,[status(thm)],[])).
% 294.90/187.43 tff(28314,plain,
% 294.90/187.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_3, c_h, s13)) | m_c_h_element_v_in1(c_e_h_3, c_h, s12) | (~node14(c_e_h_3, c_h, s12, s13))),
% 294.90/187.43 inference(modus_ponens,[status(thm)],[28313, 28312])).
% 294.90/187.43 tff(28315,plain,
% 294.90/187.43 ($false),
% 294.90/187.43 inference(unit_resolution,[status(thm)],[28314, 223, 20818, 21166, 21205])).
% 294.90/187.43 tff(28316,plain,((~node14(c_e_h_3, c_h, s12, s13)) | (~m_c_h_element_v_out(c_e_h_3, c_h, s13)) | m_c_h_element_v_in1(c_e_h_3, c_h, s12)), inference(lemma,lemma(discharge,[]))).
% 294.90/187.43 tff(28317,plain,
% 294.90/187.43 ($false),
% 294.90/187.43 inference(unit_resolution,[status(thm)],[28316, 28308, 28300, 20818])).
% 294.90/187.43 tff(28318,plain,(m_c_h_element_v_out(c_e_h_3, c_h, s12) | (~m_c_h_element_v_out(c_e_h_3, c_h, s13)) | m_c_h_element_v_in2(c_e_h_3, c_h, s12)), inference(lemma,lemma(discharge,[]))).
% 294.90/187.43 tff(28319,plain,
% 294.90/187.43 (~m_c_h_element_v_out(c_e_h_3, c_h, s13)),
% 294.90/187.43 inference(unit_resolution,[status(thm)],[28318, 28290, 21894])).
% 294.90/187.43 tff(28320,plain,
% 294.90/187.43 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_i, s13)) | m_c_h_element_v_out(c_e_h_3, c_h, s13))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s13)) | m_c_h_element_v_out(c_e_h_3, c_h, s13))),
% 294.90/187.43 inference(rewrite,[status(thm)],[])).
% 294.90/187.43 tff(28321,plain,
% 294.90/187.43 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_i, s13)) | m_c_h_element_v_out(c_e_h_3, c_h, s13))),
% 294.90/187.43 inference(quant_inst,[status(thm)],[])).
% 294.90/187.43 tff(28322,plain,
% 294.90/187.43 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_i, s13)) | m_c_h_element_v_out(c_e_h_3, c_h, s13)),
% 294.90/187.43 inference(modus_ponens,[status(thm)],[28321, 28320])).
% 294.90/187.43 tff(28323,plain,
% 294.90/187.43 (~m_and_h_gate_v_in1(c_e_h_3, c_i, s13)),
% 294.90/187.43 inference(unit_resolution,[status(thm)],[28322, 619, 28319])).
% 294.90/187.43 tff(28324,plain,
% 294.90/187.43 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s13)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s13))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_i, s13)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s13))),
% 294.90/187.43 inference(rewrite,[status(thm)],[])).
% 294.90/187.43 tff(28325,plain,
% 294.90/187.43 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_i, s13)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s13))),
% 294.90/187.43 inference(quant_inst,[status(thm)],[])).
% 294.90/187.43 tff(28326,plain,
% 294.90/187.43 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_i, s13)) | m_and_h_gate_v_in1(c_e_h_3, c_i, s13)),
% 294.90/187.43 inference(modus_ponens,[status(thm)],[28325, 28324])).
% 294.90/187.43 tff(28327,plain,
% 294.90/187.43 (~node20(c_e_h_3, c_i, s13)),
% 294.90/187.43 inference(unit_resolution,[status(thm)],[28326, 38, 28323])).
% 294.90/187.43 tff(28328,plain,
% 294.90/187.43 (m_or_h_gate_v_out(c_e_h_3, c_g, s9)),
% 294.90/187.43 inference(unit_resolution,[status(thm)],[26343, 7655])).
% 294.90/187.43 tff(28329,plain,
% 294.90/187.43 (node4(c_e_h_3, c_g, s9)),
% 294.90/187.43 inference(unit_resolution,[status(thm)],[20563, 28328, 20172])).
% 294.90/187.43 tff(28330,plain,
% 294.90/187.43 (~m_or_h_gate_v_in1(c_e_h_3, c_g, s9)),
% 294.90/187.43 inference(unit_resolution,[status(thm)],[20571, 28329])).
% 294.90/187.43 tff(28331,plain,
% 294.90/187.43 (~m_and_h_gate_v_out(c_e_h_3, c_c, s9)),
% 294.90/187.43 inference(unit_resolution,[status(thm)],[20479, 28330])).
% 294.90/187.43 tff(28332,plain,
% 294.90/187.43 (~m_and_h_gate_v_out(c_e_h_3, c_c, s8)),
% 294.90/187.43 inference(unit_resolution,[status(thm)],[20471, 28331])).
% 294.90/187.43 tff(28333,plain,
% 294.90/187.43 (~m_and_h_gate_v_out(c_e_h_3, c_c, s5)),
% 294.90/187.43 inference(unit_resolution,[status(thm)],[20626, 28332])).
% 294.90/187.43 tff(28334,plain,
% 294.90/187.43 (m_and_h_gate_v_out(c_e_h_3, c_c, s7)),
% 294.90/187.43 inference(unit_resolution,[status(thm)],[26241, 7655])).
% 294.90/187.43 tff(28335,plain,
% 294.90/187.43 (~m_and_h_gate_v_in1(c_e_h_3, c_c, s7)),
% 294.90/187.43 inference(unit_resolution,[status(thm)],[20621, 28332, 28334])).
% 294.90/187.43 tff(28336,plain,
% 294.90/187.43 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s7)),
% 294.90/187.43 inference(unit_resolution,[status(thm)],[20580, 28335])).
% 294.90/187.43 tff(28337,plain,
% 294.90/187.43 (~m_mutex_h_half_v_out(c_e_h_3, c_a, s4)),
% 294.90/187.43 inference(unit_resolution,[status(thm)],[19741, 28336])).
% 294.90/187.43 tff(28338,plain,
% 294.90/187.43 ($false),
% 294.90/187.43 inference(unit_resolution,[status(thm)],[20154, 28337, 28336, 28334, 28333])).
% 294.90/187.43 tff(28339,plain,((~m_c_h_element_v_out(c_e_h_3, c_h, s10)) | m_or_h_gate_v_out(c_e_h_3, c_g, s10)), inference(lemma,lemma(discharge,[]))).
% 294.90/187.43 tff(28340,plain,
% 294.90/187.43 (~m_c_h_element_v_out(c_e_h_3, c_h, s10)),
% 294.90/187.43 inference(unit_resolution,[status(thm)],[28339, 20172])).
% 294.90/187.43 tff(28341,plain,
% 294.90/187.43 (~m_and_h_gate_v_in1(c_e_h_3, c_i, s10)),
% 294.90/187.43 inference(unit_resolution,[status(thm)],[11223, 619, 28340])).
% 294.90/187.43 tff(28342,plain,
% 294.90/187.43 (~node20(c_e_h_3, c_i, s10)),
% 294.90/187.43 inference(unit_resolution,[status(thm)],[11227, 38, 28341])).
% 294.90/187.43 tff(28343,plain,
% 294.90/187.43 (~m_and_h_gate_v_in1(c_e_h_3, c_i, s11)),
% 294.90/187.43 inference(unit_resolution,[status(thm)],[7283, 619, 21080])).
% 294.90/187.43 tff(28344,plain,
% 294.90/187.43 (~node20(c_e_h_3, c_i, s11)),
% 294.90/187.43 inference(unit_resolution,[status(thm)],[7279, 38, 28343])).
% 294.90/187.43 tff(28345,plain,
% 294.90/187.43 (m_and_h_gate_v_out(c_e_h_3, c_i, s11)),
% 294.90/187.43 inference(unit_resolution,[status(thm)],[11467, 28344, 11439])).
% 294.90/187.43 tff(28346,plain,
% 294.90/187.43 ($false),
% 294.90/187.43 inference(unit_resolution,[status(thm)],[11435, 28345, 28342, 11422])).
% 294.90/187.43 tff(28347,plain,(m_or_h_gate_v_out(c_e_h_3, c_g, s10) | m_and_h_gate_v_out(c_e_h_3, c_i, s10) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s12))), inference(lemma,lemma(discharge,[]))).
% 294.90/187.43 tff(28348,plain,
% 294.90/187.43 (~m_and_h_gate_v_out(c_e_h_3, c_i, s12)),
% 294.90/187.43 inference(unit_resolution,[status(thm)],[28347, 20172, 24271])).
% 294.90/187.43 tff(28349,assumption,(~node20(c_e_h_3, c_i, s12)), introduced(assumption)).
% 294.90/187.43 tff(28350,assumption,(m_and_h_gate_v_out(c_e_h_3, c_i, s13)), introduced(assumption)).
% 294.90/187.43 tff(28351,assumption,(node21(c_e_h_3, c_i, s12, s13)), introduced(assumption)).
% 294.90/187.43 tff(28352,plain,
% 294.90/187.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s13)) | node20(c_e_h_3, c_i, s12) | (~node21(c_e_h_3, c_i, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s13)) | node20(c_e_h_3, c_i, s12) | (~node21(c_e_h_3, c_i, s12, s13)))),
% 294.90/187.43 inference(rewrite,[status(thm)],[])).
% 294.90/187.43 tff(28353,plain,
% 294.90/187.43 ((node20(c_e_h_3, c_i, s12) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s13)) | (~node21(c_e_h_3, c_i, s12, s13))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_i, s13)) | node20(c_e_h_3, c_i, s12) | (~node21(c_e_h_3, c_i, s12, s13)))),
% 294.90/187.43 inference(rewrite,[status(thm)],[])).
% 294.90/187.43 tff(28354,plain,
% 294.90/187.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s12) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s13)) | (~node21(c_e_h_3, c_i, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s13)) | node20(c_e_h_3, c_i, s12) | (~node21(c_e_h_3, c_i, s12, s13))))),
% 294.90/187.43 inference(monotonicity,[status(thm)],[28353])).
% 294.90/187.43 tff(28355,plain,
% 294.90/187.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s12) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s13)) | (~node21(c_e_h_3, c_i, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s13)) | node20(c_e_h_3, c_i, s12) | (~node21(c_e_h_3, c_i, s12, s13)))),
% 294.90/187.43 inference(transitivity,[status(thm)],[28354, 28352])).
% 294.90/187.43 tff(28356,plain,
% 294.90/187.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s12) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s13)) | (~node21(c_e_h_3, c_i, s12, s13)))),
% 294.90/187.43 inference(quant_inst,[status(thm)],[])).
% 294.90/187.43 tff(28357,plain,
% 294.90/187.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s13)) | node20(c_e_h_3, c_i, s12) | (~node21(c_e_h_3, c_i, s12, s13))),
% 294.90/187.43 inference(modus_ponens,[status(thm)],[28356, 28355])).
% 294.90/187.43 tff(28358,plain,
% 294.90/187.43 ($false),
% 294.90/187.43 inference(unit_resolution,[status(thm)],[28357, 52, 28350, 28351, 28349])).
% 294.90/187.43 tff(28359,plain,((~node21(c_e_h_3, c_i, s12, s13)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s13)) | node20(c_e_h_3, c_i, s12)), inference(lemma,lemma(discharge,[]))).
% 294.90/187.43 tff(28360,plain,
% 294.90/187.43 (~node21(c_e_h_3, c_i, s12, s13)),
% 294.90/187.43 inference(unit_resolution,[status(thm)],[28359, 28350, 28349])).
% 294.90/187.43 tff(28361,plain,
% 294.90/187.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s12, s13)) | node21(c_e_h_3, c_i, s12, s13) | node22(c_e_h_3, c_i, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s12, s13)) | node21(c_e_h_3, c_i, s12, s13) | node22(c_e_h_3, c_i, s12, s13))),
% 294.90/187.43 inference(rewrite,[status(thm)],[])).
% 294.90/187.43 tff(28362,plain,
% 294.90/187.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s12, s13)) | node21(c_e_h_3, c_i, s12, s13) | node22(c_e_h_3, c_i, s12, s13))),
% 294.90/187.43 inference(quant_inst,[status(thm)],[])).
% 294.90/187.43 tff(28363,plain,
% 294.90/187.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s12, s13)) | node21(c_e_h_3, c_i, s12, s13) | node22(c_e_h_3, c_i, s12, s13)),
% 294.90/187.43 inference(modus_ponens,[status(thm)],[28362, 28361])).
% 294.90/187.43 tff(28364,plain,
% 294.90/187.43 (node21(c_e_h_3, c_i, s12, s13) | node22(c_e_h_3, c_i, s12, s13)),
% 294.90/187.43 inference(unit_resolution,[status(thm)],[28363, 82, 11856])).
% 294.90/187.43 tff(28365,plain,
% 294.90/187.43 (node22(c_e_h_3, c_i, s12, s13)),
% 294.90/187.43 inference(unit_resolution,[status(thm)],[28364, 28360])).
% 294.90/187.43 tff(28366,plain,
% 294.90/187.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s13)) | (~node22(c_e_h_3, c_i, s12, s13)) | m_and_h_gate_v_out(c_e_h_3, c_i, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s13)) | (~node22(c_e_h_3, c_i, s12, s13)) | m_and_h_gate_v_out(c_e_h_3, c_i, s12))),
% 294.90/187.43 inference(rewrite,[status(thm)],[])).
% 294.90/187.43 tff(28367,plain,
% 294.90/187.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s13)) | (~node22(c_e_h_3, c_i, s12, s13)) | m_and_h_gate_v_out(c_e_h_3, c_i, s12))),
% 294.90/187.43 inference(quant_inst,[status(thm)],[])).
% 294.90/187.43 tff(28368,plain,
% 294.90/187.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s13)) | (~node22(c_e_h_3, c_i, s12, s13)) | m_and_h_gate_v_out(c_e_h_3, c_i, s12)),
% 294.90/187.43 inference(modus_ponens,[status(thm)],[28367, 28366])).
% 294.90/187.43 tff(28369,plain,
% 294.90/187.43 ($false),
% 294.90/187.43 inference(unit_resolution,[status(thm)],[28368, 108, 28350, 11833, 28365])).
% 294.90/187.43 tff(28370,plain,((~m_and_h_gate_v_out(c_e_h_3, c_i, s13)) | m_and_h_gate_v_out(c_e_h_3, c_i, s12) | node20(c_e_h_3, c_i, s12)), inference(lemma,lemma(discharge,[]))).
% 294.90/187.43 tff(28371,plain,
% 294.90/187.43 (~m_and_h_gate_v_out(c_e_h_3, c_i, s13)),
% 294.90/187.43 inference(unit_resolution,[status(thm)],[28370, 28348, 26882])).
% 294.90/187.43 tff(28372,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_i, s13)), introduced(assumption)).
% 294.90/187.43 tff(28373,assumption,(m_and_h_gate_v_out(c_e_h_3, c_i, s14)), introduced(assumption)).
% 294.90/187.43 tff(28374,assumption,(node22(c_e_h_3, c_i, s13, s14)), introduced(assumption)).
% 294.90/187.43 tff(28375,plain,
% 294.90/187.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s14)) | (~node22(c_e_h_3, c_i, s13, s14)) | m_and_h_gate_v_out(c_e_h_3, c_i, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s14)) | (~node22(c_e_h_3, c_i, s13, s14)) | m_and_h_gate_v_out(c_e_h_3, c_i, s13))),
% 294.90/187.44 inference(rewrite,[status(thm)],[])).
% 294.90/187.44 tff(28376,plain,
% 294.90/187.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s14)) | (~node22(c_e_h_3, c_i, s13, s14)) | m_and_h_gate_v_out(c_e_h_3, c_i, s13))),
% 294.90/187.44 inference(quant_inst,[status(thm)],[])).
% 294.90/187.44 tff(28377,plain,
% 294.90/187.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s14)) | (~node22(c_e_h_3, c_i, s13, s14)) | m_and_h_gate_v_out(c_e_h_3, c_i, s13)),
% 294.90/187.44 inference(modus_ponens,[status(thm)],[28376, 28375])).
% 294.90/187.44 tff(28378,plain,
% 294.90/187.44 ($false),
% 294.90/187.44 inference(unit_resolution,[status(thm)],[28377, 108, 28374, 28373, 28372])).
% 294.90/187.44 tff(28379,plain,((~node22(c_e_h_3, c_i, s13, s14)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s14)) | m_and_h_gate_v_out(c_e_h_3, c_i, s13)), inference(lemma,lemma(discharge,[]))).
% 294.90/187.44 tff(28380,plain,
% 294.90/187.44 (~node22(c_e_h_3, c_i, s13, s14)),
% 294.90/187.44 inference(unit_resolution,[status(thm)],[28379, 28373, 28372])).
% 294.90/187.44 tff(28381,assumption,(~node20(c_e_h_3, c_i, s13)), introduced(assumption)).
% 294.90/187.44 tff(28382,assumption,(node21(c_e_h_3, c_i, s13, s14)), introduced(assumption)).
% 294.90/187.44 tff(28383,plain,
% 294.90/187.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s14)) | node20(c_e_h_3, c_i, s13) | (~node21(c_e_h_3, c_i, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s14)) | node20(c_e_h_3, c_i, s13) | (~node21(c_e_h_3, c_i, s13, s14)))),
% 294.90/187.44 inference(rewrite,[status(thm)],[])).
% 294.90/187.44 tff(28384,plain,
% 294.90/187.44 ((node20(c_e_h_3, c_i, s13) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s14)) | (~node21(c_e_h_3, c_i, s13, s14))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_i, s14)) | node20(c_e_h_3, c_i, s13) | (~node21(c_e_h_3, c_i, s13, s14)))),
% 294.90/187.44 inference(rewrite,[status(thm)],[])).
% 294.90/187.44 tff(28385,plain,
% 294.90/187.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s13) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s14)) | (~node21(c_e_h_3, c_i, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s14)) | node20(c_e_h_3, c_i, s13) | (~node21(c_e_h_3, c_i, s13, s14))))),
% 294.90/187.44 inference(monotonicity,[status(thm)],[28384])).
% 294.90/187.44 tff(28386,plain,
% 294.90/187.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s13) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s14)) | (~node21(c_e_h_3, c_i, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s14)) | node20(c_e_h_3, c_i, s13) | (~node21(c_e_h_3, c_i, s13, s14)))),
% 294.90/187.44 inference(transitivity,[status(thm)],[28385, 28383])).
% 294.90/187.44 tff(28387,plain,
% 294.90/187.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s13) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s14)) | (~node21(c_e_h_3, c_i, s13, s14)))),
% 294.90/187.44 inference(quant_inst,[status(thm)],[])).
% 294.90/187.44 tff(28388,plain,
% 294.90/187.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s14)) | node20(c_e_h_3, c_i, s13) | (~node21(c_e_h_3, c_i, s13, s14))),
% 294.90/187.44 inference(modus_ponens,[status(thm)],[28387, 28386])).
% 294.90/187.44 tff(28389,plain,
% 294.90/187.44 ($false),
% 294.90/187.44 inference(unit_resolution,[status(thm)],[28388, 52, 28382, 28373, 28381])).
% 294.90/187.44 tff(28390,plain,((~node21(c_e_h_3, c_i, s13, s14)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s14)) | node20(c_e_h_3, c_i, s13)), inference(lemma,lemma(discharge,[]))).
% 294.90/187.44 tff(28391,plain,
% 294.90/187.44 (~node21(c_e_h_3, c_i, s13, s14)),
% 294.90/187.44 inference(unit_resolution,[status(thm)],[28390, 28373, 28381])).
% 294.90/187.44 tff(28392,plain,
% 294.90/187.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s13, s14)) | node21(c_e_h_3, c_i, s13, s14) | node22(c_e_h_3, c_i, s13, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s13, s14)) | node21(c_e_h_3, c_i, s13, s14) | node22(c_e_h_3, c_i, s13, s14))),
% 294.90/187.44 inference(rewrite,[status(thm)],[])).
% 294.90/187.44 tff(28393,plain,
% 294.90/187.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s13, s14)) | node21(c_e_h_3, c_i, s13, s14) | node22(c_e_h_3, c_i, s13, s14))),
% 294.90/187.44 inference(quant_inst,[status(thm)],[])).
% 294.90/187.44 tff(28394,plain,
% 294.90/187.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s13, s14)) | node21(c_e_h_3, c_i, s13, s14) | node22(c_e_h_3, c_i, s13, s14)),
% 294.90/187.44 inference(modus_ponens,[status(thm)],[28393, 28392])).
% 294.90/187.44 tff(28395,plain,
% 294.90/187.44 (node21(c_e_h_3, c_i, s13, s14) | node22(c_e_h_3, c_i, s13, s14)),
% 294.90/187.44 inference(unit_resolution,[status(thm)],[28394, 82, 12831])).
% 294.90/187.44 tff(28396,plain,
% 294.90/187.44 ($false),
% 294.90/187.44 inference(unit_resolution,[status(thm)],[28395, 28391, 28380])).
% 294.90/187.44 tff(28397,plain,((~m_and_h_gate_v_out(c_e_h_3, c_i, s14)) | node20(c_e_h_3, c_i, s13) | m_and_h_gate_v_out(c_e_h_3, c_i, s13)), inference(lemma,lemma(discharge,[]))).
% 294.90/187.44 tff(28398,plain,
% 294.90/187.44 (~m_and_h_gate_v_out(c_e_h_3, c_i, s14)),
% 294.90/187.44 inference(unit_resolution,[status(thm)],[28397, 28371, 28327])).
% 294.90/187.44 tff(28399,plain,
% 294.90/187.44 (~m_c_h_element_v_in2(c_e_h_3, c_f, s12)),
% 294.90/187.44 inference(unit_resolution,[status(thm)],[11839, 28348])).
% 294.90/187.44 tff(28400,plain,
% 294.90/187.44 (~m_and_h_gate_v_out(c_e_h_3, c_i, s11)),
% 294.90/187.44 inference(unit_resolution,[status(thm)],[11435, 28342, 24271])).
% 294.90/187.44 tff(28401,plain,
% 294.90/187.44 (~m_c_h_element_v_in2(c_e_h_3, c_f, s11)),
% 294.90/187.44 inference(unit_resolution,[status(thm)],[11474, 28400])).
% 294.90/187.44 tff(28402,plain,
% 294.90/187.44 (~m_c_h_element_v_out(c_e_h_3, c_f, s12)),
% 294.90/187.44 inference(unit_resolution,[status(thm)],[11830, 28401, 24273])).
% 294.90/187.44 tff(28403,plain,
% 294.90/187.44 (~m_c_h_element_v_out(c_e_h_3, c_f, s13)),
% 294.90/187.44 inference(unit_resolution,[status(thm)],[11914, 28402, 28399])).
% 294.90/187.44 tff(28404,assumption,(~node20(c_e_h_3, c_i, s14)), introduced(assumption)).
% 294.90/187.44 tff(28405,plain,
% 294.90/187.44 (~m_and_h_gate_v_out(c_e_h_3, c_i, s14)),
% 294.90/187.44 inference(unit_resolution,[status(thm)],[28397, 28372, 28381])).
% 294.90/187.44 tff(28406,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_i, s14)), introduced(assumption)).
% 294.90/187.44 tff(28407,assumption,(m_and_h_gate_v_out(c_e_h_3, c_i, s15)), introduced(assumption)).
% 294.90/187.44 tff(28408,assumption,(node22(c_e_h_3, c_i, s14, s15)), introduced(assumption)).
% 294.90/187.44 tff(28409,plain,
% 294.90/187.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s15)) | (~node22(c_e_h_3, c_i, s14, s15)) | m_and_h_gate_v_out(c_e_h_3, c_i, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s15)) | (~node22(c_e_h_3, c_i, s14, s15)) | m_and_h_gate_v_out(c_e_h_3, c_i, s14))),
% 294.90/187.44 inference(rewrite,[status(thm)],[])).
% 294.90/187.44 tff(28410,plain,
% 294.90/187.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s15)) | (~node22(c_e_h_3, c_i, s14, s15)) | m_and_h_gate_v_out(c_e_h_3, c_i, s14))),
% 294.90/187.44 inference(quant_inst,[status(thm)],[])).
% 294.90/187.44 tff(28411,plain,
% 294.90/187.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s15)) | (~node22(c_e_h_3, c_i, s14, s15)) | m_and_h_gate_v_out(c_e_h_3, c_i, s14)),
% 294.90/187.44 inference(modus_ponens,[status(thm)],[28410, 28409])).
% 294.90/187.44 tff(28412,plain,
% 294.90/187.44 ($false),
% 294.90/187.44 inference(unit_resolution,[status(thm)],[28411, 108, 28408, 28406, 28407])).
% 294.90/187.44 tff(28413,plain,((~node22(c_e_h_3, c_i, s14, s15)) | m_and_h_gate_v_out(c_e_h_3, c_i, s14) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s15))), inference(lemma,lemma(discharge,[]))).
% 294.90/187.44 tff(28414,plain,
% 294.90/187.44 (~node22(c_e_h_3, c_i, s14, s15)),
% 294.90/187.44 inference(unit_resolution,[status(thm)],[28413, 28407, 28406])).
% 294.90/187.44 tff(28415,assumption,(node21(c_e_h_3, c_i, s14, s15)), introduced(assumption)).
% 294.90/187.44 tff(28416,plain,
% 294.90/187.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s14) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s15)) | (~node21(c_e_h_3, c_i, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_i, s14) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s15)) | (~node21(c_e_h_3, c_i, s14, s15)))),
% 294.90/187.44 inference(rewrite,[status(thm)],[])).
% 294.90/187.44 tff(28417,plain,
% 294.90/187.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_i, s14) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s15)) | (~node21(c_e_h_3, c_i, s14, s15)))),
% 294.90/187.44 inference(quant_inst,[status(thm)],[])).
% 294.90/187.44 tff(28418,plain,
% 294.90/187.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_i, s14) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s15)) | (~node21(c_e_h_3, c_i, s14, s15))),
% 294.90/187.44 inference(modus_ponens,[status(thm)],[28417, 28416])).
% 294.90/187.44 tff(28419,plain,
% 294.90/187.44 ($false),
% 294.90/187.44 inference(unit_resolution,[status(thm)],[28418, 52, 28415, 28407, 28404])).
% 294.90/187.44 tff(28420,plain,((~node21(c_e_h_3, c_i, s14, s15)) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s15)) | node20(c_e_h_3, c_i, s14)), inference(lemma,lemma(discharge,[]))).
% 294.90/187.44 tff(28421,plain,
% 294.90/187.44 (~node21(c_e_h_3, c_i, s14, s15)),
% 294.90/187.44 inference(unit_resolution,[status(thm)],[28420, 28407, 28404])).
% 294.90/187.44 tff(28422,plain,
% 294.90/187.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s14, s15)) | node21(c_e_h_3, c_i, s14, s15) | node22(c_e_h_3, c_i, s14, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s14, s15)) | node21(c_e_h_3, c_i, s14, s15) | node22(c_e_h_3, c_i, s14, s15))),
% 294.90/187.44 inference(rewrite,[status(thm)],[])).
% 294.90/187.44 tff(28423,plain,
% 294.90/187.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s14, s15)) | node21(c_e_h_3, c_i, s14, s15) | node22(c_e_h_3, c_i, s14, s15))),
% 294.90/187.44 inference(quant_inst,[status(thm)],[])).
% 294.90/187.44 tff(28424,plain,
% 294.90/187.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s14, s15)) | node21(c_e_h_3, c_i, s14, s15) | node22(c_e_h_3, c_i, s14, s15)),
% 294.90/187.44 inference(modus_ponens,[status(thm)],[28423, 28422])).
% 294.90/187.44 tff(28425,plain,
% 294.90/187.44 (node21(c_e_h_3, c_i, s14, s15) | node22(c_e_h_3, c_i, s14, s15)),
% 294.90/187.44 inference(unit_resolution,[status(thm)],[28424, 82, 12926])).
% 294.90/187.44 tff(28426,plain,
% 294.90/187.44 ($false),
% 294.90/187.44 inference(unit_resolution,[status(thm)],[28425, 28421, 28414])).
% 294.90/187.44 tff(28427,plain,((~m_and_h_gate_v_out(c_e_h_3, c_i, s15)) | node20(c_e_h_3, c_i, s14) | m_and_h_gate_v_out(c_e_h_3, c_i, s14)), inference(lemma,lemma(discharge,[]))).
% 294.90/187.44 tff(28428,plain,
% 294.90/187.44 (~m_and_h_gate_v_out(c_e_h_3, c_i, s15)),
% 294.90/187.44 inference(unit_resolution,[status(thm)],[28427, 28405, 28404])).
% 294.90/187.44 tff(28429,assumption,(m_c_h_element_v_out(c_e_h_3, c_f, s16)), introduced(assumption)).
% 294.90/187.44 tff(28430,assumption,(m_c_h_element_v_in2(c_e_h_3, c_f, s13)), introduced(assumption)).
% 294.90/187.44 tff(28431,plain,
% 294.90/187.44 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s13)) | m_and_h_gate_v_out(c_e_h_3, c_i, s13))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s13)) | m_and_h_gate_v_out(c_e_h_3, c_i, s13))),
% 294.90/187.45 inference(rewrite,[status(thm)],[])).
% 294.90/187.45 tff(28432,plain,
% 294.90/187.45 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s13)) | m_and_h_gate_v_out(c_e_h_3, c_i, s13))),
% 294.90/187.45 inference(quant_inst,[status(thm)],[])).
% 294.90/187.45 tff(28433,plain,
% 294.90/187.45 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s13)) | m_and_h_gate_v_out(c_e_h_3, c_i, s13)),
% 294.90/187.45 inference(modus_ponens,[status(thm)],[28432, 28431])).
% 294.90/187.45 tff(28434,plain,
% 294.90/187.45 ($false),
% 294.90/187.45 inference(unit_resolution,[status(thm)],[28433, 2143, 28372, 28430])).
% 294.90/187.45 tff(28435,plain,((~m_c_h_element_v_in2(c_e_h_3, c_f, s13)) | m_and_h_gate_v_out(c_e_h_3, c_i, s13)), inference(lemma,lemma(discharge,[]))).
% 294.90/187.45 tff(28436,plain,
% 294.90/187.45 (~m_c_h_element_v_in2(c_e_h_3, c_f, s13)),
% 294.90/187.45 inference(unit_resolution,[status(thm)],[28435, 28372])).
% 294.90/187.45 tff(28437,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_f, s13)), introduced(assumption)).
% 294.90/187.45 tff(28438,plain,
% 294.90/187.45 (^[I0: $i, X: $i] : refl(((~m_and_h_gate_v_out(I0, c_i, X)) | m_c_h_element_v_in2(I0, c_f, X)) <=> ((~m_and_h_gate_v_out(I0, c_i, X)) | m_c_h_element_v_in2(I0, c_f, X)))),
% 294.90/187.45 inference(bind,[status(th)],[])).
% 294.90/187.45 tff(28439,plain,
% 294.90/187.45 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_i, X)) | m_c_h_element_v_in2(I0, c_f, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_i, X)) | m_c_h_element_v_in2(I0, c_f, X))),
% 294.90/187.45 inference(quant_intro,[status(thm)],[28438])).
% 294.90/187.45 tff(28440,plain,
% 294.90/187.45 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_i, X)) | m_c_h_element_v_in2(I0, c_f, X)) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_i, X)) | m_c_h_element_v_in2(I0, c_f, X))),
% 294.90/187.45 inference(rewrite,[status(thm)],[])).
% 294.90/187.45 tff(28441,plain,
% 294.90/187.45 (^[I0: $i, X: $i] : rewrite((m_c_h_element_v_in2(I0, c_f, X) | (~m_and_h_gate_v_out(I0, c_i, X))) <=> ((~m_and_h_gate_v_out(I0, c_i, X)) | m_c_h_element_v_in2(I0, c_f, X)))),
% 294.90/187.45 inference(bind,[status(th)],[])).
% 294.90/187.45 tff(28442,plain,
% 294.90/187.45 (![I0: $i, X: $i] : (m_c_h_element_v_in2(I0, c_f, X) | (~m_and_h_gate_v_out(I0, c_i, X))) <=> ![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_i, X)) | m_c_h_element_v_in2(I0, c_f, X))),
% 294.90/187.45 inference(quant_intro,[status(thm)],[28441])).
% 294.90/187.45 tff(28443,axiom,(![I0: $i, X: $i] : (m_c_h_element_v_in2(I0, c_f, X) | (~m_and_h_gate_v_out(I0, c_i, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_cell_25')).
% 294.90/187.45 tff(28444,plain,
% 294.90/187.45 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_i, X)) | m_c_h_element_v_in2(I0, c_f, X))),
% 294.90/187.45 inference(modus_ponens,[status(thm)],[28443, 28442])).
% 294.90/187.45 tff(28445,plain,
% 294.90/187.45 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_i, X)) | m_c_h_element_v_in2(I0, c_f, X))),
% 294.90/187.45 inference(modus_ponens,[status(thm)],[28444, 28440])).
% 294.90/187.45 tff(28446,plain,(
% 294.90/187.45 ![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_i, X)) | m_c_h_element_v_in2(I0, c_f, X))),
% 294.90/187.45 inference(skolemize,[status(sab)],[28445])).
% 294.90/187.45 tff(28447,plain,
% 294.90/187.45 (![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_i, X)) | m_c_h_element_v_in2(I0, c_f, X))),
% 294.90/187.45 inference(modus_ponens,[status(thm)],[28446, 28439])).
% 294.90/187.45 tff(28448,plain,
% 294.90/187.45 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_i, X)) | m_c_h_element_v_in2(I0, c_f, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s13)) | m_c_h_element_v_in2(c_e_h_3, c_f, s13))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_i, X)) | m_c_h_element_v_in2(I0, c_f, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s13)) | m_c_h_element_v_in2(c_e_h_3, c_f, s13))),
% 294.90/187.45 inference(rewrite,[status(thm)],[])).
% 294.90/187.45 tff(28449,plain,
% 294.90/187.45 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_i, X)) | m_c_h_element_v_in2(I0, c_f, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s13)) | m_c_h_element_v_in2(c_e_h_3, c_f, s13))),
% 294.90/187.45 inference(quant_inst,[status(thm)],[])).
% 294.90/187.45 tff(28450,plain,
% 294.90/187.45 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_i, X)) | m_c_h_element_v_in2(I0, c_f, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s13)) | m_c_h_element_v_in2(c_e_h_3, c_f, s13)),
% 294.90/187.45 inference(modus_ponens,[status(thm)],[28449, 28448])).
% 294.90/187.45 tff(28451,plain,
% 294.90/187.45 ($false),
% 294.90/187.45 inference(unit_resolution,[status(thm)],[28450, 28447, 28350, 28437])).
% 294.90/187.45 tff(28452,plain,((~m_and_h_gate_v_out(c_e_h_3, c_i, s13)) | m_c_h_element_v_in2(c_e_h_3, c_f, s13)), inference(lemma,lemma(discharge,[]))).
% 294.90/187.45 tff(28453,plain,
% 294.90/187.45 (~m_and_h_gate_v_out(c_e_h_3, c_i, s13)),
% 294.90/187.45 inference(unit_resolution,[status(thm)],[28452, 28437])).
% 294.90/187.45 tff(28454,plain,
% 294.90/187.45 (~m_and_h_gate_v_out(c_e_h_3, c_i, s14)),
% 294.90/187.45 inference(unit_resolution,[status(thm)],[28397, 28453, 28381])).
% 294.90/187.45 tff(28455,plain,
% 294.90/187.45 (~node18(c_e_h_3, c_f, s13, s14)),
% 294.90/187.45 inference(unit_resolution,[status(thm)],[12869, 12850, 12849])).
% 294.90/187.45 tff(28456,plain,
% 294.90/187.45 (m_c_h_element_v_in1(c_e_h_3, c_f, s13)),
% 294.90/187.45 inference(unit_resolution,[status(thm)],[12906, 12850, 12849])).
% 294.90/187.45 tff(28457,plain,
% 294.90/187.45 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_3, c_f, s13) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s13)) | (~node17(c_e_h_3, c_f, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_f, s13) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s13)) | (~node17(c_e_h_3, c_f, s13)))),
% 294.90/187.45 inference(rewrite,[status(thm)],[])).
% 294.90/187.45 tff(28458,plain,
% 294.90/187.45 (((~m_c_h_element_v_in1(c_e_h_3, c_f, s13)) | m_c_h_element_v_in2(c_e_h_3, c_f, s13) | (~node17(c_e_h_3, c_f, s13))) <=> (m_c_h_element_v_in2(c_e_h_3, c_f, s13) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s13)) | (~node17(c_e_h_3, c_f, s13)))),
% 294.90/187.45 inference(rewrite,[status(thm)],[])).
% 294.90/187.45 tff(28459,plain,
% 294.90/187.45 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s13)) | m_c_h_element_v_in2(c_e_h_3, c_f, s13) | (~node17(c_e_h_3, c_f, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_3, c_f, s13) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s13)) | (~node17(c_e_h_3, c_f, s13))))),
% 294.90/187.45 inference(monotonicity,[status(thm)],[28458])).
% 294.90/187.45 tff(28460,plain,
% 294.90/187.45 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s13)) | m_c_h_element_v_in2(c_e_h_3, c_f, s13) | (~node17(c_e_h_3, c_f, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_f, s13) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s13)) | (~node17(c_e_h_3, c_f, s13)))),
% 294.90/187.45 inference(transitivity,[status(thm)],[28459, 28457])).
% 294.90/187.45 tff(28461,plain,
% 294.90/187.45 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s13)) | m_c_h_element_v_in2(c_e_h_3, c_f, s13) | (~node17(c_e_h_3, c_f, s13)))),
% 294.90/187.45 inference(quant_inst,[status(thm)],[])).
% 294.90/187.45 tff(28462,plain,
% 294.90/187.45 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_f, s13) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s13)) | (~node17(c_e_h_3, c_f, s13))),
% 294.90/187.45 inference(modus_ponens,[status(thm)],[28461, 28460])).
% 294.90/187.45 tff(28463,plain,
% 294.90/187.45 ((~m_c_h_element_v_in1(c_e_h_3, c_f, s13)) | (~node17(c_e_h_3, c_f, s13))),
% 294.90/187.45 inference(unit_resolution,[status(thm)],[28462, 919, 28437])).
% 294.90/187.45 tff(28464,plain,
% 294.90/187.45 (~node17(c_e_h_3, c_f, s13)),
% 294.90/187.45 inference(unit_resolution,[status(thm)],[28463, 28456])).
% 294.90/187.45 tff(28465,plain,
% 294.90/187.45 ($false),
% 294.90/187.45 inference(unit_resolution,[status(thm)],[12881, 28464, 28455])).
% 294.90/187.45 tff(28466,plain,((~m_c_h_element_v_out(c_e_h_3, c_f, s14)) | m_c_h_element_v_in2(c_e_h_3, c_f, s13) | m_c_h_element_v_out(c_e_h_3, c_f, s13)), inference(lemma,lemma(discharge,[]))).
% 294.90/187.45 tff(28467,plain,
% 294.90/187.45 (~m_c_h_element_v_out(c_e_h_3, c_f, s14)),
% 294.90/187.45 inference(unit_resolution,[status(thm)],[28466, 28437, 12849])).
% 294.90/187.45 tff(28468,plain,
% 294.90/187.45 (m_c_h_element_v_in2(c_e_h_3, c_f, s14)),
% 294.90/187.45 inference(unit_resolution,[status(thm)],[12984, 28467, 12908])).
% 294.90/187.45 tff(28469,assumption,(m_c_h_element_v_in2(c_e_h_3, c_f, s14)), introduced(assumption)).
% 294.90/187.45 tff(28470,plain,
% 294.90/187.45 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s14)) | m_and_h_gate_v_out(c_e_h_3, c_i, s14))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s14)) | m_and_h_gate_v_out(c_e_h_3, c_i, s14))),
% 294.90/187.45 inference(rewrite,[status(thm)],[])).
% 294.90/187.45 tff(28471,plain,
% 294.90/187.45 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s14)) | m_and_h_gate_v_out(c_e_h_3, c_i, s14))),
% 294.90/187.45 inference(quant_inst,[status(thm)],[])).
% 294.90/187.45 tff(28472,plain,
% 294.90/187.45 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s14)) | m_and_h_gate_v_out(c_e_h_3, c_i, s14)),
% 294.90/187.45 inference(modus_ponens,[status(thm)],[28471, 28470])).
% 294.90/187.45 tff(28473,plain,
% 294.90/187.45 ($false),
% 294.90/187.45 inference(unit_resolution,[status(thm)],[28472, 2143, 28406, 28469])).
% 294.90/187.45 tff(28474,plain,((~m_c_h_element_v_in2(c_e_h_3, c_f, s14)) | m_and_h_gate_v_out(c_e_h_3, c_i, s14)), inference(lemma,lemma(discharge,[]))).
% 294.90/187.45 tff(28475,plain,
% 294.90/187.45 ($false),
% 294.90/187.45 inference(unit_resolution,[status(thm)],[28474, 28468, 28454])).
% 294.90/187.45 tff(28476,plain,(m_c_h_element_v_in2(c_e_h_3, c_f, s13) | (~m_c_h_element_v_out(c_e_h_3, c_f, s15)) | node20(c_e_h_3, c_i, s13) | m_c_h_element_v_out(c_e_h_3, c_f, s13)), inference(lemma,lemma(discharge,[]))).
% 294.90/187.45 tff(28477,plain,
% 294.90/187.45 (~m_c_h_element_v_out(c_e_h_3, c_f, s15)),
% 294.90/187.45 inference(unit_resolution,[status(thm)],[28476, 28436, 28381, 12849])).
% 294.90/187.45 tff(28478,assumption,(node18(c_e_h_3, c_f, s15, s16)), introduced(assumption)).
% 294.90/187.45 tff(28479,plain,
% 294.90/187.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_f, s15) | (~m_c_h_element_v_out(c_e_h_3, c_f, s16)) | (~node18(c_e_h_3, c_f, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s15) | (~m_c_h_element_v_out(c_e_h_3, c_f, s16)) | (~node18(c_e_h_3, c_f, s15, s16)))),
% 294.90/187.45 inference(rewrite,[status(thm)],[])).
% 294.90/187.45 tff(28480,plain,
% 294.90/187.45 (((~m_c_h_element_v_out(c_e_h_3, c_f, s16)) | m_c_h_element_v_out(c_e_h_3, c_f, s15) | (~node18(c_e_h_3, c_f, s15, s16))) <=> (m_c_h_element_v_out(c_e_h_3, c_f, s15) | (~m_c_h_element_v_out(c_e_h_3, c_f, s16)) | (~node18(c_e_h_3, c_f, s15, s16)))),
% 294.90/187.45 inference(rewrite,[status(thm)],[])).
% 294.90/187.45 tff(28481,plain,
% 294.90/187.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s16)) | m_c_h_element_v_out(c_e_h_3, c_f, s15) | (~node18(c_e_h_3, c_f, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_3, c_f, s15) | (~m_c_h_element_v_out(c_e_h_3, c_f, s16)) | (~node18(c_e_h_3, c_f, s15, s16))))),
% 294.90/187.45 inference(monotonicity,[status(thm)],[28480])).
% 294.90/187.45 tff(28482,plain,
% 294.90/187.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s16)) | m_c_h_element_v_out(c_e_h_3, c_f, s15) | (~node18(c_e_h_3, c_f, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s15) | (~m_c_h_element_v_out(c_e_h_3, c_f, s16)) | (~node18(c_e_h_3, c_f, s15, s16)))),
% 294.90/187.45 inference(transitivity,[status(thm)],[28481, 28479])).
% 294.90/187.46 tff(28483,plain,
% 294.90/187.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s16)) | m_c_h_element_v_out(c_e_h_3, c_f, s15) | (~node18(c_e_h_3, c_f, s15, s16)))),
% 294.90/187.46 inference(quant_inst,[status(thm)],[])).
% 294.90/187.46 tff(28484,plain,
% 294.90/187.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_3, c_f, s15) | (~m_c_h_element_v_out(c_e_h_3, c_f, s16)) | (~node18(c_e_h_3, c_f, s15, s16))),
% 294.90/187.46 inference(modus_ponens,[status(thm)],[28483, 28482])).
% 294.90/187.46 tff(28485,plain,
% 294.90/187.46 ($false),
% 294.90/187.46 inference(unit_resolution,[status(thm)],[28484, 753, 28429, 12997, 28478])).
% 294.90/187.46 tff(28486,plain,((~node18(c_e_h_3, c_f, s15, s16)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s16)) | m_c_h_element_v_out(c_e_h_3, c_f, s15)), inference(lemma,lemma(discharge,[]))).
% 294.90/187.46 tff(28487,plain,
% 294.90/187.46 (~node18(c_e_h_3, c_f, s15, s16)),
% 294.90/187.46 inference(unit_resolution,[status(thm)],[28486, 28429, 12997])).
% 294.90/187.46 tff(28488,plain,
% 294.90/187.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s15, s16)) | node19(c_e_h_3, c_f, s15, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s15, s16)) | node19(c_e_h_3, c_f, s15, s16))),
% 294.90/187.46 inference(rewrite,[status(thm)],[])).
% 294.90/187.46 tff(28489,plain,
% 294.90/187.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s15, s16)) | node19(c_e_h_3, c_f, s15, s16))),
% 294.90/187.46 inference(quant_inst,[status(thm)],[])).
% 294.90/187.46 tff(28490,plain,
% 294.90/187.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s15, s16)) | node19(c_e_h_3, c_f, s15, s16)),
% 294.90/187.46 inference(modus_ponens,[status(thm)],[28489, 28488])).
% 294.90/187.46 tff(28491,plain,
% 294.90/187.46 (node19(c_e_h_3, c_f, s15, s16)),
% 294.90/187.46 inference(unit_resolution,[status(thm)],[28490, 190, 13499])).
% 294.90/187.46 tff(28492,plain,
% 294.90/187.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_3, c_f, s15, s16) | (~node19(c_e_h_3, c_f, s15, s16)) | node17(c_e_h_3, c_f, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_3, c_f, s15, s16) | (~node19(c_e_h_3, c_f, s15, s16)) | node17(c_e_h_3, c_f, s15))),
% 294.90/187.46 inference(rewrite,[status(thm)],[])).
% 294.90/187.46 tff(28493,plain,
% 294.90/187.46 ((node17(c_e_h_3, c_f, s15) | node18(c_e_h_3, c_f, s15, s16) | (~node19(c_e_h_3, c_f, s15, s16))) <=> (node18(c_e_h_3, c_f, s15, s16) | (~node19(c_e_h_3, c_f, s15, s16)) | node17(c_e_h_3, c_f, s15))),
% 294.90/187.46 inference(rewrite,[status(thm)],[])).
% 294.90/187.46 tff(28494,plain,
% 294.90/187.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s15) | node18(c_e_h_3, c_f, s15, s16) | (~node19(c_e_h_3, c_f, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_3, c_f, s15, s16) | (~node19(c_e_h_3, c_f, s15, s16)) | node17(c_e_h_3, c_f, s15)))),
% 294.90/187.46 inference(monotonicity,[status(thm)],[28493])).
% 294.90/187.46 tff(28495,plain,
% 294.90/187.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s15) | node18(c_e_h_3, c_f, s15, s16) | (~node19(c_e_h_3, c_f, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_3, c_f, s15, s16) | (~node19(c_e_h_3, c_f, s15, s16)) | node17(c_e_h_3, c_f, s15))),
% 294.90/187.46 inference(transitivity,[status(thm)],[28494, 28492])).
% 294.90/187.46 tff(28496,plain,
% 294.90/187.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_3, c_f, s15) | node18(c_e_h_3, c_f, s15, s16) | (~node19(c_e_h_3, c_f, s15, s16)))),
% 294.90/187.46 inference(quant_inst,[status(thm)],[])).
% 294.90/187.46 tff(28497,plain,
% 294.90/187.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_3, c_f, s15, s16) | (~node19(c_e_h_3, c_f, s15, s16)) | node17(c_e_h_3, c_f, s15)),
% 294.90/187.46 inference(modus_ponens,[status(thm)],[28496, 28495])).
% 294.90/187.46 tff(28498,plain,
% 294.90/187.46 (node18(c_e_h_3, c_f, s15, s16) | node17(c_e_h_3, c_f, s15)),
% 294.90/187.46 inference(unit_resolution,[status(thm)],[28497, 776, 28491])).
% 294.90/187.46 tff(28499,plain,
% 294.90/187.46 (node17(c_e_h_3, c_f, s15)),
% 294.90/187.46 inference(unit_resolution,[status(thm)],[28498, 28487])).
% 294.90/187.46 tff(28500,assumption,(~m_c_h_element_v_in2(c_e_h_3, c_f, s15)), introduced(assumption)).
% 294.90/187.46 tff(28501,plain,
% 294.90/187.46 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_3, c_f, s15) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s15)) | (~node17(c_e_h_3, c_f, s15)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_f, s15) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s15)) | (~node17(c_e_h_3, c_f, s15)))),
% 294.90/187.46 inference(rewrite,[status(thm)],[])).
% 294.90/187.46 tff(28502,plain,
% 294.90/187.46 (((~m_c_h_element_v_in1(c_e_h_3, c_f, s15)) | m_c_h_element_v_in2(c_e_h_3, c_f, s15) | (~node17(c_e_h_3, c_f, s15))) <=> (m_c_h_element_v_in2(c_e_h_3, c_f, s15) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s15)) | (~node17(c_e_h_3, c_f, s15)))),
% 294.90/187.46 inference(rewrite,[status(thm)],[])).
% 294.90/187.46 tff(28503,plain,
% 294.90/187.46 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s15)) | m_c_h_element_v_in2(c_e_h_3, c_f, s15) | (~node17(c_e_h_3, c_f, s15)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_3, c_f, s15) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s15)) | (~node17(c_e_h_3, c_f, s15))))),
% 294.90/187.46 inference(monotonicity,[status(thm)],[28502])).
% 294.90/187.46 tff(28504,plain,
% 294.90/187.46 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s15)) | m_c_h_element_v_in2(c_e_h_3, c_f, s15) | (~node17(c_e_h_3, c_f, s15)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_f, s15) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s15)) | (~node17(c_e_h_3, c_f, s15)))),
% 294.90/187.46 inference(transitivity,[status(thm)],[28503, 28501])).
% 294.90/187.46 tff(28505,plain,
% 294.90/187.46 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_3, c_f, s15)) | m_c_h_element_v_in2(c_e_h_3, c_f, s15) | (~node17(c_e_h_3, c_f, s15)))),
% 294.90/187.46 inference(quant_inst,[status(thm)],[])).
% 294.90/187.46 tff(28506,plain,
% 294.90/187.46 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_3, c_f, s15) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s15)) | (~node17(c_e_h_3, c_f, s15))),
% 294.90/187.46 inference(modus_ponens,[status(thm)],[28505, 28504])).
% 294.90/187.46 tff(28507,plain,
% 294.90/187.46 ((~m_c_h_element_v_in1(c_e_h_3, c_f, s15)) | (~node17(c_e_h_3, c_f, s15))),
% 294.90/187.46 inference(unit_resolution,[status(thm)],[28506, 919, 28500])).
% 294.90/187.46 tff(28508,plain,
% 294.90/187.46 (~m_c_h_element_v_in1(c_e_h_3, c_f, s15)),
% 294.90/187.46 inference(unit_resolution,[status(thm)],[28507, 28499])).
% 294.90/187.46 tff(28509,assumption,(node15(c_e_h_3, c_f, s15, s16)), introduced(assumption)).
% 294.90/187.46 tff(28510,plain,
% 294.90/187.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s16)) | (~node15(c_e_h_3, c_f, s15, s16)) | m_c_h_element_v_out(c_e_h_3, c_f, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s16)) | (~node15(c_e_h_3, c_f, s15, s16)) | m_c_h_element_v_out(c_e_h_3, c_f, s15))),
% 294.90/187.46 inference(rewrite,[status(thm)],[])).
% 294.90/187.46 tff(28511,plain,
% 294.90/187.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_3, c_f, s16)) | (~node15(c_e_h_3, c_f, s15, s16)) | m_c_h_element_v_out(c_e_h_3, c_f, s15))),
% 294.90/187.46 inference(quant_inst,[status(thm)],[])).
% 294.90/187.46 tff(28512,plain,
% 294.90/187.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_3, c_f, s16)) | (~node15(c_e_h_3, c_f, s15, s16)) | m_c_h_element_v_out(c_e_h_3, c_f, s15)),
% 294.90/187.46 inference(modus_ponens,[status(thm)],[28511, 28510])).
% 294.90/187.46 tff(28513,plain,
% 294.90/187.46 ($false),
% 294.90/187.46 inference(unit_resolution,[status(thm)],[28512, 147, 28429, 12997, 28509])).
% 294.90/187.46 tff(28514,plain,((~node15(c_e_h_3, c_f, s15, s16)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s16)) | m_c_h_element_v_out(c_e_h_3, c_f, s15)), inference(lemma,lemma(discharge,[]))).
% 294.90/187.46 tff(28515,plain,
% 294.90/187.46 (~node15(c_e_h_3, c_f, s15, s16)),
% 294.90/187.46 inference(unit_resolution,[status(thm)],[28514, 28429, 12997])).
% 294.90/187.46 tff(28516,assumption,(node17(c_e_h_3, c_f, s15)), introduced(assumption)).
% 294.90/187.46 tff(28517,assumption,(node16(c_e_h_3, c_f, s15)), introduced(assumption)).
% 294.90/187.46 tff(28518,plain,
% 294.90/187.46 (m_c_h_element_v_in2(c_e_h_3, c_f, s15) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s15))),
% 294.90/187.46 inference(unit_resolution,[status(thm)],[28506, 919, 28516])).
% 294.90/187.46 tff(28519,plain,
% 294.90/187.46 (~m_c_h_element_v_in1(c_e_h_3, c_f, s15)),
% 294.90/187.46 inference(unit_resolution,[status(thm)],[28518, 28500])).
% 294.90/187.46 tff(28520,plain,
% 294.90/187.46 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s15)) | m_c_h_element_v_in1(c_e_h_3, c_f, s15) | m_c_h_element_v_in2(c_e_h_3, c_f, s15))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s15)) | m_c_h_element_v_in1(c_e_h_3, c_f, s15) | m_c_h_element_v_in2(c_e_h_3, c_f, s15))),
% 294.90/187.46 inference(rewrite,[status(thm)],[])).
% 294.90/187.46 tff(28521,plain,
% 294.90/187.46 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_3, c_f, s15)) | m_c_h_element_v_in1(c_e_h_3, c_f, s15) | m_c_h_element_v_in2(c_e_h_3, c_f, s15))),
% 294.90/187.46 inference(quant_inst,[status(thm)],[])).
% 294.90/187.46 tff(28522,plain,
% 294.90/187.46 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_3, c_f, s15)) | m_c_h_element_v_in1(c_e_h_3, c_f, s15) | m_c_h_element_v_in2(c_e_h_3, c_f, s15)),
% 294.90/187.46 inference(modus_ponens,[status(thm)],[28521, 28520])).
% 294.90/187.46 tff(28523,plain,
% 294.90/187.46 (m_c_h_element_v_in1(c_e_h_3, c_f, s15) | m_c_h_element_v_in2(c_e_h_3, c_f, s15)),
% 294.90/187.46 inference(unit_resolution,[status(thm)],[28522, 178, 28517])).
% 294.90/187.46 tff(28524,plain,
% 294.90/187.46 ($false),
% 294.90/187.46 inference(unit_resolution,[status(thm)],[28523, 28519, 28500])).
% 294.90/187.46 tff(28525,plain,(m_c_h_element_v_in2(c_e_h_3, c_f, s15) | (~node16(c_e_h_3, c_f, s15)) | (~node17(c_e_h_3, c_f, s15))), inference(lemma,lemma(discharge,[]))).
% 294.90/187.46 tff(28526,plain,
% 294.90/187.46 (m_c_h_element_v_in2(c_e_h_3, c_f, s15)),
% 294.90/187.46 inference(unit_resolution,[status(thm)],[28525, 28517, 28516])).
% 294.90/187.46 tff(28527,plain,
% 294.90/187.46 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s15) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s15)) | (~node17(c_e_h_3, c_f, s15)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_3, c_f, s15) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s15)) | (~node17(c_e_h_3, c_f, s15)))),
% 294.90/187.46 inference(rewrite,[status(thm)],[])).
% 294.90/187.46 tff(28528,plain,
% 294.90/187.46 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s15) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s15)) | (~node17(c_e_h_3, c_f, s15)))),
% 294.90/187.46 inference(quant_inst,[status(thm)],[])).
% 294.90/187.47 tff(28529,plain,
% 294.90/187.47 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_3, c_f, s15) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s15)) | (~node17(c_e_h_3, c_f, s15))),
% 294.90/187.47 inference(modus_ponens,[status(thm)],[28528, 28527])).
% 294.90/187.47 tff(28530,plain,
% 294.90/187.47 (m_c_h_element_v_in1(c_e_h_3, c_f, s15) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s15))),
% 294.90/187.47 inference(unit_resolution,[status(thm)],[28529, 859, 28516])).
% 294.90/187.47 tff(28531,plain,
% 294.90/187.47 (m_c_h_element_v_in1(c_e_h_3, c_f, s15)),
% 294.90/187.47 inference(unit_resolution,[status(thm)],[28530, 28526])).
% 294.90/187.47 tff(28532,plain,
% 294.90/187.47 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s15)) | (~node16(c_e_h_3, c_f, s15)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s15)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s15)) | (~node16(c_e_h_3, c_f, s15)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s15)))),
% 294.90/187.47 inference(rewrite,[status(thm)],[])).
% 294.90/187.47 tff(28533,plain,
% 294.90/187.47 (((~node16(c_e_h_3, c_f, s15)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s15)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s15))) <=> ((~m_c_h_element_v_in2(c_e_h_3, c_f, s15)) | (~node16(c_e_h_3, c_f, s15)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s15)))),
% 294.90/187.47 inference(rewrite,[status(thm)],[])).
% 294.90/187.47 tff(28534,plain,
% 294.90/187.47 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_f, s15)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s15)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s15)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s15)) | (~node16(c_e_h_3, c_f, s15)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s15))))),
% 294.90/187.47 inference(monotonicity,[status(thm)],[28533])).
% 294.90/187.47 tff(28535,plain,
% 294.90/187.47 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_f, s15)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s15)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s15)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s15)) | (~node16(c_e_h_3, c_f, s15)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s15)))),
% 294.90/187.47 inference(transitivity,[status(thm)],[28534, 28532])).
% 294.90/187.47 tff(28536,plain,
% 294.90/187.47 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_3, c_f, s15)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s15)) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s15)))),
% 294.90/187.47 inference(quant_inst,[status(thm)],[])).
% 294.90/187.47 tff(28537,plain,
% 294.90/187.47 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s15)) | (~node16(c_e_h_3, c_f, s15)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s15))),
% 294.90/187.47 inference(modus_ponens,[status(thm)],[28536, 28535])).
% 294.90/187.47 tff(28538,plain,
% 294.90/187.47 ((~m_c_h_element_v_in2(c_e_h_3, c_f, s15)) | (~m_c_h_element_v_in1(c_e_h_3, c_f, s15))),
% 294.90/187.47 inference(unit_resolution,[status(thm)],[28537, 2307, 28517])).
% 294.90/187.47 tff(28539,plain,
% 294.90/187.47 ($false),
% 294.90/187.47 inference(unit_resolution,[status(thm)],[28538, 28531, 28526])).
% 294.90/187.47 tff(28540,plain,((~node16(c_e_h_3, c_f, s15)) | (~node17(c_e_h_3, c_f, s15))), inference(lemma,lemma(discharge,[]))).
% 294.90/187.47 tff(28541,plain,
% 294.90/187.47 (~node16(c_e_h_3, c_f, s15)),
% 294.90/187.47 inference(unit_resolution,[status(thm)],[28540, 28499])).
% 294.90/187.47 tff(28542,plain,
% 294.90/187.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_3, c_f, s15, s16) | node14(c_e_h_3, c_f, s15, s16) | (~node19(c_e_h_3, c_f, s15, s16)) | node16(c_e_h_3, c_f, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_3, c_f, s15, s16) | node14(c_e_h_3, c_f, s15, s16) | (~node19(c_e_h_3, c_f, s15, s16)) | node16(c_e_h_3, c_f, s15))),
% 294.90/187.47 inference(rewrite,[status(thm)],[])).
% 294.90/187.47 tff(28543,plain,
% 294.90/187.47 ((node16(c_e_h_3, c_f, s15) | node14(c_e_h_3, c_f, s15, s16) | node15(c_e_h_3, c_f, s15, s16) | (~node19(c_e_h_3, c_f, s15, s16))) <=> (node15(c_e_h_3, c_f, s15, s16) | node14(c_e_h_3, c_f, s15, s16) | (~node19(c_e_h_3, c_f, s15, s16)) | node16(c_e_h_3, c_f, s15))),
% 294.90/187.47 inference(rewrite,[status(thm)],[])).
% 294.90/187.47 tff(28544,plain,
% 294.90/187.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s15) | node14(c_e_h_3, c_f, s15, s16) | node15(c_e_h_3, c_f, s15, s16) | (~node19(c_e_h_3, c_f, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_3, c_f, s15, s16) | node14(c_e_h_3, c_f, s15, s16) | (~node19(c_e_h_3, c_f, s15, s16)) | node16(c_e_h_3, c_f, s15)))),
% 294.90/187.47 inference(monotonicity,[status(thm)],[28543])).
% 294.90/187.47 tff(28545,plain,
% 294.90/187.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s15) | node14(c_e_h_3, c_f, s15, s16) | node15(c_e_h_3, c_f, s15, s16) | (~node19(c_e_h_3, c_f, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_3, c_f, s15, s16) | node14(c_e_h_3, c_f, s15, s16) | (~node19(c_e_h_3, c_f, s15, s16)) | node16(c_e_h_3, c_f, s15))),
% 294.90/187.47 inference(transitivity,[status(thm)],[28544, 28542])).
% 294.90/187.47 tff(28546,plain,
% 294.90/187.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_3, c_f, s15) | node14(c_e_h_3, c_f, s15, s16) | node15(c_e_h_3, c_f, s15, s16) | (~node19(c_e_h_3, c_f, s15, s16)))),
% 294.90/187.47 inference(quant_inst,[status(thm)],[])).
% 294.90/187.47 tff(28547,plain,
% 294.90/187.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_3, c_f, s15, s16) | node14(c_e_h_3, c_f, s15, s16) | (~node19(c_e_h_3, c_f, s15, s16)) | node16(c_e_h_3, c_f, s15)),
% 294.90/187.47 inference(modus_ponens,[status(thm)],[28546, 28545])).
% 294.90/187.47 tff(28548,plain,
% 294.90/187.47 (node15(c_e_h_3, c_f, s15, s16) | node14(c_e_h_3, c_f, s15, s16) | node16(c_e_h_3, c_f, s15)),
% 294.90/187.47 inference(unit_resolution,[status(thm)],[28547, 204, 28491])).
% 294.90/187.47 tff(28549,plain,
% 294.90/187.47 (node14(c_e_h_3, c_f, s15, s16)),
% 294.90/187.47 inference(unit_resolution,[status(thm)],[28548, 28541, 28515])).
% 294.90/187.47 tff(28550,assumption,(~m_c_h_element_v_in1(c_e_h_3, c_f, s15)), introduced(assumption)).
% 294.90/187.47 tff(28551,assumption,(node14(c_e_h_3, c_f, s15, s16)), introduced(assumption)).
% 294.90/187.47 tff(28552,plain,
% 294.90/187.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s15) | (~m_c_h_element_v_out(c_e_h_3, c_f, s16)) | (~node14(c_e_h_3, c_f, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_f, s15) | (~m_c_h_element_v_out(c_e_h_3, c_f, s16)) | (~node14(c_e_h_3, c_f, s15, s16)))),
% 294.90/187.47 inference(rewrite,[status(thm)],[])).
% 294.90/187.47 tff(28553,plain,
% 294.90/187.47 (((~node14(c_e_h_3, c_f, s15, s16)) | m_c_h_element_v_in1(c_e_h_3, c_f, s15) | (~m_c_h_element_v_out(c_e_h_3, c_f, s16))) <=> (m_c_h_element_v_in1(c_e_h_3, c_f, s15) | (~m_c_h_element_v_out(c_e_h_3, c_f, s16)) | (~node14(c_e_h_3, c_f, s15, s16)))),
% 294.90/187.47 inference(rewrite,[status(thm)],[])).
% 294.90/187.47 tff(28554,plain,
% 294.90/187.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s15, s16)) | m_c_h_element_v_in1(c_e_h_3, c_f, s15) | (~m_c_h_element_v_out(c_e_h_3, c_f, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_3, c_f, s15) | (~m_c_h_element_v_out(c_e_h_3, c_f, s16)) | (~node14(c_e_h_3, c_f, s15, s16))))),
% 294.90/187.48 inference(monotonicity,[status(thm)],[28553])).
% 294.90/187.48 tff(28555,plain,
% 294.90/187.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s15, s16)) | m_c_h_element_v_in1(c_e_h_3, c_f, s15) | (~m_c_h_element_v_out(c_e_h_3, c_f, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_f, s15) | (~m_c_h_element_v_out(c_e_h_3, c_f, s16)) | (~node14(c_e_h_3, c_f, s15, s16)))),
% 294.90/187.48 inference(transitivity,[status(thm)],[28554, 28552])).
% 294.90/187.48 tff(28556,plain,
% 294.90/187.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_3, c_f, s15, s16)) | m_c_h_element_v_in1(c_e_h_3, c_f, s15) | (~m_c_h_element_v_out(c_e_h_3, c_f, s16)))),
% 294.90/187.48 inference(quant_inst,[status(thm)],[])).
% 294.90/187.48 tff(28557,plain,
% 294.90/187.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_3, c_f, s15) | (~m_c_h_element_v_out(c_e_h_3, c_f, s16)) | (~node14(c_e_h_3, c_f, s15, s16))),
% 294.90/187.48 inference(modus_ponens,[status(thm)],[28556, 28555])).
% 294.90/187.48 tff(28558,plain,
% 294.90/187.48 ($false),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[28557, 223, 28429, 28551, 28550])).
% 294.90/187.48 tff(28559,plain,((~node14(c_e_h_3, c_f, s15, s16)) | (~m_c_h_element_v_out(c_e_h_3, c_f, s16)) | m_c_h_element_v_in1(c_e_h_3, c_f, s15)), inference(lemma,lemma(discharge,[]))).
% 294.90/187.48 tff(28560,plain,
% 294.90/187.48 ($false),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[28559, 28549, 28508, 28429])).
% 294.90/187.48 tff(28561,plain,((~m_c_h_element_v_out(c_e_h_3, c_f, s16)) | m_c_h_element_v_in2(c_e_h_3, c_f, s15) | m_c_h_element_v_out(c_e_h_3, c_f, s15)), inference(lemma,lemma(discharge,[]))).
% 294.90/187.48 tff(28562,plain,
% 294.90/187.48 (m_c_h_element_v_in2(c_e_h_3, c_f, s15)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[28561, 28477, 28429])).
% 294.90/187.48 tff(28563,assumption,(m_c_h_element_v_in2(c_e_h_3, c_f, s15)), introduced(assumption)).
% 294.90/187.48 tff(28564,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_i, s15)), introduced(assumption)).
% 294.90/187.48 tff(28565,plain,
% 294.90/187.48 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s15)) | m_and_h_gate_v_out(c_e_h_3, c_i, s15))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s15)) | m_and_h_gate_v_out(c_e_h_3, c_i, s15))),
% 294.90/187.48 inference(rewrite,[status(thm)],[])).
% 294.90/187.48 tff(28566,plain,
% 294.90/187.48 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_3, c_f, s15)) | m_and_h_gate_v_out(c_e_h_3, c_i, s15))),
% 294.90/187.48 inference(quant_inst,[status(thm)],[])).
% 294.90/187.48 tff(28567,plain,
% 294.90/187.48 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_3, c_f, s15)) | m_and_h_gate_v_out(c_e_h_3, c_i, s15)),
% 294.90/187.48 inference(modus_ponens,[status(thm)],[28566, 28565])).
% 294.90/187.48 tff(28568,plain,
% 294.90/187.48 ($false),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[28567, 2143, 28564, 28563])).
% 294.90/187.48 tff(28569,plain,((~m_c_h_element_v_in2(c_e_h_3, c_f, s15)) | m_and_h_gate_v_out(c_e_h_3, c_i, s15)), inference(lemma,lemma(discharge,[]))).
% 294.90/187.48 tff(28570,plain,
% 294.90/187.48 ($false),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[28569, 28562, 28428])).
% 294.90/187.48 tff(28571,plain,(m_and_h_gate_v_out(c_e_h_3, c_i, s13) | (~m_c_h_element_v_out(c_e_h_3, c_f, s16)) | node20(c_e_h_3, c_i, s14) | node20(c_e_h_3, c_i, s13) | m_c_h_element_v_out(c_e_h_3, c_f, s13)), inference(lemma,lemma(discharge,[]))).
% 294.90/187.48 tff(28572,plain,
% 294.90/187.48 (~m_c_h_element_v_out(c_e_h_3, c_f, s16)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[28571, 28403, 20171, 28371, 28327])).
% 294.90/187.48 tff(28573,plain,
% 294.90/187.48 (~m_c_h_element_v_in2(c_e_h_3, c_f, s13)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[28435, 28371])).
% 294.90/187.48 tff(28574,plain,
% 294.90/187.48 (~m_c_h_element_v_out(c_e_h_3, c_f, s15)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[28476, 28403, 28327, 28573])).
% 294.90/187.48 tff(28575,plain,
% 294.90/187.48 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s15)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[13002, 28574])).
% 294.90/187.48 tff(28576,plain,
% 294.90/187.48 (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s13)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[13377, 24278])).
% 294.90/187.48 tff(28577,plain,
% 294.90/187.48 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s13)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[13329, 28403])).
% 294.90/187.48 tff(28578,plain,
% 294.90/187.48 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s14)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[13405, 28577, 28576, 26412])).
% 294.90/187.48 tff(28579,plain,
% 294.90/187.48 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s16)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[12845, 28572])).
% 294.90/187.48 tff(28580,plain,
% 294.90/187.48 (~m_c_h_element_v_out(c_e_h_3, c_f, s14)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[28466, 28403, 28573])).
% 294.90/187.48 tff(28581,plain,
% 294.90/187.48 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s14)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[13622, 28580])).
% 294.90/187.48 tff(28582,plain,
% 294.90/187.48 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s17)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[13579, 28581, 28579, 28578, 26415, 28575])).
% 294.90/187.48 tff(28583,plain,
% 294.90/187.48 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s10)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[13170, 5601, 13130])).
% 294.90/187.48 tff(28584,plain,
% 294.90/187.48 (~node9(c_e_h_3, c_n, s10)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[13174, 4972, 28583])).
% 294.90/187.48 tff(28585,plain,
% 294.90/187.48 (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s11)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[13196, 28584])).
% 294.90/187.48 tff(28586,plain,
% 294.90/187.48 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s10)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[13007, 11686])).
% 294.90/187.48 tff(28587,plain,
% 294.90/187.48 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s11)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[13157, 28586, 13130])).
% 294.90/187.48 tff(28588,plain,
% 294.90/187.48 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s11)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[13162, 5601, 28587])).
% 294.90/187.48 tff(28589,plain,
% 294.90/187.48 (~node9(c_e_h_3, c_n, s11)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[13166, 4972, 28588])).
% 294.90/187.48 tff(28590,plain,
% 294.90/187.48 (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s12)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[13217, 28589, 28585])).
% 294.90/187.48 tff(28591,plain,
% 294.90/187.48 (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s11)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[13270, 28585])).
% 294.90/187.48 tff(28592,plain,
% 294.90/187.48 (~m_c_h_element_v_out(c_e_h_3, c_f, s11)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[11758, 11686, 11751])).
% 294.90/187.48 tff(28593,plain,
% 294.90/187.48 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s11)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[13228, 28592])).
% 294.90/187.48 tff(28594,plain,
% 294.90/187.48 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[26261, 28593, 28587, 28591])).
% 294.90/187.48 tff(28595,plain,
% 294.90/187.48 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s12)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[13292, 5601, 28594])).
% 294.90/187.48 tff(28596,plain,
% 294.90/187.48 (~node9(c_e_h_3, c_n, s12)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[13296, 4972, 28595])).
% 294.90/187.48 tff(28597,plain,
% 294.90/187.48 (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s13)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[13320, 28596, 28590])).
% 294.90/187.48 tff(28598,plain,
% 294.90/187.48 (~m_c_h_element_v_out(c_e_h_3, c_f, s12)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[11830, 28592, 11784])).
% 294.90/187.48 tff(28599,plain,
% 294.90/187.48 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s12)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[13340, 28598])).
% 294.90/187.48 tff(28600,plain,
% 294.90/187.48 (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s12)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[13223, 28590])).
% 294.90/187.48 tff(28601,plain,
% 294.90/187.48 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s13)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[13369, 28600, 28594, 28599])).
% 294.90/187.48 tff(28602,plain,
% 294.90/187.48 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s13)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[13609, 5601, 28601])).
% 294.90/187.48 tff(28603,plain,
% 294.90/187.48 (~node9(c_e_h_3, c_n, s13)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[13613, 4972, 28602])).
% 294.90/187.48 tff(28604,plain,
% 294.90/187.48 (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s14)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[13605, 28603, 28597])).
% 294.90/187.48 tff(28605,plain,
% 294.90/187.48 (~m_c_h_element_v_out(c_e_h_3, c_f, s13)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[11914, 28598, 11905])).
% 294.90/187.48 tff(28606,plain,
% 294.90/187.48 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s13)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[13329, 28605])).
% 294.90/187.48 tff(28607,plain,
% 294.90/187.48 (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s13)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[13377, 28597])).
% 294.90/187.48 tff(28608,plain,
% 294.90/187.48 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s14)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[13405, 28607, 28606, 28601])).
% 294.90/187.48 tff(28609,plain,
% 294.90/187.48 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s14)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[13411, 5601, 28608])).
% 294.90/187.48 tff(28610,plain,
% 294.90/187.48 (~node9(c_e_h_3, c_n, s14)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[13415, 4972, 28609])).
% 294.90/187.48 tff(28611,plain,
% 294.90/187.48 (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s15)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[13435, 28610, 28604])).
% 294.90/187.48 tff(28612,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s17)), introduced(assumption)).
% 294.90/187.48 tff(28613,plain,
% 294.90/187.48 (~m_c_h_element_v_out(c_e_h_3, c_f, s15)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[28476, 28605, 28381, 28437])).
% 294.90/187.48 tff(28614,plain,
% 294.90/187.48 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s15)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[13002, 28613])).
% 294.90/187.48 tff(28615,plain,
% 294.90/187.48 (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s12)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[13223, 13299])).
% 294.90/187.48 tff(28616,plain,
% 294.90/187.48 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s14)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[13405, 13370, 13378, 13330])).
% 294.90/187.48 tff(28617,plain,
% 294.90/187.48 (~m_c_h_element_v_out(c_e_h_3, c_f, s14)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[28466, 13322, 28437])).
% 294.90/187.48 tff(28618,plain,
% 294.90/187.48 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s14)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[13622, 28617])).
% 294.90/187.48 tff(28619,plain,
% 294.90/187.48 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s13)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[13609, 5601, 13370])).
% 294.90/187.48 tff(28620,plain,
% 294.90/187.48 (~node9(c_e_h_3, c_n, s13)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[13613, 4972, 28619])).
% 294.90/187.48 tff(28621,plain,
% 294.90/187.48 (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s14)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[13605, 28620, 13332])).
% 294.90/187.48 tff(28622,plain,
% 294.90/187.48 (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s14)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[13442, 28621])).
% 294.90/187.48 tff(28623,plain,
% 294.90/187.48 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s15)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[13471, 28622, 28618, 28616])).
% 294.90/187.48 tff(28624,plain,
% 294.90/187.48 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s14)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[13411, 5601, 28616])).
% 294.90/187.48 tff(28625,plain,
% 294.90/187.48 (~node9(c_e_h_3, c_n, s14)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[13415, 4972, 28624])).
% 294.90/187.48 tff(28626,plain,
% 294.90/187.48 (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s15)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[13435, 28621, 28625])).
% 294.90/187.48 tff(28627,plain,
% 294.90/187.48 (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s15)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[13479, 28626])).
% 294.90/187.48 tff(28628,plain,
% 294.90/187.48 ($false),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[13513, 28627, 28623, 13482, 13331])).
% 294.90/187.48 tff(28629,plain,(m_c_h_element_v_out(c_e_h_3, c_f, s12) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s16) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s15)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s13) | m_c_h_element_v_in2(c_e_h_3, c_f, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12)) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s12)) | m_c_h_element_v_in2(c_e_h_3, c_f, s12)), inference(lemma,lemma(discharge,[]))).
% 294.90/187.48 tff(28630,plain,
% 294.90/187.48 (m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s13)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[28629, 13336, 11905, 13482, 28437, 11841, 28615, 13331])).
% 294.90/187.48 tff(28631,plain,
% 294.90/187.48 (node9(c_e_h_3, c_n, s12)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[13320, 28630, 13299])).
% 294.90/187.48 tff(28632,plain,
% 294.90/187.48 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s12)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[13292, 5601, 13336])).
% 294.90/187.48 tff(28633,plain,
% 294.90/187.48 ($false),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[13296, 4972, 28632, 28631])).
% 294.90/187.48 tff(28634,plain,((~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s12) | m_c_h_element_v_in2(c_e_h_3, c_f, s12) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s16) | m_c_h_element_v_in2(c_e_h_3, c_f, s13) | m_c_h_element_v_out(c_e_h_3, c_f, s12) | (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s15))), inference(lemma,lemma(discharge,[]))).
% 294.90/187.48 tff(28635,plain,
% 294.90/187.48 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s16)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[28634, 28590, 28437, 28598, 28594, 28614, 11905])).
% 294.90/187.48 tff(28636,plain,
% 294.90/187.48 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s16)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s16)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s16)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s16)))),
% 294.90/187.48 inference(rewrite,[status(thm)],[])).
% 294.90/187.48 tff(28637,plain,
% 294.90/187.48 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s16)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s16)))),
% 294.90/187.48 inference(quant_inst,[status(thm)],[])).
% 294.90/187.48 tff(28638,plain,
% 294.90/187.48 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s16)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s16))),
% 294.90/187.48 inference(modus_ponens,[status(thm)],[28637, 28636])).
% 294.90/187.48 tff(28639,plain,
% 294.90/187.48 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s16)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[28638, 5601, 28635])).
% 294.90/187.48 tff(28640,plain,
% 294.90/187.48 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s16)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s16))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s16)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s16))),
% 294.90/187.48 inference(rewrite,[status(thm)],[])).
% 294.90/187.48 tff(28641,plain,
% 294.90/187.48 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s16)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s16))),
% 294.90/187.48 inference(quant_inst,[status(thm)],[])).
% 294.90/187.48 tff(28642,plain,
% 294.90/187.48 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s16)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s16)),
% 294.90/187.48 inference(modus_ponens,[status(thm)],[28641, 28640])).
% 294.90/187.48 tff(28643,plain,
% 294.90/187.48 (~node9(c_e_h_3, c_n, s16)),
% 294.90/187.48 inference(unit_resolution,[status(thm)],[28642, 4972, 28639])).
% 294.90/187.48 tff(28644,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s16)), introduced(assumption)).
% 294.90/187.48 tff(28645,assumption,(node11(c_e_h_3, c_n, s16, s17)), introduced(assumption)).
% 294.90/187.48 tff(28646,plain,
% 294.90/187.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s17)) | (~node11(c_e_h_3, c_n, s16, s17)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s17)) | (~node11(c_e_h_3, c_n, s16, s17)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s16))),
% 294.90/187.48 inference(rewrite,[status(thm)],[])).
% 294.90/187.48 tff(28647,plain,
% 294.90/187.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s17)) | (~node11(c_e_h_3, c_n, s16, s17)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s16))),
% 294.99/187.49 inference(quant_inst,[status(thm)],[])).
% 294.99/187.49 tff(28648,plain,
% 294.99/187.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s17)) | (~node11(c_e_h_3, c_n, s16, s17)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s16)),
% 294.99/187.49 inference(modus_ponens,[status(thm)],[28647, 28646])).
% 294.99/187.49 tff(28649,plain,
% 294.99/187.49 ($false),
% 294.99/187.49 inference(unit_resolution,[status(thm)],[28648, 5017, 28644, 28612, 28645])).
% 294.99/187.49 tff(28650,plain,((~node11(c_e_h_3, c_n, s16, s17)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s16) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s17))), inference(lemma,lemma(discharge,[]))).
% 294.99/187.49 tff(28651,plain,
% 294.99/187.49 (~node11(c_e_h_3, c_n, s16, s17)),
% 294.99/187.49 inference(unit_resolution,[status(thm)],[28650, 28612, 28644])).
% 294.99/187.49 tff(28652,assumption,(~node9(c_e_h_3, c_n, s16)), introduced(assumption)).
% 294.99/187.49 tff(28653,assumption,(node10(c_e_h_3, c_n, s16, s17)), introduced(assumption)).
% 294.99/187.49 tff(28654,plain,
% 294.99/187.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s16) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s17)) | (~node10(c_e_h_3, c_n, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_3, c_n, s16) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s17)) | (~node10(c_e_h_3, c_n, s16, s17)))),
% 294.99/187.49 inference(rewrite,[status(thm)],[])).
% 294.99/187.49 tff(28655,plain,
% 294.99/187.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s16) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s17)) | (~node10(c_e_h_3, c_n, s16, s17)))),
% 294.99/187.49 inference(quant_inst,[status(thm)],[])).
% 294.99/187.49 tff(28656,plain,
% 294.99/187.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_3, c_n, s16) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s17)) | (~node10(c_e_h_3, c_n, s16, s17))),
% 294.99/187.49 inference(modus_ponens,[status(thm)],[28655, 28654])).
% 294.99/187.49 tff(28657,plain,
% 294.99/187.49 ($false),
% 294.99/187.49 inference(unit_resolution,[status(thm)],[28656, 4986, 28612, 28653, 28652])).
% 294.99/187.49 tff(28658,plain,((~node10(c_e_h_3, c_n, s16, s17)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s17)) | node9(c_e_h_3, c_n, s16)), inference(lemma,lemma(discharge,[]))).
% 294.99/187.49 tff(28659,plain,
% 294.99/187.49 (~node10(c_e_h_3, c_n, s16, s17)),
% 294.99/187.49 inference(unit_resolution,[status(thm)],[28658, 28612, 28652])).
% 294.99/187.49 tff(28660,plain,
% 294.99/187.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s16, s17)) | node10(c_e_h_3, c_n, s16, s17) | node11(c_e_h_3, c_n, s16, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s16, s17)) | node10(c_e_h_3, c_n, s16, s17) | node11(c_e_h_3, c_n, s16, s17))),
% 294.99/187.49 inference(rewrite,[status(thm)],[])).
% 294.99/187.49 tff(28661,plain,
% 294.99/187.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s16, s17)) | node10(c_e_h_3, c_n, s16, s17) | node11(c_e_h_3, c_n, s16, s17))),
% 294.99/187.49 inference(quant_inst,[status(thm)],[])).
% 294.99/187.49 tff(28662,plain,
% 294.99/187.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s16, s17)) | node10(c_e_h_3, c_n, s16, s17) | node11(c_e_h_3, c_n, s16, s17)),
% 294.99/187.49 inference(modus_ponens,[status(thm)],[28661, 28660])).
% 294.99/187.49 tff(28663,plain,
% 294.99/187.49 (node10(c_e_h_3, c_n, s16, s17) | node11(c_e_h_3, c_n, s16, s17)),
% 294.99/187.49 inference(unit_resolution,[status(thm)],[28662, 5002, 11967])).
% 294.99/187.49 tff(28664,plain,
% 294.99/187.49 ($false),
% 294.99/187.49 inference(unit_resolution,[status(thm)],[28663, 28659, 28651])).
% 294.99/187.49 tff(28665,plain,((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s17)) | node9(c_e_h_3, c_n, s16) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s16)), inference(lemma,lemma(discharge,[]))).
% 294.99/187.49 tff(28666,plain,
% 294.99/187.49 (m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s16)),
% 294.99/187.49 inference(unit_resolution,[status(thm)],[28665, 28643, 28612])).
% 294.99/187.49 tff(28667,plain,
% 294.99/187.49 (~node11(c_e_h_3, c_n, s15, s16)),
% 294.99/187.49 inference(unit_resolution,[status(thm)],[13553, 13548, 13474])).
% 294.99/187.49 tff(28668,plain,
% 294.99/187.49 (~node10(c_e_h_3, c_n, s15, s16)),
% 294.99/187.49 inference(unit_resolution,[status(thm)],[13572, 13548, 13563])).
% 294.99/187.49 tff(28669,plain,
% 294.99/187.49 ($false),
% 294.99/187.49 inference(unit_resolution,[status(thm)],[13577, 28668, 28667])).
% 294.99/187.49 tff(28670,plain,((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s16)) | node9(c_e_h_3, c_n, s15) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s15)), inference(lemma,lemma(discharge,[]))).
% 294.99/187.49 tff(28671,plain,
% 294.99/187.49 (node9(c_e_h_3, c_n, s15)),
% 294.99/187.49 inference(unit_resolution,[status(thm)],[28670, 28666, 28611])).
% 294.99/187.49 tff(28672,plain,
% 294.99/187.49 (~m_c_h_element_v_out(c_e_h_3, c_f, s14)),
% 294.99/187.49 inference(unit_resolution,[status(thm)],[28466, 28605, 28437])).
% 294.99/187.49 tff(28673,plain,
% 294.99/187.49 (m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s14)),
% 294.99/187.49 inference(unit_resolution,[status(thm)],[13622, 28672])).
% 294.99/187.49 tff(28674,plain,
% 294.99/187.49 (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s14)),
% 294.99/187.49 inference(unit_resolution,[status(thm)],[13442, 28604])).
% 294.99/187.49 tff(28675,plain,
% 294.99/187.49 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s15)),
% 294.99/187.49 inference(unit_resolution,[status(thm)],[13471, 28674, 28608, 28673])).
% 294.99/187.49 tff(28676,plain,
% 294.99/187.49 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s15)),
% 294.99/187.49 inference(unit_resolution,[status(thm)],[13557, 5601, 28675])).
% 294.99/187.49 tff(28677,plain,
% 294.99/187.49 ($false),
% 294.99/187.49 inference(unit_resolution,[status(thm)],[13561, 4972, 28676, 28671])).
% 294.99/187.49 tff(28678,plain,(m_c_h_element_v_out(c_e_h_3, c_f, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s17)) | m_c_h_element_v_in2(c_e_h_3, c_f, s13) | m_c_h_element_v_in2(c_e_h_3, c_f, s12) | node20(c_e_h_3, c_i, s13) | m_c_h_element_v_in2(c_e_h_3, c_f, s11) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s10)) | m_c_h_element_v_in2(c_e_h_3, c_f, s10)), inference(lemma,lemma(discharge,[]))).
% 294.99/187.49 tff(28679,plain,
% 294.99/187.49 (m_c_h_element_v_out(c_e_h_3, c_f, s10) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s17)) | m_c_h_element_v_in2(c_e_h_3, c_f, s13) | m_c_h_element_v_in2(c_e_h_3, c_f, s12) | node20(c_e_h_3, c_i, s13) | m_c_h_element_v_in2(c_e_h_3, c_f, s11) | m_c_h_element_v_in2(c_e_h_3, c_f, s10)),
% 294.99/187.49 inference(unit_resolution,[status(thm)],[28678, 13095])).
% 294.99/187.49 tff(28680,plain,
% 294.99/187.49 (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s17)),
% 294.99/187.49 inference(unit_resolution,[status(thm)],[28679, 28401, 28327, 21942, 24272, 28573, 28399])).
% 294.99/187.49 tff(28681,plain,
% 294.99/187.49 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s17) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s17))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s17) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s17))),
% 294.99/187.49 inference(rewrite,[status(thm)],[])).
% 294.99/187.49 tff(28682,plain,
% 294.99/187.49 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s17) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s17))),
% 294.99/187.49 inference(quant_inst,[status(thm)],[])).
% 294.99/187.49 tff(28683,plain,
% 294.99/187.49 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s17) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s17)),
% 294.99/187.49 inference(modus_ponens,[status(thm)],[28682, 28681])).
% 294.99/187.49 tff(28684,plain,
% 294.99/187.49 (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s17) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s17)),
% 294.99/187.49 inference(unit_resolution,[status(thm)],[28683, 5704])).
% 294.99/187.49 tff(28685,plain,
% 294.99/187.49 (m_and_h_gate_h_init_v_in2(c_e_h_3, c_m, s17)),
% 294.99/187.49 inference(unit_resolution,[status(thm)],[28684, 28680])).
% 294.99/187.49 tff(28686,plain,
% 294.99/187.49 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s17)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s17)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s17)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s17)))),
% 294.99/187.49 inference(rewrite,[status(thm)],[])).
% 294.99/187.49 tff(28687,plain,
% 294.99/187.49 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s17)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s17)))),
% 294.99/187.49 inference(quant_inst,[status(thm)],[])).
% 294.99/187.49 tff(28688,plain,
% 294.99/187.49 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_n, X)) | (~m_and_h_gate_h_init_v_out(I0, c_m, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s17)) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s17))),
% 294.99/187.49 inference(modus_ponens,[status(thm)],[28687, 28686])).
% 294.99/187.49 tff(28689,plain,
% 294.99/187.49 (~m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s17)),
% 294.99/187.49 inference(unit_resolution,[status(thm)],[28688, 5601, 28582])).
% 294.99/187.49 tff(28690,plain,
% 294.99/187.49 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s17)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s17))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s17)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s17))),
% 294.99/187.49 inference(rewrite,[status(thm)],[])).
% 294.99/187.49 tff(28691,plain,
% 294.99/187.49 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_3, c_n, s17)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s17))),
% 294.99/187.49 inference(quant_inst,[status(thm)],[])).
% 294.99/187.49 tff(28692,plain,
% 294.99/187.49 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_3, c_n, s17)) | m_and_h_gate_h_init_v_in2(c_e_h_3, c_n, s17)),
% 294.99/187.49 inference(modus_ponens,[status(thm)],[28691, 28690])).
% 294.99/187.49 tff(28693,plain,
% 294.99/187.49 (~node9(c_e_h_3, c_n, s17)),
% 294.99/187.49 inference(unit_resolution,[status(thm)],[28692, 4972, 28689])).
% 294.99/187.49 tff(28694,assumption,(~node9(c_e_h_3, c_n, s17)), introduced(assumption)).
% 294.99/187.49 tff(28695,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s17)), introduced(assumption)).
% 294.99/187.49 tff(28696,assumption,(m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s18)), introduced(assumption)).
% 294.99/187.49 tff(28697,assumption,(node11(c_e_h_3, c_n, s17, s18)), introduced(assumption)).
% 294.99/187.49 tff(28698,plain,
% 294.99/187.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s18)) | (~node11(c_e_h_3, c_n, s17, s18)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s18)) | (~node11(c_e_h_3, c_n, s17, s18)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s17))),
% 294.99/187.49 inference(rewrite,[status(thm)],[])).
% 294.99/187.49 tff(28699,plain,
% 294.99/187.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s18)) | (~node11(c_e_h_3, c_n, s17, s18)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s17))),
% 294.99/187.49 inference(quant_inst,[status(thm)],[])).
% 294.99/187.49 tff(28700,plain,
% 294.99/187.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s18)) | (~node11(c_e_h_3, c_n, s17, s18)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s17)),
% 294.99/187.49 inference(modus_ponens,[status(thm)],[28699, 28698])).
% 294.99/187.49 tff(28701,plain,
% 294.99/187.49 ($false),
% 294.99/187.49 inference(unit_resolution,[status(thm)],[28700, 5017, 28695, 28696, 28697])).
% 294.99/187.49 tff(28702,plain,((~node11(c_e_h_3, c_n, s17, s18)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s17) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s18))), inference(lemma,lemma(discharge,[]))).
% 294.99/187.49 tff(28703,plain,
% 294.99/187.49 (~node11(c_e_h_3, c_n, s17, s18)),
% 294.99/187.49 inference(unit_resolution,[status(thm)],[28702, 28696, 28695])).
% 294.99/187.49 tff(28704,plain,
% 294.99/187.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s17, s18)) | node10(c_e_h_3, c_n, s17, s18) | node11(c_e_h_3, c_n, s17, s18))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s17, s18)) | node10(c_e_h_3, c_n, s17, s18) | node11(c_e_h_3, c_n, s17, s18))),
% 294.99/187.50 inference(rewrite,[status(thm)],[])).
% 294.99/187.50 tff(28705,plain,
% 294.99/187.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s17, s18)) | node10(c_e_h_3, c_n, s17, s18) | node11(c_e_h_3, c_n, s17, s18))),
% 294.99/187.50 inference(quant_inst,[status(thm)],[])).
% 294.99/187.50 tff(28706,plain,
% 294.99/187.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s17, s18)) | node10(c_e_h_3, c_n, s17, s18) | node11(c_e_h_3, c_n, s17, s18)),
% 294.99/187.50 inference(modus_ponens,[status(thm)],[28705, 28704])).
% 294.99/187.50 tff(28707,plain,
% 294.99/187.50 (node10(c_e_h_3, c_n, s17, s18) | node11(c_e_h_3, c_n, s17, s18)),
% 294.99/187.50 inference(unit_resolution,[status(thm)],[28706, 5002, 26135])).
% 294.99/187.50 tff(28708,plain,
% 294.99/187.50 (node10(c_e_h_3, c_n, s17, s18)),
% 294.99/187.50 inference(unit_resolution,[status(thm)],[28707, 28703])).
% 294.99/187.50 tff(28709,plain,
% 294.99/187.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s18)) | node9(c_e_h_3, c_n, s17) | (~node10(c_e_h_3, c_n, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s18)) | node9(c_e_h_3, c_n, s17) | (~node10(c_e_h_3, c_n, s17, s18)))),
% 294.99/187.50 inference(rewrite,[status(thm)],[])).
% 294.99/187.50 tff(28710,plain,
% 294.99/187.50 ((node9(c_e_h_3, c_n, s17) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s18)) | (~node10(c_e_h_3, c_n, s17, s18))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s18)) | node9(c_e_h_3, c_n, s17) | (~node10(c_e_h_3, c_n, s17, s18)))),
% 294.99/187.50 inference(rewrite,[status(thm)],[])).
% 294.99/187.50 tff(28711,plain,
% 294.99/187.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s17) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s18)) | (~node10(c_e_h_3, c_n, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s18)) | node9(c_e_h_3, c_n, s17) | (~node10(c_e_h_3, c_n, s17, s18))))),
% 294.99/187.50 inference(monotonicity,[status(thm)],[28710])).
% 294.99/187.50 tff(28712,plain,
% 294.99/187.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s17) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s18)) | (~node10(c_e_h_3, c_n, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s18)) | node9(c_e_h_3, c_n, s17) | (~node10(c_e_h_3, c_n, s17, s18)))),
% 294.99/187.50 inference(transitivity,[status(thm)],[28711, 28709])).
% 294.99/187.50 tff(28713,plain,
% 294.99/187.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_3, c_n, s17) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s18)) | (~node10(c_e_h_3, c_n, s17, s18)))),
% 294.99/187.50 inference(quant_inst,[status(thm)],[])).
% 294.99/187.50 tff(28714,plain,
% 294.99/187.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s18)) | node9(c_e_h_3, c_n, s17) | (~node10(c_e_h_3, c_n, s17, s18))),
% 294.99/187.50 inference(modus_ponens,[status(thm)],[28713, 28712])).
% 294.99/187.50 tff(28715,plain,
% 294.99/187.50 ($false),
% 294.99/187.50 inference(unit_resolution,[status(thm)],[28714, 4986, 28696, 28708, 28694])).
% 294.99/187.50 tff(28716,plain,((~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s18)) | node9(c_e_h_3, c_n, s17) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s17)), inference(lemma,lemma(discharge,[]))).
% 294.99/187.50 tff(28717,plain,
% 294.99/187.50 (~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s18)),
% 294.99/187.50 inference(unit_resolution,[status(thm)],[28716, 28693, 28680])).
% 294.99/187.50 tff(28718,plain,
% 294.99/187.50 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s17)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s17))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s17)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s17))),
% 294.99/187.50 inference(rewrite,[status(thm)],[])).
% 294.99/187.50 tff(28719,plain,
% 294.99/187.50 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s17)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s17))),
% 294.99/187.50 inference(quant_inst,[status(thm)],[])).
% 294.99/187.50 tff(28720,plain,
% 294.99/187.50 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s17)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s17)),
% 294.99/187.50 inference(modus_ponens,[status(thm)],[28719, 28718])).
% 294.99/187.50 tff(28721,plain,
% 294.99/187.50 (~m_and_h_gate_v_in2(c_e_h_3, c_q, s17)),
% 294.99/187.50 inference(unit_resolution,[status(thm)],[28720, 5621, 28680])).
% 294.99/187.50 tff(28722,plain,
% 294.99/187.50 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s17)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s17))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s17)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s17))),
% 294.99/187.50 inference(rewrite,[status(thm)],[])).
% 294.99/187.50 tff(28723,plain,
% 294.99/187.50 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s17)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s17))),
% 294.99/187.50 inference(quant_inst,[status(thm)],[])).
% 294.99/187.50 tff(28724,plain,
% 294.99/187.50 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s17)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s17)),
% 294.99/187.50 inference(modus_ponens,[status(thm)],[28723, 28722])).
% 294.99/187.50 tff(28725,plain,
% 294.99/187.50 (~node20(c_e_h_3, c_q, s17)),
% 294.99/187.50 inference(unit_resolution,[status(thm)],[28724, 4563, 28721])).
% 294.99/187.50 tff(28726,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_q, s15)), introduced(assumption)).
% 294.99/187.50 tff(28727,plain,
% 294.99/187.50 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_q, s15)) | m_c_h_element_v_out(c_e_h_3, c_f, s15))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_q, s15)) | m_c_h_element_v_out(c_e_h_3, c_f, s15))),
% 294.99/187.50 inference(rewrite,[status(thm)],[])).
% 294.99/187.50 tff(28728,plain,
% 294.99/187.50 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_q, s15)) | m_c_h_element_v_out(c_e_h_3, c_f, s15))),
% 294.99/187.50 inference(quant_inst,[status(thm)],[])).
% 294.99/187.50 tff(28729,plain,
% 294.99/187.50 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_q, s15)) | m_c_h_element_v_out(c_e_h_3, c_f, s15)),
% 294.99/187.50 inference(modus_ponens,[status(thm)],[28728, 28727])).
% 294.99/187.50 tff(28730,plain,
% 294.99/187.50 ($false),
% 294.99/187.50 inference(unit_resolution,[status(thm)],[28729, 1586, 12997, 28726])).
% 294.99/187.50 tff(28731,plain,((~m_and_h_gate_v_in1(c_e_h_3, c_q, s15)) | m_c_h_element_v_out(c_e_h_3, c_f, s15)), inference(lemma,lemma(discharge,[]))).
% 294.99/187.50 tff(28732,plain,
% 294.99/187.50 (~m_and_h_gate_v_in1(c_e_h_3, c_q, s15)),
% 294.99/187.50 inference(unit_resolution,[status(thm)],[28731, 28574])).
% 294.99/187.50 tff(28733,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_q, s15)), introduced(assumption)).
% 294.99/187.50 tff(28734,assumption,(node20(c_e_h_3, c_q, s15)), introduced(assumption)).
% 294.99/187.50 tff(28735,plain,
% 294.99/187.50 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s15)) | m_and_h_gate_v_in1(c_e_h_3, c_q, s15))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_q, s15)) | m_and_h_gate_v_in1(c_e_h_3, c_q, s15))),
% 295.01/187.50 inference(rewrite,[status(thm)],[])).
% 295.01/187.50 tff(28736,plain,
% 295.01/187.50 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s15)) | m_and_h_gate_v_in1(c_e_h_3, c_q, s15))),
% 295.01/187.50 inference(quant_inst,[status(thm)],[])).
% 295.01/187.50 tff(28737,plain,
% 295.01/187.50 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_q, s15)) | m_and_h_gate_v_in1(c_e_h_3, c_q, s15)),
% 295.01/187.50 inference(modus_ponens,[status(thm)],[28736, 28735])).
% 295.01/187.50 tff(28738,plain,
% 295.01/187.50 ($false),
% 295.01/187.50 inference(unit_resolution,[status(thm)],[28737, 38, 28734, 28733])).
% 295.01/187.50 tff(28739,plain,((~node20(c_e_h_3, c_q, s15)) | m_and_h_gate_v_in1(c_e_h_3, c_q, s15)), inference(lemma,lemma(discharge,[]))).
% 295.01/187.50 tff(28740,plain,
% 295.01/187.50 (~node20(c_e_h_3, c_q, s15)),
% 295.01/187.50 inference(unit_resolution,[status(thm)],[28739, 28732])).
% 295.01/187.50 tff(28741,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_q, s15)), introduced(assumption)).
% 295.01/187.50 tff(28742,assumption,(m_and_h_gate_v_out(c_e_h_3, c_q, s16)), introduced(assumption)).
% 295.01/187.50 tff(28743,assumption,(node22(c_e_h_3, c_q, s15, s16)), introduced(assumption)).
% 295.01/187.50 tff(28744,plain,
% 295.01/187.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s16)) | (~node22(c_e_h_3, c_q, s15, s16)) | m_and_h_gate_v_out(c_e_h_3, c_q, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s16)) | (~node22(c_e_h_3, c_q, s15, s16)) | m_and_h_gate_v_out(c_e_h_3, c_q, s15))),
% 295.01/187.50 inference(rewrite,[status(thm)],[])).
% 295.01/187.50 tff(28745,plain,
% 295.01/187.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s16)) | (~node22(c_e_h_3, c_q, s15, s16)) | m_and_h_gate_v_out(c_e_h_3, c_q, s15))),
% 295.01/187.50 inference(quant_inst,[status(thm)],[])).
% 295.01/187.50 tff(28746,plain,
% 295.01/187.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s16)) | (~node22(c_e_h_3, c_q, s15, s16)) | m_and_h_gate_v_out(c_e_h_3, c_q, s15)),
% 295.01/187.50 inference(modus_ponens,[status(thm)],[28745, 28744])).
% 295.01/187.50 tff(28747,plain,
% 295.01/187.50 ($false),
% 295.01/187.50 inference(unit_resolution,[status(thm)],[28746, 108, 28742, 28741, 28743])).
% 295.01/187.50 tff(28748,plain,((~node22(c_e_h_3, c_q, s15, s16)) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s16)) | m_and_h_gate_v_out(c_e_h_3, c_q, s15)), inference(lemma,lemma(discharge,[]))).
% 295.01/187.50 tff(28749,plain,
% 295.01/187.50 (~node22(c_e_h_3, c_q, s15, s16)),
% 295.01/187.50 inference(unit_resolution,[status(thm)],[28748, 28742, 28741])).
% 295.01/187.50 tff(28750,assumption,(~node20(c_e_h_3, c_q, s15)), introduced(assumption)).
% 295.01/187.50 tff(28751,assumption,(node21(c_e_h_3, c_q, s15, s16)), introduced(assumption)).
% 295.01/187.50 tff(28752,plain,
% 295.01/187.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s16)) | node20(c_e_h_3, c_q, s15) | (~node21(c_e_h_3, c_q, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s16)) | node20(c_e_h_3, c_q, s15) | (~node21(c_e_h_3, c_q, s15, s16)))),
% 295.01/187.50 inference(rewrite,[status(thm)],[])).
% 295.01/187.50 tff(28753,plain,
% 295.01/187.50 ((node20(c_e_h_3, c_q, s15) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s16)) | (~node21(c_e_h_3, c_q, s15, s16))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_q, s16)) | node20(c_e_h_3, c_q, s15) | (~node21(c_e_h_3, c_q, s15, s16)))),
% 295.01/187.50 inference(rewrite,[status(thm)],[])).
% 295.01/187.50 tff(28754,plain,
% 295.01/187.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s15) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s16)) | (~node21(c_e_h_3, c_q, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s16)) | node20(c_e_h_3, c_q, s15) | (~node21(c_e_h_3, c_q, s15, s16))))),
% 295.01/187.51 inference(monotonicity,[status(thm)],[28753])).
% 295.01/187.51 tff(28755,plain,
% 295.01/187.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s15) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s16)) | (~node21(c_e_h_3, c_q, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s16)) | node20(c_e_h_3, c_q, s15) | (~node21(c_e_h_3, c_q, s15, s16)))),
% 295.01/187.51 inference(transitivity,[status(thm)],[28754, 28752])).
% 295.01/187.51 tff(28756,plain,
% 295.01/187.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s15) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s16)) | (~node21(c_e_h_3, c_q, s15, s16)))),
% 295.01/187.51 inference(quant_inst,[status(thm)],[])).
% 295.01/187.51 tff(28757,plain,
% 295.01/187.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s16)) | node20(c_e_h_3, c_q, s15) | (~node21(c_e_h_3, c_q, s15, s16))),
% 295.01/187.51 inference(modus_ponens,[status(thm)],[28756, 28755])).
% 295.01/187.51 tff(28758,plain,
% 295.01/187.51 ($false),
% 295.01/187.51 inference(unit_resolution,[status(thm)],[28757, 52, 28742, 28751, 28750])).
% 295.01/187.51 tff(28759,plain,((~node21(c_e_h_3, c_q, s15, s16)) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s16)) | node20(c_e_h_3, c_q, s15)), inference(lemma,lemma(discharge,[]))).
% 295.01/187.51 tff(28760,plain,
% 295.01/187.51 (~node21(c_e_h_3, c_q, s15, s16)),
% 295.01/187.51 inference(unit_resolution,[status(thm)],[28759, 28742, 28750])).
% 295.01/187.51 tff(28761,plain,
% 295.01/187.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s15, s16)) | node21(c_e_h_3, c_q, s15, s16) | node22(c_e_h_3, c_q, s15, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s15, s16)) | node21(c_e_h_3, c_q, s15, s16) | node22(c_e_h_3, c_q, s15, s16))),
% 295.01/187.51 inference(rewrite,[status(thm)],[])).
% 295.01/187.51 tff(28762,plain,
% 295.01/187.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s15, s16)) | node21(c_e_h_3, c_q, s15, s16) | node22(c_e_h_3, c_q, s15, s16))),
% 295.01/187.51 inference(quant_inst,[status(thm)],[])).
% 295.01/187.51 tff(28763,plain,
% 295.01/187.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s15, s16)) | node21(c_e_h_3, c_q, s15, s16) | node22(c_e_h_3, c_q, s15, s16)),
% 295.01/187.51 inference(modus_ponens,[status(thm)],[28762, 28761])).
% 295.01/187.51 tff(28764,plain,
% 295.01/187.51 (node21(c_e_h_3, c_q, s15, s16) | node22(c_e_h_3, c_q, s15, s16)),
% 295.01/187.51 inference(unit_resolution,[status(thm)],[28763, 82, 13499])).
% 295.01/187.51 tff(28765,plain,
% 295.01/187.51 ($false),
% 295.01/187.51 inference(unit_resolution,[status(thm)],[28764, 28760, 28749])).
% 295.01/187.51 tff(28766,plain,((~m_and_h_gate_v_out(c_e_h_3, c_q, s16)) | node20(c_e_h_3, c_q, s15) | m_and_h_gate_v_out(c_e_h_3, c_q, s15)), inference(lemma,lemma(discharge,[]))).
% 295.01/187.51 tff(28767,plain,
% 295.01/187.51 (~m_and_h_gate_v_out(c_e_h_3, c_q, s16)),
% 295.01/187.51 inference(unit_resolution,[status(thm)],[28766, 28740, 26863])).
% 295.01/187.51 tff(28768,plain,
% 295.01/187.51 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_q, s16)) | m_c_h_element_v_out(c_e_h_3, c_f, s16))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_q, s16)) | m_c_h_element_v_out(c_e_h_3, c_f, s16))),
% 295.01/187.51 inference(rewrite,[status(thm)],[])).
% 295.01/187.51 tff(28769,plain,
% 295.01/187.51 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_q, s16)) | m_c_h_element_v_out(c_e_h_3, c_f, s16))),
% 295.01/187.51 inference(quant_inst,[status(thm)],[])).
% 295.01/187.51 tff(28770,plain,
% 295.01/187.51 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_q, s16)) | m_c_h_element_v_out(c_e_h_3, c_f, s16)),
% 295.01/187.51 inference(modus_ponens,[status(thm)],[28769, 28768])).
% 295.01/187.51 tff(28771,plain,
% 295.01/187.51 (~m_and_h_gate_v_in1(c_e_h_3, c_q, s16)),
% 295.01/187.51 inference(unit_resolution,[status(thm)],[28770, 1586, 28572])).
% 295.01/187.51 tff(28772,plain,
% 295.01/187.51 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s16)) | m_and_h_gate_v_in1(c_e_h_3, c_q, s16))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_q, s16)) | m_and_h_gate_v_in1(c_e_h_3, c_q, s16))),
% 295.01/187.51 inference(rewrite,[status(thm)],[])).
% 295.01/187.51 tff(28773,plain,
% 295.01/187.51 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s16)) | m_and_h_gate_v_in1(c_e_h_3, c_q, s16))),
% 295.01/187.51 inference(quant_inst,[status(thm)],[])).
% 295.01/187.51 tff(28774,plain,
% 295.01/187.51 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_q, s16)) | m_and_h_gate_v_in1(c_e_h_3, c_q, s16)),
% 295.01/187.51 inference(modus_ponens,[status(thm)],[28773, 28772])).
% 295.01/187.51 tff(28775,plain,
% 295.01/187.51 (~node20(c_e_h_3, c_q, s16)),
% 295.01/187.51 inference(unit_resolution,[status(thm)],[28774, 38, 28771])).
% 295.01/187.51 tff(28776,assumption,(~node20(c_e_h_3, c_q, s16)), introduced(assumption)).
% 295.01/187.51 tff(28777,assumption,(m_and_h_gate_v_out(c_e_h_3, c_q, s17)), introduced(assumption)).
% 295.01/187.51 tff(28778,assumption,(node21(c_e_h_3, c_q, s16, s17)), introduced(assumption)).
% 295.01/187.51 tff(28779,plain,
% 295.01/187.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s17)) | node20(c_e_h_3, c_q, s16) | (~node21(c_e_h_3, c_q, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s17)) | node20(c_e_h_3, c_q, s16) | (~node21(c_e_h_3, c_q, s16, s17)))),
% 295.01/187.51 inference(rewrite,[status(thm)],[])).
% 295.01/187.51 tff(28780,plain,
% 295.01/187.51 ((node20(c_e_h_3, c_q, s16) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s17)) | (~node21(c_e_h_3, c_q, s16, s17))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_q, s17)) | node20(c_e_h_3, c_q, s16) | (~node21(c_e_h_3, c_q, s16, s17)))),
% 295.01/187.51 inference(rewrite,[status(thm)],[])).
% 295.01/187.51 tff(28781,plain,
% 295.01/187.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s16) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s17)) | (~node21(c_e_h_3, c_q, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s17)) | node20(c_e_h_3, c_q, s16) | (~node21(c_e_h_3, c_q, s16, s17))))),
% 295.01/187.51 inference(monotonicity,[status(thm)],[28780])).
% 295.01/187.51 tff(28782,plain,
% 295.01/187.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s16) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s17)) | (~node21(c_e_h_3, c_q, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s17)) | node20(c_e_h_3, c_q, s16) | (~node21(c_e_h_3, c_q, s16, s17)))),
% 295.01/187.51 inference(transitivity,[status(thm)],[28781, 28779])).
% 295.01/187.51 tff(28783,plain,
% 295.01/187.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s16) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s17)) | (~node21(c_e_h_3, c_q, s16, s17)))),
% 295.01/187.51 inference(quant_inst,[status(thm)],[])).
% 295.01/187.51 tff(28784,plain,
% 295.01/187.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s17)) | node20(c_e_h_3, c_q, s16) | (~node21(c_e_h_3, c_q, s16, s17))),
% 295.01/187.51 inference(modus_ponens,[status(thm)],[28783, 28782])).
% 295.01/187.51 tff(28785,plain,
% 295.01/187.51 ($false),
% 295.01/187.51 inference(unit_resolution,[status(thm)],[28784, 52, 28777, 28778, 28776])).
% 295.01/187.51 tff(28786,plain,((~node21(c_e_h_3, c_q, s16, s17)) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s17)) | node20(c_e_h_3, c_q, s16)), inference(lemma,lemma(discharge,[]))).
% 295.02/187.51 tff(28787,plain,
% 295.02/187.51 (~node21(c_e_h_3, c_q, s16, s17)),
% 295.02/187.51 inference(unit_resolution,[status(thm)],[28786, 28777, 28776])).
% 295.02/187.51 tff(28788,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_q, s16)), introduced(assumption)).
% 295.02/187.51 tff(28789,assumption,(node22(c_e_h_3, c_q, s16, s17)), introduced(assumption)).
% 295.02/187.51 tff(28790,plain,
% 295.02/187.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s17)) | (~node22(c_e_h_3, c_q, s16, s17)) | m_and_h_gate_v_out(c_e_h_3, c_q, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s17)) | (~node22(c_e_h_3, c_q, s16, s17)) | m_and_h_gate_v_out(c_e_h_3, c_q, s16))),
% 295.02/187.51 inference(rewrite,[status(thm)],[])).
% 295.02/187.51 tff(28791,plain,
% 295.02/187.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s17)) | (~node22(c_e_h_3, c_q, s16, s17)) | m_and_h_gate_v_out(c_e_h_3, c_q, s16))),
% 295.02/187.51 inference(quant_inst,[status(thm)],[])).
% 295.02/187.51 tff(28792,plain,
% 295.02/187.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s17)) | (~node22(c_e_h_3, c_q, s16, s17)) | m_and_h_gate_v_out(c_e_h_3, c_q, s16)),
% 295.02/187.51 inference(modus_ponens,[status(thm)],[28791, 28790])).
% 295.02/187.51 tff(28793,plain,
% 295.02/187.51 ($false),
% 295.02/187.51 inference(unit_resolution,[status(thm)],[28792, 108, 28788, 28777, 28789])).
% 295.02/187.51 tff(28794,plain,((~node22(c_e_h_3, c_q, s16, s17)) | m_and_h_gate_v_out(c_e_h_3, c_q, s16) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s17))), inference(lemma,lemma(discharge,[]))).
% 295.02/187.51 tff(28795,plain,
% 295.02/187.51 (~node22(c_e_h_3, c_q, s16, s17)),
% 295.02/187.51 inference(unit_resolution,[status(thm)],[28794, 28777, 28788])).
% 295.02/187.51 tff(28796,plain,
% 295.02/187.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s16, s17)) | node21(c_e_h_3, c_q, s16, s17) | node22(c_e_h_3, c_q, s16, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s16, s17)) | node21(c_e_h_3, c_q, s16, s17) | node22(c_e_h_3, c_q, s16, s17))),
% 295.02/187.51 inference(rewrite,[status(thm)],[])).
% 295.02/187.51 tff(28797,plain,
% 295.02/187.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s16, s17)) | node21(c_e_h_3, c_q, s16, s17) | node22(c_e_h_3, c_q, s16, s17))),
% 295.02/187.51 inference(quant_inst,[status(thm)],[])).
% 295.02/187.51 tff(28798,plain,
% 295.02/187.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s16, s17)) | node21(c_e_h_3, c_q, s16, s17) | node22(c_e_h_3, c_q, s16, s17)),
% 295.02/187.51 inference(modus_ponens,[status(thm)],[28797, 28796])).
% 295.02/187.51 tff(28799,plain,
% 295.02/187.51 (node21(c_e_h_3, c_q, s16, s17) | node22(c_e_h_3, c_q, s16, s17)),
% 295.02/187.51 inference(unit_resolution,[status(thm)],[28798, 82, 11967])).
% 295.02/187.51 tff(28800,plain,
% 295.02/187.51 ($false),
% 295.02/187.51 inference(unit_resolution,[status(thm)],[28799, 28795, 28787])).
% 295.02/187.51 tff(28801,plain,((~m_and_h_gate_v_out(c_e_h_3, c_q, s17)) | m_and_h_gate_v_out(c_e_h_3, c_q, s16) | node20(c_e_h_3, c_q, s16)), inference(lemma,lemma(discharge,[]))).
% 295.02/187.51 tff(28802,plain,
% 295.02/187.51 (~m_and_h_gate_v_out(c_e_h_3, c_q, s17)),
% 295.02/187.51 inference(unit_resolution,[status(thm)],[28801, 28775, 28767])).
% 295.02/187.51 tff(28803,assumption,(~node20(c_e_h_3, c_q, s17)), introduced(assumption)).
% 295.02/187.51 tff(28804,assumption,(m_and_h_gate_v_out(c_e_h_3, c_q, s18)), introduced(assumption)).
% 295.02/187.51 tff(28805,assumption,(node21(c_e_h_3, c_q, s17, s18)), introduced(assumption)).
% 295.02/187.51 tff(28806,plain,
% 295.02/187.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s18)) | node20(c_e_h_3, c_q, s17) | (~node21(c_e_h_3, c_q, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s18)) | node20(c_e_h_3, c_q, s17) | (~node21(c_e_h_3, c_q, s17, s18)))),
% 295.02/187.52 inference(rewrite,[status(thm)],[])).
% 295.02/187.52 tff(28807,plain,
% 295.02/187.52 ((node20(c_e_h_3, c_q, s17) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s18)) | (~node21(c_e_h_3, c_q, s17, s18))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_q, s18)) | node20(c_e_h_3, c_q, s17) | (~node21(c_e_h_3, c_q, s17, s18)))),
% 295.02/187.52 inference(rewrite,[status(thm)],[])).
% 295.02/187.52 tff(28808,plain,
% 295.02/187.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s17) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s18)) | (~node21(c_e_h_3, c_q, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s18)) | node20(c_e_h_3, c_q, s17) | (~node21(c_e_h_3, c_q, s17, s18))))),
% 295.02/187.52 inference(monotonicity,[status(thm)],[28807])).
% 295.02/187.52 tff(28809,plain,
% 295.02/187.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s17) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s18)) | (~node21(c_e_h_3, c_q, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s18)) | node20(c_e_h_3, c_q, s17) | (~node21(c_e_h_3, c_q, s17, s18)))),
% 295.02/187.52 inference(transitivity,[status(thm)],[28808, 28806])).
% 295.02/187.52 tff(28810,plain,
% 295.02/187.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s17) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s18)) | (~node21(c_e_h_3, c_q, s17, s18)))),
% 295.02/187.52 inference(quant_inst,[status(thm)],[])).
% 295.02/187.52 tff(28811,plain,
% 295.02/187.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s18)) | node20(c_e_h_3, c_q, s17) | (~node21(c_e_h_3, c_q, s17, s18))),
% 295.02/187.52 inference(modus_ponens,[status(thm)],[28810, 28809])).
% 295.02/187.52 tff(28812,plain,
% 295.02/187.52 ($false),
% 295.02/187.52 inference(unit_resolution,[status(thm)],[28811, 52, 28804, 28805, 28803])).
% 295.02/187.52 tff(28813,plain,((~node21(c_e_h_3, c_q, s17, s18)) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s18)) | node20(c_e_h_3, c_q, s17)), inference(lemma,lemma(discharge,[]))).
% 295.02/187.52 tff(28814,plain,
% 295.02/187.52 (~node21(c_e_h_3, c_q, s17, s18)),
% 295.02/187.52 inference(unit_resolution,[status(thm)],[28813, 28804, 28803])).
% 295.02/187.52 tff(28815,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_q, s17)), introduced(assumption)).
% 295.02/187.52 tff(28816,assumption,(node22(c_e_h_3, c_q, s17, s18)), introduced(assumption)).
% 295.02/187.52 tff(28817,plain,
% 295.02/187.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s18)) | (~node22(c_e_h_3, c_q, s17, s18)) | m_and_h_gate_v_out(c_e_h_3, c_q, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s18)) | (~node22(c_e_h_3, c_q, s17, s18)) | m_and_h_gate_v_out(c_e_h_3, c_q, s17))),
% 295.02/187.52 inference(rewrite,[status(thm)],[])).
% 295.02/187.52 tff(28818,plain,
% 295.02/187.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s18)) | (~node22(c_e_h_3, c_q, s17, s18)) | m_and_h_gate_v_out(c_e_h_3, c_q, s17))),
% 295.02/187.52 inference(quant_inst,[status(thm)],[])).
% 295.02/187.52 tff(28819,plain,
% 295.02/187.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s18)) | (~node22(c_e_h_3, c_q, s17, s18)) | m_and_h_gate_v_out(c_e_h_3, c_q, s17)),
% 295.02/187.52 inference(modus_ponens,[status(thm)],[28818, 28817])).
% 295.02/187.52 tff(28820,plain,
% 295.02/187.52 ($false),
% 295.02/187.52 inference(unit_resolution,[status(thm)],[28819, 108, 28815, 28804, 28816])).
% 295.02/187.52 tff(28821,plain,((~node22(c_e_h_3, c_q, s17, s18)) | m_and_h_gate_v_out(c_e_h_3, c_q, s17) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s18))), inference(lemma,lemma(discharge,[]))).
% 295.02/187.52 tff(28822,plain,
% 295.02/187.52 (~node22(c_e_h_3, c_q, s17, s18)),
% 295.02/187.52 inference(unit_resolution,[status(thm)],[28821, 28804, 28815])).
% 295.02/187.52 tff(28823,plain,
% 295.02/187.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s17, s18)) | node21(c_e_h_3, c_q, s17, s18) | node22(c_e_h_3, c_q, s17, s18))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s17, s18)) | node21(c_e_h_3, c_q, s17, s18) | node22(c_e_h_3, c_q, s17, s18))),
% 295.02/187.52 inference(rewrite,[status(thm)],[])).
% 295.02/187.52 tff(28824,plain,
% 295.02/187.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s17, s18)) | node21(c_e_h_3, c_q, s17, s18) | node22(c_e_h_3, c_q, s17, s18))),
% 295.02/187.52 inference(quant_inst,[status(thm)],[])).
% 295.02/187.52 tff(28825,plain,
% 295.02/187.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s17, s18)) | node21(c_e_h_3, c_q, s17, s18) | node22(c_e_h_3, c_q, s17, s18)),
% 295.02/187.52 inference(modus_ponens,[status(thm)],[28824, 28823])).
% 295.02/187.52 tff(28826,plain,
% 295.02/187.52 (node21(c_e_h_3, c_q, s17, s18) | node22(c_e_h_3, c_q, s17, s18)),
% 295.02/187.52 inference(unit_resolution,[status(thm)],[28825, 82, 26135])).
% 295.02/187.52 tff(28827,plain,
% 295.02/187.52 ($false),
% 295.02/187.52 inference(unit_resolution,[status(thm)],[28826, 28822, 28814])).
% 295.02/187.52 tff(28828,plain,((~m_and_h_gate_v_out(c_e_h_3, c_q, s18)) | m_and_h_gate_v_out(c_e_h_3, c_q, s17) | node20(c_e_h_3, c_q, s17)), inference(lemma,lemma(discharge,[]))).
% 295.02/187.52 tff(28829,plain,
% 295.02/187.52 (~m_and_h_gate_v_out(c_e_h_3, c_q, s18)),
% 295.02/187.52 inference(unit_resolution,[status(thm)],[28828, 28802, 28725])).
% 295.02/187.52 tff(28830,plain,
% 295.02/187.52 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s18))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s18))),
% 295.02/187.52 inference(rewrite,[status(thm)],[])).
% 295.02/187.52 tff(28831,plain,
% 295.02/187.52 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s18))),
% 295.02/187.52 inference(quant_inst,[status(thm)],[])).
% 295.02/187.52 tff(28832,plain,
% 295.02/187.52 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s18)),
% 295.02/187.52 inference(modus_ponens,[status(thm)],[28831, 28830])).
% 295.02/187.52 tff(28833,plain,
% 295.02/187.52 (node3(c_e_h_3, c_e_h_1, s18)),
% 295.02/187.52 inference(unit_resolution,[status(thm)],[28832, 2922, 1056])).
% 295.02/187.52 tff(28834,plain,
% 295.02/187.52 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s18)) | (~node3(c_e_h_3, c_e_h_1, s18)) | m_and_h_gate_v_out(c_e_h_3, c_q, s18))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s18)) | (~node3(c_e_h_3, c_e_h_1, s18)) | m_and_h_gate_v_out(c_e_h_3, c_q, s18))),
% 295.02/187.52 inference(rewrite,[status(thm)],[])).
% 295.02/187.52 tff(28835,plain,
% 295.02/187.52 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s18)) | (~node3(c_e_h_3, c_e_h_1, s18)) | m_and_h_gate_v_out(c_e_h_3, c_q, s18))),
% 295.02/187.52 inference(quant_inst,[status(thm)],[])).
% 295.02/187.52 tff(28836,plain,
% 295.02/187.52 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s18)) | (~node3(c_e_h_3, c_e_h_1, s18)) | m_and_h_gate_v_out(c_e_h_3, c_q, s18)),
% 295.02/187.52 inference(modus_ponens,[status(thm)],[28835, 28834])).
% 295.02/187.52 tff(28837,plain,
% 295.02/187.52 ((~m_cell_v_ack(c_e_h_1, s18)) | m_and_h_gate_v_out(c_e_h_3, c_q, s18)),
% 295.02/187.52 inference(unit_resolution,[status(thm)],[28836, 1073, 28833])).
% 295.02/187.52 tff(28838,plain,
% 295.02/187.52 (~m_cell_v_ack(c_e_h_1, s18)),
% 295.02/187.52 inference(unit_resolution,[status(thm)],[28837, 28829])).
% 295.02/187.52 tff(28839,plain,
% 295.02/187.52 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s18)) | m_cell_v_ack(c_e_h_1, s18))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s18)) | m_cell_v_ack(c_e_h_1, s18))),
% 295.02/187.52 inference(rewrite,[status(thm)],[])).
% 295.02/187.52 tff(28840,plain,
% 295.02/187.52 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s18)) | m_cell_v_ack(c_e_h_1, s18))),
% 295.02/187.52 inference(quant_inst,[status(thm)],[])).
% 295.02/187.52 tff(28841,plain,
% 295.02/187.52 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s18)) | m_cell_v_ack(c_e_h_1, s18)),
% 295.02/187.52 inference(modus_ponens,[status(thm)],[28840, 28839])).
% 295.02/187.52 tff(28842,plain,
% 295.02/187.52 (~m_or_h_gate_v_in2(c_e_h_1, c_j, s18)),
% 295.02/187.52 inference(unit_resolution,[status(thm)],[28841, 1085, 28838])).
% 295.02/187.52 tff(28843,plain,
% 295.02/187.52 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s16))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s16))),
% 295.02/187.52 inference(rewrite,[status(thm)],[])).
% 295.02/187.52 tff(28844,plain,
% 295.02/187.52 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s16))),
% 295.02/187.52 inference(quant_inst,[status(thm)],[])).
% 295.02/187.52 tff(28845,plain,
% 295.02/187.52 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s16)),
% 295.02/187.52 inference(modus_ponens,[status(thm)],[28844, 28843])).
% 295.02/187.52 tff(28846,plain,
% 295.02/187.52 (node3(c_e_h_3, c_e_h_1, s16)),
% 295.02/187.52 inference(unit_resolution,[status(thm)],[28845, 2922, 1056])).
% 295.02/187.52 tff(28847,plain,
% 295.02/187.52 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s16)) | (~node3(c_e_h_3, c_e_h_1, s16)) | m_and_h_gate_v_out(c_e_h_3, c_q, s16))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s16)) | (~node3(c_e_h_3, c_e_h_1, s16)) | m_and_h_gate_v_out(c_e_h_3, c_q, s16))),
% 295.02/187.52 inference(rewrite,[status(thm)],[])).
% 295.02/187.52 tff(28848,plain,
% 295.02/187.52 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s16)) | (~node3(c_e_h_3, c_e_h_1, s16)) | m_and_h_gate_v_out(c_e_h_3, c_q, s16))),
% 295.02/187.52 inference(quant_inst,[status(thm)],[])).
% 295.02/187.52 tff(28849,plain,
% 295.02/187.52 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s16)) | (~node3(c_e_h_3, c_e_h_1, s16)) | m_and_h_gate_v_out(c_e_h_3, c_q, s16)),
% 295.02/187.52 inference(modus_ponens,[status(thm)],[28848, 28847])).
% 295.02/187.52 tff(28850,plain,
% 295.02/187.52 ((~m_cell_v_ack(c_e_h_1, s16)) | m_and_h_gate_v_out(c_e_h_3, c_q, s16)),
% 295.02/187.52 inference(unit_resolution,[status(thm)],[28849, 1073, 28846])).
% 295.02/187.52 tff(28851,plain,
% 295.02/187.52 (~m_cell_v_ack(c_e_h_1, s16)),
% 295.02/187.52 inference(unit_resolution,[status(thm)],[28850, 28767])).
% 295.02/187.52 tff(28852,plain,
% 295.02/187.52 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s16)) | m_cell_v_ack(c_e_h_1, s16))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s16)) | m_cell_v_ack(c_e_h_1, s16))),
% 295.02/187.52 inference(rewrite,[status(thm)],[])).
% 295.02/187.52 tff(28853,plain,
% 295.02/187.52 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s16)) | m_cell_v_ack(c_e_h_1, s16))),
% 295.02/187.52 inference(quant_inst,[status(thm)],[])).
% 295.02/187.52 tff(28854,plain,
% 295.02/187.52 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s16)) | m_cell_v_ack(c_e_h_1, s16)),
% 295.02/187.52 inference(modus_ponens,[status(thm)],[28853, 28852])).
% 295.02/187.53 tff(28855,plain,
% 295.02/187.53 (~m_or_h_gate_v_in2(c_e_h_1, c_j, s16)),
% 295.02/187.53 inference(unit_resolution,[status(thm)],[28854, 1085, 28851])).
% 295.02/187.53 tff(28856,plain,
% 295.02/187.53 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s13) | m_c_h_element_v_out(c_e_h_1, c_e, s13))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s13) | m_c_h_element_v_out(c_e_h_1, c_e, s13))),
% 295.02/187.53 inference(rewrite,[status(thm)],[])).
% 295.02/187.53 tff(28857,plain,
% 295.02/187.53 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s13) | m_c_h_element_v_out(c_e_h_1, c_e, s13))),
% 295.02/187.53 inference(quant_inst,[status(thm)],[])).
% 295.02/187.53 tff(28858,plain,
% 295.02/187.53 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s13) | m_c_h_element_v_out(c_e_h_1, c_e, s13)),
% 295.02/187.53 inference(modus_ponens,[status(thm)],[28857, 28856])).
% 295.02/187.53 tff(28859,plain,
% 295.02/187.53 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s13) | m_c_h_element_v_out(c_e_h_1, c_e, s13)),
% 295.02/187.53 inference(unit_resolution,[status(thm)],[28858, 7856])).
% 295.02/187.53 tff(28860,plain,
% 295.02/187.53 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s13)),
% 295.02/187.53 inference(unit_resolution,[status(thm)],[28859, 25762])).
% 295.02/187.53 tff(28861,assumption,(~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s13)), introduced(assumption)).
% 295.02/187.53 tff(28862,plain,
% 295.02/187.53 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s13) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s13) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13))),
% 295.02/187.53 inference(rewrite,[status(thm)],[])).
% 295.02/187.53 tff(28863,plain,
% 295.02/187.53 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s13) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13))),
% 295.02/187.53 inference(quant_inst,[status(thm)],[])).
% 295.02/187.53 tff(28864,plain,
% 295.02/187.53 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s13) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)),
% 295.02/187.53 inference(modus_ponens,[status(thm)],[28863, 28862])).
% 295.02/187.53 tff(28865,plain,
% 295.02/187.53 ($false),
% 295.02/187.53 inference(unit_resolution,[status(thm)],[28864, 7868, 28861, 25403])).
% 295.02/187.53 tff(28866,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s13)), inference(lemma,lemma(discharge,[]))).
% 295.02/187.53 tff(28867,plain,
% 295.02/187.53 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s13)),
% 295.02/187.53 inference(unit_resolution,[status(thm)],[28866, 25401])).
% 295.02/187.53 tff(28868,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14)), introduced(assumption)).
% 295.02/187.53 tff(28869,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s13)), introduced(assumption)).
% 295.02/187.53 tff(28870,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s13)), introduced(assumption)).
% 295.02/187.53 tff(28871,assumption,(node10(c_e_h_1, c_n, s13, s14)), introduced(assumption)).
% 295.02/187.53 tff(28872,plain,
% 295.02/187.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s13)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14) | (~node10(c_e_h_1, c_n, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s13)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14) | (~node10(c_e_h_1, c_n, s13, s14)))),
% 295.02/187.53 inference(rewrite,[status(thm)],[])).
% 295.02/187.53 tff(28873,plain,
% 295.02/187.53 (((~node10(c_e_h_1, c_n, s13, s14)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s13)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14)) <=> ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s13)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14) | (~node10(c_e_h_1, c_n, s13, s14)))),
% 295.02/187.53 inference(rewrite,[status(thm)],[])).
% 295.02/187.53 tff(28874,plain,
% 295.02/187.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s13, s14)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s13)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s13)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14) | (~node10(c_e_h_1, c_n, s13, s14))))),
% 295.02/187.53 inference(monotonicity,[status(thm)],[28873])).
% 295.02/187.53 tff(28875,plain,
% 295.02/187.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s13, s14)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s13)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s13)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14) | (~node10(c_e_h_1, c_n, s13, s14)))),
% 295.02/187.53 inference(transitivity,[status(thm)],[28874, 28872])).
% 295.02/187.53 tff(28876,plain,
% 295.02/187.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s13, s14)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s13)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14))),
% 295.02/187.53 inference(quant_inst,[status(thm)],[])).
% 295.02/187.53 tff(28877,plain,
% 295.02/187.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s13)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14) | (~node10(c_e_h_1, c_n, s13, s14))),
% 295.02/187.53 inference(modus_ponens,[status(thm)],[28876, 28875])).
% 295.02/187.53 tff(28878,plain,
% 295.02/187.53 ($false),
% 295.02/187.53 inference(unit_resolution,[status(thm)],[28877, 5718, 28869, 28871, 28868, 28870])).
% 295.02/187.53 tff(28879,plain,((~node10(c_e_h_1, c_n, s13, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s13))), inference(lemma,lemma(discharge,[]))).
% 295.02/187.53 tff(28880,plain,
% 295.02/187.53 (~node10(c_e_h_1, c_n, s13, s14)),
% 295.02/187.53 inference(unit_resolution,[status(thm)],[28879, 28868, 28870, 28869])).
% 295.02/187.53 tff(28881,plain,
% 295.02/187.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s13, s14)) | node10(c_e_h_1, c_n, s13, s14) | node11(c_e_h_1, c_n, s13, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s13, s14)) | node10(c_e_h_1, c_n, s13, s14) | node11(c_e_h_1, c_n, s13, s14))),
% 295.02/187.53 inference(rewrite,[status(thm)],[])).
% 295.02/187.53 tff(28882,plain,
% 295.02/187.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s13, s14)) | node10(c_e_h_1, c_n, s13, s14) | node11(c_e_h_1, c_n, s13, s14))),
% 295.02/187.53 inference(quant_inst,[status(thm)],[])).
% 295.02/187.53 tff(28883,plain,
% 295.02/187.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s13, s14)) | node10(c_e_h_1, c_n, s13, s14) | node11(c_e_h_1, c_n, s13, s14)),
% 295.02/187.53 inference(modus_ponens,[status(thm)],[28882, 28881])).
% 295.02/187.53 tff(28884,plain,
% 295.02/187.53 (node10(c_e_h_1, c_n, s13, s14) | node11(c_e_h_1, c_n, s13, s14)),
% 295.02/187.53 inference(unit_resolution,[status(thm)],[28883, 5002, 12831])).
% 295.02/187.53 tff(28885,plain,
% 295.02/187.53 (node11(c_e_h_1, c_n, s13, s14)),
% 295.02/187.53 inference(unit_resolution,[status(thm)],[28884, 28880])).
% 295.02/187.53 tff(28886,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13)), introduced(assumption)).
% 295.02/187.53 tff(28887,plain,
% 295.02/187.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14) | (~node11(c_e_h_1, c_n, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14) | (~node11(c_e_h_1, c_n, s13, s14)))),
% 295.02/187.53 inference(rewrite,[status(thm)],[])).
% 295.02/187.53 tff(28888,plain,
% 295.02/187.53 ((m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14) | (~node11(c_e_h_1, c_n, s13, s14)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14) | (~node11(c_e_h_1, c_n, s13, s14)))),
% 295.02/187.53 inference(rewrite,[status(thm)],[])).
% 295.02/187.53 tff(28889,plain,
% 295.02/187.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14) | (~node11(c_e_h_1, c_n, s13, s14)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14) | (~node11(c_e_h_1, c_n, s13, s14))))),
% 295.02/187.53 inference(monotonicity,[status(thm)],[28888])).
% 295.02/187.53 tff(28890,plain,
% 295.02/187.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14) | (~node11(c_e_h_1, c_n, s13, s14)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14) | (~node11(c_e_h_1, c_n, s13, s14)))),
% 295.02/187.53 inference(transitivity,[status(thm)],[28889, 28887])).
% 295.02/187.53 tff(28891,plain,
% 295.02/187.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14) | (~node11(c_e_h_1, c_n, s13, s14)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13)))),
% 295.02/187.53 inference(quant_inst,[status(thm)],[])).
% 295.02/187.53 tff(28892,plain,
% 295.02/187.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14) | (~node11(c_e_h_1, c_n, s13, s14))),
% 295.02/187.53 inference(modus_ponens,[status(thm)],[28891, 28890])).
% 295.02/187.53 tff(28893,plain,
% 295.02/187.53 ($false),
% 295.02/187.53 inference(unit_resolution,[status(thm)],[28892, 5742, 28886, 28885, 28868])).
% 295.02/187.53 tff(28894,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s13)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s13))), inference(lemma,lemma(discharge,[]))).
% 295.02/187.53 tff(28895,plain,
% 295.02/187.53 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s13))),
% 295.02/187.54 inference(unit_resolution,[status(thm)],[28894, 26480, 28867])).
% 295.02/187.54 tff(28896,plain,
% 295.02/187.54 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14)),
% 295.02/187.54 inference(unit_resolution,[status(thm)],[28895, 28860])).
% 295.02/187.54 tff(28897,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s14)), introduced(assumption)).
% 295.02/187.54 tff(28898,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14)), introduced(assumption)).
% 295.02/187.54 tff(28899,plain,
% 295.02/187.54 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s14)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s14)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14)))),
% 295.02/187.54 inference(rewrite,[status(thm)],[])).
% 295.02/187.54 tff(28900,plain,
% 295.02/187.54 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s14)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14)))),
% 295.02/187.54 inference(quant_inst,[status(thm)],[])).
% 295.02/187.54 tff(28901,plain,
% 295.02/187.54 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s14)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14))),
% 295.02/187.54 inference(modus_ponens,[status(thm)],[28900, 28899])).
% 295.02/187.54 tff(28902,plain,
% 295.02/187.54 ($false),
% 295.02/187.54 inference(unit_resolution,[status(thm)],[28901, 4958, 28898, 28897])).
% 295.02/187.54 tff(28903,plain,((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s14)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14))), inference(lemma,lemma(discharge,[]))).
% 295.02/187.54 tff(28904,plain,
% 295.02/187.54 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s14)),
% 295.02/187.54 inference(unit_resolution,[status(thm)],[28903, 28896])).
% 295.02/187.54 tff(28905,assumption,(node9(c_e_h_1, c_m, s14)), introduced(assumption)).
% 295.02/187.54 tff(28906,assumption,(~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s14)), introduced(assumption)).
% 295.02/187.54 tff(28907,plain,
% 295.02/187.54 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s14)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s14))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s14)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s14))),
% 295.02/187.54 inference(rewrite,[status(thm)],[])).
% 295.02/187.54 tff(28908,plain,
% 295.02/187.54 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s14)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s14))),
% 295.02/187.54 inference(quant_inst,[status(thm)],[])).
% 295.02/187.54 tff(28909,plain,
% 295.02/187.54 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s14)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s14)),
% 295.02/187.54 inference(modus_ponens,[status(thm)],[28908, 28907])).
% 295.02/187.54 tff(28910,plain,
% 295.02/187.54 ($false),
% 295.02/187.54 inference(unit_resolution,[status(thm)],[28909, 4972, 28906, 28905])).
% 295.02/187.54 tff(28911,plain,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s14) | (~node9(c_e_h_1, c_m, s14))), inference(lemma,lemma(discharge,[]))).
% 295.02/187.54 tff(28912,plain,
% 295.02/187.54 (~node9(c_e_h_1, c_m, s14)),
% 295.02/187.54 inference(unit_resolution,[status(thm)],[28911, 28904])).
% 295.02/187.54 tff(28913,assumption,(~node9(c_e_h_1, c_m, s14)), introduced(assumption)).
% 295.02/187.54 tff(28914,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)), introduced(assumption)).
% 295.02/187.54 tff(28915,assumption,(node10(c_e_h_1, c_m, s14, s15)), introduced(assumption)).
% 295.02/187.54 tff(28916,plain,
% 295.02/187.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)) | node9(c_e_h_1, c_m, s14) | (~node10(c_e_h_1, c_m, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)) | node9(c_e_h_1, c_m, s14) | (~node10(c_e_h_1, c_m, s14, s15)))),
% 295.02/187.54 inference(rewrite,[status(thm)],[])).
% 295.02/187.54 tff(28917,plain,
% 295.02/187.54 ((node9(c_e_h_1, c_m, s14) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)) | (~node10(c_e_h_1, c_m, s14, s15))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)) | node9(c_e_h_1, c_m, s14) | (~node10(c_e_h_1, c_m, s14, s15)))),
% 295.02/187.54 inference(rewrite,[status(thm)],[])).
% 295.02/187.54 tff(28918,plain,
% 295.02/187.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s14) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)) | (~node10(c_e_h_1, c_m, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)) | node9(c_e_h_1, c_m, s14) | (~node10(c_e_h_1, c_m, s14, s15))))),
% 295.02/187.54 inference(monotonicity,[status(thm)],[28917])).
% 295.02/187.54 tff(28919,plain,
% 295.02/187.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s14) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)) | (~node10(c_e_h_1, c_m, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)) | node9(c_e_h_1, c_m, s14) | (~node10(c_e_h_1, c_m, s14, s15)))),
% 295.02/187.54 inference(transitivity,[status(thm)],[28918, 28916])).
% 295.02/187.54 tff(28920,plain,
% 295.02/187.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s14) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)) | (~node10(c_e_h_1, c_m, s14, s15)))),
% 295.02/187.54 inference(quant_inst,[status(thm)],[])).
% 295.02/187.54 tff(28921,plain,
% 295.02/187.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)) | node9(c_e_h_1, c_m, s14) | (~node10(c_e_h_1, c_m, s14, s15))),
% 295.02/187.54 inference(modus_ponens,[status(thm)],[28920, 28919])).
% 295.02/187.54 tff(28922,plain,
% 295.02/187.54 ($false),
% 295.02/187.54 inference(unit_resolution,[status(thm)],[28921, 4986, 28914, 28915, 28913])).
% 295.02/187.54 tff(28923,plain,((~node10(c_e_h_1, c_m, s14, s15)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)) | node9(c_e_h_1, c_m, s14)), inference(lemma,lemma(discharge,[]))).
% 295.02/187.54 tff(28924,plain,
% 295.02/187.54 (~node10(c_e_h_1, c_m, s14, s15)),
% 295.02/187.54 inference(unit_resolution,[status(thm)],[28923, 28914, 28913])).
% 295.02/187.54 tff(28925,plain,
% 295.02/187.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s14, s15)) | node10(c_e_h_1, c_m, s14, s15) | node11(c_e_h_1, c_m, s14, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s14, s15)) | node10(c_e_h_1, c_m, s14, s15) | node11(c_e_h_1, c_m, s14, s15))),
% 295.02/187.54 inference(rewrite,[status(thm)],[])).
% 295.02/187.54 tff(28926,plain,
% 295.02/187.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s14, s15)) | node10(c_e_h_1, c_m, s14, s15) | node11(c_e_h_1, c_m, s14, s15))),
% 295.02/187.54 inference(quant_inst,[status(thm)],[])).
% 295.02/187.54 tff(28927,plain,
% 295.02/187.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s14, s15)) | node10(c_e_h_1, c_m, s14, s15) | node11(c_e_h_1, c_m, s14, s15)),
% 295.02/187.54 inference(modus_ponens,[status(thm)],[28926, 28925])).
% 295.02/187.54 tff(28928,plain,
% 295.02/187.54 (node10(c_e_h_1, c_m, s14, s15) | node11(c_e_h_1, c_m, s14, s15)),
% 295.02/187.54 inference(unit_resolution,[status(thm)],[28927, 5002, 12926])).
% 295.02/187.54 tff(28929,plain,
% 295.02/187.54 (node11(c_e_h_1, c_m, s14, s15)),
% 295.02/187.54 inference(unit_resolution,[status(thm)],[28928, 28924])).
% 295.02/187.54 tff(28930,plain,
% 295.02/187.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)) | (~node11(c_e_h_1, c_m, s14, s15)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)) | (~node11(c_e_h_1, c_m, s14, s15)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14))),
% 295.02/187.54 inference(rewrite,[status(thm)],[])).
% 295.02/187.54 tff(28931,plain,
% 295.02/187.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)) | (~node11(c_e_h_1, c_m, s14, s15)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14))),
% 295.02/187.54 inference(quant_inst,[status(thm)],[])).
% 295.02/187.54 tff(28932,plain,
% 295.02/187.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)) | (~node11(c_e_h_1, c_m, s14, s15)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)),
% 295.02/187.54 inference(modus_ponens,[status(thm)],[28931, 28930])).
% 295.02/187.54 tff(28933,plain,
% 295.02/187.54 ($false),
% 295.02/187.54 inference(unit_resolution,[status(thm)],[28932, 5017, 28914, 28929, 26516])).
% 295.02/187.54 tff(28934,plain,((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14) | node9(c_e_h_1, c_m, s14)), inference(lemma,lemma(discharge,[]))).
% 295.02/187.54 tff(28935,plain,
% 295.02/187.54 ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)) | node9(c_e_h_1, c_m, s14)),
% 295.02/187.54 inference(unit_resolution,[status(thm)],[28934, 26514])).
% 295.02/187.54 tff(28936,plain,
% 295.02/187.54 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)),
% 295.02/187.54 inference(unit_resolution,[status(thm)],[28935, 28912])).
% 295.02/187.54 tff(28937,plain,
% 295.02/187.54 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s15)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s15)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15))),
% 295.02/187.54 inference(rewrite,[status(thm)],[])).
% 295.02/187.54 tff(28938,plain,
% 295.02/187.54 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s15)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15))),
% 295.02/187.54 inference(quant_inst,[status(thm)],[])).
% 295.02/187.54 tff(28939,plain,
% 295.02/187.54 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s15)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)),
% 295.02/187.54 inference(modus_ponens,[status(thm)],[28938, 28937])).
% 295.02/187.54 tff(28940,plain,
% 295.02/187.54 (~m_and_h_gate_v_in2(c_e_h_1, c_l, s15)),
% 295.02/187.54 inference(unit_resolution,[status(thm)],[28939, 4549, 28936])).
% 295.02/187.54 tff(28941,plain,
% 295.02/187.54 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s15)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s15))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s15)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s15))),
% 295.02/187.54 inference(rewrite,[status(thm)],[])).
% 295.02/187.54 tff(28942,plain,
% 295.02/187.54 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s15)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s15))),
% 295.02/187.54 inference(quant_inst,[status(thm)],[])).
% 295.02/187.54 tff(28943,plain,
% 295.02/187.54 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s15)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s15)),
% 295.02/187.54 inference(modus_ponens,[status(thm)],[28942, 28941])).
% 295.02/187.54 tff(28944,plain,
% 295.02/187.54 (~node20(c_e_h_1, c_l, s15)),
% 295.02/187.54 inference(unit_resolution,[status(thm)],[28943, 4563, 28940])).
% 295.02/187.54 tff(28945,assumption,(m_and_h_gate_v_out(c_e_h_1, c_l, s16)), introduced(assumption)).
% 295.02/187.54 tff(28946,assumption,(~node20(c_e_h_1, c_l, s15)), introduced(assumption)).
% 295.02/187.54 tff(28947,assumption,(node21(c_e_h_1, c_l, s15, s16)), introduced(assumption)).
% 295.02/187.54 tff(28948,plain,
% 295.02/187.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s15) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s16)) | (~node21(c_e_h_1, c_l, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s15) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s16)) | (~node21(c_e_h_1, c_l, s15, s16)))),
% 295.02/187.55 inference(rewrite,[status(thm)],[])).
% 295.02/187.55 tff(28949,plain,
% 295.02/187.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s15) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s16)) | (~node21(c_e_h_1, c_l, s15, s16)))),
% 295.02/187.55 inference(quant_inst,[status(thm)],[])).
% 295.02/187.55 tff(28950,plain,
% 295.02/187.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s15) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s16)) | (~node21(c_e_h_1, c_l, s15, s16))),
% 295.02/187.55 inference(modus_ponens,[status(thm)],[28949, 28948])).
% 295.02/187.55 tff(28951,plain,
% 295.02/187.55 ($false),
% 295.02/187.55 inference(unit_resolution,[status(thm)],[28950, 52, 28947, 28945, 28946])).
% 295.02/187.55 tff(28952,plain,((~node21(c_e_h_1, c_l, s15, s16)) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s16)) | node20(c_e_h_1, c_l, s15)), inference(lemma,lemma(discharge,[]))).
% 295.02/187.55 tff(28953,plain,
% 295.02/187.55 (~node21(c_e_h_1, c_l, s15, s16)),
% 295.02/187.55 inference(unit_resolution,[status(thm)],[28952, 28945, 28946])).
% 295.02/187.55 tff(28954,plain,
% 295.02/187.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s15, s16)) | node21(c_e_h_1, c_l, s15, s16) | node22(c_e_h_1, c_l, s15, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s15, s16)) | node21(c_e_h_1, c_l, s15, s16) | node22(c_e_h_1, c_l, s15, s16))),
% 295.02/187.55 inference(rewrite,[status(thm)],[])).
% 295.02/187.55 tff(28955,plain,
% 295.02/187.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s15, s16)) | node21(c_e_h_1, c_l, s15, s16) | node22(c_e_h_1, c_l, s15, s16))),
% 295.02/187.55 inference(quant_inst,[status(thm)],[])).
% 295.02/187.55 tff(28956,plain,
% 295.02/187.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s15, s16)) | node21(c_e_h_1, c_l, s15, s16) | node22(c_e_h_1, c_l, s15, s16)),
% 295.02/187.55 inference(modus_ponens,[status(thm)],[28955, 28954])).
% 295.02/187.55 tff(28957,plain,
% 295.02/187.55 (node21(c_e_h_1, c_l, s15, s16) | node22(c_e_h_1, c_l, s15, s16)),
% 295.02/187.55 inference(unit_resolution,[status(thm)],[28956, 82, 13499])).
% 295.02/187.55 tff(28958,plain,
% 295.02/187.55 (node22(c_e_h_1, c_l, s15, s16)),
% 295.02/187.55 inference(unit_resolution,[status(thm)],[28957, 28953])).
% 295.02/187.55 tff(28959,plain,
% 295.02/187.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s16)) | (~node22(c_e_h_1, c_l, s15, s16)) | m_and_h_gate_v_out(c_e_h_1, c_l, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s16)) | (~node22(c_e_h_1, c_l, s15, s16)) | m_and_h_gate_v_out(c_e_h_1, c_l, s15))),
% 295.02/187.55 inference(rewrite,[status(thm)],[])).
% 295.02/187.55 tff(28960,plain,
% 295.02/187.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s16)) | (~node22(c_e_h_1, c_l, s15, s16)) | m_and_h_gate_v_out(c_e_h_1, c_l, s15))),
% 295.02/187.55 inference(quant_inst,[status(thm)],[])).
% 295.02/187.55 tff(28961,plain,
% 295.02/187.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s16)) | (~node22(c_e_h_1, c_l, s15, s16)) | m_and_h_gate_v_out(c_e_h_1, c_l, s15)),
% 295.02/187.55 inference(modus_ponens,[status(thm)],[28960, 28959])).
% 295.02/187.55 tff(28962,plain,
% 295.02/187.55 ($false),
% 295.02/187.55 inference(unit_resolution,[status(thm)],[28961, 108, 28958, 26552, 28945])).
% 295.02/187.55 tff(28963,plain,((~m_and_h_gate_v_out(c_e_h_1, c_l, s16)) | m_and_h_gate_v_out(c_e_h_1, c_l, s15) | node20(c_e_h_1, c_l, s15)), inference(lemma,lemma(discharge,[]))).
% 295.02/187.55 tff(28964,plain,
% 295.02/187.55 ((~m_and_h_gate_v_out(c_e_h_1, c_l, s16)) | node20(c_e_h_1, c_l, s15)),
% 295.02/187.55 inference(unit_resolution,[status(thm)],[28963, 26550])).
% 295.02/187.55 tff(28965,plain,
% 295.02/187.55 (~m_and_h_gate_v_out(c_e_h_1, c_l, s16)),
% 295.02/187.55 inference(unit_resolution,[status(thm)],[28964, 28944])).
% 295.02/187.55 tff(28966,assumption,(m_or_h_gate_v_in1(c_e_h_1, c_j, s16)), introduced(assumption)).
% 295.02/187.55 tff(28967,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_l, s16)), introduced(assumption)).
% 295.02/187.55 tff(28968,plain,
% 295.02/187.55 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s16)) | m_and_h_gate_v_out(c_e_h_1, c_l, s16))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s16)) | m_and_h_gate_v_out(c_e_h_1, c_l, s16))),
% 295.02/187.55 inference(rewrite,[status(thm)],[])).
% 295.02/187.55 tff(28969,plain,
% 295.02/187.55 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s16)) | m_and_h_gate_v_out(c_e_h_1, c_l, s16))),
% 295.02/187.55 inference(quant_inst,[status(thm)],[])).
% 295.02/187.55 tff(28970,plain,
% 295.02/187.55 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s16)) | m_and_h_gate_v_out(c_e_h_1, c_l, s16)),
% 295.02/187.55 inference(modus_ponens,[status(thm)],[28969, 28968])).
% 295.02/187.55 tff(28971,plain,
% 295.02/187.55 ($false),
% 295.02/187.55 inference(unit_resolution,[status(thm)],[28970, 1100, 28967, 28966])).
% 295.02/187.55 tff(28972,plain,((~m_or_h_gate_v_in1(c_e_h_1, c_j, s16)) | m_and_h_gate_v_out(c_e_h_1, c_l, s16)), inference(lemma,lemma(discharge,[]))).
% 295.02/187.55 tff(28973,plain,
% 295.02/187.55 (~m_or_h_gate_v_in1(c_e_h_1, c_j, s16)),
% 295.02/187.55 inference(unit_resolution,[status(thm)],[28972, 28965])).
% 295.02/187.55 tff(28974,assumption,(~m_or_h_gate_v_out(c_e_h_1, c_j, s16)), introduced(assumption)).
% 295.02/187.55 tff(28975,assumption,(m_or_h_gate_v_out(c_e_h_1, c_j, s17)), introduced(assumption)).
% 295.02/187.55 tff(28976,assumption,(node6(c_e_h_1, c_j, s16, s17)), introduced(assumption)).
% 295.02/187.55 tff(28977,plain,
% 295.02/187.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s16) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s17)) | (~node6(c_e_h_1, c_j, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s16) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s17)) | (~node6(c_e_h_1, c_j, s16, s17)))),
% 295.02/187.55 inference(rewrite,[status(thm)],[])).
% 295.02/187.55 tff(28978,plain,
% 295.02/187.55 (((~node6(c_e_h_1, c_j, s16, s17)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s17)) | m_or_h_gate_v_out(c_e_h_1, c_j, s16)) <=> (m_or_h_gate_v_out(c_e_h_1, c_j, s16) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s17)) | (~node6(c_e_h_1, c_j, s16, s17)))),
% 295.02/187.55 inference(rewrite,[status(thm)],[])).
% 295.02/187.55 tff(28979,plain,
% 295.02/187.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s16, s17)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s17)) | m_or_h_gate_v_out(c_e_h_1, c_j, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s16) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s17)) | (~node6(c_e_h_1, c_j, s16, s17))))),
% 295.02/187.55 inference(monotonicity,[status(thm)],[28978])).
% 295.02/187.55 tff(28980,plain,
% 295.02/187.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s16, s17)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s17)) | m_or_h_gate_v_out(c_e_h_1, c_j, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s16) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s17)) | (~node6(c_e_h_1, c_j, s16, s17)))),
% 295.02/187.55 inference(transitivity,[status(thm)],[28979, 28977])).
% 295.02/187.55 tff(28981,plain,
% 295.02/187.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s16, s17)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s17)) | m_or_h_gate_v_out(c_e_h_1, c_j, s16))),
% 295.02/187.55 inference(quant_inst,[status(thm)],[])).
% 295.02/187.55 tff(28982,plain,
% 295.02/187.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s16) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s17)) | (~node6(c_e_h_1, c_j, s16, s17))),
% 295.02/187.55 inference(modus_ponens,[status(thm)],[28981, 28980])).
% 295.02/187.55 tff(28983,plain,
% 295.02/187.55 ($false),
% 295.02/187.55 inference(unit_resolution,[status(thm)],[28982, 1121, 28975, 28974, 28976])).
% 295.02/187.55 tff(28984,plain,((~node6(c_e_h_1, c_j, s16, s17)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s17)) | m_or_h_gate_v_out(c_e_h_1, c_j, s16)), inference(lemma,lemma(discharge,[]))).
% 295.02/187.55 tff(28985,plain,
% 295.02/187.55 (~node6(c_e_h_1, c_j, s16, s17)),
% 295.02/187.55 inference(unit_resolution,[status(thm)],[28984, 28975, 28974])).
% 295.02/187.55 tff(28986,assumption,(~m_or_h_gate_v_in2(c_e_h_1, c_j, s16)), introduced(assumption)).
% 295.02/187.55 tff(28987,assumption,(~m_or_h_gate_v_in1(c_e_h_1, c_j, s16)), introduced(assumption)).
% 295.02/187.55 tff(28988,assumption,(node5(c_e_h_1, c_j, s16, s17)), introduced(assumption)).
% 295.02/187.55 tff(28989,plain,
% 295.02/187.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_1, c_j, s16) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s17)) | (~node5(c_e_h_1, c_j, s16, s17)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_1, c_j, s16) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s17)) | (~node5(c_e_h_1, c_j, s16, s17)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s16))),
% 295.02/187.55 inference(rewrite,[status(thm)],[])).
% 295.02/187.55 tff(28990,plain,
% 295.02/187.55 ((m_or_h_gate_v_in1(c_e_h_1, c_j, s16) | m_or_h_gate_v_in2(c_e_h_1, c_j, s16) | (~node5(c_e_h_1, c_j, s16, s17)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s17))) <=> (m_or_h_gate_v_in2(c_e_h_1, c_j, s16) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s17)) | (~node5(c_e_h_1, c_j, s16, s17)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s16))),
% 295.02/187.55 inference(rewrite,[status(thm)],[])).
% 295.02/187.55 tff(28991,plain,
% 295.02/187.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s16) | m_or_h_gate_v_in2(c_e_h_1, c_j, s16) | (~node5(c_e_h_1, c_j, s16, s17)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_1, c_j, s16) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s17)) | (~node5(c_e_h_1, c_j, s16, s17)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s16)))),
% 295.02/187.55 inference(monotonicity,[status(thm)],[28990])).
% 295.02/187.55 tff(28992,plain,
% 295.02/187.55 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s16) | m_or_h_gate_v_in2(c_e_h_1, c_j, s16) | (~node5(c_e_h_1, c_j, s16, s17)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_1, c_j, s16) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s17)) | (~node5(c_e_h_1, c_j, s16, s17)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s16))),
% 295.02/187.55 inference(transitivity,[status(thm)],[28991, 28989])).
% 295.02/187.55 tff(28993,plain,
% 295.02/187.55 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s16) | m_or_h_gate_v_in2(c_e_h_1, c_j, s16) | (~node5(c_e_h_1, c_j, s16, s17)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s17)))),
% 295.02/187.55 inference(quant_inst,[status(thm)],[])).
% 295.02/187.56 tff(28994,plain,
% 295.02/187.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_1, c_j, s16) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s17)) | (~node5(c_e_h_1, c_j, s16, s17)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s16)),
% 295.02/187.56 inference(modus_ponens,[status(thm)],[28993, 28992])).
% 295.02/187.56 tff(28995,plain,
% 295.02/187.56 ($false),
% 295.02/187.56 inference(unit_resolution,[status(thm)],[28994, 1159, 28975, 28988, 28986, 28987])).
% 295.02/187.56 tff(28996,plain,((~node5(c_e_h_1, c_j, s16, s17)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s17)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s16) | m_or_h_gate_v_in1(c_e_h_1, c_j, s16)), inference(lemma,lemma(discharge,[]))).
% 295.02/187.56 tff(28997,plain,
% 295.02/187.56 (~node5(c_e_h_1, c_j, s16, s17)),
% 295.02/187.56 inference(unit_resolution,[status(thm)],[28996, 28975, 28987, 28986])).
% 295.02/187.56 tff(28998,plain,
% 295.02/187.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s16, s17)) | node5(c_e_h_1, c_j, s16, s17) | node6(c_e_h_1, c_j, s16, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s16, s17)) | node5(c_e_h_1, c_j, s16, s17) | node6(c_e_h_1, c_j, s16, s17))),
% 295.02/187.56 inference(rewrite,[status(thm)],[])).
% 295.02/187.56 tff(28999,plain,
% 295.02/187.56 ((node6(c_e_h_1, c_j, s16, s17) | node5(c_e_h_1, c_j, s16, s17) | (~trans(s16, s17))) <=> ((~trans(s16, s17)) | node5(c_e_h_1, c_j, s16, s17) | node6(c_e_h_1, c_j, s16, s17))),
% 295.02/187.56 inference(rewrite,[status(thm)],[])).
% 295.02/187.56 tff(29000,plain,
% 295.02/187.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s16, s17) | node5(c_e_h_1, c_j, s16, s17) | (~trans(s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s16, s17)) | node5(c_e_h_1, c_j, s16, s17) | node6(c_e_h_1, c_j, s16, s17)))),
% 295.02/187.56 inference(monotonicity,[status(thm)],[28999])).
% 295.02/187.56 tff(29001,plain,
% 295.02/187.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s16, s17) | node5(c_e_h_1, c_j, s16, s17) | (~trans(s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s16, s17)) | node5(c_e_h_1, c_j, s16, s17) | node6(c_e_h_1, c_j, s16, s17))),
% 295.02/187.56 inference(transitivity,[status(thm)],[29000, 28998])).
% 295.02/187.56 tff(29002,plain,
% 295.02/187.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s16, s17) | node5(c_e_h_1, c_j, s16, s17) | (~trans(s16, s17)))),
% 295.02/187.56 inference(quant_inst,[status(thm)],[])).
% 295.02/187.56 tff(29003,plain,
% 295.02/187.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s16, s17)) | node5(c_e_h_1, c_j, s16, s17) | node6(c_e_h_1, c_j, s16, s17)),
% 295.02/187.56 inference(modus_ponens,[status(thm)],[29002, 29001])).
% 295.02/187.56 tff(29004,plain,
% 295.02/187.56 (node5(c_e_h_1, c_j, s16, s17) | node6(c_e_h_1, c_j, s16, s17)),
% 295.02/187.56 inference(unit_resolution,[status(thm)],[29003, 1141, 11967])).
% 295.02/187.56 tff(29005,plain,
% 295.02/187.56 ($false),
% 295.02/187.56 inference(unit_resolution,[status(thm)],[29004, 28997, 28985])).
% 295.02/187.56 tff(29006,plain,((~m_or_h_gate_v_out(c_e_h_1, c_j, s17)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s16) | m_or_h_gate_v_in2(c_e_h_1, c_j, s16) | m_or_h_gate_v_out(c_e_h_1, c_j, s16)), inference(lemma,lemma(discharge,[]))).
% 295.02/187.56 tff(29007,plain,
% 295.02/187.56 ((~m_or_h_gate_v_out(c_e_h_1, c_j, s17)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s16) | m_or_h_gate_v_out(c_e_h_1, c_j, s16)),
% 295.02/187.56 inference(unit_resolution,[status(thm)],[29006, 28973])).
% 295.02/187.56 tff(29008,plain,
% 295.02/187.56 (~m_or_h_gate_v_out(c_e_h_1, c_j, s17)),
% 295.02/187.56 inference(unit_resolution,[status(thm)],[29007, 28855, 26867])).
% 295.02/187.56 tff(29009,plain,
% 295.02/187.56 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s17))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s17))),
% 295.02/187.56 inference(rewrite,[status(thm)],[])).
% 295.02/187.56 tff(29010,plain,
% 295.02/187.56 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s17))),
% 295.02/187.56 inference(quant_inst,[status(thm)],[])).
% 295.02/187.56 tff(29011,plain,
% 295.02/187.56 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s17)),
% 295.02/187.56 inference(modus_ponens,[status(thm)],[29010, 29009])).
% 295.02/187.56 tff(29012,plain,
% 295.02/187.56 (node3(c_e_h_3, c_e_h_1, s17)),
% 295.02/187.56 inference(unit_resolution,[status(thm)],[29011, 2922, 1056])).
% 295.02/187.56 tff(29013,plain,
% 295.02/187.56 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s17)) | (~node3(c_e_h_3, c_e_h_1, s17)) | m_and_h_gate_v_out(c_e_h_3, c_q, s17))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s17)) | (~node3(c_e_h_3, c_e_h_1, s17)) | m_and_h_gate_v_out(c_e_h_3, c_q, s17))),
% 295.02/187.56 inference(rewrite,[status(thm)],[])).
% 295.02/187.56 tff(29014,plain,
% 295.02/187.56 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s17)) | (~node3(c_e_h_3, c_e_h_1, s17)) | m_and_h_gate_v_out(c_e_h_3, c_q, s17))),
% 295.02/187.56 inference(quant_inst,[status(thm)],[])).
% 295.02/187.56 tff(29015,plain,
% 295.02/187.56 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s17)) | (~node3(c_e_h_3, c_e_h_1, s17)) | m_and_h_gate_v_out(c_e_h_3, c_q, s17)),
% 295.02/187.56 inference(modus_ponens,[status(thm)],[29014, 29013])).
% 295.02/187.56 tff(29016,plain,
% 295.02/187.56 ((~m_cell_v_ack(c_e_h_1, s17)) | m_and_h_gate_v_out(c_e_h_3, c_q, s17)),
% 295.02/187.56 inference(unit_resolution,[status(thm)],[29015, 1073, 29012])).
% 295.02/187.56 tff(29017,plain,
% 295.02/187.56 (~m_cell_v_ack(c_e_h_1, s17)),
% 295.02/187.56 inference(unit_resolution,[status(thm)],[29016, 28802])).
% 295.02/187.56 tff(29018,plain,
% 295.02/187.56 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s17)) | m_cell_v_ack(c_e_h_1, s17))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s17)) | m_cell_v_ack(c_e_h_1, s17))),
% 295.02/187.56 inference(rewrite,[status(thm)],[])).
% 295.02/187.56 tff(29019,plain,
% 295.02/187.56 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s17)) | m_cell_v_ack(c_e_h_1, s17))),
% 295.02/187.56 inference(quant_inst,[status(thm)],[])).
% 295.02/187.56 tff(29020,plain,
% 295.02/187.56 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s17)) | m_cell_v_ack(c_e_h_1, s17)),
% 295.02/187.56 inference(modus_ponens,[status(thm)],[29019, 29018])).
% 295.02/187.56 tff(29021,plain,
% 295.02/187.56 (~m_or_h_gate_v_in2(c_e_h_1, c_j, s17)),
% 295.02/187.56 inference(unit_resolution,[status(thm)],[29020, 1085, 29017])).
% 295.02/187.56 tff(29022,plain,
% 295.02/187.56 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14) | m_c_h_element_v_out(c_e_h_1, c_e, s14))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14) | m_c_h_element_v_out(c_e_h_1, c_e, s14))),
% 295.02/187.56 inference(rewrite,[status(thm)],[])).
% 295.02/187.56 tff(29023,plain,
% 295.02/187.56 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14) | m_c_h_element_v_out(c_e_h_1, c_e, s14))),
% 295.02/187.56 inference(quant_inst,[status(thm)],[])).
% 295.02/187.56 tff(29024,plain,
% 295.02/187.56 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14) | m_c_h_element_v_out(c_e_h_1, c_e, s14)),
% 295.02/187.56 inference(modus_ponens,[status(thm)],[29023, 29022])).
% 295.02/187.56 tff(29025,plain,
% 295.02/187.56 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14) | m_c_h_element_v_out(c_e_h_1, c_e, s14)),
% 295.02/187.56 inference(unit_resolution,[status(thm)],[29024, 7856])).
% 295.02/187.56 tff(29026,plain,
% 295.02/187.56 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14)),
% 295.02/187.56 inference(unit_resolution,[status(thm)],[29025, 25856])).
% 295.02/187.56 tff(29027,assumption,(m_c_h_element_v_in2(c_e_h_1, c_f, s10)), introduced(assumption)).
% 295.02/187.56 tff(29028,plain,
% 295.02/187.56 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s10)) | m_and_h_gate_v_out(c_e_h_1, c_i, s10))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s10)) | m_and_h_gate_v_out(c_e_h_1, c_i, s10))),
% 295.02/187.56 inference(rewrite,[status(thm)],[])).
% 295.02/187.56 tff(29029,plain,
% 295.02/187.56 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s10)) | m_and_h_gate_v_out(c_e_h_1, c_i, s10))),
% 295.02/187.56 inference(quant_inst,[status(thm)],[])).
% 295.02/187.56 tff(29030,plain,
% 295.02/187.56 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s10)) | m_and_h_gate_v_out(c_e_h_1, c_i, s10)),
% 295.02/187.57 inference(modus_ponens,[status(thm)],[29029, 29028])).
% 295.02/187.57 tff(29031,plain,
% 295.02/187.57 ($false),
% 295.02/187.57 inference(unit_resolution,[status(thm)],[29030, 2143, 24091, 29027])).
% 295.02/187.57 tff(29032,plain,(~m_c_h_element_v_in2(c_e_h_1, c_f, s10)), inference(lemma,lemma(discharge,[]))).
% 295.02/187.57 tff(29033,assumption,(m_c_h_element_v_in2(c_e_h_1, c_f, s9)), introduced(assumption)).
% 295.02/187.57 tff(29034,plain,
% 295.02/187.57 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s9)) | m_and_h_gate_v_out(c_e_h_1, c_i, s9))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s9)) | m_and_h_gate_v_out(c_e_h_1, c_i, s9))),
% 295.02/187.57 inference(rewrite,[status(thm)],[])).
% 295.02/187.57 tff(29035,plain,
% 295.02/187.57 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s9)) | m_and_h_gate_v_out(c_e_h_1, c_i, s9))),
% 295.02/187.57 inference(quant_inst,[status(thm)],[])).
% 295.02/187.57 tff(29036,plain,
% 295.02/187.57 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s9)) | m_and_h_gate_v_out(c_e_h_1, c_i, s9)),
% 295.02/187.57 inference(modus_ponens,[status(thm)],[29035, 29034])).
% 295.02/187.57 tff(29037,plain,
% 295.02/187.57 ($false),
% 295.02/187.57 inference(unit_resolution,[status(thm)],[29036, 2143, 29033, 23251])).
% 295.02/187.57 tff(29038,plain,((~m_c_h_element_v_in2(c_e_h_1, c_f, s9)) | m_and_h_gate_v_out(c_e_h_1, c_i, s9)), inference(lemma,lemma(discharge,[]))).
% 295.02/187.57 tff(29039,plain,
% 295.02/187.57 (~m_c_h_element_v_in2(c_e_h_1, c_f, s9)),
% 295.02/187.57 inference(unit_resolution,[status(thm)],[29038, 23250])).
% 295.02/187.57 tff(29040,assumption,(~m_c_h_element_v_out(c_e_h_1, c_f, s8)), introduced(assumption)).
% 295.02/187.57 tff(29041,assumption,(m_c_h_element_v_out(c_e_h_1, c_f, s9)), introduced(assumption)).
% 295.02/187.57 tff(29042,assumption,(node15(c_e_h_1, c_f, s8, s9)), introduced(assumption)).
% 295.02/187.57 tff(29043,plain,
% 295.02/187.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s9)) | (~node15(c_e_h_1, c_f, s8, s9)) | m_c_h_element_v_out(c_e_h_1, c_f, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s9)) | (~node15(c_e_h_1, c_f, s8, s9)) | m_c_h_element_v_out(c_e_h_1, c_f, s8))),
% 295.02/187.57 inference(rewrite,[status(thm)],[])).
% 295.02/187.57 tff(29044,plain,
% 295.02/187.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s9)) | (~node15(c_e_h_1, c_f, s8, s9)) | m_c_h_element_v_out(c_e_h_1, c_f, s8))),
% 295.02/187.57 inference(quant_inst,[status(thm)],[])).
% 295.02/187.57 tff(29045,plain,
% 295.02/187.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s9)) | (~node15(c_e_h_1, c_f, s8, s9)) | m_c_h_element_v_out(c_e_h_1, c_f, s8)),
% 295.02/187.57 inference(modus_ponens,[status(thm)],[29044, 29043])).
% 295.02/187.57 tff(29046,plain,
% 295.02/187.57 ($false),
% 295.02/187.57 inference(unit_resolution,[status(thm)],[29045, 147, 29041, 29042, 29040])).
% 295.02/187.57 tff(29047,plain,((~node15(c_e_h_1, c_f, s8, s9)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s9)) | m_c_h_element_v_out(c_e_h_1, c_f, s8)), inference(lemma,lemma(discharge,[]))).
% 295.02/187.57 tff(29048,plain,
% 295.02/187.57 (~node15(c_e_h_1, c_f, s8, s9)),
% 295.02/187.57 inference(unit_resolution,[status(thm)],[29047, 29041, 29040])).
% 295.02/187.57 tff(29049,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_f, s8)), introduced(assumption)).
% 295.02/187.57 tff(29050,assumption,(node14(c_e_h_1, c_f, s8, s9)), introduced(assumption)).
% 295.02/187.57 tff(29051,plain,
% 295.02/187.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s9)) | m_c_h_element_v_in1(c_e_h_1, c_f, s8) | (~node14(c_e_h_1, c_f, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s9)) | m_c_h_element_v_in1(c_e_h_1, c_f, s8) | (~node14(c_e_h_1, c_f, s8, s9)))),
% 295.02/187.57 inference(rewrite,[status(thm)],[])).
% 295.02/187.57 tff(29052,plain,
% 295.02/187.57 (((~node14(c_e_h_1, c_f, s8, s9)) | m_c_h_element_v_in1(c_e_h_1, c_f, s8) | (~m_c_h_element_v_out(c_e_h_1, c_f, s9))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_f, s9)) | m_c_h_element_v_in1(c_e_h_1, c_f, s8) | (~node14(c_e_h_1, c_f, s8, s9)))),
% 295.02/187.57 inference(rewrite,[status(thm)],[])).
% 295.02/187.57 tff(29053,plain,
% 295.02/187.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s8, s9)) | m_c_h_element_v_in1(c_e_h_1, c_f, s8) | (~m_c_h_element_v_out(c_e_h_1, c_f, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s9)) | m_c_h_element_v_in1(c_e_h_1, c_f, s8) | (~node14(c_e_h_1, c_f, s8, s9))))),
% 295.02/187.57 inference(monotonicity,[status(thm)],[29052])).
% 295.02/187.57 tff(29054,plain,
% 295.02/187.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s8, s9)) | m_c_h_element_v_in1(c_e_h_1, c_f, s8) | (~m_c_h_element_v_out(c_e_h_1, c_f, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s9)) | m_c_h_element_v_in1(c_e_h_1, c_f, s8) | (~node14(c_e_h_1, c_f, s8, s9)))),
% 295.02/187.57 inference(transitivity,[status(thm)],[29053, 29051])).
% 295.02/187.57 tff(29055,plain,
% 295.02/187.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s8, s9)) | m_c_h_element_v_in1(c_e_h_1, c_f, s8) | (~m_c_h_element_v_out(c_e_h_1, c_f, s9)))),
% 295.02/187.57 inference(quant_inst,[status(thm)],[])).
% 295.02/187.57 tff(29056,plain,
% 295.02/187.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s9)) | m_c_h_element_v_in1(c_e_h_1, c_f, s8) | (~node14(c_e_h_1, c_f, s8, s9))),
% 295.02/187.57 inference(modus_ponens,[status(thm)],[29055, 29054])).
% 295.02/187.57 tff(29057,plain,
% 295.02/187.57 ($false),
% 295.02/187.57 inference(unit_resolution,[status(thm)],[29056, 223, 29041, 29050, 29049])).
% 295.02/187.57 tff(29058,plain,((~node14(c_e_h_1, c_f, s8, s9)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s9)) | m_c_h_element_v_in1(c_e_h_1, c_f, s8)), inference(lemma,lemma(discharge,[]))).
% 295.02/187.57 tff(29059,plain,
% 295.02/187.57 (~node14(c_e_h_1, c_f, s8, s9)),
% 295.02/187.57 inference(unit_resolution,[status(thm)],[29058, 29041, 29049])).
% 295.02/187.57 tff(29060,plain,
% 295.02/187.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s8, s9)) | node19(c_e_h_1, c_f, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s8, s9)) | node19(c_e_h_1, c_f, s8, s9))),
% 295.02/187.57 inference(rewrite,[status(thm)],[])).
% 295.02/187.57 tff(29061,plain,
% 295.02/187.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s8, s9)) | node19(c_e_h_1, c_f, s8, s9))),
% 295.02/187.57 inference(quant_inst,[status(thm)],[])).
% 295.02/187.57 tff(29062,plain,
% 295.02/187.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s8, s9)) | node19(c_e_h_1, c_f, s8, s9)),
% 295.02/187.57 inference(modus_ponens,[status(thm)],[29061, 29060])).
% 295.02/187.57 tff(29063,plain,
% 295.02/187.57 (node19(c_e_h_1, c_f, s8, s9)),
% 295.02/187.57 inference(unit_resolution,[status(thm)],[29062, 190, 1993])).
% 295.02/187.57 tff(29064,plain,
% 295.02/187.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_1, c_f, s8, s9) | (~node19(c_e_h_1, c_f, s8, s9)) | node14(c_e_h_1, c_f, s8, s9) | node16(c_e_h_1, c_f, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_f, s8, s9) | (~node19(c_e_h_1, c_f, s8, s9)) | node14(c_e_h_1, c_f, s8, s9) | node16(c_e_h_1, c_f, s8))),
% 295.02/187.57 inference(rewrite,[status(thm)],[])).
% 295.02/187.57 tff(29065,plain,
% 295.02/187.57 ((node16(c_e_h_1, c_f, s8) | node14(c_e_h_1, c_f, s8, s9) | node15(c_e_h_1, c_f, s8, s9) | (~node19(c_e_h_1, c_f, s8, s9))) <=> (node15(c_e_h_1, c_f, s8, s9) | (~node19(c_e_h_1, c_f, s8, s9)) | node14(c_e_h_1, c_f, s8, s9) | node16(c_e_h_1, c_f, s8))),
% 295.02/187.57 inference(rewrite,[status(thm)],[])).
% 295.02/187.57 tff(29066,plain,
% 295.02/187.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s8) | node14(c_e_h_1, c_f, s8, s9) | node15(c_e_h_1, c_f, s8, s9) | (~node19(c_e_h_1, c_f, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_1, c_f, s8, s9) | (~node19(c_e_h_1, c_f, s8, s9)) | node14(c_e_h_1, c_f, s8, s9) | node16(c_e_h_1, c_f, s8)))),
% 295.02/187.57 inference(monotonicity,[status(thm)],[29065])).
% 295.02/187.57 tff(29067,plain,
% 295.02/187.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s8) | node14(c_e_h_1, c_f, s8, s9) | node15(c_e_h_1, c_f, s8, s9) | (~node19(c_e_h_1, c_f, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_f, s8, s9) | (~node19(c_e_h_1, c_f, s8, s9)) | node14(c_e_h_1, c_f, s8, s9) | node16(c_e_h_1, c_f, s8))),
% 295.02/187.57 inference(transitivity,[status(thm)],[29066, 29064])).
% 295.02/187.57 tff(29068,plain,
% 295.02/187.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s8) | node14(c_e_h_1, c_f, s8, s9) | node15(c_e_h_1, c_f, s8, s9) | (~node19(c_e_h_1, c_f, s8, s9)))),
% 295.02/187.57 inference(quant_inst,[status(thm)],[])).
% 295.02/187.57 tff(29069,plain,
% 295.02/187.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_f, s8, s9) | (~node19(c_e_h_1, c_f, s8, s9)) | node14(c_e_h_1, c_f, s8, s9) | node16(c_e_h_1, c_f, s8)),
% 295.02/187.57 inference(modus_ponens,[status(thm)],[29068, 29067])).
% 295.02/187.57 tff(29070,plain,
% 295.02/187.57 (node15(c_e_h_1, c_f, s8, s9) | node14(c_e_h_1, c_f, s8, s9) | node16(c_e_h_1, c_f, s8)),
% 295.02/187.57 inference(unit_resolution,[status(thm)],[29069, 204, 29063])).
% 295.02/187.57 tff(29071,plain,
% 295.02/187.57 (node16(c_e_h_1, c_f, s8)),
% 295.02/187.57 inference(unit_resolution,[status(thm)],[29070, 29059, 29048])).
% 295.02/187.57 tff(29072,assumption,(node16(c_e_h_1, c_f, s8)), introduced(assumption)).
% 295.02/187.57 tff(29073,assumption,(node17(c_e_h_1, c_f, s8)), introduced(assumption)).
% 295.02/187.57 tff(29074,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_f, s8)), introduced(assumption)).
% 295.02/187.57 tff(29075,plain,
% 295.02/187.57 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s8)) | m_c_h_element_v_in1(c_e_h_1, c_f, s8) | m_c_h_element_v_in2(c_e_h_1, c_f, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s8)) | m_c_h_element_v_in1(c_e_h_1, c_f, s8) | m_c_h_element_v_in2(c_e_h_1, c_f, s8))),
% 295.02/187.58 inference(rewrite,[status(thm)],[])).
% 295.02/187.58 tff(29076,plain,
% 295.02/187.58 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s8)) | m_c_h_element_v_in1(c_e_h_1, c_f, s8) | m_c_h_element_v_in2(c_e_h_1, c_f, s8))),
% 295.02/187.58 inference(quant_inst,[status(thm)],[])).
% 295.02/187.58 tff(29077,plain,
% 295.02/187.58 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s8)) | m_c_h_element_v_in1(c_e_h_1, c_f, s8) | m_c_h_element_v_in2(c_e_h_1, c_f, s8)),
% 295.02/187.58 inference(modus_ponens,[status(thm)],[29076, 29075])).
% 295.02/187.58 tff(29078,plain,
% 295.02/187.58 (m_c_h_element_v_in1(c_e_h_1, c_f, s8) | m_c_h_element_v_in2(c_e_h_1, c_f, s8)),
% 295.02/187.58 inference(unit_resolution,[status(thm)],[29077, 178, 29072])).
% 295.02/187.58 tff(29079,plain,
% 295.02/187.58 (m_c_h_element_v_in1(c_e_h_1, c_f, s8)),
% 295.02/187.58 inference(unit_resolution,[status(thm)],[29078, 29074])).
% 295.02/187.58 tff(29080,plain,
% 295.02/187.58 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s8)) | m_c_h_element_v_in2(c_e_h_1, c_f, s8) | (~node17(c_e_h_1, c_f, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s8)) | m_c_h_element_v_in2(c_e_h_1, c_f, s8) | (~node17(c_e_h_1, c_f, s8)))),
% 295.02/187.58 inference(rewrite,[status(thm)],[])).
% 295.02/187.58 tff(29081,plain,
% 295.02/187.58 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s8)) | m_c_h_element_v_in2(c_e_h_1, c_f, s8) | (~node17(c_e_h_1, c_f, s8)))),
% 295.02/187.58 inference(quant_inst,[status(thm)],[])).
% 295.02/187.58 tff(29082,plain,
% 295.02/187.58 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s8)) | m_c_h_element_v_in2(c_e_h_1, c_f, s8) | (~node17(c_e_h_1, c_f, s8))),
% 295.02/187.58 inference(modus_ponens,[status(thm)],[29081, 29080])).
% 295.02/187.58 tff(29083,plain,
% 295.02/187.58 ((~m_c_h_element_v_in1(c_e_h_1, c_f, s8)) | m_c_h_element_v_in2(c_e_h_1, c_f, s8)),
% 295.02/187.58 inference(unit_resolution,[status(thm)],[29082, 919, 29073])).
% 295.02/187.58 tff(29084,plain,
% 295.02/187.58 ($false),
% 295.02/187.58 inference(unit_resolution,[status(thm)],[29083, 29079, 29074])).
% 295.02/187.58 tff(29085,plain,(m_c_h_element_v_in2(c_e_h_1, c_f, s8) | (~node17(c_e_h_1, c_f, s8)) | (~node16(c_e_h_1, c_f, s8))), inference(lemma,lemma(discharge,[]))).
% 295.02/187.58 tff(29086,plain,
% 295.02/187.58 (m_c_h_element_v_in2(c_e_h_1, c_f, s8)),
% 295.02/187.58 inference(unit_resolution,[status(thm)],[29085, 29073, 29072])).
% 295.02/187.58 tff(29087,plain,
% 295.02/187.58 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s8)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s8)) | (~node16(c_e_h_1, c_f, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s8)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s8)) | (~node16(c_e_h_1, c_f, s8)))),
% 295.02/187.58 inference(rewrite,[status(thm)],[])).
% 295.02/187.58 tff(29088,plain,
% 295.02/187.58 (((~node16(c_e_h_1, c_f, s8)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s8)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s8))) <=> ((~m_c_h_element_v_in2(c_e_h_1, c_f, s8)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s8)) | (~node16(c_e_h_1, c_f, s8)))),
% 295.02/187.58 inference(rewrite,[status(thm)],[])).
% 295.02/187.58 tff(29089,plain,
% 295.02/187.58 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_f, s8)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s8)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s8)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s8)) | (~node16(c_e_h_1, c_f, s8))))),
% 295.02/187.58 inference(monotonicity,[status(thm)],[29088])).
% 295.02/187.58 tff(29090,plain,
% 295.02/187.58 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_f, s8)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s8)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s8)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s8)) | (~node16(c_e_h_1, c_f, s8)))),
% 295.02/187.58 inference(transitivity,[status(thm)],[29089, 29087])).
% 295.02/187.58 tff(29091,plain,
% 295.02/187.58 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_f, s8)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s8)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s8)))),
% 295.02/187.58 inference(quant_inst,[status(thm)],[])).
% 295.02/187.58 tff(29092,plain,
% 295.02/187.58 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s8)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s8)) | (~node16(c_e_h_1, c_f, s8))),
% 295.02/187.58 inference(modus_ponens,[status(thm)],[29091, 29090])).
% 295.02/187.58 tff(29093,plain,
% 295.02/187.58 ((~m_c_h_element_v_in2(c_e_h_1, c_f, s8)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s8))),
% 295.02/187.58 inference(unit_resolution,[status(thm)],[29092, 2307, 29072])).
% 295.02/187.58 tff(29094,plain,
% 295.02/187.58 (~m_c_h_element_v_in1(c_e_h_1, c_f, s8)),
% 295.02/187.58 inference(unit_resolution,[status(thm)],[29093, 29086])).
% 295.02/187.58 tff(29095,plain,
% 295.02/187.58 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s8)) | m_c_h_element_v_in1(c_e_h_1, c_f, s8) | (~node17(c_e_h_1, c_f, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s8)) | m_c_h_element_v_in1(c_e_h_1, c_f, s8) | (~node17(c_e_h_1, c_f, s8)))),
% 295.02/187.58 inference(rewrite,[status(thm)],[])).
% 295.02/187.58 tff(29096,plain,
% 295.02/187.58 ((m_c_h_element_v_in1(c_e_h_1, c_f, s8) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s8)) | (~node17(c_e_h_1, c_f, s8))) <=> ((~m_c_h_element_v_in2(c_e_h_1, c_f, s8)) | m_c_h_element_v_in1(c_e_h_1, c_f, s8) | (~node17(c_e_h_1, c_f, s8)))),
% 295.02/187.58 inference(rewrite,[status(thm)],[])).
% 295.02/187.58 tff(29097,plain,
% 295.02/187.58 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s8) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s8)) | (~node17(c_e_h_1, c_f, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s8)) | m_c_h_element_v_in1(c_e_h_1, c_f, s8) | (~node17(c_e_h_1, c_f, s8))))),
% 295.02/187.58 inference(monotonicity,[status(thm)],[29096])).
% 295.02/187.58 tff(29098,plain,
% 295.02/187.58 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s8) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s8)) | (~node17(c_e_h_1, c_f, s8)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s8)) | m_c_h_element_v_in1(c_e_h_1, c_f, s8) | (~node17(c_e_h_1, c_f, s8)))),
% 295.02/187.58 inference(transitivity,[status(thm)],[29097, 29095])).
% 295.02/187.58 tff(29099,plain,
% 295.02/187.58 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s8) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s8)) | (~node17(c_e_h_1, c_f, s8)))),
% 295.02/187.58 inference(quant_inst,[status(thm)],[])).
% 295.02/187.58 tff(29100,plain,
% 295.02/187.58 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s8)) | m_c_h_element_v_in1(c_e_h_1, c_f, s8) | (~node17(c_e_h_1, c_f, s8))),
% 295.02/187.58 inference(modus_ponens,[status(thm)],[29099, 29098])).
% 295.02/187.58 tff(29101,plain,
% 295.02/187.58 ((~m_c_h_element_v_in2(c_e_h_1, c_f, s8)) | m_c_h_element_v_in1(c_e_h_1, c_f, s8)),
% 295.02/187.58 inference(unit_resolution,[status(thm)],[29100, 859, 29073])).
% 295.02/187.58 tff(29102,plain,
% 295.02/187.58 ($false),
% 295.02/187.58 inference(unit_resolution,[status(thm)],[29101, 29094, 29086])).
% 295.02/187.58 tff(29103,plain,((~node17(c_e_h_1, c_f, s8)) | (~node16(c_e_h_1, c_f, s8))), inference(lemma,lemma(discharge,[]))).
% 295.02/187.58 tff(29104,plain,
% 295.02/187.58 (~node17(c_e_h_1, c_f, s8)),
% 295.02/187.58 inference(unit_resolution,[status(thm)],[29103, 29071])).
% 295.02/187.58 tff(29105,plain,
% 295.02/187.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_f, s8, s9)) | node18(c_e_h_1, c_f, s8, s9) | node17(c_e_h_1, c_f, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s8, s9)) | node18(c_e_h_1, c_f, s8, s9) | node17(c_e_h_1, c_f, s8))),
% 295.02/187.58 inference(rewrite,[status(thm)],[])).
% 295.02/187.58 tff(29106,plain,
% 295.02/187.58 ((node17(c_e_h_1, c_f, s8) | node18(c_e_h_1, c_f, s8, s9) | (~node19(c_e_h_1, c_f, s8, s9))) <=> ((~node19(c_e_h_1, c_f, s8, s9)) | node18(c_e_h_1, c_f, s8, s9) | node17(c_e_h_1, c_f, s8))),
% 295.02/187.58 inference(rewrite,[status(thm)],[])).
% 295.02/187.58 tff(29107,plain,
% 295.02/187.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s8) | node18(c_e_h_1, c_f, s8, s9) | (~node19(c_e_h_1, c_f, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_f, s8, s9)) | node18(c_e_h_1, c_f, s8, s9) | node17(c_e_h_1, c_f, s8)))),
% 295.02/187.58 inference(monotonicity,[status(thm)],[29106])).
% 295.02/187.58 tff(29108,plain,
% 295.02/187.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s8) | node18(c_e_h_1, c_f, s8, s9) | (~node19(c_e_h_1, c_f, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s8, s9)) | node18(c_e_h_1, c_f, s8, s9) | node17(c_e_h_1, c_f, s8))),
% 295.02/187.58 inference(transitivity,[status(thm)],[29107, 29105])).
% 295.02/187.58 tff(29109,plain,
% 295.02/187.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s8) | node18(c_e_h_1, c_f, s8, s9) | (~node19(c_e_h_1, c_f, s8, s9)))),
% 295.02/187.58 inference(quant_inst,[status(thm)],[])).
% 295.02/187.58 tff(29110,plain,
% 295.02/187.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s8, s9)) | node18(c_e_h_1, c_f, s8, s9) | node17(c_e_h_1, c_f, s8)),
% 295.02/187.58 inference(modus_ponens,[status(thm)],[29109, 29108])).
% 295.02/187.58 tff(29111,plain,
% 295.02/187.58 (node18(c_e_h_1, c_f, s8, s9) | node17(c_e_h_1, c_f, s8)),
% 295.02/187.58 inference(unit_resolution,[status(thm)],[29110, 776, 29063])).
% 295.02/187.58 tff(29112,plain,
% 295.02/187.58 (node18(c_e_h_1, c_f, s8, s9)),
% 295.02/187.58 inference(unit_resolution,[status(thm)],[29111, 29104])).
% 295.02/187.58 tff(29113,plain,
% 295.02/187.58 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s9)) | m_c_h_element_v_out(c_e_h_1, c_f, s8) | (~node18(c_e_h_1, c_f, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s9)) | m_c_h_element_v_out(c_e_h_1, c_f, s8) | (~node18(c_e_h_1, c_f, s8, s9)))),
% 295.02/187.58 inference(rewrite,[status(thm)],[])).
% 295.02/187.58 tff(29114,plain,
% 295.02/187.58 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s9)) | m_c_h_element_v_out(c_e_h_1, c_f, s8) | (~node18(c_e_h_1, c_f, s8, s9)))),
% 295.02/187.59 inference(quant_inst,[status(thm)],[])).
% 295.02/187.59 tff(29115,plain,
% 295.02/187.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s9)) | m_c_h_element_v_out(c_e_h_1, c_f, s8) | (~node18(c_e_h_1, c_f, s8, s9))),
% 295.02/187.59 inference(modus_ponens,[status(thm)],[29114, 29113])).
% 295.02/187.59 tff(29116,plain,
% 295.02/187.59 ($false),
% 295.02/187.59 inference(unit_resolution,[status(thm)],[29115, 753, 29041, 29112, 29040])).
% 295.02/187.59 tff(29117,plain,((~m_c_h_element_v_out(c_e_h_1, c_f, s9)) | m_c_h_element_v_out(c_e_h_1, c_f, s8) | m_c_h_element_v_in1(c_e_h_1, c_f, s8)), inference(lemma,lemma(discharge,[]))).
% 295.02/187.59 tff(29118,plain,
% 295.02/187.59 (m_c_h_element_v_in1(c_e_h_1, c_f, s8)),
% 295.02/187.59 inference(unit_resolution,[status(thm)],[29117, 29041, 29040])).
% 295.02/187.59 tff(29119,plain,
% 295.02/187.59 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s8)) | m_and_h_gate_v_out(c_e_h_1, c_i, s8))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s8)) | m_and_h_gate_v_out(c_e_h_1, c_i, s8))),
% 295.02/187.59 inference(rewrite,[status(thm)],[])).
% 295.02/187.59 tff(29120,plain,
% 295.02/187.59 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s8)) | m_and_h_gate_v_out(c_e_h_1, c_i, s8))),
% 295.02/187.59 inference(quant_inst,[status(thm)],[])).
% 295.02/187.59 tff(29121,plain,
% 295.02/187.59 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s8)) | m_and_h_gate_v_out(c_e_h_1, c_i, s8)),
% 295.02/187.59 inference(modus_ponens,[status(thm)],[29120, 29119])).
% 295.02/187.59 tff(29122,plain,
% 295.02/187.59 (~m_c_h_element_v_in2(c_e_h_1, c_f, s8)),
% 295.02/187.59 inference(unit_resolution,[status(thm)],[29121, 2143, 22917])).
% 295.02/187.59 tff(29123,plain,
% 295.02/187.59 ((~m_c_h_element_v_in1(c_e_h_1, c_f, s8)) | (~node17(c_e_h_1, c_f, s8))),
% 295.02/187.59 inference(unit_resolution,[status(thm)],[29082, 919, 29122])).
% 295.02/187.59 tff(29124,plain,
% 295.02/187.59 (~node17(c_e_h_1, c_f, s8)),
% 295.02/187.59 inference(unit_resolution,[status(thm)],[29123, 29118])).
% 295.02/187.59 tff(29125,plain,
% 295.02/187.59 (node18(c_e_h_1, c_f, s8, s9)),
% 295.02/187.59 inference(unit_resolution,[status(thm)],[29111, 29124])).
% 295.02/187.59 tff(29126,plain,
% 295.02/187.59 ($false),
% 295.02/187.59 inference(unit_resolution,[status(thm)],[29115, 753, 29041, 29125, 29040])).
% 295.02/187.59 tff(29127,plain,((~m_c_h_element_v_out(c_e_h_1, c_f, s9)) | m_c_h_element_v_out(c_e_h_1, c_f, s8)), inference(lemma,lemma(discharge,[]))).
% 295.02/187.59 tff(29128,plain,
% 295.02/187.59 (~m_c_h_element_v_out(c_e_h_1, c_f, s9)),
% 295.02/187.59 inference(unit_resolution,[status(thm)],[29127, 25193])).
% 295.02/187.59 tff(29129,assumption,(~m_c_h_element_v_out(c_e_h_1, c_f, s9)), introduced(assumption)).
% 295.02/187.59 tff(29130,assumption,(m_c_h_element_v_out(c_e_h_1, c_f, s10)), introduced(assumption)).
% 295.02/187.59 tff(29131,assumption,(node18(c_e_h_1, c_f, s9, s10)), introduced(assumption)).
% 295.02/187.59 tff(29132,plain,
% 295.02/187.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_f, s9) | (~m_c_h_element_v_out(c_e_h_1, c_f, s10)) | (~node18(c_e_h_1, c_f, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s9) | (~m_c_h_element_v_out(c_e_h_1, c_f, s10)) | (~node18(c_e_h_1, c_f, s9, s10)))),
% 295.02/187.59 inference(rewrite,[status(thm)],[])).
% 295.02/187.59 tff(29133,plain,
% 295.02/187.59 (((~m_c_h_element_v_out(c_e_h_1, c_f, s10)) | m_c_h_element_v_out(c_e_h_1, c_f, s9) | (~node18(c_e_h_1, c_f, s9, s10))) <=> (m_c_h_element_v_out(c_e_h_1, c_f, s9) | (~m_c_h_element_v_out(c_e_h_1, c_f, s10)) | (~node18(c_e_h_1, c_f, s9, s10)))),
% 295.02/187.59 inference(rewrite,[status(thm)],[])).
% 295.02/187.59 tff(29134,plain,
% 295.02/187.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s10)) | m_c_h_element_v_out(c_e_h_1, c_f, s9) | (~node18(c_e_h_1, c_f, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_f, s9) | (~m_c_h_element_v_out(c_e_h_1, c_f, s10)) | (~node18(c_e_h_1, c_f, s9, s10))))),
% 295.02/187.59 inference(monotonicity,[status(thm)],[29133])).
% 295.02/187.59 tff(29135,plain,
% 295.02/187.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s10)) | m_c_h_element_v_out(c_e_h_1, c_f, s9) | (~node18(c_e_h_1, c_f, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s9) | (~m_c_h_element_v_out(c_e_h_1, c_f, s10)) | (~node18(c_e_h_1, c_f, s9, s10)))),
% 295.02/187.59 inference(transitivity,[status(thm)],[29134, 29132])).
% 295.02/187.59 tff(29136,plain,
% 295.02/187.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s10)) | m_c_h_element_v_out(c_e_h_1, c_f, s9) | (~node18(c_e_h_1, c_f, s9, s10)))),
% 295.02/187.59 inference(quant_inst,[status(thm)],[])).
% 295.02/187.59 tff(29137,plain,
% 295.02/187.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s9) | (~m_c_h_element_v_out(c_e_h_1, c_f, s10)) | (~node18(c_e_h_1, c_f, s9, s10))),
% 295.02/187.59 inference(modus_ponens,[status(thm)],[29136, 29135])).
% 295.02/187.59 tff(29138,plain,
% 295.02/187.59 ($false),
% 295.02/187.59 inference(unit_resolution,[status(thm)],[29137, 753, 29129, 29130, 29131])).
% 295.02/187.59 tff(29139,plain,((~node18(c_e_h_1, c_f, s9, s10)) | m_c_h_element_v_out(c_e_h_1, c_f, s9) | (~m_c_h_element_v_out(c_e_h_1, c_f, s10))), inference(lemma,lemma(discharge,[]))).
% 295.02/187.59 tff(29140,plain,
% 295.02/187.59 (~node18(c_e_h_1, c_f, s9, s10)),
% 295.02/187.59 inference(unit_resolution,[status(thm)],[29139, 29130, 29129])).
% 295.02/187.59 tff(29141,plain,
% 295.02/187.59 (~node18(c_e_h_1, c_f, s9, s10)),
% 295.02/187.59 inference(unit_resolution,[status(thm)],[29139, 29129, 29130])).
% 295.02/187.59 tff(29142,plain,
% 295.02/187.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s9, s10)) | node19(c_e_h_1, c_f, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s9, s10)) | node19(c_e_h_1, c_f, s9, s10))),
% 295.02/187.59 inference(rewrite,[status(thm)],[])).
% 295.02/187.59 tff(29143,plain,
% 295.02/187.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s9, s10)) | node19(c_e_h_1, c_f, s9, s10))),
% 295.02/187.59 inference(quant_inst,[status(thm)],[])).
% 295.02/187.59 tff(29144,plain,
% 295.02/187.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s9, s10)) | node19(c_e_h_1, c_f, s9, s10)),
% 295.02/187.59 inference(modus_ponens,[status(thm)],[29143, 29142])).
% 295.02/187.59 tff(29145,plain,
% 295.02/187.59 (node19(c_e_h_1, c_f, s9, s10)),
% 295.02/187.59 inference(unit_resolution,[status(thm)],[29144, 190, 7676])).
% 295.02/187.59 tff(29146,plain,
% 295.02/187.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_1, c_f, s9, s10) | (~node19(c_e_h_1, c_f, s9, s10)) | node17(c_e_h_1, c_f, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_f, s9, s10) | (~node19(c_e_h_1, c_f, s9, s10)) | node17(c_e_h_1, c_f, s9))),
% 295.02/187.59 inference(rewrite,[status(thm)],[])).
% 295.02/187.59 tff(29147,plain,
% 295.02/187.59 ((node17(c_e_h_1, c_f, s9) | node18(c_e_h_1, c_f, s9, s10) | (~node19(c_e_h_1, c_f, s9, s10))) <=> (node18(c_e_h_1, c_f, s9, s10) | (~node19(c_e_h_1, c_f, s9, s10)) | node17(c_e_h_1, c_f, s9))),
% 295.02/187.59 inference(rewrite,[status(thm)],[])).
% 295.02/187.59 tff(29148,plain,
% 295.02/187.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s9) | node18(c_e_h_1, c_f, s9, s10) | (~node19(c_e_h_1, c_f, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_1, c_f, s9, s10) | (~node19(c_e_h_1, c_f, s9, s10)) | node17(c_e_h_1, c_f, s9)))),
% 295.02/187.59 inference(monotonicity,[status(thm)],[29147])).
% 295.02/187.59 tff(29149,plain,
% 295.02/187.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s9) | node18(c_e_h_1, c_f, s9, s10) | (~node19(c_e_h_1, c_f, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_f, s9, s10) | (~node19(c_e_h_1, c_f, s9, s10)) | node17(c_e_h_1, c_f, s9))),
% 295.02/187.59 inference(transitivity,[status(thm)],[29148, 29146])).
% 295.02/187.59 tff(29150,plain,
% 295.02/187.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s9) | node18(c_e_h_1, c_f, s9, s10) | (~node19(c_e_h_1, c_f, s9, s10)))),
% 295.02/187.59 inference(quant_inst,[status(thm)],[])).
% 295.02/187.59 tff(29151,plain,
% 295.02/187.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_f, s9, s10) | (~node19(c_e_h_1, c_f, s9, s10)) | node17(c_e_h_1, c_f, s9)),
% 295.02/187.59 inference(modus_ponens,[status(thm)],[29150, 29149])).
% 295.02/187.59 tff(29152,plain,
% 295.02/187.59 (node18(c_e_h_1, c_f, s9, s10) | node17(c_e_h_1, c_f, s9)),
% 295.02/187.59 inference(unit_resolution,[status(thm)],[29151, 776, 29145])).
% 295.02/187.59 tff(29153,plain,
% 295.02/187.59 (node17(c_e_h_1, c_f, s9)),
% 295.02/187.59 inference(unit_resolution,[status(thm)],[29152, 29141])).
% 295.02/187.59 tff(29154,assumption,(node15(c_e_h_1, c_f, s9, s10)), introduced(assumption)).
% 295.02/187.59 tff(29155,plain,
% 295.02/187.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s10)) | (~node15(c_e_h_1, c_f, s9, s10)) | m_c_h_element_v_out(c_e_h_1, c_f, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s10)) | (~node15(c_e_h_1, c_f, s9, s10)) | m_c_h_element_v_out(c_e_h_1, c_f, s9))),
% 295.02/187.59 inference(rewrite,[status(thm)],[])).
% 295.02/187.59 tff(29156,plain,
% 295.02/187.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s10)) | (~node15(c_e_h_1, c_f, s9, s10)) | m_c_h_element_v_out(c_e_h_1, c_f, s9))),
% 295.02/187.59 inference(quant_inst,[status(thm)],[])).
% 295.02/187.59 tff(29157,plain,
% 295.02/187.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s10)) | (~node15(c_e_h_1, c_f, s9, s10)) | m_c_h_element_v_out(c_e_h_1, c_f, s9)),
% 295.02/187.59 inference(modus_ponens,[status(thm)],[29156, 29155])).
% 295.02/187.59 tff(29158,plain,
% 295.02/187.59 ($false),
% 295.02/187.59 inference(unit_resolution,[status(thm)],[29157, 147, 29129, 29130, 29154])).
% 295.02/187.59 tff(29159,plain,((~node15(c_e_h_1, c_f, s9, s10)) | m_c_h_element_v_out(c_e_h_1, c_f, s9) | (~m_c_h_element_v_out(c_e_h_1, c_f, s10))), inference(lemma,lemma(discharge,[]))).
% 295.02/187.59 tff(29160,plain,
% 295.02/187.59 (~node15(c_e_h_1, c_f, s9, s10)),
% 295.02/187.59 inference(unit_resolution,[status(thm)],[29159, 29129, 29130])).
% 295.02/187.59 tff(29161,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_f, s9)), introduced(assumption)).
% 295.02/187.59 tff(29162,assumption,(node17(c_e_h_1, c_f, s9)), introduced(assumption)).
% 295.02/187.59 tff(29163,plain,
% 295.02/187.59 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s9)) | m_c_h_element_v_in2(c_e_h_1, c_f, s9) | (~node17(c_e_h_1, c_f, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s9)) | m_c_h_element_v_in2(c_e_h_1, c_f, s9) | (~node17(c_e_h_1, c_f, s9)))),
% 295.02/187.59 inference(rewrite,[status(thm)],[])).
% 295.02/187.59 tff(29164,plain,
% 295.02/187.59 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s9)) | m_c_h_element_v_in2(c_e_h_1, c_f, s9) | (~node17(c_e_h_1, c_f, s9)))),
% 295.02/187.59 inference(quant_inst,[status(thm)],[])).
% 295.02/187.59 tff(29165,plain,
% 295.02/187.60 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s9)) | m_c_h_element_v_in2(c_e_h_1, c_f, s9) | (~node17(c_e_h_1, c_f, s9))),
% 295.02/187.60 inference(modus_ponens,[status(thm)],[29164, 29163])).
% 295.02/187.60 tff(29166,plain,
% 295.02/187.60 ((~m_c_h_element_v_in1(c_e_h_1, c_f, s9)) | m_c_h_element_v_in2(c_e_h_1, c_f, s9)),
% 295.02/187.60 inference(unit_resolution,[status(thm)],[29165, 919, 29162])).
% 295.02/187.60 tff(29167,plain,
% 295.02/187.60 (~m_c_h_element_v_in1(c_e_h_1, c_f, s9)),
% 295.02/187.60 inference(unit_resolution,[status(thm)],[29166, 29161])).
% 295.02/187.60 tff(29168,assumption,(~node15(c_e_h_1, c_f, s9, s10)), introduced(assumption)).
% 295.02/187.60 tff(29169,plain,
% 295.02/187.60 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s9)) | m_c_h_element_v_in1(c_e_h_1, c_f, s9) | m_c_h_element_v_in2(c_e_h_1, c_f, s9))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s9)) | m_c_h_element_v_in1(c_e_h_1, c_f, s9) | m_c_h_element_v_in2(c_e_h_1, c_f, s9))),
% 295.02/187.60 inference(rewrite,[status(thm)],[])).
% 295.02/187.60 tff(29170,plain,
% 295.02/187.60 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s9)) | m_c_h_element_v_in1(c_e_h_1, c_f, s9) | m_c_h_element_v_in2(c_e_h_1, c_f, s9))),
% 295.02/187.60 inference(quant_inst,[status(thm)],[])).
% 295.02/187.60 tff(29171,plain,
% 295.02/187.60 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s9)) | m_c_h_element_v_in1(c_e_h_1, c_f, s9) | m_c_h_element_v_in2(c_e_h_1, c_f, s9)),
% 295.02/187.60 inference(modus_ponens,[status(thm)],[29170, 29169])).
% 295.02/187.60 tff(29172,plain,
% 295.02/187.60 (~node16(c_e_h_1, c_f, s9)),
% 295.02/187.60 inference(unit_resolution,[status(thm)],[29171, 178, 29161, 29167])).
% 295.02/187.60 tff(29173,plain,
% 295.02/187.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_f, s9, s10)) | node16(c_e_h_1, c_f, s9) | node14(c_e_h_1, c_f, s9, s10) | node15(c_e_h_1, c_f, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s9, s10)) | node16(c_e_h_1, c_f, s9) | node14(c_e_h_1, c_f, s9, s10) | node15(c_e_h_1, c_f, s9, s10))),
% 295.02/187.60 inference(rewrite,[status(thm)],[])).
% 295.02/187.60 tff(29174,plain,
% 295.02/187.60 ((node16(c_e_h_1, c_f, s9) | node14(c_e_h_1, c_f, s9, s10) | node15(c_e_h_1, c_f, s9, s10) | (~node19(c_e_h_1, c_f, s9, s10))) <=> ((~node19(c_e_h_1, c_f, s9, s10)) | node16(c_e_h_1, c_f, s9) | node14(c_e_h_1, c_f, s9, s10) | node15(c_e_h_1, c_f, s9, s10))),
% 295.02/187.60 inference(rewrite,[status(thm)],[])).
% 295.02/187.60 tff(29175,plain,
% 295.02/187.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s9) | node14(c_e_h_1, c_f, s9, s10) | node15(c_e_h_1, c_f, s9, s10) | (~node19(c_e_h_1, c_f, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_f, s9, s10)) | node16(c_e_h_1, c_f, s9) | node14(c_e_h_1, c_f, s9, s10) | node15(c_e_h_1, c_f, s9, s10)))),
% 295.02/187.60 inference(monotonicity,[status(thm)],[29174])).
% 295.02/187.60 tff(29176,plain,
% 295.02/187.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s9) | node14(c_e_h_1, c_f, s9, s10) | node15(c_e_h_1, c_f, s9, s10) | (~node19(c_e_h_1, c_f, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s9, s10)) | node16(c_e_h_1, c_f, s9) | node14(c_e_h_1, c_f, s9, s10) | node15(c_e_h_1, c_f, s9, s10))),
% 295.02/187.60 inference(transitivity,[status(thm)],[29175, 29173])).
% 295.02/187.60 tff(29177,plain,
% 295.02/187.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s9) | node14(c_e_h_1, c_f, s9, s10) | node15(c_e_h_1, c_f, s9, s10) | (~node19(c_e_h_1, c_f, s9, s10)))),
% 295.02/187.60 inference(quant_inst,[status(thm)],[])).
% 295.02/187.60 tff(29178,plain,
% 295.02/187.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s9, s10)) | node16(c_e_h_1, c_f, s9) | node14(c_e_h_1, c_f, s9, s10) | node15(c_e_h_1, c_f, s9, s10)),
% 295.02/187.60 inference(modus_ponens,[status(thm)],[29177, 29176])).
% 295.02/187.60 tff(29179,plain,
% 295.02/187.60 (node16(c_e_h_1, c_f, s9) | node14(c_e_h_1, c_f, s9, s10) | node15(c_e_h_1, c_f, s9, s10)),
% 295.02/187.60 inference(unit_resolution,[status(thm)],[29178, 204, 29145])).
% 295.02/187.60 tff(29180,plain,
% 295.02/187.60 (node14(c_e_h_1, c_f, s9, s10)),
% 295.02/187.60 inference(unit_resolution,[status(thm)],[29179, 29172, 29168])).
% 295.02/187.60 tff(29181,plain,
% 295.02/187.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s9, s10)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s10)) | m_c_h_element_v_in1(c_e_h_1, c_f, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_1, c_f, s9, s10)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s10)) | m_c_h_element_v_in1(c_e_h_1, c_f, s9))),
% 295.02/187.60 inference(rewrite,[status(thm)],[])).
% 295.02/187.60 tff(29182,plain,
% 295.02/187.60 (((~node14(c_e_h_1, c_f, s9, s10)) | m_c_h_element_v_in1(c_e_h_1, c_f, s9) | (~m_c_h_element_v_out(c_e_h_1, c_f, s10))) <=> ((~node14(c_e_h_1, c_f, s9, s10)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s10)) | m_c_h_element_v_in1(c_e_h_1, c_f, s9))),
% 295.02/187.60 inference(rewrite,[status(thm)],[])).
% 295.02/187.60 tff(29183,plain,
% 295.02/187.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s9, s10)) | m_c_h_element_v_in1(c_e_h_1, c_f, s9) | (~m_c_h_element_v_out(c_e_h_1, c_f, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s9, s10)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s10)) | m_c_h_element_v_in1(c_e_h_1, c_f, s9)))),
% 295.02/187.60 inference(monotonicity,[status(thm)],[29182])).
% 295.02/187.60 tff(29184,plain,
% 295.02/187.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s9, s10)) | m_c_h_element_v_in1(c_e_h_1, c_f, s9) | (~m_c_h_element_v_out(c_e_h_1, c_f, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_1, c_f, s9, s10)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s10)) | m_c_h_element_v_in1(c_e_h_1, c_f, s9))),
% 295.02/187.60 inference(transitivity,[status(thm)],[29183, 29181])).
% 295.02/187.60 tff(29185,plain,
% 295.02/187.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s9, s10)) | m_c_h_element_v_in1(c_e_h_1, c_f, s9) | (~m_c_h_element_v_out(c_e_h_1, c_f, s10)))),
% 295.02/187.60 inference(quant_inst,[status(thm)],[])).
% 295.02/187.60 tff(29186,plain,
% 295.02/187.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~node14(c_e_h_1, c_f, s9, s10)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s10)) | m_c_h_element_v_in1(c_e_h_1, c_f, s9)),
% 295.02/187.60 inference(modus_ponens,[status(thm)],[29185, 29184])).
% 295.02/187.60 tff(29187,plain,
% 295.02/187.60 ($false),
% 295.02/187.60 inference(unit_resolution,[status(thm)],[29186, 223, 29130, 29180, 29167])).
% 295.02/187.60 tff(29188,plain,(m_c_h_element_v_in2(c_e_h_1, c_f, s9) | (~m_c_h_element_v_out(c_e_h_1, c_f, s10)) | node15(c_e_h_1, c_f, s9, s10) | (~node17(c_e_h_1, c_f, s9))), inference(lemma,lemma(discharge,[]))).
% 295.02/187.60 tff(29189,plain,
% 295.02/187.60 (m_c_h_element_v_in2(c_e_h_1, c_f, s9)),
% 295.02/187.60 inference(unit_resolution,[status(thm)],[29188, 29153, 29130, 29160])).
% 295.02/187.61 tff(29190,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_f, s9)), introduced(assumption)).
% 295.02/187.61 tff(29191,plain,
% 295.02/187.61 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s9)) | m_c_h_element_v_in1(c_e_h_1, c_f, s9) | (~node17(c_e_h_1, c_f, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s9)) | m_c_h_element_v_in1(c_e_h_1, c_f, s9) | (~node17(c_e_h_1, c_f, s9)))),
% 295.02/187.61 inference(rewrite,[status(thm)],[])).
% 295.02/187.61 tff(29192,plain,
% 295.02/187.61 ((m_c_h_element_v_in1(c_e_h_1, c_f, s9) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s9)) | (~node17(c_e_h_1, c_f, s9))) <=> ((~m_c_h_element_v_in2(c_e_h_1, c_f, s9)) | m_c_h_element_v_in1(c_e_h_1, c_f, s9) | (~node17(c_e_h_1, c_f, s9)))),
% 295.02/187.61 inference(rewrite,[status(thm)],[])).
% 295.02/187.61 tff(29193,plain,
% 295.02/187.61 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s9) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s9)) | (~node17(c_e_h_1, c_f, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s9)) | m_c_h_element_v_in1(c_e_h_1, c_f, s9) | (~node17(c_e_h_1, c_f, s9))))),
% 295.02/187.61 inference(monotonicity,[status(thm)],[29192])).
% 295.02/187.61 tff(29194,plain,
% 295.02/187.61 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s9) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s9)) | (~node17(c_e_h_1, c_f, s9)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s9)) | m_c_h_element_v_in1(c_e_h_1, c_f, s9) | (~node17(c_e_h_1, c_f, s9)))),
% 295.02/187.61 inference(transitivity,[status(thm)],[29193, 29191])).
% 295.02/187.61 tff(29195,plain,
% 295.02/187.61 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s9) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s9)) | (~node17(c_e_h_1, c_f, s9)))),
% 295.02/187.61 inference(quant_inst,[status(thm)],[])).
% 295.02/187.61 tff(29196,plain,
% 295.02/187.61 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s9)) | m_c_h_element_v_in1(c_e_h_1, c_f, s9) | (~node17(c_e_h_1, c_f, s9))),
% 295.02/187.61 inference(modus_ponens,[status(thm)],[29195, 29194])).
% 295.02/187.61 tff(29197,plain,
% 295.02/187.61 ((~m_c_h_element_v_in2(c_e_h_1, c_f, s9)) | (~node17(c_e_h_1, c_f, s9))),
% 295.02/187.61 inference(unit_resolution,[status(thm)],[29196, 859, 29190])).
% 295.02/187.61 tff(29198,plain,
% 295.02/187.61 ($false),
% 295.02/187.61 inference(unit_resolution,[status(thm)],[29197, 29189, 29153])).
% 295.02/187.61 tff(29199,plain,(m_c_h_element_v_out(c_e_h_1, c_f, s9) | m_c_h_element_v_in1(c_e_h_1, c_f, s9) | (~m_c_h_element_v_out(c_e_h_1, c_f, s10))), inference(lemma,lemma(discharge,[]))).
% 295.02/187.61 tff(29200,plain,
% 295.02/187.61 (m_c_h_element_v_in1(c_e_h_1, c_f, s9)),
% 295.02/187.61 inference(unit_resolution,[status(thm)],[29199, 29130, 29129])).
% 295.02/187.61 tff(29201,plain,
% 295.02/187.61 ((~m_c_h_element_v_in1(c_e_h_1, c_f, s9)) | (~node17(c_e_h_1, c_f, s9))),
% 295.02/187.61 inference(unit_resolution,[status(thm)],[29165, 919, 29161])).
% 295.02/187.61 tff(29202,plain,
% 295.02/187.61 (~node17(c_e_h_1, c_f, s9)),
% 295.02/187.61 inference(unit_resolution,[status(thm)],[29201, 29200])).
% 295.02/187.61 tff(29203,plain,
% 295.02/187.61 ($false),
% 295.02/187.61 inference(unit_resolution,[status(thm)],[29152, 29202, 29140])).
% 295.02/187.61 tff(29204,plain,((~m_c_h_element_v_out(c_e_h_1, c_f, s10)) | m_c_h_element_v_in2(c_e_h_1, c_f, s9) | m_c_h_element_v_out(c_e_h_1, c_f, s9)), inference(lemma,lemma(discharge,[]))).
% 295.02/187.61 tff(29205,plain,
% 295.02/187.61 ((~m_c_h_element_v_out(c_e_h_1, c_f, s10)) | m_c_h_element_v_in2(c_e_h_1, c_f, s9)),
% 295.02/187.61 inference(unit_resolution,[status(thm)],[29204, 29128])).
% 295.02/187.61 tff(29206,plain,
% 295.02/187.61 (~m_c_h_element_v_out(c_e_h_1, c_f, s10)),
% 295.02/187.61 inference(unit_resolution,[status(thm)],[29205, 29039])).
% 295.11/187.61 tff(29207,assumption,(m_c_h_element_v_out(c_e_h_1, c_f, s11)), introduced(assumption)).
% 295.11/187.61 tff(29208,assumption,(~m_c_h_element_v_out(c_e_h_1, c_f, s10)), introduced(assumption)).
% 295.11/187.61 tff(29209,assumption,(node18(c_e_h_1, c_f, s10, s11)), introduced(assumption)).
% 295.11/187.61 tff(29210,plain,
% 295.11/187.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_f, s10) | (~m_c_h_element_v_out(c_e_h_1, c_f, s11)) | (~node18(c_e_h_1, c_f, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s10) | (~m_c_h_element_v_out(c_e_h_1, c_f, s11)) | (~node18(c_e_h_1, c_f, s10, s11)))),
% 295.11/187.61 inference(rewrite,[status(thm)],[])).
% 295.11/187.61 tff(29211,plain,
% 295.11/187.61 (((~m_c_h_element_v_out(c_e_h_1, c_f, s11)) | m_c_h_element_v_out(c_e_h_1, c_f, s10) | (~node18(c_e_h_1, c_f, s10, s11))) <=> (m_c_h_element_v_out(c_e_h_1, c_f, s10) | (~m_c_h_element_v_out(c_e_h_1, c_f, s11)) | (~node18(c_e_h_1, c_f, s10, s11)))),
% 295.11/187.61 inference(rewrite,[status(thm)],[])).
% 295.11/187.61 tff(29212,plain,
% 295.11/187.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s11)) | m_c_h_element_v_out(c_e_h_1, c_f, s10) | (~node18(c_e_h_1, c_f, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_f, s10) | (~m_c_h_element_v_out(c_e_h_1, c_f, s11)) | (~node18(c_e_h_1, c_f, s10, s11))))),
% 295.11/187.61 inference(monotonicity,[status(thm)],[29211])).
% 295.11/187.61 tff(29213,plain,
% 295.11/187.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s11)) | m_c_h_element_v_out(c_e_h_1, c_f, s10) | (~node18(c_e_h_1, c_f, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s10) | (~m_c_h_element_v_out(c_e_h_1, c_f, s11)) | (~node18(c_e_h_1, c_f, s10, s11)))),
% 295.11/187.61 inference(transitivity,[status(thm)],[29212, 29210])).
% 295.11/187.61 tff(29214,plain,
% 295.11/187.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s11)) | m_c_h_element_v_out(c_e_h_1, c_f, s10) | (~node18(c_e_h_1, c_f, s10, s11)))),
% 295.11/187.61 inference(quant_inst,[status(thm)],[])).
% 295.11/187.61 tff(29215,plain,
% 295.11/187.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s10) | (~m_c_h_element_v_out(c_e_h_1, c_f, s11)) | (~node18(c_e_h_1, c_f, s10, s11))),
% 295.11/187.61 inference(modus_ponens,[status(thm)],[29214, 29213])).
% 295.11/187.61 tff(29216,plain,
% 295.11/187.61 ($false),
% 295.11/187.61 inference(unit_resolution,[status(thm)],[29215, 753, 29207, 29208, 29209])).
% 295.11/187.61 tff(29217,plain,((~node18(c_e_h_1, c_f, s10, s11)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s11)) | m_c_h_element_v_out(c_e_h_1, c_f, s10)), inference(lemma,lemma(discharge,[]))).
% 295.11/187.61 tff(29218,plain,
% 295.11/187.61 (~node18(c_e_h_1, c_f, s10, s11)),
% 295.11/187.61 inference(unit_resolution,[status(thm)],[29217, 29208, 29207])).
% 295.11/187.61 tff(29219,plain,
% 295.11/187.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s10, s11)) | node19(c_e_h_1, c_f, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s10, s11)) | node19(c_e_h_1, c_f, s10, s11))),
% 295.11/187.61 inference(rewrite,[status(thm)],[])).
% 295.11/187.61 tff(29220,plain,
% 295.11/187.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s10, s11)) | node19(c_e_h_1, c_f, s10, s11))),
% 295.11/187.61 inference(quant_inst,[status(thm)],[])).
% 295.11/187.61 tff(29221,plain,
% 295.11/187.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s10, s11)) | node19(c_e_h_1, c_f, s10, s11)),
% 295.11/187.61 inference(modus_ponens,[status(thm)],[29220, 29219])).
% 295.11/187.61 tff(29222,plain,
% 295.11/187.61 (node19(c_e_h_1, c_f, s10, s11)),
% 295.11/187.61 inference(unit_resolution,[status(thm)],[29221, 190, 7748])).
% 295.11/187.61 tff(29223,plain,
% 295.11/187.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s10) | (~node19(c_e_h_1, c_f, s10, s11)) | node18(c_e_h_1, c_f, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_f, s10) | (~node19(c_e_h_1, c_f, s10, s11)) | node18(c_e_h_1, c_f, s10, s11))),
% 295.11/187.61 inference(rewrite,[status(thm)],[])).
% 295.11/187.61 tff(29224,plain,
% 295.11/187.61 ((node17(c_e_h_1, c_f, s10) | node18(c_e_h_1, c_f, s10, s11) | (~node19(c_e_h_1, c_f, s10, s11))) <=> (node17(c_e_h_1, c_f, s10) | (~node19(c_e_h_1, c_f, s10, s11)) | node18(c_e_h_1, c_f, s10, s11))),
% 295.11/187.61 inference(rewrite,[status(thm)],[])).
% 295.11/187.61 tff(29225,plain,
% 295.11/187.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s10) | node18(c_e_h_1, c_f, s10, s11) | (~node19(c_e_h_1, c_f, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s10) | (~node19(c_e_h_1, c_f, s10, s11)) | node18(c_e_h_1, c_f, s10, s11)))),
% 295.11/187.61 inference(monotonicity,[status(thm)],[29224])).
% 295.11/187.61 tff(29226,plain,
% 295.11/187.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s10) | node18(c_e_h_1, c_f, s10, s11) | (~node19(c_e_h_1, c_f, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_f, s10) | (~node19(c_e_h_1, c_f, s10, s11)) | node18(c_e_h_1, c_f, s10, s11))),
% 295.11/187.61 inference(transitivity,[status(thm)],[29225, 29223])).
% 295.11/187.61 tff(29227,plain,
% 295.11/187.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s10) | node18(c_e_h_1, c_f, s10, s11) | (~node19(c_e_h_1, c_f, s10, s11)))),
% 295.11/187.61 inference(quant_inst,[status(thm)],[])).
% 295.11/187.61 tff(29228,plain,
% 295.11/187.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_f, s10) | (~node19(c_e_h_1, c_f, s10, s11)) | node18(c_e_h_1, c_f, s10, s11)),
% 295.11/187.61 inference(modus_ponens,[status(thm)],[29227, 29226])).
% 295.11/187.61 tff(29229,plain,
% 295.11/187.61 (node17(c_e_h_1, c_f, s10) | node18(c_e_h_1, c_f, s10, s11)),
% 295.11/187.61 inference(unit_resolution,[status(thm)],[29228, 776, 29222])).
% 295.11/187.61 tff(29230,plain,
% 295.11/187.61 (node17(c_e_h_1, c_f, s10)),
% 295.11/187.61 inference(unit_resolution,[status(thm)],[29229, 29218])).
% 295.11/187.61 tff(29231,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_f, s10)), introduced(assumption)).
% 295.11/187.61 tff(29232,plain,
% 295.11/187.61 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_f, s10) | (~node17(c_e_h_1, c_f, s10)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_f, s10) | (~node17(c_e_h_1, c_f, s10)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s10)))),
% 295.11/187.61 inference(rewrite,[status(thm)],[])).
% 295.11/187.61 tff(29233,plain,
% 295.11/187.61 (((~m_c_h_element_v_in1(c_e_h_1, c_f, s10)) | m_c_h_element_v_in2(c_e_h_1, c_f, s10) | (~node17(c_e_h_1, c_f, s10))) <=> (m_c_h_element_v_in2(c_e_h_1, c_f, s10) | (~node17(c_e_h_1, c_f, s10)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s10)))),
% 295.11/187.61 inference(rewrite,[status(thm)],[])).
% 295.11/187.61 tff(29234,plain,
% 295.11/187.61 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s10)) | m_c_h_element_v_in2(c_e_h_1, c_f, s10) | (~node17(c_e_h_1, c_f, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_f, s10) | (~node17(c_e_h_1, c_f, s10)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s10))))),
% 295.11/187.62 inference(monotonicity,[status(thm)],[29233])).
% 295.11/187.62 tff(29235,plain,
% 295.11/187.62 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s10)) | m_c_h_element_v_in2(c_e_h_1, c_f, s10) | (~node17(c_e_h_1, c_f, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_f, s10) | (~node17(c_e_h_1, c_f, s10)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s10)))),
% 295.11/187.62 inference(transitivity,[status(thm)],[29234, 29232])).
% 295.11/187.62 tff(29236,plain,
% 295.11/187.62 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s10)) | m_c_h_element_v_in2(c_e_h_1, c_f, s10) | (~node17(c_e_h_1, c_f, s10)))),
% 295.11/187.62 inference(quant_inst,[status(thm)],[])).
% 295.11/187.62 tff(29237,plain,
% 295.11/187.62 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_f, s10) | (~node17(c_e_h_1, c_f, s10)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s10))),
% 295.11/187.62 inference(modus_ponens,[status(thm)],[29236, 29235])).
% 295.11/187.62 tff(29238,plain,
% 295.11/187.62 ((~node17(c_e_h_1, c_f, s10)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s10))),
% 295.11/187.62 inference(unit_resolution,[status(thm)],[29237, 919, 29231])).
% 295.11/187.62 tff(29239,plain,
% 295.11/187.62 (~m_c_h_element_v_in1(c_e_h_1, c_f, s10)),
% 295.11/187.62 inference(unit_resolution,[status(thm)],[29238, 29230])).
% 295.11/187.62 tff(29240,assumption,(node15(c_e_h_1, c_f, s10, s11)), introduced(assumption)).
% 295.11/187.62 tff(29241,plain,
% 295.11/187.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s11)) | (~node15(c_e_h_1, c_f, s10, s11)) | m_c_h_element_v_out(c_e_h_1, c_f, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s11)) | (~node15(c_e_h_1, c_f, s10, s11)) | m_c_h_element_v_out(c_e_h_1, c_f, s10))),
% 295.11/187.62 inference(rewrite,[status(thm)],[])).
% 295.11/187.62 tff(29242,plain,
% 295.11/187.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s11)) | (~node15(c_e_h_1, c_f, s10, s11)) | m_c_h_element_v_out(c_e_h_1, c_f, s10))),
% 295.11/187.62 inference(quant_inst,[status(thm)],[])).
% 295.11/187.62 tff(29243,plain,
% 295.11/187.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s11)) | (~node15(c_e_h_1, c_f, s10, s11)) | m_c_h_element_v_out(c_e_h_1, c_f, s10)),
% 295.11/187.62 inference(modus_ponens,[status(thm)],[29242, 29241])).
% 295.11/187.62 tff(29244,plain,
% 295.11/187.62 ($false),
% 295.11/187.62 inference(unit_resolution,[status(thm)],[29243, 147, 29207, 29208, 29240])).
% 295.11/187.62 tff(29245,plain,((~node15(c_e_h_1, c_f, s10, s11)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s11)) | m_c_h_element_v_out(c_e_h_1, c_f, s10)), inference(lemma,lemma(discharge,[]))).
% 295.11/187.62 tff(29246,plain,
% 295.11/187.62 (~node15(c_e_h_1, c_f, s10, s11)),
% 295.11/187.62 inference(unit_resolution,[status(thm)],[29245, 29208, 29207])).
% 295.11/187.62 tff(29247,assumption,(node17(c_e_h_1, c_f, s10)), introduced(assumption)).
% 295.11/187.62 tff(29248,assumption,(node16(c_e_h_1, c_f, s10)), introduced(assumption)).
% 295.11/187.62 tff(29249,assumption,(m_c_h_element_v_in1(c_e_h_1, c_f, s10)), introduced(assumption)).
% 295.11/187.62 tff(29250,plain,
% 295.11/187.62 (m_c_h_element_v_in2(c_e_h_1, c_f, s10) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s10))),
% 295.11/187.62 inference(unit_resolution,[status(thm)],[29237, 919, 29247])).
% 295.11/187.62 tff(29251,plain,
% 295.11/187.62 (m_c_h_element_v_in2(c_e_h_1, c_f, s10)),
% 295.11/187.62 inference(unit_resolution,[status(thm)],[29250, 29249])).
% 295.11/187.62 tff(29252,plain,
% 295.11/187.62 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_f, s10)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s10)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~node16(c_e_h_1, c_f, s10)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s10)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s10)))),
% 295.11/187.62 inference(rewrite,[status(thm)],[])).
% 295.11/187.62 tff(29253,plain,
% 295.11/187.62 (((~node16(c_e_h_1, c_f, s10)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s10)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s10))) <=> ((~node16(c_e_h_1, c_f, s10)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s10)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s10)))),
% 295.11/187.62 inference(rewrite,[status(thm)],[])).
% 295.11/187.62 tff(29254,plain,
% 295.11/187.62 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_f, s10)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s10)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_f, s10)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s10)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s10))))),
% 295.11/187.62 inference(monotonicity,[status(thm)],[29253])).
% 295.11/187.62 tff(29255,plain,
% 295.11/187.62 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_f, s10)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s10)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~node16(c_e_h_1, c_f, s10)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s10)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s10)))),
% 295.11/187.62 inference(transitivity,[status(thm)],[29254, 29252])).
% 295.11/187.62 tff(29256,plain,
% 295.11/187.62 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_f, s10)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s10)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s10)))),
% 295.11/187.62 inference(quant_inst,[status(thm)],[])).
% 295.11/187.62 tff(29257,plain,
% 295.11/187.62 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~node16(c_e_h_1, c_f, s10)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s10)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s10))),
% 295.11/187.62 inference(modus_ponens,[status(thm)],[29256, 29255])).
% 295.11/187.62 tff(29258,plain,
% 295.11/187.62 ((~m_c_h_element_v_in2(c_e_h_1, c_f, s10)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s10))),
% 295.11/187.62 inference(unit_resolution,[status(thm)],[29257, 2307, 29248])).
% 295.11/187.62 tff(29259,plain,
% 295.11/187.62 ($false),
% 295.11/187.62 inference(unit_resolution,[status(thm)],[29258, 29251, 29249])).
% 295.11/187.62 tff(29260,plain,((~m_c_h_element_v_in1(c_e_h_1, c_f, s10)) | (~node16(c_e_h_1, c_f, s10)) | (~node17(c_e_h_1, c_f, s10))), inference(lemma,lemma(discharge,[]))).
% 295.11/187.62 tff(29261,plain,
% 295.11/187.62 (~m_c_h_element_v_in1(c_e_h_1, c_f, s10)),
% 295.11/187.62 inference(unit_resolution,[status(thm)],[29260, 29248, 29247])).
% 295.11/187.62 tff(29262,plain,
% 295.11/187.62 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_f, s10)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s10)) | m_c_h_element_v_in1(c_e_h_1, c_f, s10))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_f, s10)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s10)) | m_c_h_element_v_in1(c_e_h_1, c_f, s10))),
% 295.11/187.62 inference(rewrite,[status(thm)],[])).
% 295.11/187.62 tff(29263,plain,
% 295.11/187.62 ((m_c_h_element_v_in1(c_e_h_1, c_f, s10) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s10)) | (~node17(c_e_h_1, c_f, s10))) <=> ((~node17(c_e_h_1, c_f, s10)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s10)) | m_c_h_element_v_in1(c_e_h_1, c_f, s10))),
% 295.11/187.62 inference(rewrite,[status(thm)],[])).
% 295.11/187.62 tff(29264,plain,
% 295.11/187.62 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s10) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s10)) | (~node17(c_e_h_1, c_f, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_f, s10)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s10)) | m_c_h_element_v_in1(c_e_h_1, c_f, s10)))),
% 295.11/187.62 inference(monotonicity,[status(thm)],[29263])).
% 295.11/187.62 tff(29265,plain,
% 295.11/187.62 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s10) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s10)) | (~node17(c_e_h_1, c_f, s10)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_f, s10)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s10)) | m_c_h_element_v_in1(c_e_h_1, c_f, s10))),
% 295.11/187.62 inference(transitivity,[status(thm)],[29264, 29262])).
% 295.11/187.62 tff(29266,plain,
% 295.11/187.62 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s10) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s10)) | (~node17(c_e_h_1, c_f, s10)))),
% 295.11/187.62 inference(quant_inst,[status(thm)],[])).
% 295.11/187.62 tff(29267,plain,
% 295.11/187.62 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_f, s10)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s10)) | m_c_h_element_v_in1(c_e_h_1, c_f, s10)),
% 295.11/187.62 inference(modus_ponens,[status(thm)],[29266, 29265])).
% 295.11/187.62 tff(29268,plain,
% 295.11/187.62 ((~m_c_h_element_v_in2(c_e_h_1, c_f, s10)) | m_c_h_element_v_in1(c_e_h_1, c_f, s10)),
% 295.11/187.62 inference(unit_resolution,[status(thm)],[29267, 859, 29247])).
% 295.11/187.62 tff(29269,plain,
% 295.11/187.62 (~m_c_h_element_v_in2(c_e_h_1, c_f, s10)),
% 295.11/187.62 inference(unit_resolution,[status(thm)],[29268, 29261])).
% 295.11/187.62 tff(29270,plain,
% 295.11/187.62 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s10)) | m_c_h_element_v_in1(c_e_h_1, c_f, s10) | m_c_h_element_v_in2(c_e_h_1, c_f, s10))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s10)) | m_c_h_element_v_in1(c_e_h_1, c_f, s10) | m_c_h_element_v_in2(c_e_h_1, c_f, s10))),
% 295.11/187.62 inference(rewrite,[status(thm)],[])).
% 295.11/187.62 tff(29271,plain,
% 295.11/187.62 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s10)) | m_c_h_element_v_in1(c_e_h_1, c_f, s10) | m_c_h_element_v_in2(c_e_h_1, c_f, s10))),
% 295.11/187.62 inference(quant_inst,[status(thm)],[])).
% 295.11/187.62 tff(29272,plain,
% 295.11/187.62 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s10)) | m_c_h_element_v_in1(c_e_h_1, c_f, s10) | m_c_h_element_v_in2(c_e_h_1, c_f, s10)),
% 295.11/187.62 inference(modus_ponens,[status(thm)],[29271, 29270])).
% 295.11/187.62 tff(29273,plain,
% 295.11/187.62 (m_c_h_element_v_in1(c_e_h_1, c_f, s10) | m_c_h_element_v_in2(c_e_h_1, c_f, s10)),
% 295.11/187.62 inference(unit_resolution,[status(thm)],[29272, 178, 29248])).
% 295.11/187.62 tff(29274,plain,
% 295.11/187.62 ($false),
% 295.11/187.62 inference(unit_resolution,[status(thm)],[29273, 29269, 29261])).
% 295.11/187.62 tff(29275,plain,((~node16(c_e_h_1, c_f, s10)) | (~node17(c_e_h_1, c_f, s10))), inference(lemma,lemma(discharge,[]))).
% 295.11/187.62 tff(29276,plain,
% 295.11/187.62 (~node16(c_e_h_1, c_f, s10)),
% 295.11/187.62 inference(unit_resolution,[status(thm)],[29275, 29230])).
% 295.11/187.62 tff(29277,plain,
% 295.11/187.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_1, c_f, s10, s11) | node16(c_e_h_1, c_f, s10) | node14(c_e_h_1, c_f, s10, s11) | (~node19(c_e_h_1, c_f, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_f, s10, s11) | node16(c_e_h_1, c_f, s10) | node14(c_e_h_1, c_f, s10, s11) | (~node19(c_e_h_1, c_f, s10, s11)))),
% 295.11/187.63 inference(rewrite,[status(thm)],[])).
% 295.11/187.63 tff(29278,plain,
% 295.11/187.63 ((node16(c_e_h_1, c_f, s10) | node14(c_e_h_1, c_f, s10, s11) | node15(c_e_h_1, c_f, s10, s11) | (~node19(c_e_h_1, c_f, s10, s11))) <=> (node15(c_e_h_1, c_f, s10, s11) | node16(c_e_h_1, c_f, s10) | node14(c_e_h_1, c_f, s10, s11) | (~node19(c_e_h_1, c_f, s10, s11)))),
% 295.11/187.63 inference(rewrite,[status(thm)],[])).
% 295.11/187.63 tff(29279,plain,
% 295.11/187.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s10) | node14(c_e_h_1, c_f, s10, s11) | node15(c_e_h_1, c_f, s10, s11) | (~node19(c_e_h_1, c_f, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_1, c_f, s10, s11) | node16(c_e_h_1, c_f, s10) | node14(c_e_h_1, c_f, s10, s11) | (~node19(c_e_h_1, c_f, s10, s11))))),
% 295.11/187.63 inference(monotonicity,[status(thm)],[29278])).
% 295.11/187.63 tff(29280,plain,
% 295.11/187.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s10) | node14(c_e_h_1, c_f, s10, s11) | node15(c_e_h_1, c_f, s10, s11) | (~node19(c_e_h_1, c_f, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_f, s10, s11) | node16(c_e_h_1, c_f, s10) | node14(c_e_h_1, c_f, s10, s11) | (~node19(c_e_h_1, c_f, s10, s11)))),
% 295.11/187.63 inference(transitivity,[status(thm)],[29279, 29277])).
% 295.11/187.63 tff(29281,plain,
% 295.11/187.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s10) | node14(c_e_h_1, c_f, s10, s11) | node15(c_e_h_1, c_f, s10, s11) | (~node19(c_e_h_1, c_f, s10, s11)))),
% 295.11/187.63 inference(quant_inst,[status(thm)],[])).
% 295.11/187.63 tff(29282,plain,
% 295.11/187.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_f, s10, s11) | node16(c_e_h_1, c_f, s10) | node14(c_e_h_1, c_f, s10, s11) | (~node19(c_e_h_1, c_f, s10, s11))),
% 295.11/187.63 inference(modus_ponens,[status(thm)],[29281, 29280])).
% 295.11/187.63 tff(29283,plain,
% 295.11/187.63 (node15(c_e_h_1, c_f, s10, s11) | node16(c_e_h_1, c_f, s10) | node14(c_e_h_1, c_f, s10, s11)),
% 295.11/187.63 inference(unit_resolution,[status(thm)],[29282, 204, 29222])).
% 295.11/187.63 tff(29284,plain,
% 295.11/187.63 (node14(c_e_h_1, c_f, s10, s11)),
% 295.11/187.63 inference(unit_resolution,[status(thm)],[29283, 29276, 29246])).
% 295.11/187.63 tff(29285,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_f, s10)), introduced(assumption)).
% 295.11/187.63 tff(29286,assumption,(node14(c_e_h_1, c_f, s10, s11)), introduced(assumption)).
% 295.11/187.63 tff(29287,plain,
% 295.11/187.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s11)) | m_c_h_element_v_in1(c_e_h_1, c_f, s10) | (~node14(c_e_h_1, c_f, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s11)) | m_c_h_element_v_in1(c_e_h_1, c_f, s10) | (~node14(c_e_h_1, c_f, s10, s11)))),
% 295.11/187.63 inference(rewrite,[status(thm)],[])).
% 295.11/187.63 tff(29288,plain,
% 295.11/187.63 (((~node14(c_e_h_1, c_f, s10, s11)) | m_c_h_element_v_in1(c_e_h_1, c_f, s10) | (~m_c_h_element_v_out(c_e_h_1, c_f, s11))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_f, s11)) | m_c_h_element_v_in1(c_e_h_1, c_f, s10) | (~node14(c_e_h_1, c_f, s10, s11)))),
% 295.11/187.63 inference(rewrite,[status(thm)],[])).
% 295.11/187.63 tff(29289,plain,
% 295.11/187.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s10, s11)) | m_c_h_element_v_in1(c_e_h_1, c_f, s10) | (~m_c_h_element_v_out(c_e_h_1, c_f, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s11)) | m_c_h_element_v_in1(c_e_h_1, c_f, s10) | (~node14(c_e_h_1, c_f, s10, s11))))),
% 295.11/187.63 inference(monotonicity,[status(thm)],[29288])).
% 295.11/187.63 tff(29290,plain,
% 295.11/187.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s10, s11)) | m_c_h_element_v_in1(c_e_h_1, c_f, s10) | (~m_c_h_element_v_out(c_e_h_1, c_f, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s11)) | m_c_h_element_v_in1(c_e_h_1, c_f, s10) | (~node14(c_e_h_1, c_f, s10, s11)))),
% 295.11/187.63 inference(transitivity,[status(thm)],[29289, 29287])).
% 295.11/187.63 tff(29291,plain,
% 295.11/187.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s10, s11)) | m_c_h_element_v_in1(c_e_h_1, c_f, s10) | (~m_c_h_element_v_out(c_e_h_1, c_f, s11)))),
% 295.11/187.63 inference(quant_inst,[status(thm)],[])).
% 295.11/187.63 tff(29292,plain,
% 295.11/187.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s11)) | m_c_h_element_v_in1(c_e_h_1, c_f, s10) | (~node14(c_e_h_1, c_f, s10, s11))),
% 295.11/187.63 inference(modus_ponens,[status(thm)],[29291, 29290])).
% 295.11/187.63 tff(29293,plain,
% 295.11/187.63 ($false),
% 295.11/187.63 inference(unit_resolution,[status(thm)],[29292, 223, 29207, 29286, 29285])).
% 295.11/187.63 tff(29294,plain,((~node14(c_e_h_1, c_f, s10, s11)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s11)) | m_c_h_element_v_in1(c_e_h_1, c_f, s10)), inference(lemma,lemma(discharge,[]))).
% 295.11/187.63 tff(29295,plain,
% 295.11/187.63 ($false),
% 295.11/187.63 inference(unit_resolution,[status(thm)],[29294, 29284, 29239, 29207])).
% 295.11/187.63 tff(29296,plain,(m_c_h_element_v_out(c_e_h_1, c_f, s10) | (~m_c_h_element_v_out(c_e_h_1, c_f, s11)) | m_c_h_element_v_in2(c_e_h_1, c_f, s10)), inference(lemma,lemma(discharge,[]))).
% 295.11/187.63 tff(29297,plain,
% 295.11/187.63 ((~m_c_h_element_v_out(c_e_h_1, c_f, s11)) | m_c_h_element_v_in2(c_e_h_1, c_f, s10)),
% 295.11/187.63 inference(unit_resolution,[status(thm)],[29296, 29206])).
% 295.11/187.63 tff(29298,plain,
% 295.11/187.63 (~m_c_h_element_v_out(c_e_h_1, c_f, s11)),
% 295.11/187.63 inference(unit_resolution,[status(thm)],[29297, 29032])).
% 295.11/187.63 tff(29299,assumption,(m_c_h_element_v_in2(c_e_h_1, c_f, s11)), introduced(assumption)).
% 295.11/187.63 tff(29300,plain,
% 295.11/187.63 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s11)) | m_and_h_gate_v_out(c_e_h_1, c_i, s11))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s11)) | m_and_h_gate_v_out(c_e_h_1, c_i, s11))),
% 295.11/187.63 inference(rewrite,[status(thm)],[])).
% 295.11/187.63 tff(29301,plain,
% 295.11/187.63 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s11)) | m_and_h_gate_v_out(c_e_h_1, c_i, s11))),
% 295.11/187.63 inference(quant_inst,[status(thm)],[])).
% 295.11/187.63 tff(29302,plain,
% 295.11/187.63 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s11)) | m_and_h_gate_v_out(c_e_h_1, c_i, s11)),
% 295.11/187.63 inference(modus_ponens,[status(thm)],[29301, 29300])).
% 295.11/187.63 tff(29303,plain,
% 295.11/187.63 ($false),
% 295.11/187.63 inference(unit_resolution,[status(thm)],[29302, 2143, 29299, 24142])).
% 295.11/187.63 tff(29304,plain,((~m_c_h_element_v_in2(c_e_h_1, c_f, s11)) | m_and_h_gate_v_out(c_e_h_1, c_i, s11)), inference(lemma,lemma(discharge,[]))).
% 295.11/187.63 tff(29305,plain,
% 295.11/187.63 (~m_c_h_element_v_in2(c_e_h_1, c_f, s11)),
% 295.11/187.63 inference(unit_resolution,[status(thm)],[29304, 24127])).
% 295.11/187.63 tff(29306,assumption,(~m_c_h_element_v_out(c_e_h_1, c_f, s11)), introduced(assumption)).
% 295.11/187.63 tff(29307,assumption,(m_c_h_element_v_out(c_e_h_1, c_f, s12)), introduced(assumption)).
% 295.11/187.63 tff(29308,assumption,(node18(c_e_h_1, c_f, s11, s12)), introduced(assumption)).
% 295.11/187.63 tff(29309,plain,
% 295.11/187.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_f, s11) | (~m_c_h_element_v_out(c_e_h_1, c_f, s12)) | (~node18(c_e_h_1, c_f, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s11) | (~m_c_h_element_v_out(c_e_h_1, c_f, s12)) | (~node18(c_e_h_1, c_f, s11, s12)))),
% 295.11/187.63 inference(rewrite,[status(thm)],[])).
% 295.11/187.63 tff(29310,plain,
% 295.11/187.63 (((~m_c_h_element_v_out(c_e_h_1, c_f, s12)) | m_c_h_element_v_out(c_e_h_1, c_f, s11) | (~node18(c_e_h_1, c_f, s11, s12))) <=> (m_c_h_element_v_out(c_e_h_1, c_f, s11) | (~m_c_h_element_v_out(c_e_h_1, c_f, s12)) | (~node18(c_e_h_1, c_f, s11, s12)))),
% 295.11/187.63 inference(rewrite,[status(thm)],[])).
% 295.11/187.63 tff(29311,plain,
% 295.11/187.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s12)) | m_c_h_element_v_out(c_e_h_1, c_f, s11) | (~node18(c_e_h_1, c_f, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_f, s11) | (~m_c_h_element_v_out(c_e_h_1, c_f, s12)) | (~node18(c_e_h_1, c_f, s11, s12))))),
% 295.11/187.63 inference(monotonicity,[status(thm)],[29310])).
% 295.11/187.63 tff(29312,plain,
% 295.11/187.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s12)) | m_c_h_element_v_out(c_e_h_1, c_f, s11) | (~node18(c_e_h_1, c_f, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s11) | (~m_c_h_element_v_out(c_e_h_1, c_f, s12)) | (~node18(c_e_h_1, c_f, s11, s12)))),
% 295.11/187.63 inference(transitivity,[status(thm)],[29311, 29309])).
% 295.11/187.63 tff(29313,plain,
% 295.11/187.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s12)) | m_c_h_element_v_out(c_e_h_1, c_f, s11) | (~node18(c_e_h_1, c_f, s11, s12)))),
% 295.11/187.63 inference(quant_inst,[status(thm)],[])).
% 295.11/187.63 tff(29314,plain,
% 295.11/187.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s11) | (~m_c_h_element_v_out(c_e_h_1, c_f, s12)) | (~node18(c_e_h_1, c_f, s11, s12))),
% 295.11/187.63 inference(modus_ponens,[status(thm)],[29313, 29312])).
% 295.11/187.63 tff(29315,plain,
% 295.11/187.63 ($false),
% 295.11/187.63 inference(unit_resolution,[status(thm)],[29314, 753, 29307, 29306, 29308])).
% 295.11/187.63 tff(29316,plain,((~node18(c_e_h_1, c_f, s11, s12)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s12)) | m_c_h_element_v_out(c_e_h_1, c_f, s11)), inference(lemma,lemma(discharge,[]))).
% 295.11/187.63 tff(29317,plain,
% 295.11/187.63 (~node18(c_e_h_1, c_f, s11, s12)),
% 295.11/187.63 inference(unit_resolution,[status(thm)],[29316, 29307, 29306])).
% 295.11/187.63 tff(29318,plain,
% 295.11/187.63 (~node18(c_e_h_1, c_f, s11, s12)),
% 295.11/187.63 inference(unit_resolution,[status(thm)],[29316, 29306, 29307])).
% 295.11/187.63 tff(29319,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_f, s11)), introduced(assumption)).
% 295.11/187.63 tff(29320,assumption,(node15(c_e_h_1, c_f, s11, s12)), introduced(assumption)).
% 295.11/187.63 tff(29321,plain,
% 295.11/187.63 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s12)) | (~node15(c_e_h_1, c_f, s11, s12)) | m_c_h_element_v_out(c_e_h_1, c_f, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s12)) | (~node15(c_e_h_1, c_f, s11, s12)) | m_c_h_element_v_out(c_e_h_1, c_f, s11))),
% 295.11/187.63 inference(rewrite,[status(thm)],[])).
% 295.11/187.63 tff(29322,plain,
% 295.11/187.63 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s12)) | (~node15(c_e_h_1, c_f, s11, s12)) | m_c_h_element_v_out(c_e_h_1, c_f, s11))),
% 295.11/187.64 inference(quant_inst,[status(thm)],[])).
% 295.11/187.64 tff(29323,plain,
% 295.11/187.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s12)) | (~node15(c_e_h_1, c_f, s11, s12)) | m_c_h_element_v_out(c_e_h_1, c_f, s11)),
% 295.11/187.64 inference(modus_ponens,[status(thm)],[29322, 29321])).
% 295.11/187.64 tff(29324,plain,
% 295.11/187.64 ($false),
% 295.11/187.64 inference(unit_resolution,[status(thm)],[29323, 147, 29307, 29306, 29320])).
% 295.11/187.64 tff(29325,plain,((~node15(c_e_h_1, c_f, s11, s12)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s12)) | m_c_h_element_v_out(c_e_h_1, c_f, s11)), inference(lemma,lemma(discharge,[]))).
% 295.11/187.64 tff(29326,plain,
% 295.11/187.64 (~node15(c_e_h_1, c_f, s11, s12)),
% 295.11/187.64 inference(unit_resolution,[status(thm)],[29325, 29306, 29307])).
% 295.11/187.64 tff(29327,assumption,(~node15(c_e_h_1, c_f, s11, s12)), introduced(assumption)).
% 295.11/187.64 tff(29328,assumption,(node17(c_e_h_1, c_f, s11)), introduced(assumption)).
% 295.11/187.64 tff(29329,plain,
% 295.11/187.64 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s11)) | (~node17(c_e_h_1, c_f, s11)) | m_c_h_element_v_in1(c_e_h_1, c_f, s11))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s11)) | (~node17(c_e_h_1, c_f, s11)) | m_c_h_element_v_in1(c_e_h_1, c_f, s11))),
% 295.11/187.64 inference(rewrite,[status(thm)],[])).
% 295.11/187.64 tff(29330,plain,
% 295.11/187.64 ((m_c_h_element_v_in1(c_e_h_1, c_f, s11) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s11)) | (~node17(c_e_h_1, c_f, s11))) <=> ((~m_c_h_element_v_in2(c_e_h_1, c_f, s11)) | (~node17(c_e_h_1, c_f, s11)) | m_c_h_element_v_in1(c_e_h_1, c_f, s11))),
% 295.11/187.64 inference(rewrite,[status(thm)],[])).
% 295.11/187.64 tff(29331,plain,
% 295.11/187.64 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s11) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s11)) | (~node17(c_e_h_1, c_f, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s11)) | (~node17(c_e_h_1, c_f, s11)) | m_c_h_element_v_in1(c_e_h_1, c_f, s11)))),
% 295.11/187.64 inference(monotonicity,[status(thm)],[29330])).
% 295.11/187.64 tff(29332,plain,
% 295.11/187.64 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s11) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s11)) | (~node17(c_e_h_1, c_f, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s11)) | (~node17(c_e_h_1, c_f, s11)) | m_c_h_element_v_in1(c_e_h_1, c_f, s11))),
% 295.11/187.64 inference(transitivity,[status(thm)],[29331, 29329])).
% 295.11/187.64 tff(29333,plain,
% 295.11/187.64 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s11) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s11)) | (~node17(c_e_h_1, c_f, s11)))),
% 295.11/187.64 inference(quant_inst,[status(thm)],[])).
% 295.11/187.64 tff(29334,plain,
% 295.11/187.64 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s11)) | (~node17(c_e_h_1, c_f, s11)) | m_c_h_element_v_in1(c_e_h_1, c_f, s11)),
% 295.11/187.64 inference(modus_ponens,[status(thm)],[29333, 29332])).
% 295.11/187.64 tff(29335,plain,
% 295.11/187.64 ((~m_c_h_element_v_in2(c_e_h_1, c_f, s11)) | m_c_h_element_v_in1(c_e_h_1, c_f, s11)),
% 295.11/187.64 inference(unit_resolution,[status(thm)],[29334, 859, 29328])).
% 295.11/187.64 tff(29336,plain,
% 295.11/187.64 (~m_c_h_element_v_in2(c_e_h_1, c_f, s11)),
% 295.11/187.64 inference(unit_resolution,[status(thm)],[29335, 29319])).
% 295.11/187.64 tff(29337,plain,
% 295.11/187.64 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s11)) | m_c_h_element_v_in1(c_e_h_1, c_f, s11) | m_c_h_element_v_in2(c_e_h_1, c_f, s11))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s11)) | m_c_h_element_v_in1(c_e_h_1, c_f, s11) | m_c_h_element_v_in2(c_e_h_1, c_f, s11))),
% 295.11/187.64 inference(rewrite,[status(thm)],[])).
% 295.11/187.64 tff(29338,plain,
% 295.11/187.64 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s11)) | m_c_h_element_v_in1(c_e_h_1, c_f, s11) | m_c_h_element_v_in2(c_e_h_1, c_f, s11))),
% 295.11/187.64 inference(quant_inst,[status(thm)],[])).
% 295.11/187.64 tff(29339,plain,
% 295.11/187.64 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s11)) | m_c_h_element_v_in1(c_e_h_1, c_f, s11) | m_c_h_element_v_in2(c_e_h_1, c_f, s11)),
% 295.11/187.64 inference(modus_ponens,[status(thm)],[29338, 29337])).
% 295.11/187.64 tff(29340,plain,
% 295.11/187.64 (~node16(c_e_h_1, c_f, s11)),
% 295.11/187.64 inference(unit_resolution,[status(thm)],[29339, 178, 29319, 29336])).
% 295.11/187.64 tff(29341,plain,
% 295.11/187.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s11, s12)) | node19(c_e_h_1, c_f, s11, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s11, s12)) | node19(c_e_h_1, c_f, s11, s12))),
% 295.11/187.64 inference(rewrite,[status(thm)],[])).
% 295.11/187.64 tff(29342,plain,
% 295.11/187.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s11, s12)) | node19(c_e_h_1, c_f, s11, s12))),
% 295.11/187.64 inference(quant_inst,[status(thm)],[])).
% 295.11/187.64 tff(29343,plain,
% 295.11/187.64 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s11, s12)) | node19(c_e_h_1, c_f, s11, s12)),
% 295.11/187.64 inference(modus_ponens,[status(thm)],[29342, 29341])).
% 295.11/187.64 tff(29344,plain,
% 295.11/187.64 (node19(c_e_h_1, c_f, s11, s12)),
% 295.11/187.64 inference(unit_resolution,[status(thm)],[29343, 190, 11461])).
% 295.11/187.64 tff(29345,plain,
% 295.11/187.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_1, c_f, s11, s12) | node15(c_e_h_1, c_f, s11, s12) | (~node19(c_e_h_1, c_f, s11, s12)) | node16(c_e_h_1, c_f, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_f, s11, s12) | node15(c_e_h_1, c_f, s11, s12) | (~node19(c_e_h_1, c_f, s11, s12)) | node16(c_e_h_1, c_f, s11))),
% 295.11/187.64 inference(rewrite,[status(thm)],[])).
% 295.11/187.64 tff(29346,plain,
% 295.11/187.64 ((node16(c_e_h_1, c_f, s11) | node14(c_e_h_1, c_f, s11, s12) | node15(c_e_h_1, c_f, s11, s12) | (~node19(c_e_h_1, c_f, s11, s12))) <=> (node14(c_e_h_1, c_f, s11, s12) | node15(c_e_h_1, c_f, s11, s12) | (~node19(c_e_h_1, c_f, s11, s12)) | node16(c_e_h_1, c_f, s11))),
% 295.11/187.64 inference(rewrite,[status(thm)],[])).
% 295.11/187.64 tff(29347,plain,
% 295.11/187.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s11) | node14(c_e_h_1, c_f, s11, s12) | node15(c_e_h_1, c_f, s11, s12) | (~node19(c_e_h_1, c_f, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_1, c_f, s11, s12) | node15(c_e_h_1, c_f, s11, s12) | (~node19(c_e_h_1, c_f, s11, s12)) | node16(c_e_h_1, c_f, s11)))),
% 295.11/187.64 inference(monotonicity,[status(thm)],[29346])).
% 295.11/187.64 tff(29348,plain,
% 295.11/187.64 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s11) | node14(c_e_h_1, c_f, s11, s12) | node15(c_e_h_1, c_f, s11, s12) | (~node19(c_e_h_1, c_f, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_f, s11, s12) | node15(c_e_h_1, c_f, s11, s12) | (~node19(c_e_h_1, c_f, s11, s12)) | node16(c_e_h_1, c_f, s11))),
% 295.11/187.64 inference(transitivity,[status(thm)],[29347, 29345])).
% 295.11/187.65 tff(29349,plain,
% 295.11/187.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s11) | node14(c_e_h_1, c_f, s11, s12) | node15(c_e_h_1, c_f, s11, s12) | (~node19(c_e_h_1, c_f, s11, s12)))),
% 295.11/187.65 inference(quant_inst,[status(thm)],[])).
% 295.11/187.65 tff(29350,plain,
% 295.11/187.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_f, s11, s12) | node15(c_e_h_1, c_f, s11, s12) | (~node19(c_e_h_1, c_f, s11, s12)) | node16(c_e_h_1, c_f, s11)),
% 295.11/187.65 inference(modus_ponens,[status(thm)],[29349, 29348])).
% 295.11/187.65 tff(29351,plain,
% 295.11/187.65 (node14(c_e_h_1, c_f, s11, s12) | node15(c_e_h_1, c_f, s11, s12) | node16(c_e_h_1, c_f, s11)),
% 295.11/187.65 inference(unit_resolution,[status(thm)],[29350, 204, 29344])).
% 295.11/187.65 tff(29352,plain,
% 295.11/187.65 (node14(c_e_h_1, c_f, s11, s12)),
% 295.11/187.65 inference(unit_resolution,[status(thm)],[29351, 29340, 29327])).
% 295.11/187.65 tff(29353,plain,
% 295.11/187.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s12)) | m_c_h_element_v_in1(c_e_h_1, c_f, s11) | (~node14(c_e_h_1, c_f, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s12)) | m_c_h_element_v_in1(c_e_h_1, c_f, s11) | (~node14(c_e_h_1, c_f, s11, s12)))),
% 295.11/187.65 inference(rewrite,[status(thm)],[])).
% 295.11/187.65 tff(29354,plain,
% 295.11/187.65 (((~node14(c_e_h_1, c_f, s11, s12)) | m_c_h_element_v_in1(c_e_h_1, c_f, s11) | (~m_c_h_element_v_out(c_e_h_1, c_f, s12))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_f, s12)) | m_c_h_element_v_in1(c_e_h_1, c_f, s11) | (~node14(c_e_h_1, c_f, s11, s12)))),
% 295.11/187.65 inference(rewrite,[status(thm)],[])).
% 295.11/187.65 tff(29355,plain,
% 295.11/187.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s11, s12)) | m_c_h_element_v_in1(c_e_h_1, c_f, s11) | (~m_c_h_element_v_out(c_e_h_1, c_f, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s12)) | m_c_h_element_v_in1(c_e_h_1, c_f, s11) | (~node14(c_e_h_1, c_f, s11, s12))))),
% 295.11/187.65 inference(monotonicity,[status(thm)],[29354])).
% 295.11/187.65 tff(29356,plain,
% 295.11/187.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s11, s12)) | m_c_h_element_v_in1(c_e_h_1, c_f, s11) | (~m_c_h_element_v_out(c_e_h_1, c_f, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s12)) | m_c_h_element_v_in1(c_e_h_1, c_f, s11) | (~node14(c_e_h_1, c_f, s11, s12)))),
% 295.11/187.65 inference(transitivity,[status(thm)],[29355, 29353])).
% 295.11/187.65 tff(29357,plain,
% 295.11/187.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s11, s12)) | m_c_h_element_v_in1(c_e_h_1, c_f, s11) | (~m_c_h_element_v_out(c_e_h_1, c_f, s12)))),
% 295.11/187.65 inference(quant_inst,[status(thm)],[])).
% 295.11/187.65 tff(29358,plain,
% 295.11/187.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s12)) | m_c_h_element_v_in1(c_e_h_1, c_f, s11) | (~node14(c_e_h_1, c_f, s11, s12))),
% 295.11/187.65 inference(modus_ponens,[status(thm)],[29357, 29356])).
% 295.11/187.65 tff(29359,plain,
% 295.11/187.65 ($false),
% 295.11/187.65 inference(unit_resolution,[status(thm)],[29358, 223, 29307, 29352, 29319])).
% 295.11/187.65 tff(29360,plain,(m_c_h_element_v_in1(c_e_h_1, c_f, s11) | (~m_c_h_element_v_out(c_e_h_1, c_f, s12)) | node15(c_e_h_1, c_f, s11, s12) | (~node17(c_e_h_1, c_f, s11))), inference(lemma,lemma(discharge,[]))).
% 295.11/187.65 tff(29361,plain,
% 295.11/187.65 (~node17(c_e_h_1, c_f, s11)),
% 295.11/187.65 inference(unit_resolution,[status(thm)],[29360, 29326, 29307, 29319])).
% 295.11/187.65 tff(29362,plain,
% 295.11/187.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_f, s11, s12)) | node18(c_e_h_1, c_f, s11, s12) | node17(c_e_h_1, c_f, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s11, s12)) | node18(c_e_h_1, c_f, s11, s12) | node17(c_e_h_1, c_f, s11))),
% 295.11/187.65 inference(rewrite,[status(thm)],[])).
% 295.11/187.65 tff(29363,plain,
% 295.11/187.65 ((node17(c_e_h_1, c_f, s11) | node18(c_e_h_1, c_f, s11, s12) | (~node19(c_e_h_1, c_f, s11, s12))) <=> ((~node19(c_e_h_1, c_f, s11, s12)) | node18(c_e_h_1, c_f, s11, s12) | node17(c_e_h_1, c_f, s11))),
% 295.11/187.65 inference(rewrite,[status(thm)],[])).
% 295.11/187.65 tff(29364,plain,
% 295.11/187.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s11) | node18(c_e_h_1, c_f, s11, s12) | (~node19(c_e_h_1, c_f, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_f, s11, s12)) | node18(c_e_h_1, c_f, s11, s12) | node17(c_e_h_1, c_f, s11)))),
% 295.11/187.65 inference(monotonicity,[status(thm)],[29363])).
% 295.11/187.65 tff(29365,plain,
% 295.11/187.65 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s11) | node18(c_e_h_1, c_f, s11, s12) | (~node19(c_e_h_1, c_f, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s11, s12)) | node18(c_e_h_1, c_f, s11, s12) | node17(c_e_h_1, c_f, s11))),
% 295.11/187.65 inference(transitivity,[status(thm)],[29364, 29362])).
% 295.11/187.65 tff(29366,plain,
% 295.11/187.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s11) | node18(c_e_h_1, c_f, s11, s12) | (~node19(c_e_h_1, c_f, s11, s12)))),
% 295.11/187.65 inference(quant_inst,[status(thm)],[])).
% 295.11/187.65 tff(29367,plain,
% 295.11/187.65 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s11, s12)) | node18(c_e_h_1, c_f, s11, s12) | node17(c_e_h_1, c_f, s11)),
% 295.11/187.65 inference(modus_ponens,[status(thm)],[29366, 29365])).
% 295.11/187.65 tff(29368,plain,
% 295.11/187.65 (node18(c_e_h_1, c_f, s11, s12) | node17(c_e_h_1, c_f, s11)),
% 295.11/187.65 inference(unit_resolution,[status(thm)],[29367, 776, 29344])).
% 295.11/187.65 tff(29369,plain,
% 295.11/187.65 ($false),
% 295.11/187.65 inference(unit_resolution,[status(thm)],[29368, 29361, 29318])).
% 295.11/187.65 tff(29370,plain,(m_c_h_element_v_out(c_e_h_1, c_f, s11) | (~m_c_h_element_v_out(c_e_h_1, c_f, s12)) | m_c_h_element_v_in1(c_e_h_1, c_f, s11)), inference(lemma,lemma(discharge,[]))).
% 295.11/187.65 tff(29371,plain,
% 295.11/187.65 (m_c_h_element_v_in1(c_e_h_1, c_f, s11)),
% 295.11/187.65 inference(unit_resolution,[status(thm)],[29370, 29307, 29306])).
% 295.11/187.65 tff(29372,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_f, s11)), introduced(assumption)).
% 295.11/187.65 tff(29373,plain,
% 295.11/187.65 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s11)) | (~node17(c_e_h_1, c_f, s11)) | m_c_h_element_v_in2(c_e_h_1, c_f, s11))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s11)) | (~node17(c_e_h_1, c_f, s11)) | m_c_h_element_v_in2(c_e_h_1, c_f, s11))),
% 295.11/187.65 inference(rewrite,[status(thm)],[])).
% 295.11/187.65 tff(29374,plain,
% 295.11/187.65 (((~m_c_h_element_v_in1(c_e_h_1, c_f, s11)) | m_c_h_element_v_in2(c_e_h_1, c_f, s11) | (~node17(c_e_h_1, c_f, s11))) <=> ((~m_c_h_element_v_in1(c_e_h_1, c_f, s11)) | (~node17(c_e_h_1, c_f, s11)) | m_c_h_element_v_in2(c_e_h_1, c_f, s11))),
% 295.11/187.65 inference(rewrite,[status(thm)],[])).
% 295.11/187.65 tff(29375,plain,
% 295.11/187.65 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s11)) | m_c_h_element_v_in2(c_e_h_1, c_f, s11) | (~node17(c_e_h_1, c_f, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s11)) | (~node17(c_e_h_1, c_f, s11)) | m_c_h_element_v_in2(c_e_h_1, c_f, s11)))),
% 295.11/187.65 inference(monotonicity,[status(thm)],[29374])).
% 295.11/187.65 tff(29376,plain,
% 295.11/187.65 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s11)) | m_c_h_element_v_in2(c_e_h_1, c_f, s11) | (~node17(c_e_h_1, c_f, s11)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s11)) | (~node17(c_e_h_1, c_f, s11)) | m_c_h_element_v_in2(c_e_h_1, c_f, s11))),
% 295.11/187.65 inference(transitivity,[status(thm)],[29375, 29373])).
% 295.11/187.65 tff(29377,plain,
% 295.11/187.65 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s11)) | m_c_h_element_v_in2(c_e_h_1, c_f, s11) | (~node17(c_e_h_1, c_f, s11)))),
% 295.11/187.65 inference(quant_inst,[status(thm)],[])).
% 295.11/187.65 tff(29378,plain,
% 295.11/187.65 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s11)) | (~node17(c_e_h_1, c_f, s11)) | m_c_h_element_v_in2(c_e_h_1, c_f, s11)),
% 295.11/187.65 inference(modus_ponens,[status(thm)],[29377, 29376])).
% 295.11/187.65 tff(29379,plain,
% 295.11/187.65 ((~m_c_h_element_v_in1(c_e_h_1, c_f, s11)) | (~node17(c_e_h_1, c_f, s11))),
% 295.11/187.65 inference(unit_resolution,[status(thm)],[29378, 919, 29372])).
% 295.11/187.65 tff(29380,plain,
% 295.11/187.65 (~node17(c_e_h_1, c_f, s11)),
% 295.11/187.65 inference(unit_resolution,[status(thm)],[29379, 29371])).
% 295.11/187.65 tff(29381,plain,
% 295.11/187.65 ($false),
% 295.11/187.65 inference(unit_resolution,[status(thm)],[29368, 29380, 29317])).
% 295.11/187.65 tff(29382,plain,((~m_c_h_element_v_out(c_e_h_1, c_f, s12)) | m_c_h_element_v_in2(c_e_h_1, c_f, s11) | m_c_h_element_v_out(c_e_h_1, c_f, s11)), inference(lemma,lemma(discharge,[]))).
% 295.11/187.65 tff(29383,plain,
% 295.11/187.65 ((~m_c_h_element_v_out(c_e_h_1, c_f, s12)) | m_c_h_element_v_out(c_e_h_1, c_f, s11)),
% 295.11/187.65 inference(unit_resolution,[status(thm)],[29382, 29305])).
% 295.11/187.65 tff(29384,plain,
% 295.11/187.65 (~m_c_h_element_v_out(c_e_h_1, c_f, s12)),
% 295.11/187.65 inference(unit_resolution,[status(thm)],[29383, 29298])).
% 295.11/187.65 tff(29385,plain,
% 295.11/187.65 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_m, s12) | m_c_h_element_v_out(c_e_h_1, c_f, s12))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_m, s12) | m_c_h_element_v_out(c_e_h_1, c_f, s12))),
% 295.11/187.65 inference(rewrite,[status(thm)],[])).
% 295.11/187.65 tff(29386,plain,
% 295.11/187.65 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_m, s12) | m_c_h_element_v_out(c_e_h_1, c_f, s12))),
% 295.11/187.65 inference(quant_inst,[status(thm)],[])).
% 295.11/187.65 tff(29387,plain,
% 295.11/187.65 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_m, X) | m_c_h_element_v_out(I0, c_f, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_m, s12) | m_c_h_element_v_out(c_e_h_1, c_f, s12)),
% 295.11/187.65 inference(modus_ponens,[status(thm)],[29386, 29385])).
% 295.11/187.65 tff(29388,plain,
% 295.11/187.65 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_m, s12) | m_c_h_element_v_out(c_e_h_1, c_f, s12)),
% 295.11/187.65 inference(unit_resolution,[status(thm)],[29387, 5689])).
% 295.11/187.65 tff(29389,plain,
% 295.11/187.65 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_m, s12)),
% 295.11/187.65 inference(unit_resolution,[status(thm)],[29388, 29384])).
% 295.11/187.65 tff(29390,assumption,(~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s14)), introduced(assumption)).
% 295.11/187.65 tff(29391,plain,
% 295.11/187.65 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s14) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s14) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14))),
% 295.11/187.66 inference(rewrite,[status(thm)],[])).
% 295.11/187.66 tff(29392,plain,
% 295.11/187.66 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s14) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14))),
% 295.11/187.66 inference(quant_inst,[status(thm)],[])).
% 295.11/187.66 tff(29393,plain,
% 295.11/187.66 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s14) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)),
% 295.11/187.66 inference(modus_ponens,[status(thm)],[29392, 29391])).
% 295.11/187.66 tff(29394,plain,
% 295.11/187.66 ($false),
% 295.11/187.66 inference(unit_resolution,[status(thm)],[29393, 7868, 26516, 29390])).
% 295.11/187.66 tff(29395,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s14)), inference(lemma,lemma(discharge,[]))).
% 295.11/187.66 tff(29396,plain,
% 295.11/187.66 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s14)),
% 295.11/187.66 inference(unit_resolution,[status(thm)],[29395, 26514])).
% 295.11/187.66 tff(29397,plain,
% 295.11/187.66 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12)),
% 295.11/187.66 inference(unit_resolution,[status(thm)],[26440, 23363, 26431])).
% 295.11/187.66 tff(29398,plain,
% 295.11/187.66 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s12)),
% 295.11/187.66 inference(unit_resolution,[status(thm)],[25368, 4958, 29397])).
% 295.11/187.66 tff(29399,plain,
% 295.11/187.66 (~node9(c_e_h_1, c_m, s12)),
% 295.11/187.66 inference(unit_resolution,[status(thm)],[25372, 4972, 29398])).
% 295.11/187.66 tff(29400,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14)), introduced(assumption)).
% 295.11/187.66 tff(29401,plain,
% 295.11/187.66 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s12)),
% 295.11/187.66 inference(unit_resolution,[status(thm)],[26474, 25377])).
% 295.11/187.66 tff(29402,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_m, s12)), introduced(assumption)).
% 295.11/187.66 tff(29403,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15)), introduced(assumption)).
% 295.11/187.66 tff(29404,assumption,(node10(c_e_h_1, c_m, s12, s13)), introduced(assumption)).
% 295.11/187.66 tff(29405,plain,
% 295.11/187.66 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s13)),
% 295.11/187.66 inference(unit_resolution,[status(thm)],[28864, 7868, 25403])).
% 295.11/187.66 tff(29406,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s12)), introduced(assumption)).
% 295.11/187.66 tff(29407,plain,
% 295.11/187.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in1(c_e_h_1, c_m, s12)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s12)) | (~node10(c_e_h_1, c_m, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_m, s12)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s12)) | (~node10(c_e_h_1, c_m, s12, s13)))),
% 295.11/187.66 inference(rewrite,[status(thm)],[])).
% 295.11/187.66 tff(29408,plain,
% 295.11/187.66 (((~node10(c_e_h_1, c_m, s12, s13)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_m, s12)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)) <=> ((~m_and_h_gate_h_init_v_in1(c_e_h_1, c_m, s12)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s12)) | (~node10(c_e_h_1, c_m, s12, s13)))),
% 295.11/187.66 inference(rewrite,[status(thm)],[])).
% 295.11/187.66 tff(29409,plain,
% 295.11/187.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_m, s12, s13)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_m, s12)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in1(c_e_h_1, c_m, s12)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s12)) | (~node10(c_e_h_1, c_m, s12, s13))))),
% 295.11/187.66 inference(monotonicity,[status(thm)],[29408])).
% 295.11/187.66 tff(29410,plain,
% 295.11/187.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_m, s12, s13)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_m, s12)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_m, s12)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s12)) | (~node10(c_e_h_1, c_m, s12, s13)))),
% 295.11/187.66 inference(transitivity,[status(thm)],[29409, 29407])).
% 295.11/187.66 tff(29411,plain,
% 295.11/187.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_m, s12, s13)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_m, s12)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13))),
% 295.11/187.66 inference(quant_inst,[status(thm)],[])).
% 295.11/187.66 tff(29412,plain,
% 295.11/187.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_m, s12)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s12)) | (~node10(c_e_h_1, c_m, s12, s13))),
% 295.11/187.66 inference(modus_ponens,[status(thm)],[29411, 29410])).
% 295.11/187.66 tff(29413,plain,
% 295.11/187.66 ($false),
% 295.11/187.66 inference(unit_resolution,[status(thm)],[29412, 5718, 29402, 29406, 29404, 25403])).
% 295.11/187.66 tff(29414,plain,((~node10(c_e_h_1, c_m, s12, s13)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_m, s12)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s12)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)), inference(lemma,lemma(discharge,[]))).
% 295.11/187.66 tff(29415,plain,
% 295.11/187.66 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s12)),
% 295.11/187.66 inference(unit_resolution,[status(thm)],[29414, 25403, 29404, 29402])).
% 295.11/187.66 tff(29416,plain,
% 295.11/187.66 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s12) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s12) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12))),
% 295.11/187.66 inference(rewrite,[status(thm)],[])).
% 295.11/187.66 tff(29417,plain,
% 295.11/187.66 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s12) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12))),
% 295.11/187.66 inference(quant_inst,[status(thm)],[])).
% 295.11/187.66 tff(29418,plain,
% 295.11/187.66 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_m, X) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s12) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12)),
% 295.11/187.66 inference(modus_ponens,[status(thm)],[29417, 29416])).
% 295.11/187.66 tff(29419,plain,
% 295.11/187.66 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s12) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12)),
% 295.11/187.66 inference(unit_resolution,[status(thm)],[29418, 5704])).
% 295.11/187.66 tff(29420,plain,
% 295.11/187.66 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12)),
% 295.11/187.66 inference(unit_resolution,[status(thm)],[29419, 29415])).
% 295.11/187.66 tff(29421,plain,
% 295.11/187.66 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13)),
% 295.11/187.66 inference(unit_resolution,[status(thm)],[26469, 29420, 26437, 26442])).
% 295.11/187.66 tff(29422,plain,
% 295.11/187.66 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14)),
% 295.11/187.66 inference(unit_resolution,[status(thm)],[28894, 29421, 29405, 28869])).
% 295.11/187.66 tff(29423,assumption,(node11(c_e_h_1, c_n, s14, s15)), introduced(assumption)).
% 295.11/187.66 tff(29424,plain,
% 295.11/187.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14)) | (~node11(c_e_h_1, c_n, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14)) | (~node11(c_e_h_1, c_n, s14, s15)))),
% 295.11/187.66 inference(rewrite,[status(thm)],[])).
% 295.11/187.66 tff(29425,plain,
% 295.11/187.66 ((m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15) | (~node11(c_e_h_1, c_n, s14, s15)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14))) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14)) | (~node11(c_e_h_1, c_n, s14, s15)))),
% 295.11/187.66 inference(rewrite,[status(thm)],[])).
% 295.11/187.66 tff(29426,plain,
% 295.11/187.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15) | (~node11(c_e_h_1, c_n, s14, s15)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14)) | (~node11(c_e_h_1, c_n, s14, s15))))),
% 295.11/187.66 inference(monotonicity,[status(thm)],[29425])).
% 295.11/187.66 tff(29427,plain,
% 295.11/187.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15) | (~node11(c_e_h_1, c_n, s14, s15)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14)) | (~node11(c_e_h_1, c_n, s14, s15)))),
% 295.11/187.66 inference(transitivity,[status(thm)],[29426, 29424])).
% 295.11/187.66 tff(29428,plain,
% 295.11/187.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15) | (~node11(c_e_h_1, c_n, s14, s15)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14)))),
% 295.11/187.66 inference(quant_inst,[status(thm)],[])).
% 295.11/187.66 tff(29429,plain,
% 295.11/187.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14)) | (~node11(c_e_h_1, c_n, s14, s15))),
% 295.11/187.66 inference(modus_ponens,[status(thm)],[29428, 29427])).
% 295.11/187.66 tff(29430,plain,
% 295.11/187.66 ($false),
% 295.11/187.66 inference(unit_resolution,[status(thm)],[29429, 5742, 29423, 28898, 29403])).
% 295.11/187.66 tff(29431,plain,((~node11(c_e_h_1, c_n, s14, s15)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15)), inference(lemma,lemma(discharge,[]))).
% 295.11/187.66 tff(29432,plain,
% 295.11/187.66 (~node11(c_e_h_1, c_n, s14, s15)),
% 295.11/187.66 inference(unit_resolution,[status(thm)],[29431, 29422, 29403])).
% 295.11/187.66 tff(29433,plain,
% 295.11/187.66 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s14, s15)) | node10(c_e_h_1, c_n, s14, s15) | node11(c_e_h_1, c_n, s14, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s14, s15)) | node10(c_e_h_1, c_n, s14, s15) | node11(c_e_h_1, c_n, s14, s15))),
% 295.11/187.66 inference(rewrite,[status(thm)],[])).
% 295.11/187.66 tff(29434,plain,
% 295.11/187.66 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s14, s15)) | node10(c_e_h_1, c_n, s14, s15) | node11(c_e_h_1, c_n, s14, s15))),
% 295.11/187.67 inference(quant_inst,[status(thm)],[])).
% 295.11/187.67 tff(29435,plain,
% 295.11/187.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s14, s15)) | node10(c_e_h_1, c_n, s14, s15) | node11(c_e_h_1, c_n, s14, s15)),
% 295.11/187.67 inference(modus_ponens,[status(thm)],[29434, 29433])).
% 295.11/187.67 tff(29436,plain,
% 295.11/187.67 (node10(c_e_h_1, c_n, s14, s15) | node11(c_e_h_1, c_n, s14, s15)),
% 295.11/187.67 inference(unit_resolution,[status(thm)],[29435, 5002, 12926])).
% 295.11/187.67 tff(29437,plain,
% 295.11/187.67 (node10(c_e_h_1, c_n, s14, s15)),
% 295.11/187.67 inference(unit_resolution,[status(thm)],[29436, 29432])).
% 295.11/187.67 tff(29438,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s14)), introduced(assumption)).
% 295.11/187.67 tff(29439,assumption,(node10(c_e_h_1, c_n, s14, s15)), introduced(assumption)).
% 295.11/187.67 tff(29440,plain,
% 295.11/187.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15) | (~node10(c_e_h_1, c_n, s14, s15)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15) | (~node10(c_e_h_1, c_n, s14, s15)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s14)))),
% 295.11/187.67 inference(rewrite,[status(thm)],[])).
% 295.11/187.67 tff(29441,plain,
% 295.11/187.67 (((~node10(c_e_h_1, c_n, s14, s15)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15)) <=> ((~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15) | (~node10(c_e_h_1, c_n, s14, s15)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s14)))),
% 295.11/187.67 inference(rewrite,[status(thm)],[])).
% 295.11/187.67 tff(29442,plain,
% 295.11/187.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s14, s15)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15) | (~node10(c_e_h_1, c_n, s14, s15)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s14))))),
% 295.11/187.67 inference(monotonicity,[status(thm)],[29441])).
% 295.11/187.67 tff(29443,plain,
% 295.11/187.67 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s14, s15)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15) | (~node10(c_e_h_1, c_n, s14, s15)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s14)))),
% 295.11/187.67 inference(transitivity,[status(thm)],[29442, 29440])).
% 295.11/187.67 tff(29444,plain,
% 295.11/187.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s14, s15)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15))),
% 295.11/187.67 inference(quant_inst,[status(thm)],[])).
% 295.11/187.67 tff(29445,plain,
% 295.11/187.67 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15) | (~node10(c_e_h_1, c_n, s14, s15)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s14))),
% 295.11/187.67 inference(modus_ponens,[status(thm)],[29444, 29443])).
% 295.11/187.67 tff(29446,plain,
% 295.11/187.67 ($false),
% 295.11/187.67 inference(unit_resolution,[status(thm)],[29445, 5718, 29400, 29439, 29403, 29438])).
% 295.11/187.67 tff(29447,plain,((~node10(c_e_h_1, c_n, s14, s15)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s14))), inference(lemma,lemma(discharge,[]))).
% 295.11/187.67 tff(29448,plain,
% 295.11/187.67 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s14)),
% 295.11/187.67 inference(unit_resolution,[status(thm)],[29447, 29437, 29403, 29400])).
% 295.11/187.67 tff(29449,plain,
% 295.11/187.67 (m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)),
% 295.11/187.67 inference(unit_resolution,[status(thm)],[29393, 7868, 29448])).
% 295.11/187.67 tff(29450,plain,
% 295.11/187.67 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s13)),
% 295.11/187.67 inference(unit_resolution,[status(thm)],[26483, 4958, 29421])).
% 295.11/187.67 tff(29451,plain,
% 295.11/187.67 (~node9(c_e_h_1, c_m, s13)),
% 295.11/187.67 inference(unit_resolution,[status(thm)],[26487, 4972, 29450])).
% 295.11/187.67 tff(29452,plain,
% 295.11/187.67 (~node10(c_e_h_1, c_m, s13, s14)),
% 295.11/187.67 inference(unit_resolution,[status(thm)],[26506, 29449, 29451])).
% 295.11/187.67 tff(29453,plain,
% 295.11/187.67 (node11(c_e_h_1, c_m, s13, s14)),
% 295.11/187.67 inference(unit_resolution,[status(thm)],[26511, 29452])).
% 295.11/187.67 tff(29454,plain,
% 295.11/187.67 ($false),
% 295.11/187.67 inference(unit_resolution,[status(thm)],[26493, 5017, 29453, 29449, 25403])).
% 295.11/187.67 tff(29455,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s13)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s12)) | (~node10(c_e_h_1, c_m, s12, s13)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_m, s12))), inference(lemma,lemma(discharge,[]))).
% 295.11/187.67 tff(29456,plain,
% 295.11/187.67 (m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)),
% 295.11/187.67 inference(unit_resolution,[status(thm)],[29455, 29404, 29402, 28869, 26437, 26442, 29400, 29403])).
% 295.11/187.67 tff(29457,plain,
% 295.11/187.67 ($false),
% 295.11/187.67 inference(unit_resolution,[status(thm)],[25392, 4986, 29404, 29456, 25376])).
% 295.11/187.67 tff(29458,plain,((~node10(c_e_h_1, c_m, s12, s13)) | node9(c_e_h_1, c_m, s12) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_m, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s13)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15)), inference(lemma,lemma(discharge,[]))).
% 295.11/187.67 tff(29459,plain,
% 295.11/187.67 (~node10(c_e_h_1, c_m, s12, s13)),
% 295.11/187.67 inference(unit_resolution,[status(thm)],[29458, 29403, 29402, 28869, 26437, 29401, 29400, 25376])).
% 295.11/187.67 tff(29460,plain,
% 295.11/187.67 (node11(c_e_h_1, c_m, s12, s13)),
% 295.11/187.67 inference(unit_resolution,[status(thm)],[25388, 29459])).
% 295.11/187.67 tff(29461,plain,
% 295.11/187.67 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)),
% 295.11/187.67 inference(unit_resolution,[status(thm)],[25383, 29460, 25377])).
% 295.11/187.67 tff(29462,plain,
% 295.11/187.67 (~node10(c_e_h_1, c_n, s14, s15)),
% 295.11/187.67 inference(unit_resolution,[status(thm)],[29447, 29403, 29438, 29400])).
% 295.11/187.67 tff(29463,plain,
% 295.11/187.67 (node11(c_e_h_1, c_n, s14, s15)),
% 295.11/187.67 inference(unit_resolution,[status(thm)],[29436, 29462])).
% 295.11/187.67 tff(29464,plain,
% 295.11/187.67 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14)),
% 295.11/187.67 inference(unit_resolution,[status(thm)],[29431, 29463, 29403])).
% 295.11/187.67 tff(29465,plain,
% 295.11/187.67 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s13)),
% 295.11/187.67 inference(unit_resolution,[status(thm)],[28894, 29464, 28869, 28886])).
% 295.11/187.67 tff(29466,plain,
% 295.11/187.67 ($false),
% 295.11/187.67 inference(unit_resolution,[status(thm)],[28864, 7868, 29465, 29461])).
% 295.11/187.67 tff(29467,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_m, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s13)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14)) | node9(c_e_h_1, c_m, s12) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s14))), inference(lemma,lemma(discharge,[]))).
% 295.11/187.67 tff(29468,plain,
% 295.11/187.67 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_m, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s13)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14))),
% 295.11/187.67 inference(unit_resolution,[status(thm)],[29467, 26480, 29399, 26436, 29396, 23399])).
% 295.11/187.67 tff(29469,plain,
% 295.11/187.67 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s13)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14))),
% 295.11/187.67 inference(unit_resolution,[status(thm)],[29468, 29389])).
% 295.11/187.67 tff(29470,plain,
% 295.11/187.67 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15)),
% 295.11/187.67 inference(unit_resolution,[status(thm)],[29469, 29026, 28860])).
% 295.11/187.67 tff(29471,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15)), introduced(assumption)).
% 295.11/187.67 tff(29472,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s15)), introduced(assumption)).
% 295.11/187.67 tff(29473,plain,
% 295.11/187.67 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s15)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s15)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15)))),
% 295.11/187.67 inference(rewrite,[status(thm)],[])).
% 295.11/187.67 tff(29474,plain,
% 295.11/187.67 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s15)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15)))),
% 295.11/187.67 inference(quant_inst,[status(thm)],[])).
% 295.11/187.67 tff(29475,plain,
% 295.11/187.67 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s15)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15))),
% 295.11/187.67 inference(modus_ponens,[status(thm)],[29474, 29473])).
% 295.11/187.67 tff(29476,plain,
% 295.11/187.67 ($false),
% 295.11/187.67 inference(unit_resolution,[status(thm)],[29475, 4958, 29472, 29471])).
% 295.11/187.67 tff(29477,plain,((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s15)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15))), inference(lemma,lemma(discharge,[]))).
% 295.11/187.67 tff(29478,plain,
% 295.11/187.67 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s15)),
% 295.11/187.67 inference(unit_resolution,[status(thm)],[29477, 29470])).
% 295.11/187.67 tff(29479,assumption,(node9(c_e_h_1, c_m, s15)), introduced(assumption)).
% 295.11/187.67 tff(29480,assumption,(~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s15)), introduced(assumption)).
% 295.11/187.67 tff(29481,plain,
% 295.11/187.67 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s15)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s15))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s15)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s15))),
% 295.11/187.67 inference(rewrite,[status(thm)],[])).
% 295.11/187.67 tff(29482,plain,
% 295.11/187.67 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s15)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s15))),
% 295.11/187.67 inference(quant_inst,[status(thm)],[])).
% 295.11/187.67 tff(29483,plain,
% 295.11/187.67 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s15)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s15)),
% 295.11/187.67 inference(modus_ponens,[status(thm)],[29482, 29481])).
% 295.11/187.67 tff(29484,plain,
% 295.11/187.67 ($false),
% 295.11/187.67 inference(unit_resolution,[status(thm)],[29483, 4972, 29480, 29479])).
% 295.11/187.67 tff(29485,plain,((~node9(c_e_h_1, c_m, s15)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s15)), inference(lemma,lemma(discharge,[]))).
% 295.11/187.67 tff(29486,plain,
% 295.11/187.67 (~node9(c_e_h_1, c_m, s15)),
% 295.11/187.67 inference(unit_resolution,[status(thm)],[29485, 29478])).
% 295.11/187.67 tff(29487,assumption,(~node9(c_e_h_1, c_m, s15)), introduced(assumption)).
% 295.11/187.68 tff(29488,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)), introduced(assumption)).
% 295.11/187.68 tff(29489,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)), introduced(assumption)).
% 295.11/187.68 tff(29490,assumption,(node11(c_e_h_1, c_m, s15, s16)), introduced(assumption)).
% 295.11/187.68 tff(29491,plain,
% 295.11/187.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)) | (~node11(c_e_h_1, c_m, s15, s16)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)) | (~node11(c_e_h_1, c_m, s15, s16)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15))),
% 295.11/187.68 inference(rewrite,[status(thm)],[])).
% 295.11/187.68 tff(29492,plain,
% 295.11/187.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)) | (~node11(c_e_h_1, c_m, s15, s16)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15))),
% 295.11/187.68 inference(quant_inst,[status(thm)],[])).
% 295.11/187.68 tff(29493,plain,
% 295.11/187.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)) | (~node11(c_e_h_1, c_m, s15, s16)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)),
% 295.11/187.68 inference(modus_ponens,[status(thm)],[29492, 29491])).
% 295.11/187.68 tff(29494,plain,
% 295.11/187.68 ($false),
% 295.11/187.68 inference(unit_resolution,[status(thm)],[29493, 5017, 29488, 29489, 29490])).
% 295.11/187.68 tff(29495,plain,((~node11(c_e_h_1, c_m, s15, s16)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16))), inference(lemma,lemma(discharge,[]))).
% 295.11/187.68 tff(29496,plain,
% 295.11/187.68 (~node11(c_e_h_1, c_m, s15, s16)),
% 295.11/187.68 inference(unit_resolution,[status(thm)],[29495, 29489, 29488])).
% 295.11/187.68 tff(29497,plain,
% 295.11/187.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s15, s16)) | node10(c_e_h_1, c_m, s15, s16) | node11(c_e_h_1, c_m, s15, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s15, s16)) | node10(c_e_h_1, c_m, s15, s16) | node11(c_e_h_1, c_m, s15, s16))),
% 295.11/187.68 inference(rewrite,[status(thm)],[])).
% 295.11/187.68 tff(29498,plain,
% 295.11/187.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s15, s16)) | node10(c_e_h_1, c_m, s15, s16) | node11(c_e_h_1, c_m, s15, s16))),
% 295.11/187.68 inference(quant_inst,[status(thm)],[])).
% 295.11/187.68 tff(29499,plain,
% 295.11/187.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s15, s16)) | node10(c_e_h_1, c_m, s15, s16) | node11(c_e_h_1, c_m, s15, s16)),
% 295.11/187.68 inference(modus_ponens,[status(thm)],[29498, 29497])).
% 295.11/187.68 tff(29500,plain,
% 295.11/187.68 (node10(c_e_h_1, c_m, s15, s16) | node11(c_e_h_1, c_m, s15, s16)),
% 295.11/187.68 inference(unit_resolution,[status(thm)],[29499, 5002, 13499])).
% 295.11/187.68 tff(29501,plain,
% 295.11/187.68 (node10(c_e_h_1, c_m, s15, s16)),
% 295.11/187.68 inference(unit_resolution,[status(thm)],[29500, 29496])).
% 295.11/187.68 tff(29502,plain,
% 295.11/187.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)) | node9(c_e_h_1, c_m, s15) | (~node10(c_e_h_1, c_m, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)) | node9(c_e_h_1, c_m, s15) | (~node10(c_e_h_1, c_m, s15, s16)))),
% 295.11/187.68 inference(rewrite,[status(thm)],[])).
% 295.11/187.68 tff(29503,plain,
% 295.11/187.68 ((node9(c_e_h_1, c_m, s15) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)) | (~node10(c_e_h_1, c_m, s15, s16))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)) | node9(c_e_h_1, c_m, s15) | (~node10(c_e_h_1, c_m, s15, s16)))),
% 295.11/187.68 inference(rewrite,[status(thm)],[])).
% 295.11/187.68 tff(29504,plain,
% 295.11/187.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s15) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)) | (~node10(c_e_h_1, c_m, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)) | node9(c_e_h_1, c_m, s15) | (~node10(c_e_h_1, c_m, s15, s16))))),
% 295.11/187.68 inference(monotonicity,[status(thm)],[29503])).
% 295.11/187.68 tff(29505,plain,
% 295.11/187.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s15) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)) | (~node10(c_e_h_1, c_m, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)) | node9(c_e_h_1, c_m, s15) | (~node10(c_e_h_1, c_m, s15, s16)))),
% 295.11/187.68 inference(transitivity,[status(thm)],[29504, 29502])).
% 295.11/187.68 tff(29506,plain,
% 295.11/187.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s15) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)) | (~node10(c_e_h_1, c_m, s15, s16)))),
% 295.11/187.68 inference(quant_inst,[status(thm)],[])).
% 295.11/187.68 tff(29507,plain,
% 295.11/187.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)) | node9(c_e_h_1, c_m, s15) | (~node10(c_e_h_1, c_m, s15, s16))),
% 295.11/187.68 inference(modus_ponens,[status(thm)],[29506, 29505])).
% 295.11/187.68 tff(29508,plain,
% 295.11/187.68 ($false),
% 295.11/187.68 inference(unit_resolution,[status(thm)],[29507, 4986, 29489, 29501, 29487])).
% 295.11/187.68 tff(29509,plain,((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)) | node9(c_e_h_1, c_m, s15) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)), inference(lemma,lemma(discharge,[]))).
% 295.11/187.68 tff(29510,plain,
% 295.11/187.68 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)),
% 295.11/187.68 inference(unit_resolution,[status(thm)],[29509, 29486, 28936])).
% 295.11/187.68 tff(29511,plain,
% 295.11/187.68 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s16)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s16)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16))),
% 295.11/187.68 inference(rewrite,[status(thm)],[])).
% 295.11/187.68 tff(29512,plain,
% 295.11/187.68 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s16)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16))),
% 295.11/187.68 inference(quant_inst,[status(thm)],[])).
% 295.11/187.68 tff(29513,plain,
% 295.11/187.68 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s16)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)),
% 295.11/187.68 inference(modus_ponens,[status(thm)],[29512, 29511])).
% 295.11/187.68 tff(29514,plain,
% 295.11/187.68 (~m_and_h_gate_v_in2(c_e_h_1, c_l, s16)),
% 295.11/187.68 inference(unit_resolution,[status(thm)],[29513, 4549, 29510])).
% 295.11/187.68 tff(29515,plain,
% 295.11/187.68 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s16)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s16))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s16)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s16))),
% 295.11/187.68 inference(rewrite,[status(thm)],[])).
% 295.11/187.68 tff(29516,plain,
% 295.11/187.68 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s16)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s16))),
% 295.11/187.68 inference(quant_inst,[status(thm)],[])).
% 295.11/187.68 tff(29517,plain,
% 295.11/187.68 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s16)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s16)),
% 295.11/187.68 inference(modus_ponens,[status(thm)],[29516, 29515])).
% 295.11/187.68 tff(29518,plain,
% 295.11/187.68 (~node20(c_e_h_1, c_l, s16)),
% 295.11/187.68 inference(unit_resolution,[status(thm)],[29517, 4563, 29514])).
% 295.11/187.68 tff(29519,assumption,(m_and_h_gate_v_out(c_e_h_1, c_l, s17)), introduced(assumption)).
% 295.11/187.68 tff(29520,assumption,(~node20(c_e_h_1, c_l, s16)), introduced(assumption)).
% 295.11/187.68 tff(29521,assumption,(node22(c_e_h_1, c_l, s16, s17)), introduced(assumption)).
% 295.11/187.68 tff(29522,plain,
% 295.11/187.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s17)) | (~node22(c_e_h_1, c_l, s16, s17)) | m_and_h_gate_v_out(c_e_h_1, c_l, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s17)) | (~node22(c_e_h_1, c_l, s16, s17)) | m_and_h_gate_v_out(c_e_h_1, c_l, s16))),
% 295.11/187.68 inference(rewrite,[status(thm)],[])).
% 295.11/187.68 tff(29523,plain,
% 295.11/187.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s17)) | (~node22(c_e_h_1, c_l, s16, s17)) | m_and_h_gate_v_out(c_e_h_1, c_l, s16))),
% 295.11/187.68 inference(quant_inst,[status(thm)],[])).
% 295.11/187.68 tff(29524,plain,
% 295.11/187.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s17)) | (~node22(c_e_h_1, c_l, s16, s17)) | m_and_h_gate_v_out(c_e_h_1, c_l, s16)),
% 295.11/187.68 inference(modus_ponens,[status(thm)],[29523, 29522])).
% 295.11/187.68 tff(29525,plain,
% 295.11/187.68 ($false),
% 295.11/187.68 inference(unit_resolution,[status(thm)],[29524, 108, 29521, 28967, 29519])).
% 295.11/187.68 tff(29526,plain,((~node22(c_e_h_1, c_l, s16, s17)) | m_and_h_gate_v_out(c_e_h_1, c_l, s16) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s17))), inference(lemma,lemma(discharge,[]))).
% 295.11/187.68 tff(29527,plain,
% 295.11/187.68 (~node22(c_e_h_1, c_l, s16, s17)),
% 295.11/187.68 inference(unit_resolution,[status(thm)],[29526, 29519, 28967])).
% 295.11/187.68 tff(29528,plain,
% 295.11/187.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s16, s17)) | node21(c_e_h_1, c_l, s16, s17) | node22(c_e_h_1, c_l, s16, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s16, s17)) | node21(c_e_h_1, c_l, s16, s17) | node22(c_e_h_1, c_l, s16, s17))),
% 295.11/187.68 inference(rewrite,[status(thm)],[])).
% 295.11/187.68 tff(29529,plain,
% 295.11/187.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s16, s17)) | node21(c_e_h_1, c_l, s16, s17) | node22(c_e_h_1, c_l, s16, s17))),
% 295.11/187.68 inference(quant_inst,[status(thm)],[])).
% 295.11/187.68 tff(29530,plain,
% 295.11/187.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s16, s17)) | node21(c_e_h_1, c_l, s16, s17) | node22(c_e_h_1, c_l, s16, s17)),
% 295.11/187.68 inference(modus_ponens,[status(thm)],[29529, 29528])).
% 295.11/187.68 tff(29531,plain,
% 295.11/187.68 (node21(c_e_h_1, c_l, s16, s17) | node22(c_e_h_1, c_l, s16, s17)),
% 295.11/187.68 inference(unit_resolution,[status(thm)],[29530, 82, 11967])).
% 295.11/187.68 tff(29532,plain,
% 295.11/187.68 (node21(c_e_h_1, c_l, s16, s17)),
% 295.11/187.68 inference(unit_resolution,[status(thm)],[29531, 29527])).
% 295.11/187.68 tff(29533,plain,
% 295.11/187.68 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s16) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s17)) | (~node21(c_e_h_1, c_l, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s16) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s17)) | (~node21(c_e_h_1, c_l, s16, s17)))),
% 295.11/187.68 inference(rewrite,[status(thm)],[])).
% 295.11/187.68 tff(29534,plain,
% 295.11/187.68 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s16) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s17)) | (~node21(c_e_h_1, c_l, s16, s17)))),
% 295.11/187.69 inference(quant_inst,[status(thm)],[])).
% 295.11/187.69 tff(29535,plain,
% 295.11/187.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s16) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s17)) | (~node21(c_e_h_1, c_l, s16, s17))),
% 295.11/187.69 inference(modus_ponens,[status(thm)],[29534, 29533])).
% 295.11/187.69 tff(29536,plain,
% 295.11/187.69 ($false),
% 295.11/187.69 inference(unit_resolution,[status(thm)],[29535, 52, 29532, 29520, 29519])).
% 295.11/187.69 tff(29537,plain,((~m_and_h_gate_v_out(c_e_h_1, c_l, s17)) | node20(c_e_h_1, c_l, s16) | m_and_h_gate_v_out(c_e_h_1, c_l, s16)), inference(lemma,lemma(discharge,[]))).
% 295.11/187.69 tff(29538,plain,
% 295.11/187.69 (~m_and_h_gate_v_out(c_e_h_1, c_l, s17)),
% 295.11/187.69 inference(unit_resolution,[status(thm)],[29537, 29518, 28965])).
% 295.11/187.69 tff(29539,assumption,(m_or_h_gate_v_in1(c_e_h_1, c_j, s17)), introduced(assumption)).
% 295.11/187.69 tff(29540,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_l, s17)), introduced(assumption)).
% 295.11/187.69 tff(29541,plain,
% 295.11/187.69 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s17)) | m_and_h_gate_v_out(c_e_h_1, c_l, s17))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s17)) | m_and_h_gate_v_out(c_e_h_1, c_l, s17))),
% 295.11/187.69 inference(rewrite,[status(thm)],[])).
% 295.11/187.69 tff(29542,plain,
% 295.11/187.69 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s17)) | m_and_h_gate_v_out(c_e_h_1, c_l, s17))),
% 295.11/187.69 inference(quant_inst,[status(thm)],[])).
% 295.11/187.69 tff(29543,plain,
% 295.11/187.69 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s17)) | m_and_h_gate_v_out(c_e_h_1, c_l, s17)),
% 295.11/187.69 inference(modus_ponens,[status(thm)],[29542, 29541])).
% 295.11/187.69 tff(29544,plain,
% 295.11/187.69 ($false),
% 295.11/187.69 inference(unit_resolution,[status(thm)],[29543, 1100, 29540, 29539])).
% 295.11/187.69 tff(29545,plain,((~m_or_h_gate_v_in1(c_e_h_1, c_j, s17)) | m_and_h_gate_v_out(c_e_h_1, c_l, s17)), inference(lemma,lemma(discharge,[]))).
% 295.11/187.69 tff(29546,plain,
% 295.11/187.69 (~m_or_h_gate_v_in1(c_e_h_1, c_j, s17)),
% 295.11/187.69 inference(unit_resolution,[status(thm)],[29545, 29538])).
% 295.11/187.69 tff(29547,assumption,(~m_or_h_gate_v_in2(c_e_h_1, c_j, s17)), introduced(assumption)).
% 295.11/187.69 tff(29548,assumption,(~m_or_h_gate_v_in1(c_e_h_1, c_j, s17)), introduced(assumption)).
% 295.11/187.69 tff(29549,assumption,(m_or_h_gate_v_out(c_e_h_1, c_j, s18)), introduced(assumption)).
% 295.11/187.69 tff(29550,assumption,(node5(c_e_h_1, c_j, s17, s18)), introduced(assumption)).
% 295.11/187.69 tff(29551,plain,
% 295.11/187.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_1, c_j, s17) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s18)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s17) | (~node5(c_e_h_1, c_j, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_1, c_j, s17) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s18)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s17) | (~node5(c_e_h_1, c_j, s17, s18)))),
% 295.11/187.69 inference(rewrite,[status(thm)],[])).
% 295.11/187.69 tff(29552,plain,
% 295.11/187.69 ((m_or_h_gate_v_in1(c_e_h_1, c_j, s17) | m_or_h_gate_v_in2(c_e_h_1, c_j, s17) | (~node5(c_e_h_1, c_j, s17, s18)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s18))) <=> (m_or_h_gate_v_in2(c_e_h_1, c_j, s17) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s18)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s17) | (~node5(c_e_h_1, c_j, s17, s18)))),
% 295.11/187.69 inference(rewrite,[status(thm)],[])).
% 295.11/187.69 tff(29553,plain,
% 295.11/187.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s17) | m_or_h_gate_v_in2(c_e_h_1, c_j, s17) | (~node5(c_e_h_1, c_j, s17, s18)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_1, c_j, s17) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s18)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s17) | (~node5(c_e_h_1, c_j, s17, s18))))),
% 295.11/187.69 inference(monotonicity,[status(thm)],[29552])).
% 295.11/187.69 tff(29554,plain,
% 295.11/187.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s17) | m_or_h_gate_v_in2(c_e_h_1, c_j, s17) | (~node5(c_e_h_1, c_j, s17, s18)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_1, c_j, s17) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s18)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s17) | (~node5(c_e_h_1, c_j, s17, s18)))),
% 295.11/187.69 inference(transitivity,[status(thm)],[29553, 29551])).
% 295.11/187.69 tff(29555,plain,
% 295.11/187.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s17) | m_or_h_gate_v_in2(c_e_h_1, c_j, s17) | (~node5(c_e_h_1, c_j, s17, s18)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s18)))),
% 295.11/187.69 inference(quant_inst,[status(thm)],[])).
% 295.11/187.69 tff(29556,plain,
% 295.11/187.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_1, c_j, s17) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s18)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s17) | (~node5(c_e_h_1, c_j, s17, s18))),
% 295.11/187.69 inference(modus_ponens,[status(thm)],[29555, 29554])).
% 295.11/187.69 tff(29557,plain,
% 295.11/187.69 ($false),
% 295.11/187.69 inference(unit_resolution,[status(thm)],[29556, 1159, 29549, 29550, 29548, 29547])).
% 295.11/187.69 tff(29558,plain,((~node5(c_e_h_1, c_j, s17, s18)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s18)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s17) | m_or_h_gate_v_in2(c_e_h_1, c_j, s17)), inference(lemma,lemma(discharge,[]))).
% 295.11/187.69 tff(29559,plain,
% 295.11/187.69 (~node5(c_e_h_1, c_j, s17, s18)),
% 295.11/187.69 inference(unit_resolution,[status(thm)],[29558, 29549, 29548, 29547])).
% 295.11/187.69 tff(29560,assumption,(~m_or_h_gate_v_out(c_e_h_1, c_j, s17)), introduced(assumption)).
% 295.11/187.69 tff(29561,assumption,(node6(c_e_h_1, c_j, s17, s18)), introduced(assumption)).
% 295.11/187.69 tff(29562,plain,
% 295.11/187.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s17) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s18)) | (~node6(c_e_h_1, c_j, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s17) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s18)) | (~node6(c_e_h_1, c_j, s17, s18)))),
% 295.11/187.69 inference(rewrite,[status(thm)],[])).
% 295.11/187.69 tff(29563,plain,
% 295.11/187.69 (((~node6(c_e_h_1, c_j, s17, s18)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s18)) | m_or_h_gate_v_out(c_e_h_1, c_j, s17)) <=> (m_or_h_gate_v_out(c_e_h_1, c_j, s17) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s18)) | (~node6(c_e_h_1, c_j, s17, s18)))),
% 295.11/187.69 inference(rewrite,[status(thm)],[])).
% 295.11/187.69 tff(29564,plain,
% 295.11/187.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s17, s18)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s18)) | m_or_h_gate_v_out(c_e_h_1, c_j, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s17) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s18)) | (~node6(c_e_h_1, c_j, s17, s18))))),
% 295.11/187.69 inference(monotonicity,[status(thm)],[29563])).
% 295.11/187.69 tff(29565,plain,
% 295.11/187.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s17, s18)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s18)) | m_or_h_gate_v_out(c_e_h_1, c_j, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s17) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s18)) | (~node6(c_e_h_1, c_j, s17, s18)))),
% 295.20/187.69 inference(transitivity,[status(thm)],[29564, 29562])).
% 295.20/187.69 tff(29566,plain,
% 295.20/187.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s17, s18)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s18)) | m_or_h_gate_v_out(c_e_h_1, c_j, s17))),
% 295.20/187.69 inference(quant_inst,[status(thm)],[])).
% 295.20/187.69 tff(29567,plain,
% 295.20/187.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s17) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s18)) | (~node6(c_e_h_1, c_j, s17, s18))),
% 295.20/187.69 inference(modus_ponens,[status(thm)],[29566, 29565])).
% 295.20/187.69 tff(29568,plain,
% 295.20/187.69 ($false),
% 295.20/187.69 inference(unit_resolution,[status(thm)],[29567, 1121, 29560, 29549, 29561])).
% 295.20/187.69 tff(29569,plain,((~node6(c_e_h_1, c_j, s17, s18)) | m_or_h_gate_v_out(c_e_h_1, c_j, s17) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s18))), inference(lemma,lemma(discharge,[]))).
% 295.20/187.69 tff(29570,plain,
% 295.20/187.69 (~node6(c_e_h_1, c_j, s17, s18)),
% 295.20/187.69 inference(unit_resolution,[status(thm)],[29569, 29549, 29560])).
% 295.20/187.69 tff(29571,plain,
% 295.20/187.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s17, s18)) | node6(c_e_h_1, c_j, s17, s18) | node5(c_e_h_1, c_j, s17, s18))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s17, s18)) | node6(c_e_h_1, c_j, s17, s18) | node5(c_e_h_1, c_j, s17, s18))),
% 295.20/187.69 inference(rewrite,[status(thm)],[])).
% 295.20/187.69 tff(29572,plain,
% 295.20/187.69 ((node6(c_e_h_1, c_j, s17, s18) | node5(c_e_h_1, c_j, s17, s18) | (~trans(s17, s18))) <=> ((~trans(s17, s18)) | node6(c_e_h_1, c_j, s17, s18) | node5(c_e_h_1, c_j, s17, s18))),
% 295.20/187.69 inference(rewrite,[status(thm)],[])).
% 295.20/187.69 tff(29573,plain,
% 295.20/187.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s17, s18) | node5(c_e_h_1, c_j, s17, s18) | (~trans(s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s17, s18)) | node6(c_e_h_1, c_j, s17, s18) | node5(c_e_h_1, c_j, s17, s18)))),
% 295.20/187.69 inference(monotonicity,[status(thm)],[29572])).
% 295.20/187.69 tff(29574,plain,
% 295.20/187.69 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s17, s18) | node5(c_e_h_1, c_j, s17, s18) | (~trans(s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s17, s18)) | node6(c_e_h_1, c_j, s17, s18) | node5(c_e_h_1, c_j, s17, s18))),
% 295.20/187.69 inference(transitivity,[status(thm)],[29573, 29571])).
% 295.20/187.69 tff(29575,plain,
% 295.20/187.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s17, s18) | node5(c_e_h_1, c_j, s17, s18) | (~trans(s17, s18)))),
% 295.20/187.69 inference(quant_inst,[status(thm)],[])).
% 295.20/187.69 tff(29576,plain,
% 295.20/187.69 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s17, s18)) | node6(c_e_h_1, c_j, s17, s18) | node5(c_e_h_1, c_j, s17, s18)),
% 295.20/187.69 inference(modus_ponens,[status(thm)],[29575, 29574])).
% 295.20/187.69 tff(29577,plain,
% 295.20/187.69 (node6(c_e_h_1, c_j, s17, s18) | node5(c_e_h_1, c_j, s17, s18)),
% 295.20/187.69 inference(unit_resolution,[status(thm)],[29576, 1141, 26135])).
% 295.20/187.69 tff(29578,plain,
% 295.20/187.69 ($false),
% 295.20/187.69 inference(unit_resolution,[status(thm)],[29577, 29570, 29559])).
% 295.20/187.69 tff(29579,plain,((~m_or_h_gate_v_out(c_e_h_1, c_j, s18)) | m_or_h_gate_v_out(c_e_h_1, c_j, s17) | m_or_h_gate_v_in1(c_e_h_1, c_j, s17) | m_or_h_gate_v_in2(c_e_h_1, c_j, s17)), inference(lemma,lemma(discharge,[]))).
% 295.20/187.69 tff(29580,plain,
% 295.20/187.69 ((~m_or_h_gate_v_out(c_e_h_1, c_j, s18)) | m_or_h_gate_v_out(c_e_h_1, c_j, s17) | m_or_h_gate_v_in2(c_e_h_1, c_j, s17)),
% 295.20/187.70 inference(unit_resolution,[status(thm)],[29579, 29546])).
% 295.20/187.70 tff(29581,plain,
% 295.20/187.70 (~m_or_h_gate_v_out(c_e_h_1, c_j, s18)),
% 295.20/187.70 inference(unit_resolution,[status(thm)],[29580, 29021, 29008])).
% 295.20/187.70 tff(29582,plain,
% 295.20/187.70 (~m_c_h_element_v_out(c_e_h_1, c_e, s14)),
% 295.20/187.70 inference(unit_resolution,[status(thm)],[25855, 25772, 25770])).
% 295.20/187.70 tff(29583,plain,
% 295.20/187.70 (~m_c_h_element_v_out(c_e_h_1, c_e, s15)),
% 295.20/187.70 inference(unit_resolution,[status(thm)],[25927, 29582, 25876])).
% 295.20/187.70 tff(29584,plain,
% 295.20/187.70 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s13)),
% 295.20/187.70 inference(unit_resolution,[status(thm)],[28859, 25772])).
% 295.20/187.70 tff(29585,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16)), introduced(assumption)).
% 295.20/187.70 tff(29586,plain,
% 295.20/187.70 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14)),
% 295.20/187.70 inference(unit_resolution,[status(thm)],[29025, 29582])).
% 295.20/187.70 tff(29587,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s15)), introduced(assumption)).
% 295.20/187.70 tff(29588,plain,
% 295.20/187.70 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)),
% 295.20/187.70 inference(unit_resolution,[status(thm)],[25396, 25330, 25324, 23372])).
% 295.20/187.70 tff(29589,plain,
% 295.20/187.70 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s13)),
% 295.20/187.70 inference(unit_resolution,[status(thm)],[28866, 25403])).
% 295.20/187.70 tff(29590,plain,
% 295.20/187.70 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s14)),
% 295.20/187.70 inference(unit_resolution,[status(thm)],[28894, 28886, 29589, 28869])).
% 295.20/187.70 tff(29591,plain,
% 295.20/187.70 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s14)),
% 295.20/187.70 inference(unit_resolution,[status(thm)],[28903, 29590])).
% 295.20/187.70 tff(29592,plain,
% 295.20/187.70 (~node9(c_e_h_1, c_m, s14)),
% 295.20/187.70 inference(unit_resolution,[status(thm)],[28911, 29591])).
% 295.20/187.70 tff(29593,plain,
% 295.20/187.70 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s13)),
% 295.20/187.70 inference(unit_resolution,[status(thm)],[26483, 4958, 28886])).
% 295.20/187.70 tff(29594,plain,
% 295.20/187.70 (~node9(c_e_h_1, c_m, s13)),
% 295.20/187.70 inference(unit_resolution,[status(thm)],[26487, 4972, 29593])).
% 295.20/187.70 tff(29595,plain,
% 295.20/187.70 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)),
% 295.20/187.70 inference(unit_resolution,[status(thm)],[26513, 29594, 25403])).
% 295.20/187.70 tff(29596,plain,
% 295.20/187.70 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)),
% 295.20/187.70 inference(unit_resolution,[status(thm)],[28934, 29595, 29592])).
% 295.20/187.70 tff(29597,plain,
% 295.20/187.70 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s15) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s15) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15))),
% 295.20/187.70 inference(rewrite,[status(thm)],[])).
% 295.20/187.70 tff(29598,plain,
% 295.20/187.70 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s15) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15))),
% 295.20/187.70 inference(quant_inst,[status(thm)],[])).
% 295.20/187.70 tff(29599,plain,
% 295.20/187.70 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s15) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)),
% 295.20/187.70 inference(modus_ponens,[status(thm)],[29598, 29597])).
% 295.20/187.70 tff(29600,plain,
% 295.20/187.70 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s15) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)),
% 295.20/187.70 inference(unit_resolution,[status(thm)],[29599, 7868])).
% 295.20/187.70 tff(29601,plain,
% 295.20/187.70 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s15)),
% 295.20/187.70 inference(unit_resolution,[status(thm)],[29600, 29596])).
% 295.20/187.70 tff(29602,assumption,(node11(c_e_h_1, c_n, s15, s16)), introduced(assumption)).
% 295.20/187.70 tff(29603,plain,
% 295.20/187.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15)) | (~node11(c_e_h_1, c_n, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15)) | (~node11(c_e_h_1, c_n, s15, s16)))),
% 295.20/187.70 inference(rewrite,[status(thm)],[])).
% 295.20/187.70 tff(29604,plain,
% 295.20/187.70 ((m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16) | (~node11(c_e_h_1, c_n, s15, s16)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15))) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15)) | (~node11(c_e_h_1, c_n, s15, s16)))),
% 295.20/187.70 inference(rewrite,[status(thm)],[])).
% 295.20/187.70 tff(29605,plain,
% 295.20/187.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16) | (~node11(c_e_h_1, c_n, s15, s16)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15)) | (~node11(c_e_h_1, c_n, s15, s16))))),
% 295.20/187.70 inference(monotonicity,[status(thm)],[29604])).
% 295.20/187.70 tff(29606,plain,
% 295.20/187.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16) | (~node11(c_e_h_1, c_n, s15, s16)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15)) | (~node11(c_e_h_1, c_n, s15, s16)))),
% 295.20/187.70 inference(transitivity,[status(thm)],[29605, 29603])).
% 295.20/187.70 tff(29607,plain,
% 295.20/187.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16) | (~node11(c_e_h_1, c_n, s15, s16)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15)))),
% 295.20/187.70 inference(quant_inst,[status(thm)],[])).
% 295.20/187.70 tff(29608,plain,
% 295.20/187.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15)) | (~node11(c_e_h_1, c_n, s15, s16))),
% 295.20/187.70 inference(modus_ponens,[status(thm)],[29607, 29606])).
% 295.20/187.70 tff(29609,plain,
% 295.20/187.70 ($false),
% 295.20/187.70 inference(unit_resolution,[status(thm)],[29608, 5742, 29585, 29602, 29471])).
% 295.20/187.70 tff(29610,plain,((~node11(c_e_h_1, c_n, s15, s16)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15))), inference(lemma,lemma(discharge,[]))).
% 295.20/187.70 tff(29611,plain,
% 295.20/187.70 (~node11(c_e_h_1, c_n, s15, s16)),
% 295.20/187.70 inference(unit_resolution,[status(thm)],[29610, 29585, 29471])).
% 295.20/187.70 tff(29612,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s15)), introduced(assumption)).
% 295.20/187.70 tff(29613,assumption,(node10(c_e_h_1, c_n, s15, s16)), introduced(assumption)).
% 295.20/187.70 tff(29614,plain,
% 295.20/187.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s15)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s15)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16) | (~node10(c_e_h_1, c_n, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s15)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s15)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16) | (~node10(c_e_h_1, c_n, s15, s16)))),
% 295.20/187.70 inference(rewrite,[status(thm)],[])).
% 295.20/187.70 tff(29615,plain,
% 295.20/187.70 (((~node10(c_e_h_1, c_n, s15, s16)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s15)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s15)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16)) <=> ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s15)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s15)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16) | (~node10(c_e_h_1, c_n, s15, s16)))),
% 295.20/187.70 inference(rewrite,[status(thm)],[])).
% 295.20/187.70 tff(29616,plain,
% 295.20/187.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s15, s16)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s15)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s15)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s15)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s15)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16) | (~node10(c_e_h_1, c_n, s15, s16))))),
% 295.20/187.70 inference(monotonicity,[status(thm)],[29615])).
% 295.20/187.70 tff(29617,plain,
% 295.20/187.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s15, s16)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s15)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s15)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s15)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s15)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16) | (~node10(c_e_h_1, c_n, s15, s16)))),
% 295.20/187.70 inference(transitivity,[status(thm)],[29616, 29614])).
% 295.20/187.70 tff(29618,plain,
% 295.20/187.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s15, s16)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s15)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s15)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16))),
% 295.20/187.70 inference(quant_inst,[status(thm)],[])).
% 295.20/187.70 tff(29619,plain,
% 295.20/187.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s15)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s15)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16) | (~node10(c_e_h_1, c_n, s15, s16))),
% 295.20/187.70 inference(modus_ponens,[status(thm)],[29618, 29617])).
% 295.20/187.70 tff(29620,plain,
% 295.20/187.70 ($false),
% 295.20/187.70 inference(unit_resolution,[status(thm)],[29619, 5718, 29612, 29587, 29585, 29613])).
% 295.20/187.70 tff(29621,plain,((~node10(c_e_h_1, c_n, s15, s16)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s15)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s15)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16)), inference(lemma,lemma(discharge,[]))).
% 295.20/187.70 tff(29622,plain,
% 295.20/187.70 (~node10(c_e_h_1, c_n, s15, s16)),
% 295.20/187.70 inference(unit_resolution,[status(thm)],[29621, 29585, 29612, 29587])).
% 295.20/187.70 tff(29623,plain,
% 295.20/187.70 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s15, s16)) | node10(c_e_h_1, c_n, s15, s16) | node11(c_e_h_1, c_n, s15, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s15, s16)) | node10(c_e_h_1, c_n, s15, s16) | node11(c_e_h_1, c_n, s15, s16))),
% 295.20/187.70 inference(rewrite,[status(thm)],[])).
% 295.20/187.70 tff(29624,plain,
% 295.20/187.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s15, s16)) | node10(c_e_h_1, c_n, s15, s16) | node11(c_e_h_1, c_n, s15, s16))),
% 295.20/187.70 inference(quant_inst,[status(thm)],[])).
% 295.20/187.70 tff(29625,plain,
% 295.20/187.70 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s15, s16)) | node10(c_e_h_1, c_n, s15, s16) | node11(c_e_h_1, c_n, s15, s16)),
% 295.20/187.71 inference(modus_ponens,[status(thm)],[29624, 29623])).
% 295.20/187.71 tff(29626,plain,
% 295.20/187.71 (node10(c_e_h_1, c_n, s15, s16) | node11(c_e_h_1, c_n, s15, s16)),
% 295.20/187.71 inference(unit_resolution,[status(thm)],[29625, 5002, 13499])).
% 295.20/187.71 tff(29627,plain,
% 295.20/187.71 ($false),
% 295.20/187.71 inference(unit_resolution,[status(thm)],[29626, 29622, 29611])).
% 295.20/187.71 tff(29628,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s15)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s15)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15))), inference(lemma,lemma(discharge,[]))).
% 295.20/187.71 tff(29629,plain,
% 295.20/187.71 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s15)),
% 295.20/187.71 inference(unit_resolution,[status(thm)],[29628, 29601, 29587, 29585])).
% 295.20/187.71 tff(29630,plain,
% 295.20/187.71 (~node11(c_e_h_1, c_n, s14, s15)),
% 295.20/187.71 inference(unit_resolution,[status(thm)],[29431, 29629, 29590])).
% 295.20/187.71 tff(29631,plain,
% 295.20/187.71 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s14)),
% 295.20/187.71 inference(unit_resolution,[status(thm)],[29395, 29595])).
% 295.20/187.71 tff(29632,plain,
% 295.20/187.71 (~node10(c_e_h_1, c_n, s14, s15)),
% 295.20/187.71 inference(unit_resolution,[status(thm)],[29447, 29629, 29631, 29400])).
% 295.20/187.71 tff(29633,plain,
% 295.20/187.71 ($false),
% 295.20/187.71 inference(unit_resolution,[status(thm)],[29436, 29632, 29630])).
% 295.20/187.71 tff(29634,plain,((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s15)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s13))), inference(lemma,lemma(discharge,[]))).
% 295.20/187.71 tff(29635,plain,
% 295.20/187.71 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s13)),
% 295.20/187.71 inference(unit_resolution,[status(thm)],[29634, 29588, 28869, 29585, 29587, 29400])).
% 295.20/187.71 tff(29636,plain,
% 295.20/187.71 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s12)),
% 295.20/187.71 inference(unit_resolution,[status(thm)],[25364, 25335, 25324, 25329])).
% 295.20/187.71 tff(29637,plain,
% 295.20/187.71 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s12)),
% 295.20/187.71 inference(unit_resolution,[status(thm)],[26469, 29636, 26437, 29635])).
% 295.20/187.71 tff(29638,plain,
% 295.20/187.71 (m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s12)),
% 295.20/187.71 inference(unit_resolution,[status(thm)],[26474, 29637])).
% 295.20/187.71 tff(29639,plain,
% 295.20/187.71 (node9(c_e_h_1, c_m, s11)),
% 295.20/187.71 inference(unit_resolution,[status(thm)],[23397, 29638, 23372])).
% 295.20/187.71 tff(29640,plain,
% 295.20/187.71 ($false),
% 295.20/187.71 inference(unit_resolution,[status(thm)],[23370, 4972, 25330, 29639])).
% 295.20/187.71 tff(29641,plain,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s11) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s15)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s14)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11))), inference(lemma,lemma(discharge,[]))).
% 295.20/187.71 tff(29642,plain,
% 295.20/187.71 (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s15)),
% 295.20/187.71 inference(unit_resolution,[status(thm)],[29641, 29586, 29585, 26437, 23372, 25330, 29584, 25324])).
% 295.20/187.71 tff(29643,plain,
% 295.20/187.71 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s15) | m_c_h_element_v_out(c_e_h_1, c_e, s15))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s15) | m_c_h_element_v_out(c_e_h_1, c_e, s15))),
% 295.20/187.71 inference(rewrite,[status(thm)],[])).
% 295.20/187.71 tff(29644,plain,
% 295.20/187.71 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s15) | m_c_h_element_v_out(c_e_h_1, c_e, s15))),
% 295.20/187.71 inference(quant_inst,[status(thm)],[])).
% 295.20/187.71 tff(29645,plain,
% 295.20/187.71 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s15) | m_c_h_element_v_out(c_e_h_1, c_e, s15)),
% 295.20/187.71 inference(modus_ponens,[status(thm)],[29644, 29643])).
% 295.20/187.71 tff(29646,plain,
% 295.20/187.71 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s15) | m_c_h_element_v_out(c_e_h_1, c_e, s15)),
% 295.20/187.71 inference(unit_resolution,[status(thm)],[29645, 7856])).
% 295.20/187.71 tff(29647,plain,
% 295.20/187.71 ($false),
% 295.20/187.71 inference(unit_resolution,[status(thm)],[29646, 29642, 29583])).
% 295.20/187.71 tff(29648,plain,(m_c_h_element_v_out(c_e_h_1, c_e, s13) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s11) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11)) | m_c_h_element_v_in2(c_e_h_1, c_e, s14) | m_c_h_element_v_in2(c_e_h_1, c_e, s13)), inference(lemma,lemma(discharge,[]))).
% 295.20/187.71 tff(29649,plain,
% 295.20/187.71 (m_c_h_element_v_out(c_e_h_1, c_e, s13) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s11) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11)) | m_c_h_element_v_in2(c_e_h_1, c_e, s14) | m_c_h_element_v_in2(c_e_h_1, c_e, s13)),
% 295.20/187.71 inference(unit_resolution,[status(thm)],[29648, 23106])).
% 295.20/187.71 tff(29650,plain,
% 295.20/187.71 (m_c_h_element_v_out(c_e_h_1, c_e, s13) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16) | m_c_h_element_v_in2(c_e_h_1, c_e, s14) | m_c_h_element_v_in2(c_e_h_1, c_e, s13)),
% 295.20/187.71 inference(unit_resolution,[status(thm)],[29649, 23367, 26431, 26436])).
% 295.20/187.71 tff(29651,plain,
% 295.20/187.71 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16)),
% 295.20/187.71 inference(unit_resolution,[status(thm)],[29650, 25863, 25762, 25769])).
% 295.20/187.71 tff(29652,plain,
% 295.20/187.71 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s16)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s16)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16)))),
% 295.20/187.71 inference(rewrite,[status(thm)],[])).
% 295.20/187.71 tff(29653,plain,
% 295.20/187.71 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s16)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16)))),
% 295.20/187.71 inference(quant_inst,[status(thm)],[])).
% 295.20/187.71 tff(29654,plain,
% 295.20/187.71 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s16)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16))),
% 295.20/187.71 inference(modus_ponens,[status(thm)],[29653, 29652])).
% 295.20/187.71 tff(29655,plain,
% 295.20/187.71 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s16)),
% 295.20/187.71 inference(unit_resolution,[status(thm)],[29654, 4958, 29651])).
% 295.20/187.71 tff(29656,plain,
% 295.20/187.71 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s16)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s16))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s16)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s16))),
% 295.20/187.71 inference(rewrite,[status(thm)],[])).
% 295.20/187.71 tff(29657,plain,
% 295.20/187.71 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s16)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s16))),
% 295.20/187.71 inference(quant_inst,[status(thm)],[])).
% 295.20/187.71 tff(29658,plain,
% 295.20/187.71 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s16)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s16)),
% 295.20/187.71 inference(modus_ponens,[status(thm)],[29657, 29656])).
% 295.20/187.71 tff(29659,plain,
% 295.20/187.71 (~node9(c_e_h_1, c_m, s16)),
% 295.20/187.71 inference(unit_resolution,[status(thm)],[29658, 4972, 29655])).
% 295.20/187.71 tff(29660,assumption,(~node9(c_e_h_1, c_m, s16)), introduced(assumption)).
% 295.20/187.71 tff(29661,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)), introduced(assumption)).
% 295.20/187.71 tff(29662,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17)), introduced(assumption)).
% 295.20/187.71 tff(29663,assumption,(node11(c_e_h_1, c_m, s16, s17)), introduced(assumption)).
% 295.20/187.71 tff(29664,plain,
% 295.20/187.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17)) | (~node11(c_e_h_1, c_m, s16, s17)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17)) | (~node11(c_e_h_1, c_m, s16, s17)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16))),
% 295.20/187.71 inference(rewrite,[status(thm)],[])).
% 295.20/187.71 tff(29665,plain,
% 295.20/187.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17)) | (~node11(c_e_h_1, c_m, s16, s17)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16))),
% 295.20/187.71 inference(quant_inst,[status(thm)],[])).
% 295.20/187.71 tff(29666,plain,
% 295.20/187.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17)) | (~node11(c_e_h_1, c_m, s16, s17)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)),
% 295.20/187.71 inference(modus_ponens,[status(thm)],[29665, 29664])).
% 295.20/187.71 tff(29667,plain,
% 295.20/187.71 ($false),
% 295.20/187.71 inference(unit_resolution,[status(thm)],[29666, 5017, 29662, 29661, 29663])).
% 295.20/187.71 tff(29668,plain,((~node11(c_e_h_1, c_m, s16, s17)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)), inference(lemma,lemma(discharge,[]))).
% 295.20/187.71 tff(29669,plain,
% 295.20/187.71 (~node11(c_e_h_1, c_m, s16, s17)),
% 295.20/187.71 inference(unit_resolution,[status(thm)],[29668, 29662, 29661])).
% 295.20/187.71 tff(29670,plain,
% 295.20/187.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s16, s17)) | node10(c_e_h_1, c_m, s16, s17) | node11(c_e_h_1, c_m, s16, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s16, s17)) | node10(c_e_h_1, c_m, s16, s17) | node11(c_e_h_1, c_m, s16, s17))),
% 295.20/187.71 inference(rewrite,[status(thm)],[])).
% 295.20/187.71 tff(29671,plain,
% 295.20/187.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s16, s17)) | node10(c_e_h_1, c_m, s16, s17) | node11(c_e_h_1, c_m, s16, s17))),
% 295.20/187.71 inference(quant_inst,[status(thm)],[])).
% 295.20/187.71 tff(29672,plain,
% 295.20/187.71 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s16, s17)) | node10(c_e_h_1, c_m, s16, s17) | node11(c_e_h_1, c_m, s16, s17)),
% 295.20/187.71 inference(modus_ponens,[status(thm)],[29671, 29670])).
% 295.20/187.71 tff(29673,plain,
% 295.20/187.71 (node10(c_e_h_1, c_m, s16, s17) | node11(c_e_h_1, c_m, s16, s17)),
% 295.20/187.71 inference(unit_resolution,[status(thm)],[29672, 5002, 11967])).
% 295.20/187.71 tff(29674,plain,
% 295.20/187.71 (node10(c_e_h_1, c_m, s16, s17)),
% 295.20/187.71 inference(unit_resolution,[status(thm)],[29673, 29669])).
% 295.20/187.71 tff(29675,plain,
% 295.20/187.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17)) | node9(c_e_h_1, c_m, s16) | (~node10(c_e_h_1, c_m, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17)) | node9(c_e_h_1, c_m, s16) | (~node10(c_e_h_1, c_m, s16, s17)))),
% 295.20/187.71 inference(rewrite,[status(thm)],[])).
% 295.20/187.71 tff(29676,plain,
% 295.20/187.71 ((node9(c_e_h_1, c_m, s16) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17)) | (~node10(c_e_h_1, c_m, s16, s17))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17)) | node9(c_e_h_1, c_m, s16) | (~node10(c_e_h_1, c_m, s16, s17)))),
% 295.20/187.71 inference(rewrite,[status(thm)],[])).
% 295.20/187.71 tff(29677,plain,
% 295.20/187.71 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s16) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17)) | (~node10(c_e_h_1, c_m, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17)) | node9(c_e_h_1, c_m, s16) | (~node10(c_e_h_1, c_m, s16, s17))))),
% 295.20/187.72 inference(monotonicity,[status(thm)],[29676])).
% 295.20/187.72 tff(29678,plain,
% 295.20/187.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s16) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17)) | (~node10(c_e_h_1, c_m, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17)) | node9(c_e_h_1, c_m, s16) | (~node10(c_e_h_1, c_m, s16, s17)))),
% 295.20/187.72 inference(transitivity,[status(thm)],[29677, 29675])).
% 295.20/187.72 tff(29679,plain,
% 295.20/187.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s16) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17)) | (~node10(c_e_h_1, c_m, s16, s17)))),
% 295.20/187.72 inference(quant_inst,[status(thm)],[])).
% 295.20/187.72 tff(29680,plain,
% 295.20/187.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17)) | node9(c_e_h_1, c_m, s16) | (~node10(c_e_h_1, c_m, s16, s17))),
% 295.20/187.72 inference(modus_ponens,[status(thm)],[29679, 29678])).
% 295.20/187.72 tff(29681,plain,
% 295.20/187.72 ($false),
% 295.20/187.72 inference(unit_resolution,[status(thm)],[29680, 4986, 29662, 29674, 29660])).
% 295.20/187.72 tff(29682,plain,((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17)) | node9(c_e_h_1, c_m, s16) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)), inference(lemma,lemma(discharge,[]))).
% 295.20/187.72 tff(29683,plain,
% 295.20/187.72 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17)),
% 295.20/187.72 inference(unit_resolution,[status(thm)],[29682, 29659, 29510])).
% 295.20/187.72 tff(29684,plain,
% 295.20/187.72 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s17)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s17)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17))),
% 295.20/187.72 inference(rewrite,[status(thm)],[])).
% 295.20/187.72 tff(29685,plain,
% 295.20/187.72 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s17)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17))),
% 295.20/187.72 inference(quant_inst,[status(thm)],[])).
% 295.20/187.72 tff(29686,plain,
% 295.20/187.72 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s17)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17)),
% 295.20/187.72 inference(modus_ponens,[status(thm)],[29685, 29684])).
% 295.20/187.72 tff(29687,plain,
% 295.20/187.72 (~m_and_h_gate_v_in2(c_e_h_1, c_l, s17)),
% 295.20/187.72 inference(unit_resolution,[status(thm)],[29686, 4549, 29683])).
% 295.20/187.72 tff(29688,plain,
% 295.20/187.72 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s17)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s17))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s17)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s17))),
% 295.20/187.72 inference(rewrite,[status(thm)],[])).
% 295.20/187.72 tff(29689,plain,
% 295.20/187.72 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s17)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s17))),
% 295.20/187.72 inference(quant_inst,[status(thm)],[])).
% 295.20/187.72 tff(29690,plain,
% 295.20/187.72 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s17)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s17)),
% 295.20/187.72 inference(modus_ponens,[status(thm)],[29689, 29688])).
% 295.20/187.72 tff(29691,plain,
% 295.20/187.72 (~node20(c_e_h_1, c_l, s17)),
% 295.20/187.72 inference(unit_resolution,[status(thm)],[29690, 4563, 29687])).
% 295.20/187.72 tff(29692,assumption,(m_and_h_gate_v_out(c_e_h_1, c_l, s18)), introduced(assumption)).
% 295.20/187.72 tff(29693,assumption,(~node20(c_e_h_1, c_l, s17)), introduced(assumption)).
% 295.20/187.72 tff(29694,assumption,(node22(c_e_h_1, c_l, s17, s18)), introduced(assumption)).
% 295.20/187.72 tff(29695,plain,
% 295.20/187.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s18)) | (~node22(c_e_h_1, c_l, s17, s18)) | m_and_h_gate_v_out(c_e_h_1, c_l, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s18)) | (~node22(c_e_h_1, c_l, s17, s18)) | m_and_h_gate_v_out(c_e_h_1, c_l, s17))),
% 295.20/187.72 inference(rewrite,[status(thm)],[])).
% 295.20/187.72 tff(29696,plain,
% 295.20/187.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s18)) | (~node22(c_e_h_1, c_l, s17, s18)) | m_and_h_gate_v_out(c_e_h_1, c_l, s17))),
% 295.20/187.72 inference(quant_inst,[status(thm)],[])).
% 295.20/187.72 tff(29697,plain,
% 295.20/187.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s18)) | (~node22(c_e_h_1, c_l, s17, s18)) | m_and_h_gate_v_out(c_e_h_1, c_l, s17)),
% 295.20/187.72 inference(modus_ponens,[status(thm)],[29696, 29695])).
% 295.20/187.72 tff(29698,plain,
% 295.20/187.72 ($false),
% 295.20/187.72 inference(unit_resolution,[status(thm)],[29697, 108, 29694, 29540, 29692])).
% 295.20/187.72 tff(29699,plain,((~node22(c_e_h_1, c_l, s17, s18)) | m_and_h_gate_v_out(c_e_h_1, c_l, s17) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s18))), inference(lemma,lemma(discharge,[]))).
% 295.20/187.72 tff(29700,plain,
% 295.20/187.72 (~node22(c_e_h_1, c_l, s17, s18)),
% 295.20/187.72 inference(unit_resolution,[status(thm)],[29699, 29692, 29540])).
% 295.20/187.72 tff(29701,plain,
% 295.20/187.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s17, s18)) | node21(c_e_h_1, c_l, s17, s18) | node22(c_e_h_1, c_l, s17, s18))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s17, s18)) | node21(c_e_h_1, c_l, s17, s18) | node22(c_e_h_1, c_l, s17, s18))),
% 295.20/187.72 inference(rewrite,[status(thm)],[])).
% 295.20/187.72 tff(29702,plain,
% 295.20/187.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s17, s18)) | node21(c_e_h_1, c_l, s17, s18) | node22(c_e_h_1, c_l, s17, s18))),
% 295.20/187.72 inference(quant_inst,[status(thm)],[])).
% 295.20/187.72 tff(29703,plain,
% 295.20/187.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s17, s18)) | node21(c_e_h_1, c_l, s17, s18) | node22(c_e_h_1, c_l, s17, s18)),
% 295.20/187.72 inference(modus_ponens,[status(thm)],[29702, 29701])).
% 295.20/187.72 tff(29704,plain,
% 295.20/187.72 (node21(c_e_h_1, c_l, s17, s18) | node22(c_e_h_1, c_l, s17, s18)),
% 295.20/187.72 inference(unit_resolution,[status(thm)],[29703, 82, 26135])).
% 295.20/187.72 tff(29705,plain,
% 295.20/187.72 (node21(c_e_h_1, c_l, s17, s18)),
% 295.20/187.72 inference(unit_resolution,[status(thm)],[29704, 29700])).
% 295.20/187.72 tff(29706,plain,
% 295.20/187.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s17) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s18)) | (~node21(c_e_h_1, c_l, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s17) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s18)) | (~node21(c_e_h_1, c_l, s17, s18)))),
% 295.20/187.72 inference(rewrite,[status(thm)],[])).
% 295.20/187.72 tff(29707,plain,
% 295.20/187.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s17) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s18)) | (~node21(c_e_h_1, c_l, s17, s18)))),
% 295.20/187.72 inference(quant_inst,[status(thm)],[])).
% 295.20/187.72 tff(29708,plain,
% 295.20/187.72 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s17) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s18)) | (~node21(c_e_h_1, c_l, s17, s18))),
% 295.20/187.72 inference(modus_ponens,[status(thm)],[29707, 29706])).
% 295.20/187.72 tff(29709,plain,
% 295.20/187.72 ($false),
% 295.20/187.72 inference(unit_resolution,[status(thm)],[29708, 52, 29705, 29693, 29692])).
% 295.20/187.72 tff(29710,plain,((~m_and_h_gate_v_out(c_e_h_1, c_l, s18)) | node20(c_e_h_1, c_l, s17) | m_and_h_gate_v_out(c_e_h_1, c_l, s17)), inference(lemma,lemma(discharge,[]))).
% 295.20/187.72 tff(29711,plain,
% 295.20/187.72 (~m_and_h_gate_v_out(c_e_h_1, c_l, s18)),
% 295.20/187.72 inference(unit_resolution,[status(thm)],[29710, 29691, 29538])).
% 295.20/187.72 tff(29712,assumption,(m_or_h_gate_v_in1(c_e_h_1, c_j, s18)), introduced(assumption)).
% 295.20/187.72 tff(29713,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_l, s18)), introduced(assumption)).
% 295.20/187.72 tff(29714,plain,
% 295.20/187.72 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s18)) | m_and_h_gate_v_out(c_e_h_1, c_l, s18))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s18)) | m_and_h_gate_v_out(c_e_h_1, c_l, s18))),
% 295.20/187.72 inference(rewrite,[status(thm)],[])).
% 295.20/187.72 tff(29715,plain,
% 295.20/187.72 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s18)) | m_and_h_gate_v_out(c_e_h_1, c_l, s18))),
% 295.20/187.72 inference(quant_inst,[status(thm)],[])).
% 295.20/187.72 tff(29716,plain,
% 295.20/187.72 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s18)) | m_and_h_gate_v_out(c_e_h_1, c_l, s18)),
% 295.20/187.72 inference(modus_ponens,[status(thm)],[29715, 29714])).
% 295.20/187.72 tff(29717,plain,
% 295.20/187.72 ($false),
% 295.20/187.72 inference(unit_resolution,[status(thm)],[29716, 1100, 29713, 29712])).
% 295.20/187.72 tff(29718,plain,((~m_or_h_gate_v_in1(c_e_h_1, c_j, s18)) | m_and_h_gate_v_out(c_e_h_1, c_l, s18)), inference(lemma,lemma(discharge,[]))).
% 295.20/187.72 tff(29719,plain,
% 295.20/187.72 (~m_or_h_gate_v_in1(c_e_h_1, c_j, s18)),
% 295.20/187.72 inference(unit_resolution,[status(thm)],[29718, 29711])).
% 295.20/187.72 tff(29720,assumption,(~m_or_h_gate_v_in2(c_e_h_1, c_j, s18)), introduced(assumption)).
% 295.20/187.72 tff(29721,assumption,(~m_or_h_gate_v_in1(c_e_h_1, c_j, s18)), introduced(assumption)).
% 295.20/187.72 tff(29722,assumption,(~m_or_h_gate_v_out(c_e_h_1, c_j, s18)), introduced(assumption)).
% 295.20/187.72 tff(29723,assumption,(m_or_h_gate_v_out(c_e_h_1, c_j, s19)), introduced(assumption)).
% 295.20/187.72 tff(29724,assumption,(node6(c_e_h_1, c_j, s18, s19)), introduced(assumption)).
% 295.20/187.72 tff(29725,plain,
% 295.20/187.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s18) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s19)) | (~node6(c_e_h_1, c_j, s18, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s18) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s19)) | (~node6(c_e_h_1, c_j, s18, s19)))),
% 295.20/187.72 inference(rewrite,[status(thm)],[])).
% 295.20/187.72 tff(29726,plain,
% 295.20/187.72 (((~node6(c_e_h_1, c_j, s18, s19)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s19)) | m_or_h_gate_v_out(c_e_h_1, c_j, s18)) <=> (m_or_h_gate_v_out(c_e_h_1, c_j, s18) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s19)) | (~node6(c_e_h_1, c_j, s18, s19)))),
% 295.20/187.72 inference(rewrite,[status(thm)],[])).
% 295.20/187.72 tff(29727,plain,
% 295.20/187.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s18, s19)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s19)) | m_or_h_gate_v_out(c_e_h_1, c_j, s18))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s18) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s19)) | (~node6(c_e_h_1, c_j, s18, s19))))),
% 295.20/187.72 inference(monotonicity,[status(thm)],[29726])).
% 295.20/187.72 tff(29728,plain,
% 295.20/187.72 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s18, s19)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s19)) | m_or_h_gate_v_out(c_e_h_1, c_j, s18))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s18) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s19)) | (~node6(c_e_h_1, c_j, s18, s19)))),
% 295.20/187.73 inference(transitivity,[status(thm)],[29727, 29725])).
% 295.20/187.73 tff(29729,plain,
% 295.20/187.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s18, s19)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s19)) | m_or_h_gate_v_out(c_e_h_1, c_j, s18))),
% 295.20/187.73 inference(quant_inst,[status(thm)],[])).
% 295.20/187.73 tff(29730,plain,
% 295.20/187.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s18) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s19)) | (~node6(c_e_h_1, c_j, s18, s19))),
% 295.20/187.73 inference(modus_ponens,[status(thm)],[29729, 29728])).
% 295.20/187.73 tff(29731,plain,
% 295.20/187.73 ($false),
% 295.20/187.73 inference(unit_resolution,[status(thm)],[29730, 1121, 29723, 29722, 29724])).
% 295.20/187.73 tff(29732,plain,((~node6(c_e_h_1, c_j, s18, s19)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s19)) | m_or_h_gate_v_out(c_e_h_1, c_j, s18)), inference(lemma,lemma(discharge,[]))).
% 295.20/187.73 tff(29733,plain,
% 295.20/187.73 (~node6(c_e_h_1, c_j, s18, s19)),
% 295.20/187.73 inference(unit_resolution,[status(thm)],[29732, 29723, 29722])).
% 295.20/187.73 tff(29734,plain,
% 295.20/187.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s18, s19)) | node5(c_e_h_1, c_j, s18, s19) | node6(c_e_h_1, c_j, s18, s19))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s18, s19)) | node5(c_e_h_1, c_j, s18, s19) | node6(c_e_h_1, c_j, s18, s19))),
% 295.20/187.73 inference(rewrite,[status(thm)],[])).
% 295.20/187.73 tff(29735,plain,
% 295.20/187.73 ((node6(c_e_h_1, c_j, s18, s19) | node5(c_e_h_1, c_j, s18, s19) | (~trans(s18, s19))) <=> ((~trans(s18, s19)) | node5(c_e_h_1, c_j, s18, s19) | node6(c_e_h_1, c_j, s18, s19))),
% 295.20/187.73 inference(rewrite,[status(thm)],[])).
% 295.20/187.73 tff(29736,plain,
% 295.20/187.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s18, s19) | node5(c_e_h_1, c_j, s18, s19) | (~trans(s18, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s18, s19)) | node5(c_e_h_1, c_j, s18, s19) | node6(c_e_h_1, c_j, s18, s19)))),
% 295.20/187.73 inference(monotonicity,[status(thm)],[29735])).
% 295.20/187.73 tff(29737,plain,
% 295.20/187.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s18, s19) | node5(c_e_h_1, c_j, s18, s19) | (~trans(s18, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s18, s19)) | node5(c_e_h_1, c_j, s18, s19) | node6(c_e_h_1, c_j, s18, s19))),
% 295.20/187.73 inference(transitivity,[status(thm)],[29736, 29734])).
% 295.20/187.73 tff(29738,plain,
% 295.20/187.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s18, s19) | node5(c_e_h_1, c_j, s18, s19) | (~trans(s18, s19)))),
% 295.20/187.73 inference(quant_inst,[status(thm)],[])).
% 295.20/187.73 tff(29739,plain,
% 295.20/187.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s18, s19)) | node5(c_e_h_1, c_j, s18, s19) | node6(c_e_h_1, c_j, s18, s19)),
% 295.20/187.73 inference(modus_ponens,[status(thm)],[29738, 29737])).
% 295.20/187.73 tff(29740,plain,
% 295.20/187.73 (node5(c_e_h_1, c_j, s18, s19) | node6(c_e_h_1, c_j, s18, s19)),
% 295.20/187.73 inference(unit_resolution,[status(thm)],[29739, 1141, 26787])).
% 295.20/187.73 tff(29741,plain,
% 295.20/187.73 (node5(c_e_h_1, c_j, s18, s19)),
% 295.20/187.73 inference(unit_resolution,[status(thm)],[29740, 29733])).
% 295.20/187.73 tff(29742,plain,
% 295.20/187.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_1, c_j, s19)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s18) | m_or_h_gate_v_in1(c_e_h_1, c_j, s18) | (~node5(c_e_h_1, c_j, s18, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s19)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s18) | m_or_h_gate_v_in1(c_e_h_1, c_j, s18) | (~node5(c_e_h_1, c_j, s18, s19)))),
% 295.20/187.73 inference(rewrite,[status(thm)],[])).
% 295.20/187.73 tff(29743,plain,
% 295.20/187.73 ((m_or_h_gate_v_in1(c_e_h_1, c_j, s18) | m_or_h_gate_v_in2(c_e_h_1, c_j, s18) | (~node5(c_e_h_1, c_j, s18, s19)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s19))) <=> ((~m_or_h_gate_v_out(c_e_h_1, c_j, s19)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s18) | m_or_h_gate_v_in1(c_e_h_1, c_j, s18) | (~node5(c_e_h_1, c_j, s18, s19)))),
% 295.20/187.73 inference(rewrite,[status(thm)],[])).
% 295.20/187.73 tff(29744,plain,
% 295.20/187.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s18) | m_or_h_gate_v_in2(c_e_h_1, c_j, s18) | (~node5(c_e_h_1, c_j, s18, s19)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_1, c_j, s19)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s18) | m_or_h_gate_v_in1(c_e_h_1, c_j, s18) | (~node5(c_e_h_1, c_j, s18, s19))))),
% 295.20/187.73 inference(monotonicity,[status(thm)],[29743])).
% 295.20/187.73 tff(29745,plain,
% 295.20/187.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s18) | m_or_h_gate_v_in2(c_e_h_1, c_j, s18) | (~node5(c_e_h_1, c_j, s18, s19)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s19)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s18) | m_or_h_gate_v_in1(c_e_h_1, c_j, s18) | (~node5(c_e_h_1, c_j, s18, s19)))),
% 295.20/187.73 inference(transitivity,[status(thm)],[29744, 29742])).
% 295.20/187.73 tff(29746,plain,
% 295.20/187.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s18) | m_or_h_gate_v_in2(c_e_h_1, c_j, s18) | (~node5(c_e_h_1, c_j, s18, s19)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s19)))),
% 295.20/187.73 inference(quant_inst,[status(thm)],[])).
% 295.20/187.73 tff(29747,plain,
% 295.20/187.73 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s19)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s18) | m_or_h_gate_v_in1(c_e_h_1, c_j, s18) | (~node5(c_e_h_1, c_j, s18, s19))),
% 295.20/187.73 inference(modus_ponens,[status(thm)],[29746, 29745])).
% 295.20/187.73 tff(29748,plain,
% 295.20/187.73 ($false),
% 295.20/187.73 inference(unit_resolution,[status(thm)],[29747, 1159, 29723, 29741, 29721, 29720])).
% 295.20/187.73 tff(29749,plain,((~m_or_h_gate_v_out(c_e_h_1, c_j, s19)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s18) | m_or_h_gate_v_in2(c_e_h_1, c_j, s18) | m_or_h_gate_v_out(c_e_h_1, c_j, s18)), inference(lemma,lemma(discharge,[]))).
% 295.20/187.73 tff(29750,plain,
% 295.20/187.73 ((~m_or_h_gate_v_out(c_e_h_1, c_j, s19)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s18) | m_or_h_gate_v_out(c_e_h_1, c_j, s18)),
% 295.20/187.73 inference(unit_resolution,[status(thm)],[29749, 29719])).
% 295.20/187.73 tff(29751,plain,
% 295.20/187.73 (~m_or_h_gate_v_out(c_e_h_1, c_j, s19)),
% 295.20/187.73 inference(unit_resolution,[status(thm)],[29750, 29581, 28842])).
% 295.20/187.73 tff(29752,plain,
% 295.20/187.73 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s19)) | m_or_h_gate_v_out(c_e_h_1, c_j, s19))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s19)) | m_or_h_gate_v_out(c_e_h_1, c_j, s19))),
% 295.20/187.73 inference(rewrite,[status(thm)],[])).
% 295.20/187.73 tff(29753,plain,
% 295.20/187.73 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s19)) | m_or_h_gate_v_out(c_e_h_1, c_j, s19))),
% 295.20/187.73 inference(quant_inst,[status(thm)],[])).
% 295.20/187.73 tff(29754,plain,
% 295.20/187.73 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s19)) | m_or_h_gate_v_out(c_e_h_1, c_j, s19)),
% 295.20/187.73 inference(modus_ponens,[status(thm)],[29753, 29752])).
% 295.20/187.73 tff(29755,plain,
% 295.20/187.73 (~m_c_h_element_v_in2(c_e_h_1, c_h, s19)),
% 295.20/187.73 inference(unit_resolution,[status(thm)],[29754, 1174, 29751])).
% 295.20/187.73 tff(29756,assumption,(m_c_h_element_v_in2(c_e_h_1, c_h, s17)), introduced(assumption)).
% 295.20/187.73 tff(29757,plain,
% 295.20/187.73 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s17)) | m_or_h_gate_v_out(c_e_h_1, c_j, s17))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s17)) | m_or_h_gate_v_out(c_e_h_1, c_j, s17))),
% 295.20/187.73 inference(rewrite,[status(thm)],[])).
% 295.20/187.73 tff(29758,plain,
% 295.20/187.73 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s17)) | m_or_h_gate_v_out(c_e_h_1, c_j, s17))),
% 295.20/187.73 inference(quant_inst,[status(thm)],[])).
% 295.20/187.73 tff(29759,plain,
% 295.20/187.73 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s17)) | m_or_h_gate_v_out(c_e_h_1, c_j, s17)),
% 295.20/187.73 inference(modus_ponens,[status(thm)],[29758, 29757])).
% 295.20/187.73 tff(29760,plain,
% 295.20/187.73 ($false),
% 295.20/187.73 inference(unit_resolution,[status(thm)],[29759, 1174, 29560, 29756])).
% 295.20/187.73 tff(29761,plain,(m_or_h_gate_v_out(c_e_h_1, c_j, s17) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s17))), inference(lemma,lemma(discharge,[]))).
% 295.20/187.73 tff(29762,plain,
% 295.20/187.73 (~m_c_h_element_v_in2(c_e_h_1, c_h, s17)),
% 295.20/187.73 inference(unit_resolution,[status(thm)],[29761, 29008])).
% 295.20/187.73 tff(29763,assumption,(m_c_h_element_v_out(c_e_h_1, c_h, s18)), introduced(assumption)).
% 295.20/187.73 tff(29764,assumption,(~m_c_h_element_v_out(c_e_h_1, c_h, s17)), introduced(assumption)).
% 295.20/187.73 tff(29765,assumption,(node18(c_e_h_1, c_h, s17, s18)), introduced(assumption)).
% 295.20/187.73 tff(29766,plain,
% 295.20/187.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_h, s17) | (~m_c_h_element_v_out(c_e_h_1, c_h, s18)) | (~node18(c_e_h_1, c_h, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s17) | (~m_c_h_element_v_out(c_e_h_1, c_h, s18)) | (~node18(c_e_h_1, c_h, s17, s18)))),
% 295.20/187.73 inference(rewrite,[status(thm)],[])).
% 295.20/187.73 tff(29767,plain,
% 295.20/187.73 (((~m_c_h_element_v_out(c_e_h_1, c_h, s18)) | m_c_h_element_v_out(c_e_h_1, c_h, s17) | (~node18(c_e_h_1, c_h, s17, s18))) <=> (m_c_h_element_v_out(c_e_h_1, c_h, s17) | (~m_c_h_element_v_out(c_e_h_1, c_h, s18)) | (~node18(c_e_h_1, c_h, s17, s18)))),
% 295.20/187.73 inference(rewrite,[status(thm)],[])).
% 295.20/187.73 tff(29768,plain,
% 295.20/187.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s18)) | m_c_h_element_v_out(c_e_h_1, c_h, s17) | (~node18(c_e_h_1, c_h, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_h, s17) | (~m_c_h_element_v_out(c_e_h_1, c_h, s18)) | (~node18(c_e_h_1, c_h, s17, s18))))),
% 295.20/187.73 inference(monotonicity,[status(thm)],[29767])).
% 295.20/187.73 tff(29769,plain,
% 295.20/187.73 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s18)) | m_c_h_element_v_out(c_e_h_1, c_h, s17) | (~node18(c_e_h_1, c_h, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s17) | (~m_c_h_element_v_out(c_e_h_1, c_h, s18)) | (~node18(c_e_h_1, c_h, s17, s18)))),
% 295.20/187.74 inference(transitivity,[status(thm)],[29768, 29766])).
% 295.20/187.74 tff(29770,plain,
% 295.20/187.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s18)) | m_c_h_element_v_out(c_e_h_1, c_h, s17) | (~node18(c_e_h_1, c_h, s17, s18)))),
% 295.20/187.74 inference(quant_inst,[status(thm)],[])).
% 295.20/187.74 tff(29771,plain,
% 295.20/187.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s17) | (~m_c_h_element_v_out(c_e_h_1, c_h, s18)) | (~node18(c_e_h_1, c_h, s17, s18))),
% 295.20/187.74 inference(modus_ponens,[status(thm)],[29770, 29769])).
% 295.20/187.74 tff(29772,plain,
% 295.20/187.74 ($false),
% 295.20/187.74 inference(unit_resolution,[status(thm)],[29771, 753, 29764, 29763, 29765])).
% 295.20/187.74 tff(29773,plain,((~node18(c_e_h_1, c_h, s17, s18)) | m_c_h_element_v_out(c_e_h_1, c_h, s17) | (~m_c_h_element_v_out(c_e_h_1, c_h, s18))), inference(lemma,lemma(discharge,[]))).
% 295.20/187.74 tff(29774,plain,
% 295.20/187.74 (~node18(c_e_h_1, c_h, s17, s18)),
% 295.20/187.74 inference(unit_resolution,[status(thm)],[29773, 29763, 29764])).
% 295.20/187.74 tff(29775,assumption,(node15(c_e_h_1, c_h, s17, s18)), introduced(assumption)).
% 295.20/187.74 tff(29776,plain,
% 295.20/187.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s18)) | (~node15(c_e_h_1, c_h, s17, s18)) | m_c_h_element_v_out(c_e_h_1, c_h, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s18)) | (~node15(c_e_h_1, c_h, s17, s18)) | m_c_h_element_v_out(c_e_h_1, c_h, s17))),
% 295.20/187.74 inference(rewrite,[status(thm)],[])).
% 295.20/187.74 tff(29777,plain,
% 295.20/187.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s18)) | (~node15(c_e_h_1, c_h, s17, s18)) | m_c_h_element_v_out(c_e_h_1, c_h, s17))),
% 295.20/187.74 inference(quant_inst,[status(thm)],[])).
% 295.20/187.74 tff(29778,plain,
% 295.20/187.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s18)) | (~node15(c_e_h_1, c_h, s17, s18)) | m_c_h_element_v_out(c_e_h_1, c_h, s17)),
% 295.20/187.74 inference(modus_ponens,[status(thm)],[29777, 29776])).
% 295.20/187.74 tff(29779,plain,
% 295.20/187.74 ($false),
% 295.20/187.74 inference(unit_resolution,[status(thm)],[29778, 147, 29764, 29763, 29775])).
% 295.20/187.74 tff(29780,plain,((~node15(c_e_h_1, c_h, s17, s18)) | m_c_h_element_v_out(c_e_h_1, c_h, s17) | (~m_c_h_element_v_out(c_e_h_1, c_h, s18))), inference(lemma,lemma(discharge,[]))).
% 295.20/187.74 tff(29781,plain,
% 295.20/187.74 (~node15(c_e_h_1, c_h, s17, s18)),
% 295.20/187.74 inference(unit_resolution,[status(thm)],[29780, 29763, 29764])).
% 295.20/187.74 tff(29782,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_h, s17)), introduced(assumption)).
% 295.20/187.74 tff(29783,assumption,(~node15(c_e_h_1, c_h, s17, s18)), introduced(assumption)).
% 295.20/187.74 tff(29784,assumption,(node17(c_e_h_1, c_h, s17)), introduced(assumption)).
% 295.20/187.74 tff(29785,plain,
% 295.20/187.74 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_h, s17)) | m_c_h_element_v_in1(c_e_h_1, c_h, s17) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s17)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_h, s17)) | m_c_h_element_v_in1(c_e_h_1, c_h, s17) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s17)))),
% 295.20/187.74 inference(rewrite,[status(thm)],[])).
% 295.20/187.74 tff(29786,plain,
% 295.20/187.74 ((m_c_h_element_v_in1(c_e_h_1, c_h, s17) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s17)) | (~node17(c_e_h_1, c_h, s17))) <=> ((~node17(c_e_h_1, c_h, s17)) | m_c_h_element_v_in1(c_e_h_1, c_h, s17) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s17)))),
% 295.20/187.74 inference(rewrite,[status(thm)],[])).
% 295.20/187.74 tff(29787,plain,
% 295.20/187.74 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s17) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s17)) | (~node17(c_e_h_1, c_h, s17)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_h, s17)) | m_c_h_element_v_in1(c_e_h_1, c_h, s17) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s17))))),
% 295.20/187.74 inference(monotonicity,[status(thm)],[29786])).
% 295.20/187.74 tff(29788,plain,
% 295.20/187.74 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s17) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s17)) | (~node17(c_e_h_1, c_h, s17)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_h, s17)) | m_c_h_element_v_in1(c_e_h_1, c_h, s17) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s17)))),
% 295.20/187.74 inference(transitivity,[status(thm)],[29787, 29785])).
% 295.20/187.74 tff(29789,plain,
% 295.20/187.74 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s17) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s17)) | (~node17(c_e_h_1, c_h, s17)))),
% 295.20/187.74 inference(quant_inst,[status(thm)],[])).
% 295.20/187.74 tff(29790,plain,
% 295.20/187.74 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_h, s17)) | m_c_h_element_v_in1(c_e_h_1, c_h, s17) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s17))),
% 295.20/187.74 inference(modus_ponens,[status(thm)],[29789, 29788])).
% 295.20/187.74 tff(29791,plain,
% 295.20/187.74 (m_c_h_element_v_in1(c_e_h_1, c_h, s17) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s17))),
% 295.20/187.74 inference(unit_resolution,[status(thm)],[29790, 859, 29784])).
% 295.20/187.74 tff(29792,plain,
% 295.20/187.74 (~m_c_h_element_v_in2(c_e_h_1, c_h, s17)),
% 295.20/187.74 inference(unit_resolution,[status(thm)],[29791, 29782])).
% 295.20/187.74 tff(29793,plain,
% 295.20/187.74 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s17)) | m_c_h_element_v_in1(c_e_h_1, c_h, s17) | m_c_h_element_v_in2(c_e_h_1, c_h, s17))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s17)) | m_c_h_element_v_in1(c_e_h_1, c_h, s17) | m_c_h_element_v_in2(c_e_h_1, c_h, s17))),
% 295.20/187.74 inference(rewrite,[status(thm)],[])).
% 295.20/187.74 tff(29794,plain,
% 295.20/187.74 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s17)) | m_c_h_element_v_in1(c_e_h_1, c_h, s17) | m_c_h_element_v_in2(c_e_h_1, c_h, s17))),
% 295.20/187.74 inference(quant_inst,[status(thm)],[])).
% 295.20/187.74 tff(29795,plain,
% 295.20/187.74 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s17)) | m_c_h_element_v_in1(c_e_h_1, c_h, s17) | m_c_h_element_v_in2(c_e_h_1, c_h, s17)),
% 295.20/187.74 inference(modus_ponens,[status(thm)],[29794, 29793])).
% 295.20/187.74 tff(29796,plain,
% 295.20/187.74 (~node16(c_e_h_1, c_h, s17)),
% 295.20/187.74 inference(unit_resolution,[status(thm)],[29795, 178, 29782, 29792])).
% 295.20/187.74 tff(29797,plain,
% 295.20/187.74 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s17, s18)) | node19(c_e_h_1, c_h, s17, s18))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s17, s18)) | node19(c_e_h_1, c_h, s17, s18))),
% 295.20/187.74 inference(rewrite,[status(thm)],[])).
% 295.20/187.74 tff(29798,plain,
% 295.20/187.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s17, s18)) | node19(c_e_h_1, c_h, s17, s18))),
% 295.20/187.74 inference(quant_inst,[status(thm)],[])).
% 295.20/187.74 tff(29799,plain,
% 295.20/187.74 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s17, s18)) | node19(c_e_h_1, c_h, s17, s18)),
% 295.20/187.74 inference(modus_ponens,[status(thm)],[29798, 29797])).
% 295.20/187.74 tff(29800,plain,
% 295.20/187.74 (node19(c_e_h_1, c_h, s17, s18)),
% 295.20/187.74 inference(unit_resolution,[status(thm)],[29799, 190, 26135])).
% 295.20/187.75 tff(29801,plain,
% 295.20/187.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s17) | (~node19(c_e_h_1, c_h, s17, s18)) | node15(c_e_h_1, c_h, s17, s18) | node14(c_e_h_1, c_h, s17, s18))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s17) | (~node19(c_e_h_1, c_h, s17, s18)) | node15(c_e_h_1, c_h, s17, s18) | node14(c_e_h_1, c_h, s17, s18))),
% 295.20/187.75 inference(rewrite,[status(thm)],[])).
% 295.20/187.75 tff(29802,plain,
% 295.20/187.75 ((node16(c_e_h_1, c_h, s17) | node14(c_e_h_1, c_h, s17, s18) | node15(c_e_h_1, c_h, s17, s18) | (~node19(c_e_h_1, c_h, s17, s18))) <=> (node16(c_e_h_1, c_h, s17) | (~node19(c_e_h_1, c_h, s17, s18)) | node15(c_e_h_1, c_h, s17, s18) | node14(c_e_h_1, c_h, s17, s18))),
% 295.20/187.75 inference(rewrite,[status(thm)],[])).
% 295.20/187.75 tff(29803,plain,
% 295.20/187.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s17) | node14(c_e_h_1, c_h, s17, s18) | node15(c_e_h_1, c_h, s17, s18) | (~node19(c_e_h_1, c_h, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s17) | (~node19(c_e_h_1, c_h, s17, s18)) | node15(c_e_h_1, c_h, s17, s18) | node14(c_e_h_1, c_h, s17, s18)))),
% 295.20/187.75 inference(monotonicity,[status(thm)],[29802])).
% 295.20/187.75 tff(29804,plain,
% 295.20/187.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s17) | node14(c_e_h_1, c_h, s17, s18) | node15(c_e_h_1, c_h, s17, s18) | (~node19(c_e_h_1, c_h, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s17) | (~node19(c_e_h_1, c_h, s17, s18)) | node15(c_e_h_1, c_h, s17, s18) | node14(c_e_h_1, c_h, s17, s18))),
% 295.20/187.75 inference(transitivity,[status(thm)],[29803, 29801])).
% 295.20/187.75 tff(29805,plain,
% 295.20/187.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s17) | node14(c_e_h_1, c_h, s17, s18) | node15(c_e_h_1, c_h, s17, s18) | (~node19(c_e_h_1, c_h, s17, s18)))),
% 295.20/187.75 inference(quant_inst,[status(thm)],[])).
% 295.20/187.75 tff(29806,plain,
% 295.20/187.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s17) | (~node19(c_e_h_1, c_h, s17, s18)) | node15(c_e_h_1, c_h, s17, s18) | node14(c_e_h_1, c_h, s17, s18)),
% 295.20/187.75 inference(modus_ponens,[status(thm)],[29805, 29804])).
% 295.20/187.75 tff(29807,plain,
% 295.20/187.75 (node16(c_e_h_1, c_h, s17) | node15(c_e_h_1, c_h, s17, s18) | node14(c_e_h_1, c_h, s17, s18)),
% 295.20/187.75 inference(unit_resolution,[status(thm)],[29806, 204, 29800])).
% 295.20/187.75 tff(29808,plain,
% 295.20/187.75 (node14(c_e_h_1, c_h, s17, s18)),
% 295.20/187.75 inference(unit_resolution,[status(thm)],[29807, 29796, 29783])).
% 295.20/187.75 tff(29809,plain,
% 295.20/187.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s18)) | m_c_h_element_v_in1(c_e_h_1, c_h, s17) | (~node14(c_e_h_1, c_h, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s18)) | m_c_h_element_v_in1(c_e_h_1, c_h, s17) | (~node14(c_e_h_1, c_h, s17, s18)))),
% 295.20/187.75 inference(rewrite,[status(thm)],[])).
% 295.20/187.75 tff(29810,plain,
% 295.20/187.75 (((~node14(c_e_h_1, c_h, s17, s18)) | m_c_h_element_v_in1(c_e_h_1, c_h, s17) | (~m_c_h_element_v_out(c_e_h_1, c_h, s18))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_h, s18)) | m_c_h_element_v_in1(c_e_h_1, c_h, s17) | (~node14(c_e_h_1, c_h, s17, s18)))),
% 295.20/187.75 inference(rewrite,[status(thm)],[])).
% 295.20/187.75 tff(29811,plain,
% 295.20/187.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s17, s18)) | m_c_h_element_v_in1(c_e_h_1, c_h, s17) | (~m_c_h_element_v_out(c_e_h_1, c_h, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s18)) | m_c_h_element_v_in1(c_e_h_1, c_h, s17) | (~node14(c_e_h_1, c_h, s17, s18))))),
% 295.20/187.75 inference(monotonicity,[status(thm)],[29810])).
% 295.20/187.75 tff(29812,plain,
% 295.20/187.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s17, s18)) | m_c_h_element_v_in1(c_e_h_1, c_h, s17) | (~m_c_h_element_v_out(c_e_h_1, c_h, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s18)) | m_c_h_element_v_in1(c_e_h_1, c_h, s17) | (~node14(c_e_h_1, c_h, s17, s18)))),
% 295.20/187.75 inference(transitivity,[status(thm)],[29811, 29809])).
% 295.20/187.75 tff(29813,plain,
% 295.20/187.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s17, s18)) | m_c_h_element_v_in1(c_e_h_1, c_h, s17) | (~m_c_h_element_v_out(c_e_h_1, c_h, s18)))),
% 295.20/187.75 inference(quant_inst,[status(thm)],[])).
% 295.20/187.75 tff(29814,plain,
% 295.20/187.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s18)) | m_c_h_element_v_in1(c_e_h_1, c_h, s17) | (~node14(c_e_h_1, c_h, s17, s18))),
% 295.20/187.75 inference(modus_ponens,[status(thm)],[29813, 29812])).
% 295.20/187.75 tff(29815,plain,
% 295.20/187.75 ($false),
% 295.20/187.75 inference(unit_resolution,[status(thm)],[29814, 223, 29763, 29808, 29782])).
% 295.20/187.75 tff(29816,plain,(m_c_h_element_v_in1(c_e_h_1, c_h, s17) | (~m_c_h_element_v_out(c_e_h_1, c_h, s18)) | node15(c_e_h_1, c_h, s17, s18) | (~node17(c_e_h_1, c_h, s17))), inference(lemma,lemma(discharge,[]))).
% 295.20/187.75 tff(29817,plain,
% 295.20/187.75 (~node17(c_e_h_1, c_h, s17)),
% 295.20/187.75 inference(unit_resolution,[status(thm)],[29816, 29763, 29782, 29781])).
% 295.20/187.75 tff(29818,plain,
% 295.20/187.75 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s17) | node18(c_e_h_1, c_h, s17, s18) | (~node19(c_e_h_1, c_h, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s17) | node18(c_e_h_1, c_h, s17, s18) | (~node19(c_e_h_1, c_h, s17, s18)))),
% 295.20/187.75 inference(rewrite,[status(thm)],[])).
% 295.20/187.75 tff(29819,plain,
% 295.20/187.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s17) | node18(c_e_h_1, c_h, s17, s18) | (~node19(c_e_h_1, c_h, s17, s18)))),
% 295.20/187.75 inference(quant_inst,[status(thm)],[])).
% 295.20/187.75 tff(29820,plain,
% 295.20/187.75 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s17) | node18(c_e_h_1, c_h, s17, s18) | (~node19(c_e_h_1, c_h, s17, s18))),
% 295.20/187.75 inference(modus_ponens,[status(thm)],[29819, 29818])).
% 295.20/187.75 tff(29821,plain,
% 295.20/187.75 (node17(c_e_h_1, c_h, s17) | node18(c_e_h_1, c_h, s17, s18)),
% 295.20/187.75 inference(unit_resolution,[status(thm)],[29820, 776, 29800])).
% 295.20/187.75 tff(29822,plain,
% 295.20/187.75 ($false),
% 295.20/187.75 inference(unit_resolution,[status(thm)],[29821, 29817, 29774])).
% 295.20/187.75 tff(29823,plain,((~m_c_h_element_v_out(c_e_h_1, c_h, s18)) | m_c_h_element_v_in1(c_e_h_1, c_h, s17) | m_c_h_element_v_out(c_e_h_1, c_h, s17)), inference(lemma,lemma(discharge,[]))).
% 295.20/187.75 tff(29824,plain,
% 295.20/187.75 (m_c_h_element_v_in1(c_e_h_1, c_h, s17)),
% 295.20/187.75 inference(unit_resolution,[status(thm)],[29823, 29764, 29763])).
% 295.20/187.75 tff(29825,plain,
% 295.20/187.75 (~node18(c_e_h_1, c_h, s17, s18)),
% 295.20/187.75 inference(unit_resolution,[status(thm)],[29773, 29764, 29763])).
% 295.20/187.75 tff(29826,plain,
% 295.20/187.75 (node17(c_e_h_1, c_h, s17)),
% 295.20/187.75 inference(unit_resolution,[status(thm)],[29821, 29825])).
% 295.20/187.75 tff(29827,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_h, s17)), introduced(assumption)).
% 295.20/187.75 tff(29828,plain,
% 295.20/187.75 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_h, s17)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s17)) | m_c_h_element_v_in2(c_e_h_1, c_h, s17))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_h, s17)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s17)) | m_c_h_element_v_in2(c_e_h_1, c_h, s17))),
% 295.20/187.75 inference(rewrite,[status(thm)],[])).
% 295.20/187.75 tff(29829,plain,
% 295.20/187.75 (((~m_c_h_element_v_in1(c_e_h_1, c_h, s17)) | m_c_h_element_v_in2(c_e_h_1, c_h, s17) | (~node17(c_e_h_1, c_h, s17))) <=> ((~node17(c_e_h_1, c_h, s17)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s17)) | m_c_h_element_v_in2(c_e_h_1, c_h, s17))),
% 295.20/187.75 inference(rewrite,[status(thm)],[])).
% 295.20/187.75 tff(29830,plain,
% 295.20/187.75 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s17)) | m_c_h_element_v_in2(c_e_h_1, c_h, s17) | (~node17(c_e_h_1, c_h, s17)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_h, s17)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s17)) | m_c_h_element_v_in2(c_e_h_1, c_h, s17)))),
% 295.20/187.75 inference(monotonicity,[status(thm)],[29829])).
% 295.20/187.75 tff(29831,plain,
% 295.20/187.75 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s17)) | m_c_h_element_v_in2(c_e_h_1, c_h, s17) | (~node17(c_e_h_1, c_h, s17)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_h, s17)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s17)) | m_c_h_element_v_in2(c_e_h_1, c_h, s17))),
% 295.20/187.75 inference(transitivity,[status(thm)],[29830, 29828])).
% 295.20/187.75 tff(29832,plain,
% 295.20/187.75 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s17)) | m_c_h_element_v_in2(c_e_h_1, c_h, s17) | (~node17(c_e_h_1, c_h, s17)))),
% 295.20/187.75 inference(quant_inst,[status(thm)],[])).
% 295.20/187.75 tff(29833,plain,
% 295.20/187.75 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_h, s17)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s17)) | m_c_h_element_v_in2(c_e_h_1, c_h, s17)),
% 295.20/187.75 inference(modus_ponens,[status(thm)],[29832, 29831])).
% 295.20/187.75 tff(29834,plain,
% 295.20/187.75 ((~node17(c_e_h_1, c_h, s17)) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s17))),
% 295.20/187.75 inference(unit_resolution,[status(thm)],[29833, 919, 29827])).
% 295.20/187.75 tff(29835,plain,
% 295.20/187.75 ($false),
% 295.20/187.75 inference(unit_resolution,[status(thm)],[29834, 29826, 29824])).
% 295.20/187.75 tff(29836,plain,(m_c_h_element_v_out(c_e_h_1, c_h, s17) | m_c_h_element_v_in2(c_e_h_1, c_h, s17) | (~m_c_h_element_v_out(c_e_h_1, c_h, s18))), inference(lemma,lemma(discharge,[]))).
% 295.20/187.75 tff(29837,plain,
% 295.20/187.75 (~m_c_h_element_v_out(c_e_h_1, c_h, s18)),
% 295.20/187.75 inference(unit_resolution,[status(thm)],[29836, 29762, 26731])).
% 295.20/187.75 tff(29838,plain,
% 295.20/187.75 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s18)) | m_or_h_gate_v_out(c_e_h_1, c_j, s18))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s18)) | m_or_h_gate_v_out(c_e_h_1, c_j, s18))),
% 295.20/187.75 inference(rewrite,[status(thm)],[])).
% 295.20/187.75 tff(29839,plain,
% 295.20/187.75 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s18)) | m_or_h_gate_v_out(c_e_h_1, c_j, s18))),
% 295.20/187.75 inference(quant_inst,[status(thm)],[])).
% 295.20/187.75 tff(29840,plain,
% 295.20/187.75 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s18)) | m_or_h_gate_v_out(c_e_h_1, c_j, s18)),
% 295.20/187.76 inference(modus_ponens,[status(thm)],[29839, 29838])).
% 295.20/187.76 tff(29841,plain,
% 295.20/187.76 (~m_c_h_element_v_in2(c_e_h_1, c_h, s18)),
% 295.20/187.76 inference(unit_resolution,[status(thm)],[29840, 1174, 29581])).
% 295.20/187.76 tff(29842,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_h, s18)), introduced(assumption)).
% 295.20/187.76 tff(29843,assumption,(m_c_h_element_v_out(c_e_h_1, c_h, s19)), introduced(assumption)).
% 295.20/187.76 tff(29844,assumption,(~m_c_h_element_v_out(c_e_h_1, c_h, s18)), introduced(assumption)).
% 295.20/187.76 tff(29845,assumption,(node15(c_e_h_1, c_h, s18, s19)), introduced(assumption)).
% 295.20/187.76 tff(29846,plain,
% 295.20/187.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s19)) | (~node15(c_e_h_1, c_h, s18, s19)) | m_c_h_element_v_out(c_e_h_1, c_h, s18))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s19)) | (~node15(c_e_h_1, c_h, s18, s19)) | m_c_h_element_v_out(c_e_h_1, c_h, s18))),
% 295.20/187.76 inference(rewrite,[status(thm)],[])).
% 295.20/187.76 tff(29847,plain,
% 295.20/187.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s19)) | (~node15(c_e_h_1, c_h, s18, s19)) | m_c_h_element_v_out(c_e_h_1, c_h, s18))),
% 295.20/187.76 inference(quant_inst,[status(thm)],[])).
% 295.20/187.76 tff(29848,plain,
% 295.20/187.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s19)) | (~node15(c_e_h_1, c_h, s18, s19)) | m_c_h_element_v_out(c_e_h_1, c_h, s18)),
% 295.20/187.76 inference(modus_ponens,[status(thm)],[29847, 29846])).
% 295.20/187.76 tff(29849,plain,
% 295.20/187.76 ($false),
% 295.20/187.76 inference(unit_resolution,[status(thm)],[29848, 147, 29844, 29843, 29845])).
% 295.20/187.76 tff(29850,plain,((~node15(c_e_h_1, c_h, s18, s19)) | m_c_h_element_v_out(c_e_h_1, c_h, s18) | (~m_c_h_element_v_out(c_e_h_1, c_h, s19))), inference(lemma,lemma(discharge,[]))).
% 295.20/187.76 tff(29851,plain,
% 295.20/187.76 (~node15(c_e_h_1, c_h, s18, s19)),
% 295.20/187.76 inference(unit_resolution,[status(thm)],[29850, 29843, 29844])).
% 295.20/187.76 tff(29852,assumption,(~node15(c_e_h_1, c_h, s18, s19)), introduced(assumption)).
% 295.20/187.76 tff(29853,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_h, s18)), introduced(assumption)).
% 295.20/187.76 tff(29854,plain,
% 295.20/187.76 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s18)) | m_c_h_element_v_in1(c_e_h_1, c_h, s18) | m_c_h_element_v_in2(c_e_h_1, c_h, s18))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s18)) | m_c_h_element_v_in1(c_e_h_1, c_h, s18) | m_c_h_element_v_in2(c_e_h_1, c_h, s18))),
% 295.20/187.76 inference(rewrite,[status(thm)],[])).
% 295.20/187.76 tff(29855,plain,
% 295.20/187.76 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s18)) | m_c_h_element_v_in1(c_e_h_1, c_h, s18) | m_c_h_element_v_in2(c_e_h_1, c_h, s18))),
% 295.20/187.76 inference(quant_inst,[status(thm)],[])).
% 295.20/187.76 tff(29856,plain,
% 295.20/187.76 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s18)) | m_c_h_element_v_in1(c_e_h_1, c_h, s18) | m_c_h_element_v_in2(c_e_h_1, c_h, s18)),
% 295.20/187.76 inference(modus_ponens,[status(thm)],[29855, 29854])).
% 295.20/187.76 tff(29857,plain,
% 295.20/187.76 ((~node16(c_e_h_1, c_h, s18)) | m_c_h_element_v_in1(c_e_h_1, c_h, s18)),
% 295.20/187.76 inference(unit_resolution,[status(thm)],[29856, 178, 29842])).
% 295.20/187.76 tff(29858,plain,
% 295.20/187.76 (~node16(c_e_h_1, c_h, s18)),
% 295.20/187.76 inference(unit_resolution,[status(thm)],[29857, 29853])).
% 295.20/187.76 tff(29859,assumption,(node14(c_e_h_1, c_h, s18, s19)), introduced(assumption)).
% 295.20/187.76 tff(29860,plain,
% 295.20/187.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s18) | (~m_c_h_element_v_out(c_e_h_1, c_h, s19)) | (~node14(c_e_h_1, c_h, s18, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s18) | (~m_c_h_element_v_out(c_e_h_1, c_h, s19)) | (~node14(c_e_h_1, c_h, s18, s19)))),
% 295.20/187.76 inference(rewrite,[status(thm)],[])).
% 295.20/187.76 tff(29861,plain,
% 295.20/187.76 (((~node14(c_e_h_1, c_h, s18, s19)) | m_c_h_element_v_in1(c_e_h_1, c_h, s18) | (~m_c_h_element_v_out(c_e_h_1, c_h, s19))) <=> (m_c_h_element_v_in1(c_e_h_1, c_h, s18) | (~m_c_h_element_v_out(c_e_h_1, c_h, s19)) | (~node14(c_e_h_1, c_h, s18, s19)))),
% 295.20/187.76 inference(rewrite,[status(thm)],[])).
% 295.20/187.76 tff(29862,plain,
% 295.20/187.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s18, s19)) | m_c_h_element_v_in1(c_e_h_1, c_h, s18) | (~m_c_h_element_v_out(c_e_h_1, c_h, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s18) | (~m_c_h_element_v_out(c_e_h_1, c_h, s19)) | (~node14(c_e_h_1, c_h, s18, s19))))),
% 295.20/187.76 inference(monotonicity,[status(thm)],[29861])).
% 295.20/187.76 tff(29863,plain,
% 295.20/187.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s18, s19)) | m_c_h_element_v_in1(c_e_h_1, c_h, s18) | (~m_c_h_element_v_out(c_e_h_1, c_h, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s18) | (~m_c_h_element_v_out(c_e_h_1, c_h, s19)) | (~node14(c_e_h_1, c_h, s18, s19)))),
% 295.20/187.76 inference(transitivity,[status(thm)],[29862, 29860])).
% 295.20/187.76 tff(29864,plain,
% 295.20/187.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s18, s19)) | m_c_h_element_v_in1(c_e_h_1, c_h, s18) | (~m_c_h_element_v_out(c_e_h_1, c_h, s19)))),
% 295.20/187.76 inference(quant_inst,[status(thm)],[])).
% 295.20/187.76 tff(29865,plain,
% 295.20/187.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s18) | (~m_c_h_element_v_out(c_e_h_1, c_h, s19)) | (~node14(c_e_h_1, c_h, s18, s19))),
% 295.20/187.76 inference(modus_ponens,[status(thm)],[29864, 29863])).
% 295.20/187.76 tff(29866,plain,
% 295.20/187.76 ($false),
% 295.20/187.76 inference(unit_resolution,[status(thm)],[29865, 223, 29843, 29859, 29853])).
% 295.20/187.76 tff(29867,plain,((~node14(c_e_h_1, c_h, s18, s19)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s19)) | m_c_h_element_v_in1(c_e_h_1, c_h, s18)), inference(lemma,lemma(discharge,[]))).
% 295.20/187.76 tff(29868,plain,
% 295.20/187.76 (~node14(c_e_h_1, c_h, s18, s19)),
% 295.20/187.76 inference(unit_resolution,[status(thm)],[29867, 29853, 29843])).
% 295.20/187.76 tff(29869,plain,
% 295.20/187.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s18, s19)) | node19(c_e_h_1, c_h, s18, s19))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s18, s19)) | node19(c_e_h_1, c_h, s18, s19))),
% 295.20/187.76 inference(rewrite,[status(thm)],[])).
% 295.20/187.76 tff(29870,plain,
% 295.20/187.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s18, s19)) | node19(c_e_h_1, c_h, s18, s19))),
% 295.20/187.76 inference(quant_inst,[status(thm)],[])).
% 295.20/187.76 tff(29871,plain,
% 295.20/187.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s18, s19)) | node19(c_e_h_1, c_h, s18, s19)),
% 295.20/187.76 inference(modus_ponens,[status(thm)],[29870, 29869])).
% 295.20/187.76 tff(29872,plain,
% 295.20/187.76 (node19(c_e_h_1, c_h, s18, s19)),
% 295.20/187.76 inference(unit_resolution,[status(thm)],[29871, 190, 26787])).
% 295.20/187.76 tff(29873,plain,
% 295.20/187.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s18) | node14(c_e_h_1, c_h, s18, s19) | node15(c_e_h_1, c_h, s18, s19) | (~node19(c_e_h_1, c_h, s18, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s18) | node14(c_e_h_1, c_h, s18, s19) | node15(c_e_h_1, c_h, s18, s19) | (~node19(c_e_h_1, c_h, s18, s19)))),
% 295.20/187.76 inference(rewrite,[status(thm)],[])).
% 295.20/187.76 tff(29874,plain,
% 295.20/187.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s18) | node14(c_e_h_1, c_h, s18, s19) | node15(c_e_h_1, c_h, s18, s19) | (~node19(c_e_h_1, c_h, s18, s19)))),
% 295.20/187.76 inference(quant_inst,[status(thm)],[])).
% 295.20/187.76 tff(29875,plain,
% 295.20/187.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s18) | node14(c_e_h_1, c_h, s18, s19) | node15(c_e_h_1, c_h, s18, s19) | (~node19(c_e_h_1, c_h, s18, s19))),
% 295.20/187.76 inference(modus_ponens,[status(thm)],[29874, 29873])).
% 295.20/187.76 tff(29876,plain,
% 295.20/187.76 (node16(c_e_h_1, c_h, s18) | node14(c_e_h_1, c_h, s18, s19) | node15(c_e_h_1, c_h, s18, s19)),
% 295.20/187.76 inference(unit_resolution,[status(thm)],[29875, 204, 29872])).
% 295.20/187.76 tff(29877,plain,
% 295.20/187.76 ($false),
% 295.20/187.76 inference(unit_resolution,[status(thm)],[29876, 29868, 29858, 29852])).
% 295.20/187.76 tff(29878,plain,(m_c_h_element_v_in1(c_e_h_1, c_h, s18) | node15(c_e_h_1, c_h, s18, s19) | (~m_c_h_element_v_out(c_e_h_1, c_h, s19)) | m_c_h_element_v_in2(c_e_h_1, c_h, s18)), inference(lemma,lemma(discharge,[]))).
% 295.20/187.76 tff(29879,plain,
% 295.20/187.76 (m_c_h_element_v_in1(c_e_h_1, c_h, s18)),
% 295.20/187.76 inference(unit_resolution,[status(thm)],[29878, 29851, 29843, 29842])).
% 295.20/187.76 tff(29880,plain,
% 295.20/187.76 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s18)) | m_c_h_element_v_in2(c_e_h_1, c_h, s18) | (~node17(c_e_h_1, c_h, s18)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s18)) | m_c_h_element_v_in2(c_e_h_1, c_h, s18) | (~node17(c_e_h_1, c_h, s18)))),
% 295.20/187.76 inference(rewrite,[status(thm)],[])).
% 295.20/187.76 tff(29881,plain,
% 295.20/187.76 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s18)) | m_c_h_element_v_in2(c_e_h_1, c_h, s18) | (~node17(c_e_h_1, c_h, s18)))),
% 295.20/187.76 inference(quant_inst,[status(thm)],[])).
% 295.20/187.76 tff(29882,plain,
% 295.20/187.76 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s18)) | m_c_h_element_v_in2(c_e_h_1, c_h, s18) | (~node17(c_e_h_1, c_h, s18))),
% 295.20/187.76 inference(modus_ponens,[status(thm)],[29881, 29880])).
% 295.20/187.76 tff(29883,plain,
% 295.20/187.76 ((~m_c_h_element_v_in1(c_e_h_1, c_h, s18)) | (~node17(c_e_h_1, c_h, s18))),
% 295.20/187.76 inference(unit_resolution,[status(thm)],[29882, 919, 29842])).
% 295.20/187.76 tff(29884,plain,
% 295.20/187.76 (~node17(c_e_h_1, c_h, s18)),
% 295.20/187.76 inference(unit_resolution,[status(thm)],[29883, 29879])).
% 295.20/187.76 tff(29885,plain,
% 295.20/187.76 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s18) | node18(c_e_h_1, c_h, s18, s19) | (~node19(c_e_h_1, c_h, s18, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s18) | node18(c_e_h_1, c_h, s18, s19) | (~node19(c_e_h_1, c_h, s18, s19)))),
% 295.20/187.76 inference(rewrite,[status(thm)],[])).
% 295.20/187.76 tff(29886,plain,
% 295.20/187.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s18) | node18(c_e_h_1, c_h, s18, s19) | (~node19(c_e_h_1, c_h, s18, s19)))),
% 295.20/187.76 inference(quant_inst,[status(thm)],[])).
% 295.20/187.76 tff(29887,plain,
% 295.20/187.76 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s18) | node18(c_e_h_1, c_h, s18, s19) | (~node19(c_e_h_1, c_h, s18, s19))),
% 295.20/187.77 inference(modus_ponens,[status(thm)],[29886, 29885])).
% 295.20/187.77 tff(29888,plain,
% 295.20/187.77 (node17(c_e_h_1, c_h, s18) | node18(c_e_h_1, c_h, s18, s19)),
% 295.20/187.77 inference(unit_resolution,[status(thm)],[29887, 776, 29872])).
% 295.20/187.77 tff(29889,plain,
% 295.20/187.77 (node18(c_e_h_1, c_h, s18, s19)),
% 295.20/187.77 inference(unit_resolution,[status(thm)],[29888, 29884])).
% 295.20/187.77 tff(29890,plain,
% 295.20/187.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_h, s18) | (~m_c_h_element_v_out(c_e_h_1, c_h, s19)) | (~node18(c_e_h_1, c_h, s18, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s18) | (~m_c_h_element_v_out(c_e_h_1, c_h, s19)) | (~node18(c_e_h_1, c_h, s18, s19)))),
% 295.20/187.77 inference(rewrite,[status(thm)],[])).
% 295.20/187.77 tff(29891,plain,
% 295.20/187.77 (((~m_c_h_element_v_out(c_e_h_1, c_h, s19)) | m_c_h_element_v_out(c_e_h_1, c_h, s18) | (~node18(c_e_h_1, c_h, s18, s19))) <=> (m_c_h_element_v_out(c_e_h_1, c_h, s18) | (~m_c_h_element_v_out(c_e_h_1, c_h, s19)) | (~node18(c_e_h_1, c_h, s18, s19)))),
% 295.20/187.77 inference(rewrite,[status(thm)],[])).
% 295.20/187.77 tff(29892,plain,
% 295.20/187.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s19)) | m_c_h_element_v_out(c_e_h_1, c_h, s18) | (~node18(c_e_h_1, c_h, s18, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_h, s18) | (~m_c_h_element_v_out(c_e_h_1, c_h, s19)) | (~node18(c_e_h_1, c_h, s18, s19))))),
% 295.20/187.77 inference(monotonicity,[status(thm)],[29891])).
% 295.20/187.77 tff(29893,plain,
% 295.20/187.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s19)) | m_c_h_element_v_out(c_e_h_1, c_h, s18) | (~node18(c_e_h_1, c_h, s18, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s18) | (~m_c_h_element_v_out(c_e_h_1, c_h, s19)) | (~node18(c_e_h_1, c_h, s18, s19)))),
% 295.20/187.77 inference(transitivity,[status(thm)],[29892, 29890])).
% 295.20/187.77 tff(29894,plain,
% 295.20/187.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s19)) | m_c_h_element_v_out(c_e_h_1, c_h, s18) | (~node18(c_e_h_1, c_h, s18, s19)))),
% 295.20/187.77 inference(quant_inst,[status(thm)],[])).
% 295.20/187.77 tff(29895,plain,
% 295.20/187.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s18) | (~m_c_h_element_v_out(c_e_h_1, c_h, s19)) | (~node18(c_e_h_1, c_h, s18, s19))),
% 295.20/187.77 inference(modus_ponens,[status(thm)],[29894, 29893])).
% 295.20/187.77 tff(29896,plain,
% 295.20/187.77 ($false),
% 295.20/187.77 inference(unit_resolution,[status(thm)],[29895, 753, 29844, 29843, 29889])).
% 295.20/187.77 tff(29897,plain,((~m_c_h_element_v_out(c_e_h_1, c_h, s19)) | m_c_h_element_v_out(c_e_h_1, c_h, s18) | m_c_h_element_v_in2(c_e_h_1, c_h, s18)), inference(lemma,lemma(discharge,[]))).
% 295.20/187.77 tff(29898,plain,
% 295.20/187.77 (~m_c_h_element_v_out(c_e_h_1, c_h, s19)),
% 295.20/187.77 inference(unit_resolution,[status(thm)],[29897, 29841, 29837])).
% 295.20/187.77 tff(29899,assumption,(~m_c_h_element_v_out(c_e_h_1, c_h, s19)), introduced(assumption)).
% 295.20/187.77 tff(29900,assumption,(m_c_h_element_v_out(c_e_h_1, c_h, s20)), introduced(assumption)).
% 295.20/187.77 tff(29901,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_h, s19)), introduced(assumption)).
% 295.20/187.77 tff(29902,assumption,(node14(c_e_h_1, c_h, s19, s20)), introduced(assumption)).
% 295.20/187.77 tff(29903,plain,
% 295.20/187.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s19) | (~m_c_h_element_v_out(c_e_h_1, c_h, s20)) | (~node14(c_e_h_1, c_h, s19, s20)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s19) | (~m_c_h_element_v_out(c_e_h_1, c_h, s20)) | (~node14(c_e_h_1, c_h, s19, s20)))),
% 295.20/187.77 inference(rewrite,[status(thm)],[])).
% 295.20/187.77 tff(29904,plain,
% 295.20/187.77 (((~node14(c_e_h_1, c_h, s19, s20)) | m_c_h_element_v_in1(c_e_h_1, c_h, s19) | (~m_c_h_element_v_out(c_e_h_1, c_h, s20))) <=> (m_c_h_element_v_in1(c_e_h_1, c_h, s19) | (~m_c_h_element_v_out(c_e_h_1, c_h, s20)) | (~node14(c_e_h_1, c_h, s19, s20)))),
% 295.20/187.77 inference(rewrite,[status(thm)],[])).
% 295.20/187.77 tff(29905,plain,
% 295.20/187.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s19, s20)) | m_c_h_element_v_in1(c_e_h_1, c_h, s19) | (~m_c_h_element_v_out(c_e_h_1, c_h, s20)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s19) | (~m_c_h_element_v_out(c_e_h_1, c_h, s20)) | (~node14(c_e_h_1, c_h, s19, s20))))),
% 295.20/187.77 inference(monotonicity,[status(thm)],[29904])).
% 295.20/187.77 tff(29906,plain,
% 295.20/187.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s19, s20)) | m_c_h_element_v_in1(c_e_h_1, c_h, s19) | (~m_c_h_element_v_out(c_e_h_1, c_h, s20)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s19) | (~m_c_h_element_v_out(c_e_h_1, c_h, s20)) | (~node14(c_e_h_1, c_h, s19, s20)))),
% 295.20/187.77 inference(transitivity,[status(thm)],[29905, 29903])).
% 295.20/187.77 tff(29907,plain,
% 295.20/187.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s19, s20)) | m_c_h_element_v_in1(c_e_h_1, c_h, s19) | (~m_c_h_element_v_out(c_e_h_1, c_h, s20)))),
% 295.20/187.77 inference(quant_inst,[status(thm)],[])).
% 295.20/187.77 tff(29908,plain,
% 295.20/187.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s19) | (~m_c_h_element_v_out(c_e_h_1, c_h, s20)) | (~node14(c_e_h_1, c_h, s19, s20))),
% 295.20/187.77 inference(modus_ponens,[status(thm)],[29907, 29906])).
% 295.20/187.77 tff(29909,plain,
% 295.20/187.77 ($false),
% 295.20/187.77 inference(unit_resolution,[status(thm)],[29908, 223, 29900, 29902, 29901])).
% 295.20/187.77 tff(29910,plain,((~node14(c_e_h_1, c_h, s19, s20)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s20)) | m_c_h_element_v_in1(c_e_h_1, c_h, s19)), inference(lemma,lemma(discharge,[]))).
% 295.20/187.77 tff(29911,plain,
% 295.20/187.77 (~node14(c_e_h_1, c_h, s19, s20)),
% 295.20/187.77 inference(unit_resolution,[status(thm)],[29910, 29900, 29901])).
% 295.20/187.77 tff(29912,assumption,(node15(c_e_h_1, c_h, s19, s20)), introduced(assumption)).
% 295.20/187.77 tff(29913,plain,
% 295.20/187.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s20)) | (~node15(c_e_h_1, c_h, s19, s20)) | m_c_h_element_v_out(c_e_h_1, c_h, s19))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s20)) | (~node15(c_e_h_1, c_h, s19, s20)) | m_c_h_element_v_out(c_e_h_1, c_h, s19))),
% 295.20/187.77 inference(rewrite,[status(thm)],[])).
% 295.20/187.77 tff(29914,plain,
% 295.20/187.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s20)) | (~node15(c_e_h_1, c_h, s19, s20)) | m_c_h_element_v_out(c_e_h_1, c_h, s19))),
% 295.20/187.77 inference(quant_inst,[status(thm)],[])).
% 295.20/187.77 tff(29915,plain,
% 295.20/187.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s20)) | (~node15(c_e_h_1, c_h, s19, s20)) | m_c_h_element_v_out(c_e_h_1, c_h, s19)),
% 295.20/187.77 inference(modus_ponens,[status(thm)],[29914, 29913])).
% 295.20/187.77 tff(29916,plain,
% 295.20/187.77 ($false),
% 295.20/187.77 inference(unit_resolution,[status(thm)],[29915, 147, 29899, 29900, 29912])).
% 295.20/187.77 tff(29917,plain,((~node15(c_e_h_1, c_h, s19, s20)) | m_c_h_element_v_out(c_e_h_1, c_h, s19) | (~m_c_h_element_v_out(c_e_h_1, c_h, s20))), inference(lemma,lemma(discharge,[]))).
% 295.20/187.77 tff(29918,plain,
% 295.20/187.77 (~node15(c_e_h_1, c_h, s19, s20)),
% 295.20/187.77 inference(unit_resolution,[status(thm)],[29917, 29900, 29899])).
% 295.20/187.77 tff(29919,plain,
% 295.20/187.77 (succ(s19, s20) <=> succ(s19, s20)),
% 295.20/187.77 inference(rewrite,[status(thm)],[])).
% 295.20/187.77 tff(29920,axiom,(succ(s19, s20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound20')).
% 295.20/187.77 tff(29921,plain,
% 295.20/187.77 (succ(s19, s20)),
% 295.20/187.77 inference(modus_ponens,[status(thm)],[29920, 29919])).
% 295.20/187.77 tff(29922,plain,
% 295.20/187.77 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s19, s20)) | trans(s19, s20))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s19, s20)) | trans(s19, s20))),
% 295.20/187.77 inference(rewrite,[status(thm)],[])).
% 295.20/187.77 tff(29923,plain,
% 295.20/187.77 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s19, s20)) | trans(s19, s20))),
% 295.20/187.77 inference(quant_inst,[status(thm)],[])).
% 295.20/187.77 tff(29924,plain,
% 295.20/187.77 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s19, s20)) | trans(s19, s20)),
% 295.20/187.77 inference(modus_ponens,[status(thm)],[29923, 29922])).
% 295.20/187.77 tff(29925,plain,
% 295.20/187.77 (trans(s19, s20)),
% 295.20/187.77 inference(unit_resolution,[status(thm)],[29924, 29921, 65])).
% 295.20/187.77 tff(29926,plain,
% 295.20/187.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s19, s20)) | node19(c_e_h_1, c_h, s19, s20))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s19, s20)) | node19(c_e_h_1, c_h, s19, s20))),
% 295.20/187.77 inference(rewrite,[status(thm)],[])).
% 295.20/187.77 tff(29927,plain,
% 295.20/187.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s19, s20)) | node19(c_e_h_1, c_h, s19, s20))),
% 295.20/187.77 inference(quant_inst,[status(thm)],[])).
% 295.20/187.77 tff(29928,plain,
% 295.20/187.77 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s19, s20)) | node19(c_e_h_1, c_h, s19, s20)),
% 295.20/187.77 inference(modus_ponens,[status(thm)],[29927, 29926])).
% 295.20/187.77 tff(29929,plain,
% 295.20/187.77 (node19(c_e_h_1, c_h, s19, s20)),
% 295.20/187.77 inference(unit_resolution,[status(thm)],[29928, 190, 29925])).
% 295.20/187.77 tff(29930,plain,
% 295.20/187.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s19) | node14(c_e_h_1, c_h, s19, s20) | (~node19(c_e_h_1, c_h, s19, s20)) | node15(c_e_h_1, c_h, s19, s20))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s19) | node14(c_e_h_1, c_h, s19, s20) | (~node19(c_e_h_1, c_h, s19, s20)) | node15(c_e_h_1, c_h, s19, s20))),
% 295.20/187.77 inference(rewrite,[status(thm)],[])).
% 295.20/187.77 tff(29931,plain,
% 295.20/187.77 ((node16(c_e_h_1, c_h, s19) | node14(c_e_h_1, c_h, s19, s20) | node15(c_e_h_1, c_h, s19, s20) | (~node19(c_e_h_1, c_h, s19, s20))) <=> (node16(c_e_h_1, c_h, s19) | node14(c_e_h_1, c_h, s19, s20) | (~node19(c_e_h_1, c_h, s19, s20)) | node15(c_e_h_1, c_h, s19, s20))),
% 295.20/187.77 inference(rewrite,[status(thm)],[])).
% 295.20/187.77 tff(29932,plain,
% 295.20/187.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s19) | node14(c_e_h_1, c_h, s19, s20) | node15(c_e_h_1, c_h, s19, s20) | (~node19(c_e_h_1, c_h, s19, s20)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s19) | node14(c_e_h_1, c_h, s19, s20) | (~node19(c_e_h_1, c_h, s19, s20)) | node15(c_e_h_1, c_h, s19, s20)))),
% 295.20/187.77 inference(monotonicity,[status(thm)],[29931])).
% 295.20/187.77 tff(29933,plain,
% 295.20/187.77 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s19) | node14(c_e_h_1, c_h, s19, s20) | node15(c_e_h_1, c_h, s19, s20) | (~node19(c_e_h_1, c_h, s19, s20)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s19) | node14(c_e_h_1, c_h, s19, s20) | (~node19(c_e_h_1, c_h, s19, s20)) | node15(c_e_h_1, c_h, s19, s20))),
% 295.20/187.78 inference(transitivity,[status(thm)],[29932, 29930])).
% 295.20/187.78 tff(29934,plain,
% 295.20/187.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s19) | node14(c_e_h_1, c_h, s19, s20) | node15(c_e_h_1, c_h, s19, s20) | (~node19(c_e_h_1, c_h, s19, s20)))),
% 295.20/187.78 inference(quant_inst,[status(thm)],[])).
% 295.20/187.78 tff(29935,plain,
% 295.20/187.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s19) | node14(c_e_h_1, c_h, s19, s20) | (~node19(c_e_h_1, c_h, s19, s20)) | node15(c_e_h_1, c_h, s19, s20)),
% 295.20/187.78 inference(modus_ponens,[status(thm)],[29934, 29933])).
% 295.20/187.78 tff(29936,plain,
% 295.20/187.78 (node16(c_e_h_1, c_h, s19) | node14(c_e_h_1, c_h, s19, s20) | node15(c_e_h_1, c_h, s19, s20)),
% 295.20/187.78 inference(unit_resolution,[status(thm)],[29935, 204, 29929])).
% 295.20/187.78 tff(29937,plain,
% 295.20/187.78 (node16(c_e_h_1, c_h, s19)),
% 295.20/187.78 inference(unit_resolution,[status(thm)],[29936, 29918, 29911])).
% 295.20/187.78 tff(29938,plain,
% 295.20/187.78 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s19)) | m_c_h_element_v_in1(c_e_h_1, c_h, s19) | m_c_h_element_v_in2(c_e_h_1, c_h, s19))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s19)) | m_c_h_element_v_in1(c_e_h_1, c_h, s19) | m_c_h_element_v_in2(c_e_h_1, c_h, s19))),
% 295.20/187.78 inference(rewrite,[status(thm)],[])).
% 295.20/187.78 tff(29939,plain,
% 295.20/187.78 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s19)) | m_c_h_element_v_in1(c_e_h_1, c_h, s19) | m_c_h_element_v_in2(c_e_h_1, c_h, s19))),
% 295.20/187.78 inference(quant_inst,[status(thm)],[])).
% 295.20/187.78 tff(29940,plain,
% 295.20/187.78 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s19)) | m_c_h_element_v_in1(c_e_h_1, c_h, s19) | m_c_h_element_v_in2(c_e_h_1, c_h, s19)),
% 295.20/187.78 inference(modus_ponens,[status(thm)],[29939, 29938])).
% 295.20/187.78 tff(29941,plain,
% 295.20/187.78 ((~node16(c_e_h_1, c_h, s19)) | m_c_h_element_v_in2(c_e_h_1, c_h, s19)),
% 295.20/187.78 inference(unit_resolution,[status(thm)],[29940, 178, 29901])).
% 295.20/187.78 tff(29942,plain,
% 295.20/187.78 (m_c_h_element_v_in2(c_e_h_1, c_h, s19)),
% 295.20/187.78 inference(unit_resolution,[status(thm)],[29941, 29937])).
% 295.20/187.78 tff(29943,plain,
% 295.20/187.78 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s19)) | m_c_h_element_v_in1(c_e_h_1, c_h, s19) | (~node17(c_e_h_1, c_h, s19)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s19)) | m_c_h_element_v_in1(c_e_h_1, c_h, s19) | (~node17(c_e_h_1, c_h, s19)))),
% 295.20/187.78 inference(rewrite,[status(thm)],[])).
% 295.20/187.78 tff(29944,plain,
% 295.20/187.78 ((m_c_h_element_v_in1(c_e_h_1, c_h, s19) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s19)) | (~node17(c_e_h_1, c_h, s19))) <=> ((~m_c_h_element_v_in2(c_e_h_1, c_h, s19)) | m_c_h_element_v_in1(c_e_h_1, c_h, s19) | (~node17(c_e_h_1, c_h, s19)))),
% 295.20/187.78 inference(rewrite,[status(thm)],[])).
% 295.20/187.78 tff(29945,plain,
% 295.20/187.78 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s19) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s19)) | (~node17(c_e_h_1, c_h, s19)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s19)) | m_c_h_element_v_in1(c_e_h_1, c_h, s19) | (~node17(c_e_h_1, c_h, s19))))),
% 295.29/187.78 inference(monotonicity,[status(thm)],[29944])).
% 295.29/187.78 tff(29946,plain,
% 295.29/187.78 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s19) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s19)) | (~node17(c_e_h_1, c_h, s19)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s19)) | m_c_h_element_v_in1(c_e_h_1, c_h, s19) | (~node17(c_e_h_1, c_h, s19)))),
% 295.29/187.78 inference(transitivity,[status(thm)],[29945, 29943])).
% 295.29/187.78 tff(29947,plain,
% 295.29/187.78 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s19) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s19)) | (~node17(c_e_h_1, c_h, s19)))),
% 295.29/187.78 inference(quant_inst,[status(thm)],[])).
% 295.29/187.78 tff(29948,plain,
% 295.29/187.78 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s19)) | m_c_h_element_v_in1(c_e_h_1, c_h, s19) | (~node17(c_e_h_1, c_h, s19))),
% 295.29/187.78 inference(modus_ponens,[status(thm)],[29947, 29946])).
% 295.29/187.78 tff(29949,plain,
% 295.29/187.78 ((~m_c_h_element_v_in2(c_e_h_1, c_h, s19)) | (~node17(c_e_h_1, c_h, s19))),
% 295.29/187.78 inference(unit_resolution,[status(thm)],[29948, 859, 29901])).
% 295.29/187.78 tff(29950,plain,
% 295.29/187.78 (~node17(c_e_h_1, c_h, s19)),
% 295.29/187.78 inference(unit_resolution,[status(thm)],[29949, 29942])).
% 295.29/187.78 tff(29951,plain,
% 295.29/187.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s19) | node18(c_e_h_1, c_h, s19, s20) | (~node19(c_e_h_1, c_h, s19, s20)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s19) | node18(c_e_h_1, c_h, s19, s20) | (~node19(c_e_h_1, c_h, s19, s20)))),
% 295.29/187.78 inference(rewrite,[status(thm)],[])).
% 295.29/187.78 tff(29952,plain,
% 295.29/187.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s19) | node18(c_e_h_1, c_h, s19, s20) | (~node19(c_e_h_1, c_h, s19, s20)))),
% 295.29/187.78 inference(quant_inst,[status(thm)],[])).
% 295.29/187.78 tff(29953,plain,
% 295.29/187.78 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s19) | node18(c_e_h_1, c_h, s19, s20) | (~node19(c_e_h_1, c_h, s19, s20))),
% 295.29/187.78 inference(modus_ponens,[status(thm)],[29952, 29951])).
% 295.29/187.78 tff(29954,plain,
% 295.29/187.78 (node17(c_e_h_1, c_h, s19) | node18(c_e_h_1, c_h, s19, s20)),
% 295.29/187.78 inference(unit_resolution,[status(thm)],[29953, 776, 29929])).
% 295.29/187.78 tff(29955,plain,
% 295.29/187.78 (node18(c_e_h_1, c_h, s19, s20)),
% 295.29/187.78 inference(unit_resolution,[status(thm)],[29954, 29950])).
% 295.29/187.78 tff(29956,plain,
% 295.29/187.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_h, s19) | (~m_c_h_element_v_out(c_e_h_1, c_h, s20)) | (~node18(c_e_h_1, c_h, s19, s20)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s19) | (~m_c_h_element_v_out(c_e_h_1, c_h, s20)) | (~node18(c_e_h_1, c_h, s19, s20)))),
% 295.29/187.78 inference(rewrite,[status(thm)],[])).
% 295.29/187.78 tff(29957,plain,
% 295.29/187.78 (((~m_c_h_element_v_out(c_e_h_1, c_h, s20)) | m_c_h_element_v_out(c_e_h_1, c_h, s19) | (~node18(c_e_h_1, c_h, s19, s20))) <=> (m_c_h_element_v_out(c_e_h_1, c_h, s19) | (~m_c_h_element_v_out(c_e_h_1, c_h, s20)) | (~node18(c_e_h_1, c_h, s19, s20)))),
% 295.29/187.78 inference(rewrite,[status(thm)],[])).
% 295.29/187.78 tff(29958,plain,
% 295.29/187.78 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s20)) | m_c_h_element_v_out(c_e_h_1, c_h, s19) | (~node18(c_e_h_1, c_h, s19, s20)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_h, s19) | (~m_c_h_element_v_out(c_e_h_1, c_h, s20)) | (~node18(c_e_h_1, c_h, s19, s20))))),
% 295.29/187.79 inference(monotonicity,[status(thm)],[29957])).
% 295.29/187.79 tff(29959,plain,
% 295.29/187.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s20)) | m_c_h_element_v_out(c_e_h_1, c_h, s19) | (~node18(c_e_h_1, c_h, s19, s20)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s19) | (~m_c_h_element_v_out(c_e_h_1, c_h, s20)) | (~node18(c_e_h_1, c_h, s19, s20)))),
% 295.29/187.79 inference(transitivity,[status(thm)],[29958, 29956])).
% 295.29/187.79 tff(29960,plain,
% 295.29/187.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s20)) | m_c_h_element_v_out(c_e_h_1, c_h, s19) | (~node18(c_e_h_1, c_h, s19, s20)))),
% 295.29/187.79 inference(quant_inst,[status(thm)],[])).
% 295.29/187.79 tff(29961,plain,
% 295.29/187.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s19) | (~m_c_h_element_v_out(c_e_h_1, c_h, s20)) | (~node18(c_e_h_1, c_h, s19, s20))),
% 295.29/187.79 inference(modus_ponens,[status(thm)],[29960, 29959])).
% 295.29/187.79 tff(29962,plain,
% 295.29/187.79 ($false),
% 295.29/187.79 inference(unit_resolution,[status(thm)],[29961, 753, 29899, 29900, 29955])).
% 295.29/187.79 tff(29963,plain,((~m_c_h_element_v_out(c_e_h_1, c_h, s20)) | m_c_h_element_v_out(c_e_h_1, c_h, s19) | m_c_h_element_v_in1(c_e_h_1, c_h, s19)), inference(lemma,lemma(discharge,[]))).
% 295.29/187.79 tff(29964,plain,
% 295.29/187.79 (m_c_h_element_v_in1(c_e_h_1, c_h, s19)),
% 295.29/187.79 inference(unit_resolution,[status(thm)],[29963, 29900, 29899])).
% 295.29/187.79 tff(29965,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_h, s19)), introduced(assumption)).
% 295.29/187.79 tff(29966,plain,
% 295.29/187.79 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s19)) | m_c_h_element_v_in2(c_e_h_1, c_h, s19) | (~node17(c_e_h_1, c_h, s19)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s19)) | m_c_h_element_v_in2(c_e_h_1, c_h, s19) | (~node17(c_e_h_1, c_h, s19)))),
% 295.29/187.79 inference(rewrite,[status(thm)],[])).
% 295.29/187.79 tff(29967,plain,
% 295.29/187.79 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s19)) | m_c_h_element_v_in2(c_e_h_1, c_h, s19) | (~node17(c_e_h_1, c_h, s19)))),
% 295.29/187.79 inference(quant_inst,[status(thm)],[])).
% 295.29/187.79 tff(29968,plain,
% 295.29/187.79 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s19)) | m_c_h_element_v_in2(c_e_h_1, c_h, s19) | (~node17(c_e_h_1, c_h, s19))),
% 295.29/187.79 inference(modus_ponens,[status(thm)],[29967, 29966])).
% 295.29/187.79 tff(29969,plain,
% 295.29/187.79 ((~m_c_h_element_v_in1(c_e_h_1, c_h, s19)) | (~node17(c_e_h_1, c_h, s19))),
% 295.29/187.79 inference(unit_resolution,[status(thm)],[29968, 919, 29965])).
% 295.29/187.79 tff(29970,plain,
% 295.29/187.79 (~node17(c_e_h_1, c_h, s19)),
% 295.29/187.79 inference(unit_resolution,[status(thm)],[29969, 29964])).
% 295.29/187.79 tff(29971,plain,
% 295.29/187.79 (node18(c_e_h_1, c_h, s19, s20)),
% 295.29/187.79 inference(unit_resolution,[status(thm)],[29954, 29970])).
% 295.29/187.79 tff(29972,plain,
% 295.29/187.79 ($false),
% 295.29/187.79 inference(unit_resolution,[status(thm)],[29961, 753, 29899, 29900, 29971])).
% 295.29/187.79 tff(29973,plain,((~m_c_h_element_v_out(c_e_h_1, c_h, s20)) | m_c_h_element_v_out(c_e_h_1, c_h, s19) | m_c_h_element_v_in2(c_e_h_1, c_h, s19)), inference(lemma,lemma(discharge,[]))).
% 295.29/187.79 tff(29974,plain,
% 295.29/187.79 (~m_c_h_element_v_out(c_e_h_1, c_h, s20)),
% 295.29/187.79 inference(unit_resolution,[status(thm)],[29973, 29898, 29755])).
% 295.29/187.79 tff(29975,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s20)), introduced(assumption)).
% 295.29/187.79 tff(29976,plain,
% 295.29/187.79 (~m_c_h_element_v_out(c_e_h_1, c_h, s19)),
% 295.29/187.79 inference(unit_resolution,[status(thm)],[29897, 29844, 29842])).
% 295.29/187.79 tff(29977,plain,
% 295.29/187.79 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s19)) | m_c_h_element_v_out(c_e_h_1, c_h, s19))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s19)) | m_c_h_element_v_out(c_e_h_1, c_h, s19))),
% 295.29/187.79 inference(rewrite,[status(thm)],[])).
% 295.29/187.79 tff(29978,plain,
% 295.29/187.79 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s19)) | m_c_h_element_v_out(c_e_h_1, c_h, s19))),
% 295.29/187.79 inference(quant_inst,[status(thm)],[])).
% 295.29/187.79 tff(29979,plain,
% 295.29/187.79 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s19)) | m_c_h_element_v_out(c_e_h_1, c_h, s19)),
% 295.29/187.79 inference(modus_ponens,[status(thm)],[29978, 29977])).
% 295.29/187.79 tff(29980,plain,
% 295.29/187.79 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s19)),
% 295.29/187.79 inference(unit_resolution,[status(thm)],[29979, 619, 29976])).
% 295.29/187.79 tff(29981,plain,
% 295.29/187.79 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s19)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s19))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s19)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s19))),
% 295.29/187.79 inference(rewrite,[status(thm)],[])).
% 295.29/187.79 tff(29982,plain,
% 295.29/187.79 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s19)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s19))),
% 295.29/187.79 inference(quant_inst,[status(thm)],[])).
% 295.29/187.79 tff(29983,plain,
% 295.29/187.79 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s19)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s19)),
% 295.29/187.79 inference(modus_ponens,[status(thm)],[29982, 29981])).
% 295.29/187.79 tff(29984,plain,
% 295.29/187.79 (~node20(c_e_h_1, c_i, s19)),
% 295.29/187.79 inference(unit_resolution,[status(thm)],[29983, 38, 29980])).
% 295.29/187.79 tff(29985,plain,
% 295.29/187.79 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s18)) | m_c_h_element_v_out(c_e_h_1, c_h, s18))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s18)) | m_c_h_element_v_out(c_e_h_1, c_h, s18))),
% 295.29/187.79 inference(rewrite,[status(thm)],[])).
% 295.29/187.79 tff(29986,plain,
% 295.29/187.79 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s18)) | m_c_h_element_v_out(c_e_h_1, c_h, s18))),
% 295.29/187.79 inference(quant_inst,[status(thm)],[])).
% 295.29/187.79 tff(29987,plain,
% 295.29/187.79 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s18)) | m_c_h_element_v_out(c_e_h_1, c_h, s18)),
% 295.29/187.79 inference(modus_ponens,[status(thm)],[29986, 29985])).
% 295.29/187.79 tff(29988,plain,
% 295.29/187.79 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s18)),
% 295.29/187.79 inference(unit_resolution,[status(thm)],[29987, 619, 29844])).
% 295.29/187.79 tff(29989,plain,
% 295.29/187.79 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s18)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s18))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s18)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s18))),
% 295.29/187.79 inference(rewrite,[status(thm)],[])).
% 295.29/187.79 tff(29990,plain,
% 295.29/187.79 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s18)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s18))),
% 295.29/187.79 inference(quant_inst,[status(thm)],[])).
% 295.29/187.79 tff(29991,plain,
% 295.29/187.79 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s18)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s18)),
% 295.29/187.79 inference(modus_ponens,[status(thm)],[29990, 29989])).
% 295.29/187.79 tff(29992,plain,
% 295.29/187.79 (~node20(c_e_h_1, c_i, s18)),
% 295.29/187.79 inference(unit_resolution,[status(thm)],[29991, 38, 29988])).
% 295.29/187.79 tff(29993,assumption,(~node20(c_e_h_1, c_i, s18)), introduced(assumption)).
% 295.29/187.79 tff(29994,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s19)), introduced(assumption)).
% 295.29/187.79 tff(29995,assumption,(node21(c_e_h_1, c_i, s18, s19)), introduced(assumption)).
% 295.29/187.79 tff(29996,plain,
% 295.29/187.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s18) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s19)) | (~node21(c_e_h_1, c_i, s18, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s18) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s19)) | (~node21(c_e_h_1, c_i, s18, s19)))),
% 295.29/187.79 inference(rewrite,[status(thm)],[])).
% 295.29/187.79 tff(29997,plain,
% 295.29/187.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s18) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s19)) | (~node21(c_e_h_1, c_i, s18, s19)))),
% 295.29/187.79 inference(quant_inst,[status(thm)],[])).
% 295.29/187.79 tff(29998,plain,
% 295.29/187.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s18) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s19)) | (~node21(c_e_h_1, c_i, s18, s19))),
% 295.29/187.79 inference(modus_ponens,[status(thm)],[29997, 29996])).
% 295.29/187.79 tff(29999,plain,
% 295.29/187.79 ($false),
% 295.29/187.79 inference(unit_resolution,[status(thm)],[29998, 52, 29995, 29994, 29993])).
% 295.29/187.79 tff(30000,plain,((~node21(c_e_h_1, c_i, s18, s19)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s19)) | node20(c_e_h_1, c_i, s18)), inference(lemma,lemma(discharge,[]))).
% 295.29/187.79 tff(30001,plain,
% 295.29/187.79 (~node21(c_e_h_1, c_i, s18, s19)),
% 295.29/187.79 inference(unit_resolution,[status(thm)],[30000, 29994, 29993])).
% 295.29/187.79 tff(30002,assumption,(node22(c_e_h_1, c_i, s18, s19)), introduced(assumption)).
% 295.29/187.79 tff(30003,plain,
% 295.29/187.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s19)) | (~node22(c_e_h_1, c_i, s18, s19)) | m_and_h_gate_v_out(c_e_h_1, c_i, s18))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s19)) | (~node22(c_e_h_1, c_i, s18, s19)) | m_and_h_gate_v_out(c_e_h_1, c_i, s18))),
% 295.29/187.79 inference(rewrite,[status(thm)],[])).
% 295.29/187.79 tff(30004,plain,
% 295.29/187.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s19)) | (~node22(c_e_h_1, c_i, s18, s19)) | m_and_h_gate_v_out(c_e_h_1, c_i, s18))),
% 295.29/187.79 inference(quant_inst,[status(thm)],[])).
% 295.29/187.79 tff(30005,plain,
% 295.29/187.79 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s19)) | (~node22(c_e_h_1, c_i, s18, s19)) | m_and_h_gate_v_out(c_e_h_1, c_i, s18)),
% 295.29/187.79 inference(modus_ponens,[status(thm)],[30004, 30003])).
% 295.29/187.79 tff(30006,plain,
% 295.29/187.79 ($false),
% 295.29/187.79 inference(unit_resolution,[status(thm)],[30005, 108, 30002, 26761, 29994])).
% 295.29/187.79 tff(30007,plain,((~node22(c_e_h_1, c_i, s18, s19)) | m_and_h_gate_v_out(c_e_h_1, c_i, s18) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s19))), inference(lemma,lemma(discharge,[]))).
% 295.29/187.79 tff(30008,plain,
% 295.29/187.79 (~node22(c_e_h_1, c_i, s18, s19)),
% 295.29/187.79 inference(unit_resolution,[status(thm)],[30007, 29994, 26761])).
% 295.29/187.79 tff(30009,plain,
% 295.29/187.79 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s18, s19)) | node21(c_e_h_1, c_i, s18, s19) | node22(c_e_h_1, c_i, s18, s19))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s18, s19)) | node21(c_e_h_1, c_i, s18, s19) | node22(c_e_h_1, c_i, s18, s19))),
% 295.29/187.80 inference(rewrite,[status(thm)],[])).
% 295.29/187.80 tff(30010,plain,
% 295.29/187.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s18, s19)) | node21(c_e_h_1, c_i, s18, s19) | node22(c_e_h_1, c_i, s18, s19))),
% 295.29/187.80 inference(quant_inst,[status(thm)],[])).
% 295.29/187.80 tff(30011,plain,
% 295.29/187.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s18, s19)) | node21(c_e_h_1, c_i, s18, s19) | node22(c_e_h_1, c_i, s18, s19)),
% 295.29/187.80 inference(modus_ponens,[status(thm)],[30010, 30009])).
% 295.29/187.80 tff(30012,plain,
% 295.29/187.80 (node21(c_e_h_1, c_i, s18, s19) | node22(c_e_h_1, c_i, s18, s19)),
% 295.29/187.80 inference(unit_resolution,[status(thm)],[30011, 82, 26787])).
% 295.29/187.80 tff(30013,plain,
% 295.29/187.80 ($false),
% 295.29/187.80 inference(unit_resolution,[status(thm)],[30012, 30008, 30001])).
% 295.29/187.80 tff(30014,plain,((~m_and_h_gate_v_out(c_e_h_1, c_i, s19)) | m_and_h_gate_v_out(c_e_h_1, c_i, s18) | node20(c_e_h_1, c_i, s18)), inference(lemma,lemma(discharge,[]))).
% 295.29/187.80 tff(30015,plain,
% 295.29/187.80 (~m_and_h_gate_v_out(c_e_h_1, c_i, s19)),
% 295.29/187.80 inference(unit_resolution,[status(thm)],[30014, 29992, 26761])).
% 295.29/187.80 tff(30016,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_i, s19)), introduced(assumption)).
% 295.29/187.80 tff(30017,assumption,(node22(c_e_h_1, c_i, s19, s20)), introduced(assumption)).
% 295.29/187.80 tff(30018,plain,
% 295.29/187.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s20)) | (~node22(c_e_h_1, c_i, s19, s20)) | m_and_h_gate_v_out(c_e_h_1, c_i, s19))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s20)) | (~node22(c_e_h_1, c_i, s19, s20)) | m_and_h_gate_v_out(c_e_h_1, c_i, s19))),
% 295.29/187.80 inference(rewrite,[status(thm)],[])).
% 295.29/187.80 tff(30019,plain,
% 295.29/187.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s20)) | (~node22(c_e_h_1, c_i, s19, s20)) | m_and_h_gate_v_out(c_e_h_1, c_i, s19))),
% 295.29/187.80 inference(quant_inst,[status(thm)],[])).
% 295.29/187.80 tff(30020,plain,
% 295.29/187.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s20)) | (~node22(c_e_h_1, c_i, s19, s20)) | m_and_h_gate_v_out(c_e_h_1, c_i, s19)),
% 295.29/187.80 inference(modus_ponens,[status(thm)],[30019, 30018])).
% 295.29/187.80 tff(30021,plain,
% 295.29/187.80 ($false),
% 295.29/187.80 inference(unit_resolution,[status(thm)],[30020, 108, 30017, 30016, 29975])).
% 295.29/187.80 tff(30022,plain,((~node22(c_e_h_1, c_i, s19, s20)) | m_and_h_gate_v_out(c_e_h_1, c_i, s19) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s20))), inference(lemma,lemma(discharge,[]))).
% 295.29/187.80 tff(30023,plain,
% 295.29/187.80 (~node22(c_e_h_1, c_i, s19, s20)),
% 295.29/187.80 inference(unit_resolution,[status(thm)],[30022, 29975, 30016])).
% 295.29/187.80 tff(30024,assumption,(~node20(c_e_h_1, c_i, s19)), introduced(assumption)).
% 295.29/187.80 tff(30025,assumption,(node21(c_e_h_1, c_i, s19, s20)), introduced(assumption)).
% 295.29/187.80 tff(30026,plain,
% 295.29/187.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s19) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s20)) | (~node21(c_e_h_1, c_i, s19, s20)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s19) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s20)) | (~node21(c_e_h_1, c_i, s19, s20)))),
% 295.29/187.80 inference(rewrite,[status(thm)],[])).
% 295.29/187.80 tff(30027,plain,
% 295.29/187.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s19) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s20)) | (~node21(c_e_h_1, c_i, s19, s20)))),
% 295.29/187.80 inference(quant_inst,[status(thm)],[])).
% 295.29/187.80 tff(30028,plain,
% 295.29/187.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s19) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s20)) | (~node21(c_e_h_1, c_i, s19, s20))),
% 295.29/187.80 inference(modus_ponens,[status(thm)],[30027, 30026])).
% 295.29/187.80 tff(30029,plain,
% 295.29/187.80 ($false),
% 295.29/187.80 inference(unit_resolution,[status(thm)],[30028, 52, 30025, 30024, 29975])).
% 295.29/187.80 tff(30030,plain,((~node21(c_e_h_1, c_i, s19, s20)) | node20(c_e_h_1, c_i, s19) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s20))), inference(lemma,lemma(discharge,[]))).
% 295.29/187.80 tff(30031,plain,
% 295.29/187.80 (~node21(c_e_h_1, c_i, s19, s20)),
% 295.29/187.80 inference(unit_resolution,[status(thm)],[30030, 29975, 30024])).
% 295.29/187.80 tff(30032,plain,
% 295.29/187.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s19, s20)) | node21(c_e_h_1, c_i, s19, s20) | node22(c_e_h_1, c_i, s19, s20))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s19, s20)) | node21(c_e_h_1, c_i, s19, s20) | node22(c_e_h_1, c_i, s19, s20))),
% 295.29/187.80 inference(rewrite,[status(thm)],[])).
% 295.29/187.80 tff(30033,plain,
% 295.29/187.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s19, s20)) | node21(c_e_h_1, c_i, s19, s20) | node22(c_e_h_1, c_i, s19, s20))),
% 295.29/187.80 inference(quant_inst,[status(thm)],[])).
% 295.29/187.80 tff(30034,plain,
% 295.29/187.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s19, s20)) | node21(c_e_h_1, c_i, s19, s20) | node22(c_e_h_1, c_i, s19, s20)),
% 295.29/187.80 inference(modus_ponens,[status(thm)],[30033, 30032])).
% 295.29/187.80 tff(30035,plain,
% 295.29/187.80 (node21(c_e_h_1, c_i, s19, s20) | node22(c_e_h_1, c_i, s19, s20)),
% 295.29/187.80 inference(unit_resolution,[status(thm)],[30034, 82, 29925])).
% 295.29/187.80 tff(30036,plain,
% 295.29/187.80 ($false),
% 295.29/187.80 inference(unit_resolution,[status(thm)],[30035, 30031, 30023])).
% 295.29/187.80 tff(30037,plain,((~m_and_h_gate_v_out(c_e_h_1, c_i, s20)) | node20(c_e_h_1, c_i, s19) | m_and_h_gate_v_out(c_e_h_1, c_i, s19)), inference(lemma,lemma(discharge,[]))).
% 295.29/187.80 tff(30038,plain,
% 295.29/187.80 ($false),
% 295.29/187.80 inference(unit_resolution,[status(thm)],[30037, 30015, 29984, 29975])).
% 295.29/187.80 tff(30039,plain,(m_c_h_element_v_out(c_e_h_1, c_h, s18) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s20)) | m_and_h_gate_v_out(c_e_h_1, c_i, s18) | m_c_h_element_v_in2(c_e_h_1, c_h, s18)), inference(lemma,lemma(discharge,[]))).
% 295.29/187.80 tff(30040,plain,
% 295.29/187.80 (~m_and_h_gate_v_out(c_e_h_1, c_i, s20)),
% 295.29/187.80 inference(unit_resolution,[status(thm)],[30039, 29841, 29837, 26760])).
% 295.29/187.80 tff(30041,plain,
% 295.29/187.80 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s18)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s18))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s18)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s18))),
% 295.29/187.80 inference(rewrite,[status(thm)],[])).
% 295.29/187.80 tff(30042,plain,
% 295.29/187.80 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s18)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s18))),
% 295.29/187.80 inference(quant_inst,[status(thm)],[])).
% 295.29/187.80 tff(30043,plain,
% 295.29/187.80 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s18)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s18)),
% 295.29/187.80 inference(modus_ponens,[status(thm)],[30042, 30041])).
% 295.29/187.80 tff(30044,plain,
% 295.29/187.80 (~m_and_h_gate_v_in2(c_e_h_3, c_q, s18)),
% 295.29/187.80 inference(unit_resolution,[status(thm)],[30043, 5621, 28717])).
% 295.29/187.80 tff(30045,plain,
% 295.29/187.80 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s18)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s18))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s18)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s18))),
% 295.29/187.80 inference(rewrite,[status(thm)],[])).
% 295.29/187.80 tff(30046,plain,
% 295.29/187.80 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s18)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s18))),
% 295.31/187.80 inference(quant_inst,[status(thm)],[])).
% 295.31/187.80 tff(30047,plain,
% 295.31/187.80 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s18)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s18)),
% 295.31/187.80 inference(modus_ponens,[status(thm)],[30046, 30045])).
% 295.31/187.80 tff(30048,plain,
% 295.31/187.80 (~node20(c_e_h_3, c_q, s18)),
% 295.31/187.80 inference(unit_resolution,[status(thm)],[30047, 4563, 30044])).
% 295.31/187.80 tff(30049,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_q, s18)), introduced(assumption)).
% 295.31/187.80 tff(30050,assumption,(m_and_h_gate_v_out(c_e_h_3, c_q, s19)), introduced(assumption)).
% 295.31/187.80 tff(30051,assumption,(node22(c_e_h_3, c_q, s18, s19)), introduced(assumption)).
% 295.31/187.80 tff(30052,plain,
% 295.31/187.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s19)) | (~node22(c_e_h_3, c_q, s18, s19)) | m_and_h_gate_v_out(c_e_h_3, c_q, s18))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s19)) | (~node22(c_e_h_3, c_q, s18, s19)) | m_and_h_gate_v_out(c_e_h_3, c_q, s18))),
% 295.31/187.80 inference(rewrite,[status(thm)],[])).
% 295.31/187.80 tff(30053,plain,
% 295.31/187.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s19)) | (~node22(c_e_h_3, c_q, s18, s19)) | m_and_h_gate_v_out(c_e_h_3, c_q, s18))),
% 295.31/187.80 inference(quant_inst,[status(thm)],[])).
% 295.31/187.80 tff(30054,plain,
% 295.31/187.80 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s19)) | (~node22(c_e_h_3, c_q, s18, s19)) | m_and_h_gate_v_out(c_e_h_3, c_q, s18)),
% 295.31/187.80 inference(modus_ponens,[status(thm)],[30053, 30052])).
% 295.31/187.80 tff(30055,plain,
% 295.31/187.80 ($false),
% 295.31/187.80 inference(unit_resolution,[status(thm)],[30054, 108, 30049, 30050, 30051])).
% 295.31/187.80 tff(30056,plain,((~node22(c_e_h_3, c_q, s18, s19)) | m_and_h_gate_v_out(c_e_h_3, c_q, s18) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s19))), inference(lemma,lemma(discharge,[]))).
% 295.31/187.80 tff(30057,plain,
% 295.31/187.80 (~node22(c_e_h_3, c_q, s18, s19)),
% 295.31/187.80 inference(unit_resolution,[status(thm)],[30056, 30050, 30049])).
% 295.31/187.80 tff(30058,assumption,(~node20(c_e_h_3, c_q, s18)), introduced(assumption)).
% 295.31/187.80 tff(30059,assumption,(node21(c_e_h_3, c_q, s18, s19)), introduced(assumption)).
% 295.31/187.80 tff(30060,plain,
% 295.31/187.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s19)) | node20(c_e_h_3, c_q, s18) | (~node21(c_e_h_3, c_q, s18, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s19)) | node20(c_e_h_3, c_q, s18) | (~node21(c_e_h_3, c_q, s18, s19)))),
% 295.31/187.80 inference(rewrite,[status(thm)],[])).
% 295.31/187.80 tff(30061,plain,
% 295.31/187.80 ((node20(c_e_h_3, c_q, s18) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s19)) | (~node21(c_e_h_3, c_q, s18, s19))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_q, s19)) | node20(c_e_h_3, c_q, s18) | (~node21(c_e_h_3, c_q, s18, s19)))),
% 295.31/187.80 inference(rewrite,[status(thm)],[])).
% 295.31/187.80 tff(30062,plain,
% 295.31/187.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s18) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s19)) | (~node21(c_e_h_3, c_q, s18, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s19)) | node20(c_e_h_3, c_q, s18) | (~node21(c_e_h_3, c_q, s18, s19))))),
% 295.31/187.80 inference(monotonicity,[status(thm)],[30061])).
% 295.31/187.80 tff(30063,plain,
% 295.31/187.80 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s18) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s19)) | (~node21(c_e_h_3, c_q, s18, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s19)) | node20(c_e_h_3, c_q, s18) | (~node21(c_e_h_3, c_q, s18, s19)))),
% 295.31/187.81 inference(transitivity,[status(thm)],[30062, 30060])).
% 295.31/187.81 tff(30064,plain,
% 295.31/187.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s18) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s19)) | (~node21(c_e_h_3, c_q, s18, s19)))),
% 295.31/187.81 inference(quant_inst,[status(thm)],[])).
% 295.31/187.81 tff(30065,plain,
% 295.31/187.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s19)) | node20(c_e_h_3, c_q, s18) | (~node21(c_e_h_3, c_q, s18, s19))),
% 295.31/187.81 inference(modus_ponens,[status(thm)],[30064, 30063])).
% 295.31/187.81 tff(30066,plain,
% 295.31/187.81 ($false),
% 295.31/187.81 inference(unit_resolution,[status(thm)],[30065, 52, 30050, 30059, 30058])).
% 295.31/187.81 tff(30067,plain,((~node21(c_e_h_3, c_q, s18, s19)) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s19)) | node20(c_e_h_3, c_q, s18)), inference(lemma,lemma(discharge,[]))).
% 295.31/187.81 tff(30068,plain,
% 295.31/187.81 (~node21(c_e_h_3, c_q, s18, s19)),
% 295.31/187.81 inference(unit_resolution,[status(thm)],[30067, 30050, 30058])).
% 295.31/187.81 tff(30069,plain,
% 295.31/187.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s18, s19)) | node21(c_e_h_3, c_q, s18, s19) | node22(c_e_h_3, c_q, s18, s19))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s18, s19)) | node21(c_e_h_3, c_q, s18, s19) | node22(c_e_h_3, c_q, s18, s19))),
% 295.31/187.81 inference(rewrite,[status(thm)],[])).
% 295.31/187.81 tff(30070,plain,
% 295.31/187.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s18, s19)) | node21(c_e_h_3, c_q, s18, s19) | node22(c_e_h_3, c_q, s18, s19))),
% 295.31/187.81 inference(quant_inst,[status(thm)],[])).
% 295.31/187.81 tff(30071,plain,
% 295.31/187.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s18, s19)) | node21(c_e_h_3, c_q, s18, s19) | node22(c_e_h_3, c_q, s18, s19)),
% 295.31/187.81 inference(modus_ponens,[status(thm)],[30070, 30069])).
% 295.31/187.81 tff(30072,plain,
% 295.31/187.81 (node21(c_e_h_3, c_q, s18, s19) | node22(c_e_h_3, c_q, s18, s19)),
% 295.31/187.81 inference(unit_resolution,[status(thm)],[30071, 82, 26787])).
% 295.31/187.81 tff(30073,plain,
% 295.31/187.81 ($false),
% 295.31/187.81 inference(unit_resolution,[status(thm)],[30072, 30068, 30057])).
% 295.31/187.81 tff(30074,plain,((~m_and_h_gate_v_out(c_e_h_3, c_q, s19)) | node20(c_e_h_3, c_q, s18) | m_and_h_gate_v_out(c_e_h_3, c_q, s18)), inference(lemma,lemma(discharge,[]))).
% 295.31/187.81 tff(30075,plain,
% 295.31/187.81 (~m_and_h_gate_v_out(c_e_h_3, c_q, s19)),
% 295.31/187.81 inference(unit_resolution,[status(thm)],[30074, 30048, 28829])).
% 295.31/187.81 tff(30076,plain,
% 295.31/187.81 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s19))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s19))),
% 295.31/187.81 inference(rewrite,[status(thm)],[])).
% 295.31/187.81 tff(30077,plain,
% 295.31/187.81 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s19))),
% 295.31/187.81 inference(quant_inst,[status(thm)],[])).
% 295.31/187.81 tff(30078,plain,
% 295.31/187.81 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s19)),
% 295.31/187.81 inference(modus_ponens,[status(thm)],[30077, 30076])).
% 295.31/187.81 tff(30079,plain,
% 295.31/187.81 (node3(c_e_h_3, c_e_h_1, s19)),
% 295.31/187.81 inference(unit_resolution,[status(thm)],[30078, 2922, 1056])).
% 295.31/187.81 tff(30080,plain,
% 295.31/187.81 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s19)) | (~node3(c_e_h_3, c_e_h_1, s19)) | m_and_h_gate_v_out(c_e_h_3, c_q, s19))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s19)) | (~node3(c_e_h_3, c_e_h_1, s19)) | m_and_h_gate_v_out(c_e_h_3, c_q, s19))),
% 295.31/187.81 inference(rewrite,[status(thm)],[])).
% 295.31/187.81 tff(30081,plain,
% 295.31/187.81 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s19)) | (~node3(c_e_h_3, c_e_h_1, s19)) | m_and_h_gate_v_out(c_e_h_3, c_q, s19))),
% 295.31/187.81 inference(quant_inst,[status(thm)],[])).
% 295.31/187.81 tff(30082,plain,
% 295.31/187.81 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s19)) | (~node3(c_e_h_3, c_e_h_1, s19)) | m_and_h_gate_v_out(c_e_h_3, c_q, s19)),
% 295.31/187.81 inference(modus_ponens,[status(thm)],[30081, 30080])).
% 295.31/187.81 tff(30083,plain,
% 295.31/187.81 ((~m_cell_v_ack(c_e_h_1, s19)) | m_and_h_gate_v_out(c_e_h_3, c_q, s19)),
% 295.31/187.81 inference(unit_resolution,[status(thm)],[30082, 1073, 30079])).
% 295.31/187.81 tff(30084,plain,
% 295.31/187.81 (~m_cell_v_ack(c_e_h_1, s19)),
% 295.31/187.81 inference(unit_resolution,[status(thm)],[30083, 30075])).
% 295.31/187.81 tff(30085,plain,
% 295.31/187.81 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s19)) | m_cell_v_ack(c_e_h_1, s19))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s19)) | m_cell_v_ack(c_e_h_1, s19))),
% 295.31/187.81 inference(rewrite,[status(thm)],[])).
% 295.31/187.81 tff(30086,plain,
% 295.31/187.81 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s19)) | m_cell_v_ack(c_e_h_1, s19))),
% 295.31/187.81 inference(quant_inst,[status(thm)],[])).
% 295.31/187.81 tff(30087,plain,
% 295.31/187.81 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s19)) | m_cell_v_ack(c_e_h_1, s19)),
% 295.31/187.81 inference(modus_ponens,[status(thm)],[30086, 30085])).
% 295.31/187.81 tff(30088,plain,
% 295.31/187.81 (~m_or_h_gate_v_in2(c_e_h_1, c_j, s19)),
% 295.31/187.81 inference(unit_resolution,[status(thm)],[30087, 1085, 30084])).
% 295.31/187.81 tff(30089,plain,
% 295.31/187.81 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s16) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s16) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16))),
% 295.31/187.81 inference(rewrite,[status(thm)],[])).
% 295.31/187.81 tff(30090,plain,
% 295.31/187.81 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s16) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16))),
% 295.31/187.81 inference(quant_inst,[status(thm)],[])).
% 295.31/187.81 tff(30091,plain,
% 295.31/187.81 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s16) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)),
% 295.31/187.81 inference(modus_ponens,[status(thm)],[30090, 30089])).
% 295.31/187.81 tff(30092,plain,
% 295.31/187.81 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s16) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)),
% 295.31/187.81 inference(unit_resolution,[status(thm)],[30091, 7868])).
% 295.31/187.81 tff(30093,plain,
% 295.31/187.81 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s16)),
% 295.31/187.81 inference(unit_resolution,[status(thm)],[30092, 29510])).
% 295.31/187.81 tff(30094,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s16)), introduced(assumption)).
% 295.31/187.81 tff(30095,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17)), introduced(assumption)).
% 295.31/187.81 tff(30096,plain,
% 295.31/187.81 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16)),
% 295.31/187.81 inference(unit_resolution,[status(thm)],[29649, 25876, 25770, 25330, 25324, 25772, 26437])).
% 295.31/187.81 tff(30097,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16)), introduced(assumption)).
% 295.31/187.81 tff(30098,assumption,(node11(c_e_h_1, c_n, s16, s17)), introduced(assumption)).
% 295.31/187.81 tff(30099,plain,
% 295.31/187.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16)) | (~node11(c_e_h_1, c_n, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16)) | (~node11(c_e_h_1, c_n, s16, s17)))),
% 295.32/187.81 inference(rewrite,[status(thm)],[])).
% 295.32/187.81 tff(30100,plain,
% 295.32/187.81 ((m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17) | (~node11(c_e_h_1, c_n, s16, s17)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16))) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16)) | (~node11(c_e_h_1, c_n, s16, s17)))),
% 295.32/187.81 inference(rewrite,[status(thm)],[])).
% 295.32/187.81 tff(30101,plain,
% 295.32/187.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17) | (~node11(c_e_h_1, c_n, s16, s17)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16)) | (~node11(c_e_h_1, c_n, s16, s17))))),
% 295.32/187.81 inference(monotonicity,[status(thm)],[30100])).
% 295.32/187.81 tff(30102,plain,
% 295.32/187.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17) | (~node11(c_e_h_1, c_n, s16, s17)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16)) | (~node11(c_e_h_1, c_n, s16, s17)))),
% 295.32/187.81 inference(transitivity,[status(thm)],[30101, 30099])).
% 295.32/187.81 tff(30103,plain,
% 295.32/187.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17) | (~node11(c_e_h_1, c_n, s16, s17)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16)))),
% 295.32/187.81 inference(quant_inst,[status(thm)],[])).
% 295.32/187.81 tff(30104,plain,
% 295.32/187.81 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16)) | (~node11(c_e_h_1, c_n, s16, s17))),
% 295.32/187.81 inference(modus_ponens,[status(thm)],[30103, 30102])).
% 295.32/187.81 tff(30105,plain,
% 295.32/187.81 ($false),
% 295.32/187.81 inference(unit_resolution,[status(thm)],[30104, 5742, 30097, 30095, 30098])).
% 295.32/187.81 tff(30106,plain,((~node11(c_e_h_1, c_n, s16, s17)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17)), inference(lemma,lemma(discharge,[]))).
% 295.32/187.81 tff(30107,plain,
% 295.32/187.81 (~node11(c_e_h_1, c_n, s16, s17)),
% 295.32/187.81 inference(unit_resolution,[status(thm)],[30106, 30095, 30097])).
% 295.32/187.81 tff(30108,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s16)), introduced(assumption)).
% 295.32/187.81 tff(30109,assumption,(node10(c_e_h_1, c_n, s16, s17)), introduced(assumption)).
% 295.32/187.81 tff(30110,plain,
% 295.32/187.81 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s16)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s16)) | (~node10(c_e_h_1, c_n, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s16)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s16)) | (~node10(c_e_h_1, c_n, s16, s17)))),
% 295.32/187.81 inference(rewrite,[status(thm)],[])).
% 295.32/187.82 tff(30111,plain,
% 295.32/187.82 (((~node10(c_e_h_1, c_n, s16, s17)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s16)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s16)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17)) <=> ((~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s16)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s16)) | (~node10(c_e_h_1, c_n, s16, s17)))),
% 295.32/187.82 inference(rewrite,[status(thm)],[])).
% 295.32/187.82 tff(30112,plain,
% 295.32/187.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s16, s17)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s16)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s16)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s16)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s16)) | (~node10(c_e_h_1, c_n, s16, s17))))),
% 295.32/187.82 inference(monotonicity,[status(thm)],[30111])).
% 295.32/187.82 tff(30113,plain,
% 295.32/187.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s16, s17)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s16)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s16)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s16)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s16)) | (~node10(c_e_h_1, c_n, s16, s17)))),
% 295.32/187.82 inference(transitivity,[status(thm)],[30112, 30110])).
% 295.32/187.82 tff(30114,plain,
% 295.32/187.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s16, s17)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s16)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s16)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17))),
% 295.32/187.82 inference(quant_inst,[status(thm)],[])).
% 295.32/187.82 tff(30115,plain,
% 295.32/187.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s16)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s16)) | (~node10(c_e_h_1, c_n, s16, s17))),
% 295.32/187.82 inference(modus_ponens,[status(thm)],[30114, 30113])).
% 295.32/187.82 tff(30116,plain,
% 295.32/187.82 ($false),
% 295.32/187.82 inference(unit_resolution,[status(thm)],[30115, 5718, 30108, 30094, 30095, 30109])).
% 295.32/187.82 tff(30117,plain,((~node10(c_e_h_1, c_n, s16, s17)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s16)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s16)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17)), inference(lemma,lemma(discharge,[]))).
% 295.32/187.82 tff(30118,plain,
% 295.32/187.82 (~node10(c_e_h_1, c_n, s16, s17)),
% 295.32/187.82 inference(unit_resolution,[status(thm)],[30117, 30095, 30094, 30108])).
% 295.32/187.82 tff(30119,plain,
% 295.32/187.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s16, s17)) | node10(c_e_h_1, c_n, s16, s17) | node11(c_e_h_1, c_n, s16, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s16, s17)) | node10(c_e_h_1, c_n, s16, s17) | node11(c_e_h_1, c_n, s16, s17))),
% 295.32/187.82 inference(rewrite,[status(thm)],[])).
% 295.32/187.82 tff(30120,plain,
% 295.32/187.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s16, s17)) | node10(c_e_h_1, c_n, s16, s17) | node11(c_e_h_1, c_n, s16, s17))),
% 295.32/187.82 inference(quant_inst,[status(thm)],[])).
% 295.32/187.82 tff(30121,plain,
% 295.32/187.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s16, s17)) | node10(c_e_h_1, c_n, s16, s17) | node11(c_e_h_1, c_n, s16, s17)),
% 295.32/187.82 inference(modus_ponens,[status(thm)],[30120, 30119])).
% 295.32/187.82 tff(30122,plain,
% 295.32/187.82 (node10(c_e_h_1, c_n, s16, s17) | node11(c_e_h_1, c_n, s16, s17)),
% 295.32/187.82 inference(unit_resolution,[status(thm)],[30121, 5002, 11967])).
% 295.32/187.82 tff(30123,plain,
% 295.32/187.82 ($false),
% 295.32/187.82 inference(unit_resolution,[status(thm)],[30122, 30118, 30107])).
% 295.32/187.82 tff(30124,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s16)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s16)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s16))), inference(lemma,lemma(discharge,[]))).
% 295.32/187.82 tff(30125,plain,
% 295.32/187.82 (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s16)),
% 295.32/187.82 inference(unit_resolution,[status(thm)],[30124, 30096, 30095, 30094])).
% 295.32/187.82 tff(30126,plain,
% 295.32/187.82 (~m_c_h_element_v_out(c_e_h_1, c_e, s15)),
% 295.32/187.82 inference(unit_resolution,[status(thm)],[25927, 25876, 29582])).
% 295.32/187.82 tff(30127,plain,
% 295.32/187.82 (~m_c_h_element_v_out(c_e_h_1, c_e, s16)),
% 295.32/187.82 inference(unit_resolution,[status(thm)],[26002, 30126, 25932])).
% 295.32/187.82 tff(30128,plain,
% 295.32/187.82 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s16) | m_c_h_element_v_out(c_e_h_1, c_e, s16))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s16) | m_c_h_element_v_out(c_e_h_1, c_e, s16))),
% 295.32/187.82 inference(rewrite,[status(thm)],[])).
% 295.32/187.82 tff(30129,plain,
% 295.32/187.82 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s16) | m_c_h_element_v_out(c_e_h_1, c_e, s16))),
% 295.32/187.82 inference(quant_inst,[status(thm)],[])).
% 295.32/187.82 tff(30130,plain,
% 295.32/187.82 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s16) | m_c_h_element_v_out(c_e_h_1, c_e, s16)),
% 295.32/187.82 inference(modus_ponens,[status(thm)],[30129, 30128])).
% 295.32/187.82 tff(30131,plain,
% 295.32/187.82 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s16) | m_c_h_element_v_out(c_e_h_1, c_e, s16)),
% 295.32/187.82 inference(unit_resolution,[status(thm)],[30130, 7856])).
% 295.32/187.82 tff(30132,plain,
% 295.32/187.82 ($false),
% 295.32/187.82 inference(unit_resolution,[status(thm)],[30131, 30127, 30125])).
% 295.32/187.82 tff(30133,plain,(m_c_h_element_v_in2(c_e_h_1, c_e, s14) | m_c_h_element_v_in2(c_e_h_1, c_e, s15) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s16)) | m_c_h_element_v_in2(c_e_h_1, c_e, s13) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s11) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s11)) | m_c_h_element_v_out(c_e_h_1, c_e, s13) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s12))), inference(lemma,lemma(discharge,[]))).
% 295.32/187.82 tff(30134,plain,
% 295.32/187.82 (m_c_h_element_v_in2(c_e_h_1, c_e, s14) | m_c_h_element_v_in2(c_e_h_1, c_e, s15) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s16)) | m_c_h_element_v_in2(c_e_h_1, c_e, s13) | m_c_h_element_v_out(c_e_h_1, c_e, s13)),
% 295.32/187.82 inference(unit_resolution,[status(thm)],[30133, 23367, 26431, 26436])).
% 295.32/187.82 tff(30135,plain,
% 295.32/187.82 (m_c_h_element_v_in2(c_e_h_1, c_e, s15) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17)),
% 295.32/187.82 inference(unit_resolution,[status(thm)],[30134, 25762, 25769, 30093, 25863])).
% 295.32/187.82 tff(30136,plain,
% 295.32/187.82 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17)),
% 295.32/187.82 inference(unit_resolution,[status(thm)],[30135, 25580])).
% 295.32/187.82 tff(30137,plain,
% 295.32/187.82 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s17)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s17)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17)))),
% 295.32/187.82 inference(rewrite,[status(thm)],[])).
% 295.32/187.82 tff(30138,plain,
% 295.32/187.82 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s17)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17)))),
% 295.32/187.82 inference(quant_inst,[status(thm)],[])).
% 295.32/187.82 tff(30139,plain,
% 295.32/187.82 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s17)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17))),
% 295.32/187.82 inference(modus_ponens,[status(thm)],[30138, 30137])).
% 295.32/187.82 tff(30140,plain,
% 295.32/187.82 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s17)),
% 295.32/187.82 inference(unit_resolution,[status(thm)],[30139, 4958, 30136])).
% 295.32/187.82 tff(30141,plain,
% 295.32/187.82 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s17)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s17))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s17)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s17))),
% 295.32/187.82 inference(rewrite,[status(thm)],[])).
% 295.32/187.82 tff(30142,plain,
% 295.32/187.82 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s17)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s17))),
% 295.32/187.82 inference(quant_inst,[status(thm)],[])).
% 295.32/187.82 tff(30143,plain,
% 295.32/187.82 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s17)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s17)),
% 295.32/187.82 inference(modus_ponens,[status(thm)],[30142, 30141])).
% 295.32/187.82 tff(30144,plain,
% 295.32/187.82 (~node9(c_e_h_1, c_m, s17)),
% 295.32/187.82 inference(unit_resolution,[status(thm)],[30143, 4972, 30140])).
% 295.32/187.82 tff(30145,assumption,(~node9(c_e_h_1, c_m, s17)), introduced(assumption)).
% 295.32/187.82 tff(30146,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18)), introduced(assumption)).
% 295.32/187.82 tff(30147,assumption,(node10(c_e_h_1, c_m, s17, s18)), introduced(assumption)).
% 295.32/187.82 tff(30148,plain,
% 295.32/187.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18)) | node9(c_e_h_1, c_m, s17) | (~node10(c_e_h_1, c_m, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18)) | node9(c_e_h_1, c_m, s17) | (~node10(c_e_h_1, c_m, s17, s18)))),
% 295.32/187.82 inference(rewrite,[status(thm)],[])).
% 295.32/187.82 tff(30149,plain,
% 295.32/187.82 ((node9(c_e_h_1, c_m, s17) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18)) | (~node10(c_e_h_1, c_m, s17, s18))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18)) | node9(c_e_h_1, c_m, s17) | (~node10(c_e_h_1, c_m, s17, s18)))),
% 295.32/187.82 inference(rewrite,[status(thm)],[])).
% 295.32/187.82 tff(30150,plain,
% 295.32/187.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s17) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18)) | (~node10(c_e_h_1, c_m, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18)) | node9(c_e_h_1, c_m, s17) | (~node10(c_e_h_1, c_m, s17, s18))))),
% 295.32/187.82 inference(monotonicity,[status(thm)],[30149])).
% 295.32/187.82 tff(30151,plain,
% 295.32/187.82 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s17) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18)) | (~node10(c_e_h_1, c_m, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18)) | node9(c_e_h_1, c_m, s17) | (~node10(c_e_h_1, c_m, s17, s18)))),
% 295.32/187.82 inference(transitivity,[status(thm)],[30150, 30148])).
% 295.32/187.82 tff(30152,plain,
% 295.32/187.82 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s17) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18)) | (~node10(c_e_h_1, c_m, s17, s18)))),
% 295.32/187.83 inference(quant_inst,[status(thm)],[])).
% 295.32/187.83 tff(30153,plain,
% 295.32/187.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18)) | node9(c_e_h_1, c_m, s17) | (~node10(c_e_h_1, c_m, s17, s18))),
% 295.32/187.83 inference(modus_ponens,[status(thm)],[30152, 30151])).
% 295.32/187.83 tff(30154,plain,
% 295.32/187.83 ($false),
% 295.32/187.83 inference(unit_resolution,[status(thm)],[30153, 4986, 30146, 30147, 30145])).
% 295.32/187.83 tff(30155,plain,((~node10(c_e_h_1, c_m, s17, s18)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18)) | node9(c_e_h_1, c_m, s17)), inference(lemma,lemma(discharge,[]))).
% 295.32/187.83 tff(30156,plain,
% 295.32/187.83 (~node10(c_e_h_1, c_m, s17, s18)),
% 295.32/187.83 inference(unit_resolution,[status(thm)],[30155, 30146, 30145])).
% 295.32/187.83 tff(30157,plain,
% 295.32/187.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s17, s18)) | node10(c_e_h_1, c_m, s17, s18) | node11(c_e_h_1, c_m, s17, s18))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s17, s18)) | node10(c_e_h_1, c_m, s17, s18) | node11(c_e_h_1, c_m, s17, s18))),
% 295.32/187.83 inference(rewrite,[status(thm)],[])).
% 295.32/187.83 tff(30158,plain,
% 295.32/187.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s17, s18)) | node10(c_e_h_1, c_m, s17, s18) | node11(c_e_h_1, c_m, s17, s18))),
% 295.32/187.83 inference(quant_inst,[status(thm)],[])).
% 295.32/187.83 tff(30159,plain,
% 295.32/187.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s17, s18)) | node10(c_e_h_1, c_m, s17, s18) | node11(c_e_h_1, c_m, s17, s18)),
% 295.32/187.83 inference(modus_ponens,[status(thm)],[30158, 30157])).
% 295.32/187.83 tff(30160,plain,
% 295.32/187.83 (node10(c_e_h_1, c_m, s17, s18) | node11(c_e_h_1, c_m, s17, s18)),
% 295.32/187.83 inference(unit_resolution,[status(thm)],[30159, 5002, 26135])).
% 295.32/187.83 tff(30161,plain,
% 295.32/187.83 (node11(c_e_h_1, c_m, s17, s18)),
% 295.32/187.83 inference(unit_resolution,[status(thm)],[30160, 30156])).
% 295.32/187.83 tff(30162,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17)), introduced(assumption)).
% 295.32/187.83 tff(30163,plain,
% 295.32/187.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18)) | (~node11(c_e_h_1, c_m, s17, s18)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18)) | (~node11(c_e_h_1, c_m, s17, s18)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17))),
% 295.32/187.83 inference(rewrite,[status(thm)],[])).
% 295.32/187.83 tff(30164,plain,
% 295.32/187.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18)) | (~node11(c_e_h_1, c_m, s17, s18)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17))),
% 295.32/187.83 inference(quant_inst,[status(thm)],[])).
% 295.32/187.83 tff(30165,plain,
% 295.32/187.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18)) | (~node11(c_e_h_1, c_m, s17, s18)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17)),
% 295.32/187.83 inference(modus_ponens,[status(thm)],[30164, 30163])).
% 295.32/187.83 tff(30166,plain,
% 295.32/187.83 ($false),
% 295.32/187.83 inference(unit_resolution,[status(thm)],[30165, 5017, 30162, 30146, 30161])).
% 295.32/187.83 tff(30167,plain,((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17) | node9(c_e_h_1, c_m, s17)), inference(lemma,lemma(discharge,[]))).
% 295.32/187.83 tff(30168,plain,
% 295.32/187.83 ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18)) | node9(c_e_h_1, c_m, s17)),
% 295.32/187.83 inference(unit_resolution,[status(thm)],[30167, 29683])).
% 295.32/187.83 tff(30169,plain,
% 295.32/187.83 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18)),
% 295.32/187.83 inference(unit_resolution,[status(thm)],[30168, 30144])).
% 295.32/187.83 tff(30170,plain,
% 295.32/187.83 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s18)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s18)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18))),
% 295.32/187.83 inference(rewrite,[status(thm)],[])).
% 295.32/187.83 tff(30171,plain,
% 295.32/187.83 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s18)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18))),
% 295.32/187.83 inference(quant_inst,[status(thm)],[])).
% 295.32/187.83 tff(30172,plain,
% 295.32/187.83 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s18)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18)),
% 295.32/187.83 inference(modus_ponens,[status(thm)],[30171, 30170])).
% 295.32/187.83 tff(30173,plain,
% 295.32/187.83 (~m_and_h_gate_v_in2(c_e_h_1, c_l, s18)),
% 295.32/187.83 inference(unit_resolution,[status(thm)],[30172, 4549, 30169])).
% 295.32/187.83 tff(30174,plain,
% 295.32/187.83 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s18)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s18))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s18)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s18))),
% 295.32/187.83 inference(rewrite,[status(thm)],[])).
% 295.32/187.83 tff(30175,plain,
% 295.32/187.83 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s18)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s18))),
% 295.32/187.83 inference(quant_inst,[status(thm)],[])).
% 295.32/187.83 tff(30176,plain,
% 295.32/187.83 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s18)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s18)),
% 295.32/187.83 inference(modus_ponens,[status(thm)],[30175, 30174])).
% 295.32/187.83 tff(30177,plain,
% 295.32/187.83 (~node20(c_e_h_1, c_l, s18)),
% 295.32/187.83 inference(unit_resolution,[status(thm)],[30176, 4563, 30173])).
% 295.32/187.83 tff(30178,assumption,(m_or_h_gate_v_out(c_e_h_1, c_j, s20)), introduced(assumption)).
% 295.32/187.83 tff(30179,assumption,(~m_or_h_gate_v_in2(c_e_h_1, c_j, s19)), introduced(assumption)).
% 295.32/187.83 tff(30180,plain,
% 295.32/187.83 (~m_or_h_gate_v_in1(c_e_h_1, c_j, s17)),
% 295.32/187.83 inference(unit_resolution,[status(thm)],[29545, 29540])).
% 295.32/187.83 tff(30181,plain,
% 295.32/187.83 (~m_or_h_gate_v_out(c_e_h_1, c_j, s18)),
% 295.32/187.83 inference(unit_resolution,[status(thm)],[29579, 30180, 29560, 29547])).
% 295.32/187.83 tff(30182,plain,
% 295.32/187.83 (~m_and_h_gate_v_out(c_e_h_1, c_l, s18)),
% 295.32/187.83 inference(unit_resolution,[status(thm)],[29710, 29540, 29693])).
% 295.32/187.83 tff(30183,plain,
% 295.32/187.83 (~m_or_h_gate_v_in1(c_e_h_1, c_j, s18)),
% 295.32/187.83 inference(unit_resolution,[status(thm)],[29718, 30182])).
% 295.32/187.83 tff(30184,plain,
% 295.32/187.83 (~m_or_h_gate_v_out(c_e_h_1, c_j, s19)),
% 295.32/187.83 inference(unit_resolution,[status(thm)],[29749, 30183, 30181, 29720])).
% 295.32/187.83 tff(30185,assumption,(~node20(c_e_h_1, c_l, s18)), introduced(assumption)).
% 295.32/187.83 tff(30186,assumption,(m_and_h_gate_v_out(c_e_h_1, c_l, s19)), introduced(assumption)).
% 295.32/187.83 tff(30187,assumption,(node21(c_e_h_1, c_l, s18, s19)), introduced(assumption)).
% 295.32/187.83 tff(30188,plain,
% 295.32/187.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s18) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s19)) | (~node21(c_e_h_1, c_l, s18, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s18) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s19)) | (~node21(c_e_h_1, c_l, s18, s19)))),
% 295.32/187.83 inference(rewrite,[status(thm)],[])).
% 295.32/187.83 tff(30189,plain,
% 295.32/187.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s18) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s19)) | (~node21(c_e_h_1, c_l, s18, s19)))),
% 295.32/187.83 inference(quant_inst,[status(thm)],[])).
% 295.32/187.83 tff(30190,plain,
% 295.32/187.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s18) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s19)) | (~node21(c_e_h_1, c_l, s18, s19))),
% 295.32/187.83 inference(modus_ponens,[status(thm)],[30189, 30188])).
% 295.32/187.83 tff(30191,plain,
% 295.32/187.83 ($false),
% 295.32/187.83 inference(unit_resolution,[status(thm)],[30190, 52, 30187, 30185, 30186])).
% 295.32/187.83 tff(30192,plain,((~node21(c_e_h_1, c_l, s18, s19)) | node20(c_e_h_1, c_l, s18) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s19))), inference(lemma,lemma(discharge,[]))).
% 295.32/187.83 tff(30193,plain,
% 295.32/187.83 (~node21(c_e_h_1, c_l, s18, s19)),
% 295.32/187.83 inference(unit_resolution,[status(thm)],[30192, 30186, 30185])).
% 295.32/187.83 tff(30194,plain,
% 295.32/187.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s18, s19)) | node21(c_e_h_1, c_l, s18, s19) | node22(c_e_h_1, c_l, s18, s19))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s18, s19)) | node21(c_e_h_1, c_l, s18, s19) | node22(c_e_h_1, c_l, s18, s19))),
% 295.32/187.83 inference(rewrite,[status(thm)],[])).
% 295.32/187.83 tff(30195,plain,
% 295.32/187.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s18, s19)) | node21(c_e_h_1, c_l, s18, s19) | node22(c_e_h_1, c_l, s18, s19))),
% 295.32/187.83 inference(quant_inst,[status(thm)],[])).
% 295.32/187.83 tff(30196,plain,
% 295.32/187.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s18, s19)) | node21(c_e_h_1, c_l, s18, s19) | node22(c_e_h_1, c_l, s18, s19)),
% 295.32/187.83 inference(modus_ponens,[status(thm)],[30195, 30194])).
% 295.32/187.83 tff(30197,plain,
% 295.32/187.83 (node21(c_e_h_1, c_l, s18, s19) | node22(c_e_h_1, c_l, s18, s19)),
% 295.32/187.83 inference(unit_resolution,[status(thm)],[30196, 82, 26787])).
% 295.32/187.83 tff(30198,plain,
% 295.32/187.83 (node22(c_e_h_1, c_l, s18, s19)),
% 295.32/187.83 inference(unit_resolution,[status(thm)],[30197, 30193])).
% 295.32/187.83 tff(30199,plain,
% 295.32/187.83 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s19)) | (~node22(c_e_h_1, c_l, s18, s19)) | m_and_h_gate_v_out(c_e_h_1, c_l, s18))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s19)) | (~node22(c_e_h_1, c_l, s18, s19)) | m_and_h_gate_v_out(c_e_h_1, c_l, s18))),
% 295.32/187.83 inference(rewrite,[status(thm)],[])).
% 295.32/187.83 tff(30200,plain,
% 295.32/187.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s19)) | (~node22(c_e_h_1, c_l, s18, s19)) | m_and_h_gate_v_out(c_e_h_1, c_l, s18))),
% 295.32/187.83 inference(quant_inst,[status(thm)],[])).
% 295.32/187.83 tff(30201,plain,
% 295.32/187.83 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s19)) | (~node22(c_e_h_1, c_l, s18, s19)) | m_and_h_gate_v_out(c_e_h_1, c_l, s18)),
% 295.32/187.83 inference(modus_ponens,[status(thm)],[30200, 30199])).
% 295.32/187.83 tff(30202,plain,
% 295.32/187.83 ($false),
% 295.32/187.83 inference(unit_resolution,[status(thm)],[30201, 108, 30198, 30186, 29713])).
% 295.32/187.83 tff(30203,plain,((~m_and_h_gate_v_out(c_e_h_1, c_l, s19)) | m_and_h_gate_v_out(c_e_h_1, c_l, s18) | node20(c_e_h_1, c_l, s18)), inference(lemma,lemma(discharge,[]))).
% 295.32/187.83 tff(30204,plain,
% 295.32/187.83 (~m_and_h_gate_v_out(c_e_h_1, c_l, s19)),
% 295.32/187.83 inference(unit_resolution,[status(thm)],[30203, 30182, 30185])).
% 295.32/187.83 tff(30205,assumption,(m_or_h_gate_v_in1(c_e_h_1, c_j, s19)), introduced(assumption)).
% 295.32/187.83 tff(30206,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_l, s19)), introduced(assumption)).
% 295.32/187.83 tff(30207,plain,
% 295.32/187.83 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s19)) | m_and_h_gate_v_out(c_e_h_1, c_l, s19))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s19)) | m_and_h_gate_v_out(c_e_h_1, c_l, s19))),
% 295.32/187.84 inference(rewrite,[status(thm)],[])).
% 295.32/187.84 tff(30208,plain,
% 295.32/187.84 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s19)) | m_and_h_gate_v_out(c_e_h_1, c_l, s19))),
% 295.32/187.84 inference(quant_inst,[status(thm)],[])).
% 295.32/187.84 tff(30209,plain,
% 295.32/187.84 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s19)) | m_and_h_gate_v_out(c_e_h_1, c_l, s19)),
% 295.32/187.84 inference(modus_ponens,[status(thm)],[30208, 30207])).
% 295.32/187.84 tff(30210,plain,
% 295.32/187.84 ($false),
% 295.32/187.84 inference(unit_resolution,[status(thm)],[30209, 1100, 30206, 30205])).
% 295.32/187.84 tff(30211,plain,((~m_or_h_gate_v_in1(c_e_h_1, c_j, s19)) | m_and_h_gate_v_out(c_e_h_1, c_l, s19)), inference(lemma,lemma(discharge,[]))).
% 295.32/187.84 tff(30212,plain,
% 295.32/187.84 (~m_or_h_gate_v_in1(c_e_h_1, c_j, s19)),
% 295.32/187.84 inference(unit_resolution,[status(thm)],[30211, 30204])).
% 295.32/187.84 tff(30213,assumption,(~m_or_h_gate_v_out(c_e_h_1, c_j, s19)), introduced(assumption)).
% 295.32/187.84 tff(30214,assumption,(node6(c_e_h_1, c_j, s19, s20)), introduced(assumption)).
% 295.32/187.84 tff(30215,plain,
% 295.32/187.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s19) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s20)) | (~node6(c_e_h_1, c_j, s19, s20)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s19) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s20)) | (~node6(c_e_h_1, c_j, s19, s20)))),
% 295.32/187.84 inference(rewrite,[status(thm)],[])).
% 295.32/187.84 tff(30216,plain,
% 295.32/187.84 (((~node6(c_e_h_1, c_j, s19, s20)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s20)) | m_or_h_gate_v_out(c_e_h_1, c_j, s19)) <=> (m_or_h_gate_v_out(c_e_h_1, c_j, s19) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s20)) | (~node6(c_e_h_1, c_j, s19, s20)))),
% 295.32/187.84 inference(rewrite,[status(thm)],[])).
% 295.32/187.84 tff(30217,plain,
% 295.32/187.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s19, s20)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s20)) | m_or_h_gate_v_out(c_e_h_1, c_j, s19))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s19) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s20)) | (~node6(c_e_h_1, c_j, s19, s20))))),
% 295.32/187.84 inference(monotonicity,[status(thm)],[30216])).
% 295.32/187.84 tff(30218,plain,
% 295.32/187.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s19, s20)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s20)) | m_or_h_gate_v_out(c_e_h_1, c_j, s19))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s19) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s20)) | (~node6(c_e_h_1, c_j, s19, s20)))),
% 295.32/187.84 inference(transitivity,[status(thm)],[30217, 30215])).
% 295.32/187.84 tff(30219,plain,
% 295.32/187.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s19, s20)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s20)) | m_or_h_gate_v_out(c_e_h_1, c_j, s19))),
% 295.32/187.84 inference(quant_inst,[status(thm)],[])).
% 295.32/187.84 tff(30220,plain,
% 295.32/187.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s19) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s20)) | (~node6(c_e_h_1, c_j, s19, s20))),
% 295.32/187.84 inference(modus_ponens,[status(thm)],[30219, 30218])).
% 295.32/187.84 tff(30221,plain,
% 295.32/187.84 ($false),
% 295.32/187.84 inference(unit_resolution,[status(thm)],[30220, 1121, 30213, 30178, 30214])).
% 295.32/187.84 tff(30222,plain,((~node6(c_e_h_1, c_j, s19, s20)) | m_or_h_gate_v_out(c_e_h_1, c_j, s19) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s20))), inference(lemma,lemma(discharge,[]))).
% 295.32/187.84 tff(30223,plain,
% 295.32/187.84 (~node6(c_e_h_1, c_j, s19, s20)),
% 295.32/187.84 inference(unit_resolution,[status(thm)],[30222, 30178, 30213])).
% 295.32/187.84 tff(30224,assumption,(~m_or_h_gate_v_in1(c_e_h_1, c_j, s19)), introduced(assumption)).
% 295.32/187.84 tff(30225,assumption,(node5(c_e_h_1, c_j, s19, s20)), introduced(assumption)).
% 295.32/187.84 tff(30226,plain,
% 295.32/187.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_1, c_j, s20)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s19) | m_or_h_gate_v_in1(c_e_h_1, c_j, s19) | (~node5(c_e_h_1, c_j, s19, s20)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s20)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s19) | m_or_h_gate_v_in1(c_e_h_1, c_j, s19) | (~node5(c_e_h_1, c_j, s19, s20)))),
% 295.32/187.84 inference(rewrite,[status(thm)],[])).
% 295.32/187.84 tff(30227,plain,
% 295.32/187.84 ((m_or_h_gate_v_in1(c_e_h_1, c_j, s19) | m_or_h_gate_v_in2(c_e_h_1, c_j, s19) | (~node5(c_e_h_1, c_j, s19, s20)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s20))) <=> ((~m_or_h_gate_v_out(c_e_h_1, c_j, s20)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s19) | m_or_h_gate_v_in1(c_e_h_1, c_j, s19) | (~node5(c_e_h_1, c_j, s19, s20)))),
% 295.32/187.84 inference(rewrite,[status(thm)],[])).
% 295.32/187.84 tff(30228,plain,
% 295.32/187.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s19) | m_or_h_gate_v_in2(c_e_h_1, c_j, s19) | (~node5(c_e_h_1, c_j, s19, s20)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s20)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | ((~m_or_h_gate_v_out(c_e_h_1, c_j, s20)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s19) | m_or_h_gate_v_in1(c_e_h_1, c_j, s19) | (~node5(c_e_h_1, c_j, s19, s20))))),
% 295.32/187.84 inference(monotonicity,[status(thm)],[30227])).
% 295.32/187.84 tff(30229,plain,
% 295.32/187.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s19) | m_or_h_gate_v_in2(c_e_h_1, c_j, s19) | (~node5(c_e_h_1, c_j, s19, s20)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s20)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s20)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s19) | m_or_h_gate_v_in1(c_e_h_1, c_j, s19) | (~node5(c_e_h_1, c_j, s19, s20)))),
% 295.32/187.84 inference(transitivity,[status(thm)],[30228, 30226])).
% 295.32/187.84 tff(30230,plain,
% 295.32/187.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s19) | m_or_h_gate_v_in2(c_e_h_1, c_j, s19) | (~node5(c_e_h_1, c_j, s19, s20)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s20)))),
% 295.32/187.84 inference(quant_inst,[status(thm)],[])).
% 295.32/187.84 tff(30231,plain,
% 295.32/187.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s20)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s19) | m_or_h_gate_v_in1(c_e_h_1, c_j, s19) | (~node5(c_e_h_1, c_j, s19, s20))),
% 295.32/187.84 inference(modus_ponens,[status(thm)],[30230, 30229])).
% 295.32/187.84 tff(30232,plain,
% 295.32/187.84 ($false),
% 295.32/187.84 inference(unit_resolution,[status(thm)],[30231, 1159, 30178, 30225, 30224, 30179])).
% 295.32/187.84 tff(30233,plain,((~node5(c_e_h_1, c_j, s19, s20)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s20)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s19) | m_or_h_gate_v_in2(c_e_h_1, c_j, s19)), inference(lemma,lemma(discharge,[]))).
% 295.32/187.84 tff(30234,plain,
% 295.32/187.84 (~node5(c_e_h_1, c_j, s19, s20)),
% 295.32/187.84 inference(unit_resolution,[status(thm)],[30233, 30178, 30224, 30179])).
% 295.32/187.84 tff(30235,plain,
% 295.32/187.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s19, s20)) | node5(c_e_h_1, c_j, s19, s20) | node6(c_e_h_1, c_j, s19, s20))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s19, s20)) | node5(c_e_h_1, c_j, s19, s20) | node6(c_e_h_1, c_j, s19, s20))),
% 295.32/187.84 inference(rewrite,[status(thm)],[])).
% 295.32/187.84 tff(30236,plain,
% 295.32/187.84 ((node6(c_e_h_1, c_j, s19, s20) | node5(c_e_h_1, c_j, s19, s20) | (~trans(s19, s20))) <=> ((~trans(s19, s20)) | node5(c_e_h_1, c_j, s19, s20) | node6(c_e_h_1, c_j, s19, s20))),
% 295.32/187.84 inference(rewrite,[status(thm)],[])).
% 295.32/187.84 tff(30237,plain,
% 295.32/187.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s19, s20) | node5(c_e_h_1, c_j, s19, s20) | (~trans(s19, s20)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s19, s20)) | node5(c_e_h_1, c_j, s19, s20) | node6(c_e_h_1, c_j, s19, s20)))),
% 295.32/187.84 inference(monotonicity,[status(thm)],[30236])).
% 295.32/187.84 tff(30238,plain,
% 295.32/187.84 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s19, s20) | node5(c_e_h_1, c_j, s19, s20) | (~trans(s19, s20)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s19, s20)) | node5(c_e_h_1, c_j, s19, s20) | node6(c_e_h_1, c_j, s19, s20))),
% 295.32/187.84 inference(transitivity,[status(thm)],[30237, 30235])).
% 295.32/187.84 tff(30239,plain,
% 295.32/187.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s19, s20) | node5(c_e_h_1, c_j, s19, s20) | (~trans(s19, s20)))),
% 295.32/187.84 inference(quant_inst,[status(thm)],[])).
% 295.32/187.84 tff(30240,plain,
% 295.32/187.84 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s19, s20)) | node5(c_e_h_1, c_j, s19, s20) | node6(c_e_h_1, c_j, s19, s20)),
% 295.32/187.84 inference(modus_ponens,[status(thm)],[30239, 30238])).
% 295.32/187.85 tff(30241,plain,
% 295.32/187.85 (node5(c_e_h_1, c_j, s19, s20) | node6(c_e_h_1, c_j, s19, s20)),
% 295.32/187.85 inference(unit_resolution,[status(thm)],[30240, 1141, 29925])).
% 295.32/187.85 tff(30242,plain,
% 295.32/187.85 ($false),
% 295.32/187.85 inference(unit_resolution,[status(thm)],[30241, 30234, 30223])).
% 295.32/187.85 tff(30243,plain,((~m_or_h_gate_v_out(c_e_h_1, c_j, s20)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s19) | m_or_h_gate_v_in2(c_e_h_1, c_j, s19) | m_or_h_gate_v_out(c_e_h_1, c_j, s19)), inference(lemma,lemma(discharge,[]))).
% 295.32/187.85 tff(30244,plain,
% 295.32/187.85 ($false),
% 295.32/187.85 inference(unit_resolution,[status(thm)],[30243, 30212, 30184, 30179, 30178])).
% 295.32/187.85 tff(30245,plain,(m_and_h_gate_v_out(c_e_h_1, c_l, s17) | m_or_h_gate_v_in2(c_e_h_1, c_j, s19) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s20)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s18) | node20(c_e_h_1, c_l, s18) | m_or_h_gate_v_out(c_e_h_1, c_j, s17) | m_or_h_gate_v_in2(c_e_h_1, c_j, s17) | node20(c_e_h_1, c_l, s17)), inference(lemma,lemma(discharge,[]))).
% 295.32/187.85 tff(30246,plain,
% 295.32/187.85 (m_or_h_gate_v_in2(c_e_h_1, c_j, s19) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s20)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s18) | node20(c_e_h_1, c_l, s18) | m_or_h_gate_v_out(c_e_h_1, c_j, s17) | m_or_h_gate_v_in2(c_e_h_1, c_j, s17)),
% 295.32/187.85 inference(unit_resolution,[status(thm)],[30245, 29691, 29538])).
% 295.32/187.85 tff(30247,plain,
% 295.32/187.85 (m_or_h_gate_v_in2(c_e_h_1, c_j, s19) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s20)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s18) | m_or_h_gate_v_out(c_e_h_1, c_j, s17) | m_or_h_gate_v_in2(c_e_h_1, c_j, s17)),
% 295.32/187.85 inference(unit_resolution,[status(thm)],[30246, 30177])).
% 295.32/187.85 tff(30248,plain,
% 295.32/187.85 (~m_or_h_gate_v_out(c_e_h_1, c_j, s20)),
% 295.32/187.85 inference(unit_resolution,[status(thm)],[30247, 30088, 29008, 28842, 29021])).
% 295.32/187.85 tff(30249,plain,
% 295.32/187.85 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s20)) | m_or_h_gate_v_out(c_e_h_1, c_j, s20))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s20)) | m_or_h_gate_v_out(c_e_h_1, c_j, s20))),
% 295.32/187.85 inference(rewrite,[status(thm)],[])).
% 295.32/187.85 tff(30250,plain,
% 295.32/187.85 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s20)) | m_or_h_gate_v_out(c_e_h_1, c_j, s20))),
% 295.32/187.85 inference(quant_inst,[status(thm)],[])).
% 295.32/187.85 tff(30251,plain,
% 295.32/187.85 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s20)) | m_or_h_gate_v_out(c_e_h_1, c_j, s20)),
% 295.32/187.85 inference(modus_ponens,[status(thm)],[30250, 30249])).
% 295.32/187.85 tff(30252,plain,
% 295.32/187.85 (~m_c_h_element_v_in2(c_e_h_1, c_h, s20)),
% 295.32/187.85 inference(unit_resolution,[status(thm)],[30251, 1174, 30248])).
% 295.32/187.85 tff(30253,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s22)), introduced(assumption)).
% 295.32/187.85 tff(30254,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_h, s20)), introduced(assumption)).
% 295.32/187.85 tff(30255,assumption,(~m_c_h_element_v_out(c_e_h_1, c_h, s20)), introduced(assumption)).
% 295.32/187.85 tff(30256,assumption,(m_c_h_element_v_out(c_e_h_1, c_h, s21)), introduced(assumption)).
% 295.32/187.85 tff(30257,assumption,(node18(c_e_h_1, c_h, s20, s21)), introduced(assumption)).
% 295.32/187.85 tff(30258,plain,
% 295.32/187.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_h, s20) | (~m_c_h_element_v_out(c_e_h_1, c_h, s21)) | (~node18(c_e_h_1, c_h, s20, s21)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s20) | (~m_c_h_element_v_out(c_e_h_1, c_h, s21)) | (~node18(c_e_h_1, c_h, s20, s21)))),
% 295.32/187.85 inference(rewrite,[status(thm)],[])).
% 295.32/187.85 tff(30259,plain,
% 295.32/187.85 (((~m_c_h_element_v_out(c_e_h_1, c_h, s21)) | m_c_h_element_v_out(c_e_h_1, c_h, s20) | (~node18(c_e_h_1, c_h, s20, s21))) <=> (m_c_h_element_v_out(c_e_h_1, c_h, s20) | (~m_c_h_element_v_out(c_e_h_1, c_h, s21)) | (~node18(c_e_h_1, c_h, s20, s21)))),
% 295.32/187.85 inference(rewrite,[status(thm)],[])).
% 295.32/187.85 tff(30260,plain,
% 295.32/187.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s21)) | m_c_h_element_v_out(c_e_h_1, c_h, s20) | (~node18(c_e_h_1, c_h, s20, s21)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_h, s20) | (~m_c_h_element_v_out(c_e_h_1, c_h, s21)) | (~node18(c_e_h_1, c_h, s20, s21))))),
% 295.32/187.85 inference(monotonicity,[status(thm)],[30259])).
% 295.32/187.85 tff(30261,plain,
% 295.32/187.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s21)) | m_c_h_element_v_out(c_e_h_1, c_h, s20) | (~node18(c_e_h_1, c_h, s20, s21)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s20) | (~m_c_h_element_v_out(c_e_h_1, c_h, s21)) | (~node18(c_e_h_1, c_h, s20, s21)))),
% 295.32/187.85 inference(transitivity,[status(thm)],[30260, 30258])).
% 295.32/187.85 tff(30262,plain,
% 295.32/187.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s21)) | m_c_h_element_v_out(c_e_h_1, c_h, s20) | (~node18(c_e_h_1, c_h, s20, s21)))),
% 295.32/187.85 inference(quant_inst,[status(thm)],[])).
% 295.32/187.85 tff(30263,plain,
% 295.32/187.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_h, s20) | (~m_c_h_element_v_out(c_e_h_1, c_h, s21)) | (~node18(c_e_h_1, c_h, s20, s21))),
% 295.32/187.85 inference(modus_ponens,[status(thm)],[30262, 30261])).
% 295.32/187.85 tff(30264,plain,
% 295.32/187.85 ($false),
% 295.32/187.85 inference(unit_resolution,[status(thm)],[30263, 753, 30256, 30255, 30257])).
% 295.32/187.85 tff(30265,plain,((~node18(c_e_h_1, c_h, s20, s21)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s21)) | m_c_h_element_v_out(c_e_h_1, c_h, s20)), inference(lemma,lemma(discharge,[]))).
% 295.32/187.85 tff(30266,plain,
% 295.32/187.85 (~node18(c_e_h_1, c_h, s20, s21)),
% 295.32/187.85 inference(unit_resolution,[status(thm)],[30265, 30256, 30255])).
% 295.32/187.85 tff(30267,plain,
% 295.32/187.85 (succ(s20, s21) <=> succ(s20, s21)),
% 295.32/187.85 inference(rewrite,[status(thm)],[])).
% 295.32/187.85 tff(30268,axiom,(succ(s20, s21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound21')).
% 295.32/187.85 tff(30269,plain,
% 295.32/187.85 (succ(s20, s21)),
% 295.32/187.85 inference(modus_ponens,[status(thm)],[30268, 30267])).
% 295.32/187.85 tff(30270,plain,
% 295.32/187.85 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s20, s21)) | trans(s20, s21))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s20, s21)) | trans(s20, s21))),
% 295.32/187.85 inference(rewrite,[status(thm)],[])).
% 295.32/187.85 tff(30271,plain,
% 295.32/187.85 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s20, s21)) | trans(s20, s21))),
% 295.32/187.85 inference(quant_inst,[status(thm)],[])).
% 295.32/187.85 tff(30272,plain,
% 295.32/187.85 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s20, s21)) | trans(s20, s21)),
% 295.32/187.85 inference(modus_ponens,[status(thm)],[30271, 30270])).
% 295.32/187.85 tff(30273,plain,
% 295.32/187.85 (trans(s20, s21)),
% 295.32/187.85 inference(unit_resolution,[status(thm)],[30272, 30269, 65])).
% 295.32/187.85 tff(30274,plain,
% 295.32/187.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s20, s21)) | node19(c_e_h_1, c_h, s20, s21))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s20, s21)) | node19(c_e_h_1, c_h, s20, s21))),
% 295.32/187.85 inference(rewrite,[status(thm)],[])).
% 295.32/187.85 tff(30275,plain,
% 295.32/187.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s20, s21)) | node19(c_e_h_1, c_h, s20, s21))),
% 295.32/187.85 inference(quant_inst,[status(thm)],[])).
% 295.32/187.85 tff(30276,plain,
% 295.32/187.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s20, s21)) | node19(c_e_h_1, c_h, s20, s21)),
% 295.32/187.85 inference(modus_ponens,[status(thm)],[30275, 30274])).
% 295.32/187.85 tff(30277,plain,
% 295.32/187.85 (node19(c_e_h_1, c_h, s20, s21)),
% 295.32/187.85 inference(unit_resolution,[status(thm)],[30276, 190, 30273])).
% 295.32/187.85 tff(30278,plain,
% 295.32/187.85 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s20) | node18(c_e_h_1, c_h, s20, s21) | (~node19(c_e_h_1, c_h, s20, s21)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s20) | node18(c_e_h_1, c_h, s20, s21) | (~node19(c_e_h_1, c_h, s20, s21)))),
% 295.32/187.85 inference(rewrite,[status(thm)],[])).
% 295.32/187.85 tff(30279,plain,
% 295.32/187.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s20) | node18(c_e_h_1, c_h, s20, s21) | (~node19(c_e_h_1, c_h, s20, s21)))),
% 295.32/187.85 inference(quant_inst,[status(thm)],[])).
% 295.32/187.85 tff(30280,plain,
% 295.32/187.85 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s20) | node18(c_e_h_1, c_h, s20, s21) | (~node19(c_e_h_1, c_h, s20, s21))),
% 295.32/187.85 inference(modus_ponens,[status(thm)],[30279, 30278])).
% 295.32/187.85 tff(30281,plain,
% 295.32/187.85 (node17(c_e_h_1, c_h, s20) | node18(c_e_h_1, c_h, s20, s21)),
% 295.32/187.85 inference(unit_resolution,[status(thm)],[30280, 776, 30277])).
% 295.32/187.85 tff(30282,plain,
% 295.32/187.85 (node17(c_e_h_1, c_h, s20)),
% 295.32/187.85 inference(unit_resolution,[status(thm)],[30281, 30266])).
% 295.32/187.85 tff(30283,plain,
% 295.32/187.85 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s20)) | m_c_h_element_v_in2(c_e_h_1, c_h, s20) | (~node17(c_e_h_1, c_h, s20)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s20)) | m_c_h_element_v_in2(c_e_h_1, c_h, s20) | (~node17(c_e_h_1, c_h, s20)))),
% 295.32/187.85 inference(rewrite,[status(thm)],[])).
% 295.32/187.85 tff(30284,plain,
% 295.32/187.85 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s20)) | m_c_h_element_v_in2(c_e_h_1, c_h, s20) | (~node17(c_e_h_1, c_h, s20)))),
% 295.32/187.86 inference(quant_inst,[status(thm)],[])).
% 295.32/187.86 tff(30285,plain,
% 295.32/187.86 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s20)) | m_c_h_element_v_in2(c_e_h_1, c_h, s20) | (~node17(c_e_h_1, c_h, s20))),
% 295.32/187.86 inference(modus_ponens,[status(thm)],[30284, 30283])).
% 295.32/187.86 tff(30286,plain,
% 295.32/187.86 ((~m_c_h_element_v_in1(c_e_h_1, c_h, s20)) | (~node17(c_e_h_1, c_h, s20))),
% 295.32/187.86 inference(unit_resolution,[status(thm)],[30285, 919, 30254])).
% 295.32/187.86 tff(30287,plain,
% 295.32/187.86 (~m_c_h_element_v_in1(c_e_h_1, c_h, s20)),
% 295.32/187.86 inference(unit_resolution,[status(thm)],[30286, 30282])).
% 295.32/187.86 tff(30288,plain,
% 295.32/187.86 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s20)) | m_c_h_element_v_in1(c_e_h_1, c_h, s20) | m_c_h_element_v_in2(c_e_h_1, c_h, s20))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s20)) | m_c_h_element_v_in1(c_e_h_1, c_h, s20) | m_c_h_element_v_in2(c_e_h_1, c_h, s20))),
% 295.32/187.86 inference(rewrite,[status(thm)],[])).
% 295.32/187.86 tff(30289,plain,
% 295.32/187.86 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s20)) | m_c_h_element_v_in1(c_e_h_1, c_h, s20) | m_c_h_element_v_in2(c_e_h_1, c_h, s20))),
% 295.32/187.86 inference(quant_inst,[status(thm)],[])).
% 295.32/187.86 tff(30290,plain,
% 295.32/187.86 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s20)) | m_c_h_element_v_in1(c_e_h_1, c_h, s20) | m_c_h_element_v_in2(c_e_h_1, c_h, s20)),
% 295.32/187.86 inference(modus_ponens,[status(thm)],[30289, 30288])).
% 295.32/187.86 tff(30291,plain,
% 295.32/187.86 ((~node16(c_e_h_1, c_h, s20)) | m_c_h_element_v_in1(c_e_h_1, c_h, s20)),
% 295.32/187.86 inference(unit_resolution,[status(thm)],[30290, 178, 30254])).
% 295.32/187.86 tff(30292,plain,
% 295.32/187.86 (~node16(c_e_h_1, c_h, s20)),
% 295.32/187.86 inference(unit_resolution,[status(thm)],[30291, 30287])).
% 295.32/187.86 tff(30293,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_h, s20)), introduced(assumption)).
% 295.32/187.86 tff(30294,assumption,(node14(c_e_h_1, c_h, s20, s21)), introduced(assumption)).
% 295.32/187.86 tff(30295,plain,
% 295.32/187.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s20) | (~m_c_h_element_v_out(c_e_h_1, c_h, s21)) | (~node14(c_e_h_1, c_h, s20, s21)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s20) | (~m_c_h_element_v_out(c_e_h_1, c_h, s21)) | (~node14(c_e_h_1, c_h, s20, s21)))),
% 295.32/187.86 inference(rewrite,[status(thm)],[])).
% 295.32/187.86 tff(30296,plain,
% 295.32/187.86 (((~node14(c_e_h_1, c_h, s20, s21)) | m_c_h_element_v_in1(c_e_h_1, c_h, s20) | (~m_c_h_element_v_out(c_e_h_1, c_h, s21))) <=> (m_c_h_element_v_in1(c_e_h_1, c_h, s20) | (~m_c_h_element_v_out(c_e_h_1, c_h, s21)) | (~node14(c_e_h_1, c_h, s20, s21)))),
% 295.32/187.86 inference(rewrite,[status(thm)],[])).
% 295.32/187.86 tff(30297,plain,
% 295.32/187.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s20, s21)) | m_c_h_element_v_in1(c_e_h_1, c_h, s20) | (~m_c_h_element_v_out(c_e_h_1, c_h, s21)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_h, s20) | (~m_c_h_element_v_out(c_e_h_1, c_h, s21)) | (~node14(c_e_h_1, c_h, s20, s21))))),
% 295.32/187.86 inference(monotonicity,[status(thm)],[30296])).
% 295.32/187.86 tff(30298,plain,
% 295.32/187.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s20, s21)) | m_c_h_element_v_in1(c_e_h_1, c_h, s20) | (~m_c_h_element_v_out(c_e_h_1, c_h, s21)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s20) | (~m_c_h_element_v_out(c_e_h_1, c_h, s21)) | (~node14(c_e_h_1, c_h, s20, s21)))),
% 295.32/187.86 inference(transitivity,[status(thm)],[30297, 30295])).
% 295.32/187.86 tff(30299,plain,
% 295.32/187.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s20, s21)) | m_c_h_element_v_in1(c_e_h_1, c_h, s20) | (~m_c_h_element_v_out(c_e_h_1, c_h, s21)))),
% 295.32/187.86 inference(quant_inst,[status(thm)],[])).
% 295.32/187.86 tff(30300,plain,
% 295.32/187.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_h, s20) | (~m_c_h_element_v_out(c_e_h_1, c_h, s21)) | (~node14(c_e_h_1, c_h, s20, s21))),
% 295.32/187.86 inference(modus_ponens,[status(thm)],[30299, 30298])).
% 295.32/187.86 tff(30301,plain,
% 295.32/187.86 ($false),
% 295.32/187.86 inference(unit_resolution,[status(thm)],[30300, 223, 30256, 30294, 30293])).
% 295.32/187.86 tff(30302,plain,((~node14(c_e_h_1, c_h, s20, s21)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s21)) | m_c_h_element_v_in1(c_e_h_1, c_h, s20)), inference(lemma,lemma(discharge,[]))).
% 295.32/187.86 tff(30303,plain,
% 295.32/187.86 (~node14(c_e_h_1, c_h, s20, s21)),
% 295.32/187.86 inference(unit_resolution,[status(thm)],[30302, 30287, 30256])).
% 295.32/187.86 tff(30304,plain,
% 295.32/187.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s20) | node15(c_e_h_1, c_h, s20, s21) | (~node19(c_e_h_1, c_h, s20, s21)) | node14(c_e_h_1, c_h, s20, s21))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s20) | node15(c_e_h_1, c_h, s20, s21) | (~node19(c_e_h_1, c_h, s20, s21)) | node14(c_e_h_1, c_h, s20, s21))),
% 295.32/187.86 inference(rewrite,[status(thm)],[])).
% 295.32/187.86 tff(30305,plain,
% 295.32/187.86 ((node16(c_e_h_1, c_h, s20) | node14(c_e_h_1, c_h, s20, s21) | node15(c_e_h_1, c_h, s20, s21) | (~node19(c_e_h_1, c_h, s20, s21))) <=> (node16(c_e_h_1, c_h, s20) | node15(c_e_h_1, c_h, s20, s21) | (~node19(c_e_h_1, c_h, s20, s21)) | node14(c_e_h_1, c_h, s20, s21))),
% 295.32/187.86 inference(rewrite,[status(thm)],[])).
% 295.32/187.86 tff(30306,plain,
% 295.32/187.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s20) | node14(c_e_h_1, c_h, s20, s21) | node15(c_e_h_1, c_h, s20, s21) | (~node19(c_e_h_1, c_h, s20, s21)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s20) | node15(c_e_h_1, c_h, s20, s21) | (~node19(c_e_h_1, c_h, s20, s21)) | node14(c_e_h_1, c_h, s20, s21)))),
% 295.32/187.86 inference(monotonicity,[status(thm)],[30305])).
% 295.32/187.86 tff(30307,plain,
% 295.32/187.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s20) | node14(c_e_h_1, c_h, s20, s21) | node15(c_e_h_1, c_h, s20, s21) | (~node19(c_e_h_1, c_h, s20, s21)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s20) | node15(c_e_h_1, c_h, s20, s21) | (~node19(c_e_h_1, c_h, s20, s21)) | node14(c_e_h_1, c_h, s20, s21))),
% 295.32/187.86 inference(transitivity,[status(thm)],[30306, 30304])).
% 295.32/187.86 tff(30308,plain,
% 295.32/187.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s20) | node14(c_e_h_1, c_h, s20, s21) | node15(c_e_h_1, c_h, s20, s21) | (~node19(c_e_h_1, c_h, s20, s21)))),
% 295.32/187.86 inference(quant_inst,[status(thm)],[])).
% 295.32/187.86 tff(30309,plain,
% 295.32/187.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s20) | node15(c_e_h_1, c_h, s20, s21) | (~node19(c_e_h_1, c_h, s20, s21)) | node14(c_e_h_1, c_h, s20, s21)),
% 295.32/187.86 inference(modus_ponens,[status(thm)],[30308, 30307])).
% 295.32/187.86 tff(30310,plain,
% 295.32/187.86 (node16(c_e_h_1, c_h, s20) | node15(c_e_h_1, c_h, s20, s21) | node14(c_e_h_1, c_h, s20, s21)),
% 295.32/187.86 inference(unit_resolution,[status(thm)],[30309, 204, 30277])).
% 295.32/187.86 tff(30311,plain,
% 295.32/187.86 (node15(c_e_h_1, c_h, s20, s21)),
% 295.32/187.86 inference(unit_resolution,[status(thm)],[30310, 30303, 30292])).
% 295.32/187.86 tff(30312,plain,
% 295.32/187.86 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s21)) | (~node15(c_e_h_1, c_h, s20, s21)) | m_c_h_element_v_out(c_e_h_1, c_h, s20))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s21)) | (~node15(c_e_h_1, c_h, s20, s21)) | m_c_h_element_v_out(c_e_h_1, c_h, s20))),
% 295.32/187.86 inference(rewrite,[status(thm)],[])).
% 295.32/187.86 tff(30313,plain,
% 295.32/187.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s21)) | (~node15(c_e_h_1, c_h, s20, s21)) | m_c_h_element_v_out(c_e_h_1, c_h, s20))),
% 295.32/187.86 inference(quant_inst,[status(thm)],[])).
% 295.32/187.86 tff(30314,plain,
% 295.32/187.86 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s21)) | (~node15(c_e_h_1, c_h, s20, s21)) | m_c_h_element_v_out(c_e_h_1, c_h, s20)),
% 295.32/187.86 inference(modus_ponens,[status(thm)],[30313, 30312])).
% 295.32/187.86 tff(30315,plain,
% 295.32/187.86 ($false),
% 295.32/187.86 inference(unit_resolution,[status(thm)],[30314, 147, 30256, 30255, 30311])).
% 295.32/187.86 tff(30316,plain,((~m_c_h_element_v_out(c_e_h_1, c_h, s21)) | m_c_h_element_v_out(c_e_h_1, c_h, s20) | m_c_h_element_v_in2(c_e_h_1, c_h, s20)), inference(lemma,lemma(discharge,[]))).
% 295.32/187.86 tff(30317,plain,
% 295.32/187.86 (~m_c_h_element_v_out(c_e_h_1, c_h, s21)),
% 295.32/187.86 inference(unit_resolution,[status(thm)],[30316, 30255, 30254])).
% 295.32/187.86 tff(30318,plain,
% 295.32/187.86 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s21)) | m_c_h_element_v_out(c_e_h_1, c_h, s21))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s21)) | m_c_h_element_v_out(c_e_h_1, c_h, s21))),
% 295.32/187.86 inference(rewrite,[status(thm)],[])).
% 295.32/187.86 tff(30319,plain,
% 295.32/187.86 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s21)) | m_c_h_element_v_out(c_e_h_1, c_h, s21))),
% 295.32/187.86 inference(quant_inst,[status(thm)],[])).
% 295.32/187.86 tff(30320,plain,
% 295.32/187.86 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s21)) | m_c_h_element_v_out(c_e_h_1, c_h, s21)),
% 295.32/187.86 inference(modus_ponens,[status(thm)],[30319, 30318])).
% 295.32/187.86 tff(30321,plain,
% 295.32/187.86 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s21)),
% 295.32/187.86 inference(unit_resolution,[status(thm)],[30320, 619, 30317])).
% 295.32/187.86 tff(30322,plain,
% 295.32/187.86 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s21)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s21))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s21)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s21))),
% 295.32/187.86 inference(rewrite,[status(thm)],[])).
% 295.32/187.86 tff(30323,plain,
% 295.32/187.86 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s21)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s21))),
% 295.32/187.86 inference(quant_inst,[status(thm)],[])).
% 295.32/187.86 tff(30324,plain,
% 295.32/187.86 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s21)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s21)),
% 295.32/187.86 inference(modus_ponens,[status(thm)],[30323, 30322])).
% 295.32/187.86 tff(30325,plain,
% 295.32/187.86 (~node20(c_e_h_1, c_i, s21)),
% 295.32/187.86 inference(unit_resolution,[status(thm)],[30324, 38, 30321])).
% 295.32/187.87 tff(30326,assumption,(~node20(c_e_h_1, c_i, s21)), introduced(assumption)).
% 295.32/187.87 tff(30327,assumption,(node21(c_e_h_1, c_i, s21, s22)), introduced(assumption)).
% 295.32/187.87 tff(30328,plain,
% 295.32/187.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s21) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s22)) | (~node21(c_e_h_1, c_i, s21, s22)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s21) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s22)) | (~node21(c_e_h_1, c_i, s21, s22)))),
% 295.32/187.87 inference(rewrite,[status(thm)],[])).
% 295.32/187.87 tff(30329,plain,
% 295.32/187.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s21) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s22)) | (~node21(c_e_h_1, c_i, s21, s22)))),
% 295.32/187.87 inference(quant_inst,[status(thm)],[])).
% 295.32/187.87 tff(30330,plain,
% 295.32/187.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s21) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s22)) | (~node21(c_e_h_1, c_i, s21, s22))),
% 295.32/187.87 inference(modus_ponens,[status(thm)],[30329, 30328])).
% 295.32/187.87 tff(30331,plain,
% 295.32/187.87 ($false),
% 295.32/187.87 inference(unit_resolution,[status(thm)],[30330, 52, 30253, 30327, 30326])).
% 295.32/187.87 tff(30332,plain,((~node21(c_e_h_1, c_i, s21, s22)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s22)) | node20(c_e_h_1, c_i, s21)), inference(lemma,lemma(discharge,[]))).
% 295.32/187.87 tff(30333,plain,
% 295.32/187.87 (~node21(c_e_h_1, c_i, s21, s22)),
% 295.32/187.87 inference(unit_resolution,[status(thm)],[30332, 30325, 30253])).
% 295.32/187.87 tff(30334,plain,
% 295.32/187.87 (succ(s21, s22) <=> succ(s21, s22)),
% 295.32/187.87 inference(rewrite,[status(thm)],[])).
% 295.32/187.87 tff(30335,axiom,(succ(s21, s22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound22')).
% 295.32/187.87 tff(30336,plain,
% 295.32/187.87 (succ(s21, s22)),
% 295.32/187.87 inference(modus_ponens,[status(thm)],[30335, 30334])).
% 295.32/187.87 tff(30337,plain,
% 295.32/187.87 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s21, s22)) | trans(s21, s22))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s21, s22)) | trans(s21, s22))),
% 295.32/187.87 inference(rewrite,[status(thm)],[])).
% 295.32/187.87 tff(30338,plain,
% 295.32/187.87 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s21, s22)) | trans(s21, s22))),
% 295.32/187.87 inference(quant_inst,[status(thm)],[])).
% 295.32/187.87 tff(30339,plain,
% 295.32/187.87 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s21, s22)) | trans(s21, s22)),
% 295.32/187.87 inference(modus_ponens,[status(thm)],[30338, 30337])).
% 295.32/187.87 tff(30340,plain,
% 295.32/187.87 (trans(s21, s22)),
% 295.32/187.87 inference(unit_resolution,[status(thm)],[30339, 30336, 65])).
% 295.32/187.87 tff(30341,plain,
% 295.32/187.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s21, s22)) | node21(c_e_h_1, c_i, s21, s22) | node22(c_e_h_1, c_i, s21, s22))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s21, s22)) | node21(c_e_h_1, c_i, s21, s22) | node22(c_e_h_1, c_i, s21, s22))),
% 295.32/187.87 inference(rewrite,[status(thm)],[])).
% 295.32/187.87 tff(30342,plain,
% 295.32/187.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s21, s22)) | node21(c_e_h_1, c_i, s21, s22) | node22(c_e_h_1, c_i, s21, s22))),
% 295.32/187.87 inference(quant_inst,[status(thm)],[])).
% 295.32/187.87 tff(30343,plain,
% 295.32/187.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s21, s22)) | node21(c_e_h_1, c_i, s21, s22) | node22(c_e_h_1, c_i, s21, s22)),
% 295.32/187.87 inference(modus_ponens,[status(thm)],[30342, 30341])).
% 295.32/187.87 tff(30344,plain,
% 295.32/187.87 (node21(c_e_h_1, c_i, s21, s22) | node22(c_e_h_1, c_i, s21, s22)),
% 295.32/187.87 inference(unit_resolution,[status(thm)],[30343, 82, 30340])).
% 295.32/187.87 tff(30345,plain,
% 295.32/187.87 (node22(c_e_h_1, c_i, s21, s22)),
% 295.32/187.87 inference(unit_resolution,[status(thm)],[30344, 30333])).
% 295.32/187.87 tff(30346,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_i, s20)), introduced(assumption)).
% 295.32/187.87 tff(30347,plain,
% 295.32/187.87 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s20)) | m_c_h_element_v_out(c_e_h_1, c_h, s20))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s20)) | m_c_h_element_v_out(c_e_h_1, c_h, s20))),
% 295.32/187.87 inference(rewrite,[status(thm)],[])).
% 295.32/187.87 tff(30348,plain,
% 295.32/187.87 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s20)) | m_c_h_element_v_out(c_e_h_1, c_h, s20))),
% 295.32/187.87 inference(quant_inst,[status(thm)],[])).
% 295.32/187.87 tff(30349,plain,
% 295.32/187.87 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s20)) | m_c_h_element_v_out(c_e_h_1, c_h, s20)),
% 295.32/187.87 inference(modus_ponens,[status(thm)],[30348, 30347])).
% 295.32/187.87 tff(30350,plain,
% 295.32/187.87 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s20)),
% 295.32/187.87 inference(unit_resolution,[status(thm)],[30349, 619, 30255])).
% 295.32/187.87 tff(30351,plain,
% 295.32/187.87 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s20)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s20))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s20)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s20))),
% 295.32/187.87 inference(rewrite,[status(thm)],[])).
% 295.32/187.87 tff(30352,plain,
% 295.32/187.87 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s20)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s20))),
% 295.32/187.87 inference(quant_inst,[status(thm)],[])).
% 295.32/187.87 tff(30353,plain,
% 295.32/187.87 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s20)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s20)),
% 295.32/187.87 inference(modus_ponens,[status(thm)],[30352, 30351])).
% 295.32/187.87 tff(30354,plain,
% 295.32/187.87 (~node20(c_e_h_1, c_i, s20)),
% 295.32/187.87 inference(unit_resolution,[status(thm)],[30353, 38, 30350])).
% 295.32/187.87 tff(30355,assumption,(~node20(c_e_h_1, c_i, s20)), introduced(assumption)).
% 295.32/187.87 tff(30356,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s21)), introduced(assumption)).
% 295.32/187.87 tff(30357,assumption,(node21(c_e_h_1, c_i, s20, s21)), introduced(assumption)).
% 295.32/187.87 tff(30358,plain,
% 295.32/187.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s20) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s21)) | (~node21(c_e_h_1, c_i, s20, s21)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s20) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s21)) | (~node21(c_e_h_1, c_i, s20, s21)))),
% 295.32/187.87 inference(rewrite,[status(thm)],[])).
% 295.32/187.87 tff(30359,plain,
% 295.32/187.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s20) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s21)) | (~node21(c_e_h_1, c_i, s20, s21)))),
% 295.32/187.87 inference(quant_inst,[status(thm)],[])).
% 295.32/187.87 tff(30360,plain,
% 295.32/187.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s20) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s21)) | (~node21(c_e_h_1, c_i, s20, s21))),
% 295.32/187.87 inference(modus_ponens,[status(thm)],[30359, 30358])).
% 295.32/187.87 tff(30361,plain,
% 295.32/187.87 ($false),
% 295.32/187.87 inference(unit_resolution,[status(thm)],[30360, 52, 30356, 30357, 30355])).
% 295.32/187.87 tff(30362,plain,((~node21(c_e_h_1, c_i, s20, s21)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s21)) | node20(c_e_h_1, c_i, s20)), inference(lemma,lemma(discharge,[]))).
% 295.32/187.87 tff(30363,plain,
% 295.32/187.87 (~node21(c_e_h_1, c_i, s20, s21)),
% 295.32/187.87 inference(unit_resolution,[status(thm)],[30362, 30356, 30355])).
% 295.32/187.87 tff(30364,plain,
% 295.32/187.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s20, s21)) | node21(c_e_h_1, c_i, s20, s21) | node22(c_e_h_1, c_i, s20, s21))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s20, s21)) | node21(c_e_h_1, c_i, s20, s21) | node22(c_e_h_1, c_i, s20, s21))),
% 295.32/187.87 inference(rewrite,[status(thm)],[])).
% 295.32/187.87 tff(30365,plain,
% 295.32/187.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s20, s21)) | node21(c_e_h_1, c_i, s20, s21) | node22(c_e_h_1, c_i, s20, s21))),
% 295.32/187.87 inference(quant_inst,[status(thm)],[])).
% 295.32/187.87 tff(30366,plain,
% 295.32/187.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s20, s21)) | node21(c_e_h_1, c_i, s20, s21) | node22(c_e_h_1, c_i, s20, s21)),
% 295.32/187.87 inference(modus_ponens,[status(thm)],[30365, 30364])).
% 295.32/187.87 tff(30367,plain,
% 295.32/187.87 (node21(c_e_h_1, c_i, s20, s21) | node22(c_e_h_1, c_i, s20, s21)),
% 295.32/187.87 inference(unit_resolution,[status(thm)],[30366, 82, 30273])).
% 295.32/187.87 tff(30368,plain,
% 295.32/187.87 (node22(c_e_h_1, c_i, s20, s21)),
% 295.32/187.87 inference(unit_resolution,[status(thm)],[30367, 30363])).
% 295.32/187.87 tff(30369,plain,
% 295.32/187.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s21)) | (~node22(c_e_h_1, c_i, s20, s21)) | m_and_h_gate_v_out(c_e_h_1, c_i, s20))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s21)) | (~node22(c_e_h_1, c_i, s20, s21)) | m_and_h_gate_v_out(c_e_h_1, c_i, s20))),
% 295.32/187.87 inference(rewrite,[status(thm)],[])).
% 295.32/187.87 tff(30370,plain,
% 295.32/187.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s21)) | (~node22(c_e_h_1, c_i, s20, s21)) | m_and_h_gate_v_out(c_e_h_1, c_i, s20))),
% 295.32/187.87 inference(quant_inst,[status(thm)],[])).
% 295.32/187.87 tff(30371,plain,
% 295.32/187.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s21)) | (~node22(c_e_h_1, c_i, s20, s21)) | m_and_h_gate_v_out(c_e_h_1, c_i, s20)),
% 295.32/187.87 inference(modus_ponens,[status(thm)],[30370, 30369])).
% 295.32/187.87 tff(30372,plain,
% 295.32/187.87 ($false),
% 295.32/187.87 inference(unit_resolution,[status(thm)],[30371, 108, 30356, 30346, 30368])).
% 295.32/187.87 tff(30373,plain,((~m_and_h_gate_v_out(c_e_h_1, c_i, s21)) | m_and_h_gate_v_out(c_e_h_1, c_i, s20) | node20(c_e_h_1, c_i, s20)), inference(lemma,lemma(discharge,[]))).
% 295.32/187.87 tff(30374,plain,
% 295.32/187.87 (~m_and_h_gate_v_out(c_e_h_1, c_i, s21)),
% 295.32/187.87 inference(unit_resolution,[status(thm)],[30373, 30354, 30346])).
% 295.32/187.87 tff(30375,plain,
% 295.32/187.87 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s22)) | (~node22(c_e_h_1, c_i, s21, s22)) | m_and_h_gate_v_out(c_e_h_1, c_i, s21))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s22)) | (~node22(c_e_h_1, c_i, s21, s22)) | m_and_h_gate_v_out(c_e_h_1, c_i, s21))),
% 295.32/187.87 inference(rewrite,[status(thm)],[])).
% 295.32/187.87 tff(30376,plain,
% 295.32/187.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s22)) | (~node22(c_e_h_1, c_i, s21, s22)) | m_and_h_gate_v_out(c_e_h_1, c_i, s21))),
% 295.32/187.87 inference(quant_inst,[status(thm)],[])).
% 295.32/187.87 tff(30377,plain,
% 295.32/187.87 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s22)) | (~node22(c_e_h_1, c_i, s21, s22)) | m_and_h_gate_v_out(c_e_h_1, c_i, s21)),
% 295.32/187.87 inference(modus_ponens,[status(thm)],[30376, 30375])).
% 295.32/187.87 tff(30378,plain,
% 295.32/187.87 ($false),
% 295.32/187.87 inference(unit_resolution,[status(thm)],[30377, 108, 30253, 30374, 30345])).
% 295.32/187.87 tff(30379,plain,(m_c_h_element_v_out(c_e_h_1, c_h, s20) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s22)) | m_and_h_gate_v_out(c_e_h_1, c_i, s20) | m_c_h_element_v_in2(c_e_h_1, c_h, s20)), inference(lemma,lemma(discharge,[]))).
% 295.32/187.88 tff(30380,plain,
% 295.32/187.88 (~m_and_h_gate_v_out(c_e_h_1, c_i, s22)),
% 295.32/187.88 inference(unit_resolution,[status(thm)],[30379, 30252, 30040, 29974])).
% 295.32/187.88 tff(30381,plain,
% 295.32/187.88 (~m_c_h_element_v_in2(c_e_h_1, c_e, s16)),
% 295.32/187.88 inference(unit_resolution,[status(thm)],[26013, 24266])).
% 295.32/187.88 tff(30382,plain,
% 295.32/187.88 (m_c_h_element_v_in2(c_e_h_1, c_e, s16) | (~m_c_h_element_v_out(c_e_h_1, c_e, s17))),
% 295.32/187.88 inference(unit_resolution,[status(thm)],[26085, 26004])).
% 295.32/187.88 tff(30383,plain,
% 295.32/187.88 (~m_c_h_element_v_out(c_e_h_1, c_e, s17)),
% 295.32/187.88 inference(unit_resolution,[status(thm)],[30382, 30381])).
% 295.32/187.88 tff(30384,plain,
% 295.32/187.88 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s17) | m_c_h_element_v_out(c_e_h_1, c_e, s17))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s17) | m_c_h_element_v_out(c_e_h_1, c_e, s17))),
% 295.32/187.88 inference(rewrite,[status(thm)],[])).
% 295.32/187.88 tff(30385,plain,
% 295.32/187.88 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s17) | m_c_h_element_v_out(c_e_h_1, c_e, s17))),
% 295.32/187.88 inference(quant_inst,[status(thm)],[])).
% 295.32/187.88 tff(30386,plain,
% 295.32/187.88 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s17) | m_c_h_element_v_out(c_e_h_1, c_e, s17)),
% 295.32/187.88 inference(modus_ponens,[status(thm)],[30385, 30384])).
% 295.32/187.88 tff(30387,plain,
% 295.32/187.88 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s17) | m_c_h_element_v_out(c_e_h_1, c_e, s17)),
% 295.32/187.88 inference(unit_resolution,[status(thm)],[30386, 7856])).
% 295.32/187.88 tff(30388,plain,
% 295.32/187.88 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s17)),
% 295.32/187.88 inference(unit_resolution,[status(thm)],[30387, 30383])).
% 295.32/187.88 tff(30389,plain,
% 295.32/187.88 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s17) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s17) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17))),
% 295.32/187.88 inference(rewrite,[status(thm)],[])).
% 295.32/187.88 tff(30390,plain,
% 295.32/187.88 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s17) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17))),
% 295.32/187.88 inference(quant_inst,[status(thm)],[])).
% 295.32/187.88 tff(30391,plain,
% 295.32/187.88 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s17) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17)),
% 295.32/187.88 inference(modus_ponens,[status(thm)],[30390, 30389])).
% 295.32/187.88 tff(30392,plain,
% 295.32/187.88 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s17) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17)),
% 295.32/187.88 inference(unit_resolution,[status(thm)],[30391, 7868])).
% 295.32/187.88 tff(30393,plain,
% 295.32/187.88 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s17)),
% 295.32/187.88 inference(unit_resolution,[status(thm)],[30392, 29683])).
% 295.32/187.88 tff(30394,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17)), introduced(assumption)).
% 295.32/187.88 tff(30395,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s18)), introduced(assumption)).
% 295.32/187.88 tff(30396,assumption,(node11(c_e_h_1, c_n, s17, s18)), introduced(assumption)).
% 295.32/187.88 tff(30397,plain,
% 295.32/187.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s18) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17)) | (~node11(c_e_h_1, c_n, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s18) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17)) | (~node11(c_e_h_1, c_n, s17, s18)))),
% 295.32/187.88 inference(rewrite,[status(thm)],[])).
% 295.32/187.88 tff(30398,plain,
% 295.32/187.88 ((m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s18) | (~node11(c_e_h_1, c_n, s17, s18)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17))) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s18) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17)) | (~node11(c_e_h_1, c_n, s17, s18)))),
% 295.32/187.88 inference(rewrite,[status(thm)],[])).
% 295.32/187.88 tff(30399,plain,
% 295.32/187.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s18) | (~node11(c_e_h_1, c_n, s17, s18)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s18) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17)) | (~node11(c_e_h_1, c_n, s17, s18))))),
% 295.32/187.88 inference(monotonicity,[status(thm)],[30398])).
% 295.32/187.88 tff(30400,plain,
% 295.32/187.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s18) | (~node11(c_e_h_1, c_n, s17, s18)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s18) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17)) | (~node11(c_e_h_1, c_n, s17, s18)))),
% 295.32/187.88 inference(transitivity,[status(thm)],[30399, 30397])).
% 295.32/187.88 tff(30401,plain,
% 295.32/187.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s18) | (~node11(c_e_h_1, c_n, s17, s18)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17)))),
% 295.32/187.88 inference(quant_inst,[status(thm)],[])).
% 295.32/187.88 tff(30402,plain,
% 295.32/187.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s18) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17)) | (~node11(c_e_h_1, c_n, s17, s18))),
% 295.32/187.88 inference(modus_ponens,[status(thm)],[30401, 30400])).
% 295.32/187.88 tff(30403,plain,
% 295.32/187.88 ($false),
% 295.32/187.88 inference(unit_resolution,[status(thm)],[30402, 5742, 30395, 30394, 30396])).
% 295.32/187.88 tff(30404,plain,((~node11(c_e_h_1, c_n, s17, s18)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s18) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17))), inference(lemma,lemma(discharge,[]))).
% 295.32/187.88 tff(30405,plain,
% 295.32/187.88 (~node11(c_e_h_1, c_n, s17, s18)),
% 295.32/187.88 inference(unit_resolution,[status(thm)],[30404, 30395, 30394])).
% 295.32/187.88 tff(30406,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s17)), introduced(assumption)).
% 295.32/187.88 tff(30407,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s17)), introduced(assumption)).
% 295.32/187.88 tff(30408,assumption,(node10(c_e_h_1, c_n, s17, s18)), introduced(assumption)).
% 295.32/187.88 tff(30409,plain,
% 295.32/187.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s18) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s17)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s17)) | (~node10(c_e_h_1, c_n, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s18) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s17)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s17)) | (~node10(c_e_h_1, c_n, s17, s18)))),
% 295.32/187.88 inference(rewrite,[status(thm)],[])).
% 295.32/187.88 tff(30410,plain,
% 295.32/187.88 (((~node10(c_e_h_1, c_n, s17, s18)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s17)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s17)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s18)) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s18) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s17)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s17)) | (~node10(c_e_h_1, c_n, s17, s18)))),
% 295.32/187.88 inference(rewrite,[status(thm)],[])).
% 295.32/187.88 tff(30411,plain,
% 295.32/187.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s17, s18)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s17)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s17)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s18))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s18) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s17)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s17)) | (~node10(c_e_h_1, c_n, s17, s18))))),
% 295.32/187.88 inference(monotonicity,[status(thm)],[30410])).
% 295.32/187.88 tff(30412,plain,
% 295.32/187.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s17, s18)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s17)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s17)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s18))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s18) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s17)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s17)) | (~node10(c_e_h_1, c_n, s17, s18)))),
% 295.32/187.88 inference(transitivity,[status(thm)],[30411, 30409])).
% 295.32/187.88 tff(30413,plain,
% 295.32/187.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s17, s18)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s17)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s17)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s18))),
% 295.32/187.88 inference(quant_inst,[status(thm)],[])).
% 295.32/187.88 tff(30414,plain,
% 295.32/187.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s18) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s17)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s17)) | (~node10(c_e_h_1, c_n, s17, s18))),
% 295.32/187.88 inference(modus_ponens,[status(thm)],[30413, 30412])).
% 295.32/187.88 tff(30415,plain,
% 295.32/187.88 ($false),
% 295.32/187.88 inference(unit_resolution,[status(thm)],[30414, 5718, 30395, 30407, 30406, 30408])).
% 295.32/187.88 tff(30416,plain,((~node10(c_e_h_1, c_n, s17, s18)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s18) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s17)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s17))), inference(lemma,lemma(discharge,[]))).
% 295.32/187.88 tff(30417,plain,
% 295.32/187.88 (~node10(c_e_h_1, c_n, s17, s18)),
% 295.32/187.88 inference(unit_resolution,[status(thm)],[30416, 30395, 30407, 30406])).
% 295.32/187.88 tff(30418,plain,
% 295.32/187.88 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s17, s18)) | node10(c_e_h_1, c_n, s17, s18) | node11(c_e_h_1, c_n, s17, s18))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s17, s18)) | node10(c_e_h_1, c_n, s17, s18) | node11(c_e_h_1, c_n, s17, s18))),
% 295.32/187.88 inference(rewrite,[status(thm)],[])).
% 295.32/187.88 tff(30419,plain,
% 295.32/187.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s17, s18)) | node10(c_e_h_1, c_n, s17, s18) | node11(c_e_h_1, c_n, s17, s18))),
% 295.32/187.88 inference(quant_inst,[status(thm)],[])).
% 295.32/187.88 tff(30420,plain,
% 295.32/187.88 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s17, s18)) | node10(c_e_h_1, c_n, s17, s18) | node11(c_e_h_1, c_n, s17, s18)),
% 295.32/187.89 inference(modus_ponens,[status(thm)],[30419, 30418])).
% 295.32/187.89 tff(30421,plain,
% 295.32/187.89 (node10(c_e_h_1, c_n, s17, s18) | node11(c_e_h_1, c_n, s17, s18)),
% 295.32/187.89 inference(unit_resolution,[status(thm)],[30420, 5002, 26135])).
% 295.32/187.89 tff(30422,plain,
% 295.32/187.89 ($false),
% 295.32/187.89 inference(unit_resolution,[status(thm)],[30421, 30417, 30405])).
% 295.32/187.89 tff(30423,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s18) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s17)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s17)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17))), inference(lemma,lemma(discharge,[]))).
% 295.32/187.89 tff(30424,plain,
% 295.32/187.89 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s18) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s17)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17))),
% 295.32/187.89 inference(unit_resolution,[status(thm)],[30423, 30393])).
% 295.32/187.89 tff(30425,plain,
% 295.32/187.89 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s18) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s17))),
% 295.32/187.89 inference(unit_resolution,[status(thm)],[30424, 30136])).
% 295.32/187.89 tff(30426,plain,
% 295.32/187.89 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s18)),
% 295.32/187.89 inference(unit_resolution,[status(thm)],[30425, 30388])).
% 295.32/187.89 tff(30427,plain,
% 295.32/187.89 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s18)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s18)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s18)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s18)))),
% 295.32/187.89 inference(rewrite,[status(thm)],[])).
% 295.32/187.89 tff(30428,plain,
% 295.32/187.89 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s18)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s18)))),
% 295.32/187.89 inference(quant_inst,[status(thm)],[])).
% 295.32/187.89 tff(30429,plain,
% 295.32/187.89 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s18)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s18))),
% 295.32/187.89 inference(modus_ponens,[status(thm)],[30428, 30427])).
% 295.32/187.89 tff(30430,plain,
% 295.32/187.89 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s18)),
% 295.32/187.89 inference(unit_resolution,[status(thm)],[30429, 4958, 30426])).
% 295.32/187.89 tff(30431,plain,
% 295.32/187.89 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s18)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s18))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s18)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s18))),
% 295.32/187.89 inference(rewrite,[status(thm)],[])).
% 295.32/187.89 tff(30432,plain,
% 295.32/187.89 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s18)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s18))),
% 295.32/187.89 inference(quant_inst,[status(thm)],[])).
% 295.32/187.89 tff(30433,plain,
% 295.32/187.89 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s18)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s18)),
% 295.32/187.89 inference(modus_ponens,[status(thm)],[30432, 30431])).
% 295.32/187.89 tff(30434,plain,
% 295.32/187.89 (~node9(c_e_h_1, c_m, s18)),
% 295.32/187.89 inference(unit_resolution,[status(thm)],[30433, 4972, 30430])).
% 295.32/187.89 tff(30435,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18)), introduced(assumption)).
% 295.32/187.89 tff(30436,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s19)), introduced(assumption)).
% 295.32/187.89 tff(30437,assumption,(node11(c_e_h_1, c_m, s18, s19)), introduced(assumption)).
% 295.32/187.89 tff(30438,plain,
% 295.32/187.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s19)) | (~node11(c_e_h_1, c_m, s18, s19)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s19)) | (~node11(c_e_h_1, c_m, s18, s19)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18))),
% 295.32/187.89 inference(rewrite,[status(thm)],[])).
% 295.32/187.89 tff(30439,plain,
% 295.32/187.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s19)) | (~node11(c_e_h_1, c_m, s18, s19)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18))),
% 295.32/187.89 inference(quant_inst,[status(thm)],[])).
% 295.32/187.89 tff(30440,plain,
% 295.32/187.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s19)) | (~node11(c_e_h_1, c_m, s18, s19)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18)),
% 295.32/187.89 inference(modus_ponens,[status(thm)],[30439, 30438])).
% 295.32/187.89 tff(30441,plain,
% 295.32/187.89 ($false),
% 295.32/187.89 inference(unit_resolution,[status(thm)],[30440, 5017, 30436, 30435, 30437])).
% 295.32/187.89 tff(30442,plain,((~node11(c_e_h_1, c_m, s18, s19)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s19)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18)), inference(lemma,lemma(discharge,[]))).
% 295.32/187.89 tff(30443,plain,
% 295.32/187.89 (~node11(c_e_h_1, c_m, s18, s19)),
% 295.32/187.89 inference(unit_resolution,[status(thm)],[30442, 30436, 30435])).
% 295.32/187.89 tff(30444,assumption,(~node9(c_e_h_1, c_m, s18)), introduced(assumption)).
% 295.32/187.89 tff(30445,assumption,(node10(c_e_h_1, c_m, s18, s19)), introduced(assumption)).
% 295.32/187.89 tff(30446,plain,
% 295.32/187.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s18) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s19)) | (~node10(c_e_h_1, c_m, s18, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_1, c_m, s18) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s19)) | (~node10(c_e_h_1, c_m, s18, s19)))),
% 295.32/187.89 inference(rewrite,[status(thm)],[])).
% 295.32/187.89 tff(30447,plain,
% 295.32/187.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s18) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s19)) | (~node10(c_e_h_1, c_m, s18, s19)))),
% 295.32/187.89 inference(quant_inst,[status(thm)],[])).
% 295.32/187.89 tff(30448,plain,
% 295.32/187.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_1, c_m, s18) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s19)) | (~node10(c_e_h_1, c_m, s18, s19))),
% 295.32/187.89 inference(modus_ponens,[status(thm)],[30447, 30446])).
% 295.32/187.89 tff(30449,plain,
% 295.32/187.89 ($false),
% 295.32/187.89 inference(unit_resolution,[status(thm)],[30448, 4986, 30436, 30445, 30444])).
% 295.32/187.89 tff(30450,plain,((~node10(c_e_h_1, c_m, s18, s19)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s19)) | node9(c_e_h_1, c_m, s18)), inference(lemma,lemma(discharge,[]))).
% 295.32/187.89 tff(30451,plain,
% 295.32/187.89 (~node10(c_e_h_1, c_m, s18, s19)),
% 295.32/187.89 inference(unit_resolution,[status(thm)],[30450, 30436, 30444])).
% 295.32/187.89 tff(30452,plain,
% 295.32/187.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s18, s19)) | node10(c_e_h_1, c_m, s18, s19) | node11(c_e_h_1, c_m, s18, s19))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s18, s19)) | node10(c_e_h_1, c_m, s18, s19) | node11(c_e_h_1, c_m, s18, s19))),
% 295.32/187.89 inference(rewrite,[status(thm)],[])).
% 295.32/187.89 tff(30453,plain,
% 295.32/187.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s18, s19)) | node10(c_e_h_1, c_m, s18, s19) | node11(c_e_h_1, c_m, s18, s19))),
% 295.32/187.89 inference(quant_inst,[status(thm)],[])).
% 295.32/187.89 tff(30454,plain,
% 295.32/187.89 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s18, s19)) | node10(c_e_h_1, c_m, s18, s19) | node11(c_e_h_1, c_m, s18, s19)),
% 295.32/187.89 inference(modus_ponens,[status(thm)],[30453, 30452])).
% 295.32/187.89 tff(30455,plain,
% 295.32/187.89 (node10(c_e_h_1, c_m, s18, s19) | node11(c_e_h_1, c_m, s18, s19)),
% 295.32/187.89 inference(unit_resolution,[status(thm)],[30454, 5002, 26787])).
% 295.32/187.89 tff(30456,plain,
% 295.32/187.89 ($false),
% 295.32/187.89 inference(unit_resolution,[status(thm)],[30455, 30451, 30443])).
% 295.32/187.89 tff(30457,plain,((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s19)) | node9(c_e_h_1, c_m, s18) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18)), inference(lemma,lemma(discharge,[]))).
% 295.32/187.89 tff(30458,plain,
% 295.32/187.89 ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s19)) | node9(c_e_h_1, c_m, s18)),
% 295.32/187.89 inference(unit_resolution,[status(thm)],[30457, 30169])).
% 295.32/187.89 tff(30459,plain,
% 295.32/187.89 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s19)),
% 295.32/187.89 inference(unit_resolution,[status(thm)],[30458, 30434])).
% 295.32/187.89 tff(30460,assumption,(m_and_h_gate_v_in2(c_e_h_1, c_l, s19)), introduced(assumption)).
% 295.32/187.89 tff(30461,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s19)), introduced(assumption)).
% 295.32/187.89 tff(30462,plain,
% 295.32/187.89 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s19)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s19))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s19)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s19))),
% 295.32/187.89 inference(rewrite,[status(thm)],[])).
% 295.32/187.89 tff(30463,plain,
% 295.32/187.89 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_l, s19)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s19))),
% 295.32/187.89 inference(quant_inst,[status(thm)],[])).
% 295.32/187.89 tff(30464,plain,
% 295.32/187.89 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_l, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s19)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s19)),
% 295.32/187.89 inference(modus_ponens,[status(thm)],[30463, 30462])).
% 295.32/187.89 tff(30465,plain,
% 295.32/187.89 ($false),
% 295.32/187.89 inference(unit_resolution,[status(thm)],[30464, 4549, 30461, 30460])).
% 295.32/187.89 tff(30466,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s19) | (~m_and_h_gate_v_in2(c_e_h_1, c_l, s19))), inference(lemma,lemma(discharge,[]))).
% 295.32/187.89 tff(30467,plain,
% 295.32/187.89 (~m_and_h_gate_v_in2(c_e_h_1, c_l, s19)),
% 295.32/187.89 inference(unit_resolution,[status(thm)],[30466, 30459])).
% 295.32/187.89 tff(30468,assumption,(~m_and_h_gate_v_in2(c_e_h_1, c_l, s19)), introduced(assumption)).
% 295.32/187.89 tff(30469,assumption,(node20(c_e_h_1, c_l, s19)), introduced(assumption)).
% 295.32/187.89 tff(30470,plain,
% 295.32/187.89 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s19)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s19))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s19)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s19))),
% 295.32/187.89 inference(rewrite,[status(thm)],[])).
% 295.32/187.89 tff(30471,plain,
% 295.32/187.89 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_l, s19)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s19))),
% 295.32/187.89 inference(quant_inst,[status(thm)],[])).
% 295.32/187.89 tff(30472,plain,
% 295.32/187.89 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_l, s19)) | m_and_h_gate_v_in2(c_e_h_1, c_l, s19)),
% 295.32/187.89 inference(modus_ponens,[status(thm)],[30471, 30470])).
% 295.32/187.89 tff(30473,plain,
% 295.32/187.89 ($false),
% 295.32/187.89 inference(unit_resolution,[status(thm)],[30472, 4563, 30469, 30468])).
% 295.32/187.89 tff(30474,plain,(m_and_h_gate_v_in2(c_e_h_1, c_l, s19) | (~node20(c_e_h_1, c_l, s19))), inference(lemma,lemma(discharge,[]))).
% 295.32/187.89 tff(30475,plain,
% 295.32/187.89 (~node20(c_e_h_1, c_l, s19)),
% 295.32/187.89 inference(unit_resolution,[status(thm)],[30474, 30467])).
% 295.32/187.89 tff(30476,plain,
% 295.32/187.89 ((~m_and_h_gate_v_out(c_e_h_1, c_l, s19)) | node20(c_e_h_1, c_l, s18)),
% 295.32/187.89 inference(unit_resolution,[status(thm)],[30203, 29711])).
% 295.32/187.89 tff(30477,plain,
% 295.32/187.89 (~m_and_h_gate_v_out(c_e_h_1, c_l, s19)),
% 295.32/187.89 inference(unit_resolution,[status(thm)],[30476, 30177])).
% 295.32/187.89 tff(30478,assumption,(m_and_h_gate_v_out(c_e_h_1, c_l, s20)), introduced(assumption)).
% 295.32/187.89 tff(30479,assumption,(~node20(c_e_h_1, c_l, s19)), introduced(assumption)).
% 295.32/187.89 tff(30480,assumption,(node21(c_e_h_1, c_l, s19, s20)), introduced(assumption)).
% 295.32/187.89 tff(30481,plain,
% 295.32/187.89 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s19) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s20)) | (~node21(c_e_h_1, c_l, s19, s20)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s19) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s20)) | (~node21(c_e_h_1, c_l, s19, s20)))),
% 295.32/187.90 inference(rewrite,[status(thm)],[])).
% 295.32/187.90 tff(30482,plain,
% 295.32/187.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_l, s19) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s20)) | (~node21(c_e_h_1, c_l, s19, s20)))),
% 295.32/187.90 inference(quant_inst,[status(thm)],[])).
% 295.32/187.90 tff(30483,plain,
% 295.32/187.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_l, s19) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s20)) | (~node21(c_e_h_1, c_l, s19, s20))),
% 295.32/187.90 inference(modus_ponens,[status(thm)],[30482, 30481])).
% 295.32/187.90 tff(30484,plain,
% 295.32/187.90 ($false),
% 295.32/187.90 inference(unit_resolution,[status(thm)],[30483, 52, 30480, 30478, 30479])).
% 295.32/187.90 tff(30485,plain,((~node21(c_e_h_1, c_l, s19, s20)) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s20)) | node20(c_e_h_1, c_l, s19)), inference(lemma,lemma(discharge,[]))).
% 295.32/187.90 tff(30486,plain,
% 295.32/187.90 (~node21(c_e_h_1, c_l, s19, s20)),
% 295.32/187.90 inference(unit_resolution,[status(thm)],[30485, 30478, 30479])).
% 295.32/187.90 tff(30487,plain,
% 295.32/187.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s19, s20)) | node21(c_e_h_1, c_l, s19, s20) | node22(c_e_h_1, c_l, s19, s20))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s19, s20)) | node21(c_e_h_1, c_l, s19, s20) | node22(c_e_h_1, c_l, s19, s20))),
% 295.32/187.90 inference(rewrite,[status(thm)],[])).
% 295.32/187.90 tff(30488,plain,
% 295.32/187.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s19, s20)) | node21(c_e_h_1, c_l, s19, s20) | node22(c_e_h_1, c_l, s19, s20))),
% 295.32/187.90 inference(quant_inst,[status(thm)],[])).
% 295.32/187.90 tff(30489,plain,
% 295.32/187.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s19, s20)) | node21(c_e_h_1, c_l, s19, s20) | node22(c_e_h_1, c_l, s19, s20)),
% 295.32/187.90 inference(modus_ponens,[status(thm)],[30488, 30487])).
% 295.32/187.90 tff(30490,plain,
% 295.32/187.90 (node21(c_e_h_1, c_l, s19, s20) | node22(c_e_h_1, c_l, s19, s20)),
% 295.32/187.90 inference(unit_resolution,[status(thm)],[30489, 82, 29925])).
% 295.32/187.90 tff(30491,plain,
% 295.32/187.90 (node22(c_e_h_1, c_l, s19, s20)),
% 295.32/187.90 inference(unit_resolution,[status(thm)],[30490, 30486])).
% 295.32/187.90 tff(30492,plain,
% 295.32/187.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s20)) | (~node22(c_e_h_1, c_l, s19, s20)) | m_and_h_gate_v_out(c_e_h_1, c_l, s19))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s20)) | (~node22(c_e_h_1, c_l, s19, s20)) | m_and_h_gate_v_out(c_e_h_1, c_l, s19))),
% 295.32/187.90 inference(rewrite,[status(thm)],[])).
% 295.32/187.90 tff(30493,plain,
% 295.32/187.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_l, s20)) | (~node22(c_e_h_1, c_l, s19, s20)) | m_and_h_gate_v_out(c_e_h_1, c_l, s19))),
% 295.32/187.90 inference(quant_inst,[status(thm)],[])).
% 295.32/187.90 tff(30494,plain,
% 295.32/187.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_l, s20)) | (~node22(c_e_h_1, c_l, s19, s20)) | m_and_h_gate_v_out(c_e_h_1, c_l, s19)),
% 295.32/187.90 inference(modus_ponens,[status(thm)],[30493, 30492])).
% 295.32/187.90 tff(30495,plain,
% 295.32/187.90 ($false),
% 295.32/187.90 inference(unit_resolution,[status(thm)],[30494, 108, 30491, 30478, 30206])).
% 295.32/187.90 tff(30496,plain,((~m_and_h_gate_v_out(c_e_h_1, c_l, s20)) | m_and_h_gate_v_out(c_e_h_1, c_l, s19) | node20(c_e_h_1, c_l, s19)), inference(lemma,lemma(discharge,[]))).
% 295.32/187.90 tff(30497,plain,
% 295.32/187.90 ((~m_and_h_gate_v_out(c_e_h_1, c_l, s20)) | node20(c_e_h_1, c_l, s19)),
% 295.32/187.90 inference(unit_resolution,[status(thm)],[30496, 30477])).
% 295.32/187.90 tff(30498,plain,
% 295.32/187.90 (~m_and_h_gate_v_out(c_e_h_1, c_l, s20)),
% 295.32/187.90 inference(unit_resolution,[status(thm)],[30497, 30475])).
% 295.32/187.90 tff(30499,assumption,(m_or_h_gate_v_in1(c_e_h_1, c_j, s20)), introduced(assumption)).
% 295.32/187.90 tff(30500,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_l, s20)), introduced(assumption)).
% 295.32/187.90 tff(30501,plain,
% 295.32/187.90 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s20)) | m_and_h_gate_v_out(c_e_h_1, c_l, s20))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s20)) | m_and_h_gate_v_out(c_e_h_1, c_l, s20))),
% 295.32/187.90 inference(rewrite,[status(thm)],[])).
% 295.32/187.90 tff(30502,plain,
% 295.32/187.90 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | ((~m_or_h_gate_v_in1(c_e_h_1, c_j, s20)) | m_and_h_gate_v_out(c_e_h_1, c_l, s20))),
% 295.32/187.90 inference(quant_inst,[status(thm)],[])).
% 295.32/187.90 tff(30503,plain,
% 295.32/187.90 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in1(I0, c_j, X)) | m_and_h_gate_v_out(I0, c_l, X))) | (~m_or_h_gate_v_in1(c_e_h_1, c_j, s20)) | m_and_h_gate_v_out(c_e_h_1, c_l, s20)),
% 295.32/187.90 inference(modus_ponens,[status(thm)],[30502, 30501])).
% 295.32/187.90 tff(30504,plain,
% 295.32/187.90 ($false),
% 295.32/187.90 inference(unit_resolution,[status(thm)],[30503, 1100, 30500, 30499])).
% 295.32/187.90 tff(30505,plain,((~m_or_h_gate_v_in1(c_e_h_1, c_j, s20)) | m_and_h_gate_v_out(c_e_h_1, c_l, s20)), inference(lemma,lemma(discharge,[]))).
% 295.32/187.90 tff(30506,plain,
% 295.32/187.90 (~m_or_h_gate_v_in1(c_e_h_1, c_j, s20)),
% 295.32/187.90 inference(unit_resolution,[status(thm)],[30505, 30498])).
% 295.32/187.90 tff(30507,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s19)), introduced(assumption)).
% 295.32/187.90 tff(30508,plain,
% 295.32/187.90 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s19)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s19))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s19)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s19))),
% 295.32/187.90 inference(rewrite,[status(thm)],[])).
% 295.32/187.90 tff(30509,plain,
% 295.32/187.90 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | ((~m_and_h_gate_v_in2(c_e_h_3, c_q, s19)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s19))),
% 295.32/187.90 inference(quant_inst,[status(thm)],[])).
% 295.32/187.90 tff(30510,plain,
% 295.32/187.90 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_q, X)) | m_and_h_gate_h_init_v_out(I0, c_n, X))) | (~m_and_h_gate_v_in2(c_e_h_3, c_q, s19)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s19)),
% 295.32/187.90 inference(modus_ponens,[status(thm)],[30509, 30508])).
% 295.32/187.90 tff(30511,plain,
% 295.32/187.90 (~m_and_h_gate_v_in2(c_e_h_3, c_q, s19)),
% 295.32/187.90 inference(unit_resolution,[status(thm)],[30510, 5621, 30507])).
% 295.32/187.90 tff(30512,plain,
% 295.32/187.90 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s19)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s19))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s19)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s19))),
% 295.32/187.90 inference(rewrite,[status(thm)],[])).
% 295.32/187.90 tff(30513,plain,
% 295.32/187.90 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_3, c_q, s19)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s19))),
% 295.32/187.90 inference(quant_inst,[status(thm)],[])).
% 295.32/187.90 tff(30514,plain,
% 295.32/187.90 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_3, c_q, s19)) | m_and_h_gate_v_in2(c_e_h_3, c_q, s19)),
% 295.32/187.90 inference(modus_ponens,[status(thm)],[30513, 30512])).
% 295.32/187.90 tff(30515,plain,
% 295.32/187.90 (~node20(c_e_h_3, c_q, s19)),
% 295.32/187.90 inference(unit_resolution,[status(thm)],[30514, 4563, 30511])).
% 295.32/187.90 tff(30516,assumption,(~node20(c_e_h_3, c_q, s19)), introduced(assumption)).
% 295.32/187.90 tff(30517,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_q, s19)), introduced(assumption)).
% 295.32/187.90 tff(30518,assumption,(m_and_h_gate_v_out(c_e_h_3, c_q, s20)), introduced(assumption)).
% 295.32/187.90 tff(30519,assumption,(node22(c_e_h_3, c_q, s19, s20)), introduced(assumption)).
% 295.32/187.90 tff(30520,plain,
% 295.32/187.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s20)) | (~node22(c_e_h_3, c_q, s19, s20)) | m_and_h_gate_v_out(c_e_h_3, c_q, s19))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s20)) | (~node22(c_e_h_3, c_q, s19, s20)) | m_and_h_gate_v_out(c_e_h_3, c_q, s19))),
% 295.32/187.90 inference(rewrite,[status(thm)],[])).
% 295.32/187.90 tff(30521,plain,
% 295.32/187.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s20)) | (~node22(c_e_h_3, c_q, s19, s20)) | m_and_h_gate_v_out(c_e_h_3, c_q, s19))),
% 295.32/187.90 inference(quant_inst,[status(thm)],[])).
% 295.32/187.90 tff(30522,plain,
% 295.32/187.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s20)) | (~node22(c_e_h_3, c_q, s19, s20)) | m_and_h_gate_v_out(c_e_h_3, c_q, s19)),
% 295.32/187.90 inference(modus_ponens,[status(thm)],[30521, 30520])).
% 295.32/187.90 tff(30523,plain,
% 295.32/187.90 ($false),
% 295.32/187.90 inference(unit_resolution,[status(thm)],[30522, 108, 30518, 30517, 30519])).
% 295.32/187.90 tff(30524,plain,((~node22(c_e_h_3, c_q, s19, s20)) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s20)) | m_and_h_gate_v_out(c_e_h_3, c_q, s19)), inference(lemma,lemma(discharge,[]))).
% 295.32/187.90 tff(30525,plain,
% 295.32/187.90 (~node22(c_e_h_3, c_q, s19, s20)),
% 295.32/187.90 inference(unit_resolution,[status(thm)],[30524, 30518, 30517])).
% 295.32/187.90 tff(30526,plain,
% 295.32/187.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s19, s20)) | node21(c_e_h_3, c_q, s19, s20) | node22(c_e_h_3, c_q, s19, s20))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s19, s20)) | node21(c_e_h_3, c_q, s19, s20) | node22(c_e_h_3, c_q, s19, s20))),
% 295.32/187.90 inference(rewrite,[status(thm)],[])).
% 295.32/187.90 tff(30527,plain,
% 295.32/187.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s19, s20)) | node21(c_e_h_3, c_q, s19, s20) | node22(c_e_h_3, c_q, s19, s20))),
% 295.32/187.90 inference(quant_inst,[status(thm)],[])).
% 295.32/187.90 tff(30528,plain,
% 295.32/187.90 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s19, s20)) | node21(c_e_h_3, c_q, s19, s20) | node22(c_e_h_3, c_q, s19, s20)),
% 295.32/187.90 inference(modus_ponens,[status(thm)],[30527, 30526])).
% 295.32/187.90 tff(30529,plain,
% 295.32/187.90 (node21(c_e_h_3, c_q, s19, s20) | node22(c_e_h_3, c_q, s19, s20)),
% 295.32/187.90 inference(unit_resolution,[status(thm)],[30528, 82, 29925])).
% 295.32/187.90 tff(30530,plain,
% 295.32/187.90 (node21(c_e_h_3, c_q, s19, s20)),
% 295.32/187.90 inference(unit_resolution,[status(thm)],[30529, 30525])).
% 295.32/187.90 tff(30531,plain,
% 295.32/187.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s20)) | node20(c_e_h_3, c_q, s19) | (~node21(c_e_h_3, c_q, s19, s20)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s20)) | node20(c_e_h_3, c_q, s19) | (~node21(c_e_h_3, c_q, s19, s20)))),
% 295.32/187.90 inference(rewrite,[status(thm)],[])).
% 295.32/187.90 tff(30532,plain,
% 295.32/187.90 ((node20(c_e_h_3, c_q, s19) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s20)) | (~node21(c_e_h_3, c_q, s19, s20))) <=> ((~m_and_h_gate_v_out(c_e_h_3, c_q, s20)) | node20(c_e_h_3, c_q, s19) | (~node21(c_e_h_3, c_q, s19, s20)))),
% 295.32/187.90 inference(rewrite,[status(thm)],[])).
% 295.32/187.90 tff(30533,plain,
% 295.32/187.90 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s19) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s20)) | (~node21(c_e_h_3, c_q, s19, s20)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_3, c_q, s20)) | node20(c_e_h_3, c_q, s19) | (~node21(c_e_h_3, c_q, s19, s20))))),
% 295.41/187.91 inference(monotonicity,[status(thm)],[30532])).
% 295.41/187.91 tff(30534,plain,
% 295.41/187.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s19) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s20)) | (~node21(c_e_h_3, c_q, s19, s20)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s20)) | node20(c_e_h_3, c_q, s19) | (~node21(c_e_h_3, c_q, s19, s20)))),
% 295.41/187.91 inference(transitivity,[status(thm)],[30533, 30531])).
% 295.41/187.91 tff(30535,plain,
% 295.41/187.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_q, s19) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s20)) | (~node21(c_e_h_3, c_q, s19, s20)))),
% 295.41/187.91 inference(quant_inst,[status(thm)],[])).
% 295.41/187.91 tff(30536,plain,
% 295.41/187.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_3, c_q, s20)) | node20(c_e_h_3, c_q, s19) | (~node21(c_e_h_3, c_q, s19, s20))),
% 295.41/187.91 inference(modus_ponens,[status(thm)],[30535, 30534])).
% 295.41/187.91 tff(30537,plain,
% 295.41/187.91 ($false),
% 295.41/187.91 inference(unit_resolution,[status(thm)],[30536, 52, 30518, 30530, 30516])).
% 295.41/187.91 tff(30538,plain,((~m_and_h_gate_v_out(c_e_h_3, c_q, s20)) | node20(c_e_h_3, c_q, s19) | m_and_h_gate_v_out(c_e_h_3, c_q, s19)), inference(lemma,lemma(discharge,[]))).
% 295.41/187.91 tff(30539,plain,
% 295.41/187.91 (~m_and_h_gate_v_out(c_e_h_3, c_q, s20)),
% 295.41/187.91 inference(unit_resolution,[status(thm)],[30538, 30515, 30075])).
% 295.41/187.91 tff(30540,plain,
% 295.41/187.91 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s20))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s20))),
% 295.41/187.91 inference(rewrite,[status(thm)],[])).
% 295.41/187.91 tff(30541,plain,
% 295.41/187.91 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s20))),
% 295.41/187.91 inference(quant_inst,[status(thm)],[])).
% 295.41/187.91 tff(30542,plain,
% 295.41/187.91 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_3, c_e_h_1)) | node3(c_e_h_3, c_e_h_1, s20)),
% 295.41/187.91 inference(modus_ponens,[status(thm)],[30541, 30540])).
% 295.41/187.91 tff(30543,plain,
% 295.41/187.91 (node3(c_e_h_3, c_e_h_1, s20)),
% 295.41/187.91 inference(unit_resolution,[status(thm)],[30542, 2922, 1056])).
% 295.41/187.91 tff(30544,plain,
% 295.41/187.91 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s20)) | (~node3(c_e_h_3, c_e_h_1, s20)) | m_and_h_gate_v_out(c_e_h_3, c_q, s20))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s20)) | (~node3(c_e_h_3, c_e_h_1, s20)) | m_and_h_gate_v_out(c_e_h_3, c_q, s20))),
% 295.41/187.91 inference(rewrite,[status(thm)],[])).
% 295.41/187.91 tff(30545,plain,
% 295.41/187.91 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_1, s20)) | (~node3(c_e_h_3, c_e_h_1, s20)) | m_and_h_gate_v_out(c_e_h_3, c_q, s20))),
% 295.41/187.91 inference(quant_inst,[status(thm)],[])).
% 295.41/187.91 tff(30546,plain,
% 295.41/187.91 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_1, s20)) | (~node3(c_e_h_3, c_e_h_1, s20)) | m_and_h_gate_v_out(c_e_h_3, c_q, s20)),
% 295.41/187.91 inference(modus_ponens,[status(thm)],[30545, 30544])).
% 295.41/187.91 tff(30547,plain,
% 295.41/187.91 ((~m_cell_v_ack(c_e_h_1, s20)) | m_and_h_gate_v_out(c_e_h_3, c_q, s20)),
% 295.41/187.91 inference(unit_resolution,[status(thm)],[30546, 1073, 30543])).
% 295.41/187.91 tff(30548,plain,
% 295.41/187.91 (~m_cell_v_ack(c_e_h_1, s20)),
% 295.41/187.91 inference(unit_resolution,[status(thm)],[30547, 30539])).
% 295.41/187.91 tff(30549,plain,
% 295.41/187.91 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s20)) | m_cell_v_ack(c_e_h_1, s20))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s20)) | m_cell_v_ack(c_e_h_1, s20))),
% 295.41/187.91 inference(rewrite,[status(thm)],[])).
% 295.41/187.91 tff(30550,plain,
% 295.41/187.91 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_1, c_j, s20)) | m_cell_v_ack(c_e_h_1, s20))),
% 295.41/187.91 inference(quant_inst,[status(thm)],[])).
% 295.41/187.91 tff(30551,plain,
% 295.41/187.91 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_1, c_j, s20)) | m_cell_v_ack(c_e_h_1, s20)),
% 295.41/187.91 inference(modus_ponens,[status(thm)],[30550, 30549])).
% 295.41/187.91 tff(30552,plain,
% 295.41/187.91 (~m_or_h_gate_v_in2(c_e_h_1, c_j, s20)),
% 295.41/187.91 inference(unit_resolution,[status(thm)],[30551, 1085, 30548])).
% 295.41/187.91 tff(30553,assumption,(m_c_h_element_v_out(c_e_h_1, c_h, s22)), introduced(assumption)).
% 295.41/187.91 tff(30554,assumption,(~m_or_h_gate_v_in1(c_e_h_1, c_j, s20)), introduced(assumption)).
% 295.41/187.91 tff(30555,assumption,(~m_or_h_gate_v_in2(c_e_h_1, c_j, s20)), introduced(assumption)).
% 295.41/187.91 tff(30556,assumption,(~m_or_h_gate_v_out(c_e_h_1, c_j, s20)), introduced(assumption)).
% 295.41/187.91 tff(30557,assumption,(m_or_h_gate_v_out(c_e_h_1, c_j, s21)), introduced(assumption)).
% 295.41/187.91 tff(30558,assumption,(node6(c_e_h_1, c_j, s20, s21)), introduced(assumption)).
% 295.41/187.91 tff(30559,plain,
% 295.41/187.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s20) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s21)) | (~node6(c_e_h_1, c_j, s20, s21)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s20) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s21)) | (~node6(c_e_h_1, c_j, s20, s21)))),
% 295.41/187.91 inference(rewrite,[status(thm)],[])).
% 295.41/187.91 tff(30560,plain,
% 295.41/187.91 (((~node6(c_e_h_1, c_j, s20, s21)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s21)) | m_or_h_gate_v_out(c_e_h_1, c_j, s20)) <=> (m_or_h_gate_v_out(c_e_h_1, c_j, s20) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s21)) | (~node6(c_e_h_1, c_j, s20, s21)))),
% 295.41/187.91 inference(rewrite,[status(thm)],[])).
% 295.41/187.91 tff(30561,plain,
% 295.41/187.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s20, s21)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s21)) | m_or_h_gate_v_out(c_e_h_1, c_j, s20))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (m_or_h_gate_v_out(c_e_h_1, c_j, s20) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s21)) | (~node6(c_e_h_1, c_j, s20, s21))))),
% 295.41/187.91 inference(monotonicity,[status(thm)],[30560])).
% 295.41/187.91 tff(30562,plain,
% 295.41/187.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s20, s21)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s21)) | m_or_h_gate_v_out(c_e_h_1, c_j, s20))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s20) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s21)) | (~node6(c_e_h_1, c_j, s20, s21)))),
% 295.41/187.91 inference(transitivity,[status(thm)],[30561, 30559])).
% 295.41/187.91 tff(30563,plain,
% 295.41/187.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_1, c_j, s20, s21)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s21)) | m_or_h_gate_v_out(c_e_h_1, c_j, s20))),
% 295.41/187.91 inference(quant_inst,[status(thm)],[])).
% 295.41/187.91 tff(30564,plain,
% 295.41/187.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | m_or_h_gate_v_out(c_e_h_1, c_j, s20) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s21)) | (~node6(c_e_h_1, c_j, s20, s21))),
% 295.41/187.91 inference(modus_ponens,[status(thm)],[30563, 30562])).
% 295.41/187.91 tff(30565,plain,
% 295.41/187.91 ($false),
% 295.41/187.91 inference(unit_resolution,[status(thm)],[30564, 1121, 30556, 30557, 30558])).
% 295.41/187.91 tff(30566,plain,((~node6(c_e_h_1, c_j, s20, s21)) | m_or_h_gate_v_out(c_e_h_1, c_j, s20) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s21))), inference(lemma,lemma(discharge,[]))).
% 295.41/187.91 tff(30567,plain,
% 295.41/187.91 (~node6(c_e_h_1, c_j, s20, s21)),
% 295.41/187.91 inference(unit_resolution,[status(thm)],[30566, 30557, 30556])).
% 295.41/187.91 tff(30568,assumption,(node5(c_e_h_1, c_j, s20, s21)), introduced(assumption)).
% 295.41/187.91 tff(30569,plain,
% 295.41/187.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_1, c_j, s20) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s21)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s20) | (~node5(c_e_h_1, c_j, s20, s21)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_1, c_j, s20) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s21)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s20) | (~node5(c_e_h_1, c_j, s20, s21)))),
% 295.41/187.91 inference(rewrite,[status(thm)],[])).
% 295.41/187.91 tff(30570,plain,
% 295.41/187.91 ((m_or_h_gate_v_in1(c_e_h_1, c_j, s20) | m_or_h_gate_v_in2(c_e_h_1, c_j, s20) | (~node5(c_e_h_1, c_j, s20, s21)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s21))) <=> (m_or_h_gate_v_in2(c_e_h_1, c_j, s20) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s21)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s20) | (~node5(c_e_h_1, c_j, s20, s21)))),
% 295.41/187.91 inference(rewrite,[status(thm)],[])).
% 295.41/187.91 tff(30571,plain,
% 295.41/187.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s20) | m_or_h_gate_v_in2(c_e_h_1, c_j, s20) | (~node5(c_e_h_1, c_j, s20, s21)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s21)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in2(c_e_h_1, c_j, s20) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s21)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s20) | (~node5(c_e_h_1, c_j, s20, s21))))),
% 295.41/187.91 inference(monotonicity,[status(thm)],[30570])).
% 295.41/187.91 tff(30572,plain,
% 295.41/187.91 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s20) | m_or_h_gate_v_in2(c_e_h_1, c_j, s20) | (~node5(c_e_h_1, c_j, s20, s21)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s21)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_1, c_j, s20) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s21)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s20) | (~node5(c_e_h_1, c_j, s20, s21)))),
% 295.41/187.91 inference(transitivity,[status(thm)],[30571, 30569])).
% 295.41/187.91 tff(30573,plain,
% 295.41/187.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | (m_or_h_gate_v_in1(c_e_h_1, c_j, s20) | m_or_h_gate_v_in2(c_e_h_1, c_j, s20) | (~node5(c_e_h_1, c_j, s20, s21)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s21)))),
% 295.41/187.91 inference(quant_inst,[status(thm)],[])).
% 295.41/187.91 tff(30574,plain,
% 295.41/187.91 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_or_h_gate_v_in1(I0, I1, X) | m_or_h_gate_v_in2(I0, I1, X) | (~node5(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)))) | m_or_h_gate_v_in2(c_e_h_1, c_j, s20) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s21)) | m_or_h_gate_v_in1(c_e_h_1, c_j, s20) | (~node5(c_e_h_1, c_j, s20, s21))),
% 295.41/187.91 inference(modus_ponens,[status(thm)],[30573, 30572])).
% 295.41/187.91 tff(30575,plain,
% 295.41/187.91 ($false),
% 295.41/187.91 inference(unit_resolution,[status(thm)],[30574, 1159, 30557, 30568, 30555, 30554])).
% 295.41/187.92 tff(30576,plain,((~node5(c_e_h_1, c_j, s20, s21)) | (~m_or_h_gate_v_out(c_e_h_1, c_j, s21)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s20) | m_or_h_gate_v_in1(c_e_h_1, c_j, s20)), inference(lemma,lemma(discharge,[]))).
% 295.41/187.92 tff(30577,plain,
% 295.41/187.92 (~node5(c_e_h_1, c_j, s20, s21)),
% 295.41/187.92 inference(unit_resolution,[status(thm)],[30576, 30557, 30555, 30554])).
% 295.41/187.92 tff(30578,plain,
% 295.41/187.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s20, s21)) | node6(c_e_h_1, c_j, s20, s21) | node5(c_e_h_1, c_j, s20, s21))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s20, s21)) | node6(c_e_h_1, c_j, s20, s21) | node5(c_e_h_1, c_j, s20, s21))),
% 295.41/187.92 inference(rewrite,[status(thm)],[])).
% 295.41/187.92 tff(30579,plain,
% 295.41/187.92 ((node6(c_e_h_1, c_j, s20, s21) | node5(c_e_h_1, c_j, s20, s21) | (~trans(s20, s21))) <=> ((~trans(s20, s21)) | node6(c_e_h_1, c_j, s20, s21) | node5(c_e_h_1, c_j, s20, s21))),
% 295.41/187.92 inference(rewrite,[status(thm)],[])).
% 295.41/187.92 tff(30580,plain,
% 295.41/187.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s20, s21) | node5(c_e_h_1, c_j, s20, s21) | (~trans(s20, s21)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | ((~trans(s20, s21)) | node6(c_e_h_1, c_j, s20, s21) | node5(c_e_h_1, c_j, s20, s21)))),
% 295.41/187.92 inference(monotonicity,[status(thm)],[30579])).
% 295.41/187.92 tff(30581,plain,
% 295.41/187.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s20, s21) | node5(c_e_h_1, c_j, s20, s21) | (~trans(s20, s21)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s20, s21)) | node6(c_e_h_1, c_j, s20, s21) | node5(c_e_h_1, c_j, s20, s21))),
% 295.41/187.92 inference(transitivity,[status(thm)],[30580, 30578])).
% 295.41/187.92 tff(30582,plain,
% 295.41/187.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (node6(c_e_h_1, c_j, s20, s21) | node5(c_e_h_1, c_j, s20, s21) | (~trans(s20, s21)))),
% 295.41/187.92 inference(quant_inst,[status(thm)],[])).
% 295.41/187.92 tff(30583,plain,
% 295.41/187.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node6(I0, I1, X, Y) | node5(I0, I1, X, Y) | (~trans(X, Y)))) | (~trans(s20, s21)) | node6(c_e_h_1, c_j, s20, s21) | node5(c_e_h_1, c_j, s20, s21)),
% 295.41/187.92 inference(modus_ponens,[status(thm)],[30582, 30581])).
% 295.41/187.92 tff(30584,plain,
% 295.41/187.92 (node6(c_e_h_1, c_j, s20, s21) | node5(c_e_h_1, c_j, s20, s21)),
% 295.41/187.92 inference(unit_resolution,[status(thm)],[30583, 1141, 30273])).
% 295.41/187.92 tff(30585,plain,
% 295.41/187.92 ($false),
% 295.41/187.92 inference(unit_resolution,[status(thm)],[30584, 30577, 30567])).
% 295.41/187.92 tff(30586,plain,((~m_or_h_gate_v_out(c_e_h_1, c_j, s21)) | m_or_h_gate_v_in2(c_e_h_1, c_j, s20) | m_or_h_gate_v_in1(c_e_h_1, c_j, s20) | m_or_h_gate_v_out(c_e_h_1, c_j, s20)), inference(lemma,lemma(discharge,[]))).
% 295.41/187.92 tff(30587,plain,
% 295.41/187.92 (~m_or_h_gate_v_out(c_e_h_1, c_j, s21)),
% 295.41/187.92 inference(unit_resolution,[status(thm)],[30586, 30556, 30555, 30554])).
% 295.41/187.92 tff(30588,plain,
% 295.41/187.92 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s21)) | m_or_h_gate_v_out(c_e_h_1, c_j, s21))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s21)) | m_or_h_gate_v_out(c_e_h_1, c_j, s21))),
% 295.41/187.92 inference(rewrite,[status(thm)],[])).
% 295.41/187.92 tff(30589,plain,
% 295.41/187.92 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_h, s21)) | m_or_h_gate_v_out(c_e_h_1, c_j, s21))),
% 295.41/187.92 inference(quant_inst,[status(thm)],[])).
% 295.41/187.92 tff(30590,plain,
% 295.41/187.92 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_h, X)) | m_or_h_gate_v_out(I0, c_j, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_h, s21)) | m_or_h_gate_v_out(c_e_h_1, c_j, s21)),
% 295.41/187.92 inference(modus_ponens,[status(thm)],[30589, 30588])).
% 295.41/187.92 tff(30591,plain,
% 295.41/187.92 (~m_c_h_element_v_in2(c_e_h_1, c_h, s21)),
% 295.41/187.92 inference(unit_resolution,[status(thm)],[30590, 1174, 30587])).
% 295.41/187.92 tff(30592,plain,
% 295.41/187.92 (~m_c_h_element_v_in2(c_e_h_1, c_h, s20)),
% 295.41/187.92 inference(unit_resolution,[status(thm)],[30251, 1174, 30556])).
% 295.41/187.92 tff(30593,plain,
% 295.41/187.92 (~m_c_h_element_v_out(c_e_h_1, c_h, s21)),
% 295.41/187.92 inference(unit_resolution,[status(thm)],[30316, 30592, 30255])).
% 295.41/187.92 tff(30594,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_h, s21)), introduced(assumption)).
% 295.41/187.92 tff(30595,assumption,(~m_c_h_element_v_out(c_e_h_1, c_h, s21)), introduced(assumption)).
% 295.41/187.92 tff(30596,assumption,(node15(c_e_h_1, c_h, s21, s22)), introduced(assumption)).
% 295.41/187.92 tff(30597,plain,
% 295.41/187.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s22)) | (~node15(c_e_h_1, c_h, s21, s22)) | m_c_h_element_v_out(c_e_h_1, c_h, s21))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s22)) | (~node15(c_e_h_1, c_h, s21, s22)) | m_c_h_element_v_out(c_e_h_1, c_h, s21))),
% 295.41/187.92 inference(rewrite,[status(thm)],[])).
% 295.41/187.92 tff(30598,plain,
% 295.41/187.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s22)) | (~node15(c_e_h_1, c_h, s21, s22)) | m_c_h_element_v_out(c_e_h_1, c_h, s21))),
% 295.41/187.92 inference(quant_inst,[status(thm)],[])).
% 295.41/187.92 tff(30599,plain,
% 295.41/187.92 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s22)) | (~node15(c_e_h_1, c_h, s21, s22)) | m_c_h_element_v_out(c_e_h_1, c_h, s21)),
% 295.41/187.92 inference(modus_ponens,[status(thm)],[30598, 30597])).
% 295.41/187.92 tff(30600,plain,
% 295.41/187.92 ($false),
% 295.41/187.92 inference(unit_resolution,[status(thm)],[30599, 147, 30553, 30595, 30596])).
% 295.41/187.92 tff(30601,plain,((~node15(c_e_h_1, c_h, s21, s22)) | (~m_c_h_element_v_out(c_e_h_1, c_h, s22)) | m_c_h_element_v_out(c_e_h_1, c_h, s21)), inference(lemma,lemma(discharge,[]))).
% 295.41/187.92 tff(30602,plain,
% 295.41/187.92 (~node15(c_e_h_1, c_h, s21, s22)),
% 295.41/187.92 inference(unit_resolution,[status(thm)],[30601, 30595, 30553])).
% 295.41/187.92 tff(30603,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_h, s21)), introduced(assumption)).
% 295.41/187.92 tff(30604,assumption,(~node15(c_e_h_1, c_h, s21, s22)), introduced(assumption)).
% 295.41/187.92 tff(30605,plain,
% 295.41/187.92 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s21)) | m_c_h_element_v_in1(c_e_h_1, c_h, s21) | m_c_h_element_v_in2(c_e_h_1, c_h, s21))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s21)) | m_c_h_element_v_in1(c_e_h_1, c_h, s21) | m_c_h_element_v_in2(c_e_h_1, c_h, s21))),
% 295.41/187.92 inference(rewrite,[status(thm)],[])).
% 295.41/187.92 tff(30606,plain,
% 295.41/187.92 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_h, s21)) | m_c_h_element_v_in1(c_e_h_1, c_h, s21) | m_c_h_element_v_in2(c_e_h_1, c_h, s21))),
% 295.41/187.92 inference(quant_inst,[status(thm)],[])).
% 295.41/187.92 tff(30607,plain,
% 295.41/187.92 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_h, s21)) | m_c_h_element_v_in1(c_e_h_1, c_h, s21) | m_c_h_element_v_in2(c_e_h_1, c_h, s21)),
% 295.41/187.92 inference(modus_ponens,[status(thm)],[30606, 30605])).
% 295.41/187.92 tff(30608,plain,
% 295.41/187.92 ((~node16(c_e_h_1, c_h, s21)) | m_c_h_element_v_in1(c_e_h_1, c_h, s21)),
% 295.41/187.92 inference(unit_resolution,[status(thm)],[30607, 178, 30594])).
% 295.41/187.92 tff(30609,plain,
% 295.41/187.92 (~node16(c_e_h_1, c_h, s21)),
% 295.41/187.92 inference(unit_resolution,[status(thm)],[30608, 30603])).
% 295.41/187.92 tff(30610,plain,
% 295.41/187.92 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s21, s22)) | node19(c_e_h_1, c_h, s21, s22))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s21, s22)) | node19(c_e_h_1, c_h, s21, s22))),
% 295.41/187.93 inference(rewrite,[status(thm)],[])).
% 295.41/187.93 tff(30611,plain,
% 295.41/187.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s21, s22)) | node19(c_e_h_1, c_h, s21, s22))),
% 295.41/187.93 inference(quant_inst,[status(thm)],[])).
% 295.41/187.93 tff(30612,plain,
% 295.41/187.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s21, s22)) | node19(c_e_h_1, c_h, s21, s22)),
% 295.41/187.93 inference(modus_ponens,[status(thm)],[30611, 30610])).
% 295.41/187.93 tff(30613,plain,
% 295.41/187.93 (node19(c_e_h_1, c_h, s21, s22)),
% 295.41/187.93 inference(unit_resolution,[status(thm)],[30612, 190, 30340])).
% 295.41/187.93 tff(30614,plain,
% 295.41/187.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s21) | node15(c_e_h_1, c_h, s21, s22) | node14(c_e_h_1, c_h, s21, s22) | (~node19(c_e_h_1, c_h, s21, s22)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s21) | node15(c_e_h_1, c_h, s21, s22) | node14(c_e_h_1, c_h, s21, s22) | (~node19(c_e_h_1, c_h, s21, s22)))),
% 295.41/187.93 inference(rewrite,[status(thm)],[])).
% 295.41/187.93 tff(30615,plain,
% 295.41/187.93 ((node16(c_e_h_1, c_h, s21) | node14(c_e_h_1, c_h, s21, s22) | node15(c_e_h_1, c_h, s21, s22) | (~node19(c_e_h_1, c_h, s21, s22))) <=> (node16(c_e_h_1, c_h, s21) | node15(c_e_h_1, c_h, s21, s22) | node14(c_e_h_1, c_h, s21, s22) | (~node19(c_e_h_1, c_h, s21, s22)))),
% 295.41/187.93 inference(rewrite,[status(thm)],[])).
% 295.41/187.93 tff(30616,plain,
% 295.41/187.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s21) | node14(c_e_h_1, c_h, s21, s22) | node15(c_e_h_1, c_h, s21, s22) | (~node19(c_e_h_1, c_h, s21, s22)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s21) | node15(c_e_h_1, c_h, s21, s22) | node14(c_e_h_1, c_h, s21, s22) | (~node19(c_e_h_1, c_h, s21, s22))))),
% 295.41/187.93 inference(monotonicity,[status(thm)],[30615])).
% 295.41/187.93 tff(30617,plain,
% 295.41/187.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s21) | node14(c_e_h_1, c_h, s21, s22) | node15(c_e_h_1, c_h, s21, s22) | (~node19(c_e_h_1, c_h, s21, s22)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s21) | node15(c_e_h_1, c_h, s21, s22) | node14(c_e_h_1, c_h, s21, s22) | (~node19(c_e_h_1, c_h, s21, s22)))),
% 295.41/187.93 inference(transitivity,[status(thm)],[30616, 30614])).
% 295.41/187.93 tff(30618,plain,
% 295.41/187.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_h, s21) | node14(c_e_h_1, c_h, s21, s22) | node15(c_e_h_1, c_h, s21, s22) | (~node19(c_e_h_1, c_h, s21, s22)))),
% 295.41/187.93 inference(quant_inst,[status(thm)],[])).
% 295.41/187.93 tff(30619,plain,
% 295.41/187.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_h, s21) | node15(c_e_h_1, c_h, s21, s22) | node14(c_e_h_1, c_h, s21, s22) | (~node19(c_e_h_1, c_h, s21, s22))),
% 295.41/187.93 inference(modus_ponens,[status(thm)],[30618, 30617])).
% 295.41/187.93 tff(30620,plain,
% 295.41/187.93 (node16(c_e_h_1, c_h, s21) | node15(c_e_h_1, c_h, s21, s22) | node14(c_e_h_1, c_h, s21, s22)),
% 295.41/187.93 inference(unit_resolution,[status(thm)],[30619, 204, 30613])).
% 295.41/187.93 tff(30621,plain,
% 295.41/187.93 (node14(c_e_h_1, c_h, s21, s22)),
% 295.41/187.93 inference(unit_resolution,[status(thm)],[30620, 30609, 30604])).
% 295.41/187.93 tff(30622,plain,
% 295.41/187.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s22)) | m_c_h_element_v_in1(c_e_h_1, c_h, s21) | (~node14(c_e_h_1, c_h, s21, s22)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s22)) | m_c_h_element_v_in1(c_e_h_1, c_h, s21) | (~node14(c_e_h_1, c_h, s21, s22)))),
% 295.41/187.93 inference(rewrite,[status(thm)],[])).
% 295.41/187.93 tff(30623,plain,
% 295.41/187.93 (((~node14(c_e_h_1, c_h, s21, s22)) | m_c_h_element_v_in1(c_e_h_1, c_h, s21) | (~m_c_h_element_v_out(c_e_h_1, c_h, s22))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_h, s22)) | m_c_h_element_v_in1(c_e_h_1, c_h, s21) | (~node14(c_e_h_1, c_h, s21, s22)))),
% 295.41/187.93 inference(rewrite,[status(thm)],[])).
% 295.41/187.93 tff(30624,plain,
% 295.41/187.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s21, s22)) | m_c_h_element_v_in1(c_e_h_1, c_h, s21) | (~m_c_h_element_v_out(c_e_h_1, c_h, s22)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s22)) | m_c_h_element_v_in1(c_e_h_1, c_h, s21) | (~node14(c_e_h_1, c_h, s21, s22))))),
% 295.41/187.93 inference(monotonicity,[status(thm)],[30623])).
% 295.41/187.93 tff(30625,plain,
% 295.41/187.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s21, s22)) | m_c_h_element_v_in1(c_e_h_1, c_h, s21) | (~m_c_h_element_v_out(c_e_h_1, c_h, s22)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s22)) | m_c_h_element_v_in1(c_e_h_1, c_h, s21) | (~node14(c_e_h_1, c_h, s21, s22)))),
% 295.41/187.93 inference(transitivity,[status(thm)],[30624, 30622])).
% 295.41/187.93 tff(30626,plain,
% 295.41/187.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_h, s21, s22)) | m_c_h_element_v_in1(c_e_h_1, c_h, s21) | (~m_c_h_element_v_out(c_e_h_1, c_h, s22)))),
% 295.41/187.93 inference(quant_inst,[status(thm)],[])).
% 295.41/187.93 tff(30627,plain,
% 295.41/187.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s22)) | m_c_h_element_v_in1(c_e_h_1, c_h, s21) | (~node14(c_e_h_1, c_h, s21, s22))),
% 295.41/187.93 inference(modus_ponens,[status(thm)],[30626, 30625])).
% 295.41/187.93 tff(30628,plain,
% 295.41/187.93 ($false),
% 295.41/187.93 inference(unit_resolution,[status(thm)],[30627, 223, 30553, 30621, 30603])).
% 295.41/187.93 tff(30629,plain,(m_c_h_element_v_in1(c_e_h_1, c_h, s21) | (~m_c_h_element_v_out(c_e_h_1, c_h, s22)) | node15(c_e_h_1, c_h, s21, s22) | m_c_h_element_v_in2(c_e_h_1, c_h, s21)), inference(lemma,lemma(discharge,[]))).
% 295.41/187.93 tff(30630,plain,
% 295.41/187.93 (m_c_h_element_v_in1(c_e_h_1, c_h, s21)),
% 295.41/187.93 inference(unit_resolution,[status(thm)],[30629, 30602, 30594, 30553])).
% 295.41/187.93 tff(30631,plain,
% 295.41/187.93 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s21)) | m_c_h_element_v_in2(c_e_h_1, c_h, s21) | (~node17(c_e_h_1, c_h, s21)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s21)) | m_c_h_element_v_in2(c_e_h_1, c_h, s21) | (~node17(c_e_h_1, c_h, s21)))),
% 295.41/187.93 inference(rewrite,[status(thm)],[])).
% 295.41/187.93 tff(30632,plain,
% 295.41/187.93 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_h, s21)) | m_c_h_element_v_in2(c_e_h_1, c_h, s21) | (~node17(c_e_h_1, c_h, s21)))),
% 295.41/187.93 inference(quant_inst,[status(thm)],[])).
% 295.41/187.93 tff(30633,plain,
% 295.41/187.93 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_h, s21)) | m_c_h_element_v_in2(c_e_h_1, c_h, s21) | (~node17(c_e_h_1, c_h, s21))),
% 295.41/187.93 inference(modus_ponens,[status(thm)],[30632, 30631])).
% 295.41/187.93 tff(30634,plain,
% 295.41/187.93 ((~m_c_h_element_v_in1(c_e_h_1, c_h, s21)) | (~node17(c_e_h_1, c_h, s21))),
% 295.41/187.93 inference(unit_resolution,[status(thm)],[30633, 919, 30594])).
% 295.41/187.93 tff(30635,plain,
% 295.41/187.93 (~node17(c_e_h_1, c_h, s21)),
% 295.41/187.93 inference(unit_resolution,[status(thm)],[30634, 30630])).
% 295.41/187.93 tff(30636,plain,
% 295.41/187.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s21) | node18(c_e_h_1, c_h, s21, s22) | (~node19(c_e_h_1, c_h, s21, s22)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s21) | node18(c_e_h_1, c_h, s21, s22) | (~node19(c_e_h_1, c_h, s21, s22)))),
% 295.41/187.93 inference(rewrite,[status(thm)],[])).
% 295.41/187.93 tff(30637,plain,
% 295.41/187.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_h, s21) | node18(c_e_h_1, c_h, s21, s22) | (~node19(c_e_h_1, c_h, s21, s22)))),
% 295.41/187.93 inference(quant_inst,[status(thm)],[])).
% 295.41/187.93 tff(30638,plain,
% 295.41/187.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_h, s21) | node18(c_e_h_1, c_h, s21, s22) | (~node19(c_e_h_1, c_h, s21, s22))),
% 295.41/187.93 inference(modus_ponens,[status(thm)],[30637, 30636])).
% 295.41/187.93 tff(30639,plain,
% 295.41/187.93 (node17(c_e_h_1, c_h, s21) | node18(c_e_h_1, c_h, s21, s22)),
% 295.41/187.93 inference(unit_resolution,[status(thm)],[30638, 776, 30613])).
% 295.41/187.93 tff(30640,plain,
% 295.41/187.93 (node18(c_e_h_1, c_h, s21, s22)),
% 295.41/187.93 inference(unit_resolution,[status(thm)],[30639, 30635])).
% 295.41/187.93 tff(30641,plain,
% 295.41/187.93 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s22)) | m_c_h_element_v_out(c_e_h_1, c_h, s21) | (~node18(c_e_h_1, c_h, s21, s22)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s22)) | m_c_h_element_v_out(c_e_h_1, c_h, s21) | (~node18(c_e_h_1, c_h, s21, s22)))),
% 295.41/187.93 inference(rewrite,[status(thm)],[])).
% 295.41/187.93 tff(30642,plain,
% 295.41/187.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_h, s22)) | m_c_h_element_v_out(c_e_h_1, c_h, s21) | (~node18(c_e_h_1, c_h, s21, s22)))),
% 295.41/187.93 inference(quant_inst,[status(thm)],[])).
% 295.41/187.93 tff(30643,plain,
% 295.41/187.93 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_h, s22)) | m_c_h_element_v_out(c_e_h_1, c_h, s21) | (~node18(c_e_h_1, c_h, s21, s22))),
% 295.41/187.93 inference(modus_ponens,[status(thm)],[30642, 30641])).
% 295.41/187.93 tff(30644,plain,
% 295.41/187.93 ($false),
% 295.41/187.93 inference(unit_resolution,[status(thm)],[30643, 753, 30553, 30595, 30640])).
% 295.41/187.93 tff(30645,plain,(m_c_h_element_v_out(c_e_h_1, c_h, s21) | (~m_c_h_element_v_out(c_e_h_1, c_h, s22)) | m_c_h_element_v_in2(c_e_h_1, c_h, s21)), inference(lemma,lemma(discharge,[]))).
% 295.41/187.93 tff(30646,plain,
% 295.41/187.93 ($false),
% 295.41/187.93 inference(unit_resolution,[status(thm)],[30645, 30593, 30591, 30553])).
% 295.41/187.93 tff(30647,plain,(m_or_h_gate_v_out(c_e_h_1, c_j, s20) | (~m_c_h_element_v_out(c_e_h_1, c_h, s22)) | m_c_h_element_v_out(c_e_h_1, c_h, s20) | m_or_h_gate_v_in2(c_e_h_1, c_j, s20) | m_or_h_gate_v_in1(c_e_h_1, c_j, s20)), inference(lemma,lemma(discharge,[]))).
% 295.41/187.93 tff(30648,plain,
% 295.41/187.93 (~m_c_h_element_v_out(c_e_h_1, c_h, s22)),
% 295.41/187.93 inference(unit_resolution,[status(thm)],[30647, 30552, 29974, 30506, 30248])).
% 295.41/187.93 tff(30649,plain,
% 295.41/187.93 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s22)) | m_c_h_element_v_out(c_e_h_1, c_h, s22))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s22)) | m_c_h_element_v_out(c_e_h_1, c_h, s22))),
% 295.41/187.93 inference(rewrite,[status(thm)],[])).
% 295.41/187.93 tff(30650,plain,
% 295.41/187.93 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_i, s22)) | m_c_h_element_v_out(c_e_h_1, c_h, s22))),
% 295.41/187.94 inference(quant_inst,[status(thm)],[])).
% 295.41/187.94 tff(30651,plain,
% 295.41/187.94 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_i, X)) | m_c_h_element_v_out(I0, c_h, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s22)) | m_c_h_element_v_out(c_e_h_1, c_h, s22)),
% 295.41/187.94 inference(modus_ponens,[status(thm)],[30650, 30649])).
% 295.41/187.94 tff(30652,plain,
% 295.41/187.94 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s22)),
% 295.41/187.94 inference(unit_resolution,[status(thm)],[30651, 619, 30648])).
% 295.41/187.94 tff(30653,plain,
% 295.41/187.94 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s22)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s22))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s22)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s22))),
% 295.41/187.94 inference(rewrite,[status(thm)],[])).
% 295.41/187.94 tff(30654,plain,
% 295.41/187.94 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_i, s22)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s22))),
% 295.41/187.94 inference(quant_inst,[status(thm)],[])).
% 295.41/187.94 tff(30655,plain,
% 295.41/187.94 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_i, s22)) | m_and_h_gate_v_in1(c_e_h_1, c_i, s22)),
% 295.41/187.94 inference(modus_ponens,[status(thm)],[30654, 30653])).
% 295.41/187.94 tff(30656,plain,
% 295.41/187.94 (~node20(c_e_h_1, c_i, s22)),
% 295.41/187.94 inference(unit_resolution,[status(thm)],[30655, 38, 30652])).
% 295.41/187.94 tff(30657,assumption,(~node20(c_e_h_1, c_i, s22)), introduced(assumption)).
% 295.41/187.94 tff(30658,assumption,(m_and_h_gate_v_out(c_e_h_1, c_i, s23)), introduced(assumption)).
% 295.41/187.94 tff(30659,assumption,(node21(c_e_h_1, c_i, s22, s23)), introduced(assumption)).
% 295.41/187.94 tff(30660,plain,
% 295.41/187.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s22) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s23)) | (~node21(c_e_h_1, c_i, s22, s23)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s22) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s23)) | (~node21(c_e_h_1, c_i, s22, s23)))),
% 295.41/187.94 inference(rewrite,[status(thm)],[])).
% 295.41/187.94 tff(30661,plain,
% 295.41/187.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_i, s22) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s23)) | (~node21(c_e_h_1, c_i, s22, s23)))),
% 295.41/187.94 inference(quant_inst,[status(thm)],[])).
% 295.41/187.94 tff(30662,plain,
% 295.41/187.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_i, s22) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s23)) | (~node21(c_e_h_1, c_i, s22, s23))),
% 295.41/187.94 inference(modus_ponens,[status(thm)],[30661, 30660])).
% 295.41/187.94 tff(30663,plain,
% 295.41/187.94 ($false),
% 295.41/187.94 inference(unit_resolution,[status(thm)],[30662, 52, 30658, 30659, 30657])).
% 295.41/187.94 tff(30664,plain,((~node21(c_e_h_1, c_i, s22, s23)) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s23)) | node20(c_e_h_1, c_i, s22)), inference(lemma,lemma(discharge,[]))).
% 295.41/187.94 tff(30665,plain,
% 295.41/187.94 (~node21(c_e_h_1, c_i, s22, s23)),
% 295.41/187.94 inference(unit_resolution,[status(thm)],[30664, 30658, 30657])).
% 295.41/187.94 tff(30666,plain,
% 295.41/187.94 (succ(s22, s23) <=> succ(s22, s23)),
% 295.41/187.94 inference(rewrite,[status(thm)],[])).
% 295.41/187.94 tff(30667,axiom,(succ(s22, s23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound23')).
% 295.41/187.94 tff(30668,plain,
% 295.41/187.94 (succ(s22, s23)),
% 295.41/187.94 inference(modus_ponens,[status(thm)],[30667, 30666])).
% 295.41/187.94 tff(30669,plain,
% 295.41/187.94 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s22, s23)) | trans(s22, s23))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s22, s23)) | trans(s22, s23))),
% 295.41/187.94 inference(rewrite,[status(thm)],[])).
% 295.41/187.94 tff(30670,plain,
% 295.41/187.94 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s22, s23)) | trans(s22, s23))),
% 295.41/187.94 inference(quant_inst,[status(thm)],[])).
% 295.41/187.94 tff(30671,plain,
% 295.41/187.94 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s22, s23)) | trans(s22, s23)),
% 295.41/187.94 inference(modus_ponens,[status(thm)],[30670, 30669])).
% 295.41/187.94 tff(30672,plain,
% 295.41/187.94 (trans(s22, s23)),
% 295.41/187.94 inference(unit_resolution,[status(thm)],[30671, 30668, 65])).
% 295.41/187.94 tff(30673,plain,
% 295.41/187.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s22, s23)) | node21(c_e_h_1, c_i, s22, s23) | node22(c_e_h_1, c_i, s22, s23))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s22, s23)) | node21(c_e_h_1, c_i, s22, s23) | node22(c_e_h_1, c_i, s22, s23))),
% 295.41/187.94 inference(rewrite,[status(thm)],[])).
% 295.41/187.94 tff(30674,plain,
% 295.41/187.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s22, s23)) | node21(c_e_h_1, c_i, s22, s23) | node22(c_e_h_1, c_i, s22, s23))),
% 295.41/187.94 inference(quant_inst,[status(thm)],[])).
% 295.41/187.94 tff(30675,plain,
% 295.41/187.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s22, s23)) | node21(c_e_h_1, c_i, s22, s23) | node22(c_e_h_1, c_i, s22, s23)),
% 295.41/187.94 inference(modus_ponens,[status(thm)],[30674, 30673])).
% 295.41/187.94 tff(30676,plain,
% 295.41/187.94 (node21(c_e_h_1, c_i, s22, s23) | node22(c_e_h_1, c_i, s22, s23)),
% 295.41/187.94 inference(unit_resolution,[status(thm)],[30675, 82, 30672])).
% 295.41/187.94 tff(30677,plain,
% 295.41/187.94 (node22(c_e_h_1, c_i, s22, s23)),
% 295.41/187.94 inference(unit_resolution,[status(thm)],[30676, 30665])).
% 295.41/187.94 tff(30678,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_i, s22)), introduced(assumption)).
% 295.41/187.94 tff(30679,plain,
% 295.41/187.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s23)) | (~node22(c_e_h_1, c_i, s22, s23)) | m_and_h_gate_v_out(c_e_h_1, c_i, s22))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s23)) | (~node22(c_e_h_1, c_i, s22, s23)) | m_and_h_gate_v_out(c_e_h_1, c_i, s22))),
% 295.41/187.94 inference(rewrite,[status(thm)],[])).
% 295.41/187.94 tff(30680,plain,
% 295.41/187.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s23)) | (~node22(c_e_h_1, c_i, s22, s23)) | m_and_h_gate_v_out(c_e_h_1, c_i, s22))),
% 295.41/187.94 inference(quant_inst,[status(thm)],[])).
% 295.41/187.94 tff(30681,plain,
% 295.41/187.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s23)) | (~node22(c_e_h_1, c_i, s22, s23)) | m_and_h_gate_v_out(c_e_h_1, c_i, s22)),
% 295.41/187.94 inference(modus_ponens,[status(thm)],[30680, 30679])).
% 295.41/187.94 tff(30682,plain,
% 295.41/187.94 ($false),
% 295.41/187.94 inference(unit_resolution,[status(thm)],[30681, 108, 30678, 30658, 30677])).
% 295.41/187.94 tff(30683,plain,((~m_and_h_gate_v_out(c_e_h_1, c_i, s23)) | m_and_h_gate_v_out(c_e_h_1, c_i, s22) | node20(c_e_h_1, c_i, s22)), inference(lemma,lemma(discharge,[]))).
% 295.41/187.94 tff(30684,plain,
% 295.41/187.94 (~m_and_h_gate_v_out(c_e_h_1, c_i, s23)),
% 295.41/187.94 inference(unit_resolution,[status(thm)],[30683, 30656, 30380])).
% 295.41/187.94 tff(30685,plain,
% 295.41/187.94 (~m_c_h_element_v_out(c_e_h_1, c_h, s18)),
% 295.41/187.94 inference(unit_resolution,[status(thm)],[29836, 29764, 29827])).
% 295.41/187.94 tff(30686,plain,
% 295.41/187.94 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s18)),
% 295.41/187.94 inference(unit_resolution,[status(thm)],[29987, 619, 30685])).
% 295.41/187.94 tff(30687,plain,
% 295.41/187.94 (~node20(c_e_h_1, c_i, s18)),
% 295.41/187.94 inference(unit_resolution,[status(thm)],[29991, 38, 30686])).
% 295.41/187.94 tff(30688,plain,
% 295.41/187.94 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s17)),
% 295.41/187.94 inference(unit_resolution,[status(thm)],[26734, 619, 29764])).
% 295.41/187.94 tff(30689,plain,
% 295.41/187.94 (~node20(c_e_h_1, c_i, s17)),
% 295.41/187.94 inference(unit_resolution,[status(thm)],[26738, 38, 30688])).
% 295.41/187.94 tff(30690,plain,
% 295.41/187.94 (~m_and_h_gate_v_out(c_e_h_1, c_i, s18)),
% 295.41/187.94 inference(unit_resolution,[status(thm)],[26759, 30689, 26111])).
% 295.41/187.94 tff(30691,plain,
% 295.41/187.94 ($false),
% 295.41/187.94 inference(unit_resolution,[status(thm)],[30014, 30690, 30687, 29994])).
% 295.41/187.94 tff(30692,plain,(m_c_h_element_v_out(c_e_h_1, c_h, s17) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s19)) | m_and_h_gate_v_out(c_e_h_1, c_i, s17) | m_c_h_element_v_in2(c_e_h_1, c_h, s17)), inference(lemma,lemma(discharge,[]))).
% 295.41/187.94 tff(30693,plain,
% 295.41/187.94 (~m_and_h_gate_v_out(c_e_h_1, c_i, s19)),
% 295.41/187.94 inference(unit_resolution,[status(thm)],[30692, 29762, 26731, 26740])).
% 295.41/187.94 tff(30694,assumption,(m_c_h_element_v_in2(c_e_h_1, c_e, s19)), introduced(assumption)).
% 295.41/187.94 tff(30695,plain,
% 295.41/187.94 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s19)) | m_and_h_gate_v_out(c_e_h_1, c_i, s19))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s19)) | m_and_h_gate_v_out(c_e_h_1, c_i, s19))),
% 295.41/187.94 inference(rewrite,[status(thm)],[])).
% 295.41/187.94 tff(30696,plain,
% 295.41/187.94 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s19)) | m_and_h_gate_v_out(c_e_h_1, c_i, s19))),
% 295.41/187.94 inference(quant_inst,[status(thm)],[])).
% 295.41/187.94 tff(30697,plain,
% 295.41/187.94 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s19)) | m_and_h_gate_v_out(c_e_h_1, c_i, s19)),
% 295.41/187.94 inference(modus_ponens,[status(thm)],[30696, 30695])).
% 295.41/187.94 tff(30698,plain,
% 295.41/187.94 ($false),
% 295.41/187.94 inference(unit_resolution,[status(thm)],[30697, 164, 30694, 30016])).
% 295.41/187.94 tff(30699,plain,((~m_c_h_element_v_in2(c_e_h_1, c_e, s19)) | m_and_h_gate_v_out(c_e_h_1, c_i, s19)), inference(lemma,lemma(discharge,[]))).
% 295.41/187.94 tff(30700,plain,
% 295.41/187.94 (~m_c_h_element_v_in2(c_e_h_1, c_e, s19)),
% 295.41/187.94 inference(unit_resolution,[status(thm)],[30699, 30693])).
% 295.41/187.94 tff(30701,assumption,(~m_c_h_element_v_out(c_e_h_1, c_e, s19)), introduced(assumption)).
% 295.41/187.94 tff(30702,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s20)), introduced(assumption)).
% 295.41/187.94 tff(30703,assumption,(node18(c_e_h_1, c_e, s19, s20)), introduced(assumption)).
% 295.41/187.94 tff(30704,plain,
% 295.41/187.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s19) | (~m_c_h_element_v_out(c_e_h_1, c_e, s20)) | (~node18(c_e_h_1, c_e, s19, s20)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s19) | (~m_c_h_element_v_out(c_e_h_1, c_e, s20)) | (~node18(c_e_h_1, c_e, s19, s20)))),
% 295.41/187.94 inference(rewrite,[status(thm)],[])).
% 295.41/187.94 tff(30705,plain,
% 295.41/187.94 (((~m_c_h_element_v_out(c_e_h_1, c_e, s20)) | m_c_h_element_v_out(c_e_h_1, c_e, s19) | (~node18(c_e_h_1, c_e, s19, s20))) <=> (m_c_h_element_v_out(c_e_h_1, c_e, s19) | (~m_c_h_element_v_out(c_e_h_1, c_e, s20)) | (~node18(c_e_h_1, c_e, s19, s20)))),
% 295.41/187.94 inference(rewrite,[status(thm)],[])).
% 295.41/187.94 tff(30706,plain,
% 295.41/187.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s20)) | m_c_h_element_v_out(c_e_h_1, c_e, s19) | (~node18(c_e_h_1, c_e, s19, s20)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s19) | (~m_c_h_element_v_out(c_e_h_1, c_e, s20)) | (~node18(c_e_h_1, c_e, s19, s20))))),
% 295.41/187.94 inference(monotonicity,[status(thm)],[30705])).
% 295.41/187.94 tff(30707,plain,
% 295.41/187.94 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s20)) | m_c_h_element_v_out(c_e_h_1, c_e, s19) | (~node18(c_e_h_1, c_e, s19, s20)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s19) | (~m_c_h_element_v_out(c_e_h_1, c_e, s20)) | (~node18(c_e_h_1, c_e, s19, s20)))),
% 295.41/187.94 inference(transitivity,[status(thm)],[30706, 30704])).
% 295.41/187.94 tff(30708,plain,
% 295.41/187.94 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s20)) | m_c_h_element_v_out(c_e_h_1, c_e, s19) | (~node18(c_e_h_1, c_e, s19, s20)))),
% 295.41/187.95 inference(quant_inst,[status(thm)],[])).
% 295.41/187.95 tff(30709,plain,
% 295.41/187.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s19) | (~m_c_h_element_v_out(c_e_h_1, c_e, s20)) | (~node18(c_e_h_1, c_e, s19, s20))),
% 295.41/187.95 inference(modus_ponens,[status(thm)],[30708, 30707])).
% 295.41/187.95 tff(30710,plain,
% 295.41/187.95 ($false),
% 295.41/187.95 inference(unit_resolution,[status(thm)],[30709, 753, 30702, 30701, 30703])).
% 295.41/187.95 tff(30711,plain,((~node18(c_e_h_1, c_e, s19, s20)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s20)) | m_c_h_element_v_out(c_e_h_1, c_e, s19)), inference(lemma,lemma(discharge,[]))).
% 295.41/187.95 tff(30712,plain,
% 295.41/187.95 (~node18(c_e_h_1, c_e, s19, s20)),
% 295.41/187.95 inference(unit_resolution,[status(thm)],[30711, 30702, 30701])).
% 295.41/187.95 tff(30713,plain,
% 295.41/187.95 (~node18(c_e_h_1, c_e, s19, s20)),
% 295.41/187.95 inference(unit_resolution,[status(thm)],[30711, 30701, 30702])).
% 295.41/187.95 tff(30714,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_e, s19)), introduced(assumption)).
% 295.41/187.95 tff(30715,assumption,(node15(c_e_h_1, c_e, s19, s20)), introduced(assumption)).
% 295.41/187.95 tff(30716,plain,
% 295.41/187.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s20)) | (~node15(c_e_h_1, c_e, s19, s20)) | m_c_h_element_v_out(c_e_h_1, c_e, s19))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s20)) | (~node15(c_e_h_1, c_e, s19, s20)) | m_c_h_element_v_out(c_e_h_1, c_e, s19))),
% 295.41/187.95 inference(rewrite,[status(thm)],[])).
% 295.41/187.95 tff(30717,plain,
% 295.41/187.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s20)) | (~node15(c_e_h_1, c_e, s19, s20)) | m_c_h_element_v_out(c_e_h_1, c_e, s19))),
% 295.41/187.95 inference(quant_inst,[status(thm)],[])).
% 295.41/187.95 tff(30718,plain,
% 295.41/187.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s20)) | (~node15(c_e_h_1, c_e, s19, s20)) | m_c_h_element_v_out(c_e_h_1, c_e, s19)),
% 295.41/187.95 inference(modus_ponens,[status(thm)],[30717, 30716])).
% 295.41/187.95 tff(30719,plain,
% 295.41/187.95 ($false),
% 295.41/187.95 inference(unit_resolution,[status(thm)],[30718, 147, 30702, 30701, 30715])).
% 295.41/187.95 tff(30720,plain,((~node15(c_e_h_1, c_e, s19, s20)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s20)) | m_c_h_element_v_out(c_e_h_1, c_e, s19)), inference(lemma,lemma(discharge,[]))).
% 295.41/187.95 tff(30721,plain,
% 295.41/187.95 (~node15(c_e_h_1, c_e, s19, s20)),
% 295.41/187.95 inference(unit_resolution,[status(thm)],[30720, 30701, 30702])).
% 295.41/187.95 tff(30722,assumption,(~node15(c_e_h_1, c_e, s19, s20)), introduced(assumption)).
% 295.41/187.95 tff(30723,assumption,(node17(c_e_h_1, c_e, s19)), introduced(assumption)).
% 295.41/187.95 tff(30724,plain,
% 295.41/187.95 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s19)) | m_c_h_element_v_in1(c_e_h_1, c_e, s19) | (~node17(c_e_h_1, c_e, s19)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s19)) | m_c_h_element_v_in1(c_e_h_1, c_e, s19) | (~node17(c_e_h_1, c_e, s19)))),
% 295.41/187.95 inference(rewrite,[status(thm)],[])).
% 295.41/187.95 tff(30725,plain,
% 295.41/187.95 ((m_c_h_element_v_in1(c_e_h_1, c_e, s19) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s19)) | (~node17(c_e_h_1, c_e, s19))) <=> ((~m_c_h_element_v_in2(c_e_h_1, c_e, s19)) | m_c_h_element_v_in1(c_e_h_1, c_e, s19) | (~node17(c_e_h_1, c_e, s19)))),
% 295.41/187.95 inference(rewrite,[status(thm)],[])).
% 295.41/187.95 tff(30726,plain,
% 295.41/187.95 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s19) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s19)) | (~node17(c_e_h_1, c_e, s19)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s19)) | m_c_h_element_v_in1(c_e_h_1, c_e, s19) | (~node17(c_e_h_1, c_e, s19))))),
% 295.41/187.95 inference(monotonicity,[status(thm)],[30725])).
% 295.41/187.95 tff(30727,plain,
% 295.41/187.95 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s19) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s19)) | (~node17(c_e_h_1, c_e, s19)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s19)) | m_c_h_element_v_in1(c_e_h_1, c_e, s19) | (~node17(c_e_h_1, c_e, s19)))),
% 295.41/187.95 inference(transitivity,[status(thm)],[30726, 30724])).
% 295.41/187.95 tff(30728,plain,
% 295.41/187.95 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s19) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s19)) | (~node17(c_e_h_1, c_e, s19)))),
% 295.41/187.95 inference(quant_inst,[status(thm)],[])).
% 295.41/187.95 tff(30729,plain,
% 295.41/187.95 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s19)) | m_c_h_element_v_in1(c_e_h_1, c_e, s19) | (~node17(c_e_h_1, c_e, s19))),
% 295.41/187.95 inference(modus_ponens,[status(thm)],[30728, 30727])).
% 295.41/187.95 tff(30730,plain,
% 295.41/187.95 ((~m_c_h_element_v_in2(c_e_h_1, c_e, s19)) | m_c_h_element_v_in1(c_e_h_1, c_e, s19)),
% 295.41/187.95 inference(unit_resolution,[status(thm)],[30729, 859, 30723])).
% 295.41/187.95 tff(30731,plain,
% 295.41/187.95 (~m_c_h_element_v_in2(c_e_h_1, c_e, s19)),
% 295.41/187.95 inference(unit_resolution,[status(thm)],[30730, 30714])).
% 295.41/187.95 tff(30732,plain,
% 295.41/187.95 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s19)) | m_c_h_element_v_in1(c_e_h_1, c_e, s19) | m_c_h_element_v_in2(c_e_h_1, c_e, s19))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s19)) | m_c_h_element_v_in1(c_e_h_1, c_e, s19) | m_c_h_element_v_in2(c_e_h_1, c_e, s19))),
% 295.41/187.95 inference(rewrite,[status(thm)],[])).
% 295.41/187.95 tff(30733,plain,
% 295.41/187.95 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s19)) | m_c_h_element_v_in1(c_e_h_1, c_e, s19) | m_c_h_element_v_in2(c_e_h_1, c_e, s19))),
% 295.41/187.95 inference(quant_inst,[status(thm)],[])).
% 295.41/187.95 tff(30734,plain,
% 295.41/187.95 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s19)) | m_c_h_element_v_in1(c_e_h_1, c_e, s19) | m_c_h_element_v_in2(c_e_h_1, c_e, s19)),
% 295.41/187.95 inference(modus_ponens,[status(thm)],[30733, 30732])).
% 295.41/187.95 tff(30735,plain,
% 295.41/187.95 (~node16(c_e_h_1, c_e, s19)),
% 295.41/187.95 inference(unit_resolution,[status(thm)],[30734, 178, 30731, 30714])).
% 295.41/187.95 tff(30736,plain,
% 295.41/187.95 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s19, s20)) | node19(c_e_h_1, c_e, s19, s20))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s19, s20)) | node19(c_e_h_1, c_e, s19, s20))),
% 295.41/187.95 inference(rewrite,[status(thm)],[])).
% 295.41/187.95 tff(30737,plain,
% 295.41/187.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s19, s20)) | node19(c_e_h_1, c_e, s19, s20))),
% 295.41/187.95 inference(quant_inst,[status(thm)],[])).
% 295.41/187.95 tff(30738,plain,
% 295.41/187.95 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s19, s20)) | node19(c_e_h_1, c_e, s19, s20)),
% 295.41/187.95 inference(modus_ponens,[status(thm)],[30737, 30736])).
% 295.41/187.95 tff(30739,plain,
% 295.41/187.95 (node19(c_e_h_1, c_e, s19, s20)),
% 295.41/187.95 inference(unit_resolution,[status(thm)],[30738, 190, 29925])).
% 295.41/187.96 tff(30740,plain,
% 295.41/187.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_e, s19, s20)) | node15(c_e_h_1, c_e, s19, s20) | node14(c_e_h_1, c_e, s19, s20) | node16(c_e_h_1, c_e, s19))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s19, s20)) | node15(c_e_h_1, c_e, s19, s20) | node14(c_e_h_1, c_e, s19, s20) | node16(c_e_h_1, c_e, s19))),
% 295.41/187.96 inference(rewrite,[status(thm)],[])).
% 295.41/187.96 tff(30741,plain,
% 295.41/187.96 ((node16(c_e_h_1, c_e, s19) | node14(c_e_h_1, c_e, s19, s20) | node15(c_e_h_1, c_e, s19, s20) | (~node19(c_e_h_1, c_e, s19, s20))) <=> ((~node19(c_e_h_1, c_e, s19, s20)) | node15(c_e_h_1, c_e, s19, s20) | node14(c_e_h_1, c_e, s19, s20) | node16(c_e_h_1, c_e, s19))),
% 295.41/187.96 inference(rewrite,[status(thm)],[])).
% 295.41/187.96 tff(30742,plain,
% 295.41/187.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s19) | node14(c_e_h_1, c_e, s19, s20) | node15(c_e_h_1, c_e, s19, s20) | (~node19(c_e_h_1, c_e, s19, s20)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_e, s19, s20)) | node15(c_e_h_1, c_e, s19, s20) | node14(c_e_h_1, c_e, s19, s20) | node16(c_e_h_1, c_e, s19)))),
% 295.41/187.96 inference(monotonicity,[status(thm)],[30741])).
% 295.41/187.96 tff(30743,plain,
% 295.41/187.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s19) | node14(c_e_h_1, c_e, s19, s20) | node15(c_e_h_1, c_e, s19, s20) | (~node19(c_e_h_1, c_e, s19, s20)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s19, s20)) | node15(c_e_h_1, c_e, s19, s20) | node14(c_e_h_1, c_e, s19, s20) | node16(c_e_h_1, c_e, s19))),
% 295.41/187.96 inference(transitivity,[status(thm)],[30742, 30740])).
% 295.41/187.96 tff(30744,plain,
% 295.41/187.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s19) | node14(c_e_h_1, c_e, s19, s20) | node15(c_e_h_1, c_e, s19, s20) | (~node19(c_e_h_1, c_e, s19, s20)))),
% 295.41/187.96 inference(quant_inst,[status(thm)],[])).
% 295.41/187.96 tff(30745,plain,
% 295.41/187.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s19, s20)) | node15(c_e_h_1, c_e, s19, s20) | node14(c_e_h_1, c_e, s19, s20) | node16(c_e_h_1, c_e, s19)),
% 295.41/187.96 inference(modus_ponens,[status(thm)],[30744, 30743])).
% 295.41/187.96 tff(30746,plain,
% 295.41/187.96 (node15(c_e_h_1, c_e, s19, s20) | node14(c_e_h_1, c_e, s19, s20) | node16(c_e_h_1, c_e, s19)),
% 295.41/187.96 inference(unit_resolution,[status(thm)],[30745, 204, 30739])).
% 295.41/187.96 tff(30747,plain,
% 295.41/187.96 (node14(c_e_h_1, c_e, s19, s20)),
% 295.41/187.96 inference(unit_resolution,[status(thm)],[30746, 30735, 30722])).
% 295.41/187.96 tff(30748,plain,
% 295.41/187.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s20)) | m_c_h_element_v_in1(c_e_h_1, c_e, s19) | (~node14(c_e_h_1, c_e, s19, s20)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s20)) | m_c_h_element_v_in1(c_e_h_1, c_e, s19) | (~node14(c_e_h_1, c_e, s19, s20)))),
% 295.41/187.96 inference(rewrite,[status(thm)],[])).
% 295.41/187.96 tff(30749,plain,
% 295.41/187.96 (((~node14(c_e_h_1, c_e, s19, s20)) | m_c_h_element_v_in1(c_e_h_1, c_e, s19) | (~m_c_h_element_v_out(c_e_h_1, c_e, s20))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_e, s20)) | m_c_h_element_v_in1(c_e_h_1, c_e, s19) | (~node14(c_e_h_1, c_e, s19, s20)))),
% 295.41/187.96 inference(rewrite,[status(thm)],[])).
% 295.41/187.96 tff(30750,plain,
% 295.41/187.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s19, s20)) | m_c_h_element_v_in1(c_e_h_1, c_e, s19) | (~m_c_h_element_v_out(c_e_h_1, c_e, s20)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s20)) | m_c_h_element_v_in1(c_e_h_1, c_e, s19) | (~node14(c_e_h_1, c_e, s19, s20))))),
% 295.41/187.96 inference(monotonicity,[status(thm)],[30749])).
% 295.41/187.96 tff(30751,plain,
% 295.41/187.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s19, s20)) | m_c_h_element_v_in1(c_e_h_1, c_e, s19) | (~m_c_h_element_v_out(c_e_h_1, c_e, s20)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s20)) | m_c_h_element_v_in1(c_e_h_1, c_e, s19) | (~node14(c_e_h_1, c_e, s19, s20)))),
% 295.41/187.96 inference(transitivity,[status(thm)],[30750, 30748])).
% 295.41/187.96 tff(30752,plain,
% 295.41/187.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s19, s20)) | m_c_h_element_v_in1(c_e_h_1, c_e, s19) | (~m_c_h_element_v_out(c_e_h_1, c_e, s20)))),
% 295.41/187.96 inference(quant_inst,[status(thm)],[])).
% 295.41/187.96 tff(30753,plain,
% 295.41/187.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s20)) | m_c_h_element_v_in1(c_e_h_1, c_e, s19) | (~node14(c_e_h_1, c_e, s19, s20))),
% 295.41/187.96 inference(modus_ponens,[status(thm)],[30752, 30751])).
% 295.41/187.96 tff(30754,plain,
% 295.41/187.96 ($false),
% 295.41/187.96 inference(unit_resolution,[status(thm)],[30753, 223, 30702, 30747, 30714])).
% 295.41/187.96 tff(30755,plain,(m_c_h_element_v_in1(c_e_h_1, c_e, s19) | (~m_c_h_element_v_out(c_e_h_1, c_e, s20)) | node15(c_e_h_1, c_e, s19, s20) | (~node17(c_e_h_1, c_e, s19))), inference(lemma,lemma(discharge,[]))).
% 295.41/187.96 tff(30756,plain,
% 295.41/187.96 (~node17(c_e_h_1, c_e, s19)),
% 295.41/187.96 inference(unit_resolution,[status(thm)],[30755, 30721, 30714, 30702])).
% 295.41/187.96 tff(30757,plain,
% 295.41/187.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_e, s19, s20)) | node18(c_e_h_1, c_e, s19, s20) | node17(c_e_h_1, c_e, s19))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s19, s20)) | node18(c_e_h_1, c_e, s19, s20) | node17(c_e_h_1, c_e, s19))),
% 295.41/187.96 inference(rewrite,[status(thm)],[])).
% 295.41/187.96 tff(30758,plain,
% 295.41/187.96 ((node17(c_e_h_1, c_e, s19) | node18(c_e_h_1, c_e, s19, s20) | (~node19(c_e_h_1, c_e, s19, s20))) <=> ((~node19(c_e_h_1, c_e, s19, s20)) | node18(c_e_h_1, c_e, s19, s20) | node17(c_e_h_1, c_e, s19))),
% 295.41/187.96 inference(rewrite,[status(thm)],[])).
% 295.41/187.96 tff(30759,plain,
% 295.41/187.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s19) | node18(c_e_h_1, c_e, s19, s20) | (~node19(c_e_h_1, c_e, s19, s20)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_e, s19, s20)) | node18(c_e_h_1, c_e, s19, s20) | node17(c_e_h_1, c_e, s19)))),
% 295.41/187.96 inference(monotonicity,[status(thm)],[30758])).
% 295.41/187.96 tff(30760,plain,
% 295.41/187.96 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s19) | node18(c_e_h_1, c_e, s19, s20) | (~node19(c_e_h_1, c_e, s19, s20)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s19, s20)) | node18(c_e_h_1, c_e, s19, s20) | node17(c_e_h_1, c_e, s19))),
% 295.41/187.96 inference(transitivity,[status(thm)],[30759, 30757])).
% 295.41/187.96 tff(30761,plain,
% 295.41/187.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s19) | node18(c_e_h_1, c_e, s19, s20) | (~node19(c_e_h_1, c_e, s19, s20)))),
% 295.41/187.96 inference(quant_inst,[status(thm)],[])).
% 295.41/187.96 tff(30762,plain,
% 295.41/187.96 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s19, s20)) | node18(c_e_h_1, c_e, s19, s20) | node17(c_e_h_1, c_e, s19)),
% 295.41/187.96 inference(modus_ponens,[status(thm)],[30761, 30760])).
% 295.41/187.96 tff(30763,plain,
% 295.41/187.96 (node18(c_e_h_1, c_e, s19, s20) | node17(c_e_h_1, c_e, s19)),
% 295.41/187.96 inference(unit_resolution,[status(thm)],[30762, 776, 30739])).
% 295.41/187.96 tff(30764,plain,
% 295.41/187.96 ($false),
% 295.41/187.96 inference(unit_resolution,[status(thm)],[30763, 30756, 30713])).
% 295.41/187.96 tff(30765,plain,(m_c_h_element_v_out(c_e_h_1, c_e, s19) | m_c_h_element_v_in1(c_e_h_1, c_e, s19) | (~m_c_h_element_v_out(c_e_h_1, c_e, s20))), inference(lemma,lemma(discharge,[]))).
% 295.41/187.96 tff(30766,plain,
% 295.41/187.96 (m_c_h_element_v_in1(c_e_h_1, c_e, s19)),
% 295.41/187.96 inference(unit_resolution,[status(thm)],[30765, 30702, 30701])).
% 295.41/187.96 tff(30767,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_e, s19)), introduced(assumption)).
% 295.41/187.96 tff(30768,plain,
% 295.41/187.96 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_e, s19)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s19)) | m_c_h_element_v_in2(c_e_h_1, c_e, s19))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s19)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s19)) | m_c_h_element_v_in2(c_e_h_1, c_e, s19))),
% 295.41/187.96 inference(rewrite,[status(thm)],[])).
% 295.41/187.96 tff(30769,plain,
% 295.41/187.96 (((~m_c_h_element_v_in1(c_e_h_1, c_e, s19)) | m_c_h_element_v_in2(c_e_h_1, c_e, s19) | (~node17(c_e_h_1, c_e, s19))) <=> ((~node17(c_e_h_1, c_e, s19)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s19)) | m_c_h_element_v_in2(c_e_h_1, c_e, s19))),
% 295.41/187.96 inference(rewrite,[status(thm)],[])).
% 295.41/187.96 tff(30770,plain,
% 295.41/187.96 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s19)) | m_c_h_element_v_in2(c_e_h_1, c_e, s19) | (~node17(c_e_h_1, c_e, s19)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_e, s19)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s19)) | m_c_h_element_v_in2(c_e_h_1, c_e, s19)))),
% 295.41/187.96 inference(monotonicity,[status(thm)],[30769])).
% 295.41/187.96 tff(30771,plain,
% 295.41/187.96 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s19)) | m_c_h_element_v_in2(c_e_h_1, c_e, s19) | (~node17(c_e_h_1, c_e, s19)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s19)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s19)) | m_c_h_element_v_in2(c_e_h_1, c_e, s19))),
% 295.41/187.96 inference(transitivity,[status(thm)],[30770, 30768])).
% 295.41/187.96 tff(30772,plain,
% 295.41/187.96 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s19)) | m_c_h_element_v_in2(c_e_h_1, c_e, s19) | (~node17(c_e_h_1, c_e, s19)))),
% 295.41/187.96 inference(quant_inst,[status(thm)],[])).
% 295.41/187.96 tff(30773,plain,
% 295.41/187.96 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_e, s19)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s19)) | m_c_h_element_v_in2(c_e_h_1, c_e, s19)),
% 295.41/187.96 inference(modus_ponens,[status(thm)],[30772, 30771])).
% 295.41/187.96 tff(30774,plain,
% 295.41/187.96 ((~node17(c_e_h_1, c_e, s19)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s19))),
% 295.41/187.96 inference(unit_resolution,[status(thm)],[30773, 919, 30767])).
% 295.41/187.96 tff(30775,plain,
% 295.41/187.96 (~node17(c_e_h_1, c_e, s19)),
% 295.41/187.96 inference(unit_resolution,[status(thm)],[30774, 30766])).
% 295.41/187.96 tff(30776,plain,
% 295.41/187.96 ($false),
% 295.41/187.96 inference(unit_resolution,[status(thm)],[30763, 30775, 30712])).
% 295.41/187.96 tff(30777,plain,((~m_c_h_element_v_out(c_e_h_1, c_e, s20)) | m_c_h_element_v_in2(c_e_h_1, c_e, s19) | m_c_h_element_v_out(c_e_h_1, c_e, s19)), inference(lemma,lemma(discharge,[]))).
% 295.41/187.97 tff(30778,plain,
% 295.41/187.97 (~m_c_h_element_v_out(c_e_h_1, c_e, s20)),
% 295.41/187.97 inference(unit_resolution,[status(thm)],[30777, 30700, 26862])).
% 295.41/187.97 tff(30779,assumption,(m_c_h_element_v_in2(c_e_h_1, c_e, s20)), introduced(assumption)).
% 295.41/187.97 tff(30780,plain,
% 295.41/187.97 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s20)) | m_and_h_gate_v_out(c_e_h_1, c_i, s20))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s20)) | m_and_h_gate_v_out(c_e_h_1, c_i, s20))),
% 295.41/187.97 inference(rewrite,[status(thm)],[])).
% 295.41/187.97 tff(30781,plain,
% 295.41/187.97 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s20)) | m_and_h_gate_v_out(c_e_h_1, c_i, s20))),
% 295.41/187.97 inference(quant_inst,[status(thm)],[])).
% 295.41/187.97 tff(30782,plain,
% 295.41/187.97 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s20)) | m_and_h_gate_v_out(c_e_h_1, c_i, s20)),
% 295.41/187.97 inference(modus_ponens,[status(thm)],[30781, 30780])).
% 295.41/187.97 tff(30783,plain,
% 295.41/187.97 ($false),
% 295.41/187.97 inference(unit_resolution,[status(thm)],[30782, 164, 30779, 30346])).
% 295.41/187.97 tff(30784,plain,((~m_c_h_element_v_in2(c_e_h_1, c_e, s20)) | m_and_h_gate_v_out(c_e_h_1, c_i, s20)), inference(lemma,lemma(discharge,[]))).
% 295.41/187.97 tff(30785,plain,
% 295.41/187.97 (~m_c_h_element_v_in2(c_e_h_1, c_e, s20)),
% 295.41/187.97 inference(unit_resolution,[status(thm)],[30784, 30040])).
% 295.41/187.97 tff(30786,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s21)), introduced(assumption)).
% 295.41/187.97 tff(30787,assumption,(~m_c_h_element_v_out(c_e_h_1, c_e, s20)), introduced(assumption)).
% 295.41/187.97 tff(30788,assumption,(node18(c_e_h_1, c_e, s20, s21)), introduced(assumption)).
% 295.41/187.97 tff(30789,plain,
% 295.41/187.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s20) | (~m_c_h_element_v_out(c_e_h_1, c_e, s21)) | (~node18(c_e_h_1, c_e, s20, s21)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s20) | (~m_c_h_element_v_out(c_e_h_1, c_e, s21)) | (~node18(c_e_h_1, c_e, s20, s21)))),
% 295.41/187.97 inference(rewrite,[status(thm)],[])).
% 295.41/187.97 tff(30790,plain,
% 295.41/187.97 (((~m_c_h_element_v_out(c_e_h_1, c_e, s21)) | m_c_h_element_v_out(c_e_h_1, c_e, s20) | (~node18(c_e_h_1, c_e, s20, s21))) <=> (m_c_h_element_v_out(c_e_h_1, c_e, s20) | (~m_c_h_element_v_out(c_e_h_1, c_e, s21)) | (~node18(c_e_h_1, c_e, s20, s21)))),
% 295.41/187.97 inference(rewrite,[status(thm)],[])).
% 295.41/187.97 tff(30791,plain,
% 295.41/187.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s21)) | m_c_h_element_v_out(c_e_h_1, c_e, s20) | (~node18(c_e_h_1, c_e, s20, s21)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s20) | (~m_c_h_element_v_out(c_e_h_1, c_e, s21)) | (~node18(c_e_h_1, c_e, s20, s21))))),
% 295.41/187.97 inference(monotonicity,[status(thm)],[30790])).
% 295.41/187.97 tff(30792,plain,
% 295.41/187.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s21)) | m_c_h_element_v_out(c_e_h_1, c_e, s20) | (~node18(c_e_h_1, c_e, s20, s21)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s20) | (~m_c_h_element_v_out(c_e_h_1, c_e, s21)) | (~node18(c_e_h_1, c_e, s20, s21)))),
% 295.41/187.97 inference(transitivity,[status(thm)],[30791, 30789])).
% 295.41/187.97 tff(30793,plain,
% 295.41/187.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s21)) | m_c_h_element_v_out(c_e_h_1, c_e, s20) | (~node18(c_e_h_1, c_e, s20, s21)))),
% 295.41/187.97 inference(quant_inst,[status(thm)],[])).
% 295.41/187.97 tff(30794,plain,
% 295.41/187.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s20) | (~m_c_h_element_v_out(c_e_h_1, c_e, s21)) | (~node18(c_e_h_1, c_e, s20, s21))),
% 295.41/187.97 inference(modus_ponens,[status(thm)],[30793, 30792])).
% 295.41/187.97 tff(30795,plain,
% 295.41/187.97 ($false),
% 295.41/187.97 inference(unit_resolution,[status(thm)],[30794, 753, 30786, 30787, 30788])).
% 295.41/187.97 tff(30796,plain,((~node18(c_e_h_1, c_e, s20, s21)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s21)) | m_c_h_element_v_out(c_e_h_1, c_e, s20)), inference(lemma,lemma(discharge,[]))).
% 295.41/187.97 tff(30797,plain,
% 295.41/187.97 (~node18(c_e_h_1, c_e, s20, s21)),
% 295.41/187.97 inference(unit_resolution,[status(thm)],[30796, 30787, 30786])).
% 295.41/187.97 tff(30798,plain,
% 295.41/187.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s20, s21)) | node19(c_e_h_1, c_e, s20, s21))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s20, s21)) | node19(c_e_h_1, c_e, s20, s21))),
% 295.41/187.97 inference(rewrite,[status(thm)],[])).
% 295.41/187.97 tff(30799,plain,
% 295.41/187.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s20, s21)) | node19(c_e_h_1, c_e, s20, s21))),
% 295.41/187.97 inference(quant_inst,[status(thm)],[])).
% 295.41/187.97 tff(30800,plain,
% 295.41/187.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s20, s21)) | node19(c_e_h_1, c_e, s20, s21)),
% 295.41/187.97 inference(modus_ponens,[status(thm)],[30799, 30798])).
% 295.41/187.97 tff(30801,plain,
% 295.41/187.97 (node19(c_e_h_1, c_e, s20, s21)),
% 295.41/187.97 inference(unit_resolution,[status(thm)],[30800, 190, 30273])).
% 295.41/187.97 tff(30802,plain,
% 295.41/187.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s20) | node18(c_e_h_1, c_e, s20, s21) | (~node19(c_e_h_1, c_e, s20, s21)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_e, s20) | node18(c_e_h_1, c_e, s20, s21) | (~node19(c_e_h_1, c_e, s20, s21)))),
% 295.41/187.97 inference(rewrite,[status(thm)],[])).
% 295.41/187.97 tff(30803,plain,
% 295.41/187.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s20) | node18(c_e_h_1, c_e, s20, s21) | (~node19(c_e_h_1, c_e, s20, s21)))),
% 295.41/187.97 inference(quant_inst,[status(thm)],[])).
% 295.41/187.97 tff(30804,plain,
% 295.41/187.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_e, s20) | node18(c_e_h_1, c_e, s20, s21) | (~node19(c_e_h_1, c_e, s20, s21))),
% 295.41/187.97 inference(modus_ponens,[status(thm)],[30803, 30802])).
% 295.41/187.97 tff(30805,plain,
% 295.41/187.97 (node17(c_e_h_1, c_e, s20) | node18(c_e_h_1, c_e, s20, s21)),
% 295.41/187.97 inference(unit_resolution,[status(thm)],[30804, 776, 30801])).
% 295.41/187.97 tff(30806,plain,
% 295.41/187.97 (node17(c_e_h_1, c_e, s20)),
% 295.41/187.97 inference(unit_resolution,[status(thm)],[30805, 30797])).
% 295.41/187.97 tff(30807,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_e, s20)), introduced(assumption)).
% 295.41/187.97 tff(30808,plain,
% 295.41/187.97 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s20)) | m_c_h_element_v_in2(c_e_h_1, c_e, s20) | (~node17(c_e_h_1, c_e, s20)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s20)) | m_c_h_element_v_in2(c_e_h_1, c_e, s20) | (~node17(c_e_h_1, c_e, s20)))),
% 295.41/187.97 inference(rewrite,[status(thm)],[])).
% 295.41/187.97 tff(30809,plain,
% 295.41/187.97 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s20)) | m_c_h_element_v_in2(c_e_h_1, c_e, s20) | (~node17(c_e_h_1, c_e, s20)))),
% 295.41/187.97 inference(quant_inst,[status(thm)],[])).
% 295.41/187.97 tff(30810,plain,
% 295.41/187.97 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s20)) | m_c_h_element_v_in2(c_e_h_1, c_e, s20) | (~node17(c_e_h_1, c_e, s20))),
% 295.41/187.97 inference(modus_ponens,[status(thm)],[30809, 30808])).
% 295.41/187.97 tff(30811,plain,
% 295.41/187.97 ((~m_c_h_element_v_in1(c_e_h_1, c_e, s20)) | (~node17(c_e_h_1, c_e, s20))),
% 295.41/187.97 inference(unit_resolution,[status(thm)],[30810, 919, 30807])).
% 295.41/187.97 tff(30812,plain,
% 295.41/187.97 (~m_c_h_element_v_in1(c_e_h_1, c_e, s20)),
% 295.41/187.97 inference(unit_resolution,[status(thm)],[30811, 30806])).
% 295.41/187.97 tff(30813,assumption,(~node14(c_e_h_1, c_e, s20, s21)), introduced(assumption)).
% 295.41/187.97 tff(30814,assumption,(node15(c_e_h_1, c_e, s20, s21)), introduced(assumption)).
% 295.41/187.97 tff(30815,plain,
% 295.41/187.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s21)) | (~node15(c_e_h_1, c_e, s20, s21)) | m_c_h_element_v_out(c_e_h_1, c_e, s20))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s21)) | (~node15(c_e_h_1, c_e, s20, s21)) | m_c_h_element_v_out(c_e_h_1, c_e, s20))),
% 295.41/187.97 inference(rewrite,[status(thm)],[])).
% 295.41/187.97 tff(30816,plain,
% 295.41/187.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s21)) | (~node15(c_e_h_1, c_e, s20, s21)) | m_c_h_element_v_out(c_e_h_1, c_e, s20))),
% 295.41/187.97 inference(quant_inst,[status(thm)],[])).
% 295.41/187.97 tff(30817,plain,
% 295.41/187.97 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s21)) | (~node15(c_e_h_1, c_e, s20, s21)) | m_c_h_element_v_out(c_e_h_1, c_e, s20)),
% 295.41/187.97 inference(modus_ponens,[status(thm)],[30816, 30815])).
% 295.41/187.97 tff(30818,plain,
% 295.41/187.97 ($false),
% 295.41/187.97 inference(unit_resolution,[status(thm)],[30817, 147, 30786, 30787, 30814])).
% 295.41/187.97 tff(30819,plain,((~node15(c_e_h_1, c_e, s20, s21)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s21)) | m_c_h_element_v_out(c_e_h_1, c_e, s20)), inference(lemma,lemma(discharge,[]))).
% 295.41/187.97 tff(30820,plain,
% 295.41/187.97 (~node15(c_e_h_1, c_e, s20, s21)),
% 295.41/187.97 inference(unit_resolution,[status(thm)],[30819, 30787, 30786])).
% 295.41/187.97 tff(30821,plain,
% 295.41/187.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s20) | node15(c_e_h_1, c_e, s20, s21) | node14(c_e_h_1, c_e, s20, s21) | (~node19(c_e_h_1, c_e, s20, s21)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_e, s20) | node15(c_e_h_1, c_e, s20, s21) | node14(c_e_h_1, c_e, s20, s21) | (~node19(c_e_h_1, c_e, s20, s21)))),
% 295.41/187.97 inference(rewrite,[status(thm)],[])).
% 295.41/187.97 tff(30822,plain,
% 295.41/187.97 ((node16(c_e_h_1, c_e, s20) | node14(c_e_h_1, c_e, s20, s21) | node15(c_e_h_1, c_e, s20, s21) | (~node19(c_e_h_1, c_e, s20, s21))) <=> (node16(c_e_h_1, c_e, s20) | node15(c_e_h_1, c_e, s20, s21) | node14(c_e_h_1, c_e, s20, s21) | (~node19(c_e_h_1, c_e, s20, s21)))),
% 295.41/187.97 inference(rewrite,[status(thm)],[])).
% 295.41/187.97 tff(30823,plain,
% 295.41/187.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s20) | node14(c_e_h_1, c_e, s20, s21) | node15(c_e_h_1, c_e, s20, s21) | (~node19(c_e_h_1, c_e, s20, s21)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s20) | node15(c_e_h_1, c_e, s20, s21) | node14(c_e_h_1, c_e, s20, s21) | (~node19(c_e_h_1, c_e, s20, s21))))),
% 295.41/187.97 inference(monotonicity,[status(thm)],[30822])).
% 295.41/187.97 tff(30824,plain,
% 295.41/187.97 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s20) | node14(c_e_h_1, c_e, s20, s21) | node15(c_e_h_1, c_e, s20, s21) | (~node19(c_e_h_1, c_e, s20, s21)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_e, s20) | node15(c_e_h_1, c_e, s20, s21) | node14(c_e_h_1, c_e, s20, s21) | (~node19(c_e_h_1, c_e, s20, s21)))),
% 295.41/187.98 inference(transitivity,[status(thm)],[30823, 30821])).
% 295.41/187.98 tff(30825,plain,
% 295.41/187.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s20) | node14(c_e_h_1, c_e, s20, s21) | node15(c_e_h_1, c_e, s20, s21) | (~node19(c_e_h_1, c_e, s20, s21)))),
% 295.41/187.98 inference(quant_inst,[status(thm)],[])).
% 295.41/187.98 tff(30826,plain,
% 295.41/187.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_e, s20) | node15(c_e_h_1, c_e, s20, s21) | node14(c_e_h_1, c_e, s20, s21) | (~node19(c_e_h_1, c_e, s20, s21))),
% 295.41/187.98 inference(modus_ponens,[status(thm)],[30825, 30824])).
% 295.41/187.98 tff(30827,plain,
% 295.41/187.98 (node16(c_e_h_1, c_e, s20) | node15(c_e_h_1, c_e, s20, s21) | node14(c_e_h_1, c_e, s20, s21)),
% 295.41/187.98 inference(unit_resolution,[status(thm)],[30826, 204, 30801])).
% 295.41/187.98 tff(30828,plain,
% 295.41/187.98 (node16(c_e_h_1, c_e, s20)),
% 295.41/187.98 inference(unit_resolution,[status(thm)],[30827, 30820, 30813])).
% 295.41/187.98 tff(30829,assumption,(node17(c_e_h_1, c_e, s20)), introduced(assumption)).
% 295.41/187.98 tff(30830,plain,
% 295.41/187.98 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s20) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s20)) | (~node17(c_e_h_1, c_e, s20)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s20) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s20)) | (~node17(c_e_h_1, c_e, s20)))),
% 295.41/187.98 inference(rewrite,[status(thm)],[])).
% 295.41/187.98 tff(30831,plain,
% 295.41/187.98 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s20) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s20)) | (~node17(c_e_h_1, c_e, s20)))),
% 295.41/187.98 inference(quant_inst,[status(thm)],[])).
% 295.41/187.98 tff(30832,plain,
% 295.41/187.98 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | m_c_h_element_v_in1(c_e_h_1, c_e, s20) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s20)) | (~node17(c_e_h_1, c_e, s20))),
% 295.41/187.98 inference(modus_ponens,[status(thm)],[30831, 30830])).
% 295.41/187.98 tff(30833,plain,
% 295.41/187.98 (m_c_h_element_v_in1(c_e_h_1, c_e, s20) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s20))),
% 295.41/187.98 inference(unit_resolution,[status(thm)],[30832, 859, 30829])).
% 295.41/187.98 tff(30834,plain,
% 295.41/187.98 (m_c_h_element_v_in1(c_e_h_1, c_e, s20)),
% 295.41/187.98 inference(unit_resolution,[status(thm)],[30833, 30779])).
% 295.41/187.98 tff(30835,assumption,(node16(c_e_h_1, c_e, s20)), introduced(assumption)).
% 295.41/187.98 tff(30836,plain,
% 295.41/187.98 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s20)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s20)) | (~node16(c_e_h_1, c_e, s20)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s20)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s20)) | (~node16(c_e_h_1, c_e, s20)))),
% 295.41/187.98 inference(rewrite,[status(thm)],[])).
% 295.41/187.98 tff(30837,plain,
% 295.41/187.98 (((~node16(c_e_h_1, c_e, s20)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s20)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s20))) <=> ((~m_c_h_element_v_in1(c_e_h_1, c_e, s20)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s20)) | (~node16(c_e_h_1, c_e, s20)))),
% 295.41/187.98 inference(rewrite,[status(thm)],[])).
% 295.41/187.98 tff(30838,plain,
% 295.41/187.98 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s20)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s20)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s20)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s20)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s20)) | (~node16(c_e_h_1, c_e, s20))))),
% 295.41/187.98 inference(monotonicity,[status(thm)],[30837])).
% 295.41/187.98 tff(30839,plain,
% 295.41/187.98 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s20)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s20)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s20)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s20)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s20)) | (~node16(c_e_h_1, c_e, s20)))),
% 295.41/187.98 inference(transitivity,[status(thm)],[30838, 30836])).
% 295.41/187.98 tff(30840,plain,
% 295.41/187.98 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s20)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s20)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s20)))),
% 295.41/187.98 inference(quant_inst,[status(thm)],[])).
% 295.41/187.98 tff(30841,plain,
% 295.41/187.98 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s20)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s20)) | (~node16(c_e_h_1, c_e, s20))),
% 295.41/187.98 inference(modus_ponens,[status(thm)],[30840, 30839])).
% 295.41/187.98 tff(30842,plain,
% 295.41/187.98 ((~m_c_h_element_v_in1(c_e_h_1, c_e, s20)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s20))),
% 295.41/187.98 inference(unit_resolution,[status(thm)],[30841, 2307, 30835])).
% 295.41/187.98 tff(30843,plain,
% 295.41/187.98 ($false),
% 295.41/187.98 inference(unit_resolution,[status(thm)],[30842, 30834, 30779])).
% 295.41/187.98 tff(30844,plain,((~m_c_h_element_v_in2(c_e_h_1, c_e, s20)) | (~node16(c_e_h_1, c_e, s20)) | (~node17(c_e_h_1, c_e, s20))), inference(lemma,lemma(discharge,[]))).
% 295.41/187.98 tff(30845,plain,
% 295.41/187.98 (~m_c_h_element_v_in2(c_e_h_1, c_e, s20)),
% 295.41/187.98 inference(unit_resolution,[status(thm)],[30844, 30828, 30806])).
% 295.41/187.98 tff(30846,plain,
% 295.41/187.98 ((~m_c_h_element_v_in1(c_e_h_1, c_e, s20)) | m_c_h_element_v_in2(c_e_h_1, c_e, s20)),
% 295.41/187.98 inference(unit_resolution,[status(thm)],[30810, 919, 30806])).
% 295.41/187.98 tff(30847,plain,
% 295.41/187.98 (~m_c_h_element_v_in1(c_e_h_1, c_e, s20)),
% 295.41/187.98 inference(unit_resolution,[status(thm)],[30846, 30845])).
% 295.41/187.98 tff(30848,plain,
% 295.41/187.98 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s20)) | m_c_h_element_v_in1(c_e_h_1, c_e, s20) | m_c_h_element_v_in2(c_e_h_1, c_e, s20))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s20)) | m_c_h_element_v_in1(c_e_h_1, c_e, s20) | m_c_h_element_v_in2(c_e_h_1, c_e, s20))),
% 295.41/187.98 inference(rewrite,[status(thm)],[])).
% 295.41/187.98 tff(30849,plain,
% 295.41/187.98 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s20)) | m_c_h_element_v_in1(c_e_h_1, c_e, s20) | m_c_h_element_v_in2(c_e_h_1, c_e, s20))),
% 295.41/187.98 inference(quant_inst,[status(thm)],[])).
% 295.41/187.98 tff(30850,plain,
% 295.41/187.98 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s20)) | m_c_h_element_v_in1(c_e_h_1, c_e, s20) | m_c_h_element_v_in2(c_e_h_1, c_e, s20)),
% 295.41/187.98 inference(modus_ponens,[status(thm)],[30849, 30848])).
% 295.41/187.98 tff(30851,plain,
% 295.41/187.98 (m_c_h_element_v_in1(c_e_h_1, c_e, s20) | m_c_h_element_v_in2(c_e_h_1, c_e, s20)),
% 295.41/187.98 inference(unit_resolution,[status(thm)],[30850, 178, 30828])).
% 295.41/187.98 tff(30852,plain,
% 295.41/187.98 ($false),
% 295.41/187.98 inference(unit_resolution,[status(thm)],[30851, 30847, 30845])).
% 295.41/187.98 tff(30853,plain,(m_c_h_element_v_out(c_e_h_1, c_e, s20) | node14(c_e_h_1, c_e, s20, s21) | (~m_c_h_element_v_out(c_e_h_1, c_e, s21))), inference(lemma,lemma(discharge,[]))).
% 295.41/187.98 tff(30854,plain,
% 295.41/187.98 (node14(c_e_h_1, c_e, s20, s21)),
% 295.41/187.98 inference(unit_resolution,[status(thm)],[30853, 30787, 30786])).
% 295.41/187.98 tff(30855,plain,
% 295.41/187.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s21)) | m_c_h_element_v_in1(c_e_h_1, c_e, s20) | (~node14(c_e_h_1, c_e, s20, s21)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s21)) | m_c_h_element_v_in1(c_e_h_1, c_e, s20) | (~node14(c_e_h_1, c_e, s20, s21)))),
% 295.41/187.98 inference(rewrite,[status(thm)],[])).
% 295.41/187.98 tff(30856,plain,
% 295.41/187.98 (((~node14(c_e_h_1, c_e, s20, s21)) | m_c_h_element_v_in1(c_e_h_1, c_e, s20) | (~m_c_h_element_v_out(c_e_h_1, c_e, s21))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_e, s21)) | m_c_h_element_v_in1(c_e_h_1, c_e, s20) | (~node14(c_e_h_1, c_e, s20, s21)))),
% 295.41/187.98 inference(rewrite,[status(thm)],[])).
% 295.41/187.98 tff(30857,plain,
% 295.41/187.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s20, s21)) | m_c_h_element_v_in1(c_e_h_1, c_e, s20) | (~m_c_h_element_v_out(c_e_h_1, c_e, s21)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s21)) | m_c_h_element_v_in1(c_e_h_1, c_e, s20) | (~node14(c_e_h_1, c_e, s20, s21))))),
% 295.41/187.98 inference(monotonicity,[status(thm)],[30856])).
% 295.41/187.98 tff(30858,plain,
% 295.41/187.98 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s20, s21)) | m_c_h_element_v_in1(c_e_h_1, c_e, s20) | (~m_c_h_element_v_out(c_e_h_1, c_e, s21)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s21)) | m_c_h_element_v_in1(c_e_h_1, c_e, s20) | (~node14(c_e_h_1, c_e, s20, s21)))),
% 295.41/187.98 inference(transitivity,[status(thm)],[30857, 30855])).
% 295.41/187.98 tff(30859,plain,
% 295.41/187.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s20, s21)) | m_c_h_element_v_in1(c_e_h_1, c_e, s20) | (~m_c_h_element_v_out(c_e_h_1, c_e, s21)))),
% 295.41/187.98 inference(quant_inst,[status(thm)],[])).
% 295.41/187.98 tff(30860,plain,
% 295.41/187.98 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s21)) | m_c_h_element_v_in1(c_e_h_1, c_e, s20) | (~node14(c_e_h_1, c_e, s20, s21))),
% 295.41/187.98 inference(modus_ponens,[status(thm)],[30859, 30858])).
% 295.41/187.98 tff(30861,plain,
% 295.41/187.98 ($false),
% 295.41/187.98 inference(unit_resolution,[status(thm)],[30860, 223, 30786, 30854, 30812])).
% 295.41/187.98 tff(30862,plain,(m_c_h_element_v_out(c_e_h_1, c_e, s20) | (~m_c_h_element_v_out(c_e_h_1, c_e, s21)) | m_c_h_element_v_in2(c_e_h_1, c_e, s20)), inference(lemma,lemma(discharge,[]))).
% 295.41/187.98 tff(30863,plain,
% 295.41/187.98 (~m_c_h_element_v_out(c_e_h_1, c_e, s21)),
% 295.41/187.98 inference(unit_resolution,[status(thm)],[30862, 30785, 30778])).
% 295.41/187.98 tff(30864,plain,
% 295.41/187.98 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s19)),
% 295.41/187.98 inference(unit_resolution,[status(thm)],[29979, 619, 29899])).
% 295.41/187.98 tff(30865,plain,
% 295.41/187.98 (~m_c_h_element_v_out(c_e_h_1, c_h, s20)),
% 295.41/187.98 inference(unit_resolution,[status(thm)],[29973, 29899, 29965])).
% 295.41/187.98 tff(30866,assumption,(m_and_h_gate_v_in1(c_e_h_1, c_i, s20)), introduced(assumption)).
% 295.41/187.98 tff(30867,plain,
% 295.41/187.98 ($false),
% 295.41/187.98 inference(unit_resolution,[status(thm)],[30349, 619, 30255, 30866])).
% 295.41/187.98 tff(30868,plain,(m_c_h_element_v_out(c_e_h_1, c_h, s20) | (~m_and_h_gate_v_in1(c_e_h_1, c_i, s20))), inference(lemma,lemma(discharge,[]))).
% 295.41/187.98 tff(30869,plain,
% 295.41/187.98 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s20)),
% 295.41/187.98 inference(unit_resolution,[status(thm)],[30868, 30865])).
% 295.41/187.99 tff(30870,assumption,(~m_and_h_gate_v_in1(c_e_h_1, c_i, s20)), introduced(assumption)).
% 295.41/187.99 tff(30871,assumption,(node20(c_e_h_1, c_i, s20)), introduced(assumption)).
% 295.41/187.99 tff(30872,plain,
% 295.41/187.99 ($false),
% 295.41/187.99 inference(unit_resolution,[status(thm)],[30353, 38, 30871, 30870])).
% 295.41/187.99 tff(30873,plain,(m_and_h_gate_v_in1(c_e_h_1, c_i, s20) | (~node20(c_e_h_1, c_i, s20))), inference(lemma,lemma(discharge,[]))).
% 295.41/187.99 tff(30874,plain,
% 295.41/187.99 (~node20(c_e_h_1, c_i, s20)),
% 295.41/187.99 inference(unit_resolution,[status(thm)],[30873, 30869])).
% 295.41/187.99 tff(30875,plain,
% 295.41/187.99 (m_and_h_gate_v_out(c_e_h_1, c_i, s20)),
% 295.41/187.99 inference(unit_resolution,[status(thm)],[30373, 30874, 30356])).
% 295.41/187.99 tff(30876,plain,
% 295.41/187.99 (node20(c_e_h_1, c_i, s19)),
% 295.41/187.99 inference(unit_resolution,[status(thm)],[30037, 30875, 30016])).
% 295.41/187.99 tff(30877,plain,
% 295.41/187.99 ($false),
% 295.41/187.99 inference(unit_resolution,[status(thm)],[29983, 38, 30876, 30864])).
% 295.41/187.99 tff(30878,plain,(m_c_h_element_v_out(c_e_h_1, c_h, s19) | m_and_h_gate_v_out(c_e_h_1, c_i, s19) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s21)) | m_c_h_element_v_in2(c_e_h_1, c_h, s19)), inference(lemma,lemma(discharge,[]))).
% 295.41/187.99 tff(30879,plain,
% 295.41/187.99 (~m_and_h_gate_v_out(c_e_h_1, c_i, s21)),
% 295.41/187.99 inference(unit_resolution,[status(thm)],[30878, 29898, 29755, 30693])).
% 295.41/187.99 tff(30880,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_i, s21)), introduced(assumption)).
% 295.41/187.99 tff(30881,assumption,(m_c_h_element_v_in2(c_e_h_1, c_e, s21)), introduced(assumption)).
% 295.41/187.99 tff(30882,plain,
% 295.41/187.99 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s21)) | m_and_h_gate_v_out(c_e_h_1, c_i, s21))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s21)) | m_and_h_gate_v_out(c_e_h_1, c_i, s21))),
% 295.41/187.99 inference(rewrite,[status(thm)],[])).
% 295.41/187.99 tff(30883,plain,
% 295.41/187.99 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s21)) | m_and_h_gate_v_out(c_e_h_1, c_i, s21))),
% 295.41/187.99 inference(quant_inst,[status(thm)],[])).
% 295.41/187.99 tff(30884,plain,
% 295.41/187.99 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s21)) | m_and_h_gate_v_out(c_e_h_1, c_i, s21)),
% 295.41/187.99 inference(modus_ponens,[status(thm)],[30883, 30882])).
% 295.41/187.99 tff(30885,plain,
% 295.41/187.99 ($false),
% 295.41/187.99 inference(unit_resolution,[status(thm)],[30884, 164, 30881, 30880])).
% 295.41/187.99 tff(30886,plain,((~m_c_h_element_v_in2(c_e_h_1, c_e, s21)) | m_and_h_gate_v_out(c_e_h_1, c_i, s21)), inference(lemma,lemma(discharge,[]))).
% 295.41/187.99 tff(30887,plain,
% 295.41/187.99 (~m_c_h_element_v_in2(c_e_h_1, c_e, s21)),
% 295.41/187.99 inference(unit_resolution,[status(thm)],[30886, 30879])).
% 295.41/187.99 tff(30888,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s22)), introduced(assumption)).
% 295.41/187.99 tff(30889,assumption,(~m_c_h_element_v_out(c_e_h_1, c_e, s21)), introduced(assumption)).
% 295.41/187.99 tff(30890,assumption,(node18(c_e_h_1, c_e, s21, s22)), introduced(assumption)).
% 295.41/187.99 tff(30891,plain,
% 295.41/187.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s21) | (~m_c_h_element_v_out(c_e_h_1, c_e, s22)) | (~node18(c_e_h_1, c_e, s21, s22)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s21) | (~m_c_h_element_v_out(c_e_h_1, c_e, s22)) | (~node18(c_e_h_1, c_e, s21, s22)))),
% 295.41/187.99 inference(rewrite,[status(thm)],[])).
% 295.41/187.99 tff(30892,plain,
% 295.41/187.99 (((~m_c_h_element_v_out(c_e_h_1, c_e, s22)) | m_c_h_element_v_out(c_e_h_1, c_e, s21) | (~node18(c_e_h_1, c_e, s21, s22))) <=> (m_c_h_element_v_out(c_e_h_1, c_e, s21) | (~m_c_h_element_v_out(c_e_h_1, c_e, s22)) | (~node18(c_e_h_1, c_e, s21, s22)))),
% 295.41/187.99 inference(rewrite,[status(thm)],[])).
% 295.41/187.99 tff(30893,plain,
% 295.41/187.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s22)) | m_c_h_element_v_out(c_e_h_1, c_e, s21) | (~node18(c_e_h_1, c_e, s21, s22)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s21) | (~m_c_h_element_v_out(c_e_h_1, c_e, s22)) | (~node18(c_e_h_1, c_e, s21, s22))))),
% 295.41/187.99 inference(monotonicity,[status(thm)],[30892])).
% 295.41/187.99 tff(30894,plain,
% 295.41/187.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s22)) | m_c_h_element_v_out(c_e_h_1, c_e, s21) | (~node18(c_e_h_1, c_e, s21, s22)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s21) | (~m_c_h_element_v_out(c_e_h_1, c_e, s22)) | (~node18(c_e_h_1, c_e, s21, s22)))),
% 295.41/187.99 inference(transitivity,[status(thm)],[30893, 30891])).
% 295.41/187.99 tff(30895,plain,
% 295.41/187.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s22)) | m_c_h_element_v_out(c_e_h_1, c_e, s21) | (~node18(c_e_h_1, c_e, s21, s22)))),
% 295.41/187.99 inference(quant_inst,[status(thm)],[])).
% 295.41/187.99 tff(30896,plain,
% 295.41/187.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s21) | (~m_c_h_element_v_out(c_e_h_1, c_e, s22)) | (~node18(c_e_h_1, c_e, s21, s22))),
% 295.41/187.99 inference(modus_ponens,[status(thm)],[30895, 30894])).
% 295.41/187.99 tff(30897,plain,
% 295.41/187.99 ($false),
% 295.41/187.99 inference(unit_resolution,[status(thm)],[30896, 753, 30889, 30888, 30890])).
% 295.41/187.99 tff(30898,plain,((~node18(c_e_h_1, c_e, s21, s22)) | m_c_h_element_v_out(c_e_h_1, c_e, s21) | (~m_c_h_element_v_out(c_e_h_1, c_e, s22))), inference(lemma,lemma(discharge,[]))).
% 295.41/187.99 tff(30899,plain,
% 295.41/187.99 (~node18(c_e_h_1, c_e, s21, s22)),
% 295.41/187.99 inference(unit_resolution,[status(thm)],[30898, 30889, 30888])).
% 295.41/187.99 tff(30900,plain,
% 295.41/187.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s21, s22)) | node19(c_e_h_1, c_e, s21, s22))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s21, s22)) | node19(c_e_h_1, c_e, s21, s22))),
% 295.41/187.99 inference(rewrite,[status(thm)],[])).
% 295.41/187.99 tff(30901,plain,
% 295.41/187.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s21, s22)) | node19(c_e_h_1, c_e, s21, s22))),
% 295.41/187.99 inference(quant_inst,[status(thm)],[])).
% 295.41/187.99 tff(30902,plain,
% 295.41/187.99 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s21, s22)) | node19(c_e_h_1, c_e, s21, s22)),
% 295.41/187.99 inference(modus_ponens,[status(thm)],[30901, 30900])).
% 295.41/187.99 tff(30903,plain,
% 295.41/187.99 (node19(c_e_h_1, c_e, s21, s22)),
% 295.41/187.99 inference(unit_resolution,[status(thm)],[30902, 190, 30340])).
% 295.41/187.99 tff(30904,plain,
% 295.41/187.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_e, s21, s22)) | node18(c_e_h_1, c_e, s21, s22) | node17(c_e_h_1, c_e, s21))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s21, s22)) | node18(c_e_h_1, c_e, s21, s22) | node17(c_e_h_1, c_e, s21))),
% 295.41/187.99 inference(rewrite,[status(thm)],[])).
% 295.41/187.99 tff(30905,plain,
% 295.41/187.99 ((node17(c_e_h_1, c_e, s21) | node18(c_e_h_1, c_e, s21, s22) | (~node19(c_e_h_1, c_e, s21, s22))) <=> ((~node19(c_e_h_1, c_e, s21, s22)) | node18(c_e_h_1, c_e, s21, s22) | node17(c_e_h_1, c_e, s21))),
% 295.41/187.99 inference(rewrite,[status(thm)],[])).
% 295.41/187.99 tff(30906,plain,
% 295.41/187.99 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s21) | node18(c_e_h_1, c_e, s21, s22) | (~node19(c_e_h_1, c_e, s21, s22)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_e, s21, s22)) | node18(c_e_h_1, c_e, s21, s22) | node17(c_e_h_1, c_e, s21)))),
% 295.41/188.00 inference(monotonicity,[status(thm)],[30905])).
% 295.41/188.00 tff(30907,plain,
% 295.41/188.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s21) | node18(c_e_h_1, c_e, s21, s22) | (~node19(c_e_h_1, c_e, s21, s22)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s21, s22)) | node18(c_e_h_1, c_e, s21, s22) | node17(c_e_h_1, c_e, s21))),
% 295.41/188.00 inference(transitivity,[status(thm)],[30906, 30904])).
% 295.41/188.00 tff(30908,plain,
% 295.41/188.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s21) | node18(c_e_h_1, c_e, s21, s22) | (~node19(c_e_h_1, c_e, s21, s22)))),
% 295.41/188.00 inference(quant_inst,[status(thm)],[])).
% 295.41/188.00 tff(30909,plain,
% 295.41/188.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s21, s22)) | node18(c_e_h_1, c_e, s21, s22) | node17(c_e_h_1, c_e, s21)),
% 295.41/188.00 inference(modus_ponens,[status(thm)],[30908, 30907])).
% 295.41/188.00 tff(30910,plain,
% 295.41/188.00 (node18(c_e_h_1, c_e, s21, s22) | node17(c_e_h_1, c_e, s21)),
% 295.41/188.00 inference(unit_resolution,[status(thm)],[30909, 776, 30903])).
% 295.41/188.00 tff(30911,plain,
% 295.41/188.00 (node17(c_e_h_1, c_e, s21)),
% 295.41/188.00 inference(unit_resolution,[status(thm)],[30910, 30899])).
% 295.41/188.00 tff(30912,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_e, s21)), introduced(assumption)).
% 295.41/188.00 tff(30913,plain,
% 295.41/188.00 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_e, s21) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s21)) | (~node17(c_e_h_1, c_e, s21)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s21) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s21)) | (~node17(c_e_h_1, c_e, s21)))),
% 295.41/188.00 inference(rewrite,[status(thm)],[])).
% 295.41/188.00 tff(30914,plain,
% 295.41/188.00 (((~m_c_h_element_v_in1(c_e_h_1, c_e, s21)) | m_c_h_element_v_in2(c_e_h_1, c_e, s21) | (~node17(c_e_h_1, c_e, s21))) <=> (m_c_h_element_v_in2(c_e_h_1, c_e, s21) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s21)) | (~node17(c_e_h_1, c_e, s21)))),
% 295.41/188.00 inference(rewrite,[status(thm)],[])).
% 295.41/188.00 tff(30915,plain,
% 295.41/188.00 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s21)) | m_c_h_element_v_in2(c_e_h_1, c_e, s21) | (~node17(c_e_h_1, c_e, s21)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_e, s21) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s21)) | (~node17(c_e_h_1, c_e, s21))))),
% 295.41/188.00 inference(monotonicity,[status(thm)],[30914])).
% 295.41/188.00 tff(30916,plain,
% 295.41/188.00 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s21)) | m_c_h_element_v_in2(c_e_h_1, c_e, s21) | (~node17(c_e_h_1, c_e, s21)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s21) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s21)) | (~node17(c_e_h_1, c_e, s21)))),
% 295.41/188.00 inference(transitivity,[status(thm)],[30915, 30913])).
% 295.41/188.00 tff(30917,plain,
% 295.41/188.00 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s21)) | m_c_h_element_v_in2(c_e_h_1, c_e, s21) | (~node17(c_e_h_1, c_e, s21)))),
% 295.41/188.00 inference(quant_inst,[status(thm)],[])).
% 295.41/188.00 tff(30918,plain,
% 295.41/188.00 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s21) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s21)) | (~node17(c_e_h_1, c_e, s21))),
% 295.41/188.00 inference(modus_ponens,[status(thm)],[30917, 30916])).
% 295.41/188.00 tff(30919,plain,
% 295.41/188.00 ((~m_c_h_element_v_in1(c_e_h_1, c_e, s21)) | (~node17(c_e_h_1, c_e, s21))),
% 295.41/188.00 inference(unit_resolution,[status(thm)],[30918, 919, 30912])).
% 295.41/188.00 tff(30920,plain,
% 295.41/188.00 (~m_c_h_element_v_in1(c_e_h_1, c_e, s21)),
% 295.41/188.00 inference(unit_resolution,[status(thm)],[30919, 30911])).
% 295.41/188.00 tff(30921,plain,
% 295.41/188.00 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s21)) | m_c_h_element_v_in1(c_e_h_1, c_e, s21) | m_c_h_element_v_in2(c_e_h_1, c_e, s21))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s21)) | m_c_h_element_v_in1(c_e_h_1, c_e, s21) | m_c_h_element_v_in2(c_e_h_1, c_e, s21))),
% 295.41/188.00 inference(rewrite,[status(thm)],[])).
% 295.41/188.00 tff(30922,plain,
% 295.41/188.00 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s21)) | m_c_h_element_v_in1(c_e_h_1, c_e, s21) | m_c_h_element_v_in2(c_e_h_1, c_e, s21))),
% 295.41/188.00 inference(quant_inst,[status(thm)],[])).
% 295.41/188.00 tff(30923,plain,
% 295.41/188.00 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s21)) | m_c_h_element_v_in1(c_e_h_1, c_e, s21) | m_c_h_element_v_in2(c_e_h_1, c_e, s21)),
% 295.41/188.00 inference(modus_ponens,[status(thm)],[30922, 30921])).
% 295.41/188.00 tff(30924,plain,
% 295.41/188.00 ((~node16(c_e_h_1, c_e, s21)) | m_c_h_element_v_in1(c_e_h_1, c_e, s21)),
% 295.41/188.00 inference(unit_resolution,[status(thm)],[30923, 178, 30912])).
% 295.41/188.00 tff(30925,plain,
% 295.41/188.00 (~node16(c_e_h_1, c_e, s21)),
% 295.41/188.00 inference(unit_resolution,[status(thm)],[30924, 30920])).
% 295.41/188.00 tff(30926,assumption,(node15(c_e_h_1, c_e, s21, s22)), introduced(assumption)).
% 295.41/188.00 tff(30927,plain,
% 295.41/188.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s22)) | (~node15(c_e_h_1, c_e, s21, s22)) | m_c_h_element_v_out(c_e_h_1, c_e, s21))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s22)) | (~node15(c_e_h_1, c_e, s21, s22)) | m_c_h_element_v_out(c_e_h_1, c_e, s21))),
% 295.41/188.00 inference(rewrite,[status(thm)],[])).
% 295.41/188.00 tff(30928,plain,
% 295.41/188.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s22)) | (~node15(c_e_h_1, c_e, s21, s22)) | m_c_h_element_v_out(c_e_h_1, c_e, s21))),
% 295.41/188.00 inference(quant_inst,[status(thm)],[])).
% 295.41/188.00 tff(30929,plain,
% 295.41/188.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s22)) | (~node15(c_e_h_1, c_e, s21, s22)) | m_c_h_element_v_out(c_e_h_1, c_e, s21)),
% 295.41/188.00 inference(modus_ponens,[status(thm)],[30928, 30927])).
% 295.41/188.00 tff(30930,plain,
% 295.41/188.00 ($false),
% 295.41/188.00 inference(unit_resolution,[status(thm)],[30929, 147, 30889, 30888, 30926])).
% 295.41/188.00 tff(30931,plain,((~node15(c_e_h_1, c_e, s21, s22)) | m_c_h_element_v_out(c_e_h_1, c_e, s21) | (~m_c_h_element_v_out(c_e_h_1, c_e, s22))), inference(lemma,lemma(discharge,[]))).
% 295.41/188.00 tff(30932,plain,
% 295.41/188.00 (~node15(c_e_h_1, c_e, s21, s22)),
% 295.41/188.00 inference(unit_resolution,[status(thm)],[30931, 30889, 30888])).
% 295.41/188.00 tff(30933,plain,
% 295.41/188.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_e, s21, s22)) | node15(c_e_h_1, c_e, s21, s22) | node14(c_e_h_1, c_e, s21, s22) | node16(c_e_h_1, c_e, s21))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s21, s22)) | node15(c_e_h_1, c_e, s21, s22) | node14(c_e_h_1, c_e, s21, s22) | node16(c_e_h_1, c_e, s21))),
% 295.41/188.00 inference(rewrite,[status(thm)],[])).
% 295.41/188.00 tff(30934,plain,
% 295.41/188.00 ((node16(c_e_h_1, c_e, s21) | node14(c_e_h_1, c_e, s21, s22) | node15(c_e_h_1, c_e, s21, s22) | (~node19(c_e_h_1, c_e, s21, s22))) <=> ((~node19(c_e_h_1, c_e, s21, s22)) | node15(c_e_h_1, c_e, s21, s22) | node14(c_e_h_1, c_e, s21, s22) | node16(c_e_h_1, c_e, s21))),
% 295.41/188.00 inference(rewrite,[status(thm)],[])).
% 295.41/188.00 tff(30935,plain,
% 295.41/188.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s21) | node14(c_e_h_1, c_e, s21, s22) | node15(c_e_h_1, c_e, s21, s22) | (~node19(c_e_h_1, c_e, s21, s22)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_e, s21, s22)) | node15(c_e_h_1, c_e, s21, s22) | node14(c_e_h_1, c_e, s21, s22) | node16(c_e_h_1, c_e, s21)))),
% 295.41/188.00 inference(monotonicity,[status(thm)],[30934])).
% 295.41/188.00 tff(30936,plain,
% 295.41/188.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s21) | node14(c_e_h_1, c_e, s21, s22) | node15(c_e_h_1, c_e, s21, s22) | (~node19(c_e_h_1, c_e, s21, s22)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s21, s22)) | node15(c_e_h_1, c_e, s21, s22) | node14(c_e_h_1, c_e, s21, s22) | node16(c_e_h_1, c_e, s21))),
% 295.41/188.00 inference(transitivity,[status(thm)],[30935, 30933])).
% 295.41/188.00 tff(30937,plain,
% 295.41/188.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s21) | node14(c_e_h_1, c_e, s21, s22) | node15(c_e_h_1, c_e, s21, s22) | (~node19(c_e_h_1, c_e, s21, s22)))),
% 295.41/188.00 inference(quant_inst,[status(thm)],[])).
% 295.41/188.00 tff(30938,plain,
% 295.41/188.00 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s21, s22)) | node15(c_e_h_1, c_e, s21, s22) | node14(c_e_h_1, c_e, s21, s22) | node16(c_e_h_1, c_e, s21)),
% 295.41/188.00 inference(modus_ponens,[status(thm)],[30937, 30936])).
% 295.41/188.00 tff(30939,plain,
% 295.41/188.00 (node15(c_e_h_1, c_e, s21, s22) | node14(c_e_h_1, c_e, s21, s22) | node16(c_e_h_1, c_e, s21)),
% 295.41/188.00 inference(unit_resolution,[status(thm)],[30938, 204, 30903])).
% 295.41/188.00 tff(30940,plain,
% 295.41/188.00 (node14(c_e_h_1, c_e, s21, s22)),
% 295.41/188.00 inference(unit_resolution,[status(thm)],[30939, 30932, 30925])).
% 295.41/188.00 tff(30941,plain,
% 295.41/188.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s22)) | m_c_h_element_v_in1(c_e_h_1, c_e, s21) | (~node14(c_e_h_1, c_e, s21, s22)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s22)) | m_c_h_element_v_in1(c_e_h_1, c_e, s21) | (~node14(c_e_h_1, c_e, s21, s22)))),
% 295.41/188.00 inference(rewrite,[status(thm)],[])).
% 295.41/188.00 tff(30942,plain,
% 295.41/188.00 (((~node14(c_e_h_1, c_e, s21, s22)) | m_c_h_element_v_in1(c_e_h_1, c_e, s21) | (~m_c_h_element_v_out(c_e_h_1, c_e, s22))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_e, s22)) | m_c_h_element_v_in1(c_e_h_1, c_e, s21) | (~node14(c_e_h_1, c_e, s21, s22)))),
% 295.41/188.00 inference(rewrite,[status(thm)],[])).
% 295.41/188.00 tff(30943,plain,
% 295.41/188.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s21, s22)) | m_c_h_element_v_in1(c_e_h_1, c_e, s21) | (~m_c_h_element_v_out(c_e_h_1, c_e, s22)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s22)) | m_c_h_element_v_in1(c_e_h_1, c_e, s21) | (~node14(c_e_h_1, c_e, s21, s22))))),
% 295.41/188.00 inference(monotonicity,[status(thm)],[30942])).
% 295.41/188.00 tff(30944,plain,
% 295.41/188.00 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s21, s22)) | m_c_h_element_v_in1(c_e_h_1, c_e, s21) | (~m_c_h_element_v_out(c_e_h_1, c_e, s22)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s22)) | m_c_h_element_v_in1(c_e_h_1, c_e, s21) | (~node14(c_e_h_1, c_e, s21, s22)))),
% 295.41/188.01 inference(transitivity,[status(thm)],[30943, 30941])).
% 295.41/188.01 tff(30945,plain,
% 295.41/188.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s21, s22)) | m_c_h_element_v_in1(c_e_h_1, c_e, s21) | (~m_c_h_element_v_out(c_e_h_1, c_e, s22)))),
% 295.41/188.01 inference(quant_inst,[status(thm)],[])).
% 295.41/188.01 tff(30946,plain,
% 295.41/188.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s22)) | m_c_h_element_v_in1(c_e_h_1, c_e, s21) | (~node14(c_e_h_1, c_e, s21, s22))),
% 295.41/188.01 inference(modus_ponens,[status(thm)],[30945, 30944])).
% 295.41/188.01 tff(30947,plain,
% 295.41/188.01 ($false),
% 295.41/188.01 inference(unit_resolution,[status(thm)],[30946, 223, 30888, 30940, 30920])).
% 295.41/188.01 tff(30948,plain,(m_c_h_element_v_out(c_e_h_1, c_e, s21) | (~m_c_h_element_v_out(c_e_h_1, c_e, s22)) | m_c_h_element_v_in2(c_e_h_1, c_e, s21)), inference(lemma,lemma(discharge,[]))).
% 295.41/188.01 tff(30949,plain,
% 295.41/188.01 (~m_c_h_element_v_out(c_e_h_1, c_e, s22)),
% 295.41/188.01 inference(unit_resolution,[status(thm)],[30948, 30887, 30863])).
% 295.41/188.01 tff(30950,assumption,(m_c_h_element_v_in2(c_e_h_1, c_e, s22)), introduced(assumption)).
% 295.41/188.01 tff(30951,plain,
% 295.41/188.01 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s22)) | m_and_h_gate_v_out(c_e_h_1, c_i, s22))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s22)) | m_and_h_gate_v_out(c_e_h_1, c_i, s22))),
% 295.41/188.01 inference(rewrite,[status(thm)],[])).
% 295.41/188.01 tff(30952,plain,
% 295.41/188.01 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s22)) | m_and_h_gate_v_out(c_e_h_1, c_i, s22))),
% 295.41/188.01 inference(quant_inst,[status(thm)],[])).
% 295.41/188.01 tff(30953,plain,
% 295.41/188.01 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s22)) | m_and_h_gate_v_out(c_e_h_1, c_i, s22)),
% 295.41/188.01 inference(modus_ponens,[status(thm)],[30952, 30951])).
% 295.41/188.01 tff(30954,plain,
% 295.41/188.01 ($false),
% 295.41/188.01 inference(unit_resolution,[status(thm)],[30953, 164, 30678, 30950])).
% 295.41/188.01 tff(30955,plain,((~m_c_h_element_v_in2(c_e_h_1, c_e, s22)) | m_and_h_gate_v_out(c_e_h_1, c_i, s22)), inference(lemma,lemma(discharge,[]))).
% 295.41/188.01 tff(30956,plain,
% 295.41/188.01 (~m_c_h_element_v_in2(c_e_h_1, c_e, s22)),
% 295.41/188.01 inference(unit_resolution,[status(thm)],[30955, 30380])).
% 295.41/188.01 tff(30957,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s23)), introduced(assumption)).
% 295.41/188.01 tff(30958,assumption,(~m_c_h_element_v_out(c_e_h_1, c_e, s22)), introduced(assumption)).
% 295.41/188.01 tff(30959,assumption,(node18(c_e_h_1, c_e, s22, s23)), introduced(assumption)).
% 295.41/188.01 tff(30960,plain,
% 295.41/188.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s23)) | m_c_h_element_v_out(c_e_h_1, c_e, s22) | (~node18(c_e_h_1, c_e, s22, s23)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s23)) | m_c_h_element_v_out(c_e_h_1, c_e, s22) | (~node18(c_e_h_1, c_e, s22, s23)))),
% 295.41/188.01 inference(rewrite,[status(thm)],[])).
% 295.41/188.01 tff(30961,plain,
% 295.41/188.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s23)) | m_c_h_element_v_out(c_e_h_1, c_e, s22) | (~node18(c_e_h_1, c_e, s22, s23)))),
% 295.41/188.01 inference(quant_inst,[status(thm)],[])).
% 295.51/188.01 tff(30962,plain,
% 295.51/188.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s23)) | m_c_h_element_v_out(c_e_h_1, c_e, s22) | (~node18(c_e_h_1, c_e, s22, s23))),
% 295.51/188.01 inference(modus_ponens,[status(thm)],[30961, 30960])).
% 295.51/188.01 tff(30963,plain,
% 295.51/188.01 ($false),
% 295.51/188.01 inference(unit_resolution,[status(thm)],[30962, 753, 30958, 30957, 30959])).
% 295.51/188.01 tff(30964,plain,((~node18(c_e_h_1, c_e, s22, s23)) | m_c_h_element_v_out(c_e_h_1, c_e, s22) | (~m_c_h_element_v_out(c_e_h_1, c_e, s23))), inference(lemma,lemma(discharge,[]))).
% 295.51/188.01 tff(30965,plain,
% 295.51/188.01 (~node18(c_e_h_1, c_e, s22, s23)),
% 295.51/188.01 inference(unit_resolution,[status(thm)],[30964, 30958, 30957])).
% 295.51/188.01 tff(30966,plain,
% 295.51/188.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s22, s23)) | node19(c_e_h_1, c_e, s22, s23))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s22, s23)) | node19(c_e_h_1, c_e, s22, s23))),
% 295.51/188.01 inference(rewrite,[status(thm)],[])).
% 295.51/188.01 tff(30967,plain,
% 295.51/188.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s22, s23)) | node19(c_e_h_1, c_e, s22, s23))),
% 295.51/188.01 inference(quant_inst,[status(thm)],[])).
% 295.51/188.01 tff(30968,plain,
% 295.51/188.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s22, s23)) | node19(c_e_h_1, c_e, s22, s23)),
% 295.51/188.01 inference(modus_ponens,[status(thm)],[30967, 30966])).
% 295.51/188.01 tff(30969,plain,
% 295.51/188.01 (node19(c_e_h_1, c_e, s22, s23)),
% 295.51/188.01 inference(unit_resolution,[status(thm)],[30968, 190, 30672])).
% 295.51/188.01 tff(30970,plain,
% 295.51/188.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_1, c_e, s22, s23) | (~node19(c_e_h_1, c_e, s22, s23)) | node17(c_e_h_1, c_e, s22))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_e, s22, s23) | (~node19(c_e_h_1, c_e, s22, s23)) | node17(c_e_h_1, c_e, s22))),
% 295.51/188.01 inference(rewrite,[status(thm)],[])).
% 295.51/188.01 tff(30971,plain,
% 295.51/188.01 ((node17(c_e_h_1, c_e, s22) | node18(c_e_h_1, c_e, s22, s23) | (~node19(c_e_h_1, c_e, s22, s23))) <=> (node18(c_e_h_1, c_e, s22, s23) | (~node19(c_e_h_1, c_e, s22, s23)) | node17(c_e_h_1, c_e, s22))),
% 295.51/188.01 inference(rewrite,[status(thm)],[])).
% 295.51/188.01 tff(30972,plain,
% 295.51/188.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s22) | node18(c_e_h_1, c_e, s22, s23) | (~node19(c_e_h_1, c_e, s22, s23)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_1, c_e, s22, s23) | (~node19(c_e_h_1, c_e, s22, s23)) | node17(c_e_h_1, c_e, s22)))),
% 295.51/188.01 inference(monotonicity,[status(thm)],[30971])).
% 295.51/188.01 tff(30973,plain,
% 295.51/188.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s22) | node18(c_e_h_1, c_e, s22, s23) | (~node19(c_e_h_1, c_e, s22, s23)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_e, s22, s23) | (~node19(c_e_h_1, c_e, s22, s23)) | node17(c_e_h_1, c_e, s22))),
% 295.51/188.01 inference(transitivity,[status(thm)],[30972, 30970])).
% 295.51/188.01 tff(30974,plain,
% 295.51/188.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s22) | node18(c_e_h_1, c_e, s22, s23) | (~node19(c_e_h_1, c_e, s22, s23)))),
% 295.51/188.01 inference(quant_inst,[status(thm)],[])).
% 295.51/188.01 tff(30975,plain,
% 295.51/188.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_e, s22, s23) | (~node19(c_e_h_1, c_e, s22, s23)) | node17(c_e_h_1, c_e, s22)),
% 295.51/188.01 inference(modus_ponens,[status(thm)],[30974, 30973])).
% 295.51/188.01 tff(30976,plain,
% 295.51/188.01 (node18(c_e_h_1, c_e, s22, s23) | node17(c_e_h_1, c_e, s22)),
% 295.51/188.01 inference(unit_resolution,[status(thm)],[30975, 776, 30969])).
% 295.51/188.01 tff(30977,plain,
% 295.51/188.01 (node17(c_e_h_1, c_e, s22)),
% 295.51/188.01 inference(unit_resolution,[status(thm)],[30976, 30965])).
% 295.51/188.01 tff(30978,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_e, s22)), introduced(assumption)).
% 295.51/188.01 tff(30979,plain,
% 295.51/188.01 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s22)) | m_c_h_element_v_in2(c_e_h_1, c_e, s22) | (~node17(c_e_h_1, c_e, s22)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s22)) | m_c_h_element_v_in2(c_e_h_1, c_e, s22) | (~node17(c_e_h_1, c_e, s22)))),
% 295.51/188.01 inference(rewrite,[status(thm)],[])).
% 295.51/188.01 tff(30980,plain,
% 295.51/188.01 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s22)) | m_c_h_element_v_in2(c_e_h_1, c_e, s22) | (~node17(c_e_h_1, c_e, s22)))),
% 295.51/188.01 inference(quant_inst,[status(thm)],[])).
% 295.51/188.01 tff(30981,plain,
% 295.51/188.01 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s22)) | m_c_h_element_v_in2(c_e_h_1, c_e, s22) | (~node17(c_e_h_1, c_e, s22))),
% 295.51/188.01 inference(modus_ponens,[status(thm)],[30980, 30979])).
% 295.51/188.01 tff(30982,plain,
% 295.51/188.01 ((~m_c_h_element_v_in1(c_e_h_1, c_e, s22)) | (~node17(c_e_h_1, c_e, s22))),
% 295.51/188.01 inference(unit_resolution,[status(thm)],[30981, 919, 30978])).
% 295.51/188.01 tff(30983,plain,
% 295.51/188.01 (~m_c_h_element_v_in1(c_e_h_1, c_e, s22)),
% 295.51/188.01 inference(unit_resolution,[status(thm)],[30982, 30977])).
% 295.51/188.01 tff(30984,assumption,(node15(c_e_h_1, c_e, s22, s23)), introduced(assumption)).
% 295.51/188.01 tff(30985,plain,
% 295.51/188.01 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s23)) | (~node15(c_e_h_1, c_e, s22, s23)) | m_c_h_element_v_out(c_e_h_1, c_e, s22))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s23)) | (~node15(c_e_h_1, c_e, s22, s23)) | m_c_h_element_v_out(c_e_h_1, c_e, s22))),
% 295.51/188.01 inference(rewrite,[status(thm)],[])).
% 295.51/188.01 tff(30986,plain,
% 295.51/188.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s23)) | (~node15(c_e_h_1, c_e, s22, s23)) | m_c_h_element_v_out(c_e_h_1, c_e, s22))),
% 295.51/188.01 inference(quant_inst,[status(thm)],[])).
% 295.51/188.01 tff(30987,plain,
% 295.51/188.01 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s23)) | (~node15(c_e_h_1, c_e, s22, s23)) | m_c_h_element_v_out(c_e_h_1, c_e, s22)),
% 295.51/188.01 inference(modus_ponens,[status(thm)],[30986, 30985])).
% 295.51/188.01 tff(30988,plain,
% 295.51/188.01 ($false),
% 295.51/188.01 inference(unit_resolution,[status(thm)],[30987, 147, 30958, 30957, 30984])).
% 295.51/188.01 tff(30989,plain,((~node15(c_e_h_1, c_e, s22, s23)) | m_c_h_element_v_out(c_e_h_1, c_e, s22) | (~m_c_h_element_v_out(c_e_h_1, c_e, s23))), inference(lemma,lemma(discharge,[]))).
% 295.51/188.01 tff(30990,plain,
% 295.51/188.01 (~node15(c_e_h_1, c_e, s22, s23)),
% 295.51/188.01 inference(unit_resolution,[status(thm)],[30989, 30958, 30957])).
% 295.51/188.01 tff(30991,assumption,(node17(c_e_h_1, c_e, s22)), introduced(assumption)).
% 295.51/188.01 tff(30992,assumption,(node16(c_e_h_1, c_e, s22)), introduced(assumption)).
% 295.51/188.01 tff(30993,plain,
% 295.51/188.01 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s22)) | (~node17(c_e_h_1, c_e, s22)) | m_c_h_element_v_in1(c_e_h_1, c_e, s22))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s22)) | (~node17(c_e_h_1, c_e, s22)) | m_c_h_element_v_in1(c_e_h_1, c_e, s22))),
% 295.51/188.01 inference(rewrite,[status(thm)],[])).
% 295.51/188.02 tff(30994,plain,
% 295.51/188.02 ((m_c_h_element_v_in1(c_e_h_1, c_e, s22) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s22)) | (~node17(c_e_h_1, c_e, s22))) <=> ((~m_c_h_element_v_in2(c_e_h_1, c_e, s22)) | (~node17(c_e_h_1, c_e, s22)) | m_c_h_element_v_in1(c_e_h_1, c_e, s22))),
% 295.51/188.02 inference(rewrite,[status(thm)],[])).
% 295.51/188.02 tff(30995,plain,
% 295.51/188.02 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s22) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s22)) | (~node17(c_e_h_1, c_e, s22)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s22)) | (~node17(c_e_h_1, c_e, s22)) | m_c_h_element_v_in1(c_e_h_1, c_e, s22)))),
% 295.51/188.02 inference(monotonicity,[status(thm)],[30994])).
% 295.51/188.02 tff(30996,plain,
% 295.51/188.02 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s22) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s22)) | (~node17(c_e_h_1, c_e, s22)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s22)) | (~node17(c_e_h_1, c_e, s22)) | m_c_h_element_v_in1(c_e_h_1, c_e, s22))),
% 295.51/188.02 inference(transitivity,[status(thm)],[30995, 30993])).
% 295.51/188.02 tff(30997,plain,
% 295.51/188.02 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s22) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s22)) | (~node17(c_e_h_1, c_e, s22)))),
% 295.51/188.02 inference(quant_inst,[status(thm)],[])).
% 295.51/188.02 tff(30998,plain,
% 295.51/188.02 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s22)) | (~node17(c_e_h_1, c_e, s22)) | m_c_h_element_v_in1(c_e_h_1, c_e, s22)),
% 295.51/188.02 inference(modus_ponens,[status(thm)],[30997, 30996])).
% 295.51/188.02 tff(30999,plain,
% 295.51/188.02 ((~m_c_h_element_v_in2(c_e_h_1, c_e, s22)) | m_c_h_element_v_in1(c_e_h_1, c_e, s22)),
% 295.51/188.02 inference(unit_resolution,[status(thm)],[30998, 859, 30991])).
% 295.51/188.02 tff(31000,plain,
% 295.51/188.02 (m_c_h_element_v_in1(c_e_h_1, c_e, s22)),
% 295.51/188.02 inference(unit_resolution,[status(thm)],[30999, 30950])).
% 295.51/188.02 tff(31001,plain,
% 295.51/188.02 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s22)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s22)) | (~node16(c_e_h_1, c_e, s22)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s22)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s22)) | (~node16(c_e_h_1, c_e, s22)))),
% 295.51/188.02 inference(rewrite,[status(thm)],[])).
% 295.51/188.02 tff(31002,plain,
% 295.51/188.02 (((~node16(c_e_h_1, c_e, s22)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s22)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s22))) <=> ((~m_c_h_element_v_in1(c_e_h_1, c_e, s22)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s22)) | (~node16(c_e_h_1, c_e, s22)))),
% 295.51/188.02 inference(rewrite,[status(thm)],[])).
% 295.51/188.02 tff(31003,plain,
% 295.51/188.02 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s22)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s22)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s22)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s22)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s22)) | (~node16(c_e_h_1, c_e, s22))))),
% 295.51/188.02 inference(monotonicity,[status(thm)],[31002])).
% 295.51/188.02 tff(31004,plain,
% 295.51/188.02 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s22)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s22)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s22)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s22)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s22)) | (~node16(c_e_h_1, c_e, s22)))),
% 295.51/188.02 inference(transitivity,[status(thm)],[31003, 31001])).
% 295.51/188.02 tff(31005,plain,
% 295.51/188.02 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s22)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s22)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s22)))),
% 295.51/188.02 inference(quant_inst,[status(thm)],[])).
% 295.51/188.02 tff(31006,plain,
% 295.51/188.02 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s22)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s22)) | (~node16(c_e_h_1, c_e, s22))),
% 295.51/188.02 inference(modus_ponens,[status(thm)],[31005, 31004])).
% 295.51/188.02 tff(31007,plain,
% 295.51/188.02 ((~m_c_h_element_v_in1(c_e_h_1, c_e, s22)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s22))),
% 295.51/188.02 inference(unit_resolution,[status(thm)],[31006, 2307, 30992])).
% 295.51/188.02 tff(31008,plain,
% 295.51/188.02 ($false),
% 295.51/188.02 inference(unit_resolution,[status(thm)],[31007, 31000, 30950])).
% 295.51/188.02 tff(31009,plain,((~m_c_h_element_v_in2(c_e_h_1, c_e, s22)) | (~node16(c_e_h_1, c_e, s22)) | (~node17(c_e_h_1, c_e, s22))), inference(lemma,lemma(discharge,[]))).
% 295.51/188.02 tff(31010,plain,
% 295.51/188.02 (~m_c_h_element_v_in2(c_e_h_1, c_e, s22)),
% 295.51/188.02 inference(unit_resolution,[status(thm)],[31009, 30992, 30991])).
% 295.51/188.02 tff(31011,plain,
% 295.51/188.02 ((~m_c_h_element_v_in1(c_e_h_1, c_e, s22)) | m_c_h_element_v_in2(c_e_h_1, c_e, s22)),
% 295.51/188.02 inference(unit_resolution,[status(thm)],[30981, 919, 30991])).
% 295.51/188.02 tff(31012,plain,
% 295.51/188.02 (~m_c_h_element_v_in1(c_e_h_1, c_e, s22)),
% 295.51/188.02 inference(unit_resolution,[status(thm)],[31011, 31010])).
% 295.51/188.02 tff(31013,plain,
% 295.51/188.02 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s22)) | m_c_h_element_v_in1(c_e_h_1, c_e, s22) | m_c_h_element_v_in2(c_e_h_1, c_e, s22))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s22)) | m_c_h_element_v_in1(c_e_h_1, c_e, s22) | m_c_h_element_v_in2(c_e_h_1, c_e, s22))),
% 295.51/188.02 inference(rewrite,[status(thm)],[])).
% 295.51/188.02 tff(31014,plain,
% 295.51/188.02 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s22)) | m_c_h_element_v_in1(c_e_h_1, c_e, s22) | m_c_h_element_v_in2(c_e_h_1, c_e, s22))),
% 295.51/188.02 inference(quant_inst,[status(thm)],[])).
% 295.51/188.02 tff(31015,plain,
% 295.51/188.02 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s22)) | m_c_h_element_v_in1(c_e_h_1, c_e, s22) | m_c_h_element_v_in2(c_e_h_1, c_e, s22)),
% 295.51/188.02 inference(modus_ponens,[status(thm)],[31014, 31013])).
% 295.51/188.02 tff(31016,plain,
% 295.51/188.02 (m_c_h_element_v_in1(c_e_h_1, c_e, s22) | m_c_h_element_v_in2(c_e_h_1, c_e, s22)),
% 295.51/188.02 inference(unit_resolution,[status(thm)],[31015, 178, 30992])).
% 295.51/188.02 tff(31017,plain,
% 295.51/188.02 ($false),
% 295.51/188.02 inference(unit_resolution,[status(thm)],[31016, 31012, 31010])).
% 295.51/188.02 tff(31018,plain,((~node16(c_e_h_1, c_e, s22)) | (~node17(c_e_h_1, c_e, s22))), inference(lemma,lemma(discharge,[]))).
% 295.51/188.02 tff(31019,plain,
% 295.51/188.02 (~node16(c_e_h_1, c_e, s22)),
% 295.51/188.02 inference(unit_resolution,[status(thm)],[31018, 30977])).
% 295.51/188.02 tff(31020,plain,
% 295.51/188.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s22) | node14(c_e_h_1, c_e, s22, s23) | node15(c_e_h_1, c_e, s22, s23) | (~node19(c_e_h_1, c_e, s22, s23)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_e, s22) | node14(c_e_h_1, c_e, s22, s23) | node15(c_e_h_1, c_e, s22, s23) | (~node19(c_e_h_1, c_e, s22, s23)))),
% 295.51/188.02 inference(rewrite,[status(thm)],[])).
% 295.51/188.02 tff(31021,plain,
% 295.51/188.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s22) | node14(c_e_h_1, c_e, s22, s23) | node15(c_e_h_1, c_e, s22, s23) | (~node19(c_e_h_1, c_e, s22, s23)))),
% 295.51/188.02 inference(quant_inst,[status(thm)],[])).
% 295.51/188.02 tff(31022,plain,
% 295.51/188.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_e, s22) | node14(c_e_h_1, c_e, s22, s23) | node15(c_e_h_1, c_e, s22, s23) | (~node19(c_e_h_1, c_e, s22, s23))),
% 295.51/188.02 inference(modus_ponens,[status(thm)],[31021, 31020])).
% 295.51/188.02 tff(31023,plain,
% 295.51/188.02 (node16(c_e_h_1, c_e, s22) | node14(c_e_h_1, c_e, s22, s23) | node15(c_e_h_1, c_e, s22, s23)),
% 295.51/188.02 inference(unit_resolution,[status(thm)],[31022, 204, 30969])).
% 295.51/188.02 tff(31024,plain,
% 295.51/188.02 (node14(c_e_h_1, c_e, s22, s23)),
% 295.51/188.02 inference(unit_resolution,[status(thm)],[31023, 31019, 30990])).
% 295.51/188.02 tff(31025,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_e, s22)), introduced(assumption)).
% 295.51/188.02 tff(31026,assumption,(node14(c_e_h_1, c_e, s22, s23)), introduced(assumption)).
% 295.51/188.02 tff(31027,plain,
% 295.51/188.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s23)) | (~node14(c_e_h_1, c_e, s22, s23)) | m_c_h_element_v_in1(c_e_h_1, c_e, s22))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s23)) | (~node14(c_e_h_1, c_e, s22, s23)) | m_c_h_element_v_in1(c_e_h_1, c_e, s22))),
% 295.51/188.02 inference(rewrite,[status(thm)],[])).
% 295.51/188.02 tff(31028,plain,
% 295.51/188.02 (((~node14(c_e_h_1, c_e, s22, s23)) | m_c_h_element_v_in1(c_e_h_1, c_e, s22) | (~m_c_h_element_v_out(c_e_h_1, c_e, s23))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_e, s23)) | (~node14(c_e_h_1, c_e, s22, s23)) | m_c_h_element_v_in1(c_e_h_1, c_e, s22))),
% 295.51/188.02 inference(rewrite,[status(thm)],[])).
% 295.51/188.02 tff(31029,plain,
% 295.51/188.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s22, s23)) | m_c_h_element_v_in1(c_e_h_1, c_e, s22) | (~m_c_h_element_v_out(c_e_h_1, c_e, s23)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s23)) | (~node14(c_e_h_1, c_e, s22, s23)) | m_c_h_element_v_in1(c_e_h_1, c_e, s22)))),
% 295.51/188.02 inference(monotonicity,[status(thm)],[31028])).
% 295.51/188.02 tff(31030,plain,
% 295.51/188.02 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s22, s23)) | m_c_h_element_v_in1(c_e_h_1, c_e, s22) | (~m_c_h_element_v_out(c_e_h_1, c_e, s23)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s23)) | (~node14(c_e_h_1, c_e, s22, s23)) | m_c_h_element_v_in1(c_e_h_1, c_e, s22))),
% 295.51/188.02 inference(transitivity,[status(thm)],[31029, 31027])).
% 295.51/188.02 tff(31031,plain,
% 295.51/188.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s22, s23)) | m_c_h_element_v_in1(c_e_h_1, c_e, s22) | (~m_c_h_element_v_out(c_e_h_1, c_e, s23)))),
% 295.51/188.02 inference(quant_inst,[status(thm)],[])).
% 295.51/188.02 tff(31032,plain,
% 295.51/188.02 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s23)) | (~node14(c_e_h_1, c_e, s22, s23)) | m_c_h_element_v_in1(c_e_h_1, c_e, s22)),
% 295.51/188.02 inference(modus_ponens,[status(thm)],[31031, 31030])).
% 295.51/188.02 tff(31033,plain,
% 295.51/188.02 ($false),
% 295.51/188.02 inference(unit_resolution,[status(thm)],[31032, 223, 30957, 31026, 31025])).
% 295.51/188.02 tff(31034,plain,((~node14(c_e_h_1, c_e, s22, s23)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s23)) | m_c_h_element_v_in1(c_e_h_1, c_e, s22)), inference(lemma,lemma(discharge,[]))).
% 295.51/188.03 tff(31035,plain,
% 295.51/188.03 ($false),
% 295.51/188.03 inference(unit_resolution,[status(thm)],[31034, 31024, 30983, 30957])).
% 295.51/188.03 tff(31036,plain,(m_c_h_element_v_out(c_e_h_1, c_e, s22) | (~m_c_h_element_v_out(c_e_h_1, c_e, s23)) | m_c_h_element_v_in2(c_e_h_1, c_e, s22)), inference(lemma,lemma(discharge,[]))).
% 295.51/188.03 tff(31037,plain,
% 295.51/188.03 (~m_c_h_element_v_out(c_e_h_1, c_e, s23)),
% 295.51/188.03 inference(unit_resolution,[status(thm)],[31036, 30956, 30949])).
% 295.51/188.03 tff(31038,assumption,(m_c_h_element_v_in2(c_e_h_1, c_e, s23)), introduced(assumption)).
% 295.51/188.03 tff(31039,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_i, s23)), introduced(assumption)).
% 295.51/188.03 tff(31040,plain,
% 295.51/188.03 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s23)) | m_and_h_gate_v_out(c_e_h_1, c_i, s23))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s23)) | m_and_h_gate_v_out(c_e_h_1, c_i, s23))),
% 295.51/188.03 inference(rewrite,[status(thm)],[])).
% 295.51/188.03 tff(31041,plain,
% 295.51/188.03 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s23)) | m_and_h_gate_v_out(c_e_h_1, c_i, s23))),
% 295.51/188.03 inference(quant_inst,[status(thm)],[])).
% 295.51/188.03 tff(31042,plain,
% 295.51/188.03 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s23)) | m_and_h_gate_v_out(c_e_h_1, c_i, s23)),
% 295.51/188.03 inference(modus_ponens,[status(thm)],[31041, 31040])).
% 295.51/188.03 tff(31043,plain,
% 295.51/188.03 ($false),
% 295.51/188.03 inference(unit_resolution,[status(thm)],[31042, 164, 31039, 31038])).
% 295.51/188.03 tff(31044,plain,((~m_c_h_element_v_in2(c_e_h_1, c_e, s23)) | m_and_h_gate_v_out(c_e_h_1, c_i, s23)), inference(lemma,lemma(discharge,[]))).
% 295.51/188.03 tff(31045,plain,
% 295.51/188.03 (~m_c_h_element_v_in2(c_e_h_1, c_e, s23)),
% 295.51/188.03 inference(unit_resolution,[status(thm)],[31044, 30684])).
% 295.51/188.03 tff(31046,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_e, s23)), introduced(assumption)).
% 295.51/188.03 tff(31047,assumption,(m_c_h_element_v_out(c_e_h_1, c_e, s24)), introduced(assumption)).
% 295.51/188.03 tff(31048,assumption,(~m_c_h_element_v_out(c_e_h_1, c_e, s23)), introduced(assumption)).
% 295.51/188.03 tff(31049,assumption,(~node14(c_e_h_1, c_e, s23, s24)), introduced(assumption)).
% 295.51/188.03 tff(31050,assumption,(node18(c_e_h_1, c_e, s23, s24)), introduced(assumption)).
% 295.51/188.03 tff(31051,plain,
% 295.51/188.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s23) | (~m_c_h_element_v_out(c_e_h_1, c_e, s24)) | (~node18(c_e_h_1, c_e, s23, s24)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s23) | (~m_c_h_element_v_out(c_e_h_1, c_e, s24)) | (~node18(c_e_h_1, c_e, s23, s24)))),
% 295.51/188.03 inference(rewrite,[status(thm)],[])).
% 295.51/188.03 tff(31052,plain,
% 295.51/188.03 (((~m_c_h_element_v_out(c_e_h_1, c_e, s24)) | m_c_h_element_v_out(c_e_h_1, c_e, s23) | (~node18(c_e_h_1, c_e, s23, s24))) <=> (m_c_h_element_v_out(c_e_h_1, c_e, s23) | (~m_c_h_element_v_out(c_e_h_1, c_e, s24)) | (~node18(c_e_h_1, c_e, s23, s24)))),
% 295.51/188.03 inference(rewrite,[status(thm)],[])).
% 295.51/188.03 tff(31053,plain,
% 295.51/188.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s24)) | m_c_h_element_v_out(c_e_h_1, c_e, s23) | (~node18(c_e_h_1, c_e, s23, s24)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_e, s23) | (~m_c_h_element_v_out(c_e_h_1, c_e, s24)) | (~node18(c_e_h_1, c_e, s23, s24))))),
% 295.51/188.03 inference(monotonicity,[status(thm)],[31052])).
% 295.51/188.03 tff(31054,plain,
% 295.51/188.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s24)) | m_c_h_element_v_out(c_e_h_1, c_e, s23) | (~node18(c_e_h_1, c_e, s23, s24)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s23) | (~m_c_h_element_v_out(c_e_h_1, c_e, s24)) | (~node18(c_e_h_1, c_e, s23, s24)))),
% 295.51/188.03 inference(transitivity,[status(thm)],[31053, 31051])).
% 295.51/188.03 tff(31055,plain,
% 295.51/188.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s24)) | m_c_h_element_v_out(c_e_h_1, c_e, s23) | (~node18(c_e_h_1, c_e, s23, s24)))),
% 295.51/188.03 inference(quant_inst,[status(thm)],[])).
% 295.51/188.03 tff(31056,plain,
% 295.51/188.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_e, s23) | (~m_c_h_element_v_out(c_e_h_1, c_e, s24)) | (~node18(c_e_h_1, c_e, s23, s24))),
% 295.51/188.03 inference(modus_ponens,[status(thm)],[31055, 31054])).
% 295.51/188.03 tff(31057,plain,
% 295.51/188.03 ($false),
% 295.51/188.03 inference(unit_resolution,[status(thm)],[31056, 753, 31048, 31047, 31050])).
% 295.51/188.03 tff(31058,plain,((~node18(c_e_h_1, c_e, s23, s24)) | m_c_h_element_v_out(c_e_h_1, c_e, s23) | (~m_c_h_element_v_out(c_e_h_1, c_e, s24))), inference(lemma,lemma(discharge,[]))).
% 295.51/188.03 tff(31059,plain,
% 295.51/188.03 (~node18(c_e_h_1, c_e, s23, s24)),
% 295.51/188.03 inference(unit_resolution,[status(thm)],[31058, 31048, 31047])).
% 295.51/188.03 tff(31060,plain,
% 295.51/188.03 (succ(s23, s24) <=> succ(s23, s24)),
% 295.51/188.03 inference(rewrite,[status(thm)],[])).
% 295.51/188.03 tff(31061,axiom,(succ(s23, s24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound24')).
% 295.51/188.03 tff(31062,plain,
% 295.51/188.03 (succ(s23, s24)),
% 295.51/188.03 inference(modus_ponens,[status(thm)],[31061, 31060])).
% 295.51/188.03 tff(31063,plain,
% 295.51/188.03 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s23, s24)) | trans(s23, s24))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s23, s24)) | trans(s23, s24))),
% 295.51/188.03 inference(rewrite,[status(thm)],[])).
% 295.51/188.03 tff(31064,plain,
% 295.51/188.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s23, s24)) | trans(s23, s24))),
% 295.51/188.03 inference(quant_inst,[status(thm)],[])).
% 295.51/188.03 tff(31065,plain,
% 295.51/188.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s23, s24)) | trans(s23, s24)),
% 295.51/188.03 inference(modus_ponens,[status(thm)],[31064, 31063])).
% 295.51/188.03 tff(31066,plain,
% 295.51/188.03 (trans(s23, s24)),
% 295.51/188.03 inference(unit_resolution,[status(thm)],[31065, 31062, 65])).
% 295.51/188.03 tff(31067,plain,
% 295.51/188.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s23, s24)) | node19(c_e_h_1, c_e, s23, s24))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s23, s24)) | node19(c_e_h_1, c_e, s23, s24))),
% 295.51/188.03 inference(rewrite,[status(thm)],[])).
% 295.51/188.03 tff(31068,plain,
% 295.51/188.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s23, s24)) | node19(c_e_h_1, c_e, s23, s24))),
% 295.51/188.03 inference(quant_inst,[status(thm)],[])).
% 295.51/188.03 tff(31069,plain,
% 295.51/188.03 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s23, s24)) | node19(c_e_h_1, c_e, s23, s24)),
% 295.51/188.03 inference(modus_ponens,[status(thm)],[31068, 31067])).
% 295.51/188.03 tff(31070,plain,
% 295.51/188.03 (node19(c_e_h_1, c_e, s23, s24)),
% 295.51/188.03 inference(unit_resolution,[status(thm)],[31069, 190, 31066])).
% 295.51/188.03 tff(31071,plain,
% 295.51/188.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_e, s23, s24)) | node18(c_e_h_1, c_e, s23, s24) | node17(c_e_h_1, c_e, s23))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s23, s24)) | node18(c_e_h_1, c_e, s23, s24) | node17(c_e_h_1, c_e, s23))),
% 295.51/188.03 inference(rewrite,[status(thm)],[])).
% 295.51/188.03 tff(31072,plain,
% 295.51/188.03 ((node17(c_e_h_1, c_e, s23) | node18(c_e_h_1, c_e, s23, s24) | (~node19(c_e_h_1, c_e, s23, s24))) <=> ((~node19(c_e_h_1, c_e, s23, s24)) | node18(c_e_h_1, c_e, s23, s24) | node17(c_e_h_1, c_e, s23))),
% 295.51/188.03 inference(rewrite,[status(thm)],[])).
% 295.51/188.03 tff(31073,plain,
% 295.51/188.03 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s23) | node18(c_e_h_1, c_e, s23, s24) | (~node19(c_e_h_1, c_e, s23, s24)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_e, s23, s24)) | node18(c_e_h_1, c_e, s23, s24) | node17(c_e_h_1, c_e, s23)))),
% 295.51/188.04 inference(monotonicity,[status(thm)],[31072])).
% 295.51/188.04 tff(31074,plain,
% 295.51/188.04 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s23) | node18(c_e_h_1, c_e, s23, s24) | (~node19(c_e_h_1, c_e, s23, s24)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s23, s24)) | node18(c_e_h_1, c_e, s23, s24) | node17(c_e_h_1, c_e, s23))),
% 295.51/188.04 inference(transitivity,[status(thm)],[31073, 31071])).
% 295.51/188.04 tff(31075,plain,
% 295.51/188.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_e, s23) | node18(c_e_h_1, c_e, s23, s24) | (~node19(c_e_h_1, c_e, s23, s24)))),
% 295.51/188.04 inference(quant_inst,[status(thm)],[])).
% 295.51/188.04 tff(31076,plain,
% 295.51/188.04 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_e, s23, s24)) | node18(c_e_h_1, c_e, s23, s24) | node17(c_e_h_1, c_e, s23)),
% 295.51/188.04 inference(modus_ponens,[status(thm)],[31075, 31074])).
% 295.51/188.04 tff(31077,plain,
% 295.51/188.04 (node18(c_e_h_1, c_e, s23, s24) | node17(c_e_h_1, c_e, s23)),
% 295.51/188.04 inference(unit_resolution,[status(thm)],[31076, 776, 31070])).
% 295.51/188.04 tff(31078,plain,
% 295.51/188.04 (node17(c_e_h_1, c_e, s23)),
% 295.51/188.04 inference(unit_resolution,[status(thm)],[31077, 31059])).
% 295.51/188.04 tff(31079,assumption,(node17(c_e_h_1, c_e, s23)), introduced(assumption)).
% 295.51/188.04 tff(31080,assumption,(node16(c_e_h_1, c_e, s23)), introduced(assumption)).
% 295.51/188.04 tff(31081,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_e, s23)), introduced(assumption)).
% 295.51/188.04 tff(31082,plain,
% 295.51/188.04 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s23)) | m_c_h_element_v_in1(c_e_h_1, c_e, s23) | (~node17(c_e_h_1, c_e, s23)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s23)) | m_c_h_element_v_in1(c_e_h_1, c_e, s23) | (~node17(c_e_h_1, c_e, s23)))),
% 295.51/188.04 inference(rewrite,[status(thm)],[])).
% 295.51/188.04 tff(31083,plain,
% 295.51/188.04 ((m_c_h_element_v_in1(c_e_h_1, c_e, s23) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s23)) | (~node17(c_e_h_1, c_e, s23))) <=> ((~m_c_h_element_v_in2(c_e_h_1, c_e, s23)) | m_c_h_element_v_in1(c_e_h_1, c_e, s23) | (~node17(c_e_h_1, c_e, s23)))),
% 295.51/188.04 inference(rewrite,[status(thm)],[])).
% 295.51/188.04 tff(31084,plain,
% 295.51/188.04 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s23) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s23)) | (~node17(c_e_h_1, c_e, s23)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s23)) | m_c_h_element_v_in1(c_e_h_1, c_e, s23) | (~node17(c_e_h_1, c_e, s23))))),
% 295.51/188.04 inference(monotonicity,[status(thm)],[31083])).
% 295.51/188.04 tff(31085,plain,
% 295.51/188.04 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s23) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s23)) | (~node17(c_e_h_1, c_e, s23)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s23)) | m_c_h_element_v_in1(c_e_h_1, c_e, s23) | (~node17(c_e_h_1, c_e, s23)))),
% 295.51/188.04 inference(transitivity,[status(thm)],[31084, 31082])).
% 295.51/188.04 tff(31086,plain,
% 295.51/188.04 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_e, s23) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s23)) | (~node17(c_e_h_1, c_e, s23)))),
% 295.51/188.04 inference(quant_inst,[status(thm)],[])).
% 295.51/188.04 tff(31087,plain,
% 295.51/188.04 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s23)) | m_c_h_element_v_in1(c_e_h_1, c_e, s23) | (~node17(c_e_h_1, c_e, s23))),
% 295.51/188.04 inference(modus_ponens,[status(thm)],[31086, 31085])).
% 295.51/188.04 tff(31088,plain,
% 295.51/188.04 ((~m_c_h_element_v_in2(c_e_h_1, c_e, s23)) | m_c_h_element_v_in1(c_e_h_1, c_e, s23)),
% 295.51/188.04 inference(unit_resolution,[status(thm)],[31087, 859, 31079])).
% 295.51/188.04 tff(31089,plain,
% 295.51/188.04 (~m_c_h_element_v_in2(c_e_h_1, c_e, s23)),
% 295.51/188.04 inference(unit_resolution,[status(thm)],[31088, 31081])).
% 295.51/188.04 tff(31090,plain,
% 295.51/188.04 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s23)) | m_c_h_element_v_in1(c_e_h_1, c_e, s23) | m_c_h_element_v_in2(c_e_h_1, c_e, s23))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s23)) | m_c_h_element_v_in1(c_e_h_1, c_e, s23) | m_c_h_element_v_in2(c_e_h_1, c_e, s23))),
% 295.51/188.04 inference(rewrite,[status(thm)],[])).
% 295.51/188.04 tff(31091,plain,
% 295.51/188.04 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_e, s23)) | m_c_h_element_v_in1(c_e_h_1, c_e, s23) | m_c_h_element_v_in2(c_e_h_1, c_e, s23))),
% 295.51/188.04 inference(quant_inst,[status(thm)],[])).
% 295.51/188.04 tff(31092,plain,
% 295.51/188.04 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_e, s23)) | m_c_h_element_v_in1(c_e_h_1, c_e, s23) | m_c_h_element_v_in2(c_e_h_1, c_e, s23)),
% 295.51/188.04 inference(modus_ponens,[status(thm)],[31091, 31090])).
% 295.51/188.04 tff(31093,plain,
% 295.51/188.04 (m_c_h_element_v_in1(c_e_h_1, c_e, s23) | m_c_h_element_v_in2(c_e_h_1, c_e, s23)),
% 295.51/188.04 inference(unit_resolution,[status(thm)],[31092, 178, 31080])).
% 295.51/188.04 tff(31094,plain,
% 295.51/188.04 ($false),
% 295.51/188.04 inference(unit_resolution,[status(thm)],[31093, 31089, 31081])).
% 295.51/188.04 tff(31095,plain,(m_c_h_element_v_in1(c_e_h_1, c_e, s23) | (~node16(c_e_h_1, c_e, s23)) | (~node17(c_e_h_1, c_e, s23))), inference(lemma,lemma(discharge,[]))).
% 295.51/188.04 tff(31096,plain,
% 295.51/188.04 (m_c_h_element_v_in1(c_e_h_1, c_e, s23)),
% 295.51/188.04 inference(unit_resolution,[status(thm)],[31095, 31080, 31079])).
% 295.51/188.04 tff(31097,plain,
% 295.51/188.04 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_e, s23) | (~node17(c_e_h_1, c_e, s23)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s23)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s23) | (~node17(c_e_h_1, c_e, s23)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s23)))),
% 295.51/188.04 inference(rewrite,[status(thm)],[])).
% 295.51/188.04 tff(31098,plain,
% 295.51/188.04 (((~m_c_h_element_v_in1(c_e_h_1, c_e, s23)) | m_c_h_element_v_in2(c_e_h_1, c_e, s23) | (~node17(c_e_h_1, c_e, s23))) <=> (m_c_h_element_v_in2(c_e_h_1, c_e, s23) | (~node17(c_e_h_1, c_e, s23)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s23)))),
% 295.51/188.04 inference(rewrite,[status(thm)],[])).
% 295.51/188.04 tff(31099,plain,
% 295.51/188.04 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s23)) | m_c_h_element_v_in2(c_e_h_1, c_e, s23) | (~node17(c_e_h_1, c_e, s23)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_e, s23) | (~node17(c_e_h_1, c_e, s23)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s23))))),
% 295.51/188.04 inference(monotonicity,[status(thm)],[31098])).
% 295.51/188.04 tff(31100,plain,
% 295.51/188.04 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s23)) | m_c_h_element_v_in2(c_e_h_1, c_e, s23) | (~node17(c_e_h_1, c_e, s23)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s23) | (~node17(c_e_h_1, c_e, s23)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s23)))),
% 295.51/188.04 inference(transitivity,[status(thm)],[31099, 31097])).
% 295.51/188.04 tff(31101,plain,
% 295.51/188.04 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_e, s23)) | m_c_h_element_v_in2(c_e_h_1, c_e, s23) | (~node17(c_e_h_1, c_e, s23)))),
% 295.51/188.04 inference(quant_inst,[status(thm)],[])).
% 295.51/188.04 tff(31102,plain,
% 295.51/188.04 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_e, s23) | (~node17(c_e_h_1, c_e, s23)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s23))),
% 295.51/188.04 inference(modus_ponens,[status(thm)],[31101, 31100])).
% 295.51/188.04 tff(31103,plain,
% 295.51/188.04 (m_c_h_element_v_in2(c_e_h_1, c_e, s23) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s23))),
% 295.51/188.04 inference(unit_resolution,[status(thm)],[31102, 919, 31079])).
% 295.51/188.04 tff(31104,plain,
% 295.51/188.04 (m_c_h_element_v_in2(c_e_h_1, c_e, s23)),
% 295.51/188.04 inference(unit_resolution,[status(thm)],[31103, 31096])).
% 295.51/188.04 tff(31105,plain,
% 295.51/188.04 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s23)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s23)) | (~node16(c_e_h_1, c_e, s23)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s23)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s23)) | (~node16(c_e_h_1, c_e, s23)))),
% 295.51/188.04 inference(rewrite,[status(thm)],[])).
% 295.51/188.04 tff(31106,plain,
% 295.51/188.04 (((~node16(c_e_h_1, c_e, s23)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s23)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s23))) <=> ((~m_c_h_element_v_in2(c_e_h_1, c_e, s23)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s23)) | (~node16(c_e_h_1, c_e, s23)))),
% 295.51/188.04 inference(rewrite,[status(thm)],[])).
% 295.51/188.04 tff(31107,plain,
% 295.51/188.04 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s23)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s23)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s23)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_e, s23)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s23)) | (~node16(c_e_h_1, c_e, s23))))),
% 295.51/188.04 inference(monotonicity,[status(thm)],[31106])).
% 295.51/188.04 tff(31108,plain,
% 295.51/188.04 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s23)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s23)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s23)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s23)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s23)) | (~node16(c_e_h_1, c_e, s23)))),
% 295.51/188.04 inference(transitivity,[status(thm)],[31107, 31105])).
% 295.51/188.04 tff(31109,plain,
% 295.51/188.04 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_e, s23)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s23)) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s23)))),
% 295.51/188.04 inference(quant_inst,[status(thm)],[])).
% 295.51/188.04 tff(31110,plain,
% 295.51/188.04 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_e, s23)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s23)) | (~node16(c_e_h_1, c_e, s23))),
% 295.51/188.04 inference(modus_ponens,[status(thm)],[31109, 31108])).
% 295.51/188.04 tff(31111,plain,
% 295.51/188.04 ((~m_c_h_element_v_in2(c_e_h_1, c_e, s23)) | (~m_c_h_element_v_in1(c_e_h_1, c_e, s23))),
% 295.51/188.05 inference(unit_resolution,[status(thm)],[31110, 2307, 31080])).
% 295.51/188.05 tff(31112,plain,
% 295.51/188.05 ($false),
% 295.51/188.05 inference(unit_resolution,[status(thm)],[31111, 31104, 31096])).
% 295.51/188.05 tff(31113,plain,((~node16(c_e_h_1, c_e, s23)) | (~node17(c_e_h_1, c_e, s23))), inference(lemma,lemma(discharge,[]))).
% 295.51/188.05 tff(31114,plain,
% 295.51/188.05 (~node16(c_e_h_1, c_e, s23)),
% 295.51/188.05 inference(unit_resolution,[status(thm)],[31113, 31078])).
% 295.51/188.05 tff(31115,plain,
% 295.51/188.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_1, c_e, s23, s24) | (~node19(c_e_h_1, c_e, s23, s24)) | node15(c_e_h_1, c_e, s23, s24) | node16(c_e_h_1, c_e, s23))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_e, s23, s24) | (~node19(c_e_h_1, c_e, s23, s24)) | node15(c_e_h_1, c_e, s23, s24) | node16(c_e_h_1, c_e, s23))),
% 295.51/188.05 inference(rewrite,[status(thm)],[])).
% 295.51/188.05 tff(31116,plain,
% 295.51/188.05 ((node16(c_e_h_1, c_e, s23) | node14(c_e_h_1, c_e, s23, s24) | node15(c_e_h_1, c_e, s23, s24) | (~node19(c_e_h_1, c_e, s23, s24))) <=> (node14(c_e_h_1, c_e, s23, s24) | (~node19(c_e_h_1, c_e, s23, s24)) | node15(c_e_h_1, c_e, s23, s24) | node16(c_e_h_1, c_e, s23))),
% 295.51/188.05 inference(rewrite,[status(thm)],[])).
% 295.51/188.05 tff(31117,plain,
% 295.51/188.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s23) | node14(c_e_h_1, c_e, s23, s24) | node15(c_e_h_1, c_e, s23, s24) | (~node19(c_e_h_1, c_e, s23, s24)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node14(c_e_h_1, c_e, s23, s24) | (~node19(c_e_h_1, c_e, s23, s24)) | node15(c_e_h_1, c_e, s23, s24) | node16(c_e_h_1, c_e, s23)))),
% 295.51/188.05 inference(monotonicity,[status(thm)],[31116])).
% 295.51/188.05 tff(31118,plain,
% 295.51/188.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s23) | node14(c_e_h_1, c_e, s23, s24) | node15(c_e_h_1, c_e, s23, s24) | (~node19(c_e_h_1, c_e, s23, s24)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_e, s23, s24) | (~node19(c_e_h_1, c_e, s23, s24)) | node15(c_e_h_1, c_e, s23, s24) | node16(c_e_h_1, c_e, s23))),
% 295.51/188.05 inference(transitivity,[status(thm)],[31117, 31115])).
% 295.51/188.05 tff(31119,plain,
% 295.51/188.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_e, s23) | node14(c_e_h_1, c_e, s23, s24) | node15(c_e_h_1, c_e, s23, s24) | (~node19(c_e_h_1, c_e, s23, s24)))),
% 295.51/188.05 inference(quant_inst,[status(thm)],[])).
% 295.51/188.05 tff(31120,plain,
% 295.51/188.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node14(c_e_h_1, c_e, s23, s24) | (~node19(c_e_h_1, c_e, s23, s24)) | node15(c_e_h_1, c_e, s23, s24) | node16(c_e_h_1, c_e, s23)),
% 295.51/188.05 inference(modus_ponens,[status(thm)],[31119, 31118])).
% 295.51/188.05 tff(31121,plain,
% 295.51/188.05 (node14(c_e_h_1, c_e, s23, s24) | node15(c_e_h_1, c_e, s23, s24) | node16(c_e_h_1, c_e, s23)),
% 295.51/188.05 inference(unit_resolution,[status(thm)],[31120, 204, 31070])).
% 295.51/188.05 tff(31122,plain,
% 295.51/188.05 (node15(c_e_h_1, c_e, s23, s24)),
% 295.51/188.05 inference(unit_resolution,[status(thm)],[31121, 31114, 31049])).
% 295.51/188.05 tff(31123,plain,
% 295.51/188.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s24)) | (~node15(c_e_h_1, c_e, s23, s24)) | m_c_h_element_v_out(c_e_h_1, c_e, s23))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s24)) | (~node15(c_e_h_1, c_e, s23, s24)) | m_c_h_element_v_out(c_e_h_1, c_e, s23))),
% 295.51/188.05 inference(rewrite,[status(thm)],[])).
% 295.51/188.05 tff(31124,plain,
% 295.51/188.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s24)) | (~node15(c_e_h_1, c_e, s23, s24)) | m_c_h_element_v_out(c_e_h_1, c_e, s23))),
% 295.51/188.05 inference(quant_inst,[status(thm)],[])).
% 295.51/188.05 tff(31125,plain,
% 295.51/188.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s24)) | (~node15(c_e_h_1, c_e, s23, s24)) | m_c_h_element_v_out(c_e_h_1, c_e, s23)),
% 295.51/188.05 inference(modus_ponens,[status(thm)],[31124, 31123])).
% 295.51/188.05 tff(31126,plain,
% 295.51/188.05 ($false),
% 295.51/188.05 inference(unit_resolution,[status(thm)],[31125, 147, 31048, 31047, 31122])).
% 295.51/188.05 tff(31127,plain,(m_c_h_element_v_out(c_e_h_1, c_e, s23) | (~m_c_h_element_v_out(c_e_h_1, c_e, s24)) | node14(c_e_h_1, c_e, s23, s24)), inference(lemma,lemma(discharge,[]))).
% 295.51/188.05 tff(31128,plain,
% 295.51/188.05 (node14(c_e_h_1, c_e, s23, s24)),
% 295.51/188.05 inference(unit_resolution,[status(thm)],[31127, 31047, 31048])).
% 295.51/188.05 tff(31129,assumption,(node14(c_e_h_1, c_e, s23, s24)), introduced(assumption)).
% 295.51/188.05 tff(31130,plain,
% 295.51/188.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s24)) | (~node14(c_e_h_1, c_e, s23, s24)) | m_c_h_element_v_in1(c_e_h_1, c_e, s23))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s24)) | (~node14(c_e_h_1, c_e, s23, s24)) | m_c_h_element_v_in1(c_e_h_1, c_e, s23))),
% 295.51/188.05 inference(rewrite,[status(thm)],[])).
% 295.51/188.05 tff(31131,plain,
% 295.51/188.05 (((~node14(c_e_h_1, c_e, s23, s24)) | m_c_h_element_v_in1(c_e_h_1, c_e, s23) | (~m_c_h_element_v_out(c_e_h_1, c_e, s24))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_e, s24)) | (~node14(c_e_h_1, c_e, s23, s24)) | m_c_h_element_v_in1(c_e_h_1, c_e, s23))),
% 295.51/188.05 inference(rewrite,[status(thm)],[])).
% 295.51/188.05 tff(31132,plain,
% 295.51/188.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s23, s24)) | m_c_h_element_v_in1(c_e_h_1, c_e, s23) | (~m_c_h_element_v_out(c_e_h_1, c_e, s24)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_e, s24)) | (~node14(c_e_h_1, c_e, s23, s24)) | m_c_h_element_v_in1(c_e_h_1, c_e, s23)))),
% 295.51/188.05 inference(monotonicity,[status(thm)],[31131])).
% 295.51/188.05 tff(31133,plain,
% 295.51/188.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s23, s24)) | m_c_h_element_v_in1(c_e_h_1, c_e, s23) | (~m_c_h_element_v_out(c_e_h_1, c_e, s24)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s24)) | (~node14(c_e_h_1, c_e, s23, s24)) | m_c_h_element_v_in1(c_e_h_1, c_e, s23))),
% 295.51/188.05 inference(transitivity,[status(thm)],[31132, 31130])).
% 295.51/188.05 tff(31134,plain,
% 295.51/188.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_e, s23, s24)) | m_c_h_element_v_in1(c_e_h_1, c_e, s23) | (~m_c_h_element_v_out(c_e_h_1, c_e, s24)))),
% 295.51/188.05 inference(quant_inst,[status(thm)],[])).
% 295.51/188.05 tff(31135,plain,
% 295.51/188.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_e, s24)) | (~node14(c_e_h_1, c_e, s23, s24)) | m_c_h_element_v_in1(c_e_h_1, c_e, s23)),
% 295.51/188.05 inference(modus_ponens,[status(thm)],[31134, 31133])).
% 295.51/188.05 tff(31136,plain,
% 295.51/188.05 ($false),
% 295.51/188.05 inference(unit_resolution,[status(thm)],[31135, 223, 31047, 31129, 31081])).
% 295.51/188.05 tff(31137,plain,((~node14(c_e_h_1, c_e, s23, s24)) | (~m_c_h_element_v_out(c_e_h_1, c_e, s24)) | m_c_h_element_v_in1(c_e_h_1, c_e, s23)), inference(lemma,lemma(discharge,[]))).
% 295.51/188.05 tff(31138,plain,
% 295.51/188.05 (m_c_h_element_v_in1(c_e_h_1, c_e, s23)),
% 295.51/188.05 inference(unit_resolution,[status(thm)],[31137, 31128, 31047])).
% 295.51/188.05 tff(31139,plain,
% 295.51/188.05 (~node18(c_e_h_1, c_e, s23, s24)),
% 295.51/188.05 inference(unit_resolution,[status(thm)],[31058, 31047, 31048])).
% 295.51/188.05 tff(31140,plain,
% 295.51/188.05 (node17(c_e_h_1, c_e, s23)),
% 295.51/188.05 inference(unit_resolution,[status(thm)],[31077, 31139])).
% 295.51/188.05 tff(31141,plain,
% 295.51/188.05 ($false),
% 295.51/188.05 inference(unit_resolution,[status(thm)],[31102, 919, 31140, 31138, 31046])).
% 295.51/188.05 tff(31142,plain,((~m_c_h_element_v_out(c_e_h_1, c_e, s24)) | m_c_h_element_v_in2(c_e_h_1, c_e, s23) | m_c_h_element_v_out(c_e_h_1, c_e, s23)), inference(lemma,lemma(discharge,[]))).
% 295.51/188.05 tff(31143,plain,
% 295.51/188.05 (~m_c_h_element_v_out(c_e_h_1, c_e, s24)),
% 295.51/188.05 inference(unit_resolution,[status(thm)],[31142, 31045, 31037])).
% 295.51/188.05 tff(31144,plain,
% 295.51/188.05 (~m_and_h_gate_v_out(c_e_h_3, c_i, s15)),
% 295.51/188.05 inference(unit_resolution,[status(thm)],[28427, 28398, 20171])).
% 295.51/188.05 tff(31145,plain,
% 295.51/188.05 (((~![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))) | (m_and_h_gate_v_in2(c_e_h_3, c_k, s12) | m_c_h_element_v_out(c_e_h_3, c_h, s12))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))) | m_and_h_gate_v_in2(c_e_h_3, c_k, s12) | m_c_h_element_v_out(c_e_h_3, c_h, s12))),
% 295.51/188.05 inference(rewrite,[status(thm)],[])).
% 295.51/188.05 tff(31146,plain,
% 295.51/188.05 ((~![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))) | (m_and_h_gate_v_in2(c_e_h_3, c_k, s12) | m_c_h_element_v_out(c_e_h_3, c_h, s12))),
% 295.51/188.05 inference(quant_inst,[status(thm)],[])).
% 295.51/188.05 tff(31147,plain,
% 295.51/188.05 ((~![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))) | m_and_h_gate_v_in2(c_e_h_3, c_k, s12) | m_c_h_element_v_out(c_e_h_3, c_h, s12)),
% 295.51/188.05 inference(modus_ponens,[status(thm)],[31146, 31145])).
% 295.51/188.05 tff(31148,plain,
% 295.51/188.05 (m_and_h_gate_v_in2(c_e_h_3, c_k, s12) | m_c_h_element_v_out(c_e_h_3, c_h, s12)),
% 295.51/188.05 inference(unit_resolution,[status(thm)],[31147, 6420])).
% 295.51/188.05 tff(31149,plain,
% 295.51/188.05 (m_and_h_gate_v_in2(c_e_h_3, c_k, s12)),
% 295.51/188.05 inference(unit_resolution,[status(thm)],[31148, 21894])).
% 295.51/188.05 tff(31150,assumption,(m_and_h_gate_v_out(c_e_h_3, c_l, s13)), introduced(assumption)).
% 295.51/188.05 tff(31151,assumption,(~node20(c_e_h_3, c_l, s12)), introduced(assumption)).
% 295.51/188.05 tff(31152,assumption,(node21(c_e_h_3, c_l, s12, s13)), introduced(assumption)).
% 295.51/188.05 tff(31153,plain,
% 295.51/188.05 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s12) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s13)) | (~node21(c_e_h_3, c_l, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_l, s12) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s13)) | (~node21(c_e_h_3, c_l, s12, s13)))),
% 295.51/188.05 inference(rewrite,[status(thm)],[])).
% 295.51/188.05 tff(31154,plain,
% 295.51/188.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_3, c_l, s12) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s13)) | (~node21(c_e_h_3, c_l, s12, s13)))),
% 295.51/188.05 inference(quant_inst,[status(thm)],[])).
% 295.51/188.05 tff(31155,plain,
% 295.51/188.05 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_3, c_l, s12) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s13)) | (~node21(c_e_h_3, c_l, s12, s13))),
% 295.51/188.05 inference(modus_ponens,[status(thm)],[31154, 31153])).
% 295.51/188.05 tff(31156,plain,
% 295.51/188.05 ($false),
% 295.51/188.05 inference(unit_resolution,[status(thm)],[31155, 52, 31150, 31152, 31151])).
% 295.51/188.05 tff(31157,plain,((~node21(c_e_h_3, c_l, s12, s13)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s13)) | node20(c_e_h_3, c_l, s12)), inference(lemma,lemma(discharge,[]))).
% 295.51/188.05 tff(31158,plain,
% 295.51/188.05 (~node21(c_e_h_3, c_l, s12, s13)),
% 295.51/188.05 inference(unit_resolution,[status(thm)],[31157, 31150, 31151])).
% 295.51/188.05 tff(31159,assumption,(node22(c_e_h_3, c_l, s12, s13)), introduced(assumption)).
% 295.51/188.06 tff(31160,plain,
% 295.51/188.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s13)) | (~node22(c_e_h_3, c_l, s12, s13)) | m_and_h_gate_v_out(c_e_h_3, c_l, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s13)) | (~node22(c_e_h_3, c_l, s12, s13)) | m_and_h_gate_v_out(c_e_h_3, c_l, s12))),
% 295.51/188.06 inference(rewrite,[status(thm)],[])).
% 295.51/188.06 tff(31161,plain,
% 295.51/188.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_l, s13)) | (~node22(c_e_h_3, c_l, s12, s13)) | m_and_h_gate_v_out(c_e_h_3, c_l, s12))),
% 295.51/188.06 inference(quant_inst,[status(thm)],[])).
% 295.51/188.06 tff(31162,plain,
% 295.51/188.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s13)) | (~node22(c_e_h_3, c_l, s12, s13)) | m_and_h_gate_v_out(c_e_h_3, c_l, s12)),
% 295.51/188.06 inference(modus_ponens,[status(thm)],[31161, 31160])).
% 295.51/188.06 tff(31163,plain,
% 295.51/188.06 ($false),
% 295.51/188.06 inference(unit_resolution,[status(thm)],[31162, 108, 31150, 31159, 26885])).
% 295.51/188.06 tff(31164,plain,((~node22(c_e_h_3, c_l, s12, s13)) | (~m_and_h_gate_v_out(c_e_h_3, c_l, s13)) | m_and_h_gate_v_out(c_e_h_3, c_l, s12)), inference(lemma,lemma(discharge,[]))).
% 295.51/188.06 tff(31165,plain,
% 295.51/188.06 (~node22(c_e_h_3, c_l, s12, s13)),
% 295.51/188.06 inference(unit_resolution,[status(thm)],[31164, 31150, 26885])).
% 295.51/188.06 tff(31166,plain,
% 295.51/188.06 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s12, s13)) | node21(c_e_h_3, c_l, s12, s13) | node22(c_e_h_3, c_l, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s12, s13)) | node21(c_e_h_3, c_l, s12, s13) | node22(c_e_h_3, c_l, s12, s13))),
% 295.51/188.06 inference(rewrite,[status(thm)],[])).
% 295.51/188.06 tff(31167,plain,
% 295.51/188.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s12, s13)) | node21(c_e_h_3, c_l, s12, s13) | node22(c_e_h_3, c_l, s12, s13))),
% 295.51/188.06 inference(quant_inst,[status(thm)],[])).
% 295.51/188.06 tff(31168,plain,
% 295.51/188.06 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s12, s13)) | node21(c_e_h_3, c_l, s12, s13) | node22(c_e_h_3, c_l, s12, s13)),
% 295.51/188.06 inference(modus_ponens,[status(thm)],[31167, 31166])).
% 295.51/188.06 tff(31169,plain,
% 295.51/188.06 (node21(c_e_h_3, c_l, s12, s13) | node22(c_e_h_3, c_l, s12, s13)),
% 295.51/188.06 inference(unit_resolution,[status(thm)],[31168, 82, 11856])).
% 295.51/188.06 tff(31170,plain,
% 295.51/188.06 ($false),
% 295.51/188.06 inference(unit_resolution,[status(thm)],[31169, 31165, 31158])).
% 295.51/188.06 tff(31171,plain,((~m_and_h_gate_v_out(c_e_h_3, c_l, s13)) | m_and_h_gate_v_out(c_e_h_3, c_l, s12) | node20(c_e_h_3, c_l, s12)), inference(lemma,lemma(discharge,[]))).
% 295.51/188.06 tff(31172,plain,
% 295.51/188.06 (node20(c_e_h_3, c_l, s12)),
% 295.51/188.06 inference(unit_resolution,[status(thm)],[31171, 31150, 26885])).
% 295.51/188.06 tff(31173,assumption,(~m_and_h_gate_v_in1(c_e_h_3, c_l, s12)), introduced(assumption)).
% 295.51/188.06 tff(31174,assumption,(node20(c_e_h_3, c_l, s12)), introduced(assumption)).
% 295.51/188.06 tff(31175,plain,
% 295.51/188.06 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_l, s12)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s12))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_l, s12)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s12))),
% 295.51/188.06 inference(rewrite,[status(thm)],[])).
% 295.51/188.06 tff(31176,plain,
% 295.51/188.06 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_3, c_l, s12)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s12))),
% 295.51/188.06 inference(quant_inst,[status(thm)],[])).
% 295.51/188.06 tff(31177,plain,
% 295.51/188.06 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_3, c_l, s12)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s12)),
% 295.51/188.06 inference(modus_ponens,[status(thm)],[31176, 31175])).
% 295.51/188.06 tff(31178,plain,
% 295.51/188.06 ($false),
% 295.51/188.06 inference(unit_resolution,[status(thm)],[31177, 38, 31174, 31173])).
% 295.51/188.06 tff(31179,plain,((~node20(c_e_h_3, c_l, s12)) | m_and_h_gate_v_in1(c_e_h_3, c_l, s12)), inference(lemma,lemma(discharge,[]))).
% 295.51/188.06 tff(31180,plain,
% 295.51/188.06 (m_and_h_gate_v_in1(c_e_h_3, c_l, s12)),
% 295.51/188.06 inference(unit_resolution,[status(thm)],[31179, 31172])).
% 295.51/188.06 tff(31181,assumption,(m_and_h_gate_v_in1(c_e_h_3, c_l, s12)), introduced(assumption)).
% 295.51/188.06 tff(31182,assumption,(~m_and_h_gate_v_out(c_e_h_3, c_k, s12)), introduced(assumption)).
% 295.51/188.06 tff(31183,plain,
% 295.51/188.06 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_l, s12)) | m_and_h_gate_v_out(c_e_h_3, c_k, s12))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s12)) | m_and_h_gate_v_out(c_e_h_3, c_k, s12))),
% 295.51/188.06 inference(rewrite,[status(thm)],[])).
% 295.51/188.06 tff(31184,plain,
% 295.51/188.06 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | ((~m_and_h_gate_v_in1(c_e_h_3, c_l, s12)) | m_and_h_gate_v_out(c_e_h_3, c_k, s12))),
% 295.51/188.06 inference(quant_inst,[status(thm)],[])).
% 295.51/188.06 tff(31185,plain,
% 295.51/188.06 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_l, X)) | m_and_h_gate_v_out(I0, c_k, X))) | (~m_and_h_gate_v_in1(c_e_h_3, c_l, s12)) | m_and_h_gate_v_out(c_e_h_3, c_k, s12)),
% 295.51/188.06 inference(modus_ponens,[status(thm)],[31184, 31183])).
% 295.51/188.06 tff(31186,plain,
% 295.51/188.06 ($false),
% 295.51/188.06 inference(unit_resolution,[status(thm)],[31185, 1529, 31182, 31181])).
% 295.51/188.06 tff(31187,plain,((~m_and_h_gate_v_in1(c_e_h_3, c_l, s12)) | m_and_h_gate_v_out(c_e_h_3, c_k, s12)), inference(lemma,lemma(discharge,[]))).
% 295.51/188.06 tff(31188,plain,
% 295.51/188.06 (m_and_h_gate_v_out(c_e_h_3, c_k, s12)),
% 295.51/188.06 inference(unit_resolution,[status(thm)],[31187, 31180])).
% 295.51/188.06 tff(31189,plain,
% 295.51/188.06 (((~![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))) | (m_and_h_gate_v_in2(c_e_h_3, c_k, s13) | m_c_h_element_v_out(c_e_h_3, c_h, s13))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))) | m_and_h_gate_v_in2(c_e_h_3, c_k, s13) | m_c_h_element_v_out(c_e_h_3, c_h, s13))),
% 295.51/188.06 inference(rewrite,[status(thm)],[])).
% 295.51/188.06 tff(31190,plain,
% 295.51/188.06 ((~![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))) | (m_and_h_gate_v_in2(c_e_h_3, c_k, s13) | m_c_h_element_v_out(c_e_h_3, c_h, s13))),
% 295.51/188.06 inference(quant_inst,[status(thm)],[])).
% 295.51/188.06 tff(31191,plain,
% 295.51/188.06 ((~![I0: $i, X: $i] : (m_and_h_gate_v_in2(I0, c_k, X) | m_c_h_element_v_out(I0, c_h, X))) | m_and_h_gate_v_in2(c_e_h_3, c_k, s13) | m_c_h_element_v_out(c_e_h_3, c_h, s13)),
% 295.51/188.06 inference(modus_ponens,[status(thm)],[31190, 31189])).
% 295.51/188.06 tff(31192,plain,
% 295.51/188.06 (m_and_h_gate_v_in2(c_e_h_3, c_k, s13) | m_c_h_element_v_out(c_e_h_3, c_h, s13)),
% 295.51/188.06 inference(unit_resolution,[status(thm)],[31191, 6420])).
% 295.51/188.06 tff(31193,plain,
% 295.51/188.06 (m_and_h_gate_v_in2(c_e_h_3, c_k, s13)),
% 295.51/188.06 inference(unit_resolution,[status(thm)],[31192, 28319])).
% 295.51/188.06 tff(31194,plain,
% 295.51/188.06 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s21) | m_c_h_element_v_out(c_e_h_1, c_e, s21))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s21) | m_c_h_element_v_out(c_e_h_1, c_e, s21))),
% 295.51/188.06 inference(rewrite,[status(thm)],[])).
% 295.51/188.06 tff(31195,plain,
% 295.51/188.06 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s21) | m_c_h_element_v_out(c_e_h_1, c_e, s21))),
% 295.51/188.06 inference(quant_inst,[status(thm)],[])).
% 295.51/188.06 tff(31196,plain,
% 295.51/188.06 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s21) | m_c_h_element_v_out(c_e_h_1, c_e, s21)),
% 295.51/188.06 inference(modus_ponens,[status(thm)],[31195, 31194])).
% 295.51/188.06 tff(31197,plain,
% 295.51/188.06 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s21) | m_c_h_element_v_out(c_e_h_1, c_e, s21)),
% 295.51/188.06 inference(unit_resolution,[status(thm)],[31196, 7856])).
% 295.51/188.06 tff(31198,plain,
% 295.51/188.06 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s21)),
% 295.51/188.06 inference(unit_resolution,[status(thm)],[31197, 30863])).
% 295.51/188.06 tff(31199,plain,
% 295.51/188.06 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s20) | m_c_h_element_v_out(c_e_h_1, c_e, s20))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s20) | m_c_h_element_v_out(c_e_h_1, c_e, s20))),
% 295.51/188.06 inference(rewrite,[status(thm)],[])).
% 295.51/188.06 tff(31200,plain,
% 295.51/188.06 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s20) | m_c_h_element_v_out(c_e_h_1, c_e, s20))),
% 295.51/188.06 inference(quant_inst,[status(thm)],[])).
% 295.51/188.06 tff(31201,plain,
% 295.51/188.06 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s20) | m_c_h_element_v_out(c_e_h_1, c_e, s20)),
% 295.51/188.06 inference(modus_ponens,[status(thm)],[31200, 31199])).
% 295.51/188.06 tff(31202,plain,
% 295.51/188.06 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s20) | m_c_h_element_v_out(c_e_h_1, c_e, s20)),
% 295.51/188.06 inference(unit_resolution,[status(thm)],[31201, 7856])).
% 295.51/188.06 tff(31203,plain,
% 295.51/188.06 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s20)),
% 295.51/188.06 inference(unit_resolution,[status(thm)],[31202, 30778])).
% 295.51/188.06 tff(31204,plain,
% 295.51/188.06 (~m_c_h_element_v_out(c_e_h_1, c_e, s19)),
% 295.51/188.06 inference(unit_resolution,[status(thm)],[26861, 26770, 26800])).
% 295.51/188.06 tff(31205,plain,
% 295.51/188.06 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s17)),
% 295.51/188.06 inference(unit_resolution,[status(thm)],[30139, 4958, 30394])).
% 295.51/188.06 tff(31206,plain,
% 295.51/188.06 (~node9(c_e_h_1, c_m, s17)),
% 295.51/188.06 inference(unit_resolution,[status(thm)],[30143, 4972, 31205])).
% 295.51/188.06 tff(31207,plain,
% 295.51/188.06 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18)),
% 295.51/188.06 inference(unit_resolution,[status(thm)],[30167, 30162, 31206])).
% 295.51/188.06 tff(31208,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20)), introduced(assumption)).
% 295.51/188.06 tff(31209,plain,
% 295.51/188.06 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s18) | m_c_h_element_v_out(c_e_h_1, c_e, s18))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s18) | m_c_h_element_v_out(c_e_h_1, c_e, s18))),
% 295.51/188.06 inference(rewrite,[status(thm)],[])).
% 295.51/188.06 tff(31210,plain,
% 295.51/188.06 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s18) | m_c_h_element_v_out(c_e_h_1, c_e, s18))),
% 295.51/188.06 inference(quant_inst,[status(thm)],[])).
% 295.51/188.06 tff(31211,plain,
% 295.51/188.06 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s18) | m_c_h_element_v_out(c_e_h_1, c_e, s18)),
% 295.51/188.06 inference(modus_ponens,[status(thm)],[31210, 31209])).
% 295.51/188.06 tff(31212,plain,
% 295.51/188.06 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s18) | m_c_h_element_v_out(c_e_h_1, c_e, s18)),
% 295.51/188.06 inference(unit_resolution,[status(thm)],[31211, 7856])).
% 295.51/188.06 tff(31213,plain,
% 295.51/188.06 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s18)),
% 295.51/188.06 inference(unit_resolution,[status(thm)],[31212, 26770])).
% 295.51/188.06 tff(31214,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s19)), introduced(assumption)).
% 295.51/188.06 tff(31215,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s18)), introduced(assumption)).
% 295.51/188.06 tff(31216,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s19)), introduced(assumption)).
% 295.51/188.06 tff(31217,plain,
% 295.51/188.06 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s18) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s18) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18))),
% 295.51/188.07 inference(rewrite,[status(thm)],[])).
% 295.51/188.07 tff(31218,plain,
% 295.51/188.07 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s18) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18))),
% 295.51/188.07 inference(quant_inst,[status(thm)],[])).
% 295.51/188.07 tff(31219,plain,
% 295.51/188.07 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s18) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18)),
% 295.51/188.07 inference(modus_ponens,[status(thm)],[31218, 31217])).
% 295.51/188.07 tff(31220,plain,
% 295.51/188.07 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s18) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18)),
% 295.51/188.07 inference(unit_resolution,[status(thm)],[31219, 7868])).
% 295.51/188.07 tff(31221,plain,
% 295.51/188.07 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s18)),
% 295.51/188.07 inference(unit_resolution,[status(thm)],[31220, 31207])).
% 295.51/188.07 tff(31222,assumption,(node10(c_e_h_1, c_n, s18, s19)), introduced(assumption)).
% 295.51/188.07 tff(31223,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s18)), introduced(assumption)).
% 295.51/188.07 tff(31224,plain,
% 295.51/188.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s19) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s18)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s18)) | (~node10(c_e_h_1, c_n, s18, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s19) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s18)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s18)) | (~node10(c_e_h_1, c_n, s18, s19)))),
% 295.51/188.07 inference(rewrite,[status(thm)],[])).
% 295.51/188.07 tff(31225,plain,
% 295.51/188.07 (((~node10(c_e_h_1, c_n, s18, s19)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s18)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s18)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s19)) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s19) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s18)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s18)) | (~node10(c_e_h_1, c_n, s18, s19)))),
% 295.51/188.07 inference(rewrite,[status(thm)],[])).
% 295.51/188.07 tff(31226,plain,
% 295.51/188.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s18, s19)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s18)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s18)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s19))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s19) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s18)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s18)) | (~node10(c_e_h_1, c_n, s18, s19))))),
% 295.51/188.07 inference(monotonicity,[status(thm)],[31225])).
% 295.51/188.07 tff(31227,plain,
% 295.51/188.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s18, s19)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s18)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s18)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s19))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s19) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s18)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s18)) | (~node10(c_e_h_1, c_n, s18, s19)))),
% 295.51/188.07 inference(transitivity,[status(thm)],[31226, 31224])).
% 295.51/188.07 tff(31228,plain,
% 295.51/188.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s18, s19)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s18)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s18)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s19))),
% 295.51/188.07 inference(quant_inst,[status(thm)],[])).
% 295.51/188.07 tff(31229,plain,
% 295.51/188.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s19) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s18)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s18)) | (~node10(c_e_h_1, c_n, s18, s19))),
% 295.51/188.07 inference(modus_ponens,[status(thm)],[31228, 31227])).
% 295.51/188.07 tff(31230,plain,
% 295.51/188.07 ($false),
% 295.51/188.07 inference(unit_resolution,[status(thm)],[31229, 5718, 31215, 31216, 31223, 31222])).
% 295.51/188.07 tff(31231,plain,((~node10(c_e_h_1, c_n, s18, s19)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s18)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s19) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s18))), inference(lemma,lemma(discharge,[]))).
% 295.51/188.07 tff(31232,plain,
% 295.51/188.07 (~node10(c_e_h_1, c_n, s18, s19)),
% 295.51/188.07 inference(unit_resolution,[status(thm)],[31231, 31221, 31216, 31215])).
% 295.51/188.07 tff(31233,plain,
% 295.51/188.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s18, s19)) | node10(c_e_h_1, c_n, s18, s19) | node11(c_e_h_1, c_n, s18, s19))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s18, s19)) | node10(c_e_h_1, c_n, s18, s19) | node11(c_e_h_1, c_n, s18, s19))),
% 295.51/188.07 inference(rewrite,[status(thm)],[])).
% 295.51/188.07 tff(31234,plain,
% 295.51/188.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s18, s19)) | node10(c_e_h_1, c_n, s18, s19) | node11(c_e_h_1, c_n, s18, s19))),
% 295.51/188.07 inference(quant_inst,[status(thm)],[])).
% 295.51/188.07 tff(31235,plain,
% 295.51/188.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s18, s19)) | node10(c_e_h_1, c_n, s18, s19) | node11(c_e_h_1, c_n, s18, s19)),
% 295.51/188.07 inference(modus_ponens,[status(thm)],[31234, 31233])).
% 295.51/188.07 tff(31236,plain,
% 295.51/188.07 (node10(c_e_h_1, c_n, s18, s19) | node11(c_e_h_1, c_n, s18, s19)),
% 295.51/188.07 inference(unit_resolution,[status(thm)],[31235, 5002, 26787])).
% 295.51/188.07 tff(31237,plain,
% 295.51/188.07 (node11(c_e_h_1, c_n, s18, s19)),
% 295.51/188.07 inference(unit_resolution,[status(thm)],[31236, 31232])).
% 295.51/188.07 tff(31238,plain,
% 295.51/188.07 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s17)),
% 295.51/188.07 inference(unit_resolution,[status(thm)],[30392, 30162])).
% 295.51/188.07 tff(31239,plain,
% 295.51/188.07 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s18)),
% 295.51/188.07 inference(unit_resolution,[status(thm)],[30423, 31238, 30406, 30394])).
% 295.51/188.07 tff(31240,plain,
% 295.51/188.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s19) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s18)) | (~node11(c_e_h_1, c_n, s18, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s19) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s18)) | (~node11(c_e_h_1, c_n, s18, s19)))),
% 295.51/188.07 inference(rewrite,[status(thm)],[])).
% 295.51/188.07 tff(31241,plain,
% 295.51/188.07 ((m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s19) | (~node11(c_e_h_1, c_n, s18, s19)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s18))) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s19) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s18)) | (~node11(c_e_h_1, c_n, s18, s19)))),
% 295.51/188.07 inference(rewrite,[status(thm)],[])).
% 295.51/188.07 tff(31242,plain,
% 295.51/188.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s19) | (~node11(c_e_h_1, c_n, s18, s19)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s19) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s18)) | (~node11(c_e_h_1, c_n, s18, s19))))),
% 295.51/188.07 inference(monotonicity,[status(thm)],[31241])).
% 295.51/188.07 tff(31243,plain,
% 295.51/188.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s19) | (~node11(c_e_h_1, c_n, s18, s19)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s19) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s18)) | (~node11(c_e_h_1, c_n, s18, s19)))),
% 295.51/188.07 inference(transitivity,[status(thm)],[31242, 31240])).
% 295.51/188.07 tff(31244,plain,
% 295.51/188.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s19) | (~node11(c_e_h_1, c_n, s18, s19)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s18)))),
% 295.51/188.07 inference(quant_inst,[status(thm)],[])).
% 295.51/188.07 tff(31245,plain,
% 295.51/188.07 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s19) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s18)) | (~node11(c_e_h_1, c_n, s18, s19))),
% 295.51/188.07 inference(modus_ponens,[status(thm)],[31244, 31243])).
% 295.51/188.07 tff(31246,plain,
% 295.51/188.07 ($false),
% 295.51/188.07 inference(unit_resolution,[status(thm)],[31245, 5742, 31239, 31216, 31237])).
% 295.51/188.07 tff(31247,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s19) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s18)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s17)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17))), inference(lemma,lemma(discharge,[]))).
% 295.51/188.07 tff(31248,plain,
% 295.51/188.07 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s19)),
% 295.51/188.07 inference(unit_resolution,[status(thm)],[31247, 30162, 30394, 30406, 31215])).
% 295.51/188.07 tff(31249,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s19)), introduced(assumption)).
% 295.51/188.07 tff(31250,assumption,(node10(c_e_h_1, c_n, s19, s20)), introduced(assumption)).
% 295.51/188.07 tff(31251,plain,
% 295.51/188.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s19)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s19)) | (~node10(c_e_h_1, c_n, s19, s20)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s19)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s19)) | (~node10(c_e_h_1, c_n, s19, s20)))),
% 295.51/188.07 inference(rewrite,[status(thm)],[])).
% 295.51/188.07 tff(31252,plain,
% 295.51/188.07 (((~node10(c_e_h_1, c_n, s19, s20)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s19)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s19)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20)) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s19)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s19)) | (~node10(c_e_h_1, c_n, s19, s20)))),
% 295.51/188.07 inference(rewrite,[status(thm)],[])).
% 295.51/188.07 tff(31253,plain,
% 295.51/188.07 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s19, s20)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s19)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s19)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s19)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s19)) | (~node10(c_e_h_1, c_n, s19, s20))))),
% 295.51/188.08 inference(monotonicity,[status(thm)],[31252])).
% 295.51/188.08 tff(31254,plain,
% 295.51/188.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s19, s20)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s19)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s19)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s19)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s19)) | (~node10(c_e_h_1, c_n, s19, s20)))),
% 295.51/188.08 inference(transitivity,[status(thm)],[31253, 31251])).
% 295.51/188.08 tff(31255,plain,
% 295.51/188.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s19, s20)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s19)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s19)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20))),
% 295.51/188.08 inference(quant_inst,[status(thm)],[])).
% 295.51/188.08 tff(31256,plain,
% 295.51/188.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s19)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s19)) | (~node10(c_e_h_1, c_n, s19, s20))),
% 295.51/188.08 inference(modus_ponens,[status(thm)],[31255, 31254])).
% 295.51/188.08 tff(31257,plain,
% 295.51/188.08 ($false),
% 295.51/188.08 inference(unit_resolution,[status(thm)],[31256, 5718, 31208, 31249, 31214, 31250])).
% 295.51/188.08 tff(31258,plain,((~node10(c_e_h_1, c_n, s19, s20)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s19)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s19))), inference(lemma,lemma(discharge,[]))).
% 295.51/188.08 tff(31259,plain,
% 295.51/188.08 (~node10(c_e_h_1, c_n, s19, s20)),
% 295.51/188.08 inference(unit_resolution,[status(thm)],[31258, 31208, 31214, 31249])).
% 295.51/188.08 tff(31260,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s19)), introduced(assumption)).
% 295.51/188.08 tff(31261,assumption,(node11(c_e_h_1, c_n, s19, s20)), introduced(assumption)).
% 295.51/188.08 tff(31262,plain,
% 295.51/188.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s19)) | (~node11(c_e_h_1, c_n, s19, s20)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s19)) | (~node11(c_e_h_1, c_n, s19, s20)))),
% 295.51/188.08 inference(rewrite,[status(thm)],[])).
% 295.51/188.08 tff(31263,plain,
% 295.51/188.08 ((m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20) | (~node11(c_e_h_1, c_n, s19, s20)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s19))) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s19)) | (~node11(c_e_h_1, c_n, s19, s20)))),
% 295.51/188.08 inference(rewrite,[status(thm)],[])).
% 295.51/188.08 tff(31264,plain,
% 295.51/188.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20) | (~node11(c_e_h_1, c_n, s19, s20)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s19)) | (~node11(c_e_h_1, c_n, s19, s20))))),
% 295.51/188.08 inference(monotonicity,[status(thm)],[31263])).
% 295.51/188.08 tff(31265,plain,
% 295.51/188.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20) | (~node11(c_e_h_1, c_n, s19, s20)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s19)) | (~node11(c_e_h_1, c_n, s19, s20)))),
% 295.51/188.08 inference(transitivity,[status(thm)],[31264, 31262])).
% 295.51/188.08 tff(31266,plain,
% 295.51/188.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20) | (~node11(c_e_h_1, c_n, s19, s20)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s19)))),
% 295.51/188.08 inference(quant_inst,[status(thm)],[])).
% 295.51/188.08 tff(31267,plain,
% 295.51/188.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s19)) | (~node11(c_e_h_1, c_n, s19, s20))),
% 295.51/188.08 inference(modus_ponens,[status(thm)],[31266, 31265])).
% 295.51/188.08 tff(31268,plain,
% 295.51/188.08 ($false),
% 295.51/188.08 inference(unit_resolution,[status(thm)],[31267, 5742, 31208, 31260, 31261])).
% 295.51/188.08 tff(31269,plain,((~node11(c_e_h_1, c_n, s19, s20)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s19))), inference(lemma,lemma(discharge,[]))).
% 295.51/188.08 tff(31270,plain,
% 295.51/188.08 (~node11(c_e_h_1, c_n, s19, s20)),
% 295.51/188.08 inference(unit_resolution,[status(thm)],[31269, 31208, 31260])).
% 295.51/188.08 tff(31271,plain,
% 295.51/188.08 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s19, s20)) | node10(c_e_h_1, c_n, s19, s20) | node11(c_e_h_1, c_n, s19, s20))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s19, s20)) | node10(c_e_h_1, c_n, s19, s20) | node11(c_e_h_1, c_n, s19, s20))),
% 295.51/188.08 inference(rewrite,[status(thm)],[])).
% 295.51/188.08 tff(31272,plain,
% 295.51/188.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s19, s20)) | node10(c_e_h_1, c_n, s19, s20) | node11(c_e_h_1, c_n, s19, s20))),
% 295.51/188.08 inference(quant_inst,[status(thm)],[])).
% 295.51/188.08 tff(31273,plain,
% 295.51/188.08 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s19, s20)) | node10(c_e_h_1, c_n, s19, s20) | node11(c_e_h_1, c_n, s19, s20)),
% 295.51/188.08 inference(modus_ponens,[status(thm)],[31272, 31271])).
% 295.51/188.08 tff(31274,plain,
% 295.51/188.08 (node10(c_e_h_1, c_n, s19, s20) | node11(c_e_h_1, c_n, s19, s20)),
% 295.51/188.08 inference(unit_resolution,[status(thm)],[31273, 5002, 29925])).
% 295.51/188.08 tff(31275,plain,
% 295.51/188.08 ($false),
% 295.51/188.08 inference(unit_resolution,[status(thm)],[31274, 31270, 31259])).
% 295.51/188.08 tff(31276,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s19)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s19)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s19))), inference(lemma,lemma(discharge,[]))).
% 295.51/188.08 tff(31277,plain,
% 295.51/188.08 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s19)),
% 295.51/188.08 inference(unit_resolution,[status(thm)],[31276, 31248, 31208, 31214])).
% 295.51/188.08 tff(31278,plain,
% 295.51/188.08 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s19) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s19))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s19) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s19))),
% 295.51/188.08 inference(rewrite,[status(thm)],[])).
% 295.51/188.08 tff(31279,plain,
% 295.51/188.08 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s19) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s19))),
% 295.51/188.08 inference(quant_inst,[status(thm)],[])).
% 295.51/188.08 tff(31280,plain,
% 295.51/188.08 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s19) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s19)),
% 295.51/188.08 inference(modus_ponens,[status(thm)],[31279, 31278])).
% 295.51/188.08 tff(31281,plain,
% 295.51/188.08 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s19) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s19)),
% 295.51/188.08 inference(unit_resolution,[status(thm)],[31280, 7868])).
% 295.51/188.08 tff(31282,plain,
% 295.51/188.08 (m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s19)),
% 295.51/188.08 inference(unit_resolution,[status(thm)],[31281, 31277])).
% 295.51/188.08 tff(31283,plain,
% 295.51/188.08 (~node11(c_e_h_1, c_m, s18, s19)),
% 295.51/188.08 inference(unit_resolution,[status(thm)],[30442, 31282, 30435])).
% 295.51/188.08 tff(31284,plain,
% 295.51/188.08 (node10(c_e_h_1, c_m, s18, s19)),
% 295.51/188.08 inference(unit_resolution,[status(thm)],[30455, 31283])).
% 295.51/188.08 tff(31285,plain,
% 295.51/188.08 (node9(c_e_h_1, c_m, s18)),
% 295.51/188.08 inference(unit_resolution,[status(thm)],[30450, 31284, 31282])).
% 295.51/188.08 tff(31286,plain,
% 295.51/188.08 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s18)),
% 295.51/188.08 inference(unit_resolution,[status(thm)],[30423, 31238, 30394, 30406])).
% 295.51/188.08 tff(31287,plain,
% 295.51/188.08 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s18)),
% 295.51/188.08 inference(unit_resolution,[status(thm)],[30429, 4958, 31286])).
% 295.51/188.08 tff(31288,plain,
% 295.51/188.08 ($false),
% 295.51/188.08 inference(unit_resolution,[status(thm)],[30433, 4972, 31287, 31285])).
% 295.51/188.08 tff(31289,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s19)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s17)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s18))), inference(lemma,lemma(discharge,[]))).
% 295.51/188.08 tff(31290,plain,
% 295.51/188.08 (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s19)),
% 295.51/188.08 inference(unit_resolution,[status(thm)],[31289, 31213, 30394, 31208, 30162, 31207, 30406])).
% 295.51/188.08 tff(31291,plain,
% 295.51/188.08 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s19) | m_c_h_element_v_out(c_e_h_1, c_e, s19))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s19) | m_c_h_element_v_out(c_e_h_1, c_e, s19))),
% 295.51/188.08 inference(rewrite,[status(thm)],[])).
% 295.51/188.08 tff(31292,plain,
% 295.51/188.08 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s19) | m_c_h_element_v_out(c_e_h_1, c_e, s19))),
% 295.51/188.08 inference(quant_inst,[status(thm)],[])).
% 295.51/188.08 tff(31293,plain,
% 295.51/188.08 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s19) | m_c_h_element_v_out(c_e_h_1, c_e, s19)),
% 295.51/188.08 inference(modus_ponens,[status(thm)],[31292, 31291])).
% 295.51/188.08 tff(31294,plain,
% 295.51/188.08 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s19) | m_c_h_element_v_out(c_e_h_1, c_e, s19)),
% 295.51/188.08 inference(unit_resolution,[status(thm)],[31293, 7856])).
% 295.51/188.08 tff(31295,plain,
% 295.51/188.08 ($false),
% 295.51/188.08 inference(unit_resolution,[status(thm)],[31294, 31290, 31204])).
% 295.51/188.08 tff(31296,plain,(m_c_h_element_v_out(c_e_h_1, c_e, s18) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s17)) | m_c_h_element_v_in2(c_e_h_1, c_e, s18)), inference(lemma,lemma(discharge,[]))).
% 295.51/188.08 tff(31297,plain,
% 295.51/188.08 (m_c_h_element_v_out(c_e_h_1, c_e, s18) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s17)) | m_c_h_element_v_in2(c_e_h_1, c_e, s18)),
% 295.51/188.09 inference(unit_resolution,[status(thm)],[31296, 29683])).
% 295.51/188.09 tff(31298,plain,
% 295.51/188.09 (m_c_h_element_v_out(c_e_h_1, c_e, s18) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s17)) | m_c_h_element_v_in2(c_e_h_1, c_e, s18)),
% 295.51/188.09 inference(unit_resolution,[status(thm)],[31297, 30136])).
% 295.51/188.09 tff(31299,plain,
% 295.51/188.09 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20)),
% 295.51/188.09 inference(unit_resolution,[status(thm)],[31298, 26768, 26207, 30388])).
% 295.51/188.09 tff(31300,plain,
% 295.51/188.09 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s18)),
% 295.51/188.09 inference(unit_resolution,[status(thm)],[31212, 26207])).
% 295.51/188.09 tff(31301,plain,
% 295.51/188.09 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s19) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s18)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s17)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17))),
% 295.51/188.09 inference(unit_resolution,[status(thm)],[31247, 29683])).
% 295.51/188.09 tff(31302,plain,
% 295.51/188.09 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s19) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s18)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s17))),
% 295.51/188.09 inference(unit_resolution,[status(thm)],[31301, 30136])).
% 295.51/188.09 tff(31303,plain,
% 295.51/188.09 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s19)),
% 295.51/188.09 inference(unit_resolution,[status(thm)],[31302, 31300, 30388])).
% 295.51/188.09 tff(31304,plain,
% 295.51/188.09 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s19)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s19)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s19)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s19)))),
% 295.51/188.09 inference(rewrite,[status(thm)],[])).
% 295.51/188.09 tff(31305,plain,
% 295.51/188.09 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s19)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s19)))),
% 295.51/188.09 inference(quant_inst,[status(thm)],[])).
% 295.51/188.09 tff(31306,plain,
% 295.51/188.09 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s19)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s19))),
% 295.51/188.09 inference(modus_ponens,[status(thm)],[31305, 31304])).
% 295.51/188.09 tff(31307,plain,
% 295.51/188.09 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s19)),
% 295.51/188.09 inference(unit_resolution,[status(thm)],[31306, 4958, 31303])).
% 295.51/188.09 tff(31308,plain,
% 295.51/188.09 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s19)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s19))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s19)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s19))),
% 295.51/188.09 inference(rewrite,[status(thm)],[])).
% 295.51/188.09 tff(31309,plain,
% 295.51/188.09 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s19)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s19))),
% 295.51/188.09 inference(quant_inst,[status(thm)],[])).
% 295.51/188.09 tff(31310,plain,
% 295.51/188.09 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s19)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s19)),
% 295.51/188.09 inference(modus_ponens,[status(thm)],[31309, 31308])).
% 295.51/188.09 tff(31311,plain,
% 295.51/188.09 (~node9(c_e_h_1, c_m, s19)),
% 295.51/188.09 inference(unit_resolution,[status(thm)],[31310, 4972, 31307])).
% 295.51/188.09 tff(31312,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s20)), introduced(assumption)).
% 295.51/188.09 tff(31313,assumption,(node11(c_e_h_1, c_m, s19, s20)), introduced(assumption)).
% 295.51/188.09 tff(31314,plain,
% 295.51/188.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s20)) | (~node11(c_e_h_1, c_m, s19, s20)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s19))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s20)) | (~node11(c_e_h_1, c_m, s19, s20)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s19))),
% 295.51/188.09 inference(rewrite,[status(thm)],[])).
% 295.51/188.09 tff(31315,plain,
% 295.51/188.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s20)) | (~node11(c_e_h_1, c_m, s19, s20)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s19))),
% 295.51/188.09 inference(quant_inst,[status(thm)],[])).
% 295.51/188.09 tff(31316,plain,
% 295.51/188.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s20)) | (~node11(c_e_h_1, c_m, s19, s20)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s19)),
% 295.51/188.09 inference(modus_ponens,[status(thm)],[31315, 31314])).
% 295.51/188.09 tff(31317,plain,
% 295.51/188.09 ($false),
% 295.51/188.09 inference(unit_resolution,[status(thm)],[31316, 5017, 31312, 30461, 31313])).
% 295.51/188.09 tff(31318,plain,((~node11(c_e_h_1, c_m, s19, s20)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s20)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s19)), inference(lemma,lemma(discharge,[]))).
% 295.51/188.09 tff(31319,plain,
% 295.51/188.09 (~node11(c_e_h_1, c_m, s19, s20)),
% 295.51/188.09 inference(unit_resolution,[status(thm)],[31318, 31312, 30461])).
% 295.51/188.09 tff(31320,assumption,(~node9(c_e_h_1, c_m, s19)), introduced(assumption)).
% 295.51/188.09 tff(31321,assumption,(node10(c_e_h_1, c_m, s19, s20)), introduced(assumption)).
% 295.51/188.09 tff(31322,plain,
% 295.51/188.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s20)) | node9(c_e_h_1, c_m, s19) | (~node10(c_e_h_1, c_m, s19, s20)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s20)) | node9(c_e_h_1, c_m, s19) | (~node10(c_e_h_1, c_m, s19, s20)))),
% 295.51/188.09 inference(rewrite,[status(thm)],[])).
% 295.51/188.09 tff(31323,plain,
% 295.51/188.09 ((node9(c_e_h_1, c_m, s19) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s20)) | (~node10(c_e_h_1, c_m, s19, s20))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s20)) | node9(c_e_h_1, c_m, s19) | (~node10(c_e_h_1, c_m, s19, s20)))),
% 295.51/188.09 inference(rewrite,[status(thm)],[])).
% 295.51/188.09 tff(31324,plain,
% 295.51/188.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s19) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s20)) | (~node10(c_e_h_1, c_m, s19, s20)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s20)) | node9(c_e_h_1, c_m, s19) | (~node10(c_e_h_1, c_m, s19, s20))))),
% 295.51/188.09 inference(monotonicity,[status(thm)],[31323])).
% 295.51/188.09 tff(31325,plain,
% 295.51/188.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s19) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s20)) | (~node10(c_e_h_1, c_m, s19, s20)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s20)) | node9(c_e_h_1, c_m, s19) | (~node10(c_e_h_1, c_m, s19, s20)))),
% 295.51/188.09 inference(transitivity,[status(thm)],[31324, 31322])).
% 295.51/188.09 tff(31326,plain,
% 295.51/188.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s19) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s20)) | (~node10(c_e_h_1, c_m, s19, s20)))),
% 295.51/188.09 inference(quant_inst,[status(thm)],[])).
% 295.51/188.09 tff(31327,plain,
% 295.51/188.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s20)) | node9(c_e_h_1, c_m, s19) | (~node10(c_e_h_1, c_m, s19, s20))),
% 295.51/188.09 inference(modus_ponens,[status(thm)],[31326, 31325])).
% 295.51/188.09 tff(31328,plain,
% 295.51/188.09 ($false),
% 295.51/188.09 inference(unit_resolution,[status(thm)],[31327, 4986, 31312, 31321, 31320])).
% 295.51/188.09 tff(31329,plain,((~node10(c_e_h_1, c_m, s19, s20)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s20)) | node9(c_e_h_1, c_m, s19)), inference(lemma,lemma(discharge,[]))).
% 295.51/188.09 tff(31330,plain,
% 295.51/188.09 (~node10(c_e_h_1, c_m, s19, s20)),
% 295.51/188.09 inference(unit_resolution,[status(thm)],[31329, 31312, 31320])).
% 295.51/188.09 tff(31331,plain,
% 295.51/188.09 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s19, s20)) | node10(c_e_h_1, c_m, s19, s20) | node11(c_e_h_1, c_m, s19, s20))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s19, s20)) | node10(c_e_h_1, c_m, s19, s20) | node11(c_e_h_1, c_m, s19, s20))),
% 295.51/188.09 inference(rewrite,[status(thm)],[])).
% 295.51/188.09 tff(31332,plain,
% 295.51/188.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s19, s20)) | node10(c_e_h_1, c_m, s19, s20) | node11(c_e_h_1, c_m, s19, s20))),
% 295.51/188.09 inference(quant_inst,[status(thm)],[])).
% 295.51/188.09 tff(31333,plain,
% 295.51/188.09 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s19, s20)) | node10(c_e_h_1, c_m, s19, s20) | node11(c_e_h_1, c_m, s19, s20)),
% 295.51/188.09 inference(modus_ponens,[status(thm)],[31332, 31331])).
% 295.51/188.09 tff(31334,plain,
% 295.51/188.09 (node10(c_e_h_1, c_m, s19, s20) | node11(c_e_h_1, c_m, s19, s20)),
% 295.51/188.09 inference(unit_resolution,[status(thm)],[31333, 5002, 29925])).
% 295.51/188.09 tff(31335,plain,
% 295.51/188.09 ($false),
% 295.51/188.09 inference(unit_resolution,[status(thm)],[31334, 31330, 31319])).
% 295.51/188.09 tff(31336,plain,((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s20)) | node9(c_e_h_1, c_m, s19) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s19)), inference(lemma,lemma(discharge,[]))).
% 295.51/188.09 tff(31337,plain,
% 295.51/188.09 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s20)),
% 295.51/188.09 inference(unit_resolution,[status(thm)],[31336, 31311, 30459])).
% 295.51/188.09 tff(31338,plain,
% 295.51/188.09 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s23) | m_c_h_element_v_out(c_e_h_1, c_e, s23))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s23) | m_c_h_element_v_out(c_e_h_1, c_e, s23))),
% 295.51/188.09 inference(rewrite,[status(thm)],[])).
% 295.51/188.09 tff(31339,plain,
% 295.51/188.09 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s23) | m_c_h_element_v_out(c_e_h_1, c_e, s23))),
% 295.51/188.09 inference(quant_inst,[status(thm)],[])).
% 295.51/188.09 tff(31340,plain,
% 295.51/188.09 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s23) | m_c_h_element_v_out(c_e_h_1, c_e, s23)),
% 295.51/188.09 inference(modus_ponens,[status(thm)],[31339, 31338])).
% 295.51/188.09 tff(31341,plain,
% 295.51/188.09 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s23) | m_c_h_element_v_out(c_e_h_1, c_e, s23)),
% 295.51/188.09 inference(unit_resolution,[status(thm)],[31340, 7856])).
% 295.51/188.09 tff(31342,plain,
% 295.51/188.09 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s23)),
% 295.51/188.09 inference(unit_resolution,[status(thm)],[31341, 31037])).
% 295.51/188.09 tff(31343,plain,
% 295.51/188.09 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s22) | m_c_h_element_v_out(c_e_h_1, c_e, s22))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s22) | m_c_h_element_v_out(c_e_h_1, c_e, s22))),
% 295.51/188.09 inference(rewrite,[status(thm)],[])).
% 295.51/188.09 tff(31344,plain,
% 295.51/188.09 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s22) | m_c_h_element_v_out(c_e_h_1, c_e, s22))),
% 295.51/188.09 inference(quant_inst,[status(thm)],[])).
% 295.51/188.09 tff(31345,plain,
% 295.51/188.09 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s22) | m_c_h_element_v_out(c_e_h_1, c_e, s22)),
% 295.51/188.10 inference(modus_ponens,[status(thm)],[31344, 31343])).
% 295.51/188.10 tff(31346,plain,
% 295.51/188.10 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s22) | m_c_h_element_v_out(c_e_h_1, c_e, s22)),
% 295.51/188.10 inference(unit_resolution,[status(thm)],[31345, 7856])).
% 295.51/188.10 tff(31347,plain,
% 295.51/188.10 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s22)),
% 295.51/188.10 inference(unit_resolution,[status(thm)],[31346, 30949])).
% 295.51/188.10 tff(31348,plain,
% 295.51/188.10 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s20)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s20)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20)))),
% 295.51/188.10 inference(rewrite,[status(thm)],[])).
% 295.51/188.10 tff(31349,plain,
% 295.51/188.10 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s20)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20)))),
% 295.51/188.10 inference(quant_inst,[status(thm)],[])).
% 295.51/188.10 tff(31350,plain,
% 295.51/188.10 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s20)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20))),
% 295.51/188.10 inference(modus_ponens,[status(thm)],[31349, 31348])).
% 295.51/188.10 tff(31351,plain,
% 295.51/188.10 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s20)),
% 295.51/188.10 inference(unit_resolution,[status(thm)],[31350, 4958, 31299])).
% 295.51/188.10 tff(31352,plain,
% 295.51/188.10 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s20)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s20))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s20)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s20))),
% 295.51/188.10 inference(rewrite,[status(thm)],[])).
% 295.51/188.10 tff(31353,plain,
% 295.51/188.10 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s20)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s20))),
% 295.51/188.10 inference(quant_inst,[status(thm)],[])).
% 295.51/188.10 tff(31354,plain,
% 295.51/188.10 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s20)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s20)),
% 295.51/188.10 inference(modus_ponens,[status(thm)],[31353, 31352])).
% 295.51/188.10 tff(31355,plain,
% 295.51/188.10 (~node9(c_e_h_1, c_m, s20)),
% 295.51/188.10 inference(unit_resolution,[status(thm)],[31354, 4972, 31351])).
% 295.51/188.10 tff(31356,assumption,(~node9(c_e_h_1, c_m, s20)), introduced(assumption)).
% 295.51/188.10 tff(31357,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s21)), introduced(assumption)).
% 295.51/188.10 tff(31358,assumption,(node10(c_e_h_1, c_m, s20, s21)), introduced(assumption)).
% 295.51/188.10 tff(31359,plain,
% 295.51/188.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s21)) | node9(c_e_h_1, c_m, s20) | (~node10(c_e_h_1, c_m, s20, s21)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s21)) | node9(c_e_h_1, c_m, s20) | (~node10(c_e_h_1, c_m, s20, s21)))),
% 295.51/188.10 inference(rewrite,[status(thm)],[])).
% 295.51/188.10 tff(31360,plain,
% 295.51/188.10 ((node9(c_e_h_1, c_m, s20) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s21)) | (~node10(c_e_h_1, c_m, s20, s21))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s21)) | node9(c_e_h_1, c_m, s20) | (~node10(c_e_h_1, c_m, s20, s21)))),
% 295.51/188.10 inference(rewrite,[status(thm)],[])).
% 295.51/188.10 tff(31361,plain,
% 295.51/188.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s20) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s21)) | (~node10(c_e_h_1, c_m, s20, s21)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s21)) | node9(c_e_h_1, c_m, s20) | (~node10(c_e_h_1, c_m, s20, s21))))),
% 295.60/188.10 inference(monotonicity,[status(thm)],[31360])).
% 295.60/188.10 tff(31362,plain,
% 295.60/188.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s20) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s21)) | (~node10(c_e_h_1, c_m, s20, s21)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s21)) | node9(c_e_h_1, c_m, s20) | (~node10(c_e_h_1, c_m, s20, s21)))),
% 295.60/188.10 inference(transitivity,[status(thm)],[31361, 31359])).
% 295.60/188.10 tff(31363,plain,
% 295.60/188.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s20) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s21)) | (~node10(c_e_h_1, c_m, s20, s21)))),
% 295.60/188.10 inference(quant_inst,[status(thm)],[])).
% 295.60/188.10 tff(31364,plain,
% 295.60/188.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s21)) | node9(c_e_h_1, c_m, s20) | (~node10(c_e_h_1, c_m, s20, s21))),
% 295.60/188.10 inference(modus_ponens,[status(thm)],[31363, 31362])).
% 295.60/188.10 tff(31365,plain,
% 295.60/188.10 ($false),
% 295.60/188.10 inference(unit_resolution,[status(thm)],[31364, 4986, 31357, 31358, 31356])).
% 295.60/188.10 tff(31366,plain,((~node10(c_e_h_1, c_m, s20, s21)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s21)) | node9(c_e_h_1, c_m, s20)), inference(lemma,lemma(discharge,[]))).
% 295.60/188.10 tff(31367,plain,
% 295.60/188.10 (~node10(c_e_h_1, c_m, s20, s21)),
% 295.60/188.10 inference(unit_resolution,[status(thm)],[31366, 31357, 31356])).
% 295.60/188.10 tff(31368,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s20)), introduced(assumption)).
% 295.60/188.10 tff(31369,assumption,(node11(c_e_h_1, c_m, s20, s21)), introduced(assumption)).
% 295.60/188.10 tff(31370,plain,
% 295.60/188.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s21)) | (~node11(c_e_h_1, c_m, s20, s21)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s20))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s21)) | (~node11(c_e_h_1, c_m, s20, s21)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s20))),
% 295.60/188.10 inference(rewrite,[status(thm)],[])).
% 295.60/188.10 tff(31371,plain,
% 295.60/188.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s21)) | (~node11(c_e_h_1, c_m, s20, s21)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s20))),
% 295.60/188.10 inference(quant_inst,[status(thm)],[])).
% 295.60/188.10 tff(31372,plain,
% 295.60/188.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s21)) | (~node11(c_e_h_1, c_m, s20, s21)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s20)),
% 295.60/188.10 inference(modus_ponens,[status(thm)],[31371, 31370])).
% 295.60/188.10 tff(31373,plain,
% 295.60/188.10 ($false),
% 295.60/188.10 inference(unit_resolution,[status(thm)],[31372, 5017, 31368, 31357, 31369])).
% 295.60/188.10 tff(31374,plain,((~node11(c_e_h_1, c_m, s20, s21)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s20) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s21))), inference(lemma,lemma(discharge,[]))).
% 295.60/188.10 tff(31375,plain,
% 295.60/188.10 (~node11(c_e_h_1, c_m, s20, s21)),
% 295.60/188.10 inference(unit_resolution,[status(thm)],[31374, 31357, 31368])).
% 295.60/188.10 tff(31376,plain,
% 295.60/188.10 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s20, s21)) | node10(c_e_h_1, c_m, s20, s21) | node11(c_e_h_1, c_m, s20, s21))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s20, s21)) | node10(c_e_h_1, c_m, s20, s21) | node11(c_e_h_1, c_m, s20, s21))),
% 295.61/188.10 inference(rewrite,[status(thm)],[])).
% 295.61/188.10 tff(31377,plain,
% 295.61/188.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s20, s21)) | node10(c_e_h_1, c_m, s20, s21) | node11(c_e_h_1, c_m, s20, s21))),
% 295.61/188.10 inference(quant_inst,[status(thm)],[])).
% 295.61/188.10 tff(31378,plain,
% 295.61/188.10 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s20, s21)) | node10(c_e_h_1, c_m, s20, s21) | node11(c_e_h_1, c_m, s20, s21)),
% 295.61/188.10 inference(modus_ponens,[status(thm)],[31377, 31376])).
% 295.61/188.10 tff(31379,plain,
% 295.61/188.10 (node10(c_e_h_1, c_m, s20, s21) | node11(c_e_h_1, c_m, s20, s21)),
% 295.61/188.10 inference(unit_resolution,[status(thm)],[31378, 5002, 30273])).
% 295.61/188.10 tff(31380,plain,
% 295.61/188.10 ($false),
% 295.61/188.10 inference(unit_resolution,[status(thm)],[31379, 31375, 31367])).
% 295.61/188.10 tff(31381,plain,((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s21)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s20) | node9(c_e_h_1, c_m, s20)), inference(lemma,lemma(discharge,[]))).
% 295.61/188.10 tff(31382,plain,
% 295.61/188.10 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s21)),
% 295.61/188.10 inference(unit_resolution,[status(thm)],[31381, 31355, 31337])).
% 295.61/188.10 tff(31383,assumption,(~m_c_h_element_v_out(c_e_h_1, c_e, s24)), introduced(assumption)).
% 295.61/188.10 tff(31384,plain,
% 295.61/188.10 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s24) | m_c_h_element_v_out(c_e_h_1, c_e, s24))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s24) | m_c_h_element_v_out(c_e_h_1, c_e, s24))),
% 295.61/188.10 inference(rewrite,[status(thm)],[])).
% 295.61/188.10 tff(31385,plain,
% 295.61/188.10 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s24) | m_c_h_element_v_out(c_e_h_1, c_e, s24))),
% 295.61/188.10 inference(quant_inst,[status(thm)],[])).
% 295.61/188.10 tff(31386,plain,
% 295.61/188.10 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s24) | m_c_h_element_v_out(c_e_h_1, c_e, s24)),
% 295.61/188.10 inference(modus_ponens,[status(thm)],[31385, 31384])).
% 295.61/188.10 tff(31387,plain,
% 295.61/188.10 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s24) | m_c_h_element_v_out(c_e_h_1, c_e, s24)),
% 295.61/188.10 inference(unit_resolution,[status(thm)],[31386, 7856])).
% 295.61/188.10 tff(31388,plain,
% 295.61/188.10 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s24)),
% 295.61/188.10 inference(unit_resolution,[status(thm)],[31387, 31383])).
% 295.61/188.10 tff(31389,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s21)), introduced(assumption)).
% 295.61/188.10 tff(31390,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s21)), introduced(assumption)).
% 295.61/188.10 tff(31391,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20)), introduced(assumption)).
% 295.61/188.10 tff(31392,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s20)), introduced(assumption)).
% 295.61/188.10 tff(31393,plain,
% 295.61/188.10 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s20) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s20))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s20) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s20))),
% 295.61/188.10 inference(rewrite,[status(thm)],[])).
% 295.61/188.10 tff(31394,plain,
% 295.61/188.10 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s20) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s20))),
% 295.61/188.10 inference(quant_inst,[status(thm)],[])).
% 295.61/188.10 tff(31395,plain,
% 295.61/188.10 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s20) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s20)),
% 295.61/188.10 inference(modus_ponens,[status(thm)],[31394, 31393])).
% 295.61/188.10 tff(31396,plain,
% 295.61/188.10 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s20) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s20)),
% 295.61/188.10 inference(unit_resolution,[status(thm)],[31395, 7868])).
% 295.61/188.11 tff(31397,plain,
% 295.61/188.11 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s20)),
% 295.61/188.11 inference(unit_resolution,[status(thm)],[31396, 31368])).
% 295.61/188.11 tff(31398,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s21)), introduced(assumption)).
% 295.61/188.11 tff(31399,assumption,(node11(c_e_h_1, c_n, s20, s21)), introduced(assumption)).
% 295.61/188.11 tff(31400,plain,
% 295.61/188.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s21) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20)) | (~node11(c_e_h_1, c_n, s20, s21)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s21) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20)) | (~node11(c_e_h_1, c_n, s20, s21)))),
% 295.61/188.11 inference(rewrite,[status(thm)],[])).
% 295.61/188.11 tff(31401,plain,
% 295.61/188.11 ((m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s21) | (~node11(c_e_h_1, c_n, s20, s21)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20))) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s21) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20)) | (~node11(c_e_h_1, c_n, s20, s21)))),
% 295.61/188.11 inference(rewrite,[status(thm)],[])).
% 295.61/188.11 tff(31402,plain,
% 295.61/188.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s21) | (~node11(c_e_h_1, c_n, s20, s21)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s21) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20)) | (~node11(c_e_h_1, c_n, s20, s21))))),
% 295.61/188.11 inference(monotonicity,[status(thm)],[31401])).
% 295.61/188.11 tff(31403,plain,
% 295.61/188.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s21) | (~node11(c_e_h_1, c_n, s20, s21)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s21) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20)) | (~node11(c_e_h_1, c_n, s20, s21)))),
% 295.61/188.11 inference(transitivity,[status(thm)],[31402, 31400])).
% 295.61/188.11 tff(31404,plain,
% 295.61/188.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s21) | (~node11(c_e_h_1, c_n, s20, s21)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20)))),
% 295.61/188.11 inference(quant_inst,[status(thm)],[])).
% 295.61/188.11 tff(31405,plain,
% 295.61/188.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s21) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20)) | (~node11(c_e_h_1, c_n, s20, s21))),
% 295.61/188.11 inference(modus_ponens,[status(thm)],[31404, 31403])).
% 295.61/188.11 tff(31406,plain,
% 295.61/188.11 ($false),
% 295.61/188.11 inference(unit_resolution,[status(thm)],[31405, 5742, 31391, 31398, 31399])).
% 295.61/188.11 tff(31407,plain,((~node11(c_e_h_1, c_n, s20, s21)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s21)), inference(lemma,lemma(discharge,[]))).
% 295.61/188.11 tff(31408,plain,
% 295.61/188.11 (~node11(c_e_h_1, c_n, s20, s21)),
% 295.61/188.11 inference(unit_resolution,[status(thm)],[31407, 31398, 31391])).
% 295.61/188.11 tff(31409,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s20)), introduced(assumption)).
% 295.61/188.11 tff(31410,assumption,(node10(c_e_h_1, c_n, s20, s21)), introduced(assumption)).
% 295.61/188.11 tff(31411,plain,
% 295.61/188.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s21) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s20)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s20)) | (~node10(c_e_h_1, c_n, s20, s21)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s21) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s20)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s20)) | (~node10(c_e_h_1, c_n, s20, s21)))),
% 295.61/188.11 inference(rewrite,[status(thm)],[])).
% 295.61/188.11 tff(31412,plain,
% 295.61/188.11 (((~node10(c_e_h_1, c_n, s20, s21)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s20)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s20)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s21)) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s21) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s20)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s20)) | (~node10(c_e_h_1, c_n, s20, s21)))),
% 295.61/188.11 inference(rewrite,[status(thm)],[])).
% 295.61/188.11 tff(31413,plain,
% 295.61/188.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s20, s21)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s20)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s20)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s21))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s21) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s20)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s20)) | (~node10(c_e_h_1, c_n, s20, s21))))),
% 295.61/188.11 inference(monotonicity,[status(thm)],[31412])).
% 295.61/188.11 tff(31414,plain,
% 295.61/188.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s20, s21)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s20)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s20)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s21))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s21) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s20)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s20)) | (~node10(c_e_h_1, c_n, s20, s21)))),
% 295.61/188.11 inference(transitivity,[status(thm)],[31413, 31411])).
% 295.61/188.11 tff(31415,plain,
% 295.61/188.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s20, s21)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s20)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s20)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s21))),
% 295.61/188.11 inference(quant_inst,[status(thm)],[])).
% 295.61/188.11 tff(31416,plain,
% 295.61/188.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s21) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s20)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s20)) | (~node10(c_e_h_1, c_n, s20, s21))),
% 295.61/188.11 inference(modus_ponens,[status(thm)],[31415, 31414])).
% 295.61/188.11 tff(31417,plain,
% 295.61/188.11 ($false),
% 295.61/188.11 inference(unit_resolution,[status(thm)],[31416, 5718, 31409, 31392, 31398, 31410])).
% 295.61/188.11 tff(31418,plain,((~node10(c_e_h_1, c_n, s20, s21)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s20)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s20)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s21)), inference(lemma,lemma(discharge,[]))).
% 295.61/188.11 tff(31419,plain,
% 295.61/188.11 (~node10(c_e_h_1, c_n, s20, s21)),
% 295.61/188.11 inference(unit_resolution,[status(thm)],[31418, 31398, 31392, 31409])).
% 295.61/188.11 tff(31420,plain,
% 295.61/188.11 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s20, s21)) | node10(c_e_h_1, c_n, s20, s21) | node11(c_e_h_1, c_n, s20, s21))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s20, s21)) | node10(c_e_h_1, c_n, s20, s21) | node11(c_e_h_1, c_n, s20, s21))),
% 295.61/188.11 inference(rewrite,[status(thm)],[])).
% 295.61/188.11 tff(31421,plain,
% 295.61/188.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s20, s21)) | node10(c_e_h_1, c_n, s20, s21) | node11(c_e_h_1, c_n, s20, s21))),
% 295.61/188.11 inference(quant_inst,[status(thm)],[])).
% 295.61/188.11 tff(31422,plain,
% 295.61/188.11 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s20, s21)) | node10(c_e_h_1, c_n, s20, s21) | node11(c_e_h_1, c_n, s20, s21)),
% 295.61/188.11 inference(modus_ponens,[status(thm)],[31421, 31420])).
% 295.61/188.11 tff(31423,plain,
% 295.61/188.11 (node10(c_e_h_1, c_n, s20, s21) | node11(c_e_h_1, c_n, s20, s21)),
% 295.61/188.11 inference(unit_resolution,[status(thm)],[31422, 5002, 30273])).
% 295.61/188.11 tff(31424,plain,
% 295.61/188.11 ($false),
% 295.61/188.11 inference(unit_resolution,[status(thm)],[31423, 31419, 31408])).
% 295.61/188.11 tff(31425,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s21) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s20)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s20)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20))), inference(lemma,lemma(discharge,[]))).
% 295.61/188.11 tff(31426,plain,
% 295.61/188.11 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s21)),
% 295.61/188.11 inference(unit_resolution,[status(thm)],[31425, 31397, 31392, 31391])).
% 295.61/188.11 tff(31427,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s23)), introduced(assumption)).
% 295.61/188.11 tff(31428,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s21)), introduced(assumption)).
% 295.61/188.11 tff(31429,plain,
% 295.61/188.11 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s21)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s21)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s21)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s21)))),
% 295.61/188.11 inference(rewrite,[status(thm)],[])).
% 295.61/188.11 tff(31430,plain,
% 295.61/188.11 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s21)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s21)))),
% 295.61/188.11 inference(quant_inst,[status(thm)],[])).
% 295.61/188.11 tff(31431,plain,
% 295.61/188.11 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s21)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s21))),
% 295.61/188.11 inference(modus_ponens,[status(thm)],[31430, 31429])).
% 295.61/188.11 tff(31432,plain,
% 295.61/188.11 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s21)),
% 295.61/188.11 inference(unit_resolution,[status(thm)],[31431, 4958, 31428])).
% 295.61/188.11 tff(31433,plain,
% 295.61/188.11 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s21)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s21))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s21)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s21))),
% 295.61/188.11 inference(rewrite,[status(thm)],[])).
% 295.61/188.11 tff(31434,plain,
% 295.61/188.11 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s21)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s21))),
% 295.61/188.11 inference(quant_inst,[status(thm)],[])).
% 295.61/188.11 tff(31435,plain,
% 295.61/188.11 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s21)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s21)),
% 295.61/188.11 inference(modus_ponens,[status(thm)],[31434, 31433])).
% 295.61/188.11 tff(31436,plain,
% 295.61/188.11 (~node9(c_e_h_1, c_m, s21)),
% 295.61/188.11 inference(unit_resolution,[status(thm)],[31435, 4972, 31432])).
% 295.61/188.11 tff(31437,assumption,(~node9(c_e_h_1, c_m, s21)), introduced(assumption)).
% 295.61/188.12 tff(31438,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s22)), introduced(assumption)).
% 295.61/188.12 tff(31439,assumption,(node10(c_e_h_1, c_m, s21, s22)), introduced(assumption)).
% 295.61/188.12 tff(31440,plain,
% 295.61/188.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s22)) | node9(c_e_h_1, c_m, s21) | (~node10(c_e_h_1, c_m, s21, s22)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s22)) | node9(c_e_h_1, c_m, s21) | (~node10(c_e_h_1, c_m, s21, s22)))),
% 295.61/188.12 inference(rewrite,[status(thm)],[])).
% 295.61/188.12 tff(31441,plain,
% 295.61/188.12 ((node9(c_e_h_1, c_m, s21) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s22)) | (~node10(c_e_h_1, c_m, s21, s22))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s22)) | node9(c_e_h_1, c_m, s21) | (~node10(c_e_h_1, c_m, s21, s22)))),
% 295.61/188.12 inference(rewrite,[status(thm)],[])).
% 295.61/188.12 tff(31442,plain,
% 295.61/188.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s21) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s22)) | (~node10(c_e_h_1, c_m, s21, s22)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s22)) | node9(c_e_h_1, c_m, s21) | (~node10(c_e_h_1, c_m, s21, s22))))),
% 295.61/188.12 inference(monotonicity,[status(thm)],[31441])).
% 295.61/188.12 tff(31443,plain,
% 295.61/188.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s21) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s22)) | (~node10(c_e_h_1, c_m, s21, s22)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s22)) | node9(c_e_h_1, c_m, s21) | (~node10(c_e_h_1, c_m, s21, s22)))),
% 295.61/188.12 inference(transitivity,[status(thm)],[31442, 31440])).
% 295.61/188.12 tff(31444,plain,
% 295.61/188.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s21) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s22)) | (~node10(c_e_h_1, c_m, s21, s22)))),
% 295.61/188.12 inference(quant_inst,[status(thm)],[])).
% 295.61/188.12 tff(31445,plain,
% 295.61/188.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s22)) | node9(c_e_h_1, c_m, s21) | (~node10(c_e_h_1, c_m, s21, s22))),
% 295.61/188.12 inference(modus_ponens,[status(thm)],[31444, 31443])).
% 295.61/188.12 tff(31446,plain,
% 295.61/188.12 ($false),
% 295.61/188.12 inference(unit_resolution,[status(thm)],[31445, 4986, 31438, 31439, 31437])).
% 295.61/188.12 tff(31447,plain,((~node10(c_e_h_1, c_m, s21, s22)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s22)) | node9(c_e_h_1, c_m, s21)), inference(lemma,lemma(discharge,[]))).
% 295.61/188.12 tff(31448,plain,
% 295.61/188.12 (~node10(c_e_h_1, c_m, s21, s22)),
% 295.61/188.12 inference(unit_resolution,[status(thm)],[31447, 31438, 31437])).
% 295.61/188.12 tff(31449,plain,
% 295.61/188.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s21, s22)) | node10(c_e_h_1, c_m, s21, s22) | node11(c_e_h_1, c_m, s21, s22))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s21, s22)) | node10(c_e_h_1, c_m, s21, s22) | node11(c_e_h_1, c_m, s21, s22))),
% 295.61/188.12 inference(rewrite,[status(thm)],[])).
% 295.61/188.12 tff(31450,plain,
% 295.61/188.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s21, s22)) | node10(c_e_h_1, c_m, s21, s22) | node11(c_e_h_1, c_m, s21, s22))),
% 295.61/188.12 inference(quant_inst,[status(thm)],[])).
% 295.61/188.12 tff(31451,plain,
% 295.61/188.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s21, s22)) | node10(c_e_h_1, c_m, s21, s22) | node11(c_e_h_1, c_m, s21, s22)),
% 295.61/188.12 inference(modus_ponens,[status(thm)],[31450, 31449])).
% 295.61/188.12 tff(31452,plain,
% 295.61/188.12 (node10(c_e_h_1, c_m, s21, s22) | node11(c_e_h_1, c_m, s21, s22)),
% 295.61/188.12 inference(unit_resolution,[status(thm)],[31451, 5002, 30340])).
% 295.61/188.12 tff(31453,plain,
% 295.61/188.12 (node11(c_e_h_1, c_m, s21, s22)),
% 295.61/188.12 inference(unit_resolution,[status(thm)],[31452, 31448])).
% 295.61/188.12 tff(31454,plain,
% 295.61/188.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s22)) | (~node11(c_e_h_1, c_m, s21, s22)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s21))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s22)) | (~node11(c_e_h_1, c_m, s21, s22)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s21))),
% 295.61/188.12 inference(rewrite,[status(thm)],[])).
% 295.61/188.12 tff(31455,plain,
% 295.61/188.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s22)) | (~node11(c_e_h_1, c_m, s21, s22)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s21))),
% 295.61/188.12 inference(quant_inst,[status(thm)],[])).
% 295.61/188.12 tff(31456,plain,
% 295.61/188.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s22)) | (~node11(c_e_h_1, c_m, s21, s22)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s21)),
% 295.61/188.12 inference(modus_ponens,[status(thm)],[31455, 31454])).
% 295.61/188.12 tff(31457,plain,
% 295.61/188.12 ($false),
% 295.61/188.12 inference(unit_resolution,[status(thm)],[31456, 5017, 31438, 31389, 31453])).
% 295.61/188.12 tff(31458,plain,((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s22)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s21) | node9(c_e_h_1, c_m, s21)), inference(lemma,lemma(discharge,[]))).
% 295.61/188.12 tff(31459,plain,
% 295.61/188.12 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s22)),
% 295.61/188.12 inference(unit_resolution,[status(thm)],[31458, 31389, 31436])).
% 295.61/188.12 tff(31460,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s22)), introduced(assumption)).
% 295.61/188.12 tff(31461,assumption,(node11(c_e_h_1, c_m, s22, s23)), introduced(assumption)).
% 295.61/188.12 tff(31462,plain,
% 295.61/188.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s23)) | (~node11(c_e_h_1, c_m, s22, s23)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s22))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s23)) | (~node11(c_e_h_1, c_m, s22, s23)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s22))),
% 295.61/188.12 inference(rewrite,[status(thm)],[])).
% 295.61/188.12 tff(31463,plain,
% 295.61/188.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s23)) | (~node11(c_e_h_1, c_m, s22, s23)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s22))),
% 295.61/188.12 inference(quant_inst,[status(thm)],[])).
% 295.61/188.12 tff(31464,plain,
% 295.61/188.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s23)) | (~node11(c_e_h_1, c_m, s22, s23)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s22)),
% 295.61/188.12 inference(modus_ponens,[status(thm)],[31463, 31462])).
% 295.61/188.12 tff(31465,plain,
% 295.61/188.12 ($false),
% 295.61/188.12 inference(unit_resolution,[status(thm)],[31464, 5017, 31460, 31427, 31461])).
% 295.61/188.12 tff(31466,plain,((~node11(c_e_h_1, c_m, s22, s23)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s22) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s23))), inference(lemma,lemma(discharge,[]))).
% 295.61/188.12 tff(31467,plain,
% 295.61/188.12 (~node11(c_e_h_1, c_m, s22, s23)),
% 295.61/188.12 inference(unit_resolution,[status(thm)],[31466, 31427, 31460])).
% 295.61/188.12 tff(31468,assumption,(~node9(c_e_h_1, c_m, s22)), introduced(assumption)).
% 295.61/188.12 tff(31469,assumption,(node10(c_e_h_1, c_m, s22, s23)), introduced(assumption)).
% 295.61/188.12 tff(31470,plain,
% 295.61/188.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s22) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s23)) | (~node10(c_e_h_1, c_m, s22, s23)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_1, c_m, s22) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s23)) | (~node10(c_e_h_1, c_m, s22, s23)))),
% 295.61/188.12 inference(rewrite,[status(thm)],[])).
% 295.61/188.12 tff(31471,plain,
% 295.61/188.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s22) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s23)) | (~node10(c_e_h_1, c_m, s22, s23)))),
% 295.61/188.12 inference(quant_inst,[status(thm)],[])).
% 295.61/188.12 tff(31472,plain,
% 295.61/188.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_1, c_m, s22) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s23)) | (~node10(c_e_h_1, c_m, s22, s23))),
% 295.61/188.12 inference(modus_ponens,[status(thm)],[31471, 31470])).
% 295.61/188.12 tff(31473,plain,
% 295.61/188.12 ($false),
% 295.61/188.12 inference(unit_resolution,[status(thm)],[31472, 4986, 31427, 31469, 31468])).
% 295.61/188.12 tff(31474,plain,((~node10(c_e_h_1, c_m, s22, s23)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s23)) | node9(c_e_h_1, c_m, s22)), inference(lemma,lemma(discharge,[]))).
% 295.61/188.12 tff(31475,plain,
% 295.61/188.12 (~node10(c_e_h_1, c_m, s22, s23)),
% 295.61/188.12 inference(unit_resolution,[status(thm)],[31474, 31427, 31468])).
% 295.61/188.12 tff(31476,plain,
% 295.61/188.12 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s22, s23)) | node10(c_e_h_1, c_m, s22, s23) | node11(c_e_h_1, c_m, s22, s23))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s22, s23)) | node10(c_e_h_1, c_m, s22, s23) | node11(c_e_h_1, c_m, s22, s23))),
% 295.61/188.12 inference(rewrite,[status(thm)],[])).
% 295.61/188.12 tff(31477,plain,
% 295.61/188.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s22, s23)) | node10(c_e_h_1, c_m, s22, s23) | node11(c_e_h_1, c_m, s22, s23))),
% 295.61/188.12 inference(quant_inst,[status(thm)],[])).
% 295.61/188.12 tff(31478,plain,
% 295.61/188.12 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s22, s23)) | node10(c_e_h_1, c_m, s22, s23) | node11(c_e_h_1, c_m, s22, s23)),
% 295.61/188.12 inference(modus_ponens,[status(thm)],[31477, 31476])).
% 295.61/188.12 tff(31479,plain,
% 295.61/188.12 (node10(c_e_h_1, c_m, s22, s23) | node11(c_e_h_1, c_m, s22, s23)),
% 295.61/188.12 inference(unit_resolution,[status(thm)],[31478, 5002, 30672])).
% 295.61/188.12 tff(31480,plain,
% 295.61/188.12 ($false),
% 295.61/188.12 inference(unit_resolution,[status(thm)],[31479, 31475, 31467])).
% 295.61/188.12 tff(31481,plain,((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s23)) | node9(c_e_h_1, c_m, s22) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s22)), inference(lemma,lemma(discharge,[]))).
% 295.61/188.12 tff(31482,plain,
% 295.61/188.12 (node9(c_e_h_1, c_m, s22)),
% 295.61/188.12 inference(unit_resolution,[status(thm)],[31481, 31459, 31427])).
% 295.61/188.12 tff(31483,plain,
% 295.61/188.12 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s21) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s21))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s21) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s21))),
% 295.61/188.12 inference(rewrite,[status(thm)],[])).
% 295.61/188.12 tff(31484,plain,
% 295.61/188.12 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s21) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s21))),
% 295.61/188.12 inference(quant_inst,[status(thm)],[])).
% 295.61/188.12 tff(31485,plain,
% 295.61/188.12 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s21) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s21)),
% 295.61/188.13 inference(modus_ponens,[status(thm)],[31484, 31483])).
% 295.61/188.13 tff(31486,plain,
% 295.61/188.13 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s21) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s21)),
% 295.61/188.13 inference(unit_resolution,[status(thm)],[31485, 7868])).
% 295.61/188.13 tff(31487,plain,
% 295.61/188.13 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s21)),
% 295.61/188.13 inference(unit_resolution,[status(thm)],[31486, 31389])).
% 295.61/188.13 tff(31488,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s22)), introduced(assumption)).
% 295.61/188.13 tff(31489,assumption,(node11(c_e_h_1, c_n, s21, s22)), introduced(assumption)).
% 295.61/188.13 tff(31490,plain,
% 295.61/188.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s22) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s21)) | (~node11(c_e_h_1, c_n, s21, s22)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s22) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s21)) | (~node11(c_e_h_1, c_n, s21, s22)))),
% 295.61/188.13 inference(rewrite,[status(thm)],[])).
% 295.61/188.13 tff(31491,plain,
% 295.61/188.13 ((m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s22) | (~node11(c_e_h_1, c_n, s21, s22)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s21))) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s22) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s21)) | (~node11(c_e_h_1, c_n, s21, s22)))),
% 295.61/188.13 inference(rewrite,[status(thm)],[])).
% 295.61/188.13 tff(31492,plain,
% 295.61/188.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s22) | (~node11(c_e_h_1, c_n, s21, s22)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s21)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s22) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s21)) | (~node11(c_e_h_1, c_n, s21, s22))))),
% 295.61/188.13 inference(monotonicity,[status(thm)],[31491])).
% 295.61/188.13 tff(31493,plain,
% 295.61/188.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s22) | (~node11(c_e_h_1, c_n, s21, s22)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s21)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s22) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s21)) | (~node11(c_e_h_1, c_n, s21, s22)))),
% 295.61/188.13 inference(transitivity,[status(thm)],[31492, 31490])).
% 295.61/188.13 tff(31494,plain,
% 295.61/188.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s22) | (~node11(c_e_h_1, c_n, s21, s22)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s21)))),
% 295.61/188.13 inference(quant_inst,[status(thm)],[])).
% 295.61/188.13 tff(31495,plain,
% 295.61/188.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s22) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s21)) | (~node11(c_e_h_1, c_n, s21, s22))),
% 295.61/188.13 inference(modus_ponens,[status(thm)],[31494, 31493])).
% 295.61/188.13 tff(31496,plain,
% 295.61/188.13 ($false),
% 295.61/188.13 inference(unit_resolution,[status(thm)],[31495, 5742, 31488, 31428, 31489])).
% 295.61/188.13 tff(31497,plain,((~node11(c_e_h_1, c_n, s21, s22)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s22) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s21))), inference(lemma,lemma(discharge,[]))).
% 295.61/188.13 tff(31498,plain,
% 295.61/188.13 (~node11(c_e_h_1, c_n, s21, s22)),
% 295.61/188.13 inference(unit_resolution,[status(thm)],[31497, 31488, 31428])).
% 295.61/188.13 tff(31499,plain,
% 295.61/188.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s21, s22)) | node10(c_e_h_1, c_n, s21, s22) | node11(c_e_h_1, c_n, s21, s22))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s21, s22)) | node10(c_e_h_1, c_n, s21, s22) | node11(c_e_h_1, c_n, s21, s22))),
% 295.61/188.13 inference(rewrite,[status(thm)],[])).
% 295.61/188.13 tff(31500,plain,
% 295.61/188.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s21, s22)) | node10(c_e_h_1, c_n, s21, s22) | node11(c_e_h_1, c_n, s21, s22))),
% 295.61/188.13 inference(quant_inst,[status(thm)],[])).
% 295.61/188.13 tff(31501,plain,
% 295.61/188.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s21, s22)) | node10(c_e_h_1, c_n, s21, s22) | node11(c_e_h_1, c_n, s21, s22)),
% 295.61/188.13 inference(modus_ponens,[status(thm)],[31500, 31499])).
% 295.61/188.13 tff(31502,plain,
% 295.61/188.13 (node10(c_e_h_1, c_n, s21, s22) | node11(c_e_h_1, c_n, s21, s22)),
% 295.61/188.13 inference(unit_resolution,[status(thm)],[31501, 5002, 30340])).
% 295.61/188.13 tff(31503,plain,
% 295.61/188.13 (node10(c_e_h_1, c_n, s21, s22)),
% 295.61/188.13 inference(unit_resolution,[status(thm)],[31502, 31498])).
% 295.61/188.13 tff(31504,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s21)), introduced(assumption)).
% 295.61/188.13 tff(31505,plain,
% 295.61/188.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s21)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s22) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s21)) | (~node10(c_e_h_1, c_n, s21, s22)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s21)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s22) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s21)) | (~node10(c_e_h_1, c_n, s21, s22)))),
% 295.61/188.13 inference(rewrite,[status(thm)],[])).
% 295.61/188.13 tff(31506,plain,
% 295.61/188.13 (((~node10(c_e_h_1, c_n, s21, s22)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s21)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s21)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s22)) <=> ((~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s21)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s22) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s21)) | (~node10(c_e_h_1, c_n, s21, s22)))),
% 295.61/188.13 inference(rewrite,[status(thm)],[])).
% 295.61/188.13 tff(31507,plain,
% 295.61/188.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s21, s22)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s21)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s21)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s22))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s21)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s22) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s21)) | (~node10(c_e_h_1, c_n, s21, s22))))),
% 295.61/188.13 inference(monotonicity,[status(thm)],[31506])).
% 295.61/188.13 tff(31508,plain,
% 295.61/188.13 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s21, s22)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s21)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s21)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s22))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s21)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s22) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s21)) | (~node10(c_e_h_1, c_n, s21, s22)))),
% 295.61/188.13 inference(transitivity,[status(thm)],[31507, 31505])).
% 295.61/188.13 tff(31509,plain,
% 295.61/188.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s21, s22)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s21)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s21)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s22))),
% 295.61/188.13 inference(quant_inst,[status(thm)],[])).
% 295.61/188.13 tff(31510,plain,
% 295.61/188.13 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s21)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s22) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s21)) | (~node10(c_e_h_1, c_n, s21, s22))),
% 295.61/188.13 inference(modus_ponens,[status(thm)],[31509, 31508])).
% 295.61/188.13 tff(31511,plain,
% 295.61/188.13 ($false),
% 295.61/188.13 inference(unit_resolution,[status(thm)],[31510, 5718, 31390, 31488, 31504, 31503])).
% 295.61/188.13 tff(31512,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s22) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s21)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s21)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s21))), inference(lemma,lemma(discharge,[]))).
% 295.61/188.13 tff(31513,plain,
% 295.61/188.13 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s22)),
% 295.61/188.13 inference(unit_resolution,[status(thm)],[31512, 31487, 31390, 31428])).
% 295.61/188.13 tff(31514,plain,
% 295.61/188.13 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s22)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s22)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s22)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s22)))),
% 295.61/188.13 inference(rewrite,[status(thm)],[])).
% 295.61/188.13 tff(31515,plain,
% 295.61/188.13 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s22)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s22)))),
% 295.61/188.13 inference(quant_inst,[status(thm)],[])).
% 295.61/188.13 tff(31516,plain,
% 295.61/188.13 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s22)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s22))),
% 295.61/188.13 inference(modus_ponens,[status(thm)],[31515, 31514])).
% 295.61/188.13 tff(31517,plain,
% 295.61/188.13 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s22)),
% 295.61/188.13 inference(unit_resolution,[status(thm)],[31516, 4958, 31513])).
% 295.61/188.13 tff(31518,plain,
% 295.61/188.13 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s22)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s22))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s22)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s22))),
% 295.61/188.13 inference(rewrite,[status(thm)],[])).
% 295.61/188.13 tff(31519,plain,
% 295.61/188.13 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s22)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s22))),
% 295.61/188.13 inference(quant_inst,[status(thm)],[])).
% 295.61/188.13 tff(31520,plain,
% 295.61/188.13 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s22)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s22)),
% 295.61/188.13 inference(modus_ponens,[status(thm)],[31519, 31518])).
% 295.61/188.13 tff(31521,plain,
% 295.61/188.13 ($false),
% 295.61/188.13 inference(unit_resolution,[status(thm)],[31520, 4972, 31517, 31482])).
% 295.61/188.13 tff(31522,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s21) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s23)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s21)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s21))), inference(lemma,lemma(discharge,[]))).
% 295.61/188.13 tff(31523,plain,
% 295.61/188.13 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s23)),
% 295.61/188.13 inference(unit_resolution,[status(thm)],[31522, 31426, 31390, 31389])).
% 295.61/188.14 tff(31524,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s24)), introduced(assumption)).
% 295.61/188.14 tff(31525,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s25)), introduced(assumption)).
% 295.61/188.14 tff(31526,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s22)), introduced(assumption)).
% 295.61/188.14 tff(31527,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s23)), introduced(assumption)).
% 295.61/188.14 tff(31528,plain,
% 295.61/188.14 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s21)),
% 295.61/188.14 inference(unit_resolution,[status(thm)],[31425, 31397, 31391, 31392])).
% 295.61/188.14 tff(31529,plain,
% 295.61/188.14 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s22)),
% 295.61/188.14 inference(unit_resolution,[status(thm)],[31512, 31487, 31428, 31390])).
% 295.61/188.14 tff(31530,plain,
% 295.61/188.14 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s22) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s22))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s22) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s22))),
% 295.61/188.14 inference(rewrite,[status(thm)],[])).
% 295.61/188.14 tff(31531,plain,
% 295.61/188.14 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s22) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s22))),
% 295.61/188.14 inference(quant_inst,[status(thm)],[])).
% 295.61/188.14 tff(31532,plain,
% 295.61/188.14 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s22) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s22)),
% 295.61/188.14 inference(modus_ponens,[status(thm)],[31531, 31530])).
% 295.61/188.14 tff(31533,plain,
% 295.61/188.14 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s22) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s22)),
% 295.61/188.14 inference(unit_resolution,[status(thm)],[31532, 7868])).
% 295.61/188.14 tff(31534,plain,
% 295.61/188.14 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s22)),
% 295.61/188.14 inference(unit_resolution,[status(thm)],[31533, 31459])).
% 295.61/188.14 tff(31535,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s22)), introduced(assumption)).
% 295.61/188.14 tff(31536,assumption,(node10(c_e_h_1, c_n, s22, s23)), introduced(assumption)).
% 295.61/188.14 tff(31537,plain,
% 295.61/188.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s23) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s22)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s22)) | (~node10(c_e_h_1, c_n, s22, s23)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s23) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s22)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s22)) | (~node10(c_e_h_1, c_n, s22, s23)))),
% 295.61/188.14 inference(rewrite,[status(thm)],[])).
% 295.61/188.14 tff(31538,plain,
% 295.61/188.14 (((~node10(c_e_h_1, c_n, s22, s23)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s22)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s22)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s23)) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s23) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s22)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s22)) | (~node10(c_e_h_1, c_n, s22, s23)))),
% 295.61/188.14 inference(rewrite,[status(thm)],[])).
% 295.61/188.14 tff(31539,plain,
% 295.61/188.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s22, s23)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s22)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s22)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s23))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s23) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s22)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s22)) | (~node10(c_e_h_1, c_n, s22, s23))))),
% 295.61/188.14 inference(monotonicity,[status(thm)],[31538])).
% 295.61/188.14 tff(31540,plain,
% 295.61/188.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s22, s23)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s22)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s22)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s23))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s23) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s22)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s22)) | (~node10(c_e_h_1, c_n, s22, s23)))),
% 295.61/188.14 inference(transitivity,[status(thm)],[31539, 31537])).
% 295.61/188.14 tff(31541,plain,
% 295.61/188.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s22, s23)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s22)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s22)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s23))),
% 295.61/188.14 inference(quant_inst,[status(thm)],[])).
% 295.61/188.14 tff(31542,plain,
% 295.61/188.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s23) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s22)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s22)) | (~node10(c_e_h_1, c_n, s22, s23))),
% 295.61/188.14 inference(modus_ponens,[status(thm)],[31541, 31540])).
% 295.61/188.14 tff(31543,plain,
% 295.61/188.14 ($false),
% 295.61/188.14 inference(unit_resolution,[status(thm)],[31542, 5718, 31535, 31527, 31526, 31536])).
% 295.61/188.14 tff(31544,plain,((~node10(c_e_h_1, c_n, s22, s23)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s22)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s23) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s22))), inference(lemma,lemma(discharge,[]))).
% 295.61/188.14 tff(31545,plain,
% 295.61/188.14 (~node10(c_e_h_1, c_n, s22, s23)),
% 295.61/188.14 inference(unit_resolution,[status(thm)],[31544, 31527, 31526, 31535])).
% 295.61/188.14 tff(31546,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s22)), introduced(assumption)).
% 295.61/188.14 tff(31547,assumption,(node11(c_e_h_1, c_n, s22, s23)), introduced(assumption)).
% 295.61/188.14 tff(31548,plain,
% 295.61/188.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s23) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s22)) | (~node11(c_e_h_1, c_n, s22, s23)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s23) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s22)) | (~node11(c_e_h_1, c_n, s22, s23)))),
% 295.61/188.14 inference(rewrite,[status(thm)],[])).
% 295.61/188.14 tff(31549,plain,
% 295.61/188.14 ((m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s23) | (~node11(c_e_h_1, c_n, s22, s23)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s22))) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s23) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s22)) | (~node11(c_e_h_1, c_n, s22, s23)))),
% 295.61/188.14 inference(rewrite,[status(thm)],[])).
% 295.61/188.14 tff(31550,plain,
% 295.61/188.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s23) | (~node11(c_e_h_1, c_n, s22, s23)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s22)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s23) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s22)) | (~node11(c_e_h_1, c_n, s22, s23))))),
% 295.61/188.14 inference(monotonicity,[status(thm)],[31549])).
% 295.61/188.14 tff(31551,plain,
% 295.61/188.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s23) | (~node11(c_e_h_1, c_n, s22, s23)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s22)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s23) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s22)) | (~node11(c_e_h_1, c_n, s22, s23)))),
% 295.61/188.14 inference(transitivity,[status(thm)],[31550, 31548])).
% 295.61/188.14 tff(31552,plain,
% 295.61/188.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s23) | (~node11(c_e_h_1, c_n, s22, s23)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s22)))),
% 295.61/188.14 inference(quant_inst,[status(thm)],[])).
% 295.61/188.14 tff(31553,plain,
% 295.61/188.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s23) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s22)) | (~node11(c_e_h_1, c_n, s22, s23))),
% 295.61/188.14 inference(modus_ponens,[status(thm)],[31552, 31551])).
% 295.61/188.14 tff(31554,plain,
% 295.61/188.14 ($false),
% 295.61/188.14 inference(unit_resolution,[status(thm)],[31553, 5742, 31546, 31527, 31547])).
% 295.61/188.14 tff(31555,plain,((~node11(c_e_h_1, c_n, s22, s23)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s22)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s23)), inference(lemma,lemma(discharge,[]))).
% 295.61/188.14 tff(31556,plain,
% 295.61/188.14 (~node11(c_e_h_1, c_n, s22, s23)),
% 295.61/188.14 inference(unit_resolution,[status(thm)],[31555, 31527, 31546])).
% 295.61/188.14 tff(31557,plain,
% 295.61/188.14 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s22, s23)) | node10(c_e_h_1, c_n, s22, s23) | node11(c_e_h_1, c_n, s22, s23))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s22, s23)) | node10(c_e_h_1, c_n, s22, s23) | node11(c_e_h_1, c_n, s22, s23))),
% 295.61/188.14 inference(rewrite,[status(thm)],[])).
% 295.61/188.14 tff(31558,plain,
% 295.61/188.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s22, s23)) | node10(c_e_h_1, c_n, s22, s23) | node11(c_e_h_1, c_n, s22, s23))),
% 295.61/188.14 inference(quant_inst,[status(thm)],[])).
% 295.61/188.14 tff(31559,plain,
% 295.61/188.14 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s22, s23)) | node10(c_e_h_1, c_n, s22, s23) | node11(c_e_h_1, c_n, s22, s23)),
% 295.61/188.14 inference(modus_ponens,[status(thm)],[31558, 31557])).
% 295.61/188.14 tff(31560,plain,
% 295.61/188.14 (node10(c_e_h_1, c_n, s22, s23) | node11(c_e_h_1, c_n, s22, s23)),
% 295.61/188.14 inference(unit_resolution,[status(thm)],[31559, 5002, 30672])).
% 295.61/188.14 tff(31561,plain,
% 295.61/188.14 ($false),
% 295.61/188.14 inference(unit_resolution,[status(thm)],[31560, 31556, 31545])).
% 295.61/188.14 tff(31562,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s23) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s22)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s22)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s22))), inference(lemma,lemma(discharge,[]))).
% 295.61/188.14 tff(31563,plain,
% 295.61/188.14 ($false),
% 295.61/188.14 inference(unit_resolution,[status(thm)],[31562, 31534, 31529, 31526, 31527])).
% 295.61/188.14 tff(31564,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s21) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s22)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s23) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s21)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s21))), inference(lemma,lemma(discharge,[]))).
% 295.61/188.14 tff(31565,plain,
% 295.61/188.14 (m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s21)),
% 295.61/188.14 inference(unit_resolution,[status(thm)],[31564, 31528, 31527, 31526, 31390])).
% 295.61/188.14 tff(31566,plain,
% 295.61/188.14 (~node11(c_e_h_1, c_m, s20, s21)),
% 295.61/188.14 inference(unit_resolution,[status(thm)],[31374, 31565, 31368])).
% 295.61/188.14 tff(31567,plain,
% 295.61/188.14 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s20)),
% 295.61/188.14 inference(unit_resolution,[status(thm)],[31350, 4958, 31391])).
% 295.61/188.15 tff(31568,plain,
% 295.61/188.15 (~node9(c_e_h_1, c_m, s20)),
% 295.61/188.15 inference(unit_resolution,[status(thm)],[31354, 4972, 31567])).
% 295.61/188.15 tff(31569,plain,
% 295.61/188.15 (~node10(c_e_h_1, c_m, s20, s21)),
% 295.61/188.15 inference(unit_resolution,[status(thm)],[31366, 31565, 31568])).
% 295.61/188.15 tff(31570,plain,
% 295.61/188.15 ($false),
% 295.61/188.15 inference(unit_resolution,[status(thm)],[31379, 31569, 31566])).
% 295.61/188.15 tff(31571,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s20) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s23) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s22)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s21)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s20))), inference(lemma,lemma(discharge,[]))).
% 295.61/188.15 tff(31572,plain,
% 295.61/188.15 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s23)),
% 295.61/188.15 inference(unit_resolution,[status(thm)],[31571, 31368, 31526, 31390, 31391, 31392])).
% 295.61/188.15 tff(31573,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s23)), introduced(assumption)).
% 295.61/188.15 tff(31574,plain,
% 295.61/188.15 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s23) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s23))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s23) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s23))),
% 295.61/188.15 inference(rewrite,[status(thm)],[])).
% 295.61/188.15 tff(31575,plain,
% 295.61/188.15 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s23) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s23))),
% 295.61/188.15 inference(quant_inst,[status(thm)],[])).
% 295.61/188.15 tff(31576,plain,
% 295.61/188.15 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s23) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s23)),
% 295.61/188.15 inference(modus_ponens,[status(thm)],[31575, 31574])).
% 295.61/188.15 tff(31577,plain,
% 295.61/188.15 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s23) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s23)),
% 295.61/188.15 inference(unit_resolution,[status(thm)],[31576, 7868])).
% 295.61/188.15 tff(31578,plain,
% 295.61/188.15 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s23)),
% 295.61/188.15 inference(unit_resolution,[status(thm)],[31577, 31523])).
% 295.61/188.15 tff(31579,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s23)), introduced(assumption)).
% 295.61/188.15 tff(31580,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s24)), introduced(assumption)).
% 295.61/188.15 tff(31581,assumption,(node11(c_e_h_1, c_n, s23, s24)), introduced(assumption)).
% 295.61/188.15 tff(31582,plain,
% 295.61/188.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s24) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s23)) | (~node11(c_e_h_1, c_n, s23, s24)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s24) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s23)) | (~node11(c_e_h_1, c_n, s23, s24)))),
% 295.61/188.15 inference(rewrite,[status(thm)],[])).
% 295.61/188.15 tff(31583,plain,
% 295.61/188.15 ((m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s24) | (~node11(c_e_h_1, c_n, s23, s24)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s23))) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s24) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s23)) | (~node11(c_e_h_1, c_n, s23, s24)))),
% 295.61/188.15 inference(rewrite,[status(thm)],[])).
% 295.61/188.15 tff(31584,plain,
% 295.61/188.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s24) | (~node11(c_e_h_1, c_n, s23, s24)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s23)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s24) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s23)) | (~node11(c_e_h_1, c_n, s23, s24))))),
% 295.61/188.15 inference(monotonicity,[status(thm)],[31583])).
% 295.61/188.15 tff(31585,plain,
% 295.61/188.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s24) | (~node11(c_e_h_1, c_n, s23, s24)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s23)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s24) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s23)) | (~node11(c_e_h_1, c_n, s23, s24)))),
% 295.61/188.15 inference(transitivity,[status(thm)],[31584, 31582])).
% 295.61/188.15 tff(31586,plain,
% 295.61/188.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s24) | (~node11(c_e_h_1, c_n, s23, s24)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s23)))),
% 295.61/188.15 inference(quant_inst,[status(thm)],[])).
% 295.61/188.15 tff(31587,plain,
% 295.61/188.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s24) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s23)) | (~node11(c_e_h_1, c_n, s23, s24))),
% 295.61/188.15 inference(modus_ponens,[status(thm)],[31586, 31585])).
% 295.61/188.15 tff(31588,plain,
% 295.61/188.15 ($false),
% 295.61/188.15 inference(unit_resolution,[status(thm)],[31587, 5742, 31579, 31580, 31581])).
% 295.61/188.15 tff(31589,plain,((~node11(c_e_h_1, c_n, s23, s24)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s23)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s24)), inference(lemma,lemma(discharge,[]))).
% 295.61/188.15 tff(31590,plain,
% 295.61/188.15 (~node11(c_e_h_1, c_n, s23, s24)),
% 295.61/188.15 inference(unit_resolution,[status(thm)],[31589, 31580, 31579])).
% 295.61/188.15 tff(31591,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s23)), introduced(assumption)).
% 295.61/188.15 tff(31592,assumption,(node10(c_e_h_1, c_n, s23, s24)), introduced(assumption)).
% 295.61/188.15 tff(31593,plain,
% 295.61/188.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s24) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s23)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s23)) | (~node10(c_e_h_1, c_n, s23, s24)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s24) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s23)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s23)) | (~node10(c_e_h_1, c_n, s23, s24)))),
% 295.61/188.15 inference(rewrite,[status(thm)],[])).
% 295.61/188.15 tff(31594,plain,
% 295.61/188.15 (((~node10(c_e_h_1, c_n, s23, s24)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s23)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s23)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s24)) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s24) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s23)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s23)) | (~node10(c_e_h_1, c_n, s23, s24)))),
% 295.61/188.15 inference(rewrite,[status(thm)],[])).
% 295.61/188.15 tff(31595,plain,
% 295.61/188.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s23, s24)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s23)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s23)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s24))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s24) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s23)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s23)) | (~node10(c_e_h_1, c_n, s23, s24))))),
% 295.61/188.15 inference(monotonicity,[status(thm)],[31594])).
% 295.61/188.15 tff(31596,plain,
% 295.61/188.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s23, s24)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s23)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s23)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s24))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s24) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s23)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s23)) | (~node10(c_e_h_1, c_n, s23, s24)))),
% 295.61/188.15 inference(transitivity,[status(thm)],[31595, 31593])).
% 295.61/188.15 tff(31597,plain,
% 295.61/188.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s23, s24)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s23)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s23)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s24))),
% 295.61/188.15 inference(quant_inst,[status(thm)],[])).
% 295.61/188.15 tff(31598,plain,
% 295.61/188.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s24) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s23)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s23)) | (~node10(c_e_h_1, c_n, s23, s24))),
% 295.61/188.15 inference(modus_ponens,[status(thm)],[31597, 31596])).
% 295.61/188.15 tff(31599,plain,
% 295.61/188.15 ($false),
% 295.61/188.15 inference(unit_resolution,[status(thm)],[31598, 5718, 31580, 31591, 31573, 31592])).
% 295.61/188.15 tff(31600,plain,((~node10(c_e_h_1, c_n, s23, s24)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s24) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s23)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s23))), inference(lemma,lemma(discharge,[]))).
% 295.61/188.15 tff(31601,plain,
% 295.61/188.15 (~node10(c_e_h_1, c_n, s23, s24)),
% 295.61/188.15 inference(unit_resolution,[status(thm)],[31600, 31580, 31573, 31591])).
% 295.61/188.15 tff(31602,plain,
% 295.61/188.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s23, s24)) | node10(c_e_h_1, c_n, s23, s24) | node11(c_e_h_1, c_n, s23, s24))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s23, s24)) | node10(c_e_h_1, c_n, s23, s24) | node11(c_e_h_1, c_n, s23, s24))),
% 295.61/188.15 inference(rewrite,[status(thm)],[])).
% 295.61/188.15 tff(31603,plain,
% 295.61/188.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s23, s24)) | node10(c_e_h_1, c_n, s23, s24) | node11(c_e_h_1, c_n, s23, s24))),
% 295.61/188.15 inference(quant_inst,[status(thm)],[])).
% 295.61/188.15 tff(31604,plain,
% 295.61/188.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s23, s24)) | node10(c_e_h_1, c_n, s23, s24) | node11(c_e_h_1, c_n, s23, s24)),
% 295.61/188.15 inference(modus_ponens,[status(thm)],[31603, 31602])).
% 295.61/188.15 tff(31605,plain,
% 295.61/188.15 (node10(c_e_h_1, c_n, s23, s24) | node11(c_e_h_1, c_n, s23, s24)),
% 295.61/188.15 inference(unit_resolution,[status(thm)],[31604, 5002, 31066])).
% 295.61/188.15 tff(31606,plain,
% 295.61/188.15 ($false),
% 295.61/188.15 inference(unit_resolution,[status(thm)],[31605, 31601, 31590])).
% 295.61/188.15 tff(31607,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s24) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s23)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s23)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s23))), inference(lemma,lemma(discharge,[]))).
% 295.61/188.15 tff(31608,plain,
% 295.61/188.15 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s24)),
% 295.61/188.15 inference(unit_resolution,[status(thm)],[31607, 31578, 31573, 31572])).
% 295.61/188.15 tff(31609,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s24)), introduced(assumption)).
% 295.61/188.15 tff(31610,assumption,(node10(c_e_h_1, c_n, s24, s25)), introduced(assumption)).
% 295.61/188.15 tff(31611,plain,
% 295.61/188.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s25) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s24)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s24)) | (~node10(c_e_h_1, c_n, s24, s25)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s25) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s24)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s24)) | (~node10(c_e_h_1, c_n, s24, s25)))),
% 295.61/188.15 inference(rewrite,[status(thm)],[])).
% 295.61/188.15 tff(31612,plain,
% 295.61/188.15 (((~node10(c_e_h_1, c_n, s24, s25)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s24)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s24)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s25)) <=> (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s25) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s24)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s24)) | (~node10(c_e_h_1, c_n, s24, s25)))),
% 295.61/188.15 inference(rewrite,[status(thm)],[])).
% 295.61/188.15 tff(31613,plain,
% 295.61/188.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s24, s25)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s24)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s24)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s25))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s25) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s24)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s24)) | (~node10(c_e_h_1, c_n, s24, s25))))),
% 295.61/188.15 inference(monotonicity,[status(thm)],[31612])).
% 295.61/188.15 tff(31614,plain,
% 295.61/188.15 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s24, s25)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s24)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s24)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s25))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s25) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s24)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s24)) | (~node10(c_e_h_1, c_n, s24, s25)))),
% 295.61/188.15 inference(transitivity,[status(thm)],[31613, 31611])).
% 295.61/188.15 tff(31615,plain,
% 295.61/188.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_1, c_n, s24, s25)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s24)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s24)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s25))),
% 295.61/188.15 inference(quant_inst,[status(thm)],[])).
% 295.61/188.15 tff(31616,plain,
% 295.61/188.15 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s25) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s24)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s24)) | (~node10(c_e_h_1, c_n, s24, s25))),
% 295.61/188.15 inference(modus_ponens,[status(thm)],[31615, 31614])).
% 295.61/188.15 tff(31617,plain,
% 295.61/188.15 ($false),
% 295.61/188.15 inference(unit_resolution,[status(thm)],[31616, 5718, 31525, 31609, 31524, 31610])).
% 295.61/188.15 tff(31618,plain,((~node10(c_e_h_1, c_n, s24, s25)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s25) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s24)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s24))), inference(lemma,lemma(discharge,[]))).
% 295.61/188.16 tff(31619,plain,
% 295.61/188.16 (~node10(c_e_h_1, c_n, s24, s25)),
% 295.61/188.16 inference(unit_resolution,[status(thm)],[31618, 31525, 31609, 31524])).
% 295.61/188.16 tff(31620,plain,
% 295.61/188.16 (succ(s24, s25) <=> succ(s24, s25)),
% 295.61/188.16 inference(rewrite,[status(thm)],[])).
% 295.61/188.16 tff(31621,axiom,(succ(s24, s25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound25')).
% 295.61/188.16 tff(31622,plain,
% 295.61/188.16 (succ(s24, s25)),
% 295.61/188.16 inference(modus_ponens,[status(thm)],[31621, 31620])).
% 295.61/188.16 tff(31623,plain,
% 295.61/188.16 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s24, s25)) | trans(s24, s25))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s24, s25)) | trans(s24, s25))),
% 295.61/188.16 inference(rewrite,[status(thm)],[])).
% 295.61/188.16 tff(31624,plain,
% 295.61/188.16 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s24, s25)) | trans(s24, s25))),
% 295.61/188.16 inference(quant_inst,[status(thm)],[])).
% 295.61/188.16 tff(31625,plain,
% 295.61/188.16 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s24, s25)) | trans(s24, s25)),
% 295.61/188.16 inference(modus_ponens,[status(thm)],[31624, 31623])).
% 295.61/188.16 tff(31626,plain,
% 295.61/188.16 (trans(s24, s25)),
% 295.61/188.16 inference(unit_resolution,[status(thm)],[31625, 31622, 65])).
% 295.61/188.16 tff(31627,plain,
% 295.61/188.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s24, s25)) | node10(c_e_h_1, c_n, s24, s25) | node11(c_e_h_1, c_n, s24, s25))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s24, s25)) | node10(c_e_h_1, c_n, s24, s25) | node11(c_e_h_1, c_n, s24, s25))),
% 295.61/188.16 inference(rewrite,[status(thm)],[])).
% 295.61/188.16 tff(31628,plain,
% 295.61/188.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s24, s25)) | node10(c_e_h_1, c_n, s24, s25) | node11(c_e_h_1, c_n, s24, s25))),
% 295.61/188.16 inference(quant_inst,[status(thm)],[])).
% 295.61/188.16 tff(31629,plain,
% 295.61/188.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s24, s25)) | node10(c_e_h_1, c_n, s24, s25) | node11(c_e_h_1, c_n, s24, s25)),
% 295.61/188.16 inference(modus_ponens,[status(thm)],[31628, 31627])).
% 295.61/188.16 tff(31630,plain,
% 295.61/188.16 (node10(c_e_h_1, c_n, s24, s25) | node11(c_e_h_1, c_n, s24, s25)),
% 295.61/188.16 inference(unit_resolution,[status(thm)],[31629, 5002, 31626])).
% 295.61/188.16 tff(31631,plain,
% 295.61/188.16 (node11(c_e_h_1, c_n, s24, s25)),
% 295.61/188.16 inference(unit_resolution,[status(thm)],[31630, 31619])).
% 295.61/188.16 tff(31632,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s24)), introduced(assumption)).
% 295.61/188.16 tff(31633,plain,
% 295.61/188.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s24)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s25) | (~node11(c_e_h_1, c_n, s24, s25)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s24)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s25) | (~node11(c_e_h_1, c_n, s24, s25)))),
% 295.61/188.16 inference(rewrite,[status(thm)],[])).
% 295.61/188.16 tff(31634,plain,
% 295.61/188.16 ((m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s25) | (~node11(c_e_h_1, c_n, s24, s25)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s24))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s24)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s25) | (~node11(c_e_h_1, c_n, s24, s25)))),
% 295.61/188.16 inference(rewrite,[status(thm)],[])).
% 295.61/188.16 tff(31635,plain,
% 295.61/188.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s25) | (~node11(c_e_h_1, c_n, s24, s25)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s24)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s24)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s25) | (~node11(c_e_h_1, c_n, s24, s25))))),
% 295.61/188.16 inference(monotonicity,[status(thm)],[31634])).
% 295.61/188.16 tff(31636,plain,
% 295.61/188.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s25) | (~node11(c_e_h_1, c_n, s24, s25)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s24)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s24)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s25) | (~node11(c_e_h_1, c_n, s24, s25)))),
% 295.61/188.16 inference(transitivity,[status(thm)],[31635, 31633])).
% 295.61/188.16 tff(31637,plain,
% 295.61/188.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s25) | (~node11(c_e_h_1, c_n, s24, s25)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s24)))),
% 295.61/188.16 inference(quant_inst,[status(thm)],[])).
% 295.61/188.16 tff(31638,plain,
% 295.61/188.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s24)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s25) | (~node11(c_e_h_1, c_n, s24, s25))),
% 295.61/188.16 inference(modus_ponens,[status(thm)],[31637, 31636])).
% 295.61/188.16 tff(31639,plain,
% 295.61/188.16 ($false),
% 295.61/188.16 inference(unit_resolution,[status(thm)],[31638, 5742, 31525, 31632, 31631])).
% 295.61/188.16 tff(31640,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s25) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s24)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s24)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s24))), inference(lemma,lemma(discharge,[]))).
% 295.61/188.16 tff(31641,plain,
% 295.61/188.16 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s24)),
% 295.61/188.16 inference(unit_resolution,[status(thm)],[31640, 31608, 31525, 31524])).
% 295.61/188.16 tff(31642,plain,
% 295.61/188.16 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s24) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s24))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s24) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s24))),
% 295.61/188.16 inference(rewrite,[status(thm)],[])).
% 295.61/188.16 tff(31643,plain,
% 295.61/188.16 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s24) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s24))),
% 295.61/188.16 inference(quant_inst,[status(thm)],[])).
% 295.61/188.16 tff(31644,plain,
% 295.61/188.16 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s24) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s24)),
% 295.61/188.16 inference(modus_ponens,[status(thm)],[31643, 31642])).
% 295.61/188.16 tff(31645,plain,
% 295.61/188.16 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s24) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s24)),
% 295.61/188.16 inference(unit_resolution,[status(thm)],[31644, 7868])).
% 295.61/188.16 tff(31646,plain,
% 295.61/188.16 (m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s24)),
% 295.61/188.16 inference(unit_resolution,[status(thm)],[31645, 31641])).
% 295.61/188.16 tff(31647,assumption,(~node9(c_e_h_1, c_m, s23)), introduced(assumption)).
% 295.61/188.16 tff(31648,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s23)), introduced(assumption)).
% 295.61/188.16 tff(31649,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s24)), introduced(assumption)).
% 295.61/188.16 tff(31650,assumption,(node11(c_e_h_1, c_m, s23, s24)), introduced(assumption)).
% 295.61/188.16 tff(31651,plain,
% 295.61/188.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s24)) | (~node11(c_e_h_1, c_m, s23, s24)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s23))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s24)) | (~node11(c_e_h_1, c_m, s23, s24)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s23))),
% 295.61/188.16 inference(rewrite,[status(thm)],[])).
% 295.61/188.16 tff(31652,plain,
% 295.61/188.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s24)) | (~node11(c_e_h_1, c_m, s23, s24)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s23))),
% 295.61/188.16 inference(quant_inst,[status(thm)],[])).
% 295.61/188.16 tff(31653,plain,
% 295.61/188.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s24)) | (~node11(c_e_h_1, c_m, s23, s24)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s23)),
% 295.61/188.16 inference(modus_ponens,[status(thm)],[31652, 31651])).
% 295.61/188.16 tff(31654,plain,
% 295.61/188.16 ($false),
% 295.61/188.16 inference(unit_resolution,[status(thm)],[31653, 5017, 31648, 31649, 31650])).
% 295.61/188.16 tff(31655,plain,((~node11(c_e_h_1, c_m, s23, s24)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s23) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s24))), inference(lemma,lemma(discharge,[]))).
% 295.61/188.16 tff(31656,plain,
% 295.61/188.16 (~node11(c_e_h_1, c_m, s23, s24)),
% 295.61/188.16 inference(unit_resolution,[status(thm)],[31655, 31649, 31648])).
% 295.61/188.16 tff(31657,plain,
% 295.61/188.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s23, s24)) | node10(c_e_h_1, c_m, s23, s24) | node11(c_e_h_1, c_m, s23, s24))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s23, s24)) | node10(c_e_h_1, c_m, s23, s24) | node11(c_e_h_1, c_m, s23, s24))),
% 295.61/188.16 inference(rewrite,[status(thm)],[])).
% 295.61/188.16 tff(31658,plain,
% 295.61/188.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s23, s24)) | node10(c_e_h_1, c_m, s23, s24) | node11(c_e_h_1, c_m, s23, s24))),
% 295.61/188.16 inference(quant_inst,[status(thm)],[])).
% 295.61/188.16 tff(31659,plain,
% 295.61/188.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s23, s24)) | node10(c_e_h_1, c_m, s23, s24) | node11(c_e_h_1, c_m, s23, s24)),
% 295.61/188.16 inference(modus_ponens,[status(thm)],[31658, 31657])).
% 295.61/188.16 tff(31660,plain,
% 295.61/188.16 (node10(c_e_h_1, c_m, s23, s24) | node11(c_e_h_1, c_m, s23, s24)),
% 295.61/188.16 inference(unit_resolution,[status(thm)],[31659, 5002, 31066])).
% 295.61/188.16 tff(31661,plain,
% 295.61/188.16 (node10(c_e_h_1, c_m, s23, s24)),
% 295.61/188.16 inference(unit_resolution,[status(thm)],[31660, 31656])).
% 295.61/188.16 tff(31662,plain,
% 295.61/188.16 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s23) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s24)) | (~node10(c_e_h_1, c_m, s23, s24)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_1, c_m, s23) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s24)) | (~node10(c_e_h_1, c_m, s23, s24)))),
% 295.61/188.16 inference(rewrite,[status(thm)],[])).
% 295.61/188.16 tff(31663,plain,
% 295.61/188.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s23) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s24)) | (~node10(c_e_h_1, c_m, s23, s24)))),
% 295.61/188.16 inference(quant_inst,[status(thm)],[])).
% 295.61/188.16 tff(31664,plain,
% 295.61/188.16 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | node9(c_e_h_1, c_m, s23) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s24)) | (~node10(c_e_h_1, c_m, s23, s24))),
% 295.61/188.16 inference(modus_ponens,[status(thm)],[31663, 31662])).
% 295.61/188.16 tff(31665,plain,
% 295.61/188.16 ($false),
% 295.61/188.16 inference(unit_resolution,[status(thm)],[31664, 4986, 31649, 31661, 31647])).
% 295.61/188.16 tff(31666,plain,((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s24)) | node9(c_e_h_1, c_m, s23) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s23)), inference(lemma,lemma(discharge,[]))).
% 295.61/188.16 tff(31667,plain,
% 295.61/188.16 (node9(c_e_h_1, c_m, s23)),
% 295.61/188.16 inference(unit_resolution,[status(thm)],[31666, 31646, 31523])).
% 295.61/188.16 tff(31668,plain,
% 295.61/188.16 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s23)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s23)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s23)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s23)))),
% 295.61/188.17 inference(rewrite,[status(thm)],[])).
% 295.61/188.17 tff(31669,plain,
% 295.61/188.17 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s23)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s23)))),
% 295.61/188.17 inference(quant_inst,[status(thm)],[])).
% 295.61/188.17 tff(31670,plain,
% 295.61/188.17 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s23)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s23))),
% 295.61/188.17 inference(modus_ponens,[status(thm)],[31669, 31668])).
% 295.61/188.17 tff(31671,plain,
% 295.61/188.17 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s23)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[31670, 4958, 31572])).
% 295.61/188.17 tff(31672,plain,
% 295.61/188.17 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s23)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s23))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s23)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s23))),
% 295.61/188.17 inference(rewrite,[status(thm)],[])).
% 295.61/188.17 tff(31673,plain,
% 295.61/188.17 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s23)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s23))),
% 295.61/188.17 inference(quant_inst,[status(thm)],[])).
% 295.61/188.17 tff(31674,plain,
% 295.61/188.17 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s23)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s23)),
% 295.61/188.17 inference(modus_ponens,[status(thm)],[31673, 31672])).
% 295.61/188.17 tff(31675,plain,
% 295.61/188.17 ($false),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[31674, 4972, 31671, 31667])).
% 295.61/188.17 tff(31676,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s20) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s25) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s24)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s23)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s21)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s21) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s20)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s22))), inference(lemma,lemma(discharge,[]))).
% 295.61/188.17 tff(31677,plain,
% 295.61/188.17 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s25)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[31676, 31388, 31382, 31347, 31342, 31337, 31299, 31203, 31198])).
% 295.61/188.17 tff(31678,plain,
% 295.61/188.17 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_i, X)) | m_c_h_element_v_in2(I0, c_f, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s12)) | m_c_h_element_v_in2(c_e_h_3, c_f, s12))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_i, X)) | m_c_h_element_v_in2(I0, c_f, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s12)) | m_c_h_element_v_in2(c_e_h_3, c_f, s12))),
% 295.61/188.17 inference(rewrite,[status(thm)],[])).
% 295.61/188.17 tff(31679,plain,
% 295.61/188.17 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_i, X)) | m_c_h_element_v_in2(I0, c_f, X))) | ((~m_and_h_gate_v_out(c_e_h_3, c_i, s12)) | m_c_h_element_v_in2(c_e_h_3, c_f, s12))),
% 295.61/188.17 inference(quant_inst,[status(thm)],[])).
% 295.61/188.17 tff(31680,plain,
% 295.61/188.17 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_i, X)) | m_c_h_element_v_in2(I0, c_f, X))) | (~m_and_h_gate_v_out(c_e_h_3, c_i, s12)) | m_c_h_element_v_in2(c_e_h_3, c_f, s12)),
% 295.61/188.17 inference(modus_ponens,[status(thm)],[31679, 31678])).
% 295.61/188.17 tff(31681,plain,
% 295.61/188.17 ($false),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[31680, 28447, 11905, 11439])).
% 295.61/188.17 tff(31682,plain,((~m_and_h_gate_v_out(c_e_h_3, c_i, s12)) | m_c_h_element_v_in2(c_e_h_3, c_f, s12)), inference(lemma,lemma(discharge,[]))).
% 295.61/188.17 tff(31683,plain,
% 295.61/188.17 (~m_and_h_gate_v_out(c_e_h_3, c_i, s12)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[31682, 11905])).
% 295.61/188.17 tff(31684,plain,
% 295.61/188.17 (~m_and_h_gate_v_out(c_e_h_3, c_i, s13)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[28370, 31683, 28349])).
% 295.61/188.17 tff(31685,plain,
% 295.61/188.17 (~m_c_h_element_v_in2(c_e_h_3, c_f, s13)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[28435, 31684])).
% 295.61/188.17 tff(31686,plain,
% 295.61/188.17 (~m_and_h_gate_h_init_v_in1(c_e_h_3, c_m, s15)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[28634, 31685, 13336, 13299, 11841, 13482, 11905])).
% 295.61/188.17 tff(31687,plain,
% 295.61/188.17 (~m_c_h_element_v_out(c_e_h_3, c_f, s15)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[28476, 31685, 28381, 12849])).
% 295.61/188.17 tff(31688,plain,
% 295.61/188.17 ($false),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[13002, 31687, 31686])).
% 295.61/188.17 tff(31689,plain,(m_c_h_element_v_in2(c_e_h_3, c_f, s12) | node20(c_e_h_3, c_i, s13) | m_c_h_element_v_out(c_e_h_3, c_f, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s12) | m_c_h_element_v_out(c_e_h_3, c_f, s12) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s16) | node20(c_e_h_3, c_i, s12)), inference(lemma,lemma(discharge,[]))).
% 295.61/188.17 tff(31690,plain,
% 295.61/188.17 ($false),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[31689, 12848, 11905, 28381, 13336, 13299, 28349, 11841, 13482])).
% 295.61/188.17 tff(31691,plain,(m_c_h_element_v_in2(c_e_h_3, c_f, s12) | node20(c_e_h_3, c_i, s13) | (~m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s12)) | m_and_h_gate_h_init_v_out(c_e_h_3, c_n, s12) | node20(c_e_h_3, c_i, s12) | m_c_h_element_v_out(c_e_h_3, c_f, s12) | m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s16)), inference(lemma,lemma(discharge,[]))).
% 295.61/188.17 tff(31692,plain,
% 295.61/188.17 (m_and_h_gate_h_init_v_out(c_e_h_3, c_m, s16)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[31691, 28402, 24275, 21947, 26882, 28399, 28327])).
% 295.61/188.17 tff(31693,plain,
% 295.61/188.17 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s19)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[31281, 30459])).
% 295.61/188.17 tff(31694,plain,
% 295.61/188.17 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s20)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[31396, 31337])).
% 295.61/188.17 tff(31695,plain,
% 295.61/188.17 (~m_and_h_gate_v_out(c_e_h_1, c_i, s18)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[26759, 26111, 30689])).
% 295.61/188.17 tff(31696,plain,
% 295.61/188.17 (~m_cell_v_ack(c_e_h_1, s16)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[28850, 28788])).
% 295.61/188.17 tff(31697,plain,
% 295.61/188.17 (~m_or_h_gate_v_in2(c_e_h_1, c_j, s16)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[28854, 1085, 31696])).
% 295.61/188.17 tff(31698,plain,
% 295.61/188.17 (~m_or_h_gate_v_out(c_e_h_1, c_j, s17)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[29007, 31697, 28974])).
% 295.61/188.17 tff(31699,plain,
% 295.61/188.17 (~m_c_h_element_v_in2(c_e_h_1, c_h, s17)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[29761, 31698])).
% 295.61/188.17 tff(31700,plain,
% 295.61/188.17 (~m_c_h_element_v_out(c_e_h_1, c_h, s18)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[29836, 31699, 29764])).
% 295.61/188.17 tff(31701,plain,
% 295.61/188.17 (~m_and_h_gate_v_out(c_e_h_1, c_i, s19)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[30692, 31699, 29764, 26111])).
% 295.61/188.17 tff(31702,plain,
% 295.61/188.17 (~m_c_h_element_v_in2(c_e_h_1, c_e, s19)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[30699, 31701])).
% 295.61/188.17 tff(31703,plain,
% 295.61/188.17 (~m_c_h_element_v_out(c_e_h_1, c_e, s20)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[30777, 31702, 30701])).
% 295.61/188.17 tff(31704,plain,
% 295.61/188.17 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s19)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[31294, 30701])).
% 295.61/188.17 tff(31705,plain,
% 295.61/188.17 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[31276, 31704, 31260, 31249])).
% 295.61/188.17 tff(31706,plain,
% 295.61/188.17 (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s20)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[31425, 31705, 31398, 31409])).
% 295.61/188.17 tff(31707,plain,
% 295.61/188.17 (m_c_h_element_v_out(c_e_h_1, c_e, s20)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[31202, 31706])).
% 295.61/188.17 tff(31708,plain,
% 295.61/188.17 (~node18(c_e_h_1, c_e, s19, s20)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[30711, 31707, 30701])).
% 295.61/188.17 tff(31709,plain,
% 295.61/188.17 (m_c_h_element_v_in1(c_e_h_1, c_e, s19)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[30765, 31707, 30701])).
% 295.61/188.17 tff(31710,plain,
% 295.61/188.17 (~node17(c_e_h_1, c_e, s19)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[30774, 31709])).
% 295.61/188.17 tff(31711,plain,
% 295.61/188.17 ($false),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[30763, 31710, 31708])).
% 295.61/188.17 tff(31712,plain,(m_c_h_element_v_out(c_e_h_1, c_e, s19) | m_c_h_element_v_in2(c_e_h_1, c_e, s19) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s21) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s20)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s19)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s19))), inference(lemma,lemma(discharge,[]))).
% 295.61/188.17 tff(31713,plain,
% 295.61/188.17 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s21)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[31712, 31702, 30701, 31409, 31249, 31260])).
% 295.61/188.17 tff(31714,plain,
% 295.61/188.17 (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s21)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[31522, 31713, 31427, 31389])).
% 295.61/188.17 tff(31715,plain,
% 295.61/188.17 (m_c_h_element_v_out(c_e_h_1, c_e, s21)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[31197, 31714])).
% 295.61/188.17 tff(31716,plain,
% 295.61/188.17 (m_c_h_element_v_in2(c_e_h_1, c_e, s20)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[30862, 31715, 31703])).
% 295.61/188.17 tff(31717,plain,
% 295.61/188.17 (m_and_h_gate_v_out(c_e_h_1, c_i, s20)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[30784, 31716])).
% 295.61/188.17 tff(31718,plain,
% 295.61/188.17 (m_c_h_element_v_in2(c_e_h_1, c_h, s18)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[30039, 31717, 31700, 31695])).
% 295.61/188.17 tff(31719,plain,
% 295.61/188.17 (~m_and_h_gate_v_out(c_e_h_3, c_q, s17)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[28801, 28788, 28776])).
% 295.61/188.17 tff(31720,plain,
% 295.61/188.17 (~m_cell_v_ack(c_e_h_1, s17)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[29016, 31719])).
% 295.61/188.17 tff(31721,plain,
% 295.61/188.17 (~m_or_h_gate_v_in2(c_e_h_1, c_j, s17)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[29020, 1085, 31720])).
% 295.61/188.17 tff(31722,plain,
% 295.61/188.17 (~m_or_h_gate_v_out(c_e_h_1, c_j, s18)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[29580, 31698, 31721])).
% 295.61/188.17 tff(31723,plain,
% 295.61/188.17 ($false),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[29840, 1174, 31722, 31718])).
% 295.61/188.17 tff(31724,plain,(m_and_h_gate_v_out(c_e_h_3, c_q, s16) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s23)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s21) | m_c_h_element_v_out(c_e_h_1, c_e, s19) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s20)) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s19)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s19)) | m_c_h_element_v_out(c_e_h_1, c_h, s17) | m_and_h_gate_v_out(c_e_h_1, c_i, s17) | m_or_h_gate_v_out(c_e_h_1, c_j, s16) | node20(c_e_h_3, c_q, s16)), inference(lemma,lemma(discharge,[]))).
% 295.61/188.17 tff(31725,plain,
% 295.61/188.17 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s23)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[31724, 28775, 31382, 26862, 31694, 31693, 31303, 26731, 26740, 26867, 28767])).
% 295.61/188.17 tff(31726,plain,
% 295.61/188.17 (~m_c_h_element_v_out(c_e_h_1, c_e, s20)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[30777, 30701, 30767])).
% 295.61/188.17 tff(31727,plain,
% 295.61/188.17 (~m_c_h_element_v_out(c_e_h_1, c_e, s21)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[30862, 31726, 30807])).
% 295.61/188.17 tff(31728,plain,
% 295.61/188.17 (~m_c_h_element_v_out(c_e_h_1, c_e, s22)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[30948, 31727, 30912])).
% 295.61/188.17 tff(31729,plain,
% 295.61/188.17 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s20)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[31202, 31726])).
% 295.61/188.17 tff(31730,plain,
% 295.61/188.17 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[30168, 31206])).
% 295.61/188.17 tff(31731,plain,
% 295.61/188.17 (m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s19)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s17)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s18))),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[31289, 29683])).
% 295.61/188.17 tff(31732,plain,
% 295.61/188.17 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[31731, 31704, 31215, 30394, 31730, 30406])).
% 295.61/188.17 tff(31733,plain,
% 295.61/188.17 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s18)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[30424, 30406, 30394])).
% 295.61/188.17 tff(31734,plain,
% 295.61/188.17 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s18)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[30429, 4958, 31733])).
% 295.61/188.17 tff(31735,plain,
% 295.61/188.17 (~node9(c_e_h_1, c_m, s18)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[30433, 4972, 31734])).
% 295.61/188.17 tff(31736,plain,
% 295.61/188.17 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s19)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[30457, 31735, 31730])).
% 295.61/188.17 tff(31737,plain,
% 295.61/188.17 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s19)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[31301, 30406, 30394, 31215])).
% 295.61/188.17 tff(31738,plain,
% 295.61/188.17 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s19)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[31306, 4958, 31737])).
% 295.61/188.17 tff(31739,plain,
% 295.61/188.17 (~node9(c_e_h_1, c_m, s19)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[31310, 4972, 31738])).
% 295.61/188.17 tff(31740,plain,
% 295.61/188.17 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s20)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[31336, 31739, 31736])).
% 295.61/188.17 tff(31741,plain,
% 295.61/188.17 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s21)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[31197, 31727])).
% 295.61/188.17 tff(31742,plain,
% 295.61/188.17 (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s22)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[31571, 31741, 31740, 31527, 31732, 31729])).
% 295.61/188.17 tff(31743,plain,
% 295.61/188.17 ($false),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[31346, 31742, 31728])).
% 295.61/188.17 tff(31744,plain,(m_c_h_element_v_out(c_e_h_1, c_e, s19) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s23) | m_c_h_element_v_in2(c_e_h_1, c_e, s21) | m_c_h_element_v_in2(c_e_h_1, c_e, s20) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s18)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s17)) | m_c_h_element_v_in2(c_e_h_1, c_e, s19)), inference(lemma,lemma(discharge,[]))).
% 295.61/188.17 tff(31745,plain,
% 295.61/188.17 (m_c_h_element_v_out(c_e_h_1, c_e, s19) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s23) | m_c_h_element_v_in2(c_e_h_1, c_e, s21) | m_c_h_element_v_in2(c_e_h_1, c_e, s20) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s18)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s17)) | m_c_h_element_v_in2(c_e_h_1, c_e, s19)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[31744, 30136])).
% 295.61/188.17 tff(31746,plain,
% 295.61/188.17 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s23)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[31745, 30887, 26862, 30700, 31300, 30388, 30785])).
% 295.61/188.17 tff(31747,plain,
% 295.61/188.17 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s23)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[31670, 4958, 31746])).
% 295.61/188.17 tff(31748,plain,
% 295.61/188.17 (~node9(c_e_h_1, c_m, s23)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[31674, 4972, 31747])).
% 295.61/188.17 tff(31749,plain,
% 295.61/188.17 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s24)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[31666, 31748, 31725])).
% 295.61/188.17 tff(31750,plain,
% 295.61/188.17 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s23)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[31577, 31725])).
% 295.61/188.17 tff(31751,plain,
% 295.61/188.17 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s24)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[31607, 31342, 31750, 31746])).
% 295.61/188.17 tff(31752,plain,
% 295.61/188.17 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s24)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s24)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s24)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s24)))),
% 295.61/188.17 inference(rewrite,[status(thm)],[])).
% 295.61/188.17 tff(31753,plain,
% 295.61/188.17 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s24)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s24)))),
% 295.61/188.17 inference(quant_inst,[status(thm)],[])).
% 295.61/188.17 tff(31754,plain,
% 295.61/188.17 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s24)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s24))),
% 295.61/188.17 inference(modus_ponens,[status(thm)],[31753, 31752])).
% 295.61/188.17 tff(31755,plain,
% 295.61/188.17 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s24)),
% 295.61/188.17 inference(unit_resolution,[status(thm)],[31754, 4958, 31751])).
% 295.61/188.17 tff(31756,plain,
% 295.61/188.17 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s24)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s24))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s24)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s24))),
% 295.61/188.18 inference(rewrite,[status(thm)],[])).
% 295.61/188.18 tff(31757,plain,
% 295.61/188.18 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s24)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s24))),
% 295.61/188.18 inference(quant_inst,[status(thm)],[])).
% 295.61/188.18 tff(31758,plain,
% 295.61/188.18 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s24)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s24)),
% 295.61/188.18 inference(modus_ponens,[status(thm)],[31757, 31756])).
% 295.61/188.18 tff(31759,plain,
% 295.61/188.18 (~node9(c_e_h_1, c_m, s24)),
% 295.61/188.18 inference(unit_resolution,[status(thm)],[31758, 4972, 31755])).
% 295.61/188.18 tff(31760,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s24)), introduced(assumption)).
% 295.61/188.18 tff(31761,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s25)), introduced(assumption)).
% 295.61/188.18 tff(31762,assumption,(node11(c_e_h_1, c_m, s24, s25)), introduced(assumption)).
% 295.61/188.18 tff(31763,plain,
% 295.61/188.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s25)) | (~node11(c_e_h_1, c_m, s24, s25)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s24))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s25)) | (~node11(c_e_h_1, c_m, s24, s25)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s24))),
% 295.61/188.18 inference(rewrite,[status(thm)],[])).
% 295.61/188.18 tff(31764,plain,
% 295.61/188.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s25)) | (~node11(c_e_h_1, c_m, s24, s25)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s24))),
% 295.61/188.18 inference(quant_inst,[status(thm)],[])).
% 295.61/188.18 tff(31765,plain,
% 295.61/188.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s25)) | (~node11(c_e_h_1, c_m, s24, s25)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s24)),
% 295.61/188.18 inference(modus_ponens,[status(thm)],[31764, 31763])).
% 295.61/188.18 tff(31766,plain,
% 295.61/188.18 ($false),
% 295.61/188.18 inference(unit_resolution,[status(thm)],[31765, 5017, 31761, 31760, 31762])).
% 295.61/188.18 tff(31767,plain,((~node11(c_e_h_1, c_m, s24, s25)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s25)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s24)), inference(lemma,lemma(discharge,[]))).
% 295.61/188.18 tff(31768,plain,
% 295.61/188.18 (~node11(c_e_h_1, c_m, s24, s25)),
% 295.61/188.18 inference(unit_resolution,[status(thm)],[31767, 31761, 31760])).
% 295.61/188.18 tff(31769,assumption,(~node9(c_e_h_1, c_m, s24)), introduced(assumption)).
% 295.61/188.18 tff(31770,assumption,(node10(c_e_h_1, c_m, s24, s25)), introduced(assumption)).
% 295.61/188.18 tff(31771,plain,
% 295.61/188.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s25)) | node9(c_e_h_1, c_m, s24) | (~node10(c_e_h_1, c_m, s24, s25)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s25)) | node9(c_e_h_1, c_m, s24) | (~node10(c_e_h_1, c_m, s24, s25)))),
% 295.61/188.18 inference(rewrite,[status(thm)],[])).
% 295.61/188.18 tff(31772,plain,
% 295.61/188.18 ((node9(c_e_h_1, c_m, s24) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s25)) | (~node10(c_e_h_1, c_m, s24, s25))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s25)) | node9(c_e_h_1, c_m, s24) | (~node10(c_e_h_1, c_m, s24, s25)))),
% 295.61/188.18 inference(rewrite,[status(thm)],[])).
% 295.61/188.18 tff(31773,plain,
% 295.61/188.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s24) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s25)) | (~node10(c_e_h_1, c_m, s24, s25)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s25)) | node9(c_e_h_1, c_m, s24) | (~node10(c_e_h_1, c_m, s24, s25))))),
% 295.61/188.18 inference(monotonicity,[status(thm)],[31772])).
% 295.61/188.18 tff(31774,plain,
% 295.61/188.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s24) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s25)) | (~node10(c_e_h_1, c_m, s24, s25)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s25)) | node9(c_e_h_1, c_m, s24) | (~node10(c_e_h_1, c_m, s24, s25)))),
% 295.61/188.18 inference(transitivity,[status(thm)],[31773, 31771])).
% 295.61/188.18 tff(31775,plain,
% 295.61/188.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s24) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s25)) | (~node10(c_e_h_1, c_m, s24, s25)))),
% 295.61/188.18 inference(quant_inst,[status(thm)],[])).
% 295.61/188.18 tff(31776,plain,
% 295.61/188.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s25)) | node9(c_e_h_1, c_m, s24) | (~node10(c_e_h_1, c_m, s24, s25))),
% 295.61/188.18 inference(modus_ponens,[status(thm)],[31775, 31774])).
% 295.61/188.18 tff(31777,plain,
% 295.61/188.18 ($false),
% 295.61/188.18 inference(unit_resolution,[status(thm)],[31776, 4986, 31761, 31770, 31769])).
% 295.61/188.18 tff(31778,plain,((~node10(c_e_h_1, c_m, s24, s25)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s25)) | node9(c_e_h_1, c_m, s24)), inference(lemma,lemma(discharge,[]))).
% 295.61/188.18 tff(31779,plain,
% 295.61/188.18 (~node10(c_e_h_1, c_m, s24, s25)),
% 295.61/188.18 inference(unit_resolution,[status(thm)],[31778, 31761, 31769])).
% 295.61/188.18 tff(31780,plain,
% 295.61/188.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s24, s25)) | node10(c_e_h_1, c_m, s24, s25) | node11(c_e_h_1, c_m, s24, s25))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s24, s25)) | node10(c_e_h_1, c_m, s24, s25) | node11(c_e_h_1, c_m, s24, s25))),
% 295.61/188.18 inference(rewrite,[status(thm)],[])).
% 295.61/188.18 tff(31781,plain,
% 295.61/188.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s24, s25)) | node10(c_e_h_1, c_m, s24, s25) | node11(c_e_h_1, c_m, s24, s25))),
% 295.61/188.18 inference(quant_inst,[status(thm)],[])).
% 295.61/188.18 tff(31782,plain,
% 295.61/188.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s24, s25)) | node10(c_e_h_1, c_m, s24, s25) | node11(c_e_h_1, c_m, s24, s25)),
% 295.61/188.18 inference(modus_ponens,[status(thm)],[31781, 31780])).
% 295.61/188.18 tff(31783,plain,
% 295.61/188.18 (node10(c_e_h_1, c_m, s24, s25) | node11(c_e_h_1, c_m, s24, s25)),
% 295.61/188.18 inference(unit_resolution,[status(thm)],[31782, 5002, 31626])).
% 295.61/188.18 tff(31784,plain,
% 295.61/188.18 ($false),
% 295.61/188.18 inference(unit_resolution,[status(thm)],[31783, 31779, 31768])).
% 295.61/188.18 tff(31785,plain,((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s25)) | node9(c_e_h_1, c_m, s24) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s24)), inference(lemma,lemma(discharge,[]))).
% 295.61/188.18 tff(31786,plain,
% 295.61/188.18 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s25)),
% 295.61/188.18 inference(unit_resolution,[status(thm)],[31785, 31759, 31749])).
% 295.61/188.18 tff(31787,plain,
% 295.61/188.18 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s25)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s25)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s25)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s25)))),
% 295.61/188.18 inference(rewrite,[status(thm)],[])).
% 295.61/188.18 tff(31788,plain,
% 295.61/188.18 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s25)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s25)))),
% 295.61/188.18 inference(quant_inst,[status(thm)],[])).
% 295.61/188.18 tff(31789,plain,
% 295.61/188.18 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s25)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s25))),
% 295.61/188.18 inference(modus_ponens,[status(thm)],[31788, 31787])).
% 295.61/188.18 tff(31790,plain,
% 295.61/188.18 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s25)),
% 295.61/188.18 inference(unit_resolution,[status(thm)],[31789, 4958, 31677])).
% 295.61/188.18 tff(31791,plain,
% 295.61/188.18 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s25)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s25))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s25)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s25))),
% 295.61/188.18 inference(rewrite,[status(thm)],[])).
% 295.61/188.18 tff(31792,plain,
% 295.61/188.18 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_1, c_m, s25)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s25))),
% 295.61/188.18 inference(quant_inst,[status(thm)],[])).
% 295.61/188.18 tff(31793,plain,
% 295.61/188.18 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_1, c_m, s25)) | m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s25)),
% 295.61/188.18 inference(modus_ponens,[status(thm)],[31792, 31791])).
% 295.61/188.18 tff(31794,plain,
% 295.61/188.18 (~node9(c_e_h_1, c_m, s25)),
% 295.61/188.18 inference(unit_resolution,[status(thm)],[31793, 4972, 31790])).
% 295.61/188.18 tff(31795,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s25)), introduced(assumption)).
% 295.61/188.18 tff(31796,assumption,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s26)), introduced(assumption)).
% 295.61/188.18 tff(31797,assumption,(node11(c_e_h_1, c_m, s25, s26)), introduced(assumption)).
% 295.61/188.18 tff(31798,plain,
% 295.61/188.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s26)) | (~node11(c_e_h_1, c_m, s25, s26)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s25))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s26)) | (~node11(c_e_h_1, c_m, s25, s26)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s25))),
% 295.61/188.18 inference(rewrite,[status(thm)],[])).
% 295.61/188.18 tff(31799,plain,
% 295.61/188.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s26)) | (~node11(c_e_h_1, c_m, s25, s26)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s25))),
% 295.61/188.18 inference(quant_inst,[status(thm)],[])).
% 295.61/188.18 tff(31800,plain,
% 295.61/188.18 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s26)) | (~node11(c_e_h_1, c_m, s25, s26)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s25)),
% 295.61/188.18 inference(modus_ponens,[status(thm)],[31799, 31798])).
% 295.61/188.18 tff(31801,plain,
% 295.61/188.18 ($false),
% 295.61/188.18 inference(unit_resolution,[status(thm)],[31800, 5017, 31795, 31796, 31797])).
% 295.61/188.18 tff(31802,plain,((~node11(c_e_h_1, c_m, s25, s26)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s25) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s26))), inference(lemma,lemma(discharge,[]))).
% 295.61/188.18 tff(31803,plain,
% 295.61/188.18 (~node11(c_e_h_1, c_m, s25, s26)),
% 295.61/188.18 inference(unit_resolution,[status(thm)],[31802, 31796, 31795])).
% 295.61/188.18 tff(31804,assumption,(~node9(c_e_h_1, c_m, s25)), introduced(assumption)).
% 295.61/188.18 tff(31805,assumption,(node10(c_e_h_1, c_m, s25, s26)), introduced(assumption)).
% 295.61/188.18 tff(31806,plain,
% 295.61/188.18 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s26)) | (~node10(c_e_h_1, c_m, s25, s26)) | node9(c_e_h_1, c_m, s25))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s26)) | (~node10(c_e_h_1, c_m, s25, s26)) | node9(c_e_h_1, c_m, s25))),
% 295.61/188.19 inference(rewrite,[status(thm)],[])).
% 295.61/188.19 tff(31807,plain,
% 295.61/188.19 ((node9(c_e_h_1, c_m, s25) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s26)) | (~node10(c_e_h_1, c_m, s25, s26))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s26)) | (~node10(c_e_h_1, c_m, s25, s26)) | node9(c_e_h_1, c_m, s25))),
% 295.61/188.19 inference(rewrite,[status(thm)],[])).
% 295.61/188.19 tff(31808,plain,
% 295.61/188.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s25) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s26)) | (~node10(c_e_h_1, c_m, s25, s26)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s26)) | (~node10(c_e_h_1, c_m, s25, s26)) | node9(c_e_h_1, c_m, s25)))),
% 295.61/188.19 inference(monotonicity,[status(thm)],[31807])).
% 295.61/188.19 tff(31809,plain,
% 295.61/188.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s25) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s26)) | (~node10(c_e_h_1, c_m, s25, s26)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s26)) | (~node10(c_e_h_1, c_m, s25, s26)) | node9(c_e_h_1, c_m, s25))),
% 295.61/188.19 inference(transitivity,[status(thm)],[31808, 31806])).
% 295.61/188.19 tff(31810,plain,
% 295.61/188.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (node9(c_e_h_1, c_m, s25) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s26)) | (~node10(c_e_h_1, c_m, s25, s26)))),
% 295.61/188.19 inference(quant_inst,[status(thm)],[])).
% 295.61/188.19 tff(31811,plain,
% 295.61/188.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node9(I0, I1, X) | (~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node10(I0, I1, X, Y)))) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s26)) | (~node10(c_e_h_1, c_m, s25, s26)) | node9(c_e_h_1, c_m, s25)),
% 295.61/188.19 inference(modus_ponens,[status(thm)],[31810, 31809])).
% 295.61/188.19 tff(31812,plain,
% 295.61/188.19 ($false),
% 295.61/188.19 inference(unit_resolution,[status(thm)],[31811, 4986, 31796, 31805, 31804])).
% 295.61/188.19 tff(31813,plain,((~node10(c_e_h_1, c_m, s25, s26)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s26)) | node9(c_e_h_1, c_m, s25)), inference(lemma,lemma(discharge,[]))).
% 295.61/188.19 tff(31814,plain,
% 295.61/188.19 (~node10(c_e_h_1, c_m, s25, s26)),
% 295.61/188.19 inference(unit_resolution,[status(thm)],[31813, 31796, 31804])).
% 295.61/188.19 tff(31815,plain,
% 295.61/188.19 (succ(s25, s26) <=> succ(s25, s26)),
% 295.61/188.19 inference(rewrite,[status(thm)],[])).
% 295.61/188.19 tff(31816,axiom,(succ(s25, s26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound26')).
% 295.61/188.19 tff(31817,plain,
% 295.61/188.19 (succ(s25, s26)),
% 295.61/188.19 inference(modus_ponens,[status(thm)],[31816, 31815])).
% 295.61/188.19 tff(31818,plain,
% 295.61/188.19 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s25, s26)) | trans(s25, s26))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s25, s26)) | trans(s25, s26))),
% 295.61/188.19 inference(rewrite,[status(thm)],[])).
% 295.61/188.19 tff(31819,plain,
% 295.61/188.19 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s25, s26)) | trans(s25, s26))),
% 295.61/188.19 inference(quant_inst,[status(thm)],[])).
% 295.61/188.19 tff(31820,plain,
% 295.61/188.19 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s25, s26)) | trans(s25, s26)),
% 295.61/188.19 inference(modus_ponens,[status(thm)],[31819, 31818])).
% 295.61/188.19 tff(31821,plain,
% 295.61/188.19 (trans(s25, s26)),
% 295.61/188.19 inference(unit_resolution,[status(thm)],[31820, 31817, 65])).
% 295.61/188.19 tff(31822,plain,
% 295.61/188.19 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s25, s26)) | node10(c_e_h_1, c_m, s25, s26) | node11(c_e_h_1, c_m, s25, s26))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s25, s26)) | node10(c_e_h_1, c_m, s25, s26) | node11(c_e_h_1, c_m, s25, s26))),
% 295.61/188.19 inference(rewrite,[status(thm)],[])).
% 295.61/188.19 tff(31823,plain,
% 295.61/188.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s25, s26)) | node10(c_e_h_1, c_m, s25, s26) | node11(c_e_h_1, c_m, s25, s26))),
% 295.61/188.19 inference(quant_inst,[status(thm)],[])).
% 295.61/188.19 tff(31824,plain,
% 295.61/188.19 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s25, s26)) | node10(c_e_h_1, c_m, s25, s26) | node11(c_e_h_1, c_m, s25, s26)),
% 295.61/188.19 inference(modus_ponens,[status(thm)],[31823, 31822])).
% 295.61/188.19 tff(31825,plain,
% 295.61/188.19 (node10(c_e_h_1, c_m, s25, s26) | node11(c_e_h_1, c_m, s25, s26)),
% 295.61/188.19 inference(unit_resolution,[status(thm)],[31824, 5002, 31821])).
% 295.61/188.19 tff(31826,plain,
% 295.61/188.19 ($false),
% 295.61/188.19 inference(unit_resolution,[status(thm)],[31825, 31814, 31803])).
% 295.61/188.19 tff(31827,plain,((~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s26)) | node9(c_e_h_1, c_m, s25) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s25)), inference(lemma,lemma(discharge,[]))).
% 295.61/188.19 tff(31828,plain,
% 295.61/188.19 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s26)),
% 295.61/188.19 inference(unit_resolution,[status(thm)],[31827, 31794, 31786])).
% 295.61/188.19 tff(31829,plain,
% 295.61/188.19 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18)),
% 295.61/188.19 inference(unit_resolution,[status(thm)],[30167, 31206, 30162])).
% 295.61/188.19 tff(31830,plain,
% 295.61/188.19 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s18)),
% 295.61/188.19 inference(unit_resolution,[status(thm)],[30423, 30406, 30394, 31238])).
% 295.61/188.19 tff(31831,plain,
% 295.61/188.19 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s18)),
% 295.61/188.19 inference(unit_resolution,[status(thm)],[30429, 4958, 31830])).
% 295.61/188.19 tff(31832,plain,
% 295.61/188.19 (~node9(c_e_h_1, c_m, s18)),
% 295.61/188.19 inference(unit_resolution,[status(thm)],[30433, 4972, 31831])).
% 295.61/188.19 tff(31833,plain,
% 295.61/188.19 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s19)),
% 295.61/188.19 inference(unit_resolution,[status(thm)],[30457, 31832, 31829])).
% 295.61/188.19 tff(31834,plain,
% 295.61/188.19 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s19)),
% 295.61/188.19 inference(unit_resolution,[status(thm)],[31247, 31213, 30394, 30162, 30406])).
% 295.61/188.19 tff(31835,plain,
% 295.61/188.19 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s19)),
% 295.61/188.19 inference(unit_resolution,[status(thm)],[31306, 4958, 31834])).
% 295.61/188.19 tff(31836,plain,
% 295.61/188.19 (~node9(c_e_h_1, c_m, s19)),
% 295.61/188.19 inference(unit_resolution,[status(thm)],[31310, 4972, 31835])).
% 295.61/188.19 tff(31837,plain,
% 295.61/188.19 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s20)),
% 295.61/188.19 inference(unit_resolution,[status(thm)],[31336, 31836, 31833])).
% 295.61/188.19 tff(31838,plain,
% 295.61/188.19 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s19)),
% 295.61/188.19 inference(unit_resolution,[status(thm)],[31294, 31204])).
% 295.61/188.19 tff(31839,plain,
% 295.61/188.19 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s19)),
% 295.61/188.19 inference(unit_resolution,[status(thm)],[31281, 31833])).
% 295.61/188.19 tff(31840,plain,
% 295.61/188.19 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20)),
% 295.61/188.19 inference(unit_resolution,[status(thm)],[31276, 31834, 31839, 31838])).
% 295.61/188.19 tff(31841,plain,
% 295.61/188.19 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s20)),
% 295.61/188.19 inference(unit_resolution,[status(thm)],[31350, 4958, 31840])).
% 295.61/188.19 tff(31842,plain,
% 295.61/188.19 (~node9(c_e_h_1, c_m, s20)),
% 295.61/188.19 inference(unit_resolution,[status(thm)],[31354, 4972, 31841])).
% 295.61/188.19 tff(31843,plain,
% 295.61/188.19 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s21)),
% 295.61/188.19 inference(unit_resolution,[status(thm)],[31381, 31842, 31837])).
% 295.61/188.19 tff(31844,plain,
% 295.61/188.19 (node9(c_e_h_1, c_m, s21)),
% 295.61/188.19 inference(unit_resolution,[status(thm)],[31458, 31843, 31438])).
% 295.61/188.19 tff(31845,plain,
% 295.61/188.19 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s20)),
% 295.61/188.19 inference(unit_resolution,[status(thm)],[31396, 31837])).
% 295.61/188.19 tff(31846,plain,
% 295.61/188.19 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s21)),
% 295.61/188.19 inference(unit_resolution,[status(thm)],[31712, 31845, 30767, 31204, 31834, 31839])).
% 295.61/188.19 tff(31847,plain,
% 295.61/188.19 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s21)),
% 295.61/188.19 inference(unit_resolution,[status(thm)],[31431, 4958, 31846])).
% 295.61/188.19 tff(31848,plain,
% 295.61/188.19 ($false),
% 295.61/188.19 inference(unit_resolution,[status(thm)],[31435, 4972, 31847, 31844])).
% 295.61/188.19 tff(31849,plain,(m_c_h_element_v_out(c_e_h_1, c_e, s18) | m_c_h_element_v_in2(c_e_h_1, c_e, s19) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s22)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s17)) | m_c_h_element_v_in2(c_e_h_1, c_e, s18)), inference(lemma,lemma(discharge,[]))).
% 295.61/188.19 tff(31850,plain,
% 295.61/188.19 (m_c_h_element_v_out(c_e_h_1, c_e, s18) | m_c_h_element_v_in2(c_e_h_1, c_e, s19) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s22)) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s17)) | m_c_h_element_v_in2(c_e_h_1, c_e, s18)),
% 295.61/188.19 inference(unit_resolution,[status(thm)],[31849, 29683])).
% 295.61/188.19 tff(31851,plain,
% 295.61/188.19 (m_c_h_element_v_out(c_e_h_1, c_e, s18) | m_c_h_element_v_in2(c_e_h_1, c_e, s19) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s22)) | (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s17)) | m_c_h_element_v_in2(c_e_h_1, c_e, s18)),
% 295.61/188.19 inference(unit_resolution,[status(thm)],[31850, 30136])).
% 295.61/188.19 tff(31852,plain,
% 295.61/188.19 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s22)),
% 295.61/188.19 inference(unit_resolution,[status(thm)],[31851, 30700, 26207, 26768, 30388])).
% 295.61/188.19 tff(31853,plain,
% 295.61/188.19 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s22)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s22))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s22)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s22))),
% 295.61/188.19 inference(rewrite,[status(thm)],[])).
% 295.61/188.19 tff(31854,plain,
% 295.61/188.19 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s22)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s22))),
% 295.61/188.19 inference(quant_inst,[status(thm)],[])).
% 295.61/188.19 tff(31855,plain,
% 295.61/188.19 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s22)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s22)),
% 295.61/188.19 inference(modus_ponens,[status(thm)],[31854, 31853])).
% 295.61/188.19 tff(31856,plain,
% 295.61/188.19 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s22)),
% 295.61/188.19 inference(unit_resolution,[status(thm)],[31855, 14293, 31852])).
% 295.61/188.19 tff(31857,plain,
% 295.61/188.19 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s22)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s22))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s22)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s22))),
% 295.61/188.19 inference(rewrite,[status(thm)],[])).
% 295.61/188.19 tff(31858,plain,
% 295.61/188.19 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s22)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s22))),
% 295.61/188.19 inference(quant_inst,[status(thm)],[])).
% 295.61/188.19 tff(31859,plain,
% 295.61/188.19 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s22)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s22)),
% 295.61/188.19 inference(modus_ponens,[status(thm)],[31858, 31857])).
% 295.61/188.19 tff(31860,plain,
% 295.61/188.19 (~node20(c_e_h_1, c_r, s22)),
% 295.61/188.19 inference(unit_resolution,[status(thm)],[31859, 4563, 31856])).
% 295.61/188.19 tff(31861,plain,
% 295.61/188.19 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s18)),
% 295.61/188.19 inference(unit_resolution,[status(thm)],[29987, 619, 29837])).
% 295.61/188.19 tff(31862,plain,
% 295.61/188.19 (~node20(c_e_h_1, c_i, s18)),
% 295.61/188.19 inference(unit_resolution,[status(thm)],[29991, 38, 31861])).
% 295.61/188.19 tff(31863,plain,
% 295.61/188.19 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s19)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s19))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s19)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s19))),
% 295.61/188.19 inference(rewrite,[status(thm)],[])).
% 295.61/188.19 tff(31864,plain,
% 295.61/188.19 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s19)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s19))),
% 295.61/188.19 inference(quant_inst,[status(thm)],[])).
% 295.61/188.19 tff(31865,plain,
% 295.61/188.20 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s19)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s19)),
% 295.61/188.20 inference(modus_ponens,[status(thm)],[31864, 31863])).
% 295.61/188.20 tff(31866,plain,
% 295.61/188.20 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s19)),
% 295.61/188.20 inference(unit_resolution,[status(thm)],[31865, 14293, 30459])).
% 295.61/188.20 tff(31867,plain,
% 295.61/188.20 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s19)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s19))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s19)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s19))),
% 295.61/188.20 inference(rewrite,[status(thm)],[])).
% 295.61/188.20 tff(31868,plain,
% 295.61/188.20 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s19)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s19))),
% 295.61/188.20 inference(quant_inst,[status(thm)],[])).
% 295.61/188.20 tff(31869,plain,
% 295.61/188.20 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s19)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s19)),
% 295.61/188.20 inference(modus_ponens,[status(thm)],[31868, 31867])).
% 295.61/188.20 tff(31870,plain,
% 295.61/188.20 (~node20(c_e_h_1, c_r, s19)),
% 295.61/188.20 inference(unit_resolution,[status(thm)],[31869, 4563, 31866])).
% 295.61/188.20 tff(31871,plain,
% 295.61/188.20 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s18)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s18)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18))),
% 295.61/188.20 inference(rewrite,[status(thm)],[])).
% 295.61/188.20 tff(31872,plain,
% 295.61/188.20 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s18)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18))),
% 295.61/188.20 inference(quant_inst,[status(thm)],[])).
% 295.61/188.20 tff(31873,plain,
% 295.61/188.20 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s18)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s18)),
% 295.61/188.20 inference(modus_ponens,[status(thm)],[31872, 31871])).
% 295.61/188.20 tff(31874,plain,
% 295.61/188.20 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s18)),
% 295.61/188.20 inference(unit_resolution,[status(thm)],[31873, 14293, 30169])).
% 295.61/188.20 tff(31875,plain,
% 295.61/188.20 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s18)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s18))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s18)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s18))),
% 295.61/188.20 inference(rewrite,[status(thm)],[])).
% 295.61/188.20 tff(31876,plain,
% 295.61/188.20 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s18)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s18))),
% 295.61/188.20 inference(quant_inst,[status(thm)],[])).
% 295.61/188.20 tff(31877,plain,
% 295.61/188.20 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s18)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s18)),
% 295.61/188.20 inference(modus_ponens,[status(thm)],[31876, 31875])).
% 295.61/188.20 tff(31878,plain,
% 295.61/188.20 (~node20(c_e_h_1, c_r, s18)),
% 295.61/188.20 inference(unit_resolution,[status(thm)],[31877, 4563, 31874])).
% 295.61/188.20 tff(31879,assumption,(m_and_h_gate_v_in2(c_e_h_1, c_r, s17)), introduced(assumption)).
% 295.61/188.20 tff(31880,plain,
% 295.61/188.20 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s17)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s17)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17))),
% 295.61/188.20 inference(rewrite,[status(thm)],[])).
% 295.61/188.20 tff(31881,plain,
% 295.61/188.20 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s17)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17))),
% 295.61/188.20 inference(quant_inst,[status(thm)],[])).
% 295.61/188.20 tff(31882,plain,
% 295.61/188.20 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s17)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17)),
% 295.61/188.20 inference(modus_ponens,[status(thm)],[31881, 31880])).
% 295.61/188.20 tff(31883,plain,
% 295.61/188.20 ($false),
% 295.61/188.20 inference(unit_resolution,[status(thm)],[31882, 14293, 30162, 31879])).
% 295.61/188.20 tff(31884,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s17))), inference(lemma,lemma(discharge,[]))).
% 295.61/188.20 tff(31885,plain,
% 295.61/188.20 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s17)),
% 295.61/188.20 inference(unit_resolution,[status(thm)],[31884, 29683])).
% 295.61/188.20 tff(31886,assumption,(~m_and_h_gate_v_in2(c_e_h_1, c_r, s17)), introduced(assumption)).
% 295.61/188.20 tff(31887,assumption,(node20(c_e_h_1, c_r, s17)), introduced(assumption)).
% 295.61/188.20 tff(31888,plain,
% 295.61/188.20 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s17)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s17))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s17)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s17))),
% 295.61/188.20 inference(rewrite,[status(thm)],[])).
% 295.61/188.20 tff(31889,plain,
% 295.61/188.20 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s17)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s17))),
% 295.61/188.20 inference(quant_inst,[status(thm)],[])).
% 295.61/188.20 tff(31890,plain,
% 295.61/188.20 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s17)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s17)),
% 295.61/188.20 inference(modus_ponens,[status(thm)],[31889, 31888])).
% 295.61/188.20 tff(31891,plain,
% 295.61/188.20 ($false),
% 295.61/188.20 inference(unit_resolution,[status(thm)],[31890, 4563, 31887, 31886])).
% 295.61/188.20 tff(31892,plain,(m_and_h_gate_v_in2(c_e_h_1, c_r, s17) | (~node20(c_e_h_1, c_r, s17))), inference(lemma,lemma(discharge,[]))).
% 295.61/188.20 tff(31893,plain,
% 295.61/188.20 (~node20(c_e_h_1, c_r, s17)),
% 295.61/188.20 inference(unit_resolution,[status(thm)],[31892, 31885])).
% 295.61/188.20 tff(31894,assumption,(m_and_h_gate_v_in2(c_e_h_1, c_r, s15)), introduced(assumption)).
% 295.61/188.20 tff(31895,plain,
% 295.61/188.20 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s15)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s15)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15))),
% 295.61/188.20 inference(rewrite,[status(thm)],[])).
% 295.61/188.20 tff(31896,plain,
% 295.61/188.20 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s15)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15))),
% 295.61/188.20 inference(quant_inst,[status(thm)],[])).
% 295.61/188.20 tff(31897,plain,
% 295.61/188.20 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s15)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15)),
% 295.61/188.20 inference(modus_ponens,[status(thm)],[31896, 31895])).
% 295.61/188.20 tff(31898,plain,
% 295.61/188.20 ($false),
% 295.61/188.20 inference(unit_resolution,[status(thm)],[31897, 14293, 29488, 31894])).
% 295.61/188.20 tff(31899,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s15) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s15))), inference(lemma,lemma(discharge,[]))).
% 295.61/188.20 tff(31900,plain,
% 295.61/188.20 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s15)),
% 295.61/188.20 inference(unit_resolution,[status(thm)],[31899, 28936])).
% 295.61/188.20 tff(31901,assumption,(~m_and_h_gate_v_in2(c_e_h_1, c_r, s15)), introduced(assumption)).
% 295.61/188.20 tff(31902,assumption,(node20(c_e_h_1, c_r, s15)), introduced(assumption)).
% 295.61/188.20 tff(31903,plain,
% 295.61/188.20 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s15)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s15))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s15)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s15))),
% 295.71/188.20 inference(rewrite,[status(thm)],[])).
% 295.71/188.20 tff(31904,plain,
% 295.71/188.20 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s15)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s15))),
% 295.71/188.20 inference(quant_inst,[status(thm)],[])).
% 295.71/188.20 tff(31905,plain,
% 295.71/188.20 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s15)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s15)),
% 295.71/188.20 inference(modus_ponens,[status(thm)],[31904, 31903])).
% 295.71/188.20 tff(31906,plain,
% 295.71/188.20 ($false),
% 295.71/188.20 inference(unit_resolution,[status(thm)],[31905, 4563, 31902, 31901])).
% 295.71/188.20 tff(31907,plain,(m_and_h_gate_v_in2(c_e_h_1, c_r, s15) | (~node20(c_e_h_1, c_r, s15))), inference(lemma,lemma(discharge,[]))).
% 295.71/188.20 tff(31908,plain,
% 295.71/188.20 (~node20(c_e_h_1, c_r, s15)),
% 295.71/188.20 inference(unit_resolution,[status(thm)],[31907, 31900])).
% 295.71/188.20 tff(31909,assumption,(m_and_h_gate_v_in2(c_e_h_1, c_r, s13)), introduced(assumption)).
% 295.71/188.20 tff(31910,plain,
% 295.71/188.20 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13))),
% 295.71/188.20 inference(rewrite,[status(thm)],[])).
% 295.71/188.20 tff(31911,plain,
% 295.71/188.20 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13))),
% 295.71/188.20 inference(quant_inst,[status(thm)],[])).
% 295.71/188.20 tff(31912,plain,
% 295.71/188.20 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)),
% 295.71/188.20 inference(modus_ponens,[status(thm)],[31911, 31910])).
% 295.71/188.20 tff(31913,plain,
% 295.71/188.20 ($false),
% 295.71/188.20 inference(unit_resolution,[status(thm)],[31912, 14293, 25403, 31909])).
% 295.71/188.20 tff(31914,plain,((~m_and_h_gate_v_in2(c_e_h_1, c_r, s13)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s13)), inference(lemma,lemma(discharge,[]))).
% 295.71/188.20 tff(31915,plain,
% 295.71/188.20 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s13)),
% 295.71/188.20 inference(unit_resolution,[status(thm)],[31914, 25401])).
% 295.71/188.20 tff(31916,assumption,(~m_and_h_gate_v_in2(c_e_h_1, c_r, s13)), introduced(assumption)).
% 295.71/188.20 tff(31917,assumption,(node20(c_e_h_1, c_r, s13)), introduced(assumption)).
% 295.71/188.20 tff(31918,plain,
% 295.71/188.20 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s13)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s13))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s13)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s13))),
% 295.71/188.20 inference(rewrite,[status(thm)],[])).
% 295.71/188.20 tff(31919,plain,
% 295.71/188.20 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s13)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s13))),
% 295.71/188.20 inference(quant_inst,[status(thm)],[])).
% 295.71/188.20 tff(31920,plain,
% 295.71/188.20 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s13)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s13)),
% 295.71/188.20 inference(modus_ponens,[status(thm)],[31919, 31918])).
% 295.71/188.20 tff(31921,plain,
% 295.71/188.20 ($false),
% 295.71/188.20 inference(unit_resolution,[status(thm)],[31920, 4563, 31917, 31916])).
% 295.71/188.20 tff(31922,plain,((~node20(c_e_h_1, c_r, s13)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s13)), inference(lemma,lemma(discharge,[]))).
% 295.71/188.20 tff(31923,plain,
% 295.71/188.20 (~node20(c_e_h_1, c_r, s13)),
% 295.71/188.20 inference(unit_resolution,[status(thm)],[31922, 31915])).
% 295.71/188.20 tff(31924,assumption,(m_and_h_gate_v_in1(c_e_h_1, c_r, s12)), introduced(assumption)).
% 295.71/188.20 tff(31925,plain,
% 295.71/188.20 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_r, s12)) | m_c_h_element_v_out(c_e_h_1, c_e, s12))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_r, s12)) | m_c_h_element_v_out(c_e_h_1, c_e, s12))),
% 295.71/188.21 inference(rewrite,[status(thm)],[])).
% 295.71/188.21 tff(31926,plain,
% 295.71/188.21 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_r, s12)) | m_c_h_element_v_out(c_e_h_1, c_e, s12))),
% 295.71/188.21 inference(quant_inst,[status(thm)],[])).
% 295.71/188.21 tff(31927,plain,
% 295.71/188.21 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_r, s12)) | m_c_h_element_v_out(c_e_h_1, c_e, s12)),
% 295.71/188.21 inference(modus_ponens,[status(thm)],[31926, 31925])).
% 295.71/188.21 tff(31928,plain,
% 295.71/188.21 ($false),
% 295.71/188.21 inference(unit_resolution,[status(thm)],[31927, 24, 25687, 31924])).
% 295.71/188.21 tff(31929,plain,(m_c_h_element_v_out(c_e_h_1, c_e, s12) | (~m_and_h_gate_v_in1(c_e_h_1, c_r, s12))), inference(lemma,lemma(discharge,[]))).
% 295.71/188.21 tff(31930,plain,
% 295.71/188.21 (~m_and_h_gate_v_in1(c_e_h_1, c_r, s12)),
% 295.71/188.21 inference(unit_resolution,[status(thm)],[31929, 25685])).
% 295.71/188.21 tff(31931,assumption,(~m_and_h_gate_v_in1(c_e_h_1, c_r, s12)), introduced(assumption)).
% 295.71/188.21 tff(31932,assumption,(node20(c_e_h_1, c_r, s12)), introduced(assumption)).
% 295.71/188.21 tff(31933,plain,
% 295.71/188.21 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s12)) | m_and_h_gate_v_in1(c_e_h_1, c_r, s12))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_r, s12)) | m_and_h_gate_v_in1(c_e_h_1, c_r, s12))),
% 295.71/188.21 inference(rewrite,[status(thm)],[])).
% 295.71/188.21 tff(31934,plain,
% 295.71/188.21 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s12)) | m_and_h_gate_v_in1(c_e_h_1, c_r, s12))),
% 295.71/188.21 inference(quant_inst,[status(thm)],[])).
% 295.71/188.21 tff(31935,plain,
% 295.71/188.21 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_r, s12)) | m_and_h_gate_v_in1(c_e_h_1, c_r, s12)),
% 295.71/188.21 inference(modus_ponens,[status(thm)],[31934, 31933])).
% 295.71/188.21 tff(31936,plain,
% 295.71/188.21 ($false),
% 295.71/188.21 inference(unit_resolution,[status(thm)],[31935, 38, 31932, 31931])).
% 295.71/188.21 tff(31937,plain,(m_and_h_gate_v_in1(c_e_h_1, c_r, s12) | (~node20(c_e_h_1, c_r, s12))), inference(lemma,lemma(discharge,[]))).
% 295.71/188.21 tff(31938,plain,
% 295.71/188.21 (~node20(c_e_h_1, c_r, s12)),
% 295.71/188.21 inference(unit_resolution,[status(thm)],[31937, 31930])).
% 295.71/188.21 tff(31939,assumption,(m_and_h_gate_v_in2(c_e_h_1, c_r, s10)), introduced(assumption)).
% 295.71/188.21 tff(31940,plain,
% 295.71/188.21 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10))),
% 295.71/188.21 inference(rewrite,[status(thm)],[])).
% 295.71/188.21 tff(31941,plain,
% 295.71/188.21 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10))),
% 295.71/188.21 inference(quant_inst,[status(thm)],[])).
% 295.71/188.21 tff(31942,plain,
% 295.71/188.21 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s10)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10)),
% 295.71/188.21 inference(modus_ponens,[status(thm)],[31941, 31940])).
% 295.71/188.21 tff(31943,plain,
% 295.71/188.21 ($false),
% 295.71/188.21 inference(unit_resolution,[status(thm)],[31942, 14293, 23078, 31939])).
% 295.71/188.21 tff(31944,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s10) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s10))), inference(lemma,lemma(discharge,[]))).
% 295.71/188.21 tff(31945,plain,
% 295.71/188.21 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s10)),
% 295.71/188.21 inference(unit_resolution,[status(thm)],[31944, 22659])).
% 295.71/188.21 tff(31946,assumption,(~m_and_h_gate_v_in2(c_e_h_1, c_r, s10)), introduced(assumption)).
% 295.71/188.21 tff(31947,assumption,(node20(c_e_h_1, c_r, s10)), introduced(assumption)).
% 295.71/188.21 tff(31948,plain,
% 295.71/188.21 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s10)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s10))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s10)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s10))),
% 295.71/188.21 inference(rewrite,[status(thm)],[])).
% 295.71/188.21 tff(31949,plain,
% 295.71/188.21 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s10)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s10))),
% 295.71/188.21 inference(quant_inst,[status(thm)],[])).
% 295.71/188.21 tff(31950,plain,
% 295.71/188.21 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s10)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s10)),
% 295.71/188.21 inference(modus_ponens,[status(thm)],[31949, 31948])).
% 295.71/188.21 tff(31951,plain,
% 295.71/188.21 ($false),
% 295.71/188.21 inference(unit_resolution,[status(thm)],[31950, 4563, 31947, 31946])).
% 295.71/188.21 tff(31952,plain,(m_and_h_gate_v_in2(c_e_h_1, c_r, s10) | (~node20(c_e_h_1, c_r, s10))), inference(lemma,lemma(discharge,[]))).
% 295.71/188.21 tff(31953,plain,
% 295.71/188.21 (~node20(c_e_h_1, c_r, s10)),
% 295.71/188.21 inference(unit_resolution,[status(thm)],[31952, 31945])).
% 295.71/188.21 tff(31954,assumption,(m_and_h_gate_v_in2(c_e_h_1, c_r, s9)), introduced(assumption)).
% 295.71/188.21 tff(31955,plain,
% 295.71/188.21 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s9)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s9)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9))),
% 295.71/188.21 inference(rewrite,[status(thm)],[])).
% 295.71/188.21 tff(31956,plain,
% 295.71/188.21 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s9)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9))),
% 295.71/188.21 inference(quant_inst,[status(thm)],[])).
% 295.71/188.21 tff(31957,plain,
% 295.71/188.21 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s9)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9)),
% 295.71/188.21 inference(modus_ponens,[status(thm)],[31956, 31955])).
% 295.71/188.21 tff(31958,plain,
% 295.71/188.21 ($false),
% 295.71/188.21 inference(unit_resolution,[status(thm)],[31957, 14293, 22635, 31954])).
% 295.71/188.21 tff(31959,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s9) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s9))), inference(lemma,lemma(discharge,[]))).
% 295.71/188.21 tff(31960,plain,
% 295.71/188.21 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s9)),
% 295.71/188.21 inference(unit_resolution,[status(thm)],[31959, 22670])).
% 295.71/188.21 tff(31961,assumption,(~m_and_h_gate_v_in2(c_e_h_1, c_r, s9)), introduced(assumption)).
% 295.71/188.21 tff(31962,assumption,(node20(c_e_h_1, c_r, s9)), introduced(assumption)).
% 295.71/188.21 tff(31963,plain,
% 295.71/188.21 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s9)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s9))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s9)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s9))),
% 295.71/188.21 inference(rewrite,[status(thm)],[])).
% 295.71/188.21 tff(31964,plain,
% 295.71/188.21 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s9)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s9))),
% 295.71/188.21 inference(quant_inst,[status(thm)],[])).
% 295.71/188.21 tff(31965,plain,
% 295.71/188.21 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s9)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s9)),
% 295.71/188.21 inference(modus_ponens,[status(thm)],[31964, 31963])).
% 295.71/188.21 tff(31966,plain,
% 295.71/188.21 ($false),
% 295.71/188.21 inference(unit_resolution,[status(thm)],[31965, 4563, 31962, 31961])).
% 295.71/188.21 tff(31967,plain,(m_and_h_gate_v_in2(c_e_h_1, c_r, s9) | (~node20(c_e_h_1, c_r, s9))), inference(lemma,lemma(discharge,[]))).
% 295.71/188.21 tff(31968,plain,
% 295.71/188.21 (~node20(c_e_h_1, c_r, s9)),
% 295.71/188.21 inference(unit_resolution,[status(thm)],[31967, 31960])).
% 295.71/188.21 tff(31969,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s9)), introduced(assumption)).
% 295.71/188.21 tff(31970,assumption,(node21(c_e_h_1, c_r, s8, s9)), introduced(assumption)).
% 295.71/188.21 tff(31971,plain,
% 295.71/188.21 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8))),
% 295.71/188.21 inference(rewrite,[status(thm)],[])).
% 295.71/188.21 tff(31972,plain,
% 295.71/188.21 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8))),
% 295.71/188.21 inference(quant_inst,[status(thm)],[])).
% 295.71/188.21 tff(31973,plain,
% 295.71/188.21 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s8)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s8)),
% 295.71/188.21 inference(modus_ponens,[status(thm)],[31972, 31971])).
% 295.71/188.21 tff(31974,plain,
% 295.71/188.21 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s8)),
% 295.71/188.21 inference(unit_resolution,[status(thm)],[31973, 14293, 22368])).
% 295.71/188.21 tff(31975,plain,
% 295.71/188.21 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s8)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s8))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s8)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s8))),
% 295.71/188.21 inference(rewrite,[status(thm)],[])).
% 295.71/188.21 tff(31976,plain,
% 295.71/188.21 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s8)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s8))),
% 295.71/188.21 inference(quant_inst,[status(thm)],[])).
% 295.71/188.21 tff(31977,plain,
% 295.71/188.21 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s8)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s8)),
% 295.71/188.21 inference(modus_ponens,[status(thm)],[31976, 31975])).
% 295.71/188.21 tff(31978,plain,
% 295.71/188.21 (~node20(c_e_h_1, c_r, s8)),
% 295.71/188.21 inference(unit_resolution,[status(thm)],[31977, 4563, 31974])).
% 295.71/188.21 tff(31979,plain,
% 295.71/188.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s9)) | (~node21(c_e_h_1, c_r, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s9)) | (~node21(c_e_h_1, c_r, s8, s9)))),
% 295.71/188.21 inference(rewrite,[status(thm)],[])).
% 295.71/188.21 tff(31980,plain,
% 295.71/188.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s9)) | (~node21(c_e_h_1, c_r, s8, s9)))),
% 295.71/188.21 inference(quant_inst,[status(thm)],[])).
% 295.71/188.21 tff(31981,plain,
% 295.71/188.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s8) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s9)) | (~node21(c_e_h_1, c_r, s8, s9))),
% 295.71/188.21 inference(modus_ponens,[status(thm)],[31980, 31979])).
% 295.71/188.21 tff(31982,plain,
% 295.71/188.21 ($false),
% 295.71/188.21 inference(unit_resolution,[status(thm)],[31981, 52, 31978, 31970, 31969])).
% 295.71/188.21 tff(31983,plain,((~node21(c_e_h_1, c_r, s8, s9)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s9))), inference(lemma,lemma(discharge,[]))).
% 295.71/188.21 tff(31984,plain,
% 295.71/188.21 (~node21(c_e_h_1, c_r, s8, s9)),
% 295.71/188.21 inference(unit_resolution,[status(thm)],[31983, 31969])).
% 295.71/188.21 tff(31985,plain,
% 295.71/188.21 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s8, s9)) | node21(c_e_h_1, c_r, s8, s9) | node22(c_e_h_1, c_r, s8, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_1, c_r, s8, s9) | node22(c_e_h_1, c_r, s8, s9))),
% 295.71/188.21 inference(rewrite,[status(thm)],[])).
% 295.71/188.21 tff(31986,plain,
% 295.71/188.21 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s8, s9)) | node21(c_e_h_1, c_r, s8, s9) | node22(c_e_h_1, c_r, s8, s9))),
% 295.71/188.22 inference(quant_inst,[status(thm)],[])).
% 295.71/188.22 tff(31987,plain,
% 295.71/188.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s8, s9)) | node21(c_e_h_1, c_r, s8, s9) | node22(c_e_h_1, c_r, s8, s9)),
% 295.71/188.22 inference(modus_ponens,[status(thm)],[31986, 31985])).
% 295.71/188.22 tff(31988,plain,
% 295.71/188.22 (node21(c_e_h_1, c_r, s8, s9) | node22(c_e_h_1, c_r, s8, s9)),
% 295.71/188.22 inference(unit_resolution,[status(thm)],[31987, 82, 1993])).
% 295.71/188.22 tff(31989,plain,
% 295.71/188.22 (node22(c_e_h_1, c_r, s8, s9)),
% 295.71/188.22 inference(unit_resolution,[status(thm)],[31988, 31984])).
% 295.71/188.22 tff(31990,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s8)), introduced(assumption)).
% 295.71/188.22 tff(31991,assumption,(node21(c_e_h_1, c_r, s7, s8)), introduced(assumption)).
% 295.71/188.22 tff(31992,plain,
% 295.71/188.22 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7))),
% 295.71/188.22 inference(rewrite,[status(thm)],[])).
% 295.71/188.22 tff(31993,plain,
% 295.71/188.22 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7))),
% 295.71/188.22 inference(quant_inst,[status(thm)],[])).
% 295.71/188.22 tff(31994,plain,
% 295.71/188.22 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s7)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s7)),
% 295.71/188.22 inference(modus_ponens,[status(thm)],[31993, 31992])).
% 295.71/188.22 tff(31995,plain,
% 295.71/188.22 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s7)),
% 295.71/188.22 inference(unit_resolution,[status(thm)],[31994, 14293, 19249])).
% 295.71/188.22 tff(31996,plain,
% 295.71/188.22 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s7)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s7))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s7)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s7))),
% 295.71/188.22 inference(rewrite,[status(thm)],[])).
% 295.71/188.22 tff(31997,plain,
% 295.71/188.22 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s7)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s7))),
% 295.71/188.22 inference(quant_inst,[status(thm)],[])).
% 295.71/188.22 tff(31998,plain,
% 295.71/188.22 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s7)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s7)),
% 295.71/188.22 inference(modus_ponens,[status(thm)],[31997, 31996])).
% 295.71/188.22 tff(31999,plain,
% 295.71/188.22 (~node20(c_e_h_1, c_r, s7)),
% 295.71/188.22 inference(unit_resolution,[status(thm)],[31998, 4563, 31995])).
% 295.71/188.22 tff(32000,plain,
% 295.71/188.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s7) | (~node21(c_e_h_1, c_r, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s7) | (~node21(c_e_h_1, c_r, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s8)))),
% 295.71/188.22 inference(rewrite,[status(thm)],[])).
% 295.71/188.22 tff(32001,plain,
% 295.71/188.22 ((node20(c_e_h_1, c_r, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s8)) | (~node21(c_e_h_1, c_r, s7, s8))) <=> (node20(c_e_h_1, c_r, s7) | (~node21(c_e_h_1, c_r, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s8)))),
% 295.71/188.22 inference(rewrite,[status(thm)],[])).
% 295.71/188.22 tff(32002,plain,
% 295.71/188.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s8)) | (~node21(c_e_h_1, c_r, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s7) | (~node21(c_e_h_1, c_r, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s8))))),
% 295.71/188.22 inference(monotonicity,[status(thm)],[32001])).
% 295.71/188.22 tff(32003,plain,
% 295.71/188.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s8)) | (~node21(c_e_h_1, c_r, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s7) | (~node21(c_e_h_1, c_r, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s8)))),
% 295.71/188.22 inference(transitivity,[status(thm)],[32002, 32000])).
% 295.71/188.22 tff(32004,plain,
% 295.71/188.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s7) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s8)) | (~node21(c_e_h_1, c_r, s7, s8)))),
% 295.71/188.22 inference(quant_inst,[status(thm)],[])).
% 295.71/188.22 tff(32005,plain,
% 295.71/188.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s7) | (~node21(c_e_h_1, c_r, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s8))),
% 295.71/188.22 inference(modus_ponens,[status(thm)],[32004, 32003])).
% 295.71/188.22 tff(32006,plain,
% 295.71/188.22 ($false),
% 295.71/188.22 inference(unit_resolution,[status(thm)],[32005, 52, 31999, 31991, 31990])).
% 295.71/188.22 tff(32007,plain,((~node21(c_e_h_1, c_r, s7, s8)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s8))), inference(lemma,lemma(discharge,[]))).
% 295.71/188.22 tff(32008,plain,
% 295.71/188.22 (~node21(c_e_h_1, c_r, s7, s8)),
% 295.71/188.22 inference(unit_resolution,[status(thm)],[32007, 31990])).
% 295.71/188.22 tff(32009,plain,
% 295.71/188.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_1, c_r, s7, s8) | node22(c_e_h_1, c_r, s7, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_1, c_r, s7, s8) | node22(c_e_h_1, c_r, s7, s8))),
% 295.71/188.22 inference(rewrite,[status(thm)],[])).
% 295.71/188.22 tff(32010,plain,
% 295.71/188.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s7, s8)) | node21(c_e_h_1, c_r, s7, s8) | node22(c_e_h_1, c_r, s7, s8))),
% 295.71/188.22 inference(quant_inst,[status(thm)],[])).
% 295.71/188.22 tff(32011,plain,
% 295.71/188.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s7, s8)) | node21(c_e_h_1, c_r, s7, s8) | node22(c_e_h_1, c_r, s7, s8)),
% 295.71/188.22 inference(modus_ponens,[status(thm)],[32010, 32009])).
% 295.71/188.22 tff(32012,plain,
% 295.71/188.22 (node21(c_e_h_1, c_r, s7, s8) | node22(c_e_h_1, c_r, s7, s8)),
% 295.71/188.22 inference(unit_resolution,[status(thm)],[32011, 82, 1938])).
% 295.71/188.22 tff(32013,plain,
% 295.71/188.22 (node22(c_e_h_1, c_r, s7, s8)),
% 295.71/188.22 inference(unit_resolution,[status(thm)],[32012, 32008])).
% 295.71/188.22 tff(32014,plain,
% 295.71/188.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s8)) | (~node22(c_e_h_1, c_r, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_r, s7))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s8)) | (~node22(c_e_h_1, c_r, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_r, s7))),
% 295.71/188.22 inference(rewrite,[status(thm)],[])).
% 295.71/188.22 tff(32015,plain,
% 295.71/188.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s8)) | (~node22(c_e_h_1, c_r, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_r, s7))),
% 295.71/188.22 inference(quant_inst,[status(thm)],[])).
% 295.71/188.22 tff(32016,plain,
% 295.71/188.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s8)) | (~node22(c_e_h_1, c_r, s7, s8)) | m_and_h_gate_v_out(c_e_h_1, c_r, s7)),
% 295.71/188.22 inference(modus_ponens,[status(thm)],[32015, 32014])).
% 295.71/188.22 tff(32017,plain,
% 295.71/188.22 ($false),
% 295.71/188.22 inference(unit_resolution,[status(thm)],[32016, 108, 24822, 32013, 31990])).
% 295.71/188.22 tff(32018,plain,((~m_and_h_gate_v_out(c_e_h_1, c_r, s8)) | m_and_h_gate_v_out(c_e_h_1, c_r, s7)), inference(lemma,lemma(discharge,[]))).
% 295.71/188.22 tff(32019,plain,
% 295.71/188.22 (~m_and_h_gate_v_out(c_e_h_1, c_r, s8)),
% 295.71/188.22 inference(unit_resolution,[status(thm)],[32018, 24821])).
% 295.71/188.22 tff(32020,plain,
% 295.71/188.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s9)) | (~node22(c_e_h_1, c_r, s8, s9)) | m_and_h_gate_v_out(c_e_h_1, c_r, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s9)) | (~node22(c_e_h_1, c_r, s8, s9)) | m_and_h_gate_v_out(c_e_h_1, c_r, s8))),
% 295.71/188.22 inference(rewrite,[status(thm)],[])).
% 295.71/188.22 tff(32021,plain,
% 295.71/188.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s9)) | (~node22(c_e_h_1, c_r, s8, s9)) | m_and_h_gate_v_out(c_e_h_1, c_r, s8))),
% 295.71/188.22 inference(quant_inst,[status(thm)],[])).
% 295.71/188.22 tff(32022,plain,
% 295.71/188.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s9)) | (~node22(c_e_h_1, c_r, s8, s9)) | m_and_h_gate_v_out(c_e_h_1, c_r, s8)),
% 295.71/188.22 inference(modus_ponens,[status(thm)],[32021, 32020])).
% 295.71/188.22 tff(32023,plain,
% 295.71/188.22 ($false),
% 295.71/188.22 inference(unit_resolution,[status(thm)],[32022, 108, 32019, 31989, 31969])).
% 295.71/188.22 tff(32024,plain,(~m_and_h_gate_v_out(c_e_h_1, c_r, s9)), inference(lemma,lemma(discharge,[]))).
% 295.71/188.22 tff(32025,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s10)), introduced(assumption)).
% 295.71/188.22 tff(32026,assumption,(~node20(c_e_h_1, c_r, s9)), introduced(assumption)).
% 295.71/188.22 tff(32027,assumption,(node21(c_e_h_1, c_r, s9, s10)), introduced(assumption)).
% 295.71/188.22 tff(32028,plain,
% 295.71/188.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s9) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s10)) | (~node21(c_e_h_1, c_r, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s9) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s10)) | (~node21(c_e_h_1, c_r, s9, s10)))),
% 295.71/188.22 inference(rewrite,[status(thm)],[])).
% 295.71/188.22 tff(32029,plain,
% 295.71/188.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s9) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s10)) | (~node21(c_e_h_1, c_r, s9, s10)))),
% 295.71/188.22 inference(quant_inst,[status(thm)],[])).
% 295.71/188.22 tff(32030,plain,
% 295.71/188.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s9) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s10)) | (~node21(c_e_h_1, c_r, s9, s10))),
% 295.71/188.22 inference(modus_ponens,[status(thm)],[32029, 32028])).
% 295.71/188.22 tff(32031,plain,
% 295.71/188.22 ($false),
% 295.71/188.22 inference(unit_resolution,[status(thm)],[32030, 52, 32027, 32026, 32025])).
% 295.71/188.22 tff(32032,plain,((~node21(c_e_h_1, c_r, s9, s10)) | node20(c_e_h_1, c_r, s9) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s10))), inference(lemma,lemma(discharge,[]))).
% 295.71/188.22 tff(32033,plain,
% 295.71/188.22 (~node21(c_e_h_1, c_r, s9, s10)),
% 295.71/188.22 inference(unit_resolution,[status(thm)],[32032, 32025, 32026])).
% 295.71/188.22 tff(32034,plain,
% 295.71/188.22 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s9, s10)) | node21(c_e_h_1, c_r, s9, s10) | node22(c_e_h_1, c_r, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s9, s10)) | node21(c_e_h_1, c_r, s9, s10) | node22(c_e_h_1, c_r, s9, s10))),
% 295.71/188.22 inference(rewrite,[status(thm)],[])).
% 295.71/188.22 tff(32035,plain,
% 295.71/188.22 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s9, s10)) | node21(c_e_h_1, c_r, s9, s10) | node22(c_e_h_1, c_r, s9, s10))),
% 295.71/188.22 inference(quant_inst,[status(thm)],[])).
% 295.71/188.23 tff(32036,plain,
% 295.71/188.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s9, s10)) | node21(c_e_h_1, c_r, s9, s10) | node22(c_e_h_1, c_r, s9, s10)),
% 295.71/188.23 inference(modus_ponens,[status(thm)],[32035, 32034])).
% 295.71/188.23 tff(32037,plain,
% 295.71/188.23 (node21(c_e_h_1, c_r, s9, s10) | node22(c_e_h_1, c_r, s9, s10)),
% 295.71/188.23 inference(unit_resolution,[status(thm)],[32036, 82, 7676])).
% 295.71/188.23 tff(32038,plain,
% 295.71/188.23 (node22(c_e_h_1, c_r, s9, s10)),
% 295.71/188.23 inference(unit_resolution,[status(thm)],[32037, 32033])).
% 295.71/188.23 tff(32039,plain,
% 295.71/188.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s10)) | (~node22(c_e_h_1, c_r, s9, s10)) | m_and_h_gate_v_out(c_e_h_1, c_r, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s10)) | (~node22(c_e_h_1, c_r, s9, s10)) | m_and_h_gate_v_out(c_e_h_1, c_r, s9))),
% 295.71/188.23 inference(rewrite,[status(thm)],[])).
% 295.71/188.23 tff(32040,plain,
% 295.71/188.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s10)) | (~node22(c_e_h_1, c_r, s9, s10)) | m_and_h_gate_v_out(c_e_h_1, c_r, s9))),
% 295.71/188.23 inference(quant_inst,[status(thm)],[])).
% 295.71/188.23 tff(32041,plain,
% 295.71/188.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s10)) | (~node22(c_e_h_1, c_r, s9, s10)) | m_and_h_gate_v_out(c_e_h_1, c_r, s9)),
% 295.71/188.23 inference(modus_ponens,[status(thm)],[32040, 32039])).
% 295.71/188.23 tff(32042,plain,
% 295.71/188.23 ($false),
% 295.71/188.23 inference(unit_resolution,[status(thm)],[32041, 108, 32038, 32025, 32024])).
% 295.71/188.23 tff(32043,plain,((~m_and_h_gate_v_out(c_e_h_1, c_r, s10)) | node20(c_e_h_1, c_r, s9)), inference(lemma,lemma(discharge,[]))).
% 295.71/188.23 tff(32044,plain,
% 295.71/188.23 (~m_and_h_gate_v_out(c_e_h_1, c_r, s10)),
% 295.71/188.23 inference(unit_resolution,[status(thm)],[32043, 31968])).
% 295.71/188.23 tff(32045,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s10)), introduced(assumption)).
% 295.71/188.23 tff(32046,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s11)), introduced(assumption)).
% 295.71/188.23 tff(32047,assumption,(~node20(c_e_h_1, c_r, s10)), introduced(assumption)).
% 295.71/188.23 tff(32048,assumption,(node21(c_e_h_1, c_r, s10, s11)), introduced(assumption)).
% 295.71/188.23 tff(32049,plain,
% 295.71/188.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s10) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s11)) | (~node21(c_e_h_1, c_r, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s10) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s11)) | (~node21(c_e_h_1, c_r, s10, s11)))),
% 295.71/188.23 inference(rewrite,[status(thm)],[])).
% 295.71/188.23 tff(32050,plain,
% 295.71/188.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s10) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s11)) | (~node21(c_e_h_1, c_r, s10, s11)))),
% 295.71/188.23 inference(quant_inst,[status(thm)],[])).
% 295.71/188.23 tff(32051,plain,
% 295.71/188.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s10) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s11)) | (~node21(c_e_h_1, c_r, s10, s11))),
% 295.71/188.23 inference(modus_ponens,[status(thm)],[32050, 32049])).
% 295.71/188.23 tff(32052,plain,
% 295.71/188.23 ($false),
% 295.71/188.23 inference(unit_resolution,[status(thm)],[32051, 52, 32048, 32047, 32046])).
% 295.71/188.23 tff(32053,plain,((~node21(c_e_h_1, c_r, s10, s11)) | node20(c_e_h_1, c_r, s10) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s11))), inference(lemma,lemma(discharge,[]))).
% 295.71/188.23 tff(32054,plain,
% 295.71/188.23 (~node21(c_e_h_1, c_r, s10, s11)),
% 295.71/188.23 inference(unit_resolution,[status(thm)],[32053, 32046, 32047])).
% 295.71/188.23 tff(32055,plain,
% 295.71/188.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s10, s11)) | node21(c_e_h_1, c_r, s10, s11) | node22(c_e_h_1, c_r, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s10, s11)) | node21(c_e_h_1, c_r, s10, s11) | node22(c_e_h_1, c_r, s10, s11))),
% 295.71/188.23 inference(rewrite,[status(thm)],[])).
% 295.71/188.23 tff(32056,plain,
% 295.71/188.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s10, s11)) | node21(c_e_h_1, c_r, s10, s11) | node22(c_e_h_1, c_r, s10, s11))),
% 295.71/188.23 inference(quant_inst,[status(thm)],[])).
% 295.71/188.23 tff(32057,plain,
% 295.71/188.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s10, s11)) | node21(c_e_h_1, c_r, s10, s11) | node22(c_e_h_1, c_r, s10, s11)),
% 295.71/188.23 inference(modus_ponens,[status(thm)],[32056, 32055])).
% 295.71/188.23 tff(32058,plain,
% 295.71/188.23 (node21(c_e_h_1, c_r, s10, s11) | node22(c_e_h_1, c_r, s10, s11)),
% 295.71/188.23 inference(unit_resolution,[status(thm)],[32057, 82, 7748])).
% 295.71/188.23 tff(32059,plain,
% 295.71/188.23 (node22(c_e_h_1, c_r, s10, s11)),
% 295.71/188.23 inference(unit_resolution,[status(thm)],[32058, 32054])).
% 295.71/188.23 tff(32060,plain,
% 295.71/188.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s11)) | (~node22(c_e_h_1, c_r, s10, s11)) | m_and_h_gate_v_out(c_e_h_1, c_r, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s11)) | (~node22(c_e_h_1, c_r, s10, s11)) | m_and_h_gate_v_out(c_e_h_1, c_r, s10))),
% 295.71/188.23 inference(rewrite,[status(thm)],[])).
% 295.71/188.23 tff(32061,plain,
% 295.71/188.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s11)) | (~node22(c_e_h_1, c_r, s10, s11)) | m_and_h_gate_v_out(c_e_h_1, c_r, s10))),
% 295.71/188.23 inference(quant_inst,[status(thm)],[])).
% 295.71/188.23 tff(32062,plain,
% 295.71/188.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s11)) | (~node22(c_e_h_1, c_r, s10, s11)) | m_and_h_gate_v_out(c_e_h_1, c_r, s10)),
% 295.71/188.23 inference(modus_ponens,[status(thm)],[32061, 32060])).
% 295.71/188.23 tff(32063,plain,
% 295.71/188.23 ($false),
% 295.71/188.23 inference(unit_resolution,[status(thm)],[32062, 108, 32059, 32046, 32045])).
% 295.71/188.23 tff(32064,plain,((~m_and_h_gate_v_out(c_e_h_1, c_r, s11)) | m_and_h_gate_v_out(c_e_h_1, c_r, s10) | node20(c_e_h_1, c_r, s10)), inference(lemma,lemma(discharge,[]))).
% 295.71/188.23 tff(32065,plain,
% 295.71/188.23 ((~m_and_h_gate_v_out(c_e_h_1, c_r, s11)) | node20(c_e_h_1, c_r, s10)),
% 295.71/188.23 inference(unit_resolution,[status(thm)],[32064, 32044])).
% 295.71/188.23 tff(32066,plain,
% 295.71/188.23 (~m_and_h_gate_v_out(c_e_h_1, c_r, s11)),
% 295.71/188.23 inference(unit_resolution,[status(thm)],[32065, 31953])).
% 295.71/188.23 tff(32067,plain,
% 295.71/188.23 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s11)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s11)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11))),
% 295.71/188.23 inference(rewrite,[status(thm)],[])).
% 295.71/188.23 tff(32068,plain,
% 295.71/188.23 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s11)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11))),
% 295.71/188.23 inference(quant_inst,[status(thm)],[])).
% 295.71/188.23 tff(32069,plain,
% 295.71/188.23 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s11)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s11)),
% 295.71/188.23 inference(modus_ponens,[status(thm)],[32068, 32067])).
% 295.71/188.23 tff(32070,plain,
% 295.71/188.23 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s11)),
% 295.71/188.23 inference(unit_resolution,[status(thm)],[32069, 14293, 23106])).
% 295.71/188.23 tff(32071,plain,
% 295.71/188.23 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s11)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s11))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s11)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s11))),
% 295.71/188.23 inference(rewrite,[status(thm)],[])).
% 295.71/188.23 tff(32072,plain,
% 295.71/188.23 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s11)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s11))),
% 295.71/188.23 inference(quant_inst,[status(thm)],[])).
% 295.71/188.23 tff(32073,plain,
% 295.71/188.23 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s11)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s11)),
% 295.71/188.23 inference(modus_ponens,[status(thm)],[32072, 32071])).
% 295.71/188.23 tff(32074,plain,
% 295.71/188.23 (~node20(c_e_h_1, c_r, s11)),
% 295.71/188.23 inference(unit_resolution,[status(thm)],[32073, 4563, 32070])).
% 295.71/188.23 tff(32075,assumption,(~node20(c_e_h_1, c_r, s11)), introduced(assumption)).
% 295.71/188.23 tff(32076,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s12)), introduced(assumption)).
% 295.71/188.23 tff(32077,assumption,(node21(c_e_h_1, c_r, s11, s12)), introduced(assumption)).
% 295.71/188.23 tff(32078,plain,
% 295.71/188.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s11) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s12)) | (~node21(c_e_h_1, c_r, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s11) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s12)) | (~node21(c_e_h_1, c_r, s11, s12)))),
% 295.71/188.23 inference(rewrite,[status(thm)],[])).
% 295.71/188.23 tff(32079,plain,
% 295.71/188.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s11) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s12)) | (~node21(c_e_h_1, c_r, s11, s12)))),
% 295.71/188.23 inference(quant_inst,[status(thm)],[])).
% 295.71/188.23 tff(32080,plain,
% 295.71/188.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s11) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s12)) | (~node21(c_e_h_1, c_r, s11, s12))),
% 295.71/188.23 inference(modus_ponens,[status(thm)],[32079, 32078])).
% 295.71/188.23 tff(32081,plain,
% 295.71/188.23 ($false),
% 295.71/188.23 inference(unit_resolution,[status(thm)],[32080, 52, 32076, 32077, 32075])).
% 295.71/188.23 tff(32082,plain,((~node21(c_e_h_1, c_r, s11, s12)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s12)) | node20(c_e_h_1, c_r, s11)), inference(lemma,lemma(discharge,[]))).
% 295.71/188.23 tff(32083,plain,
% 295.71/188.23 (~node21(c_e_h_1, c_r, s11, s12)),
% 295.71/188.23 inference(unit_resolution,[status(thm)],[32082, 32076, 32075])).
% 295.71/188.23 tff(32084,plain,
% 295.71/188.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s11, s12)) | node21(c_e_h_1, c_r, s11, s12) | node22(c_e_h_1, c_r, s11, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s11, s12)) | node21(c_e_h_1, c_r, s11, s12) | node22(c_e_h_1, c_r, s11, s12))),
% 295.71/188.23 inference(rewrite,[status(thm)],[])).
% 295.71/188.23 tff(32085,plain,
% 295.71/188.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s11, s12)) | node21(c_e_h_1, c_r, s11, s12) | node22(c_e_h_1, c_r, s11, s12))),
% 295.71/188.23 inference(quant_inst,[status(thm)],[])).
% 295.71/188.23 tff(32086,plain,
% 295.71/188.23 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s11, s12)) | node21(c_e_h_1, c_r, s11, s12) | node22(c_e_h_1, c_r, s11, s12)),
% 295.71/188.23 inference(modus_ponens,[status(thm)],[32085, 32084])).
% 295.71/188.23 tff(32087,plain,
% 295.71/188.23 (node21(c_e_h_1, c_r, s11, s12) | node22(c_e_h_1, c_r, s11, s12)),
% 295.71/188.23 inference(unit_resolution,[status(thm)],[32086, 82, 11461])).
% 295.71/188.23 tff(32088,plain,
% 295.71/188.23 (node22(c_e_h_1, c_r, s11, s12)),
% 295.71/188.23 inference(unit_resolution,[status(thm)],[32087, 32083])).
% 295.71/188.23 tff(32089,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s11)), introduced(assumption)).
% 295.71/188.23 tff(32090,plain,
% 295.71/188.23 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s12)) | (~node22(c_e_h_1, c_r, s11, s12)) | m_and_h_gate_v_out(c_e_h_1, c_r, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s12)) | (~node22(c_e_h_1, c_r, s11, s12)) | m_and_h_gate_v_out(c_e_h_1, c_r, s11))),
% 295.71/188.24 inference(rewrite,[status(thm)],[])).
% 295.71/188.24 tff(32091,plain,
% 295.71/188.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s12)) | (~node22(c_e_h_1, c_r, s11, s12)) | m_and_h_gate_v_out(c_e_h_1, c_r, s11))),
% 295.71/188.24 inference(quant_inst,[status(thm)],[])).
% 295.71/188.24 tff(32092,plain,
% 295.71/188.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s12)) | (~node22(c_e_h_1, c_r, s11, s12)) | m_and_h_gate_v_out(c_e_h_1, c_r, s11)),
% 295.71/188.24 inference(modus_ponens,[status(thm)],[32091, 32090])).
% 295.71/188.24 tff(32093,plain,
% 295.71/188.24 ($false),
% 295.71/188.24 inference(unit_resolution,[status(thm)],[32092, 108, 32089, 32076, 32088])).
% 295.71/188.24 tff(32094,plain,((~m_and_h_gate_v_out(c_e_h_1, c_r, s12)) | m_and_h_gate_v_out(c_e_h_1, c_r, s11) | node20(c_e_h_1, c_r, s11)), inference(lemma,lemma(discharge,[]))).
% 295.71/188.24 tff(32095,plain,
% 295.71/188.24 (~m_and_h_gate_v_out(c_e_h_1, c_r, s12)),
% 295.71/188.24 inference(unit_resolution,[status(thm)],[32094, 32074, 32066])).
% 295.71/188.24 tff(32096,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s12)), introduced(assumption)).
% 295.71/188.24 tff(32097,assumption,(~node20(c_e_h_1, c_r, s12)), introduced(assumption)).
% 295.71/188.24 tff(32098,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s13)), introduced(assumption)).
% 295.71/188.24 tff(32099,assumption,(node21(c_e_h_1, c_r, s12, s13)), introduced(assumption)).
% 295.71/188.24 tff(32100,plain,
% 295.71/188.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s13)) | node20(c_e_h_1, c_r, s12) | (~node21(c_e_h_1, c_r, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s13)) | node20(c_e_h_1, c_r, s12) | (~node21(c_e_h_1, c_r, s12, s13)))),
% 295.71/188.24 inference(rewrite,[status(thm)],[])).
% 295.71/188.24 tff(32101,plain,
% 295.71/188.24 ((node20(c_e_h_1, c_r, s12) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s13)) | (~node21(c_e_h_1, c_r, s12, s13))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_r, s13)) | node20(c_e_h_1, c_r, s12) | (~node21(c_e_h_1, c_r, s12, s13)))),
% 295.71/188.24 inference(rewrite,[status(thm)],[])).
% 295.71/188.24 tff(32102,plain,
% 295.71/188.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s12) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s13)) | (~node21(c_e_h_1, c_r, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s13)) | node20(c_e_h_1, c_r, s12) | (~node21(c_e_h_1, c_r, s12, s13))))),
% 295.71/188.24 inference(monotonicity,[status(thm)],[32101])).
% 295.71/188.24 tff(32103,plain,
% 295.71/188.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s12) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s13)) | (~node21(c_e_h_1, c_r, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s13)) | node20(c_e_h_1, c_r, s12) | (~node21(c_e_h_1, c_r, s12, s13)))),
% 295.71/188.24 inference(transitivity,[status(thm)],[32102, 32100])).
% 295.71/188.24 tff(32104,plain,
% 295.71/188.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s12) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s13)) | (~node21(c_e_h_1, c_r, s12, s13)))),
% 295.71/188.24 inference(quant_inst,[status(thm)],[])).
% 295.71/188.24 tff(32105,plain,
% 295.71/188.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s13)) | node20(c_e_h_1, c_r, s12) | (~node21(c_e_h_1, c_r, s12, s13))),
% 295.71/188.24 inference(modus_ponens,[status(thm)],[32104, 32103])).
% 295.71/188.24 tff(32106,plain,
% 295.71/188.24 ($false),
% 295.71/188.24 inference(unit_resolution,[status(thm)],[32105, 52, 32098, 32099, 32097])).
% 295.71/188.24 tff(32107,plain,((~node21(c_e_h_1, c_r, s12, s13)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s13)) | node20(c_e_h_1, c_r, s12)), inference(lemma,lemma(discharge,[]))).
% 295.71/188.24 tff(32108,plain,
% 295.71/188.24 (~node21(c_e_h_1, c_r, s12, s13)),
% 295.71/188.24 inference(unit_resolution,[status(thm)],[32107, 32098, 32097])).
% 295.71/188.24 tff(32109,plain,
% 295.71/188.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s12, s13)) | node21(c_e_h_1, c_r, s12, s13) | node22(c_e_h_1, c_r, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s12, s13)) | node21(c_e_h_1, c_r, s12, s13) | node22(c_e_h_1, c_r, s12, s13))),
% 295.71/188.24 inference(rewrite,[status(thm)],[])).
% 295.71/188.24 tff(32110,plain,
% 295.71/188.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s12, s13)) | node21(c_e_h_1, c_r, s12, s13) | node22(c_e_h_1, c_r, s12, s13))),
% 295.71/188.24 inference(quant_inst,[status(thm)],[])).
% 295.71/188.24 tff(32111,plain,
% 295.71/188.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s12, s13)) | node21(c_e_h_1, c_r, s12, s13) | node22(c_e_h_1, c_r, s12, s13)),
% 295.71/188.24 inference(modus_ponens,[status(thm)],[32110, 32109])).
% 295.71/188.24 tff(32112,plain,
% 295.71/188.24 (node21(c_e_h_1, c_r, s12, s13) | node22(c_e_h_1, c_r, s12, s13)),
% 295.71/188.24 inference(unit_resolution,[status(thm)],[32111, 82, 11856])).
% 295.71/188.24 tff(32113,plain,
% 295.71/188.24 (node22(c_e_h_1, c_r, s12, s13)),
% 295.71/188.24 inference(unit_resolution,[status(thm)],[32112, 32108])).
% 295.71/188.24 tff(32114,plain,
% 295.71/188.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s13)) | (~node22(c_e_h_1, c_r, s12, s13)) | m_and_h_gate_v_out(c_e_h_1, c_r, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s13)) | (~node22(c_e_h_1, c_r, s12, s13)) | m_and_h_gate_v_out(c_e_h_1, c_r, s12))),
% 295.71/188.24 inference(rewrite,[status(thm)],[])).
% 295.71/188.24 tff(32115,plain,
% 295.71/188.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s13)) | (~node22(c_e_h_1, c_r, s12, s13)) | m_and_h_gate_v_out(c_e_h_1, c_r, s12))),
% 295.71/188.24 inference(quant_inst,[status(thm)],[])).
% 295.71/188.24 tff(32116,plain,
% 295.71/188.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s13)) | (~node22(c_e_h_1, c_r, s12, s13)) | m_and_h_gate_v_out(c_e_h_1, c_r, s12)),
% 295.71/188.24 inference(modus_ponens,[status(thm)],[32115, 32114])).
% 295.71/188.24 tff(32117,plain,
% 295.71/188.24 ($false),
% 295.71/188.24 inference(unit_resolution,[status(thm)],[32116, 108, 32098, 32113, 32096])).
% 295.71/188.24 tff(32118,plain,((~m_and_h_gate_v_out(c_e_h_1, c_r, s13)) | m_and_h_gate_v_out(c_e_h_1, c_r, s12) | node20(c_e_h_1, c_r, s12)), inference(lemma,lemma(discharge,[]))).
% 295.71/188.24 tff(32119,plain,
% 295.71/188.24 ((~m_and_h_gate_v_out(c_e_h_1, c_r, s13)) | node20(c_e_h_1, c_r, s12)),
% 295.71/188.24 inference(unit_resolution,[status(thm)],[32118, 32095])).
% 295.71/188.24 tff(32120,plain,
% 295.71/188.24 (~m_and_h_gate_v_out(c_e_h_1, c_r, s13)),
% 295.71/188.24 inference(unit_resolution,[status(thm)],[32119, 31938])).
% 295.71/188.24 tff(32121,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s14)), introduced(assumption)).
% 295.71/188.24 tff(32122,assumption,(~node20(c_e_h_1, c_r, s13)), introduced(assumption)).
% 295.71/188.24 tff(32123,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s13)), introduced(assumption)).
% 295.71/188.24 tff(32124,assumption,(node22(c_e_h_1, c_r, s13, s14)), introduced(assumption)).
% 295.71/188.24 tff(32125,plain,
% 295.71/188.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s14)) | (~node22(c_e_h_1, c_r, s13, s14)) | m_and_h_gate_v_out(c_e_h_1, c_r, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s14)) | (~node22(c_e_h_1, c_r, s13, s14)) | m_and_h_gate_v_out(c_e_h_1, c_r, s13))),
% 295.71/188.24 inference(rewrite,[status(thm)],[])).
% 295.71/188.24 tff(32126,plain,
% 295.71/188.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s14)) | (~node22(c_e_h_1, c_r, s13, s14)) | m_and_h_gate_v_out(c_e_h_1, c_r, s13))),
% 295.71/188.24 inference(quant_inst,[status(thm)],[])).
% 295.71/188.24 tff(32127,plain,
% 295.71/188.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s14)) | (~node22(c_e_h_1, c_r, s13, s14)) | m_and_h_gate_v_out(c_e_h_1, c_r, s13)),
% 295.71/188.24 inference(modus_ponens,[status(thm)],[32126, 32125])).
% 295.71/188.24 tff(32128,plain,
% 295.71/188.24 ($false),
% 295.71/188.24 inference(unit_resolution,[status(thm)],[32127, 108, 32124, 32123, 32121])).
% 295.71/188.24 tff(32129,plain,((~node22(c_e_h_1, c_r, s13, s14)) | m_and_h_gate_v_out(c_e_h_1, c_r, s13) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s14))), inference(lemma,lemma(discharge,[]))).
% 295.71/188.24 tff(32130,plain,
% 295.71/188.24 (~node22(c_e_h_1, c_r, s13, s14)),
% 295.71/188.24 inference(unit_resolution,[status(thm)],[32129, 32121, 32123])).
% 295.71/188.24 tff(32131,plain,
% 295.71/188.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s13, s14)) | node21(c_e_h_1, c_r, s13, s14) | node22(c_e_h_1, c_r, s13, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s13, s14)) | node21(c_e_h_1, c_r, s13, s14) | node22(c_e_h_1, c_r, s13, s14))),
% 295.71/188.24 inference(rewrite,[status(thm)],[])).
% 295.71/188.24 tff(32132,plain,
% 295.71/188.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s13, s14)) | node21(c_e_h_1, c_r, s13, s14) | node22(c_e_h_1, c_r, s13, s14))),
% 295.71/188.24 inference(quant_inst,[status(thm)],[])).
% 295.71/188.24 tff(32133,plain,
% 295.71/188.24 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s13, s14)) | node21(c_e_h_1, c_r, s13, s14) | node22(c_e_h_1, c_r, s13, s14)),
% 295.71/188.24 inference(modus_ponens,[status(thm)],[32132, 32131])).
% 295.71/188.24 tff(32134,plain,
% 295.71/188.24 (node21(c_e_h_1, c_r, s13, s14) | node22(c_e_h_1, c_r, s13, s14)),
% 295.71/188.24 inference(unit_resolution,[status(thm)],[32133, 82, 12831])).
% 295.71/188.24 tff(32135,plain,
% 295.71/188.24 (node21(c_e_h_1, c_r, s13, s14)),
% 295.71/188.24 inference(unit_resolution,[status(thm)],[32134, 32130])).
% 295.71/188.24 tff(32136,plain,
% 295.71/188.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s14)) | node20(c_e_h_1, c_r, s13) | (~node21(c_e_h_1, c_r, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s14)) | node20(c_e_h_1, c_r, s13) | (~node21(c_e_h_1, c_r, s13, s14)))),
% 295.71/188.24 inference(rewrite,[status(thm)],[])).
% 295.71/188.24 tff(32137,plain,
% 295.71/188.24 ((node20(c_e_h_1, c_r, s13) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s14)) | (~node21(c_e_h_1, c_r, s13, s14))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_r, s14)) | node20(c_e_h_1, c_r, s13) | (~node21(c_e_h_1, c_r, s13, s14)))),
% 295.71/188.24 inference(rewrite,[status(thm)],[])).
% 295.71/188.24 tff(32138,plain,
% 295.71/188.24 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s13) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s14)) | (~node21(c_e_h_1, c_r, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s14)) | node20(c_e_h_1, c_r, s13) | (~node21(c_e_h_1, c_r, s13, s14))))),
% 295.71/188.25 inference(monotonicity,[status(thm)],[32137])).
% 295.71/188.25 tff(32139,plain,
% 295.71/188.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s13) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s14)) | (~node21(c_e_h_1, c_r, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s14)) | node20(c_e_h_1, c_r, s13) | (~node21(c_e_h_1, c_r, s13, s14)))),
% 295.71/188.25 inference(transitivity,[status(thm)],[32138, 32136])).
% 295.71/188.25 tff(32140,plain,
% 295.71/188.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s13) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s14)) | (~node21(c_e_h_1, c_r, s13, s14)))),
% 295.71/188.25 inference(quant_inst,[status(thm)],[])).
% 295.71/188.25 tff(32141,plain,
% 295.71/188.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s14)) | node20(c_e_h_1, c_r, s13) | (~node21(c_e_h_1, c_r, s13, s14))),
% 295.71/188.25 inference(modus_ponens,[status(thm)],[32140, 32139])).
% 295.71/188.25 tff(32142,plain,
% 295.71/188.25 ($false),
% 295.71/188.25 inference(unit_resolution,[status(thm)],[32141, 52, 32135, 32122, 32121])).
% 295.71/188.25 tff(32143,plain,((~m_and_h_gate_v_out(c_e_h_1, c_r, s14)) | node20(c_e_h_1, c_r, s13) | m_and_h_gate_v_out(c_e_h_1, c_r, s13)), inference(lemma,lemma(discharge,[]))).
% 295.71/188.25 tff(32144,plain,
% 295.71/188.25 (~m_and_h_gate_v_out(c_e_h_1, c_r, s14)),
% 295.71/188.25 inference(unit_resolution,[status(thm)],[32143, 32120, 31923])).
% 295.71/188.25 tff(32145,assumption,(m_and_h_gate_v_in2(c_e_h_1, c_r, s14)), introduced(assumption)).
% 295.71/188.25 tff(32146,plain,
% 295.71/188.25 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s14)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s14)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14))),
% 295.71/188.25 inference(rewrite,[status(thm)],[])).
% 295.71/188.25 tff(32147,plain,
% 295.71/188.25 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s14)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14))),
% 295.71/188.25 inference(quant_inst,[status(thm)],[])).
% 295.71/188.25 tff(32148,plain,
% 295.71/188.25 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s14)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)),
% 295.71/188.25 inference(modus_ponens,[status(thm)],[32147, 32146])).
% 295.71/188.25 tff(32149,plain,
% 295.71/188.25 ($false),
% 295.71/188.25 inference(unit_resolution,[status(thm)],[32148, 14293, 26516, 32145])).
% 295.71/188.25 tff(32150,plain,((~m_and_h_gate_v_in2(c_e_h_1, c_r, s14)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s14)), inference(lemma,lemma(discharge,[]))).
% 295.71/188.25 tff(32151,plain,
% 295.71/188.25 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s14)),
% 295.71/188.25 inference(unit_resolution,[status(thm)],[32150, 26514])).
% 295.71/188.25 tff(32152,assumption,(~m_and_h_gate_v_in2(c_e_h_1, c_r, s14)), introduced(assumption)).
% 295.71/188.25 tff(32153,assumption,(node20(c_e_h_1, c_r, s14)), introduced(assumption)).
% 295.71/188.25 tff(32154,plain,
% 295.71/188.25 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s14)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s14))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s14)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s14))),
% 295.71/188.25 inference(rewrite,[status(thm)],[])).
% 295.71/188.25 tff(32155,plain,
% 295.71/188.25 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s14)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s14))),
% 295.71/188.25 inference(quant_inst,[status(thm)],[])).
% 295.71/188.25 tff(32156,plain,
% 295.71/188.25 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s14)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s14)),
% 295.71/188.25 inference(modus_ponens,[status(thm)],[32155, 32154])).
% 295.71/188.25 tff(32157,plain,
% 295.71/188.25 ($false),
% 295.71/188.25 inference(unit_resolution,[status(thm)],[32156, 4563, 32153, 32152])).
% 295.71/188.25 tff(32158,plain,((~node20(c_e_h_1, c_r, s14)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s14)), inference(lemma,lemma(discharge,[]))).
% 295.71/188.25 tff(32159,plain,
% 295.71/188.25 (~node20(c_e_h_1, c_r, s14)),
% 295.71/188.25 inference(unit_resolution,[status(thm)],[32158, 32151])).
% 295.71/188.25 tff(32160,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s15)), introduced(assumption)).
% 295.71/188.25 tff(32161,assumption,(~node20(c_e_h_1, c_r, s14)), introduced(assumption)).
% 295.71/188.25 tff(32162,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s14)), introduced(assumption)).
% 295.71/188.25 tff(32163,assumption,(node22(c_e_h_1, c_r, s14, s15)), introduced(assumption)).
% 295.71/188.25 tff(32164,plain,
% 295.71/188.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s15)) | (~node22(c_e_h_1, c_r, s14, s15)) | m_and_h_gate_v_out(c_e_h_1, c_r, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s15)) | (~node22(c_e_h_1, c_r, s14, s15)) | m_and_h_gate_v_out(c_e_h_1, c_r, s14))),
% 295.71/188.25 inference(rewrite,[status(thm)],[])).
% 295.71/188.25 tff(32165,plain,
% 295.71/188.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s15)) | (~node22(c_e_h_1, c_r, s14, s15)) | m_and_h_gate_v_out(c_e_h_1, c_r, s14))),
% 295.71/188.25 inference(quant_inst,[status(thm)],[])).
% 295.71/188.25 tff(32166,plain,
% 295.71/188.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s15)) | (~node22(c_e_h_1, c_r, s14, s15)) | m_and_h_gate_v_out(c_e_h_1, c_r, s14)),
% 295.71/188.25 inference(modus_ponens,[status(thm)],[32165, 32164])).
% 295.71/188.25 tff(32167,plain,
% 295.71/188.25 ($false),
% 295.71/188.25 inference(unit_resolution,[status(thm)],[32166, 108, 32163, 32162, 32160])).
% 295.71/188.25 tff(32168,plain,((~node22(c_e_h_1, c_r, s14, s15)) | m_and_h_gate_v_out(c_e_h_1, c_r, s14) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s15))), inference(lemma,lemma(discharge,[]))).
% 295.71/188.25 tff(32169,plain,
% 295.71/188.25 (~node22(c_e_h_1, c_r, s14, s15)),
% 295.71/188.25 inference(unit_resolution,[status(thm)],[32168, 32160, 32162])).
% 295.71/188.25 tff(32170,plain,
% 295.71/188.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s14, s15)) | node21(c_e_h_1, c_r, s14, s15) | node22(c_e_h_1, c_r, s14, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s14, s15)) | node21(c_e_h_1, c_r, s14, s15) | node22(c_e_h_1, c_r, s14, s15))),
% 295.71/188.25 inference(rewrite,[status(thm)],[])).
% 295.71/188.25 tff(32171,plain,
% 295.71/188.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s14, s15)) | node21(c_e_h_1, c_r, s14, s15) | node22(c_e_h_1, c_r, s14, s15))),
% 295.71/188.25 inference(quant_inst,[status(thm)],[])).
% 295.71/188.25 tff(32172,plain,
% 295.71/188.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s14, s15)) | node21(c_e_h_1, c_r, s14, s15) | node22(c_e_h_1, c_r, s14, s15)),
% 295.71/188.25 inference(modus_ponens,[status(thm)],[32171, 32170])).
% 295.71/188.25 tff(32173,plain,
% 295.71/188.25 (node21(c_e_h_1, c_r, s14, s15) | node22(c_e_h_1, c_r, s14, s15)),
% 295.71/188.25 inference(unit_resolution,[status(thm)],[32172, 82, 12926])).
% 295.71/188.25 tff(32174,plain,
% 295.71/188.25 (node21(c_e_h_1, c_r, s14, s15)),
% 295.71/188.25 inference(unit_resolution,[status(thm)],[32173, 32169])).
% 295.71/188.25 tff(32175,plain,
% 295.71/188.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s14) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s15)) | (~node21(c_e_h_1, c_r, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s14) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s15)) | (~node21(c_e_h_1, c_r, s14, s15)))),
% 295.71/188.25 inference(rewrite,[status(thm)],[])).
% 295.71/188.25 tff(32176,plain,
% 295.71/188.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s14) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s15)) | (~node21(c_e_h_1, c_r, s14, s15)))),
% 295.71/188.25 inference(quant_inst,[status(thm)],[])).
% 295.71/188.25 tff(32177,plain,
% 295.71/188.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s14) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s15)) | (~node21(c_e_h_1, c_r, s14, s15))),
% 295.71/188.25 inference(modus_ponens,[status(thm)],[32176, 32175])).
% 295.71/188.25 tff(32178,plain,
% 295.71/188.25 ($false),
% 295.71/188.25 inference(unit_resolution,[status(thm)],[32177, 52, 32174, 32161, 32160])).
% 295.71/188.25 tff(32179,plain,((~m_and_h_gate_v_out(c_e_h_1, c_r, s15)) | node20(c_e_h_1, c_r, s14) | m_and_h_gate_v_out(c_e_h_1, c_r, s14)), inference(lemma,lemma(discharge,[]))).
% 295.71/188.25 tff(32180,plain,
% 295.71/188.25 (~m_and_h_gate_v_out(c_e_h_1, c_r, s15)),
% 295.71/188.25 inference(unit_resolution,[status(thm)],[32179, 32159, 32144])).
% 295.71/188.25 tff(32181,assumption,(~node20(c_e_h_1, c_r, s15)), introduced(assumption)).
% 295.71/188.25 tff(32182,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s15)), introduced(assumption)).
% 295.71/188.25 tff(32183,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s16)), introduced(assumption)).
% 295.71/188.25 tff(32184,assumption,(node22(c_e_h_1, c_r, s15, s16)), introduced(assumption)).
% 295.71/188.25 tff(32185,plain,
% 295.71/188.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s16)) | (~node22(c_e_h_1, c_r, s15, s16)) | m_and_h_gate_v_out(c_e_h_1, c_r, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s16)) | (~node22(c_e_h_1, c_r, s15, s16)) | m_and_h_gate_v_out(c_e_h_1, c_r, s15))),
% 295.71/188.25 inference(rewrite,[status(thm)],[])).
% 295.71/188.25 tff(32186,plain,
% 295.71/188.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s16)) | (~node22(c_e_h_1, c_r, s15, s16)) | m_and_h_gate_v_out(c_e_h_1, c_r, s15))),
% 295.71/188.25 inference(quant_inst,[status(thm)],[])).
% 295.71/188.25 tff(32187,plain,
% 295.71/188.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s16)) | (~node22(c_e_h_1, c_r, s15, s16)) | m_and_h_gate_v_out(c_e_h_1, c_r, s15)),
% 295.71/188.25 inference(modus_ponens,[status(thm)],[32186, 32185])).
% 295.71/188.25 tff(32188,plain,
% 295.71/188.25 ($false),
% 295.71/188.25 inference(unit_resolution,[status(thm)],[32187, 108, 32182, 32183, 32184])).
% 295.71/188.25 tff(32189,plain,((~node22(c_e_h_1, c_r, s15, s16)) | m_and_h_gate_v_out(c_e_h_1, c_r, s15) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s16))), inference(lemma,lemma(discharge,[]))).
% 295.71/188.25 tff(32190,plain,
% 295.71/188.25 (~node22(c_e_h_1, c_r, s15, s16)),
% 295.71/188.25 inference(unit_resolution,[status(thm)],[32189, 32183, 32182])).
% 295.71/188.25 tff(32191,plain,
% 295.71/188.25 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s15, s16)) | node21(c_e_h_1, c_r, s15, s16) | node22(c_e_h_1, c_r, s15, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s15, s16)) | node21(c_e_h_1, c_r, s15, s16) | node22(c_e_h_1, c_r, s15, s16))),
% 295.71/188.25 inference(rewrite,[status(thm)],[])).
% 295.71/188.25 tff(32192,plain,
% 295.71/188.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s15, s16)) | node21(c_e_h_1, c_r, s15, s16) | node22(c_e_h_1, c_r, s15, s16))),
% 295.71/188.25 inference(quant_inst,[status(thm)],[])).
% 295.71/188.25 tff(32193,plain,
% 295.71/188.25 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s15, s16)) | node21(c_e_h_1, c_r, s15, s16) | node22(c_e_h_1, c_r, s15, s16)),
% 295.71/188.25 inference(modus_ponens,[status(thm)],[32192, 32191])).
% 295.71/188.25 tff(32194,plain,
% 295.71/188.25 (node21(c_e_h_1, c_r, s15, s16) | node22(c_e_h_1, c_r, s15, s16)),
% 295.71/188.25 inference(unit_resolution,[status(thm)],[32193, 82, 13499])).
% 295.71/188.26 tff(32195,plain,
% 295.71/188.26 (node21(c_e_h_1, c_r, s15, s16)),
% 295.71/188.26 inference(unit_resolution,[status(thm)],[32194, 32190])).
% 295.71/188.26 tff(32196,plain,
% 295.71/188.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s15) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s16)) | (~node21(c_e_h_1, c_r, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s15) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s16)) | (~node21(c_e_h_1, c_r, s15, s16)))),
% 295.71/188.26 inference(rewrite,[status(thm)],[])).
% 295.71/188.26 tff(32197,plain,
% 295.71/188.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s15) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s16)) | (~node21(c_e_h_1, c_r, s15, s16)))),
% 295.71/188.26 inference(quant_inst,[status(thm)],[])).
% 295.71/188.26 tff(32198,plain,
% 295.71/188.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s15) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s16)) | (~node21(c_e_h_1, c_r, s15, s16))),
% 295.71/188.26 inference(modus_ponens,[status(thm)],[32197, 32196])).
% 295.71/188.26 tff(32199,plain,
% 295.71/188.26 ($false),
% 295.71/188.26 inference(unit_resolution,[status(thm)],[32198, 52, 32183, 32195, 32181])).
% 295.71/188.26 tff(32200,plain,((~m_and_h_gate_v_out(c_e_h_1, c_r, s16)) | node20(c_e_h_1, c_r, s15) | m_and_h_gate_v_out(c_e_h_1, c_r, s15)), inference(lemma,lemma(discharge,[]))).
% 295.71/188.26 tff(32201,plain,
% 295.71/188.26 ((~m_and_h_gate_v_out(c_e_h_1, c_r, s16)) | node20(c_e_h_1, c_r, s15)),
% 295.71/188.26 inference(unit_resolution,[status(thm)],[32200, 32180])).
% 295.71/188.26 tff(32202,plain,
% 295.71/188.26 (~m_and_h_gate_v_out(c_e_h_1, c_r, s16)),
% 295.71/188.26 inference(unit_resolution,[status(thm)],[32201, 31908])).
% 295.71/188.26 tff(32203,plain,
% 295.71/188.26 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s16)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s16)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16))),
% 295.71/188.26 inference(rewrite,[status(thm)],[])).
% 295.71/188.26 tff(32204,plain,
% 295.71/188.26 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s16)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16))),
% 295.71/188.26 inference(quant_inst,[status(thm)],[])).
% 295.71/188.26 tff(32205,plain,
% 295.71/188.26 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s16)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s16)),
% 295.71/188.26 inference(modus_ponens,[status(thm)],[32204, 32203])).
% 295.71/188.26 tff(32206,plain,
% 295.71/188.26 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s16)),
% 295.71/188.26 inference(unit_resolution,[status(thm)],[32205, 14293, 29510])).
% 295.71/188.26 tff(32207,assumption,(~m_and_h_gate_v_in2(c_e_h_1, c_r, s16)), introduced(assumption)).
% 295.71/188.26 tff(32208,assumption,(node20(c_e_h_1, c_r, s16)), introduced(assumption)).
% 295.71/188.26 tff(32209,plain,
% 295.71/188.26 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s16)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s16))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s16)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s16))),
% 295.71/188.26 inference(rewrite,[status(thm)],[])).
% 295.71/188.26 tff(32210,plain,
% 295.71/188.26 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s16)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s16))),
% 295.71/188.26 inference(quant_inst,[status(thm)],[])).
% 295.71/188.26 tff(32211,plain,
% 295.71/188.26 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s16)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s16)),
% 295.71/188.26 inference(modus_ponens,[status(thm)],[32210, 32209])).
% 295.71/188.26 tff(32212,plain,
% 295.71/188.26 ($false),
% 295.71/188.26 inference(unit_resolution,[status(thm)],[32211, 4563, 32208, 32207])).
% 295.71/188.26 tff(32213,plain,(m_and_h_gate_v_in2(c_e_h_1, c_r, s16) | (~node20(c_e_h_1, c_r, s16))), inference(lemma,lemma(discharge,[]))).
% 295.71/188.26 tff(32214,plain,
% 295.71/188.26 (~node20(c_e_h_1, c_r, s16)),
% 295.71/188.26 inference(unit_resolution,[status(thm)],[32213, 32206])).
% 295.71/188.26 tff(32215,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s16)), introduced(assumption)).
% 295.71/188.26 tff(32216,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s17)), introduced(assumption)).
% 295.71/188.26 tff(32217,assumption,(node22(c_e_h_1, c_r, s16, s17)), introduced(assumption)).
% 295.71/188.26 tff(32218,plain,
% 295.71/188.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s17)) | (~node22(c_e_h_1, c_r, s16, s17)) | m_and_h_gate_v_out(c_e_h_1, c_r, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s17)) | (~node22(c_e_h_1, c_r, s16, s17)) | m_and_h_gate_v_out(c_e_h_1, c_r, s16))),
% 295.71/188.26 inference(rewrite,[status(thm)],[])).
% 295.71/188.26 tff(32219,plain,
% 295.71/188.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s17)) | (~node22(c_e_h_1, c_r, s16, s17)) | m_and_h_gate_v_out(c_e_h_1, c_r, s16))),
% 295.71/188.26 inference(quant_inst,[status(thm)],[])).
% 295.71/188.26 tff(32220,plain,
% 295.71/188.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s17)) | (~node22(c_e_h_1, c_r, s16, s17)) | m_and_h_gate_v_out(c_e_h_1, c_r, s16)),
% 295.71/188.26 inference(modus_ponens,[status(thm)],[32219, 32218])).
% 295.71/188.26 tff(32221,plain,
% 295.71/188.26 ($false),
% 295.71/188.26 inference(unit_resolution,[status(thm)],[32220, 108, 32217, 32216, 32215])).
% 295.71/188.26 tff(32222,plain,((~node22(c_e_h_1, c_r, s16, s17)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s17)) | m_and_h_gate_v_out(c_e_h_1, c_r, s16)), inference(lemma,lemma(discharge,[]))).
% 295.71/188.26 tff(32223,plain,
% 295.71/188.26 (~node22(c_e_h_1, c_r, s16, s17)),
% 295.71/188.26 inference(unit_resolution,[status(thm)],[32222, 32216, 32215])).
% 295.71/188.26 tff(32224,assumption,(~node20(c_e_h_1, c_r, s16)), introduced(assumption)).
% 295.71/188.26 tff(32225,assumption,(node21(c_e_h_1, c_r, s16, s17)), introduced(assumption)).
% 295.71/188.26 tff(32226,plain,
% 295.71/188.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s16) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s17)) | (~node21(c_e_h_1, c_r, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s16) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s17)) | (~node21(c_e_h_1, c_r, s16, s17)))),
% 295.71/188.26 inference(rewrite,[status(thm)],[])).
% 295.71/188.26 tff(32227,plain,
% 295.71/188.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s16) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s17)) | (~node21(c_e_h_1, c_r, s16, s17)))),
% 295.71/188.26 inference(quant_inst,[status(thm)],[])).
% 295.71/188.26 tff(32228,plain,
% 295.71/188.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s16) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s17)) | (~node21(c_e_h_1, c_r, s16, s17))),
% 295.71/188.26 inference(modus_ponens,[status(thm)],[32227, 32226])).
% 295.71/188.26 tff(32229,plain,
% 295.71/188.26 ($false),
% 295.71/188.26 inference(unit_resolution,[status(thm)],[32228, 52, 32225, 32216, 32224])).
% 295.71/188.26 tff(32230,plain,((~node21(c_e_h_1, c_r, s16, s17)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s17)) | node20(c_e_h_1, c_r, s16)), inference(lemma,lemma(discharge,[]))).
% 295.71/188.26 tff(32231,plain,
% 295.71/188.26 (~node21(c_e_h_1, c_r, s16, s17)),
% 295.71/188.26 inference(unit_resolution,[status(thm)],[32230, 32216, 32224])).
% 295.71/188.26 tff(32232,plain,
% 295.71/188.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s16, s17)) | node21(c_e_h_1, c_r, s16, s17) | node22(c_e_h_1, c_r, s16, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s16, s17)) | node21(c_e_h_1, c_r, s16, s17) | node22(c_e_h_1, c_r, s16, s17))),
% 295.71/188.26 inference(rewrite,[status(thm)],[])).
% 295.71/188.26 tff(32233,plain,
% 295.71/188.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s16, s17)) | node21(c_e_h_1, c_r, s16, s17) | node22(c_e_h_1, c_r, s16, s17))),
% 295.71/188.26 inference(quant_inst,[status(thm)],[])).
% 295.71/188.26 tff(32234,plain,
% 295.71/188.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s16, s17)) | node21(c_e_h_1, c_r, s16, s17) | node22(c_e_h_1, c_r, s16, s17)),
% 295.71/188.26 inference(modus_ponens,[status(thm)],[32233, 32232])).
% 295.71/188.26 tff(32235,plain,
% 295.71/188.26 (node21(c_e_h_1, c_r, s16, s17) | node22(c_e_h_1, c_r, s16, s17)),
% 295.71/188.26 inference(unit_resolution,[status(thm)],[32234, 82, 11967])).
% 295.71/188.26 tff(32236,plain,
% 295.71/188.26 ($false),
% 295.71/188.26 inference(unit_resolution,[status(thm)],[32235, 32231, 32223])).
% 295.71/188.26 tff(32237,plain,((~m_and_h_gate_v_out(c_e_h_1, c_r, s17)) | node20(c_e_h_1, c_r, s16) | m_and_h_gate_v_out(c_e_h_1, c_r, s16)), inference(lemma,lemma(discharge,[]))).
% 295.71/188.26 tff(32238,plain,
% 295.71/188.26 (~m_and_h_gate_v_out(c_e_h_1, c_r, s17)),
% 295.71/188.26 inference(unit_resolution,[status(thm)],[32237, 32214, 32202])).
% 295.71/188.26 tff(32239,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s18)), introduced(assumption)).
% 295.71/188.26 tff(32240,assumption,(~node20(c_e_h_1, c_r, s17)), introduced(assumption)).
% 295.71/188.26 tff(32241,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s17)), introduced(assumption)).
% 295.71/188.26 tff(32242,assumption,(node22(c_e_h_1, c_r, s17, s18)), introduced(assumption)).
% 295.71/188.26 tff(32243,plain,
% 295.71/188.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s18)) | (~node22(c_e_h_1, c_r, s17, s18)) | m_and_h_gate_v_out(c_e_h_1, c_r, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s18)) | (~node22(c_e_h_1, c_r, s17, s18)) | m_and_h_gate_v_out(c_e_h_1, c_r, s17))),
% 295.71/188.26 inference(rewrite,[status(thm)],[])).
% 295.71/188.26 tff(32244,plain,
% 295.71/188.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s18)) | (~node22(c_e_h_1, c_r, s17, s18)) | m_and_h_gate_v_out(c_e_h_1, c_r, s17))),
% 295.71/188.26 inference(quant_inst,[status(thm)],[])).
% 295.71/188.26 tff(32245,plain,
% 295.71/188.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s18)) | (~node22(c_e_h_1, c_r, s17, s18)) | m_and_h_gate_v_out(c_e_h_1, c_r, s17)),
% 295.71/188.26 inference(modus_ponens,[status(thm)],[32244, 32243])).
% 295.71/188.26 tff(32246,plain,
% 295.71/188.26 ($false),
% 295.71/188.26 inference(unit_resolution,[status(thm)],[32245, 108, 32242, 32241, 32239])).
% 295.71/188.26 tff(32247,plain,((~node22(c_e_h_1, c_r, s17, s18)) | m_and_h_gate_v_out(c_e_h_1, c_r, s17) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s18))), inference(lemma,lemma(discharge,[]))).
% 295.71/188.26 tff(32248,plain,
% 295.71/188.26 (~node22(c_e_h_1, c_r, s17, s18)),
% 295.71/188.26 inference(unit_resolution,[status(thm)],[32247, 32239, 32241])).
% 295.71/188.26 tff(32249,plain,
% 295.71/188.26 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s17, s18)) | node21(c_e_h_1, c_r, s17, s18) | node22(c_e_h_1, c_r, s17, s18))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s17, s18)) | node21(c_e_h_1, c_r, s17, s18) | node22(c_e_h_1, c_r, s17, s18))),
% 295.71/188.26 inference(rewrite,[status(thm)],[])).
% 295.71/188.26 tff(32250,plain,
% 295.71/188.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s17, s18)) | node21(c_e_h_1, c_r, s17, s18) | node22(c_e_h_1, c_r, s17, s18))),
% 295.71/188.26 inference(quant_inst,[status(thm)],[])).
% 295.71/188.26 tff(32251,plain,
% 295.71/188.26 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s17, s18)) | node21(c_e_h_1, c_r, s17, s18) | node22(c_e_h_1, c_r, s17, s18)),
% 295.71/188.27 inference(modus_ponens,[status(thm)],[32250, 32249])).
% 295.71/188.27 tff(32252,plain,
% 295.71/188.27 (node21(c_e_h_1, c_r, s17, s18) | node22(c_e_h_1, c_r, s17, s18)),
% 295.71/188.27 inference(unit_resolution,[status(thm)],[32251, 82, 26135])).
% 295.71/188.27 tff(32253,plain,
% 295.71/188.27 (node21(c_e_h_1, c_r, s17, s18)),
% 295.71/188.27 inference(unit_resolution,[status(thm)],[32252, 32248])).
% 295.71/188.27 tff(32254,plain,
% 295.71/188.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s18)) | node20(c_e_h_1, c_r, s17) | (~node21(c_e_h_1, c_r, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s18)) | node20(c_e_h_1, c_r, s17) | (~node21(c_e_h_1, c_r, s17, s18)))),
% 295.71/188.27 inference(rewrite,[status(thm)],[])).
% 295.71/188.27 tff(32255,plain,
% 295.71/188.27 ((node20(c_e_h_1, c_r, s17) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s18)) | (~node21(c_e_h_1, c_r, s17, s18))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_r, s18)) | node20(c_e_h_1, c_r, s17) | (~node21(c_e_h_1, c_r, s17, s18)))),
% 295.71/188.27 inference(rewrite,[status(thm)],[])).
% 295.71/188.27 tff(32256,plain,
% 295.71/188.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s17) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s18)) | (~node21(c_e_h_1, c_r, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s18)) | node20(c_e_h_1, c_r, s17) | (~node21(c_e_h_1, c_r, s17, s18))))),
% 295.71/188.27 inference(monotonicity,[status(thm)],[32255])).
% 295.71/188.27 tff(32257,plain,
% 295.71/188.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s17) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s18)) | (~node21(c_e_h_1, c_r, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s18)) | node20(c_e_h_1, c_r, s17) | (~node21(c_e_h_1, c_r, s17, s18)))),
% 295.71/188.27 inference(transitivity,[status(thm)],[32256, 32254])).
% 295.71/188.27 tff(32258,plain,
% 295.71/188.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s17) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s18)) | (~node21(c_e_h_1, c_r, s17, s18)))),
% 295.71/188.27 inference(quant_inst,[status(thm)],[])).
% 295.71/188.27 tff(32259,plain,
% 295.71/188.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s18)) | node20(c_e_h_1, c_r, s17) | (~node21(c_e_h_1, c_r, s17, s18))),
% 295.71/188.27 inference(modus_ponens,[status(thm)],[32258, 32257])).
% 295.71/188.27 tff(32260,plain,
% 295.71/188.27 ($false),
% 295.71/188.27 inference(unit_resolution,[status(thm)],[32259, 52, 32253, 32240, 32239])).
% 295.71/188.27 tff(32261,plain,((~m_and_h_gate_v_out(c_e_h_1, c_r, s18)) | node20(c_e_h_1, c_r, s17) | m_and_h_gate_v_out(c_e_h_1, c_r, s17)), inference(lemma,lemma(discharge,[]))).
% 295.71/188.27 tff(32262,plain,
% 295.71/188.27 (~m_and_h_gate_v_out(c_e_h_1, c_r, s18)),
% 295.71/188.27 inference(unit_resolution,[status(thm)],[32261, 32238, 31893])).
% 295.71/188.27 tff(32263,assumption,(~node20(c_e_h_1, c_r, s18)), introduced(assumption)).
% 295.71/188.27 tff(32264,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s19)), introduced(assumption)).
% 295.71/188.27 tff(32265,assumption,(node21(c_e_h_1, c_r, s18, s19)), introduced(assumption)).
% 295.71/188.27 tff(32266,plain,
% 295.71/188.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s18) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s19)) | (~node21(c_e_h_1, c_r, s18, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s18) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s19)) | (~node21(c_e_h_1, c_r, s18, s19)))),
% 295.71/188.27 inference(rewrite,[status(thm)],[])).
% 295.71/188.27 tff(32267,plain,
% 295.71/188.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s18) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s19)) | (~node21(c_e_h_1, c_r, s18, s19)))),
% 295.71/188.27 inference(quant_inst,[status(thm)],[])).
% 295.71/188.27 tff(32268,plain,
% 295.71/188.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s18) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s19)) | (~node21(c_e_h_1, c_r, s18, s19))),
% 295.71/188.27 inference(modus_ponens,[status(thm)],[32267, 32266])).
% 295.71/188.27 tff(32269,plain,
% 295.71/188.27 ($false),
% 295.71/188.27 inference(unit_resolution,[status(thm)],[32268, 52, 32265, 32264, 32263])).
% 295.71/188.27 tff(32270,plain,((~node21(c_e_h_1, c_r, s18, s19)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s19)) | node20(c_e_h_1, c_r, s18)), inference(lemma,lemma(discharge,[]))).
% 295.71/188.27 tff(32271,plain,
% 295.71/188.27 (~node21(c_e_h_1, c_r, s18, s19)),
% 295.71/188.27 inference(unit_resolution,[status(thm)],[32270, 32264, 32263])).
% 295.71/188.27 tff(32272,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s18)), introduced(assumption)).
% 295.71/188.27 tff(32273,assumption,(node22(c_e_h_1, c_r, s18, s19)), introduced(assumption)).
% 295.71/188.27 tff(32274,plain,
% 295.71/188.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s19)) | (~node22(c_e_h_1, c_r, s18, s19)) | m_and_h_gate_v_out(c_e_h_1, c_r, s18))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s19)) | (~node22(c_e_h_1, c_r, s18, s19)) | m_and_h_gate_v_out(c_e_h_1, c_r, s18))),
% 295.71/188.27 inference(rewrite,[status(thm)],[])).
% 295.71/188.27 tff(32275,plain,
% 295.71/188.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s19)) | (~node22(c_e_h_1, c_r, s18, s19)) | m_and_h_gate_v_out(c_e_h_1, c_r, s18))),
% 295.71/188.27 inference(quant_inst,[status(thm)],[])).
% 295.71/188.27 tff(32276,plain,
% 295.71/188.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s19)) | (~node22(c_e_h_1, c_r, s18, s19)) | m_and_h_gate_v_out(c_e_h_1, c_r, s18)),
% 295.71/188.27 inference(modus_ponens,[status(thm)],[32275, 32274])).
% 295.71/188.27 tff(32277,plain,
% 295.71/188.27 ($false),
% 295.71/188.27 inference(unit_resolution,[status(thm)],[32276, 108, 32273, 32272, 32264])).
% 295.71/188.27 tff(32278,plain,((~node22(c_e_h_1, c_r, s18, s19)) | m_and_h_gate_v_out(c_e_h_1, c_r, s18) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s19))), inference(lemma,lemma(discharge,[]))).
% 295.71/188.27 tff(32279,plain,
% 295.71/188.27 (~node22(c_e_h_1, c_r, s18, s19)),
% 295.71/188.27 inference(unit_resolution,[status(thm)],[32278, 32264, 32272])).
% 295.71/188.27 tff(32280,plain,
% 295.71/188.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s18, s19)) | node21(c_e_h_1, c_r, s18, s19) | node22(c_e_h_1, c_r, s18, s19))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s18, s19)) | node21(c_e_h_1, c_r, s18, s19) | node22(c_e_h_1, c_r, s18, s19))),
% 295.71/188.27 inference(rewrite,[status(thm)],[])).
% 295.71/188.27 tff(32281,plain,
% 295.71/188.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s18, s19)) | node21(c_e_h_1, c_r, s18, s19) | node22(c_e_h_1, c_r, s18, s19))),
% 295.71/188.27 inference(quant_inst,[status(thm)],[])).
% 295.71/188.27 tff(32282,plain,
% 295.71/188.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s18, s19)) | node21(c_e_h_1, c_r, s18, s19) | node22(c_e_h_1, c_r, s18, s19)),
% 295.71/188.27 inference(modus_ponens,[status(thm)],[32281, 32280])).
% 295.71/188.27 tff(32283,plain,
% 295.71/188.27 (node21(c_e_h_1, c_r, s18, s19) | node22(c_e_h_1, c_r, s18, s19)),
% 295.71/188.27 inference(unit_resolution,[status(thm)],[32282, 82, 26787])).
% 295.71/188.27 tff(32284,plain,
% 295.71/188.27 ($false),
% 295.71/188.27 inference(unit_resolution,[status(thm)],[32283, 32279, 32271])).
% 295.71/188.27 tff(32285,plain,((~m_and_h_gate_v_out(c_e_h_1, c_r, s19)) | m_and_h_gate_v_out(c_e_h_1, c_r, s18) | node20(c_e_h_1, c_r, s18)), inference(lemma,lemma(discharge,[]))).
% 295.71/188.27 tff(32286,plain,
% 295.71/188.27 ((~m_and_h_gate_v_out(c_e_h_1, c_r, s19)) | node20(c_e_h_1, c_r, s18)),
% 295.71/188.27 inference(unit_resolution,[status(thm)],[32285, 32262])).
% 295.71/188.27 tff(32287,plain,
% 295.71/188.27 (~m_and_h_gate_v_out(c_e_h_1, c_r, s19)),
% 295.71/188.27 inference(unit_resolution,[status(thm)],[32286, 31878])).
% 295.71/188.27 tff(32288,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s20)), introduced(assumption)).
% 295.71/188.27 tff(32289,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s19)), introduced(assumption)).
% 295.71/188.27 tff(32290,assumption,(~node20(c_e_h_1, c_r, s19)), introduced(assumption)).
% 295.71/188.27 tff(32291,assumption,(node21(c_e_h_1, c_r, s19, s20)), introduced(assumption)).
% 295.71/188.27 tff(32292,plain,
% 295.71/188.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s20)) | node20(c_e_h_1, c_r, s19) | (~node21(c_e_h_1, c_r, s19, s20)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s20)) | node20(c_e_h_1, c_r, s19) | (~node21(c_e_h_1, c_r, s19, s20)))),
% 295.71/188.27 inference(rewrite,[status(thm)],[])).
% 295.71/188.27 tff(32293,plain,
% 295.71/188.27 ((node20(c_e_h_1, c_r, s19) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s20)) | (~node21(c_e_h_1, c_r, s19, s20))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_r, s20)) | node20(c_e_h_1, c_r, s19) | (~node21(c_e_h_1, c_r, s19, s20)))),
% 295.71/188.27 inference(rewrite,[status(thm)],[])).
% 295.71/188.27 tff(32294,plain,
% 295.71/188.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s19) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s20)) | (~node21(c_e_h_1, c_r, s19, s20)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s20)) | node20(c_e_h_1, c_r, s19) | (~node21(c_e_h_1, c_r, s19, s20))))),
% 295.71/188.27 inference(monotonicity,[status(thm)],[32293])).
% 295.71/188.27 tff(32295,plain,
% 295.71/188.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s19) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s20)) | (~node21(c_e_h_1, c_r, s19, s20)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s20)) | node20(c_e_h_1, c_r, s19) | (~node21(c_e_h_1, c_r, s19, s20)))),
% 295.71/188.27 inference(transitivity,[status(thm)],[32294, 32292])).
% 295.71/188.27 tff(32296,plain,
% 295.71/188.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s19) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s20)) | (~node21(c_e_h_1, c_r, s19, s20)))),
% 295.71/188.27 inference(quant_inst,[status(thm)],[])).
% 295.71/188.27 tff(32297,plain,
% 295.71/188.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s20)) | node20(c_e_h_1, c_r, s19) | (~node21(c_e_h_1, c_r, s19, s20))),
% 295.71/188.27 inference(modus_ponens,[status(thm)],[32296, 32295])).
% 295.71/188.27 tff(32298,plain,
% 295.71/188.27 ($false),
% 295.71/188.27 inference(unit_resolution,[status(thm)],[32297, 52, 32291, 32288, 32290])).
% 295.71/188.27 tff(32299,plain,((~node21(c_e_h_1, c_r, s19, s20)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s20)) | node20(c_e_h_1, c_r, s19)), inference(lemma,lemma(discharge,[]))).
% 295.71/188.27 tff(32300,plain,
% 295.71/188.27 (~node21(c_e_h_1, c_r, s19, s20)),
% 295.71/188.27 inference(unit_resolution,[status(thm)],[32299, 32288, 32290])).
% 295.71/188.27 tff(32301,plain,
% 295.71/188.27 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s19, s20)) | node21(c_e_h_1, c_r, s19, s20) | node22(c_e_h_1, c_r, s19, s20))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s19, s20)) | node21(c_e_h_1, c_r, s19, s20) | node22(c_e_h_1, c_r, s19, s20))),
% 295.71/188.27 inference(rewrite,[status(thm)],[])).
% 295.71/188.27 tff(32302,plain,
% 295.71/188.27 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s19, s20)) | node21(c_e_h_1, c_r, s19, s20) | node22(c_e_h_1, c_r, s19, s20))),
% 295.71/188.28 inference(quant_inst,[status(thm)],[])).
% 295.71/188.28 tff(32303,plain,
% 295.71/188.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s19, s20)) | node21(c_e_h_1, c_r, s19, s20) | node22(c_e_h_1, c_r, s19, s20)),
% 295.71/188.28 inference(modus_ponens,[status(thm)],[32302, 32301])).
% 295.71/188.28 tff(32304,plain,
% 295.71/188.28 (node21(c_e_h_1, c_r, s19, s20) | node22(c_e_h_1, c_r, s19, s20)),
% 295.71/188.28 inference(unit_resolution,[status(thm)],[32303, 82, 29925])).
% 295.71/188.28 tff(32305,plain,
% 295.71/188.28 (node22(c_e_h_1, c_r, s19, s20)),
% 295.71/188.28 inference(unit_resolution,[status(thm)],[32304, 32300])).
% 295.71/188.28 tff(32306,plain,
% 295.71/188.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s20)) | (~node22(c_e_h_1, c_r, s19, s20)) | m_and_h_gate_v_out(c_e_h_1, c_r, s19))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s20)) | (~node22(c_e_h_1, c_r, s19, s20)) | m_and_h_gate_v_out(c_e_h_1, c_r, s19))),
% 295.71/188.28 inference(rewrite,[status(thm)],[])).
% 295.71/188.28 tff(32307,plain,
% 295.71/188.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s20)) | (~node22(c_e_h_1, c_r, s19, s20)) | m_and_h_gate_v_out(c_e_h_1, c_r, s19))),
% 295.71/188.28 inference(quant_inst,[status(thm)],[])).
% 295.71/188.28 tff(32308,plain,
% 295.71/188.28 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s20)) | (~node22(c_e_h_1, c_r, s19, s20)) | m_and_h_gate_v_out(c_e_h_1, c_r, s19)),
% 295.71/188.28 inference(modus_ponens,[status(thm)],[32307, 32306])).
% 295.71/188.28 tff(32309,plain,
% 295.71/188.28 ($false),
% 295.71/188.28 inference(unit_resolution,[status(thm)],[32308, 108, 32305, 32289, 32288])).
% 295.71/188.28 tff(32310,plain,((~m_and_h_gate_v_out(c_e_h_1, c_r, s20)) | m_and_h_gate_v_out(c_e_h_1, c_r, s19) | node20(c_e_h_1, c_r, s19)), inference(lemma,lemma(discharge,[]))).
% 295.71/188.28 tff(32311,plain,
% 295.71/188.28 ((~m_and_h_gate_v_out(c_e_h_1, c_r, s20)) | node20(c_e_h_1, c_r, s19)),
% 295.71/188.28 inference(unit_resolution,[status(thm)],[32310, 32287])).
% 295.71/188.28 tff(32312,plain,
% 295.71/188.28 (~m_and_h_gate_v_out(c_e_h_1, c_r, s20)),
% 295.71/188.28 inference(unit_resolution,[status(thm)],[32311, 31870])).
% 295.71/188.28 tff(32313,plain,
% 295.71/188.28 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s17)),
% 295.71/188.28 inference(unit_resolution,[status(thm)],[30387, 26118])).
% 295.71/188.28 tff(32314,plain,
% 295.71/188.28 (~m_c_h_element_v_in2(c_e_h_1, c_e, s17)),
% 295.71/188.28 inference(unit_resolution,[status(thm)],[26116, 26111])).
% 295.71/188.28 tff(32315,plain,
% 295.71/188.28 (~m_c_h_element_v_out(c_e_h_1, c_e, s18)),
% 295.71/188.28 inference(unit_resolution,[status(thm)],[26203, 32314, 26118])).
% 295.71/188.28 tff(32316,plain,
% 295.71/188.28 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s18)),
% 295.71/188.28 inference(unit_resolution,[status(thm)],[31212, 32315])).
% 295.71/188.28 tff(32317,plain,
% 295.71/188.28 (~m_and_h_gate_v_out(c_e_h_1, c_i, s18)),
% 295.71/188.28 inference(unit_resolution,[status(thm)],[26759, 26111, 26741])).
% 295.71/188.28 tff(32318,plain,
% 295.71/188.28 (~m_c_h_element_v_in2(c_e_h_1, c_e, s18)),
% 295.71/188.28 inference(unit_resolution,[status(thm)],[26767, 32317])).
% 295.71/188.28 tff(32319,plain,
% 295.71/188.28 (~m_c_h_element_v_out(c_e_h_1, c_e, s19)),
% 295.71/188.28 inference(unit_resolution,[status(thm)],[26861, 32318, 32315])).
% 295.71/188.28 tff(32320,plain,
% 295.71/188.28 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s19)),
% 295.71/188.28 inference(unit_resolution,[status(thm)],[31294, 32319])).
% 295.71/188.28 tff(32321,plain,
% 295.71/188.28 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s20)),
% 295.71/188.28 inference(unit_resolution,[status(thm)],[31289, 32320, 30394, 31207, 32316, 30162, 32313])).
% 295.71/188.28 tff(32322,plain,
% 295.71/188.28 (~m_c_h_element_v_in2(c_e_h_1, c_e, s18)),
% 295.71/188.28 inference(unit_resolution,[status(thm)],[26767, 26761])).
% 295.71/188.28 tff(32323,plain,
% 295.71/188.28 (~m_c_h_element_v_out(c_e_h_1, c_e, s19)),
% 295.71/188.28 inference(unit_resolution,[status(thm)],[26861, 32322, 26770])).
% 295.71/188.28 tff(32324,plain,
% 295.71/188.28 (~m_and_h_gate_v_out(c_e_h_1, c_i, s19)),
% 295.71/188.28 inference(unit_resolution,[status(thm)],[30014, 26761, 29993])).
% 295.71/188.28 tff(32325,plain,
% 295.71/188.28 (~m_c_h_element_v_in2(c_e_h_1, c_e, s19)),
% 295.71/188.28 inference(unit_resolution,[status(thm)],[30699, 32324])).
% 295.71/188.28 tff(32326,plain,
% 295.71/188.28 ($false),
% 295.71/188.28 inference(unit_resolution,[status(thm)],[30777, 32325, 32323, 30702])).
% 295.71/188.28 tff(32327,plain,(m_and_h_gate_v_out(c_e_h_1, c_i, s18) | (~m_c_h_element_v_out(c_e_h_1, c_e, s20)) | m_c_h_element_v_out(c_e_h_1, c_e, s18) | node20(c_e_h_1, c_i, s18)), inference(lemma,lemma(discharge,[]))).
% 295.71/188.28 tff(32328,plain,
% 295.71/188.28 (~m_c_h_element_v_out(c_e_h_1, c_e, s20)),
% 295.71/188.28 inference(unit_resolution,[status(thm)],[32327, 32317, 29993, 32315])).
% 295.71/188.28 tff(32329,plain,
% 295.71/188.28 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s20)),
% 295.71/188.28 inference(unit_resolution,[status(thm)],[31202, 32328])).
% 295.71/188.28 tff(32330,plain,
% 295.71/188.28 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s18)),
% 295.71/188.28 inference(unit_resolution,[status(thm)],[30423, 31238, 30394, 32313])).
% 295.71/188.28 tff(32331,plain,
% 295.71/188.28 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s18)),
% 295.71/188.28 inference(unit_resolution,[status(thm)],[30429, 4958, 32330])).
% 295.71/188.28 tff(32332,plain,
% 295.71/188.28 (~node9(c_e_h_1, c_m, s18)),
% 295.71/188.28 inference(unit_resolution,[status(thm)],[30433, 4972, 32331])).
% 295.71/188.28 tff(32333,plain,
% 295.71/188.28 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s19)),
% 295.71/188.28 inference(unit_resolution,[status(thm)],[30457, 32332, 31207])).
% 295.71/188.28 tff(32334,plain,
% 295.71/188.28 (~m_c_h_element_v_out(c_e_h_1, c_e, s18)),
% 295.71/188.28 inference(unit_resolution,[status(thm)],[26203, 26118, 26194])).
% 295.71/188.28 tff(32335,plain,
% 295.71/188.28 (~m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s18)),
% 295.71/188.28 inference(unit_resolution,[status(thm)],[31247, 32313, 30394, 30162, 31216])).
% 295.71/188.28 tff(32336,plain,
% 295.71/188.28 ($false),
% 295.71/188.28 inference(unit_resolution,[status(thm)],[31212, 32335, 32334])).
% 295.71/188.28 tff(32337,plain,(m_c_h_element_v_out(c_e_h_1, c_e, s17) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17) | m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s19) | m_c_h_element_v_in2(c_e_h_1, c_e, s17)), inference(lemma,lemma(discharge,[]))).
% 295.71/188.28 tff(32338,plain,
% 295.71/188.28 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s19)),
% 295.71/188.28 inference(unit_resolution,[status(thm)],[32337, 32314, 30394, 26118, 30162])).
% 295.71/188.28 tff(32339,plain,
% 295.71/188.28 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s19)),
% 295.71/188.28 inference(unit_resolution,[status(thm)],[31306, 4958, 32338])).
% 295.71/188.28 tff(32340,plain,
% 295.71/188.28 (~node9(c_e_h_1, c_m, s19)),
% 295.71/188.28 inference(unit_resolution,[status(thm)],[31310, 4972, 32339])).
% 295.71/188.28 tff(32341,plain,
% 295.71/188.28 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s20)),
% 295.71/188.28 inference(unit_resolution,[status(thm)],[31336, 32340, 32333])).
% 295.71/188.28 tff(32342,plain,
% 295.71/188.28 (m_and_h_gate_h_init_v_in2(c_e_h_1, c_n, s20)),
% 295.71/188.28 inference(unit_resolution,[status(thm)],[31396, 32341])).
% 295.71/188.28 tff(32343,plain,
% 295.71/188.28 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s21)),
% 295.71/188.28 inference(unit_resolution,[status(thm)],[31425, 32342, 32329, 32321])).
% 295.71/188.28 tff(32344,plain,
% 295.71/188.28 (~m_c_h_element_v_out(c_e_h_1, c_e, s21)),
% 295.71/188.28 inference(unit_resolution,[status(thm)],[30862, 32328, 30807])).
% 295.71/188.28 tff(32345,plain,
% 295.71/188.28 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s21)),
% 295.71/188.28 inference(unit_resolution,[status(thm)],[31197, 32344])).
% 295.71/188.28 tff(32346,plain,
% 295.71/188.28 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s20)),
% 295.71/188.28 inference(unit_resolution,[status(thm)],[31350, 4958, 32321])).
% 295.71/188.28 tff(32347,plain,
% 295.71/188.28 (~node9(c_e_h_1, c_m, s20)),
% 295.71/188.28 inference(unit_resolution,[status(thm)],[31354, 4972, 32346])).
% 295.71/188.28 tff(32348,plain,
% 295.71/188.28 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s21)),
% 295.71/188.28 inference(unit_resolution,[status(thm)],[31381, 32341, 32347])).
% 295.71/188.28 tff(32349,plain,
% 295.71/188.28 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s23)),
% 295.71/188.28 inference(unit_resolution,[status(thm)],[31522, 32348, 32345, 32343])).
% 295.71/188.28 tff(32350,plain,
% 295.71/188.28 (~m_c_h_element_v_out(c_e_h_1, c_e, s22)),
% 295.71/188.28 inference(unit_resolution,[status(thm)],[30948, 32344, 30912])).
% 295.71/188.28 tff(32351,plain,
% 295.71/188.28 (m_and_h_gate_h_init_v_in1(c_e_h_1, c_n, s22)),
% 295.71/188.28 inference(unit_resolution,[status(thm)],[31346, 32350])).
% 295.71/188.28 tff(32352,plain,
% 295.71/188.28 (m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s23)),
% 295.71/188.28 inference(unit_resolution,[status(thm)],[31571, 32341, 32351, 32321, 32329, 32345])).
% 295.71/188.28 tff(32353,plain,
% 295.71/188.28 (~m_and_h_gate_h_init_v_in2(c_e_h_1, c_m, s23)),
% 295.71/188.28 inference(unit_resolution,[status(thm)],[31670, 4958, 32352])).
% 295.71/188.28 tff(32354,plain,
% 295.71/188.28 (~node9(c_e_h_1, c_m, s23)),
% 295.71/188.28 inference(unit_resolution,[status(thm)],[31674, 4972, 32353])).
% 295.71/188.28 tff(32355,plain,
% 295.71/188.28 (~m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s24)),
% 295.71/188.28 inference(unit_resolution,[status(thm)],[31666, 32354, 32349])).
% 295.71/188.28 tff(32356,plain,
% 295.71/188.28 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s24)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s24))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s24)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s24))),
% 295.71/188.28 inference(rewrite,[status(thm)],[])).
% 295.71/188.28 tff(32357,plain,
% 295.71/188.28 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s24)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s24))),
% 295.71/188.28 inference(quant_inst,[status(thm)],[])).
% 295.71/188.28 tff(32358,plain,
% 295.71/188.28 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s24)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s24)),
% 295.71/188.28 inference(modus_ponens,[status(thm)],[32357, 32356])).
% 295.71/188.28 tff(32359,plain,
% 295.71/188.28 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s24)),
% 295.71/188.28 inference(unit_resolution,[status(thm)],[32358, 14293, 32355])).
% 295.71/188.28 tff(32360,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s25)), introduced(assumption)).
% 295.71/188.28 tff(32361,assumption,(~node20(c_e_h_1, c_r, s22)), introduced(assumption)).
% 295.71/188.28 tff(32362,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s20)), introduced(assumption)).
% 295.71/188.28 tff(32363,plain,
% 295.71/188.28 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_r, s20)) | m_c_h_element_v_out(c_e_h_1, c_e, s20))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_r, s20)) | m_c_h_element_v_out(c_e_h_1, c_e, s20))),
% 295.71/188.28 inference(rewrite,[status(thm)],[])).
% 295.71/188.28 tff(32364,plain,
% 295.71/188.28 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_r, s20)) | m_c_h_element_v_out(c_e_h_1, c_e, s20))),
% 295.71/188.28 inference(quant_inst,[status(thm)],[])).
% 295.71/188.28 tff(32365,plain,
% 295.71/188.28 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_r, s20)) | m_c_h_element_v_out(c_e_h_1, c_e, s20)),
% 295.71/188.28 inference(modus_ponens,[status(thm)],[32364, 32363])).
% 295.71/188.28 tff(32366,plain,
% 295.71/188.28 (~m_and_h_gate_v_in1(c_e_h_1, c_r, s20)),
% 295.71/188.28 inference(unit_resolution,[status(thm)],[32365, 24, 32328])).
% 295.71/188.28 tff(32367,plain,
% 295.71/188.28 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s20)) | m_and_h_gate_v_in1(c_e_h_1, c_r, s20))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_r, s20)) | m_and_h_gate_v_in1(c_e_h_1, c_r, s20))),
% 295.71/188.28 inference(rewrite,[status(thm)],[])).
% 295.71/188.28 tff(32368,plain,
% 295.71/188.28 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s20)) | m_and_h_gate_v_in1(c_e_h_1, c_r, s20))),
% 295.71/188.28 inference(quant_inst,[status(thm)],[])).
% 295.71/188.28 tff(32369,plain,
% 295.71/188.28 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_r, s20)) | m_and_h_gate_v_in1(c_e_h_1, c_r, s20)),
% 295.71/188.28 inference(modus_ponens,[status(thm)],[32368, 32367])).
% 295.71/188.28 tff(32370,plain,
% 295.71/188.28 (~node20(c_e_h_1, c_r, s20)),
% 295.71/188.28 inference(unit_resolution,[status(thm)],[32369, 38, 32366])).
% 295.71/188.28 tff(32371,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s21)), introduced(assumption)).
% 295.71/188.28 tff(32372,assumption,(node22(c_e_h_1, c_r, s20, s21)), introduced(assumption)).
% 295.71/188.28 tff(32373,plain,
% 295.71/188.28 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s21)) | (~node22(c_e_h_1, c_r, s20, s21)) | m_and_h_gate_v_out(c_e_h_1, c_r, s20))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s21)) | (~node22(c_e_h_1, c_r, s20, s21)) | m_and_h_gate_v_out(c_e_h_1, c_r, s20))),
% 295.71/188.29 inference(rewrite,[status(thm)],[])).
% 295.71/188.29 tff(32374,plain,
% 295.71/188.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s21)) | (~node22(c_e_h_1, c_r, s20, s21)) | m_and_h_gate_v_out(c_e_h_1, c_r, s20))),
% 295.71/188.29 inference(quant_inst,[status(thm)],[])).
% 295.71/188.29 tff(32375,plain,
% 295.71/188.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s21)) | (~node22(c_e_h_1, c_r, s20, s21)) | m_and_h_gate_v_out(c_e_h_1, c_r, s20)),
% 295.71/188.29 inference(modus_ponens,[status(thm)],[32374, 32373])).
% 295.71/188.29 tff(32376,plain,
% 295.71/188.29 ($false),
% 295.71/188.29 inference(unit_resolution,[status(thm)],[32375, 108, 32362, 32372, 32371])).
% 295.71/188.29 tff(32377,plain,((~node22(c_e_h_1, c_r, s20, s21)) | m_and_h_gate_v_out(c_e_h_1, c_r, s20) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s21))), inference(lemma,lemma(discharge,[]))).
% 295.71/188.29 tff(32378,plain,
% 295.71/188.29 (~node22(c_e_h_1, c_r, s20, s21)),
% 295.71/188.29 inference(unit_resolution,[status(thm)],[32377, 32371, 32362])).
% 295.71/188.29 tff(32379,assumption,(~node20(c_e_h_1, c_r, s20)), introduced(assumption)).
% 295.71/188.29 tff(32380,assumption,(node21(c_e_h_1, c_r, s20, s21)), introduced(assumption)).
% 295.71/188.29 tff(32381,plain,
% 295.71/188.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s20) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s21)) | (~node21(c_e_h_1, c_r, s20, s21)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s20) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s21)) | (~node21(c_e_h_1, c_r, s20, s21)))),
% 295.71/188.29 inference(rewrite,[status(thm)],[])).
% 295.71/188.29 tff(32382,plain,
% 295.71/188.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s20) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s21)) | (~node21(c_e_h_1, c_r, s20, s21)))),
% 295.71/188.29 inference(quant_inst,[status(thm)],[])).
% 295.71/188.29 tff(32383,plain,
% 295.71/188.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s20) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s21)) | (~node21(c_e_h_1, c_r, s20, s21))),
% 295.71/188.29 inference(modus_ponens,[status(thm)],[32382, 32381])).
% 295.71/188.29 tff(32384,plain,
% 295.71/188.29 ($false),
% 295.71/188.29 inference(unit_resolution,[status(thm)],[32383, 52, 32380, 32379, 32371])).
% 295.71/188.29 tff(32385,plain,((~node21(c_e_h_1, c_r, s20, s21)) | node20(c_e_h_1, c_r, s20) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s21))), inference(lemma,lemma(discharge,[]))).
% 295.71/188.29 tff(32386,plain,
% 295.71/188.29 (~node21(c_e_h_1, c_r, s20, s21)),
% 295.71/188.29 inference(unit_resolution,[status(thm)],[32385, 32371, 32379])).
% 295.71/188.29 tff(32387,plain,
% 295.71/188.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s20, s21)) | node21(c_e_h_1, c_r, s20, s21) | node22(c_e_h_1, c_r, s20, s21))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s20, s21)) | node21(c_e_h_1, c_r, s20, s21) | node22(c_e_h_1, c_r, s20, s21))),
% 295.71/188.29 inference(rewrite,[status(thm)],[])).
% 295.71/188.29 tff(32388,plain,
% 295.71/188.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s20, s21)) | node21(c_e_h_1, c_r, s20, s21) | node22(c_e_h_1, c_r, s20, s21))),
% 295.71/188.29 inference(quant_inst,[status(thm)],[])).
% 295.71/188.29 tff(32389,plain,
% 295.71/188.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s20, s21)) | node21(c_e_h_1, c_r, s20, s21) | node22(c_e_h_1, c_r, s20, s21)),
% 295.71/188.29 inference(modus_ponens,[status(thm)],[32388, 32387])).
% 295.71/188.29 tff(32390,plain,
% 295.71/188.29 (node21(c_e_h_1, c_r, s20, s21) | node22(c_e_h_1, c_r, s20, s21)),
% 295.71/188.29 inference(unit_resolution,[status(thm)],[32389, 82, 30273])).
% 295.71/188.29 tff(32391,plain,
% 295.71/188.29 ($false),
% 295.71/188.29 inference(unit_resolution,[status(thm)],[32390, 32386, 32378])).
% 295.71/188.29 tff(32392,plain,((~m_and_h_gate_v_out(c_e_h_1, c_r, s21)) | node20(c_e_h_1, c_r, s20) | m_and_h_gate_v_out(c_e_h_1, c_r, s20)), inference(lemma,lemma(discharge,[]))).
% 295.71/188.29 tff(32393,plain,
% 295.71/188.29 (~m_and_h_gate_v_out(c_e_h_1, c_r, s21)),
% 295.71/188.29 inference(unit_resolution,[status(thm)],[32392, 32370, 32362])).
% 295.71/188.29 tff(32394,plain,
% 295.71/188.29 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_r, s21)) | m_c_h_element_v_out(c_e_h_1, c_e, s21))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_r, s21)) | m_c_h_element_v_out(c_e_h_1, c_e, s21))),
% 295.71/188.29 inference(rewrite,[status(thm)],[])).
% 295.71/188.29 tff(32395,plain,
% 295.71/188.29 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_r, s21)) | m_c_h_element_v_out(c_e_h_1, c_e, s21))),
% 295.71/188.29 inference(quant_inst,[status(thm)],[])).
% 295.71/188.29 tff(32396,plain,
% 295.71/188.29 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_r, X)) | m_c_h_element_v_out(I0, c_e, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_r, s21)) | m_c_h_element_v_out(c_e_h_1, c_e, s21)),
% 295.71/188.29 inference(modus_ponens,[status(thm)],[32395, 32394])).
% 295.71/188.29 tff(32397,plain,
% 295.71/188.29 (~m_and_h_gate_v_in1(c_e_h_1, c_r, s21)),
% 295.71/188.29 inference(unit_resolution,[status(thm)],[32396, 24, 32344])).
% 295.71/188.29 tff(32398,plain,
% 295.71/188.29 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s21)) | m_and_h_gate_v_in1(c_e_h_1, c_r, s21))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_r, s21)) | m_and_h_gate_v_in1(c_e_h_1, c_r, s21))),
% 295.71/188.29 inference(rewrite,[status(thm)],[])).
% 295.71/188.29 tff(32399,plain,
% 295.71/188.29 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s21)) | m_and_h_gate_v_in1(c_e_h_1, c_r, s21))),
% 295.71/188.29 inference(quant_inst,[status(thm)],[])).
% 295.71/188.29 tff(32400,plain,
% 295.71/188.29 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_r, s21)) | m_and_h_gate_v_in1(c_e_h_1, c_r, s21)),
% 295.71/188.29 inference(modus_ponens,[status(thm)],[32399, 32398])).
% 295.71/188.29 tff(32401,plain,
% 295.71/188.29 (~node20(c_e_h_1, c_r, s21)),
% 295.71/188.29 inference(unit_resolution,[status(thm)],[32400, 38, 32397])).
% 295.71/188.29 tff(32402,assumption,(~node20(c_e_h_1, c_r, s21)), introduced(assumption)).
% 295.71/188.29 tff(32403,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s21)), introduced(assumption)).
% 295.71/188.29 tff(32404,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s22)), introduced(assumption)).
% 295.71/188.29 tff(32405,assumption,(node22(c_e_h_1, c_r, s21, s22)), introduced(assumption)).
% 295.71/188.29 tff(32406,plain,
% 295.71/188.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s22)) | (~node22(c_e_h_1, c_r, s21, s22)) | m_and_h_gate_v_out(c_e_h_1, c_r, s21))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s22)) | (~node22(c_e_h_1, c_r, s21, s22)) | m_and_h_gate_v_out(c_e_h_1, c_r, s21))),
% 295.71/188.29 inference(rewrite,[status(thm)],[])).
% 295.71/188.29 tff(32407,plain,
% 295.71/188.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s22)) | (~node22(c_e_h_1, c_r, s21, s22)) | m_and_h_gate_v_out(c_e_h_1, c_r, s21))),
% 295.71/188.29 inference(quant_inst,[status(thm)],[])).
% 295.71/188.29 tff(32408,plain,
% 295.71/188.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s22)) | (~node22(c_e_h_1, c_r, s21, s22)) | m_and_h_gate_v_out(c_e_h_1, c_r, s21)),
% 295.71/188.29 inference(modus_ponens,[status(thm)],[32407, 32406])).
% 295.71/188.29 tff(32409,plain,
% 295.71/188.29 ($false),
% 295.71/188.29 inference(unit_resolution,[status(thm)],[32408, 108, 32404, 32403, 32405])).
% 295.71/188.29 tff(32410,plain,((~node22(c_e_h_1, c_r, s21, s22)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s22)) | m_and_h_gate_v_out(c_e_h_1, c_r, s21)), inference(lemma,lemma(discharge,[]))).
% 295.71/188.29 tff(32411,plain,
% 295.71/188.29 (~node22(c_e_h_1, c_r, s21, s22)),
% 295.71/188.29 inference(unit_resolution,[status(thm)],[32410, 32404, 32403])).
% 295.71/188.29 tff(32412,plain,
% 295.71/188.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s21, s22)) | node21(c_e_h_1, c_r, s21, s22) | node22(c_e_h_1, c_r, s21, s22))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s21, s22)) | node21(c_e_h_1, c_r, s21, s22) | node22(c_e_h_1, c_r, s21, s22))),
% 295.71/188.29 inference(rewrite,[status(thm)],[])).
% 295.71/188.29 tff(32413,plain,
% 295.71/188.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s21, s22)) | node21(c_e_h_1, c_r, s21, s22) | node22(c_e_h_1, c_r, s21, s22))),
% 295.71/188.29 inference(quant_inst,[status(thm)],[])).
% 295.71/188.29 tff(32414,plain,
% 295.71/188.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s21, s22)) | node21(c_e_h_1, c_r, s21, s22) | node22(c_e_h_1, c_r, s21, s22)),
% 295.71/188.29 inference(modus_ponens,[status(thm)],[32413, 32412])).
% 295.71/188.29 tff(32415,plain,
% 295.71/188.29 (node21(c_e_h_1, c_r, s21, s22) | node22(c_e_h_1, c_r, s21, s22)),
% 295.71/188.29 inference(unit_resolution,[status(thm)],[32414, 82, 30340])).
% 295.71/188.29 tff(32416,plain,
% 295.71/188.29 (node21(c_e_h_1, c_r, s21, s22)),
% 295.71/188.29 inference(unit_resolution,[status(thm)],[32415, 32411])).
% 295.71/188.29 tff(32417,plain,
% 295.71/188.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s22)) | node20(c_e_h_1, c_r, s21) | (~node21(c_e_h_1, c_r, s21, s22)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s22)) | node20(c_e_h_1, c_r, s21) | (~node21(c_e_h_1, c_r, s21, s22)))),
% 295.71/188.29 inference(rewrite,[status(thm)],[])).
% 295.71/188.29 tff(32418,plain,
% 295.71/188.29 ((node20(c_e_h_1, c_r, s21) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s22)) | (~node21(c_e_h_1, c_r, s21, s22))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_r, s22)) | node20(c_e_h_1, c_r, s21) | (~node21(c_e_h_1, c_r, s21, s22)))),
% 295.71/188.29 inference(rewrite,[status(thm)],[])).
% 295.71/188.29 tff(32419,plain,
% 295.71/188.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s21) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s22)) | (~node21(c_e_h_1, c_r, s21, s22)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s22)) | node20(c_e_h_1, c_r, s21) | (~node21(c_e_h_1, c_r, s21, s22))))),
% 295.71/188.29 inference(monotonicity,[status(thm)],[32418])).
% 295.71/188.29 tff(32420,plain,
% 295.71/188.29 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s21) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s22)) | (~node21(c_e_h_1, c_r, s21, s22)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s22)) | node20(c_e_h_1, c_r, s21) | (~node21(c_e_h_1, c_r, s21, s22)))),
% 295.71/188.29 inference(transitivity,[status(thm)],[32419, 32417])).
% 295.71/188.29 tff(32421,plain,
% 295.71/188.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s21) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s22)) | (~node21(c_e_h_1, c_r, s21, s22)))),
% 295.71/188.29 inference(quant_inst,[status(thm)],[])).
% 295.71/188.29 tff(32422,plain,
% 295.71/188.29 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s22)) | node20(c_e_h_1, c_r, s21) | (~node21(c_e_h_1, c_r, s21, s22))),
% 295.80/188.30 inference(modus_ponens,[status(thm)],[32421, 32420])).
% 295.80/188.30 tff(32423,plain,
% 295.80/188.30 ($false),
% 295.80/188.30 inference(unit_resolution,[status(thm)],[32422, 52, 32404, 32416, 32402])).
% 295.80/188.30 tff(32424,plain,((~m_and_h_gate_v_out(c_e_h_1, c_r, s22)) | node20(c_e_h_1, c_r, s21) | m_and_h_gate_v_out(c_e_h_1, c_r, s21)), inference(lemma,lemma(discharge,[]))).
% 295.80/188.30 tff(32425,plain,
% 295.80/188.30 (~m_and_h_gate_v_out(c_e_h_1, c_r, s22)),
% 295.80/188.30 inference(unit_resolution,[status(thm)],[32424, 32401, 32393])).
% 295.80/188.30 tff(32426,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s23)), introduced(assumption)).
% 295.80/188.30 tff(32427,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s22)), introduced(assumption)).
% 295.80/188.30 tff(32428,assumption,(node22(c_e_h_1, c_r, s22, s23)), introduced(assumption)).
% 295.80/188.30 tff(32429,plain,
% 295.80/188.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s23)) | (~node22(c_e_h_1, c_r, s22, s23)) | m_and_h_gate_v_out(c_e_h_1, c_r, s22))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s23)) | (~node22(c_e_h_1, c_r, s22, s23)) | m_and_h_gate_v_out(c_e_h_1, c_r, s22))),
% 295.80/188.30 inference(rewrite,[status(thm)],[])).
% 295.80/188.30 tff(32430,plain,
% 295.80/188.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s23)) | (~node22(c_e_h_1, c_r, s22, s23)) | m_and_h_gate_v_out(c_e_h_1, c_r, s22))),
% 295.80/188.30 inference(quant_inst,[status(thm)],[])).
% 295.80/188.30 tff(32431,plain,
% 295.80/188.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s23)) | (~node22(c_e_h_1, c_r, s22, s23)) | m_and_h_gate_v_out(c_e_h_1, c_r, s22)),
% 295.80/188.30 inference(modus_ponens,[status(thm)],[32430, 32429])).
% 295.80/188.30 tff(32432,plain,
% 295.80/188.30 ($false),
% 295.80/188.30 inference(unit_resolution,[status(thm)],[32431, 108, 32428, 32427, 32426])).
% 295.80/188.30 tff(32433,plain,((~node22(c_e_h_1, c_r, s22, s23)) | m_and_h_gate_v_out(c_e_h_1, c_r, s22) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s23))), inference(lemma,lemma(discharge,[]))).
% 295.80/188.30 tff(32434,plain,
% 295.80/188.30 (~node22(c_e_h_1, c_r, s22, s23)),
% 295.80/188.30 inference(unit_resolution,[status(thm)],[32433, 32426, 32427])).
% 295.80/188.30 tff(32435,plain,
% 295.80/188.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s22, s23)) | node21(c_e_h_1, c_r, s22, s23) | node22(c_e_h_1, c_r, s22, s23))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s22, s23)) | node21(c_e_h_1, c_r, s22, s23) | node22(c_e_h_1, c_r, s22, s23))),
% 295.80/188.30 inference(rewrite,[status(thm)],[])).
% 295.80/188.30 tff(32436,plain,
% 295.80/188.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s22, s23)) | node21(c_e_h_1, c_r, s22, s23) | node22(c_e_h_1, c_r, s22, s23))),
% 295.80/188.30 inference(quant_inst,[status(thm)],[])).
% 295.80/188.30 tff(32437,plain,
% 295.80/188.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s22, s23)) | node21(c_e_h_1, c_r, s22, s23) | node22(c_e_h_1, c_r, s22, s23)),
% 295.80/188.30 inference(modus_ponens,[status(thm)],[32436, 32435])).
% 295.80/188.30 tff(32438,plain,
% 295.80/188.30 (node21(c_e_h_1, c_r, s22, s23) | node22(c_e_h_1, c_r, s22, s23)),
% 295.80/188.30 inference(unit_resolution,[status(thm)],[32437, 82, 30672])).
% 295.80/188.30 tff(32439,plain,
% 295.80/188.30 (node21(c_e_h_1, c_r, s22, s23)),
% 295.80/188.30 inference(unit_resolution,[status(thm)],[32438, 32434])).
% 295.80/188.30 tff(32440,plain,
% 295.80/188.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s22) | (~node21(c_e_h_1, c_r, s22, s23)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s23)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s22) | (~node21(c_e_h_1, c_r, s22, s23)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s23)))),
% 295.80/188.30 inference(rewrite,[status(thm)],[])).
% 295.80/188.30 tff(32441,plain,
% 295.80/188.30 ((node20(c_e_h_1, c_r, s22) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s23)) | (~node21(c_e_h_1, c_r, s22, s23))) <=> (node20(c_e_h_1, c_r, s22) | (~node21(c_e_h_1, c_r, s22, s23)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s23)))),
% 295.80/188.30 inference(rewrite,[status(thm)],[])).
% 295.80/188.30 tff(32442,plain,
% 295.80/188.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s22) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s23)) | (~node21(c_e_h_1, c_r, s22, s23)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s22) | (~node21(c_e_h_1, c_r, s22, s23)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s23))))),
% 295.80/188.30 inference(monotonicity,[status(thm)],[32441])).
% 295.80/188.30 tff(32443,plain,
% 295.80/188.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s22) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s23)) | (~node21(c_e_h_1, c_r, s22, s23)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s22) | (~node21(c_e_h_1, c_r, s22, s23)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s23)))),
% 295.80/188.30 inference(transitivity,[status(thm)],[32442, 32440])).
% 295.80/188.30 tff(32444,plain,
% 295.80/188.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s22) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s23)) | (~node21(c_e_h_1, c_r, s22, s23)))),
% 295.80/188.30 inference(quant_inst,[status(thm)],[])).
% 295.80/188.30 tff(32445,plain,
% 295.80/188.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s22) | (~node21(c_e_h_1, c_r, s22, s23)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s23))),
% 295.80/188.30 inference(modus_ponens,[status(thm)],[32444, 32443])).
% 295.80/188.30 tff(32446,plain,
% 295.80/188.30 ($false),
% 295.80/188.30 inference(unit_resolution,[status(thm)],[32445, 52, 32439, 32361, 32426])).
% 295.80/188.30 tff(32447,plain,((~m_and_h_gate_v_out(c_e_h_1, c_r, s23)) | node20(c_e_h_1, c_r, s22) | m_and_h_gate_v_out(c_e_h_1, c_r, s22)), inference(lemma,lemma(discharge,[]))).
% 295.80/188.30 tff(32448,plain,
% 295.80/188.30 (~m_and_h_gate_v_out(c_e_h_1, c_r, s23)),
% 295.80/188.30 inference(unit_resolution,[status(thm)],[32447, 32425, 32361])).
% 295.80/188.30 tff(32449,plain,
% 295.80/188.30 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s23)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s23))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s23)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s23))),
% 295.80/188.30 inference(rewrite,[status(thm)],[])).
% 295.80/188.30 tff(32450,plain,
% 295.80/188.30 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s23)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s23))),
% 295.80/188.30 inference(quant_inst,[status(thm)],[])).
% 295.80/188.30 tff(32451,plain,
% 295.80/188.30 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s23)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s23)),
% 295.80/188.30 inference(modus_ponens,[status(thm)],[32450, 32449])).
% 295.80/188.30 tff(32452,plain,
% 295.80/188.30 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s23)),
% 295.80/188.30 inference(unit_resolution,[status(thm)],[32451, 14293, 32349])).
% 295.80/188.30 tff(32453,plain,
% 295.80/188.30 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s23)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s23))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s23)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s23))),
% 295.80/188.30 inference(rewrite,[status(thm)],[])).
% 295.80/188.30 tff(32454,plain,
% 295.80/188.30 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s23)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s23))),
% 295.80/188.30 inference(quant_inst,[status(thm)],[])).
% 295.80/188.30 tff(32455,plain,
% 295.80/188.30 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s23)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s23)),
% 295.80/188.30 inference(modus_ponens,[status(thm)],[32454, 32453])).
% 295.80/188.30 tff(32456,plain,
% 295.80/188.30 (~node20(c_e_h_1, c_r, s23)),
% 295.80/188.30 inference(unit_resolution,[status(thm)],[32455, 4563, 32452])).
% 295.80/188.30 tff(32457,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s24)), introduced(assumption)).
% 295.80/188.30 tff(32458,assumption,(~node20(c_e_h_1, c_r, s23)), introduced(assumption)).
% 295.80/188.30 tff(32459,assumption,(node21(c_e_h_1, c_r, s23, s24)), introduced(assumption)).
% 295.80/188.30 tff(32460,plain,
% 295.80/188.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s24)) | node20(c_e_h_1, c_r, s23) | (~node21(c_e_h_1, c_r, s23, s24)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s24)) | node20(c_e_h_1, c_r, s23) | (~node21(c_e_h_1, c_r, s23, s24)))),
% 295.80/188.30 inference(rewrite,[status(thm)],[])).
% 295.80/188.30 tff(32461,plain,
% 295.80/188.30 ((node20(c_e_h_1, c_r, s23) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s24)) | (~node21(c_e_h_1, c_r, s23, s24))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_r, s24)) | node20(c_e_h_1, c_r, s23) | (~node21(c_e_h_1, c_r, s23, s24)))),
% 295.80/188.30 inference(rewrite,[status(thm)],[])).
% 295.80/188.30 tff(32462,plain,
% 295.80/188.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s23) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s24)) | (~node21(c_e_h_1, c_r, s23, s24)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s24)) | node20(c_e_h_1, c_r, s23) | (~node21(c_e_h_1, c_r, s23, s24))))),
% 295.80/188.30 inference(monotonicity,[status(thm)],[32461])).
% 295.80/188.30 tff(32463,plain,
% 295.80/188.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s23) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s24)) | (~node21(c_e_h_1, c_r, s23, s24)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s24)) | node20(c_e_h_1, c_r, s23) | (~node21(c_e_h_1, c_r, s23, s24)))),
% 295.80/188.30 inference(transitivity,[status(thm)],[32462, 32460])).
% 295.80/188.30 tff(32464,plain,
% 295.80/188.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s23) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s24)) | (~node21(c_e_h_1, c_r, s23, s24)))),
% 295.80/188.30 inference(quant_inst,[status(thm)],[])).
% 295.80/188.30 tff(32465,plain,
% 295.80/188.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s24)) | node20(c_e_h_1, c_r, s23) | (~node21(c_e_h_1, c_r, s23, s24))),
% 295.80/188.30 inference(modus_ponens,[status(thm)],[32464, 32463])).
% 295.80/188.30 tff(32466,plain,
% 295.80/188.30 ($false),
% 295.80/188.30 inference(unit_resolution,[status(thm)],[32465, 52, 32459, 32458, 32457])).
% 295.80/188.30 tff(32467,plain,((~node21(c_e_h_1, c_r, s23, s24)) | node20(c_e_h_1, c_r, s23) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s24))), inference(lemma,lemma(discharge,[]))).
% 295.80/188.30 tff(32468,plain,
% 295.80/188.30 (~node21(c_e_h_1, c_r, s23, s24)),
% 295.80/188.30 inference(unit_resolution,[status(thm)],[32467, 32457, 32458])).
% 295.80/188.30 tff(32469,plain,
% 295.80/188.30 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s23, s24)) | node21(c_e_h_1, c_r, s23, s24) | node22(c_e_h_1, c_r, s23, s24))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s23, s24)) | node21(c_e_h_1, c_r, s23, s24) | node22(c_e_h_1, c_r, s23, s24))),
% 295.80/188.30 inference(rewrite,[status(thm)],[])).
% 295.80/188.30 tff(32470,plain,
% 295.80/188.30 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s23, s24)) | node21(c_e_h_1, c_r, s23, s24) | node22(c_e_h_1, c_r, s23, s24))),
% 295.80/188.31 inference(quant_inst,[status(thm)],[])).
% 295.80/188.31 tff(32471,plain,
% 295.80/188.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s23, s24)) | node21(c_e_h_1, c_r, s23, s24) | node22(c_e_h_1, c_r, s23, s24)),
% 295.80/188.31 inference(modus_ponens,[status(thm)],[32470, 32469])).
% 295.80/188.31 tff(32472,plain,
% 295.80/188.31 (node21(c_e_h_1, c_r, s23, s24) | node22(c_e_h_1, c_r, s23, s24)),
% 295.80/188.31 inference(unit_resolution,[status(thm)],[32471, 82, 31066])).
% 295.80/188.31 tff(32473,plain,
% 295.80/188.31 (node22(c_e_h_1, c_r, s23, s24)),
% 295.80/188.31 inference(unit_resolution,[status(thm)],[32472, 32468])).
% 295.80/188.31 tff(32474,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s23)), introduced(assumption)).
% 295.80/188.31 tff(32475,plain,
% 295.80/188.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s24)) | (~node22(c_e_h_1, c_r, s23, s24)) | m_and_h_gate_v_out(c_e_h_1, c_r, s23))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s24)) | (~node22(c_e_h_1, c_r, s23, s24)) | m_and_h_gate_v_out(c_e_h_1, c_r, s23))),
% 295.80/188.31 inference(rewrite,[status(thm)],[])).
% 295.80/188.31 tff(32476,plain,
% 295.80/188.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s24)) | (~node22(c_e_h_1, c_r, s23, s24)) | m_and_h_gate_v_out(c_e_h_1, c_r, s23))),
% 295.80/188.31 inference(quant_inst,[status(thm)],[])).
% 295.80/188.31 tff(32477,plain,
% 295.80/188.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s24)) | (~node22(c_e_h_1, c_r, s23, s24)) | m_and_h_gate_v_out(c_e_h_1, c_r, s23)),
% 295.80/188.31 inference(modus_ponens,[status(thm)],[32476, 32475])).
% 295.80/188.31 tff(32478,plain,
% 295.80/188.31 ($false),
% 295.80/188.31 inference(unit_resolution,[status(thm)],[32477, 108, 32474, 32473, 32457])).
% 295.80/188.31 tff(32479,plain,((~m_and_h_gate_v_out(c_e_h_1, c_r, s24)) | m_and_h_gate_v_out(c_e_h_1, c_r, s23) | node20(c_e_h_1, c_r, s23)), inference(lemma,lemma(discharge,[]))).
% 295.80/188.31 tff(32480,plain,
% 295.80/188.31 (~m_and_h_gate_v_out(c_e_h_1, c_r, s24)),
% 295.80/188.31 inference(unit_resolution,[status(thm)],[32479, 32456, 32448])).
% 295.80/188.31 tff(32481,assumption,(~node20(c_e_h_1, c_r, s24)), introduced(assumption)).
% 295.80/188.31 tff(32482,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s24)), introduced(assumption)).
% 295.80/188.31 tff(32483,assumption,(node22(c_e_h_1, c_r, s24, s25)), introduced(assumption)).
% 295.80/188.31 tff(32484,plain,
% 295.80/188.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s25)) | (~node22(c_e_h_1, c_r, s24, s25)) | m_and_h_gate_v_out(c_e_h_1, c_r, s24))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s25)) | (~node22(c_e_h_1, c_r, s24, s25)) | m_and_h_gate_v_out(c_e_h_1, c_r, s24))),
% 295.80/188.31 inference(rewrite,[status(thm)],[])).
% 295.80/188.31 tff(32485,plain,
% 295.80/188.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s25)) | (~node22(c_e_h_1, c_r, s24, s25)) | m_and_h_gate_v_out(c_e_h_1, c_r, s24))),
% 295.80/188.31 inference(quant_inst,[status(thm)],[])).
% 295.80/188.31 tff(32486,plain,
% 295.80/188.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s25)) | (~node22(c_e_h_1, c_r, s24, s25)) | m_and_h_gate_v_out(c_e_h_1, c_r, s24)),
% 295.80/188.31 inference(modus_ponens,[status(thm)],[32485, 32484])).
% 295.80/188.31 tff(32487,plain,
% 295.80/188.31 ($false),
% 295.80/188.31 inference(unit_resolution,[status(thm)],[32486, 108, 32360, 32483, 32482])).
% 295.80/188.31 tff(32488,plain,((~node22(c_e_h_1, c_r, s24, s25)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s25)) | m_and_h_gate_v_out(c_e_h_1, c_r, s24)), inference(lemma,lemma(discharge,[]))).
% 295.80/188.31 tff(32489,plain,
% 295.80/188.31 (~node22(c_e_h_1, c_r, s24, s25)),
% 295.80/188.31 inference(unit_resolution,[status(thm)],[32488, 32360, 32482])).
% 295.80/188.31 tff(32490,plain,
% 295.80/188.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s24, s25)) | node21(c_e_h_1, c_r, s24, s25) | node22(c_e_h_1, c_r, s24, s25))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s24, s25)) | node21(c_e_h_1, c_r, s24, s25) | node22(c_e_h_1, c_r, s24, s25))),
% 295.80/188.31 inference(rewrite,[status(thm)],[])).
% 295.80/188.31 tff(32491,plain,
% 295.80/188.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s24, s25)) | node21(c_e_h_1, c_r, s24, s25) | node22(c_e_h_1, c_r, s24, s25))),
% 295.80/188.31 inference(quant_inst,[status(thm)],[])).
% 295.80/188.31 tff(32492,plain,
% 295.80/188.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s24, s25)) | node21(c_e_h_1, c_r, s24, s25) | node22(c_e_h_1, c_r, s24, s25)),
% 295.80/188.31 inference(modus_ponens,[status(thm)],[32491, 32490])).
% 295.80/188.31 tff(32493,plain,
% 295.80/188.31 (node21(c_e_h_1, c_r, s24, s25) | node22(c_e_h_1, c_r, s24, s25)),
% 295.80/188.31 inference(unit_resolution,[status(thm)],[32492, 82, 31626])).
% 295.80/188.31 tff(32494,plain,
% 295.80/188.31 (node21(c_e_h_1, c_r, s24, s25)),
% 295.80/188.31 inference(unit_resolution,[status(thm)],[32493, 32489])).
% 295.80/188.31 tff(32495,plain,
% 295.80/188.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s25)) | node20(c_e_h_1, c_r, s24) | (~node21(c_e_h_1, c_r, s24, s25)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s25)) | node20(c_e_h_1, c_r, s24) | (~node21(c_e_h_1, c_r, s24, s25)))),
% 295.80/188.31 inference(rewrite,[status(thm)],[])).
% 295.80/188.31 tff(32496,plain,
% 295.80/188.31 ((node20(c_e_h_1, c_r, s24) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s25)) | (~node21(c_e_h_1, c_r, s24, s25))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_r, s25)) | node20(c_e_h_1, c_r, s24) | (~node21(c_e_h_1, c_r, s24, s25)))),
% 295.80/188.31 inference(rewrite,[status(thm)],[])).
% 295.80/188.31 tff(32497,plain,
% 295.80/188.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s24) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s25)) | (~node21(c_e_h_1, c_r, s24, s25)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s25)) | node20(c_e_h_1, c_r, s24) | (~node21(c_e_h_1, c_r, s24, s25))))),
% 295.80/188.31 inference(monotonicity,[status(thm)],[32496])).
% 295.80/188.31 tff(32498,plain,
% 295.80/188.31 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s24) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s25)) | (~node21(c_e_h_1, c_r, s24, s25)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s25)) | node20(c_e_h_1, c_r, s24) | (~node21(c_e_h_1, c_r, s24, s25)))),
% 295.80/188.31 inference(transitivity,[status(thm)],[32497, 32495])).
% 295.80/188.31 tff(32499,plain,
% 295.80/188.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s24) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s25)) | (~node21(c_e_h_1, c_r, s24, s25)))),
% 295.80/188.31 inference(quant_inst,[status(thm)],[])).
% 295.80/188.31 tff(32500,plain,
% 295.80/188.31 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s25)) | node20(c_e_h_1, c_r, s24) | (~node21(c_e_h_1, c_r, s24, s25))),
% 295.80/188.31 inference(modus_ponens,[status(thm)],[32499, 32498])).
% 295.80/188.31 tff(32501,plain,
% 295.80/188.31 ($false),
% 295.80/188.31 inference(unit_resolution,[status(thm)],[32500, 52, 32360, 32494, 32481])).
% 295.80/188.31 tff(32502,plain,((~m_and_h_gate_v_out(c_e_h_1, c_r, s25)) | node20(c_e_h_1, c_r, s24) | m_and_h_gate_v_out(c_e_h_1, c_r, s24)), inference(lemma,lemma(discharge,[]))).
% 295.80/188.31 tff(32503,plain,
% 295.80/188.31 (node20(c_e_h_1, c_r, s24)),
% 295.80/188.31 inference(unit_resolution,[status(thm)],[32502, 32480, 32360])).
% 295.80/188.31 tff(32504,plain,
% 295.80/188.31 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s24)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s24))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s24)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s24))),
% 295.80/188.31 inference(rewrite,[status(thm)],[])).
% 295.80/188.31 tff(32505,plain,
% 295.80/188.31 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s24)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s24))),
% 295.80/188.31 inference(quant_inst,[status(thm)],[])).
% 295.80/188.31 tff(32506,plain,
% 295.80/188.31 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s24)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s24)),
% 295.80/188.31 inference(modus_ponens,[status(thm)],[32505, 32504])).
% 295.80/188.31 tff(32507,plain,
% 295.80/188.31 ($false),
% 295.80/188.31 inference(unit_resolution,[status(thm)],[32506, 4563, 32503, 32359])).
% 295.80/188.31 tff(32508,plain,(m_and_h_gate_v_out(c_e_h_1, c_i, s17) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s25)) | node20(c_e_h_1, c_r, s22) | m_and_h_gate_v_out(c_e_h_1, c_r, s20) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s17) | m_c_h_element_v_in2(c_e_h_1, c_e, s21) | m_c_h_element_v_in2(c_e_h_1, c_e, s20) | node20(c_e_h_1, c_i, s18) | m_c_h_element_v_out(c_e_h_1, c_e, s17) | node20(c_e_h_1, c_i, s17)), inference(lemma,lemma(discharge,[]))).
% 295.80/188.31 tff(32509,plain,
% 295.80/188.31 (m_and_h_gate_v_out(c_e_h_1, c_i, s17) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s25)) | node20(c_e_h_1, c_r, s22) | m_and_h_gate_v_out(c_e_h_1, c_r, s20) | (~m_and_h_gate_h_init_v_out(c_e_h_1, c_n, s17)) | m_c_h_element_v_in2(c_e_h_1, c_e, s21) | m_c_h_element_v_in2(c_e_h_1, c_e, s20) | node20(c_e_h_1, c_i, s18) | m_c_h_element_v_out(c_e_h_1, c_e, s17) | node20(c_e_h_1, c_i, s17)),
% 295.80/188.31 inference(unit_resolution,[status(thm)],[32508, 29683])).
% 295.80/188.31 tff(32510,plain,
% 295.80/188.31 (m_and_h_gate_v_out(c_e_h_1, c_i, s17) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s25)) | node20(c_e_h_1, c_r, s22) | m_and_h_gate_v_out(c_e_h_1, c_r, s20) | m_c_h_element_v_in2(c_e_h_1, c_e, s21) | m_c_h_element_v_in2(c_e_h_1, c_e, s20) | node20(c_e_h_1, c_i, s18) | m_c_h_element_v_out(c_e_h_1, c_e, s17) | node20(c_e_h_1, c_i, s17)),
% 295.80/188.31 inference(unit_resolution,[status(thm)],[32509, 30136])).
% 295.80/188.31 tff(32511,plain,
% 295.80/188.31 (~m_and_h_gate_v_out(c_e_h_1, c_r, s25)),
% 295.80/188.31 inference(unit_resolution,[status(thm)],[32510, 30887, 26739, 32312, 31862, 26740, 31860, 30383, 30785])).
% 295.80/188.31 tff(32512,assumption,(m_and_h_gate_v_in2(c_e_h_1, c_r, s25)), introduced(assumption)).
% 295.80/188.31 tff(32513,plain,
% 295.80/188.31 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s25)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s25))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s25)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s25))),
% 295.80/188.31 inference(rewrite,[status(thm)],[])).
% 295.80/188.31 tff(32514,plain,
% 295.80/188.31 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | ((~m_and_h_gate_v_in2(c_e_h_1, c_r, s25)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s25))),
% 295.80/188.31 inference(quant_inst,[status(thm)],[])).
% 295.80/188.31 tff(32515,plain,
% 295.80/188.31 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in2(I0, c_r, X)) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s25)) | m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s25)),
% 295.80/188.31 inference(modus_ponens,[status(thm)],[32514, 32513])).
% 295.80/188.31 tff(32516,plain,
% 295.80/188.31 ($false),
% 295.80/188.31 inference(unit_resolution,[status(thm)],[32515, 14293, 31795, 32512])).
% 295.80/188.31 tff(32517,plain,(m_and_h_gate_h_init_v_out(c_e_h_1, c_m, s25) | (~m_and_h_gate_v_in2(c_e_h_1, c_r, s25))), inference(lemma,lemma(discharge,[]))).
% 295.80/188.31 tff(32518,plain,
% 295.80/188.31 (~m_and_h_gate_v_in2(c_e_h_1, c_r, s25)),
% 295.80/188.32 inference(unit_resolution,[status(thm)],[32517, 31786])).
% 295.80/188.32 tff(32519,assumption,(~m_and_h_gate_v_in2(c_e_h_1, c_r, s25)), introduced(assumption)).
% 295.80/188.32 tff(32520,assumption,(node20(c_e_h_1, c_r, s25)), introduced(assumption)).
% 295.80/188.32 tff(32521,plain,
% 295.80/188.32 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s25)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s25))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s25)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s25))),
% 295.80/188.32 inference(rewrite,[status(thm)],[])).
% 295.80/188.32 tff(32522,plain,
% 295.80/188.32 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | ((~node20(c_e_h_1, c_r, s25)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s25))),
% 295.80/188.32 inference(quant_inst,[status(thm)],[])).
% 295.80/188.32 tff(32523,plain,
% 295.80/188.32 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in2(I0, I1, X))) | (~node20(c_e_h_1, c_r, s25)) | m_and_h_gate_v_in2(c_e_h_1, c_r, s25)),
% 295.80/188.32 inference(modus_ponens,[status(thm)],[32522, 32521])).
% 295.80/188.32 tff(32524,plain,
% 295.80/188.32 ($false),
% 295.80/188.32 inference(unit_resolution,[status(thm)],[32523, 4563, 32520, 32519])).
% 295.80/188.32 tff(32525,plain,(m_and_h_gate_v_in2(c_e_h_1, c_r, s25) | (~node20(c_e_h_1, c_r, s25))), inference(lemma,lemma(discharge,[]))).
% 295.80/188.32 tff(32526,plain,
% 295.80/188.32 (~node20(c_e_h_1, c_r, s25)),
% 295.80/188.32 inference(unit_resolution,[status(thm)],[32525, 32518])).
% 295.80/188.32 tff(32527,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_r, s25)), introduced(assumption)).
% 295.80/188.32 tff(32528,assumption,(m_and_h_gate_v_out(c_e_h_1, c_r, s26)), introduced(assumption)).
% 295.80/188.32 tff(32529,assumption,(~node20(c_e_h_1, c_r, s25)), introduced(assumption)).
% 295.80/188.32 tff(32530,assumption,(node21(c_e_h_1, c_r, s25, s26)), introduced(assumption)).
% 295.80/188.32 tff(32531,plain,
% 295.80/188.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s25) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s26)) | (~node21(c_e_h_1, c_r, s25, s26)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s25) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s26)) | (~node21(c_e_h_1, c_r, s25, s26)))),
% 295.80/188.32 inference(rewrite,[status(thm)],[])).
% 295.80/188.32 tff(32532,plain,
% 295.80/188.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_r, s25) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s26)) | (~node21(c_e_h_1, c_r, s25, s26)))),
% 295.80/188.32 inference(quant_inst,[status(thm)],[])).
% 295.80/188.32 tff(32533,plain,
% 295.80/188.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | node20(c_e_h_1, c_r, s25) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s26)) | (~node21(c_e_h_1, c_r, s25, s26))),
% 295.80/188.32 inference(modus_ponens,[status(thm)],[32532, 32531])).
% 295.80/188.32 tff(32534,plain,
% 295.80/188.32 ($false),
% 295.80/188.32 inference(unit_resolution,[status(thm)],[32533, 52, 32530, 32528, 32529])).
% 295.80/188.32 tff(32535,plain,((~node21(c_e_h_1, c_r, s25, s26)) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s26)) | node20(c_e_h_1, c_r, s25)), inference(lemma,lemma(discharge,[]))).
% 295.80/188.32 tff(32536,plain,
% 295.80/188.32 (~node21(c_e_h_1, c_r, s25, s26)),
% 295.80/188.32 inference(unit_resolution,[status(thm)],[32535, 32528, 32529])).
% 295.80/188.32 tff(32537,plain,
% 295.80/188.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s25, s26)) | node21(c_e_h_1, c_r, s25, s26) | node22(c_e_h_1, c_r, s25, s26))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s25, s26)) | node21(c_e_h_1, c_r, s25, s26) | node22(c_e_h_1, c_r, s25, s26))),
% 295.80/188.32 inference(rewrite,[status(thm)],[])).
% 295.80/188.32 tff(32538,plain,
% 295.80/188.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s25, s26)) | node21(c_e_h_1, c_r, s25, s26) | node22(c_e_h_1, c_r, s25, s26))),
% 295.80/188.32 inference(quant_inst,[status(thm)],[])).
% 295.80/188.32 tff(32539,plain,
% 295.80/188.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s25, s26)) | node21(c_e_h_1, c_r, s25, s26) | node22(c_e_h_1, c_r, s25, s26)),
% 295.80/188.32 inference(modus_ponens,[status(thm)],[32538, 32537])).
% 295.80/188.32 tff(32540,plain,
% 295.80/188.32 (node21(c_e_h_1, c_r, s25, s26) | node22(c_e_h_1, c_r, s25, s26)),
% 295.80/188.32 inference(unit_resolution,[status(thm)],[32539, 82, 31821])).
% 295.80/188.32 tff(32541,plain,
% 295.80/188.32 (node22(c_e_h_1, c_r, s25, s26)),
% 295.80/188.32 inference(unit_resolution,[status(thm)],[32540, 32536])).
% 295.80/188.32 tff(32542,plain,
% 295.80/188.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s26)) | (~node22(c_e_h_1, c_r, s25, s26)) | m_and_h_gate_v_out(c_e_h_1, c_r, s25))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s26)) | (~node22(c_e_h_1, c_r, s25, s26)) | m_and_h_gate_v_out(c_e_h_1, c_r, s25))),
% 295.80/188.32 inference(rewrite,[status(thm)],[])).
% 295.80/188.32 tff(32543,plain,
% 295.80/188.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_r, s26)) | (~node22(c_e_h_1, c_r, s25, s26)) | m_and_h_gate_v_out(c_e_h_1, c_r, s25))),
% 295.80/188.32 inference(quant_inst,[status(thm)],[])).
% 295.80/188.32 tff(32544,plain,
% 295.80/188.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_r, s26)) | (~node22(c_e_h_1, c_r, s25, s26)) | m_and_h_gate_v_out(c_e_h_1, c_r, s25)),
% 295.80/188.32 inference(modus_ponens,[status(thm)],[32543, 32542])).
% 295.80/188.32 tff(32545,plain,
% 295.80/188.32 ($false),
% 295.80/188.32 inference(unit_resolution,[status(thm)],[32544, 108, 32541, 32528, 32527])).
% 295.80/188.32 tff(32546,plain,((~m_and_h_gate_v_out(c_e_h_1, c_r, s26)) | m_and_h_gate_v_out(c_e_h_1, c_r, s25) | node20(c_e_h_1, c_r, s25)), inference(lemma,lemma(discharge,[]))).
% 295.80/188.32 tff(32547,plain,
% 295.80/188.32 (~m_and_h_gate_v_out(c_e_h_1, c_r, s26)),
% 295.80/188.32 inference(unit_resolution,[status(thm)],[32546, 32526, 32511])).
% 295.80/188.32 tff(32548,assumption,(m_c_h_element_v_in2(c_e_h_1, c_f, s12)), introduced(assumption)).
% 295.80/188.32 tff(32549,plain,
% 295.80/188.32 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s12)) | m_and_h_gate_v_out(c_e_h_1, c_i, s12))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s12)) | m_and_h_gate_v_out(c_e_h_1, c_i, s12))),
% 295.80/188.32 inference(rewrite,[status(thm)],[])).
% 295.80/188.32 tff(32550,plain,
% 295.80/188.32 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s12)) | m_and_h_gate_v_out(c_e_h_1, c_i, s12))),
% 295.80/188.32 inference(quant_inst,[status(thm)],[])).
% 295.80/188.32 tff(32551,plain,
% 295.80/188.32 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s12)) | m_and_h_gate_v_out(c_e_h_1, c_i, s12)),
% 295.80/188.32 inference(modus_ponens,[status(thm)],[32550, 32549])).
% 295.80/188.32 tff(32552,plain,
% 295.80/188.32 ($false),
% 295.80/188.32 inference(unit_resolution,[status(thm)],[32551, 2143, 24159, 32548])).
% 295.80/188.32 tff(32553,plain,((~m_c_h_element_v_in2(c_e_h_1, c_f, s12)) | m_and_h_gate_v_out(c_e_h_1, c_i, s12)), inference(lemma,lemma(discharge,[]))).
% 295.80/188.32 tff(32554,plain,
% 295.80/188.32 (~m_c_h_element_v_in2(c_e_h_1, c_f, s12)),
% 295.80/188.32 inference(unit_resolution,[status(thm)],[32553, 24149])).
% 295.80/188.32 tff(32555,assumption,(m_c_h_element_v_out(c_e_h_1, c_f, s13)), introduced(assumption)).
% 295.80/188.32 tff(32556,assumption,(~m_c_h_element_v_out(c_e_h_1, c_f, s12)), introduced(assumption)).
% 295.80/188.32 tff(32557,assumption,(node18(c_e_h_1, c_f, s12, s13)), introduced(assumption)).
% 295.80/188.32 tff(32558,plain,
% 295.80/188.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_f, s12) | (~m_c_h_element_v_out(c_e_h_1, c_f, s13)) | (~node18(c_e_h_1, c_f, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s12) | (~m_c_h_element_v_out(c_e_h_1, c_f, s13)) | (~node18(c_e_h_1, c_f, s12, s13)))),
% 295.80/188.32 inference(rewrite,[status(thm)],[])).
% 295.80/188.32 tff(32559,plain,
% 295.80/188.32 (((~m_c_h_element_v_out(c_e_h_1, c_f, s13)) | m_c_h_element_v_out(c_e_h_1, c_f, s12) | (~node18(c_e_h_1, c_f, s12, s13))) <=> (m_c_h_element_v_out(c_e_h_1, c_f, s12) | (~m_c_h_element_v_out(c_e_h_1, c_f, s13)) | (~node18(c_e_h_1, c_f, s12, s13)))),
% 295.80/188.32 inference(rewrite,[status(thm)],[])).
% 295.80/188.32 tff(32560,plain,
% 295.80/188.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s13)) | m_c_h_element_v_out(c_e_h_1, c_f, s12) | (~node18(c_e_h_1, c_f, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_f, s12) | (~m_c_h_element_v_out(c_e_h_1, c_f, s13)) | (~node18(c_e_h_1, c_f, s12, s13))))),
% 295.80/188.32 inference(monotonicity,[status(thm)],[32559])).
% 295.80/188.32 tff(32561,plain,
% 295.80/188.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s13)) | m_c_h_element_v_out(c_e_h_1, c_f, s12) | (~node18(c_e_h_1, c_f, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s12) | (~m_c_h_element_v_out(c_e_h_1, c_f, s13)) | (~node18(c_e_h_1, c_f, s12, s13)))),
% 295.80/188.32 inference(transitivity,[status(thm)],[32560, 32558])).
% 295.80/188.32 tff(32562,plain,
% 295.80/188.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s13)) | m_c_h_element_v_out(c_e_h_1, c_f, s12) | (~node18(c_e_h_1, c_f, s12, s13)))),
% 295.80/188.32 inference(quant_inst,[status(thm)],[])).
% 295.80/188.32 tff(32563,plain,
% 295.80/188.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s12) | (~m_c_h_element_v_out(c_e_h_1, c_f, s13)) | (~node18(c_e_h_1, c_f, s12, s13))),
% 295.80/188.32 inference(modus_ponens,[status(thm)],[32562, 32561])).
% 295.80/188.32 tff(32564,plain,
% 295.80/188.32 ($false),
% 295.80/188.32 inference(unit_resolution,[status(thm)],[32563, 753, 32556, 32557, 32555])).
% 295.80/188.32 tff(32565,plain,((~node18(c_e_h_1, c_f, s12, s13)) | m_c_h_element_v_out(c_e_h_1, c_f, s12) | (~m_c_h_element_v_out(c_e_h_1, c_f, s13))), inference(lemma,lemma(discharge,[]))).
% 295.80/188.32 tff(32566,plain,
% 295.80/188.32 (~node18(c_e_h_1, c_f, s12, s13)),
% 295.80/188.32 inference(unit_resolution,[status(thm)],[32565, 32555, 32556])).
% 295.80/188.32 tff(32567,plain,
% 295.80/188.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s12, s13)) | node19(c_e_h_1, c_f, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s12, s13)) | node19(c_e_h_1, c_f, s12, s13))),
% 295.80/188.32 inference(rewrite,[status(thm)],[])).
% 295.80/188.32 tff(32568,plain,
% 295.80/188.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s12, s13)) | node19(c_e_h_1, c_f, s12, s13))),
% 295.80/188.32 inference(quant_inst,[status(thm)],[])).
% 295.80/188.32 tff(32569,plain,
% 295.80/188.32 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s12, s13)) | node19(c_e_h_1, c_f, s12, s13)),
% 295.80/188.32 inference(modus_ponens,[status(thm)],[32568, 32567])).
% 295.80/188.32 tff(32570,plain,
% 295.80/188.32 (node19(c_e_h_1, c_f, s12, s13)),
% 295.80/188.32 inference(unit_resolution,[status(thm)],[32569, 190, 11856])).
% 295.80/188.32 tff(32571,plain,
% 295.80/188.32 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s12) | (~node19(c_e_h_1, c_f, s12, s13)) | node18(c_e_h_1, c_f, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_f, s12) | (~node19(c_e_h_1, c_f, s12, s13)) | node18(c_e_h_1, c_f, s12, s13))),
% 295.80/188.33 inference(rewrite,[status(thm)],[])).
% 295.80/188.33 tff(32572,plain,
% 295.80/188.33 ((node17(c_e_h_1, c_f, s12) | node18(c_e_h_1, c_f, s12, s13) | (~node19(c_e_h_1, c_f, s12, s13))) <=> (node17(c_e_h_1, c_f, s12) | (~node19(c_e_h_1, c_f, s12, s13)) | node18(c_e_h_1, c_f, s12, s13))),
% 295.80/188.33 inference(rewrite,[status(thm)],[])).
% 295.80/188.33 tff(32573,plain,
% 295.80/188.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s12) | node18(c_e_h_1, c_f, s12, s13) | (~node19(c_e_h_1, c_f, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s12) | (~node19(c_e_h_1, c_f, s12, s13)) | node18(c_e_h_1, c_f, s12, s13)))),
% 295.80/188.33 inference(monotonicity,[status(thm)],[32572])).
% 295.80/188.33 tff(32574,plain,
% 295.80/188.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s12) | node18(c_e_h_1, c_f, s12, s13) | (~node19(c_e_h_1, c_f, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_f, s12) | (~node19(c_e_h_1, c_f, s12, s13)) | node18(c_e_h_1, c_f, s12, s13))),
% 295.80/188.33 inference(transitivity,[status(thm)],[32573, 32571])).
% 295.80/188.33 tff(32575,plain,
% 295.80/188.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s12) | node18(c_e_h_1, c_f, s12, s13) | (~node19(c_e_h_1, c_f, s12, s13)))),
% 295.80/188.33 inference(quant_inst,[status(thm)],[])).
% 295.80/188.33 tff(32576,plain,
% 295.80/188.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_f, s12) | (~node19(c_e_h_1, c_f, s12, s13)) | node18(c_e_h_1, c_f, s12, s13)),
% 295.80/188.33 inference(modus_ponens,[status(thm)],[32575, 32574])).
% 295.80/188.33 tff(32577,plain,
% 295.80/188.33 (node17(c_e_h_1, c_f, s12) | node18(c_e_h_1, c_f, s12, s13)),
% 295.80/188.33 inference(unit_resolution,[status(thm)],[32576, 776, 32570])).
% 295.80/188.33 tff(32578,plain,
% 295.80/188.33 (node17(c_e_h_1, c_f, s12)),
% 295.80/188.33 inference(unit_resolution,[status(thm)],[32577, 32566])).
% 295.80/188.33 tff(32579,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_f, s12)), introduced(assumption)).
% 295.80/188.33 tff(32580,plain,
% 295.80/188.33 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s12)) | m_c_h_element_v_in2(c_e_h_1, c_f, s12) | (~node17(c_e_h_1, c_f, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s12)) | m_c_h_element_v_in2(c_e_h_1, c_f, s12) | (~node17(c_e_h_1, c_f, s12)))),
% 295.80/188.33 inference(rewrite,[status(thm)],[])).
% 295.80/188.33 tff(32581,plain,
% 295.80/188.33 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s12)) | m_c_h_element_v_in2(c_e_h_1, c_f, s12) | (~node17(c_e_h_1, c_f, s12)))),
% 295.80/188.33 inference(quant_inst,[status(thm)],[])).
% 295.80/188.33 tff(32582,plain,
% 295.80/188.33 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s12)) | m_c_h_element_v_in2(c_e_h_1, c_f, s12) | (~node17(c_e_h_1, c_f, s12))),
% 295.80/188.33 inference(modus_ponens,[status(thm)],[32581, 32580])).
% 295.80/188.33 tff(32583,plain,
% 295.80/188.33 ((~m_c_h_element_v_in1(c_e_h_1, c_f, s12)) | (~node17(c_e_h_1, c_f, s12))),
% 295.80/188.33 inference(unit_resolution,[status(thm)],[32582, 919, 32579])).
% 295.80/188.33 tff(32584,plain,
% 295.80/188.33 (~m_c_h_element_v_in1(c_e_h_1, c_f, s12)),
% 295.80/188.33 inference(unit_resolution,[status(thm)],[32583, 32578])).
% 295.80/188.33 tff(32585,assumption,(node15(c_e_h_1, c_f, s12, s13)), introduced(assumption)).
% 295.80/188.33 tff(32586,plain,
% 295.80/188.33 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s13)) | (~node15(c_e_h_1, c_f, s12, s13)) | m_c_h_element_v_out(c_e_h_1, c_f, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s13)) | (~node15(c_e_h_1, c_f, s12, s13)) | m_c_h_element_v_out(c_e_h_1, c_f, s12))),
% 295.80/188.33 inference(rewrite,[status(thm)],[])).
% 295.80/188.33 tff(32587,plain,
% 295.80/188.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s13)) | (~node15(c_e_h_1, c_f, s12, s13)) | m_c_h_element_v_out(c_e_h_1, c_f, s12))),
% 295.80/188.33 inference(quant_inst,[status(thm)],[])).
% 295.80/188.33 tff(32588,plain,
% 295.80/188.33 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s13)) | (~node15(c_e_h_1, c_f, s12, s13)) | m_c_h_element_v_out(c_e_h_1, c_f, s12)),
% 295.80/188.33 inference(modus_ponens,[status(thm)],[32587, 32586])).
% 295.80/188.33 tff(32589,plain,
% 295.80/188.33 ($false),
% 295.80/188.33 inference(unit_resolution,[status(thm)],[32588, 147, 32556, 32585, 32555])).
% 295.80/188.33 tff(32590,plain,((~node15(c_e_h_1, c_f, s12, s13)) | m_c_h_element_v_out(c_e_h_1, c_f, s12) | (~m_c_h_element_v_out(c_e_h_1, c_f, s13))), inference(lemma,lemma(discharge,[]))).
% 295.80/188.33 tff(32591,plain,
% 295.80/188.33 (~node15(c_e_h_1, c_f, s12, s13)),
% 295.80/188.33 inference(unit_resolution,[status(thm)],[32590, 32555, 32556])).
% 295.80/188.33 tff(32592,assumption,(node17(c_e_h_1, c_f, s12)), introduced(assumption)).
% 295.80/188.33 tff(32593,assumption,(node16(c_e_h_1, c_f, s12)), introduced(assumption)).
% 295.80/188.33 tff(32594,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_f, s12)), introduced(assumption)).
% 295.80/188.33 tff(32595,plain,
% 295.80/188.33 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s12)) | m_c_h_element_v_in1(c_e_h_1, c_f, s12) | (~node17(c_e_h_1, c_f, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s12)) | m_c_h_element_v_in1(c_e_h_1, c_f, s12) | (~node17(c_e_h_1, c_f, s12)))),
% 295.80/188.33 inference(rewrite,[status(thm)],[])).
% 295.80/188.33 tff(32596,plain,
% 295.80/188.33 ((m_c_h_element_v_in1(c_e_h_1, c_f, s12) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s12)) | (~node17(c_e_h_1, c_f, s12))) <=> ((~m_c_h_element_v_in2(c_e_h_1, c_f, s12)) | m_c_h_element_v_in1(c_e_h_1, c_f, s12) | (~node17(c_e_h_1, c_f, s12)))),
% 295.80/188.33 inference(rewrite,[status(thm)],[])).
% 295.80/188.33 tff(32597,plain,
% 295.80/188.33 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s12) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s12)) | (~node17(c_e_h_1, c_f, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s12)) | m_c_h_element_v_in1(c_e_h_1, c_f, s12) | (~node17(c_e_h_1, c_f, s12))))),
% 295.80/188.33 inference(monotonicity,[status(thm)],[32596])).
% 295.80/188.33 tff(32598,plain,
% 295.80/188.33 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s12) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s12)) | (~node17(c_e_h_1, c_f, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s12)) | m_c_h_element_v_in1(c_e_h_1, c_f, s12) | (~node17(c_e_h_1, c_f, s12)))),
% 295.80/188.33 inference(transitivity,[status(thm)],[32597, 32595])).
% 295.80/188.33 tff(32599,plain,
% 295.80/188.33 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s12) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s12)) | (~node17(c_e_h_1, c_f, s12)))),
% 295.80/188.33 inference(quant_inst,[status(thm)],[])).
% 295.80/188.33 tff(32600,plain,
% 295.80/188.33 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s12)) | m_c_h_element_v_in1(c_e_h_1, c_f, s12) | (~node17(c_e_h_1, c_f, s12))),
% 295.80/188.33 inference(modus_ponens,[status(thm)],[32599, 32598])).
% 295.80/188.33 tff(32601,plain,
% 295.80/188.33 ((~m_c_h_element_v_in2(c_e_h_1, c_f, s12)) | m_c_h_element_v_in1(c_e_h_1, c_f, s12)),
% 295.80/188.33 inference(unit_resolution,[status(thm)],[32600, 859, 32592])).
% 295.80/188.33 tff(32602,plain,
% 295.80/188.33 (~m_c_h_element_v_in2(c_e_h_1, c_f, s12)),
% 295.80/188.33 inference(unit_resolution,[status(thm)],[32601, 32594])).
% 295.80/188.33 tff(32603,plain,
% 295.80/188.33 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s12)) | m_c_h_element_v_in1(c_e_h_1, c_f, s12) | m_c_h_element_v_in2(c_e_h_1, c_f, s12))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s12)) | m_c_h_element_v_in1(c_e_h_1, c_f, s12) | m_c_h_element_v_in2(c_e_h_1, c_f, s12))),
% 295.80/188.33 inference(rewrite,[status(thm)],[])).
% 295.80/188.33 tff(32604,plain,
% 295.80/188.33 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s12)) | m_c_h_element_v_in1(c_e_h_1, c_f, s12) | m_c_h_element_v_in2(c_e_h_1, c_f, s12))),
% 295.80/188.33 inference(quant_inst,[status(thm)],[])).
% 295.80/188.33 tff(32605,plain,
% 295.80/188.33 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s12)) | m_c_h_element_v_in1(c_e_h_1, c_f, s12) | m_c_h_element_v_in2(c_e_h_1, c_f, s12)),
% 295.80/188.33 inference(modus_ponens,[status(thm)],[32604, 32603])).
% 295.80/188.33 tff(32606,plain,
% 295.80/188.33 (m_c_h_element_v_in1(c_e_h_1, c_f, s12) | m_c_h_element_v_in2(c_e_h_1, c_f, s12)),
% 295.80/188.33 inference(unit_resolution,[status(thm)],[32605, 178, 32593])).
% 295.80/188.33 tff(32607,plain,
% 295.80/188.33 ($false),
% 295.80/188.33 inference(unit_resolution,[status(thm)],[32606, 32602, 32594])).
% 295.80/188.33 tff(32608,plain,(m_c_h_element_v_in1(c_e_h_1, c_f, s12) | (~node16(c_e_h_1, c_f, s12)) | (~node17(c_e_h_1, c_f, s12))), inference(lemma,lemma(discharge,[]))).
% 295.80/188.33 tff(32609,plain,
% 295.80/188.33 (m_c_h_element_v_in1(c_e_h_1, c_f, s12)),
% 295.80/188.33 inference(unit_resolution,[status(thm)],[32608, 32593, 32592])).
% 295.80/188.33 tff(32610,plain,
% 295.80/188.33 ((~m_c_h_element_v_in1(c_e_h_1, c_f, s12)) | m_c_h_element_v_in2(c_e_h_1, c_f, s12)),
% 295.80/188.33 inference(unit_resolution,[status(thm)],[32582, 919, 32592])).
% 295.80/188.33 tff(32611,plain,
% 295.80/188.33 (m_c_h_element_v_in2(c_e_h_1, c_f, s12)),
% 295.80/188.33 inference(unit_resolution,[status(thm)],[32610, 32609])).
% 295.80/188.33 tff(32612,plain,
% 295.80/188.33 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s12)) | (~node16(c_e_h_1, c_f, s12)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s12)) | (~node16(c_e_h_1, c_f, s12)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s12)))),
% 295.80/188.33 inference(rewrite,[status(thm)],[])).
% 295.80/188.33 tff(32613,plain,
% 295.80/188.33 (((~node16(c_e_h_1, c_f, s12)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s12)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s12))) <=> ((~m_c_h_element_v_in1(c_e_h_1, c_f, s12)) | (~node16(c_e_h_1, c_f, s12)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s12)))),
% 295.80/188.33 inference(rewrite,[status(thm)],[])).
% 295.80/188.33 tff(32614,plain,
% 295.80/188.33 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_f, s12)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s12)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s12)) | (~node16(c_e_h_1, c_f, s12)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s12))))),
% 295.80/188.33 inference(monotonicity,[status(thm)],[32613])).
% 295.80/188.33 tff(32615,plain,
% 295.80/188.33 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_f, s12)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s12)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s12)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s12)) | (~node16(c_e_h_1, c_f, s12)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s12)))),
% 295.80/188.34 inference(transitivity,[status(thm)],[32614, 32612])).
% 295.80/188.34 tff(32616,plain,
% 295.80/188.34 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_f, s12)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s12)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s12)))),
% 295.80/188.34 inference(quant_inst,[status(thm)],[])).
% 295.80/188.34 tff(32617,plain,
% 295.80/188.34 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s12)) | (~node16(c_e_h_1, c_f, s12)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s12))),
% 295.80/188.34 inference(modus_ponens,[status(thm)],[32616, 32615])).
% 295.80/188.34 tff(32618,plain,
% 295.80/188.34 ((~m_c_h_element_v_in1(c_e_h_1, c_f, s12)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s12))),
% 295.80/188.34 inference(unit_resolution,[status(thm)],[32617, 2307, 32593])).
% 295.80/188.34 tff(32619,plain,
% 295.80/188.34 ($false),
% 295.80/188.34 inference(unit_resolution,[status(thm)],[32618, 32611, 32609])).
% 295.80/188.34 tff(32620,plain,((~node16(c_e_h_1, c_f, s12)) | (~node17(c_e_h_1, c_f, s12))), inference(lemma,lemma(discharge,[]))).
% 295.80/188.34 tff(32621,plain,
% 295.80/188.34 (~node16(c_e_h_1, c_f, s12)),
% 295.80/188.34 inference(unit_resolution,[status(thm)],[32620, 32578])).
% 295.80/188.34 tff(32622,plain,
% 295.80/188.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s12) | node15(c_e_h_1, c_f, s12, s13) | (~node19(c_e_h_1, c_f, s12, s13)) | node14(c_e_h_1, c_f, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_f, s12) | node15(c_e_h_1, c_f, s12, s13) | (~node19(c_e_h_1, c_f, s12, s13)) | node14(c_e_h_1, c_f, s12, s13))),
% 295.80/188.34 inference(rewrite,[status(thm)],[])).
% 295.80/188.34 tff(32623,plain,
% 295.80/188.34 ((node16(c_e_h_1, c_f, s12) | node14(c_e_h_1, c_f, s12, s13) | node15(c_e_h_1, c_f, s12, s13) | (~node19(c_e_h_1, c_f, s12, s13))) <=> (node16(c_e_h_1, c_f, s12) | node15(c_e_h_1, c_f, s12, s13) | (~node19(c_e_h_1, c_f, s12, s13)) | node14(c_e_h_1, c_f, s12, s13))),
% 295.80/188.34 inference(rewrite,[status(thm)],[])).
% 295.80/188.34 tff(32624,plain,
% 295.80/188.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s12) | node14(c_e_h_1, c_f, s12, s13) | node15(c_e_h_1, c_f, s12, s13) | (~node19(c_e_h_1, c_f, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s12) | node15(c_e_h_1, c_f, s12, s13) | (~node19(c_e_h_1, c_f, s12, s13)) | node14(c_e_h_1, c_f, s12, s13)))),
% 295.80/188.34 inference(monotonicity,[status(thm)],[32623])).
% 295.80/188.34 tff(32625,plain,
% 295.80/188.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s12) | node14(c_e_h_1, c_f, s12, s13) | node15(c_e_h_1, c_f, s12, s13) | (~node19(c_e_h_1, c_f, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_f, s12) | node15(c_e_h_1, c_f, s12, s13) | (~node19(c_e_h_1, c_f, s12, s13)) | node14(c_e_h_1, c_f, s12, s13))),
% 295.80/188.34 inference(transitivity,[status(thm)],[32624, 32622])).
% 295.80/188.34 tff(32626,plain,
% 295.80/188.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s12) | node14(c_e_h_1, c_f, s12, s13) | node15(c_e_h_1, c_f, s12, s13) | (~node19(c_e_h_1, c_f, s12, s13)))),
% 295.80/188.34 inference(quant_inst,[status(thm)],[])).
% 295.80/188.34 tff(32627,plain,
% 295.80/188.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_f, s12) | node15(c_e_h_1, c_f, s12, s13) | (~node19(c_e_h_1, c_f, s12, s13)) | node14(c_e_h_1, c_f, s12, s13)),
% 295.80/188.34 inference(modus_ponens,[status(thm)],[32626, 32625])).
% 295.80/188.34 tff(32628,plain,
% 295.80/188.34 (node16(c_e_h_1, c_f, s12) | node15(c_e_h_1, c_f, s12, s13) | node14(c_e_h_1, c_f, s12, s13)),
% 295.80/188.34 inference(unit_resolution,[status(thm)],[32627, 204, 32570])).
% 295.80/188.34 tff(32629,plain,
% 295.80/188.34 (node14(c_e_h_1, c_f, s12, s13)),
% 295.80/188.34 inference(unit_resolution,[status(thm)],[32628, 32621, 32591])).
% 295.80/188.34 tff(32630,assumption,(node14(c_e_h_1, c_f, s12, s13)), introduced(assumption)).
% 295.80/188.34 tff(32631,plain,
% 295.80/188.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s13)) | m_c_h_element_v_in1(c_e_h_1, c_f, s12) | (~node14(c_e_h_1, c_f, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s13)) | m_c_h_element_v_in1(c_e_h_1, c_f, s12) | (~node14(c_e_h_1, c_f, s12, s13)))),
% 295.80/188.34 inference(rewrite,[status(thm)],[])).
% 295.80/188.34 tff(32632,plain,
% 295.80/188.34 (((~node14(c_e_h_1, c_f, s12, s13)) | m_c_h_element_v_in1(c_e_h_1, c_f, s12) | (~m_c_h_element_v_out(c_e_h_1, c_f, s13))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_f, s13)) | m_c_h_element_v_in1(c_e_h_1, c_f, s12) | (~node14(c_e_h_1, c_f, s12, s13)))),
% 295.80/188.34 inference(rewrite,[status(thm)],[])).
% 295.80/188.34 tff(32633,plain,
% 295.80/188.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s12, s13)) | m_c_h_element_v_in1(c_e_h_1, c_f, s12) | (~m_c_h_element_v_out(c_e_h_1, c_f, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s13)) | m_c_h_element_v_in1(c_e_h_1, c_f, s12) | (~node14(c_e_h_1, c_f, s12, s13))))),
% 295.80/188.34 inference(monotonicity,[status(thm)],[32632])).
% 295.80/188.34 tff(32634,plain,
% 295.80/188.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s12, s13)) | m_c_h_element_v_in1(c_e_h_1, c_f, s12) | (~m_c_h_element_v_out(c_e_h_1, c_f, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s13)) | m_c_h_element_v_in1(c_e_h_1, c_f, s12) | (~node14(c_e_h_1, c_f, s12, s13)))),
% 295.80/188.34 inference(transitivity,[status(thm)],[32633, 32631])).
% 295.80/188.34 tff(32635,plain,
% 295.80/188.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s12, s13)) | m_c_h_element_v_in1(c_e_h_1, c_f, s12) | (~m_c_h_element_v_out(c_e_h_1, c_f, s13)))),
% 295.80/188.34 inference(quant_inst,[status(thm)],[])).
% 295.80/188.34 tff(32636,plain,
% 295.80/188.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s13)) | m_c_h_element_v_in1(c_e_h_1, c_f, s12) | (~node14(c_e_h_1, c_f, s12, s13))),
% 295.80/188.34 inference(modus_ponens,[status(thm)],[32635, 32634])).
% 295.80/188.34 tff(32637,plain,
% 295.80/188.34 ($false),
% 295.80/188.34 inference(unit_resolution,[status(thm)],[32636, 223, 32630, 32555, 32594])).
% 295.80/188.34 tff(32638,plain,((~node14(c_e_h_1, c_f, s12, s13)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s13)) | m_c_h_element_v_in1(c_e_h_1, c_f, s12)), inference(lemma,lemma(discharge,[]))).
% 295.80/188.34 tff(32639,plain,
% 295.80/188.34 ($false),
% 295.80/188.34 inference(unit_resolution,[status(thm)],[32638, 32629, 32584, 32555])).
% 295.80/188.34 tff(32640,plain,((~m_c_h_element_v_out(c_e_h_1, c_f, s13)) | m_c_h_element_v_in2(c_e_h_1, c_f, s12) | m_c_h_element_v_out(c_e_h_1, c_f, s12)), inference(lemma,lemma(discharge,[]))).
% 295.80/188.34 tff(32641,plain,
% 295.80/188.34 ((~m_c_h_element_v_out(c_e_h_1, c_f, s13)) | m_c_h_element_v_in2(c_e_h_1, c_f, s12)),
% 295.80/188.34 inference(unit_resolution,[status(thm)],[32640, 29384])).
% 295.80/188.34 tff(32642,plain,
% 295.80/188.34 (~m_c_h_element_v_out(c_e_h_1, c_f, s13)),
% 295.80/188.34 inference(unit_resolution,[status(thm)],[32641, 32554])).
% 295.80/188.34 tff(32643,assumption,(m_c_h_element_v_in2(c_e_h_1, c_f, s13)), introduced(assumption)).
% 295.80/188.34 tff(32644,plain,
% 295.80/188.34 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s13)) | m_and_h_gate_v_out(c_e_h_1, c_i, s13))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s13)) | m_and_h_gate_v_out(c_e_h_1, c_i, s13))),
% 295.80/188.34 inference(rewrite,[status(thm)],[])).
% 295.80/188.34 tff(32645,plain,
% 295.80/188.34 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s13)) | m_and_h_gate_v_out(c_e_h_1, c_i, s13))),
% 295.80/188.34 inference(quant_inst,[status(thm)],[])).
% 295.80/188.34 tff(32646,plain,
% 295.80/188.34 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s13)) | m_and_h_gate_v_out(c_e_h_1, c_i, s13)),
% 295.80/188.34 inference(modus_ponens,[status(thm)],[32645, 32644])).
% 295.80/188.34 tff(32647,plain,
% 295.80/188.34 ($false),
% 295.80/188.34 inference(unit_resolution,[status(thm)],[32646, 2143, 24190, 32643])).
% 295.80/188.34 tff(32648,plain,((~m_c_h_element_v_in2(c_e_h_1, c_f, s13)) | m_and_h_gate_v_out(c_e_h_1, c_i, s13)), inference(lemma,lemma(discharge,[]))).
% 295.80/188.34 tff(32649,plain,
% 295.80/188.34 (~m_c_h_element_v_in2(c_e_h_1, c_f, s13)),
% 295.80/188.34 inference(unit_resolution,[status(thm)],[32648, 24181])).
% 295.80/188.34 tff(32650,assumption,(m_c_h_element_v_out(c_e_h_1, c_f, s14)), introduced(assumption)).
% 295.80/188.34 tff(32651,assumption,(~m_c_h_element_v_out(c_e_h_1, c_f, s13)), introduced(assumption)).
% 295.80/188.34 tff(32652,assumption,(node18(c_e_h_1, c_f, s13, s14)), introduced(assumption)).
% 295.80/188.34 tff(32653,plain,
% 295.80/188.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s14)) | (~node18(c_e_h_1, c_f, s13, s14)) | m_c_h_element_v_out(c_e_h_1, c_f, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s14)) | (~node18(c_e_h_1, c_f, s13, s14)) | m_c_h_element_v_out(c_e_h_1, c_f, s13))),
% 295.80/188.34 inference(rewrite,[status(thm)],[])).
% 295.80/188.34 tff(32654,plain,
% 295.80/188.34 (((~m_c_h_element_v_out(c_e_h_1, c_f, s14)) | m_c_h_element_v_out(c_e_h_1, c_f, s13) | (~node18(c_e_h_1, c_f, s13, s14))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_f, s14)) | (~node18(c_e_h_1, c_f, s13, s14)) | m_c_h_element_v_out(c_e_h_1, c_f, s13))),
% 295.80/188.34 inference(rewrite,[status(thm)],[])).
% 295.80/188.34 tff(32655,plain,
% 295.80/188.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s14)) | m_c_h_element_v_out(c_e_h_1, c_f, s13) | (~node18(c_e_h_1, c_f, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s14)) | (~node18(c_e_h_1, c_f, s13, s14)) | m_c_h_element_v_out(c_e_h_1, c_f, s13)))),
% 295.80/188.34 inference(monotonicity,[status(thm)],[32654])).
% 295.80/188.34 tff(32656,plain,
% 295.80/188.34 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s14)) | m_c_h_element_v_out(c_e_h_1, c_f, s13) | (~node18(c_e_h_1, c_f, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s14)) | (~node18(c_e_h_1, c_f, s13, s14)) | m_c_h_element_v_out(c_e_h_1, c_f, s13))),
% 295.80/188.34 inference(transitivity,[status(thm)],[32655, 32653])).
% 295.80/188.34 tff(32657,plain,
% 295.80/188.34 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s14)) | m_c_h_element_v_out(c_e_h_1, c_f, s13) | (~node18(c_e_h_1, c_f, s13, s14)))),
% 295.80/188.35 inference(quant_inst,[status(thm)],[])).
% 295.80/188.35 tff(32658,plain,
% 295.80/188.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s14)) | (~node18(c_e_h_1, c_f, s13, s14)) | m_c_h_element_v_out(c_e_h_1, c_f, s13)),
% 295.80/188.35 inference(modus_ponens,[status(thm)],[32657, 32656])).
% 295.80/188.35 tff(32659,plain,
% 295.80/188.35 ($false),
% 295.80/188.35 inference(unit_resolution,[status(thm)],[32658, 753, 32652, 32650, 32651])).
% 295.80/188.35 tff(32660,plain,((~node18(c_e_h_1, c_f, s13, s14)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s14)) | m_c_h_element_v_out(c_e_h_1, c_f, s13)), inference(lemma,lemma(discharge,[]))).
% 295.80/188.35 tff(32661,plain,
% 295.80/188.35 (~node18(c_e_h_1, c_f, s13, s14)),
% 295.80/188.35 inference(unit_resolution,[status(thm)],[32660, 32651, 32650])).
% 295.80/188.35 tff(32662,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_f, s13)), introduced(assumption)).
% 295.80/188.35 tff(32663,assumption,(~node16(c_e_h_1, c_f, s13)), introduced(assumption)).
% 295.80/188.35 tff(32664,assumption,(node15(c_e_h_1, c_f, s13, s14)), introduced(assumption)).
% 295.80/188.35 tff(32665,plain,
% 295.80/188.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s14)) | (~node15(c_e_h_1, c_f, s13, s14)) | m_c_h_element_v_out(c_e_h_1, c_f, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s14)) | (~node15(c_e_h_1, c_f, s13, s14)) | m_c_h_element_v_out(c_e_h_1, c_f, s13))),
% 295.80/188.35 inference(rewrite,[status(thm)],[])).
% 295.80/188.35 tff(32666,plain,
% 295.80/188.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s14)) | (~node15(c_e_h_1, c_f, s13, s14)) | m_c_h_element_v_out(c_e_h_1, c_f, s13))),
% 295.80/188.35 inference(quant_inst,[status(thm)],[])).
% 295.80/188.35 tff(32667,plain,
% 295.80/188.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s14)) | (~node15(c_e_h_1, c_f, s13, s14)) | m_c_h_element_v_out(c_e_h_1, c_f, s13)),
% 295.80/188.35 inference(modus_ponens,[status(thm)],[32666, 32665])).
% 295.80/188.35 tff(32668,plain,
% 295.80/188.35 ($false),
% 295.80/188.35 inference(unit_resolution,[status(thm)],[32667, 147, 32664, 32650, 32651])).
% 295.80/188.35 tff(32669,plain,((~node15(c_e_h_1, c_f, s13, s14)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s14)) | m_c_h_element_v_out(c_e_h_1, c_f, s13)), inference(lemma,lemma(discharge,[]))).
% 295.80/188.35 tff(32670,plain,
% 295.80/188.35 (~node15(c_e_h_1, c_f, s13, s14)),
% 295.80/188.35 inference(unit_resolution,[status(thm)],[32669, 32650, 32651])).
% 295.80/188.35 tff(32671,plain,
% 295.80/188.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s13, s14)) | node19(c_e_h_1, c_f, s13, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s13, s14)) | node19(c_e_h_1, c_f, s13, s14))),
% 295.80/188.35 inference(rewrite,[status(thm)],[])).
% 295.80/188.35 tff(32672,plain,
% 295.80/188.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s13, s14)) | node19(c_e_h_1, c_f, s13, s14))),
% 295.80/188.35 inference(quant_inst,[status(thm)],[])).
% 295.80/188.35 tff(32673,plain,
% 295.80/188.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s13, s14)) | node19(c_e_h_1, c_f, s13, s14)),
% 295.80/188.35 inference(modus_ponens,[status(thm)],[32672, 32671])).
% 295.80/188.35 tff(32674,plain,
% 295.80/188.35 (node19(c_e_h_1, c_f, s13, s14)),
% 295.80/188.35 inference(unit_resolution,[status(thm)],[32673, 190, 12831])).
% 295.80/188.35 tff(32675,plain,
% 295.80/188.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_f, s13, s14)) | node15(c_e_h_1, c_f, s13, s14) | node14(c_e_h_1, c_f, s13, s14) | node16(c_e_h_1, c_f, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s13, s14)) | node15(c_e_h_1, c_f, s13, s14) | node14(c_e_h_1, c_f, s13, s14) | node16(c_e_h_1, c_f, s13))),
% 295.80/188.35 inference(rewrite,[status(thm)],[])).
% 295.80/188.35 tff(32676,plain,
% 295.80/188.35 ((node16(c_e_h_1, c_f, s13) | node14(c_e_h_1, c_f, s13, s14) | node15(c_e_h_1, c_f, s13, s14) | (~node19(c_e_h_1, c_f, s13, s14))) <=> ((~node19(c_e_h_1, c_f, s13, s14)) | node15(c_e_h_1, c_f, s13, s14) | node14(c_e_h_1, c_f, s13, s14) | node16(c_e_h_1, c_f, s13))),
% 295.80/188.35 inference(rewrite,[status(thm)],[])).
% 295.80/188.35 tff(32677,plain,
% 295.80/188.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s13) | node14(c_e_h_1, c_f, s13, s14) | node15(c_e_h_1, c_f, s13, s14) | (~node19(c_e_h_1, c_f, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_f, s13, s14)) | node15(c_e_h_1, c_f, s13, s14) | node14(c_e_h_1, c_f, s13, s14) | node16(c_e_h_1, c_f, s13)))),
% 295.80/188.35 inference(monotonicity,[status(thm)],[32676])).
% 295.80/188.35 tff(32678,plain,
% 295.80/188.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s13) | node14(c_e_h_1, c_f, s13, s14) | node15(c_e_h_1, c_f, s13, s14) | (~node19(c_e_h_1, c_f, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s13, s14)) | node15(c_e_h_1, c_f, s13, s14) | node14(c_e_h_1, c_f, s13, s14) | node16(c_e_h_1, c_f, s13))),
% 295.80/188.35 inference(transitivity,[status(thm)],[32677, 32675])).
% 295.80/188.35 tff(32679,plain,
% 295.80/188.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s13) | node14(c_e_h_1, c_f, s13, s14) | node15(c_e_h_1, c_f, s13, s14) | (~node19(c_e_h_1, c_f, s13, s14)))),
% 295.80/188.35 inference(quant_inst,[status(thm)],[])).
% 295.80/188.35 tff(32680,plain,
% 295.80/188.35 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s13, s14)) | node15(c_e_h_1, c_f, s13, s14) | node14(c_e_h_1, c_f, s13, s14) | node16(c_e_h_1, c_f, s13)),
% 295.80/188.35 inference(modus_ponens,[status(thm)],[32679, 32678])).
% 295.80/188.35 tff(32681,plain,
% 295.80/188.35 (node15(c_e_h_1, c_f, s13, s14) | node14(c_e_h_1, c_f, s13, s14) | node16(c_e_h_1, c_f, s13)),
% 295.80/188.35 inference(unit_resolution,[status(thm)],[32680, 204, 32674])).
% 295.80/188.35 tff(32682,plain,
% 295.80/188.35 (node14(c_e_h_1, c_f, s13, s14)),
% 295.80/188.35 inference(unit_resolution,[status(thm)],[32681, 32670, 32663])).
% 295.80/188.35 tff(32683,plain,
% 295.80/188.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s14)) | m_c_h_element_v_in1(c_e_h_1, c_f, s13) | (~node14(c_e_h_1, c_f, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s14)) | m_c_h_element_v_in1(c_e_h_1, c_f, s13) | (~node14(c_e_h_1, c_f, s13, s14)))),
% 295.80/188.35 inference(rewrite,[status(thm)],[])).
% 295.80/188.35 tff(32684,plain,
% 295.80/188.35 (((~node14(c_e_h_1, c_f, s13, s14)) | m_c_h_element_v_in1(c_e_h_1, c_f, s13) | (~m_c_h_element_v_out(c_e_h_1, c_f, s14))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_f, s14)) | m_c_h_element_v_in1(c_e_h_1, c_f, s13) | (~node14(c_e_h_1, c_f, s13, s14)))),
% 295.80/188.35 inference(rewrite,[status(thm)],[])).
% 295.80/188.35 tff(32685,plain,
% 295.80/188.35 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s13, s14)) | m_c_h_element_v_in1(c_e_h_1, c_f, s13) | (~m_c_h_element_v_out(c_e_h_1, c_f, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s14)) | m_c_h_element_v_in1(c_e_h_1, c_f, s13) | (~node14(c_e_h_1, c_f, s13, s14))))),
% 295.80/188.36 inference(monotonicity,[status(thm)],[32684])).
% 295.80/188.36 tff(32686,plain,
% 295.80/188.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s13, s14)) | m_c_h_element_v_in1(c_e_h_1, c_f, s13) | (~m_c_h_element_v_out(c_e_h_1, c_f, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s14)) | m_c_h_element_v_in1(c_e_h_1, c_f, s13) | (~node14(c_e_h_1, c_f, s13, s14)))),
% 295.80/188.36 inference(transitivity,[status(thm)],[32685, 32683])).
% 295.80/188.36 tff(32687,plain,
% 295.80/188.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s13, s14)) | m_c_h_element_v_in1(c_e_h_1, c_f, s13) | (~m_c_h_element_v_out(c_e_h_1, c_f, s14)))),
% 295.80/188.36 inference(quant_inst,[status(thm)],[])).
% 295.80/188.36 tff(32688,plain,
% 295.80/188.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s14)) | m_c_h_element_v_in1(c_e_h_1, c_f, s13) | (~node14(c_e_h_1, c_f, s13, s14))),
% 295.80/188.36 inference(modus_ponens,[status(thm)],[32687, 32686])).
% 295.80/188.36 tff(32689,plain,
% 295.80/188.36 ($false),
% 295.80/188.36 inference(unit_resolution,[status(thm)],[32688, 223, 32682, 32650, 32662])).
% 295.80/188.36 tff(32690,plain,((~m_c_h_element_v_out(c_e_h_1, c_f, s14)) | m_c_h_element_v_in1(c_e_h_1, c_f, s13) | node16(c_e_h_1, c_f, s13) | m_c_h_element_v_out(c_e_h_1, c_f, s13)), inference(lemma,lemma(discharge,[]))).
% 295.80/188.36 tff(32691,plain,
% 295.80/188.36 (node16(c_e_h_1, c_f, s13)),
% 295.80/188.36 inference(unit_resolution,[status(thm)],[32690, 32651, 32650, 32662])).
% 295.80/188.36 tff(32692,plain,
% 295.80/188.36 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s13)) | m_c_h_element_v_in1(c_e_h_1, c_f, s13) | m_c_h_element_v_in2(c_e_h_1, c_f, s13))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s13)) | m_c_h_element_v_in1(c_e_h_1, c_f, s13) | m_c_h_element_v_in2(c_e_h_1, c_f, s13))),
% 295.80/188.36 inference(rewrite,[status(thm)],[])).
% 295.80/188.36 tff(32693,plain,
% 295.80/188.36 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s13)) | m_c_h_element_v_in1(c_e_h_1, c_f, s13) | m_c_h_element_v_in2(c_e_h_1, c_f, s13))),
% 295.80/188.36 inference(quant_inst,[status(thm)],[])).
% 295.80/188.36 tff(32694,plain,
% 295.80/188.36 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s13)) | m_c_h_element_v_in1(c_e_h_1, c_f, s13) | m_c_h_element_v_in2(c_e_h_1, c_f, s13)),
% 295.80/188.36 inference(modus_ponens,[status(thm)],[32693, 32692])).
% 295.80/188.36 tff(32695,plain,
% 295.80/188.36 ((~node16(c_e_h_1, c_f, s13)) | m_c_h_element_v_in2(c_e_h_1, c_f, s13)),
% 295.80/188.36 inference(unit_resolution,[status(thm)],[32694, 178, 32662])).
% 295.80/188.36 tff(32696,plain,
% 295.80/188.36 (m_c_h_element_v_in2(c_e_h_1, c_f, s13)),
% 295.80/188.36 inference(unit_resolution,[status(thm)],[32695, 32691])).
% 295.80/188.36 tff(32697,plain,
% 295.80/188.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_f, s13, s14)) | node18(c_e_h_1, c_f, s13, s14) | node17(c_e_h_1, c_f, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s13, s14)) | node18(c_e_h_1, c_f, s13, s14) | node17(c_e_h_1, c_f, s13))),
% 295.80/188.36 inference(rewrite,[status(thm)],[])).
% 295.80/188.36 tff(32698,plain,
% 295.80/188.36 ((node17(c_e_h_1, c_f, s13) | node18(c_e_h_1, c_f, s13, s14) | (~node19(c_e_h_1, c_f, s13, s14))) <=> ((~node19(c_e_h_1, c_f, s13, s14)) | node18(c_e_h_1, c_f, s13, s14) | node17(c_e_h_1, c_f, s13))),
% 295.80/188.36 inference(rewrite,[status(thm)],[])).
% 295.80/188.36 tff(32699,plain,
% 295.80/188.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s13) | node18(c_e_h_1, c_f, s13, s14) | (~node19(c_e_h_1, c_f, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_f, s13, s14)) | node18(c_e_h_1, c_f, s13, s14) | node17(c_e_h_1, c_f, s13)))),
% 295.80/188.36 inference(monotonicity,[status(thm)],[32698])).
% 295.80/188.36 tff(32700,plain,
% 295.80/188.36 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s13) | node18(c_e_h_1, c_f, s13, s14) | (~node19(c_e_h_1, c_f, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s13, s14)) | node18(c_e_h_1, c_f, s13, s14) | node17(c_e_h_1, c_f, s13))),
% 295.80/188.36 inference(transitivity,[status(thm)],[32699, 32697])).
% 295.80/188.36 tff(32701,plain,
% 295.80/188.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s13) | node18(c_e_h_1, c_f, s13, s14) | (~node19(c_e_h_1, c_f, s13, s14)))),
% 295.80/188.36 inference(quant_inst,[status(thm)],[])).
% 295.80/188.36 tff(32702,plain,
% 295.80/188.36 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s13, s14)) | node18(c_e_h_1, c_f, s13, s14) | node17(c_e_h_1, c_f, s13)),
% 295.80/188.36 inference(modus_ponens,[status(thm)],[32701, 32700])).
% 295.80/188.36 tff(32703,plain,
% 295.80/188.36 (node18(c_e_h_1, c_f, s13, s14) | node17(c_e_h_1, c_f, s13)),
% 295.80/188.36 inference(unit_resolution,[status(thm)],[32702, 776, 32674])).
% 295.80/188.36 tff(32704,plain,
% 295.80/188.36 (node17(c_e_h_1, c_f, s13)),
% 295.80/188.36 inference(unit_resolution,[status(thm)],[32703, 32661])).
% 295.80/188.36 tff(32705,plain,
% 295.80/188.36 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s13)) | m_c_h_element_v_in1(c_e_h_1, c_f, s13) | (~node17(c_e_h_1, c_f, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s13)) | m_c_h_element_v_in1(c_e_h_1, c_f, s13) | (~node17(c_e_h_1, c_f, s13)))),
% 295.80/188.36 inference(rewrite,[status(thm)],[])).
% 295.80/188.36 tff(32706,plain,
% 295.80/188.36 ((m_c_h_element_v_in1(c_e_h_1, c_f, s13) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s13)) | (~node17(c_e_h_1, c_f, s13))) <=> ((~m_c_h_element_v_in2(c_e_h_1, c_f, s13)) | m_c_h_element_v_in1(c_e_h_1, c_f, s13) | (~node17(c_e_h_1, c_f, s13)))),
% 295.80/188.36 inference(rewrite,[status(thm)],[])).
% 295.80/188.36 tff(32707,plain,
% 295.80/188.36 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s13) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s13)) | (~node17(c_e_h_1, c_f, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s13)) | m_c_h_element_v_in1(c_e_h_1, c_f, s13) | (~node17(c_e_h_1, c_f, s13))))),
% 295.80/188.36 inference(monotonicity,[status(thm)],[32706])).
% 295.80/188.36 tff(32708,plain,
% 295.80/188.36 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s13) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s13)) | (~node17(c_e_h_1, c_f, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s13)) | m_c_h_element_v_in1(c_e_h_1, c_f, s13) | (~node17(c_e_h_1, c_f, s13)))),
% 295.80/188.36 inference(transitivity,[status(thm)],[32707, 32705])).
% 295.80/188.36 tff(32709,plain,
% 295.80/188.36 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s13) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s13)) | (~node17(c_e_h_1, c_f, s13)))),
% 295.80/188.36 inference(quant_inst,[status(thm)],[])).
% 295.80/188.36 tff(32710,plain,
% 295.80/188.36 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s13)) | m_c_h_element_v_in1(c_e_h_1, c_f, s13) | (~node17(c_e_h_1, c_f, s13))),
% 295.80/188.36 inference(modus_ponens,[status(thm)],[32709, 32708])).
% 295.80/188.36 tff(32711,plain,
% 295.80/188.36 ((~m_c_h_element_v_in2(c_e_h_1, c_f, s13)) | (~node17(c_e_h_1, c_f, s13))),
% 295.80/188.36 inference(unit_resolution,[status(thm)],[32710, 859, 32662])).
% 295.80/188.36 tff(32712,plain,
% 295.80/188.36 ($false),
% 295.80/188.36 inference(unit_resolution,[status(thm)],[32711, 32704, 32696])).
% 295.80/188.36 tff(32713,plain,(m_c_h_element_v_out(c_e_h_1, c_f, s13) | m_c_h_element_v_in1(c_e_h_1, c_f, s13) | (~m_c_h_element_v_out(c_e_h_1, c_f, s14))), inference(lemma,lemma(discharge,[]))).
% 295.80/188.36 tff(32714,plain,
% 295.80/188.36 (m_c_h_element_v_in1(c_e_h_1, c_f, s13)),
% 295.80/188.36 inference(unit_resolution,[status(thm)],[32713, 32651, 32650])).
% 295.80/188.36 tff(32715,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_f, s13)), introduced(assumption)).
% 295.80/188.36 tff(32716,plain,
% 295.80/188.36 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_f, s13) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s13)) | (~node17(c_e_h_1, c_f, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_f, s13) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s13)) | (~node17(c_e_h_1, c_f, s13)))),
% 295.80/188.36 inference(rewrite,[status(thm)],[])).
% 295.80/188.36 tff(32717,plain,
% 295.80/188.36 (((~m_c_h_element_v_in1(c_e_h_1, c_f, s13)) | m_c_h_element_v_in2(c_e_h_1, c_f, s13) | (~node17(c_e_h_1, c_f, s13))) <=> (m_c_h_element_v_in2(c_e_h_1, c_f, s13) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s13)) | (~node17(c_e_h_1, c_f, s13)))),
% 295.80/188.36 inference(rewrite,[status(thm)],[])).
% 295.80/188.36 tff(32718,plain,
% 295.80/188.36 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s13)) | m_c_h_element_v_in2(c_e_h_1, c_f, s13) | (~node17(c_e_h_1, c_f, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_f, s13) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s13)) | (~node17(c_e_h_1, c_f, s13))))),
% 295.80/188.36 inference(monotonicity,[status(thm)],[32717])).
% 295.80/188.36 tff(32719,plain,
% 295.80/188.36 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s13)) | m_c_h_element_v_in2(c_e_h_1, c_f, s13) | (~node17(c_e_h_1, c_f, s13)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_f, s13) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s13)) | (~node17(c_e_h_1, c_f, s13)))),
% 295.80/188.36 inference(transitivity,[status(thm)],[32718, 32716])).
% 295.80/188.36 tff(32720,plain,
% 295.80/188.36 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s13)) | m_c_h_element_v_in2(c_e_h_1, c_f, s13) | (~node17(c_e_h_1, c_f, s13)))),
% 295.80/188.36 inference(quant_inst,[status(thm)],[])).
% 295.80/188.36 tff(32721,plain,
% 295.80/188.36 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_f, s13) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s13)) | (~node17(c_e_h_1, c_f, s13))),
% 295.80/188.36 inference(modus_ponens,[status(thm)],[32720, 32719])).
% 295.80/188.36 tff(32722,plain,
% 295.80/188.36 ((~m_c_h_element_v_in1(c_e_h_1, c_f, s13)) | (~node17(c_e_h_1, c_f, s13))),
% 295.80/188.36 inference(unit_resolution,[status(thm)],[32721, 919, 32715])).
% 295.80/188.36 tff(32723,plain,
% 295.80/188.36 (~node17(c_e_h_1, c_f, s13)),
% 295.80/188.36 inference(unit_resolution,[status(thm)],[32722, 32714])).
% 295.80/188.36 tff(32724,plain,
% 295.80/188.36 ($false),
% 295.80/188.36 inference(unit_resolution,[status(thm)],[32703, 32723, 32661])).
% 295.80/188.36 tff(32725,plain,(m_c_h_element_v_out(c_e_h_1, c_f, s13) | m_c_h_element_v_in2(c_e_h_1, c_f, s13) | (~m_c_h_element_v_out(c_e_h_1, c_f, s14))), inference(lemma,lemma(discharge,[]))).
% 295.80/188.36 tff(32726,plain,
% 295.80/188.36 (~m_c_h_element_v_out(c_e_h_1, c_f, s14)),
% 295.80/188.37 inference(unit_resolution,[status(thm)],[32725, 32649, 32642])).
% 295.80/188.37 tff(32727,assumption,(m_c_h_element_v_in2(c_e_h_1, c_f, s14)), introduced(assumption)).
% 295.80/188.37 tff(32728,plain,
% 295.80/188.37 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s14)) | m_and_h_gate_v_out(c_e_h_1, c_i, s14))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s14)) | m_and_h_gate_v_out(c_e_h_1, c_i, s14))),
% 295.80/188.37 inference(rewrite,[status(thm)],[])).
% 295.80/188.37 tff(32729,plain,
% 295.80/188.37 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s14)) | m_and_h_gate_v_out(c_e_h_1, c_i, s14))),
% 295.80/188.37 inference(quant_inst,[status(thm)],[])).
% 295.80/188.37 tff(32730,plain,
% 295.80/188.37 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s14)) | m_and_h_gate_v_out(c_e_h_1, c_i, s14)),
% 295.80/188.37 inference(modus_ponens,[status(thm)],[32729, 32728])).
% 295.80/188.37 tff(32731,plain,
% 295.80/188.37 ($false),
% 295.80/188.37 inference(unit_resolution,[status(thm)],[32730, 2143, 24217, 32727])).
% 295.80/188.37 tff(32732,plain,((~m_c_h_element_v_in2(c_e_h_1, c_f, s14)) | m_and_h_gate_v_out(c_e_h_1, c_i, s14)), inference(lemma,lemma(discharge,[]))).
% 295.80/188.37 tff(32733,plain,
% 295.80/188.37 (~m_c_h_element_v_in2(c_e_h_1, c_f, s14)),
% 295.80/188.37 inference(unit_resolution,[status(thm)],[32732, 24216])).
% 295.80/188.37 tff(32734,assumption,(~m_c_h_element_v_out(c_e_h_1, c_f, s14)), introduced(assumption)).
% 295.80/188.37 tff(32735,assumption,(m_c_h_element_v_out(c_e_h_1, c_f, s15)), introduced(assumption)).
% 295.80/188.37 tff(32736,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_f, s14)), introduced(assumption)).
% 295.80/188.37 tff(32737,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_f, s14)), introduced(assumption)).
% 295.80/188.37 tff(32738,assumption,(~node15(c_e_h_1, c_f, s14, s15)), introduced(assumption)).
% 295.80/188.37 tff(32739,plain,
% 295.80/188.37 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s14)) | m_c_h_element_v_in1(c_e_h_1, c_f, s14) | m_c_h_element_v_in2(c_e_h_1, c_f, s14))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s14)) | m_c_h_element_v_in1(c_e_h_1, c_f, s14) | m_c_h_element_v_in2(c_e_h_1, c_f, s14))),
% 295.80/188.37 inference(rewrite,[status(thm)],[])).
% 295.80/188.37 tff(32740,plain,
% 295.80/188.37 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s14)) | m_c_h_element_v_in1(c_e_h_1, c_f, s14) | m_c_h_element_v_in2(c_e_h_1, c_f, s14))),
% 295.80/188.37 inference(quant_inst,[status(thm)],[])).
% 295.80/188.37 tff(32741,plain,
% 295.80/188.37 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s14)) | m_c_h_element_v_in1(c_e_h_1, c_f, s14) | m_c_h_element_v_in2(c_e_h_1, c_f, s14)),
% 295.80/188.37 inference(modus_ponens,[status(thm)],[32740, 32739])).
% 295.80/188.37 tff(32742,plain,
% 295.80/188.37 ((~node16(c_e_h_1, c_f, s14)) | m_c_h_element_v_in1(c_e_h_1, c_f, s14)),
% 295.80/188.37 inference(unit_resolution,[status(thm)],[32741, 178, 32737])).
% 295.80/188.37 tff(32743,plain,
% 295.80/188.37 (~node16(c_e_h_1, c_f, s14)),
% 295.80/188.37 inference(unit_resolution,[status(thm)],[32742, 32736])).
% 295.80/188.37 tff(32744,plain,
% 295.80/188.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s14, s15)) | node19(c_e_h_1, c_f, s14, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s14, s15)) | node19(c_e_h_1, c_f, s14, s15))),
% 295.80/188.37 inference(rewrite,[status(thm)],[])).
% 295.80/188.37 tff(32745,plain,
% 295.80/188.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s14, s15)) | node19(c_e_h_1, c_f, s14, s15))),
% 295.80/188.37 inference(quant_inst,[status(thm)],[])).
% 295.80/188.37 tff(32746,plain,
% 295.80/188.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s14, s15)) | node19(c_e_h_1, c_f, s14, s15)),
% 295.80/188.37 inference(modus_ponens,[status(thm)],[32745, 32744])).
% 295.80/188.37 tff(32747,plain,
% 295.80/188.37 (node19(c_e_h_1, c_f, s14, s15)),
% 295.80/188.37 inference(unit_resolution,[status(thm)],[32746, 190, 12926])).
% 295.80/188.37 tff(32748,plain,
% 295.80/188.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_1, c_f, s14, s15) | node16(c_e_h_1, c_f, s14) | (~node19(c_e_h_1, c_f, s14, s15)) | node14(c_e_h_1, c_f, s14, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_f, s14, s15) | node16(c_e_h_1, c_f, s14) | (~node19(c_e_h_1, c_f, s14, s15)) | node14(c_e_h_1, c_f, s14, s15))),
% 295.80/188.37 inference(rewrite,[status(thm)],[])).
% 295.80/188.37 tff(32749,plain,
% 295.80/188.37 ((node16(c_e_h_1, c_f, s14) | node14(c_e_h_1, c_f, s14, s15) | node15(c_e_h_1, c_f, s14, s15) | (~node19(c_e_h_1, c_f, s14, s15))) <=> (node15(c_e_h_1, c_f, s14, s15) | node16(c_e_h_1, c_f, s14) | (~node19(c_e_h_1, c_f, s14, s15)) | node14(c_e_h_1, c_f, s14, s15))),
% 295.80/188.37 inference(rewrite,[status(thm)],[])).
% 295.80/188.37 tff(32750,plain,
% 295.80/188.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s14) | node14(c_e_h_1, c_f, s14, s15) | node15(c_e_h_1, c_f, s14, s15) | (~node19(c_e_h_1, c_f, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node15(c_e_h_1, c_f, s14, s15) | node16(c_e_h_1, c_f, s14) | (~node19(c_e_h_1, c_f, s14, s15)) | node14(c_e_h_1, c_f, s14, s15)))),
% 295.80/188.37 inference(monotonicity,[status(thm)],[32749])).
% 295.80/188.37 tff(32751,plain,
% 295.80/188.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s14) | node14(c_e_h_1, c_f, s14, s15) | node15(c_e_h_1, c_f, s14, s15) | (~node19(c_e_h_1, c_f, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_f, s14, s15) | node16(c_e_h_1, c_f, s14) | (~node19(c_e_h_1, c_f, s14, s15)) | node14(c_e_h_1, c_f, s14, s15))),
% 295.80/188.37 inference(transitivity,[status(thm)],[32750, 32748])).
% 295.80/188.37 tff(32752,plain,
% 295.80/188.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s14) | node14(c_e_h_1, c_f, s14, s15) | node15(c_e_h_1, c_f, s14, s15) | (~node19(c_e_h_1, c_f, s14, s15)))),
% 295.80/188.37 inference(quant_inst,[status(thm)],[])).
% 295.80/188.37 tff(32753,plain,
% 295.80/188.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node15(c_e_h_1, c_f, s14, s15) | node16(c_e_h_1, c_f, s14) | (~node19(c_e_h_1, c_f, s14, s15)) | node14(c_e_h_1, c_f, s14, s15)),
% 295.80/188.37 inference(modus_ponens,[status(thm)],[32752, 32751])).
% 295.80/188.37 tff(32754,plain,
% 295.80/188.37 (node15(c_e_h_1, c_f, s14, s15) | node16(c_e_h_1, c_f, s14) | node14(c_e_h_1, c_f, s14, s15)),
% 295.80/188.37 inference(unit_resolution,[status(thm)],[32753, 204, 32747])).
% 295.80/188.37 tff(32755,plain,
% 295.80/188.37 (node14(c_e_h_1, c_f, s14, s15)),
% 295.80/188.37 inference(unit_resolution,[status(thm)],[32754, 32743, 32738])).
% 295.80/188.37 tff(32756,plain,
% 295.80/188.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s14) | (~node14(c_e_h_1, c_f, s14, s15)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_f, s14) | (~node14(c_e_h_1, c_f, s14, s15)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s15)))),
% 295.80/188.37 inference(rewrite,[status(thm)],[])).
% 295.80/188.37 tff(32757,plain,
% 295.80/188.37 (((~node14(c_e_h_1, c_f, s14, s15)) | m_c_h_element_v_in1(c_e_h_1, c_f, s14) | (~m_c_h_element_v_out(c_e_h_1, c_f, s15))) <=> (m_c_h_element_v_in1(c_e_h_1, c_f, s14) | (~node14(c_e_h_1, c_f, s14, s15)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s15)))),
% 295.80/188.37 inference(rewrite,[status(thm)],[])).
% 295.80/188.37 tff(32758,plain,
% 295.80/188.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s14, s15)) | m_c_h_element_v_in1(c_e_h_1, c_f, s14) | (~m_c_h_element_v_out(c_e_h_1, c_f, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s14) | (~node14(c_e_h_1, c_f, s14, s15)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s15))))),
% 295.80/188.37 inference(monotonicity,[status(thm)],[32757])).
% 295.80/188.37 tff(32759,plain,
% 295.80/188.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s14, s15)) | m_c_h_element_v_in1(c_e_h_1, c_f, s14) | (~m_c_h_element_v_out(c_e_h_1, c_f, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_f, s14) | (~node14(c_e_h_1, c_f, s14, s15)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s15)))),
% 295.80/188.37 inference(transitivity,[status(thm)],[32758, 32756])).
% 295.80/188.37 tff(32760,plain,
% 295.80/188.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s14, s15)) | m_c_h_element_v_in1(c_e_h_1, c_f, s14) | (~m_c_h_element_v_out(c_e_h_1, c_f, s15)))),
% 295.80/188.37 inference(quant_inst,[status(thm)],[])).
% 295.80/188.37 tff(32761,plain,
% 295.80/188.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_f, s14) | (~node14(c_e_h_1, c_f, s14, s15)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s15))),
% 295.80/188.37 inference(modus_ponens,[status(thm)],[32760, 32759])).
% 295.80/188.37 tff(32762,plain,
% 295.80/188.37 ($false),
% 295.80/188.37 inference(unit_resolution,[status(thm)],[32761, 223, 32735, 32755, 32736])).
% 295.80/188.37 tff(32763,plain,(m_c_h_element_v_in1(c_e_h_1, c_f, s14) | (~m_c_h_element_v_out(c_e_h_1, c_f, s15)) | node15(c_e_h_1, c_f, s14, s15) | m_c_h_element_v_in2(c_e_h_1, c_f, s14)), inference(lemma,lemma(discharge,[]))).
% 295.80/188.37 tff(32764,plain,
% 295.80/188.37 (node15(c_e_h_1, c_f, s14, s15)),
% 295.80/188.37 inference(unit_resolution,[status(thm)],[32763, 32735, 32736, 32737])).
% 295.80/188.37 tff(32765,assumption,(node15(c_e_h_1, c_f, s14, s15)), introduced(assumption)).
% 295.80/188.37 tff(32766,plain,
% 295.80/188.37 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s15)) | (~node15(c_e_h_1, c_f, s14, s15)) | m_c_h_element_v_out(c_e_h_1, c_f, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s15)) | (~node15(c_e_h_1, c_f, s14, s15)) | m_c_h_element_v_out(c_e_h_1, c_f, s14))),
% 295.80/188.37 inference(rewrite,[status(thm)],[])).
% 295.80/188.37 tff(32767,plain,
% 295.80/188.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s15)) | (~node15(c_e_h_1, c_f, s14, s15)) | m_c_h_element_v_out(c_e_h_1, c_f, s14))),
% 295.80/188.37 inference(quant_inst,[status(thm)],[])).
% 295.80/188.37 tff(32768,plain,
% 295.80/188.37 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s15)) | (~node15(c_e_h_1, c_f, s14, s15)) | m_c_h_element_v_out(c_e_h_1, c_f, s14)),
% 295.80/188.37 inference(modus_ponens,[status(thm)],[32767, 32766])).
% 295.80/188.37 tff(32769,plain,
% 295.80/188.37 ($false),
% 295.80/188.37 inference(unit_resolution,[status(thm)],[32768, 147, 32735, 32765, 32734])).
% 295.80/188.37 tff(32770,plain,((~node15(c_e_h_1, c_f, s14, s15)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s15)) | m_c_h_element_v_out(c_e_h_1, c_f, s14)), inference(lemma,lemma(discharge,[]))).
% 295.80/188.37 tff(32771,plain,
% 295.80/188.37 ($false),
% 295.80/188.37 inference(unit_resolution,[status(thm)],[32770, 32764, 32735, 32734])).
% 295.80/188.37 tff(32772,plain,((~m_c_h_element_v_out(c_e_h_1, c_f, s15)) | m_c_h_element_v_out(c_e_h_1, c_f, s14) | m_c_h_element_v_in1(c_e_h_1, c_f, s14) | m_c_h_element_v_in2(c_e_h_1, c_f, s14)), inference(lemma,lemma(discharge,[]))).
% 295.80/188.38 tff(32773,plain,
% 295.80/188.38 (m_c_h_element_v_in2(c_e_h_1, c_f, s14)),
% 295.80/188.38 inference(unit_resolution,[status(thm)],[32772, 32735, 32736, 32734])).
% 295.80/188.38 tff(32774,plain,
% 295.80/188.38 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_f, s14)) | m_c_h_element_v_in1(c_e_h_1, c_f, s14) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s14)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_f, s14)) | m_c_h_element_v_in1(c_e_h_1, c_f, s14) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s14)))),
% 295.80/188.38 inference(rewrite,[status(thm)],[])).
% 295.80/188.38 tff(32775,plain,
% 295.80/188.38 ((m_c_h_element_v_in1(c_e_h_1, c_f, s14) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s14)) | (~node17(c_e_h_1, c_f, s14))) <=> ((~node17(c_e_h_1, c_f, s14)) | m_c_h_element_v_in1(c_e_h_1, c_f, s14) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s14)))),
% 295.80/188.38 inference(rewrite,[status(thm)],[])).
% 295.80/188.38 tff(32776,plain,
% 295.80/188.38 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s14) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s14)) | (~node17(c_e_h_1, c_f, s14)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_f, s14)) | m_c_h_element_v_in1(c_e_h_1, c_f, s14) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s14))))),
% 295.80/188.38 inference(monotonicity,[status(thm)],[32775])).
% 295.80/188.38 tff(32777,plain,
% 295.80/188.38 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s14) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s14)) | (~node17(c_e_h_1, c_f, s14)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_f, s14)) | m_c_h_element_v_in1(c_e_h_1, c_f, s14) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s14)))),
% 295.80/188.38 inference(transitivity,[status(thm)],[32776, 32774])).
% 295.80/188.38 tff(32778,plain,
% 295.80/188.38 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s14) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s14)) | (~node17(c_e_h_1, c_f, s14)))),
% 295.80/188.38 inference(quant_inst,[status(thm)],[])).
% 295.80/188.38 tff(32779,plain,
% 295.80/188.38 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_f, s14)) | m_c_h_element_v_in1(c_e_h_1, c_f, s14) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s14))),
% 295.80/188.38 inference(modus_ponens,[status(thm)],[32778, 32777])).
% 295.80/188.38 tff(32780,plain,
% 295.80/188.38 ((~node17(c_e_h_1, c_f, s14)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s14))),
% 295.80/188.38 inference(unit_resolution,[status(thm)],[32779, 859, 32736])).
% 295.80/188.38 tff(32781,plain,
% 295.80/188.38 (~node17(c_e_h_1, c_f, s14)),
% 295.80/188.38 inference(unit_resolution,[status(thm)],[32780, 32773])).
% 295.80/188.38 tff(32782,plain,
% 295.80/188.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s14) | (~node19(c_e_h_1, c_f, s14, s15)) | node18(c_e_h_1, c_f, s14, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_f, s14) | (~node19(c_e_h_1, c_f, s14, s15)) | node18(c_e_h_1, c_f, s14, s15))),
% 295.80/188.38 inference(rewrite,[status(thm)],[])).
% 295.80/188.38 tff(32783,plain,
% 295.80/188.38 ((node17(c_e_h_1, c_f, s14) | node18(c_e_h_1, c_f, s14, s15) | (~node19(c_e_h_1, c_f, s14, s15))) <=> (node17(c_e_h_1, c_f, s14) | (~node19(c_e_h_1, c_f, s14, s15)) | node18(c_e_h_1, c_f, s14, s15))),
% 295.80/188.38 inference(rewrite,[status(thm)],[])).
% 295.80/188.38 tff(32784,plain,
% 295.80/188.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s14) | node18(c_e_h_1, c_f, s14, s15) | (~node19(c_e_h_1, c_f, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s14) | (~node19(c_e_h_1, c_f, s14, s15)) | node18(c_e_h_1, c_f, s14, s15)))),
% 295.80/188.38 inference(monotonicity,[status(thm)],[32783])).
% 295.80/188.38 tff(32785,plain,
% 295.80/188.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s14) | node18(c_e_h_1, c_f, s14, s15) | (~node19(c_e_h_1, c_f, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_f, s14) | (~node19(c_e_h_1, c_f, s14, s15)) | node18(c_e_h_1, c_f, s14, s15))),
% 295.80/188.38 inference(transitivity,[status(thm)],[32784, 32782])).
% 295.80/188.38 tff(32786,plain,
% 295.80/188.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s14) | node18(c_e_h_1, c_f, s14, s15) | (~node19(c_e_h_1, c_f, s14, s15)))),
% 295.80/188.38 inference(quant_inst,[status(thm)],[])).
% 295.80/188.38 tff(32787,plain,
% 295.80/188.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_f, s14) | (~node19(c_e_h_1, c_f, s14, s15)) | node18(c_e_h_1, c_f, s14, s15)),
% 295.80/188.38 inference(modus_ponens,[status(thm)],[32786, 32785])).
% 295.80/188.38 tff(32788,plain,
% 295.80/188.38 (node17(c_e_h_1, c_f, s14) | node18(c_e_h_1, c_f, s14, s15)),
% 295.80/188.38 inference(unit_resolution,[status(thm)],[32787, 776, 32747])).
% 295.80/188.38 tff(32789,plain,
% 295.80/188.38 (node18(c_e_h_1, c_f, s14, s15)),
% 295.80/188.38 inference(unit_resolution,[status(thm)],[32788, 32781])).
% 295.80/188.38 tff(32790,plain,
% 295.80/188.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_f, s14) | (~m_c_h_element_v_out(c_e_h_1, c_f, s15)) | (~node18(c_e_h_1, c_f, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s14) | (~m_c_h_element_v_out(c_e_h_1, c_f, s15)) | (~node18(c_e_h_1, c_f, s14, s15)))),
% 295.80/188.38 inference(rewrite,[status(thm)],[])).
% 295.80/188.38 tff(32791,plain,
% 295.80/188.38 (((~m_c_h_element_v_out(c_e_h_1, c_f, s15)) | m_c_h_element_v_out(c_e_h_1, c_f, s14) | (~node18(c_e_h_1, c_f, s14, s15))) <=> (m_c_h_element_v_out(c_e_h_1, c_f, s14) | (~m_c_h_element_v_out(c_e_h_1, c_f, s15)) | (~node18(c_e_h_1, c_f, s14, s15)))),
% 295.80/188.38 inference(rewrite,[status(thm)],[])).
% 295.80/188.38 tff(32792,plain,
% 295.80/188.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s15)) | m_c_h_element_v_out(c_e_h_1, c_f, s14) | (~node18(c_e_h_1, c_f, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_f, s14) | (~m_c_h_element_v_out(c_e_h_1, c_f, s15)) | (~node18(c_e_h_1, c_f, s14, s15))))),
% 295.80/188.38 inference(monotonicity,[status(thm)],[32791])).
% 295.80/188.38 tff(32793,plain,
% 295.80/188.38 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s15)) | m_c_h_element_v_out(c_e_h_1, c_f, s14) | (~node18(c_e_h_1, c_f, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s14) | (~m_c_h_element_v_out(c_e_h_1, c_f, s15)) | (~node18(c_e_h_1, c_f, s14, s15)))),
% 295.80/188.38 inference(transitivity,[status(thm)],[32792, 32790])).
% 295.80/188.38 tff(32794,plain,
% 295.80/188.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s15)) | m_c_h_element_v_out(c_e_h_1, c_f, s14) | (~node18(c_e_h_1, c_f, s14, s15)))),
% 295.80/188.38 inference(quant_inst,[status(thm)],[])).
% 295.80/188.38 tff(32795,plain,
% 295.80/188.38 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s14) | (~m_c_h_element_v_out(c_e_h_1, c_f, s15)) | (~node18(c_e_h_1, c_f, s14, s15))),
% 295.80/188.38 inference(modus_ponens,[status(thm)],[32794, 32793])).
% 295.80/188.38 tff(32796,plain,
% 295.80/188.38 ($false),
% 295.80/188.38 inference(unit_resolution,[status(thm)],[32795, 753, 32735, 32789, 32734])).
% 295.80/188.38 tff(32797,plain,((~m_c_h_element_v_out(c_e_h_1, c_f, s15)) | m_c_h_element_v_out(c_e_h_1, c_f, s14) | m_c_h_element_v_in1(c_e_h_1, c_f, s14)), inference(lemma,lemma(discharge,[]))).
% 295.80/188.38 tff(32798,plain,
% 295.80/188.38 (m_c_h_element_v_in1(c_e_h_1, c_f, s14)),
% 295.80/188.38 inference(unit_resolution,[status(thm)],[32797, 32735, 32734])).
% 295.80/188.38 tff(32799,plain,
% 295.80/188.38 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_f, s14) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s14)) | (~node17(c_e_h_1, c_f, s14)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_f, s14) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s14)) | (~node17(c_e_h_1, c_f, s14)))),
% 295.80/188.38 inference(rewrite,[status(thm)],[])).
% 295.80/188.38 tff(32800,plain,
% 295.80/188.38 (((~m_c_h_element_v_in1(c_e_h_1, c_f, s14)) | m_c_h_element_v_in2(c_e_h_1, c_f, s14) | (~node17(c_e_h_1, c_f, s14))) <=> (m_c_h_element_v_in2(c_e_h_1, c_f, s14) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s14)) | (~node17(c_e_h_1, c_f, s14)))),
% 295.80/188.38 inference(rewrite,[status(thm)],[])).
% 295.80/188.38 tff(32801,plain,
% 295.80/188.38 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s14)) | m_c_h_element_v_in2(c_e_h_1, c_f, s14) | (~node17(c_e_h_1, c_f, s14)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_f, s14) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s14)) | (~node17(c_e_h_1, c_f, s14))))),
% 295.80/188.38 inference(monotonicity,[status(thm)],[32800])).
% 295.80/188.38 tff(32802,plain,
% 295.80/188.38 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s14)) | m_c_h_element_v_in2(c_e_h_1, c_f, s14) | (~node17(c_e_h_1, c_f, s14)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_f, s14) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s14)) | (~node17(c_e_h_1, c_f, s14)))),
% 295.80/188.38 inference(transitivity,[status(thm)],[32801, 32799])).
% 295.80/188.38 tff(32803,plain,
% 295.80/188.38 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s14)) | m_c_h_element_v_in2(c_e_h_1, c_f, s14) | (~node17(c_e_h_1, c_f, s14)))),
% 295.80/188.38 inference(quant_inst,[status(thm)],[])).
% 295.80/188.38 tff(32804,plain,
% 295.80/188.38 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_f, s14) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s14)) | (~node17(c_e_h_1, c_f, s14))),
% 295.80/188.38 inference(modus_ponens,[status(thm)],[32803, 32802])).
% 295.80/188.38 tff(32805,plain,
% 295.80/188.38 ((~m_c_h_element_v_in1(c_e_h_1, c_f, s14)) | (~node17(c_e_h_1, c_f, s14))),
% 295.80/188.38 inference(unit_resolution,[status(thm)],[32804, 919, 32737])).
% 295.80/188.38 tff(32806,plain,
% 295.80/188.38 (~node17(c_e_h_1, c_f, s14)),
% 295.80/188.38 inference(unit_resolution,[status(thm)],[32805, 32798])).
% 295.80/188.38 tff(32807,plain,
% 295.80/188.38 (node18(c_e_h_1, c_f, s14, s15)),
% 295.80/188.38 inference(unit_resolution,[status(thm)],[32788, 32806])).
% 295.80/188.38 tff(32808,plain,
% 295.80/188.38 ($false),
% 295.80/188.38 inference(unit_resolution,[status(thm)],[32795, 753, 32735, 32807, 32734])).
% 295.80/188.38 tff(32809,plain,((~m_c_h_element_v_out(c_e_h_1, c_f, s15)) | m_c_h_element_v_out(c_e_h_1, c_f, s14) | m_c_h_element_v_in2(c_e_h_1, c_f, s14)), inference(lemma,lemma(discharge,[]))).
% 295.80/188.38 tff(32810,plain,
% 295.80/188.39 (~m_c_h_element_v_out(c_e_h_1, c_f, s15)),
% 295.80/188.39 inference(unit_resolution,[status(thm)],[32809, 32733, 32726])).
% 295.80/188.39 tff(32811,assumption,(~m_c_h_element_v_out(c_e_h_1, c_f, s15)), introduced(assumption)).
% 295.80/188.39 tff(32812,assumption,(m_c_h_element_v_out(c_e_h_1, c_f, s17)), introduced(assumption)).
% 295.80/188.39 tff(32813,plain,
% 295.80/188.39 (~m_cell_v_ack(c_e_h_1, s12)),
% 295.80/188.39 inference(unit_resolution,[status(thm)],[22071, 22023])).
% 295.80/188.39 tff(32814,plain,
% 295.80/188.39 (~m_or_h_gate_v_in2(c_e_h_1, c_j, s12)),
% 295.80/188.39 inference(unit_resolution,[status(thm)],[22075, 1085, 32813])).
% 295.80/188.39 tff(32815,plain,
% 295.80/188.39 (~m_or_h_gate_v_out(c_e_h_1, c_j, s13)),
% 295.80/188.39 inference(unit_resolution,[status(thm)],[23154, 32814, 22868])).
% 295.80/188.39 tff(32816,plain,
% 295.80/188.39 (~m_and_h_gate_v_out(c_e_h_3, c_q, s13)),
% 295.80/188.39 inference(unit_resolution,[status(thm)],[22048, 22023, 22032])).
% 295.80/188.39 tff(32817,plain,
% 295.80/188.39 (~m_cell_v_ack(c_e_h_1, s13)),
% 295.80/188.39 inference(unit_resolution,[status(thm)],[22058, 32816])).
% 295.80/188.39 tff(32818,plain,
% 295.80/188.39 (~m_or_h_gate_v_in2(c_e_h_1, c_j, s13)),
% 295.80/188.39 inference(unit_resolution,[status(thm)],[22062, 1085, 32817])).
% 295.80/188.39 tff(32819,plain,
% 295.80/188.39 (~m_or_h_gate_v_out(c_e_h_1, c_j, s14)),
% 295.80/188.39 inference(unit_resolution,[status(thm)],[23476, 32818, 32815])).
% 295.80/188.39 tff(32820,plain,
% 295.80/188.39 (~m_c_h_element_v_in2(c_e_h_1, c_h, s14)),
% 295.80/188.39 inference(unit_resolution,[status(thm)],[23485, 32819])).
% 295.80/188.39 tff(32821,plain,
% 295.80/188.39 (~m_c_h_element_v_in2(c_e_h_1, c_h, s13)),
% 295.80/188.39 inference(unit_resolution,[status(thm)],[23489, 1174, 32815])).
% 295.80/188.39 tff(32822,plain,
% 295.80/188.39 (~m_c_h_element_v_out(c_e_h_1, c_h, s14)),
% 295.80/188.39 inference(unit_resolution,[status(thm)],[23955, 32821, 23877])).
% 295.80/188.39 tff(32823,plain,
% 295.80/188.39 (~m_c_h_element_v_out(c_e_h_1, c_h, s15)),
% 295.80/188.39 inference(unit_resolution,[status(thm)],[24031, 32822, 32820])).
% 295.80/188.39 tff(32824,plain,
% 295.80/188.39 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s15)),
% 295.80/188.39 inference(unit_resolution,[status(thm)],[24036, 619, 32823])).
% 295.80/188.39 tff(32825,plain,
% 295.80/188.39 (~node20(c_e_h_1, c_i, s15)),
% 295.80/188.39 inference(unit_resolution,[status(thm)],[24040, 38, 32824])).
% 295.80/188.39 tff(32826,plain,
% 295.80/188.39 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s14)),
% 295.80/188.39 inference(unit_resolution,[status(thm)],[24044, 619, 32822])).
% 295.80/188.39 tff(32827,plain,
% 295.80/188.39 (~node20(c_e_h_1, c_i, s14)),
% 295.80/188.39 inference(unit_resolution,[status(thm)],[24048, 38, 32826])).
% 295.80/188.39 tff(32828,plain,
% 295.80/188.39 (~m_and_h_gate_v_out(c_e_h_1, c_i, s15)),
% 295.80/188.39 inference(unit_resolution,[status(thm)],[24239, 32827, 24217])).
% 295.80/188.39 tff(32829,assumption,(m_c_h_element_v_in2(c_e_h_1, c_f, s15)), introduced(assumption)).
% 295.80/188.39 tff(32830,plain,
% 295.80/188.39 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s15)) | m_and_h_gate_v_out(c_e_h_1, c_i, s15))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s15)) | m_and_h_gate_v_out(c_e_h_1, c_i, s15))),
% 295.80/188.39 inference(rewrite,[status(thm)],[])).
% 295.80/188.39 tff(32831,plain,
% 295.80/188.39 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s15)) | m_and_h_gate_v_out(c_e_h_1, c_i, s15))),
% 295.80/188.39 inference(quant_inst,[status(thm)],[])).
% 295.80/188.39 tff(32832,plain,
% 295.80/188.39 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s15)) | m_and_h_gate_v_out(c_e_h_1, c_i, s15)),
% 295.80/188.39 inference(modus_ponens,[status(thm)],[32831, 32830])).
% 295.80/188.39 tff(32833,plain,
% 295.80/188.39 ($false),
% 295.80/188.39 inference(unit_resolution,[status(thm)],[32832, 2143, 24251, 32829])).
% 295.80/188.39 tff(32834,plain,((~m_c_h_element_v_in2(c_e_h_1, c_f, s15)) | m_and_h_gate_v_out(c_e_h_1, c_i, s15)), inference(lemma,lemma(discharge,[]))).
% 295.80/188.39 tff(32835,plain,
% 295.80/188.39 (~m_c_h_element_v_in2(c_e_h_1, c_f, s15)),
% 295.80/188.39 inference(unit_resolution,[status(thm)],[32834, 24251])).
% 295.80/188.39 tff(32836,assumption,(m_c_h_element_v_out(c_e_h_1, c_f, s16)), introduced(assumption)).
% 295.80/188.39 tff(32837,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_f, s15)), introduced(assumption)).
% 295.80/188.39 tff(32838,assumption,(node15(c_e_h_1, c_f, s15, s16)), introduced(assumption)).
% 295.80/188.39 tff(32839,plain,
% 295.80/188.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s16)) | (~node15(c_e_h_1, c_f, s15, s16)) | m_c_h_element_v_out(c_e_h_1, c_f, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s16)) | (~node15(c_e_h_1, c_f, s15, s16)) | m_c_h_element_v_out(c_e_h_1, c_f, s15))),
% 295.90/188.39 inference(rewrite,[status(thm)],[])).
% 295.90/188.39 tff(32840,plain,
% 295.90/188.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s16)) | (~node15(c_e_h_1, c_f, s15, s16)) | m_c_h_element_v_out(c_e_h_1, c_f, s15))),
% 295.90/188.39 inference(quant_inst,[status(thm)],[])).
% 295.90/188.39 tff(32841,plain,
% 295.90/188.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s16)) | (~node15(c_e_h_1, c_f, s15, s16)) | m_c_h_element_v_out(c_e_h_1, c_f, s15)),
% 295.90/188.39 inference(modus_ponens,[status(thm)],[32840, 32839])).
% 295.90/188.39 tff(32842,plain,
% 295.90/188.39 ($false),
% 295.90/188.39 inference(unit_resolution,[status(thm)],[32841, 147, 32811, 32836, 32838])).
% 295.90/188.39 tff(32843,plain,((~node15(c_e_h_1, c_f, s15, s16)) | m_c_h_element_v_out(c_e_h_1, c_f, s15) | (~m_c_h_element_v_out(c_e_h_1, c_f, s16))), inference(lemma,lemma(discharge,[]))).
% 295.90/188.39 tff(32844,plain,
% 295.90/188.39 (~node15(c_e_h_1, c_f, s15, s16)),
% 295.90/188.39 inference(unit_resolution,[status(thm)],[32843, 32836, 32811])).
% 295.90/188.39 tff(32845,assumption,(node18(c_e_h_1, c_f, s15, s16)), introduced(assumption)).
% 295.90/188.39 tff(32846,plain,
% 295.90/188.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_f, s15) | (~m_c_h_element_v_out(c_e_h_1, c_f, s16)) | (~node18(c_e_h_1, c_f, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s15) | (~m_c_h_element_v_out(c_e_h_1, c_f, s16)) | (~node18(c_e_h_1, c_f, s15, s16)))),
% 295.90/188.39 inference(rewrite,[status(thm)],[])).
% 295.90/188.39 tff(32847,plain,
% 295.90/188.39 (((~m_c_h_element_v_out(c_e_h_1, c_f, s16)) | m_c_h_element_v_out(c_e_h_1, c_f, s15) | (~node18(c_e_h_1, c_f, s15, s16))) <=> (m_c_h_element_v_out(c_e_h_1, c_f, s15) | (~m_c_h_element_v_out(c_e_h_1, c_f, s16)) | (~node18(c_e_h_1, c_f, s15, s16)))),
% 295.90/188.39 inference(rewrite,[status(thm)],[])).
% 295.90/188.39 tff(32848,plain,
% 295.90/188.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s16)) | m_c_h_element_v_out(c_e_h_1, c_f, s15) | (~node18(c_e_h_1, c_f, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_f, s15) | (~m_c_h_element_v_out(c_e_h_1, c_f, s16)) | (~node18(c_e_h_1, c_f, s15, s16))))),
% 295.90/188.39 inference(monotonicity,[status(thm)],[32847])).
% 295.90/188.39 tff(32849,plain,
% 295.90/188.39 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s16)) | m_c_h_element_v_out(c_e_h_1, c_f, s15) | (~node18(c_e_h_1, c_f, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s15) | (~m_c_h_element_v_out(c_e_h_1, c_f, s16)) | (~node18(c_e_h_1, c_f, s15, s16)))),
% 295.90/188.39 inference(transitivity,[status(thm)],[32848, 32846])).
% 295.90/188.39 tff(32850,plain,
% 295.90/188.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s16)) | m_c_h_element_v_out(c_e_h_1, c_f, s15) | (~node18(c_e_h_1, c_f, s15, s16)))),
% 295.90/188.39 inference(quant_inst,[status(thm)],[])).
% 295.90/188.39 tff(32851,plain,
% 295.90/188.39 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s15) | (~m_c_h_element_v_out(c_e_h_1, c_f, s16)) | (~node18(c_e_h_1, c_f, s15, s16))),
% 295.90/188.40 inference(modus_ponens,[status(thm)],[32850, 32849])).
% 295.90/188.40 tff(32852,plain,
% 295.90/188.40 ($false),
% 295.90/188.40 inference(unit_resolution,[status(thm)],[32851, 753, 32811, 32836, 32845])).
% 295.90/188.40 tff(32853,plain,((~node18(c_e_h_1, c_f, s15, s16)) | m_c_h_element_v_out(c_e_h_1, c_f, s15) | (~m_c_h_element_v_out(c_e_h_1, c_f, s16))), inference(lemma,lemma(discharge,[]))).
% 295.90/188.40 tff(32854,plain,
% 295.90/188.40 (~node18(c_e_h_1, c_f, s15, s16)),
% 295.90/188.40 inference(unit_resolution,[status(thm)],[32853, 32836, 32811])).
% 295.90/188.40 tff(32855,plain,
% 295.90/188.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s15, s16)) | node19(c_e_h_1, c_f, s15, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s15, s16)) | node19(c_e_h_1, c_f, s15, s16))),
% 295.90/188.40 inference(rewrite,[status(thm)],[])).
% 295.90/188.40 tff(32856,plain,
% 295.90/188.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s15, s16)) | node19(c_e_h_1, c_f, s15, s16))),
% 295.90/188.40 inference(quant_inst,[status(thm)],[])).
% 295.90/188.40 tff(32857,plain,
% 295.90/188.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s15, s16)) | node19(c_e_h_1, c_f, s15, s16)),
% 295.90/188.40 inference(modus_ponens,[status(thm)],[32856, 32855])).
% 295.90/188.40 tff(32858,plain,
% 295.90/188.40 (node19(c_e_h_1, c_f, s15, s16)),
% 295.90/188.40 inference(unit_resolution,[status(thm)],[32857, 190, 13499])).
% 295.90/188.40 tff(32859,plain,
% 295.90/188.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s15) | (~node19(c_e_h_1, c_f, s15, s16)) | node18(c_e_h_1, c_f, s15, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_f, s15) | (~node19(c_e_h_1, c_f, s15, s16)) | node18(c_e_h_1, c_f, s15, s16))),
% 295.90/188.40 inference(rewrite,[status(thm)],[])).
% 295.90/188.40 tff(32860,plain,
% 295.90/188.40 ((node17(c_e_h_1, c_f, s15) | node18(c_e_h_1, c_f, s15, s16) | (~node19(c_e_h_1, c_f, s15, s16))) <=> (node17(c_e_h_1, c_f, s15) | (~node19(c_e_h_1, c_f, s15, s16)) | node18(c_e_h_1, c_f, s15, s16))),
% 295.90/188.40 inference(rewrite,[status(thm)],[])).
% 295.90/188.40 tff(32861,plain,
% 295.90/188.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s15) | node18(c_e_h_1, c_f, s15, s16) | (~node19(c_e_h_1, c_f, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s15) | (~node19(c_e_h_1, c_f, s15, s16)) | node18(c_e_h_1, c_f, s15, s16)))),
% 295.90/188.40 inference(monotonicity,[status(thm)],[32860])).
% 295.90/188.40 tff(32862,plain,
% 295.90/188.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s15) | node18(c_e_h_1, c_f, s15, s16) | (~node19(c_e_h_1, c_f, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_f, s15) | (~node19(c_e_h_1, c_f, s15, s16)) | node18(c_e_h_1, c_f, s15, s16))),
% 295.90/188.40 inference(transitivity,[status(thm)],[32861, 32859])).
% 295.90/188.40 tff(32863,plain,
% 295.90/188.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s15) | node18(c_e_h_1, c_f, s15, s16) | (~node19(c_e_h_1, c_f, s15, s16)))),
% 295.90/188.40 inference(quant_inst,[status(thm)],[])).
% 295.90/188.40 tff(32864,plain,
% 295.90/188.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_1, c_f, s15) | (~node19(c_e_h_1, c_f, s15, s16)) | node18(c_e_h_1, c_f, s15, s16)),
% 295.90/188.40 inference(modus_ponens,[status(thm)],[32863, 32862])).
% 295.90/188.40 tff(32865,plain,
% 295.90/188.40 (node17(c_e_h_1, c_f, s15) | node18(c_e_h_1, c_f, s15, s16)),
% 295.90/188.40 inference(unit_resolution,[status(thm)],[32864, 776, 32858])).
% 295.90/188.40 tff(32866,plain,
% 295.90/188.40 (node17(c_e_h_1, c_f, s15)),
% 295.90/188.40 inference(unit_resolution,[status(thm)],[32865, 32854])).
% 295.90/188.40 tff(32867,assumption,(~node15(c_e_h_1, c_f, s15, s16)), introduced(assumption)).
% 295.90/188.40 tff(32868,assumption,(node17(c_e_h_1, c_f, s15)), introduced(assumption)).
% 295.90/188.40 tff(32869,plain,
% 295.90/188.40 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_f, s15)) | m_c_h_element_v_in1(c_e_h_1, c_f, s15) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s15)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_f, s15)) | m_c_h_element_v_in1(c_e_h_1, c_f, s15) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s15)))),
% 295.90/188.40 inference(rewrite,[status(thm)],[])).
% 295.90/188.40 tff(32870,plain,
% 295.90/188.40 ((m_c_h_element_v_in1(c_e_h_1, c_f, s15) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s15)) | (~node17(c_e_h_1, c_f, s15))) <=> ((~node17(c_e_h_1, c_f, s15)) | m_c_h_element_v_in1(c_e_h_1, c_f, s15) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s15)))),
% 295.90/188.40 inference(rewrite,[status(thm)],[])).
% 295.90/188.40 tff(32871,plain,
% 295.90/188.40 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s15) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s15)) | (~node17(c_e_h_1, c_f, s15)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_f, s15)) | m_c_h_element_v_in1(c_e_h_1, c_f, s15) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s15))))),
% 295.90/188.40 inference(monotonicity,[status(thm)],[32870])).
% 295.90/188.40 tff(32872,plain,
% 295.90/188.40 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s15) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s15)) | (~node17(c_e_h_1, c_f, s15)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_f, s15)) | m_c_h_element_v_in1(c_e_h_1, c_f, s15) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s15)))),
% 295.90/188.40 inference(transitivity,[status(thm)],[32871, 32869])).
% 295.90/188.40 tff(32873,plain,
% 295.90/188.40 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s15) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s15)) | (~node17(c_e_h_1, c_f, s15)))),
% 295.90/188.40 inference(quant_inst,[status(thm)],[])).
% 295.90/188.40 tff(32874,plain,
% 295.90/188.40 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_f, s15)) | m_c_h_element_v_in1(c_e_h_1, c_f, s15) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s15))),
% 295.90/188.40 inference(modus_ponens,[status(thm)],[32873, 32872])).
% 295.90/188.40 tff(32875,plain,
% 295.90/188.40 (m_c_h_element_v_in1(c_e_h_1, c_f, s15) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s15))),
% 295.90/188.40 inference(unit_resolution,[status(thm)],[32874, 859, 32868])).
% 295.90/188.40 tff(32876,plain,
% 295.90/188.40 (~m_c_h_element_v_in2(c_e_h_1, c_f, s15)),
% 295.90/188.40 inference(unit_resolution,[status(thm)],[32875, 32837])).
% 295.90/188.40 tff(32877,plain,
% 295.90/188.40 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s15)) | m_c_h_element_v_in1(c_e_h_1, c_f, s15) | m_c_h_element_v_in2(c_e_h_1, c_f, s15))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s15)) | m_c_h_element_v_in1(c_e_h_1, c_f, s15) | m_c_h_element_v_in2(c_e_h_1, c_f, s15))),
% 295.90/188.40 inference(rewrite,[status(thm)],[])).
% 295.90/188.40 tff(32878,plain,
% 295.90/188.40 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s15)) | m_c_h_element_v_in1(c_e_h_1, c_f, s15) | m_c_h_element_v_in2(c_e_h_1, c_f, s15))),
% 295.90/188.40 inference(quant_inst,[status(thm)],[])).
% 295.90/188.40 tff(32879,plain,
% 295.90/188.40 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s15)) | m_c_h_element_v_in1(c_e_h_1, c_f, s15) | m_c_h_element_v_in2(c_e_h_1, c_f, s15)),
% 295.91/188.40 inference(modus_ponens,[status(thm)],[32878, 32877])).
% 295.91/188.40 tff(32880,plain,
% 295.91/188.40 (~node16(c_e_h_1, c_f, s15)),
% 295.91/188.40 inference(unit_resolution,[status(thm)],[32879, 178, 32837, 32876])).
% 295.91/188.40 tff(32881,plain,
% 295.91/188.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s15) | (~node19(c_e_h_1, c_f, s15, s16)) | node15(c_e_h_1, c_f, s15, s16) | node14(c_e_h_1, c_f, s15, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_f, s15) | (~node19(c_e_h_1, c_f, s15, s16)) | node15(c_e_h_1, c_f, s15, s16) | node14(c_e_h_1, c_f, s15, s16))),
% 295.91/188.40 inference(rewrite,[status(thm)],[])).
% 295.91/188.40 tff(32882,plain,
% 295.91/188.40 ((node16(c_e_h_1, c_f, s15) | node14(c_e_h_1, c_f, s15, s16) | node15(c_e_h_1, c_f, s15, s16) | (~node19(c_e_h_1, c_f, s15, s16))) <=> (node16(c_e_h_1, c_f, s15) | (~node19(c_e_h_1, c_f, s15, s16)) | node15(c_e_h_1, c_f, s15, s16) | node14(c_e_h_1, c_f, s15, s16))),
% 295.91/188.40 inference(rewrite,[status(thm)],[])).
% 295.91/188.40 tff(32883,plain,
% 295.91/188.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s15) | node14(c_e_h_1, c_f, s15, s16) | node15(c_e_h_1, c_f, s15, s16) | (~node19(c_e_h_1, c_f, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s15) | (~node19(c_e_h_1, c_f, s15, s16)) | node15(c_e_h_1, c_f, s15, s16) | node14(c_e_h_1, c_f, s15, s16)))),
% 295.91/188.40 inference(monotonicity,[status(thm)],[32882])).
% 295.91/188.40 tff(32884,plain,
% 295.91/188.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s15) | node14(c_e_h_1, c_f, s15, s16) | node15(c_e_h_1, c_f, s15, s16) | (~node19(c_e_h_1, c_f, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_f, s15) | (~node19(c_e_h_1, c_f, s15, s16)) | node15(c_e_h_1, c_f, s15, s16) | node14(c_e_h_1, c_f, s15, s16))),
% 295.91/188.40 inference(transitivity,[status(thm)],[32883, 32881])).
% 295.91/188.40 tff(32885,plain,
% 295.91/188.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s15) | node14(c_e_h_1, c_f, s15, s16) | node15(c_e_h_1, c_f, s15, s16) | (~node19(c_e_h_1, c_f, s15, s16)))),
% 295.91/188.40 inference(quant_inst,[status(thm)],[])).
% 295.91/188.40 tff(32886,plain,
% 295.91/188.40 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_f, s15) | (~node19(c_e_h_1, c_f, s15, s16)) | node15(c_e_h_1, c_f, s15, s16) | node14(c_e_h_1, c_f, s15, s16)),
% 295.91/188.40 inference(modus_ponens,[status(thm)],[32885, 32884])).
% 295.91/188.40 tff(32887,plain,
% 295.91/188.40 (node16(c_e_h_1, c_f, s15) | node15(c_e_h_1, c_f, s15, s16) | node14(c_e_h_1, c_f, s15, s16)),
% 295.91/188.40 inference(unit_resolution,[status(thm)],[32886, 204, 32858])).
% 295.91/188.40 tff(32888,plain,
% 295.91/188.40 (node14(c_e_h_1, c_f, s15, s16)),
% 295.91/188.40 inference(unit_resolution,[status(thm)],[32887, 32880, 32867])).
% 295.91/188.40 tff(32889,plain,
% 295.91/188.40 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s15) | (~m_c_h_element_v_out(c_e_h_1, c_f, s16)) | (~node14(c_e_h_1, c_f, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_f, s15) | (~m_c_h_element_v_out(c_e_h_1, c_f, s16)) | (~node14(c_e_h_1, c_f, s15, s16)))),
% 295.91/188.40 inference(rewrite,[status(thm)],[])).
% 295.91/188.40 tff(32890,plain,
% 295.91/188.40 (((~node14(c_e_h_1, c_f, s15, s16)) | m_c_h_element_v_in1(c_e_h_1, c_f, s15) | (~m_c_h_element_v_out(c_e_h_1, c_f, s16))) <=> (m_c_h_element_v_in1(c_e_h_1, c_f, s15) | (~m_c_h_element_v_out(c_e_h_1, c_f, s16)) | (~node14(c_e_h_1, c_f, s15, s16)))),
% 295.91/188.41 inference(rewrite,[status(thm)],[])).
% 295.91/188.41 tff(32891,plain,
% 295.91/188.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s15, s16)) | m_c_h_element_v_in1(c_e_h_1, c_f, s15) | (~m_c_h_element_v_out(c_e_h_1, c_f, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s15) | (~m_c_h_element_v_out(c_e_h_1, c_f, s16)) | (~node14(c_e_h_1, c_f, s15, s16))))),
% 295.91/188.41 inference(monotonicity,[status(thm)],[32890])).
% 295.91/188.41 tff(32892,plain,
% 295.91/188.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s15, s16)) | m_c_h_element_v_in1(c_e_h_1, c_f, s15) | (~m_c_h_element_v_out(c_e_h_1, c_f, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_f, s15) | (~m_c_h_element_v_out(c_e_h_1, c_f, s16)) | (~node14(c_e_h_1, c_f, s15, s16)))),
% 295.91/188.41 inference(transitivity,[status(thm)],[32891, 32889])).
% 295.91/188.41 tff(32893,plain,
% 295.91/188.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s15, s16)) | m_c_h_element_v_in1(c_e_h_1, c_f, s15) | (~m_c_h_element_v_out(c_e_h_1, c_f, s16)))),
% 295.91/188.41 inference(quant_inst,[status(thm)],[])).
% 295.91/188.41 tff(32894,plain,
% 295.91/188.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_1, c_f, s15) | (~m_c_h_element_v_out(c_e_h_1, c_f, s16)) | (~node14(c_e_h_1, c_f, s15, s16))),
% 295.91/188.41 inference(modus_ponens,[status(thm)],[32893, 32892])).
% 295.91/188.41 tff(32895,plain,
% 295.91/188.41 ($false),
% 295.91/188.41 inference(unit_resolution,[status(thm)],[32894, 223, 32836, 32888, 32837])).
% 295.91/188.41 tff(32896,plain,(m_c_h_element_v_in1(c_e_h_1, c_f, s15) | (~m_c_h_element_v_out(c_e_h_1, c_f, s16)) | node15(c_e_h_1, c_f, s15, s16) | (~node17(c_e_h_1, c_f, s15))), inference(lemma,lemma(discharge,[]))).
% 295.91/188.41 tff(32897,plain,
% 295.91/188.41 ($false),
% 295.91/188.41 inference(unit_resolution,[status(thm)],[32896, 32866, 32844, 32837, 32836])).
% 295.91/188.41 tff(32898,plain,((~m_c_h_element_v_out(c_e_h_1, c_f, s16)) | m_c_h_element_v_in1(c_e_h_1, c_f, s15) | m_c_h_element_v_out(c_e_h_1, c_f, s15)), inference(lemma,lemma(discharge,[]))).
% 295.91/188.41 tff(32899,plain,
% 295.91/188.41 (m_c_h_element_v_in1(c_e_h_1, c_f, s15)),
% 295.91/188.41 inference(unit_resolution,[status(thm)],[32898, 32836, 32811])).
% 295.91/188.41 tff(32900,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_f, s15)), introduced(assumption)).
% 295.91/188.41 tff(32901,plain,
% 295.91/188.41 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_f, s15) | (~node17(c_e_h_1, c_f, s15)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s15)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_f, s15) | (~node17(c_e_h_1, c_f, s15)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s15)))),
% 295.91/188.41 inference(rewrite,[status(thm)],[])).
% 295.91/188.41 tff(32902,plain,
% 295.91/188.41 (((~m_c_h_element_v_in1(c_e_h_1, c_f, s15)) | m_c_h_element_v_in2(c_e_h_1, c_f, s15) | (~node17(c_e_h_1, c_f, s15))) <=> (m_c_h_element_v_in2(c_e_h_1, c_f, s15) | (~node17(c_e_h_1, c_f, s15)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s15)))),
% 295.91/188.41 inference(rewrite,[status(thm)],[])).
% 295.91/188.41 tff(32903,plain,
% 295.91/188.41 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s15)) | m_c_h_element_v_in2(c_e_h_1, c_f, s15) | (~node17(c_e_h_1, c_f, s15)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_f, s15) | (~node17(c_e_h_1, c_f, s15)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s15))))),
% 295.91/188.41 inference(monotonicity,[status(thm)],[32902])).
% 295.91/188.41 tff(32904,plain,
% 295.91/188.41 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s15)) | m_c_h_element_v_in2(c_e_h_1, c_f, s15) | (~node17(c_e_h_1, c_f, s15)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_f, s15) | (~node17(c_e_h_1, c_f, s15)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s15)))),
% 295.91/188.41 inference(transitivity,[status(thm)],[32903, 32901])).
% 295.91/188.41 tff(32905,plain,
% 295.91/188.41 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s15)) | m_c_h_element_v_in2(c_e_h_1, c_f, s15) | (~node17(c_e_h_1, c_f, s15)))),
% 295.91/188.41 inference(quant_inst,[status(thm)],[])).
% 295.91/188.41 tff(32906,plain,
% 295.91/188.41 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_f, s15) | (~node17(c_e_h_1, c_f, s15)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s15))),
% 295.91/188.41 inference(modus_ponens,[status(thm)],[32905, 32904])).
% 295.91/188.41 tff(32907,plain,
% 295.91/188.41 ((~node17(c_e_h_1, c_f, s15)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s15))),
% 295.91/188.41 inference(unit_resolution,[status(thm)],[32906, 919, 32900])).
% 295.91/188.41 tff(32908,plain,
% 295.91/188.41 ($false),
% 295.91/188.41 inference(unit_resolution,[status(thm)],[32907, 32866, 32899])).
% 295.91/188.41 tff(32909,plain,((~m_c_h_element_v_out(c_e_h_1, c_f, s16)) | m_c_h_element_v_in2(c_e_h_1, c_f, s15) | m_c_h_element_v_out(c_e_h_1, c_f, s15)), inference(lemma,lemma(discharge,[]))).
% 295.91/188.41 tff(32910,plain,
% 295.91/188.41 (~m_c_h_element_v_out(c_e_h_1, c_f, s16)),
% 295.91/188.41 inference(unit_resolution,[status(thm)],[32909, 32835, 32811])).
% 295.91/188.41 tff(32911,plain,
% 295.91/188.41 (~m_and_h_gate_v_out(c_e_h_1, c_i, s16)),
% 295.91/188.41 inference(unit_resolution,[status(thm)],[24264, 24251, 24242])).
% 295.91/188.41 tff(32912,assumption,(m_c_h_element_v_in2(c_e_h_1, c_f, s16)), introduced(assumption)).
% 295.91/188.41 tff(32913,plain,
% 295.91/188.41 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s16)) | m_and_h_gate_v_out(c_e_h_1, c_i, s16))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s16)) | m_and_h_gate_v_out(c_e_h_1, c_i, s16))),
% 295.91/188.41 inference(rewrite,[status(thm)],[])).
% 295.91/188.41 tff(32914,plain,
% 295.91/188.41 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s16)) | m_and_h_gate_v_out(c_e_h_1, c_i, s16))),
% 295.91/188.41 inference(quant_inst,[status(thm)],[])).
% 295.91/188.41 tff(32915,plain,
% 295.91/188.41 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s16)) | m_and_h_gate_v_out(c_e_h_1, c_i, s16)),
% 295.91/188.41 inference(modus_ponens,[status(thm)],[32914, 32913])).
% 295.91/188.41 tff(32916,plain,
% 295.91/188.41 ($false),
% 295.91/188.41 inference(unit_resolution,[status(thm)],[32915, 2143, 26007, 32912])).
% 295.91/188.41 tff(32917,plain,((~m_c_h_element_v_in2(c_e_h_1, c_f, s16)) | m_and_h_gate_v_out(c_e_h_1, c_i, s16)), inference(lemma,lemma(discharge,[]))).
% 295.91/188.41 tff(32918,plain,
% 295.91/188.41 (~m_c_h_element_v_in2(c_e_h_1, c_f, s16)),
% 295.91/188.41 inference(unit_resolution,[status(thm)],[32917, 32911])).
% 295.91/188.41 tff(32919,assumption,(~m_c_h_element_v_out(c_e_h_1, c_f, s16)), introduced(assumption)).
% 295.91/188.41 tff(32920,assumption,(node18(c_e_h_1, c_f, s16, s17)), introduced(assumption)).
% 295.91/188.41 tff(32921,plain,
% 295.91/188.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_f, s16) | (~m_c_h_element_v_out(c_e_h_1, c_f, s17)) | (~node18(c_e_h_1, c_f, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s16) | (~m_c_h_element_v_out(c_e_h_1, c_f, s17)) | (~node18(c_e_h_1, c_f, s16, s17)))),
% 295.91/188.41 inference(rewrite,[status(thm)],[])).
% 295.91/188.41 tff(32922,plain,
% 295.91/188.41 (((~m_c_h_element_v_out(c_e_h_1, c_f, s17)) | m_c_h_element_v_out(c_e_h_1, c_f, s16) | (~node18(c_e_h_1, c_f, s16, s17))) <=> (m_c_h_element_v_out(c_e_h_1, c_f, s16) | (~m_c_h_element_v_out(c_e_h_1, c_f, s17)) | (~node18(c_e_h_1, c_f, s16, s17)))),
% 295.91/188.41 inference(rewrite,[status(thm)],[])).
% 295.91/188.41 tff(32923,plain,
% 295.91/188.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s17)) | m_c_h_element_v_out(c_e_h_1, c_f, s16) | (~node18(c_e_h_1, c_f, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_f, s16) | (~m_c_h_element_v_out(c_e_h_1, c_f, s17)) | (~node18(c_e_h_1, c_f, s16, s17))))),
% 295.91/188.41 inference(monotonicity,[status(thm)],[32922])).
% 295.91/188.41 tff(32924,plain,
% 295.91/188.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s17)) | m_c_h_element_v_out(c_e_h_1, c_f, s16) | (~node18(c_e_h_1, c_f, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s16) | (~m_c_h_element_v_out(c_e_h_1, c_f, s17)) | (~node18(c_e_h_1, c_f, s16, s17)))),
% 295.91/188.41 inference(transitivity,[status(thm)],[32923, 32921])).
% 295.91/188.41 tff(32925,plain,
% 295.91/188.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s17)) | m_c_h_element_v_out(c_e_h_1, c_f, s16) | (~node18(c_e_h_1, c_f, s16, s17)))),
% 295.91/188.41 inference(quant_inst,[status(thm)],[])).
% 295.91/188.41 tff(32926,plain,
% 295.91/188.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s16) | (~m_c_h_element_v_out(c_e_h_1, c_f, s17)) | (~node18(c_e_h_1, c_f, s16, s17))),
% 295.91/188.41 inference(modus_ponens,[status(thm)],[32925, 32924])).
% 295.91/188.41 tff(32927,plain,
% 295.91/188.41 ($false),
% 295.91/188.41 inference(unit_resolution,[status(thm)],[32926, 753, 32919, 32812, 32920])).
% 295.91/188.41 tff(32928,plain,((~node18(c_e_h_1, c_f, s16, s17)) | m_c_h_element_v_out(c_e_h_1, c_f, s16) | (~m_c_h_element_v_out(c_e_h_1, c_f, s17))), inference(lemma,lemma(discharge,[]))).
% 295.91/188.41 tff(32929,plain,
% 295.91/188.41 (~node18(c_e_h_1, c_f, s16, s17)),
% 295.91/188.41 inference(unit_resolution,[status(thm)],[32928, 32812, 32919])).
% 295.91/188.41 tff(32930,plain,
% 295.91/188.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s16, s17)) | node19(c_e_h_1, c_f, s16, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s16, s17)) | node19(c_e_h_1, c_f, s16, s17))),
% 295.91/188.41 inference(rewrite,[status(thm)],[])).
% 295.91/188.41 tff(32931,plain,
% 295.91/188.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s16, s17)) | node19(c_e_h_1, c_f, s16, s17))),
% 295.91/188.41 inference(quant_inst,[status(thm)],[])).
% 295.91/188.41 tff(32932,plain,
% 295.91/188.41 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s16, s17)) | node19(c_e_h_1, c_f, s16, s17)),
% 295.91/188.41 inference(modus_ponens,[status(thm)],[32931, 32930])).
% 295.91/188.41 tff(32933,plain,
% 295.91/188.41 (node19(c_e_h_1, c_f, s16, s17)),
% 295.91/188.41 inference(unit_resolution,[status(thm)],[32932, 190, 11967])).
% 295.91/188.41 tff(32934,plain,
% 295.91/188.41 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_1, c_f, s16, s17) | (~node19(c_e_h_1, c_f, s16, s17)) | node17(c_e_h_1, c_f, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_f, s16, s17) | (~node19(c_e_h_1, c_f, s16, s17)) | node17(c_e_h_1, c_f, s16))),
% 295.91/188.41 inference(rewrite,[status(thm)],[])).
% 295.91/188.42 tff(32935,plain,
% 295.91/188.42 ((node17(c_e_h_1, c_f, s16) | node18(c_e_h_1, c_f, s16, s17) | (~node19(c_e_h_1, c_f, s16, s17))) <=> (node18(c_e_h_1, c_f, s16, s17) | (~node19(c_e_h_1, c_f, s16, s17)) | node17(c_e_h_1, c_f, s16))),
% 295.91/188.42 inference(rewrite,[status(thm)],[])).
% 295.91/188.42 tff(32936,plain,
% 295.91/188.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s16) | node18(c_e_h_1, c_f, s16, s17) | (~node19(c_e_h_1, c_f, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node18(c_e_h_1, c_f, s16, s17) | (~node19(c_e_h_1, c_f, s16, s17)) | node17(c_e_h_1, c_f, s16)))),
% 295.91/188.42 inference(monotonicity,[status(thm)],[32935])).
% 295.91/188.42 tff(32937,plain,
% 295.91/188.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s16) | node18(c_e_h_1, c_f, s16, s17) | (~node19(c_e_h_1, c_f, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_f, s16, s17) | (~node19(c_e_h_1, c_f, s16, s17)) | node17(c_e_h_1, c_f, s16))),
% 295.91/188.42 inference(transitivity,[status(thm)],[32936, 32934])).
% 295.91/188.42 tff(32938,plain,
% 295.91/188.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s16) | node18(c_e_h_1, c_f, s16, s17) | (~node19(c_e_h_1, c_f, s16, s17)))),
% 295.91/188.42 inference(quant_inst,[status(thm)],[])).
% 295.91/188.42 tff(32939,plain,
% 295.91/188.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node18(c_e_h_1, c_f, s16, s17) | (~node19(c_e_h_1, c_f, s16, s17)) | node17(c_e_h_1, c_f, s16)),
% 295.91/188.42 inference(modus_ponens,[status(thm)],[32938, 32937])).
% 295.91/188.42 tff(32940,plain,
% 295.91/188.42 (node18(c_e_h_1, c_f, s16, s17) | node17(c_e_h_1, c_f, s16)),
% 295.91/188.42 inference(unit_resolution,[status(thm)],[32939, 776, 32933])).
% 295.91/188.42 tff(32941,plain,
% 295.91/188.42 (node17(c_e_h_1, c_f, s16)),
% 295.91/188.42 inference(unit_resolution,[status(thm)],[32940, 32929])).
% 295.91/188.42 tff(32942,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_f, s16)), introduced(assumption)).
% 295.91/188.42 tff(32943,plain,
% 295.91/188.42 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_f, s16) | (~node17(c_e_h_1, c_f, s16)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s16)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_f, s16) | (~node17(c_e_h_1, c_f, s16)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s16)))),
% 295.91/188.42 inference(rewrite,[status(thm)],[])).
% 295.91/188.42 tff(32944,plain,
% 295.91/188.42 (((~m_c_h_element_v_in1(c_e_h_1, c_f, s16)) | m_c_h_element_v_in2(c_e_h_1, c_f, s16) | (~node17(c_e_h_1, c_f, s16))) <=> (m_c_h_element_v_in2(c_e_h_1, c_f, s16) | (~node17(c_e_h_1, c_f, s16)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s16)))),
% 295.91/188.42 inference(rewrite,[status(thm)],[])).
% 295.91/188.42 tff(32945,plain,
% 295.91/188.42 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s16)) | m_c_h_element_v_in2(c_e_h_1, c_f, s16) | (~node17(c_e_h_1, c_f, s16)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in2(c_e_h_1, c_f, s16) | (~node17(c_e_h_1, c_f, s16)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s16))))),
% 295.91/188.42 inference(monotonicity,[status(thm)],[32944])).
% 295.91/188.42 tff(32946,plain,
% 295.91/188.42 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s16)) | m_c_h_element_v_in2(c_e_h_1, c_f, s16) | (~node17(c_e_h_1, c_f, s16)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_f, s16) | (~node17(c_e_h_1, c_f, s16)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s16)))),
% 295.91/188.42 inference(transitivity,[status(thm)],[32945, 32943])).
% 295.91/188.42 tff(32947,plain,
% 295.91/188.42 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s16)) | m_c_h_element_v_in2(c_e_h_1, c_f, s16) | (~node17(c_e_h_1, c_f, s16)))),
% 295.91/188.42 inference(quant_inst,[status(thm)],[])).
% 295.91/188.42 tff(32948,plain,
% 295.91/188.42 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | m_c_h_element_v_in2(c_e_h_1, c_f, s16) | (~node17(c_e_h_1, c_f, s16)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s16))),
% 295.91/188.42 inference(modus_ponens,[status(thm)],[32947, 32946])).
% 295.91/188.42 tff(32949,plain,
% 295.91/188.42 ((~node17(c_e_h_1, c_f, s16)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s16))),
% 295.91/188.42 inference(unit_resolution,[status(thm)],[32948, 919, 32942])).
% 295.91/188.42 tff(32950,plain,
% 295.91/188.42 (~m_c_h_element_v_in1(c_e_h_1, c_f, s16)),
% 295.91/188.42 inference(unit_resolution,[status(thm)],[32949, 32941])).
% 295.91/188.42 tff(32951,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_f, s16)), introduced(assumption)).
% 295.91/188.42 tff(32952,assumption,(node17(c_e_h_1, c_f, s16)), introduced(assumption)).
% 295.91/188.42 tff(32953,plain,
% 295.91/188.42 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_f, s16)) | m_c_h_element_v_in1(c_e_h_1, c_f, s16) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s16)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_f, s16)) | m_c_h_element_v_in1(c_e_h_1, c_f, s16) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s16)))),
% 295.91/188.42 inference(rewrite,[status(thm)],[])).
% 295.91/188.42 tff(32954,plain,
% 295.91/188.42 ((m_c_h_element_v_in1(c_e_h_1, c_f, s16) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s16)) | (~node17(c_e_h_1, c_f, s16))) <=> ((~node17(c_e_h_1, c_f, s16)) | m_c_h_element_v_in1(c_e_h_1, c_f, s16) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s16)))),
% 295.91/188.42 inference(rewrite,[status(thm)],[])).
% 295.91/188.42 tff(32955,plain,
% 295.91/188.42 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s16) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s16)) | (~node17(c_e_h_1, c_f, s16)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_f, s16)) | m_c_h_element_v_in1(c_e_h_1, c_f, s16) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s16))))),
% 295.91/188.42 inference(monotonicity,[status(thm)],[32954])).
% 295.91/188.42 tff(32956,plain,
% 295.91/188.42 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s16) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s16)) | (~node17(c_e_h_1, c_f, s16)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_f, s16)) | m_c_h_element_v_in1(c_e_h_1, c_f, s16) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s16)))),
% 295.91/188.42 inference(transitivity,[status(thm)],[32955, 32953])).
% 295.91/188.42 tff(32957,plain,
% 295.91/188.42 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s16) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s16)) | (~node17(c_e_h_1, c_f, s16)))),
% 295.91/188.42 inference(quant_inst,[status(thm)],[])).
% 295.91/188.42 tff(32958,plain,
% 295.91/188.42 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_f, s16)) | m_c_h_element_v_in1(c_e_h_1, c_f, s16) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s16))),
% 295.91/188.42 inference(modus_ponens,[status(thm)],[32957, 32956])).
% 295.91/188.42 tff(32959,plain,
% 295.91/188.42 (m_c_h_element_v_in1(c_e_h_1, c_f, s16) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s16))),
% 295.91/188.42 inference(unit_resolution,[status(thm)],[32958, 859, 32952])).
% 295.91/188.42 tff(32960,plain,
% 295.91/188.42 (~m_c_h_element_v_in2(c_e_h_1, c_f, s16)),
% 295.91/188.42 inference(unit_resolution,[status(thm)],[32959, 32951])).
% 295.91/188.42 tff(32961,assumption,(node16(c_e_h_1, c_f, s16)), introduced(assumption)).
% 295.91/188.42 tff(32962,plain,
% 295.91/188.42 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s16)) | m_c_h_element_v_in1(c_e_h_1, c_f, s16) | m_c_h_element_v_in2(c_e_h_1, c_f, s16))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s16)) | m_c_h_element_v_in1(c_e_h_1, c_f, s16) | m_c_h_element_v_in2(c_e_h_1, c_f, s16))),
% 295.91/188.42 inference(rewrite,[status(thm)],[])).
% 295.91/188.42 tff(32963,plain,
% 295.91/188.42 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s16)) | m_c_h_element_v_in1(c_e_h_1, c_f, s16) | m_c_h_element_v_in2(c_e_h_1, c_f, s16))),
% 295.91/188.42 inference(quant_inst,[status(thm)],[])).
% 295.91/188.42 tff(32964,plain,
% 295.91/188.42 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s16)) | m_c_h_element_v_in1(c_e_h_1, c_f, s16) | m_c_h_element_v_in2(c_e_h_1, c_f, s16)),
% 295.91/188.42 inference(modus_ponens,[status(thm)],[32963, 32962])).
% 295.91/188.42 tff(32965,plain,
% 295.91/188.42 (m_c_h_element_v_in1(c_e_h_1, c_f, s16) | m_c_h_element_v_in2(c_e_h_1, c_f, s16)),
% 295.91/188.42 inference(unit_resolution,[status(thm)],[32964, 178, 32961])).
% 295.91/188.42 tff(32966,plain,
% 295.91/188.42 ($false),
% 295.91/188.42 inference(unit_resolution,[status(thm)],[32965, 32960, 32951])).
% 295.91/188.42 tff(32967,plain,(m_c_h_element_v_in1(c_e_h_1, c_f, s16) | (~node16(c_e_h_1, c_f, s16)) | (~node17(c_e_h_1, c_f, s16))), inference(lemma,lemma(discharge,[]))).
% 295.91/188.42 tff(32968,plain,
% 295.91/188.42 (~node16(c_e_h_1, c_f, s16)),
% 295.91/188.42 inference(unit_resolution,[status(thm)],[32967, 32950, 32941])).
% 295.91/188.42 tff(32969,assumption,(node14(c_e_h_1, c_f, s16, s17)), introduced(assumption)).
% 295.91/188.42 tff(32970,plain,
% 295.91/188.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s17)) | m_c_h_element_v_in1(c_e_h_1, c_f, s16) | (~node14(c_e_h_1, c_f, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s17)) | m_c_h_element_v_in1(c_e_h_1, c_f, s16) | (~node14(c_e_h_1, c_f, s16, s17)))),
% 295.91/188.42 inference(rewrite,[status(thm)],[])).
% 295.91/188.42 tff(32971,plain,
% 295.91/188.42 (((~node14(c_e_h_1, c_f, s16, s17)) | m_c_h_element_v_in1(c_e_h_1, c_f, s16) | (~m_c_h_element_v_out(c_e_h_1, c_f, s17))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_f, s17)) | m_c_h_element_v_in1(c_e_h_1, c_f, s16) | (~node14(c_e_h_1, c_f, s16, s17)))),
% 295.91/188.42 inference(rewrite,[status(thm)],[])).
% 295.91/188.42 tff(32972,plain,
% 295.91/188.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s16, s17)) | m_c_h_element_v_in1(c_e_h_1, c_f, s16) | (~m_c_h_element_v_out(c_e_h_1, c_f, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s17)) | m_c_h_element_v_in1(c_e_h_1, c_f, s16) | (~node14(c_e_h_1, c_f, s16, s17))))),
% 295.91/188.42 inference(monotonicity,[status(thm)],[32971])).
% 295.91/188.42 tff(32973,plain,
% 295.91/188.42 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s16, s17)) | m_c_h_element_v_in1(c_e_h_1, c_f, s16) | (~m_c_h_element_v_out(c_e_h_1, c_f, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s17)) | m_c_h_element_v_in1(c_e_h_1, c_f, s16) | (~node14(c_e_h_1, c_f, s16, s17)))),
% 295.91/188.42 inference(transitivity,[status(thm)],[32972, 32970])).
% 295.91/188.42 tff(32974,plain,
% 295.91/188.42 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s16, s17)) | m_c_h_element_v_in1(c_e_h_1, c_f, s16) | (~m_c_h_element_v_out(c_e_h_1, c_f, s17)))),
% 295.91/188.43 inference(quant_inst,[status(thm)],[])).
% 295.91/188.43 tff(32975,plain,
% 295.91/188.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s17)) | m_c_h_element_v_in1(c_e_h_1, c_f, s16) | (~node14(c_e_h_1, c_f, s16, s17))),
% 295.91/188.43 inference(modus_ponens,[status(thm)],[32974, 32973])).
% 295.91/188.43 tff(32976,plain,
% 295.91/188.43 ($false),
% 295.91/188.43 inference(unit_resolution,[status(thm)],[32975, 223, 32812, 32969, 32951])).
% 295.91/188.43 tff(32977,plain,((~node14(c_e_h_1, c_f, s16, s17)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s17)) | m_c_h_element_v_in1(c_e_h_1, c_f, s16)), inference(lemma,lemma(discharge,[]))).
% 295.91/188.43 tff(32978,plain,
% 295.91/188.43 (~node14(c_e_h_1, c_f, s16, s17)),
% 295.91/188.43 inference(unit_resolution,[status(thm)],[32977, 32812, 32950])).
% 295.91/188.43 tff(32979,plain,
% 295.91/188.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_f, s16, s17)) | node15(c_e_h_1, c_f, s16, s17) | node14(c_e_h_1, c_f, s16, s17) | node16(c_e_h_1, c_f, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s16, s17)) | node15(c_e_h_1, c_f, s16, s17) | node14(c_e_h_1, c_f, s16, s17) | node16(c_e_h_1, c_f, s16))),
% 295.91/188.43 inference(rewrite,[status(thm)],[])).
% 295.91/188.43 tff(32980,plain,
% 295.91/188.43 ((node16(c_e_h_1, c_f, s16) | node14(c_e_h_1, c_f, s16, s17) | node15(c_e_h_1, c_f, s16, s17) | (~node19(c_e_h_1, c_f, s16, s17))) <=> ((~node19(c_e_h_1, c_f, s16, s17)) | node15(c_e_h_1, c_f, s16, s17) | node14(c_e_h_1, c_f, s16, s17) | node16(c_e_h_1, c_f, s16))),
% 295.91/188.43 inference(rewrite,[status(thm)],[])).
% 295.91/188.43 tff(32981,plain,
% 295.91/188.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s16) | node14(c_e_h_1, c_f, s16, s17) | node15(c_e_h_1, c_f, s16, s17) | (~node19(c_e_h_1, c_f, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_f, s16, s17)) | node15(c_e_h_1, c_f, s16, s17) | node14(c_e_h_1, c_f, s16, s17) | node16(c_e_h_1, c_f, s16)))),
% 295.91/188.43 inference(monotonicity,[status(thm)],[32980])).
% 295.91/188.43 tff(32982,plain,
% 295.91/188.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s16) | node14(c_e_h_1, c_f, s16, s17) | node15(c_e_h_1, c_f, s16, s17) | (~node19(c_e_h_1, c_f, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s16, s17)) | node15(c_e_h_1, c_f, s16, s17) | node14(c_e_h_1, c_f, s16, s17) | node16(c_e_h_1, c_f, s16))),
% 295.91/188.43 inference(transitivity,[status(thm)],[32981, 32979])).
% 295.91/188.43 tff(32983,plain,
% 295.91/188.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s16) | node14(c_e_h_1, c_f, s16, s17) | node15(c_e_h_1, c_f, s16, s17) | (~node19(c_e_h_1, c_f, s16, s17)))),
% 295.91/188.43 inference(quant_inst,[status(thm)],[])).
% 295.91/188.43 tff(32984,plain,
% 295.91/188.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s16, s17)) | node15(c_e_h_1, c_f, s16, s17) | node14(c_e_h_1, c_f, s16, s17) | node16(c_e_h_1, c_f, s16)),
% 295.91/188.43 inference(modus_ponens,[status(thm)],[32983, 32982])).
% 295.91/188.43 tff(32985,plain,
% 295.91/188.43 (node15(c_e_h_1, c_f, s16, s17) | node14(c_e_h_1, c_f, s16, s17) | node16(c_e_h_1, c_f, s16)),
% 295.91/188.43 inference(unit_resolution,[status(thm)],[32984, 204, 32933])).
% 295.91/188.43 tff(32986,plain,
% 295.91/188.43 (node15(c_e_h_1, c_f, s16, s17)),
% 295.91/188.43 inference(unit_resolution,[status(thm)],[32985, 32978, 32968])).
% 295.91/188.43 tff(32987,plain,
% 295.91/188.43 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s17)) | (~node15(c_e_h_1, c_f, s16, s17)) | m_c_h_element_v_out(c_e_h_1, c_f, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s17)) | (~node15(c_e_h_1, c_f, s16, s17)) | m_c_h_element_v_out(c_e_h_1, c_f, s16))),
% 295.91/188.43 inference(rewrite,[status(thm)],[])).
% 295.91/188.43 tff(32988,plain,
% 295.91/188.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s17)) | (~node15(c_e_h_1, c_f, s16, s17)) | m_c_h_element_v_out(c_e_h_1, c_f, s16))),
% 295.91/188.43 inference(quant_inst,[status(thm)],[])).
% 295.91/188.43 tff(32989,plain,
% 295.91/188.43 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s17)) | (~node15(c_e_h_1, c_f, s16, s17)) | m_c_h_element_v_out(c_e_h_1, c_f, s16)),
% 295.91/188.43 inference(modus_ponens,[status(thm)],[32988, 32987])).
% 295.91/188.43 tff(32990,plain,
% 295.91/188.43 ($false),
% 295.91/188.43 inference(unit_resolution,[status(thm)],[32989, 147, 32919, 32812, 32986])).
% 295.91/188.43 tff(32991,plain,((~m_c_h_element_v_out(c_e_h_1, c_f, s17)) | m_c_h_element_v_out(c_e_h_1, c_f, s16) | m_c_h_element_v_in2(c_e_h_1, c_f, s16)), inference(lemma,lemma(discharge,[]))).
% 295.91/188.43 tff(32992,plain,
% 295.91/188.43 ($false),
% 295.91/188.43 inference(unit_resolution,[status(thm)],[32991, 32918, 32910, 32812])).
% 295.91/188.43 tff(32993,plain,(m_and_h_gate_v_out(c_e_h_1, c_i, s15) | (~m_c_h_element_v_out(c_e_h_1, c_f, s17)) | m_c_h_element_v_out(c_e_h_1, c_f, s15) | node20(c_e_h_1, c_i, s15)), inference(lemma,lemma(discharge,[]))).
% 295.91/188.43 tff(32994,plain,
% 295.91/188.43 ($false),
% 295.91/188.43 inference(unit_resolution,[status(thm)],[32993, 32828, 32825, 32812, 32811])).
% 295.91/188.43 tff(32995,plain,(m_and_h_gate_v_out(c_e_h_3, c_q, s12) | (~m_c_h_element_v_out(c_e_h_1, c_f, s17)) | m_c_h_element_v_out(c_e_h_1, c_f, s15) | m_and_h_gate_v_out(c_e_h_1, c_i, s14) | m_c_h_element_v_out(c_e_h_1, c_h, s13) | m_or_h_gate_v_out(c_e_h_1, c_j, s12) | node20(c_e_h_3, c_q, s12)), inference(lemma,lemma(discharge,[]))).
% 295.91/188.43 tff(32996,plain,
% 295.91/188.43 (m_and_h_gate_v_out(c_e_h_3, c_q, s12) | (~m_c_h_element_v_out(c_e_h_1, c_f, s17)) | node20(c_e_h_3, c_q, s12)),
% 295.91/188.43 inference(unit_resolution,[status(thm)],[32995, 32810, 24216, 23875, 22867])).
% 295.91/188.43 tff(32997,plain,
% 295.91/188.43 ((~m_c_h_element_v_out(c_e_h_1, c_f, s17)) | node20(c_e_h_3, c_q, s12)),
% 295.91/188.43 inference(unit_resolution,[status(thm)],[32996, 22022])).
% 295.91/188.43 tff(32998,plain,
% 295.91/188.43 (~m_c_h_element_v_out(c_e_h_1, c_f, s17)),
% 295.91/188.43 inference(unit_resolution,[status(thm)],[32997, 21955])).
% 295.91/188.43 tff(32999,plain,
% 295.91/188.43 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s17)) | m_c_h_element_v_out(c_e_h_1, c_f, s17))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s17)) | m_c_h_element_v_out(c_e_h_1, c_f, s17))),
% 295.91/188.43 inference(rewrite,[status(thm)],[])).
% 295.91/188.43 tff(33000,plain,
% 295.91/188.43 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s17)) | m_c_h_element_v_out(c_e_h_1, c_f, s17))),
% 295.91/188.43 inference(quant_inst,[status(thm)],[])).
% 295.91/188.43 tff(33001,plain,
% 295.91/188.43 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s17)) | m_c_h_element_v_out(c_e_h_1, c_f, s17)),
% 295.91/188.43 inference(modus_ponens,[status(thm)],[33000, 32999])).
% 295.91/188.43 tff(33002,plain,
% 295.91/188.43 (~m_and_h_gate_v_in1(c_e_h_1, c_q, s17)),
% 295.91/188.43 inference(unit_resolution,[status(thm)],[33001, 1586, 32998])).
% 295.91/188.43 tff(33003,plain,
% 295.91/188.43 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s17)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s17))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s17)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s17))),
% 295.91/188.44 inference(rewrite,[status(thm)],[])).
% 295.91/188.44 tff(33004,plain,
% 295.91/188.44 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s17)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s17))),
% 295.91/188.44 inference(quant_inst,[status(thm)],[])).
% 295.91/188.44 tff(33005,plain,
% 295.91/188.44 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s17)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s17)),
% 295.91/188.44 inference(modus_ponens,[status(thm)],[33004, 33003])).
% 295.91/188.44 tff(33006,plain,
% 295.91/188.44 (~node20(c_e_h_1, c_q, s17)),
% 295.91/188.44 inference(unit_resolution,[status(thm)],[33005, 38, 33002])).
% 295.91/188.44 tff(33007,plain,
% 295.91/188.44 (~m_c_h_element_v_in2(c_e_h_1, c_f, s15)),
% 295.91/188.44 inference(unit_resolution,[status(thm)],[32834, 24241])).
% 295.91/188.44 tff(33008,plain,
% 295.91/188.44 ((~m_c_h_element_v_out(c_e_h_1, c_f, s16)) | m_c_h_element_v_in2(c_e_h_1, c_f, s15)),
% 295.91/188.44 inference(unit_resolution,[status(thm)],[32909, 32810])).
% 295.91/188.44 tff(33009,plain,
% 295.91/188.44 (~m_c_h_element_v_out(c_e_h_1, c_f, s16)),
% 295.91/188.44 inference(unit_resolution,[status(thm)],[33008, 33007])).
% 295.91/188.44 tff(33010,assumption,(m_and_h_gate_v_in1(c_e_h_1, c_q, s16)), introduced(assumption)).
% 295.91/188.44 tff(33011,plain,
% 295.91/188.44 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s16)) | m_c_h_element_v_out(c_e_h_1, c_f, s16))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s16)) | m_c_h_element_v_out(c_e_h_1, c_f, s16))),
% 295.91/188.44 inference(rewrite,[status(thm)],[])).
% 295.91/188.44 tff(33012,plain,
% 295.91/188.44 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s16)) | m_c_h_element_v_out(c_e_h_1, c_f, s16))),
% 295.91/188.44 inference(quant_inst,[status(thm)],[])).
% 295.91/188.44 tff(33013,plain,
% 295.91/188.44 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s16)) | m_c_h_element_v_out(c_e_h_1, c_f, s16)),
% 295.91/188.44 inference(modus_ponens,[status(thm)],[33012, 33011])).
% 295.91/188.44 tff(33014,plain,
% 295.91/188.44 ($false),
% 295.91/188.44 inference(unit_resolution,[status(thm)],[33013, 1586, 32919, 33010])).
% 295.91/188.44 tff(33015,plain,(m_c_h_element_v_out(c_e_h_1, c_f, s16) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s16))), inference(lemma,lemma(discharge,[]))).
% 295.91/188.44 tff(33016,plain,
% 295.91/188.44 (~m_and_h_gate_v_in1(c_e_h_1, c_q, s16)),
% 295.91/188.44 inference(unit_resolution,[status(thm)],[33015, 33009])).
% 295.91/188.44 tff(33017,assumption,(~m_and_h_gate_v_in1(c_e_h_1, c_q, s16)), introduced(assumption)).
% 295.91/188.44 tff(33018,assumption,(node20(c_e_h_1, c_q, s16)), introduced(assumption)).
% 295.91/188.44 tff(33019,plain,
% 295.91/188.44 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s16)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s16))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s16)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s16))),
% 295.91/188.44 inference(rewrite,[status(thm)],[])).
% 295.91/188.44 tff(33020,plain,
% 295.91/188.44 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s16)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s16))),
% 295.91/188.44 inference(quant_inst,[status(thm)],[])).
% 295.91/188.44 tff(33021,plain,
% 295.91/188.44 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s16)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s16)),
% 295.91/188.44 inference(modus_ponens,[status(thm)],[33020, 33019])).
% 295.91/188.44 tff(33022,plain,
% 295.91/188.44 ($false),
% 295.91/188.44 inference(unit_resolution,[status(thm)],[33021, 38, 33018, 33017])).
% 295.91/188.44 tff(33023,plain,(m_and_h_gate_v_in1(c_e_h_1, c_q, s16) | (~node20(c_e_h_1, c_q, s16))), inference(lemma,lemma(discharge,[]))).
% 295.91/188.44 tff(33024,plain,
% 295.91/188.44 (~node20(c_e_h_1, c_q, s16)),
% 295.91/188.44 inference(unit_resolution,[status(thm)],[33023, 33016])).
% 295.91/188.44 tff(33025,plain,
% 295.91/188.44 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s11)) | m_c_h_element_v_out(c_e_h_1, c_f, s11))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s11)) | m_c_h_element_v_out(c_e_h_1, c_f, s11))),
% 295.91/188.44 inference(rewrite,[status(thm)],[])).
% 295.91/188.44 tff(33026,plain,
% 295.91/188.44 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s11)) | m_c_h_element_v_out(c_e_h_1, c_f, s11))),
% 295.91/188.44 inference(quant_inst,[status(thm)],[])).
% 295.91/188.44 tff(33027,plain,
% 295.91/188.44 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s11)) | m_c_h_element_v_out(c_e_h_1, c_f, s11)),
% 295.91/188.44 inference(modus_ponens,[status(thm)],[33026, 33025])).
% 295.91/188.44 tff(33028,plain,
% 295.91/188.44 (~m_and_h_gate_v_in1(c_e_h_1, c_q, s11)),
% 295.91/188.44 inference(unit_resolution,[status(thm)],[33027, 1586, 29298])).
% 295.91/188.44 tff(33029,plain,
% 295.91/188.44 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s11)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s11))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s11)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s11))),
% 295.91/188.44 inference(rewrite,[status(thm)],[])).
% 295.91/188.44 tff(33030,plain,
% 295.91/188.44 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s11)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s11))),
% 295.91/188.44 inference(quant_inst,[status(thm)],[])).
% 295.91/188.44 tff(33031,plain,
% 295.91/188.44 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s11)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s11)),
% 295.91/188.44 inference(modus_ponens,[status(thm)],[33030, 33029])).
% 295.91/188.44 tff(33032,plain,
% 295.91/188.44 (~node20(c_e_h_1, c_q, s11)),
% 295.91/188.44 inference(unit_resolution,[status(thm)],[33031, 38, 33028])).
% 295.91/188.44 tff(33033,plain,
% 295.91/188.44 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s10)) | m_c_h_element_v_out(c_e_h_1, c_f, s10))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s10)) | m_c_h_element_v_out(c_e_h_1, c_f, s10))),
% 295.91/188.44 inference(rewrite,[status(thm)],[])).
% 295.91/188.44 tff(33034,plain,
% 295.91/188.44 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s10)) | m_c_h_element_v_out(c_e_h_1, c_f, s10))),
% 295.91/188.44 inference(quant_inst,[status(thm)],[])).
% 295.91/188.44 tff(33035,plain,
% 295.91/188.44 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s10)) | m_c_h_element_v_out(c_e_h_1, c_f, s10)),
% 295.91/188.44 inference(modus_ponens,[status(thm)],[33034, 33033])).
% 295.91/188.44 tff(33036,plain,
% 295.91/188.44 (~m_and_h_gate_v_in1(c_e_h_1, c_q, s10)),
% 295.91/188.44 inference(unit_resolution,[status(thm)],[33035, 1586, 29206])).
% 295.91/188.44 tff(33037,plain,
% 295.91/188.44 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s10)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s10))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s10)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s10))),
% 295.91/188.44 inference(rewrite,[status(thm)],[])).
% 295.91/188.44 tff(33038,plain,
% 295.91/188.44 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s10)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s10))),
% 295.91/188.44 inference(quant_inst,[status(thm)],[])).
% 295.91/188.44 tff(33039,plain,
% 295.91/188.44 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s10)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s10)),
% 295.91/188.44 inference(modus_ponens,[status(thm)],[33038, 33037])).
% 295.91/188.44 tff(33040,plain,
% 295.91/188.44 (~node20(c_e_h_1, c_q, s10)),
% 295.91/188.44 inference(unit_resolution,[status(thm)],[33039, 38, 33036])).
% 295.91/188.44 tff(33041,assumption,(m_and_h_gate_v_out(c_e_h_1, c_q, s11)), introduced(assumption)).
% 295.91/188.44 tff(33042,assumption,(node22(c_e_h_1, c_q, s10, s11)), introduced(assumption)).
% 295.91/188.44 tff(33043,assumption,(m_and_h_gate_v_out(c_e_h_1, c_q, s10)), introduced(assumption)).
% 295.91/188.44 tff(33044,plain,
% 295.91/188.44 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s9)) | m_c_h_element_v_out(c_e_h_1, c_f, s9))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s9)) | m_c_h_element_v_out(c_e_h_1, c_f, s9))),
% 295.91/188.44 inference(rewrite,[status(thm)],[])).
% 295.91/188.44 tff(33045,plain,
% 295.91/188.44 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s9)) | m_c_h_element_v_out(c_e_h_1, c_f, s9))),
% 295.91/188.44 inference(quant_inst,[status(thm)],[])).
% 295.91/188.44 tff(33046,plain,
% 295.91/188.44 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s9)) | m_c_h_element_v_out(c_e_h_1, c_f, s9)),
% 295.91/188.44 inference(modus_ponens,[status(thm)],[33045, 33044])).
% 295.91/188.44 tff(33047,plain,
% 295.91/188.44 (~m_and_h_gate_v_in1(c_e_h_1, c_q, s9)),
% 295.91/188.44 inference(unit_resolution,[status(thm)],[33046, 1586, 29128])).
% 295.91/188.44 tff(33048,plain,
% 295.91/188.44 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s9)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s9))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s9)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s9))),
% 295.91/188.44 inference(rewrite,[status(thm)],[])).
% 295.91/188.44 tff(33049,plain,
% 295.91/188.44 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s9)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s9))),
% 295.91/188.44 inference(quant_inst,[status(thm)],[])).
% 295.91/188.44 tff(33050,plain,
% 295.91/188.44 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s9)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s9)),
% 295.91/188.44 inference(modus_ponens,[status(thm)],[33049, 33048])).
% 295.91/188.44 tff(33051,plain,
% 295.91/188.44 (~node20(c_e_h_1, c_q, s9)),
% 295.91/188.44 inference(unit_resolution,[status(thm)],[33050, 38, 33047])).
% 295.91/188.44 tff(33052,assumption,(node21(c_e_h_1, c_q, s9, s10)), introduced(assumption)).
% 295.91/188.44 tff(33053,plain,
% 295.91/188.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s10)) | node20(c_e_h_1, c_q, s9) | (~node21(c_e_h_1, c_q, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s10)) | node20(c_e_h_1, c_q, s9) | (~node21(c_e_h_1, c_q, s9, s10)))),
% 295.91/188.44 inference(rewrite,[status(thm)],[])).
% 295.91/188.44 tff(33054,plain,
% 295.91/188.44 ((node20(c_e_h_1, c_q, s9) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s10)) | (~node21(c_e_h_1, c_q, s9, s10))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_q, s10)) | node20(c_e_h_1, c_q, s9) | (~node21(c_e_h_1, c_q, s9, s10)))),
% 295.91/188.44 inference(rewrite,[status(thm)],[])).
% 295.91/188.44 tff(33055,plain,
% 295.91/188.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s9) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s10)) | (~node21(c_e_h_1, c_q, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s10)) | node20(c_e_h_1, c_q, s9) | (~node21(c_e_h_1, c_q, s9, s10))))),
% 295.91/188.44 inference(monotonicity,[status(thm)],[33054])).
% 295.91/188.44 tff(33056,plain,
% 295.91/188.44 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s9) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s10)) | (~node21(c_e_h_1, c_q, s9, s10)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s10)) | node20(c_e_h_1, c_q, s9) | (~node21(c_e_h_1, c_q, s9, s10)))),
% 295.91/188.44 inference(transitivity,[status(thm)],[33055, 33053])).
% 295.91/188.44 tff(33057,plain,
% 295.91/188.44 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s9) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s10)) | (~node21(c_e_h_1, c_q, s9, s10)))),
% 295.91/188.45 inference(quant_inst,[status(thm)],[])).
% 295.91/188.45 tff(33058,plain,
% 295.91/188.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s10)) | node20(c_e_h_1, c_q, s9) | (~node21(c_e_h_1, c_q, s9, s10))),
% 295.91/188.45 inference(modus_ponens,[status(thm)],[33057, 33056])).
% 295.91/188.45 tff(33059,plain,
% 295.91/188.45 ($false),
% 295.91/188.45 inference(unit_resolution,[status(thm)],[33058, 52, 33043, 33052, 33051])).
% 295.91/188.45 tff(33060,plain,((~node21(c_e_h_1, c_q, s9, s10)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s10))), inference(lemma,lemma(discharge,[]))).
% 295.91/188.45 tff(33061,plain,
% 295.91/188.45 (~node21(c_e_h_1, c_q, s9, s10)),
% 295.91/188.45 inference(unit_resolution,[status(thm)],[33060, 33043])).
% 295.91/188.45 tff(33062,plain,
% 295.91/188.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s9, s10)) | node21(c_e_h_1, c_q, s9, s10) | node22(c_e_h_1, c_q, s9, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s9, s10)) | node21(c_e_h_1, c_q, s9, s10) | node22(c_e_h_1, c_q, s9, s10))),
% 295.91/188.45 inference(rewrite,[status(thm)],[])).
% 295.91/188.45 tff(33063,plain,
% 295.91/188.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s9, s10)) | node21(c_e_h_1, c_q, s9, s10) | node22(c_e_h_1, c_q, s9, s10))),
% 295.91/188.45 inference(quant_inst,[status(thm)],[])).
% 295.91/188.45 tff(33064,plain,
% 295.91/188.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s9, s10)) | node21(c_e_h_1, c_q, s9, s10) | node22(c_e_h_1, c_q, s9, s10)),
% 295.91/188.45 inference(modus_ponens,[status(thm)],[33063, 33062])).
% 295.91/188.45 tff(33065,plain,
% 295.91/188.45 (node21(c_e_h_1, c_q, s9, s10) | node22(c_e_h_1, c_q, s9, s10)),
% 295.91/188.45 inference(unit_resolution,[status(thm)],[33064, 82, 7676])).
% 295.91/188.45 tff(33066,plain,
% 295.91/188.45 (node22(c_e_h_1, c_q, s9, s10)),
% 295.91/188.45 inference(unit_resolution,[status(thm)],[33065, 33061])).
% 295.91/188.45 tff(33067,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_q, s9)), introduced(assumption)).
% 295.91/188.45 tff(33068,plain,
% 295.91/188.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s10)) | (~node22(c_e_h_1, c_q, s9, s10)) | m_and_h_gate_v_out(c_e_h_1, c_q, s9))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s10)) | (~node22(c_e_h_1, c_q, s9, s10)) | m_and_h_gate_v_out(c_e_h_1, c_q, s9))),
% 295.91/188.45 inference(rewrite,[status(thm)],[])).
% 295.91/188.45 tff(33069,plain,
% 295.91/188.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s10)) | (~node22(c_e_h_1, c_q, s9, s10)) | m_and_h_gate_v_out(c_e_h_1, c_q, s9))),
% 295.91/188.45 inference(quant_inst,[status(thm)],[])).
% 295.91/188.45 tff(33070,plain,
% 295.91/188.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s10)) | (~node22(c_e_h_1, c_q, s9, s10)) | m_and_h_gate_v_out(c_e_h_1, c_q, s9)),
% 295.91/188.45 inference(modus_ponens,[status(thm)],[33069, 33068])).
% 295.91/188.45 tff(33071,plain,
% 295.91/188.45 ($false),
% 295.91/188.45 inference(unit_resolution,[status(thm)],[33070, 108, 33067, 33043, 33066])).
% 295.91/188.45 tff(33072,plain,((~m_and_h_gate_v_out(c_e_h_1, c_q, s10)) | m_and_h_gate_v_out(c_e_h_1, c_q, s9)), inference(lemma,lemma(discharge,[]))).
% 295.91/188.45 tff(33073,plain,
% 295.91/188.45 (~m_and_h_gate_v_out(c_e_h_1, c_q, s10)),
% 295.91/188.45 inference(unit_resolution,[status(thm)],[33072, 25288])).
% 295.91/188.45 tff(33074,plain,
% 295.91/188.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s11)) | (~node22(c_e_h_1, c_q, s10, s11)) | m_and_h_gate_v_out(c_e_h_1, c_q, s10))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s11)) | (~node22(c_e_h_1, c_q, s10, s11)) | m_and_h_gate_v_out(c_e_h_1, c_q, s10))),
% 295.91/188.45 inference(rewrite,[status(thm)],[])).
% 295.91/188.45 tff(33075,plain,
% 295.91/188.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s11)) | (~node22(c_e_h_1, c_q, s10, s11)) | m_and_h_gate_v_out(c_e_h_1, c_q, s10))),
% 295.91/188.45 inference(quant_inst,[status(thm)],[])).
% 295.91/188.45 tff(33076,plain,
% 295.91/188.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s11)) | (~node22(c_e_h_1, c_q, s10, s11)) | m_and_h_gate_v_out(c_e_h_1, c_q, s10)),
% 295.91/188.45 inference(modus_ponens,[status(thm)],[33075, 33074])).
% 295.91/188.45 tff(33077,plain,
% 295.91/188.45 ($false),
% 295.91/188.45 inference(unit_resolution,[status(thm)],[33076, 108, 33073, 33041, 33042])).
% 295.91/188.45 tff(33078,plain,((~node22(c_e_h_1, c_q, s10, s11)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s11))), inference(lemma,lemma(discharge,[]))).
% 295.91/188.45 tff(33079,plain,
% 295.91/188.45 (~node22(c_e_h_1, c_q, s10, s11)),
% 295.91/188.45 inference(unit_resolution,[status(thm)],[33078, 33041])).
% 295.91/188.45 tff(33080,assumption,(~node20(c_e_h_1, c_q, s10)), introduced(assumption)).
% 295.91/188.45 tff(33081,assumption,(node21(c_e_h_1, c_q, s10, s11)), introduced(assumption)).
% 295.91/188.45 tff(33082,plain,
% 295.91/188.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s11)) | node20(c_e_h_1, c_q, s10) | (~node21(c_e_h_1, c_q, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s11)) | node20(c_e_h_1, c_q, s10) | (~node21(c_e_h_1, c_q, s10, s11)))),
% 295.91/188.45 inference(rewrite,[status(thm)],[])).
% 295.91/188.45 tff(33083,plain,
% 295.91/188.45 ((node20(c_e_h_1, c_q, s10) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s11)) | (~node21(c_e_h_1, c_q, s10, s11))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_q, s11)) | node20(c_e_h_1, c_q, s10) | (~node21(c_e_h_1, c_q, s10, s11)))),
% 295.91/188.45 inference(rewrite,[status(thm)],[])).
% 295.91/188.45 tff(33084,plain,
% 295.91/188.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s10) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s11)) | (~node21(c_e_h_1, c_q, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s11)) | node20(c_e_h_1, c_q, s10) | (~node21(c_e_h_1, c_q, s10, s11))))),
% 295.91/188.45 inference(monotonicity,[status(thm)],[33083])).
% 295.91/188.45 tff(33085,plain,
% 295.91/188.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s10) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s11)) | (~node21(c_e_h_1, c_q, s10, s11)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s11)) | node20(c_e_h_1, c_q, s10) | (~node21(c_e_h_1, c_q, s10, s11)))),
% 295.91/188.45 inference(transitivity,[status(thm)],[33084, 33082])).
% 295.91/188.45 tff(33086,plain,
% 295.91/188.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s10) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s11)) | (~node21(c_e_h_1, c_q, s10, s11)))),
% 295.91/188.45 inference(quant_inst,[status(thm)],[])).
% 295.91/188.45 tff(33087,plain,
% 295.91/188.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s11)) | node20(c_e_h_1, c_q, s10) | (~node21(c_e_h_1, c_q, s10, s11))),
% 295.91/188.45 inference(modus_ponens,[status(thm)],[33086, 33085])).
% 295.91/188.45 tff(33088,plain,
% 295.91/188.45 ($false),
% 295.91/188.45 inference(unit_resolution,[status(thm)],[33087, 52, 33041, 33081, 33080])).
% 295.91/188.45 tff(33089,plain,((~node21(c_e_h_1, c_q, s10, s11)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s11)) | node20(c_e_h_1, c_q, s10)), inference(lemma,lemma(discharge,[]))).
% 295.91/188.45 tff(33090,plain,
% 295.91/188.45 (~node21(c_e_h_1, c_q, s10, s11)),
% 295.91/188.45 inference(unit_resolution,[status(thm)],[33089, 33041, 33080])).
% 295.91/188.45 tff(33091,plain,
% 295.91/188.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s10, s11)) | node21(c_e_h_1, c_q, s10, s11) | node22(c_e_h_1, c_q, s10, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s10, s11)) | node21(c_e_h_1, c_q, s10, s11) | node22(c_e_h_1, c_q, s10, s11))),
% 295.91/188.45 inference(rewrite,[status(thm)],[])).
% 295.91/188.45 tff(33092,plain,
% 295.91/188.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s10, s11)) | node21(c_e_h_1, c_q, s10, s11) | node22(c_e_h_1, c_q, s10, s11))),
% 295.91/188.45 inference(quant_inst,[status(thm)],[])).
% 295.91/188.45 tff(33093,plain,
% 295.91/188.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s10, s11)) | node21(c_e_h_1, c_q, s10, s11) | node22(c_e_h_1, c_q, s10, s11)),
% 295.91/188.45 inference(modus_ponens,[status(thm)],[33092, 33091])).
% 295.91/188.45 tff(33094,plain,
% 295.91/188.45 (node21(c_e_h_1, c_q, s10, s11) | node22(c_e_h_1, c_q, s10, s11)),
% 295.91/188.45 inference(unit_resolution,[status(thm)],[33093, 82, 7748])).
% 295.91/188.45 tff(33095,plain,
% 295.91/188.45 ($false),
% 295.91/188.45 inference(unit_resolution,[status(thm)],[33094, 33090, 33079])).
% 295.91/188.45 tff(33096,plain,((~m_and_h_gate_v_out(c_e_h_1, c_q, s11)) | node20(c_e_h_1, c_q, s10)), inference(lemma,lemma(discharge,[]))).
% 295.91/188.45 tff(33097,plain,
% 295.91/188.45 (~m_and_h_gate_v_out(c_e_h_1, c_q, s11)),
% 295.91/188.45 inference(unit_resolution,[status(thm)],[33096, 33040])).
% 295.91/188.45 tff(33098,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_q, s11)), introduced(assumption)).
% 295.91/188.45 tff(33099,assumption,(m_and_h_gate_v_out(c_e_h_1, c_q, s12)), introduced(assumption)).
% 295.91/188.45 tff(33100,assumption,(node22(c_e_h_1, c_q, s11, s12)), introduced(assumption)).
% 295.91/188.45 tff(33101,plain,
% 295.91/188.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s12)) | (~node22(c_e_h_1, c_q, s11, s12)) | m_and_h_gate_v_out(c_e_h_1, c_q, s11))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s12)) | (~node22(c_e_h_1, c_q, s11, s12)) | m_and_h_gate_v_out(c_e_h_1, c_q, s11))),
% 295.91/188.45 inference(rewrite,[status(thm)],[])).
% 295.91/188.45 tff(33102,plain,
% 295.91/188.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s12)) | (~node22(c_e_h_1, c_q, s11, s12)) | m_and_h_gate_v_out(c_e_h_1, c_q, s11))),
% 295.91/188.45 inference(quant_inst,[status(thm)],[])).
% 295.91/188.45 tff(33103,plain,
% 295.91/188.45 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s12)) | (~node22(c_e_h_1, c_q, s11, s12)) | m_and_h_gate_v_out(c_e_h_1, c_q, s11)),
% 295.91/188.45 inference(modus_ponens,[status(thm)],[33102, 33101])).
% 295.91/188.45 tff(33104,plain,
% 295.91/188.45 ($false),
% 295.91/188.45 inference(unit_resolution,[status(thm)],[33103, 108, 33099, 33098, 33100])).
% 295.91/188.45 tff(33105,plain,((~node22(c_e_h_1, c_q, s11, s12)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s12)) | m_and_h_gate_v_out(c_e_h_1, c_q, s11)), inference(lemma,lemma(discharge,[]))).
% 295.91/188.45 tff(33106,plain,
% 295.91/188.45 (~node22(c_e_h_1, c_q, s11, s12)),
% 295.91/188.45 inference(unit_resolution,[status(thm)],[33105, 33099, 33098])).
% 295.91/188.45 tff(33107,assumption,(~node20(c_e_h_1, c_q, s11)), introduced(assumption)).
% 295.91/188.45 tff(33108,assumption,(node21(c_e_h_1, c_q, s11, s12)), introduced(assumption)).
% 295.91/188.45 tff(33109,plain,
% 295.91/188.45 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s12)) | node20(c_e_h_1, c_q, s11) | (~node21(c_e_h_1, c_q, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s12)) | node20(c_e_h_1, c_q, s11) | (~node21(c_e_h_1, c_q, s11, s12)))),
% 295.91/188.46 inference(rewrite,[status(thm)],[])).
% 295.91/188.46 tff(33110,plain,
% 295.91/188.46 ((node20(c_e_h_1, c_q, s11) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s12)) | (~node21(c_e_h_1, c_q, s11, s12))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_q, s12)) | node20(c_e_h_1, c_q, s11) | (~node21(c_e_h_1, c_q, s11, s12)))),
% 295.91/188.46 inference(rewrite,[status(thm)],[])).
% 295.91/188.46 tff(33111,plain,
% 295.91/188.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s11) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s12)) | (~node21(c_e_h_1, c_q, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s12)) | node20(c_e_h_1, c_q, s11) | (~node21(c_e_h_1, c_q, s11, s12))))),
% 295.91/188.46 inference(monotonicity,[status(thm)],[33110])).
% 295.91/188.46 tff(33112,plain,
% 295.91/188.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s11) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s12)) | (~node21(c_e_h_1, c_q, s11, s12)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s12)) | node20(c_e_h_1, c_q, s11) | (~node21(c_e_h_1, c_q, s11, s12)))),
% 295.91/188.46 inference(transitivity,[status(thm)],[33111, 33109])).
% 295.91/188.46 tff(33113,plain,
% 295.91/188.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s11) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s12)) | (~node21(c_e_h_1, c_q, s11, s12)))),
% 295.91/188.46 inference(quant_inst,[status(thm)],[])).
% 295.91/188.46 tff(33114,plain,
% 295.91/188.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s12)) | node20(c_e_h_1, c_q, s11) | (~node21(c_e_h_1, c_q, s11, s12))),
% 295.91/188.46 inference(modus_ponens,[status(thm)],[33113, 33112])).
% 295.91/188.46 tff(33115,plain,
% 295.91/188.46 ($false),
% 295.91/188.46 inference(unit_resolution,[status(thm)],[33114, 52, 33099, 33108, 33107])).
% 295.91/188.46 tff(33116,plain,((~node21(c_e_h_1, c_q, s11, s12)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s12)) | node20(c_e_h_1, c_q, s11)), inference(lemma,lemma(discharge,[]))).
% 295.91/188.46 tff(33117,plain,
% 295.91/188.46 (~node21(c_e_h_1, c_q, s11, s12)),
% 295.91/188.46 inference(unit_resolution,[status(thm)],[33116, 33099, 33107])).
% 295.91/188.46 tff(33118,plain,
% 295.91/188.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s11, s12)) | node21(c_e_h_1, c_q, s11, s12) | node22(c_e_h_1, c_q, s11, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s11, s12)) | node21(c_e_h_1, c_q, s11, s12) | node22(c_e_h_1, c_q, s11, s12))),
% 295.91/188.46 inference(rewrite,[status(thm)],[])).
% 295.91/188.46 tff(33119,plain,
% 295.91/188.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s11, s12)) | node21(c_e_h_1, c_q, s11, s12) | node22(c_e_h_1, c_q, s11, s12))),
% 295.91/188.46 inference(quant_inst,[status(thm)],[])).
% 295.91/188.46 tff(33120,plain,
% 295.91/188.46 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s11, s12)) | node21(c_e_h_1, c_q, s11, s12) | node22(c_e_h_1, c_q, s11, s12)),
% 295.91/188.46 inference(modus_ponens,[status(thm)],[33119, 33118])).
% 295.91/188.46 tff(33121,plain,
% 295.91/188.46 (node21(c_e_h_1, c_q, s11, s12) | node22(c_e_h_1, c_q, s11, s12)),
% 295.91/188.46 inference(unit_resolution,[status(thm)],[33120, 82, 11461])).
% 295.91/188.46 tff(33122,plain,
% 295.91/188.46 ($false),
% 295.91/188.46 inference(unit_resolution,[status(thm)],[33121, 33117, 33106])).
% 295.91/188.46 tff(33123,plain,((~m_and_h_gate_v_out(c_e_h_1, c_q, s12)) | node20(c_e_h_1, c_q, s11) | m_and_h_gate_v_out(c_e_h_1, c_q, s11)), inference(lemma,lemma(discharge,[]))).
% 295.91/188.46 tff(33124,plain,
% 295.91/188.46 ((~m_and_h_gate_v_out(c_e_h_1, c_q, s12)) | node20(c_e_h_1, c_q, s11)),
% 295.91/188.46 inference(unit_resolution,[status(thm)],[33123, 33097])).
% 295.91/188.46 tff(33125,plain,
% 295.91/188.46 (~m_and_h_gate_v_out(c_e_h_1, c_q, s12)),
% 295.91/188.46 inference(unit_resolution,[status(thm)],[33124, 33032])).
% 295.91/188.46 tff(33126,plain,
% 295.91/188.46 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s12)) | m_c_h_element_v_out(c_e_h_1, c_f, s12))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s12)) | m_c_h_element_v_out(c_e_h_1, c_f, s12))),
% 295.91/188.46 inference(rewrite,[status(thm)],[])).
% 295.91/188.46 tff(33127,plain,
% 295.91/188.46 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s12)) | m_c_h_element_v_out(c_e_h_1, c_f, s12))),
% 295.91/188.46 inference(quant_inst,[status(thm)],[])).
% 295.91/188.46 tff(33128,plain,
% 295.91/188.46 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s12)) | m_c_h_element_v_out(c_e_h_1, c_f, s12)),
% 295.91/188.46 inference(modus_ponens,[status(thm)],[33127, 33126])).
% 295.91/188.46 tff(33129,plain,
% 295.91/188.46 (~m_and_h_gate_v_in1(c_e_h_1, c_q, s12)),
% 295.91/188.46 inference(unit_resolution,[status(thm)],[33128, 1586, 29384])).
% 295.91/188.46 tff(33130,plain,
% 295.91/188.46 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s12)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s12))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s12)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s12))),
% 295.91/188.46 inference(rewrite,[status(thm)],[])).
% 295.91/188.46 tff(33131,plain,
% 295.91/188.46 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s12)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s12))),
% 295.91/188.46 inference(quant_inst,[status(thm)],[])).
% 295.91/188.46 tff(33132,plain,
% 295.91/188.46 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s12)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s12)),
% 295.91/188.46 inference(modus_ponens,[status(thm)],[33131, 33130])).
% 295.91/188.46 tff(33133,plain,
% 295.91/188.46 (~node20(c_e_h_1, c_q, s12)),
% 295.91/188.46 inference(unit_resolution,[status(thm)],[33132, 38, 33129])).
% 295.91/188.46 tff(33134,assumption,(~node20(c_e_h_1, c_q, s12)), introduced(assumption)).
% 295.91/188.46 tff(33135,assumption,(m_and_h_gate_v_out(c_e_h_1, c_q, s13)), introduced(assumption)).
% 295.91/188.46 tff(33136,assumption,(node21(c_e_h_1, c_q, s12, s13)), introduced(assumption)).
% 295.91/188.46 tff(33137,plain,
% 295.91/188.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s13)) | node20(c_e_h_1, c_q, s12) | (~node21(c_e_h_1, c_q, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s13)) | node20(c_e_h_1, c_q, s12) | (~node21(c_e_h_1, c_q, s12, s13)))),
% 295.91/188.46 inference(rewrite,[status(thm)],[])).
% 295.91/188.46 tff(33138,plain,
% 295.91/188.46 ((node20(c_e_h_1, c_q, s12) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s13)) | (~node21(c_e_h_1, c_q, s12, s13))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_q, s13)) | node20(c_e_h_1, c_q, s12) | (~node21(c_e_h_1, c_q, s12, s13)))),
% 295.91/188.46 inference(rewrite,[status(thm)],[])).
% 295.91/188.46 tff(33139,plain,
% 295.91/188.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s12) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s13)) | (~node21(c_e_h_1, c_q, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s13)) | node20(c_e_h_1, c_q, s12) | (~node21(c_e_h_1, c_q, s12, s13))))),
% 295.91/188.46 inference(monotonicity,[status(thm)],[33138])).
% 295.91/188.46 tff(33140,plain,
% 295.91/188.46 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s12) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s13)) | (~node21(c_e_h_1, c_q, s12, s13)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s13)) | node20(c_e_h_1, c_q, s12) | (~node21(c_e_h_1, c_q, s12, s13)))),
% 295.91/188.47 inference(transitivity,[status(thm)],[33139, 33137])).
% 295.91/188.47 tff(33141,plain,
% 295.91/188.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s12) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s13)) | (~node21(c_e_h_1, c_q, s12, s13)))),
% 295.91/188.47 inference(quant_inst,[status(thm)],[])).
% 295.91/188.47 tff(33142,plain,
% 295.91/188.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s13)) | node20(c_e_h_1, c_q, s12) | (~node21(c_e_h_1, c_q, s12, s13))),
% 295.91/188.47 inference(modus_ponens,[status(thm)],[33141, 33140])).
% 295.91/188.47 tff(33143,plain,
% 295.91/188.47 ($false),
% 295.91/188.47 inference(unit_resolution,[status(thm)],[33142, 52, 33135, 33136, 33134])).
% 295.91/188.47 tff(33144,plain,((~node21(c_e_h_1, c_q, s12, s13)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s13)) | node20(c_e_h_1, c_q, s12)), inference(lemma,lemma(discharge,[]))).
% 295.91/188.47 tff(33145,plain,
% 295.91/188.47 (~node21(c_e_h_1, c_q, s12, s13)),
% 295.91/188.47 inference(unit_resolution,[status(thm)],[33144, 33135, 33134])).
% 295.91/188.47 tff(33146,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_q, s12)), introduced(assumption)).
% 295.91/188.47 tff(33147,assumption,(node22(c_e_h_1, c_q, s12, s13)), introduced(assumption)).
% 295.91/188.47 tff(33148,plain,
% 295.91/188.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s13)) | (~node22(c_e_h_1, c_q, s12, s13)) | m_and_h_gate_v_out(c_e_h_1, c_q, s12))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s13)) | (~node22(c_e_h_1, c_q, s12, s13)) | m_and_h_gate_v_out(c_e_h_1, c_q, s12))),
% 295.91/188.47 inference(rewrite,[status(thm)],[])).
% 295.91/188.47 tff(33149,plain,
% 295.91/188.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s13)) | (~node22(c_e_h_1, c_q, s12, s13)) | m_and_h_gate_v_out(c_e_h_1, c_q, s12))),
% 295.91/188.47 inference(quant_inst,[status(thm)],[])).
% 295.91/188.47 tff(33150,plain,
% 295.91/188.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s13)) | (~node22(c_e_h_1, c_q, s12, s13)) | m_and_h_gate_v_out(c_e_h_1, c_q, s12)),
% 295.91/188.47 inference(modus_ponens,[status(thm)],[33149, 33148])).
% 295.91/188.47 tff(33151,plain,
% 295.91/188.47 ($false),
% 295.91/188.47 inference(unit_resolution,[status(thm)],[33150, 108, 33146, 33135, 33147])).
% 295.91/188.47 tff(33152,plain,((~node22(c_e_h_1, c_q, s12, s13)) | m_and_h_gate_v_out(c_e_h_1, c_q, s12) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s13))), inference(lemma,lemma(discharge,[]))).
% 295.91/188.47 tff(33153,plain,
% 295.91/188.47 (~node22(c_e_h_1, c_q, s12, s13)),
% 295.91/188.47 inference(unit_resolution,[status(thm)],[33152, 33135, 33146])).
% 295.91/188.47 tff(33154,plain,
% 295.91/188.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s12, s13)) | node21(c_e_h_1, c_q, s12, s13) | node22(c_e_h_1, c_q, s12, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s12, s13)) | node21(c_e_h_1, c_q, s12, s13) | node22(c_e_h_1, c_q, s12, s13))),
% 295.91/188.47 inference(rewrite,[status(thm)],[])).
% 295.91/188.47 tff(33155,plain,
% 295.91/188.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s12, s13)) | node21(c_e_h_1, c_q, s12, s13) | node22(c_e_h_1, c_q, s12, s13))),
% 295.91/188.47 inference(quant_inst,[status(thm)],[])).
% 295.91/188.47 tff(33156,plain,
% 295.91/188.47 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s12, s13)) | node21(c_e_h_1, c_q, s12, s13) | node22(c_e_h_1, c_q, s12, s13)),
% 295.91/188.47 inference(modus_ponens,[status(thm)],[33155, 33154])).
% 295.91/188.47 tff(33157,plain,
% 295.91/188.47 (node21(c_e_h_1, c_q, s12, s13) | node22(c_e_h_1, c_q, s12, s13)),
% 295.91/188.47 inference(unit_resolution,[status(thm)],[33156, 82, 11856])).
% 295.91/188.47 tff(33158,plain,
% 295.91/188.47 ($false),
% 295.91/188.47 inference(unit_resolution,[status(thm)],[33157, 33153, 33145])).
% 295.91/188.47 tff(33159,plain,((~m_and_h_gate_v_out(c_e_h_1, c_q, s13)) | m_and_h_gate_v_out(c_e_h_1, c_q, s12) | node20(c_e_h_1, c_q, s12)), inference(lemma,lemma(discharge,[]))).
% 295.91/188.47 tff(33160,plain,
% 295.91/188.47 (~m_and_h_gate_v_out(c_e_h_1, c_q, s13)),
% 295.91/188.47 inference(unit_resolution,[status(thm)],[33159, 33133, 33125])).
% 295.91/188.47 tff(33161,plain,
% 295.91/188.47 (~m_c_h_element_v_out(c_e_h_1, c_f, s14)),
% 295.91/188.47 inference(unit_resolution,[status(thm)],[32725, 32651, 32715])).
% 295.91/188.47 tff(33162,plain,
% 295.91/188.47 (~m_c_h_element_v_out(c_e_h_1, c_f, s15)),
% 295.91/188.47 inference(unit_resolution,[status(thm)],[32809, 33161, 32737])).
% 295.91/188.47 tff(33163,plain,
% 295.91/188.47 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s15)) | m_c_h_element_v_out(c_e_h_1, c_f, s15))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s15)) | m_c_h_element_v_out(c_e_h_1, c_f, s15))),
% 295.91/188.47 inference(rewrite,[status(thm)],[])).
% 295.91/188.47 tff(33164,plain,
% 295.91/188.47 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s15)) | m_c_h_element_v_out(c_e_h_1, c_f, s15))),
% 295.91/188.47 inference(quant_inst,[status(thm)],[])).
% 295.91/188.47 tff(33165,plain,
% 295.91/188.47 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s15)) | m_c_h_element_v_out(c_e_h_1, c_f, s15)),
% 295.91/188.47 inference(modus_ponens,[status(thm)],[33164, 33163])).
% 295.91/188.47 tff(33166,plain,
% 295.91/188.47 (~m_and_h_gate_v_in1(c_e_h_1, c_q, s15)),
% 295.91/188.47 inference(unit_resolution,[status(thm)],[33165, 1586, 33162])).
% 295.91/188.47 tff(33167,assumption,(m_and_h_gate_v_out(c_e_h_1, c_q, s16)), introduced(assumption)).
% 295.91/188.47 tff(33168,assumption,(m_and_h_gate_v_in1(c_e_h_1, c_q, s14)), introduced(assumption)).
% 295.91/188.47 tff(33169,plain,
% 295.91/188.47 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s14)) | m_c_h_element_v_out(c_e_h_1, c_f, s14))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s14)) | m_c_h_element_v_out(c_e_h_1, c_f, s14))),
% 295.91/188.47 inference(rewrite,[status(thm)],[])).
% 295.91/188.47 tff(33170,plain,
% 295.91/188.47 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s14)) | m_c_h_element_v_out(c_e_h_1, c_f, s14))),
% 295.91/188.47 inference(quant_inst,[status(thm)],[])).
% 295.91/188.47 tff(33171,plain,
% 295.91/188.47 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s14)) | m_c_h_element_v_out(c_e_h_1, c_f, s14)),
% 295.91/188.47 inference(modus_ponens,[status(thm)],[33170, 33169])).
% 295.91/188.47 tff(33172,plain,
% 295.91/188.47 ($false),
% 295.91/188.47 inference(unit_resolution,[status(thm)],[33171, 1586, 32734, 33168])).
% 295.91/188.47 tff(33173,plain,((~m_and_h_gate_v_in1(c_e_h_1, c_q, s14)) | m_c_h_element_v_out(c_e_h_1, c_f, s14)), inference(lemma,lemma(discharge,[]))).
% 295.91/188.47 tff(33174,plain,
% 295.91/188.47 (~m_and_h_gate_v_in1(c_e_h_1, c_q, s14)),
% 295.91/188.47 inference(unit_resolution,[status(thm)],[33173, 33161])).
% 295.91/188.47 tff(33175,assumption,(node20(c_e_h_1, c_q, s14)), introduced(assumption)).
% 295.91/188.47 tff(33176,assumption,(~m_and_h_gate_v_in1(c_e_h_1, c_q, s14)), introduced(assumption)).
% 295.91/188.47 tff(33177,plain,
% 295.91/188.47 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s14)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s14))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s14)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s14))),
% 295.91/188.47 inference(rewrite,[status(thm)],[])).
% 295.91/188.47 tff(33178,plain,
% 295.91/188.47 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s14)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s14))),
% 295.91/188.47 inference(quant_inst,[status(thm)],[])).
% 295.91/188.47 tff(33179,plain,
% 295.91/188.47 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s14)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s14)),
% 295.91/188.47 inference(modus_ponens,[status(thm)],[33178, 33177])).
% 295.91/188.47 tff(33180,plain,
% 295.91/188.47 ($false),
% 295.91/188.47 inference(unit_resolution,[status(thm)],[33179, 38, 33176, 33175])).
% 295.91/188.47 tff(33181,plain,((~node20(c_e_h_1, c_q, s14)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s14)), inference(lemma,lemma(discharge,[]))).
% 295.91/188.47 tff(33182,plain,
% 295.91/188.47 (~node20(c_e_h_1, c_q, s14)),
% 295.91/188.47 inference(unit_resolution,[status(thm)],[33181, 33174])).
% 295.91/188.47 tff(33183,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_q, s13)), introduced(assumption)).
% 295.91/188.47 tff(33184,assumption,(m_and_h_gate_v_in1(c_e_h_1, c_q, s13)), introduced(assumption)).
% 295.91/188.47 tff(33185,plain,
% 295.91/188.47 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s13)) | m_c_h_element_v_out(c_e_h_1, c_f, s13))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s13)) | m_c_h_element_v_out(c_e_h_1, c_f, s13))),
% 295.91/188.47 inference(rewrite,[status(thm)],[])).
% 295.91/188.47 tff(33186,plain,
% 295.91/188.47 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s13)) | m_c_h_element_v_out(c_e_h_1, c_f, s13))),
% 295.91/188.47 inference(quant_inst,[status(thm)],[])).
% 295.91/188.47 tff(33187,plain,
% 295.91/188.47 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s13)) | m_c_h_element_v_out(c_e_h_1, c_f, s13)),
% 295.91/188.47 inference(modus_ponens,[status(thm)],[33186, 33185])).
% 295.91/188.47 tff(33188,plain,
% 295.91/188.47 ($false),
% 295.91/188.47 inference(unit_resolution,[status(thm)],[33187, 1586, 32651, 33184])).
% 295.91/188.47 tff(33189,plain,((~m_and_h_gate_v_in1(c_e_h_1, c_q, s13)) | m_c_h_element_v_out(c_e_h_1, c_f, s13)), inference(lemma,lemma(discharge,[]))).
% 295.91/188.47 tff(33190,plain,
% 295.91/188.47 (~m_and_h_gate_v_in1(c_e_h_1, c_q, s13)),
% 295.91/188.47 inference(unit_resolution,[status(thm)],[33189, 32651])).
% 295.91/188.47 tff(33191,assumption,(~m_and_h_gate_v_in1(c_e_h_1, c_q, s13)), introduced(assumption)).
% 295.91/188.47 tff(33192,assumption,(node20(c_e_h_1, c_q, s13)), introduced(assumption)).
% 295.91/188.47 tff(33193,plain,
% 295.91/188.47 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s13)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s13))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s13)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s13))),
% 295.91/188.47 inference(rewrite,[status(thm)],[])).
% 295.91/188.47 tff(33194,plain,
% 295.91/188.47 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s13)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s13))),
% 295.91/188.47 inference(quant_inst,[status(thm)],[])).
% 295.91/188.47 tff(33195,plain,
% 295.91/188.47 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s13)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s13)),
% 295.91/188.47 inference(modus_ponens,[status(thm)],[33194, 33193])).
% 295.91/188.47 tff(33196,plain,
% 295.91/188.47 ($false),
% 295.91/188.47 inference(unit_resolution,[status(thm)],[33195, 38, 33192, 33191])).
% 295.91/188.47 tff(33197,plain,((~node20(c_e_h_1, c_q, s13)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s13)), inference(lemma,lemma(discharge,[]))).
% 295.91/188.47 tff(33198,plain,
% 295.91/188.47 (~node20(c_e_h_1, c_q, s13)),
% 295.91/188.47 inference(unit_resolution,[status(thm)],[33197, 33190])).
% 295.91/188.47 tff(33199,assumption,(~node20(c_e_h_1, c_q, s13)), introduced(assumption)).
% 295.91/188.47 tff(33200,assumption,(m_and_h_gate_v_out(c_e_h_1, c_q, s14)), introduced(assumption)).
% 295.91/188.47 tff(33201,assumption,(node21(c_e_h_1, c_q, s13, s14)), introduced(assumption)).
% 295.91/188.47 tff(33202,plain,
% 295.91/188.47 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s14)) | node20(c_e_h_1, c_q, s13) | (~node21(c_e_h_1, c_q, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s14)) | node20(c_e_h_1, c_q, s13) | (~node21(c_e_h_1, c_q, s13, s14)))),
% 295.91/188.47 inference(rewrite,[status(thm)],[])).
% 295.91/188.48 tff(33203,plain,
% 295.91/188.48 ((node20(c_e_h_1, c_q, s13) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s14)) | (~node21(c_e_h_1, c_q, s13, s14))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_q, s14)) | node20(c_e_h_1, c_q, s13) | (~node21(c_e_h_1, c_q, s13, s14)))),
% 295.91/188.48 inference(rewrite,[status(thm)],[])).
% 295.91/188.48 tff(33204,plain,
% 295.91/188.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s13) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s14)) | (~node21(c_e_h_1, c_q, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s14)) | node20(c_e_h_1, c_q, s13) | (~node21(c_e_h_1, c_q, s13, s14))))),
% 295.91/188.48 inference(monotonicity,[status(thm)],[33203])).
% 295.91/188.48 tff(33205,plain,
% 295.91/188.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s13) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s14)) | (~node21(c_e_h_1, c_q, s13, s14)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s14)) | node20(c_e_h_1, c_q, s13) | (~node21(c_e_h_1, c_q, s13, s14)))),
% 295.91/188.48 inference(transitivity,[status(thm)],[33204, 33202])).
% 295.91/188.48 tff(33206,plain,
% 295.91/188.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s13) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s14)) | (~node21(c_e_h_1, c_q, s13, s14)))),
% 295.91/188.48 inference(quant_inst,[status(thm)],[])).
% 295.91/188.48 tff(33207,plain,
% 295.91/188.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s14)) | node20(c_e_h_1, c_q, s13) | (~node21(c_e_h_1, c_q, s13, s14))),
% 295.91/188.48 inference(modus_ponens,[status(thm)],[33206, 33205])).
% 295.91/188.48 tff(33208,plain,
% 295.91/188.48 ($false),
% 295.91/188.48 inference(unit_resolution,[status(thm)],[33207, 52, 33200, 33201, 33199])).
% 295.91/188.48 tff(33209,plain,((~node21(c_e_h_1, c_q, s13, s14)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s14)) | node20(c_e_h_1, c_q, s13)), inference(lemma,lemma(discharge,[]))).
% 295.91/188.48 tff(33210,plain,
% 295.91/188.48 (~node21(c_e_h_1, c_q, s13, s14)),
% 295.91/188.48 inference(unit_resolution,[status(thm)],[33209, 33200, 33199])).
% 295.91/188.48 tff(33211,assumption,(node22(c_e_h_1, c_q, s13, s14)), introduced(assumption)).
% 295.91/188.48 tff(33212,plain,
% 295.91/188.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s14)) | (~node22(c_e_h_1, c_q, s13, s14)) | m_and_h_gate_v_out(c_e_h_1, c_q, s13))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s14)) | (~node22(c_e_h_1, c_q, s13, s14)) | m_and_h_gate_v_out(c_e_h_1, c_q, s13))),
% 295.91/188.48 inference(rewrite,[status(thm)],[])).
% 295.91/188.48 tff(33213,plain,
% 295.91/188.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s14)) | (~node22(c_e_h_1, c_q, s13, s14)) | m_and_h_gate_v_out(c_e_h_1, c_q, s13))),
% 295.91/188.48 inference(quant_inst,[status(thm)],[])).
% 295.91/188.48 tff(33214,plain,
% 295.91/188.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s14)) | (~node22(c_e_h_1, c_q, s13, s14)) | m_and_h_gate_v_out(c_e_h_1, c_q, s13)),
% 295.91/188.48 inference(modus_ponens,[status(thm)],[33213, 33212])).
% 295.91/188.48 tff(33215,plain,
% 295.91/188.48 ($false),
% 295.91/188.48 inference(unit_resolution,[status(thm)],[33214, 108, 33200, 33211, 33183])).
% 295.91/188.48 tff(33216,plain,((~node22(c_e_h_1, c_q, s13, s14)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s14)) | m_and_h_gate_v_out(c_e_h_1, c_q, s13)), inference(lemma,lemma(discharge,[]))).
% 295.91/188.48 tff(33217,plain,
% 295.91/188.48 (~node22(c_e_h_1, c_q, s13, s14)),
% 295.91/188.48 inference(unit_resolution,[status(thm)],[33216, 33200, 33183])).
% 295.91/188.48 tff(33218,plain,
% 295.91/188.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s13, s14)) | node21(c_e_h_1, c_q, s13, s14) | node22(c_e_h_1, c_q, s13, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s13, s14)) | node21(c_e_h_1, c_q, s13, s14) | node22(c_e_h_1, c_q, s13, s14))),
% 295.91/188.48 inference(rewrite,[status(thm)],[])).
% 295.91/188.48 tff(33219,plain,
% 295.91/188.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s13, s14)) | node21(c_e_h_1, c_q, s13, s14) | node22(c_e_h_1, c_q, s13, s14))),
% 295.91/188.48 inference(quant_inst,[status(thm)],[])).
% 295.91/188.48 tff(33220,plain,
% 295.91/188.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s13, s14)) | node21(c_e_h_1, c_q, s13, s14) | node22(c_e_h_1, c_q, s13, s14)),
% 295.91/188.48 inference(modus_ponens,[status(thm)],[33219, 33218])).
% 295.91/188.48 tff(33221,plain,
% 295.91/188.48 (node21(c_e_h_1, c_q, s13, s14) | node22(c_e_h_1, c_q, s13, s14)),
% 295.91/188.48 inference(unit_resolution,[status(thm)],[33220, 82, 12831])).
% 295.91/188.48 tff(33222,plain,
% 295.91/188.48 ($false),
% 295.91/188.48 inference(unit_resolution,[status(thm)],[33221, 33217, 33210])).
% 295.91/188.48 tff(33223,plain,((~m_and_h_gate_v_out(c_e_h_1, c_q, s14)) | m_and_h_gate_v_out(c_e_h_1, c_q, s13) | node20(c_e_h_1, c_q, s13)), inference(lemma,lemma(discharge,[]))).
% 295.91/188.48 tff(33224,plain,
% 295.91/188.48 (~m_and_h_gate_v_out(c_e_h_1, c_q, s14)),
% 295.91/188.48 inference(unit_resolution,[status(thm)],[33223, 33198, 33183])).
% 295.91/188.48 tff(33225,assumption,(~node20(c_e_h_1, c_q, s14)), introduced(assumption)).
% 295.91/188.48 tff(33226,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_q, s14)), introduced(assumption)).
% 295.91/188.48 tff(33227,assumption,(m_and_h_gate_v_out(c_e_h_1, c_q, s15)), introduced(assumption)).
% 295.91/188.48 tff(33228,assumption,(node22(c_e_h_1, c_q, s14, s15)), introduced(assumption)).
% 295.91/188.48 tff(33229,plain,
% 295.91/188.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s15)) | (~node22(c_e_h_1, c_q, s14, s15)) | m_and_h_gate_v_out(c_e_h_1, c_q, s14))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s15)) | (~node22(c_e_h_1, c_q, s14, s15)) | m_and_h_gate_v_out(c_e_h_1, c_q, s14))),
% 295.91/188.48 inference(rewrite,[status(thm)],[])).
% 295.91/188.48 tff(33230,plain,
% 295.91/188.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s15)) | (~node22(c_e_h_1, c_q, s14, s15)) | m_and_h_gate_v_out(c_e_h_1, c_q, s14))),
% 295.91/188.48 inference(quant_inst,[status(thm)],[])).
% 295.91/188.48 tff(33231,plain,
% 295.91/188.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s15)) | (~node22(c_e_h_1, c_q, s14, s15)) | m_and_h_gate_v_out(c_e_h_1, c_q, s14)),
% 295.91/188.48 inference(modus_ponens,[status(thm)],[33230, 33229])).
% 295.91/188.48 tff(33232,plain,
% 295.91/188.48 ($false),
% 295.91/188.48 inference(unit_resolution,[status(thm)],[33231, 108, 33226, 33227, 33228])).
% 295.91/188.48 tff(33233,plain,((~node22(c_e_h_1, c_q, s14, s15)) | m_and_h_gate_v_out(c_e_h_1, c_q, s14) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s15))), inference(lemma,lemma(discharge,[]))).
% 295.91/188.48 tff(33234,plain,
% 295.91/188.48 (~node22(c_e_h_1, c_q, s14, s15)),
% 295.91/188.48 inference(unit_resolution,[status(thm)],[33233, 33227, 33226])).
% 295.91/188.48 tff(33235,plain,
% 295.91/188.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s14, s15)) | node21(c_e_h_1, c_q, s14, s15) | node22(c_e_h_1, c_q, s14, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s14, s15)) | node21(c_e_h_1, c_q, s14, s15) | node22(c_e_h_1, c_q, s14, s15))),
% 295.91/188.48 inference(rewrite,[status(thm)],[])).
% 295.91/188.48 tff(33236,plain,
% 295.91/188.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s14, s15)) | node21(c_e_h_1, c_q, s14, s15) | node22(c_e_h_1, c_q, s14, s15))),
% 295.91/188.48 inference(quant_inst,[status(thm)],[])).
% 295.91/188.48 tff(33237,plain,
% 295.91/188.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s14, s15)) | node21(c_e_h_1, c_q, s14, s15) | node22(c_e_h_1, c_q, s14, s15)),
% 295.91/188.48 inference(modus_ponens,[status(thm)],[33236, 33235])).
% 295.91/188.48 tff(33238,plain,
% 295.91/188.48 (node21(c_e_h_1, c_q, s14, s15) | node22(c_e_h_1, c_q, s14, s15)),
% 295.91/188.48 inference(unit_resolution,[status(thm)],[33237, 82, 12926])).
% 295.91/188.48 tff(33239,plain,
% 295.91/188.48 (node21(c_e_h_1, c_q, s14, s15)),
% 295.91/188.48 inference(unit_resolution,[status(thm)],[33238, 33234])).
% 295.91/188.48 tff(33240,plain,
% 295.91/188.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s15)) | node20(c_e_h_1, c_q, s14) | (~node21(c_e_h_1, c_q, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s15)) | node20(c_e_h_1, c_q, s14) | (~node21(c_e_h_1, c_q, s14, s15)))),
% 295.91/188.48 inference(rewrite,[status(thm)],[])).
% 295.91/188.48 tff(33241,plain,
% 295.91/188.48 ((node20(c_e_h_1, c_q, s14) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s15)) | (~node21(c_e_h_1, c_q, s14, s15))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_q, s15)) | node20(c_e_h_1, c_q, s14) | (~node21(c_e_h_1, c_q, s14, s15)))),
% 295.91/188.48 inference(rewrite,[status(thm)],[])).
% 295.91/188.48 tff(33242,plain,
% 295.91/188.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s14) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s15)) | (~node21(c_e_h_1, c_q, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s15)) | node20(c_e_h_1, c_q, s14) | (~node21(c_e_h_1, c_q, s14, s15))))),
% 295.91/188.48 inference(monotonicity,[status(thm)],[33241])).
% 295.91/188.48 tff(33243,plain,
% 295.91/188.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s14) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s15)) | (~node21(c_e_h_1, c_q, s14, s15)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s15)) | node20(c_e_h_1, c_q, s14) | (~node21(c_e_h_1, c_q, s14, s15)))),
% 295.91/188.48 inference(transitivity,[status(thm)],[33242, 33240])).
% 295.91/188.48 tff(33244,plain,
% 295.91/188.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s14) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s15)) | (~node21(c_e_h_1, c_q, s14, s15)))),
% 295.91/188.48 inference(quant_inst,[status(thm)],[])).
% 295.91/188.48 tff(33245,plain,
% 295.91/188.48 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s15)) | node20(c_e_h_1, c_q, s14) | (~node21(c_e_h_1, c_q, s14, s15))),
% 295.91/188.48 inference(modus_ponens,[status(thm)],[33244, 33243])).
% 295.91/188.48 tff(33246,plain,
% 295.91/188.48 ($false),
% 295.91/188.48 inference(unit_resolution,[status(thm)],[33245, 52, 33227, 33239, 33225])).
% 295.91/188.48 tff(33247,plain,((~m_and_h_gate_v_out(c_e_h_1, c_q, s15)) | node20(c_e_h_1, c_q, s14) | m_and_h_gate_v_out(c_e_h_1, c_q, s14)), inference(lemma,lemma(discharge,[]))).
% 295.91/188.48 tff(33248,plain,
% 295.91/188.48 (~m_and_h_gate_v_out(c_e_h_1, c_q, s15)),
% 295.91/188.48 inference(unit_resolution,[status(thm)],[33247, 33224, 33182])).
% 295.91/188.48 tff(33249,assumption,(~node20(c_e_h_1, c_q, s15)), introduced(assumption)).
% 295.91/188.48 tff(33250,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_q, s15)), introduced(assumption)).
% 295.91/188.48 tff(33251,assumption,(node22(c_e_h_1, c_q, s15, s16)), introduced(assumption)).
% 295.91/188.48 tff(33252,plain,
% 295.91/188.48 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s16)) | (~node22(c_e_h_1, c_q, s15, s16)) | m_and_h_gate_v_out(c_e_h_1, c_q, s15))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s16)) | (~node22(c_e_h_1, c_q, s15, s16)) | m_and_h_gate_v_out(c_e_h_1, c_q, s15))),
% 295.91/188.49 inference(rewrite,[status(thm)],[])).
% 295.91/188.49 tff(33253,plain,
% 295.91/188.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s16)) | (~node22(c_e_h_1, c_q, s15, s16)) | m_and_h_gate_v_out(c_e_h_1, c_q, s15))),
% 295.91/188.49 inference(quant_inst,[status(thm)],[])).
% 295.91/188.49 tff(33254,plain,
% 295.91/188.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s16)) | (~node22(c_e_h_1, c_q, s15, s16)) | m_and_h_gate_v_out(c_e_h_1, c_q, s15)),
% 295.91/188.49 inference(modus_ponens,[status(thm)],[33253, 33252])).
% 295.91/188.49 tff(33255,plain,
% 295.91/188.49 ($false),
% 295.91/188.49 inference(unit_resolution,[status(thm)],[33254, 108, 33167, 33250, 33251])).
% 295.91/188.49 tff(33256,plain,((~node22(c_e_h_1, c_q, s15, s16)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s16)) | m_and_h_gate_v_out(c_e_h_1, c_q, s15)), inference(lemma,lemma(discharge,[]))).
% 295.91/188.49 tff(33257,plain,
% 295.91/188.49 (~node22(c_e_h_1, c_q, s15, s16)),
% 295.91/188.49 inference(unit_resolution,[status(thm)],[33256, 33167, 33250])).
% 295.91/188.49 tff(33258,plain,
% 295.91/188.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s15, s16)) | node21(c_e_h_1, c_q, s15, s16) | node22(c_e_h_1, c_q, s15, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s15, s16)) | node21(c_e_h_1, c_q, s15, s16) | node22(c_e_h_1, c_q, s15, s16))),
% 295.91/188.49 inference(rewrite,[status(thm)],[])).
% 295.91/188.49 tff(33259,plain,
% 295.91/188.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s15, s16)) | node21(c_e_h_1, c_q, s15, s16) | node22(c_e_h_1, c_q, s15, s16))),
% 295.91/188.49 inference(quant_inst,[status(thm)],[])).
% 295.91/188.49 tff(33260,plain,
% 295.91/188.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s15, s16)) | node21(c_e_h_1, c_q, s15, s16) | node22(c_e_h_1, c_q, s15, s16)),
% 295.91/188.49 inference(modus_ponens,[status(thm)],[33259, 33258])).
% 295.91/188.49 tff(33261,plain,
% 295.91/188.49 (node21(c_e_h_1, c_q, s15, s16) | node22(c_e_h_1, c_q, s15, s16)),
% 295.91/188.49 inference(unit_resolution,[status(thm)],[33260, 82, 13499])).
% 295.91/188.49 tff(33262,plain,
% 295.91/188.49 (node21(c_e_h_1, c_q, s15, s16)),
% 295.91/188.49 inference(unit_resolution,[status(thm)],[33261, 33257])).
% 295.91/188.49 tff(33263,plain,
% 295.91/188.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s16)) | node20(c_e_h_1, c_q, s15) | (~node21(c_e_h_1, c_q, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s16)) | node20(c_e_h_1, c_q, s15) | (~node21(c_e_h_1, c_q, s15, s16)))),
% 295.91/188.49 inference(rewrite,[status(thm)],[])).
% 295.91/188.49 tff(33264,plain,
% 295.91/188.49 ((node20(c_e_h_1, c_q, s15) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s16)) | (~node21(c_e_h_1, c_q, s15, s16))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_q, s16)) | node20(c_e_h_1, c_q, s15) | (~node21(c_e_h_1, c_q, s15, s16)))),
% 295.91/188.49 inference(rewrite,[status(thm)],[])).
% 295.91/188.49 tff(33265,plain,
% 295.91/188.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s15) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s16)) | (~node21(c_e_h_1, c_q, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s16)) | node20(c_e_h_1, c_q, s15) | (~node21(c_e_h_1, c_q, s15, s16))))),
% 295.91/188.49 inference(monotonicity,[status(thm)],[33264])).
% 295.91/188.49 tff(33266,plain,
% 295.91/188.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s15) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s16)) | (~node21(c_e_h_1, c_q, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s16)) | node20(c_e_h_1, c_q, s15) | (~node21(c_e_h_1, c_q, s15, s16)))),
% 295.91/188.49 inference(transitivity,[status(thm)],[33265, 33263])).
% 295.91/188.49 tff(33267,plain,
% 295.91/188.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s15) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s16)) | (~node21(c_e_h_1, c_q, s15, s16)))),
% 295.91/188.49 inference(quant_inst,[status(thm)],[])).
% 295.91/188.49 tff(33268,plain,
% 295.91/188.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s16)) | node20(c_e_h_1, c_q, s15) | (~node21(c_e_h_1, c_q, s15, s16))),
% 295.91/188.49 inference(modus_ponens,[status(thm)],[33267, 33266])).
% 295.91/188.49 tff(33269,plain,
% 295.91/188.49 ($false),
% 295.91/188.49 inference(unit_resolution,[status(thm)],[33268, 52, 33167, 33262, 33249])).
% 295.91/188.49 tff(33270,plain,((~m_and_h_gate_v_out(c_e_h_1, c_q, s16)) | node20(c_e_h_1, c_q, s15) | m_and_h_gate_v_out(c_e_h_1, c_q, s15)), inference(lemma,lemma(discharge,[]))).
% 295.91/188.49 tff(33271,plain,
% 295.91/188.49 (node20(c_e_h_1, c_q, s15)),
% 295.91/188.49 inference(unit_resolution,[status(thm)],[33270, 33248, 33167])).
% 295.91/188.49 tff(33272,plain,
% 295.91/188.49 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s15)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s15))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s15)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s15))),
% 295.91/188.49 inference(rewrite,[status(thm)],[])).
% 295.91/188.49 tff(33273,plain,
% 295.91/188.49 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s15)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s15))),
% 295.91/188.49 inference(quant_inst,[status(thm)],[])).
% 295.91/188.49 tff(33274,plain,
% 295.91/188.49 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s15)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s15)),
% 295.91/188.49 inference(modus_ponens,[status(thm)],[33273, 33272])).
% 295.91/188.49 tff(33275,plain,
% 295.91/188.49 ($false),
% 295.91/188.49 inference(unit_resolution,[status(thm)],[33274, 38, 33271, 33166])).
% 295.91/188.49 tff(33276,plain,(m_c_h_element_v_out(c_e_h_1, c_f, s13) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s16)) | m_and_h_gate_v_out(c_e_h_1, c_q, s13) | m_c_h_element_v_in2(c_e_h_1, c_f, s14) | m_c_h_element_v_in2(c_e_h_1, c_f, s13)), inference(lemma,lemma(discharge,[]))).
% 295.91/188.49 tff(33277,plain,
% 295.91/188.49 (m_c_h_element_v_out(c_e_h_1, c_f, s13) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s16)) | m_c_h_element_v_in2(c_e_h_1, c_f, s14) | m_c_h_element_v_in2(c_e_h_1, c_f, s13)),
% 295.91/188.49 inference(unit_resolution,[status(thm)],[33276, 33160])).
% 295.91/188.49 tff(33278,plain,
% 295.91/188.49 (~m_and_h_gate_v_out(c_e_h_1, c_q, s16)),
% 295.91/188.49 inference(unit_resolution,[status(thm)],[33277, 32733, 32642, 32649])).
% 295.91/188.49 tff(33279,assumption,(~node20(c_e_h_1, c_q, s16)), introduced(assumption)).
% 295.91/188.49 tff(33280,assumption,(m_and_h_gate_v_out(c_e_h_1, c_q, s17)), introduced(assumption)).
% 295.91/188.49 tff(33281,assumption,(node21(c_e_h_1, c_q, s16, s17)), introduced(assumption)).
% 295.91/188.49 tff(33282,plain,
% 295.91/188.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s17)) | node20(c_e_h_1, c_q, s16) | (~node21(c_e_h_1, c_q, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s17)) | node20(c_e_h_1, c_q, s16) | (~node21(c_e_h_1, c_q, s16, s17)))),
% 295.91/188.49 inference(rewrite,[status(thm)],[])).
% 295.91/188.49 tff(33283,plain,
% 295.91/188.49 ((node20(c_e_h_1, c_q, s16) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s17)) | (~node21(c_e_h_1, c_q, s16, s17))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_q, s17)) | node20(c_e_h_1, c_q, s16) | (~node21(c_e_h_1, c_q, s16, s17)))),
% 295.91/188.49 inference(rewrite,[status(thm)],[])).
% 295.91/188.49 tff(33284,plain,
% 295.91/188.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s16) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s17)) | (~node21(c_e_h_1, c_q, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s17)) | node20(c_e_h_1, c_q, s16) | (~node21(c_e_h_1, c_q, s16, s17))))),
% 295.91/188.49 inference(monotonicity,[status(thm)],[33283])).
% 295.91/188.49 tff(33285,plain,
% 295.91/188.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s16) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s17)) | (~node21(c_e_h_1, c_q, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s17)) | node20(c_e_h_1, c_q, s16) | (~node21(c_e_h_1, c_q, s16, s17)))),
% 295.91/188.49 inference(transitivity,[status(thm)],[33284, 33282])).
% 295.91/188.49 tff(33286,plain,
% 295.91/188.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s16) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s17)) | (~node21(c_e_h_1, c_q, s16, s17)))),
% 295.91/188.49 inference(quant_inst,[status(thm)],[])).
% 295.91/188.49 tff(33287,plain,
% 295.91/188.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s17)) | node20(c_e_h_1, c_q, s16) | (~node21(c_e_h_1, c_q, s16, s17))),
% 295.91/188.49 inference(modus_ponens,[status(thm)],[33286, 33285])).
% 295.91/188.49 tff(33288,plain,
% 295.91/188.49 ($false),
% 295.91/188.49 inference(unit_resolution,[status(thm)],[33287, 52, 33280, 33281, 33279])).
% 295.91/188.49 tff(33289,plain,((~node21(c_e_h_1, c_q, s16, s17)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s17)) | node20(c_e_h_1, c_q, s16)), inference(lemma,lemma(discharge,[]))).
% 295.91/188.49 tff(33290,plain,
% 295.91/188.49 (~node21(c_e_h_1, c_q, s16, s17)),
% 295.91/188.49 inference(unit_resolution,[status(thm)],[33289, 33280, 33279])).
% 295.91/188.49 tff(33291,plain,
% 295.91/188.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s16, s17)) | node21(c_e_h_1, c_q, s16, s17) | node22(c_e_h_1, c_q, s16, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s16, s17)) | node21(c_e_h_1, c_q, s16, s17) | node22(c_e_h_1, c_q, s16, s17))),
% 295.91/188.49 inference(rewrite,[status(thm)],[])).
% 295.91/188.49 tff(33292,plain,
% 295.91/188.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s16, s17)) | node21(c_e_h_1, c_q, s16, s17) | node22(c_e_h_1, c_q, s16, s17))),
% 295.91/188.49 inference(quant_inst,[status(thm)],[])).
% 295.91/188.49 tff(33293,plain,
% 295.91/188.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s16, s17)) | node21(c_e_h_1, c_q, s16, s17) | node22(c_e_h_1, c_q, s16, s17)),
% 295.91/188.49 inference(modus_ponens,[status(thm)],[33292, 33291])).
% 295.91/188.49 tff(33294,plain,
% 295.91/188.49 (node21(c_e_h_1, c_q, s16, s17) | node22(c_e_h_1, c_q, s16, s17)),
% 295.91/188.49 inference(unit_resolution,[status(thm)],[33293, 82, 11967])).
% 295.91/188.49 tff(33295,plain,
% 295.91/188.49 (node22(c_e_h_1, c_q, s16, s17)),
% 295.91/188.49 inference(unit_resolution,[status(thm)],[33294, 33290])).
% 295.91/188.49 tff(33296,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_q, s16)), introduced(assumption)).
% 295.91/188.49 tff(33297,plain,
% 295.91/188.49 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s17)) | (~node22(c_e_h_1, c_q, s16, s17)) | m_and_h_gate_v_out(c_e_h_1, c_q, s16))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s17)) | (~node22(c_e_h_1, c_q, s16, s17)) | m_and_h_gate_v_out(c_e_h_1, c_q, s16))),
% 295.91/188.49 inference(rewrite,[status(thm)],[])).
% 295.91/188.49 tff(33298,plain,
% 295.91/188.49 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s17)) | (~node22(c_e_h_1, c_q, s16, s17)) | m_and_h_gate_v_out(c_e_h_1, c_q, s16))),
% 295.91/188.50 inference(quant_inst,[status(thm)],[])).
% 295.91/188.50 tff(33299,plain,
% 295.91/188.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s17)) | (~node22(c_e_h_1, c_q, s16, s17)) | m_and_h_gate_v_out(c_e_h_1, c_q, s16)),
% 295.91/188.50 inference(modus_ponens,[status(thm)],[33298, 33297])).
% 295.91/188.50 tff(33300,plain,
% 295.91/188.50 ($false),
% 295.91/188.50 inference(unit_resolution,[status(thm)],[33299, 108, 33296, 33280, 33295])).
% 295.91/188.50 tff(33301,plain,((~m_and_h_gate_v_out(c_e_h_1, c_q, s17)) | m_and_h_gate_v_out(c_e_h_1, c_q, s16) | node20(c_e_h_1, c_q, s16)), inference(lemma,lemma(discharge,[]))).
% 295.91/188.50 tff(33302,plain,
% 295.91/188.50 ((~m_and_h_gate_v_out(c_e_h_1, c_q, s17)) | node20(c_e_h_1, c_q, s16)),
% 295.91/188.50 inference(unit_resolution,[status(thm)],[33301, 33278])).
% 295.91/188.50 tff(33303,plain,
% 295.91/188.50 (~m_and_h_gate_v_out(c_e_h_1, c_q, s17)),
% 295.91/188.50 inference(unit_resolution,[status(thm)],[33302, 33024])).
% 295.91/188.50 tff(33304,assumption,(~node20(c_e_h_1, c_q, s17)), introduced(assumption)).
% 295.91/188.50 tff(33305,assumption,(m_and_h_gate_v_out(c_e_h_1, c_q, s18)), introduced(assumption)).
% 295.91/188.50 tff(33306,assumption,(node21(c_e_h_1, c_q, s17, s18)), introduced(assumption)).
% 295.91/188.50 tff(33307,plain,
% 295.91/188.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s18)) | node20(c_e_h_1, c_q, s17) | (~node21(c_e_h_1, c_q, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s18)) | node20(c_e_h_1, c_q, s17) | (~node21(c_e_h_1, c_q, s17, s18)))),
% 295.91/188.50 inference(rewrite,[status(thm)],[])).
% 295.91/188.50 tff(33308,plain,
% 295.91/188.50 ((node20(c_e_h_1, c_q, s17) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s18)) | (~node21(c_e_h_1, c_q, s17, s18))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_q, s18)) | node20(c_e_h_1, c_q, s17) | (~node21(c_e_h_1, c_q, s17, s18)))),
% 295.91/188.50 inference(rewrite,[status(thm)],[])).
% 295.91/188.50 tff(33309,plain,
% 295.91/188.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s17) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s18)) | (~node21(c_e_h_1, c_q, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s18)) | node20(c_e_h_1, c_q, s17) | (~node21(c_e_h_1, c_q, s17, s18))))),
% 295.91/188.50 inference(monotonicity,[status(thm)],[33308])).
% 295.91/188.50 tff(33310,plain,
% 295.91/188.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s17) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s18)) | (~node21(c_e_h_1, c_q, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s18)) | node20(c_e_h_1, c_q, s17) | (~node21(c_e_h_1, c_q, s17, s18)))),
% 295.91/188.50 inference(transitivity,[status(thm)],[33309, 33307])).
% 295.91/188.50 tff(33311,plain,
% 295.91/188.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s17) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s18)) | (~node21(c_e_h_1, c_q, s17, s18)))),
% 295.91/188.50 inference(quant_inst,[status(thm)],[])).
% 295.91/188.50 tff(33312,plain,
% 295.91/188.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s18)) | node20(c_e_h_1, c_q, s17) | (~node21(c_e_h_1, c_q, s17, s18))),
% 295.91/188.50 inference(modus_ponens,[status(thm)],[33311, 33310])).
% 295.91/188.50 tff(33313,plain,
% 295.91/188.50 ($false),
% 295.91/188.50 inference(unit_resolution,[status(thm)],[33312, 52, 33305, 33306, 33304])).
% 295.91/188.50 tff(33314,plain,((~node21(c_e_h_1, c_q, s17, s18)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s18)) | node20(c_e_h_1, c_q, s17)), inference(lemma,lemma(discharge,[]))).
% 295.91/188.50 tff(33315,plain,
% 295.91/188.50 (~node21(c_e_h_1, c_q, s17, s18)),
% 296.01/188.50 inference(unit_resolution,[status(thm)],[33314, 33305, 33304])).
% 296.01/188.50 tff(33316,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_q, s17)), introduced(assumption)).
% 296.01/188.50 tff(33317,assumption,(node22(c_e_h_1, c_q, s17, s18)), introduced(assumption)).
% 296.01/188.50 tff(33318,plain,
% 296.01/188.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s18)) | (~node22(c_e_h_1, c_q, s17, s18)) | m_and_h_gate_v_out(c_e_h_1, c_q, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s18)) | (~node22(c_e_h_1, c_q, s17, s18)) | m_and_h_gate_v_out(c_e_h_1, c_q, s17))),
% 296.01/188.50 inference(rewrite,[status(thm)],[])).
% 296.01/188.50 tff(33319,plain,
% 296.01/188.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s18)) | (~node22(c_e_h_1, c_q, s17, s18)) | m_and_h_gate_v_out(c_e_h_1, c_q, s17))),
% 296.01/188.50 inference(quant_inst,[status(thm)],[])).
% 296.01/188.50 tff(33320,plain,
% 296.01/188.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s18)) | (~node22(c_e_h_1, c_q, s17, s18)) | m_and_h_gate_v_out(c_e_h_1, c_q, s17)),
% 296.01/188.50 inference(modus_ponens,[status(thm)],[33319, 33318])).
% 296.01/188.50 tff(33321,plain,
% 296.01/188.50 ($false),
% 296.01/188.50 inference(unit_resolution,[status(thm)],[33320, 108, 33316, 33305, 33317])).
% 296.01/188.50 tff(33322,plain,((~node22(c_e_h_1, c_q, s17, s18)) | m_and_h_gate_v_out(c_e_h_1, c_q, s17) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s18))), inference(lemma,lemma(discharge,[]))).
% 296.01/188.50 tff(33323,plain,
% 296.01/188.50 (~node22(c_e_h_1, c_q, s17, s18)),
% 296.01/188.50 inference(unit_resolution,[status(thm)],[33322, 33305, 33316])).
% 296.01/188.50 tff(33324,plain,
% 296.01/188.50 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s17, s18)) | node21(c_e_h_1, c_q, s17, s18) | node22(c_e_h_1, c_q, s17, s18))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s17, s18)) | node21(c_e_h_1, c_q, s17, s18) | node22(c_e_h_1, c_q, s17, s18))),
% 296.01/188.50 inference(rewrite,[status(thm)],[])).
% 296.01/188.50 tff(33325,plain,
% 296.01/188.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s17, s18)) | node21(c_e_h_1, c_q, s17, s18) | node22(c_e_h_1, c_q, s17, s18))),
% 296.01/188.50 inference(quant_inst,[status(thm)],[])).
% 296.01/188.50 tff(33326,plain,
% 296.01/188.50 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s17, s18)) | node21(c_e_h_1, c_q, s17, s18) | node22(c_e_h_1, c_q, s17, s18)),
% 296.01/188.50 inference(modus_ponens,[status(thm)],[33325, 33324])).
% 296.01/188.50 tff(33327,plain,
% 296.01/188.50 (node21(c_e_h_1, c_q, s17, s18) | node22(c_e_h_1, c_q, s17, s18)),
% 296.01/188.50 inference(unit_resolution,[status(thm)],[33326, 82, 26135])).
% 296.01/188.50 tff(33328,plain,
% 296.01/188.50 ($false),
% 296.01/188.50 inference(unit_resolution,[status(thm)],[33327, 33323, 33315])).
% 296.01/188.50 tff(33329,plain,((~m_and_h_gate_v_out(c_e_h_1, c_q, s18)) | m_and_h_gate_v_out(c_e_h_1, c_q, s17) | node20(c_e_h_1, c_q, s17)), inference(lemma,lemma(discharge,[]))).
% 296.01/188.50 tff(33330,plain,
% 296.01/188.50 ((~m_and_h_gate_v_out(c_e_h_1, c_q, s18)) | node20(c_e_h_1, c_q, s17)),
% 296.01/188.50 inference(unit_resolution,[status(thm)],[33329, 33303])).
% 296.01/188.50 tff(33331,plain,
% 296.01/188.50 (~m_and_h_gate_v_out(c_e_h_1, c_q, s18)),
% 296.01/188.50 inference(unit_resolution,[status(thm)],[33330, 33006])).
% 296.01/188.50 tff(33332,plain,
% 296.01/188.50 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s18))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s18))),
% 296.01/188.50 inference(rewrite,[status(thm)],[])).
% 296.01/188.50 tff(33333,plain,
% 296.01/188.50 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s18))),
% 296.01/188.50 inference(quant_inst,[status(thm)],[])).
% 296.01/188.50 tff(33334,plain,
% 296.01/188.50 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s18)),
% 296.01/188.50 inference(modus_ponens,[status(thm)],[33333, 33332])).
% 296.01/188.50 tff(33335,plain,
% 296.01/188.50 (node3(c_e_h_1, c_e_h_2, s18)),
% 296.01/188.50 inference(unit_resolution,[status(thm)],[33334, 4166, 1056])).
% 296.01/188.50 tff(33336,plain,
% 296.01/188.50 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s18)) | (~node3(c_e_h_1, c_e_h_2, s18)) | m_and_h_gate_v_out(c_e_h_1, c_q, s18))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s18)) | (~node3(c_e_h_1, c_e_h_2, s18)) | m_and_h_gate_v_out(c_e_h_1, c_q, s18))),
% 296.01/188.50 inference(rewrite,[status(thm)],[])).
% 296.01/188.50 tff(33337,plain,
% 296.01/188.50 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s18)) | (~node3(c_e_h_1, c_e_h_2, s18)) | m_and_h_gate_v_out(c_e_h_1, c_q, s18))),
% 296.01/188.50 inference(quant_inst,[status(thm)],[])).
% 296.01/188.50 tff(33338,plain,
% 296.01/188.50 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s18)) | (~node3(c_e_h_1, c_e_h_2, s18)) | m_and_h_gate_v_out(c_e_h_1, c_q, s18)),
% 296.01/188.50 inference(modus_ponens,[status(thm)],[33337, 33336])).
% 296.01/188.50 tff(33339,plain,
% 296.01/188.50 ((~m_cell_v_ack(c_e_h_2, s18)) | m_and_h_gate_v_out(c_e_h_1, c_q, s18)),
% 296.01/188.50 inference(unit_resolution,[status(thm)],[33338, 1073, 33335])).
% 296.01/188.50 tff(33340,plain,
% 296.01/188.50 (~m_cell_v_ack(c_e_h_2, s18)),
% 296.01/188.50 inference(unit_resolution,[status(thm)],[33339, 33331])).
% 296.01/188.50 tff(33341,plain,
% 296.01/188.50 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s18)) | m_cell_v_ack(c_e_h_2, s18))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s18)) | m_cell_v_ack(c_e_h_2, s18))),
% 296.01/188.51 inference(rewrite,[status(thm)],[])).
% 296.01/188.51 tff(33342,plain,
% 296.01/188.51 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s18)) | m_cell_v_ack(c_e_h_2, s18))),
% 296.01/188.51 inference(quant_inst,[status(thm)],[])).
% 296.01/188.51 tff(33343,plain,
% 296.01/188.51 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s18)) | m_cell_v_ack(c_e_h_2, s18)),
% 296.01/188.51 inference(modus_ponens,[status(thm)],[33342, 33341])).
% 296.01/188.51 tff(33344,plain,
% 296.01/188.51 (~m_or_h_gate_v_in2(c_e_h_2, c_j, s18)),
% 296.01/188.51 inference(unit_resolution,[status(thm)],[33343, 1085, 33340])).
% 296.01/188.51 tff(33345,assumption,(m_c_h_element_v_out(c_e_h_1, c_f, s19)), introduced(assumption)).
% 296.01/188.51 tff(33346,assumption,(m_c_h_element_v_out(c_e_h_1, c_f, s18)), introduced(assumption)).
% 296.01/188.51 tff(33347,plain,
% 296.01/188.51 (~m_c_h_element_v_out(c_e_h_1, c_f, s15)),
% 296.01/188.51 inference(unit_resolution,[status(thm)],[32809, 32737, 32734])).
% 296.01/188.51 tff(33348,plain,
% 296.01/188.51 (~m_c_h_element_v_out(c_e_h_1, c_f, s17)),
% 296.01/188.51 inference(unit_resolution,[status(thm)],[32991, 32918, 32910])).
% 296.01/188.51 tff(33349,plain,
% 296.01/188.51 (~m_and_h_gate_v_out(c_e_h_1, c_i, s17)),
% 296.01/188.51 inference(unit_resolution,[status(thm)],[26108, 32911, 26087])).
% 296.01/188.51 tff(33350,assumption,(m_c_h_element_v_in2(c_e_h_1, c_f, s17)), introduced(assumption)).
% 296.01/188.51 tff(33351,plain,
% 296.01/188.51 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s17)) | m_and_h_gate_v_out(c_e_h_1, c_i, s17))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s17)) | m_and_h_gate_v_out(c_e_h_1, c_i, s17))),
% 296.01/188.51 inference(rewrite,[status(thm)],[])).
% 296.01/188.51 tff(33352,plain,
% 296.01/188.51 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s17)) | m_and_h_gate_v_out(c_e_h_1, c_i, s17))),
% 296.01/188.51 inference(quant_inst,[status(thm)],[])).
% 296.01/188.51 tff(33353,plain,
% 296.01/188.51 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s17)) | m_and_h_gate_v_out(c_e_h_1, c_i, s17)),
% 296.01/188.51 inference(modus_ponens,[status(thm)],[33352, 33351])).
% 296.01/188.51 tff(33354,plain,
% 296.01/188.51 ($false),
% 296.01/188.51 inference(unit_resolution,[status(thm)],[33353, 2143, 26111, 33350])).
% 296.01/188.51 tff(33355,plain,(m_and_h_gate_v_out(c_e_h_1, c_i, s17) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s17))), inference(lemma,lemma(discharge,[]))).
% 296.01/188.51 tff(33356,plain,
% 296.01/188.51 (~m_c_h_element_v_in2(c_e_h_1, c_f, s17)),
% 296.01/188.51 inference(unit_resolution,[status(thm)],[33355, 33349])).
% 296.01/188.51 tff(33357,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_f, s17)), introduced(assumption)).
% 296.01/188.51 tff(33358,assumption,(~m_c_h_element_v_out(c_e_h_1, c_f, s17)), introduced(assumption)).
% 296.01/188.51 tff(33359,assumption,(node15(c_e_h_1, c_f, s17, s18)), introduced(assumption)).
% 296.01/188.51 tff(33360,plain,
% 296.01/188.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s18)) | (~node15(c_e_h_1, c_f, s17, s18)) | m_c_h_element_v_out(c_e_h_1, c_f, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s18)) | (~node15(c_e_h_1, c_f, s17, s18)) | m_c_h_element_v_out(c_e_h_1, c_f, s17))),
% 296.01/188.51 inference(rewrite,[status(thm)],[])).
% 296.01/188.51 tff(33361,plain,
% 296.01/188.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s18)) | (~node15(c_e_h_1, c_f, s17, s18)) | m_c_h_element_v_out(c_e_h_1, c_f, s17))),
% 296.01/188.51 inference(quant_inst,[status(thm)],[])).
% 296.01/188.51 tff(33362,plain,
% 296.01/188.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s18)) | (~node15(c_e_h_1, c_f, s17, s18)) | m_c_h_element_v_out(c_e_h_1, c_f, s17)),
% 296.01/188.51 inference(modus_ponens,[status(thm)],[33361, 33360])).
% 296.01/188.51 tff(33363,plain,
% 296.01/188.51 ($false),
% 296.01/188.51 inference(unit_resolution,[status(thm)],[33362, 147, 33346, 33358, 33359])).
% 296.01/188.51 tff(33364,plain,((~node15(c_e_h_1, c_f, s17, s18)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s18)) | m_c_h_element_v_out(c_e_h_1, c_f, s17)), inference(lemma,lemma(discharge,[]))).
% 296.01/188.51 tff(33365,plain,
% 296.01/188.51 (~node15(c_e_h_1, c_f, s17, s18)),
% 296.01/188.51 inference(unit_resolution,[status(thm)],[33364, 33358, 33346])).
% 296.01/188.51 tff(33366,assumption,(~node15(c_e_h_1, c_f, s17, s18)), introduced(assumption)).
% 296.01/188.51 tff(33367,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_f, s17)), introduced(assumption)).
% 296.01/188.51 tff(33368,assumption,(node14(c_e_h_1, c_f, s17, s18)), introduced(assumption)).
% 296.01/188.51 tff(33369,plain,
% 296.01/188.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s18)) | m_c_h_element_v_in1(c_e_h_1, c_f, s17) | (~node14(c_e_h_1, c_f, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s18)) | m_c_h_element_v_in1(c_e_h_1, c_f, s17) | (~node14(c_e_h_1, c_f, s17, s18)))),
% 296.01/188.51 inference(rewrite,[status(thm)],[])).
% 296.01/188.51 tff(33370,plain,
% 296.01/188.51 (((~node14(c_e_h_1, c_f, s17, s18)) | m_c_h_element_v_in1(c_e_h_1, c_f, s17) | (~m_c_h_element_v_out(c_e_h_1, c_f, s18))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_f, s18)) | m_c_h_element_v_in1(c_e_h_1, c_f, s17) | (~node14(c_e_h_1, c_f, s17, s18)))),
% 296.01/188.51 inference(rewrite,[status(thm)],[])).
% 296.01/188.51 tff(33371,plain,
% 296.01/188.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s17, s18)) | m_c_h_element_v_in1(c_e_h_1, c_f, s17) | (~m_c_h_element_v_out(c_e_h_1, c_f, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s18)) | m_c_h_element_v_in1(c_e_h_1, c_f, s17) | (~node14(c_e_h_1, c_f, s17, s18))))),
% 296.01/188.51 inference(monotonicity,[status(thm)],[33370])).
% 296.01/188.51 tff(33372,plain,
% 296.01/188.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s17, s18)) | m_c_h_element_v_in1(c_e_h_1, c_f, s17) | (~m_c_h_element_v_out(c_e_h_1, c_f, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s18)) | m_c_h_element_v_in1(c_e_h_1, c_f, s17) | (~node14(c_e_h_1, c_f, s17, s18)))),
% 296.01/188.51 inference(transitivity,[status(thm)],[33371, 33369])).
% 296.01/188.51 tff(33373,plain,
% 296.01/188.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s17, s18)) | m_c_h_element_v_in1(c_e_h_1, c_f, s17) | (~m_c_h_element_v_out(c_e_h_1, c_f, s18)))),
% 296.01/188.51 inference(quant_inst,[status(thm)],[])).
% 296.01/188.51 tff(33374,plain,
% 296.01/188.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s18)) | m_c_h_element_v_in1(c_e_h_1, c_f, s17) | (~node14(c_e_h_1, c_f, s17, s18))),
% 296.01/188.51 inference(modus_ponens,[status(thm)],[33373, 33372])).
% 296.01/188.51 tff(33375,plain,
% 296.01/188.51 ($false),
% 296.01/188.51 inference(unit_resolution,[status(thm)],[33374, 223, 33346, 33368, 33367])).
% 296.01/188.51 tff(33376,plain,((~node14(c_e_h_1, c_f, s17, s18)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s18)) | m_c_h_element_v_in1(c_e_h_1, c_f, s17)), inference(lemma,lemma(discharge,[]))).
% 296.01/188.51 tff(33377,plain,
% 296.01/188.51 (~node14(c_e_h_1, c_f, s17, s18)),
% 296.01/188.51 inference(unit_resolution,[status(thm)],[33376, 33367, 33346])).
% 296.01/188.51 tff(33378,plain,
% 296.01/188.51 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s17)) | m_c_h_element_v_in1(c_e_h_1, c_f, s17) | m_c_h_element_v_in2(c_e_h_1, c_f, s17))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s17)) | m_c_h_element_v_in1(c_e_h_1, c_f, s17) | m_c_h_element_v_in2(c_e_h_1, c_f, s17))),
% 296.01/188.51 inference(rewrite,[status(thm)],[])).
% 296.01/188.51 tff(33379,plain,
% 296.01/188.51 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s17)) | m_c_h_element_v_in1(c_e_h_1, c_f, s17) | m_c_h_element_v_in2(c_e_h_1, c_f, s17))),
% 296.01/188.51 inference(quant_inst,[status(thm)],[])).
% 296.01/188.51 tff(33380,plain,
% 296.01/188.51 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s17)) | m_c_h_element_v_in1(c_e_h_1, c_f, s17) | m_c_h_element_v_in2(c_e_h_1, c_f, s17)),
% 296.01/188.51 inference(modus_ponens,[status(thm)],[33379, 33378])).
% 296.01/188.51 tff(33381,plain,
% 296.01/188.51 ((~node16(c_e_h_1, c_f, s17)) | m_c_h_element_v_in1(c_e_h_1, c_f, s17)),
% 296.01/188.51 inference(unit_resolution,[status(thm)],[33380, 178, 33357])).
% 296.01/188.51 tff(33382,plain,
% 296.01/188.51 (~node16(c_e_h_1, c_f, s17)),
% 296.01/188.51 inference(unit_resolution,[status(thm)],[33381, 33367])).
% 296.01/188.51 tff(33383,plain,
% 296.01/188.51 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s17, s18)) | node19(c_e_h_1, c_f, s17, s18))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s17, s18)) | node19(c_e_h_1, c_f, s17, s18))),
% 296.01/188.51 inference(rewrite,[status(thm)],[])).
% 296.01/188.51 tff(33384,plain,
% 296.01/188.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s17, s18)) | node19(c_e_h_1, c_f, s17, s18))),
% 296.01/188.51 inference(quant_inst,[status(thm)],[])).
% 296.01/188.51 tff(33385,plain,
% 296.01/188.51 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s17, s18)) | node19(c_e_h_1, c_f, s17, s18)),
% 296.01/188.51 inference(modus_ponens,[status(thm)],[33384, 33383])).
% 296.01/188.51 tff(33386,plain,
% 296.01/188.51 (node19(c_e_h_1, c_f, s17, s18)),
% 296.01/188.51 inference(unit_resolution,[status(thm)],[33385, 190, 26135])).
% 296.01/188.52 tff(33387,plain,
% 296.01/188.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_f, s17, s18)) | node15(c_e_h_1, c_f, s17, s18) | node14(c_e_h_1, c_f, s17, s18) | node16(c_e_h_1, c_f, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s17, s18)) | node15(c_e_h_1, c_f, s17, s18) | node14(c_e_h_1, c_f, s17, s18) | node16(c_e_h_1, c_f, s17))),
% 296.01/188.52 inference(rewrite,[status(thm)],[])).
% 296.01/188.52 tff(33388,plain,
% 296.01/188.52 ((node16(c_e_h_1, c_f, s17) | node14(c_e_h_1, c_f, s17, s18) | node15(c_e_h_1, c_f, s17, s18) | (~node19(c_e_h_1, c_f, s17, s18))) <=> ((~node19(c_e_h_1, c_f, s17, s18)) | node15(c_e_h_1, c_f, s17, s18) | node14(c_e_h_1, c_f, s17, s18) | node16(c_e_h_1, c_f, s17))),
% 296.01/188.52 inference(rewrite,[status(thm)],[])).
% 296.01/188.52 tff(33389,plain,
% 296.01/188.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s17) | node14(c_e_h_1, c_f, s17, s18) | node15(c_e_h_1, c_f, s17, s18) | (~node19(c_e_h_1, c_f, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_f, s17, s18)) | node15(c_e_h_1, c_f, s17, s18) | node14(c_e_h_1, c_f, s17, s18) | node16(c_e_h_1, c_f, s17)))),
% 296.01/188.52 inference(monotonicity,[status(thm)],[33388])).
% 296.01/188.52 tff(33390,plain,
% 296.01/188.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s17) | node14(c_e_h_1, c_f, s17, s18) | node15(c_e_h_1, c_f, s17, s18) | (~node19(c_e_h_1, c_f, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s17, s18)) | node15(c_e_h_1, c_f, s17, s18) | node14(c_e_h_1, c_f, s17, s18) | node16(c_e_h_1, c_f, s17))),
% 296.01/188.52 inference(transitivity,[status(thm)],[33389, 33387])).
% 296.01/188.52 tff(33391,plain,
% 296.01/188.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s17) | node14(c_e_h_1, c_f, s17, s18) | node15(c_e_h_1, c_f, s17, s18) | (~node19(c_e_h_1, c_f, s17, s18)))),
% 296.01/188.52 inference(quant_inst,[status(thm)],[])).
% 296.01/188.52 tff(33392,plain,
% 296.01/188.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s17, s18)) | node15(c_e_h_1, c_f, s17, s18) | node14(c_e_h_1, c_f, s17, s18) | node16(c_e_h_1, c_f, s17)),
% 296.01/188.52 inference(modus_ponens,[status(thm)],[33391, 33390])).
% 296.01/188.52 tff(33393,plain,
% 296.01/188.52 (node15(c_e_h_1, c_f, s17, s18) | node14(c_e_h_1, c_f, s17, s18) | node16(c_e_h_1, c_f, s17)),
% 296.01/188.52 inference(unit_resolution,[status(thm)],[33392, 204, 33386])).
% 296.01/188.52 tff(33394,plain,
% 296.01/188.52 ($false),
% 296.01/188.52 inference(unit_resolution,[status(thm)],[33393, 33382, 33377, 33366])).
% 296.01/188.52 tff(33395,plain,(m_c_h_element_v_in1(c_e_h_1, c_f, s17) | node15(c_e_h_1, c_f, s17, s18) | m_c_h_element_v_in2(c_e_h_1, c_f, s17) | (~m_c_h_element_v_out(c_e_h_1, c_f, s18))), inference(lemma,lemma(discharge,[]))).
% 296.01/188.52 tff(33396,plain,
% 296.01/188.52 (m_c_h_element_v_in1(c_e_h_1, c_f, s17)),
% 296.01/188.52 inference(unit_resolution,[status(thm)],[33395, 33365, 33357, 33346])).
% 296.01/188.52 tff(33397,plain,
% 296.01/188.52 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_f, s17)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s17)) | m_c_h_element_v_in2(c_e_h_1, c_f, s17))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_f, s17)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s17)) | m_c_h_element_v_in2(c_e_h_1, c_f, s17))),
% 296.01/188.52 inference(rewrite,[status(thm)],[])).
% 296.01/188.52 tff(33398,plain,
% 296.01/188.52 (((~m_c_h_element_v_in1(c_e_h_1, c_f, s17)) | m_c_h_element_v_in2(c_e_h_1, c_f, s17) | (~node17(c_e_h_1, c_f, s17))) <=> ((~node17(c_e_h_1, c_f, s17)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s17)) | m_c_h_element_v_in2(c_e_h_1, c_f, s17))),
% 296.01/188.52 inference(rewrite,[status(thm)],[])).
% 296.01/188.52 tff(33399,plain,
% 296.01/188.52 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s17)) | m_c_h_element_v_in2(c_e_h_1, c_f, s17) | (~node17(c_e_h_1, c_f, s17)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_f, s17)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s17)) | m_c_h_element_v_in2(c_e_h_1, c_f, s17)))),
% 296.01/188.52 inference(monotonicity,[status(thm)],[33398])).
% 296.01/188.52 tff(33400,plain,
% 296.01/188.52 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s17)) | m_c_h_element_v_in2(c_e_h_1, c_f, s17) | (~node17(c_e_h_1, c_f, s17)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_f, s17)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s17)) | m_c_h_element_v_in2(c_e_h_1, c_f, s17))),
% 296.01/188.52 inference(transitivity,[status(thm)],[33399, 33397])).
% 296.01/188.52 tff(33401,plain,
% 296.01/188.52 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s17)) | m_c_h_element_v_in2(c_e_h_1, c_f, s17) | (~node17(c_e_h_1, c_f, s17)))),
% 296.01/188.52 inference(quant_inst,[status(thm)],[])).
% 296.01/188.52 tff(33402,plain,
% 296.01/188.52 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_f, s17)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s17)) | m_c_h_element_v_in2(c_e_h_1, c_f, s17)),
% 296.01/188.52 inference(modus_ponens,[status(thm)],[33401, 33400])).
% 296.01/188.52 tff(33403,plain,
% 296.01/188.52 ((~node17(c_e_h_1, c_f, s17)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s17))),
% 296.01/188.52 inference(unit_resolution,[status(thm)],[33402, 919, 33357])).
% 296.01/188.52 tff(33404,plain,
% 296.01/188.52 (~node17(c_e_h_1, c_f, s17)),
% 296.01/188.52 inference(unit_resolution,[status(thm)],[33403, 33396])).
% 296.01/188.52 tff(33405,plain,
% 296.01/188.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_f, s17, s18)) | node18(c_e_h_1, c_f, s17, s18) | node17(c_e_h_1, c_f, s17))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s17, s18)) | node18(c_e_h_1, c_f, s17, s18) | node17(c_e_h_1, c_f, s17))),
% 296.01/188.52 inference(rewrite,[status(thm)],[])).
% 296.01/188.52 tff(33406,plain,
% 296.01/188.52 ((node17(c_e_h_1, c_f, s17) | node18(c_e_h_1, c_f, s17, s18) | (~node19(c_e_h_1, c_f, s17, s18))) <=> ((~node19(c_e_h_1, c_f, s17, s18)) | node18(c_e_h_1, c_f, s17, s18) | node17(c_e_h_1, c_f, s17))),
% 296.01/188.52 inference(rewrite,[status(thm)],[])).
% 296.01/188.52 tff(33407,plain,
% 296.01/188.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s17) | node18(c_e_h_1, c_f, s17, s18) | (~node19(c_e_h_1, c_f, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_f, s17, s18)) | node18(c_e_h_1, c_f, s17, s18) | node17(c_e_h_1, c_f, s17)))),
% 296.01/188.52 inference(monotonicity,[status(thm)],[33406])).
% 296.01/188.52 tff(33408,plain,
% 296.01/188.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s17) | node18(c_e_h_1, c_f, s17, s18) | (~node19(c_e_h_1, c_f, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s17, s18)) | node18(c_e_h_1, c_f, s17, s18) | node17(c_e_h_1, c_f, s17))),
% 296.01/188.52 inference(transitivity,[status(thm)],[33407, 33405])).
% 296.01/188.52 tff(33409,plain,
% 296.01/188.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s17) | node18(c_e_h_1, c_f, s17, s18) | (~node19(c_e_h_1, c_f, s17, s18)))),
% 296.01/188.52 inference(quant_inst,[status(thm)],[])).
% 296.01/188.52 tff(33410,plain,
% 296.01/188.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s17, s18)) | node18(c_e_h_1, c_f, s17, s18) | node17(c_e_h_1, c_f, s17)),
% 296.01/188.52 inference(modus_ponens,[status(thm)],[33409, 33408])).
% 296.01/188.52 tff(33411,plain,
% 296.01/188.52 (node18(c_e_h_1, c_f, s17, s18) | node17(c_e_h_1, c_f, s17)),
% 296.01/188.52 inference(unit_resolution,[status(thm)],[33410, 776, 33386])).
% 296.01/188.52 tff(33412,plain,
% 296.01/188.52 (node18(c_e_h_1, c_f, s17, s18)),
% 296.01/188.52 inference(unit_resolution,[status(thm)],[33411, 33404])).
% 296.01/188.52 tff(33413,plain,
% 296.01/188.52 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s18)) | m_c_h_element_v_out(c_e_h_1, c_f, s17) | (~node18(c_e_h_1, c_f, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s18)) | m_c_h_element_v_out(c_e_h_1, c_f, s17) | (~node18(c_e_h_1, c_f, s17, s18)))),
% 296.01/188.52 inference(rewrite,[status(thm)],[])).
% 296.01/188.52 tff(33414,plain,
% 296.01/188.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s18)) | m_c_h_element_v_out(c_e_h_1, c_f, s17) | (~node18(c_e_h_1, c_f, s17, s18)))),
% 296.01/188.52 inference(quant_inst,[status(thm)],[])).
% 296.01/188.52 tff(33415,plain,
% 296.01/188.52 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s18)) | m_c_h_element_v_out(c_e_h_1, c_f, s17) | (~node18(c_e_h_1, c_f, s17, s18))),
% 296.01/188.52 inference(modus_ponens,[status(thm)],[33414, 33413])).
% 296.01/188.52 tff(33416,plain,
% 296.01/188.52 ($false),
% 296.01/188.52 inference(unit_resolution,[status(thm)],[33415, 753, 33346, 33358, 33412])).
% 296.01/188.52 tff(33417,plain,(m_c_h_element_v_out(c_e_h_1, c_f, s17) | (~m_c_h_element_v_out(c_e_h_1, c_f, s18)) | m_c_h_element_v_in2(c_e_h_1, c_f, s17)), inference(lemma,lemma(discharge,[]))).
% 296.01/188.52 tff(33418,plain,
% 296.01/188.52 ($false),
% 296.01/188.52 inference(unit_resolution,[status(thm)],[33417, 33356, 33348, 33346])).
% 296.01/188.52 tff(33419,plain,(m_and_h_gate_v_out(c_e_h_1, c_i, s15) | (~m_c_h_element_v_out(c_e_h_1, c_f, s18)) | node20(c_e_h_1, c_i, s16) | m_c_h_element_v_out(c_e_h_1, c_f, s15) | node20(c_e_h_1, c_i, s15)), inference(lemma,lemma(discharge,[]))).
% 296.01/188.52 tff(33420,plain,
% 296.01/188.52 (m_and_h_gate_v_out(c_e_h_1, c_i, s15)),
% 296.01/188.52 inference(unit_resolution,[status(thm)],[33419, 33347, 33346, 26087, 24242])).
% 296.01/188.52 tff(33421,plain,
% 296.01/188.52 (m_and_h_gate_v_out(c_e_h_1, c_i, s14)),
% 296.01/188.52 inference(unit_resolution,[status(thm)],[24239, 33420, 24226])).
% 296.01/188.52 tff(33422,plain,
% 296.01/188.52 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_i, X)) | m_c_h_element_v_in2(I0, c_f, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s14)) | m_c_h_element_v_in2(c_e_h_1, c_f, s14))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_i, X)) | m_c_h_element_v_in2(I0, c_f, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s14)) | m_c_h_element_v_in2(c_e_h_1, c_f, s14))),
% 296.01/188.52 inference(rewrite,[status(thm)],[])).
% 296.01/188.52 tff(33423,plain,
% 296.01/188.52 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_i, X)) | m_c_h_element_v_in2(I0, c_f, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_i, s14)) | m_c_h_element_v_in2(c_e_h_1, c_f, s14))),
% 296.01/188.52 inference(quant_inst,[status(thm)],[])).
% 296.01/188.52 tff(33424,plain,
% 296.01/188.52 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_out(I0, c_i, X)) | m_c_h_element_v_in2(I0, c_f, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_i, s14)) | m_c_h_element_v_in2(c_e_h_1, c_f, s14)),
% 296.01/188.52 inference(modus_ponens,[status(thm)],[33423, 33422])).
% 296.01/188.52 tff(33425,plain,
% 296.01/188.52 ($false),
% 296.01/188.52 inference(unit_resolution,[status(thm)],[33424, 28447, 33421, 32737])).
% 296.01/188.52 tff(33426,plain,(m_c_h_element_v_in2(c_e_h_1, c_f, s14) | node20(c_e_h_1, c_i, s14) | (~m_c_h_element_v_out(c_e_h_1, c_f, s18)) | node20(c_e_h_1, c_i, s16) | node20(c_e_h_1, c_i, s15) | m_c_h_element_v_out(c_e_h_1, c_f, s14)), inference(lemma,lemma(discharge,[]))).
% 296.01/188.53 tff(33427,plain,
% 296.01/188.53 (~m_c_h_element_v_out(c_e_h_1, c_f, s18)),
% 296.01/188.53 inference(unit_resolution,[status(thm)],[33426, 26087, 32737, 32734, 24242, 24226])).
% 296.01/188.53 tff(33428,assumption,(~m_c_h_element_v_out(c_e_h_1, c_f, s18)), introduced(assumption)).
% 296.01/188.53 tff(33429,assumption,(node18(c_e_h_1, c_f, s18, s19)), introduced(assumption)).
% 296.01/188.53 tff(33430,plain,
% 296.01/188.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_f, s18) | (~m_c_h_element_v_out(c_e_h_1, c_f, s19)) | (~node18(c_e_h_1, c_f, s18, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s18) | (~m_c_h_element_v_out(c_e_h_1, c_f, s19)) | (~node18(c_e_h_1, c_f, s18, s19)))),
% 296.01/188.53 inference(rewrite,[status(thm)],[])).
% 296.01/188.53 tff(33431,plain,
% 296.01/188.53 (((~m_c_h_element_v_out(c_e_h_1, c_f, s19)) | m_c_h_element_v_out(c_e_h_1, c_f, s18) | (~node18(c_e_h_1, c_f, s18, s19))) <=> (m_c_h_element_v_out(c_e_h_1, c_f, s18) | (~m_c_h_element_v_out(c_e_h_1, c_f, s19)) | (~node18(c_e_h_1, c_f, s18, s19)))),
% 296.01/188.53 inference(rewrite,[status(thm)],[])).
% 296.01/188.53 tff(33432,plain,
% 296.01/188.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s19)) | m_c_h_element_v_out(c_e_h_1, c_f, s18) | (~node18(c_e_h_1, c_f, s18, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_1, c_f, s18) | (~m_c_h_element_v_out(c_e_h_1, c_f, s19)) | (~node18(c_e_h_1, c_f, s18, s19))))),
% 296.01/188.53 inference(monotonicity,[status(thm)],[33431])).
% 296.01/188.53 tff(33433,plain,
% 296.01/188.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s19)) | m_c_h_element_v_out(c_e_h_1, c_f, s18) | (~node18(c_e_h_1, c_f, s18, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s18) | (~m_c_h_element_v_out(c_e_h_1, c_f, s19)) | (~node18(c_e_h_1, c_f, s18, s19)))),
% 296.01/188.53 inference(transitivity,[status(thm)],[33432, 33430])).
% 296.01/188.53 tff(33434,plain,
% 296.01/188.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s19)) | m_c_h_element_v_out(c_e_h_1, c_f, s18) | (~node18(c_e_h_1, c_f, s18, s19)))),
% 296.01/188.53 inference(quant_inst,[status(thm)],[])).
% 296.01/188.53 tff(33435,plain,
% 296.01/188.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_1, c_f, s18) | (~m_c_h_element_v_out(c_e_h_1, c_f, s19)) | (~node18(c_e_h_1, c_f, s18, s19))),
% 296.01/188.53 inference(modus_ponens,[status(thm)],[33434, 33433])).
% 296.01/188.53 tff(33436,plain,
% 296.01/188.53 ($false),
% 296.01/188.53 inference(unit_resolution,[status(thm)],[33435, 753, 33428, 33345, 33429])).
% 296.01/188.53 tff(33437,plain,((~node18(c_e_h_1, c_f, s18, s19)) | m_c_h_element_v_out(c_e_h_1, c_f, s18) | (~m_c_h_element_v_out(c_e_h_1, c_f, s19))), inference(lemma,lemma(discharge,[]))).
% 296.01/188.53 tff(33438,plain,
% 296.01/188.53 (~node18(c_e_h_1, c_f, s18, s19)),
% 296.01/188.53 inference(unit_resolution,[status(thm)],[33437, 33345, 33428])).
% 296.01/188.53 tff(33439,plain,
% 296.01/188.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s18, s19)) | node19(c_e_h_1, c_f, s18, s19))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s18, s19)) | node19(c_e_h_1, c_f, s18, s19))),
% 296.01/188.53 inference(rewrite,[status(thm)],[])).
% 296.01/188.53 tff(33440,plain,
% 296.01/188.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s18, s19)) | node19(c_e_h_1, c_f, s18, s19))),
% 296.01/188.53 inference(quant_inst,[status(thm)],[])).
% 296.01/188.53 tff(33441,plain,
% 296.01/188.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s18, s19)) | node19(c_e_h_1, c_f, s18, s19)),
% 296.01/188.53 inference(modus_ponens,[status(thm)],[33440, 33439])).
% 296.01/188.53 tff(33442,plain,
% 296.01/188.53 (node19(c_e_h_1, c_f, s18, s19)),
% 296.01/188.53 inference(unit_resolution,[status(thm)],[33441, 190, 26787])).
% 296.01/188.53 tff(33443,plain,
% 296.01/188.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_f, s18, s19)) | node17(c_e_h_1, c_f, s18) | node18(c_e_h_1, c_f, s18, s19))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s18, s19)) | node17(c_e_h_1, c_f, s18) | node18(c_e_h_1, c_f, s18, s19))),
% 296.01/188.53 inference(rewrite,[status(thm)],[])).
% 296.01/188.53 tff(33444,plain,
% 296.01/188.53 ((node17(c_e_h_1, c_f, s18) | node18(c_e_h_1, c_f, s18, s19) | (~node19(c_e_h_1, c_f, s18, s19))) <=> ((~node19(c_e_h_1, c_f, s18, s19)) | node17(c_e_h_1, c_f, s18) | node18(c_e_h_1, c_f, s18, s19))),
% 296.01/188.53 inference(rewrite,[status(thm)],[])).
% 296.01/188.53 tff(33445,plain,
% 296.01/188.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s18) | node18(c_e_h_1, c_f, s18, s19) | (~node19(c_e_h_1, c_f, s18, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | ((~node19(c_e_h_1, c_f, s18, s19)) | node17(c_e_h_1, c_f, s18) | node18(c_e_h_1, c_f, s18, s19)))),
% 296.01/188.53 inference(monotonicity,[status(thm)],[33444])).
% 296.01/188.53 tff(33446,plain,
% 296.01/188.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s18) | node18(c_e_h_1, c_f, s18, s19) | (~node19(c_e_h_1, c_f, s18, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s18, s19)) | node17(c_e_h_1, c_f, s18) | node18(c_e_h_1, c_f, s18, s19))),
% 296.01/188.53 inference(transitivity,[status(thm)],[33445, 33443])).
% 296.01/188.53 tff(33447,plain,
% 296.01/188.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_1, c_f, s18) | node18(c_e_h_1, c_f, s18, s19) | (~node19(c_e_h_1, c_f, s18, s19)))),
% 296.01/188.53 inference(quant_inst,[status(thm)],[])).
% 296.01/188.53 tff(33448,plain,
% 296.01/188.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (~node19(c_e_h_1, c_f, s18, s19)) | node17(c_e_h_1, c_f, s18) | node18(c_e_h_1, c_f, s18, s19)),
% 296.01/188.53 inference(modus_ponens,[status(thm)],[33447, 33446])).
% 296.01/188.53 tff(33449,plain,
% 296.01/188.53 (node17(c_e_h_1, c_f, s18) | node18(c_e_h_1, c_f, s18, s19)),
% 296.01/188.53 inference(unit_resolution,[status(thm)],[33448, 776, 33442])).
% 296.01/188.53 tff(33450,plain,
% 296.01/188.53 (node17(c_e_h_1, c_f, s18)),
% 296.01/188.53 inference(unit_resolution,[status(thm)],[33449, 33438])).
% 296.01/188.53 tff(33451,assumption,(node15(c_e_h_1, c_f, s18, s19)), introduced(assumption)).
% 296.01/188.53 tff(33452,plain,
% 296.01/188.53 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s19)) | (~node15(c_e_h_1, c_f, s18, s19)) | m_c_h_element_v_out(c_e_h_1, c_f, s18))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s19)) | (~node15(c_e_h_1, c_f, s18, s19)) | m_c_h_element_v_out(c_e_h_1, c_f, s18))),
% 296.01/188.53 inference(rewrite,[status(thm)],[])).
% 296.01/188.53 tff(33453,plain,
% 296.01/188.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s19)) | (~node15(c_e_h_1, c_f, s18, s19)) | m_c_h_element_v_out(c_e_h_1, c_f, s18))),
% 296.01/188.53 inference(quant_inst,[status(thm)],[])).
% 296.01/188.53 tff(33454,plain,
% 296.01/188.53 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s19)) | (~node15(c_e_h_1, c_f, s18, s19)) | m_c_h_element_v_out(c_e_h_1, c_f, s18)),
% 296.01/188.54 inference(modus_ponens,[status(thm)],[33453, 33452])).
% 296.01/188.54 tff(33455,plain,
% 296.01/188.54 ($false),
% 296.01/188.54 inference(unit_resolution,[status(thm)],[33454, 147, 33428, 33345, 33451])).
% 296.01/188.54 tff(33456,plain,((~node15(c_e_h_1, c_f, s18, s19)) | m_c_h_element_v_out(c_e_h_1, c_f, s18) | (~m_c_h_element_v_out(c_e_h_1, c_f, s19))), inference(lemma,lemma(discharge,[]))).
% 296.01/188.54 tff(33457,plain,
% 296.01/188.54 (~node15(c_e_h_1, c_f, s18, s19)),
% 296.01/188.54 inference(unit_resolution,[status(thm)],[33456, 33345, 33428])).
% 296.01/188.54 tff(33458,assumption,(~m_c_h_element_v_in1(c_e_h_1, c_f, s18)), introduced(assumption)).
% 296.01/188.54 tff(33459,assumption,(node14(c_e_h_1, c_f, s18, s19)), introduced(assumption)).
% 296.01/188.54 tff(33460,plain,
% 296.01/188.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s19)) | m_c_h_element_v_in1(c_e_h_1, c_f, s18) | (~node14(c_e_h_1, c_f, s18, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s19)) | m_c_h_element_v_in1(c_e_h_1, c_f, s18) | (~node14(c_e_h_1, c_f, s18, s19)))),
% 296.01/188.54 inference(rewrite,[status(thm)],[])).
% 296.01/188.54 tff(33461,plain,
% 296.01/188.54 (((~node14(c_e_h_1, c_f, s18, s19)) | m_c_h_element_v_in1(c_e_h_1, c_f, s18) | (~m_c_h_element_v_out(c_e_h_1, c_f, s19))) <=> ((~m_c_h_element_v_out(c_e_h_1, c_f, s19)) | m_c_h_element_v_in1(c_e_h_1, c_f, s18) | (~node14(c_e_h_1, c_f, s18, s19)))),
% 296.01/188.54 inference(rewrite,[status(thm)],[])).
% 296.01/188.54 tff(33462,plain,
% 296.01/188.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s18, s19)) | m_c_h_element_v_in1(c_e_h_1, c_f, s18) | (~m_c_h_element_v_out(c_e_h_1, c_f, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~m_c_h_element_v_out(c_e_h_1, c_f, s19)) | m_c_h_element_v_in1(c_e_h_1, c_f, s18) | (~node14(c_e_h_1, c_f, s18, s19))))),
% 296.01/188.54 inference(monotonicity,[status(thm)],[33461])).
% 296.01/188.54 tff(33463,plain,
% 296.01/188.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s18, s19)) | m_c_h_element_v_in1(c_e_h_1, c_f, s18) | (~m_c_h_element_v_out(c_e_h_1, c_f, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s19)) | m_c_h_element_v_in1(c_e_h_1, c_f, s18) | (~node14(c_e_h_1, c_f, s18, s19)))),
% 296.01/188.54 inference(transitivity,[status(thm)],[33462, 33460])).
% 296.01/188.54 tff(33464,plain,
% 296.01/188.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_1, c_f, s18, s19)) | m_c_h_element_v_in1(c_e_h_1, c_f, s18) | (~m_c_h_element_v_out(c_e_h_1, c_f, s19)))),
% 296.01/188.54 inference(quant_inst,[status(thm)],[])).
% 296.01/188.54 tff(33465,plain,
% 296.01/188.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (~m_c_h_element_v_out(c_e_h_1, c_f, s19)) | m_c_h_element_v_in1(c_e_h_1, c_f, s18) | (~node14(c_e_h_1, c_f, s18, s19))),
% 296.01/188.54 inference(modus_ponens,[status(thm)],[33464, 33463])).
% 296.01/188.54 tff(33466,plain,
% 296.01/188.54 ($false),
% 296.01/188.54 inference(unit_resolution,[status(thm)],[33465, 223, 33345, 33459, 33458])).
% 296.01/188.54 tff(33467,plain,((~node14(c_e_h_1, c_f, s18, s19)) | (~m_c_h_element_v_out(c_e_h_1, c_f, s19)) | m_c_h_element_v_in1(c_e_h_1, c_f, s18)), inference(lemma,lemma(discharge,[]))).
% 296.01/188.54 tff(33468,plain,
% 296.01/188.54 (~node14(c_e_h_1, c_f, s18, s19)),
% 296.01/188.54 inference(unit_resolution,[status(thm)],[33467, 33345, 33458])).
% 296.01/188.54 tff(33469,plain,
% 296.01/188.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s18) | (~node19(c_e_h_1, c_f, s18, s19)) | node15(c_e_h_1, c_f, s18, s19) | node14(c_e_h_1, c_f, s18, s19))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_f, s18) | (~node19(c_e_h_1, c_f, s18, s19)) | node15(c_e_h_1, c_f, s18, s19) | node14(c_e_h_1, c_f, s18, s19))),
% 296.01/188.54 inference(rewrite,[status(thm)],[])).
% 296.01/188.54 tff(33470,plain,
% 296.01/188.54 ((node16(c_e_h_1, c_f, s18) | node14(c_e_h_1, c_f, s18, s19) | node15(c_e_h_1, c_f, s18, s19) | (~node19(c_e_h_1, c_f, s18, s19))) <=> (node16(c_e_h_1, c_f, s18) | (~node19(c_e_h_1, c_f, s18, s19)) | node15(c_e_h_1, c_f, s18, s19) | node14(c_e_h_1, c_f, s18, s19))),
% 296.01/188.54 inference(rewrite,[status(thm)],[])).
% 296.01/188.54 tff(33471,plain,
% 296.01/188.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s18) | node14(c_e_h_1, c_f, s18, s19) | node15(c_e_h_1, c_f, s18, s19) | (~node19(c_e_h_1, c_f, s18, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s18) | (~node19(c_e_h_1, c_f, s18, s19)) | node15(c_e_h_1, c_f, s18, s19) | node14(c_e_h_1, c_f, s18, s19)))),
% 296.01/188.54 inference(monotonicity,[status(thm)],[33470])).
% 296.01/188.54 tff(33472,plain,
% 296.01/188.54 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s18) | node14(c_e_h_1, c_f, s18, s19) | node15(c_e_h_1, c_f, s18, s19) | (~node19(c_e_h_1, c_f, s18, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_f, s18) | (~node19(c_e_h_1, c_f, s18, s19)) | node15(c_e_h_1, c_f, s18, s19) | node14(c_e_h_1, c_f, s18, s19))),
% 296.01/188.54 inference(transitivity,[status(thm)],[33471, 33469])).
% 296.01/188.54 tff(33473,plain,
% 296.01/188.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_1, c_f, s18) | node14(c_e_h_1, c_f, s18, s19) | node15(c_e_h_1, c_f, s18, s19) | (~node19(c_e_h_1, c_f, s18, s19)))),
% 296.01/188.54 inference(quant_inst,[status(thm)],[])).
% 296.01/188.54 tff(33474,plain,
% 296.01/188.54 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_1, c_f, s18) | (~node19(c_e_h_1, c_f, s18, s19)) | node15(c_e_h_1, c_f, s18, s19) | node14(c_e_h_1, c_f, s18, s19)),
% 296.01/188.54 inference(modus_ponens,[status(thm)],[33473, 33472])).
% 296.01/188.54 tff(33475,plain,
% 296.01/188.54 (node16(c_e_h_1, c_f, s18) | node15(c_e_h_1, c_f, s18, s19) | node14(c_e_h_1, c_f, s18, s19)),
% 296.01/188.54 inference(unit_resolution,[status(thm)],[33474, 204, 33442])).
% 296.01/188.54 tff(33476,plain,
% 296.01/188.54 (node16(c_e_h_1, c_f, s18)),
% 296.01/188.54 inference(unit_resolution,[status(thm)],[33475, 33468, 33457])).
% 296.01/188.54 tff(33477,assumption,(node17(c_e_h_1, c_f, s18)), introduced(assumption)).
% 296.01/188.54 tff(33478,assumption,(node16(c_e_h_1, c_f, s18)), introduced(assumption)).
% 296.01/188.54 tff(33479,assumption,(~m_c_h_element_v_in2(c_e_h_1, c_f, s18)), introduced(assumption)).
% 296.01/188.54 tff(33480,plain,
% 296.01/188.54 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s18)) | (~node17(c_e_h_1, c_f, s18)) | m_c_h_element_v_in2(c_e_h_1, c_f, s18))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s18)) | (~node17(c_e_h_1, c_f, s18)) | m_c_h_element_v_in2(c_e_h_1, c_f, s18))),
% 296.01/188.54 inference(rewrite,[status(thm)],[])).
% 296.01/188.54 tff(33481,plain,
% 296.01/188.54 (((~m_c_h_element_v_in1(c_e_h_1, c_f, s18)) | m_c_h_element_v_in2(c_e_h_1, c_f, s18) | (~node17(c_e_h_1, c_f, s18))) <=> ((~m_c_h_element_v_in1(c_e_h_1, c_f, s18)) | (~node17(c_e_h_1, c_f, s18)) | m_c_h_element_v_in2(c_e_h_1, c_f, s18))),
% 296.01/188.54 inference(rewrite,[status(thm)],[])).
% 296.01/188.54 tff(33482,plain,
% 296.01/188.54 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s18)) | m_c_h_element_v_in2(c_e_h_1, c_f, s18) | (~node17(c_e_h_1, c_f, s18)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s18)) | (~node17(c_e_h_1, c_f, s18)) | m_c_h_element_v_in2(c_e_h_1, c_f, s18)))),
% 296.01/188.54 inference(monotonicity,[status(thm)],[33481])).
% 296.01/188.54 tff(33483,plain,
% 296.01/188.54 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s18)) | m_c_h_element_v_in2(c_e_h_1, c_f, s18) | (~node17(c_e_h_1, c_f, s18)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s18)) | (~node17(c_e_h_1, c_f, s18)) | m_c_h_element_v_in2(c_e_h_1, c_f, s18))),
% 296.01/188.54 inference(transitivity,[status(thm)],[33482, 33480])).
% 296.01/188.54 tff(33484,plain,
% 296.01/188.54 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_1, c_f, s18)) | m_c_h_element_v_in2(c_e_h_1, c_f, s18) | (~node17(c_e_h_1, c_f, s18)))),
% 296.01/188.54 inference(quant_inst,[status(thm)],[])).
% 296.01/188.54 tff(33485,plain,
% 296.01/188.54 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s18)) | (~node17(c_e_h_1, c_f, s18)) | m_c_h_element_v_in2(c_e_h_1, c_f, s18)),
% 296.01/188.54 inference(modus_ponens,[status(thm)],[33484, 33483])).
% 296.01/188.54 tff(33486,plain,
% 296.01/188.54 ((~m_c_h_element_v_in1(c_e_h_1, c_f, s18)) | m_c_h_element_v_in2(c_e_h_1, c_f, s18)),
% 296.01/188.54 inference(unit_resolution,[status(thm)],[33485, 919, 33477])).
% 296.01/188.54 tff(33487,plain,
% 296.01/188.54 (~m_c_h_element_v_in1(c_e_h_1, c_f, s18)),
% 296.01/188.54 inference(unit_resolution,[status(thm)],[33486, 33479])).
% 296.01/188.54 tff(33488,plain,
% 296.01/188.54 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s18)) | m_c_h_element_v_in1(c_e_h_1, c_f, s18) | m_c_h_element_v_in2(c_e_h_1, c_f, s18))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s18)) | m_c_h_element_v_in1(c_e_h_1, c_f, s18) | m_c_h_element_v_in2(c_e_h_1, c_f, s18))),
% 296.01/188.54 inference(rewrite,[status(thm)],[])).
% 296.01/188.54 tff(33489,plain,
% 296.01/188.54 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_1, c_f, s18)) | m_c_h_element_v_in1(c_e_h_1, c_f, s18) | m_c_h_element_v_in2(c_e_h_1, c_f, s18))),
% 296.01/188.54 inference(quant_inst,[status(thm)],[])).
% 296.01/188.54 tff(33490,plain,
% 296.01/188.54 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_1, c_f, s18)) | m_c_h_element_v_in1(c_e_h_1, c_f, s18) | m_c_h_element_v_in2(c_e_h_1, c_f, s18)),
% 296.01/188.54 inference(modus_ponens,[status(thm)],[33489, 33488])).
% 296.01/188.54 tff(33491,plain,
% 296.01/188.54 (m_c_h_element_v_in1(c_e_h_1, c_f, s18) | m_c_h_element_v_in2(c_e_h_1, c_f, s18)),
% 296.01/188.54 inference(unit_resolution,[status(thm)],[33490, 178, 33478])).
% 296.01/188.54 tff(33492,plain,
% 296.01/188.54 ($false),
% 296.01/188.54 inference(unit_resolution,[status(thm)],[33491, 33487, 33479])).
% 296.01/188.54 tff(33493,plain,(m_c_h_element_v_in2(c_e_h_1, c_f, s18) | (~node16(c_e_h_1, c_f, s18)) | (~node17(c_e_h_1, c_f, s18))), inference(lemma,lemma(discharge,[]))).
% 296.01/188.54 tff(33494,plain,
% 296.01/188.54 (m_c_h_element_v_in2(c_e_h_1, c_f, s18)),
% 296.01/188.54 inference(unit_resolution,[status(thm)],[33493, 33478, 33477])).
% 296.01/188.54 tff(33495,plain,
% 296.01/188.54 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_f, s18)) | m_c_h_element_v_in1(c_e_h_1, c_f, s18) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s18)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_f, s18)) | m_c_h_element_v_in1(c_e_h_1, c_f, s18) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s18)))),
% 296.01/188.55 inference(rewrite,[status(thm)],[])).
% 296.01/188.55 tff(33496,plain,
% 296.01/188.55 ((m_c_h_element_v_in1(c_e_h_1, c_f, s18) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s18)) | (~node17(c_e_h_1, c_f, s18))) <=> ((~node17(c_e_h_1, c_f, s18)) | m_c_h_element_v_in1(c_e_h_1, c_f, s18) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s18)))),
% 296.01/188.55 inference(rewrite,[status(thm)],[])).
% 296.01/188.55 tff(33497,plain,
% 296.01/188.55 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s18) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s18)) | (~node17(c_e_h_1, c_f, s18)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_1, c_f, s18)) | m_c_h_element_v_in1(c_e_h_1, c_f, s18) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s18))))),
% 296.01/188.55 inference(monotonicity,[status(thm)],[33496])).
% 296.01/188.55 tff(33498,plain,
% 296.01/188.55 (((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s18) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s18)) | (~node17(c_e_h_1, c_f, s18)))) <=> ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_f, s18)) | m_c_h_element_v_in1(c_e_h_1, c_f, s18) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s18)))),
% 296.01/188.55 inference(transitivity,[status(thm)],[33497, 33495])).
% 296.01/188.55 tff(33499,plain,
% 296.01/188.55 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (m_c_h_element_v_in1(c_e_h_1, c_f, s18) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s18)) | (~node17(c_e_h_1, c_f, s18)))),
% 296.01/188.55 inference(quant_inst,[status(thm)],[])).
% 296.01/188.55 tff(33500,plain,
% 296.01/188.55 ((~![I0: $i, X: $i, I1: $i] : (m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_in2(I0, I1, X)) | (~node17(I0, I1, X)))) | (~node17(c_e_h_1, c_f, s18)) | m_c_h_element_v_in1(c_e_h_1, c_f, s18) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s18))),
% 296.01/188.55 inference(modus_ponens,[status(thm)],[33499, 33498])).
% 296.01/188.55 tff(33501,plain,
% 296.01/188.55 (m_c_h_element_v_in1(c_e_h_1, c_f, s18) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s18))),
% 296.01/188.55 inference(unit_resolution,[status(thm)],[33500, 859, 33477])).
% 296.01/188.55 tff(33502,plain,
% 296.01/188.55 (m_c_h_element_v_in1(c_e_h_1, c_f, s18)),
% 296.01/188.55 inference(unit_resolution,[status(thm)],[33501, 33494])).
% 296.01/188.55 tff(33503,plain,
% 296.01/188.55 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_f, s18)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s18)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s18)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~node16(c_e_h_1, c_f, s18)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s18)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s18)))),
% 296.01/188.55 inference(rewrite,[status(thm)],[])).
% 296.01/188.55 tff(33504,plain,
% 296.01/188.55 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | ((~node16(c_e_h_1, c_f, s18)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s18)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s18)))),
% 296.01/188.55 inference(quant_inst,[status(thm)],[])).
% 296.01/188.55 tff(33505,plain,
% 296.01/188.55 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | (~m_c_h_element_v_in1(I0, I1, X)) | (~m_c_h_element_v_in2(I0, I1, X)))) | (~node16(c_e_h_1, c_f, s18)) | (~m_c_h_element_v_in1(c_e_h_1, c_f, s18)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s18))),
% 296.01/188.55 inference(modus_ponens,[status(thm)],[33504, 33503])).
% 296.01/188.55 tff(33506,plain,
% 296.01/188.55 ((~m_c_h_element_v_in1(c_e_h_1, c_f, s18)) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s18))),
% 296.01/188.55 inference(unit_resolution,[status(thm)],[33505, 2307, 33478])).
% 296.01/188.55 tff(33507,plain,
% 296.01/188.55 ($false),
% 296.01/188.55 inference(unit_resolution,[status(thm)],[33506, 33502, 33494])).
% 296.01/188.55 tff(33508,plain,((~node16(c_e_h_1, c_f, s18)) | (~node17(c_e_h_1, c_f, s18))), inference(lemma,lemma(discharge,[]))).
% 296.01/188.55 tff(33509,plain,
% 296.01/188.55 ($false),
% 296.01/188.55 inference(unit_resolution,[status(thm)],[33508, 33476, 33450])).
% 296.01/188.55 tff(33510,plain,((~m_c_h_element_v_out(c_e_h_1, c_f, s19)) | m_c_h_element_v_in1(c_e_h_1, c_f, s18) | m_c_h_element_v_out(c_e_h_1, c_f, s18)), inference(lemma,lemma(discharge,[]))).
% 296.01/188.55 tff(33511,plain,
% 296.01/188.55 (m_c_h_element_v_in1(c_e_h_1, c_f, s18)),
% 296.01/188.55 inference(unit_resolution,[status(thm)],[33510, 33428, 33345])).
% 296.01/188.55 tff(33512,plain,
% 296.01/188.55 (~node18(c_e_h_1, c_f, s18, s19)),
% 296.01/188.55 inference(unit_resolution,[status(thm)],[33437, 33428, 33345])).
% 296.01/188.55 tff(33513,plain,
% 296.01/188.55 (node17(c_e_h_1, c_f, s18)),
% 296.01/188.55 inference(unit_resolution,[status(thm)],[33449, 33512])).
% 296.01/188.55 tff(33514,plain,
% 296.01/188.55 ((~m_c_h_element_v_in1(c_e_h_1, c_f, s18)) | (~node17(c_e_h_1, c_f, s18))),
% 296.01/188.55 inference(unit_resolution,[status(thm)],[33485, 919, 33479])).
% 296.01/188.55 tff(33515,plain,
% 296.01/188.55 ($false),
% 296.01/188.55 inference(unit_resolution,[status(thm)],[33514, 33513, 33511])).
% 296.01/188.55 tff(33516,plain,(m_c_h_element_v_out(c_e_h_1, c_f, s18) | m_c_h_element_v_in2(c_e_h_1, c_f, s18) | (~m_c_h_element_v_out(c_e_h_1, c_f, s19))), inference(lemma,lemma(discharge,[]))).
% 296.01/188.55 tff(33517,plain,
% 296.01/188.55 (m_c_h_element_v_in2(c_e_h_1, c_f, s18)),
% 296.01/188.55 inference(unit_resolution,[status(thm)],[33516, 33427, 33345])).
% 296.01/188.55 tff(33518,plain,
% 296.01/188.55 (~m_and_h_gate_v_out(c_e_h_1, c_i, s17)),
% 296.01/188.55 inference(unit_resolution,[status(thm)],[26108, 26087, 26007])).
% 296.01/188.55 tff(33519,plain,
% 296.01/188.55 (~m_and_h_gate_v_out(c_e_h_1, c_i, s18)),
% 296.01/188.55 inference(unit_resolution,[status(thm)],[26759, 33518, 26741])).
% 296.01/188.55 tff(33520,assumption,(m_c_h_element_v_in2(c_e_h_1, c_f, s18)), introduced(assumption)).
% 296.01/188.55 tff(33521,plain,
% 296.01/188.55 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s18)) | m_and_h_gate_v_out(c_e_h_1, c_i, s18))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s18)) | m_and_h_gate_v_out(c_e_h_1, c_i, s18))),
% 296.01/188.55 inference(rewrite,[status(thm)],[])).
% 296.01/188.55 tff(33522,plain,
% 296.01/188.55 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s18)) | m_and_h_gate_v_out(c_e_h_1, c_i, s18))),
% 296.01/188.55 inference(quant_inst,[status(thm)],[])).
% 296.01/188.55 tff(33523,plain,
% 296.01/188.55 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s18)) | m_and_h_gate_v_out(c_e_h_1, c_i, s18)),
% 296.01/188.55 inference(modus_ponens,[status(thm)],[33522, 33521])).
% 296.01/188.55 tff(33524,plain,
% 296.01/188.55 ($false),
% 296.01/188.55 inference(unit_resolution,[status(thm)],[33523, 2143, 33520, 26761])).
% 296.01/188.55 tff(33525,plain,((~m_c_h_element_v_in2(c_e_h_1, c_f, s18)) | m_and_h_gate_v_out(c_e_h_1, c_i, s18)), inference(lemma,lemma(discharge,[]))).
% 296.01/188.55 tff(33526,plain,
% 296.01/188.55 ($false),
% 296.01/188.55 inference(unit_resolution,[status(thm)],[33525, 33519, 33517])).
% 296.01/188.55 tff(33527,plain,(node20(c_e_h_1, c_i, s16) | node20(c_e_h_1, c_i, s17) | (~m_c_h_element_v_out(c_e_h_1, c_f, s19)) | m_and_h_gate_v_out(c_e_h_1, c_i, s16) | m_c_h_element_v_in2(c_e_h_1, c_f, s14) | m_c_h_element_v_out(c_e_h_1, c_f, s14) | node20(c_e_h_1, c_i, s15) | node20(c_e_h_1, c_i, s14)), inference(lemma,lemma(discharge,[]))).
% 296.01/188.55 tff(33528,plain,
% 296.01/188.55 (node20(c_e_h_1, c_i, s16) | node20(c_e_h_1, c_i, s17) | (~m_c_h_element_v_out(c_e_h_1, c_f, s19)) | m_and_h_gate_v_out(c_e_h_1, c_i, s16) | node20(c_e_h_1, c_i, s15) | node20(c_e_h_1, c_i, s14)),
% 296.01/188.55 inference(unit_resolution,[status(thm)],[33527, 32726, 32733])).
% 296.01/188.55 tff(33529,plain,
% 296.01/188.55 (node20(c_e_h_1, c_i, s16) | node20(c_e_h_1, c_i, s17) | (~m_c_h_element_v_out(c_e_h_1, c_f, s19)) | m_and_h_gate_v_out(c_e_h_1, c_i, s16) | node20(c_e_h_1, c_i, s15)),
% 296.01/188.55 inference(unit_resolution,[status(thm)],[33528, 24049])).
% 296.01/188.55 tff(33530,plain,
% 296.01/188.55 (~m_c_h_element_v_out(c_e_h_1, c_f, s19)),
% 296.01/188.55 inference(unit_resolution,[status(thm)],[33529, 25573, 26739, 24041, 24266])).
% 296.01/188.55 tff(33531,assumption,(m_c_h_element_v_in2(c_e_h_1, c_f, s19)), introduced(assumption)).
% 296.01/188.55 tff(33532,plain,
% 296.01/188.55 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s19)) | m_and_h_gate_v_out(c_e_h_1, c_i, s19))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s19)) | m_and_h_gate_v_out(c_e_h_1, c_i, s19))),
% 296.01/188.55 inference(rewrite,[status(thm)],[])).
% 296.01/188.55 tff(33533,plain,
% 296.01/188.55 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s19)) | m_and_h_gate_v_out(c_e_h_1, c_i, s19))),
% 296.01/188.55 inference(quant_inst,[status(thm)],[])).
% 296.01/188.55 tff(33534,plain,
% 296.01/188.55 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s19)) | m_and_h_gate_v_out(c_e_h_1, c_i, s19)),
% 296.01/188.55 inference(modus_ponens,[status(thm)],[33533, 33532])).
% 296.01/188.55 tff(33535,plain,
% 296.01/188.55 ($false),
% 296.01/188.55 inference(unit_resolution,[status(thm)],[33534, 2143, 33531, 30016])).
% 296.01/188.55 tff(33536,plain,((~m_c_h_element_v_in2(c_e_h_1, c_f, s19)) | m_and_h_gate_v_out(c_e_h_1, c_i, s19)), inference(lemma,lemma(discharge,[]))).
% 296.01/188.55 tff(33537,plain,
% 296.01/188.55 (~m_c_h_element_v_in2(c_e_h_1, c_f, s19)),
% 296.01/188.55 inference(unit_resolution,[status(thm)],[33536, 30693])).
% 296.01/188.55 tff(33538,plain,
% 296.01/188.55 (~m_c_h_element_v_in2(c_e_h_1, c_f, s16)),
% 296.01/188.55 inference(unit_resolution,[status(thm)],[32917, 24266])).
% 296.01/188.55 tff(33539,plain,
% 296.01/188.55 (~m_c_h_element_v_in2(c_e_h_1, c_f, s17)),
% 296.01/188.55 inference(unit_resolution,[status(thm)],[33355, 26740])).
% 296.01/188.55 tff(33540,plain,
% 296.01/188.55 (~m_c_h_element_v_in2(c_e_h_1, c_f, s18)),
% 296.01/188.55 inference(unit_resolution,[status(thm)],[33525, 26760])).
% 296.01/188.55 tff(33541,assumption,(m_and_h_gate_v_out(c_e_h_1, c_q, s20)), introduced(assumption)).
% 296.01/188.55 tff(33542,plain,
% 296.01/188.55 (~m_c_h_element_v_out(c_e_h_1, c_f, s17)),
% 296.01/188.55 inference(unit_resolution,[status(thm)],[32991, 32919, 32942])).
% 296.01/188.55 tff(33543,plain,
% 296.01/188.55 (~m_c_h_element_v_out(c_e_h_1, c_f, s18)),
% 296.01/188.55 inference(unit_resolution,[status(thm)],[33417, 33542, 33357])).
% 296.01/188.55 tff(33544,plain,
% 296.01/188.55 (~m_c_h_element_v_out(c_e_h_1, c_f, s19)),
% 296.01/188.55 inference(unit_resolution,[status(thm)],[33516, 33543, 33479])).
% 296.01/188.55 tff(33545,plain,
% 296.01/188.55 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s19)) | m_c_h_element_v_out(c_e_h_1, c_f, s19))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s19)) | m_c_h_element_v_out(c_e_h_1, c_f, s19))),
% 296.01/188.55 inference(rewrite,[status(thm)],[])).
% 296.01/188.55 tff(33546,plain,
% 296.01/188.55 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s19)) | m_c_h_element_v_out(c_e_h_1, c_f, s19))),
% 296.01/188.55 inference(quant_inst,[status(thm)],[])).
% 296.01/188.55 tff(33547,plain,
% 296.01/188.55 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s19)) | m_c_h_element_v_out(c_e_h_1, c_f, s19)),
% 296.01/188.55 inference(modus_ponens,[status(thm)],[33546, 33545])).
% 296.01/188.55 tff(33548,plain,
% 296.01/188.55 (~m_and_h_gate_v_in1(c_e_h_1, c_q, s19)),
% 296.01/188.55 inference(unit_resolution,[status(thm)],[33547, 1586, 33544])).
% 296.01/188.55 tff(33549,assumption,(~m_and_h_gate_v_in1(c_e_h_1, c_q, s19)), introduced(assumption)).
% 296.01/188.55 tff(33550,assumption,(node20(c_e_h_1, c_q, s19)), introduced(assumption)).
% 296.01/188.55 tff(33551,plain,
% 296.01/188.55 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s19)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s19))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s19)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s19))),
% 296.01/188.55 inference(rewrite,[status(thm)],[])).
% 296.01/188.55 tff(33552,plain,
% 296.01/188.55 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s19)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s19))),
% 296.01/188.55 inference(quant_inst,[status(thm)],[])).
% 296.01/188.55 tff(33553,plain,
% 296.01/188.55 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s19)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s19)),
% 296.01/188.56 inference(modus_ponens,[status(thm)],[33552, 33551])).
% 296.01/188.56 tff(33554,plain,
% 296.01/188.56 ($false),
% 296.01/188.56 inference(unit_resolution,[status(thm)],[33553, 38, 33550, 33549])).
% 296.01/188.56 tff(33555,plain,(m_and_h_gate_v_in1(c_e_h_1, c_q, s19) | (~node20(c_e_h_1, c_q, s19))), inference(lemma,lemma(discharge,[]))).
% 296.01/188.56 tff(33556,plain,
% 296.01/188.56 (~node20(c_e_h_1, c_q, s19)),
% 296.01/188.56 inference(unit_resolution,[status(thm)],[33555, 33548])).
% 296.01/188.56 tff(33557,assumption,(~node20(c_e_h_1, c_q, s19)), introduced(assumption)).
% 296.01/188.56 tff(33558,assumption,(node21(c_e_h_1, c_q, s19, s20)), introduced(assumption)).
% 296.01/188.56 tff(33559,plain,
% 296.01/188.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s20)) | node20(c_e_h_1, c_q, s19) | (~node21(c_e_h_1, c_q, s19, s20)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s20)) | node20(c_e_h_1, c_q, s19) | (~node21(c_e_h_1, c_q, s19, s20)))),
% 296.01/188.56 inference(rewrite,[status(thm)],[])).
% 296.01/188.56 tff(33560,plain,
% 296.01/188.56 ((node20(c_e_h_1, c_q, s19) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s20)) | (~node21(c_e_h_1, c_q, s19, s20))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_q, s20)) | node20(c_e_h_1, c_q, s19) | (~node21(c_e_h_1, c_q, s19, s20)))),
% 296.01/188.56 inference(rewrite,[status(thm)],[])).
% 296.01/188.56 tff(33561,plain,
% 296.01/188.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s19) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s20)) | (~node21(c_e_h_1, c_q, s19, s20)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s20)) | node20(c_e_h_1, c_q, s19) | (~node21(c_e_h_1, c_q, s19, s20))))),
% 296.01/188.56 inference(monotonicity,[status(thm)],[33560])).
% 296.01/188.56 tff(33562,plain,
% 296.01/188.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s19) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s20)) | (~node21(c_e_h_1, c_q, s19, s20)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s20)) | node20(c_e_h_1, c_q, s19) | (~node21(c_e_h_1, c_q, s19, s20)))),
% 296.01/188.56 inference(transitivity,[status(thm)],[33561, 33559])).
% 296.01/188.56 tff(33563,plain,
% 296.01/188.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s19) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s20)) | (~node21(c_e_h_1, c_q, s19, s20)))),
% 296.01/188.56 inference(quant_inst,[status(thm)],[])).
% 296.01/188.56 tff(33564,plain,
% 296.01/188.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s20)) | node20(c_e_h_1, c_q, s19) | (~node21(c_e_h_1, c_q, s19, s20))),
% 296.01/188.56 inference(modus_ponens,[status(thm)],[33563, 33562])).
% 296.01/188.56 tff(33565,plain,
% 296.01/188.56 ($false),
% 296.01/188.56 inference(unit_resolution,[status(thm)],[33564, 52, 33541, 33558, 33557])).
% 296.01/188.56 tff(33566,plain,((~node21(c_e_h_1, c_q, s19, s20)) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s20)) | node20(c_e_h_1, c_q, s19)), inference(lemma,lemma(discharge,[]))).
% 296.01/188.56 tff(33567,plain,
% 296.01/188.56 (~node21(c_e_h_1, c_q, s19, s20)),
% 296.01/188.56 inference(unit_resolution,[status(thm)],[33566, 33541, 33557])).
% 296.01/188.56 tff(33568,plain,
% 296.01/188.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s19, s20)) | node21(c_e_h_1, c_q, s19, s20) | node22(c_e_h_1, c_q, s19, s20))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s19, s20)) | node21(c_e_h_1, c_q, s19, s20) | node22(c_e_h_1, c_q, s19, s20))),
% 296.01/188.56 inference(rewrite,[status(thm)],[])).
% 296.01/188.56 tff(33569,plain,
% 296.01/188.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s19, s20)) | node21(c_e_h_1, c_q, s19, s20) | node22(c_e_h_1, c_q, s19, s20))),
% 296.01/188.56 inference(quant_inst,[status(thm)],[])).
% 296.01/188.56 tff(33570,plain,
% 296.01/188.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s19, s20)) | node21(c_e_h_1, c_q, s19, s20) | node22(c_e_h_1, c_q, s19, s20)),
% 296.01/188.56 inference(modus_ponens,[status(thm)],[33569, 33568])).
% 296.01/188.56 tff(33571,plain,
% 296.01/188.56 (node21(c_e_h_1, c_q, s19, s20) | node22(c_e_h_1, c_q, s19, s20)),
% 296.01/188.56 inference(unit_resolution,[status(thm)],[33570, 82, 29925])).
% 296.01/188.56 tff(33572,plain,
% 296.01/188.56 (node22(c_e_h_1, c_q, s19, s20)),
% 296.01/188.56 inference(unit_resolution,[status(thm)],[33571, 33567])).
% 296.01/188.56 tff(33573,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_q, s19)), introduced(assumption)).
% 296.01/188.56 tff(33574,plain,
% 296.01/188.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s20)) | (~node22(c_e_h_1, c_q, s19, s20)) | m_and_h_gate_v_out(c_e_h_1, c_q, s19))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s20)) | (~node22(c_e_h_1, c_q, s19, s20)) | m_and_h_gate_v_out(c_e_h_1, c_q, s19))),
% 296.01/188.56 inference(rewrite,[status(thm)],[])).
% 296.01/188.56 tff(33575,plain,
% 296.01/188.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s20)) | (~node22(c_e_h_1, c_q, s19, s20)) | m_and_h_gate_v_out(c_e_h_1, c_q, s19))),
% 296.01/188.56 inference(quant_inst,[status(thm)],[])).
% 296.01/188.56 tff(33576,plain,
% 296.01/188.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s20)) | (~node22(c_e_h_1, c_q, s19, s20)) | m_and_h_gate_v_out(c_e_h_1, c_q, s19)),
% 296.01/188.56 inference(modus_ponens,[status(thm)],[33575, 33574])).
% 296.01/188.56 tff(33577,plain,
% 296.01/188.56 ($false),
% 296.01/188.56 inference(unit_resolution,[status(thm)],[33576, 108, 33541, 33573, 33572])).
% 296.01/188.56 tff(33578,plain,((~m_and_h_gate_v_out(c_e_h_1, c_q, s20)) | m_and_h_gate_v_out(c_e_h_1, c_q, s19) | node20(c_e_h_1, c_q, s19)), inference(lemma,lemma(discharge,[]))).
% 296.01/188.56 tff(33579,plain,
% 296.01/188.56 (m_and_h_gate_v_out(c_e_h_1, c_q, s19)),
% 296.01/188.56 inference(unit_resolution,[status(thm)],[33578, 33556, 33541])).
% 296.01/188.56 tff(33580,plain,
% 296.01/188.56 (((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s18)) | m_c_h_element_v_out(c_e_h_1, c_f, s18))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s18)) | m_c_h_element_v_out(c_e_h_1, c_f, s18))),
% 296.01/188.56 inference(rewrite,[status(thm)],[])).
% 296.01/188.56 tff(33581,plain,
% 296.01/188.56 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | ((~m_and_h_gate_v_in1(c_e_h_1, c_q, s18)) | m_c_h_element_v_out(c_e_h_1, c_f, s18))),
% 296.01/188.56 inference(quant_inst,[status(thm)],[])).
% 296.01/188.56 tff(33582,plain,
% 296.01/188.56 ((~![I0: $i, X: $i] : ((~m_and_h_gate_v_in1(I0, c_q, X)) | m_c_h_element_v_out(I0, c_f, X))) | (~m_and_h_gate_v_in1(c_e_h_1, c_q, s18)) | m_c_h_element_v_out(c_e_h_1, c_f, s18)),
% 296.01/188.56 inference(modus_ponens,[status(thm)],[33581, 33580])).
% 296.01/188.56 tff(33583,plain,
% 296.01/188.56 (~m_and_h_gate_v_in1(c_e_h_1, c_q, s18)),
% 296.01/188.56 inference(unit_resolution,[status(thm)],[33582, 1586, 33543])).
% 296.01/188.56 tff(33584,plain,
% 296.01/188.56 (((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s18)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s18))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s18)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s18))),
% 296.01/188.56 inference(rewrite,[status(thm)],[])).
% 296.01/188.56 tff(33585,plain,
% 296.01/188.56 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | ((~node20(c_e_h_1, c_q, s18)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s18))),
% 296.01/188.56 inference(quant_inst,[status(thm)],[])).
% 296.01/188.56 tff(33586,plain,
% 296.01/188.56 ((~![I0: $i, X: $i, I1: $i] : ((~node20(I0, I1, X)) | m_and_h_gate_v_in1(I0, I1, X))) | (~node20(c_e_h_1, c_q, s18)) | m_and_h_gate_v_in1(c_e_h_1, c_q, s18)),
% 296.01/188.56 inference(modus_ponens,[status(thm)],[33585, 33584])).
% 296.01/188.56 tff(33587,plain,
% 296.01/188.56 (~node20(c_e_h_1, c_q, s18)),
% 296.01/188.56 inference(unit_resolution,[status(thm)],[33586, 38, 33583])).
% 296.01/188.56 tff(33588,plain,
% 296.01/188.56 (~m_and_h_gate_v_in1(c_e_h_1, c_q, s16)),
% 296.01/188.56 inference(unit_resolution,[status(thm)],[33015, 32919])).
% 296.01/188.56 tff(33589,plain,
% 296.01/188.56 (~node20(c_e_h_1, c_q, s16)),
% 296.01/188.56 inference(unit_resolution,[status(thm)],[33023, 33588])).
% 296.01/188.56 tff(33590,plain,
% 296.01/188.56 (~m_and_h_gate_v_out(c_e_h_1, c_q, s17)),
% 296.01/188.56 inference(unit_resolution,[status(thm)],[33301, 33589, 33296])).
% 296.01/188.56 tff(33591,plain,
% 296.01/188.56 (~m_and_h_gate_v_in1(c_e_h_1, c_q, s17)),
% 296.01/188.56 inference(unit_resolution,[status(thm)],[33001, 1586, 33542])).
% 296.01/188.56 tff(33592,plain,
% 296.01/188.56 (~node20(c_e_h_1, c_q, s17)),
% 296.01/188.56 inference(unit_resolution,[status(thm)],[33005, 38, 33591])).
% 296.01/188.56 tff(33593,plain,
% 296.01/188.56 (~m_and_h_gate_v_out(c_e_h_1, c_q, s18)),
% 296.01/188.56 inference(unit_resolution,[status(thm)],[33329, 33592, 33590])).
% 296.01/188.56 tff(33594,assumption,(~node20(c_e_h_1, c_q, s18)), introduced(assumption)).
% 296.01/188.56 tff(33595,assumption,(~m_and_h_gate_v_out(c_e_h_1, c_q, s18)), introduced(assumption)).
% 296.01/188.56 tff(33596,assumption,(m_and_h_gate_v_out(c_e_h_1, c_q, s19)), introduced(assumption)).
% 296.01/188.56 tff(33597,assumption,(node22(c_e_h_1, c_q, s18, s19)), introduced(assumption)).
% 296.01/188.56 tff(33598,plain,
% 296.01/188.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s19)) | (~node22(c_e_h_1, c_q, s18, s19)) | m_and_h_gate_v_out(c_e_h_1, c_q, s18))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s19)) | (~node22(c_e_h_1, c_q, s18, s19)) | m_and_h_gate_v_out(c_e_h_1, c_q, s18))),
% 296.01/188.56 inference(rewrite,[status(thm)],[])).
% 296.01/188.56 tff(33599,plain,
% 296.01/188.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s19)) | (~node22(c_e_h_1, c_q, s18, s19)) | m_and_h_gate_v_out(c_e_h_1, c_q, s18))),
% 296.01/188.56 inference(quant_inst,[status(thm)],[])).
% 296.01/188.56 tff(33600,plain,
% 296.01/188.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_v_out(I0, I1, Y)) | (~node22(I0, I1, X, Y)) | m_and_h_gate_v_out(I0, I1, X))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s19)) | (~node22(c_e_h_1, c_q, s18, s19)) | m_and_h_gate_v_out(c_e_h_1, c_q, s18)),
% 296.01/188.56 inference(modus_ponens,[status(thm)],[33599, 33598])).
% 296.01/188.56 tff(33601,plain,
% 296.01/188.56 ($false),
% 296.01/188.56 inference(unit_resolution,[status(thm)],[33600, 108, 33595, 33596, 33597])).
% 296.01/188.56 tff(33602,plain,((~node22(c_e_h_1, c_q, s18, s19)) | m_and_h_gate_v_out(c_e_h_1, c_q, s18) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s19))), inference(lemma,lemma(discharge,[]))).
% 296.01/188.56 tff(33603,plain,
% 296.01/188.56 (~node22(c_e_h_1, c_q, s18, s19)),
% 296.01/188.56 inference(unit_resolution,[status(thm)],[33602, 33596, 33595])).
% 296.01/188.56 tff(33604,plain,
% 296.01/188.56 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s18, s19)) | node21(c_e_h_1, c_q, s18, s19) | node22(c_e_h_1, c_q, s18, s19))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s18, s19)) | node21(c_e_h_1, c_q, s18, s19) | node22(c_e_h_1, c_q, s18, s19))),
% 296.01/188.56 inference(rewrite,[status(thm)],[])).
% 296.01/188.56 tff(33605,plain,
% 296.01/188.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | ((~trans(s18, s19)) | node21(c_e_h_1, c_q, s18, s19) | node22(c_e_h_1, c_q, s18, s19))),
% 296.01/188.56 inference(quant_inst,[status(thm)],[])).
% 296.01/188.56 tff(33606,plain,
% 296.01/188.56 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node21(I0, I1, X, Y) | node22(I0, I1, X, Y))) | (~trans(s18, s19)) | node21(c_e_h_1, c_q, s18, s19) | node22(c_e_h_1, c_q, s18, s19)),
% 296.01/188.56 inference(modus_ponens,[status(thm)],[33605, 33604])).
% 296.01/188.56 tff(33607,plain,
% 296.01/188.56 (node21(c_e_h_1, c_q, s18, s19) | node22(c_e_h_1, c_q, s18, s19)),
% 296.01/188.56 inference(unit_resolution,[status(thm)],[33606, 82, 26787])).
% 296.01/188.57 tff(33608,plain,
% 296.01/188.57 (node21(c_e_h_1, c_q, s18, s19)),
% 296.01/188.57 inference(unit_resolution,[status(thm)],[33607, 33603])).
% 296.01/188.57 tff(33609,plain,
% 296.01/188.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s19)) | node20(c_e_h_1, c_q, s18) | (~node21(c_e_h_1, c_q, s18, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s19)) | node20(c_e_h_1, c_q, s18) | (~node21(c_e_h_1, c_q, s18, s19)))),
% 296.01/188.57 inference(rewrite,[status(thm)],[])).
% 296.01/188.57 tff(33610,plain,
% 296.01/188.57 ((node20(c_e_h_1, c_q, s18) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s19)) | (~node21(c_e_h_1, c_q, s18, s19))) <=> ((~m_and_h_gate_v_out(c_e_h_1, c_q, s19)) | node20(c_e_h_1, c_q, s18) | (~node21(c_e_h_1, c_q, s18, s19)))),
% 296.01/188.57 inference(rewrite,[status(thm)],[])).
% 296.01/188.57 tff(33611,plain,
% 296.01/188.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s18) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s19)) | (~node21(c_e_h_1, c_q, s18, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | ((~m_and_h_gate_v_out(c_e_h_1, c_q, s19)) | node20(c_e_h_1, c_q, s18) | (~node21(c_e_h_1, c_q, s18, s19))))),
% 296.01/188.57 inference(monotonicity,[status(thm)],[33610])).
% 296.01/188.57 tff(33612,plain,
% 296.01/188.57 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s18) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s19)) | (~node21(c_e_h_1, c_q, s18, s19)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s19)) | node20(c_e_h_1, c_q, s18) | (~node21(c_e_h_1, c_q, s18, s19)))),
% 296.01/188.57 inference(transitivity,[status(thm)],[33611, 33609])).
% 296.01/188.57 tff(33613,plain,
% 296.01/188.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (node20(c_e_h_1, c_q, s18) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s19)) | (~node21(c_e_h_1, c_q, s18, s19)))),
% 296.01/188.57 inference(quant_inst,[status(thm)],[])).
% 296.01/188.57 tff(33614,plain,
% 296.01/188.57 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node20(I0, I1, X) | (~m_and_h_gate_v_out(I0, I1, Y)) | (~node21(I0, I1, X, Y)))) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s19)) | node20(c_e_h_1, c_q, s18) | (~node21(c_e_h_1, c_q, s18, s19))),
% 296.01/188.57 inference(modus_ponens,[status(thm)],[33613, 33612])).
% 296.01/188.57 tff(33615,plain,
% 296.01/188.57 ($false),
% 296.01/188.57 inference(unit_resolution,[status(thm)],[33614, 52, 33596, 33608, 33594])).
% 296.01/188.57 tff(33616,plain,((~m_and_h_gate_v_out(c_e_h_1, c_q, s19)) | node20(c_e_h_1, c_q, s18) | m_and_h_gate_v_out(c_e_h_1, c_q, s18)), inference(lemma,lemma(discharge,[]))).
% 296.01/188.57 tff(33617,plain,
% 296.01/188.57 ($false),
% 296.01/188.57 inference(unit_resolution,[status(thm)],[33616, 33593, 33587, 33579])).
% 296.01/188.57 tff(33618,plain,(m_c_h_element_v_out(c_e_h_1, c_f, s16) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s20)) | m_c_h_element_v_in2(c_e_h_1, c_f, s18) | m_and_h_gate_v_out(c_e_h_1, c_q, s16) | m_c_h_element_v_in2(c_e_h_1, c_f, s17) | m_c_h_element_v_in2(c_e_h_1, c_f, s16)), inference(lemma,lemma(discharge,[]))).
% 296.01/188.57 tff(33619,plain,
% 296.01/188.57 (m_c_h_element_v_out(c_e_h_1, c_f, s16) | (~m_and_h_gate_v_out(c_e_h_1, c_q, s20)) | m_c_h_element_v_in2(c_e_h_1, c_f, s18) | m_c_h_element_v_in2(c_e_h_1, c_f, s17) | m_c_h_element_v_in2(c_e_h_1, c_f, s16)),
% 296.01/188.57 inference(unit_resolution,[status(thm)],[33618, 33278])).
% 296.01/188.57 tff(33620,plain,
% 296.01/188.57 ((~m_and_h_gate_v_out(c_e_h_1, c_q, s20)) | m_c_h_element_v_in2(c_e_h_1, c_f, s18) | m_c_h_element_v_in2(c_e_h_1, c_f, s17) | m_c_h_element_v_in2(c_e_h_1, c_f, s16)),
% 296.01/188.57 inference(unit_resolution,[status(thm)],[33619, 33009])).
% 296.01/188.57 tff(33621,plain,
% 296.01/188.57 (~m_and_h_gate_v_out(c_e_h_1, c_q, s20)),
% 296.01/188.57 inference(unit_resolution,[status(thm)],[33620, 33540, 33539, 33538])).
% 296.01/188.57 tff(33622,plain,
% 296.01/188.57 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s20))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s20))),
% 296.01/188.57 inference(rewrite,[status(thm)],[])).
% 296.01/188.57 tff(33623,plain,
% 296.01/188.57 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s20))),
% 296.01/188.57 inference(quant_inst,[status(thm)],[])).
% 296.01/188.57 tff(33624,plain,
% 296.01/188.57 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s20)),
% 296.01/188.57 inference(modus_ponens,[status(thm)],[33623, 33622])).
% 296.01/188.57 tff(33625,plain,
% 296.01/188.57 (node3(c_e_h_1, c_e_h_2, s20)),
% 296.01/188.57 inference(unit_resolution,[status(thm)],[33624, 4166, 1056])).
% 296.01/188.57 tff(33626,plain,
% 296.01/188.57 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s20)) | (~node3(c_e_h_1, c_e_h_2, s20)) | m_and_h_gate_v_out(c_e_h_1, c_q, s20))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s20)) | (~node3(c_e_h_1, c_e_h_2, s20)) | m_and_h_gate_v_out(c_e_h_1, c_q, s20))),
% 296.01/188.57 inference(rewrite,[status(thm)],[])).
% 296.01/188.57 tff(33627,plain,
% 296.01/188.57 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s20)) | (~node3(c_e_h_1, c_e_h_2, s20)) | m_and_h_gate_v_out(c_e_h_1, c_q, s20))),
% 296.01/188.57 inference(quant_inst,[status(thm)],[])).
% 296.01/188.57 tff(33628,plain,
% 296.01/188.57 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s20)) | (~node3(c_e_h_1, c_e_h_2, s20)) | m_and_h_gate_v_out(c_e_h_1, c_q, s20)),
% 296.01/188.57 inference(modus_ponens,[status(thm)],[33627, 33626])).
% 296.01/188.57 tff(33629,plain,
% 296.01/188.57 ((~m_cell_v_ack(c_e_h_2, s20)) | m_and_h_gate_v_out(c_e_h_1, c_q, s20)),
% 296.01/188.57 inference(unit_resolution,[status(thm)],[33628, 1073, 33625])).
% 296.01/188.57 tff(33630,plain,
% 296.01/188.57 (~m_cell_v_ack(c_e_h_2, s20)),
% 296.01/188.57 inference(unit_resolution,[status(thm)],[33629, 33621])).
% 296.01/188.57 tff(33631,plain,
% 296.01/188.57 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s20)) | m_cell_v_ack(c_e_h_2, s20))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s20)) | m_cell_v_ack(c_e_h_2, s20))),
% 296.01/188.57 inference(rewrite,[status(thm)],[])).
% 296.01/188.57 tff(33632,plain,
% 296.01/188.57 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s20)) | m_cell_v_ack(c_e_h_2, s20))),
% 296.01/188.57 inference(quant_inst,[status(thm)],[])).
% 296.01/188.57 tff(33633,plain,
% 296.01/188.57 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s20)) | m_cell_v_ack(c_e_h_2, s20)),
% 296.01/188.57 inference(modus_ponens,[status(thm)],[33632, 33631])).
% 296.01/188.57 tff(33634,plain,
% 296.01/188.57 (~m_or_h_gate_v_in2(c_e_h_2, c_j, s20)),
% 296.01/188.57 inference(unit_resolution,[status(thm)],[33633, 1085, 33630])).
% 296.01/188.57 tff(33635,plain,
% 296.01/188.57 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s15)),
% 296.01/188.57 inference(unit_resolution,[status(thm)],[24036, 619, 25492])).
% 296.01/188.57 tff(33636,plain,
% 296.01/188.57 (~node20(c_e_h_1, c_i, s15)),
% 296.01/188.57 inference(unit_resolution,[status(thm)],[24040, 38, 33635])).
% 296.01/188.57 tff(33637,plain,
% 296.01/188.57 (~m_c_h_element_v_out(c_e_h_1, c_h, s16)),
% 296.01/188.57 inference(unit_resolution,[status(thm)],[25564, 25492, 25554])).
% 296.01/188.57 tff(33638,plain,
% 296.01/188.57 (~m_and_h_gate_v_in1(c_e_h_1, c_i, s16)),
% 296.01/188.57 inference(unit_resolution,[status(thm)],[25568, 619, 33637])).
% 296.01/188.57 tff(33639,plain,
% 296.01/188.57 (~node20(c_e_h_1, c_i, s16)),
% 296.01/188.57 inference(unit_resolution,[status(thm)],[25572, 38, 33638])).
% 296.01/188.57 tff(33640,plain,
% 296.01/188.57 ($false),
% 296.01/188.57 inference(unit_resolution,[status(thm)],[33419, 33639, 33636, 32811, 24251, 33346])).
% 296.01/188.57 tff(33641,plain,(m_c_h_element_v_out(c_e_h_1, c_h, s15) | m_c_h_element_v_out(c_e_h_1, c_f, s15) | m_and_h_gate_v_out(c_e_h_1, c_i, s15) | (~m_c_h_element_v_out(c_e_h_1, c_f, s18)) | m_c_h_element_v_in2(c_e_h_1, c_h, s15)), inference(lemma,lemma(discharge,[]))).
% 296.01/188.57 tff(33642,plain,
% 296.01/188.57 (m_c_h_element_v_out(c_e_h_1, c_h, s15) | m_and_h_gate_v_out(c_e_h_1, c_i, s15) | (~m_c_h_element_v_out(c_e_h_1, c_f, s18)) | m_c_h_element_v_in2(c_e_h_1, c_h, s15)),
% 296.01/188.57 inference(unit_resolution,[status(thm)],[33641, 32810])).
% 296.01/188.57 tff(33643,plain,
% 296.01/188.57 (m_c_h_element_v_out(c_e_h_1, c_h, s15) | (~m_c_h_element_v_out(c_e_h_1, c_f, s18)) | m_c_h_element_v_in2(c_e_h_1, c_h, s15)),
% 296.01/188.57 inference(unit_resolution,[status(thm)],[33642, 24241])).
% 296.01/188.57 tff(33644,plain,
% 296.01/188.57 (~m_c_h_element_v_out(c_e_h_1, c_f, s18)),
% 296.01/188.57 inference(unit_resolution,[status(thm)],[33643, 25490, 24033])).
% 296.01/188.57 tff(33645,plain,
% 296.01/188.57 (~m_and_h_gate_v_in1(c_e_h_1, c_q, s18)),
% 296.01/188.57 inference(unit_resolution,[status(thm)],[33582, 1586, 33644])).
% 296.01/188.57 tff(33646,plain,
% 296.01/188.57 (~node20(c_e_h_1, c_q, s18)),
% 296.01/188.57 inference(unit_resolution,[status(thm)],[33586, 38, 33645])).
% 296.01/188.57 tff(33647,plain,
% 296.01/188.57 (~m_and_h_gate_v_out(c_e_h_1, c_q, s19)),
% 296.01/188.57 inference(unit_resolution,[status(thm)],[33616, 33646, 33331])).
% 296.01/188.57 tff(33648,assumption,(m_c_h_element_v_in2(c_e_h_1, c_f, s20)), introduced(assumption)).
% 296.01/188.57 tff(33649,plain,
% 296.01/188.57 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s20)) | m_and_h_gate_v_out(c_e_h_1, c_i, s20))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s20)) | m_and_h_gate_v_out(c_e_h_1, c_i, s20))),
% 296.01/188.57 inference(rewrite,[status(thm)],[])).
% 296.01/188.57 tff(33650,plain,
% 296.01/188.57 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_1, c_f, s20)) | m_and_h_gate_v_out(c_e_h_1, c_i, s20))),
% 296.01/188.57 inference(quant_inst,[status(thm)],[])).
% 296.01/188.57 tff(33651,plain,
% 296.01/188.57 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_f, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_1, c_f, s20)) | m_and_h_gate_v_out(c_e_h_1, c_i, s20)),
% 296.01/188.57 inference(modus_ponens,[status(thm)],[33650, 33649])).
% 296.01/188.57 tff(33652,plain,
% 296.01/188.57 ($false),
% 296.01/188.57 inference(unit_resolution,[status(thm)],[33651, 2143, 33648, 30346])).
% 296.01/188.57 tff(33653,plain,((~m_c_h_element_v_in2(c_e_h_1, c_f, s20)) | m_and_h_gate_v_out(c_e_h_1, c_i, s20)), inference(lemma,lemma(discharge,[]))).
% 296.01/188.57 tff(33654,plain,
% 296.01/188.57 (~m_c_h_element_v_in2(c_e_h_1, c_f, s20)),
% 296.01/188.57 inference(unit_resolution,[status(thm)],[33653, 30040])).
% 296.01/188.57 tff(33655,assumption,(~m_or_h_gate_v_in2(c_e_h_2, c_j, s18)), introduced(assumption)).
% 296.01/188.57 tff(33656,plain,
% 296.01/188.57 (~m_and_h_gate_v_out(c_e_h_1, c_q, s17)),
% 296.01/188.57 inference(unit_resolution,[status(thm)],[33302, 33279])).
% 296.01/188.57 tff(33657,plain,
% 296.01/188.57 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s17))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s17))),
% 296.01/188.57 inference(rewrite,[status(thm)],[])).
% 296.01/188.57 tff(33658,plain,
% 296.01/188.57 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s17))),
% 296.01/188.57 inference(quant_inst,[status(thm)],[])).
% 296.01/188.57 tff(33659,plain,
% 296.01/188.57 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s17)),
% 296.01/188.57 inference(modus_ponens,[status(thm)],[33658, 33657])).
% 296.01/188.57 tff(33660,plain,
% 296.01/188.57 (node3(c_e_h_1, c_e_h_2, s17)),
% 296.01/188.57 inference(unit_resolution,[status(thm)],[33659, 4166, 1056])).
% 296.01/188.57 tff(33661,plain,
% 296.01/188.57 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s17)) | (~node3(c_e_h_1, c_e_h_2, s17)) | m_and_h_gate_v_out(c_e_h_1, c_q, s17))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s17)) | (~node3(c_e_h_1, c_e_h_2, s17)) | m_and_h_gate_v_out(c_e_h_1, c_q, s17))),
% 296.01/188.57 inference(rewrite,[status(thm)],[])).
% 296.01/188.58 tff(33662,plain,
% 296.01/188.58 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s17)) | (~node3(c_e_h_1, c_e_h_2, s17)) | m_and_h_gate_v_out(c_e_h_1, c_q, s17))),
% 296.01/188.58 inference(quant_inst,[status(thm)],[])).
% 296.01/188.58 tff(33663,plain,
% 296.01/188.58 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s17)) | (~node3(c_e_h_1, c_e_h_2, s17)) | m_and_h_gate_v_out(c_e_h_1, c_q, s17)),
% 296.01/188.58 inference(modus_ponens,[status(thm)],[33662, 33661])).
% 296.01/188.58 tff(33664,plain,
% 296.01/188.58 ((~m_cell_v_ack(c_e_h_2, s17)) | m_and_h_gate_v_out(c_e_h_1, c_q, s17)),
% 296.01/188.58 inference(unit_resolution,[status(thm)],[33663, 1073, 33660])).
% 296.01/188.58 tff(33665,plain,
% 296.01/188.58 (~m_cell_v_ack(c_e_h_2, s17)),
% 296.01/188.58 inference(unit_resolution,[status(thm)],[33664, 33656])).
% 296.01/188.58 tff(33666,plain,
% 296.01/188.58 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s17)) | m_cell_v_ack(c_e_h_2, s17))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s17)) | m_cell_v_ack(c_e_h_2, s17))),
% 296.01/188.58 inference(rewrite,[status(thm)],[])).
% 296.01/188.58 tff(33667,plain,
% 296.01/188.58 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s17)) | m_cell_v_ack(c_e_h_2, s17))),
% 296.01/188.58 inference(quant_inst,[status(thm)],[])).
% 296.01/188.58 tff(33668,plain,
% 296.01/188.58 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s17)) | m_cell_v_ack(c_e_h_2, s17)),
% 296.01/188.58 inference(modus_ponens,[status(thm)],[33667, 33666])).
% 296.01/188.58 tff(33669,plain,
% 296.01/188.58 (~m_or_h_gate_v_in2(c_e_h_2, c_j, s17)),
% 296.01/188.58 inference(unit_resolution,[status(thm)],[33668, 1085, 33665])).
% 296.01/188.58 tff(33670,plain,
% 296.01/188.58 (~m_and_h_gate_v_in1(c_e_h_1, c_q, s13)),
% 296.01/188.58 inference(unit_resolution,[status(thm)],[33189, 32642])).
% 296.01/188.58 tff(33671,plain,
% 296.01/188.58 (~node20(c_e_h_1, c_q, s13)),
% 296.01/188.58 inference(unit_resolution,[status(thm)],[33197, 33670])).
% 296.01/188.58 tff(33672,plain,
% 296.01/188.58 ((~m_and_h_gate_v_out(c_e_h_1, c_q, s14)) | node20(c_e_h_1, c_q, s13)),
% 296.01/188.58 inference(unit_resolution,[status(thm)],[33223, 33160])).
% 296.01/188.58 tff(33673,plain,
% 296.01/188.58 (~m_and_h_gate_v_out(c_e_h_1, c_q, s14)),
% 296.01/188.58 inference(unit_resolution,[status(thm)],[33672, 33671])).
% 296.01/188.58 tff(33674,plain,
% 296.01/188.58 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s14))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s14))),
% 296.01/188.58 inference(rewrite,[status(thm)],[])).
% 296.01/188.58 tff(33675,plain,
% 296.01/188.58 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s14))),
% 296.01/188.58 inference(quant_inst,[status(thm)],[])).
% 296.01/188.58 tff(33676,plain,
% 296.01/188.58 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s14)),
% 296.01/188.58 inference(modus_ponens,[status(thm)],[33675, 33674])).
% 296.01/188.58 tff(33677,plain,
% 296.01/188.58 (node3(c_e_h_1, c_e_h_2, s14)),
% 296.01/188.58 inference(unit_resolution,[status(thm)],[33676, 4166, 1056])).
% 296.01/188.58 tff(33678,plain,
% 296.01/188.58 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s14)) | (~node3(c_e_h_1, c_e_h_2, s14)) | m_and_h_gate_v_out(c_e_h_1, c_q, s14))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s14)) | (~node3(c_e_h_1, c_e_h_2, s14)) | m_and_h_gate_v_out(c_e_h_1, c_q, s14))),
% 296.01/188.58 inference(rewrite,[status(thm)],[])).
% 296.01/188.58 tff(33679,plain,
% 296.01/188.58 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s14)) | (~node3(c_e_h_1, c_e_h_2, s14)) | m_and_h_gate_v_out(c_e_h_1, c_q, s14))),
% 296.01/188.58 inference(quant_inst,[status(thm)],[])).
% 296.01/188.58 tff(33680,plain,
% 296.01/188.58 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s14)) | (~node3(c_e_h_1, c_e_h_2, s14)) | m_and_h_gate_v_out(c_e_h_1, c_q, s14)),
% 296.01/188.58 inference(modus_ponens,[status(thm)],[33679, 33678])).
% 296.01/188.58 tff(33681,plain,
% 296.01/188.58 ((~m_cell_v_ack(c_e_h_2, s14)) | m_and_h_gate_v_out(c_e_h_1, c_q, s14)),
% 296.01/188.58 inference(unit_resolution,[status(thm)],[33680, 1073, 33677])).
% 296.01/188.58 tff(33682,plain,
% 296.01/188.58 (~m_cell_v_ack(c_e_h_2, s14)),
% 296.01/188.58 inference(unit_resolution,[status(thm)],[33681, 33673])).
% 296.01/188.58 tff(33683,plain,
% 296.01/188.58 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s14)) | m_cell_v_ack(c_e_h_2, s14))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s14)) | m_cell_v_ack(c_e_h_2, s14))),
% 296.01/188.58 inference(rewrite,[status(thm)],[])).
% 296.01/188.58 tff(33684,plain,
% 296.01/188.58 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s14)) | m_cell_v_ack(c_e_h_2, s14))),
% 296.01/188.58 inference(quant_inst,[status(thm)],[])).
% 296.01/188.58 tff(33685,plain,
% 296.01/188.58 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s14)) | m_cell_v_ack(c_e_h_2, s14)),
% 296.01/188.58 inference(modus_ponens,[status(thm)],[33684, 33683])).
% 296.01/188.58 tff(33686,plain,
% 296.01/188.58 (~m_or_h_gate_v_in2(c_e_h_2, c_j, s14)),
% 296.01/188.58 inference(unit_resolution,[status(thm)],[33685, 1085, 33682])).
% 296.01/188.58 tff(33687,plain,
% 296.01/188.58 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s12))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s12))),
% 296.01/188.58 inference(rewrite,[status(thm)],[])).
% 296.01/188.58 tff(33688,plain,
% 296.01/188.58 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s12))),
% 296.01/188.58 inference(quant_inst,[status(thm)],[])).
% 296.01/188.58 tff(33689,plain,
% 296.01/188.58 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s12)),
% 296.01/188.58 inference(modus_ponens,[status(thm)],[33688, 33687])).
% 296.01/188.58 tff(33690,plain,
% 296.01/188.58 (node3(c_e_h_1, c_e_h_2, s12)),
% 296.01/188.58 inference(unit_resolution,[status(thm)],[33689, 4166, 1056])).
% 296.01/188.58 tff(33691,plain,
% 296.01/188.58 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s12)) | (~node3(c_e_h_1, c_e_h_2, s12)) | m_and_h_gate_v_out(c_e_h_1, c_q, s12))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s12)) | (~node3(c_e_h_1, c_e_h_2, s12)) | m_and_h_gate_v_out(c_e_h_1, c_q, s12))),
% 296.01/188.58 inference(rewrite,[status(thm)],[])).
% 296.01/188.58 tff(33692,plain,
% 296.01/188.58 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s12)) | (~node3(c_e_h_1, c_e_h_2, s12)) | m_and_h_gate_v_out(c_e_h_1, c_q, s12))),
% 296.01/188.58 inference(quant_inst,[status(thm)],[])).
% 296.01/188.58 tff(33693,plain,
% 296.01/188.58 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s12)) | (~node3(c_e_h_1, c_e_h_2, s12)) | m_and_h_gate_v_out(c_e_h_1, c_q, s12)),
% 296.01/188.58 inference(modus_ponens,[status(thm)],[33692, 33691])).
% 296.01/188.58 tff(33694,plain,
% 296.01/188.58 ((~m_cell_v_ack(c_e_h_2, s12)) | m_and_h_gate_v_out(c_e_h_1, c_q, s12)),
% 296.01/188.58 inference(unit_resolution,[status(thm)],[33693, 1073, 33690])).
% 296.01/188.58 tff(33695,plain,
% 296.01/188.58 (~m_cell_v_ack(c_e_h_2, s12)),
% 296.01/188.58 inference(unit_resolution,[status(thm)],[33694, 33125])).
% 296.01/188.58 tff(33696,plain,
% 296.01/188.58 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s12)) | m_cell_v_ack(c_e_h_2, s12))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s12)) | m_cell_v_ack(c_e_h_2, s12))),
% 296.01/188.58 inference(rewrite,[status(thm)],[])).
% 296.01/188.58 tff(33697,plain,
% 296.01/188.58 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s12)) | m_cell_v_ack(c_e_h_2, s12))),
% 296.01/188.58 inference(quant_inst,[status(thm)],[])).
% 296.01/188.58 tff(33698,plain,
% 296.01/188.58 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s12)) | m_cell_v_ack(c_e_h_2, s12)),
% 296.01/188.58 inference(modus_ponens,[status(thm)],[33697, 33696])).
% 296.01/188.58 tff(33699,plain,
% 296.01/188.58 (~m_or_h_gate_v_in2(c_e_h_2, c_j, s12)),
% 296.01/188.58 inference(unit_resolution,[status(thm)],[33698, 1085, 33695])).
% 296.01/188.58 tff(33700,plain,
% 296.01/188.58 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s11))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s11))),
% 296.01/188.58 inference(rewrite,[status(thm)],[])).
% 296.01/188.58 tff(33701,plain,
% 296.01/188.58 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s11))),
% 296.01/188.58 inference(quant_inst,[status(thm)],[])).
% 296.01/188.58 tff(33702,plain,
% 296.01/188.58 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s11)),
% 296.01/188.58 inference(modus_ponens,[status(thm)],[33701, 33700])).
% 296.01/188.58 tff(33703,plain,
% 296.01/188.58 (node3(c_e_h_1, c_e_h_2, s11)),
% 296.01/188.58 inference(unit_resolution,[status(thm)],[33702, 4166, 1056])).
% 296.01/188.58 tff(33704,plain,
% 296.01/188.58 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s11)) | (~node3(c_e_h_1, c_e_h_2, s11)) | m_and_h_gate_v_out(c_e_h_1, c_q, s11))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s11)) | (~node3(c_e_h_1, c_e_h_2, s11)) | m_and_h_gate_v_out(c_e_h_1, c_q, s11))),
% 296.01/188.58 inference(rewrite,[status(thm)],[])).
% 296.01/188.58 tff(33705,plain,
% 296.01/188.58 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s11)) | (~node3(c_e_h_1, c_e_h_2, s11)) | m_and_h_gate_v_out(c_e_h_1, c_q, s11))),
% 296.01/188.58 inference(quant_inst,[status(thm)],[])).
% 296.01/188.58 tff(33706,plain,
% 296.01/188.58 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s11)) | (~node3(c_e_h_1, c_e_h_2, s11)) | m_and_h_gate_v_out(c_e_h_1, c_q, s11)),
% 296.01/188.58 inference(modus_ponens,[status(thm)],[33705, 33704])).
% 296.01/188.58 tff(33707,plain,
% 296.01/188.58 ((~m_cell_v_ack(c_e_h_2, s11)) | m_and_h_gate_v_out(c_e_h_1, c_q, s11)),
% 296.01/188.58 inference(unit_resolution,[status(thm)],[33706, 1073, 33703])).
% 296.01/188.58 tff(33708,plain,
% 296.01/188.58 (~m_cell_v_ack(c_e_h_2, s11)),
% 296.01/188.58 inference(unit_resolution,[status(thm)],[33707, 33097])).
% 296.01/188.58 tff(33709,plain,
% 296.01/188.58 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s11)) | m_cell_v_ack(c_e_h_2, s11))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s11)) | m_cell_v_ack(c_e_h_2, s11))),
% 296.01/188.58 inference(rewrite,[status(thm)],[])).
% 296.01/188.58 tff(33710,plain,
% 296.01/188.58 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s11)) | m_cell_v_ack(c_e_h_2, s11))),
% 296.01/188.58 inference(quant_inst,[status(thm)],[])).
% 296.01/188.58 tff(33711,plain,
% 296.01/188.58 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s11)) | m_cell_v_ack(c_e_h_2, s11)),
% 296.01/188.58 inference(modus_ponens,[status(thm)],[33710, 33709])).
% 296.01/188.58 tff(33712,plain,
% 296.01/188.58 (~m_or_h_gate_v_in2(c_e_h_2, c_j, s11)),
% 296.01/188.58 inference(unit_resolution,[status(thm)],[33711, 1085, 33708])).
% 296.01/188.58 tff(33713,plain,
% 296.01/188.58 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s9)) | m_cell_v_ack(c_e_h_2, s9))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s9)) | m_cell_v_ack(c_e_h_2, s9))),
% 296.01/188.59 inference(rewrite,[status(thm)],[])).
% 296.01/188.59 tff(33714,plain,
% 296.01/188.59 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s9)) | m_cell_v_ack(c_e_h_2, s9))),
% 296.01/188.59 inference(quant_inst,[status(thm)],[])).
% 296.01/188.59 tff(33715,plain,
% 296.01/188.59 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s9)) | m_cell_v_ack(c_e_h_2, s9)),
% 296.01/188.59 inference(modus_ponens,[status(thm)],[33714, 33713])).
% 296.01/188.59 tff(33716,plain,
% 296.01/188.59 (~m_or_h_gate_v_in2(c_e_h_2, c_j, s9)),
% 296.01/188.59 inference(unit_resolution,[status(thm)],[33715, 1085, 25297])).
% 296.01/188.59 tff(33717,assumption,(m_or_h_gate_v_out(c_e_h_2, c_j, s10)), introduced(assumption)).
% 296.01/188.59 tff(33718,plain,
% 296.01/188.59 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s8))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s8))),
% 296.01/188.59 inference(rewrite,[status(thm)],[])).
% 296.01/188.59 tff(33719,plain,
% 296.01/188.59 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | ((~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s8))),
% 296.01/188.59 inference(quant_inst,[status(thm)],[])).
% 296.01/188.59 tff(33720,plain,
% 296.01/188.59 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_left(I0, J0)) | node3(I0, J0, X))) | (~m_cell_v_left(c_e_h_1, c_e_h_2)) | node3(c_e_h_1, c_e_h_2, s8)),
% 296.01/188.59 inference(modus_ponens,[status(thm)],[33719, 33718])).
% 296.01/188.59 tff(33721,plain,
% 296.01/188.59 (node3(c_e_h_1, c_e_h_2, s8)),
% 296.01/188.59 inference(unit_resolution,[status(thm)],[33720, 4166, 1056])).
% 296.01/188.59 tff(33722,plain,
% 296.01/188.59 (((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s8)) | (~node3(c_e_h_1, c_e_h_2, s8)) | m_and_h_gate_v_out(c_e_h_1, c_q, s8))) <=> ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s8)) | (~node3(c_e_h_1, c_e_h_2, s8)) | m_and_h_gate_v_out(c_e_h_1, c_q, s8))),
% 296.01/188.59 inference(rewrite,[status(thm)],[])).
% 296.01/188.59 tff(33723,plain,
% 296.01/188.59 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | ((~m_cell_v_ack(c_e_h_2, s8)) | (~node3(c_e_h_1, c_e_h_2, s8)) | m_and_h_gate_v_out(c_e_h_1, c_q, s8))),
% 296.01/188.59 inference(quant_inst,[status(thm)],[])).
% 296.01/188.59 tff(33724,plain,
% 296.01/188.59 ((~![I0: $i, X: $i, J0: $i] : ((~m_cell_v_ack(J0, X)) | (~node3(I0, J0, X)) | m_and_h_gate_v_out(I0, c_q, X))) | (~m_cell_v_ack(c_e_h_2, s8)) | (~node3(c_e_h_1, c_e_h_2, s8)) | m_and_h_gate_v_out(c_e_h_1, c_q, s8)),
% 296.01/188.59 inference(modus_ponens,[status(thm)],[33723, 33722])).
% 296.01/188.59 tff(33725,plain,
% 296.01/188.59 ((~m_cell_v_ack(c_e_h_2, s8)) | m_and_h_gate_v_out(c_e_h_1, c_q, s8)),
% 296.01/188.59 inference(unit_resolution,[status(thm)],[33724, 1073, 33721])).
% 296.01/188.59 tff(33726,plain,
% 296.01/188.59 (~m_cell_v_ack(c_e_h_2, s8)),
% 296.01/188.59 inference(unit_resolution,[status(thm)],[33725, 25283])).
% 296.01/188.59 tff(33727,plain,
% 296.01/188.59 (((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s8)) | m_cell_v_ack(c_e_h_2, s8))) <=> ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s8)) | m_cell_v_ack(c_e_h_2, s8))),
% 296.01/188.59 inference(rewrite,[status(thm)],[])).
% 296.01/188.59 tff(33728,plain,
% 296.01/188.59 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | ((~m_or_h_gate_v_in2(c_e_h_2, c_j, s8)) | m_cell_v_ack(c_e_h_2, s8))),
% 296.01/188.59 inference(quant_inst,[status(thm)],[])).
% 296.01/188.59 tff(33729,plain,
% 296.01/188.59 ((~![I0: $i, X: $i] : ((~m_or_h_gate_v_in2(I0, c_j, X)) | m_cell_v_ack(I0, X))) | (~m_or_h_gate_v_in2(c_e_h_2, c_j, s8)) | m_cell_v_ack(c_e_h_2, s8)),
% 296.01/188.59 inference(modus_ponens,[status(thm)],[33728, 33727])).
% 296.01/188.59 tff(33730,plain,
% 296.01/188.59 (~m_or_h_gate_v_in2(c_e_h_2, c_j, s8)),
% 296.01/188.59 inference(unit_resolution,[status(thm)],[33729, 1085, 33726])).
% 296.01/188.59 tff(33731,assumption,(m_or_h_gate_v_out(c_e_h_2, c_j, s9)), introduced(assumption)).
% 296.01/188.59 tff(33732,assumption,(node6(c_e_h_2, c_j, s8, s9)), introduced(assumption)).
% 296.01/188.59 tff(33733,assumption,(~m_or_h_gate_v_out(c_e_h_2, c_j, s8)), introduced(assumption)).
% 296.01/188.59 tff(33734,plain,
% 296.01/188.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_2, c_j, s9)) | m_or_h_gate_v_out(c_e_h_2, c_j, s8) | (~node6(c_e_h_2, c_j, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s9)) | m_or_h_gate_v_out(c_e_h_2, c_j, s8) | (~node6(c_e_h_2, c_j, s8, s9)))),
% 296.01/188.59 inference(rewrite,[status(thm)],[])).
% 296.01/188.59 tff(33735,plain,
% 296.01/188.59 (((~node6(c_e_h_2, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s9)) | m_or_h_gate_v_out(c_e_h_2, c_j, s8)) <=> ((~m_or_h_gate_v_out(c_e_h_2, c_j, s9)) | m_or_h_gate_v_out(c_e_h_2, c_j, s8) | (~node6(c_e_h_2, c_j, s8, s9)))),
% 296.01/188.59 inference(rewrite,[status(thm)],[])).
% 296.01/188.59 tff(33736,plain,
% 296.01/188.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s9)) | m_or_h_gate_v_out(c_e_h_2, c_j, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~m_or_h_gate_v_out(c_e_h_2, c_j, s9)) | m_or_h_gate_v_out(c_e_h_2, c_j, s8) | (~node6(c_e_h_2, c_j, s8, s9))))),
% 296.01/188.59 inference(monotonicity,[status(thm)],[33735])).
% 296.01/188.59 tff(33737,plain,
% 296.01/188.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s9)) | m_or_h_gate_v_out(c_e_h_2, c_j, s8))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s9)) | m_or_h_gate_v_out(c_e_h_2, c_j, s8) | (~node6(c_e_h_2, c_j, s8, s9)))),
% 296.01/188.59 inference(transitivity,[status(thm)],[33736, 33734])).
% 296.01/188.59 tff(33738,plain,
% 296.01/188.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | ((~node6(c_e_h_2, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s9)) | m_or_h_gate_v_out(c_e_h_2, c_j, s8))),
% 296.01/188.59 inference(quant_inst,[status(thm)],[])).
% 296.01/188.59 tff(33739,plain,
% 296.01/188.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node6(I0, I1, X, Y)) | (~m_or_h_gate_v_out(I0, I1, Y)) | m_or_h_gate_v_out(I0, I1, X))) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s9)) | m_or_h_gate_v_out(c_e_h_2, c_j, s8) | (~node6(c_e_h_2, c_j, s8, s9))),
% 296.01/188.59 inference(modus_ponens,[status(thm)],[33738, 33737])).
% 296.01/188.59 tff(33740,plain,
% 296.01/188.59 ($false),
% 296.01/188.59 inference(unit_resolution,[status(thm)],[33739, 1121, 33731, 33733, 33732])).
% 296.01/188.59 tff(33741,plain,((~node6(c_e_h_2, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s9)) | m_or_h_gate_v_out(c_e_h_2, c_j, s8)), inference(lemma,lemma(discharge,[]))).
% 296.01/188.59 tff(33742,plain,
% 296.01/188.59 ((~node6(c_e_h_2, c_j, s8, s9)) | (~m_or_h_gate_v_out(c_e_h_2, c_j, s9))),
% 296.01/188.59 inference(unit_resolution,[status(thm)],[33741, 27827])).
% 296.01/188.59 tff(33743,plain,
% 296.01/188.59 (~node6(c_e_h_2, c_j, s8, s9)),
% 296.01/188.59 inference(unit_resolution,[status(thm)],[33742, 33731])).
% 296.01/188.59 tff(33744,assumption,(~m_or_h_gate_v_in2(c_e_h_2, c_j, s8)), introduced(assumption)).
% 296.01/188.59 tff(33745,assumption,(m_and_h_gate_v_out(c_e_h_2, c_l, s8)), introduced(assumption)).
% 296.01/188.59 tff(33746,assumption,(m_c_h_element_v_out(c_e_h_2, c_e, s5)), introduced(assumption)).
% 296.01/188.59 tff(33747,plain,
% 296.01/188.59 (~m_c_h_element_v_in2(c_e_h_2, c_e, s3)),
% 296.01/188.59 inference(unit_resolution,[status(thm)],[27600, 4740])).
% 296.01/188.59 tff(33748,plain,
% 296.01/188.59 (~m_c_h_element_v_out(c_e_h_2, c_e, s4)),
% 296.01/188.59 inference(unit_resolution,[status(thm)],[27676, 33747])).
% 296.01/188.59 tff(33749,plain,
% 296.01/188.59 (~m_and_h_gate_v_out(c_e_h_2, c_i, s4)),
% 296.01/188.59 inference(unit_resolution,[status(thm)],[4762, 4740, 4742])).
% 296.01/188.59 tff(33750,assumption,(m_c_h_element_v_in2(c_e_h_2, c_e, s4)), introduced(assumption)).
% 296.01/188.59 tff(33751,plain,
% 296.01/188.59 (((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s4)) | m_and_h_gate_v_out(c_e_h_2, c_i, s4))) <=> ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s4)) | m_and_h_gate_v_out(c_e_h_2, c_i, s4))),
% 296.01/188.59 inference(rewrite,[status(thm)],[])).
% 296.01/188.59 tff(33752,plain,
% 296.01/188.59 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | ((~m_c_h_element_v_in2(c_e_h_2, c_e, s4)) | m_and_h_gate_v_out(c_e_h_2, c_i, s4))),
% 296.01/188.59 inference(quant_inst,[status(thm)],[])).
% 296.01/188.59 tff(33753,plain,
% 296.01/188.59 ((~![I0: $i, X: $i] : ((~m_c_h_element_v_in2(I0, c_e, X)) | m_and_h_gate_v_out(I0, c_i, X))) | (~m_c_h_element_v_in2(c_e_h_2, c_e, s4)) | m_and_h_gate_v_out(c_e_h_2, c_i, s4)),
% 296.01/188.59 inference(modus_ponens,[status(thm)],[33752, 33751])).
% 296.01/188.59 tff(33754,plain,
% 296.01/188.59 ($false),
% 296.01/188.59 inference(unit_resolution,[status(thm)],[33753, 164, 33750, 4766])).
% 296.01/188.59 tff(33755,plain,((~m_c_h_element_v_in2(c_e_h_2, c_e, s4)) | m_and_h_gate_v_out(c_e_h_2, c_i, s4)), inference(lemma,lemma(discharge,[]))).
% 296.01/188.59 tff(33756,plain,
% 296.01/188.59 (~m_c_h_element_v_in2(c_e_h_2, c_e, s4)),
% 296.01/188.59 inference(unit_resolution,[status(thm)],[33755, 33749])).
% 296.01/188.59 tff(33757,assumption,(node15(c_e_h_2, c_e, s4, s5)), introduced(assumption)).
% 296.01/188.59 tff(33758,plain,
% 296.01/188.59 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s5)) | (~node15(c_e_h_2, c_e, s4, s5)) | m_c_h_element_v_out(c_e_h_2, c_e, s4))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s5)) | (~node15(c_e_h_2, c_e, s4, s5)) | m_c_h_element_v_out(c_e_h_2, c_e, s4))),
% 296.01/188.59 inference(rewrite,[status(thm)],[])).
% 296.01/188.59 tff(33759,plain,
% 296.01/188.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s5)) | (~node15(c_e_h_2, c_e, s4, s5)) | m_c_h_element_v_out(c_e_h_2, c_e, s4))),
% 296.01/188.59 inference(quant_inst,[status(thm)],[])).
% 296.01/188.59 tff(33760,plain,
% 296.01/188.59 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | (~node15(I0, I1, X, Y)) | m_c_h_element_v_out(I0, I1, X))) | (~m_c_h_element_v_out(c_e_h_2, c_e, s5)) | (~node15(c_e_h_2, c_e, s4, s5)) | m_c_h_element_v_out(c_e_h_2, c_e, s4)),
% 296.01/188.59 inference(modus_ponens,[status(thm)],[33759, 33758])).
% 296.01/188.59 tff(33761,plain,
% 296.01/188.59 ($false),
% 296.01/188.59 inference(unit_resolution,[status(thm)],[33760, 147, 33757, 27679, 33746])).
% 296.01/188.59 tff(33762,plain,((~node15(c_e_h_2, c_e, s4, s5)) | m_c_h_element_v_out(c_e_h_2, c_e, s4) | (~m_c_h_element_v_out(c_e_h_2, c_e, s5))), inference(lemma,lemma(discharge,[]))).
% 296.01/188.59 tff(33763,plain,
% 296.01/188.59 (~node15(c_e_h_2, c_e, s4, s5)),
% 296.01/188.59 inference(unit_resolution,[status(thm)],[33762, 33746, 27679])).
% 296.01/188.59 tff(33764,assumption,(~m_c_h_element_v_in2(c_e_h_2, c_e, s4)), introduced(assumption)).
% 296.01/188.59 tff(33765,assumption,(~m_c_h_element_v_in1(c_e_h_2, c_e, s4)), introduced(assumption)).
% 296.01/188.59 tff(33766,assumption,(~node15(c_e_h_2, c_e, s4, s5)), introduced(assumption)).
% 296.01/188.59 tff(33767,plain,
% 296.01/188.59 (((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_e, s4)) | m_c_h_element_v_in1(c_e_h_2, c_e, s4) | m_c_h_element_v_in2(c_e_h_2, c_e, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s4)) | m_c_h_element_v_in1(c_e_h_2, c_e, s4) | m_c_h_element_v_in2(c_e_h_2, c_e, s4))),
% 296.01/188.59 inference(rewrite,[status(thm)],[])).
% 296.01/188.59 tff(33768,plain,
% 296.01/188.59 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | ((~node16(c_e_h_2, c_e, s4)) | m_c_h_element_v_in1(c_e_h_2, c_e, s4) | m_c_h_element_v_in2(c_e_h_2, c_e, s4))),
% 296.10/188.60 inference(quant_inst,[status(thm)],[])).
% 296.10/188.60 tff(33769,plain,
% 296.10/188.60 ((~![I0: $i, X: $i, I1: $i] : ((~node16(I0, I1, X)) | m_c_h_element_v_in1(I0, I1, X) | m_c_h_element_v_in2(I0, I1, X))) | (~node16(c_e_h_2, c_e, s4)) | m_c_h_element_v_in1(c_e_h_2, c_e, s4) | m_c_h_element_v_in2(c_e_h_2, c_e, s4)),
% 296.10/188.60 inference(modus_ponens,[status(thm)],[33768, 33767])).
% 296.10/188.60 tff(33770,plain,
% 296.10/188.60 ((~node16(c_e_h_2, c_e, s4)) | m_c_h_element_v_in1(c_e_h_2, c_e, s4)),
% 296.10/188.60 inference(unit_resolution,[status(thm)],[33769, 178, 33764])).
% 296.10/188.60 tff(33771,plain,
% 296.10/188.60 (~node16(c_e_h_2, c_e, s4)),
% 296.10/188.60 inference(unit_resolution,[status(thm)],[33770, 33765])).
% 296.10/188.60 tff(33772,plain,
% 296.10/188.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s4, s5)) | node19(c_e_h_2, c_e, s4, s5))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s4, s5)) | node19(c_e_h_2, c_e, s4, s5))),
% 296.10/188.60 inference(rewrite,[status(thm)],[])).
% 296.10/188.60 tff(33773,plain,
% 296.10/188.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | ((~trans(s4, s5)) | node19(c_e_h_2, c_e, s4, s5))),
% 296.10/188.60 inference(quant_inst,[status(thm)],[])).
% 296.10/188.60 tff(33774,plain,
% 296.10/188.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node19(I0, I1, X, Y))) | (~trans(s4, s5)) | node19(c_e_h_2, c_e, s4, s5)),
% 296.10/188.60 inference(modus_ponens,[status(thm)],[33773, 33772])).
% 296.10/188.60 tff(33775,plain,
% 296.10/188.60 (node19(c_e_h_2, c_e, s4, s5)),
% 296.10/188.60 inference(unit_resolution,[status(thm)],[33774, 190, 1028])).
% 296.10/188.60 tff(33776,plain,
% 296.10/188.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s4) | node14(c_e_h_2, c_e, s4, s5) | node15(c_e_h_2, c_e, s4, s5) | (~node19(c_e_h_2, c_e, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_e, s4) | node14(c_e_h_2, c_e, s4, s5) | node15(c_e_h_2, c_e, s4, s5) | (~node19(c_e_h_2, c_e, s4, s5)))),
% 296.10/188.60 inference(rewrite,[status(thm)],[])).
% 296.10/188.60 tff(33777,plain,
% 296.10/188.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node16(c_e_h_2, c_e, s4) | node14(c_e_h_2, c_e, s4, s5) | node15(c_e_h_2, c_e, s4, s5) | (~node19(c_e_h_2, c_e, s4, s5)))),
% 296.10/188.60 inference(quant_inst,[status(thm)],[])).
% 296.10/188.60 tff(33778,plain,
% 296.10/188.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node16(I0, I1, X) | node14(I0, I1, X, Y) | node15(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node16(c_e_h_2, c_e, s4) | node14(c_e_h_2, c_e, s4, s5) | node15(c_e_h_2, c_e, s4, s5) | (~node19(c_e_h_2, c_e, s4, s5))),
% 296.10/188.60 inference(modus_ponens,[status(thm)],[33777, 33776])).
% 296.10/188.60 tff(33779,plain,
% 296.10/188.60 (node16(c_e_h_2, c_e, s4) | node14(c_e_h_2, c_e, s4, s5) | node15(c_e_h_2, c_e, s4, s5)),
% 296.10/188.60 inference(unit_resolution,[status(thm)],[33778, 204, 33775])).
% 296.10/188.60 tff(33780,plain,
% 296.10/188.60 (node14(c_e_h_2, c_e, s4, s5)),
% 296.10/188.60 inference(unit_resolution,[status(thm)],[33779, 33771, 33766])).
% 296.10/188.60 tff(33781,plain,
% 296.10/188.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s4) | (~m_c_h_element_v_out(c_e_h_2, c_e, s5)) | (~node14(c_e_h_2, c_e, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s4) | (~m_c_h_element_v_out(c_e_h_2, c_e, s5)) | (~node14(c_e_h_2, c_e, s4, s5)))),
% 296.10/188.60 inference(rewrite,[status(thm)],[])).
% 296.10/188.60 tff(33782,plain,
% 296.10/188.60 (((~node14(c_e_h_2, c_e, s4, s5)) | m_c_h_element_v_in1(c_e_h_2, c_e, s4) | (~m_c_h_element_v_out(c_e_h_2, c_e, s5))) <=> (m_c_h_element_v_in1(c_e_h_2, c_e, s4) | (~m_c_h_element_v_out(c_e_h_2, c_e, s5)) | (~node14(c_e_h_2, c_e, s4, s5)))),
% 296.10/188.60 inference(rewrite,[status(thm)],[])).
% 296.10/188.60 tff(33783,plain,
% 296.10/188.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s4, s5)) | m_c_h_element_v_in1(c_e_h_2, c_e, s4) | (~m_c_h_element_v_out(c_e_h_2, c_e, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | (m_c_h_element_v_in1(c_e_h_2, c_e, s4) | (~m_c_h_element_v_out(c_e_h_2, c_e, s5)) | (~node14(c_e_h_2, c_e, s4, s5))))),
% 296.10/188.60 inference(monotonicity,[status(thm)],[33782])).
% 296.10/188.60 tff(33784,plain,
% 296.10/188.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s4, s5)) | m_c_h_element_v_in1(c_e_h_2, c_e, s4) | (~m_c_h_element_v_out(c_e_h_2, c_e, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s4) | (~m_c_h_element_v_out(c_e_h_2, c_e, s5)) | (~node14(c_e_h_2, c_e, s4, s5)))),
% 296.10/188.60 inference(transitivity,[status(thm)],[33783, 33781])).
% 296.10/188.60 tff(33785,plain,
% 296.10/188.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | ((~node14(c_e_h_2, c_e, s4, s5)) | m_c_h_element_v_in1(c_e_h_2, c_e, s4) | (~m_c_h_element_v_out(c_e_h_2, c_e, s5)))),
% 296.10/188.60 inference(quant_inst,[status(thm)],[])).
% 296.10/188.60 tff(33786,plain,
% 296.10/188.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node14(I0, I1, X, Y)) | m_c_h_element_v_in1(I0, I1, X) | (~m_c_h_element_v_out(I0, I1, Y)))) | m_c_h_element_v_in1(c_e_h_2, c_e, s4) | (~m_c_h_element_v_out(c_e_h_2, c_e, s5)) | (~node14(c_e_h_2, c_e, s4, s5))),
% 296.10/188.60 inference(modus_ponens,[status(thm)],[33785, 33784])).
% 296.10/188.60 tff(33787,plain,
% 296.10/188.60 ($false),
% 296.10/188.60 inference(unit_resolution,[status(thm)],[33786, 223, 33780, 33746, 33765])).
% 296.10/188.60 tff(33788,plain,(m_c_h_element_v_in1(c_e_h_2, c_e, s4) | (~m_c_h_element_v_out(c_e_h_2, c_e, s5)) | node15(c_e_h_2, c_e, s4, s5) | m_c_h_element_v_in2(c_e_h_2, c_e, s4)), inference(lemma,lemma(discharge,[]))).
% 296.10/188.60 tff(33789,plain,
% 296.10/188.60 (m_c_h_element_v_in1(c_e_h_2, c_e, s4)),
% 296.10/188.60 inference(unit_resolution,[status(thm)],[33788, 33746, 33764, 33763])).
% 296.10/188.60 tff(33790,assumption,(node18(c_e_h_2, c_e, s4, s5)), introduced(assumption)).
% 296.10/188.60 tff(33791,plain,
% 296.10/188.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_e, s4) | (~m_c_h_element_v_out(c_e_h_2, c_e, s5)) | (~node18(c_e_h_2, c_e, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_e, s4) | (~m_c_h_element_v_out(c_e_h_2, c_e, s5)) | (~node18(c_e_h_2, c_e, s4, s5)))),
% 296.10/188.60 inference(rewrite,[status(thm)],[])).
% 296.10/188.60 tff(33792,plain,
% 296.10/188.60 (((~m_c_h_element_v_out(c_e_h_2, c_e, s5)) | m_c_h_element_v_out(c_e_h_2, c_e, s4) | (~node18(c_e_h_2, c_e, s4, s5))) <=> (m_c_h_element_v_out(c_e_h_2, c_e, s4) | (~m_c_h_element_v_out(c_e_h_2, c_e, s5)) | (~node18(c_e_h_2, c_e, s4, s5)))),
% 296.10/188.60 inference(rewrite,[status(thm)],[])).
% 296.10/188.60 tff(33793,plain,
% 296.10/188.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s5)) | m_c_h_element_v_out(c_e_h_2, c_e, s4) | (~node18(c_e_h_2, c_e, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | (m_c_h_element_v_out(c_e_h_2, c_e, s4) | (~m_c_h_element_v_out(c_e_h_2, c_e, s5)) | (~node18(c_e_h_2, c_e, s4, s5))))),
% 296.10/188.60 inference(monotonicity,[status(thm)],[33792])).
% 296.10/188.60 tff(33794,plain,
% 296.10/188.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s5)) | m_c_h_element_v_out(c_e_h_2, c_e, s4) | (~node18(c_e_h_2, c_e, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_e, s4) | (~m_c_h_element_v_out(c_e_h_2, c_e, s5)) | (~node18(c_e_h_2, c_e, s4, s5)))),
% 296.10/188.60 inference(transitivity,[status(thm)],[33793, 33791])).
% 296.10/188.60 tff(33795,plain,
% 296.10/188.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | ((~m_c_h_element_v_out(c_e_h_2, c_e, s5)) | m_c_h_element_v_out(c_e_h_2, c_e, s4) | (~node18(c_e_h_2, c_e, s4, s5)))),
% 296.10/188.60 inference(quant_inst,[status(thm)],[])).
% 296.10/188.60 tff(33796,plain,
% 296.10/188.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_out(I0, I1, Y)) | m_c_h_element_v_out(I0, I1, X) | (~node18(I0, I1, X, Y)))) | m_c_h_element_v_out(c_e_h_2, c_e, s4) | (~m_c_h_element_v_out(c_e_h_2, c_e, s5)) | (~node18(c_e_h_2, c_e, s4, s5))),
% 296.10/188.60 inference(modus_ponens,[status(thm)],[33795, 33794])).
% 296.10/188.60 tff(33797,plain,
% 296.10/188.60 ($false),
% 296.10/188.60 inference(unit_resolution,[status(thm)],[33796, 753, 33790, 27679, 33746])).
% 296.10/188.60 tff(33798,plain,((~node18(c_e_h_2, c_e, s4, s5)) | m_c_h_element_v_out(c_e_h_2, c_e, s4) | (~m_c_h_element_v_out(c_e_h_2, c_e, s5))), inference(lemma,lemma(discharge,[]))).
% 296.10/188.60 tff(33799,plain,
% 296.10/188.60 (~node18(c_e_h_2, c_e, s4, s5)),
% 296.10/188.60 inference(unit_resolution,[status(thm)],[33798, 33746, 27679])).
% 296.10/188.60 tff(33800,plain,
% 296.10/188.60 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s4) | node18(c_e_h_2, c_e, s4, s5) | (~node19(c_e_h_2, c_e, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_e, s4) | node18(c_e_h_2, c_e, s4, s5) | (~node19(c_e_h_2, c_e, s4, s5)))),
% 296.10/188.60 inference(rewrite,[status(thm)],[])).
% 296.10/188.60 tff(33801,plain,
% 296.10/188.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | (node17(c_e_h_2, c_e, s4) | node18(c_e_h_2, c_e, s4, s5) | (~node19(c_e_h_2, c_e, s4, s5)))),
% 296.10/188.60 inference(quant_inst,[status(thm)],[])).
% 296.10/188.60 tff(33802,plain,
% 296.10/188.60 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (node17(I0, I1, X) | node18(I0, I1, X, Y) | (~node19(I0, I1, X, Y)))) | node17(c_e_h_2, c_e, s4) | node18(c_e_h_2, c_e, s4, s5) | (~node19(c_e_h_2, c_e, s4, s5))),
% 296.10/188.60 inference(modus_ponens,[status(thm)],[33801, 33800])).
% 296.10/188.60 tff(33803,plain,
% 296.10/188.60 (node17(c_e_h_2, c_e, s4) | node18(c_e_h_2, c_e, s4, s5)),
% 296.10/188.60 inference(unit_resolution,[status(thm)],[33802, 776, 33775])).
% 296.10/188.60 tff(33804,plain,
% 296.10/188.60 (node17(c_e_h_2, c_e, s4)),
% 296.10/188.60 inference(unit_resolution,[status(thm)],[33803, 33799])).
% 296.10/188.60 tff(33805,plain,
% 296.10/188.60 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_e, s4)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s4)) | m_c_h_element_v_in2(c_e_h_2, c_e, s4))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_e, s4)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s4)) | m_c_h_element_v_in2(c_e_h_2, c_e, s4))),
% 296.10/188.60 inference(rewrite,[status(thm)],[])).
% 296.10/188.60 tff(33806,plain,
% 296.10/188.60 (((~m_c_h_element_v_in1(c_e_h_2, c_e, s4)) | m_c_h_element_v_in2(c_e_h_2, c_e, s4) | (~node17(c_e_h_2, c_e, s4))) <=> ((~node17(c_e_h_2, c_e, s4)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s4)) | m_c_h_element_v_in2(c_e_h_2, c_e, s4))),
% 296.10/188.60 inference(rewrite,[status(thm)],[])).
% 296.10/188.60 tff(33807,plain,
% 296.10/188.60 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s4)) | m_c_h_element_v_in2(c_e_h_2, c_e, s4) | (~node17(c_e_h_2, c_e, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~node17(c_e_h_2, c_e, s4)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s4)) | m_c_h_element_v_in2(c_e_h_2, c_e, s4)))),
% 296.10/188.60 inference(monotonicity,[status(thm)],[33806])).
% 296.10/188.60 tff(33808,plain,
% 296.10/188.60 (((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s4)) | m_c_h_element_v_in2(c_e_h_2, c_e, s4) | (~node17(c_e_h_2, c_e, s4)))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_e, s4)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s4)) | m_c_h_element_v_in2(c_e_h_2, c_e, s4))),
% 296.10/188.61 inference(transitivity,[status(thm)],[33807, 33805])).
% 296.10/188.61 tff(33809,plain,
% 296.10/188.61 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | ((~m_c_h_element_v_in1(c_e_h_2, c_e, s4)) | m_c_h_element_v_in2(c_e_h_2, c_e, s4) | (~node17(c_e_h_2, c_e, s4)))),
% 296.10/188.61 inference(quant_inst,[status(thm)],[])).
% 296.10/188.61 tff(33810,plain,
% 296.10/188.61 ((~![I0: $i, X: $i, I1: $i] : ((~m_c_h_element_v_in1(I0, I1, X)) | m_c_h_element_v_in2(I0, I1, X) | (~node17(I0, I1, X)))) | (~node17(c_e_h_2, c_e, s4)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s4)) | m_c_h_element_v_in2(c_e_h_2, c_e, s4)),
% 296.10/188.61 inference(modus_ponens,[status(thm)],[33809, 33808])).
% 296.10/188.61 tff(33811,plain,
% 296.10/188.61 ((~node17(c_e_h_2, c_e, s4)) | (~m_c_h_element_v_in1(c_e_h_2, c_e, s4))),
% 296.10/188.61 inference(unit_resolution,[status(thm)],[33810, 919, 33764])).
% 296.10/188.61 tff(33812,plain,
% 296.10/188.61 ($false),
% 296.10/188.61 inference(unit_resolution,[status(thm)],[33811, 33804, 33789])).
% 296.10/188.61 tff(33813,plain,((~m_c_h_element_v_out(c_e_h_2, c_e, s5)) | m_c_h_element_v_in2(c_e_h_2, c_e, s4) | m_c_h_element_v_out(c_e_h_2, c_e, s4)), inference(lemma,lemma(discharge,[]))).
% 296.10/188.61 tff(33814,plain,
% 296.10/188.61 ($false),
% 296.10/188.61 inference(unit_resolution,[status(thm)],[33813, 33756, 33748, 33746])).
% 296.10/188.61 tff(33815,plain,(m_and_h_gate_v_out(c_e_h_2, c_i, s3) | (~m_c_h_element_v_out(c_e_h_2, c_e, s5)) | node20(c_e_h_2, c_i, s3)), inference(lemma,lemma(discharge,[]))).
% 296.10/188.61 tff(33816,plain,
% 296.10/188.61 ((~m_c_h_element_v_out(c_e_h_2, c_e, s5)) | node20(c_e_h_2, c_i, s3)),
% 296.10/188.61 inference(unit_resolution,[status(thm)],[33815, 4257])).
% 296.10/188.61 tff(33817,plain,
% 296.10/188.61 (~m_c_h_element_v_out(c_e_h_2, c_e, s5)),
% 296.10/188.61 inference(unit_resolution,[status(thm)],[33816, 4739])).
% 296.10/188.61 tff(33818,assumption,(~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5)), introduced(assumption)).
% 296.10/188.61 tff(33819,assumption,(~m_c_h_element_v_out(c_e_h_2, c_e, s5)), introduced(assumption)).
% 296.10/188.61 tff(33820,plain,
% 296.10/188.61 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5) | m_c_h_element_v_out(c_e_h_2, c_e, s5))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5) | m_c_h_element_v_out(c_e_h_2, c_e, s5))),
% 296.10/188.61 inference(rewrite,[status(thm)],[])).
% 296.10/188.61 tff(33821,plain,
% 296.10/188.61 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5) | m_c_h_element_v_out(c_e_h_2, c_e, s5))),
% 296.10/188.61 inference(quant_inst,[status(thm)],[])).
% 296.10/188.61 tff(33822,plain,
% 296.10/188.61 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in1(I0, c_n, X) | m_c_h_element_v_out(I0, c_e, X))) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5) | m_c_h_element_v_out(c_e_h_2, c_e, s5)),
% 296.10/188.61 inference(modus_ponens,[status(thm)],[33821, 33820])).
% 296.10/188.61 tff(33823,plain,
% 296.10/188.61 ($false),
% 296.10/188.61 inference(unit_resolution,[status(thm)],[33822, 7856, 33819, 33818])).
% 296.10/188.61 tff(33824,plain,(m_c_h_element_v_out(c_e_h_2, c_e, s5) | m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5)), inference(lemma,lemma(discharge,[]))).
% 296.10/188.61 tff(33825,plain,
% 296.10/188.61 (m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5)),
% 296.10/188.61 inference(unit_resolution,[status(thm)],[33824, 33817])).
% 296.10/188.61 tff(33826,plain,
% 296.10/188.61 (((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s5) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5))) <=> ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s5) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5))),
% 296.10/188.61 inference(rewrite,[status(thm)],[])).
% 296.10/188.61 tff(33827,plain,
% 296.10/188.61 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s5) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5))),
% 296.10/188.61 inference(quant_inst,[status(thm)],[])).
% 296.10/188.61 tff(33828,plain,
% 296.10/188.61 ((~![I0: $i, X: $i] : (m_and_h_gate_h_init_v_in2(I0, c_n, X) | m_and_h_gate_h_init_v_out(I0, c_m, X))) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s5) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)),
% 296.10/188.61 inference(modus_ponens,[status(thm)],[33827, 33826])).
% 296.10/188.61 tff(33829,plain,
% 296.10/188.61 (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s5) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s5)),
% 296.10/188.61 inference(unit_resolution,[status(thm)],[33828, 7868])).
% 296.10/188.61 tff(33830,plain,
% 296.10/188.61 (m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s5)),
% 296.10/188.61 inference(unit_resolution,[status(thm)],[33829, 27457])).
% 296.10/188.61 tff(33831,assumption,(m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5)), introduced(assumption)).
% 296.10/188.61 tff(33832,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5)), introduced(assumption)).
% 296.10/188.61 tff(33833,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6)), introduced(assumption)).
% 296.10/188.61 tff(33834,assumption,(node11(c_e_h_2, c_n, s5, s6)), introduced(assumption)).
% 296.10/188.61 tff(33835,plain,
% 296.10/188.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6) | (~node11(c_e_h_2, c_n, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6) | (~node11(c_e_h_2, c_n, s5, s6)))),
% 296.10/188.61 inference(rewrite,[status(thm)],[])).
% 296.10/188.61 tff(33836,plain,
% 296.10/188.61 ((m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6) | (~node11(c_e_h_2, c_n, s5, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5))) <=> ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6) | (~node11(c_e_h_2, c_n, s5, s6)))),
% 296.10/188.61 inference(rewrite,[status(thm)],[])).
% 296.10/188.61 tff(33837,plain,
% 296.10/188.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6) | (~node11(c_e_h_2, c_n, s5, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6) | (~node11(c_e_h_2, c_n, s5, s6))))),
% 296.10/188.61 inference(monotonicity,[status(thm)],[33836])).
% 296.10/188.61 tff(33838,plain,
% 296.10/188.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6) | (~node11(c_e_h_2, c_n, s5, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6) | (~node11(c_e_h_2, c_n, s5, s6)))),
% 296.10/188.61 inference(transitivity,[status(thm)],[33837, 33835])).
% 296.10/188.61 tff(33839,plain,
% 296.10/188.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6) | (~node11(c_e_h_2, c_n, s5, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5)))),
% 296.10/188.61 inference(quant_inst,[status(thm)],[])).
% 296.10/188.61 tff(33840,plain,
% 296.10/188.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : (m_and_h_gate_h_init_v_out(I0, I1, Y) | (~node11(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_out(I0, I1, X)))) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6) | (~node11(c_e_h_2, c_n, s5, s6))),
% 296.10/188.61 inference(modus_ponens,[status(thm)],[33839, 33838])).
% 296.10/188.61 tff(33841,plain,
% 296.10/188.61 ($false),
% 296.10/188.61 inference(unit_resolution,[status(thm)],[33840, 5742, 33832, 33833, 33834])).
% 296.10/188.61 tff(33842,plain,((~node11(c_e_h_2, c_n, s5, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6)), inference(lemma,lemma(discharge,[]))).
% 296.10/188.61 tff(33843,plain,
% 296.10/188.61 (~node11(c_e_h_2, c_n, s5, s6)),
% 296.10/188.61 inference(unit_resolution,[status(thm)],[33842, 33833, 33832])).
% 296.10/188.61 tff(33844,plain,
% 296.10/188.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s5, s6)) | node10(c_e_h_2, c_n, s5, s6) | node11(c_e_h_2, c_n, s5, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s5, s6)) | node10(c_e_h_2, c_n, s5, s6) | node11(c_e_h_2, c_n, s5, s6))),
% 296.10/188.61 inference(rewrite,[status(thm)],[])).
% 296.10/188.61 tff(33845,plain,
% 296.10/188.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | ((~trans(s5, s6)) | node10(c_e_h_2, c_n, s5, s6) | node11(c_e_h_2, c_n, s5, s6))),
% 296.10/188.61 inference(quant_inst,[status(thm)],[])).
% 296.10/188.61 tff(33846,plain,
% 296.10/188.61 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~trans(X, Y)) | node10(I0, I1, X, Y) | node11(I0, I1, X, Y))) | (~trans(s5, s6)) | node10(c_e_h_2, c_n, s5, s6) | node11(c_e_h_2, c_n, s5, s6)),
% 296.10/188.61 inference(modus_ponens,[status(thm)],[33845, 33844])).
% 296.10/188.61 tff(33847,plain,
% 296.10/188.61 (node10(c_e_h_2, c_n, s5, s6) | node11(c_e_h_2, c_n, s5, s6)),
% 296.10/188.61 inference(unit_resolution,[status(thm)],[33846, 5002, 1406])).
% 296.10/188.61 tff(33848,plain,
% 296.10/188.61 (node10(c_e_h_2, c_n, s5, s6)),
% 296.10/188.61 inference(unit_resolution,[status(thm)],[33847, 33843])).
% 296.10/188.61 tff(33849,assumption,(m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s5)), introduced(assumption)).
% 296.10/188.61 tff(33850,plain,
% 296.10/188.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6) | (~node10(c_e_h_2, c_n, s5, s6)))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6) | (~node10(c_e_h_2, c_n, s5, s6)))),
% 296.10/188.61 inference(rewrite,[status(thm)],[])).
% 296.10/188.61 tff(33851,plain,
% 296.10/188.61 (((~node10(c_e_h_2, c_n, s5, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6)) <=> ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6) | (~node10(c_e_h_2, c_n, s5, s6)))),
% 296.10/188.61 inference(rewrite,[status(thm)],[])).
% 296.10/188.61 tff(33852,plain,
% 296.10/188.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s5, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6) | (~node10(c_e_h_2, c_n, s5, s6))))),
% 296.10/188.61 inference(monotonicity,[status(thm)],[33851])).
% 296.10/188.61 tff(33853,plain,
% 296.10/188.61 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s5, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6))) <=> ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6) | (~node10(c_e_h_2, c_n, s5, s6)))),
% 296.10/188.62 inference(transitivity,[status(thm)],[33852, 33850])).
% 296.10/188.62 tff(33854,plain,
% 296.10/188.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | ((~node10(c_e_h_2, c_n, s5, s6)) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6))),
% 296.10/188.62 inference(quant_inst,[status(thm)],[])).
% 296.10/188.62 tff(33855,plain,
% 296.10/188.62 ((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~node10(I0, I1, X, Y)) | (~m_and_h_gate_h_init_v_in2(I0, I1, X)) | (~m_and_h_gate_h_init_v_in1(I0, I1, X)) | m_and_h_gate_h_init_v_out(I0, I1, Y))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6) | (~node10(c_e_h_2, c_n, s5, s6))),
% 296.10/188.62 inference(modus_ponens,[status(thm)],[33854, 33853])).
% 296.10/188.62 tff(33856,plain,
% 296.10/188.62 ($false),
% 296.10/188.62 inference(unit_resolution,[status(thm)],[33855, 5718, 33849, 33833, 33848, 33831])).
% 296.10/188.62 tff(33857,plain,(m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_n, s5)) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5))), inference(lemma,lemma(discharge,[]))).
% 296.10/188.62 tff(33858,plain,
% 296.10/188.62 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s5))),
% 296.10/188.62 inference(unit_resolution,[status(thm)],[33857, 33830])).
% 296.10/188.62 tff(33859,plain,
% 296.10/188.62 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6) | (~m_and_h_gate_h_init_v_in1(c_e_h_2, c_n, s5))),
% 296.10/188.62 inference(unit_resolution,[status(thm)],[33858, 27723])).
% 296.10/188.62 tff(33860,plain,
% 296.10/188.62 (m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6)),
% 296.10/188.62 inference(unit_resolution,[status(thm)],[33859, 33825])).
% 296.10/188.62 tff(33861,plain,
% 296.10/188.62 (((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6)))) <=> ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6)))),
% 296.10/188.62 inference(rewrite,[status(thm)],[])).
% 296.10/188.62 tff(33862,plain,
% 296.10/188.62 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | ((~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6)))),
% 296.10/188.62 inference(quant_inst,[status(thm)],[])).
% 296.10/188.62 tff(33863,plain,
% 296.10/188.62 ((~![I0: $i, X: $i] : ((~m_and_h_gate_h_init_v_in2(I0, c_m, X)) | (~m_and_h_gate_h_init_v_out(I0, c_n, X)))) | (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s6)) | (~m_and_h_gate_h_init_v_out(c_e_h_2, c_n, s6))),
% 296.10/188.62 inference(modus_ponens,[status(thm)],[33862, 33861])).
% 296.10/188.62 tff(33864,plain,
% 296.10/188.62 (~m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s6)),
% 296.10/188.62 inference(unit_resolution,[status(thm)],[33863, 4958, 33860])).
% 296.10/188.62 tff(33865,plain,
% 296.10/188.62 (((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s6)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s6))) <=> ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s6)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s6))),
% 296.10/188.62 inference(rewrite,[status(thm)],[])).
% 296.10/188.62 tff(33866,plain,
% 296.10/188.62 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | ((~node9(c_e_h_2, c_m, s6)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s6))),
% 296.10/188.62 inference(quant_inst,[status(thm)],[])).
% 296.10/188.62 tff(33867,plain,
% 296.10/188.62 ((~![I0: $i, X: $i, I1: $i] : ((~node9(I0, I1, X)) | m_and_h_gate_h_init_v_in2(I0, I1, X))) | (~node9(c_e_h_2, c_m, s6)) | m_and_h_gate_h_init_v_in2(c_e_h_2, c_m, s6)),
% 296.10/188.62 inference(modus_ponens,[status(thm)],[33866, 33865])).
% 296.10/188.62 tff(33868,plain,
% 296.10/188.62 (~node9(c_e_h_2, c_m, s6)),
% 296.10/188.62 inference(unit_resolution,[status(thm)],[33867, 4972, 33864])).
% 296.10/188.62 tff(33869,assumption,(~node9(c_e_h_2, c_m, s6)), introduced(assumption)).
% 296.10/188.62 tff(33870,assumption,(~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6)), introduced(assumption)).
% 296.10/188.62 tff(33871,assumption,(m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7)), introduced(assumption)).
% 296.10/188.62 tff(33872,assumption,(node11(c_e_h_2, c_m, s6, s7)), introduced(assumption)).
% 296.10/188.62 tff(33873,plain,
% 296.10/188.62 (((~![Y: $i, I0: $i, X: $i, I1: $i] : ((~m_and_h_gate_h_init_v_out(I0, I1, Y)) | (~node11(I0, I1, X, Y)) | m_and_h_gate_h_init_v_out(I0, I1, X))) | ((~m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s7)) | (~node11(c_e_h_2, c_m, s6, s7)) | m_and_h_gate_h_init_v_out(c_e_h_2, c_m, s6))) <